《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_SiC-SiC-37

Availableonlineatwww.sciencedirect.com e Science Direct COMPOSITES CIENCE AND TECHNOLOGY ELSEVIER Composites Science and Technology 67(2007)1009-1017 www.elsevier.com/locate/compscitech Modeling stress-dependent matrix cracking and stress-strain behavior in 2D woven Sic fiber reinforced CVI SiC composites Gregory N. Morscher a,, Mrityunjay Singh b, J. Douglas Kiser Marc Freedman Ram bhatt Ohio Aerospace Institute, NASA Glenn Research Center, Cleveland, OH, United States b OSS Group, NASA Glenn Research Center, Cleveland, OH, United States Nasa Glenn research center. cleveland. oh United states d Us army. NASA Glenn Research Center. Cleveland. OH. United States 2005: received in revised form 27 April 2006: 14 June 200( Abstract 2D woven Hi-Nicalon and Sylramic-iBN SiC fiber reinforced chemical vapor-infiltrated( Cvn) SiC matrix composites were tested room temperature with modal acoustic emission monitoring in order to determine relationships for stress-dependent matrix cracking The Hi-Nicalon composites varied in the number of plies(1-36), specimen thickness, and constituent content. The Sylramic-iBN com- posites were fabricated with balanced and unbalanced 2D weaves in order to vary the fiber volume fraction in the orthogonal directions Not surprisingly, matrix cracking stresses tended to be but were not always, higher for composites with higher fiber volume fractions in the loading direction. It was demonstrated that simple relationships for stress-dependent matrix cracking could be related to the stress in the load-bearing CVI SiC matrix. For low-density composites, the 90 minicomposites do not share significant loads and matrix cracking matrix cracking was dependent on the unbridged"flaw"size, i.e., the 90 tow size or unbridged transverse crack size Qinicomposites was very similar to single tow minicomposites. For higher-density composites, where significant load is carried by the o% minicomposites o 2006 Elsevier Ltd. All rights reserved Keywords: A. Ceramic-matrix composites; B Matrix cracking: C. Acoustic emission; D. Stress-strain behavior 1. Introduction verse matrix cracks in the woven composite and it is there- fore essential to characterize the stress-strain dependence In the companion paper [l] a relationship for elastic for matrix cracking in order to effectively model stress- modulus was determined for a wide variety of 2D woven strain behavior [2,3]. This pertains not only to stress-strain SiC fiber reinforced SiC matrix composites which varied response for the purpose of modeling stress-redistribution in numbers of plies, constituent content, thickness, density, in a component, but also for the purpose of modeling ele- and number of woven tows in either direction (i.e, balanced vated temperature life properties [4] which depend on the weaves versus unbalanced weaves). A second critical prop- presence of matrix cracks to enable oxidation mechanisms erty for design is the onset of non-linearity in the stress- to cause time-dependent strength-degradation of the strain curve in addition to the stress-strain behavior composite beyond the linear region of the stress-strain curve. Non Recently, the stress-dependent matrix cracking behavior linearity is due to the initiation and propagation of trans- has been quantified for 2D woven Sic fiber reinforced melt-infiltrated (MI) composites reinforced with the high ant Sylramic-iBN fibe ondas padres: Greg nor. Tel:+1216 433 5512: fax: +1 2164335544. cial emphasis was made to vary the 2D woven architecture gory.N Morscher@grc. nasa. gov(G N Morscher). [6, 7] and composites reinforced with the lower modulus 02663538/S. see front matter 2006 Elsevier Ltd. All rights reserved doi:10.1016j.compscitech.2006.06.007

Modeling stress-dependent matrix cracking and stress–strain behavior in 2D woven SiC fiber reinforced CVI SiC composites Gregory N. Morscher a,*, Mrityunjay Singh b , J. Douglas Kiser c , Marc Freedman c , Ram Bhatt d a Ohio Aerospace Institute, NASA Glenn Research Center, Cleveland, OH, United States b QSS Group, NASA Glenn Research Center, Cleveland, OH, United States c NASA Glenn Research Center, Cleveland, OH, United States d US Army, NASA Glenn Research Center, Cleveland, OH, United States Received 19 April 2005; received in revised form 27 April 2006; accepted 14 June 2006 Available online 1 September 2006 Abstract 2D woven Hi-Nicalon and Sylramic-iBN SiC fiber reinforced chemical vapor-infiltrated (CVI) SiC matrix composites were tested at room temperature with modal acoustic emission monitoring in order to determine relationships for stress-dependent matrix cracking. The Hi-Nicalon composites varied in the number of plies (1–36), specimen thickness, and constituent content. The Sylramic-iBN com￾posites were fabricated with balanced and unbalanced 2D weaves in order to vary the fiber volume fraction in the orthogonal directions. Not surprisingly, matrix cracking stresses tended to be, but were not always, higher for composites with higher fiber volume fractions in the loading direction. It was demonstrated that simple relationships for stress-dependent matrix cracking could be related to the stress in the load-bearing CVI SiC matrix. For low-density composites, the 90 minicomposites do not share significant loads and matrix cracking was very similar to single tow minicomposites. For higher-density composites, where significant load is carried by the 0 minicomposites, matrix cracking was dependent on the unbridged ‘‘flaw’’ size, i.e., the 90 tow size or unbridged transverse crack size. 2006 Elsevier Ltd. All rights reserved. Keywords: A. Ceramic-matrix composites; B. Matrix cracking; C. Acoustic emission; D. Stress–strain behavior 1. Introduction In the companion paper [1], a relationship for elastic modulus was determined for a wide variety of 2D woven SiC fiber reinforced SiC matrix composites which varied in numbers of plies, constituent content, thickness, density, and number of woven tows in either direction (i.e, balanced weaves versus unbalanced weaves). A second critical prop￾erty for design is the onset of non-linearity in the stress– strain curve in addition to the stress–strain behavior beyond the linear region of the stress–strain curve. Non￾linearity is due to the initiation and propagation of trans￾verse matrix cracks in the woven composite and it is there￾fore essential to characterize the stress–strain dependence for matrix cracking in order to effectively model stress– strain behavior [2,3]. This pertains not only to stress–strain response for the purpose of modeling stress-redistribution in a component, but also for the purpose of modeling ele￾vated temperature life properties [4] which depend on the presence of matrix cracks to enable oxidation mechanisms to cause time-dependent strength-degradation of the composite. Recently, the stress-dependent matrix cracking behavior has been quantified for 2D woven SiC fiber reinforced melt-infiltrated (MI) composites reinforced with the high modulus, creep-resistant Sylramic-iBN fiber type [5]. Spe￾cial emphasis was made to vary the 2D woven architecture [6,7] and composites reinforced with the lower modulus 0266-3538/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2006.06.007 * Corresponding author. Tel.: +1 216 433 5512; fax: +1 216 433 5544. E-mail address: Gregory.N.Morscher@grc.nasa.gov (G.N. Morscher). www.elsevier.com/locate/compscitech Composites Science and Technology 67 (2007) 1009–1017 COMPOSITES SCIENCE AND TECHNOLOGY

