This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total str...This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.展开更多
The principle of interaction between plastic volumetric and shear strains for rock and soil has been extended to the field of unsaturated soils.Two new interactions of suction-plastic volumetric strain and pore air pr...The principle of interaction between plastic volumetric and shear strains for rock and soil has been extended to the field of unsaturated soils.Two new interactions of suction-plastic volumetric strain and pore air pressure-plastic volumetric strain appear in the unsaturated state of a soil except the interaction between plastic volumetric and shear strains.It is very important to find that the suction possesses a dual property,which is the origin of generating its special functions.Thereby the effect of the suction on volumetric strain includes two opposite aspects.By means of this property of suction,the physical significance of effective stress parameter,effects of suction on volume change and preconsolidation pressure,and the mechanism of collapse upon wetting all can be explained.In addition,it is theoretically proved by application of this principle of interaction that the critical state line for unsaturated soils exists,and is unique and independent of the stress history.展开更多
A method for calculation of temperature distribution in adiabatic shear band is proposed in terms of gradient-dependent plasticity where the characteristic length describes the interactions and interplaying among micr...A method for calculation of temperature distribution in adiabatic shear band is proposed in terms of gradient-dependent plasticity where the characteristic length describes the interactions and interplaying among microstructures. First, the increment of the plastic shear strain distribution in adiabatic shear band is obtained based on gradient-dependent plasticity. Then, the plastic work distribution is derived according to the current flow shear stress and the obtained increment of plastic shear strain distribution. In the light of the well-known assumption that 90% of plastic work is converted into the heat resulting in increase in temperature in adiabatic shear band, the increment of the temperature distribution is presented. Next, the average temperature increment in the shear band is calculated to compute the change in flow shear stress due to the thermal softening effect. After the actual flow shear stress considering the thermal softening effect is obtained according to the Johnson-Cook constitutive relation, the increment of the plastic shear strain distribution, the plastic work and the temperature in the next time step are recalculated until the total time is consumed. Summing the temperature distribution leads to rise in the total temperature distribution. The present calculated maximum temperature in adiabatic shear band in titanium agrees with the experimental observations. Moreover, the temperature profiles for different flow shear stresses are qualitatively consistent with experimental and numerical results. Effects of some related parameters on the temperature distribution are also predicted.展开更多
Gradient-dependent plasticity is introduced into the phenomenological Johnson-Cook model to study the effects of strain-hardening, strain rate sensitivity, thermal-softening, and microstructure. The microstructural ef...Gradient-dependent plasticity is introduced into the phenomenological Johnson-Cook model to study the effects of strain-hardening, strain rate sensitivity, thermal-softening, and microstructure. The microstructural effect (interactions and interplay among microstructures) due to heterogeneity of texture plays an important role in the process of development or evolution of an adiabatic shear band with a certain thickness depending on the grain diameter. The distributed plastic shear strain and deformation in the shear band are derived and depend on the critical plastic shear strain corresponding to the peak flow shear stress, the coordinate or position, the internal length parameter, and the average plastic shear strain or the flow shear stress. The critical plastic shear strain, the distributed plastic shear strain, and deformation in the shear band are numerically predicted for a kind of steel deformed at a constant shear strain rate. Beyond the peak shear stress, the local plastic shear strain in the shear band is highly nonuniform and the local plastic shear deformation in the band is highly nonlinear. Shear localization is more apparent with the increase of the average plastic shear strain. The calculated distributions of the local plastic shear strain and deformation agree with the previous numerical and experimental results.展开更多
The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding,the applicability of complete plastic model assumption and the shear stress formula were research...The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding,the applicability of complete plastic model assumption and the shear stress formula were researched.Based on the shear stress formula of circular shaft under pure torsion in elastic stage,the formula of torque in elastic stage and the definition of yield,it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship,and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension.The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section.The distribution of shear stress is still linear with the maximum shear stress τs.The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion.The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory(LSEST).The traditional yield stress formula for plastic shaft under torsion is reasonable.The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.展开更多
Two improvements have been made on the calculation of plastic strain ratio(r value)inBCC monocrystals by considering the differences in the critical shear stresses among thethree slip systems and the rotation of cryst...Two improvements have been made on the calculation of plastic strain ratio(r value)inBCC monocrystals by considering the differences in the critical shear stresses among thethree slip systems and the rotation of crystal lattice.It is found that the results calulatedby the improved method are more rational.展开更多
