Thermomechanical processing of crystalline materials induces microstructural evolution such as grain nucleation and growth. In the numerical simulation of these processes, grain nucleation is generally treated as an additional step in which circular or spherical grains are added in regions where a critical dislocation density, stress or strain are reached. In this paper, systematic finite element simulations are performed showing that the Kobayashi–Warren–Carter (KWC) phase field model and its coupling with Cosserat crystal plasticity predict spontaneous nucleation of new grains in single crystals in the presence of lattice orientation/rotation gradients. The numerical analysis of the stability of gradients of lattice rotation and dislocation-based stored energy indicates that a gradient of stored energy alone is not sufficient to trigger grain formation. As an application, the KWC–Cosserat model is used to simulate the torsion and annealing of a copper single crystal bar with a circular cross section. This mechanical loading produces a large, fairly uniform axial rotation gradient which induces nucleation in the form of a stack of cylindrical grains. Plastic strain gradients in cross-sections predicted by the 3D finite element simulation, are not strong enough to compete with the longitudinal nucleation process, as confirmed by experimental observations from the literature.

中文翻译：

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塑性变形单晶晶粒成核的 Cosserat 相场建模

晶体材料的热机械加工会引起微观结构的演变，例如晶粒成核和生长。在这些过程的数值模拟中，晶粒成核通常被视为附加步骤，其中在达到临界位错密度、应力或应变的区域中添加圆形或球形晶粒。在本文中，系统的有限元模拟表明，Kobayashi-Warren-Carter (KWC) 相场模型及其与 Cosserat 晶体塑性的耦合可以预测在存在晶格取向/旋转梯度的情况下单晶中新晶粒的自发成核。对晶格旋转梯度和基于位错的存储能量的稳定性的数值分析表明，仅存储能量的梯度不足以触发晶粒形成。作为一个应用，KWC-Cosserat 模型用于模拟圆形截面铜单晶棒的扭转和退火。这种机械载荷产生一个大的、相当均匀的轴向旋转梯度，从而引起圆柱形颗粒堆叠形式的成核。正如文献中的实验观察所证实的那样，3D 有限元模拟预测的横截面中的塑性应变梯度不足以与纵向成核过程竞争。