Issue 78

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

The experimental curve exhibits characteristic oscillations associated with successive crossings of the five identified grain boundaries. These oscillations - local acceleration, retardation near the boundary, and re-acceleration after crossing - are consistent with the crack–microstructure interaction mechanisms reported by Chen et al. [14,15]. The classical Paris law (dashed grey, n = 2.38, R² = 0.665) captures the mean propagation trend but fails to reproduce the local fluctuations. In contrast, the enriched model (red, N* = 21, R² = 0.907, NRMSE = 7.87%) accurately reproduces all five observed peaks, each aligned with a grain boundary position GB k . This correspondence indicates that the Chebyshev modulation captures a physically meaningful propagation mechanism rather than a numerical fitting artefact. The improvement in R² from 0.665 to 0.907 corresponds to a relative gain of approximately 36%. The maximum modulation value, μ max = 3.140, indicates that the local propagation rate may reach more than three times the classical Paris prediction during crossing of the highest-amplitude boundary (GB ₅ ). This result is consistent with the observations of Chen et al. [14], who reported twist misorientation angles up to 64.77° at R = 0.1, associated with pronounced crack-path perturbations near grain boundaries. Crack growth rate da/dN - Type B specimen Figs. 8 and 9 present the corresponding results for the type B specimen (  ⊥ R D , crack ∥ R D , d  = 395 µm, 0 a = 31.5 µm). The d a /dN curve was obtained numerically from a (N) data using the Savitzky-Golay smoothing and central finite difference procedure described in "Hierarchical identification strategy" above."

Figure 8: Crack length a vs. number of cycles N -type B (99 pts). Savitzky-Golay smoothing (green). Dashed line: grain boundary position GB ₁ .

Figure 9: Crack growth rate d a /dN vs. a - type B. Dashed grey: Paris law ( n = 1.07, R² = 0.147). Green: enriched model ( N* = 21, R² = 0.835, NRMSE = 8.5 %).

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