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Abstract:
Void growth and morphology evolution in fcc bi-crystals are investigated using crystal plasticity finite element method. For that purpose, representative volume element of bi-crystals with a void at the grain boundary are considered in the analysis. Grain boundary is assumed initially perpendicular/coaxial with the straight sides of the cell. Fully periodic boundary conditions are prescribed in the representative volume element and macroscopic stress triaxiality and Lode parameter are kept constant during the whole deformation process. Three different pairs of crystal orientations characterized as hard-hard, soft-soft and soft-hard have been employed for modelling the mechanical response of the bi-crystal. Simulations are performed to study the implications of triaxiality, Lode parameter and crystallographic orientation on slip mechanism, hardening and hence void evolution. The impact of void presence and its growth on the heterogeneity of lattice rotation and resulting grain fragmentation in neighbouring areas is also analysed and discussed.

Keywords:
crystal plasticity, bi-crystals, void growth, stress triaxiality, Lode parameter, unit cell calculations

Abstract:
The classical J2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure-sensitive yielding or plastic dilatancy. Another difficulty is the so-called strength differential effect (SD), leading to the asymmetry of the elaasstic range. The Burzyński yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto-plastic constitutive equations for the paraboloid case of Burzyński yield condition is frmulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial FE code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plasticity theory with the paraboloid case of Burzyński's yield condition describes adequately the strength diffrential effect, which is present in many kinds of materials significant for recent applications.

Keywords:
metal matrix, mechanical, plastic behaviour, Burzyński paraboloid yield condition, strength differential effect