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= 3 mm. The Young’s modulus and Poisson’s ratio of the substrate material were taken to be 200 GPa and 0.3, respectively.For the analysis of strain energy release rate of the 4 PB specimen, a finite element (FE) model has been constructed and solved using the software package ABAQUS 6.5. The symmetry about the midsection of the bend specimen depicted in allows the requisite solutions to be obtained by considering one half of the specimen (). Based on the actual situation, the interlayer in was subdivided into three layers in the present FE model. They are adhesive layer, top coat (TC) layer and bond coat (BC) layer. The mechanical properties of these layers as input data are listed in The bend specimen is discretized using two-dimensional eight-noded isoparametric elements. The size of elements varies along the thickness of the bend specimen with a very fine mesh used near the crack tip. The crack tip is modeled with a ring of collapsed quadrilateral elements to capture the singularity of stress and strain. The roller support at the inner loading line is constrained to fix the displacement in the vertical direction, whereas the symmetry is enforced by inhibiting horizontal displacements along the midsection. The crack surfaces are traction-free. The setting scheme of crack propagation path during bend loading can hence be examined.The cross sectional microstructures of the as-deposited coatings showed that a lot of pores and curved inter-splat microcracks distributed uniformly in both the top coat and bond coat layers, as is shown in a. In the top coat layer, the curved microcracks were longer and sharper in the horizontal direction than in the vertical direction, whereas there was not such a difference in the bond coat layer. Closer examination indicated that the top coat was composed of lamellae, typically several micrometers thick, as is shown in b. The measurement of Raman spectra indicated that there were tetragonal phase and a small amount of monolithic phase of ZrO2 in the top coat layer.During bend loading, the crack evolution and propagation path were observed on one polished surface of the specimen using an optical microscope. It was found that the onset of the crack growth occurred from the initial fatigue pre-cracks. The delamination cracks were always extended within the top coat layer close and roughly parallel to the interface between the bond coat and top coat layers, as is shown in a. The crack propagation path was slightly wavy, which was caused by the curved splat structure. The entire crack usually propagated within 10–60 μm away from the interface. Occasionally, the crack approached to a plane very near the interface between the bond coat and top coat layers, but it did not enter the interface, as is shown in zone B in a. This crack trajectory is consistent with the failure mode most frequently observed in plasma-sprayed TBCs Closer examination indicated that the delamination cracks propagated predominantly along inter-splat boundaries. Multiple, parallel short cracks were found in the crack tip region. Between the overlapping parallel cracks there were the unbroken ligaments, which bridged the parallel cracks, as is shown in b and c. The crack bridging existed even in the wake zone far behind the main crack tip although it was more sparsely separated (a). During the crack growth, some previously formed ligaments began to fracture under the increased bend loading, as is shown in a. With the fracture of bridging ligament, linking of the parallel cracks became visible. A typical cracking surface of the bend specimen is shown in b. From this figure, two kinds of cracking surfaces can be easily observed. They are relatively smooth and curved inter-splat cracking surface and rougher intra-splat cracking surface. The smooth and curved morphology of the former reflects the inter-splat boundaries. This indicates that the cracking occurred along the inter-splat boundaries, which is consistent with the observed cross sectional crack path (). The linking of inter-splat boundary cracks became more evident with the increasing of crack length and the opening of cracking surfaces. The morphology of rough intra-splat cracking surface, which exposed the internal fine structures of the spraying splats, suggested that inter-splat boundary cracks on different planes linked to each other by intra-splat cracking of bridging ligaments, as is shown in ) indicate that the bridging ligaments were prevalent in the TBCs system under the initial bend loading, and then some of them would fracture with further increase of bend loading.The maximum load in each loading–unloading cycle was used to calculate the strain energy release rate at the corresponding crack length. A typical curve of the measured strain energy release rate as a function of crack extension is shown in . An obvious rising R-curve is visible. Multiple specimens for the measurement demonstrated the same behavior.The R-curve, starting at a very low value, increased rapidly over a crack growth distance of about 6 mm, and then gradually rose to a steady state value, GSS∞, about 170 J/m2, at a crack length of about 8 mm. The steady state value of GSS∞ obtained in this work was close to the strain energy release rate measured in Refs. Although the tested materials were all composed of the standard composition (7–8 wt.% YSZ), the coating process and spray parameters might be different, which caused the variation in TBCs’ microstructure. As fractographic observations indicated in Ref. b, there were many smooth surfaces and fresh rough surfaces on the fracture surface. The smooth surfaces were the faces of micropores, or inter-splat boundaries. The rough surfaces were formed as a result of discrete trans-lamellar microcracks between neighboring micropores or inter-splat boundaries. Macro-fracture occurred when sufficient micropores or inter-splat boundaries have been connected by trans-lamellar micropores to separate that region from the remainder of the coating. Therefore, the micropores or weak splat boundaries acted as the crack initiation site and contributed to the major reductions in fracture resistance of TBCs. Thus the size, shape, orientation and size distribution of pores, and porosity level should be responsible for the difference in the reported fracture toughness.It should also be argued that different test methods might generate different results. A notched specimen (2.6 × 4.6 × 3.5 mm3) with a notch depth of 1.8 mm was used in wedge opening load technique in Ref. The rising R-curve measured in the present research was attributed to the formation of bridging zone. In the wake zone behind the main crack tip there existed many bridging zones where there were unbroken bridging ligaments. The bridging of cracks in the wake zone prohibited crack opening and contributed to the toughening. The length of each bridging zone increased with crack growth, and the bridging-caused toughening contribution was enhanced accordingly. As a result, a rising R-curve formed. With a further increase in crack length, some unbroken ligaments began to fracture. Gradually, the bridging zone approached to a saturation state, and the size of this zone attained the saturation. Thus, the toughness reached its steady state value.The evolution process of the bridging zone under bend loading can be modeled using the finite element method. As is shown schematically in , a bridging ligament (region between the dotted lines in ) was set between two cracks. The width (L) and number of bridging ligaments (BL) were changed during crack growth simulation. As is shown in , it was assumed that there were six bridging ligaments emerging successively during the crack propagation. Every new emerged bridging ligament lied behind the main crack tip about 1 mm. With the continuously emerging of new bridging ligaments during the crack propagation, the width of previously formed ligaments increased progressively until they fractured. In addition, a finite element model without crack bridging was also built for comparison.For both the considered finite element models, the strain energy release rate was calculated once the crack length (the distance from the midsection to the main crack tip) reached 2 mm. Hereafter, the strain energy release rate was calculated again following each crack extension of 1 mm. The simulation results are shown in that, for the model with crack bridging, the predicted results have a similar trend to that of the experimental results although the absolute values of them are slightly different. When the simulated crack length was less than 5 mm, the strain energy release rate increased continuously. Such an increase in the simulated value corresponded to the continuous increase in the number of bridging ligaments along the crack propagation path, which shielded the crack tip from the far-field loading. As is shown in , the bridging ligaments bore the bending load partly. When the simulated crack length was larger than 5 mm, the strain energy release rate became stabilized due to the balance between the emerging of new bridging ligaments and the fracture of previously formed bridging ligaments. In contrast, for the model without crack bridging, the strain energy release rate did not obviously increase with crack extension (As is demonstrated and analyzed above, the rising crack growth resistance curve of plasma-sprayed thermal barrier coatings strongly depends on the crack bridging behavior, and the bridging behavior relies on the microstructure of these coatings. Thus, control of the coating microstructure plays an important role in improving the crack growth resistance in the thermal barrier coatings system.The interfacial crack growth resistance in APS ZrO2–8 wt.% Y2O3 TBCs was studied using the sandwiched four-point bend specimen. Delamination cracks always propagated in the top coat layer but tended to approach to the interface between the bond coat and top coat layers. The strain energy release rate increased with crack extension, showing an obvious rising R-curve behavior. The rising R-curve in the APS TBCs was caused by the crack bridging in the wake zone, which shielded the crack tip from the far-field loading.Non-linear cable response to multiple support periodic excitationThe coupled non-linear differential equations of cable vibration due to transverse and vertical multiple support excitations are formulated. The phase difference between the input support excitations at cable ends is considered in the formulation of the equations of motion. Damping is not considered in this analysis. The spatial problem is solved by Galerkin method using a two degree of freedom model for the cable. The temporal problem is solved using the method of multiple time scales to obtain the steady state solution. The stability of the steady state solution is examined. Numerical examples are presented to compare the results with those of a finite element analysis. The effects of cable sag and phase difference between the input support excitations on the response are analyzed. The results show good agreement between the analytical and numerical solutions especially near the resonance frequency. Considering phase differences between the support excitations at the cable ends is important because in this case the anti-symmetric modes are excited.The dynamic analysis of cables has attracted the attention of several researchers. Numerical techniques such as the finite element and the finite difference methods were used extensively to analyze the dynamic behaviour of cables A major difficulty that is encountered in the dynamic analysis of long span cables, such as transmission line cables, is that during earthquakes there is a time lag between the input ground motions at different supports. The system is subjected to multiple support excitation. The tower was found to respond to the seismic excitation mainly in its own fundamental mode of vibration The free vibration characteristics of cables were determined analytically in two and three dimensions. In earlier studies, Irvine and Caughey The objective of this study is to evaluate the effect of multiple support excitation on the response of transmission line cables. This formulation is applicable to cables with small sag to span ratios where a parabolic approximation of the static equilibrium position can be assumed. This represents the majority of transmission line cables. The support motion is applied in both the vertical and transverse directions. The equations of motion are solved using Galerkin method for the spatial problem and the method of multiple time scales for the temporal problem Consider the dynamic equilibrium of a single cable hanging in a vertical plane between two supports at the same level as shown in . The cable is subjected to transverse and vertical support excitations v1, v2, w1 and w2. Damping of the cable is not considered in the analysis as the damping ratio of transmission line cables is very small where m is the cable mass per unit length; T is the static cable tension; E is Young's modulus of the cable material; A is the cross sectional area; u, v, and w are small displacements in the x, y, and z directions, respectively, as shown in . The additional dynamic cable tension is R and S is the tangent to the cable coordinate at the point of interest.Assuming small sag to span ratio, which is the actual case in transmission line cables, then dS≈dx and T≈H. Rao and Iyengar and taking into account the static equilibrium of the cable, the following three dynamic equilibrium equations are derived:Neglecting the longitudinal inertia term (ü) and following the same procedure as used by Luongo et al. The implication of neglecting the contribution of the longitudinal inertia is that the tension along the cable is a function of time only which agrees with the results of the finite element analysis carried out by Aziz et al. with respect to x, with the boundary conditions u(0,t)=u(L,t)=0, results in: can be simplified to the following form:Since the cable response to seismic ground motion acting in the longitudinal direction is negligible compared to its response to the vertical and transverse components of ground motion, the longitudinal component of ground motion is not considered in this analysis. The two components of displacement v(x, t) and w(x, t) of a cable subjected to a ground motion at both supports acting in the y and z directions as shown in where vs(x, t) and ws(x, t) are the pseudo-static displacements in the y and z directions respectively, and vd(x, t) and wd(x, t) are the relative dynamic displacements in the y and z directions respectively.From the geometry of a cable under different support motion where v1(t) and w1(t) are the displacement time histories at the left support in the y and z directions, and v2(t) and w2(t) are the displacement time histories at the right support. These expressions satisfy the boundary conditions as at x=0, vs=v1 and ws=w1 (left support motion); and at x=L, vs=v2 and ws=w2 (right support motion). For the special case of short span cables, uniform support excitation may be assumed where v1(t)=v2(t) and w1(t)=w2(t).In the solution for the vertical and transverse motions of the cable, the following non-dimensional parameters are introduced:where Φ(x) is the first in-plane mode of vibration and Θ(x) is the first out-of-plane mode of vibration.From the static equilibrium shape of the cable, can be reduced to two coupled non-linear ordinary differential equations in the following form:where the constants c1 to c7 are given by and the constants F1 to F7 are given by indicate that there are two kinds of non-linearities in the system, quadratic and cubic non-linearities. The quadratic non-linearity terms are due to the initial curvature of the cable and the cubic non-linearity terms are due to stretching of the cable under tension.The method of multiple time scales by Nayfeh and Mook The following scaling scheme is considered: W(t)=ϵW*(t); V(t)=ϵV*(t); vi(t)=ϵ3vi*(t); wi(t)=ϵ3wi*(t) where i=1, 2. Dropping the asterisks, the time dependent component of the response V(t) and W(t) are expanded in the form:, two differential equations with different powers of ϵ are arrived at. Equating the sum of the coefficients of the same power of ϵ to zero, the following equations are obtained: for the out-of-plane and the in-plane motions takes the form:where cc represents the complex conjugate of all the terms before the plus sign. is the complex conjugate of Ai, i=1, 2.Eliminating the secular term results in D1A1=0; and the solution for Eliminating the secular term results in D1A2=0; and the solution for At this stage, it is appropriate to simplify the solution by differentiating between two cases. The first case is that when the excitation is in the transverse direction only, while the second case is that when the excitation is in the vertical direction only.The support excitations are defined as accelerations using the travelling wave approach in the following form:where n=2, 3 for the vertical and transverse excitations, respectively, τ is the phase difference due to wave travel effect which is equal to the length between cable supports divided by the wave propagation velocity, σ is a detuning parameter. Resonance occurs when σ=0. Substituting and eliminating the secular term, the following equations are obtained:A1 and A2 are expressed in the polar form as follows:where a, b and φ1, φ2 are the amplitudes and phase angles of A1 and A2., and equating the real and imaginary parts to zero, the following set of equations is arrived at:The steady state solution is given by the condition: shows that the system exhibits either softening or hardening behaviour depending on the value of S1 which in turn depends on the terms of the quadratic and cubic non-linearities. After solving to determine the values of a and γ1, the general solution of the non-dimensional time dependent component of the response V(t) and W(t) are given by substituting shows that due to transverse excitation, the cable vibrates in the transverse direction with its natural frequency (ω3). Meanwhile, there is a vertical vibration of order ϵ and frequency 2ω3 coupled with the transverse vibration. Moreover, there is a non-zero amplitude term in the vertical direction due to the quadratic non-linearity.The support excitations are defined in the following form:Performing the analysis in a similar manner to the case of transverse excitation, the steady state solution is given by: simultaneously results in the values of b and γ2. The solution for W(t) and V(t) is given by: shows that due to transverse excitation, no transverse vibration is associated with the vertical vibration. The cable vibrates in the vertical direction with its natural frequency ω2. In addition, there is a vibration of order ϵ and frequency 2ω2. The cable motion is also characterized by a non-zero amplitude term due to the quadratic non-linearity.Due to the non-linearity, the response may be multi-valued for the same amplitude and frequency of excitation. In some cases, there are three possible amplitudes of the response. However, not all possible solutions are stable. It is necessary to examine the stability of the steady state solution. For the case of support excitation in the transverse direction, consider with b=0 and a and γ1 expressed in the following form:where a and γ1 are the steady state solution and a11 and γ11 are small perturbations of the steady state solution. into the steady state solution given by , the following expressions are obtained:The stability of the solution depends on the eigenvalues of . The position of the points separating the stable and unstable regions is given by the characteristic equation h1h4−h2h3=0, which can be written as:The solution given by σ1* is the backbone curve which is the solution of The stability of the solution due to support motion in the vertical direction is obtained in a similar way to the stability analysis in the transverse direction. The position of the points separating the stable and unstable regions for the case of zero damping is given by the equation:In the numerical examples, unless otherwise stated, only the first out-of-plane mode and the first in-plane symmetric mode are considered. Three cable examples are analyzed with the properties shown in . These cables cover a wide range of sag to span ratios from 0.03 to represent sagged cables to 0.003 to represent taut cables. The first symmetric mode shapes are those given by Irvine and Caughey , the constants c1 to c7 and F1 to F7 given by , respectively are evaluated. The calculated values of some important constants are given in . The non-dimensional solutions for the displacements W(t) and V(t) are given by for the transverse and vertical excitations, respectively. The dimensional solution can be found by using and considering the scaling scheme used in the analysis.The results of the analytical solution may be compared with the results obtained using numerical integration of the equations of motion The derivation of the analytical solution is general and valid for both uniform and different support excitations. However, since the available finite element program allows only for uniform support excitation, verification of the results is conducted for this case only. show the displacement time history of the cable mid-point of the three cables to uniform transverse and vertical support excitation, respectively. The support excitation is a cosine function scaled to a peak acceleration of 0.1g. These figures show good agreement between the perturbation solution and the finite element approach. While the frequencies are almost identical, the difference in amplitude is reasonably small. The accuracy increases for cables with small sag to span ratios (Cables II and III) because the effect of quadratic non-linearity is reduced. For taut cables (Cable III), since the modes are widely separated, the perturbation solution can be extended for a wider range of frequencies around the resonance frequency []. It is expected that if enough terms are included in the perturbation solution, the results would approach those of the finite element analyses.The sag in the cable creates quadratic non-linearity in addition to the cubic non-linearity. In the numerical examples, the first cable with a sag to span ratio of 0.03 represents a sagged cable while the third cable with a sag to span ratio of 0.003 approaches the behaviour of a string. shows the frequency–amplitude relationship of different cables to vertical support excitation scaled to peak acceleration values of 0.1 and 0.2g. shows a softening behaviour for Cable I (sagged cable) due to the vertical ground motion. The softening characteristics of the cable are due to the quadratic non-linearity. Multi-valued response of the cable is obtained for certain values of the detuning parameter σ. However, only two of these three solutions are stable and either one of them can be reached depending on the initial conditions. Reducing the sag to span ratio, as in Cable III [], results in hardening characteristics of the cable due to the cubic non-linearity. also indicates that for Cable II the solution is almost linear and stable in all regions. The reason for that is due to the interaction between the quadratic and cubic non-linearity terms. The amplitude of vibration of Cable III is generally smaller than that of Cables I and II which is the case for taut cables.One of the distinctive features of long span cables is the possible difference in the support excitations acting at cable ends due to the wave travel effect. In simplistic form, the wave travel effect can be accounted for by a phase shift between the motions affecting different ends of the cable. The phase shift in support excitations influences different modes of cable vibration.Consider the first symmetric mode given by and for the three cases of cables considered, F3=0.159=The first transverse anti-symmetric frequency and mode of vibration of the cable are given by Irvine and Caughey Following a similar analysis to the transverse vibration case, for the vertical vibration takes the form:The first vertical anti-symmetric frequency and mode of vibration of the cable are given by Irvine and Caughey Similarly, for this mode, I3=0 and therefore F2=0. The effect of the phase shift in support excitation on the frequency–response relationship for Cable I is shown in for transverse and vertical excitations, respectively. The support excitation is in the form of a cosine wave scaled to a peak acceleration of 0.1g. These figures show that, for the first symmetric mode, the amplitude of the dynamic response is reduced when considering the phase shift. For the case of τ=π (i.e. the two components of ground motion are completely out-of-phase) there is no stable solution for the cable equation of motion. The response being discussed is the dynamic response component. To obtain the total response, the pseudo-static component of the response should be added to the dynamic component.For the first anti-symmetric mode, the effect of different phase shifts on the frequency response relationship of Cable I for 0.1g peak support acceleration is shown in . This figure shows that for uniform excitation (τ=0), the anti-symmetric modes are not excited. As the phase shift increases, the anti-symmetric mode response increases until it reaches its maximum value at τ=π (i.e. the two components of ground motion are completely out-of-phase). This emphasizes the importance of considering the phase shift in the support input motion. This represents the case when the anti-symmetric modes are excited which, depending on the specific cable characteristics, may result in a higher overall response of the cable.The analysis of non-linear cable response to support excitation in the vertical and transverse directions is presented. The coupled non-linear equations of motion are formulated and solved. The spatial problem is solved using Galerkin method for a two-degree of freedom model. The temporal problem is solved using the method of multiple time scales. The stability of the steady state solution is developed and discussed. Different cable examples with different sag to span ratios and damping ratios are used in the analysis to demonstrate aspects of the solution and stability phenomenon. The effect of the phase difference between the support excitation at different cable ends on the response is examined.The analysis shows that the analytical solution with a two-degree of freedom model yields accurate results as compared to the finite element approach. The accuracy of the analytical solution increases for cables with small sag to span ratio where the modes of vibration become widely separated. The results show that due to vertical excitation, only vertical vibration exists, while due to transverse excitation, both vertical and transverse vibrations exist. The analysis shows a softening behaviour for sagged cables due to the quadratic non-linearity resulting from the initial curvature of the cable. Taut cables show hardening behaviour due to the stretching of the cable. It is also demonstrated from the analysis that the uniform support motion excites only the symmetric cable modes. The anti-symmetric modes are excited due to the phase difference between the input motions at cable ends.Numerical analysis of the creep crack constraint effects and the creep crack initiation for pressurized pipelines with circumferential surface cracksThe creep crack constraint effects using a load-independent creep constraint parameter Q* and the creep crack initiation (CCI) times were characterized by 3D finite element method for pipelines with circumferential surface cracks of different geometrical sizes. The results revealed that the distribution regulation of Q* along the crack front for circumferential internal surface cracks and external surface cracks was similar. The maximum constraint level occurred near the deepest crack front part for cracks with smaller a/c, while it occurred near the free surface for cracks with larger a/c. The constraint values at the same position (2Φ/π) increased with the increasing of the crack depth when a/c kept constant. The circumferential internal surface cracks of pipelines were proved more dangerous than the external surface cracks with the same geometrical size. Furthermore, the CCI times were decided by the peak values of constraint, or the CCI firstly occurred at the position where the constraint level was maximum. In addition, the empirical relationships between the CCI times and crack sizes were fitted, which was also verified effectively.eight-node linear brick reduced integration elementsa user subroutine in ABAQUS for creep analysiscoefficient in power-law creep definitiontransient creep crack tip characterising parametersteady state creep crack tip characterising parameterMany failures occurred in in-service components at elevated temperatures are mainly caused by the creep crack initiation (CCI) and creep crack growth (CCG) In general, the CCI time occupies the majority of the safe lifetime of structural integrity. Hence, the investigation of CCI is significant for the application of components under the high temperature. In a ductile material when micro-cracks (which may be generated by the nucleation, growth and coalescence of voids ahead of a pre-existing defect) first link up and form the main defect, the elapsed time is defined as the creep crack initiation (CCI) time In this paper, the constraint effects and CCI times of the pressurized pipelines with circumferential surface cracks served at elevated temperature are studied. The distributions of C* along the crack front in pipelines with internal and external surface cracks are analyzed. Besides, the creep crack-tip constraint effects with different geometrical sizes are characterized using the load-independent creep constraint parameter Q*. The creep damage accumulations and the CCI times at the positions with the maximum values of C* or Q* are also investigated. The empirical relationships between the CCI times and crack sizes are obtained. The effectivity of the empirical equations is verified.The stress distribution around the crack tip under the steady-state creep condition is expressed as where σij is the stress component, r is the distance away from the crack tip, and θ is the angle away from the crack line. σ˜ij(θ;n) is a dimensionless function of n and θ, and In is a parameter related to the creep stress-hardening exponent n. As shown in , C* is the characterization parameter of the crack propagation driving force under steady creep state.The C*–Q two-parameter approach is developed under creep conditions. The expression of the stress field is as follows where δij is the Kronecker delta. Q is a non-dimensional parameter that measures the constraint conditions around the crack. Moreover, Q is always determined by the difference of σ22 between the specimen and the analytical steady-state creep field where σ22(r,0) is the theoretical steady creep stress field calculated by . σFEM22(r,0) is the stress distribution predicted by FE simulation.The creep crack-tip stress field, including the load-independent creep constraint parameter Q*, is expressed as σijσ0=(C*ɛ˙0LInσ0)1n+1[(Lr)1n+1σ˜ij(θ;n)+Q*δij]where L is a normalized length (generally set as 1 mm Q*=(C*ɛ˙0σ0InL)−1n+1Q=(C*ɛ˙0σ0InL)−1n+1σθθ(r,0)−σθθFEM(r,0)σ0It has been revealed that Q* is load-independent out of the blunting region, and a fixed distance r = 0.2 mm is chosen to define the Q*ω=∫ɛ˙cɛ*critdt=∫ɛ˙0MSF(h)ɛcrit(σ¯(t)σ0)ndtwhere ɛ˙c is the creep strain rate, ε∗crit is the multiaxial creep ductility of the material, and εcrit is the uniaxial creep ductility. MSF is the multiaxial stress factor (MSF) depending on the triaxiality h. The triaxiality h is determined by the ratio of the mean (hydrostatic) stress to the equivalent Mises stress, i.e. σm/σ¯. MSF(h) is obtained by the Cocks and Ashby relation MSF(h)=ɛcrit*ɛcrit=sinh{(2/3)[(n−1/2)/(n+1/2)]}sinh{2h[(n−1/2)/(n+1/2)]}The material properties of P92 steel are used in this study, which has high creep resistance and corrosion resistance at high temperature Where A is the creep constant in Norton model, and n is the creep exponent. σ0 is the yield stress, and ɛ˙0is the creep strain rate at σ0. The mechanical and creep parameters of P92 steel at 650 °C are given in The microstructurally significant distance d is chosen as the average grain size of P92 steel, about 50 µm , simplified semi-elliptical circumferential surface cracks include internal surface crack (see (b)) according to the location of the crack in pipelines.a is the crack depth and 2c is the crack length. Ri and t represent the inner radius and the thickness of the pipeline. In this work, a set of simplified steam pipelines are employed with Ri = 90 mm and t= 30mm. Φ represents the angular parameter by taking the ellipse center as its coordinate origin. Hence, 2Φ/π=1 denotes the deepest point of the crack front while 2Φ/π=0 is the position of free surface. For avoiding boundary effects, the pipeline length L of all the models employed in this study is set as 40t.One quarter of the 3D finite element models are established for pipelines with circumferential surface cracks of different geometrical sizes due to geometric symmetry. The typical 3D FE meshes of the pipeline with circumferential internal surface crack and external surface crack are described in (b), respectively. The un-cracked ligament and the cross section around the crack are set as the symmetric boundary condition, while the encastre boundary is set on the cross section away from the crack. The arc fine mesh region was set ahead of the crack front. The smallest mesh size of 10 µm is employed near the crack front, which is about one-fifth of the average grain size of P92 steel Wide-ranging geometrical sizes of a/t = 0.2, 0.4, 0.6, 0.8 and a/c = 0.2, 0.4, 0.6, 0.8, 1.0 are selected to study the distribution of the creep crack-tip constraint parameter Q* with the different geometrical sizes. depict the distribution of the creep constraint parameters Q and Q* along the crack front of the internal surface crack with the geometrical size of a/t = 0.2 and a/c = 1. Two different internal pressure values of 8, 15 MPa are adopted under the steady creep state (i.e. t = tred, where tred is the redistribution time. It represents the time when the stress state reaches the steady creep state). It is obvious that the creep constraint parameter Q is dependent on the loads. The higher the load level is, the smaller the corresponding constraint parameter Q value will be show the contour integral C* along the crack front for circumferential internal surface cracks. It is clear that the peak value of C* along the crack front increases with the increasing of the crack length c (or with the decreasing of the ratio of crack depth to length, a/c) at a specific value of the crack depth ratio a/t. The position of the peak C* value is related to the surface crack size. For long crack with a/c value is smaller than 0.6, the peak C* value will occur at the deepest point of the crack front (2Φ/π=1). When a/c value is larger than 0.6 (or for short crack) it occurs near the free surface (around 2Φ/π=0.2). Besides, the minimum value of C* occurs at the free surface (2Φ/π=0) for all the cracks. depicts the distribution of C* along the crack front for circumferential internal surface cracks with different a/t at a specific a/c of 0.2. The C* parameter increases gradually as 2Φ/π increases. The increment amplitude of C* values is comparatively large when 2Φ/π< 0.2, while it becomes smaller when 2Φ/π> 0.2. The peak C* value occurs at the deepest point, and the minimum value is at the free surface. Additionly, it is obvious that the C* values increase with the increasing of crack depth (a/t) at the same a/c. In general, C* is the integral parameter of the crack propagation driving force under the creep state, so the crack will initiate at the position with the peak C* value, which means that the crack will initiate at the deepest point for long crack (a/c < 0.6) and the point around the free surface for short crack (a/c > 0.6). For the same ratio of a/c, the cracks with deeper crack depth will initiate first because of the larger C* values show the distribution of the calculated creep constraint parameter Q* along the crack front for circumferential internal surface cracks with different geometrical sizes under the internal pressure P = 15 MPa. The distribution of the constraint parameter Q* is similar to that of C* ahead of crack front. The peak value of the constraint parameter Q* increases with the increasing of a/c under the same crack depth ratio a/t. Moreover, the position of the peak Q* values is also dependent on the crack sizes. The position of peak Q* value is at the deepest point of crack front (around 2Φ/π = 1) for long crack, while it is at the free surface (around 2Φ/π=0.2) for short crack. The minimum Q* value occurs at the free surface for all cases. As shown in the ), the stress level ahead of the crack tip is related to the C* and Q*. When C* is a constant under the specific condition, the larger Q* parameter will indeed cause the larger stress. Hence, it can be concluded that the higher creep constraint level always means the higher stress level around the crack front. depict the distribution of the constraint parameter Q* ahead of the crack front for circumferential internal surface cracks with various geometrical sizes at a/c=0.2 and a/c=1.0.The Q* values increase with the increasing of crack depth a/t. It can be seen that Q* increases gradually with the increasing of 2Φ/π and reaches the peak value at 2Φ/π = 1 for shallow cracks (a/t = 0.2, 0.4), while the changes of Q* are not obvious for deep cracks (a/t = 0.6, 0.8) when 2Φ/π ≥ 0.4. In addition, the differences of peak Q* values between the deep cracks are little at 2Φ/π = 1. Moreover, the maximum values of Q* for cracks with a/t ≥ 0.4 at the same a/c of 0.2 (long crack) are generally the same near the deepest point of the crack front. For the short cracks (a/c = 1), the C* or Q* values increase firstly and the peak values occur near the free surface, and then the values decrease gradually.The distribution of constraint parameter Q* along the crack front is consistent with the investigations proposed by Liu using R* compares the creep damage accumulations of pipelines with circumferential internal surface cracks of different geometric sizes. The research positions of damage accumulation is where the maximum values of C* and Q* exist. It can be concluded that, under the same a/t, as a/c decreases (or crack length, c, increases), creep damage accumulation increases sharply and the failure time (or CCI times, when the value of ω firstly reaches unity around the crack front) decreases obviously. Besides, under the same a/c, as a/t increases the damage accumulation also increases sharply and the CCI time decreases. Generally, a large crack or high constraint causes a larger concentration of stress around the crack front, which may increase the crack-opening stress and accelerate the initiation. Therefore, it is notable that large surface crack with high constraints have high crack propagation rates and short CCI times. compare the CCI times of internal surface cracks with different crack sizes. The CCI times, normalized by ɛ˙0/ɛcrit against cack length a/c, are plotted. The creep crack initiation time is obtained when one element located at 0.05 mm ahead of the crack front is failed. The CCI times are decided by the peak values of constraint, or the CCI firstly occurs at the position where the constraint level is maximum. It can be concluded that as the a/c increases, the CCI times increase with the same a/t. As the a/t increases, the CCI times decrease with the same a/c. The change regulation of the CCI times with the crack sizes is related to the results of C* or Q*. compare the CCI times of internal surface cracks under the different pressures. It is clear that as the pressure increases the CCI times decrease. The variation law between the CCI times and the pressures is regular, and the empirical relationship between the CCI times and the pressures and the crack sizes can be obtained.Based on the FE results of CCI times, a fitting formula between the normalized CCI times tiɛ˙0/ɛcrit and a/t, crack length a/c, pressure P is established:tiɛ˙0ɛcrit=54.291(P′)−4.4e(8.852−3.407a/t+(2.027+5.769a/t)a/c+(−0.577−3.671a/t)(a/c)2)Where P′ is normalized dimensionless pressure P: P′ = P/(1 MPa).Additionly, a related prediction method of CCI times of circumferential internal surface cracks has been proposed in BS 7910 Where σref is reference stress, tR(ref) is the time to creep rupture at reference stress, and K is the stress intensity factor.σref=Pm{π(1−a/t)+2(a/t)sin(c/r)}(1−a/t){π−(c/r)(a/t)}+2Pb3(1−a′′)2Where Pm is membrane stress, Pb is bending stress, r is the radius of the analytical position, and a″ is calculated by following:Where M, fw, and Mm are coefficients related to the sizes of the circumferential surface cracks, and these can be obtained in Ref compares the CCI times between the FE results, the results calculated from and BS 7910 under the pressure P = 18 MPa. It is clear that the results calculated by the BS 7910 are largely conservative compared with the FE results. The results calculated from the empirical relationship can accurately predict the CCI times of pipeline with the circumferential internal surface cracks. Hence, the empirical relationship can effectively predict the CCI times of pipeline with circumferential internal surface cracks.The circumferential external surface cracks also occurs in pressurized pipelines which may cause safety problem. The circumferential external surface crack and its meshes are illustrated in (b), respectively. The geometrical sizes of a/t = 0.2, 0.4, 0.6, 0.8 and a/c = 0.2, 0.4, 0.6, 0.8, 1.0 are also adopted in circumferential external surface cracks. Distribution of the contour integral C* and the creep constraint parameter Q* along the crack front for circumferential external surface cracks with different geometrical sizes is depicted in under the same internal pressure P = 15 MPa. It can been seen that the distribution regulation of C* and Q* along the crack front for circumferential external surface cracks is similar to those of circumferential internal surface cracks. The peak value of C* or Q* along the crack front increases with the increasing of the crack length at a certain a/t value. The position of peak values (C* or Q*) varies from the place near the free surface to the deepest point with the increasing of the crack length c at a constant a/t. show the distribution of the contour integral C* and Q* along the crack front for circumferential external surface cracks with different depth a/t at specific values of a/c = 0.2 and 0.4, respectively. For the long cracks (a/c = 0.2), the C* or Q* values increase with the position of crack front away from the free surface, the peak values occur near the deepest point of cracks. However, for deep cracks with a/t = 0.6 and 0.8, the Q* values are basically unchanged when 2Φ/π ≥ 0.4. Moreover, the maximum values of Q* for cracks with a/t ≥ 0.4 at the same a/c of 0.2 are generally the same near the deepest point of the crack front. For the short cracks (a/c = 1), the C* or Q* values increase firstly and the peak values occur near the free surface, and then the values decrease gradually. Based on the above analysis, the internal surface cracks and the external surface cracks have the similar law of crack initiation, that the long crack will initiate from the deepest point of crack front while short crack will initiate from the position near the free surface. shows the comparison of creep damage accumulation for pipelines with different geometric sizes of circumferential external surface cracks. The variation law of damage with the external surface cracks is similar to that with the internal surface cracks. It can be concluded that, under the same a/t, as a/c decreases (or crack length, c, increases), creep damage accumulation increases sharply and the failure time (or CCI times, when the value of ω firstly reaches unity around the crack front) decreases obviously. Besides, under the same a/c, as a/t increases the damage accumulation also increases sharply and the CCI time decreases. compare the CCI times of external surface cracks with different crack sizes and the FE results. It can be concluded that as the a/c increases, the CCI times increase with the same a/t. As the a/t increases, the CCI times decrease with the same a/c. The changing regulation of the CCI times with the crack sizes is related to the results of C* and Q*. compare the CCI times of external surface cracks under the different pressures. It is clear that as the pressure increases the CCI times decrease. The empirical relationship between the CCI times and the pressures and the crack sizes can also be obtained.Based on the FE results of CCI times, a fitting formula between tiɛ˙0/ɛcrit and a/t, crack length a/c, pressure P is established:tiɛ˙0ɛcrit=202(P′)−4.7e(11.533−7.641a/t+(−0.834+12.897a/t)a/c+(1.517−8.72a/t)(a/c)2)Where P′ is normalized dimensionless pressure P: P′ = P/(1 MPa). compare the C* and Q* values between the internal and external surface cracks with the same geometrical size of a/t = 0.2 and a/c = 1. It can be seen that both the C* integral and the constraint parameter Q* of the internal surface crack are higher than those of the external surface crack. The phenomenon may be caused by the difference between the loading configurations of internal and external surface cracks. Since the C* could represent the driving force of the creep crack propagation (which can be clearly observed in )), and the position with high constraint level is always accompanied by the high stress concentration along the crack front )). Hence, it can be concluded that the damage accumulating time or CCI time of the external surface cracks will be shorter than that of the internal surface cracks at a specific crack geometrical size, or the circumferential internal surface cracks are more dangerous than the external surface cracks with the same geometrical size. compares the CCI times between the circumferential internal and external surface cracks. It is clear that the internal surface cracks initiate earlier than the external surface cracks, because it is also related to the higher values of C* and Q* of the internal surface cracks, which accelerate the damage accumulation and the creep crack initiation.The constraint level and creep crack initiation for pressurized pipelines with circumferential surface cracks served at elevated temperature were studied using 3D FEM. The creep constraint effects along the crack front were characterized using a load-independent creep constraint parameter Q*. The empirical equations for expressing the relationships between the CCI times and crack sizes as well as loads were obtained by nonlinear fitting. The main results obtained were summarized as follows:For circumferential internal surface cracks, the distribution regulation of the load-independent creep constraint parameter Q* was similar to that of C*. The peak value of C* or Q* occurred near the deepest crack front part for long cracks (a/c< 0.4), while it occurred near the free surface for short cracks (a/c> 0.4). For cracks with the same ratio of crack depth to length a/c, the contour integral C* or Q* increased with the increasing of the crack depth a/t.The values of C* and Q* along the crack front for circumferential internal surface cracks and circumferential external surface cracks had the same distribution tendency. The values of C* and Q* along the crack front for circumferential internal surface cracks were larger than those for circumferential external surface cracks with the same geometrical sizes at the same position (2Φ/π).The position ahead of the crack front with the higher constraint level meant the higher stress level and it was dangerous for the creep crack initiation occurred firstly.Under the same a/t, as a/c decreased creep damage accumulation increased sharply and the CCI times decreased obviously. Besides, under the same a/c, as a/t increased the damage accumulation also increased sharply and the CCI time decreased. As the a/c increased, the CCI times increased with the same a/t. As the a/t increased, the CCI times decreased with the same a/c. The CCI times of the external surface cracks were larger than those of the internal surface cracks. The fitting equations of FE results of the circumferential surface cracks could accurately predict the CCI times.Inelastic behavior and fracture of high modulus polymeric fiber bundles at high strain-ratesThe tensile behavior and fracture mechanisms of poly(phenylene terephthalamide) (PPTA) and high modulus polyethylene (HMPE) fiber bundles were studied at high strain-rates using a tension Kolsky bar. For all fiber bundles investigated, a significant amount of strain energy was found to be dissipated by inelastic processes in addition to that due to fracture. The differences in microstructure and properties between the fibers were shown to have a noticeable influence on the inelasticity and fracture behavior in PPTA fiber bundles. No significant strain-rate effect on inelastic behavior and maximum strength was found in HMPE fiber bundles. Scanning electron micrographs of the fracture surfaces of PPTA fiber showed that the failure occurs mainly by fibrillation resulting in pointed breaks, and showed no fundamental difference in fracture mechanism at quasi-static and high strain-rates. However, the fracture mechanism in the HMPE fiber was different at quasi-static and high strain-rates, crazing was dominant at high strain-rates and plate formation under quasi-static conditions. This difference was more substantial in HMPE fibers with lower degree of crystalline order, which suggested that the inelastic behavior is governed by a precise mechanism of load transfer between the crystalline and amorphous phases present in HMPE fibers as a function of loading rate. At high strain-rates, HMPE fibers appear to be able to dissipate more strain energy than PPTA fibers due to this intrinsic change of deformation mechanism. Our results also support the idea that the mechanical behavior of a PPTA fiber bundle is inherently statistical including variations in strength distribution and alignment of the individual filaments.The specific tensile strengths of high-performance fibers produced from poly(phenylene terephthalamide) (PPTA) and high modulus polyethylene (HMPE) exceed that of steel, and appear to dissipate large amounts of energy during ballistic impact. These two fibers are marketed commercially, for example PPTA as Kevlar® (DuPont) and HMPE as Spectra® (Honeywell), respectively. Although the structure of these fibers is now well-characterized Both PPTA and HMPE are highly crystalline. The chemical formula for the PPTA monomer is shown in . Molecules including aromatic structures or amide groups are usually strong; PPTA contains both. The aramid chains form rigid planar sheets with the chain-extended molecules hydrogen bonded together. The sheets are stacked to form a crystalline array but there is only weak van der Waals forces between the sheets, which are arranged in a radial system of axially pleated lamellae as illustrated in Based on experimental data and simulation on single filaments, Cheng et al. The chemical formula for the monomer of a HMPE fiber is shown in . This polymer is processed by gel spinning followed by drawing to produce longitudinally oriented chains b. The drawn fibers consist of microfibrils and intrafibrillar matter. The microfibrils are composed of crystalline and amorphous regions oriented along the fiber axis. The aligned crystalline regions are on the order of 60–400 nm in length Compared to PPTA, little has been published regarding the fracture of HMPE fiber. Within the fiber, the microfibrils are aligned longitudinally and linked together by the intrafibrillar chains Polyethylene is known to dissipate energy through chain unfolding and crazing in its amorphous domains, and through crystal separation and slippage in its crystalline regions This study describes an effort to understand the mechanical behavior and fracture of PPTA and HMPE fiber bundles under uniaxial tension at both quasi-static and high strain-rates. Atomic force microscopy (AFM) was used to characterize the cross-sectional structure of the filaments. Uniaxial tensile tests were conducted at high strain-rates using a tension Kolsky bar. The failure modes and mechanisms were investigated by scanning electron microscopy (SEM) and related to the structure of each of the fiber samples. Section presents the details of the experimental procedure. The results obtained from mechanical testing and fracture surface analyses are presented in Section . The relationships between microstructure, mechanisms, and strain-rate dependence of deformation and fracture in PPTA and HMPE are discussed in Section Three grades of PPTA fiber bundles (DuPont) labeled Fiber-A, -B and -C, were tested High strain-rate tensile tests were carried out using a tension Kolsky bar ) and tested in tension. The PPTA samples were glued using quick-set epoxy and clamped, while the HMPE samples were simply clamped in place. The initial fiber bundle length ranged from 3.416 mm to 4.539 mm depending on the samples.The onset of failure is assumed to occur at the peak of the stress. The filaments in the bundle did not all break simultaneously, and the strain did not drop to zero immediately after the peak stress. The total failure of the fiber bundles occurs when the stress returned to zero after the peak stress. The total strain energy dissipated was calculated by integrating the tensile stress–strain curve from zero strain to the breaking strain and by dividing this value by the material volume. The inelastic strain energy density was calculated by subtracting the elastic strain energy density from the total strain energy density. The apparent elastic modulus was determined from the linear portion of the loading curve neglecting the curvature near zero-load.Fracture mechanisms of the fibers were investigated by examining the fractured regions using SEM observations (JEOL JSM6060). For this purpose, the fractured fibers were mounted on double-sided conductive tape and gold-sputtered in vacuum to produce a 100 nm conductive coating. Also, several tests were performed on PPTA and HMPE fiber bundles at quasi-static strain-rates using a standard materials testing machine (Instron), and the fibers were examined under SEM for comparison. Furthermore, the cross-sectional microstructure of the undeformed filaments was observed by AFM (Universal SPM Quesant) in intermittent mode using a silicon cantilever with a tip radius of 10 nm and force constant of 40 N/m (NSC16, Mikromasch). For this purpose the fiber bundle was embedded in epoxy resin, the cross-section was mechanically polished with wet sand paper up to 1200 grit, and subsequently polished with diamond pastes up to 0.25 μm.The mechanical parameters determined from the tensile stress–strain curves at high strain-rates on PPTA and HMPE fiber bundles are shown in , respectively. These parameters are used to understand the differences in the performance of the three PPTA fibers and the two HMPE fibers used for this study. In the tests with Kolsky apparatus, the number of wave reverberations within the sample before failure was found to be between 4 and 7 for all the tests reported here. Thus the fiber bundles can be assumed to have reached dynamic equilibrium by the time the specimen begins to fail. Even though the modulus obtained at high strain-rates in this study may not be reliable, the strength and the energy absorbed are meaningful.The tensile stress–strain curves in PPTA fiber bundles deformed at different strain-rates are presented in . Fibers A and B belong to the same family as Kevlar® 49 and 29, respectively. Based on this similarity, and drawing from the published literature, we can conclude that A and B have lower degree of crystallinity and orientation than C All the PPTA fiber bundles broke in high strain-rate tests. Fiber-B and Fiber-C dissipated more inelastic strain energy than Fiber-A during deformation at all strain-rate. Therefore, there is a strong microstructure dependence in terms of inelastic behavior and fracture. In addition, as shown in , the breaking strain corresponding to the complete failure is between 5% and 11%, which is greater than the value reported in the literature on single filaments. This is likely a consequence of stochastic failure process, as discussed below. presents the cross-sectional AFM images of PPTA Fiber-A obtained from intermittent contact mode. The radial structure of PPTA The predominance of a fracture mechanism in a particular fiber under given condition was investigated statistically via SEM analysis. summarizes the statistical distribution of each of the fracture mechanisms observed in all the SEM micrographs. Under tension, PPTA fibers show three types of fracture morphology: fibrillated break, pointed break and breaks with transverse striations. Fibrillation, which is most common, is characterized by decohesion, a reduction in diameter and splintering of the microfibrils along the longitudinal axis of the fiber and the fracture surfaces has a bamboo-like appearance (). Pointed break, frequently seen when filaments fail at slow strain-rate (especially in PPTA Fiber-C), is accompanied by a significant necking and reduction in fiber diameter and tapered diameter near the fractured area, which results from significant localization of deformation in the crystalline phase of the polymer () resemble kink-bands that are usually seen under compressive loads, and occurs when the filaments break prematurely due to the presence of dislocations in the ordered molecular chains The tensile stress–strain curves of the HMPE fiber bundles deformed at different strain-rates are presented in . The analysis of these curves is summarized in . It has been reported that the degree of orientation and other measures of crystalline order such as crystallinity and crystallite size are higher in Fiber-B than in Fiber-A show that, similar to the results obtained in PPTA, some of the properties such as the strength and the dissipated strain energy in HMPE fiber bundles are more significantly influenced by the fiber morphology than the strain-rate. The moduli obtained here for HMPE at all strain-rates are smaller than those reported in the literature, perhaps due to fiber slippage. This discrepancy, however, will not alter the main conclusions concerning the modes of failure in HMPE fiber bundles.This figure also shows that the strength of HMPE fiber bundles does not increase with strain-rate, and are perhaps lower at high strain-rates. HMPE Fiber-B fiber bundles are also markedly stronger than HMPE Fiber-A fiber bundles at all strain-rates, indicating that the inelastic behavior and fracture processes are also highly dependent on the fiber morphology. Specific strain-rate effect on the dissipated strain energy in HMPE fiber bundles could not be deduced from the data because most of the HMPE fiber bundles tested under high strain-rate loading did not break. In HMPE Fiber-B, only a limited amount of fiber (<25%) in the bundles completely failed in each of the two high strain-rate tests; none of the HMPE Fiber-A bundles failed under high strain-rate tensile loading. However, HMPE fiber bundles break at larger strain than PPTA at high strain-rates, and clearly possess a larger propensity to dissipate strain energy during deformation than PPTA fibers. The main explanation for such a difference is related to the significant energy dissipation taking place in the inelastic processes. The slower decrease of stress at the onset of failure in HMPE than in PPTA () suggests that the failure mechanism in this material is different and as a result dissipate more energy than PPTA, albeit slowly.b presents the cross-sectional AFM images of HMPE Fiber-A obtained in intermittent mode. No specific core-skin difference in microstructure is observed in this figure. Furthermore, similar to the PPTA cross-section, a submicron scale structure, the fibrillar morphology, can be clearly observed in the close up view. It can be observed that this submicron scale structure appears to be coarser than in PPTA fibers. This observation supports the assumption that the crystalline phases are significantly smaller in size and denser in PPTA fiber bundles than HMPE fibers.The fracture mechanisms of HMPE fibers investigated by SEM include crazing, fibrillation and plate formation. There is clear evidence of crazing at the surface of HMPE fibers in . Fibrillation and plate formation mechanisms can be seen in HMPE in , respectively. Plate formation results from slippage between the crystalline regions in the fiber matrix. This slippage results from secondary bond breakage between the ordered macromolecules as explained in the Section shows that the predominant fracture mechanism in HMPE fibers strongly depends on the strain-rate. The fibers broken at quasi-static rates are characterized predominantly by plate formation with fibrillation and to a lesser extent, crazing. At high strain-rates, however, there is a significant change of mechanism from plate formation to crazing. This effect appears to be more drastic in HMPE Fiber-A, which has a lower crystalline order than HMPE Fiber-B. Some fibrillation also appears in the HMPE fibers tested, but the occurrence of this mechanism does not appear to be influenced by the strain-rate.The key result of this study is that the fracture processes are different at low and high strain-rates, especially in HMPE fibers. These differences most likely explain the observed difference in strength and absorbed energy in these fibers. Also, we observed that the mechanical behavior of the bundles is quite different from that of single filaments.Testing fiber bundles introduces an intrinsic mechanical effect as compared to experiments on single filaments It is important to note the difference between the results of Cheng et al. ). Therefore, our study reveals a strong dependence of the fracture process on fiber morphology and structure in PPTA fiber bundles. Our SEM fracture surface analysis also shows that fibrillation is the primary failure mechanism in all PPTA fibers. This result is consistent with the findings of Cheng et al. Our results show that strain-rate has no significant effect on elastic modulus in PPTA fiber bundles. The differences in the modulus in the three fibers tested do, however, indicate that modulus is related to the fiber morphology (orientation and crystalline order). There are two possible explanations for this difference in fracture behavior at different strain-rates: first, bundle effect could be more pronounced at low strain-rates in which case the fracture is the result of the bursts of filament bundles; second, the fracture mechanism could change with strain-rate, but we observed no fundamental difference in deformation mechanism from quasi-static to high strain-rates for each of the PPTA fibers tested. The underlying fracture mechanisms are related to fibrillation and, to a lesser extent, pointed break regardless of the strain-rate. This implies that the intrinsic fracture mechanisms in these fibers have only a limited contribution in terms of strain energy dissipation since these mechanisms are associated with a brittle decohesion process. The change in inelastic behavior and fracture process with strain-rate in PPTA is largely accounted for on the basis of bundle mechanics effects.This study shows limited strain-rate effect on maximum strength in HMPE fiber bundles. As opposed to PPTA, however, there is clear strain-rate dependency in the form of a change in fracture mechanisms from quasi-static regime to high strain-rate regime. In the two HMPE samples studied, analysis of the fracture surfaces showed that crazing is more common at high strain-rates than at quasi-static strain-rates, whereas plate formation is more often seen at quasi-static strain-rates. This trend is more substantial in the HMPE fibers with the lower crystallinity (HMPE Fiber-A). Crazing is known to occur in the amorphous region of the fibers, while plate formation is related to the slippage of the crystalline phases. It can be concluded that the absence of strong strain-rate effect on the inelastic behavior in HMPE fiber bundles results from load transfer at the microstructure-level, which involves crazing in the noncrystalline regions and plate-slippage.We can attempt to understand the above results using the data reported in the literature on crystalline polyethylene. Using a stochastic model of failure for perfectly ordered and oriented polyethylene, Termonia et al. . The underlying strengthening mechanism at high strain-rate could therefore be correlated to a load transfer to the amorphous regions which exhibit a viscous behavior through chain unfolding. In this process, strength in the HMPE fiber bundles at elevated strain-rates is governed by the strength of the primary bonds in the molecular chains.The fracture of PPTA and HMPE fiber bundles at room temperature were studied under high strain-rate deformation using a tension Kolsky bar. The underlying fracture mechanisms were investigated statistically by SEM analysis of the fracture surfaces. The major findings of this study are as follows.For all fiber bundles investigated a significant amount of strain energy was found to be dissipated during deformation due to inelastic and fracture processes.Fiber morphology effects were clearly evidenced on the inelastic behavior and fracture process in PPTA fiber bundles. Fracture surface examinations by SEM indicated that the main fracture mechanisms in PPTA fibers were associated with fibrillation and, to a lesser extent, pointed breaks. The difference in mechanical behavior observed from quasi-static to high strain-rates was not due to an intrinsic change of deformation mechanism, but rather to an intrinsic effect of fiber bundle mechanics. Our results support the idea that the mechanical behavior of a PPTA fiber bundle is inherently statistical including variations in strength distribution and alignment of the individual filaments.In HMPE fiber bundles, no significant strain-rate effect on the maximum strength was observed. As opposed to PPTA, however, there is clear evidence of a change of fracture mechanism at the single fiber level, from the quasi-static regime to the high strain-rate regime. HMPE fibers appear to dissipate more strain energy that PPTA at high strain-rates. In the two types of HMPE materials studied, analysis of the fracture surfaces showed that crazing is more common at high strain-rates than at quasi-static strain-rates, whereas plate formation is more often seen at quasi-static strain-rates. This trend is more substantial in the HMPE fibers with the lower crystallinity. It was shown that crazing is a more important energy absorbing mechanism in HMPE at high strain-rates than at quasi-static rates. Therefore, it can be concluded that the absence of the strain-rate dependence on strength and fracture in HMPE fiber bundles is predominantly linked to a precise mechanism of load transfer as a function of strain-rate from slippage of crystal plates to crazing in the crystalline regions of the HMPE fibers.Thermal degradation of cellulose derivatives/starch blends and sisal fibre biocompositesThermal analysis of cellulose derivatives/starch blends with different sisal short fibre content, were performed by TGA/DTGA under dynamic conditions. Apparent kinetic parameters were determined using a variety of conventional thermogravimetric methods. Two peaks were found: the first close to 334 °C and the second at 369 °C. The apparent activation energy value of the first peak slightly increased as well as the maximum temperature value. The apparent activation energy values for the second peak decreased as well as the maximum temperature value. The addition of the sisal fibres has not produced a high effect on the thermal degradation of the composites materials in comparison with the matrix alone.Biodegradable polymers constitute a new family of polymers designed to be degraded by living organisms. They offer a possible alternative to traditional non- degradable polymers when recycling is impractical or not economical, and they can be composted together with food and yard waste An increasing interest in the recycling and the use of biodegradable materials; with the aim of improving thermo-mechanical properties and decreasing water sensitivity of polymers, thereby preserving the biodegradability, has lead to the use of natural fibres as biodegradable filler. It was observed that mixing natural fibres with polysaccharides (such as thermoplastic starch and/or cellulose derivatives) improves their mechanical properties Natural fibres are a complex mix of organic materials and, as a result of that, thermal treatment produces a variety of chemical and physical changes. Fibre thermal stability can be studied using TGA. TGA curves show two decomposition steps: The first peak appears at 300 °C and corresponds to the thermal decomposition of hemicellulose and the glycosidic links of cellulose. The second one appears at around 360 °C and is due to the thermal decomposition of α-cellulose. The lignin peak is wider and appears between 200 °C and 500 °C, with a maximum at 350 °C, it appears superposed on the other two peaks Pyrolysis reaction between cellulose and lignin produces gases and follows first-order kinetics Organoleptic properties as smell and colour increases when fibres degrade. Another effect is the change on mechanical properties by mass and crystallinity changes and reduction of degree of polymerisation due to chain breakage by cellulose glycosidic union decomposition producing carbon dioxide and water. Sridhar et al. To improve fibre thermal stability, it is possible to make treatments with monomers, like acrylonitrile. Sabaa et al. The aim of the present work is to determine a global kinetic expression for the thermal degradation of the cellulose derivatives/starch blends and sisal fibre, as well as the effect of the content of fibres.When a reaction occurs in a differential thermal analysis (DTA); the change in heat content and in thermal properties of the sample is indicated by a deflection or peak. If the reaction proceeds at a rate varying with temperature; i.e., has an activation energy, the position of the peak varies with the heating rate if other experimental conditions are maintained fixed. This variation in peak temperature could be used to determine the energy of activation for reaction of different reaction orders The thermal decomposition of plastics is complex and may involve many reactions. It is very difficult to obtain the exact kinetic parameters Thermogravimetric analysis (TGA) has come into wide use in the last decades for rapidly assessing the thermal stability of various substances. The trace follows a characteristic path common to a wide range of decompositions; including many polymer pyrolyses The sample weight drops slowly as pyrolysis begins; then drops precipitously over a narrow range and finally turns back to zero slope as the reactant is exhausted. The shape of the curve is determined by the kinetic parameters of the pyrolysis such as; reaction order, frequency factor; and activation energy The derivation of kinetic data in the study of polymer decomposition using TGA has received increasing attention in the last decade; along with much criticism regarding its use in the determination of rate constants; activation energies; reaction orders and Arrhenius pre-exponential constants The values obtained depend upon atmosphere; sample mass; sample shape; flow rate; heating rate but also on the mathematical treatment used to evaluate the data.The data obtained by TGA have been studied using a variety of techniques. In the kinetic methods, the following symbols are usual All kinetic studies utilize the basic rate equation: expresses the rate of conversion, dα/dt, at a constant temperature as a function of the reactant concentration loss and rate constant.In the case of polymer degradation, it is assumed that the rate of conversion is proportional to the concentration of material that has to react.The combination of these equations and the empirical Arrhenius expression gives the following relationship:This is the fundamental expression of analytical methods to calculate kinetic parameters on the basis of TGA data., the most common methods are summarised.MaterBi-Y, supplied by Novamont SPA, Novara, Italy was used as biodegradable thermoplastic matrix. MaterBi-Y is a commercial blend based on cellulose derivatives, starch and additives Brascoda, Brazil supplied the sisal fibres. Fibres were used as received without further treatment. The average length and fibre diameter of the sisal fibre were determined by optical microscopy over 100 fibres. The length was 7.2±0.6 mm and the average diameter was 0.3±0.05 mm. The density of the fibre was determined by pycnometry in water, and was 1370 kg/m3.The cellulose derivatives/starch matrix and the sisal fibres were incorporated in an injection moulding machine (Sandretto 60 ton) without previous mixing. This procedure was chosen in order to preserve, as much as possible, the length and the diameter of the fibres. In fact, the conventional compounding technique (extrusion and injection) can ensure a good dispersion of fibres, but it also results in considerable reduction of fibre length and diameter.Dynamic thermogravimetric measurements were performed by using a Shimadzu TGA-DTGA instrument. Temperature programs for dynamic tests were run from 298 to 1273 K at heating rates in the range of 5–25 K/min. TG/DTG tests were carried out under nitrogen atmosphere (20 ml/min) in order to prevent any thermoxidative degradation.TG and DTG curves obtained for different used materials at 10 °C/min are presented in . Starch presents one decomposition peak with maximum at 320 °C. Cellulose acetate shows one peak at 365 °C. Sisal fibres present two decomposition steps: the first at 300 °C corresponding to hemicellulose and glucosidic link depolymerisation and second one at 360 °C corresponding to the thermal degradation of the α-cellulose. Lignin presents a broad peak in all the range shows the values of heating rate and temperature at the maximum degradation rate, obtained for all materials with different components. Even if the shape of the mass loss curves does not change and exhibits the same starting temperature of decomposition, the maximum degradation rate is slightly shifted to higher values as the heating rate increases. This behaviour may be attributed to heat transfer problems between the sample and the instrument It is important to note that decomposition curves of biodegradable matrix and sisal fibre are partially overlapped (), due to the component of each compound: starch and cellulose derivatives from the matrix and, lignin, hemicellulose and cellulose from the fibre. Lignin and starch are overlapped and cellulose derivative and lignin are overlapped with cellulose and hemicellulose. For a given heating rate, the temperature at the maximum degradation rate is slightly shifted to higher values as fibre content increases, may be due to the decreasing in starch content in the composite. The temperature of second peak increases with the fibre content, may be due to that cellulose derivatives is less thermal resistant than cellulose and hemicellulose of fibres.Kinetic parameters were predicted from the dynamic TG/DTG data. In spite of the overlapping of the component decomposition, it is possible to take into account two main peaks. This approach was used to predict kinetic parameters for copolymers, such as ethylene-vinyl acetate copolymer (EVA) for cellulose derivatives/starch blend heating at 10 K/min. The range of conversion for each step was determined based on the TG/DTG curves obtained at the lower heating rate (5 K/min).The differential method of Friedman allows obtaining the dependence of the kinetic parameters with the conversion from TG curves measured at different heating rates, making no assumptions about the reaction order. As an example, the iso-conversional Friedman plots for the second peak are shown in the . The average apparent activation energy value for the decomposition process for both peaks is shown in Activation energy does not change drastically with conversion (as can be concluded from the slopes in ). This result indicates that degradation mechanism remains unchanged throughout the whole process and could be attributed to the cleavage of linkages with similar bond energies. The same tendency is observed for the first peak.On the other hand, apparent activation energy for the first peak was not mainly affected for fibre content and an average value of 107.1±1.0 kJ/mol can be used for all fibre fractions from 0 to 15 wt.