《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_j.1151-2916.1997.tb03148.x[1]

Journal J. An. Ceran. Soc, 80 [10] 2171-87(1997) Fibrous monolithic ceramics Desiderio Kovar, * t Bruce H. King, *. Rodney W. Trice, *and John W.Halloran Materials Science and Engineering Department, University of Michigan, Ann Arbor, Michigan 48109-2136 Fibrous monolithic ceramics are an example of a laminate Si3N4) into fibrouscells' separated by boron nitride(BN) in which a controlled, three-dimensional structure has been 'cell boundaries results in monolithic ceramics with wood- introduced on a submillimeter scale. This unique structure like fibrous structures. which are called fibrous monolithic allows this all-ceramic material to fail in a nonbrittle man- ceramics "3 Fibrous monoliths are fabricated using a coextru- ner. Materials have been fabricated and tested with a va- sion process, 5 to produce green filaments. The filaments then structure of the constituent phases and the architecture in Among the many materials that have been manufactured using hich they are arranged are discussed. The elastic proper- icon nitride-boron nitride(Si3Na-BI Cxisting models. These models also can be extendedipasg brous monoliths are the most promising ties of these materials can be effectively predicted In this article we examine the structure of Si. N-BN fibrous orientation and architecture. However the mechanisms cell-cell boundary features to the nanometer scale of the BN that govern the energy absorption capacity of fibrous cell boundaries. We also show how the elastic properties and monoliths are unique, and experimental results do not fol- strength vary with the architecture of the cells, and how this low existing models. Energy dissipation occurs through two can be described using laminate theory. We present the fracture dominant mechanisms--delamination of the weak inter- behavior in some detail, relating the strength and fracture en- chases and then frictional sliding after cracking occurs ergy to fracture of the SisNa cells and crack deflection within The properties of the constituent phases that maximize en the bn cell boundaries ergy absorption are discussed IL. Structure of SiaN-BN Fibrous Monoliths . Introduction () Submillimeter Structure looK AND gORDon first introduced the idea that crack propagation in brittle materials could be controlled by in- Figure 1. constructed from low-magnification scanning elec- ron microscopy(SEM) micrographs of polished sections corporating a fabric of microstructural features that change the shows three-dimensional representations of the submillimeter crack path. More recently, Clegg demonstrated that, by ar- structure of two architectures of fibrous monoliths. The poly ranging layers of a strong phase and separating them with weak crystalline SisN, cells appear in dark contrast, and the continu- ous Bn cell boundaries appear in bright contrast. The cross brittle manner. Another way to accomplish this is to generalize section of Fig. 1(a) shows the Si Na cells as flattened hexagons the idea of a laminate by adding a three-dimensional structure with an aspect ratio of -2. The cells are -200 um wide; there- f crack-modifying features. The division of silicon nitride fore, there are several hundred B-Si3N4 grains through the thickness of each Sis N, cell. For the uniaxially aligned archi- tecture shown in Fig. 1(a), the SigNa cells run continuous down the length of the specimen. Figure 1(b) illustrates the D.J. Greer--Contributing editor [0790] architecture, where uniaxially aligned layers are rotated 90 between lamina. The architecture of fibrous monoliths is altered easily by changing the stacking sequence of filament layers. Much of our work has focused on the [0/45/90] archi- Manuscript No. 19182 Received February 24, 1%b a ed June Research tecture, which has isotropic elastic properties in the plane of the jects Agency under Contract No. No014-95-0302. tNow with the University The cell boundaries are typically 15-25 um thick layers of Now with Sandia National Laboratory polycrystalline BN consisting of many well-aligned BN grains eature 2471

Fibrous Monolithic Ceramics Desiderio Kovar,*,† Bruce H. King,*,‡ Rodney W. Trice,* and John W. Halloran* Materials Science and Engineering Department, University of Michigan, Ann Arbor, Michigan 48109-2136 Fibrous monolithic ceramics are an example of a laminate in which a controlled, three-dimensional structure has been introduced on a submillimeter scale. This unique structure allows this all-ceramic material to fail in a nonbrittle man￾ner. Materials have been fabricated and tested with a va￾riety of architectures. The influence on mechanical prop￾erties at room temperature and at high temperature of the structure of the constituent phases and the architecture in which they are arranged are discussed. The elastic proper￾ties of these materials can be effectively predicted using existing models. These models also can be extended to pre￾dict the strength of fibrous monoliths with an arbitrary orientation and architecture. However, the mechanisms that govern the energy absorption capacity of fibrous monoliths are unique, and experimental results do not fol￾low existing models. Energy dissipation occurs through two dominant mechanisms—delamination of the weak inter￾phases and then frictional sliding after cracking occurs. The properties of the constituent phases that maximize en￾ergy absorption are discussed. I. Introduction COOK AND GORDON1 first introduced the idea that crack propagation in brittle materials could be controlled by in￾corporating a fabric of microstructural features that change the crack path. More recently, Clegg2 demonstrated that, by ar￾ranging layers of a strong phase and separating them with weak interphases, brittle ceramics could be made to fail in a non￾brittle manner. Another way to accomplish this is to generalize the idea of a laminate by adding a three-dimensional structure of crack-modifying features. The division of silicon nitride (Si3N4) into fibrous ‘‘cells’’ separated by boron nitride (BN) ‘‘cell boundaries’’ results in monolithic ceramics with wood￾like fibrous structures, which are called ‘‘fibrous monolithic ceramics.’’3 Fibrous monoliths are fabricated using a coextru￾sion process4,5 to produce green filaments. The filaments then are arranged using methods similar to those used to manufac￾ture textiles, creating analogs of many composite architectures. Among the many materials that have been manufactured using this technique,6–9 silicon nitride–boron nitride (Si3N4–BN) fi￾brous monoliths are the most promising. In this article, we examine the structure of Si3N4–BN fibrous monoliths from the submillimeter scale of the crack-deflecting cell–cell boundary features to the nanometer scale of the BN cell boundaries. We also show how the elastic properties and strength vary with the architecture of the cells, and how this can be described using laminate theory. We present the fracture behavior in some detail, relating the strength and fracture en￾ergy to fracture of the Si3N4 cells and crack deflection within the BN cell boundaries. II. Structure of Si3N4–BN Fibrous Monoliths (1) Submillimeter Structure Figure 1, constructed from low-magnification scanning elec￾tron microscopy (SEM) micrographs of polished sections, shows three-dimensional representations of the submillimeter structure of two architectures of fibrous monoliths. The poly￾crystalline Si3N4 cells appear in dark contrast, and the continu￾ous BN cell boundaries appear in bright contrast. The cross section of Fig. 1(a) shows the Si3N4 cells as flattened hexagons with an aspect ratio of ∼2. The cells are ∼200 mm wide; there￾fore, there are several hundred b-Si3N4 grains through the thickness of each Si3N4 cell. For the uniaxially aligned archi￾tecture shown in Fig. 1(a), the Si3N4 cells run continuously down the length of the specimen. Figure 1(b) illustrates the [0/90] architecture, where uniaxially aligned layers are rotated 90° between lamina. The architecture of fibrous monoliths is altered easily by changing the stacking sequence of filament layers. Much of our work has focused on the [0/±45/90] archi￾tecture, which has isotropic elastic properties in the plane of the lamina. The cell boundaries are typically 15–25 mm thick layers of polycrystalline BN consisting of many well-aligned BN grains. D. J. Green–Contributing editor Manuscript No. 191182. Received February 24, 1997; approved June 6, 1997. Supported by U.S. Office of Naval Research and Defense Advanced Research Projects Agency under Contract No. N0014-95-0302. *Member, American Ceramic Society. † Now with the University of Texas at Austin. ‡ Now with Sandia National Laboratory. J. Am. Ceram. Soc., 80 [10] 2471–87 (1997) Journal 2471

