Finite deformation finite element calculations are carried out to analyze nonuniform plane strain tensile deformation of single crystals using an elastic–viscoplastic crystal plasticity constitutive relation. The planar crystals considered have two potentially active slip systems with the driving force for slip including a non-Schmid stress. The non-Schmid stress on a slip system is taken to be the Schmid resolved shear stress on the other slip system. In the calculations, the parameters characterizing the non-Schmid term, including its magnitude and the slip interval over which it acts, are varied. The effects of non-Schmid governed slip on the overall stress–strain response and on the strain at which a rapid drop in overall stress occurs is investigated. Additionally, the dissipation rate associated with non-Schmid governed slip is calculated both pointwise and integrated over the entire domain. Results show that one consequence of non-Schmid governed slip is the change in the slip mode and another consequence is that a non-negative dissipation rate for all possible deformation histories is not guaranteed. However, stable calculations up to the rapid drop in overall stress can be carried out even with the dissipation rate being negative at one or more points in the domain over some strain range and, in some cases, even when the integrated dissipation rate is negative. Implications for possible constitutive restrictions are briefly considered.

中文翻译：

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非 Schmid 连续滑移晶体可塑性及其对耗散速率的影响


进行有限变形有限元计算，以使用弹性-粘塑性晶体塑性本构关系分析单晶的非均匀平面应变拉伸变形。所考虑的平面晶体具有两个潜在的活性滑移系统，其滑移的驱动力包括非 Schmid 应力。滑移系统上的非 Schmid 应力被认为是另一个滑移系统上的 Schmid 分辨剪切应力。在计算中，表征非 Schmid 项的参数（包括其大小和它作用的滑移区间）是多种多样的。研究了非 Schmid 控制的滑移对整体应力-应变响应和总应力快速下降的应变的影响。此外，与非 Schmid 控制的滑移相关的耗散率是逐点计算的，也是在整个域上积分的。结果表明，非 Schmid 控制的滑移的一个结果是滑移模式的变化，另一个结果是不能保证所有可能的变形历史的非负耗散率。然而，即使在某个应变范围内域中一个或多个点的耗散率为负，或者在某些情况下，即使积分耗散率为负，也可以进行稳定的计算，直到总应力的快速下降。简要考虑了对可能的构成限制的影响。