%. The values of apparent activation energies for the second peak are affected by the fibre content; this energy decreases when fibre content increases. The reaction order determined from the intercept was close to 1 for both processes.Kissinger method was also used for determining the kinetic parameters. The fact that this method assumes that the reaction order is close to 1 may be overlooked, in agreement with the reaction order predicted by Friedman method. shows the results of application this method to both peaks. summarizes the values of apparent activation energies obtained for all used materials.Osawa method is essentially the same as Flynn–Wall , while the calculated apparent activation energies and log A are given in the . Activation energies of each material are almost invariable with the conversion in the rage of 0.1<α<0.8, as can be concluded from . This result agrees with that obtained by applying Friedman method. For first peak, it was possible to calculate an average apparent activation energy for all sisal fibre contents, this value was: 106.8±1.2 kJ/mol, while for the second peak, activation energy decreases when fibre content increases.Van Krevelen method was also applied to the different cellulose derivatives/starch blend–sisal fibre composites. shows the results obtained for a heating rate of 5 K/min. The activation energies predicted for both stages are summarised in the . Average energy values are in the same range than those obtained by Friedman, Kissinger and Osawa methods.The integral method of Horowitz–Metzger was also applied to determine the kinetic parameters. The results are summarised in the . It is possible to calculate the average activation energy for all the heating rates and both peaks analysed: for the first peak for all sisal fibre content, this value was: 107.3 kJ/mol and for the second peak, activation energy decreases when fibre content increases. Although the trend is similar; the values are slightly higher than those obtained using the previous methods. shows the results of Kamal method for the second peak. Average energy values of the second peak are in the same range than those obtained by other used methods. A decreasing in the activation energy of the second peak is associated to a decreasing in the thermal stability due to the low thermal stability of the sisal fibre compounds in comparison with the cellulose derivative in the biodegradable matrix, as it was stated before.The effect of sisal fibre content on the thermal degradation of cellulose derivatives/starch blends has been analysed. Cellulose derivatives/starch blends thermal degradation was considered as step-degradation process of the two different peaks, depending on the temperature range. Based on the experimental findings, each stage of weight loss was analysed by using different classical kinetic models for predicting apparent activation energies and reaction orders associated with each step of the degradation process.There is no great variation in the predicted energy values, either using differential or integral kinetic methods. Horowitz–Metzger method predicts values slightly higher than the other methods. Friedman and Osawa make no assumption about the reaction order and are applicable to all points of the TG curve. Friedman method has the additional advantage of predicting the reaction order, which were close to 1 for both stages. Kissinger's method uses only one point (Tmax) and assumes a kinetic of pseudo-first order. Kissinger method is able to predict values in close agreement with those obtained by Osawa, Van Krevelen and Friedman. The obtained kinetic parameter can be used processing for determining the degree of degradation of such materials when they are processed.The activation energy values were almost invariable with the conversion, within each stage of the degradation process in spite that decomposition curves of components are overlapped in a central region. This is an indication that the same mechanism of decomposition was involved in the thermal degradation.It was found that the increase in fibre content does not affect too much the thermal degradation of the cellulose derivatives/starch blends at the first step of the thermal degradation. A slightly higher temperature and activation energy was obtained for the first peak and a lower temperature and activation energy was obtained for the second peak when the sisal fibre content increases in the composites.Experimental investigation of the size effect of layered roller compacted concrete (RCC) under high-strain-rate loadingThe strain rate and specimen size are two main influential factors when measuring the compressive strength of concrete-like materials. Understanding the dynamic size effect of concrete is essential for better analysis and design of concrete structures. However, few systematic laboratory tests have investigated the dynamic size effect in layered roller compacted concrete (RCC) under various levels of high-strain-rate loading. In this study, three sizes of cylindrical RCC specimens with diameters of 50 mm, 75 mm and 100 mm are prepared and tested under high loading rates to directly investigate the size effects. The size dependence and strain rate sensitivity are characterized in terms of the failure pattern, dynamic compressive strength, ultimate strain, maximum strains, and toughness. The dynamic compressive strength increases with increasing specimen size under impact loading, which is opposite to the size effect under static loading. The statistical significance is further investigated in terms of the variation in the dynamic mechanical properties of the RCC material based on analysis of variance (ANOVA). A modified Weibull size effect law, which incorporates both the specimen size and strain rate, is proposed and verified to illustrate the underlying mechanism of the dynamic size effect for the RCC material under impact loading.dynamic strength increase from the material strain-rate effect (MPa)dynamic strength increase from the structural effect (MPa)initial cross-sectional area of the specimen (mm2)real-time cross-sectional area of the specimen (mm2)initial thickness area of the specimen (mm)real-time thickness area of the specimen (mm)engineering stress of the specimen (MPa)engineering strain of the specimen (mm/mm)engineering strain rate of the specimen (/s)wave propagation velocity in the steel bars (m/s)cross-sectional area of the steel bars (mm2)transmitted strain in the steel bars (mm/mm)reflected strain in the steel bars (mm/mm)corresponding critical value at the 5% significance levelcumulative probability density of the failure for a specimenscaling value in Weibull distribution concerned with the mean (MPa)threshold strength of the failure for the specimen (MPa)scaling value in the Weibull size effect law (MPa)critical strain rate of the specimen (/s)strain-rate correction factor in the modified size effect lawIt is well accepted, based on experimental and theoretical investigations, that the mechanical response of concrete-like materials under compression, shear, tension and torsion under quasi-static loading is significantly affected by the specimen size. Generally, a smaller specimen requires higher stress to fracture under quasi-static loading. The mechanism of the concrete size effect law for the quasi-static strength can be classified into three categories: (1) Weakest-link hypothesis However, when exposed to high-strain-rate loading, concrete-like materials have a higher dynamic compressive strength than their corresponding static compressive strength Based on the concept of the size effect from Vliet where fd is the dynamic compressive strength; fc is the quasi-static strength; Δfε̇ is the dynamic strength increment due to the material strain-rate effect; and Δfi is the dynamic strength increment due to the structural effect With respect to the material size effect, many types of micro-structure analysis have been conducted to further understand the macroscopic failure phenomena occurring under impact loading Much effort has been devoted to explain the relationship among the strength, strain rate and specimen size in the context of the complex micro-structural hierarchy and finiteness of the crack propagation speed Roller compacted concrete (RCC), as a special type of concrete material, has different mixture from traditional concrete, i.e., less water and more fly ash are used to replace Portland cement. The mechanical properties of RCC show higher discreteness in the vertical direction due to the construction technology of thin-layer pouring and vibration rolling In this investigation, ordinary Portland cement was used to prepare the specimens for the SHPB tests; the selected coarse aggregate was artificial coarse aggregate produced by a local aggregate production system. Comprehensive consideration was taken to design the mixture to experimentally investigate the dynamic size effect, as shown in . Based on the code for the mix design of hydraulic concrete shows the specimen preparation process, which was described in our previous work e). To minimize the testing errors from the specimens, the surfaces of the cylindrical specimens should be sufficiently smoothly ground (The axial inertia effect can disprove the homogeneity assumption of stress and strain, which is the foundation of the SHPB tests. To minimize the axial inertia effect and reflect the actual dynamic responses of the RCC, the optimal L/D ratio of 0.5 was used to design specimens for the SHPB tests High-strain-rate impact tests were conducted using the SHPB test system. To avoid oscillation of the stress-strain curves, a half-sine stress waveform was selected as the ideal loading method to perform SHPB tests on quasi-brittle materials. In addition, the incident waves must also have a certain rising time to avoid destroying the sample before the stress balance between the two specimen surfaces. To reduce friction, Vaseline was uniformly daubed on the two specimen/bar contact surfaces. The strikers, which are propelled by the gas gun, impact against the incident bar. In this way, a stress pulse can be generated in the incident bar that spreads towards the specimens. Due to the differential wave impedance between the specimen and the incident bar, part of the stress pulse is transmitted via the specimen as a compressive pulse, and part of stress pulse is reflected into an incident bar as a tensile pulse. The strain gauges mounted on the incident and transmitted bars can record the incident, reflected and transmitted pulses during the entire impact process. shows the typical stress signals in incident and transmitted bars obtained from an SHPB test. Due to the stress equilibrium requirement during specimen failure, the stress pulse typically must reflect at least 3–4 times before destruction. The one-dimensional wave propagation assumption and the homogeneity assumption of stress and strain for the RCC specimens in SHPB tests were verified in our previous work Because it is challenging to accurately measure the real-time cross-sectional area (As) and thickness (Hs) of the specimen during the high-speed deformation, we replace them with the initial thickness Hs0 and cross-sectional area As0 in the calculation of engineering stress-strain curves, which is justified by the fact that the change in specimen thickness and cross-sectional area in SHPB tests is minimal. The “one-wave analysis” method where cb is the wave propagation velocity in the steel bars; Hs0 and As0 denote the original length and cross-sectional area of the specimen, respectively; Ab is the cross-sectional area of the steel bars; and Eb is the elastic modulus of the steel bars. In addition, εT(t) and εR(t) are the transmitted strain and reflected strain, respectively.Regarding the dynamic mechanical properties, various cross-sectional strikers or thin copper pulse shapers were used in the tests to achieve the half-sine stress wave loading. By varying the gas pressure of the gas gun (1.5–8 bar) and diameters of the specimens (D50 mm, D75 mm, and D100 mm), we caused specimens with different sizes to undergo various strain rates. The schematic design of the experimental tests is illustrated as . The specimens prepared for the SHPB tests can be classified into three categories based on the specimen diameter. For each category with identical diameter, the specimens can be divided into four groups based on the gas pressure in the SHPB tests. We prepared 10 specimens for each group (i.e., 120 specimens for the SHPB tests in total) at first. However, some specimens for the SHPB tests failed due to incorrect operation or other reasons, and only 101 specimens successfully satisfied the one-dimensional wave propagation assumption and homogeneity assumption of stress and strain. The 101 successfully tested specimens were not uniformly distributed. The specific number for each group has been listed in graphically illustrates the definitions of key mechanical properties in this study: the peak strength, ultimate strain, maximum strain and toughness. The peak value of the stress time history is considered the material strength. The ultimate strain is taken as the strain at peak stress, and the maximum strain of the stress-strain curve is the strain at the end of the softening stage. Moreover, the toughness related to the ductility and strength can be expressed as the specific energy absorption, which is the capacity to absorb the energy of the stress wave for the RCC per unit volume. It is also observed that the material strength occurs nearly at the peak strain rate duration and that the breakage process of the specimen maintains approximately constant strain rate loading since the variation in strain rate with time near the failure point is minimal.Because the strain rates obtained in the SHPB tests are not constant, the representative strain rate for each specimen can be defined in different ways. However, the strain rate at failure cannot be used to characterize the strain rate during the entire loading process Quasi-static compressive tests on the specimens (diameter × length = 100 mm × 200 mm) were conducted by using an electro-hydraulic servo-controlled loading test machine at Tianjin University. The testing machine delivers a constant crosshead movement with the loading rate of 1 mm/min, corresponding to a quasi-static strain rate of 8.30 × 10−5/s. The 90 d uniaxial compressive strength of the RCC prepared in this study was 11.13 MPa, and the corresponding Young’s modulus and ultimate strain (corresponding to the peak strength) were 2.61 GPa and 0.71%, respectively.The quasi-static strength will be used to calculate the dynamic increase factor (DIF) of material strength for RCC material based on the experimental tests. Discussions on strain-rate effect and dynamic size effect in terms of DIFs are given in Section The RCC specimens with various sizes were prepared and tested under different loading rates by varying the gas gun pressure. The failure patterns at different strain rates, as was concluded in Ref. shows the schematic failure patterns of the RCC at various strain rates, which can be summarized as follows. Visible cracks form in the ITZs and propagate along the interfaces under static loading (a). At the critical strain rate, the propagating path becomes straighter, and the fracture surface is less ragged (b). At a high strain rate, the cracks propagate along several direct paths with more fractured aggregates and the specimens ultimately are crushed into several fragments (c). With increasing strain rate, the specimens can be further crushed into finer granularities, which dissipate more energy (d). To sum up, stress increases so rapidly at higher strain rates that the cracks do not have sufficient time to propagate along the path of least resistance and propagate in aggregates instead, resulting in smaller fragments.Notably, the critical strain rate can be reduced by increasing the specimen size. Therefore, the failure pattern or other dynamic mechanical properties under impact loading may be significantly affected by both strain rate and specimen size. For example, the fracture status of the samples changes from fine fragments to large blocks when the specimen diameter is decreased from 100 mm to 50 mm at a similar strain rate of approximately 70/s in the SHPB tests, as shown in Considering the significant discreteness of the RCC from the construction technology, the stress-strain responses of the RCC material for each group are represented by the means and standard deviations. For the specimens with identical sizes, the stress-strain responses of four groups characterized by different average strain rates are compared in a–c to illustrate the strain-rate effect along with significant discreteness. The average stress-strain responses of the RCC specimens with different sizes share common characteristics: they change significantly with increasing strain rates. The peak stress increases at a higher strain rate, which we refer to as strain-rate dependence resulting from the comprehensive effects of the inertial effect, crack propagation effect and viscosity effect. The slopes of the ascending and descending parts of the stress-strain curves tend to be steeper when the strain rate increases.The average stress–strain curves for specimens of different dimensions at a similar strain rate (approximately 70/s) are compared in d. A notable change in these curves demonstrates the dynamic size effect. The stress-strain curves of the larger specimens are much steeper than those of smaller specimens, i.e., the peak stress increases when the specimen size increases. summarizes the testing results of dynamic compressive strength and corresponding strain rate for the D50 specimens, which have been classified into four groups according to the gas gun pressure as shown in that the mean values of dynamic compressive strength for each RCC group increases with the increasing average strain rate. The same rules have been seen in specimens with diameters of 75 mm and 100 mm as well.Various concrete-like materials have been studied using laboratory tests to quantify the strain-rate effects, and the polynomial fitting method has been widely used to illustrate the empirical relationship between the strain rates and the DIFs compares the obtained DIFs with the existing empirical models from other studies. In general, the test results are distributed among these empirical models. Moreover, the DIF increases with increasing strain rate, and the DIFs of the RCC appear more sensitive to the strain rate than the DIFs of normal concrete. also shows that the DIFs tend to be more sensitive to the strain rate for larger specimens. The test results are consistent with the observations of previous studies compares the experimental results of the dynamic compressive properties, which are represented by the mean values and standard deviations, for specimens with various sizes and strain rates. For specimens with 50 mm in diameter (D50 mm), when the strain rate increases from 70.15 to 143.78/s, the average peak strength continuously increases from 10.08 to 22.28 MPa. The ultimate strain and maximum strain continually increase from 0.0070 to 0.0113 and from 0.0205 to 0.0278, respectively. In addition, the average toughness slightly increases by as much as 0.19 MJ/m3. The same trend is observed in the D75mm specimens. Immediately after the average strain rate increases from 46.68 to 111.20/s, the average peak strength increases from 10.75 to 36.71 MPa, as much as 241%. In addition, the average ultimate strain consistently increases from 0.0065 to 0.0131. Because of the increasing ductility and strength, the average toughness increases from 0.11 to 0.98 MJ/m3. The average peak strength of the D100mm specimens increases from 15.31 to 30.44 MPa when the strain rate increases from 33.11/s to 74.08/s, as well as ultimate strain, maximum strains, and toughness all increase with the strain rate.All experimental results of the dynamic mechanical properties for the RCC material share significant variability at different strain rates. Moreover, the experimental results suggest that the specimen size is another key factor for the increase in dynamic mechanical properties, e.g., the peak strength, ultimate strain and toughness, as shown in . When the specimen size is larger, the lateral inertia confinement becomes more significant, which ultimately leads to a higher peak strength. For example, the testing results of different dimensional specimens at a similar strain rate (approximately 70/s) show that when the diameter of the specimen increases from 50 mm to 75 mm to 100 mm, the average peak strength monotonically increases from 10.08 MPa to 20.33 MPa to 30.44 MPa. This phenomenon is more prominent in a. Similar trends are observed for other dynamic mechanical properties, such as the ultimate strain and toughness. For the ductility, the maximum strain increases with increasing strain rate for same-size specimens, whereas the size dependence of the maximum strain is indistinct for specimens at a similar strain rate. This phenomenon is graphically illustrated in d. Because of the increasing ductility and strength, the specimens at a high strain rate exhibit a greater toughness than those at a relative low strain rate.To further investigate the statistical significance of the strain-rate sensitivity and size dependence on the dynamic mechanical parameters of RCC at high strain rates, the widely accepted method of ANOVA was performed summarizes all ANOVA results of specimens of various dimensions for the RCC material. The peak strength, maximum strain, and toughness can be significantly affected by the strain rates for specimens of different dimensions. A smaller P-value provides stronger justification to reject the null hypothesis. The strain-rate effect is notable for almost all of the dynamic mechanical properties, whereas the ultimate strain for the D100 mm specimens is less sensitive to the strain rates. The size effect is detectable for most of the dynamic mechanical properties, apart from the maximum strain. The P-value of the maximum strain, recorded as 0.30 > 0.05, indicates that specimens of different sizes have similar maximum strains. Thus, the size dependence of the maximum strain for the RCC is insignificant.. In addition, by taking the logarithm twice, the Weibull distribution can be rewritten in linear form as Eq. where σ is the peak strength, σ0 is the scaling value concerned with the mean, and m is the shape parameter or Weibull modulus. Then, the mean and standard deviation can be derived as follows:where σ¯ is the mean strength, s is the standard deviation, and Γ(∗) is the gamma function.The cumulative probability density P can be estimated aswhere N is the total number of tests and i is the current test number.The cumulative distribution plots of the experimental results show satisfactory qualitative agreement. compares the fitted cumulative distribution functions (CDFs) for each group in , and the Weibull distribution is shown to accurately describe the discrete material strength. also shows that the fitted cumulative probability curve shifts toward a higher stress value when the strain rate increases for same-size specimens, which indicates a positive effect of the strain rate on material strength. However, the peak strength shows more significant discreteness at higher strain rates since the fitted cumulative probability curve tends to be less steep. summarizes the calculated parameters of the fitted Weibull distributions. For the dynamic experimental data, σ0 increases with increasing strain rate for same-size specimens. However, the statistical results show that the strain-rate effect on the shape parameter is not pronounced, without notable increasing or decreasing trend as the strain rate increases, which indicates an approximately uniform distribution at the selected strain rates. The average shape parameters for the D50 mm, D75 mm, and D100 mm specimens are 10.15, 4.28, and 8.07, respectively, indicating no strong relationship with the specimen size. also shows the effect of the strain rate and specimen size on the mean strength (σ¯) and standard deviation (s). Both the mean strength and standard deviation increase somewhat with increasing strain rate and specimen size. graphically presents the mean and standard deviation of strength from Weibull analysis. Relative to the results shown in a, the means and standard deviations of strength derived from the Weibull distribution are notably near to those of the experimental data. Based on the analysis results in this study, empirical formulae in terms of the dynamic compressive strength for the RCC material under impact loading are suggested as follows:σ¯=[8.36(lgε̇)2-29.94(lgε̇)+27.70]fc,forD50specimensat70/s<ε̇<150/sσ¯=[13.67(lgε̇)2-44.57(lgε̇)+37.26]fc,forD75specimensat40/s<ε̇<120/sσ¯=[8.59(lgε̇)2-25.26(lgε̇)+19.93]fc,forD100specimensat30/s<ε̇<80/sIn this study, the dynamic compressive strength increases with increasing specimen size in the condition of identical strain rates, which is opposite to the behavior of the size effect under quasi-static loading. In addition, the dynamic size effect indicates that the gap in dynamic compressive strength for specimens of different dimensions tends to be less significant under relatively low impact loading. As concluded in Ref. From the viewpoint of structural hierarchy, the weakest link of hardened RCC structure is the ITZ, where micro-cracks first initiate Most statistical analysis of brittle fracture is based on the weakest-link assumption, which is a well-accepted method to analyze the variability of concrete strength. The static size effect of concrete based on the weakest-link assumption can be illustrated as follows:where P is the cumulative probability of the failure of a specimen with volume V; dV is the differential volume; V0 is a constant representing the average volume of each microcrack; σth and σ1 denote the threshold strength and scale parameter, respectively; and m is the shape parameter or Weibull modulus. Then, the cumulative probability P is normalized for σth⩽σ⩽∞. In addition, the corresponding probability density function (p) concerning the fracture strength (σ) can be derived as follows:p(σ)=VV0mσ1σ-σthσ1m-1exp-VV0σ-σthσ1m(σ⩾σth)From the safety viewpoint, σth can be set to zero Many researchers have performed refined research on the size effect on the dynamic compressive strength of concrete-like materials. Notably, larger specimens are associated with a greater strain-rate sensitivity of the dynamic strength p(σ)=VV0αlnε̇0/ε̇mσ1σσ1m-1exp-VV0αlnε̇0/ε̇σσ1m(σ⩾0)where ε̇0 is the critical strain rate, below which the static size effect dominates. ε̇ is the strain rate, and α is the correction factor of the strain-rate effect. can be rewritten as a logarithmic linear relation, as shown in Eq. , the modified Weibull size law in the linear form can be seen as a modified two-parameter Weibull distribution to statistically analyze the dynamic strength of concrete material considering the size and strain-rate effects. In Ref. ln[-ln(1-P)]=α(lnV0-lnV)(lnε̇-lnε̇0)+m(lnσ-lnσ1)The strength is related to the specimen size and strain rate according to the proposed Weibull size effect law. Derived from Eq. using the moment method, the mean value σ¯ and standard deviation s can be obtained using Eqs. , respectively. Then, the average strength increases for larger specimens when ε̇>ε̇0; the size effect disappears at the critical strain rate; and the average strength decreases with increasing specimen size when ε̇<ε̇0. In addition, the size effect is enhanced at a higher strain rate, as is the standard deviation.Based on the statistical results of the experimental data in , the scaling value σ0 increases with increasing strain rate for same-size specimens. Comparing the mean and standard deviation of strength derived from the proposed Weibull size effect law in Eqs. to those derived from Weibull statistics as Eqs. , we find that σ0 includes the coupling effect of the strain rate and specimen size, as illustrated in Eqs. . Here, σ1 becomes a constant, and shares no relationship with the specimen size and strain rate.The parameter estimation has been the primary issue to verify the practicability of the proposed effect law. The shape parameter m is insensitive to the strain rate and uncoupled to the specimen size. Here, we select the mean value of the shape parameter (m = 7.50) according to , and the critical strain rate can be obtained as 40/s from Ref. Several methods are available to determine the parameter of the modified Weibull size effect law from a set of experimental strength data, in which the most widely used method is the least-squares method (LSM) analysis. Using the statistical results from the experimental data in , a linear least-squares regression analysis can be performed on Eq. to determine the parameters in the proposed size effect law. As a complement, the volume of a specimen can be calculated as V=πD3/8, where D is the diameter of the specimen.The results of parameter estimation with the experimental data from 101 successful SHPB tests are σ1=14.16MPa, α=4.12 and V0=3.54×10-5m3. By substituting the fitting parameters into Eq. , the modified Weibull size effect law is graphically shown in . As an objective of this study, the strength from proposed Weibull size effect law is an estimated mean strength essentially (Eq. ) based on the concept of the weakest-link assumption and has an inherent relationship with the results of the Weibull analysis. In this study, the mean strength for each group has been estimated based on the Weibull analysis, as listed in . Therefore, it is necessary to compare the mean dynamic strength from Weibull analysis () with that from proposed Weibull size effect law (Eq. a shows that the experimental mean strength points from Weibull analysis are consistent with the theoretical surface of the modified size effect law. The modified size effect law can also present the basic rules that the dynamic compressive strength increases with increasing specimen size under impact loading, as shown in b, which is diametrically opposed to the common size effect under quasi-static loading. Moreover, the enhancement of dynamic strength becomes more sensitive to the strain rate for larger specimens.Focusing on the dynamic size effect of the RCC material, SHPB tests on 101 cylindrical specimens with the diameters of 50 mm, 75 mm and 100 mm was conducted under high strain rate loading in this study. The dynamic size effect of the RCC material was investigated based on the experimental results within a wide range of strain rates and was reconfirmed based on ANOVA and Weibull analysis. A modified Weibull size effect law was proposed to illustrate the underlying mechanism of the dynamic size effect for the RCC material under impact loading. The main contributions and findings are as follows:The observed dynamic mechanical properties of RCC material were size dependent. The dynamic size effect under impact loading is notably different from the well-known static size effect, in which the dynamic mechanical properties, e.g., the peak strength, ultimate strain and toughness, increases with the increasing sample size at a similar strain rate.Besides contributions from material heterogeneity, the dynamic size effect partly consists of contributions from lateral inertial confinement due to strain rate effect, which is significantly important for larger specimens. A larger specimen corresponds to a more prominent strain-rate effect on the dynamic compressive strength, i.e., the experimental peak strength for larger specimens is more sensitive to the strain rate.More significant scatter of the stress-strain curves and DIFs was directly observed from the dynamic compressive tests at higher strain rates. The Weibull analysis also showed that the variance of dynamic compressive strength for RCC specimens tended to be larger under higher impact loading. Therefore, more attentions should be paid to the variance of dynamic compressive strength from material heterogeneity in structural dynamic analysis, considering the dynamic size effect.A modified size effect law considering the strain-rate effect was proposed to illustrate the underlying mechanism of the size effect for the RCC material. The proposed size effect law can be formulated as a modified two-parameter Weibull distribution to statistically analyze the strength of the concrete material, considering the strain rate and specimen size. Finally, the relationships of the material strength, specimen size and strain rate were further described under a unified theoretical framework containing static and dynamic loading.On significant retention of impact strength in clay–reinforced high-density polyethylene (HDPE) nanocompositesThe mechanical response of clay–reinforced polyethylene nanocomposite is investigated and the behavior compared with the un-reinforced polyethylene under identical conditions of processing. The micromechanism of plastic deformation during impact loading of neat polyethylene and clay–reinforced polyethylene nanocomposite are studied with scanning electron microscopy (SEM). The impact strength of composites is linked to structural studies by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA) and transmission electron microscopy (TEM) and SEM observations. The addition of clay to polyethylene retains adequately high-impact strength in the investigated temperature range of −40 to +70 °C. The micromechanism of deformation is altered from a combination of craze and drawing of fibrils in neat polyethylene to microvoid coalescence-fibrillated process in the nanocomposite. The aspects related to micromechanism of deformation are discussed.High-density polyethylene (HDPE) is considered a primary material in the materials substitution chain because of availability and recyclability. The performance criterion to encourage the application of HDPE requires superior modulus and yield strength in conjunction with high-impact strength. A substantial enhancement in mechanical properties (modulus, yield strength, and toughness) of thermoplastic materials can be realized by reinforcement with inorganic minerals including talc In recent years, polymer nanocomposites have received significant attention, both in the industry and in academia during the past decade. They are a new class of multiphase materials containing dispersion of an ultra fine phase, typically in the range of 1–100 nm. They represent an attractive set of inorganic–organic materials (or organic–organic in some cases), not only from their obvious potential as technological materials, but also provide a convenient macroscopic system to study basic scientific issues concerning confined and tethered polymers at a new scale intermediate between the nano and microscale. A number of experimental investigations on these materials have indicated that polymer nanocomposites exhibit new and sometimes improved properties that are not displayed by the individual phases or by their conventional composite counterparts In clay–reinforced polymer nanocomposites, the significant increase in modulus is recognized and is reasonably understood. However, an understanding of the toughness behavior is still fragmented and less examined. The study of impact toughness is fundamentally important considering that the majority of semi-crystalline polymeric materials (polyethylene and polypropylene) are ductile at low-strain rates, but at high-strain rates such as those experienced in Izod impact test, exhibit a brittle behavior. Thus, the study of impact toughness at high-strain rates is of particular interest. Izod impact tests are also important because yield stress increases with strain rate, promoting brittle mode of fracture. Lastly, high-tensile toughness may not necessarily mean high-impact toughness.The toughening behavior in polyvinylidene fluoride (PVDF) In the present paper, impact on the toughness behavior of high-density polyethylene copolymer (PE)–4 wt% clay are described in terms of the response of the polymer matrix, in terms of nucleating capability of the reinforcement, crystal structure, percentage crystallinity, lamellae thickness, and matrix–particle interface.Commercially available grade of high-density polyethylene copolymer produced by Solvay (formal product name: ethane–hexene-1 copolymer) and developed for blow molding automotive fuel tanks and other large parts, where the finished part demands environmental stress crack resistance (ESCR), excellent processability and superior impact properties was used to process PE–4 wt% clay nanocomposites. This grade has a melt flow rate of 9 g/10 min at 190/2.16 kg. A natural montmorillonite clay surface modified with dimethyl dialkyl ammonium (Nanomer I.44P, Nanocor) was used as the reinforcement filler. The nanocomposites were prepared by mixing the appropriate amounts in twin screw extruder (counter rotating, 100 rpm) followed by injection molding of bars. The storage modulus of neat PE and PE–clay nanocomposites was studied by dynamic mechanical analysis (DMA). The DMA was carried out using TA instruments 2980 in single cantilever mode from −125 to 120 °C. The testing frequency was 1 Hz and the heating rate was 3 °C/min.The study of degree of crystallinity assumes particular significance because higher crystallinity, in general, increases modulus and yield stress, and reduces toughness. The change in percentage crystallinity, and structural characteristics induced by clay is important in understanding the deformation behavior. The crystallization behavior of neat PE and clay–reinforced PE nanocomposites was studied by differential scanning calorimetry (DSC). The PE and PE–clay nanocomposites were heated from room temperature (∼20 °C) to 200 °C and held at the high temperature for about 3 min in order to erase the previous thermomechanical history and to obtain a completely relaxed melt. Then the melt was cooled to 30 °C at the rate of 10 °C/min, and a second scan was carried out at the rate of 10 °C/min.The dispersibility and intercalation of PE into the clay layers was studied by transmission electron microscopy (TEM). The staining was carried out in the vapor phase. The trimmed specimen was stained by staying with solid ruthenium tetroxide (RuO4) for 10 h in a vial The tensile bars of neat and PE–clay nanocomposites were tested in uniaxial tension at 20 °C using a computerized MTS 210 tensile testing machine at selected displacement rate of ∼5 mm/min to determine tensile properties (modulus, yield strength) in accordance with ASTM D-638. The Izod impact tests were carried out using an instrumented falling weight Tinius Olsen impact tester (Model 899) with an impact velocity of 1 m/s. The notched specimens were subjected to the impact test in the temperature range of −40 to +70 °C.The fracture surface of Izod impact tested specimens as a function of temperature was studied using field emission SEM (JEOL 6300F) after coating with gold to minimize electrostatic charging.The fracture surface of Izod impact tested specimens at −40 °C was studied using field emission SEM (JEOL 6300F) after coating with gold to minimize electrostatic charging. The surface morphology of isothermal crystallized samples (120 °C) of both neat PE and PE–4 wt% clay nanocomposite was observed using SEM after etching with potassium permanganate.The DSC plots for neat PE and PE–4 wt% clay are presented in and the crystallization data (percentage crystallinity, melting and crystallization temperatures) summarized in . The percentage crystallinity was estimated using a value of heat of fusion of 293 J/g . The interfacial interaction plays a critical role in the free energy of cluster formation and the rate of nucleation; the weak interaction lowers the rate of nucleation. The DMA results also indicated weaker interaction between PE matrix and nanoclay, compared with polypropylene–clay nanocomposite ( are lamellar thickness (l). The lamellar thickness is given by the Thomson–Gibbs equation where Tm0 is the equilibrium melting temperature, Tm is the detected melting temperature by DSC, γ the surface free energy, ΔH the heat of fusion for 100% crystalline polyethylene, and the density. The slightly increase in melting temperature is correlated to the slightly increase in lamellae thickness and indicates the perfection of crystals improved with the addition of clay particles.Representative SEM micrographs of the crystal structure of 120 °C crystallized neat PE and PE–4 wt% clay nanocomposite are presented in . It is found that the addition of clay slightly affects the crystal structure (shape and size) of the matrix polymer by making it finer.The dispersion of clay nanoparticles in the nanocomposite is presented in (a). The particles are uniformly distributed in the matrix and do not give an indication of aggregation. Uniform dispersion is important because in case of a matrix with aggregates of particles, the stress field will be concentrated around any aggregates, such that the cracks will propagate easily and rapidly, causing premature failure. The higher magnification TEM micrograph ((b)) shows the intercalation of clay. Furthermore, it is also interesting to note that crystalline lamellae parallel to the clay layers ((b1)) and are present between the intercalated galleries of clay ((b2)). The existence of parallel lamellae in the vicinity of the clay makes us to believe that interphase around the particle is a characteristic of the crystalline nature of the particle–matrix interface.The tensile modulus and yield stress data are listed in also includes data for 4 wt% clay–reinforced polyethylene. The elastic modulus increased from 606.3 MPa in neat polyethylene to 767.0 MPa in 4 wt% clay nanocomposite. However, the yield stress remained unaffected because of weak interaction between filler and the polymer matrix. A similar behavior was observed for wollastonite- ) on reinforcement with clay nanoparticles. The observed significant increase in crystallinity is most likely to be because of higher nucleation density induced by the clay particles. To rationalize these observations, it is appropriate to say that the reinforcement of polyethylene with consequent increase in percentage crystallinity increases the modulus of nanocomposites. In summary, it is the reinforcement effect that dominates the mechanical behavior. Friedrich shows that the lamellar thickness was slight increased with percentage clay reinforcement. The lamellar thickness is an important controlling parameter in the activation of yield, and yield stress in neat semi-crystalline polymers is proportional to lamellar thickness Izod impact strength for PE and PE–4 wt% clay nanocomposite are presented in for tests conducted in the temperature range of −40 to +70 °C. It may be noted that the addition of clay to PE though decreases the impact strength for the entire temperature range of Izod impact tests, however, the toughness continues to be high even at −40 °C (10 kJ/m2).The examination of fracture surface at −40 °C reveals strikingly different features and fracture zones in neat PE (). Macroscopically, the fracture surface appeared highly ductile in neat PE () and less ductile or brittle-like in PE–clay nanocomposite (). This macroscopic difference suggests that the crack propagation occurred at a rapid rate in the nanocomposite. We shall first describe the fracture characteristics of neat PE copolymer.The macroscopic fracture surface of neat PE impacted tested at −40 °C is presented in and is clearly indicative of a highly ductile mode of fracture. From , two primary zones can be defined and include initiation zone (zone 1) and the crack propagation zone (zone 2) ((a)–(c)). Both the initiation and propagation zones can be further subclassified. Initiation zone consists of zones 1A and B. The zone 1A resembles a craze-like region with large vein-type features involving tearing of the material ((c)). Within the shallow vein-type features, extensive drawing of fibrils can be seen implying considerable degree of plastic deformation ((d)). Ahead of zone 1A, is zone 1B, characterized by a less ductile zone with small shallow features ((e) and (f)). In zone 1B, the drawing of fibrils is significantly less ((f)). The high toughness of PE results in slower breakdown of the initiation zone and is characterized by a initial propagation zone 2A ((a), (g) and (h)), followed by zones 2B and 2C. The zone 2A at high-magnification images ((g) and (h)) is similar to zone 1A. An important characteristic feature of the fracture surface is the formation of parabolic or conical markings in zone 2B ((a) and (i)), ahead of the propagation zone 2A. The fracture morphology observed at the edge of the sample in zones 1A, 1B, and 2A ((a)). It is envisaged that the growth and propagation of the macroscopic crack is accompanied by nucleation of secondary ‘plastic’ microcracks ahead and on the sides of the primary macroscopic crack (notch) at a local region of heterogeneity, as depicted in . An example of a nucleation site and outward growth is presented in (i)–(k) and the magnified view of the parabolic region marked with a box is shown in (l) and (m). Another example of the nucleation point emanating in the vicinity of the edge of the sample and growing inwards to the center is presented in (n) and (o). The primary crack and the new secondary microcracks grow and eventually interact such that the locus of interaction of the main crack front and the microcracks is the parabola (). In the high-magnification view of the parabolic markings, a secondary detail in the form of fine striations or fibrillation is clearly visible ((l) and (m)). The striations or fibrils are parallel to the local direction of the crack growth and are result of severe plastic deformation processes. When the microcracks are nucleated out of the plane of the main crack, the microcracks overlap each other, as schematically shown in . The final fracture occurs when overlapping primary and secondary cracks bow out and river-like steps at the scale of nanometer develop within the highly deformed polymer matrix, as identified in (m). The last stage of propagation, zone 2C, was characterized by stop–go-events. The crack fronts were well defined indicating that some irreversible deformation occurred at the propagating crack tip leaving residual markings on the fracture surface (a). With increase in temperature up to +70 °C, the extent of the craze-like zone (zone 1A, zone 1B) was reduced. A schematic representative is shown in In contrast to neat polyethylene, the overall macroscopic fracture surface behavior of PE–clay nanocomposite at −40 °C appears brittle-like and rougher with seemingly little macroscopic plastic deformation before fracture but as described below the fracture process involved extensive plastic deformation in different zones ((a)). We can define two primary zones, initiation (zone 1) and propagation zones (zone 2). The nature of the fracture surface morphology in the two zones was different from neat PE copolymer. In general, the characteristics of the fracture surface were similar at all test temperatures except for the extent of the individual zones. The macroscopic and microscopic features are presented in The crack initiation zone has two small subzones (zones 1A and B) with significant differences in the ductile morphology. In a manner similar to neat PE, the first subfracture initiation zone (zone 1A) was characterized by a craze-like ductile zone ((b)) with tearing leading to large shallow features of size 100–200 μm (zone 1A) (). The elongated fibrils here are much finer implying considerable amount of plastic deformation but significantly less dense, when compared with zone 1A in neat PE. At high magnification, zone 1A is ductile involving microvoids and extensively deformed fibrils (fibrillation) ((d)). The combination of microvoid coalescence and fibrillated appearance results from the nucleation and growth of a large number of microvoids and extensive localized deformation of ligaments between the microvoids. The microvoids later on coalesce and the crack propagates unstably. Even in the impact test, the elements of the material or ligaments between the microvoids draw down to fine points, before separation of polymer molecules past each other occur, producing fibrillated fracture. The highly stretched material then shrinks producing an appearance presented in the high-magnification image of zone 1A in (e). The combination of microvoid and fibrillated fracture can be understood in terms of two interactive processes. First, the nucleation of microvoids in the vicinity of particles provides stress concentration centers that determine the density of microvoids. Second, the viscoelastic plastic processes associated with the growth of microvoids and the deformation of ligaments bridging the microvoids. The ligaments or islands of material between the microvoids must fracture before the final separation occurs. An explanation for the mechanics of fracture necessitates a model that can predict the nucleation, density, and growth of microvoids, all of which are dependent on the state of stress. We are currently examining this aspect. A schematic of the envisaged microvoid coalescence-fibrillated fracture process is presented in . The initiation zone 1A is dominated by microvoid coalescence. This may suggest that the ability of the material to experience high-ductile behavior, but the higher crystallinity and reinforcement clay offers resistance to plastic deformation. The reduced density of fibrils/fibrous structure implies lower amount of energy is absorbed in clay–reinforced PE copolymer. The formation of dense fibrils in PE copolymer must be responsible for the observed significantly high toughness in relation to the nanocomposite. On the other hand, the reduced density of fibrils in the nanocomposite suggests formation of greater number of shallow microvoids and dimpled pattern. The second initiation zone 1B ((e) and (f)) has reduced ductility in relation to zone 1A.The rapid breakdown of the craze initiation zone does not provide adequate time for the material ahead of the initiation zone 1A to respond such that a second smooth region 1B surrounds the zone 1A. The second initiation zone (zone 1B) has reduced ductility in relation to zone 1A.The propagation zone 2 with brittle-like appearance ((a)) also involved microvoid coalesence ((h) and (i)) in a manner similar to zone 1A, but with reduced plasticity. A schematic of the relative extent of different zones is summarized in . The zone was observed to decrease with increase in temperature with consequent increase in the shear-lip propagation zone (zone 2B). In general, the fracture surface of PE copolymer–4 wt% clay nanocomposite was predominantly characterized by microvoid and fibrillation, with fibrillation being significantly being less in zone 1B.It is clear from the relative comparison of the initiation and propagation zone in neat PE copolymer and PE–4 wt% clay nanocomposite that the reinforcement leads to transformation of the fracture surface from predominantly dense fibrous structure to predominantly microvoid coalescence fracture. In both neat PE copolymer and in the nanocomposite, the fibrils in the initiation craze zone have the ability to significantly plastically deform before fracture, except that in the nanocomposite, the ability is reduced. Thus, it is believed that clay must be the source of microvoid nucleation. The matrix ligaments between these voids are extensively deformed in the propagation zone leading to a combination of microvoid coalescence and fibrillated fracture. In general, both the initiation and propagation zones exhibit various degrees of ductility, where small size microvoids and severely deformed fibrils are indicative of higher microplasticity. for PE copolymer and nanocomposites, respectively, it may be noted that the fibrous structure is highly dense with no apparent large size microvoids in PE copolymer. On the other hand, in the nanocomposite, the density of fibrils is dramatically reduced but significant plastic deformation of a few stretched fibrils can be seen. But the fact that toughness is reduced and densely populated fibrous structure is not observed in the nanocomposite implies that some structural features of the nanocomposite offer resistance to plastic deformation. It may be noted that our recent work on polypropylene–4 wt% clay nanocomposites processed under identical conditions indicated an increase in toughness in the temperature range of −40 to +70 °C. From DSC results (), the crystallization temperature of PE–clay nanocomposite remains almost same with the addition of clay. While in polypropylene–clay nanocomposites, the crystallization temperature of polypropylene increased over 15 °C. This implies that the nucleating effect of clay in PE–clay nanocomposites is less obvious than that in polypropylene–clay nanocomposites. On the other hand, from the DMA results () it can be observed that the tan |
δ peak of the nanocomposite (glass transition temperature, Tg) shifts only slightly to lower temperature on reinforcement with clay (). This can be explained in terms of the weak interaction between nanoclay particles and the PE matrix. In addition, the storage modulus of the nanocomposite remains unaffected on the addition of clay. Comparing with polypropylene–clay nanocomposite system, the reason why the addition of clay to PE decreases the impact strength for the entire temperature range of Izod impact tests maybe ascribed to the interaction between nanoclay particles and polymer matrix. During mechanical deformation, the relative weak part (particle–filler interface) though believed to be crystalline from The toughness of a material is generally related to the energy dissipating events that occur in the vicinity of a sharp crack. In HDPE copolymer, the highly dense fibrous structure is responsible for high toughness and the final fracture occurs due to nanoscale cracks formed between the stretched fibrils, as arrowed in (m). While in the nanocomposite, the microvoids nucleated due to clay releasing the plastic constraint in the matrix, triggering large scale plastic deformation with consequent tearing of matrix ligaments between microvoids resulting in stretching of fibrils (fibrillation) interdispersed with microvoids ((h) and (i)). Each of the above outlined processes, fibrillation, or microvoiding, and matrix yielding contribute to energy absorption In mineral-reinforced semi-crystalline thermoplastic materials, the microdeformation processes identified as energy dissipating mechanisms include crazing, cavitation or debonding of minerals with consequent microvoid formation, deformation bands and fibrillation , the reinforcement with clay increased percentage crystallinity and slightly increased lamellae thickness and the crystal structure morphology remain unaffected (). Previous work on neat polymers indicated that higher crystallinity and large spherulite size are detrimental to toughness (b2)), the growth of lamellae on the nanoclay particle surface.The addition of clay to polyethylene though decreases the impact strength for the entire temperature range of Izod impact tests, however, the toughness continues to be high even at −40 °C (10 kJ/m2).Impact fracture surface of neat polyethylene and clay–reinforced polyethylene composite exhibit two primary zones: initiation and propagation zones. The fracture of polyethylene initiates with crazing, while the propagation involves a combination of different process: fast propagation of crack and shear process.The fracture initiation and propagation of clay–polyethylene nanocomposite is characterized by stretching of fibrils (fibrillation) interdispersed with microvoids. The low toughness of the clay–reinforced polyethylene in relation to neat polyethylene is related to the crystal structure and interfacial interaction between the filler and the polymer matrix.The reinforcement of polyethylene with nanoclay alters the primary mechanism of deformation from a combination of craze and drawing of fibrils in polyethylene to microvoid coalescence-fibrillated process.Fatigue characterization and modeling of AZ31B magnesium alloy spot-weldsCyclic behavior of AZ31B spot-welds was studied using different specimen configurations, and compared with steel and aluminum spot-welds. Fatigue strength of magnesium spot-welds was similar to aluminum and less than steel. Three failure modes were observed in tensile–shear specimens and one mode of failure in cross-tension specimens. Fatigue crack initiation life was 50% and 30% of the total life for tensile–shear and cross-tension specimens, respectively. A number of available fatigue models were assessed by predicting fatigue life of magnesium spot-welds. Although these models do not account for the asymmetric cyclic hardening behavior, some of them performed successfully for magnesium spot-welds.Magnesium (Mg), with the lowest density among engineering metals, has attracted significant attention in the automotive industry. The trend in the average Mg usage per car has been rapidly increasing from 3 kg in 2005 to 20 kg in 2010, and is projected to reach 50 kg in 2015 From a joining perspective, resistance spot welding (RSW) is the predominant joining technique in automobile body assembly lines Service reports of automobiles show that a major portion of structural durability issues are related to spot-welds Many researchers have focused on developing models to estimate the fatigue life of spot-welds. The main approaches in these models include: fracture mechanics Available fatigue models for spot-welds have been verified for steel and aluminum with symmetric tension–compression hardening behavior. Due to the asymmetric cyclic behavior of wrought Mg alloys, applicability of these models must be examined for Mg spot-welds. To the best of authors’ knowledge, there is no published work available for fatigue modeling of magnesium spot-welds.The present research was aimed at characterizing the fatigue behavior of AZ31B and its spot-welds from a macroscopic point of view. Cyclic behavior of AZ31B was examined through fatigue testing. Fatigue strength and modes of failure under cyclic loading were studied on spot-welded specimens in tensile–shear and cross-tension configurations. Different approaches for fatigue modeling of spot-welds were introduced and one fatigue model based on each approach was reviewed and examined for magnesium spot-welds. Investigated fatigue models were correlated with experimental data.The material investigated in this research was AZ31B-H24 hot-rolled magnesium sheet. The sheets were provided by Magnesium Elektron of North America (MENA) in 2 mm and 4 mm thicknesses. The chemical composition and mechanical properties are shown in , which has a continuous curvature within the reduced section, was adopted in this research for fatigue testing.Two types of spot-welded specimens were investigated in this research: tensile–shear (TS) and cross-tension (CT). Two different designs for the TS specimens were employed, as shown in (a), is according to the American Welding Society (AWS) standard (b), is more common in the literature. To compensate for the coupons’ offset and prevent initial bending of the specimens, two spacers with the same thickness as the coupons were attached to the ends of the TS specimens. illustrates the design of the CT specimens, which is in accordance with the resistance spot welding manual Five sets of spot-welded specimens in TS and CT configurations were prepared with an AC spot-welding machine. Different welding parameters were used to achieve different spot-weld nugget diameters. summarizes the specifications of the specimens and the coding. Nugget sizes were measured after monotonic testing as the average diameters of the bonding area, along and perpendicular to the loading direction.Fatigue testing of the base metal, AZ31B-H24, was conducted on the specimen shown in . Engineering strain was measured using an extensometer with 6 mm gauge length and ±0.8 mm travel. Fatigue testing was performed in strain-control mode for approximately 104 cycles, and then stopped and switched to load-control mode, once the load response had stabilized. The main reason for controlling the load was to increase the frequency. The testing frequency was 0.1–0.15 Hz and 3–10 Hz for strain- and load-control testing, respectively. The tests were run in the fully reversed loading condition, i.e., the strain ratio, R, was −1 (R |
= |
Lmin/Lmax, where Lmin and Lmax are minimum and maximum loads, respectively). Tests were stopped if the life exceeded 107 cycles, and considered run-outs. Another criterion for stopping the test in the strain-control mode was a 50% load drop.Fatigue testing of spot-welded specimens was performed on the specimen sets shown in . Fatigue tests were conducted under load-control with a load ratio R |
= 0.2; except for specimen set F for which R |
= 0.1. A sinusoidal waveform was applied and the loading frequency was between 2 and 30 Hz depending on the load level. Final separation of coupons was considered as failure. Tests were stopped after 107 cycles and considered run-outs. The load and cross head displacement histories, number of cycles, as well as the failure modes were recorded in all fatigue tests. illustrates the second and half-life hysteresis loops for different strain amplitudes. This figure reveals a number of features of the cyclic behavior of AZ31B-H24.First, comparing the second and the half-life hysteresis indicates that the material shows some cyclic hardening behavior, in terms of tensile or compressive peak stresses. Narrower hysteresis loops for the stabilized cycle compared with the second cycle confirms this.Dissimilar peak stresses in tension and compression, even though the strain amplitude is symmetric, is an attribute of AZ31B sheet under cyclic loading. The unusual asymmetric shape of the hysteresis loop is pronounced, especially at higher strain amplitudes, where plasticity prevails.Another cyclic feature is that in the loading reversal, i.e., from compression to tension, there is a distinct “inflection point” where the slope of the hardening curve starts increasing. Similar to other asymmetric cyclic features, the inflection point is more distinguishable at high strain amplitudes. This inflection point did not appear on the unloading curve in this study, even at the highest strain amplitudes. However, other experimental results for very large strain amplitudes, e.g., 3.5%, reveal an inflection point on the unloading reversal These observations are attributed to different plastic deformation mechanisms, i.e., twinning and untwinning during in-plane compression and tension reversals, respectively. More detailed explanation of the cyclic behavior of AZ31B sheet can be found in Fatigue testing of spot-welded specimens resulted in the raw data shown in . The load–life curves shown in this figures were obtained from a bi-linear regression fit using a log–log scale. Comparing the load–life curves corresponding to TS specimens, i.e., sets A, C, and E, reveals that enlarging the nugget size has insignificant effect on fatigue strength (in terms of load range).Comparison between specimen sets A–E and set F indicates that increasing the coupon width and decreasing the mean load improve the fatigue strength for LCF, and this effect gradually diminishes for HCF. Fatigue test results on CT specimens, i.e., set G, show a significant drop in fatigue strength as compared to TS specimens with the same nugget size, i.e., sets E and F. This observation demonstrates that cyclic loading normal to spot-welds is more destructive than shear dominated loading. The endurance limit is 0.34 kN, 0.44 kN, 0.48 kN, 0.72 kN, and 0.16 kN for specimen sets A, C, E, F, and G, respectively. Similar effects have been reported for steel shows a comparison of fatigue strengths (in terms of load range) for magnesium, aluminum The load–life data for aluminum and steel alloys was obtained from the literature so that the d/t ratio and R-ratio are close to those for magnesium spot-welds (set A). This figure demonstrates that spot-welds of high strength steel alloys (DP600, TRIP600, and HSLA340) have significantly higher fatigue strength than magnesium and aluminum spot-welds. The large difference within the LCF regime can be attributed to different modes of failure. Magnesium and aluminum The TS spot-welded specimens failed in three different failure modes under cyclic loading: interfacial, partially-interfacial, and coupon failures.(a), a crack initiated from the nugget edge in the load-bearing side of the nugget. The crack then propagated through the nugget until complete separation of coupons, while the crack also grew through the coupon thickness. Therefore, the fatigue strength in this mode of failure mainly depends on the size and strength of the nugget. This failure mode was observed only when a very high cyclic load was applied.(c), is the most common mode of failure in TS specimens. In this failure mode, a crack started either from the base metal or from the interface of the base metal and HAZ, depending on the load level. The crack then propagated through the coupon thickness and extended perpendicular to the loading direction, until the coupons were separated. Fatigue life is therefore independent of nugget strength, but rather depends on cyclic loading level and dimensional parameters, such as coupon width and sheet thickness. Coupon failure was observed at lower loads, in the intermediate and HCF regimes.Partially-interfacial failure rarely occurred under cyclic loading as a transition between interfacial and coupon failures. Cracks in this mode, as shown in (b), nucleated from the same location as for interfacial failure, and grew first inside the nugget and then through the sheet thickness, following the bonding area. It can be seen that, similar to interfacial failure, there was another crack in this mode through the thickness, which was not as critical as the main crack. This mode of failure was observed in a narrow region between very low and low cycle regimes, i.e., when fatigue life was between 3 × 103 and 104 cycles.The CT spot-welded specimens failed only in button-pullout mode, as shown in . The fatigue crack in this failure mode started from the nugget edge, on the gripping sides of one coupon, and propagated through the sheet thickness, following the FZ and around the nugget. The spot-weld nugget was left on one coupon and a hole on the other after the coupons were separated. The specimens that failed within the LCF regime exhibited button-pullout failure in both coupons, (a). However, the CT specimens in HCF failed in button-pullout mode, Fatigue crack initiation is a progressive phenomenon during which slip deformation happens within several grains under cyclic loading reversals. As they are the weakest, surface grains are more prone to slip plastic deformation. The slip deformation which happens in a cyclic loading reversal is not recovered when loading is reversed; rather, reverse slip occurs in adjacent planes Practically, there is no unique definition for fatigue crack initiation. This inconsistency is more evident for welded specimens/structures, especially RSW in which the crack initiation location is not visible. Crack initiation in some studies is assumed when the crack reaches the length of 0.25 mm where E is elastic modulus, t is sheet thickness, δa is displacement amplitude, and Pa is load amplitude. Therefore, to obtain the crack initiation life for a specimen, compliance should be calculated for the entire test and plotted versus loading cycles. schematically represents the compliance curve and how the fatigue crack initiation life is measured.By following this procedure, crack initiation life was found for all the experimental points shown in . The results for crack initiation life were normalized by the total life to demonstrate the contribution of crack initiation over different ranges of the fatigue life. illustrates the results for various RSW specimen sets.This graph shows that for Nf< 106 cycles, crack initiation life for magnesium spot-welds in TS configuration (sets A to F) and CT configuration (set G) was around 50% and 30% of the total life, respectively. This fraction increased at higher lives such that for run-out tests, i.e., Nf> 107 cycles, the crack initiation life was equal to the total interrupted life.Numerous models have been developed for predicting the fatigue life of spot-welds. These models can be categorized into three major groups: fracture mechanics, structural stress, and local strain approaches. An introduction to these approaches is given in the following sections, and a well-known fatigue model from each approach is explained.In the past four decades, several researchers have considered the spot-weld as a crack-like slit based on some experimental observations and simplifications. The RSW process produces a circular joint between two or more sheets with a notch at the spot-weld edge. displays the edge notch in a magnesium spot-weld. Because the notch radius is small compared to the sheet dimensions, the spot-weld in some studies is considered a sharp notch. Therefore, the spot-weld is treated as a circular region surrounded by a pre-existing crack.Fatigue failure, in general, consists of fatigue crack initiation and crack propagation processes. For the case of smooth specimens and blunt notched components, where the crack initiation process dominates, fatigue life is closely related to the material strength The fracture mechanics approach considers a measure of stress intensity factor (SIF) or J-integral as the fatigue damage parameter, and relates this parameter to the fatigue life or the crack growth rate.The fracture mechanics approach has a number of advantages and drawbacks. The main advantage of this approach is that the crack propagation process may be closely followed. A drawback of this approach is that the nugget edge is considered as a crack and therefore crack initiation life is assumed insignificant, which is not supported by experimental observations and analysis. The work by Swellam et al. Resultant forces and moments, including axial load, P, shear load, Q, and bending moment, M, at the spot-weld center, were found from static equilibrium of a coupon. The stress intensity factors for two half spaces joined by a circular region were used in this study,where r is the nugget radius. The equivalent mode I SIF, Keq, was defined asin which β is an empirical material constant, which reflects the material’s sensitivity to mode II loading. Experimental results from two or more different spot-weld specimen configurations are required to obtain β. Some of the specimen sets must involve only the mode I SIF (such as cross-tension or coach-peel configurations), and some other specimens must reflect only the effect of mode II or a combination of modes I and II SIFs. The parameter β is found such that the best correlation is achieved for equivalent stress intensities, Keq, when plotted versus the fatigue life for all specimen configurations.A geometrical correction factor, G, was defined to incorporate the effects of specimen and nugget sizewhere t is the sheet thickness, and W is the specimen width. To account for geometrical factors and load ratio, R, the general stress intensity parameter, Ki, was defined asand considered as a damage parameter. The SIFs and the damage parameter were assumed constant, i.e., independent of the crack length during the course of cyclic loading. Therefore, fatigue life was obtained fromwhere AS and bS are material constants for Swellam’s model. These coefficients are obtained by fitting a linear trend line to log (Ki) – log (N) curve,Therefore, the constants are determined by knowing the slope and intercept of the trend line,Swellam’s model was evaluated in this study by predicting the fatigue life for magnesium spot-welds in TS and CT configurations. Taking advantage of the simple specimen geometry, resultant loads at the spot-weld center were determined from hand calculations; hence, no finite element (FE) modeling was required for damage parameter calculation.Since 1989, a number of fatigue models have been developed for spot-welds based on the structural stress concept. Structural stress is a linearly distributed stress over the thickness, obtained by neglecting the effect of stress concentration. Structural stress reflects the effects of forces and moments at the spot-weld center or edge. Structural stress is usually calculated by superposing the effects of different forces and moments, obtained from linear elastic FE simulations. To suit this approach, the sheets and spot-welds in the FE model are represented by shell and beam elements, respectively. The structural stress approach, as opposed to many fracture mechanics-based models, often provides enough flexibility to be applicable to different specimens and structures. Therefore, these models are widely employed in industry, including the automobile industry ΔSij=ΔPijωti+6ΔM^ij∗ti2W+1.2ΔPAiti2;i,j=1,2,where ΔSij is the structural stress range. ΔPij and ΔPAi; are membrane load and axial force ranges, respectively. ω is the effective coupon width and according to Wang et al. where Mij is the summation of positive moments on the sheet i and the side j, and Mavg is the average of all positive nodal moments at elements adjacent to the spot-weld. The moments causing tension at the interface are considered as positive moments. illustrates the forces and bending moments at the edges of a spot-weld.Forces and moments were determined from linear elastic FE simulations. The sheets were represented with four-node linear shell elements, and the spot-weld was modeled with a two-node linear beam element. Material properties for AZ31B-H24 magnesium alloy was linear elastic (E |
= 43 GPa and ν |
= 0.35); hence, any strain hardening and asymmetric hardening behavior was suppressed. Nonlinear geometry was included for a correct failure location prediction The results for forces and moments are stored in nodal force (NFORC) output variables in Abaqus 6.10 software. One should note that the default setting for averaging element output at nodes has to be deactivated, so that the contribution of each element is represented correctly., four values were obtained for the structural stress range at each spot-weld. Maximum structural stress range,were found for SIF and life calculations. Initial and final crack sizes were assumed to be ai |
= 0.25 mm and af |
= |
t, respectively. Therefore, the relationship to find crack propagation life through Paris’ equation was simplified towhere Np is crack propagation life. ASh and mSh are material constants for Sheppard’s model which are determined following the same procedure explained for Swellam’s model.Some studies, in contrast to the fracture mechanics approach, consider a spot-weld as a blunt notch with a finite radius. Therefore, a detailed FE model with a fine mesh at the vicinity of the spot-weld is required. A measure of local strain at the spot-weld edge is often assumed to control fatigue failure in this approach. Local stress/strain values are calculated from an elastic–plastic FE simulation, or from an elastic solution along with a variant of Neuber’s rule A detailed FE model was employed in this model to obtain a realistic approximation of local stress and strain values at the hot-spot. The FE model included details of the nugget root radius, which was found from experimental observation. The notch radius was obtained by sectioning spot-welds, and measuring the distance between the two sheets in the vicinity of the nugget. The notch radius in Pan’s work was 0.076 mm for steel spot-welds The maximum principal strain range at the hot-spot was used as the fatigue damage parameter. Therefore, fatigue life was predicted using the following equation,in which Δεmaxpr is maximum principal strain range and AP and bP are material constants for Pan’s model. These constants are found by fitting a linear trend line to log (Δεmaxpr)–log(N) curve. The hot-spot was identified as the location with the maximum local principal strain at the end of the first reversal. Maximum principal strain range, according to Pan The FE model for a TS specimen is shown in (a). Half of the TS specimen was modeled, taking advantage of a plane of symmetry. Eight-node linear brick elements with reduced integration were used in this model. Elastic properties of magnesium along with the tensile stabilized cyclic stress–strain curve were assigned to AZ31B-H24 sheets (symmetric tension–compression behavior is assumed in Abaqus software). The same material properties were assigned to the base metal and the weld area, i.e., HAZ and FZ, due to lack of suitable mechanical properties for the weld region. Moreover, the work by Pan (b) illustrates the boundary conditions at the two ends, and on the plane of symmetry. All degrees of freedom (DOFs) were fixed in one end, and the other end was only free to move in the x-direction. The z-symmetry condition (Uz = 0) was applied to the plane of symmetry. Half of the load that was applied in the experiments was exerted due to the half model. Simulations were run for three steps to simulate three consecutive reversals, i.e., loading, unloading, and reloading, while considering the effect of nonlinear geometry. The principal strain ranges at the hot-spot were calculated for available experimental loads.(b) displays the FE model for a quarter CT specimen, which used two planes of symmetry. The notch radius, element type, and material properties were the same as the TS specimen model. The boundary conditions on the CT specimens were applied such that the experimental conditions were simulated. All DOFs on one sheet were fixed within the gripping distance, and on the other sheet the translational DOF normal to the sheet was free, and the other DOFs were fixed. A quarter of the experimental load was applied uniformly on the moving end of the specimen. Two different symmetry boundary conditions (x-symmetry, and z-symmetry) were applied to the symmetry planes. Similar to the TS model, three loading steps were run for CT specimens to simulate one cycle.The fatigue models proposed by Swellam, Sheppard, and Pan were assessed by predicting the fatigue life for magnesium spot-welds. Results are shown and compared in The damage parameter for Swellam’s model was found from Eq. (a) illustrate the results for the five specimen sets investigated. (a1) displays the data points in terms of the damage parameter along with a bilinear trend line as a result of a sharp bend at a life of 106 cycles. As depicted in this figure, data points for CT specimens (Set G) were not appropriately correlated to TS specimens, resulting in a low correlation coefficient of R2 |
= 0.53. Similarly, (a2) shows that while TS data points were mostly located within the factor of 2 bound lines, CT specimen results were left outside the region. The reason for the poor performance is the proposed method for SIF calculation. Swellam suggested obtaining SIFs from resultant forces and moments at the center of the spot-weld; therefore, the effect of self-equilibrating forces and moments is ignored in this model. For CT specimens, the resultant bending moment, M, and the corresponding SIF, Kmoment, are zero. Thus, the contribution of bending moment in SIF, which is dominant for CT specimens, is neglected in this model.For evaluating Sheppard’s model, the coefficient for the axial stress term, ΔPAiti2, was found for magnesium spot-welds to represent boundary conditions and geometric effects. The coefficient was obtained from the work by Young and Budynas The forces and bending moment at the nugget edge were found through FE simulations. The structural stress range was calculated for all the experimental data points employing Eq. and using the coefficients presented in (b) displays the results obtained from Sheppard’s model. (b1) shows that Sheppard’s model was successful in correlating experimental results from different specimen sets, with R2 |
= 0.95. However, data points corresponding to the CT specimens (set G) are slightly shifted from TS specimens. (b2) illustrates predicted versus experimental fatigue life utilizing Sheppard’s model. This figure shows that almost all experimental data points corresponding to TS specimens (sets A–F) are located within the factor of 2 bound lines, while fatigue life for CT specimens is under-predicted and the points are outside the boundary lines.(c1) displays the maximum principal strain range for Pan’s model, obtained from elastic–plastic FE simulations. Similar to Swellam’s and Sheppard’s models, a bilinear trend line was fitted to the data points. This chart indicates that Pan’s model was very successful in consolidating the experimental results for different specimen sets, with R2 |
= 0.97. This figure demonstrates that Pan’s model was capable of providing a good correlation between the CT data points (set G) and the TS data points (sets A–F). (c2) illustrates that almost all experimental data points, including the CT specimens, are located within the factor of 2 boundary lines.(a1) shows that the Swellam’s model provides a good correlation between TS specimens in HCF. This is in contrast to what expected as the fracture mechanics approach neglects the crack initiation, and illustrates that crack initiation dominates in HCF. On the other hand, (c1) demonstrates that Pan’s model was successful in LCF, even though crack propagation, which is not appropriately modeled in local approach, dominates in LCF. Nevertheless, one should note that this observation does not justify applicability of fracture mechanics approach in HCF and local approach in LCF. Because fracture mechanics and local approaches only explain the effective damage mechanism in LCF and HCF, respectively. demonstrates that, although asymmetric hardening behavior of magnesium was neglected by Sheppard’s and Pan’s model, fatigue life of spot-welds was well predicted. This is likely due to the limited range of experimental data used. The spot-weld configurations investigated in the present research were limited to TS and CT specimens. Moreover, all fatigue tests were performed with a positive R-ratio due to the specific geometry of specimens. Thus, available experimental data do not provide a situation where significant plastic deformations occur at the hot-spot during unloading and reloading reversals. Therefore, the symmetric hardening assumption did not have a significant effect on the stress–strain response and fatigue life prediction. More various configurations of spot-welded specimens and negative R-ratios could make this effect clearer.Magnesium spot-welds were characterized in tensile–shear and cross-tension configurations under cyclic loading. Where possible, magnesium spot-weld behavior was compared to that of steel and aluminum spot-welds. The most common fatigue models were assessed and compared for magnesium spot-welds. The following conclusions can be drawn from this study:Fully-reversed fatigue testing of AZ31B-H24 revealed an asymmetric shape of hysteresis loop. This feature was more pronounced at high strain amplitudes.Fatigue strength of magnesium spot-welds is comparable to that of aluminum spot-welds, but is significantly less than steel spot-welds for the similar d/t ratio.Fatigue crack initiation life for tensile–shear and cross-tension specimens was 50% and 30% of the total life, respectively. This fraction increased at lives higher than 106 cycles such that for run-out tests, the crack initiation life was equal to the interrupted life.The fatigue model proposed by Swellam based on fracture mechanics approach did not provide a satisfactory correlation of the experimental data for tensile–shear and cross-tension specimens. The poor correlation was attributed to neglecting the effect of self-equilibrating forces and moments.The models developed by Sheppard and Pan were quite successful in predicting the fatigue life for magnesium spot-welded specimens, even though the asymmetric hardening behavior of magnesium was suppressed in these models. It is likely that the correlation would suffer if a wider range of geometries or loading modes were considered.Experimental investigation on corroded cold-formed steel beam-columns under compression and major axis bendingSteel structure exposed to aggressive environment for a long time show serious corrosion problems due to the lack of effective protective measures []. Corrosion is a most predominate damage in existing steel structure [], which results in thickness reduction, uneven surface, strength degradation and brittle failure.The types of corrosion mechanisms mainly include general and pitting corrosion. The general corrosion often causes a large number of metal losses and greatly reduces the bearing capacity of components. The pitting corrosion usually takes place in a specific position, and the corrosion rate of each part is obviously different. The pitting corrosion causes less metal loss, but more serious damage. The stress concentration caused by the pitting corrosion leads to the decrease of mechanical properties.In the past, the corrosion degree was generally evaluated by simply measuring weight (thickness), and the mass loss rate (thickness loss rate) was used to characterize the corrosion degree []. With the development of detection technology, the surface morphology of corroded steel plate can be accurately measured. Therefore, a variety of methods for characterizing the corrosion degree have been proposed, including the maximum pit depth [] and the degree of pitting corrosion intensity (DOP) []. The conventional corrosion wastage modeling was assumed a linear relationship between the thickness lost and time []. However, through the statistical analysis of more measured data, it is found that the non-linear model was more suitable for the corrosion wastage modeling [] studied the influence of corrosion on the bearing capacity of the corroded H-shaped columns under eccentric load. Corrosion damage leaded to the decrease in the stiffness and strain strengthening effect. Shi et al. [] carried out an experimental and finite element study that was performed to analyze the buckling behavior of H-piles with localized corrosion. They have concluded that the location and extent of the corrosion region have a little effect on the ultimate strength. Beaulieu et al. [] estimated the remaining capacity of corroded steel angle columns under axial compression. Comparing the results calculated by the design specifications, it is found that the remaining capacity of corroded angle steel columns can be predicted using the ASCE 10–97. Jiang et al. [] investigated the effects of the radius, depth and location of pitting corrosion on the remaining capacity of mild steel rectangular plates under uniaxial and biaxial compression. They have concluded that the volume loss was the main parameter affecting the ultimate capacity. The degradation law of the bearing capacity of other corroded steel component was also studied, including steel beams [The use of cold-formed steel for load-bearing members in light-steel structure has been under growing interest due to its light weight, high strength, high rigidity and easy processing []. Cold-formed steel can obtain excellent mechanical properties through reasonable section shape. Cold working results in the increase of strength and decrease of ductility, so the mechanical properties of cold-formed steel are different from that of hot-rolled steel. Research shows cold working affects the corrosion resistance of steels [] carried out the electrochemical corrosion test and microscopic observation on the corrosion resistance of cold-worked stainless steel. The results showed that cold working led to the destruction of passive film and reduced the corrosion resistance. Many cold-formed steels which have been in aggressive environment for a long time have appeared serious corrosion problems []. However, the research on buckling behaviors of corroded cold-formed steel member, especially in terms of the cold-formed steel beam-columns under compression and major axis bending, has not yet been reported.The objective of this study was to investigate the buckling behaviors of the corroded beam-columns under compression and major axis bending. The residual thickness distribution and mechanical properties of the corroded specimens were obtained by thickness measurements, monotonic tensile tests and beam-column tests. A finite element model for the corroded cold-formed steel beam-columns was established and the parametric analyses, including the parts, locations and lengths of the corrosion region, were performed.All the corroded cold-formed steels, including monotonic tensile tests and beam-column tests, came from a chemical plant building in Jiangxi, China (shown in ). The cold-formed sections with a nominal dimension of 160 mm × 60 mm × 20 mm and a nominal internal corner radius of 2.5 mm have been in service for 4 years in the corrosive environment (high temperature, high humidity and salt-rich environment). It can be seen from that corrosion leads to a significant reduction in the thickness of the cold-formed sections, and even the formation of small perforations or voids because they are usually thin. The cold-formed steel beam-columns formed by pressing galvanized steel sheet with a nominal plate thickness of 2.5 mm were low-alloy steel (named Q345 in China).. After removing the corrosion products and anticorrosive coating by using the electric wire brushes, the thickness of 10 points in the gauge section was measured. The monotonic tensile test was performed on an electronic universal testing machine (DNS300) in displacement control with a loading rate of 0.2 mm/min. The elongation value was recorded using an extensometer.Thickness is an important parameter for steel structure members. Therefore, the thickness loss ratio η, which defined as the ratio of the average thickness of the corroded specimens to the original thickness, is adopted as a damage parameter for corrosion. gives the thickness loss ratio and mechanical properties obtained based on the experimental results, including the elastic modulus, yield strength, ultimate strength, corrosion reduction factor for elastic modulus and yield strength, and yield ratio. For the specimen H10 with the thickness loss ratio of 0.593, the elastic modulus, yield strength and ultimate strength were reduced by 33.4%, 28.3% and 35.2%, respectively, compared with the non-corroded specimens. This indicates that the elastic modulus, yield strength and ultimate strength decreased greatly. The change rule of the yield ratio that varied from 0.627 to 0.960 was not obvious as the thickness loss ratio increased. The relationship between the corrosion reduction factors and the thickness loss ratio is depicted in , the decrease of the corrosion reduction factor for the elastic modulus was smaller when the sectional loss ratio was below 0.467, but it decreased remarkably when the sectional loss ratio was beyond 0.467. In addition, the corrosion reduction factor for the yield strength decreased linearly as the thickness loss ratio increased.where Es and Es0 are the elastic modulus of the corroded specimens and non-corroded specimens, respectively, fy and fy0 are the yield strength of the corroded specimens and non-corroded specimens, respectively, η is the thickness loss ratio. It is worth noting that the calculation formulas about the corrosion reduction factors are only suitable for the specimens with the thickness loss ratio below 0.611.Six specimens with different corrosion degrees (C160-EC-1, C160-EC-2, C160-EC-3, C160-EC-4, C160-EC-5, C160-EC-6) were selected to study the buckling behaviors of corroded cold-formed steel beam-columns. The short column was studied in the paper. Therefore, the nominal length of the specimens was 500 mm according to the recommendations of Galambos [ shows the definition of cross-section symbols. The nominal dimensions of a1(a2), b1 (b2), h1–1(h1−2), h2–1(h2−2), h3, and s were 20 mm, 60 mm, 64 mm, 8 mm, 16 mm, and 1 mm, respectively. The cross-section dimensions and internal corner radius were measured by a Vernier calliper and a radius gauge, respectively. shows the average measured dimensions of four randomly selected positions. Two end plates with a nominal dimension of 200 mm × 100 mm were welded to ends of the specimens to ensure uniform compression.. Before measuring the initial imperfections, the specimens were divided into ten parts uniformly along the length direction, and the grid was drawn on the specimens. Due to the influence of deformation caused by welding at the end, the initial geometric imperfections at both ends of all the specimens were not measured. First, put the rigid plane on the specimens and read the data on the percentile meter (Δ2), then remove the rigid plane and read the data again (Δ3). The local and distortional imperfection of the specimens were recorded as Δ = Δ2 − Δ3 − Δ1, shown in shows the typical initial geometric imperfections. The convex deformation of each initial geometric imperfection is positive values. It can be found from Fig. 8 that the change of the local geometric imperfections along the length direction of the specimens was irregular, but the distortional geometric imperfection tends to increase or decrease along the length direction. Seven displacement transducers (LVDTs) were utilized to measure the probable the movements and deformations of the specimens at mid-height (shown in In this study, the eccentric force was applied to realize the compression and major axis bending. As shown in , the loading rig for the beam-column tests includes the reaction frame, top and bottom knife edge for applying eccentric force and providing pin-pin boundaries, loading jack and a data acquisition system. The reaction frame can be moved up and down to suit the test with different specimen lengths. As shown in (b, c), the top and bottom knife edge were utilized to allow the rotational degree of freedom about major axis consists of two parts – a steel plate with a knifeedged wedge connected to the test setup, and a steel plate with a long V-shaped groove contacted with the test specimens. All the specimens were tested with loading eccentricities of 40 mm. The position of the specimens was moved to align the eccentric line of two end plates with the center line of the top and bottom knife edge. The reaction frame was slowly pushed downwards until the knifeedged wedge fitted into V-shaped groove. After a pre-compression load was applied, the load was released until about 1 kN to ensure that there is no initial load. The beam-columns test was carried out in displacement control at a constant rate of 0.05 mm/min. The applied load, strain and displacement were recorded by a data acquisition system.The buckling modes of the corroded cold-formed steel beam-columns under compression and major axis bending are shown in showed that the axial load versus the axial displacement of the specimens. It can be seen from that the initial stiffness of the non-corroded specimens was obviously larger than that of the corroded specimens. Interestingly, the stiffness of descending section of the non-corroded specimens was close to that of the corroded specimens.It is worthy of note that there is a great randomness in the thickness of the specimens due to corrosion. Therefore, it is necessary to find a suitable parameter that has a great influence on the bearing capacity of the corroded component. It is generally considered that the average thickness [] are crucial parameter. The influence of two parameters on the bearing capacity of the corroded specimens was analyzed. shows the results for the beam-columns test, including the eccentricity (e), average thickness loss ratio (δave) defined as the ratio of the average thickness to the original thickness, minimum thickness loss ratio (δmin) defined as the ratio of the minimum thickness to the original thickness, failure mode, axial displacement corresponding to the ultimate load (Δu), and ultimate load (Pu). reports the relationship between the corrosion reduction factor for the ultimate load and the thickness loss ratio. The corrosion reduction factor for the ultimate load decreased with the increase of the minimum thickness loss ratio. The law of degradation of the corrosion reduction factor for the ultimate load was not obvious as the average thickness loss ratio increased, especially the specimen C160-EC-3. This is because the minimum thickness of the specimen C160-EC-3 is much smaller than the average thickness. The above analysis shows that the bearing capacity of the corroded specimens mainly depends on the minimum thickness.The axial displacement corresponding to the ultimate load for the corroded specimens decreased compared with that of non-corroded specimens although the initial stiffness of the corroded specimens decreased. This is because the ultimate load decreased more obviously than the initial stiffness. The minimum thickness loss ratio has a great influence on bearing capacity of the corroded specimens. Therefore, adequate attention should be paid to the thickness loss caused by corrosion.The commercial finite element software ABAQUS v6.13 was applied to simulate the corroded cold-formed steel beam-columns under compression and major axis bending. The cross-section dimensions and length of the finite element models were determined from the measured dimensions of the specimens (shown in ). Not that the surface of the corroded specimens is rough, and the thickness of different positions is not same. To simplify the finite element model, the real thickness was equivalent to the uniform thickness (average thickness) along lengths of the specimens, and the average thickness in S4R shell element valid for analysis of both thin and thick shell problems was adopted to simulate the corroded cold-formed steel beam-columns. S4R shell element, four node reduced integration shell elements, is well-suited for nonlinear analysis. The finite element modes with various mesh sizes from 15 mm × 15 mm to 6 mm × 6 mm were analyzed. The results show that the bearing capacity changed little with the decrease of the mesh sizes when the mesh sizes were less than 8 mm × 8 mm. Therefore, the element size of 8 mm × 8 mm was applied for the study of the corroded cold-formed steel beam-columns with time-saving and precision (shown in ). Two end plates with nominal thickness of 10 mm were applied at ends of the specimens. The Pin-pin boundaries were realized by controlling the degree of freedom of the top and bottom reference points located at the eccentric position of the end plates. For the top and bottom reference points, the rotational degree of freedom in the major axes was released. The axial translation in the z direction of the bottom reference point was restrained, while the axial translation in the z direction of the top reference point was released to apply the axial load (shown in ). The stress-strain curve for the corroded specimens was defined using a perfect bi-linear model. The parameters of the bi-linear model need to be determined: the elastic modulus, yield strength, and slope of strain-hardening branch. The elastic modulus and yield strength of the specimens with different corrosion levels was obtained from the monotonic tensile test (shown in ).The slope of strain-hardening branch was assumed to be 2% of the elastic modulus and the Poisson's ratio was 0.03.Firstly, an appropriate buckling eigenmode that was used to create a geometric imperfection was obtained by elastic buckling analysis. The maximum geometric imperfection applied in the non-linear buckling analysis was listed in . Then the arc length method was used to study inelastic buckling behavior of the corroded cold-formed steel beam-columns.Four different locations were selected to study the influence of location of the corroded region on the mechanical properties of the corroded beam-columns. The centerline of the corrosion region was moved from the mid-height to 125 mm, 175 mm, 225 and 250 mm from the upper end cross-section. For example, shows a specimen with a corrosion region 175 mm away from the upper end cross-section. shows ultimate load and failure mode of the specimens with different locations of the corroded region. Interestingly, the results show that locations of the corroded region has a little effect on the ultimate load and failure mode of corroded cold-formed steel beam-columns. This indicates that no matter where the corroded region is, its influence on the bearing capacity is the same.The effect of the lengths of the corroded region was investigated by four lengths, 110 mm, 150 mm, 190 mm, 230 mm, located at the mid-height and four kinds of corrosion degrees. provides comparison of ultimate load and failure mode of the corroded specimens with different lengths of the corroded region. When the length of the corroded region increased from 110 to 230, the maximum difference of ultimate load was only 8.1%, and the failure mode was the same. Therefore, the length of the corroded region has a little effect on the ultimate load and failure mode of the corroded cold-formed steel beam-columns. This indicates that even if the corrosion is serious in a small region, the bearing capacity is greatly reduced.Inelastic buckling of corroded cold-formed steel beam-columns was studied using experiment and non-linear finite element method. Six beam-columns with different corrosion degrees were tested under compression and major axis bending. A finite element method for buckling analysis of corroded cold-formed steel beam-columns was proposed, and the accuracy of the finite element model was verified by comparing the test results with the simulation results. Finally, the influence of the parameters of the localized corrosion on ultimate load and failure mode were discussed. The following conclusions are drawn:The elastic modulus, yield strength and ultimate strength of the corroded specimens decreased greatly. When the sectional loss ratio was below 0.467, the decrease of the corrosion reduction factor for the elastic modulus was small, and then accelerated obviously. The corrosion reduction factor for the yield strength decreased linearly as the thickness loss ratio increased.Local deformation of the non-corroded specimen web occurred as the load was approximately 85% of the ultimate strength, while that of the corroded specimen web was observed as the load was not higher than 70% of the ultimate strength. The corrosion reduction factor for the ultimate load was significantly affected by minimum thickness loss ratio. The axial displacement corresponding to the ultimate load for the non-corroded specimens was smaller than that of non-corroded specimens.We would like to submit the enclosed manuscript entitled “Experimental Investigation on corroded cold-formed steel beam-columns under compression and major axis bending”, which we wish to be considered for publication in “Journal of Constructional Steel Research”. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication. I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.Semi-infinite random unidirectional fiber-reinforced compositesDynamic effective properties of semi-infinite random unidirectional fiber-reinforced composites subjected to anti-plane shear wavesBased on the theory of elastodynamics, and employing the effective medium method and the image method, the propagation of shear waves in semi-infinite random unidirectional fiber-reinforced composites is investigated. The dispersion relation for the effective wave number in the random composites is derived. The numerical solutions of the dynamic effective properties are obtained by using an iterative scheme. The image method is applied to satisfy the traction free boundary condition of the semi-infinite composite. The effective wave fields are expressed by using the wave function expansion method, and the expanded modal coefficients are determined by satisfying the continuous boundary conditions around the fibers. Analyses show that the variation of the dynamic effective properties in the semi-infinite composite is significantly different from that in the infinite composite. The maximum dynamic effective properties near the surface increase with the increase of the incident wave number, the volume fraction of fibers, and the properties ratio of the two phases.Semi-infinite random unidirectional fiber-reinforced compositesThe study of the elastic wave propagation through composite materials is interesting due to its vast important applications. The solution of this problem allows us to predict the response of composite materials to various dynamic loading, and has been proven to give the theoretical background for the non-destructive analysis of micro-structures of composites by using the ultrasonic technique The determination of the static effective parameters of composites has been a subject which attracted a considerable attention in the past several decades. Maxwell In practical applications the engineering materials subjected to dynamic loading are more common, so the investigations on the dynamic effective parameters of composite materials are crucial for designing more practical materials. However, due to the coherence of wave scattering in dynamics and the multiple scattering in random media, the investigations of the dynamic effective properties of materials become more complex. Foldy To the author’s knowledge, up to present time the investigations on effective wave field in the random media mainly focus on the infinite structure models. It is well known that the model of the semi-infinite structure is one of the most common types of macro-structures encountered in many practical engineering structures. However, because of the effects of the boundaries of the investigated areas, the complex problems such as the multiple scattering resulting from the semi-infinite surface may arise. In the past, very few investigations about the semi-infinite composites have been engaged in. Kaganova and Litinskaia Effective medium method (EMM) is a more accurate method for evaluating the effective field and computing the dynamic effective parameters in the elastic media with randomly distributed inclusions, and has been successfully used in analyzing the wave field in composite materials The main objective of this paper is to investigate the propagation of an anti-plane shear wave in a semi-infinite random unidirectional fiber-reinforced composite. The dispersion relation for the effective wave number in the random media is obtained by using the effective medium method. The image method is applied to satisfy the traction free boundary condition of the semi-infinite composite. Through numerical examples, the effects of the phase properties, the volume fraction of fibers and the incident wave number on the dynamic effective modulus and density are analyzed.Consider a semi-infinite random unidirectional fiber-reinforced composite material, as depicted in . The two-dimensional composite material is common in many previous works , the unidirectional fibers are randomly distributed. For simplicity, the discrete fibers are assumed to be identical cylinders fully bonded to the matrix. Let μ0 and ρ0 be the shear modulus and the density of matrix phase, and μ, ρ those of fiber phase. The volume fraction of fibers is denoted by Vf.Suppose that an anti-plane shear wave of frequency ω with polarization parallel to the fibers is incident into the semi-infinite composite material. For the anti-plane shear wave propagating in the material, the wave field within the x–y plane can be formulated in the framework of scalar wave propagation, and only the component of the amplitude of the displacement field in the z direction exists (“anti-plane” strain state). When the shear wave propagates in the semi-infinite composite material, the interaction between the fibers and the multiple scattering resulting from the boundary of the structures give rise to the dispersion relations for shear waves. The propagating wave number is denoted as the effective wave number k∗.The shear wave propagating in the x direction is considered, and the dependence on time is defined by the multiplier eiωt. In the absence of body forces, the wave motion equation for the displacement u(r) in the z direction is expressed as ∂iCi3j3(r)∂ju(r)+ρ(r)ω2u(r)=0,(∂i=∂/∂x),where Ci3j3(r)=μ(r)δij are the components of the elastic moduli tensor Cijkl(r) of the media, and r=(x,y).μ(r) and ρ(r) are the shear modulus and density of the medium, and may be presented as the following sums:μ(r)=μ0+μ1S(r),ρ(r)=ρ0+ρ1S(r),μ1=μ-μ0,ρ1=ρ-ρ0.Here S(r) is the characteristic function of the region S occupied by the fibers (S(r)=1ifr∈S,S(r)=0ifr∉S).μ0∇2u(r)+ρ0ω2u(r)=-μ1∂i[εi(r)S(r)]-ω2ρ1u(r)S(r),where ∇2=∂2/∂x2+∂2/∂y2 is the two-dimensional Laplace operator, and εi(r)=∂iu(r). Applying the operator (μ0Δ+ρ0ω2)-1 to both sides of Eq. , we obtain the integral equation for the displacement field u(r) in the formu(r)=u0(r)+∫s[∂iG(r-r′)μ1εi(r′)+ω2G(r-r′)ρ1u(r′)]S(r′)dr′.where u0(r) is the incident field that would have existed in the media without fibers (μ1=0,ρ1=0), s is the whole area of the composites. G(r) is the Green function of the semi-infinite structure. Applying the image method shown in G(r)=-i4μ0[H0(1)(k0|r|)+H0(1)(k0|r′|)],k0=ωρ0/μ0.where |r′|=(r2+4b2+4brcosθ)1/2 with b being the distance between the center of the typical fiber and the semi-infinite edge, and H0(1)(·) is the zero order Hankel function of the first kind.According to the hypotheses of EMM, the interaction between many fibers is reduced to a one-fiber problem. This problem is the diffraction of a monochromatic plane shear wave on an isolated fiber embedded in the effective medium with the effective shear modulus μ∗ and density ρ∗. The effective wave field is u∗(r)=U∗ei(k∗·r-ωt), and k∗=k∗n in which k∗ is the effective wave number, and n denotes the propagation direction of shear waves.Thus, the integral equation denoted by the effective field in the one-fiber region is described asu(r)=u∗(r)+∫s0[∂iG∗(r-r′)μ∗1εi(r′)+ω2G∗(r-r′)ρ∗1u(r′)]dr′.Here s0 is the area of the fiber cross-section, G∗(r) is the Green function of the effective medium, and be known, and the field u(r) inside the fiber with the center at point r0 |
= 0 be presented in the formHere Λ is a linear operator that depends on the dynamic properties of the effective medium and fiber.Suppose that the fiber occupies the area s0 with the center at a point r0≠0, According to Bloch’s theory of wave propagation, one can present the field u(r) inside such an inclusion in the form (r∈s0)u(r)=Λ[U∗eik∗·(r-r0)eik∗·r0]=Λ[eik∗·(r-r0)]U∗eike·r0=Λ[eik∗·(r-r0)]e-ik∗·(r-r0)U∗eik∗·r=Λu(r-r0)u∗(r),Λu(z)=Λ[eik∗·z]e-ik∗·z.In the same way, from εi(r)=∂iu(r), the following can be obtained:εi(r)=∂iΛ[U∗eik∗·(r-r0)eik∗·r0]=Λιε(r-r0)u∗(r),Λιε(z)=∂iΛ[eik∗·z]e-ik∗·z.Note that Λu(z) and Λιε(z) do not depend on the position r |
= 0 of the center of the fiber. They can be constructed from the solution of the one-fiber problem for the fiber centered at the point r |
= 0.Let us introduce the random functions λu(r) and λε(r) in the two-dimensional space. These functions coincide with Λu(r-ri) and Λε(r-ri) if r is inside the fiber centered at point ri(i=1,2,3,…), and they are equal to zero in the matrix. Substituting Eqs. u(r)=u0(r)+∫s0[∂iG(r-r′)μ1λiε(r′)u∗(r′)+ω2G(r-r′)ρ1λu(r′)u∗(r′)]S(r′)dr′.In order to find the mean wave field, let us average both sides of Eq. over the ensemble realization of the random set of fibers, and take into account the condition of ue(r)=u(r), the following can be obtained:〈u(r)〉=u0(r)+Vf∫[∂iG(r-r′)μ1ΛiC+ω2G(r-r′)ρ1Λρ]〈u(r′)〉dr′.Λρ(k∗)=limΩ→∞1VfΩ∫Ωλu(r)dr=1〈S〉∫sΛu(r)dr.Λic(k∗)=limΩ→∞1VfΩ∫Ωλiε(r)dr=1〈S〉∫sΛιε(r)dr.where Λρ and Λic are the constant scalar and vector, Ω is the two-dimensional plane in the composite, Vf is the volume fraction of fibers, and S is the area occupied by the fibers.Let us apply the Fourier transform to Eq. and multiply the result with L0(k)=μ0k2-ρ0ω2. Taking into account the equationsL∗(k)〈u(k)〉=0,L∗(k)=L0(k)+Vfμ1ikiΛic(k∗)-Vfρ1ωi2Λρ(k∗). is a function of the vector k∗ only, Λic may be written in the formwhere HC(k∗) is a scalar function. If the mean wave field 〈u(r)〉 is a plane wave (〈u(r)〉=U∗ei(k∗·r-ωt)), its Fourier transform is 〈u(k)〉=(2π)-1U∗δ(k-k∗), and L∗(k)δ(k-k∗)=0, namely,L∗(k∗)=L0(k∗)+Vfμ1(k∗)2HC(k∗)-Vfρ1ω2Λρ(k∗)=0.μ∗(k∗)k∗2-ρ∗(k∗)ω2=0,μ∗(k∗)=μ+Vfμ1HC(k∗),ρ∗(k∗)=ρ0+Vfρ1Λρ(k∗)., the dynamic effective properties of the semi-infinite composite can be obtained.To solve the multiple scattering of the one-fiber problem in the semi-infinite composite structures, the image method is used to satisfy the traction free boundary condition, as shown in . The radius of the cylindrical fiber is a. The distance between the semi-infinite edge and the center of the fiber is b.Let the effective wave field be incident in the positive x direction. The incident waves can be expressed asu1∗(i)=U∗ei(k∗·r-ωt)=U∗∑n=-∞∞inJn(k∗r)einθexp(-iωt),where U∗ is the displacement amplitude of the effective wave field, and Jn(·) is the nth Bessel function. Note that the subscript 1 denotes the wave field around the real fiber, and the superscript (i) denotes the effective incident waves.The reflected waves at the edge of the semi-infinite composite structure are described by the virtual image fiber. For the image fiber, the incident waves propagate in the negative x′ direction, and can be expressed asu2∗(i)=U∗ei(-k∗·r-ωt)=U∗∑n=-∞∞i-nJn(k∗r′)einθ′exp(-iωt).Note that the subscript 2 denotes the effective incident waves around the image fiber.Considering the multiple scattering between the real and image fibers, the scattered fields of elastic waves produced by the real fiber are described, in the localized coordinate system (r,θ), asu1∗(s)=∑n=-∞∞An1Hn(1)(k∗r)einθexp(-iωt).Note that the superscript (s) denotes the scattered waves.And that the scattered waves produced by the image fiber, in the localized coordinate system (r′,θ′) of the image fiber, are described asu2∗(s)=∑n=-∞∞An2Hn(1)(k∗r′)einθ′exp(-iωt),Note that An1 and An2 are the modal coefficients of the scattered waves for the real and image fibers, respectively. They are determined by satisfying the continuous boundary conditions of the fibers. In this paper, they are also dependent on the boundary conditions of the semi-infinite material.Likewise, the refracted waves in the real and image fibers are the standing waves, which can be described aswhere An3 and An4 are the modal coefficients of the refracted waves for the real and image fibers, respectively. Note that the superscript (r) denotes the refracted waves.Λρ=∑n=-∞∞An3gn,HC=∑n=-∞∞An3g1n,gn=2ina·1k2-k∗2[kJn+1(ka)Jn(k∗a)-k∗Jn(ka)Jn+1(k∗a)],g1n=gn+2inak∗Jn(ka)Jn′(k∗a).According to the continuous boundary conditions of the displacement and stress around the real and image fibers, the boundary conditions for the anti-plane shear waves can be written asu1∗(t)|r=a=u1∗(i)|r=a+u1∗(s)|r=a+u2∗(s)|r=a=u1∗(r)|r=a,τrz1∗(t)|r=a=τrz1∗(i)|r=a+τrz1∗(s)|r=a+τr′z′2∗(s)|r=a=τrz1∗(r)|r=a,u2∗(t)|r′=a=u2∗(i)|r′=a+u2∗(s)|r′=a+u1∗(s)|r′=a=u2∗(r)|r′=a,τr′z′2∗(t)|r′=a=τr′z′2∗(i)|r′=a+τr′z′2∗(s)|r′=a+τrz1∗(s)|r′=a=τr′z′2∗(r)|r′=a,where u1∗(t) is the total wave field around the real fiber, and τrz1∗(t)=μ∗∂u1∗(t)∂r is the total shear stress around the real fiber.To make the computation tractable, the expressions of wave fields in the localized coordinate system (r′,θ′) should be translated into the coordinate system (r,θ). According to the addition theorem of Graf Hn(1)(kr′)einθ′=∑m=-∞∞(-1)m-nHm-n(1)(2kb)Jm(kr)eimθ.Hn(1)(kr)einθ=∑m=-∞∞Hm-n(1)(2kb)Jm(kr′)eimθ′.The expressions of the displacement and stress are substituted into Eqs. . Multiplying e-isθ on both sides of Eqs. , and then integrating over θ∈[-π,π], a set of algebraic equation system is obtained. After arrangement, the equations can be simplified aswhere E is a coefficient matrix of 4 × 4, and f is a vector of 4 ranks, whose elements are shown in . After solving the linear equation system, the modal coefficients As1, As2, As3 and As4(s=0,±1,±2,…) can be determined.According to the dispersion relation in Eq. , we construct numerical solutions of the effective parameters. The numerical solutions are obtained by the iterative procedure, i.e.,μ∗n=μ∗n-1+ε[μ∗n-1-μ0(1+Vfμ¯1HC(k∗n-1,μ∗n-1))],ρ∗n=ρ∗n-1+ε[ρ∗n-1-ρ0(1+Vfρ¯1Λρ(k∗n-1,μ∗n-1))],k∗n=ω(ρ∗nμ∗n)1/2,μ¯1=μ1μ0,ρ¯1=ρ1ρ0,where k∗n,ρ∗n and μ∗n are the effective parameters for the nth iteration, function HC(k∗,μ∗) and Λρ(k∗,μ∗) are defined in Eq. . Parameter ε(∣ε∣<1) is to be chosen for convergence of the iterative process. During the process of iterative, the convergence criterion ∣k∗n-k∗n-1∣/k∗n⩽10-4 is applied. It should be noted that the number of iteration increases with the increase of the incident frequency. As an initial (zero) approximation, we apply the static solutions μ∗(0)=μs and k∗(0)=ω(ρ0+Vfρ1)/μs. μs is the static shear modulus and is proposed as In the following analysis it is convenient to make the variables dimensionless. To accomplish this step, we may introduce a representative length scale a, where a is the radius of the reinforcing fibers. The following dimensionless variables and quantities have been chosen for computation: k0a=0.01-2.0, x/a=1.1-11.0, μ¯=μ/μ0=0.1-10.0, ρ¯=ρ/ρ0=0.1-2.0., we plot respectively the dynamic effective shear modulus and density of the semi-infinite composite material under different dimensionless wave number as a function of x/a with parameters: μ¯=5.0, ρ¯=2.0 and Vf |
= 0.1. It can be seen that the greater the incident wave number (higher frequency), the greater the effect of the semi-infinite boundary on the dynamic effective properties is. If the dimensionless wave number ka is greater than 1, the maximum values of the dynamic effective properties do not occur at the surface of the semi-infinite structure. The phenomenon is caused by the multiple scattering of shear waves between the semi-infinite surface and the fibers. The dynamic effective properties first increase with the increase of x/a, then reach the maximum, and tend to be invariable as x/a further increases. The value of x/a corresponding to the invariable effective properties increases with the increase of the incident wave number. However, if the dimensionless wave number ka is smaller than 1, the maximum value of the dynamic effective properties occurs at the surface of the semi-infinite structure. When the dynamic effective properties tend to be invariable, the variation of the dimensionless wave number has greater effect on the effective shear modulus than that on the effective density, which is consistent with those obtained from Ref. we plot respectively the dynamic effective shear modulus and density of the semi-infinite composite structure under different phase properties as a function of x/a with parameters: k0a=1.0 and Vf |
= 0.15. The value of x/a corresponding to the invariable effective properties increases with the increase of the values of μ¯ and ρ¯. It also can be seen that if the values of μ¯ and ρ¯ are greater than 1, the effect of the semi-infinite boundary on the dynamic effective properties is comparatively great. However, if the values of μ¯ and ρ¯ are smaller than 1, the effect of the semi-infinite boundary on the dynamic effective properties becomes little. From , it is clear that the variation of the values of μ¯ nearly has no effect on the variation of dynamic effective density. we show respectively the dynamic effective shear modulus and density of the semi-infinite composite structure under different volume fraction of fibers as a function of x/a with parameters: k0a=2.0, μ¯=10.0 and ρ¯=2.0. The effective medium method used in this paper does not consider the direct interaction between the fibers, so only the low volume fraction of fibers is analyzed. It can be seen that the maximum dynamic effective properties increase with the increase of the volume fraction Vf. The effect of the volume fraction on the dynamic shear modulus is greater than that on the dynamic effective density.To illustrate the effective shear modulus and density of the semi-infinite composite structure under the static loading, are plotted. As kAa→0, the dynamic effective elastic modulus and density tend to the static solutions. It can be seen that the variation of the dynamic effective properties with the value of x/a is more complex than that of the static properties. As expected, the effective properties under the static load express no variation with the value of x/a. The static effective properties increase greatly with the increase of the volume fraction of fibers, which is significantly different from the dynamic effective properties.To validate the present method, comparisons with the static effective shear modulus and density following from the micromechanics analysis are given. shows the static effective shear modulus as a function of the volume fraction of the fiber with parameters: kAa=0.01, μ¯=5.0 and x/a=5.0. A comparison of the effective shear modulus is made with the expression of the static solution in Eq. . It should be emphasized that the agreement between the results of the present method and the static solution appears to be good. shows the static effective density as a function of the volume fraction of the fiber with parameters: kAa=0.01, ρ¯=2.0 and x/a=10.0. A comparison of the effective density is made with the expression of the static solution: ρs=Vfρ+(1-Vf)ρ0. The excellent agreement between them is also found.A computational method is presented to analyze the propagation of anti-plane shear waves in semi-infinite random unidirectional fiber-reinforced composites. The problem of random media is simplified to the one-fiber problem by employing the effective medium method, and the dispersion relation in the semi-infinite random composites is obtained. The one-fiber problem is solved by employing the wave function expansion method and the image method. The numerical examples of the dynamic effective properties of the semi-infinite composite structure are graphically presented and analyzed. The satisfactory agreement with the static solution following from the micromechanics analysis has been observed.It has been found that the dynamic effective properties near the surface of the semi-infinite random unidirectional fiber-reinforced composite are significantly different from those in the infinite random unidirectional fiber-reinforced composite. The maximum dynamic effective shear modulus and density near the surface increase with the increase of the incident wave number, the properties ratio of the two phases and the volume fraction of fibers. However, the static effective properties of the semi-infinite unidirectional fiber-reinforced composite are the same as those of the infinite unidirectional fiber-reinforced composite.The elements of coefficient matrix E and vector f are given byE22=∑n=-∞∞(-1)s-nHs-n(1)(2kb)μ∗k∗2[Js-1(k∗a)-Js+1(k∗a)],E41=∑n=-∞∞Hs-n(1)(2kb)μ∗k∗2[Js-1(k∗a)-Js+1(k∗a)],Mechanical modeling of flexible OLED devicesGeneral expressions are deduced for the stresses developed in the individual thin layers of a multi-layer structure as a result of bending to a specified radius. These are appropriate for analysing flexible organic light emitting diode (FOLED) devices on flexible substrates. Residual stress (caused internally by temperature change and differential thermal expansion) after material deposition and return to ambient temperatures is not considered. The reduced elastic modulus of the typical small molecule OLED materials: N,N′-bis(naphthalen-1-yl)-N,N′-bis(phenyl)benzidine (NPD) and tris-(8-hydroxyquinoline)aluminum (Alq3) are measured as thin-films using nano-indentation techniques. A conventional device: polyethylene terephthalate (PET)/Buffer layer (BL)/ITO/OLED/Al is considered from a modeling standpoint, as a preliminary to actual fabrication and subsequent comparative testing of OLED performance on rigid and flexible supports.Recently, glass substrate based OLED devices have been improved to achieve commercial application standard in most respects. With reported device lifetimes longer than 200 khr To understand the mechanism of bending a device comprising more than one layer, one can imagine a 175 μm thick polyethylene terephthalate (PET) substrate covered with a 100 nm ITO thin-film to have a structure somewhat analogous to a leaf spring, with 1750 soft leaves and one hard leaf, each 100 nm thick and connected in parallel. In contrast to the leaf spring, however, here the adjacent surfaces of neighbouring leaves are firmly bound to one another. When the structure is bent so that the uppermost surface of the thin layer is concave, it is reasonable to assume that there will be one “leaf” out of the 1751, which maintains its original length, and all others laid above it are stretched whilst those below it are compressed. The one with its original length is called the neutral layer (NL). The position of this layer is crucial because the strain in any of these springs is proportional to the distance from itself to the neutral layer. This will be deduced later.To determine the position of NL in a multi-layer structure, others such as Kim and co-workers For the longitudinal stress in a plain film being bent, the stress is given by:where the Young’s modulus of the film material is E, ν is the Poisson’s ratio, E′ is the reduced elastic modulus and the strain of the film is ε. This strain is defined by:where l is the original unbent length, and Δl is the change of length after bending. Although these thin-films are not real springs, the strain caused by bending is only about 0.01 even when the radius is 10 mm. This means the higher order terms are negligible and Hooke’s Law is still valid. When an arbitrary segment of a homogeneous film with a symmetric cross section is analysed, the NL should be right at the centre of the film. Assume the layer denoted by ab¯ in a is the NL, and by definition its length remains unchanged on bending to an extent where R defines the radius of curvature experienced by the NL. Set the length of ab¯ to be l. Now consider the strain of another layer in the film, cd¯, say, when the radius of curvature at the NL (ab¯) is R. Before bending (b) the new length of cd¯ becomes c′d′¯, so thatwhere y is the distance from the layer to NL. The strain in the cd element at this distance from the NL thus becomes:Therefore, the stress in any layer in a film with its distance from the NL being y isThe total bending moment M at one end of the segment iswhere h is the thickness of the film, C is the displacement from the bottom of the film to the NL, w is the width of the cross section and Ix is the second moment of area of the cross section. So we have the following equation to describe the stress developed in the layer as a result of bending completely:From the above, the most critical property is the position of the NL. In a single-material, the position of NL is easy to determine. It is just at the centroidal axis of the cross section, so the distance from the layer of interest to the NL, y, will be known. When the architecture comprises two or more layers of different materials, for example ITO on a PET substrate, slightly more effort is required.a shows the cross section of the typical ITO coated PET substrate where hs is the thickness of the substrate, and hi is the thickness of ITO. Assume both layers are with the same width w and different Young’s modulus: Es and Ei. The total bending moment isM=∫σwydy=Es′R∫-Chs-Cwy2dy+Ei′R∫hs-Chs-C+hiwy2dy=Es′RIxs+Ei′RIxi=Ei′REs′Ei′Ixs+Ixi≡Ei′RIxeffectiveC is the position of NL from the bottom of substrate. The position of C is chosen at the y |
= 0 axis in the integration to determine the second moment of area instead of the conventional choice of the centroidal axis of the individual cross section. Formally, it is determined by equating the net force acting on the cross section under bending, to zero as follows: shows that the total bending moment M of an ITO/PET composite film is the same as the pure ITO film with the effective cross section Ixeffective. Compared with Eq. , it can be seen that the effective cross section is really the original cross section of ITO plus the cross section of PET with the new width w′ given by:Therefore, in the case of longitudinal stress, an ITO/PET composite film (as shown in a) is identical to the pure ITO film (as shown in b). This greatly reduces the effort of solving the position of NL from Eq. to simply determining the centroidal axis of the effective cross section as if it were made from a single-material. When dealing with structures of more than two layers, with each layer having a different Young’s modulus, the task of determining the position of NL using the Eq. becomes even more complicated. However, the method we used here requires only the calculation of the effective cross section by determining w′ of each layer, using the reduced elastic modulus of the layer of interest as the denominator in Eq. . Once the equivalent cross section is determined, with the assumption that all the layers are now made from an identical material to the layer of interest, the NL is targeted at the position of centroidal axis of this effective cross section, and the stress in the layer of interest is just a factor times its distance from the NL in the effective cross section: the calculation has transformed the multi-material composite film into a single-material film made solely from the layer under investigation.Due to the poor performance of plastic substrates with respect to permeation of water and oxygen, mentioned earlier, one or more extra barrier layers would usually be inserted between the ITO layer and the PET substrate. The question is: is it possible that a single additional layer could both reduce the stress in the ITO to give it an extra relief when bending and provide an adequate oxygen/water barrier at the same time?Glass, for example, has a permeation rate of oxygen and water vapour lower than the detection limit The reduced elastic modulus of ITO, glass, and PET film are assumed to be 120 GPa . If the total thickness of glass plus PET composite substrate is kept constant at 175 μm, with a typical ITO thickness of 100 nm, and the whole composite subjected to a bend radius of 10 cm, then from Eq. the thicknesses of glass and PET optimized by simulation are 35 μm and 140 μm, respectively, as shown in . This structure would reduce the stress in ITO from the plain PET substrate – and, indeed, also a plain glass substrate – by a factor of 2.5.To further understand how the overlaid OLED and cathode layers would affect the ITO stress, a knowledge of the Young’s modulus of these organic layers is required. The lack of such information is partly because the PET substrate is softer than the organic layer which leads to the difficulty for the elasticity measurement. However, with the aid of triboindenter technology, the surface of the sample can be probed on the scale of several nanometers, thus allowing the effect of the soft base to be filtered out. Three samples are prepared, as listed in , in order to gauge the elastic property of N,N′-bis(naphthalen-1-yl)-N,N′-bis(phenyl)benzidine (NPD) and tris-(8-hydroxyquinoline)aluminum (Alq3). The PET substrate was cleaned first with acetone, and then with isopropanol in an ultrasonic bath for 5 min each. Three separate samples were prepared by evaporating 100 nm of Alq3, 200 nm of Alq3 and 200 nm of NPD, respectively, on the PET substrate separately using the Kurt J. Lesker thermal evaporator under the vacuum of 5 × 10−7 |
mbar.The Young’s moduli of the samples were measured by standard nano-indentation techniques. For each material nano-indentation tests were performed under displacement control with maximum displacements from 10 nm to 1000 nm using a Hysitron Triboindenter fitted with a sharp Berkovich diamond indenter (tip end radius ∼50 nm). The diamond tip shape was carefully calibrated with a fused silica test sample (using the standard Oliver and Pharr method The indenter displacement is made up of two components, the plastic depth of the indent (contact depth) and the elastic deflection of the surface at the edge of the contact. The contact depth is typically <0.67 of the maximum displacement. Nano-indentation load–displacement curves were recorded for each indent and only those where evidence of plastic deformation was observed (i.e. the loading and unloading curves are different) were used in the analysis of Young’s modulus by the Oliver and Pharr method . The reduced elastic modulus in the y-axis direction only differs from the real Young’s modulus by a factor of (1 − |
ν2)−1. Because the thickness of the organic layers are 100 nm and 200 nm, the readings of the reduced elastic modulus at the contact depth deeper than a third of the coating thickness are greatly dominated by the PET substrate. The Young’s modulus commonly used for PET film is 4 GPa, and the Poisson’s ratio lies between 0 and 0.5. However, the reduced elastic modulus in this regime is measured to be lower than 4 GPa, rather than larger values in the range 4–5 GPa as the common values above suggest. We believe this might be due to the thin planarization layer (smoothing layer) coated by the supplier (DuPont Teijin Films), which could be softer than PET.When the contact depth is within a third of the coating thickness, the measured reduced elastic modulus contains an increasing contribution from the thin coating itself. So the value of the reduced modulus when the contact depth is extrapolated to zero can approximate the Young’s modulus of the coating layer deposited. From , all the three samples have about same value of 12 GPa when the contact depth approaches zero regardless of the difference in their thickness. For such a thin coating on a compliant substrate it is difficult to completely filter out the effect of the substrate and there may be considerable scatter in the extrapolated modulus due to the quality of the data available for extrapolation. Fracture in the coating can lead to discontinuities in observed behaviour and, at low indenter penetrations where most data is needed for accurate extrapolation, plastic deformation is limited. Thus, although this extrapolation process has been adopted in ISO 14577-4 (2007) for the assessment of the reduced modulus of thin coatings there remain some questions about its validity; for instance for a substrate harder or softer than the coated layer, the modulus determined by nano-indentation can be different For OLED operation in a flexible regime, the value of 12 GPa suggests that the materials in small molecule based OLEDs are not remarkably different in their elastic moduli relative to either the long chain polymer materials in PLEDs (typ. 2–6 GPa) or, say, a PET support (4 GPa). Only the ITO (120 GPa) and metal cathode layers such as aluminum (70 GPa) require more careful attention.The five-layers structure: PET (100 μm)/Buffer (x)/ITO (100 nm)/OLED (100 nm)/Aluminium (100 nm) is simulated with different values of reduced elastic modulus of the buffer layer (BL) and different thicknesses, x. The extension to accommodate the multiple thin layers in this case is particularly straightforward. The combined thickness of the thin layer stack is nearly three orders of magnitude less than that of the support, so the position of the neutral layer is determined almost exclusively by the composition of the thicker support. The stress in each of the thin layers is then determined by the reduced elastic modulus of the thin layer, the distance from the neutral plane to the surface on which the thin layer is coated and the bend radius, just as for the single thin layer case. The reduced elastic modulus of the PET substrate is set to be 5 GPa. Assuming the bending radius is 15 mm, the stress in ITO against the thickness of BL is shown in . This shows a series of different buffer layer moduli, in the whole device structure. In contrast to , the PET layer now has a constant thickness and the buffer thickness is increased from zero. As the buffer material modulus increases, values in the range 14–70 GPa exhibit minima in ITO stress at a thicknesses of 15–20% of the PET layer. When the reduced elastic modulus of BL is smaller than 14 GPa, the ITO stress is increased. For a BL modulus of 70 GPa, the stress has the maximum reduction – about 50% – for a thickness of 20 μm. However, a larger stress occurs when it is thicker than 70 μm. This is the result of the competition between the changing of the NL position and the distance of ITO layer from NL as mentioned before. The stress in ITO against the bending radius with BL thickness of 20 μm and 100 μm is shown in a and b. This simulation presents a very interesting result. For the former thickness, it seems that the larger the Young’s modulus, the better. But the effect will saturate eventually. However, the latter suggests that when BL is as thick as the PET layer (100 μm), the stress in ITO will never be reduced no matter what material is chosen. The value of Young’s modulus and reduced elastic modulus used in the simulation is in An alternative approach to calculate the stress developed in a thin-film multi-layer has been adopted. With this method, the position of the NL can be determined and a concept of visualising changes in stress as the structural architecture is fine-tuned has emerged. A plastic/glass composite substrate with the thickness of 140 μm and 35 μm respectively, acting to provide a flexible barrier to oxygen and water vapour, has been predicted to reduce the stress in ITO deposited on the glass surface by a factor of 2.5, compared with 175 μm of either glass or PET on its own. The yield strength of ITO (the limit beyond which material deformation is irreversible) corresponding to a failure strain of ca. 1%, is 1.2 GPa Finally, a practical five-layer OLED device structure has been simulated using the reduced elastic modulus values for NPD and Alq3 measured here. It shows that the choice of the BL material’s modulus, and its thickness relative to that of the underlying PET, are crucial in reducing the stress in ITO. For BL thicknesses equal to that of the PET, the BL is unable to decrease the ITO stress, regardless of its modulus. One has to bear in mind that all the materials in this simulation are assumed to be elastic. The mechanism of creep (changing of strain under fixed applied stress) and stress relaxation (changing of stress under fixed applied strain) is omitted. The mechanism of cracking is also not considered. There would be some cracks generated initially on each film during their fabrication, and the initial pattern of these cracks would not be expected to be the same for every sample. Nevertheless, reducing the stress in the most brittle layer should still slow down or prevent cracks from migrating further, thereby extending the device lifetime.Practically, for commercial FOLED devices, it is generally necessary to cover the device with an extra encapsulation layer. With a careful choice of the thickness and elastic property of this encapsulating layer, it is possible to further reduce the distance between NL and the brittle anode layer thus diminish the stress even to zero. However, the problem of deformation or delamination between layers, either due to thermal stress or bending, may become the dominant concern in the FOLED device degradation.Arbitrary Lagrangian–Eulerian formulationAn ALE formulation for implicit time integration of quasi-steady-state wear problemsA fully coupled implicit scheme is developed for quasi-steady-state wear problems. The formulation admits finite configuration changes due to both deformation and wear. The unconditionally stable implicit backward-Euler scheme is used for time integration of the shape evolution problem. Thus, the solution may proceed with large time increments, contrary to the commonly used explicit forward-Euler scheme, in which the time increment is restricted by the stability condition. This comes at the cost that the shape transformation mapping constitutes an additional unknown. As a result, a kind of an arbitrary Lagrangian–Eulerian (ALE) formulation is obtained in which the problem is solved simultaneously for the nodal positions and displacements. The incremental coupled problem is solved using the Newton method which leads to a highly efficient computational scheme, as illustrated by two- and three-dimensional numerical examples.Arbitrary Lagrangian–Eulerian formulationWear is a process of material removal from a surface subjected to frictional contact interaction. Wear processes are usually slow, and noticeable effects result from repeated contacts and accumulation of wear over a long period. Simulation of this class of contact problems is a challenging task as it involves shape changes due to accumulated wear and the associated evolution of the contact zone, pressure, etc. This work is concerned with computational modeling of progressive wear, and the adopted approach belongs to the class of incremental solution strategies. Note that alternative direct approaches have been developed for asymptotic or steady-state wear processes, cf. The incremental solution procedures for progressive wear problems are usually based on the explicit forward-Euler time integration scheme. Specifically, at each time step, the contact problem is solved at the known current shape of the contacting bodies, and the wear rate is computed as a postprocessing quantity. The wear depth increment is then obtained by multiplying the wear rate by the time increment, the shape is updated accordingly, and the solution proceeds to the next time step. This procedure has been used in combination with the finite element method The explicit forward-Euler scheme is simple and quite straightforward to implement, hence its popularity in modeling of progressive wear. However, as it is well known, this scheme is only conditionally stable, and the related instabilities are commonly encountered in computational practice On the contrary, the implicit backward-Euler scheme is unconditionally stable so that the time increment is constrained only by the desired accuracy of the solution. Application of the implicit scheme requires that the wear increment (or shape transformation resulting from wear) constitutes an additional unknown in the problem. In the context of wear evolution problems, the implicit time integration scheme has, so far, been employed only by Strömberg In this work, a fully coupled implicit scheme is developed for quasi-steady-state wear problems. The finite-deformation formulation of the contact and wear problem follows that recently developed by Lengiewicz and Stupkiewicz Consider two hyperelastic bodies B1 and B2 subjected to frictional contact and wear. Following the continuum formulation proposed in configuration Ωˆi, the time-dependent undeformed configuration Ωi, and the current (deformed) configuration ωi. The shape change due to wear is described by the shape transformation mappingΨi, and the deformation is described by the deformation mappingφi, so thatwhere Xˆi∈Ωˆi,Xi∈Ωi, xi∈ωi. Both the deformation and the shape change due to wear are allowed to result in finite configuration changes. The initial configuration Ωˆi is assumed to be a stress-free (natural) configuration. The undeformed configuration Ωi is thus also a stress-free configuration.The undeformed configuration Ωi evolves in time as a result of accumulation of wear at the contact interface. Shape evolution due to wear is governed bywhere Γˆi is the boundary of Ωˆi, Γˆci⊂Γˆi denotes the potential contact surface, and Ni is the unit outer normal defined in the undeformed configuration Ωi. The nominal wear rate Ẇi⩾0 in Eq. denotes the wear volume per unit area and unit time, where both the volume and the area refer to the undeformed configuration Ωi.Considering that wear is typically a slow process, i.e., the shape and contact conditions change due to slow accumulation of wear, two time scales can be introduced Xi=Ψi(Xˆi,t),xi=φti(Xi,τ),t∈[0,T],τ∈[t,t+Δτ],where Xi∈Ωti,Ωti=Ψi(Ωˆi,t), and Δτ is a characteristic time of the deformation problem, for instance, one cycle of a cyclic loading program. The details can be found in This work is concerned with a special class of wear problems, namely with quasi-steady-state wear problems. In a quasi-steady-state wear problem, the deformation problem corresponding to a fixed slow time t is a steady-state frictional contact problem once formulated in an appropriate Eulerian frame. Specifically, the Eulerian description is adopted in the reference configuration Ωˆi and in the undeformed configuration Ωti to account for the rigid-body motion of one or both contacting bodies, so that the (Lagrangian) deformation mappings φti do not depend on the fast time τ, and we havewhere Xi∈Ωti,Ωti=Ψi(Ωˆi,t). Clearly, the deformation problem is parameterized by the slow time t of the shape evolution problem. Typical examples of quasi-steady-state wear problems are the pin-on-disc tribological test and rolling contact. For instance, in the former case, the reference frame is attached to the pin, and the disc is analyzed in an Eulerian frame.Consider a steady-state quasi-static frictional contact problem in which the motion is decomposed into rigid-body motion (in an Eulerian description) and deformation (in a Lagrangian description). As the contacting bodies are hyperelastic, i.e., their behavior is time- and history-independent, and the inertial effects are neglected, the rigid-body motion in the Eulerian undeformed configuration does not affect the deformation problem, except that relative sliding must be defined properly. As discussed above, the deformation mappings φti do not depend on the fast time τ. To simplify the notation, the dependence on the slow time t, which parameterizes the deformation problem, is not indicated explicitly in this subsection.The contact formulation adopted in this work is rather standard, and it is briefly introduced below. The details can be found, for instance, in the monographs In the master–slave formulation, contact points are associated through the closest-point projection of a point x1 of the deformed slave surface γc1=φ1(Γc1) onto the deformed master surface γc2=φ2(Γc2). The projection point is denoted by x¯2=x2(ξ¯), where the master surface γc2 has been parameterized by convective coordinates ξ={ξ1,ξ2}, and ξ¯ denotes the coordinates of the projection point x¯2.The normal gap is defined in a standard manner,where n=n2, and n2 is a unit outward normal to γc2. The tangential sliding velocity is defined aswhere τα=∂x2/∂ξα is the tangent basis, τα is the cobasis, τα·τβ=δβα,vi denotes the velocity of the material point xi, and v¯2=v2(x¯2) is the velocity of the projection point x¯2. Considering that the deformation problem is a steady-state problem, velocity vi results solely from the rigid-body motion with velocity Vi in the undeformed configuration Ωi, and we haveThe contact traction vector t=t2 is decomposed into normal and tangential components,where t2=σ2n,σ2 is the Cauchy stress, and t2=-t1 in view of the action-reaction principle. The kinematical contact variables (gN,vT) and the contact tractions (tN, tT) are related by the unilateral contact law,‖tT‖+μtN⩽0,‖vT‖tT=vT‖tT‖,‖vT‖(‖tT‖+μtN)=0.Finally, the virtual work principle of the two-body system reads ∑i=12∫ΩiPi·∇δφidV-∫ΓsiT∗i·δφidS+∫Γc1(TNδgN+TTαδξ¯α)dS=0,where δφi=0 on Γui,T∗i is the traction prescribed on Γsi,Pi=∂ϕi/∂Fi is the first Piola–Kirchhoff stress, and ϕi(Fi) is the elastic strain energy function. The contact contribution in is integrated over the undeformed contact surface Γc1 of the slave body, so the nominal contact tractions TN and TT,are introduced, which refer to the unit area in the undeformed configuration Ω1 of the slave body. Here, ji=dsi/dSi is the area transformation factor (which follows from the Nanson’s formula, nds=JF-TNdS).Wear rate is a postprocessing quantity that can be computed once the contact problem is solved. According to the classical Archard’s wear model, the wear rate is proportional to the product of the normal contact pressure and sliding velocity or, equivalently, proportional to the frictional dissipation rate which is equal to the product of friction stress and sliding velocity. The wear model of the Archard type, consistently formulated in the finite-deformation setting, takes the following form where Ki is the wear coefficient, and the nominal wear rate Ẇi is the wear volume per unit area and unit time, where both the volume and the area refer to the undeformed configuration Ωi. The frictional dissipation rate ḋ is the dissipated power per unit area in the current configuration ωi, while Ḋi is referred to the area in the undeformed configuration Ωi.The shape evolution problem is governed by Eq. which defines only the normal component of the shape transformation mapping Ψ̇i on the boundary Γˆi. It is convenient to uniquely specify also the tangential component of Ψ̇i by adopting the shape evolution law in the following formIn order to arrive at a feasible computational scheme, a suitable time integration of the above time-continuous setting must be introduced, and two first-order integration schemes are discussed below. Two subsequent discrete time instants tn and tn+1=tn+Δt are thus considered, and a subscript is used to denote the quantities evaluated at a discrete time instant, e.g., Ψni(Xˆi)=Ψi(Xˆi,tn).Application of the explicit forward-Euler time integration scheme to Ψn+1i(Xˆi)=Ψni(Xˆi)-ΔtẆni(Xˆi)Nni(Xˆi)onΓˆci,where Nni and Ẇni depend on the position Xˆi in the initial configuration through the shape transformation mapping Ψni.for Xni∈Γc,ni. This form is the basis of a simple and popular shape update scheme employing remeshing after the contact problem is solved at each time step, e.g. is applied to the boundary nodes. Subsequently, the positions of the interior nodes are determined in a remeshing procedure.The above explicit scheme is simple, but it is only conditionally stable. As shown by Johansson . In realistic conditions, the critical time increment may be very small so that the scheme becomes computationally expensive.Application of the implicit backward-Euler time integration scheme to Ψn+1i(Xˆi)=Ψni(Xˆi)-ΔtẆn+1i(Xˆi)Nn+1i(Xˆi)onΓˆci.In this scheme, the normal Nn+1i and the solution of the deformation problem at tn+1, including the wear rate Ẇn+1i, depend on Ψn+1i. Thus the problem must be solved simultaneously for φn+1i (displacements) and Ψn+1i (shape transformation). Of course, the size of the problem increases due to additional unknowns.However, the benefit is that the scheme is unconditionally stable, so the time increment is limited only by the desired accuracy and not by the stability condition. In practice, significantly larger time increments can be used as compared to the explicit scheme, thus leading to a computationally efficient scheme.In the shape evolution problem discussed above, the shape transformation mapping is prescribed only on the boundary Γˆi. This uniquely defines the shape changes. In order to define the shape transformation mapping Ψi in the whole domain Ωˆi, we introduce an auxiliary elasticity problem which governs the motion due to shape transformation that is prescribed on the boundary Γˆi.For that purpose, we introduce an artificial elastic strain energy function ϕˆi(Fˆi), where the deformation gradient Fˆi is associated with the shape transformation mapping Ψi,The auxiliary elastic strain energy function ϕˆi(Fˆi) can in general be different than the elastic strain energy function ϕi(Fi) that specifies the actual behavior of the respective body Bi.For each body Bi, the shape evolution problem is then governed by the following constrained minimization problemminΨn+1i∫Ωˆiϕˆi(Fˆn+1i)dVˆsubject toΨn+1i=Ψn+1∗ionΓˆci,where Ψn+1i=0 on Γˆi⧹Γˆci. The deformation in this auxiliary elasticity problem is driven by the shape transformation Ψn+1∗i that results from wear and is prescribed on the contact boundary Γˆci,Ψn+1∗i(Xˆi)=Ψni(Xˆi)-ΔtẆn+αi(Xˆi)Nn+αi(Xˆi).Here, the implicit time integration scheme is obtained by setting α=1, and the explicit time integration scheme is obtained for α=0. This provides a uniform framework for implementation and analysis of both integration schemes. is introduced in the auxiliary elasticity problem as a constraint rather than as a Dirichlet boundary condition because Ψn+1∗i is actually an unknown in the complete wear problem. This condition is enforced using Lagrange multipliers μ and the stationarity of the corresponding Lagrangian Lˆ=∫ΩˆiϕˆidVˆ-∫Γˆciμ·(Ψn+1i-Ψn+1∗i)dSˆ yields the following variational statement,∫ΩˆiPˆi·∇ˆδΨidVˆ-∫Γˆci[μ·δΨi+δμ·(Ψn+1i-Ψn+1∗i)]dSˆ=0,where Pˆi=∂ϕˆi/∂Fˆi and δΨi=0 on Γˆi⧹Γˆci.In the present formulation, the shape evolution problem are coupled, and the two problems are solved simultaneously. This is necessary in the case of the implicit scheme which is the main concern of this work. In the case of the explicit scheme , the two problems decouple and could be solved separately in a sequential manner, thus leading to a more efficient implementation.In order to reduce the computational cost, the shape transformation mapping Ψi can be prescribed to identity away from the actual contact zone. This would correspond to solving the auxiliary elasticity problem on a subdomain of Ωˆi.The present finite element implementation and the numerical examples reported in Section are restricted to rigid-deformable contact (one body is rigid) and gross sliding (as, for instance, in the pin-on-disc configuration). Below, the specific formulation is detailed, including the augmented Lagrangian treatment of the contact constraints.In the following, a typical time instant t=tn+1 is considered, and it is assumed that the solution at the previous time step t=tn is known. To simplify the notation, the subscript denoting the quantities evaluated at the current time step tn+1 is dropped.The contact problem is defined by the virtual work principle . In this work, the augmented Lagrangian method . Since gross sliding is assumed, the friction stress is explicitly expressed in terms of the normal contact traction and sliding direction, and no special treatment is needed. Upon the augmented Lagrangian treatment, the deformation problem is governed by the following augmented virtual work principle,where Gφint and Gφext denote, respectively, the virtual work of internal and external forces,Gφint(φ,Ψ;δφ)=∫ΩP·∇δφdV,Gφext(φ,Ψ;δφ)=-∫ΓsT∗·δφdS.The contact contribution to the virtual work involves an additional field of Lagrange multipliers λN defined on the contact surface Γc,Gφcont(φ,Ψ,λN;δφ,δλN)=∫Γc(λˆNeffδgN+TT·δgT+CNδλN)dS,λˆNeff=λˆN,λˆN⩽0,0,λˆN>0,CN=gN,λˆN⩽0,-λN/ϱ,λˆN>0,λˆN=λN+ϱgN is the augmented Lagrange multiplier, and ϱ>0 is a regularization parameter. Note that CN is a state-dependent constraint enforcing either gN=0 in the case of contact or λN=0 in the case of separation, in agreement with the unilateral contact condition . In view of the gross-sliding condition, the friction stress is given by TT=-μλˆNeffvT/‖vT‖. Finally, in the case of rigid-deformable contact, the variations of the kinematical quantities are simply given by δgN=n·δx and δgT=(1-n⊗n)δx.GΨcont(φ,Ψ,λN,μ;δΨ,δμ)=-∫Γˆc[μˆ·δΨ+δμ·(Ψ-Ψ∗)]dSˆ.In the present implementation, the constraint Ψ=Ψ∗ has been actually enforced using the augmented Lagrangian method, hence the augmented Lagrange multiplier μˆ=μ+∊(Ψ-Ψ∗) in Eq. rather than the Lagrange multiplier μ alone as in Eq. . This treatment proved to have beneficial effect on the convergence of the Newton method used to solve the nonlinear finite element equations.The deformation problem depends on the current shape of the undeformed configuration Ω and this is indicated by the dependence of Gφ on the shape transformation mapping Ψ in Eqs. . The dependence of GΨcont on the deformation mapping φ and on the Lagrange multiplier λN is through the term Ψ∗, and specifically through the wear rate Ẇ in Eq. The finite element implementation has been carried out using the AceGen/AceFEM system The AD-based formulation of the solid and contact elements used in this work is provided below. Note that this compact formulation is sufficient for the actual implementation, as the specific formulae and the corresponding computer codes are generated automatically by the AceGen system.Solid elements implement the internal-work contributions Gφint and GΨint in the weak forms , respectively. Application of the standard finite element interpolation and numerical integration gives the global residual vector Rint associated with the global vector of nodal unknowns p,The global residual Rint is an assembly of element residuals Re, and each element residual is a sum of Gauss-point contributions Rg,where Ss is the set of solid elements, and wg denotes the Gauss-point weight.The element unknowns pe comprise the nodal displacements pφe related to the deformation mapping φ and displacement-like quantities pΨe related to the shape transformation mapping Ψ, thus pe={pφe,pΨe}. The Gauss-point residual Rg is obtained by applying the automatic differentiation (AD) technique according towhere Jg=det(∂X/∂ξ) is the Jacobian of the transformation from the reference element Ω□ to the undeformed configuration Ω, and similarly Jˆg=det(∂Xˆ/∂ξ) is the Jacobian relating Ω□ and the initial configuration Ωˆ. The operator δ(·)/δ(·) denotes the differentiation performed by the AD algorithm, cf. 1, and this is enforced by introducing the AD exception in the first term on the right-hand side in Eq. . It is easy to check that the above AD-based formulation indeed corresponds to the internal-work contributions In the present implementation, the F-bar formulation The contact surface Γˆc is discretized into 2-node linear segments in 2D and 4-node bilinear facets in 3D. The same interpolation is used for the Lagrange multipliers λN and μ. Nodal integration is used in order to avoid spurious oscillations typical for Gauss quadrature As in the case of solid elements, we havewhere Sc is the set of contact elements.In addition to the nodal displacements pφe and displacement-like quantities pΨe, the element unknowns pe comprise now the contact Lagrange multipliers assembled in pλe and the Lagrange multipliers that enforce the shape transformation, which are assembled in pμe, thus pe={pφe,pΨe,pλe,pμe}. The Gauss-point residual Rg corresponding to the contact contribution specified by Eqs. is obtained using the following formulationRg=jg(λˆNeffn+TT)·δxδpeDxDpΨe=0+CNδλNδpe+jˆgμˆ·δΨδpe+(Ψ-Ψ∗)·δμδpe,where jg=‖∂X/∂ξ×∂X/∂η‖ and jˆg=‖∂Xˆ/∂ξ×∂Xˆ/∂η‖ is the Jacobian of the parametrization of the element, respectively, in the undeformed configuration Ω and in the initial configuration Ωˆ. More details on automation of contact formulations can be found in The nonlinear equations R(p)=0 are solved simultaneously for all unknowns p={pφ,pΨ,pλ,pμ} using the Newton’s method. The global residual vector R=Rint+Rext+Rcont results from the finite element discretization: Rint and Rcont have been introduced above; the external-work residual Rext corresponding to Gφext is obtained trivially, particularly for conservative loading (the details are omitted here). At each Newton iteration, the following linear problem is solved for Δp(i),where R(i) and K(i) are evaluated at p(i), and the approximate solution is updated, p(i+1)=p(i)+Δp(i), until convergence is obtained. The tangent matrix K(i) is an assembly of element tangent matrices Ke(i),which are obtained using automatic differentiation. Thanks to exact linearization, quadratic convergence of the Newton scheme is achieved.The purpose of the first example is to study quantitatively the stability and accuracy of the two time integration schemes introduced in Section . A two-dimensional frictionless contact and wear problem in plane-strain conditions is considered. A hyperelastic pin is pressed into a rigid plane which is moving laterally with velocity v=1000mm/s. The geometry and the mesh of 40 × 40 elements are shown in (a). The contact surface at the bottom of the pin is a parabola y=x2/(2R) with the radius of curvature in the centre R=5mm. The maximum height of the pin is H=10mm and its width is L=10mm. The lateral boundaries are constrained in the lateral direction and free to move in the vertical direction. A uniform traction is applied at the top of the pin, the total force is F=20N/mm.Since frictionless contact is considered in this example, the wear rate is assumed to be proportional to the product of normal contact pressure and sliding velocity, Ẇ=kv|TN|, and the wear coefficient is k=10-7MPa-1. The duration of the simulated wear process is tmax=1000s.The hyperelastic material model is of the neo-Hookean type. The elastic strain energy is adopted in the following formwhere C=FTF,J=detF, and λ and μ are the Lamé’s parameters that are specified by prescribing the Young’s modulus E and Poisson’s ratio ν according to μ=E/(2(1+ν)), λ=2μν/(1-2ν). The Poisson’s ratio is fixed at ν=0.3 while the Young’s modulus is varied between E=10MPa and E=640MPa.The initial Hertzian pressure corresponding to E=640MPa is p0=30MPa, so that the ratio p0/E=0.047 is higher than in typical elastic contacts. However, considering that the pressure significantly decreases during the wear process (as the contact area increases), the case of E=640MPa will be referred to as the small-deformation regime. shows the undeformed configuration and the deformed configuration at the initial and final time instants. Evolution of the shape of the contact surface is presented in . It is seen that the time increment Δt=200s is higher than the critical one for the explicit scheme, and the corresponding results exhibit numerical instability, see (b). The instability of the explicit scheme does not occur for a smaller time increment of Δt=5. From (a) it is seen that the implicit scheme is capable of accurately reproducing significant configuration changes in just 5 time steps.The finite-deformation regime corresponds to the lower values of the elastic modulus E. Indeed, finite deformations are clearly visible in which shows the solution obtained for E=20MPa. Shape evolution is presented in , and it is seen that instability of the explicit scheme does not occur even for the large time increment of Δt=200s, and both integration schemes produce similar results.The effect of the elastic modulus E, mesh density and time increment Δt on the accuracy of the solution is illustrated in . The time increment Δt has been varied between 1.56 s and 200 s. The solution is completed in 640 time steps for Δt=1.56s and in 5 time steps for Δt=200s. The solution error is computed with respect to the reference solution obtained for Δt=0.78s (1280 steps), and the Euclidean norm of the difference of the nodal positions at the contact surface in the final undeformed configuration is taken as the measure of the error.In the case of the implicit scheme, the solution error increases with increasing time increment in an approximately linear manner. This is expected because the Euler scheme is first-order accurate. Similar behavior is observed for the explicit scheme at relatively small time increments. However, a sudden increase of the error is observed at larger time increments. This is related to the instability of the explicit forward-Euler scheme. In agreement with the theoretical result of , the critical time increment is proportional to the element size and inversely proportional to the elastic modulus.This example is a three-dimensional counterpart of the one studied in the previous subsection. The aim is to demonstrate the feasibility of the proposed approach for realistic three-dimensional contact and wear problems. A hyperelastic ball of radius R=5mm is pressed into a rigid plane which is moving with velocity v=1000mm/s. Frictional contact with friction coefficient μ=0.5 is considered. The duration of the simulated wear process is tmax=1000s, which is solved in 10 time steps with Δt=0.1tmax.Two cases are considered. In the small-deformation regime, the elastic properties are specified by E=100GPa and ν=0.3, the normal force is F=100N, and the wear coefficient in the Archard model is K=10-7MPa-1. Considering that the counter-body is rigid, the reduced elastic stiffness of the contact pair is approximately equal to that of two elastic bodies made of steel. The Hertzian pressure is p0=2.1GPa, and the Hertzian contact radius is a=0.15mm.In the finite-deformation regime, the elastic parameters are E=10MPa and ν=0.45, the normal force is F=25N, and the wear coefficient is K=4·10-7MPa-1 (the Hertzian pressure would be now p0=3.1MPa). The adopted parameters are such that the total wear volume at the end of the process is identical in both cases and equal to 5 mm3.Loading is applied at the mid-plane of the ball. The tangential displacements are prescribed to be equal to zero, and a uniform normal displacement is enforced using Lagrange multipliers under the condition that the total normal force is equal to the prescribed force. The actual problem involves thus one half of the ball fully constrained at the mid-plane. Considering the symmetry with respect to a plane parallel to the sliding direction, only one quarter of the ball is analyzed. The finite element mesh of 16,384 hexahedral elements and 18,021 nodes is shown in . The total number of unknowns is 88,421 including the displacements, displacement-like quantities describing shape changes, and Lagrange multipliers enforcing contact conditions, shape evolution at the contact interface, and uniform normal displacement at the mid-plane. The total number of unknowns is reduced from 107,245 to 88,421 by constraining the shape transformation far from the actual contact zone, cf. Evolution of the shape of the ball in the small-deformation regime is shown in . As the elastic strains are small, the undeformed and deformed configurations are nearly identical. The contact pressure at three time instants is shown in . The initial pressure at t=0 is not included in because the finite element mesh is too coarse to reasonably reproduce the Hertzian pressure distribution (the element size in the contact area is 0.125 mm, while the Hertzian contact radius is a=0.15mm). It is seen that the pressure is uniform, and its value decreases with increasing contact area. This response is easily explained by observing that wear causes a rigid-body motion of the ball in the normal direction. The rigid-body motion is then associated with a uniform wear rate which, through the wear model, induces a uniform contact pressure, see The critical time increment of the explicit time integration scheme has been estimated to be approximately equal to Δtcr≈0.1s. Accordingly, the explicit scheme would require about 10,000 time steps to complete the solution. Using the implicit scheme, the solution has been obtained in 17 time steps (at the beginning of the process, the fixed time increment Δt=100s was too large to obtain convergence so that sub-stepping was needed). The gain in computational cost is thus significant (about two orders of magnitude) even considering that the computational cost of one time increment in the implicit scheme is higher than that of the explicit scheme due to increased number of global unknowns. presents the shape evolution in the finite-deformation regime. Finite changes of both the undeformed and the deformed configuration are clearly visible. The corresponding evolution of contact pressure is shown in . The pressure distribution is not symmetric with respect to the x=0 plane due to friction (μ=0.5). The effect of friction is also visible in The present wear evolution problem has been successfully solved in 10 equal time steps of the implicit time integration scheme (i.e., substepping was not needed). The accuracy of the solution is satisfactory despite the significant changes of the shape. This is illustrated in (a) in which the pressure profile is compared to the one obtained in 100 time increments. It is seen that the two solutions agree well (the maximum relative difference is below 3%). (b) presents a similar comparison for the explicit scheme. Here, the pressure increases with decreasing time increment, while an opposite effect is observed for the implicit scheme.The instability of the explicit scheme is not a major issue in the present example for Δt=100s. Nevertheless, the results obtained using the explicit scheme with Δt=100s exhibit moderate oscillations of contact pressure at the edge of the contact zone. This can be seen in (b). It has been checked that the explicit scheme becomes unstable when the elastic modulus E is increased from 10 to 20 MPa (while keeping Δt=100s). In view of the results presented in Section , this suggests that, for E=10MPa, the critical time increment Δtcr is close to 100 s.In this last example, periodic sliding contact of a rigid ball with a hyper-elastic half-space is considered. The coordinate system is attached to the ball so that the half-space is analyzed in an Eulerian frame. Specifically, as discussed in Section , the Eulerian description of the rigid-body motion in the undeformed configuration is adopted, while the deformation due to contact interaction is treated in the Lagrangian manner. The set-up corresponding to the finite-deformation regime (specified in detail below) is shown in . Due to symmetry, only one half of the block representing the half-space is analyzed.As the problem is assumed to be a quasi-steady-state wear problem, cf. Section , the wear groove is uniform along the sliding direction. Accordingly, the shape transformation mapping Ψ is also uniform along the sliding direction, and it is sufficient to prescribe it as a two-dimensional field at one cross-section only. The number of corresponding degrees of freedom in a finite element model is thus a small fraction of the total number of degrees of freedom, and the additional computational cost of solving the coupled deformation and shape evolution problem, as referred to the cost of the deformation problem alone, is small.The problem under consideration can be treated as a model of the pin-on-disc tribological test in which the curvature of the sliding path is neglected. Wear of the disc is due to repeated contact at each revolution of the disc. Hence, the wear rate governing the evolution of the wear groove must be averaged along the sliding path, and the corresponding parameter L, the sliding length per cycle, must be specified. In the case of the pin-on-disc test, L is the circumference of the circular sliding path. This parameter is independent from the actual dimensions of the computational domain that is restricted to the neighborhood of the contact zone in order to reduce the computational cost.The material and process parameters are the following. The elastic moduli are equal to those adopted in Section , i.e., E=100GPa and ν=0.3 in the small-deformation regime, and E=10MPa and ν=0.45 in the finite-deformation regime. The ball radius is R=5mm, the sliding velocity is v=1000mm/s, the friction coefficient is μ=0.5, and the duration of the simulated wear process is tmax=1000s. In the small-deformation regime, the normal force is F=100N, the sliding length per cycle is L=70mm, and the wear coefficient is K=4·10-7MPa-1. In the finite-deformation regime, the corresponding parameters are: F=50N, L=100mm, and K=2·10-7MPa-1.The deformation in the contact zone and the evolution of the wear groove in the finite-deformation regime are shown in , and the corresponding evolution of contact pressure is shown in . The finite element mesh consists of 43,200 hexahedral elements and 47,275 nodes, and the total number of unknowns is 142,508 of which only about 1500 are the displacement-like quantities corresponding to the shape transformation mapping Ψ. The wear evolution problem has been solved with a nominal time increment Δt=50s; however, substepping was needed at the initial stage due to convergence problems so that 32 time steps were needed to complete the solution.The solution obtained in the small-deformation regime is presented in . The contact zone is initially circular, which corresponds to the Hertzian contact, and it is elongated once the wear groove forms. The computational domain has been adjusted accordingly so that the evolution of contact conditions can be accurately followed. The length of the elastic block along the sliding direction is 1.4 mm and its half-width is 2 mm, cf. (a). The finite element mesh consists of 65,600 hexahedral elements and 71,463 nodes, and the total number of unknowns is 219,432 of which about 3400 are the displacement-like quantities corresponding to the shape transformation mapping Ψ. The initial Hertzian pressure is p0=2.1GPa and the contact radius is a=0.15mm, and both features are accurately represented by the present finite element solution (element size in the contact zone is 0.015 mm). The nominal time increment was Δt=50s. As in the previous examples, substepping was needed at the initial stage, and the solution was completed in 26 time steps.