《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.tb02666.x[1]

ournal Stress Concentration due to fiber-Matrix Fusion in Ceramic-Matrix Composites William H. Glime and James D. Cawley Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106-7204 Stress concentration in ceramic-matrix composites due to fiber-matrix fusion is investigated using finite-element modeling(FEM) in conjunction with experiment. FEM re- sults indicate substantial stress concentration can be ex pected when the fiber and matrix are locally fused. The focus of the investigation is sealing through the formation of a reaction product layer(e.g, SiO2 in a SiC-SiC system) Direct sealing also is considered. Tensile experiments in volving a novel SiC-SiC microcomposite system confirm FEM predictions and unambiguously indicate the observed reduction in load-bearing capacity is the result of a SiO2 reaction product that locally fuses the fiber and matrix. . Introduction stration of interfacial sealing in a unidirectional (e. g, SiC-C-SIC). Following interphase burnout adjacent A MAJOR obstacle to the development of ceramic-matrix trix crack, growth of a reaction product layer(e.g, SiO2) composites(CMCs)for high-temperature applications is mechanical link between fibe atmospheric degradation of the fiber-matrix interphase mate pore.34 rial(e.g, carbon)almost universally used in functional sys tems.Interfacial sealing has been touted, by some, as a mean n actively oxidized fiber-matrix high-temperature composite service - One suc 四即m山(单g oncentration asso- ral. which leads to oroduct formation(e.g, SiO, on SiC)to seal an interfac tion marked reduction in load-carrying capability demonstrated by zzi et al. utilizes inherent reaction that develops following exposure of the interphase throug IL. Modeling matrix cracking(Fig. 1). Protection of the interphase from ex ure to the atmosphere through a matrix crack requires that Consider a unidirectional array of SiC fibers bridging a crack the fiber and matrix become locally fused in a SiC matrix(Fig. 1). Following recession of the interphase Recently, stressed oxidation studies in bulk composite sys via oxidation, the region of matrix directly adjacent to the tems with Sic fibers have demonstrated a severe decrease in matrix crack becomes completely relaxed, and the load is car- interphase b ried entirely by the bridging fibers. Oxidation of the system and fiber and/or matrix oxidation 6,7 Failure in the so called results in the growth of a SiO, layer that generates a mechani- Such a system be oxidation-embrittled systems typically occurs with fiber failure qualitative similarity to familiar situations leading to stress sembling that for a monolith. Sealing between the fiber and concentrations in homogeneous systems. The case of a matrix due to the formation of a reaction product(e.g, SiO,) notched cylindrical bar under tensile loading is an example Typical of these calculations is the of homo has been suggested as one mechanism that contributes to the That is, the joint is assumed to be perfect, and the materials are embrittlement of some of the CMc systems tested.b The research presented here is aimed at determining the characterized by a single set of parameters. In a fused com- magnitudes, understanding the governing parameters, and posite system, however, the fiber(e.g, NicalonTM), reaction aluating the effect of fusion-induced stress concentration on SiO2), and matrix(e.g, chemically vapor depos composite mechanical performance. A unique test speci has been designed, characterized, and tested to identify unam- plied directly. However, the computational power offered biguously the mechanism for the reduction in load-carrying modern computers allows parametric studies, via finite- apability of fused composite systems. The results demons element modeling (FEM), in a heterogeneous system to be performed readily FEM has been used to examine stress distributions for a T.A. Parthasarathy-contributing editor specific geometrical configuration designed to represent a single-fiber microcomposite to be used in the experimental ortion of this study(see Figs 4 and 5). Results from addition FEM representing unidirectional bulk composites are presented 98th Annual Meeting of the American Ceramic Society April 14-17,1996 Figure 2 is a schematic of fem designed to represent a nce and engineering, Case Western Reserve University, Cleveland, OH, SiC-SiC microcomposite made up of a single fiber fused to a lindrical section of matrix material by a layer of SiO2. Rad Institute Collaborative Core Research Prog Grant Nos. NCC3-139 and Noczranve Ag证mce ct to the fiber axis is materials involved are treated as linear elastic with dimensio elastic constants, and boundary conditions as described in FI 2597

Stress Concentration Due to Fiber–Matrix Fusion in Ceramic-Matrix Composites William H. Glime* and James D. Cawley* Department of Materials Science and Engineering, Case Western Reserve University, Cleveland, Ohio 44106-7204 Stress concentration in ceramic-matrix composites due to fiber–matrix fusion is investigated using finite-element modeling (FEM) in conjunction with experiment. FEM re￾sults indicate substantial stress concentration can be ex￾pected when the fiber and matrix are locally fused. The focus of the investigation is sealing through the formation of a reaction product layer (e.g., SiO2 in a SiC–SiC system). Direct sealing also is considered. Tensile experiments in￾volving a novel SiC–SiC microcomposite system confirm FEM predictions and unambiguously indicate the observed reduction in load-bearing capacity is the result of a SiO2 reaction product that locally fuses the fiber and matrix. I. Introduction A MAJOR obstacle to the development of ceramic-matrix composites (CMCs) for high-temperature applications is atmospheric degradation of the fiber–matrix interphase mate￾rial (e.g., carbon) almost universally used in functional sys￾tems.1 Interfacial sealing has been touted, by some, as a means to preserve an actively oxidized fiber–matrix interphase during high-temperature composite service.2–5 One such approach, demonstrated by Filipuzzi et al., 4 utilizes inherent reaction product formation (e.g., SiO2 on SiC) to seal an interfacial pore that develops following exposure of the interphase through matrix cracking (Fig. 1). Protection of the interphase from ex￾posure to the atmosphere through a matrix crack requires that the fiber and matrix become locally fused. Recently, stressed oxidation studies in bulk composite sys￾tems with SiC fibers have demonstrated a severe decrease in ultimate strength and toughness following interphase burnout and fiber and/or matrix oxidation.6,7 Failure in the so called oxidation-embrittled systems typically occurs with fiber failure at a matrix crack plane and a composite fracture surface re￾sembling that for a monolith. Sealing between the fiber and matrix due to the formation of a reaction product (e.g., SiO2) has been suggested as one mechanism that contributes to the embrittlement of some of the CMC systems tested.6 The research presented here is aimed at determining the magnitudes, understanding the governing parameters, and evaluating the effect of fusion-induced stress concentration on composite mechanical performance. A unique test specimen has been designed, characterized, and tested to identify unam￾biguously the mechanism for the reduction in load-carrying capability of fused composite systems. The results demonstrate what appears to be an unavoidable stress concentration asso￾ciated with sealing techniques, in general, which leads to marked reduction in load-carrying capability. II. Modeling Consider a unidirectional array of SiC fibers bridging a crack in a SiC matrix (Fig. 1). Following recession of the interphase via oxidation, the region of matrix directly adjacent to the matrix crack becomes completely relaxed, and the load is car￾ried entirely by the bridging fibers. Oxidation of the system results in the growth of a SiO2 layer that generates a mechani￾cal link between the fibers and matrix. Such a system bears qualitative similarity to familiar situations leading to stress concentrations in homogeneous systems.8 The case of a notched cylindrical bar under tensile loading is an example. Typical of these calculations is the assumption of homogeneity. That is, the joint is assumed to be perfect, and the materials are characterized by a single set of parameters. In a fused com￾posite system, however, the fiber (e.g., Nicalon™), reaction product (e.g., SiO2), and matrix (e.g., chemically vapor depos￾ited (CVD) SiC) typically offer different material properties. Thus, the solutions for homogeneous systems cannot be ap￾plied directly. However, the computational power offered by modern computers allows parametric studies, via finite￾element modeling (FEM), in a heterogeneous system to be performed readily. FEM has been used to examine stress distributions for a specific geometrical configuration designed to represent a single-fiber microcomposite to be used in the experimental portion of this study (see Figs. 4 and 5). Results from additional FEM representing unidirectional bulk composites are presented in Appendix A. Figure 2 is a schematic of FEM designed to represent a SiC–SiC microcomposite made up of a single fiber fused to a cylindrical section of matrix material by a layer of SiO2. Radial symmetry with respect to the fiber axis is assumed, and all materials involved are treated as linear elastic with dimensions, elastic constants, and boundary conditions as described in Fig. T. A. Parthasarathy—contributing editor Manuscript No. 190947. Received June 6, 1997; approved March 2, 1998. Presented in part at the 98th Annual Meeting of the American Ceramic Society, Indianapolis, IN, April 14–17, 1996. Based in part on the dissertation submitted by W. H. Glime for the Ph.D degree in materials science and engineering, Case Western Reserve University, Cleveland, OH, 1996. Supported by Ohio Aerospace Institute Collaborative Core Research Program un￾der Grant No. CCRP93-1-027 and a NASA-CWRU Cooperative Agreement on Ce￾ramics Processing under Grant Nos. NCC3-139 and NCC3-404. *Member, American Ceramic Society. Fig. 1. Illustration of interfacial sealing in a unidirectional composite (e.g., SiC–C–SiC). Following interphase burnout adjacent to the ma￾trix crack, growth of a reaction product layer (e.g., SiO2) generates a mechanical link between fiber and matrix, sealing the interfacial pore.3,4 J. Am. Ceram. Soc., 81 [10] 2597–604 (1998) Journal 2597

