In this work, we have developed a temperature-dependent higher-order Cauchy–Born (THCB) rule for multiscale crystal defect dynamics (MCDD) of crystalline solids based on the harmonic approximation. As a template, we employed the THCB rule to develop an atomistic-informed constitutive model for the body-centered cubic (BCC) single crystal tantalum ( $\alpha$-Ta). Considering the effect of strain gradients in different process zone elements, the corresponding higher order stress are used to model crystal plasticity of single crystal $\alpha$-Ta. Different from face-centered cubic crystals, BCC crystals are strongly influenced by temperature. It is shown in this article that the developed finite temperature atomistic-informed crystal plasticity finite element method is able to capture the temperature-dependent dislocation substructure and hence crystal plastic deformation. The main contributions and novelties of the present work are highlighted by following findings: (1) A THCB rule and an atomistic-informed strain gradient theory have been developed, and the corresponding temperature-related higher-order stress and elastic tensor formulations are derived; (2) The finite temperature MCDD provides an atomistic-informed crystal plasticity finite element method that can simulate anisotropic crystal plasticity in any orientation within stereographic triangle at micron scale and above; (3) The developed MCDD is able to capture the non-Schmid effects of BCC single crystal tantalum ( $\alpha$-Ta); (4) The developed MCDD is able to capture the size effect of single crystal plasticity; and (5) The finite temperature MCDD can simulate the temperature dependent dislocation substructure, and it captures cross-slip in single crystal tantalum at low temperature (∼20 K) and captures dislocation cell structure at high temperature (∼500 K).

中文翻译：

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微米尺度单晶钽 (α-Ta) 的有限温度原子信息晶体塑性有限元建模

在这项工作中，我们开发了一种基于谐波近似的结晶固体多尺度晶体缺陷动力学 (MCDD) 的温度相关高阶柯西-伯恩 (THCB) 规则。作为模板，我们采用 THCB 规则为体心立方 (BCC) 单晶钽开发了一个原子本构模型（$\alpha$-Ta)。考虑到不同工艺区单元应变梯度的影响，采用相应的高阶应力来模拟单晶的晶体塑性$\alpha$-Ta。与面心立方晶体不同，BCC 晶体受温度的影响很大。本文表明，开发的有限温度原子通知晶体塑性有限元方法能够捕获与温度相关的位错子结构，从而捕获晶体塑性变形。本工作的主要贡献和新颖之处在于以下发现：（1）发展了 THCB 规则和原子通知应变梯度理论，并导出了相应的与温度相关的高阶应力和弹性张量公式；(2) 有限温度MCDD提供了一种原子信息晶体塑性有限元方法，可以模拟微米级及以上立体三角形内任意取向的各向异性晶体塑性；$\alpha$-Ta); (4) 开发的 MCDD 能够捕捉到单晶塑性的尺寸效应；(5) 有限温度 MCDD 可以模拟温度相关的位错子结构，它可以在低温 (~20 K) 下捕获单晶钽中的交叉滑移，在高温 (~500 K) 下捕获位错单元结构。