(a) presents evolution of contact pressure. A characteristic distribution of pressure is observed for t⩾100s which results from elastic contact interaction of the ball with a nearly cylindrical groove. The pressure profile is uniform along the direction perpendicular to the sliding direction, except at the outer edge where a small pressure spike is formed. This pressure distribution is shown in detail in (c). At the initial stage, the pressure evolves from the Hertzian distribution towards the characteristic distribution discussed above. An intermediate distribution corresponding to t=50s is shown in It has already been mentioned that the additional computational cost related to the application of the implicit time integration scheme is small in the present example. This is because the number of additional unknowns associated with the shape transformation mapping is small compared to the total number of unknowns (less than 2%). The benefit due to stability of the integration scheme is thus obvious. Specifically, it has been checked that the critical time increment of the explicit scheme is not greater than 0.5–1 s in the present example, thus at least 1000–2000 time steps would be needed to obtain a stable solution using the explicit scheme. The corresponding computational cost would thus be approximately two orders of magnitude higher than that of the implicit scheme.An incremental solution strategy employing the implicit backward-Euler time integration scheme has been developed for finite-deformation finite-wear problems. The advantage is that arbitrarily large time increments can be used for the incremental solution of the shape evolution problem, in contrast to the commonly used explicit scheme which is only conditionally stable. In fact, the critical time increment of the explicit scheme may be prohibitively small in practical problems, as illustrated by the numerical examples. Hence, the implicit scheme, though more involved, appears beneficial, particularly when the elastic strains are small, i.e., the elastic modulus is high in relation to the loading.Application of the implicit integration scheme implies that the time-dependent shape transformation mapping is an additional unknown so that the size of the problem is increased. It has been demonstrated that the associated increase of the computational cost of one time step can be fully compensated by a significant reduction of the number of time steps.In practical terms, at each time step, the problem is solved simultaneously for the nodal positions and displacements, hence the formulation is of the arbitrary Lagrangian–Eulerian type. In the present approach, the nodal positions are determined by solving an auxiliary elasticity problem. The number of the corresponding additional unknowns can be reduced by constraining the shape transformation mapping away from the contact zone. Furthermore, when the wear groove is uniform along the sliding direction, then the shape transformation mapping is prescribed at one cross-section only, and the number of additional unknowns is, in practice, negligible.The present finite-element implementation is restricted to quasi-steady-state rigid-deformable wear problems. The potential benefit of applying the implicit scheme has been clearly demonstrated for representative examples of this class of problems. Further work on extension of the formulation to multi-body contact and to a more general class of wear problems seems thus to be a promising research topic.Quantitative evaluation of hydrogen embrittlement susceptibility in various steels for energy use using an in-situ small punch testRecently, as hydrogen has been increasingly applied in the field of new energy, it has become necessary to evaluate the mechanical characteristics of hydrogen embrittlement (HE) when materials are used to reduce costs as well as ensure safety in hydrogen facilities. However, to obtain a large amount of data in a short period of time and ensure reliability when selecting materials used in hydrogen energy applications, a simple test method for screening the HE susceptibility of materials under high-pressure hydrogen environments should be established and applied. In this study, the HE behaviors of three structural steels to be used in the hydrogen energy field were examined at room temperature and low temperatures under high-pressure hydrogen environments using the newly established in-situ small punch test method. The effects of test temperature and punch velocity on the HE susceptibility of each steel were quantitatively evaluated using the characterizing factor, known as the relative reduction of thickness.When adopting a material to be used in energy devices, it is essential to perform a characterization test in the applicable environmental atmosphere so that the influence of that environment on the fundamental characteristics and properties of the material can be understood. However, as the test environment becomes extreme, equipment requirements, costs and man-power required to install, operate, and maintain that equipment increase, making it difficult to obtain a large amount of reliable test data in those conditions.Recently, to regulate CO2 emissions and lessen the amount of micro-sized particles emitted by automobiles and power plants, countries have focused on supplying fuel cells for electric vehicles and establishing hydrogen stations. Utilizing hydrogen energy as a source of new energy has led to research into the mechanical properties of metallic materials that can be applied in the production, transportation, and storage of hydrogen. Generally, metals with austenitic structures such as austenitic stainless steels have been widely used in hydrogen energy facilities because they can provide sufficient cryogenic toughness []. To mass-produce devices to be used for hydrogen energy, cost must be reduced; efforts have focused on replacing the austenitic stainless steels with low-alloy steels or carbon steels []. It also includes the development of an austenitic stainless steel with lower amounts of nickel and molybdenum compared to the existing AISI 316L steel for high pressure hydrogen use and greater resistance to embrittlement than AISI304 steel for a comparable alloy surcharge []. Additionally, a more practical means for selecting and evaluating materials for use in high-pressure hydrogen (H2) environments — tank liners, pipes, valves, pressure gauges and other devices— remains an unfulfilled need.Because H2 atoms are very small, they can penetrate and diffuse into the microstructures of metallic materials when under high-pressure, causing embrittlement that results in poorer mechanical properties, most notably a loss of ductility due to premature fracture []. As use for H2 expands, it is important to assure that materials used in H2 energy applications are safe, thus preventing accidents, such as gas leak and explosions, caused by hydrogen embrittlement (HE) damage. To this end, it is essential that reliable mechanical properties data are collected in a practical environment equivalent to that used in the H2 facility.To evaluate the mechanical properties, including HE, of structural materials under high-pressure H2 environments, a specimen is typically placed in a large autoclave with explosion-proof capabilities, and a slow strain-rate test (SSRT) or various material fracture tests, such as fracture toughness and fatigue crack-propagation tests, are carried out []. Constructing and operating a high-pressure testing facility presents difficulties in that high costs and a considerable amount of human resources are necessary, given the amount of time needed to create the test conditions. Thus far, austenitic stainless steels have been subjected to SSRTs, primarily in high-pressure H2 environments []. Because materials used with H2 differ in chemical composition and microstructure, and because test conditions (operating gas pressure and temperature) also vary, a simple test method that can accumulate large amounts of data that can be used for compatibility screening is required.With H2 use expanding, the test method used to screen for HE-resistant materials should be cost effective. An evaluation technique using a test method that is comparatively simpler than the conventional SSRT method in an autoclave must be developed. Simple test methods such as a tensile test performed in the atmosphere while filling a hollow-type test piece with high-pressure H2 [] or one using specimens that have been H2 pre-charged via electro-chemical hydrolysis or a H2 exposure chamber has been proposed []. A small-punch (SP) test used for evaluating aging structural materials in power plants has been used to evaluate HE behaviors using miniature specimens that have been electro-chemically H2 pre-charged []. Although SP tests performed in air on H2 pre-charged specimens cannot give accurate results, they can give results that are qualitatively similar to those found in a H2 environment using SSRT []. If the H2 pre-charged samples are ferritic or martensitic-structured steels, evaluating the effects of H2 on hydrogen-assisted fracture behaviors might not be appropriate, depending on the crystal structure or its diffusion coefficient and whether the test is carried out in the ambient environment [We have recently established an in-situ SP test method using small-sized specimens under high-pressure H2 environments []. It can be used to evaluate HE behaviors in an external H2 condition, where one side of the specimen is exposed directly to high-pressure H2. Additionally, the relative reduction of thickness (RRT), a ductility-based embrittlement characteristic suitable for use with in-situ SP tests, was proposed as an influencing factor []. This simple test method is known for its advantages: It requires a small amount of H2 (less than 50 cc), the test environment (temperature and pressure) is simple to set up, and obtaining the influence of punch velocity is easy []. In-situ SP tests were first used to determine the HE behaviors of austenitic stainless steels under various test temperatures, by comparing the RRTs with the relative reductions of area (RRAs), obtained using SSRTs. Quantitatively similar temperature-dependent results were obtained for STS304L and SUS316L steels at any given H2 pressure, ensuring that the obtained data were reliable []. Therefore, when applying the in-situ SP test method to various structural steels, it is necessary to accumulate enough data to assure the suitability of those candidate materials for use with H2.On the other hand, to obtain insights into material fractures due to HE, it is also important to develop a quantitative characterization that can establish a direct correlation between mechanical properties and failure mechanisms. Fractal geometry will provide a powerful tool to quantify the complexity of fracture surfaces based on self-similar mechanisms of fracture. However, the fracture caused by HE in high-strength steels is essentially failures naturally involving from the diffusion and enrichment of H2 atoms in the steel. Recently, Fu et al. attempted to quantitatively characterize HE fractures of high-manganese (Mn) TWIP/TRIP steels using multifractal and generalized fractal analyses []. A quantitative relationship between relative ductility reduction (Eloss) and fractal parameters in high-Mn steels helped establish the HE process, indicating that the greater the Eloss, the smoother the fracture surface.The HE characteristics of various structural steels have been evaluated primarily under internal H2 conditions using H2 pre-charged specimens; however, a few reports describe the effects of test temperature and strain rate on HE under high-pressure external H2 conditions. Because the HE susceptibility of steels under external H2 conditions is highly dependent on the H2 diffusion rate and the corresponding H2 concentration level, creating a H2 diffusion barrier layer on a material surface to reduce H2 absorption when exposed to external H2 conditions would be a promising method. When a steel shows some extent of HE susceptibility, HE resistance can be improved by modifying the exposed surface through a treatment such as electroplating or carburizing []. These surface modifications can reduce HE susceptibility in high-strength steels by reducing H2 absorption and increasing its austenitic stability.The in-situ SP test will also serve as a simple alternative for industrial purposes if standard tests cannot be performed in extreme or adverse environmental situations. Therefore, a quantitative evaluation of HE characteristics using in-situ SP tests on various kinds of steels becomes very important for determining their use in H2 applications. In particular, high-Mn steel, which is expected to be used in various fields due to its excellent properties at cryogenic temperatures [], SA372 steel used in thin-wall pressure vessels [], and 9% nickel (Ni) steel used for liquid natural gas storage tanks [], need to be examined for their HE susceptibilities under high-pressure H2 environments. These three types of structural steels have been primarily evaluated for deformation and fracture behaviors in low-temperature environments, but few reports describe their HE susceptibilities based on test temperature and strain rate under external H2 conditions.In this study, the HE behaviors of three structural steels were evaluated using the newly established in-situ SP tests over a broad temperature range (from room temperature (RT) to −120 °C) under high-pressure (10 MPa) nitrogen (N2) and H2 environments, applying various punch velocities. Using the obtained load-displacement curves and the fractographic morphologies observed after SP testing, the HE behaviors of the steels could be examined qualitatively. Variations in RRT and SP energy absorbed, based on the test temperature and punch velocity, could be quantitatively examined. After assessing the HE susceptibility of each steel, the applicability of each was scrutinized.Three types of steels; a 24.5 wt% Mn steel with an austenitic structure, an SA372 steel with a ferritic structure, and a 9% Ni steel which was quenched and tempered (QT) with the needle-like martensitic and retained austenitic microstructures, were supplied for testing. The high-Mn steel was designed to have an appropriate stacking fault energy at cryogenic temperatures and is expected to be used in a variety of fields, given its high strength, high ductility, and rolling toughness [ detail the chemical compositions and mechanical properties of these steels, respectively. Specimens measuring 10 mm × 10 mm and 0.5 mm in thickness were fabricated using wirecut electric discharged machining. shows a schematic as well as cross-sectional views of the in-situ SP test fixture used in both RT and low temperature tests. The high-pressure H2 charging method and the test procedure are described in detail elsewhere []. In short, the specimen was mounted between the lower and upper dies of the SP test fixture at RT, and the space within the lower die was vacuumed and purged three times with high-purity N2 to remove impurities, then H2 was charged into the space to a specified pressure.To conduct the in-situ SP test at low temperatures, once the SP test fixture was mounted to the material testing machine (Shimadzu AG-IS, 5 kN loadcell), a cooling device was installed, as shown in (b). During cooling, a capsule-type container made of Styrofoam was installed around the SP test fixture containing the specimen, but the pressure gauge, ball valve and one-touch connector remained in the ambient environment. To cool the specimen and the interior of the container to the specified test temperature, liquid N2 was pumped into the Cu-tube coil and allowed to vaporize in the insulated container. Two T-type thermocouples were used to measure the temperature. One was installed inside the capsule container; the other was inserted in the hole of the upper die to monitor the temperature of the specimen. By controlling the N2 pump pressure, it was possible to reach −120 °C in 30 min, and maintain that temperature within ±1 °C until the end of the test. When test temperature was reached, it was held for a predetermined time (about 10 min) before the SP test was begun. details the in-situ SP test conditions adopted in this study. In the case of a 10 MPa N2 environment, the punch velocity was 1.0 mm/min, but under the 10 MPa H2 environments, all three punch velocities (1.0, 0.1, and 0.01 mm/min) were used. At each test condition, the in-situ SP test was conducted once. At each specified punch velocity, a compressive load was applied to the specimen via the punch and steel ball. Both the applied load and the displacement of the specimen were measured. The punch displacement obtained from the testing machine was used to infer specimen displacement at the midpoint of its lower surface. After the in-situ SP test, a load-displacement curve was obtained for each test condition. The area under the curve until specimen fracture was calculated as energy absorbed, designated as SP energy. If final fracture did not occur abruptly, the fracture point was defined as the displacement attained when the load dropped 20% from its maximum. After in-situ SP testing, surface morphologies of those specimens fractured were observed using scanning electron microscopy (SEM) at both macroscopic and microscopic levels. shows the load-displacement curves obtained using in-situ SP tests at RT and low-temperatures under 10 MPa N2 and H2 environments. The in-situ SP tests under 10 MPa N2 environments yielded load-displacement curves that, overall, did not indicate HE influences; specimens showed typical ductile fracture behaviors, where the load resulted in elastic and plastic bending regions, and in the plastic membrane stretching region due to the biaxial stress state induced, final rupture occurred through thinning (also known as necking) []. In SP tests, the contact area between the punch ball and the specimen changes as the punch creates displacement; therefore, interpreting the load-displacement curves is not as straightforward as with uniaxial tensile tests.When the testing condition was a 10 MPa H2 environment, the effects of test temperature and punch velocity were noticeable across all steel samples. Though the load initially increased as it did under the 10 MPa N2 environment, it began to decrease due to HE in the latter part of the plastic bending region or where it transitioned to a plastic membrane stretching region, showing early fracture. As a result, both the maximum load and the fracture displacement were reduced due to HE. In these cases, the displacement attained when maximum load dropped 20% was adopted as the point of fracture., the surface morphologies of specimens exposed to N2 and H2 environments during SP testing as seen using SEM, shows that fracture patterns correspond well to the load-displacement curves obtained at each test condition (see ). Generally, under a 10 MPa N2 environment, where ductile fractures occurred, fracture morphologies appeared as large circumferential cracks formed after the punch ball created a deep plastic indentation, no matter the test temperature or steel type. On the other hand, under a 10 MPa H2 environment, where HE could have been induced, lower punch velocities (0.1 mm/min and 0.01 mm/min) generally resulted in small-sized circular cracks or brittle fractures at a later part in the plastic bending region.The HE behaviors were examined in each steel tested. The 24.5 wt% Mn steel under the 10 MPa N2 environment showed a consistent maximum load across the test temperature range; when the displacement reached 2.2–2.4 mm, the load dropped sharply without showing any necking behavior and resulted in final fracture ((a)). Under the 10 MPa H2 environment, however, fracture displacement decreased significantly at lower temperatures, presumably due to HE. Additionally, as lower punch velocities were applied, smaller circular cracks were generated in the plastic bending region. The HE behaviors were more pronounced at −40 °C and −60 °C, particularly at low punch velocities. However, as temperature was further decreased, maximum load and fracture displacement tended to gradually increase, mitigating the changes, most notably at 1.0 mm/min punch velocity. A large circumferential crack, similar to that seen under the 10 MPa N2 environment, was formed at the lowest temperature (−120 °C) under the 10 MPa H2 environment. We conclude that HE is most significant in the 24.5 wt% Mn steel when temperatures range from −40 °C to −60 °C.The load-displacement curves obtained for SA372 steel ((b)) showed that under the 10 MPa N2 environment, maximum load increased from 2.5 kN at RT to 3.3 kN at −120 °C while fracture displacement decreased from 2.2 mm to 1.8 mm, apparently due to low-temperature hardening. As shown in (b), fracture morphologies under 10 MPa N2 reveal circular cracks of nearly the same size across the tested temperature range, indicating ductile fractures. On the other hand, under 10.MPa H2, maximum load and fracture displacement were significantly reduced due to HE, and fracture occurred in the plastic membrane stretching region, though some variations across the test temperature and punch velocity ranges were seen. Small circular cracks occurred at RT, and they were smaller when punch velocity was lower. At −40 °C, maximum load and fracture displacement increased slightly due to low-temperature hardening, and at −60 °C, HE was most noticeable at 0.1 and 0.01 mm/min, showing that fracture occurred in the plastic membrane stretching region. Unlike the 24.5 wt% Mn steel, brittle fracture (earlier fracture) did not occur in this steel. Circular cracks formed in the plastic membrane stretching region propagated through the thickness of the specimen, and radial cracks formed as the punch continued to indent the specimen to the final fracture point (20% less than the maximum load). At lower punch velocities, smaller circular cracks were observed. In particular, at 0.01 mm/min and −60 °C, the smallest circular crack formed, indicating significant sensitivity to HE in this temperature range. When test temperature was further lowered to −100 °C or −120 °C, maximum load and fracture displacement increased. Fracture occurred in the latter part of the plastic membrane stretching region, indicating that HE behavior was mitigated. This is evident in the fracture morphologies in (c) shows the load-displacement curves for 9% Ni steels. Under the 10 MPa N2 environment, when the load reached its maximum, the final fracture occurred through further deformation due to necking. The behaviors resembled those of SA372 steel: the maximum load gradually increased from 2.7 kN to 3.4 kN as test temperature decreased. (c) shows circular cracks regardless of test temperature under the 10 MPa N2 environment, indicating ductile fracture. On the other hand, under the 10 MPa H2 environment at the same test temperatures, as punch velocity decreased, maximum load and fracture displacement significantly decreased. As test temperature decreased to −60 °C, small differences based on punch velocity emerged, but at −100 °C and −120 °C, maximum load and fracture displacement increased differently depending on punch velocity, showing that HE was relieved. At punch velocities of 1.0 and 0.1 mm/min and a test temperature of −100 °C, maximum load and fracture displacement increased and became similar to those seen under the 10 MPa.(c), in the 10 MPa H2 environment, lower punch velocities (0.1 and 0.01 mm/min) created crack patterns similar to those seen in SA372 steel, where small circular cracks and radial cracks were typically generated. At lower temperatures, a large circular crack formed, indicating that HE was mitigated.In 10 MPa N2 and H2 gas environments, circular cracks were formed and penetrated on the gas-exposed surface of each specimen. Furthermore, to clarify whether they resulted from HE, the fracture surfaces inside the gaps of the penetrating cracks were directly observed using SEM. Fractographic morphologies observed at RT and −40 °C, when HE was significant in each steel, are shown in . Under a 10 MPa N2 gas environment and at all test temperatures, the fracture surfaces showed dimples, formed by the coalescence of microvoids, indicating ductile fracture.Specimens tested under a 10 MPa H2 gas environment were observed inside the gaps of the cracks, as indicated by dashed boxes in . Most fracture surfaces in the 24.5 wt% Mn steel ((a)) showed intergranular cracking, indicating brittle fracture due to HE, but at −40 °C and 1.0 mm/min punch velocity, where circular cracks formed, quasi-cleavage fracture was shown, indicating transgranular fracture as well as intergranular cracking at the grain boundaries. Therefore, 24.5 wt% Mn steel has a low maximum load and small fracture displacement resulting from early fracture under a 10 MPa H2 gas environment, where cracking is primarily intergranular and induced by HE []. On the other hand, the fracture surfaces of SA372 and 9% Ni steels ((b) and (c)) showed similar quasi-cleavage fracture regardless of test temperature or punch velocity, indicating brittle fracture due to HE. In particular, at −40 °C and 0.01 mm/min punch velocity, the 9%Ni steel showed a brittle fracture pattern before formation of the circular cracks, as shown in (c); therefore, it underwent a quasi-cleavage fracture mixed with several facets. This is a characteristic HE fracture surface for SA372 and 9% Ni steels formed by a fracture mechanism that differs from that observed in 24.5 wt% Mn steel. Each fractography firmly supports the load-displacement curves shown in By investigating the HE behaviors of these three steels under 10 MPa H2 environments, we found that although changing test temperature and punch velocity resulted in somewhat different results, overall, the HE behaviors were qualitatively similar. Two types of steel, SA372 steel and 9% Ni steel, behaved in similar ways, but the 24.5 wt% Mn steel showed significant HE when lower punch velocities were applied. Therefore, considering practical H2 application environments, the HE susceptibility of each steel must be quantitatively evaluated and compared.The load-displacement curves and fracture morphologies obtained using in-situ SP tests under the 10 MPa H2 environment showed that damage and fracture behaviors due to HE were qualitatively similar across these three steels, but quantitative comparisons of HE susceptibility must also be carried out to assess HE resistance. Therefore, a ductility-based RRT was established to serve as a quantitative influencing factor in the in-situ SP test; it will enable the screening steels for HE resistance during H2 use [The SP energy absorbed until fracture (or gas leakage) corresponds to the area under the load-displacement curve obtained from the SP test, and this value has primarily been used as a quantitative comparison factor. shows the effect of test temperature on the SP energy absorbed by each tested steel. Under the 10 MPa N2 environment, the SP energy absorbed by 24.5 wt% Mn steel and SA372 steel were consistent at all test temperatures to −120 °C, but the 9% Ni steel showed increasing amounts of energy (from 4 J to 5 J) as test temperature decreased. In particular, the SA372 steel absorbed slightly less, but constant SP energy of ~3 J, indicating that although it has a ferrite structure, the ductile-brittle transition behavior was not observed in the tested temperature range. On the other hand, in the 10 MPa H2 environment, at RT, all steels absorbed about 1 J or less regardless of punch velocity, indicating that HE greatly reduced their abilities to absorb energy in the deformation and fracture processes. At lower temperatures, the effect of punch velocity became somewhat noticeable even though it remained around 1 J at temperatures as low as −60 °C. When the punch velocity was 0.01 mm/min, all three steels showed small amounts of SP energy to −80 °C, but as test temperature decreased further, higher punch velocities increased P energy, indicating that the HE effect was lessened.Comparatively, the SSRT has been used to evaluate HE susceptibility in steels meant for use under high-pressure H2 environments. After testing under high-pressure H2, the reduction in area at the fracture part of the specimens tested was measured and compared to that obtained under the same conditions and an inert gas (He, Ar, N2, etc.) to derive the RRA, providing a quantitative evaluation of the material's sensitivity to HE [We similarly focused on the ductility-based HE susceptibility evaluation, measuring the final specimen thickness (tf) at the fractured part after SP testing under high-pressure H2 or N2. The reduction of thickness (ROT) can be derived from the initial specimen thickness (to) using Eq. . The ROT found under the high-pressure H2 can be compared to that found from the high-pressure inert gas (N-2, etc.) to find the relative reduction of thickness, RRT, using Eq. . This quantitative measure of HE susceptibility is suitable for in-situ SP testing on steels. shows the ROTs obtained from recovered steel specimens after SP testing across our specified test temperature range. Under 10 MPa N2 and RT, the measured ROT for 24.5 wt% Mn steel was around 45%; for 9% Ni steel it was 60%, a value that was nearly constant throughout the tested temperature range, indicating that no loss of ductility occurred at low temperatures. However, the ROT for SA372 steel decreased from 50% at RT to 35% at −120 °C, indicating that some loss of ductility occurred due to low-temperature hardening. Under 10 MPa H2 and RT, all tested steels showed ROTs ranging from 20% to 25% regardless of punch velocity, indicating that ductility significantly decreased by more than half due to HE. As test temperature decreased, the effect of punch velocity became barely noticeable even though the ROT remained nearly constant to −60 °C, below which higher punch velocities resulted in increased ROTs, indicating a relaxed HE effect. All three steels tested in this study showed that, at a punch velocity of 0.01 mm/min, low ROTs were maintained between RT and −80 °C, indicating that the low strain rate influences ROT due to HE under high-pressure H2 when measured using the in-situ SP test. Similar results were observed when SSRT was applied to austenitic stainless steels [ shows variations in RRT for all three steels tested under the 10 MPa H2 environment across the test temperature range. The relative loss in ductility due to HE under this environment can be quantitatively evaluated by comparing these results to the same obtained under the 10 MPa N2 environment. At RT, both SA372 steel and 9% Ni steel showed RRTs of about 0.5 no matter the punch velocity used, and as test temperature decreased to −60 °C, RRT remained nearly constant, again no matter the punch velocity. Below that, RRT increased when punch velocity was 1.0 mm/min, reaching 0.80 to 0.90 at −100 °C.Because SA372 steel and 9% Ni steel have a ferrite and a martensite structure, respectively, they have high diffusion coefficients. Their microstructures are affected by HE from the beginning of plastic deformation during in-situ SP testing under a 10 MPa H2 environment. Hydrogen atoms easily penetrated into the specimen and accumulated at the stress-concentrated regions to form cracks no matter what the punch velocity is. As a result, HE was pronounced and similarly in both steels between RT and −60 °C regardless of punch velocity, resulting in low RRT and low SP energy. When the test temperature was lowered, it seems that at the punch velocity of 1 mm/min, the crack formation was delayed due to the interactions between the low-temperature hardening and other deformation mechanisms, resulting in relaxation of the HE susceptibility.On the other hand, the 24.5 wt% Mn steel was affected by punch velocity at RT, resulting in an RRT ranging between 0.3 and 0.5. It decreased further at −40 °C and 0.01 mm/min, producing its lowest value, indicating HE vulnerability. Thereafter, RRT increased with lower temperatures, becoming greater than 0.5 to 0.8 at −100 °C and around 1.0 at −120 °C, showing that RRT was the same, as was the case in the N2 environment. The high-Mn steel exhibited relatively low resistance to HE despite its high austenite stability and stacking fault energy and even no martensite transformation occurred during deformation. It seems that activation of the planar slip by the addition of Mn promotes local H2-induced deformation. In high-Mn steels, the planar slip is further activated because mechanical twins or microbands are formed. Therefore, these materials have been described as having low HE resistance due to local H2-induced deformation and severe dislocation accumulation at grain boundaries or twin boundaries []. Michler et al. evaluated the tensile properties of various austenite alloys including high-Mn steels under H2 gas, and analyzed the HE resistance based on their intrinsic deformation mechanisms []. They found that HE occurred despite the high austenite stability and no martensite transformation during deformation, indicating that HE and resistance to it cannot be evaluated based on austenite stability alone, and the influence of other factors along with external test conditions must be fully considered.These quantitative evaluations were helpful to understand the overall HE behaviors of three types of steels under high-pressure H2 environments. In every case, the characteristic factor RRT was around 0.5 at RT no matter the punch velocity. It remained at nearly the same value to −60 °C, defining the test temperature range that is affected by HE. However, the embrittlement tended to recover at even lower temperatures. In particular, the 24.5 wt% Mn steel showed mitigating behaviors and recovery from HE as RRT approached 1.0 at the lowest test temperature. Comparatively, between RT and −60 °C, 9% Ni and SA372 steels showed similar HE susceptibilities, but their performances at −120 °C could not match the excellent HE resistance exhibited by 24.5 wt% Mn steel.When three steels were tested using the in-situ SP test at a punch velocity of 0.01 mm/min, RRT showed significant HE susceptibility at temperatures ranging from RT to −80 °C. This might have occurred when the punch velocity (or strain-rate) was low, allowing the H2 to penetrate into the specimen and to diffuse, accumulating hydrogen in the plastic bending region or plastic membrane stretching region where the strain-induced transformation began to occur []. In this region, both a biaxial stress state and a stress gradient were imposed on the specimen surface exposed to H2 along with the outer circumference of the punch contact region. Consequently, at punch velocity of 0.01 mm/min, the complicated stress situation caused H2 to penetrate into the specimen and diffuse into the plastically deformed region, accelerating crack formation and resulting in failure due to HE. The stress state in the specimen during the SP test can be considered a more severe test condition than that used in uniaxial tensile tests such as SSRTs. In the future, efforts to understand the differences should be performed using numerical analyses.Given the three types of steels tested in this study, RRTs should be verified or adjusted by comparing them to the RRAs obtained using SSRTs, but such data is lacking in the literature. In one study, in-situ SP tests were conducted on two types of austenitic stainless steels (304L and 316L), and RRTs obtained at a punch velocity of 1.0 mm/min were similar to the RRAs obtained using the SSRTs in the same test temperature range we used []. Based on these observations, it might be possible to quantitatively predict the HE susceptibilities of our candidate steels under a high-pressure H2 environment using the RRTs obtained in this study at a punch velocity of 1.0 mm/min. Although some variations in RRT were found, it was generally greater than 0.5. In particular, the 24.5 wt% Mn steel and SA372 steel showed increasing RRTs as test temperature decreased.Finally, to apply this simple test method to the screening of low-cost steels for H2 applications, HE susceptibility evaluations under a practical H2 use environment should be performed, and comparisons between RRTs and RRAs should be considered.The three kinds of steels, each with a different microstructure, were examined for use in the H2 energy fields based on their HE behaviors at RT and low temperatures (to −120 °C) using in-situ SP tests in high-pressure H2 environments. Load-displacement curves as well as fracture morphologies obtained consistently and qualitatively expose the HE behaviors at various test temperatures and punch velocities. Under a 10 MPa H2 environment, most fracture surfaces in the 24.5 wt% Mn steel are intergranular cracks, indicating brittle fracture due to HE, but fracture surfaces in SA372 and 9%Ni steels are similar to each other: primarily quasi-cleavage fractures regardless of test temperature or punch velocity. The HE susceptibilities, found using quantitative data such as RRTs and SP energies, show that test temperature and punch velocity affects HE susceptibility differently in a 10 MPa H2 environment, presumably due to their individual microstructures. Results show that in temperatures ranging from RT to −60 °C, 9% Ni and SA372 steels have similar HE susceptibilities, demonstrating similarly low RRT values, no matter the punch velocity. However, the 24.5 wt% Mn steel has relatively low HE resistance despite its high austenite stability and stacking fault energy, yet it has excellent HE sensitivity at cryogenic temperatures below −100 °C. At a punch velocity of 1.0 mm/min, RRT is typically greater than 0.5 across these tested steels although some variations occur. The RRT is an influencing factor in the quantitative evaluation of HE susceptibility, and it is suitable for use with the in-situ SP test. To assure that reliable quantitative design data are collected on these three steels using the in-situ SP tests, RRTs obtained using this simple test method should be checked by comparing them with RRAs obtained using SSRTs.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.A study on reliability-based design systems of very large floating structures under extreme wave loadsThis paper deals with reliability-based design systems of very large floating structures based on the dynamic response and strength analysis considering the hydroelastic wave propagation of the structure under wave-induced loads. Firstly, a limit state and reliability-based sensitivity analysis is shortly presented. Next, a simplified estimation method is introduced for the dynamic response and strength of the structure in regular and irregular waves. Then, the validity of the method is demonstrated through experimental results for a mat-type floating structure model in regular waves. Finally, the features of the dynamic behaviors and reliability-based sensitivity factors are investigated by a numerical example applied to a 5000-m-class very large floating structure under trial design.Recently, many studies for the dynamic response of very large floating structures (VLFS) under wave-induced loads are reported at this and other conferences, such as OMAE, and ISOPE (see As a part of studies on reliability-based design systems, this paper is concerned with reliability-based sensitivity analysis of very large floating structures based on the dynamic response and strength analysis considering the hydroelastic wave propagation of the structure under wave-induced loads.Firstly, a limit state and reliability-based sensitivity analysis is shortly presented. Next, a simplified estimation method is presented for the dynamic response and strength of the structure in regular waves. The validity of the method is also demonstrated through comparison between experimental and analytical results for a flexible barge model in regular waves.Then, a simplified estimation method for the dynamic behavior under irregular sea-state conditions is presented by using the above analytical results and combining with irregular sea wave spectra.Finally, the applicability of the methods is investigated through numerical examples for a 5000 m-class floating structure under trial design for some irregular sea conditions. Characteristics of the short-term responses and reliability-based sensitivity factors are numerically shown.As limit-state failure modes of the mat-type floating structure, the ultimate collapse strength considering the buckling and ultimate strength of panels in the structure is treated as given in the following form:where φ is the ultimate collapse strength parameter, σy the yield stress, φ the load combination factor (to be assumed φ=1.0), σsthe still water bending stress, σw=Mw/Zs the wave bending stress and Zs the section modulus of the structure.As an example for the buckling and ultimate strength parameter φ, the following form is considered where bS is the panel breadth (stiffener space), t the thickness of panel, AS the cross-sectional area of stiffener, λp=(bS/t)(σy/E)1/2 the plate slenderness ratio and E the Young's modulus (see The statistical data of fabrication and service factors are usually insufficient, and it is important to collect as many of these data as possible and add to the database systems.The failure equations (safety margins, limit-state functions) are defined as from the failure condition and stress distribution., the failure probability for each failure mode is given as in the following. in Eq.(1), which is the reliability evaluation model (failure function) for buckling or compressive ultimate strength of deck or bottom panels, is generally nonlinear for random variables, reliability index β and/or failure probability are calculated by AFOSM (see Next, we consider a linearized function in the following form, when the function in is expressed in the nonlinear form of random variables Xi (the mean value and standard deviation are assumed to be μi and σj) ( into independent standard random vector . In this case, reliability index β is expressed in the following form:On the other hand, sensitivity factor for random variable ui on the reliability index β is given asFurthermore, sensitivity factor for design parameter θ on the reliability index β is given asWe consider the dynamic behavior of a mat-type floating structure which is idealized as a uniform beam (length L, breadth B, bending rigidity EI, linear density ρA) under regular waves as shown in The governing equation of the vertical deflection of the structure is assumed to be given in the following form (see where w is the vertical deflection of the structure, ρwg the specific gravity of water and Φ the velocity potential of flow field under the structure.Next, the deflection wave propagation w |
(x, |
t) is defined as the progressive wave formwhere ∣w∣ is the deflection amplitude of the structure.Based on the analogy of linear water wave theory, the following velocity potential Φv in the flow field under the structure is approximately given as Φ in where k, ω is the wave number and circular frequency of the deflection wave of the structure.Moreover, ∣w∣ is indeterminate constant in this time. For reference, the velocity potential Φ0 of the incident wave is given as follows: is the wave number and amplitude of the incident wave.Then, the dispersion relation of the deflection wave of the structure is obtained in the following form:This relation is different from that of the incident wave as shown in the following form:Then the above Δ can be expressed as follows: and S4 are the integral constants which are determined by boundary conditions considering bending moments and shearing forces at both ends of the structure.For example, these are determined by the following conditions:A dynamic response prediction method of mat-type floating structures under long-crested irregular wave loads is presented by using the above dynamic response results. Response spectra are expressed as follows and SMM(ω) are, respectively, the energy spectra for the incident wave ζ, the deflection w and the bending moment M. HWW(ω) and HMM(ω) are the response functions given byThe probability density of peak value Xp for data X can be assumed to be of the Rayleigh type,R(·)2 is the expected value of X2. The probability distribution function of peak value Xp for data X is obtained by integrating Then, the probability distribution function FMax(XMax) of the maximum peak value XMax in n peak values is obtained as follows:where TW is the expected wave period, and HS is the significant wave height under an irregular sea state. From these equations, we can predict short-term responses under some irregular sea states.Moreover, approximation values of mean and standard deviation are as follows:Finally, using the above-mentioned methods, numerical studies are carried out for a 5000 m-class mat-type floating structure whose rough arrangement and numerical data are shown in , and the characteristics of the dynamic responses and reliability are investigated under extreme wave loads., the frequency response amplitude of the bending stress due to deflection wave at x=100 m from the weather side end is shown. It should be noted that the bending stress amplitude is maximum at the Suzuki's characteristic circular frequency ωp (see , the bending stress amplitude distribution in the longitudinal direction from the weather side end is shown. At sufficient distances from the weather side end (characteristic length, see Moreover, in both figures, analytical results obtained using ΦV or Φ0 as the velocity potential Φ in are also shown. It is seen from these figures that the calculation results obtained using Φ0 is larger than those obtained using ΦV around the characteristic circular frequency ωp.As the simplified estimation results using ΦV are in good correspondence with the experimental results for the hydroelastic response of long barge structures as shown in , the hydroelastic response is estimated using ΦV.Next, the expected maximum peak value under some short-term irregular sea states is shown in . It is seen that expected values of the bending stresses increase according to the increase of the significant wave height HS.Then, an example of the relation between the reliability index β of the bottom panel for buckling and ultimate strength and the significant wave height is also shown in . It is seen that the reliability index β of the panel decreases according to the increase of the significant wave height HS.Finally, an example of the relation between the sensitivity factor α for various parameters and mean value of panel thickness t under the significant wave height HS=2.3 m is shown in . It is also seen that the most sensitive factor is that for stiffener space b and in the case of thick panel those for panel thickness t and yield stress αy become large.From these results for the 5000 m-class mat-type structure under some regular and irregular sea-state conditions, characteristics of the short-term responses, reliability levels and sensitivity factors can be quantitatively investigated.As a part of studies on reliability-based design systems, reliability-based sensitivity analysis of very large floating structures was investigated in this study, based on the dynamic response and strength analysis considering the hydroelastic wave propagation of the structure under wave-induced loads.Firstly, a method was presented for limit-state and reliability-based sensitivity analysis.Next, a simplified estimation method was presented for the dynamic response and strength of the structure in regular waves. The validity of the method was also demonstrated through comparison between experimental and analytical results for a flexible barge model in regular waves.Then, a simplified estimation method for the dynamic behavior under irregular sea-state conditions was presented by using the above analytical results and combining with irregular sea wave spectra.Finally, the applicability of the methods was investigated through numerical examples for a 5000 m-class floating structure under trial design for some irregular sea conditions. Characteristics of the short-term responses and reliability-based sensitivity factors were also numerically shown.In order to investigate the validity of the simplified estimation for the dynamic response of very large floating structures, experimental studies are carried out for a flexible structure model as shown in This model is composed of five aluminum alloy strips as the longitudinal member with a polystyrol foam plate as buoyancy members, as shown in . Numerical data for this model is shown in Bending stresses are measured by strain gauges attached at a surface of the central longitudinal strip. shows experimental results of the relation between response amplitudes of the bending moment and incident wave frequencies ω at the midship. shows experimental results of the frequency response amplitude distribution at . In both figures, analytical results obtained by using ΦV or Φ0, as the velocity potential Φ in From these figures it is seen that the simplified estimation results using ΦV are in good agreement for the dynamic response of long barge structures.Bisphosphonate treatment affects trabecular bone apparent modulus through micro-architecture rather than matrix propertiesBisphosphonates are emerging as an important treatment for osteoporosis. But whether the reduced fracture risk associated with bisphosphonate treatment is due to increased bone mass, improved trabecular architecture and/or increased secondary mineralization of the calcified matrix remains unclear. We examined the effects of bisphosphonates on both the trabecular architecture and matrix properties of canine trabecular bone. Thirty-six beagles were divided into a control group and two treatment groups, one receiving risedronate and the other alendronate at 5–6 times the clinical dose for osteoporosis treatment. After one year, the dogs were killed, and samples from the first lumbar vertebrae were examined using a combination of micro-computed tomography, finite element modeling, and mechanical testing. By combining these methods, we examined the treatment effects on the calcified matrix and trabecular architecture independently. Conventional histomorphometry and microdamage data were obtained from the second and third lumbar vertebrae of the same dogs [Bone 28 (2001) 524]. Bisphosphonate treatment resulted in an increased apparent Young's modulus, decreased bone turnover, increased calcified matrix density, and increased microdamage. We could not detect any change in the effective Young's modulus of the calcified matrix in the bisphosphonate treated groups. The observed increase in apparent Young's modulus was due to increased bone mass and altered trabecular architecture rather than changes in the calcified matrix modulus. We hypothesize that the expected increase in the Young's modulus of the calcified matrix due to the increased calcified matrix density was counteracted by the accumulation of microdamage.Bisphosphonates, specific inhibitors of bone resorption, are gaining importance in the treatment of osteoporosis Recently, it has become possible to quantify the effect of changes in architecture and bone mass on the apparent mechanical behavior of bone independent of the mechanical properties of the calcified matrix. Micro-computed tomography (microCT) scanning and automated finite element (FE) methods In this study we examined the effect of long-term treatment with high doses of two bisphosphonates, alendronate and risedronate, in a canine model. We investigated the changes induced by bisphosphonate treament to both bone architecture and matrix modulus as well as their contributions to the apparent Young's modulus. To interpret our findings, we examined the effect of bisphosphonates on remodelling, matrix mineralization, and microdamage accumulation. Specifically, we tested the hypothesis that high dose bisphosphonate treatment leads to increased secondary mineralization and consequently an increase in the matrix modulus.The experimental design used in this study has been reported previously and will be briefly summarized One cubic trabecular bone specimen with dimensions 5 × 5 × 5 mm was produced from the center of each first lumbar (L1) vertebral body, aligned with the anatomical axes in the cranial–caudal (CC), anteroposterior (AP), and medial–lateral (ML) planes. Low speed, water cooled diamond saws (EXAKT Apparatenbau, Norderstedt, Germany; Ernst Leitz Wetzlar GmbH, Wetzlar, Germany) were used for all sample preparation. Samples were stored in sealed plastic tubes at −20 °C, and care was taken to keep specimens moist during scanning and testing.A high-resolution microCT system (μ-CT 20, Scanco Medical AG., Zürich, Switzerland) was used to scan the specimens, resulting in reconstructions with 18 × 18 × 18 μm cubic voxels. The microCT images were segmented using thresholds chosen such that the volume of the dataset matched that determined physically using Archimedes' principle After scanning, each cubic specimen was tested in compression in an 858 Bionix MTS hydraulic material testing machine (MTS Systems Corporation, Minneapolis, MN). Specimens were tested non-destructively in compression to 6000 μstrain (apparent strain) at a strain rate of 2000 μstrain/s in the AP and ML directions to determine the apparent Young's modulus. The apparent Young's modulus of each sample was calculated as the tangent of the linear portion of the stress–strain curve at 5000 μstrain for the non-destructive tests (AP and ML directions). The specimens were then tested to failure in the CC direction with the same strain rate. The apparent Young's modulus in this direction was defined as the slope of the steepest portion of the stress–strain curve. Yield stress was defined as the intercept between the stress–strain curve and the line used to define the Young's modulus offset by 0.2% strain. Ultimate stress was defined as the peak stress encountered during testing. All testing was performed on polished platens lubricated with a low viscosity mineral oil to reduce the effect of friction The matrix modulus was calculated for all three directions using a combination of finite element modeling and mechanical testing. This combination was used because it enables the total apparent modulus to be partitioned into contributions due to the matrix modulus and trabecular architecture Bisphosphonate treatment has been previously observed to result in both increased mineralization and a loss of the normal mineralization gradient between superficial and interstitial bone Dynamic histomorphometry and microdamage data from the second and third lumbar vertebrae respectively were obtained from a previous study of the same animals. The following parameters were used in the current paper to aid interpretation of the results: activation frequency (Ac.F), bone formation rate/bone surface (BFR/BS), osteoid surface/bone surface (OS/BS), crack number (Cr.N), crack length (Cr.Le), crack density (Cr.Dn), and crack surface density (Cr.S.Dn) The statistical analyses included two-way analyses of variance for repeated measures for the experimental apparent modulus, apparent modulus predicted by the FE models, and matrix modulus. The group (normal, risedronate, or alendronate) was used as the between-subjects factor and testing direction (cranial–caudal, anterior–posterior, medial–lateral) as the within-subjects factor. Bone volume fraction, matrix density, histomorphometric parameters, and microdamage parameters were analyzed using standard analysis of variance. When significant main effects were found, specific comparisons were made with Dunnett two-sided t-tests. In all cases, the exact p-values are given; we considered p<0.05 to represent significant effects.A stepwise multiple regression analysis was used to assess the suitability of the FE models for the prediction of the apparent modulus measured in three directions in the laboratory. In this model the dependent variable was the measured apparent modulus and the independent variables were apparent modulus predicted by FE, testing direction, and the treatment group. Correlation analysis was used to examine the relations between the matrix density, matrix modulus, and both remodelling and microdamage parameters. Statistical analyses were performed using SPSS version 8.0 (SPSS Inc., Chicago, IL, USA).One dog was excluded due to distemper at the start of treatment, and one vertebra was destroyed during preparation. This left 11 control, 11 risedronate-treated, and 12 alendronate-treated dogs. Bisphosphonate treatment resulted in an increase in the bone volume fraction and calcified matrix density as determined using Archimedes' principle. The increase of approximately 2% in matrix density was significant for both treatments, but the change in BV/TV was only significant for the risedronate group where the increase was 18% (The experimentally measured apparent modulus was affected by bisphosphonate treatment (p=0.001). A significant effect of direction (p<0.001) and an interaction between direction and treatment (p=0.018) were found. On average, the risedronate treated group was 37% stiffer than the control group (p=0.001). No significant difference was found in the alendronate group (p=0.215; ). The apparent modulus predicted by the FE models (contribution of trabecular architecture and bone mass) was also affected by bisphosphonate treatment (p=0.001) with effects similar to the mechanical tests (). As in the mechanical testing, there was a significant effect of direction (p<0.001), but no interaction between direction and treatment (p=0.246). The predicted apparent modulus in the risedronate group was approximately 40% higher than the control group (p<0.001). No significant effect of alendronate treatment was found (p=0.283; ). The matrix modulus was not significantly affected by treatment (p=0.517), nor was there significant interaction between direction and treatment group (p=0.893). Direction significantly affected the matrix modulus, which was 20–30% larger in the CC than in the AP or ML directions (p<0.001; ). Bisphosphonate treatment resulted in an increase in both the ultimate stress and the yield stress. However, after correcting for architecture, this difference was not significant (In the multiple regression analysis, the FE models (i.e., effect of architecture and bone mass) accounted for 89.3% (p<0.0001) of the variance in the experimentally measured modulus. A small architecture independent effect of direction was found, which contributed to 0.5% of the variance (p=0.04). Treatment group and direction-group interaction were not significant. The residual variance was 10.2%.To estimate the statistical power of our results, we simulated the predicted effect of increased mineralization on the matrix modulus. We assumed an increase of 5% in the mineralization of the bisphosphonate treated group. For bone with a mineral fraction of approximately 40%, this agreed well with our observed matrix density measurements. Based on the simulations we predicted that the matrix modulus should increase by between 5% (conservative linear model) and 14% (cubic model) in the treated animals. From these simulations we could estimate that, for the sample size used, the power (β) to detect a difference in the group mean matrix modulus with a two-sided t-test (α=0.05) was between 0.12 (for the conservative linear model) and 0.65 (for the cubic model). Because of the limited power of our results, care must be taken when comparing the group means for matrix modulus.Because one sample from the control group was destroyed during preparation, we reworked our previous data . From these data a large significant decrease in bone remodelling activity is apparent in the bisphosphonate treated groups, as well as an increased microdamage burden in the treated animals as indicated by significant increases in Cr.N, Cr.Dn and Cr.S.Dn.Linear regression analysis revealed that the matrix density was significantly correlated to both the remodelling (ES/BS r=−0.555, p=0.001; OS/BS r=−0.594, p<0.001; BFR/BV r=0.487, p=0.004; Ac.F r=−0.353, p=0.044) and microdamage parameters (Cr.N r=0.456, p=0.007; Cr.Dn r=0.412, p=0.015; Cr.S.Dn r=0.511, p=0.002). The matrix modulus, however, was not significantly correlated to the matrix density, remodelling, or microdamage parameters.The major purpose of this study was to determine whether the increased levels of matrix mineralization seen after long-term bisphosphonate therapy affected the matrix mechanical properties. We used a high dose to simulate long-term effects in the bone. Bone remodelling was greatly reduced, resulting in both a 2% increase in the matrix density (indicative of increased mineralization) and increased microdamage accumulation. By using a combination of FE modelling, microCT scanning, and mechanical testing, we investigated the effects of treatment on the apparent Young's modulus, bone architecture, and calcified matrix properties. A significant increase of the apparent modulus was observed in the risedronate treated group. This increase was predicted by the FE models, indicating a strong effect of trabecular architecture and bone mass. The importance of architecture was further indicated by the results of the multiple regression analysis where 89.3% of the variance in the mechanical testing was accounted for by the FE models with no independent effect of treatment group (an effect of treatment group would indicate a group specific difference independent of the FE results, i.e., matrix modulus). Although the matrix density was increased, there were no significant differences in the group mean matrix moduli.A limitation of our study design is that we used intact, `normal' dogs. In an osteoporotic population bone turnover is likely increased, resulting in lower mean mineralization of the calcified matrix. Hypomineralization in an osteoporotic population could lead to a decrease of the matrix modulus compared to the `normal' population used in this study.Using microCT scans to create trabecular level FE models requires that the scan be of sufficient resolution and quality to resolve individual trabeculae accurately. Our use of 36 μm voxels and individual thresholds was sufficient to create accurate meshes We found that the matrix modulus was influenced by the testing direction (). This could be due to preferential loss of material due to thresholding in the presence of strong anisotropy at the trabecular level Clinically a large increase in BMD has been observed in the first year of antiresorptive therapy. Following this, BMD either slowly increases or reaches a plateau While it is logical that normalizing the mineralization of hypomineralized bone in osteoporotics to normal levels should be beneficial to the patient, the exclusion of the contribution of increased bone mass is not supported by our data. Although we predicted an increase of at least 5% for the matrix modulus based on our measurements of increased matrix density, we observed only small insignificant changes in the moduli of the calcified matrix in the bisphosphonate treated groups (5% decrease in risedronate treated group and a 1% increase in the alendronate treated group; Based on our data, we conclude that the increased apparent modulus seen in bisphosphonate therapy results from increased bone mass and altered trabecular architecture. This is supported by a concurrent study of the three-dimensional morphology of specimens from the same animals Open-grade wearing course of asphalt mixture containing ferrite for use as ferromagnetic pavementThis study examines the rheological and physical properties of an asphalt mixture containing ferrite for using in an open-grade wearing courses. The ferrite particles partially substituted the limestone filler in the mixture. Laboratory test results indicate that the ferrite addition produces mixtures with good mechanical characteristics for using in open-graded wearing courses. The addition of 0.5% of ferrite in total weight improve the mixture’s resistance to rutting, decreasing the permanent deformation. The mixture shows a slight lack of binder-aggregates adhesion under moisture conditions. The ferrite addition reduced the electrical resistivity nearly 100 times and conferred ferromagnetic performance to the mixture once subjected to an external magnetic field.Open-graded wearing courses (OGWCs) are increasingly used layers to provide pavements with the required surface characteristics. OGWCs are constructed from hot bituminous mixtures (HMAs) with relatively uniform aggregate grading and little mineral filler content. OGWCs are designed to have more void spaces in the compacted mixture—as compared to dense-graded asphalt concrete—and normally paved in thin lifts. The main benefits of their use are the construction or renewal of surface pavement with a good functional performance—good drainage, great resistance to plastic deformation, and low tire-pavement noise.The asphalt mastic, which consists of an intimate homogeneous mixture of aggregates, filler and bitumen, determines the main properties of the HMA.Bitumen is a thermoplastic material consisting of hydrocarbon chains of different length and molecular weight. In a first approach, this material can be considered as a coexistence of a solid phase—called asphaltenes—and a liquid phase—called maltenes—resulting in a composite material. Asphaltenes are high molecular weight substances and highly aromatic formed by assembling short polycyclic aromatic hydrocarbon groups. Maltenes—smaller than asphaltenes—can also be fractionated into asphaltenes, polar aromatics, naphthalene aromatics and saturates (paraffins) Mineral filler is usually added into asphalt mixture with particle sizes in the range of 0–100 μm. The properties of mineral fillers can greatly influence the asphalt mastics characteristics—providing several physical–chemical interactions between fillers and binders—and the performance of asphaltic mixtures Ferrites are a wide range of iron oxides with magnetic properties The addition of ferrite in a polymeric system—such as an asphalt mastic—is considered the quickest and most economical way of obtaining a magnetic polymer When adding micrometer ferrite particles in a system, a multidomain magnetic system appears divided in different magnetic domains On the other hand, ferrites can absorb microwave radiation by rapidly heating. It allows heat transfer from microwave power supply to a mixture containing ferrite particles Additionally, magnetic pavements can be obtained by the inclusion of conductive coils connected to an electrical circuit embedded within the pavement, both with direct or alternate current The inclusion of small amounts of filler addition into the HMA provides materials with novel applications, such as conductive mixtures This paper aims to study the effect of the partial replacement of small amount of mineral filler by ferrite powder in an OGWC, setting its physical–mechanical properties and performance towards ferromagnetic pavement developing.The asphalt mixture materials complied with both Spanish and European CE marking specifications The aggregates were porphyry and limestone. The coarse aggregate was crushed porphyry with nominal minimum size of 4 mm and maximum size of 11 mm. The fine aggregate was crushed limestone sand of 4 mm maximum particle size. The filler was limestone of less than 0.063 mm particle size. The aggregate characteristics were appropriate and complied to Spanish specifications for asphalt mixtures, as shown in The asphalt binder was a modified bitumen type BM3c – PG 72-26-, which can be used for many different traffic volumes and climates—. The binder properties are shown in Ferrite powder (Fe3O4, No CAS 1317-61-9) was used as partial filler substitute. The ferrite particle size was less than 0.2 μm. The particles were dark brown and rounded, as shown in . The ferrite specific gravity was 5.35 g/cm3, according laboratory test carried out (UNE-EN 1097-7: 2009).The research checked the ferrite addition effects in a conventional OGWC – BBTM 11 B-type – in order to obtain a mixture with electrical and magnetic properties.The design and characterization methods were established according to both Spanish and European CE marking specifications The aggregate particle-size fit was carried out according to the spindle specified in standards for each mixture (The optimal binder content was determined by the study of the conventional mixture with natural aggregates according to specifications. Specimen sets of the A mixture were produced for five binder content points — 3; 4; 5; 6 and 7%—according to the specification UNE-EN 12697–30:2006 + 1:2007. Each specimen set was composed of three cylindrical compacted specimens (Ø101.6 mm, 1200 g in weight) to assure the reproducibility of the results. The specimens were characterized in respect to bulk density (UNE-EN 12697–6:2012, Procedure A), air void content (UNE-EN 12697–8:2003), plastic deformation resistance (UNE-EN 12697–22:2008 + A1:2008), air particle loss (EN 12697–17::2006 + A1:2007) and moisture sensibility (UNE-EN 12697–12:2009) by indirect tensile resistance ratio (ITSr) (UNE-EN 12697–23:2004). The characteristic value for each binder point was the average of the three specimen values, as shown in . The optimal binder content was 5% with a filler/binder ratio of 1.38 for optimal conditions.Once the optimal binder content was developed, the ferrite content was adjusted. The approach adopted was to obtain a minimum ferrite content within the mixture – in partial substitution of natural filler by weight – that allowed the generation of a magnetic field not higher than 100 μT, when the sample was subjected to an external field of 50 mT for 1 min. The limit value of 100 μT is established by World Health Organization as a reference value for living beings safety.The variation of the magnetic field generated under different ferrite contents are shown in . The first point corresponds to a mixture without ferrite addition (conventional mixture). The residual value of magnetization in the conventional mixture is considered to be caused by steel particulate contamination during the industrial process of the aggregates (crushing, mixing and classification). The ferrite content was eventually established in 0.5% in total mixture weight to provide a magnetic field of 100 μT.According to the established conditions, two different mixtures were both tested and studied: mixture A was a conventional mixture with natural aggregates; and, mixture B0.5%Fe was a BBTM 11 B mixture wherein 0.5% in weight of mineral filler was replaced by ferrite powder.Noteworthy, that due to the partial replacement of filler by ferrite in weight and the higher density of ferrite, the final volume of total filler decreased and the particle size distribution in the B0.5%Fe became more continuous.Some mixture parameters were obtained to study the mixtures properties according to related specifications: binder content (BIN) of produced mixtures—determined by ignition—(UNE-EN 12697–39:2006); bulk density (BD) from compacted specimen (UNE-EN 12697–6:2012, Procedure A); and, air void content (VOID) as a percentage of total volume of a compacted specimen (UNE-EN 12697–8:2003). The air void content should be higher than the minimum value of 12% established in Spanish specifications.The test method for water sensitivity (UNE-EN 12697–12:2009) determines the effect of saturation and accelerated moisture-conditioning in the mixture tensile resistance. The Indirect Tensile Strength test (UNE-EN 12697–23:2004) consists of the rupture of cylindrical specimens by applying a diametric load along the cylinder axis direction, with a constant displacement rate until the breakage occurs. The indirect tensile strength was the maximum stress calculated based on the maximum applied load when the breakage occurs and the dimensions of the specimen. Six compacted cylindrical specimens (Ø101.6 mm, 1,120 g in weight) were produced (UNE-EN 12697–30:2006 + 1:2007). Dry specimens were acclimatized at 20 °C for 24 h. Moisture-conditioned specimens were acclimatized by immersion in water 4 days at 40 °C. Three dry and three moisture-conditioned specimens of each mixture were tested with a displacement rate of 50 mm/min at 15 °C. The indirect tensile strength ratio (ITSr) relates both conditioned and dry average tensile strengths. The moisture susceptibility study allows checking the aggregate-binder adherence with water presence.The European standard Wheel-tracking rutting test (UNE-EN 12697–22:2008 + A1:2008) evaluates the resistance to permanent deformation of a mixture. The B method in air was used. Two prismatic specimens (41 × 26 × 5 cm, over 7291–6911 g in weight) for each mixture were produced by roller compactor method (UNE-EN 12697–33:2006 + A1:2007). The specimens were exposed to the alternating passage of a wheel for over 10,000 cycles inside a climatic chamber at 60 °C. The permanent deformation was the average deformation velocity of the two specimens at the interval between 5000 and 10000 cycles. The average rut depth in the specimen surfaces was a permanent deformation indicator for each mixture.The dry particle loss of porous asphalt specimen test (EN 12697–17:2006 + A1:2007) measures the loss in weight of three dry cylindrical specimens exposed to tumbling without steel spheres in the Los Angeles abrasion machine at 25 °C. The value of particle loss express the difference in weight after tumbling in percentage. This test allows checking the abrasive and disruptive effect of traffic in the mixture.Additionally, the moisture-conditioned particle loss (NLT-362/92) measures the loss of cohesion by the action of water in the mixture. Three specimens of each mixture remained submerged in water for 4 days at 49 °C. This test is carried out in Los Angeles abrasion machine without steel spheres. A compacted specimen was tumbled inside the steel drum for 300 revolutions at a speed of 30–33 rpm. The percentage loss by before and after specimen weigh is calculated. An increase in losses compared to dry particle loss indicates a lack of resistance to the action of water.The electrical conductivity was measured in three compacted specimens (Ø101.6 mm, 500 g in weight) of B0.5%Fe mixture with a Hiresta High Resistivity Meter (MCP-HT 450) at 25 °C (a). This equipment is commonly used for obtaining resistivity measurements in non-conductive composite materials.Three B0.5%Fe mixture specimens were subjected to an external field of 50 mT for 1 min. Then, a PCE-MFM 3000 equipment, which is indicated for obtaining measures of intensity and polarity of static magnetic fields, provided the magnetization measures of the specimens.. Both mixtures comply with Spanish specifications to be used as OGWC.The asphalt mastic provides cohesion to the mastic-aggregate system. Besides, it determines the aggregate-binder adhesion against the water action—significantly influencing the mechanical characteristics of the mixture. Therefore, understanding how the new ferrite-added asphalt mastic is performing results decisive to characterize the mixture properties.The ferrite powder addition—despite having very different structural and mechanical characteristics comparing to limestone filler—provides an asphalt mastic well-behaved in respect to the coating of aggregates and does not alter the rheology of the binder. The ferrite particles have much higher density than the limestone filler particles, so the by-weight filler substitution reduces the total number of effective particles in the asphalt mastic in volume. Therefore, the addition of ferrite powder—by substitution of 0.5% mineral filler in weight—caused a reduction of the bulk density by 3% and increased the air void content by 5%, despite having a more continuous particle size distribution.Regarding the mechanical properties of the mixtures, it is noteworthy in the reviewed literature that the addition of ferrite in some composite materials has led to an increase of stiffness and hardness. Besides, this addition involved the transference of some ferrite properties to the entire composite.Likewise, the partial substitution of some limestone filler by ferrite powder in the studied mixture caused a decrease in plastic deformation and increased electrical and magnetic performance.According to the results of the wheel-tracking rutting test (), the addition of ferrite improves the permanent deformation of the mixture. The rut depth of the ferrite-added mixture was 24% less than the one in the conventional mixture. Besides, the slope of the rutting curve (WTS) was 56% lower for the B0.5%Fe mixture (0.036 mm/103 cycles) than for the A mixture (0.056 mm/103 cycles), as shown in . Thus, the ferrite addition causes a greater resistance to the permanent deformation in the mixture. This implies an important improvement in the performance of the OGWC, since it reduces rutting.The particle loss test permits the characterization of the capability of the binder to hold together aggregate particles in the mixture. When the asphalt mastic joints are ductile and tough, losses are low, but higher when weak or inconsistent. Part of the impact energy over the mixture is absorbed in the plastic deformation; the remaining energy causes both cracking and breaking. Generally, the filler particles increase stiffness of the mastic causing a lower elasticity that increases loss of particles. In the studied mixture, the results indicate that the incorporation of ferrite does not weaken the cohesion of the mixture in dry conditions; additionally, the loss of particles decreases by 23%. However, the ferrite addition worsens the cohesion of the mixture with moisture conditions, showing a higher loss of particles (27% higher than the conventional mixture). The adhesion was worst with the ferrite addition, since ferrites are inorganic oxides that causes lower adhesion with the binder and ease the penetration of the water molecules in the interface binder-ferrite.Therefore, the ferrite addition increases the moisture susceptibility in the mixture in respect to the particle loss, showing a worse cohesion against the water action.Water immersion does not affect appreciably to the ferrites particles. The physics interaction produced between bitumen and ferrite are able to protect these structures from the corrosion. Ferrites are spinel type inorganic oxides characterized by very high stability, so that the chemical interaction between bitumen and ferrite are produced at near the fusion point temperature. The values reached in this research are far below the fusion temperature.On the other hand, the results of the water sensitivity test () indicate that the ferrite-added mixture has nearly the same indirect tensile strength ratio (ITSr)—ratio of strength immersed in water versus dry—than the conventional mixture. The tensile strength reports about the cohesiveness of the asphalt mixture, reproducing the state of tension in the lower fiber layer of asphalt. Thus, strength losses could indicate a lack of cohesion. The maximum indirect tensile strength in the B0.5%Fe was 17% lower than in the A mixture, as shown in . The lack of cohesion may result from the difficulty of the binder to wrap filler particles distributed therein and covering aggregates.In the ferrite-added mixture, the small size of the ferrite particles—setting a greater specific surface of the total filler—causes a lower binder to wrap the particles, so less cohesion and tensile strength. However, this effect is not very pronounced because the substantially spherical shape of the ferrite particles leads to easy wrapping. Further, the ferrite-added mixture has an ITSr 3% higher. This could indicate that the mastic-aggregate interface is not weakened by the action of water. However, that was not shown in the loss of particles values under wet conditions. Thus, the mastic-aggregates adhesion could be a point of concern against water effect that should be deeply studied. Nevertheless, both mixtures meet Spanish specifications for OGWC.The electrical values obtained a decrease of the resistivity value in the order of 100 times, as shown in . While this is a substantial improvement of the electrical conductivity, it is insufficient to consider the asphalt as a conductive element.The electrical resistivity results of the quasi-contact between the ferrite particles, which are capable of transferring electrical charge through a highly insulating medium as bitumen. The percentage of ferrite in the mixture (0.5%) is not enough to form electrical pathways interconnecting the ferrite particles. However, the ferrite particles do affect the conductivity indirectly, distorting the conducting matrix. Probably the ferrite particle size of 0.2 μm does not favor this phenomenon. Thus, other particle sizes could be investigated in future studies to test their electrical behavior. As well, the addition of other additives capable of creating these bridges could be subject for further research.On the other hand, the remnant magnetic field—after being subjected to an external field of 50 mT for 1 min—was 100 μT in the ferrite-added mixture. 100 μT is a reference value according to World Health Organization (WHO) for safe living, as the permanent magnetic field exposure can have adverse health effects.Ferrite particles—randomly distributed within a three dimensional network of binder—and other particles of similar size provide a system with randomly orientations of the multidomains, resulting in a zero net dipole moment. However, once exposed to an external field of sufficient intensity all the domains are oriented in the same direction as the external field. The magnetic characteristics of the material added have a decisive influence on the magnetic parameters of the resulting material. Another parameter also worth considering is time exposure and the intensity of the external field.In this paper, a ferromagnetic OGWC has been designed and studied. Replacing 0.5% of limestone filler by ferrite powder in an OGWC—BBTM 11 B-type with BM3c bitumen-type—provide an asphalt mixture with structural and mechanical properties complying with Spanish and European requirements.The mastic formed by ferrite and limestone filler presents a good covering and wrapping of aggregates in the mixture without affecting the basic rheological properties of the mixture. The replacement of 0.5% in weight of limestone filler by ferrite results in lower volume of filler, since the ferrite particles nearby doubled the specific weight of the limestone filler. The mixture with ferrite addition has a greater number of voids and a lower density, despite having a more continuous granulometry than the conventional mixture.The 0.5% ferrite-addition improves the permanent deformation resistance of the mixture, constituting a tool for improving the rutting performance of the wearing courses.Despite of the low moisture susceptibility obtained by the indirect tensile analysis, the ferrite-with mixture demonstrated higher particle losses in moisture conditioned samples. The performance of the mixture versus water conditions is a point of interest for future research as well as the potential effects of oxidation in ferrite particles.The incorporation of ferrite provides a material having nearly 100 times less electrical resistivity. It constitutes a future research line obtaining conductive asphalt, either by adding or combining higher percentages of ferrite or other fillers.Furthermore, the addition of ferrite powder causes a ferromagnetic performance within the mixture. The resulting material allows the orientation of all the dipole moments in the same direction of an external field when applied. The magnetization of the mixture reaches 100 μT when subjected to an external field of 50 mT for 1 min. This behavior enables its reversible magnetization with a particular orientation as a function of the intensity and direction of the applied external field. This property can allow multiples applications—such as the wireless sensing pavement, the vehicle-pavement interaction or the inductive energy transfer—that constitute the subject of future research. Likewise, the possibility of incorporating other types of magnets with different characteristics opens a new line of research with the mentioned additives.Fabrication of aligned carbon nanotube-filled rubber compositeRubber composite sheets filled with 5 wt.% and 30 wt.% of highly aligned carbon nanotubes (CNTs) were fabricated through conventional rubber technology. The alignment of CNTs was possibly derived from dragged shear force during the optimized milling process. The selective alignment of CNTs led to enhancements in the elastic modulus, thermal conductivity, electrical conductivity, and electromagnetic shielding property, compared to neat rubber sheet.A great deal of attention has been paid to tiny but fascinating carbon nanotubes (CNTs), which consist of rolled-up graphene sheet built from sp2 carbon units At present, a large quantity of carbon nanotubes is available due to the recent progress in developing synthetic methods High purity and crystalline multi-walled carbon nanotubes with diameters of ≈100–200 nm, obtained by combining the synthesis of a catalytic chemical vapor deposition method Using a conventional laboratory Banbury mixer (1800 cm2), different amounts of carbon nanotubes (5 wt.% and 30 wt.%) were mixed homogeneously in the rubber matrix by controlling the mixing conditions (e.g., mixing time, mixing volume). Subsequently, by controlling the milling conditions (e.g., nip gap, mixing time) of a conventional laboratory mill (200 mm × 330 mm), the dispersion of the CNTs in rubber matrix was accomplished by shear force. Then, we obtained CNT-aligned rubber sheet along the X-direction by applying a calendaring and shaping process. In the case of CNT-aligned rubber sheet along the Z-direction, three steps were carried out consecutively: first, extruding nanotube and rubber compounds into a cylindrical shape; then opening die of extruder for alignment of carbon nanotubes along the radial direction; and finally opening it up. Finally, the experimental specimens were cured at 150 °C for 30 min.The fractured surface was prepared by slicing the alignment direction of composite rubbers vertically with a microtome (Leica). Field-emission scanning electron microscope (FE-SEM) (5 kV, a JEOL JSM-6335Fs) observations were carried out in order to confirm the dispersion and alignment of carbon nanotubes in rubber. The degree of orientation for CNTs was determined by the wide angle X-ray diffraction (WAXD) method using CuKα radiation (Rigaku, RU-200B). The orientation coefficient (f) of CNT crystallites was calculated by using the (0 0 2) reflection at 2θ |
