Abstract
A study of the critical behavior of effective thermal conductivities of isotropic composites containing spherical inclusions is presented. Three types of problems are investigated: the debonded inclusion, coated inclusion, and contact resistance problems. For the first two problems, a critical relative interfacial layer thickness, (δ/a)c, is shown to exist and is derived to be a simple function of the reduced thermal conductivities of the inclusion, σ2, and of the interfacial layer, σ3. It depends much more strongly on σ3 than on σ2. As to the third problem, a critical Biot number, (Bi)c, is found to exist and can be simply expressed as 1/(σ2−1). Finally, the critical condition for the contact resistance problem is shown to be a special case of that of the debonded inclusion problem.
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