PSI - Issue 75

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

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Fig. 1. Typical crack growth curve (a) and mean stress effect on crack growth rate (b). Mean stress also has a strong influence on the crack growth rate as graphically shown in Fig. 1b. This is usually quantified for a particular cycle using the ratio, , of the minimum stress to the maximum stress in the cycle: = min max = min max (1) The most relevant laws proposed to describe the crack growth curve (or portions of it) are detailed below. 2.1. Paris Crack Growth Law Paris and Erdogan (1963) proposed a simple crack growth law to describe the crack propagation region (Region II) of the crack growth curve. The Paris law does not describe the threshold region (Region I), while the onset of fast fracture (Region III) is usually modelled as a discrete termination point corresponding to the plane strain or plane stress fracture toughness, and it does not consider mean stress effects. The Paris law is expressed as: = ∙ ∆ (2) where is the Paris coefficient and is the Paris exponent, that are obtained from tests and constitute material dependent constants. According to the hypothesis of crack closure, compressive stresses in the cycle do not contribute to crack propagation and therefore, can be ignored. As a consequence, when ≤0 , ∆ should be replaced with max (assuming max >0 as a necessary condition for crack propagation), leading to the following formulation: = { ∙ ∆ for > 0 ∙ max for ≤0 (3)