Stress distributions in notched structural components under pure bending and combined traction and bending

The availability of analytical expressions is often desirable in the analyses of fatigue crack initiation and early propagation. This paper presents approximate analytical expressions capable of describing the overall distribution of the maximum principal stress in finite size notched bodies subjected to bending and combined traction and bending. The formulae reported here represent an extension of an analytical complex function approach already presented in the literature, suitable for describing highly stressed zones surrounding the notch tip. Such an extension, derived by simply imposing global equilibrium conditions, enables us to increase the range of validity of the principal stress expression from the notch tip to the entire ligament width. The accuracy of the proposed expressions is tested against data from finite element analyses carried out on plates and bars weakened by semicircular, V- and U-shaped notches. The agreement seems to be good.