Three-Dimensional Stress Concentration Around a Cylindrical Hole in a Semi-Infinite Elastic Body

[+] Author and Article Information
C. K. Youngdahl

Argonne National Laboratory, Argonne, Ill.

E. Sternberg

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, Calif.

J. Appl. Mech 33(4), 855-865 (Dec 01, 1966) (11 pages) doi:10.1115/1.3625193 History: Received May 20, 1965; Revised December 06, 1965; Online September 15, 2011


This paper contains a three-dimensional solution, exact within classical elastostatics, for the stresses and deformations arising in a half-space with a semi-infinite transverse cylindrical hole, if the body—at infinite distances from its cylindrical boundary—is subjected to an arbitrary uniform plane field of stress that is parallel to the bounding plane. The solution presented is in integral form and is deduced with the aid of the Papkovich stress functions by means of an especially adapted, unconventional, integral-transform technique. Numerical results for the nonvanishing stresses along the boundary of the hole and for the normal displacement at the plane boundary, corresponding to several values of Poisson’s ratio, are also included. These results exhibit in detail the three-dimensional stress boundary layer that emerges near the edges of the hole in the analogous problem for a plate of finite thickness, as the ratio of the plate thickness to the diameter of the hole grows beyond bounds. The results obtained thus illustrate the limitations inherent in the two-dimensional plane-strain treatment of the spatial plane problem; in addition, they are relevant to failure considerations and of interest in connection with experimental stress analysis.

Copyright © 1966 by ASME
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