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

[+] Author and Article Information
G. C. Sih

Lehigh University, Bethlehem, Pa.

J. Appl. Mech 30(3), 419-425 (Sep 01, 1963) (7 pages) doi:10.1115/1.3636572 History: Received October 22, 1962; Online September 16, 2011


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.

Copyright © 1963 by ASME
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