Thermal resistance of bridged cracks in fiber-reinforced ceramic composites

The thermal resistance of a bridged matrix crack in a fiber-reinforced cera mic composite is analyzed. The problem is cast in terms of a unit cell comp rising an infinitely long composite cylinder with a single matrix crack per pendicular to the fiber axis. At the outset, it is demonstrated that the th ermal resistance of such a crack can be represented by a simple circuit con sisting of two parallel resistors; one resistor represents the thermal resi stance of the gas phase R-g within the matrix crack, and the other resistor represents the constriction resistance R-c of the bridging fiber. The main focus of the article is on determination of R-c and bounds on this resista nce are obtained by the use of variational calculus. The analogy between pr oblems involving steady-state heat flow and elasticity in multiphase materi als is emphasized. The results for the constriction resistance are compared with the predictions of an approximate analytical model presented by [T. J . Lu and J. W. Hutchinson, Philos. Trans. R. Soc. London, Ser. A 351, 595 ( 1995)]. In their model the radial temperature variation within the matrix i s neglected. The domain in which such variations can be justifiably neglect ed is found. (C) 2001 American Institute of Physics.