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= 10−4. The results obtained with the rational representation (the Padé approximants) for several values of the Padé tolerance parameter () are then studied. Without Padé approximants, 67 steps have to be performed to have the entire curve from ω |
= 0 up to ω |
= 2ωl. Note that with μ |
= 10−3 the steps number is nearly half of polynomials one. shows that the quality of the Padé approximants with μ |
= 10−4 and μ |
= 10−5 is really better than the polynomial.Finally, the relative computational times, for different numbers of harmonics, are given in . To obtain representative times, the considered number of nodes is equal to 435 (i.e. 2610 dof for one harmonic). This increases the number of terms in the matrix, and consequently the computational cost. In one step of the asymptotic numerical method, one has to perform only one matrix decomposition, to calculate all second members and to apply the Padé approximant. This last computation step does not require a great deal of computational time. For the matrix decomposition, the time increases with the harmonics number because the tangent matrix is constructed from (2 ∗ |
H |
− 1)2 blocs. In this study, a classical Crout’s method is used. The relative CPU times are then defined as the ratio between the triangulation time of the tangent operator K¯t0 in nonlinear problems given in Eqs. , and the triangulation time of tangent operator K in linear dynamical problems which contain only one harmonic: shows that for six harmonics, the time of the nonlinear matrix decomposition is 127 times that required for the computation of the solution in a linear problem. This is very large time, but this matrix decomposition must be also done with other methods (for example the Newton–Raphson). Furthermore, the Newton–Raphson method requires a great many steps The right hand side calculus time depends in one hand on the number of harmonics, and on the other hand of the truncation order. The ratio of the right hand side calculus time, with respect to the matrix decomposition time, is presented in . It can be noted that when the harmonics number is increased, the right hand side calculus time became more negligible compared to the decomposition time.This paper develops an asymptotic numerical method to solve nonlinear forced vibration problems, taking into account structural damping of plates subjected to time-harmonic transversal excitation. A large part of the nonlinear solution is obtained by solving a sequence of linear problems having the same stiffness matrix. Iteration of this method, leading to a path-following technique, made it possible to obtain the nonlinear resonance curves at any desired range of amplitudes with the limit imposed by the von Karman theory. We reported numerical tests for forced vibrations of damped rectangular plates subjected to time-harmonic lateral excitations, and compared to calculations with numerical results available in the literature. Numerical results for nonlinear frequency and nonlinear displacements were presented and compared for various values of damping coefficients. To illustrate the value of this method, several applications were described. In addition to principal resonances, the present approach enables the user to obtain the higher harmonics resonances while taking into account a greater number of harmonics. Increasing the number of harmonics leads to increase the matrix decomposition and the second member calculus time. The time required to obtain a large section of the solution is also increased, but as a whole, the asymptotic numerical method takes less computational time than a classical incremental iterative algorithm Even if the second member time increases, it is negligible compared to the decomposition time. Then to reduce this computational time, one can use another linear solver which is well-adapted to repeated right hand side problems The presented work concerns only plates with moderate rotations, but complex models of plates and shells could be investigated are symmetric and diagonal by blocs. For instance, with three harmonics, one has:B¯l=Bl00000Bl00000Bl00000Bl00000Bl,D¯=D00000D00000D00000D00000D,C¯=0000000C000C00000002C000-2C0,M¯=000000M00000M000004M000004M corresponds to the product of two vectors A and B, written in the form of series given in Eq. . For instance, with H |
= 3, the product A(t) × |
B(t) results in:AB=a0b0+12ac1bc1+as1bs1+ac2bc2+as2bs2+a0bc1+ac1b0+12ac1bc2+as1bs2+ac2bc1+as2bs1cos(ωt)+a0bs1+as1b0+12ac1bs2-as1bc2-ac2bs1+as2bc1sin(ωt)+a0bc2+ac2b0+12ac1bc1-as1bs1cos(2ωt)+a0bs2+as2b0+12ac1bs1+as1bc1sin(2ωt)The vector B can be put in as a factor, and the last equation can be written as follows:AB0ABc1ABs1ABc2ABs2=a012ac112as112ac212as2ac1a0+12ac212as212ac112as1as112as2a0-12ac2-12as112ac1ac212ac1-12as1a00as212as112ac10a0×b0bc1bs1bc2bs2 and applying harmonic balance, one finds, for H |
= 3, the matrix B¯nl(U¯) as follows:B¯nl(U¯)=Bnl(U0)Bnl12Uc1Bnl12Us1Bnl12Uc2Bnl12Us2BnlUc1BnlU0+12Uc2Bnl12Us2Bnl12Uc1Bnl12Us1BnlUs1Bnl12Us2BnlU0-12Uc2Bnl-12Us1Bnl12Uc1BnlUc2Bnl12Uc1Bnl-12Us1Bnl(U0)0BnlUs2Bnl12Us1Bnl12Uc10Bnl(U0)Note that B¯nl(U¯) is not a symmetric matrix; its blocs are functions of the Bnl(U) defined in , it can be computed easily for any number of harmonics. is arranged according to harmonics blocs i (i |
= 0, H |
− 1). In order to reduce the number of elements stored in the matrices, after discretization, the displacement vector is organized in the following form:q=qc10,qc11,qs11,…,qc1i,qs1i,…,qs1H-1,qc20,…,qs2H-1,…,qcj0,…,qsjH-1︸tqj,…,qcm0,…,qsmH-1Twhere j is the degree of freedom (j |
= 1, m). This leads, with for instance 726 degrees of freedom and H |
= 3, to decrease the number of terms saved in the tangent operator K¯t by 80%. Superplasticity-like creep behavior of coarse grained ternary Al alloys QIAO Jun(乔 军) 1 , E. M. TALEFF 2 1. College of Materials Science and Engineering, University of Science and Technology Liaoning, Anshan 114051, China; 2. Department of Mechanical Engineering, University of Texas at Austin, Austin 78705, USA Received 25 March 2009; accepted 26 June 2009 Abstract: Enhanced tensile ductilities in coarse grained Al-Mg-Zn and Al-Mg-Fe materials were studied. The materials were Al-2Mg-5Zn, Al-3Mg-5Zn, Al-4Mg-5Zn, Al-3Mg-0.11Fe, Al-3Mg-0.27Fe, and Al-3Mg-0.40Fe. Tensile elongation-to-failure tests were conducted at constant cross-head speed and constant temperatures from 300 to 450 ℃. Strain rate change tests were conducted at a constant temperature from 300 to 450 ℃ and in strain-rate range from 4.31×10 −5 to 1.97×10 −2 s −1 . Experimental results show that over 100% ductilities are consistently achieved in these materials. This superplasticity-like behavior is rate-controlled by solute-drag creep. Although ternary Zn and Fe additions do not have an adverse effect on solute-drag creep and ductility, they increase stress exponent and its sensitivity to Mg content during solute-drag creep. Key words: Al-Mg alloys; superplasticity; solute-drag creep; tensile ductility; strain-rate sensitivity 1 Introduction High temperature deformation in polycrystalline solids is generally viewed as a power-law relationship between the creep rate ε& and flow stress σ, as given in the phenomenological equation for creep. exp n Q A ERT σ ε ⎛⎞ ⎛ ⎞ =− ⎜⎟ ⎜ ⎟ ⎝⎠ ⎝ ⎠ & (1) where A is material constant related to stacking fault energy; n is the stress exponent, commonly taking values from 2 to 8; E is the dynamic elastic modulus; Q is the creep activation energy; R is the gas constant; and T is the absolute temperature. For 5000-series Al-Mg alloys, enhanced ductilities during high-temperature creep deformation can be achieved from either fine grained superplasticity or solute-drag creep. Fine grained superplasticity typically provides a low stress exponent of n=2 and some Al-Mg alloys present very high ductility (~500%), where the deformation is dominated by a grain-boundary-sliding (GBS) creep mechanism. GBS in polycrystalline solids is rate-controlled by the accommodation process of dislocation migration, which is controlled by either lattice diffusion or grain boundary diffusion. GBS typically requires a fine-grained, equiaxed microstructure which is resistant to grain growth[1−3]. It is of great interest now to develop solute-drag creep in Al-Mg materials. Solute-drag creep is rate dominated by viscous glide of dislocation interacting elastically with stress field of a solute atmosphere, which exerts a drag force to slow dislocation motion[4]. Compared to superplasticity, solute-drag creep is insensitive to grain size, which precludes the necessity of the special alloying or processing steps typically used to refine grain size and achieve superplasticity. Requirements for a solid solution to exhibit solute-drag-creep behavior include large atom-misfit parameter, relatively high solute concentration, high stacking fault energy and uniform distribution of dislocations. Al-3Mg alloys may fulfill all these requirements. The linear misfit factor of Mg in Al is +0.12. According to the binary Al-Mg phase diagram, 3% (mass fraction) Mg could be completely dissolved in Al matrix at temperatures over 190 ℃, which contributes to the solute-drag effect. High stacking-fault energy of Al-3Mg makes cross-slip and climb easier and Foundation item: Project(DMR-9702156) supported by the National Science Foundation of USA; Project(50801034) supported by the National Natural Science Foundation of China; Project(20060425) supported by the Scientific and Technological Research Key Lab Foundation of Liaoning Education Department Corresponding author: QIAO Jun; Tel: +86-412-5929532; E-mail: [email protected] DOI: 10.1016/S1003-6326(09)60179-5 QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 565 helps provide a uniform dislocation distribution, which is important to inhibit discontinuous dynamic recrystalliza- tion because of the high mobility of dislocations, although continuous dynamic recrystallization and geometric dynamic recrystallization may occur during high temperature deformation[5−9]. TALEFF et al[10−11] studied the ductility and creep mechanisms of coarse grained binary Al-Mg alloys and 5000-series commercial alloys. It is shown that when Mg content is higher than 2% (mass fraction), solute-drag creep dominates deformation and stress exponent does not greatly change with the increase of Mg content. Ductilities over 100% are consistently achieved when deformation takes place in the solute-drag creep region. Although 5000-series Al-Mg alloys offer enhanced high temperature ductility, their application is inhibited by low strength at room temperature. In contrast, 7000-series Al-Mg-Zn alloys offer a much higher room temperature strength because of their potentially improved age hardenability and strength from Zn addition. In present work, two groups of alloys are studied: three Al-xMg-5Zn alloys with approximately 5.25% Zn (mass fraction) and 2%−4% (mass fraction) Mg, three Al-3Mg-xFe alloys with approximately 3%Mg (mass fraction) and 0.11%−0.40%Fe (mass fraction). Compared to 7000-series alloys, the Al-xMg-5Zn materials have similar Zn content and higher Mg content, which is designed to investigate the effects of Zn on warm deformation mechanisms under different Mg content. The Al-3Mg-xFe materials with dilute Fe contents are designed to study the effect of Fe on creep mechanisms because Fe often exists as impurity in processing. For these materials, the relationships between strain-rate sensitivity and solute concentration are analyzed in detail, and the creep mechanisms operating under hot deformation are discussed. 2 Experimental 2.1 Materials The compositions of the investigated Al-Mg-X alloys are shown in Table 1. These materials were prepared as book mold castings, and each casting was scalped and homogenized at 550 ℃ for 8 h. Then, the castings were hot rolled at temperatures from 450 to 350 ℃ and cold rolled to a thickness of 4 mm. The grain sizes after recrystallization were measured to be in the range of 30 to 45 μm. Because of limited cold deformation and lack of grain-refining alloy additions, the microstructures were significantly less refined than that of typical commercial sheet Al materials. The tensile test specimens were machined from the cold rolled plate along the rolling direction, as shown in Fig.1. Fig.1 Dimensions of specimen for high-temperature mechanical test 2.2 Elongation-to-failure (EF) tests In high temperature mechanical tests, samples were heated in the middle zone of a three-zone split-tube furnace. Two thermocouples were placed in contact with the two ends of the specimen. Temperature was controlled to be within ±2 ℃. The tensile elongation-to-failure tests were conducted on a testing machine for the Al-Mg-Zn and Al-Mg-Fe specimens at constant cross-head speed for strain rates from 10 −3 s −1 to 10 −2 s −1 , at constant temperatures from 300 ℃ to 450 ℃. Ductilities for each failed sample were calculated based on uniform deformation in the gage section. 2.3 Strain-rate-change (SRC) tests Strain-rate-change tests were conducted on the Al-Mg-Zn and Al-Mg-Fe specimens under strain rates from 4.31×10 −5 to 1.97×10 −2 s −1 and at constant temperature ranging from 300 ℃ to 450 ℃. In each SRC test, strain rate was varied from slow to fast in ten steps of constant cross-head speeds, with a 15%−20% prestrain in first step and 2%−5% strain in each subsequent step. The initial prestrain was imposed at a low rate in order to stabilize the microstructure before strain-rate jumps. Table 1 Compositions of ternary alloys in present investigation (mass fraction, %) Material Al Si Fe Cu Mg Zn Ti Al-2Mg-5Zn Bal. 0.071 0.039 0.012 2.02 5.270 0.013 Al-3Mg-5Zn Bal. 0.064 0.033 0.010 3.00 5.250 0.012 Al-4Mg-5Zn Bal. 0.051 0.038 0.007 4.02 5.210 0.012 Al-3Mg-0.11Fe Bal. 0.029 0.108 0.001 2.99 0.024 0.014 Al-3Mg-0.27Fe Bal. 0.028 0.270 0.001 2.94 0.025 0.019 Al-3Mg-0.40Fe Bal. 0.030 0.396 0.001 3.01 0.011 0.013 QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 566 2.4 Polarized light microscopy The microstructures of each Al-xMg-5Zn and Al-3Mg-xFe material after EF test were examined using polarized light microscopy. Metallographic samples were taken from the undeformed grip regions, which assured sufficient time to completely recrystallize, to observe surfaces in longitudinal, short-transverse and long- transverse orientations. Samples were also taken from the deformed gage regions along tensile direction to observe failure features. Each polished specimen was electrolytically etched in Barker’s reagent, 5 mL fluoboric acid (HBF 4 , 48%) and 200 mL deionized water, under an electric potential of 20 V for 35 s. Micrographs were taken to observe cavitation and measure grain size using linear intercept method. 3 Results 3.1 Elongation-to-failure tests For Al-2Mg-5Zn material, the photo of one untested specimen and two specimens after EF tests with different elongations is shown in Fig.2. Complete elongation-to- failure data are given in Fig.3 for the Al-xMg-5Zn materials and in Fig.4 for the Al-3Mg-xFe materials, as EF versus logarithm of strain rate compensated by the diffusivity of Mg in Al, for which D 0 =5×10 −5 m −2 /s[12], and Q=136 kJ/mol[13]. The compensation of strain rate, ,/Dε& is similar to the Zener-Hollomon parameter, ),/exp( 0 RTQz ε&= which accounts for the temperature dependence of diffusivity. 00 00 exp Qz DD RT D εε ⎛⎞ =⋅ = ⎜⎟ ⎝⎠ && (2) where 0 ε& is the strain rate, D is the diffusivity of Mg atoms in Al; D 0 is the frequency factor; z is the Zener-Hollomon parameter; R is the gas constant and T is absolute temperature. Fig.2 Photo of samples before and after EF tests (Al-2Mg-5Zn, 400 ℃, =ε& 10 −3 s −1 ): (a) Untested sample; (b) EF=153%; (c) EF=312% Fig.3 shows that the ductilities over 100% are consistently achieved at high temperatures and low strain rates, i.e. D/ 0 ε&＜10 13 m −2 , where solute drag creep Fig.3 Elongations at different temperatures and strain rates: (a) Al-2Mg-5Zn; (b) Al-3Mg-5Zn; (c) Al-4Mg-5Zn dominates the deformation. In the region of D/ 0 ε&＞10 13 m −2 . The ductilities are reduced to below 100% with the limits of data provided. It is noted that the tensile ductilities of these Zn-containing alloys are similar to those of the binary Al-Mg alloys[14], indicating that the Zn addition of approximately 5% (mass fraction) does not strongly affect the tensile ductility of Al-Mg materials. Fig.4 shows that the tensile ductilities over 100% are also consistently achieved and the ductilities do not differ significantly from each other for the three Al-3Mg-xFe alloys, indicating that the ductilities are not QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 567 Fig.4 Elongations at different temperatures and strain rates: (a) Al-3Mg-0.11Fe; (b) Al-3Mg-0.27Fe; (c) Al-3Mg-0.40Fe strongly affected by the dilute concentration of Fe in the range of 0.11%−0.40% (mass fraction). To give a convenient comparison of the Al-xMg-5Zn and Al-3Mg-xFe materials, two hand-fit curves representing the limits of all the EF data from the three Al-xMg-5Zn materials are given in each plot of Fig.3 and Fig.4. The ductilities of the Al-3Mg-xFe materials are slightly higher, in general, than those of Al-xMg-5Zn materials. 3.2 Strain-rate change tests Fig.5 presents the SRC results from the Al-xMg-5Zn materials as the logarithm of diffusion-compensated strain rate, ,/Dε& against the logarithm of modulus-compensated flow stress, σ/E. The strain rate is compensated by the diffusivity of Mg in Al. Fig.5 SRC test data of Al-xMg-5Zn samples: (a) Al-2Mg-5Zn; (b) Al-3Mg-5Zn; (c) Al-4Mg-5Zn In these plots, the transitions to power-law breakdown (PLB) are evident at low temperatures and high strain rates, i.e. D/ε&＞10 13 m −2 . As marked in Fig.5(a), the Al-2Mg-5Zn material at 300 ℃ and 325 ℃ is found to exhibit a strong offset from the master QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 568 curve, and persist in repeated tests, which is not observed for the Al-3Mg-5Zn and Al-4Mg-5Zn materials. The evidence indicates that the test temperatures below 325 ℃ may not be high enough to dissolve all precipitates in the as-received materials. Linear regression method was applied to calculate the stress exponents in the data range of D/ε&＜10 13 m −2 . The values of n and its standard errors are listed in Table 2, where data for four Al-Mg materials[15−16] and three commercial Al-Mg alloys[17] from literature are included. For the Al-xMg-5Zn materials, the stress exponent decreases from 4.3 to 3.7 with the increase of Mg concentration, while the stress exponent for dilute, binary Al-xMg materials does not change greatly with the Mg concentration. It is indicated that ternary Zn additions increase the sensitivity of stress exponent to Mg content. Table 2 Stress exponent n, of different alloys (SE: standard error) Material n SE Material n SE Al-2Mg-5Zn 4.3 0.05 Al-2.8Mg[15] 3.5 0.2 Al-3Mg-5Zn 4.0 0.04 Al-3.0Mg[16] 3.1 0.04 Al-4Mg-5Zn 3.7 0.03 Al-5.1Mg[16] 3.2 0.02 Al-3Mg-0.11Fe 3.9 0.04 Al-5.5Mg[15] 3.5 0.09 Al-3Mg-0.27Fe 4.1 0.06 5182[17] 3.7 0.04 Al-3Mg-0.40Fe 4.2 0.06 5182cc[17] 4.1 0.10 - - - 5754[17] 4.1 0.10 3.3 Polarized light microscopy Horizontally oriented in the longitudinal direction, optical micrographs of a failed Al-3Mg-5Zn sample after EF test are shown in Fig.6. The grains in the grip region were somewhat elongated along the rolling direction, as shown in Fig.6(a). Table 3 gives the grain sizes in the grip region measured by linear-intercept method. It is evident that the grains are much larger than the size typically required for fine grained superplasticity, d≤10 μm. Observations of the failed EF specimens indicate that most specimens failed by necking to a point, which Table 3 Grain sizes in grip regions for long-transverse (LT), short-transverse (ST) and longitudinal (L) orientations (μm) Material LT ST L Al-2Mg-5Zn 50.9±3.5 34.3±1.3 48.6±1.5 Al-3Mg-5Zn 66.6±16.1 32.6±4.6 49.0±5.9 Al-4Mg-5Zn 68.2±3.2 30.0±3.0 44.7±6.6 Al-3Mg-0.11Fe 51.3±6.1 33.4±2.0 35.1±4.7 Al-3Mg-0.27Fe 54.3±5.5 33.4±2.0 43.8±1.2 Al-3Mg-0.40Fe 41.9±4.1 32.6±1.4 41.2±2.1 Fig.6 Optical micrographs of failed Al-3Mg-5Zn sample after EF test at 400 ℃ and 2×10 −4 s −1 : (a) Grip region; (b) Gage point far from failure end; (c) Failure end is similar to the necking behavior of superplastic binary Al-Mg alloys[15, 18−19]. Some specimens show moderate necking with cavities at the failure end. Fig.6(b) shows a gage point far from the failure end, and Fig.6(c) shows the failure end of the same sample at a larger magnification. The dark lines in both pictures are believed to be cavity bands. Some cavities with sizes of approximately 100 μm are apparent in Fig.6(c). The shape of the failure end in the picture is consistent with the jagged failure surface, which indicates that cavity growth and interlinkage cause the failure of the sample. 4 Discussion To make a better comparison of the data from the Al-xMg-5Zn and Al-3Mg-xFe alloys, hyperbolic-sine curves were fitted to the SRC test data, as shown in Fig.7. QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 569 Fig.7 Fitted curves of SRC test data: (a) Al-xMg-5Zn; (b) Al- 3Mg-xFe In Fig.7(a), the three Al-xMg-5Zn materials exhibit similar creep behaviors at low strain rates and high temperatures, i.e. D/ε&＜10 13 m −2 , 350 ℃＜T＜450 ℃. In this region, Mg concentration does not affect the creep behavior strongly, which indicates that 2%−4% (mass fraction) Mg is enough to ensure solute-drag creep. This conclusion is supported by the theory of Mg atoms saturation around an edge dislocation. There exists a temperature- dependent critical Mg concentration around an edge dislocation, over which the stress exponent is not sensitive to the concentration of Mg[13]. At low temperatures and high strain rates, i.e. D/ε&＞10 13 m −2 , 350 ℃＜T＜350 ℃, Fig.7(a) shows a significant difference in creep behaviors for the three Al-xMg-5Zn materials. Al-4Mg-5Zn has the highest strength and Al-2Mg-5Zn is the weakest. For materials with high Mg content, more Mg atoms are available to retain solute-drag creep and slow the transition to power law breakdown (PLB), which requires that the material be of equal or higher strength during the transition. Therefore, the decrease of stress exponent in the three Al-xMg-5Zn materials with increasing Mg content is related to the suppression of the transition to PLB. SRC data from the Al-3Mg-xFe materials were fitted using Garofalo’s hyperbolic-sine relation, as shown in Fig.7(b). The three materials exhibit similar creep behavior in both the solute-drag creep and PLB regions. Al-3Mg-0.27Fe and Al-3Mg-0.40Fe are slightly stronger than Al-3Mg-0.11Fe at high temperatures and low strain rates, which may be related to an increase in the volume fraction of iron-aluminide particulates with increasing Fe content. SRC test data from pure Al, Al-xMg, Al-xZn, Al-3Mg-xMn and commercial 5000-series materials are available in the literature. Many of these materials were tested in a similar regime of D/ε& to the present study. Fig.8(a) shows the SRC test data from pure Al[20] and Al-5Zn alloys[10]. The areas covered by data from the Fig.8 Comparison of SRC test data: (a) Al[20], Al-5Zn[10]; (b) Al-xMg[15−16]; (c) 5182, 5182cc, and 5754[17] QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 570 Al-xMg-5Zn and Al-3Mg-xFe materials are hatched with vertical lines, which provide a clear way to compare data from different materials. The strain rates of Al and Al-5Zn are compensated by the diffusivity of Mg in Al, Q=136 kJ/mol and D 0 =5.0×10 −5 m 2 /s. As expected, pure Al exhibits dislocation climb-controlled creep with a typical stress exponent of n≈5. The similarity between the stress exponents of Al and Al-5Zn indicates that the Zn addition of 5% (mass fraction) in Al does not produce a significant solute-drag effect. Therefore, both the Al and Al-5Zn materials exhibit dislocation-climb- controlled creep and the creep activation energy is equal to the activation energy of lattice self-diffusion in Al[21]. The compensation of strain rates in Fig.8(a) is valid for the Al-xMg-5Zn and Al-3Mg-xFe materials because the solute-drag behavior is induced by Mg, and it is also approximately valid for the Al and Al-5Zn data because the activation energy for lattice self-diffusion in Al is similar, which is 142 kJ/mol. It is noted in Fig.8(a) that the Zn addition does not strongly affect the strength of Al over the given range of temperatures and strain rates. In contrast, the Al-xMg-5Zn and Al-3Mg-xFe materials have higher strengths and exhibit solute-drag behavior with lower stress exponents, n≈4. The Al-3Mg-xFe materials are slightly stronger than the Al-xMg-5Zn materials when D/ε & ≤10 13 m −2 . In the transition region from solute-drag creep to PLB, D/ε&≥10 13 m −2 , the three Al-3Mg-xFe materials show a similar behavior to the Al-4Mg-5Zn material, being stronger than the Al-3Mg-5Zn and Al-2Mg-5Zn materials. This stronger behavior of the Fe-containing ternary materials is attributed to both of the strengthening effect of iron-aluminide particulates, which exist even at high temperatures, and the slower transition to PLB for the Al-4Mg-5Zn material. The effectiveness of Mg at producing solute-drag creep is illustrated in Fig.8(b)[15−16]. The binary Al-Mg alloys all exhibit a stress exponent characteristic of solute-drag creep, n≈3.3. For values of D/ε&≤10 13 m −2 , the Al-xMg-5Zn and Al-3Mg-xFe materials exhibit approximately similar strengths but higher stress exponents than Al-Mg alloys as shown in Table 2. When D/ε&≥10 13 m −2 , the Al-2Mg-5Zn material is the weakest and exhibits the earliest transition to PLB, which is generally associated with an increase in excess vacancy concentration caused by dislocation interactions at high strain rates and low temperatures[22]. Deformation- induced increases of excess vacancy concentration in Al have been confirmed by MURTY et al using nuclear magnetic resonance methods[23]. If Al-2Mg-5Zn cannot retain the solute-drag effect at low temperatures and high strain rates because of the low mobility of Mg atoms, dislocation glide becomes easier, allowing dislocation climb to control the rate of deformation. At high stresses, however, excess vacancies generated by dislocation intersections produce a high effective diffusivity, which enhances dislocation climb and accelerates the creep rate into PLB. The Al-4Mg-5Zn material, with the highest Mg content, is able to retain the solute-drag effect at low temperatures and high strain rates, exhibiting a low stress exponent and a slow transition to PLB. SRC test data from fine and coarse grained Al-2.8Mg material are included in Fig.8(b). It is noted that despite a large difference in grain size, 450 μm versus 30 μm, they exhibit a similar steady-state stress exponent, n≈3.5. Neither strength nor strain-rate sensitivity in the solute-drag-creep regime is significantly affected by grain size within the range examined. Commercial alloys, 5182, 5182cc, and 5754[17] show higher strength than the Al-xMg-5Zn and Al-3Mg-xFe materials, as shown in Fig.8(c). This can be attributed to the Cu, Mn additions in the commercial alloys. It is important to note that the Al-xMg-5Zn, Al-3Mg-xFe and commercial materials in Fig.8(c) exhibit consistent solute drag creep behaviors, from which enhanced tensile ductilities of over 100% have been repeatedly achieved. 5 Conclusions 1) In the regime of D/ε&＜10 13 m −2 , solute-drag creep dominates the deformation of these ternary materials, and the Al-xMg-5Zn and Al-3Mg-xFe materials have similar strengths. 2) Ternary additions of Zn and Fe do not strongly affect tensile ductilities. Enhanced tensile ductilities of over 100% are repeatedly achieved from the Al-xMg-5Zn and Al-3Mg-xFe materials when deformed in the solute-drag-creep regime. 3) The dominated failure mechanism in these materials during elongation-to-failure tests is necking to a point. Cavity growth and interlinkage can also cause failures. 4) Ternary Zn additions increase the sensitivity of stress exponent to Mg content, and n decreases with the increase of Mg content. This decrease of n value is related to the suppression of the transition to dislocation-climb creep and PLB with increasing Mg content. References [1] PARK K T, HWANG D Y, CHANG S Y, SHIN D H. Low-temperature superplastic behavior of a submicrometer-grained 5083 Al alloy fabricated by severe plastic deformation [J]. Metallurgical and Materials Transactions A, 2002, 33(9): 2859−2867. [2] GREEN W P, KULAS M A, NIAZI A, OH-ISHI K, TALEFF E M, QIAO Jun, et al/Trans. Nonferrous Met. Soc. China 20(2010) 564−571 571 KRAJEWSKI P E, MCNELLEY T R. Deformation and failure of a superplastic AA5083 aluminum alloy with Cu additions [J]. Metallurgical and Materials Transactions A, 2006, 37: 2727−2738. [3] FRIEDMAN P A, COPPLE W B. Superplastic response in Al-Mg sheet alloys [J]. Journal of Materials Engineering and Performance, 2004, 13(3): 335−347. [4] GARCÍA-BERNAL M A, HERNANDEZ-SILVA D, SAUCE- RANGEL V. Superplastic behavior of coarse-grained Al-Mg-Zn alloys [J]. Journal of Materials Science, 2007, 42: 3958−3963. [5] SOER W A, CHEZAN A R, HOSSON J T M D. Deformation and reconstruction mechanisms in coarse-grained superplastic Al-Mg alloys [J]. Acta Materialia, 2006, 54(14): 3827−3833. [6] MCQUEEN H J. Development of dynamic recrystallization theory [J]. Materials Science and Engineering A, 2004, 387/389(15): 203−208. [7] JAZAERI H, HUMPHREYS F J. The transition from discontinuous to continuous recrystallization in some aluminium alloys (I): The deformed state [J]. Acta Materialia, 2004, 52(11): 3239−3250. [8] CRUZ-PALACIOS M I, HERNÁNDEZ-SILVAA D, BARRALES-MORA L A, GARCÍA-BERNAL M A. Grain refinement during superplastic deformation of coarse-grained Al-Mg-Cu alloys [J]. Materials Science Forum, 2006, 509: 75−80. [9] AGARWAL S, KRAJEWSKI P E, BRIANT1 C L. Dynamic recrystallization of AA5083 at 450 ℃: The effects of strain rate and particle size [J]. Metallurgical and Materials Transactions A, 2008, 39(6): 1277−1289. [10] TALEFF E M, NEVLAND P J, KRAJEWSKI P E. Solute-drag creep and tensile ductility in aluminum alloys [C]// MISHRA R S, MUKHERJEE A K, MURTY K L. Creep Behavior of Advanced Materials of the 21st Century. San Diego, CA: TMS. Warrendale, PA, 1999: 349−358. [11] KULAS M A, GREEN W P, TALEFF E M, KRAJEWSKI P E, MCNELLEY T R. Deformation mechanisms in superplastic AA5083 materials [J]. Metallurgical and Materials Transactions A, 2005, 36(5): 1249−1261. [12] FUNAMIZU Y, WATANABE K. Interdiffusion in the Al-Mg system [J]. Trans JIM, 1972, 13: 278−283. [13] MCNELLEY T R, MICHEL D J, SALAMA A. The Mg-concentration dependence of the strength of Al-Mg alloys during glide-controlled deformation [J]. Scripta Metall, 1989, 23: 1657−1662. [14] TALEFF E M, NEVLAND P J. The high-temperature deformation and tensile ductility of Al alloys [J]. JOM, 1999, 51: 34−36. [15] TALEFF E M, HENSHALL G A, NIEH T G, LESUER D R, WADSWORTH J. Warm-temperature tensile ductility in Al-Mg alloys [J]. Metall Mater Trans A, 1998, 29: 1081−1091. [16] YAVARI P, MOHAMED F A, LANGDON T G. Creep and substructure formation in an Al-5% Mg solid solution alloy [J]. Acta Metall, 1981, 29: 1495−1507. [17] TALEFF E M, NEVLAND P J, KRAJEWSKI P E. Tensile ductility of several commercial aluminum alloys at elevated temperatures [J]. Metall Mater Trans A, 2001, 32: 1119−1130. [18] BAE D H, GHOSH A K. Cavity formation and early growth in a superplastic Al-Mg alloy [J]. Acta Materialia, 2002, 50(3): 511−523. [19] KULAS M-A, GREEN W P, TALEFF E M, KRAJEWSKI P E, MCNELLEY T R. Failure mechanisms in superplastic AA5083 materials [J]. Metallurgical and Materials Transactions A, 2006, 37(3): 645−655. [20] SERVI I S, GRANT N J. Creep and stress rupture behavior of aluminum as a function of purity [J]. Trans AIME, 1951, 191: 909−916. [21] FROST H J, ASHBY M F. Deformation-mechanism maps. The plasticity and creep of metals and ceramics [M]. Chapter 1. New York: Pergamon Press Inc, 1982: 1−19. [22] SHERBY O D, BURKE P M. Mechanical behavior of crystalline solids at elevated temperature [J]. Prog Mater Sci, 1968, 13: 325−390. [23] MURTY K L, DETEMPLE K, KANERT O, DEHOSSON J T M. In-situ nuclear magnetic resonance investigation of strain, temperature, and strain-rate variations of deformation-induced vacancy concentration in aluminum [J]. Metallurgical and Materials Transactions A, 1998, 29: 153−159. (Edited by FANG Jing-hua) Superplasticity-like creep behavior of coarse grained ternary Al alloysEnhanced tensile ductilities in coarse grained Al-Mg-Zn and Al-Mg-Fe materials were studied. The materials were Al-2Mg-5Zn, Al-3Mg-5Zn, Al-4Mg-5Zn, Al-3Mg-0.11Fe, Al-3Mg-0.27Fe, and Al-3Mg-0.40Fe. Tensile elongation-to-failure tests were conducted at constant cross-head speed and constant temperatures from 300 to 450 °C. Strain rate change tests were conducted at a constant temperature from 300 to 450 °C and in strain-rate range from 4.31×10−5 to 1.97×10−2 s−1. Experimental results show that over 100% ductilities are consistently achieved in these materials. This superplasticity-like behavior is rate-controlled by solute-drag creep. Although ternary Zn and Fe additions do not have an adverse effect on solute-drag creep and ductility, they increase stress exponent and its sensitivity to Mg content during solute-drag creep.Positive or negative role of preoxidation in the crack arresting of Cr coating for accident tolerant fuel claddingThe effect of preoxidation on the tensile property of Cr-coated Zr-4 alloy was investigated. Under tensile stress, cracks rarely occurred in the Cr coating preoxidized at 900 °C, which benefited from recrystallization transforming columnar grains into equiaxial grains. In contrast, when preoxidized at 1000 °C or higher temperature, microcracks were initiated in the interfacial diffusion layer and penetrated into both Cr coating and Zr-4 substrate under tension, resulting in premature failure of the sample. The earlier failure was triggered by multiple factors, including grain coarsening in the coating, Zr-Cr interdiffusion, transportation of oxygen, and phase transformation in the Zr-4 substrate.Since the Fukushima–Daiichi nuclear accident in 2011, developing accident tolerant fuel (ATF) cladding materials has attracted increasing worldwide attention Cr coating has been one of the optimal considerations as a near-term solution for the ATF cladding due to its superior oxidation and corrosion resistance, irradiation resistance and mechanical properties under accident scenarios Although the oxidation and corrosion behaviours of ATF coatings have been extensively studied in recent years Taking advantage of the in situ mechanical tests previously developed by the authors The Zr-4 alloy was chosen as the substrate material, with the chemical composition listed in (a), with a gauge length of 20 mm, a thickness of 0.7 mm and a longitudinal axis along with the LD. Subsequently, the samples underwent a grinding process with 1200# grit SiC papers. The substrate surface was rough enough to enhance the interfacial adhesion of the coating. After that, the substrates were cleaned by ultrasonic cleaning with ethyl alcohol before deposition.Cr coatings were deposited on the surfaces of the Zr-4 substrates through the multi-arc ion plating technique. As shown in (a), a 1.5 mm diameter hole was drilled in the middle of the clamp of each substrate for hanging on a holder, and the substrates rotated at a constant speed to acquire homogenous deposited coatings. Sputter cleaning was carried out on the samples before deposition at a bias potential of 500 V to clean the oxides from the surfaces of the substrates. Two high-purity Cr cathodes were used for deposition under a deposition temperature of 340 °C, a pressure of 2.7 Pa, a substrate bias voltage of −75 V, an arc current of 100 A, and a deposition time of 6 h.High-temperature preoxidation tests were performed in air in a muffle furnace. The temperature of the furnace environment was measured by an S-type thermocouple built into the furnace. The uncertainty of temperature at the heating zone was ±1 °C. The samples were heated in the furnace from room temperature to the target temperature and oxidized in a uniform hot zone for a certain period, followed by a cooling process in the furnace. The heating and cooling rates were set as 10 °C/min. Three oxidation conditions were selected, namely, oxidized at 900 °C for 1 h, oxidized at 900 °C for 2 h, and oxidized at 1000 °C for 1 h., tensile tests for the as-deposited and preoxidized Cr-coated samples were performed at room temperature on an in situ mechanical testing system (see (b)) equipped with a high-magnification (3000x in maximum) optical microscope (OM), a tensile loading system, and a data acquisition system. As shown in (c), the sample was fixed in the tensile loading unit by two clamps. During the tensile process, the optical microscope was suspended over the loading unit to observe the microdeformation and cracking behaviour on the surface of Cr coating in real-time. Tensile tests were performed under a displacement-control mode at a rate of 5 × 10−3 mm/s. The tensile test was suspended to capture the initiation and propagation of cracks and spallation of oxides via the microscope. Note that an area of 1450 μm × 1100 μm in the middle area of the gauge section was focused on observing the surface morphology. The tensile tests ended until final fractures occurred. The tensile tests for each heat-treated sample were carried out at least three times. After testing, the longitudinal sectional morphologies of the samples were observed by scanning electron microscopy (SEM).The phase structures of the coatings before and after oxidation were analysed by X-ray diffraction (XRD, Ultima IV). The distributions of the main elements, such as Cr, Zr and O, were characterized by energy-dispersive X-ray spectroscopy (EDS) mapping. Although EDS analysis was not sufficient for accurate quantification of light elements, such as O, it could provide a conclusive assessment of the presence of oxide phase. The surfaces and longitudinal sectional morphologies of the as-deposited and oxidized coated samples were characterized by OM and SEM (Mira 3). The evolution of grain sizes and orientations of Cr coatings were analysed using electron backscattered diffraction (EBSD, EDAX). To prepare the samples for EBSED tests, the longitudinal sections of the coated samples were mechanically polished and then Ar ion beam polished using a polishing machine (Gatan 697 Ilion II, Ar beam voltage: 6 keV, and milling time: 2 h). For EBSD characterization of Cr coating surfaces, the oxide layers were wiped off, and then the coating surfaces were vibration polished with Al2O3 polishing agent. The microstructures of the coatings at the nanoscale were examined using high-resolution transmission electron microscopy (TEM, FEI Tecnai G2 F20, at 200 kV). The TEM specimens were prepared by the focused ion beam (FIB, Crossbeam 540) technique. displays the microstructure of the as-deposited Cr-coated sample. The coating had a dense structure and a relatively uniform thickness of approximately 10 μm. The coating bonded tightly on the Zr-4 substrate without any microcracks or microvoids either on the coating surface or at the interface. Based on the EBSD results, the Cr coating possessed columnar crystal grains with a BCC structure exhibiting a strong texture with a (001) orientation vertical to the coating surface. The average grain size near the coating surface was approximately 2.5 μm, and the grains near the interface became increasingly thinner. The microstructures of the Cr coating prepared by the multi-arc ion plating technique were similar to those prepared by other PVD methods displays the XRD patterns of the as-deposited and preoxidized Cr coatings. For the as-deposited Cr coating, the (200) diffraction peak was extremely strong, which indicated a strong texture of the (200) planes, agreed with the EBSD results in (b). Note that some published results also showed a (110) crystallographic texture for Cr coatings deposited by PVD , the oxide layers of all samples were highly dense, and no microcracks or spallation were found. As the oxidation time and temperature increased, the sizes of the oxides grew slightly and became more even. To obtain more insights into the microstructures of the oxidized coatings, SEM and corresponding TEM images of the longitudinal section morphologies of the oxidized sample before tensile testing are presented in (a), the oxidized coating system consisted of four layers, namely, the outer Cr2O3 layer with rhombohedral structure identified by the selected area electron diffraction (SAED) pattern, as shown in (e), the sub-oxide residual Cr coating layer with BCC structure identified by the SAED pattern, as shown in (f), the intermetallic ZrCr2 layer between the coating and the substrate, and the Zr-4 substrate layer. During preoxidation, the Cr2O3 layer was continuously formed on the Cr coating surface due to the oxidation reaction, and the Cr2O3 layer became thicker with increasing oxidation temperature and time, as shown in (d). The thickness of the Cr2O3 layer was uneven, and the interface between the Cr2O3 layer and the Cr coating was rough, which might be due to nonuniform diffusion and oxidation rates at the interface. The TEM image in (b) shows that the Cr2O3 layer was dense without apparent defects inside. Besides, the high-resolution TEM image in (c) reveals integrated interface between the Cr2O3 layer and the Cr coating. At the same time, few microcavities were formed at the oxide/coating interface, believed to be produced by a Kirkendall-type mechanism in which the outward cationic diffusion of Cr and inward diffusion of oxygen induced back diffusion of vacancies at the interface displays the engineering stress-strain curves of all samples. Both the tensile strengths and elongations of the samples were highly influenced by preoxidation. After preoxidation at 900 °C for 1 h, the strength decreased slightly from 541 MPa to 525 MPa, but the elongation increased significantly from 15.2% to 23.8%. In addition, longer preoxidation at 900 °C slightly decreased the strength and shortened the elongation. The above changes might be attributed to the elimination of residual stress and recrystallization in the Zr-4 substrate. Besides, the improvement of microstructure of Cr coating by high temperature annealing also played a positive role in the increase in elongation, evidences of which were presented in the following sections. However, after preoxidation at 1000 °C for 1 h, the strength decreased significantly to 437 MPa, and the elongation also declined to 10.6%. Different preoxidation conditions had different effects on the elongation of the coated samples, which was closely related to the oxidation-induced microstructure evolution and cracking behaviour of the coated samples. Detailed analyses are presented in the following section. Furthermore, it is worth noting that both the strength and elongation of the preoxidized coated sample were significantly improved compared to those of the uncoated sample, attributed to the effective protection of the Cr coating from further oxidation. The results revealed that the Cr coating enhanced not only the oxidation resistance but also the mechanical properties of the sample.Next, in situ observations of the surface cracking behaviours in the coated samples were presented. summarizes our previous results of tensile cracking in the as-deposited coated sample published in Ref. (a)-(d), the first visible long channel crack vertical to the loading direction appeared on the coating surface when the tensile strain, ε, reached 0.4%. Under continuous tension, new cracks constantly initiated and grew in areas between two existing parallel cracks, resulting in a rapid increase in the surface crack density. Subsequently, the crack density reached a plateau stage, and new cracks could hardly be formed anymore. The character of surface cracking in the Cr coating under tension was consistent with those in a brittle coating-ductile substrate system (e) and (f), vertical channel cracks slightly penetrated the substrate and stopped further propagating, while few short interfacial cracks were found to initiate from the vertical crack tips.The surface crack evolutions showed a similar trend in the Cr coatings preoxidized at 900 °C for 1 h and 2 h. For the 900 °C/2 h preoxidized Cr coating shown in , when ε reached 1.93%, two short parallel cracks appeared on the green oxide layer covering the coating surface. With the increase in ε, new surface cracks formed rapidly to release the local tensile stresses, thereby leading to a high crack density. At ε= 8.53%, local spallation began to occur to further release the stresses. Subsequently, the spallation areas became larger with the increase in ε until the final fracture. The high crack density and remarkable spallation in the preoxidized coating indicated that the oxide layer was more brittle than the coating and that the interfacial adhesion between them was weak. Furthermore, it was surprising that no visible surface cracks penetrated through the Cr coating, and it appeared that the deformation compatibility between the coating and the substrate was highly improved and that the crack arresting ability of the coating was remarkably enhanced by preoxidation.For the 1000 °C/1 h preoxidized sample shown in , the green oxide layer became dark due to further oxidation. The initiation of parallel surface cracks and spallation of oxides occurred earlier than those in the 900 °C/2 h preoxidized Cr coating and then followed a similar trend with increasing strain. The earlier cracking and spallation indicated a lower strength of the oxide layer and a weaker interfacial bonding strength between the oxide and the coating. As seen in (f), severe oxide spallation was found in the shrinking area due to large local plastic deformation. Furthermore, it is worth noting that the first formed surface crack penetrated through the Cr coating and became increasingly deeper, which indicated that the crack arresting ability of the Cr coating was weaker than that preoxidized at 900 °C for 2 h.The variation in oxide spallation area could reflect the interfacial adhesion between oxide and the coating. Thus, the oxide spallation ratio, namely, the percentage of the oxide spallation area in the originally selected area, was calculated by colouring the spallation areas in red in ImageJ software, as shown in compares the evolution of oxide spallation ratios with ε for different preoxidized coatings. When oxidized at 900 °C, a shorter oxidation time led to a higher spallation ratio. The oxide spallation was the results of interfacial crack propagation and delamination between the oxide layer and the coating. Driven by the large local peeling and shear stresses, numerous interfacial cracks initiated from the vertical crack tips. Based on the shear-lag theory (a) and (b)), which might lead to a higher local stress concentration at the interface under tension, thereby causing easier and earlier interfacial delamination and spallation than those in the 900 °C preoxidized coating. shows the surface and longitudinal sectional morphologies of the 900 °C/1 h preoxidized sample. Apart from severe spallation of the oxides, rarely visible surface cracks (namely, vertical cracks in the longitudinal sectional view) in the Cr coating were found. As shown in 12(c), only a fine surface crack, which could not indicate whether it penetrated through the coating, was formed near the fracture surface. According to the longitudinal sectional views in (d) and (e), the coating/substrate interface tended to be rough near the fracture surface due to large plastic flow in the Zr-4 substrate. The formation of cracks in the oxide layer might lead to local stress concentrations near the coating surface, but no vertical cracks were formed passing through the coating. However, as shown in (e), numerous microcracks were generated at the interface, and some coalesced together to form a large microcrack, which was quite different from those in the unoxidized coatings (see (e) and (f) for example). According to the image quality (IQ) figure and corresponding EBSD orientation map shown in (f) and (g), the column grains in the Cr coating were surprisingly varied to be equiaxial after preoxidation. The variation in the grain morphologies might be beneficial to improving the crack arrest of the Cr coating. shows the morphologies of the 900 °C/2 h preoxidized sample. The surface cracks in the oxide layer were found to be transgranular (see (b)). In addition, few surface cracks (namely, vertical cracks) penetrated although the Cr coating near the fracture surface (see (c) and (e)). Based on the IQ figure and EBSD orientation map in (f) and (g), the vertical cracks in the Cr coating were also transgranular. In addition, numerous microcracks were initiated in the intermetallic ZrCr2 layer between the coating and the substrate. The formation of these microcracks might lead to degradation of the interfacial adhesion, inducing the initiation of interfacial cracks from the vertical crack tip (see , for the 1000 °C/1 h preoxidized sample, the oxide layer was thicker than that of the other samples, and interfacial cracks between the oxide layer and the coating coalesced with vertical cracks, resulting in local spallation of the oxide. There were more penetrated cracks in the Cr coating than in the preoxidized samples at 900 °C. (c) presents a transgranular surface crack in the Cr coating whose crack tip was blocked by the grain boundary of the Cr coating. Furthermore, the microcracks in the thicker intermetallic ZrCr2 layer were longer than those in the preoxidized samples at 900 °C. As shown in (e), these vertical microcracks easily penetrated the substrate, leading to earlier fracture of the sample.The pre-oxidized samples exhibited distinct tensile properties and failure mechanisms, which can be related to the change of coating microstructures by the pre-oxidation processes. displays the EBSD results of the preoxidized coating surfaces after removing the surface oxide layers. The average grain sizes reached 16 µm, 24 µm and 55 µm for the 900 °C/1 h, 900 °C/2 h, and 1000 °C/1 h oxidized Cr coatings, respectively. Significant grain size increase was noted, compared with the as-deposited coating (2.5 µm) in (b). It is inferred that recrystallization and grain growth had occurred in the Cr coating. When exposed to 900 °C for 1 h, the grain sizes of the Cr coating were quite uneven ((a)), but when exposed for a longer time, they became more uniform ((c), when the exposure temperature increased to 1000 °C, the grain sizes increased significantly because a higher temperature accelerated the migration of the grain boundaries and the grain growth rate. It is worth noting that the grain sizes of these preoxidized coatings seemed much larger than those of the Cr coatings prepared by other deposition techniques, such as the magnetron sputtering method (d)-(g), apart from grain growth, grain orientations also varied after preoxidation. Compared with the as-deposited coating in , the preoxidized coatings still exhibited (001) preferential orientations, but the texture intensities decreased to some extent. In addition, preoxidation also led to the redistribution of the misorientation angle. The recrystallization process at high temperature led to a decrease in the dislocation density of the coating, associated with the transformation from low-angle grain boundaries to high-angle grain boundaries, thereby increasing the probability of large misorientation angles. shows the orientation maps of the longitudinal sections of Cr coatings. Preoxidation evidently changed the grain morphologies from columnar structures to equiaxial structures, and the thickness reduction was due to oxidization. The grain growth and microstructure change of the Cr coating caused by recrystallization might positively affect arresting cracks in the Cr coating. For the as-deposited brittle Cr coating with columnar grains, vertical cracks were easy to initiate and penetrate through the coating under tensile stresses. After preoxidation, recrystallization process remarkably released the internal stress and the equiaxial grains transferred from columnar grains were beneficial to the ductility of Cr coating. The equiaxial grains possessed more grain boundaries in the thickness direction, which helped to hinder the slips in the grains and block vertical crack propagation, thereby enhancing the crack arresting of Cr coating. However, when preoxidized at 1000 °C for 1 h, the grain size was so large that there were few grain boundaries to prevent crack propagation through the coating (see , caused by the interdiffusion between the Cr coating and the Zr-4 substrate at high temperature, a nanoscale Cr-Zr interlayer was formed at the coating/substrate interface. Based on the TEM and EDS results, this layer mainly consisted of intermetallic ZrCr2 C15 (FCC structure) and C14 (HCP structure) Laves phases. Some references (e), oxygen diffused through the Cr coating and the ZrCr2 layer into the Zr-4 substrate. The semiquantitative EDS point analysis listed in shows that the oxygen content in the substrate adjacent to the ZrCr2 layer reached 19.03 at% at Point 5 in (a). The dissolution of oxygen in the substrate might induce a phase transition from β-Zr to oxygen-stabilized α-Zr(O) at high temperature.After preoxidation, the formed intermetallic ZrCr2 layer was quite brittle so that cracking could be easily initiated under tensile loading. As shown in (a)-(c), dislocation pile-ups and twinning were found in the grains of the ZrCr2 layer after tension. It is worth mentioning that annealing twins might already exist in the ZrCr2 layer of the preoxidized sample before tension, and deformation twins might also be formed under tension b). However, these cracks were all blocked in the ZrCr2 layer without any penetration to the coating and the substrate, which indicated that the ZrCr2 layer had a lower fracture toughness than both the Cr coating with equiaxial grains and the annealed Zr-4 substrate.Compared to the 900 °C/2 h preoxidized sample, the ZrCr2 layer (mainly in the C15 Laves phase) was thicker, and its grains were more uneven, as shown in . The rough interfacial morphology might lead to a significant local stress concentration and thus easier crack initiation at the interface under external loadings. Driven by the residual stress and tensile loading, twin bands were found more remarkably in the ZrCr2 grain (see (a)-(c)), and stacking faults were formed and blocked by the Cr coating (see (d)). Eventually, vertical transgranular cracks were generated in the ZrCr2 layer. Note that these cracks also had difficulty propagating to the Cr coating, but some of them penetrated the Zr-4 substrate beneath the ZrCr2 layer, which could also be found in the SEM results in (d) and (e). The crack penetration to the substrate indicated that the fracture toughness of the Zr-4 substrate was decreased after preoxidation. Based on the EDS map and the point analysis listed in , the content of the oxygen-enrichment at Point 5 in (a) reached 39.35%, which far exceeded its solubility limit in β-Zr According to the above experimental results, the cracking behaviours both on the surfaces and at the interfaces of the preoxidized samples were quite different from those in the unoxidized sample. It was proven that preoxidation considerably changed the microstructures and mechanical properties of the coated samples, thereby leading to different cracking behaviours, as illustrated in (a)-(c), for the unoxidized sample, vertical cracks were likely to be generated and propagated through the Cr coating under tension, but they could not penetrate the Zr-4 substrate due to crack blunting at the interface. Instead, few interfacial cracks initiated from the crack tips under larger tensile strain, driven by huge local stress concentrations.(d)-(f), for the 900 °C preoxidized sample, recrystallization and residual stress elimination occurred in both the Cr coating and the substrate (g)-(i), for the 1000 °C preoxidized sample, the Cr2O3 layer and ZrCr2 layer became thicker, the Cr coating became thinner, and the grain sizes in all layers were larger than those of the 900 °C preoxidized sample. The nonuniform interdiffusion ZrCr2 layer led to a rough coating/substrate interface, which might cause a remarkable local stress concentration. Under tensile loading, the Cr2O3 layer had more severe spallation, and the ZrCr2 layer more easily generated vertical cracks. These cracks could penetrate the Cr coating with coarse grains and the brittle α-Zr(O) substrate induced by oxygen enrichment. Therefore, although the improvement in the microstructure of Cr might positively affect its ductility, the initiation and propagation of microcracks at the coating/substrate interface led to premature failure of the sample under tensile loading. Therefore, preoxidation at 1000 °C played a negative role in the crack arresting of the Cr coatings.Based on the above analyses, it can be predicted that under extreme accident conditions, high-temperature steam oxidation leads to more severe degradation of the mechanical properties of the coated sample. However, with the protection of the Cr coating from extensive oxidation in the Zr-4 substrate, the coated samples might still have better mechanical properties than the uncoated samples. Furthermore, the experimental results might suggest that the mechanical properties of the Cr coating may be effectively improved by optimizing the deposition parameters and heat treatment process. Once the grains of the Cr coating transform from a columnar structure to an equiaxial structure and the residual stress is eliminated by recrystallization annealing, the ductility of the Cr coating and the deformation compatibility with the Zr substrate is greatly improved. Meanwhile, the oxidation resistance might also be enhanced due to the decrease in the number of grain boundaries in the Cr coating and thus the decrease in oxygen diffusion paths through the coating.This study explored the role of preoxidation in the mechanical properties and cracking behaviours of Cr-coated Zr-4 alloys. To this end, in situ tensile tests were conducted to obtain tensile properties and the evolution in surface cracking. In addition, the oxidation-induced microstructure evolution of the Cr coating was analysed, and the cracking behaviour at the coating/substrate interface was further investigated. The main conclusions were summarized as follows:Preoxidation considerably changed the microstructures of the Cr coated Zr-4 samples, resulting in the formation of an interfacial ZrCr2 diffusion layer and recrystallization in the Cr coating, transforming columnar crystals into equiaxial crystals at 900 °C or high temperatures.For the sample preoxidized at 900 °C, although microcracks were formed in the brittle Cr2O3 layer and the ZrCr2 layer under tension, they could hardly penetrate into the coating. The equiaxial grains of the preoxidized Cr coating hindered slip deformation and blocked crack initiation, which enhanced crack arresting of the Cr coating and thus increased the elongation of the coated sample. It should be pointed out that the positive role of preoxidation at 900 °C was only based on the presented in-situ testing method.For the sample preoxidized at 1000 °C or higher temperature, the generated cracks in the ZrCr2 layer were prone to penetrate into both the Cr coating and Zr-4 substrate under tension, leading to premature failure of the sample. In this case, preoxidation played a negative role in crack arresting of the Cr coating. The prefailure was attributed to the following factors: (a) the considerable local thermal mismatch stress at the rough interface, (b) the decrease in fracture toughness of the Cr coating with coarse grains, (c) the easier crack penetration from a brittle ZrCr2 diffusion layer into the coating and the substrate, and (d) the oxygen enrichment in the Zr-4 substrate promoting the phase transition from ductile β-Zr to brittle α-Zr(O).Jishen Jiang: Methodology, Investigation, Visualization, Validation, Data curation, Writing − original draft preparation. Xianfeng Ma: Conceptualization, Supervision, Writing − review & editing, Funding acquisition. Biao Wang: Conceptualization, Supervision.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Microstructure and high strength–toughness combination of a new 700 MPa Nb-microalloyed pipeline steelA new ultrahigh strength niobium-microalloyed pipeline steel of yield strength ∼700 MPa has been processed. The Charpy impact toughness at 0 °C was 27 J and tensile elongation was 16%. The ultrahigh strength is derived from the cumulative combination of fine grain size, solid solution strengthening with additional interstitial hardening, precipitation hardening from carbides, dislocation hardening, and mixed microstructure. The microstructure was characterized by polygonal ferrite, upper bainite, degenerated pearlite, and martensite–austenite (MA) constituents. The microstructure of weld and heat-affected zone (HAZ) was similar to the base metal such that the hardness is retained in the weld region implying insignificant softening in the weld zone. Niobium and titanium precipitates of different morphology and size range evolved during thermomechanical processing and include rectangular (∼500 nm), irregular (∼240–500 nm), cuboidal/spherical (∼125–300 nm), and very fine (<10 nm). They were generally MC type of carbides. An important aspect of the developed steel is significantly lean chemistry.Currently there is a demand to transport crude oil and gas by pipeline at a higher operating pressure to increase the capacity. This requires the use of ultrahigh strength steels. Increasing the strength of the pipeline steel enables a significant reduction in wall thickness with consequent reduction in weight. Thus, a major goal within the steel industry is to develop ultrahigh strength microalloyed pipeline steels (∼700–800 MPa). It is, however, important that the increase in the yield strength is not accompanied by a decrease in fracture toughness and formability because a decrease in toughness will encourage stress-induced cracking, and reduced formability will cause difficulties in forming (e.g. pipe-bowing). Thus, high strength in association with high toughness and formability are important requirements of the pipeline industry High strength–toughness combination is essential for pipeline steels for transporting natural gas and crude oil over a long distance under high pressure The evolution of microstructure depends on alloy chemistry and thermomechanical processing. Alloying additions such as Mn, Nb, V, Ti, Mo, Ni, Cr and Cu are commonly employed in pipeline steels to obtain the desired microstructure and mechanical properties Controlled thermomechanical processing is considered as the primary route for the development of API grade pipeline steels because it provides the desirable and fine-grained microstructure. Furthermore, it allows high strength–toughness combination to be achieved with accelerated cooling In thermomechanically processed pipeline steels The Nb-microalloyed pipeline steel described here was continuously cast and hot rolled to a minimum of ∼7.6 mm gage and subsequently fabricated to ∼150 mm diameter pipes. The alloy design and nominal chemical composition of the steel was based on our recently patented hot rolled steel Standard tensile tests were conducted at room temperature on longitudinal specimens machined according to ASTM E8 specification using computerized tensile testing system. The initial crosshead speed was 4.2 × 10−2 |
mm/s up to a strain of ∼5%, then the speed was increased to 4.2 × 10−1 |
mm/s. Impact toughness was measured using standard Charpy v-notch impact test (ASTM 23) at 0 °C.Transmission electron microscopy was carried out on samples cut from the fabricated steel pipe and relate to regions corresponding base, HAZ, and weld metal zones. Thin foils were prepared by cutting thin wafers from the steel samples using precision saw (Buehler Isomet 1000) and grinding to ∼100 μm in thickness. Three-millimeter discs were punched from the wafers and electropolished using a solution of 10% perchloric acid in acetic acid electrolyte. Carbon extraction replicas were also prepared for characterization of precipitates. The surface of the polished specimens was etched with 2% nital and carbon was evaporated onto the etched surface. Finally, the surface was scored to ∼3 mm squares and the sample etched first with 10% nital and then with 2% nital. Subsequently, the extracted replicas were rinsed with distilled water and placed on the copper grid and dried. Foils and carbon extraction replicas were examined with a Hitachi 7600 TEM operated at 100 kV.The yield and tensile strength of the hot end of the coil was ∼735 MPa (105 ksi) and ∼791 MPa (113 ksi), respectively. The Charpy v-notch impact toughness of Nb-microalloyed pipeline steel at 0 °C was 27 J and the tensile elongation was 16%. It may be noted that the listed mechanical properties are the minimum values that were obtained on any coil.Representative light micrographs of base, HAZ, and weld metal are presented in . The microstructure was predominantly fine-grained ferrite in all the three zones. As expected, the base metal (as-hot rolled) contained some elongated ferrite grains (b). A hardness profile encompassing base, HAZ, and weld metal zones is presented in . The hardness–distance profile indicates that the weld zone and HAZ did not experience significant softening, consistent with the microstructure of the three zones, as described below.Representative low-magnification bright field TEM micrographs of the base metal are presented in . In general, the microstructure was of mixed type consisting of ferrite, upper bainite, and degenerated pearlite. The ferrite grains were of non-equiaxed (a) and were characterized by sub-boundaries and dislocation substructures (b), and carbides at the ferrite grain boundaries (c). A region of the base metal characterized by upper bainite/degenerated pearlite is presented in are high-magnification bright field TEM micrographs of ferrite grains that contained high density dislocations at the grain boundaries (a), dislocations in the body of the grain (Representative bright field TEM micrographs of HAZ are presented in . The ferrite microstructure was similar to the base metal and contained high density of dislocations and substructure (a and b). Small differences due to the welding process include coarse-grained quasi-polygonal ferrite with small M/A islands at grain boundaries (b). At high magnification, the martensite contained microtwins of different orientations (c). The twinned martensite is an indication of high carbon content and the morphology is typical of that observed previously in pipeline steels d implied that the bainitic ferrite exhibits [0 0 1] orientation with the ferrite matrix.Representative TEM micrographs of precipitates in the base metal are presented in . The precipitates were of different size and morphology and include cuboidal (∼150 nm), spherical (∼125 nm), irregular (∼240 nm), fine (∼10 nm) and very fine (<10 nm). The EDS analysis obtained for precipitates identified in a indicated that they were (Ti, Nb)C. Bright field TEM micrographs presenting illustrations of fine precipitates within the grain, at grain boundaries, and dark field micrograph of very fine scale precipitation are presented in b–d, respectively. The SAD pattern analysis (inset in d) obtained for fine scale precipitates confirmed that they were MC type of cubic carbides, having [0 1 2]a//[0 1 1]MC orientation relationship with the ferrite matrix.a and b are bright field TEM micrographs showing regions of precipitation on dislocations and precipitate–dislocation interaction. Similar observations were made on carbon extraction replica and are briefly presented here. Examples of coarse and fine precipitates are presented in a and b. The coarse precipitates were identified as titanium and niobium rich carbides, while the SAD of fine precipitates confirmed that they were MC-type cubic carbides. A plot of precipitate size distribution corresponding to fine and very fine precipitates plot is presented in c, with average particle size of ∼6.5 nm.The microstructure of the weld metal predominantly consisted of coarse non-equiaxed ferrite grains with M/A islands at a number of grain boundaries. In addition, weld metal also contained small volume fraction of degenerated pearlite, bainite, and martensite. Representative TEM micrographs at low magnification showing the general ferrite microstructure containing a number of M/A islands, sub-boundaries, and significant amount of dislocations and dislocation substructures are presented in . In general, weld metal contained higher volume fraction of M/A constituent, bainite, and martensite as compared to the base metal. This may be a consequence of the different cooling rate experienced by the steel during the multi-pass welding process.Representative bright field TEM micrographs of various microstructural constituents present in the weld metal zone are presented in a and b describe typical characteristic morphology of martensite/austenite constituent and needle-like martensite, respectively, while c and d show typical morphology of degenerated pearlite and upper bainite, respectively. Since M/A constituent is predominantly present as a second phase in pipeline steel, a detailed TEM study was carried out to understand its microstructure. show bright and dark field TEM micrographs of M/A constituent and the corresponding SAD pattern analysis is presented in c. The SAD pattern analysis revealed the presence of retained austenite together with martensite and the orientation relationships were [1¯22]γ//[001]αand[1¯11]γ//[001]α. The M/A constituent formed as alternative layers of retained austenite and martensite. A schematic of M/A layers is depicted in d based on the morphological features observed from presents representative bright field micrographs together with EDS analysis of coarse precipitates observed in the weld metal. The precipitates were larger in size as compared to base metal and exhibited rectangular (∼500 nm), irregular (∼500 nm), cuboidal (∼300 nm), spherical (∼200 nm) and fine (<10 nm) morphology. The EDS analysis revealed that these precipitates were rich in titanium, niobium, and contained small amount of chromium. Unlike the base metal, the weld metal typically contained precipitates of size range ∼18–28 nm in high density. b shows bright field TEM micrograph of these coarse precipitates. EDS analysis obtained on these precipitates indicated that they contained niobium, titanium, iron and manganese. The SAD pattern obtained on these precipitates revealed a complex pattern as shown in the inset in b. The precipitate size distribution plot is presented in c and the average precipitate size was ∼14 nm. are bright and dark field TEM micrographs of carbon extraction replica of weld metal illustrating the fine scale precipitation in weld metal. The SAD pattern analysis of fine precipitates presented in c indicated that these precipitates were MC-type cubic carbides. The precipitate size distribution plot is depicted in d. Majority of the fine precipitates were in the size range of 6–8 nm and the average precipitate size was ∼7 nm.In summary, it can be said that the microstructure of base, HAZ, and weld metal was similar and characterized by a combination of non-equiaxed ferrite, degenerated pearlite/upper bainite, and martensite–austenite constituent (M/A) in the order of increasing cooling rate and decreasing transformation temperature ). The small variation in the hardness is a consequence of a number of factors that include recrystallization and grain refinement/growth, phase composition, and precipitates The non-equiaxed ferrite microstructure presented in is defined as quasi-polygonal ferrite or massive ferrite. Quasi-polygonal ferrite is the first high temperature (below Ae3, equilibrium temperature) ferrite phase to form during continuous cooling. It nucleates heterogeneously at the boundaries of the austenite grains. It is a reconstructive transformation involving diffusion of the atoms, such that the grains of ferrite grow freely across the austenite grain boundaries The other microstructural constituents present in the investigated steel were degenerated pearlite/upperbainite (), martensite/austenite constituent (M/A) () and they can be considered as microphases Degenerated pearlite is formed by nucleation of cementite at ferrite/austenite interfaces followed by carbide-free ferrite layers enclosing the cementite particles. It nucleates in the transformation temperature range between normal pearlite and upper bainite Martensite–austenite constituent (M/A): In pipeline steel during continuous cooling austenite first transforms to ferrite and the remaining austenite becomes carbon rich. On further lowering of transformation temperature, the retained austenite transforms to non-equiaxed or lath ferrite or acicular ferrite and the retained austenite is fully stabilized with highest carbon concentration. Thus, during cooling when the transformation temperature reaches martensite start temperature (Ms), the high carbon austenite transforms into lenticular microtwinned martensite with different size and orientation ( the typical M/A constituent consisting of alternate layers of martensite and retained austenite is illustrated. It is suggested that the martensite plate first formed will intersect and segment the austenite grain by blocking the plates that forms in the later period. Thus, the martensite formed at different stages results in different morphology and orientation b) shows the retained austenite layer in between the martensite plates. Martensite–austenite constituent (M/A) is considered to play an important role in obtaining high strength–toughness combination in pipeline steels Alloying elements used in the investigated steel such as Mn, Nb, Ti and Cr play an important role in the formation of resultant microstructure. For example, it is shown that the increase in Mn content (∼1.5%) of steel shifts the polygonal ferrite curve of CCT diagram to the right, promoting the formation of intermediate transformation products such as acicular ferrite and bainite The precipitates observed in the present pipeline steel are similar to those observed in conventionally hot rolled microalloyed steels and pipeline steels Fine strain-induced niobium carbides were observed in the ferrite phase of base steel (). Precipitate size distribution plots () indicated that the average particle size was in the range of ∼6–7 nm. This is an effective size range for precipitation hardening In summary, strength of the pipeline steel is a cumulative contribution of grain refinement, M/A constituent, bainite, precipitation hardening, and dislocation strengthening.A new ultrahigh strength niobium-microalloyed steel of yield strength of ∼700 MPa consisting of polygonal ferrite together with upper bainite, degenerated pearlite, and martensite–austenite constituent has been developed. The microstructure of HAZ and weld zone was similar to that of the base metal, consistent with the hardness data. The precipitates in the niobium-microalloyed pipeline steel can be classified on the basis of size and morphology and include rectangular, irregular, cuboidal/spherical, and fine morphology with size range of ∼500, ∼240–500, 125–300 nm, and <10 nm, respectively. Strain-induced MC (NbC) type of carbides precipitated on dislocations, and at grain boundaries. The observed high strength–toughness combination is derived from the cumulative effect of fine-grained ferrite microstructure, M/A strengthening, dislocation strengthening, and precipitation strengthening.Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flowsThe Uzawa-like algorithm is implemented for two-dimensional flows of viscoplastic fluids. The rheological model employed is the ideal Bingham model. As a test the lid-driven square-cavity benchmark problem is considered. The results for the steady-state problem are faithfully reproduced as compared to those in the literature for the shape and location of the yield surface. The proposed method is very successful at capturing both yielded and unyielded regions.Viscoplastic materials behave as rigid solids when the imposed stress is smaller than the yield stress, and they flow as fluids when yielded. The flow field is divided into two regions: the unyielded (rigid) and the yielded (fluid) zone. As a rule, the following two types of rigid zones are traditionally distinguished: the stagnation (dead) zones, where the medium is at rest, and the plug region (core), where the medium moves as a rigid body. The separation surfaces between rigid and fluid zones are related to the yield surfaces. The location and shape of the unyielded region have to be found as part of the solution of the initial boundary-value problem. Thus, the characteristic feature in the problem of viscoplastic medium flows is the necessity of constructing a solution in a domain with an unknown boundary.The main difficulty in the numerical simulation of viscoplastic fluid flow is related to the non-differentiable form of constitutive law and inability to evaluate the stresses in regions where the material has not yielded. There are two principal approaches that have been proposed in the literature to overcome the mathematical problem of viscoplastic fluid flow. The first one, known as regularization method, consists in approximating the constitutive equation by a smoother one. The second method is based on the theory of variational inequalities The isothermal flow of an incompressible viscoplastic fluid is governed by the following equations: Here Ω denotes a bounded domain in Rd (d=2,3), Γ the boundary of the domain, [0,T] a time interval, u is the velocity vector, ρ is the density, p is the pressure, τ is the extra stress tensor, f is the given field of external forces, τ0 is the yield stress and μ is the plastic viscosity, D is rate-of-strain tensor D(u)=(∇u+(∇u)T)/2 with norm |D|=D:D, and A:B=∑i=1d∑j=1daijbij, for all A=(aij), B=(bij). The first equation represents the momentum equation, the second one is continuity equation, while the third one is the rheological constitutive relations (Bingham model). Hereinafter we consider d=2. The above system of equations must be provided with suitable initial and boundary conditions: we consider the following variational inequality model: find u∈(H01(Ω))2 such that a.e. on (0,T) we haveρ∫Ω∂tu(t)⋅(v−u(t))dxρ∫Ω(u(t)⋅∇)u(t)⋅(v−u(t))dx+μ∫Ω∇(u(t)):∇(v−u(t))dx+τ02∫Ω(|D(v)|−|D(u(t))|)dx≥∫Ωf(t)⋅(v−u(t))dx,∀v∈UB,∇⋅u(t)=0in Ω,u(0)=u0in Ω,u(t)=uB(t)on Γ,UB={v∈(H1(Ω))d|v=uB(t) on Γ}.λ=λT,|λ|≤1,λ:D(u)=|D(u)|a.e. in Ω×(0,T),ρ[∂u∂t+(u⋅∇)u]−μΔu−τ02∇⋅λ+∇p=fin Ω×(0,T),∇⋅u=0in Ω×(0,T),u(0)=u0in Ω,u=0on Γ×(0,T). are equivalent to λ=PΛ(λ+rτ02D) for ∀r≥0 with the closed convex set Λ and the projection operator PΛ:(L2(Ω))4→Λ,Λ={q∈(L2(Ω))4,|q|≤1,q=qT},PΛ(q)={q, if |q|≤1,q/|q|, if |q|>1}.In most of the papers devoted to numerical modeling of Bingham medium, the convective terms are neglected. In this case, we use backward Euler scheme for time-discretization of problem . We have supposed the time interval of interest (0,T) has been divided into N subintervals [tn,tn+1], where tn+1−tn=Δt, n=0,1,…,N−1. Assume then, for n≥1 we compute un from un−1 as the solution to the following inequalityρΔt∫Ω(un−un−1)(v−un)dx+μ∫Ω∇un:∇(v−un)dx+τ02∫Ω(|D(v)|−|D(un)|)dx≥∫Ωfn⋅(v−un)dx,∀v∈UB. Here we denote f=fn+ρΔtun−1, later we omit the subscript n.We consider the following Lagrangian functional L:(H1(Ω))2×(L2(Ω))4→R asL(v;η)=12∫ΩρΔtv2dx+μ2∫Ω|∇(v)|2dx+τ02∫Ωλ:D(v)dx−∫Ωf⋅vdx. In accordance with the minimax theorem (u,λ)∈UB×Λ,L(u;η)≤L(u;λ)≤L(v;λ),∀(v,η)∈UB×Λ, and the first component of the pair u is uniquely determined and it is the solution to problem for k≥0, assuming that λk(∈Λ) is known, we compute uk and pk as followsρΔtuk−μΔuk−τ02∇⋅λk+∇pk=f,∇⋅uk=0in Ω,uk=uBon Γ; after that, the new approximation λk+1 is determined as The convergence of the algorithm was proved for the interval 0<r<μ/2τ02The problems at hand are made dimensionless: the lengths are scaled by a characteristic length, L, and the velocity is scaled by a characteristic velocity, U. Then the time is scaled by ρL2/μ, and the pressure and stress are scaled by μU/L. In the case of the lid-driven square-cavity flow, L is the square size and U is the speed of the moving lid. We introduce Bn (denotes the Bingham number) and Re which is defined as follows: Bn=(τ0L)/(μU), Re=(ρUL)/(μ). For the time scheme, we decouple the system into two subsystems: the Navier–Stokes problem and the plasticity problem. For the Navier–Stokes equations Baker, Dougalis and Karakashian suggested and investigated Find a preliminary (intermediate step) un+1/3 as the solution of the following semi-discrete problem12Δt(3un+1/3−4un+un−1)−12ReΔun+1/3+∇pn=fn+1−((2un−un−1)⋅∇)(2un−un−1)in Ω,Determine un+2/3 and pn+1 as the solution ofΔϕn+1=32Δt∇⋅un+1/3,∂ϕn+1∂n|Γ=0,32Δt(un+2/3−un+1/3)+∇ϕn+1=0,pn+1=pn+ϕn+1−1Re∇un+1/3.∫Ω(un+1−un+2/3)(v−un+1)dx−12Re∫Ω∇un+1:∇(v−un+1)dx+Bn2Re∫Ω(D(v)−D(un+1))dx≥0,∀v∈(H1(Ω)2),v=uBn+1 on Γ. The plasticity step here is equivalent to the plasticity step in is obtained by Uzawa algorithm similar to then, assuming that λn,k(∈Λ) is known, for k≥1, find un+1,k as solution1Δt(un+1,k−un+2/3)−12ReΔun+1,k−Bn2Re∇⋅λn+1,k=0,un+1,k=uB on Γ,. The above step is iterated for k until the solutions are converged. The convergence criterion used in this study is |λn,k−λn,k−1|<ε.There is another way to use the BDF2 for solving viscoplastic problem. We can use BDF2 scheme directly to discretize Eqs. , transport convective terms to the right-hand side and apply ALM to the resulting system of equations. At each time step and in each iteration the generalized Stokes problem is solved. In our opinion the fractional step method is more efficient. The most expensive is the third sub-step, where in each iteration two Poisson problems are solved. The solving a Poisson problem is simpler and cheaper than solving a generalized Stokes problem. It is possible that in the case of a small influence of inertia (for low Reynolds numbers or high Bingham numbers) the BDF2-ALM and the fractional step method will be equally effective.The space discretization of the governing equations will be achieved by a finite difference method on a uniform staggered grid with mesh size h=h1=h2, where h1 and h2 are the step discretization in each direction. The discrete values of the pressure are located at the center of each cell and the velocity components u and v are located at the middle of the cell faces as shown in . The components (D11,D22,λ11,λ22) of strain-rate and Lagrange multipliers tensors are located at the cell centers whereas the non-diagonal components D12, λ12 (D12=D21) are located at the grid nodes A second order (with respect to h) choice for the discretization of Δp evaluated in the node (i,j) is given by(Δhp)i,j=pi+1,j−2pi,j+pi−1,jh12+pi,j+1−2pi,j+pi,j−1h22. In the same node, suppose that the discrete divergence operator (∇⋅)h applied to the vector u=(u,v) is defined by(∇h⋅uh)i,j=(ui+1/2,j−ui−1/2,j)/h1+(vi,j+1/2−vi,j−1/2)/h2, and, correspondingly, the discrete gradient operator ∇h is defined componentwise by(∂hp∂x)i+1/2,j=pi+1,j−pi,jh1,(∂hp∂y)i,j+1/2=pi,j+1−pi,jh2. At the same points we define the discrete divergence operator applied to tensor λ:(∂hλ11∂x+∂hλ12∂y)i+1/2,j=λi+1,j11−λi,j11h1+λi+1/2,j+1/212−λi+1/2,j−1/212h2,(∂hλ21∂x+∂hλ22∂y)i,j+1/2=λi+1/2,j+1/221−λi−1/2,j+1/221h1+λi,j+122−λi,j22h2. For the velocity we obtain the following discrete Laplace operator:(Δhu)i−1/2,j=ui+1/2,j−2ui−1/2,j+ui−3/2,jh12+ui−1/2,j+1−2ui−1/2,j+ui−1/2,j−1h22. The numerical simulation of high Reynolds numbers flows requires in particular a good approximation of the convective terms. The discretization of all others was described above. In the present work, the convective terms are treated explicitly and approximated by third-order upwind schemes to get both low diffusion effects and stability. The stability of first-order schemes is very good, but their accuracy is poor. On the contrary, second-order schemes are more accurate but their stability is in general not ensured. We illustrate below third-order schemes on the discretization of the terms u∂u∂x and v∂u∂y at point (i+1/2,j):(u∂u∂x)i+1/2,j=−ui−1/2,j(13ui+1/2,j+12ui−1/2,j−ui−3/2,j+16ui−5/2,j)1h1,if ui−1/2,j>0,ui−1/2,j(13ui−3/2,j+12ui−1/2,j−ui+1/2,j+16ui+3/2,j)1h1otherwise, where vi−1/2,j=14(vi−1,j−1/2+vi−1,j+1/2+vi,j−1/2+vi,j+1/2)(v∂u∂y)i+1/2,j=−vi−1/2,j(13ui−1/2,j+1+12ui−1/2,j−ui−1/2,j−1+16ui−1/2,j−2)1h2,if vi−1/2,j>0,vi−1/2,j(13ui−1/2,j−1+12ui−1/2,j−ui−1/2,j+1+16ui−1/2,j+2)1h2,otherwise. To take into account the boundary conditions, we use to fiction cells outside of the domain where the velocity is nearly extrapolated according to its value at the boundary., diagonal and non-diagonal components of tensor D are evaluated at the different mesh location:(Dh11(vh))i,j=(ui+1/2,j−ui−1/2,j)/h1,(Dh22(vh))i,j=(vi,j+1/2−vi,j−1/2)/h2,(Dh12(vh))i+1/2,j+1/2=(ui+1/2,j+1−ui+1/2,j)/2h2+(vi+1,j+1/2−vi,j+1/2)/2h1.For each strain-rate tensor component Dij the corresponding component λij and expression qij=λij+rBn2ReDij are computed at the same mesh. Let us note that q11+q22=0 and q12=q21, so |λ+rBn2ReD(u)|=|q|=2q112+2q122. However, the computation of |q| is rather delicate problem since q11 are computed at the cell centers and q12 are located at the cell nodes. To compute |q| at the cell centers, we consequently substitute in expression for |q| the magnitude of q12 from points (i+1/2,j+1/2), (i+1/2,j−1/2), (i−1/2,j−1/2) and (i−1/2,j+1/2):|qh|ij=24((qij11)2+(qi+1/2,j+1/212)2+(qij11)2+(qi−1/2,j+1/212)2+(qij11)2+(qi−1/2,j−1/212)2+(qij11)2+(qi+1/2,j−1/212)2). The computation of the |q| at the nodes (i+1/2,j+1/2) is based on the same rule:|qh|i+1/2,j+1/2=24((qij11)2+(qi+1/2,j+1/212)2+(qi+1,j11)2+(qi+1/2,j+1/212)2+(qi+1,j+111)2+(qi+1/2,j+1/212)2+(qi,j+111)2+(qi+1/2,j+1/212)2).This benchmark has been extensively used first for Newtonian fluids and then for Bingham fluids . We assume that u0=0, μ=ρ=1. For the time discretization we took Δt=0.001. We have shown in (a) the time variation of the computed norm of the velocity ‖uh(t)‖L2 for Bn=1,2,5. It is clear from this figure that we have fast convergence to a steady flow. We suppose that Bn=2 and have plotted in (b) the behavior of the convergence indicators: Δuk=‖uhn,k−uhn,k−1‖L∞, δuk=‖uhn,k−uhn,k−1‖L2, δD(u)k=‖Dh(uhn,k)−Dh(uhn,k−1)‖L2, Δλk=‖λhn,k−λhn,k−1‖L∞ at t=0.01. In we show the values of these convergence indicators Δu, δu, δD(u) in the last iterations of algorithm , for several time steps, as well as the total number of iterations in each of these time steps. For the convergence criterion we took Δλk<ε, where ε=0.001 and ε=0.005. Note that to reduce the computational cost a less stringent convergence criterion (say ε=0.005) can be used. Our results confirm that the vortex intensity and the position of the vortex center calculated from ε=0.001 and ε=0.005 are the same. The yield surfaces are slightly different. We need accurately determine the position of the yield surface and in all further calculations use ε=0.001. ALM and Uzawa-like method are generally slower than codes with regularization methods. Regularization methods produce smoother solutions for the velocity field. This smoothness allows the application of more sophisticated flow solvers and leads to faster computations. Another important computation issue is the accurate tracking of the yield surfaces. In this aspect, methods based on variational inequalities are more preferred than the regularization methods In the cases of high viscosity materials and low velocity the Reynolds number is very low and the convection term is very small. We neglect convection terms in the momentum equation. Such flows are used to be called creeping flows. Firstly we consider creeping flows, which will allow us to compare our results with previously published ones. we provide the streamlines distribution together with rigid zones (where the shear strain-rate vanishes, gray color) for different yield stress Bn=0.1,1,2,5,10,20,50,200,500 (we take μ=1 so Bn=τ0). The yield surface (the boundary of rigid zone) is defined as the isostress of |τ|=Bn2. The dead zones are located in the two lower corners and the other is the rigid-body motion zone near the vortex center. This figure illustrates the dependence of the rigid zones on yield stress: it can be easily seen that the rigid zones enlarge with increasing yield stress. We compare our results with the contribution of Glowinski and Wachs shows the vortex intensity and the y-position as a function of Bn. There is a very good agreement between our results and those in the above reference. shows the results for the vortex intensity and the center position as a function of Bn, for a fixed Re=1000. The vortex intensity is slightly more than in the previous case (creeping flow). It can be noticed that for the highest values of Bn, the inertia effects are softened, intensity and vortex location are almost the same as for creeping flow. The vortex intensity monotonically increases with decreasing Bn, inertia effects get stronger, and the vortex center goes to the right, reaches a maximum for Bn=20 and then moves down and back to the left toward the center of domain. The center positions obtained in the present study and by Vola et al. agree well with each other. The vortex intensities obtained in the present study are slightly less than those obtained in we plot the maps of the streamlines and the rigid (gray) zones for Re=1000 and various yield stress values (Bn=0.1,1,10,100). As well as for creeping flows the unyielded areas increase as Bn increases. It also can be noted that inertia significantly influences the distributions of the streamlines and yield surfaces for the lower and middle values of Bn. At a low Bingham number (Bn=0.1) we can see three vortices: the principal and the two secondary vortices located at the right and left bottom corners of the cavity. The tiny rigid zones are located in the lower corners (dead zones) and near the centers of the secondary vortices. As Bn increases secondary vortices in the bottom corners associated with a Newtonian fluid become rigid stagnant regions. At a middle Bingham number the center of the main vortex goes toward to right wall, the streamlines are distorted, the upper rigid zone moves to the left and the bottom rigid region non-symmetric, with the left part larger than the right ones. As the vortex center located at the upper right corner streamlines are distorted especially strong near the top and right walls. It implies higher stress and strain-rate levels in this regions. With the gradual removal of the center of the vortex to the left and down the stress and strain reduce. If the stress drops below the yield stress, then there are rigid zones. At a high Bingham (Bn=100) number the picture becomes more symmetric and a solution more similar to that of creeping flow. The shape of the yield surfaces is in qualitative agreement with We use operator-splitting idea to simplify the computation, but we employ different time-discretization and space-discretization. The method is verified by comparing our results on the lid-driven cavity flow to the data available in the literature. This method looks promising to us and we intend to apply it in the nearest future to solution of more complicated problems (flows in complex domains and flow of another rheological constitutive relations, such as Herschel–Bulkley law).Predict effective thickness of sacrificial cellular claddings to shallow/deep water blastThe cellular materials are well known to mitigate shock loadings. However, they may attenuate or enhance the shock transmitted to the protected structures. This paper is devoted to derive an explicit expression of the effective foam thickness when subjected to deep underwater explosion. Hereinafter, the effective foam thickness represents the crushed foam when the shock energy is just completely absorbed, i.e. the attenuation/enhancement boundary. One-dimensional (1D) analytical model which can consider the core crushing, the fluid-structure interaction (FSI), the cavitation phenomenon and the initially applied static pressure is proposed to solve the problem. The analytical model is then used for the parametric study. Finally, the empirical formulae of the effective foam thickness is derived from the results of the parametric study. In practical applications, the empirical formulae for the effective foam thickness can guide the design of such cellular claddings to water blast.Warships and submarines can be severely damaged by underwater explosion shock loadings (). To enhance the shock resistance ability of such weapons, one method is to design effective surface shields to protect the warships (). Cellular materials possess superior energy absorption capability and are widely used in resistance of shock/impact loadings (). However, some studies demonstrated that if the total energy of the blast impact loading is not effectively absorbed by the cellular material, it results in an enhancement of the transmitted force to the protective structure (). This is an unwanted situation in practical applications. Motivated by this fact, we devote to derive an explicit expression of the effective foam thickness needed to fully absorb the underwater shock energy in this paper. Hereinafter, the effective foam thickness represents the thickness of the crushed foam when the underwater shock energy is just fully absorbed, i.e. the attenuation/enhancement boundary.There has been several papers studying the attenuation/enhancement boundary of sandwich structures with cellular cores to air blast loading ( has derived an analytical solution for the response of a sandwich composite with a cellular core to the air blast. However, to derive an analytical solution for the similar structures to water blast is more difficult or even impossible since the involved the fluid-structure interaction (FSI) and cavitation phenomena are complex. A considerable body of literature exists on investigating sandwich structures to underwater explosion. The one dimensional (1D) analyses of paid attention to how to calculate the problem more accurately by considering the FSI effects and cavitation phenomena. The models are gradually improved from the original Taylor's model () to a simplified analytical model proposed by which could consider cavitation effects. Taking the above analyses into account, proposed a full theoretical model which can considering the cellular material compression, the FSI effects, and the initiation and closure of cavitation bubbles for the cellular cladding to water blast. For the two dimensional sandwich beams, divided the response into different regimes according to the intensity of the shock impulse and properties of the sandwich beams. They also found that there exists an optimum core strength for a given blast impulse and sandwich beam geometry, and a sandwich beam designed to be optimal for a given impulse is suboptimal for the other shock loadings. Therefore, the design work of such protective structures will become more concise and convenient if we know when a designed cellular protective structure attenuates/enhances the underwater shock loading. Up to now, there is no study dealing with this problem. In this paper, we will analyze this problem from the simplest 1D case by calculating the effective foam thickness under different intensities of water blast.There are two primary objectives in the present paper. First, the analytical model in is modified by adding the initially applied static pressure to consider both shallow and deep water blast. Then, the sensitivity of the effective foam thickness to different parameters (including the intensity of the shock wave and the static pressure, and the properties of the cellular materials) is discussed using the analytical model to derive the explicit expression of the effective foam thickness. The derived explicit expression of the effective foam thickness is very useful for optimal designs of cellular claddings against underwater shock loadings. gives the potential schematic map of using sacrificial cellular cladding as protective structures of ship hulls or submersible structures. Under water blast, the cellular materials will be sacrificed to absorb shock energy, thus decrease the energy and the stress transmitted to the ship hulls. If the cellular cladding is thin and cannot completely absorb the shock energy, the stress enhancement will take place in the ship hull and even enlarge the local hull response (). Therefore, the prediction of the effective thickness of the cellular cladding during the design is important. In this paper, we will analyze this problem from a 1D case, where the ship/submersible structure hulls are assumed to be clamped. When subjected to underwater explosion shock wave, the cellular cladding has been identified as the cellular material crushing phase and the FSI phase in a coupled way. In this section, we present the details of the analytical model, including the compaction mechanism of the cellular cladding, the FSI and cavitation phenomena.The cladding is comprised of a rigid front face sheet with area density of mf and a compressible cellular foam core, as shown in (a), where the rear end of the core is clamped. The foam core is modelled by an idealized rigid-perfectly plastic-locking (RPPL) material model. In the RPPL idealized material model presented by , two material parameters are used to define the material properties: the plateau stress σpl and the densification strain εD (The initial static pressure in water is pst, resulting in the initial stress in the foam before the blast loading. For a 1D problem, the initial stress in the foam equals to the initial static pressure. If the static pressure exceeds the yield strength of the foam, the cladding will be crushed before the arrival of the blast loading and cannot dissipate the shock energy anymore. Therefore, the static pressure analyzed in this paper is less than the yield strength of the foam. An underwater shock wave travelling in the positive x direction at a speed cw impinges on the front face sheet. The origin of Eulerian coordinates locates at the wet face (static equilibrium position), and the water with density ρw occupies the region x≤0. The exponentially decaying incident wave with time constant θ can be expressed by (Under water blast, there are two waves, the elastic precursor wave and the compaction plastic wave, travelling through the cellular material ((b)). The latter is a plastic unloading wave with a strong discontinuity if the applied load causes stress exceeding the yield stress of the material. The governing equations for the response of the cellular material are expressed in term of Lagrangian coordinates and the compressive stresses/strains are assumed to be positive.Suppose that the plastic wave front has a velocity D in space. According to , the displacement continuity across the plastic wave front can be expressed asand the conservation of the momentum is given bywhere subscripts 1 and 0 denote the region immediately behind and ahead of the wave front, respectively. V is the material velocity (the velocity of the particle motion). σ0 and σ1 are the quasi-static yield stress and the dynamic stress behind the wave front, respectively. According to Eqs. , the velocity of the shock front and the stress behind the plastic wave front areSince the elastic strains are much smaller than the plastic strains due to the compaction, the elastic strains in the deformed foam material behind the wave front can be neglected, i.e. ε0=0 and V0=0. In the RPPL model, ε1 is a constant value and equals to εD. A rigid unloading can be assumed and a rigid body motion of the compacted region is defined. The motion equation of the front face sheet and the compressed foam is obtained aswhere pwet is the pressure at the wetted face, u is the displacement of the front face sheet. The calculation of total pressure at the wet face, pwet, will be given in The pressure at the fluid-structure interface is given by (pwet(x=0,t)=pst+pin(x=0,t)+pr(x=0,t)-ρwcwdu/dtwhere pr is the reflected wave and pst is the initial static pressure. However, the incident wave, pin, will be cut off by the cavitation and the radiated pressure due to the cavitation closure will impinge on the cladding, as shown in (c). The pressure and velocity field in water between the reflected wave front and wet face can be expressed byfor −cwt≤x≤0. The cavitation time tcav(x) at any location x in the water can be calculated by solving equation pw(tcav,x)=0. Combining equation pw(tcav,x)=0 with Eq. , the velocity of the water particle at the instant of its cavitation isVcav(x)=2pin(tcav,x)+pstρwcw=2p0ρwcwe−(tcav/θ−x/(cwθ))+pstρwcwwhere tcav is the cavitation time at location x. Compared with the result in , there is a new item due to static pressure in Eq. . Details about the cavitation expansion and closure can be referred to . The radiated pressure due to the cavitation closure ispCF,out=(1−η)ρwcwλ22λ+(cw−2λ)η−pCF,in−pstwhere λ the auxiliary quantity, η is the fraction of the space occupied by cavitation bubbles, and pCF,in is the pressure wave approaching the cavitated region, given by{λ=(2pCF,in+pst)/(ρwcw)+Vcavη(x,t)=∫tcav(x)t∂Vcav∂xdτ>0pCF,in=pr−ρwcwdu/dtThe wave train pCF,out will replace the incident wave pin when it arrives at the wet face. Define that ta is the time instant when the radiated pressure wave by the closing front reaches the wet face for the first time, the actual incident wave impinging on the cladding can be rewritten byThe total pressure at the fluid-structure interface when considering cavitation reloading isif the front face sheet is treated as a rigid body., the water blast response of cellular claddings can be solved numerically with initial conditionsIn this section, the analytical model proposed in will be validated. Though there are ample experimental studies involving foam core structures to water blast, these structures are air-backed or water-backed rather than clamped boundary condition at the back face. Until now, there is no experiment which considers a foam core structure with clamped boundary condition at the back face under combined loads of static pressure and water blast. Therefore, we cannot directly verify the analytical model. The verification of the analytical model has to be achieved by two steps. First, the numerical results by FE method are compared with experiment data to verify the numerical modeling techniques. Then, the validated numerical modeling techniques are used to validate the analytical model.The one-dimensional shock tube experiment of is used to validate the numerical modeling techniques of a cellular foam under combined loads of water blast and initially applied hydrostatic pressure. (a) shows the schematic of the laboratory setup, where the water-backed cladding is comprised of aluminum face sheets and foam core ((b)). Experiment 5 is simulated by Abaqus/Explicit () and the simulations are compared with the experimental results. The initially applied hydrostatic pressure is 1.05 MPa, the peak pressure of the shock wave and decay constant are 8.8 MPa and 0.12 ms, respectively. One can refer to the paper by for other details. The front and back face velocities and displacements histories for specimen 1 is plotted in , which indicates that the numerical model can adequately predict the experimental results and the numerical modeling techniques are validated.The numerical modeling techniques which have been validated in are then used to verify the analytical model proposed in . The schematic of the finite element model used to verify the analytical model is shown in . The front face sheet is made of steel with thickness of 1 mm and modelled as linear elastic solid with density ρf=7800 kg/m3, Young's modulus Ef=210 GPa and Poisson's ratio υf=0.3. Since the Young's modulus of the steel is much larger than the foam strength and also the bulk modulus of the water, the front face sheet can be considered as rigid. The foam is Alporas with density ρ0=245 kg/m3 (). The experimentally obtained quasi-static nominal stress-strain curve of the Alporas is presented in . The crushable foam model with isotropic hardening available in Abaqus/Explicit is used to simulate the foam. The plastic Poisson's ratio is set to be zero and the yield ratio is 3. The elastic modulus of 5 GPa is used in the simulation to diminish the influence of the elastic deformations. The constitutive response of water is modelled by the acoustic medium. The density and the bulk modulus of water are 1000 kg/m3 and 2.25×109 |
Pa, giving a wave speed 1500 m/s. In order to simulate the cavitation phenomena, the cavitation limit for water is set to be zero in line with the analytical model, and the initial acoustic static pressure is taken into account. The water column is 3 m and sufficiently long to guarantee that the reflected wave at the free end of the water column does not reach the wet face and the closing front does not go beyond the free end of the column during the calculation. The cladding is clamped at the back face and symmetric boundary conditions are applied at the cladding to constrain the deformations perpendicular to the direction of the propagation of the shock wave.Four-noded, 2D quadrilateral element with reduced integration (type CPE4R in Abaqus) is used to discretize the cladding while the acoustic elements (type AC2D4R in Abaqus) are used to simulate water. The fluid column, the face sheet and the foam are tied at their interfaces. All the element size lew in the direction of the wave propagation is set to be 0.1 mm. The parameters for the incident wave are p0=10 MPa and θ=1 ms. The RPPL material parameters of foam are σpl=1.75 MPa and εD=0.535 which can be obtained based on the work of The presence of the initial static pressure is modelled in Abaqus/Standard first. Then the corresponding displacement, strain and stress results are transferred to the Abaqus/Explicit as the initial conditions of the cladding in the dynamic analysis. It should be noted that numerical convergence studies have been conducted to ensure that the results converge to the true solution., the water can cavitate when the pressure is lower than a threshold value and cavitated bubbles will collapse due to the deceleration of the cladding. (a) shows the propagation of the breaking front and the closing front under the different initial static pressure, for both analytical and FE predictions. The results illustrate that the propagation of the breaking and closing front is insensitive to the static pressure. In the research of , they analyzed the response of a rigid plate supported by a linear spring under combined loads of the water blast and the initial static pressure and found that the uncavitated part adjacent to the wet face would expand when increasing the static pressure (Fig. 6(b) in their paper). However, situations are different for the cellular cladding. The results in (a) demonstrate that increasing initial static pressure does not change the cavitation region. This is because the cladding moves faster when increasing the static pressure, leading to a larger rarefaction wave. The FE and analytical predictions in (b) gives the spatial cavitation velocity distribution of water particles. The results imply that only the velocities of water particles adjacent to the wet face are noticeable, which is in line with the result by . Moreover, the cavitation velocity of water particles is an increasing function of initial hydrostatic pressure, and the increment equals to pst/(ρwcw) according to Eq. , the incident wave, pin, will be cut off by the cavitation. However, the closure of cavitation bubbles can radiate new pressure, pCF,out, which will reload the cladding. The actual incident wave are plotted in . The results indicate that the enhancements of the actual incident wave due to closure of cavitation bubbles are prominent compared with the given incident wave pin. Therefore, the cavitation phenomena in the analyses of underwater explosion are important.The temporal evolution of the interface pressure pwet and the cladding velocity predicted by the analytical model are compared with the FE results in where excellent agreements are observed. The peak pressure at the wet face is almost 2p0 since the front face sheet is much stiffer than water. For the sake of clarity, the peak pressure has been truncated. The results in (a) indicate that pwet is strongly related to the FSI effects. The curve of pwet typically exhibits a rapid decline at the initial stage, followed by a long plateau pressure. Consequently, the shock wave is converted into a low amplitude load with a long duration. The rapid decline is due to the negative rarefaction wave and is beneficial for shock isolation. The value of the plateau pressure approaches to the yield strength of the foam being compressed. When increasing the initial static pressure, the plateau pressure lasts longer since the foam can be compressed more easily.The velocity histories of the wetted face sheet are shown in (b). It is observed that the front face sheet accelerates to its peak velocity very quickly; then the velocity will decrease as the shock energy being dissipated gradually. It means that the acceleration of the front face sheet is very large and decreases quickly at the initial phase. During this moment, the total pressure pwet declines rapidly. Subsequently, the acceleration of the front face sheet becomes negative, leading to the velocity decrease. The first two terms on the left side of Eq. take up a smaller and smaller proportion in pwet compared with σ0, leading to a long plateau pressure in (a). Additionally, the velocity of the front face sheet will increase as increasing the static pressure. This is because the foam has subjected to the static pressure prior to the blast loading; upon the arrival of the water blast, the core can be compressed more easily.The analytical and FE predictions of reaction force transmitted to the ship hull for pst=0 and pst=1.5 MPa are shown in (a) and (b), respectively. It is shown that during the core crushing, the transmitted stress to the structures keeps about 1.75 MPa which is yield strength of the foam. The results present an advantage of the cellular claddings, i.e. the ability to greatly reduce the transmitted stress to the structure.Define the maximum achievable impulse I0 (achieved in the stationary rigid plate limit) asThe non-dimensional impulse transmitted to the wet face can be defined aswhere tp is the time when the pressure at the wet face exactly decreases to zero after the cladding has stopped crushing (The external work done by the shock loading per unit area iswhere u is the displacement of the wetted face sheet. When the cladding stops crushing, all the work done by the external impulse on the cladding is absorbed by the cellular material.The results of the impulse imparted to the cladding and the absorbed energy by the cellular material are listed in , for both analytical and FE predictions. Good agreements between the analytical model and FE simulations are observed.The results of effective foam thickness predicted by the analytical and FE models are listed in the second column of . The results illustrate that the foam thickness will increase when increasing the static pressure. have assessed the fidelity of the analytical model, which also reveals the physics of the problem. After the shock arrive at the wet face, velocity of the front face sheet increases rapidly, leading to the occurrence of first cavitation in the water. The cavitation expands to some extent and then collapses at the closing front. The radiated wave from the closing front will alter the original incident wave pin. The actual incident pressure wave pa is larger than pin. The total pressure at the wet face decreases rapidly, followed by a long plateau pressure, resulting in decrease in the momentum transmitted to the claddings. The transmitted stress to the ship hull is determined by the yield strength of the cladding and much less than the incident shock wave during the core crushing.In this section, we proceed to present a parametric study by the analytical model to investigate the dependence of the effective foam thickness as a function of the FSI parameter, ψ, the non-dimensional initial density, ρ0/ρw, and the yield strength, σ0/p0, of the foam, the incident peak pressure, p0, and the initial static pressure, pst/p0.The analytical model is dependent upon the following non-dimensional parameters:ψ=ρwcwθ/mf,t¯=t/θ,u¯=u/cwθ,V¯1=V1/I0/mf,σ¯0=σ0/p0,ρ¯0=ρ0/ρwwhere I0 is the maximum impulse achieved in the stationary rigid plate limit and equals to 2p0θ. After non-dimensionalization, the incident peak pressure, p0, is left. We choose the reference peak pressure as pref=30 MPa in the discussion. The ultimate stroke, u, represents the compression of the foam, and the effective foam thickness can be expressed by u/εD. In the following, the ultimate stroke is used to assess the effective foam thickness.The effects of the FSI parameter, ψ, on the non-dimensional stroke is shown in . It is observed that the FSI parameter has little effects on the stroke except for small values. Small ψ means a considerable heavy front face sheet; however, the face sheet of sacrificial claddings cannot be too heavy. Therefore, the effects of the FSI parameter on the effective foam thickness can be neglected. give the effects of foam properties, including foam density, ρ0/ρw, and the yield strength, σ0/p0, on the non-dimensional stroke. Obviously, the foam density has little effects on the stroke (). Compared with the foam density, the foam strength has much more effects. As shown in , the stroke decreases reciprocally with increasing yield strength of the foam, and the decrement of the stroke is insignificant when the foam is strong enough. In the design of cellular claddings, the stroke will be too long if the foam is soft though the stress transmitted to the protected structure is small. However, when the foam is strong, the stroke is short with large transmitted stress. Therefore, on the condition that the stress transmitted to the structure is lower than the limited value, we can increase the foam strength to save the work space in the practical applications. Additionally, comparing the results between illustrates that the stiffness characteristics have dominant effects on foam thickness compared with the mass effects of foam materials. Actually, the quasi-static yield strength of foam is a function of the density. We discuss these two parameters separately to reveals the influence of the inertia and the strength of the foam. The results indicate that mass effects of the foam can be neglected. can be best fitted by reciprocal functions with the following expression{ucwθ=10.533+175.5(σ0/pref)forpst/pref=0ucwθ=10.488+160.7(σ0/pref)forpst/pref=0.05ucwθ=10.410+134.8(σ0/pref)forpst/pref=0.15The stroke with the different incident peak pressure, p0, is presented in . Apparently the stroke is an increasing function of the peak pressure, and the function is almost linear when the non-dimensional yield strength is constant. Define the stroke under peak pressure p01 and p02 are u01 and u02, they satisfy indicate that the effective foam thickness is an increasing function of the initial static pressure. Define the increment rate of the effective foam thickness when considering the different static pressure iswhere Leff|pst=0 and Leff|pst denote the effective foam thickness without and with the static pressure, respectively. The static pressure, pst, can be any value but smaller than the yield strength of the foam. After calculation, we find that the increment rate, δ, is only related to the non-dimensional static pressure, pst/p0, as plotted in . Length increment of ~1.78 to ~42% is observed when pst/p0 increases from 0.01 to 0.2. The results in can be best fitted by parabolic functions with the following expressionSince the FSI parameter, ψ, and the foam density, ρ0/ρw, have little effects on the foam thickness, it is worth to note that the results shown in are not limited to a particular foam or shock loading. They can apply to the kind of cellular materials with insignificant strain hardening. Therefore, when we know the effective foam thickness under a certain static pressure, the results under any other static pressure can be estimated according to Eq. . Note: the static pressure should be less than the foam strength. indicates that the FSI parameter and the foam density have little effects on the effective foam thickness while the effective foam thickness is an increasing function of the incident peak pressure and the initial static pressure but a decreasing function of the foam strength. The fitting functions of Eqs. can help us derive the explicit expression of the effective foam thickness needed to fully absorb the shock energy. For a given shock environment (p0, θ, pst) and cellular material properties (ρ0, σ0, εD), the effective foam thickness can be calculated according to Eqs. , calculate the ultimate stroke, u1, of the cellular material under the reference peak pressure, pref, reference foam strength, σref, and zero static pressure, pst=0, calculate the ultimate stroke, u2, of the cellular material under the given incident wave, p0, the foam strength, σ0, and zero static pressure, pst=0u2=p0prefu1=p0prefcwθ0.533+175.5σ0/p0forpst=0., calculate the ultimate stroke, u3, of the cellular material under the given incident wave, p0, the foam strength, σ0, and the static pressure, pstu3=(1+δ)u2=cwp0θpref[1+1.7586(pst/p0)+1.68842(pst/p0)2]0.533+175.5(σ0/p0).Calculate the effective foam thickness, Leff,Leff(p0,θ,pst,σ0,εD)=u3εD=cwp0θprefεD[1+1.7586(pst/p0)+1.68842(pst/p0)2]0.533+175.5(σ0/p0).where pref=30 MPa, cw is the wave speed in water and equals to cw=1500 m/s. Note: The static pressure and the foam strength should satisfy pst<σ0. is the empirical formula of the effective foam thickness. We use it to predict the effective thickness of the Alporas foam mentioned in under different shock waves, as shown in . The contour plot can display the effective thickness (attenuation/enhancement boundary) clearly for different shock waves.During Underwater blast event, the shock factor is the most widely used parameter for describing shock severity, which is the function of charge weight and charge distance. The Hull Shock Factor (HSF) represents the available energy that a shock wave contains which may do work in damaging hull plating on the ship, as defined bywhere W is the mass of explosive in TNT equivalence in (kg) and R is the stand-off distance from the charge to the ship in (m).The peak pressure, p0, and the decay constant, θ, of shock wave can be described by charge weight and charge distance aswhere K1, K2 and A1, A2 are constants, dependent on explosive charge type. In case of TNT charge, these constants are K1=52.16, K2=0.0965 and A1=1.13, A2=– 0.22 ( gives the peak pressure and decay constant for different HSF. The results illustrate that a shock wave with high peak pressure and small decay constant has the same damage to the ship hull as the shock wave with low peak pressure and big decay constant., to calculate the effective thickness of the Alporas foam mentioned in . The results indicate that the effective foam thickness changes very little for the identical shock factor when the static pressure equals to zero, which obeys the definition of the HSF. When the hydrostatic pressure is non-zero, the effective foam thickness is larger for low peak pressure. This is because the ratio of pst/p0 is large for low peak pressure.The major limitation of this paper is that the current results are obtained by a one-dimensional model, and it cannot predict the whole response of the three dimensional problem. Despite, the empirical formula has the potential to provide quick estimation of sacrificial cellular claddings during full-ship calculation. For example, the research results by indicate that the one-dimensional results can predict whether the cellular cladding can attenuate or enhance the shock loading for the three-dimensional submersible hull. Of course, it would be very promising if it can extend such model into 2D or even 3D space, which is the future work.Another limitation of the paper is that the input shock wave is in the form of planar wave which is an inherent assumption of far field underwater explosion. The effects of the explosion bubble, such as bubble pulse, is not included in the empirical formula. Therefore, Eq. probably underestimates the effective thickness for real charge underwater explosion.In this paper, the shock mitigation capability of the cellular cladding plastered on the ship hull to the shallow/deep water blast is investigated, with special emphases on deriving the empirical formulae of the effective foam thickness needed to fully absorb the shock energy. According to the analyses, several conclusions are obtained as follows:Increasing initial static pressure does not change the cavitation region but increase the cavitation velocity of water particles, and the increment of the cavitation velocity equals to pst/(ρwcw). The FSI parameter and the foam density have little effects on effective foam thickness while the effective foam thickness is an increasing function of the incident peak pressure and the initial static pressure but a decreasing function of the foam strength.The empirical formula of the effective foam thickness in Eq. has potential advantage in designing the cellular claddings to water blast in practical applications without having to numerically solve the series of governing equations (including Eqs. ). Additionally, it is also beneficial for understanding the effects of different parameters (including loading conditions and structure properties) on the water blast response of such structures.Estimation and veering analysis of nonlinear resonant frequencies of cracked platesIn this paper, veering phenomena in the nonlinear vibration frequencies of a cantilevered cracked plate are investigated, and an efficient method for estimating these frequencies is proposed. Of particular interest is the vibration response in parameter regions where the natural frequency loci show veerings. For a representative finite element model, it is shown that the veerings due to crack length variation involve the switching of mode shapes and modal interactions. The nonlinearity caused by the crack closing effect is then introduced, and its effect on the vibration response near the veerings is discussed. The nonlinear forced response analysis is carried out using a hybrid frequency/time domain method, which is based on the method of harmonic balance. The nonlinear vibration response near loci veerings and crossings due to the variation of crack length is investigated in detail. Finally, a novel method for estimating the nonlinear resonant frequency is introduced by generalizing the concept of bilinear frequency approximation, and the method is validated with the results of nonlinear forced response analysis for several veering regions.It is well known that the natural frequencies of cracked elastic structures differ from their healthy counterparts. A comprehensive literature survey of research activities regarding the vibration problems of various structures with cracks is found in the work by Dimarogonas Eigenvalue loci veerings, also known as avoided crossings, or eigenvalue avoidance, are observed in plots of eigenvalues versus a system parameter. In particular, a veering refers to a region in which two eigenvalue loci approach each other and almost cross as the system parameter is changed, but instead of crossing they appear to veer away from each other, with each locus then following the previous path of the other For vibration problems of cracked rectangular plates, variations in natural frequencies and mode shapes due to crack length variations have been known for a long time. The initial contribution to the study of vibration problems of cracked rectangular plates was made by Lynn and Kumbasar In the studies of cracked rectangular plate vibrations reviewed above, the in-plane bending vibration was not considered and thus the crack closing effect was not examined. In contrast, the issue of crack closing effect naturally arose in the studies of vibration problems of cracked beams, for which in-plane bending vibration is typically of primary research interest. For the study of cracked Bernoulli–Euler beams, a pioneering contribution was made by Christides and Barr in their application of the Hu–Washizu–Barr variational principle to the cracked beam problem One of the methods to estimate the (primary) resonant frequencies of the cracked beams is the application of the bilinear frequency approximation. This was initially introduced for calculating the effective resonant frequencies of piecewise linear oscillators (e.g., The closing crack was also modeled by equivalent linear model by Kisa and Brandon With regard to the veering phenomena for nonlinear structural systems, very little is known about how the nonlinearities influence the response near the veering regions. Lacarbonara et al. In this paper, the vibration of cracked cantilevered plates in frequency veering regions is investigated. As reviewed above, veering phenomena have not been studied thoroughly for cracked structures, in either the linear or nonlinear dynamics regime. Regarding the vibration of cantilevered cracked plates, the research reviewed above focused only on the out-of-plane vibration, and crack closing effects were intentionally neglected. On the other hand, studies of cracked beams have focused on in-plane bending in most cases. Thus, the crack closing effect on the vibration response has been investigated in many studies of cracked beams. However, veering and modal interaction phenomena between in-plane and out-of-plane vibration modes have not been studied in this context. Moreover, in general, the veering phenomena in nonlinear structural systems have not been studied well. Therefore, in this paper, first the eigenvalue loci veering due to cracking is examined using a cracked cantilevered plate example without considering the crack closing effect. The crack closing effect is then included and associated nonlinear resonant frequencies are identified. A novel method for accurately estimating the nonlinear resonant frequencies is then introduced, by generalizing the concept of bilinear frequency approximation that utilizes the results of linear eigenvalue analyses of the system. The method is validated by comparing the results with those calculated by the nonlinear forced response analysis. Furthermore, the applicability of the method near the veering regions is discussed, and the effects of the crack closing on the resonant frequencies are discussed in detail for some specific veering regions., the cracked plate vibration problem and the finite element model are introduced. In , the linear free response of a cracked plate is considered using a finite element model of a three-dimensional cantilevered plate with a planar surface-breaking crack that runs parallel to the cantilevered edge, and the associated frequency veering and crossing phenomena are shown. In , a solution technique for the nonlinear forced response analysis, called the hybrid frequency/time (HFT) method, is briefly reviewed. The nonlinear forced response calculation is then carried out and the effects of nonlinearity to the response in the neighborhood of representative veering regions are discussed in detail. In , the method for estimating the nonlinear resonant frequency is introduced as a generalization to the bilinear frequency approximation. Finally, conclusions are summarized in In this paper, the vibration of a cantilevered rectangular plate composed of linear isotropic elastic material is considered. The plate is discretized with a standard finite element method, and the deformation is assumed to be infinitesimally small. In this study, nonlinearities other than the one due to intermittent contact at the crack surfaces are not considered. Namely, the governing equation of the cracked plate isMu¨(t)+Cu˙(t)+Ku(t)=b(t)+f(u);M,C,K∈Rn×n,u,b,f∈Rnwhere u is the displacement vector, M, C, and K denote the mass, damping, and stiffness matrices, b(t) denotes the time-dependent external force, and f(u) denotes the nonlinear force caused by the intermittent contact at the crack.A finite element (FE) model of a cantilevered plate with a transverse crack is shown in , where h=1.5×10-1m, l=6.0×10-2m, t=3.0×10-3m. The material model is steel with Young's modulus E=200GPa, density ρ=7800kg/m3, and Poisson's ratio ν=0.3. The FE model is composed of 6750 brick linear elements and has approximately 28,000 DOF. This FE model is used for all the numerical results in this paper, and the generation of the FE model as well as component mode synthesis were performed with the commercial code ANSYS First, in order to visualize the variations in the natural frequencies for crack parameter variations, which are closely related to the variations in the nonlinear resonant frequencies, the underlying linear system is studied in this section. Namely, the nonlinear contact force f(u) in Eq. is ignored, and for the FE model shown in , eigenvalue analysis was performed for various values of lc/l and hc/h. The results for the first 15 natural frequencies for two representative cases are shown in a shows the results where the crack length was fixed at lc/l=40 percent, and the crack location was varied as 1.33≤hc/h≤97.3 percent. As can be seen, the changes in the natural frequencies due to the variation in hc/h are quite complicated, and multiple loci veerings and crossings are observed. In order to examine the individual veering regions, some cases with realistic crack length ratio, lc/l<60 percent, are discussed below. For example in a, starting around hc/h=15 percent, modes 10 and 11 approach each other, but rather than crossing they veer away near hc/h=19 percent with high curvature. Second, the crack location was fixed at hc/h=50 percent, and the crack length was varied, the results of which are shown in b. The most notable distinction from the case in a is that the natural frequency variation due to crack length change is monotonic, i.e., as lc/l increases, all natural frequencies tend to decrease. Although the amount of frequency drop is dependent on the mode of interest, this is due to the fact that the stiffness of the plate decreases monotonically for all modes as the crack length increases.In order to see the veering regions more closely, and to see the variations in the mode shapes, representative cases are shown in a shows the veering between the modes 10 and 11 for lc/l=40 percent, where 1.33≤hc/h≤40 percent. An important characteristic of the loci veering is the mode shapes associated with the natural frequencies on each locus before veering are interchanged during the veering in a continuous manner a, which shows that mode shapes 10 and 11 become mixed and then appear to begin switching as the crack location ratio is increased through the veering region. On the other hand in b, the region for the mode shape switching between modes five and six is narrow, and it appears to be a loci crossing. This can be explained by considering that mode five (before switching) corresponds to the second out-of-plane bending mode whereas mode six (before switching) corresponds to the first in-plane bending mode, and there is little or no coupling between these modes due to their geometric dissimilarity. shows another veering region due to crack length variation, for modes seven and eight with crack location hc/h=0.63. For this case, both mode mixing and switching can be observed in a more continuous manner than the cases observed in In the previous section, the interchanging of modes as well as mode coupling were observed in frequency veering and crossing regions. However, only natural frequencies of the linear system were considered. The nonlinearity due to contact of the crack surfaces was neglected. In this section, a method to calculate the nonlinear resonant frequencies of the cracked plate is described. The method is then applied to the calculation of nonlinear resonant frequencies in veering/crossing regions, and their characteristics are discussed.In order to generate a reduced-order model, the plate is separated into two components (substructures) Ω1 and Ω2 along the crack path, as shown in , and a hybrid-interface method of component mode synthesis (CMS) . Namely, the dynamics of the FE degrees of freedom are projected onto constraint modes Ψc, inertia relief attachment modes Ψa (if rigid-body motion exists), and a truncated set of free-interface normal modes Φk. Interested readers may consult, e.g., Craig Let the displacement vector u be partitioned into boundary DOF, ub, and interior DOF ui. By denoting the inertia relief attachment coordinates and a truncated set of free-interface modal coordinates as qa and qk, the linear projection is expressed aswhere Ψ^a=Ψia-ΨicΨba, Ψ^k=Φik-ΨicΦbk, I is the identity matrix, Ψic is the boundary partition of Ψc, Ψia, and Ψba denote the interior and the boundary partitions of Ψa, and Φik and Φbk denote the interior and the boundary partitions of Φk. Denoting Eq. with a compact notation, u=Ψq, the application of Eq. yields a smaller number of equations, i.e.,where M′=ΨTMΨ, C′=ΨTCΨ, K′=ΨTKΨ, b′=ΨTb, and f′=ΨTf. The superscript “′” is omitted for convenience in the subsequent formulations.For the calculation of steady-state response to harmonic excitation, an extension to the alternating frequency/time-domain method , as well as the external force b and the nonlinear force due to intermittent contact f are approximated as truncated Fourier series, i.e.,where 2π/ω is the fundamental frequency, nh is the number of non-zero harmonics, and j=-1. Note that Qkc and -Qks are the vectors of real and imaginary parts of kth Fourier coefficients of q, where superscripts c and s denote cosine and sine components of the vibration, respectively. The same notation is applied to Bkc, Bks, Fkc, and Fks. Substituting Eqs. and considering the orthogonality of harmonic functions, it results in a nonlinear algebraic equation with respect to the Fourier coefficients for kth harmonic number, i.e.,where Q0=Q0c, B0=B0c, F0=F0c, Λ0=K, Qk=[(Qkc)T,(Qks)T]T, Bk=[(Bkc)T,(Bks)T]T, Fk=[(Fkc)T,(Fks)T]T, andwhere Λ is a pseudo-block diagonal matrix with Λk on its diagonal blocks for k=0,…nh, Q=[Q0T,…,QnhT]T, B=[B0T,…,BnhT]T, and F=[F0T,…,FnhT]T. Eq. can then be solved with nonlinear algebraic equation solvers. For the numerical examples shown in this paper, the Hybrid Powell method In this subsection, the result of nonlinear forced response analysis for the cantilevered cracked plate is presented, with the methods described in Sections . The damping was chosen to be C=αM+βK where α=1.22 and β=8.16×10-9, which result in damping that is approximately equivalent to modal (structural) damping ratio ζ=1.00×10-4 (γ=2.00×10-4) within the frequency range of 1900≤f≤2000Hz. Vectors of harmonic forcing, the resultant of which is equal to 1 N, is applied to the nodes on the tip face of the plate to excite the modes of interest. The number of harmonics was chosen as nh=9, which showed convergence in the resonant frequency predicted in the frequency response for the modes of interest. A representative result of a convergence study in terms of the number of harmonic numbers is shown in for the sixth mode with hc/h=0.5 and lc/l=0.167. For the case shown in , the predicted resonant frequency converged within 0.003 percent relative error. Representative results are shown in a shows the resonant peaks corresponding to modes five and six, which correspond to the third out-of-plane bending and the first in-plane bending modes, respectively, whereas the order of the modes is interchanged in As an alternative way of predicting the nonlinear vibration frequencies, the bilinear frequency approximation is generalized for the analysis of three-dimensional cracked structures, and an analysis framework based on reduced-order modeling as well as prediction of mode switching during the veering regions is proposed in this section. The resonant peaks predicted by the forced response to harmonic excitation is then compared with those calculated by the bilinear frequency approximations.The bilinear frequency was originally introduced as the effective vibration frequency of a piecewise linear, single-DOF system and defined as (e.g., Ref. where ωb is the bilinear frequency, ω1 is the natural frequency of one of the linear systems associated with the piecewise linear system, and ω2 is that of the other linear system of the piecewise linear system. This expression is the exact solution, for the frequency of free oscillation of the piecewise linear single-DOF oscillator with vanishing clearance/gap at the equilibrium. The application of Eq. to a multi-DOF piecewise linear system is rather straightforward if there is only one pair of linear systems. However in the cases of cracked plates formulated with multiple DOF on crack surfaces, it involves multiple piecewise linear systems, or a conewise linear systems a), allowing the inter-penetration of the crack surfaces. On the other hand with the closed state, the relative DOF along the direction that is perpendicular to the crack surfaces are fixed to be zero, whereas the other two DOF of each node are allowed to move freely in the plane tangent to the constrained direction (Fig. b). In other words, the crack surfaces are allowed to slide with respect to each other, which is consistent with the assumption employed in the formulation in Section . Associated mathematical formulation is given as follows.For a given crack length, eigenvalues of Eq. for undamped case with open crack assumption are obtained aswhere φ is the eigenvector and ω12 is the associated eigenvalue. On the other hand, the eigenvalues and eigenvectors for the other case, namely the case with allowing sliding of crack surfaces, are obtained by imposing appropriate constraints on Eq. as follows. Let A and B denote the crack surfaces facing each other, by assuming that the amplitude of vibration is much smaller than the finite element mesh size on the crack surfaces, it is possible to identify the finite element nodes that may be in contact during the vibration cycle. Hence such pairs of nodes are numbered and a set Ccp is defined where all numbers that denote the contact pairs are included. Defining gn as the gap between the nodes on the surfaces A and B for the nth contact pair, the constraints to be imposed on the nodes of nth contact pair are expressed aswhere (un)A and (un)B denote the displacements of the nodes on the surface A and B, projected onto the normal direction pointing outward from the surface A or B. It is noted that appropriate coordinate transformation must be applied to the displacement vector based on the normal vector at each node, in order to correctly calculate gn. It should also be noted that the motion of the nodes in tangential plane that is perpendicular to the normal direction is not constrained at all by Eq. , i.e., the nodes are free to slide with each other on the tangential plane. This also indicates that the crack surfaces are assumed to be frictionless, which is widely employed assumption for the vibration problem of cracked beams and plates. Applying the constraints Eq. , a constrained eigenvalue problem is obtained aswhere N is the matrix of coefficients that are associated with Eq. and the appropriate transformation matrix, and λ is the vector of Lagrange multipliers of size |Ccp|. One method to solve this indefinite eigenvalue problem is to use an eigenvalue solver for indefinite systems. Another method is to first eliminate the redundant equations due to the constraint equations Eq. , and the resulting positive definite eigenvalue problem is then solved by an eigenvalue solver for definite systems. It should be noted that this methodology can easily be incorporated with the reduced-order modeling framework described in Section as the motion of the nodes on the crack surfaces in the three-dimensional space can be captured with the reduced-order model., the ith bilinear resonant frequency ωbi of the cracked plate is approximated based on Eq. where ω1i and ω2i denote the frequencies of the ith mode of the states 1 and 2. It is emphasized that the index i does not denote the index of eigenvalues, but it denotes the index of the eigenvectors of the non-cracked plate. Namely, the eigenvectors of the non-cracked plate are indexed based on their natural frequencies, i.e., for non-cracked plate, the eigenvalues are ordered as ω1≤ω2≤⋯≤ωN-1≤ωN where N is the size of the non-cracked plate model, and corresponding eigenvectors are labeled as [φ1,φ2,…,φN-1,φN]. The reason for introducing this ordering will become apparent shortly. The bilinear frequency ωbi for a given crack length is calculated by using the natural frequencies of the corresponding ith mode of the states 1 and 2.The advantage of this method is that the frequency of the nonlinear response is obtained without calculating the associated response shapes, thus it only involves eigenvalue extraction of two linear systems. However, as mentioned, this method is known to be accurate for systems with a relatively short crack. In addition, a drawback of this method is that the choice of proper pairs of ω1i and ω2i is not apparent with the presence of a veering or crossing, because the mode shapes associated with the natural frequencies switch their orders. A way to overcome the latter problem is to track each mode by observing the correlation between the modes during the variation of crack length or crack location. In this paper, the modal assurance criterion (MAC) Denoting the crack length as p (=lc), it is noted that N and λ are dependent on p. That is, N=N(p) and λ=λ(p). The eigenvector is also dependent on p, or φ=φ(p), and the correlation between the ith mode shape of the system with p=p0 and the jth mode shape with the perturbed crack length p=p0+Δp can be characterized byMACijk=|φik(p0)Tφjk(p0+Δp)|2∥φik(p0)∥2∥φjk(p0+Δp)∥2,k=1,2where φ is the eigenvector of the system defined by Eq. , the subscripts i and j denote the indices for modes, the superscript k indicates the state, and MACijk takes the value between 0 and 1, which, respectively, correspond to no correlation, and consistent correlation between φi(p0) and φj(p0+Δp). Namely, the ith eigenvector is tracked based on the value of MAC throughout the variation of the crack length (p), such that the correct natural frequencies for the ith eigenvector in Eq. In order to better clarify the behavior of the natural frequencies of the system with open and sliding boundary conditions, as well as the bilinear frequencies, the above-mentioned analysis framework was applied to the reduced-order model of the cracked plate with hc/h=0.50. As an example, the veering region between the fifth and sixth modes are shown in , the modes of interest are the in-plane and out-of-plane bending modes. In , two significant insights into the behavior of the frequencies are shown. The first is that the existence and location vary between the cases with open and sliding boundary conditions, and bilinear frequency. For the case with sliding boundary condition, the veering between fifth and sixth modes does not exist. On the other hand for the open boundary condition case, the loci of fifth and sixth modes approach and veer away where 10≤lc/l≤15 percent. Therefore the bilinear frequency also has the veering region due to that for the open boundary condition, but slightly shifted toward larger crack length ratio because of the absence of the veering for the sliding boundary condition case (Fig. b). The second is that the bilinear frequency is always bounded by the frequencies corresponding to the cases with sliding and open boundary conditions, which are, respectively, the upper and lower bounds (Fig. a). This can also be easily verified from Eq. , i.e., if ω1i≤ω2i, then ω1i≤ωbi and ωbi≤ω2i. Furthermore, it is noted that the width between the upper and lower bounds indicates the strength of the effect of contact nonlinearity on the resonant frequency. For instance, for the fifth bilinear frequency that corresponds to the in-plane bending mode, the width between the bounds is much larger than that for the sixth bilinear frequency, which corresponds to the out-of-plane bending mode. This is due to the fact that the motion of the in-plane bending mode is greatly influenced by the existence of the contact force at the crack surfaces, whereas the out-of-plane bending modes is not so much affected by the contact force considering that the motion of the crack surfaces is almost perpendicular to the crack surfaces.It is noted that there have been other approaches for obtaining approximate bilinear frequencies for multi-DOF systems, such as the one presented in Refs. Using the bilinear frequency approximation described above, the nonlinear vibration frequencies of the cracked plate are calculated, and they are compared with those obtained by the HFT method. It is noted that the comparison between the resonant frequencies obtained by forced response analysis, and the bilinear frequencies, namely the vibration frequencies of unforced system, has been made based on the assumption that the resonant frequencies reside in the vicinity of the frequencies associated with the nonlinear normal modes It is also noted that the HFT method is capable of calculating the gradual opening and closing of crack faces during a vibration cycle, by considering the three-dimensional time trajectory of nodes on crack faces at the steady state. A detailed formulation can be found in Ref. Three representative veering regions are considered, which are the cases where (a) the interaction between the loci is weak and the corresponding modes are: (1) in-plane and out-of-plane bending modes and (2) both out-of-plane bending modes and (b) the interaction between the loci is strong and veering occurs in a continuous way and the associated modes are both out-of-plane bending modes.First, the veering between an in-plane bending mode and an out-of-plane bending mode is considered, using the modes five and six, for hc/h=0.50, as shown in b. The results of forced response analysis as well as the calculation based on bilinear frequency assumption are shown in a. As can be seen, the order-switching of modes can be observed even for this nonlinear system. The most notable distinction from the linear assumption, i.e., b, is that the veering occurs with longer crack length at around 20 percent in a, than the one at around 10 percent with the linear assumption in b. This is due to the stiffening effect because of the contact/impact of crack surfaces during the vibration cycle, which represents the dynamics of the cracked plates appropriately. Regarding the bilinear frequency approximation, a notable result has been observed: the bilinear frequency assumption predicts the resonant frequency calculated by HFT method quite well even for relatively large crack length ratio (lc/l≤40 percent).Second, the veering between two out-of-plane bending modes is considered, using the modes nine and 10 for hc/h=0.60, and the calculation results are shown in b. This result also shows that bilinear frequency approximates the resonant frequencies quite well for the case of veering between out-of-plane bending modes, with relatively large crack length. Even though the effect of nonlinearity on the vibration frequency is smaller than that on the in-plane bending modes, as it does not involve much contact/impact between crack surfaces, this clearly indicates that the bilinear frequency approximation can also be used for the prediction of nonlinear vibration frequencies of out-of-plane bending modes.Third, the veering between the torsion and out-of-plane bending modes are examined, using the modes seven and eight for hc/h=0.63 and results are shown in c. This veering region features a switching of modes in a continuous way, or in other words, the mode shapes gradually change as the crack length is varied. This result shows that the bilinear frequency approximation predicts the nonlinear vibration frequency quite well even for the modes that exhibit complicated geometry due to coupling between modes. Moreover, the results show that the approximation is accurate even for large cracks.Lastly, it is restated here that the possibility of a non-vanishing gap at the crack faces at the equilibrium, which is known to change the nonlinear resonant frequency, is ignored in the above formulations. Detailed discussions on the effects of gap for the piecewise linear oscillators can be found in Refs. In this paper, the linear and nonlinear vibration response of a cracked cantilevered rectangular plate have been investigated. In particular, the veering phenomena for the natural frequencies of the cracked plate were investigated. It was observed that veerings appear in plots of natural frequencies versus crack length or crack location ratio. It was shown that a wider veering region entails continuous interchanging between the modes, whereas a smaller veering (or crossing) region shows fast mode switching. Then, the nonlinear vibration response of the cracked plate due to contact of the crack surfaces was considered. A hybrid frequency/time-domain method was applied to the calculation of nonlinear resonant frequencies in representative veering/crossing regions. It was shown that the characteristics of veerings/crossings are affected to some extent by the nonlinearity induced by the crack closing effect, although in general they are similar to those of the linear counterparts. Furthermore, an alternative method for estimating the nonlinear resonant frequencies was proposed by generalizing the bilinear frequency approximation. The results of the proposed method were validated with the resonant frequencies obtained by the nonlinear forced response analysis for three typical veering scenarios. Moreover, it was shown that the method works even for relatively large crack length ratio.Effect of deformation and aging treatment on the microstructure and properties of Cu-0.45Cr-0.14Ti (wt.