Abstract
A solution is given for the steady-state heat conduction problem of the interface crack between dissimilar anisotropic media. Based on the Hilbert problem formulation and a special technique of analytical continuation, exact expressions are obtained for the temperature and temperature gradients for both the heat flux prescribed and temperature prescribed boundary conditions. It is found that the temperature gradients near the crack tip always possess the characteristic inverse square root singularity in rectilinearly anisotropic bodies provided the heat conductivity coefficients are positive definite and symmetric. Moreover, the temperatures or temperature gradients associated with the dissimilar media can be easily obtained from the corresponding problem associated with the homogeneous media by a simple substitution. Special examples are given to the homogeneous and isotropic materials and the solutions reduce to the results given in the literature. The strength of heat flux singularities related to the crack dimension is also discussed.
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