Thermoplastic Instability for the Transient Contact Problem of Two Sliding Half-Planes

[+] Author and Article Information
A. Azarkhin

Product Engineering Division, Aluminum Company of America, Alcoa Center, PA 15069

J. R. Barber

Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109

J. Appl. Mech 53(3), 565-572 (Sep 01, 1986) (8 pages) doi:10.1115/1.3171812 History: Received March 04, 1985; Revised January 31, 1986; Online July 21, 2009


We study the time dependent problem of a nonconducting half-plane sliding on the surface of a conductor with heat generation at the interface due to friction. The conducting half-plane is slightly rounded to give a Hertzian initial pressure distribution. Relationships are established for temperature and thermoelastic displacements due to a heat input of cosine type through the surface, and then these are used to obtain the solution in the form of a double Fourier integral. Numerical results show that, if the ratio of the initial size of the area of contact to that in the steady state is less than some critical value, the area of contact and the pressure distribution change smoothly toward the steady state solution. Otherwise the area of contact goes through bifurcation. The bifurcation accelerates the process. Numerical results are compared with previous approximate solutions.

Copyright © 1986 by ASME
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