Abstract
The study of the mechanical and thermal behaviour of polymers is of prime importance for engineering applications. Therefore, the ability of predicting these properties for several decades of loading frequencies and/or several tens of degree Celsius, is a strong motivation. Based on experimental combination of mechanical and thermal rheological-analysis (DMTA), phenomenological models are thus developed to predict the linear viscoelastic behaviour of polymers with the traditional use of the so-called “time-temperature superposition principle (TTSP)”. While implementing these models, the consideration of (i) effects linked to the real temperature of the sample or of (ii) the time effects induced by thermo-mechanical couplings are not taken into account. However, polymer materials are very sensitive to temperature variations and even slight temperature variations can be due to thermo-mechanical coupling or dissipation sources. The TTSP applicability in such a context is thus not straightforward. Therefore, an accurate knowledge of the mechanical and thermal behaviour of this class of materials, under the Thermodynamics of Irreversible processes, taking into account the dissipative effect and thermo-mechanical coupling, can become of prime importance.To achieve these objectives, the present study was performed starting from a literature review on the thermo-mechanical behaviour of vitreous and amorphous polymers and the TTSP. This was followed by understanding the theoretical framework of thermodynamics of irreversible processes and its implementation in the Generalized Standard Material (GSM) formalism. The theoretical framework of GSM allowed us to consider the temperature as an internal state variable and to derive the constitutive behavioural equations from a thermodynamic and a dissipation potential. This formalism also induced the possibilities to define and then compute the different heat sources involved in the heat diffusion equation.Second, measurements were performed to characterize the linear viscoelastic properties below the glass transition temperature of selected amorphous and rheologically simple polymers (PS, PMMA and PA-6.6). This was followed by the application of a classical TTSP using an Arrhenius law to predict the linear viscoelastic behaviour on a very large temperature/frequency range, which cannot be experimentally reachable. A first set of measurements was performed on PS in several laboratories to check for its monochromatic response to a monochromatic loading and build a reference database for the calibration and validation of different correction procedures (machine stiffness and electronic phase shift) of our DMTA. Later, synchronized thermography measurements were performed to measure the temperature variations of the sample during DMTA measurements. This allows for the estimation of the average mechanical energy dissipated during one cycle together with the heat losses and thermoelastic coupling.Finally, these experimental results were used to identify the optimum branches of a generalized Maxwell model (GMM) using non negative least squares method for the 3 different polymers. In each branch of this model, the viscoelastic time constant and the associated elastic modulus depend on the temperature (through an Arrhenius law and an activation energy determined previously experimentally). Using the GSM formalism, the different heat sources (thermomechanical couplings, dissipation) were also computed. The energy rate balance showed the predominance of the thermomechanical couplings sources. To conclude this study, we stressed that a GMM assuming the rheological simple material hypothesis is TTSP compatible.