PSI - Issue 57

Lorenzo Bercelli et al. / Procedia Structural Integrity 57 (2024) 437–444

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6 L. Bercelli, C. Guellec, B. Levieil, C. Doudard, F. Bridier, S. Calloch / Structural Integrity Procedia 00 (2019) 000 – 000

(a) (b) Fig. 5. Effectivestress range Δ illustrated on the nominal sinusoidal loading (a) and illustration of the characteristic turning points , and in the temperature signal in the presence of a crack-closure phenomenon (b). Once the DCT reconstruction is performed, the turning points in the averaged DCT signal of one loading cycle, namely the opening and closure of the crack, are identified. This process is done via the use of a signal processing method based on Continuous Wavelet Transform (CWT), as described by Du et al. (2006). This method proposes the detection of peaks in a signal via identification of significant ridge lines in the CWT scalogram (plot of the correlation in time between the signal and a chosen wavelet at different characteristic frequencies). In practice, because of conduction effects, the instant corresponding to the opening of the crack is more marked in the temperature signal than is the instant of closing of the crack (Fig. 5.b and Fig. 3.a). To avoid the pitfall of an erroneous estimation of , it is taken advantage of the fact that the period of crack closure is centered on the instant of maximum compression ( i.e. the instant of maximum temperature rise ), as suggested by Pippan and Hohenwarter (2017), which is easily determined on the DCT reconstructed signal. Finally, following this signal processing protocol, the crack-opening time Δ is determined as Δ = 1 −2| − | . (5)

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(e) (g) Fig. 6. Temperature signals close to fatigue cracks, at =0.1 and Δ / =0.29 with no crack-closure(a), and identification of closing and opening instants and at =10 in the as-welded configuration for Δ / =0.29 (b), Δ / =0.86 (c), Δ / =1.13 (d) and in the compression pre-loading configuration for Δ / =0.29 (e), Δ / =0.86 (f) and Δ / =1.13 (g). The application of this protocol is illustrated in Fig. 6 for experimentalsignals taken at pixels close to cracks for welded-joints tested at = 10 (as cracks do not show a closure phenomenon at = 0.1 , as shown in Fig. 6.a). It is found that, for stress ranges in / {0.29,0.86} (Fig. 6.a, c, e and f), the opening rate is around (f)