G.N. Morscher et al. Composites Science and Technology 67(2007)1009-1017 Hi-Nicalon fiber [6]. In this study, composites reinforced imens, 4 kN/min for 8 ply specimens, and 10 kN/min for with 2D woven Sylramic-iBN and Hi-Nicalon in a CVi thick specimens. Acoustic emission was monitored during iC matrix were studied. The Syl-iBN composites were var- the tensile test using a Digital Wave Fracture Wave Detec- ied so that the number of tows per length in the two tor. Three wide-band (100 kHz to 2 MHz sensitivity; model orthogonal directions were either the same(balanced) or B1025, Digital Wave, Englewood, CO) sensors were used differed(unbalanced), the latter to simulate enhanced fiber to capture AE activity. Two sensors were placed on the loading in a given direction. The composites reinforced face of the specimen outside of both extensometer knife with Hi-Nicalon in a CVI SiC matrix varied from I to 36 edges whereas the third was placed in the center of the gage plies and differed in constituent content and density section on the opposite face of the extensometer knife edges Only ae data that hit the middle aE sensor first, 2. Experimental i.e., data that occurred in the gage section, were used for the matrix cracking analysis. To determine non-linearity The details on composite processing, constituent con- in the stress-strain curve, a 0.002% offset stress technique tent, and variety of composite panels tested can be found was employed. The 0.002% offset stress is where the linear in Table I [1]. All of the panels consisted of 2D five or eight regression fit curve used to determine elastic modulus, E(5 harness satin woven fabric and were fabricated by ge to <50 MPa)offset by +0.002% intersects with the stress- Power Systems Composites, Newark Delaware. Most pan- strain curve els were either fabricated with BN or carbon interphases After composite failure, some of the specimens were cut Table I also describes the type of tensile specimens, straight and polished along the longitudinal direction in order to sided or dogbone, that were cut from each panel. measure the matrix crack density. The specimens with Tensile testing was performed on an Instron Model 8562 Syl-iBN fibers and a BN-interphase required a plasma (Instron Ltd Canton Mass)universal testing machine. (CF4) etch treatment (500 W for 30 min) in order to reveal The tab ends were enveloped in wire mesh and gripped with the matrix cracks Matrix crack density was measured over pneumatic grips. Clip-on extensometers were used to mea- a 10 mm length along the outer surface of the composite as sure displacement (25 mm gage length). Monotonic or well as within the interior plies. The matrix crack density load-unload-reload hysteresis tests were performed at was determined by counting the number of cracks over that loading and unloading rates of 2 kN /min for the thin spec- distance and dividing by the length Table I pecimen(interphaseINo. specimens Specimen shape f Hi-Nicalon composites standard& ply panels 8 ply (C)121 SHS Dog.A 0.44 8 ply (BND)(21 Dog.B 0.33 8 ply (BN2)(21 2.53 0.31 8 ply (BN3)111 SHS 2.14 0.37 Standard thick panels 30 ply (C)11 Dog.B 8.68 0.34 0.04 0.45 0.17 36 ply(C)(11 sssss 10.56 0.34 0.04 Thin I ply(C)111 Straighte 0.38 0.26 0.04 0.2 2 ply (C) 21 Straight 0.2 0.04 .33 3 ply (C) 21 Straigh 0.9 0.32 0.04 0.35 Iniltrated panels HS(BND)(1 Dog-B 2.45 0.32 0.05 0.25 y-5HS( BN2)1 H Dog-B 2.4 0.32 0.27 BHS(BN)I SHS 2.3 0.33 Sydramic-iBN composites (standard 8 ply panels) 8 ply 7.epcm(1)(11 2.18 0.363 0.377 0.189 8 ply 7.epcm(2)(2 2.17 0.365 .387 0.179 8ply79pcm(3){2} 2.19 0.361 0.443 8 ply 7.epcm(C)111 H 0.229 0.346 0.093 8 ply unbalanced HS Dog.A 0.335 0.069 0.464 0.132 Dogbone tensile mm in length, approximately 15.5 mm in width at grip section and 10.3 mm in width at gage section Dogbone tensile spec c Straight-sided tensile mm边ndm2m1m题tomp03m1wags

Hi-Nicalon fiber [6]. In this study, composites reinforced with 2D woven Sylramic-iBN and Hi-Nicalon in a CVI SiC matrix were studied. The Syl-iBN composites were var￾ied so that the number of tows per length in the two orthogonal directions were either the same (balanced) or differed (unbalanced), the latter to simulate enhanced fiber loading in a given direction. The composites reinforced with Hi-Nicalon in a CVI SiC matrix varied from 1 to 36 plies and differed in constituent content and density. 2. Experimental The details on composite processing, constituent con￾tent, and variety of composite panels tested can be found in Table 1 [1]. All of the panels consisted of 2D five or eight harness satin woven fabric and were fabricated by GE Power Systems Composites, Newark Delaware. Most pan￾els were either fabricated with BN or carbon interphases. Table 1 also describes the type of tensile specimens, straight sided or dogbone, that were cut from each panel. Tensile testing was performed on an Instron Model 8562 (Instron Ltd., Canton Mass) universal testing machine. The tab ends were enveloped in wire mesh and gripped with pneumatic grips. Clip-on extensometers were used to mea￾sure displacement (25 mm gage length). Monotonic or load–unload–reload hysteresis tests were performed at loading and unloading rates of 2 kN/min for the thin spec￾imens, 4 kN/min for 8 ply specimens, and 10 kN/min for thick specimens. Acoustic emission was monitored during the tensile test using a Digital Wave Fracture Wave Detec￾tor. Three wide-band (100 kHz to 2 MHz sensitivity; model B1025, Digital Wave, Englewood, CO) sensors were used to capture AE activity. Two sensors were placed on the face of the specimen outside of both extensometer knife edges whereas the third was placed in the center of the gage section on the opposite face of the extensometer knife edges. Only AE data that hit the middle AE sensor first, i.e., data that occurred in the gage section, were used for the matrix cracking analysis. To determine non-linearity in the stress–strain curve, a 0.002% offset stress technique was employed. The 0.002% offset stress is where the linear regression fit curve used to determine elastic modulus, E (5 to 650 MPa) offset by +0.002% intersects with the stress– strain curve. After composite failure, some of the specimens were cut and polished along the longitudinal direction in order to measure the matrix crack density. The specimens with Syl-iBN fibers and a BN-interphase required a plasma (CF4) etch treatment (500 W for 30 min) in order to reveal the matrix cracks. Matrix crack density was measured over a 10 mm length along the outer surface of the composite as well as within the interior plies. The matrix crack density was determined by counting the number of cracks over that distance and dividing by the length. Table 1 Physical properties of composite specimens from Ref. [1] Specimen (interphase) {No. specimens} Weave Specimen shape t, mm ff fi fSiC fp Hi-Nicalon composites Standard 8 ply panels 8 ply (C) {2} 8HS Dog-Aa 2.84 0.28 0.13 0.44 0.15 8 ply (BN1) {2} 5HS Dog-Bb 2.37 0.33 0.05 0.47 0.15 8 ply (BN2) {2} 5HS Dog-B 2.53 0.31 0.06 0.48 0.15 8 ply (BN3) {1} 8HS Dog-A 2.14 0.37 0.05 0.41 0.17 Standard thick panels 30 ply (C) {1} 5HS Dog-B 8.68 0.34 0.04 0.45 0.17 36 ply (C) {1} 5HS Dog-B 10.56 0.34 0.04 0.43 0.19 Thin panels 1 ply (C) {1} 5HS Straightc 0.38 0.26 0.04 0.29 0.41 2 ply (C) {2} 5HS Straight 0.73 0.28 0.04 0.33 0.35 3 ply (C) {2} 5HS Straight 0.92 0.32 0.04 0.35 0.29 Epoxy Iniltrated Panels E8Ply-5HS(BN1) {1} 5HS Dog-B 2.45 0.32 0.05 0.25 0.38 E8Ply-5HS(BN2) {1} 5HS Dog-B 2.45 0.32 0.05 0.27 0.35 E8Ply-8HS(BN) {1} 8HS Dog-B 2.37 0.33 0.05 0.29 0.33 Sylramic-iBN composites (standard 8 ply panels) 8 ply 7.9epcm (1) {1} 5HS Dog-A 2.18 0.363 0.071 0.377 0.189 8 ply 7.9epcm (2) {2} 5HS Dog-A 2.17 0.365 0.069 0.387 0.179 8 ply 7.9epcm (3) {2} 5HS Dog-A 2.19 0.361 0.070 0.443 0.126 8 ply 7.9epcm (C) {1} 5HS Dog-A 2.38 0.332 0.229 0.346 0.093 8 ply unbalanced 5HS Dog-A 2.24 0.335 0.069 0.464 0.132 a Dogbone tensile specimen 203 mm in length, approximately 15.5 mm in width at grip section and 10.3 mm in width at gage section. b Dogbone tensile specimen 152 mm in length, approximately 12.6 mm in width at grip section and 10.3 mm in width at gage section. c Straight-sided tensile specimen 152 mm in length and approximately 12.6 mm in width throughout. 1010 G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017

