Crack-Tip, Stress-Intensity Factors for Plane Extension and Plate Bending Problems

A complex variable method for evaluating the strength of stress singularities at crack tips in plane problems and plate bending problems is derived. The results of these evaluations give Irwin’s stress-intensity factors for plane problems and analogous quantities for bending problems, a form familiar to the practitioner of “fracture mechanics.” The methods derived are integrated with the complex variable approach of Muskhelishvili to obtain the stress-intensity factors for various basic examples applicable to the extension and bending of plates with through-the-thickness cracks. The results suggest the possibility of extension of the Griffith-Irwin fracture theory to arbitrary plane extensional and/or bending problems in plates.