Journal J.Am. Cera. Soc,84S]1043-5102001) Mechanical Properties of Two Plain-Woven Chemical Vapor Infiltrated Silicon Carbide-Matrix Composites Torben K. Jacobsen and Povl brondsted Materials Research Department, Rise National Laboratory, DK-4000 Roskilde, Denmark The elastic and inelastic properties of a chemical vapor but it fails in providing average interfacial properties because of infiltrated (Cvn Sic matrix reinforced with either plain the few interfaces tested woven carbon fibers(C/siC)or SiC fibers (SiC/SiC) have been A further complication occurs for cross-ply or plain-woven investigated. It has been investigated whether the mechanics of composites that are most likely to be used in design of real a plain weave can be described using the theory of a cross-ply components. In cross-ply laminates, cracks in the transverse plies laminate, because it enables a simple mechanics approach to decrease the stiffness of the composite. 6, 12-22 For CMCs, this the nonlinear mechanical behavior. The influences of inter. stiffness decrease is quite severe because the ceramic matrix has a phase, fiber anisotropy, and porosity are included. The ap- similar or higher elastic modulus than the fiber. However, in iber/matrix system with an interface. The tensile behavior is more complex because of bundle waviness, cross-sectional shape fib described by five damage stages. C/SiC can be modeled using of the bundles, porous matrix, and large voids between the one damage stage and a constant damage parameter. The infiltrated bundles. 1, An efficient approach for analyzing the tensile behavior of SiC/SiC undergoes four damage stages. continuum behavior of these materials is continuum damage Stiffness reduction due to transverse cracks in the transverse mechanics, where various damage modes and directions are bundles is very different from cross-ply behavior. Compressive described by phenomenological damage parameters. 1,3 failure is initiated by interlaminar cracks between the fiber In this article, we attempt to treat the plain weave as bundles. The crack path is dictated by the bundle waviness. symmetric cross-ply laminate. Furthermore, the thickness an For siC/SiC, the compressive behavior is mostly linear to elastic properties of the interphase are included and the interphase failure. C/SiC exhibits initial nonlinear behavior because of and fiber are connected to form a modified fiber with properties residual crack openings, Above the point where the cracks dependent on these two constituents. The porosity in the matrix close, the compressive behavior is linear Global compressive counted for, resulting in a matrix with modified properties. The failure is characterized by a major crack oriented at a certain advantage of this approach is the straightforward use of multiple ingle to the axial loading. In shear, the matrix cracks orientate models for inelasticity reported in the literature. 2, 18.122735-39 in the principal tensile stress direction (i.e, 45 to the fiber Models for characteristic damage stages have been collected direction) with very high crack densities before failure, but from the literature and used for setting up a general methodology only Sic/SiC shows significant degradation in shear modulus. for modeling the tensile behavior of cross plies and possibly plain Hysteresis is observed during unloading/reloading sequences weaves. For one of the materials, the tensile behavior can be and increasing permanent strain described by a single, constant damage parameter, TLo. To provide a complete description of the in-plane mechanical properties, shear and compressive tests have been conducted. The nonlinear shear L. Introduction behavior is characterized experimentally with regard to stiffness degradation, permanent strain, and failure mode. Compressive failure appearance is studied, and directions for future modeling or composites( CMCs)is strongly linked to the elastic properties are suggested constant interfacial frictional shear stress t between fiber and matrix depends on volume fractions and elastic properties of the IL. Experimental Procedure constituents -6 variations in t on similar materials observed from Material experimenter to experimenter may reflect variations in the elastic properties and the underlying modeling assumptions Two plain-weave-based CMCs were tested. The materials were Pullout or pushout tests are widely used for estimating interfa- supplied by MAN-Technologie AG, Munich, Germany. The ma- cial properties of single fibers within a composi terials were processed using the CVI method. The fibers were precoated with a thin interphase layer of pyrolytic carbon using pproach particularly appropriate for the chemical vapor infiltra. CVI. Subsequently, the weave was infiltrated with Sic as matrix on(CvI)process is to coat a single fiber with an annulus of interphase( typically carbon or BN) and matrix material(typically material. Two different fibers were used: a carbon fiber(Torayca Sic) and load this microcomposite in tension. Common to all M30, Toray Industries, Ohtsu, Japan) and a Sic fiber(Tyran TY-SIHI6EL, UBE Industries, Yamaguchi, Japan). The Tyran one test specimen to the fiber was different from the Nicalon fiber used in other investig next are observed. The main advantage of the single-fiber test is tions 2, 6 23,24 26737,40 The material with the sic fiber was that it allows for qualitative process optimization of the interphase denoted SiC/SiC, and that with the carbon fiber C/SiC. The plates were 5 mm thick, which is twice the thickness of previous studies of SiC/SiC. Figure I shows the interior plain-woven structure of C/SiC. The bundles are point-wise connected from sheet to B. N. Cox--contributing editor sheet(similar appearance for SiC/SiC). This was also observed in Ref. 29 The fiber packing was nonuniform, with the highest fiber volume fraction in the center of the bundles. Small porosities Manuscript No 190608 Received October 28, 1997; approved March 15, 2000. existed within the bundles, and large interbundle pores existed
Mechanical Properties of Two Plain-Woven Chemical Vapor Infiltrated Silicon Carbide-Matrix Composites Torben K. Jacobsen and Povl Brøndsted Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark The elastic and inelastic properties of a chemical vapor infiltrated (CVI) SiC matrix reinforced with either plainwoven carbon fibers (C/SiC) or SiC fibers (SiC/SiC) have been investigated. It has been investigated whether the mechanics of a plain weave can be described using the theory of a cross-ply laminate, because it enables a simple mechanics approach to the nonlinear mechanical behavior. The influences of interphase, fiber anisotropy, and porosity are included. The approach results in a reduction of the composite system to a fiber/matrix system with an interface. The tensile behavior is described by five damage stages. C/SiC can be modeled using one damage stage and a constant damage parameter. The tensile behavior of SiC/SiC undergoes four damage stages. Stiffness reduction due to transverse cracks in the transverse bundles is very different from cross-ply behavior. Compressive failure is initiated by interlaminar cracks between the fiber bundles. The crack path is dictated by the bundle waviness. For SiC/SiC, the compressive behavior is mostly linear to failure. C/SiC exhibits initial nonlinear behavior because of residual crack openings. Above the point where the cracks close, the compressive behavior is linear. Global compressive failure is characterized by a major crack oriented at a certain angle to the axial loading. In shear, the matrix cracks orientate in the principal tensile stress direction (i.e., 45° to the fiber direction) with very high crack densities before failure, but only SiC/SiC shows significant degradation in shear modulus. Hysteresis is observed during unloading/reloading sequences and increasing permanent strain. I. Introduction THE modeling of the mechanical performance of ceramic-matrix composites (CMCs) is strongly linked to the elastic properties of the nominally damage-free material. The magnitude of the constant interfacial frictional shear stress t between fiber and matrix depends on volume fractions and elastic properties of the constituents.1–6 Variations in t on similar materials observed from experimenter to experimenter may reflect variations in the elastic properties and the underlying modeling assumptions.7 Pullout or pushout tests are widely used for estimating interfacial properties of single fibers within a composite.7–10 Another approach particularly appropriate for the chemical vapor infiltration (CVI) process is to coat a single fiber with an annulus of interphase (typically carbon or BN) and matrix material (typically SiC) and load this microcomposite in tension.11 Common to all these methods is that large variations from one test specimen to the next are observed. The main advantage of the single-fiber test is that it allows for qualitative process optimization of the interphase, but it fails in