《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.1151-2916.1999.tb02280.x[1]

ournal JAm.cnm.So,82m23567-3574(1999 Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composite Michael J. O'Brient and Brian W. Sheldon Division of Engineering, Brown University, Providence, Rhode Island 02912 A porous Al2O3 coating for Al2O3 composites was prepared For successful toughening in a fiber-reinforced composite by aerosol-spray deposition of submicrometer-sized Al O3 all of these mechanisms require that a crack deflect preferen- owder. A model composite specimen was hot-pressed to tially along the fiber-matrix interface rather than penetrate the change the coatings porosity and, thereby, change the in fiber.Similarly, a layered composite requires crack deflection terphase fracture resistance The mixed-mode fracture re between laminae sistance of the interphase ranged from 0.5 to 14.8 J/m2.The Crack deflection requires a weak interface between fiber and interphase fracture was characterized using electron and matrix or a weak interface between laminae. The He- acoustic microscopy. Finite-element analysis(FEA)showed Hutchinson criterion identifies the interfacial fracture resis that the testing method possessed a short transient behavior tance required for crack deflection as a function of the elastic and was immune to asymmetrical cracks. This approach mismatch between two isotropic materials. For the specific provided a fundamental investigation of the relationships case of no elastic mismatch, the criterion predicts that the frac- among interphase microstructure, processing, and fracture ture resistance of the interface must be less than one-fourth the esistance. The results also provided a detailed test of the fracture resistance of the reinforcing phase to which it is at- He-Hutchinson criterion for crack deflection ached. An example of a fiber-reinforced CMC with no elastic mismatch is an Al,O3 matrix reinforced with Al,O3 fibers . Introduction Laminated composites also can be made with a single type ERAMICS are attractive candidates for high-temperataure ap. The goal of the research presented here was to use a standard con "lications because they offer high compressive strength, fracture specimen to study crack deflection and interfacial bined with a high melting point and superior creep resis- fracture in a composite with no elastic mismatch. The standard tance. Oxide ceramics are particularly attractive because of fracture specimen also provided a powerful tool to probe and their inherent resistance to degradation in oxidizing atmo- test the He-Hutchinson criterion pheres. However, monolithic ceramics have limited potential Current ceramic composites successfully use either graphite for use in highly stressed applications because of their poor or bN as the interphase between ceramic fiber and ceramic fracture toughness and notch sensitivity. In contrast, compos- matrix. Both graphite and BN offer the reduced interphase ites of ceramic fibers in a ceramic matrix, known as ceramic fracture resistance needed to deflect a crack. Unfortunately, in matrix composites(CMCs), offer markedly improved fracture an oxidizing atmosphere at 600oC, graphite is prone to form a esistance. For example, laminae of SiC with graphite inter- volatile oxide, and BN can oxidize to form a borate glass. There d greater than an order of magnitude fore, oxidation limits the use of current ceramic composites increase in the work of fracture at room temperature, as com- Many strategies for developing oxidation-resistant coatings pared to monolithic SiC have been explored. These methods include the use of mona Q. Ceramic composites can have a particle-, whisker-, lamina-, zite, which is an oxide ceramic with a low native fracture or fiber-reinforced architecture. Several toughening mecha- toughness, 0 and the use of protective barriers and passivation nisms are available in these ceramic composites that are not strategies that prevent the oxidation of graphite and bN at high present in monolithic ceramics temperatures. Previous work demonstrates that a porous ZrO2 (1) An advancing crack that is deflected by the reinforcing coating can provide crack deflection as an interfac phase dissipates fracture energy through an increase in surface Al,O3. 2 Previous researchers have used starches with mean particle sizes of 5-33 um as a fugitive material that burns out 2) Intact whiskers in the crack's during processing to give a layered Al2O3 CMC, with alter offer crack-face bridging shields the crack tip fr nating dense and porous layers and a layer thickness of remotely applied load ar vIng crack advance the present work, we develop ceramic coatings 3) Pulled-out fibers or whiskers deeper in the cracks small amount of porosity deliberately introduced. This sti wake dissipate additional energy through frictional sliding exploits the observation that introducing as little as 1 rosity into monolithic Al,O, can lead to a fracture resistance less than one fourth that of fully dense monolithIc Al,O Hence, a ceramic interphase with only a small amount o A G. Evans--contributing editor porosity can satisfy the requirements of the He-Hutchinson criterion. Control of porosity also provides an interphase whose fracture resistance can be tailored, which provides an excellent opportunity to investigate the He-Hutchinson criterion. Fur thermore, a porous Al2O3 coating is attractive for Al2O3 com- ianapolis, IN, April 15, 1996( Ceramic-Matrix Co osites because it eliminates the potential mismatch in the co- am of the National Science Foundation efficient of thermal expansion. The porous Al2O ogram of the National Science demonstrates stability to at least 1300C, a significant mark for ceramic applications. The work presented here Member, American Ceramic Society Current address: Lawrence Livermore National Laboratory, Livermore, CA portes submicrometer porosity into an interphase several micrometers thick. Both of these length scales are considerably 3567

Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composites Michael J. O’Brien† and Brian W. Sheldon* Division of Engineering, Brown University, Providence, Rhode Island 02912 A porous Al2O3 coating for Al2O3 composites was prepared by aerosol-spray deposition of submicrometer-sized Al2O3 powder. A model composite specimen was hot-pressed to change the coating’s porosity and, thereby, change the in￾terphase fracture resistance. The mixed-mode fracture re￾sistance of the interphase ranged from 0.5 to 14.8 J/m2 . The interphase fracture was characterized using electron and acoustic microscopy. Finite-element analysis (FEA) showed that the testing method possessed a short transient behavior and was immune to asymmetrical cracks. This approach provided a fundamental investigation of the relationships among interphase microstructure, processing, and fracture resistance. The results also provided a detailed test of the He–Hutchinson criterion for crack deflection. I. Introduction CERAMICS are attractive candidates for high-temperataure ap￾plications because they offer high compressive strength, combined with a high melting point and superior creep resis￾tance. Oxide ceramics are particularly attractive because of their inherent resistance to degradation in oxidizing atmo￾spheres.1 However, monolithic ceramics have limited potential for use in highly stressed applications because of their poor fracture toughness and notch sensitivity. In contrast, compos￾ites of ceramic fibers in a ceramic matrix, known as ceramic￾matrix composites (CMCs), offer markedly improved fracture resistance. For example, laminae of SiC with graphite inter￾phases have demonstrated greater than an order of magnitude increase in the work of fracture at room temperature, as com￾pared to monolithic SiC.2 Ceramic composites can have a particle-, whisker-, lamina-, or fiber-reinforced architecture. Several toughening mecha￾nisms are available in these ceramic composites that are not present in monolithic ceramics. (1) An advancing crack that is deflected by the reinforcing phase dissipates fracture energy through an increase in surface area. (2) Intact whiskers, fibers, or laminae in the crack’s wake offer crack-face bridging, which shields the crack tip from the remotely applied load and lowers the driving force for further crack advance. (3) Pulled-out fibers or whiskers deeper in the crack’s wake dissipate additional energy through frictional sliding. For successful toughening in a fiber-reinforced composite, all of these mechanisms require that a crack deflect preferen￾tially along the fiber–matrix interface rather than penetrate the fiber.3 Similarly, a layered composite requires crack deflection between laminae. Crack deflection requires a weak interface between fiber and matrix4 or a weak interface between laminae. The He– Hutchinson criterion5 identifies the interfacial fracture resis￾tance required for crack deflection as a function of the elastic mismatch between two isotropic materials. For the specific case of no elastic mismatch, the criterion predicts that the frac￾ture resistance of the interface must be less than one-fourth the fracture resistance of the reinforcing phase to which it is at￾tached. An example of a fiber-reinforced CMC with no elastic mismatch is an Al2O3 matrix reinforced with Al2O3 fibers. Laminated composites also can be made with a single type of ceramic lamina.2,6 The goal of the research presented here was to use a standard fracture specimen7 to study crack deflection and interfacial fracture in a composite with no elastic mismatch. The standard fracture specimen also provided a powerful tool to probe and test the He–Hutchinson criterion. Current ceramic composites successfully use either graphite or BN as the interphase between ceramic fiber and ceramic matrix.8 Both graphite and BN offer the reduced interphase fracture resistance needed to deflect a crack. Unfortunately, in an oxidizing atmosphere at 600°C, graphite is prone to form a volatile oxide, and BN can oxidize to form a borate glass.9 There￾fore, oxidation limits the use of current ceramic composites. Many strategies for developing oxidation-resistant coatings have been explored. These methods include the use of mona￾zite, which is an oxide ceramic with a low native fracture toughness,10 and the use of protective barriers and passivation strategies that prevent the oxidation of graphite and BN at high temperatures.11 Previous work demonstrates that a porous ZrO2 coating can provide crack deflection as an interface for Al2O3. 12 Previous researchers have used starches with mean particle sizes of 5–33 mm as a fugitive material that burns out during processing to give a layered Al2O3 CMC, with alter￾nating dense and porous layers and a layer thickness of ∼100 mm.13 In the present work, we develop ceramic coatings with a small amount of porosity deliberately introduced. This strategy exploits the observation that introducing as little as 10% po￾rosity into monolithic Al2O3 can lead to a fracture resistance less than one fourth that of fully dense monolithic Al2O3. 14 Hence, a ceramic interphase with only a small amount of porosity can satisfy the requirements of the He–Hutchinson criterion. Control of porosity also provides an interphase whose fracture resistance can be tailored, which provides an excellent opportunity to investigate the He–Hutchinson criterion. Fur￾thermore, a porous Al2O3 coating is attractive for Al2O3 com￾posites because it eliminates the potential mismatch in the co￾efficient of thermal expansion. The porous Al2O3 also demonstrates stability to at least 1300°C, a significant bench￾mark for ceramic applications. The work presented here incor￾porates submicrometer porosity into an interphase several micrometers thick. Both of these length scales are considerably A. G. Evans—contributing editor Manuscript No. 190686. Received September 23, 1997; approved June 24, 1999. Presented in part at the 98th Annual Meeting of The American Ceramic Society, Indianapolis, IN, April 15, 1996 (Ceramic-Matrix Composites Symposium: Fibers and Interfaces, Paper No. SVII-18-96). Supported primarily by the MRSEC Program of the National Science Foundation, under Award No. DMR-9632524 and by the MRG Program of the National Science Foundation, under Award No. DMR-9223683. *Member, American Ceramic Society. † Current address: Lawrence Livermore National Laboratory, Livermore, CA 94550. J. Am. Ceram. Soc., 82 [12] 3567–3574 (1999) Journal 3567

