ournal J An. Ceram Soc, 80[121 2987-96(1997) Control of Interfacial Properties through Fiber Coatings Monazite Coatings in Oxide-Oxide Composites Dong-Hau Kuo and Waltraud M. Kriven Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana. Illinois 61801 Thomas J Mackin Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana. Illinois 61801 Fiber pushout tests were used to quantify the effects of fiber temperature strength and creep resistance, in comparison with oating thickness on the mechanical properties of two other oxide fibers. This fiber is the only oxide fiber with sub- model composite systems: a monazite-coated (LaPO4 stantial creep resistance at temperatures >1600 C 9, 10 To sus- oated) alumina(Al,O3)fiber in an Al,O3 matrix and a tain the concept of an all-oxide system, a weak oxide inter- LaPOr-coated yttrium aluminum garnet(YAG) fiber in an phase is required for strong, tough, and high-temperature AlO3 matrix. Interface properties were quantified using oxidation-resistant fiber composites. A promising, new high he Liang and Hutchinson(LH) pushout model and mecha- temperature fiber-coating material (monazite, LapO4)was re- nistically rationalized by considering the change in residual cently developed by Morgan and coworkers. 1-13 The LaPO hermal stresses with changes in the coating thickness. coating material presents the opportunity of producing a hi Measures of the pure Mode ll interfacial fracture energy, temperature oxide-constituent composite with an inhere he coefficient of friction, and a radial clamping pressure weak interfa re extracted by fitting the lh equations to the experimen Fiber pushout testing has been widely used to quantify in- tal results. Using the approach that has been developed terfacial properties in composites. - Pushout testing affords herein, a methodology is available for measuring the inter- a simple screening test for model composite systems and al- facial properties, predicting the effect of coating thickness, lows the calculation of the key interface properties, which in- and selecting the coating thickness to alter the interfacial clude the following: th e intera ace fracture energy, T the co- properties efficient of sliding friction, u; and the radial clamping pressure at the interface, clamping. Theoretical models8-22 that incor . Introduction porate the elastic properties of the fiber-matrix system have been developed to explain the results of pushout tests and HE fiber/matrix interface is the key to improving the me. quantify the relevant interface properties. Although a modified chanical performance of continuous-fiber-reinforced ce- model is needed for a three-component system(i.e, one whick ramic-matrix composites(CFCCs) I-s A strong interface re- consists of the fiber, the coating, and the matrix),reasonable interfacial debonding and subsequent fiber pullout In genera estimates of the interfacial properties can be made by using the ults in little toughening, whereas a weak interface existing models several fac In this study, fiber pushout tests were used to measure tors, which include the availability of ceramic fibers and the interfacial properties of two model composite systems ( alu- need for thermal and chemical stability among the constituents The choice of constituents is broadened by using a coating stem), and (ii)YAG fiber/LaPO4 coating/Al2 O3 matrix stem that assures chemical stability and, at the same time, AG fiber system). The effect of the LapO4 coating thickness promotes easy debonding. In addition to controlling the inter- face properties, fiber coatings protect fibers from mechanical mens with fiber coatings that varied in thickness from 2 un 24 um. Residual thermal stresses were calculated by the bead- Carbon and boron nitride(bn) are the most commonly used seal solution2, 24 and were used to explain the effect of coating thickness on the interfacial properties. Liang and Hutchin- oxidize in high-temperature environments. Extensive research son's2(LH)model of the fiber pushout test was used to quan- has been undertaken to address these problems. 6-8 Natural tify and rationalize the experimental results an oxide fiber in an oxide matrix circumvents the problem of high-temperature oxidation Single-crystal yttrium aluminum II. Experimental Procedures garnate(YAG, Y3AlsO,2)fibers have shown superior high- (I Sample preparation Model composite systems were fabricated by dip coatin fibers, placing them into a powder compact, and sintering D. K. Shetty--contributing editor them. A LapOa slurry was prepared by ball milling a mixture of LapO, powder(70 wt%), ethanol (27 wt%), and poly(viny butyral)(3 wt%). Continuous single-crystal Al, O,(diameter of Manuscript No. 192227 August 5, 1996, approved April 13, 1997 and YaG (diameter of-160 um) fibers(Saphikon, carch through Dr. A. Milford, NH)were cut, cleaned, and dip coated with the LaPo Pechenik under Grant No slurry. Different coating thicknesses were obtained by repeate letting of the American Ceramic Society, In fiber dipping. To ensure a uniform coating thickness, a quick- drying ethanol-based solution was used. Dip coating was e 2987
Control of Interfacial Properties through Fiber Coatings: Monazite Coatings in Oxide–Oxide Composites Dong-Hau Kuo* and Waltraud M. Kriven* Department of Materials Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801 Thomas J. Mackin* Department of Mechanical and Industrial Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801 Fiber pushout tests were used to quantify the effects of fiber coating thickness on the mechanical properties of two model composite systems: a monazite-coated (LaPO4- coated) alumina (Al2O3) fiber in an Al2O3 matrix and a LaPO4-coated yttrium aluminum garnet (YAG) fiber in an Al2O3 matrix. Interface properties were quantified using the Liang and Hutchinson (LH) pushout model and mechanistically rationalized by considering the change in residual thermal stresses with changes in the coating thickness. Measures of the pure Mode II interfacial fracture energy, the coefficient of friction, and a radial clamping pressure are extracted by fitting the LH equations to the experimental results. Using the approach that has been developed herein, a methodology is available for measuring the interfacial properties, predicting the effect of coating thickness, and selecting the coating thickness to alter the interfacial properties. I. Introduction THE fiber/matrix interface is the key to improving the mechanical performance of continuous-fiber-reinforced ceramic-matrix composites (CFCCs).1–5 A strong interface results in little toughening, whereas a weak interface promotes interfacial debonding and subsequent fiber pullout. In general, the choice of a fiber–matrix system is limited by several factors, which include the availability of ceramic fibers and the need for thermal and chemical stability among the constituents. The choice of constituents is broadened by using a coating system that assures chemical stability and, at the same time, promotes easy debonding. In addition to controlling the interface properties, fiber coatings protect fibers from mechanical damage during handling and processing.2 Carbon and boron nitride (BN) are the most commonly used interfacial coatings in CFCCs. However, these coatings readily oxidize in high-temperature environments. Extensive research has been undertaken to address these problems.6–8 Naturally, an oxide fiber in an oxide matrix circumvents the problem of high-temperature oxidation. Single-crystal yttrium aluminum garnate (YAG, Y3Al5O12) fibers have shown superior hightemperature strength and creep resistance, in comparison with other oxide fibers. This fiber is the only oxide fiber with substantial creep resistance at temperatures >1600°C.9,10 To sustain the concept of an all-oxide system, a weak oxide interphase is required for strong, tough, and high-temperature oxidation-resistant fiber composites. A promising, new hightemperature fiber-coating material (monazite, LaPO4) was recently developed by Morgan and coworkers.11–13 The LaPO4 coating material presents the opportunity of producing a hightemperature oxide-constituent composite with an inherently weak interface. Fiber pushout testing has been widely used to quantify interfacial properties in composites.14–17 Pushout testing affords a simple screening test for model composite systems and allows the calculation of the key interface properties, which include the following: the interface fracture energy, Gi ; the coefficient of sliding friction, m; and the radial clamping pressure at the interface, sclamping. Theoretical models18–22 that incorporate the elastic properties of the fiber–matrix system have been developed to explain the results of pushout tests and quantify the relevant interface properties. Although a modified model is needed for a three-component system (i.e., one which consists of the fiber, the coating, and the matrix), reasonable estimates of the interfacial properties can be made by using the existing models. In this study, fiber pushout tests were used to measure the interfacial properties of two model composite systems: (i) alumina (Al2O3) fiber/LaPO4 coating/Al2O3 matrix (Al2O3 fiber system), and (ii) YAG fiber/LaPO4 coating/Al2O3 matrix (YAG fiber system). The effect of the LaPO4 coating thickness on the interfacial properties was evaluated by fabricating specimens with fiber coatings that varied in thickness from 2 mm to 24 mm. Residual thermal stresses were calculated by the beadseal solution23,24 and were used to explain the effect of coating thickness on the interfacial properties. Liang and Hutchinson’s20 (LH) model of the fiber pushout test was used to quantify and rationalize the experimental results. II. Experimental Procedures (1) Sample Preparation Model composite systems were fabricated by dip coating fibers, placing them into a powder compact, and sintering them. A LaPO4 slurry was prepared by ball milling a mixture of LaPO4 powder (70 wt%), ethanol (27 wt%), and poly(vinyl butyral) (3 wt%). Continuous single-crystal Al2O3 (diameter of ∼140 mm) and YAG (diameter of ∼160 mm) fibers (Saphikon, Milford, NH) were cut, cleaned, and dip coated with the LaPO4 slurry. Different coating thicknesses were obtained by repeated fiber dipping. To ensure a uniform coating thickness, a quickdrying ethanol-based solution was used. Dip coating was exD. K. Shetty—contributing editor Manuscript No. 192227. Received August 5, 1996; approved April 13, 1997. Supported by the U.S. Air Force Office of Scientific Research through Dr. A. Pechenik under Grant No. AFOSR-F49620-93-1-0027. Presented at the 98th Annual Meeting of the American Ceramic Society, Indianapolis, IN, April 14–17, 1996. *Member, American Ceramic Society. J. Am. Ceram. Soc., 80 [12] 2987–96 (1997) Journal 2987
