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Abstract

During the deformation of polycrystals, pronounced strain gradients may occur at grain boundaries or phase boundaries due to mis-orientations and eigen strains of phase transformation. Hence, even under globally uni-axial and homogeneous strains, internal stresses will arise that must be characterized by nonlocal plasticity models. In this work, such a nonlocal constitutive model is formulated based on the concept of densities of geometrically necessary super-dislocations in an isotropic elastic-plastic medium. Since the deformation of individual grains is considered, crystal plasticity models are applied that take into account plastic slip on crystallographic planes. This new nonlocal constitutive model is applied to describe the deformation of a polycrystal under the influence of plastic strain gradients caused by isotropic and kinematic strain hardening. It is found that isotropic hardening originating from plastic strain gradients amplifies deformation heterogeneities stemming from different Schmid factors in neighbouring grains. However, the kinematic hardening resulting from plastic strain gradients tends to reduce such deformation heterogeneity. Thus, the capability of a polycrystal to deform uniformly is determined by the competition between isotropic and kinematic hardening. A constitutive model for Transformation Induced Plasticity (TRIP) assisted steels is proposed that considers the elastic-plastic deformation of ferrite and austenite, the austenite-martensite phase transformation and the elastic deformation of martensite. Within this model, an explicit relation between martensite nucleation and plastic deformation within an austenite grain has been established based on the inverse Nishiyama-Wassermann (NW) relationship. In particular, strain-induced martensite nucleation and stress-assisted martensite growth have been included in one model with the help of a thermodynamic principle. With this model, we found consistently with experiment that the TRIP effect enhances the effective work hardening rate and hence is beneficial for improving strength and ductility of steels. The mechanical anisotropy produced by stress-assisted and strain-induced phase transformations are significantly different.