Thermal stress calculations based on a linear viscoelastic deviatoric response and a fictive temperature component for the volumetric response

A temperature dependent thermal expansion coefficient is introduced into the Lee, Rogers and Woo linear viscoelastic model for calculating thermal stresses in glass. Volumetric strain, is calculated as follows: ? = α_liq (T_f - T_O) + α_gl (T - T_f) where α_liq and α_gl are the thermal expansion coefficients for the liquid and glassy states respectively, T is the glass temperature, T_O is the initial temperature, and T_f is the fictive temperature as defined by Tool. Fictive temperatures are calculatedfrom theory and measurements independent of thermal stress experiments. Comparison of calculated with experimentally measured stresses shows that the modified model is useful for predicting thermal tempering propensity for different glass compositions as well as different processing parameters.