Two-dimensional rigid polycrystals whose grains have one ductile direction

We consider polycrystals with perfectly plastic grains. We study the two-dimensional problem that results if the textures and applied stresses are compatible with antiplane deformation. We show that the order of magnitude of recently introduced outer bounds on the strength domain of polycrystals is sharp even under the assumption of square symmetry on the texture. We also conclude that the fact that the texture has square symmetry is not enough information to predict the behaviour of polycrystals if the grains are highly anisotropic.