Capability for Capturing Temperability as a Criterion for the Validity of Thermoviscoelastic Constitutive Equations

The presence of varying temperature fields together with both elastic and viscous properties result in significant stress variations during temperature changes in mechanical and structural members made of viscoelastic materials. Such members when subjected to sudden cooling (tempering) may exhibit residual stresses that have important effects on the operational behaviour of the member, including effects such as changes on fatigue life and on fracture toughness. Accurate modelling the transient and residual mechanical response for such materials has important implications in both reliable design and reliable analyses. In this regard, a crucial role is played by the choice of the chosen constitutive equations that together with other fundamental equations of mechanics will determine the mechanical response of a given mechanical member. In this work it is postulated that constitutive equations used to compute the mechanical response of thermoviscoelastic media in order to be considered valid, must be able to reasonably capture the formation of residual stresses. On this basis, two published thermoviscoelastic constitutive equations, of thermorheologically simple class, are examined in terms of their capability for predicting the residual stresses in a long cylinder of float glass subjected to sudden cooling. It is shown that one of the tested theories complies with the proposed validity test while the other fails to reasonably predict the magnitude of the stated residual stresses.