Abstract: A so-called “local probabilistic Paris relation method" was presented for measuring the random thresholds of long fatigue crack propagation. A check was made to the conventional method, in which the thresholds were measured statistically and directly by the test data. It was revealed that this method was not reasonable because the test data have seldom a unified level of crack growth rates. Differently,in the presented method the Paris-Erdogan equation was applied to model the local test data around the thresholds. Local probabilistic relations with both the survival probability and the confidence were established on a lognormal distribution of the stress density factors. And then, the probabilistic thresholds were derived from the probabilistic factors with a given critical level of growth rate. An analysis on the test data of LZ50 axle steel for the Chinese railway vehicles verifies that the present method is feasible and available.

Key words: local probabilistic Paris relation, long fatigue crack, random threshold, LZ50 steel