Probabilistic Analysis for Comparing Fatigue Data Based on Johnson-Weibull Parameters

Probabilistic failure analysis is essential when analysis of stress-life (S-N) curves is inconclusive in determining the relative ranking of two or more materials. In 1964, L. Johnson published a methodology for establishing the confidence that two populations of data are different. Simplified algebraic equations for confidence numbers were derived based on the original work of L. Johnson. Using the ratios of mean life, the resultant values of confidence numbers deviated less than one percent from those of Johnson. It is possible to rank the fatigue lives of different materials with a reasonable degree of statistical certainty based on combined confidence numbers. These equations were applied to rotating beam fatigue tests that were conducted on three aluminum alloys at three stress levels each. These alloys were AL 2024, AL 6061, and AL 7075. The results were analyzed and compared using ASTM Standard E739-91 and the Johnson-Weibull analysis. The ASTM method did not statistically distinguish between AL 6010 and AL 7075. Based on the Johnson-Weibull analysis confidence numbers greater than 99 percent, AL 2024 was found to have the longest fatigue life, followed by AL 7075, and then AL 6061. The ASTM Standard and the Johnson-Weibull analysis result in the same stress-life exponent p for each of the three aluminum alloys at the median or L₅₀ lives.