%) alloyThe microstructure and properties of Cu-0.42Cr (wt.%) and Cu-0.45Cr-0.14Ti (wt.%) alloy subjected to cold rolling and aging treatment are investigated through tensile testing, electrical conductivity measurement, scanning electron microscopy, and transmission electron microscopy. Results show that the tensile strength of Cu-0.45Cr-0.14Ti (wt.%) alloy enhances as the degree of deformation increases, but the degree of deformation slightly influences electrical conductivity. When deformation is changed, electrical conductivity is basically unchanged. The good combination of strength and electrical conductivity, which reach 610 MPa and 55.4% IACS, respectively, can be obtained in the Cu-0.45Cr-0.14Ti (wt.%) alloy after 80% cold rolling and aging at 450 °C for 15 min. Ti inhibits the growth of the Cr precipitation phase and enhances the precipitation strengthening effect. Ti mainly exists in the matrix in the form of solute atoms, which do not form a separate lattice structure after aging treatment.Cu–Cr series alloys have been widely used in electric engineering, transportation, and machinery manufacturing industries because of their excellent electrical performance and mechanical properties. Their high electrical conductivity is due to the very low solubility of added Cr elements in Cu, whereas their excellent strength is attributed to the strengthening mechanisms of precipitation and particle dispersion []. Studies have shown that the overall performance of Cu–Cr alloys can be enhanced by adding a third element, such as Zr []. Among them, Cu–Cr–Zr alloy is the most widely studied because of its high strength and high thermal and electrical conductivities []. The strength and electrical conductivity of Cu-0.51Cr-0.06Zr alloy can be improved to 138 HV and 80% IACS after solution treatments at 950 °C for 1 h and aging treatments at 500 °C for 60 min []. The properties of Cu-0.2Cr-0.6Zr-0.5Ti alloy subjected to hydrogen heat treatment at 400 °C for 5 h are 665 MPa and 56% IACS []. However, zirconium can be easily burned during smelting, and accurately controlling its content is difficult, thereby inevitably wasting the cost and energy of Cu–Cr–Zr alloy. Ti is an available alloying element with low melting loss and cost []. Ti and Zr have similar chemical properties, so high-performance Cu–Cr–Ti alloys can be obtained through appropriate processing methods, thereby reducing the intensive demand for copper alloys in various industries []. In comparison with hot rolling and hydrothermal treatment, cold rolling + aging heat treatment has the characteristics of simple operation and outstanding performance []. This process reduces equipment requirements and facilitates large-scale industrial production [Some studies have explored the strength, conductivity, and microstructure of Cu–Cr–Ti alloys. Zhang [] investigated the influence of the Ti content on Cu–Cr alloy during plastic deformation and proposed the effect of solid solution strengthening of Ti. Zhang [] proposed that the degree of deformation slightly affects the conductivity of Cu–Cr–Ti alloy, and the solid solution scattering caused by Ti atoms is the main reason for the decrease in the conductivity of this alloy. Zhang [] believed that the difference between the interface and strain energies of the precipitated phase in Cu–Cr–Ti alloy is the main reason affecting the morphological characteristics of the precipitated phase; furthermore, the precipitates can appear square and round. Wang [] indicated that precipitates can be cigar shaped and elongated because of Ti atoms. However, studies have not yet to present a unified statement about the influence of Ti atoms on the morphological characteristics of the second phase. Further studies should also be performed to analyze the structure of nano-precipitates in Cu–Cr–Ti alloy after deformation and aging treatment.The current research aims to determine the effects of cold rolling deformation and aging treatment on the precipitation, electrical conductivity, and mechanical properties of Cu-0.45Cr-0.14Ti (wt.%) alloy. This study also establishes the relationship among process, microstructure, and properties by analyzing the relevant influencing mechanism. It is expected to provide a guideline for exploring efficient methods for preparing high-performance Cu–Cr–Ti alloys. This study further compares Cu-0.45Cr-0.14Ti (wt.%) alloy with Cu–Cr–Ti alloys described in previous studies and analyzes the existence of Ti atoms in Cu–Cr series alloys and their effects on structures and properties.Two different Cu–Cr alloy systems were prepared with electrolytic copper (99.97 wt%), intermediate alloy (Cu-32.25 wt% Cr), and pure titanium (99.7 wt%) in a vacuum induction furnace. The nominal compositions of the experimental alloy were as follows (mass fraction, 100%): Cu-0.65Cr and Cu-0.65Cr-0.25Ti. The actual compositions of the alloy detected by inductively coupled plasma emission spectrometer were as follows: Cu-0.42Cr and Cu-0.45Cr-0.14Ti (wt.%). Ingots were homogenized at 950 °C and rapidly hot forged into a thickness of 20 mm. Then, the plates were solution treated at 950 °C for 60 min and subjected to water quenching. Both sides of the specimens were mechanically polished to remove surface defects. They were cut into small samples, cold rolled with 60%, 70%, and 80% reductions, and isothermally aged at 450 °C for various times. shows the SEM and EDS images of the as-cast structure of Cu-0.45Cr-0.14Ti (wt.%) alloy. In a, a large number of coarse white particles appear in the microstructure of the alloy. They are the second-phase particles during the rapid solidification of the alloy. These phases are mainly dispersed in chains at grain boundaries and small second phase particles are distributed on dendrites. b is an enlarged view of the boxed area of b, the insoluble phase mainly exhibits irregular bands with an average size of about 0.5–3 μm. c and d illustrate the energy spectrum analysis of the coarse insoluble phase (point 1) and the matrix (area 2) in b. The results show that the insoluble phase is mainly rich in Cr. Ti is mainly dissolved in the alloy matrix. is an enlarged view of the Cr particles after cold rolling. In comparison with the Cr phase of the as-cast alloy, the edge of the Cr phase has a spheroidizing tendency because of the effect of the curvature effect caused by surface tension. The dissolution rate of Cr particles at the edges and sharp corners is faster than that inside the particles. During the solution treatment, the edges of the irregular Cr phase gradually become smooth. The severe cold-rolling deformation causes the Cr phase to crack, and the stuck Cr phase breaks and disperses. Under different deformation conditions, the shape of the coarse Cr phase is basically the same, mainly showing a short rod shape and a spherical shape. shows the SEM images of Cu-0.45Cr-0.14Ti (wt.%) alloy after deformation and heat treatment. After aging treatment, the distribution of undissolved phase becomes dispersed, and they are dispersed in large amounts on the surface of the alloy matrix. The greater the degree of deformation, the more dispersed the second phase. At the same time, the morphological characteristics of the second phases change significantly, and fine square and spherical phases appear in the deformed alloy (points 1 and 2). Zhang proved that the morphological characteristics of the Cr phase in Cu–Cr–Ti alloys are related to the energy contrast between the Cr phase and the matrix. When the interfacial energy is large, the Cr phase is spherical. When the elastic strain energy is large, the Cr phase is cubic []. The serious deformation treatment causes a significant change in energy at the interface of the Cr phase. The energy spectrum analysis at the location of 1.2.3.4 is shown in . The spherical, square, and elongated Cr phases contain Ti. During aging, the Cr phase grows up and gradually becomes inconsistent with the boundaries of the Cu matrix. A large number of dislocations and vacancies are generated in the interface region, thereby promoting the diffusion of Ti atoms. Ti atoms segregate at the interface between the Cr phase and the matrix to form a sandwich structure []. This sandwich structure prevents Cr atoms from diffusing into the core of the Cr phase, that is, the addition of the alloying element Ti reduces the diffusion coefficient D of the Cr phases; as a result, the growth rate of the Cr phase slows down. Wang [] revealed that Ti atoms can effectively affect the morphological characteristics of the second phase, causing it to be a cigar type, which is one of the reasons why the Cr phase is elongated. In , the larger the degree of deformation, the higher the number of Cr phases in the shape of short rods and strips. This phenomenon is also considered the plastic flow of Cr particles with the deformation of the matrix during deformation and aging process [ shows the TEM images of Cu–Cr–Ti alloy with different deformation degrees and aged at 450 °C for 15 min. As the degree of deformation increases, the number of nano-sized precipitates in the alloy gradually increases. The greater the degree of deformation, the more the dislocation defects in the alloy and the greater the distortion energy stored. On the one hand, the defects provide a large number of nucleation sites for the precipitated phase and promote the dispersion of the precipitated phase. On the other hand, the distortion energy stored at the defect can be used as the nucleation base energy of the precipitates, which reduces the nucleation barrier; furthermore, the precipitate phase more easily forms and grows [ presents a TEM image of an 80% deformed alloy aged at 450 °C for 15 min. In a, a large number of atoms precipitate in the form of atom clusters and metastable states and disperse on the substrate. The precipitated phase shows two typical morphologies []: a large amount of ellipse precipitation and a small amount of coffee beans []. The shape of coffee beans is also called the shape of double petals. The size of the fine precipitated phase is between 3 and 5 nm.b shows the HRTEM image of the ellipse precipitation by the fast fourier transformation (FFT) and inverse fast fourier transform (IFFT) techniques with the zone axis of [111]Cu. c illustrates the HRTEM image of the coffee bean precipitation by the FFT and IFFT techniques with the zone axis of [211]Cu. The selected area electron diffraction in b and c reveals that the two precipitations are Cr phases with a uniform face-centered cubic structure, and they maintain a coherent relationship with the matrix []. The coherent strengthening of the fine precipitate is considered the main reason for the strength improvement of the Cu–Cr alloy [].The other Cr precipitates with Moiré fringes are also observed in d, aligning along the [110]Cu directions, which can be considered the bcc precipitate and exhibit an NW–OR or KS–OR []. Moiré fringes are interference phenomena due to the small difference (1.25–1.45 nm) between the nano-sized precipitates and the Cu plane spacing. The bcc Cr precipitates with the orientation relationship with Cu matrix can be analyzed as the N–W relationship based on the SEAD pattern with the zone axis of [112]Cu in e and f. After the aging treatment, the precipitates of Cu–Cr–Ti alloy have the elliptical and double petal-like precipitates of the fcc structure and the moiré stripes of the bcc structure. However, according to the classic nucleation equation and the interface energy of Cu and Cr particles, an fcc–Cr core more easily forms in the Cu–Cr series alloy, which is two orders of magnitude smaller than the nucleation barrier of a bcc core. Therefore, in the Cu–Cr-based alloy at the early stage of aging, the precipitate phase has an fcc structure, and the precipitate is completely converted into a bcc structure, which has undergone this transformation process []. In addition, ellipse precipitates can reduce nucleation barriers at the early stage of aging and enhance the effect of precipitation hardening. As such, most of the precipitates appear as small and ellipse particles. The rapid diffusion of titanium atoms in the matrix promotes the growth of fcc chromium-rich nuclei. Thus, the formed lean zone hinders the further nucleation of bcc chromium-rich precipitates in equilibrium [g illustrates the coarse Cr phase that fails to dissolve after solution and aging treatment. These coarse particles adhere to grain boundaries and defects because of the low solubility of Cr in Cu alloy at room temperature [g also shows that the size of the Cr phase is between 200 and 700 nm. According to the selected area electron diffraction (SAED) diagram of the Cr phase, the crystal structure of the Cr phase is the bcc structure. The inverse Fourier transform change shows that the Cr phase is not completely coherent with the matrix. The Cr particles coordinately deform with the matrix during deformation and aging.The effect of different degrees of cold rolling deformation on the tensile strength of Cu-0.45Cr-0.14Ti (wt.%) alloy aging at 450 °C is shown in a. The strength variation trends of Cr-0.45Cr-0.14Ti (wt.%) alloys with different degrees of deformation are basically the same. Among them, CR60% corresponds to the specimen subjected to the solution treatment at 960 °C for 1 h + cold rolling thickness deformation of 60% + aging at 450 °C for different durations. In a, as the amount of cold rolling deformation increases, the time required for the alloy to reach the peak strength is shorter, and the peak value is larger. The strength of Cu-0.45Cr-0.14Ti (wt.%) alloy subjected to 60% deformation and aging for 60 min reaches 546 MPa, whereas the strength of Cu-0.45Cr-0.14Ti (wt.%) alloy exposed to 80% deformation and aging for 15 min reach 610 MPa.Defects caused by highly cold-rolled deformation store a large amount of deformation energy and provide more nucleation particles and diffusion channels, so the faster the precipitation speed after aging treatment, the shorter the time required to reach the peak of aging. The precipitates are more uniform and dispersed because of the large amount of rolling deformation, and the effect of precipitation strengthening is more prominent. At the early stage of aging, a huge lattice distortion can provide the strong nucleation and growth kinetic energy of the precipitated particles, and the intensity reaches the peak of aging in a short time. In previous studies [], the contribution of Cr precipitates to strength likely follows the Orowan bypass mechanism, which can be expressed aswhere Δбs is the increase in yield strength (MPa); G is the shear modulus of Cu matrix; and r is the radius of precipitates, which can be measured from the bright-field TEM image. More than 30 precipitates should be analyzed to obtain statistically reliable data. ν is Poisson’s ratio; b is the Burger vector of copper matrix; r0 is the radius of the core precipitate in the dislocation area (usually equal to b); λ is the average crystal plane spacing between precipitates, which can be estimated using Eq. ; and f is the volume fraction of precipitates, which can be calculated by applying the values of electrical conductivity. lists the values of tensile strength, 0.2% proof stress, electrical conductivity, average r, f, and inter-precipitate spacing k for the present alloy. After the related parameters (G = 5 × 104 MPa, ν = 0.3, b = r0 = 0.2556, r = 3 nm, and λ = 46.9 nm) are substituted in Eq. , the increasing strengthening effect by Orowan strengthening is about 151.9 MPa, which is lesser than the experimental data 295.5 MPa (б0.2-б0.2∗ = 526.5 MPa–231 MPa = 295.5 MPa). Therefore, the increase in yield strength is due to the formation of fine Cr precipitates and the interaction of dislocations with Cr and Ti at the peak aging stage [As aging progresses, the precipitated particles are fully analyzed and coarsened, gradually losing the coherent relationship with the matrix and reducing hardness. With continued aging, a low degree of recovery and recrystallization occurs in the alloy, stress is released, the work hardening phenomenon disappears, precipitation reaches an equilibrium state, and strength stabilizes. Cu-0.45Cr-0.14Ti (wt.%) alloy shows a sharp increase in strength at the initial stage of aging, and the larger the deformation, the faster the ascent rate. Intensity decreases sharply after the peak intensity is reached. The larger the deformation, the faster the falling speed. Furthermore, the strength tends to be stable at the later stage of aging.The effect of different degrees of cold rolling deformation on the electrical conductivity of Cu-0.45Cr-0.14Ti (wt.%) alloy is shown in ] reports that the resistivity of Cu alloy iswhere ρphoρdis,ρint,ρimpandρpsf are the scattering resistivities caused by phonons, dislocations, interface, impurities, and the precipitation of the corresponding variable field, respectively. ρphois only related to temperature, ρint and ρimp play a key role in the electrical conductivity of the alloy, and the effects of ρdis and ρpsf are low.At the beginning of the aging treatment, electrical conductivity increases sharply. The huge interfacial energy in the alloy promotes the rapid decomposition and desolvation of Cr and Ti, greatly reduces ρimp and rapidly improves electrical conductivity. Solute atoms gain more diffusion and precipitation channels because of the huge defect density. The rate of increase in conductivity is related to the rate of precipitation. Precipitation is faster, and conductivity increases more rapidly. Therefore, the electrical conductivity of the sample with a deformation rate of 80% reaches 55.4% IACS after 15 min. This value is significantly higher than the electrical conductivity of the alloy that deforms simultaneously by 60% and 70%. However, the alloy with a large degree of deformation has a large ρdis, so its initial conductivity is low.As the aging time is prolonged, the content of the elements in the solid solution in the alloy decreases, and ρimp gradually decreases. The precipitated phase gradually yet sufficiently reacts, and ρpsf of the precipitated particles gradually increases. Under the combined effects of these two mechanisms, the scattering effect of impurities is more prominent than that of interface scattering; as a result, conductivity slowly increases. As the aging time is further extended, the lattice defects weaken the precipitation of the precipitated phase; consequently, precipitation becomes completely stable, the solid solution gradually approaches the pure copper matrix, and electrical conductivity stabilizes. At this time, the influence of the degree of deformation on electrical conductivity is low and can be basically ignored.Cu–Cr alloys were prepared under the same process conditions to obtain the specific effects of the third trace element, i.e., Ti, on the strength and conductivity of Cu–Cr series alloys. Their properties were compared and analyzed. shows the curve of the tensile strength (a) and electrical conductivity (b) of Cu–Cr alloy with different degrees of deformation aging at 450 °C. When the Cu-0.42Cr alloy is deformed by 60%, the tensile strength can reach 478 MPa, which requires aging for 60 min (a). However, under the same deformation conditions, Cu-0.45Cr-0.14Ti (wt.%) alloy only needs to undergo aging for 30 min, and its tensile strength can reach 564 MPa (a, the addition of Ti not only increases the peak strength point of the Cu–Cr alloy but also shortens the time to reach this point. This finding shows that Ti can accelerate the response of the aging process and improve the effect of aging enhancement. When deformation is 80%, tensile strength can reach 610 MPa. It does not greatly reduce at the later stage of aging because the dissolved Ti atoms cause lattice distortion and pin dislocations. Dislocation movement is hindered to increase strength. After the aging treatment, the strength of Cu-0.45Cr-0.14Ti (wt.%) alloy is basically stable at a higher level. A large number of Ti atoms are dispersed on the surface of Cr, which hinders the diffusion and roughening of Cr atoms.b reveals that Cu-0.45Cr-0.14Ti and Cu-0.42Cr (wt.%) alloys have basically the same development trends of conductivity. Over time, their conductivity rapidly increases and then slowly increases to a stable value. When the deformation of the alloy is 60% and the aging time is 2 h, the conductivity of Cu-0.42Cr alloy reaches 89.2% IACS. However, under the same conditions, the conductivity of Cu-0.45Cr-0.14Ti (wt.%) alloy is only 63.3% IACS. This finding indicates that the solid solution atoms increase the scattering effect of conductive electrons and greatly reduce the conductivity of Cu–Cr alloy.The strength and electrical conductivity of Cu–Cr–Ti and Cu–Cr alloys were examined and compared with those of Cu–Cr–Zr in Reference 4. The results demonstrate that the addition of Ti greatly improves the strength of Cu–Cr alloys. It is almost as perfect as Cu–Cr–Zr alloy, but the gap in electrical conductivity is obvious. Furthermore, meeting the industrial requirements of a high electrical conductivity is difficult. Future studies should be conducted to apply this deformation and heat treatment method in industrial production. Nevertheless, Cu–Cr–Ti alloy has a faster aging rate than that of the other alloy, suggesting that the former has a greater advantage than the latter in terms of heat treatment time. The former can also save energy in a certain range, so it is suitable for further research.Cu-0.45Cr-0.14Ti (wt.%) alloy is subjected to solid solution treatment + cold rolling treatment with different degrees of deformation + aging treatment with different times to obtain the best comprehensive performance, i.e., a tensile strength of 610 MPa and an electrical conductivity of 55.4% IACS.In comparison with the strength of Cu-0.42Cr (wt.%) alloy, the strength of Cu-0.45Cr-0.14Ti (wt.%) alloy is significantly improved, which is almost close to that of Cu–Cr–Zr alloy. Ti can significantly shorten the time to reach the aging peak of the alloy. However, the electron scattering effect induced by the solid solution of Ti atoms possibly causes a large range of decrease in electrical conductivity.In the as-cast alloy, Ti atoms are mainly dissolved on the surface of the copper substrate. The nucleation particles and diffusion channels formed by the solid solution and the high cold deformation treatment promote the movement of Ti atoms. After the aging treatment, Ti segregates at the boundary between the Cr particles and the copper matrix, restricting the micromorphology of Cr particles. The nano-sized Cr precipitates coextensive with the matrix are the main reasons for the strength improvement of the alloy after aging. The precipitates in the Cu–Cr–Ti alloy exist in fcc and bcc structures. Ti atoms inhibit the formation of the nucleus of the fcc crystal to a certain extent.The authors declare that they have no known conflict of interes or personal relationships that could have appeared to influence the work reported in this paper.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.(iii) Twenty questions on tendon injuries in the handRecovery to full function following a tendon injury in the hand continues to be a challenge; therefore, the surgeon requires a detailed knowledge of anatomy, tendon healing, repair techniques, injury patterns and evolving rehabilitation methods to best treat these injuries. Particularly with flexor tendon injuries, current surgical techniques have significantly decreased rupture rates and controlled postoperative mobilization has reduced tendon adhesions that historically complicated repair attempts. In addition to open flexor and extensor tendon lacerations, this review also discusses closed tendon injuries in the hand, including flexor digitorum profundus (FDP) and extensor pollicis longus (EPL) ruptures, and mallet and boutonniere deformities.Normal tendon is composed of 65–70% water overall. Of its dry weight 80% is extracellular matrix, the majority of which is type I collagen (70%) with 2% elastin and 2–5% ground substance (glycoprotein, proteoglycan and plasma proteins), and the remaining weight is tenocyte fibroblastic cells. The role of these cells is to produce procollagen and remodel the extracellular matrix. Two chains of α1(I) procollagen polypeptide coil with one α2(I) procollagen forming a right-handed triple helix. This triple helix structure forms partly as a result of the abundance of proline and hydroxyproline amino acids and is stabilised by cross-linking bonds and glycine molecules. The crosslinking, which increases with maturity of the tendon, also increases its tensile strength. Within tendon these structures are organised longitudinally in a staggered pattern to form micro-fibrils, which are visible under electron microscopy. The collagen fibres are arranged in progressively larger bundles to form sub-fibrils and fibrils. These are packed in tight bundles with proteoglycans to form fascicles bound by endotenon, which also provides conduits for vessels and nerve fibres. In contrast, the arrangements of collagen fibres in ligament are not strictly parallel. Several fascicles form a tendon with a synovial epitenon membrane, which allows it to glide smoothly (see The epitenon layer continues at the musculo-tendinous junction with the perimysium, providing continuity with muscle. At the tendon–bone interface the epitenon continues onto periosteum with perforating fibres of Sharpey. There are four zones at a tendon insertion (see ). These gradually increase the stiffness of tissue so reducing the stress concentrated at the insertion site.Tendons are simply cables by which force produced by muscle contraction is transmitted to bone resulting in joint movement. The power and precision of the hand is a result of organisation of layers of extrinsic tendons and intrinsic muscles within it. The large forearm muscles can generate high tensile loads, as much as 120 N in the index flexor digitorum profundus (FDP) with strong pinch grip.The stress–strain curve for tendon, which is very similar to collagen, is divided into four regions (see ). Firstly, a toe region where initial loading causes the collagen fibres to un-crimp, straightening the wavy pattern of relaxed fibres. Secondly, a linear region where the extension of the straighten fibres (strain) is proportional to the load (stress), producing its Young's modulus. This is also called the elastic region, as removal of the load results in return to original tendon length. In the third region the tendon becomes plastic, with failure of some of the most stretched fibres strain is no longer proportional to stress. The point of transmission from elastic to plastic deformation occurs at the yield point. Finally the tendon fails at its maximum strength, the ultimate tensile strength, following which there may be a very low resistance to extension if the connective tissue surrounding the tendon is intact, region 4.Tendon exhibits rate- and time-dependant properties known as viscoelasticity, which is characterised by creep, stress relaxation and hysteresis. Creep occurs when extension (strain) of the tendon increases over time when it is held at a constant load (stress), this is a property used in the application of serial splinting. Stress relaxation is when a constant length (strain) is maintained by a reduced load over time. With cyclical loading, creep elongates the tendon causing increased extension with each constant load applied. The difference between the upswing and the downswing loop with each cycle is known as hysteresis and represents the energy absorbed by the tendon.In order to prevent bowstringing of the tendons across the finger with flexion, they are held to the phalanges and joints by a system of pulleys. These increase the range of movement of the joints by decreasing the lever arm. However, as the reduced lever arm reduces the power transmitted from the muscle, this has to be overcome by relatively more muscle bulk, contained in the forearm. The tendon sheath is made up of two osseous pulleys A2 and A4. The A2 pulley holds FDP and FDS to the proximal phalanx. The A4 is the next most important, holding the FDP to the middle phalanx. In between these the A1 is at the MCP joint and is involved in trigger fingers and A3 and A5 attach to the volar plates of the PIP and DIP joints, respectively. There are cruciate pulleys between these which compress with flexion. Based on the position of the tendon within the hand, injuries are divided into five zones (see Tendons receive their blood supply mainly through the vinculae (akin to a mesentery), as there is minimal intra-tendinous supply and only passive diffusion of nutrients from synovial fluid within the paratenon. The vinculae contain branches from each digital artery, with a superficial and a deep vessel to the dorsal side of each tendon. These are of particular importance in cases of delayed FDP rupture where the tendon has retracted into the palm and thus the vinculae are injured.Tendons heal by both intrinsic and extrinsic methods. Although clinically it is impossible to separate the cellular events involved in each method, the degree of each is influenced by injury and treatment. thereby leading to more rapid recovery of tensile strength, and thus this has been applied to rehabilitation protocols. The third stage is the remodelling phase, which occurs from 28 days to 3 months as the scar matures and collagen realigns. In addition to this period of time, return to normal ultimate tensile strength also requires physiological loading. when the ends are held only by flimsy fibrin and clot. Between 5 and 21 days, therefore, the repair strength is dependant almost entirely on the suture. Active motion rehabilitation should be started before day 5, as starting after this point increases the risk of rupture.The technique of tendon repair using a core suture was first described by Kirchmayr in 1917, but was popularised by Kessler. Much research is published on the subject, with many different suturing techniques described, including Tajima's modifications of Kessler, Strickland, cruciate and Tsuge. However, some general conclusions can be drawn from the literature. Firstly, that the initial strength of the repair is proportional to the number of suture strands that cross the tendon gap. Savage showed that a six strand repair is stronger than a four strand, which is stronger than a two strand. Since this early work there have been a number of studies correlating the number of suture stands crossing the repair with repair strength. However, the more complicated the repair, the more difficult the technique and increased chance of tendon damage, or stitch division, with a subsequent pass of the needle. So, based on current evidence, we would suggest that a four strand core suture should be used as a minimum.The strength of the repair increases with the calibre of the suture, however, quantity of suture increases the bulk of the repair so reducing tendon glide, therefore 3/0 or 4/0 non-absorbable sutures have been suggested for adequate strength and ease of placement balanced with volume of suture material. Ruptures usually occur at the knots, but this may be reduced by using braided sutures.In addition to a core suture, an epitendinous suture is used to smooth the tendon repair, improve glide, reduce gapping and increase strength by 10–59%. A locking epitendinous suture has been described, which gives greater strength; however, it is technically difficult. The aim of the repair is to have a strong enough repair that prevents tendon gapping and allows early active mobilisation, which encourages intrinsic healing and reduces adhesions.A closed FDP avulsion is often referred to as rugger jersey finger, as they commonly occur in the ring finger when it gets caught in a fellow player's jersey. As this is a closed injury a high index of suspicion is needed to avoid delayed diagnosis, especially as the tendon can retract back to the palm with rupture of both vinculae, resulting in loss of blood supply, haematoma in the sheath and subsequent scar formation and joint contracture if untreated.This classification can used to direct treatment, with type 1 requiring urgent surgical reattachment of FDP to distal phalanx, as vinculae to FPD are ruptured. A number of different techniques are described. Our preferred method is to expose the tendon ends and sheath through a Bruner incision from the level of the DIPJ to the A1 pulley in the palm. The end of the tendon is passed through the intact flexor sheath using a paediatric feeding tube and reattached to the distal phalanx using a Bunnell suture passed through the phalanx with an eyed needle and tied over a dental roll on the nail. As described by Elliot, if there is difficulty in passing the tendon beneath the A4 pulley then dividing the tendon in half longitudinally along the natural cleavage line can help. In cases where the diagnosis is delayed more than 3 weeks, tendon reattachment tends to fail due to loss of blood supply and contraction of the tendon. Hence, cases diagnosed late require reconstruction of FDP with a graft, or DIPJ fusion which can be rehabilitated in a shorter time and gives more reliable results. In cases where the FDP end causes a painful nodule in the palm, this can be excised.Type 2 has a better prognosis, as the long vinculae remain intact and as such can be repaired up to 3 months. In late cases, as described above, the FDP tendon can be reduced in size to get the tendon beneath a collapsed A4 pulley. Type 3 injuries require bony attachment of the fragment with sutures or mini screws.Zone 2 injuries lie between the A1 pulley and the insertion of FDS on the middle phalanx and therefore incorporate two tendons within the flexor sheath. Bunnell named this “no man's land” after his First World War experience in France, where it was used to describe the strip of devastated land between enemy trenches, as he recognised that restrictive adhesions followed tendon injuries in this area. He advised repair only of FDP and post-operative immobilisation in wrist flexion with “sufficient motion to stimulate growth and lessen adhesions” during healing. However, because of generally unsatisfactory results, up to the 1960s primary tendon repair in zone 2 was not practiced, but rather the tendons were excised and FDP grafted. Following Kleinert's initial work, much research has been done on tendon repair and healing, especially in zone 2, with improved techniques and suture materials showing reduced gap formation allowing early mobilisation. Current practice is to repair both tendons, as this allows independent movement of both PIP and DIP joints, encouraging tendon glide and helping to prevent adhesions. An intact FDS also wraps around FDP, acting like a dynamic pulley.With careful examination there are various observations that should alert one to a likely flexor tendon injury, including loss of the normal finger cascade, loss of the tenodesis effect, no passive movement in the fingers on squeeze compression of the forearm muscle bulk, as well as loss of individual active movement of DIP and PIP joints by isolated FDP and FDS testing. With lacerations caused by glass, the wound may be deceptively small and yet the damage done extensive.At exploration blood seen within the flexor sheath is an indication of tendon laceration. In those cases where the proximal end of the tendon has retracted away from the wound, flexing the wrist and milking it down can deliver the tendon end. Similar milking can be used to deliver a retracted distal end, but it will only come down if the tendon division occurred with the finger straight. If this fails the ends will need to be found by surgical exposure and then passed it through the flexor sheath. The tendons can be passed through the A2 pulley using a paediatric feeding catheter. The flexor sheath can be opened and reflected as a window between the A2 and A4 pulleys to allow retrieval, passage and repair of tendons.If the laceration is under the A4 or A2 pulley, in addition to flexing the finger to move the repair site out of the pulley, the end third of these pulleys can be divided to allow access to the tendon end for repair. Following tendon repair, sheath repair has been suggested to act as a barrier to adhesions; however, various studies have not confirmed a clinical advantage. Therefore, as repair may reduce volume and thus tendon glide we suggest that the sheath should be replaced back but not sutured. Once the tendon has been repaired its excursion through the pulleys is checked with passive range of movement. If the pulleys are too tight for the repaired tendon to pass through they can be dilated. If it is still too tight it is preferable to vent the pulley, by dividing up to a third along its edge either distally or proximally, rather than risking the repair catching and rupturing.Tendon injuries in zone 3 are prevented from retracting due to the lumbrical attachment and lacerations in the carpal tunnel are unusual. When repairing wrist lacerations in zone 5 it is important to be aware that isolated tendon injuries are uncommon. So, as nerve and artery damage should be anticipated, pre-operative assessment includes examination of sensation, motor assessment and an Allen's test, in addition to testing tendon integrity as described earlier. Exploration with loupe magnification is advisable. Tendon repairs in this area are repaired as elsewhere with a 3/0 or 4/0 non-absorbable core 4-strand suture and a 6/0 non-absorbable epitendinous suture.Immobilisation was historically used after flexor tendon repair as the fear was of tendon rupture; however, due to the marked adhesions that formed and the severe stiffness that developed following this, mobilisation protocols were developed. There remain a few specific indications for immobilisation, for example children or adults that cannot comprehend or comply with active or passive rehabilitation programmes. Other relative indications are where it is necessary because of associated injuries and disorders that can affect tendon healing e.g. rheumatoid arthritis.As suture techniques improved gap resistance, early controlled forces were shown to not only increase intrinsic tendon healing and recovery of tensile strength, but also reduced adhesions by allowing tendon excursion. Two basic passive motion programs were subsequently developed Duran–Houser and Kleinert.In the 1970s, Duran and Houser showed that passive movement would produce 3–5 mm of tendon glide by extending the DIP or PIP joint while the other joint was held flexed, as this moves FDP and FDS independently, moves the repairs away from each other and away from the site of injury, so reducing the formation of adhesions. The patient does these passive exercises with a dorsal blocking splint. This regimen is occasionally used now when tendon damage is such that a full repair is not possible or if the surgeon has not been able to use a strong enough repair to allow active mobilisation. This is why it is vital that the operating surgeon communicates with the hand therapist treating the patient immediately after surgery to discuss the appropriate rehabilitation protocol.Kleinert used elastic traction bands attached from the finger nails to the volar forearm, for a controlled passive motion program, the patient also has a dorsal blocking splint with the wrist at 30° and MCP joints at 30–40° flexion. The elastic traction holds the fingers in flexion so the flexor muscles cannot generate any force and they relax with the active extension of the fingers up to the dorsal hood. This programme produces glide as the tendons are pulled through passively. Two specific problems have led to modifications. Firstly, flexion contractures of the PIP joint tended to develop as the fingers sit with the PIP joint in flexion. So at night the elastic traction is removed and the fingers are strapped to the dorsal hood in extension. Secondly, loss of active DIP joint motion may occur, as there is less motion here with the Kleinert model. This has been treated by a second pulley added at the mid-palmar level increasing the vector of pull, thus flexing the DIP as well as PIP joints. This produces some differential glide between FDS and FDP though not nearly as much as with the active mobilisation protocols.An early active motion protocol was first used in 1989 in Belfast, and although the initial rupture rates were higher several subsequent studies have published improved results and this rehabilitation protocol has been widely adopted. The patient is treated in a dorsal blocking with wrist 20–30° flexion and MCP 50–70° flexion and for the first 6 weeks the patient does hourly exercises: combining passive flexion of individual fingers (DIP and PIPJ), and active mass extension and active mass flexion. After 6 weeks the patient starts to remove the splint for exercises also including individual active finger flexion, with return to heavier work at 10 weeks and full activities at 12 weeks.Rupture after a four strand tendon repair technique is uncommon, 4–17% in zone 2 and 3–17% with FPL; however, it is the most significant complication. It may occur with inadvertent strong gripping, lifting or functional use of the hand and so patient education is extremely important. On some occasions, despite commitment to therapy, reduced range of motion with contractures at DIP and PIP joints occur and an estimated 10% of zone 2 injuries require secondary tenolysis or tendon graft.Outcome can be measured using the total active range of motion (TAM) method by totalling the DIP and PIP joints range in degrees, which was proposed by the American Society of Surgery of the Hand and modified. As an active range over 80% compared to the normal side gives excellent function to the fingers, this is taken into account with this grading method, which divides results into excellent, good, fair and poor. As tendon healing takes time outcome should not be measured before 3 months. In a review of 15 papers’ results over the past 15 years TAM outcome measured excellent or good in three quarters of primary tendon repairs following various rehabilitation regimes.Flexor tenolysis is performed to release non-gliding adhesions formed on the tendon surface that reduces range of movement. Adhesions form after any tendon injury but the incidence increases with crush injuries, fracture callus, soft tissue injury, infection and immobilisation. Treatment starts with therapy to restore gliding and mobilise stiff joints; however, if progress plateaus and there is a significant difference between passive (full) and active (limited) motion of the finger then tenolysis is indicated. Other prerequisites are that fractures have united, skin is stable and supple, there is good muscle strength, mobile joints with a near full passive range, a compliant patient and availability of immediate therapy for active mobilisation and good pain relief post-operatively.Sometimes it is very hard to know whether the flexor repair is intact despite careful clinical examination. Ultrasound can be helpful. However, all patients undergoing tenolysis should be warned that the tendon may not be intact and that there is a risk of surgical damage leading to rupture. The patient should, therefore, also be consented for insertion of a tendon rod.If a flexor tendon repair is delayed beyond a few days certain criteria need to be met for delayed direct repair. These include no segmental loss of tendon, adequate skin and soft tissue cover, good passive range of movement of the joints with no contracture, adequate sensation and vascularity of the finger and skeletal alignment. If these are not fulfilled tendon grafting or transfer should be considered.If there is a delay of more than 3 weeks the tendon ends degenerate and the gap fills with scar tissue, and direct repair is not possible. In this situation primary tendon grafting can be considered. Other indications for primary tendon grafting are an acute injury with segmental tendon loss and delayed type 1 FDP avulsion. However, in order for a single stage tendon graft to be successful the finger needs to be in good condition. The criteria are the same as for tenolysis (see above) apart from the requirement that the flexor sheath is undamaged and patent.In a single stage tendon graft palmaris longus, plantaris or a toe extensor can be harvested as tendon graft. Palmaris is absent in 16% of people unilaterally and 9% bilaterally and plantaris is absent in 7%. Ultrasound can be used to identify plantaris. The tendon graft is attached to the distal phalanx as for a FDP reattachment, described earlier, and the proximal graft is weaved through the free tendon end using a Pulvertaft weave with 3–4 weaves, outside the flexor sheath either in the palm or wrist. This is usually strong enough to allow early active mobilisation, in a dorsal blocking splint similar to flexor tendon repair rehabilitation. The graft should be tensioned by observing the tenodesis effect and the normal cascade of the fingers. Only one graft is done per finger, and when restoring FDP function if there is an intact FDS this should not be sacrificed.More commonly a two-stage tendon graft reconstruction is necessary, as the criteria for single stage grafting are rarely found. Usually flexor reconstruction is needed as the result of the failure of an acute repair. If a tendon repair ruptures then a further attempt can be made to re-repair the tendon; however, this should only be done if the soft tissues and joints are in a suitable state. More often than not, the soft tissues are thickened and the joints stiff in which case single stage grafting is doomed to failure. Once the finger is in a satisfactory state the flexor sheath will have collapsed and a silicone rod will be needed to create a new synovial sheath. Another indication is the need to reconstruct fibrous pulleys.The patient needs to be aware that the process requires two operations and regular therapy to get a good result. The alternatives to tendon grafting are a tenodesis or arthrodesis of the DIP joint where just FDP is missing or amputation where both flexor tendons are missing.The first stage involves inserting a silicone rod through the pulley system, in order to recreate a smooth tunnel for the tendon graft to be inserted at a later date. If A2 and A4 are absent these can be reconstructed and any joint contracture is released. The silicone rod is fixed to the FDP stump distally and the other end is usually left free either in the palm or at the wrist. It is important to achieve and maintain the full passive range of motion during the 8–12 weeks needed for a “sheath” to form around the rod.At the second stage operation this newly formed “sheath” is not disturbed, as the ends of the rod are exposed proximally and distally. The harvested graft is then attached to the distal end of the rod and pulled through the “sheath” and attached and tensioned as for a one-stage graft. Our preference is to attach the graft distally first and to use the weave proximally to adjust the tension. Early hand therapy to establish tendon glide is essential for a good result.Successful function of the flexor tendon system requires an intact pulley system and if the A2 or A4 pulleys are destroyed then bowstringing will be a problem and reconstruction of one or both will be necessary. Loss of the A1, A3 or A5 pulleys will not lead to a significant problem. The A2 and A4 pulleys should be reconstructed at the first stage over a silicone rod. The material used to recreate pulleys needs to encourage tendon glide and thus synovial lined graft is preferable, for example one tail of FDS leaving the distal end attached or a strip of extensor retinaculum wrapped around the phalanx. The preservation of the pulleys is important and attention should be paid to retaining as much uninjured pulley and preserving the sheath as possible at primary surgery, by entering the sheath by raising windows between the main annular pulleys, through the cruciate pulleys.The joints are the odd numbered extensor zones and in between are the even numbered zones. Therefore, zone 1 is over the DIPJ, 2 over the middle phalanx, 3 over the PIPJ, 4 over the proximal phalanx, 5 over the MCPJ, 6 over the metacarpals, 7 over the dorsal reticulum, 8 distal forearm and 9 proximal forearm (see The result of an extensor tendon injury in zone 1 is known as a mallet deformity. An X-ray is essential to identify a bony or tendinous mallet and to look for subluxation. Closed injuries are common and 80% will heal with 6 (tendinous)—8 (bony) weeks of splintage with a further 2 weeks at night. If the tendon does not heal within this period of time further splintage can be successful, but if this fails open repair may be considered. One indication for surgery in a closed injury is the presence is palmar subluxation of the distal phalanx. There may be a large dorsal fracture fragment associated with this subluxation. The fragment can be fixed if large enough, otherwise a simple longitudinal k-wire to hold the joint reduced is adequate.Open mallet injuries require surgical repair and various methods of this are described. The tendon can be repaired separately from the skin, but as there is little subcutaneous tissue the repair material may be superficial and successful results have been achieved with a mass repair of tendon and skin. A k-wire through the DIP joint is useful to stabilise the repair while the tendon heals. If the tendon ends are damaged a turndown of one lateral band can be used to strengthen the repair and this method may also be useful for chronic mallet injuries.A boutonnière deformity occurs due to disruption of the central slip and subsequent palmar subluxation of the lateral bands. The deformity may not necessarily be apparent at the outset, as it may take time for the palmar subluxation of the lateral bands to occur, which then results in the classic hyperextension of the DIPJ.Acute closed injuries can be treated by splinting the PIPJ in extension, allowing active flexion of the DIPJ as this draws the lateral bands dorsally, for 6 weeks until the central slip has healed. Others advocate holding the PIPJ in extension with a k-wire for 3 weeks, followed by a further 4 weeks in a splint. Serial casting is sometimes necessary to correct PIPJ flexion if diagnosis is delayed. After immobilisation the PIPJ is often stiff and this can be treated with a dynamic splint for a further few weeks.Open extensor tendon division in zone 3 require washout of the PIP joint and primary repair of the central slip to restore extension. Sometimes the cut ends are not very substantial and in these cases the repair can be reinforced with splitting and centralising a lateral band or with a central slip turndown. Following repair, immobilisation in full an extension splint for 6 weeks is suggested and additional k-wire support for the first few weeks can be considered. The outcome of boutonnière injuries tends to be less predicable than mallet injuries.Wounds over the MCP joints (zone 5) should alert one to the possibility of a fight-bite injury and a careful history and hand radiographs should be taken to exclude both fractures and tooth fragments. Oral flora are abundant within normal saliva, which contains 42 different bacteria including Eikenella corrodens, which is not sensitive to penicillin, so such injuries require second or third generation cephalosporins or co-amoxiclav. These injuries should be treated with prompt surgical washout and exploration. The extensor tendon injury is often proximal to the skin wound, as the hand is in a fist at the time of injury, so when the finger is held extended the tendon covers the joint capsule laceration, thereby sealing off the joint and increasing the risk of septic arthritis. The inexperienced examiner will look in the wound and think that there has been no injury to either tendon or joint. Surgery must include a proper exploration of the extensor tendon and washout of MCP joint. In cases of active infection, tendon repair should be delayed until this is treated.Attrition rupture of extensor pollicis longus (EPL) can occur after a distal radius fracture. The mechanism may be wear over a rough distal radius fracture edge in the third dorsal compartment (zone 7), due to vascular damage or as a complication of dorsal plating. Rupture can also occur as a complication of tenosynovitis and attrition in rheumatoid arthritis. Loss of EPL function presents with sudden loss of extension of the thumb. The easiest test for EPL is to ask the patient to raise their thumb off the table inability to do this confirms the diagnosis, which can be further confirmed by ultrasound. The differential diagnosis includes posterior interosseous nerve palsy. An attrition rupture of EPL cannot be directly repaired, and is treated by tendon transfer using extensor indicis (EIP) or abductor pollicis longus. The presence of EIP is checked by testing hyperextension individually of the index finger. EIP is the most ulnar tendon at the MP joint. Many patients manage satisfactorily without a functioning EPL and so decide against surgical reconstruction.In summary, the treatment of tendon injuries is complex and requires an understanding of the basic principles to achieve good results. Hand therapy plays a key role in both non-operative treatment and post-operative rehabilitation. There is a plethora of literature, especially on flexor tendon injuries, but in this review article we aim at answering some of the important questions on tendon injuries, outlining the salient findings which have influenced current practice.Sintering behaviour and microstructure of 3Y-TZP + 8 mol% CuO nano-powder compositeNanocrystalline 3Y-TZP and copper-oxide powders were prepared by co-precipitation of metal chlorides and copper oxalate complexation–precipitation, respectively. A significant enhancement in sintering activity of 3Y-TZP nano-powders, without presence of liquid phase, was achieved by addition of 8 mol% CuO nano-powder, resulting in an extremely fast densification between 750 and 900 °C. This enhancement in sintering activity was explained by an increase in grain-boundary mobility as caused by dissolution of CuO in the 3Y-TZP matrix. The nano-powder composite was densified to 96% by pressureless sintering at 1130 °C for 1 h. Considerable tetragonal to monoclinic phase transformation of the zirconia phase was observed by high temperature XRD analysis. This zirconia phase transformation is discussed in terms of reactions between CuO and yttria as segregated to the 3Y-TZP grain boundaries.Zirconia based ceramic materials have obtained extensive interest in the past decades due to their advanced mechanical and electrical properties. The high fracture toughness and strength of 3 mol% yttria stabilised tetragonal zirconia polycrystals (3Y-TZP) make this material an important candidate for many structural applications. Yttria doped cubic zirconia ceramics showing high ionic conductivity and are widely used as electrolytes in fuel cells and oxygen sensors. It was also reported that fine-grained Y-TZP ceramics exhibit a superplastic deformation property, which has opened up the possibility of using ceramics in ductile near net shape forming operations. Recently low dry sliding friction was obtained with CuO doped 3Y-TZP ceramics, implying a possibility of engineering applications of these materials without lubricants.Many efforts have been addressed on enhancing the sinterability of zirconia-based ceramics because it is important not only for production cost, but also for development of multi-component devices. One approach to improve the sinterability of ceramics is to increase the powder reactivity via a reduction in particle size. It has been reported in many studies that nano-sized Y-TZP powders with weak agglomerates exhibit greatly enhanced sintering activity and thus sintering proceeds fast at relative low temperatures (<1100 °C). Another possible method is the presence of liquid phases during sintering via addition of sintering aids. However, addition of sintering aids can also lead to formation amorphous grain boundary phases and significant grain growth, which are undesired for several applications.In the present work a significant enhancement in sintering activity of a 3Y-TZP nano-powder, without presence of liquid phase, was achieved by addition of 8 mol% of CuO nano-powder. Weakly agglomerated nanocrystalline 3Y-TZP and CuO powders prepared by wet-chemical synthesis techniques were used in this study. The sintering behaviour was analysed by means of dilatometer measurements, while microstructure was analysed by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Zirconia phase transformation during sintering was investigated by means of high temperature X-ray diffraction. The sintering behaviour and zirconia phase transformation of the nano-powder composite are discussed in terms of reactions between CuO and 3Y-TZP grains.A nanocrystalline powder of 3 mol% yttria stabilised tetragonal zirconia polycrystals (3Y-TZP) was prepared by a co-precipitation technique of metal chlorides, as described in detail elsewhere. An aqueous solution (pH ∼2) containing proper amounts of Zr4+ and Y3+ ions was added by means of a peristaltic pump to a concentrated aqueous ammonia (pH ∼14) solution. The ammonia solution was stirred vigorously and continuously with a top-mounted turbine stirrer. The resulting wet gel was washed chloride-free with distilled water/ammonia mixtures. Subsequently the precipitate was washed with ethanol to remove water. The gel suspended in ethanol, was then oven-dried overnight at 100 °C. The resulting amorphous powder was ground and sieved through a 180 μm sieve, and subsequently calcined at 550 °C in stagnant air for 2 h. The proper composition of the 3Y-TZP powder was confirmed by an XRF (PW 1480, Philips) analysis. The calcined powder was then sieved through a 180 μm sieve and stored in a desiccator.A copper oxalate precipitation method was applied to prepare the nanocrystalline copper-oxide powders. Detailed procedure was described in. A Cu alcohol solution (0.5 M) was added at a controlled speed to an oxalic acid solution in alcohol (0.5 M) to form the copper oxalate complex precipitate. Oxalic acid was strongly stirred by a magnetic stirrer during addition of the Cu solution. The suspension was oven-dried overnight at 100 °C and then ground and sieved through a 180 μm sieve. The sieved complex powder was calcined at 250 °C for 2 h. The resulting black powder was sieved again through a 180 μm sieve and stored in a desiccator.An 8 mol%-CuO doped 3Y-TZP composite powder was prepared by milling the proper amounts of 3Y-TZP and copper-oxide powder for 24 h in a polyethylene bottle, using ethanol and zirconia balls as milling media. The milled suspension was ultrasonically dispersed for 5 min and then oven-dried at 100 °C for 24 h. The dry cake of the composite powder was ground lightly in a plastic mortar and sieved through a 180 μm sieve.The nanocrystalline 3Y-TZP and copper oxide powders were characterised by XRD, BET as described elsewhere.Cylindrical green compacts of nanocrystalline 3Y-TZP powder and the composite powders were prepared by isostatic pressing at 400 MPa. The diameter and length of the compacts are 7–8 and 12–15 mm, respectively. The green densities (measured by the Achimedes’ technique in mercury) of the compacts are 44–46% of the theoretical density of tetragonal zirconia. The sintering behaviour of the compacts was studied using a Netzsch 402E dilatometer in an oxygen flow. For all dilatometer measurements a three segments temperature program was applied, including heating from room temperature at 15 °C min−1, holding at 1130 °C for 1 h, and cooling to room temperature at 5 °C min−1. Linear shrinkage was recorded as function of time and temperature. The density as a function of temperature was calculated from the green density and linear shrinkage data.Slices of 3Y-TZP and composites with dimensions of 10 mm × 8 mm × 0.5 mm were prepared by isostatic pressing followed by careful polishing with sand papers (silicon carbide paper, P# 1000). These slices were used for X-ray diffraction (XRD, X’Pert_MPD, PANalytical) analysis at various temperatures in order to investigate possible zirconia phase changes during sintering. During the XRD experiments, the samples were heated and cooled at 5 °C min−1. At each measuring temperature the slice was held at that temperature for 15 min before measurement started. The volume fraction of monoclinic and tetragonal zirconia phases was calculated based on the peak intensities of M[1 1 1], M[1¯11] and T[1 1 1] XRD signals using the relationship as proposed by Toraya et al.Scanning electron microscopy (SEM-EDX, Thermo NORAN Instruments) analysis was conducted on cross sections of the sintered samples. Prior to SEM experiments, the surfaces were carefully polished and thermally etched at 850 °C for 2 h. Transmission electron microscopy (TEM, CM30 Twin/STEM, Philips) analysis was carried out on the sintered CuO doped 3Y-TZP sample to investigate the grain boundary properties.The characteristics of the nanocrystalline 3Y-TZP and copper-oxide powders have been reported in details elsewhere. It was observed that the 3Y-TZP powder contains pure tetragonal zirconia particles with an equivalent diameter as calculated by the BET surface area (DBET) of 10 nm. The CuO powder synthesised in this work has a DBET of 50 nm and exhibits a multiphase composition including CuO, Cu2O and metallic Cu. The specific amounts of those phases are not important for the sintering behaviour or zirconia phase changes of the CuO doped 3Y-TZP as treated in this work. During early stage heating both Cu2O and Cu is oxidised to CuO phase below 350 °C as shown by thermogravic analysis of the copper oxalate complex, while sintering and zirconia phase changes have not started yet. shows the relative density (corrected for weight loss and thermal expansion) and the linear densification rate (d(ΔL/L0)/dt) of the 8 mol% CuO doped 3Y-TZP nano-composite as functions of temperature, during heating in an oxygen flow. The data of undoped 3Y-TZP were also shown in the figure for comparison. As can be seen in the addition of nanocrystalline CuO drastically changes the sintering behaviour of nanocrystalline 3Y-TZP. In general it can be stated that sintering of the CuO doped 3Y-TZP composite can be divided into three stages, e.g. stage I (700–900 °C), stage II (900–1020 °C) and stage III (1020–1100 °C).In stage I it is shown that the addition of CuO decreased the onset temperature of densification of 3Y-TZP from 850 °C (undoped) to 700 °C (CuO doped). Shortly after the start of densification, the composite sample showed a drastic increase in densification rate until 850 °C. Within the next 50 °C temperature range (around 3 min of heating) the densification slowed down rapidly. After this sintering stage the density of the CuO doped sample was increased from 50% to 75%, while densification of the undoped 3Y-TZP did not started hardly in the same temperature range.In sintering stage II densification of CuO doped 3Y-TZP proceeded at a relatively low rate. However, the contribution in this stage to the total densification is also significant (an increase from 75% to 90%) of the CuO doped sample was achieved in this sintering stage, indicating that sintering has almost been finished after heating at 15 °C min−1 to around 1000 °C. In contrast, densification of the undoped 3Y-TZP sample just started in this temperature range and the density is only below 60%.The densification of the CuO doped sample slowed down gradually in stage III since densification is almost finished in stage II. After the dilatometer experiment the CuO doped 3Y-TZP had a relative density of 96% (the presence of 80 vol% monoclinic zirconia phase in the sintered sample is taken into account for the calculation of theoretical density). shows a SEM image of the cross-section surface of the CuO doped 3Y-TZP composite after the dilatometer experiment. The sintered composite exhibits a quite dense structure. However the grain size varies in a wide range from 200 nm to 1 μm, indicating that abnormal grain growth occurred during sintering. Occasionally some bright faceted grains are visible in the SEM image (as pointed out by the white arrow in ). It is revealed by EDX analysis that these faceted grains are almost pure CuO. As revealed by TEM analysis, the grain boundaries of the composite sample are clean (see ). No amorphous phase can be observed in the grain boundary region or triple grain junctions. EDX analysis combined with TEM showed that copper oxide exists as crystalline particles with a diameter of 100–200 nm among the matrix of zirconia grains.The volume fractions (VM) of monoclinic zirconia in the CuO doped 3Y-TZP composite and the undoped 3Y-TZP are plotted as a function of temperature in . As can be seen from the figure, both CuO doped and undoped green compacts contain significant amounts of monoclinic zirconia, although they were prepared using a pure tetragonal zirconia powder. The presence of monoclinic zirconia in the green compacts was caused by the stress applied during polishing prior to XRD measurements. With increasing temperatures the monoclinic zirconia phase was reduced in both cases due to stress relaxation. Whereas the monoclinic zirconia disappeared in the undoped 3Y-TZP after the sample was heated to 950 °C, VM of the CuO doped 3Y-TZP composite started to increase at 850 °C. Especially in the temperature range of 900–1100 °C the monoclinic zirconia increases drastically from 30% to 80%, indicating some reactions extremely destabilises the tetragonal zirconia phase in this temperature range. After dilatometer experiment the CuO doped 3Y-TZP composite contains also around 80 vol% monoclinic zirconia, indicating that no zirconia phase transformation occurred during cooling. Correspondingly no volume expansion caused by zirconia phase changes was observed during, as was the case for a coarse-grained 0.8 mol% CuO doped 3Y-TZP sintered at 1400 °C.It has been reported that during sintering several reactions occur in the CuO doped Y-TZP systems, and those reactions have profound influences on densification behaviour of coarse-grained 0.8 mol% CuO doped 3Y-TZP ceramics. Basically the difference between sintering behaviours of undoped and CuO doped nanocrystalline 3Y-TZP systems as shown here in can also be interpreted in terms of reactions occurring during heating.The first effect of CuO addition on the sintering behaviour of 3Y-TZP is the fact that the onset temperature of densification is lower. This phenomenon was also observed in our previous studies on coarse- and nano-powder composites of 3Y-TZP doped with lower amounts of CuO (0.8 mol%). The low onset temperature can be attributed to the dissolution of CuO in the Y-TZP matrix by forming CuO-rich grain boundaries in the zirconia grains, which increases the ion mobility of zirconia grains and especially the grain boundary region. The higher ion mobility results in activation in sintering of the zirconia grains and therefore the onset of densification shifts towards lower temperatures.The extremely fast densification rate of the CuO doped 3Y-TZP composite observed in sintering stage I is a very unique phenomenon. To our knowledge Y-TZP systems did not exhibit significant densification at such low temperatures (<900 °C) even when sintering aids were used. It is important to point out that in sintering stage I all the components in the composite studied here are in the solid phases. Therefore liquid-phase sintering kinetics, normally a reason of lower densification temperatures does not occur in this case. As discussed before the dissolution of CuO in the Y-TZP matrix significantly activates the sintering process by increasing the grain boundary diffusivity. This dissolution mainly takes place in the grain boundary region of zirconia. Therefore the area of Y-TZP grain boundaries per unit of volume as well as the Y-TZP/CuO contact area per unit volume are important for the dissolution and consequently for the activation of the sintering process. In the composite studied in this paper both Y-TZP and CuO grain size are on a nano scale. Additionally this composite contains a relatively large amount of CuO (8 mol%). Assuming the CuO grains are uniformly distributed among the 3Y-TZP matrix, it is obvious that the composite are possessing both a high Y-TZP grain boundary area and a high Y-TZP/CuO contact area. As a result of all these factors, large amounts of 3Y-TZP grains can significantly be activated for sintering by the dissolution of CuO in Y-TZP matrix in sintering stage I and correspondingly an extremely fast densification is possible.Another result of the enhancement in ion mobility as caused by the strong CuO dissolution in the 3Y-TZP is the significant growth of zirconia grains. Although the Y-TZP/CuO contact area is relatively high in the nano-powder composite, still large amounts of Y-TZP grains are not in contact with CuO grains and so CuO dissolution did not occur for all Y-TZP grains. The large grains with a size up to 1 μm as shown in are expected to be originally in contact with CuO grains. On the contrary, the Y-TZP grains that were not in contact with CuO shows a grain diameter of 100–200 nm, which is similar with the grain size of an undoped 3Y-TZP nano-powders sintered in the same way.The tetragonal to monoclinic (t–m) phase transformation of zirconia during heating was also observed in a previous study of a coarse powder composite of 0.8 mol% CuO doped 3Y-TZP. However, compared with the coarse powder composite, the t–m zirconia phase transformation in the nano–nano composite started at much lower temperatures (800 °C compared with 1100 °C) and proceeded more intensively. As discussed in our previous work the t–m transformation of zirconia in CuO doped Y-TZP systems can be related to the reaction between the CuO and yttria as segregated to Y-TZP grain boundaries. According to the pseudo-binary phase diagram of the Y2O3–CuO system in air a reaction between Y2O3 and CuO takes place at elevated temperatures (>800 °C), resulting in the formation of an yttria-copper-oxide phase. As a result of this reaction in the CuO Y-TZP composite Y-TZP grains are depleted of yttria and tetragonal zirconia phase is destabilised. However this reaction occurs only to a large extent when the material possesses sufficient Y-TZP/CuO contact area and significant yttria segregation to the grain boundaries. In the CuO-doped 3Y-TZP composite studied in this paper large amounts of Y-TZP/CuO contact are present as discussed above. The yttria segregation is actually a rate-limiting process of the reaction between CuO and yttria, and consequently controls the t–m phase transformation of zirconia. It has been shown that significant yttria segregation to Y-TZP grain boundaries occurs intensively above 850 °C. Therefore a significant reaction between Y2O3 and CuO and subsequently pronounced t–m phase transformation of zirconia started around this temperature as shown in . Heating up to 1100 °C results in the formation of 80% of monoclinic zirconia. After cooling to room temperature at the end of the sintering process also 80% of monoclinic zirconia is observed. So during cooling no further formation of monoclinic zirconia arises. This last phenomenon was also proven by the fact that during cooling no expansion was observed in dilatometer experiments.The sintering behaviour of an 8 mol% CuO-doped 3Y-TZP nano-powder composite was investigated by means of dilatometer measurements. The nano-powder composite was prepared from 3Y-TZP and CuO powders with BET equivalent particle diameters of 10 and 50 nm, respectively. This nano-powder composite exhibits a low onset temperature of densification (750 °C) followed by an extremely fast densification at relatively low temperatures (<900 °C). This unique sintering behaviour was interpreted in terms of the dissolution of CuO in the 3Y-TZP matrix due to the large 3Y-TZP/CuO contact area per unit of volume in the nano-powder composite. This CuO dissolution also results in a strong grain growth during sintering.High temperature XRD analysis revealed that a pronounced tetragonal to monoclinic phase transformation of zirconia occurs above 900 °C during heating. This phenomenon can be explained by the depletion of yttria in the Y-TZP grains, which is caused by the reaction between CuO and yttria as segregated from the Y-TZP grains resulting in a thermodynamically instable tetragonal phase, which then transforms to the stable monoclinic structure. During cooling after sintering the ratio monoclinic/tetragonal zirconia does not change in these CuO/3Y-TZP nano/nano composites.Effects of residual oils on the adhesion characteristics of metal-CFRP adhesive jointsThe demands of automobile consumers have increasingly expanded from safety to high-quality, electronic equipment, convenience, and design. As automobile makers have developed various options for satisfying consumer’s needs, the average weight of vehicles has increased by about 15 kg between 1990 and 2010. However, the environmental regulations of each country enforce the improvement of fuel efficiency required of automobile industries according to simultaneous raised concerns about environmental pollution. Many efforts, such as those aimed at enhancing engine efficiency, decreasing drive resistance, and reducing weight, have been attempted. Weight reduction using advanced materials has become mainstream since the efficiency of power-generating components has peaked due to their technical limitations. For this reason, polymeric composite materials, which have previously been used in very specialized fields, such as air vehicles, aerospace equipment, and military goods, have become new candidates for use as structural materials in automobile industries, broadening their importance Polymeric composite materials have comparative mechanical properties, lower density, and higher specific strength and durability against metallic materials, so they can be used as structural materials for main bodies and other parts of automobiles, as well as improve fuel efficiency through weight reduction. Although these have various advantages, they also have some unclear issues of damages by foreign objects or environments and repairs, which have led to metal-composite hybrid structures. For fabricating metal-composite hybrid structures, adhesively bonded joints are generally adopted, due to their load distribution, impact or vibration mitigation, and the absence of stress concentration caused by hole drilling. Examples of metal-composite adhesive joints can be easily found, such as in BMW i3 or 7-series Surface treatment is most important for improving adhesion characteristics between metal-composite adhesive joints. In particular, various oils used in the machining process essentially remain on metal surfaces, and it is well known that residual oils weaken adhesive joints. Therefore, surface cleaning is critical to adhesion as well as welding, and many studies have been conducted for the purpose of finding the appropriate conditions of each surface treatment on adherends. For example, Kozma and Olefjord These studies were conducted in a well-organized laboratory for the purpose of comparing the adhesion characteristics of oily surfaces with both very clean and surface-treated surfaces of adherends with a near-zero amount of residual oil. The derived results were realized in an ideal environment and thus have some limitations in being applied in industrial sites since cleaning and surface treatments similar to those in the laboratory are very difficult in industrial sites. If it is difficult to perfectly remove residual oils on metal surfaces in factories, we have to control the amount of residual oils in order to guarantee sufficient adhesion strength. However, there have not been any reports examining the relationship between adhesion strength and the amount of residual oils. This is the motivation of our research. The objective of this research is to find out the appropriate surface treatment method to control the amount of residual oils for guaranteeing the sufficient adhesion strength of metal-CFRP hybrid joints under the assumption that metal surfaces have residual oils. To control the amount of residual oils of metal surfaces for having required adhesion characteristics, we should know not only the effects of residual oils on the adhesion strength of metal-CFRP adhesive joints but also the effects of surface treatments on the residual oils on metal surfaces. From these two relations, we can establish the optimal surface treatments to give the required adhesion strength.As mentioned in the introduction, traditional carbon steels have been substituted with aluminum and polymer composites for weight reduction and the enhancement of fuel efficiency in automobile industries. Due to the balancing of weight reduction and cost, automobile makers have adopted metal-composite hybrid structures for main body with adhesively bonded joints. For superior mechanical properties, most automobile makers have already been using carbon fiber-reinforced polymer composites (CFRP), and their use is rapidly increasing. As a result, in this work, we selected SPFC980Y cold-rolled high-strength steel, 6061-T6 aluminum, and high strength unidirectional carbon fiber epoxy pregregs (CU190L38/FC702T, Hankuk Carbon Co., Ltd., Republic of Korea) for the fabrication of metal-CFRP hybrid structures. Details of the selected materials are listed in . We applied high-strength structural epoxy film adhesives (L-F501, L&L Products, USA), which are widely used in automobile industries, for bonding metal and CFRP Metal-CFRP hybrid structures were fabricated according to ASTM D3528 for the purpose of analyzing the adhesion characteristics between metals and CFRPs (a) so as to control the fracture site by differentiating the bonding lengths of left and right adhesive layers as well as to avoid adherend failure through a thickness design of each adherend material (1.5 mm for steels, 3.0 mm for aluminums, 3.8 mm for CFRPs) considering yield and ultimate tensile strength. The fabricating process was presented in (b). Surface treated metals with epoxy film adhesives were put on the lower mold, then two CFRPs with epoxy film adhesives and Teflon spacer were placed on them. Other surface-treated metals were stacked, and an upper mold was assembled. Adhesives were cured under 1 ton of compression and 150 °C for 5 min by hot press. The cured metal-CFRP hybrid joints were demolded and cool-downed, then the Teflon spacer was removed. Finally, metal-CFRP hybrid joints were heat-treated under 200 °C for 30 min in the oven in order to simulate the painting process of automobiles.In order to investigate the effects of residual oils of metal surfaces, we first need to know the amount of residual oils both prior to and after the surface treatment, then control these residual oils exactly for quantitative analyses. shows how to measure the weight of residual oils on as-received or ethanol-cleaned metal surfaces. After weighing the as-received metals, surface treatments were done on the metal surfaces, and then surface-treated metals were weighed. The remaining oils were perfectly removed in the industrial cleaning solution (BCS-1000, Bychem Co., Ltd., South Korea). After rinsing with distilled water in the ultrasonic bath for 1 hr and drying in the oven at 100 °C for 2 h, we measured the weights of the metals without any residual oils. Then, the weights of the residual oils could be calculated through the weight differences of the metals prior to and after the removal of residual oils with respect to the surface treatment conditions.Similarly, we could control the residual oil on metal surfaces by spreading a pre-determined amount of oils on a perfectly clean metal surface. Hereafter, surfaces with a pre-determined amount of oils were designated as controlled surfaces.Metal surfaces with residual oils are hydrophobic, but cleaned and treated surfaces become hydrophilic. Generally, hydrophilic surfaces are more suitable for adhesively bonded joints since adhesives are well wetted on metal surfaces and the bondings at the molecular level are stronger The adhesion strengths of metal-CFRP hybrid structures were measured according to ASTM D3528 We measured the contact angles of the controlled metal surfaces with pre-determined residual oils as well as the adhesion strengths and failure modes of the metal-CFRP hybrid structures. show the measured contact angles of the metal surfaces and the adhesion strengths of the metal-CFRP adhesive joints with respect to the weight of residual oils and metal materials. For reference, residual oils on as-received steels and aluminums were 5.95 ± 2.5 g/m2 and 1.45 ± 0.37 g/m2, respectively.(a), the contact angles of the controlled steel surfaces increased as the amount of residual oils increased, as was expected. In particular, the contact angles of the steel surfaces with larger than 3.0 g/m2 of residual oils increased more significantly. The untreated steel surface had a larger contact angle than the controlled steel surface with 3.0 g/m2 of residual oils, which means that the as-received steel had a larger amount of residual oils than 3.0 g/m2. Naturally, the measured adhesion strengths of the controlled steel-CFRP adhesive joints decreased as the amount of residual oils increased, as shown in (b). The adhesion strengths of the steel-CFRP adhesive joints with 0.0 g/ m2 of residual oils was 26.2 MPa. Similar to contact angle tests, the adhesion strengths of the steel-CFRP adhesive joints with larger than 3.0 g/m2 of residual oils dropped considerably. The untreated steel-CFRP adhesive joint had 70% the adhesion strength (18.2 MPa) of the steel-CFRP one with 0.0 g/ m2 of residual oils (perfectly cleaned steel-to-CFRP adhesive joint), which is similar to the 3.0 g/m2 case. In addition, the amount of residual oils affected the failure modes of the steel-CFRP adhesive joints, as shown in the inset of (b). The main failure mode with 0.0 g/m2 of residual oils was “cohesive failure in adhesive”, but the area of “adhesive failure at interface” increased as the amount of residual oils increased. Uneven “adhesive failure at interface” was observed in the untreated steel-CFRP adhesive joints, which indicates that the residual oils on the as-received steel surfaces were not uniformly distributed and worsened the adhesion characteristics.The adhesion characteristics of the controlled aluminum-CFRP adhesive joints had similar trends to those of the steel-CFRP ones, as shown in . The contact angle of the aluminum surface with 0.0 g/m2 of the residual oil was about 63°, but the very small change in the residual oils of between 0.0 g/m2 and 0.5 g/m2 made a relatively larger difference (8°) on the contact angles than that between 0.5 g/m2 and 2.0 g/m2. In contrast, the adhesion strengths between the controlled aluminum-CFRP adhesive joints with 0.0 g/m2 and 0.5 g/m2 of residual oils were almost the same, but significant drops were observed when the residual oil was greater than 1.0 g/m2. Notably, the as-received aluminum-CFRP adhesive joint had similar strength as the controlled aluminum-CFRP adhesive joints with 1.5 g/m2, and this is well in agreement with the fact that the measured residual oil on the as-received aluminum surfaces (1.45 g/m2) is similar to 1.5 g/m2. show the measured residual oils and contact angles of the metal adherends and the adhesion strength of the metal-CFRP adhesive joints with respect to the number of ethanol cleansing cycles on metal adherends. As expected, the amount of residual oils decreased significantly with only one or two times of ethanol cleansing, while the contact angles of metal adherends changed meaningfully over three times of ethanol cleansing. The adhesion strength of the ethanol-cleaned metal-CFRP adhesive joints had similar tendencies to the contact angles. The changes in adhesion strength between two and three times of ethanol cleansing were larger than those between zero times and one time of ethanol cleansing. In addition, failure modes were transferred from uneven “adhesive failure at interface” to “cohesive failure in adhesive”., oils on the as-received metals without ethanol cleansing (0 case of ) were not evenly distributed on the metal surfaces. Only one or two times of ethanol cleansing were not sufficient to make the residual oil evenly distributed, although they did remove a relatively large amount of residual oils. This led to large changes in the residual oils but small changes in the contact angles on the metal surfaces with only one or two times of ethanol cleansing, which led to a relatively small improvement in adhesion strength.Since the residual oils on the metal surfaces can be removed but the surface chemistry of the metals are merely affected by ethanol cleansing, we compared the contact angles of the controlled and ethanol-cleaned metal surfaces, as well as the adhesion strength of the controlled and ethanol-cleaned metal-CFRP adhesive joints. As shown in , the contact angles and adhesion strengths of were reproduced with respect to the amount of residual oils. For both steel and aluminum, ethanol-cleaned surfaces had a few larger contact angles than the controlled surfaces, while the adhesion strengths of the ethanol-cleaned metal-composite adhesive joints were slightly lower than those of controlled metal-composite ones. Except for slight differences in the absolute values, the changing tendencies of contact angles and adhesion strength were almost the same as the controlled and ethanol-cleaned metals. As we mentioned in 3.1, residual oils on the controlled surfaces were uniformly distributed since we spread oils after cleaning surfaces out perfectly. However, the ethanol cleaned surfaces had some contaminants such as debris and dusts as well as unevenly distribution of residual oil. We thought that this difference caused relatively large contact angle, low adhesion strength and large scattering of the ethanol cleaned surfaces.The overall tendencies of the contact angles shown in (a), and may play a role as defects. Under the longer duration, burnt-out oils gradually blew off the metal surfaces, which improved the adhesion characteristics.We summarized the failure modes and adhesion strengths of the surface-treated metal-CFRP hybrid structures with respect to the combination of both surface treatment methods in . Due to the surface characteristics and initial residual oils of steel and aluminum, differences were observed in the distribution of failure modes and adhesion strengths. As is well-known, the adhesion strength was largest when “cohesive failure” occurred in both the steel and aluminum cases. However, “cohesive failures both in adhesive and adherend” were observed only in aluminum-CFRP hybrid structures while “cohesive failures only in adhesive” occurred only in steel-CFRP hybrid structures.If we estimated the amount of residual oils after ethanol cleansing for maximum adhesion strength from (a), 1.0 g/m2 was the upper limit for both steel and aluminum adherends. From the results of , 1.0 g/m2 was the upper limit when the significant drops of adhesion strength with both steel and aluminum adherends were observed, which is well in agreement with the results according to the surface treatment. Besides, the maximum adhesion strengths under the optimum combination of each surface treatment method were not less than the adhesion strength (lap shear strength of We investigated the effects of residual oils on the adhesion characteristics of metal-carbon fiber-reinforced epoxy composites adhesive joints and suggested the optimal conditions of the surface treatment which can give the required adhesion strength and can also be easily adopted into industrial fields.Effect of residual casting solvent content on the structure and properties of sulfonated poly(ether ether ketone) membranesIn the research of the effect of casting solvents on the structure and properties of proton exchange membranes, the amount of residual casting solvent is one of the important factors that have been overlooked. In this work, a series of as-cast SPEEK membranes with controlled amount of residual solvent (RS) content were prepared. Even though all RS was removed from the membranes after the treatment with 1 M H2SO4 and DI water sequentially at room temperature, the morphology and properties of these treated membranes differed from one another. Larger and better-connected hydrophilic domains and higher fractional free volume were observed for the treated membranes with larger amount of RS. The proton conductivity of water equilibrated membranes increased with the increasing RS content until reaching a maximum value that was almost twice as high as that of the membrane with the minimum RS. With further increase of RS content, the decrease in the proton conductivity was observed. In comparison, the water uptake of the membranes kept increasing with the RS content.electron layer thickness determined empiricallyintegrated enthalpy of the water vaporization enthalpy in DSCintegrated enthalpy from the ice melting enthalpy in DSCProton exchange membrane (PEM) is one of the most important components in proton exchange membrane fuel cells (PEMFCs), serving as both the conductor for protons and the separator for the electrons and gases To prepare hydrocarbon PEMs, solution casting is one of the most widely used processing methods, where polar solvents with high boiling points such as dimethylformamide (DMF), dimethylacetamide (DMAc), N-methyl-2-pyrrolidone (NMP) and dimethylsulfoxide (DMSO) are always employed to ensure the formation of thin films with good quality. It has been realized that large discrepancies existed in the proton conductivity reported in the literature for PEMs of similar composition, and such discrepancies have been attributed to the use of different solvents during the membrane preparation process In this work, we deliberately prepared the as-cast SPEEK membranes with controlled amount of RS with DMAc chosen as the casting solvent. After the treatment with acid and water, the membranes were characterized for their morphologies and properties, which were found to be closely related with the amount of RS.Poly(ether ether ketone) (PEEK) (Vitrex 450PF) was purchased from Victrex (Lancashire, UK). Concentrated sulfuric acid (95–98%) and DMAc were purchased from Boenchuangqi Company (Beijing, China). All materials were used as received.SPEEK was synthesized according to the literature To prepare SPEEK membranes, SPEEK was dissolved in DMAc and then cast at 80 °C. To take into account the inevitable mass loss during the solution transfer process, the content of RS is determined bymSPEEKincastsolution=mSPEEKinoriginalsolution⋅mcastsolutionmoriginalsolutionContentofRS=mcastmembrane−mSPEEKincastsolutionmcastmembranewhere moriginal solution is the mass of originally prepared SPEEK solution, mcast solution is the mass of the SPEEK solution in the casting dish, mSPEEK in original solution and mSPEEK in cast solution are the mass of SPEEK in the original and cast solution, respectively; mcast membrane is the mass of the cast membrane after solvent evaporation for a certain period of time, which was monitored during the casting process. When the RS content reached certain designated value, the membranes were taken out from the oven. The membranes at this stage are named as “as-cast membranes”.The as-cast membranes were immersed in 1 M H2SO4 at 25 °C for 24 h and then washed with DI water to remove any residual acid before being stored in DI water at room temperature for further tests. These membranes after such acid and water treatment are named as “treated membranes”.The elemental analysis was carried out by an elemental analyzer (vario EL/cube, elementar).IEC was determined by titration method. A dry sample (~0.2 g) was weighed before being immersed in 15 ml 5.0 M NaCl solution at 25 °C for 24 h to release all H+. The H+ was then titrated by 0.0100 M NaOH standard solution using phenolphthalein as the indicator.The water-equilibrated treated membranes at 25 °C were weighed immediately after the surface water was removed, to obtain mwet. Then the membranes were dried at 60 °C for 24 h, and weighed again to obtain mdry. Water uptake was calculated by the following equation:The membrane samples were prepared with similar size (~5.0 cm long, ~1.0 cm wide and ~60 μm thick) to minimize the experimental errors. The membrane proton conductivity in the lateral (in-plane) direction was measured at 25 °C using a custom built two-electrode in-plane conductivity cell, which was identical to that described elsewhere where L is the distance between the two electrodes; R is the resistance of the membrane; b and h are the width and thickness of the membrane, respectively.SPEEK membrane samples were immersed in 2.0 M CsCl solution at 25 °C for 24 h to replace all H+ with Cs+, followed by thorough washing with DI water and drying in a convection oven at 60 °C for 24 h. The SAXS experiments were performed on the above-treated SPEEK membranes in a SAXSess mc2 instrument (Anton Parr, Austria) with a Cu Kα (λ=1.54 Å) radiation generator at 25 °C. The distance between the sample and detector was kept at 150 cm. The average size of the hydrophilic domains (d) was calculated according to Bragg׳s law:where q is the scattering vector, defined from the scattering angle (θ) using q=(4πsinθ)/λMembrane samples were either freeze-fractured in liquid nitrogen or cut by a scissor at room temperature, with a thin layer of platinum sputtered upon the fracture surfaces. The images of the fracture surfaces were taken by a field emission scanning electron microscopy (S4800, Hitachi) at an accelerating voltage of 5 kV.Sulfur element on the membrane fracture surfaces was detected by EDX (X-Max20011, Horiba) using component analysis and mapping technology. The mapping time was 120 s.DSC was performed on a STARe System (Mettler-Toledo) under nitrogen atmosphere. After being equilibrated in water at 25 °C for 24 h, membrane samples were quickly blotted to remove all the surface water, they were immediately loaded in the calorimeter and quenched to −50 °C at the maximum cooling rate to minimize the loss of water content in the samples. The aluminum crucibles of 40 μL were used, covered with the lids which have a 50 μm pinhole to allow the relief of pressure without causing the membrane drying. The membrane samples were heated from −50 °C to 200 °C at a ramp rate of 10 °C/min.The PALS experiments were performed at room temperature with an Ortec “fast-fast” lifetime spectrometer, with a time resolution of 270 ps where Δr is the empirically determined electron layer thickness (=1.66 Å). Then the hole volume, Vf, can be calculated byThe fractional free volume, FFV, can be expressed as follows:Mechanical properties of treated membranes were characterized by conducting the tensile tests on the dumbbell-shaped specimens at 25 °C and 50% RH using a CMT4104 electrical tensile tester (SANS, Shenzhen, China) according to ASTM D882. The gauge length, width and thickness of the specimens were 25 mm, 5 mm and ~60 μm, respectively. The crosshead speed was set at 2 mm min−1 and at least five specimens were tested to give the average. Before the tensile tests, specimens were equilibrated at 25 °C and 50% RH for 5 days.To verify if the expected values for the amount of RS content were attained in the as-cast membranes, the elemental analysis of nitrogen element was performed. Because the nitrogen element only exists in DMAc, the amount of RS content could be determined by the following equation:where wtN% is the amount of nitrogen element measured by the elemental analysis. As shown in , the calculated amount of RS content based on the elemental analysis results is very close to the designated values predicted by Eqs. . Such results suggest that it is feasible to fabricate the membranes with controlled amount of RS content when the weight loss of the casting solution during the transferring process is taken into account. As for the treated membranes, no nitrogen was found, indicating that all the solvent has been removed after the acid and water treatment of the as-cast membranes, presumably due to the miscibility between DMAc and water . It is worth pointing out that, under the casting condition described in the experimental section, the lowest RS achieved in this work is still more than 11 wt% even with the solvent evaporation period longer than 48 h. For ease of discussion, in the context below, the amount of RS content in the as-cast membranes (as predicted by Eqs. ) is used to refer to the corresponding treated membranes that actually contain no RS.The microstructure of the treated SPEEK membranes was studied by SAXS. As illustrated in , all SPEEK membranes exhibit a typical X-ray scattering behavior with the q values ranging between 3.10 and 3.65 nm−1, consistent with the previous reports ). Such results could be explained as follows: during the process of solvent evaporation and membrane formation, larger amount of DMAc in the membrane will be able to better help the hydrophilic domains in SPEEK rearrange and become larger due to the strong interaction between the sulfonic acid groups of SPEEK and DMAc; when the membranes with RS are treated with acid and water, the RS dissolves in water and leaves the hydrophilic domains filled with water. Therefore, larger amount of RS in the as-cast membranes corresponds to greater size of hydrophilic domains in the treated membranes., all treated membranes exhibit relatively uniform micro-morphology, with many small aggregates that are considered to be the assembled hydrophilic domains in the membrane. With the increasing amount of RS content in the as-cast membranes, the size of these aggregates in the corresponding treated membranes increases. Such results suggest that the larger hydrophilic domains in the membranes with higher content of RS also become better-connected.To further investigate the morphology of the treated membranes, EDX analysis was performed. As shown in , the sulfur contents on the freeze-fracture surfaces for all the membranes are much higher than the theoretical value (5.50 wt%) calculated according to the IEC of the as-prepared SPEEK powder (1.72 mmol g−1), and rise with RS content, which can also be clearly seen from where the white spots refer to the sulfur element. Such interesting results may be rationalized as follows: the hydrophilic domains rich in sulfonic acid groups are the most brittle part in SPEEK and will be more inclined to be exposed on the fracture surfaces when the sample is freeze-fractured. Thus for the membranes with higher RS content, due to the enlargement and better connection of the hydrophilic domains as mentioned above, more hydrophilic domains will be exposed on the freeze-fracture surfaces, resulting in the increasing sulfur content detected by EDX. To verify such explanation, the membranes were cut by a scissor, by which both the ductile and brittle part of SPEEK should be treated equally and the sulfur contents on the cross-sections are expected to be similar to the theoretical value. The obtained EDX analysis results was found to well match with such expectation, as the sulfur contents remain almost the same, ~4.9 wt%, for all the membranes regardless of RS content.The state of water in the fully hydrated membranes could also provide some insight to the membrane structure information. As shown in the DSC curves in , even though all the membranes exhibit an endothermic peak at around 100 °C that corresponds to the water vaporization, only the membrane with 47.4 wt% RS displays an endothermic peak at around 0 °C that corresponds to the melting of ice. Such results suggest that, for the membranes with smaller amount of RS content, there only exists non-freezable water that do not crystallize upon cooling; while the membrane with 47.4 wt% RS contains freezable water. The absence of freezable water is generally ascribed to the low degree of phase separation in SPEEK Based on the enthalpies of two thermal transitions, solid ice to liquid water and liquid water to water vapor, the overall water uptake and the amount of freezable/non-freezable water content in the membrane could be calculated by the following equations:Contentoffreezablewater(%)=ΔH2ΔHf1−ΔH1ΔHv×100where ΔH1 is the integrated enthalpy from the water vaporization enthalpy in DSC, ΔHv is the heat of vaporization for bulk water (2260 J g−1) , the calculated overall water uptake based on the DSC results is only slightly less than that determined by measuring the mass difference between dry and fully hydrated membranes, indicating almost all the water has been removed from the membranes when temperature is above 150 °C in DSC. The amount of non-freezable water content increases with the increase in RS content until 38.7 wt% RS, as the larger hydrophilic domains for the membranes with higher RS content may be able to bind more water molecules strongly. However, for the membranes with 47.4 wt% RS, the hydrophilic domains are so large that some of the water molecules become loosely bound to the sulfonic acid groups and could freeze upon cooling. Therefore, the amount of non-freezable water stops increasing further even though the overall water uptake keeps increasing with the increase of RS content in the membrane.The DSC analysis also allows the determination of Tg of the membranes, which shows a decreasing trend with rising RS content. Such change cannot be related with the water contained in the membrane because there is no remaining water at these Tgs that are close to 170 °C, well above the boiling point of water. It may indicate less compact polymer structures and more mobile polymer chains available in the membranes with higher RS content, resulting in easier segmental movement and lower Tg.The mobility and packing of polymer chains has been correlated with the free volume characteristics of polymer membranes, which could be effectively probed by PALS . With the increasing RS content, the lifetime of o-Ps τ3 increases, corresponding with the increase in the size of free volume holes as observed from the change of free volume hole radius r in . Meanwhile, the intensity of o-Ps I3 shows a decreasing trend with higher RS content in the membranes, indicating the lower density of free volume holes. Based on the measured τ3 and I3, the fractional free volume FFV was calculated and found to become larger with higher RS content. Larger FFV usually corresponds to higher mobility of polymer chains . It should be noted that even though the difference in PALS parameters among all the membranes is relatively small, the changing trends of these parameters are still clear enough to draw the conclusions as mentioned above., the IEC of the as-prepared SPEEK is the highest and becomes lower for the SPEEK membranes after the casting process. As for the treated membranes, the IEC grows gradually with increasing RS content. Such increase may be related with the larger hydrophilic domains and higher degree of phase separation for the membranes with higher RS content, as there are probably less sulfonic acid groups located in the dead-end “pockets” As can be seen from the stress–strain curves displayed in , larger amount of RS generally reduces both tensile strength and elastic modulus of the treated membranes, and in the mean time increases the elongation at break. For SPEEK membranes, the mechanical properties are closely related with the intermolecular interaction due to hydrogen bonding between the sulfonic acid groups The correlation between the water uptake of fully hydrated treated membranes and the content of RS is shown in . As RS content increases, the water uptake increases gradually. Since water is mostly filled in the space where RS resides, larger amount of RS thus corresponds to higher water uptake. In addition, the enlargement of hydrophilic domains with higher RS content as verified in SAXS measurement also contributes to the increased water uptake.Compared to the water uptake, the proton conductivity of fully hydrated treated membranes exhibits a different behavior as a function of RS content, as shown in . When RS content increases from 11.7 wt% to 38.7 wt%, the proton conductivity increases significantly, from 0.0247 S cm−1 up to 0.0484 S cm−1. With further increase in RS content, the membrane proton conductivity drops. The initial increase in proton conductivity with larger amount of RS content is mainly due to the higher degree of phase separation and better-connected larger hydrophilic domains that facilitate the proton transport. However, when RS content is higher than 38.7 wt%, the dilution of sulfonic acid groups due to higher water uptake and the further increase in the size of hydrophilic domains becomes more dominant so that the proton conductivity starts declining with the increasing RS content.Further characterization of membrane properties was conducted at various RH. As shown in , the water uptake of all membranes decreases with the drop of RH, which is commonly observed for the PEMs. In addition, different from that in the liquid water equilibrated state, the water uptake of these treated membranes at any given RH increases with the increase of RS content until reaching a maximum for the membrane with 38.7 wt% RS and the further increase of RS content in the membrane leads to the slight decrease of water uptake. It is interesting to notice that such behavior is similar to the change of the amount of non-freezable water content in the liquid water-equilibrated membranes as a function of RS content, as indicated in . As mentioned earlier, the larger hydrophilic domains for the membranes with higher RS content may be able to bind more water molecules, therefore resulting in higher water uptake at low RH. However, as for the membrane with 47.4 wt% RS, the hydrophilic domains become too large and the number of tightly-bound water molecules becomes smaller, and in the mean time, the freezable water easily loses at the low water activities. These two combining effects drive the water uptake of the membrane with 47.4 wt% RS to a lower value. In fact, DSC analysis reveals that there was no freezable water in the membrane with 47.4 wt% RS equilibrated in the water vapor environment., the proton conductivity of the treated membranes exhibits the similar behavior as the water uptake at any given RH, where the membrane with 38.7 wt% RS shows the highest proton conductivity. Such results well correlate with the vehicle mechanism of proton transport, as protons diffuse at the same rate as water in the membrane To further verify the significant effect of the amount of RS content on the membrane properties, another two series of treated SPEEK membranes with DS of 43% and 70% (corresponding to the sulfonation time of 15 and 48 h, respectively) were prepared, following the same preparation procedure for the treated membranes with 53% DS. The amount of RS content in the as-cast membranes was also varied through the casting process, and subsequent acid/water treatment at room temperature was found to be able to remove all the RS for all the membranes, as confirmed by the elemental analysis.Compared to the membranes with 53% DS, these two series of treated SPEEK membranes exhibit similar behavior of water uptake and proton conductivity as a function of RS content, as illustrated in . With the larger amount of RS content, the water uptake rises continuously for all three series of membranes (a). In addition, when the RS content is the same, the water uptake is larger for the membranes with higher DS due to higher concentration of hydrophilic sulfonic acid groups. In comparison with the water uptake behavior, with the increase of RS content, the proton conductivity of fully hydrated treated membranes increases until reaching a maximum and then starts dropping (b). As discussed in the previous section, on the one hand, higher RS content results in the larger phase separation and better-connected hydrophilic domains, improving the proton transport; on the other hand, too high RS content and resulting high water uptake cause the dilution in the concentration of sulfonic acid groups, hence reducing the amount of protons available for transport. Combination of these two factors contributes to the appearance of a maximum in proton conductivity for all three series of membranes. It could also be noticed that, for the SPEEK membranes with lower DS, the RS content at which the maximum proton conductivity is reached becomes smaller, and the reduction in proton conductivity with further increase of RS content also becomes more severe. Moreover, the enhancement of proton conductivity from low to high RS content is more significant for the membranes with lower DS, as there shows ~140% increase in proton conductivity from 9.9 wt% RS to 36.9 wt% RS for the membrane with DS of 43% as compared to ~60% increase in proton conductivity from 16.0 wt% RS to 41.8 wt% RS for the membrane with DS of 70%. Such results suggest that the proton conductivity of the membranes with lower DS is more sensitive to the change in the amount of RS content. This may be associated with the fact that the beneficial effect on proton transport resulting from the morphological change due to larger amount of RS content weighs more for the membranes with relatively low proton conductivity. In comparison, the membranes with higher DS already have relatively high proton conductivity even at low RS content, and thus the conductivity improvement by the increasing RS content is not as significant.Mechanical properties of three series of membranes are also compared, and the results are listed in . Similar to the case of the membranes with DS of 53% as discussed in , both elastic modulus and tensile strength decrease with the increasing RS content for the membranes with DS of 43% and 70%. It can also be seen that, at the same RS content, the membranes with the higher DS generally exhibit higher strength and modulus but lower ductility, mainly due to the stronger hydrogen bonding interaction between polymer chains by larger amount of sulfonic acid groups As-cast SPEEK membranes with controlled amount of RS content were first prepared, and then treated with 1 M H2SO4 and DI water sequentially at room temperature to obtain the treated membranes. Even though the elemental analysis results confirmed that there was no existence of RS in all treated membranes, the morphology and properties of these treated membranes varied very much, indicating the strong effects of RS from the as-cast membranes. For the treated membranes with larger amount of RS content, the enlargement and better connection of hydrophilic domains were observed in the SAXS and SEM, and higher fractional free volume was revealed by PALS analysis. With the increasing amount of RS, the water uptake of the fully hydrated treated membranes kept increasing continuously. In comparison, both the amount of non-freezable water content determined by DSC and the proton conductivity increased with the increasing RS content until reaching a maximum at a certain RS content. With further increase of RS content, the decrease in both the non-freezable water content and the proton conductivity was observed. For the SPEEK membranes with DS of 53%, the proton conductivity of the membrane with 38.7 wt% RS was almost twice as high in the liquid water and ten times as high at RH lower than 70%, compared to that of the membranes with the minimum RS (11.7 wt%).Supplementary data associated with this article can be found in the online version at Microstructure characterization of cement paste from micro-CT and correlations with mechanical properties evaluated from virtual and real experimentsAs micro-CT devices have become widely available, the detailed 3D microstructures of cementitious materials can be more conveniently investigated. However, owing to the resolution required to appropriately represent the cement-paste microstructures, the domain size of the micro-CT sample is limited. By synergistically combining the virtual and real experiments, correlations between the microstructural characteristics and properties of cement paste with various w/c ratios (0.3, 0.4, 0.5, and 0.6) are investigated at different length scales. The porosity from the micro-CT images are correlated with the macro-scale properties obtained from real experiments. At the micro-scale, the homogenized solid phase properties are characterized from the linear attenuation coefficient (LAC) value distribution characteristic of the micro-CT images and are correlated with the modeling parameters of the phase field fracture. According to the results of virtual experiments conducted using the phase field fracture model and the characterization methods, the mechanical properties (stiffness/strength) at the micro- and macro-scale exhibited apparent relationships.The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.Micro-CT, one of the widely used non-destructive methods for material characterization, can be used to obtain the complete 3D microstructures of cementitious materials. At the micro-scale level, the microstructures of cement paste have been characterized and successfully related to its properties []. Generally, the cement paste microstructures from the micro-CT are characterized as either two-phase (pore and solid) or three-phase (pore, hydrated, and unhydrated). The pore microstructure significantly affects the properties; moreover, pore phase identification also has been one of the primary objectives of microstructure characterization using micro-CT. In this study, in addition to the pore phase characteristics, the solid phase characteristics obtained from micro-CT are used to correlate the microstructures with the properties evaluated from virtual and real experiments.The microstructure characterization of cement paste can be performed using various methods such as mercury porosimetry (MIP), nuclear magnetic resonance (NMR) spectroscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and computed tomography (CT). The pore size ranges from a few nm to tens of μm, and the various solid phases can be identified by chemical and image-based analysis methods. Micro-CT is one of the image-based analysis tools. Unlike other image-based tools mentioned above, it exhibits the merit of obtaining 3D microstructure relatively conveniently without damaging the samples. However, owing to the resolution limitation even with the state-of-the-art CT devices, the porosity identified by the CT device is less than the actual porosity as well as the porosity from the MIP test. This also causes pores smaller than the CT resolution to be embedded into the solid phase. Because of the limited resolution of the CT images compared with the resolutions of SEM or TEM images, the solid phase microstructures in cement paste are generally homogenized, with the likely exception of unhydrated clinkers. Although smaller pores are embedded into the solid phase microstructures and the pore microstructures could be different from the real microstructures, the dominant features of the pore microstructures, which affect the material properties, are observed to be effectively captured []; this aspect can be used for cement paste microstructure characterization as a compensation tool to alternatives [To identify the pores and solid phases from the micro-CT images, the grayscale value information from the micro-CT images is processed. The intensities of X-ray after transmission through a specimen are measured 360°, and the space filling information is reconstructed from the measurements through inverse analysis. The linear attenuation coefficient (LAC) values [] are mapped on to the space filling images; however, they are transformed to grayscale values (e.g., 8 bit or 16 bit) to adequately store the information in an image format. Although the LAC values are not directly proportional to the material densities, the LAC value for a specific constituent is uniquely determined from the X-ray energy level and the components of the constituent. The LAC values can be disturbed and fluctuated during the inverse analysis when the space-filling microstructures are constructed from the projected intensity data. However, the LAC can be used as an almost absolute measure, which can be compared among the specimens under investigation. In this study, the microstructures are considered as two-phase (pore and solid) materials, and the threshold value between the pore and solid phases is determined from the characteristics of the LAC (grayscale) value distribution. The multiple solid phases of the cement paste microstructures after the hydration process are homogenized as a single solid phase to reduce complexity. The pore phase characteristics obtained from the micro-CT image analysis are correlated with the macro-scale properties obtained from real experiments. The LAC value characteristics for the solid phase are used to correlate the properties of the solid phase. The solid phase properties are identified with virtual experiments using the phase field fracture model, where the model is calibrated to real experiments.], which is similar to the non-local gradient damage model, has been widely applied to various problems []. The phase field fracture model has also been recently applied to evaluate the mechanical properties of cement paste using virtual specimens obtained from micro-CT []. The conventional continuum-damage-based model [], micromechanics-based upscaling models [] have been successfully applied to evaluation of the mechanical property of cement paste. However, the multi-physics framework of the phase field fracture model has gained momentum and is currently an active area of research as an alternative modeling approach to the fracture process. Also, direct tension test results from both experiments and simulations, as previous investigated in Refs. [], are compared. Instead of performing a rigorous homogenization-localization multi-scale approach as in Refs. [], a more direct and intuitive approach is adopted here because of the lack of real experimental data available and the complexity that might be caused by additional constraints during simulations.In this study, virtual experiments using the phase field fracture model are synergistically combined with real experiments to identify the correlation with the microstructural characteristics obtained from micro-CT. The correlation between the mechanical properties and the porosity of cement paste are revisited at the macro-scale level, which is consistent with the pioneering work of []. Moreover, the homogenized solid phase properties are correlated with the LAC values at the micro-scale level. The cement paste sample preparation is first introduced in the next section; this is followed by the virtual sample construction from micro-CT. A brief background of the virtual experiments using the phase field fracture model is presented, and the model calibration and the solid phase material parameter identification procedures are presented. Finally, the microstructure–property relationships at the macro- and micro-scales are proposed, and the relationships are verified by an example.In this study, the mechanical properties of cement paste samples are evaluated through real and virtual experiments. Real samples are prepared and cured, and virtual samples are obtained by taking the micro-CT images of portions of the real samples. The preparation of the real and virtual samples is described below.Cement paste samples of ordinary Portland cement (Type-I) with different w/c ratios of 0.3, 0.4, 0.5, and 0.6 were prepared. These samples are termed WC30, WC40, WC50, and WC60, respectively. The real cement paste samples were cast into 5 × 5 × 5 cm3 molds, and the molds were removed after 1 day. After curing the real samples for 28 days, their compressive strengths were measured. The virtual samples are obtained using the synchrotron micro-CT at the Pohang Accelerator Laboratory (PAL) in Republic of Korea with an energy level of 25 keV. The samples for the micro-CT measurements are prepared by crushing the real samples into 1-mm wide particles so that high quality images with a resolution of 0.65 μm can be obtained. The test setup for the micro-CT measurements in the beam line is presented in Recently, the micro-CT became a standard tool for investigating the microstructures of cementitious materials. However, the quantitative characterization of micro-CT images in relation to solid phase properties is scarce in the literature, and the analysis framework used in this study is described below for completeness.The micro-CT images are reconstructed from the projected intensities through the real samples for 360° in 5° intervals. The original reconstructed images are converted into a linear attenuation coefficient (LAC) map (μ-map), where the LAC value is a function of the X-ray energy level and the chemical compositions of the constituents []. The LAC is defined as a constant of the X-ray beams (incident photons) fraction that is attenuated per unit thickness of the material traversed []. When the LAC information is stored in the image files, the LAC values are converted into the grayscale level. The range of values can be changed depending on the number of bits used for the storage, e.g., the values from 0 to 216-1 are used for a 16-bit image.The LAC values and the grayscale values can be linearly transformed so that the two sets of the data can be converted interchangeably. Owing to the inversion process, which is required to obtain the space filling information from the projected X-ray intensity, the fluctuations and noises in the LAC value distribution are introduced to the reconstructed micro-CT images. However, the LAC values can be considered as an absolute measure, which can be compared among the reconstructed CT images. Therefore, in this study, the LAC values are used as a measure to identify the pore and solid phases and correlated with the characteristics of the solid phase.In this study, the cement paste is idealized as a two-phase microstructure, i.e., pore and solid phases. The pore phase characteristics and solid phase properties strongly affect the macro-scale