2988 Journal of the American Ceramic Socieny'Kuo et al Vol. 80. No. 12 ecuted by dipping one fiber end and then the other in an alter- posite processing temperature to a temperature of -1000C nating manner. The coating thickness was measured from after which a temperature difference, AT, of -1000oC would lished sections of sintered samples and was uniform to develop the room-temperature thermoelastic residual ithin +20%. Two important procedures, which included fiber stresses.29 The material properties that were used in the re- sitioning within the matrix and pellet sintering, were crucial sidual-stress calculations(Youngs modulus(E), Poissons ra- to subsequent pushout testing. If the slices for fiber pushor tio(v), and the coefficient of thermal expansion, a) for both tests were not cut perpendicular to the fiber alignment, the composite systems are listed in Table I. Using these properties, misaligned fibers exhibited higher pushout resistance and af- the residual axial and radial stresses at the fiber/coating inter fected the subsequent data interpretation. In this study, five face were calculated as a function of the coating thickness(Fig oated fibers were aligned parallel to each other. To aid in fiber 1). A residual tensile axial stress was found in both composite alignment, SCS-8 fibers(Textron Specialty Materials, Lowell systems. The residual axial stress increased as the coating MA)were used as markers in the composite. These marker hickness increased in the Al2O3 fiber system; however, it de fibers were cut so that both ends were exposed after sintering creased as the coating thickness increased in the YAG fiber These exposed marker fibers revealed the relative orientation system(Fig. I(a)). A radial compressive stress that decreased of the coated fibers and greatly facilitated subsequent sample as the coating thickness increased was calculated for the Al, O3 slice cutting. As a result, the marker fibers aided fiber align- fiber system, whereas a small increase in radial tensile stress ment and positioning(before sintering)and subsequent cutting was determined for the YAG fiber system(Fig. 1(b). These of thin slices for pushout tests(after sintering) stresses had an effect on the interfacial debonding and sliding Several different matrix powders were used to fabricate the properties for each composite system, as will be demonstrated dense model specimens. Initially, an Al2O3 powder(Al6-SG, in the following sections Alcoa Aluminum Co., Pittsburgh, PA)was used, which re- uired a sintering temperature of 1600c to densify the speci- (2) Fiber Pushout Curves mens. Fiber damage that was similar to that which was ob Representative pushout curves for both AlO, and YAG fi- served by Newcomb and Tressler was noted after only 3 h at ber systems are shown in Fig. 2. These data exhibit features catey perature of 1600 C. A second set of samples was fabri that are typical of fiber pushout: the initial linear load- using a high-surface-area Al,O3 powder(75-90 m/g, as followed by a nonlinear region that Praxair Surface Technologies, Indianapolis, IN). However, was associated with progressive debonding along the interfa rge amount of sintering shrinkage and specimen bending w Debonding continued until the crack attained a critical length oted after sintering at a temperature of 1550%C, which resulted bimodal patrick s uscg derable sample distortion. Finally, a Unstable crack growth appears as a sharp load decrease in the in broken fibers and cons 40- 60 mixture of high oad-displacement curve. After complete interfacial debond- which resulted in a powder that had ng, the fiber experienced frictional sliding throughout the re- on Using the resulting bimoda mainder of the pushout test. powder, dense pellets were formed at 1550C with a moderate During frictional sliding, fibers from both systems slid at amount of sintering shrinkage, and there was no visible fiber onstant or slightly increasing loads over -20 um of damage after observation by scanning electron microscopy displacement(Fig. 2). The peak load just prior to (SEM)(Model DS-130, International Scientific Instruments fiber bonding, Pp, and the pushout load just after debonding, P,(lower case P indicates load), are identified in (2) Pushout Test Procedure Fig. 2. Representative micrographs of each pushed-out fiber are shown in Fig. 3. These micrographs indicate that debonding After sintering, pushout samples were prepared by making occurred at the fiber/coating interface for both the Yag and the slices perpendicular to the fiber orientation. Test slices were fabricated that had thicknesses in the range of 0.4-1.2 mm system(Fig 3(b) appears qualitatively rougher than that of the which provided a range of embedded fiber lengths. Following Al2 O, fiber system(Fig. 3(a). This roughness, which in- the slicing, the samples were ground and polished to a final creased the fiber sliding resistance, was responsible for the screw-driven testing machine with a I kg load cell(Model out of the YAG fibers(Fig. 2). 15,16 uring the frictional push- finish of I Am. Fiber pushout tests were conducted using a increasing load that was experienced 4502, Instron Corp, Canton, MA). A diamond probe that had Five pushout tests were conducted for each coating a 95-]m-diameter flat tip was fixed onto a cylinder that was over a broad range of specimen thicknesses. Average threaded to the load cell. Pushout specimens were aligned over loads (Pp) were measured as a function of the embedded a slotted Al2 O3 substrate. Two micropositioning, stages-one length(L)for both the Al2O3 and the YAG fiber systems(Fig for a stereomicroscope and the other for the specimen stag ) In addition, pushout experiments were conducted using a were used to align the test fiber and the diamond punch. 4, 17 range of coating thicknesses. The pushout load varied with the Testing was conducted using a constant crosshead speed of 60 coating thickness in both composite systems(Fig. 5) Although it is common to assess the interface strengt for each slice thickness, coating thickness, and fiber system lag approach, this method assumes an instanta Average values of the key pushout parameters were used for along the entire length of the fiber. Mechanisti- obsequent sample comparison. In addition to mechanical char- debonding is progressive rather than instanta- acterization, SEM was used to evaluate the material micro- Residual axial and radial stresses are known to influent also is ing and sliding of fibers from a matrix. 19, 20 The coating Table I. Properties of Fibers, Matrix, and Coating Youngs modulus, Poissons the ffects26-8 In this study, an elastic shrink-fit calculation known as the bead-seal solution, 23, 24 has been used to estimate the residual thermal stresses in the model systems A2。3 sapphire 430(a),465(c)0.258.3(a),9.0(c) 3A 8.9 ApOA 0.275 ( Residual-Stress Calculation AlO, matrix 380 It was assumed that complete stress relaxation by creep pro- Al,O3, cesses occurred when the system was cooled from the com thasarathy. I Data from morgan and marshal. s"e and a data from kingery et a/. 2
ecuted by dipping one fiber end and then the other in an alternating manner. The coating thickness was measured from polished sections of sintered samples and was uniform to within ±20%. Two important procedures, which included fiber positioning within the matrix and pellet sintering, were crucial to subsequent pushout testing. If the slices for fiber pushout tests were not cut perpendicular to the fiber alignment, the misaligned fibers exhibited higher pushout resistance and affected the subsequent data interpretation. In this study, five coated fibers were aligned parallel to each other. To aid in fiber alignment, SCS-8 fibers (Textron Specialty Materials, Lowell, MA) were used as markers in the composite. These marker fibers were cut so that both ends were exposed after sintering. These exposed marker fibers revealed the relative orientation of the coated fibers and greatly facilitated subsequent sample slice cutting. As a result, the marker fibers aided fiber alignment and positioning (before sintering) and subsequent cutting of thin slices for pushout tests (after sintering). Several different matrix powders were used to fabricate the dense model specimens. Initially, an Al2O3 powder (A16-SG, Alcoa Aluminum Co., Pittsburgh, PA) was used, which required a sintering temperature of 1600°C to densify the specimens. Fiber damage that was similar to that which was observed by Newcomb and Tressler25 was noted after only 3 h at a temperature of 1600°C. A second set of samples was fabricated using a high-surface-area Al2O3 powder (75–90 m2 /g, Praxair Surface Technologies, Indianapolis, IN). However, a large amount of sintering shrinkage and specimen bending was noted after sintering at a temperature of 1550°C, which resulted in broken fibers and considerable sample distortion. Finally, a 40:60 mixture of high-surface-area powder and the A16-SG Al2O3 powder was used, which resulted in a powder that had bimodal particle-size distribution. Using the resulting bimodal powder, dense pellets were formed at 1550°C with a moderate amount of sintering shrinkage, and there was no visible fiber damage after observation by scanning electron microscopy (SEM) (Model DS-130, International Scientific Instruments, Santa Clara, CA). (2) Pushout Test Procedure After sintering, pushout samples were prepared by making slices perpendicular to the fiber orientation. Test slices