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+ 2C12)/3. A second relationship between C11 and C12 can be obtained by applying a volume conserving tetragonal strain to calculate the tetragonal shear elastic constant, CS |
= (C11 |
− |
C12)/2. The tetragonal strain tensor is given byHere, δ is the deformation parameter. Under the tetragonal shear strain, the total energy of the system is given by E(δ) = |
E0 |
+ 2CsV0δ2 |
+ |
0(δ4). Here, E0 is the energy of unstrained state, Cs is the cubic shear constant and V0 is the zero strain volume. A linear fit to the strain energy vs. strain δ2 yields the result for tetragonal shear elastic constant. For the pure shear elastic constant, C44, we have applied the following strain tensor given bywhich yields the total energy as a function of strain as; E(δ)=E0+(1/2)(C44V0δ2+O(δ4)). Furthermore we have used the following isotropic strain tensor to calculate the bulk modulus:which yields the deformation energy equation such as E(δ)=E0+(9BV0/2)δ2, used for determination of bulk modulus at elevated pressures.We determine the pressure dependence of the elastic stiffness constants in two steps. First, using Birch–Murnaghan equation of state for a chosen value of the hydrostatic pressure corresponding volume, hence the lattice parameter is determined. Then the cubic cell with lattice constant is chosen as the reference structure for this pressure; and the three deformations defined earlier are imposed for a set of δ values to determine the bulk modulus, tetragonal and pure shear elastic modules and hence the three independent elastic stiffness constants. The elastic energy of the deformed lattice at hydrostatic pressure P is defined exactly in the same way as at zero (ambient) pressure.Kleinmann parameter is important parameter describing the relative position of the cation and anion sublattices. It is given by the following relation Shear modulus is given in the following expression; G=(GV+GR)/2. Here, GR is Reuss modulus given byThe width of the bonds on the shear modulus is related to the anisotropy constants given in the following relationship:As the anisotropy constant approaches to unity, the crystal goes to isotropic phase, and the gap between the bounds vanishes. The Young modulus E and Poisson ratio γ are related to the hardness for polycrystalline materials. These quantities are given by The total energies of ZnS in both phases of B3 and B1 are calculated for different volumes around the equilibrium cell volume V0. The plot of total energy as a function of volume for two phases is given in shows that the B3 structure is more stable than the B1 structure. The variation of total energy with the volume is fitted to a third-order Birch–Murnaghan equation (Eq. ) of state to obtain the ground state properties such as the equilibrium lattice constant a0, the bulk modulus, B0, and its pressure derivative B′0. The calculated equilibrium parameters for both structures are given in as well as other available theoretical and experimental data. It is seen that our results of lattice parameter, bulk modulus and pressure derivative of the bulk modulus for both B1 and B3 structure show percentage errors 0.45%, 0.13% The equilibrium lattice parameters, a0, are calculated as 5.449 Å for B3 structure and as 5.107 Å for B1 structure, both of which agree well with the corresponding experimental values of 5.410 and 5.06 Å . The deviation from the experimental data for C11, C12 and C44 calculated for the structure of B3 are found to be 7.0, 15.2 and 28.0% The mechanical stability conditions in the cubic structures can be expressed in terms of elastic constants as: C11 |
− |
C12 |
> 0, C44 |
> 0, C11 |
+ 2C12 |
> 0. The elastic constants of ZnS given in satisfy these stability conditions. The transition pressure from B3 structure to the B1 structure was first reported as 24.50 GPa by Bridgman , the intersection of the enthalpy-pressure curves of two structures yields the transition pressure founded as 18.50 GPa, which is consistent with the experimental , respectively. These quantities, except for C44 in B1 phase, increase linearly with increasing pressure, as seen in the . This trend obtained for elastic constants–pressure curves of two structures is consistent with that reported by Sahraoi et al. , respectively. Despite of some fluctuations in the Young modulus value, the general linear dependence trend on the pressure is observed.We also present lattice parameter, elastic constants, bulk modulus, shear modulus, young modulus, anisotropic parameter, Kleinmann parameter and Poisson ratio of ZnS in the B1 and B3 structures at elevated pressure in , respectively, with the available other theoretical calculations. To our knowledge no experimental data for the pressure dependent of the elastic constants of ZnS are given in literature. Therefore, our results can serve as a basis for future experimental and theoretical investigations. The values of shear modulus and Young modulus for both structures increase with the increase in pressure as shown in the tables. The anisotropy factor for B3 structure increases with the increasing pressure while it decreases for B1 structure. Although Kleinmann parameter for B3 structure goes up with pressure, it decreases as the pressure increases for B1. Kleinmann parameter of B3 structure calculated at zero pressure is close to the value of 0.715 reported in Ref. We have presented some results of the phase transition from B3 to B1 structures, which are based on the first-principle calculations. Some mechanical properties, such as the elastic constants, bulk modulus and pressure derivative of the bulk modulus of ZnS in the B1 and B3 structures are reported. We have determined the variation of elastic constants as a function of hydrostatic pressure. In addition, some structural parameters such as Kleinman parameter, Shear modulus, Reuss modulus, Voight modulus and anisotropy factor are also presented for the first time in this work. The phase transition from B3 structure to the B1 structure occurs at the pressure of 18.50 GPa, which is consistent with the other theoretical and experimental data. The behavior of the elastic constants under hydrostatic pressure for ZnS is also in good agreement with the theoretical calculations of Kheneta et al. Comparative study on local and global mechanical properties of bobbin tool and conventional friction stir welded 7085-T7452 aluminum thick plate7085-T7452 plates with a thickness of 12 mm were welded by conventional single side and bobbin tool friction stir welding (SS-FSW and BB-FSW, respectively) at different welding parameters. The temperature distribution, microstructure evolution and mechanical properties of joints along the thickness direction were investigated, and digital image correlation (DIC) was utilized to evaluate quantitatively the deformation of different zones during tensile tests. The results indicated that heat-affected zone (HAZ), the local softening region, was responsible for the early plastic deformation and also the fracture location for SS-FSW samples, while a rapid fracture was observed in weld nugget zone (WNZ) before yield behavior for all BB-FSW specimens. The ultimate tensile strength (UTS) of SS-FSW joints presented the highest value of 410 MPa, 82% of the base material, at a rotational speed of 300 rpm and welding speed of 60 mm/min, much higher than that of BB-FSW joints, with a joint efficiency of only 47%. This should be attributed to the Lazy S defect produced by a larger extent of heat input during the BB-FSW process. The whole joint exhibited a much higher elongation than the slices. Scanning electron microscopic (SEM) analysis of the fracture morphologies showed that joints failed through ductile fracture for SS-FSW and brittle fracture for BB-FSW.Bobbin tool friction stir welding (BB-FSW) is a type of solid-state welding technology based on the principle of conventional FSW For FSW, the temperature field determines not only the flow behavior of base material (BM) but also the microstructure evolution of different weld regions, and further influences the mechanical properties of joints Al-Zn-Mg-Cu alloy with a brilliant application prospect has been already widely used in aerospace fields The BM used in the present study was a 12 mm thick 7085-T7452 aluminum alloy plate. The nominal chemical composition of the BM is listed in . Based on previous studies, the welding parameters selected to produce various joints are shown in The temperature evolution during the welding process was detected by K-type thermocouples plugged in feature points at different positions of the plates. In order to protect thermocouples from destruction by the tool, blind holes of 1.5 mm in diameter and 25 mm in depth were designed. shows the positions of blind holes, which allow for the measurement of the temperature changing process with the AS (by points 1–9) and RS (by points 10–12) of welds, the outside of pins (by points 7–10) and the thickness direction of work pieces (by points 1–9).After welding, the specimens for metallographic analysis were cut perpendicular to the welding direction, and then grinded with #240-#7000 sandpaper, polished using a diamond paste and etched with Keller’s reagent (3 mL HNO3, 6 mL HCL, 6 mL HF and 150 mL H2O). Macro morphology was observed using a laser scanning microscope (OLS4000), and microstructure analysis was performed by an optical microscope (OLYMPUS GX71) and the Image-Pro Plus software to measure the grains size. In this study, the cross section of weld is divided into three slices along the thickness direction, which are top layer, middle layer and bottom layer, respectively, to draw a comparison analysis of the microstructure evolution for two types of FSW welds.The 2D microhardness maps were obtained at the whole weld region on the polished cross sections using a Vickers hardness tester (THV-1D) with a testing load of 200 g and a dwell time of 20 s. The spacing between adjacent indentations was 0.5 mm. The tensile samples were prepared according to ASTM E8 with a gauge of 32 mm long by 10 mm wide, and the specimens were cut into equal three slices. Tensile properties of both the whole and slices of joints were evaluated with two tensile specimens cut from the same joint. The room temperature tensile tests were carried out at a strain rate of 10−3 |
s−1 using an electron universal testing machine (Instron-3382), and the local strain fields were determined by digital image correlation (DIC). Each specimen in this test was prepared by applying a random speckle pattern on the cross section using black and white spray paints. During the test, the specimen was photographed every half second by CCD cameras. After tensile test, the fracture features of the specimens were observed by scanning electron microscopy (X-mzx20/INCA 250).The transient temperature curves of SS-FSW and BB-FSW processes are presented in . On the whole, the variation tendencies of curves for both welding processes were essentially consistent, the initial heating rate and peak temperature of BB-FSW, however, were higher than those of SS-FSW, which agrees well with previously reported results shows the peak temperatures of different thermocouple points during the welding process, it can be seen that the highest peak temperature with a value of ∼510 °C was recorded at point 9 on the AS of the BB-FSW joint under the rotational of 200 rpm and welding speed of 150 mm/min. For the SS-FSW joints, the corresponding value was much lower (∼455 °C) under the rotational of 300 rpm and welding speed of 60 mm/min. These facts indicate that bobbin tool provides more heat input during the welding process due to the existence of its lower shoulder, the stirred zone, therefore, experienced a higher thermal cycle and severer plastic deformation during the BB-FSW process., it can be observed that the peak temperature on the AS of the SS-FSW joints decreased gradually with increment of the distance from blind holes to the top surface and the weld line, respectively. The peak temperature on the RS was lower than that of the same position on the AS. The corresponding values measured at points 12, 11 and 10, for instance, were lower by 31 °C, 29 °C and 16 °C than those of points 2, 5 and 8, respectively, at the rotational speed of 300 rpm. It is attributed to the fact that the welding direction was the same to the linear velocity direction of rotating shoulder on the AS, and thus the tool experienced higher frictional resistance and plastic shear force, leading to the material on the AS obtained more friction heat than that on the RS.The temperature distribution of BB-FSW joints along the thickness direction, by contrast, was of much difference. The peak temperature of lower shoulder affected zones was slightly higher than that of upper shoulder affected ones. With the rotational speed of 200 rpm, for example, the highest temperatures recorded at points 3, 6 and 9 were higher by 6 °C, 4 °C and 5 °C than those of points 1, 4 and 7. As there is no backing plate used in BB-FSW, the main heat-dissipating form for the lower affected zone is the air convection displays the cross section macrographs of SS-FSW and BB-FSW specimens produced by using two sets of welding parameters, respectively. For each SS-FSW weld, the AS is on the left side while the RS is on the right in the figure through the whole paper, which differs from the BB-FSW welds due to opposite rotation directions of two tools. The SS-FSW weld exhibited a bowl-like shape, the top cross section of weld corresponded with an approximate width of the shoulder diameter and the weld bottom possessed the smallest width of the tip diameter of the pin. By contrast, the cross section of BB-FSW samples was nearly dumbbell shaped, characterized by wider upper and lower layers (comparable to the diameter of shoulders) and a smaller middle layer (greater than the diameter of the pin), which was attributed to the fact that the top and bottom surface of BM experienced the maximum deformation and frictional heat during BB-FSW process.The macrostructure of the BB-FSW weld is more symmetrical compared with SS-FSW weld due to the use of a symmetrical bobbin tool. Moreover, the three distinguishing regions formed during both FSW processes, i.e. the WNZ, TMAZ and HAZ are indicated in . It is worthwhile to note that there is a rather sharp transition between the WNZ and the TMAZ on the AS of each weld, which is indicated by red arrow in , while a much smoother interface shows on the RS, which is consistent with phenomena recorded in previous studies (b, c). The local material flow of the PSZ increased slightly for both SS-FSW and BB-FSW when increasing the rotational speed, leading to the dimension change of welds. Additionally, the appearance of S line through the WNZ is presented in (d) at the rotational and welding speeds of 200 rpm and 150 mm/min, respectively. It probably originated from the oxidized layer on the 7085 aluminum alloy surface, which was produced by higher thermal cycle at the rotational speed of 200 rpm, and the S line defect might give rise to the weakness of mechanical properties.High magnification images of grain morphologies of the BM and three different weld zones are presented in , which were obtained by the optical microscopy. Compared with the BM exhibiting slightly elongated grains, the WNZ affected directly by the tool showed small equiaxed recrystallized grains ((b, c)), since the material experienced a high degree of plastic deformation and frictional heating simultaneously. The TMAZ was located at edges of the pin, and thus equiaxed recrystallied grains mixed partially with rotated elongated grains ((d, e)) were produced due to the relatively insufficient plastic deformation and the plastic shear stress of the flowing material during the welding operation. The HAZ, however, was only influenced by the thermal cycle but no stirring mechanically of the tool. Therefore the grain orientation was consistent with the BM while the grains were coarsened partially ((c, g)), resulting from the annealing treated microstructure of HAZ. shows the grains characteristics of the upper, middle and lower layers of WNZs along the thickness direction for both FSW techniques. It is observed that grains in the upper layer of WNZ of SS-FSW joint were larger than the ones in the lower layer (a–c). The average grain size of upper layer, measured with the average linear intercept method, was 6.05 μm while the middle and lower regions exhibited an average grain size of 4.87 μm and 3.56 μm, respectively, at the rotational speed of 300 rpm. This is because the heat input from the single side tool decreases gradually through the thickness, leading to the grain size presents a decline trend from the upper to lower layer of WNZ. Unlike the SS-FSW specimen, the grains in the upper layer of WNZ of the BB-FSW samples were slightly smaller than those in the lower layer ((d–f)), corresponding to the results of temperature distribution, indicating that the BB-FSW technique resulted in a more uniform grain structure in the WNZ along the thickness direction. For instance, when the rotational speed was 150 rpm, the upper, middle and lower layers had an average grain size of 6.34 μm, 6.22 μm and 6.53 μm, respectively. It can be concluded that the variations in grain evolution along the thickness were more apparent for the SS-FSW samples than those of BB-FSW.Quantitative data on the grain sizes of WNZ through the thickness direction at different rotational speeds are presented in . For both FSW techniques, higher rotational speeds gave rise to a larger grain size, and specifically, the average sizes of recrystallized grains of WNZs for SS-FSW and BB-FSW increased from 4.76 μm and 6.07 μm to 5.71 μm and 7.39 μm, with the increase of rotational speeds from 300 rpm and 150 rpm to 600 rpm and 200 rpm, respectively. It is related to a larger heat input provided by a higher rotational speed.The microhardness distribution of the joints is mainly associated with the evolving characteristics of grains and the state of precipitation phases during the welding process . It can be noted that the microhardness profiles exhibited a typical “W” shape along the cross section for both of SS-FSW and BB-FSW samples, the same as the phenomenon observed by previous studies in SS-FSW and BB-FSW aluminum alloys Compared with microhardness values of the BM scattered between 150 and 165 HV, the microhardness in the WNZ of all the joints dropped significantly. However, the average microhardness of WNZ was higher than that of the TMAZ and the HAZ, and it is attributed to the fine equiaxed microstructure in the WNZ produced by a significant effect combined of the thermal cycle and plastic deformation. Moreover, the microhardness values of the HAZ on the AS were slightly lower than those on the RS, which was related to the finer grains on the RS.For SS-FSW joints, the minimum microhardness showed a decreasing trend when increasing the rotational speed, indicating an enhanced negative effect of the thermal cycle on the mechanical properties of joints, while a reverse trend was observed for BB-FSW joints when the rotational speed was increased from 150 rpm to 200 rpm. It is also noteworthy that the heterogeneity of microhardness distributions was observed in the thickness direction for SS-FSW joints, which was commonly reported by other researchers During the BB-FSW process, the heat input was principally provided by the friction between the two shoulders and surfaces of the workpiece, while the pin guaranteed the plastic flowing of the material inside. The positions of upper and lower shoulders were approximately symmetrical to the weld mid-thickness plane, resulting in a symmetrical heat generation and material flow around the middle layer of welds presents the tensile test results of the whole and different slices of joints obtained under different welding conditions as well as the BM. It can be seen that the BM exhibited the highest yield strength (YS), ultimate tensile strength (UTS) and elongation with values of 443 MPa, 500 MPa and 18.7%, respectively. Specimens welded at the rotational speed of 300 rpm for SS-FSW showed approximately identical YS as those produced at 600 rpm except for the top slice of joint. The YS of the top, middle and bottom slices of joints presented a decreasing trend with values of 318 MPa, 303 MPa and 274 MPa, respectively, the average of which was substantially the same as that of the whole joint. It was evident that the corresponding UTS, however, exhibited a slightly lower gradient along the thickness direction with values of 412 MPa, 399 MPa and 390 MPa, respectively, reaching the highest joint efficiency (UTSJOINT/UTSBM) of 82%, and the whole joint presented an approximate UTS of 410 MPa close to the one of top slice (412 MPa), as shown in When the rotational speed was increased to 600 rpm, the YS were 262 MPa, 316 MPa and 283 MPa across the thickness, while the UTS dropped to 273 MPa, 396 MPa and 386 MPa, respectively. The top slices of joint all fractured at the WNZ, resulting worse YS and UTS. The elongation was measured by the average strain over the gauge length involving all the different regions. The highest elongation was obtained from the whole joint of SS-FSW at the lower rotational speed, with a value of ∼10.2%. Compared with the slices along the thickness direction, the elongation of the whole joint increased significantly for SS-FSW at lower rotational speed, exhibiting a reverse tendency with the YS. These results may be related to the larger effective bearing area of the whole joint, which can support a higher ultimate tensile load than different slices of joint during the tensile process, since all the samples had similar UTS. The same strain rate made the whole joint have experienced more sufficient plastic deformation. Additionally, the time of crack propagation and necking till the final fracture was relatively longer for the whole joint after the local material reached the critical value of fracture strength and microcracks formed, resulting in that the whole joint owned an obviously higher elongation than slices of the joint. Since the samples welded at the rotational speed of 300 rpm exhibited a higher microhardness distribution than those at 600 rpm (see ), which contributed to slow down the formation and growth rate of cracks, resulted in a more enhanced strength and ductility.By comparison, the tensile strengths of BB-FSW specimens degraded significantly as can be seen in . All samples had failed before the tensile stress reached YS. The UTS of the whole joint was 161 MPa at the rotational speed of 150 rpm, only achieved 32% of the BM, while different slices of joints presented relatively higher UTS with joint efficiencies of 44%, 42% and 47% for the top, middle and bottom slices, respectively. Furthermore, the elongation of BB-FSW joints decreased remarkably as shown in (d). It has to be pointed out that an increased rotational speed led to worse tensile strengths. The higher thermal cycle was mainly responsible for the difference in the mechanical properties of two FSW techniques as mentioned in sections , which will also be discussed further below. shows the evolution process of a heterogeneous strain distribution of the whole and different slices of SS-FSW samples, which were measured by DIC with the purpose of evaluating quantitatively the deformation of different zones during the tensile test , where the YS values were calculated according to the strain evolution of adjacent grid points along the loading direction for every image, assuming that the local stress in every region equaled to the global stress.Firstly, the strain was relatively homogeneous without the strain concentration through the transverse section before the stress reached 216 MPa, this stage was mainly dominated by elastic deformation. Then, the deformation was localized in the HAZ of the RS at the stress of 246 MPa, where existed the minimum YS (see ). It is known during the tensile process, the weakest region of the joint is more susceptible to the stress-strain concentration. When the YS reached 285 MPa, the strain response of the specimen was located in the HAZ of the RS principally and the AS partly, with less degree of deformation in the TMAZ and the WNZ.The local strain in the HAZ of the AS became more distinct gradually than that of the RS with the increase of stress, which was attributed to the plastic deformation strengthening on the RS, followed by a more rapid localization of strain in the HAZ of the AS consequently. At the strain state close to the fracture, the occurrence of necking was observed at the corresponding region. It can be expected the strain localization took place before the plastic deformation of joints, and finally the failure took place as about 45° shear fracture in the HAZ of the AS, where existed the lowest microhardness value (shown in ) and it was more favorable for the crack initiation. Moreover, the local strain reached the maximum value of ∼37% before fracture.The strain states at the frames of YS, UTS and failure for different slices are presented in b–d. It can be seen, the fracture of different slices was in the same process as the whole joint, while the degrees of deformation before failures were less than that of the whole sample and exhibited an increased trend along the thickness direction, with values of 15%, 17% and 22%, respectively, corresponding to the elongation trend (, there was a moderate increase in YS of the WNZ along the thickness direction, which was in accordance with the evolution results of grain sizes ( shows the DIC results of strain distribution of BB-FSW samples produced at the lower rotational speed, including the states of UTS and failure of the whole and different slices of the joint. In contrast, the variation of strain for BB-FSW joints was entirely different, and the largest local strain was only with a value of ∼1.1% when a rapid fracture happened suddenly, suggesting that the fracture location of the sample was still under elastic loading. It should be mentioned although the local softening regions led to the strain concentration in the HAZ at the initial stage of deformation, for all BB-FSW specimens produced at different rotational speeds, the failure occurred in the WNZ without plastic deformation. It was evident that the location of crack initiation was not related to any softening regions in the WNZ, according to When considering the microstructure characteristics of welds, however, the crack initiation location was exactly identical to the S line defect (shown in d), suggesting the S line had a negative effect on mechanical properties of joints, as the crack growth was mainly along the boundaries of S line, which was of much difference from the fracture behavior of SS-FSW samples. Also, it is reasonable to hypothesize that the same defect existed in the WNZ of BB-FSW joint welded at the lower rotational speed, without presenting obviously in the weld morphology (shown in c), and it was probably attributed to the insufficient etching treatment during the preparation of metallographic samples. Additionally, a more significant defect of S line was produced when the rotational speed increased, resulting in a severer deterioration of mechanical properties in the WNZ of the joint.The representative SEM micrographs of the fracture surface of SS-FSW and BB-FSW samples are presented in . It was observed that the SS-FSW joint which showed higher elongation contained a fracture surface with a few small dimples as well as tearing ridges, indicating the similar characteristics as a ductile mechanism of fracture. For the BB-FSW joints, there were no remnant particles on the fracture surface, though the fracture behavior was related to the S line, signifying a brittle mode of fracture.A 12 mm thick 7085-T7452 aluminum alloy was joined by conventional single side and bobbin tool friction stir welding, respectively, and the temperature distribution, microstructures and mechanical properties of the joints along the thickness direction were investigated in detail. The conclusions of significance are drawn as follows:The distribution of temperature gradient along the thickness direction was nonuniform for the SS-FSW joints, exhibiting a decreased trend, while the temperature of lower shoulder affected zones was slightly higher than that of upper shoulder affected ones for the BB-FSW joints, introducing a much smaller temperature gradient along the thickness direction.The bowl-shaped cross section of SS-FSW joints and dumbbell-shaped cross section of BB-FSW joints were all divided into three different zones: WNZ, TMAZ and HAZ. The boundary between the WNZ and the TMAZ and the lines of plastic flow were more obvious on the AS of weld. There was no observed difference of grain size along the thickness direction at the WNZ of BB-FSW welds.The microhardness distribution of both FSW joints was similar to a W shape, and the lowest hardness was located at the HAZ on the AS. The UTS of the SS-FSW joints reached its peak value (410 MPa), at a rotational speed of 300 rpm and a welding speed of 60 mm/min, which is 82% of the parental material, which is much higher than that of the BB-FSW joints with a joint efficiency of only 47%. The whole SS-FSW joints present a much higher elongation than the slices. Moreover, the deformation was localized in the HAZ of the RS at the stress of 246 MPa (minimum YS) and about 45° shear fracture was located in the HAZ of the AS (lowest microhardness value) due to the rapid localization of strain.Failure initiated from the HAZ for the SS-FSW samples with a ductile fracture, while the fracture mode changed to a brittle fracture in the WNZ for the BB-FSW samples.Sigma phase evolution in Co–Re–Cr-based alloys at 1100 °CCo–Re-based alloys have been introduced as a novel metallic system that possesses a wide exploitable composition range and high melting temperatures. The poor oxidation resistance of the binary system can be improved by alloying chromium. However, adding chromium also leads to the occurrence of the sigma phase of type Cr2Re3. In the present study, we investigate the evolution of the sigma phase during creep and aging at 1100 °C for three selected alloys based on the ternary composition Co–17Re–23Cr (at.%). In all alloys, sigma phase populates the grain boundaries of the hexagonally close-packed (HCP) matrix phase in a blocky morphology. Additionally, a fine dispersion of lamellar sigma phase in the grain interiors has formed during the initial processing or forms during thermal exposure. This precipitation takes place by a cellular reaction that transforms a supersaturated HCP phase into alternating lamellae of a near-equilibrium HCP phase and the sigma phase. The process therefore has the character of a discontinuous precipitation. Using orientation imaging microscopy, we observe an orientation relationship between the lamellae, which describes the basal plane of the HCP phase to form a coherent interface with the base layer of atoms of the tetragonal sigma phase. After long-term thermal exposure to 1100 °C, overaging of the lamellar structure results in spheroidization of the sigma lamellae and subsequent Ostwald ripening.The search for high temperature materials exceeding the temperature capability of Ni-based superalloys promotes research into a variety of material classes, including ceramic matrix composites, intermetallics, high melting point metal alloys and refractory metal systems based on niobium or molybdenum Rhenium is a key element in modern high temperature alloys. In monocrystalline Ni-based superalloys, the creep strength is improved by Re-contents of up to 6 at.%, leading to a temperature advantage of up to 71 °C as compared to Re-free alloys of the first generation The phase diagram of the binary system Co–Re reveals full miscibility of the two elements in a hexagonally close-packed (HCP) solid solution for a large range of concentrations and temperatures Oxidation resistance of binary Co–Re-alloys is, however, rather poor. First experimental alloys, introduced in Rösler's study, are therefore based on the ternary composition Co–17Re–23Cr (in at.%), adopting a chromium content of 23 at.% from conventional Co-based high temperature alloys. By adding chromium to the binary composition, a slight decrease of the mass loss associated with the formation of volatile oxides could be achieved in air at 1000 °C Very few metallurgical studies in literature have considered the ternary system Co–Re–Cr. In an experimental study, Sokolovskaya et al. published isothermal sections of the ternary phase diagram at high temperatures that reveal the presence of the disordered sigma phase of type Cr2Re3 for a wide composition range Three alloys were produced by vacuum arc melting and a subsequent thermo-mechanical treatment. Chemical compositions and heat treatment conditions are listed in . The ternary alloy CoReCr contains 17 atomic percent of rhenium to stabilize the HCP lattice and 23 atomic percent of chromium for enhanced oxidation resistance at intermediate temperatures. It represents the basis of all considered alloy compositions. The two model alloys CoReCrC + B and CoReCrCTa + B have been originally designed for the investigation of carbide formation and particle strengthening triggered by the addition of 2.6 atomic percent of carbon and a supplemental addition of 1.2 atomic percent of tantalum, respectively. Originating from a further advancement in alloy design, 200 ppm weight percent of boron have been added to enhance the grain boundary cohesiveness and improve ductility Although oxidation at intermediate temperatures is reduced by the chromium content of the alloys investigated, alloy optimization to avoid metal loss at high temperature is still under ongoing development. For high temperature creep testing, we have modified a standard constant load creep machine of type Mayes TC20, to enable testing in an inert gas atmosphere. A detailed description of the test rig has been given in a previous publication Scanning electron microscopy (SEM) has been carried out on a field emission scanning electron microscope of type Leo Gemini 1530 VP. Occurring phases in the alloys investigated have been identified and described in earlier studies based on diffraction experiments with X-rays, electrons and neutrons, as well as energy dispersive X-ray analysis We use the term “initial state”, referring to the material state after casting and the subsequent thermo-mechanical treatment, as given in . Initial state microstructures of all alloys investigated are presented in . A distinct difference in size and distribution of sigma phase is notable by comparison of the three alloys. In (a), the ternary alloy CoReCr shows a two-phase microstructure consisting of the HCP matrix phase that embeds small particles of round-shaped sigma phase with diameters well below 10 μm. Additionally, the BSD image reveals globular pores from the processing. In alloy CoReCrC + B, regions with an inhomogeneous distribution of several phases, referred to as “inhomogeneous regions” in the following, are prominent around grain boundaries and junctions, marked by dashed lines in (b). These inhomogeneous regions are populated by sigma phase in a stretched, blocky morphology and adjacent carbides. Moreover, in the close vicinity of inhomogeneous regions or grain boundaries, a cellular dispersion of fine sigma phase precipitates extends into the grain interiors. Contrast shading of the matrix phase indicates the presence of sub-boundaries inside the grains. Porosity is less pronounced, as compared to alloy CoReCr, since the processing route included HIP. The inset shows a region of the micrograph at higher magnification, resolving very fine carbides of type M23C6. Meeting expectations, these carbides are known to be enriched in chromium, as revealed by investigations on an alloy with the same composition, but without boron (c). Large, round-shaped blocks of sigma phase span more than 20 μm in diameter. Slightly smaller particles of TaC can be distinguished as they appear brighter, due to an excess of backscatter electron intensity. A distinctively characteristic feature of this microstructure is a dispersion of fine sigma phase precipitates that interpenetrates the HCP matrix over wide areas and appears to be lamellar in some regions. Not presented here, transmission electron microscopy (TEM) revealed that globular carbides of type TaC with a diameter of about 20 nm are embedded in the HCP matrix phase. In earlier studies, we have already reported the presence of these carbides for an alloy with the same nominal composition, but without boron addition Creep tests at a temperature of 1100 °C and an initial stress of 50 MPa revealed rupture times below 10 h, for all alloys investigated. In , the deformation behavior from loading until rupture of the specimen is shown in a plot of the strain rate ɛ˙ versus the true creep strain ɛ. Alloys CoReCr and CoReCrC + B exhibit rupture strains close to 5 percent. For alloy CoReCrCTa + B, a comparably high rupture strain of 15.7 percent has been observed. All alloys show a distinct primary creep regime as the strain rate decreases until a true creep strain of 1–2 percent is reached. We have determined the secondary strain rate ɛ˙s as the absolute minimum of the curve. Values for ɛ˙s range from 6.7·10−7 s−1 to 3.3·10−6 s−1 for alloys CoReCrC + B and CoReCrCTa + B, respectively. Subsequent to the strain rate minimum, an extended secondary creep regime is observed, showing a constant gradient, typical for constant load tensile creep testing. Eventually, at a higher strain, the onset of accelerated creep marks the beginning of the tertiary regime that leads to fracture of the sample by damage accumulation.After creep testing to rupture at 1100 °C and 50 MPa, creep samples have been subjected to metallographic preparation. BSD images of longitudinal sections of the three alloys investigated are shown in . Alloys CoReCr and CoReCrC + B exhibit intergranular damage, as pores have agglomerated and cracks have formed predominantly along grain boundaries that are oriented perpendicular to the load axis. In the microstructure of alloy CoReCrCTa + B pores have formed as well, but cracks are completely absent at some distance from the rupture surface., the observer easily notices that the sigma phase fraction in all the alloys has strongly increased after creep. In alloys CoReCr, and CoReCrC + B sigma phase particles have formed in pearl-necklace morphology along the grain boundaries, as apparent in (a) and (b). Additionally, fine precipitation of sigma phase into the grains has taken place in a lamellar morphology. Lamellae of sigma phase and HCP phase alternate in regions that are surrounded by reaction fronts, indicating that this precipitation has the character of a cellular reaction. For alloy CoReCrCTa + B a fine dispersion of sigma phase was already observed in the initial state, cf. (c), former lamellar portions of finely dispersed sigma phase appear spheroidized after creep. Moreover, both blocky and fine precipitates have coarsened., we present results of an OIM study of a cellular reaction front in alloy CoReCr after creep. The investigated region includes straight lamellar sigma phase precipitation behind the reaction front. Crystal orientations have been obtained from electron backscatter diffraction patterns for the matrix phase in front of and behind the reaction front and for each sigma phase lamella. The projections of unit cells along the normal direction of the sample surface are outlined in (a). The orientation of the HCP phase changes across the reaction front without indicating any crystallographic relationship between the retreated grain and the HCP lamellae formed by the reaction. All HCP lamellae are uniformly oriented and protrude into the retreated grain by bulging out the reaction front between the sigma lamellae. The orientation of the tetragonal sigma phase lamellae deviates only slightly from lamella to lamella and the deviation is traced back to a small angle rotation around the base plane normal of the unit cell. An orientation relationship between matrix and sigma phase lamellae is visualized by the pole figure in (b). The superposition of spots measured for the two lamellar phases reveals a strong alignment of plane normals for the (0001) matrix plane and the (001) plane of the sigma phase. Moreover, the traces of the aligned planes coincide with the trace of the interface between matrix and precipitate. A weaker relationship is observed for type {2¯110} matrix poles and type {410} sigma phase poles. This corresponds to an approximate parallelism for directions of types 〈2¯110〉 and 〈410〉 in the matrix and the sigma phase, respectively. In the investigated planar section, one of these directional alignments is approximately perpendicular to the reaction front of the cell.In aging experiments, the sigma phase precipitation was quantitatively investigated for alloys CoReCrC + B and CoReCrCTa + B.(a) shows a series of BSD images for each alloy, revealing the microstructure for the initial state and after different aging times ta = 2 h, ta = 20 h and ta = 200 h at 1100 °C. In alloy CoReCrC + B, sigma phase and carbides present at inhomogeneous regions vanish while, with increasing aging times, a more homogeneous distribution of sigma phase precipitates forms and grows on grain boundaries and sub-boundaries. After long-term aging (ta = 200 h) growth and interconnection of boundary precipitates constitute a fragmentary network along the interfaces and, additionally, cellular precipitation establishes local distributions of very fine sigma precipitates (marked by an arrow in (a)). In alloy CoReCrCTa + B, a widespread dispersion of fine sigma phase is already evident the initial material state, (c). This fine morphology of sigma phase appears to steadily coarsen during the incremental aging treatment. Large blocky sigma particles seem to be less affected by the thermal exposure.Drawn from quantitative evaluation of the BSD images, we present data for the sigma phase fraction ϕp plotted versus the logarithmic scale of aging time ta in (b). Both alloys exhibit a reduction of sigma phase fraction with respect to the initial state microstructure after ta = 2 h. For alloy CoReCrC + B, a slight increase is noticed after ta = 20 h, the absolute value still remaining below the initial state level. In the case of alloy CoReCrCTa + B, sigma phase area fraction decreases even further and establishes the minimum value of our measurement at ta = 20 h. The decrease of area fraction can likely be related to the homogenization of inhomogeneous regions. After long-term aging to ta = 200 h, in both alloys the total sigma phase fraction increases significantly to values well beyond the initial state level. This reflects the high amount of precipitation found by metallographic observations.Plotted versus the same abscissa, the number density of sigma particles np is presented in (c) and the median of the logarithmic precipitate area distribution logA¯p is shown in (d). For alloy CoReCrC + B, the number density remains approximately constant up to an aging time of ta = 20 h and slightly increases after ta = 200 h. The area of individual particles increases steeply until ta = 20 h, followed by a slight decrease after a long aging time. By relating the data to microscopic observations, these findings indicate that after the initial homogenization, boundary precipitates grow during the first stages of aging, while cellular reactions rarely occur. In the later stage of aging, fine precipitation by cellular reactions becomes more dominant, thus leading to a higher number density and reducing the average precipitate size. In alloy CoReCrCTa + B, the number density of sigma phase precipitates steadily decreases until the maximum aging time in our measurement ta = 200 h. The average precipitate area immediately increases after thermal exposure and on a logarithmic time scale this increase is even amplified as aging proceeds to the maximum aging time. In this alloy, the precipitation scenario commences already with a widely completed process of fine, partly lamellar precipitation. As a part of homogenization, sigma lamellae spheroidize as aging proceeds. Classical Ostwald ripening leads to a steady growth of larger precipitates at the expense of smaller ones.Our experimental observations reveal that the sigma phase of type Cr2Re3 is a prominent feature of the microstructure in Co–Re–Cr-based alloys. Phase fraction and morphology in the initial material state after processing strongly depends on composition and parameters of thermo-mechanical treatment. The extensive precipitation of additional sigma phase during creep and aging indicates that heat-treatment conditions selected in this study lead to a non-equilibrium microstructure and need further optimization. Microscopic observations allow for distinction between two sigma phase morphologies, blocky particles that are predominantly present on grain boundaries and finely dispersed precipitates in the grain interior that originate from a cellular precipitation reaction. Analysis of phases and crystal orientations at a cellular reaction front indicates that the reaction has the character of a discontinuous precipitation, as it transforms a supersaturated HCP matrix phase ɛsup into alternating lamellae of a near-equilibrium HCP phase ɛeq and the sigma phase σ.A detailed description of the process of discontinuous precipitation is given in many textbooks covering diffusional phase transformations, e.g. Refs. First described by Frank and Casper, the unit cell of the tetragonal sigma phase can be derived by shearing a regular kagome tiling , we illustrate the correlation of Frank and Casper for atoms in the base layer with atom positions [h, k, 0]. A shear angle of 2.2° transforms the rhombic cell of a kagome tiling into a square that constitutes the base layer of the tetragonal sigma phase unit cell.A proper fit of the sigma phase base layer and the basal layer of the HCP matrix can be obtained by shearing the sigma lattice back into the undistorted kagome tiling and additionally adjusting the misfit between the HCP lattice constant a and the side length of hexagons/triangles in the kagome structure aˆ. In , we demonstrate the planar orientation relationship represented by expressions after these geometrical adjustments. The configuration described here is very similar to the one reported by Rae and Reed for (001) planes of the sigma phase and (111) planes of the FCC γ-phase in second generation Ni-based superalloys Considering that the real lattice constants of the HCP matrix is increased due to the solid solution of large Re-atoms and taking into account a decreased unit cell size for the non-stoichiometric, Co-containing sigma phase, the real lattice misfit for the alloys investigated in this study may assume a considerably lower value.Carbides in alloys CoReCrC + B and CoReCrCTa + B may indirectly influence the progress of sigma phase precipitation. In alloy CoReCrC + B a high percentage of the alloy's chromium content is bound by Cr-rich lamellar carbides of type M23C6. Mukherji et al. reported that the onset of dissolution for this type of carbides in a similar alloy starts at about 1000 °C (c)). In this case, it can be assumed that the process of discontinuous precipitation had been widely completed before creep or aging experiments were conducted. Long-term aging of this microstructure leads to ripening and spheroidization of sigma phase lamellae. Both of these processes minimize the interfacial energy and relieve the strain energy associated with the semi-coherent nature of the interface between matrix and sigma phase lamellae.Deformation mechanisms in Co–Re-based alloys during high temperature creep have not been explicitly addressed in this study and will have to be discussed on a broader experimental basis, considering dislocation plasticity, carbide strengthening, diffusion processes and grain boundary sliding. However, from our creep data and our microscopic observations we may draw the conclusion that the total rupture strain is significantly increased, when the microstructure contains a dispersion of fine sigma phase precipitates, as in the case of alloy CoReCrCTa + B. The enhanced ductility goes along with a detrimental effect on creep strength, the secondary strain rate being shifted to higher values. Here, this behavior can only be discussed with respect to potential creep mechanisms that need further investigation. Assuming dislocation creep as a dominant deformation mechanism, the ductilization may be related to the softening of the HCP matrix phase due to the depletion of rhenium, an element that is well-known for its remarkable contribution to solid solution strengthening. However, for alloy CoReCr and a B-free variant of alloy CoReCrCTa + B, low stress exponents n < 2 have been observed for creep at 1100 °C We have investigated the evolution of the sigma phase of type Cr2Re3 in Co–Re–Cr-based alloys during creep and aging at 1100 °C. From our experimental observations we draw the following conclusions:In the alloys investigated, two distinct morphologies of sigma phase can be detected. Large blocky particles predominantly populate the grain boundaries and junctions. In the grain interior, dispersions of fine sigma phase precipitates exhibit a partly lamellar morphology.The fine sigma phase dispersions originate from a cellular reaction that transforms a supersaturated HCP phase into alternating lamellae of a near-equilibrium HCP phase and the sigma phase by means of a discontinuous precipitation.The discontinuous precipitation occurs during thermal exposure at 1100 °C. However, low heat treatment temperatures for alloy CoReCrCTa + B apparently have triggered the discontinuous precipitation during the initial processing of this alloy, establishing a widespread distribution of fine sigma precipitates in the initial state microstructure.Immediately after the precipitation process, the HCP and sigma phase lamellae exhibit an orientation relationship that resembles a planar coherency of the HCP basal plane and the base layer of the tetragonal sigma phase. For this configuration, the sigma phase unit cell is sheared by 2.2° and the misfit of interatomic distances that must be compensated is δ = 0.030, considering ideal phase stoichiometry.During long-term aging, the number of blocky boundary particles of sigma phase increases and the particles grow in size. The lamellar structures of sigma phase spheroidize and ripen after the discontinuous precipitation is completed. All the observed processes of precipitation and particle growth lead to a continuous increase of the overall sigma phase fraction.The sigma phase precipitation during thermal exposure appears to increase the achievable creep rupture strain and to deteriorate the creep strength. Possible reasons for this influence are the softening of the matrix phase due to Re-depletion or the introduction of cellular reaction fronts as additional interfaces that may assist boundary diffusion creep.Static and fatigue behavior of pultruded FRP multi-bolted joints with basalt FRP and hybrid steel-FRP boltsThis study investigates the effect of bolt types on the static and fatigue performance of basalt fiber-reinforced polymer (BFRP) multi-bolted double-lap connections. Three types of bolts are used: stainless-steel (SS), BFRP, and hybrid steel-FRP (HSFRP) bolts. Firstly, static tensile tests using steel single-bolted double-lap connections are conducted to determine the mechanical properties and failure modes of the proposed bolts. Secondly, static and fatigue tests using BFRP double-lap connections with six bolts of either SS, BFRP, or HSFRP were conducted. Finally, post-fatigue static tests were conducted to evaluate the deterioration of the composite joints caused by fatigue loading. Load-displacement curves, failure modes, fatigue life, S-N curves, and stiffness degradation are used to evaluate the effect of the bolt type on the behavior of the BFRP joints. Results indicated that SS bolts can be replaced entirely with BFRP bolts without affecting the static and fatigue performance of the joints. In addition, compared to the brittle failure of both the SS and BFRP bolts, the proposed HSFRP bolts exhibited ductile behavior which could be the key to achieving ductile composite structures. Moreover, the HSFRP bolts dramatically prolonged the fatigue life of the composite joints compared to the joints with SS and BFRP bolts.Existing structures built from conventional materials, such as timber, masonry, concrete, and steel, suffer from a number of problems, such as corrosion, degradation, and other aging-related problems. These problems not only affect the serviceability and maintenance costs of the structures, but also result in a large number of potential safety issues that could result in accidents. There is, therefore, a necessity for alternative materials to overcome these problems. Fiber reinforced polymer (FRP) is considered a promising construction material to replace and overcome the problems of the aforementioned materials due to their non-corrosive nature, high strength, and lightweight. Initially, the applications of FRP composites were limited to the military and aerospace industries. More recently, FRP has been introduced into the civil engineering industry for the strengthening and repairing of existing structures, and as reinforcement bars for new structures Connections, the most important and critical parts for any structure, control the serviceability and strength of composite structures. Bonded, bolted, and hybrid bonded-bolted connections are the most common joint systems used in FRP pultruded composite structures. Bolted connections are the most frequently used connection type because of their advantages, such as being de-constructable and less affected by environmental conditions Recently, there has been an increasing effort from researchers to promote the structural applications of composite structures by developing new connection methods and evaluating short- and long-term behavior of composite joints under both normal and extreme conditions. For instance, Bai and Yang Most of the experimentally tested joint specimens were fabricated using glass/carbon FRP plates and steel bolts The use of thousands of bolts in civil engineering structures, and even more in aerospace composite structures (approximately three million bolts are used in the Airbus A380 and Boeing 747-800 aircraft), increases the overall weight of the structure In this study, two new types of bolts (BFRP and hybrid steel-basalt FRP (HSFRP) bolts) are proposed to enhance the behavior of the pultruded FRP connection. Firstly, the shear strengths and failure modes of the proposed bolts are investigated and compared to conventional stainless-steel (SS) bolts. Static and fatigue tests were then conducted to evaluate the performance of multi-bolted double-lap BFRP joints connected by SS, BFRP, and HSFRP bolts.The pultruded BFRP plates were produced by GMV Company (Nanjing, China). The pultruded BFRP plate is orthotropic and comprises resin, unidirectional (0°) basalt roving to provide strength in the longitudinal direction, and three layers of bidirectional fiber sheets to improve the strength of the plates in the transverse direction. An alignment machine with a customized mold was used to align the unidirectional roving and the bidirectional fiber sheets together before being impregnated in resin. shows a schematic diagram of the mold used and the arrangement of the three bidirectional layers and the unidirectional fibers that were used to prepare the pultruded BFRP plate. The first sheet layer was placed on the top surface, the second one on the bottom surface, and the third one in the middle. The basalt roving and the three layers of the sheets were bonded with Sanyu L-500 resin. The fiber volume fraction of the used pultruded BFRP plates, and the mechanical properties of both the basalt fibers and Sanyu L-500 resin, are presented in Tensile tests of the BFRP pultruded plates were conducted according to the guidelines of ASTM (a)]. Five samples, which were cut along the pultrusion direction, were tested under static tensile load. The width, length, and thickness of each sample were 25 mm, 400 mm, and 7 mm, respectively. A number of trial specimens were tested to determine the appropriate anchorage length that ensures the occurrence of no slippage during the test. In addition, as shown in (b), three samples were prepared and tested according to ASTM Three types of 12 mm bolts were used in this study, as shown in : SS, BFRP, and HSFRP bolts. The BFRP bolts were fabricated by cutting pultruded BFRP bars into small pieces, and the bolts shank and the threaded part were then sculptured. For the fabrication of the HSFRP bolts, a small diameter of stainless steel bar was used as a core during the pultrusion process of the BFRP bars (i.e., inner core made of stainless steel and surrounded by BFRP). For that purpose, 6 mm diameter stainless steel bars were used and coated with BFRP until reaching a 12 mm outer diameter. The yield strength and elastic modulus of the used stainless steel were 450 MPa and 200 GPa, respectively.As this study proposes for the first time the use of the HSFRP bolts, it is necessary to understand the characteristics of this type of bolt in comparison with the conventional steel or BFRP bolts before investigating their effect on the static and fatigue performance of the BFRP multi-bolted connections. Therefore, two different specimen configurations are prepared: the first to compare the shear strength and failure mode of the three bolts, and the second to investigate the effect of the bolt type on the performance of the BFRP multi-bolted connections. shows the schematic diagram and experimental set up for the single-bolted double-lap shear connection used to investigate the behavior of the bolts. As presented in , nine specimens (three for each type of bolt) are prepared and tested under axial tensile load. The specimens were prepared by drilling a single 12.6 mm hole in the steel plates, as shown in . Steel plates were used to ensure that the specimens failed due to the bolt shear failure. Accordingly, the failure mode and shear strength of the BFRP and HSFRP bolts can be determined and compared with those of the SS bolts.Based on the recorded load measurements during the tests, the shear strength of the bolts was calculated using the following equations:where Pmax is the failure load for the bolt, Pavg is the average failure load for the three specimens, A is the cross-sectional area of the bolts, τs.s is the single shear strength for one bolt, and the value 2 is used to convert from double shear strength to single shear strength of the bolts. shows the configuration of the pultruded BFRP multi-bolted double-lap joints prepared for the static and fatigue tests. Three specimens of each joint were prepared for each bolt type. A total of thirty-two specimens were prepared and tested under static and fatigue tensile load until failure. Each connection comprised one BFRP main plate and two outer cover BFRP plates connected through six bolts (two columns and three rows) of either SS, BFRP, or HSFRP bolts. The dimensional parameters were selected to satisfy the recommendations of the EUROCOMP code It should be noted that a finger tight, which was used to consider the effect of the creep and fatigue loading, was applied to all bolts. Finger-tight conditions represent the actual application of bolted connections in practice, where the beneficial effects of the pre-set torque could be lost during the service life of composite structures The static and fatigue tests were performed using a l000 kN servo-hydraulic fatigue test machine. In the static tests, the tensile load was applied using displacement-controlled protocol at a constant rate of 0.5 mm/min until failure. shows the experimental setup for a typical specimen under static or fatigue tests. The grip length was selected as 100 mm on each side for both the static and fatigue tests to prevent any slippage between the clamps and the specimen. As shown in , the relative displacement between the main plate and the cover plate was measured by a linear variable differential transducer (LVDT).For the fatigue tests, specimens were subjected to tension-tension cyclic loading at a loading frequency of 10 Hz with a constant fatigue ratio of 0.1 (i.e., PminPmax=0.1). For each type of bolt, the connections were subjected to three fatigue load ratios: 0.3, 0.5, and 0.8 of the static failure load. For specimens that reached two million cycles without failure, the fatigue test was stopped automatically, and the specimens were then loaded monotonically until failure at a loading rate of 0.5 mm/min to evaluate the post-fatigue behavior of the BFRP multi bolted connections.The aim of this section is to describe the behavior of the proposed bolts (i.e., BFRP and HSFRP) in steel single-bolted double-lap shear connections under the effect of axial tensile loads. The failure modes and the load-displacement curves are discussed in detail.(a)–(c) show the failure modes of the SS, BFRP, and HSFRP bolts. As shown in (a), SS bolts exhibited the familiar failure for steel bolts under shear loads, where the failure occurred in two failure planes because of the use of double-lap connections. Unlike the SS bolts, the BFRP bolts failed initially by damage in the fibers and resin, followed by breakage of the bolts at one plane [see (b)]. In contrast to the SS and BFRP bolts, the HSFRP bolts exhibited a different failure mode. It can be seen from (c) that the failure is different for both the outer BFRP and the inner steel core. The BFRP outer part failed and fractured into two parts. However, the steel inner core experienced bending failure mode. In addition, with the increase in the displacement, slippage between the two parts (i.e., BFRP and steel core) was observed, which could indicate the existence of bonding problems in the fabrication of the HSFRP bolts. shows the recorded load-displacement curves for the nine specimens. For the SS bolted connections, the load-displacement curve consists of two parts. The first is linear with high initial stiffness until reaching approximately 65 kN, followed by nonlinear behavior till reaching the failure point. Beyond the failure point, the SS bolts lose all of its shear strength because of the two-planes failure. As shown in (b), the BFRP bolts exhibited approximately linear behavior until reaching their ultimate load. Beyond this point, the connection started to lose its loading capacity. The difference in the failure load of the three BFRP bolts can be attributed to the existence of some geometrical errors in the bolts as a result of the sculpture process. The HSFRP bolts exhibited similar trends to the BFRP bolts until reaching the ultimate load point. However, a remarkable difference can be observed beyond this point where, unlike the pure SS and BFRP bolts, the HSFRP bolts did not completely lose their shear strength. As shown in (c), after reaching the failure point, a sudden drop in the load occurred, which resulted from the failure of the outer part (i.e., the BFRP part). A stability plateau in the load-displacement curve can then be observed. The plateau corresponds to the bending failure of the inner part (i.e., the stainless steel core). presents the results of the shear strength tests. The average shear strength for the SS bolts is 407.5 MPa, which is 3.5 times that of the BFRP bolts (i.e., 116.2 MPa). This significant difference between the SS and BFRP bolts is attributed to the relatively weak shear resistance of the FRP composite bars which, in this study, were used to manufacture the BFRP bolts In all of the tested specimens, the failure occurred in the main plate. Therefore, the cover plates were removed after the test in order to investigate the failure. (a)–(c) show the observed damage and failure modes of the SS bolted connections (SBC), BFRP bolted connections (BBC), and HSFRP bolted connections (HBC). Typically, the dominant failure mode was shear-out failure in the main BFRP plate, regardless of the bolt type.During the test, the authors attempted to observe the formation and propagation of the cracks at the end of the main plate. The failure of the BFRP main plate started with hearing a quiet sound at load lower than the failure load. At that point, there was no sign of any damage to the end of the main plates. In addition, the sound was always associated with a change in the load-displacement curve, as will be discussed in the next section. This sound could be attributed to the beginning of the bearing failure of the plate (c). In addition, the shear-out failure was occasionally accompanied by delamination in the main plate at the location of the middle bidirectional layer [see Regarding the damage of the bolts, there was no failure observed in the bolts of the SBC specimens (i.e., SS bolts). For the BBC specimens, slight bending and damage to the fibers were observed in the BFRP bolts, as shown in (e). On the other hand, for the bolts of the HBC specimens (i.e., HSFRP bolts), some cracks were formed in the BFRP outer part of the bolts. Furthermore, clear debonding and separation between the steel inner core and the outer BFRP part could be observed, as shown in The load-displacement curves for the three replicates of the SBC, BBC, and HBC specimens are shown in (a)–(c), respectively. It can be observed from these figures that, at the beginning of the load-displacement curves, there is an increase in the displacement with no apparent increase in the applied load. This behavior is attributed to the relative slippage between the BFRP main and cover plates caused by the clearance between the bolts and the holes. Afterward, the slope of the load-displacement curve increased because of the full contact of the bolts with the holes until reaching the ultimate load, where a drop occurred because of the shear-out failure of the main plate.(a) and (b), the SBC and BBC specimens exhibited linear behavior until reaching their failure load. However, the BBC specimens exhibited a change in the slope of the load-displacement curve at approximately 50% of the failure load [(b)]. This change could be attributed to the initiation of the bearing failure, as this change was always accompanied by hearing a sound. On the other hand, two of the HBC specimens (HBC-1 and HBC-3) exhibited nonlinear behavior after reaching 60 kN, as shown in (c). It was observed during the test that this nonlinear behavior starts immediately after the damage initiation of the HSFRP bolts. That is, the occurrence of the damage in the HSFRP bolts (cracks and bending) delayed the failure of the main plate. Accordingly, HBC-1 and HBC-3 specimens achieved higher displacement before encountering the failure of the main plates. Based on these results, HSFRP bolts can be used, if designed appropriately, as a fuse element to provide the FRP composite joints with ductility and to delay their failure by sustaining an acceptable level of damage, which in turn will reduce the intensity of the shear-out failure. presents the failure loads of all specimens tested in this study. (a) and (b) compare the typical load-displacement curves and the average failure loads of the SBC, BBC, and HBC specimens, respectively. As can be seen from (a), replacing the SS bolts with HSFRP or BFRP bolts did not affect the stiffness of the BFRP multi-bolted joints. Specifically, the HBC specimen exhibited the same stiffness as that of the SBC specimen up to 60% of its failure load. In addition, it is evident from that the SBC, BBC, and HBC bolted joints have approximately comparable average failure load.It can be concluded from the above results and discussions on the failure modes, failure load, and load-displacement curves of the SBC, BBC, and HBC joints that the SS bolts of the composite joints can be entirely replaced by the BFRP or the HSFRP bolts without affecting the performance of the joints. In addition, the results suggest that, if the composite joints are designed to fail by bolts Similar to the specimens tested under static loading, the cover plates of the specimens subjected to fatigue were removed to clearly visualize the failure mode. shows the failure of the SBC, BBC, and HBC specimens in the fatigue tests. Regardless of the bolt type, all the failed specimens exhibited shear-out failure mode when subjected to fatigue loading. Compared to the specimens in the static tests, the fatigue failure was more severe, as shown in . The SBC and BBC specimens, which were each subjected to fatigue load ratios of 0.5 and 0.8, exhibited shear out failure mode during the test. On the other hand, the SBC and BBC specimens, with a load ratio of 0.3, reached 2 million cycles without experiencing any failure. It should be noted that the tests were stopped after reaching two million cycles, and the specimens were then tested under increased monotonic loading until failure, as will be discussed later. For the HBC joints, specimens with a load ratio of 0.8 exhibited similar failure mode to those of the SBC and BBC specimens (i.e., shear-out). On the other hand, the HBC specimens with a load ratio of 0.3 and 0.5 reached two million cycles without failure. presents the number of loading cycles until failure (i.e., fatigue life) for each specimen of the SBC, BBC, and HBC joints. Regardless of bolt type, specimens subjected to a load ratio of 0.3 reached two million cycles without failure. At load ratios of 0.8 and 0.5, using BFRP bolts instead of SS bolts reduced the fatigue life of the joints. For instance, BBC specimens exhibited an average fatigue life of 956 and 58,001 cycles compared to 4059 and 87,940 cycles for the SBC specimens at load ratios of 0.8 and 0.5, respectively. On the other hand, using the HSFRP bolts enhanced the fatigue life of the HBC joints. For example, at a load ratio of 0.8, the average fatigue life of the HBC specimens is 17% higher than that of the SBC specimens. The most remarkable enhancement in the fatigue life was at a load ratio of 0.5, as the HBC specimens could reach two million cycles without failure. At the same load ratio, the SBC and BBC specimens achieved average fatigue life of 87,940 and 58,001 cycles, respectively [see ]. The higher fatigue life of the HBC specimens could be attributed to the damage of the HSFRP bolts. The fatigue failure process always occurred in three sequential stages: crack initiation, crack propagation, and failure stage. With an increase in the cyclic loading, cracks propagated rapidly at locations of bolts with higher load (i.e., critical bolts). However, with the damage of the HSFRP bolts, a redistribution of the bolt loads could occur, which leads to delay the crack propagation rate because of the reduction in the load transferred by these critical bolts. Accordingly, a larger number of cycles is required to achieve a level of accumulated damage enough to cause shear-out failure of the BFRP main plate.(a) and (b) show the fatigue load ratio and fatigue load versus the fatigue life, respectively, for the SBC, BBC, and HBC specimens. The fatigue load ratio is calculated as the applied maximum load (Pmax) divided by the average static failure load for each type of joint (i.e., SBC, BBC, and HBC). (a) represents the well know S-N curve for the SBC, BBC, and HBC joints. In addition, (a) and (b) are provided with a trend line for each type of joint. It is noteworthy that the trend lines are drawn using only the results of the failed specimens, and then extrapolated up to 2 million cycles. It can be seen from (a) that the relationship between the applied fatigue load ratio and the fatigue life (on a logarithmic scale) for the SBC, BBC, and HBC is approximately linear. Accordingly, by knowing the level of the fatigue load ratio, the fatigue life of the composite joints can be predicted. To facilitate the prediction of the fatigue life of the SBC, BBC, and HBC joints, the relationship between fatigue life and the fatigue load ratio or maximum applied fatigue load is established by curve-fitting the experimental results of this study. The fitted equations for the fatigue life of multi-bolted composite joints follow a log-linear relation, as shown in Equations , where S, P, and N represent the fatigue load ratio, maximum applied fatigue load, and the number of cycles, respectively. The fitting parameters and the coefficient of determination (R2) of these equations are presented in (a) and (b), the trend lines of the SBC and BBC specimens are approximately comparable up to a fatigue life of two million cycles, which means that steel bolts can be replaced entirely with BFRP bolts without significantly affecting the fatigue life of the composite joints. On the other hand, the fatigue life of the HBC specimens outperformed both the SBC and BBC specimens at almost all fatigue load ratios. It should be noted that the static loading capacity of the HBC specimens is less than those of the SBC and BBC specimens by 3.2% and 9.1%, respectively. Therefore, to eliminate the effect of this load difference, the relationship between the applied fatigue load and the fatigue life is plotted in (b). Although HBC specimens showed slightly lower static failure load compared to both the SBC and BBC specimens, the HBC specimens exhibited enhanced fatigue life under the same applied load. However, replacing the SS bolts with HSFRP bolts depends on the expected fatigue life of the structure with a separating line at N = 100 cycles. For example, for N lower than 100 cycles, the SBC connections showed a higher fatigue life than the connections with HSFRP bolts. That can be attributed to the higher static load of the SBC connections. Therefore, in this range, it is recommended to use BFRP bolts instead of HSFRP bolts. For N > 100 cycles, bolted connections with HSFRP bolts showed remarkable improvements in the fatigue life. Therefore, it is recommended for this range (i.e., N > 100) to use HSFRP bolts instead of SS bolts.The severity of the composite joints, when subjected to fatigue loading, lies in the increasingly progressive and permanent deterioration in the internal structure of the composite material. Therefore, monitoring the degradation of the stiffness, the loading capacity, and the load-displacement relationship of the composite joints, when subjected to cyclic loading, is of great significance for structural applications of the composite structures. Therefore, the stiffness of the specimens that failed in the fatigue tests is monitored through their fatigue life. In addition, specimens, whose fatigue life exceeded two million cycles, are subjected to an increased static load until failure to evaluate their post-fatigue performance after exceeding such a large number of loading cycles. shows the recorded typical load-displacement curve for the specimens during the fatigue tests. The data was recorded at a frequency of 100 Hz (i.e., 10 readings for each loading cycle). As shown in , the stiffness at each cycle is defined as the ratio between the maximum and minimum fatigue load difference (i.e., Pmax-Pmin) to the difference of the corresponding displacements (i.e., Dmax-Dmin). depicts the relationship between the stiffness and the normalized fatigue life for the SBC, BBC, and HBC specimens under different load ratios. The normalized fatigue life represents the number of loading cycles divided by the fatigue life (number of cycles until failure) of the specimen. that the stiffness of both the SBC and HBC specimens is slightly decreased over their fatigue life, which means that they are able to maintain their stiffness and suffer minimal damage in the case of cyclic loading. The sudden drop in the curve results from the brittle shear-out failure of the specimens. On the other hand, the BBC specimens exhibited a similar trend, with a slightly higher degradation rate compared to both the SBC and HBC joints.It can be seen from the same figure that the BBC specimens with load ratios of 0.8 and 0.5 had lower stiffness than both the SBC and HBC specimens. Similarly, the HBC specimens had lower stiffness than those of the SBC specimens. This behavior indicates that the stiffness of the bolts directly affects the stiffness of the joints, even though the failure of the joints is controlled by the properties of the plates. This can be attributed to the deformation of the bolts when subjected to cyclic loading (i.e., weaker bolts experience higher deformations than stiffer bolts). According to (a) and (b), using bolts with higher stiffness will increase the stiffness of the composite joints, which, in turn, will enhance the stiffness of the composite structures.Post-fatigue static tests were conducted for the SBC, BBC, and HBC specimens that exceeded the two million cycles without failure. It is noted that there was a problem in collecting the data of the SBC specimens. Therefore, only the results of the BBC and HBC specimens are discussed. shows the load-displacement curves for the one BBC and three HBC specimens tested after surviving two million cycles (i.e., post-fatigue specimens) compared to the results of the original tested specimens. From this figure, the load displacement curves of the BBC and HBC specimens with the previous fatigue loading exhibited a similar trend to those of the specimens under only static tests. However, the post-fatigue specimens exhibited higher initial stiffness and started to gain load at lower displacement. The latter can be attributed to the vanishing of the relative slippage between the BFRP main plate and cover plates after being exposed to previous loading cycles. Accordingly, both the plates and bolts became in full contact before conducting the post-fatigue static tests. Although subjecting the specimens to previous loading cycles did not affect the failure mode as all the specimens experienced the shear out failure mode, it significantly affected the joint stiffness. (a) clearly shows that all the post-fatigue HBC specimens have a higher stiffness compared to the conventional static specimens, and the same can be seen in (b) for the BBC specimens. The stiffness improvements could be the result of a number of simultaneous contributions. Firstly, in a previous study by Wu et al. (a) shows the configuration of the bolts and the transverse fiber before conducting the conventional static test where there is no contact between the bolts and the fiber. On the other hand, after two million cycles, it can be seen that the final position of the bolts could result in residual tension forces in these transverse fibers, which act against the bolts when monotonically loaded (i.e., the tensile stressed fibers have higher stiffness than un-stressed ones) [see (b) and (c)]. Accordingly, this could result in higher stiffness than in the conventionally tested specimens. Another factor that could cause the enhancement in the stiffness in the post-fatigue static tests is the change in the clearance between the bolts and holes. For instance, McCarthy et al. shows a comparison between the average static failure load and the post-fatigue failure load of the BBC and HBC connections. It can be seen that both the BBC and HBC specimens achieved a comparable failure load to those tested without being subjected to fatigue load. In other words, BBC and HBC specimens have adequate resistance to the damage caused by cyclic loading, as they survived two million loading cycles at 0.3 and 0.5 loading ratios, respectively, without a reduction in their strength capacity. Accordingly, it can be concluded that the 0.3 and 0.5 load ratios can be considered as the preliminary recommendations for the endurance limits of the BBC and HBC joints, respectively.An experimental study was conducted to investigate the effect of the bolt type on the static and fatigue performance of BFRP multi-bolted double-lap connections. Firstly, the shear strength and failure mode of the proposed BFRP and HSFRP bolts were investigated and compared with conventional SS bolts. Secondly, static and fatigue performance of the SS, BFRP, and HSFRP multi-bolted connections were investigated. Finally, the post-fatigue performance of the connections was evaluated to determine the deterioration of the composite joints after surviving two million cycles. Based on the results and discussion of this study, the following conclusions were drawn:The proposed HSFRP bolts outperformed both the SS and BFRP bolts. The average shear strength of the HSFRP bolts was 40.7% higher than that of the BFRP bolts. In addition, unlike the brittle failure of the SS and BFRP bolts, the HSFRP bolts exhibited ductile failure mode with a stability plateau in the post-peak loading stage.Under static tensile loading, both the BBC and HBC connections experienced failure mode and achieved average failure load and stiffness comparable to that of the SBC connections.At the same amplitude of fatigue loading, SS bolts could be replaced entirely by BFRP bolts without affecting the fatigue life of the composite connections. On the other hand, using the proposed HSFRP bolts could enhance the fatigue life of the composite connections.SBC, BBC, and HBC specimens could maintain their stiffness through almost all their fatigue life, and the more the stiffness of the used bolts, the more will be the stiffness of the composite joints. In addition, as both the HBC and BBC connections maintained their original strength capacity after surviving two million cycles, 0.5 and 0.3 fatigue load ratios are recommended as preliminary endurance limits for the HBC and BBC connections, respectively.The influences of extrusion-shear process on microstructures evolution and mechanical properties of AZ31 magnesium alloySevere plastic deformation (SPD) technologies are difficult to be promoted to be industrialized, and the processes are complicated, and the costs are high. To promote industrial application of the SPD technology for magnesium alloy, a new successive SPD method has been explored which includes direct extrusion and two steps equal channel angular extrusion (ECAE) continuously. The processing technology is called extrusion-shear (ES) in this paper. The components of ES dies have been designed, manufactured and installed on extruder to manufacture the AZ31 magnesium alloy rods. Microstructures of AZ31 magnesium alloy processed by ES process have been observed and investigated. The texture evolution during ES process has also been studied. The results show that fine and uniform microstructures can be obtained by ES process. Basal texture (0002) has been weakened owing to shear deformation of ES process. Research results show that relationship between grain sizes and hardnesses is consistent with hall-petch law at 420 °C. ES process with low billet temperature could improve hardness obviously and enhance compression performance, and raise strengths. And there exits strong tension-compression asymmetry of AZ31 magnesium alloy fabricated by ES process. The results indicate that ES process can produce large plastic deformation and introduce ultra-fined grains in the AZ31 magnesium alloy.As the lightest structural material of engineering significance, Magnesium alloys have been attracted considerable attentions In the current research, a compound extrusion process has been explored to fabricate rods which included direct extrusion and two steps ECAE, and the processing technology is called extrusion-shear (ES) in this paper. The components of ES process die have been designed and manufactured and installed in a horizontal extruder. Microstructures of AZ31 alloy sampled from centers of longitudinal sections for different positions in prepared rods have been observed. Deformed microstructures and texture evolution of ES process for AZ31 magnesium alloy have been studied in order to analyze the deformation mechanisms. The aim of the present study is to reveal the microstructural evolution and clarify grain refinements mechanism for AZ31 magnesium alloy during ES process. Hardnesses distribution and tension-compression asymmetry of AZ31 alloy are measured experimentally through a series of tension and compression tests.A schematic diagram of ES process is shown in which shows the configuration of designed and manufactured ES die. The diameter of rods extruded by the ES process is 15 mm. The ES die includes direct extrusion with extrusion ratio of 32 and die channel angles of 120°. A larger amount of shear deformation in materials can be introduced by ES process than those caused by direct extrusion with the same ratio. There are four deformation zones in ES die. The deformation zone I and II is the direct extrusion zone which includes upsetting zone and sizing zone, and zone III and zone IV are the first and second shearing zones, respectively. Experiments have been done on a horizontal extrusion machine with extrusion ability 500 tons and a container diameter of 85 mm. The material used in this study is AZ31 magnesium alloy. As-cast billets have been machined into round billet with diameter of 80 mm. The process parameters of ES process, which are critical to the microstructure refinements and mechanical properties In this study, The billets and ES die have been heated up to a certain temperature and insulated to preserve heat, and then ES process started immediately. In the ES process experiments, oildag has been applied on the surface of workpieces and dies. Prepared samples have been taken from the four parts (shown in ) to investigate the microstructures and mechanical properties. All the samples have been taken from the center of longitudinal sections of different positions. The samples have been prepared for microstructural observations by using standard metallographic procedures including mounting, grinding and polishing. Then polished specimens are etched with an acetic acid. Acetic acid and picric acid solution (2 ml acetic acid + 1 g picric acid + 5 ml water + 20 ml of alcohol) have been used to erosion surface of the samples for microstructure observation.Microstructure observations have been carried out by using PME OLYMPUS TOKYO-type optical microscope. The qualitative analyses of macro-texture have been achieved by using X-ray diffraction (XRD), while the micro-texture analysis for the direct extrusion zone and the second shearing zone have been examined by electron backscatter diffraction (EBSD).Microstructure observations were realized by means of a transmission electron microscope (TEM) instrument. The hardness tests have been carried out on HV-1000 type microhardness tester, and applied load was 50 g, and loading time was 20s, and average hardness of 25 points on each researched parts have been calculated.Standard compression and tensile sample of φ8 × 16 mm and δ5 tensile samples have been prepared. The mechanical properties of samples have been carried out in electronic universal testing machine CMT5150, and compression and tensile failure test have been done with 1 mm/min speed. shows the original microstructures of AZ31 magnesium alloy with as-cast state, which consists of coarse grains and the second phase. The average grain size of the as-cast billet is estimated to be more than 200 μm, intermetallics either distribute around grain boundaries or in grain interior.Microstructures of the four zones in ES-processed rods have been observed, and which are shown in . The microstructures exhibit ribbon-like grains in the upsetting zone (zone I), as shown in a, which indicates that the degree of deformation is very small in the center and heterogeneous deformation has taken place.b is promoted in sizing zone II, which indicate large deformation has occurred. As the plastic deformation continues in the first shearing zone III, the widths of the coarse microstructures become narrow, and a large percentage of fined grains appear in c, which demonstrates that dynamic recrystallization (DRX) has taken place. Lamellar microstructures in first shearing zone begin to reduce for the large shear strain caused by shear deformation, and the deformed grains begin to turn into recrystallized grains partially.In the second shear zone IV, DRX occurs almost completely, but there still exits a small amount of fine-grain strips in the center of the rod shown in d. It is noted that the black marks located grain boundaries are overetching positions caused by acetic acid. There are some inherent drawbacks for microstructure due to uneven metal flow. However, the average grain size decreased from about 200 μm to about 10 μm by using the ES process. The microstructures are not only greatly refined but also relatively uniform because the ES process includes two steps of simple shear, and deformation degree of central part of rods increases, and more DRX occur In magnesium alloys, strong basal texture is always found, which would result in poor ductility at room temperature , the strongest diffraction peak is the (0002) crystal plane, and (101¯1) plane is the second strongest diffraction peak in zone I, zone II. In the upsetting zone I, the strongest diffraction peak is (0002) crystal plane. But in the sizing zone II, the intensities of (101¯0) and (101¯1) planes increase obviously. The crystal plane (101¯1) is the strongest diffraction peak in the second shear zone, and strength of basal plane (0002) decrease obviously.The two shearings would lead to rise of peak intensity ratio, and which shows that the ES process could promote the coexistence of the (0002) basal plane and the non-basal planes. From the XRD test, it could demonstrate that basal texture of (0002) has been weakened greatly and it becomes less dominant after ES process. The weakening of basal texture could be attributed to the shear deformation during the ES process, and which is expected to enhance the formability of magnesium alloys. presents the grain boundaries maps (SEM-EBSD) of AZ31 magnesium alloy in the sizing zone II and the second shearing zone IV processed by ES process respectively. The low angle grain boundaries (LAGBs) between 1° and 15° are marked by thin black lines, and the high angle grain boundaries (HAGBs) over 15° are labeled by thick black lines, and boundaries with misorientations below 1° are removed due to the resolution limitations of EBSD. It is clear that microstructures of are consistent with the optical microstructure shown in There are numerous LAGBs in the AZ31 magnesium alloy for the sizing zone II, as shown in a, Many subgrains can be observed inside coarser grains and are elongated in the extrusion direction. The fine grains are gathered together to form band shaped structures. There are a number of large deformed ribbon grains in the sample, and there exist fine recrystallized grains on either side of the coarse ribbon grains. The ribbon grains are probably twin grains.After two shearings, there are no long ribbon grains in the sample, as shown in grain boundary maps in b. It seems that the LAGBs have evolved into HAGBs, and more finer grains appear. Ribbon grains shown in a have changed into fine equiaxed grains. With the increase of accumulated strains caused by successive two shearings, the fraction of grain boundaries increases, and distribution of fine equiaxed grains is more homogeneous. There exist many small uniform recrystallized grains. Therefore, the recrystallization mechanism in the ES process is a continuous dynamic recrystallization. Some coarse grains are surrounded by new fine grains and some fine grains are extended inside the coarser grains.A typical deformed microstructures after ES process in the TEM image are shown in . Parallel twins with narrow deformation bands whose width is about 100–300 nm on average. Very fine particles have been also found in sample. Unlike in the initial state of magnesium alloy, It is clear that microstructures fabricated by ES process are inhomogeneous. New grains can be produced dynamic recrystallization and nucleation by bulging and subgrain rotation, and dynamic recrystallization behaviors of magnesium alloys is coordinated with formations of secondary phases and twinning. Twinning deformation plays key role in the deformation coordination of ES process.The principle of ES process is to introduce compressive and accumulated shear strains into the magnesium alloy which include two parts accumulative strains of direct extrusion and two steps ECAE.where ε is the accumulative strain, λ the extrusion ratio, Φ the inner corner angle, and Ψ the outer corner angle. The temperature corrected strain rate Z is given by equation where ε. is strain rate, Q the activation energy for the deformation, T the temperature, and R the gas constant. The Zener-Hollomon parameter (Z) of first direct extrusion is equals to Z1, v1 the extrusion speed, λ the extrusion ratio, and R1 the billet radius.Z2=[2cot(ϕ2+ψ2)+ψcsc(ϕ2+ψ2)6]v2ψR2.exp(QRT)and the Z parameter of second zone for shearing is Z2, where inner corner angle (Φ), ψ outer corner angle, v1 the speed of extruded rods, R2 radius of extruded rod. Equation includes two parts, the former is the extrusion strain and the later is the strain for ECAE. In this paper, the values of λ, Φ, and Ψ are 32.1, 120°, and 20°, respectively. Theory Calculation results for strains and strain rates and Zener-Hollomon parameters during the three stages of ES process have been shown in . So large strains occurred during the ES process refine grains.The relationship between the average recrystallization grain size (d) and the Zener-Hollomon parameter during dynamic recrystallization is given by equation where d is diameter of grain size, A and B are constants, and Z is the Zener–Hollomon parameter. that the process parameters and structure parameters of ES dies have significant impacts on the dynamic recrystallizations of fined grains. So the sizes and volume fraction of dynamic recrystallizations of fined grains are inversely proportional to the accumulation strains. It is obvious that average sizes of grains for high strains are finer than those of low strains. It can be observed that the high strains could refine grains.ES process includes direct extrusion and two successive shearing deformations. This new process could improve the work hardening and dynamic recrystallization of deformation materials, and microhardness would be changed greatly. Effects of average grain sizes on hardnesses are shown in equation where Hv is room temperature hardness, d the average grain size, H0 the average hardness of the cross section of the ES-prepared rods, k the strengthening coefficient. are researched positions of hardness tests. Hardnesses of different positions for longitudinal sections in rods fabricated by ES process with billet temperature 420 °C and 450 °C respectively have been shown in . For deformation of longitudinal section in specimen edge is the most intense, and deformation extent decrease from border to center, hardness distribution of ES-processed specimen is uneven along longitudinal section. Hardnesses of the second shearing zone decrease when extrusion temperature is 450 °C by comparing with those caused by ES process with extrusion temperature 420 °C, for grains grow up abnormally with higher billet temperature. As the temperature increase, dislocation densities are enhanced and dislocation tangles decrease. If extrusion temperatures are high, grains would grow rapidly, the reductions of grain boundaries would result in decrease of hardness.Micro-hardness in longitudinal sections of rods vary with different grain sizes shown in . It is obvious that relationships between micro hardness for extrusion temperature 420 °C and grain size are consistent with Hall-Petch laws shows compressive stress-strain curves for the ES process with different temperatures in different parts of AZ31 magnesium alloy at room temperature. The tensile compression performance has been list in . It can be seen that yield strengthes and compressive strengthes in sizing zone with extrusion temperature 420 °C are smaller than those of the second shearing zone. This is because there exits coarse grains in compressive zone I. But changes of strengthes are very little in two zones for difference of grains sizes is very small when extrusion temperature is 450 °C.The relationship between strain rate and yield stress usually is shown in the where σs and σ0 are the strain rate and yield stress respectively. n is a constant and less than 1.Mechanical properties of AZ31 magnesium alloy should be associated with strain rates. Schmid factor of basal plane increase after ES process. The axial tensile deformation due to basal slip is easy to be moved, and which may decrease yield strength. Slips distance of dislocation become shorter after the grains are refined. Stress concentration near the grain boundaries would be released through the non basal slip, grain boundary sliding and dynamic recovery process.Stress-strain curves at room temperature tensile tests are shown in . From the curves, strength and elongation of prepared sample increase with dropping of temperature. ES process can improve the compression performance of magnesium alloy to a certain extent, at the same time increase the yield strength and tensile strength. Grains can be refined, and the elongation is 12%, σb is 280 MPa for ES-prepared magnesium alloy. Local compression stresses are exerted on billets for multiple directions during ES process. So the physical properties of metal and mechanical state are formed homogeneously, plasticity would be increased.Magnesium alloys have a hexagonal close-packed (hcp) crystal structure and hence a limited number of easy-to activate independent slip systems . It is obvious that compressive yield strength of wrought magnesium alloy is lower than the tensile yield strength, and the ratio is 0.5–0.7. For direct extrusion of magnesium alloy, compression yield strength is generally lower than 1/2 of the axial tensile yield strength. The asymmetries of tensile and compressive strength for magnesium alloys restrict their application. Compressive yield strength is lower than the tensile yield strength for ES process. The ratio is 0.85 when extrusion temperature is 420 °C, and the ratio is 0.41 when extrusion temperature is 450 °C.For the quantitative description of the intensities difference, spitzig and richmond defined the parameters of intensity difference SDE (shorten for strength differential effect), and the calculation formula is shown in equation , the lower temperature can effectively reduce the differences of yield strength and tension.where σc (MPa) and σt (MPa) are uniaxial compressive and tensile yield strength respectively.The ES die with two shearings has been designed and manufactured. ES process experiments have been conducted with the speed of 0.5 m/min and extrusion ratio 32.1 and temperature 420 °C and 450 °C respectively.Metallographic analyses of optical microscopies show that the ES process could improve dynamic recrystallization during ES process. Microstructures becomes more uniform and finer by comparing to the original as-cast condition owing to the two shearings of ES process. The macro-texture analyses based on X-ray diffraction method show that ES process could weaken the basal texture of (0002). The micro-texture analyses of EBSD show that ES process would decrease intensities of basal textures.Vickers hardness tests and compression and tensile tests for different positions of ES-prepared samples with different extrusion temperatures have been tested. ES process with low extrusion temperature would improve grain refinements and yield strength, tensile strength and hardness or strength. There exits strong asymmetry for tension compression in ES-prepared magnesium alloy rods.Experimental and numerical analysis of tube-core claddings under blast loadsAn investigation into the response of a sandwich cladding panel under blast loading is presented. The sandwich cores are composed of square thin-walled metallic tubes. Three primary panel layouts are identified, consisting of panels with four, five and nine tubes within the core. Annealed mild steel and 6063-T6 aluminium alloy tubes are selected as the core material. Hemispherical indentation triggers are used to induce progressive, symmetric buckling.A series of experimental blast tests are conducted on the proposed panels. A ballistic pendulum is used to measure the impulse transferred to the panel. At smaller blast impulses, irregular buckling modes are observed for both the steel and aluminium tube-core panels primarily due to variable trigger performance. For blasts which utilize the full stroke of the tubes, symmetric buckling modes are observed. In all cases panel crush distance increases with increasing impulse and decreases with an increasing number of tubes in the panel core. Further to this, at equal charge mass, the aluminium tube cores show significantly higher crush distance than identical steel tube panels. Analytical predictions of panel response give satisfactory agreement with experimental and finite-element results provided the response is within the pre-compaction regime. Finite-element results using ABAQUS/Explicit also show satisfactory correlation with experimentally obtained global response. Numerical analysis shows that energy absorption is primarily confined to the core tubes with only minimal plastic strains developing in the top plate. A numerical parametric study is conducted to determine influence of load uniformity on panel response. Energy absorption efficiency is found to be highly sensitive to the uniformity of the load, primarily in panels with fewer core tubes and thinner top plates.In the design of blast resistant structures, sacrificial claddings are often used. Cladding structures, which are composed of energy absorbing elements or material can be fixed to the main structure. The cladding is designed such that, under blast loading, the forces transferred to the main structure are controlled to the point where damage in minimised in the protected structure. If a sandwich type cladding is employed, the energy absorption properties of the core determine how the forces are transferred.Recent work has focused significant attention to the use of metallic foam core claddings. Hanssen et al. In this paper, experimental aspects are explored in the use of thin-walled tubes as the core component of a cladding structure under blast loading. illustrates the deformation mechanisms of the panels under an applied pressure pulse P(t). Thin-walled tubes of ductile material are well understood and highly utilised structural elements in energy absorbing applications. The large plastic deformations created during the progressive folding of the tube walls absorb large amounts of energy and control the transfer of forces to the protected structure. An overview of collapsible impact energy absorbers can be found in Alghamdi In the present work, initial experimental investigations are conducted to determine the suitability of using thin-walled tube structures as a core material under blast loading. In addition, analytical and numerical models are utilised to gain further understanding of the response of such structures. Theobald and Nurick illustrates the three layouts, denoted A, B, and C which have four, five and nine tubes respectively. The position of the tubes within each panel is defined by the value λ |
= |
λ1/λ2. For the present study, only panels B and C are tested experimentally, with values of λ corresponding to λ |
= 0.61 and λ |
= 0.70 respectively. The values are obtained based on early numerical observations In order to experimentally investigate the performance of the panels under study several blast tests of panels are undertaken. The tube materials used are the annealed mild steel and 6063-T6 aluminium alloy. Panels B and C as given in are examined experimentally. Panel A is not examined as it is highly sensitive to any non-uniformity in the loading. The differences in response between panels B and C is expected to provide insight into impulse capacity as a function of the number of tubes in the panel core.The tubes forming the core of all panels have the approximate geometric parameters given in . The length of the tubes, and hence the core thickness is 75.0 mm. Note that R is the aspect ratio of tubes, as measured at the midsurface. Specifically if C is the mean width of a tube of length l, then R |
= |
l/C. The top plate thickness for all panels is 4.0 mm. This top plate thickness is chosen to ensure nearly rigid body displacements during the blast event. This has the purpose of isolating the energy absorption responsibility to the tubes in order to study the response of the tubes to blast loading. The tube positions, which are defined entirely by the value of λ, are selected based on the preliminary results found in Under blast loading large stresses may develop at the plate/tube interfaces and thus a strong bond is required. Unfortunately, welding techniques require too much heat to ensure structural integrity in the thin tubes during the welding process in addition to ensure material properties remain unchanged. This is particularly true when welding aluminium to steel. Further to this, warping in the top and bottom plates due to excessive heat renders the panels unusable. As a result, soft solder is used for both interfaces and materials. gives an idealized schematic of the bonding process. For the top plate square tubes are inserted into milled grooves. In the bottom plate, the process differs significantly. Holes of approximately the same size as the tubes are laser-cut through the plates. The tubes are inserted in the holes and fixed. shows typical panels after construction.The tubes are milled from the commercially available thickness of 2.0 mm down to a nominal thickness of 0.6 mm. Once the tubes have been processed to the desired thickness, imperfections are created in the tube walls. The purpose of the imperfections is to induce buckling at a predetermined location along the tube length. If each tube in the panel buckles at the same location, it is expected that crushing stability will be maximised. In addition to this, creating a relatively large induced imperfection ensures any small imperfections in the tube wall introduced in the thickness reduction do not dominate the buckling process. It should be noted that initial experimental tests used tubes with circular cutouts of various sizes. Such imperfections created difficulties in that if the cutouts were too small, they did not influence the buckling mode while larger holes resulted in ductile fracture at various locations around the hole perimeter.To circumvent the problem of ductile fracture, small indentations are created in the opposing tubes wall at the midpoint in terms of length and width. The dent is created with a hemispherical steel indenter with a radius of 10.0 mm. The tube is inserted into a plastic clamp which contains a hole for the denter to move through. The denter is placed in the hole and the rig is placed on a Zwick universal testing machine. The denter is then displaced a distance of 2.0 mm at a constant speed of 50 mm/min. The dent depth is measured for 20 samples for each of the steel and aluminium tubes. After elastic unloading, the final mean dent depth is found to be δs |
= 1.74 mm and δa |
= 1.45 mm for the steel and aluminium tubes respectively. The mean deviation is found to be 0.063 mm and 0.066 mm for the steel and aluminium tubes respectively indicating a reasonable level of repeatability.In the blast loading experiments, the panels are subject to uniform blast loads. Although such loads are trivial to generate numerically, experimentally uniform loading due to blast loading is a difficult problem. Initially, tests were conducted using the method presented in Chung Kim Yuen and Nurick To circumvent this problem a testing rig similar to that of Jacob et al. shows a schematic of the testing rig used. The panel is fixed to a thick rigid plate at the base of the panel, and the blast tube is adjusted such that the other end of the tube is flush against the top plate of the panel. Under this configuration only the base of the panel is constrained and the top plate is free to move as the core tubes buckle.The blast tube is 190 mm long which exceeds the width of the plate and hence the pressure applied to the top plate is likely to be reasonably uniform. As previously mentioned however, this is a difficult parameter to verify experimentally and hence thick top plates for the panels are used to minimize the effect of non-uniformity in the loading. The inside area of the blast tube is 150 mm × 150 mm while the top plate of the panel is 156 mm × 156 mm. The reason the top plate is slightly larger than the exposed area is to minimize the escaping of any gases in a direction along the axis of the ballistic pendulum. If there are gaps created during the blast event the ballistic pendulum may be subjected to loads that the panel is not, resulting in an over measurement of the applied impulse.The pressure loading on the panel is generated by detonating a circular disc of PE4 explosive of diameter 75.0 mm. The explosive is placed on a 150 mm × 150 mm polystyrene pad with an approximate density of 18 kg/m3. The polystyrene is then placed at the end of the tube opposite to that of the location of the panel. After detonation of the explosive, the polystyrene pad disintegrates and as such, has no apparent effect on the loading of the panel.The technical data for PE4 explosive is reported by Wharton et al. The blast tube is attached to a ballistic pendulum. The motion of the pendulum created by the blast load is used to determine the impulse transferred to the pendulum. If the blast load only loads the pendulum by loading the experimental panels then the recorded impulse is the true impulse that the specimen is subjected to. Specifically, if x1 and x2 are the forward and backward displacements of the pendulum respectively then the initial velocity of the pendulum can be calculated as, T refers to the period of the pendulum which is 3.41 s. From this, the total applied impulse is determined simply as I=x˙0Mpend where Mpend is the total mass of the entire pendulum, including the blast tube and specimen.The analysis and modelling of structures under blast loads requires quasi-static and dynamic constitutive parameters. This section describes the experimental and analysis procedures used to obtain the constitutive behaviour of the materials used in the panels. The general mechanical properties of the materials are given in The top plate of the panels is composed of a hot-rolled mild steel. For the core materials, mild steel tubes and aluminium alloy extrusions are considered. The purpose of this is to compare core materials of similar initial yield stress but with significantly different fracture strains. To summarize, there are three materials of interest in this studyAnnealed mild steel cut from square tubes of dimension 25.4 mm × 25.4 mm × 2.04 mm. All material specimens are centred about the centreline of the tube. The tubes are annealed for 60 min at 900 °C in an autoclave. The tubes are allowed to cool in the oven and are removed when the temperature in the oven is reasonably near room temperature.6063-T6 aluminium alloy tubes of dimension 25.4 mm × 25.4 mm × 2.04 mm. The tubes are analyzed only in their as-received state.Mild steel cut from hot-rolled 4.0 mm plates.Accurate material properties are required for numerical and analytical computations. For this study, quasi-static tensile tests are conducted on the aforementioned materials. As blast loads induce high strain rates in the tube core and top plate, material properties at these strain rates need to be obtained. To obtain the constitutive behaviour at high strain rates a standard Split Hopkinson Pressure Bar Setup (SHPB) is used. As the tensile test and SHPB techniques are well established only the results are presented here. It should be noted that numerical inversion techniques similar to that of Lee and Wierzbicki shows typical quasi-static and dynamic constitutive behaviour for the materials investigated. Of particular note is the lack of rate sensitivity for the 6063-T6 aluminium.The constitutive behaviour of the top plate steel is modelled in ABAQUS/Explicit using the Johnson–Cook plasticity model , σ¯ is the equivalent plastic flow stress as defined by the von Mises yield criterion and ɛ¯pl is the equivalent plastic strain. The parameters A, B, and n are material constants. For the second term, C is the strain-rate constant for the material at the reference strain-rate ɛ˙0 and ɛ¯⋅pl is the instantaneous equivalent plastic strain-rate. The third term models the effect of temperature on the yield stress where T is material temperature, Tmelt is the melting temperature of the material and m is the thermal softening fraction.An alternative method to the Johnson–Cook model was used in the publications regarding the numerical simulations of the panels where σd is the dynamic flow stress at the uniaxial plastic strain-rate ɛ˙pl, σs is the static flow stress and D and q are material parameters. This methodology for strain-rate dependence can be combined with an appropriate hardening model.For the annealed mild steel the strain-rate is modelled using the Cowper–Symonds relation given by Eq. . The aluminium is assumed to be strain-rate insensitive. To obtain the constants the curve fitting toolbox in Matlab is used. Firstly, the stress as a function of strain-rate is determined at a single strain value. The stress values are obtained at a strain of ɛ |
= 0.12. This corresponds to the smallest possible strain after ringing up of the specimen during dynamic tests. The smallest strain value is used in order to minimize temperature effects on the flow stress. To account for the oscillatory behaviour the curve is integrated over the range ɛ |
= 0.12 ± 0.01 to obtain the mean stress. Stress values at low strain-rate (ɛ˙=8.33×10−4s−1andɛ˙=8.33×10−2s−1) are obtained from the tensile tests. The higher strain-rate tensile test is required to create a control point between the quasi-static result and the high strain-results from the SHPB results. Optimal values for D and q are determined using least-squares techniques and are given in For both the annealed steel and aluminium the material softening due to temperature is modelled using the following equationwhere σ¯temp is the flow stress including thermal softening and T∗ is given by Eq. and the thermal softening fraction is given by m. The melting temperature Tmelt for the steel is taken to be 1527 °C which corresponds to commonly accepted values in the literature For the top plate steel, the complete Johnson–Cook model is used. The values of A, B, and n are obtained by fitting the first component of Eq. , in the least-squares sense, through the quasi-static results obtained from tensile tests and simulations. The model parameters are obtained by curve fitting up to 50% strain using the curve fitting toolbox in Matlab. As the exact yield stress is not significant for the present analysis, the fit is obtained without constraint of the value of A. This gives a more accurate fit over the complete curve but results in the A value not corresponding to the true initial yield stress. The resulting Johnson–Cook constants are given in To compute the strain-rate constant C in the Johnson–Cook model, the flow stress is related to strain-rate and least-squares techniques are used to find the optimal C value assuming a reference strain-rate of ɛ˙0=1.0s−1. If the reference strain-rate is taken as the quasi-static test strain-rate, the linear (in log space) behaviour will significantly overestimate the stress at low strain rates while underestimating the stress at large strain rates. This reference strain-rate is commonly used in studies that employ the Johnson–Cook model.The thermal softening parameter m is taken to be 1.0 for the top plate steel. As previously mentioned, this gives a linear softening of the material with no load carrying capacity at the melting temperature. This m value is used by Park et al. To validate numerical and analytical models with the experiments, the impulse measured by the ballistic pendulum must be equated to a pressure distribution over the surface of the panel. The relationship between the impulse measured by the ballistic pendulum and the pressure distribution on the top plate of the panels is given bywhere Ω is a arbitrary region on the top plate of the panel and t0 is the loading duration. Since the loading is impulsive the time distribution of the load is of significantly less importance than the spatial distribution and therefore the load is assumed to be constant over the time duration t0. For all numerical simulations the blast duration t0 is taken to be 10 μs. This is only an estimate of the true pulse duration under expected blast loading scenarios however small variations in pulse duration for a fixed impulse will have little effect on the response of the structure.Although the majority of the analysis presented in this paper is assumed to be uniform, some numerical treatment of non-uniform loading is given. The non-uniform spatial pressure distribution investigated here is given by a circular region centred at the plate midpoint with an exponentially decaying pressure outside this radius. Converting to polar co-ordinates, the pressure at any given location on the panel surface at time t isP(r,t)={P0r≤a,0≤t≤t0P0e−m(r−a)r>a,0≤t≤t00t>t0where r is the radial distance from the centre of the panel, a is the radius of constant pressure, m is the pressure decay constant, and P0 is peak pressure. Clearly, as the decay constant m approaches zero, the pressure approaches uniformity over the panel. Using the relationship given by Eq. then for a given impulse and decay constant, the peak pressure P0 isP0=It0[πa2+8∫0π/4{−e(m(−w+acosθ)cosθ)(mw−cosθ)+cosθ(1+ma)m2cosθ}ⅆθ]The loading used in comparisons with experimental and analytical results is assumed to be uniform in time and space over a prescribed pulse duration t0. A square pressure pulse is applied which is often used in the modelling of plates under uniform blast loading where the constant pressure P0 is calculated asThe geometry of the quarter-symmetry finite-element models for panels B (5 tubes) and C (9 tubes), as implemented in ABAQUS/Explicit are given in . The tubes are modelled using S4R shell elements with five integration points through the thickness using Gauss quadrature integration scheme. The top plate is modelled using 8-node continuum brick elements (C3D8R). Four elements are used through the thickness with all sides of the elements 1 mm in length. A convergence study is conducted to determine the optimal number of elements in the tubes. To minimize computational costs, the convergence study is conducted without hemispherical indentations, but with circular cutouts. An attached mass is inserted at the proximal end of a single tube and subjected to a pressure pulse, resulting in initial velocities similar to that experienced in the complete model. Convergence, in terms of maximum displacement is obtained using 180 elements along the length of the tube.The 10 mm hemispherical indenters are modelled using R3D4 rigid quadrilateral elements. The inherent difficulty in modelling the indentation process is the large time duration of the event compared to that of the blast. To accommodate this, numerically indentations are created by displacing the indenters at a velocity of 0.5 m/s. Simulating at lower velocities is found to show negligible differences in indentation shape. After indentations have reached the required depth, the indenters are moved away from the model at the indentation speed and then removed from the model.A simple analytical model is presented for predicting the response of tube-core cladding under blast loading. Specifically, simple expressions are given here to predict the crush distance of the proposed panels under blast loading. Jones for square tubes buckling in a progressive symmetric mode. For a panel with nt tubes of length l in the core, it is assumed that each tube has the same mean crush force Fm given by ref. Fm=13.05σcht5/3(lR)1/3{1+(0.33V0RlD)1/q}A simple approximation for V0 can be found asWhere I is the prescribed blast impulse, ρp and hp are the top plate density and thickness respectively. The term σc in Eq. is the characteristic stress which idealises the plastic flow of the material as perfectly plastic. There are various methods to account for strain hardening in the calculation of σc. A commonly used equation and the plastic strain values are given asɛc1=0.93(z)2/3,ɛc2=0.69(z)1/3,ɛc3=1.3(z)1/3To examine the response of the panels further, some simple results from Jones where v(0) = |
V0 and v(tmax) = 0 where tmax is the response duration. That is, at t |
= |
tmax all the kinetic energy from the blast is assumed to have been dissipated by the tubes. Therefore successive integration with respect to time and using the initial conditions v(0) = |
V0 and u(0) = 0 gives the displacement-time historyu(t)=∫{V0−ntFmtApρphp}dt=V0t−ntFmt22ApρphpTo find the total panel response duration tm, du/dt |
= 0 is solved for t givingIf the energy absorption capacity of the core tubes is insufficient to absorb the blast then the predicted value of um is beyond the maximum stroke of the core and compaction occurs. This is an undesirable result as the forces at the base of the panel may exceed the peak buckling load of the tubes by several orders of magnitude. To determine the time when this occurs, the deformation-time relationship given in Eq. is compared to the maximum allowable deformation Sl. This relation is then solved for t to give the time at which compaction occurs astc=V0Apρphp−Apρphp(V02Apρphp−2ntFmSl)nmFmTherefore if tc |
≥ |
tm then the panel will be able to absorb the prescribed blast load. The complete solution to the equation of motion is given byut(t)={0t≤0V0t−ntFmt22Apρphp0<t≤tmandt<tcSlt≥tca show a significant increase in core crush distance with increasing impulse. In terms of the panel B designs, a large increase in crush is observed when moving from 53.05 Ns blast to the 62.13 Ns blast however only a small increase is found when examining the 68.24 Ns. This is expected however, as visual inspection of the 62.13 Ns test shows the core tubes have reached their maximum stroke. For test S – B – 38 it can then be assumed that deformations near the end of the crushing process are limited to localised squashing of the tube beyond the maximum stroke length which induces large forces to the base structure.For the panels C tests, a significant increase in crush distance is observed for the two smaller blasts. The larger blast corresponding to test S – C – 38 shows an unexpectedly small crush distance in comparison to test S – C – 33. Despite the relatively large increase in impulse (10.6 Ns) only a small increase in crush distance is found. A possible explanation for this can be found by examining the distal end of the tubes in test S – C – 38. Due to apparently early debonding of the tubes and the bottom plate, significant, highly localised deformations occur in the tube at the position where the tubes are normally bonded to the bottom plate. Plastic zones are formed with a large angles of rotation at these locations.The aluminium tube-core panels also show significant increase in midpoint crush distance with increasing impulse, as given in b. Only a small increase is observed however, in test A – B – 28 over test A – B – 20 indicating that compaction has occurred and that the maximum impulse of the panel B designs with the given geometry is near 41.87 Ns (). As is the case for the steel tube panels, the panel B tests in which compaction does not occur results in relatively large top plate skewness. This skewness, characterized by large differences in tube crush distances within a given panel, does not appear to be as severe for the aluminium tube panels as for the steel tube panels. For the panel C tests the observed crush distance forms a strong linear trend as none of the tests fully compact the core tubes. Visual examination of test A – C – 28 however, shows that panel is near compaction and hence the impulse capacity of the panel C designs is near 54.49 Ns. It is also worthy of note that the crush distances at the common charge mass of 28 g, with nearly identical impulse, are significantly higher in the aluminium core panels. For the panel B tests the aluminium core panel shows a crush distance approximately 49% higher than the steel tube panel subjected to the same charge mass. For the panel C test, the aluminium tube panel shows a crush distance 248% larger than the steel tube panel. This large percentage increase is partially due to the unusually small crush distance found in test S – B – 28. These large increases in crush distances when using aluminium tubes illustrate the influence that strain hardening and strain-rate effects has on the response of the panels under blast loading conditions.For the panel B design under the 28 g blast the buckling mode is found to be irregular with each tube in the panel having lobe formations at different locations. In each of the tubes except for the central tube, buckling appears to initiate at the indentation trigger. In the central tube, lobe formation occurs at the proximal end of the tube, ignoring the trigger completely. Also of note for this test is that tearing occurs along the edge of one of the outermost tubes in the panel. For the larger blasts corresponding to 61.63 Ns and 71.63 Ns, the buckling modes are observed to be much different than those of the smaller blasts. In both cases, the resulting tubes show a nearly symmetric crushing pattern. This is particularly true for the test S – B – 33. It is possible that the symmetric buckling patterns observed are due to buckling initiation occurring at the triggers in tests S – B – 33 and S – B – 38. For tubes that undergo significant crushing, the lobe formations are of the symmetric type. Further to this, for panels that crush to compaction, it is found that two to three lobes are formed in each tube where, in general, two of the lobes are large with the third having a very small lobe size.The results of the panel C tests show similar buckling behaviour to that of test S – B – 28. Specifically, the lobe formations are highly irregular, particularly so for tests S – C – 28 and S – C – 33. Buckling does appear to initiate at the trigger in several of the tubes in these panels however. In test S – C – 28, buckling initiates at the trigger only in the outermost tubes, with the largest crush distance. Buckling initiates at the trigger in all tubes in test S – C – 33 on the side of the panel corresponding to maximum crush distance. For the largest blast test, S – C – 38, most of the tubes show buckling initiating at the trigger with tubes with small crush distance buckling at the proximal ends of the tubes. It should also be noted that the progressive buckling of tube which buckle at the trigger appears to be confined to the upper half of the tube, closest to the top plate. Further to this, in cases where the lobe formations are not degenerate, the lobe formations appear to be of the symmetric type.Similarly to the panel B, steel tube tests with small crush distance, the aluminium tube panel subject to the 13 g blast shows highly irregular lobe formations. It is also found that only three of the five tubes buckle at the trigger in this test. For the tube with the smallest crush distance, extensional modes develop at the proximal and distal ends of the tube which does not occur in any of the steel tube tests. For the larger blast tests A – B – 20, and A – B – 28, buckling is found to generally be of the progressive symmetric type with some irregularity found in the test panel A – B – 28. In this test the lobes are found to be much larger and highly non-uniform in thickness across the tube width.For tests A – C – 13 and A – C – 20, the trigger is ignored in almost all tubes. In these cases where the trigger is ignored, a mixture of extensional and symmetric lobes are formed at the distal and proximal end of the tubes. This buckling pattern is consistent with the experimental and numerical study by Karagiozova et al. compares the analytically predicted crush distances with the experimentally and numerically obtained results for each of the experimental tests. For the steel tube cores, good agreement is found in panel B tests up to the point of compaction. This is expected however, as the analytical prediction does not model response beyond the maximum theoretical stroke. For panel C tests, good agreement is obtained with the finite-element predictions, however some differences are observed with the experimental results. The reasons for this are briefly discussed in Section . Similarly, for the aluminium tube cores, good correlation is found for tests resulting in crush distances below the theoretical compaction point. A further reason the analytical predictions generally over estimate the finite-element results is that the peak velocity of the top plate is assumed to be obtained instantly. In reality, the geometry and material properties of the core tubes will influence the velocity of the top plate during the application of the load, thereby reducing the velocity from this theoretical maximum.Quasi-static tests are conducted on single tubes of the same length and aspect ratio as are used in the complete panel blast tests. The purpose of this is to validate the material and finite-element model by comparing experimental force levels with those obtained through finite-element simulations. Reaction forces cannot be measured during blast tests and therefore quasi-static tests are required to compare reaction forces. Two steel tubes and two aluminium tubes are cut from a single section, after thickness reduction, to obtain a uniform thickness. The mean thickness of the steel tubes is found to be 0.63 mm while the aluminium tubes are found to have a mean thickness of 0.62 mm. The aspect ratios of the steel and aluminium tubes are found to be R |
= 3.44 and R |
= 3.45 respectively.The tubes are crushed on a Zwick universal testing machine at a constant velocity of 3.75 mm/min. This crushing velocity is chosen as it gives a strain-rate approximately equal to the quasi-static tensile tests. The tubes are crushed a distance of 50.0 mm. a and b shows the resulting force-displacement curves for the steel and aluminium tubes respectively.In terms of buckling initiation, it is found that all tubes buckle at the location of the initial indentation as expected. During the second experiment using the steel tube, partial global buckling initiates and hence progressive, symmetric buckling ceases. All other steel and aluminium tubes are found to buckle in a progressive symmetric manner, however some slight anti-symmetric lobe formation is observed in the first steel tube experiment. This behaviour is a temporary effect as the final buckling shape is reasonably symmetric. This is likely due to inconsistencies in the wall thickness which cause lobes to begin forming at a particular location on a tube wall before the corresponding locations on the other wall have buckled. This has the effect of initiating global buckling however the effect is quickly reversed as the other tube walls buckle to form a nearly symmetric lobe.Quasi-static simulations are carried out using ABAQUS/Explicit. The tubes are crushed at a velocity of 0.5 m/s with no rate effects in either material. At this velocity inertia effects are negligible and hence can be used to simulate quasi-static behaviour. Reasonable agreement is found between the experimental and numerical force-displacement displacement curves as shown in . For both materials the numerically obtained forces are found to be slightly lower throughout the majority of the crushing process. This is particularly true for the aluminium tubes. This is expected, due to the relatively large filleted interfaces on the interior tube walls. This is not accounted for in the finite-element model using shell elements. The increased stiffness at the tube corners increases the experimentally obtained crushing force. The underestimation of the force levels for the steel tubes is likely due to the slight parabolic shape in the tube wall as the tubes tend to be thicker at the midpoint. For both materials the peak buckling load is found to be slightly higher in the numerical model than in the experiments. This is a result of the hemispherical indentation depth being under-predicted in the numerical model. The subsequent peak forces however, are predicted with a high degree of accuracy. gives the finite-element predictions of the final crush distances computed using ABAQUS/Explicit. All crush distances are measured at the panel midpoint on the top plate. In the finite-element simulations the panels crush to a maximum distance and then undergo a slight rebounding, resulting in small amplitude oscillations in the top plate displacement. Crush distance values are estimated as the midpoint of the maximum and minimum crush distances within the period of oscillation.a, the finite-element analysis shows reasonable agreement with the experimental tests. Correlation is found to be particularly good for the panel B designs. For the panel C designs, the finite-element predictions are not as accurate, except for test S – C – 33 (61.63 Ns). It was noted in Section that the experimental crush distance for test S – C – 38 (71.63 Ns) is remarkably low and reasons were presented explaining this behaviour. For these reasons it is expected that the finite-element simulations will over-predict for this test. For test S – C – 28 (55.09 Ns), similar reasons can be used to partially explain the over-prediction. It is found that in the corresponding experiment, at the central tube there are very localised deformations at the distal end due to solder failure early in the test. As this is the primary point of measurement this artificially reduces the total crush distance a small amount. It should also be noted that test S – C – 28 results in the largest relative top plate skewness of all the tests.The results of the finite-element simulations from the aluminium tube panels are given in b. For the panel B designs, the finite-element model tends to over-predict the crush distance, particularly in cases where the panel reaches its compacted crush distance. The crush distance is predicted well for test case A – B – 13 (29.17 Ns) where the panel does not undergo compaction. As the finite-element model over-predicts in the test that undergo compaction, it is clear that the finite-element model does not properly simulate the tube deformation mechanisms in the region at, or beyond the maximum stroke length. The over-predicted crush distances are likely due to the differences in lobe formation between the finite-element model and experiments. This is discussed further in the Section The finite-element predictions of panel C crush distances, with aluminium tubes agree extremely well with experimental results in all test cases. This further emphasizes the result that the response of the aluminium tube-core panels can be predicted well provided that the panel does not undergo compaction. This is a desirable result as it is important to be able to numerically predict the panel response to determine if a given panel will compact under specified blast loading conditions.From a qualitative standpoint, the buckled shape of the tubes, is predicted unsatisfactorily in most test cases, as can be seen in . Poor performance of the hemispherical indentation trigger at the midpoint of each tube is observed in these test cases. In experimental tests using aluminium tubes, where the trigger is ignored, lobe formation tends to begin at the proximal and distal ends of the tubes. Numerically, buckling begins at the trigger in all cases. This behaviour may be partially due to the numerically predicted indentation depth exceeding the experimental one. It is clear that a larger indentation depth should be used in the experimental panels to obtain the same location of the initial lobe in the numerical simulations.In all numerical simulations, buckling initiates at the trigger and progresses along the lower half of the tube. This also appears to be contrary to the experimental behaviour, particularly in the steel tube panels. In these panels, the experiments show buckling to be confined to the proximal end, close to the top plate, even for tubes that buckle at the trigger. It is unclear how successive lobes form in the experimental aluminium tube panels as the given tests that are not at or near compaction only have lobe formations at the distal and proximal ends of the tube. For tests which use the full stroke of the tube it is inconclusive as to how the lobes form with respect to time. It should be noted that in the photographs of the experimental tests, the section of the tube that is initially constrained by the bottom plate is included.The size, and hence the number of lobes is determined reasonably well in the numerical simulations of the steel tube panels. For the steel tubes, the large strain hardening and strain-rate effects leads to increased lobe size in comparison with the aluminium tubes. In the fully crushed panels, the number of lobes in the numerical simulations is found to be between three and four which compares favourably with the experiments. Of interest however is that in the finite-element simulations, due to the progressive buckling being confined to the lower half of the tubes, localised compaction occurs. This is a process where lobes which have already been formed become compressed further, despite the upper half of the tube remaining unbuckled. This is found to be a temporary phenomenon as folds begin to form in the upper half of the tube. This is discussed further in the following section. In terms of buckling mode however, this process has the effect of reducing the lobe size in the lobes closest to the base of the tubes.The size of the lobes in simulations of the aluminium tube panels is found to be smaller than that of the experimental tests. This behaviour is found to be particularly true for the simulation of test case A – C – 28 (54.49 Ns). This is again partially due to the localisation of buckling to a single end of the tube where lobes become crushed despite the full stroke of the tubes not being utilised. A further contribution to the underestimation of lobe size may also be from underestimation of the hardening properties of the 6063-T6 aluminium. It was determined using tensile test simulation that the strain hardening beyond the UTS of the material to be negligible. Underestimation of the strain hardening will reduce the numerically obtained lobe size. This is further supported by examining the quasi-static force-displacement curves shown in . An underestimation of the strain hardening may explain why the numerically computed reaction force has a lower minimum value than the experimental curves. The material is also assumed to be completely rate insensitive however it is possible that slight rate sensitivity exists in the material which cannot be measured using the SHPB setup.Despite the poor prediction of the local folding behaviour of the tubes within the panel the crush distance is predicted well in nearly all test cases. This indicates that global response of the panels can be predicted accurately, however local behaviour of the panel core requires further research. Specifically, the implementation of the trigger requires further investigation into the effect of the trigger on localised deformation patterns.As it has been determined that the global response of the proposed panels is predicted reasonably well it is interesting to examine further, the finite-element simulations of the experiments. Specifically, the force transfer and energy absorption properties of the panels is numerically investigated. give plots of the force-displacement curves and energy absorption partitioning for the steel and aluminium core panels respectively. The forces shown in the figures are obtained as the summation of the reaction forces at the distal end of each tube in the panel. As the top and bottom plates do not come into contact during the simulations, these forces represent the total force transfer to the rigid body at the base of the panels. For all force and energy plots, the curves are shown up to maximum of the average tube displacement, measured at the corners of the tubes.For the steel tube panels, there is a clear increase in absorbed energy at a given displacement when increasing the applied impulse. As the annealed mild steel is rate sensitive this result is not unexpected. This rate sensitivity also results in a slight increase in peak force levels with increasing impulse. Of note for the steel tube tests is that the peak reaction force does not correspond to the dynamic buckling load of the tubes. Examination of shows an instantaneous spike in the reaction force due to the inertia of the tube itself. The magnitude of this peak reaction force is independent of the loading velocity. This spike in the reaction force is common in the dynamic crushing of tubes. For the current application, the spike in reaction force actually exceeds the critical buckling force.As is the case for the steel tube cores, the aluminium tube panels show an increase in absorbed energy at a given displacement, when increasing the impulse, and hence the velocity of the top plate. This is despite the material model for the aluminium assuming strain-rate insensitivity. Langseth et al. If the proposed panels are to be utilised in actual blast conditions, where the application of pressure loading is not controlled, it is of interest to understand how variations in loading uniformity influences panel response. The mathematical model for the non-uniform loading of the panels is presented in Section . Under non-uniform loading, the blast load is defined by the total impulse I, the radius of uniform pressure a, the pulse duration t0, and the decay constant m. Once these parameters have been defined, the peak pressure P0 is determined using Eq. Two additional non-dimensional performance measures are introduced. Ideally, the energy absorption within the panel is confined to the core as large amounts of dishing in the top plate will lead to global buckling modes in the core tubes. To quantify this, the core efficiency ξcore is given asUcore and W are the total plastic energy dissipated in the core and the external work respectively. The value of δi is the mean crush distance for tube i. The stability parameter ξst gives a simple measure of the amount of dishing that occurs in the top plate by quantifying the deviation in crush distances of each of the tubes in the panel and is given asξst=∑i=14nt|δi−δmean|δmeanδmean=14nt∑i=14ntδiFor the analysis of this section, the impulse is fixed at I |
= 50 Ns. Using a fixed impulse allows for an isolation of the effects of non-uniformity as the total momentum transfer to the panels is the same throughout. The radius of uniform pressure is fixed at a |
= 40 mm. The pulse duration is t0 |
= 10 μs. The parameter which is allowed to vary is the decay constant m. The values used in this study are m |
= 10, 20, 30, 40 m−1. The magnitudes of the parameter m are based on the radial distance measured in metres. As the value of m increases, the pressure P0 within the radius of constant pressure increases. As the impulse is identical for all values of m, this effectively shifts the pressure away from the top plate boundaries, to the centre of the panel. gives the resulting pressure distribution, using quarter-symmetry, for the m values investigated here.Panel layouts A, B, and C are studied under non-uniform loading. The λ values used correspond to the optimal values determined from a numerical parametric study. The goal of the investigation is to determine the degree to which efficiency and stability is reduced when increasing the non-uniformity of the loading on panels which have stable cores under uniform loading. As it is expected that the top plate thickness will have significant influence on the response to non-uniform loading, a thin and a thick top plate of thickness hp |
= 2.0 mm and hp |
= 4.0 mm respectively are used in the analysis. Finite-element analysis are conducted for each layout (A, B, C), and for each top plate thickness, with loading decay parameters of m |
= 10, 20, 30, 40 m−1. It should be noted that, due to computational constraints, indentation triggers are not used for the parametric study and instead circular cutouts of diameter 0.25l/R are used. An aspect ratio of R |
= 4 is used for all computations.a gives the resulting variations in core efficiency as a function of the decay parameter m. It is clear that when loading the panels with the 2.0 mm top plate, core energy absorption is found to be reduced significantly when increasing the decay constant. The reduction in efficiency is most pronounced with panel A layouts, with panel C showing only a small reduction in core efficiency. For uniform loading (m |
= 0), all three panel layouts have nearly identical core efficiency however, due to the lack of the central tube, panel A shows a large reduction in efficiency for even a small amount of non-uniformity in the load. The central supports provided by the extra tubes in panels B and C results in a relatively small reduction in efficiency for small changes in the decay constant. This is shown to be particularly true for panel C where only a negligible reduction in efficiency is observed at m |
= 10 m−1.Numerical tests using the 4.0 mm top plate also show a substantial reduction in core efficiency at large values of m, however the reductions are less than that observed using the 2.0 mm plate. Panels A and B are observed to have nearly the same core efficiency for all values of m. For m |
> 10 m−1 the core efficiency is actually marginally higher in panel A than in panel B. This indicates that when using a thicker top plate, the addition of the central tube has little effect on the resulting core efficiency when loading the panels using a non-uniform pressure distribution.The stability parameter is also analyzed as a function of the decay parameter m. It must be noted that comparing stability parameters is only valid among similar panel layouts (A, B, or C) due to the geometric symmetry of the problem. Under uniform loading, large variations in the stability parameter generally correspond to instabilities developing in the core cubes which induce mode J and mode K buckling shapes as shown in . Under non-unform loading, it is expected that, due to the pressure being concentrated at the panel centre, that core efficiency and stability parameter will show a correspondence, however changes in the buckling mode will be different to that of uniform loading.b gives the stability parameter as a function of m for the panels tested. Under uniform loading (m |
= 0), the value of ξst is close to zero in all test cases. As expected, the value of ξst is found to increase when increasing the decay parameter m. For each panel layout, the stability parameter is significantly higher when loading the panels with a 2.0 mm top plate indicating a much larger differential in the crush distance at the tube corners within the panels. For higher decay constants, as in the case with uniform loading, increases in the stability parameter correspond to decreased core efficiency as differentials in crush distance of the core tubes requires the top plate to deform, therefore reducing the total energy absorbed by the core.A series of blast experiments are conducted on a type of sacrificial cladding. The cladding is a sandwich structure composed of thin-walled tubes made of either annealed mild steel, or 6063-T6 aluminium alloy. Tests are conducted of cores containing 5 and 9 tubes. Blast loads are applied uniformly over the cladding face plate using a blast tube apparatus.Irregular buckling modes are observed in all tests corresponding to crush distances well below the stroke of the tubes in the panel. The hemispherical trigger indentations are found to not induce buckling in all tubes. It is expected that optimisation of the trigger will result in the initiation of localised buckling modes and hence increased panel stability and impulse capacity. Test panels corresponding to crush distances at or beyond the maximum stroke of the tubes result in symmetric buckling modes in nearly all tubes within a panel. This appears to indicate that progressive, symmetric collapse of the core can occur despite buckling initiating at different locations on the tubes.A numerical investigation of tube-core sacrificial claddings under blast loading is presented. Representing the blast as a pressure pulse, uniform in time and space, simple existing analytical formulae are employed to predict panel response. A finite-element model is also investigated using ABAQUS/Explicit and a numerical parametric study is conducted to investigate the response of tube-core claddings under non-uniform loading. The analytical and finite-element approximations are found to agree well with the experimental tests. Particularly good correlation is found in cases where the maximum stroke of the panels is not exceeded.Finite-element analysis of the experimental blast tests show that for the configurations investigated here, energy absorption is primarily confined to the core tubes. The capacity of the panels is found to increase slightly at higher impulses for both rate sensitive and rate insensitive core materials, primarily due to increased energy absorption during the initial compressive phase of buckling. Panels which undergo compaction however, are found to transmit forces significantly higher than the peak buckling load of the core.Under non-uniform loading, the finite-element results show that energy absorption in the top plate can be significant, reducing the energy absorbing efficiency of the panels. For a fixed impulse, increasing the pressure distribution near the panel centre induces global buckling modes in panels which undergo progressive, symmetric buckling under uniform loading. The increased dishing in the top plate is found to be enhanced in panels with fewer core tubes and in panels with a thin top plate.Precision assembly of additively manufactured components using integral kinematic couplingsThe use of additive manufacturing (AM) in engineering applications is often confronted by process capabilities that limit component accuracy and surface finish. These limitations greatly complicate locating of parts for post-processing and/or assembly. Here, we describe the use of integral additively manufactured kinematic couplings (AM-KCs) for construction of modular AM assemblies. As a representative test geometry, classic Maxwell KCs are printed using four commonly used AM processes for plastics and metals. We study how coupling accuracy and repeatability are influenced by material properties, surface quality, and loading conditions. Under systematically controlled preload, as-built polymer AM-KCs are measured to have 1σ repeatability of 3.2−16.6μm which depends on the layer thickness and material/process combination. Metal AM-KCs made by selective laser melting (SLM) are shown to repeat to 0.9μm. Finally, we demonstrate the use of AM-KCs in the fabrication of a modular, 3D printed optical assembly.Additive manufacturing (AM) has become a vital technology for creating exotic geometries inaccessible to conventional manufacturing, and for rapid prototyping and short-run manufacturing []. However, the success of AM in precision applications is challenged by its limited dimensional accuracy, surface finish, and part-to-part consistency []. As detailed below, efficacy of traditional locating geometry (e.g. alignment pins) on AM components is sharply limited by these characteristics, and this plainly restricts application of as-built AM components in precision applications. More subtly, even parts destined for post-machining to more stringent specifications must initially be located within the machine tool by a combination of imperfect printed surfaces, introducing uncertainty in component location with respect to cutting tool trajectory []. Therefore, robust means to locate AM components in mechanical assemblies, and for post-print machining, are necessary to improve the usability of AM in precision engineering applications.Efforts to adapt AM to precision engineering must involve compromise between assembly tolerances and the properties of the individual components therein. One approach is the principle of exact constraint, that states two components should make contact in a manner that uniquely constrains all required degrees of relative motion without redundancy []. For example, one may rely on the combination of theoretical plane-plane, line-line, and point-point contact to constrain a component to its mate in 3, 2, and 1 degrees of freedom (DOF), respectively. Such a configuration is advantageous for two reasons. First, upon reassembly the components re-engage at exactly the same locations. Second, deformation of the components does not occur due to forced congruence of non-ideal geometry, as may occur in clamping a slightly tapered part between parallel vise jaws. Interfaces that employ this design paradigm for deterministic reassembly are known as kinematic couplings (KCs), and they have long been prized for providing repeatable assembly between components []. Theory and experiment show that repeatability is maximized between when KCs are fabricated from hard materials and have fine surface finish []; however, these qualities are not reflected in common AM components.Two archetypal coupling configurations are shown in a and b. These designs use sphere-plane contact to clearly define six locations of kinematic constraint []. The former is known as a symmetric Maxwell coupling; it is often employed for its near equal stiffness in all directions. Complex arrangements of coupling points are possible, such as the Kelvin coupling shown in b, and more generally may comprise alternative geometric forms, e.g. point contact of crossed cylinders or split grooves to broaden the base of support [], or for mechanical convenience. AM is well suited to fabricating custom KC geometries tailored to match a specific application, such as optimizing stiffness in a direction of anticipated loading. Moreover, a KC may be readily engineered to be robust to the variance and inaccuracy of AM components without sacrificing repeatability; kinematic surfaces of the proper form provide deterministic registration even if they are modestly perturbed from their ideal size or location, provided they still engage as designed.We contrast kinematic couplings with traditional pin and slot location (c), perhaps the most common means of locating two components, with a compromise between simplicity and precision. Here, two pins are incorporated into one component; one of these pins mates to a slip-fit hole on the second component, and the other fits into a slot oriented as to prevent over-constraint []. This locating paradigm gives the coupling high stiffness, arising from plane-plane contact, and purpose-made pins and bushings can be obtained commercially that repeat to 15μm or better []. In principle, constraining components in this way may be applied to AM. An engineering compromise must be made, however, in setting the nominal clearance between the pins and their mating features. The repeatability of the interface improves as this clearance is reduced, at the cost of increased probability that the two components fail to engage (e.g. an as-built pin is larger than its mate). Design recommendations for printing pin and slot features vary greatly across AM processes and machine suppliers. Generally, design guides for polymer process recommend 400−600μm nominal clearance between mating components [], whereas direct fabrication of mating metal AM surfaces is typically ill-advised []. Specifically, the combination of finite feedstock particle size and surface tension effects in metal AM cause considerable surface roughness (20−50μmRa), and dimensional inaccuracy (≈100μm) []. Components may be further distorted from their nominal shape by residual stress [] which is prominent in laser-based metal AM. Due to the substantial clearance necessary to accommodate such defects, AM assemblies using pinned interfaces require post-processing of the locating surfaces to achieve high repeatability.In this paper, we establish the suitability of integral ball-groove KCs, as depicted in d, for precision location of AM components. AM-KCs are fabricated by a variety of mainstream AM processes in polymers and metals, and the impact of their unique characteristics on AM-KC locating performance are discussed. Specifically, we experimentally characterize the behavior of AM surfaces under point-loading, and contrast their behavior to the Hertzian contact model. AM surfaces are shown to undergo plastic deformation upon initial loading, but to provide repeatable force-deflection behavior thereafter. These results are applied to AM Maxwell-type KCs as they are well suited to interfaces requiring stiffness and load handing in several directions; however, this understanding is broadly applicable to AM-KCs of all types, including those tailored to achieve application-specific stiffness requirements. Specifically, accuracy and repeatability measurements of the AM-KCs are presented and interpreted in view of the point-loading results. Finally, we show an exemplary application of AM-KCs in the fabrication and validation of a modular optical instrument. depicts AM-KCs fabricated using the four methods studied in this work. SLA (stereolithography) components, such as those shown in a, are fabricated at 25μm and 100μm layer heights using a Formlabs Form 2 printer in Formlab's Clear V2 resin []. FFF (fused filament fabrication) couplings are printed in ABS on two systems: a Stratasys Mojo for 170μm layers (b) and an Ultimaker 2 for 40μm layers (see Ref. [] for representative material properties). As-printed (no surface treatment) metal KCs printed via selective laser melting (SLM) on an EOS M290 (17-4 stainless steel []) and binder jetting (BJ) (ExOne, 17-4 SS/Bronze [c and d, respectively. Finally, values reported for polymer KCs are averages from five assemblies fabricated for each combination of parameters; metal AM-KC data result from a single KC assembly.a. This alignment pin is used to prevent relative motion of the sphere-groove pairs in the directions orthogonal to the applied load and thereby ensure contact of the same regions of each component on each cycle; accordingly, the specimens are precision-reamed for a minimum clearance slip-fit. The UTM is configured to cyclically load the specimens to a test load, pause for 20 seconds, unload the specimen, and pause again; data are collected for 10 repetitions of this pattern.Accuracy and repeatability of full AM-KCs are assessed using the symmetric Maxwell configuration shown in b), the datums of each half are then easily probed and therefore may be accurately located. This combination of measurements then enables the final positions of the KC surfaces to be deduced, despite the lack of mechanical access.The test fixture further comprises three fasteners that pass through the assembly to preload the KC, located as to apply force directly over the well-supported regions of the coupling. c shows one of three calibrated load cells (Futek FTH300, 0.6N resolution) that are installed inline with the fasteners to enable precision control of the clamping force, along with an alignment washer that prevents overconstraint of the assembly.The positions of the datums are recorded upon reassembly of the coupling 5 times; for a given assembly trial the positions of the locating surfaces are then calculated by way of the first set of measurements. Using the procedure described by Slocum [] for MATLAB implementation), the locations of the centroids of the sphere and vee halves may then be determined. Repeatability, or the degree to which the sphere centroid returned to the same location upon reassembly, is taken to be the 1σ standard deviation of its X, Y, and Z positions summed in quadrature. Accuracy of the couplings is calculated as the distance from the theoretical sphere-half centroid location to its mean experimental position, accounting for deflections via Hertzian model.Finally, a break-in procedure is also tested, in which couplings are loaded to 150% of the nominal test load 3 times prior to measurement. By stabilizing the plastic deformation at this higher load, plasticity of the surfaces at the test load should be minimized. Moreover, the break-in procedure is expected to further average the residual surface texture, thereby improving repeatability.Design considerations for AM-KCs begin with the contact mechanics at the points of engagement between the two components. Hertzian contact mechanics are often employed to model the expected deflections and stresses, and various heuristics are used to predict KC accuracy and repeatability. These considerations often push designers to employ stiff materials capable of sustaining high contact stresses and fine surface finishes []; however, consideration of common AM processes must embrace polymers as well as rough/layered surfaces. Here, we begin by considering methacrylate components fabricated using stereolithography (SLA) and ABS specimens printed using fused filament fabrication (FFF) under point-loading. The layerwise nature of these methods results in a significant, structured surface roughness. a and b shows exemplary surface textures of these polymer processes. In contrast, c and d shows surfaces fabricated via selective laser melting (SLM) and binder jetting (BJ), respectively, where effects of the powdered feedstock create a more random texture. In either case, the contact problem must be considered on two scales, first on that of the mean (theoretical) geometry, and second at the level of interacting surface textures.Hertzian contact theory describes point contact of surfaces, assuming the surfaces are elastic, frictionless, continuous, non-conforming, and experience small strains [ are readily derived, for contact radius a, deflection δ, and maximum contact pressure p0, as functions of applied load P, effective contact radius R, and effective modulus E*. It is also necessary to consider the maximum load that may be applied without giving rise to plastic deformation, as governed by the material yield stress Y. Applying Johnson's approach [] to a plastic with typical Poisson's ratio (ν=0.35), yields the expressions for the maximum principle shear stress (τ1)max, its location under the surface zmax, and the minimum central contact pressure pY required to cause plastic deformation, given in Eqs. First, consider the case of a 12.7mm radius sphere forced into contact with a plane; both are fabricated by SLA and therefore comprised of cured methacrylate resin. Per the relations described above, this material and geometry combination can sustain a load of 422N prior to yield, with a stiffness of 4.34N/μm at yield. ABS, a typical material for the FFF AM process, has a lower yield stress; at a load of 102N, the component begin to yield, while deflecting 73.7μm, and exhibiting a normal stiffness of 2.07N/μm.However, initial contact of AM components occurs when the surface textures come into contact, as illustrated in e. The illustration shows (exaggerated for emphasis) the typical surface texture of SLA or FFF processes on a sphere and plane, where R1 and R2 represent approximately half of the layer height used to fabricate each surface. Thus, initial contact between the surfaces occurs not with the nominal radius of the sphere R3, but when the most prominent points of this texture engage with a minuscule effective contact radius determined by R1 and R2. This is results in a very small initial contact area and high contact stress, causing deformation at sub-millinewton forces for typical characteristics of polymer AM.Therefore, with AM-KCs, plastic deformation of the surface texture is certain under any practical load. However, prior work by Moore which focused on crushing simulated asperities suggests that complete elimination of the surface texture is impossible, as later verified via experiment and slip line analysis by Childs []. Greenwood and Tripp show that any remaining surface texture serves to decrease contact stiffness and increase contact radius []. While these works suggest that residual surface texture will remain and influence the nature of contact, the presence of the residual (deformed) surface texture does not necessarily violate the conditions for point-like contact identified in Ref. [], namely that a be small as compared to R and the dimensions of the supporting body. Taken in sum, the surface texture of AM components is expected to plastically deform, but ultimately stabilize for a given loading condition, and remain point-like for sufficiently low applied forces.These mechanics are experimentally studied via the method detailed in Section . A typical experimental result for a fine-layer SLA sphere-vee pair is shown in Fig. 4a wherein the test load was set to 500N, along with the theoretical force-displacement curve predicted via the Hertzian model. We observe that the force-displacement curve stabilizes under repetitive loading. Further, the hysteresis of the full cycle is stable, and there is energy dissipation (given by the area between the loading and unloading curves) arising primarily from friction and viscoelasticity. Additionally, the initial point of contact is seen to shift vertically (in the direction of UTM travel) by approximately 30μm as a result of plastic deformation of the surfaces; this deformation primarily occurs on the first cycle, further evidenced by the modestly increased energy dissipation on the initial cycle. Ideally, this plastic deformation occurs along two vectors normal to the planes of the groove specimen, as a frictionless sphere-plane interface cannot resist tangential forces. Thus, as the planes are offset by 45∘, displacements in this direction are larger by a factor of ≈2.b shows curves resulting from an identical experiment performed with the coarse (170μm layer) FFF specimens. Many of the characteristics of the cyclic force-displacement plot are similar to the SLA data, namely that the initial loading causes plastic deformation as evidenced by the shift in contact location, and that the curves stabilize upon repetitive loading. However, the functional form of these curves deviates from the theoretical P2/3 character: all force-displacement curves except the initial loading curve show a kink at a displacement of about 0.16mm. We hypothesize this inflection point indicates sub-surface plastic deformation occurs upon initial loading. At this displacement on the initial loading cycle, the machine-applied load is ≈150N versus the 144N expected to open a sub-surface void on the basis of the preceding calculations and specimen geometry. On subsequent cycles, the stiffness is first reduced by the presence of the void. Once sufficient force is applied to close the void, the interface stiffness increases substantially. This feature is also seen in the 236N peak load data; however, is absent in the more lightly loaded trials that do not theoretically induce sub-surface yield., results from the same method applied to SLA sphere-vee pairs at peak loads spanning 25N to 1057N are compared against the Hertzian model. Referring to a, it is evident that the maximum deflection (as measured at the testing machine crosshead) under load greatly exceeds the prediction of the Hertz contact model. Much of this deflection arises from plastic deformation of the surface texture, which occurs until the contact patch area is sufficient to bear the applied force. SLA surfaces clearly show this effect; the coarser (100μm layer) surfaces exhibit much greater deflection than their finer (25μm layer) counterparts. Representative error bars illustrate the 1σ standard deviation across all cycles, and indicate the force-deflection character of the surfaces remains consistent to ≈5μm after the initial loading. Consistent contact mechanics are a requisite for repeatable KCs, thus these data suggest that comparable repeatability should be achievable on full KCs.b are similarly extracted from the crosshead force-displacement data by taking the slope of the initial unload portion of the cycle. For SLA components, compliance is invariant with layer height. This is not unexpected given the large deflections observed as compared to the magnitude of surface roughness; however, as expected, the residual texture decreases the stiffness as compared to the model. These data may also be used to estimate the stiffness of a full symmetric Maxwell KC, as this configuration is often selected for its near-uniform stiffness []. For example, these results are 1/3 of the vertical stiffness of a full KC, or 11.4N/μm for a SLA KC under 500N preload.Contact radius is measured after each test using optical microscopy, which is plotted as a function of applied force in c. Given the low pressure needed to deform the surface texture, contact radius is determined via measurement of the area displaying deformation, as shown for an SLA component loaded to 500N in d, with error bars representing estimated measurement uncertainty. The residual surface roughness lowers the average contact pressure, as low lying portions of the surfaces do not help support the forces between coupling halves. Thus, a larger contact area is necessary to support a given force as compared to the idealized theory. Nonetheless, the SLA pairs satisfy the conditions for point contact for machine-applied forces below approximately 700N.Data collected for the FFF specimens are also presented in blue in ; however, these do not display the same dependence on layer height. The fine-layer specimens typically exhibit higher deflection and increased stiffness as compared to their coarse-layer counterparts. This likely results from differences in as-printed material properties between the Ultimaker and Mojo, despite both nominally printing fully-dense ABS parts. Despite this, contact radius remains similar, implying that the final load bearing area and pressure distribution are comparable. At a force of 236N, the contact radius exceeds the threshold for point-like contact, implying that KCs loaded above this threshold will feature reduced repeatability. For direct comparison with the SLA specimens, e shows surface deformation induced by the 500N trial. summarizes the locating performance of AM-KCs under 75N net preload (25N per sphere-groove pair), assessed per the method of Section . We find repeatability is largely independent of layer height. SLA couplings printed with 100μm layer heights repeat to 16.5μm, only 1μm worse than their counterparts printed with 25μm layers. KCs fabricated via FFF offer better repeatability at this load, with the curious result that the 170μm couplings repeat to 3.2μm, which is approximately two times better than the 40μm layer KCs. Nevertheless, this is consistent with the point loading measurements above, wherein the coarse-layer FFF specimens show more ideal behavior at this load. The yield stress of ABS is approximately half that of cured methacrylate, thus the FFF couplings take advantage of greater surface texture averaging to achieve high repeatability. The break-in procedure does not measurably affect repeatability at this light load. Finally, angular locating performance is summarized in ; repeatability is typically 50−100μrad.Increasing the load to 1500N (500N per sphere-groove pair) improves the locating performance of SLA couplings (7.4μm, for 25μm layer height) but degrades performance of FFF KCs, as summarized in . The latter result is expected, because like the indentation tests above, the bulk geometry of these KCs is expected to no longer satisfy conditions for point contact and experiences sub-surface yield. However, applying the break-in procedure stabilizes the damage in FFF KCs for subsequent trials at the test load, allowing for some repeatability to be recovered. Break-in of the SLA couplings modestly improves repeatability of those with coarser layers (9.8 v. 8.6μm), but does not affect the KCs with finer layers (7.4μm).Results from the metal KC specimens are similar to their polymer counterparts (see ). The SLM coupling is shown to repeat to 0.9μm and 13.2μm when subject to 75N and 1500N preloads, respectively. Likewise, the BJ coupling repeats to 3.9μm and 5.4μm at these respective loads. The effect of the break-in procedure is unclear under the lightly-loaded condition, but substantially improves repeatability under heavier loading; for instance, the SLM coupling improves to 9.7μm after break-in. Data on angular locating performance are consolidated in , and show analogous trends to the position data.Accuracy of AM-KCs is a function both of the intrinsic accuracy of the fabrication process used to create the components, and the contact mechanics of the locating surfaces. Together, these determine the relative location of an as-fabricated KC with respect to its nominal resting place. show that KC accuracy decreases with increasing load, primarily driven by the insufficiency of the Hertzian contact model for describing the plastic deformation incurred. However, because of the symmetric KC layout employed and symmetric preload applied thereto, this theoretically affects only the anticipated Z (vertical) location of the coupling centroid. Accordingly, radial KC accuracy (in XY) is also reported; this provides an understanding of coupling accuracy independent of the contact model. Using these cleaner data, we find that the in-plane accuracy of the SLA couplings is approximately 190μm, regardless of fabricated layer height or applied load. Couplings fabricated via FFF proved modestly more accurate than their SLA counterparts; the most accurate components tested were those printed by FFF on a Stratasys Mojo (40μm at 75N preload), despite having the greatest surface roughness of all combinations tested. Finally, we note that the accuracy of metal couplings is in line with the typical accuracy of the processes used to fabricated them; centroids land ≈300μm and ≈200μm from the intended locations for the SLM and BJ couplings, respectively.We find that the significant surface texture and finite yield stress of common AM materials leads to unavoidable deformation of the as-printed surface texture. However, point contact may still be achieved by balancing the theoretical effective radius of the sphere-plane contacts against load handling and stiffness requirements. Further, loading conditions can cause appreciable deflection of the surrounding geometry. Accordingly, precision preload of plastic AM-KCs is required to achieve both high stiffness and repeatability, and care should be taken to mitigate unintended deflections. Moreover, material properties of AM material, e.g. FFF ABS, are often anisotropic []. Our prior work showed this to cause variation in contact stiffness as a function of build orientation, thus stiffness of a KC fabricated asymmetrically with respect to such a variation will have correspondingly anisotropic stiffness []. Finally, we note that polymer AM-KCs can easily achieve stiffness on the order of 10N/μm, which compares favorably to typical cutting forces (10−120N []) observed in turning thermoplastic components.Despite surface plasticity, AM-KCs can exhibit excellent repeatability if point contact is maintained between contacting surfaces. Prior studies of ground or polished KCs report 3σ repeatability roughly equal to the average surface finish (Ra) []. Applying this heuristic to the 170μm FFF couplings (out-of-plane Ra≈40μm) predicts worse 3σ repeatability by a factor of 4, assuming that re-assembly errors are gaussian. Conversely, this metric over-predicts performance of the other configurations under light loads. Finally, no substantial impact on repeatability at high loads is observed, making as-printed Ra a poor proxy for AM-KC performance. In this direction, however, we note that 1σ repeatability of AM-KCs is universally better than the nominal layer height used to print the couplings, and within an order of magnitude of the estimated Ra, as plotted in In part, the discrepancy between conventional (abrasively finished) and AM-KC repeatability may arise from the specific character of surface roughness imparted. Specifically, the former generally results in surfaces with low variance and negative skew, thus load bearing area that increases rapidly with deflection []. The idealized, structured (non-random) texture (e) on as-printed surfaces features substantial variance and positive skew. Accordingly, a metric that respects these as-fabricated surface finish characteristics may result in a more general predictor of KC performance.Friction at the points of contact has also been identified as a driver of KC repeatability [] provides an order-of-magnitude estimate of repeatability, specifically in view of the coefficient of friction (μ), per:This relation predicts ≈20μm and ≈1μm repeatability for plastic and metal KCs under these conditions under 75N load (≈150μm and ≈9μm under 1500N), respectively. These values are reasonably representative of AM-KC performance, especially for polymer KCs under light loading, again as shown in Last, we demonstrate an exemplary application of AM-KCs to precision engineering via the design and validation of a modular optical system. Specifically, we employ AM-KCs to locate variety of optical components that may be configured for microscopy and imaging spectroscopy. A ray trace of the complete system, configured for use as a computed tomography imaging spectrometer (CTIS) is shown in a, along with the corresponding solid model in b. The interested reader is referred to Refs. [] for functional details of this design.The CTIS has two optical relays; the first is nominally comprised of the two 40mmfl aspherized, achromatic lenses between the object plane and image stop (identified as the microscope stage). These two lenses have equal focal lengths, resulting in unity magnification of the object plane onto the image stop. The magnification ratio of the relay may be changed simply by replacing the foremost lens with one of an alternate focal length. If this relay is directly coupled to the detector via the threaded attachment, the system functions as a microscope of variable magnification.The dispersion stage is the second optical relay, consisting of the elements placed between the image stop and detector. Light passing through the image stop is collimated via a reversed 12mm machine vision lens, dispersed by two crossed transmissive diffraction gratings, and is reimaged onto the detector by a matching machine vision lens. This spectrally disperses an input into 9 diffracted images, from which the spatial and spectral content of the object may be recovered. Operation in this mode is simplified by filtering the input light to span at most one octave in frequency. For example, 400nm light diffracted into a second order is indistinguishable from first order 800nm light; accordingly, filters are used to only pass light from 400 to 750nm. As illustrated in the solid model, it was mechanically convenient to place these order-sorting filters in their own kinematically located module, optionally located between the lenses of the first relay.Mechanically, the system was divided into the modules identified in b. The interface between each module uses a magnetically assembled kinematic coupling, shown in c, thereby providing consistent preload and enabling reassembly without tools. Each was fabricated by FFF (Stratasys Mojo), guided by the accuracy and repeatability results presented above. Print orientation of the AM-KCs was selected to optimally locate the elements. Making use of the coordinate system shown in a and b, it is critical that the optical axes of the individual lenses are substantially co-linear with the theoretical instrument optical axis (Z), or equivalently, that the XY position of the lenses and their angular orientation about the X and Y axes be correctly placed. However, instrument performance is much less sensitive to element spacing along the optical axis, as the focus of each relay may be easily adjusted. Modest misplacement of the first relay's lenses may be countered by moving the device closer to or farther from the object plane until the intermediate image plane and stop coincide, and fine focus of the second relay is set using the built-in focus adjustment on the machine vision lenses. Therefore, the Z axis (build direction) of the modules was oriented along the nominal optical axis, using the more accurate directions of the couplings to place the individual elements on-axis. After printing, the lens bores of each module are reamed for a transition fit to the corresponding lens diameter, resulting in minimal (estimated 10μm) additional uncertainty in element axis location beyond the nominal accuracy of the coupling. Lenses are then adhesively bonded (spectrometer stage lenses are additionally clamped) inside the KC-located modules, as shown in Optical design is performed using Zemax ([]) optical CAD software, which allows both for analysis of the nominal design and study of tolerance sensitivity. Tolerance information may be entered on element placement, such as uncertainty from the KC interfaces, as well as values for the elements themselves (e.g. centration or refractive index). The influence of these parameters may then be studied individually using a sensitivity analysis, or in aggregate via Monte-Carlo analysis, here comprising an ensemble of 1,000 simulated systems. System performance is quantified via spot size radius, taken from a simulated image of a theoretical point source. Consequences of a large spot size, much like an image taken with an out-of-focus camera, are burring (decreased resolution) along the spatial and spectral axes of the recovered dataset.The nominal design brings a polychromatic, on-axis point source to a series of diffracted spots with an average RMS radius of 7.55μm on the detector; here the blurring results only from the non-ideal geometry of the optical elements. Allowing for typical tolerances on element surface form, location, and refractive index increases the spot radius by 0.71μm. Adding the errors associated with KC accuracy further increase the spot radius by 0.78μm, where typical sensitivity of spot size to single-axis translation of an element is ≈0.01mm/mm and ≈0.09mm/rad to a single-axis rotation. The theoretical RMS spot size for the as-built instrument is the sum of these values, or 9.04μm. Extending the study to include the effects of repeatability shows no marginal increase in spot size, i.e. the impact lies below the precision of the simulation. Because the increase in spot radius is small both as compared to the innate blurring of the design and the pixel pitch on the CMOS detector (Sony IMX250LLR, 3.45μm), the anticipated effect of the KC repeatability is imperceptible.The fully assembled instrument is shown undergoing characterization in d. Here, a lamp is used to overfill one end of a 25μm diameter optical fiber, with the imaging spectrometer set to image its opposite end. Imaging performance is verified by comparing the measured diameter of the fiber core to its nominal value. The output distribution from an overfilled fiber should be approximately gaussian in the center, falling to zero intensity at the edges of the fiber core [], as is shown in a typical spectral-bin image (a). To validate recovery of accurate spectra, transmission measurements are performed on a set of wavelength filters by inserting them between the lamp and fiber input; the recovered spectra are consistent with stated filter performance, as illustrated in As a demonstration of instrument operation, c shows a wideband (undiffracted order) image of a pixel of an Iphone 5s, comprising a set of (≈25×75μm) subpixels, individually capable of emitting red, green, or blue light. d–f shows representative images corresponding to these portions of the visible spectrum, allowing for identification of the color and geometric extent of each sub-pixel. These results show that functional, precision assemblies may be created using as-printed KCs.In this study, we have established the use of integrated kinematic couplings as a means of precision location of additively manufactured components, called AM-KCs. We find that plastic AM-KCs can offer 1σ repeatability as tight as 3.2μm despite significant initial surface texture (≈40μmRa), and metal AM KCs may repeat to 0.9μm. Key to achieving this high repeatability is averaging the surface texture of the contact surfaces via plastic deformation, while avoiding sub-surface plasticity of the locating features. If a calibrated preload is applied to deform the contact surface and thereby mitigate roughness, adequate stiffness (greater than 10N/μm) and repeatability for precision engineering or post-processing such as machining or grinding may be readily obtained. However, the plastic deformation inherent to point loading AM surfaces precludes use of elastic contact models for estimating coupling position as a function of preload and externally applied forces. It is expected that a contact model that adequately captures this intrinsic behavior will reduce the need to experimentally determine deformation and stiffness characteristics of AM-KCs. A demonstration of AM-KCs is developed via a modular computed tomography imaging spectrometer, enabling rapid assembly and reconfiguration of the optical path. In future work, we envision application of AM-KCs to the design and production workflow for finished parts as well as tooling and fixtures, including for convenient location of AM parts in machine tools for post-processing, and for assembly of AM parts with conventionally manufactured components.Improving both strength and ductility of a Mg alloy through a large number of ECAP passesUltra-fine-grained (UFG) ZE41A aeronautic magnesium alloy was achieved through multi-pass equal-channel angular pressing (EACP) at 603 K and subsequently tested in tension from room temperature (RT) to 588 K. An extraordinary phenomenon was first observed, improving both ductility and strength of hcp-structured UFG Mg alloy after a large number of ECAP passes. The results demonstrate the pressed ZE41A alloy after 8 passes has higher tensile strength but relatively lower ductility than the unpressed sample from RT to 423 K, whereas the tensile yield strength, ultimate strength, elongation to failure of UFG alloy after enough passes are all remarkably increased (about 120% higher in yield strength and 75% larger in elongation at RT after 32 passes). Multi-pass ECAP provides a simple and effective procedure for grain refinement of hcp-structured Mg alloy at elevated temperature undergoing dynamic recrystallization, while simultaneously improve its strength and ductility at service temperature owing to higher fraction of high-angle grain boundaries and lower intragranular dislocation density, making UFG Mg alloys more attractive in high strength structural applications.Research on magnesium alloys is currently enjoying a renaissance for increased application in the transportation and aerospace industry, which seeks to reduce weight and increase specific strength. However, most Mg alloys (except for some special Li-containing alloys) exhibit a hexagonal crystal structure, leading to severe limitations in their ductility, strength and creep resistance. This inherent difficulty maybe be reasonably overcome by some special processing of severe plastic deformation (SPD), such as equal-channel angular pressing (ECAP) As well known, strength and ductility are often mutually exclusive for bulk materials. Nevertheless, there are some isolated examples where excellent mechanical behavior has been observed on UFG materials fabricated by SPD methods The objective of present work is to investigate the effect of microstructure characteristic on deformation mechanism in the simple hcp-structured Mg system at representative ambient temperatures, and develop a new strategy for strengthening magnesium alloys with simultaneously increasing its ductility through processing by ECAP method. Due to the adequate combination of properties and cost, the ZE41A aeronautic magnesium alloy is still preferred for certain application such as aircraft engines, helicopter and airframe components, and wheels and gear boxes The materials used were commercial as-cast ZE41A alloy, obtained from the UBE INDUSTRIES, Ltd., Japan. This hcp-structured magnesium alloy contains 4.9 wt.%Zn, 1.4 wt.%RE and 0.7 wt.