《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_j.1151-2916.1998.tb02561.x[1]

ournal J An. Ceran. Soc., 81 [7] 1881-87(1998) Interface Properties in High-Strength Nicalon/C/SiC Composites, As Determined by Rough Surface Analysis of Fiber Push-Out Tests Ronald J Kerans and Triplicane A Parthasarathy Wright Laboratory Materials Directorate, Wright Patterson AFB, Ohio 45433-7817 Francis Rebillat and Jacques Lamon Laboratoire des Composites Thermostructuraux, Unite Mixte de Recherche, Centre National de la recherche Scientifique-Societe Europeene de Propulsion-Universite de Bordeaux I, 33600 Pessac, France fiber Nicalon/C/SiC composites indicate behavior that is vapor-deposited silicon carbide(CVI SiC). In one case, the distinctly different from other composites. These compos- fibers were subjected to a proprietary treatment that is reported ites have been analyzed using a model that explicitly i to clean the fiber surface and remove any native oxide layer; cludes two sets of debond-crack-surface topographies that this treatment also resulted in a somewhat different structure correspond to two stages of crack propagation. The model for the deposited carbon. , The composites made with treated successfully duplicates the observed unusual push-out fibers demonstrated 30% higher strength at the same -1% load-deflection behavior by adjusting interfacial toughness strain-to-failure value, much-finer matrix-crack spacing, and and topographical parameters to fit the experimental data. different stress-strain behavior Although the topographical parameters of the debonding Interface-property measurements on the treated-fiber mate cracks are largely unconfirmed, the fitted values are con- rial have been difficult to rationalize by conventional means sistent with observations and expectations. This analysis Features of the unloading-reloading cycles, as well as predic has determined interfacial fracture energies that are un- tions of the tensile stress-strain behavior of microcomposites usually high for composites with acceptable mechanical be- and havior but are consistent with measurements on bulk py the friction stress), imply T values that can reach 300 MPa 2,6, 0 rocarbons. The analysis provides a unifying rationalization Transmission electron microscopy (TEM)analysis of tensile of the apparent inconsistencies in results reported for such specimens has indicated that the debonding fracture consists of materials fine, diffuse multiple cracking of the carbon layer itself, as pposed to the single crack at or very near the coating/fil interface that is common in the untreated -fiber material,, . Introduction Push-out tests have shown curves that differ from those ex- EX XPERIENCE with successful composites, and subsequen pected from commonly used models and observed for conven- theoretical treatments has led to the prevalent assumption tional composites. A combination of nanoindentor push-in tests that good composite behavior requires that the debond crack and conventional push-out tests(Fig. 1)revealed that an initial ghness and interfacial sliding friction should both be quite debonding crack initiates and grows very slightly as the load low(see, for example, Cao et al. ) Reports of substantially increases to what, on first inspection, seems to be the initial roved properties of Nicalon TM/C/SiC composites due to the deviation from linearity(to area"b"in Fig. 1), then jumps behavior of the material is similar to other tough composites, in 4-6 The fracture lation of two different cracking modes, with a transition from that the interfacial region is sufficiently weak that matrix one to the other in the unstable b-to-c region in Fig. 1. As with most push-out data, there is a wide variation in behavior. Many cracks deflect into debonding cracks. However, analysis indi- curves indicate greater displacement between areas a and b cates interface property values that are significantly higher than han that shown in Fig. 1; however for most curves, that dis- usually assumed to be permissible Related questions regarding placement remains quite small. Similarly, most curves demon- laminates. for a concise discussion and review see Lee et al. 7 strate upward curvature in the c-to-d region in Fig. 1, many of (for a new approach to the detailed analysis of the problem in seems reasonably representative, and the very small a-to-b dis- fibrous composites, see Pagano) acement provides an ially rigorous test of any model The original and the improved systems both consisted of Conventional analyses do not allow for curves with such fea- pyrolytic carbon-coated ic-grade Nicalon TM(Nippon tures and are not readily applied to them. 2 Push-out behavior(and debonding in general) is affected by the topography of the sliding surfaces. The relevant surfaces are formed by the debonding crack and may differ from the surface of the fiber, these surfaces potentially can vary along A. Jagota--contributing editor he length of the debond, with variations in stress state or microstructure. The potential of significant effects due to sur- face roughness was first discussed in the context of increased adial stresses due to the geometric misfit. 4 Contradictions in measured sliding friction led to an experimental confirmation of roughness effects with the" push back seating drop"of Jere Member. American Ceramic Sociel and co-workers. 15, 16(For a brief review of subsequent work

Interface Properties in High-Strength Nicalon/C/SiC Composites, As Determined by Rough Surface Analysis of Fiber Push-Out Tests Ronald J. Kerans* and Triplicane A. Parthasarathy* Wright Laboratory Materials Directorate, Wright Patterson AFB, Ohio 45433–7817 Francis Rebillat and Jacques Lamon* Laboratoire des Composites Thermostructuraux, Unite´ Mixte de Recherche, Centre National de la Recherche Scientifique–Socie´te´ Europe´ene de Propulsion–Universite´ de Bordeaux I, 33600 Pessac, France Fiber push-out curves generated on high-strength, treated￾fiber Nicalon/C/SiC composites indicate behavior that is distinctly different from other composites. These compos￾ites have been analyzed using a model that explicitly in￾cludes two sets of debond-crack-surface topographies that correspond to two stages of crack propagation. The model successfully duplicates the observed unusual push-out load–deflection behavior by adjusting interfacial toughness and topographical parameters to fit the experimental data. Although the topographical parameters of the debonding cracks are largely unconfirmed, the fitted values are con￾sistent with observations and expectations. This analysis has determined interfacial fracture energies that are un￾usually high for composites with acceptable mechanical be￾havior but are consistent with measurements on bulk py￾rocarbons. The analysis provides a unifying rationalization of the apparent inconsistencies in results reported for such materials. I. Introduction EXPERIENCE with successful composites, and subsequent theoretical treatments, has led to the prevalent assumption that good composite behavior requires that the debond crack toughness and interfacial sliding friction should both be quite low (see, for example, Cao et al.1 ). Reports of substantially improved properties of Nicalon™/C/SiC composites due to the sole processing change of pretreating the surface of the fiber2,3 have motivated reexamination of the assumptions regarding the upper limits of allowable interfacial properties.4–6 The fracture behavior of the material is similar to other tough composites, in that the interfacial region is sufficiently weak that matrix cracks deflect into debonding cracks. However, analysis indi￾cates interface property values that are significantly higher than usually assumed to be