Abstract The single crystal elastic anisotropy is one of the most important properties affecting the macroscopic response of polycrystalline materials, both in the elastic regime and the early stages of plastic deformation. In this work, the impact of monocrystalline parameters on the mechanical behaviour of cubic polycrystals is studied in detail. The analysis is conducted with an RVE-based computational homogenisation framework which includes several original strategies and criteria developed to enable the efficient statistical analysis of virtual micro-structures. In particular, these developments include a stress-driven adaptation to the usually employed strain-driven homogenisation approach, used to study the plastic polycrystalline response in stress space. The effects of number of grains and realisations considered, finite element mesh discretisation level, and algorithms used to generate both the grain morphology and orientation distribution are also assessed. Considering a number of materials with cubic symmetry, expressions for the number of grains required for an elastically isotropic response are deduced, along with bounds for the homogenised elastic stiffness components of oligocrystals, in both cases as a function of the monocrystalline elastic anisotropy. In the plastic domain, multiple microscopic and macroscopic criteria to describe the yield onset of such polycrystals are evaluated and compared. This is done for both elastically isotropic and anisotropic polycrystals, where once again the effect of different levels of monocrystalline elastic anisotropy are evaluated. The numerically derived yield surface of isotropic polycrystals is fitted to both Tresca and von Mises yield functions, and for anisotropic oligocrystals, the statistical bounds for the expected distribution of micro-yield stresses are deduced, in terms of both the number of grains and of the level of single crystal elastic anisotropy. The results obtained are thus a step towards clarifying the effect of important micro-structural parameters in establishing the minimum representative volume element (RVE) size for metallic alloys in elasto-plastic applications.

中文翻译：

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弹性各向异性对立方寡晶和多晶宏观本构响应和屈服起始的作用

摘要 单晶弹性各向异性是影响多晶材料宏观响应的最重要特性之一，无论是在弹性状态还是塑性变形的早期阶段。在这项工作中，详细研究了单晶参数对立方多晶力学行为的影响。该分析是使用基于 RVE 的计算同质化框架进行的，该框架包括为实现虚拟微结构的有效统计分析而开发的几个原始策略和标准。特别是，这些发展包括对通常采用的应变驱动均质化方法的应力驱动适应，用于研究应力空间中的塑性多晶响应。考虑的谷物数量和实现的影响，还评估了用于生成晶粒形态和取向分布的有限元网格离散化级别和算法。考虑到许多具有三次对称性的材料，推导出弹性各向同性响应所需的晶粒数量的表达式，以及寡晶均质弹性刚度分量的界限，在这两种情况下，作为单晶弹性各向异性的函数。在塑性领域，评估和比较了描述这种多晶产量开始的多个微观和宏观标准。这是对弹性各向同性和各向异性多晶进行的，其中再次评估了不同水平的单晶弹性各向异性的影响。各向同性多晶的数值导出屈服面拟合 Tresca 和 von Mises 屈服函数，对于各向异性寡晶，推导出微屈服应力预期分布的统计界限，根据晶粒数量和单晶弹性各向异性水平。因此，所获得的结果是朝着澄清重要的微观结构参数在确定弹塑性应用中金属合金的最小代表性体积元素 (RVE) 尺寸方面的影响迈出的一步。