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