were fabricated that had thicknesses in the range of 0.4–1.2 mm, which provided a range of embedded fiber lengths. Following the slicing, the samples were ground and polished to a final finish of 1 mm. Fiber pushout tests were conducted using a screw-driven testing machine with a 1 kg load cell (Model 4502, Instron Corp., Canton, MA). A diamond probe that had a 95-mm-diameter flat tip was fixed onto a cylinder that was threaded to the load cell. Pushout specimens were aligned over a slotted Al2O3 substrate. Two micropositioning stages—one for a stereomicroscope and the other for the specimen stage— were used to align the test fiber and the diamond punch.14,17 Testing was conducted using a constant crosshead speed of 60 mm/min. A minimum of four pushout tests were conducted for each slice thickness, coating thickness, and fiber system. Average values of the key pushout parameters were used for subsequent sample comparison. In addition to mechanical characterization, SEM was used to evaluate the material microstructures. Residual axial and radial stresses are known to influence the debonding and sliding of fibers from a matrix.19,20 The coating also is known to have an important role in mitigating these effects.26–28 In this study, an elastic shrink-fit calculation, known as the bead-seal solution,23,24 has been used to estimate the residual thermal stresses in the model systems. III. Results (1) Residual-Stress Calculation It was assumed that complete stress relaxation by creep processes occurred when the system was cooled from the composite processing temperature to a temperature of ∼1000°C, after which a temperature difference, DT, of ∼1000°C would develop the room-temperature thermoelastic residual stresses.29 The material properties that were used in the residual-stress calculations (Young’s modulus (E), Poisson’s ratio (n), and the coefficient of thermal expansion, a) for both composite systems are listed in Table I. Using these properties, the residual axial and radial stresses at the fiber/coating interface were calculated as a function of the coating thickness (Fig. 1). A residual tensile axial stress was found in both composite systems. The residual axial stress increased as the coating thickness increased in the Al2O3 fiber system; however, it decreased as the coating thickness increased in the YAG fiber system (Fig. 1(a)). A radial compressive stress that decreased as the coating thickness increased was calculated for the Al2O3 fiber system, whereas a small increase in radial tensile stress was determined for the YAG fiber system (Fig. 1(b)). These stresses had an effect on the interfacial debonding and sliding properties for each composite system, as will be demonstrated in the following sections. (2) Fiber Pushout Curves Representative pushout curves for both Al2O3 and YAG fiber systems are shown in Fig. 2. These data exhibit features that are typical of fiber pushout: the initial linear load– displacement region was followed by a nonlinear region that was associated with progressive debonding along the interface. Debonding continued until the crack attained a critical length and propagated unstably to complete interfacial debonding.20 Unstable crack growth appears as a sharp load decrease in the load–displacement curve. After complete interfacial debonding, the fiber experienced frictional sliding throughout the remainder of the pushout test. During frictional sliding, fibers from both systems slid at constant or slightly increasing loads over ∼20 mm of pushout displacement (Fig. 2). The peak load just prior to complete fiber bonding, pP, and the pushout load just after complete debonding, p1 (lower case P indicates load), are identified in Fig. 2. Representative micrographs of each pushed-out fiber are shown in Fig. 3. These micrographs indicate that debonding occurred at the fiber/coating interface for both the YAG and the Al2O3 fiber systems. The debond interface of the YAG fiber system (Fig. 3(b)) appears qualitatively rougher than that of the Al2O3 fiber system (Fig. 3(a)). This roughness, which increased the fiber sliding resistance, was responsible for the increasing load that was experienced during the frictional pushout of the YAG fibers (Fig. 2).15,16 Five pushout tests were conducted for each coating system over a broad range of specimen thicknesses. Average peak loads (pP) were measured as a function of the embedded fiber length (L) for both the Al2O3 and the YAG fiber systems (Fig. 4). In addition, pushout experiments were conducted using a range of coating thicknesses. The pushout load varied with the coating thickness in both composite systems (Fig. 5). Although it is common to assess the interface ‘‘strength’’ using a shear-lag approach, this method assumes an instantaneous debond along the entire length of the fiber. Mechanistically, however, debonding is progressive rather than instantaTable I. Properties of Fibers, Matrix, and Coating Material Young’s modulus, E (GPa) Poisson’s ratio, n Coefficient of thermal expansion, a (10−6/°C) Al2O3 (sapphire) fiber† 430 (a), 465 (c) 0.25 8.3 (a), 9.0 (c) Y3Al5O12 (YAG) fiber‡ 283 0.25 8.9 LaPO4 coating§ 133 0.275 9.6 Al2O3 matrix¶ 380 0.25 8.8 † For Al2O3, data in the a and c directions are given. E data are from Li and Bradt;30 n and a data are from the manufacturer (Saphikon, Milford, NH). ‡ Data from Parthasarathy.31 §Data from Morgan and Marshall.13 ¶E and a data from Kingery et al.32 2988 Journal of the American Ceramic Society—Kuo et al. Vol. 80, No. 12
December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2989 TTTT AlO fiber system YAG fiber syste Coating Thickness, t(um) 60 40 YAG fiber system LL ⊥, Coating Thickness, t(um) Fig 1. Calculated residual stress distribution as a function of coating thickness for the(---)Al,O, and (---)YAG fiber systems(a)axial stress in the fiber and(b)radial stress acting across the fiber/coating interface Al O, Fiber/ Lapo Coating/Al O, Matrix Average Coating Thickness: 6.5 um Embedded Fiber Length: 0.6 mm Crosshead Displacement (um 50 P YAG Fiber/IaPO, Coaling /Al O, Matrix verage Coating Thickness: 2 pm Embedded Fiber Length: 0.7 m Crosshead Displacement (um Fig. 2. Typical pushout curves for(a)the AlO, fiber system and (b)the YAG fiber system
Fig. 1. Calculated residual stress distribution as a function of coating thickness for the (– – –) Al2O3 and (– - –) YAG fiber systems ((a) axial stress in the fiber and (b) radial stress acting across the fiber/coating interface). Fig. 2. Typical pushout curves for (a) the Al2O3 fiber system and (b) the YAG fiber system. December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2989
2990 Journal of the American Ceramic Sociery-Kuo et al. Vol. 80. No. 12 approach that has been taken is to use the shrink-fit calculated residual stresses as inputs for the Liang and Hutchinson 20 push- ut model(hereafter refe The detailed mechanics of fiber debonding and sliding can best be by considering the LH model. Although the Hutchinson20 considered only phase system that consisted of fiber and matrix, their analysis can still be used to provide a qualitat ment of the effect of coating thickness on the pushout response of individual fibers. Two key equations are presented in the Lh model:(i) the load-displacement equation for a partially debonded fiber and (ii) the load-displacement equation for a In the first case, the peak stress that is experienced just before complete fiber debonding occurs, Pp(uppercase italic P indicates stress), is given as2o Po=Pp+ T Er To+μNg (b) where PR is the axial residual stress(negative for tension), To the roughness-induced(asperit )sliding stress, NR the adial residual stress, H the co interface, T; the pure Mode Il fracture energy, R the fiber radius, and E the elastic modulus of the fiber; B, and B2 are elastic properties of the composite. The term c* is given by R e where L is the thickness of the slice In this study, the calculation of elastic properties B, and B was based on the assumption of a transversely isotropic fiber and an isotropic matrix for the Al2O3 fiber system. B, and B2 were formulated following Liang and Hutchinson:26 Fig. 3. SEM micrographs of pushed-out fibers from(a) the Al,O fiber system and (b)the YAG fiber system B2 2v B, where the superscript r represents the transverse direction useful for providing a qualitative and general assessment of the assumption of an isotropic fiber(a cubic single-crystal YAG B, and B2 were formulated following Liang and Hutchinson ful measure of the interface properties. a detailed mechanistic understanding can be obtained only by using more-detailed pushout models, such as those of Liang and Hutchinson20or B1=(1-vEm+1+)E Kerans and Parthasarathay. 9 Such an approach is presented in the following sections 3) The Liang and Hutchinson Model of Fiber Pushout (3b It is postulated herein that the key effect that is associated Notably, the commonly used interfacial shear strength uses the with the coating thickness is the effect on the residual stress peak stress of the LH equation to define an instantaneous state of the model composite systems. This postulate is based debond propagation down the entire length of the fiber/matrix on the microstructural evaluation of the interfacial debonds interface. Thus, the interfacial shear strength disregards the Typical micrographs of the pushed-out fibers show that the detailed interfacial mechanics and determines an average in- debond, in all cases, is at the coating/fiber interface(Fig. 3) terfacial shear strength to quantify interfacial debonding. As a The coating is dense and almost uniform for different coating result, the interfacial shear strength parameter does not mecha- thicknesses. As a result, the debonding and sliding interfaces nistically capture the details of progressive debonding and does are the same, regardless of the coating thickness. Because the not separate the effects of the stress state from the debonding chemistry of the interphase does not change with changes in the properties coating thickness, it is reasonable to assume that the physical perties of the interface, which include the interfacial frac- qe Liang and Hutchinson20 presented an additional equation to cribe the frictional sliding stress that follows complete in- ture energy Ti the coefficient of sliding friction u, and the terfacial debonding. The frictional pushout stress, P, is giv- interface roughness, remain constant as the coating thickness en by hanges. Thus, any differences in the mechanical properties of the interface that are associated with changes in the coating thickness are due to a change in the local stress state. The =|+μ(NR-B1PR) μB1
