PSI - Issue 57

Lorenzo Bercelli et al. / Procedia Structural Integrity 57 (2024) 437–444 441 L. Bercelli, C. Guellec, B. Levieil, C. Doudard, F. Bridier, S. Calloch Author name / Structural Integrity Procedia 00 (2019) 000 – 000 5 stress range Δ . This is coherent with the crack closure phenomenon observed at = 10 , as only a portion of the loading cycle effectively participates to the propagation of the crack.

(a) (b) Fig. 4. Evolution of the crack size at the surface 2 against the number of cycles for a T-joint loaded at =0.1 with Δ / =0.29 (a) and plot of the constant propagation speed against the normalized nominal stress range Δ for all test configurations (b). As an interim conclusion, it is observed from the infrared data that the fatigue life of the welded joints is governed by the propagation of fatigue cracks along the weld toe, which kinetics is affected by a crack-closure phenomenon dependent on the applied stress ratio. Then, the assessment of the intensity of the crack-closure phenomenon based on the infrared data can be related to the fatigue life of the welded joints. 3.2. Assessment of the crack closure phenomenon Let’s consider a sample, submitted to a nominal sinusoidal stress ( ) of mechanicalfrequency and stress range Δ , in which a crack is initiated and propagating in Mode I, alternatively closing and opening during one loading cycle because of the local stress state. If the crack opening time within a cycle is noted Δ , then it is possible to determine the portion of nominal stress for which the crack is open (Fig. 5.a), noted as the effective stress range Δ and given by Δ = Δ = (1−cos( Δ )) 2 Δ , (3) with the opening rate. As the temperature signal in the vicinity of a crack is affected by the crack-closure phenomenon (Fig. 3.a), the opening time Δ can be estimated in-situ , and so is the effective stress range Δ , which value is closely related to the propagation kinetics and so the fatigue life of the welded-joint. In order to estimate the opening time Δ from the temperature signal close to the crack, it is necessary to overcome bias due to the sampling frequency of the camera . Indeed, a common practice in TSA is the maximization of the mechanical frequency (to limit conduction effects),resulting in a poor temporalresolution of a loading cycle fora fixed sampling frequency , which is itself dependent on the desired signal to noise ratio (due to the infrared captor integration time). As a result, the assessment of instantaneous phenomena within one loading cycle (opening and closure of cracks) requires the application of an up-sampling process. In the present study, the use of signal reconstruction via Discrete Cosine Transform (DCT) is proposed. A number of harmonics ℎ is chosen in order to study the zero-centered analytical signal ( ) θ DCT ( ) = ∑ ℎ =1 cos(2 + ) , (4) with the th harmonic of the temperature signal and the corresponding phase. This DCT reconstruction step has the benefit of filtering the signal (any non-harmonic component or above ℎ × is neglected) as well as denoising through the averaging of cycles recorded within one infrared film. Prior to this reconstruction step, pure signal denoising can be performed through adaptive wavelet thresholding, as proposed by Chang et al. (2000).