Journal of the American Ceramic Sociery-O'Brien and Sheldon VoL. 82.N smaller for our interphase than for the porous layers fabricated at applied pressures of 5.2 MPa(750 psi), 10.4 MPa(1500 13 17.2 MPa(2500 psi), 24. 2 MPa(3500 psi), or 31.1 MPa( Porous aloa does not offer the low coefficient of friction s) at either 1200°or1300°C inherent in graphite and BN coatings. A low coefficient of The appropriate hot-pressing conditions were selected by friction is important in a fiber-reinforced architecture, to pro- following the guidelines established in an earlier study of high mote fiber pullout, but it is not a critical requirement for tough purity submicrometer-scale Al2O3 powder (Linde A, Praxair, ening in layered ceramics. Experimental evidence also suggests Inc, Danbury, CT). 7 Conditions initially were selected to that fiber coatings with a relatively high coefficient of friction yield nominal interphase densities in the range 50%95%. The can still pr5,16 composite toughening behavior in some earlier work showed that Al2O3 reaches an end-point density after 2 h of hot-pressing. A 4 h hot press was selected in the present study to guarantee that end-point density was achieved Il. Experimental Procedure Aerosol-spray deposition, followed by hot-pressing, pro- duced an interphase of uniform thickness along both the 70 mm length and the 4 mm width. The interphase thicknesses typi cally were in the range 2-5 um. Figure 2 shows an interphase The interphase of Al2 O, powder was deposited on very care- of slightly <2 um and demonstrates the uniformity of the in- fully machined Al2O, bars, using an aerosol-spray technique A terphase thickness precursor suspension of very high purity, 37 nm diameter (2)Mechanical Testing Al2O3 powder(Nanotek Aluminum Oxide, Nanophase Tech nologies Corp, Burr Ridge, IL) was prepared at a concentra- To perform the standard four-point-bend delamination test of tion of 0.060 g of Al2O3 per 40 mL of reaction-grade methanol Interphase fracture resistance, a deep and sharp precrack was introduced by indenting with a large-scale Vickers diamond at in a nebulizer that formed an aerosol through a vibrating pi ezoelectric quartz crystal. A helium carrier gas with a flow rate mm width of the bar by successively positioning the bar with of 250 sccm(standard cubic centimeters per minute)swept the a precision translational stage equipped with a Vernier barrel nozzle heated to 550C. This process completely vaporized the cracks produced by a Vickers indentation. 18, 19 We found ethanol solvent during transit. The precursor powder, initially empirically, that a load of 500 N at the centermost Vickers at a diameter of 37 nm, produced agglomerates with an average indentation and loads of 400 N at the two adjoining Vickers diameter of about one-third of a micrometer(based or indentations would yield a satisfactory, deep precrack. Higher electron microscopy(SEM) images) indentation loads ran the risk of great damage to the indented Technical Ceramics Co, Oak Ridge, TN) with a grain size of series of half-penny cracks from the corners of the Vickers 20 um was machined(by Chand Kare Technical Ceramics, Worcester, MA)into bars with final dimensions of 2 mm x 4 to directly image the cracks produced by the indentations Nonetheless, the cracks radiating from neighboring corners of used as the target for deposition was lapped(by valley design adjacent vickers indentations did link up. Thus, although direct finish of R, =0.05 um(2 uin ) A composite sandwich of to form in the interior of the indented bar from the overall nominal dimensions 4 mm x 4 mm x 70 mm. with an indentations Al2O3 interphase between monolithic Al2O, substrates, was The precracked sandwich was loaded in three-point be at a crosshead displacement of 2.5 um/min in a stiff, formed by placing a second identical ALO, bar atop the de- driven load frame(Model No. 4505, Instron Corp posited interphase. Figure I shows a schematic of the test specimen. The length of the half-crack from the center is la- MA), in order to nucleate a crack that could propaga nect.The Hot-pressing formed a composite of fully dense Al2O3 bars crack in the bar was a typical intergranular fracture joined by a porous Al2O3 interphase. a die machined to toler- After successful deflection under three-point bending, the ances of #25 um from very high-quality graphite(ACF-10Q interphase crack naturally self-arrested, because the applied Poco Graphite, Inc, Decatur, TX) was used to carefully align the two bars of the sandwich. A mating graphite platen was used to provide unidirectional hot pressure across the two bars All hot-pressing was done for 4 h under a vacuum of 10"F 2 mm 89543.8KVX4,9881FmWD18 Fig. l. Test geometry to measure interphase fracture resistance under Fig. 2. Interphase with a thickness of <2.0 um for specimen hot- four-point bending; length of half-crack from the center is labeled a. pressed at 17. 2 MPa(2500 psi)and 1300C

smaller for our interphase than for the porous layers fabricated with fugitive starches.13 Porous Al2O3 does not offer the low coefficient of friction inherent in graphite and BN coatings. A low coefficient of friction is important in a fiber-reinforced architecture, to pro￾mote fiber pullout, but it is not a critical requirement for tough￾ening in layered ceramics. Experimental evidence also suggests that fiber coatings with a relatively high coefficient of friction can still provide composite toughening behavior in some applications.15,16 II. Experimental Procedure (1) Processing The interphase of Al2O3 powder was deposited on very care￾fully machined Al2O3 bars, using an aerosol-spray technique. A precursor suspension of very high purity, 37 nm diameter Al2O3 powder (Nanotek Aluminum Oxide, Nanophase Tech￾nologies Corp., Burr Ridge, IL) was prepared at a concentra￾tion of 0.060 g of Al2O3 per 40 mL of reaction-grade methanol and placed in an ultrasonic bath for 30 min to form a colloidal suspension. For deposition, a charge of suspension was placed in a nebulizer that formed an aerosol through a vibrating pi￾ezoelectric quartz crystal. A helium carrier gas with a flow rate of 250 sccm (standard cubic centimeters per minute) swept the aerosol from the nebulizer to the target through an intermediate nozzle heated to 550°C. This process completely vaporized the methanol solvent during transit. The precursor powder, initially at a diameter of 37 nm, produced agglomerates with an average diameter of about one-third of a micrometer (based on scanning electron microscopy (SEM) images). Commercially available high-purity Al2O3 (AD995, Coors Technical Ceramics Co., Oak Ridge, TN) with a grain size of 20 mm was machined (by Chand Kare Technical Ceramics, Worcester, MA) into bars with final dimensions of 2 mm × 4 mm × 70 mm. In addition, the 4 mm × 70 mm face of the bar used as the target for deposition was lapped (by Valley Design Corp., Westford, MA) with 1 mm diamond grit to a surface finish of Ra 4 0.05 mm (2 min.). A composite sandwich of overall nominal dimensions 4 mm × 4 mm × 70 mm, with an Al2O3 interphase between monolithic Al2O3 substrates, was formed by placing a second identical Al2O3 bar atop the de￾posited interphase. Figure 1 shows a schematic of the test specimen. The length of the half-crack from the center is la￾beled a. Hot-pressing formed a composite of fully dense Al2O3 bars joined by a porous Al2O3 interphase. A die machined to toler￾ances of ±25 mm from very high-quality graphite (ACF-10Q, Poco Graphite, Inc., Decatur, TX) was used to carefully align the two bars of the sandwich. A mating graphite platen was used to provide unidirectional hot pressure across the two bars. All hot-pressing was done for 4 h under a vacuum of 10−4 Pa, at applied pressures of 5.2 MPa (750 psi), 10.4 MPa (1500 psi), 17.2 MPa (2500 psi), 24.2 MPa (3500 psi), or 31.1 MPa (4500 psi) at either 1200° or 1300°C. The appropriate hot-pressing conditions were selected by following the guidelines established in an earlier study of high￾purity submicrometer-scale Al2O3 powder (Linde A, Praxair, Inc., Danbury, CT).17 Conditions initially were selected to yield nominal interphase densities in the range 50%–95%. The earlier work showed that Al2O3 reaches an end-point density after 2 h of hot-pressing. A 4 h hot press was selected in the present study to guarantee that end-point density was achieved. Aerosol-spray deposition, followed by hot-pressing, pro￾duced an interphase of uniform thickness along both the 70 mm length and the 4 mm width. The interphase thicknesses typi￾cally were in the range 2–5 mm. Figure 2 shows an interphase of slightly <2 mm and demonstrates the uniformity of the in￾terphase thickness. (2) Mechanical Testing To perform the standard four-point-bend delamination test of interphase fracture resistance,7 a deep and sharp precrack was introduced by indenting with a large-scale Vickers diamond at the midspan of one of the two monolithic bars. A row of three Vickers indentations was placed at 1 mm intervals across the 4 mm width of the bar by successively positioning the bar with a precision translational stage equipped with a Vernier barrel. Previous works described the radial-medial and lateral cracks produced by a Vickers indentation.18,19 We found, empirically, that a load of 500 N at the centermost Vickers indentation and loads of 400 N at the two adjoining Vickers indentations would yield a satisfactory, deep precrack. Higher indentation loads ran the risk of great damage to the indented bar. The row of three indentations was intended to produce a series of half-penny cracks from the corners of the Vickers indentations. Because the bars were opaque, it was impossible to directly image the cracks produced by the indentations. Nonetheless, the cracks radiating from neighboring corners of adjacent Vickers indentations did link up. Thus, although direct evidence is lacking, a single linked flaw of deep depth seemed to form in the interior of the indented bar from the series of indentations. The precracked sandwich was loaded in three-point bending at a crosshead displacement of 2.5 mm/min in a stiff, screw￾driven load frame (Model No. 4505, Instron Corp., Canton, MA), in order to nucleate a crack that could propagate across the uncracked ligament, meet the interphase, and deflect. The crack in the bar was a typical intergranular fracture. After successful deflection under three-point bending, the interphase crack naturally self-arrested, because the applied Fig. 1. Test geometry to measure interphase fracture resistance under four-point bending; length of half-crack from the center is labeled a. Fig. 2. Interphase with a thickness of <2.0 mm for specimen hot￾pressed at 17.2 MPa (2500 psi) and 1300°C. 3568 Journal of the American Ceramic Society—O’Brien and Sheldon Vol. 82, No. 12

