PSI - Issue 39

Riccardo Cappello et al. / Procedia Structural Integrity 39 (2022) 179–193 Author name / Structural Integrity Procedia 00 (2019) 000–000

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In Figure 6 the SH phase maps show a well distinguished 180° phase shift between the area ahead of the crack tip and the wake of the crack, as already pointed out in [3], [5], [8]. This peculiar phase shift is also a sign of the presence of crack closure, that can be predicted and explained analyzing the harmonic content of the crack-closing load [3]. 4.1.3. Evaluation of the harmonic content of the localized crack-closure load A simulation of the compressive load that acts on the flanks of the crack and the analysis of its harmonic content are here performed, to provide an explanation of the genesis of the thermoelastic signal behind the tip of the crack. Under the same testing conditions as those of the experiments ( R = 0, LF = 15 Hz), if the external applied load is modeled as a pure cosine wave (Figure 7 (a), blue curve), the cyclic compression load arising on the wake of the crack can be schematized as following the behavior described by the red curve of Figure 7 (a), since the crack closure has an effect only for a part of the loading cycle. The complex harmonic content of the crack closing signal (red dots) with respect to the external load (blue dots) is highlighted performing the Discrete Fourier Transform of the signals (Figure 7 (b)). The peaks in the power spectrum at harmonics higher than 15 Hz, with a significative amplitude, are supposed to generate first order thermoelastic signals, at frequencies different form the externally applied load. In particular, the harmonic peak at twice the loading frequency (i.e., 30 Hz), explains the capability of the SH amplitude analysis to detect crack closure phenomena.

(a)

(b)

(c)

Figure 7 – (a) Loading signal, (b) Discrete Fourier Transform and (c) phase-gram of: the applied external load (blue curve) and crack closure signal (red curve).

The phase shift retrieved from the SH signal in the area that experiences crack closure can be explained looking at the phase-gram of the signal. Figure 7 (c) shows how the SH crack closure phase information is codified at a specific angular position. In particular, when the frequency is 30 Hz, a phase shift of 180° with respect to a pure cosine wave is found, resulting in a thermoelastic signal modulated as a cos(2 ) . This signal is represented in Figure 8 by the dotted red curve. Finally, as a reference, in Figure 8 also the FH thermoelastic signal (blue curve) generated by the externally applied load is represented. Both the curves are opportunely shifted: in particular, the FH thermoelastic signal is represented as − sin( ) , that would be the thermoelastic signal generated by a pure sinusoidal loading wave, while the crack-closure thermoelastic becomes a − cos(2 ) .