The statistical analysis of fatigue data.

The overall objective of this study is to develop methods for providing a statistical summary of material fatigue stress-life (S-N) data for engineering design purposes. Specific goals are: (1) Development of an analytical model for characterizing fatigue strength. This model would include: (a) a description of the trend of the data (e.g., the median curve through the data), (b) a description of the scatter of the data (e.g., the standard deviation of N as a function of S), and (c) the statistical distribution of N given S or S given N. (2) Development of an algorithm for constructing a design curve from the data. The curve should be on the safe side of the data and should reflect uncertainties in the physical process as well as statistical uncertainty associated with small sample sizes. (3) Development of a statistical model that can be applied in a structural reliability analysis in which all design factors are treated as random variables. Significant achievements are: (1) Demonstration, using representative fatigue data sets, that the bilinear model seems to provide a consistently adequate description of the trend of fatigue data. (2) Demonstration, using representative fatigue data sets, that the pure X error source model seems to provide a consistently adequate description of the uncertainties observed in heteroscedastic fatigue data. The pure X error source model is based on recognition of the uncertainties in local fatigue stress. (3) Development of a procedure for constructing a design curve using the tolerance limit concept developed by D. B. Owen. A more practical simplified or approximate Owen curve was shown to have a minimum loss of confidence level, relative to exact Owen theory, under fairly general conditions. (4) Recommendations for methods of developing a statistical model for reliability analysis. A comprehensive study of this issue was not pursued.