The First-Order Variation of the Displacement Field Due to Geometrical Changes in an Elliptical Crack

[+] Author and Article Information
T. Nishioka

Department of Ocean Mechanical Engineering, Kobe University of Mercantile Marine, Kobe 658, Japan

S. N. Atluri

Center for Computational Mechanics, Georgia Institute of Technology, Atlanta, GA 30332-0356

J. Appl. Mech 57(3), 639-646 (Sep 01, 1990) (8 pages) doi:10.1115/1.2897070 History: Accepted February 03, 1989; Received February 03, 1989; Online March 31, 2008


Analytical expressions are derived for the derivatives of the crack-surface displacement field, with respect to the lengths of the major and minor axes, respectively, of an elliptical crack embedded in an infinite isotropic elastic solid, when the crack faces are subjected to arbitrary tractions. These results are shown to lead, in turn, to analytical expressions for weight functions for the stress intensity factors along the fronts of elliptical-shaped embedded or part-elliptical shaped surface flaws, when a simple two-parameter characterization of the stress intensity variation along the flaw border is used. In the case of part-elliptical surface flaws, a finite-element alternating method, based on the Schwartz-Neumann superposition technique, is proposed to determine the coefficients in the analytical expressions for crack-surface displacements, and their gradients with respect to the crack dimensions.

Copyright © 1990 by The American Society of Mechanical Engineers
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