A texture component model for anisotropic polycrystal plasticity

There are many crystallographic textures which can be approximated by a small number of texture components [see, e.g., Int. J. Mech. Sci. 31(7) (1989) 549]. In some cases, such texture components can be described by central distributions. Central distributions are characterized by a mean orientation and a half width. The classical Taylor model for viscoplastic polycrystals assumes that a discrete set of single crystals deforms homogeneously. If the viscoplastic version of the Taylor model is numerically implemented then the crystallite orientation distribution function (codf) is usually discretized by a set of Dirac distributions, where each of the Dirac distributions represents a single crystal. Due to the specific discretization of the codf this approach requires usually a large number of discrete crystal orientations even if the texture can be described by a small number of texture components. In the present work, we consider face-centered cubic (fcc) polycrystals and compare the classical upper bound model with an approach based on texture components. The texture components are modeled by Mises–Fischer distributions, which are central distributions. The stress of the polycrystal is obtained by a numerical integration of the single crystal stress state over the orientation space.