J. Ant Cerum. Soc., 85 [3]595-602(2002) ournal Effects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite Eric A.v. Carelli* Science and Technology Center, Siemens-Westinghouse Power Corporation, Pittsburgh, Pennsylvania 15235 Hiroki Fujita, James Y. Yang, and Frank W. Zok Materials Department, University of California, Santa Barbara, California 93106 properties of an all-oxide fiber-reinforced composite follow a The present article focuses on changes in the mechanical gas turbine and at the burner outlet. In current long-term exposure(1000 h) at temperatures of 1000-1200 C or near their upper use temperature, even with in air. The composite of interest derives its damage tolerance imparted by the use of thermal barrier coatings, thereby from a highly porous matrix, precluding the need for an significant temperature elevations with these alloys interphase at the fiber-matrix boundary. The key issue in- future environmental and performance standards, it is anticipated olves the stability of the porosity against densification and the that the targeted temperature elevations in turbine components will associated implications for long-term durability of the compos- be accomplished through the use of continuous-fiber-reinforced ite at elevated temperatures. For this purpose, comparisons ceramic composites(CFCCs). Among the various ceramic com- are made in the tensile properties and fracture characteristics of a 2D woven fiber composite both along the fiber direction posites that have been developed to date, the ones that have and at 45 to the fiber axes before and after the aging try in the past few years are those made from all-oxide constitu- indentation and through the determination of the matrix non-oxide ones(e.g, SiC/SiC)is their superior resistance to oxidation under typical turbine engine conditions and hence their pled with classical laminate theory. The study reveals that, potential for long-term durability despite evidence of some strengthening of the matrix and the As part of a broad activity aimed at developing and assessing fber-matrix interfaces during aging, the key tensile properties oxide composites for use in future generations of gas turbin in the 0o clud engines, the present study focuses on changes in the mechanical are unchanged. This strengthening is manifested to a more properties of a candidate all-oxide CFCC following long-term exposure(1000 h)at temperatures of 1000-1200C. The compos- orientation, wherein the modulus and the tensile strength each ite material of interest derives its damage tolerance from a highly exhibit a twofold increase after the 1200%C aging treatment. It also results in a change in the failure mechanism, from one fiber-matrix boundary. Although the efficacy of this material involving predominantly matrix damage and interply delami- concept in enabling damage tolerance has been demonstrated, -o it nation to one which is dominated by fiber fracture. Addition- remains to be established whether the matrix pore structure is ally, salient changes in the mechanical response beyond the stable against densification and whether the desirable damage maximum load suggest the existence of an optimum matrix tolerant characteristics can be retained for extended time periods at attains a maximum. The implications for long-term durability the porous-matrix concept have been shown to exhibit severe of this class of composite are discussed. degradation in composite properties once the matrix densifies appreciably. The main matrix constituent in the present composite is mullite, L. Introduction in the form of a weakly bonded particulate network. This selection n industry has been under increased pres- is based on the sluggish sintering kinetics of mullite'at the upper keeping up with market demands for increased power output and s intended to form a contiguous particulate network that should be to red efficiency. These goals can be achieved in part through reductions under subsequent service conditions. The minor matrix constituen airfoils with attendant increases in the temperatures both within the alumina, present both in the form of particulates from a slurr and as a product of pyrolysis of an aqueous precursor solution Because of its more rapid sintering kinetics, alumina serves to bond the mullite particulates and the fibers together, thereby E. Lara-Curzio--contributing editor enhancing the matrix-dominated composite properties, e.g., inter laminar strength and off-axis in-plane strength. However, if the degree of sintering becomes excessive, the damage-tolerant char acteristics may be compromised. The challenge involves selection cript No. 187723 Received May 4, 2001; approved December 21, 2001 of the relative fractions and topologies of the two phases such that under the network of mullite particles remains contiguous and hence nrough both internal research funds at the Science and Technology Center and a prevents global nkage, yet the extent of bonding within this ubcontract to the University of California at Santa Barbara, and by a gift from NGK network is sufficient to impart the requisite matrix integrity for Member. American Ceramic Society. acceptable off-axis properties. These opposing requirements or 595
Effects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite Eric A. V. Carelli* Science and Technology Center, Siemens-Westinghouse Power Corporation, Pittsburgh, Pennsylvania 15235 Hiroki Fujita,* James Y. Yang, and Frank W. Zok* Materials Department, University of California, Santa Barbara, California 93106 The present article focuses on changes in the mechanical properties of an all-oxide fiber-reinforced composite following long-term exposure (1000 h) at temperatures of 1000–1200°C in air. The composite of interest derives its damage tolerance from a highly porous matrix, precluding the need for an interphase at the fiber–matrix boundary. The key issue involves the stability of the porosity against densification and the associated implications for long-term durability of the composite at elevated temperatures. For this purpose, comparisons are made in the tensile properties and fracture characteristics of a 2D woven fiber composite both along the fiber direction and at 45° to the fiber axes before and after the aging treatments. Additionally, changes in the state of the matrix are probed through measurements of matrix hardness by Vickers indentation and through the determination of the matrix Young’s modulus, using the measured composite moduli coupled with classical laminate theory. The study reveals that, despite evidence of some strengthening of the matrix and the fiber–matrix interfaces during aging, the key tensile properties in the 0°/90° orientation, including strength and failure strain, are unchanged. This strengthening is manifested to a more significant extent in the composite properties in the 45° orientation, wherein the modulus and the tensile strength each exhibit a twofold increase after the 1200°C aging treatment. It also results in a change in the failure mechanism, from one involving predominantly matrix damage and interply delamination to one which is dominated by fiber fracture. Additionally, salient changes in the mechanical response beyond the maximum load suggest the existence of an optimum matrix strength at which the fracture energy in the 45° orientation attains a maximum. The implications for long-term durability of this class of composite are discussed. I. Introduction THE power generation industry has been under increased pressure to reduce NOx emissions from gas turbine engines while keeping up with market demands for increased power output and efficiency. These goals can be achieved in part through reductions in the amount of film cooling of combustor liners and turbine airfoils with attendant increases in the temperatures both within the gas turbine and at the burner outlet.1,2 In current gas turbine engines, many of the superalloy-based components are operating at or near their upper use temperature, even with the benefits imparted by the use of thermal barrier coatings, thereby precluding significant temperature elevations with these alloys. To meet future environmental and performance standards, it is anticipated that the targeted temperature elevations in turbine components will be accomplished through the use of continuous-fiber-reinforced