permissible. Related questions regarding details of crack deflection have been discussed recently for laminates; for a concise discussion and review, see Lee et al.7 (for a new approach to the detailed analysis of the problem in fibrous composites, see Pagano8 ). The original and the improved systems both consisted of pyrolytic carbon-coated ceramic-grade Nicalon™ (Nippon Carbon Co., Tokyo, Japan) fibers in a matrix of chemical￾vapor-deposited silicon carbide (CVI SiC). In one case, the fibers were subjected to a proprietary treatment that is reported to clean the fiber surface and remove any native oxide layer; this treatment also resulted in a somewhat different structure for the deposited carbon.4,9 The composites made with treated fibers demonstrated 30% higher strength at the same ∼1% strain-to-failure value, much-finer matrix-crack spacing, and different stress–strain behavior.2 Interface-property measurements on the treated-fiber mate￾rial have been difficult to rationalize by conventional means. Features of the unloading–reloading cycles, as well as predic￾tions of the tensile stress–strain behavior of microcomposites and minicomposites, based on a constant t approximation (t is the friction stress), imply t values that can reach 300 MPa.2,6,10 Transmission electron microscopy (TEM) analysis of tensile specimens has indicated that the debonding fracture consists of fine, diffuse multiple cracking of the carbon layer itself, as opposed to the single crack at or very near the coating/fiber interface that is common in the untreated-fiber material.2,3,11 Push-out tests have shown curves that differ from those ex￾pected from commonly used models and observed for conven￾tional composites. A combination of nanoindentor push-in tests and conventional push-out tests (Fig. 1) revealed that an initial debonding crack initiates and grows very slightly as the load increases to what, on first inspection, seems to be the initial deviation from linearity (to area ‘‘b’’ in Fig. 1), then jumps unstably to a greater length (area ‘‘b’’ to ‘‘c’’) and begins to grow with a load deflection trace that is concave upward (to area ‘‘d’’ in Fig. 1).12,13 This observation has led to a postu￾lation of two different cracking modes, with a transition from one to the other in the unstable b-to-c region in Fig. 1. As with most push-out data, there is a wide variation in behavior. Many curves indicate greater displacement between areas a and b than that shown in Fig. 1; however, for most curves, that dis￾placement remains quite small. Similarly, most curves demon￾strate upward curvature in the c-to-d region in Fig. 1, many of them to a greater degree than that shown in Fig. 1. Figure 1 seems reasonably representative, and the very small a-to-b dis￾placement provides an especially rigorous test of any model. Conventional analyses do not allow for curves with such fea￾tures and are not readily applied to them.12 Push-out behavior (and debonding in general) is affected by the topography of the sliding surfaces. The relevant surfaces are formed by the debonding crack and may differ from the surface of the fiber; these surfaces potentially can vary along the length of the debond, with variations in stress state or microstructure. The potential of significant effects due to sur￾face roughness was first discussed in the context of increased radial stresses due to the geometric misfit.14 Contradictions in measured sliding friction led to an experimental confirmation of roughness effects with the ‘‘push back seating drop’’ of Jero and co-workers.15,16 (For a brief review of subsequent work, A. Jagota—contributing editor Manuscript No. 191103. Received April 3, 1997; approved September 15, 1997. Author TAP was supported by USAF Contract No. F33615-91-C-5663, UES, Inc., Dayton, OH. *Member, American Ceramic Society. J. Am. Ceram. Soc., 81 [7] 1881–87 (1998) Journal 1881

1882 Journal of the American Ceramic Society'Kerans et al. Vol 81. No. 7 7000+++rTT 6000 R5000 3000 °m15 2000 000 cement (um) Fig. 1. Reported typical push-out curve, with elastic deformation removed, for high-strength NicalonTM/C/SiC (After Rebillat et al. 2) see Parthasarathy et al. 7)Briefly, a fiber that is pulling out of this work was to examine the rough-interface formalism for a matrix under axial loading is subjected to radial stresses that suitability in describing the behavior of such composites differ along the length of the fiber The interfacial normal stress in the unslipped region ahead of the crack tip(Region I of Fig 2)is determined by the residual stresses and the applied axial IL. Procedure tress through differences in the poisson's ratios of the con he approach to analysis was based on the following tituents In Region lll of Fig. 2, the normal stress is defined as pothesis. The fine, highly branched, diffuse the sum of those stresses plus the stresses that result from the ing reported via TEM analysis of tensile specimens, 3, I is full effect of the topographical misfit. The roughness-induced considered to be characteristic of the early stages of stresses may be larger than the thermal stresses. As shown in and small displacements. A push-out test imposes Fig 2, Region Il extends, with increasing misfit, from the crack ments between the fiber and the matrix that are larg tip to the beginning of Region Ill. This area complicates analy those that generally develop in a composite in regions away sis and results in many interesting effects. A full solution of the from the final failure site, and such large displacements require problem for one simple form of roughness has shown that the the resolution of the diffuse cracking into a single crack or into friction in Region Il actually can be very much larger than that rubble. It is imagined that the early growth of the debonding treated-fiber Nicalon TM/C/SiC A s Co f debonding p ward crack is in the diffuse, multiple-branched form; however, a in Region Ill, and calculated push-out curves show some critical displacement, it resolves into a single crack feature suggests that roughness may contribute to the unusual Hence, two stages of cracking are assumed; each stage has the curvature observed in push-out load-deflection curves of same fracture energy (G)but different roughness parameters posites. The objective of that describe the two types of crack surfaces. The roughness T R+2A Fig. 2. isfit strain created by a rough fiber, of radius R and roughness amplitude 4, sliding in a matching matrix hole, the shape drawn and unrelated to the model or experiment. In practice, the roughness is assumed to be asymmetric and small, compared to the fiber dimensions (After Parthasarathy and Kerans. s)

