A phase field dislocation dynamics model for a bicrystal interface system: An investigation into dislocation slip transmission across cube-on-cube interfaces

In this work, we present a phase field dislocation dynamics formulation designed to treat a system comprised of two materials differing in moduli and lattice parameters that meet at a common interface. We apply the model to calculate the critical stress τcrit required to transmit a perfect dislocation across the bimaterial interface with a cube-on-cube orientation relationship. The calculation of τcrit accounts for the effects of: 1) the lattice mismatch (misfit or coherency stresses), 2) the elastic moduli mismatch (Koehler forces or image stresses), and 3) the formation of the residual dislocation in the interface. Our results show that the value of τcrit associated with the transmission of a dislocation from material 1 to material 2 is not the same as that from material 2 to material 1. Dislocation transmission from the material with the lower shear modulus and larger lattice parameter tends to be easier than the reverse and this apparent asymmetry in τcrit generally increases with increases in either lattice or moduli mismatch or both. In efforts to clarify the roles of lattice and moduli mismatch, we construct an analytical model for τcrit based on the formation energy of the residual dislocation. We show that path dependence in this energetic barrier can explain the asymmetry seen in the calculated τcrit values. Significantly, the analysis reveals that τcrit scales with a(2)G(2)a(1)+a(2)(a(1)a(2)−G(1)G(2))2, where G is the shear modulus, a is the lattice parameter, and the superscripts (1) and (2) indicate quantities for material 1 and material 2, respectively.