CERAMIC COMPOSITE INTERFACES Properties and design KT Faber Department of Materials Science and Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, Illinois 60208 KEY WORDS: ceramic-matrix composites, interfaces, interphases, residual stress, roughness ABSTRACT Optimal design of the fiber-matrix interface in ceramic-matrix composites is the key to achieving desired composite performance. In this paper the interface controlling parameters are described. Techniques for measuring interfacial prop- erties are reported. Examples of interface design of both oxide and non-oxide types are illustrated INTRODUCTION It is well established that the fiber-matrix interface is the dominant design pa- ameter in ceramic-matrix composites. The characteristic that sets brittle ma- trix composites apart from ductile composites, either metal or polymer, is the reliance on a relatively weak fiber-matrix interface for enhanced mechanical be- havior. Recognition of this phenomenon came as early as the early 1970s when Sambell et al (1)noted enhanced work of fracture in carbon fiber-reinforced glass and glass-ceramics where no chemical bond existed between fiber and matrix. In contrast, carbon fibers in magnesia and zirconia fibers in magnesia and glass were found to be chemically bonded and demonstrated little, if an The chemistry of interfaces was the sole design parameter over much of the ext 25 years. More recently, physical parameters, such as the thermal sion mismatch and fiber surface roughness(both relieved through cor oatings), were found to be equally important in interfacial design. The contained herein describes the interface controlling parameters, measurement 084-6600/97/0801-049990800
P1: ARK/MBL/rkc P2: MBL/vks QC: MBL/agr T1: MBL May 16, 1997 13:47 Annual Reviews AR034-16 Annu. Rev. Mater. Sci. 1997. 27:499–524 Copyright c 1997 by Annual Reviews Inc. All rights reserved CERAMIC COMPOSITE INTERFACES: Properties and Design K. T. Faber Department of Materials Science and Engineering, Robert R. McCormick School of Engineering and Applied Science, Northwestern University, Evanston, Illinois 60208; email: k-faber@nwu.edu KEY WORDS: ceramic-matrix composites, interfaces, interphases, residual stress, roughness ABSTRACT Optimal design of the fiber-matrix interface in ceramic-matrix composites is the key to achieving desired composite performance. In this paper the interfacecontrolling parameters are described. Techniques for measuring interfacial properties are reported. Examples of interface design of both oxide and non-oxide types are illustrated. INTRODUCTION It is well established that the fiber-matrix interface is the dominant design parameter in ceramic-matrix composites. The characteristic that sets brittle matrix composites apart from ductile composites, either metal or polymer, is the reliance on a relatively weak fiber-matrix interface for enhanced mechanical behavior. Recognition of this phenomenon came as early as the early 1970s when Sambell et al (1) noted enhanced work of fracture in carbon fiber–reinforced glass and glass-ceramics where no chemical bond existed between fiber and matrix. In contrast, carbon fibers in magnesia and zirconia fibers in magnesia and glass were found to be chemically bonded and demonstrated little, if any, toughening. The chemistry of interfaces was the sole design parameter over much of the next 25 years. More recently, physical parameters, such as the thermal expansion mismatch and fiber surface roughness (both relieved through compliant coatings), were found to be equally important in interfacial design. The review contained herein describes the interface controlling parameters, measurement 499 0084-6600/97/0801-0499$08.00
500 FABER techniques for the mechanical characterization of fiber-matrix interfaces, and key examples of interface design in brittle matrix composite INTERFACE DESIGN PARAMETERS Brittle matrix composites for structural applications are deemed successful when they exhibit fiber debonding and frictional sliding as cracks propagate hrough the matrix. Such behavior is generally accompanied by notch or flaw lerance as demonstrated in a highly nonlinear stress-strain curve reminiscent of a plastically deforming metal (2). The nonlinearity, however, derives not from plasticity but from initiation and propagation of a series of through-the thickness matrix cracks that are bridged by the brittle fibers. The low toughnes interface is the first requirement to prevent fiber fracture during matrix crack growth. Debonding of fibers alone, however, is not sufficient to provide the notch tolerance. As noted by Thouless Evans(3)and by Cao et al (4), the interfacial sliding resistance t should be small enough to allow for a substantial pullout contribution through frictional dissipation by encouraging fiber fracture at significant distances from the matrix crack plane. It is generally thought that t should be between 2 and 40 MPa(3). A third requirement is that thermal mismatch stresses between fiber and matrix are not substantial enough to cause either fiber or matrix crackin To examine how these parameters are explicitly incorporated into composite performance, we first investigate the analysis of Hutchinson Jensen (5), as modified by Marshall(6), that describes the displacement u of a single crack-bridging fiber in a brittle matrix. The analysis assumes stable, interfacial debonding with interfacial sliding governed by a Coulomb friction law and can be written as +r'-sa where u characterizes the frictional properties of the interface and is inversely proportional to the coefficient of friction u, which is related to the frictional sliding resistance t. A is a dimensionless constant that includes the elastic con- stants of the composite constituents, the volume fraction of fibers, the surface roughness, and the anisotropy in thermal misfit strains, Sro is a direct measure of the radial residual stress, Sa is the applied stress normalized by the peak pplied stress. r" is related to the debond energy and is directly proportional to the interfacial toughness Gic and includes any residual stress. The term SR includes the thermal mismatch strain a and the surface roughness-induced strain 8, which relates to the amplitude of the surface roughness A. Conse quently, a complex relationship between the interface toughness, the frictional
