Residual stresses in tempered glass are generated by interactions between thermal contraction, elasticity at low temperatures, viscoelastic flow at higher temperatures, and temperature gradients caused by cooling. To date, analyses have assumed highly idealized material behavior, such as elasticity below, and inviscid fluid flow above, a critical temperature. The theory presented in this paper is based on measured relaxation characteristics of glass and temperature influence through thermorheologically simple response, which prescribes an acceleration of all relaxation phenomena with rising temperature by a factor determined by experiment. The analysis of the varying stress history for a glass plate cooled symmetrically on both sides is developed and solved for several furnace and coolant temperature combinations by numerical solution of the integral equations which arise. The determination of the residual stress distribution follows naturally in terms of a reduced time used in the analysis. Maximum compressive residual stresses under the surface increase extremely rapidly with increasing furnace temperature above 60O°C. The method is compared with previous work on the same problem.

Stress analysis problems for linear viscoelastic material behavior are solved on the basis of integral operator stress-strain relations. These characterize the material by relaxation modulus functions or creep compliances which are directly measurable over finite time ranges, and completely describe material behavior for stress determinations for the same duration. The stress analysis theory can lead to integral equations which are shown to be soluble with high accuracy by simple finite-difference numerical integration procedures. Examples are presented and compared with solutions obtained by other methods. A possible improved technique for relaxation modulus and creep compliance measurements is suggested, based on the method presented for numerical solution of the integral equations.