Utility of the Green-Rivlin Theory in Polymer Mechanics

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Abstract
For the case of stress relaxation at constant strain, the Green-Rivlin theory for nonlinear materials with memory predicts that the stress is a power series in the strain where the coefficients, called kernels, characterize the material. This prediction of the theory has been tested using data obtained on the polycarbonate of bisphenol A in the timescale range 10–1000 sec and temperature range 23°–130°C. At each temperature level of this study, the two leading terms of the power series account for actual behavior within the standard deviation of the experimental data (3%) up to the level of tensile strain where instability (cold-drawing) occurs. The first (``linear'') kernel decreases monotonously with temperature as Tg is approached, but the second and higher kernels each vary with temperature in a complex manner. The utility of summarizing the nonlinear behavior of polymers by kernel functions is appraised and discussed in the light of recent findings on the range of validity of linear viscoelasticity theory. It is concluded that the second and higher kernels of the theory do not have any obvious physical significance. It is also suggested that the first and the second kernels might represent adequately by themselves the nonlinear viscoelastic behavior of glassy, amorphous polymers up to about 5% strain, whereas the third and higher kernels appear in addition to be necessary for semicrystalline polymers.

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