ceramic composites (CFCCs). Among the various ceramic composites that have been developed to date, the ones that have attracted the greatest attention within the power generation industry in the past few years are those made from all-oxide constituents. The main advantage of the oxide-based composites over non-oxide ones (e.g., SiC/SiC) is their superior resistance to oxidation under typical turbine engine conditions and hence their potential for long-term durability. As part of a broad activity aimed at developing and assessing oxide composites for use in future generations of gas turbine engines, the present study focuses on changes in the mechanical properties of a candidate all-oxide CFCC following long-term exposure (1000 h) at temperatures of 1000–1200°C. The composite material of interest derives its damage tolerance from a highly porous matrix, precluding the need for an interphase at the fiber–matrix boundary. Although the efficacy of this material concept in enabling damage tolerance has been demonstrated,3–6 it remains to be established whether the matrix pore structure is stable against densification and whether the desirable damagetolerant characteristics can be retained for extended time periods at the targeted service temperatures. Indeed, other CFCCs based on the porous-matrix concept have been shown to exhibit severe degradation in composite properties once the matrix densifies appreciably.7 The main matrix constituent in the present composite is mullite, in the form of a weakly bonded particulate network. This selection is based on the sluggish sintering kinetics of mullite3 at the upper use temperature for the fibers (1200°C for Nextel 720). This phase is intended to form a contiguous particulate network that should be immune from appreciable densification both during processing and under subsequent service conditions. The minor matrix constituent is alumina, present both in the form of particulates from a slurry and as a product of pyrolysis of an aqueous precursor solution.3,5 Because of its more rapid sintering kinetics, alumina serves to bond the mullite particulates and the fibers together, thereby enhancing the matrix-dominated composite properties, e.g., interlaminar strength and off-axis in-plane strength. However, if the degree of sintering becomes excessive, the damage-tolerant characteristics may be compromised. The challenge involves selection of the relative fractions and topologies of the two phases such that the network of mullite particles remains contiguous and hence prevents global shrinkage, yet the extent of bonding within this network is sufficient to impart the requisite matrix integrity for acceptable off-axis properties. These opposing requirements on the E. Lara-Curzio—-contributing editor Manuscript No. 187723. Received May 4, 2001; approved December 21, 2001. Funding for this work was provided by the Air Force Office of Scientific Research under Contract No. F49620-99-1-0259, by Siemens Westinghouse Power Corp. through both internal research funds at the Science and Technology Center and a subcontract to the University of California at Santa Barbara, and by a gift from NGK Corp. *Member, American Ceramic Society. J. Am. Ceram. Soc., 85 [3] 595–602 (2002) 595 journal
Journal of the American Ceramic Society-Carelli et al. Vol. 85. No. 3 matrix suggest an optimum state, dictated in part by the combina- air furnace for 1000 h at temperatures of either 1000, 1 100%,or tion of properties that are required in the application of interest. 1200C and subsequently tested in uniaxial tension at ambien In this study, comparisons are made between the tensile temperature, following the procedures outlined above. The furnace properties of a 2D woven CFCC both along the fiber direction was heated with resistance wire coated with a ceramic mixture of (0/90o) and at 45. to the fiber axes before and after high- aluminophosphate and alumina, and insulated with aluminosilicate temperature aging treatments. These orientations are selected to Either two or three tests were performed for most conditions elicit the fiber-dominated and matrix-dominated composite prop- representative fractured specimens were examined by bot rties. Examinations of the broken specimens by optical and agnification light microscopy and scanning electron microscopy. scanning electron microscopy are used to elucidate the role of The porosity both before and after aging was measured follow- aging in the fracture characteristics. Changes in the state of the ing ASTM Standard C20-92 Changes in the microstructure of the matrix are probed through two additional complementary methods: aged specimens were elucidated from SEM observations of pol ()measurement of matrix hardness using Vickers indentation, and ished samples. Matrix hardness measurements were also made on (ii) determination of the matrix Youngs mod using the these polished samples within the matrix-rich regions between th measured composite moduli coupled with classical laminate the- fiber tows, using Vickers indentation with a load of 300 g. This ory. Additionally, some comparisons are made with the retention load was selected to produce indentations that were no larger than in properties of a comparable porous-matrix composite with an half of the spacing between tows in all materials. Additionally, the aluminosilicate matrix indents were placed away from the processing-induced cracks (described below). At least 10 such measurements were made on IL. Materials and Test Procedures samples in each aged condition The matrix modulus of both pristine and aged specimens was The composite material consists of Nextel 720 fiber cloth in an inferred from the measured composite moduli in both the 0/90 8-harness satin weave and a porous matrix of mullite and alumi- and +45 orientations using laminate theory. Details of the theory na.5 The matrix was produced in two steps. In the first,an are described in the Appendix. queous slurry containing mullite and alumina particulates was vacuum-infiltrated into a stack of 12 fiber cloths. The matrix Ill. Experimental Results and Analysis particulates were "l um diameter MU-107 mullite(Showa Denko KK )and -0. 2 um diameter AKP-50 alumina(Sumitomo Chem ypical micrographs of polished cross sections of both cal). The slurry contained 80% mullite and 20% alumina, The rocessed specimen and one aged at 1200%C are shown in Fi packing density of the matrix powder foll infiltration was 1. A notable feature is the presence of a more-or-less regular 960%. The green panels were dried and sintered at 900oC for 2 h pattern of matrix cracks, caused by the constrained shrinkage of to promote the development of alumina bridges between the the matrix during drying of the green panels. In the as-processed mullite particles, thereby imparting some structural integrity to the composite, the cracks are concentrated in the matrix-rich regions matrix for subsequent processing. In the second step, the panel were impregnated with an alumina precursor solution(aluminum hydroxychloride) and pyrolyzed at 900C for 2 h. The volt yield of alumina on pyrolysis of this solution was #%. The(a)As-processed mpregnation and pyrolysis sequence was performed twice. The panels were given a final heat treatment at 1200.C for 2 h to stabilize the precursor-derived alumina and to enhance the integ ty of the alumina bridges. The panel dimensions were 200 mm X 130mm×3. I mm thic Panels were made with fibers oriented either parallel or at 4 to the panel edges, thus facilitating preparation of tensile speci mens in both the longitudinal(0°90°) and off-axis(±45°) orientations. The key physical properties of each of the tested summarized in Table I. The fiber content, , wa determined from knowledge of the cloth volume and the final plate ASTM Standard C20-92>P, was measured in accordance with A series of mechanical tests was performed to determine the tensile properties of the as-processed composite in both the 0%/900 and the +45 orientations. The properties were measured usin tandard dog-bone tensile specimens with a gauge length of 50 mm and a gauge width of 8 mm. The longitudinal strains were 1( b)1000 h at 1200C measured us d at room temperature at a displacement rate of an extensometer over a 25 mm gauge length. The 1.25 mm/min Either two or three tests were performed for each material the effects of thermal aging on the mechanical properties, tensile specimens in both orientations were heated in an Table L. Summary of Physical Properties of CFCC Panels b Matrix porosity (% Fiber volar designation orentation Initial Final 39.5 37.9 0.2mm ABC 0°/90° 38.3 40.2 37.7 After slurry infiltration and drying. After precursor impregnation and pyrolysis Fig. 1. SEM micrographs of as-processed and thermally aged composite backscatter imaging mode)