Journal of the American Ceramic Society-Kovar et al. Vol. 80. No. 10 Fig. 2. SEM micrograph of a fracture surface showing a BN cell boundary between two Si,N, cells viewed edge on. Glassy Phase 20m Fig. 1. Low-magnification SEM composites illustrating three sec- (Si,N, cells run continuously down the length of 5um separated by BN cell boundaries)and a(b)[/90] architectu of cells are stacked with a 90 rotation between the fractue surface prateletike mor phology of the bn irais as wetl The BN grain alignment is obvious by visual examination and as the discontinuous glassy phase are visible confirmed by X-ray diffractometry (XRD). 0 It is crucial that the(0001)cleavage planes be oriented parallel to the Si3N4 interface; otherwise, cracks do not deflect in the BN inter- boundary, looking down onto the fracture surface. The platey hase. This grain alignment occurs during the coextrusion step of green fabrication, during which the BN platelets are plane oriented parallel to the cell boundary. In this secondary- (2) Microstructure at Scale of the grains darker regions are BN platelets and the brighter areas are yttria aluminosilicate glass The microstructure within the Si3N4 cells is quite conven- lon-milled samples of fibrous monoliths were prepared for tional for this particular grade of Si, N4 densified with 6 wt% ansmission electron microscopy(TEM)using techniques de- ular, grains within a matrix of a glassy, grain-boundary revealed by TE Sewhere. 12 The major features of the BN rocracks between the (0001) basal planes of BN platelets. These are shown in Fig. 4 ditions, we find B-Si Na grains 0.2-1.5 um wide, with aspect The inset diffraction pattern indicates the foil plane to be Junctions. Figure 2 is an SEM micrograph of a fracture s efie, Som G,, te how each BN grain has exfoliated along its basal ratios of 2-10. The grain-boundary phase is glassy, present as (20).No the usual thin film between grains and in pockets at Si3 N4 grain planes into many layers. A higher magnification view of a BN in shown in Fig. 5 reveals a finer pattern of microcrack showing a Bn cell boundary between two Si3 N4 cells. Visual Some layers are divided as fine as 50 nm. (A unit graphi inspection suggests that many of the B-Si3N4 grains in the cell layer in the BN crystal structure has a thickness of are oriented with their [0001] long axes aligned along the cell nm. direction. This texture has been confirmed by XRD. o Note A similar microcrack structure has been described by also the obvious orientation of the Bn platelets in the cell Mrozowski 3 in graphite that has a crystalline structure similar boundary to BN 14 Sinclair and Simmons is have attributed these basal Figure 3 is an SEM micrograph of the fractured BN-rich cell plane cracks that they observed using TEM to the thermal

The BN grain alignment is obvious by visual examination and confirmed by X-ray diffractometry (XRD).10 It is crucial that the (0001) cleavage planes be oriented parallel to the Si3N4 interface; otherwise, cracks do not deflect in the BN inter￾phase.11 This grain alignment occurs during the coextrusion step of green fabrication, during which the BN platelets are oriented by the flow field in the extrusion die. (2) Microstructure at Scale of the Grains The microstructure within the Si3N4 cells is quite conven￾tional for this particular grade of Si3N4 densified with 6 wt% Y2O3 and 2 wt% Al2O3. This grade of Si3N4 consists of acic￾ular b-Si3N4 grains within a matrix of a glassy, grain-boundary phase. For our particular raw materials and densification con￾ditions, we find b-Si3N4 grains 0.2–1.5 mm wide, with aspect ratios of 2–10. The grain-boundary phase is glassy, present as the usual thin film between grains and in pockets at Si3N4 grain junctions. Figure 2 is an SEM micrograph of a fracture surface, showing a BN cell boundary between two Si3N4 cells. Visual inspection suggests that many of the b-Si3N4 grains in the cell are oriented with their [0001] long axes aligned along the cell direction. This texture has been confirmed by XRD.10 Note also the obvious orientation of the BN platelets in the cell boundary. Figure 3 is an SEM micrograph of the fractured BN-rich cell boundary, looking down onto the fracture surface. The platey features are the BN grains, which lie with their (0001) basal plane oriented parallel to the cell boundary. In this secondary￾electron micrograph, there are two distinct contrast areas. The darker regions are BN platelets and the brighter areas are yttria aluminosilicate glass. Ion-milled samples of fibrous monoliths were prepared for transmission electron microscopy (TEM) using techniques de￾scribed in detail elsewhere.12 The major features of the BN revealed by TEM are extensive microcracks between the (0001) basal planes of BN platelets. These are shown in Fig. 4. The inset diffraction pattern indicates the foil plane to be (2110). Note how each BN grain has exfoliated along its basal planes into many layers. A higher magnification view of a BN grain shown in Fig. 5 reveals a finer pattern of microcracking. Some layers are divided as fine as 50 nm. (A unit ‘‘graphine’’ layer in the BN crystal structure has a thickness of c0 4 0.66 nm.) A similar microcrack structure has been described by Mrozowski13 in graphite that has a crystalline structure similar to BN.14 Sinclair and Simmons15 have attributed these basal plane cracks that they observed using TEM to the thermal Fig. 3. SEM micrograph of the BN cell boundary looking down onto the fracture surface. Plateletlike morphology of the BN grains as well as the discontinuous glassy phase are visible. Fig. 1. Low-magnification SEM composites illustrating three sec￾tions of a fibrous monolith with a (a) uniaxially aligned architecture (Si3N4 cells run continuously down the length of the specimen and are separated by BN cell boundaries) and a (b) [0/90] architecture (layers of cells are stacked with a 90° rotation between lamina). Fig. 2. SEM micrograph of a fracture surface showing a BN cell boundary between two Si3N4 cells viewed edge on. 2472 Journal of the American Ceramic Society—Kovar et al. Vol. 80, No. 10

October 1997 Fibrous Monolithic Ceramics 2473 Boron Nitride Boron Nitride CTO00IDirection Glassy Phase Cracks 250nm Fig. 4. TEM micrograph showing extensive microcracks between the(0001)basal planes of the BN platelets. Also note the presence of Fig. 5. Higher-magnification view of a single bN platelet showing a glassy phase between the bn platelets expansion anisotropy between the a-axis and c-axis of graph- te.5In the basal plane, the coefficient of thermal expansion (CTE)of BN is slightly negative through 800C, about -2 10-6rC. 16 Perpendicular to the basal plane, the CTE is very large and positive, about +40 x 10-b/oC. As the composite Glassy Phase Silicon Nitride Doled from the hot-pressing ter ature(1750°C, the BN contracts perpendicular to the basal plane (i.e, in the [0001] direction), while there is a small expansion within the plane. Hf the surrounding Si3 Na grains or glassy phase constrain the BN platelets, large tensile stresses are developed perpendicular to the basal plane upon cooling. This acts to separate the BN platelet into layers along the basal plane direction. Further- more, shear stresses developed parallel to the basal plane shea the surfaces of the platelets relative to each other. The BN platelets labeled A and B in Fig. 5 clearly once existed as a single platelet before they were split and translated relative to one another during cooling A representative TEM micrograph of a Sia NBN interface shown in Fig. 6. There is no cracking between the Si3N4 and Boron Nitride the BN Rather there seems to be excellent adhesion between the two phases. a thin layer of glass is observed between the two phases in some places a glassy phase also is found residing in pockets in the BN cell boundary. No glass-forming compounds were added to the Bn powders; therefore, this glass must be residual liquid in- truded into the cell boundary from the neighboring Si N, cells 250nm during hot pressing. Figure 4 shows a large pocket of glass between exfoliated layers of BN. The selected-area electron diffraction pattern in Fig. 4 shows amorphous rings from the Fig. 6. Bright-field TEM image of a typical interface between the hase exists in pockets between booklets of bn grains. The composition of the glass in Si3N4 cells and BN cell-boundary glassy phases was determined with energy dispersive spectros- borate. The Y: Al ratio of the glass in the Bn cell boundaries copy(EDS). EDS spectra of the glassy phase between the bn is similar to the composition of the glass between Si3N4 grains platelets show the presence of yttrium, aluminum, silicon, oxy- Because of the presence of silicon, aluminum, and yttrium, it is gen, and nitrogen. Boron could not be detected by this EDS clear that the sintering-aid glass is being either drawn or forced spectrometer; therefore, we do not know if the glass contains into the bn during hot pressing

expansion anisotropy between the a-axis and c-axis of graph￾ite.15 In the basal plane, the coefficient of thermal expansion (CTE) of BN is slightly negative through 800°C, about −2 × 10−6/°C.16 Perpendicular to the basal plane, the CTE is very large and positive, about +40 × 10−6/°C.17 As the composite is cooled from the hot-pressing temperature (1750°C), the BN contracts perpendicular to the basal plane (i.e., in the [0001] direction), while there is a small expansion within the plane. If the surrounding Si3N4 grains or glassy phase constrain the BN platelets, large tensile stresses are developed perpendicular to the basal plane upon cooling. This acts to separate the BN platelet into layers along the basal plane direction. Further￾more, shear stresses developed parallel to the basal plane shear the surfaces of the platelets relative to each other. The BN platelets labeled A and B in Fig. 5 clearly once existed as a single platelet before they were split and translated relative to one another during cooling. A representative TEM micrograph of a Si3N4–BN interface is shown in Fig. 6. There is no cracking between the Si3N4 and the BN. Rather, there seems to be excellent adhesion between the two phases. A thin layer of glass is observed between the two phases in some places. A glassy phase also is found residing in pockets in the BN cell boundary. No glass-forming compounds were added to the BN powders; therefore, this glass must be residual liquid in￾truded into the cell boundary from the neighboring Si3N4 cells during hot pressing. Figure 4 shows a large pocket of glass between exfoliated layers of BN. The selected-area electron diffraction pattern in Fig. 4 shows amorphous rings from the glass with diffraction spots identified with BN. The glassy phase exists in pockets between booklets of BN grains. The composition of the glass in Si3N4 cells and BN cell-boundary glassy phases was determined with energy dispersive spectros￾copy (EDS). EDS spectra of the glassy phase between the BN platelets show the presence of yttrium, aluminum, silicon, oxy￾gen, and nitrogen. Boron could not be detected by this EDS spectrometer; therefore, we do not know if the glass contains borate. The Y:A1 ratio of the glass in the BN cell boundaries is similar to the composition of the glass between Si3N4 grains. Because of the presence of silicon, aluminum, and yttrium, it is clear that the sintering-aid glass is being either drawn or forced into the BN during hot pressing. Fig. 4. TEM micrograph showing extensive microcracks between the (0001) basal planes of the BN platelets. Also note the presence of a glassy phase between the BN platelets. Fig. 5. Higher-magnification view of a single BN platelet showing fine-scale pattern of microcracking. Fig. 6. Bright-field TEM image of a typical interface between the Si3N4 and the BN. October 1997 Fibrous Monolithic Ceramics 2473

