Gradient Crystal Plasticity Modeling of Laminate Microstructures

Metallic materials may show an ultra-fine lamellar morphology leading to desirable macroscopic mechanical properties. In this paper, an analytical method for modeling the size-dependent mechanical behavior of material systems with lamellar microstructure is proposed. The main contribution of this manuscript is the combination of the exact elastic localization relations for a periodic laminate having inhomogeneous phases with a gradient plasticity constitutive model. This allows a new formulation of the equations governing the evolution of the plastic deformation as a closed system of equations. The yield functions form a system of integro-differential equations that can be solved analytically. This new framework allows to model the size-dependent mechanical behavior of multiphase lamellar materials where the subdomains are elastoplastic single crystals. This is demonstrated using a two-phase laminate. In addition, bounds for the qualitative distributions of the plastic slip and the back stress are derived using a dimensionless quantity. The kinematic hardening due to the back stress depends on the lamella width and the slip system orientation. ... mehrThe back stress vanishes not only for increasing lamella widths but also in slip systems where the slip plane normal is parallel to the lamination direction.