matrix suggest an optimum state, dictated in part by the combination of properties that are required in the application of interest. In this study, comparisons are made between the tensile properties of a 2D woven CFCC both along the fiber direction (0°/90°) and at 45° to the fiber axes before and after hightemperature aging treatments. These orientations are selected to elicit the fiber-dominated and matrix-dominated composite properties. Examinations of the broken specimens by optical and scanning electron microscopy are used to elucidate the role of aging in the fracture characteristics. Changes in the state of the matrix are probed through two additional complementary methods: (i) measurement of matrix hardness using Vickers indentation, and (ii) determination of the matrix Young’s modulus, using the measured composite moduli coupled with classical laminate theory.8 Additionally, some comparisons are made with the retention in properties of a comparable porous-matrix composite with an aluminosilicate matrix.7 II. Materials and Test Procedures The composite material consists of Nextel 720 fiber cloth in an 8-harness satin weave and a porous matrix of mullite and alumina.3,5 The matrix was produced in two steps. In the first, an aqueous slurry containing mullite and alumina particulates was vacuum-infiltrated into a stack of 12 fiber cloths. The matrix particulates were 1 m diameter MU-107 mullite (Showa Denko K.K.) and 0.2 m diameter AKP-50 alumina (Sumitomo Chemical). The slurry contained 80% mullite and 20% alumina. The packing density of the matrix powder following infiltration was 60%. The green panels were dried and sintered at 900°C for 2 h to promote the development of alumina bridges between the mullite particles, thereby imparting some structural integrity to the matrix for subsequent processing. In the second step, the panels were impregnated with an alumina precursor solution (aluminum hydroxychloride) and pyrolyzed at 900°C for 2 h. The volumetric yield of alumina on pyrolysis of this solution was 3%. The impregnation and pyrolysis sequence was performed twice. The panels were given a final heat treatment at 1200°C for 2 h to stabilize the precursor-derived alumina and to enhance the integrity of the alumina bridges. The panel dimensions were 200 mm 130 mm 3.1 mm thick. Panels were made with fibers oriented either parallel or at 45° to the panel edges, thus facilitating preparation of tensile specimens in both the longitudinal (0°/90°) and off-axis (45°) orientations. The key physical properties of each of the tested panels are summarized in Table I. The fiber content, f, was determined from knowledge of the cloth volume and the final plate dimensions. The porosity, p, was measured in accordance with ASTM Standard C20-92. A series of mechanical tests was performed to determine the tensile properties of the as-processed composite in both the 0°/90° and the 45° orientations. The properties were measured using standard dog-bone tensile specimens with a gauge length of 50 mm and a gauge width of 8 mm. The longitudinal strains were measured using an extensometer over a 25 mm gauge length. The tests were performed at room temperature at a displacement rate of 1.25 mm/min. Either two or three tests were performed for each material. To assess the effects of thermal aging on the mechanical properties, tensile specimens in both orientations were heated in an air furnace for 1000 h at temperatures of either 1000°, 1100°, or 1200°C and subsequently tested in uniaxial tension at ambient temperature, following the procedures outlined above. The furnace was heated with resistance wire, coated with a ceramic mixture of aluminophosphate and alumina, and insulated with aluminosilicate fiber. Either two or three tests were performed for most conditions. Representative fractured specimens were examined by both lowmagnification light microscopy and scanning electron microscopy. The porosity both before and after aging was measured following ASTM Standard C20-92. Changes in the microstructure of the aged specimens were elucidated from SEM observations of polished samples. Matrix hardness measurements were also made on these polished samples within the matrix-rich regions between the fiber tows, using Vickers indentation with a load of 300 g. This load was selected to produce indentations that were no larger than half of the spacing between tows in all materials. Additionally, the indents were placed away from the processing-induced cracks (described below). At least 10 such measurements were made on samples in each aged condition. The matrix modulus of both pristine and aged specimens was inferred from the measured composite moduli in both the 0°/90° and 45° orientations using laminate theory. Details of the theory are described in the Appendix. III. Experimental Results and Analysis Typical micrographs of polished cross sections of both an as-processed specimen and one aged at 1200°C are shown in Fig. 1. A notable feature is the presence of a more-or-less regular pattern of matrix cracks, caused by the constrained shrinkage of the matrix during drying of the green panels. In the as-processed composite, the cracks are concentrated in the matrix-rich regions Table I. Summary of Physical Properties of CFCC Panels Panel designation Fiber orientation Matrix porosity (%) Fiber volume Initial fraction (%) † Final‡ A 0°/90° 39.5 37.9 38.6 B 0°/90° 40.1 38.3 38.9 C 45° 40.2 37.7 38.5 † After slurry infiltration and drying. ‡ After precursor impregnation and pyrolysis and final sintering treatment. Fig. 1. SEM micrographs of as-processed and thermally aged composite specimens (viewed in backscatter imaging mode). 596 Journal of the American Ceramic Society—Carelli et al. Vol. 85, No. 3
March 2002 Efects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite 000hat1200c 1000hat1100°c 1000hat1000°c 000 0003 0.004 Tensile Strain 10 u0z0 (b) Aging Temperature(C) (c) As-Processed 48% Nextel 720 fiber (Jurf and Butner, 2000 3 mm 0°/90 Fig 3. Macrophotographs of the 0/90 tensile specimens in two orthog- 20040060080010001200 onal views: (a) as-processed, (b)after aging for 1000 h at 1100.C, and(c Aging Temperature(C) after aging for 1000 h at 1200C Fig. 2. Effects of thermal aging on the tensile properties of the 0/90 composite. The modulus was calculated from the slope of the initial linear strain is accommodated by additional opening displacement of the rtion of the stress-strain curve over a stress range of =50 MPa. racks such that the net average strain is approximately zero. This hypothesis is supported by the measurements of the composite porosity, which indicated no significant change after any of the between fiber tows. They arrest at the interface with the longitu- aging treatments. Higher-magnification SEM examinations of the dinal fibers (oriented perpendicular to the crack plane) and matrix microstructure did not reveal any other obvious changes penetrate only slightly into the transverse tows. Following aging, due to aging the pattern of matrix cracks remains essentially the same, with the Representative stress-strain curves for the as-processed and the exception that the cracks tend to grow into the transverse tows and aged specimens in the 0 /90 orientation are plotted in Fig. 2(a) their opening displacement increases somewhat(see, for example, The variations in the Youngs modulus, E, and the ultimate tensile the cracks on the right side of Fig. 1(b)). These features are strength, u, with aging temperature are summarized in Figs. 2(b) believed to be due to some matrix densification in the matrix and (c). The only significant change is the slight increase in th segments contained between the cracks along the direction per- modulus, from 60 GPa in the as-processed condition to 70 GPa pendicular to the cracks. Since this shrinkage is constrained by the after the 1200C aging treatment. The tensile strength and the (dense) fibers in the adjacent longitudinal tows, the shrinkage failure strain, Es, remained unchanged; the averages and standard
