应变软化材料变形、破坏、稳定性的理论及数值分析
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摘要
本文在下列4个方面开展了研究工作:
(1)微结构效应引起的局部化带物理、力学量的非均匀性研究
根据考虑微结构效应的非局部理论,利用各向同性假设、边界条件、实际的剪切带厚度对应局部塑性剪切应变的最大值假设及峰后线性应变软化的本构关系,推导了剪切带厚度及剪切带内部的局部(塑性)剪切应变、应变率、变形及速度分布的表达式。建立了局部(塑性)剪切变形梯度与局部(塑性)剪切应变分布之间的关系及速度梯度与应变率分布之间的关系。给出了剪切带两盘的相对(塑性)剪切变形及速度的表达式。剪切带内部的局部(塑性)剪切变形及速度分布呈现非线性特征,这对传统的线性分布假定提出了挑战。提出了常剪切应变点的概念。研究了应变率、刚度劣化(损伤)及水致弱化效应对剪切带内部的局部(塑性)剪切应变及变形分布的影响。在剪胀条件下,分析了剪切带内部的局部体积应变增量及由于剪胀而引起的剪切带的法向变形。对考虑刚度劣化时的常剪切应变点进行了讨论。
在剪胀条件下,提出了剪切带内部的局部孔隙度、孔隙比、孔隙度增量及孔隙比增量的解析式。建立了剪切带内部的最大孔隙比、平均最大孔隙比增量、平均最大孔隙比及平均最大孔隙度的解析式。理论结果较好地解释了若干实验现象。
提出了拉伸局部化带内部的局部塑性拉伸应变分布的解析式,将其和前人的数值解进行了比较。根据非局部理论,推导了拉伸局部化带内部的局部损伤变量的解析式。提出了非局部损伤变量及其时间导数以及它们最大值的解析式。对于线性软化的韧性金属材料,在单轴拉伸条件下,提出了颈缩区域不同位置直径的解析式;在直接剪切条件下,提出了考虑峰前残余塑性剪切应变时及形变剪切带传播过程中线性软化的韧性金属材料形变剪切带内部的局部塑性剪切应变及变形分布的解析式。在Johnson-Cook本构关系中引入应变梯度效应以考虑微小结构之间的相互影响和作用,计算了线性软化的韧性金属材料绝热剪切带内部的温度分布及演变。
使用Johnson-Cook模型及梯度塑性理论,分析了绝热剪切带内部的局部塑性剪切应变及变形分布规律,研究了静态剪切强度、功热转化因子、应变硬化指数、热软化指数、熔点、比热容、密度、应变率敏感系数及应变硬化模量的影响。绝热剪切带内部的总温度被划分为初始温度、应变硬化阶段的温升及由于
Four aspects of investigations were carried out in this thesis:
(1) Theoretical analysis of nonuniformities of physical and mechanical quantities in localized band due to the microstructural effect
Based on nonlocal theory considering the interactions and interplaying among microstrcutures, the analytical solutions of the thickness of shear band and the local (plastic) shear strain, strain rate, deformation and velocity in shear band were derived using the isotropic assumption, the boundary condition, the assumption that the actual thickness of shear band corresponded to the maximum value of local plastic shear strain and the post-peak linear strain-softening constitutive relation.The relation between the gradient of local (plastic) shear deformation and the local (plastic) shear strain and that between the gradient of velocity and the strain rate were established. The theoretical results showed that the distributions of local (plastic) shear deformation and velocity in shear band exhibited nonlinear characteristics, which were different from the traditional assumption of linear distribution. The concept of constant shear strain point was proposed.
The influences of strain rate, degradation of stiffness (damage) and weakening due to pore fluid on the distributions of local (plastic) shear strain and deformation in shear band were investigated. For dilative material in shear, the increment of local volumetric strain in shear band and the normal deformation of shear band due to shear dilatancy were derived. The constant shear strain point accounting for the degradation of stiffness was discussed. For dilative material in shear, the analytical solutions of local porosity, void ratio, increments of porosity and void ratio in shear band were proposed. The analytical solutions of maximum void ratio, average value of increment of maximum void ratio, average value of maximum void ratio and average value of maximum porosity were derived.
For a specimen in uniaxial tension, the analytical solution of local plastic tensile strain in tensile localized band was proposed and compared with the previously numerical results. Based on nonlocal theory, the analytical solution of local damage variable in tensile localized band, nonlocal damage variable and their derivatives with respect to time and maximum values were proposed.
For linearly strain-softening ductile metal material in uniaxial tension, the analytical solution of diameter in necked region was proposed. In direct shear condition, considering the residual shear strain at pre-peak and the propagation of deformed shear band, the analytical solutions of local plastic shear strain and deformation in deformed shear band were proposed for linearly strain-softening ductile metal material, respectively. The strain gradient was introduced into the John-Cook constitutive relation and then the distribution of temperature in adiabatic shear band and its evolution were calculated for linearly strain-softening ductile metal material.
