Internal Stress Field of Double Cross-slip using Level Set Dislocation Dynamics

Abstract

A three-dimensional level set method (LSM) was proposed for dislocation dynamics of which the dislocation curves were smoothly evolved, especially when topological changes of merging and breaking occur. The intersections of the zero levels of two level set functions are used to represent the dislocation lines in three dimensions. Fast marching method (FMM) or fast sweeping method (FSM) creating signed distance function (SDF) from the given interface can incorporate the existing different shapes into one level set function. Therefore, the dislocation lines can be represented by one set of level set functions. Within some specific restrictions, we succeeded to demonstrate some dislocation movements like cross-slip, double cross-slip and dislocation interactions on cross-slip plane, and discussed the internal stress field around such a complex topological dislocation configuration.