In the present study, the fatigue tests under tension-tension
variable amplitude loading (VAL) are carried out on 45 carbon
steel, which is similar to the AISI 1045 steel, to investigate the
probability distribution of fatigue life under VAL and investigate the validity of a new simulation model proposed in the paper for the fatigue test and the probability distribution of fatigue life under VAL. The fatigue life of notched 45 steel bar can be expressed as the function of equivalent stress amplitude. The fatigue resistant coefficient and the fatigue threshold in the fatigue life expression are found to follow the log normal distribution and to be material constants. Therefore this distribution of the fatigue resistant coefficient and threshold can be used to represent the distribution characteristics of fatigue properties of the material. Based on the above results and the assumption that the scatter of the fatigue life results from the difference of the fatigue specimens (different specimens can be distinguished by different combinations of the fatigue resistant coefficient and threshold), a new model and procedures are proposed to simulate the fatigue test and the probability distribution of fatigue life of notched 45 carbon steel under tension tension VAL and checked by test results. Statistical analyses show that both the simulated fatigue life and the test result of fatigue life of notched bar of 45 carbon steel under VAL follow the log normal distribution, and the two distributions agree well with each other, which indicate that the proposed simulation model is of practical value in the design and reliability assessment of mechanical elements when the fatigue test under VAL is very difficult, expensive and time consuming.