Abstract Heterogeneous structures (HS) have been reported to overcome the long-standing challenge of the trade-off between strength and ductility in metallic materials. The deformation incompatibility between the fine grains (FG) and coarse grains (CG), producing hetero-deformation induced (HDI) hardening, is the primary mechanism for superior mechanical properties of HS. In this paper, a kinematic hardening law within the framework of crystal plasticity is modified to quantify the HDI hardening of HS in which a new parameter is established to consider the strength mismatch between FG and CG. Taking bimodal structure (BS) as an example of HS, the good agreement between the experimental and numerical results show that the proposed model can successively predict the mechanical properties, including the evolution of back stress, yield strength and strain hardening of BS with various grain size distributions. Furthermore, the underlying strengthening mechanisms are revealed by switching the HDI hardening term and analyzing the partitioning of the strain and stress in different components of BS. By manipulating the grain size ratio of BS, it is found that the effect of HDI hardening is more sensitive to the size of FG than that of CG. The proposed hardening law can provide a significant guide for heterogeneous material design.

中文翻译：

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基于晶体塑性的双峰结构考虑异质变形诱导硬化的修正运动硬化模型

摘要 据报道，异质结构 (HS) 克服​​了金属材料强度和延展性之间权衡的长期挑战。细晶粒 (FG) 和粗晶粒 (CG) 之间的变形不相容性，产生异质变形诱导 (HDI) 硬化，是 HS 优异机械性能的主要机制。在本文中，修改了晶体塑性框架内的运动学硬化定律以量化 HS 的 HDI 硬化，其中建立了一个新参数来考虑 FG 和 CG 之间的强度失配。以双峰结构（BS）为例，实验结果与数值结果吻合良好，表明该模型可以连续预测力学性能，包括背应力的演变，具有不同晶粒尺寸分布的 BS 的屈服强度和应变硬化。此外，通过切换 HDI 硬化项并分析 BS 不同组件中应变和应力的分配，揭示了潜在的强化机制。通过控制 BS 的晶粒尺寸比，发现 HDI 硬化的影响对 FG 的尺寸比 CG 更敏感。提出的硬化定律可以为异质材料设计提供重要的指导。发现HDI硬化的效果对FG的尺寸比CG的更敏感。提出的硬化定律可以为异质材料设计提供重要的指导。发现HDI硬化的效果对FG的尺寸比CG的更敏感。提出的硬化定律可以为异质材料设计提供重要的指导。