Representation of effective flow potentials for polycrystals based on texture data

In this paper, an effective micromechanically based flow potential for face-centered cubic crystals is pro- posed. In a first step, the single crystal flow potential is represented in terms of texture coefficients of the crystallite orientation distribution function. An optimization problem on SO(3) is formulated and solved in order to identify the best approximation of the single crystal flow potential. In a second step, assuming homogeneous stress or strain rate fields, the flow potential of the corresponding polycrystal is deduced explicitly from the tensorial representation of the single crystal potential. In contrast to phenomenological yield criteria, the advantage of such an approach lies in the fact that the macroscopic yield function can be estimated directly based on a single texture measurement and the critical resolved shear stress of the single crystal.