Diffusion-induced bending of thin sheet couples : theory and experiments in Ti-Zr system

Abstract-Numerical and analytical calculations of concentration and stress distributions of thin-sheet diffusion couples have been carried out as well as the time dependence of the Kirkendall shift, ok, and the curvature has also been determined. It is shown that the concentration distribution is not sensitive to the boundary conditions (bent and planar, constrained, samples) and is influenced mainly by the feeding back effects of stresses (described by the stress term in the generalized diffusion potential) only. The stress distributions obviously are different for bent and planar samples and the effect of cutting off, caused by the dislocation glide, is also illustrated. It is found that the Kirkendall shift follows the parabolic law only in high creep rate limit. For intermediate creep rates, as a function of the time, t, a change of the slope of the xk(t) function is expected due to the stress development and relaxation. It is shown that the curvature of samples, caused by the diffusion stresses, is proportional to the annealing time and the difference of the intrinsic diffusion coefficients in a wide range of input parameters. By the example of experiments on Ti-Zr thin-sheet diffusion couples it was illustrated that the theoretical results are in good agreement with the measurements