Parameters in the Distribution of Fatigue Life

by E. J. Gumbel,

Serial Information: Journal of the Engineering Mechanics Division, 1963, Vol. 89, Issue 5, Pg. 45-64

Document Type: Journal Paper


In the third asymptotic distribution of smallest values, or Weibull distribution, three parameters exist. One is a location parameter in which the probability of surviving θ number of cycles is fixed at 1/e. A second is a shape parameter, α, and the third parameter, uo, is the lower limit of the distribution. It is this lower limit which is of great interest in fatigue studies for the design of structures, since the existence of a positive uo enables the design of a structure in which, if the number of cycles is kept below this critical value for a given stress, no fatigue failure will ever occur. The three parameters may or may not be a function of stress, and appropriate changes in notation are made when applicable. The interdependence of the three parameters is also studied. Reduction to two parameters by the introduction of a reduced life and a reduced minimum life is carried through. By introducing a standardization of the number of cycles N, the number of parameters is lessened to one. A table of this standardized life then facilitates the estimation of the three parameters by the method of moments procedure.

Subject Headings: Parameters (statistics) | Lifeline systems | Fatigue life | Fatigue (material) | Structural design | Probability | Stress analysis | Failure analysis

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