NONLOCAL VERSUS LOCAL ELASTOPLASTIC BEHAVIOR OF HETEROGENEOUS MATERIALS

The scale transition methods have been developed for many years in ord er to obtain the overall behavior of polycrystalline materials from th eir microscopic behavior and their microstructure. Nevertheless, some basic aspects are absent from such formalisms. The most significant on e seems to be the heterogeneization by plastic straining which involve s nonlocality of hardening. In this article, a nonlocal theory based u pon crystalline plasticity is developed from which a nonlocal constitu tive equation at the grain level is derived. With regard to the polycr ystal, in order to deduce the behavior of a local equivalent homogeneo us medium, an integral equation is proposed and solved for nonlocal in homogeneous materials by the self-consistent approximation. This schem e is developed in case of a two-phase nonlocal material representing t he dislocation cell structure induced during plastic straining. Numeri cal simulations based on a simplified model show significant effects o n the intragranular heterogeneization.