A viscoelasticity model for polymers: Time, temperature, and hydrostatic pressure dependent Young's modulus and Poisson's ratio across transition temperatures and pressures

Abstract

Capturing and fundamentally understanding the variation of a polymer's mechanical properties with time, temperature, and hydrostatic pressure is essential for accurate constitutive modeling. In this paper, a new linear viscoelastic constitutive model is developed that regards Young's modulus and Poisson's ratio as functions of time, temperature, and hydrostatic pressure. Modified logistic functions are employed, which provide appealing mathematical and physical simplicity. Aided by time/temperature/hydrostatic-pressure superposition, these functions can be transformed from the time domain to the temperature or pressure domain, or the converse. Our model is successfully benchmarked against numerous sets of experimental data. Our model is also correlated to polymer processing through continuous cooling transformation (CCT) diagrams. Since CCT diagrams help determine a polymer's microstructure, which in turn determines its macroscopic mechanical properties, our model can be used as a guide for tailoring the manufacturing process (e.g., controlling quenching temperature and speed) to obtain a targeted set of mechanical properties. Our new model can also be embedded within existing nonlinear viscoelastic constitutive frameworks to capture the mechanical behavior of polymers across a wide range of strain rates, temperatures, and pressures.