The External Axisymmetric Interface Crack with Heat Flow

Two half-spaces of dissimilar material properties are brought together and bonded over a circular region of radius r = a to form an exterior axisymmetric interface crack. Loads are applied at infinity such that the common boundary (i.e. the bond and any contact region that develops) transmits tractions whose resultant is an axial tension P. Interpenetration is predicted if the track is assumed to be completely open; in fact an annular contact region {a b. If the temperatures of the bodies are now changed, the extent of this contact region changes. A solution to this problem is obtained by representing the displacement in the bodies in terms of harmonic potential functions and reducing the resulting mixed boundary-value problem to an integral equation which is solved numerically. Detailed results are given for the particular case in which both bodies are raised to the same temperature. If the load P is zero, the crack either closes completely or opens almost completely, depending on the sign of certain combinations of physical constants. Results are also given for the case where one body is a rigid perfect conductor and the other is maintained at zero temperature.