properties of cement paste []. In the literature, the macro-scale cement paste properties are often correlated with the porosity and the homogenized solid phase properties []. Among the microstructural features, porosity is generally used as a parameter because it is relatively convenient to identify and is known as a first order parameter that affects the cement paste properties []. When a more detailed analysis is performed to investigate the local responses, other microstructural features could be used for the characterization. Thus, the pore phase is characterized by the porosity from the micro-CT images and is correlated to the macro-scale properties. The solid phase also exhibits highly complex microstructures and is composed of various hydrated and unhydrated phases. However, to reduce the complexity and to be consistent with the previous approach, the various solid phases are homogenized as a single phase. The homogenized solid phase properties are correlated with the LAC distribution characteristic from the micro-CT images.The determination of the threshold LAC value from a micro-CT image for identifying two phases is essential and critical for the microstructure-property correlation analysis. Different approaches to identify the pore and solid phases of cement paste are available in the literature; however, the approach that performs best varies with the microstructures under investigation. For example, a class of methods determines the phase separation threshold so that the microstructural characteristics are clearly recognized (e.g., []), and the other methods identify the characteristic locations of the cumulative LAC (grayscale) distribution [In this study, the extension of the method using LAC distribution is used as detailed in Ref. []. The illustration of the determination of the threshold value is depicted in . First, the LAC histogram is fitted by multiple Gaussian functions. The first derivative of the fitted curve is plotted at the bottom left of , and the symbol marked by the circle is the point where the first derivative is the maximum. The plot also illustrates the 2D sectional image of the microstructure binarized by the LAC value at the maximum first derivative as the threshold. Next, the point of the maximum second derivative is identified as another characteristic, as shown in the bottom right of . The intersection of the tangents from the two points, where the first and second derivatives are the maximums, is identified as the threshold value to differentiate the pore and solid phases. The location of the final LAC threshold for the phase separation used in this study is marked by the triangle at the top right of To characterize the homogenized solid phase, the mean value of the solid phase LAC distribution is proposed in this study. The schematic of the solid phase LAC distribution and its mean value are presented in . There are two types of bins: the dark gray bins represent the pore phase, whereas the brighter gray bins represent the solid phase. The LAC value on the right-hand side of the bold dashed line in is the mean value of the solid phase. By omitting the pore phase LAC (dark bins), the effective mean LAC value of the homogenized solid, χLAC, is defined as a parameter that indicates the microstructure characterization. Because the degree of hydration with age changes according to w/c ratio, microstructural characteristics such as hydration products in addition to porosity and phase connectivity can vary. The LAC distributions of homogenized solid phase can also be different from each other. Therefore, the mean LAC can be used as a representative description of the solid phase microstructure characteristics. More detailed analyses of the microstructural characteristics according to the w/c ratio will be presented in . The mean LAC value for the solid phase is correlated with the solid phase properties calibrated using the virtual experiments.To evaluate the mechanical properties of the material, the microstructures obtained from the micro-CT are converted into virtual samples, whose process is also referred to as image-based modeling in the literature (e.g., []). A representative microstructure from the real samples is prepared as a virtual sample for each w/c ratio. The threshold between the pore and solid phases are identified, and the microstructure is modeled as two-phase solids. The domain size (D) is selected as 130 μm, which is established to be adequate for the property evaluation of cement paste []. The original microstructure has a voxel size (h) of 0.65 μm; however, the voxel size is increased to 2.6 μm for computational efficiency. The mesh coarsening affects the responses of the virtual specimens, but such effects are accommodated by the calibration of input material modeling parameters. A mesh refinement study conducted on cement paste microstructures using the same mesh sizes is presented in the previous work from the authors in Ref. []. The validity of the degree of mesh size coarsening used in this study and its implication in the virtual experimental framework can be found in the reference. The virtual specimens for the various w/c ratios are constructed as 50 × 50 × 50 voxel meshes, where each voxel is represented by an 8-noded finite element. The microstructures are mapped on to the coarse meshes using the MATLAB function termed interp3. Similar a coarsening process was observed to maintain the integrity of the original microstructure as studied in Ref. [The microstructures of the samples are shown in , the dark areas represent the pore or the low density phase inside the cement paste, whereas the bright areas represent the hydrated or unhydrated solid phases, which are denser than the other phases. In the lower-w/c-ratio samples (e.g., WC30), a larger fraction of bright regions can be observed. A higher solid fraction is present in the lower-w/c-ratio hydrated cement paste compared with that of the higher-w/c-ratio samples. Using the phase separation process discussed in , the virtual samples composed of the solid phase voxels only after removing the pore phase voxels are generated as shown in the bottom row of , and are used for the virtual experiment.To verify the microstructural characteristics obtained from the micro-CT image analysis, the mercury intrusion porosimetry (MIP) test was conducted. The MIP test was performed using MicroActive AutoPore V 9600 (Micromeritics, USA). The MIP test can measure the porosity of cement paste as well as the pore size distribution []. To obtain the pore distribution, the mercury is penetrated into the pore through the pore existing on the outer surface of the samples. The capillary pore size of the cement paste can range from 10 nm to 10 μm []. The MIP test was conducted to detect pores of a minimum size of approximately 5 nm, so that the whole range of the capillary pore distribution could be obtained. Because the division between capillary and gel porosity is highly arbitrary and the difference between the minimum pore size (5 nm) from the MIP test and the lower bound of the capillary pore size from the literature (10 nm) is not significant, the total porosity obtained from the MIP test (ϕMIP) is used as the capillary porosity (ϕc) in this study. Although there are limitations of the MIP test, such as the pore shape assumption and the detected pore size, the MIP test provides relative measures of the pore distributions present in the sample []. The typical MIP test results using WC30, WC40, WC50, and WC60 are illustrated in The total volume of the intruded mercury in the sample could be used as a measure (or an index) of its porosity from the fact that the total volume intrusion is proportional to the porosity. From a, it is noted that the total mercury intrusion volume, the y-intercept of the curve, increases as the w/c ratio of the cement paste increases. This is consistent with the relation between the w/c ratio and porosity of cement paste. The threshold diameter is another measure of the pore characteristics, which can be obtained from the MIP test []. The threshold diameter is defined as the point where mercury does not penetrate the cement paste sample through the connected pores. For example, the threshold diameters for WC30 and WC60 are approximately 0.8 μm and 1.4 μm, respectively. The threshold (percolation) diameter also increases as the w/c ratio increases. From the cumulative intrusion curves from the MIP test, it is verified that the cement paste samples used in this study are effectively produced following the characteristic pore distributions available in references [The incremental mercury intrusion vs. pore size diameter plots for all the samples are shown in b. The sample with the higher w/c ratio generally has the higher pore volume fraction for a specified pore size. As shown in the right-hand side curves, pores of significantly larger size were detected for WC60 than for the others. The critical diameter, where the peak incremental intrusion is observed, also increases as the w/c ratio increases. The porosities for all the samples from the MIP test are presented in The 28 day compressive strengths (σc) of the cement paste specimens are measured from the compression tests using 5 × 5 × 5 cm3 cube samples. Five samples per w/c ratio are tested following the Korean Standard (KS L 5105), where the top and bottom surfaces are assumed to be fixed. The mean values are calculated and listed in , where the deviations of the compressive strength are within 6.0%. As shown in the table, the compressive strength decreases as the w/c ratio increases. The tensile strength value is converted by taking one-eighth of the compressive strength value and is used as the macro-scale strength (σm), as in Ref. []. The value from the common range of tensile/compressive strength ratio at the macro-scale considered in this study is 1/8–1/10. For example, in Ref. [], the value of 1/10 is selected for the micro-scale tensile/compressive strength ratio. The value of 1/8 is selected in this study for illustrative purposes so that the average upper-scale tensile strength is around 10 MPa. σm is correlated with the porosity obtained from the micro-CT image analysis and is used to calibrate the virtual samples to identify the micro-scale strength for the homogenized solid phase microstructure.The virtual experiments were conducted using the virtual samples constructed from the micro-CT. The phase field fracture model is used as a loading tool, and the mechanical properties of the virtual cement paste samples are evaluated in this study. The phase field fracture model is briefly described, and the model calibration process to obtain the solid phase properties is described next.The phase field fracture model adopted here follows the formulation in Ref. [], and only a brief description of the input modeling parameters are presented here. The deformation field and the crack phase field are governed by Eqs. where σ is the Cauchy stress tensor, ρm is the density of the material, b is the body force, η is a parameter related to the viscosity and used for the regularization process, and l is the length modeling parameter corresponding to the crack diffusivity. The crack is represented by the regularized crack phase field variable d, where d = 0 represents no crack and d = 1 represents completely broken state, at x∈B0 (). H is a crack driving force, which is a form of potential coupled with the deformation field. The formulation is implemented using a user element subroutine within the finite element framework of FEAP [] with MPI-based parallelization following the standard procedure of the Bubnov–Galerkin method.The schematic of the macro- and micro-scale stress vs. strain relationships of the model is shown in . Es and σs are the Young's modulus and critical fracture stress, respectively, of the homogenized solid phase of the cement paste. The post-peak behavior or softening region of the material response can also be regulated; however, it is left as a future study. The current formulation of the phase field fracture model requires four modeling parameters for the solid phase of cement paste. There are two elasticity related parameters (Young's modulus Es and Poisson's ratio ν) and two fracture related parameters (critical fracture stress σs and the diffusive crack width l). Through the calibration process using the real experimental data and the virtual microstructure obtained from the micro-CT, the values of stiffness (Es) and strength (σs) for the solid phase are identified. Through the iterative process of selecting the micro-scale parameters (Es and σs), the macro-scale properties (Em and σm) satisfying the real experimental result can be reproduced through the virtual experiment. The values of the other parameters, ν and l, are selected from Ref. [The purpose of this study was to show the potential of the framework to correlate macro-scale responses with micro-scale characteristics, so simple direct tension tests are conducted instead of adopting a rigorous upscaling approach of homogenization theory, as reported on cement paste in Refs. []. Direct tension tests are conducted using the phase field fracture model, as verified in Ref. []. Performing virtual compressive experiments to be compared with the real compressive test results could be more appropriate, because compressive tests are common and reliable real experiments at the macro-scale. However, the phase field model implemented for the current study incorporates the tensile failure, and incorporation of other failure modes such as shear and compression would introduce a number of additional parameters. Recently, experiments at the micro-scale such as micro-beam bending [] have been conducted, but a micro-scale mechanical experiment is difficult to conduct and is still under development. Even at the macro-scale, real tensile tests are significantly more challenging to conduct than compressive tests. Because of the complexity and limitations of the current formulation of the phase field model for performing virtual compressive tests and the difficulty in conducting micro-scale real experiments, virtual tensile tests are conducted and calibrated to the assumed value of tensile strength from macro-scale compressive tests. Similar works, where the direct tension test is used to evaluate cement paste properties, can also be found in the literature, e.g., Refs. []. The virtual test setup is schematically illustrated in . The bottom surface is fixed, and uniformly distributed displacement is imposed on the top surface. The other four surfaces remain traction free.It should be noted that the solid phase properties of the micro-CT image-based microstructures for phase field fracture modeling are not actual properties but rather input material modeling parameters. This is owing to the fact that the sub-resolution pores, which cannot be detected by micro-CT images, are embedded in the solid phase of the microstructures, and the input material properties become model specific. These issues on the characterization of cement paste microstructures from micro-CT and the determination of input material modeling parameters for mechanical property evaluation are presented by some of the coauthors in Ref. [The macro-scale stress vs. strain responses from the virtual experiment are presented in . The input parameter determination procedure is described later in . The stiffness and strength of the virtual samples increase as the w/c ratio decreases because of the reduction in porosity. The loading strain rate is set as 1.0 × 10−4 s−1 to mimic the quasi-static loading. The initial time step is set to 1.0 s and changed to 0.1 s before the peak strength is attained. The viscosity parameter η for the solution stabilization is set to 1.0 × 10−3 Ns/m2 as applied in Ref. [The failure patterns from the virtual experiments are illustrated in a shows the crack patterns at the onset of failure immediately after the peak strength. The failure patterns at the end of the simulations are shown in b and c. The surface failure patterns are shown in b, and only the crack patterns (d ≥ 0.9) inside the samples are presented in c. Non-planar multiple crack patterns can be observed, and some of them merge during the crack propagation.The input modeling material parameters are calibrated to reproduce the macro-scale properties by the virtual experiments using the phase field fracture model. The cement paste microstructure is idealized as two-phase materials, and the properties of the homogenized solid phase are identified by the calibration process. Although the solid phase material parameters identified by the calibration process could depend on the microstructure resolution and the degree of mesh refinement, the input parameters can be used as measures under similar constraints. That is, the identified input material parameters might not be the true material properties; however they can at least be used for relative comparisons among the samples under an identical virtual experiment setup. Also, cementitious materials exhibit a strong size effect [], but the macro-scale properties used to calibrate micro-scale material parameters are taken from the commonly available approaches at a larger scale. As macro-scale real experiments for material property evaluation become readily available, the calibrated parameters should be more realistic. Thus, the current approach can be treated as a framework that can be further improved as the related technologies advance.The Poisson's ratio ν of the solid phase microstructure, one of the modeling parameters for elasticity, is selected as 0.2 (within the range of representative values for cement paste) []. The other elasticity parameter, Young's modulus Es of the solid phase, is calibrated to reproduce the macro-scale elastic modulus calculated from the relationship [where E0 is the elastic modulus of the hardened cement paste with zero porosity and is approximated as 30 GPa []. ϕc is the capillary porosity, and the porosity values obtained by the MIP tests (ϕMIP) are used to evaluate Eq. . The calculated elastic moduli for the different w/c ratios are presented in . The elastic modulus for the solid phase Es is calibrated to match the macro-scale elastic modulus Em up to the second decimal place through the virtual experiments. The calibrated values of the elastic moduli for the samples with the different w/c ratios are presented in The strength (fracture)-related diffusive crack length parameter l is selected as 5.2 μm (consistent with the value presented in Ref. []). This satisfies the criterion that the diffusive crack length should be two times as large as the element size (l ≥ 2h) for the phase field fracture model [] as the voxel size for the virtual samples is 2.6 μm. The diffusive crack length parameter for phase field fracture is considered to be a material parameter []; however, the value is adopted from a previous research on cement paste. To determine the value of the diffusive crack length as a material property, which can be related to the microstructural characteristics or micro-scale experiments such as nano/micro indentation, a more detailed analysis is required and is left as a future study.The fracture strength σs of the solid phase of each sample of a specific w/c ratio is calibrated to match the macro-scale tensile strength through virtual experiments. The macro-scale tensile strength (σm) is converted from the compressive strength (σc) obtained from the real cement paste samples by applying the relationship σm = (1/8)σc. The identified strength σ-related material parameters are presented in The characterization parameters and the properties are correlated. At the macro-scale, the porosity from the CT image and the macro-scale tensile strength obtained from the real experiments are compared. The correlations between the mean LAC of the solid phase from the CT image and the micro-scale property of the solid phase are also extracted., cement paste samples with four w/c ratios from 0.3 to 0.6 are investigated. The LAC value distributions from the CT images are shown in . The distributions are fitted from the LAC value histograms obtained from the CT images of the original resolution.Among the LAC distributions from the samples, the WC30 LAC distribution exhibits a bump on the right-hand side of the curve; this is apparent where the relatively high amount of unhydrated components are present []. The unhydrated cement products such as C3S and C2S have higher density; thus, they generally have higher LAC values compared with the hydrated phases (C-S-H, CH). Moreover, the minimum w/c ratio for ensuring the complete hydration of cement paste is 0.36 and 0.42 when the gel pores are unsaturated and saturated, respectively []. Therefore, the unhydrated phases in the LAC distribution of WC30 can are more evident than in that of the other samples.The porosity obtained from the micro-CT presented in is more or less underestimated compared with the capillary porosity measured using the MIP test (), which is reported in the literature []. For example, the resolution of the micro-CT image investigated in this study is 0.65 μm, which is much larger even compared with the lower bound of capillary pore size 10 nm []. The characteristics from the micro-CT are not regarded as absolute measures and are treated as alternatives to available characterization methods; thus, the porosity from micro-CT is denoted as ϕCT to distinguish it from the porosity obtainedfrom MIP, ϕMIP. Under similar constraints imposed on the system, the relationship incorporating the information from micro-CT should provide reasonable estimates. The mean LAC values of the solid phase χLAC are also presented in . It is evident that the density or the LAC value of the solid phase decreases as the w/c ratio or the porosity increases. The porosity is correlated with the macro-scale properties of the cement paste, whereas the LAC value is correlated with the micro-scale properties of the solid phase.The microstructure characteristics and macro-scale properties are correlated using the porosities obtained from the micro-CT images and the stiffness/strength (indirectly) obtained from the experiments. Similar to available porosity vs. property relationships, the elastic moduli and tensile strengths are correlated with the porosities obtained from the micro-CT. In , the relation between the macro-scale elastic modulus () is presented using the data from the samples with the varying w/c ratios. It should be once again noted that the derived correlation between the characterization parameters and the properties are specific to cement paste and the resolution and energy levels of micro-CT. The porosity obtained from micro-CT is much less than the true one or that from the MIP test data due to limited resolution even with state-of-the-art micro-CT devices. However, the macro-scale properties are correlated with the porosities from micro-CT to identify the similar trend as in true porosity.Because the primary purpose of this study is to demonstrate the framework of using the synergistic approach of combining real and virtual experiments with micro-CT, a simple relationship that fits the data is proposed aswhere ϕCT is the porosity obtained from the micro-CT used for this study. Similarly, the relation between the macro-scale tensile strength and the porosity is determined (The fitted equations are well correlated with the data, as shown in . The R2 values (goodness of fit) for the elastic modulus and tensile strength equations are 0.97 and 0.99, respectively. It should be again noted that the porosity data are from the micro-CT, whereas the macro-scale data points are obtained using information from the strength test and micro-CT.At the micro-scale, the solid phase properties are correlated with the mean LAC value for the solid phase from the micro-CT images. The micro-scale properties determined from the virtual experiments for the various w/c ratios (). The correlation between the LAC values from micro-CT and input material modeling parameters for the solid phase of microstructures has not been reported in the literature. This correlation is specific to the cement paste and the resolution and energy levels of the micro-CT devices used in this study, but the results show the potential of the proposed framework in identifying the input material modeling parameters of other cement paste microstructures obtained from micro-CT under the same conditions. The information can be further utilized to model more complex systems such as mortars where more complex microstructures with fine aggregates and cement paste are present.The elastic modulus for the homogenized solid phase (Es) is correlated with the mean LAC values for the solid phase (χLAC) asand the fracture strength of the homogenized solid phase (σs) is correlated with the mean LAC values of the solid phase asIt is known that the cement is fully hydrated when the w/c ratio is larger than 0.42 []. WC40, WC50, and WC60 specimens are extensively hydrated, but WC30 microstructures include a larger amount of unhydrated cement clinkers. Since the unhydrated cement clinkers have significantly higher LAC values compared with the hydrated phases, the relationship between the microstructure and the properties of the two classes of samples could be different. This is illustrated in , where data points for WC40, WC50, and WC60 are aligned well along a line, while WC30 data is more or less offset from the fitted curve of the other data. Without the WC30 data, the curves were fitted with the linear equation reasonably with R2 values of 0.89 and 0.97 for the elastic modulus and fracture strength, respectively.The curve fitting including all four points could also be conducted, but the correlation would not be a simple linear relation between the mean LAC value and the properties since the inherent microstructural feature in WC30 is different from the others. For the macro-scale relation where the macro-scale strength is correlated with the porosity, the cubic relations (Eqs. ) as a function of porosity show good agreement. Although the mean LAC value for solids reflects the density of the solid phase including sub-resolution pores such as gel pores, it cannot properly portray the effect of high LAC value from the unhydrated cement. Since the high LAC value from the unhydrated cement clinkers do not contribute to increases in mechanical properties, the relation of LAC values and properties is better correlated among the almost fully hydrated samples (i.e., WC40, WC50, WC60). As mentioned earlier, the strong linear relationship between the mechanical properties of solid phase and the mean LAC values could be extracted.The current study presents a framework for identifying micro-scale material parameters for virtual experiments compared with macro-scale real experiments. Because of the limited access to real experimental data, limitations of models, and the resolution limit of micro-CT, the framework is presented with assumptions to show the plausibility of the proposed approach.Due to the strong size effect in cementitious materials [], the macro-scale real experiments to calibrate micro-scale input material modeling parameters should be conducted with the same specimen size for virtual experiments. Micro-beam bending [] tests have recently been reported and developed, and the potential of accurately comparing real and virtual experimental results is increasing. However, due to the modeling capability of reproducing such experiments and the accessibility and reliability of such experimental results, the calibration of modeling parameters is conducted against the commonly conducted larger scale experimental results. As further real and virtual experimental approaches are developed, the accuracy of the proposed framework in identifying material modeling parameters and their correlation to characterization parameters should be improved.Porosities obtained from micro-CT microstructures are underestimated compared with those from real microstructures due to the resolution limitation of micro-CT. This also causes the sub-resolution pores to be included in the solid phase. From the solid phase point of view, since the density of the hydrated products of the cement pastes are too close to each other, the linear attenuation coefficient or LAC map of the reconstructed microstructures alone cannot be used to distinguish the different hydrated solid phases. Hence, the hydration products are often modeled as a homogenized single phase including the sub-resolution pores. The correlation of the mean LAC value for the solid phase obtained from the micro-CT and the material parameters for the virtual experiments coupled with experimental data was identified through the combined approach of virtual and real experiments.Although the porosity from the micro-CT is underestimated compared with the real MIP test data, the correlation between the mechanical property and the porosity from the micro-CT showed the strong correlation similar to those from the literature (e.g., Ref. []). The voxel resolution is 0.65 μm, which is more than one order of magnitude larger than the lower range of the capillary pore (10 nm). The general definition of porosity values cannot be obtained even with the state-of-the-art micro-CT to authors' best knowledge so that other test approaches such as MIP should be used to compensate the micro-CT results. Even if the resolution of the lower bound capillary pore size can be obtained from the micro-CT devices, the virtual experiment with the RVE using the finite element framework is impractical. For the practical property evaluation through virtual experiment, the samples should be coarsened from such refined microstructures, which results in similar issues addressed in this study. If the micro-CT is used to obtain 3D microstructures for virtual experiment, the current voxel size is found to be small enough to capture the large capillary pore microstructures which would mainly contribute to the mechanical properties. Sub-resolution size pores, which are not captured as pore phase, are incorporated into the solid phase, and it is taken account during the input material parameter calibration process.At the micro-scale, the mean LAC value for the solid phase is correlated with the input material parameters of the solid phase for the phase field fracture model. The solid phase is a homogenized phase of the complex solid phases and the sub-resolution pores so that the input material parameters should be considered as modeling parameters not as true material properties for the solid phase. Nevertheless, the material modeling parameters provide insights on the virtual experiments through the correlation with LAC values. As long as the microstructural features are similar (e.g., fully hydrated), the mean LAC values seem to be proportional to the input material parameters. With a further analysis on the micro-scale properties using such tools as nano- or micro-indentation experiments, more detailed and accurate relationship between the LAC values and the input material parameters should be able to be established.In this study, cement paste microstructures with various w/c ratios obtained from micro-CT are characterized and correlated with the cement paste's properties. The mechanical properties were evaluated using the phase field fracture model, and the parameters were determined in combination with the real experiments. The porosities from the micro-CT images are well correlated with the macro-scale properties consistent with the common knowledge. The homogenized solid phase properties are identified through virtual and real experiments, and the LAC (grayscale) values for the solid phase from the micro-CT images are correlated with the solid phase properties. The characterization parameters from the micro-CT microstructures, i.e., porosity (ϕCT) and mean LAC value of the solid phase (χCT) were successfully correlated with the macro and micro-scale properties using real and virtual experiments.The porosity obtained from micro-CT underestimates the true porosity, but the correlation between the porosity from micro-CT and macro-scale properties are well correlated and similar to the trend of previous findings. Although the micro-CT has the limited resolution, it is confirmed that the porosity from micro-CT can be used as a parameter to be linked with macro-scale properties when it is used carefully.The sub-resolution pores are embedded in the solid phase in the microstructures from micro-CT, which affects the LAC value of the solid phase. The correlation between the mean LAC value of the solid phase and the micro-scale material modeling parameters is identified, and the trend between the parameters is found to be adequate. With further analysis, modeling parameter identification of multiple solid-phases seems to be promising. The identification of material modeling parameters for cement paste investigated in this study is crucial when virtual experiments are conducted on more complex microstructures such as mortar with cement paste and fine aggregates.The purpose of this study was to present a framework that can be used for new material development and performance evaluation of existing materials. Because of the limitation of real and virtual experiments, the issues on size effects and failure modes are not fully addressed, and the analyses were conducted with assumptions. The reliability of analysis results from the proposed framework should improve as more accurate real experiments are more readily available and better virtual modeling approaches can be implemented.When developing new materials, a number of experiments might have to be conducted to find the optimal design and performance reliability. The virtual experiment framework coupled with micro-CT can help to reduce the number of time and effort consuming real experiments required so that new material development can be accelerated. The proposed framework shows potential as an accelerated tool for developing new and innovative cementitious materials. The proposed analysis framework should be capable of tracing the evolution or long-term behavior of cementitious materials, including hydration and durability, and correlating microstructural characteristics with the properties at multiple scales.Flexural behaviour of cover plated CFS built-up beams composed of lipped channels: Comparison of test and design strengthsCold-formed steel (CFS) sections are being used extensively in the primary framing elements of the structural systems, as they offer numerous favourable features like light-weight construction, fast/convenient installation, design flexibility with respect to availability of large variety of cross-sectional shapes and sizes, and many more. To overcome the limitation of the inherent local buckling instability in CFS sections, many successful research attempts have delivered effective solutions to the same Built-up members are gaining popularity in the construction sector, particularly in CFS building segment, which is mainly due to the combination of the favourable features in both CFS as well as in the adoption of built-up members. Built-up members allow the cross-sectional strength to be utilized in an effective manner, resulting in the efficient utilization of steel, as a constructional material. The past research on built-up flexural members has indicated immense potential in their application. The web stiffening of the channel sections constructing the flexural built-up members improved their bending strength by delaying the local buckling failure Given the capital required for buying a cold-rolling machine that can fabricate complex geometries of the sectional profiles and time required for the fabrication of such built-up members, a simple cross-sectional geometry (cover plated CFS built-up beams), with a simple fabrication process would substantially improve the buckling resistance of these beam sections, and thereby enhance the quality of CFS construction at a much lower cost. This can boost the practice of safe, economical and durable construction, particularly in the developing countries. With this aim in consideration, the authors have made an attempt to bring out built-up flexural members (as shown in This section presents the various details of the experimental investigation, and is given in the sub-sections below.. The nominal thickness of this plate was 1.6 mm. The reason behind the incorporation of these plates was to prevent warping of the cross-section. Additional plates were welded to the top cover plate to reduce the stress concentration and ensure more uniform distribution of forces, as shown in . Since one of the objectives of this investigation was to study the influence of moment gradient and constant moment loading of theses built-up beam specimens, both three-point loading as well as four-point loading were considered accordingly. This resulted in the specimens being categorized into two groups, first the three-point loading group, and second the four-point loading group. In the three-point loading group, the cross-sectional aspect ratio (B/D) was varied at 1.25, 1.5 and 1.75, with constant width of the built-up section, while as the span was fixed at 1.2 m. In the four-point loading group, the sectional compactness of the built-up section (that was governed by the slender web element of the channel section) was varied as 50, 60 and 70, with a constant cross-sectional aspect ratio of 1.5, while the span was fixed at 2.4 m. Three values of sectional compactness were considered based on the limiting value of sectional compactness being 60, proposed by the current standards . Since the corner radius was small and press braking operation was adopted for cold-rolling, the coupon specimens were extracted longitudinally from the steel sheet. A similar procedure has been adopted previously . The average values of the Young’s Modulus, yield stress, peak stress and elongation obtained were 215GPa, 250 MPa, 364.33 MPa and 23.75% respectively.CFS sections due to their low wall thickness are susceptible to geometric imperfections. Therefore, the measurement of these imperfections is important as they influence the local as well as global behaviour of CFS members. Accordingly, the geometric imperfections were measured and noted, prior to the testing of specimens. The imperfections were noted along the midpoint of the bottom cover plate and the web to get these values in two orthogonal directions (both longitudinal as well as transverse), as shown in presents the magnitudes of imperfections noted. An optical theodolite along with a calibrated digital vernier caliper were used for the measuring the imperfections. The maximum amplitude of the measured geometric imperfection at the mid-span in the two said orthogonal directions viz., δ1 & δ2 were noted as 1/2894 mm and 1/2913 mm, respectively. These imperfections belonged to specimen 3PL-168-112-15. The minimum amplitude of the measured imperfections at the same location and in the same directions, belonged to the specimens 4PL-168-112-15 and 3PL-196-112-15, and were noted as 1/3495 and 1/3724 respectively.A heavy-duty loading frame of 50 Tonnes capacity (as shown in ) was used for the testing of the specimens. Both four-point loading tests as well as three-point loading tests were performed under the same loading set-up. For transferring the single point load from the hydraulic jack to the two loading points in the four-point loading, a rigid spreader beam was used. Simply supported end conditions were considered for the testing both these loading type specimens. To measure the vertical displacement under the loading points as well as at the mid-point of the beam specimens, LVDTs were used. The loading was applied by means of a hydraulic jack and the loading was applied slowly, until the failure. Width of loading plate and the bearing plate was 100 mm.. Clearly the web depth influenced the involvement of the web buckling in the observed failure modes. Also, the post peak branch of the plots got steeper, as the web depth increased.The load vs. displacement curves of the four-point loading group specimens are presented in b. The ultimate load resisted by the specimen 4P-120-80-15 was 11.48kN, with the corresponding displacement of 12.32 mm. The displacements noted in four-point loading cases were higher than the three-point loading cases, mainly due to larger span in the former cases. The displacements in the four-point loading cases were nearly double of that of in the three-point loading cases. Local buckling in the compression region of the built-up section within the moment zone, prominent in the cover plate, in between the fasteners was noted, as shown in . In the specimen 4P-144-96-15, a peak load with the corresponding displacement of 16.63kN and 10.29 mm was noted. Like the previous case, local bucking half-wave lengths between the fasteners within moment zone was again observed, as shown in . Since the depth of the built-up section was higher, higher bending stresses were experienced, resulting in higher degree of local buckling failure being observed. The maximum load carried by the specimen 4P-168-112-15 was noted as 21kN, with the corresponding displacement of 9.52 mm. The local buckling of the cover plate, as observed in the previous two cases was observed in this case as well. It was further noted that the magnitude of the local buckling in between the fasteners within the moment zone was large and dropped post the moment zone (within the shear zone), as shown in . The magnitude of the local buckling wave between the fasteners was higher due to constant moment within the moment zone. In the four-point loading group specimens, a small deviation in the stiffness of the load vs. displacement plots was observed, at around a displacement of approximately 7 mm. This may be due to the formation of multiple local buckling waves between the fasteners on the compression side cover plate. shows the three-point loaded specimens after failure.The cross-sectional aspect ratio of the flexural member plays a vital role in governing its stability. It primarily controls the out-of-plane displacement in flexural members. In the three-point loading cases, on varying the aspect ratio from 1.25 to 1.5, the flexural strength changed from 11.25kNm to 13.21 kNm, which resulted in a flexural strength improvement of 17.42% as shown in a. On varying the aspect ratio further from 1.5 to 1.75, the flexural strength changed to 15.78kNm, with a flexural strength improvement of 19.45%. The improvement in the flexural strengths due to the variation in the aspect ratio attributes to the increase in the width of the flexural members, that improved their second moment of area, and thus improved their flexural strengths. The percentage improvement in the flexural strength was slightly higher in the latter case (when the aspect ratio was 1.75), as the second moment of area was higher in that case. Also, the sectional compactness in both these cases were constant.The sectional compactness is a key parameter that significantly influences the behaviour in thin-walled members. It controls their local buckling response, which mainly dominates the performance of such members. In the four-point loading cases, on varying the sectional compactness of the channel section from 50 to 60, the flexural strength changed from 6.89kNm to 9.98kNm, that resulted in a flexural strength enhancement of 44.84%, as shown in b. This enhancement in flexural strength despite a small reduction in the sectional compactness was primarily due to the increase in the depth of the beam cross-section, that substantially improves its second moment of area, which drastically enhances the flexural performance of these members. Also, the local buckling occurs under compressive stresses, which occurs above the neutral axis. This makes only half of the cross-section effective for the local buckling effect. On varying the sectional compactness further from 60 to 70, the flexural strength changed to 12.6kNm, with a flexural strength improvement of 26.25%. The reason behind this improvement is the same as was in the previous case. However, the percentage improvement in the flexural strength in the former case (when sectional compactness was changed from 50 to 60) was about 1.75 times that of in the latter case, and was mainly as the sectional compactness limit (60) proposed by the current codes was exceeded.Stiffness characteristics are important features in structural members, particularly in flexural members, essentially from serviceability consideration. The stiffnesses of the specimens were obtained as the ratio of the load resisted by them until their linear part of the load vs. displacement plots, to their corresponding displacements. In the three-point loading cases, on varying the aspect ratio from 1.25 to 1.5, the stiffness changed from 8.72kN/mm to 11.44 kN/mm, which resulted in an improvement of 31.19% as shown in a. On varying the aspect ratio further from 1.5 to 1.75, the stiffness changed to 19.14kN/mm, with an improvement of 67.30%. The improvement in the stiffness due to the variation in the aspect ratio attributes to the increase in the width of the flexural members, that improved their stability, and thus improved their stiffness characteristics. The percentage improvement in the stiffness was more than double in the latter case (when the aspect ratio was 1.75), as the second moment of area was higher in that case.In the four-point loading cases, on varying the sectional compactness of the channel section from 50 to 60, the stiffness changed from 1.43kN/mm to 1.95kN/mm, that resulted in a strength enhancement of 36.36%, as shown in b. This enhancement in flexural strength despite a small reduction in the sectional compactness was primarily due to the increase in the depth of the beam cross-section, that substantially improves its second moment of area, which drastically enhances the stiffness characteristics of these members. On varying the sectional compactness further from 60 to 70, the stiffness changed to 2.88kN/mm, with an improvement of 47.69%. The reason behind this improvement is the same as was in the previous case. However, the percentage improvement in the stiffness in the latter case (when sectional compactness was changed from 60 to 670) was about 1.3 times that of in the former case. Furthermore, the stiffness of three-point loading cases was substantially higher than the four-point loading cases, primarily due to smaller beam spans in the former cases.The strength-to-weight ratio performance of CFS members is generally higher than the hot-rolled steel members, and for these reasons the former is preferred over the latter, in moderately loaded structures. One of the primary objectives in the CFS research is to improve the efficiency of CFS sections by adopting different means to achieve the same. shows the strength-to-weight comparison of different specimens. The strength-to-weight ratio performance of the three-point loading cases was better than the four-point loading cases, and was therefore, mainly due to higher stiffness that was achieved due to lower beam spans, that enabled them to carry higher loads. In the three-point loading cases, on varying the aspect ratio from 1.25 to 1.5, the strength-to-weight ratio changed from 1.04kNm/kg to 1.13 kNm/kg, which resulted in an improvement of 8.65% as shown in . On varying the aspect ratio further from 1.5 to 1.75, the strength-to-weight ratio changed to 1.26kNm/kg, with an improvement of 11.5%. The reason behind this percentage enhancement and the order of enhancement is the same as that of behind the flexural strength enhancement.In the four-point loading cases, on varying the sectional compactness of the channel section from 50 to 60, the strength-to-weight ratio changed from 0.37kNm/kg to 0.48kNm/kg, that resulted in a performance enhancement of 29.73%. On varying the sectional compactness further from 60 to 70, the strength-to-weight ratio changed to 0.54kNm/kg, with an improvement of 12.5%. The reason behind this percentage enhancement and the order of enhancement is the same as that of behind the flexural strength enhancement.The comparison of the test strengths with the ones computed using the current standards on CFS members was one of the key objectives of this study. Accordingly, the design strengths of these built-up beams were quantified for the same. Both American Standards as well as European Standards were adopted. In the European Standard, the versatile Effective Width Method was adopted, as that has been accepted worldwide with good reliability. However, in the North American Standard, the recently developed Direct Strength Method was implemented, as the sections were open sections and were prismatic as well. The primary design equations used in these standards are given below.The procedure for the design strength determination of flexural members is presented below:For lateral torsional buckling of doubly symmetric sections (open cross-section);Where, Fcre is the elastic buckling stress, Cb is the constant that is conservatively considered as unity, d is the sectional depth, Iyc is the second moment of area of the full cross-section’s compression region about the centroidal axis, E = Young’s modulus of steel, Ky = effective length factor, Ly = unbraced member length for flexure about y axis.The nominal strength [resistance], Mne, considering inelastic flexural reserve capacity is given byWhere, Mcre is the critical lateral-torsional buckling moment resistance, My is the yield moment resistance, Mp is the plastic moment resistance, Zf is the plastic modulus of the beam cross-section.The beam’s local buckling moment resistance (Mcrl) shall be governed by the lowest buckling stress among the cross-sectional elements, with reference to the extreme compression fibre, as follows:Where, Sf is the elastic cross-sectional modulus of the gross-section, with reference to the extreme compression fibre, Fcrl is the local buckling stress at compression fibre (extreme), and is given byWhere, K is the plate buckling coefficient which is given in the Appendix 1 of the AISI The nominal flexural resistance (Mnl) that considers the local buckling and global buckling interaction shall be determined by using the following equations:Mne is the nominal flexural resistance for lateral-torsional buckling, Mcrl is the critical local buckling moment resistance.The elastic distortional buckling moment resistance (Mcrd) shall be determined as follows:The nominal flexural resistance (Mnd,) shall be determined as follows:Sfy is the section modulus (elastic) of gross cross-section, relative to the extreme fibre in the first yielding.The critical elastic moment of the beam cross-section shall be determined using the following equations, Mcr = CbWhere EIy, EIw and GJ are the flexural rigidity, warping rigidity and torsional rigidity respectively, about the major axis. The factors ky and kw are conservatively taken as unity. Also the constant Cb is considered as unity.If λ-lt>0.4, χlt = 1.0/(φLT+(φLT2 +λLT2)0.5)Where,λLT2=(Wy fy /Mcr)0.5Where, Wy is the appropriate elastic sectional modulus depending on its class, Wel for class 3 and effective section modulus Weff, for class 4 cross-sections, fy is the yield strength of steel, kσ is the relative buckling factor, ε is the ratio 235/fyb with fyb in N/mm2, Ψ is the stress ratio, t is the sectional thickness, σcr is the elastic critical buckling stress of the plate element.The comparison of the test strengths with the strengths predicted by the current codes are given in This study discussed the flexural behaviour of cover plated CFS built-up simply supported beams made up of lipped channels, under both three-point as well as four-point loading. The influence of moment gradient and constant moment loading on theses built-up beam specimens was investigated. The sectional compactness of the channel section and the aspect ratio of the built-up section were varied to assess the behavioural effect in the specimens with respect to the variations incorporated. Both the European code as well as the North American Standards were used for developing the theoretical strengths and were compared with the test results. Some prominent results are given below:Both the aspect ratio (by varying the transverse spacing between channels at constant depth) as well as the sectional compactness of the channel sections (by varying the sectional depth at aspect ratio) influence the flexural behaviour of cover plated CFS built-up beams.The sectional compactness effects the flexural strength more than the aspect ratio. However, the influence of the sectional compactness is dominant provided the sectional compactness doesn’t exceed the limiting value recommended by the current codes.The stiffness characteristics are affected by both the variation in the aspect ratio as well as the sectional compactness, and this relationship is proportional.Local buckling in the compression zone was the primary mode of failure observed in the cover plated CFS beam specimens, and was noted near the loading points.The aspect ratio influences the stiffness characteristics more compared to the sectional compactness. This is primarily due to involvement of local buckling behaviour on the sectional compactness of the built-up section that controls the structural behaviour of thin-walled members.Both the strength as well as the stiffness in three-point loading cases were higher than that of the four-point loading cases. This behaviour was observed mainly due to the moment gradient in the former cases and constant moment in the latter cases. The stiffness was higher in the three-point loading cases, primarily due to smaller spans.The strength-to-weight ratio in the three-point loading cases was higher than the four-point loading cases, and again attributed to larger flexural strengths and smaller spans in the former cases compared to the latter one.Both the European code as well as the North American Specification over predicted the strengths of these beam specimens and was so as the transverse spacing is not accounted for in the design strength approach.The authors are currently working on the parametric study on the similar configuration to develop a large pool of data for the development of reliable design equations.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.First-principles investigations of the physical properties of antifluorite Li2O under various pressuresThe crystal structural, electronic, elastic characteristics and the thermodynamic properties of antifluorite Li2O (α-Li2O) under various pressures are investigated by using the first-principles plane-wave pseudopotential density function theory within the generalized gradient approximation (GGA). The ground states properties are found to agree with the available experimental data and other theoretical results. Band structures reveal that α-Li2O is an indirect band gap (G–X) system. The band gap of this compound increases with increasing pressure. Furthermore, the optical properties are reported for radiation up to 30 eV. Finally, the thermodynamic properties of α-Li2O such as free energy, entropy, enthalpy, heat capacity and Debye temperature are given for reference.Lithia (Li2O) is a material of technological interest, which can be applied in deuterium–tritium fusion reactors as blanket breeding material In this work, we calculated the crystal structural, electronic, elastic characteristics and the thermodynamic properties of α-Li2O under various pressures using the first-principles method in order to reveal a complete understanding of the pressure dependence of physical properties.The rest of the paper is organized as follow: in Section , we describe briefly the computational techniques used in this work. Sections contains our results and discussion, involving structural properties, electronic structures, optical properties, elastic properties and some thermodynamic properties such as constant volume heat capacity and Debye temperature for the α-Li2O under various pressures. Finally, the conclusion is given in Section Our first-principles calculations were carried out by using the plane-wave ultrasoft pseudopotential method (PW-PP) within DFT which was implemented in the CASTEP code α-Li2O crystal has a cubic structure with space group Fm-3m (No. 225) as shown in . There are 12 atoms in the cell of the Li2O compound. Li atoms occupy the 8c Wyckoff site (1/4, 1/4, 1/4) and the O atoms occupy the 4a Wyckoff site (0, 0, 0). To investigate ground-state properties, the equilibrium lattice configuration of α-Li2O was computed first. The lattice constants of α-Li2O are summarized in , including experimental data by other scholars for comparison. The calculated lattice constant is 4.62977 Å, which is very close to the experimental value 4.619 Å In order to show how the structural parameters under pressure in this compound behave, the equilibrium geometries of α-Li2O unit cell were computed at fixed values of applied hydrostatic pressure in the range from 0 to 20 GPa with each step of 5 GPa, with a complete optimization for the structural parameters performed at each pressure. plots the variation of the relative changes of the lattice parameters (a/a0 and V/V0) versus applied hydrostatic pressure (P). The following relations can be obtained from this calculation.The calculated unit cell volumes at fixed values of applied hydrostatic pressure in the range from 0 to 20 GPa were used to construct the equation of state (EOS), which was fitted to a third-order Birch–Murnaghan equation P=32B0[(V0V)73−(V0V)53][1+34(B′−4){(V0V)23−1}]The fixed value of V0 is determined by the zero-pressure data. The calculated values of the bulk modulus B0 and its pressure derivative B′ at zero pressure are listed in The calculated electronic band structures (BS) of α-Li2O compound are displayed in , along symmetry lines of the first Brillouin zone (BZ). The results indicate that the valence band maximum and the conduction band minimum occur at G and X points, so α-Li2O has an indirect band gap (G–X) of value 4.829 eV. shows the relations between the pressure variation and the band gap for α-Li2O. The band gap (G–X) increases as pressure increases. The variation of this gap versus pressure is well fitted to a quadratic function:The density of states (DOS) is an important theoretical quantity for understanding the bonding in a compound. In order to get the nature change of the band gap, the total density of states (TDOS) and partial density of states (PDOS) under various pressures are calculated as shown in . As it can be seen, for this compound there are two valence regions. The O 2s and Li 2s states make mainly contributions to valence band (VB) ranging from −16.20 eV to −14.15 eV. The upper VB, which is wider for a range of −3.67 eV up to Fermi level, is mainly composed of O 2p hybridized with small amount of Li 2s states. The conduction band (CB) extending from 4.83 eV to 9.06 eV is mainly composed of O 2p and Li 2s states. The unoccupied CB from 9.67 eV to 30 eV is formed by Li 2s and O 2p states. From we found that the overall DOS spectrum profiles are the same except the value of band gap under various pressures.The optical properties of α-Li2O are studied by the frequency-dependent dielectric function ɛ(ω) = ɛ1(ω) + iɛ2(ω) that is mainly connected with the electronic structures. The imaginary part ɛ2(ω) of the dielectric function is calculated from the momentum matrix elements between the occupied and unoccupied electronic states ɛ2(ω)=2e2πΩɛ0∑k,v,c|〈ψkc|uˆ·r|ψkv〉|2δ(Ekc−Ekv−E)u is the unit vector defining the polarization of the incident electromagnetic wave; ω is the light frequency of the incoming photons; e is the electronic charge; ψkc and ψkv are the conduction and valence band wave functions at k, respectively. Since the dielectric constant describes a causal response, the real and imaginary parts are linked by a Kramers–Kronig transform.The dielectric function is a very important parameter for a material, because it is the fundamental feature of the linear response to an electromagnetic wave and determines uniquely the propagation behavior of the radiation within. The calculated real part ɛ1(ω) and imaginary part ɛ2(ω) of the dielectric function in the energy range 0–30 eV are shown in , there are two peaks in the ɛ2(ω) function with their locations at 7.24 eV and 12.85 eV at 0 GPa. In the range of 0–30 eV, our calculated dielectric functions of α-Li2O compound under various pressures are rather similar to each other, but the dielectric spectrum profiles move to the high-frequency direction, as the pressure increase. The first peak in (b) at 7.24 eV originates from the following transitions: O 2p (at −0.23 eV) to Li 2s (at 7.02 eV) at L → W point. The second peak at 12.85 eV arises from the transition O 2p (at −0.50 eV) to Li 2s (at 12.35 eV) at L-point, Li 2s (at −1.5 eV) to O 2p (at 11.35 eV) at K point, Li 2s (at −1.49 eV) to O 2p (11.35 eV) at W → K point and Li 2s (at 0 eV) to O 2p (at 12.85 eV) at G → X point. These also can be used to explain the origin of the peak structures in the refractive index (). The refractive indices (n) and the extinction coefficient (k) of α-Li2O are demonstrated in . The static dielectric constant ɛ(0) and optical permittivity ɛ(∞) are given in , along with the corresponding static refractive indices n0=ɛ(0) and the optical refractive indices n∞=ɛ(∞).Elastic constants of crystals provide a link between mechanical and dynamical behaviors. Also, they give important information concerning the elastic response of a crystal to an external pressure. To calculate the elastic constants, we have applied the volume-conserving method. In this way the values of three independent elastic constants in the cubic symmetry are estimated.A given crystal structure cannot exist in a stable or metastable phase unless its elastic constants obey certain relationship. The requirement of mechanical stability in a cubic structure meets with the following restrictions on the elastic constants C˜11+2C˜12>0,C˜11−|C˜12|>0,C˜44>0,C˜12<B<C˜11where C˜αα=Cαα−P(α=1,4), C˜12=C12+P. These criteria are satisfied, indicating that these compounds are stable against elastic deformations., we list the elastic constants of α-Li2O at 0 K under various pressures. It is obvious from that C11, C12, C44 increase monotonically with increasing pressure, and all the elastic constants in satisfy all the mechanical stability conditions very well, suggesting that the calculated structure of α-Li2O is elastically stable under these pressures. The calculated C11 are very large among elastic constants, which indicate that they are very incompressible under uniaxial stress along x axis.The Young and shear moduli (E and G) are two important mechanical quantities for technological and engineering applications. The Young moduli E is defined as the ratio between stress and strain. The shear moduli G, which is related to bond bending, depends on the bond nature and decreases as a function of ionicity. For the cubic symmetry, the Voigt bounds of bulk modulus B and shear modulus G are The elastic moduli of α-Li2O can then be estimated by Hill's average, BH = 1/2(BV + BR) for bulk modulus and GH = 1/2(GV + GR) for shear modulus. Apart from this, the Young's modulus E and Poisson's ratio σ can be computed by the following equations The values of Bulk and shear moduli B and G, Young's modulus E, Poisson's ratio σ and ratio G/B are given in . The ratio of shear modulus to bulk modulus of crystalline phases can predict the brittle and ductile behavior of materials. If G/B < 0.57 the material will behave in a ductile manner or else the material demonstrates brittleness The Poisson's ratio σ provides more information about the characteristics of the bonding forces than any of the other elastic constant. The lower and upper limits of Poisson's ratio are 0.25 and 0.5 for central force in solids respectively. The obtained values of the Poisson's ratio (σ) demonstrate that the compound isn't central forces at 0 K under 20 GPa (Dynamical properties were obtained from the linear response method, within density functional perturbation theory (DFPT). Unlike the previous calculations, the calculations of phonons have been implemented using the norm-conserving pseudopotentials within CASTEP code. Phonon calculations from DFPT can be used to evaluate the temperature dependence of the entropy, free energy, enthalpy, heat capacity and Debye temperature of a crystal in a quasi-harmonic approximation.The variations of the entropy, enthalpy, free energy, heat capacity at various temperatures and pressures are shown in (a) and (b), it is noted that the enthalpy and entropy increase rapidly when the temperature increases in the range of low temperature. The values of enthalpy and entropy decrease greatly with the increase of pressure. From (c), it is obvious that the overall profiles of the curves show similar characteristics and the free energy decreases when the temperature increases. In addition, the absolute values of free energies decrease with the increasing pressure. The results are interpreted in terms of the anharmonicity of the lattice vibrations under pressure. (d) shows the temperature-dependent behavior of the constant-volume heat capacity Cv at various pressures. It is seen from this figure that when T < 400 K, Cv increases very rapidly with temperature; when T > 400 K, Cv increases slowly with temperature and it tends to the Dulong–Petit limit. At high temperature, Cv approaches approximately 11.43, 11.36, 11.30, 11.24, 11.19 and 11.14 cal/cell K at the pressure of 0–20 GPa respectively.As an important physical quantity, the Debye temperature is a suitable parameter to describe phenomena of solid-state physics which are associated with lattice vibration, elastic constants, specific heat and melting point. The Debye temperature (θD) is not a strictly determined parameter, various estimates may be obtained through well established empirical or semiempirical formulas. One of the semiempirical formulas can be used to estimate the values of Debye temperature through elastic constants and the averaged sound velocity (vm), the longitudinal sound velocity (vl) and transverse sound velocity (vt) . Unfortunately, the experimental thermodynamic data cannot be found, therefore it is difficult to evaluate the magnitude of errors between calculations and experiments. Our calculated results can be seen as a prediction for future investigations.The structural, electronic, optical elastic and thermodynamic properties of α-Li2O under various pressures have been studied by means of DFT within the generalized gradient approximation (GGA). The most relevant conclusions are summarized as follows:The calculated ground state properties of this compound at zero pressure are in agreement with the available experimental data and theoretical results.The pressure dependence of the relative lattice parameters and the value of band gap (Eg(P)) have been fitted with a quadratic relation.The electronic structure calculations showed that α-Li2O is an indirect band gap (G–X) system. The band gap of this compound increases with increasing pressure. Analysis of the DOS revealed that the conduction band and valence band are mainly composed of O 2p and Li 2s.The dielectric function and refractive index are calculated for radiation up to 30 eV. Using density functional perturbation theory, we calculated the static dielectric constant ɛ(0) and optical permittivity ɛ(∞) under various pressures.We calculated the elastic constant, shear modulus, Young's modulus and Poisson's ratio under various pressures.We predicted the Debye temperature (θD), the isochoric heat capacity (CV), and thermodynamic properties under various pressures of α-Li2O as a function of temperature.Curing behavior and thermal properties of TGDDM copolymerized with a new pyridine-containing diamine and with DDM or DDSEpoxy resin thermosets have good chemical and corrosion resistance, high tensile strength and modulus, excellent dimension stability and adhesive properties An improvement in the thermal properties of epoxy resins can also be achieved by introducing aromatic rings into crosslinked epoxy resins, either by use of aromatic epoxy monomers, such as N,N,N′,N′-tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM), triglycidyl p-aminophenol (TGAP), diglycidyl ether of bisphenol-A (DGEBA) or by using aromatic curing agents such as diaminodiphenylmethane (DDM) and diaminodiphenylsulphone (DDS). The second approach is more useful because a wide range of established, commercial epoxy resins used in various industries can be cured in this manner 2,6-Dichloropyridine, 1-methyl-2-pyrolidone (NMP), 4-aminophenol and 4-4′-diaminodiphenylmethane (DDM), potassium carbonate and toluene were purchased from Sigma–Aldrich. N,N,N′,N′-tetraglycidyl-4,4′-diaminodiphenylmethane (TGDDM, Araldite MY 721) and diaminodiphenylsulphone (DDS) were obtained from Huntsman and Vantico, respectively. These chemicals were used as received. The structures of the amines and epoxy are shown in . All other reagents and solvents were obtained from Aldrich.4,4′-(Pyridine-2,6-diylbis(oxy))dianiline (PDD) was synthesized according to the reported procedure N stretching); 1H NMR (in DMSO-d6 and referenced to the internal standard, tetramethyl silane): 4.95–5.1 ppm s(4H, amine), 6.33 ppm d(2H, pyridine), 6.59–6.56 ppm d(4H phenylene), 6.81–6.78 ppm d(4H phenylene), 7.66 ppm t(1H pyridine).TGDDM was mixed with combinations of PDD, DDM and DDS in stoichiometric amounts as shown in . The diamines were heated and stirred with TGDDM for 10 min at 90 °C, 100 °C or 120 °C for DDM, PDD or DDS, respectively. These temperatures were chosen to facilitate mixing with the more viscous TGDDM but reduce the chance of premature cure because the reactivity of the diamines with the epoxy is DDM > PDD > DDS. After mixing, the transparent and homogenous solutions were rapidly cooled to room temperature to prevent premature cure. shows the chemistry of the curing process.The curing of ∼5 mg sample (in sealed hermetically in aluminum pans) of each resin composition was studied with a Perkin Elmer Pyris I DSC in temperature ramping mode under a nitrogen flow of 20 mL/min. An empty pan as used as reference. The instrument was calibrated with zinc and indium standards with heating rates of 10, 15, and 20 °C/min. The dynamic curing scans were recorded from 50 °C to 250 °C with heating rates of 10, 15, and 20 °C/min.Specimens for dynamic mechanical thermal analysis (DMTA) were prepared by pouring the resin mixture into silicone molds (30 mm × 5 mm × 2 mm) covered with a PTFE coated glass sheet and clamped between two glass plates. The resin was cured at 100 °C for 1 h followed by 150 °C for 2 h and then post-cured at 180 °C for 1 h. DMTA scans were preformed with a Perkin Elmer DMA 8000 operated in air at a heating rate of 2 °C/min in dual cantilever mode with a frequency of 1 Hz.A Seiko TG/DTA 6300 was used to study the thermal decomposition of the approx. 5 mg specimens under either argon or air atmosphere at a ramp rate of 10 °C/min from 50 °C to 700 °C.The physical and engineering properties of epoxy thermosets depend upon their functional groups, the specific nature of their three dimensional network structure and the extent of the epoxy-amine reaction depicts DSC thermograms of TGDDM/PDD system, and indicates that curing does not significantly occur until over 120 °C. The enthalpy of cure was found to be in the range 436–456 J g−1 or 105–114 J mol−1 of epoxy groups using scanning rates of 10, 15 and 20 °C/min, and these values are in good agreement with those reported in literature and was calculated on the assumption that 100% conversion had occurred at the completion of the DSC scan.It is generally accepted that in thermal analysis the rate of reaction is the function of temperature (T) and fractional conversion (α) where k(T) is the temperature (T) dependent rate constant and f(α) gives the dependence of the rate on conversion (α). The temperature dependence of k(T) is given by the Arrhenius equation:where A and Ea are pre exponential factor and energy of activation, respectively. By combining Eqs. When the isoconversional principle – the concept that the reaction rate at a constant conversion α (i.e., the isoconversional rate) is only a function of temperature – is applied to Eqs. can be derived which is often known as the Friedman method and can be used for calculation of Eaby measuring the dependence of reaction rate on temperature scanning rate. The slope of a plot of ln [β(dα/dt)α] versus 1/Tα (see ) was used to determine Ea at each given value of α. It can be seen from that the Ea is practically constant in the interval 0.2 ≤ |
α |
≤ 0.8. This behavior suggests that the process follows a single step kinetic model. The average activation energy of the TGDDM/PDD system is 54.1 ± 0.6 kJ/mol which is similar to those reported in the literature to be 52.3 kJ/mol for TGDDM/DDM, but lower than the value of 77.0 kJ/mol for TGDDM/DDS H resonance can be used to predict the basicity of amine The DMTA curves for the networks in the glass transition region are presented in . The tan |
δ maximum associated with the glass transition and the area under the tan |
δ curve is often used an indicator of the amount of energy loss caused by molecular movement shows in general the maximum value of tan |
δ decreases as PDD is replaced by DDM. Since the width at half-height is approximately the same for each system, this suggests that this behavior may be due to the more flexible backbone of the PDD unit (see ). Surprisingly, the reverse trend is observed with the rigid DDS unit and the reason for this is unclear. The modulus data in shows that all of these polymers have high temperature mechanical performance because their moduli remain above 1 GPa well beyond 225 °C.The glass transition temperature (Tg) is one of the most important properties of a thermoset because it determines the maximum use temperature of the polymer shows that as the percentage of PDD in the network is raised, the glass transition temperature decreases. There have been a number of mathematical expressions relating the Tg to the molecular composition and crosslink density, for example where Tg(copol) is the glass transition temperature due to the polymer's chemical composition and kρ is the effect on Tg due the difference in crosslink density (k being a constant). For fully cured networks formed from TGDDM and a blend of PDD with either DDM or DDS, the crosslink density varies linearly with the weight fraction of PDD, because the crosslink density is the moles of trifunctional junctions per gram of polymer and this rises linearly with the wt% of each of the amines used. The variation of Tg(copol) on composition can be estimated where wi is the weight fraction of monomer i and Tg(i) is the effective glass transition temperature of a polymer formed from monomer i. The combination of Eqs. predicts that a linear relationship should be found between the Tg of the thermosets and their composition as the fraction of PDD is varied as is shown in shows that TGDDM/DDS has the highest Tg and TGDDM/PDD has the lowest. Based on their structures (see ), the theoretical crosslink density (i.e. moles of trifunctional junctions per unit mass) of the networks increases in the order: TGDDM/DDS > TGDDM/DDM > TGDDM/PDD, which is also consistent with the order of their Tg values. Apart from the crosslink density, the Tg of a polymer network depends on the flexibility of the backbone chain and the strength of the van de Waals bonds shows that the three amines have similar aromatic structures with methylene, sulfone or ether spacer units. DDS has a more inflexible backbone and a polar sulfone which should contribute to a higher Tg(copol) in TGDDM/DDS than the methylene unit from DDM in TGDDM/DDM. In contrast, the extra flexibility of the ether units in the PDD unit would be expected to give the TGDDM/PDD the lowest contribution to Tg(copol). This is in accord with the variation on Tg for the thermosets: TGDDM/DDS > TGDDM/DDM > TGDDM/PDD.The weight loss during heating runs in TGA gives important insights into the oxidative or degradation mechanisms and thermal stability of polymers The TGA thermogram under Argon is shown in for the cured polymers. The relative thermal stability of cured resin was evaluated by the initial decomposition temperature (IDT) which is defined as the temperature at which 5% weight loss occurs in an argon atmosphere ) which suggests that some features in the networks that gives rise to early decomposition are common in all of the cured samples. Another index of thermal stability is the char residue at the end of the TGA trace under argon atmosphere (see shows that 100PDD/0DDS system has highest estimated LOI value., the concentration of nitrogen in PDD, DDM and DDS are 9.7, 9.3 and 7.6 mmol of nitrogen per gram which supports this explanation. In addition, it has been claimed that the heterocyclic pyridine moiety is relatively stable under an argon atmosphere and does not decompose but remains in the solid residue and thus is able to enhance char formation shows that under an oxidative environment, the initial degradation occurs between 330 and 340 °C and is similar to that under argon. However, here multi-step degradation was observed for all formulations, as has been observed by other workers A novel pyridine containing primary diamine (PDD) was used as a curing agent for TGDDM and was compared with DDS and DDM. Dynamic DSC was used to determine the activation energy and pre-exponential by using model fitting method. The Ea values were found to be 54.1 kJ/mol, which is in between those for DDS and DDM, suggesting that PDD is more reactive than DDM and less reactive than DDS.The tan |
δ and storage modulus of TGDDM cured by blends of PDD with either DDS or DDM were determined by using DMTA. The samples containing PDD had the lowest Tgs, those with DDM were intermediate and DDS-containing samples had the highest Tg values due to the higher crosslink density of the networks and the greater chain rigidity.TGA analysis of the cured samples showed that TGDDM/PDD underwent two-stage decomposition in Ar compared with a main single transition for the other systems, whereas all systems showed multiple degradation stages in an air atmosphere. Overall PDD had the best thermal stability and so can be viewed as a potential candidate to be used as curing agent for TGDDM for fire-risk situations.Effect of the countersunk hole depth on tensile-tensile fatigue behavior of riveted specimens of AA2024-T3 alloyThis study investigated the effect of countersunk hole depths (0.65, 0.90, and 1.20 mm) on the fatigue performance of the riveted AA2024-T3 alloy. The fatigue fracture of the samples was observed by scanning electron microscopy. The strain at the countersink hole was analyzed by finite element (FE) method. The stress intensity and stress concentration factor of the countersunk holes were calculated. The rationality of the FE analysis and theoretical calculation was verified by measuring the strain near the countersunk holes. The high cycle fatigue life of the samples with a countersunk depth of 1.20 mm was far less than the other samples. In contrast, the low cycle fatigue life changed insignificantly.In engineering practice, riveting has the excellent characteristics of reliable connection, light weight, and cost-effective compared to ordinary fasteners. Thus, the technology had been widely used in structural connection of aircraft Many researchers investigated the fatigue performance of the riveted Al alloy, focusing on the effect of riveting process parameters on the fatigue life In summary, the effect of different riveting process parameters on the fatigue property of the riveted specimens had been widely studied; however, the depth of the countersink was one of the important parameters of the riveting process and has not been paid any attention. Many researchers reported the effect of the diameter of the through hole on the fatigue behavior of the specimens, the increase in the diameter impaired the fatigue property. The countersink is a special through hole with a tapered shape at the top end. The taper diameter is different because of the change in the countersunk depth. Therefore, investigating the mechanism of the countersunk depth impairing the fatigue performance for the preparation of the riveted specimens is important. This paper studied the effect of countersunk depth on the fatigue life, static characteristics, and microscopic mechanism of the riveted AA2024-T3 alloy. The results will provide the reference for the design and process of the riveted structural parts of the aircraft. shows the geometry of the riveted lap joints used in the fatigue tests, and lists their dimensions. The deviations from the nominal rivet hole diameter (do) ranged from 0 to 0.03 mm. The thickness of the rivet drive head (H) is 2 mm. The chemical composition of the material investigated in this work is listed in . The raw material is a 2440 × 1830 × 1.50 mm3 Al alloy plate. Three samples were used to conduct the static test of AA2024-T3 alloy without countersink holes. The average of the experimental results is listed in . Static test loading parameters are as follows: force loading (0.10 kN sec−1) and displacement loading (0.07 mm sec−1). The raw Al alloy plates were cut into 150 × 20 × 1.50 mm3 strip plate using a wire cutting device. Riveting two test pieces was fabricated using a hand-riveting machine. Two pads (45 × 20 × 1.50 mm3) were pasted on both gripping ends of the specimen to minimize the secondary bending effect, as shown in . The fatigue property of the riveted samples with triple-row and single column of countersunk holes was evaluated. The diameter of the nominal hole was 5/32 in. (4 mm) . In order to discuss the results conveniently, the different countersunk depths were coded as follows: 0.65 mm-sample S1, 0.90 mm-sample S2, and 1.20 mm-sample S3.The fatigue test was carried out at room temperature using an electro-hydraulic servo fatigue tester (EHF-EV200k2-040-1A) . The applied maximum stress was perpendicular to the sample cross-section, and the loading frequency f was set to 10 Hz. The fatigue tests were performed at a stress ratio R of 0.1 on the riveted samples with three types of countersink depths. The cyclic stress amplitudes of samples S1 (0.65 mm) and S2 (0.90 mm) were set to be 47, 57, 67, 77, 87, 97, and 107 MPa; however, the applied stress of sample S3 (1.20 mm) was 42, 47, 52, 57, 67, 77, and 87 MPa. Seven samples were subjected to fatigue test under each cyclic stress until fatigue failure occurred. The average value of the experimental data was taken as the fatigue life. The fatigue fracture of the samples was observed by field emission scanning electron microscopy (FESEM, Ultra Plus, Carl Zeiss AG), and the crack initiation sources and the path of the crack propagation were analyzed.Accurate determination of equivalent elastic strain is an important method to analyze the location of fatigue crack initiation. The fatigue crack initiation mostly occurred in a region with significant stress concentration and large equivalent strain. The riveted specimen was modeled and analyzed by the FE method. Three-dimensional contact analysis methods including contact between the rivets and the plates and at the faying surface or interface between the two plates were used. These models were approximated as rigid surfaces with no rotational degree of freedom. The mechanical properties of the Al alloy are listed in . The countersunk depth was 0.90 mm, and the external tensile load was 67 MPa. During the static simulation process, the friction was retained between the rivets and the sides of the countersunk hole, and a certain compressive stress was generated at the countersunk position. The strain at the countersunk holes was different from other parts of the test pieces during mesh generation . The dimensions of the 3D model were consistent with the test piece, as shown in . A horizontal external load was applied to one end, keeping the other end fixed.The location of the fatigue failure of the specimens was estimated by analyzing the distribution law of the strain. In the finite element model, a series of strain nephogram are used to represent the whole crack propagation process. Combining the images of strain changes at different positions with time indicated that the maximum principal stress is located in the lower row of the holes in the top sheet (Rivet 3 in ) and the upper row of holes in the bottom sheet (Rivet 1 in ). Considering the strain values, the lower rows of holes in the top sheet were selected as the research and analysis objects, as shown in . The stress varies around the hole as well as through the thickness for each hole illustrating the complexity of its distribution , the maximum elastic deformation of samples S1 and S2 were 0.05693 and 0.057705 mm, respectively, whereas that of sample S3 was 0.061967 mm. Similarly, considering the material constants in the simulated environment, the contact setting conditions were somewhat different from the actual measurement conditions. Therefore, the strain gauges were attached to the surface of the test piece to obtain a deformation map in a real environment.To validate the finite element model of static mechanics of the riveted specimens, the strains of many locations of the riveted specimen was tested using an electro-hydraulic servo fatigue tester. Strain gages were installed at the two sides of the outer rivets of the samples. The experimental equipment is shown in . The YE2539 high-speed static strain gauge was used and connected to the front and rear sides of the riveted plates laterally, as shown . The size, gate length, and grid width of the strain gauges were BX120-5AA, 5 mm, and 3 mm, respectively. Due to the limited size, the strain gauges should be posted as close as possible to the countersunk hole. The values of the strain were continuously recorded until the specimen was fractured.The finite element strain diagram and the real measured strain of the specimen with a countersunk depth of 0.90 mm were selected as the reference standards. The tested strain curves are shown in The position of the maximum deformation was located at the outermost rivet countersink holes shows that the results of the simulation agreed with the actual measured strain values, indicating that the deformation of the FE model was correct. The above analysis also provided a foundation for the discussion of the fatigue behavior. shows the average fatigue life of the riveted samples. The depths of the countersunk hole were 0.65, 0.90, and 1.20 mm. To obtain the S–N curves, the fatigue data were fitted using the least squares method, as shown in . At the high-cycle fatigue (HCF) loading condition, the deeper countersunk hole (1.20 mm) dramatically impaired the fatigue performance of the riveted samples. However, the fatigue life of sample S1 (0.65 mm) is close to that of sample S2 (0.90 mm) and higher than that of sample S3. Under the low-cycle fatigue (LCF) regime, the depths of the countersink slightly affected the fatigue life of the riveted samples.In general, the fatigue crack initiated easily at the high cyclic stress levels and then propagated quickly , since the size of countersunk hole in diameter for all the samples was 4 mm, the remaining cross-sectional area (M1) in the transverse direction of the specimen was identical. The straight shank thickness b was different in the direction of thickness for the riveted samples as the depth of the countersunk hole was not identical; however, the crack propagation path was approximately transverse rather than the thickness direction. The length of the fatigue crack propagation varies slightly. shows that the crack propagation path was primarily along the cross-sectional direction of the test piece. (A) shows a partial enlarged view of the crack propagation. This special morphology of the fatigue fracture was also observed by Yuan and co-workers . For the entire test piece, the residual stress belongs to the internal stress and tensile stress should exist on the cross-section of the riveted specimen to offset the residual compressive stress generated around the hole To clearly show the depths of the countersink hole affecting the fatigue property, the parameter φ is expressed as follows:where Nf′ is the fatigue life of the riveted samples (0.90 and 1.20 mm); Nfis the fatigue life of the riveted sample (0.65 mm). The values of φ are shown in shows that the value φ of sample S3 (1.20 mm) was the largest at Smax = 47 MPa. The effect of the countersunk depths on the fatigue life was most obvious under the low cyclic stress levels. This phenomenon is related to the crack growth rate affected by the stress intensity factors (SIFs) at the countersunk holes. According to linear elastic fracture mechanics, SIF determined the stress, strain, and displacement fields in the zone of the crack tip near the nail hole where σ is the stress at the rivet hole, a is the length of the crack, and ε is a dimensionless factor related to the samples′ geometry. shows the fatigue fracture of the riveted samples at σmax = 67 MPa. The crack initiation of the three specimens was found at the inflection point and consistent with the FE analysis result shown in . The length and path of the crack propagation zone indicate that the crack propagation was along the taper direction of the test piece under tensile stress. The micro-fractured surface shows the typical river patterns. Moreover, numerous second phase particles existed within the 2024-T3 Al alloy. As shown in (A), the second phase particle changed the path of the crack propagation. Consequently, the crack propagation did not occur in a single plane, leaving a clear ridge line. In general, crack propagation was affected by the stress intensity factor. As the applied stress levels were the same and the size was identical, the magnitude of the stress intensity factor K was mainly related to the stress value (σ) of the rivet hole (Eq. ). Moreover, the amplitude of σ was affected by the remaining surface area of the samples without the countersunk hole. shows the longitudinal section of the riveted samples. Because the countersunk depths were 0.65, 0.90, and 1.20 mm and the angle of the countersunk hole bit was 120°, the notched area of the riveted samples was not identical. The test piece with the countersunk depth of 1.20 mm had the largest notched area. According to the geometric relationship, the remaining area is determined by Eq. where the value of t0 is in the range 0–0.65 mm and the values of Cs are 0.65, 0.90, and 1.20 mm.With increasing the countersunk depth, the remaining surface area (M2) of the samples gradually reduced. When the value of the t0 is 0.3 mm, the magnitudes of M2 are close, and are 58.67 and 50.98 mm2. However, the amplitude of sample S3 (40.20 mm2) is higher than the others. According to the formulaσ=F/S, the smaller the remaining surface area, the higher the local stress at the rivet hole since the applied load F is the same. Moreover, the magnitude of the stress intensity factor also increased gradually. This also explained why the crack propagated along the taper direction of the test piece. The fatigue life of sample S3 was much lower than that of samples S1 and S2 and was related to the crack growth rate, expressed as follows where σffis the distribution of the normal stress (σff=Eσfεf, E is Young’s modulus, σf and εf are the fracture strength and fracture ductility, respectively), and Kth is the crack propagation threshold value.In this study, the values of the σf, εf, and Kth were the constant of the riveted samples with different countersunk depths. Eq. shows that the larger the stress intensity factor value, the faster the rate of the crack propagation. Due to the largest value of the stress intensity factor of sample S3, the fatigue propagation life of sample S3 was shorter than that of samples S1 and S2.The thickness of the test piece with countersunk hole is divided into two parts: the sinking thickness Cs and the straight shank thickness b are shown in . The plate thickness was t=Cs+b because of the different countersunk depths. The stress around the perimeter of the hole was redistributed (), leading to higher local stress points. The points caused the stress concentration, where the cracks were easily produced. In addition, the stress concentration value can be expressed by the stress concentration factor (Kt). Different isotropic materials with different mechanical properties should not affect the results of the stress concentration factor, and the stress concentration factor is shown in Eq. where σmax is the maximum stress near the geometric discontinuity, and σ0 is the nominal applied stress.The stress concentration factor of this study was quantitatively analyzed from different countersunk angles (φc), the thickness to rivet hole radius ratio (t/r), countersink depth to plate thickness ratio (Cs/t), and rivet hole radius to specimen width ratio (r/w). The general form of the stress concentration factor equation of the present study was similar to that presented by Shivakumar et al. where Kh is the influencing factor of the width of the riveted samples and is mainly related to the radius of the rivet hole (r) and the width (w) of the test piece; Kss is the factor of the thickness of the riveted specimens and is mainly related to the radius of the rivet hole (r) and the thickness (t) of the test piece; Kφc is the factor of the angle of the countersink of the component. The calculation formulas of the Kh, Kss, and Kφc are reported in the literature where KCs is the factor related to the rivet hole radius (r), the thickness (t), the width (w), and the countersunk depth (CS); the i, j, k, d1, and d2 parameters were determined by the multi-parameter fit of the FE results and found as 1.80, 0.10, 1.50, 0.28, and 0.10. The width, thickness, and rivet hole of the samples were 20, 1.50, and 4 mm, respectively. The relevant parameters of the three countersunk depths were incorporated in Eq. . The ratiosKCs2/KCs1and KCs3/KCs1were 1.065 and 1.129, respectively. The subscripts 1, 2, and 3 of the KCS represent the riveted samples with the countersunk depths of 0.65, 0.9, and 1.2 mm, respectively. The results reveal that the amplitude of the stress concentration factor of sample S3 is more than that of samples S1 and S2, and that of samples S1 is almost close to that of sample S2. Since the magnitude of the stress concentration factor of sample S3 is the largest, the crack was easily initiated at the inflection point of the test piece. The increase in the amplitude of the stress concentration factor at the inflection point decreased the crack initiation life.In addition to analyzing the effect of the above parameters on the stress concentration factor, the impact of the rivets on the stress concentration factor at the inflection point of the countersink should also be considered for the riveted specimens. Homan and Jongebreur Kt=γKt,pin+1-γKt,hole,tension+kKt,hole,bendingwhere γ is the percentage of the load transferred from the most dangerous rivet row to the other plates, then (1 − γ) is the percentage of the bypass load, and k is the additional bending factor.Kt,pin, Kt,hole,tension, and Kt,hole,bending depended on the geometry of the riveted joints (rivet diameter/rivet spacing). Due to the same rivet diameter and the rivet spacing, the rivet had slight effect on the stress concentration factor. Thus, this research method of establishing the relationship between the countersink without rivets and the stress concentration factor is reasonable.In conclusion, the effect of different countersunk depths on the fatigue performance of the riveted AA2024-T3 alloy specimens was investigated in detail. The results of this study are as follows:The samples with a countersunk depth of <1 mm (0.65 and 0.90 mm) showed that the difference in the fatigue life is not significant according to the fatigue test results; however, for the samples with depths > 1 mm (1.20 mm), the fatigue life decreased dramatically.The fatigue crack of the riveted specimens always initiated at an end rivet row on the mating surface of the samples, producing stress concentration at the inflection point. The deeper the countersunk depth, the greater the amplitude of the stress concentration factor at the inflection point. At the same applied load, the fatigue crack was prone to initiating at the higher amplitude of the stress concentration factor.The large difference in fatigue life mainly caused by the rate of the fatigue crack growth. The fatigue behavior for the countersunk depth of 1.20 mm was the worst. In addition to the fatigue crack initiation life, the period of fatigue crack propagation was affected by the amplitude of the stress intensity factor. The remaining area of the cross-section for the opening location of the samples varied along the taper direction of the countersink, increasing the amplitude of the stress intensity factor from the crack initiation site to the surface of the samples.Moreover, the magnitudes of the stress intensity factors of the three samples at the crack initiation site were obtained (Kt2/Kt1=1.065, Kt3/Kt1=1.129). Thus, the fatigue performance of the samples with 0.65 and 0.90 mm countersunk depths was better. Furthermore, SEM images showed that the path of fatigue crack propagation was consistent with the previous analysis.The strain gauge measurement showed that the load transmitted by the outer rivet row was higher than that transmitted by the middle row, and this observation is consistent with the equivalent elastic deformation result at the FE analysis rivet joint and also well agreed with the fatigue test results.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Supplementary data to this article can be found online at The following are the Supplementary data to this article:Effect of cold work on the stress corrosion cracking behavior of Alloy 690 in supercritical water environmentThe stress corrosion cracking (SCC) behavior of Alloy 690 with 0, 20% and 30% cold work (CW) was studied in supercritical water (SCW) environment with an emphasis on CW and creep on the CGRs (CGR). SCC and creep CGRs increased with %CW, which correlated hardness very well. Microscopic characterization of the crack tip and fracture surface showed obvious cavity-like features, which is clear evidence of creep attack. The creep CGRs in inert gas were comparable to the SCC CGRs in SCW, indicating that creep is a major factor in crack growth. Increasing level of CW was found to increase the creep susceptibility, and high activation energies for creep crack growth were observed between 500 °C and 550 °C.As one of the most promising candidate materials for supercritical water reactor (SCWR), Alloy 690 has been intensively studied due to its relatively high corrosion and stress corrosion crack (SCC) resistance It has been confirmed by several labs that heavily cold worked (>20%) Alloy 690 materials can exhibit relatively high SCC growth rates in simulated pressurized water reactor (PWR) primary water environment The purpose of the present work is to study the SCC performance of Alloy 690 in SCW environment, and evaluate the effects of CW. Further, it is of great importance to contribute to the database of SCC, and to help to predict the remaining life of components during long term operation in the nuclear industry. Moreover, it is necessary to investigate the underlying processes by experimental studies, thus help to understand the role of CW accelerating SCC.The Alloy 690 (UNS NO6690) plate used in this study was cold forged in the thickness direction at General Electric Global Research Center (GE-GRC). Its chemical composition and mechanical properties are shown in . The final heat treatment was mill annealing (996 °C for 20 min followed by air cooling). 20% and 30% thickness reductions in room temperature air using a hydraulic press forge were performed on the as-received material, and specimens were cut from the as-received, 20% and 30% CW materials. All specimens were tested in the most susceptible S-L orientation. shows the Electron Back-Scattered Diffraction (EBSD) maps and invert pole figures of as-received, 20% CW and 30% CW Alloy 690. All maps were taken at identical magnification to evaluate the CW effect on the microstructure. Homogeneous equiaxed grains were observed for the as-received material in (a,d), while compressed and elongated grains were observed for cold worked materials ((b,c,e,f)). In addition, local banding features comprised of small grains and inclusions were also observed, which might result in higher local residual strains. shows detailed microstructural characterization of as-received and 30% CW Alloy 690, mainly focusing on the features along grain boundaries (GBs). The images were taken by high-resolution scanning electron microscope (SEM) backscatter electron (BSE) imaging under low kV conditions. A semi-continuous distribution of carbide precipitates at GBs along with small isolated TiN particles were observed for the as-received Alloy 690 ((a and b)), as well as for 30% CW Alloy 690 ((c–e)). Even at 30% CW, there is no evidence of cracks or voids along the GBs or near the carbides, as shown in Standard 0.5 T compact-tension (CT) specimens with 12.7 mm thickness were machined in the S-L orientation with 5% side grooves on each side. Crack length was monitored in situ by the reversed direct current potential drop (DCPD) method, in which a fixed current is reversed and a ∼0.100 μV potential is measured across the crack. The change in potential vs time is converted to crack length vs time. In order to decrease the noise of data, about 100–3000 points of valid data were averaged to generate the crack length curve, depending on the crack growth response. The load applied on the CT specimen was adjusted to maintain constant stress intensity factor (K) with a dedicated acquisition and control program. Firstly, the specimen was fatigue pre-cracked to a length of ∼1 mm in room temperature (RT) air. Then crack extension was continued in high temperature water. To transition to an intergranular (IG) SCC crack, the load ratio (R) was increased to 0.7, followed by decreasing frequency from 0.1 Hz to 0.01 Hz, then to 0.001 Hz. A hold time of 1000s–20000s was introduced to transition from transgranular (TG) to IG cracking before switching to fully constant K test conditions. During transitioning and SCC testing, constant K = 25 MPa√m was used. A detailed description of the experimental setup can be found in Ref. After the SCC test in SCW environment, the specimen was unloaded, and the pressure was reduced to atmospheric pressure with the temperature unchanged. Then pure argon (wt. > 99.999%) was flowed into the autoclave for more than 10 h to remove water vapor to create an inert gas environment. During this unloaded period, the DCPD measurement was also paused, so no data was recorded in the crack growth figures. Then the specimen was reloaded to the same constant K (25 MPa√m) to study creep crack growth behavior. In this way, the SCC and the creep CGRs were evaluated on the same specimen at the same temperature. After the test, the crack path and fracture appearance were examined using SEM and EBSD. The crack length for each specimen was also identified by destructive evaluation, and was compared with the DCPD measurement. Usually, the error was within 10%, and both K and crack length were corrected by linear method.Three specimens were tested in this study, including as-received, 20% CW and 30% CW specimen in SCW environment and inert gas environment at 500 °C and 550 °C. SCC and creep CGRs of as-received, 20% CW and 30% CW specimen were used to evaluate the CW effect, and creep CGRs were measured at 500 °C and 550 °C to study the effect of temperature on creep. show both SCC and creep crack growth responses with “on the fly” changes in SCW environment for as-received, 20% CW and 30% CW specimens. CGRs for each testing condition are marked on the curves and summarized in , the SCC CGR was 8.3 × 10−9 mm/s at 550 °C in SCW. The subsequent creep CGR in Ar gas was 8.6 × 10−9 mm/s at the same temperature, which is almost the same as the SCC CGR, indicating that creep dominates the overall growth. Then the temperature decreased to 500 °C and the creep CGR dropped significantly to 4.3 × 10−10 mm/s. shows a similar response for the 20% CW specimen. The SCC CGR was 3.0 × 10−6 mm/s at 550 °C, and creep CGRs were 1.6 × 10−6 mm/s at 550 °C and 1.0 × 10−7 mm/s at 500 °C. For the 30% CW specimen in , the SCC CGR was 5.9 × 10−5 mm/s at 550 °C, and the creep CGRs were 5.1 × 10−6 mm/s and 4.7 × 10−5 mm/s at 500 °C and 550 °C, respectively.A summary of obtained SCC and creep CGRs as a function of %CW is shown in . The results showed that both SCC and creep CGRs increased with CW level, and creep CGRs were comparable to the SCC CGRs at 550 °C for all the specimens. It can be concluded that creep crack growth is responsible for most of the crack growth of Alloy 690 in SCW, regardless of the CW level. In addition, the creep CGRs dropped significantly (>10 times lower) when the temperature decreased from 550 °C to 500 °C, indicating that the temperature has a large influence on the crack growth behavior.It is well known that CW will increase the yield strength (YS) and hardness of materials. The Vickers hardness (HV) was measured for as-received, 20% CW and 30% CW Alloy 690 specimens on three orientations of microstructure, as shown in (a). The top plane is the cracking plane - the S-L orientation for all specimens. For hardness measurements, a 1000 g-force was applied for 10 s, and the HV was calculated in units of kg/mm2. At least three individual values at different locations were measured on the same surface to obtain an averaged value. The correlation between HV and CW level is shown in (b). The hardness increases in a linear fashion with the %CW.CW will introduce residual strains inside the materials, and the EBSD permits measurement of residual strains on a very fine scale highlights the localized regions of kernel average misorientation (KAM) or plastic strain of the as-received, 20% and 30% CW Alloy 690. All the maps were taken at an identical magnification and scaled to a maximum of 5° average misorientation at a particular point. (d) showed only slightly strain (bright green contrast) near GBs for as-received Alloy 690, while (b) shows more severe and continuous strain near GBs for 20% CW Alloy 690. Moreover, much higher strains were observed for 30% CW Alloy 690 in (c). These results reveal that CW introduced local residual strains in the material, especially near GBs. In addition, a higher level of CW results in more severe residual strains in the material, which is responsible for the accelerating effect of CW on CGRs. shows the localized regions of KAM (or plastic strain) near the crack tip of the 20% CW and 30% CW Alloy 690 specimens. It is obvious that the SCC/creep cracking are all IG and propagate along the GBs where the KAM values are high. The high KAM values are due to CW induced strain prior to the crack propagation as shown in , and also due to the plasticity from the cracking itself. It is reasonable to assume that the IG crack tip strain field was enhanced by the high local residual strain near the GBs during crack propagation, resulting in a steep strain gradient (strain rate) at the crack tip. Various investigators The SEM-BSE images of SCC and creep crack tips for all the specimens are displayed in , there were two branched crack tips as shown in (a), and cavity-like features were identified between the semi-continuous IG carbides along the GBs as shown in (d–f). These cavities were located not only ahead of the crack tip ((d) and (e)), but also away from the crack sides ((f)). Similar cavities were also observed for 20% and 30% CW specimens as shown in shows that there were no cavities or void-like defects in the GBs or near the IG carbides in the untested material, even for 30% CW Alloy 690. Thus, these observed cavities in were formed during the creep tests in high temperature environment, but not induced during the CW process.Similar cavity-like features were also identified on the fracture surfaces in each specimen, as shown in . Although covered with oxides, the fracture surfaces and secondary cracks are clearly intergranular. Moreover, discontinuous cavities along the secondary cracks of the fracture surfaces were observed as shown in . These cavity morphologies on the fracture surfaces were consistent with the crack tip observations in . There is no doubt that all these IG cavities are evidence of creep during crack growth, indicating that creep plays an important role in the crack propagation in SCW.It is well known that the SCC growth rate increases with the yield strength, particularly when induced by CW show a clear correlation between CGRs and the degree of CW for Alloy 690. However, the level of CW only represents the total deformation in the materials, and does not provide any information on the homogeneity of CW, or microstructural and mechanical changes. It is believed that CW mainly influences the YS and introduces residual strain that may be concentrated near the GBs.It is commonly accepted that the crack tip strain rate is a key parameter in SCC growth confirm that CW enhances the strain in the materials, especially near the GBs. In addition, the crack tends to propagate along GBs which have high residual strains as shown in . Thus, it is reasonable to assume that the enhanced residual strains, especially near GBs, induced by CW account for the higher CGRs in highly cold worked specimens. To quantitatively evaluate the strain field at the crack tip and its associated effect on crack growth behavior, the crack tip strain rate was calculated for different % CW specimens as follows.The plastic crack tip strain equation for a growing crack in a work hardening material was analytically derived by Gao and Hwang for plane strain conditions where εCT is the crack tip strain, β is constant (typically 5.45, as determined by Rice et al. The σy and E has been measured at room temperature for as-received, 20% CW and 30% CW Alloy 690 as shown in , and a factor of 0.7 is utilized to estimate the yield strength and elastic modulus at 550 °C vs 25 °C.ε˙CT=βσyE(nn−1)(2KdKdt+1rdadt)[ln(λK2rσy2)]1n−1where ε˙CT is the crack tip strain rate. As a result, the crack tip strain rates of as-received, 20% and 30% CW Alloy 690 specimens at 550 °C were calculated by Equation . All specimens showed that the crack tip strain rate was much higher near the crack tip, and decreased to lower value as the distance from crack tip increased. It is obvious that the crack tip strain rate was enhanced by ∼10 times for 20% CW specimen, and more than 100 times for 30% CW specimen compared to as-received specimen. It is reasonable to believe that the enhanced crack tip strain rate was mainly attributed to the enhanced KAM/strain near the GBs induced by CW. shows the SCC and creep CGRs at 550 °C as a function of cold work, hardness and the crack tip strain rate at 30 μm ahead of crack tip. It is obvious that the SCC and creep CGRs increases with %CW, hardness as well as crack tip strain rate, and linear relationship between In(da/dt), hardness and In(ε˙CT) is observed. Since cold work represents the strain within materials and increases the hardness, the hardness and crack tip strain rate correlations are the microstructural factors that appear to account for the increased SCC and creep CGRs. Similar correlations between SCC growth rates and the degree of cold work for more than 10 heats of alloy 690 with 0–32% CW were also observed by Toloczko and Bruemmer The creep CGRs were only slightly lower than the SCC growth rates of Alloy 690 specimens at 550 °C regardless of the CW level as shown in , indicating that creep represented almost all of the total crack growth, and high temperature supercritical water seems to have little effect. In 1971, Lee and Vermilyea showed cavity features near the crack tips and on the fracture surfaces, the clear evidence of creep crack. Arioka , the plastic crack tip strain rate increases with %CW, and large amounts of cavities were found near the crack tip as shown in The creep CGRs were also measured at 500 °C and 550 °C in an Ar environment for as-received, 20% and 30% CW Alloy 690. The activation energy () was 317 kJ/mol for the as-received specimen, 293 kJ/mol for the 20% CW specimen and 235 kJ/mol for the 30% CW specimen between 500 °C and 550 °C. Arioka The SCC growth behavior of Alloy 690 in SCW environment was studied with different degrees of CW. The effect of CW on the hardness and strain distribution of the material was characterized. The crack tip and fracture surface were examined to investigate the creep contribution to crack growth. Based on the experimental results and analysis, the following conclusions can be drawn.Microstructure and EBSD observations confirm high strain distributions, especially along GBs for cold worked Alloy 690. The SCC and creep CGRs were found to increase with %CW, hardness and calculated crack tip strain rate. The hardness and crack tip strain rate were somewhat better parameters than the applied CW level to correlate CGR.Characterization of the crack path and fracture surface revealed large amount of cavity-like features, especially near the grain boundary carbides, which is clear evidence of creep attack. These cavities were considered to be formed by the accumulation of vacancies induced by CW under the applied loads.Increasing level of CW was found to increase the creep susceptibility in SCW. Creep CGRs were comparable to the SCC growth rates at identical temperature regardless of %CW, indicating that the creep is the major contribution to the overall crack growth in SCW environment.Mechanical properties of elytra from Tribolium castaneum wild-type and body color mutant strains▶ Mechanical analysis distinguishes among elytra of Tribolium castaneum color mutants. ▶ Frequency sweep power law exponent differs for black color mutant from all others. ▶ Data suggests black elytra have β-alanine-deficient and dopamine-abundant metabolism. ▶ Greater melanin production occurs at the expense of cuticular protein cross-linking.Cuticle tanning in insects involves simultaneous cuticular pigmentation and hardening or sclerotization. The dynamic mechanical properties of the highly modified and cuticle-rich forewings (elytra) from Tribolium castaneum (red flour beetle) wild-type and body color mutant strains were investigated to relate body coloration and elytral mechanical properties. There was no statistically significant variation in the storage modulus E′ among the elytra from jet, cola, sooty and black mutants or between the mutants and the wild-type GA-1 strain: E′ averaged 5.1 ± 0.6 GPa regardless of body color. E′ is a power law function of oscillation frequency for all types. The power law exponent, n, averaged 0.032 ± 0.001 for elytra from all genotypes except black; this small value indicated that the elytra are cross-linked. Black elytra, however, displayed a significantly larger n of 0.047 ± 0.004 and an increased loss tangent (tan |
δ), suggesting that metabolic differences in the black mutant strain result in elytra that are less cross-linked and more pigmented than the other types. These results are consistent with the hypothesis that black elytra have a β-alanine-deficient and dopamine-abundant metabolism, leading to greater melanin (black pigment) production, probably at the expense of cross-linking of cuticular proteins mediated by N-β-alanyldopamine quinone.Tanning is a complex process that involves hardening (sclerotization) and pigmentation or coloration of insect cuticle (). Changes in mechanical properties and coloration of the exoskeleton are governed primarily by interactions between cuticular proteins and oxidized catechols (). Notably, the resulting cuticle may be quite variable in color and/or stiffness depending on the species, phenotype, body region and chemical composition. There are different measures of material ‘stiffness’, but the Young's modulus (proportionality between stress and strain when Hooke's Law holds) is the most commonly used. Young's moduli of different cuticles can vary by more than two orders of magnitude at nearly constant density, a wider range than for any other common class of materials, whether biological or synthetic (). Cuticle can be soft and elastic, as in the case of a beetle's dorsal abdominal cuticle, which can have a Young's modulus of only 62 MPa but a fracture strain of 20% (). However, a cuticular structure can also be very rigid, as in the case for a load-bearing grasshopper mandible, which has an elastic modulus measured by nanoindentation as high as 15,000 MPa (Cuticle pigmentation may range from almost transparent and colorless to opaque and black (). In the red flour beetle, Tribolium castaneum, a range of brown to black naturally occurring phenotypes has been reported (). The beetle's color is believed to be derived from the particular combination of brown and black pigments. The black pigments are melanins formed from polymerization reactions of oxidized catecholamines. The reactions are initiated by oxidation of dopamine to its quinone (). Significantly, the melanin pathway may be blocked by N-acylation of dopamine with acetate or β-alanine (). In this case, the N-acyl derivatives N-acetyldopamine (NADA) and N-β-alanyldopamine (NBAD) become precursors of quinone tanning agents (). The N-acylated precursors can lead to the production of brown pigments. Hence, it is theorized that N-acylation and oxidative enzyme activities in vivo control the relative production of brown and melanic pigments, and that this balance determines the body color phenotypes of insects such as T. castaneum (The body color of insects has been implicated in sexual selection (), but coloration is also linked to survival. For example, increased melanization has been shown to increase the resistance of Drosophila strains to dehydration (). As a model tissue for use in the study of a relationship between color and mechanical properties, we have chosen the elytra or modified forewings of the red flour beetle, T. castaneum. These composite dorsal appendages are cuticle-rich, serve as body covers to protect beetles against mechanical stress and dehydration, and are inherently important to insect viability, helping beetles to adapt to a variety of environments and stresses (). However, with the exception of basic puncture tests (), the mechanical properties of elytra from Tribolium wild-type strains and color body mutants remain unexplored. Since pigmentation and protein modification reactions share common enzymes and organic precursors (), we hypothesized that coloration changes may also indicate differences in cuticle mechanical properties. Thus the dynamic mechanical properties of elytra from several Tribolium body color phenotypes were determined for comparison with those of elytra from the GA1 wild-type strain. Dynamic mechanical analysis (DMA) can distinguish between elastic and viscous contributions to deformation resistance and thus can be utilized to evaluate the extent of cross-linking among the color phenotypes (). Hence, we hypothesize that DMA can help to establish correlations between a sample's mechanical properties and the extent of protein cross-linking and pigment production.Elytra from T. castaneum wild-type (GA1 strain) and naturally occurring body color mutant strains jet, cola, sooty and black () were used in the experiments. Insects were reared at the USDA-ARS Center for Grain and Animal Health Research in Manhattan, KS, under standard conditions on a diet of organic wheat flour fortified with 5% brewer's yeast. Pupae were shipped overnight in capped vials to the University of Kansas, where they were allowed to ecdyse and mature into adults. Adults 7–10 days post-eclosion were considered to be fully tanned and were subsequently sacrificed and tested as noted below.A TA Instruments RSAIII dynamic mechanical analyzer was used to perform all of the mechanical measurements. The instrument utilizes a direct-drive linear motor to apply a strain and a force transducer to measure the resulting force (). This combination accounts for the high force resolution of the instrument, down to 10−4 |
N, and a strain resolution down to 1 nm, capabilities which enabled acquisition of reproducible results on these small specimens. A frequency range of 0.1–600 rad/s was used for dynamic mechanical analysis.Prior to mechanical testing, the beetles were immobilized by chilling at −20 °C for 30 min (no significant differences were seen in comparison to removal of elytra from live insects). Elytra were removed with tweezers, allowed to equilibrate with the lab atmosphere for 10 h and tested. The specimens were then mounted with epoxy to strips of hard plastic that were clamped in the instrument grips. Devcon 1.5-Ton quick-setting epoxy cement was allowed to dry for 1 h prior to testing; fixing such samples without damage was confirmed optically and by reproducibility of results. The epoxy and plastic strips were confirmed to be stiff enough not to compromise results by comparison with results obtained from mounting and testing in a comparable fashion both plastic and aluminum strips of known properties. The elytra were tested whole, without being cut into a particular test shape beforehand to avoid introducing sample defects. Geometric uniformity was maintained by clamping such that a rectangular portion of the elytron remained between the grips.Once the samples were mounted, the mechanical properties were determined via both dynamic strain and frequency sweeps (). The strain-independent linear viscoelastic region determined by strain sweeps was maintained past a strain of 0.1% for all sample types tested; thus, a strain of 0.1% was used for all frequency sweep experiments. Frequency sweeps were performed from 0.1 to 600 rad/s to measure the storage (or elastic) modulus E′, the loss (or viscous) modulus E″ and the ratio E″/E′, also known as the loss tangent, tan |
δ. The variation of the storage modulus E′ with strain wave oscillation frequency ω was fit to the power law model E′ ∼ |
ωn (r2 |
> 0.95) between 10 and 100 rad/s (The modulus calculations used an engineering or nominal stress based on the initial cross-sectional area of the sample, approximated as the product of the elytra's centerline width measured by calipers (found to vary only by ±20%) and its centerline thickness that was measured under an optical microscope with a digital filar micrometer. These dimensions were confirmed in comparison to SEM measurements in the case of the wild-type strain (). It was not feasible to measure the exact dimension of each sample tested, so the average cross-sectional area of a population was used in the stress calculations.The Tribolium body color phenotypes examined in this study are shown in , where the color mutants are displayed from lightest to darkest with the wild-type appearing lightest and most reddish-brown. An elytron from the wild-type strain is not a homogeneous structure. It consists of both thick dorsal and thinner ventral cuticular layers that are connected by small beam-like structures called trabeculae, with the tracheae positioned between the two layers (; Arakane et al., unpublished data). Furthermore, there are several ribs that run in parallel along the length of the dorsal side of the elytron, and also shallow circular cavities containing setae on the dorsal surface (). Elytra from the body color mutants, when examined individually via light microscopy, exhibit the same morphology, differing only in the degree of pigmentation as shown in Dynamic mechanical experiments were done to determine the storage modulus E′ and the loss modulus E″ as a function of oscillation frequency and strain. E′ is a measure of the elastically recoverable deformation energy and hence is also known as the (dynamic) elastic modulus. In contrast, E″ is a measure of viscous energy dissipation (dampening) and hence is also known as the viscous modulus. The ratio E″/E′ is known as the “loss tangent” or simply tan |
δ, where δ is the phase angle between sinusoidally applied stress and strain. For materials such as the elytra where E′ ≫ |
E″, E′ is approximately equal to the Young's modulus obtained from the slope of simple stress–strain measurements at the same strain rate (). Hence, E′ is a measure of the stiffness of the elytra.The storage moduli at a reference frequency of 1 Hz (6.28 rad/s) for the variously colored elytra are listed in . The values vary from 4.4 to 5.8 GPa, which are values comparable to those of synthetic plastics like polystyrene (). Within the 95% confidence intervals, there is no significant variation in E′ among the differently colored elytra. The storage modulus for an individual elytron varied between 3 and 8 GPa with the 95% confidence intervals about 30% of the mean values. Most of this measured variability is attributed to small differences in hydration levels and sample geometry as opposed to inherent differences in actual material properties among individual specimens.The variation of the storage modulus of the elytra with oscillation frequency at a strain of 0.1% was also determined. Representative frequency sweeps obtained by dynamic mechanical testing of elytra from different color mutant strains are shown in . The storage modulus E′ shows marked dependence on oscillation frequency at frequencies below ∼1 and above ∼200 rad/s. However, over the bulk of the frequency range tested, E′ displays only a weak power law dependence on oscillation frequency. The exponent of this power law dependence is an indicator of the extent of cross-linking within a sample (). Although there are slight differences in the magnitude of E′ for reasons noted above, all of the elytra from the color mutant strains clearly have a similar frequency dependence as elytra from the wild-type strain with the exception of the black specimens, whose sweep crosses over those of sooty and cola. The characteristic frequency exponents, n, for the Tribolium wild-type and color mutant elytra are summarized in . Wild-type and color mutant elytra all display statistically indistinguishable frequency exponents of about 0.030, with the exception of black. Black elytra exhibit a much more pronounced frequency dependence, indicated by an n value of 0.047 ± 0.004.During the frequency sweeps, the loss moduli and tan |
δ were also measured. Representative tan |
δ curves as a function of frequency are shown in and the mean values of tan |
δ at 1 Hz are given in . Values of tan |
δ are less variable than either E′ or E″. This result indicates that the major contributor to uncertainty in E′ and E″ is the measurement of the cross-sectional area (and the fact that the cross-sectional area is not perfectly rectangular). This conclusion is drawn because tan |
δ is a ratio in which the cross-sectional areas cancel out, and hence it is independent of sample dimension measurement unlike the moduli. The data also suggest that variability in hydration was not a significant problem, as this would also have affected the magnitude of tan |
δ.The black elytron has a significantly larger tan |
δ across the recorded frequency range than that of any of the other color variants. At the representative frequency of 1 Hz, the black elytron displays a distinct tan |
δ of 0.151 ± 0.006, nearly twice that of the elytra from sooty, jet or cola. The latter three color mutant elytra exhibit a tan |
δ statistically indistinguishable from each other and from the wild-type, ranging from 0.073 to 0.086. The greater viscous dampening of the black elytron relative to the others, as demonstrated by a greater tan |
δ, is consistent with its greater power law frequency exponent n.The cuticular tanning process involves simultaneous pigmentation, cuticular protein cross-linking and dehydration. Pigmentation polymers () and cross-links have demonstrated potential to modulate the physical properties of biological materials (). DMA provides a direct measure of fundamental material mechanical properties known and understood for many types of materials, which is an advantage over tests such as puncture resistance that may not yield parameters easily correlated with other types of mechanical tests. Since DMA tests impart only small strains and stresses, irreproducibility due to variability in sample preparation, mounting and testing is minimized. Furthermore, two important parameters, tan |
δ and the E′ frequency exponent n, obtained from DMA are independent of dimensional measurement and thus can be determined with a high level of accuracy. The value of n is a highly reproducible parameter, much more so than the E′ modulus itself, which depends on an accurate measurement of a sample's dimensions. The variability observed in n is under 10%, whereas that in E′ is close to 50%. tan |
δ is also highly reproducible. Although n varies with frequency, a single value of n is found to fit one decade or more of frequencies with an r2 value of >0.98.The first significant result reported here was that the stiffness of the Tribolium elytron as quantified by the storage modulus E′ is independent of pigmentation. It may be that Tribolium adults need to have a value of E′ of several gigapascals to survive and that mutations that reduce the stiffness notably produce adults that are less viable. This is an observation consistent with our work on the manipulation of enzymatic pathways in Tribolium by RNA interference. When the cuticle does not notably tan, the insects do not survive to maturity (The frequency sweep experiments on fully tanned wild-type and color mutant Tribolium elytra yield both the storage (E′) and the loss (E″) moduli as a function of the imposed oscillation stress frequency (ω). The dependence of these moduli, as well as their ratio (tan |
δ), in polymeric materials is in general a function of the relaxation modes available to the constitutive polymeric chains (). The storage modulus (E′) for an entangled but uncross-linked polymeric material is expected to increase notably with frequency, while E′ is expected to become frequency-independent for a well cross-linked material at frequencies below ∼100 rad/s (). Experimentally, the storage modulus of lightly cross-linked biopolymers is observed to have a weak power law frequency dependence with a frequency exponent n about ∼0.1–0.3. The frequency exponent n decreases with increased cross-linking, which inhibits polymer relaxation in this frequency range (). For alginate gels, n decreases from 0.94 to 0.01 as the cross-linking is increased. Hence, the small values of n observed for all elytral samples are consistent with those of cross-linked materials.The E′ frequency dependence of the color mutant elytra, with the notable exception of that of black, was found to be indistinguishable from that of the wild-type elytra. In contrast, the black elytral frequency exponent is over 50% greater than that of the wild-type. This result is consistent with the interpretation that black elytra have an overabundance of melanic pigments that may not be cross-linked but that have relatively high molecular weights, and that these melanic pigments are produced at the expense of cuticular protein cross-linking mediated through NBAD quinone. This conclusion is further supported by the observed E″/E′ ratio for the elytra. This ratio, tan |
δ, decreases with frequency, indicating that viscous effects become increasingly significant at the lower end of the frequency range tested. In this range, entangled but uncross-linked polymeric chains are able to flow past each other at sufficiently long time scales, which is observed as softening, whereas cross-links limit such motion. Furthermore, uncross-linked materials exhibit a relatively high viscous dissipation and hence a higher tan |
δ throughout the frequency range. Cross-linking reduces the magnitude of tan |
δ and hence tan |
δ can be used as an indicator of the molecular interconnectivity in polymeric materials (). The tan |
δ of the black elytron was determined to be over 80% greater than that of the wild-type, cola, sooty or jet elytron. This result is indicative of the higher dampening ability of the black elytron and leads to the conclusion that cuticle in the black elytron is less cross-linked than that in the wild-type even though both elytra exhibit the same degree of stiffness (E′). However, the relative importance of pigmentation and cross-linking to the magnitude of E′ is not specifically established. This analysis also does not directly distinguish between physical cross-linking and covalent cross-linking. In other work, however, we argue that these dynamic mechanical results are best interpreted in terms of the catechol oxidation processes (Thus, dynamic mechanical analysis demonstrates that the black elytron is distinctly different from those of the other color mutants. Assuming that cuticle pigmentation and protein cross-linking are a direct result of catechol oxidation reactions, these results support the hypothesis that the black strain synthesizes catecholic metabolites that produce uncross-linked, high molecular weight melanic pigments at the expense of protein cross-links. It is possible that dopaminequinone, indole quinones and other short indole quinone polymers produced by the oxidation of dopamine during cuticle tanning may also cross-link cuticular proteins, although much less efficiently than the reactive quinones produced from N-acetyldopamine or N-β-alanyldopamine. The other color mutations, on the other hand, have no significant effect on the mechanical or structural properties of the elytra. This indicates that the body color variations of cola, jet and sooty could be a matter of degree rather than of kind. Such distinctions could not be drawn based on observation of the coloration alone and demonstrates the value of DMA toward understanding differences in the metabolic pathways of these species variations. The pigmentation chemistry of the black mutant, however, is more extensive relative to that in the other color mutants and diminishes the cross-linking chemistry in the former.In summary, while the jet, sooty and cola Tribolium body color mutant elytra were found to be mechanically identical to the wild-type, the black elytron was found to be unique. Dynamic mechanical analysis showed that the black elytron, while being comparable in stiffness, has a greater degree of viscous energy dissipation. The increased frequency dependence of the storage modulus and tan |
δ both suggest that the black body color mutation leads to a cuticle that is less cross-linked. This mechanical behavior suggests that the natural production of melanin pigments within the elytron comes at the expense of cuticular protein cross-linking. Like black, the sooty mutation can be rescued by injection of β-alanine (). However, the exact genetic and biochemical basis of the jet, sooty and cola body color variants is unknown. The fact that their tan |
δ values resemble wild-type rather than black might indicate that there are alternative independent pathways that can lead to a black body pigmentation. Alternatively, it may be that incomplete suppression of β-alanine production is sufficient to promote a noticeable darkening of the cuticle, whereas compete suppression of this pathway might be required before an effect on the dynamic mechanical properties becomes measurable. The black mutation used in this work is known to be deficient of aspartate-1-decarboxlyase transcripts (Hence, DMA has shown that the elytra of the black strain are structurally different from those of the other color mutants or the wild-type strain. Further work on the black elytron may be valuable in determining the genes necessary for cuticle pigmentation and/or sclerotization as well as in deconvoluting the reactions responsible for cuticular color changes from those responsible for cuticle hardening. Previously, NMR spectroscopic data were presented that was consistent with melanin and β-alanine being more abundant in the black and wild-type strains, respectively (). We have more recently reported that the black phenotype results from a deficiency in β-alanine, due to a low expression of aspartate-1-decarboxylase and an increased amount of dopamine that is oxidized to produce melanin (More generally, this work demonstrates the utility of dynamic mechanical analysis for probing the structure of biological composites such as the insect elytron. Certain parameters of such analysis such as the frequency exponent n and tan |
