A Finite Strain Quasi-Non-Linear Thermoviscoelastic Model for Semi- Crystalline Thermoplastic Polymers subjected to Cyclic Loading

Thermoplastic polymers of varying degrees of crystallinity have found applications in
secondary and, recently, primary structures owing to their reversible glass transition and
consequent thermomechanical performance in a wide range of strain rates and temperatures. Thermomechanical models address the highly nonlinear constitutive behaviour of semicrystalline polymers using a combination of viscoelastic and viscoplastic theories. A typical approach to thermoviscoelasticity is utilising linear Maxwell elements to evaluate the rate-dependent stress response using convolution integrals in shifted laboratory time. Motivated by the aforementioned linear viscoelastic model, we introduce a novel
thermodynamically consistent quasi-non-linear thermoviscoelastic formulation in finite strain using Maxwell elements with strain dependent moduli. The novelty encompasses the solution to the convolution integrals arising from quasi-non-linearity and the corresponding internal dissipation. This formulation is intended to produce large non-linearities in the elastic regime, which is apparent in semi-crystalline polymers subjected to thermomechanical cyclic loading. To model thermoviscoplasticity, we consider a Drucker-Prager yield function and Perzyna-type flow rule. Lastly, we consider a reversible Mullins-type damage as a function of the deformation energy of the quasi-non-linear thermoviscoelastic model to describe the response in unloading. For validation, we apply this model to a conventional thermoplastic semicrystalline polymer, polypropylene. The experimental campaign for calibration and validation consists of Dynamic Mechanical Analyses (DMA) and uniaxial monotonic and cyclic tests in tension-compression. To characterise the quasi-non-linear thermoviscoelastic model parameters, we outline a simple procedure using the experimental campaign.