Abstract Two-dimensional discrete dislocation plasticity (2D-DDP) has shown to be a powerful tool for studying micro-plasticity problems such as size effects in single crystals, fracture of bimaterial interfaces, delamination of thin films, fatigue crack growth etc. The power of 2D-DDP lies in the application of edge dislocation dipoles as the vehicle for plastic slip: the loss of accuracy in the description of dislocation structures is counter-balanced by its simplicity and the possibility to reach larger plastic strains. The constitutive rules for dislocation evolution in 2D-DDP used so far are tuned to FCC crystals and need to be modified to be used for BCC materials. One of the key challenges in extending the method to BCC materials is that, contrary to FCC, the mobilities of edge and screw dislocations in BCC crystals differ vastly from each other, so that the screw mobility will be rate limiting the plastic slip. Thus, a method is required to map the edge and screw mobilities of dislocation loops into an effective mobility to be used in 2D. To do so, we here propose a 3D-to-2D procedure that is based on the notion of conservation of in-plane plastic strain rate. The consequence of this approach is that the effective 2D mobility for FCC crystals is not simply equal to the uniform mobility of a dislocation loop, as has been assumed by all 2D models to date, but also on the size of edge dipoles. In order to assess the consequences of this departure from the current literature, we considered a few key problems involving plasticity size effects and crack growth, and compared the predictions assuming constant mobility versus the proposed effective mobility. After observing that, overall, the predictions do not deviate substantially, we proceed with application of the 3D-to-2D procedure to compute the effective 2D mobility for BCC materials based on their edge and screw mobilities. The validation of the approach is done by comparison of the predicted rate sensitivity of polycrystalline iron with the experimental rate sensitivity at room temperature, which are found to be in fairly good agreement.

中文翻译：

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BCC位错在二维离散位错塑性中的有效迁移率

摘要 二维离散位错塑性 (2D-DDP) 已被证明是研究微塑性问题的有力工具，例如单晶尺寸效应、双材料界面断裂、薄膜分层、疲劳裂纹扩展等。 2D-DDP 的独特之处在于应用边缘位错偶极子作为塑性滑移的载体：位错结构描述的准确性损失被其简单性和达到更大塑性应变的可能性所抵消。迄今为止使用的 2D-DDP 中位错演化的本构规则适用于 FCC 晶体，需要修改以用于 BCC 材料。将该方法扩展到 BCC 材料的主要挑战之一是，与 FCC 相反，BCC 晶体中刃位错和螺旋位错的迁移率彼此差异很大，因此螺旋迁移率将限制塑性滑移的速率。因此，需要一种方法来将位错环的边缘和螺旋迁移率映射为要在 2D 中使用的有效迁移率。为此，我们在此提出了一种基于平面内塑性应变率守恒概念的 3D 到 2D 程序。这种方法的结果是 FCC 晶体的有效 2D 迁移率不仅等于迄今为止所有 2D 模型所假设的位错环的均匀迁移率，而且还取决于边缘偶极子的大小。为了评估这种偏离当前文献的后果，我们考虑了一些涉及塑性尺寸效应和裂纹扩展的关键问题，并将假设恒定迁移率的预测与建议的有效迁移率进行比较。在观察到之后，总体而言，预测没有显着偏离，我们继续应用 3D 到 2D 程序，根据 BCC 材料的边缘和螺杆迁移率计算其有效 2D 迁移率。该方法的验证是通过将多晶铁的预测速率灵敏度与室温下的实验速率灵敏度进行比较来完成的，发现它们具有相当好的一致性。