A rate-dependent crystal-plasticity (CP) framework that captures the coupled phase transformation - plastic deformation behavior of shape memory alloys (SMAs) is presented. Here, different from previous models, the flow rule for martensitic phase transformation incorporates the entire deformation gradient for transformation, including the rotation. Predictions of transformation strain and variant selection of Nickel-Titanium (NiTi) using this model are directly compared with previous formulations that did not include the rotation. The results show that the rotation is essential to accurately calculate the single crystal and polycrystal micromechanics of variant selection and transformation strains of SMAs. The constitutive law formulation also includes current formulations for both slip and deformation twinning plasticity mechanisms, and the differences in transformation mechanisms are further shown to impact plasticity calculations through transformation-plasticity interactions. In addition to the advancement of the constitutive law, a computationally efficient implicit time integration scheme is given for numerical implementation and demonstrated using a user material subroutine (UMAT) in the commercial finite element code ABAQUS Standard. The proposed framework and the associated numerical protocols achieve stable solutions using strain increments on the order of 0.05 mm/mm in simulating inelastic deformations and strain increments 0.01 mm/mm in the elastic-inelastic transitions. Furthermore, the use of an analytic Jacobian results in stable convergence in fewer than 10 global Newton iterations while calculating solutions for elastic-inelastic transitions, making the computational benefits evident.

中文翻译：

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隐式实现耦合变换 - 塑性晶体力学模型，用于形状记忆合金，包括变换旋转


提出了一种速率依赖性晶体塑性 （CP） 框架，该框架捕获了形状记忆合金 （SMA） 的耦合相变 - 塑性变形行为。与以前的模型不同，马氏体相变的流动规则包含了用于相变的整个变形梯度，包括旋转。使用该模型对镍钛 （NiTi） 的转化应变和变体选择的预测与以前不包括旋转的公式直接比较。结果表明，旋转对于准确计算 SMA 变体选择和转换应变的单晶和多晶微观力学至关重要。本构定律公式还包括滑移和变形孪生塑性机制的当前公式，并且进一步表明了转换机制的差异，通过转换-塑互影响了塑性计算。除了本构定律的进步外，还给出了一种用于数值实现的计算高效的隐式时间积分方案，并使用商业有限元代码 ABAQUS 标准中的用户材料子程序 （UMAT） 进行了演示。所提出的框架和相关的数值协议在模拟非弹性变形时使用 0.05 mm/mm 量级的应变增量，在弹性-非弹性过渡中使用 0.01 mm/mm 的应变增量来实现稳定的解。此外，使用解析雅可比矩阵可以在不到 10 次全局牛顿迭代中实现稳定收敛，同时计算弹性-非弹性转换的解，计算优势显而易见。