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

Abstract eng:
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]. The influence of strongly non-local (SNL; long-range) interaction, and its approximation as weakly nonlocal (WNL; short-range), are studied in the context of wall pile-up at a boundary. The boundary is modeled via a spatially dependent dislocation mobility. 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 essential to account 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.

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