providing average interfacial properties because of the few interfaces tested. A further complication occurs for cross-ply or plain-woven composites that are most likely to be used in design of real components. In cross-ply laminates, cracks in the transverse plies decrease the stiffness of the composite.6,12–22 For CMCs, this stiffness decrease is quite severe because the ceramic matrix has a similar or higher elastic modulus than the fiber. However, in CVI-manufactured plain-woven CMCs, the cracking behavior is more complex because of bundle waviness, cross-sectional shape of the bundles, porous matrix, and large voids between the infiltrated bundles.21,23–33 An efficient approach for analyzing the continuum behavior of these materials is continuum damage mechanics, where various damage modes and directions are described by phenomenological damage parameters.31,34 In this article, we attempt to treat the plain weave as a symmetric cross-ply laminate. Furthermore, the thickness and elastic properties of the interphase are included and the interphase and fiber are connected to form a modified fiber with properties dependent on these two constituents. The porosity in the matrix is accounted for, resulting in a matrix with modified properties. The advantage of this approach is the straightforward use of multiple models for inelasticity reported in the literature.12,18,22,35–39 Models for characteristic damage stages have been collected from the literature and used for setting up a general methodology for modeling the tensile behavior of cross plies and possibly plain weaves. For one of the materials, the tensile behavior can be described by a single, constant damage parameter, tL0. To provide a complete description of the in-plane mechanical properties, shear and compressive tests have been conducted. The nonlinear shear behavior is characterized experimentally with regard to stiffness degradation, permanent strain, and failure mode. Compressive failure appearance is studied, and directions for future modeling are suggested. II. Experimental Procedure (1) Materials Two plain-weave-based CMCs were tested. The materials were supplied by MAN-Technologie AG, Munich, Germany. The materials were processed using the CVI method. The fibers were precoated with a thin interphase layer of pyrolytic carbon using CVI. Subsequently, the weave was infiltrated with SiC as matrix material. Two different fibers were used: a carbon fiber (Torayca M30, Toray Industries, Ohtsu, Japan) and a SiC fiber (Tyranno TY-S1H16EL, UBE Industries, Yamaguchi, Japan). The Tyranno fiber was different from the Nicalon fiber used in other investigations.12,16,21,23,24,26,37,40 The material with the SiC fiber was denoted SiC/SiC, and that with the carbon fiber C/SiC. The plates were 5 mm thick, which is twice the thickness of previous studies of SiC/SiC. Figure 1 shows the interior plain-woven structure of C/SiC. The bundles are point-wise connected from sheet to sheet (similar appearance for SiC/SiC). This was also observed in Ref. 29. The fiber packing was nonuniform, with the highest fiber volume fraction in the center of the bundles. Small porosities existed within the bundles, and large interbundle pores existed B. N. Cox—contributing editor Manuscript No. 190608. Received October 28, 1997; approved March 15, 2000. J. Am. Ceram. Soc., 84 [5] 1043–51 (2001) 1043 journal
1044 Journal of the American Ceramic Sociery-Jacobsen and Brondsted Vol 84. No 5 Compressive specimens(Fig. 2(b)were initially cast into one cylinder, then two cylinders were put into an alignment fixture, and the specimen was cast into the second cylinder. The testing entity was then placed and tested between two plane-parallel disks mounted in the testing machine. The in-plane C-z)shear tests Pointy were conducted using the losipescu test specimen, with ar optimized V-notch angle,43(Fig. 2(c)) Interbundle mental results Bundle Figs. 3(a) and 4(a) for SiC/SiC and C/SiC, respectively. Shear stress-strain curves are shown in Fig. 5. Stress-strain curves for compressive behavior are shown in Fig. 6 for both materials. The elastic composite properties from the initial part of the respective stress-strain curves are shown in Table I. where E is the initial 1mm stiffness. y the Poisson ratio. g the shear stiffness. and g and T the stress at the first measurable deviation from linearity of the ig. 1. Plain-woven structure of C/SiC. Sample tensile and the shear stress-strain curve, respectively. Calculated point-wise connectivity between the bundles and interbundle pores is properties are the coefficient of thermal expansion (a), the residual stress on the 90 ply(), and the radial residual stress acting at the fiber/matrix interface(o ) The tensile/compressive loading is applied in the y-direction, and the in-plane properties are in the between the bundles. The fabric design of SiC/SiC was 1600 J-z-plane(ig. 2). In tension, C/SiC has no initial elastic region filaments/bundle and 0.59 rovings/mm. The C/SiC fabric was 1000 gme=0). The instantaneous elastic stiffnesses at a given peak filaments/bundle and 0.90 rovings/mm. As-received SiC/SiC stress(Ey) and G of the damaged composite are the slope of the showed no matrix cracks, whereas the C/Sic was significantly unloading curve at the peak stress 36.44 The literature reports that precracked in the 90 bundles Ey is approximated by an average modulus defined as the stress range divided by the strain range, i.e., neglecting the anelastic (2) Experimental Procedure hysteresis behavior. Tension, compression, and shear testing of the two materials The strength properties of the materials are shown in Table Il, were performed in air and at room temperature using servo- where S is the tensile strength, Es the tensile strain to failure, Tthe ontrolled test machines with 100 kN load cells (Instron Corp shear strength, yr the engineering shear strain to failure, Scom the anvers, MA). The tension tests were performed at constant load compressive strength, and Ecom the compressive strain to failure rate(5 MPa/s). Constant displacement rates were applied for the compression(0.001 mm/s)and shear tests(0. 1 mm/min). Periodic (4 Damage Mechanisms unloadings at peak loads were performed to measure changes in (A) SiC/SiC: The matrix-cracking sequence obtained from stiffness and hysteresis. Tensile and compressive specimens were the replicas of SiC/SiC revealed that, above the elastic limit unloaded to 70% of the previous peak load, and replicas were continuous matrix cracking took place until fracture. First, matrix taken of a polished edge. The replicas were then examined using cracks emanated from large porosities at stresses above - 0.1IS. optical light microscopy. Fracture surfaces were examined usin Second tunneling matrix cracking in the 90 bundles occurred at anning electron microscopy(SEM; Model JSM-6300F, JEOL tresses from 0.45S to -0 82S, above which the matrix cracking abody, MA). Test specimens are shown in Fig. 2. Strain gauge in the 90o bundles saturated. Tunneling cracks in SiC/SiC are measured the in-plane and out-of-plane strains and were mounted shown in Fig. 7. At stresses above 0.55S tunneling matrix cracks on all test specimens. A 10 mm gauge length extensometer started to grow into the 0 bundles. A few cracks penetrated the 0 (Instron)measured the strain in the loading direction for the tensile bundles below 0. 55S. Third, at stresses above 0.82S and until tests fractured delamination, cracks started to grow between the 0 and Lamina Tabs # se Strain gauges in +45°and-45° directions SiC/SIC C/SIC 200 b) Fig. 2. Test geometries, coordinate system, and specimen dimensions for(a) tensile specimens, (b) compressive specimen, and (c) shear specimen