neous. Therefore, although the linear and shear-lag models are useful for providing a qualitative and general assessment of the interface, these methods do not provide an accurate or insightful measure of the interface properties. A detailed mechanistic understanding can be obtained only by using more-detailed pushout models, such as those of Liang and Hutchinson20 or Kerans and Parthasarathay.19 Such an approach is presented in the following sections. (3) The Liang and Hutchinson Model of Fiber Pushout It is postulated herein that the key effect that is associated with the coating thickness is the effect on the residual stress state of the model composite systems. This postulate is based on the microstructural evaluation of the interfacial debonds. Typical micrographs of the pushed-out fibers show that the debond, in all cases, is at the coating/fiber interface (Fig. 3). The coating is dense and almost uniform for different coating thicknesses. As a result, the debonding and sliding interfaces are the same, regardless of the coating thickness. Because the chemistry of the interphase does not change with changes in the coating thickness, it is reasonable to assume that the physical properties of the interface, which include the interfacial fracture energy Gi , the coefficient of sliding friction m, and the interface roughness, remain constant as the coating thickness changes. Thus, any differences in the mechanical properties of the interface that are associated with changes in the coating thickness are due to a change in the local stress state. The approach that has been taken is to use the shrink-fit calculated residual stresses as inputs for the Liang and Hutchinson20 pushout model (hereafter referenced as the LH model). The detailed mechanics of fiber debonding and sliding can best be explained by considering the LH model. Although the analysis of Liang and Hutchinson20 considered only a twophase system that consisted of fiber and matrix, their analysis can still be used to provide a qualitative and rational assessment of the effect of coating thickness on the pushout response of individual fibers. Two key equations are presented in the LH model: (i) the load–displacement equation for a partially debonded fiber and (ii) the load–displacement equation for a completely debonded fiber. In the first case, the peak stress that is experienced just before complete fiber debonding occurs, PP (uppercase italic P indicates stress), is given as20 PP = PR + 2S Gi Ef B2Rf D 1/2 exp z* + t0 + mNR mB1 ~exp z* − 1! (1) where PR is the axial residual stress (negative for tension), t0 the roughness-induced (asperity-induced) sliding stress, NR the radial residual stress, m the coefficient of friction at the sliding interface, Gi the pure Mode II interfacial fracture energy, Rf the fiber radius, and Ef the elastic modulus of the fiber; B1 and B2 are elastic properties of the composite. The term z* is given by z* = 2mB1S L − 1.5Rf Rf D where L is the thickness of the slice. In this study, the calculation of elastic properties B1 and B2 was based on the assumption of a transversely isotropic fiber and an istotropic matrix for the Al2O3 fiber system. B1 and B2 were formulated following Liang and Hutchinson:20 B1 = nf Em r ~1 − nf r !~Ef/Ef r !Em r + ~1 + nm r !Ef (2a) and B2 4 1−2nf B1 (2b) where the superscript r represents the transverse direction. For the YAG fiber system, B1 and B2 were based on the assumption of an isotropic fiber (a cubic single-crystal YAG fiber) and an isotropic matrix (a polycrystalline Al2O3). Again, B1 and B2 were formulated following Liang and Hutchinson:20 B1 = nfEm ~1 − nf!Em + ~1 + nm! Ef (3a) and B2 4 1−2nf B1 (3b) Notably, the commonly used interfacial shear strength uses the peak stress of the LH equation to define an instantaneous debond propagation down the entire length of the fiber/matrix interface. Thus, the interfacial shear strength disregards the detailed interfacial mechanics and determines an average interfacial shear strength to quantify interfacial debonding. As a result, the interfacial shear strength parameter does not mechanistically capture the details of progressive debonding and does not separate the effects of the stress state from the debonding properties. Liang and Hutchinson20 presented an additional equation to describe the frictional sliding stress that follows complete interfacial debonding. The frictional pushout stress, Pl , is given by P1 = F t0 + m~NR − B1PR! mB1 G~exp zd − 1! (4) Fig. 3. SEM micrographs of pushed-out fibers from (a) the Al2O3 fiber system and (b) the YAG fiber system. 2990 Journal of the American Ceramic Society—Kuo et al. Vol. 80, No. 12
December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings Alo, fiber/Lapo4 coating /Al, O, matrix Average Coating Thickness: 6.5 um Embedded Fiber Length, L (mm) 000 20 YAG fiber/ LaPO, coaling Average Coating Thickness: 2 um LLLLL Embedded Fiber Length, L(mm) Fig 4. Variation of the oad(Pp)during pushout as a function of the embedded fiber length(L) for(a)the Al,O, fiber system and(b)the YAG fiber system. The term sd is given by tion(u), and the roughness-induced sliding resistance (To)are 2μB1d the key factors that affect the maximum pushout stress, Pp tha is measured immediately before complete interfacial debond- ng occurs. For the composite systems that have been evaluated and d is the length of fiber that remains embedded in the in this study, it is postulated that Ti, u, and the fiber/coating interface roughness remain constant as the coating thickness Considering Eq.(1), the residual stresses(PR and NR, the changes. Thus, the key outcome of changing the interphase debonding fracture energy( the coefficient of interface fric hickness is the effect on the residual stresses and hence, on the ensuing debonding and sliding properties Using the LH model (Eqs. (1)and(4), it is clear that the magnitude of the applied stress that is required to initiate and propagate debonding and subsequent fiber sliding is dependent on the residual stress state. If the applied stress, Pp(positive), YAG fiber/Laro, coating/Al o, matrix and the residual axial stress, PR, generate shear stresses that act in the same direction, then PR assists debond crack propaga- Embedded Fiber Length, L=1.12 +0.03 mm tion. That is, an axial tensile stress(negative) in the fiber gen- erates an interfacial shear stress that has the same effect as that which is induced by the application of a pushout stress. With regard to the post-debond sliding stress(Eq.(4)), the effect of PR is negligible for several reasons: (i) the uB, PR term is small,(ii) the axial residual stress is being relieved during the sliding process e roug dominate the post-debond sliding The values Al, O, fiber/LalO, coating /AlO, matrix re shown in table ll Embedded Fiber length L-076+0.02 mm The residual radial stress across the interface, NR, also af fects fiber debonding and subsequent sliding. A compressiv ILLIL radial pressure of NR(positive in the Lh equations)increases the Coulombic frictional sliding resistance of the fib LaPo, Coating Thickness, t(um) the matrⅸx sets up an "effective"Mode II bridging stress behind the debond crack front during progressive interfacial Fig. 5. ation of the pl load with the thickness of the LaPO debond propagation. If the residual stress that acts across the Al,O,fiber-reinforced and(O)YAG-fiber-reinforced fiber/coating interface is tensile(negative), it reduces the ef fective roughness contribution by subtracting from To(Eq (4))
The term zd is given by zd = 2mB1d Rf and d is the length of fiber that remains embedded in the matrix. Considering Eq. (1), the residual stresses (PR and NR, the debonding fracture energy (Gi ), the coefficient of interface friction (m), and the roughness-induced sliding resistance (t0) are the key factors that affect the maximum pushout stress, PP, that is measured immediately before complete interfacial debonding occurs. For the composite systems that have been evaluated in this study, it is postulated that Gi , m, and the fiber/coating interface roughness remain constant as the coating thickness changes. Thus, the key outcome of changing the interphase thickness is the effect on the residual stresses and, hence, on the ensuing debonding and sliding properties. Using the LH model (Eqs. (1) and (4)), it is clear that the magnitude of the applied stress that is required to initiate and propagate debonding and subsequent fiber sliding is dependent on the residual stress state. If the applied stress, PP (positive), and the residual axial stress, PR, generate shear stresses that act in the same direction, then PR assists debond crack propagation. That is, an axial tensile stress (negative) in the fiber generates an interfacial shear stress that has the same effect as that which is induced by the application of a pushout stress. With regard to the post-debond sliding stress (Eq. (4)), the effect of PR is negligible for several reasons: (i) the mB1PR term is small, (ii) the axial residual stress is being relieved during the sliding process, and, finally (iii) the interface roughness term may dominate the post-debond sliding. The values of m and B1 are shown in Table II. The residual radial stress across the interface, NR, also affects fiber debonding and subsequent sliding. A compressive radial pressure of NR (positive in the LH equations) increases the Coulombic frictional sliding resistance of the fiber within the matrix. This sets up an ‘‘effective’’ Mode II bridging stress behind the debond crack front during progressive interfacial debond propagation. If the residual stress that acts across the fiber/coating interface is tensile (negative), it reduces the effective roughness contribution by subtracting from t0 (Eq. (4)). Fig. 5. Variation of the pushout load with the thickness of the LaPO4 coating in (d) Al2O3-fiber-reinforced and (s) YAG-fiber-reinforced systems. Fig. 4. Variation of the peak load ( pP) during pushout as a function of the embedded fiber length (L) for (a) the Al2O3 fiber system and (b) the YAG fiber system. December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2991
