Thermoviscoelastic theory of freezing of stress and strain in a symmetrically cooled infinite glass plate

Abstract

Abstract The Gardon and Narayanaswami theory of annealing and tempering of glass is rederived in a unifying way using the framework of the theory of thermoviscoelasticity. It is extended by including the effect of isothermal pressure relaxation in addition to the relaxation of shear stress. In the new theory, relaxation of shear stress, isotropic stress (pressure) and thermal stress, which causes thermal expansion, are treated on the same level. The thermal expansion coefficient, a frequency-dependent quantity like bulk and shear modulus, has high- and low-frequency limits identified with the thermal expansion coefficients of glass and liquid. The results of numerical calculation of stresses and strains in a symmetrically cooled infinite plate for the extended theory illustrate the decisive importance of the dispersion of the thermal expansion coefficient.