between the bundles. The fabric design of SiC/SiC was 1600 filaments/bundle and 0.59 rovings/mm. The C/SiC fabric was 1000 filaments/bundle and 0.90 rovings/mm. As-received SiC/SiC showed no matrix cracks, whereas the C/SiC was significantly precracked in the 90° bundles. (2) Experimental Procedure Tension, compression, and shear testing of the two materials were performed in air and at room temperature using servocontrolled test machines with 100 kN load cells (Instron Corp., Danvers, MA). The tension tests were performed at constant load rate (5 MPa/s). Constant displacement rates were applied for the compression (0.001 mm/s) and shear tests (0.1 mm/min). Periodic unloadings at peak loads were performed to measure changes in stiffness and hysteresis. Tensile and compressive specimens were unloaded to 70% of the previous peak load, and replicas were taken of a polished edge. The replicas were then examined using optical light microscopy. Fracture surfaces were examined using scanning electron microscopy (SEM; Model JSM-6300F, JEOL, Peabody, MA). Test specimens are shown in Fig. 2. Strain gauges measured the in-plane and out-of-plane strains and were mounted on all test specimens. A 10 mm gauge length extensometer (Instron) measured the strain in the loading direction for the tensile tests. Compressive specimens (Fig. 2(b)) were initially cast into one cylinder, then two cylinders were put into an alignment fixture, and the specimen was cast into the second cylinder. The testing entity was then placed and tested between two plane-parallel disks mounted in the testing machine. The in-plane (y– z) shear tests were conducted using the Iosipescu test specimen,41 with an optimized V-notch angle42,43 (Fig. 2(c)). (3) Experimental Results Stress–strain curves for the tension experiments are shown in Figs. 3(a) and 4(a) for SiC/SiC and C/SiC, respectively. Shear stress–strain curves are shown in Fig. 5. Stress–strain curves for compressive behavior are shown in Fig. 6 for both materials. The elastic composite properties from the initial part of the respective stress–strain curves are shown in Table I, where E is the initial stiffness, n the Poisson ratio, G the shear stiffness, and smc and tmc the stress at the first measurable deviation from linearity of the tensile and the shear stress–strain curve, respectively. Calculated properties are the coefficient of thermal expansion (a), the residual stress on the 90° ply (sR ), and the radial residual stress acting at the fiber/matrix interface (sr R ). The tensile/compressive loading is applied in the y-direction, and the in-plane properties are in the y-z-plane (Fig. 2). In tension, C/SiC has no initial elastic region (smc 5 0). The instantaneous elastic stiffnesses at a given peak stress (Ey) and Gyz of the damaged composite are the slope of the unloading curve at the peak stress.36,44 The literature reports that Ey is approximated by an average modulus defined as the stress range divided by the strain range, i.e., neglecting the anelastic hysteresis behavior. The strength properties of the materials are shown in Table II, where S is the tensile strength, εS the tensile strain to failure, T the shear strength, gT the engineering shear strain to failure, Scom the compressive strength, and εcom the compressive strain to failure. (4) Damage Mechanisms (A) SiC/SiC: The matrix-cracking sequence obtained from the replicas of SiC/SiC revealed that, above the elastic limit, continuous matrix cracking took place until fracture. First, matrix cracks emanated from large porosities at stresses above ;0.11S. Second, tunneling matrix cracking in the 90° bundles occurred at stresses from ;0.45S to ;0.82S, above which the matrix cracking in the 90° bundles saturated. Tunneling cracks in SiC/SiC are shown in Fig. 7. At stresses above ;0.55S tunneling matrix cracks started to grow into the 0° bundles. A few cracks penetrated the 0° bundles below 0.55S. Third, at stresses above ;0.82S and until fractured delamination, cracks started to grow between the 0° and Fig. 1. Plain-woven structure of C/SiC. Sample was split and the point-wise connectivity between the bundles and interbundle pores is shown. Fig. 2. Test geometries, coordinate system, and specimen dimensions for (a) tensile specimens, (b) compressive specimen, and (c) shear specimen (Iosipescu). 1044 Journal of the American Ceramic Society—Jacobsen and Brøndsted Vol. 84, No. 5
May 2001 Mechanical Properties of Two Plain-Woven Cvl SiC-Matrix Composites 1045 SiC/SIC SImubation be苏 0.5 (b) Composite Strain, E(%) Fig 3. (a) Experimental stress-strain behavior of SiC/SiC Crack closure occurs below 20 MPa(insert).(b) Simulated stress-strain behavior of SiC/SiC Permanent strains are smaller than the ones obtained experimentally. (o/o,=0.86, or- 26 MPa, and T=80 MPa. 250 C/sic Experim Simulation 435 GPa 200+tL,=4.5MPamm 150 十士叶 HHHHH 0000.050.100.150.200.250300.35 0050.100150200.25030035 Composite Strain, e( (b) 4.(a) Experimentally observed stress-strain behavior of C/Sic (b) Simulated stress-strain behavior of C/SiC with TLo =4.5 MPa mm and oT=240 8150 specimen tailed before 9as 0.8 Engineering Shear Strain, 'y(%) Engineering Shear Strain, %y(%) Fig. 5. Shear stress-strain behavior of (a) SiC/SiC and(b)C/SiC, with periodic unloading/reloading. 90 bundles. No saturation of matrix cracking was observed in the The tunneling crack density (Loo) in the 90 bundles was 0° bundles estimated by counting the number of cracks within a bundle and Delamination crack growth was caused by crack bra anching dividing this number by the bundle width Only tunneling cracks from a 90 tunneling matrix crack. The tunneling matrix crack spanning the bundle height were included, and the small, porosi the 90 bundle had a curly pattern and ran preferably around the induced cracks in the matrix-rich regions were not included, fiber or through the interphase. A similar behavior has been because they branched in various directions observed in a SiC/CAS cross-ply laminate. Except for delani- Matrix cracks and, consequently, the matrix crack spacing in the nation behavior, the above-described behavior for SiC/SiC was 0 bundles (Lo)occurred only in cross sections where the bundles onsistent with observations by several investigators. 4 26,28-31,34 were cut at the tapered end. In the middle of the bundles, the The delamination may have been due to an edge effect or fiber-packing arrangement was too dense to show transverse processing problems related to the thickness of the composit matrix cracks, if any existed. The matrix-cracking densities varied tested(difficulties in infiltrating a thick laminate) linearly with stress. The ex ntally observed evolution of
90° bundles. No saturation of matrix cracking was observed in the 0° bundles. Delamination crack growth was caused by crack branching from a 90° tunneling matrix crack. The tunneling matrix crack in the 90° bundle had a curly pattern and ran preferably around the fiber or through the interphase. A similar behavior has been observed in a SiC/CAS cross-ply laminate.13 Except for delamination behavior, the above-described behavior for SiC/SiC was consistent with observations by several investigators.24,26,28–31,34 The delamination may have been due to an edge effect or processing problems related to the thickness of the composite tested (difficulties in infiltrating a thick laminate). The tunneling crack density (L90) 21 in the 90° bundles was estimated by counting the number of cracks within a bundle and dividing this number by the bundle width. Only tunneling cracks spanning the bundle height were included, and the small, porosityinduced cracks in the matrix-rich regions were not included, because they branched in various directions. Matrix cracks and, consequently, the matrix crack spacing in the 0° bundles (L0) occurred only in cross sections where the bundles were cut at the tapered end. In the middle of the bundles, the fiber-packing arrangement was too dense to show transverse matrix cracks, if any existed. The matrix-cracking densities varied linearly with stress. The experimentally observed evolution of Fig. 4. (a) Experimentally observed stress–strain behavior of C/SiC (b) Simulated stress–strain behavior of C/SiC with tL0 5 4.5 MPazmm and sT 5 240 MPa. Fig. 5. Shear stress–strain behavior of (a) SiC/SiC and (b) C/SiC, with periodic unloading/reloading. Fig. 3. (a) Experimental stress–strain behavior of SiC/SiC. Crack closure occurs below 20 MPa (insert). (b) Simulated stress–strain behavior of SiC/SiC. Permanent strains are smaller than the ones obtained experimentally. (si /sp 5 0.86, sT 5 26 MPa, and t 5 80 MPa.) May 2001 Mechanical Properties of Two Plain-Woven CVI SiC-Matrix Composites 1045
Journal of the American Ceramic Sociery-acobsen and Brondsted Vol. 84. No. 5 Table L. Elastic Properties and Characteristic Stresses of the Materials (GPa) (GPa) vn,=v, v (GPa) (GPa)(X10-6K-)(X10-6K-)(MPa)(MiPa)(MPa)(MPa) SiC/SiC Calculated 1550.200.1 0.220.14 Compression 1700.260.20 C/SiC Calculated 1460.210.0828 111117 Tension Compression 110.1400.230.08 lated properties are shown in the first line, mea erties in the second ticients of thermal he initial slope and the slope at the sure stress(c )of the stress-strain curve, respec lso see Fig. 6). Measured by the manufacturer, Sygulla et al. Table Il. Strength Properties of Sic/SiC and C/sic (o)=18s-045)eakm)04555082 IPa 3230.681760.60 For a/s > 0.82, the crack density in the 90 bundles remained 0.32 0.82 -521-0.42 constant at(Loo)=7 cracks/mm (B) C/SiC: The as-received material contained tunneling matrix cracks in the 90 bundle and some delamination between the 0o and 90o bundles. a few transverse matrix cracks were al crack density in the 0o bundles as a function of peak stress was observed in the 0 bundles. Replicas taken during the unload fitted using the following expression eloading procedure revealed no further damage. After fracture, a piece of material lying outside the replicated region was embedded (a=31(-045)cracks/mm) az045 (1) in epoxy, polished, and investigated using optical microscopy Similar to the 90 bundles, the crack density (Loo) is given by ξ-100十acsc e-200 -500 -600 10 0.6-05-04-03-0.2-0100.10.2 Fig 8. Fracture surface of C/SiC showing a high crack density and small particles on the fibers that may be responsible for very high friction Strain(%) between fiber and matrix, leading to high local crack densities Fig. 6. Compressive stress-strain behavior of SiC/SiC and C/SiC. 39100m V Smooth SiC-fiber VV SiC-matrix AC-interphase Fig 9. Fracture surface of SiC/SiC showing carbon interphase sticking to Fig. 7. Fracture surface of SiC/SiC showing tunneling cracks the Sic fiber and sawtooth failure of the interphase
