Prediction of modulus at various strain rates from dynamic mechanical analysis data for polymer matrix composites

Understanding and modeling the behavior of polymers and composites at a wide range of quasi-static and high strain rates is of great interest to applications that are subjected to dynamic loading conditions. The Standard Linear Solid model or Prony series frameworks for modeling of strain rate dependent behavior are limited due to simplicity of the models to accurately represent a viscoelastic material with multiple relaxations. This work is aimed at developing a technique for manipulating the data derived from dynamic mechanical analysis to obtain an accurate estimate of the relaxation modulus of a material over a large range of strain rate. The technique relies on using the time-temperature superposition principle to obtain a frequency-domain master curve, and integral transform of this material response to the time domain using the theory of viscoelasticity. The relaxation function obtained from this technique is validated for two polymer matrix composites by comparing its predictions of the response to uniaxial strain at a prescribed strain rate to measurements taken from a separate set of tension experiments and excellent matching is observed.