Stress‐strain‐time relation of poly(n‐alkyl methacrylates) in rubbery state

Abstract

AbstractMeasurements of stress‐relaxation under various extension ratios and stress–strain under various rates of extension are made for polymethyl, ethyl, n‐propyl, and n‐butyl methacrylates in their rubber regions. The time–temperature superposition at the same extension ratios is possible, but the larger the extension ratio, the faster the stress relaxes. Assuming that polymer chain length is approximately distributed along a Gaussian curve and that the relaxation spectrum shifts along log τ axis by log aα without changing its shape with extension, we can express the results of stress–relaxation for different extension ratios and temperatures by the following equation: where S is the stress per the initial cross‐section, Ts is the reference temperature, aT is the time–temperature shift factor, aα is the time–extension ratio shift factor, and H(τ) is the relaxation spectrum. For stress–strain under constant rate extension, the time–extension ratio superposition is also possible with the different shift factor aαs, which is related to the aα through the equation a = (α ‐ 1)/ ∫1α dα/aα. The calculated a agrees satisfactorily with the observed. The dependence of aα and aT on the extension ratio is derived from the free volume theory, which interprets experimental results comparatively well.