2992 Journal of the American Ceramic Sociefy-Kuo et al. Vol. 80. No. 12 Table IL. Parameters of Interfacial Properties (A, aclamping eters has been reduced to four by using the calculated pr value and T) Extracted from Curve-Fitting the LH Model to as an a-priori input to the LH equations. Further reduction in Pushout Data for Al,O3 and YAG Fiber Systems the number of parameters has been accomplished by noting that Pure Mode ll the asperity term, To. is mechanistically related to the asperity Coefficient of Clamping pressure, pressure, Asperity, through a Coulombic friction law (m) To- poa AL,, fiber system(B,=0.107 and B2=0.947) Thus, Eq (1)is reduced to a simplified form that is amer 0.27 to more-robust curve fitting: YAG fiber system(B,= 0.149 and B2=0.926) expl*一 BR BI 0.18 16.5 17.7 where o is equal to the sum Nr and all the other terms remain as defined in Eq.(1 ex Although Eq (6)reduced the number of adjustable param- to three T In effect, the interface may separate from the fiber and thereby quite sensitive to the initial settings of the parameters. To re- lessen the absolute magnitude of the roughness-induced clamp- duce the number of parameters even further, a modified form Ing pressure of Eq (4)was used to fit the immediate post-debond pushout (4) Estimating T stress over a range of specimen thicknesses. Equation (4)was The LH model was used to fit the experimental pushout data which resulted in simplified by assuming a Coulombic asperity law(Eq(5)), both before and after complete interfacial debonding(Eqs. (1) and (4)). These fits were made by recording the peak debond B,PR stress(Pp)and the stress immediately following complete fiber P (exp 5a-D) debonding(P). Averages of five pushout tests were plotted B, functions of the specimen thickness and used as data for fitting Two parameters were extracted from curve-fitting Eq. (7)to the LH equations(Fig. 6). This process was repeated for each the sliding portion of the experimental data: H and o of several coating thicknesses The LH formulation has five key parameters that can be immediate pre-debond stress values, which resulted in an esti- extracted from fits to experimental data: Ti, PR, NR, To, and p. mate of T To do so, Eq. (7) was applied to experimental However, such a large number of parameters presents consid- results over a range of specimen thicknesses. values of u and erable difficulties in conducting reliable/repeatable curve fits to Clamping were then used in Eq (6)to fit experimental values of the experimental data. Thus, the number of adjustable param- Pp as a function of the specimen thickness. The results of the 40(a 3000 250 u-0.24 174 L1⊥⊥, 1.2 Embedded Fiber Length, L(mm) r18 3000 5从-0.27 Embedded Fiber Length, L(mm) Fig. 6. Variations of peak debond stress(O) just before complete debonding(Pp)and (O)sliding stress immediately following complete debonding(P) for the Al,O, fiber system, as a function of embedded fiber length(L)(coating thicknesses of(a)6.5 um and(b)16 um
In effect, the interface may separate from the fiber and thereby lessen the absolute magnitude of the roughness-induced clamping pressure. (4) Estimating Gi The LH model was used to fit the experimental pushout data both before and after complete interfacial debonding (Eqs. (1) and (4)). These fits were made by recording the peak debond stress (PP) and the stress immediately following complete fiber debonding (Pl ). Averages of five pushout tests were plotted as functions of the specimen thickness and used as data for fitting the LH equations (Fig. 6). This process was repeated for each of several coating thicknesses. The LH formulation has five key parameters that can be extracted from fits to experimental data: Gi , PR, NR, t0, and m. However, such a large number of parameters presents considerable difficulties in conducting reliable/repeatable curve fits to the experimental data. Thus, the number of adjustable parameters has been reduced to four by using the calculated PR value as an a-priori input to the LH equations. Further reduction in the number of parameters has been accomplished by noting that the asperity term, t0, is mechanistically related to the asperity pressure, sasperity, through a Coulombic friction law:33 t0 4 msasperity (5) Thus, Eq. (1) is reduced to a simplified form that is amenable to more-robust curve fitting: PP = PR + 2S Gi Ef B2Rf D 1/2 exp z* + sclamping B1 ~exp z* − 1! (6) where sclamping is equal to the sum sasperity + NR and all the other terms remain as defined in Eq. (1). Although Eq. (6) reduced the number of adjustable parameters to three (Gi , sclamping, and m), the curvefitting was still quite sensitive to the initial settings of the parameters. To reduce the number of parameters even further, a modified form of Eq. (4) was used to fit the immediate post-debond pushout stress over a range of specimen thicknesses. Equation (4) was simplified by assuming a Coulombic asperity law (Eq. (5)), which resulted in Pl = S sclamping − B1PR B1 D ~exp zd − 1! (7) Two parameters were extracted from curve-fitting Eq. (7) to the sliding portion of the experimental data: m and sclamping. The resulting parameters were then used in Eq. (6) to fit the immediate pre-debond stress values, which resulted in an estimate of Gi . To do so, Eq. (7) was applied to experimental results over a range of specimen thicknesses. Values of m and sclamping were then used in Eq. (6) to fit experimental values of PP as a function of the specimen thickness. The results of the Table II. Parameters of Interfacial Properties (µ, sclamping, and Gi ) Extracted from Curve-Fitting the LH Model to Pushout Data for Al2O3 and YAG Fiber Systems Coating thickness, t (mm) Coefficient of friction, m Clamping pressure, sclamping (MPa) Pure Mode II interfacial fracture energy, Gi (J/m2 ) Al2O3 fiber system (B1 4 0.107 and B2 4 0.947) 6.5 0.24 174 47 16 0.27 211 18 23.5 0.20 232 11 YAG fiber system (B1 4 0.149 and B2 4 0.926) 2 0.18 421 16.2 9 0.18 464 15.5 16.5 0.19 405 17.7 Fig. 6. Variations of peak debond stress (d) just before complete debonding (PP) and (s) sliding stress immediately following complete debonding (Pl ) for the Al2O3 fiber system, as a function of embedded fiber length (L) (coating thicknesses of (a) 6.5 mm and (b) 16 mm). 2992 Journal of the American Ceramic Society—Kuo et al. Vol. 80, No. 12
December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2993 experiments(Figs. 6 and 7)showed that, as the specimen thick- ing. The compressive radial stress, NR, is positive in Eq. (1)an ness increased, Pp and P, both increased. This trend is predicted increases the load that is required for debonding. As the coating by the modified LH equations(Eqs. (6)and(7). These modi- thickness increases in the Al2O3 fiber system, the tensile axial ed LH equations were used to fit the maximum stress, PP, and stress increases while the compressive radial stress decreases the sliding stress after complete debonding Ph, versus the spe Fig. 1). Using the LH model, both effects would predict a men thickness, t, as shown in Figs. 6 and 7 ecrease in the peak debond stress Pp with increasing coating Using the material properties that are shown in Table I, the thickness; this is in agreement with the trend that has beer elastic parameters B, and B2 were computed for the Al2O3 and observed experimentally(Fig. 5), where an increasing coating the YAG fiber systems(Eqs. (2)and (3). In these calculations, thickness has decreased the required pushout stress(plotted as the interphase was assumed to have no effect on these parar pushout load in Fig. 5 eters. Values of B, and B2 were estimated to be 0.107 and In addition to affecting the stress that is needed to propagate 0.947, respectively, for the Al2O, fiber system, and 0. 149 and a debond, the residual stresses also affect the frictional sliding 0.926, respectively, for the YAG fiber system. Using this ap- of the fiber following debonding. To facilitate discussion, ar h. values for l and H were estimated for each average value of the sliding stress is calculated using the rela system and each coating thickness (Table Il). If desired, tion T= P, /2mrL). The average sliding stress is plotted against can be separated into its components using the defi the coating thickness in Fig 8 and exhibits a constant value as nition of g and the elastic calculation of the residual the coating thickness changes. To understand the factors that radial clam affect frictional sliding, we again use the LH model. The tensile Using the lh equations, we obtained a detailed ch axial stress is predicted to have little effect on frictional sliding ization of the interface. As such. the effect of coating thicknes Eq (7). However, a decrease in the compressive radial stress on the pushout response could be mechanistically explained by with increasing coating thickness would be predicted to reduce applying the LH mode the frictional pushout stress(Eq.(7). Thus, the experiment observation of a constant sliding stress is not consistent with IV. Discussion his prediction and can occur only in one of two ways: (i)there is an increase in asperity pressure, To, with an increase in coat Interfacial properties of two oxide fiber/oxide matri kX mode ing thickness or(ii) To dominates the interfacial sliding me- ystems have been analyzed using fiber pushout testing. These chanics(this latter case is indeed the case with the YAG fiber properties are discussed below system, where the residual thermal clamping stress is tensile Debond nd Sliding in th yet the fiber still resists frictional pushout Al,O/LaPO,Al2O, Fiber System Interfacial fracture energies, Ti, were determined using the The AlO3 fiber system has been calculated to have a tensile procedure that has been outlined in the previous section. The residual axial stress in the fiber and a compressive residual fracture energy in the Al2O3 fiber system varied, from a valu radial stress across the sliding interface(Fig. 1). A tensile axial of 47 J/m2 at a coating thickness of 6.5 um to a value of 1l J/m2 for a large coating thickness of 23.5 um(Table Il). This stress appears as a negative PR value in Eq (I)and decreases result is contrary to the principal supposition that the Ti value would remain constant. However, a B-Al2O3 reaction product CTTTTTTTTTTTT l-16,2J/m 到 占2000 chanin=121 MPa 000 4000 55J/m2 l000 Embedded Fiber Length, L (mm) ig. 7. Variations of peak debond stress(e) just before complete debonding (Pp) and (O)sliding stress immediately following comple debonding(P) for YAG fiber system, as a function of embedded fiber length(L)(coating thicknesses of (a)2 um and( b)9 um)
