A thermodynamically compatible model for describing the response of asphalt binders

Abstract

In this paper, we develop a model from a thermodynamic standpoint that seems capable of describing the nonlinear response of asphalt binders. We test the efficacy of the model by comparing its predictions against two different sets of torsion experiments on asphalt binders. The first set of experiments that we use for corroborating the model was carried out by Narayan et al. [2012. Mechanics Research Communications, 43, 66–74] wherein for the first time it was found that the relaxation times associated with the torque and the normal forces, in a torsion experiment, are markedly different, and the second set of experiments that we use to corroborate the model documents the overshoot of torque in a torsion experiment [Krishnan and Narayan, 2007. Steady shear experiments on ashpalt. Chennai: IIT, Madras]. The model that is developed in this paper fits both sets of experiments well, and it seems to be a good candidate for describing the response of asphalt binders in general. As the deformation is nonlinear, it would be inappropriate to use the linearised viscoelastic model which is based on the linearised strain, and the models due to Maxwell, and the Oldroyd-B model are unable to capture the marked difference in the relaxation times, while the Burgers model is unable to describe the torque overshoot.

Keywords::

• stress relaxation
• normal forces
• torque
• rate type fluid
• asphalt
• experiment fitting

Notes

^1. In Rajagopal and Srinivasa (2000), the dissipation is quadratic, but it is not expressed purely in the terms of (see the definition that follows in the text).

^2. It is not possible to provide more details of the exact nature of this 80/100 pen binder as it is proprietary.

^3. Of course, one has to make a more careful claim. A solution of the form assumed for the velocity field, under the assumption that the fluid is an Oldroyd-B fluid, is unable to capture the phenomenon. One does not know whether the full equations can capture the phenomenon. However, the similarity solution that is sought seems to be a reasonable one for the initial-boundary value problem under consideration, and in the case of the new model, the similarity solution does indeed capture the phenomenon.

Additional information

Funding

This work is supported by the Ministry of Education, Youth and Sports of the Czech Republic, the ERC-CZ project [LL1202]. K. Tůma work was also supported by the Charles University Grant Agency, Contract [GAUK 152010].