%Zr. The zinc, rare earth and zirconium mainly present at the grain boundaries as compounds (such as Mg12Zn13 and REMg12) A Nikon Eclipse ME600 optical microscopy was used for microstructure observation. The polarized light was used for microstructure observation of samples after tensile testing. The composition of the etchant used was acetic acid 2.5 ml, picric acid 3 g, ethyl alcohol 50 ml and distilled water 5 ml. The etching time was 3 s. The microstructure after tensile testing was observed at the center of the tested specimen along with the longitudinal direction. The microstructure at the place near the shrinkage area was observed (not in the shrinkage area). A JEOL JSM-5200 scanning electron microscopy was applied for investigating the specimen surface after tensile testing to determine the GBS trace. shows the microstructures of the ZE41 alloy for the as-cast condition and after various passes of ECAP processing. It is apparent that primary as-cast ZE41 alloy has equiaxed grains with the size of around 80 μm ((a)). The alloyed elements of Zn and RE exist as Mg12Zn13 and REMg12 compounds at magnesium grain boundaries at room temperature, while zirconium crystals are also concentrated at the grain boundaries (b)), observed on a plane parallel to the pressing direction, shows the remarkable change. This sample is formed by two parts: large particles or large long grains with 70 μm in length, ultra-fine grains or particles (about 1 μm in diameter). The large long grains take more percentage compared with ultra-fine grains in the 8-passes sample. The ultra-fine equiaxed grains mainly result from dynamic recrystallization (DRX). As well known, Mg alloy has a low melting point (Tm corresponds to 650 °C for pure Mg) and therefore a low recrystallization temperature (0.5Tm). The severe plastic deformation at high strain rate during ECAP leads to the conversion of partial mechanical work to heat, and this effect induces the DRX of the pressed alloy with substantial temperature rise. Obviously, DRX of Mg alloys plays a key role in refining grain into micrometer range (c)) shows ultra-fine magnesium grains but includes a few large particles with 5–8 μm in size. As increasing the ECAP passes to 32, this alloy possesses a complete recrystallization microstructure ((d)), which is more uniform with average grain size of about 1.5 μm and no large particle or large grain is found. Therefore, ECAP provides a simple and effective procedure for grain refinement of hcp-structured ZE41A alloy, which are attribute to the DRX.The measured yield strength (Y.S.), ultimate tensile strength (UTS), and elongation to failure are shown in as a function of the pass number of ECAP where the tensile test conducted at room temperature (a), 423 K (b) and 588 K (c). As shown in (a), the ZE41A samples after ECAP exhibit higher Y.S. and UTS under room temperature tensile condition with increasing pressing pass. After 8 passes, the Y.S. at room temperature is about 250 MPa, which is near 100% higher than that of the as-cast alloy; and the UTS is about 50% higher than that of the as-cast alloy. After over 16 passes, this alloy exhibits much higher tensile strength (about 120% higher in yield strength). Tested in tension at the elevated temperatures, however, the Y.S. and UTS of the pressing samples after 8 passes gradually decrease with increasing the number of ECAP pass ((b) and (c)). Even so, the 16- or 32-passes samples still exhibit much higher yield strength and higher ultimate tensile strength than the as-cast alloy at 423 K.On the other hand, the elongation to failure of the pressed alloy shows an interesting change with increasing the number of ECAP. The 8-passes sample exhibits lower elongation than the as-cast alloy at every tensile temperature. The elongation of the 32-passes sample is 14%, and the as-cast alloy is 8.5%, and the 8-passes sample is 4% at room temperature ((a)). As anticipated, the elongation to failure increases with the ECAP passes after 8 and the highest elongation is achieved in the 32-passes sample (about 14%) having the smallest grain sizes. Inspection shows that over 16 passes are necessary for simultaneously obtaining high strength and good ductility at room temperature for this magnesium alloy. There is the same tendency in elongation to failure measured at the elevated temperatures ((b) and (c)), which values of the 16- or 32-passes sample are higher than the as-cast alloy at tensile temperatures of 423 K and 588 K. Both are over 200% at 588 K. The influence of tensile temperature on the elongation to failure of the pressed alloys is consistent with previous research, i.e. the hot-working processed metals would have better ductility at elevated temperature owing to the presence of equilibrium high-angle grain boundaries (including twin boundaries) In order to reveal the reason why the samples processed 8 and up to 16 passes exhibit so different mechanical properties, microstructures of these samples after tensile testing were investigated to indicate the relevant deformation mechanisms. shows the optical micrographs of the as-cast ZE41A magnesium alloy after tensile test at room temperature (a), 423 K (b) and 588 K (c). It is evident that the main plastic deformation mechanism in the as-cast magnesium alloy gradually changes from twinning to dislocation slip with increasing the test temperature from RT to 588 K. After tensile test at room temperature, the deformation twins were observed within most of all grains ((a)) but no slip band existed in the whole specimen of as-cast ZE41A alloy. Tested in tension at 423 K, twinning traces were observed only in some grains (e.g., the grains A–C marked in (b)), while the slip bands have also been found in some grains (the grains C and D). When the tensile temperature increased up to 588 K, the slip bands were significantly observed (such as the grains A–D marked in (c)), although the twinning traces still existed in some grains (the grains C–E). This conventional deformation mechanism, occurred in the hcp-structured metal with coarse grains, restricts the ductility of as-cast ZE41A alloy at service temperature due to its limited slip system.The unusual experiment results of ultra-fine-grained ZE41A alloy at various tensile temperatures can be attributed to the higher fraction of high-angle grains boundaries and lower dislocation density. As well known, crystallographic glide (dislocation slip/twinning) and GBS are two independent mechanisms for metallic systems, and the one required less stress (energy) will be the favored mode under a given experimental condition. Fine equiaxial grains with high-angle grains boundaries are capable of GBS shows the optical micrographs of the 8-passes sample tested at various tensile temperatures. As shown in (b), the 8-passes sample consists of both large grains (about 70 μm in length and 30 μm in width) and fine grains (about 1 μm in diameter). However, the fine grains occupy only a small volume fraction, which means the main deformation mechanism depends on the elongated large grains. Evidently, crystallographic deformation is dominant for the as-cast and 8-passes sample at room temperature. Therefore, the ductility of the 8-passes sample decreases with increasing its strength, which can be attributed to the lower capacity of further accumulating dislocation in severe elongated grains. As shown in (a), no obvious twinning trace and no slip band were found in the elongated grains at room temperature. When the test temperature was 423 K, the twinning deformation occurred within a few grains in the 8-passes sample as shown in (b) (marked by A–C). With increasing the test temperature to 588 K, slip bands were locally observed within a few grains in the 8-passes sample as shown in The pressed samples after 16- and 32-passes possess ultra-fine and equiaxial grains with large misorientation angles as a result of DRX, which elongation to failure are higher than the as-cast alloy from room temperature to 588 K. Therefore, the high ductility of the 16- and 32-passes samples during the tensile test means the occurrence of GBS in the ultra-fine-grained microstructure. GBS has been examined extensively in fine DRX grains, which accommodated by intragranular slip and grain boundary diffusion shows the micrographs of the ZE41A samples tested at 588 K (tensile direction is horizontal), where (a)–(c) show the surface aspects of the as-cast alloy, 8-passes sample and 32-passes sample, respectively. The 8-passes sample ((b)) shows similar aspects with the as-cast alloy ((a)). It looks like the cracks produced at the triple points of the grains, while very tiny amount of GBS traces is observed in the 8-passes sample. In contrast, the 32-passes sample ((c)) shows clear GBS traces. This result demonstrates that the GBS operates in the ultra-fine-grained sample and is the main deformation mechanism at 588 K. Therefore, the higher fraction of general HAGBs and lower intragranular dislocation density are probably the main reasons for the excellent mechanical properties of UFG Mg alloy after a large number of ECAP passes. As stated by Zhao et al. As demonstrated in the present work, the ZE41A alloy after a large number of ECAP passes is endowed to higher ductility and strength than unpressed alloy from RT to 423 K, which is its service temperature range. But the previous research about Mg–9Li–1Zn alloy produced by ECAP just found out that it has the greater increase in tensile strength of about 41.8 MPa and the least decrease in elongation of about 25% at room temperature Multi-pass ECAP provides a simple and effective procedure for grain refinement of hcp-structured ZE41A alloy at approximate recrystallization temperature. Its grain size after 32 passes is reduced to 1.5 μm due to the occurrence of DRX during ECAP, which leads to a homogeneous distribution of essentially equiaxed grains.The microstructure presented in the sample after 8 passes is a mixture of ultra-fine and elongated coarse grains. The elongated coarse grains control the plastic deformation of this sample because of the low volume fraction of ultra-fine grains. Compared with the unpressed alloy, the sample after small passes exhibits much higher strength (100% higher in yield strength) up to 423 K but lower ductility up to 588K, in accordance with the current understanding.After over 16 passes, a few large grains were found in the sample and DRX is almost completed. Therefore, the fine grains determine the deformation mechanism in the over 16-passes sample. UFG ZE41A alloy is endowed with higher ductility than unpressed alloy from RT to 588 K (75% larger in elongation at RT after 32 passes), while higher tensile strength (120% higher in Y.S.) up to 423 K but a lower Y.S. and UTS at 588 K.UFG ZE41A alloy pressed over 16 passes are capable of GBS due to the presence of high-angle grain boundaries (HAGBs). It is feasible to achieve the superior combination of high strength with enhanced ductility at service temperature, through pressing the hcp-structured Mg alloys over a certain passes by ECAP to attain UFG structure with a large fraction of HAGBs and low intragranular dislocation density.Experimental and numerical investigations on laser-welded corrugated-core sandwich panels subjected to air blast loadingExperimental investigations on the laser-welded triangular corrugated core sandwich panels and equivalent solid plates subjected to air blast loading are presented. The experiments were conducted in an explosion tank considering three levels of blast loading. Results show that the maximum deflection, core web buckling and core compaction increased as the decrease of stand-off distance. Back face deflections of sandwich panels were found to be nearly half that of equivalent solid plates at the stand-off distances of 100 mm and 150 mm. At the closest stand-off distance of 50 mm, the panel was found to fracture and fail catastrophically. Autodyn-based numerical simulations were conducted to investigate the dynamic response of sandwich panels. A good agreement was observed between the numerical calculations and experimental results. The model captured most of the deformation/failure modes of panels. Finally, the effects of face sheet thickness and core web thickness on the dynamic response of sandwich panel were discussed.Sandwich structures, which are composed of two stiff face sheets separated by a low density core, are considered to be an excellent solution in shipbuilding for structural decks, walls, bulkheads, and ramps et al. Many researchers have focused on the dynamic mechanical behavior of sandwich structures, particularly in the last decade. A variety of such structures of different metallic cores including stochastic foams, honeycombs, prismatic topologies, and lattice topologies have been investigated experimentally and numerically, in particularly to improve their blast/impact resistance. Tilbrook et al. Corrugated core sandwich structures, a type of prismatic topology structures, are considered as ideal cores of sandwich panels applied in naval ships to replace the conventional stiffened plates due to their high longitudinal shearing and bending strength In the present study, the method of making triangular corrugated core sandwich panel in laboratory using the laser welding technology was firstly described. The influence of laser welding on the material properties of base material was evaluated by analyzing the morphology and micro-hardness profile of laser welds. The dynamic responses of triangular corrugated core sandwich panels and equivalent solid plates subjected to three levels of air blast loading were investigated experimentally. Finite element simulations were performed to reveal the response process and failure mechanisms of panels, and to explore the effects of face sheet thickness and core web thickness on the dynamic response of panels.The triangular corrugated cores used in experiments were fabricated using a folding technique, as illustrated in . For all of the stainless corrugations, sheets were folded to an angle of 45° relative to the horizontal plane, and were subsequently cut by electro-discharge machining (EDM) to the dimensions of 300 mm (length, out-of-plane direction in ) × 288 mm (width). All corrugated cores are of a 0.7 mm web thickness, a 28 mm cell size and a 14 mm core thickness, as shown in . Then, the relative density of cores is about 6.6%. Stainless face sheets with a thickness of 1.4 mm were laser cut to the dimensions of 452 mm × 440 mm. The calculated equivalent solid plate thickness was 3.72 mm. A 3.75 mm thick solid plate was actually used in experiments. The material of the face sheets and cores of sandwich panels and the equivalent solid plates was the commercially available 304 stainless steel (Fe–18Cr–8Ni). The desirable mechanical performances (i.e. high ductility, significant strain, and strain-rate hardening) of 304 stainless steel make it well-suited for dynamic loading application, and thus it was chosen as the base material of test panels.The steel was supplied by TISCO company (Shanxi Taigang Stainless Steel CO., China). To characterize the mechanical properties of the steel, quasi-static tensile tests were performed using 100 KN servo-hydraulic universal testing machine (WDW-100 E III) at room temperature. The cross-head velocity of the actuator was 2.4 mm/min in tests, giving a strain rate of 1 × 10−3 s−1 in the gage area of specimens. According to Ref. . The stress–stain curve revealed that the sheet specimens exhibited diffuse necking rather early (around the strain value of 0.10 ∼ 0.15). From the features of sheet specimens shown in , it is found that the specimens finally fractured due to localised necking. The stainless steel has an elastic modulus of ∼200 GPa, a 0.2% offset yield strength of 310 MPa, a tensile strength of 740 MPa, a density of 7900 kg/m3 and a ductility up to ∼42% (failure strain).The experimental laser, which is an Ytterbium Fiber laser (YLR-4000, IPG Photonics), was used to join the face sheets and core. The laser welding head (YW50, Precitec Group) was mounted on the welding robot (IRB 4400, ABB), which is used to push the laser welding head over the welding components at desired welding speed. Before laser welding, any leftover grease/oil was removed by cleaning with acetone. A series of preliminary experiments were conducted on two lap configurations existing in this study (i.e. from 0.7 mm to 1.4 mm, and from 1.4 mm to 1.4 mm) to ascertain the appropriate welding parameters, including laser power, welding speed, shielding gas flow rate and focal point position. Based on the measurements of the laser weld properties, the promising welding parameters to join the face sheets and core were determined, as listed in . For triangular corrugated core with thin web thickness, the welding line is an approximate face-line joint. Therefore, the accuracy of positions starting and ending welding process is crucial to the quality of the core-to-facing joints. To overcome this tough problem, a thin rectangular strip with 300 mm in length, 5 mm in width and 1.4 mm in thickness was introduced to enlarge the tolerance of each welding position. The whole laser welding process adopted in this study consists of four steps, as illustrated in (a)): The thin rectangular strips were firmly bonded parallel to each other upon the working platform using the No. 502 glue. The interval distances between the adjacent strips are set to the cell size of corrugated core. Step two ((b)): Corrugated core was placed on the strips with the folded line lying in the symmetry plane of strips, and then was clamped by a well-designed fixture, as shown in . After finding the moving locus of the laser welding head, the welding procedure of this step was executed using the welding parameters of the lap configuration of 0.7 mm–1.4 mm ((c)): The front face sheet was placed upon the working plate. The assembly made in previous step was clamped on the front face sheet. Then, the core and front face were welded together using the same welding parameters as those used in step two. The final step ((c)) was to join the back face sheet and strips. The welding condition of this step corresponds to the configuration of 1.4 mm–1.4 mm (In order to evaluate the influence of laser welding on the material properties of base metal, one specimen used to analyze the morphology and micro-hardness profile of laser welds, was cut from an as-manufactured sandwich panel, as shown in (a). The morphology of laser welds was observed under a stereo microscope (LWD300LCS). The macrostructure of the laser welded joint depicting the front face sheet and corrugated core attachment is shown in (c) demonstrates the macrostructure of the laser welds among core, narrow strip and back face. It can be seen that the laser power and welding speed adopted in this study yielded incomplete penetration. The profiles of the joints are acceptable. No cracking and porosity were observed in welds. The width and depth of fusion for the joint between the front face and core were similar to that for the joint between the core and narrow strip. The measured fusion width and depth are about 0.81 mm and 1.49 mm, respectively. For the joint between the narrow strip and back face sheet, the width and depth of fusion are about 0.48 mm and 2.57 mm, separately. (d) displays the optic micrograph near the weld junction of the joint between the front face and core. It is found that the parent material and fusion zone could be discriminated easily. The microstructure of joint revealed that the transition zone and HAZ near the fusion boundary were not apparent. It is considered that the effect of HAZ on the performance of sandwich panels is negligible.The micro-hardness of the laser weld region of the joint between the front face and core was measured, as illustrated in . The measurements were performed using SCTMC Digital Microhardness Tester DHV-1000, which can measure microscale Vickers hardness. In the present experiments, constant load of 200 gf (1.96 N) and dwell time of 15 s were applied. Each measuring point and its Vickers hardness value are shown in (a). It is observed that the average micro-hardness of parent material is higher than that of the laser welding zone (about 200 HV). (b) shows the micro-hardness profile (converted to tensile strength) across the welded region. It is found that the laser welding process resulted in an indistinct softening of the steel from 700 to 650 MPa.Based on the measurements that the fusion width is small, the HAZ seems to be absent, and the softening effect is not remarkable, it is considered that the influence of laser welding on the material properties is limited.The experiments were conducted in an explosion tank with an inner diameter of 5 m and a height of 7.5 m. The detailed experimental set-up used to study the deformation and rupture of test structures is depicted in (a). The set-up consists of explosion tank body, ventilation system, drainage system, vibration isolation system, sound isolation system, illuminating system, and the fixture system used for clamping the test sandwich panels.The test panels were mounted horizontally and bolted onto a 30 mm thick plate resting on I-beam supports along all four edges. The I-beam supports were restrained from movement by stiff concrete bricks. The 30 mm thick support plate had a 288 mm × 300 mm square hole cut out at the center to allow open space for the test panels to deform. A 10 mm thick picture frame arranged upon the sandwich panel was used for edge clamping, and provided a 288 × 300 mm2 exposure area to shock wave, as shown in (b). To ensure adequate edge restraint on face sheets, the rest part of core was filled with solid metal blocks. The blast wave was created by the detonation of a 55 g cylindrical TNT explosive with a radius of 17.5 mm and a height of 37.2 mm. The charge was detonated with an electric detonator slightly buried in the surface of the explosive furthest from the test sandwich panel. The side wall and the top of tank remained at about 2.5 m and 7.0 m, respectively, away from the explosion. The scaled distance for the position of 2.5 m is 2.5/0.0551/3m = 6.574 m. The correlated overpressure of the incident shock wave is very low, about 0.18 bar The experiments were performed to investigate the effect of stand-off distance on the deformation and failure modes of the sandwich panels and their equivalent solid plates. In this study, three stand-off distances of 50 mm, 100 mm and 150 mm from the center of explosive to the top surface of the target test structures were adopted. The same process of test panel assembly, explosive charge placement and detonation were followed for each sandwich panel and solid plate.The measured center deflections of the sandwich panel's front and back face sheets and that of the equivalent monolithic plates are summarized in shows the top view of a localized face sheets failure of the triangular corrugated core sandwich panel tested at the stand-off distance of 50 mm. It is evident that the panel fractured and failed catastrophically, especially for the front face sheet. A part of center region of the front face sheet was eroded by the high intensity shock wave. A crack with dimension of about 50 mm × 60 mm was formed, as shown in (a). The rest part of center region of front face sheet underwent a large bending deflection. Careful examination of (c) shows that several macroscopic cracks emerged on the front face. In order to clearly descript the propagation of the cracks, the lap welds near the cracks and the path of crack propagation have been marked with white dash lines in (c). The crack originated in the panel center, and grew along the direction toward the lap welds. After propagating along the left side of the laser welds with a distance of about 8 mm, the crack walked across the weld line. Finally, the crack was arrested with a crack opening angle of about 45°. Under the impact loading from front face and core webs, the panel back face underwent localized plastic deformation accompanied by a visible crack with length of about 57 mm, as shown in (b) and (d). From the evidence of the discontinuity in inclination of the panel at the supports, it is revealed from (a) and (b) that the stationary plastic hinges (marked as red dash lines) were formed at four clamped edges of tested panel.To clarify the blast performance of the sandwich panels and equivalent solid plates tested at each stand-off distance, the post-mortem analysis basing on the section profiles of specimens was conducted, as shown in . As the decrease of stand-off distance, the corresponding impulse intensity was increased and exhibited more evident spatial localization. Therefore, it can be seen in that the deformation/damage level of the sandwich panels and equivalent solid plates increased as the decrease of stand-off distance. The three solid plates underwent remarkable plastic deformation but they were intact after tested. However, it is evident that the sandwich panel tested at the stand-off distance of 50 mm failed severely (see (a)), and a small crack was observed at the center of panel front face tested at stand-off distance of 100 mm, as shown in (b). Only the panel tested at the stand-off distance of 150 mm preserved its integrity. The measured permanent deflections revealed that the sandwich panels suffered smaller back face deflections than the equivalent solid plates at the stand-off distances of 100 mm and 150 mm. However, it should be noted that the sandwich panels were more susceptible to fracture in the most severely loaded scenarios. Similar phenomenon occurred at other accident loadings, such as the metal foam projectile loading (a) and (d) shows the occurrence of core debonding symmetrically located to the central fractured field due to the failure of welds. The extent of weld separations was measured and marked in (b) with green lines. It is found that the weld separations have spread over almost half panel length. At the same blast loading, the deformation of equivalent solid plate resembled a large global dome superimposed with an inner dome, as shown in (a). At the stand-off distance of 100 mm, the core of sandwich panel crushed completely at the center, resulting in the occurrence of a small inner dome at the center of back face, as shown in (b). Increasing the stand-off distance to 150 mm, the sandwich panel suffered a significant deformation but the core was not completely crushed (see (c)), while the solid plate profile resembled a global dome, without the inner dome at the center (see The enlarged views of sectional images of tested panels were shown in , providing a detailed insight into the failure modes of cores. (a) indicates that the core crushing at the panel center occurred by plastic buckling of core webs. A part of core web material was eroded by blast loading. The incompatible deformation of front and back face sheets resulted in the core debonding at panel center. At the stand-off distance of 100 mm, the core in the center remained in contact with front face, (b). The core web had begun to fold at the center. The core web folding is an efficient manner to dissipate kinetic energy of panel. Due to the stretching deformation of front face, some core webs were in tension. A plastic buckling failure can also be found at the core webs of the panel tested at the stand-off distance of 150 mm, as shown in (c). But, the folding mode varied and the fold wavelength was larger relative to that of the panel tested at the stand-off distance of 100 mm.It should be explained that the reproducibility tests were not conducted in this study, due to the expensive cost of experiments, especially of the laser welding. It is known that the most expected influence on the reproducibility includes the base material properties and fabrication technology. The base material properties used to make panels have been checked by conducting uniaxial tensile tests, and the cell size of those fabricated cores has carefully examined to monitor spring back effect during the folding process. Meanwhile, a series of preliminary experiments were conducted on all lap configurations existing in this study to ascertain the appropriate welding parameters. All those work was to ensure good repeatability in the manufacturing process and experiments.ANSYS/Autodyn software V12.1.0, which is a versatile explicit analysis code, was used for modeling the numerical models of the experiments. All numerical simulations were performed on a desktop computer which uses four processors Intel Core i7-3770, 16 GB RAM system.The simulations were performed to give insight into the deformation mechanism and fluid–structure interaction (FSI) effects, which were not measured directly during the experiments. Considering the symmetry of panels and loads, only one quarter model was established to reduce the computation time, as shown in (c). The perimeter of the panel face was modeled as fully clamped. It is assumed that the back face and core were firmly “welded” together by strips. The narrow strips used in test panels were not considered in calculations in order to reduce the complexity of simulations.Generally, structures can be defined in a Lagrangian reference frame where the mesh follows the material movement, and the Eulerian reference is a more preferable method to describe the gas flow from detonating explosives. In the present study, the face sheets and cores of sandwich panels and monolithic plates were modeled with Belytschko-Tsay shell elements based upon Mindlin theory For blast simulations, it is crucial to start the ignition and detonation process of explosive with a very fine mesh to guarantee an acceptable error of initial energy of shock wave. The computational cost for a highly resolved 3D model is very expensive. Alternatively, the remapping technique available in ANSYS/Autodyn is a perfect method to be employed to overcome this problem (a). The detonation was initiated at the center of the furthest face of explosive from panel. In order to reduce the influence of high orthotropic property of sandwich panel on the flow of shock wave, the 2D model was run until the shock front is close to the panel front face, where the symmetry condition would be violated thus the flow becomes multi-dimensional, as shown in (b). Secondly, a binary remap file (which contains the final state of variables of 2D simulations) should be created, and then was used to fill the 3D Eulerian domain as initial condition, as shown in (c). Lastly, the 3D calculation could then proceed from that point. The air block used in 3D simulations allowed the explosive to further expand and interact with structures. According to Ref. (c). Flow out boundary conditions were set at the outer boundaries of the air block. The loading phase in 3D simulation is completed once the midpoint of the plate has begun to oscillate about its final deflection and the maximum pressure in the Eulerian mesh is below 300 kPa It should be noted that it is impossible to conserve both momentum and kinetic energy during remapping. The remapping algorithm adopted by ANSYS/Autodyn is based on the assumption of momentum conservation The element sizes for 2D model were fixed at 0.1 mm × 0.1 mm, while the side length of the cubic elements in 3D model was 1 mm. The shell elements had mesh size of 1 mm × 1 mm. Additional studies indicated that the current meshing scheme yielded convergent simulation results. The CPU times for the 2D Euler simulations used to create the initial map files to fill the 3D domain for three different stand-off distances (50 mm, 100 mm, and 150 mm) are 16 min, 32 min and 43 min, respectively. Most of 3D simulations in present study ran CPU time between 20 and 25 h.The Johnson–Cook material model was used to describe the von Mises flow stress of used steel as expressed in Eq. . The dynamic flow stress is the function of strain, strain rate, and temperature. The model assumes that the strength of the material is isotropic and independent of mean stress.σy=[A+B(εpeq)n][1+cln(ε˙peqε˙0)][1−(T∗)m],where σy is the dynamic flow stress, εpeq is the equivalent plastic strain, ε˙peq is the equivalent plastic strain rate, T is the material temperature, Tm is the melting temperature of the material and Tr is the room temperature. The constants A, B, n, c, ε˙0, and m are material parameters and can be determined from an empirical fit of flow stress data. The measured true stress–strain curve () agrees very well with the constitutive behavior of annealed 304 stainless steel as reported in the literature In order to capture the rupture of test panels, the failure criterion based on equivalent plastic strain was adopted. This criterion has gained popularity due to its simple and effective formulation, and has been proven to give results with satisfying accuracy The air and post-burning explosive gas product media are assumed to behave as ideal gas. The ideal gas equation of state (EOS) is shown in Eq. where ρg is the air density, Cp and Cv are the specific heat at constant pressure and volume respectively, and T is the gas temperature. The standard constants of air model, as determined from ANSYS/Autodyn material library, are shown in . The air is assigned an initial internal energy of 206.8 kJ/kg for keeping the atmospheric pressure.The default model in ANSYS/Autodyn material library for TNT explosive is used to numerically model the TNT explosive from the experiments. The pressure of the expanding gas of the TNT is determined by the Jones-Wilkins-Lee (JWL) model as shown in Eq. p=A(1−ωρpR1ρe)e−R1ρeρp+B(1−ωρpR2ρe)e−R2ρeρp+ωρpEm0.The parameters A, B, R1, R2 and ω are all empirically derived values. ρe and ρp are the densities of the explosive and the explosive products respectively. Em0 is the specific internal energy of the explosive. The default values from ANSYS/Autodyn material library for TNT are shown in . The state (velocity, internal energy and pressure) of detonation wave in explosive can be determined using Chapman-Jouquet condition. CJ point refers to the state of the detonation wave. The values of CJ point (CJ detonation velocity Vdet, CJ energy to volume fraction Evol and CJ pressure pcJ) for TNT are also included in To verify the material properties, boundary and contact condition in simulations, numerical results were compared to the experimental results for the corrugated core sandwich panel and monolithic plates. It is evident from that the numerically predicted and experimentally measured midpoint deflections for panels and the equivalent solid plates were in good agreement. Meanwhile, two standard statistical parameters, viz. the Pearson's correlation coefficient (R2) and average relative error (Δ), were employed to quantify the predictability of the numerical model used to predict the dynamic plastic response of panels and monolithic plates. Correlation coefficient can provide information on the strength of linear relationship between predicted and measured values. R2 and Δ are mathematically expressed as:R2=∑i=1i=N(δexpi−δ¯exp)(δpi−δ¯p)∑i=1i=N(δexpi−δ¯exp)2∑i=1i=N(δpi−δ¯p)2,where δexp is the measured midpoint deflections, and δp is the predicted midpoint deflections. δ¯exp and δ¯p are the mean values of δexp and δp, respectively.The correlation coefficient R2 for sandwich panels and solid plates is 0.99, and the average relative error Δ is 5.25%. A good correlation was achieved, further indicating that the predictability of numerical model is reliable and excellent.The numerical midpoint deflections are listed in alongside the corresponding experimental values. shows the deformed panels at the end of simulations for the stand-off distances used in experiments. The simulations also show half sections of panels using a perspective similar to that of the tested panels (). It is encouraging to find that the simulations captured most of the deformation patterns observed in experiments, including the largest plastic deformation of the center region of panels, an increase in panel deflection with the decrease of stand-off distance, the appearance of an crevasse formed on the center of front face, the development of cracks on the front face and back face of panel tested at the stand-off distance of 50 mm, the undamaged features of panels tested at the stand-off distances of 100 mm and 150 mm. Careful inspection of the simulations reveals that the occurrence of cracks located to the side of laser welds on the front face should ascribe to the arrival of tension limit under stretching force. The high effective plastic strain regions were mainly distributed along the welding lines due to the stress concentration at the joints between the face sheets and core. Comparing the final deformation of cores obtained from simulations (), the results show that the simulations obtained a similar level of web buckling and core compression to that seen in experiments. Careful examination of reveals that the numerical models overpredicted the permanent deflections for all sandwich panels, presumably as a result of that the energy dissipated by the contact friction and the deformation of narrow strips was not considered in simulations.The displacement and velocity histories at the midpoint of both front and back faces of panel and equivalent solid plate at 100 mm stand-off distance are shown in . The velocity of front face instantly reached its maximum value in the early stage of response, and then decreased progressively due to the core crush and its own plastic deformation. After the core collapsing into a more stable configuration, the velocities of the front and back face sheets equalized in deformation response. Then, both the front and back faces underwent an oscillation until the kinetic energy was gradually dissipated by the introduced static damping. It can be seen that the front face of sandwich panel appeared to take off at a higher velocity than the back face, and the initial velocity of the equivalent solid plate lied between these limits. The low takeoff velocity of back face mainly resulted from the effect of communicating the movement of the front face through the dynamically crushing core.To better understand the deformation mechanism, the distributions of the in-plane strain were investigated both temporally and spatially by placing a series of gauge points. Points 1–5 were placed on the front face, and point 6–10 were placed on the back face. The in-plane strain results and exact locations of all points are shown in . In-plane strain 1 refers to the strain on the plane of face sheet along the direction perpendicular to the corrugations (viz. the X-axis), while the in-plane strain 2 is along the direction parallel to the corrugations (viz. the Y-axis). The maximum in-plane strains of front face and back face occurred at the panel center. Due to the high intensity loading at the center area, the stretching deformation has a significant contribution to the final deformation in this region. The final deformation patterns of both face sheets revealed that the front face underwent a larger deformation than the back face. Thus, the in-plane strains on the front face are relatively larger than those on the back face. Careful inspection of the strain results shows that the in-plane strains along the X-axis are larger than those along the Y-axis, owing to the lower bending stiffness along the X-axis. Due to the constraint on the panel edges, gauges 3 and 8 underwent large in-plane strain along the X-axis, while gauges 5 and 10 underwent large in-plane strain along the Y-axis. This verified the plastic hinge formation at the edges of panels tested in experiments.The reflected pressure and impulse intensity at the fluid structure interaction (FSI) interface decayed rapidly along the direction in width, showing spatial locality of shock wave, especially, for the closest stand-off distance, as shown in . The gas pressure interaction with the outskirts should be not significant. Therefore, the adopted size of air block is reasonable to simulate the dynamic response of tested panels. It is found that the pressure and impulse intensity of sandwich panel is significantly less than that of equivalent solid plate, due to a combination of beneficial FSI effects and a low core crushing stress. At the stand-off distance of 150 mm, several local peaks located between the corrugations and local valleys at the joints of core-to-facing were observed for reflected pressure and impulse of sandwich panel. A stronger reflected shock wave occurred due to the local bending of the front face between the corrugations, which increases the rigidity of the face sheet Due to the good correlation, the validated numerical models were further used to investigate the effects of face sheet thickness and core web thickness on the blast performance of corrugated core sandwich panels.The panel tested at 100 mm stand-off distance in experiments was considered as the baseline to assess the influences of face sheet thickness on the back face deflection, the peak pressure and the impulse intensity of the midpoint of panel front face under same blast load. It is shown in that the front face thickness can significantly affect the peak reflected pressure and impulse intensity while the effect of back face thickness is negligible. A beneficial FSI can be achieved by reducing the front face sheet thickness. On the other side, decreasing of face sheet thickness leads a weakening in stiffness of panel. Then, the permanent deflection of back face decreased with the increase of front face and back face thickness, as shown in . However, it is found that the change of front face thickness resulted in a more evident influence on the back face deflection than that of back face thickness. This indicates that a more efficient way to enhance the blast resistance of panel by adding weight expense is to increase the front face thickness. Moreover, a reasonable plan to retain the blast resistance of panel under weight saving scenario is to keep the front face thickness and decrease the back face thickness. A similar conclusion has been draw by Xue and Huchinson The effect of core web thickness on the peak pressure and impulse intensity of the midpoint of front face is negligible, which is similar to the effect of back face thickness. However, the back face deflection of panels decreased linearly with the increase of core web thickness, as shown in . Examining the section profiles of panels with different core web thicknesses (), it is found that the crushing resistance of core is enhanced greatly with the increase of core web thickness. Then, the deformation mode of core webs changed. The buckling wavelength increased with the increase of core web thickness. The deformation mode of front face was affected by the variation of crushing resistance of core. For core web thickness of 0.4 mm, the front face deformed similarly to the deformation mode of a solid plate under blast loading. However, for core web thickness of 1.4 mm, a local deflection between two adjacent core webs was observed at the front face center. A thicker core web will lead to a larger load transferred to back face and supports. Therefore, using a core with appropriate characteristics is a way to keep balance between the energy absorption and the load transferred to the back face and supports.The triangular corrugated core sandwich panels were designed and fabricated through folding and laser welding technology. The dynamic responses of the triangular corrugated core sandwich panels and equivalent monolithic plates were investigated by performing air blast experiments in an explosion tank. The experiments revealed that the sandwich panels suffered smaller back face deflections than the equivalent solid plates at low impulses levels, but were more susceptible to fracture in the most severely loaded scenarios. This phenomenon also existed under metal foam projectile loading and wet sand blast loading for corrugated core sandwich panels. The cores behaved several different deformation/failure modes in experiments, including plastic buckling, stretching, debonding, and full compacted. Numerical calculations matched well with the experimental results. The in-plane strain distribution indicated that the stretching deformation is evident at the panel center. Investigation into the effects of face sheet thickness and core web thickness on the dynamic response revealed that the back face deflection reduced with the increase of both face sheet thickness and core web thickness. The front face thickness is critical to the reflected pressure and impulse intensity. An effective way to enhance the blast resistance of panel is to increase the thickness of front face. In order to obtain an optimal design of sandwich panel for shipbuilding, a further study is needed in future to investigate the mass allocation of panel under different blast loads. Likewise, an elaborate design of core is needed to balance the energy absorption and the load transferred to the back face and supports.Mechanical modeling of coupled plasticity and phase transformation effects in a martensitic high strength bearing steelThe stress and strain induced solid to solid phase transformation of retained austenite in a martensitic high strength bearing steel has been studied. Monotonic tension experiments that were carried out at different temperatures using this high strength steel showed that not only the strain induced but also the stress induced phase change plays a crucial role in the phase transformation of retained austenite to martensite. In the material model, plastic deformation was defined using the Drucker Prager yield surface through a nonassociated flow rule accompanied by nonlinear kinematic and isotropic hardening. The hardening was coupled with stress and strain induced phase transformations. A nonlinear elastic effect based on elastic dilation was included in the constitutive model by extending the bulk modulus with a second order term. For the finite element analysis, the material model was written as a user defined material subroutine (UMAT). The numerical simulations were done using ABAQUS and compared to monotonic tension, compression and cyclic experiments. The results showed that the strength differential effect and the volumetric change under loading are closely related to the transformation of retained austenite to martensite. At low temperatures the effect of stress induced phase transformation on yield strength was noticeable. It was concluded that at certain temperatures both strain and stress induced phase transformations significantly affect mechanical behavior of the high strength steel.slope of the offset yield stress with respect to hydrostatic stresscoefficients in parameter A responsible for magnitude of transformation shape changeundeformed elastic modulus of austenite and martensiteelasticity tensor of austenite and martensitecoefficients define driving force of martensite nucleationshear modulus of austenite and martensitethermally induced martensite start temperaturestrain induced martensite start temperaturethe limiting value of the change in yield surfaceexponent affecting strain induced phase transformationstandard deviation in probability function Pmaterial parameter for volume fraction of shear bandsmaterial parameter for the average volume of martensite and shear band intersectionrelative volume change during phase transformationplastic strain tensor, equivalent plastic strainelastic strains of austenite and martensite phasesdimensionless driving force function for martensite nucleationmaterial property in phase change heat density functiondeviatoric stress, hydrostatic stress, equivalent stressstress induced transformation start stressmaterial property in phase change heat density functionparameters define kinetics of stress induced phase transformationAt equilibrium conditions, materials tend to stay in their crystallographically more stable phase i.e. the atomic configuration having the lowest energy level. In high strength bearing steels and other materials undergoing phase change upon cooling, solid to solid phase transformation occurs from the parent phase (austenite), which is stable at high temperatures, to the product phase (martensite) that is stable at low temperatures. During quenching of the high strength steel, when the temperature is above the martensite finish temperature and the energy level required to complete the transformation is not reached, austenite cannot transform completely to martensite. As a result, a metastable phase named retained austenite forms. The amount of austenite retained after heat treatment is affected by carbon content, quenching temperature and alloy composition. Aside from temperature change, application of load and shear band intersection triggers the phase change of retained austenite to martensite. This mechanically induced phase change enhances ductility, formability, toughness and strength of such steels and makes them attractive for automotive, aerospace and variety of other engineering applications.The martensitic transformation of retained austenite upon loading can be either stress or strain induced (assisted). When the temperature is below transformation start temperature (Msd), stress induced displacive martensitic transformation of the retained austenite to martensite takes place at nucleation sites in the parent phase. Up to Msd stress induced transformation takes place below the yield stress (σY) of the material. In this temperature range, the transformation start stress increases linearly with the temperature (). Kinetics of stress induced transformation is described using either Gibbs or Helmholtz free energy potentials by considering the thermodynamic effect of the applied stress ( proposed a model for stress induced phase transformation based on the formalism of principle of generalized standard materials with internal constraints (). The simulations that they performed using the thermomechanical model had good correlations with experimental results. In the literature, the constitutive models of stress induced transformation are studied not only for high strength steels but also for other alloys like Nitinol (Strain induced (assisted) phase change initiates through formation of highly potent new sites via shear band interactions when the temperature is above Msd. In this case, depending on temperature, the transformation start stress can be higher than the yield stress. In previous studies, the strain induced transformation, that is commonly investigated in TRIP steels, was found to undergo irreversible martensitic transformation ( proposed a model that outlines the strain induced phase transformation behavior in austenite steel through interaction of shear bands. Their model was only able to capture uniaxial stress effects under isothermal conditions. by considering the stress state sensitivity, since the evolution of martensite at a material point is effected not only by the plastic strain and temperature but also by the stress state history. The model proposed by was improved by taking into account of the influence of strain rate on toughness and ductility ( to study the multiphase TRIP steels having different retained austenite levels. In a later study () modified the same model to study the interaction between embedded retained austenite islands and the surrounding matrix.In the early attempts, formulation of transformation kinetics in TRIP steels is based on either large scale orientation of the transformation strain in the martensite phase () or the micromechanical plastic strain accommodation that emerges from martensitic phase transformation and arises in the parent phase (). Based on these two principles, most of the constitutive models for TRIP steels are derived using either macro scale (). In the vast majority of constitutive models developed for materials undergoing phase transformation, the rate of martensite volume fraction (ζ˙) is prescribed as the main internal state variable. Previous researches have documented that the rate of martensite transformation is affected by Ms temperature (), quenching temperature and rate, plastic strains () and percentage of retained austenite ( showed that evolution of martensite fraction with respect to plastic strain during stress induced transformation is more linear compared to the case of strain induced phase change. Not only the transformation kinetics, but also the morphology of the martensite microstructure formed via stress or strain assisted transformation differs. Strain induced phase change results in fine lath martensite phase formed at the shear band intersections, whereas plate martensite formation is observed when the transformation is induced by stress (Phase transformation in TRIP steels results in a strength differential effect (SDE), which is known as the asymmetry between tensile and compressive yield stresses, because the retained austenite is more susceptible to transform to martensite under tension than in compression. The stress induced transformation is affected by temperature, for this reason SDE is found to be higher when the temperature is decreased (). It is observed that SDE depends not only on temperature but also on the hydrostatic stress, therefore Drucker Prager yield surface has to be used to define the plastic flow (). In addition, in high strength steels the associated flow rule would result in a plasticity induced volume change which is different from the experimental findings, for this reason a nonassociated flow rule has to be considered in the material model (). Not only the phase transformation but also microcracking, residual stresses, volume expansion and solute dislocation interaction are some of the factors that can give rise to SDE. For instance () observed SDE in high strength bainitic steel which did not undergo any mechanically induced phase transformation.Previously, the stress dependency of elastic modulus for high strength steels is discussed by some researchers (). According to the results of push–pull cyclic experiments by on SAE 52,100 high strength steel, when the linear elastic part is subtracted, a sickle shaped asymmetric hysteresis loop is obtained in stress vs. plastic strain graphs. In a recent work, showed that the nonlinear elastic material behavior should be considered in the material model of the high strength bainitic roller bearing steels. Moreover, used combined nonlinear kinematic and nonlinear isotropic behaviors to precisely define the plastic material response in their experimental measurements. illustrates the temperature effect on the start of strain and stress induced transformations. At a certain critical temperature stress induced transformation starts at a certain stress level, σs, which can be below yield stress (). Therefore coupled transformation behavior takes place after plastic yielding. Strain induced transformation on the other hand starts at the onset of yielding. Above Msd the shape of yield stress curve representing the case of coupled transformation depends on material properties but increases up to a certain temperature above which no phase change is observed (). Therefore, coupled transformation behaviour takes place after plastic yielding. it is difficult to distinguish stress induced from strain induced transformation when the deformation increases beyond the yield point. Recently proposed a constitutive model considering strain induced martensite nucleation and stress assisted martensite growth using Helmholtz free energy potential. Although they stated that their numerical calculations fit to the experimental results of , no direct comparison were presented between the numerical results and the corresponding measurements. In the present research, stress and strain induced phase transformation mechanisms were coupled with plastic deformation that was described using a Drucker Prager yield surface with a nonassociated flow rule accompanied with combining nonlinear kinematic and isotropic hardening. For this purpose the model represented by was extended by including the stress induced transformation effect using Nguyen's formalism of standard materials, which was applied to TRIP steels by . The temperature dependence of the onset of nonlinear stress strain behavior was the main motivation for implementing coupled stress and strain induced phase change. Compared to the models existing the literature this model couples stress and strain induced phase changes with a non-associated flow rule and nonlinear elasticity. The predictions were in a good agreement with the experimental findings. Since the morphology and mechanisms of the stress and strain induced martensite phases differ, the proposed model includes the contribution of each phase separately and in combination to the other mechanical properties of the high strength steel, such as nonlinear elasticity, nonlinear hardening and pressure dependence of the yield surface.The paper is structured in the following way: First the material model is described in section two. The first subsection introduces the free energy potential and the effect of nonlinear elasticity. The second subsection describes the nonlinear kinematic and isotropic hardening rules together with nonassociated flow rule. The third subsection presents the strain induced phase transformation mechanism and combines it with the stress induced transformation mechanism. In section three experiments and determination material parameters are discussed. The describes the method and procedure of numerical simulations. Finally, conclusions are drawn.This section presents the constitutive model of the investigated martensitic high strength bearing steel (DIN 100CrMnMoSi8), with the chemical composition given in shows the microstructure of the quenched and tempered martensitic steel with retained austenite content. were among the first researchers to investigate the contribution of the applied loading to phase transformation through a free energy formulation. Using a similar approach, represented the stress state sensitivity of the transformation and the toughening effect of stress assisted transformation. In this part, the thermodynamic force conjugate to evolution of martensite fraction was computed using the formalism of generalized standard materials with the internal constraints that were derived by . A similar approach was implemented by In this study Reuss scheme was used to define the macroscopic strain tensor which is an average over the representative volume element and given aswhere the terms ɛija and ɛijm are elastic strains of austenite and martensite phases, respectively. Martensite volume fraction, ζ, that is bounded in the interval [0, 1] can be stated in inequality form as, the constraints potential, Wl, in the form of a Lagrangian formulation, was given byWl=−Λij[(1−ζ)ɛija+ζɛijm+ɛijtr+ɛijpl−ɛij]−ν1ζ−ν2(1−ζ),where Λij, ν1 and ν2 are the Lagrange multipliers. ν1 and ν2 are associated with unilateral constraints andBy considering the contribution of internal variables of plastic deformation, the free energy potential can be written asW=(1−ζ)(12ɛijaEijklaɛkla)+ζ(12ɛijmEijklmɛklm+C(T))+13∑m=13Cmχijmχijm+13K1ɛkkel3+Q(ɛeqpl+1bexp(−bɛeqpl))., Ea and Em are the linear elasticity tensors for martensite and austenite phases. C(T) is the phase change heat density that is assumed to be a linear function of temperature (, C is the slope between the back stress Xij, where X˙ij=23Cɛ˙ijpl−γXijλ˙, and the plastic strain rate ɛ˙ijpl when γ=0,C/γ defines the saturated value of evolution of the back stress. χij is the conjugate of back stress Xij and defined as, Q is the limiting value of the change in isotropic yield surface size and b is the rate of hardening before reaching the stress limit. The term K1ɛkkel3 represents the nonlinear elastic potential with the same nonlinear bulk modulus parameter K1 for both phases. ɛijel is the elastic strain tensor that is composed of the elastic strains of the martensite and austenite phases,Given the expressions of the free energy density W and of the constraints potential Wl in , the Lagrangian L=W+Wl was constructed to define the generalized forces (L(ɛij,T,ɛija,ɛijm,ζ)=(1−ζ)(12ɛijaEijklaɛkla)+ζ(12ɛijmEijklmɛklm+C(T))+13K1ɛkkel3+13∑m=13Cmχijmχijm+Q(ɛeqpl+1bexp(−bɛeqpl))−Λij[(1−ζ)(ɛija)+ζ(ɛijm)+ɛijtr+ɛijpl−ɛij]−ν1ζ−ν2(1−ζ),−∂L,ɛija=0⇒K1ɛkkel2δij+ɛklaEijkla−Λij=0,−∂L,ɛijm=0⇒K1ɛkkel2δij+ɛklmEijklm−Λij=0,−∂L,ζ=Cζ⇒12(ɛklaEijklaɛkla−ɛklmEijklmɛklm)−C(T)−(Λij−K1ɛijel2)(ɛija−ɛijm)=Cζ,−∂L,Λij=0⇒(1−ζ)(ɛija)+ζ(ɛijm)+ɛijtr+ɛijpl−ɛij=0.in the equations above Cζ is the only nonzero thermodynamic force. Using the At undeformed state, assuming the same Poisson's ratio ν0 for both phases, the equivalent Young's, E0eq, bulk, K0eq, and shear, G0eq moduli were expressed as a small but significant nonlinear elastic behavior was detected during uniaxial cyclic push pull experiments on high strength bainitic steel. The nonlinear elastic behavior was traced to the volumetric bulk behavior of the material and defined using the bulk modulus as a function of elastic strains, K(ɛkkel) and a constant shear modulus, G. Using The nonlinearity of Young's modulus and Poisson's ratio could be written in terms of their relation to K(ɛkkel) asν(ɛkkel)=3K(ɛkkel)−2G0eq2(3K(ɛkkel)+G0eq). the hydrostatic stress, σh=σii/3, was stated asThe uniaxial elastic strain can be calculated usingAppendix A shows the derivation of uniaxial elastic strain, ɛ11el, at tension or compression using The strain energy function of the nonlinear elastic material becameWNL=(1−ζ)12[(K0a−23G0a)(ɛkka)2+G0aɛijaɛija]+ζ12[(K0m−23G0m)(ɛkkm)2+G0mɛijmɛijm]+13K1ɛkkel3,which can be stated alternatively as WNL=WL+13K1ɛkkel3, where WL represents sum of the linear elastic strain energies of both phases. The change of WNL / WL with respect to hydrostatic strains is plotted in for ζ=0.60,0.80,0.99 to see the effect of phase change on nonlinear elasticity. shows that strain energy is effected by nonlinearity when the strains are high and the nonlinear elasticity is more noticeable at high ζ when the retained austenite level is low.The stress strain graph of a push pull experiment under a cyclic load with a compressive mean load, Pm=−20.8 kN and amplitude of Pa=48.5 kN performed by (a). The figure shows the 1st and 10th cycles of the experiment. The effect of nonlinear elasticity on the inelastic stress strain cycle is given in (b). The inelastic curves are derived either by subtracting linear elastic (L), ɛ11in=ɛ11−σ/Eeq, or nonlinear elastic (NL) strains, using ɛ11in=ɛ11−ɛ11el and (a). When the two cyclic responses shown in (b) are compared, it is observed that nonlinear elastic strains exist during unloading, since steeper response is obtained for the NL curves. The vertical unloading response from both tension and compression that was derived using NL illustrates the presence of nonlinear elastic strains. Hence, the cyclic response must be studied in order to separate nonlinear elasticity from plasticity. The martensite fraction ζ at start of the first cycle was taken as ≈ 0.78 and at 10th cycle it was ≈ 0.85. These values, ζ=0.78,0.85, were measured using X-ray diffraction on an undeformed reference configuration and on the specimen midsection where it had broken after 10 cycles.By virtue of the SDE observed in the push pull experiments conducted by , it was found that a Drucker Prager type () yield surface with a linear dependency on the hydrostatic stress had to be used to define the plastic behavior. Hence, the yield surface was defined aswhere a is the slope of the offset yield stress with respect to hydrostatic stress σh=σii/3. σY defines the yield stress which could be expressed using nonlinear isotropic hardening behavior (In the equation above, σY0 represents the virgin yield stress at zero hydrostatic stress. The evolution of the yield surface radius, R˙, was defined aswhere λ˙ represents the plastic multiplier, λ˙=23ɛ˙ijplɛ˙ijpl=ɛ˙eqpl. For uniaxial loading, R in where σijd is the deviatoric stress, σijd=σij−σhδij, and δij is the Kronecker delta. In , the nonlinear kinematic hardening is introduced using the back stress tensor, described by three sets of kinematic hardening parameters are usedExperimental measurements of the volume change due to the dislocation motion in austenitic steels undergoing phase change was found to be different from the predictions of the associated flow rule (), for this reason a nonassociated flow rule was used,g=σeq+3a*σh−σY+∑m=1334γmCmXijmXijm=constant,where a* was used to predict plastic dilatation ΔV/V0, which is known to be very small compared to volume expansion due to phase change (). Using the nonassociated flow rule the plastic strain was defined asThe nonassociated flow ruled used to define plastic material behavior might result in a physically instable solution and violence of principal of maximum dissipation. For this reason, the bounds on the pressure dependence in nonassociated flow rule were defined by thein order to satisfy the dissipation equation. The derivation is stated in Appendix B. Using the same procedure as () the value of a* was continuously checked during the simulations to satisfy the condition in The strain induced phase change, that occurs after plastic yielding, see , was introduced by implementing the extended version of Olson and Cohen's model (. The evolution of strain induced martensite fraction, ζ˙strain, was formulated aswhere ζ is the overall martensite volume fraction and Σ represents the stress triaxiality, Σ=σiiσeq, which has an effect not only on the nucleation of voids () but also on nucleation of martensite sites (where α, β and r are the material parameters. The volume fraction of shear bands, fsb, is a function of equivalent plastic strain. The equation that describes fsb was written aswhere ɛeqpl(a) is the equivalent plastic strain of the austenite phase. It was calculated using assuming the same hardening properties for both phases ( represents the probability function for transformation start, which was determined by assuming a Gaussian distribution of the potency of the shear bands to activate the nucleation sites that initiate transformation (). The probability function was defined aswhere g¯ is the mean value of the distribution and sg is the standard deviation. Γ depends on temperature and stress triaxiality through a dimensionless driving force function for martensite nucleationin which g0 is a material parameter, g1 and g2 are the temperature and the linear triaxiality dependency coefficients. Θ is the normalized temperature defined as Θ=TMs. When Θ˙=0,P˙ could be derived aswhere H() is the Heaviside function. Using the evolution of martensite in Δv is the relative volume change due to martensite transformation (Δv≈0.02−0.05 ()). N is defined as N=3σijd2σeq and A was calculated usingwhere A0 and A1 are material parameters and sa is the reference austenite hardness (Finally, the stress and strain transformations were united through the pseudo potential for dissipation of the phase transformation proposed by Therefore, the evolution of martensite fraction can be found using the functionwhere ξ1 and ξ2 are material parameters and Cζ is given by the term multiplied by Cζ is responsible for stress induced phase transformation and determines the value of evolution of stress induced martensite fraction, ζstress. In order to satisfy the dissipation inequality the requirement of Cζ > 0 is discussed in the To examine stress and strain induced transformations and determine the parameters related to the stress and strain induced transformation mechanisms, monotonic tests were performed at different temperatures. For this purpose, tension experiments were carried out at 22°C (RT), 100°C and 150°C using servo-hydraulic test machines and the specimens shown in The thin steel specimens with rectangular cross section used in this study were wire electro-discharged from forged rod specimens which had been hardened together with the specimens used in the experiments conducted by . Thus, the material and heat treatment were identical for all specimens used in the present and earlier experiments by . The specimens with the aforementioned steel grade DIN 100CrMnMoSi8 had been heat treated to martensitic microstructure with a retained austenite content. The monotonic test setup was placed in an oven to maintain constant temperature during the experiment and the axial strains were measured using extensometers. To avoid assembly stresses, the fixtures were carefully aligned with the load line using metal shims. In addition to these experiments, the results of tension, compression and cyclic experiments performed at 75°C were taken from the study of . The stress strain curves in monotonic tension, compression and cyclic experiments are presented in In this work, the plastic and nonlinear elastic material parameters given by were used as starting values to determine the material parameters of the corresponding model that considers phase transformation. In their work the phase transformation was not explicitly modeled, instead all the inelastic strains were included in the plastic description. The material properties for nonlinear kinematic and isotropic hardening given in . Since the present investigation focused on and modeled the phase change taking into account both stress and strain induced transformation, some parameters in the plastic description that are given in were adjusted from the values in the reference (σY0, a, a*, b, Q, C1, C2, C3, γ1, γ2, γ3). The plasticity parameters were updated iteratively using inverse modeling of the stress strain curves with respect to the experimental results in (a). The parameters quantify the effects of the different mechanical phenomena described in In previous studies it is reported that the elastic modulus of martensite is less than that of austenite () therefore different elastic moduli have to be defined for each phase. The equivalent elasticity tensor should vary during the transformation with respect to the change of martensite fraction as given in . Here the Poisson's ratio and nonlinear bulk modulus K(ɛkkel) were taken from . The same values were used for both phases. The Young’s moduli for each phase were then determined by inverse modeling of the monotonic experiments presented in , the curves describing the nonlinear elastic behavior given in The X–ray diffraction (XRD) measurements were performed using a Bruker D8 Discover instrument and Co K–alpha radiation. A 1D silicon strip detector with 192 strips were used and a programmable divergence slit maintained the sample illumination at 5 mm throughout the measurements. The instrument was operated at 40 kV and 35 mA, and the step size used was 0.03 deg. The counting time was varied depending on the cross-section area of the sample to assure proper counting statistics. The accuracy of 2.2–3% was maintained in the date analysis of single martensite fraction values. The measured X-ray diffraction values at different temperatures are shown in The parameters affecting the kinetics of the phase transformation were set from the retained austenite levels measured after deformation. The parameter β in depends on ratio of the average volume of martensite and shear band intersection. In this study, the start value for β was based on values in the literature (). The value of β=3.05 that fits the transformation kinetics given in (a) and (b) was finally determined again using inverse modeling with the FEM subroutine. The exponent r in is commonly taken as 4−4.5 for martensitic TRIP steels (). Here r=4 was found to give the best fit to the experimental data represented in , which controls the rate of shear band formation based on a stacking fault energy, is temperature dependent (). Since the temperature degree of freedom was satisfied through the functions Γ(Θ, σ) and C(T) in , α and β were here kept temperature independent. The parameters responsible for temperature dependence (g1, ρ, κ) were obtained using the results of X-ray diffraction measurements presented in (b). The g1 value was fitted to the measurements representing the change of ζ at high temperatures (75°C, 100°C and 150°C) where strain induced transformation was dominant. The parameters ρ and κ on the other hand changes the transformation start stresses in . Therefore they were determined considering the yield strength at RT to 75°C, where stress induced transformation starts before yielding, see (a). Parameters g0, g2, g¯ and sg in the probability function are determined through their fit to the X–ray diffraction measurements given in (a), especially at high temperatures where the strain induced phase transformation is dominant. The dimensionless parameters A0, A1 and sa given in were used to calculate A, which account for the strains related to shape change. These parameters were determined from the stress strain curves in . The starting values were based on the values by the difference in kinetics and morphology of stress and strain induced phase transformation affect the magnitude of transformation strains. However, in this study the same A was used to define the evolution of all transformation strains. shows the retained austenite as islands at the prior austenite grain boundary intersections. Some islands of retained austenite are circled in red in which represent small inclusions constrained in martensite matrix that effect phase change and redistributes the stress field in the transformation zone. Therefore the volume expansion of retained austenite is not free and it is mainly constricted by elastic deformation of the martensite matrix. Using the empirical equation given by , during martensitic transformation of the iron-carbon alloy with 0.91 wt % C was calculated as 0.0371. The determined value was in the range of 0.2 % to 0.4 %, that is reported by and commonly used by previous researchers.The relation between the parameters which were only related to the kinetics of the stress induced phase change, ξ1 and ξ2, was determined using where Tf=165∘C representing the temperature at the end of heat treatment when ζ2=0.78 and Ms=220∘C () at the martensite start where ζ1=0. Using ξ2=1, which is defined as the maximum martensite fraction that can be obtained as a result of phase transformation as stated by lists the minimum number of experiments required to determine the model parameters, the number of experiments used here for parameter determination, the additional number of experiments used for model verification and which parameters are fitted to the corresponding curves. Some of the calculated parameters indicated in were fitted independently (σY0, a, a*, b, Q, Ms, g1, κ, ρ, ξ1, ξ2) since they define a unique characteristic. Some parameters (C1, C2, C3, γ1, γ2, γ3, A0, A1, g2, g¯,α, β, sa, sg, g0, E0m,E0a,ν0, K1) required number of iterations. The other parameters are either calculated through expressions existing in the literature or taken directly from the literature (Δv, ξ1, ξ2, r). The experiments were monotonic tension to specimen rupture or a predefined strain, monotonic compression to a predefined strain and cyclic push-pull to rupture. Also, the tension experiments must be performed at different temperatures in the transition temperature range, see FE calculations were done using ABAQUS through a user defined material subroutine (UMAT) that followed shows the FE model used in the analysis. A 3D mesh with 67872 C3D8 elements was used after a mesh size and convergence study. The total CPU time was 13.1 × 103 s and the ratio of CPU time with and without considering phase transformation was 1.2. In the UMAT, stress and strain induced phase transformations were coupled with nonlinear elasticity, nonlinear kinematic and isotropic hardening behaviors and formulated using fully implicit integration of the constitutive relations. In the numerical solution, initially stress induced transformation was considered, the evolution of martensite fraction and transformation strains were calculated by . During dislocation movement, strain induced transformation takes place at shear band intersections along with stress induced phase change. Together they yield the evolution of martensite fraction. The flowchart of the UMAT subroutine is summarized in As seen from true stress true strain curves in , the finite element results were in good agreement with the tension experiments performed at different temperatures. (a) indicates that the yield stress increases with the increase of temperature from RT to 75°C, but over 75°C only a small difference is observed. According to during stress induced transformation, the yield strength in tension increases considerably with temperature. Therefore for TRIP steels, the change of yield point can be used to identify whether stress induced transformation takes place before strain induced transformation or not.To see the temperature dependence of stress induced transformation and the change in transformation start stress, stress strain curves representing the data obtained from the tensile experiments to rupture and those calculated using FE are plotted separately in . In the FE computations rupture of the specimens was not modeled. Instead all simulations continued to the total strain when the last experiment ruptured. During the experiments it was observed that the stress was homogeneously distributed and the specimens deformed without any necking. Therefore the localization of inhomogeneous stresses was not considered in the numerical simulations. (a) shows that the start of stress induced phase change increases with the temperature up to a certain value above which no phase change occurs prior to yielding. Thus the results obtained were compatible with the findings of indicated that it is difficult to separate the stress and strain induce transformations by only analyzing monotonic loading experiments at one specific temperature, especially if the material yields before transformation. To illustrate the transformation kinetics distinctly, the conditions considering only stress induced or strain induced transformations were modeled and are plotted in at two different temperatures. At RT in (a), the dashed green curve, representing the case where only stress induced transformation is active, coincides with black curve, including both transformation mechanics, till the start of strain induced transformation. Therefore, it is seen that for low temperature the stress induced transformation initiates before yielding and is a major part of the total transformation. At 75°C strain induced phase change becomes more dominant and the stress induced phase change takes place after yielding as is represented in For visual representation of the dependence of yield strength on transformation behavior, the uniaxial stress versus martensite fraction is plotted in (a). By comparing the onset of nonlinearity in (a) with transformation start stress in (a) it can be clearly seen that the yield strength decreases with decreasing temperature as the result of early transformation start at low temperatures of stress induced transformation. On the other hand at higher temperatures the effect of temperature on yield strength is less because no stress induced transformation occurs before yielding. Moreover, (b) supports the claim that at RT phase change starts before yielding since ɛ11tr starts evolving before ɛeqpl. It was concluded that by performing a series of different monotonic tension experiments at different temperatures it was possible to separate between stress and strain induced transformation. illustrates for low temperatures that the decrease of inelastic deformation with decreasing temperature shows that stress induced transformation is present and predominating. It was then detected separately from strain induced transformation, see the schematic start stress below yielding for stress induced transformation in . Strain induced transformation starts after yielding which in the present temperature range is relatively constant. It was then found that after yielding, strain induced transformation was more pronounced than stress induced.(a) together with the ζ curves obtained from FE using the calibrated material properties. When all data points were considered together with the model prediction in the figure, the measurements supports each other and deviation from the model is less than 0.5% for each retained austenite value. Hence, the overall accuracy of multiple measurements were much better than the single point estimate suggests.(a) and (b) represent the contour plot of martensite fraction at the early transformation stage (ɛ11=0.00275 in the test part with homogeneous strain and maximum ɛ11=0.0095 in the notch root) and at the specimen rupture under tensile loading at 75°C, see During phase change that occurs more predominantly under tension than compression, the volume increase induces an increase in strain, resulting in a nonlinear stress-strain behavior in advance and/or during dislocation motion. For this reason, in high strength steels with retained austenite undergoing phase change, the asymmetry between compressive and tensile yield stresses seen in (b) is largely a result of phase transformation. The triaxiality parameter Σ in affects the probability of martensite formation at the dislocation sites during strain induced phase change through the parameter Γ in that fitted to the martensite fraction evolution data of showed that martensite formation decreases when the triaxility is negative as in the case of compression. Additionally, reported that transformation curves for stress induced transformation exhibit linear behavior with respect to axial strains, whereas the curves for strain induced transformation was found to be nonlinear. The comparison of tension–compression tests and the calculated FE results together with X-ray diffraction measurements given in (b) pointed out that under compression a small amount of transformation occurs. The simulated behavior of ζ versus axial strain plotted in (b) differs quite markedly to the tensile loading case in (a). In compression, the transformation is dominated by the stress induced transformation that develops at the early stages of the deformation. This part of the transformation is furthermore linear with the strain, which agree with the findings of . The last part of the curve includes small strain induced transformation but at this stage the rate of transformation ζ˙ is much lower than the early part (The strength differential effect was also examined for cyclic load and compared to the experiments performed by (b) are in agreement with the simulations where the dotted the black line represents the martensite fraction under monotonic tensile loading and dashed blue curve is the evolution of martensite in the first cycle. The results confirm that the phase transformation predominantly develops during tension. Note that the retained austenite measurement for the cyclic curve in (b) was not directly used in determining the phase transformation parameters. Hence, it gave an indication on the model prediction.For high strength steels, the slope of the yield surface in the meridian plane is a ≈ 0.02 (), which is smaller than the value determined by , a ≈ 0.25. However, this value included all nonelastic effects. The effect of the pressure sensitive plasticity parameter, a on yield strength and phase transformation was investigated by using four different a values in tensile simulations. The parameter sensitivity study represented in (a) shows that the decrease in yield stress for increasing a is more significant at 75°C than RT. This result is mainly due to the stress induced transformation that occurs at lower temperatures before yielding. Therefore, the dependency of hydrostatic stress is influenced more by stress induced phase change, where the transformation is initiated by elastic stresses, compared to strain induced phase transformation. To determine the value of parameter a, not only the stress strain response but also the effect of a on phase transformation kinetics was studied. From (b) it is seen that decreasing a from a=0.12 to a=0.04 decreases the predicted martensite fraction at a certain strain value. Experimental measurements on martensite fraction ζ in (a) and the tensile and compressive stress strain responses in (b) were used to establish a=0.04 as the best yield stress slope for the present material. During strain induced phase change, which dominates for elevated temperatures, the evolution of martensite fraction occurs at dislocation sites and the effect on the yield surface slope is illustrated in (b). Therefore the experimented evolution of ζ at elevated temperatures were also considered.The effect of phase change on SDE was analyzed for two different temperatures through simulations of monotonic loading where the different parts of phase changes were executed. The evolution of such simulated SDE is plotted against inelastic strains in (a) shows that for increased temperatures, here exemplified with 75°C, strain induced transformation together with Drucker Prager plasticity coincides with the curve representing the full model and they yield closer results to the experimental measurements of performed at 75°C. The difference in SDE between experimental measurements and full model predictions in (b) by the corresponding difference in the compression curves at moderate strain. (b) also illustrates that in absolute stress values the model deviation is small. (a) and (b) includes simulated curves that only contains pressure sensitive plasticity, using Drucker Prager, i.e. the phase transformation was turned off. Comparing these curves with the full model prediction clearly illustrates that phase transformation dominates SDE effect for the current material structure. The result also show that stress induced phase change has only a small effect on SDE for high temperatures. Besides, when the temperature decreases to a level where the stress induced phase transformation is more effective on yield strength, e.g. RT in this case, the stress induced transformation is mainly responsible for SDE especially at low inelastic strains, see compares the calculated volume changes during tensile and compressive loading to experimental measurements of . It was observed that the computed volume change during compression is less than that during tensile loading which agree with the results by The present study couples the plastic deformation obeying nonlinear hardening rules and nonassociated flow rule with stress and strain induced phase change. Good agreement was obtained with the experimental results. In addition to phase transformation kinetics, the nonlinearity of elastic strains were taken into account in the material model while scrutiny of the plastic response cycles from cyclic experiments clearly showed that nonlinear elastic effects do have influences for the high elastic strains that can develop in this type of high strength bearing steel.Although the full material model includes a relatively large amount of material parameters, a limited number of well planned and well instrumented experiments were sufficient to calibrate the model. The required series include monotonic tensile experiments to some different strains and at some different temperatures together with at least one compression and one cyclic experiment. The data captured should include retained austenite levels and densities at test termination as well as the stress strain curves.The experiments showed that the solid to solid phase transformation of retained austenite to martensite affects the material behavior before and after plastic deformation through stress and strain induced phase transformations and changes in the yield strength of the material. Results indicated that the change of the yield strength with temperature is the main indicator of stress induced transformation that takes place before plasticity and defines start of the measured yielding at RT. At low temperatures, approximately below 75°C for the present material, stress induced transformation results in a reversed temperature relation with decreasing yield point for decreasing temperature. Also at these temperatures phase transformation was only stress induced, i.e. no strain induced transformation existed. At 75°C and for higher temperatures up to the martensite start temperature plastic yielding develop before phase change. Here strain induced transformation dominates the transformation, although some stress induced transformation continues to develop. By utilizing the understanding on how the yield point changes with temperature and the corresponding measured data points, stress and strain induced phase transformation were successfully separated from each other, their magnitude measured and the model parameter values were determined. Thus, the proposed model summarized in separates stress and strain induced transformation. It was concluded that the stress and strain induced phase transformation was active in the present material and that the processes can be separated by coupled modeling with a series of different monotonic experiments at different temperatures where both the stress strain curves were captured and the retained austenite levels after experiment termination was determined. Using the proposed model not only the coupled behavior but also distinctly stress and strain induced phases can be identified. Therefore, using this modeling technique, for complex loading condition like the stress distribution around a crack tip or at contact surfaces, contour plot of strain and stress induced martensite transformation zones can be plotted separately and their contribution to the mechanical behavior can be calculated independently.According to the monotonic experiments and X-ray diffraction measurements it was concluded that the amount of retained austenite that transforms to martensite is higher under tension than compression. The calculations for compressive loads at 75°C showed that a small stress induced phase transformation at the early stage of compression accompanied by strain induced phase change which is very small in total compared to the change under tensile loading. The analysis showed that phase transformation enhances and dominates the SDE over plasticity effects and that SDE can be simulated successfully by employing the coupled stress and strain induced phase transformation kinetics together with a pressure sensitive surface for plastic yielding and flow as is proposed in the current study.In the light of the aforementioned reasons it is claimed that both stress and strain induced phase change should be taken into account in the definition of constitutive behavior of the present class of high strength steels. Therefore, the material model that was capable of capturing nonlinear hardening behaviors, pressure sensitive plastic yielding and nonlinear elasticity together with stress and strain induced phase change was required to simulate the mechanical material behavior including the SDE in the high strength martensitic bearing steel accurately.and σh=K0eqɛkkel+K1ɛkkel2 was evaluated for uniaxial tension and compression. The uniaxial stress was then calculated throughσ11=3G3(K0eq+K1ɛkkel)3(K0eq+K1ɛkkel)+Gɛ11el.ɛkkel=(1−3(K0eq+K1ɛkkel)−2G3(K0eq+K1ɛkkel)+G0eq)ɛ11el., ɛkkel can be defined in terms of ɛ11el asɛkkel=−3(K0eq+G0eq)6K1+(3(K0eq+G0eq)2+36K1G0eqɛ11el6K1., noting that ɛkkel=0 for ɛ11el=0,ɛ11el=0 when σ11=0 and solved for ɛ11el the following equation was obtainedThe dissipation potential of the system defined through free energy potential by The corresponding work conjugates to the thermodynamic forces Xijm and R can be defined asWhen a nonassociative flow rule is employed in order to compute the bounds for the influence of pressure that satisfies the dissipation equation and the stresses were written in deviatoric and dilatation components so thatD=(σeq+3a*σh+∑m=1332γmCmXijmXijm−R)+Cζζ˙≥0The positivity of Cζζ˙ is discussed in appendix C. Therefore for the rest of the analysis the method used by is followed. Since λ˙>0 and f=0 during plastic deformation,This condition should be satisfied for large plastic deformations when the kinematic hardening is zero, Xij=0. Hence a ≥ a*. For this conditions the hydrostatic tension can be formulated as 3σh=σY0+Ra which yielded the equation states that in the material model that considers the nonassociated flow rule with pressure dependent plastic flow rule, the chosen parameters a* and a has to be controlled throughout the simulations to verify the stability of the solution and satisfaction of dissipation equation. the conditions of convex potential analysis ensures thatwhere (∂ΦCζ)0=0 since there is no phase change when the thermodynamic force Cζ=0. This yields the condition Cζ≥−Aζɛ˙eqpl+BζΣ˙ξ1(ξ2−ζ), where both terms in this division are positive and numerator is zero when there is no plastic deformation. It is known that stress induced phase change starts before strain induced phase change below a certain temperature and the evolution of stress induced martensite fraction defined in , ζstress ≥ 0. In addition to that the term Aζɛ˙eqpl+BζΣ˙ is positive during plastic deformation and zero otherwise. Therefore here, as a transformation function the condition of Cζ ≥ 0 should be used. This condition satisfies positivity of the term responsible from the dissipation during phase change Cζζ˙ in dissipation equation.Stability and performance of organic-inorganic thin films on polymer substratesThe use of polymer instead of glass is increasingly frequent, ranging from ophthalmic applications to electronic devices, displays and others. In the case of optical interference filters on plastic substrates (e.g., antireflective coatings) the performance of the device is limited by the coating-substrate compatibility (e.g., thermal expansion coefficient of the substrate about 100 times that of glass). In the present work, we demonstrate significantly improved resistance to temperature and humidity variation and higher elastic recovery of organic-inorganic SiO2 and ZrO2 coatings compared to their inorganic counterparts. Specifically, organic-inorganic coatings prepared by ion beam assisted chemical vapour deposition (IBACVD) show a higher thermal expansion (10− 5 |
K− 1) close to that of polymer substrates (10− 4 |
K− 1 for CR-39) and a relatively high H/E ratio (as up to 0.16). We show that both individual organic-inorganic layers as well as complete antireflective stacks exhibit a higher durability following accelerated environmental tests including exposure to high temperature/high humidity, UV and solar radiation, as well as a saline solution.Antireflective (AR) coatings are extensively used on a variety of products such as displays, ophthalmic and camera lenses, communication systems and others. In some applications such as ophthalmic lenses or smartphones screens, AR coatings are exposed to frequently changing and challenging environments. When polymer substrates are used (for example, to improve resistance to shock and reduce weight), application of inorganic AR coatings gives rise to a significant mismatch at the film/substrate interface due to a large difference between the coefficient of thermal expansion (CTE), hardness (H) and Young's modulus (E). Such mismatch can cause crazing failures of the brittle materials and delamination To further reduce the mechanical failure, one would need to use more elastic coatings in order to reduce the mismatch. One possible approach is to use organic-inorganic (O-I) materials. For example, the use of O-I SiOCH layers deposited by PECVD was proven to obtain low-k dielectrics with improved mechanical properties for new microelectronic devices In our laboratory, we have recently introduced the ion beam assisted chemical vapour deposition (IBACVD) process in which O-I optical coatings are prepared by using end-Hall ion source to dissociate the organosilicon precursor and supply energetic ions to the growing film to control its composition and microstructure. The obtained O-I coatings exhibit enhanced elastic recovery, higher strain to failure, and lower water uptake compared to standard mineral SiO2 layers We note, however, that the environmental stability of O-I coatings has not yet been systematically investigated. In this work, we performed series of tests that are representative of the conditions of use seen by ophthalmic lenses, namely temperature variation, exposure to a hot and humid environment, UV irradiation and immersion in a saline solution. Such tests allow one to discriminate between the tested samples and identify the best performing candidates for the application. The characterizations used in this work were inspired by the ISO 9211-3 The films were deposited in a box coater system (Boxer Pro, Leybold Optics), schematically presented in Inorganic ZrO2 and SiO2 layers were produced by evaporation using an electron beam (e-beam) gun mounted in the centre of the bottom plate. During the deposition of some of these layers the ion assistance (IAD) was provided by an end-Hall ion source (EH-1000, Kaufman & Robinson, Inc. . It is worth noting that all depositions involving the use of the ion source were preceded by a 1-minute pre-treatment using oxygen ions at 3 A of emission current using 20 sccm of O2.Refractive index, n, extinction coefficient, k, and thickness, df, of the deposited single layers were obtained by variable angle spectroscopic ellipsometry (VASE) using a J.A. Woollam RC2 ellipsometer. The measurements were performed at different angles of incidence from 45° to 75° with 10° intervals on samples deposited on silicon substrates. The ellipsometric model was a Gen-Osc layer consisting of Gaussian and Tauc-Lorentz oscillators and a surface roughness layer. The film density, ρ, was calculated as a ratio of the deposited mass measured with QCM and the thickness measured by ellipsometry.Haze measurements were performed before and after the aging tests using Lambda 1050 (Perkin Elmer Inc.) spectrophotometer equipped with an integrating sphere and an InGaAs detector. The haze coefficient was calculated as:where Tdiff(λ) is a spectrum measured using the light trap which removes direct transmission while Ttot(λ) includes both direct and diffuse transmissions where Rfs is the reflection of the coating, and Rbs(λ) ≈ 3.57% is the back side reflection at the CR-39/air interface. The reflection spectra were then converted into CIE XYZ and then CIE LAB, which were used to obtain the ΔE00 values.Mechanical properties, namely the hardness (H), the reduced Young's modulus (E) and the elastic recovery (%R) were obtained via nanoindentation using a Hysitron Triboindenter. The applied load varied from 0.1 to 9.5 mN using a Berkovich diamond tip, calibrated with fused quartz standard. The presented results are averages of 50 indentations. The load-displacement curves were analysed using the Oliver and Pharr methodology Stress in the deposited films was calculated using the Stoney formula where E, ν, d, and R are the Young's modulus, the Poisson coefficient, the thickness and the radius of curvature change, the subscripts s and f represent the substrate and the film, respectively. Using the measured Ef value, one can then estimate the coefficient of thermal expansion αf of the film by approximating the Poisson coefficient to its typical values of νf |
= 0.25 ± 0.15 using the following formula where α is the linear coefficient of thermal expansion:A similar approach was used to evaluate the linear coefficient of hygroscopic expansion (CHE) using the same formula (). For such evaluation, the samples on silicon were dried at room temperature from an ambient 40%RH to 0%RH using nitrogen purge. The substrate was considered not sensitive to the humidity level.Series of environmental tests were performed in order to evaluate the coating durability; this includes near-UV radiation from the Sun, exposure to high humidity and temperature variations and contact with liquids. Different samples deposited under the same conditions were subject to these tests in parallel. All aging tests were performed with films deposited on CR-39 substrates, except for the UV test, which was performed on the BK7 glass strips in order to eliminate the effect of the substrate.The conditions of the four different aging tests go as follows:Heat test: 1 h at every temperature from 50 °C to 120 °C by increment of 10 °C;humidity test: 2 h at 60 °C, and then 80 °C (> 90% RH, inspired by UV test: 200 h to Sun-like UV radiation (Suntest Heraeus CPS +, ASTM G-173 standard saline solution test: 20 min in 200 g/L NaCl solution at 50 °C (inspired by the ISO-9211-4 standard Following the first two tests, which may have resulted in mechanical failures, the samples were evaluated by visual inspection using an optical microscope in the case of the single layers, while haze was measured in the case of antireflection stacks. For tests iii and iv, the samples were characterized by ellipsometry and transmission measurements in order to assess optical properties (n, k and the thickness) change and colour variation using ΔE00.A combination of e-beam evaporation and IBACVD described in has been used to obtain films in a wide range of refractive index (n at 550 nm), ranging from 1.45 to 1.95. illustrates the film density and stress plotted as a function of n. When adding DMTS to ZrO2, n decreases from its high value of 1.98 down to that of silica (1.47) accompanied by a decrease of ρ and σ. The stress for inorganic SiO2 is highly compressive, but it is lowered for SiOCH films. Inorganic ZrO2 samples show tensile stress, that is decreased by IAD, and it transforms into compressive by the addition of SiOCH.The basic elastoplastic properties of the as-deposited films are summarized in with respect to n that itself is monotonically related to ρ. Inorganic SiO2 films possess H and E values of about 4 GPa and 45 GPa, respectively (c). In addition, the enhanced mechanical coating performance is further demonstrated by the high elastic rebound, R, in excess of 60% (The effect of the stability tests on the performance of the individual films is described in . Specifically, after exposure to elevated temperatures ranging from 50 °C to 110 °C in air, the samples show a clear trend indicating the beneficial effect of the O-I approach to increase resistance to temperature-induced crazing. All low-n samples showed good stability and virtually no damage (marked as > 110 °C) when compared to films with a higher ZrO2 content (a). The appearance of failure (cracks) in zirconia-rich samples also correlates with the estimated temperature-induced stress variation on the CR-39 substrate (. Comparing the curvature change of films deposited onto 〈100〉 Si substrate, we found that the coatings' CTE values were in the range between 2·10− 6 |
K− 1 |
< |
αf |
< 6·10− 6 |
K− 1, that is significantly lower than the CR39 substrate's CTE, αs ~ 10− 4 |
