Amorphous polymer mechanics exhibits strong non-linearities below the glass transition. We focus here on their apparition in the glass transition regime, while temperature is decreasing. We compare our experimental results with a simple model that accounts for dynamical heterogeneities and Eyring like relaxation.
We first describe the effect of dynamical heterogeneities on the linear mechanical response of polymers using a stochastic continuum mechanics model that includes a local heterogeneous dynamics. Calculations are performed using a Finite Element method. We show that in the linear regime, it gives a quantitative description of the modulus relaxation from the glassy to the rubber state measured on various polymer systems in the linear regime
We have extended this model to describe the transition from the linear to the non-linear response of polymers in the glass transition regime. In this aim, we have assumed a local Eyring stress dependence of the local relaxation times. We derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is first order Poisson -like.
We have compared the numerical predictions to experiments. First, the initial relaxation time distribution is deduced from the modulus relaxation measured in the linear regime for each polymer and is implemented in the model. We show that the stress-strain curves measured on many polymers stretched at constant strain rate in their glass transition can be quantitatively described by our numerical approach by adjusting only one parameter i.e. the critical stress involved in the local Eyring law. Finally, the additional dissipation of the mechanical work, that is induced by the formation of plastic events follows a time-temperature superposition.