On the formulations of higher-order strain gradient crystal plasticity models
On the formulations of higher-order strain gradient crystal plasticity models
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DOI：
10.1016/j.jmps.2007.07.015
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发表时间：
2008-04
影响因子：
5.3
通讯作者：
M. Kuroda;V. Tvergaard
中科院分区：
文献类型：
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作者：
M. Kuroda;V. Tvergaard
最近，一些高阶扩展的晶体塑性理论已被提出，以纳入材料的长度尺度的影响，在传统的连续介质力学中缺失的环节。扩展理论分为功共轭和非功共轭两类。前者的一个共同特点是假定存在与塑性应变梯度共轭的高阶应力功，并推导出包含这种附加虚功贡献的虚功扩展原理。同时，在后一种类型中，高阶应力量不显式出现。相反，晶体滑移率的影响，出现在响应于空间梯度的几何必要的位错密度的背应力。功共轭型和非功共轭型理论有不同的理论背景，也有非常不同的数学表示。然而，这两种类型的理论预测相同类型的材料长度尺度效应。我们最近证明了在二维单滑移小变形的特殊情况下，这两种方法之间存在某种等价性。本文将讨论扩展到更一般的情况，即多重和三维滑动变形的情况。
Recently, several higher-order extensions to the crystal plasticity theory have been proposed to incorporate effects of material length scales that were missing links in the conventional continuum mechanics. The extended theories are classified into work-conjugate and non-work-conjugate types. A common feature of the former is that existence of higher-order stresses work-conjugate to gradients of plastic strain is presumed and an extended principle of virtual work involving such an additional virtual work contribution is formulated. Meanwhile, in the latter type, the higher-order stress quantities do not appear explicitly. Instead, rates of crystallographic slip are influenced by back stresses that arise in response to spatial gradients of the geometrically necessary dislocation densities. The work-conjugate type and the non-work-conjugate type of theories have different theoretical backgrounds and very unlike mathematical representations. Nevertheless, both types of theories predict the same kind of material length scale effects. We have recently shown that there exists some equivalency between the two approaches in the special situation of two-dimensional single slip under small deformation. In this paper, the discussion is extended to a more general situation, i.e. the context of multiple and three-dimensional slip deformations.