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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• The body of the turtle (i.e. behind the crack tip): this area is placed on the wake of the crack, and it is where compressive stresses arise due to the crack closure. These compression stresses only act for a portion of the loading cycle. It comes out that the waveform representing the evolution of these compressive stresses has a significant peak at twice the loading frequency, i.e. 2 ω . Therefore the crack closure zone experiences also a 2 ω stress cycling which generates a first-order thermoelastic signal. • The head of the turtle (i.e. behind the crack tip): this part is placed ahead of the crack tip. Due to the early closure of the crack, a residual traction remains acting near the crack tip, that cannot be fully released when the remote load cycle reaches its trough. Similarly to what happens in the turtle’s body, the waveform representing the evolution of these traction stresses also develops a peak at twice the loading frequency, i.e. 2 ω, which gives rise to a first-order thermoelastic signal .
Second Harmonic
T
Second Harmonic
T
Second Harmonic
T
Sample#1: N = 503445
Sample #1: N = 137280
Sample #1: N = 368250
0.05
0.05
0.05
Numerical
Numerical
Numerical
120
120
120
Physical
Physical
Physical
0.045
0.045
0.045
140
140
140
0.04
0.04
0.04
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160
0.035
0.035
0.035
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180
0.03
0.03
0.03
200
200
0.025
200
0.025
0.025
220
0.02
220
0.02
0.02
220
0.015
0.015
0.015
240
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240
0.01
0.01
0.01
260
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260
0.005
0.005
0.005
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280
0
0
0
120
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120
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120
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Figure 5 – Second harmonic amplitude for different number of cycles: evolution and growth of the turtle
The physical (obtained from the pictures) and numerical (obtained from the Williams’ series + pattern search) crack tip positions are slightly distanced one from the other: the first one lies on the “neck” of the turtle, i.e. where the 2 ω thermoelastic signal is minimum between the body and the head of the turtle, while numerical tip is found inside the turtle’s head. This has been previously justified because the Williams’ model is based on a linear elastic solution, wherein a plastic radius Irwin correction must be considered.
Second Harmonic Phase
Second Harmonic Phase
Second Harmonic Phase
[°deg]
[°deg]
[°deg]
Sample #1: N = 368250
Sample #1: N = 503445
Sample #1: N = 137280
180
180
180
100
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90
90
90
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140
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30
160
0
0
0
180
180
-30
-30
-30
200
200
200
-60
-60
-60
220
-90
-90
-90
220
240
-120
-120
-120
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-150
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mm
Figure 6 – Second harmonic phase maps. The phase shift between the crack tip and the wake of the crack is 180°
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