Issue 78

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

Microstructure-explicit Chebyshev-enriched Paris law for short fatigue crack propagation in rolled AA2024-T351 Taoufik Nasri Applied Mechanics and Engineering Laboratory (LMAI), National Engineering School of Tunis (ENIT), University of Tunis El Manar, P.O. Box 37, Belvédère 1002, Tunis, Tunisia Higher Institute of Applied Sciences and Technology of Kasserine (ISSAT), University of Kairouan, P.O. Box 471, 1200 Kasserine, Tunisia taoufik.nasri@enit.utm.tn; https://orcid.org/0009-0004-1165-1033 Adel Hamdi Applied Mechanics and Engineering Laboratory (LMAI), National Engineering School of Tunis (ENIT), University of Tunis El Manar, P.O. Box 37, Belvédère 1002, Tunis, Tunisia Adel.hamdi@enit.utm.tn; https://orcid.org/0000-0001-6806-9694 Mohamed Anouar Borgi Advanced Materials and Nanotechnology Research Laboratory (LRMAN), Higher Institute of Applied Sciences and Technology of Kasserine (ISSAT), University of Kairouan, P.O. Box 471, 1200 Kasserine, Tunisia anoir.borgi@gmail.com; https://orcid.org/0000-0002-3723-5845

Citation: Nasri, T., Hamdi, A., Borgi, M. A., Microstructure-explicit Chebyshev-enriched Paris law for short fatigue crack propagation in rolled AA2024-T351, Fracture and Structural Integrity, 78 (2026) 275-297.

A BSTRACT . The classical Paris-Erdogan law describes long fatigue crack propagation but fails to capture the oscillatory behaviour of short cracks in microstructurally heterogeneous materials. This work proposes an enriched Paris law based on first-kind Chebyshev polynomials for short crack propagation in rolled AA2024-T351 aluminium alloy. A normalized crack length variable ξ = f(a/d) ∈ [ − 1, 1] links crack position to the average grain size d measured by EBSD. The resulting microstructural modulation factor μ ( ξ ) reproduces local fluctuations in crack growth rate at successive grain boundaries. The model is applied to two specimen orientations: type A (crack ⊥ rolling direction, dୄ = 154 µm) and type B (crack ∥ rolling direction, d ∥ = 395 µm). For type A, R² improves from 0.665 to 0.907 (N* = 21). For type B, R² improves from 0.147 to 0.835 (N* = 21). The modulation factor oscillations correlate closely with the grain boundaries identified by SEM and EBSD for type A, while for type B they suggest additional sub-surface crack microstructure interactions linked to the pronounced difference between in plane and through-thickness grain sizes for this orientation.

Received: 30.06.2026 Accepted: 31.08.2026 Published: 13.09.2026 Issue: 10.2026

Copyright: © 2026 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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