Self-Similar Crack Expansion Method for Three-Dimensional Crack Analysis

[+] Author and Article Information
Yonglin Xu, B. Moran, T. Belytschko

Department of Civil Engineering, Northwestern University, Evanston, IL 60208

J. Appl. Mech 64(4), 729-737 (Dec 01, 1997) (9 pages) doi:10.1115/1.2788976 History: Received January 19, 1996; Revised September 24, 1996; Online October 25, 2007


The self-similar crack expansion method is developed to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique. With this method, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface, and the crack expansion rate, which is related to the crack energy release rate, is estimated by using a technique based on self-similar (virtual) crack extension. For elements on the crack surface, regular integrals and singular integrals are evaluated based on closed-form expressions, which improves the accuracy. Examples show that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than one percent as compared with exact solutions. The stress intensity factors of subsurface cracks are in good agreement with other numerical solutions.

Copyright © 1997 by The American Society of Mechanical Engineers
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