G.N. Morscher et al Composites Science and Technology 67(2007)1009-1017 3. Results imen(Table 2). For a balanced weave, f is half the total volume fraction of fibers in the composite(Table 1) 3.1. Stress-strain behavior There were considerable differences in elastic modulus for specimens from different composite panels due to constitu Micrographs of the woven composites are shown in ent content and constituent composition [1]. Some speci Fig 2 of Ref. [1]. The stress-strain curves which were also mens in the same panel also exhibited some variability in presented in Ref [l]are shown here in Fig. 1. Table 2 gives elastic modulus(specimens from 7epcm(2)in Table 2).In some of the important mechanical properties for each ten- general, the specimens with the higher volume fraction of sile specimen. The fiber volume fraction of fibers oriented fibers in the loading direction display higher stresses for in the test direction for each specimen was determined non-linearity in the stress-strain curve. However there were based on the fiber architecture and thickness measurement exceptions, lower elastic modulus composites do have lower used for the tensile test as follows: stresses for non-linearity compared to higherelastic modulus composites of the same architecture(7.epcm specimens in /=Npl NYTRr (epmmo) (1) Table 2). Note also that two of the carbon interphase com- posites, hn 8 ply(C) and Syl-iBN 7epcm(C), have a greater fraction of interphase (Table 1)and consequently where Ply is the number of plies, Nr is the number of fibers lower elastic moduli and 0.002% offset stresses(Table 2) in a tow(800 for Syl-iBN and 500 for Hi-Nicalon), R is the compared to 8 ply composites with lower fractions of average fiber radius (5 um for Syl-iBN and 6.8 um for Hi- interphase. Nicalon), epmmo is tow ends per mm in the O direction, and For some of the specimens, a load-unload-reload hys- f is the thickness measured for the tensile test of each spec- teresis tensile test was performed in order to determine 8 Ply(BN1); E= 258 GPa fo =0.16: 2.5 mm thick Ply: E=221 GP fo = 0.17: 8.6 mm thi 36 Ply: E=217 GPa fo= 0.17; 10.5mm thick f。=0.16; 8 250 10. mm thick E8Ply-8HS; E=118 GP f。=0.17;2.37 mm thick 2 Ply: E= 102 GPa E8Ply-5HS; E= 108 GPa fo=0. 14: 0.76 mm thick f.=0.16: 2.45 mm thick 8 Ply(BN3); E= 225 GPa fo =0.18: 2.35 mm thick 8 Ply(C): E=177 GPa fiber in the =0.14: 2.88 mm thick 0.4 6 Strain. b E=271 GPa CVI; 9. epcm 253GP 4008py(002) 5.5 epcm fo=0.12(002) E=261 GPa Strain. Fig. 1. Stress-strain curves of: (a)HN fiber reinforced and(b) Sylramic-iBN fiber reinforced composites

3. Results 3.1. Stress–strain behavior Micrographs of the woven composites are shown in Fig. 2 of Ref. [1]. The stress–strain curves which were also presented in Ref. [1] are shown here in Fig. 1. Table 2 gives some of the important mechanical properties for each ten￾sile specimen. The fiber volume fraction of fibers oriented in the test direction for each specimen was determined based on the fiber architecture and thickness measurement used for the tensile test as follows: f 0 f ¼ NplyNfpR2 fðepmm0Þ t ð1Þ where Nply is the number of plies, Nf is the number of fibers in a tow (800 for Syl-iBN and 500 for Hi-Nicalon), Rf is the average fiber radius (5 lm for Syl-iBN and 6.8 lm for Hi￾Nicalon), epmm0 is tow ends per mm in the 0 direction, and t is the thickness measured for the tensile test of each spec￾imen (Table 2). For a balanced weave, f 0 f is half the total volume fraction of fibers in the composite (Table 1). There were considerable differences in elastic modulus for specimens from different composite panels due to constitu￾ent content and constituent composition [1]. Some speci￾mens in the same panel also exhibited some variability in elastic modulus (specimens from 7.9epcm(2) in Table 2). In general, the specimens with the higher volume fraction of fibers in the loading direction display higher stresses for non-linearity in the stress–strain curve. However there were exceptions, lower elastic modulus composites do have lower stresses for non-linearity compared to higher elastic modulus composites of the same architecture (7.9epcm specimens in Table 2). Note also that two of the carbon interphase com￾posites, HN 8 ply (C) and Syl-iBN 7.9epcm(C), have a greater fraction of interphase (Table 1) and consequently lower elastic moduli and 0.002% offset stresses (Table 2) compared to 8 ply composites with lower fractions of interphase. For some of the specimens, a load–unload–reload hys￾teresis tensile test was performed in order to determine 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 Strain, % Stress, MPa CVI 5.5 epcm fo=0.12 (002) E = 261 GPa CVI; 9.4epcm 8 ply (002) fo=0.21 E=293 GPa CVI 7.9epcm fo=0.18 E=271 GPa E = 253 GPa C-interphase fo = 0.17 E = 230 GPa 0 50 100 150 200 250 300 350 400 450 500 0 0.2 0.4 0.6 0.8 1 Strain, % Stress, MPa 30 Ply; E = 221 GPa fo = 0.17; 8.6 mm thick 36 Ply; E = 217 GPa fo = 0.17; 10.5mm thick 8 Ply (BN3); E = 225 GPa fo = 0.18; 2.35 mm thick 8 Ply (C); E = 177 GPa fo = 0.14; 2.88 mm thick fo refers to the volume fraction of fiber in the loading direction 2 Ply; E = 102 GPa fo = 0.14; 0.76 mm thick 3Ply; E = 114 GPa fo = 0.16; 0.92 mm thick 8 Ply (BN2); E = 244 GPa fo = 0.16; 2.5 mm thick 8 Ply (BN1); E = 258 GPa fo = 0.17; 2.5 mm thick E8Ply-8HS; E = 118 GPa fo = 0.17; 2.37 mm thick E8Ply-5HS; E = 108 GPa fo = 0.16; 2.45 mm thick a b Fig. 1. Stress–strain curves of: (a) HN fiber reinforced and (b) Sylramic-iBN fiber reinforced composites. G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017 1011

G.N. Morscher et al. Composites Science and Technology 67(2007)1009-1017 Table 2 Mechanical properties of specimens tested Specimen: fo E, GPa Ult. stress, Failure Residual stress, 0.002% offset First AE stress, AE onset stress, Pe, m stress. M Hi-Nicalon CV SiC composites 10 0.1725 0 0.16225416 0.1822 30 ply (C) 36 ply(C) 0.17231391 8033805287 466159894 6406086%0 2443332 I ply ( 0.13 2 ply (C) 0.14104 0 0.16109 0 E8Ply-8HS(BN)0.17118 Sy/-iBN CH SiC composites l10 10.3 0.18226433 7.9epcm(3) 7.9epcm(3) 98092 0.21289509 9.epcm 0.21293 Gage -42 588 128 04500 0.12260258 l10 0.12261298 43 115 a typical hysteresis stress-strain curve with the 8. 2 shows 3.2. Acoustic emission and matrix cracking the amount of residual stress in the specimen associated with that test. Following Steen and Valles [8]. The AE activity for all the composites is shown in Fig 3 the average slope of the top portion of the hysteresis loops as normalized cumulative AE energy versus stress and are extrapolated back towards zero. Where those lines strain. This is determined by normalizing the cumulative intersect indicates whether or not there is residual stress energy at a given stress-strain condition by the total energy in the matrix. Since the lines intersect in the positive stress of all the events that occurred during the entire test in the and positive strain quadrant, the matrix is in compression, gage section. Two aE properties are given in Table 2 for i.e., crack closure occurs at a positive stress upon unload- each specimen. The"First AE Stress"is the stress at which ng the specimen. The Sylramic-ibN composites typically the first AE event was recorded and represents the onset of exhibited some measure of residual compressive stress in microcrack formation. The"AE Onset Stress"is the stress did not. The Sylramic-ibN 94epcm specimen, with the rence of large energy AE events and is indicated by the highest fo and higher elastic modulus, had the highest drastic increase in AE activity in Fig. 3a and c. This is residual stress (Table 2) indicative of the onset of large matrix crack formation where fiber-bridged cracks propagate through-the-thick ness or at least across several plies For the hn composites( Fig 3a and b), the onset of AE E=293 Gpa 35008 activity and the range of stress or strain over which AE 3000 a activity occurs varies from composite to composite. How 500 w ever, for the higher-density HN composites(8, 30, and 36 a 0.035+0.005%. For the Syl-iBN composites(Fig. 3c 1500 and d), the strain for onset of significant AE activity was 1000 higher, -0.05+0.005%. However, the range of strain Residual Compressive Stress for the different Syl-iBN composites Normalized cumulative Ae energy has been shown to be Strain, an excellent measure of relative matrix crack density [6]. Fig 4 shows some typical matrix cracks from a polished Fig. 2. Stress-strain for a 9.epcm specimen, load-unload-reload hyster- section of the failed 7.95epcm(C) specimen. Multiplying esis tensile test with AE activity the final matrix crack density (Table 2)measured from

