Reliability of Metal Components in Fatigue: A Simple Algorithm for the Exact Solution

An efficient and accurate method for computing the fatigue‐life distribution of metal structures is presented. The problem is governed by the basic equations of the Coffin‐Manson‐Neuber local‐strain fatigue theory for notched components. The coefficients of fatigue strength and fatigue ductility, the fatigue notch factor as well as the nominal‐stress amplitude may be random variables with an arbitrary joint distribution. In order to arrive at a direct solution for the fatigue‐life distribution, hence an assessment of the reliability of a component, a collocation method has been developed which gives the total‐strain amplitude as an explicit function of the stress amplitude and the fatigue notch factor. This explicit equation has very close conformity to the corresponding, true, implicit equation. The fatigue‐life distribution is finally expressed in a multiple‐integral closed form. A simple algorithm termed the “complete‐probability fast integration” (CPFI) is developed which gives the exact solution, to any desired accuracy, for the entire ranges of fatigue‐life and reliability. CPFI is superior when compared to the results and procedures of the approximate methods currently employed.