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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.

An equivalent constant amplitude fatigue loading (Miner's stress) is developed for stationary random amplitude loadings. The effects of rainflow cycle counting and fatigue crack closure are included. A method for determining the opening stress in a random loading is also proposed. This research takes a fatigue damage factor approach. The damage factor is defined as the ratio of the wide band rainflow fatigue damage to the equivalent narrow band fatigue damage. The mathematical form of the damage factor equations is derived from theoretical derivations using the analytically tractable local range cycle counting method. Simulations of stationary Gaussian random processes are used to empirically derive the values of certain parameters dependent on the spectral shape for the rainflow cycle counting equations. There are five tasks in this research. (1) A simulation program for generating a Gaussian process has been written and is used to generate random loading histories for this study. (2) A previously proposed rainflow damage factor has been verified and refined with these simulations, without considering crack closure. (3) Using a sinusoidal approximation, the joint probability density functions between peaks, valleys and rises counted by the local range method are derived. (4) The resulting joint probability distributions are used to determine the theoretical damage with crack closure; simulations are again used to calibrate the parameters for rainflow stress cycles. (5) A procedure for finding an equivalent constant fatigue crack opening stress for stationary random loadings is described. An example application of the procedures and equations is given.

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