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 ∂W ∂I₁, and ∂W ∂I₂ of the time dependent strain potential function. ∂W ∂I₁ and ∂W ∂I₂ 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 ∂W ∂I₁ and ∂W ∂I₂ 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 ∂W ∂I₁ is negative and increases towards zero with increasing time and deformation while ∂W ∂I₂ is positive, greater in magnitude than ∂W ∂I₁ 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.