Research Article
Oct 1963

Parameters in the Distribution of Fatigue Life

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Publication: Journal of the Engineering Mechanics Division
Volume 89, Issue 5

Abstract

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.

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Journal of the Engineering Mechanics Division
Volume 89Issue 5October 1963
Pages: 45 - 64

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Published in print: Oct 1963
Published online: Feb 3, 2021

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E.J. Gumbel
Industrial and Mgr. Engrg., Dept., Columbia Univ., New York, N. Y.

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