see Parthasarathy et al.17) Briefly, a fiber that is pulling out of a matrix under axial loading is subjected to radial stresses that differ along the length of the fiber. The interfacial normal stress in the unslipped region ahead of the crack tip (Region I of Fig. 2) is determined by the residual stresses and the applied axial stress through differences in the Poisson’s ratios of the con￾stituents. In Region III of Fig. 2, the normal stress is defined as the sum of those stresses plus the stresses that result from the full effect of the topographical misfit. The roughness-induced stresses may be larger than the thermal stresses. As shown in Fig. 2, Region II extends, with increasing misfit, from the crack tip to the beginning of Region III. This area complicates analy￾sis and results in many interesting effects. A full solution of the problem for one simple form of roughness17 has shown that the friction in Region II actually can be very much larger than that in Region III, and calculated push-out curves show upward curvature in the Region II-only portion of debonding.18 This feature suggests that roughness may contribute to the unusual curvature observed in push-out load–deflection curves of treated-fiber Nicalon™/C/SiC composites. The objective of this work was to examine the rough-interface formalism for suitability in describing the behavior of such composites. II. Procedure The approach to analysis was based on the following hy￾pothesis. The fine, highly branched, ‘‘diffuse’’ multiple crack￾ing reported via TEM analysis of tensile specimens2,3,11 is considered to be characteristic of the early stages of cracking and small displacements. A push-out test imposes displace￾ments between the fiber and the matrix that are larger than those that generally develop in a composite in regions away from the final failure site, and such large displacements require the resolution of the diffuse cracking into a single crack or into rubble. It is imagined that the early growth of the debonding crack is in the diffuse, multiple-branched form; however, at some critical displacement, it resolves into a single crack. Hence, two stages of cracking are assumed; each stage has the same fracture energy (G) but different roughness parameters that describe the two types of crack surfaces. The roughness Fig. 1. Reported typical push-out curve, with elastic deformation removed, for high-strength Nicalon™/C/SiC. (After Rebillat et al.12) Fig. 2. Schematic of misfit strain created by a rough fiber, of radius R and roughness amplitude A, sliding in a matching matrix hole; the shape is arbitrarily drawn and unrelated to the model or experiment. In practice, the roughness is assumed to be asymmetric and small, compared to the fiber dimensions. (After Parthasarathy and Kerans.18) 1882 Journal of the American Ceramic Society—Kerans et al. Vol. 81, No. 7

July 1998 Interface Properties in High-Strength Nicalon/C/SiC Composites parameters have been adjusted to generate curves that fit the interfacial and axial stresses were obtained. Such effective respective portions of the experimental curve properties will correctly model phenomena that do not involve The procedure adopted was to determine two theoretical significant axial loading of the matrix, such as fiber pushout. rough-surface curves to fit the respective segments of the ex- but will yield misleading composite properties; hence, they perimental curve by adjusting the roughness parameters itera- should be used selectively. There is also an inherent probler tively. The initiation of cracking and details of early crack with the experimental data, in that the displacement during the rowth are extremely difficult to determine from the load- growth of the initial crack is comparable to the sensitivity of deflection curves, because of the small displacements that are corrected push-out data. Therefore, the procedure used here ssociated with initial cracking. Consequently, the secondar should not be expected to yield precise parameters rack was extrapolated to zero inelastic displacement, to fur- The push-out curves were calculated using a computer pro- ther guide the estimation of the stress at initiation. The nanon ramT to solve the implicit expressions that resulted from the in results of rebillat analysis of Parthasarathy et al. 17 The misfit assumed in the placements at the Region II/lll transition of the initial crack of model is such that the resulting dilatation increases linearly as 250 nm, as do some of the push-out tests. However, the mag the displacement increases. The dilatation caused by many dif- nitude of the indentation/compliance correction is three times ferent forms of roughness can be expected to be reasonabl the fiber displacement; hence, this value is highly uncertain linear in the early stages of sliding, however, the true applica Other push-out tests, as shown in Fig. 1, imply much less bility of this assumption, and the sensitivity of the results to displacement. Such variation could be a real result of test-to- are as yet unknown. Deviation from the assumed form will test differences in the roughness of the crack surface; however, certainly change some details of the curves essentially, the test is not sufficiently sensitive to distinguish such details. For this analysis, the displacement at the transition was somewhat arbitrarily considered to be-30 nm, which is a II. Results and discussion value that is seemingly consistent with a curve such as that shown in Fig. 1. A predicted fiber-stress-deflection curve for tive matrix properties that closely reproduce stresses deter- omposite tension was then generated, using the same interfa- mined by elastic analysis of a composite with an explicit car al roughness and toughness values, and examined for qual bon coating 0.5 um thick, are listed in Table 1. The properties tative consistency with known aspects of behavior. The rough- of the coating are speculative but were estimated as indicated ness parameters were also subjectively evaluated for based on comparison of the structure to carbon fibers.The feasibility actual”and‘ effective’ matrix elastic moduli differ by a properties that have be factor of 2 and the thermal expansions differ by 20%. The out are listed in Table I. the fiber and the matrix were con sidered to be isotropic. The pyrocarbon coatings were applied coating clearly has a significant effect The calculated push-out curves for the two sets of crack ia chemical vapor deposition( CVD)such that there was sig topographies are shown in Fig. 3; the postulated transition be- nificant turbostratic character throughout the thickness of the tween the two sets is indicated by the arrowed line. The rel- oating. The properties were assumed to be anisotropic and evant parameters for the initial crack are as follows: roughness ns and fibers with highly turbostratic structures. The friction The parameters for the secondary crack are h=90 nm,d oefficient was considered to be 0.05, based on an earlier 2.2 um, and G= 28 J/m2. The value of 28 J/m2 for the fracture nalysis of well-behaved fiber pushout in conventional com- energy of pyrocarbon is in good agreement with literature osites.A fiber volume fraction ( of 0. 4 and a coating mode I values. 22, 23 Nevertheless. it is much higher than the 0-3 The formalism of Parthasarathy et al 17 like almost all such J/m2 value typically inferred from composites with carbon models, does not include specific consideration of the elastic effects of the coating. It has been shown that this omission ca Predicted curves of bridging-fiber stress versus displacement significantly affect frictional stresses: 9 hence, any treatment for composite tension tests (Type Il boundary conditions), assuming the same crack characteristics, are shown in Fig. 4.I that ignores a coating that has a substantially different radial transition to the secondary crack is considered( somewhat ar- elastic modulus than the matrix will likely have serious errors bitrarily) to occur at the same crack progression-slightly after One approach to this problem that allows the use of currently he region Il/lll transition--it will occur at-2.2 GPa in the vailable models is to introduce the coating elastic effects by tension test. However, fiber strengths in composite tension tests adjusting the elastic properties of the matrix and/or fiber to are typically 1.8-2 GPa, hence, composite failure can be ex effective' elastic properties that compensate for coating ef- pected to occur before transition to the secondary crack. Ten- fects. 20 In this case, the coating effect was introduced by ad- sile specimens then should display only (or mostly) primary correct interfacial normal stress. The correct stresses for a fl- ure at a fiber stress of 2 GPa in Fig. 4 would correspond to ber/coating/matrix composite were calculated using the com- -0.5% strain in the composite, which is a value that is some- puter program NDSANDS(AdTech Corp, Dayton, OH) of what less than that which is observed and is consistent with the Tandon and Pagano. 