## 1 Introduction
The energy per cycle dissipated as heat by a unit volume of material is assumed as a fatigue damage indicator, obtaining that this parameter can be correlated to the fatigue strength independently of the geometry, despite some limitations for severe notches [13]. Research focusing on GFRP aimed to study its fatigue behaviour from both the mechanical and the thermal points of view [14]. In order to perform the fatigue characterization of GFRP composite materials, two methods have been presented for determining fatigue limit: a statistical method validated for metallic materials and a graphical method applied on phase data, both showing a good agreement with the conventional S-N curve [15]. A technique to pass from temperature information to distribution of heat sources on the composites surface to monitor the damage evolution of some carbon/epoxy composite specimens during a fatigue test has been proposed [16]. Only one study analysed the influence of a particular type of notch as a central hole [17] but no study has analysed the presence of notch with different geometries in composites. The aim of this previous study was to understand the damage evolution of unidirectional GFRP specimens with and without a circular notch under static and fatigue loads, by observing the thermal phenomena on the external surface of the GFRP composite [17]. At present, the research world is showing a growing interest in studying the mechanical behaviour of composites, employing both traditional and innovative techniques, with the final purpose of making previsions regarding their service life. A commonly used approach is based on the assessment of the temperature plateau during a stepwise loading procedure. The composite structures' fatigue failure is generally caused by a combination of different types of damage: fibre breakage, matrix cracking, delamination, ply failure or debonding. Each of these mechanisms is amplified by stress concentrations due to manufacturing defects, cut-outs, notches and flaws. Most of the structural components in the automotive and aerospace applications present notches or holes causing a stress concentration that reduces the overall fatigue strength in the material that is generally a composite material. In machines and structures, in fact, progressive local failure often takes place at the root or in the proximity of the notches or holes. This paper presents a new application of the Risitano method [1; 9] for the determination of the fatigue notch coefficient \(\mathsf{k}_{\mathsf{f}}\) in GFRP composite specimens. Traditionally, the fatigue notch effect \(\mathsf{k}_{\mathsf{f}}\) is obtained by the ratio between two fatigue limits, referred to un-notched and notched specimen. As a consequence, two fatigue curves are needed to define this parameter for each geometry. It is evident that the approach commonly used for homogeneous materials to define k\({}_{\rm f}\) is inapplicable in the case of composite, not only for the entity of the experimental effort, but also for the lack of generality of the approach. Assuming to have determined the notch effect k\({}_{\rm f}\) for a specific geometry carrying out experimental fatigue tests on a selected layup sequence, in fact, it would be not possible to extend the result to specimen having the same notch geometry but a different ply sequence. Therefore, the development of a methodology for the rapid determination of k\({}_{\rm f}\) would be useful. Using a thermographic approach, the fatigue limit could be evaluated using a stepped fatigue test. Adopting this technique both for the un-notched and notched section, it is possible to determine these two fatigue limits and the corresponding notch fatigue coefficient k\({}_{\rm f}\) using a unique specimen. This last parameter will be defined simply by the ratio between the fatigue limits corresponding to the net and gross section determined using the Risitano method [1; 2; 3]. Since fatigue tests are carried out only on a single notched specimen, the advantage of the methodology is evident.