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, σ 2 , and of the interfacial layer, σ 3 . It depends much more strongly on σ 3 than on σ 2 . As to the third problem, a critical Biot number, (Bi) c , is found to exist and can be simply expressed as 1/(σ 2 -1). Finally, the critical condition for the contact resistance problem is shown to be a special case of that of the debonded inclusion problem. © 1995 American Institute of Physics.