= ≈27° for CNTs by using equations described in Ref. Carbon nanotubes used in this study exhibit relatively linear and long tubular morphology (high aspect ratio), as shown in (a) and (b). These nanotubes contain high crystallinity and relatively high real density, higher than that of conventional graphite. In addition, metallic impurity was detected at less than 100 ppm (measured by atomic absorption spectroscopy). The ideal status of nanotube alignments in the composites along the (a) X- and (b) Z-directions are illustrated in (c) and (d), respectively. In order to check the dispersion of carbon nanotubes in rubber, the fractured surfaces obtained by slicing the alignment direction of the rubber composite containing 30 wt.% carbon nanotube vertically with a microtome were observed using the FE-SEM apparatus. As shown in (e) and (f), relatively long and straight nanotubes protruded from the fractured surface. It is noteworthy that no aggregate of carbon nanotubes was observed. Therefore, it is possible to say that high-purity carbon nanotubes were homogeneously dispersed in rubber during conventional rubber processing (mixing and milling processes).To evaluate the effect of nanotubes on the physical properties of rubber, the mechanical properties, thermal and electrical conductivities were measured and compared with neat rubber sheet and also with those of rubber containing boron nitride, a conventional filler used in the rubber industry (see ). The tensile strength at breaking of nanotube-added rubber is twice as high as those of neat rubber sheet and boron-added rubber, and, in addition, no large change in elongation at break. Simple explanations for this mechanical property are (1) the nanosized effect of fibrous carbon (≈100 nm), indicating highly increased interface area between filler and rubber when compared to boron nitride and (2) beneficial alignment of fibrous carbons (high aspect ratio) (the degree of alignment of carbon nanotubes in rubber will be described in detail using WAXD). Furthermore, thermal conductivity of nanotube-added rubber was increased by at least a factor of 1.5 in both directions, while volume resistivity of nanotube-added rubber was drastically lowered by six orders. It is assumed that conductive networks in rubber were formed, resulting in the highly decreased resistivity of the rubber sheet. In this sense, this rubber composite is highly suited to antistatic, electromagnetic shielding, pressure sensor and actuator applications ). For all samples, the initial modulus (below 10% strain) is abruptly increased as the amount of nanotubes increases. In the case of 5 wt.% added rubber composites, where nanotubes are aligned along the X-direction, the elastic modulus for the sample when force is applied to the alignment direction of carbon nanotubes is increased by approximately two times as compared with the elastic modulus for the sample with vertically applied tensile force. But, with a higher amount of nanotubes, the rubber composites show highly increased initial modulus (stiffness), but reduced tensile strength by ≈0.5 and high elongation at break by ≈0.4, possibly due to increased cross-linking intensities.It is well known that WAXD is a powerful tool for characterizing the degree of crystallinity of CNTs aligned in a polymer matrix shows the X-ray diffraction photographs taken from different X-ray incident directions for the rubber composite filled with 30 wt.% CNTs aligned along the X-direction. This figure includes the azimuthal X-ray intensity profiles. The thinner white arrow indicates the Debye–Scherrer ring of the (0 0 2) plane of the CNTs. Although the Debye–Scherrer ring is of a circular form, the whiteness of the ring is more concentrated in the equatorial direction for (a) and (b), indicating that the CNTs were aligned in the X-direction as we expected. The degree of orientation of CNTs crystallites in the composite is 0.60, determined from azimuthal profiles of (a) and (b). In the case of the composite filled with 5 wt.% CNTs, the selective orientation of CNTs also occurred in the directions we expected, but the degrees of orientation were considerably lower than that of 30 wt.% CNTs filled composite. The values were ≈0.54 for X-sheet, and 0.44 for Z-sheet, respectively, which means that the degree of orientation for the composite containing 5 wt.% CNTs was much lower that that containing 30 wt.% CNTs. The difference between the 5 wt.% and 30 wt.% CNTs filled composites may be attributed to the melt viscosity during the rubber milling processing. Since the melt viscosity with higher CNT content is higher, the higher shear force may be generated during milling, which brings about the higher orientation of CNTs. In addition, when filled with 30 wt.% CNTs, the higher viscosity may prevent the relaxation of aligned CNTs to random orientation, and retain the orientation of CNTs during solidification of the rubber component. shows the shielding characteristics of the nanotube-filled rubber sheet as compared with those of graphite particle- and ferrite-filled rubber sheets, as a function of frequency. The shielding effect of the nanotube-filled rubber is prominent, especially in the high-frequency bands of several hundred MHz or more. It is expected that the excellent shielding characteristics are mainly due to the formation of a conducting network in an insulating rubber matrix through the incorporation of the highly conductive carbon nanotubes. The required level of the shielding can be varied according to the environment. However, since the nanotube-filled rubber sheet exhibited excellent shielding effects above 60 dB at frequencies up to 1 GHz, we envisage that the nanotube-filled rubber sheet will be utilized in a wide range of electrical equipment.We evaluated the mechanical, thermal, electrical and electromagnetic shielding properties of multi-walled carbon nanotubes incorporated EPDM rubber composite sheet. By varying the amount and alignment of nanotubes in a controllable direction, we can control the mechanical/electrical/thermal/shielding properties of nanotube/rubber sheet in detail, something that is urgently required from the viewpoint of applications. Alignment of carbon nanotubes in rubber matrix resulted in significant improvements in elastic modulus, thermal and electrical conductivities, especially along the Z-direction. As the amount of nanotubes added increased, rubber composites were transformed into a rigid material, which is reflected in a marked increase of the modulus. Based on WAXD study, it has been determined that conventional rubber technology is quite useful in aligning carbon nanotubes in rubber in a controllable fashion. Furthermore, increased shear force (melt viscosity) caused by the higher amount addition of nanotube (30 wt.%) during the milling process gave rise to an improved alignment of CNTs in the rubber matrix. Therefore, it is envisaged that judicious selection of the amount and the alignment of carbon nanotubes in rubber, will make this material applicable in various fields.Microstructure, mechanical properties and strengthening mechanism of titanium particle reinforced aluminum matrix composites produced by submerged friction stir processingIn spite of the improved strength, aluminum matrix composites (AMCs) reinforced with ceramic particle generally suffer a great loss in ductility. A solution to this problem is to use rigid metallic particles as a substitute for ceramic particles. In the present study, multi-pass submerged friction stir processing (SFSP) was employed to efficiently scatter titanium (Ti) particles into 5083Al matrix to form bulk AMCs. The multi-pass processing accompanied by water cooling could ensure no only the rapid acquisition of well-distributed particle dispersion, but also the absence of Al/Ti interface reaction products as well as the formation of ultrafine grains. A continuous type of dynamic recrystallization process was responsible for grain refining. The additional water cooling had a strong suppression effect on the growth of recrystal grains, and meanwhile the addition of Ti particles could boost the recrystallization due to the generation of extra dislocations at Ti/Al interfaces. As a result, ultrafine grains with the average size of about 1 µm were created in the resultant AMCs. The SFSPed AMCs exhibited an improvement of about 78 MPa in the YS and 153 MPa in the UTS respectively as compared with as-received Al and simultaneously kept a considerable amount of ductility (23.2%). The fracture surfaces of the SFSPed AMCs indicated well-developed small and uniform dimples corroborating appreciable ductility. Strength contribution from various strengthening mechanisms for the YS improvement of SFSPed AMCs was analyzed in detail. Quantitative analysis indicated that grain boundary strengthening contributed most to the YS of SFSPed AMCs.Particulate reinforced aluminum matrix composites (AMCs), owing to the combination of respective characteristics of aluminum matrix (e.g. high specific strength, good formability, excellent thermal conductivity and electric conductivity, etc.) and reinforcement particle (e.g. high hardness, excellent resistance and superior properties at elevated temperature, etc.), have been widely applied to automobile, aerospace and other fields as structural materials Friction stir processing (FSP) first put forward by Mishra et al. Recently, some studies have reported the use of FSP to prepare metal particle (e.g. Ni, Ti, W, Mo and stainless steel, etc.) reinforced AMCs It is well known that exerting forced cooling while FSW is a common strategy to weaken the annealing effect of the thermal cycle on the joint This paper reported the preparation of titanium (Ti) particle reinforced AMCs by submerged friction stir processing (SFSP) with three main aims: (i) to verify feasibility of multi-pass SFSP to prepare metallic particle reinforced AMCs, with uniform particle distribution and no formation of discernible interfacial reaction products; (ii) to understand the effect of Ti particles on the microstructure evolution of SFSPed Al; and (iii) to identify the strength contribution from various strengthening mechanisms to the strength improvement of the resultant AMCs.Commercially 5083Al-H112 plates, with the composition of Al-4.5 Mg-0.5Mn-0.4Fe-0.1Cu-0.15Cr-0.4Si-0.15Zn-0.25Ti (wt%), were used as the matrix material in this work. This alloy is a strain hardenable aluminum alloy with high resistance and excellent formability. Spherical Ti powders with the mean size of 23 µm were used as reinforcements (In order to place the Ti particles in advance along the predetermined processing path, a row of holes, with 1.5 mm in diameter, 4 mm in depth and 0.5–1.0 mm in wall thickness between adjacent holes, was drilled through a drilling machine on the surface of the rectangular Al sheet of 60 mm width, 120 mm length and 5 mm thickness respectively. The Al plates with a row of holes was clamped on the worktable. Ti particles were compacted into the holes and then the upper openings of these holes were closed with a pinless FSP tool to avert penetration of water into the holes. Subsequently, a simplified water tank was fixed to the surface of the workpiece. The FSP tool used in the present study was made of WC-13 wt% Co matrix material, with a shoulder 18 mm in diameter and a unthreaded cylindrical pin of 5 mm in diameter and 4 mm in length. When the flowing water was injected and stabilized, multi-pass SFSP with a 100% overlap was carried out along the same path at a rotational rate of 1400 rpm and a traveling speed of 40 mm/min and the rotating direction was changed between the consecutive passes. For each pass SFSP, the tilt angle of the tool and the plunged depth of shoulder were kept constant and were 2° and 0.2 mm respectively. After optimizing the number of FSP passes, it was found that a 3-pass SFSP can uniform disperse Ti particle across the whole stir zone and avoid possible interfacial reactions. The sample is designated (and followed hereafter) as SFSPed AMCs. In order to clarify the effect of Ti particle on the microstructure evolution of SFSPed Al, SFSP with the same parameters was carried out on Al matrix plate, with no Ti particle addition for comparision. The sample is designated (and followed hereafter) as SFSPed Al. The schematic diagram of preparing the AMCs reinforced with Ti particles by SFSP is shown in After SFSP, the metallographic samples were prepared randomly from both SFSPed zones perpendicular to the processing path, followed by mechanical grinding and then finely polishing. The phase composition in SFSPed AMCs was identified by X-ray diffraction (XRD). The particle distribution, the Ti/Al interface characteristics and the chemical distribution across Ti/Al interfaces were determined by scanning electron microscope (SEM) coupled with an energy dispersion analysis (EDS). The grain structures in both SFSPed samples were revealed in detail by electron backscattered diffraction (EBSD), which were further identified by transmission electron microscope (TEM). For EBSD analysis, the metallographic samples were subjected to electrolytic polishing with a solution of 10 ml perchloric acid and 90 ml ethanol solution at 6 V for 15 s. For TEM observation, the thin foil specimen with a thickness of about 100 nm were prepared by ion thinning.The tensile test was executed on the tensile samples (2.5 mm in thickness, 4 mm in width, and 26 mm in gage length), prepared along SFSP path according to ASTM E8M standard by electrical discharge machining, at an initial strain rate of 1 × 10−3 s−1. For comparison, the tensile test was also carried out on the tensile specimen from base metal. The property data for each sample were collected by averaging three test results. The fracture surfaces were observed by SEM.XRD pattern acquired form the SFSPed AMCs is presented in . Only the obvious diffraction peaks of Al and Ti were detected, and no other diffraction peaks corresponding to Al-Ti intermetallic compounds (IMCs) were observed. This indicates that no new phases formed after SFSP. It is well known that when introducing Ti into Al, Ti easily reacts with Al to form Al3Ti IMCs due to low ultimate solid solubility of Ti in Al, about 1.3 wt% at 660 ℃ depicts the cross sectional macrostructure of the SFSPed AMCs. The symmetrical bowl-shaped stir zone (SZ), with no defects, can be clearly distinguished based on the etching contrast. Clearly, Ti particles exhibited uniform dispersion in the SZ. It should be mentioned that the SZ produced by single pass FSP is usually asymmetrical since the material flow on both sides of the SZ is distinctly different The typical microstructure and chemical distribution of SFSPed AMCs are shown in , Ti particles were homogeneously within the matrix, exhibiting no particle clustering, as shown in a. Based on the image analysis, the volume fraction of Ti particles was estimated to about 8%. Moreover, the original spherical particle did not exist and were replaced by some irregular particles with reduced size. This is due to the particle fragmentation as the result of strong mechanical stirring and intense plastic deformation. Based on quantitative analysis for SEM micrograph, the mean size of Ti particle, dp, in the SFSPed AMCs was determined to be about 5.72 µm. Furthermore, no Ti particles peeled off from the matrix after sample preparing process, thus meaning strong enough Al/Ti interfacial bonding. b–d give the EDS maps of Al, Ti and Mg elements for the entire region in a, also reflecting that the Ti particles were distributed uniformly in the Al matrix with some Ti particles broken into small pieces.The Al/Ti interface characteristics was detailedly observed by SEM at higher magnification, which was shown in a. High magnified SEM examinations revealed two interface features. One is that the Al/Ti interface was intact with no microdefects, which is mainly because the sufficient flow of plasticized Al can ensure the whole surface of the particles to be fully covered. The other is that the Al/Ti interface was free of any discernible reaction products, thus corroborating the XRD results. This also indicates that the forced water cooling exerted a real inhibiting effect on the interfacial reactions. The corresponding EDS element maps shown in b–d further confirmed that the Al/Ti interface was dominated by atomic diffusion. The Al/Ti interface was further observed by TEM and shown in e. Clearly, the sharp Al/Ti interface with no sign of the formation of a reaction layer was observed. This supports the XRD and SEM results and provides a clear evidence for the effective inhibition of water cooling on the interfacial reaction. The good Al/Ti interface, consisting of diffusion layer rather than brittle IMCs layer, is a prerequisite for giving play to the role of strengthening of Ti particles since the load carried by Ti particles must be transferred through the interface a–e show the EBSD inverse pole figures (IPFs) of as-received Al, SFSPed Al and SFSPed AMCs respectively. The grain size distribution of SFSPed Al and SFSPed AMCs was shown in d. The as-received Al consisted of coarse pancake-shaped grains, with average grain size around 27 µm. After 3-pass SFSP without Ti particle addition, primitive coarse grain disappeared, along with the appearance of fine equiaxed grains with the mean grain size of 1.3 µm, as shown in b. Such significant grain refinement can be chalked up to the dynamic recrystallization (DRX) as a result of hot plastic deformation c and d. The slight decrease in grain size is mainly due to the presence of Ti particles because the processing conditions remained the same, which will be explained later. shows the image quality (IQ) maps super-imposed with grain boundaries of SFSPed Al and SFSPed AMCs, along with the corresponding misorientation angle distribution. In the grain-boundary super-imposed IQ maps, the color green line represents high angle grain boundaries (HAGBs, misorientation angle exceeding 15°), black line represents low angle grain boundaries (LAGBs, misorientation angle between 5° and 15°), and red line is the subgrain boundaries (SBs, misorientation angle between 2° and 5°). From a and b, a large fraction of green HAGBs was observed in the microstructure of both SFSPed samples. The corresponding misorientation angle distribution in e and f showed that the HAGBs reached about 82% in the SFSPed AMCs, higher than that in the SFSPed Al reaching 74%. This signifies that more sufficient DRX occurred in the SFSPed AMCs. During FSP of Al alloys with high stacking fault energy, dislocation rearrangement into SBs (i.e., polygonalization) under FSP-induced continuous strain readily takes place to reduce the dislocation density. From e and f, a high fraction of SBs, formed as a result of dislocation rearrangement, can be clearly found. The magnified view of the maps, shown in b and c, illustrates the mixing of red SBs and black LAGBs, as marked by black arrows. Also, the mixing of black LAGBs and green HAGBs was revealed in b and c, as marked by the white arrows. The appearance of different types of grain boundaries at the same grain boundary in a mixed form indicates the occurrence of the gradual transformation of grain boundary during FSP, from SBs to LAGBs, then to HAGBs. The evolution characteristics of grain boundary is completely in conformity with CDRX, in which SBs are gradually transformed into HAGBs e and f. This is because the size of Ti particle in the SFSPed AMCs is much larger than the particle size (less than 0.5 µm) which allows the Zener pinning effect to play a role It is noted that the matrix grain size (~ 1 µm) produced by SFSP was significantly smaller than those produced by FSP in air. Bauri et al. The microstructure of SFSPed AMCs was further revealed by TEM, as shown in a, dislocation-free ultrafine equiaxed grains were observed. b shows a large quantity of dislocations, which were reserved due to the lack of DRX. The dislocation arrangement into subgrain boundaries can be clearly observed in c. The obvious diffraction contrast between many of the subgrain boundaries was revealed in d, supporting the occurrence of the gradual transformation of the grain boundary. The typical microstructural characteristics in the SFSPed AMCs revealed by TEM match well with EBSD results. Thus, it appears that the CDRX is the predominant DRX mechanisms. shows the representative tensile curves of as-received Al, SFSPed Al and SFSPed AMCs, along with a summary of the corresponding tensile properties. Clearly, compared to as-received Al with the yield strength (YS, 0.2% proof stress) of 168 MPa and the ultimate tensile strength (UTS) of 279 MPa, the SFSPed Al exhibited some improvement in the YS and UTS, reaching ~ 186 MPa and ~ 329 MPa, respectively. The as-received Al plates used in the present study were in work hardening condition, characterized by high dislocation density and residual stress. In the SFSPed Al, the dislocation density and residual stress decreased, and the grain refinement occurred as a result of DRX. The grain refinement causes strength improvement, while the reduction of dislocation density and residual stress leads to the strength reduction. Clearly, grain refinement is mainly responsible for the improvement of YS and UTS in SFSPed Al. Moreover, a more obvious increase in the YS and UTS was observed in the SFSPed AMCs than in the SFSPed Al. The SFSPed AMCs exhibited the improvement of 46% and 55% in the YS and UTS, respectively, compared to as-received Al, with the YS and UTS reaching ~ 246 MPa and ~ 432 MPa, respectively. Based on the microstructure analysis, the significant increase in strength can be attributed to the further grain refinement and strengthening effect arising from the presence of Ti particles, which will be discussed in detail in the For most engineering structural components, a combination of high strength and high ductility is desired. In fact, materials may have high strength or great ductility, but rarely have both simultaneously. Especially for the conventional ceramic reinforced AMCs, a great loss in the ductility could be generated inevitably when the strength is significantly improved. For example, in the study shows the fracture surfaces of the tensile samples. From a, a number of deep dimples with bimodal size distribution were observed in the as-received Al, suggesting a typical ductile failure. The fracture morphology of SFSPed Al (b) showed more dimples with significantly reduced size in comparision with as-received Al. This indicates the achievement of enhanced crack propagation resistance and toughness, arising from the significantly grain refinement after SFSP. It is well acknowledged that dimple size is closely related to grain size because grain boundaries can serve as crack nucleation sites, thereby dominating the dimple size a and c, it is found that similar to as-received Al, the SFSPed AMCs also showed the typical ductile fracture, with a bimodal distribution of small and large dimples. Despite similar fracture characteristics, the dimple size in SFSPed AMCs was significantly decreased compared to that in as-received Al due to larger magnification in c. The formation of large dimples in the fracture surface of SFSPed AMCs is mainly due to the existence of Ti particles since crack preferentially initiates near or at the Al/Ti interfaces under the effect of external load. Small dimples are related to the ductile failure of the matrix. In addition, several Ti particles were found in the dimples,as marked by white arrows in c, suggesting the excellent Al/Ti interface binding.In general, the strength of particulate reinforced metal matrix composites (PRMMCs) can be evaluated by two methods where σcy and σmy are YS of composite and matrix, respectively. σLT is the YS improvement caused by load transfer effect. The general expression for σLT is where fv is the volume fraction of reinforcement phase and S is aspect ratio of reinforcements. On the basis of the micromechanics, comprehensively considering the contribution of Orowan strengthening (σOR), grain boundary strengthening (σGB), and quench strengthening (σCTE), the YS of the matrix (σmy) can be expressed as where σu = 10 MPa is the strength of the pure Al. It should be pointed out that the BM used in the present study is 5083 Al-Mg alloys, in which Magnesium (Mg) is the main alloying element, playing a role of solid solution strengthening In the SFSPed AMCs, the average grain size of the Al matrix is about 1 µm, while the mean size of Ti particles is 5.72 µm. Given this, it can be considered that Ti particles mainly exists among Al matrix grains, and thus the direct interaction of Ti particles with moving dislocations is extremely unlikely to happen inside the grains. In this case, strength contribution by Ti particles due to Orowan mechanism is negligible. However, there were some spherical precipitated particles inside the grains after SFSP, as shown in . It has been reported that after FSP the needle-shaped precipitated particles in 5083Al, consisting of Al, Mn, Fe and Si, would be fragmented into small spherical particles and distributed uniformly within grains in which b = 0.286 nm is the Burger vector, G is the shear modulus of the Al matrix (~ 26.2 GPa) and L is the mean distance between precipitates. Based on TEM micrographs in , the L was estimated as 600 nm in the SFSPed AMCs. According to Eq. , the σOR is calculated to be about 21.6 MPa.It is well known that smaller grain size will provide more grain boundaries (GBs), capable of acting as strong obstacles to the dislocation motion due to the misorientation between neighboring grains and thereby improving strength. The increment in yield strength due to grain boundaries, σGB, can be described by Hall-Petch equation where d is the average grain size (~ 1 µm for the SFSPed AMCs),σO is the lattice frictional stress (~ 45 MPa for Al-Mg alloy), and ky is a material constant (~ 74 MPa μm0.5) The quench strengthening due to the dislocations generated by CTE mismatch, σCTE, can be calculated by the following expression where α is a proportional constant (~ 1.25), G is the shear modulus of the Al matrix (~ 26.2 GPa), b is the Burgers vector of Al-matrix (~ 0.286 nm), ΔT is the difference between the processing and ambient temperatures (~ 350 K), ΔC is the difference in the CTE between Al (23.6 × 10−6 K−1) and Ti (8.6 × 10−6 K−1), dp is the mean size of Ti particles (5.72 µm). If taking fv= 0.08 into Eq. The solute strengthening increment, σSS, due to concentration C of a solute atom, is often defined as where H and γ are constants, 1 and 13.8 MPa/wt% γBringing the corresponding calculated contribution of each strengthening mechanism to the YS of the matrix (σmy) into Eq. , the σmy is calculated to be 229.6 MPa. Because in the present study we use the diameter of the equivalent circle to evaluate the average size of Ti particles, the aspect ratio of Ti particles, S, is considered to be 1. If taking S = 1 and fv= 0.08 into Eq. , the σLT is calculated to be 9.2 MPa. The theoretical YS calculated based on each strengthening mechanism and the experimental values are summarized in . In general, a satisfactory agreement between the theoretical and experimental YS values was achieved. It was also noticeable that grain boundary strengthening contributes the most to the YS of the SFSPed AMCs. Meanwhile, the Ti particles also strengthen the SFSPed AMCs through load transfer mechanism and quench strengthening mechanism.In this study, the feasibility of multi-pass SFSP to prepare metallic particle reinforced AMCs with desired microstructure was verified. The effect of Ti particles on the microstructure evolution of SFSPed Al was clarified. The strengthening mechanisms of SFSPed AMCs was identified and quantified. The main conclusions can be summarized as follows:3-pass SFSP ensured Ti particles to be uniformly distributed in the SZ and the formation of defect-free Al/Ti interface, consisting of mutual diffusion of elements rather than harmful reaction products.During SFSP of 5083Al, the continuous dynamic recrystallization (CDRX) was mainly responsible for grain refining. Ti particles could boost the recrystallization due to the generation of extra dislocations at Ti/Al interfaces. The forced water cooling inhibited the growth of recrystallized grains, thus producing ultrafine grains with the average size of ~ 1 µm in the resultant AMCs.The SFSPed AMCs indicated significantly higher YS and UTS than the as-received Al while only suffering a slight loss in ductility. The fracture surface of SFSPed AMCs consisted of fine dimples indicates a typical ductile failure. The fractured and pulled out Ti particles appearing on the fracture surfaces corroborated the good Al/Ti interfacial bonding.Various strengthening mechanisms including load transferring, grain boundary strengthening and quench strengthening were responsible for the YS improvement of SFSPed AMCs. Quantitative analysis indicated that grain boundary strengthening contributed most to the YS strength of SFSPed AMCs.The effect of fiber surface treatments on the tensile and water sorption properties of polypropylene–luffa fiber compositesThe effects of coupling agents on the mechanical, morphological, and water sorption properties of luffa fiber (LF)/polypropylene(PP) composites were studied. In order to enhance the interfacial interactions between the PP matrix and the luffa fiber, three different types of coupling agents, (3-aminopropyl)-triethoxysilane (AS), 3-(trimethoxysilyl)-1-propanethiol (MS), and maleic anhydride grafted polypropylene (MAPP) were used. The PP composites containing 2–15 wt% of LF were prepared in a torque rheometer. The tensile properties of the untreated and treated composites were determined as a function of filler loading. Tensile strength and Young's modulus increased with employment of the coupling agents accompanied by a decrease in water absorption with treatment due to the better adhesion between the fiber and the matrix. The maximum improvement in the mechanical properties was obtained for the MS treated LF composites. The interfacial interactions improved the filler compatibility, mechanical properties, and water resistance of composites. The improvement in the interfacial interaction was also confirmed by the Pukanszky model. Good agreement was obtained between experimental data and the model prediction. Morphological studies demonstrated that better adhesion between the fiber and the matrix was achieved especially for the MS and AS treated LF composites. Atomic force microscope (AFM) studies also showed that the surface roughness of LFs decreased with the employment of silane-coupling agents.In recent years, significant effort has been done to investigate the use of natural fibers as reinforcement in thermoplastic composites. Natural fiber-reinforced composites have many advantages such as light weight, reasonable strength and stiffness, renewable, and biodegradable. The composites therefore provide economical and ecological properties Despite the advantages of cellulosic fibers in thermoplastics, the preparation of polymer–cellulose composite materials is handicapped by the highly hydrophilic character of these fibers, which is associated with a low compatibility of hydrophobic polymers like polypropylene, as well as with a loss of mechanical properties after moisture uptake This paper presents the preparation and characterization of luffa cylindrica (sponge gourd) fiber-reinforced polypropylene (PP) composites. In this study, luffa cylindrica, having interior tough fiber, was used as a natural fiber and PP was used as the thermoplastic polymeric matrix. Luffa cylindrica is a subtropical plant abundant in Asia, Central, and South America. The fruit of luffa fiber has a fibrous and vascular system that forms a natural mat when dried In this work, the effects of surface modification and luffa fiber concentration on the mechanical, morphological, and water uptake properties of polypropylene (PP) composites were investigated and reported. In order to improve the interaction between the matrix and the fibers, silane-coupling agents, namely, aminopropyltriethoxy silane and mercapto silane were employed in the pretreatment of luffa cylindrica fiber. Maleated PP was used for the improvement of surface of the PP matrix.Interfacial interaction between the polymer matrix and the filler is an important factor affecting the mechanical properties of the composites. Thus, theoretical yield strength and ultimate tensile strength of the composites are modeled to show the effect of interfacial interaction on the tensile strength of the composites.The effects of composition and the interfacial interaction on tensile yield stress or tensile strength of particulate filled polymers, which is described by the Pukanszky model, is indicated in Eq. . The parameter Bσy is an interaction parameter that is related to the macroscopic characteristics of the filler–matrix interface and interphase where Φf is the volume fraction of the filler, σyc and σym denote the tensile yield stress of composite and matrix, respectively. The first term in Eq. is related to the decrease in effective load bearing cross-section, while the second one is concerned with the interfacial interaction between filler and matrix. Interfacial interaction depends on the area of the interphase, and the strength of the interaction as shown in Eq. where Af is the specific surface area of the filler, ρf is its density, and t is the thickness of the interface. From the Bσ values, strength of interaction σyi can be calculated.Isotactic PP, (MH-418, PETKIM), in the pellet form with a density of 895 kg/m3, and luffa cylindrica fibers (fiber length 3–5 mm) were used for the preparation of composites. Fibers were modified using two different types of coupling agents to improve compatibility of filler with polymer. The silane-coupling agents are: 3-(trimethoxysilyl)-1-propanethiol (MS), and (3-aminopropyl)-triethoxysilane (AS). Maleic anhydride grafted polypropylene (MAPP) (AdmerQF-300E) was used for the improvement of polypropylene surface. The chemical structure and supplier of these agents were given in detail in Luffa cylindrica fibers were obtained from local specialty shop. The LFs were washed with water to remove the adhering dirt. They were dried in an oven at 70 °C for 6 h. After drying, they were cut with Waring Blendor for reducing the length of fiber to 2–3 mm. Fibers were pretreated with 0.1 M sodium hydroxide (NaOH) solution at boiling temperature for 20 min. Then, fibers were washed with distilled water until all sodium hydroxide was removed. After washing, they were dried in an oven at 70 °C for 6 h.Surface modification of LF with silane-coupling agents was carried out in solution. LF was added to the solution of silane-coupling agent (2.5 wt%) in 95 wt% ethanol and mixed for 15 min to let silane hydrolysis. Then, LFs were added to the mixture and mixed for 45 min for the condensation and chemical bonding of silanes and cellulose fibers. Treated LFs were washed with ethanol to remove the excess of coupling agents and dried in an oven at 70 °C for 12 h.Surface modification of PP was conducted by using maleated PP. Maleated PP (MAPP) was mixed (2 wt% of composite) with molten PP in rheomixer during compounding at mixing temperature of 190 °C, rotor speed of 60 rpm and mixing time of 10 min.PP composites containing 2–15 wt% pretreated and treated LF were prepared using torque rheometer (Thermo Haake Rheomix). The composites were prepared at mixing temperature of 190 °C, rotor speed of 60 rpm and mixing time of 10 min. During compounding, torque vs time data of the mix can be acquired through ‘Convert data’ software program to determine rheological response of the composites. First, PP was incorporated into the plastograph, and then previously dried fibers were introduced as soon as torque indicated melting of the polymer (about 2 min). Ten minutes of mixing was enough to reach to the stabilization torque, which indicated homogeneous mixing of filler and matrix. The composition of samples used in the experiments were tabulated in . The samples taken from the torque rheometer were compression moulded using a Carver polymer press to form rectangular sheet with dimensions of 150×150×3 mm3. The composites were pressed gradually at 190 °C in order to avoid void and bubble formation and then pressed at 100 bar pressure at the same temperature for 10 min. These samples were cooled to 40 °C in 6 min under the same pressure.Tensile tests of PP–LF composites were performed under ambient conditions on Testometric Universal Testing Machine with a 5 kN load cell, and at the cross-head speed of 50 mm/min. Tensile test specimens were prepared using a dog bone shaped hollow die punch according to ASTM D-638 procedure. The test results were taken by software program supplied from Testometric Co. At least five specimens were tested and the mean values were reported.Scanning electron microscopy (SEM) was used to examine the morphology of the PP–LF composites. Fracture surfaces of tensile tested specimens, containing 15 wt% untreated and treated LF with amino silane and mercapto silane and MAPP, were analyzed with a Philips XL-305 FEG-SEM to investigate the interface between the filler and the matrix and the dispersion of filler in the matrix.The surface topography of the untreated, sodium hydroxide and coupling agents treated LFs were investigated by using AFM Digital instrument MMSPM Nanoscope 4. The treated and untreated LFs were compressed prior to scanning and three points for each specimen was investigated on a 10×10 μm surface area.The FTIR–ATR analysis was performed by using a Digilab FTS 3000MX spectrometer with ATR attachment to analyze the interfacial reactions between fibers and silane-coupling agents. The FTIR spectra of modified luffa fibers was subtracted from the spectra of the untreated luffa fiber.The samples were cut into 10×10×0.1 cm3 sheets. First, the samples were dried at 70 °C for overnight to reach the constant weight. Then, the samples were immersed into static distilled water bath at 25 °C to observe the sorption of water. Mass uptake of the samples were measured periodically by removing them from the water bath. The water uptakes were plotted as a function of time. The samples were wiped with the tissue paper to remove the surface water before weighing. Water uptake of LFs reinforced PP composites at time t was calculated using the equation below:where; Mt is mass of sample at time t; M0 the mass of sample at t=0.Since torque is an indicator of viscosity, which reveals relative rheological behavior of composites, the effect of fiber loading or surface treatment on the rheological properties of the composites can be investigated using torque vs time data at stabilization conditions. The torque vs time data for the PP–LF composites were recorded at mixing temperature of 190 °C, rotor speed of 60 rpm and mixing time of 10 min. illustrates a typical torque vs time data of the treated fiber PP composites and compares with the neat PP matrix. As seen in , the initial torque increased rapidly by the incorporation of polymer, which is depicted as a peak at around 40 s. Torque decreased rapidly as soon as temperature of polypropylene increased and melting occurred. After complete melting at around 120 s, cellulose was fed to rheomixer, which was accompanied by an increase in the viscosity. This second peak was proportional to the fiber loading. After wetting of the fibers by the polymer, the good dispersion of filler in the polymer matrix was obtained. At this point, torque values decreased up to a stable value that is called stabilization torque. Composite reached the stabilization torque at around 400 s. A stable torque is also an indicator of homogenization of fiber in the melt Tensile tests were conducted to understand the effects of the fiber loading and coupling agent employment on the mechanical properties of LF–PP composites. Tensile strength, Young's modulus, and elongation at break of the PP–LF composites were measured at ambient conditions.The importance of the treatment with coupling agent can be assessed by comparing the results of the untreated and treated composites. illustrates the tensile strength of LF filled composites containing the untreated (ULF) and the treated LF's with two different silane-coupling agents, and MAPP treatment as a function of fiber loading. In general, the tensile strength of the treated and untreated composites decreased as the fiber content increased. The reduction in the tensile stress with an increase of filler content can be explained by the reduction in the effective matrix cross-section. However, it was clearly observed that the reduction in the tensile strength of PP composites has been decreased by the silane-coupling agents. The decrease is significantly greater in the untreated composites than the treated composites. The amino functional silane and mercapto silane treated fiber composites showed a reactive coupling effect that resulted in higher tensile strength compared to the untreated ones. The higher tensile strength was observed in only amino (AS) and mercapto (MS) treated LF–PP composites with 2 wt% fiber content. Above 2 wt% loading, true reinforcement cannot be attained despite the silane treatment.Tensile strength of the untreated LF–PP composites containing 15 wt% LF decreased from 33 to 19.5 MPa which corresponds to the 41% decrease. For the 15 wt% treated fiber composites, the decrease was about 21% for the MS and the AS treated fiber composites and 11% for the MAPP treated fiber composites. Tensile strengths of the composites containing 15 wt% LF treated with 2.5 wt% AS and MS increased by 33% compared to the untreated composites. For the MAPP treated composites, the enhancement is up to 11%. The increase in the tensile strength with the silane treatment can be explained by the better adhesion between the filler and the matrix. Without coupling agent, the only adhesion mechanism is interdiffusion. Silane-coupling agents yields to hydrogen and covalent bonding between hydroxyl groups of filler and polysiloxanes formed by hydrogenation of silanes providing better adhesion between the fiber and the matrix. Better adhesion improves stress transfer through fibers, therefore, increases the tensile strength of composites shows the comparison of experimental data of the tensile strength values of PP–LF fiber composites with the Pukanszky model. As seen in the figure, except at low volume fraction region, the model predicts the data well. Since the parameter B in the model represents the strength of interaction between the PP and the LF fiber, the higher B values indicates the better interaction. In literature, Pukanszky and Tudos . B values for the untreated LF fiber and treated LF fiber with AS, MS, and MAPP were found as −2.93, 0.43, 0.81, and −1.57, respectively. B values increased with the treatment of the fiber, and the MS treated composites have the highest B value indicates the strongest interaction between the polymer and the fiber compared to others. shows the Young's modulus of the composites as a function of filler content for the different treatment conditions. The Young's modulus of the composites increased as the fiber loading increased. Young's modulus of the composites containing 15 wt% fiber increased by 38, 52, 74, and 98% for the untreated, MAPP, AS, and MS treated composites, respectively. The highest increase was achieved for the MS treated composites, followed by the AS treated composites. The increase in the Young's modulus due to the silane treatment can be attributed to the better adhesion between the fiber and the matrix by chemical interactions. Better adhesion yields to more restriction to deformation capacity of the matrix in the elastic zone increasing Young's modulus.Variation of elongation at break values as a function of filler content for different coupling agent treatment was illustrated in , the elongation at break values for all composites decreased with the increase in LF loading. Incorporation of even low fraction (2 wt%) of fiber to the matrix caused a sharp decrease in the elongation at break values. Elongation at break of pure PP is around 338%, whereas elongation at break of 2 wt% fiber loaded composites is around 17%, almost independent of coupling agent employment. The decrease in the elongation at break was much more pronounced for AS and MS treated composites due to the adhesion between fiber and matrix restricts deformation capacity of matrix in the elastic zone as well as the plastic zone.The subtraction spectra of the AS and MS modified luffa fibers were shown in , respectively. The broad bands around 950 and 1150 cm−1 are attributed to asymmetric stretching of Si–O–Si linkage and Si–O–cellulose bonds for AS modified luffa fibers shown in . These bands prove that condensation of silanols and chemical bonding of silane groups to cellulose was achieved via silane treatment. The absorption bands at 936 and 1366 cm−1 also confirm the presence of the Si–O–cellulose bond. The band at 1370 cm−1 belongs to deformation of NH2 that characteristic peak of amino silane. The asymmetric stretching of Si–O–Si linkage and Si–O–cellulose bonds were also observed around 950 and 1150 cm−1 for MS treated luffa fibers as shown in . The existence of 1200 and 1366 cm−1 bands could be attributed to the presence of Si–O–Si and Si–O–cellulose bonds as similar to amino treated luffa fibers The effect of the surface treatment on the interface between the PP and the LF's was studied by examining the fracture surfaces of the tensile tested composites with SEM. SEM micrographs of the fracture surface of the treated and untreated composites containing 15 wt% LF can be seen in (a)–(h). Both treated and untreated LFs distributed in transverse and longitudinal directions in the polymeric matrix and fibers are well dispersed in the matrix indicating the efficient mixing of filler within the polymeric matrix. The micrographs illustrate the differences in microstructure of composites. Examination of fracture surface of untreated LF composites ((a) and (b)) indicates that there are voids between fiber and matrix which is an evidence of poor adhesion. Poor adhesion seems to facilitate debonding of the fiber. This was also confirmed by the mode of fracture in the untreated composites. Fracture seems to be dominated by matrix failure since no fiber breakage can be observed. SEM micrographs of the treated composites clearly indicated that the treatment facilitates good adhesion between fiber and matrix. Fiber–matrix adhesion seemed to be better for MAPP treated composites than the untreated LF composites as shown in (c) and (d). In fact there are still voids around the fiber to a lesser extend compared to ULF composites. Fracture mechanism was still dominated by matrix failure since no fiber breakage could be observed. Fracture surface examinations of silane treated composites exhibited the best results in terms of interfacial adhesion. The AS treated and the MS treated composites are illustrated in (f), AS treated fiber was well surrounded by the matrix without voids. The fracture surface of AS treated composites illustrate that failure of composites takes place by a fiber breakage. At the same time, no interfacial failure was observed. When fiber breakage occurs, matrix fibrillation takes place, which is a good indicator of better interfacial adhesion between fiber and matrix as shown in (e). Examination of fracture surface of MS treated composites lead to similar results with the AS treated composites with fiber failure ((g)) and good adhesion between fiber and matrix ((h)). All these observations are consistent with the mechanical test results.AFM images of natural, sodium hydroxide treated and silane treated LFs were shown in . AFM pictures illustrate the reduction of roughness via surface treatment of fibers. Untreated fibers exhibit a roughness value of 138 nm, whereas the AS and the MS treated fibers exhibit 88 and 85 nm of surface roughness, respectively. These results can be accepted as a proof for the surface coverage of the fibers with a siloxane layer resulting a decrease in the surface roughness. NaOH treatment did not cause a significant variation in roughness of LFs. shows water absorption of 10 wt% untreated and treated LF loaded composites as a function of time. It is obvious that treatment of the fibers with silanes and MAPP reduced water absorption of the composites. The untreated composites exhibited 2.8% water absorption when immersed in distilled water for 40 days. The decrease in water absorption is 34.3, 39.0, and 28.4% for MS, AS, and MAPP treated composites, respectively. Water absorption in cellulose fibers is caused by hydrogen bonding between free hydroxyl groups on cellulose molecules and water molecules. Silane-coupling agents and maleic anhydride group on MAPP form hydrogen or covalent bonds with some of free hydroxyl groups of cellulose, which reduce the water absorption capacity of cellulose. Another reason for the decrease in water absorption capacity of composites would be enhanced adhesion between fiber and matrix by the treatment that results in a decrease in voids between fiber and polymer matrix. Poor adhesion causes cracks and voids between the polymeric matrix and the luffa fiber. This causes easy penetration and storage of water through the voids. The volume of voids decrease due to enhanced adhesion and therefore water penetration or storage through the interface is restricted. Silane and MAPP treated composites with lesser water absorption values have greater tensile strength, confirming better interfacial adhesion via bonding between fiber and coupling agent.Effects of coupling agents on the mechanical, morphological, and water absorption properties of luffa fiber (LF)/polypropylene (PP) composites were studied to enhance the interfacial interactions between the PP matrix and the luffa fibers. Mechanical test results clearly showed that both silane treatment of LFs and reactive treatment of composite with MAPP during compounding increased the tensile strength and Young's modulus. Composites containing MS treated luffa fiber showed the most pronounced improvement in the mechanical properties compared to the composites containing untreated LF's due to adhesion and compatibility between the PP and the silane treated LF. The improvement in adhesion between PP and treated LF fiber with coupling agents was also confirmed with the semi-empirical model of the Pukanzy and was is in agreement with the experimental data and was also supported by scanning electron microscopy (SEM).AFM studies of surface of the fibers showed that silane treatment decreased surface roughness of the fibers. This is also an indication of the surface coverage of the fibers with a silane layer. Water absorption results showed that silane and MAPP treatment reduced the water absorption capacity compared to untreated composites. Water sorption results can be correlated with mechanical test results, which can be treated as a proof for enhanced interfacial interactions with employment of treatment.On the role of tin in the infiltration of aluminium by aluminium for rapid prototyping applicationsThe use of tin as an alloying element in the production of freeformed infiltrated aluminium components is explored. Tin slows the growth of the aluminium nitride skeleton which provides dimensional stability, as well as increasing the rate of infiltration of the aluminium liquid into the aluminium nitride skeleton.We have recently described a new infiltration route for the production of aluminium components using rapid prototyping technologies The formation of a rigid skeleton is a key factor in the successful infiltration of a free standing part because it provides structural rigidity and hence dimensional stability during the infiltration stage. This is particularly problematical in aluminium because of the presence of a thermodynamically stable oxide film that is always present on the surface. It is further complicated by the need for the skeleton to be inert with respect to the infiltrant. This generally prevents the infiltration of one metal by the same metal because the liquid will dissolve the sintered necks that formed during pre-sintering. These difficulties can be surmounted by the development of an aluminium nitride skeleton. Aluminium nitride will develop in preference to aluminium oxide in a nitrogen atmosphere if the oxygen partial pressure is exceedingly low The amount of nitride that forms is a critical parameter. If insufficient nitride forms, then the dimensional stability is compromised during the infiltration step. If excess nitride forms, then cracking occurs during infiltration, which can limit the production of large parts. Excess nitride also limits the mechanical properties, particularly the tensile ductility Here, we examine the use of tin as an aid in the infiltration of aluminium by aluminium in freeform fabrication processing.The feed stock was prepared by mixing pre-alloyed AA6061 powder, 2% Mg and 4% (10 vol%) nylon in a Turbula mixer for 30 min. All compositions are given in wt% unless stated otherwise. The Mg was atomized, with a particle size <45 μm. Tin was added either as a separate elemental addition with a particle size <45 μm at a concentration of 0.25%, 0.5% or 1% or pre-alloyed into the AA6061 powder, at a concentration of 0.25%, 0.47% or 0.87%. Parts were manufactured by heating the powder mixture in a small mould to 220 °C for ∼30 min. This melted the nylon powder resulting in a resin-bonded green body that simulated processing by rapid prototyping techniques. The shaped part was then placed in a crucible with a piece of solid infiltrant of composition Al–13.8Si–4.7Mg on one end. The mass of the infiltrant was equal to that of the green part. The assembly was covered with alumina powder with 1% Mg mixed with it. Parts were heated at 90 °C/min in a horizontal tube furnace under flowing nitrogen and isothermally treated at 540 °C for up to 12 h. For infiltration, parts were further heated to 570 °C and held for up to 7 h. All parts were furnace cooled to below 300 °C before being removed from the furnace, except those used to determine the extent of infiltration. These were removed from the hot zone of the furnace to a cold region within the furnace and cooled there to room temperature. The remanent infiltrant was then removed from the part and weighed. The degree of infiltration was then determined from the weight loss of the infiltrant (assuming that when the weight loss was 100%, the part was fully infiltrated). Samples for metallographic examination were mounted in epoxy and polished using standard techniques. They were left unetched and examined either optically or in a Phillips XL30 scanning electron microscope (SEM) with a LaB6 filament and fitted with an Oxford energy dispersive X-ray spectrometer (EDS) and a backscattered detector. Thermogravimetric analysis was performed on a Netszch 409 STA using a heating rate of 5 °C/min. The sample was evacuated to below 5 Pa and back filled with N2. A flow rate of 60 cm3/min was used for the remainder of the test. shows the weight gain of AA6061 powder under argon and nitrogen. We have shown previously that the weight gain that occurs during heating of aluminium powder encased in an alumina/magnesium blanket is due to nitridation also shows the weight gain of AA6061 powder with and without tin. The weight gain without tin exceeds 16% after 6 h at 540 °C but it is less than 2% when tin is added to the powder. The effect of tin on the nitride thickness is clearly visible in the optical micrographs of The amount of tin used is also important, although concentrations >0.5 wt% have little effect for the temperatures and particle sizes used here (). Adding the tin as a separate elemental addition to the aluminium–magnesium powder mixture or pre-alloying it into the aluminium powder makes little difference. Tin is insoluble in aluminium, it is molten at the nitridation temperature and it has a low surface tension shows that the distribution of the tin after nitridation is inconsistent with this model. While the tin lies between the aluminium and the nitride, it does not form a continuous film over the particles. Furthermore, the nitride layer is of uniform thickness throughout, whereas it might be expected to be thinner or even non-existent over the tin. Its final location is also independent on its original site: it is localised under the nitride, irrespective of whether it was pre-alloyed into the aluminium or mixed as a separate elemental addition. The precise mechanism by which tin effects nitride growth is therefore unresolved at this time. A solution will require detailed microscopy and microanalysis, which is currently in progress.In addition to the growth of the nitride, the tin also effects the infiltration rate. Without Sn, there is an incubation time prior to infiltration, . This appears to be ∼2 h for the conditions used here, although there is a large amount of scatter in the data. The behaviour of the Sn-containing alloy is very different to the Sn-free material. With tin, there is no, or at least a very much reduced, incubation period, with noticeable infiltration occurring after 30 min. Once ∼15% is infiltrated, the rate increases rapidly, producing a large amount of scatter at 90 min. Infiltration is effectively complete at 120 min. Microstructural cross-sections through a partially infiltrated tin containing sample are shown in . The infiltrated section is depleted of tin, which appears to concentrate at the advancing liquid interface. Tin has a low surface tension The formation of aluminium nitride is important in the production of freeformed infiltrated aluminium components because it largely controls the tensile properties of the infiltrated part as well as providing structural support and dimensional stability during infiltration. Tin slows the growth rate of the aluminium nitride. The mechanism by which this occurs may be related to the low melting point and low surface tension of tin, which also increases the subsequent rate of infiltration of the aluminium liquid into the nitride skeleton.Effect of hydrolytic degradation on the mechanical property of a thermoplastic polyether ester elastomerPolymers with a finite lifetime are of great interest for oil and gas industry. Thermoplastic elastomers (TPEs) combine the strength of thermoplastics with the flexibility of elastomers, a characteristic also potentially useful in oil and gas applications. We studied the hydrolytic degradation of a TPE of interest at elevated temperatures from both a mechanical and chemical perspective, and have demonstrated that the chemical degradation rates, the change in crystallinity and the storage modulus all follow the pseudo zero order kinetics with respect to varying time at three temperatures. Applying Arrhenius' empirical relationship to the determined rates gives rise to a temperature-dependent model that predicts the degradation behavior of the TPE outside of the experimental temperature range. Our results indicate that hydrolytic degradation leads to an increase of crystallinity (chemicrystallization) and a decrease of tensile strength and strain, and that the increase of crystallinity strongly correlates to the increase of the storage modulus. The polymer eventually deteriorates due to brittleness.Polymers with a finite lifetime are of great interest for the medical device, electronics []. A controlled degradation of the materials within a defined time frame could enable transient applications that increase operational efficiency and reduce the overall cost of producing oil and gas. Degradable materials are highly desired for some transient applications in hard-to-reach locations of the downhole environment []. The degradable materials will dissolve into downhole fluids or lose their integrity by degrading to small particles or powders upon passive or active triggers after fulfilling their temporary functions as a device or a seal. Although all polymers eventually fail due to wear, tear, or aging, polymers with controlled degradation, which predictably degrade with property changes as a function of time, are critical for these potential applications.We are particularly interested in degradable elastomeric materials that can be used as temporary seals and plugs. Conventional elastomers, such as hydrogenated nitrile butadiene rubber (HNBR), ethylene propylene diene monomer rubber (EPDM) etc., have lifetimes longer than the requirement of transient applications for downhole use. Thermoplastic elastomers (TPEs), on the other hand, may contain hydrolysable functional groups [] such as esters, urethanes, and amides that experience hydrothermal degradation in downhole conditions. TPEs have networks formed by physical crosslinking that could be physically or thermally reversible, thus they combine the strength of plastics with the flexibility of elastomers. TPE have been used in a variety of applications including wire insulation, automobile fascia, footwear, wheels and adhesives. [] Most of the TPEs are used in an ambient condition, and thus are perceived as tough and durable materials. However, several conditions in the downhole environment affect TPE properties: rising temperatures and water penetration into the materials soften the TPEs, while hydrolytic degradation of the polymer chains may result in a change of morphology and mechanical properties of the materials. Our goal is to understand the property change of the TPE when it undergoes hydrolytic degradation in downhole conditions, so that we can design components whose property evolutions are fully understood and predictable during their lifetime downhole. This paper reports our studies of the kinetics and evolution of properties of a particular TPE, polyether ester, poly-(butylene terephthalate)-co-(tetramethylene ether) glycol terephthalate (PBT-PTMG), when undergoing hydrothermal degradation. shows a generic structure of the PBT-PTMG.Benzyl alcohol and 0.0204 N KOH in methanol were purchased from Sigma Aldrich. Phenolphthalein indicator (0.5% (w/v) in 50% (v/v) in methanol was purchased from Ricca Chemical Company.For most experiments, rectangular beam-shaped samples (22 × 4x3 mm) were die cut randomly from large sheets and subjected to an experimental degradation procedure. The mass, volume, dimensions, and storage modulus of each original sample were measured. Then, three samples were sealed in glass vials with approximately 10 ml of DI water and placed in an oven at 98 °C for varying time intervals. After desired time, the samples were cooled to room temperature and taken out of the water, their surface was wiped using Kimwipes. Their mass, volume, dimensions, and storage modulus at room temperature were measured again. Next, the samples were dried at room temperature under vacuum until the measured weight was constant (about 1 week). The mass, volume, dimensions, and storage modulus (temperature sweep) of the dried samples were then measured. For degradation experiments conducted at higher temperatures, the samples in un-sealed vials were placed inside a pressure vessel (), and the pressure vessel was sealed and placed in an oven at either 120 °C or 150 °C for varying time intervals.For tensile strength measurements, dog bone-shaped specimens (ASTM D638-type V) having roughly a thickness of 1.5 mm were stamped using a die from the same sheets as above. Samples were placed in a 100 ml Schott vial full of DI water (3 samples per vial), then placed in a pressure vessel with extra water for different amounts of time (7 h, 14 h, 1 day, 1.2 days, 2 days, 2.6 days, 3 days, and 4 days) at 120 °C. The tests at 14 h and 2.6 days, which correspond to transitions, as described below, were repeated. At each time interval, six samples were taken out. Three samples were tested right away in the wet state, at room temperature, and three were left to dry in a vacuum oven at room temperature for at least a week before testing at room temperature. The reference sample (“Ref”) was only dried in the vacuum oven.The hydrolysis of PBT-PTMG results in an increase of the acid end groups. The rate of hydrolysis of the PBT-PTMG in water can therefore be tracked by titrating the quantity of acid end groups in the original and the degraded samples. The dried polymer sample with known weight (around 0.3 g) was dissolved in 10.0 ml of benzyl alcohol after heating at 170 °C under N2 for 30 min. Around 8 drops of phenolphthalein indicator were added into the clear solution. The concentration of the acid end groups in each sample was titrated at 170 °C under N2, using 0.0204 N KOH (NKOH) in methanol, and the end point was determined when the color of the solution turned to light pink. The blank titration was carried out using 10.0 ml of benzyl alcohol at 170 °C under N2. The concentration of the end group (mol/g) was calculated using Equation Vp is the volume (ml) of KOH solution for titrating the polymer and Vb is the volume (ml) of KOH solution for titrating the blank. Wp is the mass of the polymer sample.We measure the melting and crystallization temperatures and enthalpy of the PBT-PTMG samples before and after degradation using differential scanning calorimetry (TA Instruments, Q200). Around 10 mg of the polymer samples were sealed in an aluminum pan and loaded to the auto-sampler of the DSC. The samples were equilibrated at −50 °C, ramped to 250 °C at 10 °C/min, and then cooled back down to −50 °C at 10 °C/min. The scan was repeated once. The specific enthalpy of melting was determined by integrating the peak of melting from the first scan. The percentage of crystallinity (Xc) was calculated according to Equation using the specific melting enthalpy of PBT ((ΔHmPBT,crystal = 145.3 J/g) [We determined the storage modulus of the samples using Dynamic Mechanical Analysis (TA Instruments Q800). A 0.1% strain amplitude was applied at a frequency of 1 Hz. The temperature was ramped at 5 °C/min to 160 °C after equilibrating at 28 °C. The storage (elastic) modulus E′ at 100 °C was recorded for each sample before and after degradation.An electron micrograph on a thin slice of elastomer was obtained using a TEM (JOEL 2100, courtesy of the Center for Nanoscale Systems at Harvard University). The accelerating voltage (high tension, HT) of the TEM was set at 80 kV and the filament was set to 60%. The elastomer sample was sectioned to a thin slice (less than 20 nm in thickness) using an ultramicrotome at room temperature. The sample was trimmed into smaller blocks using a metal blade first, and then cooling with liquid N2 before sectioning into thinner slices using a diamond blade equipped with a water bath. The slices were picked up from the water using a copper grid. The grid with the sample was immersed in a 0.2% aqueous solution of phosphotungstic acid (PTA) for 15 min and then washed and air dried. The amorphous phase absorbs the stain and the crystalline phase is then visible as a light/bright fibrillary region under TEM [A 5565 series Instron machine equipped with a 5 kN load cell was used to measure the tensile strength of the samples. The tests were done at a crosshead displacement rate of 500 mm/min. The strain was calculated by dividing the crosshead displacement by the gauge length of the sample (the gauge length was estimated to be 23 mm). The stress was calculated by dividing the load by the initial cross-section of the sample.Chemical degradation of PBT-PTMG is the result of hydrolysis of the ester bonds in the polymer chains to form a carboxylic acid and an alcohol end group. Water diffusion and hydrolysis occur predominately in the amorphous phase [], similar to other hydrolytic degradable semicrystalline polymers []. Since the samples are immersed in water during the experiments and water diffusion is not the rate limiting step as demonstrated later for these thin experimental samples, the reverse condensation reactions are considered minimum. The reaction follows a pseudo zero order reaction mechanism (Equation ) wherein the concentrations of water ([H2O]) and the ester bonds [RCOOR’] inside the sample can be considered as constant, and assuming the contribution of acid end groups [RCOOH] catalyzed hydrolysis is minimum at the early stage of hydrolysis []. The number average molecular weight Mn is inversely proportional to the concentration of acid end group.−dRCOOR'dt=dRCOOHdt=kRCOOR'H2OdRCOOHdt=k',k'=kRCOOR'H2ORCOOHt=k't+RCOOH01Mnt=k't+1Mn0The slope of the plot of [RCOOH]t vs time t is the apparent rate constant k’ at the given temperature. Mn0 and Mnt are the number average molecular weight of PBT-PTMG at time 0 and time t, respectively. We can define t1/2 as the time when Mn decreases by 50%. So t1/2 = 1/Mn0k’.To demonstrate that water diffusion is not the rate limiting step and that there is uniform hydrolysis through the entire sample, we first measured the rate of water diffusion at the experimental temperatures for hydrothermal degradation. The detailed experimental procedure and theoretical details for measuring and calculating water diffusion coefficient Dx are in the Appendix. shows the measured Dx for the PBT-PTMG at three experimental temperatures. The temperature-dependence of Dx follows the Arrhenius equation (Appendix). The experimentally measured activation energy Ea for Dx is 35.2 kJ/mol. Since the diffusion coefficients at temperatures higher than 100 °C are difficult to measure accurately, we used Arrhenius' equation to predict Dx at temperatures up to 150 °C. presents the predicted Dx at 120 °C and 150 °C. The conservative estimations of the time taken to saturate a 3 mm thick sample from one-dimensional water diffusion (ts=a42πDx, ts is time to water saturation) are 6.1, 3.20 and 1.49 hrs at 98, 120 and 150 °C, respectively. In fact, the experiments also confirm that the water concentrations remain constant at even significantly longer degradation time than ts,: 1.00 ± 0.3% for one month at 98 °C, 1.12 ± 0.04% for 86 h at 120 °C, and 1.46 ± 0.09% for 18 h at 150 °C (Because the products (oligomers) from the PBT-PTMG hydrolysis have low solubility in water, the samples have little mass loss (<0.2% weight loss) throughout the entire degradation time at each temperature (). Thus, tracking the mass change of the sample following the hydrothermal degradation is not feasible to study the degradation kinetics. We attempted to track hydrolysis using ATR-FTIR to monitor the concentration of ester or acid end groups. However, due to the low concentration of the acid end groups even after hydrolysis and the overlapping of the carbonyl peaks of acid (1674 cm−1) with that of the ester (1714 cm−1) groups [], an accurate integration of the two peaks could not be obtained (). Notable changes in the FTIR spectrum after degradation appear as increases of the peak intensities at 917 cm−1 and 751 cm−1, contributed by the motions of -(CH2)4-O- in the polymer chains in both hard and soft segments. The result suggests changes of crystallinity and possible conformation after degradation (] (end group titration) on the original and the degraded sample provided a more robust method of tracking the kinetics of hydrolysis. The number average molecular weight decreases as the degradation proceeds at each temperature (, [RCOOH]t vs degradation time follows the pseudo zero order reaction kinetics at each degradation temperature as illustrated by Eq. . The apparent rate constants of hydrolysis are 3.53E-11, 1.37E-10 and 9.92E-10 s−1 at 98, 120 and 150 °C respectively (). The corresponding activation energy Ea for the hydrolysis is 84.0 kJ/mol (). Using Ea for the hydrolysis reaction, we are able to calculate the rate constant of hydrolysis at 38 °C and 70 °C (). To illustrate the impact of temperature on the rate of material degradation, we present t1/2 (the time taken to degrade 50% of the ester bonds i.e. reduce Mn by 50%) in , which indicates that 50% of the ester bonds will be hydrolyzed within two weeks at temperatures above 98 °C.The morphology of the PBT-PTMG is best described as hard segment PBT domains dispersed in a soft segment matrix of PTMG, in which some PBT blocks are covalently linked to PTMG []. The hard PBT crystalline domains function as physical crosslinks. DSC scans reveal some morphology changes of the PBT-PTMG before and after hydrolytic degradation. shows the DSC scan of the samples aged at 120 °C at varying time intervals. The melting temperature of the original sample, Tm1, is 217.2 °C with a small shoulder (Tm2) at around 220.4 °C; the crystallization temperature, Tc, on the cooling cycle, is at 172.5 °C (the peak temperature of the exothermic peak). As the degradation time increases, the intensity of Tm2 increases and the peak moves to 223 °C after almost four days of degradation in water at 120 °C. Meanwhile, Tc gradually increases as the degradation proceeds accordingly as shown in . Thus, the undercooling ΔT (ΔT = Tm0-Tc, Tm0 is the equilibrium melting temperature) decreases for the degraded samples, which indicates easier formation of a crystalline phase in the degraded samples. The rate of the change of Tc is also temperature-dependent and the samples that degraded at higher temperatures showed a faster increase of Tc (), which supports the hypothesis that hydrolysis drives the change of morphology.Tm2 of the degraded samples increases to be closer to the Tm of pure polybutylene terephthalate (230 °C) [], which suggest that the newly formed crystalline phases resemble PBT. The percentage of total crystallinity (Xc%) also increases as the degradation proceeds at each temperature. We reason that the change of crystallinity should also follow the pseudo zero order kinetics, Eq. , if the change of crystallinity is solely the result of crystallization of the separated PBT blocks originally linked to soft PTMG segments. indeed shows a reasonable linear correlation of Xc% to the degradation time at 98 °C (R2 = 0.98), 120 °C (R2 = 0.98) and 150 °C (R2 = 0.97). The slopes of the linear plots are the apparent zero order rate constant, kc (s−1), of the change of Xc % (Equation ), and the activation energy is calculated to be 84.0 kJ/mol using Arrhenius' Equation with R2 = 0.99 (Since water diffusion and hydrolytic degradation take place mostly in the amorphous phase [] and there is little weight loss at this stage of degradation, the increase of Xc% following the degradation should be the result of hydrolysis induced chemicrystallization [] of the PBT segments that were originally linked to the PTMG soft segments in the amorphous phase and are ‘freed’ after the hydrolysis of the ester bonds. These PBT segments have relatively long polymer chains and thus form larger sizes of PBT crystals []. Fayolle and Richaud have shown that the Xc% for quenched semi-crystalline polymers is inversely proportional to the square root of molecular weight [, the linear relationship of Xc% and Mn−1/2, for all the experimental samples regardless of their degradation history, suggests that the simple relationship between crystallinity and molecular weight is also correct for hydrolysis induced chemicrystallization for this polymer.Transmission electron microscopy (TEM) confirms the evolution of the morphology before and after degradation. The samples were stained with phosphotungstic acid (PTA) so the crystalline phase is visible as a light/bright fibrillary region under TEM [ shows the TEM images of the original sample (left) and the dried sample after degradation in water at 150 °C for 15 h (right). Both images present the light fibrillary crystalline lamellar as being 30–35 Å in width that are continuous and interconnected by short lengths of tie molecules (, left). The difference lies in the dark amorphous phase []. The amorphous phase of the degraded sample is occupied ( bottom also illustrates the proposed evolution of the morphology of the elastomers before and after degradation.The morphology change of the samples after degradation affects the mechanical properties of the polymer. We measured the storage modulus E′ of the dry samples before and after degradation using a DMA temperature sweep from 25 °C to 160 °C. The degraded samples show overall higher E′ than the original samples across the whole temperature range (). To further compare the E′ of the samples with different degradation history, we recorded the “median plateau modulus” [] E′ at 100 °C for each sample before and after degradation at different temperatures. The E′ at 100 °C of the degraded elastomers increases and follows the pseudo zero order kinetics to the degradation time at 98, 120 and 150 °C with R2 at 0.97, 0.96 and 0.99 respectively ( are the apparent rate constants, kE (s−1) of the change of E′ at each degradation temperature (Equation ). The activation energy is calculated to be 89.2 kJ/mol (The hydrolysis activation energy, crystallinity change and modulus change are in the narrow range of 84–89 kJ/mol, which strongly suggests that the same mechanism drives their change. Dividing Equation , which suggests that the E′ should be linearly proportional to Xc % with the slope close to kE/kc regardless of the thermal history of the samples. in the supporting materials indeed shows the approximate linear plot of E′ vs Xc% (R2 = 0.91) for all the samples before and after degradation. The slope of the E′ vs Xc% plot is 1069, close to the slope of kE vs kc plot (). This correlation strongly indicates that the increase of crystallinity drives the increase of the storage modulus and the decrease of Mn has little impact on the storage modulus.The large strain mechanical properties of the PBT-PTMG samples (1.5 mm in thickness) under uniaxial tension demonstrate a transition from ductile to brittle behavior upon hydrolytic degradation. The neat material (’Ref’) fails at around 600% engineering strain and 60 MPa engineering stress (). The stress-strain curves are conventionally described in three parts: the pseudo elastic region below the yield stress, the “draw” region, where the neck propagates and the hard phase crystallites are aligned, and the strengthening region, similar to an elastomeric curve [After three days of exposure to water at 120 °C and the subsequent drying, the samples fail at 5% strain, below the yield, and 22 MPa. The stress-strain curves of the degraded and dried samples fit on a master-curve, with a slight increase in yield stress with increasing degradation time (, right, show the samples after failure. They illustrate that the samples degraded for 1.6 days exhibit a necking region, while the 3-day sample displays a brittle failure. Both the ductile-to-brittle transition and the increase in yield stress are consistent with the crystallinity increase that accompanies the disruption of the soft segments described above. The change in the stress-strain curve is a reflection of the decrease of the number average molecular weight (Mn) and increase of the crystallinity (increase of the tie molecules) [] after the hydrolytic degradation. After the first two days of degradation at 120 °C, the Mn decreased from around 44 kg/mol to around 17 kg/mol () along with the increase of crystallinity from around 26%–33%, which results in the increase of the yield stress and decrease of the ultimate tensile stress and strain. synthesize the tensile results for all the samples tested right after water exposure (wet) and dried for one week (dry). After around one day in water at 120 °C, the samples fail at an average ultimate stress below their yield stress. In other words, they do not show any hardening behavior, further proving the disruption of the soft, elastomeric phase. In this region, the strength of the material is equal to the yield stress, which is rather constant (wet) or slightly increasing (dry) with increasing degradation time. The water acts as a plasticizer in the wet state, counteracting the increased crystallinity related to hydrolytic degradation. Between 2.6 and 3 days, the samples become brittle, i.e. they fail before yielding. Interestingly, the half time (time to degrade half of the ester bonds) is 2.4 days at 120 °C, which is close to the time it takes to make the samples brittle (between 2.6 and 3 days with Mn below 20 kg/mol). In summary, the evolution of the tensile stress and strain during the degradation is the result of the changes at the molecular level.We studied the hydrolytic degradation of the PBT-PTMG at elevated temperatures from both a mechanical and chemical perspective, and have determined the Fickian diffusion coefficient, the rate of hydrolysis, the change in crystallinity and the storage modulus with respect to varying temperature and time. Our results indicate that the chemical degradation via hydrolysis follows pseudo zero order kinetics, and the kinetics of hydrolysis correlates with the rates of change of crystallinity and modulus. In fact, chain scissions due to hydrolysis lead to the reduction of the molecular weight and decrease of tensile strength and strain; rearrangement of molecular fragments increase crystallinity (chemicrystallization); rise of crystallinity increases the storage modulus regardless of the samples' thermal history. Applying Arrhenius’ empirical relationship to the determined rates gives rise to a temperature-dependent model. The model allows for a good approximation of the behavior of the mechanical properties at temperatures outside of the experimental range based on the activation energies. The rather large temperature range (∼50 °C) used to determine the temperature dependence of each property makes the model more robust; however, extrapolation should be done with caution, especially when approaching the glass transition temperature (25 °C) and the melting point (218 °C).Measurement of water diffusion coefficient are made on dried rectangular prism samples of the PBT-PTMG measuring approximately 3 × 4 × 22 mm. Samples were subjected to isothermal water absorption experiments at 38, 70 and 98 °C. The mass and volume of each original sample were measured using a Sartorius CPA1245 analytical balance (Data Weighing Systems). The width and thickness were measured using a Mitutoyo digital caliper. Three samples were placed in glass vials containing 10 ml of deionized (DI) water. The samples in the sealed vials were placed in an oven at the desired temperature and the mass of the wet samples was measured periodically after removing the surface water using Kimwipes. The sample was considered saturated with water once the wet weight reached a plateau.Determining the Fickian Diffusion coefficient allows for the quantification of water absorption and enables a comparison of the kinetics of water absorption with that of hydrolysis. We used the 1D Fickian diffusion model (Equation ) to derive the Diffusion coefficient (Dx) at each temperature [, mt is the mass of the wet sample at time t, mi is the mass of the original dry sample, mmax is mass of the wet sample at water saturation and H2O% (max) is percentage of water absorption at saturation.mt−mimmax−mi=1−8π2∑j=0∞(2j+1)−2×exp[−(2j+1)2π2Dxta2]=H2O%(t)H2O%(max)a<b<c(dimensionsofarectanguloid),Dx≅f−2Deff is developed for an infinite plate that has one-dimensional diffusion. Since the geometry of the experimental samples deviates from an infinite plate, an edge correction factor (f ≈ 1.5 when a = 3 mm, b = 4 mm and c = 22 mm for our samples) [] is applied to get the more accurate 1D diffusion coefficient (Dx) for the experimental samples. An unconstrained optimization algorithm in MATLAB called “fminsearch”, which applies the least square function to minimize the residual distance between a predicted/estimated Dx and the actual (experimental) Dx, was used to derive the optimal Dx from the experimental data collected at each temperature.The mass of each sample increases as the sample absorbs water over time, though the dimension change is inconspicuous (within the experimental error) ( shows the mass% increase over time at 38, 70 and 98 °C. Within the time frame of the water absorption experiments, the leaching of chemicals to water is minimum as there is little weight change after the absorbed water is removed by vacuum. Applying an unconstrained optimization algorithm “fminsearch” in MATLAB to the average H2O% results in the optimal 1D diffusion coefficient Dx at each temperature (). The activation energy Ea for Dx is calculated to be 35.2 kJ/mol (R2 = 0.99, The following is the supplementary data related to this article:Supplementary data related to this article can be found at Relating asphalt binder elastic recovery properties to HMA cracking and fracture propertiesCracking in HMA pavements reduces the long-term durability of HMA pavements and undesirably increases the costs of road maintenance. Asphalt binder as one of major constituents of HMA plays an important role in the HMA cracking performance. Previous studies have indicated that higher elastic recovery of asphalt binder was favored to resist fatigue cracking. This study was undertaken to further investigate the relationships between the asphalt binder elastic recovery (ER) properties and the HMA cracking resistance and fracture properties, measured in the laboratory. The ER test (or ductility test) and MSCR test were used to measure and quantify the asphalt binder ER properties. Similarly, the OT and IDT tests were used to measure and quantify the HMA cracking resistance (cycles to crack failure) and fracture properties (tensile strength, fracture energy [FE], and FE Index), respectively. The test results indicated that HMA mixes with high ER properties (⩾59%) showed superior fracture properties and better laboratory cracking resistance performance, i.e., higher FE Index values (>1.0) and more load cycles to crack failure (>500 OT cycles), respectively. By contrast, no definitive performance trends were found for the HMA mixes with low ER properties (<59%).Cracking in the HMA pavements reduces the long-term durability of HMA pavements and undesirably increases the costs of road maintenance In order to characterize the asphalt binder properties related to HMA cracking and fracture, the parameters of |G∗|.Sinδ at intermediate temperatures is used in the Superpave Performance Grade (PG) Specification. Due to a rapid increase of traffic volume and higher summer temperatures, more polymer-modified asphalt binders are utilized in pavements to address these challenges. However, the parameter |G∗|.Sinδ was used for non-modified asphalt binders, and thus, it may not sufficiently characterize the properties of polymer-modified asphalt binders relative to HMA fatigue performance.One of the main features of polymer modified asphalt binders is a big improvement in elastic recovery (ER) property To achieve this objective, the elastic recovery (ER) test and multiple stress creep recovery (MSCR) test for characterizing asphalt binder properties, and the Overlay Tester (OT) test and indirect tension (IDT) test for measuring mixture performances, were selected and their corresponding test results were comparatively evaluated.. As can be seen in the figure, the ER and MSCR were used to measure asphalt binder ER properties while the OT and IDT tests were used for characterizing HMA fracture/cracking characteristics, and then a correlative laboratory study between them was conducted.Details of the laboratory tests used in this study including standard specifications, sample dimensions, loading mode, test temperature, and output data are presented in this section.The ER test (or ductility test) was conducted as per AASHTO T301 using a ductilometer . The test uses a water bath to condition the specimens to 10 °C for one hour. And then, the specimens were elongated at a constant speed of 5 cm/min to the specified elongation. After 5 min, the specimen was cut and allowed to be in the water bath for recovery. After 60 min, the total length of the specimen after recovery was measured. The percent elastic recovery (ER) is simply the ratio of the retracted length to the total elongated length: ER = |
RetractedlengthTotalelongatedlength.The MSCR test is used to measure the creep and recovery properties of asphalt binders according to AASHTO TP 70-10 The OT test is used for characterizing the reflection cracking potential of asphaltic materials as per Tex-248-F shows that the HMA sample was glued onto two plates, and one plate is moving while the other is fixed. In addition, a 2-mm gap between the two plates exists to simulate the existing cracking underneath the new constructed pavement. As can be seen in the b, the OT is a displacement-controlled loading test, and the horizontal displacement is 0.635 mm at a loading rate of 10 s per cycle The indirect tension test has been widely used for characterizing the fatigue resistance properties of HMA mixes. The test was performed to determine the tensile strength of compacted HMA mixes in accordance with the Texas specification Tex-226-F The tensile strength of the compacted HMA was computed using Eq. where σT is the indirect tensile strength, F is the applied load at failure; h is the thickness of specimen, and d is diameter of specimen.The other two HMA fracture parameters computed from the IDT test data were the fracture energy (FE) and FE Index. The FE is defined as the work required to produce a crack of unit surface area, measured in J/m2where Gf is the fracture energy (FE) or the work done to fracture the HMA specimen. The FE Index is defined as a parametric ratio of the fracture energy to the HMA tensile strength and tensile strain at peak failure load per unit crack length where lcr is the traversed cracking length; σt is the indirect tensile strength; and εt is failure indirect tensile strain at peak load. presents a total of 11 Texas HMA mixes (plant-produced) collected from various field projects, and are categorized into five mix types, namely Type B, C, D, F, and CAM. The aggregate gradation specification limits for these mix types are summarized in . The asphalt binders were extracted from the mixes according to ASTM It needs to be noted that, even though the focus of this study was on the influence of asphalt binder elastic recovery properties on fracture behavior of HMA, the variation in mineral composition of the aggregates do influence the mixes’ fracture performance. However, because most of the mixes evaluated in this study have the same aggregate source of limestone, and only one or two mixes have other sources of igneous rock or sandstone, the effect of aggregate sources on the fracture performance of mixes cannot be validated based on these limited data, and it was also outside the scope of this study.The test results for the ER, MSCR, OT and IDT tests are presented in this section, and includes a comparative evaluation and synthesis.The ER and MSCR tests results are presented in . The comparisons of the two test results are presented in Clotopel et al. (2012) found an obvious linear correlation (R2 |
= 0.97) between the ER-ductility and ER-DSR tests when performed at the same test temperature (i.e., 25 °C). However, when performed at different test temperatures (i.e., 25 °C for ER-DSR; 58 and 64 °C for MSCR), a much lower correlation (R2 |
= 0.78) was observed since the ER test was conducted at a much lower temperature of 10 °C compared with the MSCR test at 64 °C. Another reason for the difference could be the different mode of loading as the ER is a tensile test while the MSCR is a shear test. When comparing the MSCR test results at two different stresses of 0.1 kPa and 3.2 kPa, a good linear correlation (R2 |
= 0.94) is observed, which is mainly because of the same testing temperature and test set-up ( presents the OT test results including the OT cycles and peak load. It is observed that D1, CA1, and F1 exhibit the three largest values of OT cycles to failure, while other mixes have much lower failure cycles. For the mixes D1, CA1, and F1, they also have much lower peak loads (i.e., ⩽2.6 kN) in the OT test. On the contrary, the mixes with low failure cycles such as D3, C1, C3, and B1 have much larger peak load (i.e., ⩾3.7 kN).The OT cycles and peak load measured from OT test along with the asphalt binder ER property obtained from the two asphalt binder tests are presented in . It is observed that mixes D1, CA1 and F1 with three greatest OT cycles have the three highest ER elastic recovery values as well. However, mix D1 does not have the third largest ER value in MSCR test. Considering a much higher testing temperature of MSCR test, the low ER testing temperature is closer to OT test and is more representative of low field temperatures at which the HMA propensity to cracking is higher. Thus, it appears reasonable that the ranking of ER test results is more consistent than the MSCR with that of OT cycles. The comparison indicates that when the ER test values for asphalt binders are much higher (e.g., ⩾59%), the HMA shows a corresponding great value in the OT cycles (⩾700 cycles). These results are also consistent with the study conducted by Mogawer et al. (2011) in which three asphalt binders with ER values of 63%, 69%, and 93% had higher OT cycles of 669, 503, and 1200, respectively, in the corresponding HMA mixes When comparing the OT peak loads with the OT failure cycles and ER values (ER test), it is found that the three mixes (D1, CA1, and F1) with the highest ER values and OT failure cycles have the lowest OT peak loads (⩽2.6 kN). On the contrary, the asphalt binders whose HMA mixes had few OT cycles were associated with large OT peak loads. For example, D3, C1, and C3 with OT cycles of 5, 8, and 5 have peak loads of 3.9, 3.7, and 3.9 kN, respectively. presents the correlations of OT peak loads with failure cycles and asphalt binder ER property. It can be seen that mixes with high failure cycles tend to have low peak load. For the correlation of OT peak load and asphalt binder ER, although the coefficient of correlation (R2 |
= 0.49) is low, there is still a trend that mixes with high ER tend to exhibit low peak loads, but more testing is needed to validate this observation.From laboratory experience, it has also often been observed that the OT peak loads are generally inversely related to the OT cycles, which concurs with the findings of this study as demonstrated in presents the IDT test results including tensile strength, fracture energy, and FE index. The correlations of HMA tensile strength with fracture energy and FE Index are presented in . As can be seen, there is no clear trend between HMA tensile strength and fracture energy. However, although the coefficient of correlation between the tensile strength and FE Index is low (R2 |
