Stress in ion exchanged soda‐lime silicate and sodium aluminosilicate glasses: Experimental and theoretical comparison

Abstract

Glass samples of two different chemical compositions were strengthened by ion exchange. Residual stress profiles were experimentally determined by differential surface refractometry. The experimental results were compared with values theoretically predicted by a formalized viscoelastic mathematical model incorporating both stress buildup and stress relaxation contributions. The comparison exhibited a remarkable agreement both in terms of strengthening characteristics and stress profiles curves between experimentally measured and theoretically predicted values. The mathematical model incorporated terms directly linked to selected relaxation mechanisms either isochoric shear stress driven and fast relaxation. The comparison demonstrated the relevance of the stress relaxation mechanisms for the different glass chemical compositions. The approach presented in this study will allow the prediction of the mechanical behavior of chemically strengthened glass starting from its chemical composition together with the ion exchange process parameters.

Towards a Glass New World: The Role of Ion-Exchange in Modern Technology

“…In this context, R. Dugnani developed an analytical solution to the problem assuming a generalised function for the stress relaxation, a constant ionic inter-diffusion coefficient and, simultaneously, taking into account an analytical approximation for the composition-dependent stress relaxation behaviour of the glass [120]. On the other hand, A. K. Varshneya, G. Macrelli, and others in their studies modified the Cooper's analysis introducing a new term in the model, related to different relaxation contributions (i.e., the viscoelastic and structural one) together with the network hydrostatic yield strength in order to evaluate the subsurface maximum compressive stress when the process temperature is higher and/or close to the glass transition temperature T g [121][122][123][124]. Also noteworthy is the method, recently proposed by R. Rogozi ński, which allows to control in real time the stresses generated in a glass as a result of the ion-exchange process from the knowledge of some parameters such as the elasto-optical coefficients, the dependence of the diffusion coefficients on the temperature and, finally, the function describing the time relaxation of stresses at the glass surface [118].…”

Coupling of diffusion and chemical stress: The case of ion exchange in glass

“…The example glasses are the same as recently reported. 38 The main characteristics of the two glass compositions are listed in Tables 2 and 3. The κ constant according to Equation (32) has been calculated for ion exchange processes performed at 350, 450, and 500°C, and values are reported in Table 4.…”

“…Interdiffusion coefficients have been taken at 450°C as constant. The finite differences expression was validated by comparing against the usual analytical solution for a constant diffusion coefficient 13,14,38 : where t is the total immersion time and D is the approximated interdiffusion coefficient reported by Macrelli et al 38 The effect of the gradient stress term on the depth-dependent concentration as a function of depth in an ion-exchanged glass, assuming a constant interdiffusion coefficient, is seen by setting up the finite differences, Equation (40), for a SLS glass and assuming two cases: (a) without a stress gradient κ = 0 and (b) with stress gradient κ = 0.460 for a 24-h immersion time at 450°C, data from Macrelli et al 38 It is observed in Figure 1 that just the stress gradient itself does not have much influence on the concentration distribution.…”

“…Glass chemical compositions (mol%), from Macrelli et al38 Physical characteristics of the glasses (* determined by Sci-Glass 6.5) from Macrelli et al38 …”

Modeling of ion exchange in glass considering large viscoelastic deformation and mechano–electrochemical coupling

“…Dugnani et al [8][9][10][11] developed an analytical solution to Sane and Cooper's equa-tion with the assumption of composition-dependent stress relaxation of the glass based on a generalized Maxwell model (Prony series). Concomitantly, Varshneya et al [12][13][14][15] modified Sane and Cooper's analysis by introducing a new term to account for various relaxation effects (i.e., fast βrelaxation, slow α-relaxation, and stress release due to volume and shear viscosities) that is an account for the subsurface maximum compressive stress when the process temperature is close to or higher than T g .…”