| Summary: | Applying Goodman, Gerber, Soderberg and Elliptical failure theories does not make it possible to determine the span of failure times (cycles to failure-<inline-formula><math display="inline"><semantics><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula>) of a mechanical element, and so in this paper a fatigue-life/Weibull method to predict the span of the <inline-formula><math display="inline"><semantics><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula> values is formulated. The input’s method are: (1) the equivalent stress (<inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub></mrow></semantics></math></inline-formula>) value given by the used failure theory; (2) the expected <inline-formula><math display="inline"><semantics><mrow><msub><mi>N</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub></mrow></semantics></math></inline-formula> value determined by the Basquin equation; and (3) the Weibull shape <i>β</i> and scale <i>η</i> parameters that are fitted directly from the applied principal stress <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> values. The efficiency of the proposed method is based on the following facts: (1) the <i>β</i> and <i>η</i> parameters completely reproduce the applied <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> values. (2) The method allows us to determine the reliability index <i>R(t)</i>, that corresponds to any applied <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mn>1</mn><mi>i</mi></mrow></msub></mrow></semantics></math></inline-formula> value or observed <inline-formula><math display="inline"><semantics><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula> value. (3) The method can be applied to any mechanical element’s analysis where the corresponding <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>N</mi><mrow><mi>e</mi><mi>q</mi></mrow></msub></mrow></semantics></math></inline-formula> values are known. In the performed application, the <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>σ</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> 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 <inline-formula><math display="inline"><semantics><mrow><msub><mi>N</mi><mi>i</mi></msub></mrow></semantics></math></inline-formula> values by using the Weibull distribution are given.
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