Abstract
A model of crystal plasticity is developed in which the effects of plastic flow non-uniformity are described through the full dislocation density tensor. The micromorphic approach is used in which the dislocation density tensor is represented by the curl of an independent constitutive variable called microdeformation. The microdeformation tensor is enforced by an energetic penalty term to be close to the actual plastic distortion tensor. The curl of microdeformation tensor enters the constitutive model in two independent but complementary ways. First, it is an argument of the free energy density function, which describes the kinematic-type hardening in cyclic non-uniform deformation. Second, its rate influences the rates of critical resolved shear stresses, which corresponds to additional isotropic hardening caused by incompatibility of the plastic flow rate. The latter effect, missing in the standard slip-system hardening rule, is described in a simple manner that does not require any extra parameter in comparison to the non-gradient theory. In the proposed model there are two independent internal length scales whose interplay is examined by means of 1D and 2D numerical examples of plastic shearing of a single crystal.
Highlights
The aim of this paper is to examine a crystal plasticity model that combines in a novel way two physically related but conceptually and mathematically distinct effects of plastic flow non-uniformity on the material hardening
A new version of the micromorphic model of crystal plasticity has been developed by combining the microcurl model (Cordero et al, 2010) with the minimal gradient-enhancement of the hardening law (Petryk and Stupkiewicz, 2016)
The curl of the microdeformation tensor as a basic constitutive variable has entered the computational model in two complementary ways
Summary
The aim of this paper is to examine a crystal plasticity model that combines in a novel way two physically related but conceptually and mathematically distinct effects of plastic flow non-uniformity on the material hardening. Instead of considering a microdeformation tensor, these authors introduce a scalar micromorphic variable related to the accumulated plastic slip, and its gradient into the free energy density function. The advantage of this model is the reduction of complexity from the computational mechanics point of view. The present paper extends the earlier works to a novel combination of the ‘microcurl’ model of micromorphic type (Cordero et al, 2010) and the ‘minimal’ gradient-enhancement of the incremental hardening law (Petryk and Stupkiewicz, 2016). Throughout this paper, the attention is limited to quasi-static isothermal deformation
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