K− 1. Therefore, the observed differences in the thermally-induced stress are primarily determined by Ef and not by αf (see Eq. ). SiOCH and SiO2 samples exhibited good performance because of a more compressive initial stress and/or because of their more elastic behaviour (c and d) when compared to their zirconia-based counterparts.After exposure for 2 h to an environment saturated in humidity at 60 °C and 80 °C, the samples exhibited different types of behaviour (c). Specifically, the “> 80 °C” result means that the samples did not develop any crack or failure. All inorganic silica and zirconia, showed signs of cracking failure, while most of O-I films particularly, the mixture resulting in ZrOSiCH turned out to survive the test.One can also notice a correlation between the estimated humidity-induced stress variation on CR-39 (d) and the failure apparition, at least in the case of the zirconia-based films. This test was the most discriminating one between samples, showing a clear advantage of both SiOCH and ZrOSiCH O-I films compared to purely inorganic materials, as systematic failure of the inorganic samples was observed, while only a few O-I coatings showed sign of damage.Following the saline solution test, n does not seem to significantly change (average of 0.5% variation), with only 3 samples out of 18 showing variations higher than 1% (). For the UV test, the results were very similar, again with an average of 0.5% variation, this time only 4 samples exhibiting a change of > 1% (b). One can conclude that all the samples were rather stable under UV irradiation and saline solution immersion, though the zirconia-based samples show a slightly higher variation than the SiOCH ones.The summary of the test results is presented in . The tests on the single-layers have shown that the incorporation of organic groups helps in improving the resistance to hygroscopic variations in both silica and zirconia-based materials. It also helps to enhance the heat resistance of zirconia-based films. In addition, these materials are rather insensitive to the exposure to UV and to a saline solution.In order to evaluate the performance of the -I coatings in future applications, we prepared antireflection (AR) stacks using the pre-characterized materials described in the previous section. These filters were then subject to the same heat, humidity, saline solution and UV tests as above. The filters are based on a 4-layer design, using different materials of high and low indices (HHLLHL quarter-wave optical thickness or QWOT layers), namely inorganic stacks deposited by e-beam evaporation with and without ion beam assistance, and e-beam layers with an O-I top layer. In addition, we tested an all-O-I (4-layer) and a 3-layer filter which consist of a high-index inorganic layer (H) sandwiched between a medium (M) and a low-index (L) QWOT O-I layers, resulting in the 3 layer MHL system denoted as Sandwich AR stack. The optimal index (at the reference wavelength) of the M layer can be calculated from H and L using the formula derived from the Abelès' matrix method The thicknesses of the layers in these designs were optimized using the OpenFilters software ). One should be careful when comparing the 4-layer stacks with the MHL one, as the latter possesses a thickness only about 60% of the thickness of the other stacks (250 nm vs 430 nm).Based on the results for single layer coatings, the O-I stacks are expected to perform better than their inorganic counterparts since they should possess less stress build-up induced by the temperature and/or humidity variations. Indeed, the results of the heat-test for stacks on CR-39 () indicate that the inorganic films tend to fail at a lower temperature, with cracks appearing between 70 °C and 80 °C. It is worth noting that although ion-assisted coatings cracked, they did not delaminate, most likely because of a stronger interface with CR-39 compared to the evaporated AR stacks. Also, the use of an O-I top layer on the deposited e-beam stack allowed one to increase its stability by pushing the cracking temperature to 110 °C. The other samples, which are the all-O-I and the MHL stacks, did not fail in any case and their haze remained below the measurement error of about 0.2% (black dashed line).b) the all-O-I and the MHL stacks still performed very well, having maintained their low haze and showing no sign of cracking. The inorganic sample deposited by e-beam started failing after 5 days at 60 °C, while ion assistance or an O-I top layer have both exhibited improved resistance at 60 °C, but they developed cracks at 80 °C.Summary of the different stability tests is illustrated in . The samples that used the inorganic (thus hydrophilic) SiO2 as a top layer show salt residue, while samples with hydrophobic SiOCH (contact angle around 90°–110°) as a top layer remained clean after being dried with nitrogen. After a quick rinse, no significant scattering was observed, as the haze of all samples remained below 0.2%. On the other hand, the measured spectra revealed a certain level of quantifiable colour change, which is noticeable in the case of the all e-beam sample (, empty bars). All the other samples exhibited about a third of that colour variation, which is not easily perceived by the naked eye (ΔE < 2).Finally, the UV test results show no significant colour variation for any of the samples (, full bars), the lowest variation occurring in the case of the all O-I stack. This indicates that the coatings are not affected by the UV irradiation. A summary of the results is presented in Organic-inorganic single layer coatings were characterized prior to being implemented in antireflective coating stacks. Their lower Young's moduli resulted in lower stress variations arising from the elevated temperature and humidity levels, while their increased elasticity resulted in better resistance to the tests. The use of O-I materials in AR coatings has greatly improved their resistance to hygroscopic and thermal variations, and to saline solution. Also, all the layers exhibited good stability to UV irradiations. This work demonstrates the opportunities for O-I coatings to enhance durability when applied to polymer substrates.Regarding the properties of the CR-39 (Columbia Resin batch 39) polymer from PPG, the thermal expansion was found to be around 10− 4 |
K− 1 in the literature ). Thus, one can say that the substrate can expand up to about 1% from 0% to 100% humidity, which can lead to severe strain in the coatings.A model for the estimation of hardness of laser bent stripsIn this work, a model is developed for the estimation of hardness of the laser bent parts. The model incorporates the effects of phase fraction, cooling rate as well as strain hardening. This is accomplished by using microstructure integrated finite element method simulation of laser bending of steel strips. The methodology is illustrated with an example of laser bending of AH36 steel strips. The Johnson-Mehl-Avrami-Kolmogorov law and Scheil’s additivity rule are employed to simulate the kinetics of diffusional phase transformation, while Koistinen-Marburger equation is employed for non-diffusional phase transformation. Effects of latent heat release during phase transformations, temperature and phase fractions on the variation of thermo-physical properties are considered. The proposed model is validated through experiments. The model is able to simulate the kinetics of phase transformation in laser bending that leads to reasonably accurate estimation of phase fractions and hardness of laser bent strips.Laser forming is a flexible forming process that does not require the application of force by a tool; instead it relies on the thermal stresses introduced by a laser beam. Due to its flexibility, the process is suitable for batch production and rapid prototyping. In the past, numerical and experimental investigations of laser bending process were carried out to understand the process mechanisms Researchers have shown experimentally and numerically that the application of lasers in metal forming process induces microstructural changes that affect the geometry change and the mechanical properties of the material. Cheng and Yao A review of literature reveals that some models have been developed to predict the phase fractions in laser forming, but there is hardly any model on the estimation of hardness of laser formed products. On the other hand some research groups have developed numerical models for predicting the phase fraction The aforesaid models predict the hardness accurately but these are not directly applicable to laser bending process. Laser bending is a fast heating and cooling process unlike hot working processes. In laser bending the cooling process is similar to quenching in a typical hardening heat treatment except for significant plastic deformation in the former. Literature contains phase transformation models for cooling after hot rolling describes the kinetics of phase transformation incorporating diffusional and non-diffusional transformations. The JMAK law , an FEM model is developed to simulate the microstructure integrated laser bending process. Here, metallurgical and thermal behaviors of material are incorporated to predict the volume fraction of different phases of the laser scanned strip. A model for the estimation of hardness is developed to predict the Vickers hardness of the laser bent strips. In , the experimental conditions and corresponding FEM simulation are elaborated. The validation of developed FEM model and discussion is presented in Phase transformation occurs during continuous cooling of the laser irradiated steel sheet forming various phases such as ferrite, pearlite, bainite, cementite and martensite. The volume fraction of these phases depends on the cooling rate and the composition of the workpiece material. In order to deal with all these phases, the volume fraction of each of the phase is represented by Xf, where the subscript f ranges from 1 to 6 and indicates different phases— 1: austenite, 2: ferrite, 3: bainite, 4: pearlite, 5: cementite and 6: martensite. The phase transformation is an isochoric process; therefore, the sum of volume fractions must be unity i.e., ∑f=1f=6Xf=1, where Xf lies in between 0 and 1. The phase transformation of the steel sheet during heating from room temperature to austenitizing temperature depends on heating rate, temperature and the austenitization time. Luo et al. There are two types of transformations— diffusional and non-diffusional. In case of hypoeutectoid steels, the formation of proeutectoid ferrite, pearlite and bainite occurs due to diffusional transformation. Diffusional transformation is a time-dependent phenomenon. It strongly depends on temperature and proceeds by nucleation and grain growth. The evolution of these phase transformation can be predicted through an approximate solution using data from time-temperature-transformation (TTT) diagrams. The phase transformation analysis using this diagram is done by assuming that the cooling process may be represented by a curve divided in a sequence of isothermal steps, with a duration Δt as shown in . For each isothermal step, the kinetics of diffusional transformation is described by the JMAK law. The JMAK law can be expressed as where Xf(T) is the volume fraction of f phase during the time t at a constant temperature T, X̂fmax is the maximum volume fraction of an f phase, bf the diffusion coefficient and nf is the Avrami exponent of transformation; bf and nf are the functions of temperature, and represent the condition of nucleation and growth rates . Usually these two times are chosen as the start time tfs and finish time tff. This provides the following expressions:nf(T)=lnln1-XfsX̂fmaxln1-XffX̂fmaxlntfstff,where Xfsand Xff are the transformed volume fraction at the start and finish of the f phase transformation, respectively. It is very difficult to know the exact starting and finishing of the phase transformation. Moreover, the JMAK law may not be accurate at the very beginning and the end of the transformation. Hence, it is usual to take Xfs and Xff as 0.01 and 0.99, respectively. The parameter X̂fmax is represented bywhere Xfmax is the maximum possible amount of volume fraction for an f-phase. The Xfmax for proeutectoid ferrite can be determined using lever rule in iron-iron carbide phase carbon diagram. Consider an alloy of C0 wt% carbon (C), between 0.022 and 0.76 wt% C. Cooling an alloy of this composition is represented by moving down the vertical line yy′. At point a, the microstructure will consist entirely of grains of the austenite (γ) phase, as shown in Boundary line PQ represents the phase transformation line from austenite (γ) to proeutectoid ferrite (α) + γ. Cooling from point b to c, just above the eutectoid but still in the (α + γ) region, will produce an increased fraction of the α phase. At point c, the compositions of the α and γ can be determined by constructing a tie line at the eutectoid temperature (Te); the α phase contains 0.022 wt% C, whereas γ phase contains 0.76 wt% C. The lever rule can be used to compute the maximum fraction of proeutectoid ferrite (X2max) as follows:X2max=UU+V=0.76-C00.76-0.022=0.76-C00.738.As the temperature is lowered, all the γ phase that remained at temperature Te will transform to pearlite, bainite and martensite depending on cooling rate. In case of other phases viz., bainite, pearlite, cementite and martensite, the maximum volume fraction i.e.,X3max,X4max,X5maxandX6max, respectively, is equal to 1.The JMAK law used for describing the transformation kinetics for diffusional transformation is valid only under isothermal conditions. Transformation kinetics of continuous heating and cooling curve is assumed to follow Scheil’s additivity rule . The amount of phase transformation at each step is calculated using JMAK law. A fictitious time t* is defined that represents the time for the formation of the volume fraction Xf at temperature T, considering an isothermal transformation developed at temperature (T + ΔT). The fictitious time can be calculated using Eq. This fictitious time is the starting time of phase transformation during the isothermal time step Δt at temperature (T + ΔT) as shown in . The total amount of volume fraction at the end of the time step t + Δt is given byXfT+ΔT=X̂fmaxT+ΔT1-exp-bfT+ΔTt∗+ΔtnfT+ΔT.The start and finish time for different phases viz., ferrite, pearlite and bainite can be obtained from the TTT diagram. It is required to digitize the start and finish curves of different phases of TTT diagram. After digitizing the curves, functions can be fitted for start and finish curves of different phases in terms of temperature using curve fitting tool of the MATLAB®.Unlike diffusional transformation, non-diffusional transformation such as martensite transformation is independent of time and depends only on temperature. Koinstinen and Marburger proposed an empirical model to predict the volume fractions of martensite (X6) where Ms is the martensite start temperature in °C.This section presents the procedure for FEM modeling of the microstructure integrated laser bending process. The section is divided into three subsections. describes the standard procedure for thermo-mechanical analysis, presents the implementation of phase transformation and The thermo-elastic–plastic model of straight line laser bending process has been developed using commercial finite element package ABAQUS® version 6.10-1. The complete description of FEM model is given in Kumar and Dixit . The strip is fixed at on edge along the width direction. For the typical optimum mesh, the total number of elements is 4800 comprising 40 divisions along the length, 40 divisions along the width and 3 divisions along the thickness. The material used in the study is AH36 steel, which has a hypoeutectoid composition with carbon content of 0.2%. The temperature dependent properties are taken from In laser forming process, very high temperature is generated in a very short interval of time. The high temperature (beyond critical temperature) led to the austenitization of the strip. During cooling, the austenite phase decomposes into various other phases viz., ferrite, bainite, pearlite and martensite. The percentage of phase transformation during heating and cooling is dependent on time–temperature-transformation (TTT) diagram of the workpiece material. Luo et al. The mathematical model for the phase transformation kinetics explained in is implemented by user subroutine to define a material’s thermal behavior (UMATHT) available in ABAQUS®, which is written in FORTRAN. The main code in ABAQUS® calls the UMATHT subroutine at each node for each increment. The fractions of each phase were stored as solution dependent variables (SDVs). SDVs are a set of global variables that are stored in the state variable (STATEV) array in the ABAQUS® main code. For AH36 steel, 4 SDVs were specified and the volume fractions of austenite, bainite, ferrite and martensite were stored as SDV1, SDV2, SDV3 and SDV4, respectively. The material is initially assumed as 100% ferrite. This condition was implemented through solution dependent initial variable (SDVINI) user subroutine. The SDVINI subroutine allows initial values to be assigned to the SDVs. The SDVs that store the initial volume fractions of ferrite are then passed into the UMATHT subroutine, where the algorithm for phase transformation is implemented. The algorithm for phase transformations at a particular node is described in the flowchart shown in , where Tfs, Tbs, Tms and Tamb are ferrite start, bainite start, martensite start and ambient temperature, respectively. Xaus, Xbain, Xfer and Xmar are the volume fractions of austenite, bainite, ferrite and martensite, respectively. The steps of the algorithm are explained as follows:Step 1: The SDVINI subroutine is called at the node to initialize a microstructural state with 100% ferrite. The SDVs representing these volume fractions are passed into the UMATHT subroutine in Step 2.Step 2: Nodal temperature T is checked. If T is greater than 725 °C then austenite will be formed according to JMAK law and a fully austenitic microstructure is assigned at the particular node if temperature is greater than 925 °C and Step 3 is executed. If the temperature is less than 725 °C, the microstructure at the node remains in the state as initialized in Step 1 and then thermo-physical properties are computed followed by thermo-elasto-plastic analysis.Step 3: Volume fraction of austenite Xaus is checked. If it is greater than 1%, Step 4 is executed. Else the austenite decomposition is considered complete at the particular node.Step 4: If Tfs ≥ T > Tbs then Xfer is calculated and the current available austenite fraction Xaus is updated by subtracting Xfer from it and then Step 7 is executed. Else Step 5 is executed.Step 5: If Tbs ≥ T > Tms then Xbain is calculated and the current available austenite fraction Xaus is updated by subtracting Xbain from it and then Step 7 is executed. Else Step 6 is executed.Step 6: If Tms ≥ T ≥ Tamb then Xmar is calculated and the current available austenite fraction Xaus is updated by subtracting Xmar from it and then Step 7 is executedStep 7: The thermo-physical properties are computed followed by thermo-elasto-plastic analysis and then Step 3 is executed. The procedure continues till the temperature reaches the ambient temperature (20 °C in this work).The thermal behavior was also defined in the UMATHT subroutine after the instructions for the computation of the volume fractions of the microstructural constituents. The material properties of steel are functions of both temperature and phase volume fractions. Since the material is composed of various phase, the magnitude of a particular type of property can be computed as an aggregate of the values contributed by each phase at the particular temperature using the linear mixture law expressed aswhere ki, ci and Xi are the thermal conductivity, specific heat and volume fractions of the ith phase, respectively. However, in the present work temperature dependent material properties were already available and the same were used. The latent heat release due to phase transformation is incorporated in the equation for the change in internal energy per unit mass as follows:where ΔH is the enthalpy of formation per unit volume, ΔT is the incremental change in temperature and ΔXi is the incremental volume fraction of the ith phase. The ΔH for austenite-pearlite and austenite–martensite transformations are taken as 1.56 × 109 – 1.5 × 106T J/m3 and 640 × 106 J/m3In laser bending process, hardness of the material changes due to high temperature generation that lead to phase transformation of the workpiece and strain hardening of the material. In order to predict the Vickers hardness distribution due to phase transformation, the empirical model presented by Maynier et al. HVbain=-323+185(%C)+330(%Si)+153(%Mn)+65(%Ni)+144(%Cr)+191(%Mo)+{89+53(%C)-55(%Si)-22(%Mn)-10(%Ni)-20(%Cr)-33(%Mo)}logVR,HVfer - per=42+223(%C)+53(%Si)+30(%Mn)+12.6(%Ni)+7(%Cr)+19(%Mo)+{10-19(%Si)+4(%Mn)+8(%Cr)+130(%V)}logVRHVmar=127+949(%C)+27(%Si)+11(%Mn)+8(%Ni)+16(%Cr)+21×logVRwhere HVmar, HVbain and HVfer-per are the Vickers hardness of martensite, bainite and mixture of ferrite and pearlite, respectively. VR is the cooling rate in °C/h at 700 °C. The total Vickers hardness (HV) of the steel, dependent on the volume fractions of the constituents of the microstructure, is calculated using the rule of mixtures:HV=XbainHVbain+Xfer+XperHVfer - per+XmarHVmar,where Xper is the volume fractions of pearlite.The strain hardening of the material causes an increase in the yield strength of the material. It was theoretically found and experimentally shown in several previous contributions where C is a material dependent constant. The flow stress can be written aswhere σy is the yield stress and R = f(εp) is the hardening law of considered steel. In present work, linear strain hardening law is considered. Therefore, R at equivalent plastic strain (ɛp) can be obtained aswhere σ1 and σ2 are flow stresses at equivalent plastic strains ɛp1 and ɛp2 at room temperature, respectively. The strain hardening of the material will increase the hardness of the workpiece by f times where f is obtained as the ratio of flow stress at equivalent plastic strain (ɛp) and initial yield stress of the material.To validate the accuracy of the present model, the experimental results of the laser bent AH36 steel strips are used. Although the complete experimental procedure is explained in Fetene et al. . The laser beam was irradiated in a direction parallel to the free edge (along the width) of the clamped specimens. After the laser beam irradiation, the heated specimens were allowed to cool naturally. In case of multi pass bending, a gap of 5 s was kept in between two successive irradiations. Bend angles were measured along the width direction at 5 locations, using a coordinate measuring machine (CMM) of ZeissTM make, and the average bend angles were reported. The Vickers hardness was measured for laser bent strips to understand the effect of number of scans and workpiece thickness. The hardness was measured using a hardness tester of BuehlerTM make with an indenting force of 500 gf and a dwell period of 20 s. The measurements of the laser bent strips were taken at 0.2 mm below the irradiated surface and indentations were made at 1 mm intervals, along perpendicular to laser scan length.FEM simulations are carrried out to evolve the phase fractions, equivalent plastic strain and cooling rate of laser irradiated AH36 steel strips. The temperature dependent material properties are taken from . The TTT diagram during cooling process for 0.2% carbon steel is taken from This section presents the results of the FEM analysis. The validation of the FEM model is discussed in provides the results of phase fraction distribution. results of equivalent strain distribution. Phase fraction and equivalent strain together influence the hardness distribution. The section concludes with a discussion.The current FEM model is validated using experimental results of Vickers hardness reported in Fetene et al. shows the predicted and the experimental values of Vickers hardness for different strip thicknesses at constant values of other geometrical and laser parameters (mentioned in the caption). The predicted hardness values are in good agreement with the experimental results with most of the deviations below 10%. shows a similar comparison for different cases of the number of scans. The predicted results of hardness are in good agreement with the experimental results for the third and the fifth number of scans. However, there is some deviation in the result of first scan. It is because the simulation predicted the maximum temperature of the workpiece as only 570 °C after first scan. At this temperature, no phase transformation takes place. In experiments, temperature might have crossed 725 °C due to high value of absorptivity in the first scan. In the FEM simulations, only the average value of absorptivity has been taken.The distributions of the phase fractions was taken along the line XX' (refer ) at a depth of 0.2 mm from the top surface. These are shown in for various strip thicknesses. On an average, the surface comprises 92% bainite, 5% martensite and 3% retained austenite, at the point O. In contrast, some researchers The resulting microstructural states obtained in , which shows the variation of temperature along the line OX (refer ) when the laser beam reaches the point O in the 5th pass. The temperature is the maximum at the laser irradiated spot O and gradually decreases as one moves away from O. The horizontal line shows the lower critical temperature of 725 °C above which microtructure changes. At locations where the temperature remains below this line, the final microstructure remains in the initially assumed 100% ferritic state.The distribution of the equivalent plastic strain along the line OX for different thicknesses of the laser-bent strip keeping other geometrical and laser parameters the same are shown in . The equivalent plastic strain is the maximum at the laser irradiated spot O and decreases as one moves farther away along the line OX. The evolution of the equivalent plastic strain with time and temperature at the point O from the start to finish of the laser bending process is shown in . The temperature increases with each subsequent pass and leads to a corresponding increase in the equivalent plastic strain. With more plastic strain, the flow stress increases due to strain hardening and leads to a corresponding increase in the hardness as can be inferred from . The final bend angle and maximum value of the hardness obtained for typical cases of geometrical and laser parameters are presented in . These results have been obtained from simulations.The results obtained in this study show that microstructure, temperature and strain hardening play a significant role in the hardness. A microstructure that comprises a higher fraction of hard phases like bainite (as in the present study) results in greater surface hardness. The resulting microstructure is a direct consequence of the temperature distribution that exists during the laser bending process. The temperature is the maximum at points along the laser scan line and gradually decreases while moving away from it along the transverse direction. The hardness of the workpiece is also affected by the strain hardening that occurs during cooling of the laser bending process. This effect has not been incorporated in the previous hardness models Estimation of hardness of laser bent sheets is of paramount importance. In this work, a numerical model is developed to simulate the kinetics of phase transformations that predicts the phase fraction and hardness during laser bending of AH36 steel strip. A good agreement is found between experimental and simulation results of Vickers hardness of the laser scanned strip. The proposed model has considered phase transformation and cooling rate as well as strain hardening. It is observed that strain hardening plays a major role in inducing hardness. Neglecting this produces results contrary to experimental observation; hardness of thicker strips will be over-predicted. The proposed model (considering phase transformation, cooling rate and strain hardening) is useful in optimizing the laser bending process to achieve desirable microstructure and properties, thus reducing manufacturing costs.The methodology proposed in this work is fairly general. It, nevertheless, requires an accurate TTT diagram as well as temperature-dependent properties of the material. This information may not be available in several cases involving newly developed materials. Hence, the future work should be directed to develop faster methods to determine TTT diagram and properties. This may be possible by developing inverse techniques.Multimode Ultrasound Breast Imaging Using a New Array Transducer ConfigurationThis article presents a diagnostic ultrasound imaging technique that can be used in imaging protruding objects such as a human breast using two opposing array transducers. Because two B-mode images obtained from each of the two linear array transducers facing each other represent the same imaging area viewed in different directions, the image quality can be improved using a compounding technique. Using one array as a transmitter and the other as a receiver, the speed of sound distribution in a medium interposed between them is also reconstructed. In addition, because the spacing between the two arrays can be finely controlled, strain image can also be obtained. This new method can be used to produce a compound B-mode image, a speed of sound image, and a strain image of the same region-of-interest, making it possible to obtain more information leading to better diagnosis. Experimental results on a phantom containing a cylinder of different speed of sound and elasticity confirm that the proposed method is useful in obtaining compound and speed of sound images as well as strain images. (E-mail: Although mammography is widely used in the diagnosis of breast cancer, it may be subject to potential radiation hazard. Breast cancer has different ultrasound characteristics from normal healthy tissue in terms of speed of sound (SOS) and attenuation (). For the case of diagnosing breasts in medical ultrasound imaging, tissue parameter imaging can be used together with B-mode imaging in a complementary manner.Since the breast protrudes from a human body, it is possible to obtain attenuation and SOS images by using circular transducers or by rotating linear arrays over 360° in transmission or reflection mode using tomographic reconstruction principles (). Although this approach enables us to obtain more information about lesion, the use of circular transducers or linear arrays entails the immersion of objects to be imaged in water. Due to relatively long data acquisition time and discomfort to patients, it has not yet been put to practical use.To overcome these limitations, several researchers proposed data acquisition methods based on linear array transducers (). As with mammography, using a linear array transducer and a plane reflector, the SOS image of a human tissue positioned between them was obtained. Compared with tomographic reconstruction methods that collect data over an angle of 360°, the linear array method acquires data over a limited range of angles, making it difficult to produce a complete artifact-free image ( compensated for distortion in SOS image using structural information extracted from B-mode image. To superpose images obtained from multiple viewing angles in full angle spatial compounding, reconstructed the SOS distribution by placing a reflector behind an object of interest and using the filtered backprojection of the echo data from the reflector. obtained SOS images in transmission mode using two transducers that face each other.Compound imaging techniques acquire data using spatial or frequency diversity and average images of the same region to achieve less speckle noise and better contrast ( introduced a method of obtaining compound image together with SOS image using circular array transducers.Recently, there has been much research into elasticity imaging of the breast. Since tumor or cancer in soft tissue such as the breast and prostate tends to be stiffer than the surrounding tissue, elasticity imaging that visualizes the degree of stiffness is of great help in diagnosing it (). Human tissues tend to exhibit a higher contrast in elasticity than other tissue parameters. Therefore, the elasticity parameter is amenable to imaging.In this article, we obtain spatial compound, SOS, and strain images using two opposing linear array transducers. B-mode or strain images are obtained independently in reflection mode from each of the two array transducers, and are compounded to improve the image quality. In transmission mode, however, we use an imaging configuration where one array transducer is used as a transmitter and the other is used as a receiver. The time of flight (TOF) is measured and an SOS image is reconstructed. A combination of the B-mode, strain, and SOS imaging can increase the accuracy of lesion diagnosis. This article presents each imaging method and experimental results.Compound imaging is used to reduce speckle noise as well as artifacts such as shadowing and reverberation by averaging a certain number of images whose correlations are small. However, the degradation of resolution and signal-to-noise ratio (SNR) with increasing depth cannot be compensated for. Conventional spatial compound B-mode images are produced by averaging individual images of the same imaging region obtained by steering scan lines at different angles. However, the number of useful images obtainable with a single transducer array is limited by its characteristics or the performance of an ultrasound imaging system employing it.If two linear array transducers are arranged such that they face each other, compound images can be reconstructed separately using each of them and those compound images can be averaged again. As a result, the images can be compensated for their depth-dependent characteristics. shows the imaging configuration used in this article where the two linear array transducers face each other. A slanted imaging area that makes an angle of θ to the upper transducer array normal by steering ultrasound beams is also indicated in dashed lines in the figure.The measurement of ultrasound speed has been a topic of interest since it can aid in tissue characterization, beamforming, scan conversion, and image registration (). Recently, the work of Duric et al. has been quite noteworthy. They employ a powerful, sophisticated approach to imaging SOS distribution within the framework of ultrasound computed tomography as well as diffraction tomography. Their experimental and clinical imaging results are promising. By surrounding a breast with 256 transducers positioned on a ring in a clinical prototype system called computed ultrasound risk evaluation (CURE), they imaged three parameters of the breast, i.e., SOS, attenuation, and reflectivity, and fused them together to present as a single pseudocolor image. The resolution was approximately 3 mm corresponding to three wavelengths at a central transducer frequency of 1.5 MHz.If we use two array transducers in transmission mode, SOS and attenuation images can be reconstructed by measuring the arrival time and amplitude of the received signal on one array transducer with insonification from the other array transducer. shows an imaging configuration for two opposing linear array transducers. By exchanging the transmitting and receiving roles of the two array transducers, the range of angles over which data can be acquired is doubled compared with the case of using a single array transducer and a plane reflector (To reconstruct SOS images from the arrival time of received signals, the backprojection algorithm is employed (). We will briefly explain the procedure used here. The time it takes for the transmit ultrasound signal from the nth transmit element to arrive at the receive element after traveling a distance of Lθ at an angle of θ with respect to the transmit array transducer normal is expressed aswhere v(x,y) is the SOS at an imaging point (x,y). Letting vo denote the SOS in the background medium, the relative TOF can be written asP(θ,n)=t(θ,n)−to(θ,n)=∫Lθdlv(x,y)−∫Lθdlvo.Letting a distribution, f(x,y), related to the SOS, be equal towe can represent it in terms of the projection data as follows:Then the SOS distribution, v(x,y), can be obtained from eqn where α is a scale factor. Due to the limited view angle available for our configuration, it turns out that the SOS tends to be somewhat underestimated. Thus, to remedy this underestimation problem, the scale factor is incorporated into the above expression. It is determined experimentally.Elastography is useful in imaging the mechanical properties of tumor or cancer in soft tissue such as the breast. To obtain a strain image, mechanical compression needs to be applied to the human tissue. Stain image formation proceeds by first estimating tissue displacements due to applied compression and then taking the difference of displacements along the axial or lateral direction (). Thus, displacement estimation is a crucial step in strain imaging.In this article, complex baseband signals are used to estimate the displacement between pre- and postcompression signals reflected from tissue (). The displacement is modeled using an allpass filter whose phase varies linearly with frequency. In this case, the linear phase delay is the same as the group delay. Also, both are identical to the time delay, τ. If an input, x1(t)=r(t)cos(ω0t+ϕ(t)), is applied to the filter, then the output, which is a delayed version of the input, is given byx2(t)=x1(t−τ)=r(t−τ)cos(ω0(t−τ)+ϕ(t−τ)),where r(t) is the envelope, ω0 is the radian center frequency, and ϕ(t) is the time-varying phase. Following demodulation, their complex baseband signals can be expressed asxb1(t)=r(t)ejϕ(t)xb2(t)=r(t−τ)ej(−ω0τ+ϕ(t−τ)).The phase difference between the two signals in a finite interval can be written asΔΦ0=arg<xb1(n)⋅xb2∗(n)>=ω0τ+ϕ(t)−ϕ(t−τ),where arg denotes the phase of the argument, <⋅>, the inner product, and ∗, the complex conjugate. Expanding ϕ(t−τ) in a first-order Taylor series yieldsSolving the above equation for τ, we obtainwhere ϕ′(t)=ωB(t) is the derivative of phase with respect to time, corresponding to the instantaneous frequency. Hence,where T is the sampling period. This term is responsible for reducing errors associated with the center frequency shift with increasing imaging depth due to speckle and attenuation characteristics. If the displacement between the two signals to be compared is large, their decorrelation becomes large, resulting in large errors in estimating the phase difference. To make the phase difference as small as possible, our method of displacement estimation proceeds by shifting the postcompression signal, xb2(t), by an amount corresponding to a previously estimated coarse displacement, δ, as in the following expression:The above process is graphically depicted in represent either the in-phase or quadrature components. Considering the fact that for proper operation, |τ−δ| should be maintained less than one half of the period of the signal of interest, this shifting operation leads us to obtain valid displacement estimates. Using the relationship that a temporal shift of δ is equivalent to a phase rotation of ej(−ω0δ) and expanding in a Taylor series, we can express eqn ΔΦδδ=arg[<xb1(t)⋅xb2∗(t+δ)>⋅ej(−ωoδ)]≈ω0(τ−δ)+ϕ′(t)(τ−δ).where τ can be correctly determined from ΔΦδδ as long as the latter is within the range [−π,π] so as to avoid aliasing. To obtain satisfactory displacement estimates, it is essential that δ should be as close to τ as possible. Since the displacement estimation starts at a depth of zero, as one gets deeper into the axial direction, the displacements of the current and previous data windows tend to be nearly identical. In subsequent experiments, to obtain the current displacement estimate, τ, we have used the previously estimated version of displacement, τ, for δ.In static palpation method, the compression is externally applied manually by slowly pushing a transducer on the tissue (). When using two array transducers that face each other, the spacing between them can be adjusted. By changing the spacing, the amount of mechanical compression applied to the breast can be varied. This makes it possible to obtain strain images.Because the spacing between the two array transducers is finely controllable electromechanically, the amount of compression used to obtain every image frame is available, paving the way for improving the elastographic signal-to-noise ratio (SNRe) and elastographic contrast-to-noise ratio (CNRe) values of strain image by employing adaptive strain estimation or stretching techniques (). Also, in the configuration where both array transducers face each other, the strain image can be obtained from each of both array transducers, thus making it feasible to apply the compounding operation to obtain better image quality. shows the block diagram of an experimental setup. a illustrates a configuration used to obtain both compound and strain images, where the two array transducers are connected to a clinical ultrasound scanner (Accuvix; Medison, Seoul, Korea) and the acquired data are transferred to a PC for signal processing. In strain imaging, the position of the lower array transducer is fixed, while the upper array transducer is movable up and down under the control of a stepper motor with a precision of 25 μm. b shows a configuration where the two array transducers are connected to a pulser and receiver (Olympus 5077PR; Olympus NDT, Waltham, MA, USA) to obtain SOS images. The individual elements of the two array transducers are connected to a multiplexer switchboard controlled by a PC. Two 38.4 mm wide, 192 element, 7.5 MHz linear array transducers are configured to face each other with a phantom placed between them. c is a photograph of the experimental setup used.To assess the image quality, we fabricated two types (A and B) of ultrasound phantoms in our laboratory. Phantom A for compound and SOS imaging has two urethane rubber cylinders with an SOS of 1450 m/s and phantom B for strain imaging contains a single cylindrical hard inclusion. The two cylinders used in making phantom A were taken out of a commercial multipurpose phantom (Model 539; ATS Laboratories, Bridgeport, CT, USA) and had diameters 7 mm and 10 mm. Both cylinders were embedded in a 40 mm thick background of plastic formed by mixing together plastic softer and hardener (M-F Manufacturing, Ft. Worth, TX, USA). The SOS in the background was 1400 m/s. The background material is mainly used to make artificial soft plastic fishing lures. Glass particles with a diameter of 27 μm (Spheriglass 2000 solid glass microspheres; Potters Industries, Malvern, PA, USA) were added in the background as scatterers. The particles had no color and accounted for 0.5% of the total weight. The two parallel cylinders were positioned in perpendicular to the transducer scan plane and were displayed in ultrasound image in the form of a circle. Because the cylinders that simulate lesion do not contain scatterers, they appear darker than the background in ultrasound B-mode image, and thus it is relatively easy to identify them.To obtain compound images, ultrasound beams were steered at angles of –14°, –7°, 0°, 7° and 14°. The radio-frequency (RF) data were acquired from each of both array transducers, and were transferred to a PC, where compounding was carried out. It is to be added that actually, the steering angle of 0° corresponds to the case of no steering. The compound images were obtained by geometrically aligning five datasets, each steered at different angles, using affine transform and averaging them. represent the B-mode and compound images, respectively. The images in the top row are obtained from the upper array transducer, those in the middle row are obtained from the lower array transducer, and the image in the bottom row shows the result of compounding the right panel images in the first and second rows. Here, the B-mode images are obtained at a steering angle of 0°, i.e., without steering.To assess the image quality between different images, the SNR was evaluated in the region marked by a rectangular box as shown in the left panel of the top row in . It is defined as the average to the standard deviation of the pixel values in the region of interest (). The SNRs for the top and middle row B-mode images obtained without steering were found to be 15.2 dB and 15.9 dB, respectively, and those for the compounded images in the top and middle rows were 19.0 dB and 18.9 dB, respectively. We can see that the compounding of the compound images obtained from each of both array transducers helps increase the SNR as expected because compound images obtained from each of both array transducers are essentially uncorrelated. The final compounded image is presented in the right panel of the bottom row in and is found to have an SNR of 21.9 dB.We also obtained SOS images for the same phantom that was used to obtain the compound images. In the SOS imaging, a multiplexer board was used between the two array transducers so that when one of the two arrays acts as a transmitter, the other can be configured to function as a receiver and vice versa. The multiplexer board can selectively connect each of the array transducer elements to the data acquisition system interfaced to a PC for data processing.The measurement was repeated for each of the 192 elements in the transmit array transducers, and after exchanging the role of transmission and reception, the entire process was repeated again. To reduce the data acquisition time, for every transmit element, the data were acquired from every fifth receive element starting from the center element. The interelement spacing of the transducer used is 0.2 mm. Because the data were acquired from every fifth transducer element, the SOS image was reconstructed with a resolution cell of size 1 mm × 1 mm. To reduce noise by averaging, the data acquisition process was repeated eight times.The TOF of an ultrasound signal emitted from a selected transmit element to reach receive elements that make angles of less than 34° to the transmit array normal (see ) was estimated using cross-correlation on RF data acquired at a rate of 125 MHz. The acquired RF data were interpolated to a sampling rate of 1.75 GHz to improve the accuracy of TOF estimation. By estimating the absolute TOF from the signal on some transmit element and the signal on some receive element of interest and also the relative time delay between the signal on that receive element and the signal on any other receive element of interest, using cross-correlation, we determined the TOFs from that transmit element to any other receive elements.a shows the resulting SOS image. In reconstructing the SOS image, we used a value of 1400 m/s for vo, which is the SOS in the background, and a value of 7.3 for α, in eqn . Although the cylinders whose SOS is different from that of the surrounding background can be identified upon close inspection of the figure, their circular edges are not well defined. The cylinders look like ellipses because the data are acquired over a limited angle range. The two cylinders with different diameters of 7 mm and 10 mm were fabricated to have the same SOS but it was found that the smaller one had a lower SOS. In b, the dotted lines represent the true SOS profile of the two cylinders. The solid and dashed lines depict the reconstructed SOS profiles along the lateral direction that pass through the centers of the left and right cylinders in a, respectively. It can be seen that there is still room for improvement in the overall performance of SOS estimation due to the fact that the data are acquired only over a limited view of the object. However, the experimental results show that we are able to obtain an SOS contrast necessary to differentiate between the cylinders and the background.For strain imaging, phantom B, which is an elasticity phantom with a single inclusion, was also fabricated in our laboratory. The stiffness of the inclusion was controlled by varying the amount of the plastic hardener and softener (M-F Manufacturing, Ft. Worth, TX, USA) that were mixed together. Phantom B had a 10 mm diameter cylindrical inclusion with a Young's modulus of 58.5 kPa embedded at a depth of 15 mm in the background with a Young's modulus of 11.1 kPa. The Young's moduli were measured using Erkamp et al.'s method (). The total height of the elasticity phantom was 37 mm. The elasticity phantom was placed between the upper and lower array transducers. As the upper array transducer was moved downward using a stepper motor in steps of 0.42% in strain, the RF datasets before and after applying compression were acquired from each of both array transducers. represent strain images obtained with each of both array transducers facing each other and the resulting compounded strain image is shown in the bottom panel of . Note that the cylindrical inclusion is of diameter 10 mm. The strain images were obtained by employing Yoon et al.'s method (In our present method, because the spacing between the array transducers can be finely controlled by a stepper motor, the adaptive strain estimation technique can be applied to the successive frame data obtained at different steps of compression (). However, the effect of averaging is not significant because there is large correlation between the strain images of the same region subjected to different amounts of compression applied by only one array transducer. On the contrary, we were able to improve the strain image quality by compounding the strain images obtained in opposite directions using each of the two array transducers.The strain image quality is evaluated by the SNRe and CNRe which are defined as follows (SNRe=20log10μbσbCNRe=20log10(μb−μi)2σb2+σi2,where the subscripts b and i indicate the background and the inclusion, respectively, and μ and σ denote the mean and standard deviation of the estimated strain in a selected region of interest, respectively. presents the SNRe and CNRe values computed to compare the quality of the compounded strain images when the applied strain is 0.42% (). The SNRe values were computed in region A indicated by the two black windows in and the CNRe values were computed for region A relative to region B indicated by the white window in that the compound strain images has somewhat better SNRe and CNRe values than either of the individual uncompounded strain images.To assess the effect of compounding on strain image quality under different amounts of compression, multiple consecutive image frames were acquired while compression was being applied mechanically. Every pair of two successive image frames was made to be different in the amount of compression by 0.42%. Images that are two frames apart were taken to make the amount of compression equal to 0.84% and their strain was estimated to construct strain image. Also, images that are three frames apart were taken to make the amount of compression equal to 1.26% and their strain is estimated to construct strain image. shows the effect of compounding as the applied strain is variably set to 0.42%, 0.84%, and 1.26%. The dotted lines represent the case of using either of the two array transducers while the solid line represents the case of compounding both array transducers. a and b plot the SNRe and CNRe values, respectively, as the applied strain is increased. The vertical error bars denote one standard deviation from the mean. The SNRe value of the compounded strain image has increased by more than 2.5 dB compared with the uncompounded strain images. It is known that in general, increasing the amount of applied strain to within some range tends to improve the SNRe value. It is found, however, that compounding of strain images is more effective in reducing noise (The strain image quality can also be improved by averaging over consecutive image frames based on persistence. Persistence is a signal processing method widely used to improve ultrasound image quality by averaging consecutive moving image frames and thereby reducing noise (). In the method, the noise can be suppressed considerably but the spatial resolution is degraded because the constituent strain image frames do not exactly match geometrically. Those image frames need to be geometrically matched using an affine transform. In general, in a manual palpation method, the amount of strain applied cannot be exactly estimated so the geometrical distortion cannot be compensated for exactly.On the contrary, in our proposed method, the amount of strain applied is exactly known and, thus, the distortion can be compensated for. plots the strain profiles along the scan lines that pass through the center of the cylinder in frames 1, 6, and 11 of strain images which are obtained successively, as a constant strain of 0.42% is applied from one frame to the next in all steps of the data acquisition process. The strain between frames 1 and 2 is 0.42%, that between frames 1 and 3 is 0.84%, that between frames 1 and 4 is 1.26%, and so on. The strain increases with increasing frame number.The strain values inside the cylinder are shown to be small. However, neither the falling nor the rising edges shown in b shows the result of performing a global stretching operation in a using the applied strain where both left and right edges are seen to be aligned. Averaging these aligned strain images results in a decrease of noise without degrading the image resolution. shows the result of applying global stretching to the RF data where the applied strain is 0.42%. The diameter of the cylindrical inclusion is 10 mm. The soft region is stretched to equal its original length, but the hard region is expanded because the latter has not been compressed much. Thus, the black and white levels are reversed so that the hard region appears to be brighter. This characteristic helps us better identify the hard region. Our method has the advantage that the amount of the total compression is available.We have investigated a new linear array transducer configuration for compound, SOS, and strain imaging. Its feasibility was confirmed by experiments with two types of in-house phantoms. The proposed method is suitable for imaging protruding objects such as a human breast placed between two opposing linear array transducers. In vitro images of compounding and SOS as well as strain are reconstructed. Although there is some distortion in the SOS images due to limited view angle, those three types of images can be used complementarily to aid in better diagnosis. Unlike computed or diffraction tomography that uses water to surround a breast, our imaging method is advantageous in that there is no need to correct for refraction at the surface of it since the transducers are in direct contact with it. The surface refraction is one of the major sources of error in SOS estimation. The data required for the proposed method can be acquired very fast if a dedicated hardware system that operates in real time is built. Therefore, the diagnosis can be made within a small amount of time without causing much discomfort to the patient.Micromechanics analysis on the microscopic damage mechanism and mechanical behavior of graphite fiber-reinforced aluminum composites under transverse tension loadingIn this paper, the transverse tensile behavior and microscopic damage evolution of graphite fiber-reinforced aluminum composites were investigated by numerical and experimental methods. Micromechanical models based on realistic and assumptive fiber arrangements were established. In these models, the progressive damage procedure of the matrix alloy and the interface was incorporated. The validity of the models was assessed by comparing the predicted stress-strain curves with the experimental ones. The microscopic damage behavior of the matrix alloy and the interface was revealed and its contributions to macroscopic mechanical responses were analyzed in detail. The interaction of different damage mechanisms was further discussed on the basis of numerical and experimental results. The influences of interface, matrix alloy, and fiber volume fraction on damage evolution and mechanical behaviors were parametrically studied on the basis of the verified micromechanical model to provide insights into the damage mechanisms of the composites.Continuous carbon fiber reinforced aluminum composites (CF/Al composites) possess high specific strength and stiffness, high thermostability, and low thermal expansivity []. In addition, the mechanical behavior of composites can be tailored to satisfy particular applications by tuning constituent properties and reinforcement morphology, such as fiber volume fraction and its orientation []. Therefore, CF/Al composites show potential for applications in aerospace, defense, and automobile engineering []. Numerous efforts have also been devoted to studying these composites []. To date, experimental studies have focused on the formation of an interface and its effect on the mechanical properties of CF/Al composites. It is generally recognized that interfacial reaction may result in the formation of a complicated interface []. For example, the brittle aluminum carbide (Al4C3) phase at the interface plays an important role in determining the mechanical properties of composites []. Particularly, an excessive Al4C3 phase results in a high interfacial bonding strength, which impedes interface sliding and causes the catastrophic failure of the composites []. Therefore, the dependence of mechanical behavior on interfacial properties should be clarified explicitly. However, no available methods can precisely predict the mechanical behavior of CF/Al composites based on their constituents properties, interface properties, and microstructural features []. In general, experimental methods require considerable amounts of human, financial cost, and time resources. Furthermore, the details of the damage propagation and fracture of the microstructures can be hardly revealed []. Hence, an accurate and effective approach must be developed to reveal the microscopic failure mechanism and to predict the macroscopic mechanical behavior simultaneously.A computational micromechanics method has been developed and applied to examine the damage process of fiber-reinforced composites. In comparison with classic homogenization techniques, this method can consider the influence of microstructure morphology, and present a visual damage evolution process, and provide an assessment of its effect on macroscopic behavior []. On the basis of a micromechanical model, Zhang et al. [] investigated the damage behavior of fiber-reinforced polymer composites in which the matrix and interface are described by a viscoelastic model and cohesive law, respectively. Vaughan et al. [] developed a micromechanics model to inspect the influence of interface decohesion and matrix plasticity on the transverse behavior of a unidirectional carbon fiber-reinforced epoxy composite. Maligno et al. [] investigated the local damage in unidirectional fiber-reinforced epoxy composite by a 3D micromechanics FEM model. The influence of the non-uniform distribution of fiber and interface property on damage behavior has been analyzed, and transverse and longitudinal tensile properties have been predicted. These studies have confirmed the important role of interface debonding and matrix failure on the transverse behavior of fiber-reinforced polymer composites. In comparison with the behavior of polymer matrix composites, the interface behavior of metal matrix composites is more complex because of a complicated interfacial structure formed during fabrication process. Recently, Xu and Qu et al. [] investigated the interfacial decohesion and sliding behavior of a SiC monofiber-reinforced titanium composite and established a novel cohesive zone model to explore the shear deformation and frictional mechanism for fiber push-out tests at an elevated temperature. On the basis of this work, Xu and Qu [] furtherly investigated the inelastic deformation of SiC monofiber-reinforced titanium composite under transverse loading-unloading condition. They pointed out that the primary deformation mechanism of this composite is fiber-matrix debonding induced by interfacial plasticity and damage accumulations. For a CF/Al composite, which has a complicated interface and constituent properties that differ from those of a polymer matrix composite [], quantifying its microscopic damage initiation and evolution process presents a great challenge []. To the best of our knowledge, research on microstructure progressive damage and its influence on the mechanical behavior of CF/Al composites is limited.In this study, numerical analysis and experiments were carried out to investigate the mechanical behavior and microscopic damage progression of CF/Al composites during a transverse tension process. Based on RVE with realistic and assumptive fiber arrangements, micromechanical models considering the progressive damage of a matrix alloy and an interface were developed for the first time, and their validities were assessed by comparing the calculated stress-strain curves with the experimental ones. The damage states of the matrix alloy and the interface at different tensile stages were revealed, and their influences on the mechanical response of the composite were analyzed in detail. The microscopic damage mechanism of the composite was further discussed on the basis of the numerical results and the fracture morphology. In addition, the influences of interface, matrix alloy, and fiber volume fraction on microscopic damage and mechanical behavior were parametrically evaluated to provide in-depth insights into the failure mechanism and a guidance for the design of these composites.The material used in this study was the unidirectional CF/Al composite and the as-cast Al–Mg–Si alloy (ZL301). The alloy compositions (wt.%) are illustrated in . Graphite fiber M40J, whose nominal properties given by the manufacturer are shown in The CF/Al composite was fabricated through vacuum-assisted liquid metal infiltration method []. The cylindrical sample of ZL301, which was designed in accordance with GB/T228-2002, was also prepared under the same fabrication condition. In accordance with ASTM-D3552, the CF/Al composite was cut into plate tensile samples perpendicular to the fiber axis. The samples were annealed at 340 °C for 30 min to reduce the residual stress between the fiber and the matrix alloy. A pure aluminum sheet (thickness: 0.5 mm) was wrapped around the grip section of the composite samples to prevent grip failure. The appearance of the composite sample and the ZL301 alloy sample for uniaxial tensile testing is shown in . The CF/Al composites and the ZL301 alloy were subjected to uniaxial tensile testing on an electronic testing machine (INSTRON-8801) at a constant loading rate of 0.5 mm/min. The microhardness of the ZL301 and the matrix alloy of the composite were measured using a STRUERS Vickers hardness tester with a load of 245.3 mN and a dwell time of 10 s. The microstructure of the composite was observed under a scanning electron microscope (SEM) (Quanta200). The morphology characteristics of the fracture surface were inspected with NovaNano SEM450. shows the microstructure of the CF/Al composites along the transverse direction and the interfacial micromorphology. In a, the matrix alloy was free of microscopic porosity or microcrack, and the distribution of the graphite fiber in the matrix alloy was homogeneous. b illustrates the transmission electron microscopy (TEM) observation of the interface between the graphite fiber and the matrix alloy. A thin and clean interface formed in this composite, and no microporosity was observed in the interfacial region. A block Al4C3 phase with a length of less than 50 nm was also found in the interface and identified through selected-area electron diffraction (SAED). All the fibers in the SEM micrograph were identified using the Image Pro Plus, and their area ratio in the total area of the micrograph was calculated, accounting a fiber volume fraction of 55%. The matrix and the fibers were considered a continuum without a microvoid to construct a RVE model based on the microstructure, and the interface was homogeneous with zero thickness. Based on these assumptions, the following RVE models were set up with a fiber volume of 55%: (i) the Sq-RVE model had a square array of fiber packing geometry (a); (ii) the Hex-RVE model had a hexagonal array of fiber packing geometry (b); (iii) the Re-RVE model had a realistic fiber distribution similar to that in the microstructure (c). In the first two RVE models, the packing geometry assumed a uniform distribution and a periodic packing of the fibers. In the last model, the packing geometry considered a non-uniform distribution of the fibers, and this may influence the mechanical response at local and global levels []. In the next section, the computational accuracy of these RVE models was assessed by comparing the calculated stress-strain curve with the experimental ones. presents the global dimension of the RVE models. The fibers in the RVE had a circular cross-section with a diameter of 6 μm; the out-of-plane depth (t) of the RVE models was set as 1 μm because this parameter is not very critical when periodic boundary conditions are applied []. The commercial software ABAQUS/Standard was used for FEM calculation. Eight-node hexahedral brick elements using reduced integration (C3D8R) were selected to discretize the RVE models.Three different mesh models with element lengths of 0.1 (very fine mesh), 0.2 (fine mesh) and 0.4 μm (coarse mesh) were investigated to assess the effect of mesh size on micromechanical simulation studies. For comparison, the distributions of equivalent plastic strain simulated with different mesh models are illustrated in a, b, and 4c. The simulation using the RVE model with the very fine and fine mesh size were precisely the same, but were different from that obtained from the coarse mesh model. The simulation results obtained from the coarse mesh model could hardly capture the sufficient details because of the insufficient quantity of elements between neighboring fibers. However, the stress-strain curves obtained from the three mesh models almost overlapped with one another (d). These finding implies that mesh size slightly influenced the calculated mechanical response. The RVE model discretized with mesh size of 0.2 μm was selected in the following analysis in this work, considering the balance of computational accuracy and cost. Periodic boundary conditions were applied to the RVE models as follows [{u→X(0,Y,Z)−u→X(W0,Y,Z)=U→Xu→Y(X,0,Z)−u→Y(X,L0,Z)=U→Yu→Z(X,Y,0)−u→Z(X,Y,T0)=U→Zwhere X, Y, and Z are the coordinate axes, and U→i (i = X, Y, Z) is the displacement applied to the nodes lying on the face in X = W0, Y = L0 and Z = T0, respectively. u→i (i = X, Y, Z) denotes the displacement in X, Y, Z directions, respectively. Transverse tension loading (along X-axis) was performed by applying a displacement U→X=(+δ,0,0) on the nodes lying on the boundary face (X = W0). The displacement and reaction force (fjX) of these nodes were used to calculate the equivalent stress-strain curves,A proper constitutive and damage model of the fiber, the matrix, and the interface in the micromechanical model should be established to describe the deformation and damage response of the composites [ showed that the transverse fracture strain and stress of the composite are less than 0.2% and 30 MPa respectively, which remained considerably below the fracture elongation and strength of the fiber (). It can be expected that the fibers unlikely fracture during the transverse tensile process. This can also be verified by the fracture surface of the composite where no fiber breakage was found (). Therefore, the fiber could be modeled as a linear elastic and transverse isotropic material, and no damage model has been involved in this study. Young’s modulus of EL = 377 GPa (longitudinal), ET = 7.6 GPa (transverse), and Poisson’s ratio of νf = 0.26 were used to define the elastic behavior of the fibers []. The mechanical behavior as well as the damage and failure model of the matrix alloy and the interface were discussed in detail as follows.Numerous experimental studies have indicated that the mechanical properties of the matrix alloy in CF/Al composite differ from those of the corresponding aluminum alloy []. In our study, the microhardness values of the as-cast ZL301 and the matrix alloy were measured (). The average microhardness of the matrix alloy was higher than that of the as-cast ZL301 alloy, resulting in a hardening factor of 1.37. The as-cast ZL301 alloy prepared at the same condition as the composite was tested by the uniaxial tensile experiment. The black line in depicts the experimental engineering stress-strain curve of the as-cast ZL301alloy. The low fracture strain and strength might be mainly caused by the coarse grain morphology of the as-cast ZL301 alloy (a), leading to a fracture without evident local necking appearance (b). The in-situ tensile behavior of the matrix alloy was phenomenologically evaluated by scaling the stress level of the as-cast ZL301 alloy with the hardening factor of 1.37. This method has been successfully used to determine the in-situ properties of matrix alloy in metal matrix composites []. The in-situ stress-strain curve of the matrix alloy is represented by the red curve in , in which the elastic modulus, yield and ultimate strength was improved accordingly whereas the yield strain and fracture strain values keeps unchanged. Therefore, the difference in damage and fracture behavior between the as-cast alloy and the matrix alloy was not considered in this work.The matrix alloy was modeled as an isotropic elastic-plastic material with an equivalent strain failure criterion. In , the slope of a-b segment represents Young’s modulus of the matrix alloy, that is Em=tanα=81.7GPa. Poisson’s ratio of the matrix alloy was assumed as νm=0.33. The plastic deformation behavior was described by the yield strength σY, strain hardening modulus EmH, and plastic strain ε‾pl according to Ludwik’s law. These parameters were calculated from the in-situ stress-strain curve of the matrix alloy (the b-c segment in ), as follows: σY=79MPa, EmH=∫bctanβdεεbc=24.9GPa. It is assumed that the matrix alloy possesses the same damage and fracture performance as those of the as-cast alloy (). Local necking appearance during the tension process was inapparent (b), considering the small plastic deformation stage on the stress-strain curve. The effect of local necking on the stress softening behavior (after point c in ) could also be neglected. The material softening and stiffness degradation of the matrix phase was assumed to be mainly induced by the damage accumulation in the form of microscopic void nucleation, growth, and coalescence. A ductile damage model was utilized to predict the damage onset and evolution behaviors. In this model, the damage initiates as the equivalent plastic strain reached the critical value ε‾0 (). As plastic strain increased, damage accumulation led to stress softening and elasticity degradation. Based on the definition of equivalent plastic displacement u‾pl (u‾pl=L⋅ε‾pl, where L and ε‾pl are the element characteristic length and plastic strain, respectively), a linear softening law was adopted to formulate the damage evolution progress. With damage accumulation, the damage variable (D) increased monotonically from 0 to 1, as defined by the following formula [where ε‾f is the equivalent plastic strain corresponding to failure initiation. Based on the stress-strain curve of the matrix alloy, the equivalent plastic strains of ε‾o and ε‾f were set as 0.16% and 0.8%, respectively.Interfacial damage is the most typical failure mechanism under transverse loading condition, significantly affecting mechanical responses. In this study, the cohesive zone model [] was utilized to describe the decohesion behavior between the graphite fibers and the matrix alloy. The constitutive behavior of cohesive zone elements is governed by bi-linear traction-separation law [a. This law assumes that the initial response is linear before the interface damage is activated, and can be expressed as follows,where K denotes the interfacial elastic stiffness, tn/s/t indicates the normal and shear stress component, and δn/s/t represents the normal and shear displacement component.The following maximum nominal stress criterion was used to determine the onset of interface damage,Where, tn0, ts0, and tt0 are the interfacial normal and shear strength. The Macaulay bracket ⟨⟩ implies that a purely compressive stress cause no damage initiation.The interfacial shear strength was measured by a fiber push-out testing method []. A graphite fiber bundle with a uniform length of 2.5 mm embedded in the ZL301 alloy was pulled out using an Instron 5540 testing machine. b presents the pull-out force-displacement curve. The interfacial shear strength was approximately calculated with ts/t0=Fmax/n⋅πdfL by measuring the number of abstracted fibers (n) and their average length (L), resulting in an interfacial shear strength of 9.5 MPa. For the CF/Al composites, the interface bonding strength is extremely weak, and the transverse tensile property is closely and directly related to the interfacial bonding strength []. Therefore, the interfacial bonding strength tn0 = 16 MPa was adopted in our study based on the transverse tensile tests conducted in another study []. The interfacial elastic stiffness is defined as K=(Em+EfT)/2kdf, where Em and EfT is the elastic modulus of the matrix and the fiber, and k is assumed to be the ratio of the interface thickness to the fiber diameter (df). The df was set as 6 μm and the Em and EfT were constant in the numerical model. Hence, an increase of k would lead to an increase in the interface thickness as well as a decrease in the interfacial elastic stiffness K. By adjusting the value of k, the influence of interfacial elastic stiffness on transverse tensile behavior was parametrically investigated in the next section.As the interface damage was activated, a linear degradation in the elastic stiffness was determined by a scalar interface damage variable (d) monotonically increasing from 0 (damage initiation) to 1 (ultimate failure), as depicted in a. The traction-separation behavior of the damaged interface was evaluated by the following relations [The damage variable d is defined in a damage evolution model based on the energy dissipated Gc=0.5δeqf⋅teq0, where δeqf and teq0 are the equivalent displacement at interfacial failure and the equivalent stress at interfacial damage initiation, respectively. According to most works in metal matrix composite by Needleman [], the equivalent displacement δeqf is typically assumed to be 7–9 times that of the critical displacement δeq0 corresponding to teq0.Before other results are discussed, the validity of the micromechanical models established in the above section should be examined. In this section, the micromechanical models based on the three RVE models, i.e., Sq-RVE, Hex-RVE, and Re-RVE, are utilized to calculate the stress-strain curves under the transverse tensile condition. a presents the results of the calculated curves together with the experimental stress-strain curves. The elastic stages of the calculated curves (before the point A) almost overlap, and are in coincident with that of the experimental ones. After point A, however, the curves calculated by the Sq-RVE and Hex-RVE models begin to deviate from the experimental curves, especially as the strain exceeds 0.085% (point B). As a result, the tensile strength and the fracture strain are noticeably overestimated. For the Re-RVE model, the calculated curve can track the global stress-strain curves of the composite, and the predicted ultimate strength and fracture strain are closer to the experimental ones.The calculation errors of the ultimate tensile strength (UTS), the elastic modulus (E, at the strain of 0.07%) and the elongation (δ) by the different RVE models are presented in b. For all the RVE models, the calculation error of δ is relatively high, which can be attributed to the assumption that the matrix alloy is a continuum without microvoid in these RVE models. In fact, the possibility of microporosities in the matrix alloy likely reduces the fracture strain of the composites, which are not considered in this study. Nevertheless, the calculation error of the UTS and E of the Re-RVE are −0.56% and −0.12%, respectively, which are significantly smaller than those of the two other RVE models. Based on the comparison results of the stress-strain curves and the calculation errors, our conclusion is that the Re-RVE model is more feasible than the two other models for predicting the mechanical behavior of the composites.The damage and mechanical behavior of fiber-reinforced composites have been simulated widely by using the RVE model in which fibers are equally spaced and arranged (square or hexagonal) in the transverse cross-section []. In recent years, however, numerical analysis on a RVE with random fiber distribution of the real composites has been the current trend of work []. In the above section, the FE simulation based on the Re-RVE model, where the real fiber arrangement is included, can predict the tensile behavior and properties more accurately than the one based on Sq-RVE and Hex-RVE models. In the following section, hence, the FE simulations are performed on the region in the Re-RVE rather than on the region in the Sq-RVE and Hex-RVE models. shows the computational results of the microscopic damage initiation and evolution of the matrix alloy and interface during the transverse tensile process. At the first tensile stage (the O-A segment in a), an initial damage is found at some local interface (a). As the strain increases, the interfacial damage accumulates and leads to an onset of the interfacial failure (d = 1), as depicted in b. The onset of interfacial failure indicates that some fiber/matrix begin to debond at a strain of 0.0652%, resulting in a slight reduction in the tangent modulus as denoted by point A in a. Thereafter, the tensile stress increases monotonously, but the tangent modulus of the curve decreases continuously (A-B segment in a) because of the development of interfacial debonding. At the strain of 0.0891%, the local damage initiation of the matrix alloy is found at the vicinity of the interface (c), leading to a significant decrease in the tangent modulus (denoted by point B in Afterward, the increase in strain leads to matrix damage accumulation and macroscopic stress increases slowly as depicted by the B–C segment in a. When the tensile strain reaches 0.1528%, the matrix damage variable D in d reaches 1.0 in some local regions, indicating that matrix alloy failure occurs in the vicinity of the interface. At the final tensile stage, matrix alloy failure exacerbates at the region near the interface, especially in the interstices of fibers. The interfacial debonding is linked by matrix cracks at the strain of 0.1847% (e). This phenomenon leads to the ultimate fracture of the composite and the corresponding peak stress (denoted by point C in a), indicating that the transverse fracture is directly induced by matrix alloy failure. In addition, the interfacial property may also play an important role in determining the mechanical properties of the composite because the matrix alloy failure is stimulated by the interfacial debonding. In the next section, the influence of the matrix and interface properties on the transverse tensile behaviors was further discussed. presents the typical fracture surface of the CF/Al composite under the transverse tension condition. The fracture surface exhibits two failure characteristics, i.e., the interfacial debonding and the matrix alloy fracture. The ultimate fracture mode is similar to the above computational results, which provide a good verification for micromechanical simulation. Based on the combined computational and experimental results, our conclusion is that the matrix alloy failure in the vicinity of the interface, which is stimulated by interfacial debonding, is the main failure mechanism of the CF/Al composites during the transverse tension process.The original interfacial strength in the micromechanical model was scaled by factor of 2 and 0.5 to assess the influence of interfacial properties on the tensile behavior. The calculated stress-strain curves are presented in a. The enhancement of interfacial strength improves the UTS significantly. For example, the peak stress with the high interfacial strength is equal to 43.27 MPa, which is 1.53 times higher than that with the original interfacial strength and 2.15 times higher than that with the low interfacial strength. Moreover, the increase in interfacial strength enlarges the scope of the elastic segment and improves the fracture strain at the curves. This result implies that the failure of the interface and matrix alloy is greatly retarded in the case of the high interfacial strength. presents the damage state of the interface and the matrix alloy under the low and high interfacial strength conditions. At the same strain of 0.0652%, the interface failure regions in a are greatly enlarged compared with those in b. By comparison, no interface failure is found as shown in b. At the same strain of 0.1528%, more matrix failure regions are found in the vicinity of the interface in c, whereas the degree of matrix damage is less than that in d. Therefore, the high interfacial strength is advantageous to the inhibition of the interface debonding and matrix alloy failure and to the improvement of the transverse tensile strength and fracture strain of composites.b shows the stress-strain curves calculated with the original interfacial stiffness and with the high (a factor of 2) and low (a factor of 0.5) interfacial stiffness. The UTS increases slightly as the interfacial stiffness increases, whereas the variation in the fracture strain is not obvious. However, the elastic segments in these curves exhibit different lengths and tangent slopes. As the interfacial stiffness increases, the elastic modulus increases, whereas the scope of the elastic segment of the curves reduces gradually. This finding implies the premature onset of the interface failure in the case of the high interfacial stiffness. This observation can be verified in , that illustrates the interface damage state simulated with the low and high interfacial stiffness. At the same strain of 0.0652%, no interface failure is found in a, whereas more interfacial debonding regions are observed in presents the matrix failure initiation state and its corresponding tensile strain under the different interfacial strengths and stiffnesses. The comparison of c reveals that the tensile strain related to the matrix failure initiation increases significantly as the interfacial strength increases, As a result, the fracture strength and strain greatly improved (d, e and 14f shows that the tensile strain associated with the matrix failure initiation remains almost the same regardless of the different interfacial stiffnesses. Therefore, the influence of interfacial stiffness on matrix failure is unobvious in comparison with that of interfacial strength. Matrix failure dominates the eventual fracture process as discussed in the above section. As such, the influence of interfacial stiffness on the UTS and fracture strain is also unapparent (All the stress values on the stress-strain curve for the original matrix alloy (the blue line in ) are scaled by a factor of 2, to obtain the different mechanical properties of the matrix alloy while the strain values on this curve remain unchanged. This phenomenon results in a stress-strain curve for matrix with high property (the red line in a) in which the elastic modulus, yield stress, and ultimate strength are magnified by two times. Similarly, the stress-strain curve for matrix with low property is generated by scaling with a factor of 0.5, which is shown by a black line in a. The critical strain of damage initiation and failure in the three matrix property curves remains constant because the strain values in these curves remain unchanged. The transverse tensile stress-strain curves at the different matrix property conditions are predicted and compared by applying the elastic modulus and strength parameters of these curves in the micromechanical models (b). All the curves display two deformation stage, i.e., the linear elastic (interval I) and the inelastic deformation (interval II) stage. The two stage are divided by the strain at which interfacial debonding occurs. At the linear elastic stage, the stress-strain curve with the high matrix property exhibits a high elastic modulus of 33.23 GPa, which is 1.34 times higher than that with the original matrix property and 1.66 times higher than that with the low matrix property.The inelastic stage in these curves can be further divided into three sub-intervals, which corresponds to the interfacial debonding progression (i), matrix damage accumulation (ii), and matrix failure progression (iii), as shown in b. At the same subinterval, the tensile stress exhibits different variation modes because of the difference in the stress-strain characteristic of the matrix alloy. In comparison with the ultimate strength obtained from the original matrix property, the UTS with the high matrix property increases by 42.30%, whereas the UTS with the low matrix property decreases by 20.21%. Conversely, the fracture strain on these curves almost remains the same. Despite the different matrix properties, the strains corresponding to the initiation of interfacial debonding, matrix damage, and matrix failure are identical. This finding suggests that the influence of the matrix alloy property on damage initiation and evolution is inevident because the critical plastic strain related to the damage initiation and failure of the matrix alloy remains unchanged in the micromechanics model. Hence, the initiation and evolution of microscopic damage still follow a similar rule as described in Section , but these phenomena would not be discussed here anymore.To obtain the Re-RVE model with Vf=70%, the distances between the neighboring fiber centers (c i.e., the Re-RVE model with Vf=55%) were uniformly scaled by a factor of 0.88, but the fiber diameter and the relative orientation between the fibers remain unchanged. Accordingly, the globe size of the Re-RVE with Vf=70% was 22.1μm×19.1μm (a), which is 0.88 times reduced as compared with the Re-RVE with Vf=55% (c). Using this method, the Re-RVE model with Vf=40% (b) is generated with a scaling factor of 1.14, in which the globe size is 28.6μm×24.7μm. Micromechanical analyses on these Re-RVE models with different fiber volume fractions were carried out to investigate the effect of the fiber volume fraction on the mechanical response and damage evolution behavior during the transverse tension process by applying the same periodic boundary conditions and the constituent property condition.The tensile stress-strain curves simulated at different fiber volume fractions are presented in , and the calculated mechanical properties are listed in . The elastic modulus, ultimate strength and fracture strain decrease significantly as the fiber volume fraction increases. This result is in contrast to that described in a previous study [], which revealed that the transverse strength increases as the fiber volume fraction increases because a perfect interfacial bonding is assumed. In the case of an imperfect interface, the ultimate fracture of the composites is the result of the development of the interface debonding and the matrix alloy failure in the vicinity of the failed interface, as being clarified in Section . Therefore, the volume fraction of interface region is expected to play an important role in determining the mechanical property of the composites. The increase in fiber volume fraction likely leads to an increase in the volume fraction of the interface region. These vulnerable interface regions are liable to debonding and induce a serious matrix failure, which will reduce the bearing capacity of the composites and result in a low ultimate strength.The elastic and inelastic stages on these stress-strain curves exhibit different characteristics, implying that the microscopic damage and failure state are also affected by fiber volume fraction. For the composites with Vf = 55%, the interfacial failure is initiated when the strain reaches 0.0652% (b). For the composites with Vf = 40% and Vf = 70%, the strains corresponding to the interfacial failure are 0.0574% and 0.0744%, respectively (a and b). At the elastic deformation stage, the high fiber volume fraction means that enough interfacial regions bear the tensile loading. Therefore, an increase in the fiber volume fraction can impede the interfacial debonding germinating at the initial tensile stage. At the inelastic deformation stage, however, the strain associated with the matrix failure initiation with Vf = 40% and Vf = 70% are 0.1697% and 0.1516%, respectively (c and d). Under the low fiber volume condition, the interstice regions between neighboring fibers are enlarged, and the space is enough for the matrix damage to propagate and accumulate during the inelastic deformation stage (c). Hence, as a result of the matrix damage accumulation, the matrix alloy failure in the vicinity of the failed interface is postponed accordingly, leading to high ultimate strength and fracture strain (A microstructure-based micromechanics model was developed to analyze the transverse tensile and progressive damage behavior of the CF/Al composites. According to the computational and experimental results, the interaction mechanisms of interfacial debonding and matrix alloy damage evolution were visually revealed and their influences on the mechanical behaviors were investigated in detail. The main conclusions could be summarized as follows:During the transverse tension process, interfacial damage and debonding initially occur at the local fiber surface where the inter-fiber distance is small. Then, they induce the matrix alloy damage and failure successively as the tensile strain increases. Lastly, local interfacial debonding is linked by matrix crack propagation, which causes the fracture morphology to have the characteristic of interfacial debonding and matrix alloy fracture.The transformation from elastic to inelastic deformation is induced by interfacial debonding due to the accumulation of interfacial damage. At the inelastic stage, the interaction of interfacial debonding and matrix failure in the interstice of fibers causes a decrease in the tangent modulus of the stress-strain curve and results in the transverse failure of the composite.High interfacial strength is conducive to the retardation of interfacial debonding, which in turn inhibits matrix damage and failure. Hence, an increase in interfacial strength can enhance the ultimate strength and fracture strain of the composite. Conversely, the influence of interfacial stiffness on the mechanical properties is unapparent.As the mechanical properties of matrix increase, the elastic modulus and the ultimate strength significantly improve, whereas the variation in fracture strain is inevident. This finding can be attributed to the assumption that the plastic damage parameters of the matrix alloy remain unchanged in micromechanics analysis.As the fiber volume fraction decreases, the volume fraction of the vulnerable interface region decreases, and the matrix alloy failure process is postponed. Both events can promote the transverse bearing capability of the composite and result in high ultimate strength and fracture strain.Thermal behaviour of phase-change slurries incorporating hydrated hydrophilic polymeric particlesThe application of slurries containing phase change materials (consisting of hydrated hydrophilic polymeric particles) to both the storage and the transmission of thermal energy at temperatures below ambient has been investigated. Phase change due to freezing has been investigated experimentally for oil-based slurries employing hydrophilic copolymer particles in concentration of 1%, 5%, 10% and 25% (by volume). The principle findings are: At temperatures above the phase transition temperature the presence of particles causes a significant increase in the measured heat transfer coefficient for concentrations ⩾10%.There is a significant interaction of particles at the heat transfer surface.Under high flow rate conditions with phase change occurring, the heat transfer coefficients are enhanced considerably (i.e. by about 80%) when compared with the support fluid alone or with the support fluid incorporating similar volume fractions of non-active particles.hydraulic diameter of rectangular duct (m)ratio of cross-sectional area of the flow to wetted perimeter (m)Nusselt number, i.e. ratio of convection to conduction heat transfer in a fluid slab (=hD/k)Prandtl number, i.e. ratio of molecular momentum and thermal diffusivitiesReynolds number, i.e. ratio of inertia to viscous forces (=ρVD/μ)Stephan number, i.e. ratio of sensible heat capacity to latent heat capacitypertaining to a solid–liquid mixture or slurrypertaining to conditions at the heat transfer surfacepartially cross-linked high-density polyethyleneThe transient fluctuations that occur in the aggregate electrical demand of a generating utility counteract efforts to improve the total system efficiency. Demand side management techniques have been widely applied to reduce such fluctuations, including the conversion of electrical energy to thermal energy during periods of low demand for use during peak demand periods. For thermal processes requiring energy above ambient temperature, it is feasible to use sensible heat due to the existence of stable storage media and efficient methods of heating at the required temperatures. However where energy is required at temperatures below ambient, the efficiency of cooling limits the use of sensible heat and so latent heat storage is desirable. Conventional cold-storage systems use ice banks to store cooling energy at 0 °C in order to capture the high latent heat of fusion of water. The rate of discharge for such stores is limited by the thermal resistance of ice and the thermal capacity of secondary coolants (such as glycol solutions).In the above context, this research programme investigated the use of hydrophilic copolymers as a means for overcoming the limitations of current cold-storage technology. Such materials are chemically stable, have the capacity to absorb and retain up to 95% by mass of water (or other aqueous solutions) irrespective of how a given sample is subdivided. Furthermore, the thermal properties of the polymers in their hydrated state resemble those of the free hydration fluid, including the latent heat of fusion, and again the particles have been shown to be stable through repeated (<100) freeze–thaw cycles. By supporting granulated hydrated materials in a non-freezing non-aqueous fluid, the resultant mixture provides a medium for cold storage that can be pumped to the point of demand, and one which is not limited by the thermal resistance of an encapsulating material. A system of mobilised particles could therefore be employed as a high thermal density cold-storage system yielding rapid rates of charge/discharge and exploiting the availability of time-of-use electricity tariffs. Furthermore the ability to pump the slurry to and from the thermal load removes the need for intermediate heat exchangers, and results in a highly effective thermal transfer fluid. This may facilitate the introduction of non-CFC primary refrigerants that require remote siting from the thermal loads. These applications could provide energy efficiency benefits, reduced CO2 emissions and more controllable air conditioning and refrigeration systems.The following aspects concerning the utilisation of hydrophilic materials for these potential applications have been studied: (i) the physical properties of the materials in their hydrated state, (ii) methods of “fluidising” the material in a high-density store, and (iii) the heat transfer properties of hydrophilic-based slurries while undergoing phase transition. This paper reviews the relevant literature and reports the main findings associated with (iii).m (largest copper particles), and in concentrations from 2.3% to 10.7% (by volume). The rheological behaviour of the suspensions was pseudoplastic (as it applies generally to concentrations over about 7% and as a result of the small particle sizes used in this investigation). A horizontal tube heat exchanger 12.7 mm internal diameter was used, with the heat being applied by the application of steam in the outer annulus. (Results for water were found to be in good agreement with standard correlations for 60,000⩽Re⩽150,000). The following correlation was derived (with the viscosity value being that of the suspension as measured during each test run via an inline tube viscometer):for 14,000⩽Re⩽14,000, 3.4⩽Pr⩽12.7, 0.35⩽Ks/Kf⩽583, 282⩽D/d⩽10,500 and 0.09⩽Cps/Cpf⩽0.22.Close agreement was achieved with data sets from two independent investigations.m to 1.0 mm in volumetric concentrations of 1–10%. The heat transfers occurring in horizontal tubes of 14, 19 and 25 mm diameter were analysed. The results deviated significantly from those of Salamone and Newman for 8000⩽Re⩽50,000, 0.01⩽φ⩽0.1 and 0.0024⩽d/D⩽0.071.This correlation fitted the experimental data to within ±15%. For particle diameters of >0.35 mm, a greater heat transfer coefficient was achieved than that for water alone; the degree of enhancement was fairly independent of particle size, pipe diameter and the volume fraction of the solids. Conversely for particle diameters of <0.15 mm, reductions in the heat transfer coefficient occurred for 6000⩽Re⩽15,000. Two orthogonal diametric temperature profiles were taken in the planes orthogonal to the flow direction, where one was arranged to be parallel with the ground (“horizontal”) and the other normal (“vertical”). These showed a symmetrical profile in the horizontal direction at all Reynolds numbers, but the vertical profile became increasingly asymmetric as Re decreased. At Re=7500 and Re=4500 it was observed that the temperature profiles were almost linear, suggesting that the particles had settled and formed a moving bed where the heat transfer occurred by conduction alone. Harada et al. This work was extended to suspensions consisting of glass beads (of 0.35, 0.5 and 1.0 mm) in rectangular ducts Again at low Reynolds numbers it was found that the vertical temperature profile was asymmetric and a two-layer model was developed. This employed a correlation giving the thickness of the stationary bed based upon the system Reynolds number, and unlike the correlation for tubes the flowing part was considered to be turbulent.The above investigations each used particles with high settling velocities, which inhibit detailed analysis of heat transfer enhancement at low flow rates. Lui et al. making it a candidate for further investigations for phase-change slurries.) The particle sizes used were 3.2 and 1.3 mm with solids concentrations (by volume) from 0% (i.e. a Newtonian fluid) to 45% (i.e. a non-Newtonian fluid exhibiting a very non-linear shear–stress/shear-rate characteristic) flowing in a 6 m tube of 23.98 mm diameter. Flow rates ranged from 21.2 to giving Reynolds numbers of 28,000 to 200,000. All heat transfer tests were for heating the fluid; the heat input being provided by an electrical heater along the length of the test section. Several interesting results emerged.The first was that reductions in the pressure drop were related to particle size, volumetric concentration and flow rate. For example, for all concentrations of <30% and a flow rate of 65.6 kg/min, reductions in the pressure drop of a few percent occurred relative to water alone. For particle sizes of 3.2 mm, pressure drop reductions were only present at concentrations of less than 5% and, in general, larger particles were characterised by relatively high pressure drops. Dramatic pressure drop reductions were measured if small quantities of Separan (slip additive) were added. For example, at a flow rate of 65.5 kg/min with 65 wppm Separan, the pressure drop was observed to be 73% less than that for water alone; a 70% reduction applied for a 15% volumetric concentration (of 1.3 mm particles) and this did not diminish to zero until particle concentrations exceeded 40%.The effect of particles on heat transfer coefficients was reported in terms of the Stanton number (). For particle sizes of 3.2 mm, increases in the Stanton number were observed at all concentrations up to ∼35% for flow rates between 32 and 86.4 kg/min. This enhancement increased with concentration, and for a given concentration rose with flow rate. For φ=30%, the Stanton number increased by 6% for a flow of 32 kg/min and rose by 12% for a flow of 86.4 kg/min. Conversely, for the 1.3 mm particles, volumetric concentrations of >10% yielded a decrease in the Stanton number; a maximum reduction of 15% occurred at a 20% solids concentration and a mass flow rate 63.6 kg/min.The use of phase-change slurries for thermal energy transmission and/or storage has been suggested and investigated by Kasza and Chen Despite the feasible performance gains suggested by m particles were used for the φ=5% and φ=10% tests, while mixtures of 100 and m particles were employed for the φ=15% and φ=20% tests. This clearly will have had an effect on the viscosity of the mixture due to the scaling effect of φmax which increases as the particle size distribution increases.These findings were based upon the behaviour of the wall temperature of the heat transfer test section measured in the direction of fluid flow. In all cases the rise in wall temperature, along the test section's length, was found to be reduced by the addition of phase change particles. A comparison with a single phase fluid, of the same ρ, v, k and Cp as the suspension, indicated that the local heat transfer conditions were being enhanced along the length of the test section. The degree of enhancement was found to be fairly independent of solids concentration above 10% and the wall temperature rise was reduced by ∼50% along the whole length of the test section.This work also found that the bulk Stephan number (Stem), defined (i.e. the ratio of sensible heat capacity to the latent heat capacity) was a critical factor. As Stem increased the rise in wall temperature decreased. Experimental data were compared by Goel et al. The phase change occurred as soon as the suspension entered the test section and at exactly one temperature.The particles were totally homogeneous (the particles in the test consisted of 30% by mass of C20H42).No particle–particle interactions occurred.Limited tests were performed to investigate the effects of particle diameter. It was found that, for φ=5% and φ=10%, the larger m particles caused a reduction in wall temperature rise by 15%. Goel et al. (see later) to estimate the effective thermal conductivity. Zhang and Faghri In Region 1, the phase change occurred only in the laminar sub-layer.When phase change started to extend into the turbulent zone the rapid mixing forced the constant temperature of the bulk fluid of Region 2.On completion of phase change across the diameter of the tube in Region 3, a rise in temperature was due to normal turbulent heat transfer mechanisms. |
