International Journal of Fatigue 24 (2002) 11–19 www.elsevier.com/locate/ijfatigue Rapid determination of the fatigue curve by the thermographic method G. Fargione * , A. Geraci, G. La Rosa, A. Risitano Dipartimento di Ingegneria Industriale e Meccanica, Universita ` di Catania, Viale Andrea Doria 6, 95125 Catania, Italy Received 29 January 2001; received in revised form 19 July 2001; accepted 23 July 2001 Abstract The available methods for the rapid determination of the fatigue limit (Metall. Ital. 27 (1935) 188; Rev. Metall. XVIII (1951) 11) and for the analysis of the dynamic parameters of crack mechanics (ASTM-STP 519, 246; J. Mater. 5 (1970) 4; J. Appl. Mech. 67 (1945) A159; Exp. Mech. 5 (1965) 193; Fatigue Engng Mater. Struct. 1 (1979) 37; J. Basic Eng. Trans. ASME, Ser. D 85 (1963) 528) require the determination of parameters which are highly specialised (K I , J-integral) and often too closely linked to the micro-mechanics of the material, downgrading the engineering aspects of the problem and its design definition. Following their research into the use of the thermographic method to determine the dynamic properties of materials and components commonly used in the industrial sector (hereafter called the Risitano method [Int. J. Fatigue Mater. Struct. Components 22/1 (1999) 65]), the authors now present a procedure for the definition of the whole fatigue curve.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Fatigue curve; Thermographic method 1. Introduction As has been repeatedly noted [1–19] and reported by Risitano and La Rosa in [1], in thermographic investi- gation (on which the rapid method for the determination of the fatigue limit is based) it is possible to observe the temperature of each zone (pixel by pixel) over the entire surface of the specimen, and the evolution of the surface temperature over time T=f(N). In all the tests perfor- med, it has been found that (Fig. 1), with stresses above the fatigue limit s 0 (endurance 10 6 cycles), the thermal variation increases during the first phase of the test (phase 1), then remains almost constant until shortly before the failure (phase 2) and finally shows a further increase immediately prior to failure, (phase 3). The first phase of temperature increase is limited to a very low number of cycles compared to the number subsequently required to reach failure (in general, in the order of 10% of the entire lifespan of the specimen for loads not close to the yield stress). The second phase, of “stabilised tem- perature”, varies considerably; for applied loads close to * Corresponding author. Tel.: +39-095-7382413. E-mail address: glarosa@diim.unict.it (G. La Rosa). 0142-1123/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII:S0142-1123(01)00107-4 the yield stress this phase is extremely limited, while for loads only slightly above the fatigue limit s 0 it extends over almost the whole lifespan of the specimen. For loads greater than the fatigue limit, the rate of tempera- ture increase with the number of cycles in phase 1 and the stabilisation temperature (constant or very slightly rising, according to the first law of thermodynamics related to the quantity of heat per unit volume released to the outside) in phase 2, are higher the greater the load with respect to the fatigue limit (Fig. 2). In the third phase, that of failure (the complete plasticisation of a section of the specimen), the temperature increases rap- idly for comparatively a very small number of cycles. Failure of fatigue can occur only if, as a result of the presence of micro-cracks, local yieldings, micro-cavities, etc., the applied load produces an increase in the stress in one point (or zone) of the material, with local values exceeding the elastic limit. It is known that if the stress is static, the local plasticisation and the redistribution of the stress onto the surrounding material does not gener- ate any particularly critical condition and the material reaches failure only under decidedly greater loads. On the contrary, in the case of cyclic loading, where the stress is one of fatigue, when the material arrives at the condition of local yielding (micro-plasticisation) and a