Static behaviour of a shaft with an elliptical crack

Cracks in mechanical components produce changes in their behaviour like increases of displacements or decreases of frequencies due to the flexibility increase. Some works related to the analysis of the behaviour of cracked shafts consider the front of the transversal fatigue cracks to be straight, but experience says that the front of these kind of cracks is approximately elliptical. Many expressions have been given for the flexibility of a cracked shaft with a straight front whereas, for elliptical cracks, only an approximate expression for the flexibility has been found in the literature. In the present work, flexibility expressions for cracked shafts having elliptical cracks are obtained, based on the polynomial fitting of the stress intensity factors, taking into account the size and shape of the elliptical cracks showing results according with reality. The static displacements in bending of the shaft for different support conditions have been calculated. The comparisons between these results and those obtained by FEM analysis and by experimental tests show that the closed-form expressions for the flexibility give us a very good approximation to the behaviour of the cracked shaft.