δ show great reproducibility and sensitivity to material structural changes as they do not depend upon the accuracy of sample dimension measurements. Further application of DMA to natural and engineered tissues such as the cuticle phenotypes examined in this study will be useful in establishing structure–function relationships within other important biopolymer composites.Analysis of a beam-column system under varying axial forces of elliptic type: the exact solution of Lamé’s equationWe investigate the dynamical response of a beam-column system with hinged ends subjected to an axial pulsating force of elliptic type. It is shown that the resulting equation is of the form. In this paper, we obtain the general exact solution of this equation that reveals stable behavior of the beam-column system if the assigned initial conditions are of the form y1(0)=y10 and . It is also found that at a certain value of the modulus of the elliptic force, the lateral vibrational frequency is independent of the material properties of the beam-column system.In this paper we investigate the main physical characteristics of an elastic hinged beam-column system subjected to a pulsating load of elliptic type. It is well-known that an elastic beam-column with hinged ends can be put into stable equilibrium by applying pulsating loads at the proper driving frequency (). If the pulsating load is of the sine or cosine type, then the resulting governing equation of motion reduces to the well-known Mathieu equation whose exact solution is not known and hence, numerical schemes or perturbation techniques are used to obtain an approximate solution (However, when the pulsating load is given as a function of Jacobian elliptic functions, the resulting Lamé equation has an exact solution. In this paper, we study the main characteristics of the behavior of a hinged beam-column under the action of this type of pulsating loads.An elastic uniform beam-column with hinged ends and length L subjected to the action of a compressive varying axial force is shown in where P is a compressive stationary force and is a periodically varying force with driving frequency ) that the differential equation that describes the lateral deflection w(x,t) of the beam-column system is given byIn this equation E is the Young’s modulus, I is the area moment of inertia of the cross section, t is the running time, and m represents the mass of the column per unit length. The boundary conditions are those corresponding to the case of a hinged beam-column i.e., the lateral deflection w(x,t) and the bending moment M=EI(∂2w/∂x2) are both zero at x=0 and x=L. Therefore, the boundary conditions for These boundary conditions can be satisfied by taking for the lateral deflection w(x,t) a solution in the form of a Fourier series:If only the first mode of vibration of the beam-column system is considered, then To obtain a non-trivial solution of Eq. which represents the governing equation of motion of the beam-column system with hinged ends. Note that the frequency of the lateral vibration of the beam-column without axial load is given byRecalling that the Euler load for this beam-column is given by Pe=π2EI/L2 and introducing Eq. reduces to the case of lateral vibration of a beam-column with static load P. In this case, Eq. represents the dimensionless frequency of lateral vibrations. Note that if P<Pe then the beam-column system has a simple harmonic response that remains stable. When P reaches the value of the Euler load, the lateral frequency becomes zero. Under this load there will no longer be any vibration, and the beam-column is in equilibrium in a slightly deflected form. The case for which P>Pe produces an exponential type solution of Eq. that increases with time. Hence the motion of the beam-column system is unstable.Next, we shall study the solution of Eq. and the response of the beam-column system when Assuming certain periodic functions for can be solved exactly. These functions that provide exact solutions for are known as Jacobian elliptic functions; i.e. the Jacobian elliptic function cn(τ,k2) and sn(τ,k2) that have a period in τ equal to 4K(k2), where K(k2) is the complete elliptic integral of the first kind for the modulus k (). Also, the Jacobian elliptic function dn(τ,k2) has a period in τ equal to 2K(k2). Now, let us investigate the behavior of the beam-column system assuming a periodic driving function where a is the magnitude of the driving force. To make the Jacobian elliptic function ), the relation between the modulus k and the driving frequency Notice that when k→1, the driving frequency , and using the dimensionless time τ, givesThe initial conditions are assumed to bewith appropriate initial conditions. Eq. is a special form of the well-known Lamé equation. This is a second-order linear ordinary differential equation whose exact solution must have two linearly independent solutions. We assumed here that one of these linearly independent solution is of the form: holds for all τ if and only if each coefficient vanishes, i.e. provided that can be used to find the second linearly independent solution (see ). The idea is to look for a second solution of the formin which v is a nonconstant function of τ given bywhere E(ψ,k2) represents the incomplete elliptic intergral of the second kind and ψ=am(τ,k2) is called the amplitude. Substitution of Eq. provides the second linearly independent solutionThus, the general exact solution of Lamé’s equation becomeswhere C1 and C2 are integration constants that can be determined from the assigned initial conditions. For instance, if the initial conditions are assumed to be given by y(0)=1 and grows without bounds as time τ increases and hence, the beam-column system has unstable behavior no matter what values are chosen for a, P, and k that satisfy relations . But if we choose the initial conditions to be given by y(0)=1 and , the integration constants become C1=1 and C2=0 and hence the exact solution of Lamé’s equation becomes bounded for all time τ. Recalling Eqs. and if the value of the modulus k, or d2, is given then we can find d1 and d2, or k and d1, and then the values of a and P, from , for stable beam-column behaviour. Note that for all values of d1 and d2 obtained from Eqs. where it can be seen that these curves intersect at the value of shows the plots of d1 and d2 versus the modulus of the Jacobian elliptic function k. Note that d1 and d2 intersect at k=1/2., it is possible to obtain the relation between the Euler load Pe and the axial forces a and P: that the driving force a is in tension as long as , |a+P|>Pe. In this case, small oscillations of the beam-column system in the neighborhood of its undeflected position are stable. When the ratio approaches the resonance condition of the beam-column system, the ratio Pe/(a+P) becomes indeterminately large. This corresponds to the case for which the magnitude of the tension driving force a becomes close to the value of the compressive stationary force P. For any further increase in the frequency ratio , the magnitude of the ratio Pe/(a+P) approaches asymptotically to the value of one. Thus, the magnitude of (a+P) that is acting on the beam becomes close to the magnitude of the Euler load Pe., the value of the lateral vibrational frequency of the beam-column system is found to be ω0=0.3794 rad/s in which Eq. has been used. Note that the value of ω0 is independent of the elastic material properties of the beam-column system. Therefore, the following can be concluded:The value ofω0=0.3794 rad/s represents a universal constant frequency of the lateral vibration of a hinged beam-column system, valid for any elastic material for which the Euler loadPeand the absolute value of the pulsating loadaare equal. Substitution of this value into Eq. , gives the relation for which the pulsating and Euler loads are equalThe above equation shows that the load is independent of the Young’s modulus and therefore, the following can be concluded:The universal loadPeu, for which |a|=Pe, valid for any kind of elastic material and given bydepends only on the massmand the lengthLof the beam-column system. contains only three parameters, to say k, d1, and d2. The parameter k represents the modulus of the jacobian elliptic function cn and it is related to the driving frequency . The parameter d1 is related to the static load P while d2 depends on the magnitude of the driving force a. It is well-known that for arbitrary values of these parameters that do not follow relations is an equation with periodic coefficients, we may determine the stability–instability chart by using numerical integration in conjunction with Floquet theory ( shows a typical stability–instability chart for the Lamés equation for the value of k=1/2. The shaded (unshaded) regions of the chart indicate values of d1 and d2 for which the solutions are stable (unstable). This stability–instability chart is similar to the one obtained by with the difference that they plotted it for the value of , we may obtain a relation between the driving force a and the Euler load Pe: that in some regions of the stability–instability chart the value of the driving force a is bigger than the Euler load Pe. For instance, if we take the value of P=0 and if we pick the value of d1=−1 and the value of d2=2 and in accordance with , the driving force is twice that of the Euler load without producing lateral buckling in the beam-column system. Similar conclusion can be drawn if we take the values of P=5/9Pe, d1=−2, and d2=9. Thus, there exist set of values of d1, d2, and P for which a>Pe without causing buckling in the beam-column system.Finally, if the the driving forces are replaced by either also has exact solution. We shall describe this procedure in future work.The effects of applying an axial force of elliptic type to a hinged beam-column system have been studied. It was shown that under these type of loads, Lamé’s equation has a closed-form solution. Special focus was given for describing the dynamical response of the system by using the obtained closed-form solution. It was observed that when , the absolute value of the magnitude of the axial loads is larger than the Euler load without producing lateral deflection on the beam-column system. At the frequency ratio value of for which k=1/2, we found that the value of the lateral vibration frequency of the beam-column system is independent of the material properties and that the absolute value of the pulsating load is equal to the Euler load.It was also shown that for certain set of values of the parameters d1, d2, and P, the driving force a is bigger than the Euler load without producing lateral buckling in the beam-column system.Competing failure mechanisms in metal matrix composites and their effects on fracture toughnessDevelopment of high performance Metal Matrix Composites (MMCs) requires careful microstructure design which can improve material's fracture toughness while maintaining high strength. Microstructure and constituent properties combine to determine the overall fracture toughness of MMCs through the activation of different deformation and failure mechanisms. Although the effects of key microstructural attributes on the fracture toughness of MMCs have been discussed in previous studies, their effects on the interplay between plastic deformation and crack formation, as well as their effects on the competing failure mechanisms have not been systematically studied. In this paper, an integrated experimental and analytical framework is presented to evaluate the fracture toughness of MMCs through an assessment of energy contributions in terms of plastic deformation and crack surface formation in the matrix, reinforcement particles and interface. J-integral is calculated through displacement field measurement using Digital Image Correlation method. The competition of different failure mechanisms and their relations with material deformation are quantified through an analytical model by considering the effects of reinforcement volume fraction, interfacial property and yield stress of the matrix. Calculations carried out concern 6092Al/SiCp, but the overall approach applies to other MMCs as well. Results from this work indicate that interface debonding is a beneficial failure mechanism for fracture toughness enhancement of MMCs. It not only increases the surface energy dissipation by creating tortuous crack paths, but also promotes plastic deformation in the ductile matrix which largely contributes to the toughening of MMCs. The activation of interface debonding primarily depends on the volume fraction of SiCp, the yield stress of Al and the interface bonding energy.Dimensionless constant in Ramberg–Osgood equationshear modulus of matrix and reinforcementmaterial parameter as function of elastic properties of reinforcement and matrixmaximum internal stress of reinforcementstrain energy density, elastic strain energy density and plastic strain energy densityMetal Matrix Composites (MMCs) have great potential to replace monolithic metals in many engineering applications due to their enhanced properties, such as higher strength and stiffness, higher operating temperature, and better wear resistance Development of high performance MMCs requires careful microstructure design which can improve their fracture toughness while maintaining high strength. This task not only requires the relationship between microstructural attributes and fracture toughness/strength of MMCs to be established, but also requires elucidation of the deformation and fracture mechanisms and quantification of their effects on material response. Interface debonding and particle cracking are two competing fracture mechanisms when a crack interacts with a reinforcement particle in a composite material. From the strengthening point of view, particle cracking adversely affects material strength since cracked particles lose the capability to carry load. Interface debonding, on the other hand, alleviates stress concentration in the particle phase and promotes microcrack initiation and propagation to the matrix phase. The effect of microstructural attributes on interface debonding has been discussed both computationally and experimentally. Romanova et al. layer can block interface debonding. Wang et al. The fracture toughness of MMCs depends on the combined effect of plastic dissipation in the matrix phase and energy spent on creating new crack surfaces. We hypothesize that interface debonding can positively contribute to the toughening of MMCs. First of all, interface debonding improves the fracture toughness of composites by creating tortuous crack paths via crack deflection and coalescence of interface microcracks with the main crack In the present work, Compact Tension (CT) test specimens are fabricated from 6092Al/SiCp MMC materials with 17.5% SiCP and 25% SiCP, respectively. The CT specimen configuration follows the ASTM . Plane strain condition prevails with specimen thickness of 6 mm. All the CT specimens are tested using Instron machine under Mode-I loading. The loading rate applied in this study is 0.1016 mm/min.DIC (Digital Image Correlation) analysis is a non-contact optical method which measures the full displacement/strain field during the course of material deformation and crack formation at both macro and micro scales. DIC method measures strain/displacement field by tracking the motion of speckle patterns on the specimen surface. The essence of this method is to correlate two digital images taken from a specimen before and after loading. The image before loading is set as the reference image. In order to achieve better the accuracy of the correlating procedure, a random speckle pattern is created on the surface of a specimen. Here, randomly distributed fine speckles are created using an air gun through careful control of gas flow rate. A set of synchronized images are captured through VIC-3D stereo-microscope during fracture testing as illustrated in . A small region of the specimen which is defined as the subset is selected from the reference image and is traced to the same region at subsequent deformed images. The displacement fields in the target region is obtained by minimizing the correlation coefficient. Details of DIC fundamentals can be found in multiple literatures J-integral is equivalent to the energy release rate in nonlinear elastic materials where W is the strain energy density, Ti are components of the traction vector, ui are the displacement vector components and ds is the length increment along the contour Γ. The displacement field and strain field can be directly extracted from DIC analysis. The stress components are resolved according to the Ramberg–Osgood equation asHere, σy represents the yield stress of MMC and ɛy corresponds to the strain at σy. The σe and ɛe are equivalent stress and strain, respectively. The hardening parameter N and dimensionless constant α are chosen from . To simplify the problem, total-strain theories are employed in the following study withεij=1+νESij+1−2ν3Eσkkδij+32αεy(σeσy)N−1Sijσy,where E and ν are the Young's modulus and Poisson's ratio of 6092Al/SiCp MMC, respectively. Sij is the stress deviator and δij is the Kronecker delta.As a measure of the material's resistance to fracture, the J value calculated from includes contributions from both plastic energy dissipation and the energy spent on creating new surfaces. Specifically, the total strain energy density which is formulated asW=12E(σx2+σy2)−vE(σxσy)+1+vE(τxy2)+(NN+1)ασeN+1EσyN−1can be separated as elastic strain energy density We and plastic strain energy density Wp. Since the displacement and strain data obtained from DIC analysis are on the specimen surface, the elastic strain energy density We and the plastic strain energy density Wp are calculated under plane stress conditions according to{We=12E(σxx2+σyy2)−vEσxxσyy+1+vEτxy2,Wp=(NN+1)ασeN+1EσyN−1.The relationship between the strain energy density and notch tip opening displacement δ which is measured from DIC analysis are discussed in Reinforcement particles in most MMCs are brittle ceramics with negligible plastic deformation, such as SiC and ZrO2/SiO2.When a tensile load is applied on a MMC sample, the stress distribution around reinforcement particles is not uniform because of load transfer interactions between the matrix and heterogeneities. According to the critical normal stress criterion σp=εpcμ*f(f(1−ϕ)[(1−f)σ0+εpcμ*ϕ]εpcμ*[(1−f)+fϕ]+Kf(1−f)ϕ(1−ϕ)μ*[(1−f)+fϕ]).Here, f is the volume fraction of reinforcement particles, σ0 is the yield stress of matrix, εpc is the critical plastic strain, ϕ is the interfacial damage function related to the plastic strain of matrix ɛp, K is the strength coefficient of Ludwig equation, and μ* is a function of elastic properties of the particle and matrix. According to Brown et al. where μM and μP are the shear modulus of the matrix and particles, respectively. In 6092Al/SiCp composites, μM and μP are taken as 25.56 GPa and 179.82 GPa, respectively. γ represents an Eshelby accommodation factor, which is in the form of 1−2(4−5ν)/15(1−ν) for spherical particles illustrates the evolution of particle stress σp with the plastic strain ɛp. It is assumed that particle fracture instantaneously occurs when σpmax≥σc. Otherwise, interface debonding is activated. Here σpmax and σc are the maximum stress in the particle phase and the threshold stress for particle cracking, respectively. Specifically, σc is the material property of reinforcement particles. In the following calculations, σc=370MPa is considered for SiCPσpmax=εpcμ*f((1−ϕ*)((1−f)σ0/εpcμ*+ϕ*)+ϕ*(1−ϕ*)(1−f)(K/μ*)1−ff+ϕ*),where is ϕ* is the critical value of ϕ when σpmax is reached. that interface damage develops progressively during the load transfer from the matrix to the particles. The interfacial damage function ϕ is assumed to linearly vary with ɛp. The evolution of σp with ɛp is illustrated in (a) considers a scenario when interface debonding is the only activated failure mechanism as σpmax<σc. In (b), interfacial damage starts to initiate when σp<σc. The further increase of σp beyond σc immediately leads to particle cracking. The interface energy density Eint is therefore defined asEint={∫0εpcσpdεp,σpmax<σc,∫0εp0σpdεp,σpmax≥σc.Here, εp0 corresponds to the critical plastic strain when σp=σc as illustrated in (b). The physical implication of Eint is discussed in According to the analytical model developed in , particle volume fraction f, matrix yield stress σ0 and the critical plastic strain εpc are the primary factors that influence the competition between particle cracking and interface debonding. illustrates the effect of these factors on σpmax which is formulated in , if the predicted value of σpmax locates in the “gray” area, particle cracking is activated as σpmax≥σc. Otherwise, interface debonding occurs if σpmax is in the “rainbow” area with σpmax<σc. It is noted that the increase of f, σ0 and εpc pushes σpmax towards to the “gray” area. This indicates that particles are more prone to fracture with higher f, σ0 and εpc. For example, in (a) f=18% represents the transitional volume fraction from interface debonding to particle cracking when εpc=0.1 and σ0=276MPa are considered. Further increase of f beyond 18% leads to particle cracking. This is due to the fact that higher volume fraction usually corresponds to lower average particle spacing which suppresses the plastic deformation in the matrix. It is also noted from (a) that the corresponding critical εpc decreases as f increases. For example, εpc decreases from 0.1 to 0.058 as f increases from 18% to 30%. The decrease of εpc also signifies lower level plastic deformation in the matrix and more brittle response of the entire material. As shown in (b) and (c), the increase of σ0 promotes particle cracking. It is expected as the increase of yield stress σ0 is the consequence of higher reinforcement volume fraction f. The higher volume fraction of brittle phase leads to lower level plastic deformation in the matrix therefore creates favorable condition for particle cracking which negatively influences the material fracture toughness The effects of f, σ0 and εpc on the interface energy density Eint as defined in (a) that when f varies from 10% to 23.5%, the corresponding σp curve is completely below the σc threshold. This indicates that interface debonding is the only activated failure mechanism. When f > 23.5%, interfacial damages emerge initially but switches to particle cracking as σp reaches σc. It is worth nothing from (b) that interface energy density Eint does not monotonically increase or decrease with f. In this example,Eint increases with f when f ≤ 23.5%.This trend reverses when f > 23.5%. In fact, when interface debonding is the only activated failure mechanism, the increase of f can lead to more interface areas and potential microcrack initiation cites. Therefore, the corresponding interface energy density Eint increases with f. However, when the increase of f starts to cause particle cracking, interface debonding quickly loses its dominance and results in significant decrease of Eint. The same trend is found in , particle cracking starts to emerge and gradually becomes the dominant failure mechanism when σ0 > 342 MPa. It is noted from (b) that when σ0 increases from 260 MPa to 342 MPa, there is a slight increase of Eint. However, a significantly drop of Eint is observed when σ0 exceeds 342 MPa as particle cracking starts to take over. In addition to f and σ0, the choice of εpc also significantly influences the failure mode and the value of Eint. In , σ0 and f are kept at 276 MPa and 17.5%, respectively. εpc is systematically varied from 0.05 to 0.15 with an interval of 0.025. It can be found from that Eint initially increases with εpc as interface debonding is the only activated failure mechanism. This indicates that Eint is very sensitive to particle cracking which is the outcome of material embrittlement due to the increase of yield stress. The plastic energy dissipation during the failure process is quantified through Digital Image Correlation (DIC) analysis in the following Based on the displacement/strain data extracted from the DIC analysis and the constitutive law in , the J-integral and notch-tip-opening-displacement δ are predicted for 6092Al/SiCp MMC specimens with SiCP volume fraction f=17.5% and f=25%, respectively. As shown in , the notch-tip-opening-displacement δ is defined asHere, δn and δs are the notch-tip-opening-displacement in the normal and shear directions, respectively. Two representative points on the upper half and lower half of the notch are selected as shown in It was observed that 6092Al/SiCp MMCs with 25% SiCP exhibit a much more brittle behavior than those with 17.5% SiCP. It can be inferred from that more profound plastic deformation is observed for the specimen with f=17.5%, and higher J and δ values are predicted. This trend is consistent with other experimental observations of MMCs summarizes the elastic strain energy density, plastic strain energy density and total strain density at the two representative stages in . It can be inferred that the increase of J and δ after stage A is primarily due to the plastic deformation in the Al matrix. According to stage B which is the onset of catastrophic failure, plastic strain energy almost constitutes the entire total strain energy as illustrated in both in . Part of the elastic strain energy has been released to form a small amount of microcracks before the rapid crack propagation. On the contrary, very little plastic deformation was observed for the specimen with f=25% when catastrophic failure occurs. As shown in , the plastic energy density is negligible. Besides, no crack advancement or microcracks were observed before the onset of instability. It is also worth noting from that the elastic strain energy tends to saturate at a plateau for both specimens with f=17.5% and f=25%. This trend has several implications. First of all, the amount of stable crack propagation before catastrophic failure can be estimated since the released elastic strain energy is used to form crack surfaces. It can be inferred that there is limited room to improve the fracture toughness of MMCs through the increase of surface energy dissipation alone. In fact, plastic energy dissipation plays a more important role in material toughening. For example, the same amount of crack propagation in the ductile matrix phase and the brittle particle phase does not cause much variation in surface energy dissipation but leads to a huge discrepancy in plastic energy dissipation. Crack propagation in the ductile matrix phase can lead to profound plastic energy dissipation while the same amount of crack propagation in the brittle particle phase usually results in negligible plastic deformation. It can be concluded from the above discussions that the activation of failure mechanisms during the crack-particle interactions ultimately determines the amount of plastic energy dissipation and the fracture toughness of MMCs. The quantitative relations between fracture mechanisms and plastic energy dissipation are discussed in The surfaces near the pre-crack tip of each CT specimen are polished so that both the microstructure features and the crack trajectory can be well observed from the microscope. The optical observations of one sample with f=17.5% and one sample with f=25% are illustrated in . Based on the micrographs, a computer program is developed to delineate the crack path and distinguish the crack segments in different phases. As shown in , the crack segments associated with matrix cracking, particle cracking and interface debonding are highlighted in blue, red and green, respectively. The probability of interface debonding is calculated as the ratio between crack length in the interface and the sum of crack length in interface and particles. The percentage of matrix cracking is calculated as the ratio between crack length in the matrix and the total crack length. It is noted from that specimens with f=17.5% exhibit higher probability of interface debonding during the crack-particle interactions. In addition, a higher percentage of matrix cracking is predicted for specimens with f=17.5%. The higher percentage of matrix cracking leads to more prominent plastic deformation as the average plastic strain energy predicted from specimens with f=17.5% is significantly higher than that in specimens with f=25%. It can be inferred that interface debonding promotes crack development in the matrix which intensifies the plastic deformation. The increase of SiCp volume fraction discourages interface debonding and in turn negatively influences the fracture toughness. The analytical model developed in can be employed to predict the probability of interface debonding with different particle volume fractions. As shown in , the probability of interface debonding at a specific volume fraction is formulated aswhere S1 and S2 represent the scale of εpc in the particle cracking zone and interface debonding zone, respectively. The probability of interface bonding is predicted based on different ranges of εpc as shown in . It should be noted that the range of εpc cannot be directly determined from experiment. In the current study, εpc=0.15 which is the fracture strain of matrix 6092 Al is selected as the upper bound of the range. The lower bound of εpc varies from 0.0257 to 0.05. It is noted that the probability of interface debonding decreases with increased SiCp volume fraction regardless of the range of εpc. When the lower bound of varies between 0.0257 and 0.05, the analytical predictions agree well with the experimental predictions with f=17.5%. For cases with f=25%, the experimental predictions are primarily located in the region where the lower bound of εpc varies from 0.04 to 0.0257.The above trends are observed in SEM fractographs as well. As shown in , multiple long cracks are observed in specimens with f=17.5%. A closer look at the region near a long crack in (f) indicates that the fracture surface is dominated by dimples which are the typical ductile fracture features. Voids are found to initiate at retained porosity sites at the interface or in the matrix close to the interface due to stress concentration. Both interface debonding and particle pull-out are observed as shown in (e) and (f). It can be inferred that these voids initially initiate near the debonded interfaces. Once these voids start to grow, strain localization causes more void initiation at the weak interfaces. The coalescence of these voids eventually leads to the long crack in the matrix. The SEM fractographs with f=25% are summarized in (b) that multiple clusters of particles exist near the notch tip. A more intensified particle cracking is also observed as shown in when the volume fraction of SiCp increases from 17.5% to 25%. Particle cracking suppresses plastic deformation as fewer void initiation at the interface and coalescence with matrix cracks are observed.The above discussions point out that the development of high toughness MMCs requires microstructure design which promotes interface debonding. Volume fraction of reinforcements, strength and ductility of the matrix phase, and the interface bonding energy are the primary parameters that influence the competition between interface debonding and particle cracking during the crack–microstructure interactions. The fundamental avenue for toughening is to promote interface debonding through optimized selection of these parameters so that the combined energy dissipation in terms of plastic deformation and surface formation can be maximized.An integrated experimental and analytical framework is developed to investigate the fracture behavior of 6092Al/SiCp Metal Matrix Composites through quantification of competing failure mechanisms and quantification of their influences on the fracture toughness. Experiments carried out concern 6092Al/SiCp MMCs with 17.5% and 25% SiCP, respectively. The fracture toughness and energy dissipation in terms of plastic deformation and surface formation are predicted through Mode-I fracture testing and Digital Image Correlation analysis. The analytical model quantifies the competition between interface debonding and particle cracking by considering the effect of volume fraction of reinforcement particle, yield stress of matrix and the interface properties. It extends the scope of the experimental framework by considering a wide range of microstructure configurations. Results suggest that interface debonding is the beneficial mechanism for the toughening of MMCs. It not only leads to more tortuous crack paths which contributes to the surface energy dissipation but also significantly promotes plastic deformation in the ductile matrix. The probability of interface debonding increases with decreasing reinforcement volume fraction, lower yield stress of the matrix, as well as properly balanced interface bonding energy.Study of transfer printing using micro-dynamically-regulated micro-structural flexible moldThis study proposed a creative technical method of the transfer printing process using a micro-dynamically-regulated micro-structural flexible mold. First, the flexible mold materials were configured and selected. Then material properties were tested, and controlled in a scope suitable for micro elastic deformation. Related equations were used as reference for microscopically changed micro-structural forms. A transfer printing system was developed, and dynamic micro-structural flexible mold transfer print was tested. The experimental results showed that with the micro-dynamically regulated micro-structural flexible mold transfer printing technology proposed in this study, micro-dynamic regulations can be successfully conducted and greatly reduced under allowable micro-structural conditions. The proposed technology can greatly reduce the time and energy consumption problems in the production of relative components, with microelectromechanical systems (MEMS) processes. Moreover, the required replication features could be achieved by transfer printing, and micro-structural imprinting and forming could be conducted in a precise manner, thus, providing an alternative choice for the application of micro-dynamically regulated microcomponents.When using microelectromechanical systems (MEMS) technology to produce silicon-chip-substrate micro-structural or related microcomponent molds In the dynamic change theory of external form in this study, the uniaxial tensile method is used as the regulation basis for the external form of the micro structure of flexible molds. First, tensile testing is conducted on the flexible molds under different hardener proportions, which are specific to this specimen, in order to obtain the linear elasticity testing range (In this study, the transfer printing experiments of a micro-dynamically regulated micro-structural flexible mold are conducted by utilizing the imprinting system in combination with the self-developed dynamic mold regulation system, as shown in . The dynamic mold regulation system can be divided into the following main parts, the mold clamping part, force regulation part, and displacement measurement part. First, the mold clamping parts are mainly used to hold the two ends of the experimental mold. Since the mold in this study is made into a dog-bone shape (long strip shape), there are no micro-structural parts at the two ends, thus, they can be clamped and used as the force application areas for tensile. The force regulation part is mainly to control the outside tensile force of the mold, which causes the mold to experience elastic deformation within the range of its elasticity limits. Finally, the displacement measurement part is mainly to take measurements and recordings specific to the displacement after outward tensile.In this study, PDMS (poly-dimethylsiloxan, Sylgard™ 184, Dow Corning) is used as the mold of imprinting, which has excellent mechanical properties, good wear resistance, and anti-fatigue properties, thus, this material is often used by for research and industrial applications. Regarding the selection of imprinted materials in this study, imprinted materials are prepared using amorphous polymer as polycarbonate (PC).To accurately obtain the mechanical properties of mold materials, mechanical testing is conducted specific to the PDMS, which uses nano indentation and tensile testing in order to more completely record the actual impact of the material under stress and tension. The tensile test of the present study adopts the micro-tensile testing machine produced by the Instron Corp.The adopted nano indenter is produced by the Hysitron Corp., which mainly tests the material properties of film characteristics under the micro-nano scale of its applications. It is a highly sensitive detection instrument able to re-confirm the material properties determined through tensile testing. The nano indentation system is to obtain the hardness and Young's modulus of the material according to continuous stiffness measurement (CSM) testing and continuous recording of load and indentation depth, and conduct its development based on the Hertzian elasticity theory and established related art by Oliver and Pharr . First, the indentation contact projection area (An) could be obtained through the geometrical deduction of the Berkovich tip.Meanwhile, θ |
= 53° (For an ideal Berkovich tip)where hc: contact depth of material indentation, An: contact projection area of indentation, pmax: maximum force applied, H: material hardness obtained from testing.Meanwhile, the material stiffness could be expressed by the following formulaThe equivalent elasticity modulus could be obtained through conversionThen, the formula of equivalent elasticity modulus could be obtained through calculation, as shown in Eq. where S: initial contact stiffness, Vs: Poisson's ratio of the substrate, Vi: Poisson's ratio of the indenter, Er: indentation modulus (reduced modulus), Ei: Young's modulus of the indenter, Es: Young's modulus of the substrate.In this study, dog bone and long-stripe shapes are used as the main external forms of the mold, and the micro structure would be placed within the central area range for observation of its dynamic changes. The mold preparation process in this study is shown, as follows: (a) design with CATIA software, and the process of the CNC (Computer Numerical Control) four-axis processing machine casts a mold cavity from acrylic material (); place the complementary micro-structural original mold to be achieved at the very bottom; (b) prepare and pour an appropriate proportion of PDMS into the mold cavity; (c) remove the mold after it is cured to obtain the micro-structural PDMS mold, as shown in This study adopts a self-developed dynamic mold regulation system, in combination with an imprinting system, for imprinting and forming. Experimental process of this study, as follows: (a) use the fixture heads at the two sides of the dynamic mold regulation system to clamp and fix the two ends of the micro-structural mold; (b) place PC on the substrate of the system of the imprinting seat; (c) perform dynamic deformation regulation on the different forces of the micro-structural mold regulation, within elasticity limits, in order that predictable regulation of the micro structure could be conducted within the elastic deformation range; and (d) set the imprinting force and heating-embossing-cooling forming of imprinting to obtain the finished product.In this section, nano indentation and micro-tensile tests under different proportions of the main agent and hardener are conducted, and their impacts on the mechanical properties are explored. In the tests, the PDMS molds are produced under the three different proportions of 13:1, 10:1, and 5:1, at the same temperature condition and with the same standing time. According to the nano indentation and micro-tensile test results, it can be clearly found that, in the condition of a low-proportion of hardener, its hardness and Young's modulus are both lower than the data of the high-proportion hardener, meanwhile, with the increased hardener proportion, the structural strength and the tensile resistance of material would be relatively improved, as shown in . Besides, within the elastic deformation tensile of PDMS, shows that a small contact angle change is observed.In this section, PDMS micro-structural molds under the two different proportions of the main agent (13:1, 10:1) are continuously conducted in order to explore its imprinting, replication, and forming abilities. The experimental results show that for these two kinds of proportions, the external form in the condition of 10:1 is better. The main reason is that structural strength is weakened under the condition of a relatively low proportion, which consequently is likely to cause deformation, thus, affecting forming quality. Besides, regarding the pressure evenness test, sensitive film was placed between the PDMS plate (no structure) and the glass base the pressure distribution is quite even, distribution photo of test of pressure evenness of the sensitive film is shown in , and simulation and discussion about the soft mold mechanical tensile force of uniform situations, as a result, we using ANSYS finite element analysis (PDMS soft mold: modulus of elasticity: 1.72 Mpa; Poisson's ratio: 0.49; density: 965 kg/m3; tensile pressure: 0.03 MPa) during this simulation situations, we obtain uniform force distributions is shown in In the experiments of this section, the micro-tensile testing machine, integrated with a mobile microscope detection system, is erected to facilitate observations, as shown in ; meanwhile, the Fresnel lens micro-structural tensile situation of a uniaxial PDMS flexible mold (10:1) is discussed, which is mainly used to compare the basic data of the tensile situation in the case of different proportions. The results show that under the conditions of different tensile times (10, 20, and 30 s.), the two end points on the same circle of the radian of the Fresnel lens micro structure increases with the increased tensile time within the equal radian measurement range of the Fresnel micro structure, and the radian angle also decreases, as shown in . Moreover, a linear equation and second-order polynomial equation are used as the approach methods in this study, where the approach equations of the linear equation Eq. and second-order polynomial equation Eq. can be obtained. In addition, the second-order polynomial equation has a high degree of approach, as listed below.In this section, the self-developed dynamic mold regulation system is used to perform the tensile of the PDMS micro-structural mold, which is controlled within the elasticity range, resulting in the micro deformation of the micro-structural mold; while imprinting and forming is conducted through the micro-dynamically-regulated micro-structural imprinting process. The experimental results show that the external form variation of the micro structure is changed along with the increased tensile extent (stretch), within the elasticity range of the mold material, as shown in . In addition, imprinting and replication are performed after the tensile extent (stretch) is determined (embossing time: 60 s, embossing pressure: 6.5 MPa, embossing temperature: 147.5 °C). The obtained complementary structure also has precise performance, as shown in This study developed a technical method of the transfer printing process using a micro-dynamically regulated micro-structural flexible mold. In the process of the study, detailed discussions are made specific to the preparation and selection of flexible mold materials of different proportions, as well as tests regarding mechanical properties; meanwhile, tensile and nano indentation testing are adopted in order to more accurately explore the mechanical properties of PDMS micro-structural mold materials of different proportions; and the formability of the micro-dynamically-regulated imprinting is explored by using the self-developed dynamic mold regulation system. This study verified that, in addition to the increased hardener proportion, the structural strength and tensile resistance of material would be relatively improved; the better external form is achieved in the condition of 10:1; and the complementary structure obtained after the imprinting and replication within the elasticity range of mold material has precise performance.Effect of different loading conditions on the mechanical behavior of [0/±45/90]s woven compositesThe main objective of this paper is to investigate the behavior of [0/±45/90]s woven FRP composites under tension, bending, and combined bending/tension loading conditions. First, the mechanical properties of the composite were determined experimentally using the ASTM testing standards. Bending properties were determined using 3-point and 4-point bending tests. The results showed that the woven composites performed better under bending loading than under tension loading. Finally, special test fixtures were designed to facilitate the study of the effect of the combined bending/tension loading. The bending moments were applied using offset shims of various thicknesses placed between the plane of the specimen and the loading axis. At the beginning, the load–strain diagrams at the specimen center showed the domination of bending strains, tension on one surface and compression on the other. With the advance of the loading process, the tension strain dominated and the strain on both sides were almost equal. The failure under combined bending/tension loading was due to the high stresses near the fixture. However, in pure bending, the material failed at the center because of the excessive delamination on the compressive side.The usage of woven composites has increased over the recent years due to their lower production costs, light weight, higher fracture toughness and better control over the thermo-mechanical properties The complex behavior of the fiber-reinforced plastic materials is due to their anisotropic and inhomogeneous properties. These properties cause a variety of failure mechanisms associated with fiber-reinforced composite materials Several researchers found that bending strength was greater than tensile strength in polymeric composite materials Although most of the structures are usually subjected to biaxial or triaxial stresses, the studies of these loading conditions have been very limited. Therefore, the main objective of this paper is to further investigate the behavior of [0/±45/90]s woven FRP composites under combined bending/tension loading. The effects of three types of loadings on the standard woven specimens will also be investigated. These loading conditions are: pure tension, pure bending, and combined bending and tension. Furthermore, the paper will study the surface strains, out of plane displacements, tensile and flexural properties, and failure modes in these composites., the internal resisting moment, Mi, at any section (say at point x) is equal to:where M is the resulting bending moment at distance x, P is the applied tension load, e is the eccentricity, and y is the vertical deflection. From the moment–curvature relationship:where E is the modulus of elasticity, I is the second moment of area, and y¨ is the second derivative of the deflection y. Hence,The general solution for the above equation is:where A and B are constants to be determined from the boundary conditions. The first and the second derivatives of the deflection are:Boundary condition 1: at x |
= 0, y |
= 0, and from Eq. Boundary condition 2: at x |
= |
l (specimen length), y |
= 0, and from Eq. Since B |
= −e, and after certain manipulations, the constant A is determined as:Substituting for the constants A and B into Eq. An expression for the mid-height deflection y |
= |
δ is obtained by letting x=l2. Thus:δ=ymax=ecoshkl-1sinhklsinhkl2-ecoshkl2+ecosh2kl2-sinh2kl2=1sinhkl=2sinhkl2coshkl2coshkl=cosh2kl2+sinh2kl2=2sinh2kl2+1Substituting into δ equation and after certain manipulations:Quasi-isotropic polymeric composite material was fabricated from polyester resin reinforced by woven glass fiber using hand-lay-up technique shows the constituent materials of the composite laminates. Care must be taken when cutting and laying the woven glass fiber layers. The cutting must be through the warp and weft threads to ensure right angles of all layers. These layers were stacked at different angles to give quasi-isotropic laminate [0/±45/90]s, . The fiber volume fraction (Vf) was determined experimentally using the ignition technique according to ASTM D3171-99. The average value of Vf was 30.8%.Tension, bending, and combined bending/tension tests were carried out on woven GFRP specimens using a universal testing machine (Testometric 200 kN). The crosshead speed of the loading member was 2 mm/min. In tension, 3-point bending, and 4-point bending tests, four specimens were used in every test, while two specimens were used in each eccentric value in combined bending and tension tests. The strength values were determined based on the average values. The load displacement diagrams were monitored for all the test specimens and printed through the PC of the testing machine. The strains were measured for each test type using strain gages connected to the Digital Strain Meter (Tc-21K model 232).The tensile properties of woven composites were determined experimentally according to the ASTM D3039/D3039M-00. The apparent Young’s modulus and the ultimate tensile strength were determined from the load–displacement curve of the testing machine, while the actual tensile modulus was measured using strain gages bonded at the center of the test specimens. The dimensions of each test specimen were: the total length was 210 mm, the gage length, L, was 90 mm, the width, w, was 27 mm, and the thickness, t, was 3.5 mm.Bending properties (strength and modulus) of woven composites were determined experimentally using 3-point and 4-point bending tests according to JIS K 7055 shows the dimensions between the supporting points and the dimensions of the test specimens. The specimen width, w, was 26 mm. Two strain gages were bonded back to back on the 4-point bending specimen to monitor the surface strains on both sides during the pure bending test. represent the flexural fracture strength (σb) for 3-point and 4-point bending tests, respectively.where Pmax is the maximum load (fracture load).The flexural modulus of elasticity, E, is determined from the initial inclination of the load–deflection curve of the 3-point bending specimen using the following equation:where P/δ represents the slope of the initial portion of the load–deflection curve (N/mm).a, were designed and manufactured according to the specifications illustrated in NASA report number TM-1999-209511 b illustrates the dimensions of the combined bending/tension test specimens. Two specimens were tested for each offset value. Two strain gages were mounted back to back on one specimen and the second specimen was tested without using strain gages. The strain gages were longitudinally placed at the specimen center. During the combined bending/tension test, the strain gage on one side was under compression, while the gage on the other side was under tension. The out of plane displacements (δ) at the specimen center were measured using dial indicator. The out of plane displacements and the strains on tension and compression sides of test specimens were recorded during the loading process till failure occurred. illustrates the load–displacement diagram of woven composite in tension test. The apparent modulus of elasticity was obtained from the initial linear portion of the curve. Meanwhile, the actual modulus of elasticity was determined from the initial linear portion of the stress–strain diagram that was drawn using the strain gage results, . The ultimate tensile strength was determined at the maximum tensile load (fracture), was the nonlinearity of the load–displacement and stress–strain diagrams. This behavior was attributed to the fact that fiber-reinforced plastic materials were not only anisotropic, but, on the macro scale, they were also inhomogeneous. The failure sequences of tensile specimens were matrix cracking at about 0.43% of maximum load, , followed by debonding at fiber/matrix interfaces, which could be easily observed visually as white patches at about 80% of the ultimate load, . Excessive delamination was observed just before the specimen fracture, which was catastrophic due to the fiber breakage.It should be noted that three specimens failed at the end of the gripping length, a, and only one specimen failed near the middle of the specimen, b. Failure of specimens at the end of gripping length was due to the stress concentration, which was developed from the lateral compressive stress of the grips. The indentations of the grips on the specimen surface could be easily shown in . These indentations affected significantly the failure loads and modes of unidirectional composites rather than woven and chopped composites. To overcome this problem, particularly in unidirectional composites, it is essential to use tabs at the gripping portions to prevent the longitudinal splitting of the specimen indicate that the actual modulus of elasticity is about 3.8 times higher than the apparent modulus of elasticity of woven GFRP specimen. It is interesting to note that the actual modulus of elasticity of cross-ply specimens, with aluminum tabs, was more than six times higher than the apparent modulus shows the load–deflection diagrams of 3-point and 4-point bending tests. The results indicate that the load–deflection diagrams of the 3-point and 4-point tests have initial linear portions of up to 0.34 kN and 0.64 kN, respectively. At these loads, each curve starts to form a knee. The slope of the 3-point specimen is higher than the slope of the 4-point specimen. The knees in the load–deflection diagrams at the mentioned loads are due to the micro cracking of the matrix. Continuing to increase the load causes delamination that leads to a gradual deterioration in the test specimen. The final failure of the 3-point specimen is catastrophic.Due to the load concentration at the center of the specimen in the 3-point bending test, the bending stress is associated with shear stress. This is the main cause of the catastrophic failure in the 3-point bending specimens. Moreover, the knee (the micro cracking of the matrix) in the 3-point bending test occurs at approximately half of the loading value in the 4-point bending test. Therefore, the flexural strength of the 4-point specimen is higher than that of the 3-point specimen, . Also, 4-point bending specimens are sbjected to constant bending moments between the two tops loading points and their failure is due to pure bending stress. This explains the gradual decrease in the 4-point load–deflection curve once the load reaches its peak. illustrates the stress–strain diagrams in 4-point bending test. The results in this figure indicate that the strains in the compression side are lower than those in the tension side. This can be demonstrated by higher delaminations in the compression side than in the tension side of the test specimens, . The excessive delaminations in the compression sides are the main cause of the final failure of the test specimens. Similar behavior has been reported by Palmer et al. also shows that the delaminations in the 4-point specimens are higher than those in the 3-point specimens. This behavior is due to the higher deflections in 4-point specimens compared with the deflections in 3-point specimens, shows that woven composites are stronger in bending than in tension. The ratio of 3-point bending strength to tensile strength (1.27) readily agrees with the published values shows the load–displacement diagrams of woven composites under combined bending/tension tests at different eccentricities, “e”. The figure indicates that large displacements are associated with low loads. Increasing the eccentricity values results in decreasing the slope of load–displacement diagrams while increasing the failure displacements. The displacement increases with the increasing value of eccentricity. As the load increases, the displacement increases at a lower rate.The relationship between the tensile load and the strains in the tension and compression sides of the combined bending/tension specimen with different eccentricities is shown in (a) and (b). The main characteristic in these curves is the presence of the bending strains (positive and negative strains) at the beginning of the loading. This means that at low loads, the bending stress is more dominant than the tensile stress. The bending strains increase when the eccentricity value increases. As the load increases, the tensile stress becomes more dominant and the tensile strains occur in both sides.The effect of the applied load on the out of plane displacement (y) at the specimen center is also investigated. shows this effect for a specimen with eccentricity e |
= 21.75 mm. The figure indicates that the out of plane displacement increases significantly toward the axis of the applied load with the increasing of the load, . This decreases the bending arm, “e–y”, and hence the bending moment at the specimen center also decreases. As the load advances, the out of plane displacement reaches its maximum value, which is approximately equal to the eccentricity (y |
≈ |
e). Therefore, at the specimen center, the bending moment approaches zero and the specimen is only subjected to tensile stress. shows the effect of the eccentricity on the maximum tensile load in combined bending/tension test. For the tested range of eccentricities, the results show a linear relationship between the eccentricity and the maximum tensile load.It should be noted that the rate of change in the out of plane displacement is almost negligible once the load exceeds about 1/4 of its maximum value. The variation of y from its maximum value (y |
≈ |
e) at the specimen center to its minimum value at the fixtures, , causes the bending moment to increase from zero at the specimen center to its maximum value at the fixtures. Therefore, the failures of the test specimens are due to the combined bending and tensile stresses at the end of the gage length (near the fixtures of the test specimens), This work investigates the mechanical behavior of the woven composites under tension, bending, and combined bending/tension loadings. The failure stresses in bending are higher than those in tension. The material shows better performance under 4-point bending test than 3-point bending test. In 3-point bending, the load concentration causes early micro cracking of the matrix as well as catastrophic failure. Generally, failure under bending is mainly caused by excessive delamination in the compression side of the specimen.In combined bending/tension loading, the out of plane displacement changes from its maximum value at the specimen center to its minimum value near the fixture. As the load is gradually increased, the out of plane displacement at the center increases till it reaches the eccentricity value. Hence, the specimen is only under tension at the center, while the specimen is under the same tension and maximum bending near the fixture. Therefore, the failure of the test specimen is due to the combined bending and tensile stresses that occur at the end of the gage length.Structural, electronic and elastic properties of Zn3As2In this paper, we report ab initio studies of structural, electronic and elastic properties of a II-V group semiconductor compound, Zn3As2 along with its experimental Compton profile (CP). For experimental CP, 59.54 keV gamma ray (radiation source:5 Ci 241Am) spectrometer is used and to deal with the theoretical part, density functional theory, Hartree-Fock as well as the hybrid functional theory, implemented in CRYSTAL code, are used. A full structure optimization following an equation of state calculation is performed to get the structural parameters. Further directional CPs, band structure, density of states, Mulliken population analysis and elastic properties have also been computed. A concurrence-test with experimental CP proves hybrid scheme to provide the best results in the present case.Importance of ab initio calculations, in exploring various ground state properties is well recognized and appreciated as well. It provides an elegant and systematic way to predict the properties of a system, before going through the bushes of experimental chaos. Many times, results of first-principle approximation are found to be accurate enough to interpret the experimental observations. Moreover, agreement between theory and experiment increases our faith in the obtained results. Keeping these facts in mind, present paper is devoted to the theoretical as well as experimental study of a II-V group semiconductor compound, Zn3As2.As far as the choice of material is concerned with, Zn3As2 compound has long been considered as a promising candidate for potential applications in photovoltaic, long wavelength optoelectronics, ultrasonic multipliers, IR detectors and spintronics-devices as well Thus, this enormous potential and concurrently no significant theoretical work reported so far becomes the main motivation for us to proceed in this direction. Here, study of structural and electronic properties is carried out applying density functional theory (DFT), Hartree-Fock (HF) and hybrid schemes. On comparing the results, hybrid potential is found to provide the best agreement. Thus, we have performed the study of elastic properties using hybrid potential only. Ab initio study of the elastic properties of the compound is an unmarked work, as far as the familiarity of the author is concerned with. In electronic properties, isotropic Compton profiles (CPs), anisotropic CPs, band structure, density of states (DOS) and Mulliken population analysis are studied. DFT, HF and B3PW (Becke's 3 parameter hybrid functional Experimental set-up, as reported in Ref. Background corrections have been made by taking the readings with the holder only and then subtracting this from the sample data channel by channel. In doing so, effect of the set-up gets cancelled out and data corresponding to only sample can be retrieved effectively. Obtained data is, then refined using data reduction program All the calculations have been performed using the latest version of CRYSTAL code of Torino group http://www.tcm.phy.cam.ac.uk/∼mdt26/crystal.html. To accelerate the convergence, a level shifting of 0.5 hartree has been applied; that is removed after diagonalization. 40% mixing of Fock/Kohn-Sham matrix is applied between the subsequent self-consisted field (SCF) cycles. A full direct approach is utilized for the computation of integrals in which screening of the integrals is not performed. To control the accuracy in computation of Coulomb and exchange series, five tolerance parameters are considered. Monkhorst-Pack scheme of 4 × 4 × 4 k-point mesh is used for Brillouin zone integration.Full structure optimization (lattice parameter and atomic positions) of experimental parameters Compton scattering (i.e. inelastic scattering of photons and electrons) is considered as an efficient technique to decipher the momentum distribution of electrons in an atom where, ω1 and ω2 are the energies of incident and scattered photon respectively, K=k1−k2 is the scattering vector (conventionally chosen as the z-axis), p is the electron momentum and ℏ and m are taken in atomic units (a.u.). Clearly, unlike the well-known Compton shift formula Theoretical isotropic as well as directional CPs have been computed. Isotropic profiles are then added to the corresponding core profile Second order elastic constants are calculated by applying the homogeneous strain to the equilibrium lattice structure of Zn3As2where, V0 is the equilibrium volume, E is the energy of the crystal and η defines the lattice strain in terms of Voigt's notations. The symmetry dependent strained pattern of tetragonal crystal structure of Zn3As2, has six symmetry elements i.e. C11, C12, C13, C33, C44 and C66. Various elastic constants like bulk modulus, shear modulus, Young's modulus and Poisson's ratio are calculated from Hill's approximation Structure of Zn3As2, as mentioned above, is tetragonal (ca=2) which belongs to the space group P42/nmc (space group no. 137) . Here, green spheres show Zn atoms whereas blue spheres show As atoms. Zn3As2 unit cell consists of 8 formula units, with 24 Zn and 16 As atoms. There are three different Wyckoff positions for both Zn and As atoms. The cation atoms occupy three distinct 8g positions which are labelled as Zn1, Zn2 and Zn3 respectively. The anions are located at 4c, 4d and 8f positions which are labelled as As1, As2 and As3 respectively. Each Zn atom is in tetrahedral coordination with As atom, whereas each As atom makes 6 bonds, directing to the corners of a cube, having two vacancies at the diagonal ends.Structure has been fully optimized and corresponding optimized lattice parameters are presented in . Clearly, DFT and hybrid underestimate the lattice parameters a and c by 0.72%, 0.75% and 0.65%, 0.64% respectively, whereas HF overestimates it by 2.75% and 2.59% respectively. Overestimation by HF can be explained on the basis of the non-inclusion of correlation energy, consequently this theory generally under binds the molecule. The reason for this considerable difference may also be the presence of transition metals in our case, in which correlation due to d-electrons contributes significantly. On the other hand, introducing these effects in DFT and hybrid give better results, but the small discrepancies may be attributed to the thermal vibrations, which are present in experimental conditions while all the ab initio calculations are performed at absolute 0 K temperature.Further, after optimization, an EOS calculation is performed using DFT and hybrid schemes and corresponding parameters are presented in . The values of bulk modulus predicted by DFT are lower as compared to the hybrid scheme. Pressure derivative, on another part, shows an excellent consistency. To have a quantitative comparison of the performance of these theories, experimental verification is required. As far as the familiarity of the author is concerned with, no experimental as well as theoretical data has yet been reported for Zn3As2., CPs have been calculated using all the three algorithms. Unconvoluted CPs corresponding to hybrid scheme along with the experimental data is presented in . Errors are also included at some points. To check the comparative performance of the theory, difference from experiment has been plotted. As evident from , in low momentum region i.e. below pz = 0.4 a.u., theoretical CPs overestimate the experimental CP.The difference calculated at J(0) is 1.72%, 1.97% and 1.52% for DFT, HF and hybrid respectively. Thus, hybrid potential is providing the best agreement among these schemes. Further, χ2-test also supports the better performance of hybrid scehme. This agreement would have been more appropriate, if the relativistic correction and Lam-Platzman (LP) correction To examine the directional dependence of CP, we have figured out the theoretical momentum densities in three different crystallographic directions [100], [110] and [111]. Their corresponding differences are plotted in . Taking differences make the interpretation more clear and comprehensible, since all the common errors and core part is cancelled out. From the present calculation, it is observed that the difference profile with respect to [100] direction shows identical behaviour, though the anisotropic behaviour of J100- J110 is comparatively higher than J100- J111 in the momentum range ≤ 1.0 a.u. Hence, the maximum amplitude of anisotropy is observed for J100- J110 profile at pz = 0.7 a.u. On contrary to this, J110- J111 difference profile shows almost the opposite trend of momentum density in low momentum range 0.2 ≤ pz ≤ 1.2 a.u. The close inspection of the J(0) values shows the higher electron momentum density in [111] direction as compared to others, although the difference is quite small. This, in other words, predicts the higher availability of degenerate states near Fermi surface in the corresponding direction i.e. (Γ-A) as compared to the (Γ-X) and (Γ-M) directions. Thus, crystal formation in this direction may be of great practical applications. depicts anisotropic behaviour up to the momentum range pz = 2.0 a.u. only. Beyond this momentum region, the isotropic behaviour of core electrons dominates and eliminates the anisotropic behaviour of electron momentum density., bond lengths are calculated to be 3.96 Å and 4.59 Å, corresponding to the profiles J110- J111 and J100- J111 respectively.Band structures have been calculated using all the three algorithms and the corresponding values of band gap energy is reported in . As expected, DFT underestimates the value as compared to the experiment and provides the value too small owing to the lack of integer discontinuity of the exchange correlation energy derivative. On the other hand, HF scheme overestimates the value greatly due to uneven treatment with the self-interaction term. In this scheme, inclusion of the concept of ‘orbital’ excludes the self-interaction term completely, but only for the occupied bands. While, conduction bands are totally untouched, resulting in an increased band gap. Besides these two theories, hybrid functional approach provides better result. Looking at the concurrence provided by the hybrid potential regarding the value of band gap and CPs as discussed in the previous section, here we are discussing band structure corresponding to hybrid functional theory only.The presence of highest valence band maxima and the lowest conduction band minima at Γ point predicts a direct band gap of 1.32 eV (). Further, on moving along the directions ΓX and ΓM, the decrement in available energy states is shaper in the later one and the difference is quite significant. This fact can also be verified by the anisotropic behaviour of CPs, where the maximum anisotropy is found between the directions [100] and [110]. On the other hand, along the direction [111] i.e. at point A the available energy states are quite similar to that at point M, clarifying the small amplitude of anisotropy in [111] - [110] direction. It is to be considered from that the valence band is dominated by sp-sp*shells of As atom while the lowest lying conduction band is associated with sp-sp* shells of Zn atom, where sp* shows the corresponding diffused shell. From these shells, sp-sp* shells of Zn and As atoms are highly delocalized and spread over the entire region, where as d-shell of transition metal is localized within the region from −6.492 eV to −0.947 eV.To find out the charge neutrality level of Zn3As2 compound, we have calculated branch point energy (EB) from the electronic band structure. EB is the energy interface where the surface state of semiconductor changes from donor to acceptor like. It is an important parameter for lining up the band gaps through Schottkey barriers and heterojunctions. It is taken as the average of the mid gap energies across the entire Brillouin zone (BZ). Numerically the value of EB, in present case (for without spin-orbit coupling), is calculated as:where, ε¯CB is the average of the conduction band minima at Γ, R and Z points of BZ while ε¯VB is the average of the valence band maxima at Γ and X points of BZ. The EB of Zn3As2 found to be 0.95 eV, which lies in the band gap just below the lowest conduction band minima Population analyses have been proved to be efficient techniques . It is clear from the table that the charge depends on the orientation/position of the atom excluding As(1) and As(2) atomic positions, where the charge distribution is almost the same. A significant amount of charge is redistributed among the diffused shells. Approximately 68.4% charge has been transferred from 3sp shell of Zn atom. In case of As atom, maximum charge transfer of ∼68% has taken place from 4sp shell. On an average, 0.184e charge is transferred from each Zn atom and 0.272e charge is received by each As atom during the bond formation.Similarly, population-overlap analysis has also been performed. For example, overlapping charge between Zn1 atom and As3 atom at a distance 2.480 Å is 0.223, whereas with As2 at 2.483 Å and As1 at 2.751 Å are 0.228 and 0.096 respectively. Similarly, for As1 the overlapping charge with Zn3, Zn2 and Zn1 atoms at distances 2.427 Å, 2.462 Å and 2.751 Å are 0.246, 0.238 and 0.096 respectively. Clearly, overlapping decreases with the increment in interatomic distance.To investigate the structural stability and stiffness of Zn3As2, the elastic constants are computed using hybrid potential, owing to the agreement provided by hybrid potential in preceding calculations. The calculated elastic stiffness coefficients are listed in . According to the Born stability criteria the mechanical stability of tetragonal crystal structure is defined as follows Hence, the calculated stiffness constants of Zn3As2 justify these necessity conditions for mechanical stability at zero pressure and 0 K temperature.The stiffness constants C11 and C33 determine the resistance to linear compression in [100]/[010] and [001] directions respectively. From , C11is found to be greater than C33, which implies that [001] direction is reliable to more compression as compared to [100] and [010] directions. Thus, indicating higher bonding potential in [100] and [010] directions as compared to [001] direction. The stiffness constants C44 and C66 measure the shear modulus in the direction [100] along the (001) and (010) plane respectively. As C44> C66, it implies that the (001) plane offers higher resistance for monoclinic shear distortion as compared to the (010) plane. This in turn determines the indentation hardness of Zn3As2.Apart from the stiffness constants, the macroscopic elastic parameters like bulk modulus (B) associated with resistance to volume deformation and shear modulus (G) associated with resistance to plastic deformation defines the mechanical strength of the compound and are calculated using the Voigt and Reuss theories. The Voigt model calculates the upper limit of bulk (BV) and shear (GV) modulus as The Reuss model calculates the lower limit of bulk (BR) and shear (GR) modulus where, M=[C11+C12+2C33−4C13] and C2=[C11+C12]C33−2C132.To calculate the effective elastic moduli, Hill's discovered Voigt-Reuss-Hill's approximation where bulk (BH) and shear modulus (GH) are calculated as an average of these two upper and lowerlimits Hence, the elastic moduli evaluated from the above equations are reported in . Clearly, bulk modulus obtained from EOS and Cij's are observed to be coherent with each other. Due to non-availability of experimental as well as theoretical data, comparison of the present data could not been performed.To estimate the plastic range of a material, Pugh Further, Poisson's ratio determines the nature of chemical bonding existing in the material. For the covalent materials it is equivalent to unity, whereas for ionic bonding υ=0.25. The calculated Poisson's ratio for Zn3As2 is 0.27. This implies that ionic bonding is dominating in Zn3As2For each material existing in nature, there exists varying degree of elastic anisotropy. The shear anisotropy factors determine the degree of anisotropy of chemical bonding present in different crystallographic planes. Tetragonal structure of Zn3As2 has two shear anisotropy factors to calculate elastic anisotropy Factor A1 corresponds to (100) and (010) plane while A3 belongs to (001) plane. Anisotropic factor of unity belongs to the isotropic structure while the value higher or lower than unity measures the degree of elastic anisotropy. The calculated value of A1 is 1.39 and A3 is 0.69, this implies that Zn3As2 is an anisotropic structure with higher degree of anisotropy along (100) and (010) plane as compared to (001) plane. This nature of elastic anisotropy is associated only with (100) and (001) crystallographic plane of Zn3As2. Thus, to overview the elastic anisotropy of Zn3As2 structure as a whole, we have calculated anisotropy of bulk modulus (AB) and shear modulus (AG) using Voigt and Reuss elastic modulus from the following relations:AB and AG of Zn3As2 are 0% and 4.2% respectively. From the calculated value of AB and AG it is observed that Zn3As2 has isotropic elastic compressibility and high degree of shear anisotropy.From the calculated elastic moduli, BH and GH, θD can be determined at absolute zero temperature and pressure. Since, at low temperature, acoustic vibrations are responsible for vibrational excitations, hence, θD, is thus calculated from the average sound velocity, ϑm, using the expression where, h is Plank constant, k is Boltzmann's constant, NA is Avogadro's number, ρ is the density, M is the molecular mass per formula unit, n is the number of atoms per formula unit and ϑm is the average wave velocity. The average wave velocity ϑm , is calculated from Ref. where, ϑt and ϑl is transverse and longitudinal elastic wave velocity respectively. These are defined as The values calculated from the above equations are reported in . Hence, θD of Zn3As2 as obtained from the elastic tensors at 0 K is 324 K.Isotropic CP, corresponding to hybrid functional theory, provides the best agreement with the experiment. Directional CPs have also been computed along [100], [110] and [111] directions, from which [111] is found to have the maximum electron momentum density at pz = 0a.u. Band structure and density of states calculation elucidate its semiconducting properties, thus supports its applicablity in optoelectronic devices and solar applications. Elastic modulus calculated using both EOS calculation and elastic constants show nice coherence and proves Zn3As2 as a ductile compound. Elastic anisotropy of Zn3As2 shows high degree of shear anisotropic behaviour, while elastic compressibility is isotropic in nature. Although at some points, non-availability of experimental data hinders the verification. In this sense, experimental confirmation of the presented data is expected in near future.Effect of yaw angle misalignment on brake noise and brake time in a pad-on-disc-type apparatus with unidirectional compliance for pad supportA pad-on-disc-type brake apparatus was constructed based on a theoretical principle for suppressing frictional vibration. The pad for this apparatus was supported by parallel leaf springs with a unidirectional compliance. Braking tests were conducted using the apparatus under a constant normal load. It has been found that a yaw angle misalignment between the directions of the pad and disc motions provides a positive damping to suppress the frictional vibration and brake noise. In addition, it has been also found that when an appropriate misalignment angle is selected, a low-noise performance and a good braking performance can be achieved simultaneously.stiffness of pad support in ξ-axis directionoverall sound pressure level of brake noiseaxes of coordinate system based on disc velocity directionpad accelerations in ξ- and η-axis directions, respectivelykinetic friction coefficient when Vrel=Vkinetic friction coefficient (function of Vrel)effective kinetic friction coefficient (function of V)axis of coordinate system based on pad support directionconstant direction of ξ axis from V: “misalignment angle”Brake noise is one of the classical problems for brake systems. When brake noise occurs in an automobile, the passengers feel uncomfortable. Therefore, it has long been thought to decrease the commercial value of an automobile, and has been an important problem requiring a solution. It is obvious that brake noise is strongly related to frictional vibration because brake systems are typical sliding systems. For example, Hervé et al. A variety of methods to eliminate brake noise have been proposed from the viewpoints of the materials in contact Recently, from the viewpoint of structural design, Nakano et al. Based on the above, this study experimentally examined the method proposed by Nakano et al. briefly describes the principle for the method. It is theoretically shown that an angular misalignment provides positive damping to suppress the frictional vibration induced by the velocity-weakening friction. describes the pad-on-disc-type brake apparatus with angular misalignment. Parallel leaf springs are used to make a unidirectional compliance for supporting the pad. discusses the experimental results of braking tests using the apparatus. It is shown that when the misalignment angle is 30°–45°, the pad vibration and brake noise are minimized. In addition, it is shown that when they are minimized by angular misalignment, the brake time is also minimized. shows a model that describes the principle for suppressing frictional vibration in disc brake systems proposed by Nakano et al. The equation of motion of the pad is written aswhere ξ and m are the displacement and mass of the pad, respectively; k is the supporting stiffness in the ξ-axis direction; F(Vrel) is the frictional force acting on the pad as a function of the relative velocity Vrel; θ is the direction of the frictional force from the ξ axis; and (•) is the derivative with respect to the time t. Note that the direction of the frictional force corresponds to that of the relative velocity. From the velocity triangle consisting of the disc velocity V, pad velocity ξ̇, and relative velocity Vrel, we obtainLetting R and Ω be the radius position of the contact and the angular velocity of the disc, respectively, we obtain shows that if the pad velocity is changed, the direction of the frictional force is changed autonomously.Linearizing these equations around Vrel=V, we obtainThe two coefficients, c1 and c2, in the second term on the left-hand side of this equation are the effective damping coefficients arising from the frictional force, defined aswhere F′(V) is the slope of the function F=F(Vrel) at Vrel=V.When the slope F′(V) is negative, c1 is also negative, which gives a negative damping that causes frictional vibration. Meanwhile, the additional coefficient c2 is always positive, which gives a positive damping that suppresses frictional vibration. Therefore, in this model, even if F′(V) is negative, we find that frictional vibration does not occur when the misalignment angle φ is larger than the critical misalignment angle φcr, i.e.,φ>φcr=tan−1−F′(V)VF(V)=tan−1−μ′k(V)Vμk(V)where μk(V) is the kinetic friction coefficient at Vrel=V. It should be noted that this stability condition does not depend on the normal load, which is an advantageous characteristic for the application to disc brake systems, in which the normal load varies over time.It should be stressed that the stabilization effect described above is provided by instantaneous change in the frictional force direction θ, under the presence of the yaw angle misalignment φ, which occurs according to Eq. as a function of the pad velocity ξ̇. Considering that the change in the frictional force direction is inevitable in two-degree-of-freedom sliding systems, the stabilization effect might have been underlying in everywhere. shows a photograph and schematic diagram of the pad-on-disc-type brake apparatus that embodies the model of . This apparatus employs a plane contact between a gray cast iron disc (diameter: 250 mm, thickness: 10 mm, and arithmetic mean roughness: 2.5 μm) and a phenol resin pad (Young’s modulus: 5 GPa, diameter: 20 mm, and thickness: 5 mm). The disc is connected to a flywheel through a main shaft mounted in a bearing unit so that the disc rotates freely around the shaft, where the moment of inertia of the whole rotor is J=0.70 kg•m2. A rotary encoder connected to the shaft by a timing belt measures the disc angular velocity Ω. Meanwhile, the pad is supported by phosphor–bronze parallel leaf springs mounted on a z-axis linear guide. The position of the pad is R=75 mm below from the rotational center of the disc. A coil spring and a jack are placed in series behind the parallel leaf springs to apply the normal load W to the contact by using the spring force of the coil spring. A load cell placed in series behind the jack measures the normal load. To measure the sound pressure p of the brake noise, a microphone is mounted on the extended line of the rotational axis at a distance of 100 mm from the disc. shows the detailed structure around the pad. The xy plane is parallel to the disc surface, and the x axis corresponds to the direction of the disc velocity V at the contact between the pad and the disc. The ξ and η axes show the principal axes of the parallel leaf springs. The length, width, and thickness of the exposed part of a leaf spring are 20 mm, 60 mm, and 0.6 mm, respectively; and the distance between the two leaf springs is 40 mm. Therefore, the stiffness of the parallel leaf springs in the ξ-axis direction (k=210 kN/m) is the smallest among the three principal stiffnesses. The angle between the x and ξ axes is the misalignment angle φ. In this figure, three configurations for φ=0°, 45°, and 90° are shown as examples. An acceleration sensor is mounted behind the pad for measuring the pad accelerations in the ξ- and η-axis directions, which are denoted by αξ and αη, respectively.Using the pad-on-disc-type brake apparatus, braking tests were conducted as follows. First, after cleaning the surfaces of the pad and disc using ethanol, the running-in procedure was carried out at φ=0°, W=100 N, and V~1 m/s by rotating the disc manually until the brake noise remained stable. Then, after setting φ under a non-contact condition, W=100 N was applied again. Finally, the disc was rotated up to Ω=200 rpm manually. Then, during the free rotation of the disc, the temporal changes in the disc angular velocity (Ω), pad accelerations (αξ and αη), and sound pressure (p) were measured, at a sampling rate of 40 kHz, by using the rotary encoder, acceleration sensor, and microphone, respectively, until the disc was stopped completely by the frictional force between the pad and the disc. The braking test described above was conducted three times at values of φ ranging from 0° to 90°. All the tests were conducted at an ambient temperature of 25 °C and a relative humidity of approximately 20%. shows typical experimental results for the temporal changes in Ω, αξ, αη, and p when φ=0°, 30°, 60° and 90°, where the results for the 5-s period after Ω=180 rpm are shown., the disc angular velocities appear to decrease linearly in time from Ω=180 rpm to 0 rpm. Observing these carefully, however, we find that they are slightly convex upward. Considering that the magnitude of the negative slope of the function Ω(t) is proportional to the magnitude of the frictional force, the convex shapes indicate that the frictional force between the pad and the disc has a velocity-weakening characteristic that causes frictional vibration. In fact, using the temporal changes in Ω shown in , we obtain the effective kinetic friction coefficient μkeff as a function of the disc velocity V, as shown in . To obtain this figure, the instantaneous values of μkeff are calculated byand then they are plotted against the instantaneous values of V=RΩ, where P¯ and ΔΩ in Eq. are the mean energy consumption rate by the frictional force and change in Ω in a time window Δt (=0.25 s for ), respectively. We find negative slopes for the function μkeff(V) for all φ in the first-order approximation, indicating the velocity-weakening characteristic. In addition, we find significant differences in μkeff(V) for different φ, leading to a change in the brake time Tb. Among these, the highest value of μkeff(V) is found when φ=30°, leading to the shortest brake time Tb=3.30 s.Considering that the frictional vibration is suppressed when φ=30° as shown in the second row of , the results on the magnitude of μkeff(V) shown in are consistent with those of the experiments by Kado et al. , we find the effect of the angular misalignment on the pad vibration. When φ=0°, we find vibrations in the ξ-axis direction during the brake time, whereas in the η-axis direction, we just find vibrations with a fairly small amplitude. When φ=30°, the vibration in the ξ-axis direction seems to disappear, but when φ=60° and 90°, vibrations with large amplitudes appear in both directions. Note that when φ=0° and 90°, the amplitude of the vibration in the disc velocity direction (i.e., the x-axis direction) is larger than that in the perpendicular direction (i.e., the y-axis direction). In addition, from the bottom row of , we find brake noise for φ=0°, 60° and 90°, but when φ=30°, the brake noise seems to disappear.It is noted that these vibrations and noises are convergent just before the disc stops, which can be partly because of the positive damping effect originated from the positive slope in the kinetic friction coefficient shown in a low velocity range in . Another possible reason is change in the positive damping coefficient c2, which is, as Eq. shows, increased with decreasing V, especially in a low velocity range. shows the mean spectra of the brake noise based on the sound pressure level (SPL) calculated from p(t) for t<3 s for three measurements. The vertical broken lines show the natural frequencies obtained experimentally when the pad unit or disc is hammered independently under a non-contact condition. The abbreviations for the natural frequencies are as follows: PTξ (110 Hz) is the translational motion of the pad in the ξ-axis direction; PRξ (1340 Hz and 2380 Hz), PRη (4900 Hz), and PRζ (1860 Hz) are the rotational motions of the pad about the ξ-, η-, and ζ-axis directions, respectively; and Dij (D20: 840 Hz, D30: 1760 Hz, and D40: 3050 Hz) is the out-of-plane motion of the disc with i nodal lines and j nodal circles, where the modes of the pad motions were detected by using the phase difference between the signals from two acceleration sensors mounted on the pad holder, and the modes of the disc motions were detected by using the phase difference between the signals from two microphones mounted close to the disc surface.When φ=0°, the dominant components of the brake noise were PTξ (110 Hz) and its harmonics (220 Hz and 330 Hz). It is believed that the velocity-weakening friction confirmed in caused the dominant components. Meanwhile, from the spectrum for φ=30°, we find that applying the angular misalignment eliminates the dominant components down to the background noise level. Therefore, we can conclude that this is a suppression effect of the angular misalignment because the principle stated in requires the pad motion in the ξ-axis direction, which provides a positive damping using the change in the direction of the frictional force. However, when φ=60° and 90°, several other dominant components appeared, e.g., those close to D20 (840 Hz), D30 (1760 Hz), and D40 (3050 Hz). These were probably caused by a different mechanism for frictional vibration, i.e., the mode-coupling instability. At present, we have no theoretical background to show that the angular misalignment suppresses the frictional vibration induced by the mode-coupling instability. However, the dominant component close to D20 appeared to be minimized at φ=30°.It should be noted that based on the structures of actual disc brake systems, the result when φ=90° in this apparatus can be regarded as the baseline for estimating the effect of yaw angle misalignment because the pad support in actual systems is closer to that when φ=90° than that when φ=0°. From this viewpoint, the experimental results show a possibility that a pad setting with a yaw angle misalignment suppresses the squeal noises originated form disc vibrations in actual systems. It should be also noted that the various types of vibrations observed here are not always linear and thus nonlinear effects between them can determine the final noise levels. shows the effects of the misalignment angle (φ) on the overall SPL of the brake noise (Lp) and brake time (Tb). The plots represent the mean values of three experiments conducted for each φ, and the error bars represent their standard deviations. The upper graph shows that Lp decreases from 110.4 dB with increasing φ from 0°, with a minimum of 105.6 dB when φ=30°. Then, it increases to the maximum of 139.3 dB when φ=75°, and when φ=90°, it has a value of 129.9 dB, which is close to the value for φ=60°. This means that when φ=30°, Lp is 5 dB less than that for φ=0° and 24 dB less than that for φ=90°. Meanwhile, the lower graph shows that Tb decreases from the maximum of 3.68 s with increasing φ from 0°, with a minimum of 3.24 s for φ=45°. Then, it increases to 3.62 s when φ=75°, and when φ=90°, it has a value of 3.46 s, which is close to the value for φ=60°. This means that when φ=45°, Tb is 12% less than that for φ=0° and 6% less than that for φ=90°. showing the relationship between Lp and Tb when the angular misalignment is changed from 0° to 90°, where all the measured values are shown in this graph without averaging. Note that a small Lp means a good low-noise performance, and a small Tb means a good braking performance. This figure shows that both performances can be maximized when φ=30°–45° in the pad-on-disc-type brake apparatus. Its theoretical generalization is expected in future studies.Finally, it should be noted that experimental results qualitatively consistent with those shown in this paper have also been obtained when W=50 N, which supports the conclusion that the proposed method using the positive damping provided by the angular misalignment is insensitive to a change in the normal load, although in theory, the suppression performance of additional dampers depends on the normal load Based on a theoretical principle for suppressing the frictional vibration from the viewpoint of structural design, a pad-on-disc-type brake apparatus was constructed, the pad of which was supported by parallel leaf springs having a unidirectional compliance. In braking tests using the apparatus, the following conclusions were confirmed.The yaw angle misalignment between the directions of the pad and disc motions provides positive damping to suppress the frictional vibration caused by the velocity-weakening friction. This eliminates the corresponding frequency component and its harmonic components included in the brake noise.The appropriate misalignment angle to minimize the frictional vibration and brake noise is approximately 30°–45°. When the appropriate angle is used, the effective kinetic friction coefficient is maximized, and thus a good low-noise performance can be achieved with a good braking performance.Flutter of structurally inhomogeneous cantilevers in laminar channel flowFlutter instability of flexible cantilevers axially immersed in channel flow has been studied mainly for slender bodies with uniform properties. The present study addresses the stability of one-dimensional stepped cantilevers comprising two sections of different thickness immersed in two-dimensional viscous channel flow. The influence of the relative mass and rigidity of the two sections on the motion of the cantilever is explored through variations of length and thickness ratios. The parametric investigation shows that, for instance, making the free end of the cantilever twice thinner or thicker than the clamped end over a short fraction can produce structures that are either more stable or more unstable, depending on the fluid-to-solid mass ratio. In the case of a heavy and stiff free section and a light and flexible clamped section of comparable length, the excitation of lower structural modes by slower flows is significantly destabilising as compared to a uniform cantilever of same length and total mass. Strong destabilisation and weak stabilisation of the fluid–structure interaction system can result from either thinning or thickening the cantilever free-end which can also lead to changes in the flutter mode shape. These complex variations are quantitatively presented through stability maps.The vast majority of fundamental studies on flow-induced fluttering bodies has focused on low complexity models including idealised geometries and a limited number of parameters () causes flutter. Designs to modify and control the structural response were explored mainly through external alterations and additions to the slender body, including changes of mounts and supports (), and added masses, springs and dampers (). This study investigates the flutter instability of flexible cantilevers of non-uniform thickness axially immersed in viscous channel flow. It focuses on the identification of the conditions for which the two sections of stepped cantilevers might sustain each others’ oscillations or behave as mainly separate uncoupled structures.Most recent analyses of flutter instability of flexible structures immersed in axial flow provided innovative approaches to energy harvesting (), and building and vehicle panel-vibration suppression (). The solutions investigated for energy harvesting and fluid mixing aimed to extend the parameter ranges over which flutter instability occurs and enhance the structural oscillations. On the other hand, for most other applications, the objectives are usually delay and mitigation of flutter to avoid structural instabilities and reduce their adverse effects, such as destructive failures. Both promoting and preventing flutter oscillations require reliable prediction and efficient control of the FSI instabilities and their desired or undesired effects, such as material fatigue, power extraction (), variations of hydro-/aero-dynamic efficiency (In many fields of engineering, compliant structures interacting with aerodynamic forces can have non-uniform geometric and mechanical properties (). In biomechanics, for instance, the vibrations of the soft-palate and its conical extension, the uvula, induced by inspiratory airflow is an FSI system studied extensively in recent years for its implications in breathing disorders such as snoring and obstructive sleep apnoea. The complex shape and composite structure of the uvulopalatal system originate from the layered soft tissues with viscoelastic properties varying anisotropically (). Numerical models of this particular FSI system have been proposed to account for the intricate geometric configuration of the airway and the tissue () as well as the local variations in mechanical properties (). Most of these studies have provided detailed accounts of the passive motion of the soft palate and its effect on the flow properties, but only for a limited number of specific cases. These more elaborate and comprehensive models can be challenging to control and computationally demanding so that they are often used for particular problems and conditions. Therefore, this approach usually only provides limited understanding of the physical phenomena and the critical parameters underlying FSI instabilities in laminar flow which can be found, for instance, during slow breathing and in blood flow.In this study, the coupling of one-dimensional stepped cantilevers, comprising two sections with different mass and flexural rigidity, to two-dimensional Navier–Stokes equations is numerically simulated for a Reynolds number of 200, based on the channel height, to ascertain the nature of the cantilever’s flow-induced motion. The instability boundaries of the FSI system are determined through a comprehensive parametric analysis of its linear stability. Thus, over the wide ranges of parameters explored, results demonstrate the complex dynamics of the inhomogeneous flexible structure interacting with the surrounding fluid. This investigation ultimately provides details to elucidate whether a stepped cantilever with a thinner or thicker free-end immersed in an axial flow can be more unstable than its uniform counterpart.An infinitely-thin flexible cantilever axially immersed in two-dimensional viscous channel flow constitutes the FSI system represented schematically in (a) in dimensional form (all dimensional quantities are denoted by ∗). The cantilever beam of length LC∗ and thickness hC∗ is characterised by its density ρC∗ and flexural rigidity B∗=Eeff∗hC∗3∕12, where Eeff∗ is the effective Young’s modulus defined as Eeff∗=E∗∕(1−ν2) with E∗ and ν being, respectively, the Young’s modulus and Poisson’s ratio of the solid material. The fluid, characterised by its density ρF∗ and dynamic viscosity μF∗, is flowing in a channel of length L∗ and height H∗. The flexible cantilever is clamped to a rigid wall of length Linlet∗ positioned along the centreline of the channel and parallel to the channel walls. The upstream end of the channel is thus divided into two inlets of identical height H∗∕2 at which identical steady Poiseuille velocity profiles with average velocity U∗ are imposed. The downstream end of the channel, located at a distance Loutlet∗ from the downstream free end of the flexible cantilever, is set as the outlet where the flow is assumed to be parallel and axially traction-free.The shape of the flexible cantilever is represented solely by its centreline, parameterised by the one-dimensional Lagrangian coordinate ξ∗. The non-uniform flexural rigidity and mass are varied locally through a thickness function hC∗(ξ∗) dividing the cantilever into two sections of length Lclamp∗ and Lfree∗, and thickness hclamp∗ and hfree∗, corresponding respectively to the clamped-end and free-end as shown in (b). To avoid discontinuities in the thickness profile, a smoothstep-2 polynomial function (see Eq. ) is used over the relatively short length Ltrans∗ to smooth the transition between the two sections. The shape of the thickness profile is based on the constant reference thickness h0∗ (corresponding to the uniform cantilever for which hC∗(ξ∗)=h0∗) and parameterised by the length ratio ϑL=Lfree∗∕LC∗ and thickness ratio ϑh=hfree∗∕hclamp∗ so that Lfree∗=ϑLLC∗, Lclamp∗=(1−ϑL)LC∗ and hC∗(ξ∗)=hclamp∗=h0∗(1−ϑL)+ϑLϑh,ξ∗<ξA∗=Lclamp∗−Ltrans∗2hclamp∗+hfree∗−hclamp∗×6ξ∗−ξA∗Ltrans∗5−15ξ∗−ξA∗Ltrans∗4+10ξ∗−ξA∗Ltrans∗3,ξA∗≤ξ∗≤ξB∗hfree∗=ϑhh0∗(1−ϑL)+ϑLϑh,ξ∗>ξB∗=Lclamp∗+Ltrans∗2.This piecewise function allows keeping the average thickness hC∗¯ and total mass of the stepped cantilever beams the same as those of the uniform cantilever beam, so that hC∗¯=h0∗.To analyse the problem in non-dimensional form, all geometric dimensions and spatial coordinates are scaled with the channel height H∗, flow velocity components with the average inlet velocity U∗, the fluid stresses with the viscous scale μF∗U∗∕H∗, solid stresses and loads with effective Young’s modulus Eeff∗, and time with H∗∕U∗. This leads to five non-dimensional parameters, in addition to the length and thickness ratios ϑL and ϑh, characterising the FSI dynamics: M¯=ρF∗LC∗ρC∗hC∗¯=ρF∗LC∗ρC∗h0∗,U¯=U∗LC∗ρC∗hC∗¯B∗¯=U∗LC∗ρC∗h0∗B∗¯,Re=ρF∗U∗H∗μF∗,LH=LC∗H∗,hL=h0∗LC∗.The stability of the FSI system depends primarily on the average mass ratio M¯ and average reduced velocity U¯. For different stepped cantilevers obtained from variations of ϑL and ϑh, the average mass ratio remains constant as the thickness profile function is set to keep hC∗¯=h0∗ and the total solid mass constant. However, for a particular value of average reduced velocity, the behaviour of the FSI can differ significantly depending on ϑL and ϑh, as these two ratios affect the local mass and rigidity of the beam. The Reynolds number Re, the ratio LH between cantilever-length and channel-height and the cantilever thickness-to-length ratio hL are independent of the thickness profile and set constant for all the configurations investigated (see Section is used to carry out time-marching numerical simulations of the FSI system. An overview of the approach employed and its implementation is provided in the following sections. Further details can be found in the extensive tutorials available on the ). Rigorous validation of the FSI methods and modelling used in the present study can be found in the study conducted by The two-dimensional fluid domain shown in (a) is discretised using nine-node quadrilateral Taylor–Hood elements implemented with adaptive mesh-refinement capabilities. The body-fitted fluid-mesh is updated using an algebraic node update procedure, based on a generalisation of Kistler and Scriven’s “method of splines” (). A second-order backward differentiation formula scheme is used for the fluid time-stepping. The incompressible Navier–Stokes equations, are solved in the Eulerian coordinate system x=x1,x2 for the non-dimensional fluid velocity u and pressure p.At both inlets, a parabolic velocity profile is imposed for the axial velocity so that u=12x21−2x2e1,0≤x2≤H∕2(upper inlet)−12x21+2x2e1,−H∕2≤x2≤0(lower inlet),where e1 and e2 are the unit vectors of the Eulerian coordinate system. At the outlet, where the flow is assumed parallel, the transverse velocity is set to zero while the axial velocity is determined using the axially-traction-free outflow condition. The no-slip condition is applied on all stationary (u=0) and flexible-cantilever walls.The motion of the flexible cantilever is solved using a one-dimensional, elastic Kirchhoff–Love beam discretised using two-node Hermite finite elements. A Newmark scheme is used for the solid time-stepping. The position vector to a material point is given by r(ξ) in the undeformed cantilever and by R(ξ) in the cantilever deformed by a resultant load Teff combining the tractions acting on the top and bottom of the beam. The principle of virtual displacements that governs the cantilever motion is given by ∫0LHγδγ+hC212κδκ−1hCAaTeff−U¯hL212∂2R∂t2⋅δRadξ=0,are the squares of the lengths of infinitesimal material line elements in the undeformed and deformed configurations, respectively. Therefore, the ratio A∕a represents the stretch of the cantilever centreline while the strain γ and bending κ are given by representing the curvature of the cantilever centreline, respectively, before and after the deformation. n and N denote the unit normals (pointing into the fluid, as shown in (a)) to the top face of the undeformed and deformed cantilever centreline, respectively.The downstream end (ξ=1) of the flexible cantilever is free while its upstream end (ξ=0) is clamped to the rigid wall dividing the channel inlet, so that ) and the Newton–Raphson method is used to solve the non-linear system of equations for the FSI system, employing the SuperLU direct linear solver within the Newton iteration.The no-slip condition on the flexible walls (top and bottom of the cantilever) is given by where Rˆ is the position vector of the FSI interface. The fluid load acting on the beam in Eq. combines the fluid tractions on the top and bottom of the cantilever so that Teff=U¯hL212M¯hLReptopI−∇u+∇uTtop⋅N−pbottomI−∇u+∇uTbottom⋅N.The primary objective of this study is to characterise the critical instability, i.e. that which first appears with increasing mean flow velocity, of the immersed stepped cantilever in the M¯,U¯ parameter space when the relative length and thickness of the two beam sections, clamped and free, change through variations of the length ratio ϑL between 1/8 and 7/8, and of the thickness ratio ϑh between 0.1 and 10.The base configuration is kept constant for all the cases considered. To ensure that the slender beam approximation holds for all cases, the base cantilever thickness-to-length ratio hL is set to 0.01 (h0=0.02). Also, the Reynolds number Re and the cantilever-length-to-channel-height ratio LH are both fixed to 200 and 2, respectively. While the fluid relative viscosity, corresponding to different values of Re, and the cantilever confinement, corresponding to different values of LH, can play a significant role in the FSI instability mechanisms (), these effects are not explored in the present study. As regards the non-dimensional channel dimensions, the channel height is set to H=1, the length of the wall dividing the inlet to Linlet=1 and the distance between the outlet and the free-end of the flexible cantilever to Loutlet=3Linlet+LH=9. The latter is prescribed to ensure that the effect of the outlet boundary condition on FSI stability characteristics remains marginal while restricting excessive computational cost.Each simulation corresponding to a set of non-dimensional parameters M¯,U¯,ϑL,ϑh is initialised as follows: (I) the inlet flow velocity is gradually increased in a sequence of nine steady solutions while the flexible cantilever is constrained in its undeformed shape, and (II) the flexible cantilever is then given a small amplitude deformation and the system is again solved as a steady problem. This initial shape corresponds to the uniform-cantilever in vacuo Mode 2 (n=2, β2≈4.6941) transverse deflection with amplitude ηT0=h0=0.02 at the free-end tip η(ξ)=ηT02coshβnξLC−cosβnξLC−CnSnsinhβnξLC−sinβnξLC,where Cn=cos(βn)+cosh(βn), Sn=sin(βn)+sinh(βn) and βn satisfies the dispersion relation cos(βn)cosh(βn)=−1. The cantilever is then released and the unsteady FSI problem solved with a time step Δt=0.02 until 20 periods of the cantilever-tip oscillation are obtained.The flow domain is meshed initially using a 10 × 90 grid. As shown in , all elements are allowed to be refined or coarsened during the simulation (three times per steady solve during the initialisation and once per time step during the unsteady run) depending on local normalised error. The flexible cantilever is discretised with 80 elements and the transition in the thickness profile (see (b)) is prescribed over 4 of these elements so that the transition length Ltrans represents 5% of the flexible cantilever length LC. This total number of solid elements ensures that enough elements are present in each section of the flexible cantilever to capture accurately the kinematics of the beam deformation, even when Lfree=LC∕8 or Lclamp=LC∕8.The linear stability analysis of the FSI system is based on the time trace of the transverse deflection of the flexible-cantilever tip ηT. The stability or instability of the system is characterised by the exponential decay or growth rate αT of the tip oscillations normalised by the frequency of oscillation fT¯. In this analysis, all frequencies are scaled by the characteristic in vacuo frequency of the uniform cantilever The frequency fT¯ is determined by performing a peak detection on a 8192-FFT of the signal ηT while the growth rate αT is estimated through a linear interpolation of the log envelope detected on the same signal. For particular cases, the cantilever oscillations can very quickly be damped out or leave the linear small-amplitude regime. Therefore, when the FSI system is very stable or unstable, αT and fT¯ are quantified using fewer than 20 periods of the cantilever-tip oscillation. This process allows the mapping of the FSI stability characteristics over 41 values of M¯, logarithmically spaced between 0.1 and 10, and 51 values of U¯, logarithmically spaced between 1 and 50, for variations of the two non-dimensional parameters ϑL and ϑh, to extract the critical combinations of parameters M¯,U¯,ϑL,ϑh for which the immersed stepped cantilever become unstable.Detailed characterisation of the dynamics of the uniform cantilever (ϑh=1) for fixed LH=2 and Re=200 is obtained from the consolidation in the M¯,U¯ parameter space of the data simulated with both sections of the cantilever having the same mass and rigidity as hclamp=hfree=h0. The resulting topography shown in (a) indicates the strength of stability (αT<0) or instability (αT>0) represented by the coloured contours of the normalised exponential growth rate αT of the tip oscillations. The thick solid line denotes the neutral stability (αT=0) demarcating the boundary between stable and unstable motions of the cantilever. The shape of this curve shows that the critical flow velocity U¯crit required to initiate self-sustained oscillations is strongly linked to the structural mode most excited by the flow, hence to the relative properties of the flow and solid. The sequence of lobes representing the cascade from lower to higher order modes with increasing M¯ has been reported in previous studies based on viscous flow modelling () or using the inviscid-flow assumption (). As the channel height is reduced, the critical flow velocity required to destabilise the cantilever decreases because of the greater pressure difference across the cantilever associated with the strengthened axial momentum of the flow. For relatively low Reynolds numbers, the flow characteristics downstream of the cantilever can change considerably () and the inertial effects on the critical velocity are, in relative terms, diminished by the increased viscous contribution to the hydrodynamic forces (). Thus, stabilisation of the immersed-cantilever FSI system as the Reynolds number decreases has been shown to be stronger for high fluid-to-solid mass ratios, usually associated with higher-mode structural oscillations. The influence of the Reynolds number Re and the cantilever-length-to-channel-height ratio LH on the cantilever-tip oscillation frequency, and more generally on the stability boundary, can become significant as these two control parameters alter the interactions between the viscous flow and the individual structural modes. However, the neutral-stability curves globally retain their main features with variations of Re and LH so that the critical values U¯crit and f¯crit of the immersed uniform cantilever for LH=2 and Re=200 can reliably represent the phenomenology described below.For M¯<0.7, Mode 2 is the dominant structural mode and the higher order modes remain unexcited by the flow. Over this range of mass ratio, the frequency f¯T of the oscillations varies relatively smoothly with increasing reduced flow velocity as shown in (b). For M¯>0.8, Modes 3, 4 and 5 successively become the dominant structural mode excited by the flow as the mass ratio increases to 10. For reduced flow velocities lower than the critical velocity, the mode-cascade structure can be observed on the stability map. This translates into abrupt changes in oscillation frequency with increasing reduced flow velocity. For all modal branches of the neutral-stability curve, the critical cantilever-tip oscillation frequency f¯crit is lower than the corresponding in vacuo linear eigenfrequency of the cantilever. In comparison to in vacuo condition, the decrease in frequency at which immersed cantilevers oscillate is caused by the fluid-inertia loading that primarily depends upon the mass ratio (The stability of immersed stepped cantilevers divided in half (ϑL=1∕2) is analysed for variations of the relative thickness ϑh=hfree∕hclamp of the free and clamped sections. The thickness profile of the cantilever with both sections of the same length is given by Eq. (in dimensional form) with Lfree=Lclamp=LC∕2. The results for this particular configuration are presented first to illustrate the range of phenomena associated with the stepped-cantilever instabilities. As shown in (a), when the free section is thinner than the clamped section (ϑh<1), the neutral-stability curve is in general gradually shifted to lower average fluid-to-solid mass ratio M¯ and lower critical velocity U¯crit. Thus, compared to the uniform case, higher structural modes are triggered at lower mass ratios and become more easily excited by the flow as the free section becomes lighter and more flexible. Conversely, when the free section is thicker than the clamped section (ϑh>1), the neutral-stability curve is in general only slightly shifted to higher average fluid-to-solid mass ratio M¯. However, as the free section becomes heavier and stiffer, the critical velocity U¯crit initially increases for 1<ϑh≲2 before significantly decreasing for ϑh≳2. The influence of the relative thickness ϑh on the stability boundary does not produce the same pattern over the higher range of mass ratio for which higher structural modes dominate the motion of the stepped cantilever. This is an indication that the complexity of the three-way interactions between the flow and the two cantilever sections is increased by higher structural modes coming into play with both thinner and thicker free sections. However, at high mass ratio, uniform and stepped cantilevers remain very stable since the reduced flow velocities required to initiate the oscillations become relatively high. It must also be noted that the resolution over the higher range of U¯ is coarser in this study. Thus, overall, for behaviours corresponding to Mode 2, Mode 3 and Mode 4 of the immersed uniform cantilever, an increase in thickness of the free or clamped section of the stepped cantilever tends to destabilise the FSI system except over a narrow range of thickness ratio, 1<ϑh≲2. As shown in (b), the decrease in critical velocity through most of the range of thickness ratio considered is accompanied by a decrease of the critical frequency at which the stepped-cantilever tip oscillates when the system is neutrally stable.The relative thinning or thickening of the free part of the stepped cantilever induces non-linear variations in the FSI system behaviour. The influence of the thickness ratio on the flutter instability thresholds and on the pre- and post-critical cantilever-tip oscillations is illustrated in for M¯=1. In this figure, the instability of the reference uniform cantilever (ϑh=1) corresponds to point (v), which is demonstrated to be a Mode 3 oscillation in (case (v)), and which is also confirmed in at M¯=1. For comparison, the critical velocity and frequency curves of the uniform cantilever equivalent (LH=1) to the free and clamped sections of the stepped cantilever are included in . These curves intersect for ϑh=1 when the two sections are identical and the equivalent uniform cantilever flutters in a Mode 2 motion.When the free part of the stepped cantilever is thinner than its clamped part (ϑh<1), the critical velocity decreases with decreasing thickness ratio, as shown in (a). Thus, the stepped cantilever becomes increasingly more unstable than the uniform cantilever as its free section becomes lighter and more flexible. While the modal motions of the uniform and stepped cantilevers are comparable, the deflection and bending of the clamped part are greatly reduced with decreasing ϑh, as shown in (cases (iv) to (ii)). However, for ϑh<0.2, other modal branches emerge on the stability map because of higher modes of the free section being excited by the flow, as illustrated in (case (i)). Indeed, when the free section becomes much thinner than the clamped section, the latter is much heavier and stiffer than the former and the reference uniform cantilever. Consequently, the free part of the stepped cantilever mainly interacts with the flow while the clamped part remains very stable and contributes only marginally to the motion of its fluttering counterpart. Over this range of thickness ratio, the neutral-stability curve for the stepped cantilever gets closer to that of the uniform cantilever equivalent to the free part, showing that the behaviour of the free part is more independent from the mostly undeformed thick clamped part. It must be noted that the neutral-stability curve for the stepped cantilever does not strictly converge to that of the uniform cantilever equivalent to the free part for very low thickness ratio since the stepped cantilever’s free section is not clamped (by imposed boundary condition) to its clamped part like the equivalent uniform cantilever is to the fixed wall.When the free part of the stepped cantilever is thicker than the clamped part (ϑh>1), its deformation is reduced with increasing thickness ratio but its large displacement is driven by the highly deformed clamped section, as shown in (cases (vi) to (viii)). This results in an initial increase of the critical velocity when the thickness ratio is increased from 1. For a similar modal motion, the thick free section makes the stepped cantilever more stable than the uniform cantilever up to ϑh≈2.2 but strongly destabilises it beyond this value, as indicated in by the rapidly decreasing critical velocity with increasing thickness ratio. However, for ϑh>1.8, a lower mode, as illustrated by case (ix) in , is also excited by the flow at lower reduced velocities, causing the stepped cantilever to be significantly more unstable than the uniform cantilever. The emergence of this lower-mode instability lobe in the stability map for very low values of U¯ results from the effect of an ‘elongated’ added mass, that constitutes the heavier and stiffer free-end section, connected to the lighter and more flexible clamped section. Indeed, have shown that a concentrated mass had the most destabilising effect on the flow-induced flutter of a plate when it was added to the trailing edge. For the stepped cantilever, the relatively thicker free section destabilises the clamped section in a similar way but, unlike a concentrated mass, also interacts with the flow even if it does not deform considerably. Therefore, it has a more extensive effect on the motion of the clamped section and on the whole FSI system behaviour. This is clearly indicated by the stepped cantilever’s lower mode being increasingly unstable with increasing thickness ratio while only modes of the clamped section’s equivalent uniform cantilever higher than Mode 3 can become unstable for ϑh>4.5.The modifications of the stepped cantilever’s stability boundary caused by variations of the thickness ratio for different average mass ratios follow similar trends to that observed for M¯=1. However, for some average mass ratios, e.g. M¯=0.25 or M¯=2, the neutral stability of the reference uniform cantilever is clearly associated with a single modal motion. In these cases where the regions of transition to lower or higher mode instabilities are sufficiently separated, lower structural modes of the stepped cantilever cannot become unstable with a thicker free section so that new modal branches do not appear on the stepped cantilever’s stability map as the thickness ratio is increased beyond ϑh=1. At the other end of the stepped cantilever’s stability map, for decreasing thickness ratio below ϑh=1, higher modes of the thinner free section can become unstable and dominate the stepped cantilever motion for any average mass ratio. This can result in the stepped cantilever being more stable than the reference uniform cantilever. Thus, with a free part significantly thicker than the clamped part, the stepped cantilever is always more unstable than the reference uniform cantilever, as well as more unstable than the uniform cantilever equivalents to both the free and clamped sections. Otherwise, the changes in thickness ratio can make the stepped cantilever either more stable or more unstable than the reference and equivalent uniform cantilevers.In this section, the influence of the relative length of the free section on the stability of stepped cantilevers is examined. The analysis focuses on the two particular cases in which the free section is either twice as thin (ϑh=1∕2 or hfree=hclamp∕2) or twice as thick (ϑh=2 or hfree=2hclamp) as the clamped section. As defined in Eq. , when the stepped cantilever consists almost exclusively of its clamped part (ϑL→0+) or of its free part (ϑL→1−), it becomes identical to the reference uniform cantilever. Therefore, for any thickness ratio ϑh, the total volume of solid material remains constant and the stability characteristics of the stepped cantilever evolve cyclically from and to those of the reference uniform cantilever as the length ratio ϑL increases from 0 to 1.For the case when the free section is thinner than the clamped section, it can be seen from (a) that the neutral-stability curve is generally shifted to lower average fluid-to-solid mass ratio M¯ in comparison to the reference uniform cantilever, except when the thin free part occupies more than three quarters of the stepped cantilever. For ϑL=7∕8, the critical velocity curves for the uniform and stepped cantilever are almost superimposed, indicating that the stepped cantilever with a long and thin free part, and a short and thick clamped part behaves almost like its uniform counterpart. This is confirmed by the mode shape for case (xi) shown in which is similar to that of the reference uniform cantilever (case (v)) shown in . For ϑL<3∕4, the shift to lower mass ratio of Mode 2, Mode 3 and Mode 4 branches is accompanied by a general decrease of the critical velocity except when the free section becomes relatively short. Indeed, the neutral-stability curve corresponding to ϑL=1∕8 is the only curve with higher U¯crit than that of the uniform cantilever throughout almost the whole range of M¯. In this case, the short and thin free section makes the stepped cantilever more stable than the reference uniform cantilever for all mass ratios considered. Thus, the long and stiffer clamped section does not bend significantly and most of the deformation of the stepped cantilever occurs in the more flexible free section, as shown in (case (x)). Also, the modal transitions are smoother for ϑL=1∕8, and to a lesser extent for ϑL=1∕4, denoting a damping effect of a shorter thin free section on the motion of the stepped cantilever. As shown in (a) for different average mass ratios, relatively short and long free sections tend to stabilise stepped cantilevers with a free part twice as thin as their clamped part, and this stabilisation can be more pronounced for ϑL<3∕8. On the other hand, these stepped cantilevers tend to be more prone to instability for 3∕8<ϑL<5∕8. Over this range of length ratio, free and clamped sections are of comparable length and thickness, so that they can more easily interact to reciprocally sustain their flow induced motion, while the bandwidth of destabilising flow velocity is increased for the whole stepped cantilever system.When the free section is thicker than the clamped section, the neutral-stability curve is generally shifted to higher average fluid-to-solid mass ratio M¯ in comparison to the reference uniform cantilever, as shown in (b), except when the thick free part occupies more than three quarters of the stepped cantilever. Similar to the case hfree=hclamp∕2, the critical velocity curves for the uniform cantilever and the stepped cantilever with ϑL=3∕4 and ϑL=7∕8 are almost superimposed when hfree=2hclamp. Thus, e.g. for M¯=1, the mode shape for case (xiv) shown in is comparable to that of the reference uniform cantilever (case (v)) shown in . The shift to higher mass ratios of the different modal branches is more pronounced for relatively short and thick free section (ϑL<3∕8) and all the higher modes become unstable at lower reduced flow velocity. However, for M¯<3, the critical velocities associated with Mode 2 instability for all the values of length ratio considered almost coincide with that of the reference uniform cantilever. Thus, a free section twice as thick the clamped section, and of any length, appears to have very little influence on the stepped cantilever’s stability for the lower range of mass ratio. More generally, for mass ratios at which the neutral stability of the reference uniform cantilever is clearly associated with a single modal motion, e.g. M¯=0.25 or M¯=2, variations of ϑL appears to have limited effect on the stability boundary, as shown on (b). On the contrary, for mass ratios corresponding to regions of transition to lower or higher mode instabilities, e.g. M¯=1 or M¯=4, lower structural modes can become unstable at significantly lower reduced velocities when the thick free part occupies less than half of the length of the stepped cantilever, as illustrated in For oscillations of the stepped cantilevers in the linear regime, the influence of the modal shapes would have overall very limited impact on the flow in the channel. Indeed, for small-amplitude deflection of the cantilever, flow separation at the trailing edge and vertex shedding downstream are nearly non-existent or remain negligible. However, as shown in , for large-amplitude oscillations, the modal shapes resulting from placing the step at different locations along the length of the cantilever can significantly influence the flow patterns generated by the cantilever motions. Thus, with a relatively short and light free section (e.g. case (x)), most of the stepped cantilever’s deflection is concentrated around this free part, so that the flow directly above and below the clamped section remains mainly undisturbed. When the clamped section undergoes larger-amplitude oscillation (e.g. case (xii)), the flow is disturbed further upstream from the trailing edge. This appears to alter flow separation at the trailing edge and the shape of the vortices shedding in the wake region immediately downstream of the trailing edge. The influence of the modal shape on the vortical structures is less prominent further downstream of the trailing edge (region not shown in showed the rapid dissipation of the flow disturbances generated by oscillating cantilevers at low Reynolds numbers. Moreover, also showed that this attenuation effect was amplified with an increasing confinement of the cantilever. Therefore, for the configuration considered in this study (Re=200 and LH=2), an early attainment of plane Poiseuille flow can be expected in the downstream part of the channel. Configurations based on higher Reynolds number and wider channels to limit interference of the channel walls with the system dynamics might be more relevant to determine the influence of the stepped cantilevers’ modal shapes on the vortical patterns in the wake and the fluid–structure interactions mechanisms in the non-linear regime of oscillation.Variations of the relative thickness of two connected flexible sections forming a stepped cantilever immersed in axial channel flow can have contrasting effects on the flutter instability thresholds and induce non-linear variations of the pre- and post-critical behaviours of the FSI system. Thinning or thickening the free end of a flexible cantilever is shown to influence greatly the bending motions of the structure. By altering the cantilever dynamics, this can result in a relatively weak stabilisation or a strong destabilisation of the FSI system and can change the shape of the mode that first becomes unstable with increasing flow speed. While the neutral-stability curves corresponding to different stepped cantilevers retain a similar shape to that of the uniform cantilever when the overall fluid-to-solid mass ratio is kept consistent between all cases, they are shifted along both the mass ratio and reduced flow velocity axes of the stability map when a non-uniform thickness is introduced. The figures presented in this paper can thus be used as lookup charts to evaluate quantitatively the overall consequences of different degrees of non-uniformity in immersed cantilevers on the neutral stability of the FSI system.In general, predominance of the higher mode instabilities is triggered for lower mass ratios for the flexible cantilevers with a thinner free-end, in comparison to the uniform case. Conversely, for the flexible cantilevers with a thicker free-end, the predominance of the higher mode instabilities is triggered only for higher mass ratios. An overview of the effects on the stability characteristics expected at any particular average fluid-to-solid mass ratio for variations of the relative thickness and length of the free section of the stepped cantilever is presented in . In this table, it can be noted that the flutter instability thresholds for most modes, from 2 to 5, remain comparable (within 5%) to those of the equivalent uniform cantilever when the thickness of the free section of the stepped cantilever is kept between 0.7 and 2 times that of the clamped section. With two sections of the same length and a free part more than twice thicker than the clamped part, a stepped cantilever is expected to be significantly more unstable than the corresponding uniform cantilever, as well as uniform cantilevers equivalent to the free and clamped sections, particularly if the thickness ratio is sufficiently high to destabilise a lower structural mode excited by much slower axial flows. However, results show that a relatively long free section generally reduces the effects introduced by its thickening or thinning, and yields stability characteristics for stepped cantilevers that are similar to those of the uniform cantilever.Over the wide of range of thickness and length ratios considered in this study, it is found that stepped cantilevers can become significantly more unstable in many cases but can only be more stable, slightly or moderately, for just a few particular conditions. Therefore the introduction of a non-uniform thickness in a cantilever immersed in axial channel flow appears to be more appropriate for applications aiming to promote FSI instability and strengthening fluttering motions, such as those in energy harvesting.Extraction process optimization of Juncus plant fibers for its use in a green compositeIn the context of the development of green building materials using plant fibers, this research has focused on the characterization of natural fibers extracted from Juncus plant, commonly called Juncus. A well-known chemical extraction method was applied here for the first time at our knowledge to the Juncus plant, in order to obtain better mechanical characteristics (tensile strength and elastic modulus) and better surface morphology. Therefore, a chemical treatment with alkalization through various factors such as temperature, NaOH concentration (alkalizing agent), presence or not of sodium dithionite Na2S2O4 (for reducing lignin) and sodium hypochlorite NaOCl (chlorine bleach delignification agent) was performed. This study aims to determine the effects of different chemical treatments applied to the fiber extraction of Juncus stem, on the change in fiber diameter, surface state morphology, density, tensile strength and elastic modulus. As one of the Juncus fiber treatments considered in this work, the cold alkali-treatment did not give good results in terms of delignification of the Juncus fibers (There is always non-cellulosic products on the treated fiber) and low values of tensile stress and modulus of elasticity. The treatment with a solution of 8% NaOH, sodium hypochlorite and sodium dithionite at hot temperature present the best result due to the effective delignification of the fibers which has allowed reaching highest tensile strength and highest elastic modulus.It is well-known that plant fibers, also known as lignocellulosic fibers, have been one of the attractive reinforcements for different types of composites in substitution of those from glass and carbon, because of their availability, recyclability, low cost, environmental and friendly character, no toxicity, no abrasion, biodegradability and acceptable mechanical performance (). This study was carried out as part of a development project of green building materials, environmentally and socio-culturally integrated. The overall purpose of this article is to improve living standards of local populations through self-construction and use of materials adapted to the socio-economic context. The availability of fibers plants (alfa, palm leaflets, sunflower sticks, Posidonia oceanica, Juncus) in different regions of Tunisia and their under-exploitation, have contributed to use local plant fibers to reinforce the preparation of a building material based on local mineral raw materials (natural soil, natural lime, cement etc.). The use of plant fibers is particularly interesting because of the development of local knowledge and the agro-industrial exploitation of these species (). Thus, this option leads to a vegetal fiber production spinneret with innovative regional activities, and improved incomes of the population in the disadvantaged regions of Tunisia. In this context, we have chosen to use the Juncus plant that belongs to the family of Juncaceae (). It is also called Juncus in Latin and Smmar in Tunisia. It is currently harvested and weaved to produce traditional mats, baskets, and other craftwork items. Moreover, it could constitute a potential source for reinforcing fibers in organic matrix (polyester resins or epoxy components) or in mineral matrix (mortar or cement lime