A finite deformation formulation for amorphous glassy polymers under moderate and impact strain rates: Application to adhesive films

Abstract

This work describes a novel finite strain hypo-elastic formulation for amorphous thermoset polymers working in the glassy regime. The constitutive formulation is able to describe time and pressure-dependent behaviour under loading rates ranging from quasi-static to impact-type loading conditions and to account for thermo-mechanical coupling effects. A non-linear pressure dependent potential function is introduced to capture the non-associative visco-plastic potential flow for volumetric plastic strain control. The formulation also incorporates an internal state or deformation resistance variable to enable the description of the polymer hardening — softening behaviour, as well as a novel relation for the dissipative fraction of the plastic work in terms of the equivalent accumulated plastic strain. The constitutive model is formulated within a finite strain kinematics framework, and full details of its numerical implementation into the finite element method using a fully implicit Euler Backward algorithm are given. Model calibration is carried out for three different thermosetting resins (PR520 and RTM6 Epoxies, and MMA adhesives).To illustrate the model capabilities, two case studies are investigated: (i) the de-formation behaviour of epoxy under moderate and impact-type loading conditions under isothermal and fully adiabatic conditions, and (ii) the fracture behaviour of adhesive layers used to bond stiff metallic substrates. Results on RTM6 epoxy show that at, e.g., 60% true strain, 48.5% of the rate of plastic work is dissipative, and that the corresponding predicted increase in temperature due to the locally dissipated heat is consistent with published calorimetry data on a similar thermoset polymer. It was also found that, by coupling the proposed constitutive model with a cohesive zone model, it was possible to predict accurately the effect of an MMA adhesive layer thickness and pressure-dependency on the growth of an interfacial crack between the MMA adhesive and the metallic substrates. The proposed model should constitute a generic phenomenological formulation for the mechanical behaviour prediction of a wide range of thermoset polymers under confined and quasi-adiabatic conditions such as in composites and adhesive joints.