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