or gypsum or natural earth). In order to promote sustainable building materials by using Juncus fibers as reinforcement for composites, it has been necessary to undergo an extractive workup of rods from the natural plant. Over the last few years () tried to extract the Juncus fibers by the process of alkalization only with 2.5% of NaOH, to use it as reinforcement of a mineral matrix based on plaster. In this study we began with a fiber extraction based on a mechanical treatment which was not satisfactory. That's why we tried in the first part of this study, to focus more on the study of the possibility of chemical extraction by alkalizing process (cold and hot) which is inexpensive and effective to improve the mechanical performance of natural fiber in general used to reinforce composites (A.M. ). This alkaline treatment is carried out with two different concentrations of NaOH (c.a. 4 and 8%) in the presence and/or not of both of sodium dithionite Na2S2O4 (alkalizing agent) and sodium hypochlorite NaOCl (chlorine bleach delignification agent) (). The second part was shown the influence of these different chemical treatments on the mineralogical (degree of crystallinity), physical (diameter, density), chemical and mechanical (tensile strength and elastic modulus) properties of Juncus treated fibers.The Juncus plant, used as a raw material here, is a perennial plant, found everywhere in Tunisia and especially in wet places. This plant grows under different environmental conditions. The Juncus plant studied in this article () was collected in the field site Amroun (governorate of Nabeul-Tunisia) located at northeastern part of Tunisia. The Juncus’ stem has an average length of about 125 cm. During the study, Juncus stems were stabilized in a controlled atmosphere (RH = 65 ± 2%) and temperature (T = 20 °C ± 2) The morphology of the untreated stems and treated Juncus fibers was studied by scanning Electron microscopy (SEM) in order to evaluate and analyze the chemical treatments effects on the defibration of Juncus fibers, their diameter and evenly their surface state. This has been carried out by means of a scanning electron microscope (SEM, JEOL JSM 5400). The observations were made on fiber bundles and on single fibers, coated with a thin gold layer by sputtering using a JEOL JFC 1100 apparatus and thus, the scanning electron micrographs of fibers were recorded.The chemical composition of raw material and the obtained fibers from Juncus after each treatment was established. Thus, the contents of Klason lignin, holocellulose, as well as a-cellulose were assessed by using different standards. The ashes content was determined, according to the standard procedure Tappi211 om-07, by calcinations of the materials at 525 ± 25 °C for at least 4 h. The amounts of lignin and α-cellulose were also established by using the following respective TAPPI methods: T222 cm-99; T203 cm-99. Finally, the holocellulose content was determined according to the method described by . In the follow, we describe them very briefly:Ash in Wood and Annual Plants, Test Method T 211 om-07: To determine the ash content, the vegetal organic raw material under investigation is submitted to combustion at 525 °C.Acid-Insoluble Lignin in Wood and Pulp, Test Method T 222 om-06: The acid-insoluble lignin can be determined by submitting the raw material to acid hydrolysis and after filtering off the insoluble lignin. The obtained solid is then dried and weighted. The acid-soluble lignin can be determined in a solution, after filtering off the insoluble lignin, by a spectrophotometric method based on the absorption of ultraviolet radiation. The most often used wavelength is 205 nm. Klason lignin is the sum of acid-insoluble and acid-soluble lignins.Alpha-Cellulose in Pulp, Test Method T 203 cm-99: Alpha-cellulose is the pulp fraction resistant to 17.5 and 9.45% sodium hydroxide solutions under conditions of the test.All tests were repeated at least in duplicate and the difference between the various values was within an experimental error of 5%.The apparent diameter of treated fibers was measured by a digital microscope Leica MD500. Due to the variability of fiber cross section, a hundred diameter measurements (at least) have been performed along the longitudinal axis of each fiber, and the average value was reported along with the variability of the data. The test was repeated at least in 10 times.Fibers density was measured according to French standard NFT 20 053. This method consists of weighting a quantity of fibers to be introduced into a Gay Lussac's pycnometer which is then filled up with carbon tetrachloride (CCl4). The density of fibers is expressed by the following relationship Eq. (1):M1: weight of the pycnometer filled with CCl4,M2: weight of the pycnometer after the fibers additionAnd M3: weight of the filled with CCl4 pycnometer and containing the fibers.Those measures were performed on three samples of treated fibers.Single Juncus fibers were carefully manually separated from the bundles. They were subjected to a tensile test using a universal testing machine (Lloyd LRX Bench top mounted Vertical strip Paper Tensile Tester) at constant strain rate with test duration of 20 ± 3 s as specified in the French standard methods (NFG 07002). For this test, due to the limited length of the fiber, it was necessary to choose a length between jaws of 50 mm. This test was applied on ten samples of treated fibers and conducted under standard conditions: 20 ± 2 °C and 65 ± 2% RH (%).The chemical treatment of fibers extraction choosen in this work is alkalization. This process is a method commonly used for obtaining elementary fibers by extraction and isolation of the fiber bundles and the removal of non-cellulosic compounds such as the hemicellulose and lignin (). The alkalization method is essentially based on the use of caustic soda NaOH acting delignification plant fibers. The degree of alkalization can be increased with the use of other chemicals such as dithionite sodium (Na2S2O4) and sodium hypochlorite (NaOCl). All chemicals and reagents utilized during this study were purchased from Sigma-Aldrich and were used without further purification. A different process was performed in order to make the extraction of fibers from Juncus stem successful. In the following section, we described the chemical products used during this work:Caustic soda (NaOH): The caustic soda solution used in our study is a strong alkaline product often used as a chemical reactant in various applications. Its’ molar mass is 40.00 g/mol and its density is 2.13 g.cm−3. The concentrations used in this study are 4 and 8% of the mass's water.Sodium dithionite (Na2S2O4): Sodium hydrosulfite or sodium dithionite Na2S2O4, is a white crystalline powder with a weak sulfurous odor. It is easily soluble in water and sodium hydroxide solutions. Its density is 2.19 g/cm3 and its molar mass is 174.107 g/mol. In this case, alkaline solutions of 1.5% sodium dithionite are used in order to bleach and delignify Juncus fibers, such as observed in (). Sodium dithionite (Na2S2O4) is known as a reducing agent, especially for lignin content, resulting in the reduction of carbonyl groups CSodium hypochlorite NaOCl: Sodium hypochlorite NaOCl used in this study contains 38 g/l available chlorine. It is used for the delignification of fibers obtained by alkali treatment, by removing lignin and other non-cellulose compounds (Cold chemical extraction process: This process is based on a cold alkalization with sodium hydroxide NaOH. The optimum NaOH concentration is at 8%, because of environmental and economic reasons. Fibers were extracted by first cutting the Juncus stem into small pieces of about 10 ± 1 cm. These pieces were put into a beaker of aqueous of NaOH solution with concentrations 4% or 8% for 48 h at room temperature. Subsequently, the treated fibers were rinsed with tap water and were then dried at room temperature.Hot chemical extraction process: The hot process of chemical extraction of fibers consists in alkalization at 100 °C for 1 or 2 h using four different treatments: (i) treatment with sodium hydroxide NaOH; (ii) treatment with sodium hydroxide NaOH and sodium dithionite Na2S2O4; (iii) treatment with NaOH followed by treatment with NaOCl; and (iv) treatment with caustic soda and the sodium dithionite and finally followed by treatment with sodium hypochlorite. For each treatment, the Juncus stem was cut into small pieces of about 10 ± 1 cm and the pulping step was carried on batch. The delignification-bleaching protocol was carried out at least in duplicate and the difference between the obtained yields was within an experimental error of 5%.The Juncus fibers were investigated by X-Ray diffraction, under standard conditions by using an X-ray diffractometer (D8 Advance, Brucker AXS, Germany), with a voltage of 40 kV and 30 mA, Cu radiation Ka (1.5418 Å) at a rate scanning 2°/min, and a range of angle 2θ between 2 and 40°. Thus, the crystallinity of the treated fibers was obtained by the X-ray diffraction. Results indicated the influence of chemical treatment on the crystalline properties and crystallographic planes of cellulose. The crystallinity index CrI, was determined using the method described by Fourier transformed infrared (FTIR) spectroscopy is an important analytical technique used in this work to determine structures and chemical compositions of the fibers extracted from the Juncus plant. The fiber properties obtained during the various treatments were analyzed due to chemical treatments performed. An IR spectrum was recorded at room temperature using a Nicolet FT-IR 200 spectrometer, equipped with a diamond crystal and has a wide spectral range between 4000 and 400 cm−1.The fibers obtained after each chemical treatment are composed of single cells of cellulose that are held together in the form of a bundle by binding non cellulosic substances such as lignin and pectin. Lignin is the major binding material in fibers since most of the pectin will be removed during the alkali treatment. The conditions used in this study to obtain fibers (4 and 8% sodium hydroxide, 100°C for 60 and 120 min) are expected to remove most of the pectin since, for some authors, The pectin will be removed in 0.4% sodium hydroxide and boiling (). The yield of production of the fibers obtained depends on the fiber production conditions such as alkali concentration, time, temperature and the stalk-to-liquor ratio used. In our study, the production yield of chemically treated Juncus fibers varies according to the treatment applied and the concentration of sodium hydroxide: for example, in our case study shown in the , the yields in the case of cold alkaline treatment with 4% NaOH and 8% NaOH were 50 and 40%wt, respectively. In the case of hot treatment, the yield of production has decreased, respectively, to 38 and 36% with 4 and 8% NaOH. Then to 35 and 33% with 4 and 8% NaOH combined with NaOCl. This value reach to 37 and 35% with 4 and 8% NaOH combined Na2S2O4. Finally it can accomplish to 32 and 28% with 4 and 8% NaOH combined simultaneity with NaOCl and Na2S2O4.In addition to the yield of the fibers, the extent of removal of the non-cellulosic substances plays a major role in determining the structure and properties of treated fibers.The chemical composition of natural plant fibers varies from one plant to another and varies also within different parts in the same plant (). It depends on several factors such as specie, age, climatic conditions, soil composition and also the method of extraction used. All plant fibers are composed mainly of cellulose, hemicelluloses, lignin, pectin and waxes. The analysis of chemical composition of Juncus plant was established in terms of the amount of: ashes, Klason lignin, holocellulose, hemicellulose and α-cellulose, using the standard methods, as listed in The Juncus plant is characterized by a set of branches that are springing up together as a multitude of stems as shown in a. Each stem is composed mostly by cellulose fibers. Many of these fibers are found on the periphery and others are situated inside stem. The stems inside are isolated by empty cells of the blister strip as observed on the SEM (Scanning Electron Microscopy) images (The chemical composition of the Tunisian Juncus plant was established, as listed in At the microscopic level, with cold treatment the investigation of the chemical composition revealed that with 4% NaOH solution, cellulosic fibers groups are surrounded by lignin compounds (26.85%), hemicelluloses and non-cellulose compounds, and undergo only a very slight defibration (see a and 4a). Whereas, when increasing NaOH concentration to 8% the process of delignification is started by removing lignin (21.77%) and non-cellulose compounds cells. Some cellulosic fiber groups are liberated and as shown in the b and 4b, a light defibration is observed.With hot treatment process, it can be noticed that the elimination of a large part of the non-cellulosic materials such as lignin (16.25 with 4% NaOH and 11.56 with 8% NaOH) and hemicellulose (23.60 with 4% NaOH and 26.08 with 8% NaOH) with the release of the cellulose fibers groups. A better defibration of cellulosic fiber groups was observed (see c and g and 4c,d,g and h). Thereby, it turns out that the hot treatment is a necessary stage of the alkalization process needed to reach the defibration of cellulose fibers.Applying the cold treatment with NaOH, the diameter of the defibrated cellulosic fibers did not decrease. Furthermore, as observed in e and f, there is presence of lignin and non-cellulose compounds on the fiber surface membrane which continue to wrap groups of cellulose fiber. This can be justified also by the amount of lignocellulosic compounds which were determined using the standards methods.During the hot treatment with NaOH, a significant decrease in the fiber groups’ diameter was observed. In addition, the membrane lignin (16.25 with 4% NaOH and 11.56 with 8% NaOH) and non-cellulose compounds were also eliminated. The groups of cellulosic fibers become apparent (see g and h). However, they exhibit traces of lignin and hemicelluloses components, as seen in Under hot treatment with NaOH, in the presence of the sodium dithionite Na2S2O4, at 4% NaOH solution, a significant diameter decrease is observed as seen in i and j. On the contrary, at 8% NaOH, by adding of Na2S2O4 no further diameter reduction is noticed. Regarding the surface state of fibers treated separately with 4 and 8% concentration of NaOH, it appears that cellulosic fibers remain still, surrounded by hemicelluloses (20.92 with 4% NaOH and 20.69 with 8% NaOH) and a large amount of lignin (13.01 with 4% NaOH and 9.04 with 8% NaOH).In the case of hot treatment, in the presence of sodium hypochlorite NaOCl, with 4% concentration of NaOH, there is a significant decrease in the cellulosic fiber groups’ diameter as seen in k and l. With 8% concentration of NaOH, the addition of NaOCl does not provide a further diameter reduction. Regarding the fiber surface state treated with 4% concentration of NaOH, it has been found that the lignin and hemicelluloses compounds still persist. Despite their persistence, they wrap fewer groups of cellulosic fibers. With a concentration of 8% NaOH, it is noted that the lignin (6.06%) and hemicellulose (19.93%) compounds have been almost eliminated and that the groups of cellulosic fibers became conspicuous. Furthermore, the color of the cellulosic fibers has turned to a whitish color, indicating the sodium hypochlorite NaOCl's ability to remove lignin and hemicellulose compounds and the delignification of cellulose fibers (see With the hot treatment with NaOH, in the presence of the sodium dithionite Na2S2O4 and sodium hypochlorite NaOCl, has led us to find that with both NaOH concentrations of 4 and 8%, a considerable reduction in fiber diameter was revealed, as illustrated in Analysis of surface states of fibers treated with 4% NaOH showed that the lignin and hemicellulose membrane are not very persistent and surrounds much less that expected. This is not the case for the surface condition with a concentration of 8% NaOH where we find that as to fibers treated at 8% NaOH, the lignin (8.89%) and hemicellulose (21.42%) compounds are completely removed and the groups of cellulose fibers become conspicuous. Similarly to the treatment using only NaOCl, a whitening color of Juncus cellulose fibers was noted, indicating the sodium hypochlorite NaOCl's ability to remove lignin and hemicellulose compounds and the delignification of cellulose fibers (see f and j). The combination treatment of Juncus fibers by mixing the sodium dithionite Na2S2O4 in the caustic soda treatment as pre-treatment and sodium hypochlorite NaOCl (40%, aqueous solution) as a post-treatment is considered the optimal solution. It allows delignification and defibration of cellulosic fibers groups. Obviously, it would be also important to check the state of the cellulose fibers on mineralogical and mechanical plans.The Juncus stems used here as raw material have an average diameter of 3300 μm and a density of about 0.385 g.cm-3. Comparison between these values with those of other plant fibers as Esparto grass, bagasse, bamboo, kenaf and date palm, subjected to chemical treatments (), shows a significant difference in their ultimate fiber diameter and density. Therefore, to use the Juncus fibers as reinforcement in composites there is the need for a mechanical or chemical treatment at first.The experimental results obtained from physical and mechanical properties of various plant fibers or synthetic fibers shown in , provide an idea about values intervals of density, diameter and length that fiber should have after its treatment with a mechanical or chemical process, in order to be comparable to other fibers often used as reinforcement material in composites.For this reason we started at first by a mechanical treatment with a machine composed of rotary crusher rollers which aims husking and extraction of the Juncus stem. Then we obtain individual fibers by separating the fiber bundles the generally woody heart. It is worth mentioning that the mechanical treatment and the extraction process have led to a random effect and have produced an incomplete separation of cellulosic fibers. That is why, results were not convincing. Juncus fibers obtained following this mechanical treatment had an average length of about 250 mm, an average diameter of about 280 μm and a density of about 0.71 g.cm−3. These results are not well satisfactory, especially with regard to the very low density and the very large diameter in comparison with other vegetal fibers such as alfa, kenaf and/or bagasse having an average density: 1.25 g.cm−3; an average diameter: 60 μm (). It would therefore be necessary to continue and complete the mechanical treatment with a chemical method in order to remove lignin and hemicellulose components and for insuring effective separation of cellulosic fibers.The Juncus’ stem having diameter of about 3300 microns cannot be used directly in its raw state as reinforcement material in composites. First, the elimination of lignin and hemicelluloses substances to obtain ultimate cellulosic fibers was optimized. The ultimate cellulosic fibers have a diameter of about 300 microns as shown in As excepted, under chemical treatment, the Juncus fiber diameter is greatly decreasing. (). The diameter has decreased from an initial value of 300 μm (for an untreated fiber) to a value within the interval [45 μm; 110 μm] for c.a 4% NaOH solution. This latter value also belongs to the range [40 μm; 90 μm] for c.a. 8% NaOH solution (see a). Through chemical treatment by alkalization process, it was possible to obtain a Juncus fiber of 60 μm diameter as width. This is a satisfactory result, which agrees well with what was calculated for other plant fibers commonly used in composite materials (see ). It can also be noticed that the fiber diameter decreases in hot treatment (see a). The hot treatment with only c.a NaOH = 4% allowed to reduce the diameter to 60 ± 16 microns whereas for c.a 8% NaOH, or with a pre treatment with Na2S2O4 and/or with a post treatment with NaOCl have slightly decreased the reduction and the diameter reduction can be achieved was 40 ± 4 microns.Due to mechanical treatment and various chemical treatments applied to Juncus plant, fibers density has significantly increased as shown in b. It reflects that the expected results of defibration, delignification and cellulose extraction have been achieved without damaging the cell wall (). Indeed, the density has increased from 0.385 g.cm−3 (for untreated fiber) to 0.71 g.cm−3 (for fibers treated mechanically). It has reached results greater than 0.925 g.cm−3 after chemical treatment by alkalization until reaching a maximum of 1. 25 g.cm−3 under hot treatment with 8% NaOH combined with Na2S2O4 and NaOCl.As noted for the diameter reduction, the aim to obtain a Juncus fiber density similar to that evaluated for other plant fibers (see ) commonly used in composite materials, has been achieved through chemical treatment by alkalization. It would, however, be important to check the effects of diameter reduction and density increase of Juncus fiber, especially on its morphology, its surface state, its crystallinity, and the molecular bonds of cellulosic component, its tensile strength, and its elastic modulus. These different features will be developed in the following sections., the cellulose has a crystalline structure different from that of the hemicellulose and lignin, which are amorphous in nature. Its crystal structure is due to hydrogen bonding interactions and Van-der-Waals forces between adjacent strands of cellulose. In order to investigate the efficiency of delignification by chemical treatment adopted in this study, a comparison was made between the crystallinity of chemically treated fibers with that of untreated fibers. The a and b lead to the following comments: (i) spectra of Juncus fibers untreated and those of chemically treated fibers by hot treatment reveal three main peaks at 2Theta equal to 16.0, 22.5 and 34.8°. These peaks are attributed to the crystalline structure of cellulose Iβ with the chemical formula: (C6H10O5)n referring to XRD reference patterns. The maximum is allocated to the crystal plane or reticular (lattice plane) with (hkl) coordinates of (200). The average is assigned to the crystal plane (101) and the minimum is assigned to the crystal plane (004). (ii) The peak 2Theta = 29.5° is absent in the diffract gram of the Juncus natural fiber. However, it is present in the chemically treated fibers, where it corresponds to the presence of the residual NaOH. In fact, despite rinsing fibers with water, the NaOH remains present with a noticeable amount. (iii)The different chemical treatments have fostered the extraction and delignification of fibers without changing the crystalline state of the cellulose.a and b showed the FTIR spectra of the Juncus fibers treated with various announced process. summarizes the different peaks detected in FTIR spectra observed. By comparison with peak positions cited in the literature, it is deduced that the CO bonds which form the lignin in the natural fibers, detected at a peak wave number of 1243 cm−1, have disappeared for all of the fibers treated with NaOH either in cold or hot treatment, or with or without sodium dithionite Na2S2O4 and sodium hypochlorite NaOCl. The peaks groups between wave number from 2000 to 2500 cm−1 do not concern Juncus compounds.It is noted also that the type of cellulose existing in Juncus fibers (natural or chemically treated) is the Iβ cellulose. This cellulose is detected in the vibration region at around the wave number of 3400 cm−1. This confirms the results found by XRD analysis that allowed specifying cellulose entity that characterizes this kind of fiber. It can also be concluded from that the NaOH treatment, in cold or hot process, followed by a post treatment with NaOCl (i.e. sodium hypochlorite) is a more aggressive treatment for the delignification and the removal of lignin and hemicellulose. Yet, it may be aggressive on the cellulose fibers too. Whatever the used process, the NaOH treatment provides a selective delignification and a removal of lignin and hemicelluloses compounds, while sparing the cellulosic fibers. When NaOCl added to the NaOH post-treatment was preceded by a pre-treatment via Na2S2O4, it acts only on lignin and hemicellulose without attacking cellulose fiber.Before starting the chemical treatment, ultimate tensile strength of the fiber obtained by mechanical defibration of Juncus stem was 31 ± 8 MPa. Various modes of chemical treatments (including hot treatment), have greatly increased the tensile strength value of Juncus fibers (see Figs. ). The hot treatment alone with 4 and 8% NaOH has increased the tensile strength up to 730 ± 68 MPa and 800 ± 48 MPa, respectively. The post-treatment with NaOCl has increased again this tensile strength up to 800 ± 20 MPa and 1100 ± 40 MPa, respectively.During the pre-treatment with Na2S2O4, these values have reached 1050 ± 50 MPa and 1500 ± 45 MPa, respectively. The combination of the pre-treatment via Na2S2O4 and the post-treatment via NaOCl has spawned a further increase of the tensile strength of the Juncus fibers up to 1400 ± 90 MPa and 1800 ± 60 MPa, respectively. This gives the idea that the combination process can be suitable to protect the degradation of cellulose fiber from non-cellulosic compounds.Now, regarding the effect of treatment on the elastic modulus, it can be noticed that the fiber obtained by mechanical defibration of Juncus stem had a very low elastic modulus (i.e. 0.7 ± 0.1 GPa). Various modes of chemical treatments (including hot treatment) have considerably increased the elastic modulus value of Juncus fiber, and have therefore supplied to its composites a high specific stiffness and strength, as illustrated in b. The hot treatment with 4 and 8% NaOH has increased the elastic modulus up to 41 ± 2 GPa and 46 ± 3 GPa, respectively. Concerning the post-treatment with NaOCl has increased again this elastic modulus up to 47 ± 2 GPa and 62 ± 3.5 GPa, respectively. During the pre-treatment with Na2S2O4, these values have reached 62 ± 1.5 GPa and 70 ± 2 GPa, respectively. The combination of the pre-treatment via Na2S2O4 and the post-treatment via NaOCl has spawned a further increase of the elastic modulus of Juncus fibers up to 103 ± 2 GPa and 122 ± 4 GPa, respectively.During this work, the mechanical extraction of Juncus plant was investigated in order to valorize in green biomaterial. Different processes were established to evaluate the best way to isolate the fiber from Juncus plant. The hot alkali treatment has resulted in fibers’ delignification by removal of lignin and hemicellulose compounds enveloping the groups of cellulosic fibers. Therefore, this treatment has allowed performing a better extraction than that with mechanical husking. Under this hot treatment and with 8% NaOH, Na2S2O4 and NaOCl the isolation of fibers was the most effective, with a reduced diameter to a value of 40 μm, the increases of the density to 1.25 g.cm−3, the tensile strength to 1800 MPa and the elastic modulus to 122 GPa. These particularly interesting mechanical characteristics of Juncus fibers are better than those of some vegetal fibers (alfa, kenaf, bagasse, bamboo, date palm) and are comparable to those of some synthetic fibers commonly used for reinforcing composites. That is why our upcoming publication will be devoted to use the best fibers from this renewable material to produce biocomposite. Their characterization will also be covered.Surface mechanical attrition treatment (SMAT)A constitutive model incorporating grain refinement strengthening on metallic alloysSurface nano-crystallization techniques have been recently developed as one of the most effient ways to optimize materials’ structure, and therefore develop the local and global mechanical behavior as to increase strength without compromising ductility. In this work, we present a constitutive model incorporating grain refinement hardening to simulate the nano-crystallization technique, specifically, surface mechanical attrition treatment. The computation is implemented using user-defined VUMAT subroutines. As an example of its application, a geometry model with full coverage of random impacts are employed. The results show that the model has rather precise predictability of grain size evolution during plastic deformation. The readily embedded with a computational code of material dynamics enables this novel model to be a promising tool to study the dynamic evolution of microstructures under plastic deformation.Surface mechanical attrition treatment (SMAT)Energy-saving treatment and techniques are needed to make stronger and tougher materials. For example, grain refinement, as one of the materials strengthening solutions, is regarded as the method to introduce grain refinement in order to make better structural materials. Among methods of grain refinement, surface nano-crystallization is as widely considered to be a developed energy-saving method for the surface part of the materials has been physically refined while the chemicals’ stay the same. As one of the popular surfaces nano-crystallization techniques, surface mechanical attrition treatment (SMAT) is used to attain advanced structure with less energy consumption as well as lower cost. During SMAT process [], the repeated multidirectional impacts at high strain rates onto the sample surface can result in severe localized plastic deformation and grain refinement eventually down to the nanometer regime on the entire sample surface. Thus, elastic strain rate dependent plasticity theory must be employed in the numerical analysis of the mechanical response under SMAT.Recently, numerous empirical and semi-empirical temperature and strain-rate dependent models have been developed. For instance, Zerilli and Armstrong proposed a microstructure-based constitutive model using the framework of thermally activated dislocation motion []. This model results in equations that resemble the stress function proposed by Hall (1951) and Petch (1953) []. The constitutive equations include terms such as the flow stress, the grain size dependence, and a stress correction factor. The Mechanical Threshold Stress Model [] adopts the same concepts as the Zerilli-Armstrong Model. The Steinberg Cochran Guinan Lund (SCGL) model is a semi-empirical model that is developed by Steinberg et al. [] for high strain rate situations and extended to low strain rates and Body Centered Cubic Structure (BCC) materials by Steinberg and Lund. The Preston-Tonks-Walllace (PTW) model [] concerns extreme strain rates (up to 1011/s) and temperatures up to melting. Typically, these models define the flow stress as some functions of strain raised to a power, among which Johnson-Cook (JC) model [] is probably the most widely used as it has fewer experimentally determined parameters and an easily identified form.In this work, an effective constitutive model is developed in order to simulate strength hardening induced by grain refinement. User defined materials, i.e. UMAT/VUMAT, for commercial FEA package ABAQUS [], are implemented in this study. The integration procedure for the new constitutive model, its validation and applications are discussed. The full coverage random impact model for SMAT proposed in Most of the empirical models mentioned above show reasonable agreement with experimental data in the macro-scale. According to the experimental study, the properties of SMAT processed materials are strongly determined by their microstructure parameters, such as grain size, grain orientation and defect density. An ideal numerical simulation model should not only account the changes of strain, strain rate and temperature but also for the evolution of microstructure and/or texture. For this purpose, it is necessary to develop a new constitutive model including micro-level internal variables such as dislocation density ρ, grain size d, twin-boundary spacing Δ and so on (shown in ). Coupling poly-crystal structure and structure by Cellular Automaton Method are illustrated in as well. This type of model will be a versatile tool for the description of the mechanical response of metallic materials.From the microstructure perspective, the mechanical property changes during the SMAT process is commonly attributed to the higher effective dislocations, the grain refinement and the deformation induced by impacts (shock), such as the deformation twins, the stacking faults, point defects and/or martensitic phase transformation. These effects all contribute to the resultant strength. Much interest has been developed in the mechanical properties and corresponding mechanisms of metals with submicron grain size. A large number of experiments show that polycrystalline materials exhibit a variety of unique properties as their grain size is refined down to the nanometer regime. Of particular interest is the reported deviations from the classical Hall–Petch relationship (Eq. ), which is a scaling law that describes how strength (or hardness) increases as the mean grain size is refined.where σf is the yield flow stress, d the average grain size, σ0 the stress required to initiate dislocation movement and k the Hall-Petch slope. Zhang et al. [] employed SMAT to fabricate a nanocrystalline surface layer on a pure copper plate. The grain size is about 10 nm on the top layer and increases with an increasing depth from the treated surface. The relationship between the hardness and d−1/2 is consistent with the classical Hall-Petch relation. Plotting the hardness values of SMAT Fe as a function of measured grain size along the depth, the Hall-Petch relation is still valid in a wide range of the grain size (from 10 nm to 50 μm) in one sample []. Extrapolating the Hall-Petch line of 316 L pure austenite stainless steel [] down to the nanometer scale, it is found that the results obtained from the SMAT treated sample (both the average σf, data from 4 tensile tests and the average hardness value from thirty indent data) [] fit the Hall-Petch line very well. These observations are consistent with previous results reported for nanocrystalline iron samples [Since the Hall-Petch relation remains valid for SMAT treated materials, it can be introduced into the constitutive model. Khan et al. [] developed their phenomenological Khan-Liang-Farrokh (KLF) model based on the new experimental observations on post-yield mechanical properties of ultra-fine-grained and nc materials. They obtained the model material constants from an optimization program for both Cu and Al, then the stress-strain responses of mechanically milled Cu and Al of different grain size (from sub-micron to nanometer range), at different strain rates and temperatures were simulated by using their newly developed viscoplastic KLF model []. They concluded that the change in yield stress and work hardening behavior with variation in the grain size can be reasonably captured by the new model. However, HKL model and KLF model cannot reflect the dynamic response (microstructure evolution) during the SMAT process. Since SMAT involves complex mechanical and multi-axial loading conditions, which result in strain hardening, high strain rate hardening and grain refinement hardening, a proper hardening law describing these processes is needed.We propose a constitutive model that incorporate the grain refinement. A general frame of the proposed model is given in the following, where the components of the total strain tensor εijεij is given by the sum of the elastic and plastic components, εije and εijp, respectively. The plastic part of the strain rate tensor is expressed in the form of the Lévy-von Mises equationε˙ijp=32ε̄˙σ̄Sij,ε̄˙=0ifσ̄<σf(ε̄)≥0ifσ̄=σf(ε̄)where Sij=σij-σkkδij/3 is the deviatoric stress, σ̄=3SijSij/2 the von Mises equivalent stress, ε̄ the equivalent plastic strain and σf the flow stress, respectively. In order to represent the microstructural state of the material, an internal variable σˆ(d) related to the grain size d is introduced in the Hall-Petch form. Thus, σˆ(d) could act as the bridge between the macro-level continuum theory and the micro-level phenomena. The strain induced grain refinement is modeled to reflect the microstructure evolution during SMAT, using the accumulated equivalent strain ε̄. The empirical relation [] is employed as the grain size evolution function under plastic deformationwhere d0 is the initial grain size, d∞ the … and εc the …. d∞ and εc are material constants from conventional test data. In absence of plastic deformation, ε̄=0, d = d0 represents the initial or elastic deformation states. When the grain size converges against the equivalent plastic strain due to the saturation of work hardening, it is regarded as d∞.Introducing the scalar grain size d, the yield stress delta can be additively split into an a thermal part σ⌢(d) with strength hardening induced by grain refinement and a thermal part σ*(ε̄,ε̄˙,T) which depends on the equivalent plastic strain e, the equivalent plastic strain rate e and the temperature T.With isotropic plastic behavior assumed, the von Mises yield function is applied and given in short asThis function indicates that plastic deformation of a material begins when the sum of the squares of the principal components of the deviatoric stress reaches a certain critical value. The Johnson-Cook equation is adopted as the thermal part σ*(ε̄,ε̄˙,T). Replacing the initial yield stress A by the internal variable σ⌢d, the final hardening law equation for SMAT can be expressed asσf=σ0+Bε̄n+kd1/21+Clnε̄˙ε̄˙*1-T-TrTm-TrmIf the thermo-mechanical coupling is treated as locally adiabatic heating and the temperature is seen as an inner variable, the new temperature of the material is calculated using the temperature resulting from the plastic work.where Tint is the initial temperature, β is the converting efficiency from plastic work to heat, ρ is the material’s density, Cv is specific heat of the material, and V is the geometrical domain occupied by the material, respectively.The relationship between impact ball parameters and the indent coverage on a sample surface have been obtained from the previous work (d) presents the multiple impingements model which considers the full coverage, random impact location and random impact oblique angle simultaneously. Each circle in (d) (1–3) stands for an indent induced by one impact. The circle diameter is calculated by where dB, v, ρB and θ are the ball diameter, impact velocity, ball density and impact angle, respectively. k1 is the materials’ constants. It is clearly shown that the indent sizes are different from each other due to the different oblique angles as illustrated in (d) (1–2). For the random impacts during SMAT, the global full coverage rate Cratio is generated by Cratio=1-exp-γπ⋅k12⋅dB2⋅v⋅sinθ⋅ρB1/24SplateNwhere γ is the coverage coefficient, Splate is the area of treated sample and N is the number of impacts. Considering the limited calculation ability of computer, only the local full coverage model which described in (d) (4). Specifically, we used 194, 840 elements in the single impact model. The size of elements in the impact zone was chosen to be 1/24th of dimple size; this is considerably smaller than previous mesh convergence studies[33, 34] which utilized elements that were 1/15th and 1/10th of the dimple size. The implication of this is that we have taken a smaller mesh size parameter than all predecessor methods to ensure convergence of our calculations.The proposed model is a non-standard constitutive model which is not provided in commercial finite element (FE) packages. Therefore, special techniques such as user defined material laws are required to perform simulations on the basis of this new computational material model. User subroutines provide an extremely powerful and flexible tool for analysis. Implementation of the user defined material laws is the transformation process from the constitutive rate equation to an incremental equation by using a suitable integration method. VUMAT is chosen since ABAQUS/Explicit [] could provide more promising features such as reasonable computational time and better contact definitions especially in simulations of impact.During the solution process, ABAQUS calculates an increment in strain based on the boundary conditions (such as an increment in load) and the previous state of stress. This increment in strain is passed to the VUMAT subroutine. The subroutine then returns the states of stress and strain for the material. A large number of parameters can be passed into the VUMAT subroutine. Most of these parameters are either user defined material properties or solution variables, which provide information on the last state of the solution and increment in strain. The user definable variables include the updated stress, strain tensor, state variables, internal energy and inelastic energy. The flowchart of a user defined material implemented is shown in (b). At the end of this subroutine, several variables are saved as solution dependent variables (SDVs) for VUMAT. Any variables saved as SDVs can be used during the next time step and the time history response of SDVs during post processing can be plotted by the user.The material parameters used for studying the grain refinement induced by SMAT are listed in . These parameters are determined either directly from fitting experimental data [Testing the subroutines thoroughly on simple samples is the first step before attempting to use them in production analysis work. The influence of the new parameters associated with the grain size evolution is studied. (a, b) illustrates the effect of the εc on the stress-strain curve and the grain size evolution, respectively. In general, with other parameter fixed, the stress-strain curve tendency increases as εc decreases and the grain size is refined sharply with smaller εc.The effects of the initial grain size d0 on the stress strain curve and grain size evolution are shown in (c, d). It is revealed that the initial grain size d0 has little effect on neither the stress strain state nor the final grain size.(e, f). These results reveal that the parameters d∞ and εc have a significant impact on the yielding characteristics of austenite steels as both the stress strain curve and grain size evolution being affected.To demonstrate the capability of the presented model to describe complex material behavior under SMAT, single ball impacting on a target is firstly examined by adopting the new constitutive model. The ball is defined as rigid. The diameter is 3 mm and the initial velocity is 10 m/s.(c) presents the time evolution of impact velocity and equivalent plastic strain rate ε̄˙ (ε̄˙=dε̄/dt), respectively. It is shown that the strain rate predicted by the new constitutive model can be as high as 105 for a 3 mm ball at 10 m/s velocity. This result agrees with the experiment observation [The SMAT case with full coverage of random impacts within one indent area is studied. The initial grain size is defined as the average size (20 μm) []. The predicted spatial variations of grain size distribution during SMAT process are illustrated in (a), (d), and (g) are the schematic illustrations of local indents produced by random impacts. (b, c, e, f, h, i) clearly show the contours of grain size distributions on the impact surface and in the interior. After five random impacts, eight random impacts and twelve random impacts, the minimum grain sizes are reduced to 75.94, 51.16 and 43.46 nm, respectively.Furthermore, one more SMAT case is investigated for further investigation. The impact area is enlarged to a circle with 2 mm in diameter, at least 64 random impacts are needed to full coverage this area as illustrated in (a) and (b) shows the final grain size distribution in the interior of SMAT treated sample. It is shown that the SMAT process has induced the gradient gran size distribution from tens of nanometers (in the top surface layer) to several micrometers (in the sub-surface layer) and the uniformity of grain size in the same layer through the large amount of cyclic random impacts. Thus, the strain, strain rate as expressed in Eqs. and (6) have been regarded as the vital keys in refining the grain size. The residual stress and yield flow stress distributions along depth are plotted in . The maximum of compressive residual stress can reach to around 900 MPa while the maximum yield stress goes up to as high as 1.2 GPa. Experimental results imply that nanocrystalline steel samples processed by means of SMAT shows the highest yield strength of 1.45 GPa []. Thus, the numerical prediction has acceptable consistence with experimental measurements. The predicted grain size distributions reveal that grain refinement near the top surface is the key factor to contribute such high strength attained.An elastic-plastic constitutive model is formulated to model the grain evolution under plastic deformation. The model incorporates metallurgical characteristics and microstructural features of a material and successfully applies to the full coverage random impacts case for surface grain-refinement. The model has a rather accurate predictability of grain refinement evolution during plastic deformation. The gradient variation of the stain and stain rate are regarded as the significant factors for the gradient grain size distribution along depth of the treated sample. This model is readily embedded with a computational code of material dynamics. To our best knowledge, this is the first model developed that reveals the relationship between analyzing structure and material processing technology. We believe that this model can play an important role for further structural analysis at both meso- and micro-length scales of the use of SMAT for optimizing the mechanical properties of metallic materials.Very hard TiN thin films grown by pulsed laser deposition► TiN films thinner than 400 nm were grown at RT and 300 °C by PLD technique. ► Simulation of XRR curves acquired showed that TiN films were very dense and smooth. ► XRD spectra found that TiN were crystalline, with crystallites size from 10 to 35 nm and micro-strain values of 0.6–1.1%. ► Nanoindentation investigations found hardness values between 35 and 40 GPa.TiN films thinner than 400 nm were grown on (1 0 0) Si substrates at room temperature and 300 °C by the pulsed laser deposition (PLD) technique using a KrF excimer laser (λ |
= 248 nm, pulse duration τ |
= 25 ns, 6.0 J/cm2 fluence, and 40 Hz repetition rate) under various atmospheres. Simulation of X-ray reflectivity curves acquired from films showed they were very dense and smooth, while X-ray diffraction investigations found they were crystalline, with crystallites size from 10 to 35 nm and micro-strain values of 0.6–1.1%. The oxygen content in bulk, measured by Auger electron spectroscopy (AES), was below 3.1 at%. Nanoindentation investigations found hardness values between 35 and 40 GPa, amongst the highest values reported for TiN films. The high laser fluence used for ablation generated energetic ions and atomic species that bombarded the substrate during growth, resulting in the deposition of very dense films, exhibiting high micro-strain values and small crystallite sizes, which could explain the measured hardness values.TiN, a transitional metal nitride, is well known for its excellent mechanical and thermochemical properties: very high melting point, high hardness (20–35 GPa), low electrical resistivity, good wear resistance and thermochemical stability The films were deposited in a typical PLD system using a KrF excimer laser (λ |
= 248 nm, pulse duration τ |
= 25 ns, 6.0 J/cm2 fluence, 40 Hz repetition rate). Since Ti is an oxygen getter, great care was taken to achieve, with a combination of a turbomolecular and Ti sublimation (with a LN2 shroud) pumps, ultimate pressures of the order of 1–2 × 10−6 |
Pa, while water and oxygen partial pressures, measured with a residual gas analyzer attached to the deposition chamber, were below 8 × 10−7 |
Pa. The films were deposited from a polycrystalline TiN target (Plasmaterials Inc.) on p++ (1 0 0) Si substrates (MEMC Electronic Materials Inc.) at room temperature (RT) and 300 °C under various atmospheres. The deposition conditions are displayed in The films mass density, thickness (when possible), and surface roughness were obtained from simulations of the X-ray reflectivity (XRR) curves acquired with a Panalytical X’Pert MRD instrument operated at a voltage and current of 45 kV and 40 mA, respectively and working in a parallel beam configuration, with a mirror and a (1/32)° slit on the incident beam side and a thin film collimator and a 0.1 mm slit on the diffracted beam side. The same instrument was used for structural characterization by acquiring X-ray diffraction patterns both in symmetric and grazing incidence geometry (XRD and GIXD).The chemical composition of the films was investigated by Auger electron spectroscopy (AES) in a Perkin-Elmer PHI 660 system (10 kV, 30° take off angle) and by X-ray photoelectron spectroscopy (XPS) in a Perkin-Elmer PHI 5100 ESCA system (300 W, 45° take off angle, Mg or Al Kα). To obtain the bulk composition, measurements were collected after various time cycles of Ar ion sputtering (4 kV, 1–5 μA/cm2; for XPS measurements the Ar ion beam was rastered over an area of 10 mm × 7 mm). A dual beam, focused ion beam (FIB) Strata DB 235 was used to create cross sections of the samples for high resolution transmission electron microscopy (TEM) analysis on a JEOL 2010F.Nanoindentation was performed on the TiN samples using a nanomechanical testing system (Hysitron Triboindenter), with NorthStar™ diamond cube-corner geometry tip with a nominal tip radius of 40 nm. The tip area function was calibrated on fused quartz using the method of Oliver and Pharr XRR curves recorded from TiN films deposited at room temperature and 300 °C under various atmospheres are displayed in , while the results of their simulation using commercially available software (WinGixa™ from Panalytical) are included in . All films were very dense (100–105% of the tabulated value The GIXD patterns acquired from the films are showed in . The patterns correspond to cubic rock-salt lattice of TiN .AES survey scans, recorded after more than 10 nm were removed by Ar ion sputtering, are shown in . The results indicated oxygen bulk concentrations from 1.6 to 3.1 at%, depending on the deposition conditions. Some samples also incorporated from 10 to 15 at% C, when the deposition atmosphere contained a small amount of CH4. High resolution XPS scans of the C 1s region revealed that its position was located at 282.4 eV, slightly higher than the 281.7 eV value reported for TiC TEM images of the TiN_P1 film deposited using 10,000 pulses on Si are displayed in . From a film thickness of 190 nm, which is in excellent agreement with the XRR results, a growth rate of 0.019 nm/laser pulse was estimated. The film is nanocrystalline, with crystallites size of the order of 10–15 nm, slightly smaller than the values estimated from the Williamson–Hall plot. High resolution TEM images of the interfacial region are displayed in b and c. There is a thin layer with a brighter contrast of around 0.5 nm exactly at the interface followed by a ∼3.5 nm thick layer, exhibiting a rather high roughness towards the crystalline TiN layer. These findings corroborate the results obtained from XRR curve simulation. The use of such a high laser fluence for ablation resulted in a plasma plume that contained a significant fraction of high energy ions and atomic species that were subplanted into the substrate, resulting into the formation of a mixed composition Si–O–Ti–N interfacial layer. The presence of a rough interface also explains the absence of Kissieg fringes in the acquired XRR curves as those shown in Representative nanoindentation load–displacement curves are plotted in for TN3C sample. The measured hardness and elastic modulus values are plotted vs. contact depth in a, it is observed that at shallow depths (<∼5 nm), the measured hardness, H, is small and increases rapidly with contact depth, hc. This is common for nanoindentation on very hard materials, and was attributed to the way the hardness values are calculated at hc |
→ 0 nm by using the Oliver and Pharr method a and b. We followed the current practice by averaging the measured E and H values for each sample in the ranges from 5% to 10% of the film thickness, which for our TiN films translates to 20 nm < |
hc |
< 30 nm. The measured hardness results, which are shown in , are some of the highest values reported for TiN films. Since the films were very smooth, the surface roughness should not affect the results Nanocrystalline TiN films were deposited by PLD on Si substrates at room temperature and at 300 °C. The use of a laser fluence of 6 J/cm2 resulted in a strong bombardment of the film during growth by ions and atomic species from the plasma plume. Some of the impinging ions and atoms were subplanted into the substrate and created a denser and thicker interfacial layer, with a rough interface towards the growing film. The bombardment also decreased the crystallites sizes, induced defects, increased the mass density and decreased the surface roughness. These modifications resulted in TiN films exhibiting hardness values up to 40 GPa.Exploring the strength and ductility improvement of Cu–Al alloysSynchronous improvement of the strength and ductility for metallic materials is an everlasting object as the good service performance. In this study, the yield strength (σYS) and uniform elongation (εUE) of Cu-Al alloys with three Al contents, nine grain sizes induced by the controlled annealing treatment, and three gradient structures induced by surface spinning strengthening (3S) treatment were explored. Results show that the σYS and εUE may be enhanced synchronously by increasing Al content from 5Al, 8Al to 11Al, while the σYS decreases and εUE increases when increasing grain size from ultra-fined grain, fine grain to coarse grain, and the σYS increases obviously and εUE decreases slightly by constructing the gradient layer. The trade-off relation between strength and ductility is broken through by increasing Al content, however cannot be broken through by controlling grain size, and cannot be directly broken through by constructing gradient structure. In addition, the Cu-Al alloys with the high Al content, fine grain and gradient layers obtain the superior combination of strength and ductility, and the reason is that the solid-solution strengthening, boundary strengthening and work hardening are combined together. Inspired by these, the composition design, grain size regulation, and gradient structure construction may be considered as the three feasible approaches to enhance the strength and ductility of metallic materials.The metallic materials with high strength and ductility have been paid much attentions for both fundamental researches and industrial applications as the good service performance []. In general, the metallic materials with superior fatigue property need high strength and ductility because the high fatigue strength needs to improve the tensile strength and reduce fatigue crack propagation rate []. For example, the Fe-Mn-C twinning-induced plasticity (TWIP) steel has synchronous increment in tensile strength and ductility by increasing C content, as a result, their fatigue properties are improved, including enhanced fatigue strength and decreased fatigue crack propagation rate []. However, there is a trade-off relation between strength and ductility for identical metallic materials. The high-strength metallic materials usually have low ductility, e.g., the metallic glass has high strength but very low ductility, and the nanocrystalline Cu prepared by severe plastic deformation (SPD) has a high yield strength (σYS) of about 440 MPa and a low uniform elongation (εUE) less than 0.05 []. The high-ductility metallic materials usually have low strength, e.g., the austenitizing martensite steel has improved ductility but the strength decreased greatly [In order to improve the strength and ductility of metallic materials, some mechanisms are proposed []. The main idea for enhancing strength is to restrain the dislocation movement, and the employed internal obstacles to restrict dislocation movement are solute atoms for solid-solution strengthening, boundaries for boundary strengthening and second-phase particles for precipitation strengthening, respectively []. Conversely, the main idea for enhancing ductility is to make dislocation movement happen easily by microstructure optimization, including grain size, microstructure homogeneity, percentage of the ductile phase and brittle phase and so on []. In addition, changing the deformation mode from wavy slip, planar slip to twinning may also enhance the ductility []. Compared to the wavy slip, the planar slip and twinning can provide more ductility, especially the later [Corresponding methods and process strategies for improving the strength and ductility have been well developed in recent years. Firstly, the chemical composition design is always important, for metallic materials and some alloys have realized the simultaneous increment of strength and ductility, like the copper alloys and TWIP steels []. Specifically, the copper alloy has decreased stacking fault energy (SFE) by regulating alloying content []. As the main deformation modes of copper alloy with low SFE are planar slip and twinning; while the main deformation mode of copper alloy with high SFE is wavy slip; accordingly, they displayed quite different strength and ductility due to the difference in their plastic deformation modes []. In addition, the Fe-22Mn-0.6C TWIP steel has realized simultaneous improvement of strength and ductility via nitrogen addition, as nitrogen restrained the dynamic strain aging (DSA) []. Secondly, the grain size regulation has been considered as the microstructural design to alter the mechanical properties of metallic materials. For example, the CoCrFeMnNi high entropy alloy and Fe-22Mn-0.6C TWIP steel have realized enhanced strength and ductility by controlling grain size which has fully recrystallized ultrafine-grained structure [On the other hand, to enhance the strength and ductility of metallic materials, some novel structures are designed and constructed, e.g., laminate structure, nanotwinned structure, dual-phase structure, gradient structure and so on []. One of the characteristics of these structures is the microstructural heterogeneity, and the metallic materials behave in the distinct mechanical properties due to the coordinating role of all components in the heterogeneous structure []. In these structures, the dislocation density, grain boundary (GB) density and grain size of the gradient structure vary from the topmost surface layer to the interior []. As the distinct microstructural heterogeneity, the metallic materials with gradient structure behave in unique mechanical properties. The obvious increment in σYS induced by gradient layer may be attributed to the gradient layer with the increased strength; and this is similar with the pre-strain metallic materials which can be strengthened by high density internal defects in advance []. As the matrix except gradient layer still keeps the original strength and ductility, the metallic materials with gradient structure may still have good ductility [In this work, the Cu-Al alloys are selected as model materials to explore how to improve the strength and ductility. Although the composition design can improve strength and ductility, the specific distribution to strength induced by adding alloying element is not clear, and the three Al contents are selected to study how Al content affects the strength and ductility qualitatively. In addition, whether or not regulating grain size improves the strength and ductility of Cu-Al alloys needs to be verified. Therefore, the nine grain sizes are designed to study these two questions. When the Al content and grain size are certain, whether or not the gradient structure can improve the strength and ductility simultaneously needs to be verified, and how gradient layer quantitatively improves strength needs to be discussed. Therefore, three different gradient structures are designed to answer the two questions. Based on these works, how Al content, grain size and gradient structure affecting the strength, ductility, and the trade-off relation between strength and ductility will be clarified further.The Cu-Al ingots with different Al contents, including Cu-5 at. % Al alloy (abbreviated as Cu-5Al), Cu-8 at. % Al alloy (abbreviated as Cu-8Al), and Cu-11 at. % Al alloy (abbreviated as Cu-11Al), were prepared by vacuum melting furnace. These ingots were forged into billets with the sectional area of 40 × 40 mm2, and then the billets were cold-rolled into thin plates with the thickness of 5 mm.Each group of Cu-Al alloy plates was divided into nine parts, one of the nine parts kept the cold-rolled state, and the other eight parts were heat-treated at 200 °C for 30 min, 300 °C, 350 °C, 400 °C, 450 °C, and 500 °C for 30 min, and 600 °C and 800 °C for 60 min by the oil bath furnace, salt bath furnace and box resistance furnace, respectively.In addition, two surface layers of the cold-rolled Cu-5Al then heat-treated at 400 °C (abbreviated as 5Al-CR + A400), the cold-rolled Cu-8Al then heat-treated at 450 °C (abbreviated as 8Al-CR + A450) and the cold-rolled Cu-11Al then heat-treated at 500 °C (abbreviated as 5Al-CR + A500) were strengthened by surface spinning strengthening (3S), with the rotating speed of 600 r/min, the moving speed of 10 mm/min and the spinning depth of 200 μm (abbreviated as 3S-200), 350 μm (abbreviated as 3S-350) and 450 μm (abbreviated as 3S-450) as shown in The microstructures of the as-received Cu-Al alloys were observed by the electron back-scattered diffraction (EBSD) technique with a LEO Supra 35 field scanning electron microscope (SEM), and the surface layer microstructures of 3Sed Cu-Al alloys were also observed by the EBSD technique. The EBSD samples were firstly mechanically grinded and then electropolished with a solution of CO(NH2)2: H2O: (CH3)2CHOH: H3PO4: C2H5OH = 2.5 g: 250 mL: 25 mL: 125 mL: 125 mL. In addition, the topmost surface layer (about 25 μm from the surface) microstructures of the 3Sed Cu-Al alloys were observed by an FEI Tecnai F20 transmission electron microscopy (TEM) operated at 200 kV. The TEM samples were firstly mechanically grinded into slice with the thickness of about 50 μm, and then twin-jet electropolished with a solution of H3PO4:C2H5OH: H2O = 1: 1: 2 (vol.).The microhardness distributions in the surface layers of the 3Sed Cu-Al alloys were measured by a LECO AMH43 automatic microhardness tester which is fitted with a Vickers indenter, with a holding time of 13 s and a load of 100 g. The microhardness samples were firstly mechanically grinded and then polished. The tensile tests of all Cu-Al alloys samples, including as-received and 3Sed samples were carried out by an Instron 5982 testing machine with a contacting Instron extensometer at a strain rate of 1 × 10-3 s-1. For each condition, a total of three samples were prepared and tested. The gauge dimensions of the dog-bone shaped tensile samples were 16 × 4 × 5 mm3, and the tensile samples were mechanically grinded by the abrasive paper.The Cu-Al alloys with three different Al contents were fabricated under the same preparation process, i.e., first cold-rolling with the relatively large deformation and then annealing at 400 °C with a short period of time, and the microstructures are shown in . After the annealing treatments for the cold-rolled Cu-Al alloys, the largely deformed grains induced by cold-rolling are fully recrystallized. In addition, the average grain sizes of 5/8/11Al-CR + A400 samples are approximately same. Analogously, the fully recrystallized grains with smaller grain sizes also formed in Fe-22Mn-0.6C TWIP steel and CoCrFeMnNi high entropy alloy, and they have similar preparation process which is first induced by the SPD and then controlled annealing treatments [Moreover, the tensile properties of 5/8/11Al-CR + A400 samples are considered, and the corresponding tensile curves are shown . It is clear that all the samples have obvious work-hardening processes after yielding, and it is apparent that the Al content affects the tensile properties of the three Cu-Al alloys. With the increase of Al content from 5Al, 8Al to 11Al, the σYS, εUE and ultimate tensile strength (σUTS) all increased, i.e., the synchronous improvements of strength and ductility are realized by increasing the Al content for Cu-Al alloys. Besides increasing the Al content, the strength and ductility of Cu-Zn, Cu-Ag and Cu-Mn alloys are also improved synchronously as compared to the pure Cu by increasing contents of Zn, Ag and Mn, respectively []. This indicates that the composition design is a valid approach to enhance the strength and ductility for the metallic materials.In addition to the Al content, the grain size is also important for tensile properties, according to the classical Hall-Petch relation []. In this work, the controlled annealing treatments are carried out to obtain the different grain for Cu-Al alloys. The microstructures of 5/8/11Al samples with the different grain sizes are shown in , and there are some differences among these samples. In a view of the horizontal comparison, the grain size increases when increasing annealing temperature for each group of Cu-Al alloys, especially from 600 °C to 800 °C. In a view of the vertical comparison, the grain sizes for each group of Cu-Al alloys from 5Al, 8Al to 11Al under the same annealing temperature are approximately same.The strength and ductility have been improved synchronously by increasing Al content from the results in section , but how the grain size affects the strength and ductility of Cu-Al alloys is unclear. The tensile engineering stress-strain curves of 5/8/11Al Cu-Al alloys with different grain sizes are shown in . The CR sample with the minimum grain size has the highest σYS and lowest εUE, and then the σYS decreases and εUE increases with the increase of grain size for each group of Cu-Al alloys. In addition, the change of σYS and εUE is obvious for CR, CR+200, to CR + A300 samples, slight for CR + A350, CR + A400, CR + A450, and CR + A500 samples, and obvious again for CR + A600 and CR + A800 samples for each group samples. Taken as a whole, the Cu-Al alloys with the fine-grained structure have high strength and large ductility, like CR + A350, CR + A400, CR + A450, and CR + A500 samples for each group of Cu-Al alloys. The similar results are observed in some other metallic materials with the fully recrystallized ultrafine-grained or fine-grained grains, like pure Cu, Fe-22Mn-0.6C TWIP steel and Mg-Zn-Zr-Ca Alloy []. Undoubtedly, the grain size is important for the strength and ductility, and controlling grain size may regulate the strength and ductility for the metallic materials.In this work, the microstructures of as-received Cu-Al alloys are homogeneous, except the CR sample with elongated deformed grains and CR + A200 samples with practically recrystallized grains. Here, the heterogenous microstructure of Cu-Al alloys had been prepared by constructing gradient structure induced by the 3S treatment []. Firstly, the 5Al-CR + A400, 8Al-CR + A450, and 11Al-CR + A500 samples were selected as the matrixes to construct three different gradient structures, and the matrix microstructures of Cu-Al alloys are shown in . The grain sizes of 5Al-CR + A400 and 8Al-CR + A450 samples are approximately same, but the grain size of 11Al-CR + A500 sample is a little bit larger. Moreover, some annealing twins are formed in these three samples, especially the 11Al-CR + A500 sample. shows the microstructures of topmost surface layers of the 3Sed Cu-Al alloys under different 3S machining parameters, and the obvious grain refinement is realized in all 3Sed samples. Under each 3S intensity, the microstructures are similar for Cu-Al alloys. In particular, some dislocation cells are observed with an average size about 300 nm in 5Al-CR + A400 () samples under the 3S intensity of 3S-200; the refined grains are observed with an average size about 200 nm in 5Al-CR + A400 () samples under the 3S intensity of 3S-350; the refined grains are observed with an average size below 100 nm in 5Al-CR + A400 () samples under the 3S intensity of 3S-450. As a result, the grain refinement degree increases with the increase of 3S intensity from 3S to 200, 3S-350 to 3S-450 for each group samples, which is consistent with the experimental results of Cr5Mo1V steel treated by laser shock peening (LSP) and AISI 1017 mild steel subjected to severe shot peening (SSP) [Besides the topmost microstructures, the gradient microstructures of Cu-Al alloys under three different 3S intensities along the gradient direction are observed by SEM-EBSD as shown in . It shows that all 3Sed Cu-Al alloys have something in common, i.e., the grain refinement and deformation are much obvious with decreasing the distance from surface. For example, the obvious grain refinement is observed with a distance from 100 to 300 μm as shown in , a grain deformation with a distance from 300 to 500 μm as shown in , and then there is no obvious change with a distance greater than 500 μm as shown in for the 5Al-CR + A400 (3S-200) sample. However, the gradient microstructures still show some differences with the increase of 3S intensity for each group of Cu-Al alloys. In the case of 5Al-CR + A400 samples, the level of grain refinement becomes more and more serious with the increase of 3S intensity from 3S to 200, 3S-350, to 3S-350, like the zone with a distance of 100–300 μm as shown in , b1, and c1. As for the subsurface layers, the level of grain deformation also becomes more and more serious with the increase of 3S intensity, like the zone with a distance from 300 to 500 μm as shown in , b2, and c2. In addition, the thickness of grain deformation zone also increases with the increase of 3S intensity. The grain deformation is still obvious with a distance from 500 to 800 μm under the 3S intensity of 3S-450 as shown in . For the other two groups of Cu-Al alloys, 8Al-CR+450 (g–i) samples have the similar results with the increase of 3S intensity. In general, the external stress is applied on the surface layer, and the dislocation subdivision and twinning fragmentation are two major deformation mechanisms []. During the surface strengthening process, the grain deformation and grain refinement induced by the dislocation subdivision and twinning fragmentation are realized. Besides, each group of Cu-Al alloys obtains three different kinds of gradient microstructures after the 3S treatment.In addition, the gradient microhardness distribution caused by the grain deformation and the grain refinement is also important and common to describe the gradient structures which are induced by surface mechanical strengthening []. In this work, the microhardness distributions of the 3Sed Cu-Al alloys were measured and are shown in . The two surface layers of each 3Sed Cu-Al alloy were strengthened with the obviously increased microhardness, and the microhardness has the maximum value at the topmost surface layer and then gradually decreases along the depth direction. For the 3Sed 5Al-CR + A400 samples as shown in a, the two surface layers have the approximately maximum microhardness and microhardness distributions under each 3S intensity. With the increase of 3S intensity, the maximum microhardness increases from about 130 HV, 140 HV, to 170 HV under the 3S intensity of 3S-200, 3S-350 and 3S-450, respectively. The microhardness distributions in the surface strengthened layers are also affected by the 3S intensity, and the rank of the increased microhardness at any depth position is 3S-450, 3S-350 and 3S-200, respectively. For the other two groups of Cu-Al alloys, 8Al-CR+450 (c) samples have the similar results with the increase of 3S intensity. Obviously, each group of Cu-Al alloys obtains three different gradient microhardness distributions after the 3S treatments, and the microhardness increases with the increase of 3S intensity which is similar with the wrought magnesium alloy AZ80 treated by the shot peening (SP) and AISI 316 L stainless steel treated by surface mechanical attrition treatment (SMAT) [ show that both the Al content and grain size influence the tensile properties, but how the gradient structures affect the tensile properties of Cu-Al alloys quantitatively is still unclear. d–f shows the tensile engineering stress-strain curves of the 3Sed Cu-Al samples, and all the 3Sed samples have the obviously increased σYS but approximately or a little increased σUTS as compared to the as-received samples. Specifically, the σYS increases with the increase of 3S intensity from 3S to 200, 3S-350 to 3S-450, but the σUTS has no obvious rules with the increase of 3S intensity for each group samples. However, the εUE of all the 3Sed samples decreases as compared to the as-received samples for each group of Cu-Al alloys, and the εUE slightly decreases with the increases of 3S intensity. These results show that the gradient structure can improve the σYS greatly but the εUE decreases to some extent, which is consistent with the pure Cu treated by rotationally accelerated shot peening (RASP), 304 stainless steel treated by SMAT, interstitial free (IF) steel treated by SMAT and AZ31 magnesium alloy treated by severe impact loading (SIL) [Usually, the alloy composition design is a valid method to regulate the strength and ductility of metallic materials. One of the common and classical metallic materials is alloying steels, and their strength and ductility are regulated by controlling the alloy elements, including the types and contents []. For example, the interstitial free (IF) steel has the lower σYS and higher εUE by reducing the carbon content []; the Fe–22Mn–0.6C TWIP steel realized the simultaneous improvement of σYS and εUE by increasing nitrogen content [a shows the work-hardening rate of 5/8/11Al-CR + A400 samples, and it is obvious that the work-hardening rate increases with the increases of Al content. The increased work-hardening rate indicates that the grain deformation ability increases when increasing Al content, and it results in the simultaneous improvement of σYS and εUE as shown in b. It shows that increasing the Al content can break through the trade-off relation between strength and ductility of Cu-Al alloys [In addition, the increased strength partly owes to the solute Al atoms because the solute Al atoms restrain the movement of dislocation. The reaction between the moving dislocation and solute Al atoms gets severer, and the increment of strength increases when increasing Al content. The σYS increment induced by solute atoms (Δσs) may be evaluated by the conventional solid-solution strengthening theory as below [], G = 23 GPa, c and a are Taylor factor, shear modulus, concentration (expressed as an atomic fraction) and the lattice parameter of solute Al atoms, respectively. In addition, the parameter of εb is a measure of the relative size difference between the solute and solvent atoms, and the εG represents the fractional change in shear modulus per unit solute concentration. c shows the relation between the σYS increment and Al content, and the effect of Al content on strength is obvious. This indicates that Al as solute atom, can contribute partial strength to the total increment of σYS, and the rest part of strength may be owing to the other factors and will be discussed later. Moreover, increasing the Al content not only enhances the strength, but also improves the ductility of Cu-Al alloys. The pure Cu has high SFE, and its main deformation mode is wavy slip []. When the Al as solute atom was added into Cu, the SFE decreases and the deformation mode changes from wavy slip, planar slip to twinning. Therefore, the twinning and the corresponding twin boundaries (TBs) may get increasingly easier with the increase of Al content during the tensile process. As the TBs can effectively impede dislocation movement to enhance the work-hardening capability, leading to the simultaneous improvement of strength and ductility of Cu-Al alloys with increasing Al content [In this work, the ultra-fined grain (UFG), fine grain (FG), and coarse grain (CG) Cu-Al alloys were obtained by the controlled annealing treatments, and the relations between the σYS and εUE of Cu-Al alloys with different grain sizes are shown in a. For the Cu-5Al alloy, there is an obvious trade-off relation between σYS and εUE, and the σYS decreases with the increase of the εUE. The Cu-8Al and Cu-11Al alloys have the similar trade-off relations as shown in a, and there is no breakthrough of trade-off relation between strength and ductility by controlling the grain size.Although it is difficult to break through the trade-off relation by controlling the grain size, it is a valid method to regulate the strength and ductility of Cu-Al alloys. The traditional Hall-Petch relation shows that the strength increases when decreasing grain size as below [where σ0 is a constant of the frictional stress required to move dislocation, kYS is the H-P slope of σYS and D is the grain size. The relations between σYS and the inverse square root of grain size (D-1/2) of Cu-Al alloys are show in b, and three groups of Cu-Al alloys from 5Al, 8Al to 11Al samples have different Hall-Petch relations as below, respectively:The results indicate that the Al content affects the Hall-Petch relations of Cu-Al alloys, both σ0 and kYS increase when increasing Al content. In addition, the ductility increases with the increase of grain size of Cu-Al alloys. There are also nearly linear relations between the εUE and the D-1/2 of Cu-Al alloys as show in c, and the fitted equations of 5Al, 8Al and 11Al samples are given as below, respectively:Undoubtedly, the εUE also conforms to the Hall-Petch relation as below:where εUE is a constant, and kUE is the H-P slope of εUE. When increasing of Al content, both εUE and kUE increase.To better understand how the grain size affects the strength and ductility, the further discussion on Eqs. shows the relations between the Hall-Petch parameters and Al content, including the σ0 and KYS for σYS as shown in a and ε0 and KUE for the εUE as shown in b. Since the σ0 and KYS exponentially increase with the increase of Al content (here using c instead of c.at%), the fitted results are shown as below:Moreover, both ε0 and KUE for the εUE also exponentially increase with the increase of Al content as below:Therefore, the strength of Cu-Al alloys can be evaluated by the modified Hall-Petch relation as below:σYS=8.69+0.07e0.48c+(276.18+7.31e0.25c)D-1/2.Analogously, the ductility of Cu-Al alloys can be evaluated by the modified Hall-Petch relation as below:εUE=92.38-247.82e-0.35c-(66.29-514.34e-0.53c)D-1/2.Therefore, the σYS and εUE of Cu-Al alloys can be evaluated according to their grain size and Al content, the σYS increases when increasing Al content and decreasing grain size, but the εUE increases when increasing grain size and Al content.Usually. the gradient structures are described by the gradient microhardness, and the microhardness in the gradient layer conforms to the exponential dissipation model []. The microhardness distribution in the gradient layer may be fitted by the following equation [where H, d, Hm, HM and R are the microhardness in the gradient layer, distance from surface, matrix microhardness, maximum microhardness of the gradient layer and surface strengthening index, respectively. In addition, the thickness of the gradient layer (λ) is defined, and is the depth at the position where the microhardness is the 1.2 Hm [ shows the results of the gradient layer of the 3Sed Cu-Al alloys, and the special values of the gradient layer indicate that each 3Sed sample has obvious gradient structure and the gradient structure is affected by the 3S intensity. In detail, the gradient structures of the two sides in each 3Sed sample have the approximately same HM, R, and λ. For each group of 3Sed Cu-Al alloy, HM and λ increase but R decreases with the increase of 3S intensity. Under each 3S intensity, HM and λ increase and R decreases with the increase of Al content from 5Al, 8Al to 11Al. In general, the 3Sed Cu-Al alloys have the gradient structures with microhardness distributions and the corresponding HM and λ.In addition, the strength and ductility of the 3Sed samples with gradient structures are shown in . For Cu-5Al alloy, the σYS of the 3Sed samples increases significantly as compared to the as-received samples, and the σYS increases more when increasing of 3S intensity. However, the εUE of the 3Sed samples decreases slightly as compared to the as-received sample, and the εUE decreases more with the increase of 3S intensity. For the other two groups of Cu-Al alloy, i.e., Cu-8Al and Cu-11Al alloys, their σYS and εUE have the similar relations between the 3Sed and the as-received samples. The results of strength and ductility for the as-received and the 3Sed Cu-Al alloys indicate that the gradient structure can enhance the σYS with the slight loss of εUE. This may be because that the gradient layer with the obvious grain deformation and grain refinement has increased σYS and the matrix can still have original εUE, and the 3Sed sample with the gradient layer and matrix has a good combination of strength and ductility. In addition, the enhanced σYS with the slight loss of εUE gets much more obvious with the increase of 3S intensity.It is obvious that the increment in σYS may be attributed to the gradient structure, and the qualitative analysis between the σYS and gradient structure is very necessary. In general, the gradient structure has the graded microhardness distribution, and the average microhardness increment (ΔHG) can be calculated according to the exponentially distributed microhardness as below:where g = 9.807 is a constant which convert the microhardness from HV to MPa. Typically, the strength of metallic materials with gradient structure may be divided into two parts, including matrix strength (σm) and gradient layer strength (σG). According to the parallel rule of strength, the σYS of 3Sed samples may be described as below [where δ is the thickness, including the matrix and the gradient layer. In addition, the σYS increment induced by the gradient structure can be described as below:where k is a constant which represents the quantitative relation between the hardness and strength, and here k = 3 is employed []. Furthermore, the increment between the experimental and calculated σYS for Cu-Al alloys with different gradient structures are compared as shown in . It indicates that the calculated σYS conforms to the experimented σYS for the most samples, and the gradient layer is the main factor for the improvement of strength.In this work, the σYS and εUE of Cu-Al alloys are regulated by increasing Al content, controlling grain size, and constructing gradient structure as shown in . In particular, increasing Al content can improve the σYS and εUE greatly; thus it is the main approach to improve the strength and ductility of Cu-Al alloys. Since controlling the grain size can regulate the σYS and εUE, it is an effective method to optimize the mechanical properties of Cu-Al alloys. Meanwhile, constructing the gradient structure can improve the σYS but still sacrifice the εUE slightly, so it is also an effective approach to improve the strength and ductility of Cu-Al alloys. Moreover, the mechanisms for enhancing the strength and ductility will be explored, and each sole path and multiple paths affecting tensile properties of Cu-Al alloys will be discussed in the following section.Firstly, the σYS and εUE of Cu-Al alloys are improved synchronously by increasing Al content, and the trade-off relation between strength and ductility may be broken through as introduced in the previous study [, increasing Al content can increase both σYS and εUE. This may be because that the solute Al atoms and TBs can restrain the dislocation movement, and the increasing twinning ability enhances the work-hardening capability with the increase of Al content. When increasing the Al content, the effect on the improvement of strength and ductility gets more significant.Secondly, the σYS decreases and εUE increases with the increase of grain size for each group samples, and controlling the grain size cannot break through the trade-off relation between strength and ductility. As the path B show in , the Cu-Al alloys can obtain an optimal combination of strength and ductility by controlling the grain size, and this can avoid the shortcoming of the high-strength and low-ductility or low-strength and high-ductility. The grains in the FG Cu-Al alloys have some GBs which can restrain the dislocation movement, and they also have enough room to accommodate the dislocations and twins induced by the external stress. Therefore, the core of optimizing the strength and ductility is how to control the distribution of grain size.Thirdly, the σYS increases and εUE decreases slightly with the increase of 3S intensity for each group samples, and constructing the gradient structure cannot directly break through the trade-off relation between strength and ductility obviously. As the path C show in , constructing the gradient structure provides anther effective path to improve strength with a slight loss of ductility when the alloy composition and grain size are certain. This is due to that the gradient layer with the refined and deformed grains has increased σYS and decreased εUE. However, the matrix still keeps the original σYS and εUE. When the gradient layer and matrix are combined together, the Cu-Al alloys can obtain an improved strength and a slight loss of ductility. With the increase of the HM and λ, the increase of the percentage of gradient layer, the strength improves greatly and the decrease of ductility increases.Finally, both σYS and εUE increase synchronously by increasing Al content, regulating grain size, and constructing gradient structure. As the path D shown in , the high-Al content, FG Cu-Al alloys with the gradient structure can optimize the strength and ductility. Therefore, the composition design, grain size regulation and gradient structure construction may be considered as the three effective approaches to improve the strength and ductility of metallic materials, and rationally selection of strengthening and toughening methods can break through the trade-off relation between strength and ductility.The Cu-Al alloys with three Al contents, nine grain sizes induced by the controlled annealing treatment, and three gradient structures induced by 3S treatment were prepared, and the improvement of strength and ductility, trade-off relation between strength and ductility were explored in this work. Based on the experimental results and analysis above, the following conclusions can be drawn:Both the σYS and εUE are enhanced by increasing Al content from 5Al, 8Al to 11Al. The σYS increment may be attributed to the solid-solution strengthening. The εUE increment may be resulted from the decrease of the SFE and the change of deformation mode from wavy slip, planar slip to twinning.Both the σYS and εUE conform to the Hall-Petch relation; wherein the σYS decreases and εUE increases when increasing grain size from UFG, FG, to CG. Controlling grain size can regulate the σYS and εUE, but the trade-off relation between strength and ductility cannot be broken through.The σYS increases and εUE decreases slightly by constructing the gradient layer. With the increase of the maximum microhardness and thickness of gradient layers and the percentage of gradient layer, the σYS improves greatly and the ductility decreases. Constructing the gradient structure cannot directly break through the trade-off relation between strength and ductility obviously.Both σYS and εUE increase synchronously by increasing Al content, regulating grain size, and constructing gradient structure. The high-Al content, FG Cu-Al alloys with the gradient layers obtain the superior strength and ductility, and the reason is the multiple strengthening mechanisms including solid-solution strengthening, boundary strengthening, and work. The trade-off relation between strength and ductility can be broken through by the composition design, grain size regulation, and gradient structure construction.C.X. Ren: Investigation, Methodology, Writing - original draft. Q. Wang: Methodology, Writing - review & editing. J.P. Hou: Project administration, Methodology. Z.J. Zhang: Conceptualization, Methodology, Project administration. H.J. Yang: Data curation, Resources, Investigation. Z.F. Zhang: Conceptualization, Funding acquisition, Writing - review & editing.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Available online at www.sciencedirect.com ScienceDirect Materials Today: Proceedings 16 (2019) 612–620 www.materialstoday.com/proceedings ICAMMAS17 Experimental Analysis and Comparative Mechanical testing on Glass- Carbon Hybrid Composites K.Poyyathappana*, G. B. Bhaskarb, S.Rajeshc, K. Pazhanivela aDepartment of Mechanical Engineering, Tiruvalluvar College of Engineering and Technology, Vandavasi, Tamil Nadu, India bDepartment of Production Technology, Madras Institute of Technology, Anna University, Chennai, Tamil Nadu, India cDepartment of Mechanical Engineering, Tagore Engineering College, Chennai, Tamil Nadu, India Abstract This paper deals with the fabrication of Glass fiber reinforced plastic (GFRP), Carbon fiber reinforced plastic (CFRP), Glass-Carbon fiber reinforced plastic (G-CFRP), Carbon-Glass fiber reinforced plastic (C-GFRP) and starting glass and ending carbon reinforced composite laminates (G-C-G-CFRP) that have been organized using hand layup techniques. Test specimens were prepared by using numerous composite materials as per ASTM standards. The mechanical properties which include tensile, flexural, impact, shear and hardness strength of diverse composites have been evaluated and compared. The CFRP are best suited for flexural and tensile test and for impact test, shear test and hardness test hybrid composite is found to be higher than others. © 2019 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials, Manufacturing and Applied Sciences. Keywords: GFRP; CFRP; G-CFRP; C-GFRP; tensile test 1. Introduction: Composite materials have fascinated the attention of many researchers owing to their material properties like high specific strength and stiffness of materials, qualities that cannot be obtained by other conventional materials. Composites facilitate to attain unique properties by combining unique materials in a conventional manner. K. Alagaraja et al has shown that incorporation of sisal fiber with GFRP can improve materials for glass fiber reinforced polymer composites [1]. During the processing and service, the composite materials may exhibit some defects like matrix cracking, fiber breakage, fiber pull out, delamination and debonding [2]. An experimental and numerical study has been conducted to analyze the fracture toughness of glass-carbon (0-90) Fiber Reinforced polymer composites [3]. T. Rajasekaran et al conferred the manufacture of hybrid natural composite using sisal, kenaf, banana, rice hunk and carbon fiber reinforced natural composite using compression moulding technique [4]. The author analyses the tensile and flexural properties of glass, graphite and Kevlar fiber reinforced polymer matrix composites. Test specimen was fabricated by vaccum bag moulding as per ASTM standard. The graphite fiber reinforced laminate exhibits higher strength when compared to glass fiber reinforced laminates [5]. The natural fiber and glass hybrid composite were fabricated using cold press moulding. The striking development in tensile strength was indicated by woven fiber glass hybrid composites [6]. Here the specimens were subjected to low frequency cyclic load for a precise time before the flexural bending analysis. * K.Poyyathappan. Tel.: 91-955-105-4221 ; fax: +91-44-27409730 . E-mail address: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials, Manufacturing and Applied Sciences. K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 613 Flexural strength and modulus are calculated from the load deflection curve obtained from tensometer for respective specimens. The results illustrate that the hybrid composites have higher flexural properties than GFRP [7]. The mechanical properties of sisal and coir natural fiber composites were manufactured using epoxy resin matrix. The composites were organized with distinctive volume fraction. They observed that 20% sisal and 20% coir having 3mm fiber length in a composite create optimum tensile strength and modulus and impact strength [8]. The impact of hybrid composite specimen subjected to in-plane tensile and compressive loading was considered and found that the hybrid laminated specimen with higher percentage of steel sustain prominent loads independent of the fiber orientation [9]. The morphological review uncovered great adhesion and similarity between woven kenaf and glass reinforced unsaturated polyester which displayed high dimensional stability and load transfer in hybrid composites under varying load conditions [10]. Impact of carbon nano tubes on tensile, flexural and impact properties of short fiber reinforced composites was studied and detailed by Rahmanian et al [11]. The author carried out the tensile and flexural characterization of polymer hybrid composites made by reinforcing jute, pineapple leaf fiber and glass fiber as 1:1:1 ratio in epoxy resin. The fiber content in the composite was differed from 0.18 to 0.42 by volume fraction [12]. The low velocity point load setup was fabricated and fixed in processing machine by cam pointer arrangements. The specimens have been subjected to low velocity point load for a specific duration by exposure time. DMA test demonstrates that storage modulus and loss factor of GFRP specimens are compared with others [13]. The author investigated the stacking sequence on the flexural and fracture properties of carbon/basalt/epoxy hybrid composites [14, 15]. Uniaxial tension and compression characterization of hybrid carbon nanostructure – glass fiber-epoxy composites were contemplated by Sam Markkula et al [16]. Recently, hybrid composites are being examined all over the world as it has improved properties when compared to their parent composites. The mechanical properties like bending fatigue stiffness and strength degradation have been examined in carbon-glass/epoxy hybrid laminates [17]. Glass carbon woven fabrics hybrid composites were surveyed on its flexural properties and significant improvement is reported towards its application for light weight load bearing structures [18]. Within the scope of literature survey there are extremely constrained literatures on the examination of mechanical properties on laminates. Hence, it is intriguing to study the tensile, flexural, impact, shear and hardness properties of different blends of glass and carbon hybrid composites. In the present work, bidirectional CFRP, GFRP, G-CFRP, C-GFRP and G-C-G-CFRP are utilized owing to their different glass/carbon fiber proportions. Hand layup method was carried out for fabricating five laminates. Mechanical properties like tensile, flexural, impact, shear and hardness properties were studied by testing experimentally as per ASTM standards. 2. Materials and Methods: The bidirectional glass fiber and bidirectional carbon fiber of 600 gsm were taken. The following strategies were followed to form GFRP laminates and CFRP laminates using hand layup procedure. For fabricating the GFRP laminates all the glass fiber mats were cut into 13 layers of 300 x 300 x 5 mm each. A combination of LY556 epoxy resin and HY951 hardener is used in the ratio of 10: 1 weight. This was utilized as a matrix material. Fine surfacing was achieved by applying wax on the surface of the die, which also helps easy removal of plate from die. The glass fiber mats are arranged one upon the other until the required thickness is obtained. In between each mat a mixture of resin is coated. Excess of resin mixture was expelled by roller pressing besides guaranteeing elimination of possible air bubbles. The whole set-up was permitted to stand for about 24 hours under normal atmospheric curing condition after which, the plate was detached from the die. Finally trimming is done to achieve the required dimensions for the GFRP laminates. Similar procedures were carried out to fabricate CFRP laminates, with the contrast of using carbon fiber mat of 600 gsm instead of glass fiber mat. For G-CFRP laminates, 7 layers of glass fiber mat and 6 layer of carbon fiber mat were taken. Using the die, the glass fiber mat was positioned on the starting layer, carbon fiber and glass fiber mat were located over each other alternatively and ending layer was positioned with glass fiber. For C-GFRP laminates, 7layers of carbon fiber mat and 6 layer of glass fiber mat were used. By using the die the carbon fiber mat was positioned on the starting layer, glass fiber and carbon fiber mat were located over each other alternatively and ending layer was positioned with carbon fiber. For Starting glass and ending carbon laminates (G-C-G-CFRP), 7 layers of glass fiber mat and 7 layer of carbon fiber mat were taken. By using the die the glass fiber mat was set on the starting layer, carbon fiber and glass fiber mat were positioned over each other alternatively and ending layer was set with carbon fiber. 614 K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 3. Experimental Details: 3.1 Tensile Test: The tensile test specimen was prepared according to ASTM D638-03 standard. Every specimen was cut in the dimension of (165x19x5) mm. For testing with utmost load rating of 100KN a universal test machine is used. The different types of tensile test specimens are shown in the figure 1. For every state, three samples were tested and the average is resolved and noted. The specimen was held and the load was connected, while the corresponding deflections are noted. The load is applied until the specimen breaks. The breaking load’s ultimate tensile strength is noted. Fig 1: Tensile test specimen of various composites 3.2 Flexural Test: The flexural test specimen was arranged according to ASTM D790 standard. Every specimen was cut in rectangular shape having dimension of (100 x12.5x5) mm. Universal testing machine was used for three point bend test. At the point when a load is connected to the center of the specimen, it bends and fracture occurs. The different flexural test specimen is shown in figure 2. The breaking load’s ultimate bending strength is noted. Fig 2: Flexural test specimen of various composites 3.3 Shear test: The shear test specimen was organized according to ASTM D-3846 standard. Every specimen was of rectangular shape, with dimension of (50x 9x 5) mm. The different shear test specimens are shown in figure 3. The test signifies the maximum shear stress existing amid the layers of laminated materials. The breaking load, maximum displacement, ultimate shear stress are noted. K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 615 Fig 3: Shear test specimen of various composites 3.4 Impact test: The impact test is carried out in a charpy impact set up as per ASTM D256 standard. All the specimens are rectangular in shape having a notch with dimension of (65.5 x 12.7 x 5) mm. The different composite impact test specimens are shown in the figure 4. The specimen must be loaded into the testing machine and allowed to suspend until it fractures or breaks. Using impact test, the energy required to break the material and impact value is analyzed. Fig 4: Impact test specimen of various composites 3.5 Hardness Test: The hardness test specimen was equipped according to ASTM D 785 standard. Here Rockwell hardness testing is used to compute the hardness of specimen. All specimens were of square shape having dimension of (10 x10 x 5) mm. Different types of hardness test specimens are shown in the figure 5. Hardness testing is normally used in the evaluation of materials. Fig 5: Hardness test specimen of various composites 4. Result and Discussion: 4.1 Tensile Test: The composites specimens are tested for tensile properties in universal testing machine and the acquired tensile results are shown in Table. 1. Figure 4 shows the tensile strength of several fiber reinforced composites. The CFRP composite is observed to exhibit tensile strength value of 0.530 KN/mm2 which is high when compared to other composite material. The Hybrid composites result shows a higher tensile strength value of 0.433 KN/mm2 on comparison with the other tw hybrid composites. 616 K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 Table 1: Tensile test results for various specimen Fibers Load (KN) Tensile Strength(KN/mm2) GFRP 16.840 0.111 CFRP 30.620 0.530 G-CFRP 24.760 0.433 C-GFRP 23.015 0.409 G-C-G-CFRP 21.700 0.394 Fig 6: Graph indicates the tensile strength of various specimens 4.2 Flexural Test: This test is carried out in the universal testing machine from which the breaking load is noted. The flexural test results are shown in Table 2. Figure 6 shows the flexural strength of a choice of fiber reinforced composites. The CFRP composite was observed to have high flexural strength value of 0.030 KN/mm2 when compared to other composite material. Fig 7: Graph indicates the flexural strength of various specimens K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 617 Table 2: Flexural test results for various specimen Fibers Load (KN) Flexural Strength (KN/mm2) GFRP 1.285 0.020 CFRP 2.005 0.030 G-CFRP 1.695 0.024 C-GFRP 1.585 0.026 G-C-G-CFRP 1.480 0.023 4.3 Shear Test: The shear test results are shown in Table 3. Figure 8 shows the shear strength for various fiber reinforced composites. The G-C-G-CFRP composite was observed to have a shear strength value of 0.096 KN/mm2, which is high when compared to other composite material. On comparing the hybrid composites the results show that shear strength value is 0.085 KN/mm2, which is considerably lower than C-GFRP when compared to the other two hybrid composites. Table 3: Shear test results for various specimens Fibers Load (KN) Shear Strength (KN/mm2) GFRP 3.965 0.074 CFRP 5.975 0.090 G-CFRP 5.190 0.085 C-GFRP 5.485 0.082 G-C-G-CFRP 6.085 0.096 Fig 8: Graph indicates the shear strength of various specimens 4.4 Impact Test: Izod impact test was carried out on the test pieces. The test pieces were fabricated following the standard ASTM D4813 which is the standard used for impact test of un-notched test pieces. The loss of energy during impact, that is, the energy absorbed is depicted in Table 4. The C-GFRP composite was observed to have an impact strength value 9.4J, which is high when compared to other composite material. By comparing the hybrid composites the results show low impact strength value of 8.0J for G-CFRP when compared to other two hybrid composites. The comparison between impact test results is shown in Fig. 9. 618 K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 Table 4: Impact test results for various specimens Fibres Impact Values (J) GFRP 7.6 CFRP 8.6 G-CFRP 8.0 C-GFRP 9.4 G-C-G-CFRP 8.3 Fig 9: Graph indicates the impact strength of various specimens 4.5 Hardness Test: The composites specimens are investigated for tensile properties in Rockwell hardness testing machine and the acquired hardness results are shown in Table 5. Figure 10 shows the hardness strength of various fiber reinforced composites. The GFRP composite was observed to have a hardness strength value 101.2 which is high when compared to other composite materials. On comparing the Hybrid composites the results show a hardness strength value of 99 for C-GFRP which is high when compared to other two hybrid composites. Table 5: Hardness test results for various specimens Fibres Hardness Value in Location(HRL) GFRP 101.2 CFRP 98.5 G-CFRP 95 C-GFRP 99 G-C-G-CFRP 97.4 K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 619 Fig 10: Graph indicates the hardness strength of various specimens Conclusion: The carbon fiber and glass fiber reinforced hybrid composites have been fabricated by hand layup methods. Experimental evaluation of mechanical properties like tensile, flexural, shear, impact hardness of different composites as per ASTM standards has been successfully completed. The tensile and flexural properties of various composites have been studied and the breaking load has been measured. The inclusion of CFRP composite has significantly enhanced the ultimate tensile strength, ultimate flexural strength and peak load of the composite. The shear and impact properties of various composites have been analyzed. It is found that the hybrid composites exhibit better results in shear and impact test. In the hardness test GFRP is higher than the other composites. References: [1] K.Alagarraja, A.Dhamodharan, K.Gopinathan, R.Mathan Raj, and K.Ram Kumar, “Fabrication and Testing of Fibre Reinforced Polymer Composites Material,â€� IOSR Journal of Mechanical a nd Civil Engineering, 2014, pp. 27-34. [2] K. Pazhanivel, N. Ramadoss, K. Poyyathappan, P. Anandan and G. B. Bhaskar, “Flexural analysis on GRP composites subjected to cyclic gradual load and cyclic impact,â€� Advanced Material Research , Vol. 685, 2013, pp. 35-39. [3] P.S. Shivakumar Gouda, S. K. Kudari, S. Prabhuswamy and DayanandaJawali, “Fracture toughness of glass -carbon (0/90)s fiber reinforced polymer composite –An experimental and numerical studyâ€�, J Miner Mat Char Eng, Vol.10 , 2011, pp.671-682. [4] T. Rajasekaran, and S. Vigneshkumar,â€� Comparative Mechanical Testing On Hybrid Fiber Reinforced Polymer Compositesâ€�, International Journal of Advances in Engineering Research, Vol. 11, 2016, pp.56-65. [5] S. Channabasavaraju, Dr. H. K. Shivanand, and S. Santhosh Kumar,â€� Evaluation of Tensile and Flexural Properties of Polymer Matrix Compositesâ€�, International Journal of Modern Engineering Research, Vol. 3, 2013, pp.3177-3180. [6] R.Sakthivela, and D.Rajendran,â€� Experimental Investigation and Analysis a Mechanical Properties of Hybrid Polymer Composite P latesâ€�, International Journal of Engineering Trends and Technology, Vol. 9, 2014, pp.407-414. [7] K. Poyyathappan, G.B.Bhaskar, K. Pazhanivel and N.Venkatesan,â€�Tensile and Flexural Studies on Glass - Carbon Hybrid Composites Subjected to Low Frequency Cyclic Loadingâ€�, Internationa l Journal of Engineering and Technology, Vol.6, 2014, pp.83-90. [8] G.Velmurugan, S.P.Venkatesan, P.V.Prakash, N.Sathishkumar and N.Vijayakumar,â€� Mechanical Testing of Hybrid Composite Material (Sisal and Coir)â€�, International Journal of Scientific and Re search Publications, 2014, Vol. 4, pp.1-6. [9] K.G. Satish, B. Siddeswarappa and K. Mohamed Kaleemulla, “Characterization of in -plane mechanical properties of laminated hybrid compositesâ€�, J Miner Mat Char Eng, Vol.9 , 2010, pp.105-114. [10] Mohaiman J. Sharba, Zulkifle Leman, Mohamed T.H. Sultan, Mohamad R.Ishak, and Mohammad A.Azmah Hanim, “Partial Replacement of glass fiber by woven kenaf in hybrid composites and its effect on monotonic and fatigue propertiesâ€�. Bio R esources, Vol.11, 2016, pp. 2665-2683. [11] S. Rahmanian, K.S. Thean, A. R. Suraya, M. A. Shazed, M. A. MohdSalleh and H. M. Yusoff, “Carbon and glass hierarchical fiber s: Influence of carbon nanotubes on tensile, flexural and impact properties of short fiber reinforced compositesâ€�, Material Design, Vol. 43, 2013, pp. 10-16. [12] M. IndraReddy, M. Anil Kumar, and Ch. Rama Bhadri Raju,â€� Tensile and Flexural properties of Jute, Pineapple leaf and Glass Fi ber Reinforced Polymer Matrix Hybrid Compositesâ€�, International Conference on Processing of Materials, Minerals and Energy, 2016, pp. 1-5. [13] K.Poyyathappan, G.B.Bhaskar, N.Venkatesan, K.Pazhanivel, G.Saravanan and S.Arunachalam, “ Dynamic Mechanical and Flexural characteristics of Glass-Carbon Hybrid Compositesâ€�, Applied Mechanics and Materials, Vol. 591, 2014, pp. 72-76. [14] Jae IL Lim, Kyong Yop Rhee, Hyun Ju Kim and Dong Ho Jung, “Effect of stacking sequence on the flexural and fracture propertie s of carbon/basalt/epoxy hybrid compositesâ€�, Carbon Letter s, Vol. 15, 2014, pp.125-128. [15] Muhamad Shahirul Mat Jusoh, Carlo Santulli, Mohd Yazid Mohd Yahya, NurIzan Syahriah Hussein, and Hariz Ahmad Israr Ahmad,â€� Effect of Stacking Sequence on the Tensile and Flexural Properties of Glass Fibre Epoxy Composites Hybridized with Basalt, Flax or Jute Fibresâ€�,Material Science and Engineering with Advanced Research ,Vol.1, 2016, pp. 21-25. 620 K Poyyathappan et al / Materials Today: Proceedings 16 (2019) 612–620 [16] Sam Markkula, H.C. Malecki and Marc Zupan, “Uniaxial tension and compression characterization of hybrid CNS -glass fiber-epoxy compositesâ€�, Composite Structure, Vol.95, 2013, pp.337-345. [17] G.Belingardi and M. P. Cavatorta, “Bending fatigue stiffness an d strength degradation in carbon-glass/epoxy hybrid laminates Cross-ply vs. angle-ply specimensâ€�, International Journal of Fatigue, Vol. 28, 2006, pp. 815-825. [18] Jin Zhang, Khunlavit Chaisombat, Shuai He and Chun H. Wang, “Hybrid composite laminates re inforced with glass/carbon woven fabrics for light weight load bearing structuresâ€�, Materials Design, Vol.36, 2012, pp.75-80. 013, pp. 35-39. [3] P.S. Shivakumar Gouda, S. K. Kudari, S. Prabhuswamy and DayanandaJawali, “Fracture toughness of glass -carbon (0/90)s fiber reinforced polymer composite –An experimental and numerical studyâ€�, J Miner Mat Char Eng, Vol.10 , 2011, pp.671-682. [4] T. Rajasekaran, and S. Vigneshkumar,â€� Comparative Mechanical Testing On Hybrid Fiber Reinforced Polymer Compositesâ€�, International Journal of Advances in Engineering Research, Vol. 11, 2016, pp.56-65. [5] S. Channabasavaraju, Dr. H. K. Shivanand, and S. Santhosh Kumar,â€� Evaluation of Tensile and Flexural Properties of Polymer Matrix Compositesâ€�, International Journal of Modern Engineering Research, Vol. 3, 2013, pp.3177-3180. [6] R.Sakthivela, and D.Rajendran,â€� Experimental Investigation and Analysis a Mechanical Properties of Hybrid Polymer Composite P latesâ€�, International Journal of Engineering Trends and Technology, Vol. 9, 2014, pp.407-414. [7] K. Poyyathappan, G.B.Bhaskar, K. Pazhanivel and N.Venkatesan,â€�Tensile and Flexural Studies on Glass - Carbon Hybrid Composites Subjected to Low Frequency Cyclic Loadingâ€�, Internationa l Journal of Engineering and Technology, Vol.6, 2014, pp.83-90. [8] G.Velmurugan, S.P.Venkatesan, P.V.Prakash, N.Sathishkumar and N.Vijayakumar,â€� Mechanical Testing of Hybrid Composite Material (Sisal and Coir)â€�, International Journal of Scientific and Re search Publications, 2014, Vol. 4, pp.1-6. [9] K.G. Satish, B. Siddeswarappa and K. Mohamed Kaleemulla, “Characterization of in -plane mechanical properties of laminated hybrid compositesâ€�, J Miner Mat Char Eng, Vol.9 , 2010, pp.105-114. [10] Mohaiman J. Sharba, Zulkifle Leman, Mohamed T.H. Sultan, Mohamad R.Ishak, and Mohammad A.Azmah Hanim, “Partial Replacement of glass fiber by woven kenaf in hybrid composites and its effect on monotonic and fatigue propertiesâ€�. Bio R esources, Vol.11, 2016, pp. 2665-2683. [11] S. Rahmanian, K.S. Thean, A. R. Suraya, M. A. Shazed, M. A. MohdSalleh and H. M. Yusoff, “Carbon and glass hierarchical fiber s: Influence of carbon nanotubes on tensile, flexural and impact properties of short fiber reinforced compositesâ€�, Material Design, Vol. 43, 2013, pp. 10-16. [12] M. IndraReddy, M. Anil Kumar, and Ch. Rama Bhadri Raju,â€� Tensile and Flexural properties of Jute, Pineapple leaf and Glass Fi ber Reinforced Polymer Matrix Hybrid Compositesâ€�, International Conference on Processing of Materials, Minerals and Energy, 2016, pp. 1-5. [13] K.Poyyathappan, G.B.Bhaskar, N.Venkatesan, K.Pazhanivel, G.Saravanan and S.Arunachalam, “ Dynamic Mechanical and Flexural characteristics of Glass-Carbon Hybrid Compositesâ€�, Applied Mechanics and Materials, Vol. 591, 2014, pp. 72-76. [14] Jae IL Lim, Kyong Yop Rhee, Hyun Ju Kim and Dong Ho Jung, “Effect of stacking sequence on the flexural and fracture propertie s of carbon/basalt/epoxy hybrid compositesâ€�, Carbon Letter s, Vol. 15, 2014, pp.125-128. [15] Muhamad Shahirul Mat Jusoh, Carlo Santulli, Mohd Yazid Mohd Yahya, NurIzan Syahriah Hussein, and Hariz Ahmad Israr Ahmad,â€� EffeExperimental Analysis and Comparative Mechanical testing on Glass- Carbon Hybrid CompositesThis paper deals with the fabrication of Glass fiber reinforced plastic (GFRP), Carbon fiber reinforced plastic (CFRP), Glass-Carbon fiber reinforced plastic (G-CFRP), Carbon-Glass fiber reinforced plastic (C-GFRP) and starting glass and ending carbon reinforced composite laminates (G-C-G-CFRP) that have been organized using hand layup techniques. Test specimens were prepared by using numerous composite materials as per ASTM standards. The mechanical properties which include tensile, flexural, impact, shear and hardness strength of diverse composites have been evaluated and compared. The CFRP are best suited for flexural and tensile test and for impact test, shear test and hardness test hybrid composite is found to be higher than others.Magnesium oxide-poly(ε-caprolactone)-chitosan-based composite nanofiber for tissue engineering applicationsThe ability to produce composite nanofibers of inorganic particles and synthetic polymers represents a significant advancement in the development of composite materials for potential biomedical applications. In this study, composite nanofibers of magnesium oxide (MgO), poly(ε-caprolactone) (PCL) and chitosan (CS) with diameters in the range of 0.7–1.3 µm were fabricated by electrospinning their blend solutions in trifluroethanol and water. To support the potential use of these nanofibrous membranes for biomedical applications their physicochemical properties such as morphology, mechanical strength, and integrity in aqueous medium, were studied. Cellular compatibility was determined using cell viability assays and microscopy imaging, with the results showing that the nanofibrous membranes support 3T3 cell viability and attachments. The new composite nanofibrous membranes developed in this study have the ability to mimic the physical structure and function of tissue extracellular matrix (ECM) and thus have potential for many tissue engineering applications.Engineered composite nanofibers have shown great potential in different biomedical applications including but not limited to drug delivery, wound healing, tissue engineering, implant coatings etc. Composite nanofibers derived from natural and/or synthetic biopolymers and ceramic particulates are gaining popularity in biomedical applications because they capitalize on the favorable biological properties of the natural polymer and the ceramic, and superior mechanical properties of the synthetic polymer A large body of published work in the area of chitosan (CS) and polycaprolactone (PCL) blends demonstrates the growing interest in CS-PCL composite fibers for biomedical applications where mechanical strength, biocompatibility and stability of nanofibers in vitro and in vivo are important Among a large number of inorganic particulates used to design composite nanofibers, there has been a growing interest in magnesium oxide (MgO)-based composite materials because of its decontamination potential for catalytic detoxification of toxic chemicals as well as protection from UV light We fabricated nanofiber membranes of PCL-CS/MgO of different compositions by electrospinning the blend solutions of PCL and MgO in trifluoroethanol, and CS in water. Physicochemical properties, such as morphology, mechanical strength, and integrity in aqueous medium as well as cellular compatibility of the nanofibrous membrane were determined.Chitosan (MW 2.5 k; Lot No. HL130109G) was purchased from Creative PEGWorks Inc. (Chapel Hill, NC). 2,2,2-Trifluoroethanol (TFE) was obtained from Alfa Aesar (Ward Hill, MA). PCL (Mn 70–90 kDa), and MgO (nanopowder, <50 nm particle size) were purchased from Sigma Aldrich. Stainless steel dispensing needle (21 gauge and 3.81 cm long, product number 75165A757), fluorinated ethylene propylene tubing (0.32 cm inner diameter) and Luer lock syringe needle fittings were obtained from McMaster-Carr (Atlanta, GA). Luer-lock syringes (catalog number: 14-829-45) was obtained from Fisher Scientific (Pittsburgh, PA).PCL and CS were dissolved in separate beakers at a concentration of 10% (w/w) in TFE and DI water respectively. PCL/MgO solutions were created by mixing PCL and MgO in different ratios (). Subsequently, a PCL-CS/MgO solution was created by mixing CS solution drop-wise to the solution of PCL and MgO. The solution mixtures were vortexed manually until each solution reached a homogeneous blend ready for electrospinning. Weight ratio of PCL/CS was maintained at 80/20 for all the CS based blend solutions.A previously prepared polymer solution of PCL/MgO and PCL-CS/MgO was individually fed into the syringe of 10 mL and then placed into a syringe pump (Model 78-01001, Fisher Scientific, Pittsburgh, PA, USA). The syringe pump was set to a flow rate of 2.5 mL/h. The syringe tip was positioned ∼7 cm from a fiber collecting drum at an angle of ∼30° to the horizontal. A 25–27 kV high voltage power supply (Model CZE100PN30, Spellman High Voltage Electronics Corporation, Hauppauge, NY, USA) was used to charge the solution. The positive lead from the high voltage power supply was fixed to a 21-gauge hypodermic needle. The fibers formed were deposited onto an aluminum sheet wrapped over a rotating grounded collector.The surface morphology of nanofiber membranes was analyzed by SEM (Hitachi SU8000, Tokyo, Japan). Prior to imaging, a small section of the fibers was sputter coated with gold in a Polaron SEM coating system for 90 s at 15 mA. Images of the samples were taken at an accelerating voltage of 10 kV and 5 µA current. The diameter of these electrospun fibers was determined through SEM images with the use of ImageJ Pro Plus 6.0 software (NIH, USA). Three SEM images from different location of each composition were utilized. Twenty different nanofibers were randomly chosen in each SEM image to measure the diameter in pixels. The number of pixels was converted into µm using the scale factor. Finally, the average diameter of the nanofibers was calculated based on the converted ImageJ data.The core–shell structure of the electrospun PCL/MgO composite nanofibers was examined in a Tecnai G2 Twin transmission electron microscope (TEM) at 200 kV. The samples for TEM were prepared by directly depositing the as-spun nanofibers onto a copper grid.Stability and degradation of nanofiber membranes were also studied through SEM images. Sterilized nanofiber membrane of PCL, PCL/CS and PCL-CS/MgO (30 × 30 mm) immersed in 40 mL of 1X Phosphate Buffer Saline (PBS) solution were incubated for 3 weeks in a Shaking Incubator (Dubnoff Shakebath-2876, Thermo Fisher Scientific, Fair Lawn, NJ, USA) at 37 °C and 50 rpm. Nanofibers after incubation were removed from the PBS solution, rinsed with DI water and lyophilized. Morphological changes on these samples were studied under SEM.Mechanical properties of the fiber were determined with a universal testing machine (Instron 5542) with a 500 N load cell at a displacement rate of 4 mm/min. A custom-designed specimen holder was used to test the fiber strength. A paper template of (38 mm × 25 mm) with an opening of (6 mm × 12 mm) was prepared as described in the literature A Bruker AXS D8 Discover X-ray diffractometer with Cu-Kα radiation was used to examine the crystallography and phases of the nanofiber membranes synthesized. The X-ray diffraction patterns were recorded in locked-coupled scan mode with a scanning range (diffraction angle, 2θ) set between 10° and 80°. The instrument was operated in the continuous mode, in increments of 0.0146°. All experiments were performed at room temperature.Fourier transform infrared spectroscopy (FTIR) was used to analyze the bonding between PCL and CS in the fiber. FTIR spectra were recorded using Varian 670 FT-IR Spectrophotometer (Varian, Inc., Palo Alto, CA, USA). The spectra were collected from 400 to 4000 cm−1 with a resolution of 4 cm−1.Nanofiber samples were attached to a circular coverslip using a biocompatible silicone-based elastomeric gel The Alamar Blue (AB) colorimetric assay (Life Technologies, Grand Island, NY) was used to analyze the cell attachment and cell cytotoxicity of 3T3 fibroblast cells grown on composite nanofiber samples on coverslips and, as a control, on plain glass coverslips. After 1 and 3 days of culture, the culture plates were removed from the incubator, media was removed from the sample and washed twice with DPBS and incubated with 1 ml of 10 % (v/v) AB containing DMEM with 10% FBS for 2 h. After incubation, 400-µL sample of the assay solution was transferred to an opaque 96-well culture plate for fluorescent measurements on a SPECTRAmax GEMINI XPS microplate spectrofluorometer (Molecular Devices, Sunnyvale, CA) at λex 530 nm, λem 590 nm. The relative fluorescent units were converted to a percent of the average values for cells in control wells.Initial pH of the cell culture media (DMEM supplemented with 10% FBS, 1% antibiotics) was recorded using a Fisher Scientific™ Accumet™ AE150 pH Benchtop meter. Similarly, before the AB assay, pH of cell culture media was determined for 1, 2 and 3 days respectively.After the cell cytotoxicity assay, samples with cells were fixed and cellular morphology was examined with SEM. Cells were washed with DPBS (twice) and fixed with 4% glutaraldehyde for 30 min. After fixing, samples were briefly rinsed with DI water (twice) and dehydrated by sequential incubations in 50, 75, and 100% ethanol at room temperature. The sequential wash between different percent of ethanol was carried out at 10 min-intervals. The samples were left to dry in the sterile fume hood for 24 h and were imaged using SEM.Statistical analysis was performed using a one-way analysis of variance (ANOVA). p-values less than .05 were considered statistically significant, and the Tukey test method was conducted for pairwise comparisons. SPSS Statistics 17.0 software was used to conduct the statistical analysis.The surface morphology of as-synthesized nanofibers of PCL, PCL/MgO and PCL-CS/MgO is shown in A shows the morphology of pure PCL nanofibers whereas images of B–D show PCL nanofiber with increasing concentration of MgO. Similarly, E shows structure of polyblended PCL–CS fiber and F–H represents the morphology of PCL-CS nanofibers with increasing MgO concentration. The average diameters of PCL, PCL/MgO (90/10), PCL/MgO (75/25) and PCL/MgO (50/50) were found to be 1.30, 1.10, 1.00 and 0.97 μm, respectively (n = 20). There was a statistically significant difference (p = .0437) in fiber diameter between PCL and PCL/MgO (50/50). Similarly, the average diameters of PCL/CS, PCL-CS/MgO (90/10), PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) were 0.70, 0.90, 0.93 and 0.95 μm respectively (n = 20). There was a significant difference (p = .00627 and .02386) in fiber diameter of PCL with PCL-CS/MgO (90/10) and PCL-CS/MgO (50/50) fiber respectively.PCL fibers were bead-free, had a smooth surface, and were oriented in a single direction. PCL/MgO fiber, however, showed small protrusions and had a rough fiber structure. The distinct morphology of nanofibers produced from the solution of PCL alone is attributed to solution conductivity and solution viscosity E, random orientation of fibers can be seen as compared to PCL fibers. Furthermore, addition of CS (H) resulted in the formation of small fibrous networks (50–70 nm in diameter) between major nanofibers.The surface morphology and particle distribution was further observed by using Transmission Electron Microscopy. A, B shows TEM images of the electrospun PCL nanofibers with and without MgO nanoparticles (<50 nm). The array of MgO nanoparticles are seen to be encapsulated in the PCL nanofibers.Next, nanofiber membranes were studied for their stability. Samples were immersed in PBS (1X) for 3 weeks and these fiber membranes retained their dimensional stability as well as fibrous structure throughout the test period which is confirmed by SEM images in Mechanical properties of nanofibers were assessed by tensile testing. Results of ultimate tensile strength (UTS) and Young’s Modulus (YM) are shown in . The Young’s Modulus was determined using Hooke’s law from the slope of the linear portion of the stress–strain curve, whereas the UTS was determined as the highest stress that a nanofiber sample could bear without breaking Furthermore, the YM for PCL, PCL/MgO (90/10), PCL/MgO (75/25) and PCL/MgO (50/50) was found to be 21.6, 24.8, 25.9 and 25.3 MPa respectively. Similarly, the YM for PCL/CS, PCLCS/MgO (90/10), PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) was found to be 6.8, 7.0, 7.5, and 8.6 MPa respectively. There was a significant difference (p = .03291) in YM between samples PCL/MgO (90/10) and PCL. Furthermore, there was no significant difference in YM when the concentration of MgO was increased to 50%. There was a significant decrease in YM when CS was added to PCL. However, there was no significant difference in YM observed when different concentrations of MgO were added to PCL-CS.XRD patterns of as-spun PCL/MgO nanofibers with different ratios of PCL to MgO are shown in . The PCL nanofiber membrane showed two strong peaks at 21.5° and 23.6°, corresponding to the (1 1 0) and (2 0 0) crystallographic planes of PCL The FTIR spectra were measured to confirm the presence of PCL and CS of the composite nanofiber membrane. (A and B) shows the FTIR spectra of PCL and PCL-CS based nanofiber membranes respectively with different MgO content. Typical absorption bands for PCL nanofiber were located at: 2950 cm−1 and 2865 cm−1 for CH2 asymmetric and symmetric stretching vibrations respectively; 1727 cm−1 for the stretch of CO in ester groups; 1240 cm−1 and 1170 cm−1 for CC asymmetric and symmetric stretching vibrations, respectively Cell culture media were analyzed for pH change after days 1, 2, and 3 (See ). The initial pH of media was 7.2. For day 1, average pH for PCL, PCL/MgO (90/10), PCL/MgO (75/25) and PCL/MgO (50/50) was found to be 7.35, 7.57, 7.91, 7.98 respectively. At Day 2, these values were found to be 7.42, 7.75, 8.07, 8.09 respectively. Similarly, at Day 3 these values changed to 7.39, 7.59, 7.95, 8.01 respectively.Furthermore, at day 1 the average pH for PCL/CS, PCL-CS/MgO (90/10), PCL- CS/MgO (75/25) and PCL-CS/MgO (50/50) was found to be 7.62, 7.74, 8.16, 8.18, respectively. At day 2, these values were found to be 7.78, 7.86, 8.37, 8.39 respectively. Similarly, at day 3, these values changed to 7.66, 7.78, 8.20, 8.22 respectively. shows relative levels of AB between 3T3 cells grown on nanofiber membranes with and without MgO. Cytotoxicity was calculated for each time point using the control group (PCL) as a baseline for healthy cell culture as instructed in assay protocols. Toxicity level of 3T3 cells was similar to or slightly lower than the control groups. The average cell viability for PCL, PCL/MgO (90/10), PCL/MgO (75/25) and PCL/MgO (50/50) after day 1 was found to be 100%, 94.5%, 95.6% and 94.9% respectively. Similarly, after day 2, the average cell viability for these nanofiber was found to be 100%, 87.4%, 90.5% and 89.4% respectively. A significant difference (p = .04951) was observed between samples PCL at day 1 and PCL/MgO (90/10) at day 2. Also, there was significant difference different (p = .04951) between PCL/MgO (90/10) and PCL at day 2. Furthermore, after day 3, the average cell viability for PCL, PCL/MgO (90/10), PCL/MgO (75/25) and PCL/MgO (50/50) was found to be 100%, 106.9%, 91.0% and 90.2% respectively. Significant differences (p = .00302; p = .00039) were observed between samples PCL/MgO (75/25) and PCL, and PCL/MgO (75/25) and PCL/MgO (90/10) respectively at day 3. Significant difference (p = .00139; p = .000211) was also observed between samples PCL/MgO (50/50) and PCL, and PCL/MgO (50/50) and PCL/MgO (90/10) at day 3 respectively. There was a significant difference (p < .05) between sample, PCL/MgO (90/10) from day 3, to samples PCL/MgO (90/10), PCL/MgO (75/25) and PCL/MgO (50/50) from day 2. shows average cell viability for samples consisting of chitosan and MgO. The average cell viability for PCL, PCL/CS, PCL-CS/MgO (90/10), PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) after day 1 was found to be 100%, 103.6%, 113.0%, 94.9% and 89.6% respectively. PCL-CS/MgO (90/10) was significantly different (p = .0311; p = .00134; p = .00049) to PCL, PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) at day 1 respectively. There was also a significant difference (p = .01764) between samples PCL/CS and PCL-CS/MgO (50/50) at day 1.Similarly, after day 2, the average cell viability for PCL, PCL/CS, PCL-CS/MgO (90/10), PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) was found to be 100%, 107.6%, 100.4%, 107.1% and 100.86% respectively. PCL/CS from day 2 was significantly different (p = .03963; p = .00142) with samples PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) from day 1, respectively. Furthermore, after day 3, the average cell viability for PCL, PCL/CS, PCL-CS/MgO (90/10), PCL-CS/MgO (75/25) and PCL-CS/MgO (50/50) was found to be 100%, 89.3%, 97.4%, 96.7% and 120.9 %, respectively. PCL-CS/MgO (50/50) was significantly different (p < .05) with all other samples at day 3. PCL-CS/MgO (50/50) from day 3 was also significantly different (p < .05) to samples PCL, PCL/CS, PCL-CS/MgO (75/25) from day 1. PCL-CS/MgO (90/10) from day 1 was significantly different (p = .00318) with PCL-CS/MgO (90/10) from day 3. PCL-CS/MgO (50/50) at day 3 was significantly different (p < .05) with samples PCL, PCL-CS/MgO (90/10), PCL-CS/MgO (50/50) from day 2.Cellular compatibility including cell adhesion and spreading, as well as cell interactions with the nanofibrous membranes of the PCL, PCL/CS, PCL/MgO and PCL/CS-MgO, were studied by SEM. shows the SEM images of fibroblast cells (3T3 cells) grown on these nanofibers after 3 days in cell culture. The cells attached well and formed cell clusters on the nanofibrous structure.In this research, composite nanofibers of PCL and PCL/chitosan with different compositions of MgO powders were obtained by electrospinning technique. Preparation of homogeneous solution with appropriate viscosity is an important step in electrospinning of nanofibers. In our experiment chitosan was added drop-wise to PCL/MgO solution to form a homogeneous blend solution that could be electrospun. In our own preliminary experiment, we prepared multiple ratios of PCL and chitosan, and found that any ratios with more than 40% of chitosan was not appropriate for electrospinning because the solution did not remain homogeneous for an extended duration (phase separation was visible after ∼5 min). Therefore, we kept chitosan ratio constant, i.e. 20 % of PCL solution, and varied the amount of MgO. PCL, being a nonionic synthetic polymer, is only soluble in organic solvent. TFE, an organic solvent, is a water-miscible fluorinated alcohol that has been widely used to dissolve PCL to create nanofibers. TFE exhibits a strong acidic nature due to the presence of electronegative trifluoro groups. TFE thus helps to create a stable interactions between MgO, CS and PCL by forming hydrogen bonding among them All blended solutions in this study yielded nanofibers which were collected as a thin mat. However, fiber morphology slightly varied with blend composition. There is a significant difference in the fiber diameters between PCL fibers and corresponding fibers blended with MgO nanoparticles. This may be due to the presence of oxide particles enhancing the electrical conductivity of the solution, which further increases the acceleration of jetting during the electrospinning process Nanofiber membranes retained their dimensional stability and fibrous structure after immersion in PBS for up to 3 weeks. PCL is a known biopolymer with proven long biodegradation time of over 2 years. CS is a water soluble and relatively faster degradable polymer. Our composite nanofiber consisted of only small amount of CS relative to PCL (∼20% of PCL) which enabled the nanofiber membrane to be stable in aqueous medium. A prolonged immersion of the membrane in PBS for up to a year might be necessary to observe any drastic physical and chemical changes in fibers.XRD patterns of as-spun PCL, PCL/CS, and PCL/MgO nanofibers showed that the highly crystalline nature of PCL was significantly weakened in the blended nanofibers. The lower crystallinity of PCL indicates better miscibility of blended nanofibers . PCL/MgO and PCL-CS/MgO nanofibers showed the characteristic bands of PCL and CS. Absorption peaks of MgO are not clearly visible in composite nanofibers, because of their weak intensity compared to PCL and CS. Peak intensities of CS are also weak compared to PCL because of its small composition.Nanofibrous scaffolds need to maintain their structural and mechanical integrity during in vivo and in vitro cell growth and tissue remodeling Cell viability was assessed using an Alamar Blue (AB) assay. The dye, AB, is a chemical resazurin that enters the living cells and turns into pink fluorescent molecules due to the reduction of resazurin to resorufin with mitochondrial reductases The possible primary toxicants in these nanofibers could be the excessive leachants from the nanofibers – that includes released Mg ions. Our cell toxicity results indicate that these fibers didn’t release the Mg in sufficiently high level that could be toxic to the cells. In our previous study it was observed that there was very insignificant change of cumulative release of Mg ions from PCL-based fibers MgO-based composite fibers when in contact with aqueous medium can form a soluble form of Mg, such as magnesium hydroxide. Formation of hydroxides could easily increase the pH of the medium. We measured the pH of the culture media obtained from the cell seeding experiments to find out if the increased pH of the culture media can be correlated with cell toxicity. pH of the media collected from the composite fibers increased compared to the pH of the culture media alone (). The change of pH for both PCL and PCL/CS nanofibers was lower than the corresponding fibers with MgO. The higher pH values measured in MgO-containing nanofibers is attributed to the release of basic hydroxyl groups in the culture media Furthermore, SEM images showed that the fiber topography enhanced the cell attachment on the fibers. All the nanofibers samples showed attachment of cells to the surfaces by forming numerous and long filopodia. It is interesting to observe that the filopodia of the cells tend to attach and grow along the nanofibers direction whose diameter is comparable to that of the filipodia. Such cellular morphology is another indicative of a favorable interaction of fibroblasts with the nanofibers.PCL-CS/MgO based nanofibers were successfully fabricated by the electrospinning technique. All the fiber composition showed uniform surface morphology, structural integrity, and suitable mechanical properties. PCL/MgO showed higher Young’s modulus (∼25 MPa) compared to other compositions, whereas the ultimate tensile strength was higher for PCL/CS nanofiber (∼3 MPa). XRD confirmed the oxide state of MgO in the nanofiber sample. Alamar Blue Assay revealed no toxicity in these fibers. SEM imaging confirmed favorable cell adhesion and cell attachment on these nanofibers. Cell viability was found to be >75% for all sample types, which is considered a safe level. These nanofiber samples showed the attachment of cells to the surfaces by numerous and long filopodia. The significance of this work was to synthesize a novel biomaterial scaffold for use in tissue engineering applications such as wound healing, bone regeneration, drug delivery and regenerative medicine. Electrospun PCL-CS/MgO-based nanofibers are inexpensive and easy to synthesize, process and scale up. The ability to produce a novel material represents a significant advancement in development of composite materials with structural and material properties that will be beneficial for biomedical applications.Development of a high power wideband polarizer for electron cyclotron current drive system in JT-60SAA wideband polarizer consisting of a polarization twister and a circular polarizer has been developed for an electron cyclotron current driving system in JT-60SA, where the output frequencies of a dual frequency gyrotron for JT-60SA are 110 and 138 GHz. The groove depths are optimized for the dual frequencies by numerical simulations using a FDTD method and cold test results. The polarization properties of a mock-up polarizer are measured at the dual frequencies in cold tests. The cold test results suggest that all practical polarizations for ECCD experiments can be achieved at the dual frequencies. The prototype polarization twister has been tested up to 0.25 MW during 3 s at the frequency of 110 GHz.Flexibility of electron cyclotron heating (ECH) and current drive (ECCD) can be improved by multi-frequency operation in magnetically confined plasma devices. The dual-frequency gyrotron at the frequencies of 110 and 138 GHz has been developed for the ECH/ECCD system in JT-60SA The grooved mirror polarizer consisting of a polarization twister and a circular polarizer for ECH system was proposed by Petelin shows the conceptual view of the grooved mirror, where a, b, and h are a groove period, a groove width, and a groove depth, respectively. The z component of magnetic field of FP and electric field of SP must be zero, so that FP is reflected by the top of the groove, and SP is reflected by the bottom of it.The groove depth of the polarization twister is about a quarter wavelength, so that the phase difference between FP and SP is about 180°. Consequently, the axis of polarization ellipse can be rotated by the polarization twister. On the other hand, the groove depth of the circular polarizer is about one eighth wavelength, so that the phase difference between FP and SP is about 90°. Consequently, the axial ratio of the polarization ellipse can be controlled by the circular polarizer. In order to suppress high order diffraction waves, the groove period a must be given bywhere θ is the incident angle, ϕ is the rotation angle of the grooved mirror in The wideband polarizer of the Gaussian beam transmission system at the frequency from 105 to 140 GHz was developed for the ECCD system in ASDEX Upgrade tokamak The miter bend type polarizer for the corrugated circular waveguide transmission system was proposed by Doane The design of grooved mirror is one of the key issues of wideband polarizer development. shows the cross sectional view of the mock-up polarizer for cold tests, where R is the filet of groove edge. The main parameters of the two grooved mirrors are shown in , where the groove depths are measured by the depth gage. The groove depth of polarization twister can be designed by the simulation results. On the other hand, the circular polarizer is designed by the extrapolation from the low power test results, because that β is more sensitive to the groove depth than τ. The polarization properties of the grooved mirrors are optimized for 110 and 138 GHz. The influence of high order diffractions can be suppressed by designing the groove period of 1.17 mm, which satisfies Eq. The schematic view of the test stand for cold tests is shown in . The incident mode is HE11 mode in a circular corrugated waveguide, and it is vertically linearly polarized wave. The polarizations of radiated waves from the output port of the polarizer are evaluated by the pair of the phase plates (π and π/2) made of a-plane sapphire at the dual frequencies. The polarizations are measured by rotating the grooved mirror in steps of 10°. When the polarization of the radiated wave from the polarizer is converted to vertically linearly polarized wave by the pair of phase plates, the polarization parameters can be estimated from the two rotation angles of the phase plates.The typical tilted polarization ellipse is shown in . The key polarization parameters are τ: the tilted angle of a polarization ellipse and β: the arctangent of the axial ratio of a polarization ellipse. The cold test results of polarization twister are shown in (b) at 138 GHz. When the grooved mirror of the polarization twister is rotated from 0° to 180° in steps of 10°, the τ increases from 0° to 360°, the β changes in the range from minus several degrees to plus several degrees at both of the frequencies. The measured data indicate the realization of the wideband polarization twister.The cold test results of the circular polarizer are shown in (b) at 138 GHz. When the grooved mirror of the circular polarizer is rotated from 0° to 180° in steps of 10°, the τ changes in the range from about −80° to about 80°, while the β changes in the range from about −40° and about 40° at 110 GHz. In the case of 138 GHz, when the grooved mirror of the circular polarizer is rotated from 0° to 180° in steps of 10°, the τ changes in the range from about −120° and about 120°. On the other hand, the β changes in the range from about −40° and about 40°.The numerical simulations with the commercial electromagnetic simulation code XFdtd (Remcom) using FDTD method have been carried out using a quarter size model for comparison between the wide groove mirror (b |