December 1999 Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composites nding moment, which represents the driving force for crack -200 1 dvance, dropped off linearly from the centerpoint of the sand wich to the outermost loading points. Although the interphase crack could not be measured directly because the composite 175 andwich was opaque, acoustic microscopy verified that the rack length could be closely estimated by monitoring the com -150 aliance of the cracked sandwich(see Section Ill(3). This overall rocedure yielded an interphase crack that typically measured 4 mm long from the centerpoint, or 8 mm in total length. As plained in the Appendix, finite-element analysis(FEA)con-T of the four-point-bend delamination test. Me int bend test then could continue with confidence 75 The cracked sandwich next was tested under four-point nding at a crosshead displacement of 2.5 um/min. The outer span of the four-point bend test was set to 50 mm and the inner an to 42 mm, which gave a moment arm of 4 mm. The displacement of the sandwich's neutral axis at the centerspan was monitored with an extensometer(Model No. 2630-031 astron Corp )in order to identify the steady-state load at which the interphase crack propagated. As required by the pertinent military standard for the flexural testing of ceramics, the load ing pins were"free to rotate in order to eliminate any frictional Centerspan Displacement (mm) restraints. "20 In the absence of load-point frictional restraints the steady-state load was turned directly into a material prop- Fig 3. Typical experimental plot from load frame that displays the erty, the interphase fracture resistance, by using the closed characteristic steady-state delamination at a load of 188 N: ordinate form solution of Charalambides et aL. 7 shows the total applied load, in newtons, and abscissa shows the dis- 3) Characterization of fracture Path by Electron and placement, in micrometers, of the specimens neutral axis, as measured Acoustic Fractography The end-to-end fracture path was revealed in cross section by carefully grinding intact composite sandwiches along an entire 70 mm long side face. The depth of material removed may not have been perfectly closed during the initial linear through grinding was 0.381 mm, which exceeded 2.5(K/o from a load ofon to a load of 68N. In for Al,O3 (Ke is the fracture toughness and o, the yield stres itial compliance was calculated from beam-bending theory This material-removal depth ensured that the exposed fracture which cannot account for the complicated three-dimensional ath had, in fact, been under plane-strain loading during me fractures produced by the Vickers indentations. The Vickers hanical testing dentations, which did not close when unloaded, and their During the grinding, with both 15 and 9 um diamond, the ssociated lateral and medial cracks, made the actual specimen ample was repeatedly infiltrated with hot beeswax, which pre more co mpliant than implied by the value calculated from served the fracture surface. After the grinding depth had been eached, the fracture surface was polished down using I um At a peak load of 194 N, the crack first started to grow. At diamond grit a load of 186-190 N, the specimen displayed the characteristic Acoustic fractographs of cor te sandwiches also were steady-state fracture of the interphase crack at a closely con- taken after mechanical testing(Multiscan acoustic microsco stant load, as expected from earlier works. 7 The observed Panametrics, Inc, Waltham, MA) was completed. A 50 mHz steady-state load at which the interphase crack propagated was transducer produced the best results. The acoustic images were converted directly into a material property the interphase frac- focused on the 4 mm x 70 mm face of the specimen in the plane ture resistance by using the closed-form solution. 7 For the results drawn from Fig. 3 to be valid. no sources of error can exist during the test. One source of error is load-point IlL. Results friction during the test. This friction can be discounted as a source of error for two reasons: First, as explained in Section ( Mechanical Testin II(2), freely rolling load pins were used; second, load-point Figure 3 is a typical experimental result from the four-point friction, if present, manifests as a rising load during propaga- bend delamination test. The slope of the line from a load of 0 tion of the interphase crack, but no rising load was observed n to a load of 68 N is linear and corresponds to a compliance during interphase fracture(see Fig. 3). This observation also slightly greater than that of the uncracked specimen, calculated indicates that the specimen displayed no significant R-curve from beam-bending theory. This finding implies that the initial behavior as the interphase crack propagated. An R-curve be- linear response is caused by a crack-closure effect correspond havior presumably would have manifested itself as a rising load ing to a fully closed crack, I although the underestimate in the during interphase fracture calculated compliance suggests that the cracked specimen is A second potential source of error during the test is mis- not perfectly closed. The slope of the line from a load of 120 alignment of the four-point bend fixture. If the test fixture is n to the peak load also is linear and is presumed to correspond misaligned, a component of three-point bending occurs during to the compliance of the specimen with a fully open crack as the test. However, under the influence of any three-point bend- ng as the crack formed during three-point bending. The non- ing, again, a rising load would appear during propagation of the linear line between the loads of 68 and 120 N corresponds to the transition between a fully open and a fully closed crack shows measured interphase fracture resistance as a FEA, outlined in the Appendix, showed that the compliance function of hot-pressing pressure for hot-pressing temperatures of the specimen with a fully open crack, in Fig. 3, corresponded of 1200 and 1300 C. The error bars correspond to the com- to an interphase crack 4 mm long from the centerpoint, or8 bined estimate of experimental errors in the quantities inserted mm in total length. Because the interphase crack that formed into the closed-form solution for the interphase fracture resis- during three-point bending thus was very long, the specimen tance. For the specimens hot-pressed at 1200C, the fract

bending moment, which represents the driving force for crack advance, dropped off linearly from the centerpoint of the sand￾wich to the outermost loading points. Although the interphase crack could not be measured directly because the composite sandwich was opaque, acoustic microscopy verified that the crack length could be closely estimated by monitoring the com￾pliance of the cracked sandwich (see Section III(3)). This overall procedure yielded an interphase crack that typically measured 4 mm long from the centerpoint, or 8 mm in total length. As explained in the Appendix, finite-element analysis (FEA) con￾firmed that a 4 mm interphase crack was safely outside the transient zone of the four-point-bend delamination test. Mea￾surement of the interphase fracture resistance with the four￾point bend test then could continue with confidence. The cracked sandwich next was tested under four-point bending at a crosshead displacement of 2.5 mm/min. The outer span of the four-point bend test was set to 50 mm and the inner span to 42 mm, which gave a moment arm of 4 mm. The displacement of the sandwich’s neutral axis at the centerspan was monitored with an extensometer (Model No. 2630-031, Instron Corp.) in order to identify the steady-state load at which the interphase crack propagated. As required by the pertinent military standard for the flexural testing of ceramics, the load￾ing pins were “free to rotate in order to eliminate any frictional restraints.”20 In the absence of load-point frictional restraints, the steady-state load was turned directly into a material prop￾erty, the interphase fracture resistance, by using the closed￾form solution of Charalambides et al.7 (3) Characterization of Fracture Path by Electron and Acoustic Fractography The end-to-end fracture path was revealed in cross section by carefully grinding intact composite sandwiches along an entire 70 mm long side face. The depth of material removed through grinding was 0.381 mm, which exceeded 2.5(Kc/sy) 2 for Al2O3. (Kc is the fracture toughness and sy the yield stress.) This material-removal depth ensured that the exposed fracture path had, in fact, been under plane-strain loading during me￾chanical testing. During the grinding, with both 15 and 9 mm diamond, the sample was repeatedly infiltrated with hot beeswax, which pre￾served the fracture surface. After the grinding depth had been reached, the fracture surface was polished down using 1 mm diamond grit. Acoustic fractographs of composite sandwiches also were taken after mechanical testing (Multiscan acoustic microscope, Panametrics, Inc., Waltham, MA) was completed. A 50 mHz transducer produced the best results. The acoustic images were focused on the 4 mm × 70 mm face of the specimen in the plane of the interphase. III. Results (1) Mechanical Testing Figure 3 is a typical experimental result from the four-point￾bend delamination test. The slope of the line from a load of 0 N to a load of 68 N is linear and corresponds to a compliance slightly greater than that of the uncracked specimen, calculated from beam-bending theory. This finding implies that the initial linear response is caused by a crack-closure effect correspond￾ing to a fully closed crack,21 although the underestimate in the calculated compliance suggests that the cracked specimen is not perfectly closed. The slope of the line from a load of 120 N to the peak load also is linear and is presumed to correspond to the compliance of the specimen with a fully open crack as long as the crack formed during three-point bending. The non￾linear line between the loads of 68 and 120 N corresponds to the transition between a fully open and a fully closed crack.21 FEA, outlined in the Appendix, showed that the compliance of the specimen with a fully open crack, in Fig. 3, corresponded to an interphase crack 4 mm long from the centerpoint, or 8 mm in total length. Because the interphase crack that formed during three-point bending thus was very long, the specimen may not have been perfectly closed during the initial linear response from a load of 0 N to a load of 68 N. In addition, the initial compliance was calculated from beam-bending theory, which cannot account for the complicated three-dimensional fractures produced by the Vickers indentations. The Vickers indentations, which did not close when unloaded, and their associated lateral and medial cracks, made the actual specimen more compliant than implied by the value calculated from beam-bending theory. At a peak load of 194 N, the crack first started to grow. At a load of 186–190 N, the specimen displayed the characteristic steady-state fracture of the interphase crack at a closely con￾stant load, as expected from earlier works.7 The observed steady-state load at which the interphase crack propagated was converted directly into a material property, the interphase frac￾ture resistance, by using the closed-form solution.7 For the results drawn from Fig. 3 to be valid, no sources of error can exist during the test. One source of error is load-point friction during the test. This friction can be discounted as a source of error for two reasons: First, as explained in Section II(2), freely rolling load pins were used; second, load-point friction, if present, manifests as a rising load during propaga￾tion of the interphase crack,22 but no rising load was observed during interphase fracture (see Fig. 3). This observation also indicates that the specimen displayed no significant R-curve behavior as the interphase crack propagated. An R-curve be￾havior presumably would have manifested itself as a rising load during interphase fracture. A second potential source of error during the test is mis￾alignment of the four-point bend fixture. If the test fixture is misaligned, a component of three-point bending occurs during the test. However, under the influence of any three-point bend￾ing, again, a rising load would appear during propagation of the interphase crack.2 Figure 4 shows measured interphase fracture resistance as a function of hot-pressing pressure for hot-pressing temperatures of 1200° and 1300°C. The error bars correspond to the com￾bined estimate of experimental errors in the quantities inserted into the closed-form solution for the interphase fracture resis￾tance. For the specimens hot-pressed at 1200°C, the fracture Fig. 3. Typical experimental plot from load frame that displays the characteristic steady-state delamination at a load of 188 N; ordinate shows the total applied load, in newtons, and abscissa shows the dis￾placement, in micrometers, of the specimen’s neutral axis, as measured at the centerspan. December 1999 Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composites 3569

3570 Journal of the American Ceramic Society'O'Brien and shelda Vol. 82, No. 12 angle considerations, the interphase fracture resistance pro- vided in this paper represents the correct material property that should be inserted into the he-Hutchinson criterion per Defl, The substrate fracture resistance that is inserted into the de- nominator of the He-Hutchinson criterion is a mode I prop- erty. Thus, the fracture resistance of the monolithic Al2O3 was measured with the chevron-notch short rod specimen2in a commercially available fracture-testing machine(Fractometer 1, Terratek Systems, Inc, Salt Lake City, UT). Seven speci- mens were machined from the same tile of Al2O3(all of the four-point-bend delamination-test specimens also were ma- chined from this tile). The measured values for these mono- lithic specimens ranged from 42.8 to 65.4 J/m, with an average value of 54.7 J/n The experimentally measured fracture-resistance values are in very good agreement with the theoretical He-Hutchinson criterion for crack deflection. As seen in Fig. 4. the maximum Pressed at 1300]C value that permitted crack deflection in a porous interphase was Pressed at 1200 ughly one-fourth of the value needed for the dense Al,O The theoretical value of one-fourth was not corrected for the elastic mismatch and does not account for possible R-curve effects these issues are discussed in more detail in Section IV Hot Pressing pressure in MPa However, based on this approximate value of one-fourth, the maximum allowable interfacial fracture resistance was between Fig. 4. Interphase fracture resistance as a function of hot-pressing 10.7 and 16.4 J/m2(i.e, one-fourth of 42.8 and 65.4 J/m2) pressure and temperature These two limiting values are labeled the upper deflection cri- terion and the lower deflection criterion in Fig. 4. The solid line resistance climbed monotonically to a maximum at a hot labeled avg defl. criterion in Fig. 4 is the average value for the ressing pressure of 24.2 MPa(3500 psi)and then leveled off, maximum allowable interfacial fracture resistance and was ith a further increase in pressure, to 31. 1 MPa(4500 psi). As found by taking one-fourth of 54.7 J/m2. As shown in Fig.4, all a check of the experiment's repeatability, two runs were made of the measured interphase resistances are lower than the upper in the present case, for a pressure of 10.4 MPa(1500 psi) ar a temperature of 1200.C. As shown in Fig. 4, the duplicate runs (3) Microstructure and Estimates of Porosity ating very good repeatability. The difference in values is The porosity of the interphase was characterized using pol- attributed to true variability in the fracture resistance of the shed and etched mounts of interphase cross sections. Quanti- nterphase processed in the various specimens under identical tative assessment was quite challenging, because the interphases were very prone to pullout during polishing The interphases were prep For the specimens hot-pressed at 1300oC, the fracture resis- each specimen across the width with a tance climbed monotonically up to a hot-press 17.2 MPa(2500 psi). Specimens hot-pressed at 24.2 MPa vacuum impregnating the cross section in 12-hour epoxy 3500 psi) and 31.1 MPa(4500 psi)at 1300oC did not deflect vacuum impregnation wicked epoxy into the porosity and pre a crack at the interphase during initial three-point bending. As served the interphase for examination. The m ounts were lapped a further check, a specimen hot-pressed at 20.8 MPa(3000 psi successively with diamond grit, down to 0. 25 um, and finally ailed to deflect a crack. Presumably, the interphases hot slashed with 50 nm colloidal sio. grain structures and in- pressed at or above 20.8 MPa(3000 psi)at 1300C allowed no tergranular porosity were revealed by etching for 5 min in crack deflection because the fracture resistances were too hig boiling phosphoric acid. Before the specimens were imaged Thus, the specimen hot-pressed at 17.2 MPa(2500 psi) and the mounts were cleaned ultrasonically in alcohol and coated 1300C represented the highest fracture resistance that still with an estimated 20 nm of carbon to prevent charging allowed successful crack deflection electron microscop 2) Test of the He-Hutchinson Criterion for Figure 5 shows that the average grain size of the interphase was several hundred nanometers because of powder agglom- Crack Deflection eration and consolidation. The microstructure also exhibited a As mentioned in the Introduction, the He-Hutchinson crite- very fine intergranular porosity, on the scale of tens of nanom- rion predicts the maximum interfacial fracture resistance that eters. The interphase also displayed larger submicrometer-scale allows crack deflection The criterion describes the ratio of two pores, evident in Fig. 2. It was very difficult to establish with material properties, the critical energy-release rate of a crack confidence whether all of the larger pores were preexisting or deflected into the interface and the critical energy-release rate at least some were artifacts caused by pullout during polishing f a crack penetrating the substrate to which the interface is Figure 2 verifies that the interphase was very prone to pullout, bonded. The proper assessment of these two properties invokes which made it difficult to obtain a flat and uniform surface for several important and subtle questions metallographic analysis. The etchant also may have contribute We first address the correct measurement of the interfacial to the pullout fracture resistance. The critical condition for crack deflectio Because metallography did not provide a quantitative esti- into the interface is the branching of the deflected crack to one mate of the interphase density, a substitute approach was used side(as opposed to the branching of the crack to both sides). The Al2O3 powder specimens were pressed, under identical deflected crack is 42(Ref 5)for the special case of no elastic eter of -22 mm and a nominal height of-12 mm. The height mismatch between the ceramic substrates. The four-point-bend of the slug was kept approximately constant by using a varying delamination test used in the present study measures the mixed- charge of powder that ranged from 5 g for the sample hot- mode interfacial fracture resistance at the same phase angle, pressed at 5.2 MPa and 1200 C to 8.25 g for the sample hot- 42, when the interfacial crack is longer than the transient zone pressed at 31.3 MPa and 1300C. The densities of the bulk and there is no elastic mismatch. 7 Therefore, based on phase- slugs were measured using the ASTM oil-impregnation Archi-

resistance climbed monotonically to a maximum at a hot￾pressing pressure of 24.2 MPa (3500 psi) and then leveled off, with a further increase in pressure, to 31.1 MPa (4500 psi). As a check of the experiment’s repeatability, two runs were made in the present case, for a pressure of 10.4 MPa (1500 psi) and a temperature of 1200°C. As shown in Fig. 4, the duplicate runs gave similar values for the interfacial fracture resistance, indi￾cating very good repeatability. The difference in values is attributed to true variability in the fracture resistance of the interphase processed in the various specimens under identical conditions. For the specimens hot-pressed at 1300°C, the fracture resis￾tance climbed monotonically up to a hot-pressing pressure of 17.2 MPa (2500 psi). Specimens hot-pressed at 24.2 MPa (3500 psi) and 31.1 MPa (4500 psi) at 1300°C did not deflect a crack at the interphase during initial three-point bending. As a further check, a specimen hot-pressed at 20.8 MPa (3000 psi) failed to deflect a crack. Presumably, the interphases hot￾pressed at or above 20.8 MPa (3000 psi) at 1300°C allowed no crack deflection because the fracture resistances were too high. Thus, the specimen hot-pressed at 17.2 MPa (2500 psi) and 1300°C represented the highest fracture resistance that still allowed successful crack deflection. (2) Test of the He–Hutchinson Criterion for Crack Deflection As mentioned in the Introduction, the He–Hutchinson crite￾rion predicts the maximum interfacial fracture resistance that allows crack deflection. The criterion describes the ratio of two material properties, the critical energy-release rate of a crack deflected into the interface and the critical energy-release rate of a crack penetrating the substrate to which the interface is bonded. The proper assessment of these two properties invokes several important and subtle questions. We first address the correct measurement of the interfacial fracture resistance. The critical condition for crack deflection into the interface is the branching of the deflected crack to one side (as opposed to the branching of the crack to both sides).5 At the point of initial deflection, the phase angle for the singly deflected crack is 42° (Ref. 5) for the special case of no elastic mismatch between the ceramic substrates. The four-point-bend delamination test used in the present study measures the mixed￾mode interfacial fracture resistance at the same phase angle, 42°, when the interfacial crack is longer than the transient zone and there is no elastic mismatch.7 Therefore, based on phase￾angle considerations, the interphase fracture resistance pro￾vided in this paper represents the correct material property that should be inserted into the He–Hutchinson criterion. The substrate fracture resistance that is inserted into the de￾nominator of the He–Hutchinson criterion is a mode I prop￾erty.5 Thus, the fracture resistance of the monolithic Al2O3 was measured with the chevron-notch short rod specimen23 in a commercially available fracture-testing machine (Fractometer I, Terratek Systems, Inc., Salt Lake City, UT). Seven speci￾mens were machined from the same tile of Al2O3 (all of the four-point-bend delamination-test specimens also were ma￾chined from this tile). The measured values for these mono￾lithic specimens ranged from 42.8 to 65.4 J/m2 , with an average value of 54.7 J/m2 . The experimentally measured fracture-resistance values are in very good agreement with the theoretical He–Hutchinson criterion for crack deflection. As seen in Fig. 4, the maximum value that permitted crack deflection in a porous interphase was roughly one-fourth of the value needed for the dense Al2O3. The theoretical value of one-fourth was not corrected for the elastic mismatch and does not account for possible R-curve effects; these issues are discussed in more detail in Section IV. However, based on this approximate value of one-fourth, the maximum allowable interfacial fracture resistance was between 10.7 and 16.4 J/m2 (i.e., one-fourth of 42.8 and 65.4 J/m2 ). These two limiting values are labeled the upper deflection cri￾terion and the lower deflection criterion in Fig. 4. The solid line labeled avg. defl. criterion in Fig. 4 is the average value for the maximum allowable interfacial fracture resistance and was found by taking one-fourth of 54.7 J/m2 . As shown in Fig. 4, all of the measured interphase resistances are lower than the upper value of the maximum allowable limit. (3) Microstructure and Estimates of Porosity The porosity of the interphase was characterized using pol￾ished and etched mounts of interphase cross sections. Quanti￾tative assessment was quite challenging, because the interphases were very prone to pullout during polishing. The interphases were prepared for microscopy by slicing each specimen across the width with a diamond saw and vacuum impregnating the cross section in 12-hour epoxy. The vacuum impregnation wicked epoxy into the porosity and pre￾served the interphase for examination. The mounts were lapped successively with diamond grit, down to 0.25 mm, and finally polished with 50 nm colloidal SiO2. Grain structures and in￾tergranular porosity were revealed by etching for 5 min in boiling phosphoric acid. Before the specimens were imaged, the mounts were cleaned ultrasonically in alcohol and coated with an estimated 20 nm of carbon to prevent charging in the electron microscope. Figure 5 shows that the average grain size of the interphase was several hundred nanometers because of powder agglom￾eration and consolidation. The microstructure also exhibited a very fine intergranular porosity, on the scale of tens of nanom￾eters. The interphase also displayed larger submicrometer-scale pores, evident in Fig. 2. It was very difficult to establish with confidence whether all of the larger pores were preexisting or at least some were artifacts caused by pullout during polishing. Figure 2 verifies that the interphase was very prone to pullout, which made it difficult to obtain a flat and uniform surface for metallographic analysis. The etchant also may have contributed to the pullout. Because metallography did not provide a quantitative esti￾mate of the interphase density, a substitute approach was used. The Al2O3 powder specimens were pressed, under identical hot-pressing conditions, into bulk slugs with a nominal diam￾eter of ∼22 mm and a nominal height of ∼12 mm. The height of the slug was kept approximately constant by using a varying charge of powder that ranged from 5 g for the sample hot￾pressed at 5.2 MPa and 1200°C to 8.25 g for the sample hot￾pressed at 31.3 MPa and 1300°C. The densities of the bulk slugs were measured using the ASTM oil-impregnation Archi￾Fig. 4. Interphase fracture resistance as a function of hot-pressing pressure and temperature. 3570 Journal of the American Ceramic Society—O’Brien and Sheldon Vol. 82, No. 12