Joumal of the American Ceramic Sociery-Kovar et al. Vol. 80. No. 10 Ill. Mechanical Properties of Si3NBN facial sliding resistance. Particular emphas Fibrous Monoliths veloping a methodology to predict the properties, stre materials as Fibrous monoliths are novel materials. therefore. it is a function of architecture. Because fibrous monoliths are in- essary to identify the micromechanical properties that infl tended for use in applications where stresses are primarily gen- ring properties. These include the fracture erated because of bending, we focus on flexural properties tance of cells the interfacial fracture resistance. and the In some respects, fibrous monoliths are similar to ceramic- Panel A. Processing of fibrous monoliths Schematic illustrations of the steps used to fabricate binder, is 83 vol% sinterable Si,N-6 wt%Y203-2 wt% SigNa-BN fibrous monoliths are shown in Fig. Al. We start Al,O3(6Yn2Al-Si3 N4)and 17 wt% BN by mixing conventional ceramic powders in a polyme Sheets of uniaxially aligned green filaments are produced Starck and Co. Newton. MA. or SN-e- by winding the filaments around a mandrel and fixing them into place with a spray adhesive. Fibrous monolith speci New York, NY), consist primarily of equiaxed ax-SiaN4 par- mens are assembled from these sheets. Typically, 25 sheets ticles, nominally 0.5 um in diameter, with a BET specifi are used to produce a specimen. The uniaxially aligned surface area of m/g. The BN powder is a well- chitecture is produced by stacking the sheets without Advanced Ceramics Corp, Cleveland, OH) moplastic; therefore, after stacking, the assembly is molded The thermoplastic extrudable compound is made by into a solid block at temperatures between 1000 and 150C ing ceramic powder with thermoplastic polymers in a heated at a pressure of 2 MPa Shaped objects can be formed using mixer. The solids loading for the cell materials (Sis N conventional compression-molding dies. The filaments, Y2O3, and Al,O3)is 52 vol% ceramic, whereas the cladding which initially have a round cross section, deform during (BN)contains 50 vol% ceramic. After it is mixed, the Siy N4 this warm-pressing operation, filling the interstitial spaces compound is compression molded into a 20 mm diameter etween the filaments and producing flattened hexagon rod. A similar BN compound is compression molded into a shaped cells cylindrical shell, I mm thick, with a 20 mm inner diameter The thermoplastic binder is removed by heating slowly to The bn shell is fitted around the Si3N4 rod to make a 700C in a nitrogen atmosphere Hot pressing at 1750C fo for a piston-style extruder. The feedrod is then 2 h produces a density of 3.05 g/cm3,-98% of the estimated through a heated extrusion die to create 220 um er green filaments with the same Si3 N4 core and BN ng as the feedrod. The flexible green filament is col- onal ZrO,(contamination from the milling media a spool. The ceramic composition, excluding the Extrude feedrod into fine filament feedrod Si NA-filled polymer Form extrusion feedrod heated di spoo上 Hot-press to densify rolysis to remove polymer. binder Laminate sheets of filament to form solid billet Fig. Al. Schematic illustrations showing processing route to fabricate fibrous monoliths

III. Mechanical Properties of Si3N4–BN Fibrous Monoliths Fibrous monoliths are novel materials; therefore, it is nec￾essary to identify the micromechanical properties that influence the engineering properties. These include the fracture resis￾tance of cells, the interfacial fracture resistance, and the inter￾facial sliding resistance. Particular emphasis is placed on de￾veloping a methodology to predict the elastic properties, strength, and energy absorption capability of these materials as a function of architecture. Because fibrous monoliths are in￾tended for use in applications where stresses are primarily gen￾erated because of bending, we focus on flexural properties. In some respects, fibrous monoliths are similar to ceramic￾Panel A. Processing of Fibrous Monoliths Schematic illustrations of the steps used to fabricate Si3N4–BN fibrous monoliths are shown in Fig. A1. We start by mixing conventional ceramic powders in a polymer binder system. The commercial Si3N4 powders (M11, H. C. Starck and Co., Newton, MA, or SN-E-10, Ube Industries, New York, NY), consist primarily of equiaxed a-Si3N4 par￾ticles, nominally 0.5 mm in diameter, with a BET specific surface area of 9–13 m2 /g. The BN powder is a well￾crystallized, hexagonal BN powder consisting of platey par￾ticles 7–10 mm in diameter and 0.1–0.3 mm thick (HCP-BN, Advanced Ceramics Corp., Cleveland, OH). The thermoplastic extrudable compound is made by mix￾ing ceramic powder with thermoplastic polymers in a heated mixer. The solids loading for the cell materials (Si3N4, Y2O3, and Al2O3) is 52 vol% ceramic, whereas the cladding (BN) contains 50 vol% ceramic. After it is mixed, the Si3N4 compound is compression molded into a 20 mm diameter rod. A similar BN compound is compression molded into a cylindrical shell, 1 mm thick, with a 20 mm inner diameter. The BN shell is fitted around the Si3N4 rod to make a feedrod for a piston-style extruder. The feedrod is then forced through a heated extrusion die to create 220 mm diameter green filaments with the same Si3N4 core and BN cladding as the feedrod. The flexible green filament is col￾lected on a spool. The ceramic composition, excluding the binder, is 83 vol% sinterable Si3N4–6 wt% Y2O3–2 wt% Al2O3 (6Y/2Al–Si3N4) and 17 wt% BN. Sheets of uniaxially aligned green filaments are produced by winding the filaments around a mandrel and fixing them into place with a spray adhesive. Fibrous monolith speci￾mens are assembled from these sheets. Typically, 25 sheets are used to produce a specimen. The uniaxially aligned architecture is produced by stacking the sheets without ro￾tation, whereas, for the [0/±45/90] architecture, the filament direction is rotated between layers. The filaments are ther￾moplastic; therefore, after stacking, the assembly is molded into a solid block at temperatures between 100° and 150°C at a pressure of 2 MPa. Shaped objects can be formed using conventional compression-molding dies. The filaments, which initially have a round cross section, deform during this warm-pressing operation, filling the interstitial spaces between the filaments and producing flattened hexagon￾shaped cells. The thermoplastic binder is removed by heating slowly to 700°C in a nitrogen atmosphere. Hot pressing at 1750°C for 2 h produces a density of 3.05 g/cm3 , ∼98% of the estimated theoretical density for this composition. XRD shows the presence of b-Si3N4, hexagonal BN, and a trace of tetrag￾onal ZrO2 (contamination from the milling media). Fig. A1. Schematic illustrations showing processing route to fabricate fibrous monoliths. 2474 Journal of the American Ceramic Society—Kovar et al. Vol. 80, No. 10

