Interfacial Stresses for a Coated Irregularly Shaped Hole Embedded in an Infinite Solid under Point Heat Singularity

Particle-reinforced metals are being developed for advanced heat dissipation applications. However, an irregularly shaped void develops during eutectic solidification and enhances interfacial stress induced by visco-plastic deformation in temperature gradient conditions. An analytical solution to an irregularly shaped coated hole embedded in an infinite substrate under an arbitrarily located heat source or sink is presented. For a coated polygonal hole with any number of edges, a rapidly convergent series solution of the temperature and stress functions is expressed in an elegant form using conformal mapping, the analytic continuation theorem, and the alternation method. The iterations of the trial-and-error method are utilized to obtain the solution for the correction terms. First, temperature contours are obtained to provide an optimal suggestion that a larger thermal conductivity of the coating layer exhibits better heat absorption capacity. Furthermore, interfacial stresses between a coating layer and substrate increase if the strength of a point thermal singularity and thermal mismatch increases. This study provides a detailed explanation for the growth of an irregular void at an ambient temperature gradient.