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Discrete dislocation modeling of fracture in plastically anisotropic metals

机译：塑性各向异性金属断裂的离散位错模型

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The intrinsic lattice resistance to dislocation motion, or Peierls stress, depends on the core structure of the dislocation and is one essential feature controlling plastic anisotropy in materials such as HCP Zn, Mg, and Ti. Here, we implement an anisotropic Peierls model as a friction stress within a 2d discrete dislocation (DD) plasticity model and investigate the role of plastic anisotropy on the crack tip stress fields, crack growth, toughening, and micro-cracking. First, tension tests for a pure single crystal with no obstacles to dislocation motion are carried out to capture the general flow behavior in pure HCP-like materials having slip on basal and pyramidal planes. Then Mode-Ⅰ crack growth in such a single crystal of the HCP material is analyzed using the 2d-DD model. Results show that the fracture toughness scales inversely with the tensile yield stress, largely independent of the plastic anisotropy, so that increasing Peierls stress on the pyramidal planes gives decreasing resistance to crack growth, consistent with recent experiments on Zn. Analyzing the results within the framework of Stress Gradient Plasticity concepts shows that the equilibrium dislocation dipole spacing serves as an internal material length scale for controlling fracture toughness. Furthermore, the fracture toughness of materials with flow stress controlled by a Peierls stress (this work) and of materials with flow stress controlled by dislocation obstacles (prior literature) is unified through the Stress Gradient Plasticity concept. Finally, the DD simulations show that local stress concentrations exist sporadically along the pyramidal plane(s) that emanate from the current crack tip, suggesting an origin for experimentally observed basal-plane microcracking near the tip of large cracks.
机译：晶格对位错运动或Peierls应力的固有抵抗力取决于位错的核心结构，并且是控制HCP Zn，Mg和Ti等材料中塑性各向异性的一项重要特征。在这里，我们将各向异性Peierls模型实现为二维离散位错（DD）塑性模型中的摩擦应力，并研究塑性各向异性对裂纹尖端应力场，裂纹扩展，增韧和微裂纹的作用。首先，对无位错运动障碍的纯单晶进行拉伸测试，以捕获在基平面和棱锥平面上具有滑移的纯HCP类材料中的一般流动行为。然后使用2d-DD模型分析了这种HCP材料单晶中的Ⅰ型裂纹扩展。结果表明，断裂韧性与拉伸屈服应力成反比，在很大程度上与塑性各向异性无关，因此，在锥面上增加的Peierls应力会降低对裂纹扩展的抵抗力，这与最近对Zn进行的实验一致。在应力梯度可塑性概念的框架内分析结果表明，平衡位错偶极间距可作为控制断裂韧性的内部材料长度尺度。此外，通过应力梯度可塑性概念统一了由Peierls应力控制的流应力材料的断裂韧性（此项工作）和由位错障碍控制的流应力材料的断裂韧性（现有文献）。最后，DD模拟表明，局部应力集中沿着从当前裂纹尖端发出的锥体平面零星地存在，这为实验观察到的大裂纹尖端附近的基底平面微裂纹提供了起点。

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