Closed-form solution to the residual stresses in ion-exchanged silicate glass including concentration-dependent material properties

Abstract

In this work, the closed-form solution to the residual stresses in ion-exchanged, silicate glasses accounting for composition-dependent material properties, is derived. The solution is applicable to physical systems where the self-diffusion coefficients of the exchanged, ionic species are nearly identical, such as for Na+ ↔ K+ in both soda-lime and alumino-silicate glass. In the proposed solution, the relaxation function is expressed in terms of the Prony series and the relaxation times, Young's modulus, and the dilation coefficient are assumed as analytic functions of the chemical concentration. A significant, practical aspect of this research is that the derived closed-form solution could be used to establish the relationship between the material properties and the local ion concentration through the regression analysis of experimentally-determined, residual stress profiles. Practical illustrations of how the relationship between the ion concentration and both the dilation coefficient and the relaxation times could be established in ion-exchanged, soda-lime glass are finally presented.