Residual stress in ion-exchanged silicate glass: An analytical solution

The ion-exchanged residual stress profile influences both the strength and the wear-resistance of glass hence its description is of great importance. Currently, residual stress profiles of silicate glasses can only be estimated by numerical time-integration based on the known ionic concentration profile and the expected stress relaxation behavior of the glass. In this work, we derived and validated the constant coefficients analytical solution describing the residual stress profile in single-step ion-exchanged glasses. The proposed solution is based on Sane and Cooper's model and assumed that both the generalized Maxwell stress relaxation function applied and that a constant ionic inter-diffusion coefficient could accurately describe the behavior of the system. Furthermore, an analytical approximation for composition-dependent stress relaxation behavior of the glass was proposed. Examples of how the newly developed analytical description of the stress profile could be fitted through regression analysis to available residual stress data were also presented.