The fatigue failure mechanism of many cast metals and high-strength alloys involves initiation and propagation of a crack from an initial defect to a critical size where fatigue failure occurs. Crack growth rate and fatigue data can be combined to estimate the initial size of the defect that led to failure. This technique has been developed and used to provide statistical interpretations of fatigue data and to determine the probabilistic size distribution of critical defects and the specimen size dependence of the average critical defect size.

An expression for the fatigue curve that incorporates the initial defect size (a_i) is produced by integrating an analytical expression for the cyclic crack growth rate curve that includes a threshold stress intensity factor. For two different values of a_i, two fatigue curves are generated that can represent scatter in fatigue data from two specimens of the same size or average fatigue curves for specimens with two different sizes. This scatter or specimen size effect is best treated along lines of constant initial stress intensity factor that have a slope of −0.5 on the log stress-log life fatigue curve. The separation between fatigue curves along lines of constant initial stress intensity factor is independent of fatigue life. This treatment of fatigue data therefore predicts the commonly observed trend of increasing scatter in fatigue life with increasing lifetime and provides a treatment of scatter that is independent of fatigue life.

Probabilistic defect size analysis has been applied to data for a nickel-base superalloy to predict the size distribution of critical defects. An initial defect size is inferred for each data point, then a distribution of initial critical defect sizes is predicted for the alloy. The Weibull distribution is used to display the data in terms of 1/√a_i. The specimen size effect is treated where the square root of the average critical defect size increases with an increase in the effective area of the specimen. Thus, critical defect size distributions in components can be predicted that, in turn, allow material processing and inspection criteria to be based on required component life.