A thermo-elasto-viscoplastic constitutive model for polymers

Joakim Johnsen (1) , Arild Holm Clausen (1) , Frode Grytten (2) , Ahmed Benallal (3) , Odd Sture Hopperstad (1)

1 SIMLab - Structural Impact Laboratory
2 SINTEF Industry
3 LMT - Laboratoire de Mécanique et Technologie

Tensile tests conducted at different temperatures and strain rates on a low density cross-linked polyethylene (XLPE) have shown that increasing the strain rate raises the yield stress in a similar manner as when the temperature is decreased. The locking stretch also increases as a function of the strain rate, but not to the same extent as by decreasing the temperature. The volumetric straining and self-heating of the specimens were also measured in the experimental campaign: at room temperature the material was close to incompressible, while at the lower temperatures it was found to be moderately compressible. At the lowest strain rate isothermal conditions was observed, while adiabatic heating was seen at the highest strain rate. In this study, a thermo-elasto-viscoplastic model is developed for XLPE in an attempt to describe the combined effects of temperature and strain rate on the mechanical stress-strain response but also on the thermodynamical response. The proposed model consists of two parts. On one side, Part A models the thermoelastic and thermoviscoplastic response, and incorporates an elastic Hencky spring in series with two Ree-Eyring dashpots. The two Ree-Eyring dashpots represent the effects of the main α relaxation and the secondary β relaxation processes on the plastic flow. Part B, on the other side, consists of an eight chain spring capturing the entropic strain hardening due to alignment of the polymer chains during deformation. The constitutive model was implemented in a nonlinear finite element (FE) code using a semi-implicit stress update algorithm combined with sub-stepping and a numerical scheme to calculate the consistent tangent operator. After calibration to available experimental data, FE simulations with the constitutive model are shown to successfully describe the stress-strain curves, the volumetric strain, the local strain rate and the self-heating observed in the tensile tests. In addition, the FE simulations adequately predict the global response of the tensile tests, such as the force-displacement curves and the deformed shape of the tensile specimen.

Mots clés: Temperature; Constitutive model; Polyethylene; XLPE; Strain rate sensitivity; Self-heating

Domaines: Mécanique des matériaux [physics.class-ph]

Joakim Johnsen, Arild Holm Clausen, Frode Grytten, Ahmed Benallal, Odd Sture Hopperstad. A thermo-elasto-viscoplastic constitutive model for polymers. Journal of the Mechanics and Physics of Solids, 2019, 124, pp.681-701. ⟨10.1016/j.jmps.2018.11.018⟩. ⟨hal-03103080⟩