Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 53, Issue 7, Pages 1624-1649Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2004.12.008
Keywords
constitutive behavior; viscoplasticity; strain-gradient plasticity
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This study develops a small-deformation theory of strain-gradient plasticity for isotropic materials in the absence of plastic rotation. The theory is based on a system of microstresses consistent with a microforce balance; a mechanical version of the second law that includes, via microstresses, work performed during viscoplastic flow; a constitutive theory that allows: center dot the microstresses to depend on del E-P, the gradient of the plastic strain-rate, and center dot the free energy Psi to depend on the Burgers tensor G = curl E-P. The microforce balance when augmented by constitutive relations for the microstresses results in a nonlocal flow rule in the form of a tensorial second-order partial differential equation for the plastic strain. The microstresses are strictly dissipative when Psi is independent of the Burgers tensor, but when 0 depends on G the gradient microstress is partially energetic, and this, in turn, leads to a back stress and (hence) to Bauschinger-effects in the flow rule. It is further shown that dependencies of the microstresses on del E-p lead to strengthening and weakening effects in the flow rule. Typical macroscopic boundary conditions are supplemented by nonstandard microscopic boundary conditions associated with flow, and, as an aid to numerical solutions, a weak (virtual power) formulation of the nonlocal flow rule is derived. (c) 2005 Published by Elsevier Ltd.
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