A thermo-mechanical large deformation constitutive model for polymers based on material network description: Application to a semi-crystalline polyamide 66

A visco-hyperelastic constitutive model, based on an original approach initially developed by (Billon, 2012) and applied to amorphous rubbery polymers for a one-dimensional formalism, was extended in this study to three-dimensional constitutive equations based on a thermodynamic framework. The model was applied to a semi-crystalline polyamide polymer, PA66. The experiments included tension and shear testing coupled with synchronized digital image correlation and infrared measurements device for capturing the time, temperature, and stress state dependence, as well as the complex thermomechanical coupling exhibited by the material under large deformation. A notion of equivalent strain rate (based on the time–temperature principle superposition) was also introduced to show its capability to build master curves and therefore decrease the number of testing needed to build a material database. The model is based on the Edward Vilgis theory (1986) and accounts for chains network reorganization under external loading through the introduction of an evolution equation for the internal state variable, η¯, representing the degree of mobility of entanglement points. The model accounting for the equivalent strain rate notion was calibrated using master curves. The thermomechanical model agreed well with the experimental mechanical and temperature measurements under tension and shear conditions. The approach developed in this study may open a different way to model the polymer behavior.

• We develop a behavior model for a semi crystalline polymer with full thermo-mechanical couplings.
• The model is based on the molecular chain network description with parameters physical meaning.
• We assume that inelastic phenomena result in an increase of entropy related to “de-entanglement”.
• The model is identified on a large experimental basis based on tensile and shear tests.
• We report very good results on prediction using a reduced number of parameters.