Formation of dislocation patterns: Computer simulations

Dislocations patterns have been extensively studied by means of TEM. In parallel, theoretical approaches have been developed by using two methods; reaction diffusion schemes and computer simulation models. This distinction is not rigid since some computer models include the former approach in their evolution equations. Independently from the difficulties each approach presents in formulating the collective behavior of dislocations, the aim of these studies is to exhibit simple dislocation patterns as persistent slip bands and/or cellular organization. In this context, computer simulations brought a methodology which undoubtedly is a complement to the existing approaches for dislocations. Nevertheless, several remarks must be pointed out about the results obtained with the method. First, the conditions of simulations (e.g., cutoff procedure, periodic boundaries conditions), have been extensively criticized and responsible for spurious patterns. Second, the simulations developed do not show clearly the formation of cell structures. Third, the simulations performed do not tell us about the evolution of dislocation patterns in function of the parameters such as dislocation density, external force, or friction stress. The aim of the simulations presented here is to study at the mesoscopic scale the formation of dislocation patterns in two dimensions. For this, we used systems of large dimensions (20 mu)(2) and rigid boundaries conditions which permitted us to avoid a cutoff procedure. The simulations performed exhibit the formation of dipolar walls present in persistent slip bands and clearly show the formation of cell organizations. For each pattern observed, we have deduced relationships between the size of the patterns and the parameters used as dislocation density, external force, or friction stress. And indeed, the results obtained show a good agreement with experimental laws.