On plastic deformation and the dynamics of 3D dislocations

A three-dimensional (3D) mesoscopic model to simulate the collective dynamic behavior of a large number of curved dislocations of finite lengths has been developed for the purpose of analyzing deformation patterns and instabilities, including the formation of dislocation cell structures. Each curved dislocation is approximated by a piecewise continuous array of straight line segments. The interactions among the segments, including line-tension and self-interactions, are treated explicitly. For longer-range interactions, the space is divided into a regular cellular array and the elastic fields of the dislocations in a remote cell approximated by a multipolar expansion, leading to an order N algorithm for the description of a cell containing N dislocations. For large arrays, the simulation volume is divided into cubical cells. A discrete random starting array is selected for the master cell and its nearest neighbors, which constitute an order 2 cell. Reflection boundary conditions are imposed for near-neighbor order 2 cells and so forth, creating an NaCl-type lattice array. The boundaries between the cells are considered to be relaxed grain boundaries. That is, recovery within the boundaries and rotation across them are considered to occur so that the boundaries have no associated elastic fields. This cell hierarchy, coupled with the multipole expansion, is suitable for the use of massively parallel computation, with individual cells assigned to separate processors.