= 0.49), it seems that mixes with high FE Index tend to exhibit low tensile strength. It is obvious that the FE Index has a better correlation than fracture energy with tensile strength, which could be attributed to the involvement of tensile strength in the calculation of FE index, which nonetheless warrants more testing to supplement and validate these findings.As observed, the comparison of the ER and IDT test results is presented in . When comparing asphalt binder ER properties and HMA tensile strength, no evident trend was found. However, for CA1 and F1 with higher ER values, their tensile strengths are lower than most of the mixes. When comparing the asphalt binder ER properties with fracture energy and FE Index for all the mixes (as shown in a and b), no definitive trend was observed as the coefficients of correlation (R2) are below 0.5. In the previous section, the OT test showed that D1, CA1, and F1 with three highest values in the asphalt binder elastic recovery exhibited much larger failure cycles than the other mixes. Thus, it is supposed that D1, CA1, and F1 have the three largest fracture energies. However, CA1 has a much lower fracture energy, which is consistent with the statement that no clear correlation was observed between the asphalt binder ER properties and fracture energy. Compared with the tensile strength and fracture energy, the FE Index differentiates CA1 and F1 with the two highest asphalt binder ER values from the other mixes, and has a much better correlation with the asphalt binder ER properties. also presents the correlation for the mixes with ER <59% and ER ⩾59%, respectively. As can be seen, for the mixes with ER <59%, no definitive relationship between the fracture energy and asphalt binder ER property or between the FE Index and asphalt binder ER property was observed (R2 <0.5), and the trends were contrary to the expectation that the mixes with higher ER are expected to exhibit larger fracture energy and FE Index. For ER ⩾59%, due to the limited data, there is no definite statement made and more data is required to validate the correlation; but compared with the other mixes with ER <59%, the OT test results show a trend that these mixes with high ER (⩾59%) tend to exhibit a much better cracking resistance as measured through the number of OT cycles to failure.The OT and IDT tests are typically used to characterize the HMA fatigue characteristic properties. Thus, there is a need to establish their correlations amongst one another. shows the graphical linear correlations between the IDT test results of fracture energy and FE Index and the OT test results of failure cycles. As can be seen in , FE Index shows a much better correlation with the failure cycles than fracture energy, that is also consistent with a study conducted by Walubita et al. Overall, the general poor cracking resistance of Type B mix (i.e., elastic recovery <59%, low OT cycles <50, low FE Index value <1.0, etc) in almost all the laboratory tests was not unexpected. Type B mix is a coarse-graded mix that is not used for cracking resistance purposes but used as a base material for the purpose of decreasing the permanent deformation The correlations between the asphalt binder ER properties (i.e., ER and MSCR test results) and HMA fracture characteristics (i.e., OT and IDT test results) were investigated. The conclusions are summarized as follows:No obvious correlation was observed between the ER and MSCR tests for asphalt binder ER properties, which may be mainly attributed to a big difference in the testing temperatures (10 °C for ER and 64 °C for MSCR). A good correlation was, however, found in the MSCR test results between two different stress levels.The HMA mixes with higher ER values (⩾59%) exhibited high OT cycles to failure (>500) and low peak load (⩽2.6 kN), while no clear correlation was found for the mixes with lower ER values (<59%).The MSCR test result is not appropriate to correlate with the HMA cracking performance tests due to its high test temperature.No significant trends were observed between asphalt binder ER properties and IDT test results (i.e., indirect tensile strength and fracture energy). However, the results showed that the FE Index was able to effectively differentiate the HMA mixes with the high asphalt binder ER values (i.e., CA1 and F1) from mixes with low ER values.The FE Index showed a much better correlation with the OT failure cycles than the fracture energy.To further validate the correlation of the asphalt binder ER properties and HMA cracking characteristic properties, the investigation of influences of additives such as polymers and recycled asphalt materials on the asphalt binder ER property and their relationship with HMA cracking resistance and fracture characteristics is recommended in future studies. Correlation of the study findings with field performance observations is also warranted. Also, other alternative recovery tests such as the Torsiometer, particularly for modified asphalt binders, need to be explored in future studies.Evaluation of multifunctional properties of gallic acid crosslinked Poly (vinyl alcohol)/Tragacanth Gum blend films for food packaging applicationsThe natural polymer Tragacanth Gum is less explored as a supporting matrix, there are very less studies conducted using this polymer in literature. So the present study aims to explore the consequences of different weight percent (wt.%) of gallic acid (GA) on physicochemical properties of Poly (vinyl alcohol)/Tragacanth Gum blend films. The incorporation of GA resulted in more strengthened but less flexible films as confirmed by tensile tests. DSC studies confirmed the miscibility of composite films in the given composition range and TGA studies revealed increased thermal stability. The morphological studies revealed a homogeneous distribution of GA at lower wt.% in the blend system. X-Ray Diffraction study depicted; the added GA lost crystalline structure after incorporating it into the blend. The Water Vapor Transmission Rate (WVTR) was improved after the incorporation of GA into the blend system. Overall migration studies revealed the limited release of GA from the matrix into food simulants. Soil degradation rate increased as the wt.% of GA increased. The composite films presented strong antioxidant activity; therefore, prepared composite films could be used as an alternative to current packaging materials.In recent years there is an increased concern towards eco-friendly food packaging materials due to the negative effects of petrochemical based polymers towards nature. The main drawbacks of petrochemical based plastics are, nonbiodegradability and limited recyclability []. These setbacks can be overcome by using biopolymers []. Polymer blending is an important method to obtain new polymeric materials by mixing homogeneous solutions of two or more different polymers. Various polymers or copolymers can interact with secondary forces such as hydrogen bonds, dipole-dipole forces, or by forming charge transfer complexes to obtain homopolymeric materials with desired properties []. Poly (vinyl alcohol) (PVA) is a synthetic []. It is one of the leading synthetic polymers produced via non-petroleum route []. PVA has the excellent film-forming ability []. PVA has contributed good tensile strength and elongation property to the blends []. PVA has many numbers of hydroxyl groups in its skeleton, thus it is widely used in biomedical applications []. PVA is chemically stable in acidic and alkaline conditions []. Apart from its excellent properties, PVA film has also a few setbacks like low elongation at break, poor decomposition temperature and high glass transition temperature []. The hitches can be overcome by blending with another biopolymer. Tragacanth Gum (TG), is a less explored biopolymer with good chemical properties. It is an anionic biopolymer which is derived from renewable sources. TG is an exudate obtained from wounds created in certain trees. The gum is produced as a dried exudate from the stems and branches of Astragalus gummifer and other Asiatic species of Astragalus, such as Astragalus gossypinus and Astragalus microcephalus []. The hydrolysis of TG yields D-galactose, L-fucose (6-deoxy-L-galactose), D-xylose and L-arabinose []. TG solution in water has a higher viscosity compared to other natural plant gums, with outstanding thermal stability []. The viscosity of TG is depending on the ionic strength and pH because of the presence of many carboxylic groups in the structure []. Torres et al. (2012) reported that the TG has higher water absorption properties at 20–65 °C compared to guar gum and locust bean gum []. In the examination of a TG-based superabsorbent with water-absorbent equivalent to 864 g water/g absorbent, water absorbance was found to be affected by the type of initiator, monomer and crosslinking agent employed for the synthesis []. It has emulsifying ability, rheological behavior, non-toxicity and safe for oral take as well as long shelf life. Moreover, TG has been accepted since 1961 as Generally Recognized as Safe (GRAS) at the level of 0.2–1.3% and in Europe has E-number E413 on the list of additives approved by the scientific committee for food of the European community []. Gallic acid (GA) (3,4,5-trihydroxy benzoic acid) is an endogenous product found in plants []. It is a natural phenolic antioxidant extractable from natural products []. GA derivatives present in the form of methylated gallic acids are widely used as food additives to prevent the food from oxidation process [] Sun et al. (2014) reported that the chitosan films incorporated with GA improved the antimicrobial properties of the film significantly, and the films reduced microbial growth by 2.5-log reduction []. Toxicological studies revealed that the “no-observed-adverse effect-level” (NOAEL) of GA is at least 120 mg/kg/day for F334 rats and the level of gallates was reported to be as high as 1000 mg/kg for mice []. Interaction of GA with protein such as Bovine Serum Albumin (BSA) has studied by Precupas et al. (2019) and they reported that the interaction with GA increased the thermal stability of BSA []. GA is soluble in water; this character makes it suitable crosslinker to hydrocolloids. The current study hypothesizes that the selected three materials are water soluble and contains –OH groups in each component, so the obvious intermolecular hydrogen bonding could be an important factor in getting miscible composite films in the given composition range. Aim of the study is to evaluate the influence of GA on various physicochemical properties of PT blend films using several characterization techniques and to check the potentiality of the composite films as a packaging material. To the best of our knowledge, there are no such reports available in the literature.PVA having molecular weight 1,15,000 (Degree of Hydrolysis 98–99 mol%) procured from, Loba Chemie, Pvt. Ltd., Mumbai. Tragacanth Gum was supplied by Central Drug House (CDH), Pvt. Ltd., New Delhi. Gallic acid was purchased from Loba Chemie, Pvt. Ltd., Mumbai, India and Millipore water were used throughout the experiment.The control PVA, Poly (vinyl alcohol)/Tragacanth Gum blend (PT) and GA doped blend films (PTG) were prepared by solution casting and solvent evaporation technique. To prepare pure PVA and PT film, an exactly weighed amount of PVA and PT was dissolved in Millipore water with stirring at 80–90 °C for an hour. The clear solution kept for stirring to attain room temperature (RT, 26 ± 3). The homogeneous, viscous solution was poured onto previously cleaned and dried Petri dishes for solvent evaporation at RT. After 96 h the film was peeled off from the Petri dishes and stored in desiccators until further use. The composite films were prepared by doping different wt.% of GA (as shown in ) to the PT blend films using the above-mentioned method.The thickness of the composite films was measured using a digital micrometer (Mitutoyo Digital Micrometer, Japan). Several thickness measurements were taken at several locations for each composite film and mean value were reported.To determine the tensile properties includes Tensile strength (TS), Young's modulus (Ym), and elongation at break (Eb) a universal testing machine (UTM, DAK System Instrument, Mumbai), were determined according to ASTM D882-91. Rectangular specimens of size 2.5 cm × 10 cm were cut with a sharp knife from the prepared film samples and then placed in the extension grip of the testing machine. The film samples were stretched at a crosshead speed of 1 mm/min at RT in air.Differential Scanning Calorimetry (Instrument: DSC Q20 V24.10 Build 122 TA Instruments, Walters LLC New Castle, Delaware, USA) were used to analyze glass transition (Tg) and melting temperature (Tm) of the blend and composite films. The film samples were sealed in an aluminium crucible and heated from 25 °C to 400 °C at 10 °C/min in an inert N2 gas (50 mL/min). The percentage of crystallinity (Xc) was calculated Eq. Where ΔHexp is the experimental melting enthalpy of the crystalline phase, ΔHstd is theoretical melting enthalpy of the PVA crystalline phase, i.e., 138.7 J/g [Thermogravimetric analysis (TGA) was carried out on an equipment SDT Q600 V20.9 Build 20 TA instruments to determine the thermal stability of the blend and composite films. The samples of 2–10 mg was taken and heated from 25 °C to 700 °C at a heating rate of 10 °C/min under N2 atmosphere (100 mL/min).The surface morphology features were determined using a JEOL JSM-6360 Scanning Electron Microscopy (SEM) at an acceleration voltage of 10 kV. The film specimens were mounted on metal stubs using double-sided sticky carbon tape. All specimens were sputter-coated with a conductive layer of gold to avoid charging to the high electron beam.The correlation between crystallinity and its influence on mechanical properties of the blend and composite films were investigated by using Rigaku D/Max-IIA, X-ray diffraction (XRD) (Tokyo, Japan). The radiation was generated from Cu-Kβ source (λ = 1.5406 Å) at a voltage 40 kV and 40 mA was used to scan the samples between 5° and 80° with a scanning speed of 5°/min. Crystallinity was calculated from the diffracted intensity data using the Eq. Crystallinity%=Total Area of Crystalline PeaksTotal Area ofallPeaks×100To understand the resistivity of blend and composite films towards water, the water solubility test was carried out according to Shojaee-Aliabadi et al. with slight modifications []. The films of size (2 × 2 cm2) were dried at 110 °C in an oven for 24 h and then weighed the samples to get initial dry weight (Wi) of the samples. The samples were immersed in a beaker containing 50 mL of water with gentle stirring at RT for 6 h. The remaining film samples were filtered and dried in an oven at 110 °C for 24 h to get the final weight (Wf) of the samples. The water solubility (WS) was calculated using the Eq. Where Wi is the initial weight of samples before immersion in water and Wf is the final weight after immersion in water for 6 h.To determine the surface hydrophilicity/hydrophobicity, a contact angle analyser SEO Phoenix was used. The measurements were conducted at ambient RT and the size of the drop was 7 μL with all measured probe liquids. At least five measurements of different locations per test point were performed. Contact angle calculations were done with associated software.The WVTR test was carried out according to the method described by Muhammad Salman Sarwar et al., with some modifications []. Briefly, the glass bottle of 17.5 mm diameter was taken as container and filled with 10 mL of distilled water. The prepared films were wrapped on the mouth of container and tightened with the Teflon tape. The initial weight of glass bottles (Wi) were weighed and placed in an oven at 40 °C for 24 h. After 24 h the glass bottles were taken out of the oven and weighed again to the final weight (Wf). The WVTR was calculated using the Eq. Where A is the area of the circular mouth of the glass bottle and T is the time (24 h).The soil degradation of all the prepared films was studied using soil burial method described by Shiji Mathew with some modifications []. The samples of size 2 × 2 cm2 were dried and weight of each sample was recorded. The films were buried in soil at a depth of 5–10 cm under the soil surface and watered daily. After 20 days samples were removed from the soil, washed and dried at 45–50 °C. The weight loss was calculated using the below equation.Where mi is the weight of samples before degradation, mf is the weight of samples after 20 days of soil burial.To determine the release of active components from the matrix into the foodstuff, the overall migration was carried out according to the IS:9845-1998 specifications. The pure and composite films were exposed to three different food simulants like 50% Ethanol, 3% acetic acid and distilled water mimicking the behavior of alcoholic beverages, acidic foods and aqueous food respectively. The preweighed samples of size 2 × 2 cm2 were immersed in three food simulants at 40 °C for 10 days in a hot air oven. After the incubation period, the samples were removed and evaporated to dryness. The residue was weighed with an analytical balance. The results are expressed in mg/kg. The presented values are the average of three readings on each sample for each simulant. The amount of extractive was calculated according to the Eq. Amount of extractEx=MV×1000mg/kgormg/lorppmWhere M is the mass of residue in mg minus blank value, V is total volume in mL of simulant used in each replicate.Antioxidant activities of the PTG samples were measured on the basis of the free radical scavenging activity using the DPPH (2,2-diphenyl-1-picrylhydrazyl) method. The stock solution of DPPH was prepared by dissolving 3.9 mg of DPPH in 100 mL of methanol and stored at 4 °C until use. 2 ml of DPPH solution was mixed with 1 mL of five different concentrations (20, 40, 60, 80 and 100 mg mL−1) of the PTG samples. Ascorbic acid (20, 40, 60, 80 and 100 mg mL−1) was used as a standard reference. A mixture of 1 mL of distilled water and 2 mL of DPPH solution was used as the control. The reaction mixture was mixed and kept in the dark for 30 min and incubated at room temperature. The absorbance was recorded spectrophotometrically at 517 nm. The antioxidant activity was calculated by the following equation.Scavenging effect%=control Absorbance−sample absorbancecontrol absorbance×100The IC50 value was calculated from the graph of RSA (%) against sample concentration.Statistical analyses were performed using the ORIGIN 9.0 program (OriginLab Inc., USA). Data were presented as an average of at least three observations on one sample for each time period and analyzed by one-way analysis of variance (ANOVA). P value <0.05 was regarded as significant throughout the study.The stress-strain curves of placebo films and composite films are shown in . The corresponding data is presented in . The neat PVA film has a tensile strength of 15.3 MPa with an elongation at break of 149.3% indicating more flexible nature. The PT blend film shows an increased tensile strength and Young's modulus which might be due to the stronger interaction between the –OH groups of PVA and the polar groups of TGs. The decreased elongation at break might be attributed to the more viscous nature of TG leading to brittle film compared to the pristine PVA film.After incorporating with GA in the PT blend system, increased tensile strength, Young's modulus was observed up to 15% of GA, this can be attributed to the increased intermolecular interaction between the components and cross-linkage capacity of GA []. The added GA acted as a crosslinker between the PVA and TG through numerous hydrogen bonding. The obtained stress-strain curves are depicting that the composite films are more flexible compared to PT blend. The elongation at break was found to be increased with an increase in GA content which is contrary to the general observation of cross-linked films []. The increased elongation at break attributed to the plasticizing effect of moisture content in the film []. It is well-known that water is the most omnipresent and uncontrollable plasticizer for most water-soluble films because of its ability to modify the structure of this polymer []. Overall there is an improvement in the strength and flexibility (57% and 50.2% respectively) of composite films compared to pure PT blend.The DSC thermograms of neat PVA, PT blend and PTG composite films are shown in . The glass transition temperature (Tg) is an effective factor to determine the compatibility of polymers []. The PT blend has shown increased Tg compared to virgin PVA, which might be due to the strong intermolecular interaction between the components. A single Tg was observed for the PT blend indicating the miscibility between PVA and TG. After doping GA into the PT blend the Tg was increased as the content of GA increased upto certain content (15%) which might be due to reinforcement of GA upto miscible composition.an increase in the Tg associated with the crosslinking effect was observed. Cui et al. (2018) reported an increase in Tg of poly (propylene carbonate) (PPC) by the synergetic effect of nanocrystalline cellulose (NCC) and Poly (vinyl alcohol) (PVA) []. Hu et al. (2013) also mentioned an increase in Tg of PVA by blending it with glutaraldehyde (GA) crosslinked chitosan at 8% of GA-Chitosan and attributed it to the increased intermolecular hydrogen bonding will restrict the motion of polymer chains, thus results in an increased Tg []. Chiou et al. (2002) also reported an increase in Tg of polyurethanes after crosslinking with triols []. The overall Tg of the composite films was lower than that of neat PT blend system attributed to the decreased interaction between the components or may be due to the added GA induced an increase in amorphous phase which resulted in a decreased Tg of composite films []. Overall a decrease in Tg was observed (Except 15%) compared to PT blend. This is attributed to the reduced interactions among the components, the added GA penetrated the PT matrix and thus decreasing the interaction among the two polymers. The Tm of the composite films was not so much deviated from the PT blend system. Interestingly the Td of the composite films were monotonically increased as the wt.% of GA increases (around 49 °C increase).That might be due to the increased degree of crosslinking between the components. Levchik et al. (1999) reported an improvement in thermal degradation temperature of polystyrene after crosslinking with divinyl benzene (DVB) in presence benzoyl peroxide (BPO) as free radical initiator []. The crystallinity (%) was calculated using the above-mentioned formula and results are presented in . The crystallinity trend is in good agreement with the observed Tg trend.To investigate the effect of added GA on the thermal stability of the PT blend, the TGA was carried out. The thermograms of bare PVA, GA, PT blend and PTG composite films are shown in . All the films shown three stage degradation patterns. For pristine PVA, the initial weight loss at 60–143 °C (6.9%) can be attributed to the evaporation of physically adsorbed water molecules []. The pure GA also exhibited the water evaporation process in the temperature range of 72–112 °C with a weight loss of 7.6% []. The neat blend and composite films also exhibited this process within the range of 71–159 °C. The second degradation step of PVA occurred in the range 235–420 °C with a massive weight loss of about 77.8% is corresponding to the elimination of main chain acetate groups by chain scission mechanism of PVA []. The third stage decomposition of PVA at 440–580 °C is attributed to the degradation of by-products formed during the second step degradation []. The second degradation step of pure GA involves the melting of GA and decarboxylation of GA to pyrogallol [The third step degradation of neat GA occurred at 289–362 °C ascribed to the further loss of hydroxyl groups either as water or perhaps even as CO2 or CO. The PT blend films showed the second degradation step at 282–328 °C is attributed to the degradation of the main chain of PVA and the highly complex heterogeneous structure of TG []. The incorporation of GA into the PT matrix brought some major improvements in the stability to withstand temperature. The onset temperature of the second step degradation of PTG composite films decreased compared to the pure PT blend film which is attributed to the melting and decarboxylation phenomenon of GA which occurs at a relatively lower temperature. As the GA content increased in the PT matrix the onset and offset temperature increased attributed to the greater number of interactions induced by GA by the presence of –OH groups among the blend components resulting in more thermally stable composite films []. The stronger interactions impede the elimination reactions of the composite films leading to suppression in the thermal degradation process []. The percentage of weight loss decreased by about 4% in the II degradation stage after doping with GA. The third step degradation onset temperature increased as GA incorporated into the blend films and the percentage of residual mass increased from 9.9% to 12.5% (PTG-5), which is higher than that of PT blend film indicating the increased thermal stability of the composite films.The SEM micrographs of PVA, PT blend and composite films are shown in . The neat PVA film has a smooth, homogeneous and compact structure. The binary blend PT film has shown a compact and coarse structure with some visible patches. The incorporation of GA into PT matrix resulted in major changes in the morphology. At lower wt.% of GA (5 to 15%), the composite films were homogeneous, continuous without any visible cracks indicating the homogeneous dispersion of GA in the PT matrix. The white spots in the composite films might be due to the excess GA indicating some heterogeneity in the composite films [With increase in the amount of GA, the surface roughness increased with small agglomeration of GA and is due to the increased covalent and noncovalent interactions between matrix and dopant []. The composite films (except PTG-1) shows very small pores in the microstructure of the films which resulted in decreased mechanical properties of composite films. The pores or holes in the composite films might be due to the release of GA in distilled water from composite films []. At higher loading of GA (PTG-5), composite film has shown a phase separation morphology due to immiscibility of GA with the PT matrix. In XRD (.) also the PTG-5 composite film has shown peaks related to GA indicating the decreased miscibility of GA with the PT matrix. With increase in the amount of GA, the surface roughness increased with small agglomeration.To study the consequence of GA on the structural behavior of the PT blend system, the XRD analysis was performed. The diffractograms of pure PVA, GA, PT blend system and PTG composite films are presented in . The variation of crystallinity (%) by the incorporation of GA is presented in . The pristine PVA shows a broad peak at 2θ = 19.6 and a small hump at 2θ = 40.6 which is attributed to the crystalline nature of PVA []. The bare GA shows crystalline diffraction peaks which is in relevant with the literature []. In the PT blend system, the appearance of two new peaks at 2θ = 9.7 and 28.7 are ascribed to the microcrystalline structure of TG [After the incorporation of GA into PT blend, palpable changes were observed. At lower content of GA, (up to 20 wt.% of GA) the crystalline peaks related to GA are not distinctly observed in the diffractograms of PTG composite films as compared to pure GA, which might be due to the overlapping of the peaks of PT blend and GA resulting in broadening of the peaks []. As the content of GA increased, the intensity of the diffractograms of the composite films was decreased indicating the added GA exhibited structural changes in the composite films. The composite films exhibited decreased crystallinity compared to PT blend system agrees with the fact that generally when crystalline and non-crystalline (amorphous) polymers exhibit good compatibility results in decreased crystallinity []. The higher GA loaded composite film viz PTG-5 (25 wt.% of GA) showed an additional two peaks related to GA at 2θ = 14.0 and 16.9° which might be due to the non-uniform distribution of GA in the PT blend system. The percentage of crystallinity of the composite films was decreased after doping with GA corresponding to the restriction of a regular arrangement of the crystalline regions within the polymer system. The crystallinity (%) calculated by using XRD data is coherent with DSC results.Water solubility is an important factor to determine the potency of biopolymer films for a specific application. The WS details are presented in . The incorporation of GA into the PT matrix affected the water solubility. The PVA has shown 39.0 ± 5.0% of water solubility indicating the high hydrophilicity of PVA. The PT blend has shown decreased solubility compared to pure PVA. As the GA wt.% increases in the matrix, the solubility increased and reached a maximum of 40 ± 3% for PTG-5 film. The increased solubility of PTG composite films attributed to the highly polar nature of GA. As the selected three materials (PVA, TG and GA) are water soluble, during the solubility test period, some amount of materials might dissolve in water that led to the greater solubility of composite films.To explore the influence of GA on wettability of PT blend, the contact angle measurements were carried out using sessile drop method. The images and contact angle in degrees are presented in . Neat PVA has a contact angle of 54.3° showing the hydrophilicity of PVA. The blend system has a contact angle of 81° which is still hydrophilic. The decreased hydrophilicity of PVA after blending it with TG might be due to the decreased free –OH groups of PVA and TG on the surface of films []. The addition of GA into the PT blend system resulted in a further increase of contact angle at lower wt.% of GA (5%) to a maximum of 88.1 ± 3.2°. The increase in contact angle might be due to the non-availability of free –OH groups to interact with water molecules as shown in Further doping of higher wt.% of GA (10–25%) resulted in increased hydrophilicity of the composite films which might be due to the hydrophilicity of GA. The increase in GA content resulted in a greater number of –OH groups which in turn interacted with –OH groups of water molecule resulting in an increased wettability of composite films. The possible scheme for increased hydrophilicity is given in The WVTR is a vivid factor for food packaging materials as it determines the rate of transmission of water vapor from the surroundings to the food through the packaging material. To be used as a packaging material, the WVTR must be as low as possible [The influence of GA on the WVTR property of the PT blend was studied and results are presented in . The neat PVA has exhibited WVTR of 43.8 ± 2.1 (g/m2h) and the PT blend has shown 34.5 ± 4.7 (g/m2h) respectively, which is due to the hydrophilicity of the film as evidenced by WCA and WS results. The GA doping into the PT blend system has improved the resistance of composite film towards water vapor transmission. The composite films presented the lowest WVTR value of 19.5 ± 3.8 (PTG-2), about 56% decrease in WVTR was observed. The compact structure of the composite films as evidenced by morphology studies and decreased hydrophilicity of the composite films are the main two reasons for this observation. Another explanation for the decreased WVTR is the sinuous path created by the complex structure of the composite films as shown in a. The present findings are in good agreement with previous research works [To investigate the effect of GA on soil degradation rate of PT blend, the soil degradation test was carried out under natural atmospheric conditions. Neat PVA film was buried in soil for the comparison purpose. After 20 days the samples were removed from the soil and washed with water to remove the soil adhered to the film and dried, the weight loss was calculated and presented in . The neat PVA film show only 15% of degradation after 20 days. The PT blend exhibited 16.6% degradation. The composite films presented high rate of degradation compared to PT blend and PVA. At lower content of GA, composite films degradation was low due to the less sensitive towards water/moisture as indicated by WCA and WS results. At higher content of GA (PTG-3 and PTG-5) demonstrated higher degradation rate. The incorporation of GA into the PT blend accelerated the soil degradation rate.A migration test means the determination of the release of substances from the packaging material or article into food/food simulant. Food simulants are test medium that imitates food behavior, mimicking migration from food contact materials []. The overall migration values of all samples are presented in An ideal food packaging material should possess inertness towards food/food simulant in contact with. Therefore, to scrutinize the migration of active components from material to food/food simulants, the overall migration study was carried out. After incubation for 10 days at 40 °C in food simulants the maximum migration was 161.0 μg/kg for PTG-2 in 50% Ethanol. In 3% AcOH maximum migration was 196.0 μg/kg for PTG-1 and in distilled water maximum migration was 220 μg/kg for PTG-3. The mentioned values are well within the migration limits for food contact materials established by the Bureau of Indian standards (second revision, December 1998) IS:9845-1998. Thermodynamic properties, such as polarity and solubility, play an important role on migration due to interactions between the polymer, migrants and the food simulant (FS). If the migrant has a poor solubility in the FS it will be retained in the polymer matrix, while a simultaneous effect based on the high affinity between FS and the polymer could be also present leading to the absorption by the polymer matrix. In addition, sorption of certain organic solvents could cause swelling of the polymer matrix, thereby enlarging the gaps between the molecules and enhancing the additive migration [The migration value of composite films in 50% Ethanol was higher than neat PVA this might due to the easily soluble nature of GA in Ethanol and water. The highest overall migration of an active component from the matrix into food simulant was exhibited in distilled water compared to other two food simulants, this observation might be due to the hydrophilicity of three components in the matrix. Compared to PT blend, PTG composite films exhibited higher overall migration (except PTG-5) in all three food simulants is an indication of release of GA from the matrix. The overall migration values were well within the limits.The free radical scavenging activity of PT blend and PTG composite films was determined. The results are presented in . The activity of all the samples discussed only for the highest concentration viz 100 μg/mL due to concise. The control Ascorbic acid has exhibited a maximum RSA of 93.8% with an IC50 value of 35.09 (μg/mL).The PT blend presented a maximum RSA of 75.4% with an IC50 value of 56.13 (μg/mL) with moderate activity as shown in b. The scavenging ability of the blend might be due to the hydroxyl groups present in the TG backbone. After the incorporation of GA into the PT blend the antioxidant activity was remarkably improved. The Added GA reinforced the antioxidant nature in the blend. The antioxidant activity of composite films (PTG-1 & PTG-2) is more than the standard Ascorbic acid. The IC50 values were also less than the Ascorbic acid indicating the strong activity of composite films. The increase in GA wt.% in the blend has resulted in stronger antioxidant activity of composite films.The different wt.% of GA incorporated PT blend films were prepared by the solvent casting technique and analyzed by various characterization techniques. Tensile properties such as tensile strength and elongation at break were improved up to 57% and 50.2% respectively, compared to the blend. The DSC measurements presented miscibility between the blend and GA by exhibiting a single Tg. The thermal stability of the blend was greatly enhanced by the incorporation of GA. The morphology was homogeneous, coarse and compact at lower wt.% of GA. At higher content of GA (PTG-5) phase separation and aggregation of GA were observed. The XRD results suggested that at lower content of GA, homogeneously distributed in the matrix and lost its crystalline domains. The WCA results depicted that at lower wt.% of GA the composite films were near hydrophobic and at higher wt.% of GA, they are hydrophilic. The percentage of water solubility was decreased after the incorporation of GA compared to the blend. The WVTR was improved by the incorporation of GA. The release of GA from the matrix into 3 food simulants was well within migration regulations as confirmed by the overall migration study. The added GA enhanced the soil degradation rate of the blend. The composite films exhibited a remarkable antioxidant activity. The prepared composite films have the capability to use as a packaging material.Naganagouda Goudar: Conceptualization, Data curation, Formal analysis, Methodology, Resources, Software, Writing - original draft,Writing - review & editing.Vinayak N. Vanjeri: Methodology, Resources,Validation, Investigation, Writing - review & editing.Sarala Sataraddi: Preparation of Figures and Graphical Abstract.Ravindra B. Chougale: Supervision, Validation, Investigation, Writing - review & editing.Saraswati P. Masti: Writing-review and editing.Shyam Kumar Vootla: Supervision and Data Curation.All the authors declare no conflict of interest.Supplementary data to this article can be found online at Notional load method for industrial steel storage racksThe discussion in this paper is on the stability analysis and design of industrial steel storage racks. Studies were carried out to evaluate the current Effective Length Method, and to examine the Notional Load Method as an alternative design procedure. Presently, the design of industrial steel storage racks in the United States is carried out according to the Rack Manufacturers Institute (RMI) specification using the effective length method. The notional load method is a new method for stability analysis and design of structural steel systems introduced in the AISC Specification for Structural Steel Buildings (ANSI/AISC 360-05). The difference between these two methods is that in the effective length method the beam-column member within the frame is designed based on effective member length while in the notional load method it is designed based on actual member length and the analysis is based on a reduced stiffness in the structure. The finite element method, which considers both geometric and material nonlinearities, was used as the basis for evaluating the accuracy of these two design methods. The study was carried out for numerous cold-formed steel industrial storage rack configurations. The application to cold-formed steel structures had to include the frequently encountered torsional–flexural buckling and semi-rigid joints. Results showed that the effective length method is more conservative than the notional load method and the notional load method agrees better with the finite element results than the effective length method does. It is, therefore, recommended that the notional load method be considered as an alternative means for industrial steel storage rack design.Presently, the design of industrial steel storage racks in the United States is carried out according to the 2006 edition of the specifications published by the Rack Manufacturers Institute (RMI) The discussion in this paper is on the RMI specifications and recent research at Cornell on improving the RMI specification. The research project discussed in this paper was co-sponsored by the Rack Manufacturers Institute and the American Iron and Steel Institute. The objective of this study was to compare the Effective Length Method and the Notional Load Method for accuracy and appropriateness for storage rack design. The storage rack industry currently uses the effective length method.This paper begins with a discussion on the effective length method and notional load method design procedures employed in this study. For a thorough discussion of the philosophies behind these two methods the reader is referred to ASCE Storage rack columns are considered to be subjected to a combined compressive axial load and bending. The required compressive axial strength Pu and required flexural strength Mu for the column designed by using the effective length approach Load and Resistance Factor Design (LFRD) method must satisfy the following interaction equation:where Pn is the nominal axial strength, Mn is the nominal flexural strength, φc is the resistance factor for axial strength, and φb is the resistance factor for bending strength.The required strengths Pu and Mu can be determined by using second-order elastic analysis, which considers both P−δ and P−Δ effects, or by using first-order analysis provided that the moment magnification factor is used. The analysis must consider flexibility of connections and incorporate initial geometric imperfection in the structure due to fabrication and erection tolerances. Story out-of-plumbness of 0.5 in in 10 ft (ψ=1/240) as shown in is used for industrial steel storage racks. This corresponds to the maximum fabrication and erection tolerances permitted by the RMI specification.The required strengths Pu and Mu for the column designed by using the notional load approach LRFD method must satisfy the following interaction equation:where Pn(L) is the nominal axial strength computed based on the value of Kx, which is the effective length factor for bending about the axis perpendicular to the plane of the frame (x-axis), taken as 1.0, and Kt, which is the effective length factor for twisting, taken as 0.8. Analysis is performed on a geometrically perfect frame subject to notional horizontal load ξW at each story as shown in , where W is the gravity load at that story, and ξ is the notional load coefficient. Notional load coefficient of 1/240 is used for storage rack design. This value corresponds to the maximum initial out-of-plumbness allowed by the RMI specification and is roughly twice the value of 1/500 recommended by the AISC specification used for structural steel buildings. Other out-of-plumb values that are typical for the particular structure may be used and notional loads adjusted accordingly. The minimum value of the notional load coefficient is to be taken as 1/500.Analysis is performed on a 20% reduced flexural stiffness model in accordance with Appendix 7 of the AISC specification. This can be done by using a reduced flexural stiffness EI* for all members and connections in the analysis model:where E is the modulus of elasticity and I is the moment of inertia. The reason for imposing the reduced stiffness for analysis, as explained in the commentary section of the AISC specification, is to limit the system available strength to 0.8 times the elastic stability limit, which is roughly equivalent to the safety margin for slender column design by the effective length method, where the design strength φcPn=0.9(0.877)Pe=0.79Pe. Stiffness reduction factor τb to account for inelastic softening under high compression load (when Pu>0.5Py where Py is the member yield strength) was not used in this study because stocky columns were not considered. It should be noted that in the notional load method the nominal strengths Pn(L) and Mn used in the interaction equation do not need to be calculated based on the reduced value of E.Performing the analysis on a frame with initial out-of-plumbness or on a geometrically perfect frame with notional load is the same if ψ is equal to ξ because they are statically equivalent. Therefore, there are only two differences between the effective length method and the notional load method: one is the value of the column nominal axial strength used in the interaction equation because it is a function of Kx and the other is the stiffness of the analysis model used to determine the required strengths. The column nominal flexural strength is not the function of Kx when it is bending about the axis perpendicular to the plane of the frame.A parametric study was carried out to compare the effective length method and the notional load method for accuracy and appropriateness for beam-column design. An isolated rotationally restrained sway column as shown in was used as the vehicle for carrying out the parametric study. The parameters included: nine column sections as shown in , three material yield stresses: 33, 55, and 70 ksi (228, 379, and 483 MPa), and 20 different rotational end-restraints as given in . Combinations of these parameters yielded a total of 540 beam-column configurations.The finite element method, which considers both geometric and material nonlinearities, was used as the basis for evaluating the accuracy of the design method. The finite element modeling assumptions included using a three-dimensional model, using open-section beam elements to capture torsional–flexural buckling behavior of the open-section columns, using linear torsional springs to model the rotational end-restraints for bending about the major axis, using pin-ended supports for bending about the minor axis and for twisting, using a combination of the out-of-straightness and the out-of-plumbness as shown in for the member initial geometric imperfection, and using an elastic–plastic material model.The effective length approach relies significantly on the prediction of the critical buckling load of the member. The critical buckling load is usually determined by using the AISI torsional–flexural buckling provisions, or could be more accurately obtained by performing an elastic buckling analysis. Both procedures were investigated.The following assumptions were used in this study: all resistance factors were taken as 1.0 and the value of Kt used in the AISI torsional-flexural buckling provisions was taken as 1.0 because the column was simply supported for twisting. In Appendix 7 of the AISC specification, the flexural stiffness of the analysis model for the notional load method should be reduced by a factor of 0.8. This reduction factor is, however, for research purposes in this study taken as 0.9 because the resistance factor was taken as 1.0. Local buckling and distortional buckling failure modes were not considered in this study. All these assumptions, except for the assumption on Kt, were also used in the following study on storage racks., where PEL1, PEL2, PNL, and PFE are the axial load carrying capacity of the column obtained by using the effective length method with the elastic buckling load determined from AISI torsional–flexural buckling provisions, the effective length method with elastic buckling load determined from elastic buckling analysis, the notional load method, and the finite element method, respectively. The statistical summary of the correlations between the design method and the finite element results is summarized in Comparison between the first effective length method, which is with the elastic buckling load determined from AISI torsional–flexural buckling provisions, and the second effective length method, which is with the elastic buckling load determined from the elastic buckling analysis, indicates that the second method agrees better with the finite element results than the first method does. The first method has lower design loads than the second method because of the conservatism in the AISI torsional–flexural buckling provisions. Further study on the accuracy of the AISI buckling provisions is given in Sarawit Comparison between the effective length method and the notional load method indicates that overall the notional load method agrees better with the finite element results than the effective length method does. Some unconservative results can be obtained in a few instances in the notional load method if the stiffness of members was not reduced in the analysis.A parametric study was carried out to compare the effective length method and the notional load method for accuracy and appropriateness for cold-formed steel industrial storage rack design. Pallet racks as shown in were used as the vehicle for carrying out the parametric study. The parameters included: three frame dimensions as shown in , two column frame configurations as shown in , three material yield stresses: 33, 55, and 70 ksi (228, 379, and 483 MPa), six beam to column connection stiffnesses: 100, 200, 300, 400, 500, and 600 kip in./rad (11298, 22596, 33894, 45192, 56490, and 67788 N m/rad), and braces and shelf beams as shown in . Combinations of these parameters yielded a total of 972 pallet rack configurations. The loading condition is the gravity load case on a frame with initial out-of-plumbness of 0.5 in in 10 ft (ψ=1/240). The limit state of all frames in the study is assumed to be governed by the strength of the column. In practice, this may not always be the case, strength of other components such as the shelf beams and the connections must also be checked.The finite element method, which considers both geometric and material nonlinearities, was used as the basis for evaluating the accuracy of the design methods. The finite element analysis modeling assumptions included using a three-dimensional model, using open-section beam elements to capture torsional–flexural buckling behavior of the open-section columns and braces, using linear torsional springs to model the connection stiffness, using the base fixity equation given by Sarawit In this parametric study, the elastic buckling load was computed using the AISI torsional–flexural buckling provisions where for the effective length method the value of Kx was determined from elastic flexural buckling analysis, for the notional load method the value of Kx was taken as 1.0, and for both methods the value of Ky and Kt were taken as 1.0 and 0.8, respectively. of the RMI specifications permits the use of Kt equal to 0.8 provided that the connection details between the columns and the braces are such that the twisting of the column is prevented at the brace points. Second-order elastic analyses to determine the required strengths and elastic buckling analyses to compute the value of Kx were performed using the computer program CU-SRF, developed by the authors., where WEL, WNL, and WFE are the ultimate load carrying capacity per bay of the frame obtained by using the effective length method, notional load method, and the finite element method, respectively. The statistical summary of the correlations between design method and finite element results is summarized in Comparison between the effective length method and the notional load method indicates that the notional load method agrees better with the finite element results than the effective length method does. Results for the notional load method show that a reduction of 10% in member flexural stiffness resulted in a minimum conservatism of 10% in the calculated load carrying capacity. Additional reduction in member stiffness would lead to an increased conservatism in the calculated load carrying capacity. Reducing the stiffness by 20%, that is, after including an additional 10% reduction to account for the resistance factor for axial strength, would give satisfactory results for cold-formed steel frames. Additional reduction to account for the fact that the resistance factor for cold-formed steel columns is 0.85 less than 0.9 used in the AISC specification is not needed.A parametric study was also carried out to compare the effective length method and the notional load method for assessing the frame stability under real large horizontal forces. The differences between the two methods are not as significant in this load case as has been shown for the gravity load case. The reason for this is because the real horizontal force coming from the earthquake loads or the wind loads causes the storage rack to fail from column flexural strength rather than axial strength. The column flexural strength used in both the effective length method and the notional load method is the same.When the notional load method is used for an earthquake load design or wind load design, applying additional notional horizontal loads is usually not necessary if the real horizontal forces are much greater, making the additive notional horizontal loads insignificant. However, if the magnitude of the real horizontal forces is comparable with the required notional horizontal loads then that notional horizontal load must be applied as an additive load.A study comparing the effective length method and the notional load method for cold-formed steel industrial storage rack design was carried out. The finite element method, which considers both geometric and material nonlinearities, was used as the basis for evaluating the accuracy of these two design methods. Results showed that the effective length method is more conservative than the notional load method and that the notional load method agrees better with the finite element results than the effective length method does. The notional load approach would lead to more economical structures than the effective length approach. It is, therefore, recommended that the notional load method be considered as an alternative means for cold-formed steel industrial storage racks. In the notional load method, the notional load coefficient ξ is equal to 1/240 and the second-order elastic analysis is performed on a 20% reduced flexural stiffness model.An experimental study on the bond strength between reinforcement bars and concrete as a function of concrete cover, strength and corrosion levelThe effect of corrosion on the bond strength between reinforcement bars and concrete was studied in a series of experiments. An accelerated corrosion method was used to corrode the reinforcement bars embedded in concrete specimens. Pullout tests were performed to develop an empirical model for the ultimate bond strength by evaluating bond strengths in two different concrete mixes, three concrete cover depths and different mass losses of reinforcement bars after corrosion. Bond-slip relationships for the different corrosion levels were compared. It was found that the relationship between bond strength and concrete strength in uncorroded specimens differed from that of corroded specimens set in high-strength concrete because of brittleness in the corroded specimens, which caused a sudden loss of bond strength. The results revealed that specimens with higher concrete strength levels and corroded reinforcements showed a higher percentage of bond strength degradation due to concrete cracking during the pullout tests.The corrosion of reinforcement bars embedded in concrete is regarded as the most important factor in the deterioration of concrete structures and can lead to serious damage Although considerable research has been conducted to predict concrete bond strengths, contradictions are found in the literature. In particular, the degradation of bond strength due to corrosion and in concrete mixtures of different strength levels, taking into account the effect of differences in the concrete cover depths used, requires further investigation. Moreover, the available models (e.g., A total of 90 specimens were tested in the current study. The experimental program consisted of two phases. In the first phase, different corrosion levels were investigated by considering the permeability of the concrete matrix and concrete covers. In this phase, the test specimens were divided into two main groups based on the type of concrete mixture used, with w/c ratios of 0.40 or 0.75. Each main group was subdivided into three smaller groups corresponding to the three different concrete covers: c |
= 15 mm, c |
= 30 mm and c |
= 45 mm. The samples in each subgroup were then subjected to corrosion for different time periods using an accelerated corrosion method. The contact resistivity was recorded for each specimen at one minute intervals to monitor the corrosion level. The crack width (Wcr) of the specimens was visually observed and measured with an EL35-2505 crack detection microscope. In the second phase, pullout tests were applied for each specimen to predict the ultimate bond strength and bond-slip relationships for different corrosion levels and considering the effects of different concrete covers and concrete strength levels.Deformed steel bars 14 mm in diameter and 250 mm long were used for all specimens. Tensile tests were performed on six randomly selected reinforcement bars, and the mechanical properties of the reinforcement bars were determined as follows: the yield strength (fsy) was equal to 458 MPa, the rupture strength (fsu) was equal to 606 MPa, the yield strain (εsy) was equal to 0.00187, and the strain at the onset of strain hardening (εsh) was equal to 0.0299. Slag cement 42.5 was used with crushed limestone aggregate. shows the mixture proportions of concrete for the two different concrete strengths. In , the water contents given are the net water contents after considering moisture adjustments. No air-entraining or water-reducing admixtures were used. The prepared concrete mixes were cast in 150 mm cubes made of waterproof plywood. shows the setup for the 27 concrete specimens with a w/c ratio of 0.40 before casting the concrete.Before mixing the concrete, the reinforcement bars were carefully cleaned. The mass of the reinforcement bars in each specimen was recorded, and the bars were aligned and fastened to the moulds. A mould-releasing compound was applied to the inside surfaces of the specimen moulds. Compaction was performed with a table vibrator. After pouring and compacting the concrete, the specimen surface was smoothed with a steel trowel. The concrete specimens were kept in a curing room maintained at 22 °C (± 2 °C) and 90% relative humidity for 24 h. Demoulding and transportation of the specimens were conducted with great care to avoid any disturbance of the reinforcement bars. After demoulding, the specimens were cured in a water tank at 22 °C (± 2 °C) for 28 days.An electrochemical method was used to accelerate the corrosion of the reinforcement bars. The specimens were fully immersed in an aqueous solution of 3.5% sodium chloride by weight for four days before being subjected to the accelerated corrosion procedure. Before and during this procedure, the temperature of the water over each concrete specimen was held constant at 22 °C (± 2 °C). The shapes of specimens representing the three different concrete covers are shown in (a), deformed reinforcement bars 14 mm in diameter were placed in the cubes with different concrete covers. The embedded length was set at 50 mm to ensure bond failure. To prevent contact between the concrete and the reinforcement bars while maintaining the required concrete cover on the surface of the concrete specimen, 50 mm lengths of the reinforcement bars were placed inside polyvinyl chloride (PVC) pipes. The specimens were then fully immersed in a glass tank filled with water. An adjustable direct current supply providing 60 V constant potential at 0 to 5 A was used for the accelerated corrosion process. The direct current was applied to the main reinforcement bar embedded in the concrete, using the reinforcement bar as the anode and a copper plate as the cathode. The current was passed from the reinforcement bars to the copper plate placed inside of 5% salt solution (NaCl). The setup for the accelerated corrosion process is shown in The designed (theoretical) mass loss of the reinforcement bars due to corrosion was calculated according to Faraday's law using Eq. mass loss =t(s)×I(A)×55.847(g/mol for iron)2×96,487(coulomb)where t is the time, I is the current, 55.847 (g/mol) is the molar mass for iron and 96,487 (coulomb) is the Faraday's constant. The actual corrosion level or percentage mass loss of each specimen was calculated by Eq. where G0 is the initial weight of the reinforcement bars before corrosion and G1 is the weight of the reinforcement bars after the removal of the corrosion products.Pullout tests were performed for both corroded and uncorroded specimens based on ASTM C234-91a , this apparatus was especially designed and adapted to avoid any changes in bond strength during the pullout test. The results of the displacement and stress values of the designed apparatus at any point was negligible under an applied 25 kN load. None of the reinforcement bars reached the yield point during the pullout tests, and the maximum pullout forces were recorded to calculate the ultimate bond strength (τbu) according to Eq. where Pmax is the ultimate pullout load and D and L are the diameter and bond length of the reinforcement bars, respectively.The specimens were designated R1SP1 to R9SP3 for the concrete specimens having w/c ratios of 0.75 (see ) and R10SP1 to R18SP3 for the concrete specimens having a w/c ratio of 0.40 (see ). The specimen was named such as R1SP1, where R stands for different w/c ratio and cover depth, and SP stands for specimen number. The test results were analysed for the following parameters:Applied corrosion levels and the effects of concrete covers and strengths on corrosion levelsA comparison between theoretical and actual corrosion mass lossesThe effects of corrosion levels, concrete covers, crack width and concrete strengths on bond strengthBond-slip relationships at different corrosion levelsTo calculate the mass losses of the reinforcement bars, chemical cleaning was performed using hydrochloric acid to remove the corrosion products from the surface of the reinforcement bars, according to ASTM G1-03 shows selected corroded reinforcement bars after the pullout tests. show the gravimetric test results and comparisons between the theoretical and actual mass losses of specimens with w/c ratios of 0.75 and 0.40, respectively.(a–b) shows the effect of concrete cover depth on the corrosion level for samples with the same w/c ratios under the same applied corrosion time (t |
= 289 h). As shown here and in , the effect of concrete cover depth on the corrosion level was significant; increasing concrete cover depth decreased the corrosion level.Even though plastic pipes were used to prevent contact between the concrete and the reinforcement bars on the surface of the concrete specimens, local corrosion occurred for some specimens at the outside of the concrete. As shown in (a–b), corrosion of the reinforcement that occurred outside of the concrete led to higher mass loss for specimen R17SP1 than R8SP1, even though more mass loss would be expected for R8SP1 due to its higher w/c ratio (and presumed higher permeability). The differences in the corrosion levels obtained at a fixed corrosion time showed that more energy was needed to initiate corrosion in the concrete mixture with a w/c ratio of 0.40 than that with a w/c ratio of 0.75. (a–c) illustrates the effects of both concrete covers and w/c ratios on the corrosion levels for different applied corrosion times for selected specimens. Here, for the same applied corrosion time, the corrosion level decreased with increasing concrete cover depth. The reduced permeability of the concrete with the 0.40 w/c ratio likely reduced corrosion of the reinforcement bars, because increasing the w/c ratio increases capillary porosity (a–b), due to the premature cracking of R16SP3 and R8SP2 compared with R13SP1 and R8SP1, respectively, more corrosion was observed at an earlier stage due to the increased permeability of the concrete in the former. The recorded concrete resistivity values were used to estimate the time required for the growth of fine cracks (tcr). For instance, the resistivity of R8SP2 began to decrease at 70 h, whereas it decreased at 105 h for R8SP1.It should be noted that concrete resistivity and premature cracking had no influence on the bond strength. Therefore, the corrosion levels determined from the actual mass losses in the reinforcement bars and the recorded concrete crack widths were used to develop the proposed strength model., there were differences between the measured and theoretically estimated corrosion mass losses based on Faraday's law. Such differences have been reported previously in the literature (e.g., can be used to correlate the actual and theoretically estimated mass losses in future studies.Actual mass loss=0.703×theoretical mass loss –0.15 gr R2=0.94Although the concrete resistivity was not our main interest in this study, it was used to monitor the corrosion level. Under the same environmental conditions, the relationships between concrete resistivity and corrosion time for both the low and high strength concrete levels were determined, as shown in The resistivity results obtained by calculating the average current over 24 h from the current recorded at one-minute intervals are presented in . The results clearly show that reducing the w/c ratio of the concrete was more effective than increasing the concrete cover depth for improving the protection against chloride attack provided by the concrete. shows the resistivities of specimens R5SP2 and R8SP1 (w/c |
= 0.75 and c |
= 30 mm); although they had a 30 mm concrete cover, the measured resistivity for these concretes suggests lower protection against chloride attack than that of the concrete specimens with the lower w/c ratio and a 15 mm concrete cover depth (e.g., R16SP1). Thus, a 50% reduction in concrete cover depth with the lower w/c ratio provided 34% more resistivity than the higher w/c ratio. It was observed that the resistivity increased quickly during the initial period of the corrosion process; this continued for a long time, and then the resistivity dropped quickly beginning with the initiation of visible surface cracks. However, in the concrete specimens R7SP1 and R7SP3, the resistivity started to drop at the beginning of corrosion process, likely due to the closer contact surface of the reinforcement bars. Although the concrete specimens were cured under the same conditions, due to the complex concrete matrix, including many unknown variables, nonuniform corrosion behaviour was observed during the accelerated corrosion procedure. In this study, only two concrete specimens (i.e., R7SP2, R9SP1) displayed this nonuniform behaviour.The ultimate bond strengths of corroded and uncorroded specimens were calculated using the initial cross-sectional dimensions of the reinforcement bars. shows the relationship between concrete compressive strength and the maximum bond strength for different concrete covers in the case of uncorroded specimens. are the average bond strengths of 18 concrete specimens for each concrete strength level. As shown here, the bond strength depends on both the concrete compressive strength and the concrete cover depth. The results showed that up to a c/D ratio of 3.2, the bond strength increased with increasing concrete compressive strength, and no significant increase was recorded for the c/D ratios above 3.2. As shown in , the effect of concrete cover depth on bond strength was more significant in the concrete specimens of lower concrete strength level. For example, when the concrete cover depth was increased from 15 mm to 30 mm, the bond strength of the concrete with a w/c ratio of 0.75 was increased by 43.7%, whereas it increased 6% for the concrete specimens having a w/c ratio of 0.40. With further increases in concrete cover depth, differences in bond strength increases between the two concrete strengths were moderate. For example, when the concrete cover depth was increased from 15 mm to 45 mm, the bond strengths of concrete specimens with w/c ratios of 0.40 and 0.75 increased by 41% and 52%, respectively. As expected, for concrete covers of the same depth, bond strength increased as the w/c ratio was reduced. On reducing the w/c ratio from 0.75 to 0.40, bond strengths increased by 58% and 73% with concrete covers 30 mm and 45 mm thick, respectively. In the case of the uncorroded specimens, increasing the concrete compressive strength with a given concrete cover depth yielded a higher bond strength than increasing the concrete cover depth for a given concrete strength. The following equation was developed to predict the ultimate bond strength of uncorroded specimens using linear regression analysis, where the coefficient of correlation (R2) was 0.96.τbu= -2.7143+0.3621fc'+2.3296 (cD) (MPa)In contrast to previous models, the model developed in Eq. provides a way to predict the ultimate bond strength not only as a function of concrete strength but also as a function of the c/D ratio. show the bond strengths of corroded reinforcement bars with ratios of w/c |
= 0.75 and w/c |
= 0.40, respectively.(a), up to a corrosion level of 4%, bond strength increased and then decreased for a given corrosion level. However, increases in bond strength occurred at lower levels of corrosion with higher c/D ratios. For the low levels of corrosion, the average bond strength likely increased due to the increased roughness of the steel bar caused by the confined corrosion products (a), the bond strength at the lowest c/D ratio increased by approximately 41% at a corrosion level of 4%. For a higher c/D ratio (c/D |
= 2.143 or c |
= 30 mm), bond strength was increased by 51% at the lower corrosion level of 1.4% and then decreased nonlinearly beyond 1.4%. This can be explained by the frictional properties of the interface between the reinforcement bars and the concrete and by the crack width. The lugs of the reinforcement bars at the lowest c/D ratio were highly corroded, which decreased the transfer of stress from the reinforcement bars to the surrounding concrete. With respect to these results, it should be noted that the cracking of concrete increased with concrete depth. shows the effect of various c/D ratios on concrete cracking after the pullout tests., crack width increased with increasing c/D ratio at the lower corrosion levels when compared with lower c/D ratios at higher corrosion levels. For example, in , even though the corrosion level of R4SP2 was 54% more than that of R6SP3, the observed crack width was wider for R6SP3 after the pullout test. As shown in (a), for the same w/c ratio, an increase in the c/D ratio yielded a different behaviour than at the lower c/D ratio. The likely reason for this is that the cracks observed in the specimens with the higher c/D ratio caused a reduction in bond strengths at lower corrosion levels. After the accelerated corrosion process, the maximum recorded crack widths on the surfaces of R5SP2 and R6SP3 were 0.24 mm and 0.30 mm, respectively, whereas no cracks were observed on R4SP2 (Another important result of this study was the observation that with increasing concrete compressive strength, the degradation of bond strength at higher concrete strengths was more than that with lower-strength concrete (see (b)). The specimens with higher-strength concrete became more brittle than in the uncorroded condition where sudden loss of bond strength occurred. Chang shows the reductions in bond strengths for two concrete strength levels at almost the same corrosion levels. and given the bond-slip relationships in the next section, it is clear that the effect of corrosion is more dramatic in concrete with a higher strength level. The measured maximum crack widths on the surface of the concrete samples clearly support this interpretation. At the same corrosion levels, the maximum crack width of the high-strength concrete was greater than that in the low-strength concrete during the accelerated corrosion process. As shown in , the crack width of R15SP2 was 0.80 mm, whereas the crack width of R6SP3 was 0.30 mm (see (a–b), the experimental results of this study are compared with the previously developed models found in the literature. As shown in (b); the concrete strength in this study was 52.1 MPa. This comparison shows that the previous empirical bond strength equations underestimate or overestimate bond strengths for different conditions. Among them, the latest study by Chung et al. (a), the previous empirical models developed (e.g., ) based on the c/D ratios and the given limits of the corrosion levels.if c/D < 2 and 0≤CL≤0.8 for fc'=51MPa0≤CL≤4 for fc'=23MPaτbu= 0.40551fc'−0.25306(cD)+0.97926 CL (MPa) R2=0.98if c/D≥ 2 and0≤CL≤0.68 for fc'= 51 MPa0≤CL≤1.4 for fc'= 23 MPaτbu=e(0.01572fc'+0.22957(cD)+0.13946CL+1.75913) (MPa) R2=0.94For the descending branch of the bond strength curve in . If the corrosion levels are above the limits given by Eqs. can be used to calculate the bond strength for the descending branch. In other words, if 1 ≤ |
c/D |
≤ 3.2, then:τbu=e(0.01667fc'-1.06499Wcr+0.20658cD−0.12928CL+1.80139) (MPa) R2=0.96The experimentally obtained results were compared with those obtained with the proposed analytical models, as shown in (a–b), it is possible to predict the bond strength as a function of crack width and corrosion levels for different c/D ratios and concrete strengths in the light of developed bond strength models and their limitations. As shown in (a), whereas previous models show a decrease in bond strength with increasing corrosion level, the newly proposed model shows a more realistic behaviour reflecting the actual bond strength. Using the relations given by Eqs. , it is possible to monitor bond strength behaviour at both low and high corrosion levels with cracked or uncracked concrete conditions for different c/D ratios and concrete strengths.The bond-slip relationships for selected uncorroded specimens are shown in . Here, the slippage of the reinforcement bars decreases with increasing c/D ratio and concrete strength. The results presented in are in accord with the relationships obtained for bond strength. It can be seen in , the slip displacement at the maximum bond strength of R1SP1 was reduced by 35% due to the increased c/D ratio of R3SP2. For the same concrete cover depth (c |
= 30 mm), the recorded slip displacement at the maximum bond strength of R2SP2 was reduced by 20% with an increase in concrete compressive strength for R11SP2. Similarly, comparing the two concrete strength levels at a 45 mm cover depth, the slip displacement at maximum bond strength of R3SP2 was reduced by 19% from that of the higher-strength R12SP2. Thus, it can be said that percentage reduction in slip displacement with changing cover depths were almost the same among different strength levels for the uncorroded specimens.The bond-slip relationships for corroded specimens are given in (a–b). These relationships are important in verifying our findings regarding the bond strength degradation of higher-strength concrete due to corrosion. As shown in (a), when the c/D ratio was less than two (c |
= 15 mm), more slip displacement occurred at lower corrosion levels for higher-strength concrete due to the opening of longitudinal cracks during the pullout tests. As mentioned earlier, the occurrence of cracks during accelerated corrosion played an important role in the case of the corroded specimens. In (a), the measured maximum crack width on the surface of R16SP3 was 0.6 mm, whereas no cracks were observed on R4SP3 and R4SP2. In (a), the slip displacement of R1SP2 at the maximum bond strength was reduced by 48% due to the increased corrosion level of R4SP2 (4%). However, at the maximum bond strength of the higher-strength concrete (R16SP3), the slip displacement increased by 34% at the lower corrosion level of 3.4%. In (a), it can be seen that when the corrosion level was relatively a large value (e.g., R4SP1 and R16SP1), the effect of corrosion on slip displacement was almost the same for the different concrete strength levels due to more localised and extensive cracking of the concrete surface during the pullout test. As illustrated in (b), the bond-slip relationship showed different behaviours with increasing c/D ratio for the two different concrete strength levels. As shown in (b), the bond strength with the higher w/c ratio was greater than that with the lower w/c ratio at almost the same corrosion level (see R6SP3 and R15SP2). However, the results were different for slip displacement. When the slip displacements for the two concrete strength levels are compared for the same concrete cover depth (c |
= 30 mm), e.g., R5SP3 and R14SP3, it can be seen that less displacement occurred in the higher-strength concrete at an almost identical corrosion level. Similar results were also observed for several other specimens, such as R6SP3 and R15SP2, with a concrete cover of 45 mm. This can be explained by the increased resistance to the slippage of the reinforcement bars set in higher-strength concrete until the time it split. In (a–b), splitting of the concrete specimens along the corrosion cracks is shown. As shown in , at the almost same corrosion levels, wider cracks occurred for higher-strength concrete, which caused a loss of bond strength. Up to a given value of applied load, the higher-strength concrete provided less displacement, but for further increases in load it exhibited more brittle behaviour, with a sharp decrease occurring at the peak of the curve, as displayed by specimen R17SP3. A good relationship was obtained when the results were compared for different concrete cover depths. (b) shows that with a concrete cover depth of 30 mm and w/c |
= 0.75 (R5SP2), the value of slip displacement was almost the same at the maximum bond strength of R15SP2 (c = 45 mm and w/c |
= 0.40) at a higher corrosion level of 3.45%. The same behaviour was also observed with R6SP2 and R17SP3. In contrast with the previous samples (R5SP2, R15SP2), slip displacement was less for the higher-strength concrete (R17SP3) at the almost same corrosion level due to a lower cover depth.A series of tests was performed to develop models for the prediction of the ultimate bond strengths of corroded and uncorroded reinforced concrete specimens. Based on the test results, the following conclusions were drawn:Using the newly developed bond strength equations, based on the limitations specified before, it is possible to predict the bond strength as a function of corrosion levels, concrete strength levels, crack width and c/D ratios.Previously developed bond strength equations yielded significantly underestimated or overestimated results; the bond strength decreases rapidly in these models.In the case of the uncorroded specimens, bond strength increased with increasing concrete strength level and c/D ratio, where the c/D ratio of 3.2 and a w/c ratio of 0.40 yielded the highest ultimate bond strength in this study.In the case of the uncorroded specimens, bond strength increased up to a c/D ratio of 3.2, and no significant enhancement observed above this ratio.When the c/D ratio was increased in the uncorroded specimens, the percentage increase in ultimate bond strength of the lower-strength concrete was more than that of the higher-strength concrete. Indeed, this is a normal behaviour since the reinforcement bars used were deformed. The radial pressure from the lugs of the reinforcing bars causes high tensile stresses on concrete. The resistance of the specimen to these radial stresses depends on both the compressive strength and c/D ratio. Thus, as the c/D ratio increases for lower-strength level of concrete, resistance to these radial pressure will increase.In the case of the uncorroded specimens, increasing the concrete compressive strength for a given concrete cover depth yielded higher bond strength than increasing the concrete cover for a given concrete strength.At the same corrosion level, the measured maximum surface crack width of the higher-strength concrete was more than that of the lower-strength concrete. This was due to higher permeability of concrete specimens with higher w/c ratios of 0.75. Accelerated corrosion method showed that with a higher w/c ratio, the corrosion products were flowing throughout the concrete. Meanwhile, the colour of water in glass tank was changed to red. On the other hand, lower permeability of concrete (w/c |
