On the statistical interpretation of fatigue tests

Abstract
Progressive damage under repeated load cycles which leads to spreading, visible fatigue cracks and finally to fracture in both metals and non-metals is a highly structure-sensitive process, the large-scale manifestations of which depend primarily on happenings on the submicroscopic and microscopic scale. This produces a considerable scatter in the results of fatigue tests performed under assumedly identical conditions. Thus, if n specimens are subjected to a sequence of stress cycles of the same amplitude S, they break at varying numbers of cycles; these numbers N taken in decreasing order, and the frequencies of survival at each number, determine, for each stress level S, a characteristic cumulative frequency distribution l(N)$_{S}$, the 'survivorship function'. By formulating the phenomenon of consecutive fatigue fractures of the weakest within a finite (large) set of specimens as a problem of extreme values, the statistical theory of extreme values can be applied to the interpretation of the observed frequencies of survival at any stress amplitude. If, in first approximation, it is assumed that the probability of survival reaches unity only for N = 0 (no 'sensitivity threshold' in N), the survivorship functions are reproduced by the 'third asymptotic probability function of smallest values', which is represented on extremal probability paper by a straight-line relation between a reduced statistical variate y and log$_{10}$ N. Methods are presented for the computation of the two parameters of the survivorship function l(N)$_{S}$ from a set of fatigue data. The fit between the computed theoretical straight lines and the test results is satisfactory for fatigue tests of copper, aluminium and a high-strength structural aluminium alloy.

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