Abstract This paper outlines a single crystal plasticity theory for the mesoscale resolution of the diffusionless transformation process of deformation twinning. Unlike prevalent crystal plasticity models of lattice transformation that characterize volume fraction evolution of coexisting parent and product lattices at a material point, our model alternates between two deformation gradient decompositions, depending on whether or not the lattice is transforming, so that only a single lattice exists at a material point at all times. This approach permits a proper spatiotemporal resolution of the transformation, and further captures its associated residual lattice distortions. Our formulation was implemented as a VUMAT subroutine on the finite element solver ABAQUS\Explicit and used to model the twinning of a magnesium single crystal that was loaded under compression at different angles. As verified against multiple experiments from the literature, our model successfully characterizes for moderate strain: (a) the anisotropic stress-strain behavior of the Mg crystal, (b) the resulting spatial cross-hatch pattern of spindle shaped twins, and (c) the natural completion times of the twinning transformation. These results indicate that our mesoscale theory is capable of an in-depth spatiotemporal investigation of twinning and can be potentially extended to similar diffusionless transformation processes in single crystals.

中文翻译：

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解决单晶塑性理论中孪晶的无扩散转化过程

摘要 本文概述了变形孪晶无扩散转变过程的中尺度分辨率的单晶塑性理论。与表征材料点共存母体和产物晶格的体积分数演化的普遍晶格转变晶体塑性模型不同，我们的模型在两种变形梯度分解之间交替，取决于晶格是否正在转变，因此只有一个晶格存在在任何时候都处于重要位置。这种方法允许转换的适当时空分辨率，并进一步捕获其相关的残余晶格畸变。我们的公式在有限元求解器 ABAQUS\Explicit 上作为 VUMAT 子程序实现，并用于模拟以不同角度压缩加载的镁单晶的孪晶。与文献中的多个实验相比，我们的模型成功地表征了中等应变：（a）镁晶体的各向异性应力应变行为，（b）由此产生的纺锤形孪晶的空间交叉影线图案，以及（c）孪生变换的自然完成时间。这些结果表明，我们的中尺度理论能够对孪晶进行深入的时空研究，并且有可能扩展到单晶中类似的无扩散转化过程。我们的模型成功地表征了中等应变：（a）镁晶体的各向异性应力应变行为，（b）由此产生的纺锤形孪晶的空间交叉影线图案，以及（c）孪晶转变的自然完成时间。这些结果表明，我们的中尺度理论能够对孪晶进行深入的时空研究，并且有可能扩展到单晶中类似的无扩散转化过程。我们的模型成功地表征了中等应变：（a）镁晶体的各向异性应力应变行为，（b）由此产生的纺锤形孪晶的空间交叉影线图案，以及（c）孪晶转变的自然完成时间。这些结果表明，我们的中尺度理论能够对孪晶进行深入的时空研究，并且可以潜在地扩展到单晶中类似的无扩散转化过程。