Issue 78

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

A single major grain boundary (GB ₁ ) is observed along the type B propagation path, consistent with the limited number of grains crossed ( N g-B = 1.55) resulting from the large grain size in the ∥ R D direction ( d  = 395 µm). The enriched model (green, N* = 21, R² = 0.835, NRMSE = 8.5 %) reproduces the main oscillatory features, including the pronounced peak centred on GB ₁ . The classical Paris law yields R² = 0.147 for type B, significantly lower than for type A ( R² = 0.665). This low baseline value must, however, be interpreted cautiously, since it partly reflects the reduced quality of da/dN data obtained by numerical differentiation of a (N). The enriched model raises R² to 0.835, a substantial and physically meaningful improvement; as discussed above, this additional oscillatory content plausibly reflects sub-surface crack-microstructure interactions given the pronounced difference between in-plane and through-thickness grain sizes for this orientation ( d L = 395 µm vs. d TC = 133 µm). Crack length evolution a(N) - comparison of both orientations The oscillatory character of crack propagation remains more clearly interpretable for type A, where the five peaks in μ ( ξ ) map directly onto the five grain boundaries identified by EBSD and SEM. Both orientations ultimately require the same statistically optimal order ( N = 21), but for type B this order is not independently confirmed by the physical peak-counting criterion, reflecting the more limited microstructural sampling available along this propagation path ( N g-B = 1.55 vs. N g-A = 3.72) rather than a genuinely richer set of physical grain-boundary interactions. da/dN vs. Δ K diagram - complete comparison Fig. 10 shows the d a /dN– Δ K diagram for all specimens in log-log representation, placing the results within the framework of fatigue fracture mechanics.

Figure 10: da /dN vs. Δ K - AA2024-T351. Type A (red, n = 2.38), type B (green, n = 1.07) and long crack (purple, n = 2.53, R² = 0.984). Three main observations can be drawn. First, short-crack data (types A and B) occupy the range Δ K ∈ [4.6; 22] MPa √ m, whereas the long-crack regime extends over Δ K ∈ [10; 35] MPa √ m. Short-crack propagation behaviour therefore cannot be extrapolated directly from long-crack Paris-law descriptions, consistent with the observations of Borges et al. [18]. For comparison, the standardised NASGRO baseline for AA2024-T351 plate (LT orientation, R = 0.1) from the FAA fatigue crack growth database [32] gives C = 7.24 × 10 ⁻⁵ µm/cycle·(MPa √ m) -n and n = 3.60 over Δ K ∈ [3.3; 44] MPa √ m. Both type A and type B short-crack data remain significantly below this long-crack reference at equivalent Δ K levels. At Δ K = 10 MPa √ m and R = 0.1, the Walker equation from the FAA database predicts d a /dN = 0.087 µm/cycle for long cracks, whereas the average measured rate for type A is approximately 0.008 µm/cycle, i.e. nearly one order of magnitude lower. This pronounced retardation is characteristic of microstructurally short cracks in regime II, where grain-boundary barriers

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