CERAMIC COMPOSITE INTERFACES 503 the fiber and matrix. To first order E= A/R, where a is the amplitude of the surface roughness and R is the fiber radius. The amplitude of the face roughness then appears explicitly in Equation 1, because Sro is directl proportional to the clamping stress o Fiber surface roughness can be altered with compliant, low-fracture resis- tance coatings. A rationale for a coating scheme is best seen in Figure 2, where increasing coating thickness allows for systematic modification of the asperity asperity interactions of fiber and matrix. An increase in the coating thickness reduces the roughness asperity interactions between the fiber and matrix dur- ing interfacial sliding. This results in a smaller roughness-induced strain and clamping stress, which reduces the frictional resistance to sliding. A coating with a thickness greater than the amplitude of the fiber surface roughness can completely negate the contribution to the frictional sliding stress. This is best illustrated by the following example Fiber-sliding measurements were made on a model composite system by Mumm Faber(16). SiC monofilaments coated with four different thick- nesses of carbon(relative to the amplitude of the asperity roughness)in a soda-borosilicate glass matrix were used for model fiber pullout experiments In the extreme, the coating is meant to completely eliminate asperity contact during debonding and sliding. The fiber force-displacement measurements for the series are shown in Figure 3. First, the controlled thickness coatings induce systematic changes in the load fluctuations; their amplitude decreases ith increasing thickness and is essentially eliminated for coatings thicker thaI he roughness amplitude. The increased slope of the load-deflection curves likely due to an increase in the coefficient of friction with increasing coating thickness owing to changes in the real area of contact(18) Residual stress Few ceramic composites are free of residual stresses. The stresses derive from hermal expansion mismatch between fiber and matrix. The role of such stresses is obvious: As clamping stresses increase, the interfacial frictional stress in- creases. At the extreme, such stresses result in spontaneous cracking of the matrix for a fiber under residual compressive stresses(19). Conversely, sponta neous fiber debonding results when tensile stresses in the fiber exceed a critical value. In addition to interfacial sliding, residual stresses influence the condi- tions for deflection and/or penetration shown in Figure 1. Compressive residual stresses in the reinforcement enhance conditions for deflection, shifting the con- tour upward, while tensile stresses enhance penetration(20) Residual stresses can be controlled through the appropriate choice of the fiber-matrix pair. Moreover, the residual stress profile can be altered with fiber loading. Singh et al (21) found a decrease in debonding and frictionalP1: ARK/MBL/rkc P2: MBL/vks QC: MBL/agr T1: MBL May 16, 1997 13:47 Annual Reviews AR034-16 CERAMIC COMPOSITE INTERFACES 503 the fiber and matrix. To first order εsr = Asr/Rf, where Asr is the amplitude of the surface roughness and Rf is the fiber radius. The amplitude of the sur￾face roughness then appears explicitly in Equation 1, because SRo is directly proportional to the clamping stress σn. Fiber surface roughness can be altered with compliant, low-fracture resis￾tance coatings. A rationale for a coating scheme is best seen in Figure 2, where increasing coating thickness allows for systematic modification of the asperity￾asperity interactions of fiber and matrix. An increase in the coating thickness reduces the roughness asperity interactions between the fiber and matrix dur￾ing interfacial sliding. This results in a smaller roughness-induced strain and clamping stress, which reduces the frictional resistance to sliding. A coating with a thickness greater than the amplitude of the fiber surface roughness can completely negate the contribution to the frictional sliding stress. This is best illustrated by the following example. Fiber-sliding measurements were made on a model composite system by Mumm & Faber (16). SiC monofilaments coated with four different thick￾nesses of carbon (relative to the amplitude of the asperity roughness) in a soda-borosilicate glass matrix were used for model fiber pullout experiments. In the extreme, the coating is meant to completely eliminate asperity contact during debonding and sliding. The fiber force-displacement measurements for the series are shown in Figure 3. First, the controlled thickness coatings induce systematic changes in the load fluctuations; their amplitude decreases with increasing thickness and is essentially eliminated for coatings thicker than the roughness amplitude. The increased slope of the load-deflection curves is likely due to an increase in the coefficient of friction with increasing coating thickness owing to changes in the real area of contact (18). Residual Stress Few ceramic composites are free of residual stresses. The stresses derive from thermal expansion mismatch between fiber and matrix. The role of such stresses is obvious: As clamping stresses increase, the interfacial frictional stress in￾creases. At the extreme, such stresses result in spontaneous cracking of the matrix for a fiber under residual compressive stresses (19). Conversely, sponta￾neous fiber debonding results when tensile stresses in the fiber exceed a critical value. In addition to interfacial sliding, residual stresses influence the condi￾tions for deflection and/or penetration shown in Figure 1. Compressive residual stresses in the reinforcement enhance conditions for deflection, shifting the con￾tour upward, while tensile stresses enhance penetration (20). Residual stresses can be controlled through the appropriate choice of the fiber-matrix pair. Moreover, the residual stress profile can be altered with fiber loading. Singh et al (21) found a decrease in debonding and frictional