On precipitate induced hardening in crystal plasticity: theory

A material description for the elasto-plastic deformation of crystals with non-shearable precipitates at finite strains is presented in this article. On the basis of the elastic inclusion model of Bate et al., [Acta Metall. 29 (1981), 1797–1814] the constitutive equations are formulated in a crystal plasticity setting. The anisotropic kinematic hardening for the actual yield condition of the slip systems is described by the averaged accommodation tensor over all precipitates of an aggregate. For needle and disk-like shaped precipitates the incorporation of precipitate rotations is suggested to describe the evolution of back stress terms in the deformation process. The dependencies of the kinematic hardening description on shape, size, and orientation of the precipitates within the deformation process are discussed.