= 0.40) maintained expansive corrosion products. These products increased the internal pressure which resulted in premature cracking of concrete due to volumetric expansion.The splitting of the higher-strength concrete was more dramatic than that of the lower-strength concrete at the same corrosion level since initial cracks have been already observed during accelerated corrosion method as explained above.An increase in crack width was observed with increasing c/D ratio at lower corrosion levels when compared with a lower c/D ratio at higher corrosion levels.Pull-out tests on corroded high-strength concrete specimens showed more brittle behaviour (sharp decrease in bond strength-slip curve occurred at the peak bond strength values as shown in (b)) compared with its uncorroded condition.The degradation of bond strength in the higher-strength concrete was more pronounced than in the lower-strength concrete. The underlying mechanism of this again was the cause of expansion of the corrosion products as explained above in conclusion number 7.In the case of the uncorroded specimens, the slippage of reinforcement bars decreased with increasing c/D ratio and concrete strength.In the case of the corroded specimens, the slip displacement was less for the lower-strength concrete at the lowest c/D ratio.When the c/D ratio was increased in the case of the corroded specimens, the slip displacement was less for the higher-strength concrete at the same corrosion level and c/D ratio.It is expected that the differences in bond strength and slip behaviour for corroded reinforcements with different concrete classes and c/D ratios highlighted in this study may provide guidance for the performance evaluation of existing reinforced concrete buildings, especially in the earthquake-prone regions. Although this study was based on pullout tests with prepared specimens and may therefore not reflect the actual behaviour of reinforced concrete sections under the influence of bending, where both concrete and the reinforcement are in tension, the results and findings of this study are general and may be used directly and as a guide for further studies.The following are the supplementary materials related to this article.Effect of cover-to-diameter ratio on concrete cracking.Splitting of concrete specimens along the corrosion cracks.Supplementary materials related to this article can be found online at Mechanical characteristics of well cement under cyclic loading and its influence on the integrity of shale gas wellboresThis paper focuses on the effect of repeated loading and unloading conditions on cement sheaths during staged fracturing. Triaxial compression and cyclic loading/unloading tests were designed for cement at room temperature and elevated temperatures of 95 °C and 130 °C. Based on the mechanical characteristics of cyclic loading and unloading, in the staged fracturing simulation process, numerical simulation of the cement sheath in both shallow and deep formations was performed. The following observations were made. (1) The elastic modulus of the cement was high at room temperature but lower under 95 °C and 130 °C. However, the deformation performance was greatly improved at higher temperatures, showing significant mechanical properties of an elastoplastic material. (2) In the cyclic loading test, the residual strain of the cement increased as the number of cycles at room temperature increased, and the unloading secant modulus was larger than that of the initial loading segment. The cement cumulative residual strain was larger under a higher temperature, and there was a significant “rebound hysteresis” in the unloading curve; the unloading secant modulus value also increased. The numerical simulation of staged fracturing produced the following conclusions. (1) The cement sheath in the shallow formation undergoing fracturing was at risk of circumferential tensile failure, and the severity of tensile failure increased with an increasing number of fracturing stages. (2) The cement sheath in the deep formation was at risk of plastic failure under compression, and the cement sheath gradually entered the plastic yield state as the number of fracturing stages increased.Shale gas reservoirs are low-porosity and low-permeability reservoirs. Horizontal drilling and staged fracturing technology are commonly used to achieve cost-effective development of such reservoirs Aiming at the sealing failure mechanism of cement sheaths, some scholars have conducted physical simulation experiments to directly observe and test the failure modes of wellbore sealing Theoretical and computational cement models have evolved from the original linear elastic model to the elastoplastic model. The effects of cement sheath shrinkage and pre/post-cementing operations are further considered Based on previous studies aiming at the repeated loading and unloading conditions inside casing during staged fracturing, this paper designed and carried out triaxial compression and triaxial cyclic loading/unloading tests that take temperature into consideration to reveal the mechanical properties of cement under different temperatures and cyclic loads. Based on the test results, a step-by-step finite element model of the casing-cement sheath-formation system was further established. The elastoplastic mechanical response of the cement sheath during the staged fracturing simulation was studied, and the potential failure mode of the cement sheath sealing was obtained. The study results could help to evaluate the integrity of cement sheaths under the influence of staged fracturing and improve cementing design quality.The purpose of this experiment was to reveal the mechanical properties of cement, especially its deformation law, under cyclic loading at different temperatures. However, some key parameters (such as the upper limit of the load) in the cyclic loading test needed to be set with reference to the compression test results. Therefore, two types of tests were designed in this experiment, i.e., a triaxial compression test and a triaxial cyclic loading test. The test temperatures were set to room temperature and elevated temperatures of 95 °C and 130 °C, and the triaxial confining pressure was set to 15 MPa. The temperature of a cement sheath at a reservoir depth of approximately 3000 m is 95 °C, which is approximately the temperature of the fracturing section of the current horizontal shale gas wells in China. The confining pressure of 15 MPa was mainly used to simulate the triaxial stress state of the cement.The formula of the well cement slurry was 100% G grade well cement +4% fluid loss agent +40% water. A total of 35% silicon powder was added to prevent strength degradation at 130 °C and maintain the solid/liquid ratio. The fluid loss agent was liquid and was added to ensure the stability of the cement slurry and to prevent settlement and delamination. The mixing procedure meets API standards. Casting molding of evenly mixed slurry was performed in a Φ50 mm × 120 mm cylindrical mold, and curing proceeded at 95 °C and 130 °C, 20 MPa for 72 h. After demolding and end face cutting and polishing, cylindrical samples of Φ50 mm × 100 mm were obtained for the triaxial compression and cyclic loading tests.At the same time, pouring molding of “8″-shaped cement samples was conducted; these samples were cured under the same conditions and used for testing the axial tensile strength of the cement. In addition, the following methods were used to test the interface bonding strength of the cement sheath: first, cast half an “8”-shaped cement sample, and cure it for 72 h; then, cast the other half of the “8”-shaped cement sample, and cure it for 72 h. The same cement tensile strength test method was used to test the interface tensile bonding strength of the cement. The mechanical testing of the cement was performed on the MTS815.03 testing machine at the Wuhan Institute of Rock and Soil Mechanics, Chinese Academy of Sciences.For the high-temperature test, the surfaces of the cement samples were wrapped with Teflon heat-shrinkable tubes instead of conventional rubber heat- shrinkable tubing to isolate the hydraulic oil. The heating coil was fixed on the outer surface of the triaxial chamber, and heat was transmitted to the cement through the triaxial chamber by the hydraulic oil. The heating process was controlled by a temperature controller. The test continued after the temperature reached and maintained the preset value for 1 h to ensure that the cement samples were heated evenly. In the triaxial compression test, axial displacement control was adopted during the loading process, and the loading rate was 0.12 mm/min. Once the sample reached the peak stress, loading was continued for a period to obtain a full stress-strain curve.The triaxial compression stress-strain curves at different temperatures and the morphology of the samples after testing are shown in . At room temperature, the initial stress-strain curve increased linearly; the slope of the straight line (i.e., the elastic modulus) was 8.37 GPa, and the Poisson’s ratio was 0.191. After the deviatoric stress exceeded approximately 41.4 MPa, the loading curve gradually deviated from the original linear state, and the cement entered the nonlinear deformation stage. The loading curve then gradually increased to a peak, with a peak stress of 56.8 MPa. After reaching the peak, it dropped quickly and gradually stabilized, and the deviatoric stress eventually remained at approximately 44.2 MPa. After the test, an oblique macroscopic fracture caused by shear failure of the sample under triaxial compression was observed on the sample surface.Under the 95 °C environment, the stress-strain curve also showed a straight linear increase in the initial stage; the slope of the straight line (i.e., the elastic modulus) was 7.41 GPa, and Poisson’s ratio was 0.105. After the deviatoric stress reached approximately 28.9 MPa, the loading curve began to deviate from a straight line, and this critical value was lower than the corresponding test result at room temperature. The subsequent parts of the stress-strain curves showed a significant strain hardening phenomenon; that is, as the axial strain increased, the bearing capacity of the cement continued to increase. The axial strain developed to over 4.0%, and the deviatoric stress reached approximately 66.4 MPa; however, there was still no macroscopic crack visible at the sample surface, and the sample height was significantly shortened. Under 130 °C, the same characteristics as those under 90 °C were exhibited, indicating a greater plastic deformation ability.The triaxial compression tests at room temperature and high temperature suggested that the mechanical properties of the cement showed a great difference under different temperature conditions: At room temperature, the elastic modulus of the cement was relatively high, with obvious brittle fracture characteristics. At high temperature, the elastic modulus of the cement was somewhat lower; however, the deformation properties of the cement were greatly improved.The mechanical properties of this cement are compared with published data to confirm the measurements. It should be noted that the formulation of the cement slurry system, cement curing conditions, test temperature and pressure conditions vary among the studies in the literature. A comparison of the data shows that the mechanical parameters of the cement given in this paper are within the acceptable range (In the cyclic load test, the loading and unloading rates were set at 0.5 kN/s, and the upper limit of cyclic loading was set at approximately 70% of the reference stress. The reference stress at room temperature was the peak deviatoric stress of the triaxial stress-strain curve. Since no obvious peak was observed on the triaxial stress-strain curve at high temperature, the corresponding deviatoric stress at the axial strain of 2.0% was selected as the reference stress. Based on the cement stress-strain curve at high temperature, the cement performance after 2% axial strain showed slow strain-hardening characteristics; that is, the strain increased as the stress increased slowly. The lower limit of the load was set at a relatively small stress value, and the number of fracturing stages was generally not more than 20. The number of loading/unloading cycles was set to 20. The parameters set in the cyclic loading testing is shown in The cyclic loading stress-strain curve measured at room temperature is shown in (a). For comparative analysis, the triaxial compression stress-strain curve at room temperature is also drawn in the same coordinate system. In the initial loading stage of the cyclic loading test, the stress-strain curve basically coincided with the triaxial test curve at room temperature; however, the curve in the unloading phase no longer coincided with the curve in the loading phase, and there was a significant hysteresis, indicating that an unrecoverable residual deformation was generated inside the sample. In particular, after the first loading and unloading, the residual strain was large. With the increasing number of cycles, the “hysteresis loop” formed by the loading curve and the unloading curve continuously moved to the right; additional strain accumulated in each cycle, and the residual deformation continuously increased. Cement has its own inherent defect properties. Cement contains a large number of pores and microcracks before being subjected to an external load. Under the action of a load, stress concentration occurs at the defects and crack tips. When the stress of cement exceeds a certain proportion of its strength, the internal the pore structure collapses, the microcracks expand and viscous flow occurs, which will result in plastic deformation and unrecoverable residual strain after unloading. Under repeated cyclic loading, the damage at the crack tips increases, the cracks tend to grow, the plastic deformation increases, and the cumulative residual strain increases gradually after unloading. Due to the narrow width and dense arrangement of the “hysteresis loop”, the curve of one loading/unloading cycle was taken for analysis, as shown in (b). The process from the initial loading point A to the upper limit point B is called the loading phase, which has a an approximately linear loading curve; the process from the upper limit point B to the unloading endpoint C is called the unloading phase, and the curve of the unloading section shows a nonlinear change.To accurately calculate the residual strain after each cycle, the elastic strain at the stress level should be deducted on the basis of the strain corresponding to the lower limit of the stress cycle. The intersection point D of the tangent and the abscissa at point C in (b) is the residual strain, and the detailed calculation method is as follows:where εDi refers to the residual strain after the ith cycle, %; εCi is the strain corresponding to the unloading endpoint C, %; σCi is the stress corresponding to the unloading endpoint C, MPa; and ECi is the slope of the tangent at the unloading endpoint C.The residual strain was calculated and analyzed after each cyclic loading. The residual strain increased with increasing number of cycles. After the first cycle of loading and unloading, the residual strain was 0.1282%; after 20 cycles of loading and unloading, the residual strain reached 0.4253%, 3.3 times that of the first cycle. The evolution of the residual strain can be fitted by the following linear formula:where Di refers to the residual strain after the ith cycle, %, and i is the number of cycles, from 1 to 20. The residual strain and fitting curve after each loading/unloading are shown in The variation law of the unloading secant modulus is also a key parameter to be studied. It represents the evolution of the overall elastic properties of cement, and the unloading secant modulus is calculated by the following formula:where EBDi refers to the unloading secant modulus of the ith cycle, GPa; σBi is the upper limit of the cyclic load stress, MPa; εBi is the strain corresponding to the upper limit of the cyclic load, %; and εDi is the residual strain after cycling, %.The variation law of the unloading secant modulus (varying in the range of 8.4–9.6 GPa) with the number of cycles is shown in . During the first 10 cycles, the unloading secant modulus showed a rapid decline but stabilized at approximately 8.5 GPa during the last 10 cycles. Relative to the secant modulus of 7.34 GPa during the initial loading (the slope of the line connecting the peak point of the initial load and the coordinate origin), the unloading secant modulus was generally greater, indirectly indicating the continuous accumulation of residual strain in the sample.Compared with the test results at room temperature, the cyclic loading/unloading stress-strain curve at 95 °C presented a different morphology, as shown in (a), and the hysteresis in the loading-unloading process was more obvious. For example, the analysis of the third loading cycle ((b)) illustrated that the loading and unloading curve can be divided into four stages: initial stage of loading (section AB), with a small sample deformation and a rapid increase in stress; later stage of loading (section BC), with a relatively slow increase in stress and relatively rapid sample deformation; initial stage of unloading (section CD), with a rapidly decreasing stress, the deformation recovery of the sample showed obvious lag, and no obvious rebound was observed; and later stage of unloading (section DE), with a rapidly decreasing axial strain of the sample with the decrease in stress, indicating a significant rebound. At the same time, the hysteresis loops became denser in stress-strain space as the number of cycles increased.The calculation method of residual strain is the same as that at room temperature. The detailed calculation formula is as follows:where εFi is the residual strain after the ith cycle, %; εEi is the strain corresponding to the unloading endpoint E, %; σEi is the stress corresponding to the unloading endpoint E, MPa; and EEi is the tangent slope at the unloading endpoint E.The evolution law of the residual strain with the number of cycles is shown in . In general, the residual strain showed a tendency of a sharp increase first and slow increase later. The law of sharp increase in the first 8 loading/unloading cycles and subsequent slowdown in growth rate was different from the approximate linear increase at room temperature. Another noteworthy aspect was that after the first cyclic loading, the residual strain of the sample reached 0.5120% (exceeded the residual strain of 0.4253% after 20 cycles at room temperature), and the residual strain after 20 cycles was 1.0125%, which is approximately twice that of the 1st cycle. Therefore, at high temperature, a single loading and unloading cycle can produce a considerable degree of residual deformation, but the cumulative residual deformation after repeated cycles will be greater. The variation law of residual strain can be fitted by a polynomial, as follows:where εFi is the residual strain after the ith cycle, %; i is the number of cycles, from 1 to 20; and the coefficients A0, A1, A2, A3, A4, and A5 are 0.3353, 0.1990, −0.0279, 0.0021, −7.45 × 10−5, and 1.06 × 10−6, respectively.The unloading secant modulus was calculated by the following formula:where ECFi is the unloading secant modulus after the ith cycle, GPa; σCi is the upper limit stress of the cyclic load, MPa; εCi is the strain corresponding to the upper limit stress of the cyclic load, %; and εFi is the residual strain after cycling, %.The variation trend of the unloading secant modulus at 95 °C was similar to that at room temperature, which showed a rapid decrease in the first half of the test and nearly stabilized in the second half of the test, fluctuating in a small range, as shown in . One of the notable features at room temperature was that the value of the unloading secant modulus was generally high. The unloading secant modulus was approximately 43 GPa after the 1st cycle and then ranged from 20−30 GPa because the residual strain after each cycle was large at high temperature and the sample rebound was small.The cyclic loading/unloading stress-strain curve at 130C is shown in . The “hysteresis loop” had a small width and a slender shape, which was different from that at 95 °C. As the number of cycles increased, the hysteresis loops became denser, indicating that the increase in plastic deformation accumulation slowed.The axial tensile method was used to test the tensile strength and interfacial bonding strength of the cement, the results of which are shown in and are more accurate than those of the easy Brazilian splitting test. These properties can correctly give the tensile and interfacial bonding properties of cement sheaths in wellbores. This method requires special “8″-shaped molds. The axial tensile strength test of the cement and its destruction are shown in , and the calculated tensile strength of the cement was 3.56 MPa.The forming process of the sample for the cement tensile bond strength test is shown in , and the calculated tensile bond strength of the cement was 0.89 MPa.The typical casing design of Fuling shale gas wells in China is a three-section casing design, i.e., from the outside to the inside, the surface casing, the intermediate casing, the production casing and the corresponding cement sheaths. The casing sizes are shown in . ABAQUS finite element software was used to simulate the elastoplastic mechanical response of the casing-cement sheath-formation system. Since the axial dimension of the wellbore was much larger than those in the other two directions, the cross-sectional size and shape can be basically considered constant along the length of the axis. Under the fracturing load, the main stress generated is perpendicular to the longitudinal axis, and the computing model was simplified to two dimensions. The casing programs are different in shallow and deep formations; therefore, finite element calculation models are established for both cases. There are three sections of casing in the shallow strata, namely, the production casing, technical casing, and surface casing, in sequence from inside to outside. Correspondingly, there are three annuluses corresponding to the three layers of cement sheath, namely, cement sheath A, cement sheath B and cement sheath C. The structure of the shale gas drilling well is shown in . The specific dimensions of the casing are shown in , the wellbore ID is 410 mm, and the finite element calculation model is shown in (a). In deep formations, only the production casing exists, and only one cement sheath is outside the casing. The casing size is the same as that of the production casing in , the wellbore ID is 270 mm, and the finite element calculation model is shown in (b). The dimensions of the above two calculation models are all 1000 mm × 1000 mm. Gray et al. (a), and the deep formation model is shown in (b). “Hard Contact” is a contact relationship (face to face, edge and edge) in ABAQUS. Under this contact relationship, the outside of the casing and the inside of the cement sheath are in contact and can transmit normal compressive stress but cannot transmit normal tensile stress. “Hard Contact” is set between the casing and cement sheath, and normal stress can be transmitted between them. Once the normal tensile stress exceeds the interface bonding strength, the casing and cement sheath will separate.In terms of material mechanical parameters, both the casing and formation were assigned linear elastic constitutive relationships with elastic moduli and Poisson’s ratios of 210 GPa and 0.30 and 25 GPa and 0.20, respectively. The cement sheath was assigned an elastoplastic constitutive relation, and the elastoplastic stress-strain relationship changed nonlinearly according to the laboratory-measured curve rather than the simple idealized elastoplasticity curve to accurately reflect the stress state of the cement sheath.At room temperature, the shallow formation near the wellhead was selected for analysis, and the geostress was taken as 0; at this depth, the cement sheath exhibited the maximum circumferential tensile stress, which is the most dangerous state. The corresponding burial depth of 95 °C was 3000 m, and the geostress was set to 70 MPa.The alternating rise and drop of internal casing pressure lead to repeated radial loading and unloading of the cement sheath. According to the laboratory test results, the integral stiffness of the cement would increase slightly after loading/unloading. The reason that the elastic modulus gradually increased with the number of cycles was because residual strain was incurred in the cement after each cycle; the cement was pressed more compactly, its deformation ability was lowered, and the elastic modulus was increased. The porosity and pore size distribution of the cement after cyclic loading were also studied by nuclear magnetic resonance (NMR). It was found that the porosity of cement decreased after the test, and the number of large pores decreased while the number of small pores increased. Under the load, the stress concentrated around the pores, which resulted in the collapse of pore walls and a reduction in the number of large pores. Therefore, as the number of loadings increased, the residual strain accumulated, the cement became denser, and the elastic modulus increased. Compared with that at room temperature, the increase in integral stiffness was more significant. To simulate this trend and simplify the calculation, the elastic modulus of the cement sheath was set to linearly increase with the increasing number of fracturing stages. The values of the starting point and endpoint in numerical calculation were selected from the test data. As shown in , the elastic modulus was set to increase at a rate of 0.05 GPa/time at room temperature, with an initial value of 8.5 GPa and a final value of 9.5 GPa. The elastic modulus was changed from 7.5 GPa to 27.5 GPa at 95 °C, and the increase rate was 1 GPa/time. The elastic modulus was changed from 4.5 GPa to 14.5 GPa at 130 °C, and the increase rate was 0.5 GPa/time. Here, the main purpose was to investigate the mechanical response of the cement sheath to the continuous improvement of cement stiffness; therefore, the elastic modulus set in the numerical simulation did not strictly follow the laboratory test results but mainly referred to the final stiffness of the cement after the cycles of loading/unloading.Initial phase: set the symmetrical boundary conditions of the model.Geostress balancing phase: apply geostress in both the X and Y directions, and then balance the geostress to obtain the initial geostress field with zero strain. At the same time, impose a fixed boundary constraint on both sides of the model.Wellbore drilling phase: remove the unit collection of the wellbore section, and apply the cement slurry hydrostatic pressure of 1.85 g/cm3 on the wellbore.Cementing cement sheath forming phase: add unit collection of cement sheath and casing into the model, set the contact relation between the casing and cement sheath, remove the cement slurry hydrostatic pressure applied previously, and apply a fracturing fluid hydrostatic pressure of 1.0 g/cm3.Fracturing phase: during fracturing, the maximum applied pressure is 80 MPa, and the number of fracturing stages is set to 20. The elastic modulus is set to change dynamically with the number of fracturing stages by using a function of field variables.Three forms of cement sheath sealing failure are considered here: compressive failure, circumferential tensile failure and interface microannulus failure.In deep formation, cement is usually under triaxial compression stress. Since equivalent stress combines the effects of the triaxial principal stresses, it is selected as the reference to judge whether compressive plastic failure occurs. The criterion of compressive damage is as follows:where σe is the equivalent stress, MPa; σs is the yield stress, referring to the stress where the stress-strain curve deviates from the initial linear segment, and is set to 30 MPa; and σr, σɵ, and σz are the radial, circumferential and axial principal stresses, MPa, respectively.Once the circumferential stress of the cement sheath exceeds the tensile strength of the cement, the cement will experience circumferential tensile damage, and the tensile failure criterion is as follows:where σɵ is the circumferential principal stress, MPa, and is the axial tensile strength of the cement, which is set at 3.56 MPa according to the laboratory test results.When the interface normal stress of the cement sheath equals the compressive stress, the interfaces will contact each other without forming a microannulus; when the interface normal stress is greater than the tensile strength of the interface, the interfaces will be separated from each other, and a microannulus will be formed. The criterion for the formation of such a microannulus is as follows:where σN is the interface normal stress, MPa, and σB is the interface tensile bonding strength, MPa. illustrates that cement sheath A has a much higher stress level than cement sheaths B and C and is most prone to sealing failure. Therefore, the focus is placed on the analysis of the stress distribution characteristics of cement sheath A. During the first fracturing step, with a maximum fracturing pressure of 80 MPa, the stresses in all directions of the cement sheath are shown in . Along the cement sheath thickness, the stresses in all directions gradually decreased from the inside to the outside, and the maximum stress occurred at the inside of the cement sheath. The sheath was under pressure in both the radial and axial directions, varying from 14.1 to 8.3 MPa; a smaller axial stress change occurred along the thickness direction of the cement sheath, and the stress level was approximately 1.1 MPa. The circumferential tensile stress increased to a maximum of 6.6 MPa, exceeding the tensile strength of the cement sheath (3.56 MPa), so the cement sheath would experience circumferential tensile damage. The equivalent stress of the cement sheath varied from 18.2 to 8.3 MPa, which is smaller than the yield stress of 30 MPa. Therefore, the cement sheath would not experience compressive plastic damage.Further analysis was performed on the evolution of the cement sheath circumferential stress under different fracturing pressures during initial fracturing, as shown in . The circumferential stress increased gradually with increasing fracturing pressure. The circumferential stress was distributed unevenly in the radial direction of the cement sheath and decreased gradually along the radial direction. At a fracturing pressure of 40 MPa or below, the maximum circumferential tensile stress of cement sheath A did not exceed the tensile strength of the cement sheath (3.56 MPa), and the cement sheath maintained its integrity. At the fracturing pressure of 60 MPa, the tensile stress exceeded its tensile strength at part of the inner side of cement sheath A (approximately 10 mm in thickness), and tensile failure occurred. As the fracturing pressure continued to rise, the magnitude of the circumferential tensile stress and the areas in which the tensile strength was exceeded were constantly increasing.The above analysis suggests that under a high fracturing load, the cement sheath in a shallow formation is exposed to the risk of complete failure caused by circumferential tensile failure. Under a fracturing pressure of 40 MPa, the circumferential stress of cement sheath A during the first fracturing step did not exceed its tensile strength. With the increase in fracturing times, the circumferential tensile stresses at the innermost and outermost parts of cement sheath A changed, as shown in . This shows that the circumferential tensile stress increased with the increasing number of fractures. When the number of fractures increased to 14, the maximum tensile stress generated at the inner side of the cement sheath exceeded the tensile strength, and tensile failure started to occur. The area of tensile damage also gradually increased with the increasing number of fractures, which caused further expansion of the radial cracks in the cement sheath. Therefore, the impact of cyclic loads during staged fracturing on the integrity of the cement sheath can be confirmed.At 3000 m burial depth, the cement sheath withstands the stress from the far field, where the stress state is different from that of the shallow formation. The stress states of the cement sheath under 0 MPa and 80 MPa surface pressures are shown in . Prior to the fracturing job, there was a 30 MPa hydrostatic pressure inside the casing. Meanwhile, the cement sheath was in a triaxial compressive state with radial stress varying from 32.4 MPa to 25.3 MPa and decreasing from the inside to the outside. The circumferential and axial stresses varied from approximately 5 MPa to 15 MPa and were generally lower than the radial stress. The maximum value of equivalent stress was 25.4 MPa at the inner side of the cement sheath and was lower than the 30 MPa yield stress. The whole cement sheath was still in an elastic state with no plastic failure. When the fracturing pressure reached the peak value of 80 MPa, the radial and axial stresses of the cement sheath increased, while the circumferential stress decreased. The triaxial stress underwent the largest variation at the inner side of the cement sheath, i.e., radial stress increased by 40.0% from 32.4 to 45.4 MPa, axial stress increased by 54.0% from 6.1 to 9.4 MPa, and circumferential stress decreased by 57.0% from 8.1 to 3.5 MPa. The triaxial stress changes caused by fracturing pressure caused the equivalent stress of the cement sheath to be 39.3–23.1 MPa, which surpassed the 30 MPa yield stress at certain areas of the cement sheath inner wall, which could lead to a risk of compressive plastic failure.During fracturing, the equivalent stress of the cement sheath increased continuously as the fracturing stage number increased, but the increasing rate gradually decreased. The maximum equivalent stress at the 20th stage of fracturing was 42.6 MPa, and compared with the 39.3 MPa maximum equivalent stress at the first stage, it increased by 8.4%. Although the maximum equivalent stress increased at a low rate, the equivalent stress at the outside of the cement sheath increased at a high rate. At the 12th stage of fracturing, the cement sheath whole equivalent stress exceeded 30 MPa, indicating that various degrees of plastic deformations occurred at each part of the cement sheath, as shown in . During fracturing, the cement sheath was exposed to the compressive plastic failure risk, and this risk became increasingly severe with the increasing number of fracturing stages. show the distribution law of the plastic strain and the contour plot of the plastic strain in the cement sheath under various fracturing stages, respectively. The evolution trend of the plastic strain is consistent with the equivalent stress.The numerical calculations at 130 °C are similar to those at 95 °C, and there are very few shale gas wells in China reaching 130 °C; thus, numerical calculations at 130 °C have not been performed. between the results of this paper and those from the literature; the previous cyclic load studies mainly used a scaled model of a casing-cement sheath structure in the laboratory. The failure mode of the cement sheath is mainly radial cracking, indicating that tensile stress exceeds the cement tensile strength, which is consistent with the conclusion of the shallow strata but is different than that of the deep strata in this paper.The numerical calculation in section 2 showed that during the entire fracturing process, the compressed part of the cement sheath in the shallow formation was maintained in the elastic state, with no residual strain generated, so there was no microannulus formed by interface bonding failure. In the deep formation, although an obvious plastic deformation occurred within the entire cement sheath, due to the squeezing effect of the far-field stress, the normal stresses at the 1st and 2nd interfaces of the cement sheaths were always compressive, and no microannulus formed at the interface. This result was calculated based only on the current tests and input data, and it did not indicate that there was no sealing failure of the microannulus caused by interface bonding failure. In a deep formation, once the internal casing pressure decreases to a certain level and macrovolume shrinkage of the cement sheath occurs after staged fracturing, it may be exposed to the risk of the formation of a microannulus.In this paper, triaxial compression and cyclic loading tests were performed on well cement at room temperature and high temperature. The elastoplastic stress response from the numerical calculations of casing-cement sheath-formation in shallow and deep formations during staged fracturing simulation were determined. The conclusions are as follows:The mechanical properties of the cement at room temperature were different from those at high temperature. The cement exhibited a relatively high elastic modulus, an obvious brittle property and a low deformation capacity at room temperature. At high temperature, the elastic modulus of the cement was lower, but the deformation performance was greatly improved, showing significant elastoplastic properties.The cyclic loading/unloading tests suggested that at room temperature, the residual strain of the cement increased with increasing number of cycles, and the unloading secant modulus was larger than that in the initial loading section. At high temperature, the cumulative residual strain of the cement increased, the unloading curve exhibited a significant “rebound lag”, and the unloading secant modulus also increased.During fracturing, the cement sheath had a tensile failure risk in the shallow formation, and the severity of the tensile damage increased with increasing fracturing stages. The cement sheath in the deep formation was exposed to the risk of compressive plastic failure, and as the number of fracturing stages increased, the cement sheath gradually entered into the plastic yielding state.At high temperature, the mechanical and deformation characteristics of well cement were quite different from those at room temperature. To ensure long-term integrity of a cement sheath in deep oil and gas wells, the mechanical properties of the cement at high temperature should be fully considered.3D printed architected hollow sphere foams with low-frequency phononic band gapsWe experimentally and numerically investigate elastic wave propagation in a class of lightweight architected materials composed of hollow spheres and binders. Elastic wave transmission tests demonstrate the existence of vibration mitigation capability in the proposed architected foams, which is validated against the numerically predicted phononic band gap. We further describe that the phononic band gap properties can be significantly altered through changing hollow sphere thickness and binder size in the architected foams. Importantly, our results indicate that by increasing the stiffness contrast between hollow spheres and binders, the phononic band gaps are broadened and shifted toward a low-frequency range. At the threshold stiffness contrast of 50, the proposed architected foam requires only a volume fraction of 10.8% while exhibiting an omnidirectional band gap size exceeding 130%. The proposed design paradigm and physical mechanisms are robust and applicable to architected foams with other topologies, thus providing new opportunities to design phononic metamaterials for low-frequency vibration control.Noise and vibration are becoming an increasingly hazardous form of pollution as cities become busier and technology advances. Sources of noise and vibration pollution can be airborne or structural-borne and include construction, traffic, and wind. These undesired noises and vibration not only have negative impacts on the physical and social health by impacting sleep patterns, hearing abilities, and concentration [], but also deteriorate the structural integrity of civil infrastructures [] and the functionality of high-precision industrial equipment []. To control noise and vibration pollution, both active and passive control methods have been developed in the past few decades. Active noise control works best for mechanical waves that travel primarily in the longitudinal direction through gas mediums, such as air. In this method, a second wave is generated to interactive with the wave source and they ultimately cancel each other out. Though the operating frequency range is limited, the perfect control effect makes this approach have many applications such as noise-canceling headphones, active mufflers, and anti-snoring devices []. Passive control involves the passing of waves through a soft or hard material so that the mechanical waves will either be dampened or reflected, respectively. Because of the broad vibration control frequency range, the passive approach has been widely employed in pumps, motors, isolation of civil engineering structures, and sensitive laboratory equipment []. While each method is effective in its own way, these control methods can contribute negatively to the cost or mass of a system and are not appropriate in all applications []. Many newly-developed composites such as carbon fiber-reinforced composites exhibit increased strength properties at the expense of noise and vibration control capabilities compared to more traditional soft bulk materials used in passive control approach []. For this reason, the architectures and mechanical properties of composite materials are being analyzed and optimized to exhibit enhanced strength and damping properties [Moving towards architected materials, which are rationally designed multiscale material systems, exhibit novel functionalities and unique properties that cannot be readily achieved in natural bulk solids []. In addition to the unusual mechanical and physical properties, architected materials have been designed and optimized for novel elastodynamic wave phenomena. One example of such architected materials is phononic metamaterial, which consists of periodically topological structures and materials dispersions and has the ability to manipulate the propagation of mechanical waves []. The periodic structures of phononic crystals produce omnidirectional band gaps-ranges of frequencies where elastic waves cannot propagate. In these band gaps, mechanical waves decay exponentially and are thus mitigated. Phononic band gaps are formed through two main mechanisms, Bragg scattering and local resonance. Band gaps induced by Bragg scattering are dependent on order and the symmetry of the lattice and can be modified with a stronger or weaker mismatch in the mechanical impedance of a composite’s materials []. Band gaps form by way of local resonance due to the excitation of resonant frequencies; these band gaps are independent of periodicity []. Phononic crystals with Bragg-type band gaps are limited, however, in their application because they do not attenuate vibration at lower frequencies without requiring large geometries. Inducing these lower frequency band gaps is being achieved through the production of phononic metamaterials that exploit locally resonant masses to absorb energy []. Despite these advances, the application of phononic metamaterials is largely hindered by their limited operation frequency ranges and inferior mechanical properties. Designing lightweight phononic metamaterials with low-frequency vibration mitigation capability is still challenging.Here we choose architected hollow sphere foams (AHSFs) as the model system to address the above challenge. In the past decades, hollow sphere foams (HSFs) have been investigated intensively, because of their exceptional mechanical, thermal, and acoustic properties. For example, earlier finite element simulations have revealed that architected hollow sphere metallic foams with a face-centered cubic lattice symmetry exhibit the highest moduli and yield strength when compared with foams with other lattice symmetries []. In addition, anisotropic feature and considerable fatigue resistance of HSFs have been reported []. Under large deformation, HSFs show good energy absorption characteristic, which is controlled by loading rate, geometric parameters, and topologies []. These prominent mechanical properties make hollow sphere foams ideal candidate for automotive applications where lightweight design and enhanced mechanical properties are simultaneously pursued. In addition to these mechanical properties, theoretical models along with finite elements simulations indicate that architected hollow sphere foams can be designed with low thermal conductivity by tailoring the packing fraction, shell, and binder geometry []. In parallel, it has been demonstrated that both random and rationally designed HSFs can manipulate mechanical wave propagation. For instance, perforated HSFs with wide acoustic attenuation ranges show great promise to serve as acoustic liners for airplane engines []. Our recent numerical work further demonstrates that perforated AHSFs can simultaneously control sound and elastic wave propagation []. In addition to these multifunctionalities, HSFs offer manufacturing flexibility in material selection and can be assembled into relatively defect-free periodic structures [], making them ideal for use in multiple fields of application. Because of the multifunctionalities, versatile design space, and manufacturing flexibility, AHSFs offer an ideal model system to investigate how to achieve lightweight phononic metamaterials with low-frequency vibration mitigation.In this work, we designed and fabricated AHSFs composed of hollow spheres connected by binders with a body-centered-cubic (BCC) lattice symmetry ((a)). The unit cell for Bloch wave propagation analysis and detailed geometric description of each component can be found in (b) and (c). We demonstrate both experimentally and numerically the existence of phononic band gaps in the proposed AHSFs. Numerical simulations indicate that the band gap properties are controlled by the geometric features of the hollow sphere and binder. Remarkably, phononic band gap can be altered to a low-frequency range by tailoring the stiffness contrast between the hollow sphere and binder. In addition to the AHSF with a BCC lattice symmetry, we will show that the elastic wave phenomena persist in AHSFs with other topologies.We start by focusing on the existence of phononic band gaps in the proposed AHSFs through a combined experimental and numerical effort. For our simulations and experiment, the lattice constant of the unit cell is 3 cm and the volume fraction of the sample is 10.8%. The lattice constant is determined by the operating frequency range of the dynamic signal analyzer and the maximum build volume of our 3D printer. To avoid unsintered powder to be encapsulated inside the hollow spheres, AHSF model composed of 6 × 3 × 3 unit cells was cut into six equivalent layers and fabricated by using an HP Jet Fusion 3D 4200 printer ((a)). Then, the six layers were glued together using glue gel, and the assembled sample was kept at room temperature for seven days to allow for the saturation of the curing. The mechanical properties of the constitutive material Nylon PA12 were measured by following ASTM D695. The basic properties of Nylon PA12 are characterized by Young’s modulus E = 1.312 GPa, Poisson’s ratio ν = 0.33, and density of ρ = 979 kg m−3.To evaluate the vibration mitigation capability, elastic wave transmission tests were performed on the 3D printed AHSF, as shown in the experimental setup ((b)). An impact hammer with a hard tip (PCB Piezotronics, Model 086E80) was used to provide impulse forces exerted at the input end of the sample. To simulate the longitudinal polarization of the incident waves, we hit the left surface center of the sample along x-direction. The hammer can generate an impulse force with the frequency range up to 15 kHz that is sufficient to cover the frequency range of interest. To capture the longitudinally polarized wave signal transmitted from the input excitation, a piezoelectric accelerometer was attached to the right surface center of the sample using adhesive wax. To ensure that the hammer can hit the sample center and accelerometer can be attached well to the sample, we added two 3D printed patches (3 × 3 × 0.1 cm) on the left and right surfaces, respectively. A dynamic signal analyzer (Crystal Instrument corporation, COCO-80) was adopted to record both the input force and output acceleration. (c) shows the measured wave transmission spectrum, where a strong attenuation zone between 8.6 and 14.1 kHz can be observed.To confirm the experimentally observed attenuation zone, we performed numerical simulations on the single unit cell and the finite size AHSF with 6 × 1×1 unit cells using a commercial finite element package. Briefly, the phononic dispersion relation is constructed by performing eigenfrequency analyses to a unit cell, where Floquet-Bloch periodic boundary conditions are applied. The unit cell is discretized using 4-node tetrahedral elements, which are one-tenth of the minimum wavelength. The dynamic response of the proposed AHSF under elastic wave excitations is calculated by performing frequency domain analyses. Perfectly matched layers (PMLs) are applied at the two ends of the homogeneous parts to prevent reflections by scattering waves from the domain boundaries. More computational details on the eigenfrequency and frequency domain analyses can be found in our previous work [(d) and (e) report the simulated phononic dispersion relation and transmission spectrum, respectively. Notably, we have a good qualitative agreement for the partial band gap between the simulations and experiments (highlighted in gray). The dynamic responses of the AHSF under harmonic excitation frequencies inside and outside the band gap further solidify this phenomenon ((f)). When the incident frequency lies outside the band gap (point A), elastic wave can propagate freely through the AHSF. By contrast, the incident wave energy will be reflected when the incident wave frequency is located inside the band gap (point B).It should be noted that the attenuation zones in the measured transmission spectra are slightly shifted toward high frequencies. This discrepancy is due to the manufacturing defects in the thin walls of hollow spheres (∼ 1 mm), including non-uniform wall thickness and voids among powder. These structural defects will not affect elastic wave propagation in the AHSF, since the wavelength is much larger than the powder size. These defects, however, could affect the effective stiffness of the structure, which leads to the difference between the lower band gap boundary frequencies. In addition, intrinsic material damping affects mechanical wave attenuation at the high-frequency range, as one can see the attenuation from 14.1 kHz to 15 kHz. This attenuation zone is not attributed to the partial phononic band gap. Instead, inherent material damping of Nylon PA12 could be responsible for this. A detailed dynamic mechanical analysis is preferred to characterize the damping properties of this material but is not the focus of this study []. It should be pointed out the large difference between the transmission amplitude for experiment and simulation is due to the different model setups. Nevertheless, our dynamic tests evidence the existence of phononic band gap and thus wave attenuation capability of the proposed AHSFs. Since both the printing technique and wave transmission testing procedure are all well-established, in the rest of this work, we will only use numerical simulations to investigate the wave propagation phenomena in the AHSFs.We then numerically investigate the effects of architected foam geometric features on the evolution of the first phononic band gap. The unique design of architected foams allows us to study the roles of the hollow sphere and binder independently. The mechanical properties of the constitutive material are defined by Young’s modulus E = 1.6 GPa, Poisson’s ratio ν = 0.33, and density of ρ = 1174 kg m−3 unless otherwise specified. As shown in (a), by increasing the fillet angle of binder, the relative size of the omnidirectional band gap decreases gradually. The relative band gap size was changed from 0.68 to 0.31 when the fillet angle is doubled from 10˚ to 20˚. By contrast, the binder slenderness ratio has a pronounced impact on the band gap properties. For a wide binder (l/w=2) representing a strong connection between binders and hollow spheres, the first omnidirectional band gap has a relatively small size of 0.1. When the binders become slender (l/w=10) corresponding to a soft connection, the band gap size increases to 1.47, which is one order of magnitude larger ((b)). To further understand these trends, one can assume that the proposed AHSF behaves as a 3D mass-spring system, where hollow spheres act as lumped masses and binders work as springs. Each mass is accompanied by its eight nearest neighbors and connected by the spring. Analytical formulations reveal that the first omnidirectional phononic band gap results from oscillation and interaction among these masses [] and thus the opening of the first band gaps are controlled by the geometric features of the binders and hollow spheres. To confirm this, (c) shows the effect of hollow sphere thickness and thus the mass on the band gap properties. As expected, by increasing the sphere thickness and thus the lumped mass of the system, a larger omnidirectional band gap can be observed. These parametric analyses not only demonstrate the design flexibility of the proposed AHSFs with targeted phononic band gaps, but also imply that a weak connection among hollow spheres can lead to large band gap size in a low-frequency range.We have shown the targeted phononic band gaps can be achieved by tailoring the geometric parameters of the AHSFs. Next, we fix the geometric parameters of the AHSFs and change the stiffness contrast between spheres and binders (Es/Eb) to study the effect of this contrast on the band gaps. Here we choose d=3 cm, R=3/5d, R/t=10, l/w=2 and θ=18∘. As displayed in , the first omnidirectional band gap is enlarged from Ω = 0.36∼0.55 to Ω = 0.18∼0.53 when the binder stiffness varies from one to one-tenth that of the sphere. By further decreasing the stiffness of the binders, the first band gap rapidly shifts toward a much lower frequency range. For example, when the stiffness ratio is Es/Eb=1000, the frequency range of the band gap decreases to Ω = 0.02∼0.094. To gain physical insights into this trend, we plot the eigenmodes at high symmetry points of the band edges, as shown in . The initial AHSF with a single constitutive material shows a Bragg type band gap because of the global vibration modes at the band edges ((a)–(b)). With the increase of stiffness contrast, the vibration modes demonstrate a strong localized characteristic. For example, as one can see in (c) and (d), the vibrational energy is localized in the hollow spheres at the upper band edges; at the lower band edges, the wave energy is concentrated on the soft binders. Essentially, these eigenmodes analyses suggest that by tailoring the stiffness contrast between components, the band gap formation mechanisms can be switched from Bragg scattering to local resonance.A more detailed analysis of the effect of stiffness contrast on the first band gap properties is summarized in . The band gap is abruptly shifted toward low-frequency range with the increase of stiffness ratio, while the relative band gap size increases linearly until a critical value is reached. At this threshold, the stiffness contrast is 50. Compared with conventional approaches such as harnessing structural instability to tune band gap properties [], the proposed approach does not need to change the architectures by applying external stimuli. Importantly, compared with existing 3D phononic crystals [], the proposed AHSF only requires a volume fraction of 10.8% while exhibiting a comparable band gap size exceeding 130%. This remarkable low-frequency band gap feature along with the lightweight design offers a promising approach for low-frequency vibration control, such as ground transportation induced vibrations and low amplitude seismic waves []. In addition to choose different constitutive materials, the stiffness contrast can be accomplished by using active materials, such as shape memory polymers []. As demonstrated by recent experimental work, the stiffness of 3D printed shape memory polymer can be tuned over three orders of magnitude by resistance wire heating []. For our case, by wrapping the binders with designed resistance wire, one can tune the binder stiffness and hence achieve tunable low-frequency band gaps, as predicted by our numerical simulations.The elastic wave propagation results reported so far are focused on AHSFs with a BCC lattice symmetry. We now proceed to examine the effect of lattice symmetry on the band gap properties. reports the phononic dispersion relations of AHSFs with a simple cubic (SC) and a face-centered-cubic (FCC) lattice symmetry. For the AHSF with an SC lattice symmetry, an omnidirectional band gap is observed in Ω = 0.28∼0.47, which is shifted to Ω = 0.05∼0.25 when the stiffness contrast increases to 100. Notably, the relative band gap size is enlarged from 0.52 to 1.36. Similar evolution trend of the first band gap can be observed in the dispersion relations of the AHSF with an FCC lattice symmetry. The relative band gap size is increased from 0.22 to 1.23. Physically, the global vibration modes of the initial AHSFs with SC and FCC lattice symmetries indicate Bragg type band gaps, while the localized deformation patterns in AHSFs with a high stiffness contrast suggest locally resonant band gaps. These results imply that the proposed design strategy and physical mechanisms are robust and can be extended to architected foams with other topologies.In summary, we have numerically and experimentally demonstrated the existence of an omnidirectional band gap in the 3D printed architected hollow sphere foam. The wave attenuation zone in the measured transmission spectrum agrees well with our our numerical predictions. Because of the unique design of the proposed architected foams, we have shown the design flexibility to change the band gap properties by tailoring the geometric and material parameters of the binder and hollow sphere. Remarkably, without changing the architecture or breaking lattice symmetry, the omnidirectional phononic band gaps can be shifted toward a low-frequency range by simply tailoring the stiffness contrast between hollow sphere and binder. We also evidenced that the proposed design paradigm and the physical mechanisms are robust and are applicable to AHSFs with other lattice symmetries. The findings reported in this work not only provide useful guidelines to design a new type of lightweight phononic metamaterials with low-frequency band gaps but also offers implications to develop active architected materials with tailored dynamic behaviors for a broad range of applications ranging from selective noise and vibration control to shock wave mitigation.OM and HJ designed the models and performed numerical simulations, FQ conducted the wave transmission test, ZJ, LW, HM, and DC analyzed the data and discussed the results, YC and LZ supervised the research. All authors discussed the results and contributed to the final manuscript.The authors declare no competing interests.On slip initiation in equiaxed α/β Ti-6Al-4VA computational study of 3D virtual instantiations of microtextured Ti-6Al-4V with varying initial slip system strengths is presented. Electron backscatter diffraction (EBSD) scans of a rolled and heat-treated mill annealed plate were used in order to determine the approximate geometric morphology of both the grain structure and the microtextured regions. Data from the EBSD experiments were used to calculate representative orientation distribution functions (ODFs) and grain size distributions for the α (HCP) crystallographic phase. Laguerre tessellations were employed to create idealized geometric representations of the microstructure and microtextured regions, while orientations were sampled from the experimentally derived ODFs. A highly parallelized crystal plasticity finite element framework was used to model the deformation response of single phase polycrystals under uniaxial tension, with attention paid to the intragrain slip system activity. Simulations were conducted with changes in the orientations within microtextured regions, as well as with various sets of initial slip system strengths to reflect differences in reported values in literature. Results were compared to a strength-to-stiffness parameter designed to predict succession of yield as a function of orientation. Presented are slip activity trends as a function of microstructure and initial slip system strengths, as well as results concerning the development of long-range localization of plasticity as a function of the microstructure. Predictions are compared to slip system activity measured by scanning electron microscope based digital image correlation.Ti-6Al-4V is the most widely produced titanium alloy, used in a wide array of industries and applications due to good resistance to corrosion, high strength, and low density Of the most common microstructures, those produced by the mill annealed processing path exhibit near equiaxed grains of hexagonal crystallographic phase - in contrast to the complex geometric structures that may form in other variations (e.g. the β annealed and bi-modal microstructures) The plastic behavior of many hexagonal crystals is debated in literature. In order to accommodate generalized plastic deformation Considering the mechanical constraints that exist due to compatibility and equilibrium between grains - as well as between microtextured regions - is crucial in determining the influence of microtextured regions and initial slip system strengths on the deformation response of the material. Computational simulations provide a window into the development of plasticity at the crystal scale Prediction and explanation of the succession of crystal yield, as evidenced by the initiation of slip, is achieved through the use of a directional strength-to-stiffness metric In this study, electron backscatter diffraction data in large 2D scans and in 3D datasets are used to inform the geometric representation of polycrystals through the use of Laguerre tessellations Ti-6Al-4V alloys subject to deformation processing and subsequent annealing in the α/β phase field develop a spectrum of relatively fine-scale α/β microstructures. The material used in this study () was homogenized in the β phase field, cooled, and then rolled into plate at a temperature just below the α/β transus. Subsequently, the plate was heat treated at 926° C for 4 h and cooled to room temperate at 0.3° C/minute to homogenize residual strain present from the hot working steps. Analysis of the top of the rolled plate details a composition of 6.28 wt% aluminum, 4.09 wt% vanadium, 0.18 wt% oxygen, 0.19 wt% combination iron, carbon, nitrogen, and yttrium, and balance titanium.Dominant in terms of volume fraction, the α phase - which exhibits HCP crystal symmetry - represents approximately 92% of the material volume. The geometry of the microstructure of Ti-6Al-4V is very sensitive to the thermomechanical processes used during production. Microstructures (e.g. β annealed or bimodal) comprised of primary grains with complex sub-grain structures are attainable through the use of hot rolling or long recrystallization steps, and present many challenges with respect to understanding their deformation responses. The equiaxed mill annealed microstructure represents a geometrically simple microstructural variation available for Ti-6Al-4V. Electron backscatter diffraction (EBSD) scans elucidate the geometric morphology of the α grains in the microstructure ((a)), which shows that the mill annealed microstructure is comprised of α phase grains of both similar size and shape.Additionally, crystallographic orientations of the grains are gathered from EBSD scans. (b) details a subset of the EBSD scan in (a), and exhibits areas of contiguous grains with similar crystallographic orientations (labeled “Region A” and “Region B”) - or microtextured regions. The two outlined regions show two different microtextured regions. Similarly oriented microtextured regions appear multiple times through EBSD surface scans covering larger areas 2(a). The microtextured regions outlined in (b) were identified visually. Microtextured regions result due to the persistence of α phase transformation structures (that arise from high temperature β phase structures) through thermomechanical processing By considering the orientations measured in the entire scan, as well as only those within the selected regions, functional representations of the microtextured regions may be constructed (c) shows the deduced orientation distribution functions (ODFs) for the entire scan, as well as each of the identified microtextured regions plotted in the hexagonal symmetry fundamental region of Rodrigues' space Three-dimensional characterization was performed by TriBeam, an in-situ FIB-SEM microscope femtosecond laser based mesoscale tomography technique (d)) shows that the microtextured regions run lengthwise not only in the rolling direction (as shown in (b)) but also in the transverse direction. In other words, the microtextured regions are planar regions with normals in the same direction as the sample ND.Surface strain measurements were made using a SEM based digital image correlation (SEM DIC) technique in a previous study ). Slip activity characterized as a function of the applied macroscopic strain was detected by SEM DIC, and has been directly compared to the simulations performed in this article.The model employed in this study is an elastic-viscoplastic model embedded in a highly parallelized finite element framework. This method is capable of modeling large inelastic, quasi-static deformations of a polycrystal discretized into a finite element mesh. The deformation of the material is described using a set of constitutive equations, and we consider both an elastic response and inelastic response of a single crystal. Anisotropy is included in the elastic response, as well as the inelastic response, which considers only rate-dependent crystallographic slip restricted to dominant slip systems. Although deformation twinning is commonly seen in commercially pure titanium and other titanium alloys, it is not observed in Ti-6Al-4V due to its high aluminum content The equations for the elastic and plastic responses are written in a configuration reached by elastically unloading, without rotation, from the current, or spatial, configuration by the inverse of the elastic stretch, ve. The elastic portion of deformation is governed by Hooke's law,where the Kirchhoff stress, τ, is related to the elastic strain, ee. The Kirchhoff stress is related to the Cauchy stress, σ, by τ=det(ve)σ; the elastic strain is computed from the elastic stretch as ee=ve−I, assuming small elastic strains The plastic portion of deformation is governed by a rate-dependent restricted slip model. The plastic deformation rate, DP (defined again in unloaded configuration), is a linear combination of the simple shearing modes defined by the symmetric portion of the Schmid tensors,where γ˙ is the shearing rate. For each slip system, k, the Schmid tensor is defined as the dyadic product between a slip plane normal vector, mk, and a slip direction vector, sk.Slip systems considered in this study are shown in . The α phase utilizes three slip families to represent those which have been experimentally observed to be active during the onset of plasticity The kinetics of slip are defined using a power law relationship between the shearing rate of a given slip system and the resolved shear stress, τk, on that system:γ˙k=γ˙0(|τk|gk)1msgn(τk)whereτk=tr(Pkτ′)where τ′ is the deviatoric portion of τ. The resolved shear stress on a slip system is scaled by the slip system strength, gk. The fixed-state strain rate sensitivity is controlled by m, and γ˙0k is the fixed-state strain rate scaling coefficient. For a given element, gk evolves at the same rate for all slip systems within a family.Similarly, for a given element, each slip system within a family will evolve at the same rate. Evolution of a slip system's strength is modeled using a linear Voce hardening assumption g˙k=γ˙h0(gsk(γ˙)−gkgsk(γ˙)−g0k)wheregsk(γ˙)=gs0k(γ˙γ˙s0)m′andγ˙=∑k|γ˙k|The initial slip system strength and saturation strength are defined by g0k and gsk, respectively, and h0 is the strength hardening rate coefficient. The saturation strength is a function of the sum of the slip system shear rates for a given element, and is controlled by the initial saturation strength, gs0k, the saturation strength strain rate scaling coefficient, γ˙s0, and the saturation strength rate scaling exponent, m′. For a given element, the saturation strengths of all slip systems within a family will evolve at the same rate.Model parameters were gathered from the analysis of tensile tests on equiaxed Ti-6Al-4V and from literature on Ti-Al alloys , and were optimized in an associated optimization study on the same material studied here . The primary set of initial slip system strengths (Strength Set 1) were also determined in a related study on the same material , Strength Set 1 prismatic strength is slightly higher than the basal strength and the pyramidal strength is moderately higher than the basal strength.The relative values of slip system strengths reported in the literature for the hexagonal phase of Ti-Al alloys spans a considerable range, as summarized in ) were chosen to limit the magnitude of hardening and effectively suppress evolution of the saturation strength. Recent studies suggest the possibility that the strain rate sensitivity may be variable across slip families To better predict the succession of grains which have yielded as a function of orientation, a strength-to-stiffness metric is employed. A strength-to-stiffness metric is critical in predicting the behavior of crystals in low-strain regimes, and is useful in determining the initial development of plasticity throughout a polycrystal. While the strength to stiffness ratio may not be of critical importance in predicting high strain behavior such as that experienced during processing, it is absolutely critical to predicting yielding, fatigue, and ductility. A structural analog is useful in illustrating the importance of a strength-to-stiffness metric in polycrystalline materials (a)). The two masses may not yield in succession as expected when considering only their directional yield strengths. In this case, the mass with a larger yield stress also has a larger directional modulus, such that it reaches its yield stress at a lower strain than the mass with a lower yield stress and lower directional modulus ((b)). The succession of yield in the two masses is better described by a strength-to-stiffness metric, which predicts the mass to yield first would be that with the lower ratio of directional strength to directional stiffness.The appropriate extension from this illustrative system is to consider many masses under similar loads, such as a polycrystalline material subjected to uniaxial tension. Each grain in the aggregate may have a complex stress state due to the effects of elastic anisotropy, plastic anisotropy, and the loading of its neighbors. A first-order directional strength-to-stiffness metric may be calculated, however, assuming a uniaxial stress state in the same direction as the applied load. Previous study on FCC crystals reveals that for high degrees of single crystal anisotropy, the isostress assumption leads to the over-prediction of strength-to-stiffness values for certain crystallographic fibers compared to those predicted using more specific fiber averaged stress values To obtain the directional modulus in general, the elastic compliance tensor, S (the inverse of the stiffness tensor, C, in Equation ), is considered in the crystal reference frame. Crystals exhibiting hexagonal symmetry are elastically transversely isotropic, meaning the directional stiffness for a uniaxial stress state, Edir, is dependent only on the angle, θ(r), between the crystal's c-axis and the loading direction 1Edir(r)=(1−cos2(θ(r)))2s11+cos4(θ(r))s33+cos2(θ(r))(1−cos2(θ(r)))(2s13+s44)where sij are components of the symmetry reduced compliance tensor in the crystal reference frame. details the directional stiffness as a function of θ.To obtain the strength for a given orientation, the uniaxial stress state is transformed from the sample reference frame to the crystal reference frame, and the normalized resolved shear stresses, τk(r)gk, for each slip system are each computed for an applied uniaxial stress. From this, the directional strength for a given orientation is defined as the inverse of the Schmid factor where m(r) is the orientation dependent Schmid factor. From the separate evaluations of stiffness and strength, the directional strength-to-stiffness parameter is constructed as,Since the single crystal elastic constants are held fixed in this study, the contribution of the directional stiffness to the strength-to-stiffness parameter remains constant across the simulations. However, the relative slip system strengths are variable () and each strength set will have a unique influence on the strength-to-stiffness values.Pole distributions are useful in displaying the results graphically. Each point on the unit sphere corresponds to a crystallographic orientation, in which the c-axis, c, will form some angle between the loading direction, d - which is in this case parallel to the RD direction. The computation consists of evaluating the strength-to-stiffness ratio for each crystallographic orientation defined by the points on the unit sphere, thus defining a pole distribution. For display, the distribution is presented as a stereographic projection onto a plane perpendicular to the loading axis. details the directional strength-to-stiffness ratios for the various sets of initial slip system strength.Note that the pole figures are nearly axisymmetric about their RD axes, with only minor azimuthal fluctuations in magnitude. To this point, details the directional strength-to-stiffness assuming both elastic and plastic transverse isotropy to more compactly illustrate the metric. Practically, this is achieved by calculating averages of the strength-to-stiffness values azimuthally about the RD axes of the pole figures found in . Note the general differences - in both character and magnitude - between the curves of the strength-to-stiffness parameters calculated using different strength sets. Specifically, note the values when the loading is parallel to the c-axis (θ = 0°, or the center of the pole figures), and when the loading is fully transverse (θ = 90°, or the periphery of the pole figures).Geometric representation of the microstructure is achieved through the use of Laguerre tessellations. Control over grain size (relative equivalent diameter) was achieved through the use of a normal distribution with mean 1 and standard deviation 0.045, while control over grain shape (sphericity) was achieved through the use of a lognormal distribution with mean −0.145 and standard deviation of 0.03 ), similar to those experimentally observed in and representative of the measured grain size distribution in , which exhibits a roughly normal distribution of grain sizes for the α phase.), contributing to long-ranging strain localization. However, the extent of resistance to transmission that the β phase presents between neighboring α phases is a complicated research topic Grains are assigned to spatial regions based on the spatial location of their centroid. The microtextured regions at the center of these instantiations are designed to have approximately four grains across their width to mimic the microtextured regions observed in EBSD scans. Generally, orientations are assigned to grains by randomly sampling from the ODFs informed by the EBSD surface scans. Microtextured regions are modeled in the instantiations by assigning grains to spatial regions based on the location of their centroids. Orientations are then assigned to grains within each spatial region by sampling from only one microtextured region ODF per region - ensuring localized microtexturing. Each microtextured region contains approximately 400 grains, or a third of the total volume.To account for potential bias introduced by sampling only a single microtextured region per instantiation, two instantiations are created - one with an embedded microtextured region sampled from the region B ODF ((a)), and one with an embedded microtextured region sampled from the region A ODF (Symmetry boundary conditions are employed detail (0 0 0 1) pole figures with the discrete orientations of grains considered to have active slip systems. Two thresholds must be met for a grain to be considered active for a given family of slip systems. First, a slip system from any family at each element of the mesh is considered active based on a threshold relating its shear rate to the applied strain rate (ε˙app):Note that elemental results presented consider the model's results calculated at an element's centroid. Next, a grain is considered active based on a volumetric threshold, calculated by considering the sum of the volumes of all the elements in a given grain (Vgrain) and the sum of the volumes of the elements with active slip systems (Vactive):Vactive{<110Vgraininactive≥110VgrainactiveResults were insensitive to either threshold through the range of [0.01:0.25], and as such 0.10 was chosen arbitrarily within this range.Each plot details the full spherical pole figure from a viewpoint looking down the rolling direction axis, similar to details the approximate engineering strains at which each slip family first activates for each instantiation and strength set.In this study the rolling direction is coincident with the loading direction, and henceforth “rolling direction” will refer to both the rolling direction of the material and the sample's loading direction. Additionally, the region between the periphery (outer circumference) of the pole figure plots and the center of the pole figure plots - that is, the region where the c-axis is neither aligned nor orthogonal to the rolling direction - will be referred to as the “intermediary region of the pole figure”.Little difference is observed between simulations conducted with Instantiation 1 and simulations conducted with Instantiation 2, and as such the results are discussed simultaneously. Inspection of the pole figures shown in reveals immediate trends concerning grain activation. Broadly speaking, orientations with the lowest strength-to-stiffness values are the first to register slip activity, and orientations with higher strength-to-stiffness values activate at higher strains. Key differences, however, are apparent between each simulated strength set.Inspecting the pole figures in the first columns of - those corresponding to the simulations conducted with Strength Set 1 - reveals that crystals in the intermediary region of the pole figure are the first to activate. This is consistent with the strength-to-stiffness plot for Strength Set 1 presented at the tops of the first columns, as the intermediary region of the pole figure has the lowest strength-to-stiffness values. Orientations with their c-axis orthogonal to the rolling direction are the second to activate, and orientations with their c-axis aligned with the rolling direction activate last - again, both consistent with the strength-to-stiffness values.The pole figures in the second columns of - those corresponding to the simulations conducted with Strength Set 2 - reveal a different trend. Grains in the intermediary region of the pole figure activate at roughly the same strain as those with their c-axis orthogonal to the loading direction, while grains with their c-axis aligned with the rolling direction are again the last to activate - notably at a much higher strain than in simulations conducted with other strength sets. The strength-to-stiffness plot for Strength Set 2 presented at the tops of the second columns shows that the strength-to-stiffness values for the intermediary region of the pole figure are comparable to the values for the periphery of the pole figure, while the center of the pole figure has the highest strength-to-stiffness values. Again, the order in which orientations activate are supported by the relative values for the strength-to-stiffness parameter.Finally, the pole figures in the third columns of - those corresponding to the simulations conducted with Strength Set 3 - reveal that grains in the intermediary region of the pole figure again activate at roughly the same strain as those with their c-axis orthogonal to the loading direction, followed by grains with their c-axis aligned with the rolling direction, though at a lower strain than in the pole figures in the second columns of . This again obeys the strength-to-stiffness plot for Strength Set 3 presented at the tops of the third columns.The order in which slip system families activate with relation to the strength-to-stiffness parameter may also be explored. details the engineering strains at which the each slip family first registers activity in the polycrystal for each simulated instantiation and strength set. Again, little difference is noted between simulations conducted with Instantiation 1 or Instantiation 2. However, differences are evident between simulations conducted with different strength sets. The strains at which activation is first registered for each slip family correlates well with the initial slip system strengths used for each simulation - relative strains at activation match the ordering of relative slip system strengths.The pole figures also reveal phenomena pertaining to the clustering of orientations with the same slip family active. Grains in the center and periphery of the (0 0 0 1) pole figures are from the microtextured regions sampled from the region A and B ODFs, respectively, while grains in the intermediary region of the pole figure may come from either microtextured region. The clustering of like orientations in the center and along the periphery of the pole figures reveals microtextured regions activating with a certain slip family. The pole figures in the first column of , for example, reveal that the grains at the periphery of the pole figure initially activate with only prismatic slip systems, while grains at the center of the pole figure initially activate with only pyramidal slip systems. This indicates that grains that exhibit pyramidal activity reside in microtextured regions corresponding to the region A ODF, while grains that exhibit prismatic activity reside in microtextured regions corresponding to the region B ODF. Grains in the intermediary region of the pole figure initially activate with only basal slip systems. These trends hold true for the other simulated instantiations and strength sets.In previous work, high resolution scanning electron microscope images were collected to measure the onset of plastic strain localization, using the digital image correlation technique (SEM DIC) (a). Bands of localized plastic deformation and their relative slip systems were identified from the strain field measurements at 0.65% and 0.71% engineering strain. Comparison to the experimentally measured slip activity, shown in Simulations conducted with Strength Set 1 have average activation engineering strains of 0.54%, 0.66%, and 0.71% for the basal, prismatic, and pyramidal families, respectively. (b) shows pole figures for the simulation conducted with Instantiation 1 and Strength Set 1 at 0.65% and 0.71% engineering strains. At 0.65% engineering strain, a relatively large number of grains register basal activity in the intermediary region of the pole figure, while a small number of grains register prismatic activity around the periphery of the pole figure. A single grain at the center of the pole figure registers pyramidal activity at 0.71% engineering strain, with continued basal and prismatic activity in the intermediary region and periphery of the pole figure, respectively.Other simulated strength sets produce results that do not match experimental observations. Simulations conducted with Strength Set 2 have an average engineering strain of 1.00% at which pyramidal activity is first witnessed - much higher than the average engineering strains at which the other two families first activate (0.54% and 0.55% for basal and prismatic, respectively). Additionally, Strength Set 2 produces a comparable amount of grains with basal and prismatic activity at 0.65% engineering strain, and no pyramidal activity at 0.71% engineering strain. Simulations conducted with Strength Set 3 have an average engineering strain at which prismatic activity is first witnessed of 0.40%, below the average engineering strain at which grains with basal activity first appear (0.54%). Additionally, Strength Set 3 produces more grains with prismatic activity at 0.65% engineering strain. In other words, the strength set with a weak basal system, and a moderately high pyramidal strength (Strength Set 1) best captures the observed trends in slip system family activation, while the strength set with a high pyramidal strength (Strength Set 2) registers pyramidal activation at an engineering strain far above what was observed experimentally, and the strength set with a weak pyramidal system (Strength Set 3) registers pyramidal activation before basal activation, which produces relative numbers of active grains for each family that differ from experimental observations.Results considering different subsets of grains were compiled to account for any potential bias introduced by considering interior and surface grains separately or together. details the strains at which each slip family first registers activity for each instantiation and strength set when considering only the grains on traction free surfaces (to mimic experimental EBSD scans), as well as when considering all interior grains. Little difference is witnessed when considering subsets of the aggregate or the entire aggregate, though the calculated strains at which slip families activate when considering only the traction free surface tend to be marginally higher than those calculated when considering the interior grains, which in turn tend to match (with few deviations) the calculated strains when considering the entire aggregate.To probe the influence of microtextured regions, two additional instantiations were produced in which the same orientation sets for Instantiations 1 and 2 were randomly assigned to grains - that is, with no microtextured regions. shows viewgraphs of these new instantiations containing the same orientation sets, but no microtextured regions. details the engineering strains at which each slip family activates for simulations conducted with these two new instantiations and each strength set. Activation strains deviate somewhat from those in , but the observed trends concerning the order of slip family activation are consistent with the trends observed in simulations performed with microtextured regions, implying that microtextured regions have little influence on this metric.Microtextured regions, however, have an effect on the localization of plasticity within the aggregate. details the grains within polycrystals of two representative simulations (one conducted with the presence of microtextured regions, and one without), colored if they are considered active for a certain slip family (Equations )). Note that for the simulation conducted with the presence of microtextured regions, active grains within each microtextured regions are active in the same slip family - that is, the regions in which the c-axis is perpendicular to the loading direction have grains which exhibit prismatic slip, while the region in which the c-axis is aligned with the loading direction exhibits primarily basal slip. The microtextured regions also facilitate the development of long-range regions of localized plastic strain spanning multiple contiguous grains. Most evident is the strain caused by shear on basal slip planes that is shown to have developed in the center microtextured region, which spans across neighboring grains, but terminates at the boundaries of the microtextured region. This strain localization occurs while the aggregate is still in the elastic regime (Conversely, the simulations conducted without the presence of microtextured regions exhibit a more disperse distribution of plasticity. Whereas the microtextured regions facilitate the localization of plasticity by means of specific slip family activity, their absence allows for plasticity to develop anywhere in the polycrystal. Additionally, the dispersion of slip activity across the polycrystal suppresses the formation of long-range plasticity localization before the onset of macroscopic yielding (). The shift from plasticity within single grains to coordinated long-ranging plasticity localization across grains with similar grain orientations in microtextured regions is likely to be detrimental to ductility.These results align well with experimental results (, in which the pole figures display the clustering of orientations with the same slip family activated, as well as the results plotted in Recent studies of hexagonal materials have proposed and utilized more complex hardening assumptions than the Voce form utilized in this study ), and the case of self hardening, where each slip system hardens independently details the results of these simulations in terms of the strains at which each slip family activates.Both the case of no hardening and the case of self hardening result in slightly higher strains at activation than the results presented in - though not significantly. Furthermore, the relative strains at activation are consistent with the results found with the case of isotropic hardening. In all cases, the trends observed in the results from the simulations conducted with isotropic hardening are the same with the two other hardening assumptions. When viewing the results at coarser strain states (), the results are nearly indistinguishable from those found with the isotropic hardening assumption (first column of Additionally, the grain averaged magnitude of hardening is calculated for the simulations with isotropic hardening or self hardening. In the case of isotropic hardening, the hardening magnitude is simply averaged across the grain (weighted by the element volume). In the case of self hardening, the hardening magnitude considers the largest slip system hardening magnitude per element, which is in turn averaged across the grain (again, weighted by the element volume). shows the grain averaged hardening for all simulations performed with hardening at 1.00% strain - the maximum strain investigated in this study.Hardening is seen to contribute minimally to the results of this study due in large part to the deformation regime in which this study focuses (elastic and elastic/plastic transition), in which the results are shown to be insensitive to the hardening assumption, and the magnitude of hardening is low compared to the slip system strengths.A study of the effect of microtextured regions and relative initial slip system strengths for equiaxed mill annealed Ti-6Al-4V is presented. Single phase instantiations - namely the generation of the microstructural morphology and the formation of representative orientation distribution functions - were informed by experimental data gathered through 2D and 3D EBSD data. Simulations were conducted multiple times on each instantiation with different sets of initial slip system strengths. Results from the simulations were used to determine slip activity in grains at various strains, and the strains at which each slip system family activates were deduced. These results proved to be sensitive to the relative initial slip system strengths for the basal, prismatic, and pyramidal slip families. A strength-to-stiffness parameter - previously demonstrated to be successful for use with FCC materials and extended here for use with HCP materials - correctly predicted the succession of yield in all cases. Compared to experimental results, the order of grain activation and the relative number of grains which exhibited slip activity in each family were best modeled using a weak basal family strength, a slightly higher prismatic family strength (1.2x basal), and moderately high pyramidal family strength (1.7x basal). Other sets of slip system strengths - including one with a high pyramidal family strength (3x basal), and another with a weak prismatic family strength (0.9x basal) - differed from experimental results in the relative magnitude of strain at activation, as well as the relative number of active grains for a given family at a given strain. Considering subsets of the aggregate - specifically grains which appear on traction free surfaces and interior grains - had little effect on these observed trends. Furthermore, the presence of microtextured regions had little effect on the initiation of slip, but proved to facilitate the formation of long-range plasticity localization within microtextured regions before the onset of macroscopic yield, compared to the disperse distribution of plasticity in simulations conducted without the presence of microtextured regions, which compares well with experimental observations.Serial block-face scanning electron microscopyStructure–function studies of blood and air capillaries in chicken lung using 3D electron microscopySerial block-face scanning electron microscopyIt is remarkable that the two classes of vertebrates capable of sustained high oxygen consumptions, the mammals and birds, have radically different lungs. The mammalian lung uses reciprocating ventilation with large terminal air spaces (alveoli). By contrast, the avian lung has a flow-through system with small air capillaries. As a consequence, the environment of the pulmonary capillaries is very different between mammals and birds.The present study was prompted by three important differences between avian and mammalian pulmonary capillaries. First, the blood–gas barrier is much thinner in birds than in mammals. For example, an analysis of data from 34 species of birds and 37 of mammals found that the mean harmonic thickness of the barrier was 0.19 and 0.47 μm respectively, that is it differed by a factor of 2.5 (). The extreme thinness of the barrier is paradoxical because flying is very energetic, and the thinness of the barrier predisposes it to stress failure. It is known that mammals that have thicker pulmonary capillary walls can develop stress failure of the barrier during heavy exercise (Second, the blood–gas barrier is much more uniform in thickness in the chicken than in mammals such as rabbit, dog, and horse (). The reason is that mammals have a type I collagen cable that threads its way along the alveolar wall thickening one side of each capillary in the process. It has been suggested that this cable is necessary for the mechanical integrity of the long alveolar wall (), but it is not required for the avian pulmonary capillaries which are nested in a honeycomb-like arrangement of small, supporting air capillaries.It seems likely that these differences between avian and mammalian capillaries are related to the immediate environment of the small blood vessels. In mammals, the pulmonary capillaries are strung out along the long alveolar wall and are unsupported at right angles to wall. By contrast in birds, the pulmonary capillaries are intimately surrounded by air capillaries of approximately the same diameter, and the presumption is that the blood capillaries are therefore supported in some way. However the micromechanics of this support, if