Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue

Abstract

Spontaneous pattern formation by a large number of dislocations is commonly observed during the initial stages of metal fatigue under cyclic straining. It was experimentally found that the geometry of the dislocation pattern undergoes a crossover from a 2D spot-scattered pattern to a 1D ladder-shaped pattern as the amplitude of external shear strain increases. However, the physical mechanism that causes the crossover between different dislocation patterns remains unclear. In this study, we theorized a bifurcation diagram that explains the crossover between the two dislocation patterns. The proposed theory is based on a weakly nonlinear stability analysis that considers the mutual interaction of dislocations as a nonlinearity. It was found that the selection rule among the two dislocation patterns, “spotted” and “ladder-shaped”, can be described by inequalities with respect to nonlinearity parameters contained in the governing equations.

Keywords

• pattern formation
• metal fatigue
• bifurcation theory
• turing instability
• reaction–diffusion dynamics