Monday, 11 October 2004 - 2:15 PM

This presentation is part of : Graduate Student Competition

The Nonlinear Effect of Applied Stresses on Stress-Assisted Diffusion

Peng Liu and Chien H. Wu. Department of Civil and Materials Engineering (MC 246) University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL 60607

When a solid of nonuniform concentration is stressed, a flux of atoms is produced by not only just the concentration gradient but also a potential gradient. This latter effect is traditionally termed a stress-assisted diffusion by a chemical potential gradient. This potential depends, among other possible causes, the external load-induced stresses as well as those necessitated by a nonuniform concentration. A nonuniform concentration is accompanied by a state of eigen-transformation, which, in view of its dependence on the associated molar volumes, may be called a chemical eigentransformation (or chemical strain for short). Chemical eigentransformations are, in general, incompatible and must be, in turn, accompanied by geometrically necessary elastic transformations. The load- and concentration-induced stresses are coupled by this last requirement in the strain energy portion of the free energy. The derivative of the free energy with respect to the chemical eigentransformation is a generalized energy momentum tensor, which tends to the energy momentum tensor of Eshelby as the eigentransformation tends to the identity transformation. At the same time, the chemical potential deduced from the free energy is a functional of the load and concentration. It becomes a functional of only the load when the concentration is uniform. The diffusion, assisted by such a load-induced potential, from an initially uniform state is investigated in this paper. The effect is by nature nonlinear and more prominent for singularly nonuniform stress states.

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