Metallurgical and Materials Transactions A

, Volume 37, Issue 9, pp 2701–2714

Numerical modeling of diffusion-induced deformation


  • J. A. Dantzig
    • the Department of Mechanical and Industrial EngineeringUniversity of Illinois at Urbana-Champaign
  • W. J. Boettinger
    • Metallurgy Division
  • J. A. Warren
    • Thermodynamics and Kinetics GroupMetallurgy Division
  • G. B. McFadden
    • Mathematical and Computation Sciences Division, Information Technology Laboratory
  • S. R. Coriell
    • the National Institute of Standards and Technology
  • R. F. Sekerka
    • Carnegie Mellon University

DOI: 10.1007/BF02586104

Cite this article as:
Dantzig, J.A., Boettinger, W.J., Warren, J.A. et al. Metall and Mat Trans A (2006) 37: 2701. doi:10.1007/BF02586104


We present a numerical approach to modeling the deformation induced by 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 in which 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 one-dimensional (1-D) diffusion couples are solved for verification, and a problem involving two-dimensional (2-D) diffusion in a lap joint is solved to illustrate the power of the method in a more complex geometry.

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© ASM International & TMS-The Minerals, Metals and Materials Society 2006