A constitutive model for poly-methyl-methacrylate over a wide range of strain rates and temperatures

Abstract

This study proposes a three-dimensional elasto-viscoplastic constitutive model to depict the rate- and temperature-dependent behaviour of poly-methyl-methacrylate (PMMA) under a variety of strain rates and temperature ranges at finite deformations. Yield stress is described via incorporating an appropriate Young's modulus into the Argon's model. The effects of temperature and strain rate are incorporated into the Young's modulus. Subsequently, a new empirical equation has been suggested to describe the softening behaviour over a wide range of strain rates and temperatures. Further, the temperature dependence of the fraction of plastic work rate converted to heat (β factor) has been studied. In addition, the expressions of hardening parameters (Cr and N) under a changing temperature in the full network model that represents the strain-hardening characteristics of polymers have been proposed. Moreover, a method to calibrate the values of newly introduced parameters has been introduced as well. The experimental results demonstrate that the new softening model can predict softening behaviour at various strain rates (from 0.0003 s−1 to 4300 s−1) and temperatures (from 298 K to the glass transition temperature θg).