A ONE-DIMENSIONAL INTRODUCTION TO CHEMICAL STRAINS AND STRESSES WITH APPLICATIONS TO DIFFUSION IN CRACKED SOLIDS C. H. WU & P. LIU Department of Civil and Materials Engineering, University of Illinois at Chicago, Chicago, IL 60607, USA ABSTRACT 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 eigentransformation, 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. Such types of concentration-induced stresses are coupled to the ordinary load-affected stresses 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 promoted by such a load-induced potential are commonly known to be linearly coupled to the elastic field. The coupling disappears when the load-induced elastic field is quasi-static. Our coupled equations are built on the full nonlinear energy momentum tensor and the stress-assisted diffusion persists, as long as the elastic deformation is nonuniform. A one-dimensional introduction to chemical strains and stresses is used in this paper to illustrate the roles of a generalized energy momentum tensor in chemical potentials and the associated bulk and surface diffusion. The general three-dimensional equations are used to demonstrate the effects of singularly nonuniform stress states on diffusion. 1 INTRODUCTION The effect of a nonuniform elastic stress on diffusion is a flux of atoms driven by a stress potential V. In the context of linear elasticity, this potential is commonly taken to be the trace of the stress tensor σ and the associated diffusion equation is kk c c D c t k ∂ ∇ = ∇ ∇ + ∂ V T       , (1) where c(x,y,z,t) is the concentration and all the symbols have the usual meaning. Applying the above to the situation where c is initially uniform everywhere, one reaches the conclusion that the solution for very short times is governed by 2 c Dc V t kT ∂ = ∇ ∂ . (2) Since , elastic stresses do not drive diffusion even if they are singularly nonuniform. It was shown in [1], however, that the stress potential V is actually more than just the trace of the 2 kk 0 ∇σ =