Strength of Stress Singularities at Crack Tips for Flexural and Torsional Problems

Abstract

Continuing a series of studies on the fracture analysis of elastic bodies, the present paper provides a complex variable method for evaluating the strength of stress singularities at crack tips encountered in the flexure and torsion of cylindrical bars. As a result of the complex flexure functions being sectionally holomorphic for crack problems, the singular character of the shearing stresses is found to be of the type r−1/2, where r is radial distance from the crack point. Crack-tip stress-intensity-factor solutions are given for problems involving both imbedded and surface cracks in bars. The results suggest the possibility of extending the Griffith-Irwin theory of static fracture to flexural and torsional problems.