Mechanics of dislocation pile-ups : a unification of scaling regimes

Research output: Contribution to journalArticleAcademicpeer-review

23 Citations (Scopus)

Abstract

This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a micro-to-meso-upscaling, and we obtain five expressions for the mesoscopic (continuum) internal stress. The upscaling method we illustrate here can be made mathematically rigorous, as we show in the companion paper (Geers et al., 2013. Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. Arch. Ration. Mech. Anal. 209, 495–539). The focus of the present paper is on the mechanical interpretation of the resulting internal stresses. In the continuum limit we recover some expressions for the internal stress that are already in use in the mechanical community, as well as some new models. The results in this paper offer a unifying approach to such models, since they can be viewed as the outcome of the same discrete dislocation setup, for different values of the dimensionless parameter (i.e., for different local dislocations arrangements). In addition, the rigorous nature of the upscaling removes the need for ad hoc assumptions. Keywords: Dislocations; Pile-up; Internal stress; Plasticity; Upscaling
Original languageEnglish
Pages (from-to)42-61
Number of pages20
JournalJournal of the Mechanics and Physics of Solids
Volume70
DOIs
Publication statusPublished - 2014

Fingerprint

piles
residual stress
Piles
Residual stresses
Mechanics
scaling
Edge dislocations
edge dislocations
continuums
rations
arches
Arches
plastic properties
Plasticity

Cite this

@article{6bab718f885a42fca5655b78d99934c4,
title = "Mechanics of dislocation pile-ups : a unification of scaling regimes",
abstract = "This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a micro-to-meso-upscaling, and we obtain five expressions for the mesoscopic (continuum) internal stress. The upscaling method we illustrate here can be made mathematically rigorous, as we show in the companion paper (Geers et al., 2013. Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. Arch. Ration. Mech. Anal. 209, 495–539). The focus of the present paper is on the mechanical interpretation of the resulting internal stresses. In the continuum limit we recover some expressions for the internal stress that are already in use in the mechanical community, as well as some new models. The results in this paper offer a unifying approach to such models, since they can be viewed as the outcome of the same discrete dislocation setup, for different values of the dimensionless parameter (i.e., for different local dislocations arrangements). In addition, the rigorous nature of the upscaling removes the need for ad hoc assumptions. Keywords: Dislocations; Pile-up; Internal stress; Plasticity; Upscaling",
author = "L. Scardia and R.H.J. Peerlings and M.A. Peletier and M.G.D. Geers",
year = "2014",
doi = "10.1016/j.jmps.2014.04.014",
language = "English",
volume = "70",
pages = "42--61",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier",

}

Mechanics of dislocation pile-ups : a unification of scaling regimes. / Scardia, L.; Peerlings, R.H.J.; Peletier, M.A.; Geers, M.G.D.

In: Journal of the Mechanics and Physics of Solids, Vol. 70, 2014, p. 42-61.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Mechanics of dislocation pile-ups : a unification of scaling regimes

AU - Scardia, L.

AU - Peerlings, R.H.J.

AU - Peletier, M.A.

AU - Geers, M.G.D.

PY - 2014

Y1 - 2014

N2 - This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a micro-to-meso-upscaling, and we obtain five expressions for the mesoscopic (continuum) internal stress. The upscaling method we illustrate here can be made mathematically rigorous, as we show in the companion paper (Geers et al., 2013. Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. Arch. Ration. Mech. Anal. 209, 495–539). The focus of the present paper is on the mechanical interpretation of the resulting internal stresses. In the continuum limit we recover some expressions for the internal stress that are already in use in the mechanical community, as well as some new models. The results in this paper offer a unifying approach to such models, since they can be viewed as the outcome of the same discrete dislocation setup, for different values of the dimensionless parameter (i.e., for different local dislocations arrangements). In addition, the rigorous nature of the upscaling removes the need for ad hoc assumptions. Keywords: Dislocations; Pile-up; Internal stress; Plasticity; Upscaling

AB - This paper unravels the problem of an idealised pile-up of n infinite, equi-spaced walls of edge dislocations at equilibrium. We define a dimensionless parameter that depends on the geometric, constitutive and loading parameters of the problem, and we identify five different scaling regimes corresponding to different values of that parameter for large n. For each of the cases we perform a micro-to-meso-upscaling, and we obtain five expressions for the mesoscopic (continuum) internal stress. The upscaling method we illustrate here can be made mathematically rigorous, as we show in the companion paper (Geers et al., 2013. Asymptotic behaviour of a pile-up of infinite walls of edge dislocations. Arch. Ration. Mech. Anal. 209, 495–539). The focus of the present paper is on the mechanical interpretation of the resulting internal stresses. In the continuum limit we recover some expressions for the internal stress that are already in use in the mechanical community, as well as some new models. The results in this paper offer a unifying approach to such models, since they can be viewed as the outcome of the same discrete dislocation setup, for different values of the dimensionless parameter (i.e., for different local dislocations arrangements). In addition, the rigorous nature of the upscaling removes the need for ad hoc assumptions. Keywords: Dislocations; Pile-up; Internal stress; Plasticity; Upscaling

U2 - 10.1016/j.jmps.2014.04.014

DO - 10.1016/j.jmps.2014.04.014

M3 - Article

VL - 70

SP - 42

EP - 61

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

ER -