PSI - Issue 75

Andrew Halfpenny et al. / Procedia Structural Integrity 75 (2025) 234–244 Author name / Structural Integrity Procedia (2025)

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2.1. Crack growth model The crack growth rate, , is given by a monotonic series of logarithmic portions defined as: = ∙ ∆ (1) where and are the intercept and the slope of the ℎ portion of the crack growth curve, respectively, and ∆ is the crack-tip driving force defined by Walker (1970) as: ∆ = m1−ax ∙ ( max − min ) (2) where is Walker’s mean stress correction coefficient. While max and min are the maximum stress intensity factor during crack opening and the minimum stress intensity factor of the preceding reversal, respectively, defined as: max = max ∙ ∙ ∙ √ + ; min = min ∙ ∙ ∙ √ (3) where max and min are the maximum and minimum stress in the cycle, respectively, is the current crack length, is the Mode I (tensile stress perpendicular to the crack plane) stress intensity factor solution, is the retardation stress intensity factor due to the crack travelling through the plastic zone produced by previous cycles (defined later in Eq. 13) and is the small crack correction factor defined by Bogdanov (2014): = 1 + 12 √ ∗ (4) Noroozi et al. (2005), based on the idea that the crack tip does not close completely under compression loading, proposed to model the stress field as a circular notch of radius ∗ with notch factor , as defined in Eq. 5. This is in contrast to most crack growth models where, in the case of crack closure under compressive loading ( min <0 ), an effective minimum stress intensity factor min ′ =0 is used. m′ in ={ min if min ≥0 min if min <0 (5) Noroozi et al. (2005) originally proposed to use a notch factor =3 . However, about a decade later, Glinka (2015a) demonstrated experimentally that is material-dependent and usually varies between 2 and 3. Therefore, the effective minimum stress intensity factor can be defined as: m′ in ={ min if min ≥0 2 ∙ min ∙ ∙ √ ∗ if min <0 (6) It is worth noticing that by setting =0 the compression effects are ignored.