Closed-form equations for the calculation of stress intensity factors for embedded cracks in round bars subjected to tensile load

Abstract

Fatigue crack propagation initiated from internal defects is a typical mechanism observed in high cycle fatigue (HCF) and very high cycle fatigue (VHCF) of cylindrical tensile specimens subjected to uniaxial cyclic loads. To study the fatigue crack propagation of these embedded cracks by means of a fracture mechanics approach, solutions for the Stress Intensity Factor (SIF) for different crack configurations are needed. In this paper, a set of closed-form equations for the calculation of the SIF of embedded cracks in round bars subjected to tensile load is presented. Two sets of solutions are provided, which allow for different levels of approach to be considered. The first solution provides the SIF for the vertex points of an internal elliptical crack as a function of three dimensionless parameters related to crack size, crack position and crack aspect ratio. The second solution is a simplification for eccentric circular cracks located at any position of the cross section. The methodology necessary for the application to the study of fatigue crack propagation is also presented, and a comparison with those obtained from experimental tests is included, which exhibits a very good capacity for prediction.