The microstructure ofx-Ti/mild steel composite fabricated by using constant stand-off cladding technique was observed with optical microscopy, SEM and TEM analvses. Veryfine equiaxed grains (【0.1μm) with a low dislo...The microstructure ofx-Ti/mild steel composite fabricated by using constant stand-off cladding technique was observed with optical microscopy, SEM and TEM analvses. Veryfine equiaxed grains (【0.1μm) with a low dislocation density were observed in the adiabatic shear bands (.4SB);this enables a thermomechanical response that may lead to a superPlastic de formation.展开更多
JOHNSON-COOK(J-C) model was used to calculate flow shear stress—shear strain curve for Ti-6Al-4V in dynamic torsion test. The predicted curve was compared with experimental result. Gradient-dependent plasticity(GDP) ...JOHNSON-COOK(J-C) model was used to calculate flow shear stress—shear strain curve for Ti-6Al-4V in dynamic torsion test. The predicted curve was compared with experimental result. Gradient-dependent plasticity(GDP) was introduced into J-C model and GDP was involved in the measured flow shear stress—shear strain curve, respectively, to calculate the distribution of local total shear deformation(LTSD) in adiabatic shear band(ASB). The predicted LTSDs at different flow shear stresses were compared with experimental measurements. J-C model can well predict the flow shear stress—shear strain curve in strain-hardening stage and in strain-softening stage where flow shear stress slowly decreases. Beyond the occurrence of ASB, with a decrease of flow shear stress, the increase of local plastic shear deformation in ASB is faster than the decrease of elastic shear deformation, leading to more and more apparent shear localization. According to the measured flow shear stress—shear strain curve and GDP, the calculated LTSDs in ASB are lower than experimental results. At earlier stage of ASB, though J-C model overestimates the flow shear stress at the same shear strain, the model can reasonably assess the LTSDs in ASB. According to the measured flow shear stress—shear strain curve and GDP, the calculated local plastic shear strains in ASB agree with experimental results except for the vicinity of shear fracture surface. In the strain-softening stage where flow shear stress sharply decreases, J-C model cannot be used. When flow shear stress decreases to a certain value, shear fracture takes place so that GDP cannot be used.展开更多
Fe40Ni40P14B6 bulk metallic glass rods have been prepared by water quenching the fluxed alloy. The deformation behavior was investigated by nanoindentation tests and compressing tests. The average hardness and elastic...Fe40Ni40P14B6 bulk metallic glass rods have been prepared by water quenching the fluxed alloy. The deformation behavior was investigated by nanoindentation tests and compressing tests. The average hardness and elastic modulus of the as-prepared Fe40Ni40P14B6 BMG (bulk metallic glass) measured by nanoindentation tests are 8.347 and 176.61 GPa respectively. The displace- ment-load curve shows “pop-in” characteristics which correspond to the loading rate bursts. Many shear bands around the indent were observed. The as-prepared Fe-based BMG exhibits a compressive plastic strain of 5.21%, which is much larger than that of other Fe-based glassy alloys and most of other BMGs.展开更多
The distributed shear stress and the displacement across shear band, the evolution of plastic zones, and the load-carrying capacity of rock specimen were investigated in plane strain direct shear test according to Fas...The distributed shear stress and the displacement across shear band, the evolution of plastic zones, and the load-carrying capacity of rock specimen were investigated in plane strain direct shear test according to Fast Lagrangian Analysis of Continua (FLAC). And then the shear displacement distribution in normal direction of system composed of localized shear band and elastic rock was analyzed based on gradient-dependent plasticity. The adopted failure criterion was a composite of Mohr-Coulomb criterion, that is, the relation between tension cut-off and post-peak constitutive of rock was linear strain-softening. Numerical results show that shear stress field approximately undergoes three different stages. At first, shear stress is only concentrated in the middle of top and base of specimen. Next, shear stress in the middle of specimen tends to increase, owing to superposition of shear stresses. Interestingly, two peaks of shear stress appear far from the loading ends of specimen, and the peaks approach with the increase in timestep until elements at the center of specimen yield. Finally, relatively lower shear stress level is reached in large part of specimen except in the regions near the two ends. As flow stress decreases, the analytical shear displacement distribution in shear band based on gradient-dependent plasticity becomes steep; outside the band, it is linear and its slope tends to decrease. These theoretical results qualitatively agree with that of the present numerical predicted results. Main advantage of the analytical solution over the numerical results according to FLAC is that it is continuous, smooth and non-linear (except at elastic stage).展开更多
The correlation between crystal rotation and redundant shear strain in rolled single crystals was investigated by using the crystal plasticity finite element(CPFE) model in this paper. The deformation in aluminium sin...The correlation between crystal rotation and redundant shear strain in rolled single crystals was investigated by using the crystal plasticity finite element(CPFE) model in this paper. The deformation in aluminium single crystals of four representative orientations(rotated-Cube, Goss, Copper, and Brass) after rolling and plain strain compression was simulated, and the predictions have been validated by the experimental observations. In the rotated-Cube and Goss, the redundant shear strain and crystal rotation were in the same pattern, alternating along the thickness, while the relation between them was not obvious for the Copper and Brass due to their asymmetrical distributions of activated slip systems. The relations between slip system activation, crystal rotation, and shear strain were investigated based on the CPFE model, and the correlation between shear strain and crystal rotation has been built.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant No.52074269).
