One of the central unsolved problems of engineering design is prediction of the probability distribution of fatigue life of structural members and machine components. Fatigue data scatter is a manifestation of the probabilistic nature of fatigue failure. A relationship is known to exist between the distributions of the number of cycles-to-failure and the applied stress through the probabilistic stress-life (S-N) curve.

A method was developed for predicting the scatter of fatigue life for structures and components subjected to constant, complex or narrow band random amplitude cyclic loading. The method provides a unique way of predicting the statistical properties of fatigue life using a Monte Carlo simulation technique. In this method the randomness of material properties as well as that of the applied loading are incorporated into a stochastic model in conjunction with appropriate fatigue failure criterion to determine the fatigue life distribution.

A modified probabilistic S-N diagram is used to reflect the variability of the endurance limit and the fatigue strength coefficient. Any damage criterion can be used with the simulated S-N diagrams. When the linear damage law is used, the analysis yields a damage criterion analogous to Miner's rule but with a random cycle ratio. The proposed method was used to analytically predict the characteristics of the cycle ratio distribution. Good agreement with available experimental results is obtained. This result is of particular importance since no assumption regarding the fatigue failure mechanism is made. A phenomenological treatment of damage accumulation below the endurance limit is presented.

The validity of the method is demonstrated for different load histories and materials. Fatigue life data for axial and bending test specimens of SAE 1008 steel sheets subjected to constant amplitude, block and narrow band random loading were generated experimentally. The distributions of the endurance limit, ultimate strength and fatigue strength coefficient were obtained. The endurance life and cyclic stress-strain curve were also determined experimentally. The suggested method has proved successful in predicting fatigue life distributions for each case.

The effects of the randomness of loads, material properties, and the shape of load probability density function were investigated. This study indicates that the large scatter exhibited in fatigue test data is mostly explained by the scatter in the material properties. It was found that the randomness of the fatigue strength coefficient does not significantly affect the scatter of predicted life or its estimated mean value. On the other hand, the variance of the endurance limit has a pronounced effect on the variability of fatigue life. Its effect on the estimated mean is also considerable.

It was shown that the scatter in fatigue life under random loading is less than that under sinusoidal constant amplitude loading. The mean value of fatigue life decreases slightly as a result of increasing the variance of the applied load. Changes in the shape of the load probability density function affect the scatter of life more than its mean value. The predicted fatigue life distribution under random loading depends upon the accuracy of the load probability density function.

The method has the capability of simulating complex load histories of the kind that occur in service. It can also be extended to include possible correlation between peaks of the applied load.

The suggested method is believed to be an efficient tool that can be used at the design stage;​ it is ideal for parametric studies and provides an attractive alternative to the costly and time consuming prototype fatigue tests. Minimum experimental data is needed for the analysis.

It is concluded that implementation of this new technique will substantially improve the ability of the engineer to design reliable fatigue resistant components efficiently.