The behaviour of the pressure drop could also be explained by this mechanism. In the first region little change occurred in the majority of the fluid, hence no changes in the differential pressure drops were observed. In Region 3 the situation was similar, although the phase change particles were now fluid giving a lower pressure drop. In Region 2, the decrease in pressure drop was associated with a transition between the fluid containing solid particles to one containing fluid particles. This was supported by the fact that at a higher wall heat flux, the transition from Region 1 to 2 occurred within a shorter distance from the inlet and the transition period (Region 2) was much shorter. Heat transfer coefficients based on the bulk temperature and the constant wall heat flux were computed. These showed that h rose from the start to a maximum Region 1, then decreased steadily reaching a minimum at the end of Region 2 and finally increased very slightly with distance in Region 3. The peak of the enhancement at the end of Region 1 was less pronounced at higher wall heat fluxes.From the published literature previous experimental investigations on slurry heat transfer appear to be limited to heating rather than cooling; few investigations have considered phase change effects and it appears that none has studied phase change due to freezing. Little is known of the influence of particles on the heat transfer coefficient.No experimental results appear to have been published for phase conditions employing particles of >0.1 mm, but the work of Lui et al. When the movement of the particle is independent of fluid particles (i.e. a large particle or a high-density particle) it is more likely to impact the laminar sub-layer as particles are thrown around. Under such conditions an increase in the local heat transfer rate will occur, but a stable increase will be achieved only at high flow rates due to the degree of turbulence required. Some analysis of particle behaviour in vortices has been undertaken The effects of the latent heat exchange in the boundary layer are also unclear, but it is evident from the work of Choi et al. An experimental programme was therefore developed to assess the thermal behaviour of slurries containing phase change particles when subjected to cooling. The focus was placed on the freezing phase change by utilizing 1–3 mm by hydrated particles of the hydrophilic copolymer methylmethacrylate-vinylpyrolidone in concentrations of up to 25% (by volume) in a non-aqueous Newtonian support fluid.A heat transfer test apparatus was constructed and calibrated to permit collection of detailed heat transfer data. The differential temperatures involved were small and so the test rig had to achieve a high sensitivity.Initial design considerations supported the use of a tube geometry for ease of construction and freedom from settlement. Also comparisons can then be made with existing single phase correlations for this geometry: the most common such correlation being that of Sieder and Tate can lead to errors of ±25% in the predicted value of h, and is only valid for fully developed turbulent flow. A better correlation is that of Petukhov This has an error of ±10% and is valid in the transitional flow regime. The rig was therefore designed to achieve a sensitivity large enough to allow the measurement of heat transfer coefficients of a single phase support fluid and detect any enhancement due to the addition of phase change particles.The experimental method adopted was to find the solution for h in the standard convective heat transfer equationThe temperature difference, ΔT, changes along the axis (direction of flow) because of the energy transfer occurring between the surface and the fluid. One method of accounting for this variation is to use the log mean temperature difference, ΔTlmHere ΔTo and ΔTi represent the surface to fluid outlet and surface to fluid inlet temperature differences, respectively. The derivation of this equality makes the assumption that the surface temperature is constant and that there are no discontinuities in the physical properties of the fluid indicate that to calculate the mean heat transfer coefficient requires a measurement of the rate of energy flow across the surface, the surface temperature and the inlet and outlet temperature of the fluid. Furthermore to relate h to other data the flow rate must be known.To measure the heat transfer coefficients of the hydrophilic-based slurries various parameters were measured around a circuit, part of which constituted the heat exchange test section (HETS) – see . The HETS was a concentric circular annulus with the slurry flowing through the tube and the refrigerant flowing through the annulus. The basic design requirements for the HETS were: (a) a length-to-diameter ratio of >60, (b) either a constant wall temperature or a constant rate of heat transfer through the wall, and (c) a knowledge of the temperature variation of the heat transfer surface (Tw). The high thermal conductivity and relatively low cost of drawn copper tubing made it the first choice as the core of the heat exchanger test section. A standard pipe diameter of 28 mm was chosen, leading to a test section length of 2 m to satisfy criterion (a). The outer annulus was cooled with a pumped glycol brine solution supplied by a chiller unit (Coniar Churchill TCW9) and the mass flow rate of the brine was measured with a turbine flow meter. The slurry was held in a stirred bulk holding tank, which provided a thermal mass to the circuit and enabled mass-flow rate measurements to be taken with minimal change to the slurry head, and minimal thermal impact upon measured data from the returned slurry sample. The tank was insulated with 50 mm thick foil-coated glass-fibre insulation and fitted with a 40 mm thick styrofoam lid, while the circulating network was insulated with a closed cell elastomeric foam. From this tank the slurry was pumped by four identical pumps, connected in series. To achieve repeatable flow conditions, the controlling parameter used was the number of pumps in operation: “high” flow rate (four pumps), “medium” flow rate (three pumps) and, “low” flow rate (two pumps). Acrylonitrile butadiene styrene (ABS) pipes of 25 mm internal diameter were employed for the slurry circulation loop and the bulk tank (760 mm high by 460 mm diameter) was open-topped and fitted with a motorised agitation unit to prevent particle settlement. (The total heat gain to the system at an ambient temperature of 18 °C was calculated to be approximately 450 W, for slurry and brine temperatures of −10 and −20 °C, respectively).Hydrated polymer particles of 1–3 mm were employed to charge the system. The thermal properties of the particles do not change significantly upon repeated freeze–thaw thermal cycling, but they are hard and brittle when frozen as opposed to soft and elastic when unfrozen. For this reason, pumps with silicone-elastomer impellers were employed to limit mechanical degradation of the particles due to pumping. However, the particle size distribution changed, due to an increased proportion of fines existing after testing (see ). Although this did not alter the water content of the slurry, further attention should be given in a subsequent study to the rheology of phase-change slurries incorporating hydrophilic particles.Measurement of the temperatures in the HETS and around the system was performed with type E thermocouples calibrated to ±0.04 °C. The inlet and outlet temperatures of the slurry were measured at the mid-stream point (centre of the tube). The inlet temperature of the slurry was measured just before entry to the HETS, and the exit temperature was measured 2 m downstream of the HETS. The wall temperature was measured in the axial direction at respective positions of 20%, 50% and 80% of the length of the HETS as shown in After leaving the HETS the slurry continued around the loop and passed through a 2 m rheological test section, the first 1 m of which was designed to allow flow conditions to stabilise prior to measurement of the pressure drop in the second 1 m section. When steady-state conditions were required and heat was being extracted from the slurry in the HETS, a 2.5 kW electric in-line heater present in the thermal circuit was employed to return the temperature of the slurry leaving the HETS to the reference temperature. Before returning to the bulk tank, the slurry passed through a chute mechanism which allowed it to be drawn off for a selected period so that the mass flow rate could be measured.The performance of the test rig was initially verified with water to check its ability to reproduce heat transfer coefficients within the errors of standard correlations. When compared with predictions from , Nu values were accurate to within 9% at low flow rates improving to 3% at high flow rates. Also a number of tests employing water or oil were performed with 28 and 21 mm diameter heat transfer tubes to enable comparisons with h predictions from standard correlations (). The results indicated that the rig could be used to reproduce the standard heat transfer correlation for turbulent heat transfer in tubes.For the subsequent slurry heat transfer investigation, a non-aqueous Newtonian fluid was required to support the various concentrations of hydrated hydrophilic particles. A calibration fluid, Shell Fusus oil, was selected for which fluid properties were readily available in the temperature range of interest. (In this paper, a fluid containing hydrophilic particles of say 75% maximum water uptake is termed “75% hydrophilic”, to indicate that each polymer particle is characterised by a water content of 75% when measured as a proportion of its fully hydrated wet weight.)To account for the addition of solids to the system the data analysis software was developed to utilise slurry property data when calculating the heat transfer coefficients. These were based on the principal fluid properties (i.e. density, viscosity, thermal capacity and thermal conductivity) calculated by interpolation and the properties of the solid particles (i.e. density, thermal conductivity and thermal capacity). Predictions were not attempted for temperatures at or below 0 °C as the discontinuities occurring due to the phase change could not be accounted for.Fundamental to any slurry property correlation is the solids concentration, φ, which changed as the density of the oil changed:It was assumed that the change in density of the solid particles was negligible compared to the change in density of the support fluid.The thermal capacity was calculated by a simple mass ratio of the fluid and solid components:The 1–3 mm particles employed in this study are commonly classed as largeThe effects on the apparent thermal conductivity, due to the presence of solid particles, were accounted for by employing Maxwell's equation which is valid for mixtures where the interparticle separation is larger than the particle diameter (i.e. φ<10%). Although this correlation was developed for static systems it has been used successfully for flowing solid/liquid mixtures.The mean fluid temperature was employed for all interpolations and calculations of fluid and mixture properties. The physical properties of the solid particles were those for a 75% hydrophilic material. It was anticipated that below 0 °C the effect of latent heat during phase change would make the correlations for Nu invalid. The respective density, thermal capacity and thermal conductivity of the hydrophilic particles were taken as (as measured experimentally for 0–10 °C). The calculated physical properties were saved in the processed data file together with several non-dimensional numbers (Re, Pr, Nu) which were subsequently employed to analyse the data.This investigation was based on slurries with solids concentrations of 1%, 5%, 10% and 25% (by volume) of 75% water-uptake hydrophilic co-polymers. The particles were prepared by hydrating, rinsing and then draining (to remove any interstitial water) before placing them in polythene bags. Each bag contained ∼1 kg of hydrated material. The batches were thermally cycled 20 times to ensure a stable freeze–thaw characteristic each cycle consisting of cooling from 18 to −27 °C and then thawing to 18 °C. Measurements had shown that 16 h were required for cooling (the longest part of the cycle); hence for convenience it was arranged for each part of the cycle to span one day (i.e. 24 h of cooling followed by 24 h of thawing).After thermal cycling, the materials were placed in water again to replenish any dehydration occurring during the thermal cycles. To remove excess water from the materials, before they were introduced to the test rig, a centrifugal drying device was employed. A comparison of the dry weight of the particles with the weights before and after centrifuging confirmed that the increased mass of the samples after centrifuging was solely due to water absorption by the polymer and not due to water in the interstices between adjacent particles. Sufficient particles were then added to the system to achieve the desired concentration.The adopted test procedure was to set the flow conditions for the rig and allow the slurry to circulate for 1 h. At the same time the glycol circuit was circulated with the compressor of the chiller unit switched off. This allowed the whole system to reach thermal equilibrium before the cooling commenced. Then the chiller was operated to cool the slurry to below 0 °C. A number of samples were taken to measure the mass flow rate and confirm the solids concentration of the following mixture (i.e. to check that the agitation device was fully mixing the contents of the bulk tank). For heat transfer analyses, samples were only taken at the start and end of the test. All measurements showed a near-linear relation between flow rate and temperature (see ), and deviations were found only for solids concentrations of 25% and at temperatures below 0 °C.Generally, the correlations for the physical properties of solid–liquid mixtures are considered to fail at a point where the mean particle separation is similar to the characteristic size of the particles. For systems of mono-sized particles this occurs at concentrations of >10%. For this reason particular attention was paid to concentrations of 5% and 10%.General consideration of the behaviour of the slurry during cooling suggests a three-stage process:While the slurry remains above its phase change temperature.The transitional phase during which the heat exchanger surface is at, or below, the phase change temperature, but while the inlet temperature remains above this temperature.The final stage, when the inlet temperature also drops below the phase change temperature. |
The first stage shows only the effects of the solid particles on the behaviour of the slurry's heat transfer coefficient. illustrates the measured heat transfer coefficients for concentrations of 1%, 5% and 10% under very similar flow conditions (with a mass flow rate of at 10 °C). The point at which any part of the wall reached 0 °C (the start of the second stage) is marked. At this point it can be seen that no significant change in h occurs for the 1% and 5% slurries although there is a change for the 10% slurry. For inlet temperatures below 0 °C (start of third stage) there is a distinct change in behaviour with concentration. The 1% curve shows a smooth profile indicating that phase change had occurred over a very restricted temperature range. However the 5% and 10% curves show a significant increase reflecting the high thermal capacity of the mixtures due to latent heat exchange in the materials. For all concentrations the effect of increasing the flow rate was, as it applies generally for a single phase fluid, to increase the overall value of h.In this section the measured heat transfer data are compared with predictions using a single-phase heat transfer correlation (for both a single phase fluid and a fluid with properties accounting for the presence of particles). Attention focussed on concentrations of 5% where a good correlation was expected, and at 10% where the rheological properties were expected to deviate from a Newtonian fluid. The analysis is limited to temperatures above 0 °C to eliminate the influence of phase transition effects. With φ=5% it was found that the predicted and measured values were in close agreement for a high mass flow rate ( at 10 °C) a rapid decrease in h was observed, which suggests that the degree of turbulence was then insufficient to overcome settling. Under such conditions the particles were believed to have formed a moving bed (see tests D and E in ) where heat transfer through the mass was via conduction alone. This itself would yield a low rate of overall heat transfer, although more significantly the surface area available for convective heat transfer would be reduced.The transition was observed to occur over a very narrow range of flow rates. At 10 °C for all of the tests, the value of h decreased from (i.e. a decrease of nearly 50% for a change in the flow rate of only 20%). The effect of settling on the heat transfer behaviour of the slurry is shown clearly in . The Reynolds analogy has been used to analyse similar conditions by Analysis of the heat transfer tests for φ=10% mixtures revealed that the standard heat transfer equation fails to give any correlation at the flow rates tested (see ). At the high flow rate h was found to be significantly enhanced when compared with both predictions for a single phase fluid and when applying property modifications to account for the incorporation of solid particles. The results obtained for φ=10% clearly indicate that the correlations used for single phase fluids cannot be applied. As this work was primarily concerned with applying actively phase-changing slurries to thermal storage systems no further analysis will be presented for temperatures above the phase transition. (Results are not presented for the 10% concentration at low flow rates since the system was found to fail due to blockage at the control valve.)It is evident that the 10% mixture gave a significant enhancement in h at transitional temperatures. This section describes the data obtained from further investigations made at this concentration, with particular attention being given to the higher flow rate conditions.Several practical problems occurred which complicated the process of obtaining reliable results. The chiller performance limited the lowest temperatures of the glycol circuit to −20 °C, thus limiting the differential temperatures used in calculating h. Despite careful shielding of the chiller, agitation unit and local 240 V mains, the low differential temperatures led to a reduced signal-to-noise ratio and so electrical noise could have a significant effect on the final value of h calculated around the phase change temperature. Furthermore particles were believed to be adhering to the temperature probes in the mixture for small periods causing additional fluctuations. To negate these effects tests were repeated under the same system flow condition to obtain consistent sets of data and averages calculated where required. As with the previous tests the low flow rates were not always stable; mass flow rate measurements often disturbed the conditions in the system enough to lead to blockages. The equivalence between the conditions is illustrated in The heat transfer coefficient for a slurry of φ=10% at high flow rates, averaged for 5 test runs, is shown in . The results show that above 0 °C the heat transfer coefficient is enhanced between 10% and 20%. More significant though is the enhancement below 0 °C; it is typically 60% although at −2.5 °C it reaches 70%. This general increase in h results from the effective thermal capacity of the fluid having increased due to the latent heat of the particles. Of interest are the dual peaks evident during the phase transition which occurred at −0.5 and −2.4 °C (see ). This is consistent with there being two peaks in the particle size distribution due to shearing in the pumps and the stresses of freeze–thaw cycling (see ). Below −2.5 °C a very sharp decrease in h was measured, which indicated the completion of the phase transition.The heat transfer coefficient was also enhanced above 0 °C for the medium and low flow rates. For both, the increase was more significant than had been recorded for the high flow rate, being consistently of the order of 20%. This may reflect the operation of micro-convection lower temperatures would exhibit an increased micro-convection enhancement, unlike the medium or low flows where micro-convection would be evident throughout.The behaviour of h below 0 °C differed with flow rate. For the high and medium flow rates, respective enhancements of up to 70% and 30% were recorded, whereas for the low flow rate a significant drop in the heat transfer coefficient occurred (). A number of repeat tests at this flow rate yielded a virtually linear relationship between flow rate and temperature with no fluctuations. It is considered that the variations in the heat transfer coefficient value below 0 °C are due to flow disturbances where particles fleetingly stick to the cold walls of the HETS, and to each other by the mechanism where surface moisture froze to create ice bridges. (The surface water forms when the maximum hydration level of the particles decreases with temperature Only two tests were successfully conducted at φ=25%, and solely at the high flow rate due to the probability of system failure. The rig failed on many occasions due to either particles agglomerating and blocking the chute or particles forming lower density (i.e. air containing) structures which floated in the bulk tank and thereby caused the flowing concentration to become inconsistent.The measured heat transfer coefficients at φ=25% () followed a similar trend to those associated with the 10% mixture. There as a general enhancement in h above that of the clear fluid down to ≈2 °C at which point a sudden decrease was seen to occur. The cause of this is again believed to be related to ice bridges occurring between particles causing agglomerations to form in the heat transfer test section. The flow rates for these tests were similar to those for the 10% mixture at low flow conditions (cf. at 12.3 °C), although due to the higher concentration the turbulence was reduced. This caused particles to remain closer to the heat transfer surface for longer periods allowing the conditions for ice bridging to occur sooner at a given inlet temperature. The evidence for this is further suggested from analysing the differential temperature between the wall and the slurry. If the particles in the boundary layer were forming agglomerations, the movement of other particles into the boundary layer would be prevented. This effect would end once the surfaces of the particles were below 0 °C allowing movement of other particles into the layer. Furthermore, because the whole mass was at the phase transition temperature a very rapid rise would occur at 0 °C – this is clearly evident in – and may be a reflection of the transition point, where the freezing at the particle surface is occurring as it passes into the boundary layer before it can form bridges.This investigation has assessed the relevant literature and extended the published range of date for the heat transfer properties of solid–liquid mixtures. Generally the data collected indicate that phase-change slurries based on hydrophilic polymers in thermal energy storage or transmission systems can be used at the temperatures required for cold storage.The heat transfer behaviour of a solid–liquid mixture at low concentrations (<10%), without phase change can be modelled by applying appropriate property modifications which account for the presence of particles. This fails when turbulence is not sufficient to overcome settling, and under these conditions a reduction in the heat transfer coefficient occurs. At solids concentrations of 10% or greater, the heat transfer coefficient is substantially enhanced relative to predictions for a single phase fluid (with or without including property modifications to account for the particles). This suggests that the particle interaction with the boundary layer becomes significant once conditions at the boundary layer allow phase change to occur. The scale of the effect was found to be very dependent on the flow conditions and it is believed that ice bridging between particles is a controlling factor.To improve the thermal performance of phase-change slurries incorporating hydrated hydrophilic polymeric particles requires a support fluid of lower viscosity and higher thermal capacity/conductivity than the oil used in this investigation. This in turn will require higher flow rates to be applied to maintain homogeneity within the flow. The flow rates tested were not sufficient for fully developed turbulence to be established. It is believed that, under such conditions, particle interaction with the boundary layer will increase, thereby further increasing the heat transfer rate. This extension of the current investigation is recommended for further study.Experimental constraints on the diagenetic self-sealing capacity of faults in high porosity rocksA thorough understanding of fault seal processes is important in many practical and geological applications, which depend on subsurface flow of fluids. While the mechanisms involved in fault sealing are well known, the microscale processes involved and their relative contribution to sealing remain debatable. In particular, the extent to which diagenetic processes overprint cataclastic fault sealing has not been resolved, mainly due to the long time scales required to measure these effects. Here, we report results from a novel suite of room temperature experiments that combined continuous analysis of dissolved silica using on-line high performance liquid chromatography, with low strain rate creep loading on sandstone cores. This technique allowed changes in silica concentration during different phases of deformation to be resolved, and revealed a 7-fold increase in overall silica concentration immediately after dynamic faulting by localised cataclasis. Calculations based on these results show that the mass of dissolved silica from the resultant fault gouge increased by up to two orders of magnitude relative to that from the intact rock over the same time scale. This increase represents the first stage of the inherent diagenetic sealing capacity of the fault, presumably through localised diffusive mass transfer. Post-test microstructural studies suggest that the magnitude of diagenetic self-sealing depends on lithological and mechanical attributes of the host rock, which control fault gouge microstructure. Our experiments suggest that diagenetic processes may account for permeability reduction of up to two orders of magnitude, comparable to reductions due to cataclasis alone. Together, these two processes account for the 5–6 orders of magnitude reduction of permeability observed in natural faults and deformation bands.Faults play an important role in the movement and channelling of fluids in the subsurface. Thus predicting their hydraulic behaviour has become a major pursuit in recent years Despite some recent success in this endeavour, many issues remain to be resolved with regard to fault seal prediction. For example, with the exception of direct measurement from hydraulic pump tests, information about the actual petrophysical properties of fault rocks is often only available from direct studies of faulting processes and sealing mechanisms, as revealed by microstructural observations of fault rocks in the field or laboratory. Based on mainly field observations, several workers have proposed a generic classification of the mechanisms by which faults can seal So far, significant progress has been made in understanding the mechanics of clay smear seals, leading to development of fairly robust predictive algorithms that have been calibrated against known hydrocarbon column data To date, relatively few experiments have attempted explicitly to quantify the magnitude of fault sealing due to local diagenetic processes in reservoir sandstones, largely because it has proven difficult to measure at the relevant pressures (≤700 bars) and temperatures (≤120°C). Experiments relevant to seismogenic (greenschist metamorphic) conditions only show permeability decreases of about one order of magnitude We first describe the experimental methodology and the results, and then show using mass balance calculations that these are consistent with a two orders of magnitude potential reduction in permeability following the cataclastic failure of porous rock samples at low strain rates.Our objective was to determine changes in mineral dissolution associated with deformation in general and cataclastic faulting in particular, and to use these observations to place constraints on diagenetic self-sealing of faults. Since cataclasis generates fine grains (fault gouge), we expect the faulting process to be associated with an increase in solute concentration in the fluid. This may occur as a result of increased dissolution rate expected for finer grains Two problems must be overcome before attempting to quantify changes in mineral dissolution due to faulting. Firstly, the time span of conventional laboratory deformation experiments is too short relative to mineral dissolution rates at low temperatures to allow the effects of initial loading to be resolved from those due to subsequent faulting. Secondly, frequent sampling of the pore fluids is required, especially during or after faulting, but this is limited by the volume of fluid needed for analysis while maintaining the low flow rates necessary to observe changes in mineral dissolution. The novelty in our approach lies in combining high resolution sampling using on-line high performance liquid chromatography (HPLC), which only requires μl analytical volumes In order to determine changes associated with cataclastic faulting, we measured the extent of mineral dissolution for intact samples and then compared this with dissolution after fracture. Central to our interpretation of the diagenetic sealing is the assumption that in a subsurface environment, an increase in dissolution due to faulting will represent ‘supersaturation’ with respect to grains in the intact rock. We show below that this assumption has a sound theoretical basis when our experimental data are extrapolated to natural conditions.The experiments were based on the scenario that a core sample of given length (L, cm) and cross-sectional area (A, cm2) is loaded to a constant stress () while a fluid of known composition is pumped through it at a constant flow rate, Q (cm−3 s−1). Assuming, for simplicity, that the rock is monomineralic and neglecting aqueous phase reactions, which are relatively fast In this equation, C is the concentration (mol l−1) of the dissolved species in the advective fluid at position x and time t, φ is the porosity of the sample (dimensionless), α is the stoichiometric constant of the dissolution–precipitation reaction (dimensionless), υ is the linear flow velocity along the sample (cm s−1), while R+ and R− are the dissolution and precipitation rates in the sample, respectively (mol cm−3 s−1). For simple oxides such as quartz, the precipitation rate varies linearly with concentration of dissolved silica in solution where R∼=R−/C is the modified precipitation rate (l cm−3 s−1). Explicit in is the fact that the concentration of the dissolved solute will vary along the length of the column. However, for times long enough for reactions to be sufficiently resolved from initial loading effects, the concentration in the fluid will reach steady-state at all points along the core, including at the outlet (x=L). Thus departures from this steady-state condition at fracture can be exploited to assess the effects of faulting on dissolution.The full solution to this inhomogeneous equation under these conditions is given in the EPSL online Background Dataset, based on the analysis by Franklin et al. equals the equilibrium concentration, Ce. Since distilled water was injected into the core, the boundary condition at the inlet end is C(x=0)=0, whencewhere Css is now the steady-state concentration. We analysed at the outlet of the core sample in our experiments, whence x=L in . The derivation assumes that the porosity of the sample remains effectively constant during the lifetime of these experiments. This is justified since the mass dissolved is very low, although it can be accurately measured (see later). allows us to predict steady-state concentrations in our experiments at a given temperature and pressure if the precipitation rate R∼ is known. Since the rate varies along the length of the core sample, it cannot be calculated simply from exit concentrations. However, for a given mineral, R∼ is related to sample characteristics by the equation where k− is the apparent precipitation rate constant (l cm−2 s−1), ρ is the density of the dissolving or precipitating mineral (g cm−3), and As is surface area per unit mass (cm2 g−1), as measured from gas adsorption (BET) studies , it is possible to show whether our measured solution concentrations follow the predicted values, and to validate the assumption of fault-induced supersaturation under natural flow rates.Two Permian aeolian sandstones (Clashach and Locharbriggs, UK) were used as test samples. These have almost identical detrital mineralogy of quartz and K-feldspar, but differing diagenetic and petrophysical attributes (). Clashach is notable for its quartz overgrowths, producing a well-cemented sandstone with porosities of 12–18% and permeabilities ranging from 200 mD to 1 D The experiments were conducted in a triaxial flow rig (σ1>σ2=σ3) at room temperature and involved creep-to-failure, followed by frictional sliding on the new fault. Cores measuring between 75 and 80 mm long and 38 mm diameter were loaded to differential stresses ranging from 85 to 95% of their short-term failure strength, with a radial confining pressure of 6.9 MPa. The differential stress was maintained constant until the samples failed by accelerating creep. Axial strain was measured continuously using an externally mounted linear variable differential transducer, while helium-purged distilled water flowed through the cores at 0.1 ml min−1. For the range of porosity and cross-sectional area in our samples, this volumetric flow rate translates into linear flow velocities (υ) of about 3.0 cm h−1. These velocities were too high for solutions to reach equilibrium with the minerals over the lengths of samples used, but were dictated by the need to deliver an accurate and constant flow rate.At regular intervals, 100 μl samples of the exit pore fluid were extracted and loaded onto an on-line Water’s IC-PAK™ anion column for analysis of dissolved silica using 2.5 mM lithium hydroxide eluent flowing at 1.2 ml min−1, and a Water’s 431 conductivity detector. A three-standard calibration was run prior to analysis and the eluent, which degrades with time, was changed every 4–5 h. The method detection limit was 80 ppb of H4SiO4 and analytical errors were below 2%.At the end of the tests, the samples were removed from the pressure cell while still encased in the confining rubber sleeve. After drying to constant weight at 60°C, the samples were impregnated under vacuum with an extra low-viscosity epoxy resin so that the gouge and other fine particles would not be displaced during impregnation. Thin sections made perpendicular to the shear fractures were used to study microstructural and fault gouge characteristics under backscattered scanning electron microscopy (SEM).In order to quantify microcrack distributions, photomicrographs were taken across and near the fractures. These photographs were scanned into a software package called OPTIMAS™ for measurement and counting of microcracks, after calibration of the field of view. Depending on the magnification of the photomicrograph, the smallest microcracks resolvable by this technique were about 0.3 μm long.Measurements of axial strain and pore fluid dissolved silica (H4SiO4) for the two sandstones are shown in . Before failure, strain was found to follow the three classic stages of creep: transient, steady-state and accelerating creep. Transient creep was found to obey a logarithmic law We note that the concentration of dissolved silica in the exit fluid is correlated with the different stages of creep for the Clashach sandstone (). After an initial rise due to loading, the concentration drops exponentially during the transient creep phase, attains a steady-state value during steady-state creep and increases steadily during the accelerating creep phase. Comparison with the Locharbriggs sandstone () run at the same stress magnitude (90% of failure strength) shows a higher concentration due to loading and no increase in dissolved silica during tertiary creep. However, most of the features of are reproduced. The higher concentration due to loading for Locharbriggs samples may be due to the smaller grain size relative to Clashach samples (), which favours pressure solution. For the Clashach sandstone, the exit fluid reaches a steady-state concentration of about 1 ppm; rising to about 1.4 ppm during accelerating creep (), while the steady-state concentration for the Locharbriggs sandstone is about 0.7 ppm (The development of the macroscopic fault is marked by a dramatic increase in silica concentration in the exit fluid. This behaviour is observed for both sandstones, but the Clashach samples showed a higher increase in concentration than the Locharbriggs samples. This increase was transient, and concentrations dropped to the pre-fracture levels within 5 days. In this respect, our observations are similar to those of Dewers and Hajash Further experiments conducted at different stresses show that these geochemical changes are reproducible and hence characteristic of the creep-to-failure process (). The Clashach sample deformed at 92% of failure strength () fails earlier than that at 90%, and the steady-state concentration appears not to have been attained before failure occurred. A rather interesting observation is that after failure, the exit tubing was blocked (tested by reversing flow), resulting in a progressive increase in pore pressure within the sample. This induced frictional sliding along the fault and the resulting continuous ‘grinding’ is manifest in a continuous increase in dissolved silica in the exit fluid. Meantime, the second Locharbriggs sample () loaded to 85% of failure strength lasted longer, reaches lower steady-state concentrations, and shows a much smaller silica signal at failure. These differences in failure times are consistent with the stress dependence of failure times found in other studies Frictional sliding also manifests in an increase in silica concentration, but to levels lower than those due to fracture. However, the increased levels due to sliding appear to be sustainable over longer periods relative to the dynamic failure (), consistent with a more efficient grinding process. also highlights the advantages of combining creep tests with on-line chemical analysis. We can resolve the 3–4 h transient increase in silica concentration, associated with the initial phase of loading. In a comparative conventional deformation test, using a strain rate of 10−5 s−1, fracture occurred within 1–2 h of initial loading and the silica concentration at fracture could not be resolved from that due to initial loading. shows backscattered electron photomicrographs of the fractured samples taken around areas in the vicinity of micro-faults created. The samples failed by a single fracture oriented at about 40° to the maximum principal stress, although small subsidiary axial fractures were also present. The two photographs were taken at the same scale and the slightly larger grain size for the Clashach samples () is evident, while the Locharbriggs samples have a higher porosity, with less obvious grain–grain contacts (). The Clashach sample shows pervasive intra-granular and trans-granular microcracking and the fault gouge consists wholly of comminuted grains (). This suggests that the formation and linkage of microcracks was the dominant deformation mechanism that led to the failure of this sandstone. Microcracking increases surface area to volume ratio in the whole sample, but particularly in the fracture, by producing grains much finer than the bulk grains. In contrast, microcracks in the Locharbriggs sandstone were restricted to within 0.5 mm of the fault and the fault gouge still contained whole grains of the matrix material (). These observations are suggestive of deformation by compaction and grain translation, producing gouge with a lower surface area to volume ratio.These qualitative observations of deformation mechanisms were quantified by analysis of microcrack distributions around the micro-faults. We counted the number, and measured the total length of microcracks in eight separate photographs taken on a transect across each micro-fault (). Firstly, both microcrack density and total crack length are higher at all points in the Clashach relative to the Locharbriggs samples. Secondly, both parameters decrease exponentially away from the micro-fault, and take the general form N=ae−bx, where N is the number or density of microcracks per unit area, x is the distance (mm) away from the micro-fault and a and b are constants. This is consistent with previous observations of microcrack distributions in samples of deformed granites as well around fault zones generally We have shown that the fracture process leads to a significant increase in the concentration of dissolved silica in distilled water flowing through the core, and that concentrations are nearly back to the bulk, steady-state levels approximately 120 h after fracture (). Since differential pressures across the samples were not measured, it is not possible to quantify permeability changes due to deformation and/or dissolution. However, in one case during the test shown in , the pump used had a pressure transducer to indicate backpressure downstream of the fluid reservoir. A record of this pressure is shown in , from which we observe a 6-fold increase in backpressure immediately at failure. This pressure increase is a qualitative indication of a decrease in permeability associated with cataclastic faulting. Although the pressure drops to about 0.1 MPa as the fault gouge dissolves the small changes in dissolved silica and the erratic subsequent changes in backpressure suggest that these permeability changes are mostly of mechanical origin. Nevertheless, we can use observed changes in dissolution to estimate the potential for diagenetic self-sealing.Our main objective was to investigate whether the fracture process contributes significantly to the amount of diagenetic sealing seen in natural faults, where solutions are likely to be at equilibrium with bulk rock minerals. We can get a semi-quantitative idea of the diagenetic sealing potential of faults if we use the steady-state concentration before failure () to represent an equivalent ‘equilibrium’ concentration with respect to the bulk rock grains. Since the flow rate was maintained constant throughout our experiments, the measured increase in dissolution after fracture can be thought of as representing the degree of supersaturation with respect to the bulk rock grains. This assumption is justified because Dewers and Hajash Further justification of this assumption and extrapolation to equilibrium situations comes from theoretical analysis in shows the variation of silica concentration at the outlet, calculated from parameters given in ). The calculation assumes a monomineralic rock, which can be justified for Clashach samples as they contain ≥90% quartz predicts an outlet [H4SiO4] of 0.80±0.1 ppm. True equilibrium concentrations require flow rates of ≤0.001 ml min−1, i.e. three orders of magnitude less than we were able to achieve with available pumps. The calculated silica concentrations agree reasonably well with our measured values of 1 ppm, particularly as our calculations did not account for the presence of K-feldspar and effects of non-hydrostatic loading on grain contacts. Outlet silica concentrations at 100°C were also calculated based on quartz solubility and enthalpy data from Langmuir . Under these conditions, which are more representative of diagenetic environments in the top few kilometres of the earth, exit fluids reach equilibrium with quartz even at flow rates as high as 1 ml min−1. The calculated values are similar to flow rate-independent concentrations measured by Franklin et al. Mechanistically, fault-induced supersaturation may be evaluated using the Freundlich–Ostwald equation, where the smallest (most reactive and most abundant) particles determine solubility, so that the new equilibrium solubility is given by Here, C is now the solubility (mol l−1) of finer grains produced due to faulting, with diameter r (cm), Vm is the molar volume of the dissolving mineral (cm−3 mol−1), σ is its surface free energy (J cm−2), B is a geometric constant (dimensionless), R is the gas constant (J mol−1 K−1), T (K) is the temperature and other terms are as defined before. As pointed out by Parks indicate that significant increases in dissolution occur only at grain radii of less than 0.1 μm are corresponding curves for 0.1 μm grains at both 25°C and 100°C. It is noticeable that even at this grain size, supersaturation with respect to bulk grains exists in any fault zone under diagenetic flow rate and temperature conditions, even without having to adjust the calculation for reaction rate dependence on grain size We estimated the additional mass of dissolved silica due to fracture by integrating the [H4SiO4]–time curve over the 120 h duration when [H4SiO4] is above steady-state values and multiplying this by the flow rate. The curve exhibits a linear relationship with time up to peak concentration, followed by a power-law decay post-peak:where M is the mass of H4SiO4 (mg), Q is the volumetric flow rate (l min−1), k is the slope of the linear component, Co is a constant and n is the exponent. The total mass of additional H4SiO4 calculated this way is about 2 mg. By comparison, the total amount of H4SiO4 that would be released from dissolution of the bulk core over the same duration is about 0.7 mg. While this difference is small, the additional silica over this time frame must be interpreted in terms of its source volume. The 0.7 mg came from the whole sample while the additional 2 mg came from the fault zone only. By normalising the masses calculated to their respective source volumes (9.1×10−2 dm3 for the whole sample and 2.7×10−3 dm3 for the fault, calculated from the fracture thickness and inclination), we get values of 7.7 mg dm−3 for the bulk sample and 748 mg dm−3 for the fracture. In this case, faulting increases total dissolved silica per unit volume of rock by about two orders of magnitude. For the case where minerals were initially in equilibrium with the fluid, the excess silica represents a potential source for the diagenetic cementation of the fault even at room temperature, albeit at times much longer than our experiments. Our experiments have also shown that continuous shear along the fault produces more fine particles, leading to continuous increases in fluid silica concentrations (). Such long-term ductile compaction is thought to be an important mechanism for generating excess pore pressures in seismogenic zones It is not possible from our experimental data to identify mechanisms that operate in nature during diagenetic self-sealing of faults. However, the increased silica concentration associated with fracturing and frictional sliding can be attributed to two processes that have previously been suggested as diagenetic fault seal mechanisms. Ostwald ripening is the process where small grains in a multi-modal population dissolve in the fluid and the dissolved solute re-precipitates on larger grains is the difference in solubility at faulting and frictional sliding between the two sandstones. It is probable that the difference in silica concentration between the two tests is consistent with the differing microscopic deformation mechanisms described in , and suggests that lithological and mechanical attributes of the host rock have a first order control on self-sealing deformation Finally, our experiments may be used to resolve some of the outstanding issues regarding sources of quartz cement for fault sealing in reservoir sandstones. Among the chemical seals, quartz is one of the most important causes of porosity and permeability reduction in faults. However, the source of the quartz is debatable, and the local versus external source arguments for explaining quartz diagenesis in reservoir sandstones have recently been applied to the fault seal problem We have demonstrated that the dynamic formation of fault gouge leads to transient increases in dissolution of minerals in the gouge relative to that in the host rock by up to two orders of magnitude. This increase provides an upper bound for the inherent diagenetic sealing capacity of the fault, since the dissolved material can precipitate within the fault and reduce its permeability. However, the overall magnitude of this self-sealing depends on a range of lithological and mechanical attributes of the host rock, which control fault gouge microstructure. Overall, our experiments suggest that diagenetic processes may account for up to two orders of magnitude of the total sealing observed in natural faults.Method for analysis of dynamic mechanical thermal analysis data using the Havriliak–Negami modelA new method is presented for analysis of single frequency dynamic mechanical thermal analysis (DMTA) data in the complex plane. The applicability of the method is restricted to cases where the polymer is thermorheologically simple and whose dynamic mechanical properties are well described by the Havriliak–Negami (HN) model. The method involved two steps: (1) the HN model was used to describe the shape of the complex plane representations of the DMTA data; and (2) the HN relaxation time (τ) was solved for at each temperature over which experimental measurements were made. This procedure resulted in the determination of four temperature independent HN parameters (α, β, E0, and E∞) and one temperature dependent parameter, τ(T). These model parameters were then used to calculate the dynamic mechanical properties over a range of temperatures and frequencies. The calculated moduli and loss factors were generally in good agreement with the experimental values for two elastomeric materials, neoprene and plasticized polyvinylchloride, that were subjected to the analysis procedure, over an 80° temperature range and three decades of frequency. It was also demonstrated that complex plane analysis of frequency multiplexed DMTA data could be used to calculate shift factors for time–temperature superposition. The corresponding master curves for storage modulus and loss factor created by horizontal shifts along the log(frequency) axis were smooth, providing additional support to the validity of the analysis procedure.Time–temperature superposition is commonly used with dynamic mechanical thermal analysis (DMTA) of polymeric materials to extend the frequency range of the measurement. This is typically accomplished by an empirical approach in which constant temperature data segments are shifted along the log(frequency) axis, such that adjacent segments overlap and a smooth master curve is obtained The dynamic mechanical and dielectric relaxation behavior of polymers in the frequency or time domains has been described by a number of models, including the single relaxation time Cole and Cole is the unit imaginary number, α is related to the width of the loss peak, β controls the asymmetry of the loss peak, and τ is the relaxation time. The parameters α and β can take on values between 0 and 1. Hartmann et al. have shown that the five parameter HN model can accurately describe the dynamic mechanical behavior of polymers in the frequency domain, including the height, width, position, and shape of the loss peak In order to use the HN model for analysis of DMTA data, it is necessary to somehow incorporate the temperature dependence of the complex modulus, E∗(T). This may be accomplished by making some or all of the HN parameters temperature dependent. Alig et al. used this approach in A new approach is described in this paper for the analysis of DMTA data in the context of the HN model. The method involves the fit of four temperature independent HN parameters in the complex plane of E∗, followed by a direct calculation of the temperature dependent relaxation time τ(T) from the HN equation. There is no specific functional dependence for τ on temperature assumed, and there are no additional parameters introduced. The method described yields not only the HN model parameters from single frequency DMTA data, but allows one to predict the complex modulus over a wide range of temperatures and frequencies.Isodamp C-1002, a plasticized polyvinylchloride, was obtained from EAR Division of Cabot Corp. A neoprene elastomer, an underwater transducer material, was nominally manufactured to specifications of 5109S All experimental data were collected on a TA Instruments DMA 2980 machine, using the tension-film clamping arrangement. Specimens were excited using a 20 μm dynamic displacement, and a small pre-load (0.2 N) to ensure that the specimens were always in tension. For the Isodamp C-1002, measurements of the complex Young’s modulus were made over a temperature range from −60 to 40 °C, in 5 °C intervals, at the following frequencies: 0.2, 0.3, 0.6, 1, 2, 3, 6, 10, 20, 30, 60, 125, 150, and 175 Hz. For the neoprene elastomer, measurements were made over a temperature range from −80 to 50 °C in 5 °C intervals, except in the region of the glass transition (−45 to −12 °C), where the measurements were made in 2 °C intervals. The frequencies used for the neoprene elastomer were 0.2, 0.3, 0.6, 1, 2, 3, 6, 10, 20, 30, 60, 125, and 150 Hz. The temperature was allowed to come to equilibrium and held constant while measurements were made at each frequency. The temperature was then incremented in a stepwise fashion throughout the temperature range, with measurements being made under isothermal conditions.For thermorheologically simple materials where tan δ is also known as the loss factor. Jones If one has data for the complex modulus over a narrow range of frequencies, or for that matter at a single frequency over a wide range of temperatures (i.e. DMTA data), it is not immediately obvious from how one might extract the five HN parameters from this data. However, it is possible to do this in two steps: (1) plot the modulus in the complex plane, and solve for α, β, E0, and E∞; and (2) solve for τ at each temperature over which measurements were made. This approach is based on the following assumptions.The complex plane representation of the modulus is independent of τ. An analysis of demonstrates that either the Wicket plot or Cole–Cole representation of the complex modulus computed from depends on four of the five HN parameters: α, β, E0, and E∞. However, the Wicket plot is essentially invariant of the HN relaxation time τ, as demonstrated in The only temperature dependent HN parameter is τ. While there is no a priori reason for this to be true, it will be shown that temperature independent values for α, β, E0, and E∞ may be successfully employed to describe the temperature and frequency dependent complex modulus.The detailed procedure for step (1) is discussed below. The procedure for step (2) is discussed in the next section.Trial values for α, β, E0, and E∞ were used to compute E∗(ω) according to , setting τ=1 and over the frequency range 10−20–1015 |
Hz. The degree of fit of the calculated complex modulus to the experimental modulus for each set of trial parameters was examined in the complex plane, using either the Cole–Cole (E″ versus E′) or Wicket plot (log(tan |
δ) versus log |
E′) analysis. For the Cole–Cole plot, the error function used was related to the sum of the squares of the differences between the experimental and calculated loss moduli, E″, over a given range of storage moduli, E′.where Eexp″ is the experimentally determined loss modulus and Ecalc″ is the calculated loss modulus. For each set of trial parameters, the error function was computed over the range of E′ for which there was an overlap of experimental and calculated data. The corresponding error function used for the Wicket plot was as follows.where tan δexp is the experimentally determined loss factor, and tan |
δcalc is the calculated loss factor.A multi-parameter optimization was carried out using the Matlab software’s optimization toolbox to find values for the parameters α, β, E0, and E∞ that minimized the error functions f1 and f2. The most consistent results and the fastest convergences were reached by first optimizing with respect to the Cole–Cole function f1, then with respect to the Wicket function f2. shows the storage and loss modulus of Isodamp C-1002 over a range of temperatures and at a frequency of 1 Hz. The results of the fitting procedure described above are shown in that the four temperature independent HN parameters (α, β, E0, and E∞) describe the complex plane behavior of Isodamp C-1002 quite well. The same procedure was applied to the neoprene elastomer, and the results tabulated in ) describes the dynamic mechanical behavior of the neoprene elastomer specimen quite well, except at the lowest and highest moduli. This is especially true for moduli less than 2×107 |
Pa, where the HN model data is markedly different from the experimental data. The DMTA experiments and the complex plane fitting procedure was repeated a number of times for replicate specimens of each elastomer (). The statistical variability of results in is due mainly to factors such as the precision of the instrument, reproducibility of the clamping conditions and isotropy of the sample, rather than robustness of the analysis technique. The experimental results for two specific elastomer specimens and their associated HN parameters in are the subject of further analysis described below., and the associated experimental complex moduli, E∗(ω, T), it should be possible to calculate the relaxation times τ(T) from . This may be accomplished analytically if τ can be isolated from other variables in that expression. Using the Matlab symbolic toolbox to solve this problem yielded the following expression for τ: to the data for Isodamp C-1002 resulted in the relaxation times shown in . Note that the results of this calculation were complex, and only the real part is considered here. The temperature dependence of the relaxation time follows an Arrhenius relationship:where T is absolute temperature, R the gas constant, Ea the Arrhenius activation energy, and A is a constant. The activation energy determined by least squares analysis of a plot of log(τ) versus 1/T was Ea=2.25×105 |
J mol−1. This value is higher than the value of Ea=1.53×105 |
J mol−1, which has been reported elsewhere The relaxation time was also derived from using numerical methods. For Isodamp C-1002, this yielded nearly identical results to the analytical method. The analytical solution given by is compared to a numerical solution for τ using for the case of the neoprene elastomer in . It can be seen that the analytical solution is in agreement with the numerical solution from −43 to −10 °C, but outside this temperature range the analytical solution gives negative results for τ (not shown on semi-log plot). This can be attributed to a poor fit of the HN equation outside the transition region for the neoprene elastomer (for the numerical solution, the value of τ was constrained to be positive).So far, it has been shown that analysis of DMTA data in the complex plane may be used to derive four temperature independent HN parameters, and the temperature dependent relaxation time. In this section, the applicability of the analysis method to the prediction of dynamic mechanical properties at various frequencies and temperatures will be explored. Specifically, it will be shown that it is possible to use single frequency DMTA data to predict the complex modulus over a range of frequencies and temperatures. The temperature range for prediction will be limited to the range over which the HN relaxation time has been determined.Calculation of the complex modulus at a given temperature (T) and frequency (ω) using is straightforward once α, β, E0, E∞, and t(T) have been determined from the procedure described above. shows the real part of the complex moduli for Isodamp C-1002 that were determined experimentally by DMTA over three decades of frequency (0.2–175 Hz), and at several different temperatures. The complex moduli that were predicted from the complex plane analysis of 1 Hz DMTA data compares favorably with the experimental data over the range of frequencies studied, especially at 0 °C, which is in the glass transition region for this polymer. The relaxation time for each temperature was found by interpolation of the data in . For Isodamp C-1002, the relaxation times at −30, 0, and 20 °C were found to be 1.65×102, 1.02×10−3, and 1.34×10−6 |
s, respectively. The corresponding experimental data and calculations for neoprene elastomer are shown in for the loss factor. Again, the agreement between experimental data and calculations based on complex plane analysis is very good. Note that the calculations accurately predict the location and shape of the peak in the loss factor curve for a temperature of −25 °C.It is also possible to calculate the modulus-temperature dependence at frequencies other than 1 Hz, by utilizing the full temperature range of relaxation times derived in the complex plane analysis. shows the experimental and calculated storage modulus data for Isodamp C-1002 over the temperature range −60 to 40 °C, and at 0.2, 1, 30, and 150 Hz. The temperature dependence of the calculated storage moduli agree quite well with the experimental data, with the exception perhaps of the 150 Hz data at low temperature. The calculations were based entirely on the analysis of 1 Hz DMTA data, using the HN parameters derived from complex plane analysis. Calculated DMTA curves for neoprene elastomer also agree quite well with experimental data (), except in the low modulus, high temperature region, where the degree of fit to the HN model in the complex plane was poor. The shape and location of the loss factor peaks for neoprene elastomer were well captured by the analysis, including the broadening of the peak with increasing frequency (An additional means of investigating the robustness of the analysis method presented here is to examine its success in producing smooth master curves from frequency multiplexed DMTA data. a shows experimental unshifted storage modulus data for Isodamp C-1002 over the frequency range 0.2–175 Hz, and at 5 °C temperature increments between −60 and 40 °C. The discrete temperature segments can readily be distinguished from one another in the glass transition region, and are labeled accordingly. A master curve at 0 °C was created by shifting the temperature segments along the frequency axis by a shift factor aT given bywhere τ is the relaxation time at temperature T (taken from ), and τ0 is the relaxation time at the reference temperature of 0 °C (1.59×10−3 |
s). As shown in b, the resultant master curve is a smooth function of frequency. This master curve also agrees quite well with the predictions based on for Isodamp C-1002, and the relaxation time τ0=1.59×10−3 |
s (c). Note that the HN parameters, relaxation times, and shift factors were all derived from 1 Hz DMTA data, but were successfully applied to frequency multiplexed DMTA data.It has been shown that complex plane analysis of DMTA data may be used to predict the complex modulus of thermorheologically simple polymers as a function of temperature and frequency. The method described involved deriving four temperature independent HN parameters (α, β, Eo, and E∞) and the temperature dependent relaxation time τ from single frequency DMTA data. These five HN parameters were then used to calculate the complex modulus as a function of temperature and frequency. Agreement with experimental data was generally good for two elastomeric materials investigated, Isodamp C-1002 and a neoprene elastomer.The method described is restricted to thermorheologically simple polymers, whose dynamic mechanical properties may be described by the HN model. The accuracy of the predicted properties is limited by the degree to which the experimental data may be fit to the HN model in the complex plane. In the case of the neoprene elastomer, there was generally a good fit of the experimental data to the HN model in the complex plane, with the exception of the low modulus region. As a result, the high temperature predictions for the neoprene elastomer were less accurate than the lower temperature predictions.Shift factors were derived from the temperature dependent relaxation times, and applied to frequency multiplexed data to create master curves. The resultant curves had overlapping temperature segments and were smooth functions of frequency.Mechanical and durability performance of carbon nanotubes (CNTs) and nanosilica (NS) admixed cement mortarFor many decades, investigations for improving the behaviour of conventional cementitious composites both in terms of strength and durability is continuously carried out by adding various nanomaterials, replacing some amount of cement with different nanomaterials. Nanotechnology or Nanoscience is one of the most promising areas trending these days for studying enhanced properties of cementitious composites and is almost touching every field of study like medicine, environment, petroleum industry, etc. In Civil Engineering, the addition of nanomaterial in the cementitious matrix leads to enhanced mechanical properties like flexural strength, compressive strength, Young’s modulus, etc., as well as improved durability properties. In the present study, mortars incorporating NS (1% by cement weight) and MWCNTs (0.3% by cement weight) of 4 different types, i.e., functionalized and un-functionalized with two different diameters (10–20 nm and 30–50 nm), were prepared for assessing mechanical and durability properties at 28, 56, 90 and 120 days. Compressive and flexural strength was enhanced for nano admixed mortar than control samples (CS). Also, the nano admixed mortar was proved to be excellent in resisting sulphate attack and abrasion. Ultrasonic pulse velocity (UPV) results showed good quality for nano admixed mortar samples. In all the study cases, the mortar sample prepared with treated MWCNTs and having a diameter of 30 nm–50 nm (T2) performed better than CS and other nano admixed mortar. Microstructure images strongly correlated with the experimental results.Nanotechnology, especially nanomaterials, are being used in various fields of studies for the past few decades and performed excellently in many aspects, viz. enhancing mechanical and durability properties of cementitious composites. Carbon nanotubes (CNTs) unique mechanical properties made them the most promising nanomaterial to be used in improving the properties of mortar and concrete. Young’s modulus, tensile strength, ultimate strain capacity of CNTs are 1TPa, 60GPa, and 12%, respectively Recently, a review paper discussed the effect of nanosilica (NS) addition on cement concrete and concluded that NS increases the flexural, compressive, split tensile strength of the concrete and gives a denser matrix than plain concrete. The use of nanomaterials also enhanced the durability of concrete, thus providing a sustainable solution in the Civil engineering field Various researchers performed durability studies of cementitious composites incorporated with different types of nanomaterials. In one of the studies, the effect of nanoparticles on microstructural surface characteristics, abrasion resistance, and skid resistance of concrete pavements were seen. Nano modified concrete yielded the most considerable improvement in abrasion resistance (about 23%) Since there is a scarcity of combined mechanical and durability investigation with CNTs and NS admixed mortars. Therefore, further investigation in this area is important to utilize the full potential of these nanomaterials on the behaviour of cementitious composites. Hence, in the current study, an effort has been made to gather both mechanical and durability properties test results carried on the different types of CNTs and NS admixed cement mortar. Also, Scanning Electron Microscopy (SEM) was done to analyze the efficiency of nanomaterials within the cementitious matrix.OPC 43-grade cement by Ultra Tech Company conforming to IS: 8112-1989 (Reaffirmed 2005, Bureau of Indian Standard, New Delhi) having a specific gravity of 2.15 was used. The soundness of cement was obtained as 1.2 mm, which is well within the requirements of IS: 8112-1989.Indian Standard Sand conforming to IS: 650-1991 of three sizes 2 to 1 mm, 1 to 0.5 mm, 0.5 to 0.09 mm from Pinal Corporation, Ahmedabad was used. Properties of sand are listed in Nanosilica (NS) obtained from Fibre Zone India, Ahmedabad, Gujarat, was used. The specifications of the NS are listed in Four types of MWCNTs (Un-functionalized and functionalized by – COOH) by Adano Technology were used. Specifications are listed in For exposure in sulphate environment, magnesium sulphate powder with 97% purity was purchased from Triveni Interchem, Pvt. Ltd. Valsad, Gujarat.Proper dispersion of these nanomaterials cannot be ensured by hand mixing. The most common technique is sonication, which was used here. The required quantity of MWCNTs and NS were first taken with a mixture of water and superplasticizer (0.4% SP by cement weight). The resulting solution was then subjected to sonication by Sonica Bath Sonicator for 20 min. Steps of sonication are shown in The mix proportions were designed according to IS: 2250-1981 with a w/c ratio of 0.55 and cement to sand ratio of 1:3 and are presented in . Sonicated solution was mixed with a dry mixture of cement and sand and then poured in the moulds of 160 mm × 40 mm × 40 mm, conforming to IS: 10078-1982. The moulds were lightly oiled before use. The mortar sample was compacted in 3 layers and kept in mould at 100% relative humidity for 24 h and then transferred to a curing tank of water for 28 days and then in sulphate solution for 28, 56, 90, 120 days for the flexural strength test. Number of specimens casted for various test is mentioned below (The test was performed on a flexural testing machine consisting of two roller supports of a diameter of 10 mm spanning 100 mm. The third roller with the equal diameter and at the equal distance from the first two supports was used to transmit the load ‘P’ on the opposite side of the sample, as shown in (a). The load was applied at a rate of 50 ± 10 N/s. The flexure testing machine with the specimen is shown in (b). Flexural strength is determined by using the relation mentioned in M= Maximum bending moment under central point loadingB= Side of the square cross-section of the prismCubes of size 40 mm × 40 mm × 40 mm were cut from the un-cracked portion of the sample after the flexure strength test, as shown in (a). The test was done by placing the cube between two rigid metal plates in a compression testing machine. The rate of loading was 200 kg/cm2/min. (b) shows the compression testing machine with a sample. Compressive strength will be given by the ultimate load divided by the cross-sectional area.For this test, flexural samples were cured in magnesium sulphate solution (10%/litre of water), the pH of the solution is maintained at 6.5 ± 0.5, and sulphate water was changed every month. Samples were tested for change in length at 56, 90, and 120 days by measuring the distance between the demic points glued to mortar samples using an extensiometer having the least count of 0.002 mm, as shown in Percentage change in length is given as-Los Angeles abrasion test was done to find the abrasion resistance of mortar specimens. The apparatus consists of a hollow steel cylinder, closed at both ends. It has an inside diameter of 70 cm and an inside length of 50 cm, mounted on stub shafts about which it rotates on a horizontal axis. Six abrasive charges, consisting of cast iron spheres with an approximate diameter of 4.8 cm and 5Kg weight of the specimen, were taken and rotated in a drum for 16 min. The percentage of mass loss was determined as:W1 weight of the specimen taken initially, i.e., 5 Kg; W2 weight taken after the test.This test was performed with the Resipod instrument to measure concrete permeability towards the ingress of aggressive ions. It is an effective and quick way to assess concrete permeability. (a) and (b) represent the testing of the mortar sample using Resipod.In this method, concrete’s permeability is indirectly measured in terms of resistance provided by the matrix towards the movement of aggressive ions (like sulphate, chloride, etc.) within the composite. The likelihood of corrosion (transmission of ions) according to the different resistivity value is mentioned in the operating manual of Resipod as (UPV is a non-destructive test to assess the quality of the mortar specimen. This involves measuring the time travel of pulse within a known path length from which pulse velocity was evaluated, as shown in . The path length is taken as 160 mm. Five readings were taken for each specimen. Depending upon UPV values, its quality can be given as Excellent, Good, Medium, and Poor as per IS: 13311(part1) - 1992.The changes in the microstructure of the mortar sample due to the addition of NS and MWCNTs with that of control was assessed by scanning electron microscopy (SEM). Crushed sample after compressive strength test at 28 and 120 days was taken to University Sophisticated Instruments Facility (USIF) Centre, AMU, Aligarh. The Scanning Electron Microscope (SEM) from JOEL, Japan, was used to study the microstructural characterization.Six batches of mortar samples were tested for evaluating various mechanical and durability properties viz. flexural strength, compressive strength, length expansion, abrasion resistance, resistivity, ultrasonic pulse velocity test at 28, 56, 90, and 120 days. Also, a cost analysis was done to find the economic feasibility of using NS and MWCNTs in cement mortar. represents the average flexural strength of each type of mortar sample at 28, 56, 90, and 120 days. The values follow an increasing trend upto 56 days and then decreased. The order of increment of strength was CS < NS < U1 < T1 < U2 < T2. Sample T2 exhibited maximum strength i. e. 9.08 MPa, which was 38.63% higher than the CS at 56 days. At 120 days, a 31.43% increment was observed for T2 than CS even after sulphate attack. Out of each type of specimen, T2 performed better in enhancing the strength at all curing ages. The improvement in the strength is because of the increased hydration due to NS and CNTs. These nanoparticles not only fill the pores but act as a catalyst in promoting hydration reaction, thus increasing the strength of the matrix. Further, the reduction in strength after 56 days due to immersion of the sample in sulphate water is because of two reasons. Firstly, an expansive material, namely ettringite, might be formed due to the reaction between calcium aluminate and calcium sulphate. The presence of sulphates increases the formation of ettringite. Secondly, magnesium sulphate causes significant damage and debonding of C–S–H gel leading to reduced flexural strength at 90 and 120 days.The average compressive strength of each type of mortar specimen is shown in . The same trend, as observed in the previous section, was obtained. The compressive strength of T2 was higher than that of CS at each age and from other mixes too. About 16.4% increment in compressive strength was seen for T2 than CS at 56 days. Also, at 120 days, 15.35% enhancement was seen for T2 than CS. The addition of these nanomaterials confined the matrix and increased the capacity of taking load efficiently and, in turn, enhanced the strength. The mechanism for degrading strength from 56 to 120 days is the same as discussed in the previous section. The results showed that T2 outperforms other types at all ages.Although due to the variation in the bending moment during the flexure test, the entire length may get disturbed. The disturbance is not much dominant near the end of the beam as the effect of bending moment decreases as we move away from the load positions. Hence, the compressive strength obtained from the cubes cut from the un-cracked portion of the beam is correct.With the increased age of curing, the strength of the specimen should have been increased ideally, but specimens are cured in sulphate solution; hence, the results are showing a decreasing trend after 56 days. Even then, the compressive strength at 90 and 120 days is still higher than the control specimens at the same ages due to the addition of NS and CNTs. Initially, the strength of the specimen increases until 56 days because of the increased hydration due to the addition of these nanomaterials. After 56 days, strength gets decreased slightly due to the degrading effect of sulphate and that too to a lesser extent as these nanomaterials are responsible for the increase in strength. The reduction in the compressive strength for 90 and 120 days is due to the formation of the expansive product like ettringite and gypsum. Additionally, significant damage and debonding of C-S-H gel are caused due to the magnesium sulphate present in the matrix.. CS exhibited more expansion value than other specimens at each age. T2 showed lesser expansion values than CS and other nano admixed mortar at each age, representing T2 as a good reinforcing material. Expansion value of 0.078% was seen for T2 at 120 days, and for CS, the maximum value was achieved as 0.091% (63% increase in expansion than CS at 56 days), which was lesser than the limit provided in ASTM C 1012, i.e., 0.1%. In the presence of sulphate, a reaction between Ca(OH)2 and C–S–H gel takes place, leading to the formation of gypsum and ettringite. These compounds cause internal stresses resulting in the length expansion of the sample. On the other hand, T2 has a more densified structure than CS leading to increased strength and less ingress of SO42- ions, in turn giving a lesser value of expansion.Abrasion resistance results are shown in with the observation of concrete mass loss taking during the 16 min. All the specimens represented increased abrasion resistance shown by decreased mass loss of sample till 56 days. Then resistance to abrasion gets slightly reduced due to decrement in the strength from 56 to 120 days. The reduced mass loss is showing a direct relation of abrasion resistance with the compressive strength. Also, T2 exhibited more abrasion resistance than CS and other nano admixed cement mortar at each age. About a 29% decrease in mass loss is observed for T2 than CS at 120 days.The resistivity values decrease for all the specimens due to the enhanced ingress of sulphate ions with time. Although negligible to low risk of corrosion was seen, which in turn reflected a fairly durable matrix even after sulphate attack. The reason behind its behaviour is the effective filling of pores by NS and MWCNTs, making the structure more reluctant to ingress of more SO42- ions. The results of the resistivity are given in . Most of the resistivity values are found to be more than 100KΩcm, which indicates a negligible risk of corrosion.The UPV values get decreased with the increase in the age, showing that the quality of the mortar sample decreased with the increased age of curing in sulphate solution. CS showed less value of velocity than nano – admixed cement mortar, especially T2, exhibited higher values than other samples representing good quality as its strength was also enhanced. Even after the decrement, the values of each sample were very close to 4 km/s representing the good quality of the specimen, as shown in . The good quality was a result of good strength achieved in the case of nano admixed cement mortar, as observed in . (a) to (d) showed the selected SEM images of CS and T2 with 2000× magnification. (a) represented the formation of characteristic products like C–S–H gel and CH (Portlandite) in the form of cylindrical rods of a larger diameter, which gets reduced in size over time, resulting in the comparatively uniform matrix at 120 days as reflected by (b) gave the justification of reduced strength in the case of CS at 120 days than at 28 days, as shown in (a). NS and MWCNTs were distributed properly in the matrix filling the pores of the structure leading to enhanced strength in the case of T2 than CS at 28 and 120 days, as shown in . A needle-like structure named ettringite was also found in the matrix, which is a result of the reaction between SO42- ions, Ca(OH)2 and C–S–H gel, which in turn reduces the strength of CS and T2 from 28 to 120 days. A more uniform C–S–H gel in case of T2 at 28 and 120 days than CS, as shown by (c) and (d) even after sulphate attack, is a reason for enhanced strength values for T2 at all ages as reflected from due to its pore filling ability. Thus, microstructure images proved to be clear evidence of experimental results obtained by conducting various tests on samples.Cost is a prime constraint in introducing any new technology either in the form of software, material, etc., to the real world. Therefore, cost analysis is an essential task to check the economic feasibility of the work. The cost of these nanomaterials is significantly high. Still, the advantages we get in the form of increased strength are much more, making it worthful to be used in cementitious composites (From the various tests performed on mortar samples, the following conclusions are drawn:The flexural and compressive strength of nano admixed cement mortar enhanced significantly than the CS at each age. Out of all the CNTs and NS admixed cement mortar, sample T2 performed better in all cases. For T2, the flexure strength increment was found to be 38.63% and 31.43% at 56 and 120 days. Also, Compressive strength was enhanced by 16.4% and 15.35% for T2. This enhancement is because of the increased hydration and pore-filling ability of these nanomaterials, making the matrix more densified and capable of taking larger loads efficiently.Length expansion is one of the adverse effects seen in mortar samples due to sulphate attack. CS exhibited maximum expansion. While T2 showed an increase of 0.078%, which is less than the value of CS and well within the limit given in ASTM C 1012, i.e., 0.1%. Less expansion in T2 is because of densified mortar matrix leading to less ingress of SO42- ions.Abrasion resistance was improved until 56 days, and then resistance slightly decreased due to the decrement in strength, showing a direct relationship between strength and abrasion resistance. Overall, a 29% decrement in the mass loss was observed for T2 than CS at 120 days.Resistivity results showed a decrement in the value from 28 to 120 days for all the specimens because of the movement of ions in the pores of the matrix. In general, the negligible to low risk of corrosion was represented by the values of each sample, which reflected a fairly durable matrix.UPV results showed that T2 gave higher values at each age than CS because of the enhanced strength. Even after decrement due to sulphate attack, the values of each sample are very close to 4 km/s, representing the good quality of the specimen, thus a good durable matrix.Improved and denser microstructure was obtained for nanomaterials admixed mortars as observed through various microstructural images, which correlate the improved properties of the matrix.The cost of NS and MWCNTs are appreciably high. Still, the advantages obtained in terms of increased strength and improved durability are of utmost importance, making these nanomaterials worthful to be used in cementitious composites.From the comprehensive study, one can conclude that the MWCNTs proved to be good reinforcing material as it improves both the mechanical and durability properties of mortar. Also, T2 performed better in all cases of the study.Varisha: Conceptualization, Resources, Writing - review & editing. Mohd Moonis Zaheer: Conceptualization, Supervision. Syed Danish Hasan: 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.Effects of mechanical alloying on the characteristics of a nanocrystalline Ti–50 at.%Al during hot pressing consolidationTwo different powder metallurgy processes, i.e., reactive and non-reactive sintering, were investigated for the production of titanium aluminides. Ti–Al intermetallics have been successfully produced by mechanical alloying and hot pressing of powders with a nominal composition of Ti–50 at.%Al. A Ti(Al) solid solution was formed at the early stage of milling that transformed to an amorphous phase at longer milling times. On further milling, the amorphous structure transformed to a supersaturated hcp-Ti(Al) solid solution with trace amounts of TiAl after 80 h of milling, which was completely transformed to TiAl, Ti3Al, and TiAl3 intermetallic compounds after additional milling up to 100 h milling with particles of about 200 nm. Blended elemental powders and 100 h MA-ed powders were used for the reactive and non-reactive sintering processes, respectively. The results showed that the HP-ed pre-alloyed powder had better properties in terms of density, hardness, homogeneity of microstructure, yield stress, and ductility than that produced by reactive sintering. The major contribution to the yield stress of the sintered pre-alloyed powder comes from the nanometer-sized grains of intermetallics in accordance with the Hall–Petch relation.Titanium aluminide intermetallics are recognized as compounds with such desirable properties as low density, high strength, high modulus, and good oxidation resistance. Many efforts have been devoted to the fabrication of Ti–Al alloys using powder metallurgy (PM) processes, especially mechanical alloying (MA) Production of Ti–50 at.%Al has been reported by several researchers, all of whom introduced the supersaturated hcp-Ti(Al) solid solution as their final MA product Ti (60–200 μm, 99.9% purity) and Al (40–100 μm, 99.9% purity) powders were mixed to give the composition Ti50Al50 (at.%) which was then charged into a WC vial with WC balls under a high purity argon atmosphere. The ball to powder weight ratio (BPR) was 10:1. The milling was performed in a Fritsch P6 planetary ball mill for periods varying from 0 to 100 h at a speed of 300 rpm. Dispersants, such as Hexane For the purposes of reactive and non-reactive sintering, HP was performed on two different series of powders: (1) 100 h-milled (pre-alloyed) powders for the non-reactive sintering process, and (2) blended elemental powders for the reactive sintering process. The powders were hot pressed under 50 MPa for 10 min at 1000 °C under a high purity argon atmosphere. The HP-ed samples were 20 mm in diameter and about 12 mm in thickness. After hot pressing, the consolidated samples were ground and polished.The milled and HP-ed samples were characterized by means of X-ray diffraction (XRD) using a Seifert 3003TT diffractometer with Cu Kα, operating at 40 kV and 30 mA. The crystallite size of the as-milled powders was determined by X-ray line broadening and calculated using the Scherrer equation where β=(βM2−βI2)1/2, βM is the full width at half maximum (FWHM), βI is the correction factor for instrument broadening, θ is the angle of the peak maximum, and λ is the Cu Kα weighted wavelength (λ |
= 0.15406 nm).Using a Vega©Tescan machine, scanning electron microscopy (SEM) was carried out to characterize the morphology of the milled powder, the surfaces of the consolidated samples, and the fracture surface topography. Energy-dispersive X-ray spectroscopy (EDS) coupled with SEM was used for the semi-quantitative investigation of the microstructure of the HP-ed samples.The density of the HP-ed samples was determined using the immersion method in distilled water based on Archimedes principle. Open porosity of HP-ed samples was calculated using the mass measurements performed during density determination. Hardness measurements were conducted using a Koopa model UV1 machine.Compressive tests were carried out on cylinder samples (D: 4 mm, L: 6 mm) both at room temperature and at 700 °C using an Instron model 8503 tensile/compressive testing machine at a constant strain rate of 10−2 |
