Issue 78

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

B specimens were fatigue-monitored. One specimen per orientation (Type A and Type B) was retained for the detailed identification of the enriched model presented in this study, with data from the additional specimens used as a complementary consistency check. The central hole was produced by conventional drilling, its diameter (10 mm) chosen to reproduce a stress concentration representative of a typical bolted or riveted joint in aeronautical structures. Fatigue tests were conducted under sinusoidal tension–tension loading ( R = 0.1, f = 10 Hz, ambient temperature). Test parameters by specimen type are summarized in Tab. 4. Crack length   a N was measured by optical microscopy on polished specimen surfaces. The nominal stress intensity factor range, used throughout the identification procedure described in "Parameter Identification" below, is given by Eqn. (1):

 



a  

1.12 t K K

(1)

௠௔௫ (MPa) ௧ 300 ≈ 1.1

d (µm) ଴ (µm) — —

d /dN measurement Direct Derived from ሺ ሻ Direct

Specimen

Smooth (dogbone) Type A ( ∥ ஽ ) Type B ( ⊥ ஽ )

200 200

2.3 2.3

154 395

35.4 31.5

Table 4: Test parameters by specimen type .

where  1 max R      and a is the half-crack length measured from the hole centre. The factor 1.12 corresponds to the classical Bowie (1956) solution [30] for a crack emanating from the edge of a circular hole in an infinite plate, remaining very close to the full numerical solution in the short-crack regime, consistent with the boundary correction framework of Tada et al. [31]. This expression is valid for a ≪ R hole ( / max hole a R ≈ 0.12 for type A and ≈ 0.16 for type B), for which the hole-edge stress concentration t K dominates; a transition to a full boundary-corrected geometry solution ( / ) Y a W was therefore not required within the range covered by the present tests. The specimen thickness t = 5 mm satisfies plane-stress conditions (plane strain would require B > 2.5(K ₁ c/YS)² ≈ 37 mm for AA2024-T351 [32]). The apparent fracture toughness at this thickness is K c ≈ 116 MPa √ m [32], which remains well above the maximum Δ K max ≈ 22 MPa √ m reached in the tests. The present Δ K range therefore lies entirely within the Paris regime II, with no influence of fracture toughness on the crack driving force. Complementary microstructural observations Crack initiation was observed at the hole edge, perpendicular to the loading direction, for both specimen types. The number of initiation cycles is similar for types A and B, indicating that the difference in propagation behaviour is of microstructural origin. Type B exhibits a higher average propagation rate than type A over the tested cycle range (mean rate ≈ 1.16 × 10 ⁻ ² µm/cycle vs. ≈ 0.82 × 10 ⁻ ² µm/cycle, ratio ≈ 1.4). In the ⊥ R D direction (type A), the crack crosses the ⟨ 111 ⟩∥ TL texture and frequently encounters high-angle interfaces ( θ > 30°), generating large local oscillations in d a /dN . In the ∥ R D direction (type B), fewer boundaries are crossed ( g B N  =1.55 vs g A N  = 3.72), but the overall propagation rate is higher. This is consistent with the experimental   a N curves and with Chen et al. [14]. his section presents the formulation of the enriched model proposed to describe short fatigue crack propagation in AA2024-T351. The approach is based on three elements: (i) an orthogonal basis adapted to the representation of propagation oscillations, (ii) a normalised variable linking crack length to grain size, and (iii) a multiplicative term enriching the classical Paris law. Choice of the Chebyshev basis First-kind Chebyshev polynomials T ₙ (x) are defined on [ − 1, 1] as follows: T  E NRICHED MODEL FORMULATION

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