December 1999 Porous Alumina Coating with Tailored fracture Resistance for Alumina Composites 88862Kv38,0891mM10 92383.8KV 83 88818mMD′9 Fig. 5. Electron micrograph used to characterize the microstructure of the interphase hot-pressed at 10.4 MPa and 1200oC Fig. 7. Cross-sectional view of fracture in the interphase; interphase crack runs along the lower interface ( Specimen hot-pressed at 17.2 MPa(2500 psi) and 1300C) medean technique. 24 These bulk slugs had densities between 40% and 80%. The densification of these samples was some what different from that of the thin layers, which were con- This interphase had the highest fracture resistance for which However, the exnppper and lower bars of monolithic Al2O3 trained by th crack deflection was observed. The micrograph is oriented so ents still provided some insight into the that the precracked bar containing the Vickers indentations is expected range of porosities uppermost. Hence, the term lower interface always means the nterface between the porous interphase and the bar opposite (4 Acoustic Fractography and Finite-Element Analysis he initial Vickers indentation Figure 6 is an acoustic fractograph that shows the interphase Then the crack pops in from the Vickers indentations during fracture after four-point bending in the specimen hot-pressed three-point bending, the advancing crack must penetrate the 10.4 MPa(1500 psi)and 1200 C. The interphase crack caused upper interface between the precracked substrate and the po a strong reflected echo, revealed by the light-gray tones. The rous interphase, according to the He-Hutchinson criterion. The fractograph displays the centerspan row of three vickers strikes 7 shows that the crack in this specimen was along the lower used to precrack the sandwich. The interphase fracture was 40 interface. A specimen hot-pressed at 10.4 MPa(1500 psi) and mm in total length, from end to end, and centered symmet 1200C also displayed the crack at the lower interface cally. The light-gray region in the upper left corner of Fig. 6 is The interphase crack occasionally kinked away from the attributed to an edge effect. Corners occasionally reflect ar lower interface and approached the upper interface. Figure 8 anomalous echo. Although the fractographs are presented here shows a typical kink in the same specimen shown in Fig. 7. in gray scale, they were captured originally with a color scale Typically, the crack ran along the lower interface for a span of that showed the fracture a bit more clearly and dramatically 200-500 um and then departed from the lower interface. The In order to interpret the acoustic fractograph, the experimen length of a typical departure was 30 to 50 um, over which compliance recorded during mechanical testing he Appen- as used to distance the crack meandered toward the upper interface and estimate the interphase crack length through FEA. hen returned to the lower interface. The crack then trapped outlines the numerical scheme used to calculate the mens compliance, as a function of crack length. The sandwich shown in Fig. 6 had a calculated crack length of 32 mm, based on the experimental compliance, a value that compares favor ably with the length of 40 mm measured from the acousti fractograph. The underestimate in crack length may be attrib- utable to the large mode Il loading component, which can lead o significant frictional contact between crack faces during me- hanical testing. This frictional contact can cause roughness- induced crack closure and lower the specimens complian (5) Electron Fractography Figure 7 is a cross-sectional view of the fracture path in an interphase hot-pressed at 17.2 MPa(2500 psi) and 1300oC 9143.K′x3,6018 ustic fractograph of interphase fracture in specimen Fig. 8. Interphase fracture that displays kinking away from 10.4 MPa and 1200oC, specimen displays symmetrical interface and toward the upper interface. (Specimen hot fracture 17.2 MPa(2500 psi) and 1300C

medean technique.24 These bulk slugs had densities between 40% and 80%. The densification of these samples was some￾what different from that of the thin layers, which were con￾strained by the upper and lower bars of monolithic Al2O3. However, the experiments still provided some insight into the expected range of porosities. (4) Acoustic Fractography and Finite-Element Analysis Figure 6 is an acoustic fractograph that shows the interphase fracture after four-point bending in the specimen hot-pressed at 10.4 MPa (1500 psi) and 1200°C. The interphase crack caused a strong reflected echo, revealed by the light-gray tones. The dark-gray tone shows where the reflected echo was absent. The fractograph displays the centerspan row of three Vickers strikes used to precrack the sandwich. The interphase fracture was 40 mm in total length, from end to end, and centered symmetri￾cally. The light-gray region in the upper left corner of Fig. 6 is attributed to an edge effect. Corners occasionally reflect an anomalous echo. Although the fractographs are presented here in gray scale, they were captured originally with a color scale that showed the fracture a bit more clearly and dramatically. In order to interpret the acoustic fractograph, the experimen￾tal compliance recorded during mechanical testing was used to estimate the interphase crack length through FEA. The Appen￾dix outlines the numerical scheme used to calculate the speci￾men’s compliance, as a function of crack length. The sandwich shown in Fig. 6 had a calculated crack length of 32 mm, based on the experimental compliance, a value that compares favor￾ably with the length of 40 mm measured from the acoustic fractograph. The underestimate in crack length may be attrib￾utable to the large mode II loading component, which can lead to significant frictional contact between crack faces during me￾chanical testing. This frictional contact can cause roughness￾induced crack closure25 and lower the specimen’s compliance. (5) Electron Fractography Figure 7 is a cross-sectional view of the fracture path in an interphase hot-pressed at 17.2 MPa (2500 psi) and 1300°C. This interphase had the highest fracture resistance for which crack deflection was observed. The micrograph is oriented so that the precracked bar containing the Vickers indentations is uppermost. Hence, the term lower interface always means the interface between the porous interphase and the bar opposite the initial Vickers indentations. When the crack pops in from the Vickers indentations during three-point bending, the advancing crack must penetrate the upper interface between the precracked substrate and the po￾rous interphase, according to the He–Hutchinson criterion. The crack then is expected to deflect at the lower interface. Figure 7 shows that the crack in this specimen was along the lower interface. A specimen hot-pressed at 10.4 MPa (1500 psi) and 1200°C also displayed the crack at the lower interface. The interphase crack occasionally kinked away from the lower interface and approached the upper interface. Figure 8 shows a typical kink in the same specimen shown in Fig. 7. Typically, the crack ran along the lower interface for a span of 200–500 mm and then departed from the lower interface. The length of a typical departure was 30 to 50 mm, over which distance the crack meandered toward the upper interface and then returned to the lower interface. The crack then trapped Fig. 7. Cross-sectional view of fracture in the interphase; interphase crack runs along the lower interface. (Specimen hot-pressed at 17.2 MPa (2500 psi) and 1300°C.) Fig. 8. Interphase fracture that displays kinking away from the lower interface and toward the upper interface. (Specimen hot-pressed at 17.2 MPa (2500 psi) and 1300°C.) Fig. 5. Electron micrograph used to characterize the microstructure of the interphase hot-pressed at 10.4 MPa and 1200°C. Fig. 6. Acoustic fractograph of interphase fracture in specimen hot-pressed at 10.4 MPa and 1200°C; specimen displays symmetrical fracture. December 1999 Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composites 3571

Journal of the American Ceramic Sociery-O'Brien and Sheldon Vol. 82. No. 12 itself at the lower interface for another span of 200-500 um lation is Lawn's global observer,35 with the shielding contri- before another kink formed. Interestingly, the specimen hot bution viewed as an extrinsic part of the material resistance, pressed at 10.4 MPa(1500 psi)and 1200C displayed no kinks Relobal. Thus, The reasons for the complicated crack path through the in- R terphase are not well understood. One possibility is that local- ized inhomogeneities in the interphase cause kinking away where Rb is the resistance contributed from from the lower interface. When the ceramic interphase is hot the material's intrinsic resistance at the crac he instron pressed, local densification inhomogeneities are unavoidable load frame acts as global observer and, thus, Thus, an advancing interfacial crack encounters regions with it records the critical load for crack advance along the inter fracture resistance. In this way, a kink around a denser region chevron-notch test used to measure the substrate properties exhibit a lower energy than would direct passage through a denser region Hutchinson ratio is evaluated with the sured global quantities (i.e, G and global substrate) The He-Hutchinson analysis is based on the fracture resis IV. D tance of a pupative deflected interface crack. However, the four-point bend test measures the resistance of an interphase Aerosol-spray deposition produces a porous interphase i crack several millimeters long. In addition, Fig. 8 shows that which the microstructure and corresponding fracture resistance are readily controlled. Because this is a line-of-sight technique interphase fracture resistance from roughness-induced crack a natural application for this interphase is in layered structures closure. Although the interphase crack in Fig. 8 displayed no method also produces composites of Al,O3 laminae joined by R-curve behavior as it grew from several millimeters to several centimeters, a pupative interfacial crack still may have a dif- the thin-tailored interphase of porous Al, 03 26 These layered ferent fracture resistance than the longer crack that was actually composites successfully demonstrate composite toughening be- monitored. Therefore, the measured interphase fracture resis- havior at 1200.C in air. 27 Further development should make it tance is not necessarily the physical quantity that should be possible to incorporate a rotary degree of freedom into the inserted into the He-Hutchinson criterion. This problem dem- deposition process and coat fibers with this type of interphase onstrates that R-curve effects can cause experimental results to deviate from the threshold value predicted by He and Hutch- duce a tailorable interface coating on the small-diameter oxide inson(e.g, for the case of no elastic mismatch, a deflected fibers currently used for CMCs crack could exhibit a maximum measured fracture resistance With this type of porous interphase, the fracture properties of either greater or less than one-fourth of the measured substrate a composite can be controlled by tailoring the fracture resistance value). A more detailed analysis of possible R-curve effects is of the interphase. To achieve high toughness, the composite warranted but beyond the scope of the work presented here must be designed with interphase fracture-resistance values The elastic mismatch and R-curve behavior appear to have afely below the upper limit for crack deflection. The natural little influence on the observed fracture-resistance limit for ariability in the mechanical properties of ceramics implies a crack deflection. The largest measured fracture resistance of spread in the fracture resistance of the ceramic to which the 14.8 J/m is 27% of the average fracture resistance for the erphase is bonded. Thus, a fiber-reinforced CMC that contain numerous fiber segments samples a range of fracture-resistance dense Al2O3. Thus, the experimental results provide a good fit values 28 Based on these variations. the He-Hutchinson crite with the theoretical threshold, given the inherent variability in the fracture resistance of the dense Al,O3, the experimental fracture resistance. Hence, the probability of successful crack error in the interphase measurements, the undetermined influ- deflection in a CMC decreases as the interphase fracture resis- ence of R-curve effects, and the elastic-mismatch adjustment tance approaches the upper limit of the range permitted by the He-Hutchinson criterion. As this upper limit is approached V. Conclusions the benefit of the additional work of fracture resulting from the erosol-spray de ion allowed us to fabricate a porous ability of succes eventually is offset by the decreased prob- ceramic interphase whose fracture resistance was tailored by that only limited crack deflection occurs when the interphase which, in turn, controlled the mechanical response of the in- fracture resistance is targeted at the type of upper deflection terphase. Two different-length scale porosities were present, criterion shown in Fig. 4, whereas extensive crack deflection both a nanometer-scale intergranular porosity and a larger sub- occurs when the interphase fracture resistance is targeted at or micrometer-scale porosity below the lower deflection criterion Finite-element analysis(FEA)confirmed that the four-point- As noted in Section Ill(2), the measured interfacial fracture bend delamination test has a particularly short transient re- resistance values are in very good agreement with an appro ne to asymmetrical crack advance. These mate He-Hutchinson limit of one-fourth. The one-fourth value findings strengthen the utility of the test. is not adjusted for the elastic- modulus difference between the Model composite specimens demonstrate an excellent match porous interphase and the dense substrate. Because both inter- with the predictions of the He-Hutchinson criterion. However, phase and substrate are composed of polycrystalline Al2O3, the the large variation in the fracture resistance of monolithic ce- elastic mismatch is only caused by microstructural differences ramics naturally is responsible for a corresponding range in the (i.e, porosity). For an interphase with roughly 20% porosity, critical interfacial fracture resistance at which crack deflection is activated. This range must be recognized in the design of a eral percent(assuming that the elastic modulus is roughly tailored interfacial fracture resistance for use in a real-world proportional to the bulk density of the porous material) The original mechanics analysis of He and Hutchinson'does not address R-curve effects. However, the experimentally de APPENDIX termined fracture resistances almost certainly are influenced by crack-wake bridging, because large-grained AL, substrates Finite-Element Analysis of Asymmetrical Interphase Cracks and Short Interphase Cracks tions are evaluated by applying the integral32 and solving for The original analyses of the four-point-bend delamination the stress intensity at the crack tip. 33,34 An equivalent formu- test, 22 did not consider the influence of an asymmetrical in-

