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

Abstract

Abstract-Numericaland 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.

Bending of a Bimetallic Beam Due to the Kirkendall Effect

“…In that work, the pressure gradient effect was neglected and thus the diffusion and stress analysis were decoupled. Good agreement with *Daruka et al [2] define average intrinsic diffusion coefficients by experiments was obtained. We extend this simpler approach to diffusion in a single-phase bi-metal strip and in a twophase bi-metal strip with a moving interface.…”

“…Evaluation of the general result (Eq 24) is made for materials parameters corresponding to the experiments of Daruka et al [2] for diffusion couple beams made initially of pure Ti and Zr and annealed at 1223 K. [2] giving DD= e D ¼ 0:375). In agreement with Daruka et al, [2] the slope of the linear portion does not depend on the interdiffusion coefficient as seen in Eq 26.…”

“…Experiments and models elucidating bending have been executed for solid solution alloys of Au-Ag by Stevens and Powell, [1] of Cu-Ni by Daruka et al, [2] and of Zr-Ti by Opposis et al [3] Suo et al [4] describes a practical application of this subject where the stresses and bending due to the difference of diffusion rates of oxygen and metals in thermal barrier coatings have been investigated. A beam that undergoes transverse diffusion may also bend if the lattice parameter (or alternately, the molar volume) depends on mole fraction even if the intrinsic diffusion coefficients are equal.…”

“…Daruka et al [2] performed numerical, analytical, and experimental investigations of the bending of single-phase plates undergoing diffusion with unequal diffusion rates for two species. Their experiments clamped an entire edge of a plate and thus their analysis focused on the cylindrical geometry and required an analysis of the clamping moment.…”

Optimisation of interface roughness and coating thickness to maximise coating–substrate adhesion – a failure prediction and reliability assessment modelling

“…[7][8][9][10] The evolution of diffusion-induced stresses in coatings was originally analysed by Podstrigach and Shevchuk [11]. Since then, some researchers [12][13][14][15][16][17] had made a series of studies of diffusion-induced stresses in coatings and had come up with experiments and numerical models to analyse coating-substrate debondment. Also, in recent research work, models for coating-substrate debondment involving diffusion-induced stresses, developed by Nguyen et al [18], Prawoto et al [19,20], Cui et al [21], Yang and Li [22] and Rusanov [23] are based on various numerical methods and techniques.…”