Quantitative relation between the relaxation time and the strain rate for polymeric solids under quasi‐static conditions

Relaxation time is an essential physical quantity reflecting the hysteresis of the microstructure of materials. To associate the relaxation time with the strain rate, the stress–strain curves of six types of polymers at low strain rate were normalized, and a nondimensional generalized Maxwell model incorporating strain‐rate‐dependent relaxation times was obtained by the internal variable theory of irreversible thermodynamics. The results indicate that the constitutive equation may capture well the normalized stress–strain behaviors that are not related to the strain rate. The ratio of the initial modulus to the secant modulus at the maximum stress was also found to not rely on the strain rate anymore. Furthermore, strain‐rate independence occurred only when the relaxation time was proportional to the time interval for stress from zero to the maximum stress. The relaxation time varied in a power law with the strain rate. The explicit relation is helpful for providing a concise and promising solution for predicting the quasi‐static mechanical response of viscoelastic solids. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44114.