Microstructure-explicit Chebyshev-enriched Paris law for short fatigue crack propagation in rolled AA2024-T351

https://doi.org/10.3221/IGF-ESIS.78.17

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, d_⊥ = 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.