indeed it exists, are not understood.The purpose of the present study was to obtain better information on the structures surrounding the pulmonary capillaries in birds in the hope that we can gain a better understanding of how the avian blood–gas barrier can be so much thinner and more uniform than in mammals, and why avian pulmonary capillaries are so rigid. Studies were made by transmission electron microscopy of chicken lung fixed by intratracheal instillation of glutaraldehyde. In addition, we exploited two relatively new techniques for obtaining three-dimensional information, namely electron tomography, and serial block-face scanning electron microscopy. Both techniques are well suited to studying the environment of avian pulmonary capillaries but we are not aware of any previous studies of this material using these methods.The animal protocols for these experiments were approved by the Animal Subject Committees of the University of California San Diego. White Leghorn chickens (Gallus gallus domesticus) were anesthetized with intravenous pentobarbital sodium (40 mg/kg) and a cannula was inserted into the trachea. The lungs were then fixed by intratracheal installation of 3% glutaraldehyde using a pressure of 25 cm H2O for 15 min.Lung samples were taken from the paleopulmo portion of lung from each animal at about one-third distance from the most caudal aspect of the lung. A section of tissue 0.5 cm thick was excised from the entire width of each lung transverse to the cranial–caudal axis. This section was then cut into approximately 10 vertical slices and trimmed into blocks.Blocks were rinsed overnight in 0.1 M phosphate buffer (350 mOsm, pH 7.4) and postfixed for 2 h in osmium tetroxide (1% osmium tetroxide in 0.125 sodium cacodylate buffer; 400 mOsm, pH 7.4). The samples were then passed through stepwise dehydration in increasing concentrations of ethanol (50–100%), rinsed with propylene oxide and embedded in Araldite. Blocks were then cut into ultra thin sections (50–70 nm) and contrast stained with saturated uranyl acetate and bismuth subnitrate. Sections were examined at an accelerating voltage of 60 kV using a Zeiss EM 10C transmission electron microscope. Micrographs of a carbon grating replica were taken for calibration.Electron tomography was carried out on sections of 0.5 and 1.0 μm thickness. Images were acquired using a JEM4000EX IVEM (400 kV) microscope equipped with a NCMIR custom design 4K lens coupled CCD camera (). The sections were successively tilted through 2° increments from −64° to +64°. Part of an epithelial bridge was collected as a single tilt series and a central portion of the epithelial bridges was collected as a double tilt series. The backprojected volume images were reconstructed using both the Boulder Laboratory's IMOD Tomography package suite and NCMIR's Transform Based Reconstruction (TxBR) software. Visualizations of the backprojected volumes were completed using Visage Imaging's Amira software suite. General information about electron tomography is available in Blocks of lung tissue were specially prepared for serial block-face scanning EM as follows. After primary aldehyde fixation the tissue was rinsed in 0.1 sodium cacodylate and postfixed in 0.1% potassium ferrocyanide-reduced 2% osmium tetroxide in cacodylate buffer for 1 h. Tissue was then rinsed in distilled water and treated with 0.1% aqueous thiocarbohydrazide for 20 min. After further rinsing in distilled water the tissue was again treated with 2% osmium tetroxide for 30 min, rinsed in distilled water, dehydrated in an ethanol series and infiltrated with Durcupan ACM resin.The tissue blocks were mounted on an aluminum pin and trimmed to 1 mm × 0.5 mm in size. The specimen was placed in a scanning electron microscope (FEI Quanta FEG) equipped with a serial block-face sectioning unit (Gatan 3 View) and a backscatter electron image of the face obtained. An automatic microtome then removed a 60 nm thick slice from the face and another image was recorded. This procedure was then repeated 500 times to give a data set from which a complete three-dimensional reconstruction 30 μm thick could be derived. The separate images were processed using Amira (Visage Imaging) to create maximum intensity projections, slice by slice renderings and segmentations of epithelial bridges. A general description of serial block-face scanning EM is given in The epithelial structures that join two adjacent capillaries and that form part of the wall of the air capillaries are known as epithelial bridges. These are very thin in cross-section but the epithelial cells that make up each bridge have a large area and are here called epithelial plates. It is convenient to describe the central portions of the bridges first and then the junctions of the bridges with the capillary walls. shows central portions of epithelial bridges. A is a relatively low power EM but nicely shows three bridges and their attachments to a single capillary. This figure is a screen shot from which is an electron tomography study that shows more clearly how the bridges link to the capillary.B and C shows the central portions of the bridges at high magnification. It can be seen that the bridges are made up of two separate epithelial cells with a small amount of matrix material between them. The total thickness of the central part of the bridges in these cross-sections is of the order of 50 nm. The four layers comprising the inner and outer cell membranes of both epithelial bridge cells are clearly seen. In B the bridge has a remarkably uniform thickness over most of its length whereas in C there is some variation in thickness. This may be because the micrograph of B happened to be at exactly right angles to the plane of the bridge, whereas in C this was not the case, and some thickening of the epithelial cell is seen because the plane of the section cuts slightly obliquely across the cell. In the thin central parts of the bridge the cytoplasm of the cells has a uniform appearance with no visible inclusions, but as the cells widen, approaching the junctions with the capillary wall, small circular structures in the cells are apparent. A notable feature of the bridges is that they do not include any intercellular junctions, and this is also the case in micrographs published by other investigators (. It can be seen that the epithelial cells of the bridges are contiguous with the epithelium that forms the outer cellular layer of the pulmonary capillary. A shows that there is a marked widening of one of the epithelial bridge cells near the capillary wall. This is also seen in B to a lesser extent. Both figures show a communication between the extracellular matrix of the capillary wall and the space between the two epithelial cells of the bridge. However the material in the space between the cells is less electron dense as we move away from the junction. It is not clear how far the extracellular matrix of the capillary wall actually extends into the epithelial bridge or whether the matrix material in the center of the bridge has a different composition. This is potentially important because the extracellular matrix of the capillary wall is believed to contain type IV collagen which has a high ultimate tensile strength (B shows an enlargement of the extracellular matrix material at the junction between the bridge and the capillary wall. Both micrographs show very small circular structures of about 20 nm diameter within the epithelial cells close to the capillary wall. It is possible that these are microtubules. shows part of an epithelial bridge from an electron tomography study. The figure is a screen shot from a file submitted as . The epithelial bridge is shown as a thin ribbon 1 μm wide. This is because the thickness of the tissue section is only 1 μm. However clearly show the three-dimensional configuration of the junction between the bridge and the capillary. This emphasizes that the enlargements of the junctions shown in A and B extend along the capillary wall. It would be desirable to have thicker tissue sections so that a greater width of the epithelial bridge could be seen. However the thickness of the section is limited by the energy of the electrons. In this particular microscope the 300 kV electrons will not penetrate a thicker tissue slice satisfactorily especially when the slice is tilted so that the distance through which the electrons need to penetrate is increased.The appearance of the whole of the epithelial bridges in three dimensions was studied using serial block-face SEM. A screen shot from a file is shown in . For this preparation, the perimeter of a single epithelial bridge was traced by an operator using a video pen and assigning it a green color to distinguish it from the surrounding capillaries that were colored blue. The complete epithelial bridge comprises two epithelial plates is clearly seen. The printed version of is in black and white whereas the online version and show the colors. In part of the video sequence we can see through the thin semi-transparent epithelial bridge to the capillaries behind. In another part of the sequence we look down through the center of an air capillary and see the epithelial bridge completely closing the gap between pulmonary capillaries at the far end. In another part of the sequence the blue pulmonary capillaries were removed by appropriate software allowing the bridge and its component plates to be clearly seen. The plates are seen in both plan view and from the side. emphasize that the epithelial bridge is part of the wall of the air capillary. They also show how the junction of the bridge with the capillary wall follows any curvature of the wall. This is important when we consider the role of the junction in influencing the mechanical properties of the pulmonary capillaries as discussed below.The three-dimensional relationships between the blood capillaries and air capillaries are difficult to determine from conventional thin sections. However serial block-face SEM studies show the configuration clearly. A screen shot is shown in . It can be seen that the blood capillaries form a series of short interconnecting tubes of random orientation. The air capillaries are freely communicating spaces between the blood capillaries. No obvious constriction points in the air capillaries are seen. The whole arrangement emphasizes the very efficient apposition of air and blood in the gas-exchanging tissue.Another informative sequence is obtained when the viewer is enabled to move through the complete volume slice by slice. A screen shot of this is shown in . As indicated earlier, this study was done by taking a series of separate SEM images while the tissue block was shaved by the automatic microtome which removed 60 nm thick slices sequentially for 500 slices. This means that we can gradually move through a 30 μm thickness of the block. At any particular point in time, we can see the blood capillaries with their red cells, the epithelial bridges, and the air capillaries. If we concentrate on a single capillary as we gradually move through the block, its configuration changes and we eventually reach an epithelial bridge that connects it to the next capillary. In some instance there is no epithelial bridge at the end of the capillary but simply the space of an air capillary. The appearances of this sequence are essentially predictable from the image shown in , but in the video clip the transition from blood capillary to epithelial cell is emphasized. These experiments were not designed to measure the size of the blood and air capillaries. However, in a previous study on similar material we found that the average diameter of the blood capillaries in a thin microscopic section varied from 3.9 to 5.4 μm when the capillary transmural pressure was altered over a range of 60 cm water ( reported the diameter of blood capillaries to be about 3 μm, and for air capillaries the mean diameter was 15 μm.Previous investigators have described the structures outside the pulmonary capillaries in avian lung notably . However the present study is the first to clarify the three-dimensional arrangement of the junctions of the epithelial bridges with the pulmonary capillaries and as such it allows a better analysis of the forces acting on the capillaries than has previously been available. In a recent review (), possible modes of support of the blood capillaries were discussed but the present article is the first to provide the ultrastructural basis of the physiology. obtained electron micrographs of lung tissue from pigeon, barn owl, domestic chicken, and quail and their results are similar to those reported here although the resolution in their published micrographs is not as high. Another difference is that in that study, many of the epithelial bridges show a much larger space between the two epithelial plates than is the case here. A likely explanation of this is that the lungs developed some degree of interstitial pulmonary edema before the tissue was fixed. In support of this, the study of showed a progressive increase in the width of the space between the epithelial bridges of chickens following graded intravenous infusion of avian Ringer's solution to produce increasing degrees of interstitial edema. In none of the micrographs reproduced in either of these studies was there any example of an epithelial cell junction in the epithelial bridge itself, and this is consistent with our findings.The epithelial plates are the two very thin cells that have an extensive area and that make up the bridges as shown in . These plates are single epithelial cells with no cellular junctions and are remarkable for their extraordinary thinness but large extent. We have not been able to find similar illustrations of these plates although there have been several published three-dimensional studies of the gas-exchanging tissue of avian lung. For example, performed three-dimensional reconstructions of Muscovy duck lung using serial sections of light micrographs. In addition there have been scanning electron micrograph studies of blood capillaries that give a three-dimensional perspective (), and also an image of a cast of air capillaries in chicken lung (). However none of these studies clearly show the anatomy of the epithelial plates. An interesting feature of is that the plates are so thin that they are transparent to some extent and other tissue can be seen behind them. Perhaps we should not be too surprised that these epithelial plates can be extremely thin and have such a large area because this is the typical appearance of the type I alveolar epithelial cells that cover most of the surface of the alveoli in mammalian lungs.As discussed below, these junctions may have a critical role in reducing the hoop stresses that otherwise might damage the capillary wall when the capillary transmural pressure is raised. As show, these junctions are characterized by expansions of the epithelial cells as they join the capillary wall. In addition there is some evidence that the extracellular matrix of the capillary wall that contains the stress-bearing type IV collagen is thickened at the junction and perhaps may extend somewhat into the gap between the two epithelial cells at the beginning of the bridge. This is best seen in B. Another feature of the epithelial cells at the junction is the large number of cytoplasmic inclusions that appear as extremely small circular structures that are possibly microtubules. The significance of these is not known.As noted earlier, there are three major differences between avian and mammalian pulmonary capillaries. These are (1) avian capillaries have very much thinner walls than in the case in mammals, and furthermore the thickness of the extracellular matrix which is believed to be responsible for the mechanical strength of the capillaries is very much less in birds. For example, reported that the average thickness of the extracellular matrix in pulmonary capillaries of chicken was 0.045 ± 0.02 μm as compared with 0.319 ± 0.51 μm in dog. This is a difference of over sevenfold. (2) The blood–gas barrier is much more uniform in thickness in birds compared with mammals (). (3) Avian pulmonary capillaries are much more rigid than those of mammals in that the change in average diameter when the capillary transmural pressure is altered is very much less. A feasible mechanism for these differences is that avian pulmonary capillaries receive some support from the outside. This is in contrast to the situation in mammals where the capillaries are unsupported at right angles to the alveolar wall.There seem to be two possible ways in which the pulmonary capillaries can receive mechanical support from the outside.The epithelial bridges themselves could support the capillaries by a guy wire (extension) or buttressing (compression) action.The junctions between the epithelial bridges and the capillary walls could themselves share some of the hoop stress that otherwise might damage the capillary wall.A striking feature of the behavior of pulmonary capillaries in chickens is that their diameter is little reduced when the pressure outside them exceeds the pressure inside (). For example when the pressure in the air capillaries was raised from 0 to 35 cm H2O above the pressure inside the blood capillaries, the change in diameter was less than 20%. Contrast this with the behavior of mammalian pulmonary capillaries which completely collapse under these conditions, a situation known as Zone 1 (). It seems reasonable to ascribe this behavior to the guy wire-like action of the epithelial bridges as suggested by A although the connections of the bridges to the capillaries are by means of plates rather than wires. This support requires that the epithelial plates that make up the bridges be strong in extension. A diagram is shown in with arrows depicting the tensile forces that could hold the pulmonary capillary open.However when we consider forces tending to increase the hoop stress in the pulmonary capillary wall, the situation is less clear. It is well known that capillary stress failure occurs in mammalian lungs under both physiological and pathological conditions in spite of the much thicker wall of the capillaries in mammals compared with birds (). The fact that avian pulmonary capillaries can maintain their mechanical integrity with an extremely thin wall, and in particular with far less of the stress-bearing extracellular matrix, is difficult to explain. This would presumably require the epithelial bridges to be strong in compression, but they are so thin that this seems unlikely, and they would be expected to buckle. The situation might be different if there were appreciable surface tension forces in the air capillaries that resulted in a rigid assemblage. But in the absence of these forces it is not clear how the epithelial bridges could prevent large hoop stresses in the capillary wall that would result in failure.We have seen that there is an expansion of tissue at the junctions between the bridges and the walls with an obvious increase in the thickening of the epithelial cell itself, and also possibly the stress-bearing extracellular matrix (). These junctions track along the capillary walls, and if they were sufficiently numerous and appropriately oriented, they could share some of the hoop stress which otherwise would cause stress failure in the walls. An analogy here is the iron hoops around a barrel of beer although the cellular junctions are part of the barrel rather than being outside it. A diagram is shown in B. Note that in this diagram the junction runs around the circular perimeter of the capillary rather than along the axis as shown in A. In practice the junctions have random orientations as implied by The effects of surface tension in the air capillaries could have a major influence on the support of the blood capillaries. Because the diameter of the air capillaries is approximately 10–20 μm, the average radius of curvature of say, 5–10 μm could result in large pressures tending to close the capillary. For example, if we consider an air capillary as a thin-walled cylindrical tube with a radius of curvature of 10 μm and a thin aqueous lining layer, the pressure tending to close the capillary can be calculated from the Laplace relationship. This states that the pressure is given by the surface tension divided by the radius of curvature. For water at 37 °C, the surface tension is 70 mN m−1 (70 dyn cm−1), and for a radius of curvature of 10 μm this means that the pressure is about 7 kPa (53 mm Hg). For an air capillary of 5 μm radius of curvature, the pressure would be double this. Another way of looking at this is that a tube by itself would require a pressure inside it of 7 kPa to prevent it from collapsing. An assemblage of such tubes could be very rigid as is the case with the avian lung.Unfortunately we are almost entirely ignorant about the role of surface tension in the avian lung. It is not known whether the air capillaries are lined with a liquid or are dry. We do know that avian lungs contain surfactant as do mammalian lungs (). It is also known that avian lung has a peculiar trilaminar substance (TLS) that is not found in other lungs, and the electron microscopic appearance of this suggests that it may have surfactant properties ( has suggested that the TLS might be concerned with keeping the air capillaries free of liquid. have reviewed differences in surfactant between birds and mammals. introduced the term “interdependence” to refer to the stabilizing effect exerted on a structure embedded in an elastic continuum by virtue of the many connections between the embedded structure and the surrounding material. The original description considered a structure such as an airway or blood vessel, or perhaps a region of collapsed alveoli within an expanded lung. The analysis showed that the forces acting on the embedded structure could be very high. For example if the embedded region tended to collapse below its equilibrium volume, substantial forces would come into play to prevent this. In the same way, if the embedded region tended to expand beyond its normal volume, this would be opposed by the forces in the elastic continuum around it. This type of analysis might be very relevant to how an avian blood capillary shows very small changes in its caliber in spite of large changes in capillary transmural pressure. However whereas in the analysis of structures within the mammalian lung the pressure–volume properties of the lung are known, this information is not available for the parabronchial tissue in birds. Note also that the interdependence explanation does not concern itself with the geometry of the attachments as was discussed above, but simply the overall effects of a surrounding elastic continuum on an embedded structure that has a tendency to increase or decrease its size.In summary, our studies clarify how the pulmonary capillaries of chicken lung can differ so much from those of mammals. Avian pulmonary capillaries have thinner and more uniform blood–gas barriers, and they show much less change in diameter when the capillary transmural pressure is altered. Compression of the capillaries from the outside is apparently resisted by the guy wire-like arrangement of the epithelial bridges as shown for example in A. A similar mechanism could support the capillaries when the pressure inside them is increased if the epithelial bridges resist compression. This would be most effective if there was appreciable surface tension in the air capillaries that promoted their rigidity. Another mechanism that could support the capillary walls when the pressure inside them was increased is the cord-like junctions between the epithelial bridges and the capillary wall. These junctions run along the wall and could share some of the hoop stress which otherwise would tend to damage the unprotected wall. This could explain why the blood–gas barrier, and in particular the extracellular matrix layer in it, can afford to be so thin. As noted earlier, the uniform thickness of the blood–gas barrier is explained by the absence of type I collagen cable that is necessary in an alveolar lung but not here where external support of the pulmonary capillaries is available. Another potential explanation for the support of the pulmonary capillaries is the interdependence mechanism that exerts a stabilizing action on an embedded structure in an elastic continuum. The net result of having a very thin blood–gas barrier of uniform thickness is advantageous for pulmonary gas exchange.Supplementary data associated with this article can be found, in the online version, at SM1. Electron tomograph showing the pulmonary capillary with its three bridges that make up A. By rotating the capillary in three dimensions, the junctions between the bridges and the capillary wall are more clearly seen.SM2. Electron tomograph showing a ribbon of epithelial bridge running between two capillaries. Rotation of the image shows the nature of the junctions between the bridge and the capillary walls clearly.SM3. Serial block-face SEM study showing an epithelial plate surrounded by blood capillaries. The plate has been colored green while the capillaries are blue. This was done by tracing around the periphery of the plate with a video pen. In part of the clip it is possible to see structures through the plate because it is so thin. In a later part of the clip the capillaries have removed by the operator and the plate is well seen both in plane view and side view.SM4. Serial block-face SEM study showing the blood and air capillaries in a block of tissue 30 μm thick. The configuration of the two sets of capillaries can be seen as the section is rotated.SM5. Serial block-face SEM study in which we appear to move through a 30 μm thick tissue block in a series of small steps. As we do this and concentrate on a single capillary, its thickness changes and eventually we see the connecting epithelial bridge. For some of the capillaries there is no bridge on the far side but simply the empty air capillary.Work-hardening and plastic deformation behavior of Ti-based bulk metallic glass composites with bimodal sized B2 particlesIn this work, the role of individual B2 particles with bimodal length scale on work-hardening and plastic deformation behaviors of Ti-based bulk metallic glass composites has been studied by systemic microstructural and mechanical investigations. At the early stage of plastic deformation, work-hardening characteristic was clearly observed. This work-hardening behavior can be supported by the martensitic transformation and the deformation induced twinning in both small- and large-sized B2 particles during deformation. On progress of plastic deformation after work-hardening, small-sized B2 particles (1–10 μm) were penetrated by propagation of main shear bands while large-sized B2 particles (100–200 μm) were severely interacted with shear bands leading to formation of multiple shear bands and impeding the propagation of principal shear bands. This reveals that each B2 particle with different length scale plays a distinct role on the stage of plastic deformation depending on the particle size.Bulk metallic glasses (BMGs) have been highlighted as an highly accessible engineering material for advanced structural application due to their high strength, high hardness and large elastic limit Recently, it was reported that the CuZr-/Ti-based BMGCs containing intermetallic B2 phase phase represent obvious plastic deformation and exceptionally pronounced work-hardening behavior under compression as well as tension In order to investigate the effect of individual B2 particles with distinct length scale (small and large) on the deformation behavior of Ti-based BMGCs with bimodal length scale of B2 particles, we selected two alloys (Ti45Cu40Ni7Zr5Sn2.5Si0.5 and Ti45.3Cu39.5Ni7.8Zr4.9Sn2.5) with similar total volume fraction of B2 particles but with different volume ratio of small- and large-sized B2 particles. Here we report the influence of volume ratio of B2 particles between small and large one on plastic deformation behavior of Ti-based BMGCs via systemic mechanical and topological investigations for deformed samples with different degree of plastic deformation i.e., early stage of plastic deformation (work-hardening state) and late stage of pronounced plastic deformation (after work-hardening). In addition, deformation mechanism of work-hardening behavior in Ti-based BMGCs with bimodal B2 particles will be discussed.Ti45Cu40Ni7Zr5Sn2.5Si0.5 and Ti45.3Cu39.5Ni7.8Zr4.9Sn2.5 shows the XRD patterns, SEM backscattered electron (BSE) images, TEM bright field (BF) images of the as-cast samples (A and B alloys), together with selected area electron diffraction (SAED) patterns of amorphous matrix and large-/small-sized B2 particles obtained from as-cast B alloy. As depicted in (a), the XRD traces of as-cast A and B alloys exhibit typical BMGC characteristics having crystalline phases. The crystalline peaks superimposed on the broad diffraction of amorphous phase are identified as the B2 phase. At the same time, (b and c) reveal SEM BSE images obtained from cross sectional area of the both samples which demonstrate a BMGC microstructure containing spherical-type crystalline particles (dark contrast). The spherical crystalline particles reinforced in amorphous matrix (bright contrast) can be inferred as a B2 phase based on XRD analysis. As indicated by the arrows, the B2 particles exhibit the distinct size deviation in length scale, i.e., small- and large-sized B2 particles. The average size of small and large B2 particles can be measured to be 1 ∼ 10 μm and 100 ∼ 200 μm, as shown in inset images corresponding dotted circles in (b and c), respectively. The volume fraction of B2 particles and volume ratio of small- and large-sized B2 particles for both alloys are measured as 28 ± 5 vol.%, 60: 40 for A alloy, and ∼31 ± 5 vol.%, 20: 80 for B alloy, respectively. The TEM BF images [(c), obtained from B alloy present the enlarged views of B2 particles (dark contrast) embedded in amorphous matrix (bright contrast). The inset SAED patterns display a typical diffuse hallow ring corresponding amorphous phase and spots representing CsCl-type B2 crystalline phases, respectively. Furthermore, the superlattice of the {100} and {110} plane of B2 phases is obviously visible. Based on above phase and microstructural analyses, it is confirmed that the both alloys have similar total volume fraction of B2 particle but different volume ratio in particle size between large (100 ∼ 200 μm) and small (1 ∼ 10 μm) particles. shows the true compressive stress–strain curves of the as-cast A and B alloys with diameter of 2 mm. The values of yield strength and plastic strain are 1670 ± 25 MPa, 4 ± 1% for A alloy and 1645 ± 25 MPa, and 13 ± 2% for B alloy, respectively. The yield strengths of both alloys exhibit slightly lower than that (∼2 GPa) of monolithic BMG (not shown), which is caused by early deformation of softer B2 particles In order to investigate macroscopic deformation behavior (shear banding) of Ti-based MGMCs including bimodal-sized B2 particles at the early stage of plastic deformation, interrupted experiment was carried out and the evolution of shear band on the lateral surface was observed. The stress–strain curve for interruption is shown in (b) shows the lateral surface morphologies of the 1% plastically deformed B alloy. Multiple shear bands (marked by dashed arrows) were observed in BMG matrix along the perpendicular direction of loading direction and copious slip bands in large-sized B2 particle can be found. It is supposed that primary shear bands were developed and propagation of shear bands was properly hampered due to the stress concentration and strain accommodation at the interface between amorphous matrix and B2 particles To obtain deep insight into the origin of early plastic deformation i.e., work hardening, we performed the TEM analysis for 1% plastically deformed B alloy (see exhibits the TEM BF [(a), (h)], high resolution (HR) TEM images (b)-(d), fast Fourier transformation (FFT) (e)-(g) and SAED patterns (i)-(j) of the deformed sample. (a) shows the morphology of large-sized B2 particle embedded in amorphous matrix. (b)–(d) exhibit HRTEM images corresponding to the i), ii), and iii) areas in (e) presents the FFT patterns obtained from HRTEM image [(b)], which indexed as [110] zone axis of the B2 phase. The FFT patterns [(c) reveals weak sub diffraction spots (marked by dotted circles) superimposed on diffraction spots (marked by arrows) corresponding [110] zone axis of B2 phase. These sub diffraction spots are identified as [100] zone axis corresponding monoclinic B19′ phase, which indicates occurrence of the stress-induced martensitic transformation. For further closed region in crystalline phase with interface, the FFT pattern of the corresponding HRTEM image [(d)] exhibits the [001] zone axis of twinned monoclinic B19′ phase (marked by black solid and dotted arrows in center) superimposed on the [110] zone axis of B2 phase (marked by white arrows). Similarly, (h) exhibits the morphology of small-sized B2 particle embedded in BMGCs. The SAED patterns [(h) which is vicinity of interface between amorphous matrix and small-sized B2 particle are also confirmed as the [110] zone axis of B2 phase and [001] zone axis of twinned monoclinic B19′ phase (marked by solid and dotted arrows in center area) superimposed on the [110] zone axis of B2 phase, respectively. This clearly demonstrates the occurrence of stress-induced martensitic transformation and deformation twinning even in small-sized B2 particles. From these point of views, it is confirmed that the stress-induced martensitic transformation from B2 phase to B19′ phase in both small- and large-sized B2 particles occurs in the vicinity of interface between amorphous matrix and B2 phases at the early stage of plastic deformation. Moreover, the deformation induced twinning structure of B19′ at the interface reveals that the stress concentration happened around interface areas rather than inside of B2 particles.It is known that the nano-indentation test combined with microscopic analysis is effective way to evaluate the relationship between micro-/nano-scale structural evolution and corresponding mechanical properties. (a) shows the average hardness values of the amorphous matrix and B2 particles obtained from the as-cast and 1% plastically deformed B alloys. It is clear that the hardness of the amorphous matrix is not changed while the deformed B2 particles exhibit higher hardness value than as-cast B2 particles. In addition, (b) exhibits the hardness value gradient within the B2 particles depending on the region of indented area. The higher hardness values are observed in the vicinity of interface within the B2 particles, which are probably connected with the plateau of the martensitic transformation and deformation twinning (see ). Therefore, it is believed that the work-hardening phenomenon at the early stage of plastic deformation is a result of the hardening of the B2 particles into the amorphous matrix.In order to understand the formation and propagation of shear bands related with global plasticity at the late stage of plastic deformation, we compared the lateral surface morphologies of failed both samples. exhibit the SEM SE and BSE images obtained from the lateral surface of the failed A [(a), (c)] and B [(b), (d)] alloys, respectively. Lateral surface morphologies show a large number of shear bands throughout the entire surface region of the failed samples (not shown). Closer SEM observation of failed samples displays slight difference in plastic deformation behavior related with localized shear banding. In particular, distribution and propagation behavior of shear bands is obviously different. For A alloy with crystalline phase volume concentration ratio of 60:40 on the particle size, wavy fashioned shear bands with wide inter shear band spacing was observed. It is hard to find interaction between the primary shear bands and principal shear bands. Only tiny primary shear bands formed around small-sized B2 particles are observed [(c)]. In contrast, B alloy with crystalline phase volume concentration ratio of 20:80 on the particle size exhibits a high density of fine scale shear bands containing primary shear bands with perpendicular direction to loading direction (marked by dotted circles) and main shear bands (indicated by arrows), which is resulted from the strong interaction between large-sized B2 particles and main shear bands as well as shear bands blocking effect of homogeneously distributed large-sized B2 particles [see (i) and (j)], small-sized B2 phase was also transformed to B19′ phase during deformation and leads to work hardening at initial plastic deformation. However, they do not effective to contribute the further plastic deformation after work hardening [see inset image in (d)]. Main shear bands propagated along with maximum shear stress plane to the loading direction penetrates the small-sized B2 particles despite undergoing martensitic transformation equivalent to that of the large-sized B2 particles, as marked by dashed box region in (d). This observation reveals that small-sized B2 particles with size variation of 1 ∼ 10 μm are not sufficiently effective to impede the movement of the main shear bands due to their low strain accommodation capacity. In contrast, the large-sized B2 particles, as marked by circles in (c) and (d), sufficiently suppress the propagation of main shear bands. From these results, it is supposed that the shear banding behavior during plastic deformation is obviously related with size, distribution and volume fraction of reinforced bimodal B2 particles In the present work, the influence of B2 particles on the early and the late stages of plastic deformation of Ti-based BMGCs containing B2 particles with length scale difference, i.e., small-sized particles (1 ∼ 10 μm) and large-sized particles (100 ∼ 200 μm), was systemically investigated. The noticeable work-hardening phenomenon, at the early stage of plastic deformation, is the result of the individual hardening effect of the both small- and large-sized B2 crystalline particles which are originated from stress-induced martensitic transformation from B2 phase to B19′ phase and deformation twinning of crystalline phases. On progress of plastic deformation after work-hardening stage, the pronounced plastic deformation was attributed to the vigorous shear banding activity. In particular, we clearly found that shear banding behaviors related with plastic strain were governed by size of B2 particles. For small-sized B2 particles, the major shear bands propagated rapidly without hampering. In case of large-sized B2 particles, the propagation of shear bands was impeded by B2 particles with severe interaction and multiple primary shear bands were formed. This demonstrates that the B2 particles with distinct length scale play a different role on the stage of plastic deformation. In other word, the role of B2 particles with different length scale on the early stage of plastic deformation is almost same but clearly different at the late stage of plastic deformation (plasticity).Pullout behavior of inclined steel fiber in an ultra-high strength cementitious matrixIn this study, as a part of research to characterize the tensile properties of steel fiber reinforced ultra-high strength cementitious composites, pullout tests of steel fiber were performed to evaluate the effect of fiber inclination angle on the load direction and an analytical pullout model was derived considering this effect. The fiber inclination angles considered in the pullout tests were 0°, 15°, 30°, 45°, and 60°. From the pullout tests, it was observed that the largest peak load was obtained at an angle of 30° or 45°, and the peak slip increased as the fibers were oriented at a more inclined angle. Based on the experimental results, an analytical pullout behavior model considering fiber inclination was proposed. In order to take into account the effect of fiber inclination in the pullout model, apparent shear strengths (τ(app)) and slip coefficient (β) were introduced to express the variation of pullout peak load and the augmentation of peak slip as the inclined angle increases. These variables are expressed as functions of the inclined angle (ϕ).Brittle materials such as mortars and ceramics exhibit low toughness and poor resistance to cracking. However, the incorporation of fibers can delay the occurrence of cracks in concrete and restrain their propagation, thus endowing substantially higher energy absorption capability and toughness compared to plain concrete. This beneficial effect can be attributed to fiber bridging at cracks by the pullout process of the fibers, the main mechanism of fiber reinforcement.Fiber reinforced concrete (FRC) resists tensile forces through a composite action of the matrix and the fibers. A part of the tensile force is resisted by the matrix, while the other part is resisted by the fibers. Each of these resistances is determined by the stress transfer at the fiber–matrix interface, which is achieved by the bond defined as the shear stress acting at the interface. Before any cracking has taken place, elastic stress transfer is dominant. At more advanced stages of loading, debonding across the interface usually takes place, and frictional slip governs stress transfer at the interface. Therefore, the mechanical properties of FRC, especially its tensile strength, tensile stress–strain curve, and toughness, are sensitively influenced by the bond characteristics at the fiber–matrix interface Ultra-high strength cementitious matrix is composed of fine particles having a size of less than 0.5 mm, without coarse aggregate The bond characteristics depend on several factors involving the orientation of the fibers relative to the direction of the applied load, the embedded length of the fibers, the shape of the fibers, and the strength of the matrix. Many researches concerning bond properties have been conducted to reveal the effects of parameters related to fiber geometry or the strength of matrix The inclination angle of a fiber in a cementitious matrix has a strong influence on the pullout resistance. Although several researchers have performed experiments to investigate the effect of fiber inclination angle, the focus was mostly on the peak pullout load, and the effect is still disputable As a preliminary research to find out the tensile behavior of steel fiber reinforced ultra-high strength cementitious composites, the analytical pullout model which can consider the effect of various fiber orientations on the pullout behaviors is suggested in this study. The pullout test results were then exploited to derive pullout models by changing the inclined angle of steel fiber in each specimen.Most analytical pullout models proposed to date deal with the behavior of aligned fiber pulled out from the matrix Numerous researchers have performed analytical studies to clarify the bond mechanism of the fibers in a cementitous matrix. Wang et al. With respect to steel fibers, Nammur and Naaman Numerous studies have also been conducted on deformed fibers with different shapes, such as hook-shaped fibers, and analytical models were proposed by Alwan et al. To model the pullout behavior of steel fiber in an ultra-high strength cementitious matrix, this study applies the pullout behavior model proposed by Naaman et al. The mathematical derivation has been explained in detail in Naaman et al. . The bond shear stress–slip curve is linear elastic up to the point where the bond strength τmax of the interface is reached, beyond which a purely frictional condition prevails, with a constant frictional shear stress equal to τf. It is also assumed that τf cannot exceed τmax. Based on this relationship, Naaman et al. The following relation can be derived considering the equilibrium of forces in the free-body diagram in where F is the local axial force acting on the fiber at a distance x from the embedded end of the fiber; τ is the local bond shear stress at an arbitrary position acting on the fiber–matrix interface; and df is the diameter of the fiber.The local bond shear stress (τ) versus local slip (S) relationship in the elastic region (fully bonded) of can be related through the bond modulus κ as follows.where κ is assumed to be constant, and the slip S is defined as follows.where δf and δm are the local displacement in the fiber and the matrix, respectively, and ɛf and ɛm denote the corresponding strains.Taking the static equilibrium condition at any section together with Eqs. , the local axial force F acting on the fiber at a distance x from the embedded end of the fiber and the corresponding shear stress τ acting at the interface can be obtained using the following equations.where λ=KQ,K=πdfκAmEm, and Q=1+AmEmAfEf.The unknowns A and B can be obtained using the two boundary conditions, F(0) = 0 and F(l) = |
P.The critical load Pcrit stands for the load when the shear stress acting on the fiber and matrix at x |
= |
l reaches its maximum value, τmax. The critical load can be calculated by substituting τ(x |
= |
l) = |
τmax in Eq. Pcrit=πdfτmaxλ1-e-2λl1-1Q1+e-2λl+1Q2e-λlWhen a force P |
⩽ |
Pcrit, the fibers remain perfectly bonded to the matrix and the interface is kept in an elastic bond condition.The pullout behavior of the fiber can be divided into three distinct regions. The first region is the elastic range, where the fiber and matrix are perfectly bonded. The second region is the partial debonding region, during which a part of the fiber is bonded while the other part remains perfectly bonded. The third region is the fully debonded region, where the pullout behavior is governed by only frictional bond shear stress at the interface.When P |
⩽ |
Pcrit, the fiber preserves a perfect bond with the matrix. In this case, the pullout load–slip behavior is linear and can be defined as follows.When P > Pcrit, a part of the fiber is debonded from the matrix while the remaining part is still fully bonded to the matrix. Here, the pullout resistant load (P) is the result of the resistance due to the fiber in the bonded zone (Pb) and the resistance due to the fiber in the debonded zone (Pd).Let u be the length of the debonded zone. Assuming that the bond force acting on this length is provided by the friction with a constant value of τf, the force acting on length u (Pd) can be calculated. Furthermore, Pb can be computed by replacing l by l–u in Eq. . Accordingly, the pullout load and the corresponding slip displacement in the partially debonded state are given byP=πdfτfu+πdfτmaxλ1-e-2λ(l-u)2Qe-λ(l-u)+1-1Q{1+e-2λ(l-u)}Δ=P(Q-1)u-πdfτfu22(Q-2)+(P-πdfτfu)1-e-λ(l-u)1+e-λ(l-u)Q-2λ-πdfτfulAmEmOnce complete debonding has occurred at the fiber–matrix interface, the fiber acts as a rigid body. At this time, the relative displacement due to the elastic elongation of the fiber is neglected. Accordingly, the pullout behavior can be expressed by the following equation.where Δ is the end slip of the fiber after full debonding; Δo is the end slip of the fiber at the end of full debonding, which can be calculated by substituting u |
= |
l in Eq. ; and τfd is the decaying frictional bond stress relative to the end slip Δ. While the assumption of a constant value for τf can be made for small slips, it cannot be applied in the case of large slips. Accordingly, the decrease of the frictional bond stress with larger slip should be considered, which leads to the following definition of τfd (Δ).τfd(Δ)=τfe-(Δ-Δo)η-ςe-(l)η1-ςe-(l-Δ+Δo)η1-exp-4νfμ(l-Δ+Δo)Efdf1+νmEm+1-νfEf1-exp-4νfμlEfdf1+νmEm+1-νfEfwhere ζ is defined as the damage coefficient, a dimensionless constant to give the analytical descending branch with the same asymptotic value as the experimentally obtained descending branch; η is a coefficient representing the exponential shape of the descending branch of the bond shear stress versus slip curve. Generally, a value of 0.2 can be applied for η in the case of straight fibers The bond characteristics at the fiber–matrix interface can generally be verified by means of a pullout test. A fiber pullout test can be performed through various methods according to the method of application of tensile force and the number of fibers. Pullout tests can be classified into single-sided and double-sided tests according to the method of applying tensile force, and can also be performed according to the number of fibers, which can be single fiber or multiple fibers A review of the relevant literature shows that pullout tests of fibers have mostly been executed by means of a single-sided test on single fiber, owing to the relative simplicity of the test. However, a pullout test on a single fiber necessitates an apparatus capable of precision measurement due to the extremely small pullout force. Furthermore, there is typically a large variation in the obtained experimental results, and thus a tremendous number of specimens are required in order to secure reliability of the results The mix proportion adopted in this study is summarized in and is applied identically to all the tested matrixes. The fibers used in the test are steel fibers with a tensile strength of 2500 MPa, a diameter of 0.2 mm, and a length of 13 mm. A total of 32 steel fibers are embedded in each specimen at an inclination angle with respect to the pullout direction of 0°, 15°, 30°, 45°, and 60°.The pullout test specimens were fabricated as double-sided pullout specimens using multiple fibers. depicts the manufacturing process of the specimens. The process can be briefly described as follows. First, a PE sheet is adhered to a steel plate () to ensure sealing, and the fibers are placed into the plate at a depth equivalent to half of their length. The plate has holes that enable the location and inclination angle to be set accurately. The plate is then positioned at the center of the PVC mold and divided into two portions before casting mortar on one face. After 24 h of wet curing at ambient temperature, the central steel plate is removed. At this time, the PE sheet and the steel fibers are bonded to the matrix and retain their shapes. Thereafter, the matrix is casted on the other side and subjected identically to 24 h of wet curing at ambient temperature. Finally, after the mold is removed, the specimen is subjected to steam curing at 90 °C during 48 h. illustrates the configuration and dimensions of the specimen fabricated through this process.Tests were performed through displacement control using a universal testing machine with a capacity of 10 kN, as shown in . The load–slip relationships were obtained from the experiments. The slip was measured by means of a clip gauge positioned at the center of the specimen.Test results on pullout tests for multiple fibers are reported in , where peak slip is the slip corresponding to the peak load and the unit peak load refers to the value obtained by dividing the peak load by the number of fibers and the pullout work is defined as the area under the pullout load versus slip curve.Pullout behaviors corresponding to each orientation of the fibers to the pullout direction, that is, 0°, 15°, 30°, 45°, and 60°, are plotted in . From the pullout response obtained for the inclination angle, it was clear that the fiber orientation with respect to the crack plane has a definite influence on the response. It could also be observed that the largest maximum pullout loads and pullout work occurred at orientation angles of 30° or 45° () and that increased fiber inclination angle accelerated peak slip. In addition, the initial ascending slope of the load–slip curve appears to be smaller with a larger fiber inclination angle.The obtained results including peak pullout load and slip and the ascending and descending shape of the pullout curve can be used to derive a modified pullout model that takes into account the effect of fiber inclination angle. The derived model is based on the pullout model of Naaman et al. The pullout behavior of steel fiber is analyzed based on the results of pullout tests and the pullout model described through Eq. , and by subdividing the model into the ascending and descending behavior. The ascending behavior consists of the perfectly bonded state and partially debonded state, and the descending behavior is equal to the load–slip curve in a fully debonded state.The pullout model presented through Eq. is for single-sided pullout behavior; however, the experimental results in this study are for double-sided pullout. It is thus necessary to convert the original results to values corresponding to single-sided pullout. The load–slip relationship for single-sided pullout until full debonding was obtained by applying 1/2 of the measured slip, since it could be assumed that the bond simultaneously remains in the fibers at both sides under a partially bonding state. In addition, during the slip due to friction after complete debonding, it can be reasonably assumed that only one side of the fiber has been pulled out while the other remains in a partially bonded state, which means that the measured slip can be applied as it is. Although there may be a small displacement at the side in a partially bonded state, the displacement is very small relative to the slip displacement due to friction, and therefore can be neglected.After analyzing the pullout behavior in the case of aligned fiber based on the model given by Naaman et al., the effect of fiber inclination angle on the pullout curve was quantitatively estimated and this effect was reflected in the modified pullout model.As mentioned earlier, the ascending region in the pullout load–slip curve can be identified by two regions corresponding to the perfectly bonded state and partially debonded state. In the perfectly bonded state, the bond force–slip behavior is defined by Eq. , where Q can be obtained by means of the physical properties of the matrix and fibers. After deciding Q, λ can be determined using the value of the initial linear slope of the experimental load–slip curve.In the partially debonded region, the values of τmax and τf in Eqs. should be determined. The peak load, Pmax, normally occurs in the partially debonded region.In general, if τf is smaller than τmax, the pullout load after reaching the peak load drops suddenly to a level corresponding to the frictional slip resistance generated when the fiber is fully debonded shows the experimental results obtained in this study; note that a sudden load drop did not appear. Therefore, τmax and τf can be assumed to be identical for the modeling of the fiber pullout behavior in the ultra-high strength cementitious matrix, and the peak load, Pmax, is obtained when the fiber is fully debonded along the embedded length. Consequently, the values of τmax and τf can be calculated using only Eq. , without requiring the equation related to Δmax, which is likely to include slight experimental errors in the measured values. The obtained values of τmax and τf are both 6.80 MPa, and when Pmax |
= 27.77 kN, the slip Δmax is calculated to be 0.0148 mm. compares the pullout load–slip curve obtained by means of the model with the experimental results. are established based on the following equation considering a Poisson’s effect after full debonding and exponential decay of the frictional bond shear stress (τf).where x is the embedded length of the fiber with x |
= |
l |
− Δ + Δo and is valid for Δ ⩾ Δo. In this relation, it should be noted that while x varies from l to zero, Δ changes between Δo and l |
+ Δo. However, if we consider that there is a small pullout load when the fiber is almost pulled out, the slip at that time should be equal to the original embedded fiber length as the elastic deformation of the fiber is recovered. Therefore, it is reasonable that Δ varies from Δo to l while x varies from l to zero. The embedded length, x, is thus expressed asδ is the relative displacement between the fiber and matrix due to radial shrinkage of the matrix. This variable decreases due to abrasion of the matrix around the fiber according to the progress of frictional slip behavior. Considering this phenomenon, Naaman et al. where δo can be obtained by substituting x |
= |
l and applying P |
= |
πdfτf in Eq. This study analyzed the experimental results using Eqs. shows the influence of the value of ζ on the bond–slip curve in the descending region when η |
= 0.2, and presents the influence of the value of η on the bond–slip curve when ζ |
= 0. It should be noted, in comparing the experimental results with , that the formula for the frictional slip behavior proposed by Naaman et al. where α is a constant determining the initial slope of the frictional slip behavior; and η is a constant related to the shape of the exponentially descending branch in the bond–slip curve. Once η is determined, α can be obtained by comparing the initial slope of the descending branch, which is obtained by substituting Δ |
= |
Δo after differentiating Eq. with respect to Δ, with experimental results. When η = |
0.05, an overall decreasing trend of the experimental results was satisfactorily simulated. compares the behavior obtained by the model with the experimental results.In the case where the fibers are not positioned in the tensile load direction but instead are inclined, the bridging force will be increased In addition, fiber with an angle inclined toward the pullout load direction causes a stress concentration at the fiber exit and consequent local failure of the supporting matrix The combined effects of the snubbing and matrix spalling were considered when modeling the bond behavior of the inclined fibers.Modeling was implemented through a comparison of the pullout test results according to the change of the inclination of the fibers. Modeling for the bond behavior of inclined fiber was based on the pullout model for aligned fiber. The modeling of the bond behavior for inclined fibers considered the variation of load due to the snubbing effect and matrix spalling effect based on the model when the fiber inclined angle (ϕ) is equal to zero. This was accomplished by introducing the apparent bond strength (τmax(app), τf(app)), which is described as a function of the inclined angle ϕ. In addition, the increase of the slip displacement was reflected by multiplying the slip displacement corresponding to ϕ |
= 0 by the coefficient β, which is also a function of the inclined angle ϕ. gives the values of τmax(app), τf(app), and β obtained through comparison with the experimental results for each fiber inclination angle, as well as the corresponding Pmax. In this study, τmax(app) is equal to τf(app) for each fiber inclination angle, since τmax and τf were the same for the aligned fiber. The Levenberg–Marquardt algorithm was selected for the nonlinear regression method to fit the test results with the parameters τmax(app) and τf(app). A parameter study was performed to minimize the sum of squares of errors, as shown in Eq. where n is the number of test data sets, Pm is the measured pullout load from the pullout test, and Pe is the calculated pullout load from Eq. with the parameters τmax(app) and τf(app). The parameter β was determined by calculating Δpeak(φ)/Δpeak(0) ratio obtained from the experiments, where Δpeak(φ) denotes the peak slip displacement corresponding to the peak load with ϕ and Δpeak(0) is the peak slip displacement corresponding to the peak load for the aligned fiber. compares the experimentally obtained load–slip curves and the predicted curves from the model using τmax(app), τf(app) and β with different fiber inclination angles.This study attempts to express τmax(app), τf(app) and β as functions of ϕ based on the results of . To express these quantities as functions of ϕ considering the snubbing effect and matrix spalling effect for Pmax, the snubbing effect could be considered by the following equation where f is the snubbing friction coefficient. While the value of f varies according to the type of fiber and the strength of the matrix, its value ranges between 0.5 and 1 for nylon, polypropylene, PVA or steel fiber in mortar with normal strength.The matrix spalling effect can be considered by the following equation, assuming that a load reduction does not occur when ϕ= |
0 and that the pullout force does not act on the fiber when ϕ= π/2.where k is the spalling coefficient and ϕ is expressed in radian.In order to apply the snubbing effect and matrix spalling effect to the bond behavior instead of P(ϕ), τapp can be expressed as a function of ϕ using Eqs. A comparison with the experimental values revealed that the strongest agreement can be realized when f |
= 1.6 and k |
= 1.8. compares the shear strengths obtained by fitting the experimental results using Eq. and the apparent shear strengths by Eq. for variation of the fiber inclination angle.In addition, Δ(ϕ) is defined by the following expression considering both the snubbing effect and the effect of matrix spalling.Through a comparison of the results yielded by the above equations with the experimental values, it is seen that good agreement is obtained for n = |
2 and γ |
= 100. shows the variation of slip coefficient, β, according to ϕ obtained by Eq. using the determined values of n and γ. The predicted curve of β is also compared with the experimentally obtained Δpeak(φ)/Δpeak(0) ratio.Accordingly, the pullout behavior with inclined fiber in the ascending branch can be expressed by the following equations: Eqs. are for the perfectly bonded region while Eqs. represent the behavior in the partially debonding region, by adopting apparent shear strengths that reflect the effects of fiber inclination angle, such as the snubbing and matrix spalling effects, on both load and slip displacement.Pcrit(ϕ)=πdfτmax(app)(ϕ)λ1-e-2λl1-1Q(1+e-2λl)+1Q2e-λlP(ϕ)=πdfτf(app)(ϕ)u+πdfτmax(app)(ϕ)λ1-e-2λ(l-u)2Qe-λ(l-u)+1-1Q{1+e-2λ(l-u)}Δ(ϕ)=1+γ2ϕπn1AmEmP(ϕ)(Q-1)u-πdfτf(app)(ϕ)u22(Q-2)+(P(ϕ)-πdfτf(app)(ϕ)u)1-e-λ(l-u)1+e-λ(l-u)Q-2λ-πdfτf(app)(ϕ)ulThe pullout behavior with inclined steel fiber in the descending branch can be modeled by Eqs. , as in the case of aligned fiber. The effect of the fiber inclination angle on η was investigated. It was observed that inclination angle of the fiber has almost no effect on η. Accordingly, Eq. can be applied with η = |
0.05 regardless of the inclined angle of the fibers. compares the pullout behavior due to the frictional slip after the peak load with the experimental values for each fiber inclination angle.The pullout behavior with inclined fiber in the descending branch can be modeled as given by the following equations introducing the apparent frictional shear strength.τfd(Δ)=τf(app)(ϕ)exp{-η(Δ-Δo)α}1-exp-4νfμxEfdf1+νmEm+1-νfEf1-exp-4νfμlEfdf1+νmEm+1-νfEfIn this study, as a part of research to characterize the tensile properties of steel fiber reinforced ultra-high strength cementitious composites, pullout tests of steel fiber were performed to evaluate the effect of fiber inclination angle with respect to the load direction on the pullout behavior. Based on the experimental results, an analytical pullout behavior model considering fiber inclination was proposed. Through experimental and theoretical investigations, the following conclusions are drawn:The fiber inclination angles considered in the pullout tests were 0°, 15°, 30°, 45°, and 60°. The largest peak load was observed at an angle of 30° or 45°, and therefore it is concluded that the largest pullout load can be achieved at the inclination angle which ranges from 30° to 45° due to the combined mechanism of snubbing and matrix spalling in the inclined fiber composites.The pullout behaviors of steel fiber in an ultra-high strength cementitious matrix did not show a sudden load drop after peak load, indicating that the maximum shear strength (τmax) is equal to the frictional shear strength (τf).In order to take into account the effect of fiber inclination in the pullout model, apparent shear strengths (τ(app)) and slip coefficient (β) were introduced to express the variation of the pullout peak load and the augmentation of peak slip as the inclined angle increases. They were expressed as functions of the inclined angle (ϕ).To effectively describe the descending behavior, a new equation for the decay of the frictional shear stress, suitable for ultra-high strength cementitious mortar, was proposed. It was found that the decay behavior was irrelevant to the degree of fiber inclination.Low-relaxation hot-dip galvanized prestressed steel wiresPost-fire mechanical properties of low-relaxation hot-dip galvanized prestressed steel wiresLow-relaxation hot-dip galvanized prestressed steel wires are the basic component materials of high-strength steel cables, which have wide applications as key load-bearing members in prestressed steel structures. Provided that the general appearance of the prestressed steel structure is acceptable after a fire event, how the behaviors of the steel cables in these structures have been affected must be estimated accurately to ensure safety. Therefore, a series of experiments with a total of 360 specimens was conducted to investigate the post-fire mechanical properties of low-relaxation hot-dip galvanized prestressed steel wires with various grades, namely, 1670, 1770, 1860, and 1960. Tensile coupon tests were performed on specimens after exposure to 13 preselected temperatures up to 1000 °C, where two different cooling methods, namely, air cooling and water cooling, were considered. The post-fire stress–strain curves, elastic moduli, yield strengths, ultimate strengths, and ductility were obtained. Additional tests were also conducted to study the effects of cyclic heating-cooling. The post-fire mechanical properties of the studied steel wires changed significantly after exposure to temperatures exceeding 400 °C, and the change characteristics of different steel wire grades were similar. Moreover, the influences of different cooling methods were notable: the water-cooled steel wires lose most of their ductility and strength when the exposure temperature exceeded 700 °C; whereas the effects of cyclic heating-cooling were insignificant. Thus, predictive equations that incorporate the influences of different cooling methods were developed to evaluate the post-fire mechanical properties of the steel wires studied.Low-relaxation hot-dip galvanized prestressed steel wiresLow-relaxation hot-dip galvanized prestressed steel wires (hereafter referred to as LG-SW) are the basic component materials of various high-strength steel cables (including steel strands, steel wire ropes, and semiparallel/parallel steel wire ropes), which have been widely used as key load-bearing members in prestressed steel structures, such as large-span prestressed space grid structures, suspended-cable structures, and cable-stayed bridge structures. Compared with the steel wires commonly used in prestressed concrete structures, LG-SW possesses such characteristics of higher strength (with a characteristic strength higher than 1670 MPa), lower relaxation, and better corrosion resistance. Fire represents one of the extreme conditions that may be encountered by structures and structural members. During fire hazards, steel materials, including both structural steels and steel wires, are inevitably exposed to elevated temperatures and lose strength and stiffness quickly. Hence, the performance of steel materials at elevated temperatures is critical for the safe design and evaluation of the fire resistance of prestressed steel structures. Extensive studies have been conducted to investigate the high-temperature mechanical properties of various grades of structural steels To date, existing studies on post-fire mechanical properties mainly focused on various structural steels, such as hot-rolled mild steels In general, without comprehensive knowledge of the post-fire mechanical properties of LG-SW, the residual behavior of the steel cables that act as the key load-bearing members in prestressed steel structures cannot be evaluated convincingly after fire events. The results of such an unreliable evaluation may lead to an uneconomical consequence or a potential safety problem. This paper presents the details of a comprehensive experimental investigation on the post-fire mechanical properties of four widely used LG-SW grades, namely, 1670, 1770, 1860, and 1960. Tensile coupon tests were conducted on specimens cooled down from 13 predetermined elevated temperatures up to 1000 °C. Both the air cooling and water cooling methods were considered. Associated mechanical properties, including stress–strain curves, elastic moduli, yield strengths, ultimate strengths, and ductility, were obtained. The influences of exposure temperatures, steel wire grades, and cooling methods on the post-fire mechanical properties were discussed. The effects of cyclic heating-cooling were also investigated through additional tests. On the basis of the experimental results, predictive equations that considered the influences of different cooling methods are developed to estimate the residual behavior of the steel wires that were studied.The LG-SW specimens were cut from longer 5.0-1670-II, 5.0-1770-II, 5.0-1860-II, and 5.0-1960-II low-relaxation hot-dip galvanized prestressed steel wires ordered for this study with a nominal diameter of 5 mm. The steel wires satisfied the requirements of GB/T 17101-2008 The actual diameters of each specimen were measured with a vernier caliper at three points within the gauge length. The average values of the measured dimensions were used to calculate the mechanical properties of LG-SW.The entire experiment procedure mainly comprised two steps. In the first step, the specimens were initially heated to the preselected elevated temperatures and subsequently cooled down to ambient temperature. In the second step, tensile coupon tests were conducted on the specimens at ambient temperature. The heating process was accomplished by a temperature-controlled electric furnace (). The thermocouple located inside the furnace measured the air temperature in the furnace and fed back the information to the control system to facilitate the adjustment of the heating rate; thus, a closed control loop was formed. In this study, the 13 elevated temperatures were 100, 200, 300, 400, 500, 600, 650, 700, 750, 800, 850, 900, and 1000 °C. In the heating process, the furnace temperature was initially increased at a rate of 15 °C/min to a temperature 50 °C less than the target temperature and then maintained for 10 min. Subsequently, the furnace temperature was raised to the target temperature at a rate of 5 °C/min and held for another 20 min. Adopting heating process like this ensures a uniform temperature distribution in the specimens and prevents the actual temperature from exceeding the target temperature. Subsequently, the specimens were removed from the furnace and cooled down to ambient temperature. Both air cooling and water cooling methods were considered. The specimens for the air cooling method were exposed to air and allowed to cool down at their own rates to simulate the situation in which a fire dies out naturally. The specimens for the water cooling method were cooled down by water spraying using a water jet () to simulate the scenario where fire is extinguished by fire nozzles. The entire heating-cooling procedure is plotted in . The water volume used in water cooling was determined based on the principle that the volume sprayed on each unit area of the specimen surface is proportional to the volume sprayed on the members in actual fire extinguishment. Given the firefighting parameters and flux of the water jet, the spraying time can be calculated with the following:where T1 refers to the fire extinguishing time in actual fire events (s); Q1 refers to the water flux in actual fire extinguishment (m3/s), R refers to the cover radius of the fire guns (m); T2 refers to the water spraying time in this test (s); Q2 refers to the flux of the water jet (m3/s), which remained constant during the test at 2 × 10− 5 |
m3/s; and A refers to the surface area of one specimen (m2). The values of the firefighting parameters were derived from those suggested in GB 50045-95 The tensile test was conducted via a computer-controlled electronic universal testing machine (). An electronic extensometer was attached to the specimens to measure strain precisely. The tensile load was applied at a rate of 10 MPa/s during the elastic stage and thereafter at a constant stain rate of 0.005/s until failure occurred, which satisfied the requirement of GB/T 228.1-2010 Additional tests were also performed to explore the possible degeneration in the mechanical properties of LG-SW induced by cyclic heating-cooling. Tensile coupon tests were conducted on Grade 1670 and 1960 LG-SW specimens after being heated to preselected elevated temperatures and cooled down to ambient temperature repeatedly up to three times, and then the effects of cyclic heating-cooling were analyzed. Heating-cooling cycles more than three times were not included because that on one hand, repeating heating-cooling process for three times is enough to discover the change trend of the mechanical properties of LG-SW; on the other hand, the purpose of the additional tests is to explore the possible degeneration in the mechanical properties of LG-SW induced by repeated fire hazards, and the probability of the fact that a structure encounters fire events for more than three times is extremely low, thus, there is no need to repeat the cooling-heating process for more times. Air cooling method alone along with three elevated temperatures, namely, 300, 600, and 900 °C, were considered. Similarly, three specimens with the same exposure temperature and cycle index were tested and regarded as a group. A total of 120 groups with 360 specimens (including four groups without exposure to elevated temperatures and 12 groups after cyclic heating-cooling) were tested.All four grades of LG-SW showed obvious thermochromism after cooling down from elevated temperatures ( is useful in estimating the highest exposure temperature the LG-SW had experienced after a fire event.The failure modes of the LG-SW are shown in . For comparison, the specimens that were not exposed to elevated temperatures were also included. All four grades of LG-SW showed a similar trend in failure modes with respect to exposure temperatures, while the influences of different cooling methods are significant. Under air cooling condition, all grades of LG-SW showed ductile failures with different degrees of necking regardless of the temperature to which they had been exposed. For water-cooled specimens, however, obvious brittle failures with a smooth fracture surface and nearly no necking were observed when the exposure temperatures exceeded 700 °C, thereby indicating that considerable attention should be given to the prevention of brittle fractures in the reuse of LG-SW extinguished by fire nozzles. Actually, as detailed in the following sections, the mechanical properties of these LG-SW with brittle failure modes also significantly changed, which made them totally unusable after fire events.The post-fire stress–strain relationships of the steel wires are plotted in . (Each curve plotted is one of the three curves obtained from the specimens in a group). The post-fire stress–strain curves differed considerably with respect to the exposure temperatures and cooling methods, whereas the change characteristics were similar among various steel wire grades. As shown in , after cooling from temperatures less than 400 °C, the stress–strain curves of all these four grades of LG-SW were almost unchanged compared with that of ambient-temperature specimens. However, with the growth of exposure temperature, significant changes in strength, ductility, and shape of the stress–strain curves were observed. The influences of different cooling methods on the post-fire mechanical properties were also significant. When the exposure temperature reached 750 °C, the water-cooled LG-SW showed a brittle fracture at the elastic stage without any plastic deformation although considerable ultimate strength (higher than 700 MPa) was reserved. As the exposure temperature continued to increase, complete embrittlement occurred for all steel wire grades, which exhibited extremely low ultimate strengths (no more than 100 MPa) and no plastic deformation capacity. Therefore, the curves of these specimens were not included in . Such observations, which were also consistent with the failure modes shown in , indicate that great caution must be exercised to avoid the post-fire reuse of LG-SW that were cooled down from relatively high fire temperatures by water spraying.The post-fire elastic moduli of LG-SW tested in this experiment are defined as the initial slope of their stress–strain curves (). The method adopted to calculate the initial slope was in accordance with GB/T 22315-2008 list the post-fire elastic moduli and corresponding residual factors obtained from this experiment, respectively. The residual factors are also plotted as the function of exposure temperature in (each listed and plotted value is the average value of the three specimens in a group).Results show that the elastic moduli of the LG-SW remained almost unchanged after exposure to temperatures up to 1000 °C (including the severely embrittled LG-SW, which were cooled down from temperatures exceeding 700 °C by water spraying), with only slight variations of 3.4%, 3.5%, 3.4%, and 3.3% for steel wire grades 1670, 1770, 1860 and 1960, respectively. Similar observations were also found in the previous studies of steel wires used in prestressed concrete structures For comparison, the 0.2% proof stress method was used to define the yield strengths of LG-SW studied in this experiment although an obvious yield plateau was observed when LG-SW were cooled down from temperatures exceeding 500 °C. The 0.2% proof stress f0.2 was determined from the intersection of the stress–strain curve and proportional line off-set by 0.2% strain level (). The post-fire yield strength residual factor is defined as the ratio of the yield strength after cooling down from elevated temperatures (fy |
, |
PT) to that at ambient temperature (fy) without fire exposure. list the yield strengths and corresponding residual factors of all four grades of LG-SW obtained from this experiment, respectively. The residual factors are also plotted as the function of exposure temperature in (each value listed and plotted is the average value of the three specimens in a group).Results show that the yield strength of all four grades of LG-SW generally followed a similar trend with exposure temperatures; moreover, the influences of different cooling methods were significant. The tested LG-SW did not lose their yield strengths until 400 °C under both air and water cooling conditions; thereafter, significant decreases in yield strength were observed. For air-cooled LG-SW, the yield strength was reduced to the lowest value at the temperature of 750 °C, with nearly identical reductions of 67.5%, 69.9%, 70.6%, and 71.7% for steel wire grades 1670, 1770, 1860, and 1960, respectively. Notably, an obvious rebound in yield strength was observed for all four grades of LG-SW cooled by air when the exposure temperature exceeded 750 °C, and at least 40% of their original yield strength can be regained at 1000 °C. This phenomenon was due to the formation of martensite crystalline which bears high hardness and strength but low ductility in the microstructure of LG-SW, when LG-SW was cooled down from exposure temperatures that exceed their critical temperature (usually considered as 727 °C for structural steels) at a relatively rapid rate (as in air cooling). Hence, when exposure temperature exceeded 750 °C which is higher than the critical temperature of steel wires, obvious rebound in yield strength of LG-SW was observed.By contrast, when water cooling method was adopted, the yield strength of LG-SW decreased in the range of 400 °C–700 °C, following the trend similar to that of air-cooled specimens. With the increase in exposure temperature, however, significant embrittlement occurred and all four grades of LG-SW fractured at the elastic stage without plastic deformation. Therefore, no yield strengths were obtained for LG-SW after water cooling from temperatures exceeding 700 °C. The embrittlement of the steel wire was mainly attributed to two factors. First, the 82MnA steel used to manufacture the LG-SW has a high carbon content. Hence, when the LG-SW were cooled down from temperatures exceeding their critical temperatures at an extremely rapid rate (as in water cooling), a large quantity of cementite phase precipitated out of the crystal structure of the LG-SW and formed a brittle microstructure. Second, numerous needle-type martensite followed by internal stress and microcracks in the crystal structures formed because of rapid cooling. Both factors lead to the brittleness and the significant strength reduction of LG-SW. Hence, the embrittling effect of water cooling, which severely reduces the strength and ductility of LG-SW, is a problem that requires attention in the reuse of LG-SW after fire events.The ultimate strength represents the maximum (peak) value of stress in the stress–strain curve (). The post-fire ultimate strength residual factor is defined as the ratio of the ultimate strength after cooling down from elevated temperatures (fu |
, |
PT) to that at ambient temperature without exposure to fire (fu). present the ultimate strengths obtained from this experiment and their corresponding residual factors, respectively. The residual factors are also plotted in as the function of exposure temperatures (each listed and plotted value is the average value of the three specimens in a group).The degradation trend of the ultimate strength is similar to that of the yield strength. The ultimate strength of LG-SW remained almost unchanged when the exposure temperatures were lower than 400 °C for both air and water cooling. Thereafter, the strength of air-cooled LG-SW decreased rapidly and reached the lowest value at 750 °C, with a reduction of approximately 60% for all steel wire grades. This finding indicated that LG-SW can regain more of their ultimate strength than yield strength after fire exposure. A rebound of ultimate strength caused by the aforementioned change in the crystal structure of LG-SW was also observed when the exposure temperatures exceeded 750 °C. Under water cooling condition, the ultimate strength of all grades of LG-SW firstly decreased at almost the same rate as that of air-cooled specimens in the range of 400 °C–700 °C. However, when the exposure temperatures exceeded 750 °C, significant embrittlement caused by the aforementioned reasons occurred, and nearly no strength can be regained for all four grades of LG-SW, thereby representing complete failure of the material.The ductility of the steel wire is the indicator that reflects its plastic deformation capacity, which is defined based on the deformation that the steel wire specimens can undergo before fracture (). The post-fire ductility residual factor is defined as the ratio of the fracture strains after cooling down from elevated temperatures (δu |
, |
PT) to that at ambient temperature without exposure to fire (δu). present the post-fire fracture strains obtained from this experiment and the corresponding residual factors, respectively. The residual factors are also plotted in as the function of exposure temperatures (each listed and plotted value is the average value of three specimens in a group).The ductility of all grades of LG-SW followed similar trends with respect to exposure temperatures whereas the variations obviously differed with steel wire grades, which was different from the case of yield and ultimate strength. In addition, the influence of different cooling methods was significant. The ductility was not affected for both air and water cooling when exposure temperatures were below 500 °C. Subsequently, air-cooled specimens showed a remarkable increase in ductility until 750 °C, with a growth of 137.0%, 163.9%, 205%, and 219.6% for steel wire grades 1670, 1770, 1860, and 1960, respectively. The increase in ductility is mainly attributed to the increase of ferrite and decrease of pearlite in the microstructures of steel wire. Moreover, results showed that higher-grade steel wire presented a more obvious growth in ductility than lower-grade specimens did with increasing exposure temperature. When the exposure temperatures exceeded 750 °C, all the air-cooled LG-SW presented a sharp decrease in ductility because of the aforementioned formation of a martensite structure in the crystal structure. Nevertheless, even after cooling from a temperature of 1000 °C, the ductility was still higher than its original value, thereby indicating that lack of ductility is not a problem in the reuse of LG-SW cooled by air after fire events.As for the LG-SW cooled by water spraying, an increasing trend of ductility was also observed up to 700 °C, with a growth less than that of air-cooled LG-SW but still significant, i.e., 102.6%, 109.7%, 77.7%, and 95.4% for steel wire grades 1670, 1770, 1860, and 1960, respectively. After exposure to temperatures exceeding 700 °C, however, LG-SW lost nearly all their plastic deformation capacity because of the embrittling effect of water cooling.Additional tensile coupon tests were conducted on grades 1670 and 1960 LG-SW after multiple heating-cooling cycles to explore the possible degeneration in mechanical properties of LG-SW; air cooling method alone and three elevated temperatures, i.e., 300 °C, 600 °C, and 900 °C were considered.The thermochromism and failure modes of the steel wire specimens after cyclic heating-cooling are shown in , respectively. The Roman numbers on each steel wire refers to the cycle index of the heating-cooling process that the specimen had undergone. When the exposure temperatures were 600 °C and 900 °C, the color of the LG-SW darkened with increasing heating-cooling cycle index, which could be attributed to the increase of accumulated heating time; while for a low exposure temperature of 300 °C, no significant changes in color were observed. In addition, the failure modes of the LG-SW subjected to multiple heating-cooling cycles showed nearly no difference from those of the LG-SW subjected to only one heating-cooling cycle.Related mechanical properties, such as elastic modulus, yield strength, ultimate strength, and ductility after cyclic heating-cooling, were obtained. Degeneration factors are defined as the ratio of the mechanical properties after multiple heating-cooling cycles (EMPT, fy |
, |
MPT, fu |
, |
MPT, and δu |
, |
MPT) to that after one heating-cooling cycle (EPT, fy |
, |
PT, fu |
, |
PT, and δu |
, |
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