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A unified treatment of strain gradient plasticity
KTH, Superseded Departments, Solid Mechanics.ORCID iD: 0000-0002-0307-8917
2004 (English)In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 52, no 6, 1379-1406 p.Article in journal (Refereed) Published
Abstract [en]

A theoretical framework is presented that has potential to cover a large range of strain gradient plasticity effects in isotropic materials. Both incremental plasticity and viscoplasticity models are presented. Many of the alternative models that have been presented in the literature are included as special cases. Based on the expression for plastic dissipation, it is in accordance with Gurtin (J. Mech. Phys. Solids 48 (2000) 989; Int. J. Plast. 19 (2003) 47) argued that the plastic flow direction is governed by a microstress q(ij) and not the deviatoric Cauchy stress sigma'(ij) that has been assumed by many others. The structure of the governing equations is of second order in the displacements and the plastic strains which makes it comparatively easy to implement in a finite element programme. In addition, a framework for the formulation of consistent boundary conditions is presented. It is shown that there is a close connection between surface energy of an interface and boundary conditions in terms of plastic strains and moment stresses. This should make it possible to study boundary layer effects at the interface between grains or phases. Consistent boundary conditions for an expanding elastic-plastic boundary are as well formulated. As examples, biaxial tension of a thin film on a thick substrate, torsion of a thin wire and a spherical void under remote hydrostatic tension are investigated.

Place, publisher, year, edition, pages
2004. Vol. 52, no 6, 1379-1406 p.
Keyword [en]
strain gradients, material length scales, constitutive behaviour, elastic-plastic material, elastic-viscoplastic material, discrete dislocation analysis, thin-films, nonlocal continuum, single-crystals, free-energy, deformation, predictions, viscoplasticity, microforces, composite
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-23344DOI: 10.1016/j.jmps.2003.11.002ISI: 000220933700007Scopus ID: 2-s2.0-1642633214OAI: oai:DiVA.org:kth-23344DiVA: diva2:342042
Note
QC 20100525 QC 20111026Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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Gudmundson, Peter

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