PSI - Issue 75

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

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• Delayed retardation: the crack has to propagate into the plastic zone created by the tensile overload of a certain amount before crack growth retardation takes place. • Overshoot: this is a crack growth rate increase occurring when the crack reaches the end of the plastic zone generated by the tensile overload. • Crack acceleration: following a significant compressive underload, a residual tensile stress region is generated around the crack tip causing the crack growth rate to increase. This is the opposite of crack retardation; however, this effect is significantly smaller than the crack retardation caused by a tensile overload and usually leads to a reduction of the effects of a previous crack retardation. At the basis of any retardation model is the definition of the size of the plastic zone ahead of the crack tip caused by a tensile overload. Irwin (1960) proposed to estimate the size of the plastic zone, , ahead of a crack tip as a function of the stress intensity factor, , and the yield stress, : = 1∙ ∙ ( ) 2 (23) where is a parameter representative of the stress/strain state (Bannantine et al. (1990), NASGRO3 (1999), Harter (2000), nCode (2003)). 3.1. Wheeler Model Wheeler (1972), based on empirical observations, proposed to modify the crack growth rate through a retardation coefficient, , defined as: =( + − ) (24) where is the size of the plastic zone generated by the current cycle, is the crack length at the current cycle, is the size of the plastic zone generated by the tensile overload, is the crack length when the overload occurred and is an empirically derived fitting factor. The retardation coefficient, , ranges between 0 for no crack growth (crack arrest) and 1 when the crack reaches the boundary of the plastic zone created by the tensile overload. The fitting factor can be evaluated only through tests and this is often rather difficult, making this model not very appealing. In addition, the Wheeler model contradicts the observed effect of delayed retardation, as it predicts maximum retardation immediately following an overload. Finally, it is worth highlighting that this model does not consider crack acceleration due to compressive underload. Willenborg Model The retardation model proposed by Willenborg et al. (1971) assumes that, following a tensile overload, a plastic zone characterised by a residual compressive stress forms around the crack tip and that the crack propagates only if the stress at the crack tip overcomes this residual stress. The maximum and minimum effective stress intensity factors at the crack tip are respectively defined as: max = max − (25) min = min − (26) 3.2.