PHASE-CHANGES IN A THIN PLATE WITH NONLOCAL SELF-STRESS EFFECTS

Because the stress resulting from compositional inhomogeneities are long range, the local stress, diffusional flux and equilibrium conditions at a point depend on the entire composition distribution in a specimen. For a thin plate with a one-dimensional composition profile, this dependence is simple; the local stress depends on the local composition and on both the average composition and the first moment of the composition profile, neither of which are local. A theory of diffusion and equilibrium in a thin plate is developed, based on a free energy that depends on composition, its gradients and strain, and has a term for chemical effects at the plate boundary. Under certain assumptions, a standard diffusion equation is derived, with all of the non-local stress effects in the boundary conditions. Solutions are altered by these new conditions. Spontaneous bending is often a natural result of diffusion.