between fiber tows. They arrest at the interface with the longitudinal fibers (oriented perpendicular to the crack plane) and penetrate only slightly into the transverse tows. Following aging, the pattern of matrix cracks remains essentially the same, with the exception that the cracks tend to grow into the transverse tows and their opening displacement increases somewhat (see, for example, the cracks on the right side of Fig. 1(b)). These features are believed to be due to some matrix densification in the matrix segments contained between the cracks along the direction perpendicular to the cracks. Since this shrinkage is constrained by the (dense) fibers in the adjacent longitudinal tows, the shrinkage strain is accommodated by additional opening displacement of the cracks such that the net average strain is approximately zero. This hypothesis is supported by the measurements of the composite porosity, which indicated no significant change after any of the aging treatments. Higher-magnification SEM examinations of the matrix microstructure did not reveal any other obvious changes due to aging. Representative stress–strain curves for the as-processed and the aged specimens in the 0°/90° orientation are plotted in Fig. 2(a). The variations in the Young’s modulus, E, and the ultimate tensile strength, u, with aging temperature are summarized in Figs. 2(b) and (c). The only significant change is the slight increase in the modulus, from 60 GPa in the as-processed condition to 70 GPa after the 1200°C aging treatment. The tensile strength and the failure strain, εf , remained unchanged; the averages and standard Fig. 2. Effects of thermal aging on the tensile properties of the 0°/90° composite. The modulus was calculated from the slope of the initial linear portion of the stress–strain curve, over a stress range of 50 MPa. Fig. 3. Macrophotographs of the 0°/90° tensile specimens in two orthogonal views: (a) as-processed, (b) after aging for 1000 h at 1100°C, and (c) after aging for 1000 h at 1200°C. March 2002 Effects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite 597
598 Journal of the American Ceramic Society-Carelli et al. Vol. 85. No. 3 deviations from 14 tests are g.= 145+8 MPa and E=0.26 Following aging at 1200.C, the fiber tow failures in the 0/90 +.03%. Also shown for comparison in Fig. 2(c)is the retained specimens remained largely uncorrelated with one another at the strength of a comparable all-oxide ceramic composite consisting of macroscopic level(Fig. 3(c). However, there was a noticeable the same Nextel 720 fibers in an aluminosilicate matrix(in place ncrease in the correlation in the fiber failure sites within each tow of the mullite/alumina matrix used in the present study ), after the(Fig. 4(c). The most highly correlated failure sites appeared in same aging treatments. The strength of the aluminosilicate-basee small clusters, each containing perhaps 3-10 fibers. Additionall material decreases rapidly for aging temperatures beyond 1000%C the amount of matrix material remaining adhered to the fiber eportedly due to extensive densification of the matrix and an surfaces was significantly greater than that in the as-processed attendant loss in damage tolerance. material. These features clearly indicate that both the matrix and the In the 0/90 as-processed tensile specimens, the locations of fiber-matrix interface have been strengthened as a consequence of the the tow failures were uncorrelated with one another, as evident in aging treatment, thereby reducing somewhat the extent of damage the macrophotograph in Fig. 3(a). Indeed, the tow failure sites tolerance. Nevertheless, the effects do not appear to be sufficiently were offset by distances up to several centimeters along the large to noticeably alter the 0/90% composite strength. loading direction. larly, highly uncorrelated fiber fra In the +45 orientation, the effects of matrix strengthening on were obtained within each longitudinal tow. An example of a aging were more pronounced(Fig. 5). In all cases, the tensile broken tow near the fracture surface is shown in Fig. 4(a). a response was characterized by elastic-plastic behavior, reminis- articularly striking feature is the seemingly large lateral separa- cent of metal plasticity (albeit at lower levels of strain). The tion between adjacent fibers. This feature is somewhat misleading transition from elastic to plastic behavior was gradual and the in the sense that there are large longitudinal separations between ultimate tensile strength was controlled by a plastic instability the fiber fracture sites and hence many of the broken fibers within analogous to necking in metals, at an average strain of 0.32+ a broken tow are well outside the field of view when imaging the 0.03%, independent of aging treatment. By contrast, Youngs tow at even modest magnifications. These observations attest to modulus and the tensile strength increased dramatically following the efficacy of the matrix in mitigating stress concentrations aging, by as much as a factor of 2 at the highest aging temperature around fiber breaks and hence yielding damage tolerant behavior. This trend reaffirms that some strengthening of both the matrix and Higher-magnification SEM observations revealed only small amounts of matrix particulates remaining adhered to the fiber off-axis composite strength, such changes may be beneficial surface (Fig. 4(b). This result suggests that failure involves In the as-processed +45tensile specimens and the ones aged at debonding and sliding either at or very near the fiber-matrix temperatures up to 1100C, failure occurred mainly through the interface during fiber fracture, analogous to that in dense-matrix matrix and was accompanied by extensive interply delamination CFCCs with weak interphases. Similar features were observed on and fiber" scissoring, but with minimal fiber fracture(Figs. 6(a) the specimens that had been aged at either 1000 or 1100C(.g, and(b). A consequence of this"scissoring"is through-thi g.3(b) swelling in the region near the fracture surface. Following th 5 50 um 10m (d) 0 Fig. 4. SEM micrographs of the fracture surfaces of the 0/90 specimens: (a, b) in as-processed condition, and (c, d) after aging for 1000 h at 1200
deviations from 14 tests are u 145 8 MPa and εf 0.26% 0.03%. Also shown for comparison in Fig. 2(c) is the retained strength of a comparable all-oxide ceramic composite consisting of the same Nextel 720 fibers in an aluminosilicate matrix (in place of the mullite/alumina matrix used in the present study), after the same aging treatments.7 The strength of the aluminosilicate-based material decreases rapidly for aging temperatures beyond 1000°C, reportedly due to extensive densification of the matrix and an attendant loss in damage tolerance. In the 0°/90° as-processed tensile specimens, the locations of the tow failures were uncorrelated with one another, as evident in the macrophotograph in Fig. 3(a). Indeed, the tow failure sites were offset by distances up to several centimeters along the loading direction. Similarly, highly uncorrelated fiber fractures were obtained within each longitudinal tow. An example of a broken tow near the fracture surface is shown in Fig. 4(a). A particularly striking feature is the seemingly large lateral separation between adjacent fibers. This feature is somewhat misleading in the sense that there are large longitudinal separations between the fiber fracture sites and hence many of the broken fibers within a broken tow are well outside the field of view when imaging the tow at even modest magnifications. These observations attest to the efficacy of the matrix in mitigating stress concentrations around fiber breaks and hence yielding damage tolerant behavior. Higher-magnification SEM observations revealed only small amounts of matrix particulates remaining adhered to the fiber surface (Fig. 4(b)). This result suggests that failure involves debonding and sliding either at or very near the fiber–matrix interface during fiber fracture, analogous to that in dense-matrix CFCCs with weak interphases. Similar features were observed on the specimens that had been aged at either 1000° or 