On the prediction of P–S–N curves of 45 steel notched elements and probability distribution of fatigue life under variable amplitude loading from tensile properties

In the present study, attempts are made to use the fatigue formula developed before for predicting the expressions of fatigue life curves with given survivability (Sv), the so-called P–S–N curves of 45 steel notched elements from tensile properties. Then, the probability distribution of fatigue life under variable amplitude loading (VAL) can be predicted by using the predicted P–S–N curves and the linear cumulative damage rule and compared with test results. It is shown that the predicted P–S–N curves of 45 steel notched elements are in good agreement with test results but a little conservative. Both the predicted fatigue lives and the test results of 45 steel notched elements under VAL follow the log–normal distribution. The predicted fatigue life of 45 steel notched elements with 50% survivability agrees well with the test results. However, the standard deviation of the predicted fatigue life of 45 steel notched elements under VAL is a little higher than that of test results. The reason behind it should be further investigated. Based on the results mentioned above, it confirms again that the fatigue formula used in this study is a good one, which provides the possibility and the basis to predict the P–S–N curves and the probability distribution of fatigue life of 45 steel notched elements under VAL from tensile properties. Besides, the fatigue formula mentioned above could cover the whole range of fatigue life from 1/4 cycle to infinite, showing a horizontal asymptote in really geometrical and physical significance, which is expressed by the fatigue threshold. Finally, the measures are proposed to reduce the dispersion of fatigue test results and improve the prediction accuracy of the fatigue life under both constant and variable amplitude loading.