itself at the lower interface for another span of 200–500 mm before another kink formed. Interestingly, the specimen hot￾pressed at 10.4 MPa (1500 psi) and 1200°C displayed no kinks. The reasons for the complicated crack path through the in￾terphase are not well understood. One possibility is that local￾ized inhomogeneities in the interphase cause kinking away from the lower interface. When the ceramic interphase is hot￾pressed, local densification inhomogeneities are unavoidable. Thus, an advancing interfacial crack encounters regions with density variations and, presumably, corresponding variations in fracture resistance. In this way, a kink around a denser region can exhibit a lower energy than would direct passage through a denser region. IV. Discussion Aerosol-spray deposition produces a porous interphase in which the microstructure and corresponding fracture resistance are readily controlled. Because this is a line-of-sight technique, a natural application for this interphase is in layered structures, recently of technological interest.2,6,10 The aerosol-spray method also produces composites of Al2O3 laminae joined by the thin-tailored interphase of porous Al2O3. 26 These layered composites successfully demonstrate composite toughening be￾havior at 1200°C in air.27 Further development should make it possible to incorporate a rotary degree of freedom into the deposition process and coat fibers with this type of interphase. Thus, the aerosol-spray technique also could be used to pro￾duce a tailorable interface coating on the small-diameter oxide fibers currently used for CMCs. With this type of porous interphase, the fracture properties of a composite can be controlled by tailoring the fracture resistance of the interphase. To achieve high toughness, the composite must be designed with interphase fracture-resistance values safely below the upper limit for crack deflection. The natural variability in the mechanical properties of ceramics implies a spread in the fracture resistance of the ceramic to which the interphase is bonded. Thus, a fiber-reinforced CMC that contains numerous fiber segments samples a range of fracture-resistance values.28 Based on these variations, the He–Hutchinson crite￾rion also implies a spread in the maximum allowed interphase fracture resistance. Hence, the probability of successful crack deflection in a CMC decreases as the interphase fracture resis￾tance approaches the upper limit of the range permitted by the He–Hutchinson criterion. As this upper limit is approached, the benefit of the additional work of fracture resulting from the tougher interphase eventually is offset by the decreased prob￾ability of successful crack deflection. This phenomenon implies that only limited crack deflection occurs when the interphase fracture resistance is targeted at the type of upper deflection criterion shown in Fig. 4, whereas extensive crack deflection occurs when the interphase fracture resistance is targeted at or below the lower deflection criterion. As noted in Section III(2), the measured interfacial fracture￾resistance values are in very good agreement with an approxi￾mate He–Hutchinson limit of one-fourth. The one-fourth value is not adjusted for the elastic-modulus difference between the porous interphase and the dense substrate. Because both inter￾phase and substrate are composed of polycrystalline Al2O3, the elastic mismatch is only caused by microstructural differences (i.e., porosity). For an interphase with roughly 20% porosity, the elastic mismatch increases the He–Hutchinson limit by sev￾eral percent29 (assuming that the elastic modulus is roughly proportional to the bulk density of the porous material). The original mechanics analysis of He and Hutchinson5 does not address R-curve effects. However, the experimentally de￾termined fracture resistances almost certainly are influenced by crack-wake bridging, because large-grained Al2O3 substrates exhibit significant R-curve behavior.30,31 Shielding contribu￾tions are evaluated by applying the J integral32 and solving for the stress intensity at the crack tip.33,34 An equivalent formu￾lation is Lawn’s global observer,35 with the shielding contri￾bution viewed as an extrinsic part of the material resistance, Rglobal. Thus, Rglobal 4 Rb + Rtip (1) where Rb is the resistance contributed from shielding and Rtip the material’s intrinsic resistance at the crack tip. The Instron load frame acts as global observer and, thus, measures Rglobal as it records the critical load for crack advance along the inter￾phase. The R-curve effect also is fully operative during the chevron-notch test used to measure the substrate properties. Thus, R-curve effects are inherently included when the He– Hutchinson ratio is evaluated with the experimentally mea￾sured global quantities (i.e., Gcr global,interphase and Gcr global,substrate). The He–Hutchinson analysis5 is based on the fracture resis￾tance of a pupative deflected interface crack. However, the four-point bend test measures the resistance of an interphase crack several millimeters long. In addition, Fig. 8 shows that the interphase crack can display kinks that might increase the interphase fracture resistance from roughness-induced crack closure.2 Although the interphase crack in Fig. 8 displayed no R-curve behavior as it grew from several millimeters to several centimeters, a pupative interfacial crack still may have a dif￾ferent fracture resistance than the longer crack that was actually monitored. Therefore, the measured interphase fracture resis￾tance is not necessarily the physical quantity that should be inserted into the He–Hutchinson criterion. This problem dem￾onstrates that R-curve effects can cause experimental results to deviate from the threshold value predicted by He and Hutch￾inson (e.g., for the case of no elastic mismatch, a deflected crack could exhibit a maximum measured fracture resistance either greater or less than one-fourth of the measured substrate value). A more detailed analysis of possible R-curve effects is warranted but beyond the scope of the work presented here. The elastic mismatch and R-curve behavior appear to have little influence on the observed fracture-resistance limit for crack deflection. The largest measured fracture resistance of 14.8 J/m2 is 27% of the average fracture resistance for the dense Al2O3 and 23% of the maximum recorded value for the dense Al2O3. Thus, the experimental results provide a good fit with the theoretical threshold, given the inherent variability in the fracture resistance of the dense Al2O3, the experimental error in the interphase measurements, the undetermined influ￾ence of R-curve effects, and the elastic-mismatch adjustment. V. Conclusions Aerosol-spray deposition allowed us to fabricate a porous ceramic interphase whose fracture resistance was tailored by hot-pressing. Hot-pressing controlled the interphase porosity, which, in turn, controlled the mechanical response of the in￾terphase. Two different-length scale porosities were present, both a nanometer-scale intergranular porosity and a larger sub￾micrometer-scale porosity. Finite-element analysis (FEA) confirmed that the four-point￾bend delamination test7 has a particularly short transient re￾sponse and is immune to asymmetrical crack advance. These findings strengthen the utility of the test. Model composite specimens demonstrate an excellent match with the predictions of the He–Hutchinson criterion. However, the large variation in the fracture resistance of monolithic ce￾ramics naturally is responsible for a corresponding range in the critical interfacial fracture resistance at which crack deflection is activated. This range must be recognized in the design of a tailored interfacial fracture resistance for use in a real-world CMC. APPENDIX Finite-Element Analysis of Asymmetrical Interphase Cracks and Short Interphase Cracks The original analyses of the four-point-bend delamination test7,22 did not consider the influence of an asymmetrical in- 3572 Journal of the American Ceramic Society—O’Brien and Sheldon Vol. 82, No. 12

December 1999 Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composites Fig. Al. Representative finite-element mesh. Fig. A3. Asymmetrical finite-element mesh used to show that en ergy-release rate at crack tip is uninfluenced by asymmetrical cracks terphase crack and did not explicitly solve for the effect of a short interphase crack, although the analyses did suggest that a deliberately loaded well past the point at which steady-state short crack would have an important influence Finite-element fracture was exhausted, to ensure that the interphase crack analysis(FEA) proved very important to our understanding of extended at least across the inner span of the four-point bend the four-point-bend delamination test FEA confirmed that the fixture. The interphase fracture was, in fact, 58 mm long and four-point-bend delamination test can be extended confident actually overran the outer supports of the four-point-bend-test to both asymmetrical interphase cracks and relatively short fixture. which was set to 50 mm. Of course. the crack wa unloaded outside the outer supports of the four-point fixture The geometry used for mechanical testing was solved nu- and was subjected to no driving force for crack advance outside merically as a plane-strain linear-elastic problem. Al O3 is a the outer supports. The specimen had the lowest recorded in- very strong and brittle material that satisfies the requirements terphase fracture resistance in these experiments, which may of small-scale yielding. Under small-scale yielding, all of the explain why the crack ran very far below the applied load. The haracteristic lengths of the geometry, such as width,un- crack also ran asymmetrically and was longer on one side of cracked ligament, and crack length, are >2.5(Koy) center than on the other The present geometry was analyzed using a commercial fi- In order to elucidate the asymmetrical interphase fracture nite-element code(ABAQUS, Hibbitt, Karlsson, and Sorensen, displayed in Fig. A2, various asymmetrical meshes were used Inc, Pawtucket, RI). Figure Al shows a representative mesh used to solve the problem of an interphase crack. For illustra- to test whether the four-point bend test is sensitive to asyl metries Figure A3 shows a representative mesh with a crack 3 tion, the entire mesh is shown, although the problem contains mm long to the left of center and 10 mm long to the right of center plane of symmetry that allows solution of the equiva- center. The asymmetrical meshes demonstrate that the energy lent half-body problem with reduced computational time Eight-node quadrilateral elements were used. The half-body release rates at each crack tip are exactly (to the d test is mesh typically contained a total of 816 elements, with 384 of immune to asymmetries, and the closed-form these elements arranged in a radial ring around the crack tip. A extended safely to asymmetrical interphase es. This radial mesh of wedge-shaped elements in a spider-web pattern finding enhances the utility of the test was used at a crack tip. 36 The radial length of the first wedge In order to elucidate the transient behavior of a short inter- was 1. 424 x 103 mm. The radial length from the crack tip to phase crack before the steady-state response is reached, the distance of I mm was spanned by 16 circular strips of wedges energy-release rate was calculated numerically as a function of under an exponential scaling. Within each circular strip, the the half-crack length, a, of a symmetrical interphase crack for angular distance from 0 to 2m was spanned by 24 equally an applied load of 200 N under the four-point-bend geometry spaced, wedge-shaped elements. The mesh for the domain fre used for mechanical testing. As shown in Fig. A4, the inter- the crack tip to a radius of I mm therefore consisted of 384 phase crack reaches the steady-state energy-release rate of 16.8 elements. The domain beyond the radius of I mm from the J/m2 if the half-crack length exceeds I mm, which corresponds crack tip typically was modeled with an additional 432 ele ments, for a total of 816 elements. The code's implementation of the domain integral technique 7 was used to solve the J integral for the energy-release rate at the crack tip. variou lesh refinements confirmed the accuracy of this typical mesh which seems to represent a very conservative design. The typi- al mesh required several minutes to solve(Alphastation 200 Digital Equipment Corp, Maynard, MA) igure A2 is an acoustic fractograph of the specimen hot ssed at 5.2 MPa(750 psi) and 1200@C after the four-point nd test. During the four-point bend test, the specimen was 器u Haif-Crack Length, a(mm A2. Acoustic fractograph of interphase fracture in specimen ssed at 5.2 MPa and 1200oC, specimen displays asymmetrical 4. Energy-release rate calculated as a function of equal in length to one-half the bar height

