Issue 78

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

Stress range: Δ  = max  (1 − R )

MPa MPa

 

max  

Maximum applied stress

/ min max   = 0.1)

Load ratio ( R =

— — — — — — — — — — —

R

First-kind Chebyshev polynomial Normalised crack-length variable ( ξ ∈ [ − 1, 1]) K th Chebyshev coefficient Modulation factor: μ ( ξ ) = 1 + Σ ₖ a ₖ T ₖ ( ξ ) Mean modulation factor Maximum modulation factor Minimum modulation factor Optimal polynomial order (AICc) Optimal order — type A (21) Optimal order — type B (21) Mean grain size in propagation direction Grain size perpendicular to R D (154 µm) Grain size parallel to R D (395 µm) K th grain boundary along crack path Grain boundary misorientation angle Grain boundary density -type A (6.5) Grain boundary density -type B (2.5) Corrected Akaike information criterion Coefficient of determination (log-space) Normalised root mean square error Akaike information criterion Rolling direction Transverse direction Through-thickness direction

  n T x

ξ

k a

μ ( ξ )

mean  max 

min  * N

* N

A

* B N

µm µm µm

d

TL d d  

L d d  

D R

— — — —

TL TC

GB ₖ

°



f 

boundaries/mm boundaries/mm

f 

AIC

— — — — — — — — — Hz % —

AICc

R²

NRMSE

RSS

Residual sum of squares

Number of experimental points Number of parameters ( k = N + 1)

M

k

T  - Spectral terms per grain crossed ( type-dependent: ≈ 5.65 for type A, ≈ 13.55 Chebyshev weight function w(x) = (1 − x²) ⁻ ½

T 

  w x

μ ᵢ

Experimental modulation factor Normalised variable at point i Loading frequency (10 Hz)

ξ ᵢ

f

297