Using the widely used Johnson-Cook model and gradient-dependent plasticity, the distributions of local plastic shear strain and deformation in adiabatic shear band were analyzed. The effects of static shear strength, work to heat conversion factor, strain-hardening exponent, thermal-softening exponent, melting point, thermal capacity, mass density, strain rate sensitive
(1)微结构效应引起的局部化带物理、力学量的非均匀性研究
根据考虑微结构效应的非局部理论,利用各向同性假设、边界条件、实际的剪切带厚度对应局部塑性剪切应变的最大值假设及峰后线性应变软化的本构关系,推导了剪切带厚度及剪切带内部的局部(塑性)剪切应变、应变率、变形及速度分布的表达式。建立了局部(塑性)剪切变形梯度与局部(塑性)剪切应变分布之间的关系及速度梯度与应变率分布之间的关系。给出了剪切带两盘的相对(塑性)剪切变形及速度的表达式。剪切带内部的局部(塑性)剪切变形及速度分布呈现非线性特征,这对传统的线性分布假定提出了挑战。提出了常剪切应变点的概念。研究了应变率、刚度劣化(损伤)及水致弱化效应对剪切带内部的局部(塑性)剪切应变及变形分布的影响。在剪胀条件下,分析了剪切带内部的局部体积应变增量及由于剪胀而引起的剪切带的法向变形。对考虑刚度劣化时的常剪切应变点进行了讨论。
在剪胀条件下,提出了剪切带内部的局部孔隙度、孔隙比、孔隙度增量及孔隙比增量的解析式。建立了剪切带内部的最大孔隙比、平均最大孔隙比增量、平均最大孔隙比及平均最大孔隙度的解析式。理论结果较好地解释了若干实验现象。
提出了拉伸局部化带内部的局部塑性拉伸应变分布的解析式,将其和前人的数值解进行了比较。根据非局部理论,推导了拉伸局部化带内部的局部损伤变量的解析式。提出了非局部损伤变量及其时间导数以及它们最大值的解析式。对于线性软化的韧性金属材料,在单轴拉伸条件下,提出了颈缩区域不同位置直径的解析式;在直接剪切条件下,提出了考虑峰前残余塑性剪切应变时及形变剪切带传播过程中线性软化的韧性金属材料形变剪切带内部的局部塑性剪切应变及变形分布的解析式。在Johnson-Cook本构关系中引入应变梯度效应以考虑微小结构之间的相互影响和作用,计算了线性软化的韧性金属材料绝热剪切带内部的温度分布及演变。
使用Johnson-Cook模型及梯度塑性理论,分析了绝热剪切带内部的局部塑性剪切应变及变形分布规律,研究了静态剪切强度、功热转化因子、应变硬化指数、热软化指数、熔点、比热容、密度、应变率敏感系数及应变硬化模量的影响。绝热剪切带内部的总温度被划分为初始温度、应变硬化阶段的温升及由于
Four aspects of investigations were carried out in this thesis:
(1) Theoretical analysis of nonuniformities of physical and mechanical quantities in localized band due to the microstructural effect
Based on nonlocal theory considering the interactions and interplaying among microstrcutures, the analytical solutions of the thickness of shear band and the local (plastic) shear strain, strain rate, deformation and velocity in shear band were derived using the isotropic assumption, the boundary condition, the assumption that the actual thickness of shear band corresponded to the maximum value of local plastic shear strain and the post-peak linear strain-softening constitutive relation.The relation between the gradient of local (plastic) shear deformation and the local (plastic) shear strain and that between the gradient of velocity and the strain rate were established. The theoretical results showed that the distributions of local (plastic) shear deformation and velocity in shear band exhibited nonlinear characteristics, which were different from the traditional assumption of linear distribution. The concept of constant shear strain point was proposed.
The influences of strain rate, degradation of stiffness (damage) and weakening due to pore fluid on the distributions of local (plastic) shear strain and deformation in shear band were investigated. For dilative material in shear, the increment of local volumetric strain in shear band and the normal deformation of shear band due to shear dilatancy were derived. The constant shear strain point accounting for the degradation of stiffness was discussed. For dilative material in shear, the analytical solutions of local porosity, void ratio, increments of porosity and void ratio in shear band were proposed. The analytical solutions of maximum void ratio, average value of increment of maximum void ratio, average value of maximum void ratio and average value of maximum porosity were derived.
For a specimen in uniaxial tension, the analytical solution of local plastic tensile strain in tensile localized band was proposed and compared with the previously numerical results. Based on nonlocal theory, the analytical solution of local damage variable in tensile localized band, nonlocal damage variable and their derivatives with respect to time and maximum values were proposed.
For linearly strain-softening ductile metal material in uniaxial tension, the analytical solution of diameter in necked region was proposed. In direct shear condition, considering the residual shear strain at pre-peak and the propagation of deformed shear band, the analytical solutions of local plastic shear strain and deformation in deformed shear band were proposed for linearly strain-softening ductile metal material, respectively. The strain gradient was introduced into the John-Cook constitutive relation and then the distribution of temperature in adiabatic shear band and its evolution were calculated for linearly strain-softening ductile metal material.
Using the widely used Johnson-Cook model and gradient-dependent plasticity, the distributions of local plastic shear strain and deformation in adiabatic shear band were analyzed. The effects of static shear strength, work to heat conversion factor, strain-hardening exponent, thermal-softening exponent, melting point, thermal capacity, mass density, strain rate sensitive
引文
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