A finite deformation theory of higher-order gradient crystal plasticity
A finite deformation theory of higher-order gradient crystal plasticity
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DOI：
10.1016/j.jmps.2008.03.010
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发表时间：
2008-08
影响因子：
5.3
通讯作者：
M. Kuroda;V. Tvergaard
中科院分区：
文献类型：
--
作者：
M. Kuroda;V. Tvergaard
对于高阶梯度晶体塑性，提出了有限变形公式。该理论与传统的晶体塑性理论相差不大。只有背应力效应和附加的几何必要位错（GND）密度演化的微分方程补充了非功共轭框架内的传统理论，其中不需要引入高阶微观应力，这将是功共轭滑移率梯度。我们讨论了它与基于高阶应力存在的假设的有限变形梯度晶体塑性的功共轭型的联系。在此基础上，用数值方法研究了受约束薄带的简单剪切边值问题，并通过与小变形理论解的比较，证明了有限变形的一些特征。与先前的小变形公式一样，本公式适用于多重和三维滑动变形的情况。
For higher-order gradient crystal plasticity, a finite deformation formulation is presented. The theory does not deviate much from the conventional crystal plasticity theory. Only a back stress effect and additional differential equations for evolution of the geometrically necessary dislocation (GND) densities supplement the conventional theory within a non-work-conjugate framework in which there is no need to introduce higher-order microscopic stresses that would be work-conjugate to slip rate gradients. We discuss its connection to a work-conjugate type of finite deformation gradient crystal plasticity that is based on an assumption of the existence of higher-order stresses. Furthermore, a boundary-value problem for simple shear of a constrained thin strip is studied numerically, and some characteristic features of finite deformation are demonstrated through a comparison to a solution for the small deformation theory. As in a previous formulation for small deformation, the present formulation applies to the context of multiple and three-dimensional slip deformations.