A comparison between crystal and isotropic strain gradient plasticity theories with accent on the role of the plastic spin

Lorenzo Bardella

DICATA, University of Brescia, Via Branze 43, Brescia 25123, Italy


In the small deformation range, we consider crystal and isotropic "higher-order" theories of strain gradient plasticity, in which two different types of size effects are accounted for: (i) that dissipative, entering the model through the definition of an effective measure of plastic deformation peculiar of the isotropic hardening function and (ii) that energetic, included by defining the defect energy (i.e., a function of Nye's dislocation density tensor added to the free energy; see, e.g., Gurtin, 2002). In order to compare the two modellings, we recast both of them into a unified deformation theory framework and apply them to a simple boundary value problem for which we can exploit the Gamma-convergence results of Bardella and Giacomini (2008), in which the crystal model is made isotropic by imposing that any direction be a possible slip system. We show that the isotropic modelling can satisfactorily approximate the behaviour described by the isotropic limit obtained from the crystal modelling if the former constitutively involves the plastic spin, as in the theory put forward in section 12 of Gurtin (2004). The analysis suggests a criterium for choosing the material parameter governing the plastic spin dependence into the relevant Gurtin model.

Author Keywords: Crystal plasticity; Deformation theory; Strain gradient plasticity