the amount of residual stress in the specimen. Fig. 2 shows a typical hysteresis stress–strain curve with the AE activity associated with that test. Following Steen and Valles [8], the average slope of the top portion of the hysteresis loops are extrapolated back towards zero. Where those lines intersect indicates whether or not there is residual stress in the matrix. Since the lines intersect in the positive stress and positive strain quadrant, the matrix is in compression, i.e., crack closure occurs at a positive stress upon unload￾ing the specimen. The Sylramic-iBN composites typically exhibited some measure of residual compressive stress in the matrix whereas the Hi-Nicalon composites typically did not. The Sylramic-iBN 9.4epcm specimen, with the highest f 0 f and higher elastic modulus, had the highest residual stress (Table 2). 3.2. Acoustic emission and matrix cracking The AE activity for all the composites is shown in Fig. 3 as normalized cumulative AE energy versus stress and strain. This is determined by normalizing the cumulative energy at a given stress–strain condition by the total energy of all the events that occurred during the entire test in the gage section. Two AE properties are given in Table 2 for each specimen. The ‘‘First AE Stress’’ is the stress at which the first AE event was recorded and represents the onset of microcrack formation. The ‘‘AE Onset Stress’’ is the stress at which significant AE activity occurs due to the occur￾rence of large energy AE events and is indicated by the drastic increase in AE activity in Fig. 3a and c. This is indicative of the onset of large matrix crack formation where fiber-bridged cracks propagate through-the-thick￾ness or at least across several plies. For the HN composites (Fig. 3a and b), the onset of AE activity and the range of stress or strain over which AE activity occurs varies from composite to composite. How￾ever, for the higher-density HN composites (8, 30, and 36 ply), the strain for onset of significant AE activity was 0.035 ± 0.005%. For the Syl-iBN composites (Fig. 3c and d), the strain for onset of significant AE activity was higher, 0.05 ± 0.005%. However, the range of strain and stress over which cumulative AE activity occurs varies for the different Syl-iBN composites. Normalized cumulative AE energy has been shown to be an excellent measure of relative matrix crack density [6]. Fig. 4 shows some typical matrix cracks from a polished section of the failed 7.95epcm(C) specimen. Multiplying the final matrix crack density (Table 2) measured from Table 2 Mechanical properties of specimens tested Specimen: Panel f 0 f E, GPa Ult. stress, MPa Failure location Residual stress, MPa 0.002% offset stress, MPa First AE stress, MPa AE onset stress, MPa qc, mm1 s, MPa Hi-Nicalon CVI SiC composites 8 ply (C) 0.14 199 300 Gage 10 68 24 61 2.2 14 8 ply (BN1) 0.17 258 415 Gage 0 90 66 94 4.6 35 8 ply (BN2) 0.16 225 416 Gage 0 73 63 70 4.3 31 8 ply (BN3) 0.18 225 367 Gage – 83 51 86 3.6 20 30 ply (C) 0.17 237 328 Radius – 88 15 70 3.4 30 36 ply (C) 0.17 231 391 Radius – 80 19 78 3.5 27 1 ply (C) 0.13 96 110 Grip – 55 28 56 2.0 25 2 ply (C) 0.14 104 274 Grip 0 92 29 95 10.6 – 3 ply (C) 0.16 109 380 Grip 0 83 24 80 11.6 – E8Ply-8HS(BN) 0.17 118 364 Gage 0 77 48 85 10.8 33 Syl-iBN CVI SiC composites 7.9epcm(1) .18 247 432 Gage – 138 69 110 10.3 48 7.9epcm(2) 0.18 254 424 Gage – 135 91 120 9.0 45 7.9epcm(2) 0.18 226 433 Gage 25 131 84 117 – – 7.9epcm(3) 0.18 278 445 Gage – 158 107 150 8.1 43 7.9epcm(3) 0.18 276 – Gage 30 153 97 145 – – 9.4epcm 0.21 289 509 Radius – 188 122 155 10.6 – 9.4epcm 0.21 293 500 Gage 42 180 128 150 10.1 59 5.5epcm 0.12 260 258 Gage – 140 110 110 8.3 – 5.5epcm 0.12 261 298 Gage 30 143 115 123 9.4 63 7.9epcm(C) 0.17 230 387 Gage 30 120 69 114 6.7 28 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 Strain, % Stress, MPa 0 500 1000 1500 2000 2500 3000 3500 4000 Cumulative AE Energy E = 293 Gpa fo = 0.21 Residual Compressive Stress Fig. 2. Stress–strain for a 9.4epcm specimen, load–unload–reload hyster￾esis tensile test with AE activity. 1012 G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017

G.N. Morscher et al. Composites Science and Technology 67 (2007)1009-1017 a b uE3OEz 5HS epoxy 8HS epoxy 00 00.10.20.3040.50.60.7080.91 Stress. MPa Strain, d 5.5epcm(1) 5.5 epcm epcm(1) 9.4 epcm(1) 59.4 epcm 9 epcm(3) 03179epcm(1 7.9 epcm (3 9 epcm(1) Stress. MPa Strain.% Fig 3. Acoustic emission activity (normalized cumulative energy) versus composite stress and strain for Hi-Nicalon composites, ()and(b)respective 100μmoo ?, Fig 4. Through-thickness matrix cracks(arrows) in polished 7.95epcm( C) specimen after failure. Note the thick C-interphase. the polished sections of the failed specimens by the normal- shear stress of the fiber-interphase interface [6]. After Refs ized cumulative AE energy results in an estimated matrix [3, 9] the strain behavior of the composite can be modeled crack density that can be used to estimate the interfacial according to the following relationship

the polished sections of the failed specimens by the normal￾ized cumulative AE energy results in an estimated matrix crack density that can be used to estimate the interfacial shear stress of the fiber-interphase interface [6]. After Refs. [3,9] the strain behavior of the composite can be modeled according to the following relationship: 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 100 200 300 400 Stress, MPa Norm Cum AE Energy 8ply BN1 8ply C 2 ply 3 ply 5HS epoxy 36 ply 30 ply 8HS epoxy 8ply BN2 8ply BN3 1 ply 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Strain, % Norm Cum AE Energy 8ply C 2 ply 3 ply 8HS epoxy 5HS epoxy 36 ply 30 ply 8ply 8ply 8ply BN3 1 ply 8ply 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 Strain, % Norm Cum AE Energy 5.5 epcm (1) 5.5 epcm (2) C-interphase 7.9 epcm 7.9 epcm (1) 7.9 epcm (2) 7.9 epcm (3) 9.4 epcm (1) 9.4 epcm (2) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 100 150 200 250 300 350 400 Stress, MPa Norm Cum AE Energy 5.5 epcm (1) 5.5 epcm (2) C-interphase 7.9 epcm 7.9 epcm (1) 7.9 epcm (2) 7.9 epcm (3) 9.4 epcm (1) 9.4 epcm (2) a b c d Fig. 3. Acoustic emission activity (normalized cumulative energy) versus composite stress and strain for Hi-Nicalon composites, (a) and (b) respectively, and Sylramic-iBN composites, (c) and (d) respectively. Fig. 4. Through-thickness matrix cracks (arrows) in polished 7.95epcm(C) specimen after failure. Note the thick C-interphase. G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017 1013

