Crystal plasticity: micro-shear banding in polycrystals using voronoi tessellation

Abstract

Abstract A Taylor-type polycrystalline model, together with a new time-integration scheme, has been developed and implemented into a finite element program to simulate the development of micro shear bands in single- and polycrystal of fcc metals. In order to take numerical advantages associated with a symmetric stiffness matrix, the stiffness tensor which arises from the crystal plasticity formulation is symmetrized and the constitutive equation is rearranged accordingly. It is shown that this approach yields significant reduction in computational time without affecting the numerical results. The mesoscopic behavior of polycrystals is analyzed using Voronoi tessellation in which the randomness of the microstructure is generated using a Delaunay network from which a random distribution of grains is generated. The use of 3-node and 4-node elements to analyze the phenomena of shear banding in polycrystals is investigated. It is shown that the use of triangular elements to capture the shear banding phenomenon in polycrystals depends critically on the mesh design, since the resulting mesh is highly nonuniform. However, this problem is resolved by using a 4-node element with reduced integration, illustrating the formation of micro shear bands in a polycrystal using a nonuniform mesh.