Issue 78

T. Nasri et alii, Frattura ed Integrità Strutturale, 78 (2026) 275-297; DOI: 10.3221/IGF-ESIS.78.17

[25] Zhou, S., Yang, B., Xiao, S., Yang, G., Zhu, T. (2024). Interpretable Machine Learning Method for Modelling Fatigue Short Crack Growth Behaviour . Metals and Materials International, 30(7), 1944-1964. DOI: https://doi.org/10.1007/s12540-024-01628-6 [26] Babu Rao, V., Spear, A.D. (2025). An interleaved physics-based deep-learning framework as a new cycle jumping approach for microstructurally small fatigue crack growth simulations. npj Computational Materials, 11, 255. DOI: https://doi.org/10.1038/s41524-025-01741-z [27] Hurvich, C.M. and Tsai, C.L. (1989). Regression and time series model selection in small samples. Biometrika, 76, pp. 297–307. DOI: https://doi.org/10.1093/biomet/76.2.297. [28] Hobson, P.D., Brown, M.W. and de los Rios, E.R. (1986). Two phases of short crack growth in a medium carbon steel. In: The Behaviour of Short Fatigue Cracks. EGF Pub. 1, pp. 441–459. [29] Nizery, E., Proudhon, H., Buffière, J.-Y., Cloetens, P., Morgeneyer, T.F. and Forest, S. (2015). Three-dimensional characterization of fatigue-relevant intermetallic particles in high-strength aluminium alloys using synchrotron X-ray nanotomography. Philosophical Magazine, 95(25), pp. 2731–2746. DOI: https://doi.org/10.1080/14786435.2015.1061716. [30] Bowie, O.L. (1956). Analysis of an infinite plate containing radial cracks originating at the boundary of an internal circular hole. Journal of Mathematics and Physics, 35(1-4), 60-71. [31] Tada, H., Paris, P.C. and Irwin, G.R. (2000). The Stress Analysis of Cracks Handbook. 3rd ed. ASME Press, New York. [32] Forman, R.G., Shivakumar, V., Cardinal, J.W., Williams, L.C. and McKeighan, P.C. (2005). Fatigue Crack Growth Database for Damage Tolerance Analysis. Report DOT/FAA/AR-05/15, Federal Aviation Administration, Washington D.C.

N OMENCLATURE

Symbol

Unit GPa MPa MPa

Definition

Young's modulus

E

0.2 P R

0.2% proof stress (yield strength)

m R

Ultimate tensile strength Elongation at fracture

%

A %

µm µm µm µm µm

Half crack length measured from hole centre Initial crack length at the onset of measurable propagation Initial crack length — type A specimen (35.4 µm) Initial crack length — type B specimen (31.5 µm) Crack length as a function of fatigue cycles

a

0 a

0 A a  0 B a    a N

/ da dN

µm/cycle

Crack growth rate

cycles

Number of fatigue cycles

N

g N

— — — — — — —

Number of grain boundaries crossed along crack path

g A N  g B N 

Grain boundaries crossed — type A (3.72)

N g-B (1.51–1.55 , two specimens)

µm/cycle·(MPa √ m) ⁻ ⁿ

Paris law coefficient

C

Paris exponent

n

, A A C n

Type A constants (3.55×10 ⁻⁵ , 2.382) Type B constants (1.07×10 ⁻ ³, 1.071) Long-crack reference constants

, B B C n

, FL FL C n

MPa √ m

Stress intensity factor range

K 

t K

Stress concentration factor ( K t = 2.3)

—

296