1014 G.N. Morscher et al. Composites Science and Technology 67(2007)1009-1017 E=a/Ec+ad(a)Pc/Er(o+ oth); for pc> 2 (2) Table 3 where the sliding length g. MPa 6=m(+)/2 (3) Hi- Nicalon CVI SiC composites ply(C) 35 4.1 4.1 30 and 36 ply (C o is the applied stress, oth is the residual stress, r is the fiber radius,E is elastic modulus, subscripts c, f, and m refer to Sy/-iBN CVI SiC composites omposite, fiber, and modulus, and Pe is the stress-depen- 9.epcm 4 dent matrix crack density estimated from the ae data. 5.epcm 8.9 q(2)can be best fit to the actual stress-strain curve by 7epcm(c) varying t in order to estimate a value for t(Fig. 5). This was done for most of the specimens with good fits of the a 90 minicomposite. A similar approach was attempted stress-strain curve with the exception of the Hi-Nicalon to relate matrix cracking in CVI SiC composites with less PLY and Hi-Nicalon 3PLY specimens(Table 3). The rea- success than for melt-infiltrated systems [7]. This was prob- son for this is probably that the ae data does not just rep- ably due to more non-uniformity in lower density CVi resent transverse matrix cracks. For these thin specimens, matrix systems and the variety of matrix crack sources sources of Ae at the higher stresses such as straight available in CVI SiC composites which include the out of minicomposites and longitudinal cracks"notches"that exist at the large pores as well as the inner een the 0 and 90 minicomposites which are apparent region of 90 minicomposites. The CVI SiC matrix when from polished sections. The single ply specimen was not fully-loaded is the region where through-thickness matrix modeled because the failure occurred in the grips at a cracks form and propagate. Therefore, in order to quantify low stress. Note that the relatively thick carbon interphase matrix-crack activity, the acoustic emission activity was composites had the lowest interfacial shear strength for analyzed based on the stress (or local strain) in the load- both fiber-composite systems bearing CVI SiC. This was accomplished by assuming the For nearly fully dense melt-infiltrated SiC/SiC compos- equivalence of local elastic strain (Ec=Esic) in an ites [6]it was found that the onset stress for matrix cracking uncracked region of the composite just prior to matrix and the stress-distribution for matrix cracking could be crack formation through the relationship related to the average stress on the region of the composite that excludes the load-bearing fiber-interphase-CVI SiC Sic =(a/EC)Esic minicomposite. This corresponded to the stress required where Esic=425 GPa. Note that once matrix cracks have to form and/or propagate a matrix crack emanating from formed, the average total composite strain includes the ex- tra displacement associated with matrix cracks that devi ates from elasticity. This is why the local elastic strain in the uncracked cvi SiC must be used s the normalized cumulative Ae energy plot best fit for t= 59 MPa ted versus stress in the load-bearing CVI SiC for the Hi- Nicalon(Fig. 6a) and Sylramic-iBN (Fig 6b)composites. For composites which saturate in matrix cracks, 1.e., where the normalized cumulative AE energy nearly plateaus with increasing stress, there are some definite convergences of the ae activity with stress. In particular higher-density Hi-Nicalon composites, the Sylramic-iBN stress-strain data composites when oriented in the high fiber volume direc tions, and the Sylramic-iBN composites when oriented in the lower fiber volume fraction direction each converge into distinct"distributions". The low-density Hi-Nicalon 100 composites do not converge, but also, with the exception of the epoxy-infiltrated specimen, may not all saturate in matrix cracks as was the case for low volume fraction com- posites in Ref. [6]. Therefore, the normalized cumulative AE energy was multiplied by the final matrix crack de and plotted versus the stress on the load-bearing CVI SiC Fig.5. Example of method used to determine interfacial shear stress based for the Hi-Nicalon fiber reinforced CVI SiC matrix com- on AE activity and final matrix crack density (9.4epcm(D). Dashed lines posites(Fig. 7). A good correlation exists, at least at lower represent a t value +20% of best fit value stresses, for all of the lower density composites. Also plot

e ¼ r=Ec þ fadðrÞqc=Efgðr þ rthÞ; for q1 c > 2d ð2Þ where the sliding length d ¼ arðr þ rthÞ=2s ð3Þ and a ¼ ð1 f ÞEm=fEc ð4Þ r is the applied stress, rth is the residual stress, r is the fiber radius, E is elastic modulus, subscripts c, f, and m refer to composite, fiber, and modulus, and qc is the stress-depen￾dent matrix crack density estimated from the AE data. Eq. (2) can be best fit to the actual stress–strain curve by varying s in order to estimate a value for s (Fig. 5). This was done for most of the specimens with good fits of the stress–strain curve with the exception of the Hi-Nicalon 2PLY and Hi-Nicalon 3PLY specimens (Table 3). The rea￾son for this is probably that the AE data does not just rep￾resent transverse matrix cracks. For these thin specimens, other sources of AE at the higher stresses such as straight￾ening out of minicomposites and longitudinal cracks between the 0 and 90 minicomposites which are apparent from polished sections. The single ply specimen was not modeled because the failure occurred in the grips at a low stress. Note that the relatively thick carbon interphase composites had the lowest interfacial shear strength for both fiber-composite systems. For nearly fully dense melt-infiltrated SiC/SiC compos￾ites [6] it was found that the onset stress for matrix cracking and the stress-distribution for matrix cracking could be related to the average stress on the region of the composite that excludes the load-bearing fiber-interphase-CVI SiC minicomposite. This corresponded to the stress required to form and/or propagate a matrix crack emanating from a 90 minicomposite. A similar approach was attempted to relate matrix cracking in CVI SiC composites with less success than for melt-infiltrated systems [7]. This was prob￾ably due to more non-uniformity in lower density CVI matrix systems and the variety of matrix crack sources available in CVI SiC composites which include the ‘‘notches’’ that exist at the large pores as well as the inner region of 90 minicomposites. The CVI SiC matrix when fully-loaded is the region where through-thickness matrix cracks form and propagate. Therefore, in order to quantify matrix-crack activity, the acoustic emission activity was analyzed based on the stress (or local strain) in the load￾bearing CVI SiC. This was accomplished by assuming the equivalence of local elastic strain (ec = eSiC) in an uncracked region of the composite just prior to matrix crack formation through the relationship rSiC ¼ ðr=EcÞESiC ð5Þ where ESiC = 425 GPa. Note that once matrix cracks have formed, the average total composite strain includes the ex￾tra displacement associated with matrix cracks that devi￾ates from elasticity. This is why the local elastic strain in the uncracked CVI SiC must be used. Fig. 6 shows the normalized cumulative AE energy plot￾ted versus stress in the load-bearing CVI SiC for the Hi￾Nicalon (Fig. 6a) and Sylramic-iBN (Fig. 6b) composites. For composites which saturate in matrix cracks, i.e., where the normalized cumulative AE energy nearly plateaus with increasing stress, there are some definite convergences of the AE activity with stress. In particular, all of the higher-density Hi-Nicalon composites, the Sylramic-iBN composites when oriented in the high fiber volume direc￾tions, and the Sylramic-iBN composites when oriented in the lower fiber volume fraction direction each converge into distinct ‘‘distributions’’. The low-density Hi-Nicalon composites do not converge, but also, with the exception of the epoxy-infiltrated specimen, may not all saturate in matrix cracks as was the case for low volume fraction com￾posites in Ref. [6]. Therefore, the normalized cumulative AE energy was multiplied by the final matrix crack density and plotted versus the stress on the load-bearing CVI SiC for the Hi-Nicalon fiber reinforced CVI SiC matrix com￾posites (Fig. 7). A good correlation exists, at least at lower stresses, for all of the lower density composites. Also plot- 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 Strain, % Stress, MPa stress-strain data best fit for τ= 59 MPa Fig. 5. Example of method used to determine interfacial shear stress based on AE activity and final matrix crack density (9.4epcm(1)). Dashed lines represent a s value ±20% of best fit value. Table 3 Model parameters Specimen s, MPa rth, MPa qc, mm1 Hi-Nicalon CVI SiC composites 8 ply (C) 14 10 2.2 8 ply BN1 35 0 4.1 8 ply BN3 20 0 4.1 30 and 36 ply (C) 26 0 3.5 Syl-iBN CVI SiC composites 7.9epcm 45 30 9.0 9.4epcm 60 42 10.4 5.5epcm 60 30 8.9 7.9epcm(C) 28 30 6.7 1014 G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017

