Probabilistic measurements of the fatigue limit data from a small sampling up-and-down test method

Fatigue limit in engineering is in general understood as the fatigue strength at a given expected fatigue life. A given life is a primary condition for defining probabilistic fatigue limits. Available approaches, i.e. conventional approach (CA), Dixon-Mood approach (DMA), and Zhang-Kececioglu approach (ZKA), are reviewed and discussed by their effects on test data with respect to their supporting theoretical frameworks. They are verified to being not strictly match the primary condition. A new approach, maximum likelihood approach (MLA), is then developed for determining probabilistic measurements of the fatigue limit data from a small sampling up-and-down test method (SSUDM). SSUDM holds a self-closed condition for ending the up-and-down fatigue tests. This closed condition constructs a paired theory, which can successfully identify the fatigue limit range. MLA uses a maximum likelihood estimation to measure the fatigue limits. The data are from the deduced stress amplitudes with a given fatigue life on the local S–N curves of paired failure and survival specimens. Comparison analysis of effects on the test data of Chinese railway LZ50 axle steel and grade B bogie cast steel indicates that ZKA may be not suitable to measure the probabilistic limits because of its abnormal scattered measurements. MLA, CA, and DMA have closer estimations with little relative errors and MLA matches strictly the primary condition.