1100°C (e.g., Fig. 3(b)). Following aging at 1200°C, the fiber tow failures in the 0°/90° specimens remained largely uncorrelated with one another at the macroscopic level (Fig. 3(c)). However, there was a noticeable increase in the correlation in the fiber failure sites within each tow (Fig. 4(c)). The most highly correlated failure sites appeared in small clusters, each containing perhaps 3–10 fibers. Additionally, the amount of matrix material remaining adhered to the fiber surfaces was significantly greater than that in the as-processed material. These features clearly indicate that both the matrix and the fiber–matrix interface have been strengthened as a consequence of the aging treatment, thereby reducing somewhat the extent of damage tolerance. Nevertheless, the effects do not appear to be sufficiently large to noticeably alter the 0°/90° composite strength. In the 45° orientation, the effects of matrix strengthening on aging were more pronounced (Fig. 5). In all cases, the tensile response was characterized by elastic–plastic behavior, reminiscent of metal plasticity (albeit at lower levels of strain). The transition from elastic to plastic behavior was gradual and the ultimate tensile strength was controlled by a plastic instability analogous to necking in metals,4 at an average strain of 0.32 0.03%, independent of aging treatment. By contrast, Young’s modulus and the tensile strength increased dramatically following aging, by as much as a factor of 2 at the highest aging temperature. This trend reaffirms that some strengthening of both the matrix and the fiber–matrix interfaces occurs during aging. In the context of off-axis composite strength, such changes may be beneficial. In the as-processed 45° tensile specimens and the ones aged at temperatures up to 1100°C, failure occurred mainly through the matrix and was accompanied by extensive interply delamination and fiber “scissoring,” but with minimal fiber fracture (Figs. 6(a) and (b)). A consequence of this “scissoring” is through-thickness swelling in the region near the fracture surface. Following the Fig. 4. SEM micrographs of the fracture surfaces of the 0°/90° specimens: (a,b) in as-processed condition, and (c,d) after aging for 1000 h at 1200°C. 598 Journal of the American Ceramic Society—Carelli et al. Vol. 85, No. 3
March 2002 Efects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite 1000hat1200°C 1000hat1100°c As-processed 0 0.001 0.003 ens 9 Strength Modulus 200400600800 (b) Aging Temperature (C) 1000hat1200°c 1000hat1100°C (c) 3 mm 020.30. 050.60.7 Post-Localization Displacement (mm Fig. 6. Macrophotographs of the +45 tensile specimens in two orthog h at 1100°c,and(c Fig. 5. Effects of thermal aging on the tensile properties of the +45 after aging for 1000 h at 1200C features but with greater amounts of matrix on the fibers, consis- 1200C aging, there was a reduction in the extent of delamination. tent with the trend seen in the 0/90 orientation. Furthermore the failure mechanism now included extensive fiber Salient changes in the fracture properties in the t45orientation fracture(Fig. 6(c)). This feature is consistent with the increases in are revealed in the tensile response following strain localizatio the matrix and interface strengths due to aging, which improve the (beyond the load maximum). The load-displacement response in this effectiveness of load transfer from the matrix to the fibers and regime(Fig 5(c)) can be viewed as the traction law that would b hence increase the propensity for fiber fracture pertinent to the fracture process zone in a notched specimen and hence When viewed in the SEM (Fig. 7(a, b)), the fracture surfaces of provides information about the steady-state fracture energy. The the +45 as-processed specimens revealed somewhat greater results indicate that, as the matrix strength is initially increased, e. g amounts of matrix particulates adhered to the fiber surfaces than from the as-processed condition to the one obtained after 1000 h at that in the 0/90 orientation. It is surmised that these differences 1100oC, the stress-displacement response is simply shifted up to are related to the differences in the stress states at the fiber-matrix higher strength levels, commensurate with the increase in the ultimate interfaces in the two orientations, coupled with differences in the tensile strength. The fracture energy increases proportionately, by surfaces of the specimens aged at 1200C exhibited similar hS% However, as the matrix strength is increased further, e. g, after amounts of sliding that occur between adjacent fibers. The fracture 1200C aging, the stress-displacement response begins at a higher
1200°C aging, there was a reduction in the extent of delamination. Furthermore, the failure mechanism now included extensive fiber fracture (Fig. 6(c)). This feature is consistent with the increases in the matrix and interface strengths due to aging, which improve the effectiveness of load transfer from the matrix to the fibers and hence increase the propensity for fiber fracture. When viewed in the SEM (Fig. 7(a,b)), the fracture surfaces of the 45° as-processed specimens revealed somewhat greater amounts of matrix particulates adhered to the fiber surfaces than that in the 0°/90° orientation. It is surmised that these differences are related to the differences in the stress states at the fiber–matrix interfaces in the two orientations, coupled with differences in the amounts of sliding that occur between adjacent fibers. The fracture surfaces of the specimens aged at 1200°C exhibited similar features but with greater amounts of matrix on the fibers, consistent with the trend seen in the 0°/90° orientation. Salient changes in the fracture properties in the 45° orientation are revealed in the tensile response following strain localization (beyond the load maximum). The load–displacement response in this regime (Fig. 5(c)) can be viewed as the traction law that would be pertinent to the fracture process zone in a notched specimen and hence provides information about the steady-state fracture energy. The results indicate that, as the matrix strength is initially increased, e.g., from the as-processed condition to the one obtained after 1000 h at 1100°C, the stress–displacement response is simply shifted up to higher strength levels, commensurate with the increase in the ultimate tensile strength. The fracture energy increases proportionately, by 25%. However, as the matrix strength is increased further, e.g., after the 1200°C aging, the stress–displacement response begins at a higher Fig. 5. Effects of thermal aging on the tensile properties of the 45° composite. Fig. 6. Macrophotographs of the 45° tensile specimens in two orthogonal views: (a) as-processed, (b) after aging for 1000 h at 1100°C, and (c) after aging for 1000 h at 1200°C. March 2002 Effects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite 599
Journal of the American Ceramic Society-Carelli et al. Vol. 85. No. 3 pm 50 um 10画(d) 10 um Fig. 7. SEM micrographs of the fracture surfaces of the 45 specimens:(a)in as-processed condition, and(b) after aging for 1000 h at 1200.C stress level but rapidly diminishes with increasing displacement, with the 1200C aging. These results reveal yet again that changes complete rupture ensuing at a relatively small displacement. The occur in the state of the matrix as a result of the aging treatment corresponding fracture energy is reduced significantly, by more than a factor of 2 relative to that after the 1 100C heat treatment. This reduction in fracture energy can be attributed to the transition in the IV. Discussion and conclusions fracture mechanisms, from one of matrix cracking, delamination and fiber scissoring, to one involving extensive fiber fracture. This trend The mullite/alumina matrix undergoes some degree of sintering suggests the existence of an optimum matrix condition(e.g, strength) during the aging treatments. The main manifestations are increases at which the fracture energy in the +45 orientation attains a in modulus and hardness, by as much as a factor of 2. These maximum changes cause similar elevations in the modulus and the tensile The changes in matrix hardness with aging temperature ar strength of the composite in the +45 orientation, but with no plotted in Fig. 8(a). The hardness was essentially