= 0.91 mm) and the narrow one (b |
= 0.585 mm) at the same groove period: a |
= 1.17 mm and the same groove depth: h |
= 0.49 mm, as shown in . The wide grooved mirror has the almost same polarization properties at the dual frequencies. On the other hand, the polarization properties of narrow grooved mirror are different between 110 and 138 GHz, so that the wide groove is one of the key points for designing a wideband polarizer. The suitable groove depth of the circular polarizer is different between the cold test result (h |
= 0.54 mm) and the numerical simulation one (h |
= 0.49 mm), due to the effect of rounded edge making an electrical groove depth shallower.For evaluating the ability of universal polarizer in both frequency bands, the enable polarizations with combined operation of the polarization twister and the circular polarizer are plotted on the Poincaré spheres. shows the plotted data on the northern hemisphere and the southern one of the Poincaré sphere at 110 GHz. (c) and (d) shows the plotted data at 138 GHz. The widespread plots on the Poincaré spheres suggest that all practical polarizations for ECCD experiments can be achieved at the dual frequencies.Since the Ohmic loss on the grooved mirror surface of the polarization twister is expected to be larger than that of the circular polarizer, the prototype polarization twister is designed and fabricated for high power tests. shows the design of the prototype polarization twister consisting of the grooved mirror, the magnetic liquid rotary seal, and the rotation motorized stage. The width, the period and the depth of the groove are 0.91, 1.17, and 0.85 mm, respectively. The grooved mirror is made of chromium copper alloy for high electrical conductivity and high yield stress. The magnetic liquid rotary seal (FMT-075-CANN-S1, Rigaku Mechatronics) is adopted as the vacuum seal for reducing rotating torque and suppressing oil vapor in evacuated waveguides. The groove mirror can be rotated with the precision rotation motorized stage (KST-120YAW-G10, Sigma Koki) using a stepping motor. The cooling channel has the coaxial structure, for cooling of the center of the back plane of the grooved mirror. The thermo-coupler is attached in the small hole of the back plane of the grooved mirror for monitoring the mirror temperature.The high power test stand consisting of the dual frequency gyrotron, the MOU, the directional coupler, the prototype polarization twister, the miter bend with the arc sensors, the vacuum evacuation system, and the dummy load is shown in . The polarization of incident wave into the polarization twister from the gyrotron is perpendicular to the incident plane. When the electric field of incident wave is parallel to the groove direction (z-axis in ), the mirror rotation angle is defined to be 0°. The joule loss of the polarization twister, the miter bend with the arc sensors, and the dummy load are evaluated by calorimetric measurements. The high power test of the prototype polarization twister had been carried out up to 0.25 MW, 3 s at a frequency of 110 GHz. The RF power and pulse length is restricted by the mechanical trouble of the dummy load. shows the Joule losses of the prototype polarization twister and the miter bend with rotating the grooved mirror of the polarization twister. The Joule loss of the polarization twister increases with the mirror rotation angle from 0° to 90°. The maximum loss of the polarization twister is about 1.06% at the mirror rotation angle of 90°, which agree with theoretical predictions, qualitatively The wideband polarizer has been developed at the frequencies of 110 GHz and 138 GHz for the ECH/ECCD system in JT-60SA. The groove depths are optimized for the dual frequencies by the numerical simulations and the cold test results. The polarization properties of the grooved mirror are confirmed at the dual frequencies in the cold tests. The measured results suggest that all practical polarizations for actual ECCD experiments can be achieved at the dual frequencies. The polarization twister has been tested up to 0.25 MW during 3 s at 110 GHz. In future plans, the smaller, lighter and low cost polarizer will be designed, fabricated and tested up to 1 MW, 10 s at the dual frequencies.Behaviour of CFST stub columns with initial concrete imperfection: Analysis and calculationsGap between the steel tube and concrete core can be considered as a kind of initial concrete imperfection in concrete-filled steel tubular (CFST) structures.This paper performs a nonlinear analysis of CFST stub columns with a circumferential gap or spherical-cap gap under axial compression. A nonlinear finite element model is developed, where the nonlinear material behaviour and the effect of gap on the interface behaviour of the concrete and steel tube are included. Close agreement is achieved between the test and calculated results in terms of load−deformation response and ultimate strength. In light of the numerical results, the behaviour of CFST columns with a circumferential gap or spherical-cap gap is analysed. Parametric studies are then carried out to investigate the influence of different parameters on the ultimate strength of CFST stub columns with gaps. Finally, the maximum limit of the gap ratio is proposed for CFST stub columns with circumferential gaps, and a simplified formula is proposed to estimate the effect of spherical-cap gap on the ultimate strength of CFST stub columns as well.characteristic concrete strength (=0.67fcufor normal strength concrete)gap ratio (χ=2dc/D for circumferential gaps; or χ=2ds/D for spherical-cap gaps)In real concrete filled steel tubular (CFST) structures, two types of gaps (a) and (b), respectively. Normally, the circumferential gap is caused by the concrete shrinkage in the circumferential direction, and the spherical-cap gap mainly originates from the constructional process. In the practical engineering, the circumferential gap may appear at vertical CFST members such as CFST columns and CFST piers, and the spherical-cap gap is found to occur at horizontal CFST members such as CFST arch bridges and CFST truss structures. In the companion paper ForCFSTwithacircumferentialgap(asshowninFig.1(a)):χ=2dcDForCFSTwithaspherical-capgap(asshowninFig.1(b)):χ=dsDwhere dc and ds are the dimensions of the circumferential gap and spherical-cap gap respectively, and dc and ds are designated as the maximum distance from the concrete edge to the inner surface of the steel tube, as shown in ; D is the outer diameter of the tube section. The test results showed that the gaps can affect the failure modes and ultimate strength of CFST columns under axial compression. However, how the gaps imposed these effects, especially their effects on the confinement of the steel tube to concrete, cannot be clarified by the physical tests.In the past, many numerical studies had been carried out on CFST stub columns under axial compression by using finite element analysis. Schneider This paper aims to carry out a nonlinear analysis of CFST stub columns with a circumferential gap or spherical-cap gap under axial compression. The main objectives of this research are threefold. First, to develop a three-dimensional nonlinear finite element model, in which the nonlinear material behaviour and the effect of gap on the interface behaviour of concrete and the steel tube are included. Previous test results will be used to verify the feasibility of the finite element model. Second, to study the mechanical behaviour of the CFST stub columns with gaps, especially to reveal the influence of gaps on the interaction behaviour between concrete and the steel tube. Third, to perform a parametric study, and then propose the maximum allowed gap ratio for CFST stub columns with a circumferential gap, as well as a simplified formula to estimate the effect of spherical-cap gap on the ultimate strength of CFST stub columns.ABAQUS software is employed throughout the finite element analysis. The steel tube is simulated by using 4-node shell elements with reduced integration. The concrete core is modelled using 8-node brick elements, with three translation degrees of freedom at each node. A mesh convergence study is performed to identify an appropriate mesh density to achieve reliable results. Loading was applied in a displacement control mode at the top of a column to simulate the axial loading condition. For an axially loaded column with a relatively large slenderness, a lateral deflection of L/1000 at the mid-height was adopted to consider the global initial imperfection, where L is the effective length of the column . The rigid plate was assumed to be an elastic rigid block, and its modulus of elasticity and Poisson's ratio were taken as 1012 |
N/mm2 and 0.00001, respectively. All degrees of freedom except the rotation around the y-axis were constrained at the loading line of the bottom rigid plate, whilst at the top rigid plate an appointed displacement was applied on the loading line along the z-axis, and the translations along x- and y-axes and the rotations about the x- and z-axes were restrained. The boundary conditions are shown in (c). For a stub column, the ends of the column were fixed against all degrees of freedom except for the vertical displacement at the top end.The steel was simulated by an elastic–plastic model using a stress−strain relation that consists of five stages The damage plasticity model was used for modelling concrete material in the current finite element model where x=ε/ε0, y=σ/fc′; ε0, β0, η are model parameters where expressions can be found in Han et al. The results of previous physical tests presented in the companion paper where Y=σc/fc', X=εc/εco; σc and εc are stress and strain of concrete respectively; and εco, A’, B’, C’ and D’ are parameters where expressions can be found in Attard and Setunge For the CFST with a spherical-cap gap, it was observed from the physical tests For concrete in tension, the cracking strength of concrete (σt) was determined by using the method given by Shen et al. In the past, surface-based interaction with a contact pressure model in the normal direction and a Coulomb friction model in the tangential directions to the surface between the steel tube and core concrete has been successfully used to simulate CFST columns where u is the friction coefficient and taken as 0.6 in this analysis Unlike that in a CFST with a spherical-cap gap, the surface of concrete core in a CFST with a circumferential gap has no direct contact with the inner surface of the steel tube at the initial stage. Therefore, both normal contact pressure and tangential shear stress are taken as zero at the beginning in the finite element model. Then after the contact occurs, the tangential frictional stress (τfric) relies on the value of normal pressure stress (p) and can be expressed as τfric=u·p, in which the frictional factor (u) is taken as 0.6.A comparison between the test results presented in the accompanying paper shows a comparison between the numerical deformed shapes and the observations of typical CFST short columns with gap under axial compression. It can be seen that the columns with gap generally show outward local buckling for the steel tubes while the overall lateral deflection at mid-height is also observed. The predicted failure mode generally shows a reasonable agreement with the observed one despite small differences of them in term of the position of the local buckling. compares the predicted axial load (N) versus axial shortening (Δ) curves with typical measured curves presented by Liao et al. . A mean value (Nue/Nuc) of 0.989 is obtained with a standard deviation of 0.030. Generally, it can be found that good agreement is obtained between the predicted and tested results.Typical CFST stub columns selected herein to conduct behaviour analysis generally have the same parameters as those tested by Liao et al. compares the axial load (N)−axial strain (ε) curves of the CFSTs with a circumferential gap (χ=1.1%) or without gap. The axial loads carried by the steel tube and concrete core are also presented in this figure as a function of ε. The strength level of Asfy, Acfc and Asfy+Acfc are shown in as well. For the convenience of analysis, several characteristic points are marked on the N−ε curves by dot points, shown in (a). Points A and A’ correspond to the time when the peak load is attained. At Point B, the axial load (N) of the column with a circumferential gap begins to increase again after experiencing a sudden drop. Points C and C’ refer to the time when the axial strain (ε) attains 0.05.(a) that, the axial load (N) of the column with a circumferential gap drops suddenly after the peak load (Nmax, Point A). Then when the concrete is in contact with the outer steel tube, the axial load (N) increases again (Point B) until a large axial strain (ε=0.05, Point C) is achieved. This is confirmed by the observations of previous tests (b) presents the axial loads (Ns and Nc) carried by the steel tube and its core concrete respectively, against the axial strain (ε) of the column. It is found that the load (Ns) carried by the steel tube is approximately the same for the columns with gap or not, both of which have a peak load (Ns-max) around As·fy. However, the circumferential gap causes a concrete strength loss by 33% in this example due to the lack of confinement. Therefore, it may be concluded that the strength reduction of the CFST with a circumferential gap is mainly due to the less strength contribution from its concrete. From (b), it can also be seen that, Nc of the CFST with gap is close to that of the CFST without gap at an axial strain of 0.05.Typical failure modes of CFST stub columns are compared in (1), where the deformation have been amplified three times to show the deformed shapes of columns more clearly. The elephant-foot shaped buckling is found near the top and bottom of the CFST stub column with a circumferential gap, whilst the CFST without gap shows an outward buckling at the mid-height of the steel tube. The deformed shapes of concrete at different times are shown in (2). It can be seen that, before the concrete contacts the outer steel tube (Point B) the biggest transverse deformation of concrete is observed at the mid-height. Then after the concrete is in contact with the outer steel tube, the transverse deformation of concrete at the mid-height is restrained by the tube. As a result, the failure location of concrete tends to move towards the column ends. At Point C, the failure of concrete is observed at the top and bottom sections where the steel tube local buckling occurs, shown as in (2c) (i). For the CFST without gap, the failure of its core concrete is at the mid-height as the axial strain attains 0.05 (Point C’), shown in (3) gives the longitudinal stress (S33) distribution of concrete at the mid-height as the ultimate strength (Nu) is achieved. At a same location, the concrete stress of the column without gap is obviously greater than that of the column with gap due to the confinement effect.From the above analysis, it can be concluded that the confinement of the steel tube to concrete is the key issue for the circumferential gap to affect the ultimate strength and failure mode of CFST stub columns. Therefore, it is important to analyse the interaction stress (p) between the steel tube and concrete since the confinement effect is directly associated with the magnitude of p. presents the development of the interaction stress (p) at the mid-height of stub columns, where the moments corresponding to Points A and B shown in are marked in this figure as well. At Point A, p remains zero for columns with a circumferential gap, indicating that the concrete is not in contact with the steel tube as the peak load (Nmax) is attained. Then after Point B, p begins to increase significantly until the axial strain reaches 0.05. At Point C, p of the CFST with a gap is slightly smaller than that of the CFST without the gap. With an increase of the gap ratio (χ), the moment when interaction takes place tends to be postponed. For the CFST without a gap and those with a gap ratio (χ) of 1.1% and 2.2% respectively, the interaction occurs when the axial strains (ε) attain 0.0019, 0.0058 and 0.01, respectively. compares the p−ε curves of the CFST stub column with a circumferential gap at different heights of L/2, L/3 and L/6 respectively, where L is the length of column. The interaction firstly occurs at L/2, and then the contact happens at L/3 and L/6 respectively. After the occurrence of the interaction, it seems that the values of p at L/3 and L/6 increase more significantly than that at L/2, due to the higher transverse deformation of concrete. For the composite column without a gap, the transverse deformation of concrete tends to develop evenly, therefore the concrete at various heights generally contact the steel tube at the same time, shown in (in which H is the distance to the bottom end). However, for the CFST with a gap, the concrete tends to contact the tube later at a position closer to the column end, whilst no interaction occurs in the range from 0.13H/L to the column end during the whole loading process.The transverse stress (σst) of the steel tube is another parameter that reflects the confinement of the steel tube to concrete. A higher σst indicates a more significant confinement provided by the steel tube. demonstrates the longitudinal stress (σsl) and transverse stress (σst) of the steel tube at the mid-height, in which both of them are plotted at the positive side of the vertical axis for the convenience of comparison. As expected, longitudinal steel stresses (σsl) are generally close for the CFST without a gap and that with a circumferential gap, and values of σsl for both columns attain the steel yield strength (fy=360 MPa) at peak load (Nmax). For the CFST stub column without a gap, at the initial stage the longitudinal stress (σsl) tends to increase significantly whilst the transverse stress (σst) remains small. But after concrete contacts the steel tube σst develops rapidly due to the interaction between the concrete and tube. During the whole loading process, σst of the CFST with a circumferential gap is always lower than that of the column without the gap, indicating the less confinement of the steel tube to concrete in the former.The above analysis demonstrates that, due to the existence of a circumferential gap, the core concrete in a CFST stub column will not be in contact with its outer steel tube when the peak load (Nmax) is attained if the gap is big enough. Consequently, this will affect the ultimate strength and deformation capacity of the stub column. In a real CFST column, the circumferential gap cannot always be avoided due to the radial shrinkage or non-compactness of its concrete core. Therefore, it is necessary to provide a maximum limit for the gap ratio (χ) to ensure the gap would not impose a significant effect on the mechanical behaviour of CFST columns. In defining this limit, the main goal is to make sure that concrete can contact the steel tube before the CFST column reaches its peak load. In this regarding, a series of parametric studies are performed with a range of gap ratio from 0.02% to 1.1% to derive a proper limit. shows the relative axial strain (εcontact/εmax) as a function of the gap ratio (χ), where εcontact is the axial strain corresponding to the moment when concrete contacts the steel tube, and εmax is the axial strain corresponding to the peak load (Nmax) of the CFST stub column. If εcontact/εmax equals to unity, it means that concrete contacts the steel tube exactly at the same time as the peak load (Nmax) is obtained. But if εcontact/εmax is less than unity, the interaction occurs before Nmax is attained. As can be seen from that, with the decrease of the gap ratio (χ), concrete tends to contact the steel tube earlier. When χ is decreased to 0.05%, a magnitude of 0.76 is achieved for εcontact/εmax. From the parametric results, it is also found that the steel tube shows an elephant-foot shaped buckling at both ends [as shown in (1a)] when the gap ratio (χ) is greater than or equals to 0.7%, and the buckling mode is changed to the outward buckling at the mid-height [similar to the failure mode of the CFST stub column without a gap, as shown in For convenience of analysis, a strength index SI is defined as following in this paper:where Nuc-gap is the calculated ultimate strength of the CFST stub columns with a gap, and Nuc-no gap is the calculated ultimate strength of the CFST stub columns without a gap.The values of SI for CFST columns with different gap ratios (χ) are given in . When χ reduces to 0.05%, the magnitude of SI is 0.965 indicating that the strength loss of the stub column is less than 5%. So if χ equals to or is smaller than 0.05%, the existence of the circumferential gap has no significant effect on the failure mode, ultimate strength and corresponding deformation of CFST stub columns. Therefore, the maximum limit of χ is proposed herein as 0.05% for the engineers to check and control the size of circumferential gaps in real CFST structures.According to the test results reported by Han compares the failure modes of CFST stub columns with spherical-cap gaps with that of a perfect CFST column. The basic parameters used in the calculation are similar to those of the CFST stub column with a circumferential gap, which have been described in . Three typical gap ratios (χ), i.e. 2.2%, 4.4% and 6.6%, are selected in the analysis, whilst the corresponding CFST stub column without a gap was shown for comparison purposes. The bigger the gap ratio (χ) of a CFST stub column, the more significant inward buckling the steel tube exhibits at the position of the spherical-cap gap, shown in . It is owing to the less support from the core concrete to its outer tube when χ is increased. shows the axial load (N)−axial strain (ε) curves for the CFST stub columns with different spherical-cap gap ratios (χ), where the axial loads carried by the steel tube and concrete core are also presented in it. There is no significant difference in term of the shape of N−ε curves between the CFST with a spherical-cap gap and not. However, the ultimate strength (Nu) tends to decrease with the increase of the gap ratio (χ), mainly due to the strength loss of its core concrete. Compared to that of the CFST without a gap, the Nu of CFST stub columns with a spherical-cap gap decreases by around 3%, 7% and 10% as the χ is 2.2%, 4.4% and 6.6% respectively. As far as the axial strain (εu) corresponding to Nu is concerned, the CFST with a χ of 2.2% has a same εu as the CFST without gap. But εu of the CFST with a χ of 4.4% or 6.6% is around 36% less than that of the perfect CFST.A typical CFST stub column having a spherical-cap gap ratio (χ) of 4.4% is selected and its interaction stresses (p) between the steel tube and concrete across the cross-section are analysed. The predicted p−ε curves at different points are presented in (b) and (c), where the point positions are shown in (a). The interaction stress of the corresponding CFST without a gap is also given in for comparison purposes. From the calculation results, it is found that the interaction stresses of CFST without a gap distribute evenly across the cross-section. For the CFST with a spherical-cap gap, the concrete at the edge of the gap (Points 1–4) does not contact the steel tube during the whole loading process. Point 5 has a far greater value of p than other points while the value of p at Point 6 is very minor. From Point 7 to Point 11 the interaction stresses (p) generally distribute evenly and all of them are significantly lower than those of the CFST without a gap. Since Points 7–11 are relatively near to the gap, the influence of the gap in this area is consequently remarkable. As far as Points 12–20 are concerned, the values of p are almost constant cross this area, so only p at Point 20 is presented in (b). It can be seen that p at Point 20 is significantly greater than those at Points 7–11, which indicates a stronger confinement provided by the steel tube at Point 20. Under a same axial strain (ε), p of Point 20 is slightly lower than that of CFST without a gap. But this difference is considerably minor, especially before the axial strain attains 0.01. Since the area ranging from Point 12 to Point 20 is far away from the gap, the influence of the gap on the confinement to concrete in this area is thus relatively small.From the above analysis, it seems that the effect of a spherical-cap gap on the interaction varies along the concrete's circumference. Therefore, the average interaction stresses (Pave) at different regions are compared in , in which pavr-all means the average interaction stress of all the points (Points 1–20), pavr-upper represents the average interaction stress of the points at the upper half-circle which includes the gap (Points 1–11), and pavr-lower represents the average interaction stress of the points at the lower haft-circle which is far away from the gap (Points 12–20). As expected, the average interaction stress (pavr-all) of the CFST with a gap is smaller than that of the CFST without a gap (pavr-nogap), indicating the reduced confinement to concrete caused by the gap. pavr-upper is significantly lower than pavr-lower, whilst pavr-lower is close to pavr-nogap under a same axial strain (ε). As the column with the gap attaining its ultimate strength (ε=0.0032), the values of pavr-all, pavr-upper and pavr-lower are 1.51 MPa, 1.27 MPa and 1.8 MPa respectively, and the value of pavr-nogap is 2.09 MPa. Then at the ultimate strength for the column without the gap (ε=0.0051), pavr-all, pavr-upper, pavr-lower and pavr-nogap increase to 3.48 MPa, 2.78 MPa, 4.33 MPa and 4.65 MPa, respectively. shows the longitudinal stress (S33) distributions of concrete when CFST columns with different χ ratios reach the ultimate strength, where the interaction stresses (p) at different points are presented as well. Due to the even confinement from the steel tube, the core concrete of the CFST without a gap generally exhibits a constant longitudinal stress (S33) along the circumference. Values of S33 at different locations are all greater than the corresponding concrete cylinder strength (fc=54 MPa), and higher stresses are obtained at positions closer to the centre of the section, shown as in (a). For composite columns with spherical-cap gaps, obviously the stress S33 distributes unevenly due to the existence of the gaps, as shown in (b)–(d). In the region next to the gap, the value of S33 generally equals to the concrete cylinder strength (fc=54 MPa), which indicates the absence of confinement from the steel tube. This area may be recognised as a “no confinement” region. Then as the distance to the gap increases, the influence of gap tends to diminish. As a result, the confinement to concrete becomes stronger, resulting in an increased concrete stress. The value of S33 in this area is greater than fc but it is still smaller than that of the CFST without a gap. It seems that the concrete in this area is only “partially confined”. Finally, in the region far away from the gap, the concrete stress (S33) is generally close to that of the CFST without the gap due to the fact that the effect of the gap is considerably minor in this area. Therefore, a “full confinement” may be recognised for this region. Based on the above discussion, three parts, i.e. “no confinement” part, “partial confinement” part and “full confinement” part, for the concrete section of a typical CFST stub column with a spherical-cap gap are shown in After comparing the concrete stresses (S33) and interaction stresses (p) shown in , it can be also found that the value of p for the CFST with a small spherical-cap gap ratio (χ) of 2.2% is very close to that of the CFST without a gap. Especially in the lower half-circle far away from the gap, both p and S33 of the former are generally the same as those of the latter at ultimate strength. However, when the ratio of χ increases to 4.4% or 6.6%, a bigger gap tends to have a more significant effect on the confinement from the steel tube to concrete, thus making the column attain its ultimate strength earlier. Consequently, both p and S33 at the ultimate strength in these two cases are significantly lower than those of the CFST without a gap. Meanwhile, the “no confinement” area of the column with an χ ratio of 4.4% or 6.6% is obviously larger than that of the column with an χ of 2.2%, shown in shows the effect of the gap ratio (χ) on the axial load (Nc) carried by concrete, in which Nc is normalised with respect to the corresponding nominal strength of concrete [Nc/(Acfc)]. The value of Nc/(Acfc) of the CFST stub column without a gap is 1.26, indicating a 26% improvement of the concrete strength contributed by the confinement from the steel tube. Nc/(Acfc) decreases with increasing gap ratio (χ). When χ ratio is 2.2%, the value of Nc/(Acfc) is close to but slightly less than that of the CFST without the gap. As χ ratio increases to 6.6%, Nc/(Acfc) significantly decreases to 1.04. In this case, the strength enhancement of concrete resulting from the confinement is very minor due to the remarkable influence of the gap.Since a spherical-cap gap affects the confinement of concrete in a CFST stub column and decreases the ultimate strength to some extent, a simplified model may be proposed to account for this effect. Before doing this, a parametric study is carried out first, where the basic calculating conditions are chosen as: D=400 mm, t=9.3 mm, fy =345 MPa, fcu=60 MPa, and α=0.1. Meanwhile, six gap ratios (χ) ranging from 1% to 6% were selected.(a), (b) and (c) presents the influence of the steel strength (fy), concrete strength (fcu) and steel ratio (α) on the strength index SI (see Eq. ) for columns with different gap ratios (χ), respectively. It is worth noting that there are two groups that no softening branch is obtained in their axial load versus axial strain relations owing to the strong confinement of concrete core from the outer steel tube. These two groups demonstrating “strain hardening” is the group with a fcu of 30 MPa in analysing the influence of concrete strength and the one with a α ratio of 0.1 in analysing the influence of the steel ratio, respectively, which have been marked in (b) and (c) by arrows. In these cases, the ultimate strength (Nuc) is determined corresponding to an ultimate strain εcu (=1300+12.5fck+(600+33.3fck)⋅ξ0.2) proposed previously by Han . Apart from the N−ε relations with strain-hardening branches, the strengths of all other examples are taken as the peak loads of the N−ε relations. In general, to increase the gap ratio (χ) has no significant influence on the shape of N−ε relations; however, the ultimate strength (Nuc) decreases with an increase in χ. that, with the increase of χ, generally SI deceases linearly. The higher the steel strength (fy) is, the smaller the SI is obtained. With a same gap ratio (χ), SI tends to decrease with the decrease of fcu or the increase of α except for those two “strain hardening” groups. Generally, the influence of a gap on the strength of the CFST column will be more severe if the column has a lower fcu or a higher fy and α.A factor k is introduced herein to consider the effect of spherical-cap gaps on the ultimate strength of CFST stub columns, shown as following:where Nu-gap is the predicted ultimate strength of the CFST stub column with a spherical-cap gap, and Nu-nogap is the predicted ultimate strength of the CFST stub column without the gap.Based on the parametric analysis, a simplified model is proposed as follows to predict k:in which, χ (=ds/D) is the gap ratio, andf(ξ) is a function related to the confinement factor (ξ). presents the effect of ξ on the SI values for columns with different χ ratios. When ξ is below 1.22–1.26 (varying while χ ranges from 1 to 6), SI tends to decrease with increasing ξ. For a perfect column with a higher ξ, more confinement is expected to be provided to the concrete core. So for a column with a spherical-cap gap, the existence of the gap will have more significant influence and cause a higher reduction in confinement if ξ is higher. On the other hand, ξ represents the ratio of the nominal capacity between concrete and steel as well. When ξ exceeds a certain limit, the strength of CFST stub columns will be contributed mainly by the steel tube, which might result in the less influence of a gap on SI. For this reason, as ξ exceeds a value between 1.22 and 1.26, SI will increase with the increase of ξ, as shown in . Based on a regression analysis, formulae are developed to determine f(ξ)as follows:, the ultimate strength of a CFST stub column with a spherical-cap gap can be obtained. The validity limits of the simplified formulae are: χ=1–6%, fy=235–500 MPa, fcu=30–90 MPa, α=0.05–0.2, and 0<ξ≤1.725.The comparison between the calculated strengths (kformula) using Eq. and finite element results (kFE) is shown in . A mean value (kformula/kFE) of 0.995 is obtained with a standard deviation of 0.005. Clearly, the agreement between kformula and kFE is reasonably good.The following conclusions can be drawn based on the results of the study:A finite element model of CFST columns with a circumferential gap or spherical-cap gap under axial compression was developed in this paper. Close agreement was achieved between the test and calculated results in terms of load−deformation response and ultimate strength.The circumferential gap tends to impose a significant effect on CFST stub columns in terms of failure mode, ultimate strength and load−deformation response, mainly due to the fact that the core concrete is not in contact with its outer steel tube at the peak load (Nmax) of the column. With the increase of the gap ratio (χ), the moment when interaction takes place tends to be postponed.For a CFST stub column with a circumferential gap, as the gap ratio (χ) is equal to or less than 0.05%, the concrete will contact its outer tube before the peak load (Nmax) of the column is attained, and the strength loss of the stub column is within 3.5% under this circumstance. Therefore, the maximum limit of the χ ratio proposed in this paper is 0.05%, which can be used by engineers to control the circumferential gap in real CFST structures.A spherical-cap gap only have significant influence on the confinement of concrete from the steel tube in the area near the gap. Based on a regression analysis, a simplified formula was proposed to estimate the effect of spherical-cap gaps on the ultimate strength of CFST stub columns, and the accuracy of the predictions was verified by the finite element results.Application of crystal plasticity to plastic behavior at notched plate and crack propagationStrain concentration characteristics of ductile polycrystalline materials are studied experimentally and numerically by considering a notched square segment of material. The micromechanical modeling is performed using the finite element method based on crystal plasticity, while the material sample is taken to be FCC polycrystallline copper segment. The constitutive behavior is taken to be large-strain strain-rate-dependent elastic–plastic material. To effectively simulate polycrystalline behavior, the grain shape is generated from Voronoi tessellation, bearing a different lattice orientation in each grain. Strain concentration patterns around the notched bottom are observed experimentally and numerically, which are enlarged near the notch by accompanying a formation of localized strain accumulation toward an oblique direction. For the sample analyzed, with a relatively small macroscopic strain of 0.10, the notched bottom region experiences plastic strains as large as 1.00, and provides a strong indication that failure will initiate from the corner. Implications of this modeling study to microcracking failure are discussed by considering two fundamental modes of shear and cleavage to provide plausible microcracking examples.Uniform patterns of plastic deformations may evolve localized modes of deformation as natural and inevitable outcome of large-strain plasticity in many classes of materials. One of the most significant implications of the localization of plastic flow is that, among other things, it significantly affects the macroscopic behavior and limits ductility and toughness of materials. The localized phenomenon, especially, involves texture development and the nucleation of micro-voids or micro-cracks which, acting together, lead to catastrophic mechanical failure.Micro-mechanical modeling within the framework of crystal plasticity has been extensively employed in simulating the mechanical response of materials In the present study, we seek to measure and analyze the deformation behavior of a crystalline specimen having severe strain concentration due to a geometrical singularity. Particular attention is devoted to the capability of crystal plasticity analysis methodology simulating strain concentration problem. Rice et al. The present study is to provide experimental data for notched plate in tensile loading to obtain the stress–strain curve and also to obtain the microscopic observation near the notch from SEM photographs.The present study is also to give a computational approach to simulate notched plate based on crystal plasticity approach, where the specimen with the rectangular notch is approximated by Voronoi tessellation, and to analyze strain concentration problem for the notch to compare with the experimental observation.Insights into some fundamental aspects of micro-cracking can be gained, by introducing two types of fracture mode of cleavage and shearing. |
In this work, strain localization around the notch is studied experimentally and numerically. The nature of the localization, its dependence on the micro-structure, computational prediction for strain concentration problem, and its implications to micro-cracking are discussed.In order to investigate the characteristic behavior of notched plate as shown in material samples are machined to have a rectangular cross section, whose width w and thickness t are 12 and 6 mm, respectively. The length of the notched plate in tension loading is kept at 3 mm, while gap height is 0.15 and 0.30 mm. In the experiments, OFHC Copper, whose lattice structure is the face centered cubic material, is selected. The test specimens are machined from a distributed industrial rolling plate designated as C-1020P, whose chemical composition is 99.99% Cu in the unit of weight %. The rolling direction coincides with the loading direction.Electric screw-type static testing machine (Shimadzu AG-100 kNG, maximum load capacity 100 kN) is used, where the accuracy of load cell is within the errors of 1% accuracy for loading. The extension meter measures the displacement in the standard span with a length of 50 mm of the specimen, and the corresponding strain is calculated. An electric furnace anneals the specimens in order to remove the work hardening in machining. The samples are elevated to 600°C for 2 h and subjected to 1 h duration, and cooled down for 6 h. The specimens were then aged for one day at room temperature. After these heat treatments, the crystals were then electro-polished in a 33.3% nitric acid–66.7% methyl alcohol solution to remove thin oxidized film on Cu specimen as well as to reveal grain boundary just prior to mechanical testing. of the stress–strain curve, it may be found that the stress rapidly decreases after reaching the maximum strength in the notched specimen, while the specimen not having the notch takes a moderate smooth curve compared with those with the notch. The width of the notch does not affect the stress–strain curve response from shows SEM photograph of the grain size of Cu specimens before loading. The specimen having a width of 0.15 mm has about grains in diameter, and the notch has a rectangular shape. shows the deformation in grain, where the slip line on the lateral face is observed in the grain, and the fluctuation is intensified at the same portion to hide the grain boundaries as shown in (b) shows that the crack initiates at the corner of the notch. shows the schematic deformation around the notch appeared in Based on the formulation of rate-dependent material by Peirce et al. The mesoscopic behavior of polycrystals is analyzed using Voronoi tessellation in which the randomness of the micro-structure is generated. The use of 4-node elements to analyze the phenomena of shear banding in polycrystals is investigated. The mesh dependency appeared in a 3-node element can be resolved by using a 4-node element with reduced integration, illustrating the formation of micro shear bands in a polycrystal even if a non-uniform mesh is applied In the present study, the deformation of an fcc crystal under plane strain conditions is analyzed by using the 3-slip model of Harren et al. where the angle between the adjacent slip directions is set to be 60°. The constitutive description on each slip system (α) is given in terms of a power law is the corresponding reference rate of shearing, m is the strain rate sensitivity parameter, τ(α) is the resolved shear stress on the slip plane calculated from the macroscopic stress, and g(α) is the current strain hardened state of the crystal and its evolution is given by. The hardening modulus hαβ in the present calculation is assumed to be of the form hαβ=qh+(1−q)hδαβ where the fundamental hardening modulus h is to have the formwith γ(=∑α|γ(α)|) being the accumulated sum of slip. Material constants of the single crystal copper are the values used by Harren Deve and Asaro , q=1.0 (Taylor hardening), and m=0.005.In the present study, the rectangular test specimen with a rectangular notch is first divided into a two-dimensional Delaunay triangulation network. Then, the Voronoi tessellation is constructed by connecting the perpendicular bisector to the adjacent two Delaunay points. Each polygon in the Voronoi tessellation is further sub-divided into a mesh of 4-node elements. Meshing in each grain is accomplished by cutting a polygon in both of the radial and circumferential directions from the viewpoint of grain center, ensuring continuity across the grain boundaries. shows the mesh subdivision by 4-node element for 50 grains and 100 grains. From the experimental observation of , the obtained Voronoi tessellation is fine enough to approximate the grain size in the specimens. Each grain has a random lattice orientation created from a uniform random distribution from 0 to 1, which is converted to the angle of the first slip system varying from 0 to 60°.The prescribed displacement rate on the upper and lower edges is taken to be either of the following two modes. The first boundary condition is defined as simple extension labeled as ‘Boundary 1’ where the upper and lower edge surfaces move vertically at a constant velocity aswhere u1 and u2 are displacements in horizontal and vertical directions, respectively. The other mode is that the displacements of the mode I derived from linear fracture mechanics labeled as ‘Boundary 2’ are applied at the upper and lower edge in the polar coordinate system taking the coordinate basics in the middle of the notch to be expressed byThese displacements are employed in the crystal plasticity simulation by Tomita shows the results of contour of equivalent plastic strain for 50 grains model using ‘Boundary 1’ condition, and the painted color is white for less than 0.0 straining and perfect black for more than 1.0 straining, and the intermediate is equally subdivided into 10 intervals. (b) shows the current lattice orientation in each element, whose orientation in each slip system is magnified by the accumulated sum of slip, which is normalized by the nominal axial strain. Plastic strain accumulation is caused near the notch, and the shear band takes oblique directions from the bottom to reach the left side. The shape of the bottom, which is straight before loading, is sharpened to have an edge to the right, and this is contrary to the experimental facts of (a). Corresponding to the plastic strain contour, the slip system shown in (b) is active in the right side of the notch, and particularly its direction within the macroscopic shear band is almost parallel to the bands.(a). The slip system is very active near the notch, and the slip direction in the neighboring portion of the bottom surface is slightly inclined from the vertical line at u/L=0.0769, and the lattice orientation is rotated and becomes directed vertically at the stage of u/L=0.1538. This result coincides with the experimental fact of (a). As in the shear banding analyses, this indicates that the predominant effect of lattice rotations is to increase the resolved shear stress on the most active systems in the bands In material without defects, the thrust at the surface due to slip deformation causes the nucleation of micro-voids or micro-cracks, which grows and consolidates as deformation proceeds, finally leading to catastrophic mechanical failure. At an elevated temperature, micro-crack at the grain boundary, which has much lower yield stress than that of the inter-granular boundary, induces the intercrystalline failure. The present study proposes a law of nucleation and propagation of micro-voids or micro-cracks applicable for both inter-granular boundary and grain boundary. The proposed analysis method is to consider crystalline fracture based on microscopic quantities. Since microscopic stress and strain in polycrystal is influenced by internal conditions involving shear band, sub grain and cell structure, the nucleation and propagation law is assumed to have a base on this microscopic stress and strain in the grains. In the continuum approach, the constitutive equation of Gurson One of the two fundamental fracture modes Then, we have the two procedures for the propagation of micro-crack and the nucleation of micro-voids or micro-crack. As for the propagation of micro-crack at the tip, the procedure in As for the generation of micro-crack from inside, the procedure in Though the stress field would be singular at the tips of the micro-crack when a micro-crack is generated, the employed element at the tips is the regular 4-node bilinear element. To simulate a singular stress field, it would be better to employ a singular element around these tips. Since the present study is to expect many micro-cracks in the specimen caused by the internal stress or strain condition, the mesh arrangement becomes a regular mesh configuration.The stress-based criterion is applied in the calculation, and the critical value for the side-evaluation is the same regardless of grain boundary or inter-granular boundary. Critical stress dependence on the grain may incorporate the transcrystalline fracture in creep problem. shows the mesh subdivision for 20-grain model using 4-node element. shows the crack propagation starting from internal crack placed in the internal grain under the simple extension loading as is depicted of ‘Boundary 1’. The crack propagates to both sides horizontally, and at the final stage, short surface cracks enter at the left side, where the algorithm for nucleation of micro-crack is neglected. The proposed propagation algorithm is mesh-dependent, thus the propagation path is restricted to initial mesh design. When the crack extends to the center of the grain, the path has a choice to kink, however, the crack extends horizontally to the right. shows micro-crack under the same condition of by including the algorithm for generation of micro-crack. A similar crack extension is observed by accompanying additional microcracks around the original crack, which is also propagating horizontally. Contour of equivalent stress is also included in the same figure, where high-stress region move according to the crack front. Since the critical value is taken to be , the micro-crack obeys the cleavage fracture criteria and brittle fracture appeared. Currently, we are gathering more calculated results and modifying the program to include plastic strain-based criteria to simulate a wide range of parameter surveys.Plastic behavior at notched plate is studied experimentally and numerically. Using OFHC Copper with a rectangular notch of 0.15 and 0.30 mm width, the experiment is carried out under tensile loading to obtain the deformation at the notch. The calculation by the finite element analysis incorporating crystal plasticity with Voronoi tesellation is also performed. The surface at the notch bottom is curved in the experiment by intense strain accumulation, which is conformed by crystal plasticity calculation. The modeling study is extended to micro-cracking failure by considering two fundamental fracture modes of shear and cleavage to bring about a plausible crack propagation and micro-cracking.Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell elementA general shell model, including both theories of thin and thick shells, Kirchhoff–Love and Reissner–Mindlin undergoing finite rotations is presented. Based on Higher-order shear theory, where the fiber is cubic plane, the developed model does not need any transverse shear coefficients. The implementation is applicable to the analysis of isotropic and functionally graded shells undergoing fully geometrically nonlinear mechanical response. Material properties of the shells are assumed to be graded in the thickness direction according to a simple power-law and sigmoid distribution. The accuracy and overall robustness of the developed shell element are illustrated through the solution of several non trivial benchmark problems taken from the literature. The effect of the material distribution on the deflections and stresses is analyzed.Shells are widely used in various mechanical structures, civil engineering, aerospace and naval. These structures are more and more replaced by composites because of their superior mechanical properties. First, the abrupt change of the properties across the interface between different materials in conventional composite material is the source of cracks. Second, the presence of residual stresses due to the difference in coefficient of thermal expansion of different materials in conventional composite generates a decrease of the lifetime. Third, conventional composites are made to support a moderate temperature. To overcome these thermo-mechanical disadvantages, special kind of composites, known as functionally graded materials (FGMs) with a gradual transition of material properties from one material to another, are made.The analysis of classical shell structures is based on four kinematic assumptions, which are membrane, Kirchhoff–Love, Reissner–Mindlin and the refined model. Membrane theory, where the bending and shear strain are neglected, is not applicable to thin flexible structures. Kirchhoff–Love theory, where the shear strain are assumed zero, is not acceptable for composite shell The linear mechanical behavior of FGM plates was analyzed by several researchers. Based on the third-order shear deformation of plate theory, the static behavior of FGM plate was investigated in More general models were developed to analyze the linear mechanical behavior of shell structures. Typically functionally graded shell structures were presented with shear deformation theories by using the first-order shear deformation theory (FSDT) Because of the high modulus and high strength properties that FGM have, FGM shells undergo large deflection and rotation before the inelastic behavior. Therefore, an accurate prediction of geometrically non-linear behavior is required. Even if theories and formulations of geometrically non-linear analysis are numerous, a good representation of finite rotation of shells is a dominant factor.The geometrically non-linear of shells is largely used for isotropic and composite laminates materials The present work is based on a double directors shell model, in which the fiber is cubic plane This paper is organized as follows. First, kinematic strain of a double directors shell model is described in Section . The weak form is introduced in Section . The details of the finite element formulation are given in Section . The materials properties of FGM shell used in the present paper are presented in Section . Numerical results are illustrated in Section To distinguish the initial configuration C0 from the deformed Ct, capital letters (resp. lowercase letters) are used for quantities relative to the configuration C0 (resp. Ct).The reference surface in an arbitrary configuration, initial or deformed, is described by the same parametric coordinates ξ1 and ξ2. The position vector of an arbitrary point (p) of the mean reference surface, in the initial configuration C0 is defined by its components in the Cartesian global basis (Ei): where Aξ is the parametric surface. A differential element at point p is given by: The vectors of the covariant basis A1 and A2 are tangent at coordinate lines ξ1 and ξ2. The square of the incremental element length is given by: dSp2 is known as the first fundamental form (quadratic form) and the coefficients Aαβ are the components of the covariant metric tensor A. The unit normal vector at the mean reference surface, in the initial configuration C0 is given by: The parametric basis (A1,A2,N) is covariant at the point (p) of the reference surface in the initial configuration. Two unit vectors (T1,T2), located in the tangent plane can be defined at any point on the middle surface. These vectors, with the normal vector N, make an orthonormal basis (T1,T2,N). This basis can be obtained from the unit vectors N and E3: The position vector at any point (p), of the reference mean surface in the deformed configuration Ct, is defined by its components in the Cartesian basis (Ei): A differential element at point (p) is given by: where a1 and a2 are the covariant vectors. The square of the incremental element length is given by: The coefficients aαβ are the covariant components of metric tensor a.The 3D position of any point (q) of the structure is obtained by a power series expansion in the vicinity of the reference mean surface: where dk (k=1,2,…,n) are the n unit vectors field at each point of the surface, referred to as the directors field. For n=0, corresponding to membrane theory, the shell is represented by the mean surface. The case n=1, corresponding to single director shell model or first order theory, includes the Kirchhoff–Love and Reissner–Mindlin assumptions. The case n=2 leads to two director vectors, which allow to have a better representation of transverse shear strain and remove the correction factor associated to Reissner–Mindlin theory.In the initial configuration, the shell geometry description is done with a single vector. The position of any point (q) of shell domain is given by (show The covariant basis at point (q) is obtained from the position vector by (G1,G2,G3)=(∂Xq/∂ξ1,∂Xq/∂ξ2,∂Xq/∂z), which yields in base vectors relative to the initial state: In the initial configuration, the covariant components of metric tensor become: where the kinematic variables Aαβ, Bαβ, Cαβ, ωα0, Bα and λ02 are given by: {Aαβ=Aα⋅Aβ,Bαβ=Aα⋅D,β+Aβ⋅D,α,Cαβ=D,α⋅D,βωα0=Aα⋅D,Bα=D⋅D,α=λ0λ0,α,λ02=D⋅D, where Aαβ, Bαβ and Cαβ are the curvature tensors. ωα0 is initial shear term. Bα and λ02 are the variation of the thickness in the initial configuration. With the assumption of a constant thickness along the element, the metric tensor becomes: To force a particular behavior of the shell along the thickness, some assumptions must be introduced. The first assumption, known as the plane curve fiber, reflects a higher-order distribution of the position vector in the deformed configuration. This assumption is based on double director shell model. In the second assumption, known as cubic fiber, it is assumed that the position vector is cubic in function of the thickness variable z. The third assumption consists on imposing a zero shear stress at the top and bottom surfaces.The fiber, which is assumed initially straight, becomes curve after deformation. This plane curve is defined in a plane formed by two director vectors d1 and d2. These vectors are initially identical and equal to D. Vectors d1, d2 and D are unit if the thickness is assumed constant. The angle between the both director vectors d1 and d2, noted by γ=(d1,d2), is assumed small. This assumption makes neglect the thickness variation viewed through the both fibers (d1,d2). The curve fiber is tangent to one from both director vectors (d1), in the vicinity of the reference surface. With these geometric assumptions, the real position (q) after deformation is given by (show where d3 is located in the fiber plane defined by d1 and d2. The vector d3, which has the same modulus as d1 and d2, can be obtained by a rigid rotation of the vector d1 of an angle α(z) around the unit vector e, normal to the plane (d1,d2): e¯ is the skew-symmetric tensor such that e¯⋅e=0. According to double vector product formula, Eq. With the assumption ‖d1‖≈‖d2‖, the ratio r12 is equal to 1. Using Eqs. , can be written in the following form: where the form functions f1(z) and f2(z) are defined by: {f1(z)=zcos(α(z))−cos(γ)f2(z)f2(z)=zsin(α(z))/sin(γ).Assuming that the variation of the angle γ with the parametric coordinates ξα is neglected (γ,α≈0), the vectors of the covariant basis associated to the geometric description becomes: gα=aα+f1(z)d1,α+f2(z)d2,α,g3=f1′(z)d1+f2′(z)d2.The angle γ is not dependent on the thickness variable z. Using Eq. , the derivatives of f1 and f2 are given by: {f1′(z)=cos(α)−zα′sin(α)−f2′(z)cos(γ)f2′(z)=(sin(α)+zα′cos(α))/sin(γ).Assuming the director vector d1 is tangent to the fiber at the mean surface (g3(0)=d1), f1′(0) and f2′(0) become: , α(z) is zero at the origin (z=0). Under the assumption of small angle α, the functions f1 and f2 and those derivatives can be simplified as: {f1(z)=z−cos(γ)f2(z)f2(z)=zα/sin(γ),{f1′(z)=1−cos(γ)f2′(z)f2′(z)=(α+zα′)/sin(γ).The angle α, used in the expression of f1, f2, f1′ and f2′, can be expressed as a power series expansion of the thickness variable z. The second hypothesis assumes a cubic function of the deformed fiber. Since the angle α is zero at the origin, α(z) becomes: To reduce or remove the kinematic variables α1 and α2 from Eq. , some kinematic assumptions must be imposed. Contrary to Başar et al. , the shear components of the metric tensor can be written in the deformed configuration: gα3=gα⋅g3=f1′aα⋅d1+f2′aα⋅d2+(f1d1,α+f2d2,α)⋅(f1′d1+f2′d2). The transverse shear strain is given by: γα=2Eα3=gα3−Gα3=f1′aα⋅d1+f2′aα⋅d2−Aα⋅D+(f1d1,α+f2d2,α)⋅(f1′d1+f2′d2)−zD,α⋅D.These strains can be written in the third order as follows (f1′=1−cos(γ)f2′): {γ1α=aα⋅d1−Aα⋅Dγ2α=aα⋅d2−cos(γ)Aα⋅D≈aα⋅d2−Aα⋅Dχα=d1,α⋅d1−D,α⋅D, where the assumption cos(γ)≈1. It is assumed that the director vector d2 does not induce shear strain (Kirchhoff–Love), the strain γα and γ2α can be written as:γα=(1−(2α1z+3α2z2)cos(γ)/sin(γ))γ1α+zχα.The zero shear in the top and bottom of the shell can be written as: α1=χαtg(γ)2γ1α,α2=4tg(γ)3h2,α=(zχα2γ1α+4z23h2)tg(γ)≈4z2tg(γ)3h2.Since χα measures a small strain. (χα is zero for a constant thickness), the term zχα/(2γ1α) is neglected in front 4z2/(3h2). The functions f1 and f2 become: The shear strain angle γ, formed by d1 and d2, is assumed small and the term cos(γ) in f2(z) is equal to 1. The position vector of any shell point, defined by Eq. , will be considered with the functions f1(z) and f2(z) given by . The double directors model is an expansion of Reissner–Mindlin model, which include Kirchhoff–Love model. It is noticed that Reissner–Mindlin, Kirchhoff–Love and double director models have the same relations: The general model with functions f1 and f2, defined in , can be reduced in linear case to obtain plate model by projection in the tangent plane. The following displacement field is obtained: {u=u0+(z−4z33h2)β1+4z33h2α1v=v0+(z−4z33h2)β2+4z33h2α2w=w0,αk=−w,k,k=1,2, where u0, v0 and w0 are the mean surface displacement. β1 and β2 are the rotations and α1 and α2 are the derivative of transverse displacement w. This displacement field is initially proposed in linear case Using the kinematic assumptions, the Lagrangian strain E can be written as follows E=12(g−G),Eij=12(gij−Gij),{Eαβ=eαβ+f1(z)χαβ1+f2(z)χαβ22Eα3=f1′(z)γα1+f2′(z)γα2E33=12[(f1′+f2′)d−1], where eαβ, χαβk and γαk denote the membrane, the bending and the shear strains, which can be computed as: {δeαβ=12(aαβ−Aαβ),γαk=cαk−Cαkχαβk=12(bαβk−Bαβk),k=1,2, where aαβ, bαβk, Bαβk, cαk, Cαk and d are defined by: {aαβ=aα⋅aβ,bαβk=aα⋅d,βk+aβ⋅d,αk,Bαβk=Aα⋅D,βk+Aβ⋅D,αkcαk=aα⋅dk,Cαk=Aα⋅Dk,d=d1⋅d1,k=1,2.In matrix notation, the membrane, bending and shear strains vectors are given by: e=[e11e222e12],χk=[χ11kχ22k2χ12k],γk=[γ1kγ2k],k=1,2.Vanishing of the transverse shear stress on the top and bottom shell faces, σ13(±h/2)=σ23(±h/2)=0, the shear strain can be obtained as follows: This kinematic constraint will be imposed in a discrete form in the finite element approximation.The generalized strain and virtual strain vectors Σ and δΣ are defined by: Σ=[eχ1χ2γ1]11×1δΣ=[δeδχ1δχ2δγ1]11×1γ2=[00], where the virtual strains can be written as: {δeαβ=1/2(aα⋅δx,β+aβ⋅δx,α),δγαk=aα⋅δdk+δx,α⋅dkδχαβk=1/2(aα⋅δdk,β+aβ⋅δdk,α+δx,α⋅dk,β+δx,β⋅dk,α),k=1,2.Using the total Lagrangian formulation, the weak form of equilibrium equations is given by: where dV is the shell volume element in the initial configuration, δEij are the covariant components of the virtual Green–Lagrange strain tensor, Sij are the contravariant components of the second Piola–Kirchhoff stress tensor and Gext is the external virtual work. Performing the integration through the thickness of the shell, and using Eqs. G=∫A(N⋅δe+∑k=12(Mk⋅δχk)+T1⋅δγ1)dA−Gext=0, where δe, δχk and δγ1 are the variations of shell strains. N, Mk and T1 are the membrane, bending and shear stress resultants, which can be written in matrix form as: N=[N11N22N12],Mk=[Mk11Mk22Mk12],T1=[T11T12],k=1,2. These components are defined as follows: Nαβ=∫−h/2h/2σαβdz,Mkαβ=∫−h/2h/2fk(z)σαβdz,T1α=∫−h/2h/2f1′(z)σα3dz.The generalized resultant of stress R is defined by: The weak form of the equilibrium equation can then be rewritten as: where Φ=(u,d1,d2) is the displacement and directors vectors. Gext consists of the conservative boundary traction and surface pressure load. The details of the finite element approximation of Gext, which exists in the literature of shell element, is not detailed in the present manuscript. describes the nonlinear shell model, which can be solved by the Newton iterative algorithm. The consistent tangent operator for the Newton solution procedure can be constructed by the directional derivative of the weak form in the direction of the increment ΔΦ=(Δu,Δd1,Δd2). To analyze large displacement, the tangent stiffness should be composed of material and geometric stiffness matrices, denoted by DMG⋅Δϕ and DGG⋅Δϕ, respectively: The material part of the tangent operator results from the variation in the stress resultants and thus takes the form: The material tangent modulus is expressed as: ΔR=HTΔΣ,HT=[H11H12H130H12H22H230H13H23H330000H44],(H11,H12,H13,H22,H23,H33)=∫−h/2h/2(1,f1,f2,f12,f1f2,f22)Hdz., are in plane and out-of-plane linear elastic sub-matrices, which can be expressed in a Cartesian system as: H=E(z)1−ν2(z)[1ν(z)0ν(z)1000(1−ν(z))/2],Hτ=E(z)2(1+ν(z))[1001], where E(z) and ν(z) are the Young’s modulus and the Poisson’s ratio, respectively.The geometrical part results from the variation of the virtual strain by maintaining constant the stress resultants: This expression can be decomposed in membrane, bending and shear terms as follows: DGG⋅ΔΦ=DGGm⋅ΔΦ+DGGb1⋅ΔΦ+DGGb2⋅ΔΦ+DGGs1⋅ΔΦ. are developed after the finite element approximation.In this section, the numerical implementation of the presented shell theoretical formulation based upon a four node shell element is established. Using the isoparametric concept, the mid-surface (X) and surface displacement field (u=x−X) are approximated by: where NI are the standard bilinear isoparametric shape functions. The first director vector d1 is approximated with the same functions: For the variation and increment of the second director vector d2, we choose a quadratic interpolation as the same one proposed in δd2=∑I=14NIδd2I+∑K=58PKδαKtK,Δd2=∑I=14NIΔd2I+∑K=58PKΔαKtK, where (I) and (K) represent a node of the element and the mid-point of the element boundaries, respectively. δαK are variables associated to δd2 on the element boundaries and are given as in over the element boundaries under integral form. The shape functions PK are quadratic and are given in Taking into account the finite element approximation, the membrane, bending and shear strain components become: where Bm, Bk and Bs are the discrete strain–displacement matrices given in . For the shear strain, the assumed natural transverse shear strain method of Bathe and Dvorkin the shear matrix is given for all nodes. Nevertheless, the membrane and bending matrices are given at node I. A typical isoparametric finite element is considered as depicted in . A, B, C and D denote the mid-points of the element boundaries set.The virtual and incremental generalized strains are expressed as follows: leads to the following internal forces vector: The material tangent operator is deduced from Eqs. In matrix form, the geometric tangent operator, based on Eq. Membrane, bending and shear contributions can be grouped to form the geometric tangent operator: The global geometric tangent operator is detailed in the The Jacobian transformation J0 from basis (n10,n20) to (A1,A2) is expressed as: The derivatives of shape functions N¯,1I and N¯,2I ( The unit vectors of the actual basis (n1,n2) in The relationship between the incremental director vectors Δdk and the incremental rotation is given by Δdk=ΛkΔΘk, where ΔΘk=[ΔΘk1ΔΘk2] and k=1,2. For more details, the reader can refer to TI=[I000Λ1I000Λ2I]9×7,ΔUI=[ΔuΔΘ1ΔΘ2]7×1.This transformation leads to an element with seven-degrees-of-Freedom per node. The matrices Λ1I and director vectors d1I at nodes, at integration points and at mid-side for the ANS method, are done following The functionally graded materials can be produced by continuously varying the constituents of multi-phase materials in a predetermined profile. These material properties are assumed to vary through the shell thickness according to the rule of mixture. Most researchers use the power-law (P-FGM) or sigmoid functions (S-FGM) to describe the volume fractions. This article also uses FGM plates and shells with power-law or sigmoid function.The material properties of the P-FGM are assumed to obey to a power-law function written as: where P(z), Pm and Pc denote respectively the effective material property, the properties of the metal and ceramic. Vc is the volume fraction, which varies according to the two general four-parameter power-laws distribution FGMI(a,b,c,p):Vc(z)=[1−a(12+zh)+b(12+zh)c]p,FGMII(a,b,c,p):Vc(z)=[1−a(12−zh)+b(12−zh)c]p, where p is the power-law index. The parameters a, b and c determine the material variation profile through the functionally graded shell thickness. Instead of the rule of mixture, Eqs. , another analytical method for estimating the effective properties can be used as Mori–Tanaka or self-consistent methods The volume fraction of sigmoid function (S-FGM) is defined by: Vf1(z)=1−12(h/2−zh/2)p,0≤z≤h2,Vf2(z)=1−12(h/2+zh/2)p,−h2≤z≤0. The material properties of S-FGM can be calculated using the rule mixture as: P(z)=Vf1(z)Pm+(1−Vf1(z))Pc,0≤z≤h2,P(z)=Vf2(z)Pm+(1−Vf2(z))Pc,−h2≤z≤0.The applicability of the proposed theory and the performance of the finite element implementation are assessed by numerical simulation including large rotation. Numerical examples are divided into two classes: two isotropic shell examples and three functionally graded structures. In isotropic structure examples, we focus on applications with warped elements and on the finite rotation capability. The FGM structures are simulated to analyze its mechanical behavior. The results are compared with several formulations from the literature. The used laws distribution of the FGM shells are the classical power-law P-FGM and sigmoid S-FGM. The P-FGM can be obtained by the general four-parameter power-law distribution Eq. According to the choice of the functions f1 and f2 in , three elements are implemented. These elements are SQAD4, S4 and SHO4 corresponding to the discrete Kirchhoff quadrilateral The pinched hemisphere problem, a popular benchmark problem for shell analysis, is considered with an 18° hole at the top subjected to two inward and two outward forces F90° apart. From the geometrical symmetry of the sphere, the analysis is reduced to one quadrant (show The spherical geometry is defined by the radius R=10 and the thickness t=0.04. The material properties are the Young’s modulus E=6.82510107 and the Poisson’s ratio ν=0.3.The loads F are increased to 450 to compare with results by Saleeb et al. shows a good performance for SQAD4, S4 and SHO4 in large displacement and finite rotation analysis. The present results based on SHO4, are located between S4 and SQAD4 results. The initial and deformed configurations, subjected to F=450, obtained using SHO4 element mesh are shown in The ring plate geometry, which is shown in (b). The displacements W at points A, B and C versus the load factor f are plotted in . The W displacement is located along the normal to the non-deformed ring plate.Two types of elements are used in this example, which are S4 and SHO4. The displacements using SHO4 element are in good agreement with the S4 element solutions. These displacements at points A, B and C agree very well with results reported in A cantilever plate strip subjected to a distributed end shear load F as shown in , where L=10, b=1 and h=0.1. First, an isotropic material is considered. This problem was studied in many works depict the axial and vertical deflections of the plate tip −U and W for isotropic case. Results obtained by the present model (SHO4) are compared to analytical and numerical models. Results obtained by S4 and SQAD4 are close and in excellent agreement with analytical solution in The analysis of FGM cantilevered plate was conducted using the same geometry of the isotropic plate and a power law variation of Aluminum and Zirconia (P-FGM). The material properties of Aluminum and Zirconia are given in . The lower surface of the plate is assumed to be metal rich and the top surface is assumed to be ceramic. shows Axial and vertical deflection −U and W of FGM plate using double director shell element of P-FGM, under mechanical loading. The deflection of metallic plate is greater than ceramic due to the high bending stiffness of ceramic plate. It is shown that the deflection decreases with the power index p from metal to ceramic.The distribution across the plate thickness of the non-dimensional shear stress τ13hb/F for various values of the power index at the fixed end is illustrated in . It is shown that the zero-transverse condition shear stress on top and bottom faces of the FGM plate is verified using SHO4 element. The shear stress field of isotropic material (metal and ceramic) is symmetric with a parabolic distribution along the thickness.A static analysis was performed on a S-FGM square plate of side length a=100cm and thickness h=2cm, simply supported on all its edges. Due to the symmetry, one quarter of the square plate is modeled with 8×8 mesh. The material properties are E1=2.1×106kg/cm2 and ν=0.3. The deflection of S-FGM plate under uniform load q0=1.0kg/cm2 for p=2 is computed. The results of S-FGM plates using Reissner–Mindlin solution with a constant transverse shear correction factor of 5/6. The present results agree very well with Kim et al. A second square plate of side length a=0.2m and thickness h=0.01m, simply supported on all its edges is analyzed here. As the previous plate, the same mesh is considered. The results are presented in terms of non-dimensionalized parameters which are: center deflection, w/h; load parameter, P=q0a4/(Emh4); thickness co-ordinate, z¯=z/h; and stress, σ¯=σh2/(|q0|a2). q0 and Em denote the intensity of the applied mechanical load and the Young modulus of metal, respectively. The analysis was conducted using Aluminum/Zirconia and Aluminum/Alumina. The material properties of Aluminum, Zirconia and Alumina are given in . In all cases, the lower surface of the plate is assumed to be metal rich and the top surface is assumed to be ceramic. This analysis is based on P-FGM. shows the comparison between the linear and non-linear analysis using double director shell element of P-FGM, under mechanical loading. The deflection magnitudes using linear analysis are always overpredicted. The effect of nonlinearity is more pronounced for metallic plate, having the less important stiffness. The difference between linear and non-linear deflection decreases as the plate becomes more and more ceramic. The present results agree very well with those given in depicts the non-dimensional axial stress through the non-dimensional thickness of the plate under uniform loading applied on the top surface made of Aluminum and Zirconia. The present results agree very well with those of Praveen and Reddy , except for the magnitude by replacing the Zirconia by the Alumina. The present results are in good agreement with those of Praveen and Reddy The non linear mechanical response of cylindrical panel subjected to a concentrated load is examined (show ). Variants of this problem are found throughout the literature ). Numerical simulation are conducted using one quarter of the physical domain. The complete model is obtained using appropriate symmetry boundary conditions. a uniform 2×2 mesh for the quarter model and a 4×4 discretization for the full domain. depicts the deflection of the isotropic shell at the loaded point versus the applied load P for cylindrical panel where h=25.4mm using 2×2 and 20×32 mesh for the quarter model. Results obtained using 2×2 mesh are similar to those obtained from the refined mesh. The present results agree strongly with those reported in Numerical results for metal–ceramic functionally graded panels, for h=12.7mm, are shown in . Displacement control method is used in this example. The metal is taken as the bottom material and the ceramic (zirconia) as the top constituent. The power law is used in this model and the index of FGM is varied between 0.2 and 5 by considering the extremely cases of ceramic and metal. For ceramic panel, it is shown that the load increases until a deflection of 10mm. Then the applied load decreases until a deflection of 20mm. Next, the load increases monotonic with deflection. Due to the high stiffness of ceramic compared to metal, the applied load to ceramic panel is more important to metal. All the cylindrical panels with intermediate properties undergo corresponding intermediate values of loads and deflection. These results are visually in unison with the deflection curves provided in The geometrically non-linear theory of 3D-FGM-shell structures undergoing the finite rotation was analyzed using a finite element model based on a discrete double director shell element. The present model, based on higher-order shear deformation theory, does not need any shear coefficients. The grading function is assumed along the thickness direction. A pinched hemisphere shell and a ring plate with isotropic material are used to validate the model for shells subjected to finite rotation. Functionally graded shells as a cantilevered plate strip, a simply supported square and a cylindrical panel are computed by the present model. To validate the results of the present study and demonstrate its accuracy, the results are compared with the literature. A very good agreement among the results confirms the high accuracy of the current non-linear model. Deflection and axial stress are analyzed by varying the grading index.For a couple of nodes (i,j), the matrix [KG] becomes: [KGij]=[UUMijI+UUF2ij(UBF1ij+UBC1ij)I(UBF2ij)(BUF1ij+BUC1ij)I(BBF1ij+BBC1ij)I0(BUF2ij)0(BBF2ij)], where UUM, (UBF1,BBF1,UUF2,UBF2,BBF2) and (UBC1,BBC1) correspond to membrane, bending and shear respectively. The expression of the membrane term is written as: UUMij=∫A(Ni,1(N11Nj,1+N12Nj,2)+Ni,2(N12Nj,1+N22Nj,2))dA. The bending terms of the first director vector d1 are given by: UBF1ij=∫A(Ni,1(M111Nj,1+M112Nj,2)+Ni,2(M112Nj,1+M122Nj,2))dA,BBF1ii=−∫A(Ni,1((a1⋅d1i)M111+(a2⋅d1i)M112)+Ni,2((a1⋅d1i)M112+(a2⋅d2i)M122))dA,The bending term of the second director vector d2 is given by: UUF2ij=∫A(Nju,1(Ni,1M211+Ni,2M212)+Nju,2(Ni,1M212+Ni,2M222))dA+∫A(Niu,1T(Nj,1M211+Nj,2M212)+Niu,2T(Nj,1M212+Nj,2M222))dA.The expression of Niu is given by the following relation: where tm and dm are the unit vectors defined by the segment of the element with center m and the normal in this point, respectively. {UBF2ij=∫A(Njd,1(Ni,1M211+Ni,2M212)+Njd,2(Ni,1M212+Ni,2M222))dABUF2ij=UBF2ji.The expression of Nid is given by the following relation: , the rotating term BBF2ij is zero for i≠j: BBF2ij=∫A((M211a1+M212a2)⋅Nid,1+(M212a1+M222a2)⋅Nid,2)didA.The measurement of transverse shear strain relatively to substitution strain model allows to deduce UBC1 and BBC1. The shear Terms UBC1ij can be grouped in matrix form: [UBC1]=18[−α−β−β0−αββ−γ−γ00γγ+δδα0−δα−δ], where the coefficients α, β, γ and δ are defined by the following expressions: {α=∫A(1−ξ)T2dA,β=∫A(1−η)T1dAγ=∫A(1+ξ)T2dA,δ=∫A(1+η)T1dA,The shear terms BBC1ij are zero for i≠j (BBC1ij=0). The non-zero terms can form the column vector: {BBC1}=−14{(αa2A+βa1B)⋅d1(βa1B+γa2C)⋅d2(γa2C+δa1D)⋅d3(δa1D+αa2A)⋅d4}.Dynamic response of metallic lattice sandwich structures to impulsive loadingThe dynamic response of metallic lattice sandwich plates under impulsive loading is studied by experimental investigation. The sandwich structures composed of two identical face sheets and tetrahedral lattice cores, were designed and fabricated through perforated metal sheet forming and welding technology. The air blast experiment of lattice sandwich structures was performed by use of a four-cable ballistic pendulum system. The deformation/failure mechanisms were investigated through experimental observation and analysis. The impulsive resistance of the tetrahedral lattice sandwich structures is quantified by the maximum permanent transverse deflection of the back face sheet as a function of transmitted impulse. The maximum transverse deflections of tetrahedral lattice sandwich plates are compared with that of hexagonal honeycomb ones with identical parent materials and core relative density. The comparison implies that the tetrahedral lattice sandwich structures possess a better impulsive resistance.With the fast development of modern technology in military area, the monolithic plates cannot meet the requirements of blast protection any longer. In such case, the lattice sandwich structures have attracted broad interest for their excellent impulsive resistant performance. The sandwich structures have various energy dissipation mechanisms, such as bending and stretching of the face sheet, compression and shear of the core. Especially, in the case of impulsive loading, the voids in the porous lattice core can provide adequate space for the large plastic deformation of the core, which is an efficient mechanism to dissipate the energy produced by blast impact For optimization and application of the lattice sandwich structures, it is necessary to have abundant experimental information. Recently in experimental investigation, Dharmasena et al. In this study, we designed and fabricated the tetrahedral lattice sandwich square plate, which have the same material and core relative density as that of the hexagonal honeycomb sandwich plate tested by Zhu et al. . The specimens and testing set-up are presented at first, and the qualitative and quantitative experimental results are discussed subsequently. Finally, the general conclusions are summarized in Section The previous experimental investigation of lattice sandwich structures subject to air explosion was mainly focused on two-dimensional metal lattice materials; hence the present study concentrates on the three-dimensional metal lattice sandwich structure that exhibits a different core deformation characteristic.The fabrication methods of three-dimensional metal lattice include sheet perforation and node folding method The metal material and geometry of the tetrahedral lattice is designed according to the aluminium alloy hexagonal honeycombs used in the experiment performed by Zhu et al. . The thickness of the face sheets and the core are hf = 1 mm and hc = 12.5 mm, respectively. The lattice is a regular tetrahedron composed of three struts, with a length of l = 15.3 mm, a width of b = 2 mm and a thickness of h = 2 mm. The predicted relative density is given byThe side length of the square sandwich plate is 310 mm, but the side length of the lattice core is only 2L = 250 mm. The rest part of the core was filled with solid metal material to protect the specimen from collapse when clamping.The experiment was performed on a four-cable ballistic pendulum system, which has been used by Zhu et al. . The sandwich plate was clamped between two rectangular steel frames, which were fixed at the front of the pendulum. The TNT charge was placed in front of the specimen centre with a constant stand-off distance of 200 mm.When the charge was detonated, the shock wave produced in the air impacted the specimen and the whole pendulum is pushed to translate. The oscillation amplitude of the pendulum was measured by a laser displacement transducer, and recorded by an oscilloscope. The impulse transmitted to the pendulum front face can be calculated according to the oscillation period, weight and length of the pendulum and the effective impulse on the specimen can be further estimated.The relative density of the fabricated lattice sandwich specimen is 0.034, which is a little lower than the designed value due to the manufacturing error. A set of TNT charge mass, i.e. 15 g, 20 g, 25 g and 30 g, is used in the explosion experiment. The measured maximum deflection of the back face sheet and transmitted impulse are given in The impulses transmitted to the sandwich plate vary with the mass of charge, and the corresponding deformation/failure modes are discussed below for the front face sheet, back face and lattice core, respectively.The front face sheet of the lattice sandwich plate exhibits a large global deformation and local concave-convex deformation, as shown in . It can be seen that the local concave-convex deformation emerges at the central region of the front face sheet, and its area increases with the magnitude of the impulse transmitted to the sandwich plate as shown in (b–e). The front face sheet would suffer tearing failure at an abundant high impulse level. The contact of the core and face sheet can be regarded as point-surface contact, and thus intense impulsive impact could induce local concave–convex deformation for a relative thin face sheet. It implies that besides the global deformation, the front face sheet can also dissipate the impact energy by local deformation. Further efforts should be made to establish the analytical models including this mechanism.The deformation of the back face sheet is shown in . When the applied impulse has less intensity, only global deflection was observed, similar as that of the sandwich plates with other cores (b). It is again because of the point-surface contact of the face sheet and lattice core. At the given mass of charge, the produced impulse is not intense enough to induce fracture in the back face sheet. Therefore, we adjusted the stand-off distance of the charge to 150 mm without changing its mass. A crack was then observed at the centre of back face sheet under an impulse of 28.63 Ns, as shown in The deformation of the lattice core is shown in . Three regions can be identified according to the deformation pattern of the core, from centre to the edge: (1) fully densified region in the centre; (2) free deformation region at the edge and (3) transition region between the centre and edge. Shear failure was observed in the transition region due to the incompatible deformation of the front and back face sheets.In the blast experiment of hexagonal honeycomb sandwich plate, Zhu et al observed delamination failure between the front sheet and the honeycomb core The tested maximum deflection of back face sheet of tetrahedral lattice sandwich plate is compared with that of hexagonal honeycomb obtained by Zhu et al. . The maximum deflection wo and the applied impulse I are normalized byrespectively, where A denotes the effective core area, and M¯ denotes the sandwich mass per unit area.It can be seen that the maximum deflection of the back face sheet increases with the applied impulse following an approximately linear relation for the tetrahedral lattice and hexagonal honeycomb sandwich plate. The maximum back face sheet deflection of the tetrahedral lattice sandwich plate is smaller than that of the hexagonal honeycomb sandwich plate. It indicates that the tetrahedral lattice sandwich plate possesses a better impulsive resistance.The tetrahedral lattice sandwich structures are designed and fabricated through perforated metal sheet forming and welding technology. The dynamic response of the lattice sandwich structures is investigated by performing air explosion experiment. The transmitted impulses were measured by use of a four-cable ballistic pendulum system, and the maximum transverse deflection of the back face sheet is measured after test.The experiment results indicate that, besides global transverse deflection, local concave-convex deformation and punctate convex deformation occur at the central region of the front face sheet and back face sheet, respectively. These deformation models are induced by the approximate point-surface contact between the core and the face sheet. Non-uniform compression deformation and shear deformation appear in the tetrahedral lattice core due to the inconsistent deformation of the front and back face sheets. The maximum permanent transverse deflection is engaged to evaluate the impulsive resistance of the tetrahedral lattice sandwich structures, and the measurement results of tetrahedral lattice sandwich plates are compared with that of hexagonal honeycomb ones with identical parent materials and core relative density. The comparison demonstrates that the tetrahedral lattice sandwich structures possess a better impulsive resistance.Thermal- and mechanical-responsive polyurethane elastomers with self-healing, mechanical-reinforced, and thermal-stable capabilitiesPrevious studies have shown that the commonly used Diels-Alder (DA) bonds (furan and maleimide) cleaved at low temperatures (about 100 °C), which limits further application of these self-healing materials at higher temperatures. Hence, a series of thermo stable self-healing polyurethane elastomers (PUAn-DA-x) have been developed by using the reversible DA/retro-DA reactions initiated by thermal and mechanical stimuli between anthryl and maleimide functions. The synthesized linear polyurethane bearing pendant anthryl groups (PUAn-0) was effectively toward DA reactions with a bismaleimide crosslinker (BMI) to get covalently crosslinked PUAn-DA-x networks. Tensile test showed that the stress at break of PUAn-DA-1/1 was increased by more than 261% after the PUAn-0 was effectively networked by DA bonds. At the same time, with the aid of hydrogen bonds and chains’ rearrangement, the healing efficiency of PUAn-DA-1/1 could reach as high as 91.28% via the recombination of mechanically decoupled anthracene and maleimide without causing deformation of bulk specimens. In addition, the thermal stabilities of the DA bonds and PUAn-DA-x were studied.Self-healing polymeric materials have attracted great research attentions because of their built-in capability to repair physical breaks and microcracks. Over the duration of operation and utilization of materials, such micro-damages are arisen from the impact, abrasion and fatigue alone or in a combination. Such self-healing ability is a highly desired property which avoids catastrophic failure and extends materials’ lifespan []. Consequently, in order to enhance the safety performance, conserve natural resources and reduce the contamination of environment, three-dimensionally crosslinked networks were equipped with the self-healing property is extensively necessary. Nowadays, compared with extrinsic self-healing mechanisms, intrinsic self-healing systems grounded on the stimuli-responsively reversible chemical interactions have attracted more and more interests, as intrinsic self-healing systems can heal same damaged places multiple times and avoid exhausting healing agents and catalysts []. These dynamically stimuli-responsive chemistries contain: reversible covalent bonds like thermal-triggered reversible Diels-Alder (DA) cycloaddition reactions, photothermal-triggered ring-opening reactions, heating-triggered metathesis reactions and so on; or noncovalent interactions such as hydrogen bonds, metal-ligand coordination bonds, redox-triggered host-guest complexations, etc. [] Of particular interest among these mechanisms is the [4 + 2] cycloaddition DA reaction because it is simple, efficient, reversible and repetitive [DA chemistry is a [4 + 2] cycloaddition reaction between diene and dienophile, resulting in cyclohexane derivatives. Normally, DA bonds formed between furan (diene) and maleimide (dienophile) are thermally unstable when they are heated to approximately 100 °C. As a result, the thermal instability of the DA bonds (furan and maleimide) places a limitation of these self-healing materials on some practical use temperature (over roughly 100 °C). Thermo-induced retro-DA reactions may lead to enormous deformation of virgin shape and dramatic decrease of mechanical performance, which are ascribed to the loss of crosslinking structure or the decrease molecular weight []. On the other aspect, taking the advantages of this thermally reversible nature, some recyclable thermosetting materials have been designed and prepared based on DA/retro-DA reactions of furan and maleimide []. However, in order to expand the using temperature range of DA chemistry based self-healing materials, anthracene is selected to replace furan as a diene to prepare self-mending polymers. The DA bonds formed between anthracene (diene) and maleimide (dienophile) molecules are thermally stable and do not undergo thermal-induced retro-DA reactions even though beyond 200 °C. On the other aspect, according to the literature, the DA bonds (anthracene and maleimide) are more easily cleaved into the corresponding anthracene and maleimide moieties when they are suffered from mechanical tension destroy. This interesting phenomenon is due to its lower bond energy than other covalent bonds []. It is reported that the bond energy of the covalent DA bonds (anthracene and maleimide) varies from 77 kJ mol−1 to 117 kJ mol−1 depending on the substituents, while others covalent are 348 kJ mol−1 for C-C bonds, 293 kJ mol−1 for C-N bonds and 389 kJ mol−1 for N-H bonds []. As a result, the covalent DA bonds are more easily cleaved along with the propagation of microcracks or breaks. Surely, the reversed anthryl and maleimide molecules can reconnect to reform the DA products when the damaged regions are repaired under appropriate heat stimuli []. This characteristic reversible DA reaction is shown in (a). Hence, on the basis of the thermal- and mechanical-triggered DA/retro-DA reactions between anthryl and maleimide, a self-healing protocol has been proposed. Yoshie's et al. have prepared a self-healing system based on this reversible chemistry. However, the relative healing efficiency was undesirable even though it was repaired at 100 °C for more than 7 days which could only reach to 45% []. The unsatisfactory healing efficiency and slow healing process might be arisen from poor movement of polymer chains. In another word, a crosslinker with tri-maleimide functionalities (with rigid and mutifunctional structures) was taken to develop DA bonds resulted networks, which limited the reconnection of maleimide with anthracene to restore mechanical properties.Herein, it is tremendously necessary to develop a thermostable and efficient self-healing polyurethane (PU) network grounded on reversible DA/retro-DA reactions between anthryl and maleimide groups. By introducing 3-(N, N-Bis (2-hydroxyethyl) amine) propionic acid-9-anthracenemethanol ester (BHPAE) diol into polymer chains, linear polyurethane bearing pendant anthryl groups (PUAn-0) is going to be synthesized. A series of polyurethane networks with different crosslinking density (PUAn-DA-x) will be synthesized after PUAn-0 is effectively crosslinked by the maleimide terminated and flexible cross-linker (BMI). Taking the advantages of thermal- and mechanical-triggered reversible DA/retro-DA reactions between anthracene and maleimide molecules, the mechanical properties will be enhanced and self-healing abilities will be obtained of materials. The characteristic DA reactions between anthracene and maleimide are going to be systemically studied by 1H NMR, FT-IR and UV-vis spectroscopy. In addition, self-healing properties will be extensively investigated qualitatively and quantitatively, and the repairing process will be recorded by micrographs. At last, thermal stabilities of the DA bonds and the corresponding PUAn-DA-x elastomers are going to be explored simultaneously. It is expected that the introduction of DA bonds (anthracene and maleimide) into PUAn-DA-x systems will achieve integral self-healing capability, enhanced mechanical performance and well thermal stability.9-hydroxymethylanthracene (Macklin Biochemical Co., Ltd., China), acryloyl chloride (Adamas Beta Reagent Co., Ltd., China) and diethanolamine (DEA, Kelong Reagent Co., Ltd., China) were used without further purification. Maleic anhydride, furan and ethanolamine were supplied by Kelong Reagent Co., Ltd. (Chengdu, China) and used as received. Polypropylene glycol (PPG210, Hersbit Chemical Co., Ltd., China), as the macro polyol, was dehydrated under vacuum at 120 °C for 2 h prior to use. Isophorone diisocyanate (IPDI) and dibutyltin dilaurate (DBTDL) were purchased from Hersbit Chemical Co., Ltd. (China). 1,4-butanediol (BDO, Kelong Reagent Co., Ltd., China), as the chain extender, was dried under vacuum at 80 °C for more than 2 h and stored in a desiccator. Methyl ethyl ketone (MEK), tetrahydrofuran (THF), ethyl acetate and other solvents were purchased from Kelong Reagent Co., Ltd. (Chengdu, China) and stored in the presence of 4 Å molecular sieves.4,10-Dioxatricyclo[5.2.1.02,6]dec-8-ene-3,5-dione (Furan-A): HEMI was synthesized according to the literature procedure as shown in (400 MHz, DMSO‑d6, d). 6.559 (s, 2H, -CH-C (400 MHz, CDCl3, d). 6.551 (s, 2H, -CH-C2-CH2-OH), 3.732 (t, 2H, J = 3.6 Hz, N-CH2-CSynthesis of N-(2-Hydroxyethyl)-maleimide (HEMI): HEMI-A (5.0 g, 96 mmol) was refluxed in toluene (200 mL) for more than 12 h until all the DA bonds were completely cleaved. In order to confirm this retro-DA reactions process, 1H NMR spectroscopy was taken to study it. Chemical shift at 6.551 ppm and 5.307 ppm, which was ascribed to DA bonds, were totally disappeared once the furan was absolutely removed from the HEMI-A. While the solution was cooled in a freezer, the white powder was crystallized and collected via suction filtration. The crude HEMI was washed with diethyl ether and dried under vacuum (3.6 g, 26 mmol and yield 71.88%). The 1H NMR spectrum of HEMI was shown in (400 MHz, CDCl3, d). 6.733 (s, 2H, -CO-C2-CH2-OH), 3.712 (t, J = 4.8 Hz, 2H, N-CH2-CThe process of preparation of BMI chain crosslinker was presented in the -NCO groups terminated oligomers was obtained. Following, HEMI (3.4 g, 24 mmol) was dissolved with DMF (10.0 mL) and dropped into former solution to terminate the -NCO groups. The BMI was successfully synthesized when the system was stirred for another 5 h at 85 °C. The concentration of maleimide functional groups of the resultant solution was 0.585 mmol g−1 and the chemical structure was analyzed via 1H NMR spectrum as shown in (400 MHz, CDCl3, d). 7.950 (urethane, s, 4H, -OCON-), 6.668 (maleimide groups, t, 4H, J = 2.8 Hz, -CO-C2-CH-) and 1.083 (PPG210, d, J = 2.8 Hz, -CH-CPUAn-0 was synthesized through conventional two-step polymerization of polyurethane. According to , this procedure was illustrated as following: in particular, dehydrated PPG210 (33.0 g, 33 mmol), BHPAE (2.4 g, 6.5 mmol, synthesized according to our previous work and the synthesis process was presented in Shceme S1 (b) [ (400 MHz, CDCl3, d). 8.465–7.410 (9H, anthryl ring, 2-CH-) and 1.083 (PPG210, d, J = 2.8 Hz, -CH-CPUAn-DA-1/1 was taken as an example to illustrate the preparation of networked elastomers. Firstly, the solution of PUAn-0 (5.0 g, 0.18 mmol of anthryl functional groups) and BMI solution (0.30 g, 0.18 mmol of maleimide functional groups, 1 eq) were mixed and stirred for 30 min to get a clear and uniform solution. Following, the mixture was poured into a freshly clean polytetrafluoroethene (PTEF) mold and the solvent was removed after being dried at room temperature for 48 h, and then in a vacuum oven at room temperature for another 48 h. The dried films were transferred into an oven and maintained at 90 °C for 24 h to extremely carry out DA reaction between anthryl and maleimide functionalities and get the crosslinked PUAn-DA-1/1 film. The resulted elastomers were stored in a desiccator containing silica gel for the following characterizations. In the same way, other polyurethane films with different mole ratios of maleimide over anthryl (M: An, proportional to the content of crosslink points), i.e., 3: 4, 1: 2 and 1: 4 were prepared and named PUAn-DA-3/4, PUAn-DA-1/2 and PUAn-DA-1/4 respectively. Besides, two control samples of PUAn-0 (linear structure, no BMI was added and no DA bonds were formed) and PU-0 (no BMI was added and no BHPAE was incorporated) were prepared following the same steps mentioned above.Proton nuclear magnetic resonance (1H NMR) spectra were recorded with Bruker AV 400 spectrometers (400 MHz, Germany) using CDCl3 or DMSO‑d6 as the solvent and tetramethyl silane (TMS) as the internal reference at an ambient condition.Fourier transform infrared (FT-IR) spectra were recorded on Nicolet 560 FT-IR Spectrum Scanner (Thermo Scientific, USA) in the region of 4000 to 400 cm−1 with a resolution of 4 cm−1.UV-vis spectra of the thin PUAn-DA-x films fabricated by solution casting on the quartz wall were recorded using an Analytic-jena Specord S600 (Germany) over region of wavelength from 200 to 500 nm in an absorption mode.Molecular weight and polydispersity index (PDI) of PUAn-0 and BMI were determined by gel permeation chromatography (GPC, HLC-8320, Japan) with DMF as the solvent (flowing rate: 0.4 mL min−1, at 40 °C) and polystyrene as a standard.Stress-strain and loading-unloading tensile curves were measured on dumbbell-shaped specimens (25 mm × 4 mm × 0.4–0.6 mm) using an Instron tensile testing machine (Model 5569, USA) with a crosshead speed of 100 mm min−1. Measurements were performed on five replicates for each sample.Thermal stability was studied by thermal gravimetric analysis (TGA) instruments (NETZSCH TG 209 F3, Germany). The curves were recorded from room temperature to 600 °C with a heating rate of 10 °C min−1 under a flowing nitrogen atmosphere (40 mL min−1).Dynamic mechanical analysis (DMA) was measured on a Q-800 instrument (TA Instruments, USA) in a stretching mode under a nitrogen atmosphere. The storage modulus (E′) and loss factor (tan δ) were measured in the temperature range from −80 °C to 80 °C with a heating rate of 3 °C min−1 and a frequency of 1 Hz.For qualitative evaluation of the self-healing process, the healing progress of cracks (made by razor blade) was recorded by optical microscope (Phenix PH50-3A-A, China). Micrographs of healing process were recorded by a digital camera (Phenix JKF 500, China) under white light and ultraviolet light (λ > 300 nm), respectively.The chemical structure of BMI and PUAn-0 was confirmed by 1H NMR spectra. exhibited the 1H NMR spectrum of BMI, which presented special chemical shift of maleimide groups (d = 6.668 ppm, (a)), urethane bonds (d = 7.950 ppm, (d)), IPDI (d = 0.997 ppm, (f)) and PPG210 (d = 2.894 ppm (g) and d = 1.083 ppm (i)). It proved that the flexible BMI with maleimide termination was successfully synthesized. Simultaneously, the 1H NMR spectrum of PUAn-0 was shown in which contains unique peaks of anthryl groups (d = 8.465–7.410 ppm, (a, b, c, d and e)), urethane bonds (d = 7.950 ppm, (i)), IPDI (d = 0.992 ppm, (k)) and PPG210 (d = 2.892 ppm (h) and d = 1.083 ppm (f)). These results demonstrated PUAn-0 bearing pendant anthryl functions was successfully prepared.The DA reactions between anthryl and maleimide groups were investigated via 1H NMR spectroscopy yet. (a) exhibited the 1H NMR spectra of the BMI, PUAn-0 and PUAn-DA-1/1. From 1H NMR curves, it was observed that the signal peaks of anthracene rings (d = 8.465–7.410 ppm, (b, c, d, e and f)) were emerged in the curve of PUAn-0 (middle in (a)) and the resonance signal of maleimide (d = 6.668 ppm, (a)) was appeared in the curve of BMI (bottom in (a)). However, the characteristic peaks of anthracene rings and maleimide groups disappeared from PUAn-DA-1/1's 1H NMR spectrum (top in (a)) after the mixture of BMI and PUAn-0 was maintained in a screw-top NMR tube at 90 °C for 24 h. At the same time, the resonance signals at d = 7.082 ppm (b') and 6.956 ppm (c') in PUAn-DA-1/1's curve were attributed to the protons of [4 + 2] cycloaddition DA products. Thus, from the 1H NMR analysis, it is known that the DA reactions between the anthracene and maleimide derivatives have actually occurred.The molecular weight and polydispersity index (PDI) of PUAn-0 and BMI were presented in . The chemical structures of BMI, PUAn-0 and PUAn-DA-1/1 were also analyzed by FT-IR spectroscopy. As shown in (b), for all the spectra of BMI, PUAn-0 and PUAn-DA-1/1, there was no absorption peak at 2270 cm−1. It confirmed that no residual -NCO groups were existed in the resulting products. Moreover, the special peaks at 3338 cm−1 for stretching of N-H, 1531 cm−1 for bending of N-H and 1716 cm−1 for stretching of C=O of urethane groups confirmed that the urethane links for BMI, PUAn-0 and PUAn-DA-1/1 were formed between -OH and -NCO. At the same time, from the BMI's curve, the obvious peaks of C=C bonds of maleimide group at 697 cm−1 and 829 cm−1 proved that the maleimide groups were successfully introduced. Above analysis via FT-IR spectroscopy clearly indicate successful preparing of BMI, PUAn-0 and PUAn-DA-1/1 []. Besides, the DA reactions were studied by FT-IR spectroscopy too. As exhibited in the inserted graph of (b), the weak absorption peak at 1772 cm−1 assigned to DA products appeared in the PUAn-DA-1/1 spectrum. The peaks at 829 cm−1 and 697 cm−1 assigned to maleimide groups did not appear in PUAn-DA-1/1 spectrum. It demonstrated that the [4 + 2] cycloaddition DA reactions between the anthracene of PUAn-0 and maleimide of BMI were successfully carried out.The [4 + 2] cycloaddition DA reactions between anthryl and maleimide were further verified by UV-vis spectroscopy. Upon the DA reactions occurred, the conjugation effect of anthracene chromophores was broken, resulting in a depletion of absorption intensity of ultraviolet light []. On the basis of this feature, the conversions and kinetics of this special [4 + 2] cycloaddition DA reaction were studied through UV-vis spectroscopy. The mixed solution of PUAn-0 and BMI (ratio equal to PUAn-DA-1/1) was casted on the quartz wall and the solvent was evaporated within a few minutes to prepare thin films for UV-vis spectroscopy measurements []. The time zero (t = 0) was set at the time when the solvent was apparently evaporated. (a) exhibited the UV-vis spectra of PUAn-DA-1/1 heated at 90 °C for different time interval The absorption bands of anthracene at λ = 333 nm, 350 nm, 368 nm and 387 nm was gradually decreased with the prolongation of maintenance time Depletion of the absorption bands justified that anthryl functional groups were consumed and the [4 + 2] cycloaddition DA products were formed. Among these four obvious absorption peaks, absorption at λ = 368 nm has the strongest intensity. Therefore, it was selected to investigate the kinetics of DA reactions between anthryl and maleimide.The conversions of anthryl chromophores, x, as a function of maintaining time were calculated following eqn. , where the A0 was the initial absorption intensity at t = 0 and the At related to the absorbance after being heated for time t at λ = 368 nm [ (b) showed the conversions of anthryl functional groups versus maintenance time at diverse temperatures (70 °C, 90 °C, and 110 °C). The reaction rate of the [4 + 2] cycloaddition DA reactions increased with elevating the temperature from 70 °C to 110 °C. When these thin films were heated for 300 min, the conversion yields were 73.0%, 79.8% and 85.2% for 70 °C, 90 °C and 110 °C respectively.The conversion yield of 110 °C was higher than other two temperatures, indicating that the new DA bonds formed between maleimide and anthryl groups were thermally stable above 110 °C. Considering the unstable urethane bonds at a higher temperature, the cross-linked PUAn-DA-x samples were prepared by keeping the films at 90 °C for 24 h []. From the UV-vis results, the first- and second-order kinetics of the [4 + 2] cycloaddition were estimated from eqn. respectively, where k was the rate constant.First-order kinetics regression coefficients of linear fitting were 0.974, 0.990 and 0.987 for 70 °C, 90 °C and 110 °C respectively, as presented in (c). However, regression coefficients were 0.999 for the second-order kinetics for three different temperatures ( (d)), indicating that the second-order kinetics seems be more reasonable for this characteristic DA reaction. The activation energy derived from the second-order kinetics was 26.7 kJ mol−1 [When PUAn-0 was efficiently networked through DA links, the mechanical performance of PUAn-DA-x with different DA bonds density was distinctly reinforced. Load-displacement curves of PUAn-DA-x with different crosslinking density were presented in (a). The ultimate tensile strengths were 3.84 MPa, 4.21 MPa, 6.27 MPa and 10.66 MPa, whereas the elongations were 1049.5%, 882.1% 844.8% and 662.1% for PUAn-DA-1/4, PUAn-DA-1/2, PUAn-DA-3/4 and PUAn-DA-1/1 respectively. The tensile strength of PUAn-DA-1/1 increased by more than 261% and the Young's modulus increased by 442% compared with PUAn-0. The enhanced mechanical properties indicated that the chains of PUAn-0 were effectively networked by DA links. Crosslinked PUAn-DA-1/1 was a highly stretchable elastomer at ambient temperature, which could be stretched over 600% without a fracture, as shown in (b) showed successive loading-unloading tensile curves. Dissipation energy was decreased with increasing the load-unload cycles because the resistance of polymer chains' slippage was decreased. There was about 82% residue strain originated from hysteresis effect and plastic flow of polymer chains []. The thermal mechanical properties of PUAn-DA-x were investigated by dynamic mechanical analysis (DMA). Storage modulus (E′) and loss factor (tan δ) as a function versus temperature were presented in (c and d). From the storage modulus (E′) outcomes, it could be concluded that the crosslinking structure has been formed and DA links' density increased along with more BMI was incorporated. From the tan δ curves, the glass transition temperature (Tg) was approximately 16 °C. It could be observed that the Tg increased negligibly even though more DA links formed form PUAn-DA-1/4 to PUAn-DA-1/1. It was resulted from the crosslinking density was not high enough to affect segments' movement [In addition, the crosslinking process initiated by DA reactions was further studied by the sol-gel transformation experiments. The mixture (35 wt%) of PUAn-0 and BMI were prepared according to the ratio mentioned above to make different PUAn-DA-x solutions. The sol-gel transformation progress of the PUAn-DA-x solutions at 90 °C with prolonging time could be found in . The initial mixture solutions were clear, transparent and freely fluid, where the DA bonds didn't form at all. However, after these solutions were kept at 90 °C for 90 min, PUAn-DA-1/1 and PUAn-DA-3/4 have transformed into gel completely and lost the fluidity []. However, PUAn-DA-1/2 and PUAn-DA-1/4 were still sol and could flow freely. At last, while the heating time increased to 180 min, the four formulations turn into gels without fluidity. The sol-gel transformation results indicated that the crosslinking density increased with enlarging ratio of maleimide over anthryl functional groups.Previous studies have demonstrated that the DA bonds (anthryl and maleimide) represent weak links which were broken preferentially when subjected to mechanical attacks []. Heo et al. have designed a self-healing polyurethane system and demonstrated that the DA cycloaddition products formed between anthryl and maleimide groups were cleaved with the cracks propagation []. Besides, free anthryl groups and the DA products (cyclohexane derivatives) exhibited different fluorescence properties since [4 + 2] cycloaddition DA reactions destroyed the conjugated π-system of anthracene chromophores []. The micrographs of cracked PUAn-DA-1/1 and PU-0 were presented in . Compared with the ultraviolet photomicrographs of PU-0, strong fluorescence emission was detected surrounding the crack of PUAn-DA-1/1. This phenomenon evidenced that mechanical destruction causes free anthracene and maleimide functional groups at the cracked region. Surely, the cross-linking points of DA bonds could be reformed from the reversed functionalities to efficiently recover the excellent properties of the PUAn-DA-x elastomers. (b) showed the macroscopic self-healing process of PUAn-DA-1/1. The PUAn-DA-1/1 cross-linked films (50 mm × 5 mm × 0.6 mm) were dyed with different colors and cut break. Under an external intervention, fresh surfaces were immediately contacted at 90 °C for 20 min Subsequently, after removing the external force, the specimen was kept in an oven at 90 °C for 24 h to regenerate the DA crosslinking points and make the fresh surfaces disappear. The repaired PUAn-DA-1/1 could be bent and stretched without breaking at the connected position. In addition, in order to qualitatively evaluate the healing process, the microscopic repairing process was also monitored. As shown in (c), cracks were applied on the surface of PUAn-DA-1/1 and PUAn-DA-1/4 films with razor blade. The cracked samples were heated at 90 °C for 24 h to close the cracks and reconnect the DA bonds. It could be observed that the cracks disappeared gradually with prolonging heating time. However, compared with the PUAn-DA-1/4 film, a slight scar could be detected on the surface of the repaired PUAn-DA-1/1 film, which was related to the different chain mobility caused by the different cross-linking density. Furthermore, fluorescence emission disappeared from the repaired region in the ultraviolet-irradiated micrographs, manifesting that the most anthryl groups were converted into DA products again and the notches were repaired []. In the repairing progress, chains’ diffusion and hydrogen bonds played an important auxiliary role for achieving interesting self-healing performance, as exhibited in In order to evaluate the healing efficiency quantitatively, load-displacement curves of different PUAn-DA-x samples were measured. Crosslinked specimens were gashed by razor blade and kept in an oven at 90 °C. During the heating process, the PU chains and hydrogen bonds were rearranged along with the expansion of the crack surfaces. By subsequent heat treatment, the recombination of the DA bonds regenerated the network structure and restored the mechanical properties. The healing efficiencies were calculated from the ratio of ultimate tensile strength of the repaired specimens over the virgin specimens []. The healing efficiencies were 83.85%, 82.66%, 82.62% and 91.28% for PUAn-DA-1/4, PUAn-DA-1/2 PUAn-DA-3/4 and PUAn-DA-1/1 respectively, as shown in . Satisfactory healing efficiencies justified that thermal-induced r-DA reaction was not necessary, but the reformation of DA bonds from mechanical destroy initiated anthryl and maleimide could lead to self-healing []. The healing efficiency of PUAn-DA-1/1 was highest, which was attributed to the largest amount of available anthryl and maleimide molecules surrounding the crack surfaces. However, the healing efficiency of PUAn-DA-1/4 could also reach to as high as 83.85%, which was resulted from the low crosslinking density and the well chains' mobility. In other word, the hydrogen bonds and chains’ diffusion have played a key role in the self-healing process of PUAn-DA-1/4. Pleased healing efficiency proved that PUAn-DA-x elastomers had the ability to recover the physical properties and the DA bonds play a significant role in the self-repairing process.According to the self-healing process, the schematic of self-healing mechanism was illustrated in . After the cracks were inserted by razor blade, the major of [4 + 2] cycloaddition DA products were cleaved into free anthracene and maleimide molecules surrounding the cracked places. The following heating treatment at 90 °C made the fracture surfaces expand to contact intimately, and hydrogen bonds and PU chains were reshuffled freely. With increasing the heating dose, the DA bonds were reconnected to recover the mechanical properties of PUAn-DA-x. After networked structure was reconstructed of the repaired PUAn-DA-x, the self-healing process was actually completed. However, some irreversible covalent bonds could not be reconnected which would sacrifice some the healing efficiency.A disadvantage of self-healing polymers based on the thermo-reversible DA reaction of furan and maleimide molecules was that the DA bond was thermally unstable. If the application temperature was higher than 100 °C, the retro-DA reactions would lead to sharp deterioration of the comprehensive mechanical performance. However, the DA bonds formed between anthryl and maleimide remained relatively stable at temperatures above 200 °C, which made these self-healing polymers exhibit a broad range of application temperature. The thermal stability of networked UAn-DA-1/1's elastomer and gel was investigated and the results were presented in , the crosslinked elastomer was immersed in dimethylsulfoxide (DMSO). After the mixture was heated for 1 h at 200 °C, the elastomer couldn't be dissolved while just swollen. On the other hand, as shown in , the initial mixture of PUAn-0 and BMI (according to the ratio of PUAn-DA-1/1) was clear and free of fluidity. However, after the mixture was kept at 90 °C for 3 h, crosslinking DA reactions led to the transformation of sol into gel and loss of fluidity. Similarly, when the networked gel was heated at 200 °C for 1 h, the gel couldn't be dissolved and flowed freely, but some bubbles appeared which were ascribed to the volatilization of some solvent at that high temperature. These results proved that the network structures were thermally stable even above 200 °C because the DA crosslinking bonds of anthryl and maleimide moieties did not occurred retro-DA reactions at such high temperature.Besides, the thermal stability of PUAn-0 and PUAn-DA-x was assessed by TGA under a nitrogen atmosphere between room temperature and 600 °C as shown in . TGA curves revealed that typical two-step decomposition of these prepared polyurethane was occurred in the temperature range of 250–450 °C. Correspondingly, two distinct degradation stages could also be observed from the first derivative of weight loss thermograms (DTG, ). The first decomposition stage ascribed to urethane bonds occurred in 250–300 °C, which were decomposed into primary amines (or secondary amines), olefins and carbon dioxide. The second decomposition stage was related to the scission of polypropylene glycol []. After more BMI being introduced into the PUAn-DA-x systems, the decomposition speed of the urethane bonds became slower and the temperatures of the first peaks in DTG thermograms increased. For the soft microdomains, the decomposition temperature of second peaks in DTG thermograms became higher with enlarging the ratio of maleimide to anthracene. These results could be observed from the insertion figure in . The details of the decomposition process were summarized in . When the ratio of maleimide over anthracene increased from 0 to 1/1, the Tmax1, the Tmax2 and the char residue were increased by 5.7 °C, 2.3 °C and 0.81%. In short, the thermal stability of PUAn-DA-x shown some enhancement after being cross-linked via DA bonds, which might be resulted from the better thermal stability of the network structure and the maleimide groups by comparing with PUAn-0 [A series of novel self-healing polyurethane elastomers (PUAn-DA-x) networked by [4 + 2] cycloaddition DA reactions between anthryl and maleimide derivatives was successfully prepared. Characteristic DA reaction has been extensively studied by 1H NMR, FT-IR and UV-vis spectroscopy, and the conversion of anthryl groups could reach to 85.2% according to UV-vis results. This designed PUAn-DA-x systems have shown interesting self-healing capability and well thermal stability. The healing efficiency of PUAn-DA-1/1 was 91.28%, which owing to the reformation of DA bonds from maleimide and anthracene with the assistance of hydrogen bonds and chains’ rearrangement. From the thermal stability characterizations, it was known that the DA bonds and PUAn-DA-x exhibited no thermal degradation below 200 °C. In addition, tensile test results also proved that the self-healing PUAn-DA-x elastomers had pleased mechanical and elastic properties which own a potential application as smart materials.The following is the supplementary data to this article:Supplementary data to this article can be found online at Late proterozoic–Early paleozoic magmatismA Late Proterozoic–Early Paleozoic magmatic cycle in Sierra de la Ventana, ArgentinaLate Proterozoic–Early Paleozoic intrusive and volcanic rocks of Sierra de la Ventana can be grouped into two magmatic assemblages: the Meyer and Cochenleufú suites. The older (700–570 Ma) is composed of S-type quartz-monzodiorites, synogranites, and monzogranites associated with andesites and rhyolites and related to volcanic-arc and postcollisional settings. The younger (540–470 Ma) corresponds to highly fractionated homogeneous A-type monzogranites, linked to final plutonic events during postorogenic extension in collisional belts. Strong similarities between Sierra de la Ventana magmatic rocks and the S- and A-type granites of the Cape granite suite in South Africa allow positive correlation. In both areas, primitive volcanic arcs or collisional orogens are recognized. Continuous transpressional shearing between the Swartland and Tygerberg terranes in the Saldania belt may have triggered the generation and emplacement of both suites.Late proterozoic–Early paleozoic magmatismIn southeastern Buenos Aires province, Argentina, Sierra de la Ventana is a 180 km long sigmoidal mountain belt, composed of basement and sedimentary cover (). The basement consists of Late Precambrian–Early Paleozoic deformed granites, rhyolites, and andesites. The Paleozoic sedimentary sequences can be divided into three groups. Conglomerates and quartzites compose the Curamalal (Ordovician–Silurian) and Ventana (Silurian–Devonian) Groups. The Pillahuincó Group (Upper Carboniferous–Permian) is composed of glacial deposits, black shales, and sandstones. Deformational episodes occurred during the Upper Devonian and Permian. correlated the Sierra de la Ventana sequences with the Karoo Basin in South Africa, and integrated both areas in the Samfrau Geosyncline. , among others, carried out geological studies in Sierra de la Ventana. In addition, studied the petrography, geochemistry and geochronology, and reported preliminary geotectonic interpretations of the igneous rocks. Finally, presented relevant data for understanding the tectonic setting of the Sierra de la Ventana granite.In this paper, we present new petrographical and geochemical data about the intrusive and volcanic rocks of Sierra de la Ventana. These are integrated with regional geological data to postulate the magmatic source of the rocks and propose a model for the Late Proterozoic–Early Paleozoic tectonomagmatic evolution of this part of Gondwana.The igneous rocks crop out at La Mascota, La Ermita, Agua Blanca, Pan de Azucar, Cerro del Corral, San Mario, and Cerro Colorado (). Most are exposed on the western side of the Sierra de la Ventana due to tectonic transport to the northeast by thrust faults (). The outcrops at Cerro Colorado, La Ermita, and Agua Blanca are granitic and rhyolitic rocks overlain by Quaternary sediments. The igneous rocks at San Mario, Pan de Azucar, and Cerro del Corral show tectonic contacts with the Paleozoic sedimentary cover (Field relationships in the San Mario, Pan de Azúcar, and Cerro del Corral granites, as well as in the Cerro del Corral rhyolite and Pan de Azúcar andesite, together with petrologic, structural, chemical, and geochronological data, suggest grouping these rocks as part of the Meyer suite. Most outcrops of the rocks are located near Abra Meyer. The Cochenleufú suite includes the Agua Blanca and Cerro Colorado granites and the La Ermita rhyolite, which outcrops near Arroyo Cochenleufú. They are slightly deformed and characterized by a distinctive magmatic fabric and chemical characteristics. This suite partially corresponds to the Sierra de la Ventana granite suite of a), the greenschists, metaquartzites, mafic bodies, and mylonitized granites (Pan de Azúcar Formation) described by found no evidence of intrusive contact. suggested a dextral overthrust to the northeast. Our interpretation is a NE-vergent overthrust suggested by the presence of ultramylonitic belts (344°/61°SW) in the granitic rocks.a), these rocks plot in the synogranite and monzogranite fields. In protoclastic and protomylonitic varieties, quartz, plagioclase, and K-feldspar were disrupted to produce porphyroclasts with patchy extinction and fracturing. In the mylonitic granites, a fine-grained matrix composed of quartz, biotite, sericite, and chlorite wraps rotated porphyroclasts of quartz, plagioclase, and K-feldspar. The ultramylonitic granites display a few strongly fractured porphyroclasts of K-feldspar in a fine-grained matrix of quartz, muscovite, and chlorite with minor calcite and biotite.Basic and acidic volcanic rocks also were recognized in this profile. Acidic rocks consist of a 1 m thick belt of porphyritic rocks with 30% euhedral quartz, plagioclase (An10–15), and K-feldspar phenocrysts in a groundmass of microcrystalline quartz, alkaline feldspar, and fine micas. Quartz shows embayment, whereas plagioclase forms agglomerates. Its microscopic characteristics and QAP diagram classification correspond with a rhyolite.Basic vulcanites appear as a 10 m thick, 90 m long body with notable coarse fenocrysts of plagioclase. first described these rocks as diabases. The groundmass displays a pilotaxitic texture with laths of plagioclase and elongated crystals of tremolite, epidote, and quartz. The plagioclase (An20–23) shows alteration to epidote and sericite. Oscillatory zoning and lamellar twinning are common. On the basis of these characteristics, the rocks are classified as andesites.b). They are coarse- to medium-sized grains with fractured quartz, K-feldspar, and twinned plagioclase (An8–10). Secondary quartz, biotite, and muscovite appear in veinlets or disseminated crystals. On a QAP diagram, these rocks plot in the synogranite and monzogranite fields.Micaceous-rich, coarse bands of quartz and alkali feldspar compose the mylonitized rhyolites. The original igneous quartz and alkali feldspar represent porphyroclasts or augens surrounded by a deformed matrix.In Cerro San Mario, an east–west, elongated, granitic body (600 m long, 150 m wide) is overthrust on conglomerates of the Curamalal Group. The San Mario granite is a medium- to coarse-grained biotite monzogranite with protoclastic to protomylonitic textures (c). The mineralogy consists of quartz, K-feldspar, plagioclase, and biotite. Plagioclase ranges from An15–33 in syenogranites to An26–40 in monzogranites. Large alkali feldspar is usually perthitic and shows shadowy, crosshatched twinning.Several foliated belts cut the granite N–S (353°/66°SW). Minor aplite and pegmatite dikes cross-cut the granites. recognized two deformational events. The first is evidenced by a regional NNW schistosity, and NE shear planes represent the second.The Agua Blanca granite occurs 10 km north of Cerro Pan de Azúcar. It is a porphyritic to aplitic granite, composed of microcline, anorthoclase, quartz, and plagioclase. Quartz appears as isolated phenocrysts, whereas plagioclase (An0–5) is subhedral to euhedral. Biotite with strong pleocroism and muscovite are scarce. Fluorite is present as disseminated crystals or veinlets in the microcline (). Most samples from the Agua Blanca granite plot on the monzogranite field in a QAP diagram ( described kink bands, deformational twinning, and flexures in microcline and biotite crystals, suggesting ductile deformation during the solid-state stage (La Ermita is located 10 km NNW of Agua Blanca. It forms a N–S, 500 m long hill with no relationships to the Paleozoic cover. These rocks display fluidal and microporphyritic textures with quartz and K-feldspar phenocrysts. Quartz is anhedral and presents undulose extinction and parallel deformational bands. The groundmass is completely recrystallized to fine-grained quartz. Fluorite and iron oxides appear as disseminated crystals. These rocks are classified as rhyolites.Cerro Colorado is located 20 km W of Cerro San Mario. The predominant lithology is a medium to coarse granite ( described similar features in the Agua Blanca granite.Major, trace, and rare earth elements (REE) geochemical data for both suites appear in . X-ray fluorescence was used to determine major, minor, and trace elements: SiO2, TiO2, Al2O3, FeO, MnO, MgO, CaO, Na2O, K2O, P2O5, Ba, Cl, Co, Cr, Cu, Ga, Nb, Pb, Rb, Sr, Th, U, V, Y, Zn, and Zr. International geostandards, including AC-E, MA-N, GS-N, GA, and GH granitoids, were used for instrumental calibration. The analyses were carried out at University of Barcelona. Instrumental neutron activation analyses (INAA) were carried out on 31 selected samples to determine the REE, Ta, Hf, Sc, Cs, and Sn at ACTBLABS.The granitoids of the Meyer suite are the most mafic of the Sierra de la Ventana igneous rocks, ranging in composition from monzonite to granite (). Harker diagrams of major elements display decreasing TiO2, Al2O3, Fe2O3, MgO (a–d), and CaO and increasing K2O with increasing fractionation, thus implying a comagmatic origin for these rocks. SiO2 concentrations are between 57–77 wt% in the Pan de Azucar granite, 67–76 wt% in the Cerro del Corral granite, and 68–76 wt% in San Mario. The granitoids are characterized by high K2O (Cerro del Corral and Pan de Azucar: 6.29 wt%, San Mario: 5.28 wt%) and fall in the shoshonitic and high-K calc–alkaline fields of The AFM diagram (not shown) indicates a calc–alkaline evolution, with A ranging from 55 to 85 and evolving from the Pan de Azucar andesite to the Cerro del Corral rhyolite. The granitic rocks occupy the transitional terms of this series. All samples are subalkaline.The ASI index ranges 0.83–2.3 for the Cerro Corral and Pan de Azucar granites and 1.9–1.1 for San Mario; for the Pan de Azucar andesite, it is 1.3, and for the Cerro del Corral rhyolites, it ranges 1.0–3.0. This range plots in the peraluminous field on The normative corundum reaches 8.9% in the Cerro del Corral granite, 9.4% in Pan de Azucar, and 7.1% in San Mario, though modal corundum was not recognized. On the basis of their petrographical and geochemical characteristics, the Cerro del Corral, Pan de Azucar, and San Mario granites are interpreted as S-types as suggested by . The Cerro del Corral rhyolites plot in the peraluminous field of diagram and in the banakite and high-K rhyolite field of Granites of the Meyer suite display significant variations in trace element contents (). Fractional crystallization is well represented by the K/Rb ratio, which decreases from 401 to 184 in the Pan de Azucar granite, from 261 to 189 in the Cerro del Corral granite, and from 252 to 197 in the San Mario granite. With increasing fractionation, Ba, Sc, Mn, and Zr decrease, and Ga, Ta, Nb, and Y increase (e–h). This indicates fractional crystallization of plagioclase and K-feldspar in the melt, with enrichment of Rb and depletion of Sr in later stages (The total REE reaches 539 ppm in Pan de Azucar, 195 ppm in Cerro del Corral, and 180 ppm in San Mario. Chondrite-normalized spider diagrams of Pan de Azucar (a) indicate strong enrichment of LREE. The LaN/LuN between 16 and 100 suggests that garnet remained as a residual phase during the melting of the parental rocks.b) also display important LREE enrichments, though not as high as those of Pan de Azucar. Their LaN/LuN relationships vary between 8.6 and 28.0 with small Eu anomalies, reflecting some plagioclase fractionation. San Mario displays patterns similar to those of Cerro del Corral, with LaN/LuN relationships varying between 7.6 and 10.2 (The Pan de Azucar andesite was classified by as andesite and alkaline basalt. The total REE concentration reaches 83 ppm, with LaN/LuN of 5.35 and Eu/Eu* of 0.82 (The Cerro del Corral rhyolite has a high concentration of silica and alkalies, thus classifying it as a high-K subalkaline (). The total REE concentration reaches 164 ppm. Chondrite-normalized diagrams (b) display severe negative Eu anomalies (Eu/Eu*: 0.097–0.42), which indicate that plagioclase was strongly fractionated.The Agua Blanca and Cerro Colorado granites present very restricted chemical compositions () with SiO2=73–77 wt%, Al2O3=11–17 wt%, and K2O=3.84–6.36 wt%. Fractional crystallization is not evident from the Harker diagrams (a–d). The Agua Blanca and Cerro Colorado granites are peraluminous and subalkaline with 6.8 and 4.4 wt% corundum normative, respectively.The Agua Blanca and Cerro Colorado granites present restricted trace element concentrations, with Rb, Y, Nb, and Ga higher than those of the Meyer suite, whereas the Sr, Zr, and Ba concentrations are lower (e–h). Logarithmic plots of Rb–Sr and Ba–Rb indicate restricted fractional crystallization of plagioclase and K-feldspar (see ). Total REE concentrations are between 104 and 177 ppm in Cerro Colorado and between 98 and 370 ppm in Agua Blanca. The chondrite-normalized diagram for the Cochenleufú suite indicates enrichments of 60–150 times in Cerro Colorado and 50–400 times in Agua Blanca (e and f). Both bodies have strong negative Eu anomalies with Eu/Eu*=0.049–0.094 in Agua Blanca and 0.051–0.127 in Cerro Colorado. These strong negative Eu anomalies indicate that plagioclase was severely fractionated from the original magma. obtained radiometric ages for the granitic and volcanic rocks of Sierra de la Ventana using K/Ar and Rb/Sr methods. , using the U–Pb SHRIMP method, established a clear distinction between Neoproteroic and Lower Paleozoic ages (Late Proterozoic ages were obtained for the Cerro del Corral rhyolite (671±35,655±30,638±30 Ma), Cerro del Corral granite (612.3±5.3, 607±5.2 Ma), Pan de Azucar andesite (603±30 Ma), and Pan de Azucar granite (598 Ma). also constructed a Rb/Sr isochron using samples from both the San Mario and Agua Blanca granites to obtain an age of 574±10 Ma. Lower Paleozoic ages were obtained for the Cerro del Colorado granite (487±15, 407±21, 529.6±3.3, 531.1±4.1 Ma), Agua Blanca granite (492 Ma), San Mario granite (524.3±5.3, 526.5±5.5 Ma), and La Ermita rhyolite (509±5.3 Ma).The age population indicates two magmatic cycles at 700–560 and 530–470 Ma, which are concordant with the field-, petrographical-, and geochemical-based separation into two suites. Discrepancies arise when the younger age of the San Mario granite is compared with other members of the Meyer suite (). On the basis of the strong geochemical, petrographical, and deformational similarities among the San Mario granite and Pan de Azúcar and Cerro del Corral granites, the San Mario granite is included in the Meyer suite.Equivalent magmatic cycles have been recognized in South Africa, where they constitute the Cape granite suite ( subdivided the granitoids, according to their tectonic setting, into intrusion in ocean ridge, volcanic arc, within plate, orogenic, and syncollisional granites. In the Y+Nb versus Rb diagram (a), samples plot dominantly in the volcanic arc field, whereas in the Y versus Nb diagram, they plot in both the volcanic arc and syncollisional fields ( discriminated between A-type granites and most orogenic granitoids (M-,I-, and S-types) using the Ga/Al relationships and Y, Nb, and Zr concentrations. In discrimination diagrams, the Meyer suite granites plot in the S- and I-type granite fields (). These results indicate that the Meyer suite consists of S-type granites, as defined by reported the calc–alkaline character of these rocks, as well as their S-type signature. According to , the San Mario granite is a differentiated I-type granite and not consanguineous with the Agua Blanca granite. recognized four groups of granitic rocks in the Himalayan, Alpine, and Hercynian belts: (1) precollisional, calc–alkaline, dioritic to granodioritic plutons associated with volcanic arcs; (2) syncollisional, peraluminous leucogranites; (3) late- or postcollisional, calc-alkaline, biotite-hornblende tonalite to granodioritic plutons; and (4) postcollisional alkaline rocks. In the triangular diagram Rb/30-Hf–Ta*3 (a), samples plot in the precollisional (volcanic arc) and the late- or postcollisional fields, though a few appear in the within-plate field. In the SiO2 |
