Time-dependent nonlinear deformation behaviour of glassy polymers

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Abstract
This paper develops a generalized nonlinear Maxwell model that is capable of treating glassy polymer deformation under diverse kinematics, including creep. The nonlinearization of the constitutive equation is accomplished by incorporation of a Williams-Watts relaxation element for the viscous dissipation. This equation describes the relaxation behaviour in polymer glasses over four orders of magnitude in time with the addition of only one new rheological parameter β. The parameter β is an exponent to the time variable and typically ranges between 0·02 and 0·2 for these materials. Decreasing molecular weight and/or increasing temperatures tends to increase the magnitude of β. The time constant τ ranges over many orders of magnitude and is generally inversely related to β. The physical significance of β is linked to the relative magnitude of short- versus long-term relaxation behaviour and can therefore be correlated to the creep and impact behaviour of materials. Finally the generalized Maxwell model is shown to predict nonlinear creep behaviour and gives new meaning to the Deborah number.