MESOSCOPIC DYNAMICS ON DISLOCATION PATTERNING IN FATIGUED MATERIAL BY CELLULAR AUTOMATA(Special Issue on Hierarchical Estimations of Materials Strength)

A typical pattern formation of collective dislocations under cyclic loading, the persistent slip bands (PSBs), is simulated by the cellular automata (CA) method. The local rule of CA taken in the present paper is the weighted addition modulo two rule. Each weight is chosen referring to the reaction-diffusion coupled differential equations with respect to immobile and mobile dislocation densities. The mesoscopic evolution of the immobile dislocation density is driven by the space-oriented bifurcation (Turing instability) and results in the ladder-type self-organization. Instability related to the space- and the time-oriented bifurcations is in detail discussed in a one-dimensional model. A stress amplitude-like parameter and two diffusion coefficients of the immobile and mobile dislocation densities highly affect the sequential evolution process. Finally, a two-dimensional hexagonal cell model representing a {111} glide plane of the fcc crystal is proposed. The same local rule is applied along the three preferential sliding directions for easy description of mutual interaction between cells. The evolution yields a localized isotropic and a one-directional anisotropic flow patterns of dislocation densities according to the combination of the three diffusion coefficients.