Three-Dimensional Analysis of Surface Cracks in an Elastic Half-Space

[+] Author and Article Information
Quanxin Guo, Jian-Juei Wang

TerraTek, Inc, 420 Wakara Way, Salt Lake City, UT 84108

R. J. Clifton

Division of Engineering, Brown University, Providence, RI 02912

J. Appl. Mech 63(2), 287-294 (Jun 01, 1996) (8 pages) doi:10.1115/1.2788862 History: Received June 23, 1994; Revised May 15, 1995; Online October 26, 2007


A numerical method is presented for analyzing arbitrary planar cracks in a half-space. The method is based on the fundamental solution for a dislocation loop in a half-space, which is derived from the Mindlin solution (Mindlin, Physics , Vol. 7, 1936) for a point force in a half-space. By appropriate replacement of the Burgers vectors of the dislocation by the differential crack-opening displacement, a singular integral equation is obtained in terms of the gradient of the crack opening. A numerical method is developed by covering the crack with triangular elements and by minimizing the total potential energy. The singularity of the kernel, when the integral equation is expressed in terms of the gradient of the crack opening, is sufficiently weak that all integrals exist in the regular sense and no special numerical procedures are required to evaluate the contributions to the stiffness matrix. The integrals over the source elements are converted into line integrals along the perimeter of the element and evaluated analytically. Numerical results are presented and compared with known results for both surface breaking cracks and near surface cracks.

Copyright © 1996 by The American Society of Mechanical Engineers
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