terphase crack and did not explicitly solve for the effect of a short interphase crack, although the analyses did suggest that a short crack would have an important influence. Finite-element analysis (FEA) proved very important to our understanding of the four-point-bend delamination test. FEA confirmed that the four-point-bend delamination test can be extended confidently to both asymmetrical interphase cracks and relatively short interphase cracks. The geometry used for mechanical testing was solved nu￾merically as a plane-strain linear-elastic problem. Al2O3 is a very strong and brittle material that satisfies the requirements of small-scale yielding. Under small-scale yielding, all of the characteristic lengths of the geometry, such as width, un￾cracked ligament, and crack length, are >2.5(Kc/sy) 2 . The present geometry was analyzed using a commercial fi￾nite-element code (ABAQUS, Hibbitt, Karlsson, and Sorensen, Inc., Pawtucket, RI). Figure A1 shows a representative mesh used to solve the problem of an interphase crack. For illustra￾tion, the entire mesh is shown, although the problem contains a center plane of symmetry that allows solution of the equiva￾lent half-body problem with reduced computational time. Eight-node quadrilateral elements were used. The half-body mesh typically contained a total of 816 elements, with 384 of these elements arranged in a radial ring around the crack tip. A radial mesh of wedge-shaped elements in a spider-web pattern was used at a crack tip.36 The radial length of the first wedge was 1.424 × 10−3 mm. The radial length from the crack tip to a distance of 1 mm was spanned by 16 circular strips of wedges under an exponential scaling. Within each circular strip, the angular distance from 0 to 2p was spanned by 24 equally spaced, wedge-shaped elements. The mesh for the domain from the crack tip to a radius of 1 mm therefore consisted of 384 elements. The domain beyond the radius of 1 mm from the crack tip typically was modeled with an additional 432 ele￾ments, for a total of 816 elements. The code’s implementation of the domain integral technique37 was used to solve the J integral for the energy-release rate at the crack tip. Various mesh refinements confirmed the accuracy of this typical mesh, which seems to represent a very conservative design. The typi￾cal mesh required several minutes to solve (Alphastation 200, Digital Equipment Corp., Maynard, MA). Figure A2 is an acoustic fractograph of the specimen hot￾pressed at 5.2 MPa (750 psi) and 1200°C after the four-point bend test. During the four-point bend test, the specimen was deliberately loaded well past the point at which steady-state fracture was exhausted, to ensure that the interphase crack extended at least across the inner span of the four-point bend fixture. The interphase fracture was, in fact, 58 mm long and actually overran the outer supports of the four-point-bend-test fixture, which was set to 50 mm. Of course, the crack was unloaded outside the outer supports of the four-point fixture and was subjected to no driving force for crack advance outside the outer supports. The specimen had the lowest recorded in￾terphase fracture resistance in these experiments, which may explain why the crack ran very far below the applied load. The crack also ran asymmetrically and was longer on one side of center than on the other. In order to elucidate the asymmetrical interphase fracture displayed in Fig. A2, various asymmetrical meshes were used to test whether the four-point bend test is sensitive to asym￾metries. Figure A3 shows a representative mesh with a crack 3 mm long to the left of center and 10 mm long to the right of center. The asymmetrical meshes demonstrate that the energy￾release rates at each crack tip are exactly identical (to the accuracy of the computation). Thus, the four-point bend test is immune to asymmetries, and the closed-form solution can be extended safely to asymmetrical interphase fractures. This finding enhances the utility of the test. In order to elucidate the transient behavior of a short inter￾phase crack before the steady-state response is reached, the energy-release rate was calculated numerically as a function of the half-crack length, a, of a symmetrical interphase crack for an applied load of 200 N under the four-point-bend geometry used for mechanical testing. As shown in Fig. A4, the inter￾phase crack reaches the steady-state energy-release rate of 16.8 J/m2 if the half-crack length exceeds 1 mm, which corresponds Fig. A1. Representative finite-element mesh. Fig. A2. Acoustic fractograph of interphase fracture in specimen hot-pressed at 5.2 MPa and 1200°C; specimen displays asymmetrical fracture. Fig. A3. Asymmetrical finite-element mesh used to show that en￾ergy-release rate at crack tip is uninfluenced by asymmetrical cracks. Fig. A4. Energy-release rate calculated as a function of half-crack length, a; energy-release rate reached the steady-state value for a half￾crack equal in length to one-half the bar height. December 1999 Porous Alumina Coating with Tailored Fracture Resistance for Alumina Composites 3573

574 Journal of the American Ceramic Sociery-O'Brien and Sheldon Vol. 82. No. 12 to one-half the sandwich bar height of 2 mm. In comparisor Meeting of th indianapolis, IN, April 15, 1996 the closed-form solution? for the energy-release rate is 16.8 J/m2 which shows an excellent correlation between the analytical and numerical solutions. Other estimates of the Energy of Al,O3, "J. Am. Ceram Soc., 56 [117-11(1973) length of the transient behavior usually have been oneo to Composites with a (C -swc), multilayered Interphase: Pioces four times the bar height. Therefore, at least for the geometry ture, and Tensile Behavior at Room Temperature, "unpublished work. and materials used for the present experiment, the steady-state I6D. P. Stinton, Oak Ridge National Laboratory, unpublished res J D. McClelland and E H. Zehms, "End-Point Density of Hot-Pressed finding again strengthens the utility of the four-point bcl tx is Alumina,"J.Amt Ceram. Soc, 46(2)77-80(1963) olution can be extended to very short interphase cracks. This xG. R. Anstis, P. Chantikul, D. B. Marshall, and B R. Lawn, "A Critical The energy-release rate of 16.8 J/m is higher than any inter Evaluation of Indentation Direct Crack Measurements, "J. Am. Ceram Soc., 649]533-38(1981) our test of the steady-state response is quite severe and dem- 26-46 in Microindentation Techniques in Materials Science and Engineering onstrates that the four-point bend test is very robust. ASTM STP 889. Edited by P J and B. R Lawn. American Society fo Testing and Materials, Philadelphia, PA, 19 Acknowledgments: We thank Ms D M. Ferris, Mr M. J. Starkey, and MIL-STD-1942A: Flexural Strength of High Performance Ceramics at Mr. B. D. Dracup for their M. F. Kanninen and C H. Popelar, Adranced Fracture Mechanics, pp Professors A.S. Argon, A F. Bower, J. W. Hutchinson, K.S. Kim, M. N. Pelloux, and C. F Shih, Dr J. L H C Cao, J. Lund, and A G. Evans, Development mothy Hynes, Mr. Michael Longo, and Mr Steven Berube of Panametrics, of a Test method for Measuring the mixed mode fracture resistance of bi- Waltham, MA, and the donation of their acoustic-microscopy services. Fracture Mechanics of Ceramics, Vol 3. Edited by R.C. Bradt, D PHHa ndard Test Method for Density, Oil Content, and Interconnected Po- rosity of Sintered Metal Structural Parts of Oil-Impregnated Bearings, "ASTM References Designation B328-94. American Society for Testing and Materials, West Con- IR. Raj, Fundamental Research in Structural Ceramics for Service Near shohocken, PA A.G. Evans, M. Role, B J. Dalgleish, and P, G. Charalambides, "The 2A. J. Phillipp, w. J. Clegg, and T. w. Clyne, "Fracture Behavior of Ceramic Fracture Energy of Bimaterial Interfaces, "Mater. Sci. Eng, A, A126[1 53-64 Laminates in Bending: Il, Comparison of Model Predictions with Experimen Data, "Acta Metall. Mater, 41 13] 819-27(199 4. J. O'Brien, ""Fabrication of a Tailored Oxidation-Resistant Interface and 'A G. Evans and D. B. Marshall. "The nical Behavior of Ceramic High-Temperature Testing of a Laminated Alumina Composite"; Ph. D. Thesis. 4V.Gupta, A.S. Argon, and J. A. Cornie, "Interfaces with Controlled Tc 2M. 1. O'Brien, E M. Capaldi, and B w. Sheldon, "Layered Alumina Com- as Mechanical Fuses to Isolate Fiber from Damage, " J.Mater. Scl, 24[6 posites Tested at High Temperature in Air, Am. Ceram Soc., In press. Dissimilar Elastic Materials, "Int J. Solids Struc., 25 19] 1053-67(1989) Z. Suo and J W. Hutchinson, ""Sandwich Test Specimens for Measuring 6H. Liu and S M. Hsu, "Fracture Behavior of yer Silicon Nitride/ Interface Crack Toughness, "Mater. Sci. Eng, A, A107 [1 135-43(1989) rp g. thdralamabides. , LAnd. g. Evans and R. 4. Mcmeekin, "A Test Resistance during slow crack growth in a a, end specimens 0. Maer Specimen for Determining the Fracture Resistance of Bimaterial Interfaces, "J. pp.Meh,56l77-82(1989) in,"R-Curve Behavior in a Poly-Crystalline Alumina Material, T M. Besmann, B. W. Sheldon, R. A. Lowden, and D. P. Stinton, "Vapor- J Mater. Sci. Lett., 5[12J1313-15(1986) utchinson, and A G. Evans, "Matrix Fracture in ites, "Science(Washington, D. C ) 253, 1104-109(1991 orced Ceramics, "J.Mech. Phys. Solids, 34[2 KK. Chawla, Ceramics Matrix Composites; p 319. Chapman and Hal Reinforced Brittle Matrix Composites, "J Mater. Sci., 29, 3857-96(1994) P.E. D. Morgan and D. B. Marshall, " Ceramic Composites of Monami shall, B N. Cox, and A G. Evans, "The Mechani Cracking in Brittle-Matrix Fiber Composites, " Acta Metall, 33 [11] 2013-2 ISR Nutt, "Environmental Effects on Mechanical Behavior of Ceramics pp. 365-406 in High-Temperature Mechanical Behavior of Ceramic Compos University es. Edited by s. V. Nair and K Jakus. Butterworth-Heinemann, Newton, sC. F. Shih and R J. Asaro, "Elastic-Plastic Analysis of n Bima B. Davis, J. P. A. Lofvander, A. G. Evans, E, Bischoff, and M. L. Emil- 76 15)1249-63 1gg)ts for Brtle- Matrix Composites,"J.Am. Ceram.(1988) terial Interfaces: Part I-Small-Scale Yielding, " J. App/. Mech., 55[2] 299-316 ISA. Kristoffersson, K. Lindqvist, and J B. Davis, "Processing of Porous from Momentum and Energy Balance, Eng. Fract. Mech., 37 [6]615-42 Ceramics with Starches as Fugitive Materials", presented at the 98th Annual (1987)

