Quantitative law of diffusion induced fracture

Abstract

Through dimension analysis, an almost analytical model for the maximum diffusion induced stress (DIS) and critical temperature (or concentration) difference at which cracks begin to initiate in the diffusion process is developed. It interestingly predicts that the spacing of diffusion-induced cracks is constant, independent of the thickness of specimen and the temperature difference. These conclusions are validated by our thermal shock experiments on alumina plates. Furthermore, the proposed model can interpret observed hierarchical crack patterns for high temperature jump cases, and a three-stage relation between the residual strength and the temperature difference. The prediction for crack spacing can guide the biomimetic thermal-shock-failure proof design, in which the hard platelets smaller than the predicted diffusion induced by constant crack-spacing are embedded in a soft matrix, and, therefore, no fracture will happen. This may guide the design of the thermal protection system and the lithium ion battery. Finally we present the maximum normalized DISes for various geometry and boundary conditions by single-variable curves for the stress-independent diffusion process and two-variable contour plots for the stress-dependent diffusion process, which can provide engineers and materialists a simple and easy way to quickly evaluate the reliability of related materials and devices.