Analytical solutions for the ideal orientations of f.c.c. rolling textures

Abstract

The ideal orientations of rolling textures for f.c.c. metals (cube, Goss, brass, copper and Taylor) are investigated. Analytical solutions for the stress states, slip distributions and lattice spins are obtained using both a rate-sensitive crystal plasticity model and the classical Bishop and Hill rate-independent theory. As expected, slip and stress state ambiguities are found with the Bishop and Hill theory. Three types of boundary conditions are considered for the rate-sensitive model: plane strain compression, “lath” compression, and “pancake” compression. However, only plane strain conditions are analyzed with the rate-independent theory. It is shown that, in the limit of zero strain-rate sensitivity, the analytical rate-sensitive results tend to those of the Bishop and Hill theory. Furthermore, all of the possible Bishop and Hill slip systems turn out to be active in the limiting rate-sensitive solutions. Symmetrical slip distributions (2, 4, or 8 slip systems with equal shear rates) and symmetrical stress states (the average of all the yield surface stress vertices involved) are characteristic behaviours for symmetrical orientations under the boundary conditions considered.