Modelling the finite strain response of PEEK with strain-dependent viscosity within the EGP model

Abstract

The University of Twente performed experimental uniaxial compression tests of Poly(ether-ether-ketone) (PEEK) and the TU Delft made a comparison with a numerical model; the viscoplastic Eindhoven Glassy Polymer (EGP) model. A higher strain-rate dependency and a higher yield stress at lower temperatures are observed in the experimental results. It is of importance to correctly model the stress-strain behaviour of PEEK for future research in long term behaviour of fibre reinforced PEEK by adapting the EGP model to account for these differences. The viscosity of the EGP model is based on the Ree-Eyring equation in which the three Ree-Eyring parameters (activation volume, activation energy and initial viscosities) are constants within the EGP model. It is observed that all three Ree-Eyring parameters are not constant over the strain when the original Ree-Eyring equation is fitted to the experimental data. Thus, non-constant Ree-Eyring parameters should be included in the EGP model. Evolving all three Ree-Eyring parameters leads to accurate stress-strain results, except for the pre-yield regime. The EGP model does not behave as stiff as the experiment in this region. Thus, a higher stiffness is included by evolving the shear moduli over the pre-yield regime. The evolution of the Ree-Eyring parameters is expressed by a $\tanh()$ function and quadratic function, while the evolution of the shear moduli is only expressed by a $\tanh()$ function. The evolution based on the $\tanh()$ function mostly influences the behaviour at small strains and the evolution based on the quadratic function mostly influences the behaviour at large strains. The evolution of the Ree-Eyring parameters at large strains leads to the insertion of viscous strain hardening in the EGP model. The viscous strain hardening qualitatively describes the Bauschinger effect for a cyclic loading case. The Bauschinger effect can be explained as the change of material behaviour when stresses are present. What occurs when the loading direction reverses within a cyclic loading case. An invariant function that is proportional to the strain determines the strain dependency of the evolution of the Ree-Eyring parameters and shear moduli. This invariant function is prevented from reducing for the evolution based on the $\tanh()$ function when the loading direction is reversed but does reduce for the evolution based on the quadratic function to correctly model cyclic loading. Furthermore, the linearization of the stiffness tensor is updated for the changes to the EGP model and a part of the stiffness tensor which was omitted in the original implementation is added.

Including the evolution of the Ree-Eyring parameters and shear moduli with the mentioned characteristics in the EGP model makes the EGP model correspond very well with the experimental results for all investigated temperatures and strain-rates.