文摘This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.
文摘The principle of interaction between plastic volumetric and shear strains for rock and soil has been extended to the field of unsaturated soils.Two new interactions of suction-plastic volumetric strain and pore air pressure-plastic volumetric strain appear in the unsaturated state of a soil except the interaction between plastic volumetric and shear strains.It is very important to find that the suction possesses a dual property,which is the origin of generating its special functions.Thereby the effect of the suction on volumetric strain includes two opposite aspects.By means of this property of suction,the physical significance of effective stress parameter,effects of suction on volume change and preconsolidation pressure,and the mechanism of collapse upon wetting all can be explained.In addition,it is theoretically proved by application of this principle of interaction that the critical state line for unsaturated soils exists,and is unique and independent of the stress history.
文摘A method for calculation of temperature distribution in adiabatic shear band is proposed in terms of gradient-dependent plasticity where the characteristic length describes the interactions and interplaying among microstructures. First, the increment of the plastic shear strain distribution in adiabatic shear band is obtained based on gradient-dependent plasticity. Then, the plastic work distribution is derived according to the current flow shear stress and the obtained increment of plastic shear strain distribution. In the light of the well-known assumption that 90% of plastic work is converted into the heat resulting in increase in temperature in adiabatic shear band, the increment of the temperature distribution is presented. Next, the average temperature increment in the shear band is calculated to compute the change in flow shear stress due to the thermal softening effect. After the actual flow shear stress considering the thermal softening effect is obtained according to the Johnson-Cook constitutive relation, the increment of the plastic shear strain distribution, the plastic work and the temperature in the next time step are recalculated until the total time is consumed. Summing the temperature distribution leads to rise in the total temperature distribution. The present calculated maximum temperature in adiabatic shear band in titanium agrees with the experimental observations. Moreover, the temperature profiles for different flow shear stresses are qualitatively consistent with experimental and numerical results. Effects of some related parameters on the temperature distribution are also predicted.
基金This work was financially supported by the Educational Department of Liaoning Province (No.2004F052) and the National Natural Science Foundation of China (No. 50309004).
文摘Gradient-dependent plasticity is introduced into the phenomenological Johnson-Cook model to study the effects of strain-hardening, strain rate sensitivity, thermal-softening, and microstructure. The microstructural effect (interactions and interplay among microstructures) due to heterogeneity of texture plays an important role in the process of development or evolution of an adiabatic shear band with a certain thickness depending on the grain diameter. The distributed plastic shear strain and deformation in the shear band are derived and depend on the critical plastic shear strain corresponding to the peak flow shear stress, the coordinate or position, the internal length parameter, and the average plastic shear strain or the flow shear stress. The critical plastic shear strain, the distributed plastic shear strain, and deformation in the shear band are numerically predicted for a kind of steel deformed at a constant shear strain rate. Beyond the peak shear stress, the local plastic shear strain in the shear band is highly nonuniform and the local plastic shear deformation in the band is highly nonlinear. Shear localization is more apparent with the increase of the average plastic shear strain. The calculated distributions of the local plastic shear strain and deformation agree with the previous numerical and experimental results.
文摘The distribution of shear stress on the cross-section of plastic metal solid circular shaft under pure torsion yielding,the applicability of complete plastic model assumption and the shear stress formula were researched.Based on the shear stress formula of circular shaft under pure torsion in elastic stage,the formula of torque in elastic stage and the definition of yield,it is obtained that the yielding stage of plastic metal shaft under pure torsion is only a surface phenomenon of torque-torsion angle relationship,and the distribution of shear stress is essentially different from that of tensile stress when yielding under uniaxial tension.The pure torsion platform-torsion angle and the shape of torque-torsion angle curve cannot change the distribution of shear stress on the shaft cross-section.The distribution of shear stress is still linear with the maximum shear stress τs.The complete plasticity model assumption is not in accordance with the actual situation of shaft under torsion.The experimental strength data of nine plastic metals are consistent with the calculated results of the new limiting strain energy strength theory(LSEST).The traditional yield stress formula for plastic shaft under torsion is reasonable.The shear stress formula based on the plane assumption in material mechanics is applicable for all loaded stages of torsion shaft.