to one-half the sandwich bar height of 2 mm. In comparison, the closed-form solution7 for the energy-release rate is also 16.8 J/m2 , which shows an excellent correlation between the analytical and numerical solutions. Other estimates of the length of the transient behavior usually have been one10 to four22 times the bar height. Therefore, at least for the geometry and materials used for the present experiment, the steady-state solution can be extended to very short interphase cracks. This finding again strengthens the utility of the four-point bend test. The energy-release rate of 16.8 J/m2 is higher than any inter￾phase fracture resistance measured in our experiments. Hence, our test of the steady-state response is quite severe and dem￾onstrates that the four-point bend test is very robust. Acknowledgments: We thank Ms. D. M. Ferris, Mr. M. J. Starkey, and Mr. B. D. Dracup for their great help in completing the experiments. We are grateful to Professors A. S. Argon, A. F. Bower, J. W. Hutchinson, K. S. Kim, R. M. N. Pelloux, and C. F. Shih, Dr. J. L. O’Brien, and the late Mr. M. Rossetti for many helpful discussions. We also acknowledge the kind assistance of Mr. Timothy Hynes, Mr. Michael Longo, and Mr. Steven Berube of Panametrics, Waltham, MA, and the donation of their acoustic-microscopy services. References 1 R. Raj, “Fundamental Research in Structural Ceramics for Service Near 2000°C,” J. Am. Ceram. Soc., 76 [9] 2147–73 (1993). 2 A. J. Phillipp, W. J. Clegg, and T. W. Clyne, “Fracture Behavior of Ceramic Laminates in Bending: II, Comparison of Model Predictions with Experimental Data,” Acta Metall. Mater., 41 [3] 819–27 (1993). 3 A. G. Evans and D. B. Marshall, “The Mechanical Behavior of Ceramic￾Matrix Composites,” Acta Metall., 37 [10] 2567–83 (1989). 4 V. Gupta, A. S. Argon, and J. A. Cornie, “Interfaces with Controlled Tough￾ness as Mechanical Fuses to Isolate Fiber from Damage,” J. Mater. Sci., 24 [6] 2031–40 (1989). 5 M. Y. He and J. W. Hutchinson, “Crack Deflection at an Interface between Dissimilar Elastic Materials,” Int. J. Solids Struct., 25 [9] 1053–67 (1989). 6 H. Liu and S. M. Hsu, “Fracture Behavior of Multilayer Silicon Nitride/ Boron Nitride Ceramics,” J. Am. Ceram. Soc., 79 [9] 2452–57 (1996). 7 P. G. Charalambides, J. Lund, A. G. Evans, and R. M. McMeeking, “A Test Specimen for Determining the Fracture Resistance of Bimaterial Interfaces,” J. Appl. Mech., 56 [1] 77–82 (1989). 8 T. M. Besmann, B. W. Sheldon, R. A. Lowden, and D. P. Stinton, “Vapor￾Phase Fabrication and Properties of Continuous-Filament Ceramic Compos￾ites,” Science (Washington, D.C.), 253, 1104–109 (1991). 9 K. K. Chawla, Ceramics Matrix Composites; p. 319. Chapman and Hall, London, 1993. 10P. E. D. Morgan and D. B. Marshall, “Ceramic Composites of Monazite and Alumina,” J. Am. Ceram. Soc., 78 [6] 1553–63 (1995). 11S. R. Nutt, “Environmental Effects on Mechanical Behavior of Ceramics”; pp. 365–406 in High-Temperature Mechanical Behavior of Ceramic Compos￾ites. Edited by S. V. Nair and K. Jakus. Butterworth-Heinemann, Newton, MA, 1995. 12J. B. Davis, J. P. A. Lo¨fvander, A. G. Evans, E. Bischoff, and M. L. Emil￾iani, “Fiber-Coating Concepts for Brittle-Matrix Composites,” J. Am. Ceram. Soc., 76 [5] 1249–63 (1993). 13A. Kristoffersson, K. Lindqvist, and J. B. Davis, “Processing of Porous Ceramics with Starches as Fugitive Materials”; presented at the 98th Annual Meeting of the American Ceramic Society, Indianapolis, IN, April 15, 1996 (Basic Science Division, Poster No. BP-22-96.) 14L. A. Simpson, “Effect of Microstructure on Measurements of Fracture Energy of Al2O3,” J. Am. Ceram. Soc., 56 [1] 7–11 (1973). 15C. Droillard, X. Bourrat, J. Lamon, and R. Naslain, “2D-SiC/SiC CVI Composites with a (C − SiC)n Multilayered Interphase: Processing, Microstruc￾ture, and Tensile Behavior at Room Temperature,” unpublished work. 16D. P. Stinton, Oak Ridge National Laboratory, unpublished results. 17J. D. McClelland and E. H. Zehms, “End-Point Density of Hot-Pressed Alumina,” J. Am. Ceram. Soc., 46 [2] 77–80 (1963). 18G. R. Anstis, P. Chantikul, D. B. Marshall, and B. R. Lawn, “A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements,” J. Am. Ceram. Soc., 64 [9] 533–38 (1981). 19D. B. Marshall and B. R. Lawn, “Indentation of Brittle Materials”; pp. 26–46 in Microindentation Techniques in Materials Science and Engineering. ASTM STP 889. Edited by P. J. Brau and B. R. Lawn. American Society for Testing and Materials, Philadelphia, PA, 1986. 20“MIL-STD-1942A: Flexural Strength of High Performance Ceramics at Ambient Temperature,” Department of the Army, Washington, DC, 1990. 21M. F. Kanninen and C. H. Popelar, Advanced Fracture Mechanics; pp. 505–506. Oxford University Press, New York, 1985. 22P. G. Charalambides, H. C. Cao, J. Lund, and A. G. Evans, “Development of a Test Method for Measuring the Mixed Mode Fracture Resistance of Bi￾material Interfaces,” Mech. Mater., 8 [4] 269–83 (1990). 23L. M. Barker, “Short Rod KIC Measurements of Al2O3”; pp. 483–94 in Fracture Mechanics of Ceramics, Vol. 3. Edited by R. C. Bradt, D. P. H. Has￾selman, and F. F. Lange. Plenum Press, New York, 1974. 24“Standard Test Method for Density, Oil Content, and Interconnected Po￾rosity of Sintered Metal Structural Parts of Oil-Impregnated Bearings,” ASTM Designation B328-94. American Society for Testing and Materials, West Con￾shohocken, PA. 25A. G. Evans, M. Ru¨hle, B. J. Dalgleish, and P. G. Charalambides, “The Fracture Energy of Bimaterial Interfaces,” Mater. Sci. Eng., A, A126 [1] 53–64 (1990). 26M. J. O’Brien, “Fabrication of a Tailored Oxidation-Resistant Interface and High-Temperature Testing of a Laminated Alumina Composite”; Ph.D. Thesis. Brown University, Providence, RI, 1997. 27M. J. O’Brien, F. M. Capoldi, and B. W. Sheldon, “Layered Alumina Com￾posites Tested at High Temperature in Air,” J. Am. Ceram. Soc., in press. 28W. A. Curtin, “Toughening by Crack Bridging in Heterogeneous Ceram￾ics,” J. Am. Ceram. Soc., 78 [5] 1313–23 (1995). 29Z. Suo and J. W. Hutchinson, “Sandwich Test Specimens for Measuring Interface Crack Toughness,” Mater. Sci. Eng., A, A107 [1] 135–43 (1989). 30R. Steinbrech, R. Khehans, and W. Schaarwachter, “Increase of Crack Resistance during Slow Crack Growth in Al2O3 Bend Specimens,” J. Mater. Sci., 18 [1] 265–70 (1983). 31M. V. Swain, “R-Curve Behavior in a Poly-Crystalline Alumina Material,” J. Mater. Sci. Lett., 5 [12] 1313–15 (1986). 32B. Budiansky, J. W. Hutchinson, and A. G. Evans, “Matrix Fracture in Fiber-Reinforced Ceramics,” J. Mech. Phys. Solids, 34 [2] 167–89 (1986). 33A. G. Evans and F. W. Zok, “The Physics and Mechanics of Fiber￾Reinforced Brittle Matrix Composites,” J. Mater. Sci., 29, 3857–96 (1994). 34D. B. Marshall, B. N. Cox, and A. G. Evans, “The Mechanics of Matrix Cracking in Brittle-Matrix Fiber Composites,” Acta Metall., 33 [11] 2013–21 (1985). 35B. Lawn, Fracture of Brittle Solids; pp. 72–77. Cambridge University Press, Cambridge, U.K., 1993. 36C. F. Shih and R. J. Asaro, “Elastic–Plastic Analysis of Cracks on Bima￾terial Interfaces: Part 1—Small-Scale Yielding,” J. Appl. Mech., 55 [2] 299–316 (1988). 37B. Moran and C. F. Shih, “Crack Tip and Associated Domain Integrals from Momentum and Energy Balance,” Eng. Fract. Mech., 37 [6] 615–42 (1987). h 3574 Journal of the American Ceramic Society—O’Brien and Sheldon Vol. 82, No. 12