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

Abstract

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.