crack density in the 0° bundles as a function of peak stress was fitted using the following expression: ~L0! 21 5 31.6S s S 2 0.45D ~cracks/mm! s S $ 0.45 (1) Similar to the 90° bundles, the crack density (L90) 21 is given by ~L90! 21 5 18.9S s S 2 0.45D ~cracks/mm! 0.45 # s S # 0.82 (2) For a/S . 0.82, the crack density in the 90° bundles remained constant at (L90) 21 5 7 cracks/mm. (B) C/SiC: The as-received material contained tunneling matrix cracks in the 90° bundle and some delamination between the 0° and 90° bundles. A few transverse matrix cracks were also observed in the 0° bundles. Replicas taken during the unloading/ reloading procedure revealed no further damage. After fracture, a piece of material lying outside the replicated region was embedded in epoxy, polished, and investigated using optical microscopy. Fig. 6. Compressive stress–strain behavior of SiC/SiC and C/SiC. Fig. 7. Fracture surface of SiC/SiC showing tunneling cracks. Fig. 8. Fracture surface of C/SiC showing a high crack density and small particles on the fibers that may be responsible for very high friction between fiber and matrix, leading to high local crack densities. Fig. 9. Fracture surface of SiC/SiC showing carbon interphase sticking to the SiC fiber and sawtooth failure of the interphase. Table I. Elastic Properties and Characteristic Stresses of the Materials† Ex (GPa) Ey 5 Ez (GPa) nxy 5 nxz nyz Gxy 5 Gxz (GPa) Gyz (GPa) ax (31026 K21 ) ay 5 az (31026 K21 ) smc (MPa) tmc (MPa) sR (MPa) sr R (MPa) SiC/SiC Calculated 124 155 0.20 0.16 56 60 4.2 3.7 14 26 Tension 147 0.22 0.14 60 4‡ 4‡ 41 48 Compression 170 0.26 0.20 C/SiC Calculated 56 146 0.21 0.08 28 37 4.5 1.7 111 117 Tension 113 0.16 0.04 40 5‡ 3‡ 0 44 Compression 110,140 0.23 0.08 † Calculated properties are shown in the first line, measured tensile properties in the second line along with shear properties and coefficients of thermal expansion, and compressive properties in the third line for each of the materials. Two values for the compressive stiffness along the y- or z-direction denote the initial slope and the slope at the crack closure stress (scl) of the stress–strain curve, respectively (also see Fig. 6). ‡ Measured by the manufacturer, Sygulla et al. Table II. Strength Properties of SiC/SiC and C/SiC S (MPa) εS (%) T (MPa) gT (%) Scom (MPa) εcom (%) SiC/SiC 323 0.68 176 0.60 2632 20.39 C/SiC 200 0.32 150 0.82 2521 20.42 1046 Journal of the American Ceramic Society—Jacobsen and Brøndsted Vol. 84, No. 5
May 2001 Mechanical Properties of Two Plain-Woven Cvl SiC-Matrix Composites 047 This investigation revealed regions with a low crack spacing Lo of Tunneling cracking releases residual on the lamina 10-20 um)and regions with no matrix cracks in the 0 bundles level, leading to permanent deformation ons and tun unneling crack SEM investigations of the fracture surface also revealed a high openings at complete unloading Rewriting Its obtained in crack density(Fig. 8). The tunneling crack spacing Lgo in the 90 Ref 18, the permanent strain ep at complete unloading is given by bundles remained constant at an average of 124 um. Conse- quently, there were no experimental observations of evolution of matrix cracks in the bundles as a function of stress for this SoCE+E h material The above solution is unbounded, but an upper bound is the situation where the stress in the o' ply is zero, i.e., the permanent Ill. Theory of Tensile Behavior strain is the negative of the initial strain in the 0' plies. Therefore, (1 Damage-Free Properties the solution is bounded by the limit The stacked, plain-woven composite is treated as E +ero symmetric cross-ply laminate. The height of each ply equal to the maximum height of a bundle. The analytica Ey for calculating damage-free properties based on the properties is shown elsewhere" and reviewed briefly here. The interphase adheres preferably to the fiber after debonding and stage Il, multiple matrix cracking occurs simultaneo therefore, assumed to connect to the fiber(Fig. 9). The porosity is compliance of the 0 ply Eo can be written as in stage Il.The and 90. plies. We assume that lo =loo in assumed to alter the matrix properties. Such a procedure leads to a fiber/matrix system with an interface that subsequently can be used for interpretation of the inelastic behavior E-E+ D (10) (2) Tensile Behavior The nonlinear behavior is divided into five damage stages Stage 0 defines the damage-free composite exhibiting a linea D.=E(-en2+b)(= (11) elastic behavior. In Stage I, the cracking is confined to the 90o olies until stage Il is reached, where the 90 ply cracks penetrate where a and b are nondimensional constants defined in Ref. 35. Vr into the 0 plies. Stage Ill defines 90 ply crack saturatio is the volume fraction of fibers, Em the Young modulus of the delamination between the plies, and continuous cracking in the 0 matrix, and T a constant interfacial shear stress. The composite lies. Stage IV is fiber fracture and pullout. This idealized compliance is given by- composite behavior is consistent with experimental observations on brittle-matrix fiber-reinforced cross-ply materials. 2,13, 15-7 (A) Stage F90 Ply-Tunneling Cracks: The increase 1+C1+2D (12) composite compliance due to tunneling cracks can be written as Assuming that the strains in the 90 and 0 plies are equal, the 11 1+C1 effective stress(o) acting on the 0 ply is appr An approximation for CI based on finite-element calculations 1+ Cit+ 2DIEL (C) Stage I-0 Ply Cracking and Delamination: In stage C (4) the mechanical behavior is fully controlled by the o ply, and compliance becomes The nondimensional constant Ci depends weakly on strongly on the ply modulus ratio ELeT. A relationship EOR 1+D Loo and the applied composite stress o is derived in Ref. p between can be rewritten as and the stress on the 0 ply is given by uo= 2o E+E The analysis of the nonlinear monotonic tensile behavior of the 0 ply is based on the stress-displacement analysis by Hutchinson and Jensenof a fiber being pulled out of a brittle matrix against friction. The analysis can be rewritten in terms of stress and strain, 时时m finite-element solutions for small debond lengths with the fiber radius R(R< 1).The ove train E for a multiple-cracked unidirectional laminate onsists of three strain contributions that can be written ass Ee tEttE ET or E+(En-E1+2H2o0-o)n+-(5) From Eq(5), the critical stress for the onset of tunneling cracking where the strain subscipts e, T, and s refer to the elastic, thermal (onst) can be derived as loo→∞ and sliding contributions, respectively, and E t E Rb2(1-V4a1)2 4EmVTLo Using Eq. (5), the compliance change can be simulated as a In Eq (15), the stresses are given by function of composite stress. At crack densities h/Lgo 2, further cracking in the 90 plies has little effect on stiffness
This investigation revealed regions with a low crack spacing (L0 of ;10–20 mm) and regions with no matrix cracks in the 0° bundles. SEM investigations of the fracture surface also revealed a high crack density (Fig. 8). The tunneling crack spacing L90 in the 90° bundles remained constant at an average of 124 mm. Consequently, there were no experimental observations of evolution of matrix cracks in the bundles as a function of stress for this material. III. Theory of Tensile Behavior (1) Damage-Free Properties The stacked, plain-woven composite is treated as a classical symmetric cross-ply laminate. The height of each ply (2h) is set equal to the maximum height of a bundle. The analytical approach for calculating damage-free properties based on the constituent properties is shown elsewhere45 and reviewed briefly here. The interphase adheres preferably to the fiber after debonding and is, therefore, assumed to connect to the fiber (Fig. 9). The porosity is assumed to alter the matrix properties. Such a procedure leads to a fiber/matrix system with an interface that subsequently can be used for interpretation of the inelastic behavior. (2) Tensile Behavior The nonlinear behavior is divided into five damage stages. Stage 0 defines the damage-free composite exhibiting a linear elastic behavior. In Stage I, the cracking is confined to the 90° plies until stage II is reached, where the 90° ply cracks penetrate into the 0° plies. Stage III defines 90° ply crack saturation, delamination between the plies, and continuous cracking in the 0° plies. Stage IV is fiber fracture and pullout. This idealized composite behavior is consistent with experimental observations on brittle-matrix fiber-reinforced cross-ply materials.12,13,15–17 (A) Stage I—90° Ply-Tunneling Cracks: The increase in composite compliance due to tunneling cracks can be written as22 1 Ey 5 1 Ey 0 S 1 1 C1 h L90D (3) An approximation for C1 based on finite-element calculations is18,22 C1 5 C1 0 tanhS ET C1 0 EL L90 h D (4) The nondimensional constant C1 0 depends weakly on Vf , but strongly on the ply modulus ratio EL/ET. 22 A relationship between L90 and the applied composite stress s is derived in Ref. 18, and can be rewritten as s 5 3 G90E# y 0 hC1 0 tanhS ET C1 0 EL L90 h D4 1/ 2 2 EL 1 ET 2ET sR (5) where G90 is the toughness of the 90° ply in the tunneling cracking mode and E# y 0 the plane strain modulus of the cross ply, given as E# y 0 5 1 2 ELS1 1 EL ET D EL ET 2 nL 2 (6) From Eq. (5), the critical stress for the onset of tunneling cracking (sonset) can be derived as L90 3 `: sonset 5 S G90E# y 0 hC1 0 D 1/ 2 2 EL 1 ET 2ET sR (7) Using Eq. (5), the compliance change can be simulated as a function of composite stress. At crack densities h/L90 . 