s−1. All the data reported are averaged out of at least three results.The evolution of the transformations occurring during milling was followed by XRD. shows the diffraction pattern for Ti50Al50. It can be seen that the XRD pattern of as-received powder is almost similar to that of 10–40 h-milled powders. However, peak broadening and decreasing intensity were observed with milling time due to the decrease in crystallite size from 26 nm after 10 h to about 13 nm after 40 h milling. Shifting of the main reflexion of Ti peaks towards higher angles was also observed, which was due to the reduction in the lattice parameter attributed to a distortion of the Ti lattice by Al diffusion. From the widely accepted Ti–Al phase diagram , after 60 h of MA, the peaks completely broadened between angles of 35–40°; this is an indication of the amorphization of the powders. The XRD results were verified by transmission electron diffraction (TED) (not shown). It is interesting to note that the free energy curve of the amorphous phase in the Ti–Al system is lower than those of the solid solution and intermetallic phases Some studies have reported the formation of a stable fcc-TiN during the milling of Ti and Al ), determined from the XRD patterns according to Bragg's relation, decreased gradually up to 40 h of milling and an abrupt decrease was observed between 40 and 80 h of milling; this finding confirms the formation of the supersaturated Ti(Al) solid solution after 80 h of milling due to the dissolution of large amounts of Al into the Ti lattice. This phase can also be confirmed by vanishing of the Al peaks. According to , the ratio of c/a decreased with milling time and a dramatic decrease was observed after 40 h of milling.The morphology of as-received and MA-ed powders at different milling times was investigated by SEM analysis, as shown in a, Ti powders appear in irregular shapes and in various sizes, but the particles of Al are mainly round-shaped. The early stages of MA (before 10 h of MA) result in the formation of powder agglomerates (b) due to the ductility of Al. Further milling leads to increased deformation and work hardening, and the agglomerated powders then disintegrate into fragments producing finer particles after 10 h or after up to 80 h of milling (c–f). Upon further milling, particle size abruptly reduces down to about 200 nm after 100 h of milling (g). This is because of the formation of TiAl, Ti3Al, and TiAl3 intermetallic compounds. It is known that the titanium aluminides as intermetallic compounds are brittle phases. Formation of these compounds leads to a sharp increase in the reduction of particle size, as shown in present the XRD patterns of the HP-consolidated pre-alloyed and elemental powders, respectively. Comparing a with that of the MA-ed powder before HP, one can see the reduction in peak widths. This reduction is due to the increasing crystallite size and decreasing lattice strain; but nanostructured grains are retained after HP. It has been postulated that the higher than expected stability of nanostructured grains is the result of a number of factors such as uniformity of the crystallite size, solute segregation to grain boundaries, achievement of a low grain boundary energy during annealing, straightness of grain boundaries, and large number of grain intersections, the latter effectively pinning the grain boundaries b that TiAl, Ti3Al, and TiAl3 were produced after HP of elemental powders for reactive sintering.The density and amount of porosities obtained during reactive and non-reactive sintering have been shown in . The density of the HP-ed sample made with reactive sintering is lower than that of the HP-ed pre-alloyed powder. Both kinds of the HP-ed samples possess relatively adequate densities to exhibit considerable mechanical properties.Nanocrystalline powders have a high potential for agglomeration during MA The hardness of both HP-ed samples has also been shown in . The hardness value of the HP-ed pre-alloyed powder is almost three times higher than that of the HP-ed elemental one, which is in consistence with the density results. On the other hand, the increased density induces increased hardness. Moreover, as can be observed in the SEM micrographs (), the intermetallic particles in the HP-ed pre-alloyed powder are very fine compared to those of the HP-ed elemental one (b). So refinement of the non-reactively sintered sample is associated with a decrease in the mean intermetallic inter-particle distance.The harmful effect of pores and porosities is indicated by a proportional relationship between density and hardness. Porosities lead to the weakening of the sample because the available stress bearing area is reduced, thereby lowering the amount of stress that a sample is able to withstand.The results of compressive tests at room temperature and at 700 °C are presented in . All the tests revealed relatively brittle fracture characteristics. The compressive yield strength of the non-reactively sintered sample is higher than that of the reactively sintered one. In addition, the ductility of the first one is also greater than the second one, which reveals the improvement of ductility as a result of using the non-reactive sintering process. Enhanced compressive yield strength and improved ductility were mainly caused by nano-particle powders. This is because the volume of grain boundaries increased which naturally gave rise to fast diffusion paths. These fast paths made a few initial tiny cracks which quickly closed during the deformation process and, therefore, crack growth and propagation were avoided to a certain extent, contributing to the fine grain toughness.It is worth noting that the mechanical properties of metallic materials are influenced by grain boundaries, solute atoms, dislocations, second-phase particles, dispersoids, etc. Out of these, only the refinement of grain size strengthening mechanism is relevant to the present work. Grain size is known to have a significant effect on the mechanical behavior of materials and on yield stress, in particular. The dependence of yield stress on grain size in metals is well established. Yield stress, σ, for materials with the grain size d is found to follow the Hall–Petch relation:where σ0 is the friction stress and k is the Hall–Petch constant a and b illustrates the microstructure of the HP-ed samples by both reactive and non-reactive processes, respectively. As expected, the particle size of the blended elemental powder after HP is obviously larger than that of the pre-alloyed powder. In addition, more homogeneous phase distributions are observed in the latter Figure. It should be mentioned that the increase in milling time increases the lattice strain and the reduction in the crystallite size, which can improve the sinterability of the 100 h-milled powder.The EDS analysis was used to identify the three different areas revealed in both HP-ed samples shown in . The results of this analysis are presented in . According to these results, the likely phases are TiAl, Ti3Al, and TiAl3 corresponding to areas 1, 2, and 3, respectively. It is obvious from a that the TiAl intermetallic compound has the greatest amounts of the phases. Ti3Al is only found in some separate islands in the TiAl matrix, but TiAl3 surrounds the TiAl phase. This distribution of intermetallics during reactive sintering is due to the non-homogenous powders that consolidate during the HP process. The above-mentioned observations are not made in the HP-ed pre-alloyed powder in which a good particle distribution is obtained. The EDS results obtained are in good agreement with XRD analysis of both HP-ed samples () that reveal the formation of TiAl, Ti3Al, and TiAl3 intermetallics after both reactive and non-reactive sintering processes. illustrates the fracture surface of the samples made by reactive and non-reactive sintering processes. Both figures exhibit a mixture of intergranular and transgranular fractures. But, as observed in , the reactively sintered sample is more brittle and, so the cleavage surfaces are evidently more conspicuous.The results of this study show that titanium aluminide powders can be produced by mechanical alloying of elemental Ti and Al at times longer than 80 h. Increasing MA time led to a dramatic decrease in the particle size of titanium aluminide powders down to about 200 nm after 100 h of milling. By reactive and non-reactive sintering processes, titanium aluminide samples could be produced from Ti and Al elemental powders and titanium aluminide powders, respectively. According to results obtained, the non-reactive sintering process promotes better physical and mechanical properties.Intrinsic and extrinsic size effects in the deformation of amorphous CuZr/nanocrystalline Cu nanolaminatesIntroducing a soft crystalline phase into an amorphous alloy can promote the compound’s ductility. Here we synthesized multilayered nanolaminates consisting of alternating amorphous Cu54Zr46 and nanocrystalline Cu layers. The Cu layer thickness was systematically varied in different samples. Mechanical loading was imposed by nanoindentation and micropillar compression. Increasing the Cu layer thickness from 10 to 100 nm led to a transition from sharp, cross-phase shear banding to gradual bending and co-deformation of the two layer types (amorphous/nanocrystalline). Specimens with a sequence of 100 nm amorphous Cu54Zr46 and 50 nm Cu layers show a compressive flow stress of 2.57 ± 0.21 GPa, matching the strength of pure CuZr metallic glass, hence exceeding the linear rule of mixtures. In pillar compression, 40% strain without fracture was achieved by the suppression of percolative shear band propagation. The results show that inserting a ductile nanocrystalline phase into a metallic glass prevents catastrophic shear banding. The mechanical response of such nanolaminates can be tuned by adjusting the layer thickness.The plastic deformation of metallic glasses profoundly differs from that of crystalline materials due to the absence of long-range atomic periodicity. While plasticity of crystals is mainly achieved by dislocations, metallic glass is deformed through shear transformation zones An important approach to increasing the ductility of a metallic glass is to introduce a softer crystalline phase into it Another way to enhance the plastic deformation of metallic glasses, besides inserting crystalline portions, is shape confinement: A decrease in the aspect ratio of the sample (i.e. samples with small dimensions in the directions perpendicular to the applied load) generates interacting, deflected shear bands with a wavy shape Some pure nanocrystalline (nc) materials probed in sub-micron scale mechanical experiments indeed exhibit a different trend. For example, Jang and Greer These two ideas, namely promoting ductilization by amorphous–crystalline composite design and by size control, motivated us to synthesize a multilayered glass-containing composite with confined metallic glass fractions. The aim is to investigate the mechanical response and the governing deformation mode of such materials at the sub-micron scale.Recently, investigations on such amorphous/nanocrystalline (am/nc) CuZr/Cu multilayers (also referred to as nanolaminates) have attracted considerable interest Therefore, in this work, amorphous CuZr/nc Cu nanolaminates with varying Cu layer thickness were synthesized. We first used nanoindentation testing to study the mechanical response of these multilayers. Also, we fabricated micron- and submicron-scale pillars to study the effect of the crystalline (Cu) layer thickness on the deformation behavior of these nanolaminates. Based on the experimental observations, we study the deformation behavior as a function of the intrinsic Cu layer thickness and also of the extrinsic pillar size effect.Amorphous CuZr/nc Cu nanolaminates were deposited on Si (100) wafers by direct current magnetron sputtering. Targets of pure Cu (99.99%) and Zr (99.99%), each 5.08 cm in diameter, were used to deposit alternating layers of amorphous CuZr layer and pure nc Cu layers. The base pressure was ⩽10−7 |
mbar and the processing pressure was 3 × 10−3 |
mbar using pure Ar gas. The substrate rotated at a frequency of 10 min-1. Three kinds of nanolaminates with different layer thickness were prepared, namely, 100 nm CuZr (amorphous)/10 nm nc Cu (referred to as MS10), 100 nm CuZr (amorphous)/50 nm nc Cu (MS50) and 100 nm CuZr (amorphous)/100 nm nc Cu (MS100). The total stacked thickness of the CuZr/Cu multilayer compounds is ∼1200 nm with an amorphous CuZr cap layer. The structure of the as-deposited thinfilms was characterized by X-ray diffraction (XRD; Bruker D8 diffractometer), field-emission scanning electron microscopy (SEM; FEI Helios Nanolab 600) and transmission electron microscopy (TEM;J EOL JEM-2200FS).The hardness and indentation modulus of the multilayers were measured with a diamond Berkovich indenter tip in conjunction with a load and depth sensing nanoindenter system (Hysitron TriboIndenter 800). The indentation depth amounted to ∼5–15% of the total film thickness. A minimum of 12 indents were performed on each specimen to obtain averages and standard deviations for hardness and reduced modulus. Fused silica was employed for tip area function calibration according to the method of Oliver and Pharr The engineering stress, σ=F/A0, was calculated from the measured force F and the pillar cross-sectional area A0 at 20% of its height away from the top of the pillar (deformation was confined to the top due to the tapered geometry). To avoid an ambiguous determination of a first deviation from linear elasticity (yield stress) and reduce the influence of early plasticity and the artificial, i.e. geometric, work-hardening due to the tapered geometry, we select 5% plastic strain as a compromise to determine the flow stress. For calculating the engineering strain, the displacement was firstly corrected by using Eq. where P is the applied load and di and dsi are the diameters of the pillar top and bottom, respectively. Ei and Esi are the Young’s modulus of diamond (1220 GPa The XRD patterns of the as-deposited CuZr/Cu nanolaminates (see ) reveal that the thickness increase of the Cu layers matches the intensity increase of the Cu (111), Cu (200) and Cu (222) peaks. Comparing the ratio of the (200) and (222) XRD intensities in the CuZr/Cu nanolaminates with that in pure Cu shows that the as-deposited layers are textured with a majority of the crystals oriented with their {111}-planes in the layer plane. This is confirmed by selected area diffraction patterns (SADP, see inset in a). The extra (111) spots in reciprocal space indicate the existence of nanotwins. Cross-sectional microstructures of the nanolaminates were examined in detail. A representative bright field TEM micrograph of MS50 (a) shows a drastic contrast difference between the amorphous CuZr layer and the nc Cu layer, clearly revealing the layered structure. The double spots around (111) in the inset SADP and fringes in the dark grains (the ones in Bragg condition) indicate (111) nanotwins in the as-deposited state, which is common in magnetron sputtered Cu thin films b) show that neither crystalline phases in the amorphous layer nor transitional crystalline structures at the am/nc interfaces are present. The chemical composition of the materials was determined by atom probe tomography (LEAP 3000X HR, Cameca Instruments). The results show that the Cu concentration is 54.2 ± 0.3 at.% in the amorphous CuZr layer and 99.2 ± 0.5 at.% in the nc Cu layer.Representative loading/unloading curves and the corresponding hardness of the am/nc CuZr/Cu nanolaminates are summarized in for different penetration depths. No obvious “pop-in” (strain burst) events were detected in the load–displacement curves, indicating that no catastrophic shear bands occur during loading summarizes the nominal hardness values derived from ∼10% penetration depth of the film thickness (data from 3 mN load). We find the trend of a decreasing hardness level as a function of an increasing Cu layer thickness and Cu volume fraction in the laminates.The cross-sectional samples of MS10 and MS50 after 5 mN indentation were cut by FIB for subsequent SEM and TEM probing. shows a series of micrographs with increasing magnification in the indented sample MS10. a shows, as marked by red arrows, that the glass layers are locally deformed along the plane of maximum shear load. The localized stress cannot be dissipated by the top Cu layer alone; hence the load is transmitted to the layers beneath. The layered morphology remains intact along the shear plane, with no apparent discontinuities or cracks. This indicates that even Cu layers with only 10 nm thickness can suppress catastrophic shear band failure of the metallic glass matrix. This is fully consistent with the observed absence of pop-in or pronounced strain burst events when the MS10 samples are subjected to nanoindentation. The Cu layer away from the kinked region undergoes a strain below ∼0.3 in the layer thickness direction, while the strain around the kinked region is above 0.8 in layer thickness direction. c shows a higher resolution image of this sheared region: the Moiré fringes shows a cross-sectional TEM micrograph of sample MS50 after 5 mN loading. In contrast to sample MS10, no plastic instability was observed. Instead, the Cu layer tends to rotate to comply with the local load. Apparently, the two different layers were co-deformed, as shown by the thickness reduction of both the nc Cu and the amorphous layer in b. The variance in thickness reduction at different positions arises from the inhomogeneous deformation state below indents. The absence of preferential thinning of the Cu layers and the absence of shear bands indicate a homogeneous deformation of the CuZr layer for this sample.d shows the engineering stress–strain curves from the pillar compression tests for the three sample types. From the literature, the stress–strain curves of a fully amorphous homogeneous CuZr pillar The compressed MS50pillar shows only two well-defined shear bands nucleated in the amorphous layer. They do not penetrate the underlying Cu layer but remain confined inside the amorphous zone. Accordingly, the stress–strain curve does not show significant strain bursts, d. This means that each shear band event in sample MS50 released less elastic stored energy than a corresponding event in sample MS10. We choose the stress at 5% plastic strain to compare the flow stress of different material systems. Interestingly, the flow stress of sample MS50 is comparable with that of sample MS10, indicating that the amorphous/crystalline interfaces are characterized by a certain strengthening plus confinement effect.Sample MS100 has a flow stress of 1.72 GPa, mainly due to preferential deformation of the Cu layers, as revealed by their slight individual barreling, c. As the strain increases, strong work-hardening occurs, due to the high work-hardening capacity of nc Cu. Also, the topmost amorphous CuZr layer deformed homogeneously, expanding its diameter from ∼600 to ∼700 nm. When compared to the stress–strain curve of the nc Cu pillars (data taken from Ref. 2 μm diameter pillars were fabricated for each of the multilayer samples. shows a 52° tilted SEM image of the 2 μm diameter pillars deformed to ∼40% strain (MS50, MS100). Sample MS50 shows multiple shear bands at the pillar surface, a. Most of the shear bands are either deflected or “captured” by the Cu layers, but a few of the bands penetrate through multiple layers. Accordingly, the plateau after yielding in the stress–strain curve (stage II in d) indicates that there is no work-hardening during further plastic deformation. For sample MS100, there are no visible shear bands on the entire pillar surface. As the deformation of the pillar increases, barreling of the entire nanolaminate occurs, but there is no obvious extrusion of the copper layers. This indicates that no preferential deformation of the nc Cu layers takes place. shows the effect of the pillar diameter on the deformation behavior of the three types of nanolaminates. For the MS10 pillars, a–c shows that few large shear bands control the deformation of the pillars for all sizes. For the smallest MS50 and MS100 pillars (300 nm, d and g), strong barreling of the Cu layers is observed. However, the barreling of the Cu layers decreases with the increase in pillar size, suggesting more deformation and dislocation interactions within the Cu layer and also enhanced strain compatibility between the nc and amorphous layers. For larger pillar sizes (900 nm, f), the shear bands are either deflected or absorbed by the underlying Cu layers. More confined shear bands with length scales close to the amorphous layer thickness are formed for strain accommodation. For the large pillars in the MS100 samples, the absence of shear steps and the diameter changes after deformation indicate a more homogeneous co-deformation The compressive stress–strain curves for the pillar compression tests are shown in . The strong barreling observed for the large pillars and the associated increase in the cross-sectional area lead to a high unloading modulus and will not be further analyzed here. However, the flow stress values taken at 5% flow strain are rather reliable in describing the stress state of the pillars. When the pillar diameter is reduced from 2000 to 750 nm, the flow stress of the MS10 pillars firstly decreased from 3.01 to 2.25 GPa. As the pillar diameter further shrinks to 300 nm, the flow stress increases to 2.62 GPa. The same trends are also observed in samples MS50 and MS100 when decreasing the pillar size from 2000 to 300 nm. summarizes the flow stress values obtained from both the pillar tests (using ∼8% strain offset; symbols) and the nanoindentation tests where the flow stress was calculated as hardness/2.7 (dotted lines) Another possible explanation involves the {111} nanotwins that may contribute to out-of-plane deformation in the as-deposited nc Cu layers. You et al. . However, if the loading direction is 45° relative to the twin boundary plane, “soft mode” slip is enabled, where dislocations move parallel to the twin boundaries, leading to a low flow stress. Such anisotropy associated with dislocation slip in nc Cu was also reported elsewhere gives an example of the nanotwin alignment and of the high nanotwin density observed inside the Cu layer in sample MS10. The average twin spacing amounts to ∼5 ± 2 nm in samples MS10 and MS50 and 7 ± 3 nm in sample MS100. This means that the nanotwin spacing does not change substantially with the Cu layer thickness. This is plausible since the same deposition conditions were employed for all samples.The high flow stress of am/crystalline nanolaminates results in part from the hetero-interfaces confining dislocation slip inside the nc Cu layers. In laminates composed of soft/ductile layers and hard/brittle phases, plastic flow is initially governed by the soft/ductile phase where M |
≈ 3.7 is the Taylor factor of the {111} textured Cu, h is the Cu layer thickness, h′=hsinθ is the thickness of the layer parallel to the glide plane, θ is the angle between the slip plane and the interface, b |
= ∼0.2556 nm is the magnitude of the Burgers vector, ν |
∼ 0.343 is the Poisson ratio of Cu and μ∗ is the effective shear modulus of the (111) Cu layer. The geometrical factor α |
≈ 0–1 represents the core cut-off parameter and contains the contribution of the extrinsic size constraint effect on the layer strength; is the mean spacing of glide loops in a parallel array; and f |
≈ 0.5–1.1 J m−2 is the characteristic am/crystalline interface stress results for the CLS model. The predicted values, 2.38 GPa for sample MS50 and 2.00 GPa for MS100, generally agree with the flow stress measured in the pillar compression tests. However, the value suggested by the CLS model for sample MS10 is 4.40 GPa, i.e. it strongly overestimates the flow stress level observed experimentally, namely, 2.37–3.01 GPa. We interpret this deviation in terms of a transition from the dislocation-dominated CLS mechanism for the case of the thicker Cu layers to a co-deformation mechanism where shear band penetration initiated by the amorphous phase prevails when the Cu layer thickness is reduced down to 10 nm. This means that those samples with the largest volume fraction of amorphous phase are prone to develop shear bands that can more easily intersect numerous nc Cu layers. When increasing the nc Cu layer thickness, however, such multi-layer penetration of shear bands is reduced b). Such a process may even alter the local structures and induce mechanical alloying of the shear banded regions, as will be discussed in more detail below clearly reveal that thicker Cu layers are indeed more efficient in arresting emerging shear bands. More confined, i.e. localized shear bands have to be formed if larger shear bands cannot penetrate through the Cu layers. The instability associated with the nucleation and expansion of large shear bands that penetrate multiple layers will thus be suppressed since the imposed load is dissipated in the form of a high dispersion of more confined shear bands. Thus, the strain bursts observed in the load-controlled experiments are weaker compared to those observed in homophase metallic glasses. Finally, in all interpretations it has to be considered that the tapered geometry of the pillars is associated with a stress decrease from top to bottom so that mechanical inhomogeneity cannot be entirely excluded.In order to check such effects in the present study, we calculated the flow stress values based on the topmost diameter, for avoiding underestimation of the pillar flow stresses. However, as shown in , no extrinsic size effect can be observed when the pillar diameters are reduced from 2000 to 300 nm for all three multilayer systems. This finding is in contrast to observations made in a previous work: CuZr/Cu multilayered samples with a 5 nm thickness period were reported to exhibit a yield strength of 4.8 GPa for Φ = 350 nm pillars and of 3 GPa for Φ = 1425 nm pillars As a lower bound estimate, i.e. neglecting the hetero-interface strengthening, we approximate the flow stress of the laminates by a linear rule-of-mixtures where σNL describes the lower bound flow stress of the compound, σa |
= 2370 MPa is the flow stress of the amorphous CuZr layer The observed flow stress values exceed the linear rule-of-mixture approximation for all multilayered samples: For the MS10 specimens we found an experimental range of 2370–3010 MPa for the flow stress, which roughly matches the lower bound value suggested by the linear rule-of-mixtures, i.e. 2240 MPa, . For the MS50 specimens the linear rule-of-mixtures suggests only 1887 MPa for the flow stress, underestimating the experimentally observed strength of the pillar samples which fall into the range 2360–2780 MPa, . We attribute this to the large scatter of the experimental data. For the MS100 specimens the values are 1720–2290 MPa vs. 1645 MPa predicted as lower bound by the linear rule-of-mixtures.When the thickness of the Cu layer is only 10 nm (MS10), dislocation slip inside the nc Cu layers cannot accommodate the imposed strain intrinsically. Therefore, these thin Cu layers cannot easily prevent the cross-phase propagation of shear bands stemming from the amorphous CuZr layers. The stress concentration acting on the amorphous/crystalline interfaces leads to a localized dislocation flux along the path of the shear band When increasing the Cu layer thickness to 100 nm (MS100), pillar deformation is initially practically only carried by the Cu layers, due to their lower initial flow stress compared to that of the amorphous CuZr layers. Conventional plastic deformation mechanisms, such as dislocation multiplication, intra-phase glide and pile-up-induced work-hardening, first dominate the Cu deformation. As deformation proceeds, the flow stress in the nc Cu layers hence rapidly approaches that of the metallic glass layers due to intra-layer strain hardening.When the Cu layers assume an “ideal” thickness, such as 50 nm, as observed here, the effect of plastic co-deformation on the strength increase is even more pronounced since the strengthening potential of both layer types is ideally coupled. The CuZr metallic glass layers sustain considerable intrinsic, i.e. intra-phase, plasticity via shear banding which, however, remains confined inside the layers. The Cu layers can further dissipate these localized loads, such as originating from the incoming confined shear bands, by intrinsic plastic deformation without strong localization. Due to the coupled deformation mechanisms of the Cu layers and the metallic glass layers, a strong and yet ductile mechanical response can be achieved in the MS50 samples. A proper design and sequence of the laminate architecture seem thus to be crucial for the enhancement of the mechanical properties by utilizing these different mechanisms simultaneously.The influence of the am/nc hetero-interfaces on dislocation motion inside the Cu is two-fold. At low strains, the debris from elongated expanding dislocation loops get deposited at the hetero-interfaces. Reactions with inclined dislocations produce dislocations with Burgers vectors in the interface plane, i.e. interfacial dislocations . Therefore, such am/nc interfaces may reveal better strain dissipation potential compared to crystalline/crystalline interfaces since the incoming strain from the amorphous phase is not limited by fixed Burgers vectors and slip planes. Instead, omnidirectional atomic motions and shear transformation zones can facilitate both dislocation movement in the crystal and inelastic shear/dislocation shuffling among the layers The analysis also shows that both extrinsic size effects (pillar size, taper, loading type, tool design, compression vs. indentation, surface-to-volume ratio etc. We synthesized multilayer nanolaminates consisting of alternating layers of amorphous Cu54Zr46 and nc Cu by direct current sputtering. The probed combinations were based on 100 nm CuZr amorphous layers and nc Cu layers of varying thickness (10, 50 and 100 nm). Loading was exerted by nanoindentation and pillar compression. The main findings are as follows:An increase in Cu layer thickness can suppress catastrophic propagation of shear bands. For 10 nm Cu layers, small confined shear bands can readily develop into larger, i.e. percolative shear bands. For 50 and 100 nm thick Cu layers a higher fraction of confined shear bands forms in the amorphous layers at low strains (10%), distributing the load more homogeneously. Generally, the interplay of shear bands with the crystalline Cu layers increases the compound’s toughness and ductility.In the three multilayer systems studied here, the experimentally observed compressive flow strength of the submicron/micron pillars exceeds the lower bounds given by a linear rule-of-mixture approximation. Specially, the MS50 pillars not only have flow stresses (2.57 ± 0.21 GPa) that match the value of pure CuZr metallic glass, but also accommodate high compressive plastic strains (>40%) by the confinement of small shear bands inside the metallic glass layers. This composite behavior reveals a path to design am/nc composite structures that are “strong and ductile” by utilizing the cooperation of the deformation modes in the two different types of layers.Decreasing the pillar diameter from 2000 to 300 nm shows no obvious extrinsic size effect among the three types of multilayer systems. Both extrinsic and intrinsic influence factors should be generally considered when interpreting apparent mechanical size effects.The “confined layer” dislocation slip mode well explains the flow stress of Cu in the 100/50 and 100/100 nm CuZr/Cu nanolaminates but overestimates the flow stress in the 100/10 nm CuZr/Cu nanolaminates, where shear band penetration prevails the nanolaminate co-deformation.Wear resistance of nano- and micro-crystalline diamond coatings onto WC–Co with Cr/CrN interlayersCr/CrN bi-layers have been used recently to promote the growth of high quality Hot Filament Chemical Vapour Deposition (HFCVD) diamond coatings onto Co-cemented tungsten carbide (WC–6 wt.%Co) substrates. In the present investigation, the influence of the crystalline size of the diamond coatings on their wear endurance is looked into.Nano- (NDC) and micro-crystalline Diamond Coatings (MDC) were deposited by HFCVD onto untreated and Fluidized Bed (FB) treated Cr/CrN interlayers. NDCs, characterized by a cauliflower-like morphology, showed improved wear resistance. However, the superimposition of NDCs onto Cr/CrN interlayers micro-corrugated by FB treatment was found to be the most promising choice, leading to the formation of highly adherent and wear resistant coatings.The deposition of highly adherent and wear resistant diamond coatings onto Co-cemented tungsten carbide tools has been largely investigated in the recent literature Chemical etching of the WC–Co substrates to remove the outermost layers of the Co binder phase, heat treatments to reduce the Co surface concentration and deposition of intermediate layers of different materials to erect a diffusion barrier so as to suppress any interaction between the CVD atmosphere and/or the following diamond films with the WC–Co substrate are the most frequent approaches to reduce the deleterious effect of cobalt Although recent efforts have entailed noteworthy progress, many factors are known to have a significant influence on the performance of diamond coatings onto WC–Co substrate in term of adhesion and wear endurance. In particular, the effect of superimposing layers of different materials between the diamond film and the WC–Co substrate, the ability to modify their morphology to achieve a customized surface texture on which to deposit the diamond film and, above all, the final morphology of the overlying diamond films on the overall performance of the whole coating system are still scarcely investigated and/or poorly understood.In this respect, among the different interlayers, the Cr-based ones are of utmost interest. They were used in the recent past as C and Fe diffusion barrier in the diamond deposition on ferrous substrates WC–5.8 wt.%Co as-ground substrates (Fabbrica Italiana Leghe Metalliche Sinterizzate SpA, Anzola d'Ossola, VB, Italy) 10 × 10 × 3 mm3 with 1 μm average grain size, 90.0 HRA Rockwell A hardness and 2900 MPa transverse rupture strength (TRS, according to ISO 3327) were coated with Cr/CrN films (overall thickness about 8 μm) by using a PVD-arc plant (Microcoat S.p.A., Italy). During the initial stages of PVD, a thin metallic Cr layer (≤ 200 nm) was preventively deposited on the substrate to improve the adhesion of the following Cr/CrN film. Cr/CrN interlayers are sort of graded coatings. They were achieved by progressively reducing the nitrogen concentration inside the deposition chamber from 100% to 0% of the gas phase, and, concurrently, increasing the argon concentration. The resulting CrN layer is progressively poorer in nitrogen going towards the topmost layers. At last, when the nitrogen is completely replaced by the argon in the gas phase, a resulting layer of metallic Cr is superimposed on the graded CrN layer. By varying the deposition time of each different thickness of the CrN and Cr layers were achieved ( shows the cross-sections of Cr/CrN interlayers deposited by PVD-arc onto WC–Co substrates.40 × 40 × 100 mm3 fast regime FB of diamond powders (mesh size 120, factor shape 0.67, supplied by Poligem Srl, Italy) was used to mechanically pre-treat a fraction of Cr/CrN coated WC–Co substrates before CVD (PVD-Cr/CrN + FB Treatment) by rotating them at moderate speed (180 rpm) in the suspended phase (). Operating pressure of 2 bar and processing times never longer than 60 s were set to avoid the ductile topmost Cr layer was damaged by the impact with the multi-faceted diamond powders. However, details of the experimental apparatus and fluidization conditions are elsewhere reported Prior to diamond deposition, all substrates were washed with acetone and de-ionized water in an ultrasonic vessel and, then, ultrasonically seeded for 15 min in a ¼ μm diamond suspension (50 ct/l in absolute ethanol).The deposition of diamond films was performed in a stainless steel HFCVD. The gas phase, a mixture of hydrogen and methane, was activated by a set of linear tungsten filaments (0.79 mm in diameter), whose temperature was kept at about 2500 K and monitored by a two-colour pyrometer (Land Infrared model RP 12). Flow rate was 4000 standard cm3 |
min− 1 (sccm). NDCs on just seeded Cr/CrN interlayers were achieved by setting the CH4/H2 volume ratio at 2.0% and the total pressure of the gas mixture in the reactor at 5 kPa. Conversely, MCDs were achieved both on just seeded and FB treated Cr/CrN interlayers by setting the CH4/H2 volume ratio at 1.0% and the pressure of the gas mixture in the reactor at 10 kPa. During the diamond deposition, the substrates were located on a molybdenum grid with their surface located at 12 mm from the tungsten filaments. The substrates temperature (600 °C) was monitored by a Type K (Chromel/Alumel) thermocouple. Deposition rates, under those CVD conditions, were 0.6 ± 0.1 μm/h, whilst deposition times were 10 h.After CVD, FT-IR interferometry (BIORAD FTS-40 Fourier transform infrared spectrometer) with a glancing angle of 20°, wavelength ranging 500–4000 cm− 1 and a resolution of 4 cm− 1 was used to check the thickness of the diamond coatings. Raman spectroscopy was used to characterize the NCD and MCD films. Raman spectra were recorded with a Spex Triplemate spectrograph, equipped with a liquid nitrogen cooled (512 × 512 pixels) EG&G Princeton Applied Research CCD optical multichannel analyzer (OMA) detector. The 514 nm line of an Ar-ion laser was used for excitation in a backscattering geometry.Field Emission Gun Scanning Electron Microscopy (FEG-SEM, LEO model Supra 35) and Energy Dispersive X-Ray Spectroscopy (EDS, Oxford Instruments Ltd., model Inca 300) were used to take high resolution images and perform preliminary chemical analyses of the PVD and CVD films. A contact gauge surface profiler (Taylor Hobson Surface Topography System model TalySurf CLI 2000) was used to measure the 3D morphology of the PVD and CVD coatings. Surface profiles with a lateral spacing of 1 μm were recorded. Next, TalyMap software Release 3.1 was used for data analysis and image processing.Wear behaviour of the coated substrates was evaluated by 10 N dry ‘pin-on-disk’ tribological tests (Standard Tribometer, CSM Instruments). The counterpart was spherical Al2O3 (diameter 6 mm). The diameter of the wear pattern was 3 mm, the sliding velocity 2.78 mm/s and the sliding distance 5000 m. Volume, dimensions and average depth of the wear patterns were measured by the above contact gauge profiler. Data were elaborated by using the features of the TalyMap software Release 3.1.The changes in the surface morphologies of the Cr/CrN interlayers after FB treatment are displayed in . As deposited Cr/CrN interlayers were characterized by a rather smooth morphology with some isolated features protruding out from the surface (i.e., droplets) due to the PVD-arc process summarizes the roughness parameters. Whatever the Cr:CrN ratio, FB treatment was able to remove most of the Cr-droplets and entailed the establishment of a highly micro-corrugated surface morphology on which to grow potentially adherent diamond films. The removal of the droplets produced an improvement in the average roughness Ra of about 40%. The slope RΔq improved less (≈ 15%). Although the FB treatment was able to remove the droplets, thus reducing the amplitude parameters, it was found to cause a micro-corrugation of the surface due to the repeated impacts of the media. Such micro-corrugation brought up the actual length of the surface profile. The hybrid parameters RΔq takes into account that issue, being a measure of the ratio between the actual length of the profile and the evaluation length. Accordingly, RΔq decreased as result of the droplets removal, but not as much as expected because of the contribution of the micro-grooving induced on the ductile Cr-surface by FB treatment. Micro-corrugation of FB treated interlayers was also supported by the measured decrease in the spacing parameter RSm (≈ 25%). Lower RSm means spikier surface morphologies are expected. Indeed, FB treatment was also liable for the spikiness of the surface, which is a ‘side-effect’ of the micro-grooving. The micro-corrugation of the surface to be deposited is well known to be helpful to improve the adhesion of overlying CVD diamond films as it increases the specific contact area at the interface and counterbalance better to the large thermal residual stresses induced in the diamond coating by the cooling phase and the large mismatch of the coefficient of thermal expansion c), the topmost Cr layer was too thin to absorb the impact of the abrasive particles and it was easily removed or displaced sideways by plastic deformation. The innermost CrN layer was therefore exposed to some impacts with the incoming diamond powders, thus explicating its brittleness. Although the fragile CrN interlayer is partially shielded by the overlying ductile Cr layer, it was subjected to the machining action of the diamond powders and some material was removed by brittle spallation, thus originating sparse craters with faceted rims. This phenomenon was less apparent on samples belonging to Scenarios C and D, where Cr layers with larger thicknesses and more suitable to deaden the impacts with the abrasives were used.The morphology of the MDCs after 10 h CVD is reported in . The diamond films deposited on FB treated Cr/CrN interlayers were characterized by a finer average crystallite size, which can be ascribed to the capability of a fluidized bed of diamond powders to leave extra diamond seeds in the form of small splinters onto the impinged surface. As reported previously Raman spectrum of MDC deposited onto FB treated Cr/CrN interlayers are shown in . Raman spectra of MDCs are insensitive to the Cr:CrN ratio, therefore only scenario C is reported. Their first-order diamond Raman lines were always at 1336.9 cm− 1. The frequency of the peaks were blue-shifted of about 4.5 cm− 1 with respect to natural diamond (1332.4 cm− 1 at atmospheric pressure and 25 °C), which corresponds to a biaxial compressive stresses of about 2.6 GPa The morphology of NDCs on just seeded Cr/CrN interlayers after 10 h CVD is reported in . The thicknesses of these films were similar to those of MDCs. In fact, the CH4 partial pressures in the gas phase were identical (0.1 kPa). However, the larger CH4/H2 ratio induced a cauliflower-like morphology of NDCs, which is not unlikely to occur Raman spectra of NDCs deposited onto FB treated Cr/CrN interlayers are shown in , as well. Raman spectra of NDCs are insensitive to the Cr:CrN ratio, therefore only scenario C is reported. Again, their first-order diamond Raman bands were at 1336.9 cm− 1. Therefore, the average stress in NDCs and MDCs was the same. However, a more intense D band of micro-crystalline sp² carbon along with quite evident ν1 and ν3 peaks attributable to TPA were present. The larger intensity of ν1 and ν3 modes in NDCs spectra was clearly related to the huge ‘secondary’ nucleation and to the consequent larger grain boundary area, where TPA is supposed to lay reports the 3D maps of the wear pattern of NDCs and MDCs on just seeded and FB treated CrN/Cr interlayers. NDCs deposited on just seeded Cr/CrN interlayers were more wear resistant than MDCs, which, under the action of the counterpart, exhibit larger wear pattern, whatever is the investigated scenario (). This is particularly true on Cr/CrN films with thicker CrN layer (Scenario B), where the MDC displays an overall wear volume of 26 × 10− 3 |
mm3, that is, exactly the double of wear volume the of the corresponding NDC. The worse behaviour is more likely ascribable to the high temperature reaction of Cr with CrN in excess to form a bare Cr2N layer during CVD reports the general trend of the friction coefficient for the CVD diamond coatings on Cr/CrN interlayers and the displayed experimental data refer to scenario D for both ‘just seeded’ and FB treated interlayers. It is possible to note that increasing the sliding distance (i.e., wear time), the friction coefficient tends to progressively reduce, as the morphology of the diamond film is progressively worn out and, therefore, smoothed. However, after a first decreasing branch, the trend of the friction coefficient of the MDC deposited onto the ‘just seeded’ Cr/CrN interlayer starts increasing. This should not surprise as, under that circumstance, the diamond coating underwent significant damage () during the tribological test. The increase in friction at the contact between the coating and the counterpart can be therefore ascribed to the formation of the rupture on the diamond coating along the wear pattern.Cauliflower-like NDCs exhibit better wear endurance, with wear volumes in Scenarios C and D, which is not measurable or very small (< 1.5 × 10− 3 |
mm3). However, this should not surprise as cauliflower-like diamond has already found to be characterized by good mechanical behaviour and wear resistance, although the reason why it exhibits improved resistance is still poorly understood Indeed, the main mechanism by which NDCs and MDCs are damaged during the tribological tests is by spallation of entire portion of the diamond film which delaminate at the interface with the interlayer rather than by progressive wear of the diamond film. This is witnessed by the shape of the wear pattern, shown in , which, where damaged, seems to be delaminated and by its depth, which is close or bigger than the thickness of the diamond film (~ 5 μm). Accordingly, the damage can be supposed to start at the interface between diamond and underlying layer and, then, propagate in the surrounding at different extent according to the adhesion performance of the whole coating system. It could be therefore speculated that the best endurance to the tribological test of the NDCs can be ascribed to the combination of two distinct aspects: (i) the increase in the nucleation density of NDCs and (ii) their peculiar micro-structure. Since NDCs and MDCs should present the same primary nucleation (i.e., the same seeding density), NDCs are characterized by a definitely higher secondary nucleation and this is the reason why their average grain size is smaller. Such ‘enhanced’ secondary nucleation takes place from the beginning of the diamond deposition process. Therefore, it is reasonable to argue that the crystallite density at the interface with the underling interlayers is largely higher for the NDCs. The increase in the number of crystallites per unit of area can entail the presence of smaller voids at the interface between diamond coating and underlying interlayer, thus promoting a larger adhesive toughness of the NDCs compared to MDCs in agreement with what found by Kamiya et al. in similar coating systems FB treated Cr/CrN interlayers displayed diamond films with better adhesion and wear resistance whatever the Cr:CrN ratio, as FB was able to deeply micro-corrugate the topmost ductile Cr layer. Accordingly, after tribological tests, there are no appreciable wear volumes whatever the scenario investigated (). The better wear resistance of NDCs and MDCs on FB treated Cr/CrN interlayers can be ascribed to the increased specific contact area between the interlayer and the overlying diamond films. The substrate-modification process created a three-dimensional graded interface that allowed inhibiting catastrophic propagation of interfacial cracks.The present investigation dealt with the analysis of growth, morphology, adhesion and wear resistance of CVD Cr/CrN interlayers. The following conclusions can be drawn:Wear endurance of diamond coatings deposited on FB treated Cr/CrN interlayers was definitely enhanced, thus exhibiting very promising adhesion and wear resistance.FB treatment is an effective way to customize the surface morphology of Cr/CrN interlayers, thus inducing a vast micro-corrugation and a three-dimensional graded interface between CrN film and the overlay diamond coating.The peculiar micro-corrugated morphology of the Cr/CrN film is also expected to inhibit the propagation of interfacial cracks, thus potentially conferring extra-adhesion on diamond.The effectiveness of FB to pre-treat Cr/CrN interlayers is superior when interlayers with larger Cr:CrN ratios are treated, as thicker ductile Cr layers are more prone to receive the vigorous FB treatment and preserve the underlying fragile CrN layer by potentially deleterious brittle spallation.Adhesion and wear endurance of NDCs deposited on Cr/CrN interlayers is definitely better than those of MDCs, whose mechanical behaviour is severely compromised at any time they are deposited on interlayers with the smaller Cr:CrN ratio, and the complete trasformation of Cr into Cr2N occurs.In conclusion, the best endurance to the tribological test of the NDCs can be ascribed to the combination of two distinct aspects: (i) the increase in the nucleation density of NDCs and (ii) their peculiar micro-structure.Yield criterion for a perforated sheet with a uniform triangular pattern of round holes and a low ligament ratioThe plastic behavior of a perforated sheet with round holes in a triangular pattern depends largely on the hole size of the perforated sheet. This study investigates the plastic behavior of perforated sheets with low ligament ratios. A yield criterion for the perforated sheets is also proposed in terms of apparent stresses by employing the equivalent-continuum approach. The effectiveness of the proposed yield criterion is then demonstrated by comparing the predicted values of apparent yield stresses and apparent strain ratios with results obtained from finite-element analysis and experiment.Tube sheets in heat-exchanger equipment , the ligament ratio ρ is defined as the ratio of the ligament width W to the perforated pitch P in a unit cell ABCD. However, the yield criterion as defined by Chen is inappropriate for a perforated sheet with a low ligament ratio. On the other hand, the apparent strain ratios predicted by the related flow rule defined by Baik et al. do not correlate well with those obtained in experiments under uniaxial loading for a perforated sheet with a low ligament ratio.The yielding of a perforated sheet depends on the ligament ratio of the perforated sheet and the loading states. Hence, the plastic behavior of a perforated sheet is extremely complicated, thereby making it difficult to propose a yield criterion for a perforated sheet over the whole range of ligament ratios. In general uses of perforated sheets, e.g. tube sheets in heat-exchanger equipment and shadow-masks in high-resolution color picture tubes, the ligament ratios of the perforated sheets are in the low range. Hence, this study investigates the plastic behavior of perforated sheets with a uniform triangular pattern and low ligament ratios, a yield criterion also being proposed for the perforated sheets.The plastic behavior of a perforated sheet cannot be characterized by treating each hole because a perforated sheet has a large number of holes. The plastic behavior of a perforated sheet is analyzed by treating the perforated sheet metal as an equivalent continuum that is compressible and anisotropic . Then, yield criteria for perforated sheets were defined by considering the yield stress states of the minimum ligaments along AB and AO.Chen also considered the apparent volume change of an equivalent continuum during the deformation process owing to the volume change of the holes of a perforated sheet. Hence, in addition to the hydrostatic pressure producing plastic deformation, the effect of hydrostatic pressure is also modeled in the general yield criterion for anisotropic materials proposed by Hill where Sx and Sy are the apparent normal stresses in x and y directions, respectively, Sxy an apparent shear stress, Yb the yield stress of the base metal in the perforated sheet, and F, H, G and N are parameters. Chen developed two deformation models, i.e. the yielding of a perforated sheet in the minimum ligaments along AB and AO, to determine the coefficients in the yield criterion equation (1).In the two deformation models, the stresses are assumed to be uniform across the ligament widths. In one model, with respect to yielding in the minimum ligament along AB, the mean true stresses σx and σy in the base metal of the minimum ligament along AB are expressed bywhere ρx=Wx/Px and ρy=Wy/Py. In another model, with respect to yielding in the minimum ligament along AO, the mean true stresses σξ and ση in the base metal of the minimum ligament along AO are obtained by transforming the apparent stresses Sx and Sy into stresses in ξ–η coordinates, as illustrated in into the von Mises yield criterion, the following yield equations are derived.For yielding of the minimum ligament along AB:For yielding of the minimum ligament along AO:where factor f is a function of the ligament ratio. Substituting the corrected stresses into the von Mises yield criterion allows one to obtain the following yield criteria.The parameter f is approximately zero for low ligament ratios but increases to unity with increasing ligament ratio. Hence, the normal stresses σx and σξ in are close to zero. The stresses are substituted in the yield criterion equations (7) to obtain the coefficient of the SxSy term, being about zero. As a result, the apparent strain ratio under uniaxial loading, Sx=0, predicated by the yield criterion This study investigates perforated sheets with a uniform triangular pattern of round holes and of low ligament ratios. The yielding of the perforated sheets is also assumed to occur in the minimum ligament along AO under uniaxial and biaxial loadings. Next, the average values of the stress components across the ligament width along AO are calculated to define the yield stress states of a perforated sheet. However, the definition of stress states differs from those in Chen For stress analysis of the minimum ligament along AO, as shown in , the normal stress ση and the shear stress σξη across the ligament width along AO are assumed to be uniform because the ligament width is narrow for low ligament ratios. Under biaxial loading in the x- and y-directions, according to , the apparent stresses Sx and Sy are transformed into stresses in ξ–η coordinates. The apparent stresses in ξ–η coordinates can be obtained asMoreover, the stresses ση and σξη across the minimum ligament width along AO can be defined asOn the other hand, the distribution of transverse normal stress σξ varies across the ligament width along AO and can be derived by use of the theoretical analysis of Isida The complex stress potentials in the form of a Laurent series expansion are expressed bywhere ϕ(z) and φ(z) are two complex stress potentials that must be analytical in the triangular unit region (ΔOMN) chosen, as shown in , and z=ξ+iη. Next, the unknown coefficients A2n, B2n, C2n and D2n in the Laurent series are determined by considering the traction-free condition along the hole edge and the boundary conditions at the outer edges of the triangular unit regions used where [σξ]η=0 denotes the stress distribution in the ξ direction along M0M and k is a function of the ligament ratio that can be calculated following the method proposed in The von Mises yield criterion under the plane-stress condition applies for the base metal of the perforated sheet: are then substituted in the von Mises yield criterion equation (17), whereby the yield criterion for the perforated sheets can be obtained as allows the determination of coefficients F, G and H asIf the hole size is zero, ρy=ρx=1, the apparent stresses of a perforated sheet are the same as the mean true stresses in the base metal of the sheet and k in is equal to unity. By allowing the x- and y-axes to be the principal axes, the yield criterion is reduced to the von Mises yield criterion, F=1, G=−1, and H=1. This observation suggests that the yield criterion function corresponds to the limiting case for a solid isotropic material. plots the yield locus according to the yield criterion proposed above on the stress plane for a ligament ratio, ρy of 0.213. The yield locus is smooth and no singular points exist on the yield surface. However, the yield loci plotted by Chen presents both yield loci, which consist of two yield criteria results of singular points on the yield surface.The related flow rules are established by assuming the yield function f(Sij) to be a plastic potential: is a proportionality constant. When the strains remain small, the strain eij may be substituted for the strain rates In uniaxial tension in the y direction, Sx=0, the apparent yield stress Sy and the apparent strain ratio Ry defined as the ratio of the apparent strain ex in the x direction to the apparent strain ey in the y direction, can be expressed asSimilarly, in uniaxial tension in the x direction, Sy=0, the apparent yield stress Sx and the ratio of the apparent strains Rx are determined byThis study confirms the effectiveness of the yield criterion and its related flow rule developed herein by finite-element analysis and by uniaxial tension tests in the x- and y-directions.Theoretical analysis for the global deformation of a perforated sheet must correspond to the behavior of local deformation. To examine the analytical results, the finite-element method is used to analyze the local deformation. Simulation results obtained by the finite-element method are then compared with those predicted by the theoretical analysis and as determined by tensile tests, respectively.By considering the symmetry in the geometric configuration of a perforated sheet, a repetitive portion of the unit cell, OFAE, as depicted in , is adopted as the analytical pattern. To determine the boundary conditions of the unit cell, the model of a perforated sheet with many holes is analyzed by the finite-element method under uniaxial and biaxial tensile loading. According to , the displacements are uniform at the symmetric lines of the model during the deformation process. Whilst neglecting the free boundary conditions of the outer edges, the boundary conditions of the unit cell are determined by the results of the finite-element analysis, as summarized in In this study, the general purpose finite-element computer code is employed by using a 10-node quadrilateral element to generate the two-dimensional solutions. The steel alloy used in the experiment described in the following section is taken as the simulated material. Young’s modulus and Possion’s ratio of the material are 198 GPa and 0.3, respectively. The effective-stress () relationship is expressed approximately by Experimental results of uniaxial tensile tests, the apparent yield stress and the apparent strain ratio, are used not only to verify the predicted values derived from the theoretical analysis developed herein, but also to compare the results with the values determined by the finite-element method. Herein, the ligament ratios of perforated sheets are in the low range. Hence, the different lower ligament ratios of perforated sheets are prepared for the experimental tests, including the ligament ratios of 0.25, 0.3, 0.4 and 0.5. The test specimens are cut from the x- and y-directions in a perforated sheet, as illustrated in . To neglect the effect of the free boundary along the gauge edges of test specimens, at least 10 holes are present in the gauge width. The distance between the centers of two adjacent holes is then recorded to determine the material flow during deformation. The tensile tests are performed with an MTS 810 material test machine, the stretching rate being approximately 1.5×10−3 |
s−1.After testing, the averaged distance between the centers of two adjacent holes is measured in the loading and transverse direction, and then it is compared with those before testing to obtain the apparent strain ratios. The results of the tensile experiments enable the verification of the apparent strain ratio and the apparent yield stress ratio. display the true effective stress contours obtained by the finite-element analysis under uniaxial and biaxial tension for two different ligament ratios, ρy=0.285 and ρy=0.515, respectively. According to , the maximum effective stress is almost in the minimum ligament along AO for a perforated sheet with a low ligament ratio under uniaxial and biaxial tensions. (b) reveals that, when the ligament ratio is greater (ρy=0.515) under y-direction loading, the maximum effective stress may occur in the minimum ligament along AB and AO. Hence, the effective stress contours confirm the assumption that the yielding location of a perforated sheet is in the minimum ligament along AO when the ligament ratio ρy is approximately lower than 0.5 under uniaxial and biaxial loading.This study proposes a yield criterion to describe the plastic behavior of a perforated sheet with a low ligament ratio. The effectiveness of the proposed yield criterion and related flow rules is demonstrated by comparing the predicated values of the apparent yield stress ratios (Yx/Yy) and the apparent strain ratios (Rx and Ry) with the results obtained from the finite-element analysis and from experimental tests. summarizes the apparent yield stress ratios predicted by the proposed yield criterion, the finite-element analysis and the experimental tests. These results are also compared with those predicted by Chen Chen’s analytical work assumed that the stress distribution is uniform across the minimum ligament width, resulting in an insignificant effect of stress concentration in the minimum ligament On the other hand, the apparent yield stress ratios predicted by Baik et al. and by the present study correlate well with those obtained by finite-element analysis and experimental tests, for greater ligament ratios. However, the predicted results of Baik et al., as shown in , are inappropriate for a perforated sheet with ligament ratios lower than 0.4, compared to those predicted by the present analysis, the finite-element analysis and the experimental tests. Notably, according to , the apparent yield stress ratios predicted by this study are well within the range for a low ligament ratio. present the apparent strain ratios, Rx and Ry, obtained by the theoretical analysis, the finite-element analysis and the experimental tests, respectively. These figures also summarize the results obtained by Chen , the results predicted by Baik et al. and this study correlate with those obtained by the finite-element analysis and the experimental tests, both in trend and in magnitude. However, under uniaxial loading in the x direction, the uniform stress distribution of the minimum ligament analyzed by Chen is inconsistent with that computed by the finite-element analysis developed herein, particularly for a perforated sheet with a lower ligament ratio. Hence, the apparent strain ratio Rx, under uniaxial loading in the x direction, as predicted by Chen, is inappropriate for a perforated sheet with a lower ligament ratio, as shown in , the apparent strain ratio Ry predicted by Baik et al. is almost zero and differs markedly from those obtained by Chen (this study) in the finite-element analysis and the experimental tests. This phenomenon is due to the correct factor of stress, f, used in , being close to zero, resulting in the very small coefficient of term SxSy in . Hence, the apparent strain ratio Ry derived by the yield criterion equation (7) is very small. On the other hand, under uniaxial loading in the y direction, with the deformation model proposed by Chen, the yielding in the minimum ligament along AB, is properly applicable for a perforated sheet with a larger ligament ratio, as shown in (b). Hence, the correlation of the apparent strain ratio Rx predicted by Chen with those obtained by the finite-element analysis and the experimental tests is better than the results calculated by this study for a perforated sheet with a larger ligament ratio. However, when the ligament ratio of the perforated sheet is lower, the correlation of the apparent strain ratio Rx predicted by this study with those obtained by the finite-element analysis and the experimental tests is better than the analytical results of Chen.The plastic behavior of a perforated sheet depends largely on the hole size and arrangement. Hence, the actual yielding condition of a perforated sheet is extremely complex and the yielding location is not fixed for various ligament ratios and different stress states. Hence, the assumptions of the yield location of a perforated sheet are not always practical over the whole range of ligament ratio.In this study, perforated sheets with a uniform triangular pattern of round holes and low ligament ratios have been investigated. Yielding of the perforated sheets occurs close to the minimum ligament. Then, the stress components in the base metal across the minimum ligament width are calculated by the stress functions, their average values describing the yielding stress states of a perforated sheet. The von Mises yield criterion is assumed to govern the base metal of a perforated sheet. Next, the average values of stress components are substituted into the von Mises yield criterion to derive the yield criterion for a perforated sheet. Furthermore, the yield locus can be plotted by the yield criterion proposed herein. The yield locus is smooth and no singular point is present on the yield surface.Simultaneously, the finite-element method and experiments were performed to discuss the validity of the yield criterion and the flow rules. The apparent yield stress ratios and the apparent strain ratios predicted by the proposed yield criterion are compared with those obtained by the finite-element analysis, experiments and those predicated by Chen Thermo-physical properties of plasma electrolytic oxide coatings on aluminiumPlasma electrolytic oxide coatings appear to offer attractive combinations of hardness, wear resistance, corrosion resistance and interfacial adhesion. In order to optimise such characteristics, however, more basic thermo-physical property data are required, together with an understanding of how they are affected by processing conditions and microstructure. In the present study, coatings were produced on 6082 aluminium and characterised using profilometry, scanning electron microscopy, X-ray diffraction and nanoindentation. The in-plane thermal expansivity of detached coatings was measured by dilatometry to be about 8 microstrain K−1. There is thus a rather substantial mismatch between the expansivities of coating and substrate, amounting to about 15 microstrain K−1. The global in-plane Young's modulus was estimated using cantilever bending of sandwich coated substrates and also by measuring the curvature generated in a bi-material beam on cooling to low temperature. It was found to lie in the approximate range of 10–40 GPa. Values of this order, which are low compared with the figure of around 370 GPa expected for fully dense polycrystalline alumina, are thought to be associated with the presence of a network of microcracks and voids. A low value is expected to be beneficial in terms of conferring good strain tolerance, and hence resistance to spallation driven by differential thermal expansion.There are increasing levels of interest in plasma electrolytic oxide (PEO) coatings. They can be quickly and economically produced on components with almost any shape and size, made of various metals, and the thickness range is substantial However, much remains to be established before these coatings can be efficiently exploited and find widespread use. In particular, despite extensive study of the deposition process In the present study, coating microstructures have been examined using X-ray diffraction, optical microscopy and scanning electron microscopy. Optical interferometry and nanoindentation have been used to characterise the surface roughness, porosity, hardness and local stiffness. Finally, cantilever beam bending, dilatometry and curvature measurements after cooling of bi-material beams have been used to evaluate global elastic constants and thermal expansivities. An attempt is made to establish correlations between these properties and microstructural features.Coatings were generated on square coupons (50×50×4 mm) of aluminium alloy BS Al-6082, using the Keronite™ process. AC power was applied with a 50 Hz modulation. The voltage was in the 400–600 V RMS range in the anodic half-cycle and 150–250 V RMS in the cathodic half-cycle, controlled so as to maintain a constant current density (of approximately 1 kA m−2). The electrolyte consisted of an aqueous solution of tetra-sodium pyrophosphate (3–5 g l−1), sodium silicate solution (specific gravity 1.5, 3–5 g l−1), and potassium hydroxide (1–2 g l−1). Treatment times were selected to give coating thicknesses of approximately 5, 10, 40, 60, 80 and 100 μm based on an approximate growth rate of 1 μm/min. Thicknesses were measured using an Oxford Instruments CMI 100 thickness gauge, which uses eddy currents induced in the substrate to measure coating thickness with an accuracy of 1 μm. The accuracy of this technique was verified by microscopy of polished sections. Coated specimens were sectioned, using a low-speed rotating diamond saw, hot-mounted in resin, ground, using SiC papers, and polished using diamond paste and colloidal silica. For some purposes, coatings were detached from the substrate. This was done by immersion in a warm, saturated solution of NaOH for 1–2 min.SEM observations were made using a JEOL 5500 microscope. Some observations were made in low vacuum mode, while others were made in high vacuum on specimens sputter-coated with platinum (to minimise surface charging). Topographic studies were carried out, using a Wyko RS-2 interferometric profilometer, on untreated coating surfaces, in order to measure the surface roughness and explore surface features. A Phillips PW 1710 X-ray diffractometer was used to perform θ–2θ scans from 10° to 120° with a 0.02° step size. A CuKα radiation source was used, with a 40 kV accelerating voltage and a 40 mA filament current. Data were obtained from as-deposited free surfaces. Serial dry grinding of the coating surface was then used to collect data at nominal depths through the thickness of the coating. Phase proportions were determined by Rietveld analysis The thermal expansion behaviour of detached coatings was investigated using a Netszch 402L push-rod dilatometer, over the temperature range 20–700 °C. This allowed evaluation of the (in-plane) thermal expansivity, which was found to be approximately constant over this temperature range.The global in-plane Young's modulus of coatings was measured using two techniques. Firstly, cantilever bending experiments were carried out on sandwich bi-material beams, consisting of relatively thick (100 μm) PEO coatings on both sides of relatively thin (∼400 μm) substrates. Loads were applied incrementally (by adding ball bearings to a small receptacle suspended from the beam) and displacements were measured using a scanning laser extensometer. Elastic behaviour was confirmed by checking that load-deflection plots were linear and reversible. The following standard expression gives the deflection, δy, exhibited by such a beam, at a distance x along its length, when subjected to a load P at a distance L along its length.where Ec, Es are the Young's moduli of coating and substrate, respectively, and the corresponding moments of inertia (about the neutral axis at the mid-plane) are given byin which b is the beam width, d is the total beam thickness and h is the thickness of the substrate.Secondly, stiffness values were also obtained via measurement of the specimen curvature, κ, induced by immersing asymmetrical bi-material beams (substrates coated on one side only) in liquid nitrogen, using the following relationship κ=6EcEs(tc+ts)tcts(αc−αs)ΔTEc2tc4+4EcEstc3ts+6EcEstc2ts2+4EcEstcts3+Es2ts4where ΔT is the temperature change, tc, ts are the thicknesses and αc, αs are the thermal expansivities of coating and substrate, respectively. The curvature, which is uniform along its length, was established from displacement measurements (made with a scanning laser beam device), using the geometrical relationshipin which δy is the lateral displacement at a distance x along the length of the specimen. The Young's modulus of the coating was obtained from Eq. , after substituting the experimentally measured curvature value. This process was repeated for several similar specimens. The expansivity values obtained for coating and substrate, using the dilatometer, were employed in the calculation.Nanoindentation was performed on polished cross-sections and in-plane sections, using a Micromaterials Nanotest 600 machine. A Berkovitch indenter was used with loads of 10 mN and 50 mN. Hardness was calculated from load and indentation depth data, while the local stiffness was determined from the unloading response, using the standard Oliver and Pharr technique The surfaces of PEO coatings exhibit several features indicative of the physical phenomena occurring during growth. An example is shown in . Repeated volcano-like eruptions appear to occur, which are a consequence of discrete localised discharge events. These lead to the formation of craters, with deep central shrinkage holes or pipes. There are also numerous microcracks, many of them radially oriented, as might be expected during solidification of a melt pool in a brittle material. Furthermore, irregularly shaped regions can be seen around these pools, with the appearance of having been ejected from them as liquid globules.On studying such free surfaces on coatings of variable thickness, some clear trends become apparent (). For example, it can be seen that the areal density of discharge craters drops off as the thickness increases. It is also noticeable that the surface roughness rises as the coating thickness increases, presumably reflecting the increasing energy and violence of individual discharges. This is consistent with the energy associated with individual discharges increasing as the coating thickness goes up, with the overall power level being held constant. More substantial craters and pipes would thus be expected, and a higher incidence of ejecta, leading to increased surface roughness. These characteristics are quantified in , which shows plots of the crater population density and the surface roughness as a function of coating thickness.It appears that the process is approaching a limit for stable coating growth, which, for this particular alloy/electrolyte combination and power profile, is known to be about 100 μm. As this limit is approached, the discharges begin to localise. Typical reported growth rates shows a micrograph of the underside of a detached 100 μm coating. This exhibits globular features approximately 10 μm in diameter, with a similar areal population density to that of the crater cores on the outer surface. (Some large precipitates are also apparent in this image, which were formed during dissolution of the substrate.) This suggests that the discharges penetrate through the entire thickness of the coating. This is confirmed by (b), which is a higher magnification image of a region where the thin oxide crust had been damaged in the de-bonding process, showing a channel which appears to penetrate through the complete thickness of the coating. From both micrographs, it would seem that the detaching process has little, if any, effect on the overall integrity of the coating. shows a backscattered SEM micrograph of a polished cross-section of a coating. Even at this low magnification, and recognising the possibility of the polishing process generating some artefacts, it can be seen that these coatings contain a fairly dense network of shrinkage pipes and microcracks. While it would not be expected that any single discharge channel would lie within the sectioned plane throughout its length, some such channels can be seen in the image, since backscattered mode allows a degree of sub-surface imaging. It can be seen that some channels do appear to penetrate the entire thickness of the coating. This cross-section also reveals two distinct structural layers. There is an inner region, with a dense network of small channels and microcracks, which is presumably the product of the many previous discharges during coating growth. The outer region, marked only with the most recent discharges, appears to have been subjected to an annealing treatment of some sort, perhaps by heating from more energetic surface discharges. Such an effect has been suggested by Yerokhin et al. is a typical X-ray diffraction θ–2θ trace for the coatings under consideration. It has been fully indexed and is shown to consist of α-Al2O3 and γ-Al2O3. There is also a substantial fraction of amorphous material, indicated by the broad background peaks at approximately 30° and 60°. Finally, there appears to be a significant amount of textured aluminium, but this is probably due to X-ray penetration through to the aluminium substrate. shows the results of phase analysis by Rietveld refinement, together with the serial grinding of the surface of a 100-μm thick coating. It is presented in the form of a plot of the phase proportion as a function of nominal depth below the free surface. It should be noted that there is an inherent error in the nominal depth since the depth probed by each scan is finite and increases with angle of incidence. The presence of amorphous material also makes penetration harder to quantify. As noted earlier, it is likely that the measured proportion of “aluminium” is merely a consequence of X-ray penetration through to the substrate and thus provides an indication of the error in this method. In particular, the rapid increase in aluminium proportion beyond a nominal depth of 70 μm is indicative of the substrate being probed. Even taking into account this uncertainty, there are significant trends in the data. These trends are confirmed by a simpler analysis based on the relative integrated intensities of the (113)α and (400)γ peaks alone.The proportion of amorphous material remains constant at about 30% throughout the thickness. However, while the remaining material is predominantly composed of the more stable α-Al2O3 phase in the outer 40 μm or so, there is then a switch to the metastable γ-Al2O3 phase becoming predominant over the next 30 μm.These phase profiles bear little resemblance to those previously reported . Moreover, the appearance of this outer layer does suggest that it has effectively been subjected to a series of high temperature annealing treatments, of short duration, but distinguishable from rapid quenching. This might be expected to yield a high proportion of the stable α-Al2O3 phase. It is also significant that a high proportion of amorphous material is detected. Rapid quenching is expected to favour the formation of amorphous phases and γ-Al2O3. It would appear that the γ-Al2O3 can be converted to α-Al2O3 by the heat treatment to which the outer layers are effectively subjected during the violent discharge events, whereas the amorphous material does not transform so readily. It is also possible that the distinct layers are a consequence of different modes of growth within and outside the original aluminium substrate. However, it is clear that further work is needed in order to confirm any of these suggestions.Approximately linear plots were obtained of length change against temperature. The gradients all indicated an in-plane thermal expansivity for the coatings of about 8.2±0.1 microstrain K−1. This was not dependent on coating thickness. The value is actually fairly typical of handbook data for alumina and it is unsurprising that little deviation is observed, since expansivity is not expected to be sensitive to the presence of defects such as microcracks and porosity.However, it is certainly worth noting that the value is appreciably smaller than the figure of about 23 microstrain K−1 typically expected for aluminium and its alloys. A moderate temperature change of, say, 200 K would thus be expected to generate a misfit strain of about 3 millistrain. Assuming a massive substrate, and a coating stiffness of 370 GPa (typical of dense alumina), this would lead to in-plane stresses within the coating having a magnitude of about 1 GPa, which would in turn generate a large driving force for debonding (∼150 J m−2 for a 100 μm thick coating). These figures suggest that the danger of spallation during temperature excursions might be substantial. of Young's modulus values deduced for the coatings, using (a) bending of a sandwich cantilever beam (substrate coated on both sides) and (b) cooling of a bi-material beam (substrate coated on one side only). These plots show the range of measured data and the corresponding deductions of Young's modulus. On each plot, a curve showing the dependence of Young's modulus on the measured parameter for a specific case is included to give some indication of the significance of results.It can be seen that, while there is some scatter in the data, and the values obtained using the two different approaches are not in close agreement, the experimentally measured in-plane stiffness is relatively low, compared with the figure expected for dense alumina (∼370 GPa). The cantilever bending data suggest a value of around 10 GPa, while the bi-material beam cooling experiments indicate a figure of around 40 GPa. The discrepancy between these two figures looks a little large, but it is worth noting that the cooling experiments put the coating into compression, which may raise its apparent stiffness as the microcracks etc become closed. During the sandwich beam bending, on the other hand, the average of tensile and compressive moduli is being measured. In any event, the main conclusion is that the global in-plane stiffness is about an order of magnitude lower than that expected for dense alumina. This is not really surprising when account is taken of the network of micro-cracks and micro-pores present in the coatings. It may also be noted that beneficial effects are expected to arise from having a relatively low value. For example, if the coating stiffness is 30 GPa, then the calculations outlined in the previous section become altered such that the inplane stress level in the coating is reduced to about 100 MPa and the corresponding strain energy release rate falls to about 15 J m−2. These relatively low values are at least consistent with the observation that even relatively thick coatings do not appear to be severely prone to debonding during either heating or cooling. for the local hardness and stiffness, obtained using nanoindentation on a polished transverse section from a 80 μm thick coating, as a function of depth below the surface. While there is clearly a lot of scatter in the data, associated with the possibility that the indent could be close to a pore or other microstructural defect, it can be seen that there is a tendency for the hardness to be higher near the free surface, where there is a high proportion of α-Al2O3—see . Furthermore, the hardness in this region reaches about 23 GPa, which is comparable to that expected for sintered α-Al2O3 (measured as 21 GPa using the same instrument).The Young's modulus plots follow a similar trend, with a slightly higher average value near the free surface, but again a lot of scatter. It is certainly noticeable that the values obtained are of the same order as is expected for dense alumina and hence are much higher than the global values reported in the previous section. This is broadly as expected, since the procedure is sensing the local stiffness and will thus be little affected in most cases by porosity or cracks. Furthermore, the material is being loaded predominantly in compression, which also makes it less likely that very low values would be obtained as a consequence of the presence of cracks, etc.The following conclusions can be drawn from this work, relating to PEO coatings on aluminium-based substrates.The coatings form via a series of electrical discharge events, which create columnar melt pools extending through the thickness of the coating and cause some eruption of molten material at the free surface.These discharge events become more energetic and less frequent as the coating thickness increases. For the conditions employed in the present study, their population density started at about 1.5×1010 m−2 (spacing∼8 μm), but fell to about 1×109 m−2 (spacing∼30 μm) as the coating thickness rose to about 100 μm. The surface roughness increased during this process, from ∼2 μm to ∼8 μm Ra. As the discharge events become more localsied and more violent, further stable growth becomes difficult, imposing an upper limit on the coating thickness.The process generates a network of fine cracks, pipes and pores within the coating.The coatings contain about 30% of amorphous material throughout the thickness. The remaining material is predominantly α-Al2O3 near the free surface, but contains more of the metastable γ-Al2O3 phase near the substrate. Furthermore, the microstructure is coarser near the free surface, to such an extent that the coating exhibits a noticeable two-layer appearance. These differences are provisionally attributed to the near-surface regions having been subjected to an annealing-type process, as a consequence of the relatively large heat-affected zones around the energetic discharge events which occur as the coating becomes relatively thick.The thermal expansivity of the coatings has been measured to be about 8 microstrain K−1. This is similar to previously reported values for dense alumina. This property is not expected to exhibit much sensitivity to the phase constitution or microstructrure.The global in-plane stiffness of the coatings has been found to be relatively low. Cantilever bending experiments on coating/substrate composite beams suggested a figure around 10 GPa, while a procedure involving curvature measurement on cooling of coated substrates, which involved putting the coating into compression, suggested a figure closer to 40 GPa. The difference between these figures and a typical value for dense alumina of 370 GPa is attributed to the effect of the network of cracks and fine pores.Nanoindentation was used to measure the hardness and the local stiffness. Coating hardness (∼20 GPa) and stiffness (∼300 GPa) were both found to be similar to those of dense alumina. This is consistent with the fact that these experiments sense the local properties and are not in most cases strongly affected by defects such as cracking or porosity.Nano-indentation characterization of Ni–Cu–Sn IMC layer subject to isothermal agingLead-free Sn–Ag–Cu(SAC) solder joint on Cu–OSP and ENIG subject to thermal testing leads to IMC growth and causes corresponding reliability concerns at the interface. Modulus and hardness of these IMCs were characterized by Nanoindentation CSM from plan view in this study. A plan-view IMC surface was prepared by deep etching and slight polishing method. When SAC/Ni(Au) solder joint were subject to thermal aging, elastic modulus of the NiCuSn IMC at SAC/ENIG specimen changed from 207 to 146 GPa with different aging time up to 500 h. The hardness decreased from 10.0 to 7.3 GPa. For SAC/Cu–OSP reaction couple, elastic modulus of Cu6Sn5 kept constant at 97.0 GPa and hardness about 5.7 GPa. The modulus of Cu3Sn after 500 h thermal aging was 115.7 GPa. The change of modulus is caused by solid state diffusion process during thermal aging where the morphology and crystal structure of Ni,–Cu–Sn IMC is changing. The calculation of modulus and hardness for IMC layers was based on nanoindentation CSM test results and was compared with reported results.With the implementation of lead-free Sn–Ag–Cu surface mounted components like Plastic Ball Grid Array (PBGA) packages, solder joint reliability of such electronic assemblies is under further research CSM standard hardness and modulus test program was used, in which the harmonic depth and frequency were 2 nm and 45 Hz, respectively. The hardness and modulus of IMCs reported in this study were the average value when displacement into surface is from 100 to 300 nm. For each specimen, 15 points (3 * 5 arrays) were tested. The selection of position to indent could be controlled under a high resolution optical microscope, by which various IMCs and Cu or Ni substrate could be recognized by their colors. Further, since the elastic moduli and hardness for IMCs, Cu and Ni substrate are different, curves for IMCs could be distinguished from the test array. The calculation of elastic modulus and hardness for Nanoindentation CSM was based on the Oliver and Pharr Method show the plan view IMC microstructure of the as-reflowed samples. After selective deep etching to remove the Sn phase, the IMCs layer was exposed for investigation. The scallop-type IMC observed in (a) is typically Cu6Sn5 (or called η-phase) generated at the SAC/Cu reaction couple during solder reflow. When the reaction couple experienced long time thermal aging, a Cu3Sn (ɛ-phase) layer formed between Cu substrate and η-phase. In (b), the needle or rod type IMC is typically Ni–Cu–Sn ternary IMC phase generated at the SAC/Ni reaction couple. It was reported that crystal structure of Ni–Cu–Sn ternary IMC is sensitive with the concentration of Cu in SAC, change of 0.2% Cu may shift the IMC from (Ni1 − |
xCux)3Sn4 to (Cu1 − |
yNiy)6Sn5, XRD, EPMA and phase theories were involved to determine its structure shows the representative test curves for Cu6Sn5, Cu3Sn and NiCuSn. The load–displacement curves were shown in (1a–1c). The curves for Cu6Sn5 before and after aging were roughly identical, thus only one curve for 500 h was presented. For Cu3Sn, the test was only conducted on the specimen after 500 h aging, since it was too thin for as-reflowed specimen and the one after 260 h aging. The elastic moduli, as a function of depth, were shown in (2a–2c). The value of modulus becomes “stable” when the displacement increases to 50–100 nm. The Poisson's ratio of all the phases were approximated as 0.3 when calculating true elastic modulus, E, from reduced elastic modulus, Er. The hardness shown in (3a–3c) was a function of the load applied on the surface and the corresponding projected contact area. The value of hardness, however, decreases with the increment of depth into surface. For the specimen used in this study, since it is multilayer structure, the Cu layer beneath the IMC is softer (hardness of Cu is 1.4 GPa), when the indenter tip penetrates into the top layer, the plastic or elastic deformation in Cu substrate produce extra displacement and makes the measured hardness lower.A summary of the elastic modulus and hardness for the three IMCs subject to thermal aging is shown in . Elastic modulus of Cu6Sn5 after 0, 260 and 500 h thermal aging was measured as 95.7, 97.0 and 97.4 GPa, respectively. The modulus of Cu3Sn after 500 h thermal aging was 115.7 GPa. The hardness of Cu6Sn5 after aging was measured to be 6.09, 5.67 and 5.77 GPa, respectively. Considering the measurement deviation, although Cu6Sn5 grows in thickness during thermal aging, there was no significant change in the modulus and hardness. Reported result from the literature shows some variability Change in modulus and hardness for Ni–Cu–Sn layer at SAC/Ni couple was observed as compared to Cu6Sn5 as shown in (a). The modulus measured from as-reflowed (0 h aging), 260 and 500 h aging specimens were 206.8, 164.9 and 145.8 GPa, respectively. The measured hardness were 10.07, 8.65, 7.31 GPa, respectively. The Ni–Cu–Sn IMC decreases in modulus and hardness with increase in aging time. The interfacial microstructure of the Ni–Cu–Sn grows and changes dramatically in morphology as shown in . For as-reflowed specimen, the IMC on the solder/nickel interface was irregular and needle-like in feature. After 260 h of aging, coalescence of the IMC needles leads to lateral thickening and ripening. After 500 h of aging, the IMC layer growth is a planar or layer-like manner. The change of modulus for Ni–Cu–Sn IMC subject to thermal aging time is dependent on the dynamic changes in the IMC growth and diffusion process, which could change the IMC crystal structure. In our earlier study The reported modulus for Cu6Sn5, (Cu1 − |
xNix)6Sn5, (Ni1 − |
yCuy)3Sn4 and Ni3Sn4 IMCs are given in . Note that the values for various IMCs are quite different. For example, although Cu6Sn5 and (Cu1 − |
xNix)6Sn5 have the same crystal structure (hexagonal structure), the modulus of (Cu1 − |
xNix)6Sn5 with Nickel substitution is almost two times higher than Cu6Sn5, while Ni3Sn4 and (Ni1 − |
yCuy)3Sn4 have similar modulus magnitudes. Both (Cu1 − |
xNix)6Sn5 and (Ni1 − |
yCuy)3Sn4 are ternary IMCs but their moduli are different due to different crystal structure. These results indicate that change of content in Ni–Cu–Sn IMC could affect modulus and hardness. From our measured results, the modulus for as-reflowed specimen was 206.8 GPa, and is consistent with the reported value for (Cu1 − |
xNix)6Sn5. For the aged specimen after 500 h, the elastic modulus was 145.8 GPa, this is also consistent with reported value for (Cu1 − |