October 1997 Fibrous monolithic ceramics 247: matrix-fiber-reinforced composites. For example, we find that point bend test Charalambides et al. 21 This test is the elastic properties of fibrous monoliths can be predicted with specimen, and then loading it in tor pi the elastic behar four-point bend ination occurs. The steady-state einforced laminates. But the fra d necessary delamination crack and the of fibrous monoliths is quite different, because these materials specimen dimer used to compute the interfacial ontain neither strong fibers nor a weak matrix. The failure fracture resistar mechanisms and associated dissipative mechanisms that are important in fiber-reinforced composites, I9 do not occur r in (2) Elastic Properties fibrous monoliths; therefore, those theories are not applicable To predict the elastic response of fibrous monolithic ceram- Instead, we find that the fracture process that occurs in fibrous s with multiaxial architectures, it is necessary to first under monoliths can be described by existing theories for the fracture stand the elastic behavior of uniaxially aligned fibrous mono- count for the unique structure of fibrous monoliths on to ac- liths along principal directions. These predictions are made of two-dimensional layered materials after modificatio using appropriate micromechanical models and a knowledge of the elastic properties of the constituent materials. Once these () Experimental Procedure predictions are made, laminate theory is used to predict the Elastic properties of both the fibrous monolithic ceramics off-axis elastic properties for uniaxially aligned materials and and monolithic ceramics were measured using the impulse- the elastic moduli for fibrous monolithic ceramics with multi- excitation technique using a commercially available tester axial architectures. The predictions are verified by measuring Grindo-sonic Model MK4x, J. w. Lemmon, St Louis, MO) he elastic moduli in many test coupons ccording to ASTM E 494-92a 20 In this test, the specimen is We assume that uniaxial fibrous monolithic ceramics pos- excited using a small driver, and the resonant frequency is sess a plane of isotropy perpendicular to the axis of the fibrous measured using a piezoelectric transducer. The modulus is then texture. The additional assumption that out-of-plane stresses calculated from the resonant frequency, the specimen dimen- can be ignored reduces the number of required elastic constants sions, and the specimen density. Youngs modulus was deter to four and allows the use of classical laminate theory to predict mined using bars with dimensions 3 mm x 4 mm x 45 mm, and he properties at an arbitrary angle for materials with uniaxial shear modulus was determined on plates 3 mm x 20 mm x 45 architectures and the moduli for materials with biaxial archi- mm. Bars with a uniaxially aligned architecture were machined tectures 22 These four elastic constants are calculated in terms parallel or perpendicular to the fibrous texture to determine of the engineering properties E1, E2, G12, and v12.We express Young's modulus in the I and 2 directions(E and E2, respec these properties for each architecture in terms of the composi- of the BN (EBN) and sin angle(0) with respect to the I direction to determine E(0). The (EsN) constituent materials shear modulus was determined using plates machined with the (A) Elastic Properties along Principal Directions: Uni- ng axis parallel to the direction of interest. For biaxial archi- axial Architecture: All elastic property predictions for fibrous tectures, one layer was designated the 0o layer, and the axis of monolithic ceramics are made from the elastic moduli of the Strength measurements at room temperature and at elevated Si3N4 of 320 GPa is used. This value is obtained from mea- emperature were performed using a computer-controlled surements performed on bars of monolithic Si3 Na of the same screw-driven, testing machine(Model 4483, Instron Corp, composition as that of the fibrous monolithic cells and hot- Canton, MA)operated in displacement control. The crosshead pressed under the same conditions and onsistent with val displacement rate was 0.5 mm/min for all tests. Specimens cited in the literature. 23 It is difficult to measure the elastic were tested in four-point flexure with an inner span of 20 mm properties of bulk BN. Similar to fabricated graphite, 4 the and an outer span of 40 mm. For elevated-temperature tests, the elastic properties of bulk BN vary greatly with fabrication tech- and an outer strowds allowed to stabilize for 10 min prior nique. Furthermore, the high degree of internal damping makes to testing. The energy absorption capability of a specimen was measurement using the impulse-excitation technique difficult characterized by the work-of-fracture(WOF), which was com- Only a few examples of successful modulus measurements on outed by taking the total area under the load-displacement BN are known in the literature. Two of the more commonl ng by twice the cross-sectional area of the reported values are 19.6 GPa26 and 22 GPa.27 However, these specimen values should be used with caution because the microstructure Interfacial fracture resistance was determined using a four- of the BN present in hot-pressed fibrous monolithic ceramics is Panel B. Material Combinations Although this article focuses on fibrous monoliths made Table bl. Material Combinations that have been used om SiaN4 and BN, fibrous monoliths have been fabricated to Fabricate Fibrous monoliths using many different material combinations. Some ex- Cell boundary Reference amples of all-ceramic fibrous monoliths and metal-ceramic fibrous monoliths that have been successfully fabricated are All-ceramic fibrous monoliths presented below. The usual limitations to processing of composite materials also apply to fibrous monoliths: i.e. the Hb2 constituent materials must be phase compatible. In addition, the constituent materials must be compatible with the poly C(graphite) mer binders that are used in the extrusion process ALO -ZrO Ceramic-metal fibrous monoliths ALo Advanced Ceramic Research, Tucson, AZ

matrix–fiber-reinforced composites. For example, we find that the elastic properties of fibrous monoliths can be predicted with existing theories used for predicting the elastic behavior of traditional fiber-reinforced laminates. But the fracture behavior of fibrous monoliths is quite different, because these materials contain neither strong fibers nor a weak matrix. The failure mechanisms and associated dissipative mechanisms that are important in fiber-reinforced composites18,19 do not occur in fibrous monoliths; therefore, those theories are not applicable. Instead, we find that the fracture process that occurs in fibrous monoliths can be described by existing theories for the fracture of two-dimensional layered materials after modification to ac￾count for the unique structure of fibrous monoliths. (1) Experimental Procedure Elastic properties of both the fibrous monolithic ceramics and monolithic ceramics were measured using the impulse￾excitation technique using a commercially available tester (Grindo-sonic Model MK4x, J. W. Lemmon, St. Louis, MO) according to ASTM E 494-92a.20 In this test, the specimen is excited using a small driver, and the resonant frequency is measured using a piezoelectric transducer. The modulus is then calculated from the resonant frequency, the specimen dimen￾sions, and the specimen density. Young’s modulus was deter￾mined using bars with dimensions 3 mm × 4 mm × 45 mm, and shear modulus was determined on plates 3 mm × 20 mm × 45 mm. Bars with a uniaxially aligned architecture were machined parallel or perpendicular to the fibrous texture to determine Young’s modulus in the 1 and 2 directions (E1 and E2, respec￾tively). Young’s modulus also was measured as a function of angle (u) with respect to the 1 direction to determine E(u). The shear modulus was determined using plates machined with the long axis parallel to the direction of interest. For biaxial archi￾tectures, one layer was designated the 0° layer, and the axis of the bar was machined parallel to this layer. Strength measurements at room temperature and at elevated temperature were performed using a computer-controlled, screw-driven, testing machine (Model 4483, Instron Corp., Canton, MA) operated in displacement control. The crosshead displacement rate was 0.5 mm/min for all tests. Specimens were tested in four-point flexure with an inner span of 20 mm and an outer span of 40 mm. For elevated-temperature tests, the furnace temperature was allowed to stabilize for 10 min prior to testing. The energy absorption capability of a specimen was characterized by the work-of-fracture (WOF), which was com￾puted by taking the total area under the load–displacement curve and dividing by twice the cross-sectional area of the specimen. Interfacial fracture resistance was determined using a four￾point bend test developed by Charalambides et al.21 This test is performed by first notching a specimen, and then loading it in four-point bending until delamination occurs. The steady-state load necessary to propagate the delamination crack and the specimen dimensions are then used to compute the interfacial fracture resistance. (2) Elastic Properties To predict the elastic response of fibrous monolithic ceram￾ics with multiaxial architectures, it is necessary to first under￾stand the elastic behavior of uniaxially aligned fibrous mono￾liths along principal directions. These predictions are made using appropriate micromechanical models and a knowledge of the elastic properties of the constituent materials. Once these predictions are made, laminate theory is used to predict the off-axis elastic properties for uniaxially aligned materials and the elastic moduli for fibrous monolithic ceramics with multi￾axial architectures. The predictions are verified by measuring the elastic moduli in many test coupons. We assume that uniaxial fibrous monolithic ceramics pos￾sess a plane of isotropy perpendicular to the axis of the fibrous texture. The additional assumption that out-of-plane stresses can be ignored reduces the number of required elastic constants to four and allows the use of classical laminate theory to predict the properties at an arbitrary angle for materials with uniaxial architectures and the moduli for materials with biaxial archi￾tectures.22 These four elastic constants are calculated in terms of the engineering properties E1, E2, G12, and n12. We express these properties for each architecture in terms of the composi￾tion (VBN) and the elastic properties of the BN (EBN) and Si3N4 (ESN) constituent materials. (A) Elastic Properties along Principal Directions: Uni￾axial Architecture: All elastic property predictions for fibrous monolithic ceramics are made from the elastic moduli of the constituent Si3N4 and BN. A value for the Young’s modulus of Si3N4 of 320 GPa is used. This value is obtained from mea￾surements performed on bars of monolithic Si3N4 of the same composition as that of the fibrous monolithic cells and hot￾pressed under the same conditions and is consistent with values cited in the literature.23 It is difficult to measure the elastic properties of bulk BN. Similar to fabricated graphite,24 the elastic properties of bulk BN vary greatly with fabrication tech￾nique. Furthermore, the high degree of internal damping makes measurement using the impulse-excitation technique difficult. Only a few examples of successful modulus measurements on BN are known in the literature.25 Two of the more commonly reported values are 19.6 GPa26 and 22 GPa.27 However, these values should be used with caution, because the microstructure of the BN present in hot-pressed fibrous monolithic ceramics is Panel B. Material Combinations Although this article focuses on fibrous monoliths made from Si3N4 and BN, fibrous monoliths have been fabricated using many different material combinations. Some ex￾amples of all-ceramic fibrous monoliths and metal–ceramic fibrous monoliths that have been successfully fabricated are presented below. The usual limitations to processing of composite materials also apply to fibrous monoliths; i.e., the constituent materials must be phase compatible. In addition, the constituent materials must be compatible with the poly￾mer binders that are used in the extrusion process. Table BI. Material Combinations that have been Used to Fabricate Fibrous Monoliths Cell Cell boundary Reference All-ceramic fibrous monoliths ZrB2 BN † HfB2 BN † SiC BN 8, 53 SiC C (graphite) 7, 53 Al2O3 C (graphite) 54 Al2O3 Al2TiO5 6 Al2O3 Al2O3–ZrO2 6 Ceramic–metal fibrous monoliths Al2O3 Fe–Ni 55 Al2O3 Fe 55 Al2O3 Ni 56 † Advanced Ceramic Research, Tucson, AZ. October 1997 Fibrous Monolithic Ceramics 2475