constant (50 change in the failure strain. Additionally, there is a noticeable g/mm)up to 1100 C. It subsequently increased and reached increase in the propensity for fiber fracture in this orientation aft value of s 100 kg/mm- following the 1200C aging. This twofold the highest temperature aging treatment and evidence of reduced increase in hardness is consistent with the twofold increase in the damage tolerance in the post-load-maximum regime By contrast, composite tensile strength in the +45 orientation following the in the 0/90 orientation, the composite modulus increases only same aging treatment. The corresponding changes in the matrix slightly and the tensile strength and the failure strain remain Youngs modulus are plotted in Fig. &(b). In light of the presence unchanged. Perhaps the most notable change in the latter orienta- of the processing-induced matrix cracks(Fig. 1), this modulus tion is the increase in the spatial correlation in the fiber failure sites presents an average value that incorporates the effects of the within an individual tow and the increased amount of matrix racks and is therefore expected to be somewhat lower than that of material adhered to the fibers. Nevertheless, the failure sites appea the porous matrix itself. Nevertheless, since the density of cracks to be sufficiently decorrelated from one another to suggest that th does not change appreciably during aging, the relative changes matrix largely continues to serve its role of mitigating stress the inferred matrix modulus are expected to reflect the changes due concentrations around fiber breaks. In light of the known sintering to matrix sintering. For the pristine composite, the inferred matrix kinetics of mullite and alumina, it is surmised that the sintering modulus the range 5-9 GPa(more than an order of within the matrix is associated predominantly with the Al O3, both magnitude lower than that of fully dense mullite). Furthermore, the from the particulates and that derived from the precursor value inferred from the +45 tensile tests is consistently higher The rather large differences in the effects of the matrix changes than that from the 0/90tests. It is surmised that this difference is on the 0/90 and +45 composite properties can be rationalized due to the different effects of the processing-induced matrix cracks with the aid of the schematic in Fig. 9. Since the properties in the (Fig. 1)on the average matrix modulus in the two testing +45 orientation are dominated by the matrix, it follows that orientations. The modulus increased with increasing aging temper- changes in the matrix properties will be translated in a roughly ature, especially above about 1 100%C, and essentially doubled after proportionate amount in the composite properties. This behavior
stress level but rapidly diminishes with increasing displacement, with complete rupture ensuing at a relatively small displacement. The corresponding fracture energy is reduced significantly, by more than a factor of 2 relative to that after the 1100°C heat treatment. This reduction in fracture energy can be attributed to the transition in the fracture mechanisms, from one of matrix cracking, delamination and fiber scissoring, to one involving extensive fiber fracture. This trend suggests the existence of an optimum matrix condition (e.g., strength) at which the fracture energy in the 45° orientation attains a maximum. The changes in matrix hardness with aging temperature are plotted in Fig. 8(a). The hardness was essentially constant (50 kg/mm2 ) up to 1100°C. It subsequently increased and reached a value of 100 kg/mm2 following the 1200°C aging. This twofold increase in hardness is consistent with the twofold increase in the composite tensile strength in the 45° orientation following the same aging treatment. The corresponding changes in the matrix Young’s modulus are plotted in Fig. 8(b). In light of the presence of the processing-induced matrix cracks (Fig. 1), this modulus represents an average value that incorporates the effects of the cracks and is therefore expected to be somewhat lower than that of the porous matrix itself. Nevertheless, since the density of cracks does not change appreciably during aging, the relative changes in the inferred matrix modulus are expected to reflect the changes due to matrix sintering. For the pristine composite, the inferred matrix modulus is in the range 5–9 GPa (more than an order of magnitude lower than that of fully dense mullite). Furthermore, the value inferred from the 45° tensile tests is consistently higher than that from the 0°/90° tests. It is surmised that this difference is due to the different effects of the processing-induced matrix cracks (Fig. 1) on the average matrix modulus in the two testing orientations. The modulus increased with increasing aging temperature, especially above about 1100°C, and essentially doubled after the 1200°C aging. These results reveal yet again that changes occur in the state of the matrix as a result of the aging treatment. IV. Discussion and Conclusions The mullite/alumina matrix undergoes some degree of sintering during the aging treatments. The main manifestations are increases in modulus and hardness, by as much as a factor of 2. These changes cause similar elevations in the modulus and the tensile strength of the composite in the 45° orientation, but with no change in the failure strain. Additionally, there is a noticeable increase in the propensity for fiber fracture in this orientation after the highest temperature aging treatment and evidence of reduced damage tolerance in the post-load-maximum regime. By contrast, in the 0°/90° orientation, the composite modulus increases only slightly and the tensile strength and the failure strain remain unchanged. Perhaps the most notable change in the latter orientation is the increase in the spatial correlation in the fiber failure sites within an individual tow and the increased amount of matrix material adhered to the fibers. Nevertheless, the failure sites appear to be sufficiently decorrelated from one another to suggest that the matrix largely continues to serve its role of mitigating stress concentrations around fiber breaks. In light of the known sintering kinetics of mullite and alumina, it is surmised that the sintering within the matrix is associated predominantly with the Al2O3, both from the particulates and that derived from the precursor. The rather large differences in the effects of the matrix changes on the 0°/90° and 45° composite properties can be rationalized with the aid of the schematic in Fig. 9. Since the properties in the 45° orientation are dominated by the matrix, it follows that changes in the matrix properties will be translated in a roughly proportionate amount in the composite properties. This behavior is Fig. 7. SEM micrographs of the fracture surfaces of the 45° specimens: (a) in as-processed condition, and (b) after aging for 1000 h at 1200°C. 600 Journal of the American Ceramic Society—Carelli et al. Vol. 85, No. 3
March 2002 Efects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite 150 blunting cracks that emanate from fiber breaks. Evidently the extent of the changes in the matrix strength following aging are insufficient to noticeably alter the fiber bundle strength. This suggests the existence of a rather broad maximum or plateau in t fiber bundle strength, wherein the properties are insensitive to the matrix properties(top curve in Fig 9). The much larger changes in the extent of matrix sintering in aluminosilicate matrix CFCCs lead to extremely brittle fracture characteristics and low strength illustrated by the decreasing part of the top curve in Fig. 9 It is anticipated that there are two other behavioral regimes with 50 regard to the o°90°and±45° tensile response. In the former orientation, the strength is expected to increase with increasing matrix strength in the regime where the matrix strength is very low. This expectation is based in part on analogous behavior of dense-matrix CFCCs with weak interphases. Notably, when the interfacial sliding 00400600800100012001400 stress, To, is sufficiently low to ensure global load sharing character Aging Temperature(C) istics, the bundle strength is predicted to scale with T. (m+D)where m is the Weibull modulus of the fibers. For typical values of m (4-10), the exponent 1/(m+ 1)0. 