A Plane strain at an interface

For plane strain, if the two polymorphs deformed without diffusion, would need to equal -I- tr x)/2 but if self-diffusion occurs, this stress condition no longer leads to plane strain. Where cylindrical constriction requires a simple exponential profile of compressive stress, plane-strain deformation at an interface requires a more complicated curve. 

The analyses emphasize the idea that when a volume-element changes volume by diffusive mass transfer at constant density, the change is not isotropic the strain components Cyy, and e are linked by three separate equations to the components and gradients of the driving stress field. 

The fifth right-hand term in eqn. (12.7) contains a factor that is not fully defined, but for applications of the type illustrated no difficulty arises because the entire fifth term is very small in comparison with the other four. 

Otherwise conditions are as in the constriction problem in particular we continue to assume that no quantities vary along y or z. We apply eqn. (12.7) 

The solutions of (13A.3) and (13A.4) are similar to each other and to the solution of (13.4), but the value of the parameter B that results from (13A.4) is new and differs from that for (13A.3). In other words, T diminishes with distance from the interface on a different length scale from R. 

---