Statistical Method to Evaluate the Scattering Fatigue Data Considering Both of Life and Strength Distributions

Abstract

In this paper, a statistical method to evaluate the fatigue data has been proposed by considering a two dimensional distribution on the life-strength plane (S-N plane). This evaluation method is based on the assumption that the data of S-N curve can be treated as the members of the set, which has a two dimensional normal distribution around the peak point in the coordinates of life and strength axis, and the variance of this two dimensional normal distribution can be given from the life and strength distributions of the original S-N data. A contour line of this two dimensional distribution is of elliptical shape, and represents the probability range.
Furthermore, the contour line having the same probability of S-N curve can be obtained from the envelope curve of the contour lines having the same probability of subgroups which have also the two dimensional normal distribution. The region enclosed with this curve expresses the probability of fracture occurrence. The fatigue limit is defined as the tangent line of this contour line, which is paralled to the life axis.
As an example, the S-N data obtained by Nishijima et al. were analyzed. It was confirmed that the contour lines of the same probability obtained by the above mentioned method were in good agreement to that of the sample S-N data.