experiments (Figs. 6 and 7) showed that, as the specimen thickness increased, PP and Pl both increased. This trend is predicted by the modified LH equations (Eqs. (6) and (7)). These modified LH equations were used to fit the maximum stress, PP, and the sliding stress after complete debonding Pl , versus the specimen thickness, t, as shown in Figs. 6 and 7. Using the material properties that are shown in Table I, the elastic parameters B1 and B2 were computed for the Al2O3 and the YAG fiber systems (Eqs. (2) and (3)). In these calculations, the interphase was assumed to have no effect on these parameters. Values of B1 and B2 were estimated to be 0.107 and 0.947, respectively, for the Al2O3 fiber system, and 0.149 and 0.926, respectively, for the YAG fiber system. Using this approach, values for Gi , sclamping, and m were estimated for each fiber system and each coating thickness (Table II). If desired, sclamping can be separated into its components using the definition of sclamping and the elastic calculation of the residual radial clamping stress. Using the LH equations, we obtained a detailed characterization of the interface. As such, the effect of coating thickness on the pushout response could be mechanistically explained by applying the LH model. IV. Discussion Interfacial properties of two oxide fiber/oxide matrix model systems have been analyzed using fiber pushout testing. These properties are discussed below. (1) Debonding and Sliding in the Al2O3 /LaPO4 /Al2O3 Fiber System The Al2O3 fiber system has been calculated to have a tensile residual axial stress in the fiber and a compressive residual radial stress across the sliding interface (Fig. 1). A tensile axial stress appears as a negative PR value in Eq. (1) and decreases the magnitude of the applied stress that is required for debonding. The compressive radial stress, NR, is positive in Eq. (1) and increases the load that is required for debonding. As the coating thickness increases in the Al2O3 fiber system, the tensile axial stress increases while the compressive radial stress decreases (Fig. 1). Using the LH model, both effects would predict a decrease in the peak debond stress PP with increasing coating thickness; this is in agreement with the trend that has been observed experimentally (Fig. 5), where an increasing coating thickness has decreased the required pushout stress (plotted as pushout load in Fig. 5). In addition to affecting the stress that is needed to propagate a debond, the residual stresses also affect the frictional sliding of the fiber following debonding. To facilitate discussion, an average value of the sliding stress is calculated using the relation t 4 p1/(2prL). The average sliding stress is plotted against the coating thickness in Fig. 8 and exhibits a constant value as the coating thickness changes. To understand the factors that affect frictional sliding, we again use the LH model. The tensile axial stress is predicted to have little effect on frictional sliding (Eq. (7)). However, a decrease in the compressive radial stress with increasing coating thickness would be predicted to reduce the frictional pushout stress (Eq. (7)). Thus, the experimental observation of a constant sliding stress is not consistent with this prediction and can occur only in one of two ways: (i) there is an increase in asperity pressure, t0, with an increase in coating thickness or (ii) t0 dominates the interfacial sliding mechanics (this latter case is indeed the case with the YAG fiber system, where the residual thermal clamping stress is tensile yet the fiber still resists frictional pushout). Interfacial fracture energies, Gi , were determined using the procedure that has been outlined in the previous section. The fracture energy in the Al2O3 fiber system varied, from a value of 47 J/m2 at a coating thickness of 6.5 mm to a value of 11 J/m2 for a large coating thickness of 23.5 mm (Table II). This result is contrary to the principal supposition that the Gi value would remain constant. However, a b-Al2O3 reaction product Fig. 7. Variations of peak debond stress (d) just before complete debonding (PP) and (s) sliding stress immediately following complete debonding (Pl ) for YAG fiber system, as a function of embedded fiber length (L) (coating thicknesses of (a) 2 mm and (b) 9 mm). December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2993
Journal of the American Ceramic Sociery-Kuo et al. Vol. 80. No. 12 ∽05苏品 20 LL1,11L,L1I1111 Lapo Coating Thickness (um ig. 8. Variation of average sliding stress as a function of interfacial coating thickness for(O)the Al2O, and (O)the YAG fiber systems (LaAl1O18)2,34 was observed at both the fiber and the matrix length and 1-2 um in width. Some porosity existed at the sides of the (Fig 9(a)). The reaction product was thin reaction layer; however, the specimen was dense elsewhere with elongated ix at the fiber side but formed elongated This LaAl, O1s reaction product affected the residual stress, I um) and saigo at the mat ide. This B-Al2O3 layer was -8 um thick the interfacial bonding at both sides of the coating, and the grains that had dimensions of 10-15 um subsequent debond crack propagation. Additionally, the forma- tion of a reaction product occurred at the expense of the Al2O3 fiber and is expected to have an effect on the in-situ strength (a statistics of the Al2O, fibers. 35 In this study, this reaction prod- uct at the coating/matrix interface penetrated to a constant depth for each coating thickness, thereby representing a larger volume fraction at a small coating thickness. It is postulated that the high r values that are calculated for thinner coatings are due to some amount of debond crack propagation along the LaPO,/LaAl,Oug interface For a thin coating thickness, the crack might wander to each side of the coating, which would result in crack jumping. " Similar crack propagation has been noted in the four-point flexure tests that were conducted by Morgan and Marshall.13 Such a crack-propagation mechanism LaAlo is expected to increase the Ti value. As the coating thickness increases. the debond crack is confined to the interface that is nearest the fiber, which results in a distinctly different crack propagation path (2) Debonding and Sliding in the YAGlLaPO,/Al,O, Fiber System The residual stresses for the Y AG fiber system are shown in Fig. 1, which illustrates that both the axial (PR)and radial (NR) stresses are tensile. The axial residual stress decreases as the coating thickness increases, the effect of which would increase the required peak pushout stress. The radial tensile stress was small and increases only slightly as the coating thickness in- ceases, the result of which would be only a slight decrease in he peak pushout stress. Combining these effects, the stress that is required to debond the fiber should increase slightly as the coating thickness increases. This trend is illustrated by the experimental results that are summarized in Fig. 5. In regard to the radial tensile stress, such a stress would effectively recoil o Thus, the YAG fiber system must generate sliding resistance face. The high asperity value in the YAG fiber system is a factor of -2-4 greater than that for the AlO, fiber system and is postulated to result entirely from surface-roughness effects ( Fig. 3). For this reason, the sliding resistance after debonding is not a strong function of the residual stresses for the yag fiber system; i.e., the sliding resistance was not strongly de- Fig 9. SEM mi of the interface region for(a) the Al,O endent on the coating thickness. This behavior is observed product at the f oating interface) and experimentally, where the average sliding stress(p/(2TrL)), as (b)the YAG fiber reactio t is obvious at the a function of the coating thickness, is plotted in Fig.8 and coating/matrix interface for both fiber systems exhibits a constant sliding stress at all coating thicknesses