2 The effective matrix properties were idea that Fig. I represents somewhat higher friction values and calculated by using a procedure equivalent to iterating the ra- lower displacement values than average dial coefficient of thermal expansion a, and elastic modulus Er There are potential issues in comparing the G value esti- for the matrix of a fiber/matrix composite until the correct mated from this analysis with literature values obtained using different techniques. The first of these issues involves the frac- ture mode: at least early stages of cracking in pushout can be Table L. Properties Used for Analysis expected to be somewhat mixed mode, The second issue is that in this case, the deflections are so small that the assigned value Elast ulus, therm Constituent of G is heavily influenced by an extrapolation from interme- diate crack lengths. A third issue is the wide variety of struc- Fiber tures reported for pyrocarbons, which range from soot to dense turbostratic carbon. The effects of these factors are unknown Effective matrix (or coating) tThis computer program is available from the authors upon

parameters have been adjusted to generate curves that fit the respective portions of the experimental curve. The procedure adopted was to determine two theoretical rough-surface curves to fit the respective segments of the ex￾perimental curve by adjusting the roughness parameters itera￾tively. The initiation of cracking and details of early crack growth are extremely difficult to determine from the load– deflection curves, because of the small displacements that are associated with initial cracking. Consequently, the secondary crack was extrapolated to zero inelastic displacement, to fur￾ther guide the estimation of the stress at initiation. The nanoin￾dentor push-in results of Rebillat et al.12 imply fiber-end dis￾placements at the Region II/III transition of the initial crack of ∼250 nm, as do some of the push-out tests. However, the mag￾nitude of the indentation/compliance correction is three times the fiber displacement; hence, this value is highly uncertain. Other push-out tests, as shown in Fig. 1, imply much less displacement. Such variation could be a real result of test-to￾test differences in the roughness of the crack surface; however, essentially, the test is not sufficiently sensitive to distinguish such details. For this analysis, the displacement at the transition was somewhat arbitrarily considered to be ∼30 nm, which is a value that is seemingly consistent with a curve such as that shown in Fig. 1. A predicted fiber-stress–deflection curve for composite tension was then generated, using the same interfa￾cial roughness and toughness values, and examined for quali￾tative consistency with known aspects of behavior. The rough￾ness parameters were also subjectively evaluated for feasibility. The constituent properties that have been assumed through￾out are listed in Table I. The fiber and the matrix were con￾sidered to be isotropic. The pyrocarbon coatings were applied via chemical vapor deposition (CVD) such that there was sig￾nificant turbostratic character throughout the thickness of the coating. The properties were assumed to be anisotropic and were estimated based on interpolation between bulk pyrocar￾bons and fibers with highly turbostratic structures. The friction coefficient was considered to be 0.05, based on an earlier analysis of well-behaved fiber pushout in conventional com￾posites.19 A fiber volume fraction ( f) of 0.4 and a coating thickness (tc) of 0.5 mm were assumed throughout. The formalism of Parthasarathy et al., 17 like almost all such models, does not include specific consideration of the elastic effects of the coating. It has been shown that this omission can significantly affect frictional stresses;19 hence, any treatment that ignores a coating that has a substantially different radial elastic modulus than the matrix will likely have serious errors. One approach to this problem that allows the use of currently available models is to introduce the coating elastic effects by adjusting the elastic properties of the matrix and/or fiber to ‘‘effective’’ elastic properties that compensate for coating ef￾fects.20 In this case, the coating effect was introduced by ad￾justing the radial elastic modulus of the matrix to produce the correct interfacial normal stress. The correct stresses for a fi￾ber/coating/matrix composite were calculated using the com￾puter program NDSANDS (AdTech Corp., Dayton, OH) of Tandon and Pagano.21 The effective matrix properties were calculated by using a procedure equivalent to iterating the ra￾dial coefficient of thermal expansion ar and elastic modulus Er for the matrix of a fiber/matrix composite until the correct interfacial and axial stresses were obtained. Such effective properties will correctly model phenomena that do not involve significant axial loading of the matrix, such as fiber pushout, but will yield misleading composite properties; hence, they should be used selectively. There is also an inherent problem with the experimental data, in that the displacement during the growth of the initial crack is comparable to the sensitivity of corrected push-out data. Therefore, the procedure used here should not be expected to yield precise parameters. The push-out curves were calculated using a computer pro￾gram18† to solve the implicit expressions that resulted from the analysis of Parthasarathy et al.17 The misfit assumed in the model is such that the resulting dilatation increases linearly as the displacement increases. The dilatation caused by many dif￾ferent forms of roughness can be expected to be reasonably linear in the early stages of sliding; however, the true applica￾bility of this assumption, and the sensitivity of the results to it, are as yet unknown. Deviation from the assumed form will certainly change some details of the curves. III. Results and Discussion The properties assumed for the constituents, and the effec￾tive matrix properties that closely reproduce stresses deter￾mined by elastic analysis of a composite with an explicit car￾bon coating 0.5 mm thick, are listed in Table I. The properties of the coating are speculative but were estimated as indicated, based on comparison of the structure to carbon fibers. The ‘‘actual’’ and ‘‘effective’’ matrix elastic moduli differ by a factor of 2 and the thermal expansions differ by 20%. The coating clearly has a significant effect. The calculated push-out curves for the two sets of crack topographies are shown in Fig. 3; the postulated transition be￾tween the two sets is indicated by the arrowed line. The rel￾evant parameters for the initial crack are as follows: roughness amplitude (h) of 50 nm, period (d) of 50 nm, and G 4 28 J/m2 . The parameters for the secondary crack are h 4 90 nm, d 4 2.2 mm, and G 4 28 J/m2 . The value of 28 J/m2 for the fracture energy of pyrocarbon is in good agreement with literature mode I values.22,23 Nevertheless, it is much higher than the 0–3 J/m2 value typically inferred from composites with carbon coatings, often considered to be a necessary condition.1 Predicted curves of bridging-fiber stress versus displacement for composite tension tests (Type II boundary conditions24), assuming the same crack characteristics, are shown in Fig. 4. If transition to the secondary crack is considered (somewhat ar￾bitrarily) to occur at the same crack progression—slightly after the Region II/III transition—it will occur at ∼2.2 GPa in the tension test. However, fiber strengths