1-0. 2, and thus the sensitivity to To is weak. Indeed, over the typical range of m values, twofold 凵20 may not be detected readily among the scatter in the experimental measurements. Furthermore, once To becomes sufficiently large, the load-sharing characteristics among broken fibers become more local- ●From pt ized and the fiber bundle strength then gradually diminishes. 0 nsion analogy, the fiber bundle strength in the porous-matrix composites is expected to follow a similar dependence on the matrix shear strength. initially increasing and then decreasing with increasing matrix strength. Furthermore, the seeming independence of the composite strength on the matrix strength in the present experiments may be a 5 consequence of a similarly weak dependence in composite propertie on matrix properties in the regime probed by these experiments coupled with some scatter in the experimental measurements. Con- sequently, it remains to be established more definitively whether the 0200400600800100012001400 present experimental results do indeed reside along the broad plateau Aging Temperature(C) in Fig.9 or whether they are in one of the adjacent regimes in which the strength is either gradually increasing or gradually decreasing with Fig. 8. Effects of thermal aging on(a) the matrix hardness and(b) the the degree of matrix sintering. matrix Young's modulus For similar reasons, a maximum in the +45 composite strength is also expected. That is, once the matrix strength achieves a sufficiently high value, the inelastic straining capabilities of the are diminished and the becomes increasingly sensitive to the presence of flaws, introduce Mullite/Alumina either during processing or as a consequence of mechanical 090° loading. In this regime, the strength is expected to be low and exhibit large variability. These hypotheses require further theoret 5品 From a technological viewpoint, the retention of the fiber- dominated properties after the 1200C aging treatment is partici Aluminosilicate larly encouraging. It reaffirms that, with the selection of a matrix Matrix with a stable pore structure coupled with a stable oxide fiber, these composites have the potential for long-term durability at temper atures to which they will be subjected in the targeted applications Otherwise, if the matrix is susceptible to appreciable sintering, the composites are prone to severe property degradation. Moreover, it ±45° is anticipated that further enhancement in the stability of the pore structure could be achieved through modifications to the matrix formulation, e.g., increasing the ratio of mullite to alumina, to ensure that the properties are retained for even longer time periods Degree of Matrix Sintering than those probed by the present experiments. However, these improvements may come at the expense of reduced off- Fig.9. Schematic showing the trends in the +45 and o%/90 tensile properties. This is the subject of current investigation strengths with the degree of matrix sintering Append llustrated by the lower(solid) curve in Fig. 9. In the 0 /90 orientation, the properties are largely fiber-dominated, with onl Youngs modulus of the matrix was inferred from the measured small contributions coming from the matrix. For instance, because Youngs moduli of the composites, measured both in the 0/90 of the extremely low value of matrix modulus in the as-processed and +45%orientations, using classical laminate theory. For this composite, even a twofold increase in this modulus following purpose, the composite is treated as a balanced, symmetric lay-up aging has only a small effect on the composite modulus. The main of unidirectional fiber composite plies. The calculation proceeds in role of the matrix in this orientation is to act as a medium for two steps. In the first, the properties of the laminate are expressed
illustrated by the lower (solid) curve in Fig. 9. In the 0°/90° orientation, the properties are largely fiber-dominated, with only small contributions coming from the matrix. For instance, because of the extremely low value of matrix modulus in the as-processed composite, even a twofold increase in this modulus following aging has only a small effect on the composite modulus. The main role of the matrix in this orientation is to act as a medium for blunting cracks that emanate from fiber breaks. Evidently the extent of the changes in the matrix strength following aging are insufficient to noticeably alter the fiber bundle strength. This suggests the existence of a rather broad maximum or plateau in the fiber bundle strength, wherein the properties are insensitive to the matrix properties (top curve in Fig. 9). The much larger changes in the extent of matrix sintering in aluminosilicate matrix CFCCs lead to extremely brittle fracture characteristics and low strength, illustrated by the decreasing part of the top curve in Fig. 9. It is anticipated that there are two other behavioral regimes with regard to the 0°/90° and 45° tensile response. In the former orientation, the strength is expected to increase with increasing matrix strength in the regime where the matrix strength is very low. This expectation is based in part on analogous behavior of dense-matrix CFCCs with weak interphases. Notably, when the interfacial sliding stress, 0, is sufficiently low to ensure global load sharing characteristics, the bundle strength is predicted to scale with 0 1/(m 1) where m is the Weibull modulus of the fibers.9 For typical values of m (4–10), the exponent 1/(m 1) 0.1–0.2, and thus the sensitivity to 0 is weak. Indeed, over the typical range of m values, twofold changes in 0 only alter the bundle strength by 10%, an effect which may not be detected readily among the scatter in the experimental measurements. Furthermore, once 0 becomes sufficiently large, the load-sharing characteristics among broken fibers become more localized and the fiber bundle strength then gradually diminishes.10 By analogy, the fiber bundle strength in the porous-matrix composites is expected to follow a similar dependence on the matrix shear strength, initially increasing and then decreasing with increasing matrix strength. Furthermore, the seeming independence of the composite strength on the matrix strength in the present experiments may be a consequence of a similarly weak dependence in composite properties on matrix properties in the regime probed by these experiments, coupled with some scatter in the experimental measurements. Consequently, it remains to be established more definitively whether the present experimental results do indeed reside along the broad plateau in Fig. 9 or whether they are in one of the adjacent regimes in which the strength is either gradually increasing or gradually decreasing with the degree of matrix sintering. For similar reasons, a maximum in the 45° composite strength is also expected. That is, once the matrix strength achieves a sufficiently high value, the inelastic straining capabilities of the composite are diminished and the strength of the composite becomes increasingly sensitive to the presence of flaws, introduced either during processing or as a consequence of mechanical loading. In this regime, the strength is expected to be low and exhibit large variability. These hypotheses require further theoretical and experimental investigation. From a technological viewpoint, the retention of the fiberdominated properties after the 1200°C aging treatment is particularly encouraging. It reaffirms that, with the selection of a matrix with a stable pore structure coupled with a stable oxide fiber, these composites have the potential for long-term durability at temperatures to which they will be subjected in the targeted applications. Otherwise, if the matrix is susceptible to appreciable sintering, the composites are prone to severe property degradation. Moreover, it is anticipated that further enhancement in the stability of the pore structure could be achieved through modifications to the matrix formulation, e.g., increasing the ratio of mullite to alumina, to ensure that the properties are retained for even longer time periods than those probed by the present experiments. However, these improvements may come at the expense of reduced off-axis properties. This is the subject of current investigation. Appendix Young’s modulus of the matrix was inferred from the measured Young’s moduli of the composites, measured both in the 0°/90° and 45° orientations, using classical laminate theory. For this purpose, the composite is treated as a balanced, symmetric lay-up of unidirectional fiber composite plies. The calculation proceeds in two steps. In the first, the properties of the laminate are expressed Fig. 8. Effects of thermal aging on (a) the matrix hardness and (b) the matrix Young’s modulus. Fig. 9. Schematic showing the trends in the 45° and 0°/90° tensile strengths with the degree of matrix sintering. March 2002 Effects of Thermal Aging on the Mechanical Properties of a Porous-Matrix Ceramic Composite 601
