An internal state variable material model for predicting the time, thermomechanical, and stress state dependence of amorphous glassy polymers under large deformation
Bouvard, J.-L., Francis, D.K., Tschopp, M. A., Marin, E., Bammann, D., & Horstemeyer, M. (2013). An internal state variable material model for predicting the time, thermomechanical, and stress state dependence of amorphous glassy polymers under large deformation. International Journal of Plasticity. 42, 168--193. DOI:10.1016/j.ijplas.2012.10.005.
This paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress state dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thrackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based internal state variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for i) the material strain softening induced by the polymer chain slippage; ii) the material strain hardening at large strains induced by chain stretching between entanglement points; iii) the time, temperature, and stress state dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress states. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions.