PSI - Issue 39

188 10

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

1.6

2

10

head

head

body

1.4

body

1.2

0

10

1

0.8

-2

10

0.6

0.4

power spectrum

-4

10

temperature variation [°C]

0.2

0

-6

10

-0.2

0

10

20

30

40

50

60

70

80

90

100

0

0.05

0.1

0.15

0.2

0.25

0.3

Frequency [Hz]

time [s]

Figure 10 – DFT of the signals and reconstruction via LSF approach.

Finally, the phase values retrieved from the LSF of the blue and red curves are used to verify the prediction of Figure 8. The FH and SH of the turtle’s head signal (blue and red solid lines) and the SH of the turtle’s body signal (red dotted line) are represented in Figure 11. Again, the curves perfectly follow the behavior predicted earlier in this section, and also the SH of the temperature signal at the crack tip is opposite in phase to the SH ahead of the crack tip.

head FH

head SH

body SH

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4

normalized amplitude

-0.6

-0.8

-1

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

time [s]

Figure 11 – Effective phase values of the signals in the crack tip ( head ) and the wake of the crack ( body ).

4.1.4. Crack growth and Paris law The comparison between the crack length obtained via LSF of the Williams’ series solution and the measurement obtained from the high-resolution images captured by the digital camera is shown in Figure 12. As already explained, the numerical crack length is always a bit longer than the optical measurement, due to the Irwin plastic radius correction required in the linear elastic solution. Due to a higher uncertainty in accurately identifying the crack tip position from the photographs, due to the blurred edges caused by the narrow depth of field, the numerical curve appears to provide a smoother trend of crack length