(LaAl11O18) 12,34 was observed at both the fiber and the matrix sides of the coating (Fig. 9(a)). The reaction product was thin (1 mm) and uniform at the fiber side but formed elongated grains at the matrix side. This b-Al2O3 layer was ∼8 mm thick with elongated grains that had dimensions of 10–15 mm in length and 1–2 mm in width. Some porosity existed at the reaction layer; however, the specimen was dense elsewhere. This LaAl11O18 reaction product affected the residual stress, the interfacial bonding at both sides of the coating, and the subsequent debond crack propagation. Additionally, the formation of a reaction product occurred at the expense of the Al2O3 fiber and is expected to have an effect on the in-situ strength statistics of the Al2O3 fibers.35 In this study, this reaction product at the coating/matrix interface penetrated to a constant depth for each coating thickness, thereby representing a larger volume fraction at a small coating thickness. It is postulated that the high Gi values that are calculated for thinner coatings are due to some amount of debond crack propagation along the LaPO4/LaAl11O18 interface. For a thin coating thickness, the crack might wander to each side of the coating, which would result in ‘‘crack jumping.’’ Similar crack propagation has been noted in the four-point flexure tests that were conducted by Morgan and Marshall.13 Such a crack-propagation mechanism is expected to increase the Gi value. As the coating thickness increases, the debond crack is confined to the interface that is nearest the fiber, which results in a distinctly different crackpropagation path. (2) Debonding and Sliding in the YAG/LaPO4 /Al2O3 Fiber System The residual stresses for the YAG fiber system are shown in Fig. 1, which illustrates that both the axial (PR) and radial (NR) stresses are tensile. The axial residual stress decreases as the coating thickness increases, the effect of which would increase the required peak pushout stress. The radial tensile stress was small and increases only slightly as the coating thickness increases, the result of which would be only a slight decrease in the peak pushout stress. Combining these effects, the stress that is required to debond the fiber should increase slightly as the coating thickness increases. This trend is illustrated by the experimental results that are summarized in Fig. 5. In regard to the radial tensile stress, such a stress would effectively recoil the coating from the interface (neglecting elastic expansion). Thus, the YAG fiber system must generate sliding resistance from the asperity pressure sasperity along the debonded interface. The high sasperity value in the YAG fiber system is a factor of ∼2–4 greater than that for the Al2O3 fiber system and is postulated to result entirely from surface-roughness effects (Fig. 3). For this reason, the sliding resistance after debonding is not a strong function of the residual stresses for the YAG fiber system; i.e., the sliding resistance was not strongly dependent on the coating thickness. This behavior is observed experimentally, where the average sliding stress (pl /(2prL)), as a function of the coating thickness, is plotted in Fig. 8 and exhibits a constant sliding stress at all coating thicknesses. Fig. 8. Variation of average sliding stress as a function of interfacial coating thickness for (d) the Al2O3 and (s) the YAG fiber systems. Fig. 9. SEM micrographs of the interface region for (a) the Al2O3 (arrows mark the reaction product at the fiber/coating interface) and (b) the YAG fiber systems; the reaction product is obvious at the coating/matrix interface for both fiber systems. 2994 Journal of the American Ceramic Society—Kuo et al. Vol. 80, No. 12
December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2995 The coefficient of friction, u, in the YAG fiber system(0. 18) the fiber/coating interface, is-45o, which is similar to the mode was lower than that of the Al,O3 fiber system(0. 24). These mixity of the interface crack in the UCSB specimen. 37, 42As the differences are expected, because the sliding interface is dif- residual stress state changes, the mode mixity of the kink ferent in each case: YAG on LaPO4, for the YAG fiber com- crack also changes; it becomes more Mode ll with residual ite,and Al2O3 against LaPO4, for the Al,O3 fiber compos- compression and more Mode I with residual tension. The key point is that the pure Mode Il fracture resistance that is mea- The interfacial fracture energy Ti in the YAG fiber system ured using the pushout test gives an extremely conservative was constant as the coating thickness changed and was-165(and inaccurate)estimate for the He and Hutchinson debonding J/m2(Table II) Debonding and sliding were observed to occur criterion It the YAG/LapO4 interface. This system did not develop any eaction product between the coating and the fiber at the V. Conclusions debonding interface(Fig. 9(b))and, therefore, had a T value that remained constant as the coating thickness changed. a This study quantified the effect of the thickness of a mona- -Al2O, reaction layer was found at the coating/matrix side of zite(LaPO4) coating on the interfacial properties of alumina he interface: however, it had no effect on debonding and slid- (AL,O3)and YAG fibers that were embedded in an Al,O, ma- trix. The different thermal and elastic properties of the con- stituents resulted in different distributions of residual stresses ( Summary for each fiber system. An increase in the coating thickness It is known that coatings will modify the thermomechanical decreased the load that was required for debonding in the and thermochemical properties of ceramic composites. 2 Test Al2O3 fiber system, whereas a slight increase in the required res ults in a carbon-coated silicon carbide(SiC) fiber system load was observed for the YAG fiber system. These showed that the interfacial shear strength and the coefficient of mentally observed changes were consistent with predictions friction u decreased as the coating thickness increased 26,2 that have been extracted from the Liang and Hutchinson(LH) The carbon interlayer was hypothesized to form a compliant pushout model20 and illustrated how the interface properties layer that mitigated the effect of thermal stress: thicker carbon can be altered through changes in the coating thickness oatings reduced the thermal stresses more than thinner coat- An experimental methodology was presented for extracting ings. 28 The same effect was e entally observed for the the key interfacial parameters from pushout tests on fiber tems that have been evaluated in this study: i.e., the coating reinforced composites. The extracted parameters included the ts as a compliant layer that alters the residual stress state of interfacial fracture energy(), the coefficient of interfacial Morgan and Marshall 3 measured a mixed-mode T value which incorporated interfacial roughness). The proposed meth using the UCSB four-point flexure tests, which resulted in a odology used the Lh pushout model to curve-fit results of mixed-mode t value of 5 J/m2 The relation between the in pushout tests that had been conducted on specimens of varying terfacial fracture resistance, T, and the phase angle, y, has sample thickness. This method mechanistically rationalized the been established by evans et al s and has been applied to effect of the coating thickness on the mechanical properties d- the fiber/coating interface, which led to a detailed understa Mode ll (Y /2)i value can be a factor of >4 larger than ing of the mechanics of fiber debonding and sliding. As such, 45)36, 37Therefore, the relatively large Mode II Ti value that can be used to establish target levels of pushout stresses; more has been obtained in this study is reasonable, when compared importantly, it can be used to determine the required coat with the mixed-mode Ti value that was measured by Morgan hickness for obtaining a target interfacial sliding stress and Marshall. 13 The resulting Ti values from the fiber pushout tests represen Acknowledgments: The authors would like to acknowledge Dr R hay of wright-Patterson Air Force Base(Wright-Patterson AFB, OH) for supply values must be related to the he and hutchinson interfacial the YAg fibers. Prof John Hutch bonding criterion s to ascertain the value of these coatings for critical comments, and Dr. David Marshall for his insight and interest. for use in structural composites. He and Hutchinsons found References that a propagating crack will deflect up the fiber/coating inter M. D. Thouless, O. Sbaizero, L. S. Sigl, and A. G. Evans, Inter- ace if the ratio of the interfacial debond toughness to the fiber toughness is <0.25. Fracture-energy values for sapphire and YAG fibers, along with the measured Mode ll interfacial frac- R. w. Rice, J.R. Spann, D. Lewis, and w. Coblenz, " The Fiber Coatings on the Room Temperature Mechanical Behavior of Ceramic- ture toughness, are given in Table Ill. Clearly, neither the Fiber Composites, " Ceram Eng. Sci. Proc. 5(7-8)614-24(1984) Al2O3 nor the YAG fiber systems satisfy the He and Hutchin- R.J.Kerans, R. S Hay, N. J. Pagano, and T. A Parthasarathy, The Role of son debonding crite if the pure Mode Il toughness is used. However, the fracture testing that was reported by Mor- 1 e 429e-42 (1989 tertace n Ceramic Composites," Am. Ceram. So:, Bul, 68 an and Marshalls clearly showed interfacial debonding and 'A G. Evans and D. B. Marshall. The CB和M,3710 ical behavior of ceramic (1989) sliding for Al,O, fibers that were coated with LaPOa. Thus, the ole of Interfaces in Fiber. issue of the mode mixity of the kinked crack is relevant to Reinforced Brittle Matrix Composites, Compos. Sci. TechnoL., 42, 3-24 deciding the validity of a given coating system. In a residual stress-free system, the mode mixity of a crack, as it kinks up T Mah, M. G. Mendiratta, A P. Katz, and K.S. Mazdiyasni, "Recent De- Cera.Soc.Ba,662]304308(1987 7R F. Cooper and K. Chyung, "Structure and Chemistry of Fiber-Matrix Interfaces in Silicon Carbide Fiber Reinforced Glass-Ceramic Composites: An Table Ill. Comparisons of Fiber Fracture Energy(Td and Electron Microscopy Study, J. Mater. Sci., 22 [913148-60(1987). Mode Il Interfacial Fracture Energy (i ) between AlO3 and structural YAG Fiber Systems with a LaPO4 coating SiC-Fiber-Reinforced Lithium Aluminum Silicate gl ic,J.Am. Ceram. Soc., 72 5]741-45( Mode ll interfacial E L. Courtright, ""Engineering Property Limitations of Structural Ceramics Fiber fracture Ceramic Composites Above 1600C, ""Ceram. Eng. Sct. Proc., 12 [9-101 Fiber LaPO coating system T(/m2) G S. Corman, ""High-Temperature Creep of Some Single Crystal Oxides, 12-20t 10-12 fFrom davis et al 39 *From Reimanis et al-o and blumenthal P E D Morgan, D B. Marshall, and R. M. Housley, " "High Temperature
