A closed expression for the stress intensity factor of concave fatigue cracks in rotating shafts
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A new analytical model is developed that allows us to obtain the Stress Intensity Factor (SIF) in a point on a concave shaped crack contained in a rotating shaft as a function of the characteristics of the crack (depth and aspect), the point position on the crack front, and the rotation angle. The model can be used for all kinds of linear elastic materials. The Finite Element Method (FEM) has been used to make a tridimensional quasi-static model of a shaft that contains a concave shaped crack in its central section, subjected to rotary bending. Different rotation angles are taken into account in order to simulate the rotation of the shaft. The SIF is determined in every position of the front of the concave crack, for each crack geometry and for each rotation angle. Then an analytical model is developed using all the results of SIF obtained with the numerical model, and is verified comparing its results with solutions found in the literature. The proposed model may be very useful to study the dynamic behavior of shafts with concave shaped cracks, and can be employed to analyze the propagation of these types of cracks.