Joumal of the American Ceramic Sociery-Kovar et al. Vol. 80. No. 10 Cell Boundary ■圜 ■國圜塵圖 Fig. 7. Schematic of the "brick model" used to calculate the Youngs modulus of fibrous monoliths Table 1. Measured and predicted values of elastic EBN, ESN, and VBN with a model that combines elastic elements Properties for Uniaxially Aligned Fibrous Monoliths in series and in parallel, 9 and yields the following equation: Er(GPa) Ez(GPa) G12(GPa) Measured 276 PredictionVoigt or Reuss 268 E2,3EBN+P*EsNEBN(I-I*) Prediction-brick model 268 124 likely to be different from other BN materials. The presence of This predicts a value for the se modulus, E,, of 124 etermined value of 127 the section on microstructure)also can influence the modulus GPa for uniaxially aligned tested in the off-axis direction an approximate number of 20 GPa is used To calculate the Youngs moduli, E, and E2, for uniaxially D) Poisson's Ratio and Shear Modulus for Uniaxially aligned fibrous monoliths from the constituent values for SiaN Aligned Architecture: Predicting Poissons ratio for a com- lex architecture is not as straightforward as it is for the nd BN, the cross-sectional structure of the materials is mod- Youngs modulus. However, because there is only a weak de eled using a"brick model, in which the cells are represented pendence of architecture on Poissons ratio, we use a simple by square brick and the cell boundaries are treated as mortar rule-of-mixtures approach. Assuming a condition of uniform surrounding the brick. This brick model is shown schematically in Fig. 7. The measured values of the elastic constants are listed strain exists in Table I, with predicted values from the sections that follo (3) (B) Direction 1-Longitudinal Modulus of Uniaxial Archi tecture: The well-known Voigt rule-of-mixtures is used as a nd v,i can be found from first approximation for El, the Youngs modulus in the longi- tudinal direction E= EBN BN ESN(-VBNd (1) This is a plausible model for the longitudinal Young's modulus solids. 22Mogeneral result from the elasticity for orthotropic which is for the uniaxially aligned architecture, because the SiaN4 cells fiber-reinforced composites, but these all require accurate and BN cell boundaries reasonably approximate the assump- knowledge of the shear modulus of the constituents. The shear tions made in the Voigt model (equal strain in elastic elements modulus of polycrystalline BN is unknown. Because an inde- connected in parallel). Table I lists the predicted value from the dent measurement of the shear modulus for bn could not Voigt model, which shows agreement within% compared to be obtained the shear modulus of fibrous monolithic ceramics not actually a tensile modulus, because the impulse-excitation suring G, on bars aligned at 0o and then at 90.Because hnique excites the specimen in a flexural model. The lor the two measured values should be itudinal flexural modulus of the uniaxial architecture is mod eled by calculating the effective section modulus using the average was (E) Elastic Modulus as a Function of Ply Angle for Uni brick model shown in Fig. 7.28 This leads to a straightforward but quite lengthy expression in terms of EBN, EsN, and v 29 axially Aligned Architecture: Classical laminate theory can This model converges to the Voight rule of mixtures for fibrous aligned architecture as a function of ply angle using the elastic monoliths with six or layers. Because our specimens are typically 25 layers, the Voight model is used properties calculated in the previous section(El, E2, G12, and (C) Direction 2-Transverse Modulus of Uniaxial Archi v12). In terms of the angular orientation of the ply angle, the tecture: The well-known Reuss model (uniform stress to elas- Youngs modulus is given by tic elements connected in series)serves as a lower bound for m2n2 the transverse modulus Ex, but usually badly underestimates the Youngs modulus of composites. 2 Other models for pre Ee dicting E2 for fiber-reinforced composites typically require ad- where itional experimental data and empirical factors. We have been able to accurately predict the transverse modulus using only

likely to be different from other BN materials. The presence of secondary phases and microcracks (discussed in more detail in the section on microstructure) also can influence the modulus of BN. Given the uncertainty in the Young’s modulus of BN, an approximate number of 20 GPa is used. To calculate the Young’s moduli, E1 and E2, for uniaxially aligned fibrous monoliths from the constituent values for Si3N4 and BN, the cross-sectional structure of the materials is mod￾eled using a ‘‘brick model,’’ in which the cells are represented by square brick and the cell boundaries are treated as mortar surrounding the brick. This brick model is shown schematically in Fig. 7. The measured values of the elastic constants are listed in Table I, with predicted values from the sections that follow. (B) Direction 1—Longitudinal Modulus of Uniaxial Archi￾tecture: The well-known Voigt rule-of-mixtures is used as a first approximation for E1, the Young’s modulus in the longi￾tudinal direction: E1 4 EBNVBN + ESN(1 − VBN) (1) This is a plausible model for the longitudinal Young’s modulus for the uniaxially aligned architecture, because the Si3N4 cells and BN cell boundaries reasonably approximate the assump￾tions made in the Voigt model (equal strain in elastic elements connected in parallel). Table I lists the predicted value from the Voigt model, which shows agreement within ∼3% compared to the experimental values. However, the experimental value is not actually a tensile modulus, because the impulse-excitation technique excites the specimen in a flexural model. The lon￾gitudinal flexural modulus of the uniaxial architecture is mod￾eled by calculating the effective section modulus using the brick model shown in Fig. 7.28 This leads to a straightforward but quite lengthy expression in terms of EBN, ESN, and VBN. 29 This model converges to the Voight rule of mixtures for fibrous monoliths with six or more layers. Because our specimens are typically 25 layers, the Voight model is used. (C) Direction 2—Transverse Modulus of Uniaxial Archi￾tecture: The well-known Reuss model (uniform stress to elas￾tic elements connected in series) serves as a lower bound for the transverse modulus E2, but usually badly underestimates the Young’s modulus of composites.22 Other models for pre￾dicting E2 for fiber-reinforced composites typically require ad￾ditional experimental data and empirical factors. We have been able to accurately predict the transverse modulus using only EBN, ESN, and VBN with a model that combines elastic elements in series and in parallel,29 and yields the following equation: E2,3 = EBNV* + ~1 − V*!EBNESN V*ESN + EBN ~1 − V*! (2a) where V* = 1 − =1 − VBN (2b) This predicts a value for the transverse modulus, E2, of 124 GPa, compared to the experimentally determined value of 127 GPa for uniaxially aligned specimens tested in the off-axis direction. (D) Poisson’s Ratio and Shear Modulus for Uniaxially Aligned Architecture: Predicting Poisson’s ratio for a com￾plex architecture is not as straightforward as it is for the Young’s modulus. However, because there is only a weak de￾pendence of architecture on Poisson’s ratio, we use a simple rule-of-mixtures approach. Assuming a condition of uniform strain exists, n12 4 VSNn1,2,SN + VBNn1,2,BN (3) and n21 can be found from n12 E1 = n21 E2 (4) which is a general result from the elasticity for orthotropic solids.22 Models exist that accurately predict shear modulus for fiber-reinforced composites, but these all require accurate knowledge of the shear modulus of the constituents. The shear modulus of polycrystalline BN is unknown. Because an inde￾pendent measurement of the shear modulus for BN could not be obtained, the shear modulus of fibrous monolithic ceramics instead was measured directly. This was accomplished by mea￾suring G12 on bars aligned at 0° and then at 90°. Because, theoretically, G12 4 G21, the two measured values should be equal, and, thus, the average was used. (E) Elastic Modulus as a Function of Ply Angle for Uni￾axially Aligned Architecture: Classical laminate theory can be used to predict the Young’s modulus of the uniaxially aligned architecture as a function of ply angle using the elastic properties calculated in the previous section (E1, E2, G12, and n12). In terms of the angular orientation of the ply angle, the Young’s modulus is given by22 1 Eu = m2 E1 ~m2 − n2 n12! + n2 E2 ~n2 − m2 n21! + m2 n2 G12 (5a) where m 4 cos u (5b) Fig. 7. Schematic of the ‘‘brick model’’ used to calculate the Young’s modulus of fibrous monoliths. Table I. Measured and Predicted Values of Elastic Properties for Uniaxially Aligned Fibrous Monoliths E1 (GPa) E2 (GPa) G12 (GPa) Measured 276 127 78 Prediction—Voigt or Reuss 268 88 Prediction—brick model 268 124 2476 Journal of the American Ceramic Society—Kovar et al. Vol. 80, No. 10