wt% versus Rb/Zr diagram (not shown), most samples plot in the VAG field. In the Y–Nb–Ce and Y–Nb–3*Ga diagrams of Rocks with similar geochemical and petrologic characteristics emplaced during a subduction-collision event have been recognized in the Karakoram Axial batholith of northern Pakistan (Baltoro plutonic unit, Hunza leucogranite; ), the Pan-African belt of the Arabian shield (Through plotting in TiO2–MnO*10-P2O5*10, Ti/100-Zr–Y*3, and Th/Yb–Ta/Yb discriminant diagrams (), the Pan de Azucar andesite is classified as a calc–alkaline basalt that erupted at an active continental margin (not shown).Samples from the Cochenleufú suite plot in the within-plate granite field ( diagrams. They also fall in the A-type granite field in trace elements versus 10,000 Ga/Al discrimination diagrams ( conclusion, based on major elements, as well as with interpretation. These rocks also share some A-type granite characteristics, namely, high SiO2 and Na2O+K2O, low CaO, and high Ga/Al, Zr, Nb, Ga, Y, and Ce.), the samples plot in the syn- to postcollisional fields (b); in the SiO2 |
wt% versus Rb/Zr diagram (not shown), they are classified in the syncollisional field. Y–Nb–Ce and Y–Nb–3*Ga diagrams, most of the samples plot in the continental–continental collisional to postcollisional field (. Examples include the Gabo and Mumbulla suites in the Lachland fold belt, Australia (), and the Topsails complex of Newfoundland (In Sierra de la Ventana, the deficiency of igneous rock outcrops, as well as the lack of field relationships with host rocks, makes it difficult to establish its tectonic setting. However, the correlation with the African granitic suites () enables us to clarify the evolution of accretional events in Sierra de la Ventana (). Two igneous suites are differentiated in Sierra de la Ventana. The most basic is the Meyer suite (700–570 Ma), which displays a calc–alkaline evolution related to volcanic arc and postcollisional settings.In the Saldania belt of South Africa, sedimentary and volcanic rocks deposited in the Boland terrane (Malmesbury Group) attest to ocean floor spreading in response to the breakup of Rodinia and the progressive opening of the proto-Atlantic (Adamastor Ocean) during 780–750 Ma (). Rocks of this age, which represent this extensional event, had not been recognized in Sierra de la Ventana. A reversal of the spreading caused subduction and the closure of the Adamastor Ocean (600–570 Ma). The tholeiitic series (olivine gabbros, gabbros, diorites, and granodiorites) represents this event along an immature magmatic arc (), as does the first phase of intrusion of the Cape granite suite (600–540 Ma). S-type granitic rocks intruded during this phase have late to postorogenic signatures. The presence of a suture zone at the Swartland–Boland terrane boundary supports either oblique collision or strike–slip transpressional tectonics without the development of a collisional orogen. In Sierra de la Ventana, the most basic rocks form the Meyer suite (700–570 Ma), which displays a calc-alkaline evolution. These rocks are related to an immature volcanic arc, but they also show characteristics of a postcollisional setting. In the Cape granite suite, the final phase of intrusion (520–500 Ma) is represented by A-type granitoids (). These anorogenic alkaline granites are related to pressure release in a strike-slip tectonic environment with associated uplift and extension following collision.The Cochenleufú suite (540–470 Ma) is considered an A-type association and plots in the within-plate, syn- to postcollisional fields in several discrimination diagrams. According to classification, these rocks belong to the A2 granitoids, which generally occur as final plutonic events during postorogenic extension in collisional belts (). This magmatic event already has been interpreted as within-plate magmatism and correlated with the Cape granite suite by Equivalent postcollisional granites, intruded during an oblique N–S collision of the Kalahari and Congo cratons, have been recognized in the central Damaran orogenic belt, Namibia (). They are related to the closure of the Adamastor Ocean.The Swartland and Tygerberg terranes (Saldania belt), accreted in a transpressive regime to the Boland terrane (600–630 Ma), are potential candidates for the Meyer and Cochenleufú suites’ emplacement.Similar structural styles, magmatism, and tectonic events have been recognized in the Saldania, Ross, and Delamarian orogens, indicating a common history (). The Ross event, responsible for major magmatism in the Transantarctic Mountains, is represented partially by the granitic Harbour intrusive complex (), which was emplaced in a calc–alkaline arc. The Mid-Proterozoic–Late Cambrian history of the Transantarctic Mountains has been interpreted as a cycle of extension, continental rifting, transpression, and subduction ( interpreted the basement complex of the Sierra de la Ventana fold belt as related to Early to Mid-Cambrian continental rifting along the southwestern margin of Gondwana. They correlated the extensional event with similar scenarios in the Cape fold belt, the Atlantic coast of Brazil, the Malvinas microplate, and the Ellsworth Mountains. The A-type granites of the Cochenleufú suite and of the La Ermita rhyolite were formed, according to , by underplating mafic magma, which melted the lower crust during continental rifting. The absence of mafic rocks related to the Cambrian–Devonian sedimentary sequence precluded correlation with similar rocks in the Ellsworth Mountains, despite magnetic anomalies detected between Sierra de la Ventana and Tandilia. According to , these anomalies were produced by basaltic rocks below the Paleozoic sequence. However, evidence of such oceanic crust, which must be coetaneous with sedimentation during the Lower Paleozoic, is not present in the Sierra de la Ventana and Claromecó basin (In Sierra de la Ventana, two magmatic suites are differentiated. The older Meyer suite (700–570 Ma) displays a calc–alkaline evolution related to a volcanic arc and postcollisional setting. The younger Cochenleufú suite (540–470 Ma) displays an A-type signature related to the final plutonic events during postorogenic extension in the collisional belts.The remarkable similarities observed between the suites of Sierra de la Ventana and the Saldania belt enables a positive correlation. In both cases, primitive volcanic arc or collisional orogens are recognized. Moreover, continuous shearing between the Swartland and Tygerberg terranes was a potential trigger for the emplacement of both suites.A self-consistent Eulerian rate type model for finite deformation elastoplasticity with isotropic damageContinuum models for coupled behaviour of elastoplasticity and isotropic damage at finite deformation are usually formulated by first postulating the additive decomposition of the stretching tensor D into the elastic and the plastic part and then relating each part to an objective rate of the effective stress, etc. It is pointed out that, according to the existing models with several widely used objective stress rates, none of the rate equations intended for characterizing the damaged elastic response is exactly integrable to really deliver a damaged elastic relation between the effective stress and an elastic strain measure. The existing models are thus self-inconsistent in the sense of formulating the damaged elastic response. By consistently combining additive and multiplicative decomposition of the stretching D and the deformation gradient F and adopting the logarithmic stress rate, in this article, we propose a general Eulerian rate type model for finite deformation elastoplasticity coupled with isotropic damage. The new model is shown to be self-consistent in the sense that the incorporated rate equation for the damaged elastic response is exactly integrable to yield a damaged elastic relation between the effective Kirchhoff stress and the elastic logarithmic strain. The rate form of the new model in a rotating frame in which the foregoing logarithmic rate is defined, is derived and from it an integral form is obtained. The former is found to have the same structure as the counterpart of the small deformation theory and may be appropriate for numerical integration. The latter indicates, in a clear and direct manner, the effect of finite rotation and deformation history on the current stress and the hardening and damage behaviours. Further, it is pointed out that in the foregoing self-consistency sense of formulating the damaged elastic response, the suggested model is unique among all objective Eulerian rate type models of its kind with infinitely many objective stress rates to be chosen. In particular, it is indicated that, within the context of the proposed theory, a natural combination of the two widely used decompositions concerning can consistently and uniquely determine the elastic and the plastic parts in the two decompositions as well as all their related kinematical quantities, without recourse to any ad hoc assumption concerning a special form of the elastic part or a related relaxed intermediate configuration. As an application, the proposed general model is applied to derive a self-consistent Eulerian rate type model for void growth and nucleation in metals experiencing finite elastic–plastic deformation by incorporating a modified Gurson's yield function and an associated flow rule, etc. Two issues involved in previous relevant literature are detected and raised for consideration. As a test problem, the finite simple shear response of the just-mentioned model is studied by means of numerical integration.It is widely recognized that in a deforming material body, evolution of microstructure, such as microdefects, microvoids and microcracks, etc. is the main cause leading to irreversible inelastic deformations. On the other hand, deformation, in particular large deformation, usually causes changes of microstructure in a material body. The actual coupling mechanism between the process of deformation and the evolution of microstructure may be extremely complicated in nature. In an idealized and simplified sense, a macroscopic scalar variable φ called damage variable, among other things, may be introduced to represent the state of microstructure and is directly associated with pertinent mechanical quantities, such as the stress, the material moduli, etc. Then, a phenomenological model for the foregoing coupling mechanism may be established by formulating the evolution equation of the damage variable φ and other relevant rate type constitutive equations. Since the inception of the seminal idea by , the very promising branch of continuum mechanics, continuum damage mechanics, has been developing extensively and steadily and receiving increasing applications in numerous related fields, refer to, e.g. and the relevant literature therein for details.At the present stage of development, a set of damage variables and other internal variables of scalar type and tensorial type are introduced to characterize the state of microstructure of a material in a more realistic manner and more general models are accordingly developed, see the aforementioned monographs and recent works by, e.g., , and others. This general aspect is still under continuing development. In this article, we are mainly concerned with the classical aspect, i.e. the isotropic damage with one scalar damage variable φ. This aspect has been fully studied with reference to both small and finite deformation due to its simple, clear and direct physical meaning. Now, it may be said that isotropic damage theories with reference to small deformation are well established on firm mathematical and physical foundations. However, the case might not be so when large deformation is concerned. In fact, even the existing formulations of finite deformation elastoplasticity are somewhat controversial and a number of fundamental issues between them have been indicated and extensively debated (see, e.g., the recent comprehensive review by and the pertinent references therein for detail). As a result, finite deformation elastoplastic damage theories based on them are accordingly subject to the same issues.Based on some recent developments in kinematics of finite deformation and rate type constitutive models by these authors and other researchers (see ), we shall establish a general Eulerian rate type model for finite deformation elastoplasticity coupled with isotropic damage, with which the main fundamental discrepancies involved in existing formulations of finite elastoplasticity disappear. The main content of this article is arranged as follows: In , for later use we introduce the newly discovered logarithmic rate and the rotating frame in which the latter is defined, as well as other basic facts regarding kinematics of finite deformations of continua. In , postulating the additive decomposition of the stretching and adopting the logarithmic rate, we establish a complete system of Eulerian rate type constitutive equations governing the coupled behaviour of finite elastoplasticity and isotropic damage. It is pointed out that the logarithmic rate is a unique choice among all infinitely many objective corotational rates, in the self-consistency sense of achieving an integrable-exactly rate type formulation of damaged elastic response. In , the elastic and the plastic part in the decomposition and all their related kinematical quantities are uniquely and consistently determined. In , we supply the rate form of the suggested constitutive formulation in a rotating frame in which the logarithmic rate is defined and then derive an integral formulation. Some implications of the results obtained are indicated. In , incorporating a modified Gurson's yield function and an associated flow rule, etc. we apply the general model proposed in to derive a self-consistent Eulerian rate type model for void growth and nucleation in porous metals at finite deformation. Two issues involved in previous relevant literature are detected and raised for consideration. Finally, in , we study the finite simple shear response of the model established in be, respectively, an orthogonal tensor, two second-order tensors and a fourth-order tensor. We shall use the notations to designate, respectively, the scalar, the three second-order tensors and the fourth-order tensor given byThe following identities will be useful:Consider a deforming body with particles. We identify each particle with a position vector X in a referential configuration, e.g. an initial configuration. The current position vector of a particle X is denoted by , and hence the velocity vector of a particle X is given by Throughout, the superposed dot is used to represent the material time derivative.The local deformation state at a particle X is described by the deformation gradientwhile the rate of change of deformation state at a particle is characterized by the velocity gradientThe following left polar decomposition formula and additive decomposition formula are well known:The symmetric positive definite tensors are known as, respectively, the left stretch tensor and the left Cauchy–Green tensor, the proper orthogonal tensor is the rotation tensor, and the symmetric and antisymmetric tensors are called the stretching and the vorticity tensor. Throughout, are used to denote the transpose and the inverse of the second-order tensor Let the distinct eigenvalues of the left Cauchy–Green tensor be given by χ1,…,χm and their corresponding subordinate eigenprojections by . We introduce a general class of Eulerian strain measures by (see where g: R+→R, called scale function, is a smooth monotonic increasing function with the normalized property g(1)=2g′(1)−1=0. Taking the scale function g(χ) as certain particular forms, one can obtain almost all commonly-known Eulerian strain measures. In particular, by taking , Hencky's Eulerian logarithmic strain measureis available, which will be of particular interest. be a spin, i.e. a time-dependent antisymmetric second-order tensor. In a rotating frame with the spin , an objective Eulerian symmetric second-order tensor S in a fixed background frame, becomes , and hence its time rate in this rotating frame is given byIn the above, Q is a proper orthogonal tensor defining the spin that the latter, called the corotational rate of the tensor , is just the counterpart of the time rate of in a background frame. It is evident that there are infinitely many kinds of corotational rates. Not all of them, however, are objective. A well-known example of objective corotational rate is provided by the Zaremba–Jaumann rate with , and another well-known example is given by the Green–Naghdi rate with the polar spin . In general, the objectivity of a corotational rate depends on its defining spin tensor. The latter must be associated with the rotation and deformation of the deforming body in question, as is shown by several commonly known examples. A general class of objective corotational rates and their defining spin tensors have been derived by these authors (It is commonly accepted that the stretching tensor , the symmetric part of the velocity gradient, is a well-defined fundamental kinematic quantity measuring the rate of change of local deformation state in a deforming body. It is frequently referred to as the Eulerian strain rate, the tensor of deformation rate, or simply the deformation rate. However, it has long been unknown whether or not the stretching can be really written as a rate of a strain measure. The pertinent question is: whether or not a strain measure can be found such that the objective corotational rate of is exactly identical with the stretching tensor ) that the above expression, where both the strain measure are left to be determined, holds iff the strain measure has a unique continuous solution to the spin . Owing to the unique relationship between the stretching has been termed the logarithmic spin and accordingly the objective corotational rate defined by it the logarithmic rate.The logarithmic rate of an Eulerian symmetric second-order tensor be the proper orthogonal tensor defining the logarithmic spin , which is called the logarithmic rotation and determined by the tensor differential equationfor any Eulerian symmetric second-order tensor defines a rotating frame via the transformation of motionThis frame, whose spin is just the logarithmic spin , is called the logarithmic rotating frame. The equality indicates a kinematical feature of the logarithmic rotation or the logarithmic spin: An observer in the logarithmic rotating frame observes that the material time derivative of Hencky's logarithmic strain measure is just the stretching.Thus, the logarithmic rotation is associated with the deformation and rotation in a deforming body in a unique manner. It is evident that such an association is purely of kinematical character and independent of any material behaviour. were the first to consider the particular case of the tensor equation . Similar results were derived later by . In a different context, these authors (Xiao et al., 1996, 1997a, 1998a) studied the general case of tensor equation with both the strain measure e and the spin left to be determined and revealed the unique relationship between the stretching D and the logarithmic strain h for the first time. The significance of the logarithmic rate to formulating Eulerian rate type inelasticity models has been indicated in very recent works by these authors (; Xiao et al., 1997a,b, 1999, 2000). Based on these results, in the succeeding sections we shall develop new Eulerian rate type models for finite deformation elastoplasticity coupled with isotropic damage.We consider a damaged elastoplastic solid with an initial stress-free natural state and with initial isotropy material symmetry. The initial natural state is taken as the reference configuration. Accordingly, we have the initial conditions is used to denote the Kirchhoff stress, which is related to the Cauchy stress We assume that the damage variable is a scalar variable φ whose value belongs to the interval [0,1]. Then we define the effective Kirchhoff stress as follows:), we assume the additive decomposition of the stretching D: the elastic part and the coupled elastic–plastic part of D. Another widely used decomposition is the multiplicative decomposition of the deformation gradient F (see given later). A natural and consistent combination of the two kinds of widely used decompositions will be given in the . It will be seen that the elastic part is associated with both the elastic part In the succeeding subsections we shall establish Eulerian rate type constitutive formulations for the two parts as well as the damage variable φ etc., respectively. characterize the instantaneous elastic behaviour of the material. Most often is chosen as the constant isotropic compliance tensor, especially for small elastic strain case. Hence,where E and G are Young's modulus and the shear modulus, respectively. Throughout, are used to designate the second-order and the fourth-order symmetric identity tensor, respectively, i.e. is crucial. It should be noted that these equations are intended to characterize damaged elastic response. Namely, they must be exactly integrable to really deliver a damaged elastic, in particular hyperelastic, relation. However, if special care is not taken, the just-mentioned self-consistency requirement for rate-type characterization of damaged elastic response may not be fulfilled and some aberrant, spurious phenomena, such as the oscillatory shear stress response with increasing shearing strain, etc., may be resulted in, as disclosed by , and others, for the case of hypoelasticity and elastoplasticity without damage. Further, have proved that none of the rate equations with several commonly known stress rates, such as Zaremba–Jaumann rate, Truesdell rate and Green–Naghdi rate etc., is integrable to yield an elastic, in particular hyperelastic, relation in nonlinear range. This fact indicates that the existing formulations of Eulerian rate type elastoplasticity (and accordingly elastoplasticity coupled with damage) are self-inconsistent in the sense of characterizing elastic response.The undesirable self-inconsistency indicated above has been removed in very recent works by these authors for the case of hypoelasticity and elastoplasticity (see ; Xiao et al., 1997b, 1999). Utilizing these results, we here propose the integrable-exactly Eulerian rate type formulation of general damaged hyperelasticity as follows:, which is an isotropic scalar function of the effective Kirchhoff stress , is called the effective complementary hyperelastic potential. For small elastic strain, the gradient may be taken as the constant isotropic compliance tensor as shown by It will be shown in the next two sections that the rate equation provides a consistent definition for the elastic deformation rate and leads to a general damaged hyperelastic relation according to which the elastic logarithmic strain measure with respect to the effective Kirchhoff stress . Hence, defining a scalar function Σ′ of via the Legendre transformation relation is given by an isotropic function (see In the above, the last expression implies that the material time derivative of the scalar function Σ′ furnishes the effective elastic stress power, whereas the equation relating shows that the effective Kirchhoff stress is derivable from the scalar function Σ′ with respect to the elastic logarithmic strain measure . These facts explain why the scalar function Σ in has been termed the effective complementary hyperelastic potential.The logarithmic stress rate used in the rate equation is merely a particular objective stress rate among infinitely many objective corotational stress rates (see ). Probably another objective corotational stress rate may serve our purpose just as well. Hence, by replacing the logarithmic stress rate one obtains another form of rate type equation for the elastic part The above-mentioned nonuniqueness, if any, will result in the puzzling situation concerning which stress rate is better, as encountered in existing Eulerian rate type formulations of finite elastoplasticity (see for detail). Recently, these authors have demonstrated (see ; Xiao et al., 1999) that the above rate equation is exactly integrable to deliver an elastic relation if and only if the stress rate , i.e. the rate equation is identical with the rate equation . This fact means that the rate equation is unique among all the rate equations of its kind with infinitely many objective corotational rates to be chosen, in the self-consistency sense of formulating damaged elastic response.In addition to the damage variable φ, we introduce a scalar k and an objective symmetric second-order Eulerian tensor as internal variables to characterize isotropic and kinematic hardening behaviours. The tensor is called the back or shift stress. We assume that the current yield surface in the stress space is defined byHere f̂ is an isotropic scalar function of the Kirchhoff stress and the back stress . We further assume that in the stress space there is another surface is in the direction of the gradient of this surface with respect to the Kirchhoff stress Accordingly, g is called the flow potential, which is here also an isotropic scalar function of the Kirchhoff stress and the back stress.For a process of continued plastic flow, the stress point must remain on the current yield surface. Hence, we have the consistency condition for plastic flow. Since the yield function f is isotropic, we haveHence, we may write the just-mentioned condition in the form are, respectively, the counterparts of the yield function f and the Kirchhoff stress in the logarithmic rotating frame, given by Eqs. (59a) and , as well as the penultimate identity in , we formulate the consistency condition for plastic flow in a form convenient for later use:Moreover, we assume general forms of evolution equations for the damage variable φ, the isotropic hardening parameter k and the back stress Here, the objective symmetric second-order Eulerian tensors and each tensor-valued function above is isotropic with respect to . In addition, the fourth-order tensor has minor index symmetry. Namely,) for plastic flow, we derive an expression for the plastic multiplier where the loading–unloading indicator ψ is of the form (see Bruhns et al., 1999)The Eulerian rate type constitutive equations (28)–(30) and (35)–(37), together with Cauchy's equations of motion, constitute a complete system of equations governing the total kinematical quantities and the total stress, etc. Of them, the basic elements are the complementary hyperelastic potential Σ, the yield function f, the flow potential g and the constitutive tensors . For various kinds of materials, the latter may assume various forms. They must be determined by related experimental data. For example, various forms of evolution equations for the damage variable φ are available in . This aspect can be simplified by using a yield function of von Mises type and the associated flow rule as well as simple hardening relations, as will be done in The constitutive formulation proposed in , together with Cauchy's equations of motion and well-posed initial and boundary conditions, determine the total stress, the total kinematical quantities , etc. On the other hand, for a process of elastoplastic deformation, it is required to define and specify elastic and plastic deformations and their related kinematical quantities. It should be noted that if there is no a priori definition for elastic and plastic deformations, no definite information about the latter can be drawn from the rate quantities need to be related to “elastic deformation” and “plastic deformation” in an appropriate sense.To introduce and separate elastic and plastic deformations, the physically motivated multiplicative decomposition of the total deformation gradient is widely used, which was first introduced by with reference to a linearized theory, subsequently utilized by , and systematically and extensively used and developed by Lee and other researchers, see, e.g., for recent applications in continuum damage mechanics. According to this decomposition, the total deformation gradient for any process of elastic–plastic deformation. Usually, are called, respectively, the elastic and the plastic part of Here and henceforth we use the notations to designate the symmetric and the skewsymmetric part of a second-order tensor Now, we proceed to establish the relationship between the two decompositions (18) and (38). Towards this goal, let us compare . Clearly, the first term of the right-hand side of only, whereas the second term depends on both the elastic and the plastic part . Thus, a natural, direct relationship between the two decompositions (18) and (38) should beIn the above two relations, the former implies the latter and vice versa. The right-hand side of the latter explains why has been termed the coupled elastic–plastic part of Consider the constitutive formulation (23) for the elastic part . As pointed out before, the rate equation (23) should be exactly integrable to produce a damaged elastic relation. Define the elastic logarithmic strain measureGenerally, we may assume that the foregoing damaged elastic relation is of the form. In fact, for each process of purely elastic deformation, i.e., are also isotropic. Applying the chain rule for the gradient of a symmetric second-order tensor-valued isotropic function derived in . From the above account, it follows that the elastic relation assumed before must take the formThis and the rate equation (23) result in the relationship is just the logarithmic rate of the elastic logarithmic strain measure . Further interpretation of this relationship will be given in , the above established relationship between the two widely used decompositions (18) and (38) can consistently and uniquely determine the elastic part in the decomposition (38), as well as all their related kinematical quantities, with no ad hoc assumption about restricted special forms of . Indeed, from the outset of this section we know that the effective Kirchhoff stress , can be obtained by integrating the constitutive equations (28)–(30), (35)–(37) and Cauchy equations of motion with well-posed initial and boundary conditions. Then, the elastic deformation over a time interval [0,a] is consistently and uniquely determined by given over [0,a], where the elastic stretch tensor is obtained by integrating the linear tensorial differential equation (see Eq. (61) in , σ=1,…,m, are the distinct eigenvalues of the elastic stretch and the corresponding subordinate eigenprojections of is available, one can immediately obtain the plastic deformation Now we consider the rate quantities related to From the above analysis, we conclude that, within the context of the finite deformation elastoplasticity-damage theory suggested in this and the last sections, the elastic deformation and all their related kinematical quantities such as the spins , etc. can be consistently and uniquely determined. Moreover, it is shown in that in a full sense the proposed combination of the two widely used decompositions concerning the total stretching obeys the invariance requirement under the change of frame or under the superposed rigid body rotation.In the logarithmic rotating frame specified by an objective scalar keeps unaltered, whereas an objective symmetric second-order tensor The Eulerian rate type constitutive formulation proposed in is frame-indifferent, and hence, its form in the logarithmic rotating frame specified by remains the same. Consequently, in the logarithmic frame , we rewrite the last two equations into the forms supply the forms of the rate constitutive equations (28)–(30) and (35)–(37) in the logarithmic rotating frame. It turns out that the rate equations (60)–(65) have the same structure as the counterpart of small deformation elastoplastic damage theory. Indeed, whenever the deformation is small, the logarithmic strain measure approximate to the small strain measure , respectively, and accordingly the quantities , respectively. With these approximations are reduced to the rate constitutive equations for small deformation elastoplastic damage.Owing to the fact indicated above, the numerical integration of formulated in the logarithmic rotating frame may be carried out by means of the numerical methods developed for small deformation theory. Then, the quantities in the current configuration are available from the corresponding quantities in the logarithmic rotating frame and the logarithmic rotation , the latter being obtained by integrating In addition, in the logarithmic rotating frame, The former, being a rigorous kinematical relation, simply means that in the logarithmic rotating frame the total stretching is exactly the material time derivative of the total logarithmic strain measure, whereas the latter, which defines the elastic part , implies that in the logarithmic rotating frame, the material time derivative of the elastic logarithmic strain measure supplies the elastic part of the total stretching. These show that the relationship (45) is a natural and consistent definition motivated by and based on the rigorous kinematical relation (14). over the time interval [0,t] and using the equalities, the above integral type formulation indicates, in a clear and direct manner, the effect of the finite strain and rotation history on the current stress, the damage and the hardening behaviour.In this section, we apply the general model established in the previous sections to derive a model for void growth and nucleation in porous metals at finite deformations. In this case, the damage variable φ is interpreted as the void volume fraction.Based on certain simplified assumptions, was the first to establish a continuum model for void growth and nucleation in porous ductile media with perfectly plastic matrix. Gurson's model was modified and developed later by various researchers, refer to, e.g. . This aspect is mentioned in the review articles by and discussed by Voyiadjis and Kattan (1992a,b) (some relevant remarks on the latter will be made at the end of this section). Taking these subsequent modifications into account, we here assume a modified form of Gurson's yield function as follows (cf. is the deviatoric Kirchhoff stress, σF is the flow yield strength of the metal matrix at uniaxial tensile test, and q1 and q2 are the two modified material parameters introduced by . Moreover, the back stress, which defines the centre of the current yield surface, is assumed to be traceless, i.e. are used to denote the hyperbolic cosine and sine functions of x.As commonly done, we assume an associated flow rule and the kinematic hardening rule of Prager–Ziegler's type. Thus, we have f≡g andwith c being a kinematic hardening parameter. It is easy to demonstrate that this is just a particular form of the general evolution equation (30). Besides, the flow rule (26) becomesUsually, the elastic strain in a metal matrix is small. In this case, we can take the gradient as the constant isotropic compliance tensor given by for the damaged elastic response becomeDuring the course of deformation, both the growth of existing voids and the nucleation of new cavities contribute to the change of the void volume fraction φ. Following , we assume the evolution equation of the void volume fraction φ as follows:In the above, the first term of the right-hand side arises from the contribution of the void growth and the second term from the contribution of the void nucleation, with A being a material parameter. Here, we assume that the void nucleation is correlated directly with the flow yield strength σF.On the other hand, from the equivalence of the overall rate of plastic work and that in the matrix material the following relation is derived (see Eqs. (2.38b) and (2.36c) given in where σY0 is the initial and σY the current flow stress for the metal matrix, and the parameter b ranges from 0 to 1 with b=1,0 corresponding to, separately, purely isotropic and purely kinematic hardening. Besides, E and Et are Young's modulus and the tangent modulus associated with the Kirchhoff stress-logarithmic strain curve in a uniaxial test of the metal matrix. Here σY characterizes the isotropic hardening of metal matrix. Hence, by identifying the internal variable k with σF, is again a particular form of the general evolution equation (29)., we derive the evolution equation of the void volume fraction φ as follows:, supply a system of Eulerian rate type constitutive equations governing the Kirchhoff stress , the flow strength σF and the void volume fraction φ. This system and the consistent combination of the decompositions (18) and (38), proposed in , constitute an Eulerian rate type model for void growth and nucleation in porous metals experiencing finite elastic–plastic deformations. As a test problem, in we study the finite simple shear response of this model by means of Runge–Kutta numerical integration.We conclude this section with some remarks on recent interesting and instructive works by . In these works, a general large deformation elasto-plasticity-damage theory with a symmetric second-order damage tensor variable has been established by postulating the decomposition (18) and adopting the corotational rates defined by the spin tensors of the formwith ω being a scalar influence parameter. The general theory is applied to derive a model for void growth by relating a quadratic yield function of von Mises type with combined isotropic-kinematic hardening to a modified Gurson's yield function. Some interesting results have been obtained in this case. The idea and approach employed are insightful, instructive and quite general. However, here we would like to raise two questions for consideration.is not objective except for the case whenω=1. To substantiate this statement, consider the transformation of the above corotational rate under the change of frame specified by a time-dependent proper orthogonal tensor Q. Under the just-mentioned change of frame, an objective symmetric second-order Eulerian tensor S changes to , while the vorticity tensor W changes to In addition, an objective scalar ω, in particular, a constant ω, keeps unaltered. As a result, the corotational rate one can further deduce that the corotational rate is objective, i.e. the latter is identical to for every time-dependent proper orthogonal tensor for every time-dependent proper orthogonal tensor . The latter is possible only for the case when ω=1, i.e., is the well-known Zaremba–Jaumann rate.Next, through relating the general model to a modified Gurson's model, the material parameters q1 and q2 in the modified Gurson's yield function given by are found to assume the forms (cf. Eqs. (100) and (83) in Voyiadjis and Kattan (1992a,b), respectively; the void volume fraction ν therein has been replaced by φ here):Substituting the above expressions into The latter, however, implies that the void volume fraction φ has no influence on yielding behaviour.For the sake of simplicity, we consider Gurson's model with purely isotropic hardening, i.e.Moreover, it will be shown shortly that in the course of finite simple shear deformation, the spherical component of the stress Hence, for the case at issue, the yield condition is of the formTaking into account now the relation (cf. can be redefined for the effective Kirchhoff stress For processes with prescribed deformation, as it is the case for simple shear, it is more convenient to express here the rate of the effective stress through the stretching. This can be achieved by multiplying With this transformation, the rate equations (85) and (86) can be redefined to giveThe finite simple shear deformation is specified by are the initial and the current position vectors of a material particle, respectively. is used to represent the inverse hyperbolic sine function of ω, i.e.The process of simple shear deformation response consists of two stages: First, the elastic response (hence ) starts at ω=0 and ends at a yielding point ω=ωp, and then follows the elastic–plastic response (hence ) for all ω⩾ωp. The two stages will be studied separately.), there is no void nucleation and growth, i.e.during the whole stage of elastic response, if φ|t=0=0. Thus, we haveThe above elastic response starts at ω=0 and concludes withwhich corresponds to the yield point ω=ωp. Using the expressions (99)–(101), we infer that ωp is determined by (cf. Eq. (29) therein, in which Y0/G=0.1 with Y0 being σY0 here), we choose the initial yield stress σY0 asThe plastic flow and the void nucleation occurs whenever ω⩾ωp and are governed by the yield condition (83) and the rate equations (84), (90) and (91), with the loading–unloading indicator ψ=1. is the effective Kirchhoff stress. For simple shear deformation, however, the latter is identical with the effective Cauchy stress The above system may be further simplified. In fact, for the simple shear deformation (cf. ) are essentially symmetric second-order tensors in two dimensions. As a result, the expression (2.9)3 in can be reduced to Eq. (2.9)2 therein, i.e. the log-spin for the simple shear deformation is given bywhere the coefficient ν can be obtained by using Eq. (2.10) in . Since each x, vanishes during the whole elastic process, from the above differential equation for x, we infer that each x continues to vanish during the whole stage of the succeeding elastic–plastic process. Thus, the effective stress for each function ϕ=ϕ(ω), we arrive at simplified forms of with the initial conditions (103) and (104) determine the effective stress components as functions of the shear strain ω. Then, gives the flow yield strength σY′. In addition, the void volume fraction φ is obtained by integrating the rate equation (84). Finally, the true stress components τ11′ and τ12′ are given byVarious forms of the evolution relation of the void fraction volume φ to the flow yield strength σY are possible, refer to, e.g. is regarded as a constant, then one can readily derive a linear relation between φ and σY. Here, we assume the exponential formwhere k>0 is a dimensionless material parameter. Evidently, whenever the flow yield strength σY is close to the initial yield strength σY0, i.e. (σY−σY0)/σY0 is small, the foregoing linear relation gives a good approximation of the general relation (112).Setting ϱ=0.9 and σY0/G=0.1, we obtain the effective normal stress by means of Dormand–Prince numerical integration. Then, from , we obtain the void volume fraction φ for various possible values of the material parameter k. Here we set k=0.2. Finally, we obtain the true normal stress τ11′ and the true shear stress τ12′ from , the dimensionless effective shear stress is depicted vs the shear strain ω. In addition to the solution of the differential equations (109) and (110) for the logarithmic rate, we also have presented solutions for the Zaremba–Jaumann rate and the Green–Naghdi rate, where according to , respectively. It is illustrated that both results for the logarithmic rate and the Green–Naghdi rate as well show almost linear increasing behaviour, whereas the Zaremba–Jaumann rate tends to display oscillating properties and, for the hardening parameter ϱ under consideration, even changes the sign of the shear stress for very high strains of about ω=8.3. As has been observed by various authors the Jaumann rate may cause physically not plausible results.The effective normal stresses vs the shear strain ω are shown in . Here again the Zaremba–Jaumann rate tends to display oscillating behaviour. The Green–Naghdi rate leads to an almost constant normal stress. Only the logarithmic rate creates a monotonically increasing stress as would be expected from experimental observations.The respective dimensionless true stresses are presented in . Whereas the shear stresses for the logarithmic rate and the Green–Naghdi rate are almost identical, first increasing and then decreasing, with a maximum at about ω=1.2, and asymptotically tending to zero, the result for the Zaremba–Jaumann rate again changes its sign, as for the effective shear stress., the true normal stresses show physically plausible behaviour for both the logarithmic rate and the Green–Naghdi rate, except for the Zaremba–Jaumann rate, which again leads to an oscillating response.The void volume fraction φ vs the shear strain ω is shown in . The results for the Green–Naghdi rate and the logarithmic rate are again almost identical. For very large values of shear strain ω, the void volume fraction φ tends asymptotically to the value 1. As has been emphasized by different authors, this indeed will restrict the validity of our fundamental assumptions.It has been demonstrated that, by consistently combining additive and multiplicative decomposition of the stretching and adopting the logarithmic stress rate, a general Eulerian rate type model for finite deformation elastoplasticity coupled with isotropic damage is proposed. The new model is shown to be self-consistent in the sense that the incorporated rate equation for the damaged elastic response is exactly integrable to yield a damaged elastic relation between the effective Kirchhoff stress and the elastic logarithmic strain. The rate form of the new model in a rotating frame in which the foregoing logarithmic rate is defined, is derived and from it an integral form is obtained. The former is found to have the same structure as the counterpart of the small deformation theory and may be appropriate for numerical integration. The latter indicates, in a clear and direct manner, the effect of finite rotation and deformation history on the current stress and the hardening and damage behaviours. Further, it is pointed out that in the foregoing self-consistency sense of formulating the damaged elastic response the suggested model is unique among all objective Eulerian rate type models of its kind with infinitely many objective stress rates to be chosen. In particular, it is indicated that, within the context of the proposed theory, a natural combination of the two widely used decompositions concerning can consistently and uniquely determine the elastic and the plastic parts in the two decompositions as well as all their related kinematical quantities.As an application, the proposed model is applied to derive a self-consistent Eulerian rate type model for void growth and nucleation in metals experiencing finite elastic–plastic deformation by incorporating a modified Gurson's yield function and an associated flow rule, etc. As a test problem, the finite simple shear response of the model is studied by means of numerical integration. It turned out from these calculations that the results obtained for the effective and the true stresses can represent the experimentally observed behaviour, when the logarithmic rate is incorporated in the model. It has been demonstrated further that the Zaremba–Jaumann rate and the Green–Naghdi rate as well may lead to a physically nonplausible behaviour.In this appendix, some calculations related with the constitutive model describing the elastic–plastic damage behaviour are comprised.For the modified Gurson's yield function (Utilizing the evolution equations (74), (79) and (81), from the general formula (35), we derive an expression for the plastic multiplier where the loading–unloading indicator ψ is given by one can obtain an explicit expression for β as follows:Crystal structure and mechanical properties of nickel–cobalt alloys with different compositions: A first-principles studyThe properties of nickel–cobalt alloys depend greatly on their composition. In this study, we investigated the crystal structure and mechanical properties (elastic properties and hardness) of nickel–cobalt alloys with different compositions based on first-principles calculations. The formation enthalpy (ΔH) values were calculated and the results showed that as the cobalt content increased in the alloys, the crystal structure of the alloys changed from face centered cubic (fcc) to hexagonal close-packed (hcp), and a coexistence zone with both the fcc and hcp phases existed when the cobalt content was 50–80 at.%. The formation enthalpy values for the fcc-phase and hcp-phase were equal when the cobalt content was 65.5 at.%. The results were in good agreement with the experimental results. Calculations of the elastic properties showed that increasing the cobalt content of the alloys could increase the stiffness as well as improving the compression and shear resistance, but the ductility was reduced. The hardness increased for the fcc and hcp phases as the cobalt content increased. When the cobalt content was 50 at.%, the hardness reached the maximum value of 1032 HV. Further analyses of the electron localization function demonstrated that the increases in the compression and shear resistance, stiffness, and hardness of the nickel–cobalt alloys as the cobalt increased could be attributed to the enhanced covalent bonds between Ni–Co and Co–Co atoms.Nickel–cobalt alloys have been used widely in many fields, such as engineering materials, surface protection, and catalysis, because of their excellent properties in terms of strength, toughness, corrosion, and wear resistance.Previous investigations of nickel–cobalt alloys showed that the properties of these alloys depend greatly on the cobalt content. For example, Karpuz et al. [] investigated the structure, magnetic properties, and magnetoresistance of nickel–cobalt alloys with different cobalt contents and found that the cobalt content in the alloys greatly affected the structure and magnetic properties of the alloys. They showed that the optimum cobalt content was 28–40 at.% because the alloys had a very smooth or slightly granular surface with a lower coercivity Hc as well as higher magnetoresistance. Karpuz et al. [] studied the effects of different components due to variations in the deposition potential on the properties of nickel–cobalt films. The results showed that the structure and magnetic properties of the films were highly dependent on the nickel–cobalt ratio. Wang et al. [] reported that increasing the cobalt content of films could reduce the friction coefficient and enhance the wear resistance. Srivastava et al. [] investigated the corrosion resistance and microstructure of nickel–cobalt films with different cobalt contents, and showed that the morphology changed from a mixture of columnar and fibrous to lamellar, before finally becoming fibrous as the cobalt content increased. In addition, the microstructure transformed from the face centered cubic (fcc)-phase (0–50 wt%) to the hexagonal close-packed (hcp)-phase (70 wt%). Their findings indicated that the microhardness and corrosion resistance were maximized with cobalt contents of 50 wt% and 20 wt%, respectively. Other studies [Many experimental studies have investigated the structure and properties of nickel–cobalt alloys with a fixed composition. However, the properties of Ni–Co alloys depend greatly on their composition and few studies have evaluated the effects of different compositions on the structure and properties of nickel–cobalt alloys. Thus, in the present study, we systematically investigated the crystal structure and mechanical properties (elastic properties and hardness) of nickel–cobalt alloys. The main aims of this study were to obtain insights into the changes in the crystal structure and the overall trends in the elastic properties and hardness of nickel–cobalt alloys with different compositions, and to determine the relationships among the composition, structure, and properties of these alloys from the perspective of the microcrystalline structure. The calculations conducted in this study may provide guidance for future research and reduce the workload in experimental research. Our findings may also be applicable to other binary alloys and multi-element alloys.All of the calculations conducted in this study were performed with the Cambridge Serial Total Energy Package (CASTEP) [], which employs the plane-wave ultrasoft pseudopotential method [] based on first-principles with density functional theory []. The generalized gradient approximation (GGA) with Perdew-Wang91 (PW91) [] was employed as the exchange-correlation functional. In some of the elastic property calculations, the local density approximation [] and GGA with Perdew-Burke-Ernzerhof (PBE) [] were also considered for comparison. The cutoff energy was set to 550 eV, which guarantees good convergence. According to the Monkhorst–Pack [] sampling scheme, the k-point matrix was set to 22 × 22 × 22 for the cubic structure (Pm-3m) and 31 × 31 × 22 for the tetragonal structure (P4/mmm). For the hexagonal and orthorhombic phases, we set k-point matrices with parameters of 19 × 19 × 21 (for a = b = 4.294, 4.283, etc.) and 36 × 36 × 19 (for a = b = 2.483, 2.495), respectively. The convergence criteria for geometry optimization and the energy calculations were set as follows: (i) self-consistent field (SCF) convergence tolerance = 5 × 10−7 eV/atom; (ii) energy convergence tolerance = 1 × 10−5 eV/atom; (iii) displacement tolerance = 0.001 Å; (iv) maximum force tolerance = 0.03 eV/A; and (v) stress tolerance = 0.05 GPa. Spin polarization was considered in all of the calculations conducted in this study.The nickel–cobalt phase diagram and previous research showed that nickel and cobalt have similar atomic radii, and they form an infinite substitutional solid solution []. The crystal structure of pure nickel is fcc. Pure cobalt occurs in two allotropic forms where the fcc structure is stable at temperatures higher than 417 °C and the hcp structure is thermodynamically stable below 417 °C []. The nickel–cobalt binary alloy phase diagrams showed that the crystal structure of the nickel–cobalt alloys with low cobalt contents was fcc and those with a high cobalt content had the hcp structure. A coexistence zone existed containing the two structures. The coexistence zone with the two structures existed when the cobalt concentration ranged from 0.66 wt% to 0.71 wt% at 300 K. Comparisons of the diffraction peaks obtained for nickel–cobalt with different cobalt content demonstrated that the crystal structures of the alloys with different compositions were similar where they comprised fcc nickel and hcp cobalt [In this study, we analyzed the changes in the crystal structure of nickel–cobalt alloys with different compositions in terms of their phase stability based on first-principles calculations. The structure models are shown in , which indicates that all of the structures could be divided into two categories comprising the fcc-phase and hcp-phase. All of the structures in the fcc-phase were obtained by solid solution substitution of the conventional cell of pure nickel. One conventional cell of pure nickel contains four nickel atoms. The corresponding structures for Ni3Co, NiCo, and NiCo3 with cobalt contents of 25, 50, and 75 at.% were obtained by substituting one, two, and three nickel atoms with cobalt, respectively. Symmetry search and geometry optimization were then conducted to obtain the four structures with the fcc-phase shown in All of the structures with the hcp-phase were obtained by solid solution substitution of the 3 × 3 × 1 supercells of pure cobalt where the atomic ratios of cobalt relative to nickel were 1/2 (CoNi2), 1/1(CoNi), 2/1(Co2Ni), and 5/1(Co5Ni), and the cobalt contents were 33.3 at.%, 50 at.%, 66.7 at.%, and 83.7 at.%, respectively. The structure of CoNi2 was the same as that for Co2Ni but the atomic positions of nickel and cobalt were the opposite, and thus the structure of CoNi2 is not shown in . The optimized parameters calculated for the crystal structure, cohesive energy, and formation enthalpy are shown in . The optimized lattice parameters were in good agreement with the experimental results [In order to investigate the phase stability and alloying ability of the nickel–cobalt alloys, we calculated the cohesive energy (Ecoh) and formation enthalpy (ΔHNixCoy). The cohesive energy was calculated as follows:EcohNixCoy=EtotNixCoy−xEatomNi−yEatomCox+ywhere EcohNixCoy is the cohesive energy, EtotNixCoy is the total energy of the NixCoy alloy, and EatomNi and EatomCo represent the energy values for the isolated nickel and cobalt atoms, respectively. The values obtained for Ecoh are presented in where the negative values indicate that all of the structures were predicted to be stable. The trend in the cohesive energy for the different crystal structures is shown in . Clearly, the absolute value of the cohesive energy increased as the cobalt content increased in the crystal structure, which indicates that increasing the cobalt content in the crystal is beneficial for the stability of the structure.The formation enthalpy ΔH was calculated as follows:ΔHNixCoy=EtotNixCoy−xEsolidNi−yEsolidCox+ywhere ΔHNixCoy is the formation enthalpy, and EsolidNi and EsolidCo are the energy per atom for nickel and cobalt in the solid state, respectively. The values determined for nickel, cobalt (fcc), and cobalt (hcp) in the solid state were −1356.75, −1044.87, and −1044.85 eV/atom, respectively. In Eq. , x and y are the numbers of nickel and cobalt atoms in the unit cell, respectively. The values of ΔHNixCoy are listed in . As shown in Table, the values of ΔHNixCoy for all of the structures 1 were positive but the values were very small, with a maximum value of 5.30 kJ/mol and a minimum value of only 2.59 kJ/mol, thereby indicating that cobalt can occupy the nickel position with only a small amount of energy. In the hcp-phase, the value for ΔHCoNi−2 was less than that for ΔHCoNi−1, which indicates that the nickel–cobalt alloys more readily form in the (f)-2 structure with a cobalt content of 50 at.% and the number of (f)-2 structures will be more than that of (f)-1 structures in the actual macroscopic nickel–cobalt alloys. A similar result was obtained when the cobalt content was 66.7 at.%.The trends in the formation enthalpy for different crystal structures are shown in , where the bottom coordinate axis represents the percentage of cobalt atoms in the microstructure models and the top coordinate axis denotes the percentage cobalt content in the macroscopic nickel–cobalt alloys. The red triangular points are the formation enthalpy values corresponding to the four structures in the fcc-phase. The red curve is the polynomial curve fitted to the four red triangular points. Similarly, the blue points are the corresponding formation enthalpy values for the five structures in the hcp-phase and the blue curve is the polynomial curve fitted to the five points. shows that the formation enthalpy for the fcc-phase was determined as much lower than that for the hcp-phase in the low cobalt content region, thereby indicating that the crystal structures of the macroscopic nickel–cobalt alloys exist as fcc structures when the cobalt content is low, as shown by the red shadow region in . In the high cobalt content region, the formation enthalpy value for the hcp-phase formation was determined as much lower than that for the fcc-phase, which indicates that in the high cobalt content region, the crystal structure of the macroscopic nickel–cobalt alloys is the hcp structure, as shown by the blue shadow area in . These results are in good agreement with the nickel–cobalt binary phase diagram and those obtained in previous studies [, the two fitted curves intersect at point c (cobalt 65.5 at.%), which indicates that the amounts of energy required for the formation of the two nickel–cobalt alloy structures (fcc and hcp) are equal with this cobalt content, and the two structures coexist in the same amounts. shows that when the cobalt content is less than 65.5 at.%, the fcc-phase is dominant and this corresponds to the yellow shaded area in , whereas the hcp-phase dominates above 65.5 at.%, as indicated by the green shaded area in . The range for the two-phase region (fcc and hcp) is a–b at.%. Many factors can affect the values of a and b. For example, the deposition parameters for electrodeposited nickel–cobalt alloys will affect the values of a and b, such as the deposition current and pH value of the electrolyte. Srivastava et al. [] studied the corrosion resistance and microstructure of electrodeposited nickel–cobalt alloys, and determined that the crystal structures of nickel–cobalt alloys were fcc with cobalt contents of 0 wt% and 20 wt%. With a cobalt content of 50 wt%, the nickel–cobalt alloys exhibited a mixed cell structure dominated by fcc, which comprised an fcc-phase and peritectic phase. The peritectic phase was a combination of the fcc-phase and hcp-phase. The hcp-phase was dominant with a cobalt content of 70 wt%. As the cobalt content increased, the structure transformed from hcp + fcc to hcp. The morphology, structure, and magnetic properties of nickel–cobalt alloys were studied by Ergeneman [], where the cobalt content of the alloys varied between 50 wt% and 83 wt%. They found that when the cobalt contents were 50 and 53 wt%, the alloys comprised the fcc-phase. The mixed phase was observed with cobalt contents of 58, 62, and 79 wt%. When the cobalt contents of the alloys were 81 and 84 wt%, only the hcp-phase was found. Similar results were also obtained in other studies [] and the content ranges for the two-phase zones [. Based on previous experimental results [], we consider that a≈50 at.% and b≈80 at.%.] have provided some evidence for order in Ni–Co alloys containing the fcc-phase. For example, Ni3Co (L12) is ordered at low temperatures [] and the critical temperature for ordering is 773 ± 1 °C. Thus, Ni–Co alloys that contain the fcc-phase are considered to be ordered. However, in order to replicate substitutional disorder, we used 1 × 1 × 2 supercells of Ni7Co, Ni3Co (DO22), Ni5Co3 () to determine any significant differences and the results are shown in . Clearly, the formation enthalpy for the supercells followed the same trend described above.The elastic constants directly describe the reactions of crystals under external forces and they are indispensable in practical applications for understanding processes such as load deflection, fracture toughness, and thermo-elastic stress. In the framework of linear elasticity theory, the change in the internal energy of a crystal under general strain δ can be expressed as a function of the strain as follows:ΔE=E(V,δ)−E(V0,δ)=V02∑i6∑j6cijδiδj+o(δ3)where E(V,δ) and E(V0,δ) are the total energy of the crystal under strain and without strain, respectively, V0 is the volume of the equilibrium cell, cij is the elastic constant, which is an element of an n×6 matrix according to Voigt's notation [], and δ is the deformation added to the equilibrium cell. According to Eq. , the elastic constants cij can be obtained by applying some restricted strain modes based on the symmetry of the crystals. For each strain mode, the deformation is applied δ=±0.002n(n=0~6).The calculated elastic constants are shown in and the results are in good agreement with the experimental values []. The crystal structures of the hcp-phase containing cobalt 33.3 at.% are not listed in because we consider that this crystal structure does not exist in actual macroscopic nickel–cobalt alloys. The elastic constants satisfy the general mechanical stability criteria for cubic structures []: (c11+2c12)/3>0, c11−c12>0 and c44>0; for tetragonal structures []: c11>0, c33>0, c44>0, c66>0, c11−c12>0, c11+c12−2c13>0, and 2(c11+c12)+c33+4c13>0; for orthorhombic structures []: c11+c22−2c12>0, c11+c33−2c13>0, c22+c33−2c23>0, c11+c22+c33+2(c12+c13+c23)>0; and for hexagonal structures []: c11>0, c11−c12>0, c44>0, (c11+c22)c33−2c132>0. These conditions and results also limit the magnitude of the bulk modulus B: c12<B<c11. In , the large value for c33 in the hcp-phase indicates the high incompressibility along the c axis. The value for c44 in the hcp-phase is only half that in the fcc-phase, which indicates that the hexagonal structures have a lower capacity to resist monoclinic deformation than those in the fcc-phase.The bulk modulus B and shear modulus G can be obtained using the Voigt–Reuss–Hill approximation [where BV and BR, and GV and GR, are the bulk modulus and shear modulus for the Voigt equation and Reuss equation, respectively.] Ni, Ni3Co, and NiCo3, B, GV, and GR are defined as follows.] NiCo, BV, BR, GV, and GR, are obtained with:BV=(2(c11+c12)+c33+4c13)/9,GV=(M+3c11−3c12+12c44+6c66)/30,BR=C2/M,GR=15/((18BV/C2)+6/(c11−c12)+6/c44+3/c66)where M=c11+c12+2c33−4c13 and C2=(c11+c12)c33−2c132.] CoNi-1, Co2Ni-1, Co5Ni, Co, BV, BR, GV, and GR are defined as:where C2=(c11+c12)c33−2c132 and c66=(c11−c12)/2.] CoNi-2, Co2Ni-2, BV, BR, GV, and GR are obtained with:GR=15/(4(s11+s22+s33−s12−s13−s23)+3(s44+s55+s66))where s11, s22, etc., are the elastic compliance constants, which can be determined based on the mathematical relationship between the stiffness matrix cij and compliance coefficient sij. Young's modulus E and Poisson's ratio v can be calculated with the following formula.The calculated mechanical parameters are listed in . Clearly, E and G satisfy the relationship: G=E/2(1+v). The bulk modulus was used to assess the capacity to resist deformation under an applied pressure and the shear modulus was employed to evaluate the capacity to resist shear deformation, where higher values indicate greater resistance. Young's modulus reflects the stiffness of crystals, where larger values indicate stiffer crystals. As shown in , the anti-compression of the hcp-phase was slightly stronger than that of the fcc-phase. At the same cobalt content, the shear resistance and stiffness of the fcc-phase were stronger than those of the hcp-phase. The ratio of the bulk modulus relative to the shear modulus (B/G) for the polycrystalline phase was used to predict the ductile and brittle behavior of the solid materials, where a high (low) B/G value indicates ductility (brittleness). The critical value for assessing ductility and brittleness is 1.75. shows that all of the structures were determined as ductile. Further analyses of the responses of B, G, E, v, etc. to increases in the cobalt content are presented in our subsequent analysis of hardness.In order to investigate the effects of the cobalt contents on the hardness of nickel and cobalt alloys, the method proposed by Chen et al. [] was used to calculate the hardness of the alloys according to the following formula:where K = G/B is Pugh's modulus ratio. Full details of this method were provided by Chen et al. []. The calculated hardness values are listed in . In order to illustrate the trends in the elastic properties and hardness of the nickel–cobalt alloys as the cobalt content increased, we show the variations in B, G, E, B/G, v, and HV in represent the calculated elastic properties corresponding to the four structures in the fcc-phase, and the blue polylines are the results for the hcp-phase.Our findings demonstrate that the critical cobalt content for the transition from the fcc structure to the hcp structure is 50 at.%. The formation enthalpies were determined as ΔHNiCo=4.36 kJ/mol and ΔHCoNi−2=5.07 kJ/mol, and the difference between these values is 0.71 kJ/mol. Thus, we consider that when the difference in the formation enthalpy between two structures is more than 0.71 kJ/mol, the structure with a large ΔH will not exist in the actual macroscopic alloys. In the hcp-phase, when the cobalt content is 50% and 66.7 at.%, there are two structures comprising (f1) and (f2), and (g1) and (g2), respectively. The difference in the formation enthalpy between structures (f1) and (f2) is 0.23 kJ/mol, and thus we consider that the (f1) and (f2) structures both exist in macroscopic nickel–cobalt alloys, where the ratio of the two structures in the alloys is about 3:7. The elastic properties and hardness of the alloys with a cobalt content of 50 at.% in the hcp-phase were obtained as: (f1) × 0.3 + (f2) × 0.7. In particular, HV (CoNi) = HV (CoNi-1) × 0.3 +HV (CoNi-2) × 0.7. The (g1) and (g2) structures can be treated in the same manner. Our results indicate that when the cobalt content of the alloys is 65.5 at.%, the fcc-phase coexists with the hcp-phase and their amounts are equal. Therefore, the average values of the elastic properties or hardness for the two phases approximately represent the values of the elastic properties or hardness for the actual macroscopic alloys with a cobalt content of 65.5 at.%., the solid line shows the change in the elastic properties of the actual macroscopic alloys as the cobalt content increases. The dotted lines indicate that a phase cannot exist alone at the corresponding cobalt content in the macroscopic nickel–cobalt alloys. According to , the bulk modulus (B) increases in a monotonic manner as the cobalt content increases, which indicates that increasing the cobalt content can significantly improve the compressibility of nickel–cobalt alloys. The shear modulus (G) and Young's modulus (E) for the fcc-phase and hcp-phase both increase as the cobalt content increases. At the same cobalt content, the values of G and E are smaller for the hcp-phase than the fcc-phase. Therefore, as the cobalt content increases in macroscopic nickel–cobalt alloys, the shear resistance and stiffness both increase initially, before decreasing when reaching the two-phase region, and then slowly increasing again. The B/G and Poisson's ratios were used to evaluate the brittleness and ductility of materials. that the ductility of the hcp-phase is greater than that of the fcc-phase. The ductility of the alloys decreases as the cobalt content increases. When the alloy phase reaches the two-phase region, the ductility increases and then decreases slightly., the changes in the hardness as the cobalt content increases are consistent with the changes in G and E. The hardness of the fcc-phase is greater than that of the hcp-phase, and the hardness decreases when the alloy phase enters the two-phase region. The hardness is maximized at a cobalt content of 50 at.%. Therefore, increasing the hardness of nickel–cobalt alloys should increase the content of cobalt in the alloys, but it is necessary to avoid transforming the phase structure from fcc to hcp and entering the two-phase region. The changes in the hardness with the cobalt content of the alloys are consistent with previous findings [], but the hardness values are about twice the experimentally determined values. We consider that the overestimates of the hardness are due to the inappropriate formula used for calculating the properties of the pure metal alloys.At present, The formulae used for calculating the hardness can be roughly divided into two categories. The first category comprises the hardness calculation models proposed by Gao et al. [], where it is basically assumed that the hardness can be expressed based on the resistance of chemical bonds to the indenter. The second category of hardness models comprises those developed by Chen et al. [], which were obtained based on the linear relationship between the hardness and elasticity modulus. These hardness calculation models have been applied to superhard materials or high hardness materials, such as diamond, transition metal borides, nitrides, and carbides. However, we found that none of these models were accurate at calculating the hardness of pure metals or alloys. In this study, various models were used to calculate the hardness of nickel–cobalt alloys. We found that the results obtained using the first category of hardness calculation models were obviously incorrect because the chemical bonds in nickel–cobalt alloys are mainly metal bonds, and the formulae are mainly applicable to super-high or high hardness materials with short and strong covalent bonds. Among the second category of hardness calculation models, the calculation errors were smallest using the model proposed by Chen et al. [], so we employed this model. The hardness calculations were high but the changes in the hardness values as the cobalt content increased were consistent with the experimental values. Therefore, the hardness values obtained in this study are useful and they may facilitate experimental research.We also assessed the mechanical properties of the fcc supercells and the results are shown in . The conclusions were the same as those obtained based on the formation enthalpy. Therefore, the properties of the alloys with substitutional order or disorder did not differ significantly. The results also showed that compared with the substitutional sites in alloying atoms and the ordered or disordered alloys, the compositions of the alloys had the greatest influence on the properties of Ni–Co alloys.The electronic localization function (ELF) [] values were calculated in order to further analyze the bonding of atoms in the alloys. The ELF provides a reliable measure for characterizing electron pairing and localization. According to the definition, the ELF values are scaled between 0 and 1, where ELF = 1 indicates the perfect localization of covalent bonds or lone pairs and ELF = 0.5 corresponds to a free-electron gas or metallic bonding. The ELF sections on the (111) and (001) lattice planes of nickel–cobalt alloy phases with different compositions are depicted in . The maximum ELF value was determined as only 0.36, which indicates that the peripheral electrons have an almost free distribution in the whole crystal, with the typical characteristics of metal bonds. As shown in , as the cobalt content increases in the alloys, the area (orange region) representing the relative localization of electrons in the fcc and hcp phases clearly increases, thereby indicating that the metallic bonds between the atoms in the alloys are weakened (i.e., covalent bonds are enhanced). The distribution in the orange region shows that the covalent bonds are stronger for Co–Co than Co–Ni. The covalent bonds are weakest for Ni–Ni. Covalent bonds have positive effects on the strength and hardness, and metallic bonding has a positive effect on ductility. Thus, these findings explain why the compression and shear resistance, stiffness, and hardness of nickel–cobalt alloys increase as the cobalt content increases, whereas the ductility decreases.In this study, we systematically analyzed the effects of the composition of nickel–cobalt alloys on the crystal structure and mechanical properties based on first-principles methods.As the cobalt content increased in the alloys, the structures of the alloys changed from fcc to hcp. The initial cobalt concentration when the transformation occurred was about 50 at%. At a cobalt content of 65.5 at.%, the formation of the fcc-phase occurred to a similar extent as the hcp-phase. However, when the cobalt content increased to about 80 at.%, only the hcp-phase was present in the alloys.The elastic properties and hardness values were also calculated for the nickel–cobalt alloys. The bulk modulus (B), shear modulus (G), and Young's modulus (E) increased for the fcc-phase and hcp-phase as the cobalt content increased. At the same cobalt content, the shear modulus (G) and Young's modulus (E) were higher for the fcc-phase than the hcp-phase. The ductility was greater for the hcp-phase than the fcc-phase. The ductility decreased for the fcc-phase and hcp-phase as the cobalt content increased.The hardness values for the fcc and hcp phase both increased as the cobalt content increased. The hardness of the fcc-phase was higher than that of the hcp-phase. The hardness was maximized at a cobalt content of 50 at.%. Therefore, increasing the cobalt content in the alloys can enhance the hardness of nickel–cobalt alloys, provided that the alloy structure does not enter the two-phase region from fcc-phase.Further analyses based on the ELF values demonstrated that the compression and shear resistance, stiffness, and hardness of nickel–cobalt alloys increased as the cobalt content increased due to the enhanced covalent bonds between Ni–Co and Co–Co atoms.Comparison of nanostructured Al/B4C composite produced by ARB and Al/B4C composite produced by RRB process▶ The SEM microstructures revealed the well distributed B4C particles in the aluminum matrix for both the composites. ▶ The TEM analysis showed the nanostructured Al/B4C composite was produced by the ARB process successfully. ▶ The ductility (elongation) of the RRB processed composite is higher than that of the ARB processed composite. ▶ The microhardness of the ARB processed composite is higher than that of the RRB processed composite.In the present study, Al/B4C composites were produced and compared in the form of sheets, through accumulative roll bonding (ARB) and repeated roll bonding (RRB) processes. The microstructure of the composites fabricated by both the methods, revealed by scanning electron microscopy (SEM), showed the B4C particles properly distributed in the aluminum matrix. The average grain size of the ARB processed composite was about 186 nm by linear intercept method, based on transmission electron microscopy (TEM) observations. Mechanical properties of the Al/B4C composites produced by two methods were investigated by tensile and hardness tests. The results showed that the tensile strength and hardness of the ARB and RRB processed composites increase with the number of cycles. However, the tensile strength and hardness of the ARB processed composite are much higher than those of the RRB processed composite. The tensile test results revealed that the elongation of the ARB processed composite is lower than that of the RRB processed composite.Aluminum metal matrix composites (Al MMCs) are being considered as a group of new advanced materials due to lightweight, high strength, high specific modulus, low coefficient of thermal expansion and good wear resistance properties. A combination of these properties is not available in a conventional material Processing techniques for Al MMCs can be classified into (1) liquid-state processing, (2) semisolid processing and (3) powder metallurgy The aim of this research is using the ARB and RRB processes to fabricate Al/7.5 vol.% B4C composites and also evaluating: (i) microstructure of these composites through a typical section parallel to the rolling direction (RD), (ii) mechanical properties of the composite samples, such as hardness and strength, and (iii) comparison of the microstructure and mechanical properties of two composites.Strips of 1100-aluminum alloy with the length of 200 mm, width of 30 mm, and thickness of 0.4 mm annealed at 623 K in ambient atmosphere and analytical grade of B4C powder with an average size of 2.5 μm were used as raw materials. lists the chemical composition of the Al used. shows the SEM image of the B4C particles used in this work.This process consists of two steps. In the first step, the strips were degreased in acetone and scratch brushed with a 90 mm diameter stainless steel circumferential brush with 0.35 mm wire diameter. To fabricate the Al/7.5 vol.% B4C composites by the ARB process, eight strips were stacked over each other to achieve 3.2 mm thickness, while 0.83 vol.% B4C from 7.5 vol.% B4C powders were dispersed between every two of the layers. The stacked strips were fastened at both ends by steel wire to make it ready for the rolling process. The strip was roll-bonded with a draft percentage of 66% reduction at room temperature. The reduction of 66% was used for the creation of an appropriate bonding between the aluminum strips In the second step, the two annealed and roll-bonded strips were degreased in acetone, scratch brushed and after stacking over each other, without B4C particles between them, roll-bonded with a draft percentage of 50% reduction (Von Mises equivalent strain of 0.8). The last step of the process was repeated up to eight cycles without annealing between each cycle. After eight accumulative roll bonding cycles in total, the Al matrix composite, including well-dispersed B4C reinforcements was produced.This process was also performed in two main steps. The first step of RRB was completely the same as the ARB process. The second step of the RRB process was slightly different from the ARB process. In the second step of the RRB process, the strips were annealed between two rolling cycles; therefore, the microstructure of the matrix in the produced composite consists of micron size grains. Nevertheless, in the ARB process there was no annealing between any of the two rolling cycles; therefore, the microstructure of the produced composite would consist of ultrafine grains.The ARB and RRB experiments were carried out, without lubricant, using a laboratory rolling mill with a loading capacity of 15 tons. The roll diameter was 170 mm, and the rolling speed (ω) was 15 rpm.The microstructural characterization of the specimens was carried out by scanning and transmission electron microscopy (SEM and TEM).A SEM (Leica Cambridge S360) was used to observe microstructural evolution. SEM was used to investigate porosities in the interface of the B4C and Al layers. The dispersion of the B4C particles in the composite matrix also was investigated by SEM.TEM and corresponding selected area diffraction (SAD) patterns were obtained by utilizing a Philips-FEG operating at 200 kV. Thin foils parallel to the rolling plane (rolling direction–transverse direction or RD–TD plane) were prepared by ion milling technique.Tensile test specimens were machined by a wire cut machine from the rolled sheets according to the 1/5 scale of the JIS-No. 5 specimen, oriented along the rolling direction (). No considerable B4C pull-out was observed during cutting. The gauge length and width of the tensile test specimens were 10 and 5 mm, respectively. The tensile test at ambient temperature was carried out at a nominal strain rate of 8.3 × 10−4 |
s−1 by using an Instron tensile testing machine. The total elongation of the specimens was measured from the difference in the gage length before and after testing.Vickers hardness (HV) tests, using a load of 150 g for 15 s, were performed on the cross-section (TD plane) of the ARB processed samples. The mean value of ten separated measurements taken at randomly selected points of the composite was reported.The microstructure of the composite produced by the ARB process in the eighth cycles of ARB (tenth rolling cycles) is shown in . As it can be seen after the eight ARB cycles, a homogenous distribution of the B4C particles into the Al matrix is obtained. The SEM image of this composite after the final ARB cycles shows the defect-free (it means defects like porosities and cracks) composites have been formed during fabrication. shows the microstructure of the composite produced by the RRB process after 10 rolling cycles. As it can be seen in , the microstructure of the ARB and RRB processed composite from the viewpoint of the B4C particles distribution and porosities is the same; thus, the B4C particles have been dispersed uniformly in the Al matrix in both the composites and the number of porosities is negligible in them.The TEM microstructure and corresponding selected area diffraction pattern (SAD) at the plane perpendicular to the transverse direction (TD plane) of the ARB processed Al/B4C composite specimen of the eighth cycle are shown in . As it can be seen after eight ARB cycles, ultrafine grains extend in the Al matrix and also they aligned in rolling direction. Tsuji et al. , the SAD pattern confirms the presence of high-angle grain boundaries in the microstructure. Huang et al. shows the SEM micrograph of the RRB processed composite specimen after the final cycle. The average grain size determined by the intercept method is about 9 μm which is about 48 times that of the ARB processed composite.The engineering stress–strain curves of the Al/B4C composites produced by the ARB and RRB processes (after eight cycles of the ARB process) and also engineering stress–strain curves of an annealed commercial pure aluminum, as the raw material, are compared in . It is seen that the strength of the ARB processed composite is higher than the RRB processed composite. So that the tensile strength of the ARB processed composite is about 2.1 times higher than the RRB processed composite. However, the strength of both the composites is higher than the raw material. As it can be seen, by increasing strain, the flow stress of the ARB processed composite rapidly reached its maximum value, macroscopic necking occurred, and then tensile fracture happened with a low elongation. It has been shown that the increase of the strength in ARB processed materials is due to the strain hardening or dislocation strengthening and evolution of the grain structure and formation of ultrafine grains (grain boundary strengthening mechanism) The elongations obtained from the tensile tests of the ARB and RRB processed composites are listed in . It indicates that the elongation decreased after the first cycle, and again it increased slightly by increasing the ARB and RRB cycles in both the composites. However, the elongation of the ARB processed composite is lower than that of the RRB processed composite. The decrease in the ductility of the ARB processed Al/B4C composite sheets in the first cycle, can be due to the highly strain hardening and inadequate bonding between the Al layers. In the RRB processed Al/B4C composite sheets, the subsequent annealing decreases the strain hardening effect, therefore. The ductility is higher than the ARB processed composite sheets. However, there is inadequate bonding between the Al layers yet and caused the decrease of ductility. The increase in the ductility of both the composite sheets in higher cycles can be due to the creation of adequate bonding between the Al layers and also the decrease of the porosities with increasing rolling cycles shows the Vickers hardness of the ARB and RRB processed Al/B4C composites as a function of the rolling cycles. The ARB curve shows an immediate increase in the hardness at the initial cycles, followed by a minor additional increase up to the seventh cycle. Afterward, the hardness does not essentially change with subsequent cycle. After eight cycles, the hardness of the ARB processed composite samples reached 89 HV. The rapid increase of hardness at the initial cycles is attributed to strain hardening (based on the density of dislocations and interaction between them) which is saturated at large strains. The saturation of hardness has been previously reported in ultrafine grain materials fabricated by severe plastic straining , the increase of hardness in the initial RRB cycles is insignificant. After the initial RRB cycles, the hardness of the composite increases by increasing cycles up to the seventh cycle and it is saturated in the higher (eighth) cycle. In the initial cycles of the rolling process, the work piece has a layered structure, in which the layers of the B4C powders discrete the metal layers. By increasing the number of the Al and B4C layers in the cross-section, as a result of increasing the rolling cycles, the B4C particles are dispersed more uniformly in the aluminum matrix and therefore the hardness increases. Since the B4C particles completely disperse in the Al matrix after the seventh cycle In this study, micron and nanostructured Al/B4C composites were produced in the form of sheets through RRB and ARB processes successfully. The microstructure of the composites was investigated by SEM and TEM. Also, the mechanical properties of the ARB composite samples were investigated and compared with those of the RRB composite samples. The conclusions drawn from the results can be summarized as follows:The SEM microstructures revealed the well distributed B4C particles in the aluminum matrix for both the composites.The TEM analysis showed the nanostructured Al/B4C composite was produced by the ARB process successfully.The evolution of the grain structure and the formation of ultrafine grains in the ARB processed composite and high dislocation density are the main reasons for the increase in the strength in them rather than the RRB processed composite.The ductility (elongation) of the RRB processed composite is higher than that of the ARB processed composite.The hardness of both the composites increased in the rolling process; however, the hardness of the ARB processed composite is about 2 times higher than that of the RRB processed composite.Electroless Ni-P plating on Mg-Li alloy by two-step methodMicrostructural evolution during solution treatment of Co–Cr–Mo–C biocompatible alloysThree different Co–Cr–Mo–C alloys conforming to ASTM F75 standard were poured in an industrial environment and subjected to a conventional solution treatment at 1225 °C for several time intervals. The microstructural changes and transformations were studied in each case in order to evaluate the way in which treatment time influences the secondary phase fraction and clarify the microstructural changes that could occur. To assess how treatment time affects microstructure, optical microscopy and image analyzer software, scanning electron microscopy and energy dispersion spectrometry analysis were employed.The main phases detected in the as-cast state were: σ-phase, M6C, and M23C6 carbides. The latter presented two different morphologies, blocky type and lamellar type. Despite being considered the most detrimental feature to mechanical properties, σ-phase and lamellar carbides dissolution took place in the early stages of solution treatment. M23C6 carbides featured two different behaviors. In the alloy obtained by melting an appropriate quantity of alloyed commercial materials, a decrease in size, spheroidization and transformation into M6C carbides were simultaneously observed. In the commercial ASTM F75 alloy, in turn, despite being the same phase, only a marked decrease in precipitates size was noticed. These different behaviors could be ascribed to the initial presence of other phases in the alloy obtained from alloyed materials, such as σ-phase and “pearlitic” carbides, or to the initial precipitate size which was much larger in the first than in the commercial ASTM F75 alloy studied. M6C carbides dissolved directly in the matrix as they could not be detected in samples solution-treated for 15 min.► Three different Co–Cr–Mo alloys were poured under an industrial environment. ► Transformation of existing phases followed during conventional solution treatment. ► In as-cast/treated samples, phases were identified by color metallography, SEM and EDS. ► M23C6 |
→ M6C transformation was corroborated by SEM and EDS analysis. ► Carbide spheroidization was also detected prior a noticeably carbide size decreasing.Cobalt base alloys (Co–Cr–Mo) are widely used in several medical applications such as knee and hip joint replacement, given their excellent biocompatibility, corrosion and wear resistance, combined with their good mechanical properties With a view to removing casting defects, as-cast Co–Cr–Mo alloys are often subjected to different heat treatments, which are designed to enhance their mechanical properties and prevent fatigue failure. The main thermal treatments applied to these alloys are conventional isothermal solution treatment or homogenization, hot isostatic pressing (hipping) and carbide refining treatments Several authors have reported that the best elongation values were obtained by hipping treatments In conventional solution treatments applied to Co–Cr–Mo alloys, the temperature range available to achieve complete carbide dissolution is very narrow. To achieve the quality demanded by implants used in human beings, the processes require a rigorous control of the variables involved. Treatment temperature is one of said variables, which is determined by the melting point of the interdendritic phases. The values reported in the literature present some discrepancies in this respect too, while the success or failure of the entire process depends on the accuracy of its choice.Some authors have found that before carbides melting, a solid-state diffusion of the carbide forming elements occurs, while after that, a serrated interface develops It has been demonstrated that partial carbide dissolution improves not only ductility The microstructure of Co–Cr–Mo alloys in as-cast condition consists in a Co-rich fcc matrix, and precipitates in the interdendritic zones and grain boundary. Such precipitates are mainly formed by M23C6 carbide, the intermetallic phase σ and an eutectic lamellar precipitate, formed by M23C6 carbides and α-fcc phase Carbide precipitation represents the major strengthening mechanism in as-cast state for these kinds of alloys, and it is also responsible for low mechanical properties. The type, size and carbide volume fraction depend on the solidification conditions as well as on the chemical composition. The carbide forming elements along with the carbon content present in the alloy play a significant role in the composition and morphology of the precipitated carbides Three different Co–Cr–Mo–C alloys, all of them conforming to ASTM F75 chemical composition specifications, were poured following the methodology adopted and described in a previous work introduces the chemical analysis of the resulting alloys, as determined by spark emission spectrometry.The cylinders were cut into slices and then subjected to a solution treatment at 1225 °C and held at this temperature for intervals ranging from 0 to 240 min. Specimens were held at the predetermined temperature for 15, 30, 45, 60, 120 and 240 min, respectively. In all the cases, the samples were quenched in cold water to retain the high temperature microstructure. The samples corresponding to time 0 were the as-cast state specimens for each alloy.Samples preparation for optical and scanning electron microscopy was carried out with conventional procedures for polishing, from 600 grid Si-C paper until a 0.05 μm alumina suspension. The specimens were thoroughly cleaned to remove any polishing remnant. To reveal the microstructure and study the precipitates evolution, a two-stage etching was used, selecting a combination of etchants that, in a first stage, revealed the dendritic matrix features with a light electrolytic chromic acid etchant and then stained the second phases for their identification Optical microscopy was used for a first identification of secondary phases, and image analysis, together with carbide fraction quantification, was performed using Image Pro Plus™ software. To provide a more accurate characterization, the samples were examined by scanning electron microscopy (SE-SEM) with a JEOL JSM-6460LV microscope, and energy dispersive spectroscopy (EDS) techniques were employed, even though the EDS technique provides a semi-quantitative analysis. The system used was an EDAX Genesis XM4-Sys 60, equipped with a multichannel analyzer EDAX mod EDAM IV, Sapphire Si(Li) detector and a super ultra thin beryllium window, with a 20 kV acceleration voltage.The microstructure of all the samples studied in as-cast condition and observed by optical microscopy was mainly formed by dendritic α-fcc Co-rich grains and carbides precipitated in grain boundaries (GBs) and interdendritic spaces The main precipitates were identified by color metallography and EDS analysis as σ phase, M23C6 and coarse lamellar phase, in agreement with reports in the literature details the as-cast microstructure in an optical micrograph, while illustrates a secondary electron SEM image with the main phases marked. The EDS analysis of the “pearlitic” phase revealed that it was formed by thin interlayed plates of M23C6 carbides and α-fcc phase, in accordance with Kilner depicts the EDS analysis for the carbide and σ tetragonal phase.During the solution treatment evolution, the initial “pearlitic” colonies and σ phase dissolved in the first 15 min, and their presence could not be detected in any solution-treated sample under longer term treatment. This could be expected given the fact that the “lamellar” structure permits a faster diffusion of the carbide forming elements in the α-matrix and therefore blocky type carbides dissolve more slowly than lamellar carbides do.As the solution treatment progresses, the M23C6 carbide suffers a spheroidization and transforms according to the M23C6 |
→ M6C reaction, as it can be noticed in , respectively. Such transformation was corroborated by the EDS analysis and consistent with Clemow and Daniell demonstrates that in samples from C1 solution-treated for 45 min, recrystallization also occurs as a secondary effect. A decrease in carbide size, concomitant with the transformation, could be observed as well.The coexistence of two different types of carbides was found in as-cast condition in this alloy, probably owing to a change in the cooling rate. depicts the carbides identified by color metallography as M23C6 and M6C needle-type. , in turn, shows EDS analysis results. The latter carbide (M6C) was only detected in the as-cast state, so it could be assumed that this carbide dissolved directly in the matrix exhibiting no transformation. In regard to the M23C6 carbide present in C2, despite being the same phase identified in C1, its behavior differed completely, as no transformation was noticed. A decrease in M23C6 carbides size was detected instead, indicating that, in this case, this phase dissolved directly in the matrix.Only M23C6 carbides were identified in this alloy in as-cast samples, as illustrated in . Carbides present in solution-treated specimens from C3 alloy behaved analogously to C2 alloy. The prolonged exposure to high temperature dissolved most carbides, and those remaining featured such a small size that it hindered their visualization by optical microscopy. is a secondary electron SEM image of a 120 minute solution-treated specimen. The EDS analysis shown in The variation of the carbide content with increasing solution treatment time was studied for each alloy. Each quantitative determination of carbide content was made at 100 × magnification on 20 fields and the data obtained were processed by image analyzer software. For the three alloys under study, the carbide fraction decreased significantly in short treatments, whereas in times ranging from 120 to 240 min, variation was slight. The solution treatment promotes a pronounced decrease in the size of secondary phases for the first 90 min. Since the initial carbide size difference between the alloys was very large, the data presented in were normalized. Initial carbide sizes were 262, 127 and 45 μm in average for C1, C2 and C3 as-cast samples, respectively. Therefore the carbide variation with the solution time is reported based on the percentage of size decrease.Carbide size reduction reached 62%, nearly 71% and 97% for samples solution-treated for 240 min from C1, C2 and C3 alloys, respectively, as illustrated in It is noteworthy that as the solution treatment time increased, a high temperature oxide layer was formed in heat C2. Its thickness increased as treatment time did, up to reaching 1 mm thickness in the 240 minute solution-treated specimen. The oxide layer analysis applying EDS technique revealed that it was an oxide formed by the main alloying elements. The oxide film SEM image and the EDS analysis corresponding to the oxide layer are shown in The formation of this oxide layer cannot be tolerated in the manufacture of biocompatible devices; since oxide microparticles could be retained in ulterior sterilization processes and change the device properties. It could even be released in the human body as wear or corrosion products. Despite the fact that the chemical composition of the alloys studied does not vary significantly, indeed there is an element that, given its distribution or size, becomes the catalyst in the formation of this chromium rich layer. Further investigations should be conducted to clarify the formation mechanism of this layer.Three Co–Cr–Mo–C alloys poured in an industrial environment were solution treated at 1225 °C for several time intervals. The microstructural changes and transformations were studied in each case. According to the results obtained, the following conclusions can be drawn:The optical, SEM microscopy and EDS analysis, showed that the phases present in the as-cast state were well identified as σ-phase, M6C and M23C6 carbide, respectively. The latter presented two different morphologies, blocky type and lamellar type. Despite being mentioned as the most detrimental feature to the mechanical properties, σ-phase dissolution takes place in the first minutes of solution treatment.With respect to M23C6 carbides, two different behaviors were observed. In C1 alloy, a decrease in size, spheroidization and transformation into M6C carbides were simultaneously appreciated. In C3 alloy, despite being the same phase, only a marked decrease in the size of the precipitates was noticed. These different behaviors could be ascribed to the initial presence of other phases in C1 such as σ-phase and “pearlitic” carbides, which, once dissolved in the early stages of treatment, may have increased the transition element rates in the matrix facilitating transformation; or due to the initial precipitate size which was much larger in C1 than in the other two alloys under study.Specimens from C3 alloy showed precipitates with an initial, much smaller size and with a more homogeneous distribution in the interdendritic space of the as-cast structure with respect to the other two alloys studied. These phases could be identified only with large magnifications, which were achieved by SEM microscopy. As a consequence, shorter times were needed to dissolve most carbides.The decrease in carbides size turned out to be 62%, about 71% and 97% for C1, C2 and C3 alloys, respectively, for samples solution-treated for 240 min.Finally, samples from C2 alloy generated an oxide layer around the solution-treated samples. This oxide film was mainly formed by chromium. The anomalous behavior of this particular alloy, which was obtained by remelting C1 alloy, could be caused by carbide distribution during casting and by the high level of Si-metallic inclusions detected in the as-cast evaluation.Effect of moisture content on static compressive elasticity modulus of concreteFor concrete under humid conditions, the mechanical properties of concrete are significantly affected by the moisture content, which differs in terms of different immersion times. This paper presents an experiment to investigate the dependence of the moisture content on the immersion time and the influence of the moisture content on the static compressive elasticity modulus. The results show that the saturated moisture content declines with increasing concrete strength grades and also declines with increasing area–volume ratios. The moisture content is slightly higher for specimens cured under the natural conditions than ones cured under the standard conditions in the same immersion times. The elasticity modulus increases with the moisture content increasing. The elasticity modulus of the fully saturated concrete has an increase of 30% over the fully dry concrete. Besides, a slight reduction occurs in the elasticity modulus for the specimens cured under the natural conditions than the ones cured under the standard conditions when the moisture content is almost the same. Based on the experimental data and the analytical results, a formula for the moisture content effect on the elasticity modulus of the concrete is proposed.The modulus of elasticity is one of the most important elastic properties of concrete from the point of view of design and behavior of structures. This parameter is determined for the structural assessment and retrofitting of structures. It is also used to estimate deflections of structures for serviceability requirement and to calculate deformation and drift in seismic analysis It is well established that concrete structures are dynamic systems subjected to continuous changes in moisture content. Structures such as dams, bridge piers, offshore platforms, and waterfront structures are all with operating conditions under water. The effect of the moisture content on the elasticity modulus of concrete has been analyzed already for a long time. Early in 1929, Davis and Troxell However, there still seems to be no consensus as to the variation occurring in the mechanical behavior as the moisture content changes. Changes in amplitude of the static elasticity modulus with the moisture content varying differ between experiments. Yaman et al. where E denotes the modulus of elasticity of concrete (GPa), and M denotes the moisture content (%). As can be seen from Eq. , the elasticity modulus inversely correlated with the moisture content. Bjerkli et al. In terms of the dispersion of the experimental results and the inconsistent conclusions, it is essential to do further studies concerning the elasticity modulus of concrete under different moisture contents. The objective of this paper is to investigate the change regulations of the moisture content in concrete and the influence of moisture content on the static compressive elasticity modulus of concrete via a full set of experiments considering the different dimensions, curing conditions and strength grades of the concrete specimens. Furthermore, the research also aims at developing relations of the moisture content and the static compressive elasticity modulus to predict or determine the static compressive elasticity modulus of concrete with different moisture contents.In this investigation, an ordinary Portland Cement (P.O42.5) produced in the Lima cement plant of China was used in all compositions, and all its properties were in accordance with the standard of Common Portland Cement , are according the Specification for Proportion Design of Ordinary Concrete The strength grade of concrete in this research were C30 and C40, whose mechanical index can be referred to the Code for Design of Concrete Structure . Besides, C30 concrete specimens with the dimension of 100 × 100 × 100 mm and 100 × 100 × 300 mm were cured under the natural conditions (outdoor environment, maximum temperature and minimum temperature were 26 °C and 12 °C respectively), as shown in . The curing method was carried out according to the Standard for Evaluation of Concrete Compressive Strength The pressure apparatus used in this work is an electro-hydraulic servo testing machine controlled by a computer in the material laboratory of Beijing Jiaotong University. The maximum capacity is 1000 kN and the accuracy is ±1%, as illustrated in The electric thermostat blast drying box produced by Shanghai Jinghong Laboratory Instrument Co., Ltd. was used to dry the specimens, as shown in The balance electronic scale was employed to measure the weight of the specimens, whose maximum weight range is 15 kg and the accuracy is 1 g, as indicated in The range and the accuracy of the caliper used to measure the dimension of the specimens in the test are 300 mm and 0.1 mm respectively. The ZH DG-80 type concrete experimental shaking table was used in the experiment and its amplitude is 0.5 mm. A BYS-3 automatic temperature controller was chosen as the temperature control instrument in the standard curing room. A concrete elasticity modulus tester was also employed to measure the deformation of the specimens, as shown in Concrete specimens cured under the standard conditions were divided into 4 groups: A, B, C and D. The first three groups were C30 concrete with the dimensions of 100 × 100 × 100 mm, 100 × 100 × 300 mm, 150 × 150 × 150 mm respectively, and the last group was C40 concrete with the dimensions of 100 × 100 × 100 mm. Each group included 3 specimens. The specimens of the four groups were placed into the drying box (keep temperature in 45 °C to avoid the damage of the concrete at high temperature) until the mass changed no longer, which can be considered as being completely dry, when the mass was noted as m0. Then the concrete specimens of the four groups were put into the plastic tank, in which the top water can drown all concrete specimens even after all specimens absorbed water to reach fully saturation. The mass of the specimens was recorded every 30 min at first, and then the interval was increased to 1 h, 2 h, 4 h, etc. In this research, the immersion time was selected as 0 h, 0.5 h, 2.5 h, 23.5 h, 32.5 h, 55 h, 97.5 h, 197.5 h and 217.3 h, respectively. The C30 specimens with the dimension of 100 × 100 × 100 mm cured under the natural conditions were also divided into 4 groups, and the moisture contents were measured at the immersion time of 0 h, 24 h, 96 h and 192 h, respectively.The moisture content M of concrete specimens can be expressed in the form ofwhere m0 represents the mass of the concrete specimens dried completely; and mi represents the mass of the concrete specimens measured at a specified time interval, namely the mass under different moisture conditions.A few remarks relevant to weighing the specimens must be made. In order to keep the specimens moist and ensure no water drops existing on the surface, the specimens should be placed on the iron stand for 5 min to drain the water out, and mopped the surface by wet cloth after removed from the tank. Besides, the specimens should be handled carefully so as to avoid being chipped the corner and ensure the accuracy of measurements.According to the Standard for Test Method of Mechanical Properties on Ordinary Concrete According to the moisture content test, the fully saturated moisture content was nearly 4% and the mass changed by 100 g with the moisture decreasing by 1.5%. On the basis of this results, Group I, II, II, and IV were designed with different moisture contents. And then the values of the moisture contents were precisely obtained by drying method. The following is the specific process:Group I was put into the drying box to reach a completely dry state, i.e., the moisture content is 0%. Group II, III, and IV were immersed into water until the mass changed no longer, which can be regarded as fully saturated. Then Group II and III were re-put into the drying box and were employed to measure the elasticity modulus when the mass of the specimens reduced by about 200 g and 100 g respectively. describes that the specimens were immersed in the water and weighed on the electronic scale.The test method of the axial compressive strength and elasticity modulus was in accordance with the Standard for Test Method of Mechanical Properties on Ordinary Concrete , and the load should be applied uniformly and consecutively (0.5–0.8 MPa/s). Besides, in the elasticity modulus test, modulus tester should be installed on the midline of the specimens’ both sides and should be asymmetrical, as illustrated in . Loading method of the elasticity modulus test is depicted in Then some fragments of each group were weighed and the mass was noted as m1, and then the fragments were put into the drying box until the mass changed no longer, when the mass was recorded as m0. The moisture content M of each group was obtained by Eq. , and the curve of the association between moisture content and elasticity modulus was established. Moreover, the effect of the curing phase on concrete properties was concluded by the comparison of specimens under different curing conditions.On the basis of the above moisture test, the relation between moisture content and immersion time for different strength grades, dimensions and curing conditions were attained, as depicted in For all groups, the trend of the moisture content varying with the immersion time is similar. The moisture content increases to about 70% fully saturated moisture content at the first interval of 2.5 h, while it increases slowly after 90 h, which can be considered as fully saturated approximately.With the same immersion time, the moisture content and the fully saturated moisture content decrease when the concrete strength grade varies from C30 to C40, which can be attributed to the decrease of the void ratio for the higher strength grade concrete.The difference of the specimens’ dimension can be determined by area–volume ratio, symbolized as i (m−1).where s represents the surface area of specimens (mm2), and v represents the volume (mm3). Based on Eq. , the values of i of specimens with the dimension of 100 × 100 × 100 mm, 100 × 100 × 300 mm and 150 × 150 × 150 mm are 6, 4.67 and 4, respectively. Compared with Group A, the increase in the moisture content of Group B and C slows down because of the decrease of the area–volume ratio. Due to the area–volume ratio of Group B being close to Group C, variations in the moisture content of two groups are similar. That is to say, the specimens with same volumes and low area–volume ratios have a smaller contact area with water, resulting in a reduction of the water penetration, and therefore slowing the increase of the moisture content.Compared with the specimens cured under the standard conditions, the growth trend of the moisture content for the ones cured under the natural conditions is more significant with the increase of immersion time. Furthermore, the fully saturated moisture content is slightly larger than the one of specimens cured under the standard conditions, which can be chalked up to the standard curing diminishing the void rate of specimens.In the axial compressive strength test, the slope of stress–strain curve in elastic stage was smaller for wet concrete than dry concrete, which can attribute to the presence of the water in the internal micro-cracks . However, for wet specimens, with the stress increasing, more vertical cracks appeared on the ends and developed along the vertical direction. When the stress reached to the extremum, the intermediate section of specimens expanded and some fragments broke away on the edge, as shown in . Then the slope of the stress–strain curve dropped slower than the one of the dry specimens In the elasticity modulus test, for wet specimens, the strain in the preloading stage was smaller than the one of dry specimens. The unrecoverable strain decreased gradually in every loading and unloading. The value of the strain was smaller than the one after the previous loading, but it tended towards stability rapidly. The difference of the two dial gauges was about 10 unit values (1/1000 mm). But after three preloading it became 4 unit values. The above phenomenon was more obvious with the moisture content increasing. For some saturated specimens, vertical cracks developed rapidly after the first crack appeared in the end because the bearing capacity in the end was too low. Finally, the typical crushed zone appeared in the end, as shown in The elasticity modulus can be determined as follows:where Ec denotes the elasticity modulus of concrete (MPa); Fa denotes the load when the stress accounts for 1/3 of the axial compressive strength (kN) and Fo denotes the initial load when the stress is 0.5 MPa (kN), as shown in ; A denotes the bearing area of the specimen (mm2); L denotes the measuring gauge (mm) and Δn denotes the average deformation at both sides of the specimen when loaded from Fo to Fa after the at least twice preloading (mm), which can be calculated by Eq. where εa represents the average deformation on both sides of the specimens under Fa (mm); εo represents the average deformation on both sides of the specimens under Fo (mm). The note point location on the stress–strain curve of concrete is shown in . The values of elasticity modulus should be accurate to 100 MPa.As stipulated in the Building Material Test Annual In this research, the moisture content and the elasticity modulus were calculated on the basis of the experimental results, as summarized in and the relationship between moisture content and elasticity modulus of the specimens cured under the standard conditions was depicted in , it is obvious that higher moisture content gives higher elasticity modulus for the specimens cured under the standard conditions. The elasticity modulus of fully saturated concrete is 33,000 MPa, exceeding the dry concrete and the value of 30,000 MPa stipulated in the Code for Design of Concrete Structure , it is found that under almost similar moisture contents, the average elasticity modulus of the specimens cured under the natural conditions is 30,771 MPa, slightly lower than the one of the specimens cured under the standard conditions. The reason may be the development of micro-cracks in the curing stage.Based on the experimental data, the relation between moisture content and elasticity modulus can be expressed by Eq. where E denotes the modulus of elasticity (MPa), and M denotes the moisture content (%). The regression coefficient (R2) is 0.9992, which indicates that a proportional relation exists between elasticity modulus and moisture content. The test results obtained in this study indicate that the elasticity modulus increases by 7.1% when the moisture content increases by one degree. The moisture gradient during drying may result in non-uniform elasticity modulus, and to an even greater extent, it leads to the change of the stiffness value of specimens. However, for the special case of unconstrained uniaxial tension or compression, Young’s modulus can be thought of as a measure of the stiffness of a material. So it can provide references to the researches of the moisture effect on the static compressive elasticity modulus of the concrete. Therefore, the formula can be used to predict the elasticity modulus of concrete under the same experimental conditions. It can also give a reference for the elasticity modulus of underwater concrete and concrete after immersion or flood to assure the concrete can operate safely under the water. However, whether the results can give guidance to the design of other concrete accurately should be studied further. Besides, according to , the area–volume ratio of specimens has an effect on the moisture content and the elasticity modulus is linked to the dimensions of the specimens. The formula obtained in this paper should also be expanded to the specimens with other different dimensions in further studies.This paper, incorporating the test of moisture content and the relationship between moisture content and elasticity modulus, presents a case study to analyze the influence of moisture content on the elasticity modulus. It is found that:In the case of the same concrete strength grades and curing conditions, the moisture content of specimens increases rapidly with increasing immersion time. The growth pace slows down after 2.5 h and stabilizes after 90 h. Compared with low strength concrete, the moisture content of high strength concrete changes slower. Besides, the growth rate of the moisture content decreases with the area–volume ratio decreasing.As a result of the development of micro-cracks in transition region during drying, the elasticity modulus decreases with the moisture content increasing. And the elasticity modulus is 30% higher for fully saturated concrete than dry concrete.When the moisture contents are almost similar, the elasticity modulus of the specimens cured under the natural conditions reduces slightly, because concrete develops incompletely in the curing stage, leading to the development of micro-cracks.Based on the experimental data and the analytical results, a formula indicating the relationship between moisture content and elasticity modulus of concrete is proposed. It can give a reference for the elasticity modulus of other underwater concrete or concrete after immersion and flood to assure the concrete can operate safely under the water.Contact stress analysis of the anterior tibial post in bi-cruciate stabilized and mobile-bearing posterior stabilized total knee arthroplasty designsIn posterior-stabilized (PS) total knee arthroplasty (TKA), unexpected wear and fracture of the tibial post due to anterior post impingement have been reported. The purpose of this study was to determine the contact stress on the anterior aspect of the tibial post in four contemporary TKA designs. We evaluated one bi-cruciate stabilized design (Journey II) and three mobile-bearing PS designs (Vanguard RP, PFC Sigma RP, and NexGen LPS Mobile). The contact conditions at the anterior aspect of the tibial post were determined upon application of a posterior force of 100 N to individual implants. Each measurement was sequentially performed five times, and the data were compared within and across designs using analysis of variance and a post-hoc test. The contact stress of the Journey II and Vanguard RP was less than the compressive yield stress for polyethylene (10 MPa) at all tested flexion angles and degrees of rotation. The PFC Sigma RP did not show anterior tibial post impingement under any experimental conditions. The NexGen LPS Mobile demonstrated bilateral edge loading at the anterior tibial post and exceeded 10 MPa of contact stress in some test conditions. Thus, the differences among implants in terms of the dimensions of the femoral anterior cam or intercondylar notch and the anterior aspect of the tibial post in the axial and sagittal planes led to significant differences in contact conditions. The present study helps the surgeon to be more aware that various contact conditions of the anterior aspect of the tibial post can occur in individual TKA designs.Posterior-stabilized (PS) total knee arthroplasty (TKA), including fixed-bearing (), has satisfactory long-term results. However, unexpected wear and fracture of the ultra-high-molecular-weight polyethylene tibial post due to anterior tibial post impingement have been reported as complications of the procedure (). Our previous study determined the contact stress at the anterior aspect of the tibial post in three implants for PS TKA () and demonstrated various contact conditions. Meanwhile, other previous studies have demonstrated that anterior tibial post impingement can provide a functional substitute for the anterior cruciate ligament (ACL) to some degree in near-extension of the knee (The Journey II bi-cruciate stabilized (BCS) knee system (Smith & Nephew, Memphis, USA) has a design aimed to maintain the anteroposterior (AP) stability during extension of the knee via the anterior tibial post and femoral anterior cam construct. Several studies have reported that BCS TKA demonstrated in vivo kinematics more similar to the normal knee than the conventional PS TKA (). Although no reports have described the fracture of the tibial post in the short term using BCS designs (), surgeons remain concerned about possible clinical failure of the tibial post in TKA designs with an anterior cam-post mechanism, particularly in young and active patients. However, no studies have reported the contact condition at the anterior aspect of the tibial post for BCS designs.In a previous study demonstrating the contact stress of the post-cam, mobile-bearing PS TKA demonstrated a relatively stable contact location () similar to curve-on-curve fixed-bearing TKA (). Thus, the anterior aspect of the tibial post also may have low contact stress. Mobile-bearing PS TKA designs were developed to increase the contact area on the articular surface and decrease the contact stress of the post-cam (). Like BCS designs, the contact conditions of the anterior aspect of the tibial post in mobile-bearing PS designs have not been previously reported in the literature.The purpose of this study was to determine the contact conditions of the anterior aspect of the tibial post in contemporary TKA implants, including one BCS TKA design and three mobile-bearing PS TKA designs. We investigated whether the design characteristics of the femoral anterior cam or intercondylar notch and the tibial post affect contact area, stress, and contact location at the anterior aspect of the tibial post in TKA. In addition, we evaluated the effect of axial rotation of the tibial insert on the contact stress at the tibial post in the BCS design, as well as whether rotation of the tibial insert affected contact stress in the mobile-bearing PS designs.One BCS implant and three mobile-bearing PS implants were analyzed: (1) the Journey II BCS (Smith & Nephew, Memphis, USA) (size 5 femoral component, size 5 tibial component), (2) the Vanguard RP, PS type, mobile-bearing (Biomet, Bridgend, UK) (size 65-mm femoral component, size 65-mm tibial component), (3) the PFC Sigma RP, PS type, mobile-bearing (DePuy Synthes, Warsaw, IN, USA) (size 3 femoral component, size 3 tibial component), and (4) the NexGen LPS mobile, PS type, mobile-bearing (Zimmer, Warsaw, USA) (size D femoral component, size 4 tibial component) (). In the axial plane, the Journey II has a concave femoral anterior cam and a convex anterior aspect of the tibial post (). The Vanguard RP and the NexGen LPS Mobile designs have a medium radius of curvature of the femoral intercondylar notch. The PFC Sigma RP has a large radius of curvature of the femoral intercondylar notch. According to the manufacturers, the Journey II system was designed to contact between the femoral anterior cam and the anterior aspect of the tibial post from extension to 20° of implant flexion without AP movement of the femoral component. The Vanguard RP, PFC Sigma RP, and NexGen LPS Mobile systems were designed to avoid impingement of the anterior aspect of the post up to 12°, 11°, and 14° of hyperextension, respectively, without AP movement of the femoral component. The configuration of the femoral anterior cam and tibial post is asymmetrical in the Journey II system. By contrast, those of the femoral intercondylar notch and tibial post are symmetrical in the other implants (Vanguard RP, PFC Sigma RP, and NexGen LPS Mobile).The experimental method used in the present study was described previously (). Each femoral component was attached to a fixture that provided flexion-extension, and the tibial insert was mounted onto a parallel-link six-axis actuator. A compressive posterior load of 100 N was applied to the femoral component, parallel to the tibial insert (). A digital electronic stress sensor (K-Scan sensor; Tekscan, Boston, USA) () was placed at the interface between the femoral anterior cam or intercondylar notch and the anterior aspect of the tibial post to measure both contact stress and area (). Measurements were performed at −15°, −10°, −5°, 0°, and 5° of flexion of the femoral component, with neutral rotation of the tibial insert. The Journey II system was additionally evaluated every 5° from 10° to 20° of implant flexion, because of the design concept and the results of in vivo kinematic studies (). Each measurement was sequentially performed five times. The peak contact stress, defined as the highest stress of all the sensing locations, as well as the mean contact stress, and contact area were automatically calculated using Tekscan software. The center of the contact area was also determined. The distance from the bottom of the tibial post to the center of the contact area was defined as the contact location, and the mean contact location divided by the post height was defined as the percentage of contact location. The peak contact stress was then measured again with the tibial component externally rotated by 5° in the three symmetrical implants (Vanguard RP, PFC Sigma RP, and NexGen LPS Mobile). The Journey II system was additionally measured with 5° and 10° internal rotation, based on the classification of the design with the screw-home mechanism as a sharp femoral external rotation from full extension to 15° flexion and internal rotation from 15° flexion to full extension () and the results of rotation in kinematic studies (The contact area, mean and peak contact stress, and contact location were compared across angles of flexion within each design and across the implants at each angle of flexion of the femoral component. The peak contact stress with the tibial insert in neutral position was compared with those in external or internal rotation for each design at each angle of flexion. JMP statistical software (Version 11; SAS Institute, Inc., Cary, USA) was used to analyze the data. Significance was calculated with analysis of variance and a post-hoc test. The threshold for statistical significance was set at p<0.05. Numerical data are expressed as mean values in the results and mean ± standard deviation in the figures.The contact area of the Journey II was a horizontal band on the anterior aspect of the tibial post (). The contact area of the Vanguard RP was an oblique band on the apex of the tibial post. No contact between the anterior aspect of the tibial post and the femoral intercondylar notch occurred at any angle of flexion for the PFC Sigma RP. The contact areas of the NexGen LPS Mobile were located on the medial and lateral anterior corners of the tibial post in the coronal plane. The contact areas of the Journey II, Vanguard RP, and NexGen LPS Mobile systems at each flexion angle are illustrated in . The contact area of the Journey II was significantly larger than that of the Vanguard RP at −5° (p<0.05). Conversely, the contact area of the Vanguard RP was significantly larger than that of the Journey II at −10° (p<0.05). The contact areas of the Journey II and the Vanguard RP did not significantly differ at −15° and 0°. The contact area of the NexGen LPS Mobile was significantly smaller than those of the other three systems at −15°, −10°, −5°, and 0° (p<0.05).The mean contact stress of the Journey II, Vanguard RP, and NexGen LPS Mobile systems at each flexion angle are shown in , and the peak contact stress of those implants are shown in . The mean contact stress for the three TKA designs demonstrated an opposing trend to that for contact area. The peak contact stress ranged from 4.2 to 11.9 MPa; this range was approximately two to three times higher than the range of the mean contact stress for each flexion angle. The Journey II showed the lowest peak stress at −5° and 5°, and the Vanguard RP showed the lowest peak stress at −15°, −10°, and 0°. The peak contact stress of the Journey II and Vanguard RP were less than 10 MPa at all angles of flexion. For the PFC Sigma RP, no contact between the anterior aspect of the tibial post and the femoral intercondylar notch occurred at any angle of flexion. The peak contact stress of the NexGen LPS Mobile exceeded 10 MPa at −10°, −5°, 0°, and 5°.The actual measured value and percentage of contact location for the Journey II, Vanguard RP, and NexGen LPS Mobile systems at each flexion angle are shown in a and b, respectively. For the Journey II, although the contact location shifted upward from −10° of flexion and peaked at 20° of flexion, the percentage of contact location was significantly lower than those of the other designs at −15°, −10°, −5°, 0°, and 5° (p<0.05). The contact location of the Vanguard RP shifted upward from −15° of flexion and peaked at 0° of flexion, and the percentage of contact location at −5° and 0° of flexion were significantly larger than those of the Journey II and NexGen LPS Mobile systems at those flexion angles (p<0.05). The PFC Sigma RP demonstrated no contact at any angle of flexion. For the NexGen LPS Mobile, the contact location was fairly stable at approximately the center of the tibial post.The effect of rotation on the peak stress of the Journey II, Vanguard RP, and NexGen LPS Mobile systems at each flexion angle are shown in . The peak contact stress of the Journey II changed in the range of 1.9 MPa with rotation, and remained less than 10 MPa at all angles of flexion. With 5° of rotation, the mobile-bearing PS designs (Vanguard RP and NexGen LPS Mobile) showed increased peak contact stress up to only 1.0 MPa. For the PFC Sigma RP, contact between the anterior aspect of the tibial post and the femoral intercondylar notch did not occur at any angle of flexion even with 5° of rotation.This study is the first to demonstrate the variation of contact area, stress, and location at the anterior aspect of the tibial post in contemporary TKA implants, including one BCS TKA design and three mobile-bearing PS TKA designs. In our previous study (), all three examined fixed-bearing PS TKA designs exceeded the compressive yield stress for polyethylene (10 MPa) () in some test conditions. However, in the present study less than 10 MPa of stress was observed in all test conditions for the BCS design (Journey II) and one mobile-bearing PS design (Vanguard RP). Regarding rotation, the BCS design with adjustable contracture of the anterior cam-post mechanism was equivalent to the mobile PS designs. For the PFC Sigma RP system, no contact between the anterior tibial post and femoral intercondylar notch was observed at any angle of flexion with neutral or 5° of rotation. The contact areas of the NexGen LPS mobile were located on the anteromedial and anterolateral aspects of the tibial post, and the peak stress exceeded 10 MPa in some test conditions.The Journey II system has a concave femoral anterior cam and convex aspect of the tibial post in the axial plane and a large radius of curvature of the femoral anterior cam in the sagittal plane, and it demonstrated no excessive peak stress at any flexion angle. Although the contact location of the Journey II was more superior at some flexion angles, the percentage of contact location was lowest because of the height of the tibial post. In addition, the Journey II showed no remarkable increase of peak contact stress with internal or external rotation because of the concave-in-convex contracture of the anterior cam-post. The Journey II was designed to replicate some function of both the anterior and posterior cruciate ligaments, and incorporates both anterior and posterior post-cam mechanisms to promote normal kinematics (). Multiple factors are associated with the shear force applied at the anterior tibial post, including