Formulation of a Homogenization Theory for Discrete Dislocation Dynamics Analysis
Dai OKUMURA, Nobutada OHNO and Yoshihiro KATAGIRI
Abstract:In this study, we develop an extended version of homogenization theories for composite materials consisting of inclusions and a matrix. The extension allows discrete dislocations to move in a matrix based on dislocation dynamics. Macroscopic stress-strain response and microscopic stress distribution in representative volume elements (RVEs) are analyzed on the assumption that the periodic arrangement of RVEs is subjected to macroscopic uniform deformation. The periodicity, which enforces the periodic distributions of microscopic stress and strain as well as dislocations, is used as boundary conditions on the surface of RVEs. It is shown that elastic fields of periodically arranged dislocations in an infinite medium have no contribution to macroscopic relations, and that discontinuous displacements resulting from dislocation motions in each RVE are introduced as a macroscopic plastic strain. From these relations, a set of homogenization equations is derived, in which two boundary value problems in integral form are solved for analyzing perturbed displacements due to the presence of inclusions and due to the interaction of inclusions with dislocations, respectively. Finally, the influence of periodic boundary conditions on macroscopic and microscopic responses is investigated by performing the RVE analysis of a model composite. Key Words:Homogenization, Dislocation, Finite element method, Composite