Abstract An XFEM-based DDD scheme is developed to study multiple-dislocation emission from the crack tip and crack propagation in the ductile fracture of a single crystal. A dislocation emission model based on Rice-Thomson theory is incorporated to capture the dynamic dislocation emission from the crack-tip and a normal traction-separation distance model to depict the propagation of mode I cohesive crack. The boundary value problem containing complex surfaces/interfaces and discrete dislocations can be solved by the present XFEM-based DDD scheme directly in a unified framework with satisfactory accuracy. A careful examination shows that the local stress field at the crack tip induced by emitted dislocations can be exactly depicted by this XFEM-based DDD scheme. This local stress field can not only shield the crack from the applied load but also inhibit the emission of subsequent dislocations from the crack-tip; therefore, it plays a crucial role in the ductile-to-brittle competition during crack propagation. After careful verification, this XFEM-based DDD scheme is used to simulate dynamic propagation of mode I cohesive crack. The ductile-to-brittle competition in the crack-tip process zone is investigated with a special attention. Both the dislocation emission-crack propagation process within the crack-tip zone and the discrete dislocation dynamics details behind it are captured and show good agreements with the previous MD simulations conducted by other researchers.

中文翻译：

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基于 XFEM 的 DDD 方案模拟裂纹扩展与裂纹尖端位错发射

摘要 为了研究单晶延性断裂中裂纹尖端的多位错发射和裂纹扩展，开发了一种基于 XFEM 的 DDD 方案。结合基于 Rice-Thomson 理论的位错发射模型来捕获来自裂纹尖端的动态位错发射和一个正常的牵引-分离距离模型来描述模式 I 内聚裂纹的传播。包含复杂表面/界面和离散位错的边界值问题可以通过目前基于 XFEM 的 DDD 方案直接在统一框架中以令人满意的精度解决。仔细检查表明，这种基于 XFEM 的 DDD 方案可以准确地描述由发射的位错引起的裂纹尖端的局部应力场。这种局部应力场不仅可以保护裂纹免受外加载荷的影响，还可以抑制裂纹尖端后续位错的发射；因此，它在裂纹扩展过程中的韧脆竞争中起着至关重要的作用。经过仔细验证，这种基于 XFEM 的 DDD 方案用于模拟 I 型内聚裂纹的动态扩展。对裂纹尖端加工区的韧脆竞争进行了特别关注。裂纹尖端区域内的位错发射 - 裂纹扩展过程及其背后的离散位错动力学细节都被捕获，并与其他研究人员进行的先前 MD 模拟显示出良好的一致性。它在裂纹扩展过程中的韧脆竞争中起着至关重要的作用。经过仔细验证，这种基于 XFEM 的 DDD 方案用于模拟 I 型内聚裂纹的动态扩展。对裂纹尖端加工区的韧脆竞争进行了特别关注。裂纹尖端区域内的位错发射 - 裂纹扩展过程及其背后的离散位错动力学细节都被捕获，并与其他研究人员进行的先前 MD 模拟显示出良好的一致性。它在裂纹扩展过程中的韧脆竞争中起着至关重要的作用。经过仔细验证，这种基于 XFEM 的 DDD 方案用于模拟 I 型内聚裂纹的动态扩展。对裂纹尖端加工区的韧脆竞争进行了特别关注。裂纹尖端区域内的位错发射 - 裂纹扩展过程及其背后的离散位错动力学细节都被捕获，并与其他研究人员进行的先前 MD 模拟显示出良好的一致性。