SYMPOSIA PAPER Published: 01 January 1994

Stress Intensity Factor Solutions for Surface Cracks in Flat Plates Subjected to Nonuniform Stresses


The case of a surface crack in a flat plate has received a lot of attention from the fracture mechanics community because of its practical applicability as an idealization of a flaw in structures. Among all the solutions available, those of Raju and Newman seem to be the most accepted and cover the widest range of geometric parameters. These solutions are, however, known only for the cases of tensile and bending loads, and include the effect of finite width using an empirical equation. Residual stresses and more complex forms of loading lead to nonlinear stress distributions across the thickness in real structures. Attempts were made by a few researchers to provide solutions for arbitrary loading using the weight-function and other methods, but a comprehensive treatment of these solutions is not available. The objective of the present work is to provide complete solutions including the effect of finite width using direct tabular inter polation of the finite-element results and to demonstrate the accuracy of a weight-function approach for computing stress intensity factors for a cracked plate subject to arbitrary stresses across the thickness. The reference solutions used in the weight-function scheme were obtained using the three-dimensional finite-element method (FEM). The full range of geometric parameters such as the crack-length-to-width ratio 2c/W, the crack-depth-to-thickness ratio a/t, and the aspect ratio a/c was covered so that accurate interpolation and extrapolation could be made for any given geometry. Piecewise cubic Hermite interpolation was used to compute the quantities corresponding to intermediate values of the geometric parameters. The new solution was compared with the earlier Newman-Raju equation. The new solution in tabular form was then used directly in the weight-function method. The stress intensity factor solution developed here was incorporated into the fatigue crack growth program NASA/FLAGRO, which is widely used by the aerospace community.

Author Information

Raju, IS
Analytical Services and Materials, Inc., Hampton, VA
Mettu, SR
Lockheed Engineering & Sciences Co., Houston, TX
Shivakumar, V
Lockheed Engineering & Sciences Co., Houston, TX
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Developed by Committee: E08
Pages: 560–580
DOI: 10.1520/STP13727S
ISBN-EB: 978-0-8031-5270-0
ISBN-13: 978-0-8031-1990-1