P1: ARK/MBL/rkc P2: MBL/vks QC: MBL/agr T1: MBL May 16, 1997 13:47 Annual Reviews AR034-16 500 FABER techniques for the mechanical characterization of fiber-matrix interfaces, and key examples of interface design in brittle matrix composites. INTERFACE DESIGN PARAMETERS Brittle matrix composites for structural applications are deemed successful when they exhibit fiber debonding and frictional sliding as cracks propagate through the matrix. Such behavior is generally accompanied by notch or flaw tolerance as demonstrated in a highly nonlinear stress-strain curve reminiscent of a plastically deforming metal (2). The nonlinearity, however, derives not from plasticity but from initiation and propagation of a series of through-thethickness matrix cracks that are bridged by the brittle fibers. The low toughness interface is the first requirement to prevent fiber fracture during matrix crack growth. Debonding of fibers alone, however, is not sufficient to provide the notch tolerance. As noted by Thouless & Evans (3) and by Cao et al (4), the interfacial sliding resistance τ should be small enough to allow for a substantial pullout contribution through frictional dissipation by encouraging fiber fracture at significant distances from the matrix crack plane. It is generally thought that τ should be between 2 and 40 MPa (3). A third requirement is that thermal mismatch stresses between fiber and matrix are not substantial enough to cause either fiber or matrix cracking. To examine how these parameters are explicitly incorporated into composite performance, we first investigate the analysis of Hutchinson & Jensen (5), as modified by Marshall (6), that describes the displacement u of a single, crack-bridging fiber in a brittle matrix. The analysis assumes stable, interfacial debonding with interfacial sliding governed by a Coulomb friction law and can be written as u u∗ = −ASRo ln µ SRo − Sa SRo − 00 ¶ + 00 − Sa, 1. where u∗ characterizes the frictional properties of the interface and is inversely proportional to the coefficient of friction µ, which is related to the frictional sliding resistance τ . A is a dimensionless constant that includes the elastic constants of the composite constituents, the volume fraction of fibers, the surface roughness, and the anisotropy in thermal misfit strains, SRo is a direct measure of the radial residual stress, Sa is the applied stress normalized by the peak applied stress. 00 is related to the debond energy and is directly proportional to the interfacial toughness Gic and includes any residual stress. The term SRo includes the thermal mismatch strain εT, and the surface roughness-induced strain εsr, which relates to the amplitude of the surface roughness Asr. Consequently, a complex relationship between the interface toughness, the frictional
CERAMIC COMPOSITE INTERFACES sliding resistance, and residual stress state determines the loac cement response. Each of these components is expounded upon below Interface Toughn Conditions for fiber pullout in a fiber-reinforced material first require that a propagating crack deflects along the interface rather than penetrates the fiber uch conditions have been aptly described by He Hutchison(7, 8). They evaluated the relative energy release rate for a crack deflecting along an interface and for the crack penetrating the interface. The competition between crack growth along the interface and penetration through a fiber was found to depend upon the ratio of the fracture energy of the interface Gic and that of the adjoining material Gc, in this case the fiber. In a system where the modulus and fiber have identical moduli, the interface toughness Gic must be less than one quarte of the matrix toughness G. This finding now serves as the basis of interface design. Shown in Figure I is a contour separating regions of crack deflection 0.5 -0.5 0.5 Dundurs' Parameter a Figure I Debonding map showing crack penetration and crack deflection regimes as a function of Dundurs' parameter(after 7, 8)
P1: ARK/MBL/rkc P2: MBL/vks QC: MBL/agr T1: MBL May 16, 1997 13:47 Annual Reviews AR034-16 CERAMIC COMPOSITE INTERFACES 501 sliding resistance, and residual stress state determines the load displacement response. Each of these components is expounded upon below. Interface Toughness Conditions for fiber pullout in a fiber-reinforced material first require that a propagating crack deflects along the interface rather than penetrates the fiber. Such conditions have been aptly described by He & Hutchison (7, 8). They evaluated the relative energy release rate for a crack deflecting along an interface and for the crack penetrating the interface. The competition between crack growth along the interface and penetration through a fiber was found to depend upon the ratio of the fracture energy of the interface Gic and that of the adjoining material Gc, in this case the fiber. In a system where the modulus and fiber have identical moduli, the interface toughness Gic must be less than one quarter of the matrix toughness Gc. This finding now serves as the basis of interface design. Shown in Figure 1 is a contour separating regions of crack deflection Figure 1 Debonding map showing crack penetration and crack deflection regimes as a function of Dundurs’ parameter (after 7, 8)
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 of
P1: 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 modulus 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 reinforcement 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 properties 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 resistance 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
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 frictional
P1: 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 surface 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 resistance coatings. A rationale for a coating scheme is best seen in Figure 2, where increasing coating thickness allows for systematic modification of the asperityasperity interactions of fiber and matrix. An increase in the coating thickness reduces the roughness asperity interactions between the fiber and matrix during 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 thicknesses 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 increases. At the extreme, such stresses result in spontaneous cracking of the matrix for a fiber under residual compressive stresses (19). Conversely, spontaneous fiber debonding results when tensile stresses in the fiber exceed a critical value. In addition to interfacial sliding, residual stresses influence the conditions for deflection and/or penetration shown in Figure 1. Compressive residual stresses in the reinforcement enhance conditions for deflection, shifting the contour 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