A peridynamic approach to solving general discrete dislocation dynamics problems in plasticity and fracture: Part II. Applications

In Part II of this work we extend the method introduced in Part I to consider dislocation dynamic evolution through dislocations nucleation, glide, pile-up, and annihilation. The SP DDD-PD scheme is employed to investigate uniaxial tension in a single crystal and a polycrystal and verify its accuracy. The model is then used to simulate elastoplastic fracture by considering interactions between dislocations and crack growth. For Mode I elastoplastic fracture in a single crystal, we observe that the crack path is “attracted” towards regions of high density of gliding dislocations, leading to an undulating crack paths, as observed in experiments but never replicated by continuum-level computational models before. Tests on different sample sizes show how the proximity of constraints to the crack tip can lead to plastic hardening. Ductile-to-brittle transition happens naturally in this model when the crack, under Mode I displacement-controlled loading, approaches a free edge. A new way to calibrate the critical bond strain based on the material toughness or fracture energy is proposed. The present SP DDD-PD scheme can be used to investigate complicated elastoplastic fracture problems in which the interaction between dislocation motion and damage is critical.