STEADY-STATE HEAT-CONDUCTION PROBLEM OF THE INTERFACE CRACK BETWEEN DISSIMILAR ANISOTROPIC MEDIA

A solution is given for the steady-state heat conduction problem of th e interface crack between dissimilar anisotropic media. Based on the H ilbert problem formulation and a special technique of analytical conti nuation, exact expressions are obtained for the temperature and temper ature gradients for both the heat flux prescribed and temperature pres cribed boundary conditions. It is found that the temperature gradients near the crack tip always possess the characteristic inverse square r oot singularity in rectilinearly anisotropic bodies provided the heat conductivity coefficients are positive definite and symmetric. Moreove r, the temperatures or temperature gradients associated with the dissi milar media can be easily obtained from the corresponding problem asso ciated with the homogeneous media by a simple substitution. Special ex amples are given to the homogeneous and isotropic materials and the so lutions reduce to the results given in the literature. The strength of heat flux singularities related to the crack dimension is also discus sed.