in composite tension tests are typically 1.8–2 GPa; hence, composite failure can be ex￾pected to occur before transition to the secondary crack. Ten￾sile specimens then should display only (or mostly) primary, short-period cracking, which is, in fact, as reported.2,3,11 Fail￾ure at a fiber stress of 2 GPa in Fig. 4 would correspond to ∼0.5% strain in the composite, which is a value that is some￾what less than that which is observed and is consistent with the idea that Fig. 1 represents somewhat higher friction values and lower displacement values than average. There are potential issues in comparing the G value esti￾mated from this analysis with literature values obtained using different techniques. The first of these issues involves the frac￾ture mode: at least early stages of cracking in pushout can be expected to be somewhat mixed mode. The second issue is that, in this case, the deflections are so small that the assigned value of G is heavily influenced by an extrapolation from interme￾diate crack lengths. A third issue is the wide variety of struc￾tures reported for pyrocarbons, which range from soot to dense turbostratic carbon. The effects of these factors are unknown. † This computer program is available from the authors upon request. Table I. Properties Used for Analysis Constituent Elastic modulus, E (GPa) Coefficient of thermal expansion, a (×10−6/°C) Fiber 200 3.5 Matrix 400 4.5 Coating, axial 30 0 Coating, radial 10 12 Effective matrix (or coating) ( f 4 0.4, tc 4 0.5 mm) 200 4 July 1998 Interface Properties in High-Strength Nicalon/C/SiC Composites 1883

l884 Journal of the American Ceramic Society'Kerans et al. Vol 81. No. 7 8000 8000 7000 7000 6000 6000 乏5000 5000 4000 4000 3000 000 P90/2.2/28 2000 P:50/50/282000 1000 elastic 1000 8.5605 Displacement(micrometers) Fig 3. Push-out curves according to the roughness interface model, with parameters chosen to fit the experimental curve of Fig. 1, assuming that (i) initial cracking is governed by the roughness parameters h =50 nm, d= 50 nm, and G= 28 J/m-and(ii) subsequent cracking is governed by h =50 nm, d= 2. 2 um, and G= 28 J/m", the transition between the two conditions is indicated by the arrowed line In the rough-interface analysis, the interfacial friction will ported composites that show crack deflection along fibers and increase very quickly to extremely high values in the primary good properties. This, in turn, suggests that essentially all other short-period crack regime, then decrease to much-lower values ood"'conventional NicalonTM-reinforced composites in the secondary crack regime. For example, the effective av- debond in a manner similar to that of the untreated-fiber com- erage fiber stress to overcome friction at crack initiation in Fig posites, i.e., along an interface or in a weak layer very near an 4 is-200 MPa, whereas at the Region II/lll transition of the interface, as opposed to through the coating layer itself. rimary crack, this value is -750 MPa. Upon transition to the Perhaps the most important outcome of work related to the long-period crack, it decreases to -50 MPa, then climbs to 85 treated-fiber composites is the suggestion that the fracture en- APa at the Region il/ili transition of the ergy for debonding can be higher than often assumed and still correspond to this model, such as matrix-crack spacing or ten- suggests that the window of properties that can be possessed sile hysteresis loops, will return very high friction values. On by an oxide alternative coating, for example, is larger than such as fiber pushout(in a conventional analysis), will return because the very low fracture energies previously thought to be much-lower friction values necessary will likely be difficult to obtain with oxides or other The differences in the behavior of the treated-fiber compos- alternative materials Ite system considered here, in comparison to a more conven- o It is important to note that the crack-deflection criterion is different interfacial cracking behavior. 2,3 The results of this Hutchinson criterion, for example, was derived for deflection facial crack in untreated-fiber composites has been reported to figure of merit for the competition between crack deflection in be confined to the C/SiO, interface near the fiber surface or the the interface and crack propagation into the second material carbon layers very near to the interface 3, 11 Such composites was the ratio of interfacial (principally mode II)fracture energy have been observed, when measured, to have interfacial frac- to its mode I fracture energy. 5 However, if the relevant issue ture energies of no more than a few joules per square meter. is crack deflection within the coating, the analogous figure of The fiber treatment has been inferred to strengthen the interface merit will be the ratio of the coating(principally mode ID) egion to a level that is above the strength of the pyrocarbon fracture energy(,2)to its mode I fracture energy (T2,2). In coating itself, thereby shifting the fracture to the pyrocarbon, principle, the basic suitability of a material that is intended to which is the next-weakest link 3, 12 The measurements and in promote crack deflection via cleavage can be evaluated inde- terpretation of this work imply that the fracture energy and the pendent of the fiber fracture properties friction both are very much higher than in the untreated-fiber There are interesting implications of the fracture behavior composites and, moreover, much higher than in any other bserved in the materials of the preceding section. Crack de-

In the rough-interface analysis, the interfacial friction will increase very quickly to extremely high values in the primary, short-period crack regime, then decrease to much-lower values in the secondary crack regime. For example, the effective av￾erage fiber stress to overcome friction at crack initiation in Fig. 4 is ∼200 MPa, whereas at the Region II/III transition of the primary crack, this value is ∼750 MPa. Upon transition to the long-period crack, it decreases to ∼50 MPa, then climbs to 85 MPa at the Region II/III transition of the long-period crack. Tests that probe the primary-crack regime of specimens that correspond to this model, such as matrix-crack spacing or ten￾sile hysteresis loops, will return very high friction values. On the other hand, tests that probe the secondary-crack regime, such as fiber pushout (in a conventional analysis), will return much-lower friction values. The differences in the behavior of the treated-fiber compos￾ite system considered here, in comparison to a more conven￾tional untreated-fiber composite, have been attributed to the different interfacial cracking behavior.2,3 The results of this work are consistent with that scenario. Specifically, the inter￾facial crack in untreated-fiber composites has been reported to be confined to the C/SiO2 interface near the fiber surface or the carbon layers very near to the interface.3,11 Such composites have been observed, when measured, to have interfacial frac￾ture energies of no more than a few joules per square meter. The fiber treatment has been inferred to strengthen the interface region to a level that is above the strength of the pyrocarbon coating itself, thereby shifting the fracture to the pyrocarbon, which is the next-weakest link.3,12 The measurements and in￾terpretation of this work imply that the fracture energy and the friction both are very much higher than in the untreated-fiber composites and, moreover, much higher than in any other re￾ported composites that show crack deflection along fibers and good properties. This, in turn, suggests that essentially all other ‘‘good’’ conventional Nicalon™-reinforced composites debond in a manner similar to that of