alignment and position of the prostheses, knee stability, activity demands, and the location and geometry of the femoral notch and tibial post complex. A clinical study with long-term follow-up is necessary to determine whether the low degree of stress observed under the experimental conditions of the present study may be associated with a decreased risk of failure for the Journey II.In contrast to the Journey II, the Vanguard RP system has a convex femoral intercondylar notch and a concave anterior aspect of the tibial post in the axial plane. When this construction of the anterior tibial post and femoral intercondylar notch has a fixed bearing, contact stress might be increased with 5° rotation. However, the Vanguard RP did not show a remarkable increase of peak contact stress with 5° rotation because of the bearing mobility. The contact location is determined by multiple factors, including the shape, position, and curvature of the femoral intercondylar notch (). The contact area of the Vanguard RP was an oblique band on the anterior aspect of the tibial post due to the asymmetric geometry of the patellar groove of the femoral component. Because of the low height of the post, the percentage of contact location was higher than that of the other implants. Therefore, the shear force can be increased at the anterior aspect of the tibial post (), although the Vanguard RP did not demonstrate significantly greater contact stress.The PFC Sigma RP system demonstrated no contact of the anterior tibial post and femoral intercondylar notch at any angle of flexion, which is consistent with the findings of a previous biomechanical study (). Furthermore, no contact of the anterior aspect of tibial post and the femoral intercondylar notch was exhibited with 5° rotation because the PFC Sigma RP has a mobile-bearing mechanism. Given the findings of this study, abnormal polyethylene wear of the anterior aspect of tibial post may not occur. Although the posterior lip with high articular surface conformity prevents excessive posterior femoral positioning, the absence of anterior post impingement might cause paradoxical tibiofemoral translation during knee extension due to ACL deficiency (). Meanwhile, the incidence of patellar clunk syndrome has been a concern of the PFC Sigma RP system due to the large ratio of length of the femoral intercondylar box to the AP size of the femoral component (). Likewise, the contact areas of the NexGen LPS Mobile were located on the anteromedial and anterolateral aspects of tibial post, and its peak stress exceeded 10 MPa in some test conditions, as also demonstrated in our previous study () of the post, and thus, affecting long-term outcomes of TKA. The intercondylar notch of the femoral component and the anterior aspect of the tibial post should be designed such that they provide a larger contact area and prevent edge loading.The contact conditions were variable in all four designs. Two implants, the Journey II and Vanguard RP, showed less than 10 MPa of stress under all experimental conditions. With respect to contact location, the Journey II was stable compared with the Vanguard RP at the apex of the tibial post. The Journey II has stable contact conditions, with an anterior tibial post and femoral anterior cam construct to replicate the function of the ACL during extension of the knee. Anterior tibial post impingement can occur during daily activities after PS TKA and provides a functional substitute for the ACL to some degree (). However, unintended impingement could lead to sudden change of direction in the AP tibiofemoral translation () with excessive stress at the anterior tibial post (). Meanwhile, the PFC Sigma RP demonstrated no contact in the present study. This finding is related to the observation of paradoxical femoral translation at extension of the knee (The present study has some limitations. First, it is necessary to evaluate the force distribution of the femoral intercondylar notch and the anterior aspect of the tibial post under dynamic loading conditions with ligamentous constraint. It is necessary to consider both the sliding velocity and the contact stress when predicting the need for polyethylene wear (). In addition, the contact forces on the tibial post have been reported to increase to as much as 250 N as the knee is hyperextended (). Thus, surgeons should avoid excessive flexion of the femoral component and posterior slope of the proximal tibial resection. Second, only four implants including one BCS and three mobile-bearing PS TKA designs were evaluated in this study. Although additional TKA designs would be needed for each of the analyzed groups to determine repeatability characteristics of the research material, only the Journey II is now available for BCS TKA knee system in clinical use. Meanwhile, the findings of this study for Vanguard RP, PFC Sigma RP, and NexGen LPS Mobile are not generalizable to other mobile-bearing PS designs. Third, the dimensions of the implants differed for the four TKA designs. However, we used intermediate-sized femoral components and inserts, and we believe that the size differences among the four implants had a minimal effect on the results. Finally, this study concentrates the attention on one of the aspects of implant functionality: contact stresses at the anterior tibial post and disregards the others, e.g., manufacturing methods and durability of the polyethylene insert. Mechanical properties of the fabricated material and potential for long-term oxidation after implantation can influence wear and damage to the tibial post in PS TKA (). Further investigations are needed to evaluate the durability of clinical post wear and the incidence of fractures in a long-term follow-up.In conclusion, the contact conditions were variable for all four contemporary TKA implant designs investigated in this study. The differences among implants in terms of the dimensions of the femoral anterior cam or intercondylar notch and the anterior aspect of the tibial post in the axial and sagittal planes led to significant differences in contact area, peak contact stress, and contact location. The present study helps the surgeon to be more aware that various contact conditions of the anterior aspect of the tibial post can occur in individual TKA designs.Measurement of the critical resolved shear stress for basal slip in magnesium alloys using instrumented indentationThe critical resolved shear stress (CRSS) for basal slip for a range of magnesium alloys was determined using instrumented indentation. Good agreement was observed between the analysis from spherical indenters with different radii and literature results from single crystal tests on Mg-Al alloys. In the case of tests on a Mg-1Zn-0.5Nd alloy, the indentation size effect showed a change in behavior for indenters with a radius of <13 μm. The change in behavior was proposed to be related to the activation of second order pyramidal slip which was confirmed by three-dimensional electron backscatter diffraction-based orientation microscopy (3D-EBSD) analysis.The quantification of the critical resolved shear stress (CRSS) for the different slip and twinning systems in magnesium and its alloys is of fundamental importance to understanding and modelling plasticity in polycrystal magnesium alloys. The seminal work of Burke [] provided early experimental results for the CRSS of basal slip in magnesium. The effect of alloy additions in solid solution on the CRSS for basal slip has also been experimentally measured for a range of alloy additions []. The experimental measurement of the CRSS for basal slip is difficult as it requires the preparation and testing of oriented single crystals. Recently, a combination of density functional theory (DFT) and phenomenological modelling has been employed to predict the CRSS for basal slip for different magnesium alloys []. They found good agreement with the limited experimental data available but point to the need for experimental data on the CRSS for basal slip to validate the theoretical predictions.The difficulty of preparing single crystals has led a number of researchers to examine the possibility of using instrumented indentation to quantify the CRSS for as basal slip and extension twinning []. It has been shown that the stress to activate different deformation modes is influenced by i) indenter shape [], and iii) the crystallographic orientation of the loading axis []. The effect of indenter size has been shown to strongly affect the apparent CRSS for basal slip [] recently conducted a systematic study of the indentation size effect for Mg. In this work, it was shown that yielding commenced by operation of pre-existing dislocations prior to appearance of pop-ins []. The pop-ins were found to be associated with the formation of deformation twins. As such, a simple model based on the strain gradient under the indenter was proposed to describe the relation between the yield stress measured from the indentation stress-strain curve (at 0.2% offset) resolved on the basal slip systems, τindent, as a function of the radius of a spherical indenter, i.e.where τo, Mg is CRSS for movement of basal dislocations in Mg, α is a constant, μ is the shear modulus, b is the magnitude of the Burgers vector, K is constant and R is the radius of the indenter [], the strain gradient is proportional to R−1/2 and the behaviour is assumed to be rate insensitive. The extrapolation of Eq. to an infinitely large indenter gives the CRSS for basal slip, i.e. τindent = τo, Mg.The effect of chemistry on the indentation response has also received some attention []. However, the CRSS values obtained from these experiments are much larger than expected from single crystal experiments and this has been attributed to the indentation size effect []. The goal of the current study is to develop an experimental approach based on using instrumented spherical indentation with indenters of different radius and loading directions to quantify the CRSS for basal slip in polycrystalline magnesium alloys.The materials studied in this work are polycrystalline magnesium alloys, i.e. 99.98 Mg, Mg-1Al, Mg-3Al, Mg-7Al, Mg-1Zn, and Mg-1Zn-0.5Nd (all compositions in wt%). Instrumented indentation tests were conducted using spherical diamond indenters with radii of 1.0, 3.0, 13, 50 and 250 μm. Large grains (approximately 500 μm in diameter) with angles of ≈10°, 50°, and 80° between the loading axis and the c-axis direction were selected. The indentation tests were conducted using an MTS-XP Nanoindentor with a loading rate of 5 mN/s. The zero-load and zero-displacement point was defined using the method of Kalidindi and Pathak []. Standard metallographic techniques were used to polish specimen surfaces followed by a chemical polish using a solution of 10% nitric acid in 90% absolute ethanol for 5 min and then electropolishing in a solution of 20% nitric acid in absolute ethanol at −20 °C at 20–30 V. Following indentation, a Zeiss XB 1540 dual-beam high resolution FEGSEM was used to characterize the 3D microstructure under the indent (note, the details of 3D-EBSD experiments are reported in reference []). After reconstruction of the 3D volume under the indent, the density of geometrically necessary dislocations (GND) was calculated with the post processing software, QUBE [] and as described for indentation of Mg in reference [ illustrates the indentation stress-strain curves of Mg-1Al, Mg-3Al, and Mg-7Al alloys determined from the load-displacement data. The tests have been conducted with a spherical indenter of radius 13 μm where the angle, θ, between the loading axis and the c-axis was varied, i.e. θ = 6–9°, 50–54°, and 78–88° in a, b and c, respectively. The 0.2% offset method was used to characterize the onset of plasticity. For the case of θ = 6–9° (b), there is a distinct deviation from elastic behavior and the indentation yield stress can readily be obtained prior to the first large pop-in. The maximum resolved shear stress at the onset of plasticity on the basal plane, τindent(R = 13 μm) was determined by from the indentation yield stress and the Hertzian contact solution for the stress state under the indenter [], noting that Mg is nearly elastically isotropic []. It was observed that the magnitude of τindent(R = 13 μm) was ≈80–95 MPa (for detailed results, see the on-line supplemental material) which is much higher than the CRSS values measured on single crystals by Akhtar and Teghtsoonian [] (i.e. 0.5–2.5 MPa) due to the indentation size effect. For the cases of θ ≳70°, the maximum RSS for basal slip was less than that for 101¯2112¯0 extension twinning. Given the similarity of the CRSS values for basal slip and extension twinning [], it therefore seems likely that extension twinning is the first deformation mode to occur, consistent with the large stress drop observed at low strains seen in c. As such, the following will only consider cases where θ < 70°, i.e. where plasticity is initiated by basal slip.Additional spherical indentation tests were conducted with radii between 1.0 and 250 μm. show the τindent(R) values plotted as a function of the inverse square root of the indenter radius (see Eq. ) for Mg, Mg-1Al, Mg-3Al, and Mg-7Al, with θ = 6–9° and 50–54°, respectively. The inset in the top right of each figure shows an expanded view of the results near the intercept with the y-axis. The values of the intercept, τo, Mg−xAl, which is the total CRSS for basal slip in a Mg-Al alloy with “x” wt% Al in solid solution, were determined for each alloy by a least squares regression analysis (see ). The total CRSS for basal slip is the sum of the intrinsic friction stress for dislocation motion and the contribution of aluminum in solid solution, i.e.where τo, Mg is the friction stress for basal slip in Mg (i.e. an average of 2.3 MPa taken from the tests with θ = 9 and 54°, as shown in ) and τo, xAl is the contribution to the CRSS from “x” wt% aluminum in solid solution. According to the Labusch model, it is assumed that the solid solution strengthening contribution from aluminum is given by [where c is the solid solution concentration of aluminum in the alloy (wt-%) and K is a constant. The Fleischer model (i.e. solid strengthening proportional to c1/2 []) was also tested and found to give similar results except in the case of 7 wt% Al where Labusch fit better. c plots the results for τo, xAl as a function of c2/3 determined from the current study and the results obtained by Akhtar and Teghtsoonian [] from tensile tests on single crystals of binary Mg-Al alloys. It can be seen that the results obtained from the analysis of the indentation tests are in very good agreement with the results obtained directly from single crystals.The next stage of the research was to apply the above described methodology in order to consider the Mg-1Zn-0.5Nd ternary alloy where there are two elements in solid solution and to the best knowledge of the authors, the solid solution strengthening of Nd has never been characterized. show the results for the dependence of τindent on the indenter radius of the Mg-1Zn and Mg-1Zn-0.5Nd alloys tested at θ = 7–10° and 48–54°. The results for the Mg-1Zn alloy show a linear dependence of τindent on R−1/2 similar to the Mg-Al alloys and the analysis gives a τo, Mg−1Zn value of 3.4 MPa and 4.6 MPa for the tests at 7° and 50°. This is in close agreement with the value of 4.4 MPa from Akhtar and Teghtsoonian's single crystal experiments on a similar alloy []. Using an average values for the friction stress, τo, Mg = 2.3 MPa and τo, Mg−1Zn = 4.0 MPa gives τo,1Zn = 1.7 MPa.On the other hand, it can also be observed that for the case of Mg-1Zn-0.5Nd alloy the plots of τindent versus R−1/2 show two distinct regimes. For the indenters with radii of 13–250 μm, the slope of the plot is similar to that of the Mg-Zn or the Mg-Al alloy. However, at smaller indenter radii of 1 and 3 μm, the magnitude of τindent is much lower than the case of Mg-Zn. To examine the difference between the two alloys, the density of GNDs in the volume under the indenter was calculated based on the local lattice rotations measured by 3D-EBSD. illustrates the 3D distribution of GND densities for <a> basal type dislocations, <a> prismatic edge, and <c + a> type dislocations for Mg and Mg-1Zn-0.5Nd alloys after indentation to a depth of 1500 nm with an indenter of R = 13 μm and the angle of the indentation axis with respect to the [0001] is 54° and 48°, respectively. In , it is noted that the image represents one quarter of the volume under the indent and that the yellow arrow in the top left corner marks the location indentation axis. For the case of Mg shown in a, the GND calculation shows a relatively homogenous distribution of basal dislocations (≈1014–1015 m−2), a lower value for the density of prismatic dislocations and a very low density of <c + a> dislocations, i.e. it is near the resolution limit of the calculation []. This is consistent with the assumption that basal slip is the dominant deformation mode in magnesium for indentation under these conditions. However, d–f illustrate that the situation is very different for the case of the Mg-1Zn-0.5Nd alloy. Here the GND densities for basal, prismatic, and <c + a> slip are higher compared with Mg. In particular, the Mg-1Zn-0.5Nd alloy (f) shows a significant density of pyramidal <c + a> dislocations. It has been reported previously that the addition of rare-earth elements such as Nd (or Yttrium) to Mg facilitates the occurrence <c + a> slip [] although there remains controversy as to the detailed mechanism []. Regardless of the mechanism, the current work is consistent with the observation that Nd facilitates the activity of <c + a> dislocations in the volume under the indent.a, it can be observed that the decrease in the slope of the curve for the Mg-1Zn-0.5Nd alloy occurs as the stress increases above ≈80 MPa. It was shown previously that when θ = 0, the maximum Schmid factors for basal slip and <c + a> slip are 0.375 and 0.45, respectively [] and therefore, after accounting for the different Schmid factors, the τindent(R = 13 μm) for <c + a> slip is ≈95 MPa. Thus, it is proposed that for τindent(R = 13 μm) greater than ≈95 MPa, significant <c + a> slip is initiated at the onset of plastic deformation. The activation of <c + a> slip will allow significant plastic relaxation under the indent, leading to a sharp decrease of the slope of the τindent(R) curve. Although the CRSS of <c + a> slip is significantly higher than that of basal slip, the additional activation of <c + a> slip leads to a reduction in the size effect since basal slip alone is not sufficient to satisfy the Taylor criterion (at least 5 independent slip systems are required to accommodate general plasticity). As long as only basal slip is available, strain accommodation must occur partly by elastic straining which quickly leads to high values of τindent(R) for radii <13 μm and thus show a steep linear dependence of the indentation stress on the inverse square root of the indenter radius as shown in The estimate of ≈95 MPa for the τindent (R = 13 μm) needed to activate <c + a> slip should be viewed as an upper bound given that the indentation size effect has not been accounted for in its determination. To first approximation, the size effect can be accounted for by extrapolating the data for indenters of radius < 13 μm to an infinitely large indenter radius (see the red dashed line in a and b). This results a refined estimate of ≈75 MPa for CRSS for <c + a> (after the correction for different Schmid factors). As such the ratio of the CRSS for <c + a> to basal slip in the Mg-1Zn-0.5Nd alloy (i.e. ≈5–6 MPa) is approximately ≈13–15. This is consistent with previous estimates which have suggested a ratio of CRSS<c+a> / CRSSbasal > 14 was needed to match crystal plasticity simulations on the distribution of local strain in the polycrystalline ZE100 alloys to experiments [Returning to the estimate of Nd solid solution hardening, this can be done using the data from 250, 50 and 13 μm radii indenters which gives an average value of τo, MgZnNd = 5.7 MPa (see ). It is possible to calculate the contribution of Nd, τo,Nd, to the CRSS value of the alloy, τo, MgZnNd, using the appropriate addition for the friction stress and a combination of weak obstacles (Zn and Nd solute atoms), see reference [ and solving for τo,0.5Nd gives a value of 2.9 MPa. To the best knowledge of the authors, this is first measurement of solid solution strengthening of basal slip by Nd.In summary, the current study has demonstrated a new technique based on instrumented indentation using indenters with different radii to measure the CRSS for basal slip experimentally from polycrystalline samples. It was shown that the results are in agreement with the results from single crystals experiments on Mg-Al and Mg-Zn binary solid solution alloys. In the case of a ternary Mg-1Zn-0.5Nd alloy, it was found that size dependence of the RSS showed two regimes. For indenters with a radius > 13 μm, the results were similar to Mg-Al and Mg-Zn binary alloys. However, as the indenter radius decreased, a new regime is entered where <c + a> slip becomes prolific. This was confirmed by the high density of <c + a> dislocations observed using the GND analysis based on 3D-EBSD measurements under an indent in the Mg-Zn-Nd alloy. An estimate of 95 MPa for the CRSS for <c + a> slip was calculated. In principal, the current experimental method could also be extended to i) study the temperature dependence of the CRSS in solid solutions and ii) to precipitation hardening alloys to determine the increase in the basal slip CRSS due to precipitates.Supplementary data to this article can be found online at The influence of adhesive viscosity and elastic modulus on laser spot weld bonding processLaser spot weld bonding (LSWB) is a novel joining technology, which combines laser spot welding with a layer of structural adhesive in a single joint. The purpose of this paper is to investigate the effect of the adhesive properties on the joining process, the peel and the shear strength of the LSWB joints. The present work demonstrates that the adhesive viscosity has great influence on the vaporized adhesive gas exhaust process, and the low viscosity is good for the exhaust process. The mechanical test result shows that the tension–shear load of LSWB joint isn׳t always higher than that of the adhesive bonded joint, and LSWB joint with high elastic modulus of adhesive may get the same tension–shear load as the adhesive bonded joint gets. The reaction zone produced by the carbon diffusion between the adhesive and the metal sheet will influence the mechanism of LSWB joint.Weld bonding is first developed and used by USSR on planes of the type AN-24 A lot of researchers have investigated the influence of adhesive properties on resistance weld bonding (RWB) process, especially the viscosity and the elastic modulus of adhesive. As the technique used in the weld bonding process is the “weld-through” method, the adhesive is applied to the parts first, spot welded and subsequently cured As entrenched as resistance welding is in the weld bonding process The main objective of this study is to investigate the influence of adhesive viscosity and the elastic modulus on LSWB, two different adhesives were used in the experiment. The joining process and the mechanical properties with different adhesives were compared and analyzed.The sheet material employed in the experiment was St33 mild steel. And the chemical composition is shown in The welding equipment used in the experiment was a ROFIN-3000W CO2 laser welding machine. The configuration and dimensions of the welding specimen used throughout the work are shown in . The specimens were prepared by abrading with 150-grid emery paper, degreasing with acetone, drying and storing in a desiccator before weld bonding.Two different structural epoxy resin adhesives were employed in the experiment, shown in . The adhesive with a thickness of 0.1 mm was coated on the overlap area of the sheets. And the thickness of adhesive layer was controlled by a caliper. Then the spot-welded joints were made by laser beam. After the welding was completed, the weld-bonded specimens were cured under a fixed pressure by clamps in order to insure the well contact between adhesive and metal sheet during the curing process. In the present work, the pulsed laser is consisted of two periods with different laser power and pulse duration, as shows. The first pulse is the pre-gasify pulse, and the second one is welding pulse.The polished specimens were etched with a 4 percent Nital reagent and examined by scanning electron microscope (SEM). Two commonly applied methods of destructive testing were used, tension–shear testing and peel testing. The former indicates the maximum shear load that the joint can withstand before joint failure, while the latter is used for observing the shape and size of the torn-out nugget. Both tests were carried out on an INSTRON MODEL1186 testing machine using different tensile rate (3 mm/s in tensile-shear testing, 5 mm/s in peel testing). For comparison, those of adhesive bonded joints, laser spot-welded joints and LSWB joints under the same parameters were assessed. And the destructive test results of the LSWB joints using different adhesives were compared to analyze the influence of adhesive׳s properties.To show the influence of adhesive viscosity on LSWB process, two different adhesives with different viscosity were used at the same laser welding process parameters. illustrate the macrographs of the LSWB process with different adhesive A and B. It is obvious that the LSWB process with adhesive B is unsuccessful, due to lack of adhesive flow during the pre-gasify phase. is the schematic diagram of the LSWB joint in the pre-gasify phase of laser beam. In this phase, the upper-sheet is micro-melting, and then the heat produced by the laser beam transfers to the adhesive layer, causing the adhesive to decompose and transform to gaseity. As the upper-sheet is partially penetrated in this pulse, the adhesive gas can only exhaust through the overlap area, consequently the uncured adhesive layer around welding zone would be pushed out of the overlap area. This process will decrease the pressure of adhesive gas. In another word, the volume and pressure of the vaporized gas around the laser effect zone would be decreased, avoiding the directly percussion on the weld pool.To make it easier to analyze the adhesive flow in the pre-gasify pulse in LSWB, we assumed that the adhesive was affected by the laser beam only at the beginning of pre-gasify pulse, which means the adhesive in the welding zone decomposed completely at the beginning of pre-gasify pulse. Then the adhesive around welding zone was only expelled in the rest of pre-gasify pulse by the adhesive gas. And a model of the interaction between the adhesive gas, the adhesive layer around and the molten pool is shown in The crucial point to get a fine LSWB joint is to make sure that the adhesive gas pressure is smaller than the gravity of the molten pool, which means the molten metal would not be expelled by adhesive gas when the top sheet is penetrated.where Pg represents the pressure of adhesive gas, l0 represents the radius of the adhesive decomposition area at the beginning, l′ represents the distance that adhesive layer expelled, ρ represents the density of molten metal, g represents gravity acceleration, z represents the thickness of metal sheet.We assumed that the force at the interface between the adhesive gas and adhesive layer is in a balance status when the adhesive is pulled out to the distance l′, the equilibrium equationwhere τ represents the internal friction in the unit of adhesive, Patm represents the atmosphere, h represents the thickness of adhesive layer, L represents the length of the adhesive layer, and dθ represents the angle of sampling area.As the viscosity of adhesive meets the Bingham equation,where μ represents the colloidal viscosity, du/dy represents the normal velocity gradient.The μ solution can be obtained from Eqs. the, ρ g, and z are fixed by the metal materials, and the l0 and Δl are fixed by the laser beam parameters. So it can be deduced from Eq. that there is a threshold value of adhesive viscosity in the LSWB process, when the other parameters are fixed. If the viscosity of adhesive is bigger than the threshold value, the adhesive gas cannot exhaust through the adhesive layer, the LSWB process will fail. And it is also clearly that lower adhesive viscosity is beneficial to the stability of the LSWB process.The load–displacement curves obtained by tension–shear tests of the specimens produced by adhesive bonding, laser spot welding and the LSWB are plotted in . It is obvious that two peaks are distinguished in the load–displacement curves of the LSWB specimens using different adhesives. The first one indicates the failure of adhesive bonding area, while the second one means the break of weld joint. The results show that weld-bonded test specimens perform better than the conventional spot welding and the adhesive bonding specimens in terms of the displacement. The LSWB specimens using different adhesives also show differences in the performance. Compared with the traditional adhesive bonding specimen, the LSWB specimen using adhesive A can improve the tension–shear load and displacement, while the LSWB specimen using adhesive B can only improve the displacement.The difference on the mechanical properties of LSWB specimens using different adhesives is very likely related to the elastic modulus of the adhesives. To some extent, the tension–shear load of LSWB specimen is the reactive force to the relative motion between the two metal sheets. The elastic modulus of adhesive will influence the relative motion, and the lower elastic modulus, the bigger relative motion. Then the force load shared by welded part will be higher, due to the significant relative motions, which means the force load shared by adhesive bonded part will be lower. That׳s the reason why the LSWB joint with adhesive A gets higher tension–shear load than the LSWB joint with adhesive B does.The load–displacement curves obtained by peel tests of the specimens produced by adhesive bonding, laser spot welding and the LSWB are plotted in . Compared with the adhesive bonding and the laser spot welding specimens, the LSWB specimen has the highest peel load and the longest displacement. And the process peel test of the LSWB specimen has high similarity to the laser spot welding specimen.In region I, the cracks only concentrate in the adhesive layer. The curve of the LSWB specimen has high similarity to the laser spot welding specimen, which means the adhesive bonded part only shares a little peel load. In region II, the crack propagates to the spot-welded part. Some differences are found in this region between the load–displacement curves of the LSWB specimen using different adhesives. Compared with laser spot welding specimen, the load–displacement curve of LSWB specimen using adhesive B exhibits a plateau, while the other one doesn׳t. It is considerate to be related with the reaction zone which is composed of twinned martensite b and c, due to the carbon diffusion in the LSWB process, and it doesn׳t exist in the laser spot-welded joint shown in a. The twinned martensite is a kind of steel crystalline structure which has very high hardness. It is clearly that the reaction zone in the LSWB using adhesive B is thicker than that in the LSWB using adhesive A. are the fracture morphology and SEM of the different joints. The zone of plastic deformation was found in the fracture surface of laser spot-welded joint (a), indicating ductile fracture mechanism. While in the fracture surface of LSWB joint using adhesive A and B, cleavage fractures were found instead of plastic deformation. It is due to the existence of the reaction zone, which consists of twinned martensite with high hardness, anti-crack capacity of spot-welded joint has been improved. And this phenomenon can explain well that the distinction of the curve tendency of the load–displacement curve using different adhesives.The stability of LSWB joining process is related to the viscosity of adhesive. There is a threshold value of adhesive viscosity in the LSWB process. If the viscosity of adhesive is bigger than the threshold value, the adhesive gas cannot exhaust through the adhesive layer, the LSWB process will fail. And it is also clearly that lower adhesive viscosity is beneficial to the stability of the LSWB process.Compared with traditional laser spot welding and adhesive bonding specimen, the tensile-shear properties of the LSWB specimen has been improved a lot. The increasing range is related to the adhesive elastic modulus, and the range is increased with the decline of the adhesive elastic modulus.The peel tests of the LSWB specimens using different adhesive show that the peak load of the LSWB specimen is bigger than that of the laser spot-welded specimen or the adhesive bonded specimen. And the thickness of the reaction zone will influence the peak load of the LSWB specimen.Observation and quantification of the fracture process zone for two magnesia refractories with different brittlenessIn this paper, the formation of the fracture process zone (FPZ) of industrially produced magnesia spinel and magnesia refractories was analysed using digital image correlation (DIC). Compared to pure magnesia materials, the magnesia spinel materials exhibited a higher amount of microcracks, causing a larger FPZ. A critical displacement, where the cohesive stress between the crack faces decreases to zero, is determined by analysing the development of the localized zone. Critical displacement determined from the changes of the FPZ width and length is used to determine the onset of macro-cracking and locate the crack tip. The development of the fracture process zone for a magnesia spinel initiates before reaching the maximum load, and the onset of the macro-crack is in the post-peak region. The FPZ size increases until the formation of a macro-crack takes place, but decreases afterwards. For the magnesia refractory, no pronounced FPZ could be detected.Refractories are heterogeneous materials consisting of grains and fines. When containing pre-existing microcracks, refractory materials exhibit pronounced deviations from pure linear elastic mechanical behaviour shows the stress-strain relationship within the elastic and quasi-plastic zones ((a)) and the stress-strain relationship within the process zone (According to Hillerborg et al., the fracture process zone (FPZ) is defined as the region ahead of the traction free crack tip (a)). The frontal process zone is especially composed of distributed microcracks. In the process wake, stress is still transferred between the faces of an already localized crack. Phenomena such as grain bridging and interlocking may be responsible for the load transfer. In this work, the FPZ will be identified and depicted without distinguishing between the frontal process zone and the process wake. The definition of the FPZ as quoted above was first applied for concrete, a material showing several similarities to refractories (a)). The transition between microcrack and macro-crack, which is a prerequisite to determine the FPZ length and crack length, is important for the study of fracture process. Several different methods have been adopted to determine the onset of macro-cracking. Zechner et al. used a tension test to determine the ultimate displacement Until now, various techniques, such as scanning electron microscopy In the domain of refractory materials, DIC has been already used in some fracture studies, i.e. for a MgO-based refractory castable To investigate the influence of brittleness and microstructure on the fracture process, two typical refractory materials were selected: pure magnesia (M) and magnesia spinel (MA). The chemical compositions and properties of these two materials are shown in . The two materials investigated in this research work are commercial products manufactured by RHI AG according to ISO 10081-2.An example of the microstructure of magnesia and magnesia spinel materials are shown in (a) exhibits that the magnesia product is composed of magnesia aggregates (inferior to 4 mm) in a magnesia matrix. In magnesia spinel bricks, the inclusions are magnesium aluminate spinel grains (MgAl2O4). The magnesia spinel material is composed of spinel aggregates with a grain size between 3 to 5 mm, magnesia aggregates (grain size inferior to 4 mm) and the magnesia matrix. Due to the mismatch in the thermal expansion coefficients between magnesia (αMgO |
≈ 13 × 10−6 |
K−1) and spinel (αMgAl2O4 |
≈ 9 × 10−6 |
K−1), the microcracks are formed around the spinel inclusions during the cooling stage of the firing process of magnesia spinel materials The wedge splitting test (WST) has already been frequently applied to study the fracture behaviour of brittle or quasi-brittle materials. This test was firstly proposed by Tschegg in 1986 (a). Due to a low ratio of specimen volume to fracture area and the reduction of the elastic energy stored in the testing machine by the action of the wedge, the WST is a convenient testing method which enables a stable crack propagation for rather brittle materials. This was proved by Harmuth et al. The vertical force (FV) is measured by a load cell. The horizontal force (FH) is calculated from FV using Eq. Here β is the wedge angle, which is 10° in this study. The WST is a displacement controlled test and was carried out with a loading velocity of 0.5 mm/min, measured in the vertical direction. The horizontal displacement was measured by video extensometer. A load-displacement curve was generated, and the fracture mechanical parameters of refractories can be determined from these data.The specific fracture energy GF is determined by integrating the area under the load-displacement curve divided by the projected fracture area A during stable crack propagation, as shown in Eq. Here δH is the horizontal displacement and δult is the ultimate displacement.The nominal notch tensile strength σNT can be calculated from the maximum horizontal load FH,max using:Here b and h are the width and the height of the ligament, respectively. The vertical distance from the load vector to the centre of the ligament is denoted by y. The nominal notch tensile strength adds both the tensile stress and the flexural stress.A CMOS digital camera with a resolution of 5184 × 3456 pixels2 is used to record the images during the wedge splitting test. The image acquisition set-up is shown in (b). The scale factor is 0.03 mm/pixel. The MatchID DIC-2D software by University of Leuven is used to analyse the results. The DIC technique has already been developed and used by many researchers in different scientific domains The correlation process is performed for the zone of interest (ZOI), as shown in (a). The correlation algorithm locates a subset in the reference image and searches the same subset in the images of the deformed sample. The step size is the distance between the centre points of two consecutive subsets. The strain field is then calculated from the displacement field based on the strain window algorithm shows the results of the wedge splitting tests for pure magnesia and magnesia spinel. The maximum load for magnesia is 1384 N and is reduced to 499 N for magnesia spinel due to pre-exiting microcracks. The influence of the pre-exiting microcracks, which are induced by the spinel inclusions during the production process, was for example investigated by Gruber et al. shows the maximum vertical force Fv,max, notch tensile strength σNT, tensile strength σt, specific fracture energy GF and characteristic length lch for both materials. Here, the maximum vertical force is obtained directly from the experimental curve and the nominal notch tensile strength is calculated by Eq. . The tensile strength and total specific fracture energy are not evaluated directly from the load-displacement curve, but were obtained by an inverse evaluation technique proposed by Jin et al. , the characteristic length lch is used to represent the brittleness according to Hillerborg et al. Here E is the Young’s Modulus and σt is the tensile strength. The lower lch is, the more brittle the material is. The quantity of lch is equal to twice the thermal shock resistance parameter R′′′′ according to Hasselman Energy dissipation processes occur in the process zone ahead of the macro-crack. In this work, strain is used as an indicator to define the fracture process zone. The FPZ is characterized as the area where the strain lies between a lower and an upper limit. Here will show how these limits are defined and determined.Due to the numerical correlation and interpolation algorithms uncertainty and image distortion, the DIC evaluated strains show some scatter. The lower limit of strain is determined in the following way: ten references images representing the ZOI are evaluated with respect to the strain for the undeformed specimen. Resulting strains are due to the scatter mentioned above. From this scatter, a threshold in the X direction (εxx) of 4.5 × 10−4 was obtained and values exceeding this lower limit are significant to the fracture process. It should be noted that this threshold is larger than the ultimate elastic strain calculated by the ratio of σt/E, where E is the Young’s elastic modulus. Therefore, a pure elastic deformation will not exceed the threshold. The area bordered by the lower limit εxx |
= 4.5 × 10−4 is called the localized zone here. It includes both the FPZ and possible further macro-crack. shows the strains in the horizontal direction at different loading stages for pure magnesia (a) and magnesia spinel (b). The strain below the threshold is coloured grey. If a slightly higher threshold value is adjusted (for instance, 5%), the localized zone dimension (width and length) will not be influenced according to the investigation. Magnesia spinel exhibits crack branching. The local microstructures govern the actual crack propagating crack patterns and its branching. With our camera resolution of 5184 × 3456 pixels2 and for the industrial sample characterized here, the FPZ is small and crack branching is not observed for the magnesia material. Due to the addition of spinel in the volume, magnesia spinel material shows a reduced brittleness () and a larger FPZ. A similar phenomenon was observed for fibre reinforced concrete structure To further evaluate the upper limit of strain used to characterize the transition between macro-cracking and FPZ, the maximum length and width of the localized zone were evaluated (). Lm is defined as the maximum length of the localized zone for each loading stage while wm is the maximum width.The parameters Lm, wm and crack mouth opening displacement (CMOD) were determined for different loading stages. shows the evolution of Lm and wm for magnesia spinel. Lm increases with the CMOD and wm first increases and subsequently decreases after reaching a certain CMOD. With the chosen parameters resulting in the threshold value above, the fracture process zone starts to develop at 82% of the maximum load (P1 in (b)). The main part of the process zone continues developing until reaching a CMOD of 0.07 mm. Between a CMOD of 0.07-0.144 mm, the increase is small. For a CMOD higher than 0.144 mm, further increases of Lm are even smaller and wm decreases. The development of both parameters, Lm and wm, indicates the onset of macro-cracking in the moment where CMOD equals 0.144 mm (66% post-peak, P6 in (b)): then wm shows a maximum and the increase of Lm is nearly saturated. The displacement and strain measured in front of the initial notch tip at this moment are the critical separation and critical strain component. Then, the critical separation ucr is 0.144 mm and the critical strain component in X-direction εcr of magnesia spinel is 0.05. This strain was called tensile strain capacity by some researchers , the fracture process can be divided into two stages. The first stage comprises the initiation and development of new microcracks, and the propagation of already existing microcracks in the virgin material. This includes localization of at least one microcrack that still transfers stresses between its faces. Energy is dissipated due to the fracture process zone development. In this stage, the fracture process zone is already developed to a large part. The second stage is the initiation and propagation of the macro-crack. During this second stage, further extension of Lm is only 15% of the final localized zone length and the FPZ size even decreases due to the closure of microcracks and the unloading caused by the macro-crack propagation. When the macro-crack starts to extend, less energy is consumed for further development of the fracture process zone.It was assumed that macro-crack of pure magnesia is localized at the maximum load. Then, the critical strain εcr of the magnesia material was identified to be 3 × 10−3 by DIC. All of the regions in the photographs in where the local strain equals to or exceeds the critical strain are coloured black. This clearly shows the defined crack tip and the crack length. shows the different fracture behaviour for pure magnesia (a) and magnesia spinel (b). The magnesia spinel exhibits a higher ultimate CMOD compared to pure magnesia. The difference between the localized zone length Lm and crack extension a is denoted as the fracture process zone length here and indicates the development of the FPZ and its size. Pure magnesia shows a very small FPZ, but in magnesia spinel, a significant FPZ is developed compared to the specimen size. The FPZ of magnesia spinel develops prior to reaching the maximum load and increases with the load as long as the macro-crack does not propagate. With the extension of the macro-crack, the FPZ decreases. Because of the higher brittleness of pure magnesia, both Lm and an increase rapidly. The initiation and propagation of the macro-crack are assumed to take place at the maximum load. When the FPZ tip reaches the compressive zone induced by the linear support of the WST, the crack propagation slows down. By comparing the crack length curves in (a) and (b), it shows that the magnesia spinel has a higher CMOD tolerance: for the same CMOD, the crack propagation in the magnesia spinel specimen is shorter. Even when the strength of the magnesia spinel is lower than the strength of the magnesia material, the development of the FPZ consumes a higher amount of fracture energy ( shows the process zone for both materials at the moment of their maximum extension: the maximum FPZ length is approximately 12 mm for magnesia and 55 mm for magnesia spinel. A comparison clearly shows that a large part of the specimen volume contributes to energy consumption for the magnesia spinel material, whereas this is not the case for pure magnesia with the resolution used in this evaluation.The horizontal displacement u is measured at different loading stages in the ZOI to further illustrate the fracture process for magnesia spinel refractories. It is assumed that the horizontal displacement field is symmetrical. Twelve equally spaced lines are arranged along the ZOI vertical axis for a displacement measurement at the selected loading stages. The locations are illustrated in (a). Displacements measured between the end points of the lines are shown in (a). Here, the outer black square is the ZOI for the DIC evaluation. The (b) shows the results. The vertical dashed lines symbolize the critical separation ucr for the magnesia spinel specimen, which is 0.144 mm. When the horizontal displacement u equals or exceeds ucr, the macro-crack forms. When u is smaller than ucr, no traction-free macro-crack exists, only the fracture process zone. As shown in (b), the height of the FPZ (hFPZ) at P8 in (b) is 39 mm. This is defined as the vertical dimension of the FPZ. As the loading stage transitios from P8 to P10, the macro-crack extends and the hFPZ decreases to 20 mm.The variation in the FPZ height is plotted versus crack extension in (b)), hFPZ increases and reaches the maximum value at P6 (47 mm). From P6 to P11, the macro-crack length an increases and hFPZ decreases.The fracture behaviour of two typical industrially produced refractory ceramics was investigated in this work. The microcrack network already present in virgin magnesia spinel supports the formation of a fracture process zone, and consequently, the material behaves less brittle than the pure magnesia refractory. The mechanical properties measured by the wedge splitting test indicate a reduction in strength and an increase in fracture energy. The development of the fracture process zone in the magnesia spinel material is rather energy consuming even with the reduced tensile strength. The special microstructure characterized by pre-existing microcracks increases the strain bearing capacity, which is very important for improving the thermal shock resistance of refractories.For pure magnesia, no pronounced fracture process zone could be detected. Crack propagation occurs immediately after reaching the maximum load. For magnesia spinel, the FPZ development starts in the pre-peak region. This phenomenon contributes to the deviation from pure linear elastic mechanical behaviour. The fracture process for magnesia spinel is characterized by the development of the fracture process zone and the subsequent development of the macro-crack. The transition is indicated by the dimensions of the FPZ. Due to the closure of the microcracks and propagation of the macro-crack, the FPZ width and height both decrease. The onset of the macro-crack is in the post-peak region when the load has already decreased to 66% of the maximum value. The fracture process zone of magnesia spinel contributes to the large post-peak region, stable crack propagation and high strain tolerance before failure. All of these properties represent lower material brittleness., brittleness reduction by the addition of spinel to a magnesia refractory is achieved by a strength decrease, even as the specific fracture energy increases. More precisely, the strength and quantity σt2/E decreases, which is proportional to Irwin’s crack extension force. One question that arises is why a strength decrease is not associated with a decrease of the specific fracture energy and what would be expected for a pure linear elastic material. The large increase of the FPZ answers this question. Processes, such as crack branching as well as the friction and interlocking of the crack faces, become dominant and manage to even increase the specific fracture energy. The visual representation of the FPZ using DIC illustrates the deviation from pure linear elastic fracture behaviour and the brittleness reduction achieved.Suppression of edge cracking and improvement of ductility in high borated stainless steel composite plate fabricated by hot-roll-bondingIn the nuclear fuel reprocessing systems, the demands for high borated stainless steels are increasing due to their excellent thermal neutron shielding properties. However, the eutectic borides precipitating around the matrix grains could easily result in the severe edge cracking for the ingot-casting steels during processing. In this paper, a 3-layered composite plate consisting of 2.1 wt% B stainless steel and boron-free austenite steel was fabricated by welding and hot-roll-bonding. Besides, the microstructure evolution and the tensile properties of the composite and non-composite plates were comparatively investigated. It was found that the edge cracking of the composite plate was significantly suppressed comparing with the non-composite plate prepared by conventional hot rolling. Moreover, the ductility of the composite plate at room-temperature was greatly enhanced. The tensile elongation reached to 15.5% for the specimen after 1100 °C × 30 min solution treatment, and that was approximate 2.5 times as high as the elongation of the non-composite specimen. In addition, the inhibition mechanism of edge cracking during hot-roll-bonding, and the enhancement mechanism of tensile plasticity for the composite plates were both explained. The present work not only develops a new high borated stainless steel with the excellent mechanical properties, but also provides a promising method to suppress the edge cracking for some other metallic materials with poor hot workability.High borated stainless steels are widely used as the functional materials for the containers to store and transport spent nuclear fuel in the nuclear fuel reprocessing systems because of their excellent thermal neutron absorption properties Powder metallurgy (PM) is widely used to fabricate the borated stainless steels. The fine and dispersed borides in the PM steels could contribute to the improved workability and enhanced mechanical properties In this paper, a sandwich composite plate consisting of 2.1 wt% B borated stainless steel and boron-free austenite steel clad layers was trial-fabricated by hot-roll-bonding. The microstructure evolution, edge cracking and mechanical properties of the non-composite plate and composite plates were comparatively investigated in detail. The research results showed that the edge cracking of high borated stainless steel could be significantly suppressed during hot rolling. Moreover, the ductility at room temperature was remarkably enhanced for the composite plate. In addition, the inhibition mechanism of edge cracking and the enhancement mechanism of tensile plasticity for the composite plate were both revealed. It is of great significance to examine the suppression of edge cracking and the improvement of ductility in high borated stainless steel composite plates, and these are the main aims of the present paper.The investigated 2.1 wt% B stainless steel was melted and refined by a 40 kg vacuum induction melting furnace, then the molten steel was poured into a steel mold to produce a 60-mm-thick ingot. A square billet was cut from the ingot and then directly hot rolled. Another billet with the same size was used as the core of the sandwich composite billet and cladded by two billets of boron-free austenite stainless steel. The chemical compositions of different billets were listed in shows the preparation of the composite plate. The contact surfaces of core and clad billets were first ground, polished and then wiped with acetone and ethyl alcohol. The final thickness of the surface-treated core and clad billets were 57 mm and 9.5 mm, respectively. After that, two Φ5 mm 304SS tubes were welded at the sides of contacting surfaces between the core and clad layers. Afterwards, the argon-arc welding was performed along the sides of the contact surfaces until the end of the tube. A vacuum pump was used to pump out the air between the adjacent layers until the atmospheric pressure was below 10 Pa, and then the tube was heat-sealed to avoid oxygen penetration. Hence, a 3-layered sandwich composite billet with a total thickness of 76 mm and a stacking ratio of 1:6:1 was prepared. After being homogenized at 1130 °C for 30 min, both the non-composite and sandwich billets were rolled to 5.5 mm in 6 passes at a rolling speed of 1.2 m·s−1 by a Φ400 mm hot rolling mill. The initial and finishing rolling temperature was controlled to be around 1110 °C and 1000 °C, respectively. Following rolling, these hot rolled plates were cooled in the air. Subsequently, a part of the hot rolled specimens were conducted to solution treatment at 1000 °C and 1100 °C for 30 min respectively under argon atmosphere, and then followed by water quenching.The mechanical polishing surfaces of the specimens for microstructure observation were etched in a solution of 20 ml hydrochloric acid, 20 ml ethyl alcohol and 1.0 g CuCl2. The samples for Electron back-scattered diffraction (EBSD) examination were chemically polished in a solution of 10 vol% HClO4 and 70 vol% C2H5OH. The metallographic microstructure was observed by a Leica DM2500M optical microscope (OM). The concentration maps and the secondary electron microscopy were analyzed by a JEOL JXA-8530F Electro-Probe Micro-analyzer (EPMA) equipped with a wavelength dispersive X–ray (WDX) analysis. The fracture morphologies and the crystal orientation maps of the tensile specimens were obtained by a Zeiss Ultra 55 scanning electron microscope (SEM) equipped with an EBSD system.The appearance of the hot rolled composite and non-composite plates is shown in . The maximum length of the edge cracks along the transverse direction for the non-composite plate was about 21 mm. As for the composite plate, only a few short edge cracks with a length less than 7.0 mm were observed. There were even some crack-free regions along the edges for the composite plate. It could be concluded that the edge cracking of 2.1 wt% B stainless steel could be effectively restrained via hot-roll-bonding.The through-thickness photograph of the hot rolled composite plate is shown in . The thickness of the core layer and each clad layer was 4.20 mm and 0.65 mm, respectively. Besides, the defects such as cavities or avulsion were not observed along the interfaces between the core and clad layers, demonstrating that the 2.1 wt% B stainless steel could be effectively bonded with the boron-free austenite steel layers by hot-roll-bonding. shows the EPMA images of the as-cast 2.1 wt% B stainless steel. The solidification microstructure was characterized by the equiaxed austenite grains and bulk network-like structures, as shown in a. According to the elements concentration maps (b–f), these Cr-B-Fe-rich and Ni-Mn-depleted structures around the austenite grains were identified as the eutectic (Cr, Fe)2B type borides. shows the microstructure of the non-composite plate and the core layer in composite plate after hot rolling and solution treatment. As shown, the original bulk eutectic borides in the as-cast ingot were broken into the bar-shaped and granular particles after hot rolling. The average size of borides in the core layer of the composite plate was a little smaller than that in the non-composite plate due to the slightly larger reduction. The majority of the bar-shaped borides were 22–24 µm long in the core layer of the composite plate, while these borides in the non-composite plate were 23–26 µm. Further, it should be noted that the morphology and distribution of the borides were hardly changed after solution treatment due to their excellent thermal stability. exhibit the microstructure around the interfaces in the composite plate. It should be noted that the interface was quite clear to be seen in the hot rolled specimen, however, a 35-μm-thick transition region existed between the core and clad layers after solution treatment. Lots of the fine and dispersed (Cr,Fe)2B particles with the diameter below 2.0 µm were observed in this region. Further, both of the number and the size of borides decreased with the increasing distance from the interface. further revealed the microstructure around the transition regions. It was found that the core layers were characterized by the fine structure both before and after solution treatment. By contrast, the significant grain-coarsening occurred in the clad layers during solution treatment. the average diameter of grains was 9.5 µm in the hot rolled specimen, while the grain diameter increased to 112 µm after 1100 °C × 30 min solution treatment. Additionally, it was worth mentioning that the transition region was characterized by the medium-sized austenite grains of 14.5 µm and the fine borides (b, c). It could be inferred that the grain boundaries provided the diffusion channels for the boron atoms from the boron-oversaturated core layer into the boron-free clad layers during solution treatment. The new fine (Cr,Fe)2B particles would precipitate at the austenite grains boundaries (c). Consequently, the grain-coarsening was inhibited due to the pinning effect of the new fine borides during solution treatment, resulting in the existence of the transition regions after solution treatment.The tensile curves of the composite and non-composite specimens are shown in . The yield strength (YS) and ultimate tensile strength (UTS) of the solution-treated non-composite specimens were 242 MPa and 645 MPa, respectively. Due to the combination of the hard 2.1 wt% B stainless steel and the relatively soft clad layers, the YS and UTS of the composite specimens were lower than that of the non-composite specimens and decreased with the increase of the solution-treated temperature. In the case of the 1100 °C × 30 min solution-treated composite specimen, its YS and UTS were 205 MPa and 554 MPa, respectively. Moreover, it was worth mentioning that the composite specimens presented more excellent ductility than the non-composite specimens. As for the non-composite specimens, the engineering strain was less than 7.0%. Besides, the solution treatment had no significant effect on the tensile plasticity of the non-composite specimens. In contrast, the engineering strain of the composite specimens ranged from 10.5% to 15.5%. It should be noted that the tensile elongation could be further enhanced after solution treatment for the composite plates. The engineering strain of the 1100 °C × 30 min solution-treated specimen even reached to 15.5%. Besides, the strength-ductility balance was over 8500 MPa% which was close to the upper limit of the 2.1 wt% B Markomet 1120 alloy . The higher strength-ductility balance indicated the better capacity of absorbing the impact energy, suggesting that the composite plates would be much safer than the non-composite plates under impaction. shows the fracture profile and morphology of the non-composite tensile specimens. A very small reduction of area was observed in the hot-rolled specimen (a). For the solution-treated specimen, the reduction of area slightly increased in comparison with the hot rolled specimen (c). Besides, two kinds of fracture modes (i.e. brittle cleavage fracture for the borides and ductile fracture for the austenite matrix) were identified in the non-composite plates according to the broken borides and the dimples observed in (a, e), the fracture profile of the composite specimens was different from that of the non-composite plates. Specifically, the clad layers were characterized by the large reduction of area after fracture. It could also be inferred that the brittle core layer fractured prior to the soft ductile clad layers. Besides, the delamination and cracks were not observed between the core layer and the clad layers (a, b, e, f), further demonstrating the strong bonding interfaces in the hot rolled and solution-treated composite plates. According to the micro-morphology shown in (c, g), it could be concluded that the fracture modes of the core layers were similar to that of the non-composite specimens. In contrast, the shallow dimples shown in (d, h) not only indicated the ductile fracture mode for the clad layers, but also suggested that the cracks propagated swiftly from the brittle core layer to the ductile clad layers at the end period of tensile deformation. That was in accordance with the tensile cures of the composite specimens () which showed almost no sign of dropping at the end of strain. In addition, the larger and deeper dimples in the clad layers were mainly related to the larger grain size after solution treatment (The stress states in different locations of the core layer during hot rolling are schematically shown in . Basically, the inner part of the core layer located in tri-axial compressive stress zone, however, the edges located in a different zone where was under uniaxial compressive stress in Z direction and uniaxial tensile stress in X direction. In the inner parts, although numerous brittle borides would be crushed during hot rolling, the cavities initiated around them could be healed by the plastic flow of austenite under the tri-axial compressive stress (). In contrast, the cavities at the edges would be further promoted under the tensile stress in X direction. Consequently, the nucleation, aggregation and extension of the cracks could easily occur at the edges of core layer. schematically shows the inhibition mechanism of edge cracking for the composite plate during hot rolling. As the large thickness ratio of the core and clad layer (6:1), the lateral spread of the core layer was larger than that of clad layers at the early stage of hot rolling. It could be inferred that the lateral spread part of the core layer could not be covered and bonded by the clad layers (a). As a result, the edge cracks would propagate under the tensile stress (σx) in further deformation (b). Afterwards, when the cracks extended into the internal parts where were covered and bonded by the clad layers, the additional compressive stress (Fc) would be induced due to the restriction of clad layers, as show in c. Besides, the tensile stress (σx) could be compensated to a certain extent. Hence the edge cracks of the 2.1 wt% B stainless steel were effectively suppressed by composite rolling (As shown, the engineering strain of the composite plates especially the solution-treated specimens significantly surpassed that of the non-composite plates (). The main mechanism on this attractive phenomenon was analyzed from the point of geometrical restriction which mainly included the delay of necking for the brittle 2.1 wt% B stainless steel layer during tensile deformation schematically illustrates the enhancement mechanism of tensile elongation for the composite plate. During the tensile test, the core and the clad layers elongated uniformly and synchronously at the early stage. Specifically, plastic flow occurred in the matrix austenite grains of the 2.1 wt% B stainless steel layer, the shear stress would gradually transfer and concentrate around the borides since the brittle borides could hardly deform. Hence the cracks would be easily initiated in the large-sized borides, as shown in . It could be inferred that the core layer would reach to its ultimate strain ahead of the clad layers at the end of the uniform deformation stage. When the potential necking tended to be initiated in the brittle core layer, the elongation of the core layer would immediately increase, and the cross-sectional area would decrease faster than that of the ductile clad layers. However, as a result of the geometrical restriction provided by the clad layers, the additional tension stress would increase inside the clad layers to compensate the lacking strain along the tensile direction. Meanwhile, additional compressive stress would arise in the core layer, thus effectively restricting the necking. Consequently, the composite specimens exhibited much higher elongation than the non-composite specimens.To further examine this inference, the microstructure and the strain hardening behavior of the boron-free clad layers were further analyzed. On one hand, for the composite plate, the strong bonding interfaces were obtained after hot rolling. The bonding strength could be further enhanced due to the formation of the transition regions between the core and clad layers after solution treatment (). Besides, the deformation compatibility of the core and clad layers could be also improved during tensile deformation. On the other hand, the formation of more austenite twins was favorable to increase the strain hardening rate of the clad layers. Based on the results in , more annealing and deformation twins were observed in the clad layers of the solution-treated specimens. Obviously, the number fractions of twin boundaries increased with the increasing solution-treated temperature (1000–1100 °C). The capacity of delaying the necking of the brittle core layer would be further improved for the clad layers with the sufficient strain hardening rate. For the above reasons, the solution-treated specimens exhibited much enhanced ductility in tensile test (). These results were consistent with the previous literatures and further demonstrated the inference in their researches In this paper, a 3-layered composite plate of 2.1 wt% B stainless steel was fabricated by hot-roll-bonding. By contrast, a non-composite plate was prepared by conventional hot rolling. The aim of present work was to comparatively investigate the edge cracking and the mechanical properties for these plates. The main findings are summarized as follows:In comparison with the severe edge cracking of the non-composite plate, the edge cracking of the composite plate could be effectively suppressed by hot-roll-bonding.The boron atoms diffused from the core layer to the boron-free clad layers, then formed as the new fine (Cr,Fe)2B particles at the austenite grains boundaries, inhibiting the grain coarsening during solution treatment. The transition regions were characterized by the medium-sized austenite grains and a few fine borides between the core and clad layers after solution treatment.The transition regions between the core and clad layers could not only contribute to the enhancement of the interfacial bonding strength, but also improve the deformation compatibility of the core and clad layers during tension test.The solution-treated composite specimens exhibited more excellent plasticity than the non-composite specimens due to the geometrical restriction provided by the ductile clad layers during tensile deformation. The potential necking of core layer could be effectively suppressed by the clad layers with sufficient work-hardening capacity through the medium-grain-sized transition regions.The high borated stainless steel with an excellent combination of functional and ductility indicated that the hot-roll-bonding technology could be a promising method to fabricate some other types of metallic materials which had poor workability or mechanical properties.Role of partially amorphous structure and alloying elements on the corrosion behavior of Mg–Zn–Ca bulk metallic glass for biomedical applicationsMetallic glasses have emerged as promising biodegradable materials due to their excellent corrosion resistance properties. However, processing constraints for achieving desired section thickness have limited their real world applications. This study involves the development of partially amorphous bio-compatible and bio-degradable Mg66Zn30Ca4 and Mg60Zn35Ca5 alloys with adequate section thickness for bio-medical components. The corrosion rates of these alloys are analyzed through in-vitro corrosion studies. The combined contributions of the amorphous structure and alloying elements have been used to explain their corrosion behaviors.Bio-materials have matured from non-biodegradable to bio-degradable over the last three decades. In recent years, Magnesium based alloys for the bio-implant applications, have gained considerable appreciation Metallic glasses are more commonly produced through rapid solidification techniques. Contemporary processing routes for metallic glass formation include solid state processes (i.e. mechanical alloying/milling) and liquid state processes (i.e. melt spinning, copper mold induction melting). High cooling rates, in the order 106 |
K/s associated with the rapid solidification process arrest solid state diffusion, which enables to retain the chemical homogeneity of liquid structure The electrochemical measurements based corrosion investigations, performed previously on the Mg–Zn–Ca metallic glasses The aim of the work is to elucidate the influence of amorphous structure and chemical composition on the in-vitro corrosion behavior of Mg66Zn30Ca4 and Mg60Zn35Ca5 alloys which are suitable for biodegradable implant applications. According to the authors previous work, thermodynamic predictions of glass forming alloy based on GCEA mixture of pure Mg (99.9%), pure Zn (99.9%) and binary Mg–30Ca master alloys was melted in a controlled environment of Argon and SF6 gas atmosphere to prepare amorphous alloys with a nominal composition of Mg66Zn30Ca4 and Mg60Zn35Ca5. The melted alloy was injected into a wedge shaped, air-cooled copper mold. The amorphous behavior in these alloys was inspected by X-ray diffraction using Cu-Kα radiation (X'PERT 3 PANalytical, Netherland). A slow scanning speed of order 0.5°min− 1 was employed. Percentage of crystallinity in the samples was identified using software (X'Pert High Score). The crystallization behavior in Mg–Zn–Ca amorphous alloys with respect to temperature was studied using a differential scanning calorimetry (DSC) (Netzsch, STA 449F3, Germany). The DSC scan was carried out at a constant heating rate of 10 K min− 1, under continuously purged nitrogen environment.Partially amorphous (8 mm) and fully crystalline samples (22 mm) of both Mg66Zn30Ca4 and Mg60Zn35Ca5 compositions were used for the biocorrosion studies. The sample surfaces were ground with SiC emery papers and finely polished to a mirror finish in the disc polisher. Ultrasonic cleaning was done with ethanol for 5 min, followed by drying in air. To replicate a real time human body serum, simulated body fluid (SBF) (8.035 g of NaCl, 0.355 g of NaHCO3, 0.225 g of KCl, 0.231 g of K2HPO4. 3H2O, 0.311 g of MgCl2.6H2O, 39 ml of 1.0 M HCl, 0.292 g of CaCl2, 0.072 g of Na2SO4, 6.118 g of Tris, 0–5 ml of 1.0 M HCl) at 37 °C was used as the corrosion medium. Tris (hydroxymethyl) aminomethane (TRIS) was used as the buffer. Prior to testing, the pH of the solution was adjusted to 7.4, using 1 M HCl solution.The biocorrosion behavior of the Mg66Zn30Ca4 and Mg60Zn35Ca5 systems was studied using electrochemical measurements. Potentiodynamic polarization measurements were carried out in 200 ml SBF solution at 310 K using Gamry Potentiostat/Galvanostat/ZRA. The frequency range was chosen from 10 kHz to 10 MHz. The sample served as the working electrode. Saturated calomel electrode was used as the reference electrode, while the counter electrode was a platinum electrode. The scan rate was 0.5 mV/s after 1800 s of open circuit potential measurements. The test was carried out from − 250 mV below to 500 mV above the open circuit potential. Powersuite software was used to perform the Tafel analysis. The morphology of the corroded surface of Mg–Zn–Ca samples was examined using a Field Emission Scanning Electron Microscope (Carl Zeiss, Sigma, UK).The amorphous behavior in the Mg66Zn30Ca4 and Mg60Zn35Ca5 samples of various thicknesses was analyzed using the XRD (). In Mg66Zn30Ca4 composition, the 22 mm sample displays sharp and distinct diffraction peaks for α-Mg, MgZn2, Mg2Zn11 and Ca2Mg6Zn3 phases. 22 mm sample of Mg60Zn35Ca5 composition, shows the existence of diffraction peaks corresponding to CaZn2 and CaMg2 phases apart from the α-Mg, MgZn2, Mg2Zn11 and Ca2Mg6Zn3 phases. CaZn2 and CaMg2 are high melting point intermetallic phases (a), for 8 mm Mg66Zn30Ca4 sample, partially amorphous structure displaying distinct diffraction peaks for α-Mg, MgZn2, Mg2Zn11 and Ca2Mg6Zn3 phases with 19.3% index of crystallinity can be witnessed. The XRD pattern of the Mg66Zn30Ca4 sample of 4 mm thickness exhibits a single broad peak. This is an illustration of a highly disordered amorphous phase. Furthermore, for the 2 mm sample, amorphization is much more improved. This is evident from the decrease in the intensity of the halo peak and the absence of other crystallization peaks. Therefore, for the Mg66Zn30Ca4 composition, complete amorphous formation can be observed for thickness ranging up to 4 mm. In (b), the XRD pattern of Mg60Zn35Ca5 8 mm sample displays diffraction peaks corresponding to α-Mg, CaZn2, CaMg2, MgZn2, Mg2Zn11 and Ca2Mg6Zn3 phases. This is a two phase structure: crystalline phase plus amorphous phase with 25.7% index of crystallinity. In the 4 mm sample, though the intensity of the crystalline α-Mg peak seems to have significantly reduced, stunted CaZn2, CaMg2, MgZn2, and Ca2Mg6Zn3 peaks are observed, which signify the co-existence of crystalline and amorphous phase with 19.7% index of crystallinity. In (b), the XRD pattern of Mg60Zn35Ca5 2 mm sample depicts almost a single broad peak exhibiting a amorphous structure. Therefore, for the Mg60Zn35Ca5 composition, partially amorphous structure can be observed in larger diameter samples (i.e. above 2 mm).), the Mg66Zn30Ca4 samples up to 4 mm thickness show distinct glass transition temperature (Tg), followed by a wide super cooled liquid region. Consequent crystallization events (Tx1, Tx2, Tx3, Tx4) are also observed. Exothermic relaxation is frequently observed in glasses which have high enthalpy upon casting (b)), the Mg60Zn35Ca5 composition for any given section thickness does not distinctly display glass transition temperature and crystallization events. As interpreted from the curves, the 2 mm diameter specimen exhibits a melting range between 613 K and 664 K. For the 4 mm sample, melting range is between 616 K and 663 K, and that of 8 mm sample is between 616 K and 661 K. On comparing the DSC results of Mg66Zn30Ca4 and Mg60Zn35Ca5 samples, Mg60Zn35Ca5 system is shown to exhibit higher melting point than the Mg66Zn30Ca4 samples. This is attributed to the presence of higher melting point CaZn2 and CaMg2 phases in Mg60Zn35Ca5 samples as observed in the XRD results presents the potentiodynamic polarization curves for the Mg66Zn30Ca4 and Mg60Zn35Ca5 samples. Tafel extrapolation was used to calculate corrosion current density, a parameter, widely used to evaluate the corrosion rate. The higher the corrosion densities, higher shall be the rate of degradation or corrosion. For the given compositions, the anodic polarization curves represent the dissolution of Mg and other elemental ions, while the cathodic polarization curves are indicative of hydrogen evolution through water reduction. To summarize, for the given system, the following electrochemical reactions are expected.Anodic Reaction:We examine the significance of Mg–Zn–Ca alloy: the dissolution of Mg2 +, Zn2 + and Ca2 + due to anodic reaction can be considered safe, as these elements carry a larger tolerance limit in the human system. Previous studies have shown that the corrosion product Mg (OH)2, forms a partially impervious layer over the implant surface, thereby regulating a controlled degradation rate As can be analyzed from the Tafel regions of the polarization curves (), high corrosion current density, and therefore greater corrosion rate in the fully crystalline 22 mm samples of both Mg66Zn30Ca4 and Mg60Zn35Ca5 compositions are observed. Critical parameters of corrosion resistance of these alloys are summarized in . For the Mg66Zn30Ca4 composition, the current density and corrosion rate are 1530 μA cm− 2 and 2286 mpy respectively. On the other hand, for the Mg60Zn35Ca5 composition, the current density and corrosion rate are 222 μA cm− 2 and 331.8 mpy respectively. High corrosion rates are partially due to the crystalline nature of the matrix and partly due to the presence of secondary phases. The presence of high energy defects, such as grain boundaries, stacking faults, twinned region, vacancies etc., accounts for the contribution of poly-crystallinity to the corrosion rate. Secondary phase such as binary MgZn2, as it is evident from the XRD plot, further aids to increase corrosion rates. This can be attributed to their different electrochemical behaviors; such precipitates form micro-galvanic couples between them and with α-Mg, thus contributing to rapid degradation rates.It is evident from the Tafel plot data () that the partially amorphous 8 mm samples of both Mg66Zn30Ca4 and Mg60Zn35Ca5 compositions, exhibit significantly lower current density compared to their fully crystalline 22 mm samples. This means that the partially amorphous sample, which is a combination of metastable crystalline phase in the amorphous matrix performs better for corrosion resistance. The corrosion current density and corrosion rate of 8 mm sample of Mg66Zn30Ca4 alloy are 8.490 μA cm− 2 and 12.69 mpy respectively, while for the Mg60Zn35Ca5 8 mm sample, they are 4.1 μA cm− 2 and 6.118 mpy respectively.Chemical composition of amorphous alloy can significantly influence their corrosion behavior. This can be observed from the corrosion behaviors of Mg60Zn35Ca5 and Mg66Zn30Ca4 samples. The alloy with lower Zn (Mg66Zn30Ca4) displays higher corrosion rate, while the Zn rich alloy (Mg60Zn35Ca5) exhibits a lower rate of corrosion. The varying corrosion behaviors between Mg66Zn30Ca4 and Mg60Zn35Ca5 samples can be thus attributed to the elemental Zn concentration, i.e. the higher the Zn content, the better is the corrosion resistance. pictures the FESEM micrographs of Mg66Zn30Ca4 and Mg60Zn35Ca5 samples of 22 mm and 8 mm diameter after the polarization experiments. It can be observed and interpreted that the corrosion product layer formed on the surface of Mg66Zn30Ca4 ((b), (d)) is on a comparison scale, more intense and dense than that formed on the surface of Mg60Zn35Ca5 sample ((a), (c)). The completely crystalline 22 mm sample micrographs for both of these compositions through the corrosion product layer, depict heavy degradation. An almost uniform corrosion product layer is deposited on the surface of 8 mm Mg66Zn30Ca4 sample ((d)). Also, unlike on the Mg66Zn30Ca4 surface, the surface film on Mg60Zn35Ca5 shows few micro-cracks, signifying its impervious property, i.e. protective against electrolyte ((c)). Thus, at the outset, it is rational to deduce the decreased corrosion rate in the 8 mm sample of Mg60Zn35Ca5 sample from these micrographs. This result supplements the Tafel plot data, and thus confirms partially amorphous Mg60Zn35Ca5 composition to be suited for bio-medical components synthesis.It is clear from aforementioned results that for both Mg66Zn30Ca4 and Mg60Zn35Ca5 systems, it is the partially amorphous sample (8 mm diameter), which exhibits a lower corrosion rate or degradation rate, as compared to completely crystalline sample (22 mm diameter). These results are in accordance with a previously reported literature ), a positive shift in the electrochemical potential can be noticed for a partially amorphous sample. A similar trend is also observed in the Mg66Zn30Ca4 alloy. The 8 mm sample exhibits a less negative potential of − 1.270 V, while the crystalline sample experiences a more degradation causing potential of − 1.510 V. These results further supplement to our understanding of the corrosion behaviors.Alloying elements play a significant role in influencing the corrosion behavior. This is evident from the high corrosion resistance of Zn rich alloy (Mg60Zn35Ca5) as compared to the Zn lower alloy (Mg66Zn30Ca4). Effect of Zn concentration is in tune with the conclusions of Zberg et al. depicts the Pourbaix diagram of Mg, Mg66Zn30Ca4 and Mg60Zn35Ca5 systems with different corrosion behaviors. As per the Pourbaix diagram of pure Mg ((a)), the immunity region is below the water stability region (b) and (c)). Immunity region of these systems is higher than that of Mg. The passive region shows the formation of products such as Zn(OH)2, Ca(OH)2, ZnO2 along with the formation of Mg(OH)2 and these films may provide long term protection. However, the passivation reaction occurs at higher potential (~− 1 V) and also at higher pH (> 8) which is slightly away from our working environment. When considering our working potential range (below − 1.2 V) and pH (closer to 7.4), the region that falls under our constraint is the immunity region. The phases formed in the various potential domains of both Mg66Zn30Ca4 and Mg60Zn35Ca5 systems are almost the same, other than the existence of CaMg2 and CaZn2 phases in the immunity region of the Mg60Zn35Ca5 alloy system. CaMg2 and CaZn2 intermetallic phases exist in the potential domain below ~− 0.2 V. The lower corrosion rate of Mg60Zn35Ca5 alloy system may be attributed to the presence of these intermetallic phases. These results are in accordance with the XRD results ((b)) where Mg60Zn35Ca5 samples display the presence of diffraction peaks corresponding to CaMg2 and CaZn2 phases. According to below mentioned reaction, there exist the possibilities of CaZn2 to form a compound CaZn2(PO4)2 |
· 2H2O (Scholzite) with the constituents of the SBF solution Ca2 + |
+ 2Zn2 + |
+ 2H2PO4− |
= CaZn2(PO4)2(s) |
+ 4H+.Since Scholzite phase is less soluble in the corrosive medium, it provides better protection against corrosion CaMg2 is also responsible for the reduced corrosion rate of Mg60Zn35Ca5 samples. Cha et al. Calcium plays an important role in building denser and healthy bones. Variation of calcium content may also influence the corrosion behavior, but this study is a comparison based on a narrow compositional window of Ca. In further studies, a much wider compositional window encompassing variation of Ca percentage has to be analyzed in order to arrive at the exact role of Ca in the corrosion behavior.Though Zn contributes positively to the corrosion resistance, it is important to stress that the extent of Zn addition should be well-controlled. This is because, high zinc content renders poor glass formation ability to the Mg–Zn–Ca system With respect to the crystallinity and section thickness it is not easy to quantify the optimum value since corrosion rate will vary with respect to both composition and crystallinity. However, the present work demonstrated that Mg60Zn35Ca5 8 mm sample has lowest corrosion rate of 0.1554 mm/year, which is higher than the acceptable corrosion rate for bioimplants i.e. 0.02 mm/year This work was performed with the purpose of casting relatively larger sized partially amorphous Mg–Zn–Ca alloys for bio-medical devices which derive commendable corrosion resistance of amorphous structures. In-vitro corrosion behavior of partially amorphous and crystalline Mg66Zn30Ca4 and Mg60Zn35Ca5 alloys in SBF solution was analyzed using electrochemical studies. It is observed on a comparable scale that the corrosion resistance of partially amorphous samples was greater as compared to their crystalline equivalents. The corrosion rate and degradation rate were observed to decrease significantly with increasing Zn content and due to the presence of CaMg2 and CaZn2 phases. The combined contribution of partially amorphous structure and alloying element is the basis of explaining varied corrosion behavior. The reported results are new insights or a step for selection of Mg–Zn–Ca metallic glasses for bio-medical applications.Experiment and numerical study of a new bolted steel plate horizontal joints for precast concrete shear wall structuresIn a non-emulative precast shear wall structures, joints are the key to influence the overall mechanical performance under seismic actions. While wet joints are widely used in the precast reinforced concrete shear wall structure, they present problems such as collision of steel bars, inconsistency of the post-casting area and importantly, they cannot achieve the best potential of precast concrete structures. Hence, this paper proposes a new dry joint, which is a bolted C-shaped steel plate for the horizontal joint of precast shear walls. Four identical sub-assembly precast shear wall panels bolted with four distinct configurations of steel plates (plain, X-stiffeners, horizontal slots and vertical slots) were tested under reversed cyclic loading. It was discovered that the bolted steel plate with horizontal slots could improve the ductility and energy dissipation of the joint. Numerical models were calibrated by benchmarking with the experimental results. Through a systematic parametric study on the number and spacing of slots, thickness of steel plates and number of bolts, the results indicated that the number of bolts is the critical parameter that will affect initial stiffness, peak strength capacity and ductility of the proposed joint.Precast reinforced concrete (RC) construction is widely adopted internationally, given its more superior quality, being prefabricated in the factory with the better-controlled environment, reduction of construction time and labour costs. The research of precast RC structures under seismic actions had been actively carried out, for example, a major United States-Japan coordinated research program, i.e. PREcast Seismic Structural Systems (PRESSS) program, has been conducted since the 1990s Various joint detailing methods had been proposed for low-rise precast construction structural systems without shear walls. These systems joined precast RC beams, columns and slabs Precast concrete joints can be of dry or wet type. In general, wet connections using rebars Besides UPT walls, another class of non-emulative dry connections is precast shear walls jointed with bolts. El Semelawy et al. From the literature review, most of the dry joints using bolts may induce local concrete failure (cone breakout), but their performance is notably enhanced with the inclusion of steel plates. Hence, a dry joint of precast concrete wall with high construction efficiency and good seismic performance is seemingly worth investigating. This paper describes a new bolted steel plate horizontal joints for precast concrete shear wall structures. Four specimens are tested under reversed cyclic actions, i.e. bolted plain steel plates (baseline model), bolted steel plates with X-stiffeners, bolted steel plates with horizontal slots and bolted steel plates with vertical slots. The discussions in this paper are focused on the failure modes, strength capacity, ductility, and energy dissipation of the newly proposed joint. Finally, numerical analysis for this new dry joint is presented, with calibrated models and parametric variations of research parameters are studied in detail, which includes horizontal slots, the thickness of steel plate and number of bolts.), inspired by the jacket confinement method for column (c). Potentially, the proposed bolted steel plate method can be used on vertical joint of precast shear walls, which should be further tested in future works. The focus of this research is on the horizontal joint.In this study, four identical shear walls jointed with four distinct bolted steel plates are tested under reversed cyclic actions. The steel plates are designed with different configurations, i.e. bolted plain steel plates (baseline model), bolted steel plates with X-stiffeners, bolted steel plates with horizontal slots and bolted steel plates with vertical slots. It should be noted that the baseline model was intentionally chosen using bolted plain steel plates and not benchmarking with a monolithically connected single piece of longer shear wall. The intention of this experimental programme is to test the behaviour of the joint and not the shear wall itself. The failure modes of the joint connecting by two pieces of the precast shear wall are not comparable to a single piece of longer shear wall.Q235 mild steel with 3.5 mm thickness was used for the C-shaped steel plates, which were manufactured with identical dimensions but designed with different schemes for the four specimens (as shown in ). For PW1, a full steel plate scheme is assigned to serve as the benchmark control specimen. For PW2, X-stiffeners of 8 mm thickness by 1300 mm length stiffeners were welded on the steel plates. For PW3, two horizontal 10 mm width slots by 1000 mm length were cut, distributed evenly at 100 mm interval on the steel plates. For the final specimen PW4, four vertical 10 mm width by 200 mm length slots were cut with spacings of 250 mm on the steel plates.Concrete compression tests were conducted on six cubes of 150 mm × 150 mm × 150 mm and six standard prisms of 150 mm × 150 mm × 300 mm height to obtain the average cube (fcu) and prism compressive strengths (fc) on the day of testing. All concrete was left for curing for 28 days. Three 500 mm long steel bars of each bar types shown in , with 6 mm, 8 mm and 10 mm diameters were tested according to the Chinese standards for tensile testing The sub-assembly of the precast shear wall connected with the proposed bolted joints are tested in the loading frame shown in . Low-speed lateral reversed cyclic loading was applied using a 2000 kN servo-controlled hydraulic actuator. Note that vertical load is not applied, as it is assumed that axial force is negligible in the application of precast shear wall in lower-rise building. Furthermore, it is essential to have a better understanding of the structural behaviour of the proposed bolted joint subject to lateral force only without coupling of vertical actions. Two huge and rigid pressure beams were mounted at the shoulder (RC base beam of the wall panel) and fixed to the laboratory ground by bolts, to prevent uplift due to moment under lateral cyclic loading (see (b)). The horizontal sliding movement of the base is eliminated by having the LVDTs reference to the RC base beam.The instruments installed in this test were Linear Variable Displacement Transducers (LVDTs) and strain gauges, which were used to capture deflection, curvature profiles, slipping of the bolted steel plate connections and deformation of steel plates. The arrangements of the five numbers of LVDTs (L1 to L5) and nine strain gauges (SG1 to SG9) are shown in . LVDT L1, which was placed at the same height of actuator (1175 mm above the RC base), is primarily to control the drift displacement of the target in each cycle. Joint rotations (θ), defined as the relative displacement between the upper and lower wall panels (Δ) in the loading direction divided by the total height of the top and bottom wall panels (h), were calculated using the displacements measured by LVDTs L2 and L5. LVDTs L3 and L4 were used to detect the slip of the joint. shows the fabricated specimens PW1 to PW4, instrumented with strain gauges and installed in position in the loading frame. Additional strain gauges (results are not used in this paper) were attached along with the longitudinal bars and stirrups, as shown in The reversed cyclic loading protocol was divided into two phases, i.e. force-controlled followed by displacement-controlled, as shown in . During the force-controlled phase, each cycle of loading was incremented by 100 kN with two repetitions per cycle. Reversed cyclic loading was applied to each specimen up to 75% of the theoretical ultimate shear capacity, estimated using an approximate value of 400 kN from numerical analysis. Subsequently, the loading protocol was switched to displacement-controlled phase. In the displacement-controlled phase, each cycle is repeated twice. The test was terminated when the post-peak load drops to 80% of the peak load, or when the test specimens could not be further loaded.The concrete crack patterns of the test specimens are shown in . During the force-controlled phase, the first diagonal and horizontal cracks in the test specimens occurred when the applied load reached approximately 200 kN. Diagonal cracks that inclined at about 45 degrees, formed from the wall corner to the bolted steel plate joints. Horizontal flexural cracks were detected at the edge of the lower wall panel. As the applied load increased, major diagonal and horizontal cracks were formed across the upper and lower wall panel. It was observed that there are some differences between the four specimens, where less diagonal cracks with wider spacing were formed at the upper wall panel for specimens PW1 and PW2, with stiffer bolted joint behaviour. On the contrary, for PW3 with horizontal slotted steel plate, more severe horizontal cracks occurred; and for PW4 with vertical slotted steel plate, more severe diagonal cracks occurred. shows the load-rotation hysteresis curves for all the specimens. The load-rotation curve of all specimens exhibited substantial pinching effects after reaching the peak load. This pinching is associated with rapid stiffness degradation and reduced energy dissipation in the post-peak regime. shows the comparison of the envelope of the load-rotation curves of all specimens. PW3 had a larger deformation and buckling tend to occur in the steel plate with horizontal slots, which could improve the energy dissipation ability of the bolted steel plate joint. also reveals that the load-rotation curves for positive and negative load cycles were slightly different. The non-symmetrical response of the curves is probably due to the formation of slips between the upper and lower wall panel. The slips measured during the experiment will be discussed in subsequent sub-section. can give a general overview of the strength performance of the bolted steel plate joints of precast shear walls, it is more apparent and convenient to interpret the test results by computing the values of the essential parameters. Hence, the test results related to load-carrying capacities and rotations are summarised in . The cracking, yield and maximum load capacities are denoted as Vcr,Vy and Vmax, respectively. The cracking rotation (θcr) is defined as the corresponding rotation angle at Vcr. The yield rotation (θy) is defined as the corresponding rotation angle at 0.75Vmax of an envelope curve at the increasing pre-peak branch. The energy equivalence principle method was adopted to find the yielding point of the specimens. The maximum rotation (θmax) is the rotation corresponds to the Vmax. The ultimate rotation (θu) is defined as the corresponding rotation angle at 0.8Vmax of an envelope curve at the post-peak softening branch. The maximum ductility (µ) is equal to the ratio of ultimate rotation to yield rotation (θu/θy), where the average results of the positive and negative cycles are computed. that PW2 with X-stiffener steel plate had higher strength capacity, but its ductility was slightly reduced compared to the control specimen PW1. Specimen PW3 exhibited better ductility performance because of the horizontal slotted steel plate. Specimen PW4 had the lowest strength capacity, possibly due to the effects of vertical slotted steel plate, which may change the internal force distribution of steel plate.To compare the energy dissipation of the specimens, the energy dissipated (Wd) in each half-cycle was evaluated. The value of Wd is equivalent to the area bounded by the load-rotation curves. shows the variations of Wd across the rotation. In the initial rotation levels, all specimens were able to dissipate an increasing amount of energy. Specimen PW3 with the horizontal slotted steel plate had larger deformation at the two ends, hence showing the highest energy dissipation performance. On the contrary, specimen PW4, which had the vertical slotted steel plate, demonstrated the lowest energy dissipation ability. It is noted that the deformation of steel plate in PW4 mainly occurred in the middle portion and not at the two ends. shows the maximum slips calculated based on the difference of the values recorded by LVDTs L3 and L4 under the horizontal loading of the actuator. Generally, very little slips were observed during the elastic force control loading protocol at 100 kN. The formation of the slips started to display differences among the four specimens after the 100 kN applied loading. It is apparent that stiffened configuration of steel plate, as in the case of PW2, exhibited little slips (about 4 mm). On the contrary, the most flexible configuration of steel plate, as in the case of PW3, demonstrated the most slips (about 6 mm). PW4 showed an interesting behaviour, where it seems to slip very little (about 2.6 mm at peak load) despite having vertical slots opening, but it also failed to achieve a higher lateral load capacity.It is noted that the deformation and stresses of the C-shaped steel plate can provide interesting insights. The strain gauges SG1 to SG9 installed in an array (see ) can only give discrete points of information. Hence, numerical analysis is carried out in the following discussions, to complement the experimental results. shows an example of an FE model of specimen PW1. All other specimens PW2 to PW4 are similar to PW1, except for the steel plate configurations in . In the simulation, the compression value of the concrete was defined by concrete compression tests in . Damage parameter d was calculated using the method put forward by Sidiroff The concrete components, bolts and steel plates were meshed with eight-node solid elements, codenamed as C3D8R. The reinforcement bars are modelled using the two-node truss element, codenamed as T3D2. The basic element size is set at about 35 mm, with at least two elements in the thickness direction. The size of the bolts is approximately 8 mm. The reinforcement bars that were modelled using the T3D2 elements have element size of 30 mm. Mesh sensitivity study was conducted, and all components are considered suitably meshed since there are no poor elements highlighted after the mesh convergence test.An embedded region constraint is used to embed reinforcement elements to the whole model so that all translational degrees of freedom of reinforcement will be constrained. No rebar slip is assumed, i.e. concrete and reinforcement are compatible in deformation. This assumption is justified as in actual engineering, only small deformation is allowed in shear wall panels. Encastre boundary conditions are created to simulate the fixed condition of the bottom base beam. The out-of-plane movement at the side of the top beam was constrained to zero to ensure the out-of-plane stability of the model. A reference point was placed at the right side of the loading beam, and the horizontal displacement load was applied at that loading point.The FE models for the four specimens were constructed, and the simulation results (presented in terms of displacement) are overlaid on the envelope of the test results, as shown in . The monotonic pushover simulation curves are replicated in the negative displacement regions. It can be observed that the maximum lateral shear capacity of simulation results is slightly higher than that of the tests. One possible reason is that the conditions and material properties simulated in the model are idealised, while errors may occur in the experimental procedure, for example, during concrete pouring and reinforcement assembling process.The maximum lateral shear capacity and ultimate displacement between the simulation results and test results are summarised in for further comparison. The ultimate displacement (Δu) is consistent with the previously defined ultimate rotation (θmax), where it is referring to the displacement corresponds to 0.8Vmax of an envelope curve at the post-peak softening branch, the differences in simulation compared to test results are less than 15%, and the failure modes of the specimen agree well with the observations made during the tests. Hence, the model can be considered calibrated and thus, further investigations are to be conducted based on these calibrated models.During the experiment, a faint sound was produced from the movements between bolts, steel plates and the shear wall panels, along with relative movements between them. shows the vertical and horizontal relative displacements of the upper and lower wall panel, with an exaggerated uniform deformation factor of 10. The Von Mises stress contours of the four specimens are shown in , at the three key points (yield, peak and failure). Specimens PW1, PW2 and PW4, showed relatively cool colours of blue and green, which have low stress values. From the progression of these stress contours, it is discovered that the stress area in PW1 is at first mostly distributed in the middle, showing a 45-degree angle. The stresses in the middle area are gradually reduced, and higher stresses occurred on the two sides. In view of the stiffened effects in PW2, the stresses are generally concentrated at the edge and sides. Interestingly, the stress areas at the two sides of specimen PW3 are much larger than the rest, with some warmer colours (yellow, orange and red) appearing at the tip of the horizontal slots. This indicates that the steel plates in PW3 had actively participated in working together with the concrete. During the elastic phase, the stress areas initially concentrated on the two sides. The stresses propagate and extend to the middle part of the steel plate, especially at the areas near to the slots. The stress concentration area at the ends of the horizontal slots had also enlarged. For PW4 with vertical slots, it shows narrower stress areas in between the spacing of the slots. Compared to PW3, the area on the two sides of PW4 do not participate as much during the loading proses.It can be concluded that, through the experimental work and numerical simulation results, PW3 has demonstrated the best overall mechanical performance. The bolted steel plate with horizontal slots could improve the deformability, ductility and energy dissipation capacity of the joints of the precast shear walls. Hence, the following investigations take the focus on the configuration used in PW3 to provide further insights to find the best forms of steel plates with horizontal slots.A series of parametric study is conducted for PW3 type of steel plate configurations, by varying the number and spacing of horizontal slots, the thickness of steel plates and number of steel bolts.The original PW3 has two slots opening, spaced at 100 mm. The numbers of slots are varied from two to three with changes in the spacing of 50 mm, 100 mm and 150 mm. shows the four types of configurations of horizontal slots with the same length, where PW3 is codenamed with the variables. For example, PW3-2–150 is a steel plate with two numbers of horizontal slots, spaced at 150 mm.The load–deflection curves and the Von Mises stress contours are shown in , respectively. Generally, there are no significant effects of altering the configurations of horizontal slots, evidently shown in . The overlapping data points in the figure are not explicitly marked, but symbolic marks are enlarged when the lines have deviated apart. PW3-3–100 presents trivial strength enhancement after reaching its peak point, compared to the others. shows that the Von Mises stress contours are slightly higher in PW3-3-50 and PW3-3-100 (those with three horizontal slots) compared to PW3 and PW3-2-150 (with two horizontal slots).The original PW3 has a steel plate thickness of 3.5 mm. Three additional models with steel plate thickness of 3 mm (codenamed as PW3-3 mm), 6 mm (codenamed as PW3-6 mm) and 9 mm (codenamed as PW3-9 mm), were numerically modelled and analysed to their failure. shows the load–deflection curves of the four models with varying steel plate thickness. Generally, the maximum lateral load capacity is similar. However, when the steel plate thickness is increased, the yield displacement, peak displacement and failure displacement tend to appear earlier. shows that when the steel plate thickness is increased, say in the case of PW3-6 mm and PW3-9 mm, the Von Mises stress area in the steel plate and the maximum stress are lower. This observation suggests that the thick steel plates transfer lesser loads compared to the thinner ones. An interim conclusion can be drawn here, i.e. thicker steel plate may not provide more superior seismic performance for the proposed steel plate bolted joints for the precast wall. Also, it is obviously uneconomical to utilise thicker steel plates.The original PW3 was jointed with five numbers of bolts on each side of the C-shaped steel plates. In this study, three more specimens with different numbers of bolts (n) are modelled. summarises the specimen ID codenamed with the numbers of bolts of four to seven. For example, PW3-4 denotes the steel plate type PW3 (horizontal slots) with four number of bolts.Consistent with the previous figures presented to discuss the change of parameters, the load-deflection curves and Von Mises stress contours for different numbers of bolts are plotted in , respectively. Interestingly, an obvious change in load resisting behaviour can be clearly detected in . Using a higher number of bolts may result in higher initial stiffness and maximum lateral load capacity, for example, in PW3-n7. However, this configuration with higher strength is a trade-off for its less ductile performance, as compared to model PW3-n4 with lesser bolts. The maximum Von Mises stresses in these models are shown in , and they are close to each other without a distinct difference. Hence, taking a moderate solution half-way, i.e. the original PW3 with five number of bolts appear to be an optimum solution that gives the best overall mechanical performance in terms of strength and deformability.The experimental and numerical investigations of a new bolted C-shaped steel plate used for the horizontal joints for precast reinforced concrete shear wall structures are presented in this paper. Four identical sub-assembly of precast wall panels are jointed using bolts with four distinct types of steel plate configurations (plain steel plate, X-stiffeners, horizontal slots and vertical slots) and tested under reversed cyclic load. Using ABAQUS, the FE models of the joints mounted on the precast walls are verified and calibrated with the experimental results. The following conclusions are made based on the work in this research:Among the four types of bolted steel plate joint, PW3 has the highest energy dissipation, partly due to the reason that steel plate with horizontal slots had a larger deformation, especially at the two ends region.The numerical study in selecting steel plates variations with horizontal slots, by varying the numbers of slots and spacing between them, and different thickness of steel plates, showed that these parameters are basically trivial and not significantly affect the overall mechanical performance of the specimens. In contrast, the numbers of bolts presented substantial effects on the performance of sub-assembly precast wall panels. A decision has to be made to strike a balance in trading off strength and deformability, where this study shows that five numbers of bolts appear to be the optimal solution.For the proposed bolted horizontal joint for the precast shear wall, further efforts should be devoted to exploring the influence of axial loading on the seismic performance. The coupling of axial, shear and bending interaction may present further insights into the practical use of this proposed joint in tall buildings. Also, the authors foresee the potential use of the proposed bolted steel plate on vertical joint of precast shear walls, which should be further tested in future works.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Microstructure, mechanical property and Hall-Petch relationship of a light-weight refractory Al0.1CrNbVMo high entropy alloy fabricated by powder metallurgical processA light-weight refractory Al0.1CrNbVMo high entropy alloy (HEA) was fabricated by high energy ball milling and spark plasma sintering (SPS). The alloy had a density of 7.96 g/cm3, which is lower than that of conventional Ni-base superalloys. Optimum milling time was decided by the microstructure analysis of the HEA powders. The microstructure of the bulk alloy consisted of a body-centered cubic (BCC) matrix with a minor amount of alumina inclusions. The Al0.1CrNbVMo HEA exhibited outstanding compressive mechanical properties of 2863 MPa at room temperature, and 1405 MPa at 1000 °C, respectively. The specific yield strength of 176 MPa cm3/g at 1000 °C, is much higher than that of the other refractory HEAs. The Hall-Petch coefficient of the Al0.1CrNbVMo alloy was derived to 811 MPa μm0.5.A new paradigm of alloy design concept, named as multi-principal element alloys or high entropy alloys (HEAs), has been proposed to overcome properties limit of conventional alloys. Unlike the conventional alloys such as Fe, Al and Ti-alloys, the HEAs consisting of five or more principal components with an equiatomic or near-equiatomic ratio for maximizing the configurational entropy, which is related with the stability of solid solution phases of the HEAs []. It is reported that the HEAs exhibit excellent properties, including high strength at various temperature [], and considerable resistances to wear, oxidation and corrosion []. Owing to these unique and outstanding properties of the HEAs, many researchers have participated in investigating on HEAs and developed a variety of HEA systems, such as Cantor alloy (CoCrFeNiMn) [], combined systems of Al and 3d transition metals []. Especially the refractory HEAs, which are predominately composed of refractory elements such as Nb, Mo, V and W, have been developed recently for applying to high temperature aerospace industries. Some of the refractory HEAs were reported as having excellent compressive yield strength at room temperature and elevated temperatures compared to commercial Ni-base superalloys [Until nowadays, fabrication processes of HEAs are mostly focused on arc-melting and casting methods. In the case of the arc-melting and casting processes, however, there are issues of inhomogeneous microstructures with a dendrite structure, and degradation of mechanical properties due to coarsening of grain size. Meanwhile, through the powder metallurgical process, homogenous microstructures, grain refinement and uniformly formed reinforcements can be accomplished so it is able to maximize the mechanical properties of HEAs. A few research group fabricated nano-crystalline HEAs via powder metallurgical processes to solve the mentioned issues but the alloy systems have been still limited to the 3d transition metal HEA systems []. When it comes to the refractory HEAs, due to the high melting point of refractory elements, some of researches were conducted to fabricate the refractory HEAs through the powder metallurgical process []. But the research on the powder metallurgical process of the refractory HEAs is still in early stage. By using the powder metallurgical process to fabricate the refractory HEAs, several benefits could be achieved, such as no segregation problems [] and the easiness for the fabrication of small and precise components that are exposed to extremely high temperatures.In view of the above findings, a present study was motivated to fabricate and characterize a new refractory HEA via the powder metallurgical process to develop an advanced structural alloy with excellent mechanical properties at room and elevated temperature. Furthermore, it should be noted that the density of typical alloys for the high temperature applications (Ni-base superalloys) usually exhibit more than 8.0 g/cm3. In the present work, a refractory HEA of Al0.1CrNbVMo (theoretical density: 7.98 g/cm3) was newly designed, which has similar or lower density than the typical Ni-base superalloys. Relatively light refractory elements such as Cr (7.19 g/cm3), Nb (8.57 g/cm3), V (6.00 g/cm3) and Mo (10.28 g/cm3) were selected as the main alloy constituents with consideration of their high-melting temperature for the high-temperature properties. A minor amount of Al was added, which is a benefit for stabilizing the BCC crystalline structure, enhancing mechanical properties, and reducing the density of the refractory HEAs []. The fabrication processes of the bulk Al0.1CrNbVMo HEA through the high energy ball milling and spark plasma sintering (SPS) were established. The microstructure, phase evolution and mechanical properties of the bulk Al0.1CrNbVMo HEA were systemically investigated. Moreover, grain growth behavior of the bulk specimen and consequent change of yield strength were characterized to identify the correlation between the grain size and yield strength: Hall-Petch relationship.Al0.1CrNbVMo HEA powders were prepared by the ball milling process for 12 h with high purity (99.0–99.9%) elemental powders of Al, Cr, Nb, V and Mo. The elemental powder was loaded into an SKD-11 bowl with tungsten carbide balls (7 mm in diameters) and ball-milled in a high energy planetary ball mill machine (Pulverisette 5). The ball milling process was carried out a milling speed of 200 RPM with the ball to powder ratio of 10:1 without process control agent. So as to investigate milling behavior of the ball milled powders, 0.5 g of powders were taken out periodically after a certain time of milling. To prevent oxidation during the milling process, all of the procedures handling the powders were conducted inside of a glove box and high purity of argon was filled into the bowl before the milling. Average powders size at different milling time was analyzed by a laser diffraction particle size analyzer (LS230). After 12 h of milling, the powders were taken out and consolidated by Spark Plasma Sintering (SPS, SPS-515S) at 1200 °C at a pressure of 50 MPa under vacuum. The milled powders were heated to 600 °C within 1 min, and from 600 °C to the 1200 °C, a heating rate of 100 °C min−1 were applied, and followed by 5 min of holding time at 1200 °C. Heat-treatment for grain growth of the sintered HEA samples was carried out inside of a tube furnace at different temperatures of 1250 and 1450 °C for 16 h in an argon atmosphere followed by furnace cooling. The crystalline structure and microstructure of the HEA powders and sintered sample were investigated by X-ray diffraction (XRD) analysis, scanning electron microscopy (SEM) and transmission electron microscopy (STEM). The metallographic samples were prepared by grinding and polishing using SiC papers up to #4000 and a diamond paste up to 0.25 μm. Grain morphology after heat-treatment was revealed by a chemical etching with a solution of a mixture of H2O, H2SO4, HF and HNO3 (ratio of 50: 15: 20: 10). The grain size of the matrix, volume fraction and average radius of inclusion phase were quantitatively examined by using an image analysis software (ImagePartner, Saramsoft Co. Ltd.). Density of the bulk HEA was measured by Archimedes principle. Cylindrical samples (∅ 3 × 4.5 mm) of the bulk HEA samples were cut by an electrical discharge machine to characterize compressive mechanical properties. Compression tests were conducted at 25 °C, 600 °C, 800 °C and 1000 °C in air atmosphere by a universal testing machine (MTS 810) with an engineering strain rate of 0.001s−1. The representative data for each conditions were obtained by averaging three values of the test results. The strain was measured by a customized strain gauge directly applied on the test fixtures right beside the specimens, and calibrated by measuring the actual length of the specimens after each tests. Axial dilatation of the specimens during the test was also considered, so that the strain was calibrated using the thermal expansion coefficient of the Al0.1CrNbVMo HEA of 3.8 × 10−6/K, which was derived by rule of mixture.Several parameters have been suggested to predict formation of solid solution phases and phase stability of HEAs []. Notably, King et al. proposed two-parameter model to predict the formation and stability of single-phase HEAs based on Miedema's model []. One parameter is the atomic size difference (δ), which is defined as follows:where ci is the atomic percentage of the ith element, r¯ is the average atomic radius and ri is the atomic radius of the ith element []. The other is a thermodynamic parameter (Φ), which represent the ratio of the Gibbs free energy of a completely disordered solid solution to that of the most possible intermetallic, is detailed as followed equation:where ΔGss is the Gibbs free energy change for the formation of a fully disordered solid solution from a mixture of its individual elements, and ΔGmax is the lowest or highest Gibbs free energy change that is obtainable from the formation of binary systems from the alloy elements []. Here, the formation of a disordered solid solution is stable when Φ ≥1. Single-phase HEAs are predicted when Φ ≥1 and δ<6.6 are obeyed simultaneously []. In addition, the valence electron concentration (VEC) can predict the crystalline structure of the solid solution phase. The VEC of a multi-component HEA is derived by VEC=∑i=1n(VEC)ici, where (VEC)i is the VEC of the ith element. According to the literature [], BCC phase is stable when VEC < 6.87, whereas FCC becomes stable when VEC > 8.0. Mixed phases of BCC and FCC were formed at a range of 6.87–8.0. In the case of Al0.1CrNbVMo HEA, the calculated values of Φ, δ, and VEC are 1.49, 4.82, and 5.4, respectively. Thus, the present alloy would most likely be composed of single and stable BCC solid solution.(e), the average powders size was almost saturated to 5–10 μm c.a. after 12 h of milling. In addition, the lamellar spacing became constant to 0.5 μm c.a. after 12 h of milling. It is obvious that the distributions of the average size and lamellar spacing decrease with increasing milling time. In general, the ball milling process has a concern of contamination of powders due to wear of milling media and oxidation. As the milling time increases, the powders become finer and consequently more sensitive to the contaminations []. Although the milling was carried out in inert atmosphere, due to the high affinity of Al and Ta to oxygen, the finer powders tend to be easily oxidized with increasing of the surface area. The oxidation of as-milled powders is attributed to the presence of residual oxygen and humidity in glove box, and the short exposure to air during sample loading of SPS process. To prevent the powders from those contaminations, it is necessary to minimize the duration of the ball mill with a consideration of advantages of refinement effect of the powders. It is reported that the driving force of densification during sintering process is greater for finer powders than for coarser powders []. This means that finer powder size has an advantage on the full density of consolidated bulk specimens. Therefore, we concluded that the optimized milling time of Al0.1CrNbVMo HEA, considering the aspect of the minimum contamination and maximum densification, is 12 h when both the average powders size and the lamellar spacing were saturated. It is obvious that XRD patterns of the Al0.1CrNbVMo powders after 12 h of the milling still exhibit diffraction peaks of all alloying elements, as shown in (f). It means complete alloying of the Al0.1CrNbVMo HEA were not achieved only by the 12 h milling. Generally, other literature on the fabrication of HEA powders via high energy milling process did not consider the optimization of milling time, so that as-milled HEA powders show single- or multi-phase of the solid solution as a result of relatively longer milling duration than the present work []. Nonetheless, we assume that the complete alloying of the constituents would be achieved through following sintering process. exhibits the microstructure measured by the back-scattered electron (BSE) imaging mode and XRD patterns of bulk Al0.1CrNbVMo HEA consolidated by SPS. As shown in (a), the bulk alloy consisting of a homogeneous grey matrix with uniformly distributed black inclusions. The volume fraction of the black inclusions was measured as 5.54%. The density of the Al0.1CrNbVMo was measured to 7.96 g/cm3, which is 99.7% of the theoretical density, and no pores presented in the matrix. In terms of the crystalline structure of the Al0.1CrNbVMo HEA, the XRD patterns of the bulk alloy were only composed of a single body-centered cubic (BCC) solid solution without any other phase, as illustrated on (b). The results of the formation of single BCC solid solution are in good agreement with the phase prediction. As a reference, the XRD peaks of the 12 h milled powders were included together. Comparing the peaks of the milled powder and the bulk alloy, it is deduced that the stable BCC solid solution could be formed through the SPS process even though the HEA powders were not completely alloyed by the ball mill process. Therefore, it is reasonable to mention that when fabricating the HEA via the powder metallurgical process, it is not essential to form solid solution phases of the HEA only by the milling. Especially, given the possible contamination of the refractory elements due to the prolonged milling, optimizing the time for the milling is necessary for fabricating refractory HEAs by the powder metallurgical process. It is also worth to note that this HEA system cannot be alloyed only by the SPS process without the optimized milling process (see (c) shows the XRD patterns of the sintered bulk specimen (marked at (b)) at 2θ range from 30° to 50°. The presence of the diffraction peaks of alumina (Al2O3, PDF-# 10–0173) was obvious. To identify the chemical compositions of the matrix and inclusions, a semi-quantitative energy dispersive X-ray spectrometer (EDS) analysis was conducted. The spot EDS analysis results indicated that the chemical composition of the matrix is well matching the nominal composition of Al0.1CrNbVMo HEA (). In general, the quantitative EDS analysis of light elements, such as C and O, has a limitation to measure the concentration accurately. Although, the atomic ratio of Al and O analyzed by the EDS was almost 1:1 in the black inclusions, they were identified as alumina (Al2O3) with the XRD patterns ((c)). The formation of the alumina inclusions might be induced by oxidation of Al during the powder metallurgical process. According to Ellingham diagram [], the Al possesses the highest affinity to the oxygen among the alloy elements, so that Al takes up inherent oxygen from the other constituents. Therefore, thermodynamically the most stable alumina inclusions evolved during the processes. illustrates SEM images of the Al0.1CrNbVMo HEA after the heat-treatment at different temperature for 16 h, the grain morphology of the alloy was revealed by chemical etching except for the image of as-sintered bulk, which is measured by STEM due to the difficulty to observe the grain morphology by the chemical etching. The grain sizes of the Al0.1CrNbVMo HEA were various according to the heat-treatment temperature, i.e, 0.6μm (as-sintered), 1.1μm (1250 °C) and 2.8μm (1450 °C). In other words, the heat-treatment process was effective in coarsening the grain of the Al0.1CrNbVMo HEA. The grain size of the Al0.1CrNbVMo HEA was quite larger than that of other HEAs processed by the powder metallurgical processes []. It is due to the higher sintering temperature of 1200 °C than others, which are generally ranged from 800 to 1000 °C. In terms of the alumina inclusions, they were formed along the grain boundary of the matrix and showed the tendency of larger average size with higher heat-treatment temperature. illustrates TEM images of the as-sintered Al0.1CrNbVMo HEA. It was obvious that the Al2O3 inclusions were formed uniformly inside of grains and at grain boundaries of the single BCC Al0.1CrNbVMo HEA. As shown in (a), dislocations were piled up (marked as yellow arrow) near the grain boundary. The grain boundary of one grain was marked by yellow dashed line for clear separation of each grains. Due to the pile up of dislocations near the grain boundary, the effect of grain boundary strengthening would be large, enhancing the yield strength of the material. In addition, as marked by the red arrows in (b), the Al2O3 inside of the grain served as anchors, hindering the movement of dislocations, thereby increasing the yield strength.The mechanical properties of Al0.1CrNbVMo HEA bulk specimens at room temperature were shown in . The compressive stress-strain curves of the as-sintered and heat-treated Al0.1CrNbVMo HEAs are shown in (a). It is observed that the as-sintered bulk of Al0.1CrNbVMo HEA exhibits outstanding compressive yield strength of 2863 MPa, specific yield strength of 360 MPa cm3/g, and fracture strain of 6.1%, respectively. Here, there was no change in the density after the heat-treatment. The fabrication process, crystal structure and compressive mechanical properties of the Al0.1CrNbVMo HEA, as well as some typical refractory HEAs, are summarized in . It is obvious that the powder metallurgy-processed Al0.1CrNbVMo HEA shows improved mechanical properties of good combinations of strength and fracture strain than the other refractory HEAs, especially compared to others processed by arc-melting and casting. Furthermore, as the higher heat-treatment temperature was applied, the grain size was coarsened, leading to decrease of the yield strength of the bulk alloy. It is indicated that after the heat-treatment, the yield strength was decreased as result of the grain growth of the alloy. The ultra-high mechanical properties are attributed to the inherent solid solution strengthening of the high entropy alloys []. In addition, Orowan strengthening (σor) by the alumina inclusions which are incoherent with BCC matrix has to be considered []. Orowan strengthening is detailed by followed equation [where M = 2.9 is the mean orientation factor for the BCC phase polycrystalline matrix [], G is the shear modulus, b is the Burgers vector and v is the Poisson's ratio. The Burgers vector b is derived to 2.70 nm from the XRD patterns of the bulk Al0.1CrNbVMo HEA ((b)). r¯=r2/3 is the mean radii of a circular cross-section in a random plane for a spherical precipitates [], where r is the mean radii of precipitates. Inter-spacing of the precipitates (λ) is described as followed equation [where f is the volume fraction of the precipitates. Elastic modulus of the Al0.1CrNbVMo HEA derived to 99 GPa from the compressive stress-strain curve. Because pure Nb has the same BCC crystalline structure and similar elastic modulus of 105 GPa with the alloy [], the Poisson's ratio of Nb (0.4) was borrowed to calculate the shear modulus of the Al0.1CrNbVMo HEA of 35 GPa. Using the parameters in equations , the contribution of Orowan strengthening of each sample was calculated, and summarized in . The value of σor decreases as heat-treatment temperature increases due to the coarsening of alumina inclusions. (b) illustrates the relationship of compressive yield strength and grain size of the Al0.1CrNbVMo HEA before (marked ) and after (marked ■) excluding the contribution of Orowan strengthening (18–86 MPa). The Al0.1CrNbVMo HEA agrees well with the Hall-Petch relationship (the red line) with KHP = 811 MPa μm0.5, where KHP is Hall-Petch coefficient which is a constant specific to each material, calculated from the slope of the fitted line. The KHP value of typical HEAs were reported by several literature, and summarized in ] reported that BCC metals generally exhibit higher KHP than that of FCC and HCP metals, resulting from higher resolved shear stress necessary to propagate plastic flow across the grain boundary. For this reason, the present alloy with a BCC structure showed higher KHP value, compared with that of the other HEAs with FCC structure, as shown in . Furthermore, it would be noted that the calculated KHP of the present alloy throughout the Hall-Petch analysis was more reliable than the approximated KHP value calculated by the rule of mixture of alloy constituents []. The intercept of the fitted line is a very high value of 1680 MPa, which is intrinsic strength induced by the combined effect of the friction strength (friction of lattice to dislocation movement) [] and the solid solution strengthening due to the lattice distortion by different atomic size of each element []. In fact, the formation of single BCC solid solution can significantly increase the configurational entropy, thereby increasing the solid solution strengthening effect. In addition, as shown in , grain boundaries and the Al2O3 impede the movement of dislocations. The superior mechanical properties are attributed by nano-scale grain size inducing large grain boundary strengthening, and partially, Orowan strengthening by small amount of alumina inclusions. shows fracture morphologies of Al0.1CrNbVMo HEA after the compressive test at room temperature. Brittle cleavage fracture was particularly evident for the Al0.1CrNbVMo HEA. The fracture surfaces of the present HEA depicted that cracks were dominantly initiated at the grain boundaries, which were possessing the highest stress triaxiality []. In addition, interfacial decohesion between the matrix and the alumina inclusions was observed, which meant the interfacial property should be enhanced to maximize strengthening effect by the alumina. To further improve properties, modification in fabrication processes will be conducted at the follow-up study. Notably, as the grain size increased, fracture mode changed from the inter-granular fracture (as depicted in (a)-(d)) to the trans-granular fracture (as shown in (e)-(f)). Future works will be carried out with detailed analysis on the transitions of the fracture mode. exhibits temperature dependence of compressive specific yield strength of typical refractory HEAs processed with arc-melting and casting, Ni-base superalloys (Inconel 718 and Hayne 230) and the Al0.1CrNbVMo HEA [], and the mechanical properties of Al0.1CrNbVMo HEA are summarized in . Surprisingly, the specific yield strength of the Al0.1CrNbVMo HEA is the highest value at all temperature range from 25 °C to 1000 °C among the other refractory alloys. At 1000 °C, the Al0.1CrNbVMo HEA shows almost 76% enhanced specific yield strength than AlMo0.5NbTa0.5TiZr HEA, which has been the refractory HEA with the best specific yield strengths. Moreover, the high temperature properties of the Al0.1CrNbVMo HEA are much higher than Inconel 718 and Haynes 230, which are widely used in gas turbine applications. Therefore, Al0.1CrNbVMo HEA has the potential for structural alloys high temperature applications in gas turbines, such as turbine blades, vanes and disks. Moreover, the excellent high temperature strength of the present alloy also will be analyzed minutely. In the present study, the authors think that the outstanding mechanical properties at the elevated temperature might be attributed by both the solid solution strengthening of Al0.1CrNbVMo HEA and the presence of the alumina inclusions at grain boundaries of the matrix, which play a key role in pinning of dislocation movement and grain boundary sliding [In summary, a novel and light-weight Al0.1CrNbVMo refractory HEA processed via powder metallurgical methods has been successfully fabricated and characterized. Unlike other researches on the fabrication of the HEAs using the powder metallurgical process, minimum milling time was deduced from both average powder size and lamellar spacing of the HEA powders to minimize contamination during the ball milling. Subsequently, the bulk specimens were prepared by SPS at the sintering temperature of 1200 °C, and almost 100% of relative density was achieved. Even though the as-milled powder did not show solid solution phases due to the relatively short time of ball milling, a single BCC solid solution of the Al0.1CrNbVMo HEA was evolved after the SPS. The microstructure of the bulk Al0.1CrNbVMo consisted of the BCC matrix of nano-scale grains, and the alumina inclusions formed along the grain boundary and inside of the grains. As-sintered Al0.1CrNbVMo HEA bulk exhibited much enhanced compressive yield strength as well as specific yield strength at a temperature range from 25 °C to 1000 °C compared to the other refractory HEAs processed with arc-melting and casting. Especially, the Al0.1CrNbVMo HEA showed 76% higher specific yield strength of 176 MPa cm3/g at 1000 °C than AlMo0.5NbTa0.5TiZr HEA, which has exhibited the highest specific yield strength in the refractory HEAs. To identify grain growth behavior, the heat-treatment process was conducted at 1250 °C and 1450 °C for 16 h. After excluding the contribution of Orowan strengthening by the alumina inclusions, the Hall-Petch relationship for at a temperature range from 25 °C to 1000 °C was derived; Hall-Petch coefficient was calculated to 811 MPa μm0.5. The outstanding mechanical properties of the Al0.1CrNbVMo HEA are combined effect of the solid solution strengthening, grain boundary strengthening and partially, Orowan strengthening.The following is the supplementary data related to this article:Supplementary data related to this article can be found at Ca. 2.5 billion year old coeval ultramafic–mafic and syenitic dykes in Eastern Hebei: Implications for cratonization of the North China CratonA group of extremely rare coeval ultramafic–mafic and syenitic dykes was discovered in the Eastern Hebei region of the North China Craton. These dykes intrude the 3.8–2.55 Ga old Caozhuang complex. An olivine gabbro dyke and syenite dyke yield, respectively, SHRIMP zircon U–Pb ages of 2516 ± 26 Ma and 2504 ± 11 Ma, interpreted as the magmatic crystallization age. Their zircons have single-stage Hf model ages 2677 Ma and 2705 Ma. The olivine gabbros have Mg# values of 59–63, similar to high-magnesian tholeiitic basalt. They show relatively LREE-enriched patterns without Eu anomalies (La/YbN |
= 9.28–9.78, Gd/YbN |
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