The present contribution is toward the systematic characterization and development of a one-dimensional incremental viscoelastic (VE) model for thermo-rheologically complex materials (called “VisCoR”) for the prediction of residual stresses and shape distortions in composites. Traditionally, models that have been developed for this purpose within the composites industry are based on incremental linear elastic methods. While these methods are robust, they fall short in predicting exact behaviour of large composite parts and high temperature composites where relaxation effects also play a vital role in the final shape of the part. Moreover, these models also do not consider the dependency of stresses on temperature and degree of cure. Although viscoelastic models have been formulated, they are not in an incremental form (which is suitable for Finite Element (FE) simulations), hence requiring higher computational efforts. The presented model is an incremental form and requires lesser computational cost and characterization efforts and most importantly takes into account the effect of temperature and degree of cure. Preliminary studies indicate that the incremental 1D viscoelastic model can accurately model VE stress relaxation behaviour when compared to exact solutions.

A thermo-rheologically complex linear viscoelastic material model, accounting for temperature and degree of cure (DoC), is developed starting with series expansion of the Helmholtz free energy and systematically implementing simplifying assumptions regarding the material behavior. In addition to the temperature and DoC dependent shift factor present in rheologically simple models, the derived novel model contains three cure and temperature dependent functions. The first function is identified as the rubbery modulus. The second is a weight factor to the transient integral term in the model and reflects the current temperature and cure state, whereas the third function is under the sign of the convolution integral, thus affecting the “memory” of the material. An incremental form of this model is presented which, due to improved approximation inside the time increment, has better numerical convergence than most of the similar forms. Parametric analysis is performed simulating stress development in a polymer, geometrically constrained in the mold during curing and cool-down. The importance of using proper viscoelastic model is shown, and the role of parameters in the model is revealed and discussed. 

Stress relaxation and strain recovery phenomena during curing and changed thermal conditions are analyzed using a viscoelastic model developed for thermorheologically complex materials (VisCoR). By making several simplifying assumptions regarding the material behavior, the incremental form of the VisCoR model is reformulated to a version describing thermorheologically simple material and presented in one-dimension for simplicity. The model (called VisCoR-simple) is used to analyze material behavior under various conditions, including stress relaxation behavior at varying temperatures and time scales; tensile loading and unloading tests at high temperatures; stress build up and “frozen-in” strains during curing and following cool-down and strain recovery during the next step of heating. Furthermore, the differences between the so-called “path-dependent” model, which is a linear elastic model with different elastic properties in glassy and rubbery regions, and the presented viscoelastic model are studied. The path-dependent model is an extreme case of the viscoelastic model presented. The importance of considering viscoelasticity when considering temperature and curing effects on polymers and the shortcomings of the path-dependent model are revealed and discussed. © The Author