Thermal resistance of bridged cracks in fiber-reinforced ceramic composites

The thermal resistance of a bridged matrix crack in a fiber-reinforced ceramic composite is analyzed. The problem is cast in terms of a unit cell comprising an infinitely long composite cylinder with a single matrix crack perpendicular to the fiber axis. At the outset, it is demonstrated that the thermal resistance of such a crack can be represented by a simple circuit consisting of two parallel resistors; one resistor represents the thermal resistance of the gas phase Rg within the matrix crack, and the other resistor represents the constriction resistance Rc of the bridging fiber. The main focus of the article is on determination of Rc and bounds on this resistance are obtained by the use of variational calculus. The analogy between problems involving steady-state heat flow and elasticity in multiphase materials 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 is neglected. The domain in which such variations can be justifiably neglected is found. © 2001 American Institute of Physics. @DOI: 10.1063/1.1354648#