the untreated-fiber com￾posites, i.e., along an interface or in a weak layer very near an interface, as opposed to through the coating layer itself. Perhaps the most important outcome of work related to the treated-fiber composites is the suggestion that the fracture en￾ergy for debonding can be higher than often assumed and still perform the necessary function of crack deflection. This result suggests that the window of properties that can be possessed, by an oxide alternative coating, for example, is larger than previously thought. This observation is an important result, because the very low fracture energies previously thought to be necessary will likely be difficult to obtain with oxides or other alternative materials. It is important to note that the crack-deflection criterion is often discussed in a potentially misleading way. The He and Hutchinson criterion, for example, was derived for deflection in a true interface between two materials, and the relevant figure of merit for the competition between crack deflection in the interface and crack propagation into the second material was the ratio of interfacial (principally mode II) fracture energy to its mode I fracture energy.25 However, if the relevant issue is crack deflection within the coating, the analogous figure of merit will be the ratio of the coating (principally mode II) fracture energy (c Gr,z) to its mode I fracture energy (c Gz,z). In principle, the basic suitability of a material that is intended to promote crack deflection via cleavage can be evaluated inde￾pendent of the fiber fracture properties. There are interesting implications of the fracture behavior observed in the materials of the preceding section. Crack de￾Fig. 3. Push-out curves according to the roughness interface model, with parameters chosen to fit the experimental curve of Fig. 1, assuming that (i) initial cracking is governed by the roughness parameters h 4 50 nm, d 4 50 nm, and G 4 28 J/m2 and (ii) subsequent cracking is governed by h 4 50 nm, d 4 2.2 mm, and G 4 28 J/m2 ; the transition between the two conditions is indicated by the arrowed line. 1884 Journal of the American Ceramic Society—Kerans et al. Vol. 81, No. 7

July 1998 nterface Properties in High-Strength Nicalon/C/SiC Composites 40001 4000 3500 3500 3000 3000 32500 2500 2000 2000 1500 500 P:90/2.2/28/Pull 1000 P:50/50/28/Pu00 500 500 0,5 Inelastic Displacement(micrometers) dicted curved of bridging fiber stress versus characteristics as the push-out curves of Fig. 3 ession as in pushout: slightly after the region Ivill trans ment for composite tension tests(Type Il boundary conditions2), assuming the n to the secondary crack is assumed (somewhat arbitrarily) to occur at the same which is -2.2 GPa in tension. Fiber strengths in composite tension tests ly 1.8-2 GPa, hence, composite failure can be to occur before transition to the secondary crack flection is usually assumed to be literally that: the matrix crack near the coating/fiber interface, this observation seems to pro- p propagates into the interfacial region, then turns parallel to the fiber surface. However, it has been suggested that an in- in weak-interface equence of events for the deflection process opposites terfacial crack that develops in a composite under tension may dditional consideration of the failure process tempers th initiate as a mode I crack in the tensile(normal to the fiber conclusion somewhat and provides interesting speculation on ace)stress field ahead of the crack tip, 8,26 and observations he degree to which oxide coatings can be expected to provide on model laminate materials have confirmed the existence of protection against fiber oxidation. Consider the tensile failure such a failure sequence. 7 Because the microscopic details of process that is illustrated in Fig. 5, which shows a matrix crack fracture are difficult to probe experimentally, the exact se- quence of events in real fibrous composites has remained a The consequent debonding crack propagates some distance in matter of speculation. Nevertheless, it is a matter of some im- the coating away from the matrix crack plane. With subsequent portance in understanding the design and analysis of coating loading, the matrix crack by passes the fiber and the debonding systems. In one case, the interfacial fracture will be determined crack propagates somewhat farther within the coating. At that by the radial tensile strength, whereas in the other case, it will point, the crack is bridged by a fiber that is still coated by the be determined by the interfacial shear strengths. Understanding remaining intact portion of the coating. This remaining coating the process is also important to interpret test data. For example, could provide some protection; however, unless the coating is fiber push-in/pull-out tests may measure a somewhat different extremely strain tolerant, it must fail in tension with subsequent property than that which determines debonding during com- loading, which introduces another mode I crack. That crack posite failure may deflect into another mode Il crack that has traversed par- The carbon coatings in both composites are considered to be allel to the fiber axis; however, the process must repeat until the same, except perhaps very near the coating/fiber interface the coating is completely cracked and there is a debonding In the case of an untreated-fiber composite failing in tension, crack in the fiber/coating interface. The only possibility for the weak coating/fiber interface region fails, whereas the coat- ing itself does not, which implies that the interface must fail strains)as the fiber(1%)1.e, much more strain tolerant than before the crack enters the coating, because of the stress field would be expected from equivalent bulk materials. Although in front of the crack. If the crack had traversed through the thin coatings can be expected to exhibit increasing strain-to- coating, it would have been deflected in the coating. The proof failure with decreasing thickness(for example, see Hu et a1. 27) of this statement is provided by the treated-fiber materials, in such high values may be problematic for approaches such which the cracks deflect in the coating before reaching the those which use porous oxides. This scenario implies two con- fiber/coating interface. Provided that the debonding in the sequences: (i) even though crack deflection occurred in the weak-interface(untreated-fiber)composites is truly at or very coating, post-failure analysis may show cracks in the coating/

flection is usually assumed to be literally that: the matrix crack tip propagates into the interfacial region, then turns parallel to the fiber surface. However, it has been suggested that an in￾terfacial crack that develops in a composite under tension may initiate as a mode I crack in the tensile (normal to the fiber surface) stress field ahead of the crack tip,8,26 and observations on model laminate materials have confirmed the existence of such a failure sequence.7 Because the microscopic details of fracture are difficult to probe experimentally, the exact se￾quence of events in real fibrous composites has remained a matter of speculation. Nevertheless, it is a matter of some im￾portance in understanding the design and analysis of coating systems. In one case, the interfacial fracture will be determined by the radial tensile strength, whereas in the other case, it will be determined by the interfacial shear strengths. Understanding the process is also important to interpret test data. For example, fiber push-in/pull-out tests may measure a somewhat different property than that which determines debonding during com￾posite failure. The carbon coatings in both composites are considered to be the same, except