October 1997 Fibrous monolithic ceramics 2477 sin e Table l. Measured and Predicted values of young Modulus for Several Multilayer Fibrous Monoliths This expression is plotted in Fig. 8 with the experimentally measured values, showing that there is very good agreement ±6o][o45/ between experiment and prediction Measured modulus(GPa)198±2205±7202±3 (F Young's Modulus for Multiaxial Architectures: The 198 198 Young's modulus for multiaxial architectures is calculated terms of the engineering properties E1, E2, G12, and v12 using baut icat t ound ihestaquarid te xrs o lengtate th present Tare by an individual cell is related to the geometry of the specimen Il shows the measured and predicted Young's moduli for three 90]. The experimental values and the predictions from laminate earie d can be calculated using laminate theory as described architectures with simple stacking: [0/90), [0/460), and [0/45/ ary, and theory agree within 2.5% Unlike most monolithic ceramics or layered A(G) Summary of Elastic Properties: Because of the tex- strophic failure of the entire layer of cells on the tensile surface of the specimen. In other words, local failure of a single cell properties along the principal axes differ from the values pre- does not always cause global failure. If the stress that was have been presented that allow the elastic properties to be carried by the fractured cell can be transferred to neighboring accurately predicted. Principal moduli were determined from the elastic properties of the constituent materials and, with possible for the layer to remain intact after the failure of indi- vidual cells. Presumably, this behavior is favored when there to accurately predict modulus as a function of ply angle within are many cells in the specimen and the variability in the models can be extended to predict the elastic moduli for fibrous If loading is continued beyond the point where the fracture onolithic ceramics with multiaxial architectures of an individual cell occurs, eventually enough cells fracture so that the remaining cells on the tensile surface can no longer bear the applied stress, and an entire layer of cells fractures. In IV. Failure Mechanisms in Fibrous monoliths Two modes of failure have been observed during the flexural simple laminates, where fracture is controlled by weak-link atistics. Because the failure of fibrous monoliths is controlled of the beam because of tensile stress, or failure can initiate near by damage accumulation, the strength should be less sensitive the midsection of the beam because of shear stress. Either can to preexisting flaws than either monolithic ceramics or simple ditions. and on the fracture resistance of the cell and the cell laminates boundary. Tensile failure is favored when the cell boundaries load-bearing capacity of the bar is reduced, because the effec- are tough in comparison to that of the cells. Shear failure is tive cross section of the bar is smaller. In the case of uniaxially favored when the cell boundaries are weak compared to the aligned specimens with cells aligned at zero degrees(on-axis), cells. In a flexural test, the span-to-depth ratio of the bar de termines the relative magnitude of the normal stress to the the maximum applied load is typically achieved at the poi have a strength of -450 MPa. If the test is conducted in dis- tested as a short, thick beam. We consider each failure mecha- placement control, it is possible for the specimen to continue to nism separately bear a substantial load to large deflections even after the peak () Tensile Failure by Cell fracture load is achieved. An example of a typical stress-deflection for For an individual cell, the failure criterion is simply that a specimen in which failure initiated on the tensile surface is ailure occurs when the normal, tensile stress carried by that fa shown in Fig. 9(a). Each stress drop is associated with the cell exceeds the strength of the cell. Because the cells are made fracture of one or several layers of cells. The progressive nature from SiNa, the strength of an individual cell depends on the of the fracture process is shown in Fig. 9(b), the side surface of flaw size and fracture resistance of the cell. The stress carried this specimen after testing. The area under the stress-deflection curve is related to the energy dissipated by the sample during his noncatastrophic fracture. Typically, uniaxially aligned ecimens tested on-axis have a work-of-fracture of.5 Measure Predicted ( Tensile Failure by Cell-Boundary fracture In architectures where cells are misaligned with respect to the axis of the applied load, it is possible for the cells to remain intact, but for the specimen to fail when the surrounding cell boundary fractures. An SEM micrograph of the fracture surface of a BN cell boundary is shown in Fig 3, which shows that fracture in the interphase occurs by separation of the platelike grains between the weak, basal planes of the BN. It is likely that the preexisting Mrozowski microcracking in the Bn in terphases weakens the BN interphase by introducing large pre- existing defects that can propagate to failure Figure 10(a) shows examples of stress-deflection curves for specimens tested with cells oriented at 90 and at 30 with ersus orient hs Measu he Bn interphase on the tensile surface. Thus, the strength is

n 4 sin u (5c) This expression is plotted in Fig. 8 with the experimentally measured values, showing that there is very good agreement between experiment and prediction. (F) Young’s Modulus for Multiaxial Architectures: The Young’s modulus for multiaxial architectures is calculated in terms of the engineering properties E1, E2, G12, and n12 using laminate theory. The equations are too lengthy to present here, but can be found in standard texts on laminate theory.22 Table II shows the measured and predicted Young’s moduli for three architectures with simple stacking: [0/90], [0/±60], and [0/±45/ 90]. The experimental values and the predictions from laminate theory agree within 2.5%. (G) Summary of Elastic Properties: Because of the tex￾ture associated with fibrous monolithic ceramics, the elastic properties along the principal axes differ from the values pre￾dicted using rule-of-mixture models. However, simple models have been presented that allow the elastic properties to be accurately predicted. Principal moduli were determined from the elastic properties of the constituent materials and, with experimentally measured shear modulus data, have been used to accurately predict modulus as a function of ply angle within the plane of hot pressing. It also has been shown that these models can be extended to predict the elastic moduli for fibrous monolithic ceramics with multiaxial architectures. IV. Failure Mechanisms in Fibrous Monoliths Two modes of failure have been observed during the flexural testing of fibrous monoliths. Failure can initiate on the surface of the beam because of tensile stress, or failure can initiate near the midsection of the beam because of shear stress. Either can occur depending on the specimen geometry and loading con￾ditions, and on the fracture resistance of the cell and the cell boundary. Tensile failure is favored when the cell boundaries are tough in comparison to that of the cells. Shear failure is favored when the cell boundaries are weak compared to the cells. In a flexural test, the span-to-depth ratio of the bar de￾termines the relative magnitude of the normal stress to the shear stress; therefore, the same material might fail because of tensile stress if tested as a long, slim beam, but fail in shear if tested as a short, thick beam. We consider each failure mecha￾nism separately. (1) Tensile Failure by Cell Fracture For an individual cell, the failure criterion is simply that failure occurs when the normal, tensile stress carried by that cell exceeds the strength of the cell. Because the cells are made from Si3N4, the strength of an individual cell depends on the flaw size and fracture resistance of the cell. The stress carried by an individual cell is related to the geometry of the specimen and the constituent elastic properties of the cell and cell bound￾ary, and can be calculated using laminate theory as described earlier. Unlike most monolithic ceramics or layered ceramics, the failure of an individual cell does not necessarily cause cata￾strophic failure of the entire layer of cells on the tensile surface of the specimen. In other words, local failure of a single cell does not always cause global failure. If the stress that was carried by the fractured cell can be transferred to neighboring cells that are strong enough to bear the increased stress, it is possible for the layer to remain intact after the failure of indi￾vidual cells. Presumably, this behavior is favored when there are many cells in the specimen and the variability in the strength of the cells is high.30 If loading is continued beyond the point where the fracture of an individual cell occurs, eventually enough cells fracture so that the remaining cells on the tensile surface can no longer bear the applied stress, and an entire layer of cells fractures. In this case, failure of the layer involves the accumulation of failure of a number of cells. Contrast this with monoliths or simple laminates, where fracture is controlled by weak-link statistics. Because the failure of fibrous monoliths is controlled by damage accumulation, the strength should be less sensitive to preexisting flaws than either monolithic ceramics or simple laminates. Once a layer of cells fractures during flexural loading, the load-bearing capacity of the bar is reduced, because the effec￾tive cross section of the bar is smaller. In the case of uniaxially aligned specimens with cells aligned at zero degrees (on-axis), the maximum applied load is typically achieved at the point just prior to failure in the layer of cells closest to the tensile surface. Uniaxially aligned specimens tested on-axis typically have a strength of ∼450 MPa. If the test is conducted in dis￾placement control, it is possible for the specimen to continue to bear a substantial load to large deflections even after the peak load is achieved. An example of a typical stress–deflection for a specimen in which failure initiated on the tensile surface is shown in Fig. 9(a). Each stress drop is associated with the fracture of one or several layers of cells. The progressive nature of the fracture process is shown in Fig. 9(b), the side surface of this specimen after testing. The area under the stress–deflection curve is related to the energy dissipated by the sample during this noncatastrophic fracture. Typically, uniaxially aligned specimens tested on-axis have a work-of-fracture of ∼7.5 kJ/m2 . (2) Tensile Failure by Cell-Boundary Fracture In architectures where cells are misaligned with respect to the axis of the applied load, it is possible for the cells to remain intact, but for the specimen to fail when the surrounding cell boundary fractures. An SEM micrograph of the fracture surface of a BN cell boundary is shown in Fig. 3, which shows that fracture in the interphase occurs by separation of the platelike grains between the weak, basal planes of the BN. It is likely that the preexisting Mrozowski microcracking13 in the BN in￾terphases weakens the BN interphase by introducing large pre￾existing defects that can propagate to failure. Figure 10(a) shows examples of stress–deflection curves for specimens tested with cells oriented at 90° and at 30° with respect to the applied load. The pattern of cracking is shown in Figs. 10(b) and (c), where the side surfaces of the specimens are shown after testing. Failure is catastrophic and initiates in the BN interphase on the tensile surface. Thus, the strength is Fig. 8. Young’s modulus versus orientation for uniaxially aligned fibrous monoliths. Measured values are indicated by points. Line is the predicted behavior using the brick model and laminate theory. Table II. Measured and Predicted Values of Young’s Modulus for Several Multilayer Fibrous Monoliths [0/90] [0/±60] [0/±45/90] Measured modulus (GPa) 198 ± 2 205 ± 7 202 ± 3 Predicted modulus (GPa) 201 198 198 October 1997 Fibrous Monolithic Ceramics 2477