2, further cracking in the 90° plies has little effect on stiffness. Tunneling cracking releases residual stresses on the lamina level, leading to permanent deformations and tunneling crack openings at complete unloading. Rewriting the results obtained in Ref. 18, the permanent strain εp 90 at complete unloading is given by εp 90 5 C1 EL 1 ET 2ETE# y 0 h L90 sR (8) The above solution is unbounded, but an upper bound is the situation where the stress in the 0° ply is zero; i.e., the permanent strain is the negative of the initial strain in the 0° plies. Therefore, the solution is bounded by the limit εp,max 0 5 EL 1 ET 2EL sR E# y 0 (9) (B) Stage II—Simultaneous 0° and 90° Ply Cracking: In stage II, multiple matrix cracking occurs simultaneously in the 0° and 90° plies. We assume that L0 5 L90 in stage II. The compliance of the 0° ply E0 can be written as38 1 E0 5 1 EL S1 1 D1 R L0 D (10) where D1 5 EL Em ~1 2 Vfa1! 3 ~b2 1 b3! Vf 2 ~s 2 si ! t (11) where a and b are nondimensional constants defined in Ref. 35. Vf is the volume fraction of fibers, Em the Young modulus of the matrix, and t a constant interfacial shear stress. The composite compliance is given by22 1 Ey 5 1 Ey 0 S 1 1 C1 h L0 1 2D1 Ey 0 EL R L0 D (12) Assuming that the strains in the 90° and 0° plies are equal, the effective stress (s0) acting on the 0° ply is approximated by22 s0S 1 1 D1 R L0 D 5 EL Ey 0 S1 1 C1 h L0 1 2D1 Ey 0 EL R L0 D (13) (C) Stage III—0° Ply Cracking and Delamination: In stage III, the mechanical behavior is fully controlled by the 0° ply, and the analysis is similar to unidirectional laminates. The composite compliance becomes 1 Ey 5 1 Ey 0 S 1 1 D1 Ey 0 EL R L0 D (14) and the stress on the 0° ply is given by s0 5 2s. The analysis of the nonlinear monotonic tensile behavior of the 0° ply is based on the stress–displacement analysis by Hutchinson and Jensen35 of a fiber being pulled out of a brittle matrix against friction. The analysis can be rewritten in terms of stress and strain, including finite-element solutions for small debond lengths l compared with the fiber radius R (l/R , 1).38 The overall monotonic strain ε for a multiple-cracked, unidirectional laminate consists of three strain contributions that can be written as38 ε 5 εe 1 εT 1 εs 5 s0 E0 1 S 1 E0 2 1 EL DsT 1 2H@2~s0 2 si !sT 1 s0 2 2 si 2 # (15) where the strain subscipts e, T, and s refer to the elastic, thermal, and sliding contributions, respectively, and H 5 Rb2~1 2 Vfa1! 2 4EmVf 2 tL0 (16) In Eq. (15), the stresses are given by si 5 sD 2 sT (17) May 2001 Mechanical Properties of Two Plain-Woven CVI SiC-Matrix Composites 1047
1048 Journal of the American Ceramic Sociery-Jacobsen and Brondsted Vol 84. No 5 2VAb2 +b3)Emri simulated stress-strain curve for SiC/SiC shows good agreement Or (1 -Va1) (18) with measured behavior(Fig 3(b)) (19) (2) CAiC The constant crack spacing of the 90 plies implies that The interfacial debond fracture energy is I and the thermal strain S-received C/SiC is already in stage Ill. Using the rule of is defined as mixtures,E,=0.5(EL Er) and setting ET =0 GPa, we find E 1 17 GPa, which is within the measured range of Er, supporting an)△T the stage Ill assumption. The large residual stress g(Table (20) between the plies in the C/SiC material demonstrates why this The analysis of the hysteresis behavior of unidirectional materials aterial is precracked in the 90 plies in the as-received condition s based on the results obtained in Refs. 10 and 36. Generalized Also, the fiber/matrix interface is in residual tension(or >0)for hysteresis behavior in the case of unloading to nonzero stresses can the CsiC material (Table I). When matrix cracking in the 0 plies be found in ref 4 occurs followed interface debonding. there should be no connection between fiber and matrix in C/Sic due to the tensile stress in the interface, and an interfacial gap is predicted. 7If V. Simulation of Tensile Behavior asperities are present, there may be interfacial contact during (I SiC/SiC sliding between fiber and matrix. The transition from stages 0 to I occurs at the first deviation for he osore, a simple one-dimensional shear-lag model is applied from linearity of the stress-strain curve, i.e., at 41 MPa (Table D) and it requires that the interface is in compr With Co=1.20 and h= 0.30 the fractur for sion. 35 Models for one-dimensional stress-strain behavior have tunneling cracking is roo=3.9 J/m2 at h/Loo =0. The simulated Deen proposed. 4, 5, 48 The approach used here is based on a can be compared with the experimentally measured changes. stiffness due to relief of residual strain and interfacial debonding, emulations of stiffness change with stress are plotted in Fig. 10 Too values. The stiffness changes indicate a I A one-dimensional model neglects the Poisson contraction,i.e ncreasing from 3.9 to 32.5 J/m. Such an increase is unlikely, because the tunneling crack openings in general are small. It Up = 0. The last simplifying assumption is that the change in peculated whether there is a contribution from tunneling cracks radial stress on the outer boundary of the cylindrical unit cell is rowing into the 0 plies, where fiber bridging increases the zero, which is a type-I boundary condition, equivalent to the apparent fracture energy, as shown by Ref. 46, and thus affecting implicit assumption for earlier-derived one-dimensional models The nondimensional constants(as and bs)become simple expres- The damage characterization shows that significant matrix sions. as shown below cracking in the oo bundles starts at o/S of 0.45-0.55. The crack spacing in the 90% plies follows the evolution of the crack spacing II. To obtain the smoothest transition, a=Ea≈(1-E stage II is set active at o/S>0.55. At hLo >0.9 the residual Em sses are largely released, and a maximum permanent strain of 0.015% because of tunneling cracking has been calculated for SiC/SiC using Eq (9) The relation o, =0.86o is found from analysis of the slope of h≈. REM 4EEVTLo the hysteresis curve. The same relation has been found for a similar material. This functional relation comes directly from analysis of The stress quantities become the composite stress; i.e., the stress on the 0 ply is not explicitly needed. The frictional shear stress t= 80 MPa is derived from the (23) maximum hysteresis loop width at the last unloading peak stress (stage III) before fracture, and it is assumed to have this constant The overall monotonic stress-strain behavior can be written a value at all stresses where stages l and ll are active. Th 2H(o +0)- E E (24) ar=26MPaSic/sic where the damaged elastic modulus Eo is given by 「e=39Jm2123047 11 +4H(+σ1) Simulated Keith and Kedward have used a constant TLo to simulate the 0.5EL stress-strain behavior of a SiC-fiber-reinforced AlPOa-matri composite and have found reasonable agreement between experi- 04 Stages 02回 (25). A good fit for the elastic modulus degradation has bee obtained with TLo =6.0 MPar'mm(Fig. 11). The initial residual contribution because of a constant TLo is subtracted from all the 0.0 equations before simulation begins, i.e., at o=0 MPa. The loss of 020.4 stiffness is sensitive to TLo (Fig. 11) Therefore, an experimentally observed maximum hysteresis Fig. 10. Stiffness change and onset of tunneling cracking as a function loop width eMax and the permanent strain at zero unloading stress nneling cracking toughness Tgo in SiC/SiC, To obtain the agreement Euo have been fitted to various TLo values. bEma can be fitted with experimental results and theory it is necessary to increase T9o Euo= 4.5 MPa'mm, whereas TLo can be fitted with values ranging accordingly, At stresses >0.55S, the compliance change is mainly due to from 4.5 to 6 MPa'mm. The tensile behavior of C/SiC(0, 90)is matrix cracking and debonding in the 0 plies. simulated using TLo = 4.5 MPa, mm(Fig 4(b)
