Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue

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