PSI - Issue 75

Andrew Halfpenny et al. / Procedia Structural Integrity 75 (2025) 219–233 Author name / Structural Integrity Procedia (2025)

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= ∙ (∆ )

(9) where the effective stress intensity range, ∆ = max − min , accounts for both threshold and onset of fast fracture, with max = max + and min =max( min , ) . Austen accounted for the onset of fast fracture through the expression (modification for static failure): = max 1 − max (10) where 1 is the plane strain fracture toughness. Threshold and short cracks, instead, were considered through a crack closure stress intensity factor, , expressed as: = max − max ∙ √ + 0 + ∆ ℎ 1− (11) where is the crack length and 0 = 1 ∙ ( ℎ ∆ 0 ) 2 is the smallest crack size that will propagate as defined by Kitagawa and Takahashi (1976), with ℎ the threshold stress intensity factor and ∆ 0 the unnotched fatigue strength. The threshold stress intensity range, ∆ ℎ , is defined as a bi-linear function of (or mean stress) as: ∆ ℎ ={ 1 if ≥ 0 −( 0 − 1 ) ∙ if < (12) where 0 is the threshold stress intensity at =0 , 1 is the threshold stress intensity at > and the stress ratio at the threshold knee. Austen also made the assumption, supported by test data, that compressive stresses do not contribute to damage. Finally, it is worth highlighting that the Austen law does not explicitly correct for mean stress effects, but Austen argued that it was irrelevant and attributed it to crack closure and retardation. NASGRO3 was proposed by NASA (1999) and represents the most comprehensive crack growth law. It considers mean stress effects, threshold values, the onset of fast fracture and crack closure. Another benefit is that NASA made available a large quantity of material data expressed in this format. The only real downside of the NASGRO3 law is the complex curve fitting of the experimental data. The NASGRO3 law is expressed as: = ∙ (1 − 1 − ∙ ∆ ) ∙ (1− ∆ ℎ ∆ ) (1− max ) (13) where , , and are empirical coefficients derived from test data. The crack tip opening function, , is given by: 2.5. NASGRO3 Crack Growth Law