Continuum dislocation dynamics (CDD) aims at representing the evolution of systems of curved and connected dislocation lines in terms of density-like field variables. Here we discuss how the processes of dislocation multiplication and annihilation can be described within such a framework. We show that both processes are associated with changes in the volume density of dislocation loops: dislocation annihilation needs to be envisaged in terms of the merging of dislocation loops, while conversely dislocation multiplication is associated with the generation of new loops. Both findings point towards the importance of including the volume density of loops (or ’curvature density’) as an additional field variable into continuum models of dislocation density evolution. We explicitly show how this density is affected by loop mergers and loop generation. The equations which result for the lowest order CDD theory allow us, after spatial averaging and under the assumption of unidirectional deformation, to recover the classical theory of Kocks and Mecking for the early stages of work hardening.

中文翻译：

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continu灭和连续位错动力学的来源

连续位错动力学（CDD）旨在代表像密度场变量那样的弯曲和连接的位错线系统的演化。在这里，我们讨论如何在这种框架内描述位错倍增和an灭的过程。我们显示这两个过程都与位错环的体积密度的变化相关：位错an灭需要根据位错环的合并来设想，而相反，位错倍增与新环的产生相关。这两个发现都指出了将环的体积密度（或“曲率密度”）作为位错密度演化的连续模型的附加场变量的重要性。我们明确显示了此密度如何受循环合并和循环生成的影响。