xNix)6Sn5. The plausible explanation for this reduction in modulus of Ni–Cu–Sn IMC at SAC387/ENIG solder joint due to the dynamic changes in composition and crystal structure during thermal aging, thus causing changes to the mechanical properties.Novel plan view nanoindentation measurements for IMC layers were conducted on actual BGA Sn–Ag–Cu solder joint interfaces with OSP and ENIG surface finish. Typical studies reported in the literature employ cross-section specimens with thick IMC layers for nano-indentation tests. The plan view tests produces stable result for modulus and hardness even when the IMC layer was as thin as 1–2 μm. The measured modulus of Cu6Sn5 and Cu3Sn after solder reflow were 97 and 115.7 GPa, and the hardness are 5.7 and 7.0 GPa, respectively. After 500 h of isothermal aging at 125 °C, no significant changes were noted for Cu6Sn5. Changes in the modulus and hardness for Ni–Cu–Sn IMC were observed when subjected to isothermal thermal aging at 125 °C. The modulus for Ni–Cu–Sn IMC changes from 207 to 146 GPa after 500 h of isothermal aging. The hardness for Ni–Cu–Sn IMC changes from 10.07 to 7.31 GPa after 500 h of aging. The changes in modulus and hardness Ni–Cu–Sn IMC is due to the dynamic changes during the solid state diffusion where the morphology and crystal structure of Ni–Cu–Sn IMC is changing.Journal of African Earth Sciences, Vol. 31, No. 1, pp. 25-33, 2000 o 2000 Elsevier Science Ltd Pergamon SO899-5382(00)00070-1 All rights reserved. Printed in Great Britam 0899.5362/00 6. see front matter Fold-thrust belt geometry of the Eastern Ghats Mobile Belt, a structural study from its western margin, Orissa, India T.K. BISWAL Department of Earth Sciences, Indian Institute of Technology, Bombay, Powai, Mumbai, 400076, India ABSTRACT-The deformation pattern of the western margin of the Eastern Ghats Mobile Belt reveals the overthrusting relationship of the mobile belt with the craton. The mobile belt is characterised by a nappe structure consisting of the Lathore Group and Turekela Group nappes, which display distinctive lithological assemblages and deformational structures. While the Lathore Group nappe is dominated by charnockitic gneisses and folded by east-west reclined folds, the Turekela Group is khondalitic and folded along a northeast-southwest axis. The study area, therefore, resembles a fold-thrust belt. However, in view of the post-kinematic nature of thrusting to folding, it is comparable with the Caledonides fold-thrust belt. @ 2000 Elsevier Science Limited. All rights reserved. RESUME-Le style de deformation de la bordure occidentale de la chaine des Ghats Orientaux revele que la chaine chevauche le craton. La chaine est caracterisee par une structure en nappes avec celles du Groupe de Lathore et du Groupe de Turekela, qui montrent des assemblage lithologiques et des structures de deformations distincts. Alors que la nappe du Groupe de Lathore, dominee par les gneiss charnockitiques, a ete plissee selon des plis est-ouest, le Groupe de Turekela, khondalitique, a Bte plisse selon un axe NE-SW. La zone dtude ressemble done a une chaine plissee chevauchante. A cause de la nature post-cinematique du chevauchement par rapport au plissement, elle est comparable a la chaine plissee chevauchante des Caledonides. o 2000 Elsevier Science Limited. All rights reserved. (Received I/7/98: revised version received 1 O/9/99: accepted 17/9/99) INTRODUCTION The Eastern Ghats Mobile Belt (EGMB) extends in to the surrounding craton (Subrahmanyam and Verma, a northeast-southwest direction over a strike length 1986) and distinctive terrane boundary shear zones of 900 km along the east coast of India (Fig. 1 a). It on its western margin further distinguish it from the represents a regional granulite belt (Mukherjee, 19981, craton. The eastern continuity is, however, comprising several kinds of high-grade rocks such as interrupted by submarine rocks of the Bay of Bengal. khondalites, charnockites, basic granulites, leptynites It has been proposed by du Toit (1937) and many and enderbytes (Murty et al., 197 1; Narayanswamy, later workers (Katz, 1989; Yoshida, 1995) that the 1975). These are intruded by anorthosites, gabbro, belt once formed a single granulitic terrane with norite and alkaline rocks (Leelanandam, 1987, 1990). Enderby Land of East Antarctica in Gondwana. The The belt is surrounded on three sides by low-grade belt has been divided into four longitudinal zones Palseoproterozoic-Archsean cratons (Fig. 1 b). The belt on the basis of the dominance of particular rock is not only distinguishable on the basis of a higher types (Fig. 1 b; Nanda and Pati, 1989; Ramakrishnan grade of metamorphism, but a positive gravity relative eta/., 1998): *[email protected] Journal of African Earth Sciences 25 T. K. BIS WAL asic chamockite zone -Western khondalite zone -Central migmatlte zone ,, 4 - Eastern khondalite zone \::,NVC - Nagavalli-Vamshadhara Combined shear zone J Terrane boundary shear zonb T Wrench fault , oc)./ ? / 1I M I^\ !c 65Ta Tuiekela 3c m Chhattishgarh Groupm 6aStar Craton 1 Turekela Group r# Lathore Group m Lakhna shear zone 60 Mylonitic foliation with 10 (thrust) stretching lineation Cross;!cz along 200latitude 0 I Figure 1. Geological map of the Eastern Ghats Mobile Belt (EGMB) and adjoining craton around Lakhna, western Orissa, India. (aJ Location map of the EGMB. lb) Geological map of the EGMB (modified after Ramakrishnan et al., 1998) showing the location of the study area. (c) Stereographic projection of poles to 195 mylonitic foliations I+) and 138 stretching lineations (@I. ld) Stereographic projection of 110 c-optic axis of quartz grains: contours I- 2-5.70% showing their distribution over one major and two subsidiary girdles. The major girdle is orthogonal to the C-and deflected leftward to the S-fabric. The above deflection indicates top-to-the-northwest vergence implying overthrusting of the -EGMB. The lowest contour is indicated by a dashed line. le) Stereographic projection of 769 LF, fold axes of the Lathore Group around Dholmandal showing a maximum in the southeast quadrant, contours: l-3-5-7-10%. (f) Stereographic projection of 250 TF, fold axes of the Turekeia Group around Turekela showing a maximum in the northeast and southwest quadrants, contour: l-3-5%. (gl Cross-section along latitude 200showing the thrusting of the Lathore Group over the craton and the klippe position of the Turekela Group over the Lathore Group. i) a western basic charnockite zone; Similarly, the EGMB has been divided into two ii) a western khondalite zone; transverse blocks, namely the northern Chilka Block /ifl a central migmatite-charnockite zone; and and the southern Araku Block, by the northwest- iv) an eastern khondalite zone. southeast-trending Nagavalli-Vanshadhara combined 26 Journal of African Earth Sciences Fold-thrust belt geometry of the Eastern Ghats Mobile Belt shear zone (Fig. 1 b; Chetty, 1995). The granulites Kamineni and Rao, 1988; Dasgupta, 1995). The are conspi-cuously marked by a gneissose fabric, geochronological data across the EGMB fall into which owes its origin to syn-kinematic com-six age categories (Table 1; for a review see Sarkar pressional tectonism and granulite-facies meta-and Paul, 1998). The major deformation and morphism (Biswal et a/., 1998b). This fabric is granulite metamorphism are polychronous, be- dominantly northeast-southwest in the southern and longing to Neoarchaean as well as Meso-to Neo- central part of the EGMB and is east-west in the Proterozoic ages, while the emplacement of anor- northern part. It is axial planar to a set of isoclinal thosites and alkaline rocks are of Meso-to Neo- folds, referred to as first generation folds in the proterozoic age. A Pan-African thermal imprint is belt. These folds have been refolded coaxially by widely recorded in the belt. tight to open second generation folds and sub-The present study focuses on the deformation sequently by open cross folds producing several pattern around the northwestern margin of the belt types of small-to large-scale interference patterns lying in the Balangir and Kalahandi Districts of (Sriramdas and Murthy, 1975; Natarajan and Orissa. Lakhna (204, 82O40), an important Nanda, 1981; Halden et al., 1982; Bhattacharya et locality in the area, is nearly 500 km from al.,1 994; Biswal et a/., 1998a). Shear zones are Bhubaneswar, the capital city of Orissa (Fig. 1 b). the next important deformational features in the belt, which include a terrane boundary shear zone and many intrabelt shear zones (Aftalion et a/., GEOLOGICAL SETTING 1988; Katz, 1989; Chetty and Murthy, 1994; The study area encompasses the Palaeoproterozoic- Mahalik, 1994; Nash et a/., 1996). The pelitic Archiean Bastar Craton in the west, the EGMB in granulites of the south central part are dominated the east and the Lakhna Shear Zone in the centre. by a sapphirine-spinel-cordierite-sillimanite-bearing The Lakhna Shear Zone delineates a terrane boun- assemblage that shows 9.0 kbar pressure and dary between them (Fig.1 1. The Chhattishgarh 95O temperature of prograde metamorphism and Group, which unconformably overlies the craton in 650 temperature and 4.5 kbar pressure of the west, comprises Neoproterozoic unmeta- retrograde metamorphism with a dominantly anti-morphosed platform sequences that are not included clockwise retrograde trajectory (La1 et a/., 1987; in this paper. Table 1. A summary of the ages of tectonic, metamorphic and igneous events in the Eastern Ghats Mobile Belt Age in Ga Event Dating Method References Age of sediment protolith Rb-Sr whole rock Peeraju et al. (1979) 2.86 Mafic granulite intruding the Sm-Nd model age Paul et al. (I 990) khondalites. Crustal residence age 2.6 Granulite Metamorphism and U/Th-Pb from zircon of Vinogradov et al. (1964) folding khondalites 2.1 Intrusion of S-type granites Rb-Sr whole rock age of Bhaskar Rao et al. (1992) following transtensional granites tectonism 1.5 Granulite metamorphism Rb-Sr whole rock ages Aswathanarayana (I 964) 1.4 Intrusion of massif anorthosites Sr isotope data Sarkar et al. (1981) 1.2 Alkaline rocks Rb-Sr whole rock isochron Clark and Subbarao (1971) 1.4 Alkaline rocks Rb-Sr whole rock isochron Sarkar and Paul (1998) 1 .o Charnockitisation through CO2 U-Pb of zircon Aftalion et al. (1988) metasomatism 0.98 Charnockitisation U-Pb of zircon Paul et a/. (1990) 1 .o Granulite-facies metamorphism U/Th-Pb from perrierite Grew and Manton (1986) and development of sapphirine-and zircon spine1 bearing assemblages 0.85 Intrusion of alkaline rocks Rb-Sr whole rock isochron Sarkar et al. (1989) 0.5 Thermal rejuvenation U-Pb zircon ages Kovach et al. (1997) Journal of African Earth Sciences T. K. BIS WAL The Bastar Craton Bastar Craton predominantly consists of trond- hjemitic gneisses (3.5 Ga, U-Pb age) similar to that of Peninsular gneisses of South India and late tectonic granites (2.5 Ga, U-Pb age) (Sarkar et al., 1993). However, the study area is dominated by late tectonic granite which is coarse-grained, homogeneous and composed of quartz, alkali feldspar and plagioclase feldspar with a minor amount of biotite. It does not show much ductile deformation, although cross-cutting brittle shear fractures are common. Lakhna Shear Zone The Lakhna Shear Zone (LSZ) defines the terrane boundary between the Bastar Craton and the EGMB. Except for a narrow zone in the EGMB, most of it lies in the craton. Hence, the mylonites of the shear zone show quartzofeldspathic composition. The LSZ strikes northeast-southeasterly having a map width of 2 km. It is inclined moderately to the southeast and the EGMB and the craton form the hanging wall and footwall, respectively. The mylonites are chara- cterised by mylonitic foliation, which dip moderately to the southeast, and stretching lineations that plunge down-dip on the mylonitic foliation (Fig. 1 c). Petrofabric analysis of the mylonites indicates a wide variation in the clast to matrix ratio. The cratonic side of the shear zone is dominated byprotomylonites followed by mylonites and ultramylonites towards the centre. The L section of the mylonites (section cut perpendicular to the mylonitic cleavage but parallel to the stretching lineation) contains an S-Cfabric (Fig. 2a), various types of porphyroclasts (Fig. 2b) and intragranular faults which unequivocally prove top-to-the-northwest vergence of the LSZ (Biswal et al,, 1998a). This has been further confirmed by the asymmetric c-axis girdle of dynamically recrystallised quartz grains (Fig. Id) and indicates thrusting of the EGMB over the craton. In view of the high-grade nature of the EGMB resting over the low-grade craton, the above thrusting implies absolute movement of the EGMB with respect to the craton. Using the values of SAC angle (Table 2) measured in the orientated samples collected at regular interval across the shear zone along profile A-B, the minimum amount of throw is estimated to be around 2.5 km (Fig. 3). Occasionally, the LSZ hosts concordant nepheline syenite intrusives, which exhibit excellent preservation of magmatic foliations and lineations consistent with the mylonitic foliation and stretching lineation of the host mylonites. However, internally it is devoid of any mylonitic fabric. This feature is ascribed to syn- kinematic emplacement of melt during shearing. The shear zone has witnessed the growth of biotite and 28 Journal of African Earth Sciences chlorite at the expense of plagioclase feldspar during shearing. Hence, it is interpreted that the PTcondition of shearing lies well within greenschist-facies con- ditions. The Eastern Ghats rock in the LSZ has been retrograded to amphibolites and schists, thereby inferring the zone to be a retrograde shear zone. Eastern Ghats Mobile Belt The EGMB overlies the craton with the LSZ at the base. The mobile belt is represented by granulite- facies rock, which are grouped into two lithotectonic groups: namely the Lathore Group and the Turekela Group. While the Lathore Group is dominated by charnockitic gneisses, the Turekela Group is dominated by khondalites (Tabe 3). The contact between them is marked by a narrow low angle thrust along which the khondalites have been mylonitised and retrograded to schists and the early folds have been reorientated parallel to thrusting. The two groups differ significantly in deformation pattern too. While the rocks of the Lathore Group are folded by an early phase of coaxial folding with a southeasterly plunging axis (Fig. 1 e), the Turekela Group shows folding along a northeast-southwest axis (Fig. 1 f). Hence, the fold axes in these groups are at a high angle to each other. The third generation folds differ in respect to flow direction, which has resulted in variations in the interference pattern. Furthermore, the groups vary with regard to their brittle de-formation. The contrasts between these groups are illustrated in Table 3. DISCUSSION The above study reveals that the EGMB has over- thrust the Bastar Craton along the terrane boundary shear zone. Further, the belt is subdivided into two lithotectonic groups, the Turekela Group and the Lathore Group, which are not only separated by a low angle thrust but display contrasting lithological assemblages and deformation patterns. The fold axes in these two groups are at right angles to each other, suggesting different finite strain. Based on this, these two groups are described as nappe sheets. Furthermore, the brittle shear fractures in them show two distinct generations of growth. While the Lathore Group is marked by both east-northeast- west-southwest and northwest-southeast sets of fractures, the Turekela Group is marked by only the latter set. Secondly, the east-northeast-west- southwest set in the Lathore Group is cut out against the Turekela Group. The two phases of fracturing implies two stages of thrusting involving a nappe sheet at each stage. The Turekela Group, after being thrust over the Lathore Group, has been eroded to form a klippe (Fig. 1 g). The presence of nappes with distinct Figure 2. (al Microphotograph of an S-C fabric, illustrating a left lateral sense of shear (Passchier and Trouw, 79961. The sense of shear implies top-to-the-northwest vergence and interprets the thrusting of the mobile belt over the craton. (b/ Microphotograph of an s-type porphyroclast showing top-to-the-northwest vergence. (cl East-west-trending LF, reclined fold on the sub-horizontal surface in the talc gneiss of the Lathore Group near Dholmandal. (d/ East-west-trending reclined LF, fold on the sub-horizontal surface in the talc gneiss south of Dholmandal. (e) Sub-horizontal view of an LFZ sheath fold in the talc gneiss near Dholmandal. If) Northeast-trending TF, reclined fold on a subvertical surface in the impure marble of the Turekela Group near Turekefa. /gJ Type 3 interference pattern produced due to coaxial folding between TF, and TF, folds (Ramsay, 19671 in the Turekela Group, seen on a sub-vertical section of impure marble west of Turekela. (h) Type 2 interference pattern due to cross-folding between the northeast-southwest-trending TF, fold and the northwest-southeast-trending TF, fold (Ramsa y, 1967) in the Turekela Group seen on a sub-horizontal face of impure marble west of Turekela. T.K. BISWAL Table 2. Table showing the relationship between SAC angle, shear strain and angular displacement Sample No. SC Angle Shear Strain Angular from northwest (0) in degrees Displacement w to southeast 1~) in degrees AB -1 32 0.97 44 AB -2 23 1.93 62 A6 -3 15 3.46 74 AB -4 22 2.07 64 AB -5 28 1.35 53 AB -6 30 1.15 49 AB -7 35 0.72 36 AB -8 40 0.34 19 Table 3. A comparison ot the lithology and structure of the Lathore ans Turekela Groups Lathore Group Turekela Group Lithology Lithology 1. Charnockitic gneiss (quartz + alkali 1. Khondalites feldspar + plagioclase (quartz + sillimanite + garnet + graphite) feldspar + garnet + hypersthene), garnet-and impure marble sillimanite quartzite, talc gneiss (calcite + diopside + scapolite + plagioclase (diopside + scapolite + plagioclase feldspar + sphene). feldspar + sphene). Structure Structure 1. Prominent gneissose fabric which is axial 2. Gneissose fabric is axial planar to a set of planar to a set of reclined, southeasterly reclined isoclinal northeast-southwest plunging isoclinal LFI folds (Figs le and trending TFI folds (Figs If and 2f). 2c). 3. TFz fold is coaxial with the TFI fold. The 2. LF1 fold is coaxially refolded by an LF:! Type 3 interference pattern has resulted fold, which is open to tight and reclined from this (Fig. 29). in nature (Fig. 2d). The Type 3 4. Sheath folds are absent. interference pattern has resulted from 5. TF3 folds are in the northwest-southeast this. direction. They have produced mirror 3. LF2 fold has been transformed into sheath image patterns with TFz folds (Fig. 2h) folds (Fig. 2e). The x-axis of the sheath due to horizontal flow. plunges to the southeast. 6. Northwest-southeast fractures are present 4. LFz folds are open in the northwest-only. The east-northeast-west-southwest southeast direction. The movement fractures are not only absent in it; but direction is vertical. This has produced while tracing them from Lathore Group, rare dome and basin structures with LFz they are truncated at the base of the folds. Turekela Group. 5. Both sinistral east-northeast-west- southwest and dextral northwest- southeast brittle shear fractures are present in small-and micro-scale. The east-northeast-west-southwest set is earlier than the northwest-southeast set (Biswal and Sahoo, 1998). 30 Journal of African Earth Sciences Fold-thrust belt geometry of the Eastern Ghats Mobile Belt Shear strain along profile A-B southeast of Lakhna rue width line b 32 23 15 22 28 30 35 40 S A C angle in degree W 4.0 7 Sample locations along true width line Displacement Angular 1.8 times the true width displacement I 44 62 36 19 Figure 3. Shear strain evaluation along profile A-B across the Lakhna Shear Zone southeast of Lakhna (Fig. lg). (al The profile plane and true width line of the shear zone. The samples (1-B) are plotted on the profile line. The S-planes are drawn using the SC angle at each sampling site. The S-planes meet the shear zone wall at a 45angle because shear strain, y, is zero at the wall. Ibl Shear strain variation curve along the true width line. (cl Graphical integration of angular displacement at each sampling site. The values of shear strain and angular displacement have been given in Table 3. The above method is adopted from Ramsay and Huber (1983, 1987). lithological and deformational characteristics draws an analogy of the belt with a fold-thrust belt. However, unlike a fold-thrust belt where the folding is synchronous with thrusting (Suppe, 19831, the folding in the EGMB is pre-kinematic to thrusting. This is evident from the fact that the granulites of the EGMB in the shear zone have been mylonitised and retrograded to amphibolites and schists and earlier deformational fabrics have been reorientated parallel to the shear direction. Hence, the study area is comparable with the Caledonides fold and thrust belt where the folding is reported to predate the thrusting (Ramsay, 1997). The Lakhna Shear Zone forms a part of the larger terrane boundary shear zone along which the mobile belt has been juxtaposed against the craton (Fig. 1 a). The curvilinear map view of the shear zone is attributable to the low inclination of the thrust plane and to the presence of wrench faults (Fig. 1) across it. To the far north and south of the study area, two such wrench faults (Fig. 1 b; Nash et al., 1996 and the author unpublished work) occur con- tributing to the salient geometry of this part of the belt. The EGMB has been correlated with East Antarctica on the basis of similar metamorphic history and geochronological data (Grew and Manton, 1986; Yoshida, 1995; Mezger and Costa, 1999). The present study, revealing the presence of a thrust structure and retrograde shear zone in the EGMB, agrees with such a correlation on account of similar structures reported from East Antarctica (Sandiford, 1985; Clarke, 1988). ACKNOWLEDGEMENTS The above research work is sponsored by the Depart- ment of Science and Technology, New Delhi. REFERENCES Aftalion, M., Bowes, D.R., Dash, B., Dempster, T.J., 1988. 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Its Economic Resources. Elsevier, Amsterdam, pp. 409-Sarkar, A.N, Nanda, J.K., Paul, D.K., Bishui, P.K., 436. Gupta, S.N., 1989. Late Proterozoic alkaline Mahalik, N.H.. 1994. Geology of the contact between magmatism in the Eastern Ghat Belt: Rb-Sr isotopic the Eastern Ghats Belt and North Orissa Craton, India. study in the Koraput Complex, Orissa. Industrial Journal Geoligucal Society India 44, 41-52. Minerals 43, 265-272. 32 Journal of African Earth Sciences Fold-thrust belt geometry of the Eastern Ghats Mobile Belt Sarkar, G., Corfu, F., Paul, D.K., McNaughton, N.J., Gupta, S.N., Bishui, P.K., 1993. Early Archsean crust in Bastar Craton, Central India -a geochemical and isotopic study. Precambrian Research 62, 127-I 37. Sarkar, A., Paul, D.K., 1998. Geochronology of the Eastern Ghats Precambrian Mobile Belt -A review. Geological Survey India, Special Publication 44, 51-86. Sriramdas, A., Murthy, M.S., 1975. Lithology and structure of the Eastern Ghat of Vishakapatnam, A.P.. 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Journal of Afrzcan Earth Sciences Fold-thrust belt geometry of the Eastern Ghats Mobile Belt, a structural study from its western margin, Orissa, IndiaThe deformation pattern of the western margin of the Eastern Ghats Mobile Belt reveals the overthrusting relationship of the mobile belt with the craton. The mobile belt is characterised by a nappe structure consisting of the Lathore Group and Turekela Group nappes, which display distinctive lithological assemblages and deformational structures. While the Lathore Group nappe is dominated by charnockitic gneisses and folded by east-west reclined folds, the Turekela Group is khondalitic and folded along a northeast-southwest axis. The study area, therefore, resembles a fold-thrust belt. However, in view of the post-kinematic nature of thrusting to folding, it is comparable with the Caledonides fold-thrust belt.Le style de déformation de la bordure occidentale de la chaîne des Ghats Orientaux révèle que la chaîne chevauche le craton. La chaîne est caractérisée par une structure en nappes avec celles du Groupe de Lathore et du Groupe de Turekela, qui montrent des assemblage lithologiques et des structures de déformations distincts. Alors que la nappe du Groupe de Lathore, dominée par les gneiss charnockitiques, a été plissée selon des plis est-ouest, le Groupe de Turekela, khondalitique, a été plissé selon un axe NE-SW. La zone d'étude ressemble donc à une chaîne plissée chevauchante. A cause de la nature post-cinématique du chevauchement par rapport au plissement, elle est comparable à la chaîne plissée chevauchante des Calédonides.Improved mechanical anisotropy and texture optimization of a 3xx aluminum alloy by differential temperature rollingThe effects of roller temperature on the microstructure and mechanical properties of a 3xx serie aluminum alloy sheet were studied. Three temperature settings, namely, traditional rolling with low roller temperature (LTR), high roller temperature (HTR), and differential temperature rolling (DTR): different temperature of upper and lower rollers, were performed. The results reveal that among the three routes, the DTR introduces an internal shear strain, which significantly promotes the dynamic recrystallization and grain refinement. Moreover, a texture optimization from the rolling texture of {112} <111> to {001} <120> texture can be observed. The newly-formed {001} <120> texture has a high Schmid factor in both rolling and transverse direction (RD and TD), which contributes mostly to the improvement of the mechanical anisotropy. Compared to the LTR and HTR samples, the mechanical properties (tensile strength, yield strength and elongation) of the DTR samples in RD and TD are closer, which results in a significantly higher Erichsen value of 6.85 even without annealing. In addition, the combined experimental and calculation results indicate that the DTR sample also maintain a high yield strength due to a higher recrystallization degree and grain boundary strengthening effect. The mechanical anisotropy can be reduced by controlled grain refinement, dynamic recrystallization and texture optimization through DTR without sacrificing the strength.Owing to the advantages of low density, high specific strength and excellent processing performance, aluminum alloys have been widely used in the automotive, aerospace and other industries under the tendency of lightweight transportation fields []. 3xx Al alloys have been widely used as food packaging material due to its excellent formability and corrosion resistance []. However, there exists a long-standing dilemma in the manufacturing and forming process of Al alloys especially sheets, that is, mechanical anisotropy [], which seriously reduces the service life and production efficiency.Numerous investigations have demonstrated that the texture is the main factor dominating a deterioration of ductility and strong mechanical anisotropy of polycrystalline aluminum alloys []. Thus, the main strategy should aim at controlling and designing of texture orientation to improve the mechanical properties and the anisotropy. Recently, different rolling techniques have been developed for texture design. For example, the asynchronous rolling with different rolling speed of upper and lower rollers can result in the formation of shear stress, which directly influence the texture evolution. Asymmetric rolling is also developed to introduce shear deformation in the material, which favors shear deformation textures consisting of {001}<110>, {111}<110>, and {111}<112> along the thickness []. By using the accumulative roll-bonding (ARB) technique, which is a kind of severe plastic deformation method and involves the repetitive rolling of two equal sized metal sheets, the shear and rolling texture of {001}<110> and {112}<111> develops at the surface and center of the sheet, respectively []. In order to achieve a randomization of the recrystallization texture with improved formability properties, the rolling texture of {112}<111> in aluminum sheet can be modified by introducing a cross-rolling step in which the aluminum sheets are rolled along different rolling routes to change metal flowing state []. Briefly, the shear texture of {001}<110> introduced by the shear stress is beneficial for the formability [] while the rolling texture of {112}<111> lead to poor ductility of the sheet []. Moreover, the dynamic recrystallization (DRX) plays an important role in the microstructure evolution and mechanical response during rolling []. The imposed cold deformation can increase the strain energy and the driving force of the recrystallization nucleation, thus increasing the recrystallized fraction. Furthermore, the recrystallization process can result in a random distribution of grain orientation and the elimination of rolling texture [], which also improves the mechanical anisotropy to make the mechanical properties of the sheet become similar in different tensile directions. Thus, it is also crucial to enhance the dynamic recrystallization during the rolling process.In view of this aspect, this work adopts a new differential temperature rolling (DTR) route [] to improve the mechanical anisotropy of 3xx aluminum alloy. Compared with other conventional rolling techniques in the previous works, such as asymmetric rolling [], the advantages of the DTR route can be explained as follows: the DTR route can cause the different flowing speed of upper and lower surfaces, which contributes to the formation of shear stress. In the DTR route, the temperature of the upper surface of the sheet is higher than that of the lower surface because of higher temperature of upper roller than that of lower roller, making the upper surface of the sheet more easily deformed than the lower surface. Meanwhile, the dynamic recrystallization can also be significantly promoted due to a high roller temperature and additional driving force. On the other hand, the effect of temperature gradient of the rolling mill on the mechanical properties has hardly been reported. Thus, this work main focuses on the microstructure evolution (microstructure, texture and dislocation density), mechanical properties and formability (stress-strain curves and Erichsen value) during different rolling routes. The aim of the study is to investigate the influence of the innovative DTR route on the microstructure evolution and mechanical properties of 3xx aluminum alloy, which provides a guide of designing 3xx Al alloys sheets with a combination of high strength-ductility with improved mechanical anisotropy.The rolling aluminum alloy in this study was the house-melted 3xx aluminum alloy with a chemical composition of Al-1.271Fe-0.484Mn–0089Si-0.003Cu (wt. %). Three kinds of rolling routes, namely, LTR, HTR and DTR, were conducted. In the LTR and HTR, the upper and lower temperatures of the rollers were the same, namely 50 °C and 100 °C, respectively. In the DTR, the upper and lower rollers were set to 100 °C and 50 °C, respectively. For all the rolling routes, the 3xx aluminum sheets (100 mm × 50 mm × 1.2 mm) cut from the same sheet were rolled to a final thickness of 0.5 mm by a single pass with 50% thickness reduction without lubrication. The rolled sheets were placed on a GBS-60B Erichsen testing machine to measure the Erichsen value. The uniaxial tensile tests were performed at room temperature with a strain rate of 2 mm/min using a CMT5305 universal material testing machine, and the tensile direction was parallel to the rolling direction (RD) and the transverse direction (TD), respectively. The cross-sectional microstructure of the rolled sheet was examined using electron backscatter scanning diffraction (EBSD) with a step size of 0.08 μm. The data were illustrated using OIM software to acquire the inverse pole figure (IPF) and grains size distribution. To obtain the surface texture and the dislocation density, X-ray diffraction (XRD) with a Cu-Kα radiation (D/max-2200/PC) tests were performed. The data for texture and dislocation density were analyzed using LABOTEX software and Jade 6.0 software, respectively. shows the IPF maps and corresponding grains size distributions of aluminum alloy sheets after different rolling routes. Significantly, the three samples show different morphologies and grain orientations. Many elongated grains with a large deformation degree can be observed in the LTR sample, while a small amount of equiaxed grains are available. The DTR sample shows large amounts of equiaxed recrystallized grains with a smaller average grain size of 0.84 μm. In the HTR sample, the recrystallization also occurs but the nucleating grains grow faster to an average grain size of 1.13 μm. The origin of microstructure differences can be attributed to different (DRX) degree after the three rolling routes. displays the Kernel Average Misorientation (KAM) maps and corresponding values of the three samples. Color scale illustrates the local misorientation degree, which directly represents the internal strain at individual measured points []. The black color represents unrecognized locations. It is well known that KAM value and total strain energy in materials will exhibit an approximately linear relationship []. The DTR sample exhibits a lowest average KAM value of 0.47 among the three samples (d), which indicates that a smaller internal strain exists in the DTR sample than that in the LTR and HTR samples. By assuming the original sheets have equivalent internal strain energies, it is logical that the internal strain energy is released more effectively in the DTR sample during the rolling compared with other samples. Here, we may infer the internal strain energy is related with the DRX during the rolling, detailed discussion see section To characterize the texture distribution, the . Three types of texture components {112}<111>, {001}<110> and {001}<120> exist in all three samples. The texture components {112}<111> and {001}<110> dominate in the HTR and LTR samples, while a stronger texture of {001}<120> is -found in the DTR sample. The maximum texture intensities are 4.2, 5.5 and 3.1 of the LTR, DTR and HTR sample, respectively. Indeed, the texture has a significant impact on the deformation behavior of the rolled sheet, thus resulting in different mechanical properties of the three samples. In contrast, the weakening of the deformed texture was mainly achieved by severe plastic deformation such as ARB and multi-axial forging [ shows the engineering stress-strain curves of the three samples along the rolling and transverse direction (RD and TD). shows the important mechanical properties of the LTR, DTR and HTR samples. From the analysis of the overall mechanical properties, the three samples have similar yield strength of 150–170 MPa and ultimate tensile strength of 175–200 MPa. However, for the LTR sample, the mechanical performance both in the strength and total elongation in RD is obviously better than that in TD (a). This demonstrates a strong mechanical anisotropy. However, the tensile curves in the RD and TD are closer in the DTR and HTR samples compared with LTR, i.e., weaker anisotropy, as shown in In general, the dynamic recrystallization process plays an important role in dominating the dislocation evolution and the overall microstructure after different rolling routes, hence, strongly influencing the mechanical properties []. To evaluate the DRX degree, the dislocation density was measured using the XRD experiment. a shows the XRD patterns of the LTR, DTR and HTR samples. The microstrain η, Burgers vector (B) from the XRD data and average crystallite sizes (d) from EBSD data were used to evaluate the dislocation density ρ (m−2). The Burgers vector for the FCC structure is B = 0.286 nm [After correcting the broadening of diffraction peaks obtained from the lanthanum hexaboride, the Williamson–Hall method was used to investigate the change of the microstrain and determine the full width at half maximum (FWHM) intensity of the selected peak in degrees (rad) [FWHM=((FWHM)Measured2−(FWHM)Instrumental2)1/2According to a linear fitting of the Williamson–Hall plot shown in b, the microstrain (η) can be computed from the slope using the following equation [where θ and λ are Bragg's angle of diffraction and the wavelength of Cu–Kα radiation (λ = 0.1541 nm), respectively. shows the microstrain values and the calculation of dislocation density of the three samples., the dislocation densities of LTR, DTR and HTR samples are 1.78444 × 1013, 2.36476 × 1013 and 1.67316 × 1013 (m−2), respectively. From the above analysis, compared with other samples, the DTR sample has a higher degree of recrystallization and lower KAM value, which demonstrates a lower dislocation density. However, the calculated dislocation density results from XRD data are on the contrary. This difference can be explained as follows: the XRD data is only reliable when measuring the order of magnitude of the dislocation density, which decides the strengthening degree []. During the DTR process, the temperature difference between the upper and lower rolls cause different metal flowing speed in normal direction (ND), which causes internal shear forces that facilitates the plastic deformation of the alloy. Under this shear stress, the metal undergoes additional shear deformation. At the same reduction, a high shear strain in DTR may activate more slip systems of Al sheets, both in slip and cross slip, which provides a good plasticity of material.The numerical fraction of recrystallized, substructured and deformed grains in the LTR, DTR and HTR samples is shown in . The grains with high-angle boundaries (>15°) were defined as the recrystallized grains. It can be clearly seen that the DTR sample shows a highest recrystallization degree and a lowest substructured fraction. Dislocations accumulate in the sample to form substructural boundaries. The introduction of shear deformation in the DTR process causes the rotation of substructural boundaries in the crystalline material, thereby forming large-angle grain boundaries. However, the HTR sample also shows a high recrystallization degree but the recrystallized grains grow fast due to a high deformation temperature, which results in a largest average grain size value (). As the grain grows, the low angle grain boundaries gradually change to large angle grain boundaries.In general, the yield strength is mainly related to the comprehensive strengthening mechanisms including the solid solution, grain boundary, precipitation and dislocation strengthening, which can be quantitatively calculated based on the microstructure features such as the grain size, dislocation density and phase composition []. Meanwhile, the texture and dynamic recrystallization play dominant roles in the plasticity and mechanical anisotropy []. Thus, the correlation between the microstructure and mechanical properties can be established as follows. shows the volume fraction, intensity and Schmid factor of different texture components in the three samples after different rolling routes. Among the three rolling sheets, there are three main textures of {001}<120>, {001}<110> and {112}<111>. The Schmid factor values of {001}<120> texture toward RD and TD are equal and largest, indicating that this texture shows a soft orientation factor along both RD and TD. However, the Schmid factor value of {112}<111> rolling texture in the RD is much smaller than that of TD, which mainly results in a strong mechanical anisotropy. The shear texture of {001}<110> has the same Schmid factor values for RD and TD, and its intensity and volume fraction is gradually reduced in the three rolling techniques of LTR, DTR and HTR. The DTR sample shows a highest fraction of recrystallized grains, thus contributing to a random distribution of grain orientation and minimizing the rolling texture of {112}<111>. A texture optimization from the rolling texture of {112} <111> to {001} <120> texture can be observed. shows mechanical properties of three aluminum alloy sheets with different rolling techniques. The LTR sample shows a highest tensile strength. Based on the previous analysis on the microstructures, the strengthening mechanisms of 3xx aluminum alloy sheets consist of solid solution strengthening, grain boundary strengthening and dislocation strengthening.The theoretical yield strength satisfies Eq. where σ0 is the yield strength of the pure aluminum, σss is the strengthening due to the solid solution, σgs is the strengthening due to the grain boundary, σd is the strengthening due to the dislocation density. According to Ref. [The particular contribution to the strength from the specific types of solute atoms can be estimated by Eq. τi(sol)(T)=(kiCi2/3)exp[−kiTln(ε˙0/ε˙)/(0.51)ΔEb)]where the term ki is a constant related to specific solute element []. Ci is the concentration of the specific solute element; T is the temperature (being 298 K for room temperature); ε˙and ε˙0 are the macroscopic strain rate and the reference strain rate, respectively; △Eb is the total energy barrier for thermally activated motion of the dislocation []. The total solute atom contribution to the τss can be estimated by combining the contribution of each solute element, as in the following expression [Here, τ1, τ2, τ3 and τ4 stand for the contribution of different solute elements. M is the Taylor factor. The average value of M can be calculated based on the volume fraction of texture and the previous studies [] and the average M value of LTR, DTR and HTR sample is 3.12, 3.22 and 3.18, respectively.The Hall-Petch relationship usually is applied to evaluate the grain boundary strengthening which was estimated by σgs=kd−1/2 []. For Al–Fe alloys, k = 72.7 MPa μm1/2 []. The dislocation strengthening is governed by Eq. where αd is a constant and αd = 0.2; G is shear modulus of the Al matrix and G = 27.4 GPa []. The calculated results are also revealed in The quantitative results are not very close to the experimental results (b). The difference can be attributed to the contribution of precipitation strengthening from the second phase Al6(MnFe) (a). Because the solid solvus temperature (400°C–600 °C) of Al6(MnFe) is much higher than the recrystallization temperature [], it is reasonable to assume that the volume fraction and size of the precipitate are almost the same in the three samples (without phase transformation). Thus, the precipitation strengthening contributions are also similar when calculating the strengthening degree of the LTR, HTR and DTR samples. In conclusion, the difference of yield strength mainly originates from the grain boundary strengthening in the three samples, which is strongly related to the dynamic recrystallization. In addition, the total elongation values of the DTR sample in RD and TD are also very close, which results from a higher dynamic recrystallized fraction. Moreover, the {001}<120> texture occupies a largest intensity and volume fraction in the DTR sample while the {112}<111> texture in DTR sample has a lowest intensity of 0.76 and volume fraction of 2.23 (). The texture optimization also contributes to the highest Erichsen value of 6.85 in the DTR sample (d), which is much better than the Erichsen value of 4.80 in Ref. []. The Erichsen value gives a measure of the ductility of the sheet in the plane of drawing under biaxial stress condition []. Thus, the innovative DTR technique plays an important role in grain refinement, optimizing texture components and improving mechanical anisotropy. This work offers a useful perspective for optimizing texture components and improving mechanical anisotropy by introducing internal shear stress developed from DTR techniques.Three kinds of rolling techniques were carried out to investigate the microstructure and mechanical properties of 3xx aluminum alloys, namely, traditional rolling with low roller temperature (LTR), high roller temperature (HTR) and different temperature of upper and lower rollers (DTR). The following conclusions can be drawn from the investigations:Compared with the conventional rolling techniques, DTR techniques can introduce an internal shear strain, which promotes grain refinement, increases the recrystallized fraction, and effectively releases strain energy in the material.In the DTR samples, the {0 0 1} <1 2 0> texture with a high schmid factor has a largest volume fraction of 7.82% and a highest intensity of 5.14, while the {1 1 2} <1 1 1> rolling texture which results in a strong mechanical anisotropy has a smallest volume fraction of 2.23% and a lowest intensity of 0.76. Such a texture optimization from {1 1 2} <1 1 1> texture to {0 0 1} <1 2 0> texture happened in the DTR techniques.The difference of yield strength mainly originates from the grain boundary strengthening in the three samples, which is strongly related to the dynamic recrystallization. The DTR sample has a largest theoretical yield strength of 152.2 MPa, and the experimental mechanical properties of DTR sample are closer in RD and TD than that of LTR and HTR samples, which contributes to a significantly higher Erichsen value up to 6.85.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.Xiaoyu Fan: Conceptualization, Methodology. Yu Li: Conceptualization, Methodology, Writing - review & editing, Supervision. Chun Xu: Validation, Formal analysis, Visualization, Investigation. Binjun Wang: Investigation, Resources. Ruizhi Peng: Data curation, Writing - original draft. Jianbin Chen: Funding acquisition.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.G-phase strengthened iron alloys by designDensity functional theory (DFT) calculations were used to model G-phase precipitates of formula X6M16Si7 where X is Cr, Hf, Mn, Mo, Nb, Ta, Ti, V, W and Zr and M is either Fe or Ni. It was found that the occupancy of the d-orbital is correlated to the formation enthalpies of each structure. Past thermal expansion coefficient data was used to predict the lattice misfit between each G-phase and body centred cubic (BCC) Fe. All except Hf and Zr containing G-phases were predicted to have zero misfit between 581−843 K. Of the Ni containing G-phases, Mn6Ni16Si7 was predicted to have the most similar elastic properties to BCC Fe. DFT calculations of the substitution energies of Al, Cr Cu, Fe, Ge, Hf, Mo, Nb, P, Ta, Ti, V, Zr, and vacancies onto the Mn6Ni16Si7 G-phase from BCC Fe were performed. It was predicted that Cu, P and vacancies favour G-phase substitution. Suppression of the G-phase is predicted when Si content is reduced by half, at which point the BCC phase is favoured. It is hypothesised that including Zr to form a (Mn,Zr)6Ni16Si7 precipitate will allow for higher ageing temperature and expediate nucleation in an Fe alloy. Thermocalc was used to predict that a mixture of FebalCr9Ni4Si2(Mn0.6Zr0.4)1.2 (at.%) will produce a G-phase strengthened Fe alloy with potential for a good balance of strength, ductility and oxidation/corrosion resistance at room temperature. This alloy composition was experimentally determined to precipitate the G-phase in ≤24 h with cube-on-cube orientation to the BCC Fe matrix.A mechanistic understanding of the G-phase in steels/iron alloys is of interest to oil, chemical and nuclear industries . A considerable amount of work has been done, that is still ongoing in the nuclear industry, to understand and prevent the solute clustering of Mn, Ni and Si (thought to be a precursor to the Mn6Ni16Si7 G-phase in low-alloy ferritic steels ), which is potentially a limiting factor for the lifetime of pressurised water reactors Off-stoichiometric G-phase is commonly observed and its accommodation of various other species has been evidenced by chemical analysis techniques In this study, density functional theory (DFT) was used to calculate formation energies, lattice parameters and elastic constants for 22 different G-phase chemistries. The site preferences for substitution of Al, Cr Cu, Fe, Ge, Hf, Mo, Nb, P, Ta, Ti, V, Zr, and a vacancy into the Mn6Ni16Si7 G-phase were also calculated. The off-stoichiometric G-phase Fex+y+zMn6-xNi16-ySi7-z was examined and compared to BCC structures with the same composition. Thermocalc was used, guided by lessons learned from DFT, to predict compositions that could form dual phase BCC+G-phase microstructures in Fe alloys. One predicted composition [FebalCr9Ni4Si2(Mn0.6Zr0.4)1.2] at.% and two comparison compositions (FebalNi7Si3Mn1 and FebalNi3Si3Mn1 at.%) were experimentally produced, aged and characterised to compare with theoretical predictions.A plane-wave density functional theory method was used, as implemented in the Vienna Ab initio Simulation Package (VASP) The k-points, cut-off energy and lattice parameters of the pure elements in their ground state structures were converged independently. It was determined that a real space k-point density of 0.02 Å−3 and a cut-off energy of 500 eV would provide accurate results, within 10−3 eV, and were kept consistent to calculate formation enthalpies and lattice parameters in all alloyed structures. The Methfessel and Paxton For the calculations of the density of states (DOS) and elastic constants the cut-off energy was increased to 650 eV and k-point density decreased 0.01 Å−3. The tetrahedron smearing method with Blöchl corrections To calculate the substitution energies of the elements into the Mn6Ni16Si7 G-phase its stoichiometric, 116 atom, cubic structure was energy minimised and used as a reference structure. Fixed volume and dimension calculations were then performed with a single substitution of the impurity element on the Wycoff sites 4a (Si), 24d (Si), 32f (Ni) and 24e (Mn). Using Cu onto the Mn site as an example, the substitution energies were calculated according to the following reaction:(Cu1Fe127)BCC+(Mn24Ni64Si28)G−phase→(Mn1Fe127)BCC+[(Cu0.04Mn0.96)24Ni64Si28]G−phaseTo simulate concentrated Fe substitution (Fe0.58Mn0.42)6Ni16Si7, Mn6(Fe0.22Ni0.78)16Si7 and Mn6Ni16(Fe0.5Si0.5)7 G-phase (116 atoms) and BCC structures (128 atoms) were simulated at constant pressure. The site occupancies of the BCC supercell were kept consistent with the G-phase i.e. one sublattice was occupied by Ni and the other by Mn and Si as done in a previous study The lattice misfit parameter, δ, was calculated by the equation:where aG-phase and aFe are the lattice parameters of the G-phase and Fe (taken to be 4 × 2.83 Å of pure BCC Fe from DFT in this study), respectively.CALculation of PHase Diagrams (CALPHAD) as implemented within Thermocalc was used to calculate the equilibrium property diagrams of Fe-Cr-Ni-Si-Mn-Zr alloys. The “TCFE7” database was used.Three alloy ingots were prepared by arc-melting using commercially-pure metals (99.99% in purity), and then drop cast into a copper mould. The following compositions were chosen: FebalCr9N4iSi2(Mn0.6Zr0.4)1.1, FebalCr20N3iSi3Mn1, and FebalN7iSi2Mn1, where the foremost composition was predicted from the theoretical component of this study, and the latter two were chosen to remove the influence of Cr and Zr and compare to a previous study by Yang et al. . These cast ingots were homogenised at 1525 K for 30 min in evacuated quartz tubes, quenched into ice water and then cut into small pieces for further ageing heat treatment at 773 K for 1–24 h in air, and air-cooled on a ceramic block.A series of aged specimens were then inlaid, polished and tested in a Shimadzu micro-hardness tester under a 4.9 N load and 15 s holding time. Each specimen was tested six times and average values of the measured data were taken. The 24 h aged samples were further analysed in a JEM-2100 (HC) transmission electron microscope (TEM) operating at 200 kV. TEM specimens were initially ground to a thickness of ~50 µm and were then electro-polished at room temperatures and at 28 V using jet-polish techniques in an electrolyte containing 6% HClO4, 12% CH3COOH and 12% ethylene glycol in methanol.The formation enthalpies of the various Ni containing G-phase compositions previously observed, or hypothesised to form, were calculated and compared to past literature, see . The lattice parameters of the simulated structures are in good agreement with past experimental findings. Discrepancies are attributed to the approximation of the exchange-correlation functional and omission of thermal effects i.e. lattice parameters are calculated at 0 in the current study and often measured at room temperature experimentally. Mn6Ni16Si7 has a relatively unfavourable (−12.39 eV/formula unit) formation enthalpy compared to the other combinations. Refractory elements Hf, Zr together with Ti were found to be the most thermodynamically favourable G-phase compositions to form in the X6Ni16Si7 ternary systems, all with enthalpies less than −20 eV/formula unit, in agreement with past findings Recently, it has been proposed that a smaller magnitude of lattice misfit [δ, ()], of a coherent precipitate to the surrounding matrix, leads to a lower nucleation energy barrier for precipitation and maintenance of ductility after precipitation hardening . Therefore we continue our analysis assuming that dislocations can move from the matrix through the precipitate and δ could influence the ductility of the alloy. It follows that the Nb6Ni16Si7 and Hf6Ni16Si7 precipitates are predicted to have the lowest misfits with a surrounding BCC Fe matrix at 0 K. The misfit predicted for Mn6Ni16Si7 was within the range recorded in duplex steels (−5.13% Here it is predicted that for all X6Ni16Si7 compositions studied, except where X=Zr and Hf, there will be a Tδ=0% value between 581 – 843 K. In theory, one could tailor the composition of the G-phase or choose a suitable ageing temperature, insofar as they both coincide, to promote nucleation. It could also be postulated that the greater the misfit, at operational temperature, the greater hardening will be present at that temperature. However, composition specific thermal expansion studies will need to be conducted for better accuracy in this prediction.In past literature, there are fewer reports of G-phase precipitates that contain Fe instead of Ni; where this has been reported, the Fe containing G-phase was considered to be metastable. reports the outputs obtained from G-phase structures identical to but with Fe replacing Ni. To the authors’ knowledge, no prior ab initio calculated data on these systems exist and, as expected, they all exhibit less favourable formation enthalpies compared to Ni-based G-phases. Tδ=0% values were not calculated for these compositions due to their predicted metastability.Most chemical composition analyses on G-phase precipitates in steels include a significant Fe content (10 – 40 at.%) . Therefore, it is likely that there is a solubility limit of Fe into the X6Ni16Si7 G-phase. In the Fex(Mn6Ni16Si7)100-x system it is predicted that this limit is x = ~18 at.% it is predicted that, in the majority of cases (with the exceptions of Ti, V and Zr), when Fe replaces Ni in the G-phase, there is an increase in the magnitude of δ. Therefore, it is perhaps favourable for an enrichment of Ni and depletion of Fe, in the G-phase, for greater ductility to be achieved in an Fe alloy.To identify the cause of difference in stabilities between Ni vs Fe containing G-phase compositions, the electronic structures are examined by plotting the l-decomposed projected density of states (PDOS) of four compositions W6(Ni/Fe)16Si7 and Zr6(Ni/Fe)16Si7, which represent the least and most stable non-magnetic structures, respectively, see . The total density of states (TDOS) of all compositions are plotted in and complete datasets pertaining to all l-decomposed X6(Ni/Fe)16Si7 structures can be found in ref shows the relationship between the occupancy fraction of the X-d orbitals, in the upper and lower spin channels below EF vs the formation enthalpy. The more stable G-phase compositions have lower occupancies of their d orbitals. This relationship arises due to the occupancy of the higher energy states, available in these species, leading to anti-bonding behaviour, therefore, reduced occupancy of these orbitals is energetically preferred. This is analogous to observations in previous works on crystal stability of intermetallics . In light of these results, the trend in formation enthalpies can be loosely correlated to the number of electrons that occupy the outermost d orbital of the pure X element i.e. Hf(2)<Zr(2)<Ti(2)<Ta(3)<Nb(4)<V(3)<Mo(5)<W(4) <Mn(5)<Cr(5).For the first time, a prediction of the elastic properties of the Ni containing G-phase structures is made from DFT, see . Pure BCC Fe is included for comparison. It is difficult to generalise the elastic properties of the G-phase structure as the results show that the bulk (B), shear (E), and Young's (G) moduli vary by a magnitude of 140.1, 37.0 and 80.3 GPa, respectively, between the different compositions (see ). Interestingly, the Mn6Ni16Si7 composition's three elastic moduli deviate the least from that of BCC Fe. It is inferred that the similarity in elastic moduli of Mn6Ni16Si7 and BCC Fe may lead to reduced modulus hardening, load partitioning, debonding, and increased dislocation mobility in a ferritic steel. This could also shed some light onto the disagreement between studies in the literature that conclude that the hardening of duplex stainless steels during low-temperature annealing (~623 - 823 K) is due to either spinodal decomposition in the ferrite plus G-phase precipitation the wrought condition (no spinodal decomposition or G-phase in ferrite), aged >10,000 h (spinodal decomposition and G-phase in ferrite), and (3) post ageing, 1 h anneal at 823 K (no spinodal decomposition but G-phase in ferrite); the hardness in the 3rd step was measured to be equal to that of the first and it was therefore concluded that it was not the G-phase that contributes to hardening. However, the former two studies measured hardness with spinodal decomposition and G-phase precipitation combined, whereas the latter study removed the spinodal decomposition and only observed G-phase precipitates in the matrix. Therefore, it is possible that the G-phase precipitates located at the α and α' phase boundaries increase the hardening caused by the spinodal decomposition but do not significantly contribute to hardening when precipitating in the ferrite matrix; a hypothesis that the DFT results within the current study supports. The caveat to this is that the composition and/or precipitate sizes differ significantly between both studies, which is possible due to the lack of data pertaining to these quantities.In five of the structures (denoted by * in ), the energy landscape surrounding the atomic positions of the X component were too shallow to calculate the displacement response internal strain tensor. Therefore, the ionic contributions to the elastic constants were not included. These are estimated to be one order of magnitude smaller than the frozen-ion elastic tensor and negative. For a full breakdown of the contributions refer to ref. The G-phase has five unique lattice sites: 1 Mn, 2 Ni and 2 Si, here labelled Mn, Ni1, Ni2, Si1 and Si2, see . In this section, the substitution energies of 14 elements and a vacancy, when substituted onto these sites in the 116 atom cubic G-phase unit cell (corresponding to concentrations of 0.86 at.%), are presented.Instead of the typical calculation of substitution energy, where the reference structure of the species substituting is taken as their ground state pure form, here the reference structure is taken as their solution in BCC Fe and a negative substitution energy indicates an exothermic reaction. A comparison between the results using the conventional method and current method is shown in shows the results for 14 different species, and a vacancy onto the five unique lattice sites of the G-phase. Some of the X metals e.g. Hf, Zr and Ti, which were predicted to form low energy (more stable) G-phases, have a large energetic preference for the Mn site (Zr>Hf>Nb>Ti>Ta) and it is expected that the inclusion of these species in the melt will significantly promote G-phase formation. Interestingly, of the X metals that form low energy G-phases, Mo and V do not display this behaviour in substitution; in the case of the latter element, this is due to the stability of V in the BCC Fe lattice evidenced by the large solubility in their binary phase diagram Cu is predicted to have a slight preference for substitution onto the Mn site, and the substitution energy onto both the Ni sites is also very small. The clustering of Cu, Mn, Ni, and Si is a well-known degradation phenomenon in RPV steels Another interesting finding is the preference for P to substitute onto the Si lattice sites. Again, another species known to cluster with Mn, Ni and Si in RPV steels, and segregate to grain boundaries Vacancies show a unique behaviour in substitution preference. In the G-phase structure they are much more stable than in BCC Fe when situated on the Si1>Si2>Mn lattice sites. These results suggest that the G-phase could act as a sink for vacancies, and offers an explanation for the observed reduction in Si content from its stoichiometric composition in chemical analyses from past experimental studies Fe and Cr are two species that feature heavily in G-phase chemical analyses, yet both are predicted to be unfavourable when substituted into the G-phase from a BCC Fe matrix. This result supports the observation of a decrease in Fe and Cr content in G-phase precipitates with ageing time in past studies . However, as previously stated, the differing chemical environments due to the alloy composition in stainless steels i.e. high availability of Fe and Cr and deficiency of Mn, Ni and Si, it is likely that an equilibrium concentration of Fe and Cr could exist in the G-phase structure.Unexpectedly, the most favourable site for Fe to occupy is the Mn site. It has long been assumed that Fe will occupy the Ni site, and most recently theorised that it will occupy the Si lattice site To determine the effect of large concentrations (~12 at.%) of Fe on the stability of Mn-Ni-Si G-phase and BCC structure, 14 Fe atoms were substituted for each species and their site occupations were randomised ten times to obtain a sample of the effect of disorder on a G-phase lattice and BCC packed arrangement, respectively. The concentration of Fe was chosen as it has previously been predicted, to be at the threshold at which point the G-phase structure and BCC packing are equal in formation enthalpy shows the formation energy and lattice parameter of each G-phase and BCC packed structures simulated with an Fe concentration of ~12 at.%. In the G-phase, a trend in site preference, similar to the single Fe atom substitutions, is found i.e. Mn>Ni>Si in favourability. In the BCC packed system there is no clear favourability for Fe to occupy Ni or Mn sites, however, replacement of the Si site remains relatively unfavourable. Interestingly, when Fe replaces Ni or Si in the BCC packed structures, the lattice parameters deviate the least from a pure BCC matrix (dashed vertical line). From this result we may deduce that the maintenance of stoichiometric Mn will minimise the misfit between a BCC packed cluster and the surrounding Fe matrix. Conversely, the replacement of Mn with Fe will lead to a significantly smaller volume, which may also be associated with an energy penalty for small clusters in an Fe matrix. This may explain recent observations by Almirall et al. of the proportionality between number density of “Mn-Ni-Si precipitates” and Mn contents of the base steel Additional simulations were carried out on compositions more similar to cluster/G-phase compositions experimentally observed in low alloy and stainless steels, i.e. reduced Si content . Two situations were considered: 14 Fe occupying the Mn site and the displaced Mn atoms occupying the Si sites (left open triangles), and Ni site with the displaced Ni atoms again occupying the Si sites (right open triangles). The results from these additional simulations show that, when the compositions are kept consistent, the trend of site preference of Fe is changed. Indeed, it is possible that Fe will preferentially occupy the Si lattice site due to the chemical availability of species offering an additional explanation to the findings of Matsukawa et al. . Therefore, it is predicted that the initial steel composition and ratio of solute species will affect the site preference of Fe and overall composition of the G-phase and solute clusters in steels. The latter of which has also recently been concluded experimentally The promotion of G-phase precipitation is not historically designed for in a steel. Due to the context of past investigations, long ageing times are typically performed (2500 – 200,000 h where investigations into the promotion of G-phase, for strengthening of an Fe alloy, is documented. In this context, reducing the required ageing time is of great interest. Another desirable property for a precipitate hardened alloy is maintenance in ductility. To optimise an Fe alloy composition to for these two traits we employed the following design principles:Addition of Mn to promote Mn6Ni16Si7 formation, predicted to be similar in elastic properties to an α-Fe matrix, to try to preserve ductility.Addition of Zr to promote (Mn,Zr)6Ni16Si7 to expedite G-phase nucleation by decreasing enthalpy of formation, increasing precipitation temperature, and offsetting negative δ value between G-phase and α-Fe matrix at room temperature.Other design principles include: addition of Cr for oxide scale, omission of other embrittling intermetallic phases other than G-phase, limitation of Si to 6.7 at.% to avoid potential loss of workability, and annealing temperature ≥700 K to expedite kinetics.In this study, CALPHAD was used to explore the phase space of an Fe alloy containing Cr, Ni, Si, Mn and Zr, by varying contents in step sizes of 1.0 at.% for the first three elements, and 0.1 at% for MnZr, in the FebalCr8Ni3Si3(Mn0.5Zr0.5)1.2 system. This was done to predict a suitable composition and aging temperature, to achieve the largest phase fraction of G-phase and avoid other intermetallic phases, for the proceeding experimental section of this study. The property diagram of the optimised alloy is presented in . At equilibrium, it is predicted that a dual phase BCC Fe and G-phase could exist between 700 and 800 . This is labelled as the “region of interest”. Below 700 additional phases: σ-FeCr, a second BCC Fe phase, and Cr3Si are also predicted to form. Above 800 K, γ-Fe FCC phase, and Fe2Zr Laves phase are predicted to form.The effect of varying each elemental species in the mixture on the size of this region of interest is graphically represented in . As Cr is added to the mixture, it is predicted that there will be a significant phase fraction of σ-FeCr that forms at ~500 K, which shifts to higher temperatures until 13 at.% at which point it completely overlaps with the dual phase forming region. The addition of Si past 6.7 at.% (3.5 wt.%) has been shown to greatly reduce workability of a steel From the previous analysis of lattice misfit (δ) in the current study, it can be postulated that an equal ratio of Mn and Zr in the G-phase will lead to a minimisation of δ. The fraction of Mn in a hypothetical [Mnx'Zr(1-x')]6Ni16Si7 precipitate, in the optimised alloy FebalCr9Ni4Si4[MnxZr(1-x)]1.2 at.%, where x is the fraction Mn contributing to the 1.2 at.% total of Mn+Zr included in the initial mixture and x' is the ratio of Mn:Zr predicted in the G-phase precipitate by Thermocalc, see . It is predicted that there will be a depletion of Mn and enrichment of Zr in the G-phase for higher temperatures. When included in a 1:1 ratio (0.6:0.6), there is no temperature at which it is predicted that an equal ratio will be achieved in the G-phase. However, when increasing the Mn:Zr ratio to 3:2 (0.72:0.48) an equal concentration of both species is predicted to occur at 645 K. A higher portion of Mn is also retained at higher temperatures compared to the other tested ratios. When the Mn:Zr ratio is increased further to 4:1 (0.96:0.24) the dual phase region is greatly reduced to 636 K due to FCC phase formation.From the results within this study, it is possible to conclude that concentrations of 4 at.% Ni, 5 at.% Si, 0 at.% Cr and 1.2 at.% (Mn, Zr) yield the highest upper bounds of the dual phase forming regions. However, in the interest of including a Cr content high enough for reasonable oxidation/corrosion resistance behaviour (~9 at.% minimum The casting and heat treatments of the predicted composition, Fe81.4Cr9Ni4Si2[Mn0.6Zr0.4]1.1 (wt.%), revealed remarkable promise. displays the micro-hardness with ageing time (at 773 K) of the predicted composition and compares to two other compositions: FebalNi7Si2Mn1 and FeBalCr20Ni3Si3Mn1 (wt.%).Hardening of ~60 HV occurs extremely quickly (~1 h) for the predicted composition, whereas hardening does not occur for the other alloys within the 24 h tested. presents the TEM analysis of the predicted composition after 24 h of ageing. Lath martensite with a high dislocation density is observed, which is due to the initial quenching of the alloy from high temperature (1475 K) austenite. Fine precipitates, ~1 nm in diameter, were observed dispersed within the martensitic phase. The selected area electron diffraction pattern of this region revealed a double diffraction pattern of a G-phase structure with a cube-on-cube orientation with a BCC phase. No such precipitation was observed in the other two compositions, see From these results it is reasonable to deduce that the addition of Zr to the composition expedited G-phase precipitation. As far as the authors are aware, the shortest ageing time before that showed a Mn6Ni16Si7 G-phase precipitate is 500 h at 750 K The lattice parameter of the BCC phase formed in the predicted composition was measured to be 0.286 nm. Due to the small scale of the precipitates an accurate lattice parameter could not be obtained, however, from the observed cube-on-cube orientation we can assume it to be close to that of the matrix, which would equate to a G-phase lattice parameter of ~1.144 nm. Coherency and low interfacial energy between the two phases could explain the lack of merging/coarsening of precipitates but it is also possible that there exists a strain energy suggested by the streaking of the diffraction spots in (c), which would also supress coarsening.A combination of theory and experiment were used to design and test a new Fe alloy composition [FebalCr9Ni4Si2(Mn0.6Zr0.4)1.2 at.%] that expedites the formation of the G-phase, as a strengthening phase, with coherency with to the BCC Fe matrix, and avoid Laves phase precipitation. The following conclusions can be drawn from this work:The combination of Mn and Zr as a shared X component in the X6Ni16Si7 G-phase precipitate leads to large reduction in precipitation time (≤ 24 h) and coherency within a BCC Fe matrix, with an associated hardening of ~60 HV that occurs after ~1 h at 773 K.In general, G-phase formation in steel is best promoted by including Ni, Si, and at least one other element of species Hf, Zr, Ti, Ta, Nb, V, Mo, W, Mn, Cr (in order of decreasing energetic favourability). The differing magnitudes of energies of formation of these species is proportional to the occupancy of the d-band when in the G-phase structure.The Mn6Ni16Si7 G-phase is predicted to have the most similar elastic properties to BCC Fe and therefore minimise the G-phase nucleation barrier, modulus hardening, load partitioning, debonding, and increase dislocation mobility in a BCC Fe matrix. A mixture of Mn:Zr in 3:2 ratio should be included to allow for an increased ageing temperature to expediate precipitation.There is a high energetic preference for vacancies to occupy the G-phase Si lattice sites displacing Si to the BCC Fe phase. Therefore, the G-phase will act as a vacancy sink and reduction of Si content from stoichiometric composition will be observed.The concentration of species available in the alloy mixture is predicted to affect the solubility of Fe into the G-phase and stability of the G-phase relative to a concentrated BCC packed structure. When there is excess Si available, Fe will preferentially substitute onto the Mn or Ni sites. However, when deficient in Si (half stoichiometric G-phase), the preference for Fe substitution changes to the Si sites, which decreases the favourability of a G-phase over a BCC structure. If the suppression of the G-phase is desired, it is recommended that Si is kept as low as possible in the alloy mixture.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 material associated with this article can be found, in the online version, at When comparing the TDOS of G-phases with the same X component, distinct differences in shapes are seen when X is Mn, Cr, Mo and V. This is due to the magnetic moments of each X component, predicted by DFT, observed as an anisotropy of the upper and lower spin channels of the TDOS, which is not seen in their non-magnetic counterparts. The magnetic moments were calculated are as follows:3.5 µB for Mn, in Mn6Ni16Si7, which is within the range measured by neutron diffraction (1.7 µB1.0 µB for V in V6Fe16Si7, when in the presence of Fe;It should be noted that the non-magnetic Mn6Ni16Si7 structure was also simulated and found to have a 2.81 eV/unit less favourable formation enthalpy and lattice parameter 0.19 Å smaller than its magnetic counterpart.J. Mater. Sci. Technol., 2011, 27(4), 377-381. Effect of Silver Content on Microstructure and Properties of Brass/steel Induction Brazing Joint Using Ag-Cu-Zn-Sn Filler Metal J. Cao 1,2)†, L.X. Zhang 1) , H.Q. Wang 1) ,L.Z.Wu 2) and J.C. Feng 1) 1) State Key Lab of Advanced Welding Production Technology, Harbin Institute of Technology, Harbin 150001, China 2) Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150001, China [Manuscript received May 5, 2009, in revised form December 19, 2009] The induction brazing of brass to steel using Ag-Cu-Zn-Sn filler metal was investigated in this study. The influence of Ag content on the microstructure and properties were analyzed by means of optical microscopy, scanning electron microscopy and electron probe microanalysis. Defect free joint was achieved using Ag- Cu-Zn-Sn filler metal. The microstructure of the joint was mainly composed of Ag-based solid solution and Cu-based solid solution. The increase of Ag content and the cooling rate both led to the increase of the needle like eutectic structure. The tensile strength decreased with the increase of Ag content. The tensile strength at room temperature using Ag25CuZnSn filler metal reached 445 MPa. All fractures using Ag-Cu-Zn-Sn filler metal presented ductile characteristic. KEY WORDS: Induction brazing; Brass; Steel; Microstructure; Tensile strength 1. Introduction The joining technique of copper alloy to steel has been widely applied in nuclear, aerospace and indus- try fields [1–3] . The conventional fusion welding of these materials usually leads to the irregularity in- terface and welding deficiency between copper alloy and steel [4,5] . The microstructure evolution and so- lidification cracking susceptibility of Cu deposits on steel has been systematically investigated [6–8] .The hot isostatic pressing and explosive bonding joint of copper alloy to steel can reach high joining strength, but the shape requirement of the based metal limits the application of these methods [9–13] . No microstruc- tural deficiency joint can be obtained using diffusion bonding method [14–17] . However, the vacuum equip- ment is required and the deformation of the substrate is usually large. Especially, brass cannot be intro- duced in a vacuum condition due to the inclusion of evaporable Zn element. Thus, induction brazing in air was the optimal joining method to achieve regular †Corresponding author. Ph.D.; Tel.: +86 451 86418882; Fax: +86 451 86418146; E-mail address: cao [email protected] (J. Cao). interface, accurate dimension and low cost brass/steel joint. The selection of filler metal was the foundational step for induction brazing of brass to steel [18,19] .The Ag-Cu based filler metal has been widely applied for joining steel to other materials [20] . The low melting point of brass leads to the selection of filler metal with low melting point. The Ag-Cu-Zn-Sn filler metal, which served as the replacement of poisonous Ag-Cu- Zn-Cd filler metal, was selected in this study. Al- though the Ag-Cu-Zn-Sn filler metal has been devel- oped for a long time, few investigations on the mi- crostructure and joining properties have been system- atically carried out. Accordingly, the aim of this work was to investigate induction brazing of brass to steel using Ag-Cu-Zn-Sn filler metal. In particular, the ef- fect of Ag content on the interfacial microstructure and joining strength of brass/steel joint was investi- gated. 2. Experimental The substrates were commercial H62 brass and 10# steel. The metallographic observation and ten- 378 J. Cao et al.: J. Mater. Sci. Technol., 2011, 27(4), 377–381 Table 1 The composition and brazing temperature of applied filler metal (wt%) Type Ag Cu Zn Sn Cd Brazing Temp./ â—¦ C Ag25CuZnSn 25.7 40.6 Bal. 2.0 / 790 Ag30CuZnSn 29.9 35.7 Bal. 1.9 / 780 Ag45CuZnSn 44.3 27.2 Bal. 2.2 / 730 AgCuZnCd 35.1 26.2 Bal. / 21 750 Fig. 1 Back-scattered electron images of the joint mi- crostructure using Ag25CuZnSn filler metal: (a) general microstructure, (b) in the steel side, (c) in the brass side sile test specimens were machined to φ10.0 mm× 1.5 mm and φ10.0 mm × 20 mm, respectively. All joined surfaces were polished by SiC papers up to grit 600 and ultrasonically cleaned by acetone prior to in- duction brazing. The joining process was carried out in an induction heating apparatus with a varied heat- ing rate between 50 and 100 K/s. Induction brazing is an effective joining method with high heating velocity and the assembly gap was kept between 50 to 100 µm. The holding time was controlled no longer than 10 s in order to avoid the softening of Cu substrate. The composition and brazing temperature of filler metal are listed in Table 1. The filler metal was pro- duced by mechanical alloying method. Powder mix- ture of Ag (200 mesh, 99%), Cu (300 mesh, 99%), Zn (300 mesh, 99%) and Sn (200 mesh, 99%) was used as filler metal in this study. The powder filler metal was dry-mixed thoroughly in a tumbler ball mill for 24 h to realize mechanical alloying. The flux was the J102 type, which mainly consists of natrium biboricum and boracic acid. After joining process, the microstructure and phase composition of induction brazing joint were characterized employing optical microscopy (OM) and scanning electron microscopy (SEM) with electron probe X-ray microanalysis (EPMA). The heat treat- ment of the joint was employed to identify the charac- teristic of the needle-like structure. The parameters of heat treatment are: the treating temperature 823 K with a holding time of 30 min and a cooling rate of 5 K/min, respectively. Tensile tests were performed at a constant loading rate of 1 mm/min by a universal testing machine (Instron 1186) to assess the joining quality. 3. Results and Discussion The microstructure of joint was first analyzed due to its direct effect on the joining quality. The typ- ical microstructure of brass/steel joint using induc- tion brazing method is shown in Fig. 1. From this general view in Fig. 1(a), it can be concluded that the successful joining of brass to steel was achieved using Ag25CuZnSn filler metal. The microstructure was homogeneous and no defects were observed in the joint. The total thickness of brazing seam was about 75 µm. Figure 1(b) presents the interfacial mi- crostructure in the steel side. The joint consists of a grey phase (named as A region) and a white planular phase (named as B region). According to the results of the quantitative analysis shown in Table 2, it was Table 2 Quantitative chemical analyses of the dif- ferent elements of the joint (at.%) Position Composition Possible phase Ag Cu Zn Sn A 48.0 20.5 29.1 2.4 Ag(s.s) B 8.2 56.2 33.8 1.8 Cu(s.s) indicated that A and B regions were composed of Cu-based solid solution(s.s) and Ag-based solid so- lution(s.s), respectively. The similar results were reported by Chakravarty and Gupta when the in- termetallics formation between Fe and Ag-Cu-Sn filler metal was investigated [19] . A thin white layer, which was also Ag-based solid solution, was observed J. Cao et al.: J. Mater. Sci. Technol., 2011, 27(4), 377–381 379 Fig. 2 Microstructure of the brass/steel joint using Ag30CuZnSn filler metal at the interface between steel and filler metal. When Cu-Zn alloy was deposited on the solid state steel, the reaction layer was only 5–30 nm at the interface [4] . Therefore, there was no obvious reaction layer ob- served at the interface because of the reaction layer was too thin. The interfacial microstructure in the brass side is shown in Fig. 1(c). The interface between filler metal and brass is not clear, which indicated that the interfacial joining is perfect. The interdiffusion of elements occurred at the interface due to the concen- tration gradient. But the interdiffusion layer is not obvious. The addition of Sn resulted in the low melt- ing point and good flow ability of filler metal. The evaluation of the flow ability was based on the height of fillet and the observation of the gap filling process in the induction brazing. In order to investigate the effect of Ag content in Ag-Cu-Zn-Sn filler metal on the joining qual- ity, the filler metal with higher Ag content was ap- plied. The microstructure of the brass/steel joint us- ing Ag30CuZnSn filler metal is shown in Fig. 2. The microstructure was similar to that using Ag25CuZnSn filler metal. The defect free joint was also obtained with this filler metal. The total thickness of brazing seam is about 25 µm. It was noted that small amounts of needle-like structures appeared in the brazing seam. Figure 3 represents the general microstructure of brass/steel joint with Ag45CuZnSn filler metal. The similar microstructure was achieved and defect free joints were produced. The interface between filler metal and steel became irregular, which may be gener- ated by Ag and Cu diffusion along the grain boundary in the steel, as demonstrated [18] . The microstructure was characterized by the distribution of large amounts of white needle-like phase. The magnification of the needle-like phase is shown in Fig. 3(b). The needle- like structures formed in the Cu-based solid solution. EDS analysis was performed to identify the composi- tion of the needle-like phase. The needle-like phases consisted of Ag (24.5 at.%), Cu (33.8 at.%) , Zn (38.8 at.%) and some amounts of Sn (2.9 at.%). The com- position between the needle-like phase was composed of Ag (7.9 at.%), Cu (48.4 at.%) , Zn (40.9 at.%) and some amounts of Sn (3.0 at.%). According to the Ag- Fig. 3 Microstructure of the brass/steel joint using Ag45CuZnSn filler metal, (a) general view (b) magnification of needle like phase Fig. 4 Tensile strength of brass/steel joint using induc- tion brazing method Cu-Zn ternary phase diagram, it was indicated that the needle-like phase was the α 1 +β eutectic structure. The tensile strength of brass/steel brazing joint us- ing Ag-Cu-Zn-Sn filler metal is shown in Fig. 4. The test was performed at room temperature with a con- stant loading rate of 1 mm/min. The Ag-Cu-Zn-Cd filler metal was applied for comparison. From the re- sults, it was found that the tensile strength decreased with the increase of the Ag content for Ag-Cu-Zn- Sn filler metal. The Ag45CuZnSn filler metal pre- sented the similar tensile strength to that of the Ag- Cu-Zn-Cd filler metal. All tensile strengths exceeded 300 MPa and the tensile strength of Ag25CuZnSn reached 445 MPa. This result indicated that the ap- plication of Ag-Cu-Zn-Sn filler metal as a replacement of Ag-Cu-Zn-Cd filler metal is reasonable and reliable. The heat process had a strong influence on the 380 J. Cao et al.: J. Mater. Sci. Technol., 2011, 27(4), 377–381 Fig. 5 Distribution of the microhardness in the brass/ steel joint Fig. 6 Morphology of the fracture in the brass/steel joint: (a) Ag25CuZnSn, (b) Ag30CuZnSn, (c) Ag45CuZnSn properties of the substrate. Especially for brass, the grain size increased greatly and the soften behavior happened after heat cycle. However, serious soften- ing was unacceptable for most applications. The ef- fect of the induction heat cycle on the hardness of the substrate is shown in Fig. 5. Although the hard- ness of the substrate decreased in a certain extent, the brass still kept in semi-hardening range and fitted most of requirements. There is no denying that induc- tion brazing is beneficial for keeping the properties of the substrate. The microstructure analysis was performed to in- vestigate the fracture mechanism. The morphology of fracture using Ag-Cu-Zn-Sn filler metal is shown in Fig. 6. All fracture of the brass/steel joints pre- sented the ductile characteristic. The EDS analy- sis was applied to assist the fracture analysis. The crack in the joint using Ag25CuZnSn propagates in the brass substrate and the fracture was the typical ductile characteristic with obvious dimples. When Ag30CuZnSn filler metal was applied, the fracture was similar to that using Ag25CuZnSn. The frac- ture with Ag30CuZnSn filler metal propagated in the brazing seam. However, the fracture of the joint using Ag45CuZnSn filler metal is different from other struc- tures. Generally, the fracture still belongs to ductile characteristic with some dimples. It was noted that the needle-like structure was observed on the fracture surface. From the result of tensile test, the strength of the joint with Ag45CuZnSn filler metal was lower than that of low Ag-content filler metal. The formation of the needle-like structure affects the joining quality greatly. The investigation on the formation mechanism of this structure is necessary and meaningful. Both precipitating in the cooling process and eutectic phase solidification could result in the formation of this structure. The post joining heat treatment and quenching test were carried out to analyze the mechanism. Ag45CuZnSn filler metal was selected to evaluate the microstructure character- istic. The microstructure of joint using post joining heat treatment is shown in Fig. 7(a). The amount of needle-like structure decreased greatly, which in- dicated that the needle like structure was not pre- cipitated phase. Figure 7(b) presents the microstruc- ture of brass/steel joint using quenching test. Large amounts of needle-like structure was observed in the joint. It was confirmed that the needle-like structure was produced by the ternary eutectic phase solidifica- tion. The high cooling speed led to the formation of the needle-like structure. The other factor to generate the needle like phase was the increase of Ag content. The increase of Ag content in the filler metal resulted in the compostion point close to the eutectic point and the increase of ternary eutectic content. Thus the quantity of needle-like structure increased cor- respondingly. The properties of eutectic phase were worse than that of solid solution. Thus, the way to increase induction brazing quality was to control the quantity of needle-like structure. The tensile test at a higher temperature was car- ried out systematically to evaluate the joining quality. The testing results are shown in Fig. 8. The test was performed at 300 â—¦ C with a constant loading rate of 1 mm/min. It was noted that all tensiles strength distributed above 230 MPa. The tensile strengths for Ag25CuZnSn, Ag30CuZnSn and Ag45CuZnSn filler J. Cao et al.: J. Mater. Sci. Technol., 2011, 27(4), 377–381 381 Fig. 7 Effect of cooling rate on the needle like structure: (a) post joining heat treatment, (b) quenching test Fig. 8 Tensile strength of brass/steel joint in high tem- perature condition (300 â—¦ C) metal at 300 â—¦ C were 258.5, 245.8 and 226 MPa, re- spectively. It was noted that part of the fracture propagated in the brass substrate. This result indi- cated that the interfacial joining was excellent and the brass/steel joint could be steadily applied at a high temperature condition no higher than 300 â—¦ C. 4. Conclusions (1) The induction brazing of brass to steel was successfully achieved using Ag-Cu-Zn-Sn filler metal. (2) The typical microstructure consisted of white Ag(s.s) structure and grey Cu(s.s) structure. The needle like phase, which was confirmed to be α 1 + β eutectic phase, was observed when Ag30CuZnSn and Ag45CuZnSn filler metals were applied. The quantity of needle like structure increased with the increase of the Ag content and cooling rate. (3) All tensile strengths exceeded 300 MPa and the strength decreases with the increase of the Ag content. It was noted that all fractures were of ductile charac- teristic with obvious dimples. The softening behavior of substrates happened and the hardness of brass sub- strate distributed in the semi-hardening range. Acknowledgements The research is supported by the National Natural Sci- ence Foundation of China (No. 50805038) and Program for New Century Excellent Talents in University. We also give our acknowledgement to the Research Fund of Provin- cial Key Lab of Advanced Welding Technology in Jiangsu University of Science and Technology for financial support. REFERENCES [1 ] A.F. Rowcliffe, S.J. Zinkle, J.F. Stubbins, D.J. Ed- wards and D.J. Alexander: J. Nucl. Mater., 1998, 258-263, 183. [2 ] K. Ioki, F. Elio and V. Barabash: Fusion Eng. Des., 2007, 82, 1771. [3 ] G. LeMarois, C. Dellis, J.M. Gentzbittel and F. Moret: J. Nucl. Mater., 1996, 233-237, 927. [4 ] H.Z. Wang, K.H. Wang, R.K. Zheng, K.S. Prasad and S.P. Ringer: Mater. Charact., 2008, 59, 542. [5 ] I. Magnabosco, P. Ferro, F. Bonollo and L. Arnberg: Mater. Sci. Eng. A, 2006, 424, 163. [6 ] F.F. Noecker andJ.N. DuPont : J. Mater. Sci., 2007, 42, 510. [7 ] S.X. Lv, Z.W. Xu, H.T. Wang and S.Q. Yang: Sci. Technol. Weld. Join., 2008, 1, 10. [8 ] F.F. Noecker and J.N. DuPont: J. Mater. Sci., 2007, 42, 495. [9 ] K.D. Leedy and J.F. Stubbins: Mater. Sci. Eng., 2001, 297,19. [10] K.D. Leedy and J.F. Stubbins: Mater. Sci. Eng., 2001, 297, 10. [11] A.S. Pokrovsky, S.A. Fabritsiev, A. Peacock, A. Ger- wash and V.R. Barabash: J. Nucl. Mater., 2007, 367- 370, 947. [12] B.V. Krishna , P. Venugopal and K.P. Rao: J. Mater. Sci., 2006, 41, 1175. [13] P. Zhang, Y.H. Du, H.W. Liu, J. Zhang, D.B. Zeng, J.Z. Cui and L.M. Ba: J. Mater. Sci. Technol., 2006, 22, 235. [14] I.S. Batra, G.B. Kale, T.K. Saha, A.K. Ray, J. Derose and J. Krishnan: Mater. Sci. Eng. A, 2004, 369, 119. [15] S. Kundu and S. Chatterjee: Mater. Sci. Technol., 2007, 23, 368. [16] S. Kundu, M. Ghosh, A. Laik, K. Bhanumurthy, G.B. Kale and S. Chatterjee: Mater. Sci. Eng. A, 2005, 407, 154. [17] O. Yilmaz and M. Aksoy: J. Mater. Process. Tech- nol., 2002, 121, 136. [18] F. Molleda, J. Mora, J.R. Molleda, E. Carrillo, E. Mora and B.G. Mellor: Mater. Charact., 2008, 59, 613. [19] I. Chakravarty and S.P. Gupta: Mater. Charact., 2003, 51, 235. [20] M. Singh, T.P. Shpargel and R. Asthana: J. Mater. Sci., 2008, 43, 23. ke structure increased cor- respondingly. The properties of eutectic phase were worse than that of solid solution. Thus, the way to increase induction brazing quality was to control the quantity of needle-like structure. The tensile test at a higher temperature was car- ried out systematically to evaluate the joining quality. The testing results are shown in Fig. 8. The test was performed at 300 â—¦ C with a constant loading rate of 1 mm/min. It was noted that all tensiles strength distributed above 230 MPa. The tensile strengths for Ag25CuZnSn, Ag30CuZnSn and Ag45CuZnSn filler J. Cao et al.: J. Mater. Sci. Technol., 2011, 27(4), 377–381 381 Fig. 7 Effect of cooling rate on the needle like structure: (a) post joining heat treatment, (b) quenching test Fig. 8 Tensile strength of brass/steel joint in high tem- perature condition (300 â—¦ C) metal at 300 â—¦ C were 258.5, 245.8 and 226 MPa, re- spectively. It was noted that part of the fracture propagated in the brass substrate. This result indi- cated that the interfacial joining was excellent and the brass/steel joint could be steadily applied at a high temperature condition no higher than 300 â—¦ C. 4. Conclusions (1) The induction brazing of brass to steel was successfully achieved using Ag-Cu-Zn-Sn filler metal. (2) The typical microstructure consisted of white Ag(s.s) structure and grey Cu(s.s) structure. The needle like phase, which was confirmed to be α 1 + β eutectic phase, was observed when Ag30CuZnSn and Ag45CuZnSn filler metals were applied. The quantity of needle like structure increased with the increase of the Ag content and cooling rate. (3) All tensile strengths exceeded 300 MPa and the strength decreases with the increase of the Ag content. It was noted that all fractures were of ductile charac- teristic with obvious dimples. The softening behavior of substrates happened and the hardness of brass sub- strate distributed in the semi-hardening range. Acknowledgements The research is supported by the National Natural Sci- ence Foundation of China (No. 50805038) and Program for New Century Excellent Talents in University. We also give our acknowledgement to the Research Fund of Provin- cial Key Lab of Advanced Welding Technology in Jiangsu University of Science and Technology for financial support. REFERENCES [1 ] A.F. Rowcliffe, S.J. Zinkle, J.F. Stubbins, D.J. Ed- wards and D.J. Alexander: J. Nucl. Mater., 1998, 258-263, 183. [2 ] K. Ioki, F. Elio and V. Barabash: Fusion Eng. Des., 2007, 82, 1771. [3 ] G. LeMarois, C. Dellis, J.M. Gentzbittel and F. Moret: JEffect of Silver Content on Microstructure and Properties of Brass/steel Induction Brazing Joint Using Ag-Cu-Zn-Sn Filler MetalThe induction brazing of brass to steel using Ag-Cu-Zn-Sn filler metal was investigated in this study. The influence of Ag content on the microstructure and properties were analyzed by means of optical microscopy, scanning electron microscopy and electron probe microanalysis. Defect free joint was achieved using Ag-Cu-Zn-Sn filler metal. The microstructure of the joint was mainly composed of Ag-based solid solution and Cu-based solid solution. The increase of Ag content and the cooling rate both led to the increase of the needle like eutectic structure. The tensile strength decreased with the increase of Ag content. The tensile strength at room temperature using Ag25CuZnSn filler metal reached 445 MPa. All fractures using Ag-Cu-Zn-Sn filler metal presented ductile characteristic.Copyright@ IFAC Manoeuvring and Control of Marine Craft, Aalborg, Denmark, 2000 BOUNDARY CONTROL OF A TRANSVERSELY VIBRATING BEAM VIA LYAPUNOV METHOD Mehrdad P. Fard * , Svein Ivar Sagatun ** * DepaTtment of Engineering CybeT7~etics, Norwegian UniveTsity of Science and technology, N7034 Trondheim-Norway, e-mail: M ehTdad. FaTd@itk. ntnu. no ** NOTSk Hydro ASA, The reseaTch CenteT in BeTgen, NS020 Be-rgen-Norway, e-mail: [email protected] Abstract: This paper discusses the boundary stabilization of a beam in free transversal vibration. We consider a nonlinear partial differential equation (PDE) and based on this model construct two linear control laws to stabilize the system. The first control law guarantees globally convergent of states, while the second control law results into an exponentially stable closed loop. The latter control law is formed by feed backing slope and velocity of beam's boundary displacement. Numerical simulations are performed to test each of the control laws. The outcome of simulations are compared and discussed. The novelty of this article is that globally convergece and exponentially stabilization of transversely vibration in a beam is achieved, via boundary control without resorting to truncation of model. Copyright ©2000 IFAC Keywords: Distributed-parameter systems, Boundary value problem, Vibration. 1. INTRODUCTION This art.icle descrihes st.ahili;r,at.ion of a vihrat.ing beam via boundary control. There are no external forces applied to the beam, hence we will limit this article to treat only free vibrating beam. Vibration occurs in the beam's transversal direction, hence the beam's bending stiffness must be included in our discussion. In this article we have designed two control laws. With their simple structure they ensure both globally convergence and exponentially stabilization of free vibration in a beam. The required measurements are the slope and velocity at the beam's boundary. This research is motivated by the industrial interest in active control of vibrating slender bodies. Examples of practical applications where tensioned beams are exposed to undesirable transversal vibrations are: pretensioned marine risers used in offshore oil and gas exploration, free hanging underwater pipelines, and drill strings for oil and gas drilling. In conventional approaches to the control problem of distributed structures it is common to use an approximation of the distributed model. This model is approximated by one 'with the finite number of modes via spatial discretization. In order to describe the behavior of a flexible system in a satisfactory fashion, it is necessary to model a large number of flexible modes. Hence, it becomes impractical to control all mode. Therefore the control of discrete systems are restricted to a few critical modes. This conversion into the finite dimensional reduced model facilitates application of control theory available for discrete systems. However, due to the ignored high frequencies and uncertainties in design models, caused by truncation of the original model (PDE), the demands of high performance may not be satisfied. Due to the difficulties of implementing distributed sensors and actuators, performance of such a system can be deteriorated due to the effects known as control and observer spillover, (Balas, 1977) and (Meirovitch and Baruk, 1983). It is shown y x Fig. 1. A beam in bending vibration with axial tension in (:tI.Ieirovitch and Baruk, 1983) that in the case if the residual models are not included in the observer dynamics, observation spillover may lead to instability in the residual modes. Boundary control is an efficient method to exclude the effect of both observation and control spillover, since in this method the need for distributed actuators and sensors is excluded. A brief review about boundary control is given in (Fung and Tseng, 1999). Boundary control of flexible systems has been studied by several researchers. a function of both time and space. This occurs frequently in practical situations, for instance pre tensioned marine risers exposed to axial wave and current loads. We will limit our discussion to freely vibrating beams, therefore f(x , t) will be set to zero. In Eq. (1) notations1}tt(x, t) = a"~~~,t), ( ) a"T/(x.t) d ( ) aT/(x,t) d TJxx x, t = ax" an TJx x, t = ax are use . A beam with its dynamic and geometric boundary conditions is shown in Fig. 1. The axial strain-displacement relationship is given by 1 2 P(x, t) = Po + 2EATJx(x, t) (2) where E is the Young's modulus and A is the cross sectional area of the beam. Po is the axial pretension at the boundary x = L. Equation (2) has been used in literature to describe the variation of tension along the length of a string, (Shahruz, 1997) and (Lee, 1957). In this paper we only consider the elongation of the beam due to bending. The variatiou of the elongatioll of the beam due to axial force is assumed small and In (Shahruz and Krishna, 1996), (Shahruz and Narasimha, 1997) and (Shahruz, 1997) it is shown that feedback from the velocity at the boundary of a string can stabilize the vibration in the string. In (Fung et al., 1999), (Fung and Tseng, 1999) the asymptotic and exponential stability of an axially moving string is proven by using a linear and nonlinear state feedback boundary control, respectively. The feedback state include only the displacement, velocity and slope at the right-hand side of the string. This paper is organized as follow: In section 2 the dynamics of a vibrating beam is presented. Section 3 is dedicated to design of control laws. Numerical simulations and discussion of results are presented in section 4. Finally some concluding remarks are made in section 5. 2. EQCATIO?\S OF MOTION The dynamic equation of motion of a modified, nonlinear Euler-Bernoulli beam with axial tension P(x, t) and transversal force density f(x, t) can be written as follows: Ej2 pATJtt(x , t) + 8x2 (EITJxx(x , t)) 8 -8x (P(x, t)TJx(x, t)) -f(x, t) = ° (1) for all (x, t) E (0, L) x [0, (0). In Eq. (1) 71(X. t) represent's the transversal displacement, f(x. t) is the external transverse force distribution on the beam, El is the beam's stiffness or flexural rigidity and pA is the mass per unit length. Both El and pA are assumed to be constant throughout this article. Notice that the axial tension P(x, t) is negligible. The boundary conditions are EITJxx(O, t) = El1}xx(L, t) = ° ° (3a) 1}(0, t) = (3b) 1 3 u(t) = -EITJxxx(L, t) + PoTJx(L, t) + 2EATJx(L, t) (3c) where boundary condition (3a) represents the bending moments at the boundaries. Equation (3c) denotes the shear force at x = L of the beam. u(t) represents the boundary control force applied at x = L. The boundary condition (3c) represents the balance of the shear force and the control force u(t). The initial conditions are TJ(x,O) = gr(x) (4) TJt(x ,O) = g2(X) (5) for all (x, t) E (0, L) x [0, (0). Equations (4) and (5) denote the position and velocity functions respectively. The main goal of this paper is to construct a control law, u(t), which stabilizes the nonlinear equation of the beam (1), (3a-3c) and guarantees that TJ(x, t) --> Oast --> 00 for all x E [0, L]. 2.1 Assumption A.I Po > °for all t 2: 0. This assumption simply means that we are dealing with an axially tensioned beam. In the case where Po < ° we will be dealing with a compressed beam, which is not \\-i.thin the scope of this paper. A.2 The existence of solution for the dynamics given by (1) and (3a-3c) is assumed. It is also assumed that the displacement TJ(x. t) and its time derivative l7t{x, t) belong to a space of function which has the following properties: i) If the potential energy of the system is proven to be bounded 'Vt E [0, x), h O"7)(x,t) . b d d r t en oX" IS oun e lor n = 3,4, 'Vt E [0,(0) and 'Vx E [0. L], and ii) If the kinetic energy of the system is proven to be bounded 'Vt E [0,00), th O"7),(x,t). b d d r 1 2 3 en oX" IS oun e lor n = , . , 'Vt E [0, (0) and 'Vx E [0. L]. 3. DESIGN OF BOUr\DARY CO:.1TROL LAW Our control objective is to design a control law which guarantees stability of a continuous system consisting (1) and (3a-3c) , using the boundary control (3c). The assumptions A.I and A.2 will be used throughout the paper to establish the stability property of the system when designing the control law. 3.1 Globally Convergent Control Law The following Lyapunov functional is introduced : (6) for all t 2: O. p{q, 0) is a metric and defined as PA 2 Po rL rL2 p{q, O) = [ "2 lo l7t{x,t)dx + 2 lo l7x{x,t)dx EA El rL rL ]1 + 8 lo l7;{x , t)dx +"2 lo T}~x{x, t)dx (7) where T}{' , .) satisfies the boundary-value problem (1) and (3a-3c) and qT = ht T}x T}xx]' The metric p{q, 0) establishes a measure of the closeness of the state q from the equilibrium null state in terms of the velocity, curvature and slope of the beam. In addition the metric p corresponds to a measure of the total energy of the system, more specific p{q,O) corresponds to J2E{t), where E{t) is the system's total energy. The first term represents the kinetic energy, the second and third terms represent the potential energy due to the axial force and the last term represents the potential energy due to bending. Theorem I Let the boundary control law u(t) (3c) be u(t) = -KTft{L, t) (8) where K > 0. Then, the functional V(t) along the solution of the system (1), with corresponding boundary conditions, (3a-3c), satisfies . -' 2 V(t) = -/\ Tft(L , t) . (9) Hence, the states of the system,q(t), and Tf(x ,t) are bounded and converge, globally, to zero.• Proof The derivative of (6) with respect to time, after substitution of pAT}tt from Eq. (1) is given by (for the sake of simplicity the argument (x, t) is omitted) V(t) = -lLEIT}xxxxl7tdx + Po lL l7xxT}tdx rL rL3EA 2 + lo -2-l7x T}xxl7t dx + Po lo T}xT}xt dx +pA lL XT}tT}xtdx + E2A lL T}~l7xtdx +EI lL T}xxT}xxtdx. (10) One can conclude from boundary condition (3b) that l7t(O,t) = 0 for all t 2: O. Using this, applying boundary condition (3a) and integrating by parts, we obtain . EA 3 V(t) = -EIT}xxx(L, t)T}t(L, t) + TT}x(L , t)l7t(L, t) +P07Jx(L, t)1lt(L, t). Now substitution for EIT}xxx(L, t) from boundary condition (3c) and using control law (8) yields Eq. (9). By this we can conclude that the states of the system are bounded and remain bounded for all t 2: 0. As a consequence both kinetic and potential energy of the system, given by Eq. (7), are bounded. Due to boundedness of potential energy, we use property i of assumption A.2 to fJ"d x t' conclude that ~is bounded for n = 3,4, 'It E [0,00) and'Vx E [0, L]. Furthermore, by using property ii of assumption A.2 we conclude that o"Z~(,~,t) is bounded for n = 1,2,3, 'Vt E [0,00) and 'Vx E [0,L]. In order to prove global convergence of state, q(t), we need to establish that V(t) is uniformly continuous. To prove this it is sufficient to prove that V(t) is bounded'Vt 2: to. Time derivative of Eq. (9) is given by V(t) = -2KT}t(L, t)T}tt(L, t). Time derivative of boundary condition (3c) after substitution of control law (8) is -KT}tt(L, t) = -EIT}xxxt(L, t) 3 2 +PoT}xt(L, t) + "2 EAT}x(L, t)T}xt(L, t) . (11) It is already established that T}t(L , t) is bounded 'Vt E [0,00). Equation (1) and boundedness of o"g£~,t) can be utilized to show that l7tt{x , t) is bounded 'Vt E [0, x) and 'Vx E (O, L). Using Eq. 0" (x t) (11) and boundedness of 7), , for n = 1 2.3 , ax'l' . we conclude that T}tt{L,t) is bounded 'It E [O,x). Hence, according to Barbttiat's lemma (Barbruat, 1959) , V{t) -> Oast -> 00. Hence, the states of the system converge to zero as t -> 00. ~ow since T}(O, t) = 0, 'Vt E [0, x) and all states converges to zero as t -> 00. It is concluded that T}(x, t) converges to zero as t ----+ 00. Hence, the theorem is proven.• 3.2 ExponentiaUy Stabilizing Control Law The Lyapunov functional is now redefine as: Vet) = p2(q, 0) + I'pA foL l.·1Jt(X, t)1Jx(X, t)dx (12) where I' is a small positive constant real number. Theorem 2 Let the boundary control law u(t) (3c) be u(t) = -Kl1Jx(L, t) -K21Jt(L, t) (13) where 1 2 L2 KI ~ --I' 2PA (14a) 2 bL -1) 1 21'L -1 K2 > --I'LpA (14b) - 2bL-1)2 Then, the functional V (t) along the solution of the system (1), (3a-3c), satisfies Vet) :s V(O) exp(-I' t). (15) 1 + I'l'l Furthermore, p(q, O):S jv(O)exp( I' t) (16) V~ 2(1+1'1'1) where 1'1 = Lmax(l, ~). Hence, the transversal displacement, velocity a~d slope will exponentially go towards zero .• Lemma 1 Let I' in (12) satisfy 1 1'« -. (17) 1'1 Then, the functional V (t) satisfies (I -I'l'l )p2(q, 0) :s Vet) :s (1 + 1'1'1) /l(q, 0) (18) for all t ~ O. Furthermore Vet) is positive definite with respect to metric p(q,O) and admits an infinitesimally upper limit. Proof One has pA foL X17t(x,thr(x, t)dx :s pA foL x l1Jt(x, t)l l1Jx(x, t) 1 dx pA rL A Po rL ) :s L ( 2 io 1J~(x, t)dx + ~o 20 io 1J;(x, t)dx :s I'IP2(q, 0) 260 Transversal Otsptacemenl -.-Convergent --Exponenttal . Uncontroued ..i , C' Fig. 2. Comparison between globally convergent, exponentially controlled and uncontrolled response at 1J(L, t)). for all t ~ 0, where 1'1 = Lmax(I,7f,)' The second inequality is obtained using the following triangular inequalit.y Therefore Eq. (12) can be written as Vet) :s p2(q, 0) + I'I'IP2(q, 0) = (1 +1'1'1 )p2(q, 0) By a similar way the left side of inequality (18) can be proven. It is clear from the definition of the metric p(q, 0), Eq.