2604 Journal of the American Ceramic Socien-Kerans et aL. Vol. 85. No. 1I Consideration of protection of fibers by residual coating lay on interfacial stresses and sliding friction. Realization that rough- es the issue of the degree of protection that might be expecte ness misfit effects can be substantial in oxide coatings has led to nra has discussed the issue of Sic-fiber protection from reexamination of conventional composites for coating thicknes oxidation in some detail. It is evident that very thin coatings can compliance effects. Modeling has shown that roughness in slow oxidation only to a limited degree. Small-diameter fibers- creases the compressive radial stress in a hypothetical uncoated Sic filaments are typically 8-12 um in diameter--are desirable Nicalon fiber/SiC composite from "150 MPa before sliding to 450 for easy handling, weaving, and shape-making, but the surface/ MPa after sliding. These stresses are decreased by 1/3 by including volume ratio is very high. Consequently, oxidation depths that are a 0.5 um thick carbon coating, therefore, changes in coating thickness can be expected to affect debond length and composite properties. In general, oxides are less compliant than carbon and BN; therefore, thicker coatings are required to similarly accom- n modate misfit stresses. Assuming a Nicalon/SiC composite and a a. MC behavior also depends strongly on the fiber/matrix sliding practical lower limit of 70 GPa for the elastic modulus of a porous iction. The ultimate strength, strain-to-failure, matrix crack oxide, the compliance provided by 500 nm of carbon requires 2 spacing, and toughness are affecte Coulomb friction is um of oxide. If coatings of such thickness are not practical proportional to the radial clamping stress on the fiber, which can suitable friction levels may need to be engineered in other ways be caused by residual stress from differential thermal expansion or e.g., by controlling roughness, matrix compliance, and residual els and experiments focus on residual stresses, ,/- but, re- thickness are also a large volume fraction of the composite and can cently, more attention has been given to roughness-induced stress- affect other composite properties, such as modulus, thermal A large roughness effect on sliding friction has been conductivity, and thermal expansion. Astute design allows for the shown by fiber push back or"seating drop"measurements. 3 effects on composite properties. 6 nitial modeling of the roughness effectis based on an approx- mation that debond roughness of amplitude h causes a mismatch strain of h/R, where R, is the fiber radius, that adds to the thermal (6) Effects of Coating Properties on Composite Analysis mismatch strain. Experiments show that this captures major Many calculations of radial clamping stress during fiber/matrix debonding and sliding consider only the thermoelastic properties spects of the behavior for many interfacial crack roughness of the fiber and matrix. The discussion above implies that serious geometries and. for most systems. during sliding of long fiber lengths. However, modeling has shown that the effect of roug errors may result. A rigorous treatment of the coating elastic ness in the early stages of debond crack propagation(Fig. 7)can effects exists 7 but the results are not easily incorporated into be much more pronounced and can have a significant influence on existing models of behavior. An approach that utilizes an approx omposite properties. This effect is due to the initial unseating of imation of this work in a method that represents the coated fiber by the matching rough surfaces just behind the crack tip. In this an"effective "( transversely isotropic) fiber in simple fiber/matrix region, the work required to further compress the fiber and matrix composites allows simple inclusion of coating elasticity in exi to accommodate the misfit is done. Furthermore the sliding analyses. This work also indicates that many conventional urfaces are not parallel to the fiber axis therefore, there is a analyses that have neglected carbon and Bn coatings in a Nicalon/ Sic system are significantly in error, Plots of normalized elastic beehponent of applied force that increases the friction. Perhap the modulus and coefficient of thermal expansion(CTE)for isotro treated-fiber Sic composite system discussed earlier, a rough interface model is necessary to decrease pushout data, and rough ometries for which th work well for compliant(carbon, BN) coating thickness up to 6 ness appears to be the primary source of the high friction that of the fiber radius, and they give reasonable approximations for dictates the very good fracture properties. ,0 Models of such thickness up to 10%. The thickness constraints relax somewhat A-Tocesses are now available and can be used to study debonding with incr, sg S coating stiffness. Other limitations are discussed ughness contributions to composite behavior. 