On estimates of stress intensity factors for cracked beams and pipes

Abstract

This paper presents a discussion and an extension of a method, advanced by Kienzler and Herrmann [Acta Mech. 62, 37-46 (1986)], of evaluating the stress intensity factors of cracked beams based on an elementary beam theory estimation of strain energy release rate as the crack is widened into a fracture band. Recently, Bazant [Engng Fracture Mech. 36, 523-525 (1990)] justified the approach taken by Kienzler and Herrmann as a good approximation by showing that the strain energy release rate for crack extension is closely related to, but usually not equal to, the energy release for crack widening into a band. This indicates that an additional factor needs to be introduced to improve the approximations. We show here that this factor can be obtained through asymptotic matching with standard limiting crack solutions. As an extension, we use the beam theory estimation to compute stress intensity factors for a circumferentially cracked cylindrical pipe in bending and tension and find good agreement with the exact solutions obtained from complete shell analysis. Applications of the beam theory analysis are under progress for numerous other crack problems of practical interest. © 1992.