On the formulation of higher gradient single and polycrystal plasticity

Menzel, A. and Steinmann, P. (1998) On the formulation of higher gradient single and polycrystal plasticity. Journal De Physique. IV : JP, 8(PR8), Pr8-239-Pr8-247. (doi: 10.1051/jp4:1998830)

Abstract

This contribution aims in a geometrically linear formulation of higher gradient plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. Thereby, general continuum dislocation densities and incompatibilities are introduced from the viewpoint of continuum mechanics by considering the spatial closure failure of arbitrary line integrals of the displacement differential. Then these findings are translated to the plastic parts of the displacement gradient, the so called plastic distorsion, and the plastic strain, respectively, within an elasto-plastic solid thus defining tensor fields of plastic dislocation densities and plastic incompatibilities. Next, in the case of single crystalline material the plastic dislocation density and in the case of polycrystalline material the plastic incompatibility are considered within the exploitation of the thermodynamical principle of positive dissipation. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates for single crystals second spatial derivatives of the plastic deformation gradient and for polycrystals fourth spatial derivatives of the plastic strains into the yield condition. Moreover, these modifications mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law.

• Item Type: Articles
• Additional Information: 2nd European Mechanics of Materials Conference on Mechanics of Materials with Intrinsic Length Scale : Physics, Experiments, Modelling and Applications.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Menzel, A., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Journal De Physique. IV : JP

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