Theory of nonlinear creep in polymer glasses

Abstract

A statistical segment-scale constitutive equation theory for the nonlinear mechanics and relaxation of polymer glasses recently proposed by two of us is applied to study nonlinear creep and recovery. The key physics resides in a deformation-dependent elastic modulus and alpha relaxation time, which are determined by a segment-displacement-dependent dynamical free energy that quantifies the transient localization and activated hopping processes. For simple creep and recovery, the amplitudes of the instantaneous up- and down strain jumps are equal and exhibit upward deviations from a linear dependence on applied stress due to modulus softening. Nonexponential relaxation indicative of a distribution of alpha relaxation times is incorporated and shown to be crucial in determining the so-called delayed elastic deformation at intermediate times. The amount of delayed recovered strain appears to saturate at long times at a value equal to the total delayed elastic deformation during creep. Calculations of the time-dependent creep compliance covering the linear and nonlinear regimes are presented. Horizontal shifts can collapse the compliance curves at different stress levels onto a master plot as seen experimentally, and the extracted shift factor quantitatively agrees with the a priori computed normalized alpha relaxation time. Calculations for two-step creep at small stress are in reasonable agreement with experiments on poly(methylmethacrylate) glass, although systematic deviations occur at very high applied stresses.