Evolution of edge dislocations under elastic and inelastic strains: A nanoscale phase-field study

A phase-field approach is used to study the evolution of edge dislocations in single crystals at the nanoscale. The characteristics of an advanced phase-field approach for dislocation evolution are investigated, and some advancements are made to make it more accurate in predicting the dislocation evolution. To verify the model and numerical procedure, the height of a slip system, the Burgers vector, and the distance between the cores of dislocations are calculated, which show a very good agreement with those of the existing theoretical solutions. The analytical and numerical solutions for the equilibrium shear stress versus order parameter are obtained, and in contrast to the previous models, the current model represents a physical model for the dislocation growth. Different methods are investigated to prevent dislocation widening, revealing that the periodic step-wise function of crystalline energy coefficient performs better than the periodic step-wise function of the Burgers vector and can keep dislocations inside their physical height. Several functions for the coefficient of normal gradient energy are investigated to prevent dislocation localization inside the dislocation band. The sample size effect on the dislocation evolution is also studied which reveals a non-linear variation of the number of dislocations inside the slip system versus the sample size. The presented model and results are useful for understanding and predicting the dislocation evolution and its interaction with other phenomena such as phase transformation.