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.

Derivation of the Variants of the Burgers Model Using a Thermodynamic Approach and Appealing to the Concept of Evolving Natural Configurations

“…Next, following [6], we show that the model (74) is equivalent to the Burgers model (2). Indeed, first, we define S 1 := G 1 (B κ p 1 (t) − I) and S 2 := G 2 (B κ p 2 (t) − I) and S := S 1 + S 2 .…”

“…Let A T denote the transpose of a tensor A. Then, the left and right Cauchy-Green tensors are defined through B := FF T and C := F T F. (6) We will also introduce the standard notation for the symmetric and antisymmetric parts of L through:…”

“…In this section, we consider a setting described by three configurations: reference, current and a natural one (see Figure 4). We first recall the derivation developed in [6,9,27] and then provide its extension. Throughout the rest of this paper, we suppose that det F = 1 and div v = tr D = 0,…”

“…On the other hand, the presence of multiple relaxation times in the response of materials in creep or stress relaxation tests can be well described by rate-type fluid models of higher order. An example of a higher order model capable of describing two different relaxation times is the model due to Burgers. In the case of asphalt, Monismith and Secor [5], Narayan et al [1] and Málek et al [6] used the model due to Burgers to corroborate experimental data, while in the case of the vitreous of the bovine eye, Sharif-Kashani et al [2] correlated experimental data also using a Burgers model.…”

“…Since the introduction of the notion of natural configuration allows one to split any process into an elastic response from an evolving natural configuration and a dissipative process describing (irreversible) changes in the natural configuration, it seems reasonable to require that, if the total process is isochoric, then its instantaneous elastic part is isochoric as well. However, Málek et al [6] found that, if they gave up the requirement that both the elastic and dissipative responses be isochoric and only required that the compound response be isochoric, then they were able to develop the Maxwell and Oldroyd-B model without resorting to any approximation. We refer the reader to [15] for a detailed discussion of this issue.…”