Energy approach for the fatigue of thermoviscoelastic materials: Application to asphalt materials in pavement surface layers M. Boudabbous a,b , A. Millien a , C. Petit a,⇑ , J. Neji b a Université de Limoges, Laboratoire GEMH-GCD, Bd J. Derche, 19300 Egletons, France b Université de Tunis El Manar, ENIT, Laboratoire LAMOED, Tunis, Tunisia article info Article history: Received 10 June 2012 Received in revised form 14 September 2012 Accepted 25 September 2012 Available online 11 October 2012 Keywords: Fatigue Dissipated energy Thermoviscoelastic material Damage Intrinsic law abstract This paper focuses on a study of the dissipated energy approach according to two methods, i.e. cumula- tive energy and the ratio of dissipated energy. An experimental investigation has been performed, with a double shear cyclic test of asphalt material HMA 0/6 being chosen at a 10 Hz frequency, 10 °C and 20 °C and at various force or displacement loading levels. A comparison between the two fatigue characteriza- tion methods shows that cumulative energy yields an intrinsic fatigue law that can be further developed to obtain other relations between different loading modes: displacement or force loading. Thanks to this paper, users are able to define the fatigue law in other loading-controlled modes than those introduced during the tests analyzed to identify fatigue parameters. The possibility is available to obtain a fatigue law independent of loading mode and representative of a real loading evolution in the field. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction In most cases, fatigue occurs at a constant level of loading dur- ing a strain-controlled or stress-controlled test. Some authors have considered the effect of a rest period; in reality, when fatigue takes place within a material, both fatigue and heating are contributing to a decrease in the complex modulus. Design methods must adopt Miner’s Law [1] or a similar cumulative damage law in order to take into account actual loadings in the field. On the other hand, for the fatigue of asphalt materials for example, fatigue tests are performed under controlled displacement. The chosen design method must therefore consider a reference loading along with a level of strain assumed constant over the pavement lifespan. Such is not presently the case; consequently, this paper seeks to incor- porate a variation in loading level during fatigue by means of an energy approach. This same approach is applicable in other visco- elastic materials, since dissipated energy contains information on test parameter variations (stress, strain, phase angle), while at the same time energy can be correlated with other expressions through the number of fatigue cycles and is thus capable of provid- ing an intrinsic law for tested materials. 2. Background This study targets thermoviscoelastic materials and is intended to determine the influence of temperature and loading through application of the Time–Temperature Superposed Principle (TTSP). These materials have been well modeled using a pseudo-elastic modulus given by master curves and denoted the complex modu- lus. In this section, we will begin by a brief review of the fatigue of asphalt materials before focusing on the rationale behind the en- ergy approach. 2.1. Fatigue of viscoelastic materials Thermoviscoelastic properties are generated by the bitumen part of a Hot Mix Asphalt (HMA) material (which accounts for ap- prox. 6% by weight or 15% by volume); most studies assume a mac- roscopic approach towards homogeneous materials [1]. In the present paper, we have maintained this underlying assumption. For asphalt materials, most authors have identified and used a fa- tigue law from the Wöhler representation [2]; this graphic repre- sentation is always used for asphalt materials even when experimental results are dispersed due to the presence of hetero- geneous materials at both the micro and mesoscales. Subsequent research by Miner [1] has considered the cumulative damage in each cycle, with cycles potentially featuring different loading rates. Miner’s cumulative law has been defined for metallic materials and verified as well for asphalt materials [2]. Fatigue depends on the loading level, temperature, frequency and the loading-time signal shape [4]. In the majority of studies therefore, the pseudo-elastic analysis is conducted with TTSP, as a continuous sinusoidal loading is most often applied under controlled displacement for asphalt materials, in accordance with a standard (either European or American). A cyclic tensile-compressive loading is introduced by 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.09.013 ⇑ Corresponding author. Tel.: +33 555934519. E-mail address: christophe.petit@unilim.fr (C. Petit). International Journal of Fatigue 47 (2013) 308–318 Contents lists available at SciVerse ScienceDirect International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue