Fatigue-Life Prediction of Mechanical Element by Using the Weibull Distribution

Applying Goodman, Gerber, Soderberg and Elliptical failure theories does not make it possible to determine the span of failure times (cycles to failure-N-i) of a mechanical element, and so in this paper a fatigue-life/Weibull method to predict the span of the N-i values is formulated. The input's method are: (1) the equivalent stress (sigma(eq)) value given by the used failure theory; (2) the expected N-eq value determined by the Basquin equation; and (3) the Weibull shape beta and scale eta parameters that are fitted directly from the applied principal stress sigma(1) and sigma(2) values. The efficiency of the proposed method is based on the following facts: (1) the beta and eta parameters completely reproduce the applied sigma(1) and sigma(2) values. (2) The method allows us to determine the reliability index R(t), that corresponds to any applied sigma(1i) value or observed N-i value. (3) The method can be applied to any mechanical element's analysis where the corresponding sigma(1) and sigma(2), sigma(eq) and N-eq values are known. In the performed application, the sigma(1) and sigma(2) values were determined by finite element analysis (FEA) and from the static stress analysis. Results of both approaches are compared. The steps to determine the expected N-i values by using the Weibull distribution are given.