Circular Rigid Punch With One Smooth and Another Sharp Ends on a Half-Plane With Edge Crack

[+] Author and Article Information
Norio Hasebe, Jun Qian

Department of Civil Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466, Japan

J. Appl. Mech 64(1), 73-79 (Mar 01, 1997) (7 pages) doi:10.1115/1.2787296 History: Received October 10, 1995; Revised September 03, 1996; Online October 25, 2007


A circular rigid punch with friction is assumed to contact with a half-plane with one end sliding on the half-plane and another end with a sharp corner. The contact length is determined by satisfying the finite stress condition at the sliding end of the punch. The crack is initiated near the end with a sharp corner where infinite stresses exist. Coulomb’s frictional force is supposed to act on the contact region. The cracked half-plane is mapped into a unit circle by using a rational mapping function, and the problem is transformed into a standard Riemann-Hilbert problem, which is solved by introducing a Plemelj function. The contact length, the stress intensity factors of the crack, and the resultant moment about the origin of the coordinates on the contact region are calculated for different frictional coefficients, Poisson’s ratios of the half-plane, crack lengths, and distances from the crack to the punch, respectively. The stress distributions on the contact region are also shown.

Copyright © 1997 by The American Society of Mechanical Engineers
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