Availableonlineatwww.sciencedirect.com DIRECT● COMPOSITES SCIENCE AND TECHNOLOGY ELSEVIER Composites Science and Technology 65(2005)2541-2549 Effect of on-axis tensile loading on shear properties of an orthogonal 3D woven SiC/SiC composite Toshio Ogasawara , Takashi Ishikawa Tomohiro Yokozeki Takuya Shiraishi b, I, Naoyuki Watanabe b Advanced Composite Evaluation Technology Center, Japan Aerospace Exploration Agency(JAXA), Mitaka, Tokyo 181-0015, Japan ersity, Hino, Tokyo 191-006 Received 2 June 2005: accepted 2 June 2005 Available online 28 July 2005 Abstract The present study examines in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix com- posite. A composite beam with rectangular cross-section was subjected to a small torsional moment, and the torsional rigidities were measured using an optical lever. Based on the Lekhnitskii's equation( Saint-Venant torsion theory) for a orthotropic material, the in-plane and out-of-plane shear moduli were simultaneously calculated. The estimated in-plane shear modulus agreed with the mod ulus measured from +45 off-axis tensile testing. The effect of on-axis(0%/90) tensile stress on the shear stiffness properties was also investigated by the repeated torsional tests after step-wise tensile loading. Both in-plane and out-of-plane shear moduli decreased by about 50% with increasing the on-axis tensile stress, and it is mainly due to the transverse crack propagation in 90 fiber bundles and matrix cracking in 0 fiber bundles. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shea modulus of ceramic matrix composites, because a thick specimen is not required o 2005 Elsevier Ltd. All rights reserved Keywords: Ceramic matrix composites; Matrix cracking: Transverse cracking: Finite element analysis 1. Introduction composites, this change also involves initial cracking in he transverse (90o) plies as tunneling cracks [4-7] It is now well understood that continuous fiber ceramic Subsequently, transverse cracks penetrate the longitudi matrix composites(CMCs) exhibit nonlinear stress- nal plies as the load is increased. Based on the energy strain behavior under tensile loading as a result of multi- criterion and finite element analysis, transverse crack ple microcracking and fiber fragmentation. An overview propagation in cross-ply brittle matrix composites has of CMC mechanical properties has been provided by been analyzed [6, 7]. Shear-lag analysis is often used to Evans and Zok [1]. For unidirectional CMCs, the estimate transverse crack propagation within polymer change in stifness due to multiple matrix cracking has matrix composites [8], and this method has also beer been estimated by elastic analysis based on the Lame applied to an orthogonal 3D woven CMC as well as problem [2], and shear-lag analysis [3]. In cross-ply cross-ply CMCs [9] The effect of transverse crack on shear stiffness deg radation has been investigated for polymer matrix com Corresponding author. Tel +81 422 40 3561; fax: +81 422 40 posites. For example, Kobayashi et al. [10]investigated ressogasat(@chofu jaxa. jp(T. Ogasawara) the effect of on-axis tensile loading on degradation of Former graduate student, Currently in Mitsubishi Space Software in-plane and out-of-plane shear moduli of cross-ply car- Co, Ltd, Kanagawa, Japan. bon fiber/epoxy composites. The experimental results -3538/S- see front matter 2005 Elsevier Ltd. All rights reserved. . compscitech. 2005.06.003
Effect of on-axis tensile loading on shear properties of an orthogonal 3D woven SiC/SiC composite Toshio Ogasawara a,*, Takashi Ishikawa a , Tomohiro Yokozeki a , Takuya Shiraishi b,1, Naoyuki Watanabe b a Advanced Composite Evaluation Technology Center, Japan Aerospace Exploration Agency (JAXA), Mitaka, Tokyo 181-0015, Japan b Aerospace Systems Department, Tokyo Metropolitan University, Hino, Tokyo 191-0065, Japan Received 2 June 2005; accepted 2 June 2005 Available online 28 July 2005 Abstract The present study examines in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix composite. A composite beam with rectangular cross-section was subjected to a small torsional moment, and the torsional rigidities were measured using an optical lever. Based on the Lekhnitskiis equation (Saint–Venant torsion theory) for a orthotropic material, the in-plane and out-of-plane shear moduli were simultaneously calculated. The estimated in-plane shear modulus agreed with the modulus measured from ±45 off-axis tensile testing. The effect of on-axis (0/90) tensile stress on the shear stiffness properties was also investigated by the repeated torsional tests after step-wise tensile loading. Both in-plane and out-of-plane shear moduli decreased by about 50% with increasing the on-axis tensile stress, and it is mainly due to the transverse crack propagation in 90 fiber bundles and matrix cracking in 0 fiber bundles. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shear modulus of ceramic matrix composites, because a thick specimen is not required. 2005 Elsevier Ltd. All rights reserved. Keywords: Ceramic matrix composites; Matrix cracking; Transverse cracking; Finite element analysis 1. Introduction It is now well understood that continuous fiber ceramic matrix composites (CMCs) exhibit nonlinear stress– strain behavior under tensile loading as a result of multiple microcracking and fiber fragmentation. An overview of CMC mechanical properties has been provided by Evans and Zok [1]. For unidirectional CMCs, the change in stiffness due to multiple matrix cracking has been estimated by elastic analysis based on the Lame problem [2], and shear-lag analysis [3]. In cross-ply composites, this change also involves initial cracking in the transverse (90) plies as tunneling cracks [4–7]. Subsequently, transverse cracks penetrate the longitudinal plies as the load is increased. Based on the energy criterion and finite element analysis, transverse crack propagation in cross-ply brittle matrix composites has been analyzed [6,7]. Shear-lag analysis is often used to estimate transverse crack propagation within polymer matrix composites [8], and this method has also been applied to an orthogonal 3D woven CMC as well as cross-ply CMCs [9]. The effect of transverse crack on shear stiffness degradation has been investigated for polymer matrix composites. For example, Kobayashi et al. [10] investigated the effect of on-axis tensile loading on degradation of in-plane and out-of-plane shear moduli of cross-ply carbon fiber/epoxy composites. The experimental results 0266-3538/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.06.003 * Corresponding author. Tel.: +81 422 40 3561; fax: +81 422 40 3549. E-mail address: ogasat@chofu.jaxa.jp (T. Ogasawara). 1 Former graduate student, Currently in Mitsubishi Space Software Co., Ltd., Kanagawa, Japan. Composites Science and Technology 65 (2005) 2541–2549 COMPOSITES SCIENCE AND TECHNOLOGY www.elsevier.com/locate/compscitech
2542 T Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 were compared with the numerical results based on Tsai- A schematic drawing of a torsion beam is shown in Daniel model[ll], Hashin model [12], and Gudmundson- Fig. 1. A specimen consists of a rectangular cross-sec- Zang model[13], and conservative stiffness degradation as tion beam with dimensions b(width) by h(thickness a function of transverse crack density was predicted by in y and z directions, with L (length) in x direction these models The coordinate x is parallel to a material axis. For an Some researchers experimentally investigated the orthotropic material twisted about an axis parallel to degradation of in-plane shear modulus in CMCs by the material direction(x direction) with torsional mo- off-axis tensile test and V-notched shear(losipescu) test ment M, the torsional rigidity GJ(=M o) is given by 14, 15], and the effect of in-plane shear stress on in-plane [17] shear stiffness degradation has been understood However, the effect of on-axis loading on the in-plane GJ=GrB(c)bi and out-of-plane shear properties of CMCs have not B(c) been revealed yet. S{1-m( k=1,3,5. For evaluating the effect of on-axis loading on shear roperties, the she ear mo dulls of a composite which has microscopic damages caused by on-axis tensile stress should be measured. However it is difficult to make thick Cmc specimens because of difficulty in processing where o is a twist angle per unit length, Ga Standard test methods such as rail-shear method in-plane and out-of-plane shear moduli. As this equa (ASTM-D4255), off-axis tensile test method (ASTM on is based on Saint-Venant torsion, So-called"warp. D3518, V-notched shear(losipescu) method (ASTM ing effects"are neglected Ishikawa et al. [16]investigated the effect of warping C1292)are not applicable for measuring out-of-plane torsion on the torsional rigidity of a unidirectional com- shear modulus of thin CMC specimens A unique test method for measuring out-of plane posite beam, and revealed that torsional rigidity shear modulus has been provided by Ishikawa et al increases under the warping torsion. For an actual [16. They applied a torsional test for estimating out-of experiment, specimen grip areas shown in Fig. I are con plane shear modulus of a unidirectional carbon fiber/ strained for applying torsion moment