Viscoelastic Behavior of Poly(Methyl Methacrylate): Prediction of Extensional Response from Torsional Data
Some years ago Rivlin1 showed that for certain deformations, one can treat isochronal data from single step stress relaxation experiments on viscoelastic materials in the same fashion as if the data were obtained for an elastic material. We have conducted single step stress relaxation experiments on cylinders of poly (methyl methacrylate) (PMMA) where we measured torque and normal force responses as functions of time and angle of twist. By assuming that torsion is an isocholic motion and that volume effects are separable, we obtained isochronal values for ∂W/∂Il and ∂W/∂I2. Our results showed that ∂W/∂I1 is negative while ∂W/∂I2 is positive and greater in magnitude than ∂W/∂I1. These findings led to the possibility of explaining the phenomenon observed by Sternstein and Ho3 that the single step stress relaxation response of PMMA is different in torsion than in simple extension. Specifically, it was found that the rate of decay of the stress with respect to time is significantly higher in torsion than in extension. This phenomenon was observed at small strains where the stress responses in both torsion and extension were linear in the appropriate strain measure. The difference could not be accounted for either in terms of a time dependent Poisson’s ratio or the material compressibility.
KeywordsRelaxation Rate Methyl Methacrylate Simple Shear Viscoelastic Material Simple Extension
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