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Prediction of Fatigue Cracks Using Gamma Function

Open Access
|Nov 2023

Figures & Tables

Figure 1.

Four points fatigue bending tests. (a) Schematic assembly and dimensions; (b) real assembly with electrical follow; and (c) fractured specimen.
Four points fatigue bending tests. (a) Schematic assembly and dimensions; (b) real assembly with electrical follow; and (c) fractured specimen.

Figure 2.

Servo-hydraulic machine for fatigue tests: Instron 8500.
Servo-hydraulic machine for fatigue tests: Instron 8500.

Figure 3.

Experimental fatigue life of V-notch in four-point bending specimens’ tests of 2024 T351 Al-alloy.
Experimental fatigue life of V-notch in four-point bending specimens’ tests of 2024 T351 Al-alloy.

Figure 4.

Comparison of predicted and experimental fatigue life at R = 0.1.
Comparison of predicted and experimental fatigue life at R = 0.1.

Figure 5.

Comparison of predicted and experimental fatigue life at R = 0.2.
Comparison of predicted and experimental fatigue life at R = 0.2.

Figure 6.

Comparison of predicted and experimental fatigue life at R = 0.3.
Comparison of predicted and experimental fatigue life at R = 0.3.

Figure 7.

Comparison of predicted and experimental fatigue life at R = 0.5.
Comparison of predicted and experimental fatigue life at R = 0.5.

Figure 8.

Comparison of predicted and experimental crack growth rate at R = 0.1.
Comparison of predicted and experimental crack growth rate at R = 0.1.

Figure 9.

Comparison of predicted and experimental crack growth rate at R = 0.2.
Comparison of predicted and experimental crack growth rate at R = 0.2.

Figure 10.

Comparison of predicted and experimental crack growth rate at R = 0.3.
Comparison of predicted and experimental crack growth rate at R = 0.3.

Figure 11.

Comparison of predicted and experimental crack growth rate at R = 0.5.
Comparison of predicted and experimental crack growth rate at R = 0.5.

Figure 12.

Error band scatter of predicted life at R = 0.1.
Error band scatter of predicted life at R = 0.1.

Figure 13.

Error band scatter of predicted life for at R = 0.2.
Error band scatter of predicted life for at R = 0.2.

Figure 14.

Error band scatter of predicted life at R = 0.3.
Error band scatter of predicted life at R = 0.3.

Figure 15.

Error band scatter of predicted life at R = 0.5.
Error band scatter of predicted life at R = 0.5.

Experimental loading conditions and equivalents’ initial and final crack lengths for different stress ratios_

R-ratioa0(mm)af(mm)Pmin(KN)Pmax(KN)P(KN)N(cycles)ΔK0(MP√m)ΔKf(MP√m)
0.13.347.8750.1151.1491.034382.0005.39522.696
0.23.317.140.2371.1840.947569.7004.8516.88
0.33.3657.3650.3481.160.812547.0004.2215.90
0.52.7356.281.252.501.25240.0005.53515.82

Coefficient of Paris model_

R-ratioCm
0.11 · 10−83.645
0.21 · 10−83.7053
0.39 · 10−93.8712
0.55 · 10−82.9287

Mechanical properties of Al-Alloy 2024 T351_

σ0.2σRAEGν
36347712.57427.820.33

Dimension of fatigue specimens_

LtLlhBa0
645014.510102

Chemical composition of Al-alloy 2024 T351_

ElementsSiFeCuMnMgCrTiZnPbNiAl
%0.1050.1593.970.4491.50.050.0180.1090.0560.02Rest

Performance of Gamma model

R-ratio0.10.20.30.5Mean value
%Dev4.5203.8921.2205.2003.708
Prediction ratio0.9610.9680.9880.9510.967

The values of the constants of the adjustment curves_

R-ratioABCDEF
0.1−44,955 · 104282,743 · 103−71,01 · 1038932.6−566.9515.047
0.2−16,180 · 104139,644 · 103−42.59 · 1036101.5−424.4912.113
0.3−10,975 · 104603,626 · 103−132.9 · 10314.714−823.3919.20
0.5−56,762 · 104384,000 · 103−104.6 · 10314.404−1008.929.449
DOI: https://doi.org/10.2478/fas-2022-0004 | Journal eISSN: 2300-7591 | Journal ISSN: 2081-7738
Language: English
Page range: 29 - 46
Published on: Nov 28, 2023
Published by: Institute of Aviation
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2023 Abdelfetah Moussouni, Mustapha Benachour, Nadjia Benachour, published by Institute of Aviation
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.