Abstract In this paper, the so-called “β rule” is used to simulate the anisotropic behaviour of directionally solidified superalloys. First, the “mean-field” model is extended to the general case of heterogeneous local elasticity. Two other models also designed using the “self-consistent” framework are applied to make comparisons, either with the assumption of a purely elastic accommodation of grains (Kroner-Weng model) or the translated field theory. As a reference, full-field simulations using a representative volume element (RVE) and a crystal plasticity finite element model (CPFEM) are carried out. Results show that the β rule is able to predict the overall response of the material for various cases such as one-dimensional or two-dimensional cyclic loading with or without a mean stress. Otherwise, local estimations are studied for both mean-field and full-field models. The local responses of the β rule are consistent when they are compared to those of CPFE simulations.

中文翻译：

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镍基定向凝固材料的多尺度模型

摘要 本文采用所谓的“β规则”来模拟定向凝固高温合金的各向异性行为。首先，将“平均场”模型扩展到异质局部弹性的一般情况。应用“自洽”框架设计的另外两个模型进行比较，要么假设谷物的纯弹性调节（Kroner-Weng 模型），要么使用平移场理论。作为参考，使用代表性体积元 (RVE) 和晶体塑性有限元模型 (CPFEM) 进行全场模拟。结果表明，β 规则能够预测材料在各种情况下的整体响应，例如具有或不具有平均应力的一维或二维循环载荷。除此以外，研究了平均场和全场模型的局部估计。β 规则的局部响应与 CPFE 模拟的局部响应相比是一致的。