Journal of the American Ceramic Society-Glime and Cawle Vol 81. No. 10 2 Fiber l.5 1.3 Sic Sheath 0.86 0.71 4 0.5 Fig. 2. Schematic of two-dimensional axisymmetric FEM represent ing the Sic-SiC microcomposites used to experimentally evaluat Fig. 3. Contour plot of maximum principal stress for the model iusion-induced stress concentration( Section III). Linear elastic behav. SiC-SiC microcomposite system. Scale indicates the local stress rela- GPa and v=0. 2: for SiO,, E= 70 tive to the I gPa fiber nominal stress. arrows indicate the direction of GPa and v= 0.2) Radius of curvature in the SiO, where the fiber the maximum principal stress. Thermal stress associated with cooling enters the matrix section and the thickness of the SiO, at the interface from an oxidation temperature of 1100C to room temperature is in- are assumed to be r/35 (r is the fiber radius) cluded in the model 2. In the context of defining model geometry, it is noted that the clear that the SiO, layer. which is more compliant th molar volume of SiOz is approximately twice that of SiC. Thus, significantly decreases the magnitude of the stress rowth of a SiOz layer on SiC results in a linear increase in the tion, as is expected. Although lower than that for a ness of the SiO2 scale; i.e., a I um interfacial gap is replaced sealed system remains substantial by a 2 um SiO, layer following oxidation. FEm and result ve been generated using a Silicon Graphics UNIX worksta- on with P3/PATRAN(Mac Neal-Schwendler Corp, Los Ange IlL. Experimental Evaluation of Fusion-Induced les, CA)mesh ge n and ABAqUs 5.4(Hibbit, Karlsson Stress Concentration and Sorensen, Inc, Pawtucket, RI) analysis software The model depicted in Fig. 2 is representative of a fiber with The microcomposite system used in the experimental inves- a 70 um radius(scs-O)and an original fiber-matrix intess y by tigation of stress concentration in the fused fiber-matrix system 2 um layer of Sio 2. The radius of curvature assumed by the MA) SiC monofilament. Figure 4 schematically outlines the SiO, in the region where the fiber enters the matrix has been specimen preparation procedure. SCS-0 fibers were coated chosen, in this case, to be equivalent to the thickness of an with a layer of CVD pyro-carbon I to 3 um in thickness; this nterfacial SiO2 layer that fills the interfacial pore(2 um). The was followed by deposition of -200 um of SiC. The carbon nalysis includes residual stress due to thermal expansion mis match associated with cooling from the oxidation ar out in air at 500C for 100 h. Transverse cracks were generated temperature(1100C)to room temperature. Residual stresse in the continuous SiC coating at regular intervals by controlled ssociated with growth of the SiO2 reaction product are not impact with a steel probe. Intact sections of the coating, 1-3 onsidered. Details of the thermally induced residual stress in mm in length, were removed from the monofilament substrate the microcomposite system are presented in Appendix B with tweezers. The sections of Sic coating then were forced igure 3 is a contour plot of maximum principal stress cal manually onto pristine SCS-0 monofilaments to produce speci- culated for the aforementioned fused fiber-matrix system mens suitable for tensile testing. A SEM micrograph of a typi FEM results indicate two areas with significant stress concen cal SiC-SiC microcomposite specimen is presented in Fig. 5 tration. In the region where the fiber enters the matrix, the sio This experimental procedure was developed out of necessity layer is stressed to a value that is-1.3 times the nominal fiber Initial efforts involved testing of full mi sIte systems, stress. The stress intensity factor for the underlying fiber is 2.3 i.e., single fibers with a thick(>200 um)CVD-SiC coating as which also is manifest in the same local region. As a compar a surrogate matrix. It was discovered that the full microcom son,the predicted value of stress concentration for a homoge- posite had several shortcomings with neous cylindrical butt joint with similar geometry is 4.8.t It is stress concentration effect. First, a baseline to evaluating the alue of the scs monofilament strength following interphase and matrix depo- sition could not be unambiguously determined. Second, intrin- sic residual stress in the CVD matrix coating led to crooked specimens that were difficult to uniformly test in tension FEM after first conf nd rod aans&w seved, the full microcomposites were fragile and often failed several locations following the initial tensile failure, making

