Strongly non-local modelling of dislocation transport and pile-up

J.R. Mianroodi, R.H.J. Peerlings, B. Svendsen

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The purpose of this work is the continuum modelling of transport and pile-up of infinite discrete dislocation walls driven by non-local interaction and external loading. To this end, the underlying model for dislocation wall interaction is based on the non-singular Peierls-Nabarro (PN) model for the dislocation stress field. For simplicity, attention is restricted to walls consisting of single-sign dislocations and to continuous wall distributions on a single glide plane. In this context, 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 modelled via a spatially dependent dislocation mobility which decreases to zero at the boundary. The pile-up behaviour predicted by the current SNL-based continuous wall distribution modelling is consistent with that predicted by discrete wall distribution modelling. Both deviate substantially from the pile-up behaviour predicted by WNL-based continuous wall distribution modelling. 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.

Original languageEnglish
Pages (from-to)1171-1187
Number of pages17
JournalPhilosophical Magazine
Issue number12
Publication statusPublished - 22 Apr 2016


  • Peierls-Nabarro modelling
  • pile-up
  • strongly non-local interaction
  • transport


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