This is performed to determine the critical size of pit in terms of pit depth that would transition to a crack (not necessarily a Mode I crack) for different stresses. The stress values that could be used in the calculation are: (a) the estimated maximum applied stress that the component would be subjected to and (b) the ultimate stress for the material in question. From Hoeppner's pitting corrosion fatigue model, the following equation can be used to determine the critical pit depth (Equation 2):
where:
K_{sf} = Stress intensity factor for a surface discontinuity (MPa m^{0.5})
s = Applied stress (MPa)
a = Size of the pit in terms of pit depth (mm or m)
Q = f[(a/2c, tensile yield stress (s_{ty}))] (dimensionless)
In this calculation, it can be assumed that K_{sf} is equal to "short" crack stress intensity threshold (DK_{scth}) for the material. It is recommended value of DK_{scth} be used because the pit-to-crack transition first would result in a non-Mode I crack, that is in the "short" crack region. It is important to note that there is no standard value for the DK_{scth} in the "short" crack region for a particular material as there is no standard test method to measure the fatigue crack growth rates in this regime. Therefore, this value can either be determined from conducting "short" fatigue crack growth experiments or determined from literature for a specific material.
The shape parameter, Q, for a surface crack can be assumed depending on the pit morphology. For different stress levels, ranging from the estimated applied stress for the component to the ultimate stress of the material, the critical pit depth 'a' that would enable the transition of the pit to a "short" crack can be determined. The resultant value of 'a' can be compared with the measured depth of the pit from the failure analysis of a similar component, if there is any. Moreover, the calculated value of 'a' can be correlated to the experimentally generated pit growth rate curve to estimate the phase 1 life (L_{1}). Then, equation (1) can be used to determine the critical crack size for instability (a_{c}) given the value of K_{IC} for the material as well as the maximum applied stress for the component.
Review of Pitting Corrosion Fatigue Models, D.W. Hoeppner, V. Chandrasekaran, and A.M.H. Taylor, University of Utah and FASIDE International Inc.