Journal of the American Ceramic Society-Kovar et al. Vol. 80. No. 10 (a) Crosshead DIsplacement, d(mm) nu between the lavers 30°off-axis 90°off-uxis shead Displacenent, d (n) 2 mm mn Fig. 10.(a) Stress-deflection response is shown for uniaxially aligned specimens tested at 30 and 90 orientations. Side surface of the specimen determined by the strength of the BN-containing cell boundary hat for on-axis orientations. Also, because very little crack rather than the Si3N cell. Failure occurred at a nominal stress deflection is required to propagate a crack completely through of 70 MPa for the specimen tested at 90 and at 145 MPa for the specimen when cells are oriented perpendicular to the axis the specimen tested at 30. Because the BN cell boundary is of the applied load, little energy is absorbed during the fracture much weaker than the Si3N4 cell, the strength of uniaxially process fibrous monoliths tested off-axis are much lower than 3) Tensile Failure by Combination of Cell and Cell-Boundary fracture The side surface of a specimen with a [0/45/90 architec- the load-deflection behavio ture is shown in Fig. 11(a)after testing. The specimen shows stress. which the original specimen would hay extensive delamination cracking between the 0 plies. Because of the orientation of weak bn cell boundaries the delamination

determined by the strength of the BN-containing cell boundary, rather than the Si3N4 cell. Failure occurred at a nominal§ stress of 70 MPa for the specimen tested at 90° and at 145 MPa for the specimen tested at 30°. Because the BN cell boundary is much weaker than the Si3N4 cell, the strength of uniaxially aligned fibrous monoliths tested off-axis are much lower than that for on-axis orientations. Also, because very little crack deflection is required to propagate a crack completely through the specimen when cells are oriented perpendicular to the axis of the applied load, little energy is absorbed during the fracture process. (3) Tensile Failure by Combination of Cell and Cell-Boundary Fracture The side surface of a specimen with a [0/±45/90] architec￾ture is shown in Fig. 11(a) after testing. The specimen shows extensive delamination cracking between the 0° plies. Because of the orientation of weak BN cell boundaries, the delamination § Once fracture begins, signaled by nonlinearity in the load–deflection behavior, beam theory cannot be used to relate load to stress. The apparent stress levels are reported as the ‘‘nominal stress,’’ which the original intact specimen would have experienced at that load. Fig. 10. (a) Stress–deflection response is shown for uniaxially aligned specimens tested at 30° and 90° orientations. Side surface of the specimen tested at (b) a 90° orientation and (c) a 30° orientation. Fig. 9. (a) Flexural response for a uniaxially aligned specimen tested in the 0° orientation. Apparent flexural stress is defined as the load sustained by the specimen divided by the original cross-sectional area. (b) Side surface of this specimen after testing, showing extensive delamination cracking between the layers of cells. 2478 Journal of the American Ceramic Society—Kovar et al. Vol. 80, No. 10

October 1997 Fibrous monolithic ceramics 点200 50 0.1 Crosshead Displacement, d (mm) Fig. 11.(a) Side surface of a [0/45/90] fibrous monolith is shown after testing.(b) Stress-deflection response for [0/45/90) fibrous monolith distances between the 90 plies are generally only as long as shear Initiation the cell width. However, in many of the plies, multiple cracl ing of the off-axis cells are observed For specimens containing multiaxial architectures, it is pos- sible for the peak load to be achieved after the failure of an entire layer of cells. If cells on the tensile surface are not aligned in the direction of applied stress, failure of the cell boundary on the tensile surface can occur at a relatively low oad, but cells with 0 orientations that are just beneath the tensile surface can continue to bear substantially more load This leads to stress-deflection curves with pronounced nonlin- earities prior to the peak load. An example is shown for a h noticeable nonlinearity is observed when failure of a 45.layer occurs at -200 MPa but the load continues to increase until the failure of the first on-axis layer occurs at a nominal stress of rosshead Deflection, d(mm) 85 MPa. Using laminate theory, appropriate failure criteria can be established to predict when the nonlinearity in the Fig 12. Stress-deflection response is shown for a specimen tested at elevated temperature in which failure initiated in shear. (4) Shear failure Shear failure also has been observed in some specimens that V. Influence of Material Properties have a very low interfacial fracture resistance and/or a high As demonstrated by the stress-defection curves, fibrous pan-to-depth ratio. For a specimen loaded in four-point bend ing. there is a significant shear stress between the inner ar outer loading pins that can cause shear failure if it exceeds the original load-bearing capacity. Usually, a substantial amount of shear strength of the interphase before the tensile strength of energy is absorbed by the specimen, leading to a high work- the outermost layer is reached. When a shear crack propagates of- fracture in flexure and a large Charpy impact energy, 32 This through a weak interphase at the midplane of the specimen, the occurs as a consequence of delamination of BN cell bound- stiffness of the specimen is reduced. This reduction in stiffness anes leads to a large load drop when the test is conducted in dis- allowing the material to split apart gradually rather than fracturing catastrophically. We find that graceful failure re- placement control. When loading is continued beyond the first lres crack deflection at the bn cell boundaries as well as load drop, the stress again builds in each of the halves of the significant delamination cracking and sliding. The following specimen until cracking occurs in one of two places: sufficient shear stresses develop in each of the halves, causing them to sections discuss the conditions for delamination cracking, and split again along a weak interphase or tensile stresses devel the energy absorption mechanisms leading to high work-of- fracture Because the load-bearing capacity of the beam is greatly re- (Crack Deflection duced each time a shear crack propagates, it is usually the case When a crack initiates on the tensile surface of a fibrous that the peak load that the n can bear is achieved just monolithic ceramic, the stress-deflection behavior is dictated ior to propagation of the first shear crack. by crack deflection and subsequent delamination cracking. The Figure 12 is an example of a stress-deflection plot for a conditions that cause a crack to deflect at an interface between specimen that failed in shear when the was tested at two isotropic solids have been treated theoretically by several elevated temperatures. Using elastic-beam equations, the shea groups,33,34 These models suggest that crack deflection is stress on the midplane of this specimen when the shear crack governed by the ratio of the fracture resistance of the interface initiated was 23 MPa, while the tensile stress on the surface of to that of the cell, the elastic mismatch between the cell and the the beam was -300 MPa. The transition from tensile failure to cell boundary, and the location of interface at which fracture shear failure can be predicted if the shear strength of the cell occurs. Crack deflection is predicted when the fracture resis- boundary is known. Experimental measurements indicate that tance of the interface is low and when the elastic mismatch the shear strength of the BN cell boundary is-30 MPa at ro between the cell and the cell boundary is high temperature, but it decreases at elevated temperatures. To examine the influence of interfacial fracture resistance on

