We present a numerical approach to modeling the deformation induced the the Kirkendall effect in binary alloys. The governing equations for isothermal binary diffusion are formulated with respect to inert markers and also with respect to the volume averaged velocity. Relations necessary to convert between the two formulations are derived. Whereas the marker formulation is the natural one to pose constitutive laws, the volume formulation provides certain computational advantages. We therefore compute the diffusion and deformation with respect to the volume-centered velocity and then determine the corresponding fields with respect to the markers. Several problems involving 1-D diffusion couples are solved for verification, and problem involving 2-D diffusion in a lap joint is solved to illustrate the power of the method in a more complex geometry.
Citation: Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science
Pub Type: Journals
deformation, diffusion, Kirkendall effect, modeling