7, 4 Effects pre- dicted for oxide fiber coatings are discussed later elsewhere This approach is applicable to many models that assume transversely isotropic fibers. For example, effective fiber pr (5) Interfacial Layer Compliance ties can be directly used in the shear-lag models of fiber pullout Although the coating is not often explicitly considered in pushout, ,8 as well as the Budiansky-Hutchinson-Evans nalysis, the compliance of the coating can have significant effects (BHE)model for matrix-cracking stress (7 Necessary Values of Interfacial Toughness and Friction Many CMCs fit in one of two categories: those with negligible interfacial strength, moderate to low interfacial friction, and toug (bond Crack-tip behavior, and those with high interfacial strength and elastic behavior. From these categories, it often has been inferred that toughness. s, u, When combined with the ease of using one parameter to describe the interface, this practice has led to the ssumption of zero interfacial strength and constant low interfacial friction(T)in most fracture models. 75.,90 Nicalon/C/SiC composites made with fibers treated to enhand Matrix oating/fiber bond strength",o evidence interface properties that defy common assumptions regarding what is required for good te behavior. Composites made with treated fibers have 30% higher tensile strength(from 250 to 350 MPa) at the same strain-to-failure. much finer matrix crack Fig. 7. Illustration of the effect of interfacial cantly different stress-strain behavior(Fig. 9). The change is e debonding progressing away from a matrix e attributed to interfacial friction(T)that increases from -5 to -150 sion. Three different reg labeled I.II MPa. Strong and tough composites with high strain-to-failure Roughness amplitude, h, period, 2d, and R. are the (0.5%)are observed even when T 370 MPa. The high mportant parameters that influence interfacial friction. has been attributed to the decrease in effectiveConsideration of protection of fibers by residual coating layers raises the issue of the degree of protection that might be expected. Luthra57 has discussed the issue of SiC-fiber protection from oxidation in some detail. It is evident that very thin coatings can slow oxidation only to a limited degree. Small-diameter fibers— SiC filaments are typically 8–12 m in diameter—are desirable for easy handling, weaving, and shape-making, but the surface/ volume ratio is very high. Consequently, oxidation depths that are insignificant in monolithics damage fibers. (4) Interfacial Friction CMC behavior also depends strongly on the fiber/matrix sliding friction. The ultimate strength, strain-to-failure, matrix crack spacing, and toughness are affected.75,76 Coulomb friction is proportional to the radial clamping stress on the fiber, which can be caused by residual stress from differential thermal expansion or misfit from roughness at the debonding interface.73,77 Most mod￾els and experiments focus on residual stresses,73,78–80 but, re￾cently, more attention has been given to roughness-induced stress￾es.71,81–83 A large roughness effect on sliding friction has been shown by fiber push back or “seating drop” measurements.82,83 Initial modeling of the roughness effect73 is based on an approx￾imation that debond roughness of amplitude h causes a mismatch strain of h/Rf , where Rf is the fiber radius, that adds to the thermal mismatch strain. Experiments show that this captures major aspects of the behavior for many interfacial crack roughness geometries and, for most systems, during sliding of long fiber lengths.77 However, modeling has shown that the effect of rough￾ness in the early stages of debond crack propagation (Fig. 7) can be much more pronounced and can have a significant influence on composite properties. This effect is due to the initial unseating of the matching rough surfaces just behind the crack tip. In this region, the work required to further compress the fiber and matrix to accommodate the misfit is done. Furthermore, the sliding surfaces are not parallel to the fiber axis; therefore, there is a component of applied force that increases the friction. Perhaps the best example of a system where this effect is important is the treated-fiber SiC composite system discussed earlier; a rough￾interface model is necessary to decrease pushout data, and rough￾ness appears to be the primary source of the high friction that dictates the very good fracture properties.25,68 Models of such processes are now available and can be used to study debonding roughness contributions to composite behavior.71,84 Effects pre￾dicted for oxide fiber coatings are discussed later. (5) Interfacial Layer Compliance Although the coating is