(7), that p(q,O) is positive definite, hence from inequality (18) and with 'Y satisfying the inequality (17), it is concluded that the functional Vet) is also positive definite. The right-hand side of the inequality (18) indicates that the functional Vet) has an upper limit which is given by (1 + 'Yl'd p2(q, 0) .• The derivative of (12) with respect to time, after substitution of pA1Jtt from Eq. (1) is given by From the boundary condition (3b) one has 1Jt(O, t) = o for all t ~ O. {;sing this fact, integrating by parts, and applying boundary conditions (3c-3a) we obtain Transversal Displacement """Convergent "" Exponential " UnoonIR>Ied ......... ------.. - Fig. 3. Comparison between globally convergent, exponentially controlled and uncontrolled response at TJ(L/2, t)). Conuc» Force "." Convergen' "" ExponenIial " UnconIrolled Fig. 4. Control forces of globally convergent and exponentially stabilizing control laws. V(t) = -~pA foL TJ;dx -,~o foL TJ;dx -,~ EA foL TJ!dx -,~El foL 7];xdx EA 4 L 2 -,LSTJx(L, t) -'"2 P07]x(L, t) L + ,Lu(t)TJx(L, t) + '"2pATJ;(L, t) + u(tJryt(L, t) (20) We are now ready to prove Theorem 2. Proof of Theorem 2: Substitution of the control law (13) into the Eq. (20), collecting terms and using the inequality 1 2 1 2 7Jx(L . t)7]t(L, t) ~ -'2 TJx (L. t) -'27]t (L, t) Selecting control gains KI and K2 according to (14a) and (14b) renders V(t) negative definite and can be written as V(t) :::; _,p2(q,0). ~ow, using the inequality (18) gives V(t) S -' V(t) . (22) 1 +"1 By the comparison lemma (Khalil, 1996)[13] the inequality (15) and the theorem are proven. From (15), using (17) and inequality (18), it is easy to obtain the inequality (16). Now using (15) and (18) we can conclude that the equilibrium state, q = 0, of the dynamic system is exponentially stable according to Theorem 3.1 in (Walker, 1980)[15]. Consequently, the slope 7]x(x , t) and the velocity TJt(x, t) will exponentially go toward zero as t ---t ofor all x E [0, L]. Thus, the deflection 7](x , t) will also converge exponentially to zero as t ---+ 0 for all x E [0, L] since 7](0, t) = 0 for all t ~ 0.• 4. SIMULATION 4.1 The Simulator The FEMBEAM (Sagatun, 1999) simulator solves the Euler-Bernoulli beam equation numerically by using the method of finite elements (FE). The program simulate long slender bodies submerged in a fluid both static and in the time domain or frequency domain. The simulator has been used to simulate drill strings vibrating in a bore hole submerged in drilling mud and dynamics of marine risers submerged in sea water. The beam modelled in the simulator may consist of an arbitrarily number of different beam segment with different static, geometrical or hydrodynamic properties. Environmental loads like current and top point motion may be included. All states are available for feedback along the entire beam length. The entire simulator is written in Matlab. 4.2 Results from the Simulation To test the control laws designed in this article, numerical simulations were carried out. A 100 meter long riser is modelled with 10 element. Time step used in numerical integration was ~t = 0.001 [s] . Detailed tipecmcatioIl!:; of ritier are given in Table 1. Transversal displacement of the riser at TJ( L, t) and TJ( ~, t) are presented in Fig. 2 and 3, respectively. Comparison between responses shows that the displacement in the case of control law (13) decays faster. From Fig. 4 we can also see that the control Table 1. parameter and material properties REFERENCES Parameter Value Ollll'r Dialllell'r 152.4 x 10 3[mj 11Jlwr DiauH,wr 76.2 x 1O-3[mj L("l)!;!.h 1000[mj I\lass 1)('1' IIllit lell)!;!." 108.1i~j E 2.06 x 1012[~j Fig. 5. Exponential decay of Lyapunov function. force in case of control law (13) is smaller and decays faster. A plot of Lyapunov functional is provided in Fig.5 to compare the energy content of the system in each cases. It can be seen that the Lyapunov functional (12) decays exponentially according to analysis in Section 3. 4.3 Implementational Aspect of the Controllers We notice from the expressions for the boundary control laws represented in (8) and (13) that only measurements from the top point (the riser's termination at the drill floor) are required. The state required to implement the control system is the top point transversal velocity. The exponential stabilizing control law does also require that the top point inclination is measured. Both these measurements are easily and inexpensively available by direct measures or through a state estimator. It can be seen from Fig. 4 that the maximum commanded force is::::::: 1300 [N] and with a maximum frequency of 1.6 [radjs]. This is easily achievable with a hydraulic system. 5. CONCLUSION Two boundary control laws are designed to stabilize the transversal vibration of a beam. Exp<r nential stability is proven via Lyapunov analysis. Stability and convergent of states, in case of control law (8), is proven using Barbaliit's lemma. Since the control laws consist only of feed backs from the slope and velocity , or just velocity, of the beam at the boundary, measurements cost is minimized and deterioration effects of spillover phenomenon are avoided. Control law (13) shows a better performance. It has been proven that the mechanical energy of the system will exponentially go toward zero. Balas, Mark J. (1977). Active control of flexible systems. Proceeding of the AIAA Symposium on Dynamic and Control of Large Flexible Spacecraft, Blacksburg, Va. pp. 217-236. BarbaIat (1959). Systemes d'Equations differentielles d'Oscillations non lineaires. Re1.!Ue de Mathematiques Pures et Appliquees 4(2),267 270. Fung, R. F. and C. C. Tseng (1999). Boundary control of an axially moving string via lyapunov method. Journal of Dynamic Systems, Measurement, and Control 121, 105-110. Fung, R. F., J. W. Wu and S. L. Wu (1999). Stabilization of an axially moving string by nonlinear boundary feedback. Journal of Dynamic Systems, Measurement, and Control 121,117-121. Khalil, Hassan K. (1996). Nonlinear Systems. second ed.. Prentic Hall. Lee, E. W. (1957). Non-linear force vibration of a stretched string. British Journal of Applied Physics 8, 411-413. Meirovitch, L. and H. Baruk (1983). On the problem of observation spillover in self-adjoint distributed-parameter systems. Journal of Optimization and Applications 30(2), 26929l. Sagatun, S. I. (1999). FEMBEAM, theory manual. Technical Report Tech. Rep. R-086327B. Norsk Hydro ASA. Shahruz, S. M. (1997). Suppression of vibration in stretched strings by the boundary control. Proceedings of the 36th Conference on Decesi on and Control, San Diego, California USA pp. 535-536. Shahruz, S. M. and C. A. Narasimha (1997). Suppression of vibration in stretched strings by the boundary control. Journal of Sound and Vibration 204(5), 835-840. Shahruz, S. M. and L. G. Krishna (1996). BOWldary control of a non-linear string. Journal of Sound and Vibration 195(1), 169-174. Walker, J. A. (1980). Dynamical Systems and Evolution Equations. Plenum Press. New York. 100 meter long riser is modelled with 10 element. Time step used in numerical integration was ~t = 0.001 [s] . Detailed tipecmcatioIl!:; of ritier are given in Table 1. Transversal displacement of the riser at TJ( L, t) and TJ( ~, t) are presented in Fig. 2 and 3, respectively. Comparison between responses shows that the displacement in the case of control law (13) decays faster. From Fig. 4 we can also see that the control Table 1. parameter and material properties REFERENCES Parameter Value Ollll'r Dialllell'r 152.4 x 10 3[mj 11Jlwr DiauH,wr 76.2 x 1O-3[mj L("l)!;!.h 1000[mj I\lass 1)('1' IIllit lell)!;!." 108.1i~j E 2.06 x 1012[~j Fig. 5. Exponential decay of Lyapunov function. force in case of control law (13) is smaller and decays faster. A plot of Lyapunov functional is provided in Fig.5 to compare the energy content of the system in each cases. It can be seen that the Lyapunov functional (12) decays exponentially according to analysis in Section 3. 4.3 Implementational Aspect of the Controllers We notice from the expressions for the boundary control laws represented in (8) and (13) that only measurements from the top point (the riser's termination at the drill floor) are required. The state required to implement the control system is the top point transversal velocity. The exponential stabilizing control law does also require that the top point inclination is measured. Both these measurements are easily and inexpensively available by direct measures or through a state estimator. It can be seen from Fig. 4 that the maximum commanded force is::::::: 1300 [N] and with a maximum frequency of 1.6 [radjs]. This is easily achievable with a hydraulic system. 5. CONCLUSION Two boundary control laws are designed to stabilize the transversal vibration of a beam. Exp<r nential stability is proven via Lyapunov analysis. Stability and convergent of states, in case of control law (8), is proven using Barbaliit's lemma. Since the control laws consist only of feed backs from the slope and velocity , or just velocity, of the beam at the boundary, measurements cost is minimized and deterioration effects of spillover phenomenon are avoided. Control law (13) shows a better performance. It has been proven that the mechanical energy of the system will exponentially go toward zero. Balas, Mark J. (1977). Active control of flexible systems. Proceeding of the AIAA Symposium on Dynamic and Control of Large Flexible Spacecraft, Blacksburg, Va. pp. 217-236. BarbaIat (1959). Systemes d'Equations differentielles d'Oscillations non lineaires. Re1.!Ue de Mathematiques Pures et Appliquees 4(2),267 270. Fung, R. F. and C. C. Tseng (1999). Boundary control of an axially moving string via lyapunov method. Journal of Dynamic Systems, Measurement, and Control 121, 105-110. Fung, R. F., J. W. Wu and S. L. Wu (1999). Stabilization of an axially moving string by nonlinear boundary feedback. Journal of Dynamic Systems, Measurement, and Control 121,117-121. Khalil, Hassan K. (1996). Nonlinear Systems. second ed.. Prentic Hall. Lee, E. W. (1957). Non-linear force vibration of a stretched string. British Journal of Applied Physics 8, 411-413. Meirovitch, L. and H. Baruk (1983). On the problem of observation spillover in self-adjoint distributed-parameter systems. Journal of Optimization and Applications 30(2), 26929l. Sagatun, S. I. (1999). FEMBEAM, theory manual. Technical Report Tech. Rep. R-086327B. Norsk Hydro ASA. Shahruz, S. M. (1997). Suppression of vibration in stretched strings by the boundary control. Proceedings of the 36th Conference on Decesi on and Control, San Diego, CBoundary Control of a Transversely Vibrating Beam Via Lyapunov MethodThis paper discusses the boundary stabilization of a beam in free transversal vibration. We consider a nonlinear partial differential equation (PDE) and based on this model construct two linear control laws to stabilize the system. The first control law guarantees globally convergent of states, while the second control law results into an exponentially stable closed loop. The latter control law is formed by feedbacking slope and velocity of beam’s boundary displacement. Numerical simulations are performed to test each of the control laws. The outcome of simulations are compared and discussed. The novelty of this article is that globally convergece and exponentially stabilization of transversely vibration in a beam is achieved, via boundary control without resorting to truncation of model.Increasing strength and ductility of a Mg–9Al alloy by dynamic precipitation assisted grain refinement during multi-directional forgingA fine-grained microstructure with enhanced strength and ductility was fabricated in a Mg–9Al alloy by tailoring multi-directional forging with dynamic precipitation. The dynamic precipitation concurred with dynamic recrystallization and inhibited grain growth, thus improved the strength by grain boundary strengthening. The improved ductility was explained by the drastic morphology alteration and decreased volume fraction of the precipitates.Magnesium (Mg) alloys offer significant weight reduction in transportation industry due to its low density []. Yet their applications have long been hampered by their unsatisfactory mechanical properties, especially the low strength and low ductility []. Among strategies in optimizing the strength and ductility, grain refinement is regarded as a promising one and has been explored by severe plastic deformation processes such as equal-channel angular pressing (ECAP) [], and conventional processes such as low temperature compression [These processes are able to produce a fine-grain structure with its grain size refined down to nano-level []. Yet most of these processes are not suitable for large-scale industrial fabrication due to their limited sample size and demanding processing parameters. More feasible process should involve relatively high processing temperature in order to promote recrystallization and thus avoids cracking. Consequently, the refined grains may grow larger during manufacturing. One effective way to retard grain growth is to pin the grain boundary by second phase particles []. The particles could be introduced by static aging [] or formed dynamically during deformation []. Since dynamic precipitation has a high kinetics caused by the presence of crystal defects [] and the precipitate particles appear mostly at grain boundary [], dynamic precipitation is more preferable than the static aging.To fully utilize dynamic precipitation, the matching process could be multi-directional forging (MDF). In MDF, plastic deformation can be carried out endlessly and thus the degree of dynamic precipitation can be regulated accordingly. At the same time, the periotic change of loading direction may facilitate the activation of multiple deformation modes, especially the <c + a> dislocations which are critical in forming a three-dimensional nuclei for recrystallization []. Another benefit of adopting MDF is that the texture produced would be weaker than ECAP []. Consequently, the ductility would be higher and the mechanical properties more isotropic.To verify the efficiency of achieving fine grain size via MDF and dynamic precipitation, microstructural and mechanical examination were carried out between the MDFed and the then heat-treated samples. Results showed that the grain size was refined down to 1.5 μm with the help of the dynamic precipitation. At the same time, the strength and ductility were significantly improved when compared to that of the statically aged samples.The alloy in use was a Mg-8.8Al-0.47Zn-0.21Mn-0.17Ag (wt.%) casting ingot. Rectangular samples with a dimension of 50 × 50 × 68 mm3 (labeled as X, Y, and Z, respectively) were machined out from the ingot. After homogenized at 420 °C for 24 h to dissolve the eutectic β-phase, the samples were MDFed on a hydraulic machine for the first round to break down the grain size form ~2 mm to ~20 μm. The forging was carried out at 420 °C for 6 passes in the sequence of Z-X-Y-Z-X-Y, each pass with a true strain of 0.15. After the forging, the samples were salt-bath heated from room temperature to 300 °C and forged 6 passes at this temperature (second round) before quenching. The first round was proved to be necessary in preventing crack during the second round of forging.Tensile tests were carried out in an Instron 3369 universal testing machine at room temperature and an initial strain rate of 1.5 × 10−3 s−1. The samples for testing (15 mm in length, 4 × 2 mm in cross section) were electro-discharge machined from the forged sample along the Z direction. Texture information was acquired using a FEI Helios Nanolab 600i dual beam scanning electron microscope (SEM) equipped with HKL Channel 5.0. Samples for electron backscatter diffraction (EBSD) measurement were prepared by mechanical grinding and subsequent electro-polishing in a solution of 90% ethanol and 10% perchloric acid at 25 V and −40 °C. Information of the precipitates was collected with the same microscope in the secondary electron (SE) mode. To facilitate the SE imaging, samples were chemical etched. More detailed information on the precipitates and dislocations was examined with a Titan G2 transmission electron microscope (TEM). Specimens for examination were first mechanical-ground to 60 μm in thickness, punched into 3 mm discs, then twin-jet electron polished with a solution of 97% ethanol, 1% nitric acid, and 2% perchloric acid. presents the mechanical properties of the forged alloy in various conditions. By varying the temperature and time, various grain sizes were obtained via annealing the MDFed sample. Tensile engineering stress-strain curves of the samples with representative microstructural features are presented in a while relationship between all the samples’ yield stresses with grain size is plotted in b. After a soft annealing at 350 °C for 5 min to dissolve the precipitates, elongation of the annealed sample (Annealed-A) reaches to 35% while the yielding stress (YS) drastically decreases. More through annealing lead to a simultaneous decrease of elongation and YS of the sample Annealed-B. After aging treatment, elongation decreased to merely one third of the annealed sample, a trend similar to the alloy which included reinforcements []. Compared with these statically aged samples, yield stress of the MDFed sample is significantly higher. At the same time, elongation of MDFed sample is also larger than that of the statically aged samples. The concurrent increase in strength and ductility indicates that MDFed sample has superior mechanical properties than the statically aged ones. shows the inverse pole figures, {0002} pole figures (PF), Schmid factors for basal and prismatic slip, and grain size distribution of the processed samples. In the MDFed sample, the microstructure consists of equiaxed grains with an average size of ~1.5 μm. Also, the microstructure is homogenous and has a narrow grain size distribution. Texture of the sample is featured with a low Imax of 3.5 times of random intensity. In addition to the weak texture, the PF shows that a large proportion of the basal poles tilt towards the tensile direction with an angle of 50°. This direction favors activation of basal slip, as indicated by the high percentage of grains fall between 0.4 and 0.5 of basal slip Schmid factor. With the grain size grows to 7 and then 21 μm, the texture configuration and Imax maintained the major features. Similarly, the Schmid factor for basal and prismatic slip maintained nearly the same during the annealing. shows the SEM micrographs of the MDFed and the then-T6 treated samples. Morphology of the precipitates in the three samples are drastically different. In the MDFed sample, two groups of precipitates were observed: (i) the dominant group is the spherical β-phase particles evenly distributed in the matrix, with an averaged particles size of 340 nm (c); (ii) the minor group adopts the morphology of typical continuous precipitate but with much smaller aspect ratio, these particles have an equivalent diameter of ~100 nm and they aggregate into circular patches (a). In the T6-A sample, the lamellae grow less inerratic (f) while the lath particles take a morphology prone to the fine precipitates in the MDFed sample (Fig. 3d). In the T6-B sample, precipitates follow the typical morphological features of continuous and discontinuous precipitate particles of β-phase that have been characterized in previous studies []: the lath-shaped and isolated particles are the continuous precipitates while the colony of lamellae are the discontinuous precipitates. shows the HAADF-STEM images of the two groups of precipitates in the forged sample. The fine precipitate area is divided into micro-bands with a spacing of ~2 μm, and the basal plane trace slightly varies between different bands (a inset). In the fine precipitate area, plate-shaped and granular particles evenly distribute in the matrix, and most of the granular particles are found attached to the plates. With higher magnification, nano precipitates with an averaged diameter of 5 nm are also identified in the matrix. The similar high contrast and granular particle shape indicate that they have the same composition. EDX analysis shows that these particles are Ag-containing particles which might be Mg54Ag17 as characterized in a previous research []. In the coarse precipitate area, most of the coarse particles locate at grain boundaries, indicating that these precipitates are most likely formed after recrystallization since grain boundaries are fast diffusion channels for solute atoms to transport and thus form particles []. Similar to the fine precipitate area, coarse and fine Mg54Ag17 particles are found evenly distributed in the matrix. EDX examination shows that the composition is the same as in the fine precipitate area. present a schematic diagram of the typical microstructural features acquired at temperatures selected for examination. The diagram is adapted from the classical time-temperature-transformation curve for recrystallization at static heating process []. And a few modifications were made to emphasis the variation of microstructural features under the influence of dynamic precipitation. To refine grain size, dynamic recrystallization should be as fully-finished as possible, thus temperature should be relatively high so that migration of grain boundary could be mobilized with sufficient ease. Consequently, this would increase the tendency of grain growth after recrystallization. To retard the grain growth, either decreased temperature or boundary-pinning particles is in demand. Although particles can be quickly formed at 350 °C, a lower temperature would be more beneficial so that higher volume fraction of precipitates can be acquired. After examining a series of samples, the finest grain size and optimal mechanical properties is achieved with those forged at 300 °C. This temperature is significantly higher than the typical aging temperature of 175 °C, thus precipitation kinetics is much higher since the diffusion rate increase exponentially with temperature []. In addition, the kinetics would also be boosted by the dense grain boundaries which serve as fast diffusion channels []. This high precipitation kinetics leads to a rapid formation of large particles (especially at grain boundaries), and thus help to block the grain growth and achieve a fine-grained microstructure., the fine-grained microstructure acquired by the tailored forging temperature shows a significant improvement in strength and ductility. Data of the yield stress and grain size fit well with the Hall-Petch relationship when the grain size ranges from 7 to 175 μm (grain size of 175 μm was in cast and homogenized condition). One detail worth noting is that caution should be taken in quantifying the Hall-Petch relationship. In order to achieve a fitting reflects accurately the grain boundary strengthening, the annealed samples should avoid of second phase particles or crystal defects. In this study, this was realized by annealing samples at temperatures where the precipitates would quickly dissolve into the matrix. And the smallest grain size achieved under this requirement is 7 μm (Annealed-A). In the range of 7–175 μm, a slope of 158 MPa μm1/2 for the relationship is acquired. According to this slope, estimated yield strength at the grain size of 1.5 μm is 198 MPa. Discrepancy between this value and the test value of 216 MPa (Δσy in b) should originate mainly from the precipitate strengthening of β-phase and Mg54Ag17 particles. Compared with the precipitate strengthening of ~45 MPa, the strength enhancement due to grain refinement (from 175 to 1.5 μm) reaches to a far larger value of 120 MPa.Ductility of the MDFed sample is also significantly higher than that of the statically aged samples. As shown in the SEM and TEM images, most of the precipitate particles in MDFed sample adopt a spherical morphology and locate at grain boundary. The spherical morphology has been reported to be beneficial to ductility due to its efficiency in preventing crack growth than the colony of lamellae []. Also, locating at grain boundary renders the precipitates ineffective in blocking dislocation slid in the matrix and thus they are more beneficial than the statically formed precipitates in conserving a high ductility. In addition, the higher ductility of T6-A than T6-B indicates that finer grain size also benefits the ductility in aged condition. This ductility enhancement by refined grains may originate from its suppression on twinning or its interference on the formation of lamellae by altering the diffusion of Al atoms. Although it is difficult to separate the two effects, a general conclusion can be drawn that the overall effect of decreasing grain size on promoting ductility is beneficial.Apart from the improved mechanical properties, the resulting microstructure also presents a new perspective on processing route of age-hardenable Mg alloys. In conventional processing, deformation and aging (static) are usually separated. In the MDF, however, the two processing steps were completed simultaneously in the MDF. And the time to produce a microstructure strengthened with precipitates was shortened from days into minutes. If the superior mechanical properties and the manufacturing advantages can be extended to mass production of Mg alloys, their applications would be widened while the overall manufacturing cost decreased.The tailored MDF process demonstrates its effectiveness in refining the grain size and improving the mechanical properties of a Mg–9Al alloy. During the forging, intense dynamic precipitation occurs with enhanced kinetics which is caused by the combination of the relative high temperature and refined grain size. These precipitates appear slightly after the recrystallization and pin the grain boundary, and thus constrains the growth of the grains. Compared with the typical coarse-grained samples in the aged condition, this microstructure leads to a simultaneous improvement in strength and ductility. Moreover, producing this microstructure by MDF shortens the time and decrease the manufacturing cost, and it shows potential for mass production and the widen of application of Mg alloys.The raw data required to reproduce these findings are available from the corresponding author on reasonable request.Jiansheng Wei: Investigation, Data curation, Writing - original draft. Shunong Jiang: Supervision, Writing - review & editing. Zhiyong Chen: Validation. Chuming Liu: Project administration, Funding acquisition.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.~ Pergamon www.elsevier.com/locate/jappmathmech J. Appl. Maths Mechs, Vol. 64, No. 3, pp. 443-447, 2000 2000 Elsevier Science Ltd All rights reserved. Printed in Great Britain PII: S0021-8928(00)00067-8 0021-8928/00/S--see front matter THE, ASYMPTOTIC SOLUTION OF A CONTACT PROBLEM WITH A HALF-UNKNOWN BOUNDARY OF THE CONTACT REGION " I. I. ARGATOV St. Petersburg (Received 25 August 1999) The following problem is considered: a punch, disk-shaped in plan, whose base is an almost circular elliptical paraboloid, is pressed onto the boundary of an elastic half-space. The friction between the bodies in contact is ignored; the punch edges are allowed to separate from the elastic base. It is assumed that the contact region, which is not known a priori, is almost circular. The solution of the problem is constructed by the method of matched asymptotic expansions. The asymptotic form of the boundary of the contact region is presented in explicit form. 2000 Elsevier Science Ltd. All rights reserved. 1. FORMULATION OF THE PROBLEM Suppose a punch whose base is an elliptical paraboloid (1.1) where e is a small positive parameter, is pressed without friction into the elastic half-space x3 > 0. It is assumed that in plan the punch occupies a disk too of radius a with centre at the origin. Letting ~8 denote the forward displacement of the punch, we set ~E = 8o +eSt; 5o = 2Aa2 (1,2) Then (see, e.g. [1], Chap. 3, Sec. 2) when e = 0 the punch is in contact with the base over the entire region tOo, and the contact pressure vanishes at the boundary F0. In the general situation, the contact region to~ turns out to be some subregion of tOo which is not known a priori. Using the Papkovich-Neuber representation, one can reduce the problem [2, 3] to that of determining a harmonic function u~ that vanishes at infinity and satisfies the following boundary conditions uE(x)~ 5E -q)~(xl,x2), a3u~(x)~ 0 [u~ (x) - 8E + O~ (xI, x2)]03uE (x) = 0 x3 = 0, (xt, x2) e tOo (1.3) 03ue(x)=0, X3 =0, (XI,X2)ER2 \N0 (1.4) The boundary F, of the contact region toe is defined by the condition that the contact pressures pe(Xl,X2)=--~-1~3UE(Xl,X2,0); C~-- 2(I-- v2)E-I (1.5) must be positive, where E and v are Young's modulus and Poisson's ratio of the elastic half-space. In a previously obtained analytical solution of the problem [4], the coefficients of the trigonometric expansion of a function h~, characterizing the deviation of the contact region from the disk, were computed by the collocation method. In this paper an asymptotic method developed by Nazarov [5, 6] will be employed. A simple closed expression will be derived for a piecewise-smooth function h~. tPrikl. Mat. Mekh. Vol. 64, No. 3, pp. 462--466, 2000. 443 444 I.I. Argatov 2. THE OUTER ASYMPTOTIC EXPANSION Far from the disturbed part of the contact boundary, we prescribe the solution of problem (1.3), (1.4) in the form t?'(x) ---vx)+ cv ICx) (2.1) where the right-hand side is the solution of the linear contact problem of the punch (1.1) pressed in to the depth (1.2). Accordingly, we have the following representation for the contact pressure pe (Xl, X2 ) ~__. p0(xi, X2 ) + Epl (Xl, X2 ) (2.2) Using well known results (see [1, 2, 7], etc.), we find E 280 4a2 - x? - x~ (2.3) PXa' x2) = re(1 - v2-----~ a---T- E 8, - (%)A(x2 -x~) (2.4) P'(X"Xz)=x(1-v2) 4a2_x?_x~ Let us determine the behaviour of the function (2.1) in the neighbourhood of the contact boundary. In a three-dimensional neighbourhood of the contour F0, we introduce local coordinates Yl, Y2 = x3, or, where cr is the polar angle. In addition, in planes orthogonal to F0 we introduce polar coordinates r and ~, where Yl = r cos q0, Y2 = r sin q~ and ~p e [0, ~r]. Direct computations for the densities (2.3) and (2.4) yield the following asymptotic formulae px,, x2) = -(2r0-~ kG)r~ + O(r~), r --~ 0 (2.5) pJ(xj,x2)=-(2g)-~Kl(G)r-~ +O(r~), r---~O (2.6) where, by normalization as in [5], we have k0(G) =- E 480 (2.7) 1 - v2 4-ffa~ E ( 81 8Aa2 ) K' (G) = - i _---~..q~a 3~/-~ COS2G (2.8) Finally, for the functions vand v1 we have the following asymptotic expansions as r ~ 0 (see for example [8, 5]). o O(x) = Aa2 + 2Aar cos (1) + oc(2rUl ))-'/3-1 kG)r;)~ sin(3(p / 2) + O(r2 ) (2.9) I I I IZ . u I(x) = 81 - Aa2 cos2G + Off2rU )~K (G)r'2 sin(q0/2) + O(r) (2.10) Note that only the second inequality is violated for the function (2.3) in boundary condition (1.3), in the neighbourhood of those points of the contour F0 where the stress intensity factor (2.8) is positive. 3. THE INNER ASYMPTOTIC EXPANSION In planes normal to F0 we change to "stretched" variables "q =(rll,q2); qi =8-JYi The solution of problem (1.3), (1.4) near F0 will be sought in the form (3.1) The asymptotic solution of a contact problem with a half-unknown boundary 445 U~: (X)= W0 (13; "ItI ) + E I/2 wl (13, "111 )-I- El4'2 (13; "llI ) + e~ 14'3(13; "III ) (3.2) We substitute expansions (2.9) and (2.10) into (2.1) and apply the coordinate transformation inverse to (3.1). Setting r =: ep, we obtain v x) + evl (x) = Aa2 + e[2Aal]~ + 81 - Aa2 cos 213] + + z Y-'tx(2rt-I )[3-1 k0 (13)p~ sin(3qo / 2) + KI (13)9sin(qo / 2)] + O(e2p2) (3.3) By the method of matched asymptotic expansions (see [9-11] and others), the first terms on the right in (3.3) are determined by the leading terms of the boundary layer w13;'q)=-Aa2, w~(13;rl)-0, w2(13;~l)=2Aarll +~1 -Aa2cos213 (3.4) By the second equality in (3.4), the function w3 must be harmonic in the half-plane "q2 > 0 (see [5, Section 3]) 4. VARI[ATION OF THE BOUNDARY OF THE CONTACT REGION Let us assume that the curve F~ is described in local coordinates by the equation Yl = h~(13); h~(13) = ~h(c) (4.1) or "ql = h((r), where h((r) is a function to be determined. Besides the coordinates p and ~p, we also introduce polar coordinates Ph and ~h ~ [0, ~r] with pole at the point "ql = h((r), "q2 = 0. Proceeding as in [6], we prescribe the lower-order term of the inner asymptotic expansion (3.2) in the form w3 (13; ~ ) = ~(2n-I )3-I N(13)p~ sin(3(ph / 2) (4.2) The function (3.2) essentially satisfies the second inequality of (1.3) in the contact region "ql > h(cr), provided that N((r) < 0. When that happens the contact pressure will vanish over the disturbed part of the contour F~. In addition, because of (3.4) and (4.2), the first inequality of (1.3) will be an quantities O(e ). Finally, the functions N and h are determined by comparing the equality apart from 2 asymptotic expansions (2.1) and (3.2). Using the formulae [5] arh//:)h=-costp, Otph/~h=r-lsintp for h=0 for large values of la we derive the relation Off sin(3~h / 2) = p)~ sin(3q~ / 2) - (3~)p(13) sin((p / 2) + O(p-~ ) (4.3) Substituting (4.1) into (4.2) and making the change of variables (3.1), we find that e~ w3 (13; ~ ) = ct(2r~-t )~ 3-I N(13)r~ sin(3tp/2)- - I~ct(2rc-I )~ 2-j N(13)hO3)rsin(qa / 2) + O(e2r- (4.4) Now, comparing relations (3.3) and (3.2)2taking into account equalities (3.4) and (4.4), we conclude r /3 4/3 that in the matching, zone, where r/a = O(e ), the inner and outer expansions differ by quantities O(e ), provided that N((r) = k(r) and h(13) = (-2K' (13)/k13))+ (4.5) The subscript p]Lus denotes the operation of taking the positive value of the expression in the parentheses. We emphasize that at those points (r where K](rr) < 0, so that compressive stresses develop near the edge of the punch, formula (4.5) gives h(cr) = 0 and the boundary F~ coincides with F0. By (2.7) and (2.8), the function (4.5) may be written in the form 446 I.I. Argatov h(~) = ((~)a cos 2c - (~)8x )+ or, if (1.2) and (1.4) are taken into consideration = _~Aa (8~ 2 cos2c] h~(~) ( -8o)+-ca 3 .,+ Formula (4.6) in the main determines the position of the boundary F~. (4.6) 5. THE CONDITIONS FOR WHICH THE PUNCH EDGE DOES OR DOES NOT SEPARATE FROM THE BASE SURFACE It is not hard to see that the contact pressure (2.2) on co0 will be positive if gl - (8/3)Aa2 cos 2cr t> 0 for cre [0, 2"rr] or gl -- (8/3)Aa2- Consequently, the condition for full contact is as follows (see also [12], Sec. 1.5.2): ~0 + e(~)Aa2 <~ fie (5.1) Note that the boundary (5.1) coincides exactly with that obtained from asymptotic formula (4.6). Indeed, if inequality (5.1) is satisfied, the function (4.6) will vanish identically. On the other hand, formula (4.6) predicts that the whole edge of the punch will separate from the elastic base if 8E <~ 8o - e(~)Aa2 (5.2) Let us compare this result with the exact result obtained using Hertz's formulae ([13], Chap. V, Sec. 6.5). In this case, the contact surface is bounded by an ellipse with semi-major axes a and eccentricity e defined by the equation (I- e2)[K(e)- E(e)] = I-~: E(e)-(l -e2)K(e) I+r Using the expansions of the complete elliptic integrals K and E for small values of the modulus (see, e.g. [14]), we see that as e ~ 0 Using the relation and the equation ,2 = (~)e + O(E2). 5/-~--t( E(e) )~ a= ,~-~-~ K(e)-)-~_ e2) ) we compute the asymptotic behaviour of the displacement of the punch 8~ = 2Aa2 - e(~)Aa2 + O(e2) If (1.2) is taken into consideration, formula (5.3) is in general agreement with estimate (5.2). (5.3) 6. CONCLUSION In the neighbourhood of the disturbed part of the contact boundary, one has the phenomenon of a plane boundary layer. Here the following formula holds for the contact pressure (by relations (3.2) and (4.2)) pC (xl, x2) = _ (2 ) ~ k(~)~/Yl - hE (~) where Yl ~> h~(~) It should be noted that the essential point in the asymptotic solution of the problem is the fact that if e = 0, the contact pressure vanishes along the entire boundary F0. In the problem of separation from an elastic base for the edge of a punch with a two-dimensional base (see [15, 16]), more complicated constructions are needed. We also note that in neighbourhoods of points where the base surface separates from the punch edge, asymptotic formula (4.5), obviously, does not described the local behaviour of the boundary F~. The asymptotic solution of a contact problem with a half-unknown boundary 447 In the problem considered, the punch surface is a perturbation of a circular paraboloid by an elliptic paraboloid. Using the method described in [5], an analogous study may be made of the case in which the perturbed surface is, say, of fourth order. I wish to thank S. A. Nazarov for useful discussions. This research was supported financially by the International Association for Promoting Cooperation with Scientists from the Independent States of the Former Soviet Union (INTAS-96-0876). REFERENCES 1. SHTAERMAN, I. Ya., The Contact Problem of Elasticity Theory. Gostekhteorizdat, Moscow, 1949. 2. LURYE, A. I., Three-dimensional Problems of Elasticity Theory, Gostekhteorizdat, Moscow, 1955. 3. GALIN, L. A., Contact Problems of Elasticity Theory. Gostekhizdat, Moscow 1953. 4. KOVURA, A. B. ancE MOSSAKOVSKII, V. I., A contact problem with a half-unknown boundary of the contact region. Prikl. Mat. Mekh., 1979, 43, 1,106-111. 5. NAZAROV, S. A., r)erivation of the variational inequality for the shape of a small increment of an I-mode crack, lzv. Akad. Nauk SSSR. MTT, 1!)89, 2, 152-160. 6. NAZAROV, S. A., The perturbations of solutions of the Signorini problem for a scalar second-order equation. Mat. Zametki, 1990, 47, 1,115-126. 7. ROSTOVTSEV, N. A., Complex potentials in the problem of a punch, circular in plan. Prikl. Mat. Mekh., 1957, 21, 1,77-82. 8. PARTON, V. Z. and PERLIN, P. I., Methods of the Mathematics Theory of Elasticity. Nauka, Moscow, 1981. 9. VAN DYKE, M., Pel~urbation Methods in Fluid Mechanics. Academic Press, New York 1964. 10. IEIN, A. M., Match&g of Asymptotic Expansions of the Solutions of Boundary-vahte Problems. Nauka, Moscow, 1989. 11. MAZJA, E. G.. Nazarov, S. A. and Plamenewski, B. A.,Asymptotische Theorie elliptischerRandwertaufgaben in singuliirgest6rten Gebieten. Akademie, Berlin, 1991. 12. ALEKSANDROV, V. M. and POZHARSKII, D. A., Non-classical Three-dimensional Problems in the Mechanics of Contact Interactions of Elastic Bodies, Faktorial, Moscow, 1998. 13. LUR'YE, A. I., The Theory ofE(asticity. Nauka, Moscow, 1970. 14. JAHNKE, E., EMDF, F and LOSCH, E, Tables of Higher Functions, 6th ed. McGraw-Hill, New York, 1960. 15. RVACHEV, V. L. and PROTSENKO, V. S., The structure of the solution of a contact problem with an inclined punch Dop. Akad. Nauk UkrSSR, Ser. A, 1970, 11, 1023-1026. 16. RVACHEV, V. L. and PROTSENKO, V. S., Contact Problems of the Theory of Elasticity for Non-classical Domains. Naukova Dumka Kiev, 1977. Translated by D.L. The asymptotic solution of a contact problem with a half-unknown boundary of the contact regionThe following problem is considered: a punch, disk-shaped in plan, whose base is an almost circular elliptical paraboloid, is pressed onto the boundary of an elastic half-space. The friction between the bodies in contact is ignored; the punch edges are allowed to separate from the elastic base. It is assumed that the contact region, which is not known a priori, is almost circular. The solution of the problem is constructed by the method of matched asymptotic expansions. The asymptotic form of the boundary of the contact region is presented in explicit form.Texture comparison of an ordinary IF steel and a high-strength IF steel under ferritic rolling and high-temperature coilingThe present work was performed to investigate the texture difference of an ordinary Ti-IF steel and a high-strength Ti-IF steel under ferritic hot rolling and high-temperature coiling. Comparing with the completely recrystallized textures of the ordinary IF steel, the textures of the high-strength IF steel were still deformed textures. The texture difference for the two steels is related to high P content in the high-strength IF steel which prevents the recrystallization during the coiling process. For the ordinary IF steel, the texture components were mainly very weak {001}〈110〉 orientation at the surface, and partial 〈110〉//RD (rolling direction) textures focused on {223}〈110〉 orientation and 〈111〉/ND (normal direction) texture at the mid-section and 1/4-section. For the high-strength IF steel, the texture components were mainly of {110}〈001〉 orientation at the surface and of a sharp 〈110〉//RD texture from {001}〈110〉 to {223}〈110〉 and weak 〈111〉/ND texture at the mid-section and 1/4-section.Compared to conventional austenitic rolling of steel, the physical metallurgy of ferritic hot rolling, i.e., warm rolling, is significantly different and was extensively discussed in many literatures In the present paper, the texture characteristics were studied in two different IF steels after rolling in the ferrite range and coiling at high temperature.The experimental materials including an ordinary Ti-IF steel and a high-strength Ti-IF steel were obtained from industrial trial in a hot-strip mill line and the chemical composition was shown in . Considering the precipitation of Ti4C2S2 and to prevent the coarsening of austenite grains, slabs were reheated at 1050 °C. Slabs with a thickness of 230 mm were rolled to 46 mm during rough rolling to refine austenite grains; finish rolling was performed in ferrite region with lubrication, and finishing temperature, coiling temperature and the final thickness of slabs were 760 °C, 740 °C and 5 mm, respectively.The microstructure was analyzed by optical micrograph to observe the status of grains. X-ray and EBSD were employed to analyze textures. Macroscopic textures were measured on an X'Pert Pro X-ray diffractometer and three incomplete pole figures ({222}, {211}, and {110}) were obtained. ODFs (orientation distribution functions) were then evaluated using Roe's method The optical micrographs of the test steels are shown in a that in the ordinary Ti-IF steel, the deformed microstructure was vanished and the recrystallization microstructure was developed as uniform and equiaxed grains. However, most of the grains were still in rolling status in high-strength Ti-IF steel. The ferrite grains were elongated along the rolling direction and deformation bands were formed in the specimen with only a few grains recrystallizing in the deformed bands, as can be seen in b. This difference attributes to the different chemical composition in the two steels. shows the ϕ |
= 45° ODF figures through the thickness of the ordinary steel. For the ordinary Ti-IF steel, weak {111} texture as well as strong {001}〈110〉 and {113}〈332〉 components were formed at the surface, while the intensity of {001}〈110〉 and {113}〈332〉 components decreases greatly and {111} texture strengthens distinctively at the 1/4-section. The texture character at the mid-section is basically the same as that at the 1/4-section except that the intensity of {111} texture is higher. This texture characteristic is in agreement with the recrystallized microstructure in ordinary Ti-IF steel., the main component at the surface of high-strength Ti-IF steel is the shear texture {110}〈001〉 and no {111} textures are formed. While textures at 1/4 section consist of strong {001}〈110〉∼{223}〈110〉 components and weak {111} textures. The textures at the mid-section display the same character as that at the 1/4-section except that the intensity is higher, which is consistent with the deformed microstructure in high-strength Ti-IF steel. show the corresponding intensity changes of ε-fiber (〈110〉//TD), α-fiber (〈110〉//RD) and γ-fiber (〈111〉//ND) for the two steels, respectively. In the ε-fiber of ordinary Ti-IF steel seen in a, the intensity of {554}〈225〉 5° deviating from {111}〈112〉 is high at both mid-section with f(g) = 13 and 1/4-section with f(g) = 10 and very low in surface. While in the ε-fiber of the high-strength Ti-IF steel seen in a, the main component is {001}〈110〉 at mid-section with f(g) = 12 and 1/4-section with f(g) = 6, but {110}〈001〉 dominates at surface with f(g) = 10. In the γ-fiber of ordinary Ti-IF steel seen in c, the intensity of the main component {111}〈110〉 at the mid-section and 1/4-section is less than f(g) = 5 and f(g) = 6, respectively, while {111}〈112〉 is more intense with f(g) = 9 and f(g) = 12. In the γ-fiber of the high-strength Ti-IF steel seen in c, no γ-fiber is present at surface and the main component {111}〈110〉 is weak at the mid-section and 1/4-section. shows the inverse pole figures of the surface and mid-section of the ordinary Ti-IF steel. It is obvious that the main texture components at surface and mid-section are 〈001〉//ND and 〈111〉//ND, respectively, which is in agreement with the results achieved by X-ray diffraction.After hot rolled in ferrite region and coiled at high temperature, grains in the ordinary Ti-IF steel recrystallized completely, but those in the high-strength Ti-IF steel were still in rolling status. This is closely related to the different P contents in the two steels. Since the atomic radius of P is much smaller than that of Fe, strong interactions would be expected between P and recrystallized high-angle grain boundaries. Several literatures have described the segregation of P to the ferrite grain boundaries during coiling Complete recrystallization microstructure is produced in the ordinary Ti-IF steel after high-temperature coiling and 〈111〉//ND texture is in the ascendant. After hot rolled at lower temperature, beneficial rolling texture is developed and transforms to 〈111〉//ND recrystallization texture during coiling, which improves the mechanical properties. The yield strength, tensile strength and elongation of the ordinary Ti-IF steel in this trial are 135 MPa, 265 MPa and 44%, respectively. Due to the high content of P, most grains in the high-strength Ti-IF steel are still in rolling status and typical rolling textures are developed with high intensity. It has been reported that these textures can transform to beneficial 〈111〉//ND recrystallization texture and drawability can be improved after annealing , the texture characters at the surface are absolutely different from that at mid-section and 1/4-section. Texture at the surface is weak and strengthens gradually from 1/4-section to mid-section. The main component at the surface of the high-strength Ti-IF steel is {110} texture, which is the typical component of the shear texture in bcc metals. This indicates that the friction between the rolls and the material due to ineffective lubrication at the surface leads to shear strain, which contributes to the formation of {110} texture , the texture components at the surface of the ordinary steel are {001}〈110〉 orientation. This is estimated that {110}〈001〉 should be transformed to {001}〈110〉 because of recrystallization during the coiling process. It should be pointed out that the differences between the textures at the surface and the center may deteriorate the formability. Therefore, in order to gain higher intensity of {111} texture at surface and improve the drawability, it is essential to improve the lubrication conditions.The ordinary Ti-IF steel was recrystallized completely and strong 〈111〉//ND recrystallization texture was formed at the mid-section and 1/4-section after hot rolled in the ferrite region and coiled at high temperature.Due to high content of P in the high-strength Ti-IF steel, most of the grains were still in rolling status after coiling and 〈110〉//RD texture was in the ascendant at the mid-section and 1/4-section with very weak 〈111〉/ND recrystallization texture.Intensity and type of texture at the surface are greatly different with that at mid-section and 1/4-section. Textures at surface in both steels are very weak with 〈001〉//ND in ordinary Ti-IF steel and 〈110〉//ND in high-strength Ti-IF steel.Microstructure and mechanical properties of Co/Sn-10Bi couple and Co/Sn-10Bi/Co jointThe growth behavior of interfacial intermetallic compounds (IMCs) layer of Co/Sn-10Bi and Co/Sn-10Bi/Co couple has been studied by scanning electron microscope. The critical temperature and shear strength of Co/Sn-10Bi/Co joints were tested by universal testing machine. The results showed that the thickness of CoSn3 IMCs layer increased as the increase of aging time and temperature. The growth rate of CoSn3 IMCs layer of Co/Sn-10Bi/Co couple was suppressed and was lower than that of Co/Sn-10Bi couple as the decline in Sn concentration of residual Sn-Bi layer. The critical temperature of Co/Sn-10Bi/Co joint that could hold a load of 1 N changed as the chemical composition of residual Sn-Bi layer changed. The shear strength of Co/Sn-10Bi/Co joints bonded at 240 °C for 20 min, 30 min, 40 min, and 50 min was between 58 MPa and 82 MPa. The shear strength of Co/Sn-10Bi/Co joint bonded at 240 °C for 60 min was only about 17 MPa. The damage in shear strength of Co/Sn-10Bi/Co joint bonded for 60 min was led by the crack in residual Bi layer.For traditional transient liquid phase bonding (TLPB) process, which is always used in System-in-a-Package (SiP), thin solder alloy layer (about 5 μm) should be electroplated on the Cu pillar. Then, two Cu pillars with electroplated solder are bonded together and form Cu/IMCs/Cu joint at high temperature (a)) is available by direct reflowing without pressure. The TLPB process of solder joint with thicker solder alloy layer (above 20 μm) could be developed (in (b)), if the bonding time expanded or the bonding temperature improved. However, for traditional Cu or Cu-based under bump metallurgy (UBM), the growth rate of interfacial IMCs layer is limited Co series alloys, including pure Co, Co-P, and Co(W,P) have been widely applied in packaging industry. Wang et al. have investigated the interfacial IMCs layer growth behavior of Sn-Pb/Co Sn-Bi series solder alloy was an important Pb-free candidate in packaging industry. Chen et al. In this investigation, the pure Co substrate and high performance Sn-10Bi solder alloy was employed. The growth behavior CoSn3 IMCs layer between Sn-10Bi and Co was investigated. The mechanical properties of Co/Sn-Bi/Co and Co/IMCs/Co joints were tested systematically. The fracture mechanism was also analyzed.The Sn-10Bi solder alloy ingot was prepared by pure Sn (99.99 wt.%) and pure Bi (99.95 wt.%) with the protection of liquid mixed KCl and LiCl salts at 500 °C (a)) was prepared by Co substrate and Sn-10Bi solder alloy on heating plate at 240 °C. Then, the couple was aged at 220 °C, 240 °C, 250 °C, and 260 °C for 10 min, 20 min, 40 min, 60 min respectively. The cross section was cut and polished at last.The Co/Sn-10Bi/Co lap joint with an overlapping area of 4 mm2 (in (b)) was prepared by Co substrate and Sn-10Bi sheet on heating plate with the help of fixture. The bonding temperature was 240 °C. The bonding time was 20 min, 30 min, 40 min, 50 min, and 60 min respectively. Then the cross section was cut and polished.All the cross section was observed by scanning electron microscope (SEM). The chemical composition of special regions was analyzed by energy dispersion spectrum (EDS). The critical temperature which was the highest temperature that the Co/Sn-10Bi/Co overlap joint (as shown in (c)) could hold a load of 1 N was tested by universal testing machine with an environmental chamber. During testing, the environment temperature was increased in a speed of 10 °C/min. The control system recorded the temperature and load by two sensors at the same time. The shear strength of Co/Sn-10Bi/Co lap joints was tested as (c). The fracture surface was analyzed by SEM, EDS, and X-ray diffraction (XRD).The microstructure of Co/Sn-10Bi interface aged for 60 min is shown in . The Co/Sn-10Bi interface included Sn-10Bi solder alloy, interfacial IMCs layer, and Co substrate. Generally, the Co-Sn IMCs generated from the reaction between Co and Sn-based solder alloy was CoSn3 and CoSn2. CoSn2 always formed with high reaction temperature and low Sn concentration , the interfacial IMCs layer contained CoSn3 and small amount of Bi (three locations per sample were tested). Therefore, the IMCs resulted from the reaction between Co and Sn was CoSn3.The thickness of CoSn3 layer is shown in . The CoSn3 layer of Co/Sn-10Bi aged at 220 °C for 10 min was 8.1 μm. The CoSn3 layer of Sn-10Bi/Co aged at 260 °C for 60 min was 82.9 μm. From , it could be concluded that the thickness of CoSn3 layer was increased as the aging temperature and aging time increased.To describe the growth of CoSn3 IMCs layer, the Eq. where X is the thickness of CoSn3 layer, k is the growth rate of CoSn3 layer, t is the reaction time of Co/Sn-10Bi couple.The value of k and n was calculated from Eq. . The results showed that the exponent (n) was between 0.5 and 1 as shown in . Therefore, the growth of CoSn3 layer was controlled by chemical reaction and diffusion together (a). It could be found that the growth rate of CoSn3 layer increased as the increase of aging temperature. The growth rate of CoSn3 layer of Co/Sn-10Bi aged at 250 °C was closed to that of Co/Sn-Pb aged at 250 °C ) was employed to describe the relationship between growth rate and temperature where k0 is the constant, Q is the activation energy, T is the temperature. The activation energy was shown in . The activation energy of CoSn3 layer of Co/Sn-10Bi between 220 °C and 260 °C was 80.7 kJ/mol. The activation energy in this investigation was smaller than that of Co/Sn-Pb The Co/Sn-10Bi/Co sandwich structure couple was fabricated. Then the sandwich structure couples were kept at 240 °C for different time. The microstructure of Co/Sn-10Bi/Co with different bonding time is shown in . The structure of Co/Sn-10Bi/Co couple included Co substrate, CoSn3 IMCs layer, residual Sn-Bi layer, CoSn3 IMCs layer, and Co substrate. The interfacial IMCs thickness and residual Sn-Bi layer thickness were measured. Then the fraction of interfacial IMCs layer and residual Sn-Bi layer were calculated as shown in (a), the fraction of residual Sn-Bi layer in Co/Sn-10Bi/Co couple declined gradually as the bonding time increased. The residual Sn-Bi layer fraction of the Co/Sn-10Bi/Co couple bonded at 240 °C for 20 min was 67 vol.%. The residual Sn-Bi layer fraction of the Co/Sn-10Bi/Co couple bonded at 240 °C for 60 min was only 12 vol.%.The chemical composition of residual Sn-Bi layer (as shown in ) was analyzed by EDS. The result showed that the Bi fraction of residual Sn-Bi layer increased gradually as the bonding time increased. The phase constitution of residual Sn-Bi layer with different bonding time was also indicated in . The result showed that the residual Sn-Bi layer of Co/Sn-10Bi/Co couple bonded for 20 min, 30 min, 40 min, and 50 min was Sn-12Bi, Sn-19Bi, Sn-42Bi, and Sn-72Bi respectively. The Bi fraction of residual Sn-Bi alloy increased as the bonding time increased. During bonding, the Sn was consumed by Co as the gradual generation of CoSn3. Therefore, the Bi fraction of Sn-Bi in residual Sn-Bi layer increased gradually. It also should be noted that the residual Sn-Bi layer in (e) was consisted of CoSn3 IMCs and pure Bi as the atomic ratio of Co and Sn was about 1:3. It means that the Sn atom in Sn-Bi layer has been reacted by Co atom totally when the bonding time increased to 60 min.The thickness of CoSn3 IMCs layer and residual Sn-Bi layer in Co/Sn-10Bi/Co couple is shown in (b). It could be found that the CoSn3 IMCs layer in Co/Sn-10Bi/Co couple was thinner than that in Co/Sn-10Bi couple. The growth rate of CoSn3 IMCs layer might be inhibited by the gradually declining Sn concentration of Sn-Bi alloy in residual Sn-Bi layer.To identify the effect of Sn fraction in Sn-Bi solder alloy on the growth behavior of Co-Sn IMCs layer in Co/Sn-Bi/Co couple. The CoSn3 IMCs layer growth behavior of Co/Sn-xBi (x |
= 30, 50, and 70) couple was investigated. The interface structure of Co/Sn-30Bi, Co/Sn-50Bi, and Co/Sn-70Bi aged at 240 °C for 60 min was revealed in . The EDS test showed that the interfacial IMCs was CoSn3. The thickness of CoSn3 layer is plotted in . When the Sn fraction of Sn-Bi solder alloy decreased to 30 wt.%, the thickness of CoSn3 IMCs layer declined to 22.56 μm which was smaller than that of Co/Sn-10Bi greatly. Therefore, it can be derived that declining Sn in Sn-Bi solder alloy could suppress the growth of CoSn3 layer in Co/Sn-xBi couple.For Co/Sn-10Bi/Co couple, the Sn concentration of residual Sn-Bi declined gradually, due to the Sn consumption induced by CoSn3 IMCs layer growth. Then the growth of interfacial IMCs layer was hindered by the declining Sn concentration. Therefore, the CoSn3 IMCs layer thickness of Co/Sn-10Bi/Co couple was always lower, when compared with the Co/Sn-10Bi couple.The load-temperature curves of the four kinds of Co/Sn-10Bi/Co joints are shown in , the critical temperature that the load changed to 0 N from 1 N was indicated. The critical temperature of joint bonded at 240 °C for 20 min was 173 °C. The critical temperature of joint bonded at 240 °C for 30 min, 40 min, and 50 min was all under 160 °C. To explore the change in critical temperature, the composition of residual Sn-Bi layer was analyzed and is shown in . According to the Sn-Bi phase diagram in , the solid status point of Sn-12Bi solder alloy (in ) was about 170 °C. When the temperature reached to 173 °C, the solder alloy started to become semi-solid status and fractured with the effect of load. The residual Sn-Bi layer compositions of Co/Sn-10Bi/Co joint bonded for 30 min, 40 min, and 50 min were all indicated in . There is a semi-solid status for Sn-19Bi, Sn-42Bi, and Sn-65Bi from . When the temperature increased to the semi-solid region, the residual Sn-Bi layer became semi-solid status and fractured. Therefore, the fracture mechanism of Co/Sn-10Bi/Co joint bonded for 30 min, 40 min and 50 min was all similar to that of Co/Sn-10Bi/Co joint bonded for 20 min., the Co/Sn-10Bi/Co joint bonded for 60 min could hold the load of 1 N from 100 °C to 350 °C. The Bi + CoSn3 layer in Co/Sn-Bi/Co joint bonded for 60 min was un-continuous as demonstrated in . When the temperature was higher than the melting point of Bi, the Bi phase in the joint became liquid status. However, the joint could still hold the load of 1 N. It should be attributed to the partly connected CoSn3 IMCs phase in the Bi + CoSn3 layer of Co/Sn-Bi/Co joint bonded for 60 min. When the temperature was higher than the melting point of Bi (271 °C), the Bi phase particle in Co/Sn-Bi/Co joint bonded for 60 min became liquid. However, the connected CoSn3 IMCs was still solid and could function as a mechanical connection. Therefore, the Co/Sn-10Bi/Co joint bonded for 60 min could still hold the load of 1 N when the temperature was higher than 271 °C.The shear strength of five kinds of Co/Sn-10Bi/Co joints was shown in . The shear strength of joints bonded at 240 °C for 20 min, 30 min, 40 min, and 50 min were all higher than 50 MPa. However, the shear strength of joint bonded at 260 °C for 60 min was only about 15 MPa.. The typical fracture surface was shown in (c)) showed that the surface was CoSn3 IMCs. The cross section of fractured sample was shown in The fracture surface of Co/Sn-10Bi/Co joint hold for 60 min was rough as shown in The cross section microstructure of Co/Sn-10Bi/Co joint bonded for 60 min is shown in . Crack was found in Bi + CoSn3 layer. In the joints bonded for 20 min, 30 min, 40 min, and 50 min, there was residual liquid Sn-Bi alloy in the residual Sn-Bi layer during bonding. Therefore, the shrunk volume induced by the consumption of Sn and generation of CoSn3 IMCs could be filled by liquid Sn-Bi. However, for the joint bonded for 60 min, due to the shrunk volume that could not be filled by the solid Bi, the crack initiated during bonding. During shearing, the crack propagated and resulted in the joint failure and the mixture of Bi and CoSn3 IMCs on the fracture surface. Furthermore, the Bi phase was a kind of low strength phase The growth behavior of interfacial IMCs layer of Co/Sn-10Bi and Co/Sn-10Bi/Co couple has been studied in this investigation. The mechanical properties of Co/Sn-10Bi/Co joints were tested. Following conclusions were derived.(1) The thickness of CoSn3 IMCs layer increased as the aging time and temperature increased. The growth of interfacial CoSn3 IMCs layer of Co/Sn-10Bi was mainly controlled by chemical reaction mechanism. The growth activation energy of CoSn3 IMCs layer was 80.7 kJ/mol.(2) Due to the consumption of Sn, the Sn concentration of residual Sn-Bi layer in Co/Sn-10Bi/Co couple declined continuously. The growth rate of CoSn3 IMCs layer of Co/Sn-10Bi/Co couple was suppressed and was lower than that of Co/Sn-10Bi couple.(3) The critical temperature of Co/Sn-10Bi/Co joint that could hold a load of 1 N varied as the chemical composition of residual Sn-Bi layer changed. The test showed that the critical temperature of Co/Sn-10Bi/Co joint aged at 240 °C for 60 min with a residual Sn-Bi layer of Bi particle and CoSn3 was higher than 350 °C.(4) The Co/Sn-10Bi/Co joints aged at 240 °C for 20 min, 30 min, 40 min, and 50 min was between 58 MPa and 82 MPa. The fracture located on the interface of Co/Co-Sn IMCs layer. However, the Co/Sn-10Bi/Co joint aged at 240 °C for 60 min was only about 17 MPa. The fracture located in the residual Sn-Bi layer as the propagation of initiated micro crack in residual Sn-Bi layer.Wine glass sound excitation by mechanical coupling to plucked stringsWine glasses can be used to produce musical sounds using various excitation mechanisms. In this work a method for producing wine glass sounds is proposed, consisting of coupling a string to a wine glass. The coupled string-glass system produces sounds by transmitting vibrations from the string to the glass. The glass reacts sympathetically, much like sympathetic strings on instruments like the Sitar. Two methods for creating acoustic coupling between the string and glass are developed; one by direct contact between the two and one by using a custom designed coupling component. In the latter, a coupling mechanism transmits vibrations from the string to the glass while maintaining some geometric distance between the two. The coupling component is designed through an optimization process composed of two stages in order to maximize the intensity of the glass sound. The proposed coupling method can be used as the basis for designs of wine glass instruments, adding to the existing excitation methods of striking, bowing and rubbing. Some prototypes of such instruments are suggested here. These instruments may have the combined spectra and sound characteristics of both strings and wine glasses, offering timbres and playing techniques different from those of existing wine glass instruments.Wine glasses have been used for centuries as components of musical instruments. According to an historical review given by Gallo and Finger Development of string-glass coupling is inspired by sympathetic strings that exist in various musical instruments. In these, two coupled sets of strings are mounted on a single instrument. One set of strings (“the playing strings”) is directly excited by the player. Vibrations are then transmitted to a second set of strings (“the sympathetic strings”) which react and produce a sound In addition to string-to-string coupling, in some cases sympathetic strings are excited by non-string components. One such example is ‘Prongs & Echoes’, an instrument by designer Bart Hopkin In the next sections we describe the principles and development of several string-glass coupling mechanisms. We begin in Section by presenting two basic designs of instruments: one with direct string-glass excitation, and the second with an intermediate coupling component. Section describes the operating principles of both coupling methods. Sections describe the development of the coupling component using optimization algorithms. Section describes an experiment for evaluating the performance of the different mechanisms. Section is devoted to a discussion of the results.Two instrument concepts are suggested here in order to demonstrate the potential of string to wine glass coupling. The first, illustrated in , is based on the shape of a harp. The string-glass coupling is achieved by direct contact. This approach is explored in Section . The figure shows an instrument with 15 strings, each coupled to a different wine glass. The wine glasses are placed on both sides of the frame, replacing the sound box and pillar in a typical harp. The second concept, illustrated in , couples the strings to the glasses using a coupling component. The figure shows an instrument composed of 7 coupling components positioned on top of a sound box and 7 wine glasses positioned adjacently. Each coupling component couples one or more strings to a single glass. The existence of the sound box is made possible due to the distance between string and glass permitted by the coupling component. This coupling mechanism is studied in Sections Consider a tight string directly touching the surface of a household wine glass, as shown in . The string is fastened to a frame equipped with a tail-piece and a nut. The glass, free to vibrate, touches the string near the string’s end and exerts an upwards force on the string. The glass thus performs a similar role to that of a bridge on a string instrument. The string is free to vibrate in the section between the nut and the glass’ contact point. In initial tests we found that the preferred contact point is at the widest part of the glass. Measurements of the produced sounds are described in Section Direct contact coupling is a feasible basis for design of such musical instruments, however it requires direct contact between the string and the wine glass. This may limit design options, which prompts the need for a coupling method that allows a physical distance between the two components.In order to create a certain physical distance between the strings and the wine glasses, a coupling component (‘bridge’) is used to mount the string and to transmit the vibrations to the glass through a contact point. A generic bridge coupling a string to a wine glass is shown in . Clearly, the magnitude of the mechanical impedance of the bridge has an effect on the produced glass sounds. This impedance is adjustable by introducing geometric changes to the bridge. Simulations verify that when the bridge impedance is lowered to the order of magnitude of the glass impedance, the sound intensities produced by the glass increase. shows the simulated glass transfer impedance along with the transfer impedance of a manually designed bridge prototype, used in early stages of this research. Note that the bridge impedance is considerably higher.If the bridge design is not performed properly, sounds produced using the bridge may be weaker than those produced by direct coupling, as indeed was shown in preliminary simulations and experiments. This prompts the need for a quantitative design process, which can optimize the performance of the coupling component.In the following two sections we explore the design of a coupling component using a two-stage optimization process. First, an initial prototype is developed using the material distribution method. Then, this prototype is refined using the shape optimization method. In order not to limit the design possibilities of future instruments, the process presented here assumes a general case where a single glass is expected to generate responses over a large range of excitation frequencies. It is envisioned that for specific future designs, in cases where the glasses will be expected to respond only to specific notes or frequencies, the optimization process will be repeated with suitable criteria.A thorough description of the material distribution method is given by Bendsoe and Sigmund . Note that with any coupling method, the coupling strength may differ between horizontal and vertical string movements. For different instruments, the string movement is determined by the playing technique The material distribution method generates a new structure by way of creating a spatial elasticity function (Young’s modulus) covering the entire domain, Ω. The new structure created within the boundaries of Ω is represented by points containing material having its nominal elasticity. Points excluded from the structure (void) are represented as being composed of zero elasticity material. The material distribution method can also yield models containing points of intermediate elasticity values. However, intermediate elasticity values are difficult to manufacture by traditional methods. Thus, an approach was needed which would discourage the optimization process from seeking such intermediate values. Such an approach is the Solid Isotropic Material with Penalization (SIMP) Note that CSTR is linear in α(x,y) while Young’s modulus, E, is proportional to α(x,y)p. At each point, α(x,y) contributes to both CSTR and E. However, since p>1, points where 0<α(x,y)<1 contribute a disproportionately lower change to E than to CSTR The current optimization stage was performed in a two-dimensional space. A wine glass cannot be fully modeled as a two dimensional object , an objective function was chosen with the aim of matching the magnitude of the bridge impedance (which is mostly purely imaginary with -Π2 phase) to the average magnitude of the glass impedance (which is mostly purely imaginary with +Π2 phase). The glass is therefore accounted for in the optimization via its impedance. Let b∈B denote a bridge layout, where B is the set of all possible layouts. Let f denote the string excitation frequency. The glass transfer impedance is defined by a force Fbridge(f;b) measured on the bridge contact point divided by the velocity Vbridge(f;b) measured on a single point on the rim. The average glass transfer impedance over the frequency range is Z¯glass. The bridge frequency-dependent transfer impedance is Zbridge(f;b), defined by a force Fglass measured on the string excitation point divided by the velocity Vglass measured on the glass contact point. shows the applied forces and induced velocities defining both impedances.The difference in magnitudes is given byAveraging the magnitude difference over a set F of discrete frequencies, F=100,200…1000: The optimization goal is defined as finding b̂ that minimizes Z¯diff(b): resulted in a two dimensional layout for a new prototype of an optimized coupling component, as shown in a. A refined shape labeled ‘O1’ is shown in b. Shape O1 is extracted by thresholding b̂ at 0.95 and smoothing the edges, retaining full elasticity points representing the optimized shape and omitting the zero elasticity points representing the void. The O1 prototype served to initialize a second optimization stage, aimed at determining a final shape, as discussed next.The shape optimization method is the algorithm used in the second optimization stage and is described in detail by Bendsøe and Sigmund , includes the coupling component and a wine glass. The wine glass is based on actual dimensions of household wine glasses, to be used later in the physical implementation. An initial prototype such as the one created by the material distribution method (O1) is used as the coupling component. The initial coupling component O1 is extended to a third dimension by extrusion, with a fixed thickness of 3 mm. Afterwards, the optimization was performed over a domain of 2D shapes extruded to this fixed thickness. As in this configuration the shape optimization method’s execution times are about half than those of the material distribution method, a higher resolution of 50 Hz was chosen, with an identical 100–1000 Hz frequency range. As with the material distribution method, additional sporadic tests using intermediate frequencies generated similar end results and offered little contribution to the final shape. The bridge material properties, wood alignment and string excitation model are as described in Section Mathematically, the shape is parameterized as follows: The outer contour, Õ, is embedded with N fixed anchor points xianchor, as shown in . From each anchor point, a ray Ri is projected at a fixed direction towards the inner contour of the coupling component, Ĩ. The intersection of Ri and Ĩ results in N intersection points, xiint=Rp∩Ĩ. The distances, di=xianchor-xiint are the design variables. The algorithm changes the distances, thus changing the position of each xiint along Ri. Once the positions of xiint are changed, the inner contour Ĩ is replaced by a spline connecting all intersection points at their new positions. As a result, the shape of the bridge is tuned.The objective to be optimized is taken to be maximum glass displacements, because larger displacements produce higher sound intensities. All wine glass modes are characterized by having anti-nodes on the rim, with some higher modes characterized by additional anti-nodes on the surface, as demonstrated in . Therefore, we measure displacement using a closed line integral over the rim, necessarily covering anti-node displacements contributed by all modes Let us average Drim(f) over a set of discrete frequencies, F2=100,150…1000 |
Hz:The optimization seeks a set β=d1…dN which defines a new bridge β̂ that maximizes D¯(β): The second optimization stage used N |
= 7 anchor points and the material properties of Ipe wood. It resulted in a new set of values for the section lengths, defining a new spline and a new optimized bridge, as shown in . The length of most rays was reduced, in some cases by as much as 20%. The newly created bridge, which was the final product of the optimization process, was labeled the optimized bridge.The optimized bridge was tested by simulation and compared to the Direct Contact coupling method. Each mechanism was simulated separately using the same wine glass model and a frequency sweep over 20–3000 Hz, covering all notes in the range up to F#7 (2959.96 Hz). shows the normalized simulated displacements of the glass rim produced by each coupling mechanism. The average simulated glass rim displacements over the simulated frequency range generated by the optimized bridge are about 75% larger than the displacements generated by direct contact. Experimental results for the same comparison are described in Section . Note that the curves have a similar overall shape, with the resonance frequencies of the optimized bridge-glass system occurring at higher frequencies. The shift of the first resonance frequency is about 100 Hz, with the shift progressively increasing for each subsequent resonance frequency. The 3rd resonance frequency of the optimized bridge-glass system is split into two frequencies, forming a doublet.To complement the findings of the simulations, an experiment was conducted using the setup shown in . The experiment compared wine glass sound intensities produced using the two different coupling mechanisms.A custom built experimental rig held the glass and string in place. Each mechanism was tested with three household mass-produced wine glasses, shown in . The glasses were used without tuning or alteration. Two of the glasses (labeled Glass1a, Glass1b) were of the same make and model and seemingly identical. These glasses had different lowest resonance frequencies, (438 Hz and 547 Hz respectively), due to minute differences in thickness or material properties. The geometry of these glasses was used as a model during the optimization process. The third glass (labeled Glass2) was of a different model with a different geometry - shorter and wider. Glass2 had the lowest resonance frequency at 434 Hz. Steel strings of various gauges were used, tuned to frequencies of musical notes in the range of A1 (55 Hz) to E5 (659.25 Hz). The string and wine glass were coupled by each of the mechanisms. Each measurement consisted of plucking the string and then quickly muting it. The string sound and glass response were recorded using a microphone placed 5 cm above the glass rim. While various papers describe the development of mechanical plucking systems shows the intensities measured for Glass1a using both coupling mechanisms.The normalized average sound intensity was calculated for each glass and excitation method as follows: for each glass, let It be the intensity of the sound produced by excitation at note t. Let M be the set of all notes that produced intensities above the background noise, per glass. Let OB and DC be the optimized bridge and direct contact excitation methods, respectively. The maximal sound intensity measured per glass is defined as:The normalized average sound intensity per glass, per excitation method, is defined as:In addition, the median Imed of the normalized sound intensities was calculated for each glass and excitation method. The results are shown in The results for Glass1a and Glass1b showed similar trends, with the optimized bridge generating the highest average and median glass sound responses. Glass2, which is different in geometry from the model used in the optimization process, showed the opposite trend.For all glasses, the loudest intensities were produced when the string’s fundamental frequency or one of its overtones closely coincided with the glass resonance frequency of mode (2, 0). This mode is characterized by having 4 anti-nodes on the rim, as shown in a. The resonance frequency of mode (2, 0) is most usually the strongest resonance frequency in a wine glass spectrum. For example, the (2, 0) mode resonance frequency of Glass1a is 547 Hz. String excitation at C#5 (554.4 Hz) maximized the sound intensity produced by this glass relative to all other excitation frequencies. In addition, exceptionally high responses were produced by excitation tones which coincided with glass resonance frequencies of higher normal modes.A spectrogram of the combined sound of a string and a wine glass (Glass2) coupled by direct contact is shown in a. The string is tuned to E2 (82.41 Hz). A spectrogram of a classic guitar playing E2 is shown in b for comparison. The partials contributed by the wine glass are especially visible at 434 Hz, 990 Hz and 2267 Hz. The glass was separately shown to have partials at these frequencies. Note that some glass partials closely coincide with string harmonics. For instance, the strong glass doublet at 990 Hz and 998 Hz coincides with the string’s 12th harmonic at 984 Hz, as is clearly visible in the spectrogram. The actual sound recordings are found in the attached sound clips: The above data shows that the optimized bridge does indeed produce higher sound intensities than the direct contact method when used with glasses that have an identical geometry to the model used in the optimization process. However, with a considerably different glass such as Glass2, the optimized bridge does not offer an improvement, in terms of sound intensity, over the direct contact method.Future research could involve extending the methods described in this paper by generalizing the optimization stage to include glasses of a larger variety (different geometries, sizes and materials). Additional experiments will be needed in order to test the coupling methods over a large selection of such glasses. Furthermore, the affect of different string characteristics, such as impedance, material and gauge on the glass reaction could be explored in both experiment and simulation. Another possible direction of research is the usage of modern methods such as 3-D printing for bridge fabrication. Such methods might allow designing bridges of more elaborate geometries and from different materials.Each of the methods described in this research may be used as the basic operating mechanism for future instruments. The design may limit the choice of glasses to a specific geometry in order to fully use the capabilities of the optimized bridge. An alternative approach might require the development of additional optimized bridges, custom fitted to various glass geometries.In conclusion, we have explored a new method of exciting wine glass sounds: coupling to a plucked string. Two coupling methods were proposed: direct contact between a string to glass or using a custom designed coupling component. An optimized coupling component was developed using two optimization methods and was shown to increase the intensity of the generated sounds. Each coupling method provides a different approach for the design of new wine glass based instruments. It is our hope that the coupling methods developed in this research will be used as the basis for the design of future wine glass instruments, which will combine the sounds of string instruments with the rich sound spectra of wine glasses.Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apacoust.2017.03.016Direct observation of shear–induced nanocrystal attachment and coalescence in CuZr-based metallic glasses: TEM investigationIn-situ tensile straining tests were performed in a transmission electron microscope (TEM) to analyse the deformation processes in CuZr-based metallic glasses and to directly observe the phase transformation occurrence. We report evidence of shear induced coalescence of nanocrystals in the vicinity of deformed regions. Nanocrystals grow in shear bands, come into contact, being attached and progressively coalesce under applied shear stress.Owing to their attractive properties such as extremely high strength, high hardness, large elastic limits, and excellent superplastic formability Since metallic glasses alloys have not been in thermodynamic equilibrium, supplying such alloys with mechanical energy in the form of deformation can promote various phase transformation routes. Chen, He and Shiflet We present the results of unique in situ observations, inside a transmission electron microscope (TEM), of nanocrystals formation in CuZr based metallic glass and subsequent attachment and coalescence of these nanocrystals during progressive tensile straining in TEM. These structural observations could establish a new self-toughening mechanism of CuZr-based bulk MGs underlying shear-induced coalescence of nanoparticles in deformed region.Binary Cu50Zr50 was used as a model material owing to its low brittleness and considerable plastic strain (≈50% in compression The obtained ribbon was cut into rectangular forms with 4.8 mm in length, 1.8 mm in width and thinned by the ion milling (PIPS, Gatan Model 691) with a liquid nitrogen-cooled stage to produce a small central hole, and subsequently mounted on a tensile straining device for in-situ deformation in a 300 kV JEOL 3010 transmission electron microscope. The ion beam energy used for sample thinning was 3.5 keV and the milling angle was about 6–7°. Under these ion milling conditions, no heating or radiation induced crystallisation can occur as previously reported by Sun et al. http://www.sciencedirect.com/science/article/pii/S1359646206001643(a) shows a picture of the in-situ tensile holder used in TEM and 1(b) the tensile sample fastened to a template using small bolts. In-situ TEM observations were carried out with the rate of 1 μm/s, and stopped several times to investigate changes of microstructure during the different steps of tensile straining. illustrates the initiation of a shear deformation zone (indicated by arrows) at low magnification with the thickness of 15–20 nm formed in front of the microcrack tip. The direction of the initiated microcrack was found to be perpendicular to the loading direction. The shear bands initiate from the thin region of a TEM sample and propagate to the thick region. A few bright parts suggest the presence of nanocrystallines of 3–5 nm size. show that the deformation induced a significant microstructural changes. The formation and growth of large number of nanocrystallites (B2–CuZr (a) and (b) show TEM images of the notch-tip area after consecutive tensile straining whereas (c) show another blunted crack in front of crystals being attached. These images demonstrate how nanocrystals come into contact and progressively coalesced under shear (as designed by arrows in )(b) and (c). The formation of the nanocrystallites and their subsequent coalescence are undoubtedly induced by shear stress because the crystallites were only observed within the shear bands and cannot be found in the surrounding regions (outside the bands). (a) taken from another deformed area (shear band) confirms the existence of the “giant” nanocrystals which are larger and denser than the onset of deformation. High magnification of this area ((b)) shows the dispersion of attached-like non-spheroidal crystallites in glassy matrix. The coalescence of nanocrystals (as indicated by arrows in ) produces a large grain that may hinder further crack advance as shown in (c) and has been also reported elsewhere (a) and (b)) show boundaries within the particles, consistent with contact between the crystallites. Some of the large nanocrystals reveal a contrast, which can be attributed to twinning (b) shows many grains ahead of the crack tip being attached after additional straining. The HRTEM images of (a) resulted from the deformed sample shows the distorted lattice fringes of nanophases which can be regarded as evidence of the nanocrystal coalescence process prevailing the plastic deformation of the considered marginal glass.The formation of crystalline phase within the narrow shear bands during deformation of metallic glasses (known as deformation-induced crystallization) is not new and has been reported in many published works and the main consideration reasons are the increase of local atomic mobility and diffusion inside shear bands As it is well known, shear in metallic glasses generates free-volume and heat, reduces the viscosity and leads to liquid-like behaviour in the vicinity of shear bands sketches the mechanism process of shear-induced coalescence of nanocrystallites in the deformed region in light of the general steps of coalescence phenomenon The coalescence time, tc, outlined the time during which the inter-crystallites distance decreases to the critical value at which the merger of particles can be obtained. This time depends on the particle size, the local shear rate and the interfacial tension. The regime where the coalescence is prevailing can be characterized by the capillary number, Ca given by Ref. With ηm is the amorphous matrix viscosity, γ˙ is the local shear rate, R is the crystallites radius and σ is the interfacial tension. For particles with 2R ≈ 10 nm, ηm ≈ 103 Pa s The deformation mechanism of CuZr-based metallic glasses and its phase transformations have been investigated by in-situ straining test in TEM. We found that the strain induces in situ nanocrystallization and subsequent attachment and coalescence of these nanocrystals. The shear-induced precipitation and coalescence of nanocrystals in shear bands is more prominent for a set of favoured factors such a low shear rate and low viscosity in shear bands. This novel deformation mechanism, which is uncovered by our TEM observations, led to the delocalization of the plastic deformation and promoted a method to compensate strain softening.In addition, the present investigation may be useful to design advanced bulk metallic glasses that display higher plastic deformation through a new self-toughening mechanism.Friction and wear characteristics of various prosthetic materials sliding against smooth diamond-coated titanium alloyDuplex coating with an external nano-smooth fine-grained diamond (SFGD) layer, a thin titanium carbide interlayer and a carbon diffusion layer have been deposited by PACVD on titanium alloy at 600 °C. These coatings have already shown low wear against various counterfaces in ambient air. They might have potential applications in the field of prostheses because of their high resistance to corrosion and wear.Rotating pin-on-disc friction tests have been carried out here at room temperature in ambient air, Ringer’s solution and synthetic serum to approach the in vivo wear conditions, with a sliding velocity of 0.1 m s−1 and a normal load varying in the 0.5–13 N range. Diamond-coated Ti–6Al–4V samples were used as the discs. The counterface materials were hemispherical pins fabricated from diamond-coated Ti–6Al–4V, Ti–6Al–4V and Co–28Cr–6Mo alloys, 316L steel and UHMWPE. During the sliding tests, the total wear heights were measured and recorded on-line. After the tests, the final mean wear rates of the pins were determined from the diameter of their wear scars. The friction coefficients and wear rates of the different materials allow one to compare their performance and to demonstrate the potential of the nano-smooth diamond coatings for biomechanical applications.While ceramic parts are usual components of orthopedic implants, the use of ceramic coatings on metallic alloys for optimizing the wear resistance of sliding surfaces is restricted. Only zirconia coating on zirconium alloy and diamond-like-carbon with titanium carbide and titanium (carbo)-nitride sub-layers are currently proposed The present study deals with the interest of using such coatings in various media. Some characteristics of the diamond-coated Ti–6Al–4V alloy are presented first. The tribological behavior of these diamond-coated Ti–6Al–4V samples is then reported when sliding against different counterface materials: diamond-coated Ti–6Al–4V, Ti–6Al–4V and Co–28Cr–6Mo alloys, 316L steel and UHMWPE. Rotating pin-on-disc friction tests have been carried out at room temperature in various media: ambient air, Ringer’s solution and synthetic serum to approach the in vivo wear conditions. The friction coefficients and wear rates of the different materials allow one to compare their performance and to demonstrate the potential of the nano-smooth diamond coatings for biomechanical applications.Disks with a diameter up to 34 mm and a thickness of 5 mm were machined from commercial Ti–6Al–4V alloy. They were ground on SiC papers from 500 to 4000 grit and finally polished with diamond pastes. The resulting root mean square (rms) surface roughness was about 5 nm. They were then ultrasonically seeded following a well-known procedure Diamond coatings were characterized by Raman spectroscopy, atomic force microscopy (AFM), X-ray diffraction (XRD) and scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDX). Micro-Raman study was carried out with a DILOR XY spectrometer, in backscattering configuration, using a 514.5 nm Ar incident laser beam, with 50 mW power and a spot size of 1 μm. Raman spectra allowed characterization of the quality of the different diamond coatings by taking into account the influence of the diamond grain size and the resonance Raman effect |
μm AFM images obtained in tapping mode. The variation on the whole surface was about ±10%. The different crystalline phases before and after the diamond deposition were identified by XRD performed with a Cu Kα beam, with a Philips X-ray diffractometer. Their intrinsic mechanical properties were determined by nano-indentation and Brillouin light scattering (BLS) The friction and wear tests were carried out using a rotating pin-on-disk tribometer with a fixed pin. Diamond-coated Ti–6Al–4V samples were used as the disks. The counterface materials were hemispherical pins, 6 mm in diameter, fabricated from commercial Ti–6Al–4V and Co–28Cr–6Mo alloys, 316L and UHMWPE. The radius of curvature was 10 mm in most cases. Because of some difficulties in the manufacturing of the UHMWPE pins, their radius of curvature was about 12 mm. The friction tests were conducted at a sliding velocity of 0.1 m s−1 and a normal applied load, L, in the 0.5–13 N range. The tangential force was measured using a piezo-resistive miniature sensor fixed on the substrate holder. The total wear height, including the decrease of both the pin height and depth of wear track on the disk, was measured during the test by a displacement measuring system based on the eddy-current loss principle. The tests were conducted in ambient air at relative humidity in the 40–60% range, in Ringer’s solution and synthetic serum (Plasmion® from Rhône Poulenc which contains 25 g l−1 proteins).After the friction experiments, the worn surfaces were examined by SEM, AFM and studied by Raman spectroscopy. The final worn volumes of the disk and the pin were evaluated from cross-sectional profiles of the wear tracks, and from the diameter of the wear scars, respectively. The mean wear rate, WS, was determined from the following relation WS=V/DL, where V is the worn volume in mm3, L the load in N and D is the sliding distance in m.Contrary to the classical polycrystalline diamond coatings, the SFGD coatings exhibit a smooth surface as shown in . Their surface roughness varied in the 15–35 nm range as a function of the deposition conditions (). The lowest surface roughness is obtained when more sp2-hybridized carbons are incorporated in the coatings. It is important to note that the roughness does not vary with the coating thickness. The columnar or renucleated microstructures can be controlled, with fine grains in both cases and various [sp3/(sp2+sp3)] ratios, ranging from 70 to 95%. It has been shown, from Raman spectroscopy and XRD that all these coatings contain diamond with sp2-hybridized carbon incorporated in amorphous and polyaromatic entities without any appreciable graphitic phase shows especially the variation of the surface tension components.Another important characteristic of these coatings on titanium surfaces is related to the relatively high diffusion coefficients of carbon in titanium and in titanium carbide at moderate temperature. They permit one to obtain a duplex coating with an external diamond layer, a thin titanium carbide interlayer and a carbon diffusion layer in the α- (and β-) solid solution(s). The titanium carbide phase can be seen on the cross-section in , as a clear sub-layer. Diffusion in the carbon–titanium pair was studied at moderate temperature, both in pure titanium and Ti–6Al–4V shows the calculated concentration profile of carbon in the coating obtained on pure titanium after 12 h at 600 °C. This figure clearly shows the incorporation of carbon in a thin titanium carbide phase and in the α-solid solution, as reported in the inset in . With the Ti–6Al–4V alloy, the diffusion depth in the alloy is greater, about 400 μm in the same conditions and the titanium carbide phase is thinner accordingly. The formation of this thin titanium carbide phase and of the diffusion layer in the substrate allows very strong bonding of the diamond layer to be obtained while avoiding the brittleness of a thick titanium carbide layer. This type of duplex coating with an internal diffusion layer, a strongly bonded carbide interphase with an external diamond-based layer appears particularly attractive for applications requiring no risk of delamination. Scratch adhesion tests and indentations under heavy load are being carried out on these SFGD coatings on Ti–6Al–4V alloy. Ager and Drory The hardness of the SFGD layers and their Young’s modulus vary as a function of the [sp3/(sp2+sp3)] ratio. High values are however always obtained (), in the 70–90 and 600–900 GPa ranges, respectively In a first embodiment, both bearing surfaces of orthopedic implants could be protected with a nano-smooth diamond coating. With a normal load of 13 N, the friction coefficient of Ti–6Al–4V pin and disc both diamond-coated is low in ambient air, about 0.06, even if some titanium alloy arises in the contact at the pin tip after wearing completely through the coating on the pin, due to the difference between the areas of the two counterfaces (). Otherwise, still better results would be obtained. The friction coefficient measured in the Ringer’s solution is about 0.03 while it is slightly higher in the synthetic serum with a mean value of about 0.08. The initial Hertzian contact pressure, calculated by neglecting the influence of the thin coating and the surface roughness, was about 460 MPa in all cases. The final contact pressures were in the 60–260 MPa range, depending on the pin wear.). In that case both the counterfaces were still diamond-coated at the end of the test.These results show that two nano-smooth diamond-coated surfaces can be used for biomechanical applications. The wear rate is very low, despite relatively high contact pressures, and the self-polishing mechanism allows one to avoid any risk even when one coating has been worn as observed on the pin tested in ambient air. This is due to the good tribological behavior of metallic alloys against polished diamond coatings as will be shown in the following paragraphs. The as-deposited smooth diamond coatings also can be polished by other techniques to the 3–5 nm range because of their initial low roughness. They can then be tested against softer counterfaces.In a second embodiment, orthopedic implants could utilize a metal-on-diamond coating contact. In ambient air with a normal load of 13 N, the friction coefficient of the polished coating sliding against the Ti–6Al–4V alloy is reported in . It varies also in the 0.05–0.06 range. Even the as-deposited coatings allow fairly good results to be obtained against Ti–6Al–4V alloy due to their smoothness (). In the Ringer’s solution and the synthetic serum, the friction coefficients are in the 0.03–0.06 range. A very attractive property of these smooth and polished coatings is due to the very low wear of the counterface materials. In ambient air, the specific wear rate of the Ti-alloy against the as-deposited and polished coatings could be measured. On the polished coatings, it is always low ( shows that, on the as-deposited coatings, the initial wear rate is somewhat high but it decreases after an accommodation period of about 400 m. In this test, the average wear rate was 4.5×10−9 |
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