sD 5 2Vf~b2 1 b3! 1/ 2 ~1 2 Vfa1! S EmGi R D 1/ 2 (18) sT 5 Vfa2 1 2 Vfa1 EmεT (19) The interfacial debond fracture energy is Gi , and the thermal strain is defined as εT 5 ~afL 2 am!DT (20) The analysis of the hysteresis behavior of unidirectional materials is based on the results obtained in Refs. 10 and 36. Generalized hysteresis behavior in the case of unloading to nonzero stresses can be found in Ref. 45. IV. Simulation of Tensile Behavior (1) SiC/SiC The transition from stages 0 to I occurs at the first deviation from linearity of the stress-strain curve, i.e., at 41 MPa (Table I). With C1 0 5 1.20 and h 5 0.30 mm, the fracture energy for tunneling cracking is G90 5 3.9 J/m2 at h/L90 5 0. The simulated stiffness change for G90 5 3.9 J/m2 is shown in Fig. 10, where it can be compared with the experimentally measured changes. Simulations of stiffness change with stress are plotted in Fig. 10 for various G90 values. The stiffness changes indicate a G90 increasing from 3.9 to 32.5 J/m2 . Such an increase is unlikely, because the tunneling crack openings in general are small. It is speculated whether there is a contribution from tunneling cracks growing into the 0° plies, where fiber bridging increases the apparent fracture energy, as shown by Ref. 46, and thus affecting the composite compliance. The damage characterization shows that significant matrix cracking in the 0° bundles starts at s/S of ;0.45–0.55. The crack spacing in the 90° plies follows the evolution of the crack spacing in the 0° plies during stage II. To obtain the smoothest transition, stage II is set active at s/S . 0.55. At h/L90 . 0.9, the residual stresses are largely released, and a maximum permanent strain of 0.015% because of tunneling cracking has been calculated for SiC/SiC using Eq. (9). The relation si 5 0.86sp is found from analysis of the slope of the hysteresis curve. The same relation has been found for a similar material.12 This functional relation comes directly from analysis of the composite stress; i.e., the stress on the 0° ply is not explicitly needed. The frictional shear stress t 5 80 MPa is derived from the maximum hysteresis loop width at the last unloading peak stress (stage III) before fracture, and it is assumed to have this constant value at all stresses where stages II and III are active. The simulated stress–strain curve for SiC/SiC shows good agreement with measured behavior (Fig. 3(b)). (2) C/SiC The constant crack spacing of the 90° plies implies that as-received C/SiC is already in stage III. Using the rule of mixtures, Ey 5 0.5(EL 1 ET) and setting ET 5 0 GPa, we find Ey 5 117 GPa, which is within the measured range of Ey, supporting the stage III assumption. The large residual stress sR (Table I) between the plies in the C/SiC material demonstrates why this material is precracked in the 90° plies in the as-received condition. Also, the fiber/matrix interface is in residual tension (sr R . 0) for the C/SiC material (Table I). When matrix cracking in the 0° plies occurs followed by interface debonding, there should be no connection between fiber and matrix in C/SiC due to the tensile stress in the interface, and an interfacial gap is predicted.47 If asperities are present, there may be interfacial contact during sliding between fiber and matrix. Therefore, a simple one-dimensional shear–lag model is applied for the 0° plies, and it requires that the interface is in compression.35 Models for one-dimensional stress–strain behavior have been proposed.4,5,48 The approach used here is based on a simplified version of the present model and includes the loss of stiffness due to relief of residual strain and interfacial debonding, which are not included in the previous models. A one-dimensional model neglects the Poisson contraction, i.e., nf 5 nm 5 0. The debond fracture energy is neglected, leading to sD 5 0. The last simplifying assumption is that the change in radial stress on the outer boundary of the cylindrical unit cell is zero, which is a type-I boundary condition,35 equivalent to the implicit assumption for earlier-derived one-dimensional models. The nondimensional constants (as and bs) become simple expressions, as shown below: a1 5 Ef EL a2 5 ~1 2 Vf!Ef EL b2 5 Em Ef b3 5 Vf 1 2 Vf (21) H 5 RVm 2 Em 2 4EfEL 2 Vf 2 tL0 (22) The stress quantities become si 5 2sT sT 5 2Vfsf R (23) The overall monotonic stress–strain behavior can be written as ε 5 s E0 1 S 1 E0 2 1 EL DsT 1 2H~s 1 sT! 2 (24) where the damaged elastic modulus E0 is given by 1 E0 5 1 EL 1 4H~s 1 sT! (25) Keith and Kedward48 have used a constant tL0 to simulate the stress–strain behavior of a SiC-fiber-reinforced AlPO4-matrix composite and have found reasonable agreement between experiment and simulation, although they neglected the last term in Eq. (25). A good fit for the elastic modulus degradation has been obtained with tL0 5 6.0 MPazmm (Fig. 11). The initial residual contribution because of a constant tL0 is subtracted from all the equations before simulation begins, i.e., at s 5 0 MPa. The loss of stiffness is sensitive to tL0 (Fig. 11). Therefore, an experimentally observed maximum hysteresis loop width dεmax and the permanent strain at zero unloading stress εu0 have been fitted to various tL0 values. dεmax can be fitted with εu0 5 4.5 MPazmm, whereas tL0 can be fitted with values ranging from 4.5 to 6 MPazmm. The tensile behavior of C/SiC (0°,90°) is simulated using tL0 5 4.5 MPazmm (Fig. 4(b)). Fig. 10. Stiffness change and onset of tunneling cracking as a function of tunneling cracking toughness G90 in SiC/SiC. To obtain the agreement between experimental results and theory it is necessary to increase G90 accordingly. At stresses .0.55S, the compliance change is mainly due to matrix cracking and debonding in the 0° plies. 1048 Journal of the American Ceramic Society—Jacobsen and Brøndsted Vol. 84, No. 5
May 2001 Mechanical Properties of Two Plain-Woven Cvl SiC-Matrix Composites 1049 C/SiC gauge on the C/SiC specimen shows a slight deviation from linearity before fracture, indicating the start of further delamination. (3) Shear behavior The shear stiffness G changes continuously for SiC/SiC. Lo=6.0 MPam whereas, for C/SiC, almost no change in G, is observed( Fig. 12) tLo=4.5 MPamm The lack of stiffness reduction in C/SiC implies that the nonlinear 0.7 Lo=3.0 MPamm deformation is entirely controlled by release of residual stres The hysteresis loop starts to open at high strains for SiC/SiC, Shear hysteresis can occur only if delamination is present i whereas, for C/SiC, the loop width is continuously inci 02 0.6 consistent with delamination cracks in the as-received material Nondimensional Peak Stress, op/s Permanent strains are observed experimentally, even in the ab- sence of visible hysteresis, which must be the result of residual ig. 11. Experimental and simulated change of stiffness using a constant nterfacial damage parameter Tlo and or 240 MPa for C/SiC stress relief on the lamina level. SiC/SiC does not develop the same magnitudes of permanent strains as does C/sic The matrix shear-crack spacings in both materials after failure are low. SEM photographs of the interior of the shear zone show Discussion crack spacings of 10-45 um Matrix cracking is observed at 45 (I Tensile behavior to the fibers, consistent with the princip stress direction similar cracking behavior has been observed in SiC-fiber (A SiC/SiC: The overall behavior, including hysteresis, is reinforced carbon. Examination of the fracture appearance shows well predicted although the simulate tat some fiber bundles are cracked at 45 to the fibers. whereas smaller than indicated by experiment be due to an thers are cracked normal to the fibers. This is especially true for increase in the unloading stiffness below SiC/SiC (Fig. 13) closure(maybe due to small particles ff during matrix fracture), and, consequently, apparent anent strains at(4) Strength(Stage In ero unloading stress(Fig 3(a)). The same observation is made in Refs. 12 and 28, which report that stiffness on reloading from zero A) Tension: Figures 3(a)and 4(a)show that the tangent stress is significantly higher than the stiffness on unloading modulus of both materials has a finite value(-20 GPa for SiC/Sic Residual stress on the lamina level released due to matrix cracking and35 GPa for C/SiC) before fracture(stage IV). No distinct in the 90 bundles also affects the permanent strain. Comparing the failure plane is evident, and failure of each bundle is randomly xperimental and simulated stress-strain behavior(Fig. 3)shows each other. The implication of this failure pattern is that the tensile distributed because of delaminations decoupling the bundles from that the real residual stress on the lamina level must be much higher than calculated in Table I, because the increase in experi- trength should be modeled on the bundle level mental permanent strains are higher in the beginning of the load (B) Compression: For both materials, a distinct failure plane re there are no cracks in the 0o bundles. The thick plate follows at 15%-20% to the loading axis(Fig. 14).Optical examina- sed for the investigation may be responsible for the low elast tions of the polished edges for the two materials show that modulus(more difficult infiltration and, thus, higher