G.N. Morscher et al. Composites Science and Technology 67 (2007)1009-1017 8 ply BN2- S 0. 88 ply BN1 8 ply C 3 Ply 山莓 2 Ply 8HS epoxy 30 ply 0+ Stress on Load-Bearing CVI SiC, MPa 5.5 epcm (1) o000oo 0.9 5.5epcm(2) 7.9 epcm(1) 079.4epm(2 C-interphase 0.5 -7. 9 epcm(2) 9. 4 epcm (1) 0.2 7.9 epcm (3) 00 60 Stress on Load-Bearing CVI SiC, MPa Fig. 6. Normalized AE energy versus stress on load-bearing CVI SiC for: (a) Hi-Nicalon and (b) Sylramic-iBN composites. Arrows espond to the onset stresses for matrix cracking of the two different matrix cracking materials. Large circles correspond to the simple Weibull model the three matrix cracking distributions. ted are data from single tow minicomposites [10, 11] which also correlate well with the low-density woven composites 目EE巴品四 8HS by the 00 minicomposites [1] for these low-density woven 8 CVI SiC composites the"stress on the load-bearing SiC"(Fig. 6), even though 3423 4. discussion An excellent correlation exists for matrix cracking of the higher volume fraction oriented composite specimens with BN3 the stress-strain behavior(Fig. 2), the stress-dependent AE 0 behavior(Fig. 3), and interfacial shear stress for the differ 001200 ent C-interphase and BN-interphase composites are signif- Stress on Load-Bearing CVI SiC, MPa icantly different. The two Syl-iBN unbalanced composite Fig. 7. Estimated matrix crack density for Hi-Nicalon, CVI SiC matrix specimens oriented in the lower fiber volume fraction diree composites

ted are data from single tow minicomposites [10,11] which also correlate well with the low-density woven composites and further demonstrates that the load is primarily carried by the 0 minicomposites [1] for these low-density woven CVI SiC composites. 4. Discussion An excellent correlation exists for matrix cracking of the higher volume fraction oriented composite specimens with the ‘‘stress on the load-bearing SiC’’ (Fig. 6), even though the stress–strain behavior (Fig. 2), the stress-dependent AE behavior (Fig. 3), and interfacial shear stress for the differ￾ent C-interphase and BN-interphase composites are signif￾icantly different. The two Syl-iBN unbalanced composite specimens oriented in the lower fiber volume fraction direc- 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 100 200 300 400 500 600 Stress on Load-Bearing CVI SiC, MPa Norm Cum AE 5.5 epcm (1) 5.5 epcm (2) C-interphase 7.9 epcm 7.9 epcm (1) 7.9 epcm (2) 7.9 epcm (3) 9.4 epcm (1) 9.4 epcm (2) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 500 1000 1500 Stress on Load-Bearing CVI SiC, MPa Normalized Cumulative AE Energy 8 ply BN1 30 ply 36 ply 8 ply BN2 8 ply C 8 ply BN3 1 Ply 2 Ply 8HS epoxy 3 Ply a b Fig. 6. Normalized AE energy versus stress on load-bearing CVI SiC for: (a) Hi-Nicalon and (b) Sylramic-iBN composites. Arrows on abscissa correspond to the onset stresses for matrix cracking of the two different matrix cracking materials. Large circles correspond to the simple Weibull models for the three matrix cracking distributions. 0 2 4 6 8 10 12 0 200 400 600 800 1000 1200 1400 Stress on Load-Bearing CVI SiC, MPa Estimated Crack Denisty, mm-1 3ply 1ply 2ply single tow minicomposite (C) 8ply C 8ply BN3 8ply BN3 8ply BN2 30ply 8ply BN1 36ply 8HS epoxy single tow minicomposite (BN) Fig. 7. Estimated matrix crack density for Hi-Nicalon, CVI SiC matrix composites. G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017 1015

G.N. Morscher et al. Composites Science and Technology 67(2007)1009-1017 tion had a different, yet consistent, AE relationship with NCumAE= 1-exp(o stress on the load-bearing Sic compared to the higher vol- ume fraction Syl-iBN composites. This is similar to MI where composites [6] which were woven with different sized tows, =(gcvisic the larger tow size composites exhibiting the lower and temper stress-distribution for matrix cracking where acviSic is the stress in the load-bearing CVI SiC and The reasons for these two distributions are most likely o. the reference stress, would correspond to the average due to the effectiveness of fiber-bridging and the flaw distri- stress of the composite system for NCumAE=0.623 of the SiC matrix in the two-different orientations. The lower vol. two different distributions (285 MPa for high-density Hi ume fraction composites have not only a lower volume fraction but also would have larger unbridged tion Syl-iBN CVI SIC, and 245 MPa for low volume fraction within a matrix crack when compared to a balanced weave Syl-iBN CVI SIC). Eq. (5)was best fit for m(4 for high-den- or the high volume fraction orientation of the unbalanced sity Hi-Nicalon CVI SiC composites, 6 for high volume frac- tion Syl-iBN CVI SiC, and 9 for unbalanced low volume weave.Consequently, when a tunnel crack propagates out- fraction Syl-iBN CVI SiC) for the distributions( large circles ward from a 90 ply [12] or a microcrack forms that inter- in Fig. 6 ). Multiplying Eq (6)by the final measured matrix sects load-bearing fibers, the fiber-bridging is not sufficient crack density would then give an estimated matrix crack den- to stop the crack and through-thickness macrocracking sity distribution. Using this relationship and then transform occurs. This explains why the onset of large-energy event CaE onset stress"in Table 1)for the low volume fraction g to absolute stress for a given architecture/constituent unbalanced composite specimens correspond either with content composite Eq (5), one could then use the estimated the initial ae activity or at slightly higher stresses than behavior for each composite/orientation. Fig 8 shows the the first Ae activity for the low volume fracti predicted stress-strain behavior for some of the Hi-Nicalon ites. For the high volume fraction composite orientations, Fig 8a)and Syl-iBN Fig 8b) composites. The predicted there is a lag in stress from initial AE activity to high elastic modulus for each composite specimen from Ref [U] energy AE activity, signifying tunnel cracks or microcracks are formed at lower stresses, but higher stresses are propagate bridg racks. The st slope of the low volume fraction orientation com may also be indicative of the existence of a more prevalent HN 8 Ply(BNT lower strength flaw population to produce matrix cracks This would be due to the fact that there are more 90 tows HN 8 Ply(BN3) in the lower fiber orientation unbalanced composite speci men, sometimes aligned three abreast, compared to the 9200 higher fiber orientation composite systems(See Fig. la-c 0 150 Two important properties can be gleaned from Fig. 6. HN 8 Ply (C) The first is the stress on the load-bearing Cvi Sic for Open symbols correspond to model which significant matrix crack formation(AE onset stress) For the higher-density Hi-Nicalon composites, this stress 06 would be 140 MPa. For the Syl-iBN composites, the low volume fraction unbalanced composites the CVI SiC b 600 circles onset stress was 185 MPa: whereas for the high volume fraction composites the CvI Sic onset stress was N210 MPa. This gives a simple design parameter, more robust than a"proportional limit"since it is based on actual macrocrack formation and is a general relationship for 2D woven CVI SiC composites of different constituent contents. This CVI SiC onset stress for matrix cracking y could be used to predict the local composite stress for Syl-IBN 5.5 epcm matrix cracking if the local Ec is known [1] via Eq. (5) Second, the general AE relationships can be used to determine an estimated stress-dependent matrix crack den sity. A simple Weibull modeling approach can be employed for the two different normalized cumulative AE energy dis- tributions [7] since matrix crack saturation occurs in these Fig 8 Stress-strain predictions for: (a) Hi-Nicalon and(b)Syl-iBN high density CVI SiC matrix composites

