Volume-induced stress response in amorphous polymers

Time-dependent volume changes are important in polymer processing operations because the material is typically cooled rapidly and the resulting solid is rarely in equilibrium. The present work is part of a basic study to describe the coupling of such volume changes with the stresses they induce when the material is constrained. It is mostly an application of the generalized integral model developed by Snow and Bogue.

Stress-free volume data from the literature (the dilatometric data of Greiner and Schwarzl) were first analyzed by the integral equation of the Snow and Bogue model, and second, by a differential equation that can be derived from that model (the Kovacs equation). The data consist of volume-temperature plots, measured at different cooling rates ranging from 1.17 × 10^-5 to 3.33 × 10^-2 °C/sec. As the cooling rate is increased, the apparent glass transition temperature (the break in the V-T plots) also increases. This effect as well as the detailed shape of the curves could be well approximated with the two formulations studied. The parameters were either taken from the literature or were in the range of values previously used. There is, however, considerable flexibility in adjusting the shift factor for the glassy state.

The data of the present work came from measuring the stress build-up in a uniaxially constrained fiber, subjected to cooling rates varying from 0.08 to 3.2 °C/sec. The volume contraction was calculated from the parameters of the previous analysis. In addition one requires a modulus and a time constant (with its shift factor) for the anisotropic stress term. Using values from the literature, slightly adjusted in the case of the modulus, a quite satisfactory fit to the stress build-up data was obtained. The qualification must be added, however, that the stresses produced were not themselves large enough to affect the volume change. But with this qualification it was concluded that the Snow-Bogue model provides a satisfactory framework for dealing with volume-induced stresses.