porosity ) and delamination in the90° bundles and0°/90° interface are the free-edge delamination, which is usually not observed in other primary failure mechanism(Fig. 15). The fibers break similar to investigations on thinner plates. what is observed in bending, and no fiber-kinking mechanism (B) C/SiC: A comparison of Figs. 4(a)and(b)shows a good ood observed. The delamination cracks follow the waviness of the fiber approximation to treat C/SiC as being initially in stage Ill. The bundles. When a sinusoidal approximation to model the bundle itial part of the simulated curve shows a low tangent modulus waviness is used, >, maximum bundle misalignments (0)of 15.5 for SiC/SiC and 14.3 for C/SiC are calculated. The decrease from infinity (no cracks)to tlo=4.5 MPar-mm used in implication of the interlaminar cracking is that the compressive the simulation, a better fit would be obtain strength is controlled by the interlaminar shear strength. Ar The interfacial shear stress t for a sir material has been equation for the maximum compressive stress that can be sustained examined using a pushout test, and a value of 5 MPa has beer materials with an initial fiber misalignment angle 0 proposed by derived. Average crack spacings of L,=0.3-0.9 mm are Argon.is used here xpected using this value. These values may explain why so few cracks are observed in the replicas. The high local crack spacings (10-20 um) in some regions found after the tests imply high interfacial shear stresses in these regions that may be responsible O SIC/SIC for the overall inelasticity--the rest of the bundles have too low 口csic interfacial shear stress to create matrix cracks. We expect the latter ecause the interface is in residual tension. Therefore. it is posed that either local strong interfacial bondings and/or small particles and asperities can cause high friction between fiber and matrix and explain the high crack densities in some regions(Fig. 8) ()Compressive Behavior For C/SiC, because of the precracked 90 bundles, it is lat, during compression, these cracks close, and the co attains its damage-free value. Figure 6 shows that the increases to a crack closure stress of 150 MPa, below which the stiffness remains constant at Ec 140 GPa, approximately lat of the computed damage-free value (Table D) accordance with other experiments. The compressive behavior In-plane Shear Stress, O(MPa) for both materials is essentially linear until fracture, except for the 12. Changes in unloading shear modulus as a function of peak stress. crack-closure effect observed for C/SiC. The out-of-plane strain SiC/SiC shows significant change
V. Discussion (1) Tensile Behavior (A) SiC/SiC: The overall behavior, including hysteresis, is well predicted although the simulated permanent strains are smaller than indicated by experiments. This may be due to an increase in the unloading stiffness below 20 MPa, indicating crack closure (maybe due to small particles being torn off during matrix fracture), and, consequently, apparent larger permanent strains at zero unloading stress (Fig. 3(a)). The same observation is made in Refs. 12 and 28, which report that stiffness on reloading from zero stress is significantly higher than the stiffness on unloading. Residual stress on the lamina level released due to matrix cracking in the 90° bundles also affects the permanent strain. Comparing the experimental and simulated stress–strain behavior (Fig. 3) shows that the real residual stress on the lamina level must be much higher than calculated in Table I, because the increase in experimental permanent strains are higher in the beginning of the load history, where there are no cracks in the 0° bundles. The thick plate used for the investigation may be responsible for the low elastic modulus (more difficult infiltration and, thus, higher porosity) and free-edge delamination, which is usually not observed in other investigations on thinner plates. (B) C/SiC: A comparison of Figs. 4(a) and (b) shows a good approximation to treat C/SiC as being initially in stage III. The initial part of the simulated curve shows a low tangent modulus compared with that experimentally observed. If tL0 is allowed to decrease from infinity (no cracks) to tL0 5 4.5 MPazmm used in the simulation, a better fit would be obtained. The interfacial shear stress t for a similar material has been examined using a pushout test, and a value of 5 MPa has been derived.49 Average crack spacings of L0 5 0.3–0.9 mm are expected using this value. These values may explain why so few cracks are observed in the replicas. The high local crack spacings (10–20 mm) in some regions found after the tests imply high interfacial shear stresses in these regions that may be responsible for the overall inelasticity—the rest of the bundles have too low interfacial shear stress to create matrix cracks. We expect the latter because the interface is in residual tension. Therefore, it is proposed that either local strong interfacial bondings and/or small particles and asperities can cause high friction between fiber and matrix and explain the high crack densities in some regions (Fig. 8). (2) Compressive Behavior For C/SiC, because of the precracked 90° bundles, it is expected that, during compression, these cracks close, and the composite attains its damage-free value. Figure 6 shows that the stiffness increases to a crack closure stress of scf 5 150 MPa, below which the stiffness remains constant at Ecl 5 140 GPa, approximately that of the computed damage-free value (Table I). This is in accordance with other experiments.32 The compressive behavior for both materials is essentially linear until fracture, except for the crack-closure effect observed for C/SiC. The out-of-plane strain gauge on the C/SiC specimen shows a slight deviation from linearity before fracture, indicating the start of further delamination. (3) Shear Behavior The shear stiffness Gyz changes continuously for SiC/SiC, whereas, for C/SiC, almost no change in Gyz is observed (Fig. 12). The lack of stiffness reduction in C/SiC implies that the nonlinear deformation is entirely controlled by release of residual stress. The hysteresis loop starts to open at high strains for SiC/SiC, whereas, for C/SiC, the loop width is continuously increasing. Shear hysteresis can occur only if delamination is present.43 Therefore, hysteresis is observed from the beginning in C/SiC, consistent with delamination cracks in the as-received material. Permanent strains are observed experimentally, even in the absence of visible hysteresis, which must be the result of residual stress relief on the lamina level. SiC/SiC does not develop the same magnitudes of permanent strains as does C/SiC. The matrix shear-crack spacings in both materials after failure are low. SEM photographs of the interior of the shear zone show crack spacings of 10–45 mm. Matrix cracking is observed at 45° to the fibers, consistent with the principal stress direction. A similar cracking behavior has been observed in SiC-fiberreinforced carbon.43 Examination of the fracture appearance shows that some fiber bundles are cracked at 45° to the fibers, whereas others are cracked normal to the fibers. This is especially true for SiC/SiC (Fig. 13). (4) Strength (Stage IV) (A) Tension: Figures 3(a) and 4(a) show that the tangent modulus of both materials has a finite value (;20 GPa for SiC/SiC and ;35 GPa for C/SiC) before fracture (stage IV). No distinct failure plane is evident, and failure of each bundle is randomly distributed because of delaminations decoupling the bundles from each other. The implication of this failure pattern is that the tensile strength should be modeled on the bundle level. (B) Compression: For both materials, a distinct failure plane follows at 15°–20° to the loading axis (Fig. 14). Optical examinations of the polished edges for the two materials show that delamination in the 90° bundles and 0°/90° interface are the primary failure mechanism (Fig. 15). The fibers break similar to what is observed in bending, and no fiber-kinking mechanism is observed. The delamination cracks follow the waviness of the fiber bundles. When a sinusoidal approximation to model the bundle waviness is used,23,50 maximum bundle misalignments (u) of 15.5° for SiC/SiC and 14.3° for C/SiC are calculated. The implication of the interlaminar cracking is that the compressive strength is controlled by the interlaminar shear strength. An equation for the maximum compressive stress that can be sustained in materials with an initial fiber misalignment angle u proposed by Argon51 is used here. Fig. 11. Experimental and simulated change of stiffness using a constant interfacial damage parameter tL0 and sT 5 240 MPa for C/SiC. Fig. 12. Changes in unloading shear modulus as a function of peak stress. Only SiC/SiC shows significant change. May 2001 Mechanical Properties of Two Plain-Woven CVI SiC-Matrix Composites 1049
