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

Abstract

Applying Goodman, Gerber, Soderberg and Elliptical failure theories does not make it possible to determine the span of failure times (cycles to failure-Ni) of a mechanical element, and so in this paper a fatigue-life/Weibull method to predict the span of the Ni values is formulated. The input’s method are: (1) the equivalent stress (σeq) value given by the used failure theory; (2) the expected Neq value determined by the Basquin equation; and (3) the Weibull shape β and scale η parameters that are fitted directly from the applied principal stress σ1 and σ2 values. The efficiency of the proposed method is based on the following facts: (1) the β and η parameters completely reproduce the applied σ1 and σ2 values. (2) The method allows us to determine the reliability index R(t), that corresponds to any applied σ1i value or observed Ni value. (3) The method can be applied to any mechanical element’s analysis where the corresponding σ1 and σ2, σeq and Neq values are known. In the performed application, the σ1 and σ2 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 Ni values by using the Weibull distribution are given.

Keywords

• static and fatigue reliability
• mechanical design
• Weibull distribution
• finite element analysis
• principal stresses