Gradient elasticity: a transformative stress analysis tool to design notched components against uniaxial/multiaxial high‐cycle fatigue

This paper investigates the accuracy of gradient elasticity in estimating high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial fatigue loading. A novel design methodology is formulated by combining Ru and Aifantis’ gradient elasticity with the Theory of Critical Distances and the Modified Wohler Curve Method. The keyfeature of this innovative design methodology is that, via the Theory of Critical Distances, gradient elasticity’s length scale parameter is directly estimated from conventional material fatigue properties (i.e., the plain fatigue limit and the threshold value of the stress intensity factor). From a stress analysis point of view, the proposed approach directly post-processes the gradient-enriched stress states determined, at the hot-spots, on the surface of the component under investigation (and independently of the sharpness of the stress concentrator being assessed). The accuracy and reliability of this design method was checked by using a large number of experimental results taken from the literature and generated by testing notched metallic samples under uniaxial as well as under multiaxial fatigue loading. This comprehensive validation exercise demonstrates that the systematic usage of this transformative design approach leads to the same level of accuracy as the one which is obtained by applying the classic Theory of Critical Distances. This result is certainly remarkable since the proposed approach is not only very efficient from a computational point of view, but it also allows high-cycle fatigue damage to be assessed by directly postprocessing gradient-enriched stress states determined on the surface of the component being assessed.