Dislocation random walk under cyclic deformation

Dislocation motion under cyclic loading is of great interest from theoretical and practical viewpoints. In this paper, we develop a random walk model for the purpose of evaluating the diffusion coefficient of dislocation under cyclic loading condition. The dislocation behavior was modeled as a series of binomial stochastic processes (one-dimensional random walk), where dislocations are randomly driven by the external load. The probability distribution of dislocation motion and the diffusion coefficient per cycle were analytically derived from the random-walk description as a function of the loading condition and the microscopic material properties. The derived equation was validated by comparing the predicted diffusion coefficient with the molecular dynamics simulation result copper under cyclic deformation. As a result, we confirmed fairly good agreement between the random walk model and the molecular dynamics simulation results.