The coefficient of friction, m, in the YAG fiber system (0.18) was lower than that of the Al2O3 fiber system (0.24). These differences are expected, because the sliding interface is different in each case: YAG on LaPO4, for the YAG fiber composite, and Al2O3 against LaPO4, for the Al2O3 fiber composite. The interfacial fracture energy Gi in the YAG fiber system was constant as the coating thickness changed and was ∼16.5 J/m2 (Table II). Debonding and sliding were observed to occur at the YAG/LaPO4 interface. This system did not develop any reaction product between the coating and the fiber at the debonding interface (Fig. 9(b)) and, therefore, had a Gi value that remained constant as the coating thickness changed. A b-Al2O3 reaction layer was found at the coating/matrix side of the interface; however, it had no effect on debonding and sliding. (3) Summary It is known that coatings will modify the thermomechanical and thermochemical properties of ceramic composites.2 Test results in a carbon-coated silicon carbide (SiC) fiber system showed that the interfacial shear strength and the coefficient of friction m decreased as the coating thickness increased.26,27 The carbon interlayer was hypothesized to form a compliant layer that mitigated the effect of thermal stress: thicker carbon coatings reduced the thermal stresses more than thinner coatings.28 The same effect was experimentally observed for the systems that have been evaluated in this study: i.e., the coating acts as a compliant layer that alters the residual stress state of the system. Morgan and Marshall13 measured a mixed-mode Gi value using the UCSB four-point flexure tests, which resulted in a mixed-mode Gi value of 5 J/m2 . The relation between the interfacial fracture resistance, Gi , and the phase angle, C, has been established by Evans et al.36 and has been applied to experimental results.37 Theoretically and experimentally, the Mode II (C 4 p/2) Gi value can be a factor of >4 larger than the mixed-mode value that is measured by flexure testing (C ≈ 45°).36,37 Therefore, the relatively large Mode II Gi value that has been obtained in this study is reasonable, when compared with the mixed-mode Gi value that was measured by Morgan and Marshall.13 The resulting Gi values from the fiber pushout tests represent pure Mode II measures of the fracture energy. However, these values must be related to the He and Hutchinson interfacial debonding criterion38 to ascertain the value of these coatings for use in structural composites. He and Hutchinson38 found that a propagating crack will deflect up the fiber/coating interface if the ratio of the interfacial debond toughness to the fiber toughness is 0.25 YAG 10–12‡ 16 >0.25 † From Davis et al.39 ‡From Reimanis et al.40 and Blumenthal.41 December 1997 Control of Interfacial Properties through Fiber Coatings: Monazite Coatings 2995
2996 Journal of the American Ceramic SocienyKuo et al. Vol. 80. No. 12 Stability of Monazite-Alumina Composites, Mater Sci Eng, A. A195, 215- ZE. Lara-Curzio, M.K. Ferber, and R. A. Lowden, "The Effect of Fiber E.D. Morgan and D.B. Marshall, "Ceramic Composites of Monazite Matrix Composites Cter mtertacisl prpperties of a continuous Fiber Ce 78回9]2574(1 4J. D. Bright, D K. Shetty, C. w. Griffin, and S. Y. Limaye, Interfacial 5-s09iaphy on Debonding in Ceramic Composites, "Scr. Metall, 3214 Bonding and Friction in Silicon Carbide( Filament)-Reinforced Ceran Glass- Matrix Ce es,”"J.Am. Ceram 210189000 J Am. Ceram Soc., 72[]70-77(1989) ISJ. I. Eldridge, R. T, Bhatt, and J. D. Kiser, ""Investigation of interf Stresses in Sapphire Whisker Strength in SiC/Si3 N4 Composites, "Ceram. Eng Sc 7-8 and Alumina Fiber Reinforced Mullite and Garnet Ceramic Matrix Compos- ites, J. Eur. Ceram. Soc., 9 [ 2]143-52(1992 P D. Warren, T J. Mackin, and A G. Evans, Analysis and Ap- w.D. Kingery, H. K. Bowen, and D R. Uhlmann, Introduction to Ceram plication of an Improved Push-Through Test for th ics;2nd Ed. Wiley, New York, 1976 C M. Huang, D. Zhu, Y. Xu, T Mackin, and ST J Mackin, P D. Warren, and A G. Evans, ""Effects of Fiber Roughness roperties of SiC Monofilament Reinforced B'-SiAION Composites, Mater. on Interface Sliding in Composites, "Acta Metall. Mater, 40 [6] 1251-57 Sc.Eng,A,A201,15968(1995) 3D. H. Kuo and w. M. Kriven,""Chemical Stability, Microstructure, and Mechanical Behavior of LaPOa-Containing Ceramics, Mater. Sci. Eng, A A210[-2]12334(1996 R J. Kerans and T. A. Parthasarathy, " Theoretical Analysis of the Fiber Pullout and Pushout Tests, "JAm Ceram Soc., 74 [7J1585-96(1991) 35J. B. Davis, J. Yang, and A G. Evans, ""Effects of Composite Processing C. Liang and J W. Hutchinson, ""Mechanics of the Fiber Pushout Test, gth of Sapphire Fiber-Reinforced Composites, Acta Metall Mech. M aer.4325968(1995) 2L. B. Greszczuk *The Theoretical Studies of the Mechanics of the Fiber 36A. G. Evans, M. Y. He, and J. W. Hutchinson, Interface Debond Matrix Interface in Composi Fiber Cracking in Brittle Matrix Composites, J. Am. Ceram. Soc., 72 [ pecial Technical Publication 452. American Society for Testing and Materials, 7H. C Cao and A G. Evans, "An Experimental Study of the Fracture Re- 22p. Lawrence."Some Theoretical Considerations of Fiber Pullout from an sS Mech.Maer,7,295-304(1989) Elastic Matrix, J. Mater. Sci., 7, 1-6(1970) 2K. K. Chawla, Ceramic Matrix Composites. Chapman and Hall, London, Dissimilar Elastic Materials, "Int J Solids Struct, 25(9)1053-67(1989)en SM. Y. He and J W. Hutchinson, ""Crack Deflectic nterface Be 39J B. Davis, J. P. Lofvander. A G. Evans, E. Bischoff and M. L. En 4A. K. Varshneya, Treatise on Materials Science and Technology, Vol. 22: ots for Brittle- Matrix Composites, J. Am. Ceram. Soc. Edited by M. to a and R. H. Doremus. Ac 7615]124957(1993 New York, 1982. 401. E. Reimanis.J. J. Petrovic. and T. E. Mitchell. "The Fracture Behavior of 2>S. A. Newcomb and R. E. Tressler, ""Slow Crack Growth in Sapphire Fi ingle-Crystal Y, Al,2. " J. Non-Cryst. Solids, 177, 67-73(1994). bers at 800%C to 1500/C, ""J. Am. Ceram Soc., 76 [10J2505-12(199 Iw. M. Blumenthal, Los Alamos National Laboratory, Los Alamos, NM; Fiber Coatings and the Mechanical Properties of a Fiber- reinforced Ceramic Composite, pp. 619-30 in Ceramic Transactions, Vol. 19 42M.R. Turner, B J. Dalgleish, M. Y. He, and A G. Evans,"A Fracture Advanced Composite Materials. Edited by M D. Sacks. American Ceramic Resistance Measurement Method Fc es having Society, Westerville, OH, 1991 Debond Energy, 'Acta Metall. Mater ., 43 [9 3459-65(1995)
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Kriven, ‘‘Interfacial Properties of SiC Monofilament Reinforced b8-SiAlON Composites,’’ Mater. Sci. Eng., A, A201, 159–68 (1995). 18D. B. Marshall and W. C. Oliver, ‘‘Measurement of Interfacial Mechanical Properties in Fiber-Reinforced Ceramic Composites,’’ J. Am. Ceram. Soc., 70 [8] 542–48 (1987). 19R. J. Kerans and T. A. Parthasarathy, ‘‘Theoretical Analysis of the Fiber Pullout and Pushout Tests,’’ J. Am. Ceram. Soc., 74 [7] 1585–96 (1991). 20C. Liang and J. W. Hutchinson, ‘‘Mechanics of the Fiber Pushout Test,’’ Mech. Mater., 14, 207–21 (1993). 21L. B. Greszczuk, ‘‘The Theoretical Studies of the Mechanics of the Fiber– Matrix Interface in Composites’’; pp. 42–58 in Interfaces in Composites, ASTM Special Technical Publication 452. American Society for Testing and Materials, Philadelphia, PA, 1969. 22P. Lawrence, ‘‘Some Theoretical Considerations of Fiber Pullout from an Elastic Matrix,’’ J. Mater. Sci., 7, 1–6 (1970). 23K. K. Chawla, Ceramic Matrix Composites. Chapman and Hall, London, U.K., 1993. 24A. K. Varshneya, Treatise on Materials Science and Technology, Vol. 22; pp. 241–306. Edited by M. Tomozawa and R. H. Doremus. Academic Press, New York, 1982. 25S. A. Newcomb and R. E. Tressler, ‘‘Slow Crack Growth in Sapphire Fibers at 800°C to 1500°C,’’ J. Am. Ceram. Soc., 76 [10] 2505–12 (1993). 26R. A. Lowden, ‘‘Fiber Coatings and the Mechanical Properties of a FiberReinforced Ceramic Composite;’’ pp. 619–30 in Ceramic Transactions, Vol. 19, Advanced Composite Materials. Edited by M. D. Sacks. American Ceramic Society, Westerville, OH, 1991. 27E. Lara-Curzio, M. K. Ferber, and R. A. Lowden, ‘‘The Effect of Fiber Coating Thickness on the Interfacial Properties of a Continuous Fiber Ceramic Matrix Composite,’’ Ceram. Eng. Sci. Proc., 15 [5] 989–1000 (1994). 28R. J. Kerans, ‘‘The Role of Coating Compliance and Fiber/Matrix Interfacial Topography on Debonding in Ceramic Composites,’’ Scr. Metall., 32 [4] 505–509 (1995). 29Z. Li and R. C. Bradt, ‘‘Micromechanical Stresses in SiC-Reinforced Al2O3 Composites,’’ J. Am. Ceram. Soc., 72 [1] 70–77 (1989). 30Z. Li and R. C. Bradt, ‘‘ Micromechanical Stresses in Sapphire Whisker and Alumina Fiber Reinforced Mullite and Garnet Ceramic Matrix Composites,’’ J. Eur. Ceram. Soc., 9 [2] 143–52 (1992). 31W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics; 2nd Ed. Wiley, New York, 1976. 32T. A. Parthasarathy; personal communication, 1997. 33T. J. Mackin, P. D. Warren, and A. G. Evans, ‘‘Effects of Fiber Roughness on Interface Sliding in Composites,’’ Acta Metall. Mater., 40 [6] 1251–57 (1992). 34D. H. Kuo and W. M. Kriven, ‘‘Chemical Stability, Microstructure, and Mechanical Behavior of LaPO4-Containing Ceramics,’’ Mater. Sci. Eng., A, A210 [1–2] 123–34 (1996). 35J. B. Davis, J. Yang, and A. G. Evans, ‘‘Effects of Composite Processing on the Strength of Sapphire Fiber-Reinforced Composites,’’ Acta Metall. Mater., 43 [1] 259–68 (1995). 36A. G. Evans, M. Y. He, and J. W. Hutchinson, ‘‘Interface Debonding and Fiber Cracking in Brittle Matrix Composites,’’ J. Am. Ceram. Soc., 72 [12] 2300–303 (1989). 37H. C. Cao and A. G. Evans, ‘‘An Experimental Study of the Fracture Resistance of Bimaterial Interfaces,’’ Mech. Mater., 7, 295–304 (1989). 38M. Y. He and J. W. Hutchinson, ‘‘Crack Deflection at an Interface Between Dissimilar Elastic Materials,’’ Int. J. Solids Struct., 25 [9] 1053–67 (1989). 39J. B. Davis, J. P. Lo¨fvander, A. G. Evans, E. Bischoff, and M. L. Emiliani, ‘‘Fiber Coating Concepts for Brittle-Matrix Composites,’’ J. Am. Ceram. Soc., 76 [5] 1249–57 (1993). 40I. E. Reimanis, J. J. Petrovic, and T. E. Mitchell, ‘‘The Fracture Behavior of Single-Crystal Y3Al5O12.’’ J. Non-Cryst. Solids, 177, 67–73 (1994). 41W. M. Blumenthal, Los Alamos National Laboratory, Los Alamos, NM; unpublished results, 1993. 42M. R. Turner, B. J. Dalgleish, M. Y. He, and A. G. Evans, ‘‘A Fracture Resistance Measurement Method For Bimaterial Interfaces Having Large Debond Energy,’’ Acta Metall. Mater., 43 [9] 3459–65 (1995). h 2996 Journal of the American Ceramic Society—Kuo et al. Vol. 80, No. 12