The time dependent strain potential function for a polymeric glass

Torsion and normal force measurements were made during single step stress relaxation experiments on a polymeric glass (PMMA). Isochronal data were analysed using an approach adapted from that developed by Penn and Kearsley¹ (for incompressible elastic materials) to determine the derivatives $\text{?W}\text{?I}{}_1$, and $\text{?W}\text{?I}{}_2$ of the time dependent strain potential function. $\text{?W}\text{?I}{}_1$ and $\text{?W}\text{?I}{}_2$ are determined from existing solution to the torsion of an incompressible cylinder. A special solution to the torsion of a compressible cylinder is presented and it is shown that the values of $\text{?W}\text{?I}{}_1$ and $\text{?W}\text{?I}{}_2$ obtained using this solution to analyse the data do not differ greatly from those obtained using the incompressible solution. It is found from both solutions that $\text{?W}\text{?I}{}_1$ is negative and increases towards zero with increasing time and deformation while $\text{?W}\text{?I}{}_2$ is positive, greater in magnitude than $\text{?W}\text{?I}{}_1$ and decreases towards zero with increasing time and deformation. These results were unexpected and a full understanding of their meaning has yet to be reached.