The Penny-Shaped Interface Crack With Heat Flow, Part 1: Perfect Contact

[+] Author and Article Information
C. J. Martin-Moran

Department of Mechanical Engineering, University of Newcastle-Upon-Tyne, NE1 7RU, England

J. R. Barber

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

M. Comninou

Department of Civil Engineering, University of Michigan, Ann Arbor, Mich. 48109

J. Appl. Mech 50(1), 29-36 (Mar 01, 1983) (8 pages) doi:10.1115/1.3167013 History: Received May 01, 1982; Online July 21, 2009


A solution is given for the thermal stresses due to a penny-shaped crack at the interface between dissimilar materials loaded in tension for the case where the heat flux is into the material with higher distortivity. Regions of separation and perfect thermal contact are developed at the crack faces. A harmonic potential function representation is used to reduce the problem to a three-part boundary value problem which is formulated as a pair of coupled Abel integral equations using the method of Green and Collins. These equations are further reduced to a single Fredholm equation which is solved numerically. Results are presented illustrating the effect of heat flux and applied tractions on the contact radius and the stress intensity factors for various combinations of material constants. The effect of heat flux is profoundly influenced by the relative signs of Dundurs constant β and a constant γ describing the mismatch of distortivities. If the more distortive material is also the more rigid, the contact region at the crack face is reduced by heat flow; otherwise it is increased. In the latter case, solutions involving separation are obtained even for applied compressive tractions if the latter is within a certain range. The solution also exhibits nonuniqueness in this range.

Copyright © 1983 by ASME
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