tion had a different, yet consistent, AE relationship with stress on the load-bearing SiC compared to the higher vol￾ume fraction Syl-iBN composites. This is similar to MI composites [6] which were woven with different sized tows, the larger tow size composites exhibiting the lower and steeper stress-distribution for matrix cracking. The reasons for these two distributions are most likely due to the effectiveness of fiber-bridging and the flaw distri￾bution or nature of local stress-concentrations on the CVI SiC matrix in the two-different orientations. The lower vol￾ume fraction composites have not only a lower volume fraction but also would have larger unbridged regions within a matrix crack when compared to a balanced weave or the high volume fraction orientation of the unbalanced weave. Consequently, when a tunnel crack propagates out￾ward from a 90 ply [12] or a microcrack forms that inter￾sects load-bearing fibers, the fiber-bridging is not sufficient to stop the crack and through-thickness macrocracking occurs. This explains why the onset of large-energy events (‘‘AE onset stress’’ in Table 1) for the low volume fraction unbalanced composite specimens correspond either with the initial AE activity or at slightly higher stresses than the first AE activity for the low volume fraction compos￾ites. For the high volume fraction composite orientations, there is a lag in stress from initial AE activity to high energy AE activity, signifying tunnel cracks or microcracks are formed at lower stresses, but higher stresses are required to propagate bridged macrocracks. The steeper slope of the low volume fraction orientation composites may also be indicative of the existence of a more prevalent lower strength flaw population to produce matrix cracks. This would be due to the fact that there are more 90 tows in the lower fiber orientation unbalanced composite speci￾men, sometimes aligned three abreast, compared to the higher fiber orientation composite systems (See Fig. 1a–c in Ref. [1]). Two important properties can be gleaned from Fig. 6. The first is the stress on the load-bearing CVI SiC for which significant matrix crack formation (AE onset stress). For the higher-density Hi-Nicalon composites, this stress would be 140 MPa. For the Syl-iBN composites, the low volume fraction unbalanced composites the CVI SiC onset stress was 185 MPa; whereas, for the high volume fraction composites the CVI SiC onset stress was 210 MPa. This gives a simple design parameter, more robust than a ‘‘proportional limit’’ since it is based on actual macrocrack formation and is a general relationship for 2D woven CVI SiC composites of different constituent contents. This CVI SiC onset stress for matrix cracking could be used to predict the local composite stress for matrix cracking if the local Ec is known [1] via Eq. (5). Second, the general AE relationships can be used to determine an estimated stress-dependent matrix crack den￾sity. A simple Weibull modeling approach can be employed for the two different normalized cumulative AE energy dis￾tributions [7] since matrix crack saturation occurs in these systems: NCumAE ¼ 1 expð/Þ ð6Þ where / ¼ rCVISiC ro m ð7Þ where rCVI SiC is the stress in the load-bearing CVI SiC and ro, the reference stress, would correspond to the average stress of the composite system for NCumAE = 0.623 of the two different distributions (285 MPa for high-density Hi￾Nicalon CVI SiC composites, 345 MPa for high volume frac￾tion Syl-iBN CVI SiC, and 245 MPa for low volume fraction Syl-iBN CVI SiC). Eq. (5) was best fit for m (4 for high-den￾sity Hi-Nicalon CVI SiC composites, 6 for high volume frac￾tion Syl-iBN CVI SiC, and 9 for unbalanced low volume fraction Syl-iBN CVI SiC) for the distributions (large circles in Fig. 6). Multiplying Eq. (6) by the final measured matrix crack density would then give an estimated matrix crack den￾sity distribution. Using this relationship and then transform￾ing to absolute stress for a given architecture/constituent content composite Eq. (5), one could then use the estimated matrix crack density in Eq. (2) to determine the stress–strain behavior for each composite/orientation. Fig. 8 shows the predicted stress–strain behavior for some of the Hi-Nicalon (Fig. 8a) and Syl-iBN (Fig. 8b) composites. The predicted elastic modulus for each composite specimen from Ref. [1] 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 Strain, % Stress, MPa Syl-iBN 5.5 epcm Syl-iBN 9.4epcm Syl-iBN 7.9epcm Syl-iBN C￾interphase circles correspond to model 0 50 100 150 200 250 300 350 400 450 0 0.2 0.4 0.6 0.8 1 Strain, % Stress, MPa HN 36 Ply HN 8 Ply (BN3) HN 8 Ply (C) HN 8 Ply (BN1) Open symbols correspond to model a b Fig. 8. Stress–strain predictions for: (a) Hi-Nicalon and (b) Syl-iBN high￾density CVI SiC matrix composites. 1016 G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017

G.N. Morscher et al Composites Science and Technology 67(2007)1009-1017 was used to model stress-strain. There is excellent agreement found to be very similar to that of single tow minicomposites between this modeling approach for matrix crack density For higher density composites, a lower stress on the load and stress-strain behavior. There was a slight overestimate bearing CVI SiC was required to form and propagate matrix for some of the Hi-Nicalon composites due to the overesti- cracks since the 90 minicomposites act as the source of mate of Ec in Ref [1]. Table 2 lists the model parameters that matrix flaws. For Sylramic-iBN CVI SiC composites, which were used in Fig. 7 were all of higher density, matrix cracking was dependent on Finally, it is instructive to compare the relationships fiber volume fraction in the loading direction and the size of governing the stress-distributions for matrix cracking for the unbridged region of a matrix crack For composites with the different fiber/matrix systems [68]. Matrix cracking a high volume fraction of fibers in the loading direction a for balanced weave CVI SiC composites with Hi-Nicalon higher stress-range distribution of load-bearing CVI SiC [8] and Sylramic fiber types both can be modeled on the stress was observed. For the un balanced composites when basis of stress in the load-bearing SiC. However, the stressed in the low fiber volume direction a lower stress- ress-range for matrix cracking for Hi-Nicalon composites range, steeper distribution of load-bearing CVI SiC stress is approximately 80 MPa lower in load-bearing SiC stress was observed which may have also been influenced by the than that for Sylramic CVI SiC. If the difference in matrix increased number of 90 minicomposites resulting in larger cracking stresses for different fiber composites was just due unbridged regions of a matrix crack. to the difference in fiber stiffness, they should have the same These distributions were used to determine two impor- stress and strain in the Cvi SiC for matrix cracking. But tant design parameters: the onset stress for matrix cracking this was not the case as described above. There is essen- and an estimated stress-dependent matrix crack density tially no measurable residual stress in Hi-Nicalon Cvi which is required to effectively model stress-strain behavior Sic composites [8 whereas there is residual compressive for these composites. Combining these relationships with stress in the matrix of Sylramic CVI SiC composites. This the model for elastic modulus of these 2D composites [1] would account for some of the disparity between the two gives designers useful tools to determine the entire stress- systems. The net fiber area in a Hi-Nicalon tow cross-sec- strain response in local areas of a composite component tion is approximately 22%/ greater than Sylramic based This is especially useful if local constituent content is on average fiber diameter(14 and 10 um, respectively) known to vary due to architectural and/or process varia- and number of fibers(500 and 800, respectively) which tions which cannot easily be replicated by simple panel- should result in similar differences in tow height of the based property generation. Also, these models could be 90 bundles, i. e, larger flaw sizes in Hi-Nicalon compos- used to optimize 2D architecture and constituent content ites. In addition, the flaw sources for matrix cracks in to optimize Ec and/or matrix cracking properties for a CVI SiC composites are not only the 90o bundles. The given application sharp notches of the macro-pore structure in the CVI SiC that exist where 90 and 0o bundles are adjacent to one another [13, 14] are the lowest stress flaw sources (highest References stress-concentrators on Cv SiC) and most likely greater [1 Morscher GN. The elastic modulus of 2D woven CVI SiC compos- n size for the larger tow size Hi-Nicalon composites. ites, Comp Sci Tech (i 2] Curtin WA, Ahn BK, Takeda N. Acta Mater 1998: 46(10): 3409-20. 5. Conclusions [] Lamon J Comp Sci Tech 2001: 61: 2259-72. [4] Morscher GN, Cawley JD. J Eur Ceram Soc 2002; 22(14-15): 2777-88. M, The stress-dependence for matrix cracking in woven Hi- [5]Yun HM, Gyekenyesi JZ, Chen YL, Wheeler DR,DiCarlo JA Ceram Eng Sci Proc 2001; 22(3): 521-31 licalon and Sylramic-ibN fiber reinforced, CVI SiC matrix [6]Morscher GN Comp Sci Tech 2004: 64: 1311-9 composites was determined for balanced and unbalanced 2D [7]Morscher GN. Published in the 35th international SAMPE technical architectures. It was shown that higher volume fraction com conference proceedings(CD), Dayton, OH; 2003 posites usually exhibited higher matrix cracking stresses. [8 Steen M, Valles JL. ASTM STP 1309. In: Jenkins MG et al,editors Therefore. unbalanced architectures with increased fiber rials:1997.p.49-65 loading in the direction where an application requires a high [9]Pryce Aw, Smith PA. Br Ceram Trans 1993: 92(2): 49-54 matrix cracking stress are viable options to achieve higher [10] Martinez-Fernandez J, Morscher GN. Room and elevated matrix cracking stresses if needed ure tensile properties of single tow Hi-Nicalon, carbon interphase, Stress-dependent relationships for matrix cracking in this CVI SiC matrix minicomposites J Eur Ceram Soc 2000: 20: 2627-36 measurements. The stress-dependent matrix cracking Sion [1] Morscher GN, Martinez-Fernandez J Fiber effects on minicomposite composite system were determined from acoustic emission apor-infiltrated silicon carbide matrix systems. J Am Ceram Soc found to be dependent on the stress in the load-bearing SiC as dictated by the architecture and constituent content. For [2] Cox BN, Marshall DB. Crack initiation in fiber-reinforced brittle Hi-Nicalon CVI SiC composites, matrix cracking was aminates.J Am Ceram Soc 1996: 79(5): 1181-8 dependent on the degree of load-sharing in the 90 minicom- [13] Guillaumat L, Lamon J. In: Revue des composites et des materiaux avances, vol 3, 1993, p. 159-71 posites. For lower density composites which had little if any [14] Pluvinage P, Parvizi-Majidi A, Chou TW. J Mater Sci load-sharing in the 90 minicomposites, matrix cracking was 1996:31:232-41

