Stress and Notch-Stress Concentration Induced by Slight Depressions and Protrusions

[+] Author and Article Information
C. H. Wu

Department of Civil Engineering, Mechanics, and Metallurgy, University of Illinois at Chicago, P.O. Box 4348, Chicago, IL 60680

J. Appl. Mech 60(4), 992-997 (Dec 01, 1993) (6 pages) doi:10.1115/1.2901014 History: Received January 09, 1992; Revised October 16, 1992; Online March 31, 2008


The presence of a smooth depression on the surface of a stretched half-plane magnifies the surface stress at the trough of the depression. Similarly, the stress at the foot of a smooth protrusion is also magnified. The associated stress concentration factors are determined, via a regular perturbation procedure, in terms of a small aspect ratio that measures the slight unevenness of the surf ace. When the depression/protrusion profile has corners, the method of matched asymptotic expansions is used to obtain the desired analytic solution. The case of a shallow notch, as well as that of a triangular protrusion, is solved explicitly.

Copyright © 1993 by The American Society of Mechanical Engineers
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