not often explicitly considered in analysis, the compliance of the coating can have significant effects on interfacial stresses and sliding friction. Realization that rough￾ness misfit effects can be substantial in oxide coatings has led to reexamination of conventional composites for coating thickness/ compliance effects.85 Modeling has shown that roughness in￾creases the compressive radial stress in a hypothetical uncoated Nicalon fiber/SiC composite from 150 MPa before sliding to 450 MPa after sliding. These stresses are decreased by 1/3 by including a 0.5 m thick carbon coating; therefore, changes in coating thickness can be expected to affect debond length and composite properties. In general, oxides are less compliant than carbon and BN; therefore, thicker coatings are required to similarly accom￾modate misfit stresses. Assuming a Nicalon/SiC composite and a practical lower limit of 70 GPa for the elastic modulus of a porous oxide, the compliance provided by 500 nm of carbon requires 2 m of oxide.86 If coatings of such thickness are not practical, suitable friction levels may need to be engineered in other ways, e.g., by controlling roughness, matrix compliance, and residual stress state, or by other deformation mechanisms. Coatings of such thickness are also a large volume fraction of the composite and can affect other composite properties, such as modulus, thermal conductivity, and thermal expansion. Astute design allows for the effects on composite properties.86 (6) Effects of Coating Properties on Composite Analysis Many calculations of radial clamping stress during fiber/matrix debonding and sliding consider only the thermoelastic properties of the fiber and matrix. The discussion above implies that serious errors may result. A rigorous treatment of the coating elastic effects exists,87 but the results are not easily incorporated into existing models of behavior. An approach that utilizes an approx￾imation of this work in a method that represents the coated fiber by an “effective” (transversely isotropic) fiber in simple fiber/matrix composites allows simple inclusion of coating elasticity in existing analyses.88 This work also indicates that many conventional analyses that have neglected carbon and BN coatings in a Nicalon/ SiC system are significantly in error. Plots of normalized elastic modulus and coefficient of thermal expansion (CTE) for isotropic “effective” fibers are given in Fig. 8. There are limits to the geometries for which this approach yields good results. The plots work well for compliant (carbon, BN) coating thickness up to 6% of the fiber radius, and they give reasonable approximations for thickness up to 10%. The thickness constraints relax somewhat with increasing coating stiffness. Other limitations are discussed elsewhere.88 This approach is applicable to many models that assume transversely isotropic fibers. For example, effective fiber proper￾ties can be directly used in the shear–lag models of fiber pullout and pushout,72,81 as well as the Budiansky–Hutchinson–Evans (BHE) model89 for matrix-cracking stress. (7) Necessary Values of Interfacial Toughness and Friction Many CMCs fit in one of two categories: those with negligible interfacial strength, moderate to low interfacial friction, and tough behavior; and those with high interfacial strength and elastic behavior. From these categories, it often has been inferred that negligible interfacial strength and low friction are necessary for toughness.75,90,91 When combined with the ease of using one parameter to describe the interface, this practice has led to the assumption of zero interfacial strength and constant low interfacial friction () in most fracture models.75,90 Nicalon/C/SiC composites made with fibers treated to enhance coating/fiber bond strength25,68 evidence interface properties that defy common assumptions regarding what is required for good composite behavior.25 Composites made with treated fibers have 30% higher tensile strength (from 250 to 350 MPa) at the same strain-to-failure, much finer matrix crack spacing, and signifi￾cantly different stress–strain behavior (Fig. 9). The change is attributed to interfacial friction () that increases from 5 to 150 MPa.67 Strong and tough composites with high strain-to-failure (0.5%) are observed even when   370 MPa. The high composite strength has been attributed to the decrease in effective Fig. 7. Illustration of the effect of interfacial roughness during progres￾sive debonding progressing away from a matrix crack in a composite under tension. Three different regions, labeled I, II, and III, can be envisioned. Roughness amplitude, h, period, 2d, and fiber radius, R, are the most important parameters that influence interfacial friction.71 2604 Journal of the American Ceramic Society—Kerans et al. Vol. 85, No. 11