Journal of the American Ceramic Society-Carelli et al. Vol. 85. No. 3 In terms engineering elastic constants of an The fitting parameters, s, in Eqs.(A-3)and(A-4) are taken to be nidirecti lamina. In the second, the lamina pi elated to operties of the fibers and the matrix and The matrix modulus was inferred from the measured modulus orientation through established composite models. The results Orgo via Eqs.(A-1)and(A-3), along with the known constituent from these two steps are then combined with other(known) properties (Er= 260 GPa, vm S v S V12 8 0.2(Ref. 13)) constituent properties to obtain the matrix modulus. The pertinent Similarly, it was inferred from the measured modulus Eas via eqs esults in each of the two main steps are summarized below. (A-2)and(A-4)and the same constituent properties. The results of The unidirectional lamina is treated as being transversely these calculations are plotted in Fig. 7(b) isotropic. The relevant in-plane engineering elastic constants are denoted E1, Ex, V12 and G12, where E denotes Youngs modulus, v is Poissons ratio, G is the shear modulus, and the subscripts I and 2 refer to the directions parallel and perpendicular to the fibers, Acknowledgment espectively. From laminate theory, Youngs modulus of the acknowledge Professor Carlos G. Levi for his invaluable contribu- laminate can be expressed as tions in the de 2v12 +E 1+E1/E E E (A-1) References R. L. Bannister, N.S. Ceruvu, D. A. Little, and G. McQuiggan, "Developmen Requirements for an Advanced Gas Turbine System, Trans. ASME, 117, 724-33 For typical values of the various engineering elastic properties of W. P. Parks, R. R Ramey, D. C. Rawlins, J. R. Price, and M. Van Roode is very close to unity (within about 0. 4%]). Consequently, for most Gas nuri es Picter, 13 S// oz 4 (r991 cases only the term in brackets,[,I is required. 3C. G. Levi, J. Y. Yang, B. J. Dalgleish, F. W. Zok, and A G. Evans, "Process 9. Similarly, for in-plane uniaxial loading at 45 to the two fiber and Performance of an All-Oxide Ceramic Composite,"J. Am. Ceram Soc., 81 (8 erections, Youngs modulus Eas of the laminate is given by 4J. A Heathcote, X.-Y. Gong, J. Yang, U. Ramamurty, and F. w. Zok, "In-Plane 111-v2(E2/E1) Mechanical Properties of an All-Oxide Ceramic Composite, "J. Am Ceram. Soc., (A-2) 012721-30(199 toni. and J. P. A. Lofvande ble Porous Matrices for All-Oxide Ceramic Compos- FA i N SC I A i o) o ou Mis Ccmt The engineering elastic constants E, and vu are related to the fiber ites, "Z Metallkd, 90[12]1037-47(1999) and matrix properties using the rule of mixtures. The other constants F W. Zok and E, and G12, are calculated using the Tsai-Halpin equation 1+ SEmE/ Turbines Power,122[2]202-205(2000) University Press, Cambridge, U.K., 1981 9w. A. Curtin, "Theory of the Mechanical Properties of Ceramic Composites, Er/Em-1 J. Am Ceram.Soc,74[2837-45(1991) E/En SE (A-3b) IoM. Ibnabdeljalil and w. A, Curtin, "Strength and Reliability of Fiber-Reinforced Composites: Localized Load-Sharing and Associated Size Effects, "Int.J. Solids Struct,34,2649-68(1997) J. Lu and J. w. Hutchinson,"Thermal Conductivity and G (A-4a) Cross-Ply Composites with Matrix Cracks,J. Mech Phys. Solids 12D. Wilson, Statistical Tensile Strength of Nextel M 610 and Nextel M720 G/Gm+ Eg (A-4b)M.Bari.AMsEngieringMrdsReremeBoo2ndEd;pp195-264
in terms of the engineering elastic constants of an individual (unidirectional) lamina. In the second, the lamina properties are related to the properties of the fibers and the matrix and the fiber orientation through established composite models. The results from these two steps are then combined with other (known) constituent properties to obtain the matrix modulus. The pertinent results in each of the two main steps are summarized below. The unidirectional lamina is treated as being transversely isotropic. The relevant in-plane engineering elastic constants are denoted E1, E2, 12 and G12, where E denotes Young’s modulus, is Poisson’s ratio, G is the shear modulus, and the subscripts 1 and 2 refer to the directions parallel and perpendicular to the fibers, respectively. From laminate theory,8 Young’s modulus of the laminate can be expressed as E0/90 E1 E2 2 1 2 12 1 E1/E2 2 1 12 2 E2 E1 (A-1) For typical values of the various engineering elastic properties of the lamina, the term in braces, {. . . }, on the right side of Eq. (A-1) is very close to unity (within about 0.4%). Consequently, for most cases only the term in square brackets, [. . . ], is required. Similarly, for in-plane uniaxial loading at 45° to the two fiber directions, Young’s modulus E45 of the laminate is given by 1 E45 1 4G12 1 12 2 E2/E1 E1 E2 1 2 12 (A-2) The engineering elastic constants E1 and 12 are related to the fiber and matrix properties using the rule of mixtures. The other constants, E2 and G12, are calculated using the Tsai–Halpin equations:11 E2 Em 1 EE f 1 E f (A-3a) E Ef /Em 1 Ef /Em E (A-3b) G12 Gm 1 GG f 1 G f (A-4a) G Gf /Gm 1 Gf /Gm G (A-4b) The fitting parameters, , in Eqs. (A-3) and (A-4) are taken to be G 1 and E 2.8,11 The matrix modulus was inferred from the measured modulus E0/90 via Eqs. (A-1) and (A-3), along with the known constituent properties (Ef 260 GPa;12 m f 12 0.2 (Ref. 13)). Similarly, it was inferred from the measured modulus E45 via Eqs. (A-2) and (A-4) and the same constituent properties. The results of these calculations are plotted in Fig. 7(b). Acknowledgment We gratefully acknowledge Professor Carlos G. Levi for his invaluable contributions in the design and implementation of the porous-matrix concept utilized in this study. References 1 R. L. Bannister, N. S. Ceruvu, D. A. Little, and G. McQuiggan, “Development Requirements for an Advanced Gas Turbine System,” Trans. ASME, 117, 724–33 (1995). 2 W. P. Parks, R. R. Ramey, D. C. Rawlins, J. R. Price, and M. Van Roode, “Potential Applications of Structural Ceramic Composites in Gas Turbines,” J. Eng. Gas Turbines Power, 113 [4] 628–34 (1991). 3 C. G. Levi, J. Y. Yang, B. J. Dalgleish, F. W. Zok, and A. G. Evans, “Processing and Performance of an All-Oxide Ceramic Composite,” J. Am. Ceram. Soc., 81 [8] 2077–86 (1998). 4 J. A. Heathcote, X.-Y. Gong, J. Yang, U. Ramamurty, and F. W. Zok, “In-Plane Mechanical Properties of an All-Oxide Ceramic Composite,” J. Am. Ceram. Soc., 82 [10] 2721–30 (1999). 5 C. G. Levi, F. W. Zok, J.-Y. Yang, M. Mattoni, and J. P. A. Lo¨fvander, “Microstructural Design of Stable Porous Matrices for All-Oxide Ceramic Composites,” Z. Metallkd., 90 [12] 1037–47 (1999). 6 F. W. Zok and C. G. Levi, “Mechanical Properties of Porous Matrix Ceramic Composites,” Adv. Eng. Mater., 3 [1–2] 15–23 (2001). 7 R. A. Jurf and S. C. Butner, “Advances in Oxide–Oxide CMC,” J. Eng. Gas Turbines Power, 122 [2] 202–205 (2000). 8 D. Hull, An Introduction to Composite Materials; pp. 81–124. Cambridge University Press, Cambridge, U.K., 1981. 9 W. A. Curtin, “Theory of the Mechanical Properties of Ceramic Composites,” J. Am. Ceram. Soc., 74 [11] 2837–45 (1991). 10M. Ibnabdeljalil and W. A. Curtin, “Strength and Reliability of Fiber-Reinforced Composites: Localized Load-Sharing and Associated Size Effects,” Int. J. Solids Struct., 34, 2649–68 (1997). 11T. J. Lu and J. W. Hutchinson, “Thermal Conductivity and Expansion of Cross-Ply Composites with Matrix Cracks,” J. Mech. Phys. Solids, 43, 1175–98 (1995). 12D. Wilson, “Statistical Tensile Strength of NextelTM 610 and NextelTM 720 Fibers,” J. Mater. Sci, 32, 2532–42 (1997). 13M. Bauccio, AMS Engineering Materials Reference Book, 2nd Ed.; pp. 195–264. ASM International, Materials Park, OH, 1994. 602 Journal of the American Ceramic Society—Carelli et al. Vol. 85, No. 3