The perturbation series method based on the logarithm equation for fatigue crack growth prediction

This paper gives the perturbation series method for the fatigue crack growth prediction accounting for the error in initial crack length. The proposed method utilizes the logarithm form of the crack growth equation and the solution of it is expressed in the form of asymptotic series by introducing a small parameter. The initial crack length is considered as a sum of the nominal value and the perturbation which mainly originates from manufacturing and measurement errors. Based on the Taylor series expansion and perturbation series method, a series of perturbation equations to predict the fatigue crack growth history are obtained. Then these equations can be solved by the successive approximation approach and the a-N curve which describes the relationship between crack length and number of load cycles can be obtained. Two examples with respect to fatigue crack growth experiments are given to verify the accuracy and validation of the presented method. The results show that the perturbation series method is closer to the experimental data compared with the original solution of crack growth equation and it can provide a more accurate prediction for the fatigue crack growth process.