Numerical modeling of diffusion-induced deformation
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- W.J. Boettinger, G.B. McFadden, S.R. Coriell, R.F. Sekerka, and J.A. Warren:Acta Mater., 2005, vol. 53, pp. 1995–2008. CrossRef
- G.B. Stephenson:Acta Metall., 1988, vol. 36 (10), pp. 2663–83. CrossRef
- I. Daruka, I.A. Szabó, D.L. Beke, C. Cserháti, A. Kodentsov, and F.J.J. Van Loo:Acta Mater., 1966, vol. 44, pp. 4981–93. CrossRef
- J. Philibert:Atom Movements Diffusion and Mass Transport in Solids, Les Éditions de Physique, Les Ulis, France, 1991 (translated by S.J. Rothman).
- R.B. Bird, W.E. Stewart, and E.N. Lightfoot:Transport Phenomena, Wiley, New York, NY, 1960.
- R.F. Sekerka:Progr. Mater. Sci., 2004, vol. 49, pp. 511–36. CrossRef
- Metals Reference Book, 5th ed., C.J. Smithells, ed., Butterworth and Co., London, 1976, p. 975.
- M.S. Engelman, R. Sani, P.M. Gresho, and M. Bercovier:Int. J. Num. Meth. Eng., 1982, vol. 2, pp. 25–42.
- P.M. Gresho and R.L. Sani:Incompressible Flow and the Finite Element Method, Wiley, New York, NY, 1998.
- R. Voigt and V. Ruth:J. Phys. Condens. Matter, 1995, vol. 7, pp. 2655–66. CrossRef
- Numerical modeling of diffusion-induced deformation
Metallurgical and Materials Transactions A
Volume 37, Issue 9 , pp 2701-2714
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Industry Sectors
- Author Affiliations
- 1. the Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA
- 2. Metallurgy Division, USA
- 3. Thermodynamics and Kinetics Group, Metallurgy Division, USA
- 4. Mathematical and Computation Sciences Division, Information Technology Laboratory, USA
- 5. the National Institute of Standards and Technology, 20899, Gaithersburg, MD, USA
- 6. Carnegie Mellon University, 15213, Pittsburgh, PA, USA