502 FABER and penetration as a function of Dundurs parameter a where Ef-em and the subscripts f and m refer to the fiber and the matrix, and Ex=Ex(I-v2) he plane strain modulus for the phase x. E and v are the elastic modu- lus and Poissons ratio for the respective phases. A positive value of a re- flects conditions of a fiber stiffer than the matrix, a likely occurrence even in brittle matrix composites. The magnitude of a rarely exceeds 0.5 in these materials Recently, Lee et al (9)analyzed conditions for kinking back into the re- nforcement after deflection-a problem more common to laminates than to fiber-reinforced materials, but important nonetheless liding Resistance The coefficient of friction u at the sliding interface plays a dominant role in ceramic composite toughening by determining the sliding resistance t. For a crack-bridging fiber, the bridging tractions are determined by the relative fiber-matrix displacements as controlled through the sliding resistance. At first glance. one would then wish to maximize the friction coefficient. However. as u and hence t increase, fiber fracture is expected closer to the crack plane(3) The contribution to toughening from pullout is then diminished. Systematic changes in t in a single system can be arrived at by altering the residual stress profile or fiber surface roughness, both described bel Roughness Fiber surface roughness was first acknowledged to influence interfacial prop- erties by Jero Kerans(10)who noticed that fibers would"reseat" with a oncomitant decrease in load when they were pushed back into the matrix to heir original position. The load drop was attributed to the residual sliding resis- tance resulting from the relaxation from roughness-induced misfit strain upon reseating. Additional evidence of the role of fiber surface roughness including stress birefringence of an asperity misfit (I1)and direct evidence of the role of fiber-surface roughness of as-processed fibers(11-16) have been reported Kerans Parthasarathy(17) have included the role of roughness in Equation I by treating it as an additional component to the effective interfacial clamping k(sth +ear) where g. is the radial thermal mismatch strain. gs is the roughness-induced radial misfit strain, and k is a constant accounting for the elastic properties ofP1: ARK/MBL/rkc P2: MBL/vks QC: MBL/agr T1: MBL May 16, 1997 13:47 Annual Reviews AR034-16 502 FABER and penetration as a function of Dundurs’ parameter α where α = E¯f − E¯m E¯f + E¯m , 2. and the subscripts f and m refer to the fiber and the matrix, and E¯x = Ex(1-ν2 x ), the plane strain modulus for the phase x. E and ν are the elastic modu￾lus and Poisson’s ratio for the respective phases. A positive value of α re- flects conditions of a fiber stiffer than the matrix, a likely occurrence even in brittle matrix composites. The magnitude of α rarely exceeds 0.5 in these materials. Recently, Lee et al (9) analyzed conditions for kinking back into the re￾inforcement after deflection—a problem more common to laminates than to fiber-reinforced materials, but important nonetheless. Sliding Resistance The coefficient of friction µ at the sliding interface plays a dominant role in ceramic composite toughening by determining the sliding resistance τ . For a crack-bridging fiber, the bridging tractions are determined by the relative fiber-matrix displacements as controlled through the sliding resistance. At first glance, one would then wish to maximize the friction coefficient. However, as µ and hence τ increase, fiber fracture is expected closer to the crack plane (3). The contribution to toughening from pullout is then diminished. Systematic changes in τ in a single system can be arrived at by altering the residual stress profile or fiber surface roughness, both described below. Roughness Fiber surface roughness was first acknowledged to influence interfacial prop￾erties by Jero & Kerans (10) who noticed that fibers would “reseat” with a concomitant decrease in load when they were pushed back into the matrix to their original position. The load drop was attributed to the residual sliding resis￾tance resulting from the relaxation from roughness-induced misfit strain upon reseating. Additional evidence of the role of fiber surface roughness including stress birefringence of an asperity misfit (11) and direct evidence of the role of fiber-surface roughness of as-processed fibers (11–16) have been reported. Kerans & Parthasarathy (17) have included the role of roughness in Equation 1 by treating it as an additional component to the effective interfacial clamping stress σn, as shown here: σn = k ¡ εth r + εsr¢ , 3. where εth r is the radial thermal mismatch strain, εsr is the roughness-induced radial misfit strain, and k is a constant accounting for the elastic properties of