distances between the 90° plies are generally only as long as the cell width. However, in many of the plies, multiple crack￾ing of the off-axis cells are observed. For specimens containing multiaxial architectures, it is pos￾sible for the peak load to be achieved after the failure of an entire layer of cells. If cells on the tensile surface are not aligned in the direction of applied stress, failure of the cell boundary on the tensile surface can occur at a relatively low load, but cells with 0° orientations that are just beneath the tensile surface can continue to bear substantially more load. This leads to stress–deflection curves with pronounced nonlin￾earities prior to the peak load. An example is shown for a specimen with a [0/±45/90] architecture in Fig. 11(b). Here a noticeable nonlinearity is observed when failure of a 45° layer occurs at ∼200 MPa, but the load continues to increase until the failure of the first on-axis layer occurs at a nominal stress of 285 MPa. Using laminate theory, appropriate failure criteria can be established to predict when the nonlinearity in the stress–deflection curve will occur. (4) Shear Failure Shear failure also has been observed in some specimens that have a very low interfacial fracture resistance and/or a high span-to-depth ratio. For a specimen loaded in four-point bend￾ing, there is a significant shear stress between the inner and outer loading pins that can cause shear failure if it exceeds the shear strength of the interphase before the tensile strength of the outermost layer is reached. When a shear crack propagates through a weak interphase at the midplane of the specimen, the stiffness of the specimen is reduced. This reduction in stiffness leads to a large load drop when the test is conducted in dis￾placement control. When loading is continued beyond the first load drop, the stress again builds in each of the halves of the specimen until cracking occurs in one of two places: sufficient shear stresses develop in each of the halves, causing them to split again along a weak interphase or tensile stresses develop in each of the halves of the specimen, causing them to fail. Because the load-bearing capacity of the beam is greatly re￾duced each time a shear crack propagates, it is usually the case that the peak load that the specimen can bear is achieved just prior to propagation of the first shear crack. Figure 12 is an example of a stress–deflection plot for a specimen that failed in shear when the specimen was tested at elevated temperatures. Using elastic-beam equations, the shear stress on the midplane of this specimen when the shear crack initiated was 23 MPa, while the tensile stress on the surface of the beam was ∼300 MPa. The transition from tensile failure to shear failure can be predicted if the shear strength of the cell boundary is known. Experimental measurements indicate that the shear strength of the BN cell boundary is ∼30 MPa at room temperature,31 but it decreases at elevated temperatures. V. Influence of Material Properties As demonstrated by the stress–defection curves, fibrous monoliths can undergo noncatastrophic or ‘‘graceful failure,’’ during which the material retains a significant fraction of its original load-bearing capacity. Usually, a substantial amount of energy is absorbed by the specimen, leading to a high work￾of-fracture in flexure and a large Charpy impact energy.32 This occurs as a consequence of delamination of BN cell bound￾aries, allowing the material to split apart gradually rather than fracturing catastrophically. We find that graceful failure re￾quires crack deflection at the BN cell boundaries as well as significant delamination cracking and sliding. The following sections discuss the conditions for delamination cracking, and the energy absorption mechanisms leading to high work-of￾fracture. (1) Crack Deflection When a crack initiates on the tensile surface of a fibrous monolithic ceramic, the stress–deflection behavior is dictated by crack deflection and subsequent delamination cracking. The conditions that cause a crack to deflect at an interface between two isotropic solids have been treated theoretically by several groups.1,33,34 These models suggest that crack deflection is governed by the ratio of the fracture resistance of the interface to that of the cell, the elastic mismatch between the cell and the cell boundary, and the location of interface at which fracture occurs. Crack deflection is predicted when the fracture resis￾tance of the interface is low and when the elastic mismatch between the cell and the cell boundary is high. To examine the influence of interfacial fracture resistance on Fig. 11. (a) Side surface of a [0/±45/90] fibrous monolith is shown after testing. (b) Stress–deflection response for [0/±45/90] fibrous monolith. Fig. 12. Stress–deflection response is shown for a specimen tested at elevated temperature in which failure initiated in shear. October 1997 Fibrous Monolithic Ceramics 2479

Journal of the American Ceramic Sociery-Kovar et al. Vol. 80. No. 10 crack deflection behavior, the composition of the BN-con- tensile surface. In contrast, the sample with 40 vol% Si3N aining cell boundary was varied. Previously, it has been ob dded to the cell boundary has very few extensive delamination erved that the addition of a strong phase to a weak interphase cracks, although cracks deflect a short distance at each cell increases the interfacial fracture resistance. II As BN in the cell boundary. Similar results have been observed in Sic-graphite oundary is replaced with Si3N4, the fracture resistance of the ous mono 7 cell boundary increases, and the tendency for crack deflection Kovar et al. 35 have conducted a more detailed study decreases significantly. SEM micrographs showing the tensile conventional, two-dimensional, layered ceramics. In this work, and side ces of two specimens after flexural testing are the interphase composition was again modified by adding shown in Fig. 13. The specimen with 10 vol% Si3N4 added to Si3Na to the Bn interphase. The interfacial fracture resistanc the cell boundary, which had the lower interfacial energy or these materials was measured directly on the Si3Na-BN shows extensive delamination on the side surface and on the laminates that revealed that the interfacial fracture resistance increased from -30 to 90 J/m as the SigNa content in the interphase was increased from 0 to 50 vol%, as shown in Fig 14. The fracture resistance of the monolithic Sis Na layers is 120 J/m2 The results of the interfacial fracture resistance measurements together with the predictions of He and Hutch- inson33 are shown in Fig. 15. This plot shows that crack de flection occurs at values of the interfacial fracture resistance hat are significantly higher than the predicted values There are several factors that may contribute to the d ncy between the observations of crack deflection and heory. For example, bn is highly anisotropic in its elastic properties as well as other mechanical properties, 5 which is ot accounted for in the theory Furthermore this theory does ot account for residual stresses that may develop because of differences in thermal expansion between Si3N4 and BN. How- ever. the microcracks in the bN. which have been observed using tEM, should relieve most of the residual stress that develops because of thermal mismatch. These microcracks also should make it easier for cracks to deflect at the BN layers. 36, 37 ≡HH crack deflection at an interface, but we observe that crack deflection and crack propagation al ways occur within the BN cell boundary, rather than at the interface between Si3N4 and BN. Figure 16 shows a crack propagating within the Bn cell The cracks wander within the bn cell boundary, bu never at the interface. Cracks seem to grow by link-up of preexisting microcracks, although it is difficult to image the near-tip region of the cracks (2) Delamination Cracking versus Crack Kinking Although crack deflection is an essential mechanism for dis- sipating energy in layered materials,38,39 crack deflection by itself does not ensure that a laminate will absorb significant amounts of energy during fracture. For example, materials with up to 50% Si3 N4 in the bn interphase have observable crack deflection but relatively little work-of-fracture, because the ex- tent of the delamination cracking decreases significantly as the dissipation depends upon the extent of delamination ci Delamination has little effect on the energy dissipation of a laminate if the delamination crack kinks and reenters the Si3N4 cell after propagating only a short distance Bulk I for Si, N4 mn Fig. 13. Side and tensile surfaces of a specimen with(a)10 vol% and tcrphasc(") vith(b)40 vol% Si, Na in the cell boundary are shown after testing Delamination cracking is much more extensive in the specimen w Fig. 14. Plot of interfacial fracture resistance as a function of Si3 Na less Si, N, in the cell boundary content in the BN-containing interphase

crack deflection behavior, the composition of the BN-con￾taining cell boundary was varied. Previously, it has been ob￾served that the addition of a strong phase to a weak interphase increases the interfacial fracture resistance.11 As BN in the cell boundary is replaced with Si3N4, the fracture resistance of the cell boundary increases, and the tendency for crack deflection decreases significantly. SEM micrographs showing the tensile and side surfaces of two specimens after flexural testing are shown in Fig. 13. The specimen with 10 vol% Si3N4 added to the cell boundary, which had the lower interfacial energy, shows extensive delamination on the side surface and on the tensile surface. In contrast, the sample with 40 vol% Si3N4 added to the cell boundary has very few extensive delamination cracks, although cracks deflect a short distance at each cell boundary. Similar results have been observed in SiC–graphite fibrous monoliths.7 Kovar et al.35 have conducted a more detailed study using conventional, two-dimensional, layered ceramics. In this work, the interphase composition was again modified by adding Si3N4 to the BN interphase. The interfacial fracture resistance for these materials was measured directly on the Si3N4–BN laminates that revealed that the interfacial fracture resistance increased from ∼30 to 90 J/m2 as the Si3N4 content in the interphase was increased from 0 to 50 vol%, as shown in Fig. 14. The fracture resistance of the monolithic Si3N4 layers is ∼120 J/m2 . The results of the interfacial fracture resistance measurements together with the predictions of He and Hutch￾inson33 are shown in Fig. 15. This plot shows that crack de￾flection occurs at values of the interfacial fracture resistance that are significantly higher than the predicted values. There are several factors that may contribute to the discrep￾ancy between the observations of crack deflection and the theory. For example, BN is highly anisotropic in its elastic properties as well as other mechanical properties,25 which is not accounted for in the theory. Furthermore, this theory does not account for residual stresses that may develop because of differences in thermal expansion between Si3N4 and BN. How￾ever, the microcracks in the BN, which have been observed using TEM, should relieve most of the residual stress that develops because of thermal mismatch. These microcracks also should make it easier for cracks to deflect at the BN layers.36,37 Finally, the He and Hutchinson33 theory defines conditions for crack deflection at an interface, but we observe that crack deflection and crack propagation always occur within the BN cell boundary, rather than at the interface between Si3N4 and BN. Figure 16 shows a crack propagating within the BN cell boundary. The cracks wander within the BN cell boundary, but never at the interface. Cracks seem to grow by link-up of preexisting microcracks, although it is difficult to image the near-tip region of the cracks. (2) Delamination Cracking versus Crack Kinking Although crack deflection is an essential mechanism for dis￾sipating energy in layered materials,38,39 crack deflection by itself does not ensure that a laminate will absorb significant amounts of energy during fracture. For example, materials with up to 50% Si3N4 in the BN interphase have observable crack deflection but relatively little work-of-fracture, because the ex￾tent of the delamination cracking decreases significantly as the Si3N4 content in the interphase is increased. Clearly, energy dissipation depends upon the extent of delamination cracking. Delamination has little effect on the energy dissipation capacity of a laminate if the delamination crack kinks and reenters the Si3N4 cell after propagating only a short distance. Fig. 13. Side and tensile surfaces of a specimen with (a) 10 vol% and with (b) 40 vol% Si3N4 in the cell boundary are shown after testing. Delamination cracking is much more extensive in the specimen with less Si3N4 in the cell boundary. Fig. 14. Plot of interfacial fracture resistance as a function of Si3N4 content in the BN-containing interphase. 2480 Journal of the American Ceramic Society—Kovar et al. Vol. 80, No. 10