was used to model stress–strain. There is excellent agreement between this modeling approach for matrix crack density and stress–strain behavior. There was a slight overestimate for some of the Hi-Nicalon composites due to the overesti￾mate of Ec in Ref. [1]. Table 2 lists the model parameters that were used in Fig. 7. Finally, it is instructive to compare the relationships governing the stress-distributions for matrix cracking for the different fiber/matrix systems [6–8]. Matrix cracking for balanced weave CVI SiC composites with Hi-Nicalon [8] and Sylramic fiber types both can be modeled on the basis of stress in the load-bearing SiC. However, the stress-range for matrix cracking for Hi-Nicalon composites is approximately 80 MPa lower in load-bearing SiC stress than that for Sylramic CVI SiC. If the difference in matrix cracking stresses for different fiber composites was just due to the difference in fiber stiffness, they should have the same stress and strain in the CVI SiC for matrix cracking. But this was not the case as described above. There is essen￾tially no measurable residual stress in Hi-Nicalon CVI SiC composites [8] whereas there is residual compressive stress in the matrix of Sylramic CVI SiC composites. This would account for some of the disparity between the two systems. The net fiber area in a Hi-Nicalon tow cross-sec￾tion is approximately 22% greater than Sylramic based on average fiber diameter (14 and 10 lm, respectively) and number of fibers (500 and 800, respectively) which should result in similar differences in tow height of the 90 bundles, i.e., larger flaw sizes in Hi-Nicalon compos￾ites. In addition, the flaw sources for matrix cracks in CVI SiC composites are not only the 90 bundles. The sharp notches of the macro-pore structure in the CVI SiC that exist where 90 and 0 bundles are adjacent to one another [13,14] are the lowest stress flaw sources (highest stress-concentrators on CVI SiC) and most likely greater in size for the larger tow size Hi-Nicalon composites. 5. Conclusions The stress-dependence for matrix cracking in woven Hi￾Nicalon and Sylramic-iBN fiber reinforced, CVI SiC matrix composites was determined for balanced and unbalanced 2D architectures. It was shown that higher volume fraction com￾posites usually exhibited higher matrix cracking stresses. Therefore, unbalanced architectures with increased fiber loading in the direction where an application requires a high matrix cracking stress are viable options to achieve higher matrix cracking stresses if needed. Stress-dependent relationships for matrix cracking in this composite system were determined from acoustic emission measurements. The stress-dependent matrix cracking was found to be dependent on the stress in the load-bearing SiC as dictated by the architecture and constituent content. For Hi-Nicalon CVI SiC composites, matrix cracking was dependent on the degree of load-sharing in the 90 minicom￾posites. For lower density composites which had little if any load-sharing in the 90 minicomposites, matrix cracking was found to be very similar to that of single tow minicomposites. For higher density composites, a lower stress on the load￾bearing CVI SiC was required to form and propagate matrix cracks since the 90 minicomposites act as the source of matrix flaws. For Sylramic-iBN CVI SiC composites, which were all of higher density, matrix cracking was dependent on fiber volume fraction in the loading direction and the size of the unbridged region of a matrix crack. For composites with a high volume fraction of fibers in the loading direction a higher stress-range distribution of load-bearing CVI SiC stress was observed. For the unbalanced composites when stressed in the low fiber volume direction a lower stress￾range, steeper distribution of load-bearing CVI SiC stress was observed which may have also been influenced by the increased number of 90 minicomposites resulting in larger unbridged regions of a matrix crack. These distributions were used to determine two impor￾tant design parameters: the onset stress for matrix cracking and an estimated stress-dependent matrix crack density which is required to effectively model stress–strain behavior for these composites. Combining these relationships with the model for elastic modulus of these 2D composites [1] gives designers useful tools to determine the entire stress– strain response in local areas of a composite component. This is especially useful if local constituent content is known to vary due to architectural and/or process varia￾tions which cannot easily be replicated by simple panel￾based property generation. Also, these models could be used to optimize 2D architecture and constituent content to optimize Ec and/or matrix cracking properties for a given application. References [1] Morscher GN. The elastic modulus of 2D woven CVI SiC compos￾ites, Comp Sci Tech (in press). [2] Curtin WA, Ahn BK, Takeda N. Acta Mater 1998;46(10):3409–20. [3] Lamon J. Comp Sci Tech 2001;61:2259–72. [4] Morscher GN, Cawley JD. J Eur Ceram Soc 2002;22(14–15):2777–88. [5] Yun HM, Gyekenyesi JZ, Chen YL, Wheeler DR, DiCarlo JA. Ceram Eng Sci Proc 2001;22(3):521–31. [6] Morscher GN. Comp Sci Tech 2004;64:1311–9. [7] Morscher GN. Published in the 35th international SAMPE technical conference proceedings (CD), Dayton, OH; 2003. [8] Steen M, Valles JL. ASTM STP 1309. In: Jenkins MG et al., editors. West Conshohocken, PA: American Society for Testing and Mate￾rials; 1997. p. 49–65. [9] Pryce AW, Smith PA. Br Ceram Trans 1993;92(2):49–54. [10] Martı´nez-Ferna´ndez J, Morscher GN. Room and elevated tempera￾ture tensile properties of single tow Hi-Nicalon, carbon interphase, CVI SiC matrix minicomposites. J Eur Ceram Soc 2000;20:2627–36. [11] Morscher GN, Martinez-Fernandez J. Fiber effects on minicomposite mechanical properties for several silicon carbide fiber – chemically vapor-infiltrated silicon carbide matrix systems. J Am Ceram Soc 1999;82(1):145–55. [12] Cox BN, Marshall DB. Crack initiation in fiber-reinforced brittle laminates. J Am Ceram Soc 1996;79(5):1181–8. [13] Guillaumat L, Lamon J. In: Revue des composites et des materiaux avances, vol. 3, 1993, p. 159–71. [14] Pluvinage P, Parvizi-Majidi A, Chou TW. J Mater Sci 1996;31:232–41. G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017 1017