文摘Two improvements have been made on the calculation of plastic strain ratio(r value)inBCC monocrystals by considering the differences in the critical shear stresses among thethree slip systems and the rotation of crystal lattice.It is found that the results calulatedby the improved method are more rational.
文摘The microstructure ofx-Ti/mild steel composite fabricated by using constant stand-off cladding technique was observed with optical microscopy, SEM and TEM analvses. Veryfine equiaxed grains (【0.1μm) with a low dislocation density were observed in the adiabatic shear bands (.4SB);this enables a thermomechanical response that may lead to a superPlastic de formation.
基金Project(2004F052) supported by the Educational Department of Liaoning Province, China
文摘JOHNSON-COOK(J-C) model was used to calculate flow shear stress—shear strain curve for Ti-6Al-4V in dynamic torsion test. The predicted curve was compared with experimental result. Gradient-dependent plasticity(GDP) was introduced into J-C model and GDP was involved in the measured flow shear stress—shear strain curve, respectively, to calculate the distribution of local total shear deformation(LTSD) in adiabatic shear band(ASB). The predicted LTSDs at different flow shear stresses were compared with experimental measurements. J-C model can well predict the flow shear stress—shear strain curve in strain-hardening stage and in strain-softening stage where flow shear stress slowly decreases. Beyond the occurrence of ASB, with a decrease of flow shear stress, the increase of local plastic shear deformation in ASB is faster than the decrease of elastic shear deformation, leading to more and more apparent shear localization. According to the measured flow shear stress—shear strain curve and GDP, the calculated LTSDs in ASB are lower than experimental results. At earlier stage of ASB, though J-C model overestimates the flow shear stress at the same shear strain, the model can reasonably assess the LTSDs in ASB. According to the measured flow shear stress—shear strain curve and GDP, the calculated local plastic shear strains in ASB agree with experimental results except for the vicinity of shear fracture surface. In the strain-softening stage where flow shear stress sharply decreases, J-C model cannot be used. When flow shear stress decreases to a certain value, shear fracture takes place so that GDP cannot be used.
文摘Fe40Ni40P14B6 bulk metallic glass rods have been prepared by water quenching the fluxed alloy. The deformation behavior was investigated by nanoindentation tests and compressing tests. The average hardness and elastic modulus of the as-prepared Fe40Ni40P14B6 BMG (bulk metallic glass) measured by nanoindentation tests are 8.347 and 176.61 GPa respectively. The displace- ment-load curve shows “pop-in” characteristics which correspond to the loading rate bursts. Many shear bands around the indent were observed. The as-prepared Fe-based BMG exhibits a compressive plastic strain of 5.21%, which is much larger than that of other Fe-based glassy alloys and most of other BMGs.
文摘The distributed shear stress and the displacement across shear band, the evolution of plastic zones, and the load-carrying capacity of rock specimen were investigated in plane strain direct shear test according to Fast Lagrangian Analysis of Continua (FLAC). And then the shear displacement distribution in normal direction of system composed of localized shear band and elastic rock was analyzed based on gradient-dependent plasticity. The adopted failure criterion was a composite of Mohr-Coulomb criterion, that is, the relation between tension cut-off and post-peak constitutive of rock was linear strain-softening. Numerical results show that shear stress field approximately undergoes three different stages. At first, shear stress is only concentrated in the middle of top and base of specimen. Next, shear stress in the middle of specimen tends to increase, owing to superposition of shear stresses. Interestingly, two peaks of shear stress appear far from the loading ends of specimen, and the peaks approach with the increase in timestep until elements at the center of specimen yield. Finally, relatively lower shear stress level is reached in large part of specimen except in the regions near the two ends. As flow stress decreases, the analytical shear displacement distribution in shear band based on gradient-dependent plasticity becomes steep; outside the band, it is linear and its slope tends to decrease. These theoretical results qualitatively agree with that of the present numerical predicted results. Main advantage of the analytical solution over the numerical results according to FLAC is that it is continuous, smooth and non-linear (except at elastic stage).
文摘The correlation between crystal rotation and redundant shear strain in rolled single crystals was investigated by using the crystal plasticity finite element(CPFE) model in this paper. The deformation in aluminium single crystals of four representative orientations(rotated-Cube, Goss, Copper, and Brass) after rolling and plain strain compression was simulated, and the predictions have been validated by the experimental observations. In the rotated-Cube and Goss, the redundant shear strain and crystal rotation were in the same pattern, alternating along the thickness, while the relation between them was not obvious for the Copper and Brass due to their asymmetrical distributions of activated slip systems. The relations between slip system activation, crystal rotation, and shear strain were investigated based on the CPFE model, and the correlation between shear strain and crystal rotation has been built.
