Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model

Abstract F ull solutions to mixed rate boundary value problems over polycrystalline domains are performed via the finite element method. In order to make these finite element calculations feasible, an idealized two-dimensional crystal structure is studied. These boundary value problems rigorously satisfy the averaging theorems of Hill (Proc. R. Soc. A326 , 131, 1972) so that well defined Taylor model analogue problems may be identified and solved. Comparisons between the finite element solutions and their corresponding Taylor model analogues yield a quantitative assessment of the Taylor model's validity with respect to its predictions of texture development and global stress-strain response. The finite element calculations also provide physical insight into the mechanisms contributing to the development of nonuniform and localized deformations in polycrystals.