perhaps very near the coating/fiber interface. In the case of an untreated-fiber composite failing in tension, the weak coating/fiber interface region fails, whereas the coat￾ing itself does not, which implies that the interface must fail before the crack enters the coating, because of the stress field in front of the crack. If the crack had traversed through the coating, it would have been deflected in the coating. The proof of this statement is provided by the treated-fiber materials, in which the cracks deflect in the coating before reaching the fiber/coating interface. Provided that the debonding in the weak-interface (untreated-fiber) composites is truly at or very near the coating/fiber interface, this observation seems to pro￾vide a definitive sequence of events for the deflection process in weak-interface composites. Additional consideration of the failure process tempers this conclusion somewhat and provides interesting speculation on the degree to which oxide coatings can be expected to provide protection against fiber oxidation. Consider the tensile failure process that is illustrated in Fig. 5, which shows a matrix crack that impinges on a coated fiber and is deflected in the coating. The consequent debonding crack propagates some distance in the coating away from the matrix crack plane. With subsequent loading, the matrix crack bypasses the fiber and the debonding crack propagates somewhat farther within the coating. At that point, the crack is bridged by a fiber that is still coated by the remaining intact portion of the coating. This remaining coating could provide some protection; however, unless the coating is extremely strain tolerant, it must fail in tension with subsequent loading, which introduces another mode I crack. That crack may deflect into another mode II crack that has traversed par￾allel to the fiber axis; however, the process must repeat until the coating is completely cracked and there is a debonding crack in the fiber/coating interface. The only possibility for retaining the coating is if it is as strain tolerant (to axial tensile strains) as the fiber (>1%)—i.e., much more strain tolerant than would be expected from equivalent bulk materials. Although thin coatings can be expected to exhibit increasing strain-to￾failure with decreasing thickness (for example, see Hu et al.27), such high values may be problematic for approaches such as those which use porous oxides. This scenario implies two con￾sequences: (i) even though crack deflection occurred in the coating, post-failure analysis may show cracks in the coating/ Fig. 4. Predicted curved of bridging-fiber stress versus displacement for composite tension tests (Type II boundary conditions24), assuming the same crack characteristics as the push-out curves of Fig. 3. Transition to the secondary crack is assumed (somewhat arbitrarily) to occur at the same crack progression as in pushout: slightly after the Region II/III transition, which is ∼2.2 GPa in tension. Fiber strengths in composite tension tests are typically 1.8–2 GPa; hence, composite failure can be expected to occur before transition to the secondary crack. July 1998 Interface Properties in High-Strength Nicalon/C/SiC Composites 1885

Journal of the American Ceramic Society'Kerans et al. Vol 81. No. 7 matrix coan三 Fig. 5. Schematic of a matrix crack impinging on a coated fiber in a composite under increasing tension along the axis of the fiber(vertical)(a) initial crack deflection within a coating; (b)subsequent mode I failure of the coating, followed by a second deflection; and (c)additional mode failures and deflections, until the fiber/matrix interface is reached fiber interface, and(ii) any oxidation protection provided by in drawing conclusions regarding initial crack deflection, I the coating may be limited by the tensile strain-to-failure of the on inspection of regions of the composite away from clusions based on the arguments of the preceding section be tive of the fibers in the neighborhoodof ss that can be coating. The first of these consequences requires that the con tiating matrix crack. Furthermore, coating matrix cracks should based on sound evidence regarding the location of the initial not be expected to provide effective protection at high stresses, crack deflection, because all debonding cracks will have a ten unless they are axially very strain tolerant(i.e, the coatings dency to eventually traverse into or near the interface. This have strain-to-failure values that are comparable to that of the enario is also consistent with the analysis that is based on two fiber) successive modes of cracking behavior used in the preceding Consideration of the implications of debond-crack roughness section, wherein the initial short-period crack regime would has led to valuable insights regarding the possible roles of fiber correspond to initial crack deflection in the coating. ar inter- in turn, has led to the identification of several parameters that facial crack should be considered in the design and evaluation of alternative Although the possibility of crack deflection and tough be- fiber coatings. If they are not considered, it is entirely possible havior, despite higher-strength interfaces, is a positive result, that viable coating schemes will be discarded for invalid rea- to vary the course of damage evolution in the overall compos- appreciation of the complexity of the problem, they should not te. Such things as notch sensitivity and fatigue behavior can be considered to be prohibitive. There are simple approaches to managing eac tems will require re-evaluation of the failure behavior of the re yet to be ide composite Acknowledgments: Author RJK would like to express his appreciation collaboration that included this Rough-crack formalism seems to be useful in providing an work. Mr Kelly Brown is also acknowledged for his assistance with manuscript interpretation of the push-out behavior of high-strength, preparation treated-fiber NicalonTM/C/SiC composites. It also offers a rea- sonable resolution of the wide variety of interface properties of References such composites inferred from different test techniques and H. C. Cao E. of Interfaces on the Properties of Fiber-Reinforced Soc,7361691-99(1990 amon,""Fracture Toughness of 2D Woven SiC/SiC tests indicate that the allowable toughness of coatings for de Composites with Multilayered Interphases, 'J. Am. Ceram. Soc., 79 [4]849-58 flecting cracks may be higher than previously believed 3C. Droillard, J. Lamon, and X. Bourrat, The interfacial fracture behavior of the two types of com- dition for Efficient multilay ng Interfaces in CMCs Con- later. Res. Soc. Symp. Proc. posites that have been considered provides strong evidence that 365,371-76(1995) the debonding process in the weaker-interface material initiates R. Naslain, Fiber-Matrix Interphases and Interfaces in Cerami s a mode I crack ahead of the matrix crack Composites Processed by CVI, "" Compos. Interfaces, I 3]253-86 However, consideration of the failure pro aces and Interfacial Mechanics: Influence on the deflection in a coating indicates that car cal Behavior of Ceramic Matrix Composites, J. Phys. 11,311]

