Numerical Modeling of Diffusion-Induced Deformation

Published

September 11, 2006

Author(s)

J A. Dantzig, William J. Boettinger, James A. Warren, Geoffrey B. McFadden, Sam R. Coriell, R F. Sekerka

Abstract

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

Volume

37A

Issue

9

Pub Type

Journals

Keywords

deformation, diffusion, Kirkendall effect, modeling

Citation

Dantzig, J. , Boettinger, W. , Warren, J. , McFadden, G. , Coriell, S. and Sekerka, R. (2006), Numerical Modeling of Diffusion-Induced Deformation, Metallurgical and Materials Transactions A-Physical Metallurgy and Materials Science (Accessed October 8, 2025)