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.
Highlights
Fatigue is a random phenomenon [1,2] that causes a mechanical component to fail [3] at a stress level lower than the material strength limit (Se ) [4]
Fatigue is random and the mechanical component is subject to variable amplitude and cyclic load [σ1, σ2 ], based on single equivalent stress σeq value, its failure analysis can be performed by applying a failure theory such as the Goodman, Gerber, Soderberg, and ASME (American Society of Mechanical Engineers) elliptical theories [5]
The proposed Weibull analysis is performed by using the σ1 and σ2 principal stress values that are acting on the flat spring device; in this study they are determined by performing a finite element analysis (FEA) simulation
Summary
Fatigue is a random phenomenon [1,2] that causes a mechanical component to fail [3] at a stress level lower than the material strength limit (Se ) [4]. Because rather than using the random behavior the analysis uses only a stress value, its application does not enable either the reliability of the component or its expected cycles to failure (Ni ) values to be found. Because the reliability of the component depends on both the applied stress and the inherent strength [12,13] in the product to overcome it, the proposed method to determine the random behavior of N can be based on the Weibull distribution used to model the stress, and on the Weibull distribution used to model the Ni values. Parameters and on the cycles to failure N value, where N is obtained from the S-N curve by inserting the σeq that corresponds to the applied failure theory in Basquin’s equation This makes the proposed method highly efficient in determining the random behavior of N and the corresponding reliability indices.
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