Numerical Simulation of the Viscohyperelastic Behaviour of PET near the Glass Transition Temperature

Abstract

The presentation deals with the non linear strongly elastic and viscous behaviour of poly ethylene terephthalate near the glass transition temperature and biaxially stretched at high strain rates representative of the injection stretch blow moulding process. A non linear visco-hyperelastic model inspired from [1] and identified from the experimental results of the equi-biaxial tension test [2], have been developed and presented in [3] is implemented into a finite element code developed with Matlab. The thermal behaviour modelling, identification and simulation has also been managed. First, a numerical simulation of 2D plane stress case has been performed involving 2 fields (global velocity V and elastic Cauchy Green tensor Be). Rectangular finite elements with quadratic and linear interpolations have been employed for velocity and the elastic left Cauchy Green tensor. Second, an axi symmetric formulation involving 4 fields (global velocity V, lagrange multiplier p associated with the global incompressibility condition, and multiplier q associated with the incompressibility of the elastic part) has been performed using rectangular elements. Degree of interpolation have been tested for all possible combinations to test the LBB like condition. Both simulations are compared with equi biaxial or sequential biaxial testing in order to reproduce the strain hardening effect and the self-heating observed. The final goal of this work is to perform the free blowing simulation to compare with experimental data. Therefore, we should solve an iterative procedure for a thermo-mechanical equation. At each time step, a four-field approach is adopted for the mechanical part, and a classical heat transfer equation is discretised for the thermal part.