Dislocation-density based description of the deformation of a composite material

Composite materials consisting of hard particles in a ductile metallic matrix are of major interest since their strength and deformability can be dramatically changed by varying volume fraction, size and shape of the particles. Understanding dislocation motion in composite materials as the cause of plastic deformation therefore is an important task. Recently, advanced dislocation-based continuum theories of plasticity have been developed for performing meaningful averages over systems of straight and curved dislocation lines in a continuum approach. In this paper, we focus on a single slip heterogeneous microstructure and investigate how the dislocation interactions can be represented in an averaged dislocation density based continuum description. The representation of strong dislocation density gradients is discussed in the context of a formulation, which aims at a coarse-grained resolution. We introduce a set of dislocation density evolution equations which account for the formation and dissolution of dislocation dipoles. By applying the model to a composite structure, we demonstrate that the dislocation density based description can well describe the physical processes in the microstructure and a comparison to discrete dislocation dynamics simulations shows good agreement for the relaxation behavior of the considered composites.