1050 Journal of the American Ceramic Sociery-Jacobsen and Brondsted Vol 84. No 5 shear loading 0094 sKU 0.1m Delamination cracks Vv ig. 15. Optic dure in C/SiC Fig. 13. Shear fracture of SiC/Sic amination in the 90 bundles and fiber breaks in the o bundles No fiber kinking is observe volume-dependent strength, because the gauge volume of the losipescu test is much smaller than the gauge volume of the tensile specimens. C Optical microscopy and SEM examinations of two plain-woven MCs show that fiber packing is very irregular, that large interbundle porosity is present, and that C/SiC is precracked in the Delamination 90 bundles. Therefore, a transition scheme for converting a plain weave to a cross-ply laminate has been applied, because it enables a simpler mechanics approach to the mechanical performance. In 10 mm the first step, the porosity is included in the matrix, and the SiC/SiC interphase is attached to the fiber, resulting in a reduction of the composite system to a fiber and matrix system with an interface Bundles decoupled by interlaminar cracks The second step consists of calculating the elastic properties of ult in unidirectional ply. The third step consists of calculating the elastic of failure bundle properties of the cross ply. Compared with the measured elastic properties, the agreement is good for both materials, and it concluded that the elastic properties of plain weaves can be calculated using the theory for a cross ply Fig. 14. Failure appearance of compressive specimens and failure mech- n tension, four characteristic damage stages are identified anism by interlaminar shear failur SiC/SiC undergoes all four stages, whereas C/SiC in its as received condition is in stage Ill, where the inelastic deformation is controlled by the 0 plies. Furthermore, we can simulate the tensile stress-strain behavior of C/Sic using a constant interfacial (26) damage parameter and a residual stress term. The tensile behavior of SiC/SiC is more complex, and the damage in the 90 plies has where gm. is the maximum interlaminar shear stress. For SiC/ e energy SiC, omax= 70 MPa,2 resulting in 0=6.3. A value of om Therefore, the mechanical analysis of laminated cross plies cannot 50 MPa has been measured for C/Sic by the manufacturer be applied to plain weaves in stage Il, because it is believed that in 0=5.5. Knock-down factors of 2. 44 for SiC/SiC and he fracture energy for tunneling cracking does not vary much C/SiC are needed to obtain agreement between the model because of small crack openings In the other stages, the agreement (26) and experiments, i.e., a reasonable compressive sive between theory and simulation is good prediction for plain-woven CVI-SiC composites would be e In compression, the stress-strain behavior is linear until very se to failure. Failure occurs by interlaminar matrix cracks, followed by bundle buckling. A simple criteria based on the maximum bundle misalignment angle, interlaminar shear strength and knock-down factor of "2.5 predicts the compressive strength The angle of the failure plane is coincident with the maximum The compressive strength of the materials is more than twice as angle of bundle misalignment. Therefore, it is proposed that high as the tensile strength, but strain-to-failure is of the same compressive failure is initiated by 0-oriented interlaminar crack resulting in"pinned-end" wavy bundle columns. Subsequently, the The shear behavior of SiC/Sic shows almost no hysteresis unt cracks link up and form the major crack plane, as shown in Fig 14. very close to the failure strain, indicating that the shear deforma- (C) Shear. The expected tensile strength at +45 to the fiber tion is controlled by matrix cracking and no delamination between directions is 2T, which, for both materials, exceeds the tensile the plies. C/SiC exhibits only a slightly decreasing shear stiffness, trength in the fiber directions S(Table If). This indicates a but large permanent deformations and hysteresis, indicating that
Scom 5 sxy max u (26) where sxy max is the maximum interlaminar shear stress. For SiC/ SiC, sxy max 5 70 MPa,25 resulting in u 5 6.3°. A value of sxy max 5 50 MPa has been measured for C/SiC by the manufacturer, resulting in u 5 5.5°. Knock-down factors of 2.44 for SiC/SiC and 2.60 for C/SiC are needed to obtain agreement between the model in Eq. (26) and experiments, i.e., a reasonable compressive strength prediction for plain-woven CVI-SiC composites would be Scom 5 sxy max 2.5u (27) The angle of the failure plane is coincident with the maximum angle of bundle misalignment. Therefore, it is proposed that compressive failure is initiated by u-oriented interlaminar cracks, resulting in “pinned-end” wavy bundle columns. Subsequently, the cracks link up and form the major crack plane, as shown in Fig. 14. (C) Shear: The expected tensile strength at 645° to the fiber directions is ;2T, which, for both materials, exceeds the tensile strength in the fiber directions S (Table II). This indicates a volume-dependent strength, because the gauge volume of the Iosipescu test is much smaller than the gauge volume of the tensile specimens. VI. Summary Optical microscopy and SEM examinations of two plain-woven CMCs show that fiber packing is very irregular, that large interbundle porosity is present, and that C/SiC is precracked in the 90° bundles. Therefore, a transition scheme for converting a plain weave to a cross-ply laminate has been applied, because it enables a simpler mechanics approach to the mechanical performance. In the first step, the porosity is included in the matrix, and the interphase is attached to the fiber, resulting in a reduction of the composite system to a fiber and matrix system with an interface. The second step consists of calculating the elastic properties of a unidirectional ply. The third step consists of calculating the elastic properties of the cross ply. Compared with the measured elastic properties, the agreement is good for both materials, and it is concluded that the elastic properties of plain weaves can be calculated using the theory for a cross ply. In tension, four characteristic damage stages are identified. SiC/SiC undergoes all four stages, whereas C/SiC in its asreceived condition is in stage III, where the inelastic deformation is controlled by the 0° plies. Furthermore, we can simulate the tensile stress–strain behavior of C/SiC using a constant interfacial damage parameter and a residual stress term. The tensile behavior of SiC/SiC is more complex, and the damage in the 90° plies has to be fitted to an increasing tunnel-cracking-mode fracture energy. Therefore, the mechanical analysis of laminated cross plies cannot be applied to plain weaves in stage II, because it is believed that the fracture energy for tunneling cracking does not vary much because of small crack openings. In the other stages, the agreement between theory and simulation is good. In compression, the stress–strain behavior is linear until very close to failure. Failure occurs by interlaminar matrix cracks, followed by bundle buckling. A simple criteria based on the maximum bundle misalignment angle, interlaminar shear strength, and knock-down factor of ;2.5 predicts the compressive strength. The compressive strength of the materials is more than twice as high as the tensile strength, but strain-to-failure is of the same order. The shear behavior of SiC/SiC shows almost no hysteresis until very close to the failure strain, indicating that the shear deformation is controlled by matrix cracking and no delamination between the plies. C/SiC exhibits only a slightly decreasing shear stiffness, but large permanent deformations and hysteresis, indicating that Fig. 13. Shear fracture of SiC/SiC. Fig. 14. Failure appearance of compressive specimens and failure mechanism by interlaminar shear failure. Fig. 15. Optical microscopy photograph of compressive failure in C/SiC due to delamination in the 90° bundles and fiber breaks in the 0° bundles. No fiber kinking is observed. 1050 Journal of the American Ceramic Society—Jacobsen and Brøndsted Vol. 84, No. 5
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the plies are delaminated and that release of residual stress on the fiber/matrix level is the controlling mechanism for the nonlinear behavior. Although examination of the fracture surfaces shows extensive matrix cracking, it apparently has no effect on the shear stiffness of C/SiC. Acknowledgments The work was conducted within the Engineering Science Centre for Structural Characterization and Modeling of Materials at the Materials Research Department, Risø National Laboratory, Denmark. Professor F. W. Zok, University of California Santa Barbara (UCSB), is gratefully acknowledged for many useful suggestions and fruitful discussions during a research stay at UCSB by the first author. References 1 J. Aveston, G. A. Cooper, and A. Kelly, “Single and Multiple Failure”; pp. 15–26 in The Properties of Fiber Composites, Conference Proceedings. IPC Science and Technology Press, Guildford, U.K, 1971. 2 D. B. Marshall, B. N. Cox, and A. G. 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