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

Abstract

International audienceA 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

Deformation behavior of thermoplastic elastomer specimens: Observation of the strain behavior in a wide range of tensile speeds

“…Figure shows the NDRs of Samples A and B. In both samples, the NDR increased with the tensile speed.…”

Modeling of time dependent mechanical behavior of polymers: Comparison between amorphous and semicrystalline polyethylene terephthalate

“…According to chosen model Edwards and Vilgis’ model was chosen as equivalent network. Inelastic processes were assumed to result from kinetics of internal variables variation induced by the microstructure changes under loading.…”

“…As far as the second branch is concerned, the chain extensibility and the level of connectivity in the chain network must be correlated. This is why we consider α to be proportional to (disentanglement) at any time.…”

“…Feasibility to model rubbery PMMA over a wide range of strain rates and temperatures with a using equivalent strain rate at reference temperature as a “new” coupled parameter to account for temperature and strain rate coupled effects was also reported . Recently, Maurel‐Pantel et al completed the approach proposing the fully 3D writing of the resulting thermomechanical model in the rigorous frame of thermodynamics.…”

Phenomenological multi-mechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation

“…Indeed, to capture the overall behaviour of polymers or polymeric composites, some authors refer to the theories of viscoelasticity (Moreau et al, 2005;Khan et al, 2006), viscoplasticity (Achour et al, 2015;Drosdov and Christiansen, 2007), coupled viscoelasticity and viscoplasticity (Miled et al, 2011), damage (Nouri et al, 2009) or even both coupled viscoelsticity, viscoplasticity and damage (Launay et al, 2011(Launay et al, , 2013aKrairi and Doghri, 2014;Lawrimore II et al, 2016). It is worth noticing that some other models integrate aspects related to physics of polymers, such as the molecular chains network reorganization 2 (Maurel-Pantel et al, 2015) or the partial phase transformation between crystalline and amorphous phases (Oshmyan et al, 2005). Other works (Arruda et al, 1995) have introduced conformational rearrangement as mechanisms behind yielding and plasticity of glassy polymers.…”