摘要
本文在对结构陶瓷的四方至单斜(t→m)马氏体相变进行细观力学、热力学和微观机制分析的基础上,导出了在非比例加载条件下考虑材料的体膨胀和剪切效应的相变塑性细观本构模型。作者首次采用 Mori-Tanaka 方法以自洽的方式导出了材料构元的 Helmho-ltz 自由能及余能函数的解析表达式,它是外加宏观应力(或应变)、温度、相变夹杂体积分数以及夹杂内平均相变应变的函数,其中夹杂体积分数和平均相变应变为描述材料构元微结构变化的内变量。最后按 Hill-Rice 本构理论框架导出相变塑性屈服面方程及增量本构关系。
Based on micromechanics, thermodynamics and microscale t→m transformation mechanism considerations, amicromechanics constitutive model which takes into account both the dilatation and shear effects of the transformation is proposed to describe the macroscopic plastic behavior of structure ceramics during forward transformation under different temperatures. Under some basic assumptions, the analytic expressions of the Helmholtz and complementary free energy of the constitutive element is derived in a self-consistent manner by using the Mori-Tanaka's method which takes into account the interaction between the transformed inclusions. The derived free energy is a function of externally applied macroscopic stress (or strain), temperature, volume fraction of transformed phase and the averaged stress-free transformation strain (eigen strain) of all the transformed inclusions in the constitutive element, the latter two quantities being considered to be the internal variables describing the micro-structural rearrangement in the constitutive element. In the framework of Hill-Rice's internal variable constitutive theory, the forward transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for generalised non-proportional loading histories are obtained.Based on micromechanics, thermodynamics and microscale t→m transformation mechanism considerations, amicromechanics constitutive model which takes into account both the dilatation and shear effects of the transformation is proposed to describe the macroscopic plastic behavior of structure ceramics during forward transformation under different temperatures. Under some basic assumptions, the analytic expressions of the Helmholtz and complementary free energy of the constitutive element is derived in a self-consistent manner by using the Mori-Tanaka's method which takes into account the interaction between the transformed inclusions. The derived free energy is a function of externally applied macroscopic stress (or strain), temperature, volume fraction of transformed phase and the averaged stress-free transformation strain (eigen strain) of all the transformed inclusions in the constitutive element, the latter two quantities being considered to be the internal variables describing the micro-structural rearrangement in the constitutive element. In the framework of Hill-Rice's internal variable constitutive theory, the forward transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for generalised non-proportional loading histories are obtained.
出处
《力学学报》
EI
CSCD
北大核心
1991年第3期299-308,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
关键词
剪切效应
结构陶瓷
相变
本构构元
shear effect, internal variables, constitutive element
