Computationally efficient pseudo-viscoelastic models for evaluation of residual stresses in thermoset polymer composites during cure

In this study of the constitutive modelling of thermoset polymers during cure, we compare what we call the “cure hardening instantaneously linear elastic (CHILE)” approach with the more computationally intensive viscoelastic approach. The CHILE approach is popular compared to the viscoelastic approach as the cost of material characterization, data reduction, finite element model development and implementation, and computer run time is significantly lower. However, CHILE models suffer from the fact that the justification for their validity is essentially anecdotal, rather than based on a clear linkage to viscoelastic theory; and in related manner, materials characterization is done at an intuitively low but essentially arbitrary frequency. In this work we show that there are approximations that allow the full viscoelastic approach to be simplified progressively, and that these approximations are appropriate for the typical cure cycle undergone by a thermoset polymer. We present the functions of time at which the elastic modulus of the polymer should be calibrated for these simplified ‘pseudo-viscoelastic’ models, and show that for the uniaxial loading of a fully constrained block of polymer undergoing a given cure cycle, the predicted residual stresses compare very well with those computed using the full viscoelastic model. For further simplification, at the price of slightly lower accuracy and generality, a constant time or frequency can be chosen to evaluate the modulus. In general, we show that the CHILE approach, when properly calibrated, is a valid and efficient pseudo-viscoelastic (PVE) model, and that there is a continuum of trade-off of investment versus accuracy as we go from a full viscoelastic approach to the simplest CHILE approach.