On Improving the Celebrated Paris’ Power Law for Fatigue, by Using Moving Least Squares

In this study, we propose to approximate the a− n relation as well as the da/dn−∆K relation, in fatigue crack propagation, by using the Moving Least Squares (MLS) method. This simple approach can avoid the internal inconsistencies caused by the celebrated Paris’ power law approximation of the da/dn−∆K relation, as well as the error caused by a simple numerical differentiation of the noisy data for a−n measurements in standard fatigue tests. Efficient, accurate and automatic simulations of fatigue crack propagation can, in general, be realized by using the currently developed MLS law as the “fatigue engine” [da/dn versus ∆K], and using a high-performance “fracture engine” [computing the K-factors] such as the Finite Element Alternating Method. In the present paper, the “fatigue engine” based on the present MLS law, and the “fracture engine” based on the SafeFlaw computer program developed earlier by the authors, in conjunction with the COTS software ANSYS, were used for predicting the total life of arbitrarily cracked structures. By comparing the numerical simulations with experimental tests, it is demonstrated that the current approach can give excellent predictions of the total fatigue life of a cracked structure, while the celebrated Paris’ Power Law may miscalculate the total fatigue life by a very large amount.