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 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.

Automated summary

Spontaneous pattern formation by dislocations in metal fatigue under cyclic straining shows a crossover from a 2D spot-scattered pattern to a 1D ladder-shaped pattern. However, the physical mechanism behind this crossover remains unclear. This study proposes a bifurcation diagram that explains the crossover using a weakly nonlinear stability analysis. It is found that inequalities with respect to nonlinearity parameters can describe the selection rule between the two dislocation patterns, spot and ladder-shaped.