Strongly versus weakly non-local dislocation transport and pile-up

The purpose of this work is the continuum modeling of transport and pile-up of infinite discrete dislocation walls driven by nonlocal interaction and external loading. The underlying model for dislocation wall interaction is based on the non-singular Peierls-Nabarro (PN) model [e.g., 4, Chapter 8] for the dislocation stress field. The influence of strongly non-local (SNL; long-range) interaction, and its approximation as weakly non-local (WNL; short-range), are studied in the context of interaction- and external-load-driven wall pile-up at a boundary. The pile-up boundary is modeled via a spatially dependent dislocation mobility which decreases to zero at the boundary. The pile-up behavior predicted by the current SNL-based continuous wall distribution modeling is consistent with that predicted by discrete wall distribution modeling [e.g., 1, 6]. Both deviate substantially from the pile-up behavior predicted by WNL-based continuous wall distribution modeling [e.g., 2, Chapter 2]. As such, it is clearly essential to account in continuum models for the intrinsic SNL character of the interaction
between same-sign dislocations ”close” to the boundary. Gradient-based WNL ”approximation” of this interaction is not justified.