2. In the context of defining model geometry, it is noted that the molar volume of SiO2 is approximately twice that of SiC. Thus, growth of a SiO2 layer on SiC results in a linear increase in the total material thickness that is equivalent to one-half the thick￾ness of the SiO2 scale; i.e., a 1 mm interfacial gap is replaced by a 2 mm SiO2 layer following oxidation. FEM and results have been generated using a Silicon Graphics UNIX worksta￾tion with P3/PATRAN (MacNeal–Schwendler Corp., Los Ange￾les, CA) mesh generation and ABAQUS 5.4 (Hibbit, Karlsson, and Sorensen, Inc., Pawtuckett, RI) analysis software. The model depicted in Fig. 2 is representative of a fiber with a 70 mm radius (SCS-0) and an original fiber–matrix interphase 1 mm in thickness, which, following oxidation, is replaced by a 2 mm layer of SiO2. The radius of curvature assumed by the SiO2 in the region where the fiber enters the matrix has been chosen, in this case, to be equivalent to the thickness of an interfacial SiO2 layer that fills the interfacial pore (2 mm). The analysis includes residual stress due to thermal expansion mis￾match associated with cooling from the oxidation annealing temperature (1100°C) to room temperature. Residual stresses associated with growth of the SiO2 reaction product are not considered. Details of the thermally induced residual stress in the microcomposite system are presented in Appendix B. Figure 3 is a contour plot of maximum principal stress cal￾culated for the aforementioned fused fiber–matrix system. FEM results indicate two areas with significant stress concen￾tration. In the region where the fiber enters the matrix, the SiO2 layer is stressed to a value that is ∼1.3 times the nominal fiber stress. The stress intensity factor for the underlying fiber is 2.3, which also is manifest in the same local region. As a compari￾son, the predicted value of stress concentration for a homoge￾neous cylindrical butt joint with similar geometry is 4.8.† It is clear that the SiO2 layer, which is more compliant than SiC, significantly decreases the magnitude of the stress concentra￾tion, as is expected. Although lower than that for a homoge￾neous system, the predicted stress concentration in the SiO2 sealed system remains substantial. III. Experimental Evaluation of Fusion-Induced Stress Concentration The microcomposite system used in the experimental inves￾tigation of stress concentration in the fused fiber–matrix system was based on the SCS-0 (Textron Speciality Materials, Lowell, MA) SiC monofilament. Figure 4 schematically outlines the specimen preparation procedure. SCS-0 fibers were coated with a layer of CVD pyro-carbon 1 to 3 mm in thickness; this was followed by deposition of ∼200 mm of SiC. The carbon layer between SiC monofilament and SiC coating was burned out in air at 500°C for 100 h. Transverse cracks were generated in the continuous SiC coating at regular intervals by controlled impact with a steel probe. Intact sections of the coating, 1–3 mm in length, were removed from the monofilament substrate with tweezers. The sections of SiC coating then were forced manually onto pristine SCS-0 monofilaments to produce speci￾mens suitable for tensile testing. A SEM micrograph of a typi￾cal SiC–SiC microcomposite specimen is presented in Fig. 5. This experimental procedure was developed out of necessity. Initial efforts involved testing of full microcomposite systems, i.e., single fibers with a thick (>200 mm) CVD-SiC coating as a surrogate matrix. It was discovered that the full microcom￾posite had several shortcomings with respect to evaluating the stress concentration effect. First, a baseline value of the SCS monofilament strength following interphase and matrix depo￾sition could not be unambiguously determined. Second, intrin￾sic residual stress in the CVD matrix coating led to crooked specimens that were difficult to uniformly test in tension. Third, the full microcomposites were fragile and often failed in several locations following the initial tensile failure, making † The geometric parameters (radius of curvature at joint and rod radii) typically tabulated for homogeneous systems do not include the extreme ratios typical of a continuous-filament ceramic composite (CFCC). The value of 4.8 was obtained by FEM after first confirming tabulated values8 with calculation. Fig. 2. Schematic of two-dimensional axisymmetric FEM represent￾ing the SiC–SiC microcomposites used to experimentally evaluate fusion-induced stress concentration (Section III). Linear elastic behav￾ior is assumed (for SiC, E 4 400 GPa and n 4 0.2; for SiO2, E 4 70 GPa and n 4 0.2). Radius of curvature in the SiO2 where the fiber enters the matrix section and the thickness of the SiO2 at the interface are assumed to be r/35 (r is the fiber radius). Fig. 3. Contour plot of maximum principal stress for the model SiC–SiC microcomposite system. Scale indicates the local stress rela￾tive to the 1 GPa fiber nominal stress. Arrows indicate the direction of the maximum principal stress. Thermal stress associated with cooling from an oxidation temperature of 1100°C to room temperature is in￾cluded in the model. 2598 Journal of the American Ceramic Society—Glime and Cawley Vol. 81, No. 10

October 1998 Stress Concentration Due to Fiber-Matrix Fusion in Ceramic-Matrix Composite. 2599 CDS sc5-0 fiber wath coaling induced by oxidizing to form a layer of Sio2. All oxidation experiments were performed in air. All anneals took place at 1 100C for times ranging from 20 to 120 h, with the exception of one set that was oxidized at 1200%C for 50 h. A set of control Carhnn interphase burned out 5]"C air specimens also was tested to establish a baseline, to which the tensile performance of the sealed microcomposites could be Crack induced in costinE compared. These included as-received SCS-0 fibers, as- assembled microcomposites( which were not subjected to oxi- dation and, hence, not fused), and bare SCS-0 fibers(which were oxidized by exposure to air at 1@C for 68 h). Sets of monofilaments and microcomposites that were exposed to 1 100C air for 100 h were treated for I h in a room-temperature Scction of ocating removed from fiber 50% HF solution to remove the SiO, oxidation product. Fol lowing acid treatment, there was no visible evidence of a SiO layer, and the sections of Sic sheath moved freely along the length of the SiC monofilament. IV. Microcomposite Results and Discussion As-received scs-0 fiber Figure 6A reports the nominal tensile failure stress for single SCS-0 fiber specimens. The as-received SCS-0 fibers failed at a nominal fiber stress between 2.5 and 3 GPa, in agreement with independent data obtained previously. Bare fibers that were subjected to 1100C air for 68 h failed at stresses between for oxidized SCS-0 monofilaments. Removal of the SiO, scale by etching in HF restored the strength of the fibers to values comparable to those of the as-received fibers. This indicated Fig. 4. Schematic of the procedure used to prepare microcomposit tensile specimens suitable for experimental evaluation of fusion- site that the temperatures and times used during oxidation did not induced stress concentration cause significant fiber degradation As indicated in Fig. 6(B), the failure stress for microcom- resembled)ranged between 1.5 and 2.5 GPa. This decrease in ite specimens that were not fused via oxidation(i.e,as- strength compared to as-received fibers was expected, consid- SCS-O fiber SiC sheath manual threading of a SiC sheath with an-2 um radial toler ance on to a pristine SCS-0 monofilament Fa gins for the as-assembled microcomposites were ra located along the length of the fiber; i. e, they were ne the final location of sic sheath Microcomposites that were fused to the sheath with a layer of SiO, following oxidation exhibited failure at a nominal fiber tress centered at -700 MPa. all observed failure origins in the sealed microcomposites occurred where the SiC monofilament entered the SiC sheath( Fig. 7). Two of the five specimens oxidized for 20 h at 1.C had strengths approaching that for In bare and oxidized SCS-0. but failure was observed where the fiber entered the sheath. For the remaining three 20 h speci- Fig. 5. SEM micrograph of an as-assembled microcomposite mens failure occurred at a fiber nominal stress <1 GPa. similar to that for microcomposites oxidized for longer times Figure 8 depicts SEM micrographs of the mating fiber from he fractured microcomposite specimen in Fig. 7. The SiO scale on the fiber and matrix was-I um in thickness. Where the location of the initial failure site for microstructural evalu- the fiber enters the sheath, a SiO2 scale had formed with a ation a challenge. Fourth, direct experimental confirmation of radius of curvature of -2 um for the majority of the fiber models most relevant to true composites was not possible. circumference Thus, the experimental strategy was to test a microcomposite The fibers typically were displaced to one side of the model that contained features similar to those in a SiO2-fused d, for the shorter oxidation times(<120 h), were sealed bulk composite system and also was accessible to FEM and over a portion of their circumference. For example m en that was oxidized in air for 40 h at 1 100%C. the sheath composite sy stem allowed confidence when inferring the com- siles testing reveal asegrignof ibsr that was n side the sheath Tensile testing of the microcomposite specimens Fig 9).A""of SiO, that formed at the edge of the sheath formed at room temperature on a test frame(Instron Corp was observed to extend over approximately one-sixth the fiber Danvers, MA)with pneumatic rubber grips. The single fila circumference. Behind the SiO, lip, the portion of the Sio microcomposite and control specimens were mounted to interlayer that bridged the fiber and sheath had become ex mene tabs using epoxy to aid in the gripping process. The specimen gauge length(distance between paper tabs) was 2.5 cm. All specimens were pulled at a rate of 1 x 10- m/s, and the ad at failure was electronically recorded Sealing between the Sic monofilament and SiC sheath was one case, fiber failure occurred inside the sheath -200 Hm from the end for

the location of the initial failure site for microstructural evalu￾ation a challenge. Fourth, direct experimental confirmation of models most relevant to true composites was not possible. Thus, the experimental strategy was to test a microcomposite model that contained features similar to those in a SiO2-fused bulk composite system and also was accessible to FEM and experimental analysis. Confirmation of FEM for the micro￾composite system allowed confidence when inferring the com￾posite behavior from the results of FEM for actual composites. Tensile testing of the microcomposite specimens was per￾formed at room temperature on a test frame (Instron Corp., Danvers, MA) with pneumatic rubber grips. The single fila￾ment microcomposite and control specimens were mounted to paper tabs using epoxy to aid in the gripping process. The specimen gauge length (distance between paper tabs) was 2.5 cm. All specimens were pulled at a rate of 1 × 10−5 m/s, and the load at failure was electronically recorded. Sealing between the SiC monofilament and SiC sheath was induced by oxidizing to form a layer of SiO2. All oxidation experiments were performed in air. All anneals took place at 1100°C for times ranging from 20 to 120 h, with the exception of one set that was oxidized at 1200°C for 50 h. A set of control specimens also was tested to establish a baseline, to which the tensile performance of the sealed microcomposites could be compared. These included as-received SCS-0 fibers, as￾assembled microcomposites (which were not subjected to oxi￾dation and, hence, not fused), and bare SCS-0 fibers (which were oxidized by exposure to air at 1100°C for 68 h). Sets of monofilaments and microcomposites that were exposed to 1100°C air for 100 h were treated for 1 h in a room-temperature 50% HF solution to remove the SiO2 oxidation product. Fol￾lowing acid treatment, there was no visible evidence of a SiO2 layer, and the sections of SiC sheath moved freely along the length of the SiC monofilament. IV. Microcomposite Results and Discussion Figure 6A reports the nominal tensile failure stress for single SCS-0 fiber specimens. The as-received SCS-0 fibers failed at a nominal fiber stress between 2.5 and 3 GPa, in agreement with independent data obtained previously.9 Bare fibers that were subjected to 1100°C air for 68 h failed at stresses between 1.4 and 2 GPa, also in agreement with data previously obtained for oxidized SCS-0 monofilaments.9 Removal of the SiO2 scale by etching in HF restored the strength of the fibers to values comparable to those of the as-received fibers. This indicated that the temperatures and times used during oxidation did not cause significant fiber degradation. As indicated in Fig. 6(B), the failure stress for microcom￾posite specimens that were not fused via oxidation (i.e., as￾assembled) ranged between 1.5 and 2.5 GPa. This decrease in strength compared to as-received fibers was expected, consid￾ering the likelihood of handling damage associated with the manual threading of a SiC sheath with an ∼2 mm radial toler￾ance on to a pristine SCS-0 monofilament. Failure origins for the as-assembled microcomposites were randomly located along the length of the fiber; i.e., they were not correlated with the final location of SiC sheath. Microcomposites that were fused to the sheath with a layer of SiO2 following oxidation exhibited failure at a nominal fiber stress centered at ∼700 MPa. All observed failure origins in the sealed microcomposites occurred where the SiC monofilament entered the SiC sheath (Fig. 7).‡ Two of the five specimens oxidized for 20 h at 1100°C had strengths approaching that for bare and oxidized SCS-0, but failure was observed where the fiber entered the sheath. For the remaining three 20 h speci￾mens, failure occurred at a fiber nominal stress <1 GPa, similar to that for microcomposites oxidized for longer times. Figure 8 depicts SEM micrographs of the mating fiber from the fractured microcomposite specimen in Fig. 7. The SiO2 scale on the fiber and matrix was ∼1 mm in thickness. Where the fiber enters the sheath, a SiO2 scale had formed with a radius of curvature of ∼2 mm for the majority of the fiber circumference. The fibers typically were displaced to one side of the sheath and, for the shorter oxidation times (<120 h), were sealed only over a portion of their circumference. For example, in one specimen that was oxidized in air for 40 h at 1100°C, the sheath was dislodged from its original position on the fiber after ten￾sile testing to reveal a region of fiber that was inside the sheath (Fig. 9). A ‘‘lip’’ of SiO2 that formed at the edge of the sheath was observed to extend over approximately one-sixth the fiber circumference. Behind the SiO2 lip, the portion of the SiO2 interlayer that bridged the fiber and sheath had become ex- ‡ In one case, fiber failure occurred inside the sheath ∼200 mm from the end for reasons that are unclear. Fig. 4. Schematic of the procedure used to prepare microcomposite tensile specimens suitable for experimental evaluation of fusion￾induced stress concentration. Fig. 5. SEM micrograph of an as-assembled microcomposite specimen. October 1998 Stress Concentration Due to Fiber–Matrix Fusion in Ceramic-Matrix Composites 2599

Journal of the American Ceramic SocietyGlime and Cawley Vol 81. No. 10 s-received HEesch Stress As-assembled 68h50h120h 00°100°1200°1100° (B) Fig. 6. Plot nal failure stress for (A) single SCS-0 monofilament and (B)microcomposite specimens following the indicated treatments. All o eals were performed in air for the time and temperature indicated. Tensile testing was performed at room temperatur using a 2.5 cm 间 ngth and displacement control (1 x 10-m an average nominal stress of 700 MPa. This 2.5-fold reduc tion in strength correlates well with FEM prediction( Fig. 6 of 2.2 for the stress concentration on the fiber in this system SiC matrix, 140 um SiC fiber, assuming a 2 um SiO2 inter- layer with a 2 um radius of curvature ). However, if Weibull statistics are used to describe fiber strength, the 2.5 cm gauge length used for the bare fibers should be compared to the re- gion influenced by the stress concentration in the fused sy tem. It is assumed that flaws at the fiber surface govern failure his allows the length of fiber influenced by stress concen- tration to be directly compared to the fiber gauge length, ra ther than use the volume comparison more standard of a Wei- bull analysis. Assuming an arbitrary, but reasonable, Weibull modulus of 10 for the oxidized ScS-o and that the stress concentration in the fused system acts along 5 um of the fi- ber length based on fem results then the 25-fold decrease in strength observed experimentally corresponds to a stress concentration of -6. Thus, with sampling length considered the experimentally observed stress concentration is signifi- cantly larger than that predicted by FEM. In this context, it is important to note that FEM represents a lower bound for the stress concentration, because it assumes a constant curvature and smooth surface at the sealing point. The large flaws ob- tested to failure. Fiber failure occurred near the end of the Sic served in the SiO2 seal( Fig. 8)can induce failure at a stress that consistent with FEM predictions. is below the value predicted assuming a more homogenous mIcrostructure Because the failure stress in the oxidized microcomposites is posed. The remainder of the Sio2 layer around the fiber cir- similar for the various conditions, it appears that only a mod- cumference appeared smooth and presented no evidence that erate degree of bonding is necessary to produce the observed bonding with the SiO, on the inner surface of the SiC sheath decrease in strength. The range of tensile strengths observed in had occurred the specimens oxidized for 20 h at 1100C may indicate that Similar to the monofilaments, microcomposites that were this combination of time and temperature is close to the thresh- treated in a HF solution to remove the Sio, reaction product old necessary for bonding the fiber to the matrix that induces showed a recovery of tensile strength to that for the as- premature fiber failure. The scatter in the 20 h fused micro- assembled condition composite data is presumed to be due to the formation of a thin Using the average failure (-1.7 GPa)of oxidized SiO2 scale that does not always cause sealing. This is supported SCS-0 fibers (no sheath) ne to which the perfor- by the fact that the data tend to be clustered at two extremes, mance of sealed microcompo n be compared, fusion either similar to the oxidized fibers or typical of the microcom f the scs-o fiber to the sic yields fibers that fail at posites oxidized under more severe conditions. It also is con-

posed. The remainder of the SiO2 layer around the fiber cir￾cumference appeared smooth and presented no evidence that bonding with the SiO2 on the inner surface of the SiC sheath had occurred. Similar to the monofilaments, microcomposites that were treated in a HF solution to remove the SiO2 reaction product showed a recovery of tensile strength to that for the as￾assembled condition. Using the average failure strength (∼1.7 GPa) of oxidized SCS-0 fibers (no sheath) as a baseline to which the perfor￾mance of sealed microcomposites can be compared, fusion of the SCS-0 fiber to the SiC shealth yields fibers that fail at an average nominal stress of 700 MPa. This 2.5-fold reduc￾tion in strength correlates well with FEM prediction (Fig. 6) of 2.2 for the stress concentration on the fiber in this system (SiC matrix, 140 mm SiC fiber, assuming a 2 mm SiO2 inter￾layer with a 2 mm radius of curvature). However, if Weibull statistics are used to describe fiber strength, the 2.5 cm gauge length used for the bare fibers should be compared to the re￾gion influenced by the stress concentration in the fused sys￾tem. It is assumed that flaws at the fiber surface govern failure; this allows the length of fiber influenced by stress concen￾tration to be directly compared to the fiber gauge length, ra￾ther than use the volume comparison more standard of a Wei￾bull analysis. Assuming an arbitrary, but reasonable, Weibull modulus of 10 for the oxidized SCS-0 and that the stress concentration in the fused system acts along 5 mm of the fi￾ber length based on FEM results, then the 2.5-fold decrease in strength observed experimentally corresponds to a stress concentration of ∼6. Thus, with sampling length considered, the experimentally observed stress concentration is signifi￾cantly larger than that predicted by FEM. In this context, it is important to note that FEM represents a lower bound for the stress concentration, because it assumes a constant curvature and smooth surface at the sealing point. The large flaws ob￾served in the SiO2 seal (Fig. 8) can induce failure at a stress that is below the value predicted assuming a more homogenous microstructure. Because the failure stress in the oxidized microcomposites is similar for the various conditions, it appears that only a mod￾erate degree of bonding is necessary to produce the observed decrease in strength. The range of tensile strengths observed in the specimens oxidized for 20 h at 1100°C may indicate that this combination of time and temperature is close to the thresh￾old necessary for bonding the fiber to the matrix that induces premature fiber failure. The scatter in the 20 h fused micro￾composite data is presumed to be due to the formation of a thin SiO2 scale that does not always cause sealing. This is supported by the fact that the data tend to be clustered at two extremes, either similar to the oxidized fibers or typical of the microcom￾posites oxidized under more severe conditions. It also is con￾Fig. 6. Plot of fiber nominal failure stress for (A) single SCS-0 monofilament and (B) microcomposite specimens following the indicated treatments. All oxidation anneals were performed in air for the time and temperature indicated. Tensile testing was performed at room temperature using a 2.5 cm gauge length and displacement control (1 × 10−5 m/s). Fig. 7. SEM micrograph of a microcomposite treated for 120 h at 1100°C tested to failure. Fiber failure occurred near the end of the SiC sheath, consistent with FEM predictions. 2600 Journal of the American Ceramic Society—Glime and Cawley Vol. 81, No. 10

October 1998 Stress Concentration Due to Fiber-Matrix Fusion in Ceramic-Matrix Composites 100um Silica Silica 10 Fig 9. SEM micrographs of a microcomposite specimen treated at ig. 8. SEN 1100.C for 40 h in air. Following tensile fracture. the sheath was displaced from its initial position on the fiber to reveal the region fused matrix section sheath, the radius of curvature assumed by the Sio, scale is-2 um sistent with published data for oxidation in air, o which indi- problems involving a SiOx-fused system have been o similar resented cates these conditions would produce -0.5 um of SiO2, enoug previously and indicate that the properties of a SiO -SiC in to cause partial fusion in eccentric fibers, but not enough to terface are not conducive to debonding. 11, 12 Thus, crack initia- ensure fusion tion in the SiO2 seal also is expected to lead to microcomposite The fact that the observed strength in oxidized and HF failure etched monofilaments returns to that observed in as-received The results presented here indicate that fusion of the fiber fibers suggests that it is the presence of the SiO, layer that and matrix local to a matrix crack results in the loss of"com- governs failure in the oxidized bare fiber. The physical fail posite behavior" because of the inability of the fiber and ma- ure origins in the sealed microcomposites have not been de trix to act independently. As well as the corresponding de- termined unambiguously, but two possibilities seem most crease in toughness, the load-bearing capacity of a fused likely. The first involves failure of the SiO2 layer in the re- composite system is expected to decrease sharply because of elon where the fiber is coupled to the matrix, and a crack in stress concentration. Thus, when interfacial sealing is the he SiO2 extends into the fiber. The second possible failure means of interphase preservation, composite designs must also initiation in the fiber occurs in the region where the stress is address the issue of stress concentration, if composite systems concentrated because of sealing. Although FEM analysis of that use this approach are to be effective in the SiO2 layer that are 60% that in the SiC fiber, the stress d he microcomposite specimens in this study have been oxi- the microcomposite system predicts maximum tensile stresses in the SiO, layer at the point of maximum concentration con- room temperature. If the oxidation-induced sealing is to occur tinues to be expected to exceed 1 GPa at the nominal fiber at a constant load, a stress concentration is not predicted. It is, stress at which microcomposite failure occurs. Therefore therefore, conceivable that a composite that remains at a con- although it is not unambiguous that failure is initiated in stant load during high-temperature service would not be af- the SiO, layer in the microcomposite specimens, it is likely. If fected by stress concentration following fiber-matrix bonding the case, then microcomposite failure is a function However, if the loading conditions on the fused system are to of crack deflection(debonding)versus penetration(failure)at change(e.g, by further matrix cracking or failure in a neigh

sistent with published data for oxidation in air,10 which indi￾cates these conditions would produce ∼0.5 mm of SiO2, enough to cause partial fusion in eccentric fibers, but not enough to ensure fusion. The fact that the observed strength in oxidized and HF￾etched monofilaments returns to that observed in as-received fibers suggests that it is the presence of the SiO2 layer that governs failure in the oxidized bare fiber. The physical fail￾ure origins in the sealed microcomposites have not been de￾termined unambiguously, but two possibilities seem most likely. The first involves failure of the SiO2 layer in the re￾gion where the fiber is coupled to the matrix, and a crack in the SiO2 extends into the fiber. The second possible failure initiation in the fiber occurs in the region where the stress is concentrated because of sealing. Although FEM analysis of the microcomposite system predicts maximum tensile stresses in the SiO2 layer that are 60% that in the SiC fiber, the stress in the SiO2 layer at the point of maximum concentration con￾tinues to be expected to exceed 1 GPa at the nominal fiber stress at which microcomposite failure occurs. Therefore, although it is not unambiguous that failure is initiated in the SiO2 layer in the microcomposite specimens, it is likely. If this is the case, then microcomposite failure is a function of crack deflection (debonding) versus penetration (failure) at the SiO2–SiC interface. Energy release rate solutions to similar problems involving a SiO2-fused system have been presented previously and indicate that the properties of a SiO2–SiC in￾terface are not conducive to debonding.11,12 Thus, crack initia￾tion in the SiO2 seal also is expected to lead to microcomposite failure. The results presented here indicate that fusion of the fiber and matrix local to a matrix crack results in the loss of ‘‘com￾posite behavior’’ because of the inability of the fiber and ma￾trix to act independently. As well as the corresponding de￾crease in toughness, the load-bearing capacity of a fused composite system is expected to decrease sharply because of stress concentration. Thus, when interfacial sealing is the means of interphase preservation, composite designs must also address the issue of stress concentration, if composite systems that use this approach are to be effective. The microcomposite specimens in this study have been oxi￾dized in an unstressed condition and fractured in tension at room temperature. If the oxidation-induced sealing is to occur at a constant load, a stress concentration is not predicted. It is, therefore, conceivable that a composite that remains at a con￾stant load during high-temperature service would not be af￾fected by stress concentration following fiber–matrix bonding. However, if the loading conditions on the fused system are to change (e.g., by further matrix cracking or failure in a neigh￾Fig. 8. SEM micrographs of the mating fiber to the fracture surface depicted in Fig. 7. Rim of SiO2 scale pulled from the surface of the SiC matrix section is observed around the fiber. Where the fiber enters the sheath, the radius of curvature assumed by the SiO2 scale is ∼2 mm. Fig. 9. SEM micrographs of a microcomposite specimen treated at 1100°C for 40 h in air. Following tensile fracture, the sheath was displaced from its initial position on the fiber to reveal the region fused by the SiO2 reaction product. October 1998 Stress Concentration Due to Fiber–Matrix Fusion in Ceramic-Matrix Composites 2601

2602 Journal of the American Ceramic SocietyGlime and Cawley Vol 81. No. 10 boring fiber), the additional load carried by intact fibers ntensified at the sealing points. The reality is that a used system behaves similar to a flawed monolith The presence of a stress concentration also assumes that the materials involved do not possess the ability to deform and Matrix O ccommodate the local strains. The modeling can, of course, be xtended to include this effect, but, for SiO,, stress relaxation expected to be insignificant, even to temperat 1500°C.13 The nominal failure stress in SiC-SiC microcomposite specimens that had been oxidized to induce fusion decreased to less than half that observed in bare fibers with a similar thermal history. The loss of strength in oxidized microcompos- ites is completely recovered following etching in HF to remove the Sio, layer that binds the fiber to the matrix sheath. This result demonstrates that the decreased load at failure is entirely due to the presence of SiO, that fuses the sheath to the fiber Silica a geometrical effect. The experimental results su port FEM predictions for this system and, thus, build confi- dence in their application to systems more closely related to true composite Stress concentrations between a factor of 5 to 6 are predicted Matrix Crack by FEM for conditions similar to those typically considered for Sic-SiC systems(see Appendix). Stress concentrations of this magnitude are likely to make the systems inappropriate for many applications. Consider a uniaxial system with 30 vol%, 3 GPa fibers. The maximum room-temperature load Fig. Al. Schematic of axisymmetric FEM use carrying capacity after fusion would be -150 MPa (0.3 x concentration associated with fiber-matrix sealing, in Fig. 3 GPa+6). Application of a reasonable safety factor would Linear elastic behavior is assumed (for SiC, E restrict use to situations with very low expected loads, and 0. 2: for SiO,, E= 70 GPa and v =0.2). Radius of in most cases, a monolith would offer better performance. thickness of the sio, at the interface is r35 material(e.g, carbon or BN) in an oxidizing environment is expected to result in markedly decreased load-carrying SIC FIoRE SC.strix FEM analysis indicates that one approach to decrease stress concentrations in these systems would be to use an Silica sealant with an elastic modulus that is low compared The problem is that the number of available materials condensed-phase oxidation products with an elasti 品 below the 70 GPa of SiO, is, if not zero, very limited APPENDIX A FEM Modeling of Stress Concentration in a Sealed Composite System FEM described in the main body of the text has been de igned to emulate a single-fiber microcomposite. The work r35 S19 ported in this appendix extends the modeling to consider tw bulk unidirectional composites The model depicted resents a composite that has been stressed beyond the matrix cracking stress and held at constant load such that the crack remains open while inter- phase burnout and growth of the reaction product(SiO2)oc- curs. The result is a composite with stressed fibers fused to relaxed sections of matrix. If the stress state in the system emains constant, no stress concentration occurs. The assump- tion is that, at some point during service, the stress state in the Matrie Crack system changes, e.g., through subsequent loading, additional matrix cracking, or fiber failures. Any change in the local load ing conditions is subject to stress concentration in a fused A contour plot for the model system be rel- ess conced stress relative to the increase in the iber eports the increase in Fig. A2. C lot of maximum principal stress in a un ally fused at the matrix crack by a Sio seal at the matrix crack plane depicting Increase maximum principal stress due to an applied nominal stress with in Fig. A2. There are two areas with a notable stress concen-

boring fiber), the additional load carried by intact fibers would be intensified at the sealing points. The reality is that a fused system behaves similar to a flawed monolith. The presence of a stress concentration also assumes that the materials involved do not possess the ability to deform and accommodate the local strains. The modeling can, of course, be extended to include this effect, but, for SiO2, stress relaxation is expected to be insignificant, even to temperatures as high as 1500°C.13 V. Summary The nominal failure stress in SiC–SiC microcomposite specimens that had been oxidized to induce fusion decreased to less than half that observed in bare fibers with a similar thermal history. The loss of strength in oxidized microcompos￾ites is completely recovered following etching in HF to remove the SiO2 layer that binds the fiber to the matrix sheath. This result demonstrates that the decreased load at failure is entirely due to the presence of SiO2 that fuses the sheath to the fiber; i.e., it is a geometrical effect. The experimental results sup￾port FEM predictions for this system and, thus, build confi￾dence in their application to systems more closely related to true composites. Stress concentrations between a factor of 5 to 6 are predicted by FEM for conditions similar to those typically considered for SiC–SiC systems (see Appendix). Stress concentrations of this magnitude are likely to make the systems inappropriate for many applications. Consider a uniaxial system with 30 vol%, 3 GPa fibers. The maximum room-temperature load￾carrying capacity after fusion would be ∼150 MPa (0.3 × 3 GPa ÷ 6). Application of a reasonable safety factor would restrict use to situations with very low expected loads, and, in most cases, a monolith would offer better performance. Thus, interfacial sealing as a means to preserve an interphase material (e.g., carbon or BN) in an oxidizing environment is expected to result in markedly decreased load-carrying capability. FEM analysis indicates that one approach to decrease stress concentrations in these systems would be to use an interfacial sealant with an elastic modulus that is low compared to SiO2. The problem is that the number of available materials that form condensed-phase oxidation products with an elastic modulus below the 70 GPa of SiO2 is, if not zero, very limited. APPENDIX A FEM Modeling of Stress Concentration in a Sealed Composite System FEM described in the main body of the text has been de￾signed to emulate a single-fiber microcomposite. The work reported in this appendix extends the modeling to consider two bulk unidirectional composites. The model depicted in Fig. A1 represents a composite that has been stressed beyond the matrix cracking stress and held at constant load such that the crack remains open while inter￾phase burnout and growth of the reaction product (SiO2) oc￾curs. The result is a composite with stressed fibers fused to relaxed sections of matrix. If the stress state in the system remains constant, no stress concentration occurs. The assump￾tion is that, at some point during service, the stress state in the system changes, e.g., through subsequent loading, additional matrix cracking, or fiber failures. Any change in the local load￾ing conditions is subject to stress concentration in a fused system. A contour plot for the model system in the vicinity of the seal at the matrix crack plane depicting the relative increase in maximum principal stress due to an applied strain is presented in Fig. A2. There are two areas with a notable stress concen￾Fig. A1. Schematic of axisymmetric FEM used to evaluate the stress concentration associated with fiber–matrix sealing, as depicted in Fig. 1. Linear elastic behavior is assumed (for SiC, E 4 400 GPa and n 4 0.2; for SiO2, E 4 70 GPa and n 4 0.2). Radius of curvature at the crack plane is assumed to be r/70 (r is the fiber radius), and the thickness of the SiO2 at the interface is r/35. Fig. A2. Contour plot of maximum principal stress in a uniaxial SiC–SiC composite locally fused at the matrix crack by a SiO2 reac￾tion product (see Figs. 1 and A1). Scale reports the increase in local stress relative to the increase in the fiber nominal stress with tensile strain. 2602 Journal of the American Ceramic Society—Glime and Cawley Vol. 81, No. 10

October 1998 Stress Concentration Due to Fiber-Matrix Fusion in Ceramic-Matrix Composite. typically exists remote from the matrix crack plane. Figure A4 illustrates Fem used to evaluate the stress concentration in an Matr x interrupted interphase system. It is assumed that the radius of curvature at the seal is one-half the interphase thickness. This assumption represents a lower limit to stress concentration in act A contour plot of maximum principal stress(fiber nomi- nal 1)for a SiC-SiC system with an interrupted interphase thickness of r/25 (i.e, a 70 um fiber with a 3 um interphase) is shown in Fig. A5. A stress at the seal that is 5.3 times the feer ber nominal is observed A systematic parametric study has Fig. A3. Schematic of the interrupted interphase approach to inter- tions and that reducing the elastic modulus of the matrix/seal m Periodic fiber-matrix seals prevent runaway oxidation with respect to that of the fiber decreases the magnitude of the ase material upon exposure to the atmosphere following stress concentration leads to two probable outcomes. The first is crack propagation tration. The first occurs within the fiber adjacent to the SiO2 along the seal-fiber interface, separating the seal from the fi- seal. The increase in local stress in this region is-6 times ber. The second is crack extension across the interface and into higher than the nominal fiber stress The second occurs with the fiber. If the toughness of the seal or seal-fiber interface is the SiO2 seal near the end of the gap at the matrix crack plane ufficiently low. the an fail eav the fiber intact. That In this region, an increase in the stress is observed that is -3.5 is, crack propagation occurs parallel, rather than perpendicular modulus of the sic fiber is 6 times that of sio,. the stress in to the fiber axis. However the intended function of the seal is to localize interphase oxidation. Failure of the seal would de the SiO, seal at the crack plane is -20 times that expected for continued oxidation of the carbol the sio, in the absence of stress concentration effects. thus, a significant reduction in the effective fiber strength, or compos- interrupted interphase concept to provide oxidation resistance using a tough seal) can be achieved only at the expense of tion is larger than that expected for the microcomposite by a decreased composite strength associated with stress concentra factor >2. This is primarily due to the differences in the ge- tion at the interrupt ometry at the seal and indicates an even sharper decrease in load-bearing capacity than indicated by the data in Fig. 6 An interrupted interphase(Fig. A3) presents a slightly dif- ferent geometric situation than does the SiO, -sealed system. In this case, the matrix is bonded directly to the fiber rather than through a reaction product intermediary, and the bonded region Fice Matrix lar Interfacial Interfacial r了20 Fiber. Matrix o Fig. A4. Schematic axisymmetric FEM of an interrupted interphase system following matrix cracking and local interphase removal Linea elastic behavior is assumed (for SiC, E=400 GPa and v = 0.2, for urvature at the crack plane is assumed to be one-half the thickness of the original interphase (120), and the distance between the matrix crack plane and SiO, seal the increase in local stress relative to the increase in the fiber nominal vas chosen to be 4 times the fiber radius stress with tensile strain

tration. The first occurs within the fiber adjacent to the SiO2 seal. The increase in local stress in this region is ∼6 times higher than the nominal fiber stress. The second occurs within the SiO2 seal near the end of the gap at the matrix crack plane. In this region, an increase in the stress is observed that is ∼3.5 times the fiber nominal stress. Considering that the elastic modulus of the SiC fiber is ∼6 times that of SiO2, the stress in the SiO2 seal at the crack plane is ∼20 times that expected for the SiO2 in the absence of stress concentration effects. Thus, a significant reduction in the effective fiber strength, or compos￾ite load-carrying capacity, is predicted. The stress concentra￾tion is larger than that expected for the microcomposite by a factor >2. This is primarily due to the differences in the ge￾ometry at the seal and indicates an even sharper decrease in load-bearing capacity than indicated by the data in Fig. 6. An interrupted interphase (Fig. A3) presents a slightly dif￾ferent geometric situation than does the SiO2-sealed system. In this case, the matrix is bonded directly to the fiber rather than through a reaction product intermediary, and the bonded region typically exists remote from the matrix crack plane. Figure A4 illustrates FEM used to evaluate the stress concentration in an interrupted interphase system. It is assumed that the radius of curvature at the seal is one-half the interphase thickness. This assumption represents a lower limit to stress concentration in actual systems. A contour plot of maximum principal stress (fiber nomi￾nal 4 1) for a SiC–SiC system with an interrupted interphase thickness of r/25 (i.e., a 70 mm fiber with a 3 mm interphase) is shown in Fig. A5. A stress at the seal that is 5.3 times the fiber nominal is observed. A systematic parametric study has indicated, as expected, that thinner interphases (yielding lower radii of curvature at the seal) produce higher stress concentra￾tions and that reducing the elastic modulus of the matrix/seal with respect to that of the fiber decreases the magnitude of the stress concentration. Assuming failure of the interfacial seal precedes fiber failure leads to two probable outcomes. The first is crack propagation along the seal–fiber interface, separating the seal from the fi￾ber. The second is crack extension across the interface and into the fiber. If the toughness of the seal or seal–fiber interface is sufficiently low, the seal can fail, leaving the fiber intact. That is, crack propagation occurs parallel, rather than perpendicular, to the fiber axis. However, the intended function of the seal is to localize interphase oxidation. Failure of the seal would de￾feat this purpose by allowing continued oxidation of the carbon interphase. From this perspective, it is clear that the use of an interrupted interphase concept to provide oxidation resistance (using a tough seal) can be achieved only at the expense of decreased composite strength associated with stress concentra￾tion at the interrupt. Fig. A3. Schematic of the interrupted interphase approach to inter￾facial sealing. Periodic fiber–matrix seals prevent runaway oxidation of the interphase material upon exposure to the atmosphere following matrix cracking.5 Fig. A4. Schematic axisymmetric FEM of an interrupted interphase system following matrix cracking and local interphase removal. Linear elastic behavior is assumed (for SiC, E 4 400 GPa and n 4 0.2; for SiO2, E 4 70 GPa and n 4 0.2). Radius of curvature at the crack plane is assumed to be one-half the thickness of the original interphase (r/20), and the distance between the matrix crack plane and SiO2 seal was chosen to be 4 times the fiber radius. Fig. A5. Contour plot of maximum principal stress local to the fiber– matrix seal in an interrupted interphase system (Fig. A4). Scale reports the increase in local stress relative to the increase in the fiber nominal stress with tensile strain. October 1998 Stress Concentration Due to Fiber–Matrix Fusion in Ceramic-Matrix Composites 2603

2604 Journal of the American Ceramic Society-Glime and Cawle Vol 81. No. 10 APPENDIX B Microcomposite Residual Stress Due to Thermal Expansion Mismatch Upon cooling to room temperature, thermal expansion mis- match between the SiO2 reaction product and the SiC fiber and matrix sheath leads to residual stress in the microcomposite system FEM of the residual stress that develops upon cooling from 1100C (the oxidation anneal temperature)to room tem- perature has been performed, and a contour plot of the pre dicted maximum principal stresses is provided in Fig. Bl. Lin ear expansion coefficients have been used in the model and have been selected to represent the mean value for cooll from the anneal temperature to room temperature, 4x/o( for fused SiO, 4 and 4 x 10-6/C for the sCS SiC fiber and Si sheath D.9 A maximum thermally induced tensile stress of -100 MPa is 75 predicted in the fiber. The stress in the SiO2 near the joint is imarily compressive and <150 MPa. With the local stress concentration accounted for. the stresses in the SiO, and fiber ncrease, near fracture, to-I and 2 GPa, respectively. Although 0.45 the qualitative behavior of the system is not influenced dra- matically by the thermal stresses, the ratio of tensile stress 434 the fiber to that in the SiO, at the seal is increased compared to FEM predictions that do not consider thermally induced stress Fig. B2). For the microcomposite model, considering thermal stress in the analysis decreases the predicted maximum princi- pal stress in the SiO, from 1.7 to 1.3 GPa. Fig. B2. Contour plot of maximum principal stress for the model Acknowledgments: The authors would like to thank Mark Purdy and SiC-SiC microcomposite system. Scale indicates the local stress rela- Jeff Lewis. BFGoodrich OH, for providing chemic tive to the I gPa fiber nominal stress. Arrows indicate the direction of vapor deposition, and Greg Morscher, CWRU/NASA Lewis Research Center, the maximum principal stress. References C. Cao E. Bischoff. O. Sbaizero M. Rhile. A. G. Evans. D. B. Marshall and J J. Brennan, "Efiects of Interfaces on the Properties of Fiber-Reinforced .1g2 Ceramics, J. Am. Ceram. Soc., 73 16] 1691-9 Reactivity of Silicon Carbide and Carbon with Oxygen in Thermostructural Composites, "'Carbon, 31, 6 L. Filipuzzi and R. Naslain, " Oxidation Mechanisms and Kinetics of ID- SiC/C/SiC Composite Materials: IL, Modeling, J Am. Ceram. Soc., 77 [2] 467-80(1994 Camus, and R. Naslain, " Oxidati etics of ID-SiC/C/SIC Composite Materials: I, An Experimental Approach, JAm. Ceran.Soc.,771245966(1994) mic Transactions. Vol. 28. Advances in Ceramic Matris osites. Edited 518 by N. Bansal, Ar eramic Society, Westerville, OH, 199 bF E. Heredia, J. McNulty, F w. Zok, and A G. Evans, Oxidation Em- brittlement Probe for Ceramic-Matrix Composites, "JAm Ceram Soc., 7881 R 2097-100(1995) A.G. Evans, F W. Zok, R. M. MeMeeking, and Z Z. Du, ""Models of igh-Temperature, Environmentally Assiste ment in Ceramic-Matrix Composites, J. Am. Ceram. Soc., 79 192345-52(1996). 151. Wiley-Interscience, New York, 1997. lorscher, unpublished research, NASA Lewis Research Center 135 G. Cruciani, K. E. Spear, R. E. Tressler, and C. F. Ram- -0057 IM. D. Thouless, O. Sbaizero, L.S. Sigl, and A G. Evans, ""Effect of In- terface Mechanical Properties on Pullout in a SiC-Fiber luminum Silicate Glass-Ceramic, "J. Am. Ceram. Soc, 72 [4 525-32 (1989). Evans, M Fiber Cracking in Brittle Matrix Composites, J. Am. Ceram. Soc., 72 L N. P. Bansal and R. H. Doremus(Eds ) Handbook of Glass Properties, p I4Y. S. Tolukian(Ed. ) Thermophysical Properties of Matter-TPRC Data Fig. B1. Contour plot of maximum principal stress resulting from Series, VoL. 13: P. 358. IFI/Plenum, New York, 1970 ISM. K. Brun and M. P, Borom, ""Thermomechanical Properties of ermal expansion mismatch between SiO, and SiC upon cooling from sited Silicon Carbide Filaments, J. Am. Cera. Soc 1100C to room temperature. 1993-96(1989)

APPENDIX B Microcomposite Residual Stress Due to Thermal Expansion Mismatch Upon cooling to room temperature, thermal expansion mis￾match between the SiO2 reaction product and the SiC fiber and matrix sheath leads to residual stress in the microcomposite system. FEM of the residual stress that develops upon cooling from 1100°C (the oxidation anneal temperature) to room tem￾perature has been performed, and a contour plot of the pre￾dicted maximum principal stresses is provided in Fig. B1. Lin￾ear expansion coefficients have been used in the model and have been selected to represent the mean value for cooling from the anneal temperature to room temperature, 4 × 10−7/°C for fused SiO2 14 and 4 × 10−6/°C for the SCS SiC fiber and SiC sheath.15 A maximum thermally induced tensile stress of ∼100 MPa is predicted in the fiber. The stress in the SiO2 near the joint is primarily compressive and <150 MPa. With the local stress concentration accounted for, the stresses in the SiO2 and fiber increase, near fracture, to ∼1 and 2 GPa, respectively. Although the qualitative behavior of the system is not influenced dra￾matically by the thermal stresses, the ratio of tensile stress in the fiber to that in the SiO2 at the seal is increased compared to FEM predictions that do not consider thermally induced stress (Fig. B2). For the microcomposite model, considering thermal stress in the analysis decreases the predicted maximum princi￾pal stress in the SiO2 from 1.7 to 1.3 GPa. Acknowledgments: The authors would like to thank Mark Purdy and Jeff Lewis, BFGoodrich Aerospace, Brecksville, OH, for providing chemical vapor deposition, and Greg Morscher, CWRU/NASA Lewis Research Center, Cleveland, OH, for assistance in tensile testing. References 1 H. C. Cao, E. Bischoff, O. Sbaizero, M. Rhu¨le, A. G. Evans, D. B. Marshall, and J. J. Brennan, ‘‘Effects of Interfaces on the Properties of Fiber-Reinforced Ceramics,’’ J. Am. Ceram. Soc., 73 [6] 1691–99 (1990). 2 C. Vix-Guterl, J. Lahaye, and P. Ehrburger, ‘‘Reactivity of Silicon Carbide and Carbon with Oxygen in Thermostructural Composites,’’ Carbon, 31, 629– 35 (1993). 3 L. Filipuzzi and R. Naslain, ‘‘Oxidation Mechanisms and Kinetics of 1D￾SiC/C/SiC Composite Materials: II, Modeling,’’ J. Am. Ceram. Soc., 77 [2] 467–80 (1994). 4 L. Filipuzzi, G. Camus, and R. Naslain, ‘‘Oxidation Mechanisms and Ki￾netics of 1D-SiC/C/SiC Composite Materials: I, An Experimental Approach,’’ J. Am. Ceram. Soc., 77 [2] 459–66 (1994). 5 O. Unal, J. Cawley, K. Lagerlof, and S. Prybyla, ‘‘Intermittent Coatings for Continuous-Fiber-Reinforced Ceramic-Matrix Composites’’; pp. 223–34 in Ce￾ramic Transactions, Vol. 28, Advances in Ceramic Matrix Composites. Edited by N. Bansal. American Ceramic Society, Westerville, OH, 1993. 6 F. E. Heredia, J. McNulty, F. W. Zok, and A. G. Evans, ‘‘Oxidation Em￾brittlement Probe for Ceramic-Matrix Composites,’’ J. Am. Ceram. Soc., 78 [8] 2097–100 (1995). 7 A. G. Evans, F. W. Zok, R. M. McMeeking, and Z. Z. Du, ‘‘Models of High-Temperature, Environmentally Assisted Embrittlement in Ceramic-Matrix Composites,’’ J. Am. Ceram. Soc., 79 [9] 2345–52 (1996). 8 W. D. Pilkey, Peterson’s Stress Concentration Factors, 2nd ed.; pp. 122 and 151. Wiley-Interscience, New York, 1997. 9 G. N. Morscher, unpublished research, NASA Lewis Research Center, Cleveland, OH. 10C. E. Ramberg, G. Cruciani, K. E. Spear, R. E. Tressler, and C. F. Ram￾berg, ‘‘Passive-Oxidation Kinetics of High-Purity Silicon Carbide from 800° to 100°C,’’ J. Am. Ceram. Soc., 79 [11] 2897–911 (1996). 11M. D. Thouless, O. Sbaizero, L. S. Sigl, and A. G. Evans, ‘‘Effect of In￾terface Mechanical Properties on Pullout in a SiC-Fiber-Reinforced Lithium Aluminum Silicate Glass-Ceramic,’’ J. Am. Ceram. Soc., 72 [4] 525–32 (1989). 12A. G. Evans, M. Y. He, and J. W. Hutchinson, ‘‘Interface Debonding and Fiber Cracking in Brittle Matrix Composites,’’ J. Am. Ceram. Soc., 72 [12] 2300–303 (1989). 13N. P. Bansal and R. H. Doremus (Eds.), Handbook of Glass Properties; p. 226. Academic Press, Orlando, FL, 1986. 14Y. S. Tolukian (Ed.), Thermophysical Properties of Matter–TPRC Data Series, Vol. 13; p. 358. IFI/Plenum, New York, 1970. 15M. K. Brun and M. P. Borom, ‘‘Thermomechanical Properties of Chemi￾cally Vapor Deposited Silicon Carbide Filaments,’’ J. Am. Ceram. Soc., 72 [10] 1993–96 (1989). h Fig. B2. Contour plot of maximum principal stress for the model SiC–SiC microcomposite system. Scale indicates the local stress rela￾tive to the 1 GPa fiber nominal stress. Arrows indicate the direction of the maximum principal stress. Fig. B1. Contour plot of maximum principal stress resulting from thermal expansion mismatch between SiO2 and SiC upon cooling from 1100°C to room temperature. 2604 Journal of the American Ceramic Society—Glime and Cawley Vol. 81, No. 10