Incorporating crystallinity distributions into a thermo-mechanically coupled constitutive model for semi-crystalline polymers

Abstract Thermoplastic polymers (TP) are well-suited for thermoforming and injection moulding processes. Semi-crystalline polymers (SCP) are a specific class of TPs, which partly crystallize after cooling from the melt. During thermoforming processes, SCPs are subjected to large deformations and thermal loadings and show strong thermo-mechanical coupling effects. In addition, the evolution of the crystalline phase influences the macroscopic material response significantly. Due to these complex dependencies, a demand for computational models arises, to analyze, predict, and optimize the complex material and structural behavior of parts during these processes. To this end, a finite strain, thermo-mechanically coupled constitutive framework is derived in a thermodynamically consistent manner for SCPs. In the continuum model, a visco-hyperelastic network resistance and an elasto-plastic intermolecular resistance are introduced, where non-linear isotropic and kinematic hardening as well as non-linear relaxation behavior are considered. To account for the dependence of the material response on the degree of crystallinity, the crystallization kinetics during cooling from the melt are captured by means of a non-isothermal representation of the Avrami equation. Furthermore, the heat generation, associated with irreversible processes and exothermic crystal growth, is derived in a thermodynamically consistent manner. Uniaxial tensile test data for different temperatures, loading rates, and degrees of crystallinity, as well as isothermal and non-isothermal differential scanning calorimetry (DSC) data for Polyamide 6 is utilized to calibrate the model in a stepwise parameter identification scheme. The model response is discussed and reveals the promising potential of this new approach to efficiently and accurately predict this class of materials in the future.