Analytical and numerical investigation of the stiffness matrix for edge-cracked circular shafts

This paper examines two engineering methods of evaluating the stress intensity factors for cracked beams and bars subjected to a combined loading and proposes innovative formulations, as far as the circular cross section is concerned. Based on the definition of the stress intensity factors, the compliance matrix is determined as the inverse of the stiffness matrix, modelling the cracked section of a beam through a line-spring approximation with interactive forces computed within fracture mechanics. A comparative evaluation of numerical predictions based on the proposed methods is also performed with methods available from the literature. Results for free vibration analyses of beams with transverse non-propagating open cracks are presented and compared in order to estimate the accuracy and efficiency of the proposed methods, where a good agreement is generally found. More specifically, two different coupling effects are herein analysed for circular beams subjected to a combined bending, axial and shear loading, first, and a combined bending, shear and torsion loading, subsequently.