Fatigue from defect under multiaxial loading: Defect Stress Gradient (DSG) approach using ellipsoidal Equivalent Inclusion Method

The fatigue design of metallic parts depends on the casting process. It requires a compromise between the fatigue resistance of the component and the allowable defect size due to the process. The research team has proposed, in previous work [Leopold G, Nadot Y. J ASTM Int 7:2010], to represent the effect of a defect in the fatigue criterion by means of a stress gradient term. This general methodology called Defect Stress Gradient (DSG) can consider explicitly the type, the morphology and the size of the defect due to the fact that a Finite Element (FE) submodel describes directly the defect at the mesoscopic scale. The DSG approach gives correct results for the defects range from 100 to 1000 μm but it is limited for application to full scale components by the use of FE submodel. The aim of this paper is to present an upgraded version of the DSG approach using the Equivalent Inclusion Method (EIM) due to Eshelby [Eshelby JD. Proc Royal Soc Lond Ser A. Math Phys Sci 241:1957; 376–96], [Eshelby JD. Elastic inclusions and inhomogeneities. In: Sneddon IN, Hill R (Eds.), Progress in solid mechanics 2. Amsterdam: North-Holland Publishing Company; 1961. p. 89–140] to compute stresses around the defect. Using this analytical approach, it is possible to compute the stresses around an ellipsoidal defect without FE simulations. Furthermore, the EIM for an ellipsoidal defect is efficient to address the question of the defect size related to loading direction in the case of a non-spherical defect. Although the framework of the original EIM is for internal defect, this paper shows that its application for a surface defect gives fair results in the context of the DSG approach. The new DSG proposal is evaluated on a low carbon steel, containing ellipsoidal defects with different orientations, under tension and torsion fatigue loadings.