Stress Intensity Factor equations for incipient transverse external annular eccentric cracks contained in a shaft under bending

One of the most common failures in rotating machines is the apparition and propagation of fatigue cracks in one of its main elements: the shafts. These cracks can cause catastrophic failures and lead to costly maintenance or repair processes. Most of the studies in relation to cracks contained in shafts have focused on straight or elliptical transverse cracks. However, although it is less common, the shaft breaks also occur with cracks whose fronts are approximately circumferential, that are more difficult to analyze. These cracks are transverse with circular shape that extend over a complete circumference and that have a certain eccentricity. This work presents the equations that provide the value of the Stress Intensity Factor (SIF) of an incipient crack with circumferential shape contained in a shaft subjected to bending, along the front, as a function of the characteristics of the crack, size and eccentricity. For this, an exhaustive numerical study has been carried out, using the Finite Element Method (FEM), to determine the SIF value along the circumferential front for different sizes and eccentricities of the annular crack.