Abstract

This paper presents an approach to evaluate the failure of arbitrarily inclined interfaces using FE models with structured spatial discretization, providing accurate prediction of crack propagation along paths known a priori that are not constrained to the element boundaries. The combination of algorithms for the generation of structured discretization of representative polycrystalline microstructures with novel cohesive element formulations allow modelling the failure of complex topologies along rasterised boundaries, with noticeably higher computational efficiency and comparable accuracy. Two formulations of raster cohesive elements are presented, adopting either elastic-brittle or Tvergaard–Hutchinson traction separation laws. The formulations proposed are first validated comparing the failure of the interface within bi-crystal structures discretised using hexahedral elements either within a structured mesh (i.e. with rasterised boundaries) or an unstructured mesh (i.e. with planar boundary). Subsequently, the effectiveness of the formulations is demonstrated comparing the inter-granular crack propagation within complex polycrystalline microstructures. The behaviour of the novel cohesive element formulation in structured meshes consisting of regular hexahedral elements is in excellent agreement with the deformation and failure of classic cohesive element formulations placed along the planar boundaries of unstructured meshes consisting of tetrahedral elements. The higher computational cost of the raster cohesive elements is more than compensated by the increase in computational efficiency of structured meshes when compared to unstructured meshes, leading to a reduction of the simulation time of up to over 200 times for the simulations presented in the paper, thus allowing the simulation of large domains.

中文翻译：

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使用结构化网格对任意倾斜界面的故障进行栅格方法建模

摘要

本文提出了一种使用具有结构化空间离散化的有限元模型来评估任意倾斜界面失效的方法，提供了沿着不受单元边界约束的先验已知路径的裂纹扩展的准确预测。用于生成代表性多晶微结构的结构化离散化的算法与新颖的内聚元素公式的组合允许对沿栅格化边界的复杂拓扑的失效进行建模，并且具有显着更高的计算效率和相当的精度。提出了栅格内聚单元的两种公式，采用弹性-脆性或特弗加德-哈钦森牵引分离定律。首先验证所提出的公式，比较使用结构化网格（即具有光栅化边界）或非结构化网格（即具有平面边界）内的六面体单元离散的双晶结构内的界面失效。随后，通过比较复杂多晶微观结构内的晶间裂纹扩展，证明了该配方的有效性。由规则六面体单元组成的结构化网格中的新型粘性单元公式的行为与沿着由四面体单元组成的非结构化网格的平面边界放置的经典粘性单元公式的变形和失效非常一​​致。与非结构化网格相比，结构化网格计算效率的提高足以弥补栅格内聚元素较高的计算成本，从而使本文中提出的模拟时间减少多达 200 倍以上，从而允许模拟大域。