Prediction of fatigue life and its probability distribution of notched friction welded joints under variable-amplitude loading

Abstract

In the present study, fatigue tests under constant-amplitude loading (CAL) and variable-amplitude loading (VAL) are carried out on the notched friction welded (FW) joints of 45 (0.45%C) carbon steel, which is similar to the AISI 1045 steel. Statistical and regression analysis on the fatigue test results under CAL shows that the fatigue life of 45 steel notched FW joints with small size can be expressed as the function of the equivalent stress amplitude, and the values of the fatigue resistant coefficient and threshold are thus obtained. From the probability distribution of fatigue resistant coefficient and threshold, the expressions of the fatigue life with given survivability, i.e., the so-called P–S–N curves of 45 steel notched FW joints are obtained, which can cover the whole life region, in particular, the long life range and are used to determine the probability distribution of fatigue strength of 45 steel notched FW joints. Furthermore, the so-obtained expressions for P–S–N curves and Miner's rule are directly applied to predict the fatigue life and its probability distribution of 45 steel notched FW joints considering that 45 steel is of non-continuous strain-hardening characteristic and thus nil overloading effect. The prediction procedures for fatigue life with given survivability of 45 steel notched FW joints under VAL by using Miner's rule and the expressions of P–S–N curves are outlined. The fatigue life and the critical cumulative fatigue damage of 45 steel notched FW joints under VAL predicted by using the above procedures follow the log-normal distribution, and checked by test results under one type of programmed block loading and the statistical analysis. The procedures mentioned above may be applicable in predicting the probability distribution of fatigue life of the notched elements of metals with non-continuous strain-hardening characteristic, including the notched friction welded joints under VAL.