Interface Crack Between Two Dissimilar Half Spaces Subjected to a Uniform Heat Flow at Infinity—Open Crack

[+] Author and Article Information
An-Yu Kuo

Structural Integrity Associates, San Jose, CA 95118

J. Appl. Mech 57(2), 359-364 (Jun 01, 1990) (6 pages) doi:10.1115/1.2891997 History: Received March 08, 1989; Revised June 05, 1989; Online March 31, 2008


The thermal stress problem of an “open” crack situated at the interface of two bonded, dissimilar, semi-infinite solids subjected to a uniform heat flow is studied. Heat transmission between adjacent crack surfaces is assumed to be proportional to the temperature difference between the crack surfaces with a proportional constant h , which is defined as the contact coefficient or interface conductance. Temperature distribution of the problem is obtained by superimposing the temperature field for a perfectly bonded composite solid and the temperature fields for a series of distributed thermal dipoles at the crack location. The distribution function of the dipoles is obtained by solving a singular Fredholm integral equation. Stresses are then expressed in terms of a thermoelastic potential, corresponding to the temperature distribution, and two Muskhelishvili stress functions. Stress intensity factors are calculated by solving a Hilbert arc problem, which results from the crack surface boundary conditions and the continuity conditions at the bonded interface. Thermal stress intensity factors are found to depend upon an additional independent parameter, the Biot number λ = (ah/k) , on the crack surface, where a is half crack length and k is thermal conductivity. Dipole distribution and stress intensity factors for two example composite solids, Cu/Al and Ti/Al2 O3 , are calculated and plotted as functions of λ. Magnitude of the required mechanical loads to keep the interface crack open is also estimated.

Copyright © 1990 by The American Society of Mechanical Engineers
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