fiber interface, and (ii) any oxidation protection provided by the coating may be limited by the tensile strain-to-failure of the coating. The first of these consequences requires that the con￾clusions based on the arguments of the preceding section be based on sound evidence regarding the location of the initial crack deflection, because all debonding cracks will have a ten￾dency to eventually traverse into or near the interface. This scenario is also consistent with the analysis that is based on two successive modes of cracking behavior used in the preceding section, wherein the initial short-period crack regime would correspond to initial crack deflection in the coating and the long-period crack would correspond to the coating/fiber inter￾facial crack. Although the possibility of crack deflection and tough be￾havior, despite higher-strength interfaces, is a positive result, significant variation in the interface properties can be expected to vary the course of damage evolution in the overall compos￾ite. Such things as notch sensitivity and fatigue behavior can change significantly;28,29 hence, changes in the coating sys￾tems will require re-evaluation of the failure behavior of the composite. IV. Summary Rough-crack formalism seems to be useful in providing an interpretation of the push-out behavior of high-strength, treated-fiber Nicalon™/C/SiC composites. It also offers a rea￾sonable resolution of the wide variety of interface properties of such composites inferred from different test techniques and resolves macroscopic measurements of pyrocarbon properties with composite interface measurements. Finally, the analyzed tests indicate that the allowable toughness of coatings for de￾flecting cracks may be higher than previously believed. The interfacial fracture behavior of the two types of com￾posites that have been considered provides strong evidence that the debonding process in the weaker-interface material initiates as a mode I crack ahead of the approaching matrix crack. However, consideration of the failure process after initial crack deflection in a coating indicates that care should be exercised in drawing conclusions regarding initial crack deflection, based on inspection of regions of the composite away from the ini￾tiating matrix crack. Furthermore, coatings that can be protec￾tive of the fibers in the neighborhood of matrix cracks should not be expected to provide effective protection at high stresses, unless they are axially very strain tolerant (i.e., the coatings have strain-to-failure values that are comparable to that of the fiber). Consideration of the implications of debond-crack roughness has led to valuable insights regarding the possible roles of fiber coatings in influencing composite behavior. This observation, in turn, has led to the identification of several parameters that should be considered in the design and evaluation of alternative fiber coatings. If they are not considered, it is entirely possible that viable coating schemes will be discarded for invalid rea￾sons. Although these additional design parameters add to our appreciation of the complexity of the problem, they should not be considered to be prohibitive. There are simple approaches to managing each of these parameters and, no doubt, more-subtle ones that are yet to be identified. Acknowledgments: Author RJK would like to express his appreciation to Prof. Roger Naslain (Director, Laboratoire des Composites Thermostruc￾turaux), the U.S. Air Force Office of Scientific Research, and Wright Labora￾tory Materials Directorate for facilitating the collaboration that included this work. Mr. Kelly Brown is also acknowledged for his assistance with manuscript preparation. References 1 H. C. Cao, E. Bischoff, O. Sbaizero, M. Ru¨hle, A. G. Evans, D. B. Marshall, and J. J. Brennan, ‘‘Effect of Interfaces on the Properties of Fiber-Reinforced Ceramics,’’ J. Am. Ceram. Soc., 73 [6] 1691–99 (1990). 2 C. Droillard and J. Lamon, ‘‘Fracture Toughness of 2D Woven SiC/SiC Composites with Multilayered Interphases,’’ J. Am. Ceram. Soc., 79 [4] 849–58 (1996). 3 C. Droillard, J. Lamon, and X. Bourrat, ‘‘Strong Interfaces in CMCs, Con￾dition for Efficient Multilayered Interphases,’’ Mater. Res. Soc. Symp. Proc., 365, 371–76 (1995). 4 R. Naslain, ‘‘Fiber–Matrix Interphases and Interfaces in Ceramic Matrix Composites Processed by CVI,’’ Compos. Interfaces, 1 [3] 253–86 (1993). 5 J. Lamon, ‘‘Interfaces and Interfacial Mechanics: Influence on the Mechani￾cal Behavior of Ceramic Matrix Composites,’’ J. Phys. IV, 3 [11] 1607–16 (1993). Fig. 5. Schematic of a matrix crack impinging on a coated fiber in a composite under increasing tension along the axis of the fiber (vertical) ((a) initial crack deflection within a coating; (b) subsequent mode I failure of the coating, followed by a second deflection; and (c) additional mode I failures and deflections, until the fiber/matrix interface is reached). 1886 Journal of the American Ceramic Society—Kerans et al. Vol. 81, No. 7

July 1998 Interface Properties in High-Strength Nicalon/C/SiC Composites composites:Experimental Study and Model, "Acta Mater., 45 131025-44 17T A. Parthasarathy, DB.Marshall, and RJ.Kerans,"Analysis of the eN. Lissart and J. Lamon, "" Damage and Failure in Ceramic Matrix Mini- nd Sliding in Brittle Ma- (1997) trix Composites, " Acta Metall. Mater, 42[11]3773-84(1994) 7W. Lee S J. Howard, and W. J. Clegg. ""Growth of Interface Defects and Its ST. A. Parthasarathy and R J. Kerans, "Predicted Effects of Interfacial Effect on Crack Deflection and Toughening Criteria, " Acta Mater, 44 [10 Roughness on the of Selected Ceramic Composites, " J. Am. Ceram. J. Pagano, " On the Micromechanical Failure Modes in a Class of Ide- 9R. J. Kerans, "The Role of Coating Compliance and Fiber/Matrix Inte alized Brittle Matrix Composites, Part I: Axial Tension Loading of Coated Fiber cial Topography in Debonding in Ceramic Composites, "Scr. Metall. Mater. M. Monthioux and D. Cojean, ""Microtextures of Interfaces Related to Me. ceramic Fiber Reinforced Ceramic Matrix Composite porate Coating Thermoelastic Effects into Fiber/Matrix Composite Models, J p. 729-34 in Proceedings of the 5th European Conference on Comp materials (ECCM-5. Edited by A. R. Bunsell, J F. Jamet, and A. Massiah. 2N. J. Pagano and G. P. Tandon, "" Elastic R of Multi-Directiona European Association for Composite Materials(EACM), Bordeaux, Franc es, Compos. Sci. Technol, 31 14]273-93(1988) IOL. Guillaumat and J. Lamon, "Influence of Interfacial Characteristics on the Non-linear nations of Ceramic Matrix Composites"; pp. 649-56 in 31 R. O. Ritchie, R H. Dauskardt, w. w. Gerberich, A and E. Lil- gs of ICCM 10, Vol. IV. Edited by A. Poursartip and K. Sti sodden, ""Fracture, Fatigue and Indentation Behavior of for Biomedical Applications, Mater. Res. Soc. Symp. Proc., 383, 229-54 24J W. Hutchinson and H M. Jensen, "Models of Fiber Debonding and ac. France. 1993 Pullout in Brittle Composites with Friction, "Mech. Mater,9 [2] 139-63 12F. Rebillat, J. Lamon, R. Naslain, E. Lara-Curzio, M. K. Ferber, and T. M (1990) 2M. Y. He and J. W. Hutchinson, ""C Crack Deflection at the Interface be. As Studied by Single-Fiber Push-Out Tests, "J Am Ceram Soc., 81 14965-78 tween Dissimilar Elastic Materials, Int.J. Solids Struct, 25 19] 1053-87 F. Rebillat, E. Lara-Curzio, J. Lamon, R. Naslain, M. K. Ferber, and T M. with"Weak' andStrong Interfaces, J. Am. Ceram. Soc, in press 269-83(1993) I4R. J. Kerans and T. A. Parthasarathy, Theoretical Analysis of the Fiber M. S. Hu, M. D. Thouless, and A G. Evans, "The Decohesion of Thin sP. D Jero and R J. Kerans, "The Contribution of Interfacial Roughness Films From Brittle Substrates, Acta MetalL, 36 [5]1301-307(1988) hergue, and E. Vagaggini, ""Methodology for Re- Sliding Friction of Ceramic Fibers in a glass Matrix, " Scr. Metall. Mater, 24, lating the Tensile Constitutive Behavior of Ceramic-Matrix Composites to Ce IP. D. Jero, R J. Kerans, and T. A, Parthasarathy, ""Effect of Interfacial T. J. Mackin, T. E. Purcell, M. Y, He, and A. G. Evans, Notch Sensitivity Roughness Frictional Stress Measured Using Pushout Tests, J.Am and Stress Redistribution in Three Ceramic-Matrix Composites, "J. Am. Ceram. Cera.Soc,74ll12793-801(1991) Soc,78[]7928(1995)

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