and for fixing epoxy composite based on Lekhnitskii's torsion theor pecimen with a fixture. Therefore the effect of warping [17]. Tsai et al. also presented a closed-form solution on torsional rigidity was preliminarily investigated by for a composite laminate under torsion in terms of the nite element analysis(FI EA). A commercial FEA code lamination geometry, and the experimental methodol ABAQUS was used for the calculation The numerical results under the condition of ogy to determine the three principal shear moduli by L/H=26.7, and Gr/ G=x=2 are shown in Fig. 2 for measuring surface and edge strains in twisted prismatic coupons [18]. The torsional test is useful to estimate b/h of 1, 2, 4, and 8 On and oa are twist angles per length calculated by FEa and Lekhnitskil's torsion out-of plane shear properties, because a thick specimen theory(Eq(1), respectively. While the grip areas are is not required for the experiment In this study, the in-plane and out-of-plane shear assumed to constrain the warping deformation strictly properties of an orthogonal 3D woven Sic fiber/sic in the calculation, these boundary conditions are much matrix composite were evaluated by torsional test of a stricter than those in an actual experiment. The rectangular cross-section beam. The experimental results were compared with numerical results by finite element analysis(FEA). Furthermore, the effect of on- grip area axis tensile loading on shear modulus degradation of the SiC/SiC composite was also examined 2. Torsional test methodology Based on Lekhnitskii's torsion theory for an ortho- tropic material, Swanson established a torsion theory for composite laminated rectangular rods [19]. However, it is difficult to expand this theory for an orthogonal 3D woven composite. Therefore, Lekhnitskii's torsion the ory is directly applied rthogonal 3D woven composite as a uniform orthotropic material Fig. 1. Specimen configuration and coordinate system for torsional test
were compared with the numerical results based on Tsai– Daniel model [11], Hashin model [12], and Gudmundson– Zang model [13], and conservative stiffness degradation as a function of transverse crack density was predicted by these models. Some researchers experimentally investigated the degradation of in-plane shear modulus in CMCs by off-axis tensile test and V-notched shear (Iosipescu) test [14,15], and the effect of in-plane shear stress on in-plane shear stiffness degradation has been understood. However, the effect of on-axis loading on the in-plane and out-of-plane shear properties of CMCs have not been revealed yet. For evaluating the effect of on-axis loading on shear properties, the shear modulus of a composite which has microscopic damages caused by on-axis tensile stress should be measured. However, it is difficult to make thick CMC specimens because of difficulty in processing. Standard test methods such as rail-shear method (ASTM-D4255), off-axis tensile test method (ASTM D3518), V-notched shear (Iosipescu) method (ASTM C1292) are not applicable for measuring out-of-plane shear modulus of thin CMC specimens. A unique test method for measuring out-of plane shear modulus has been provided by Ishikawa et al. [16]. They applied a torsional test for estimating out-of plane shear modulus of a unidirectional carbon fiber/ epoxy composite based on Lekhnitskiis torsion theory [17]. Tsai et al. also presented a closed-form solution for a composite laminate under torsion in terms of the lamination geometry, and the experimental methodology to determine the three principal shear moduli by measuring surface and edge strains in twisted prismatic coupons [18]. The torsional test is useful to estimate out-of plane shear properties, because a thick specimen is not required for the experiment. In this study, the in-plane and out-of-plane shear properties of an orthogonal 3D woven SiC fiber/SiC matrix composite were evaluated by torsional test of a rectangular cross-section beam. The experimental results were compared with numerical results by finite element analysis (FEA). Furthermore, the effect of onaxis tensile loading on shear modulus degradation of the SiC/SiC composite was also examined. 2. Torsional test methodology Based on Lekhnitskiis torsion theory for an orthotropic material, Swanson established a torsion theory for composite laminated rectangular rods [19]. However, it is difficult to expand this theory for an orthogonal 3D woven composite. Therefore, Lekhnitskiis torsion theory is directly applied, assuming an orthogonal 3D woven composite as a uniform orthotropic material. A schematic drawing of a torsion beam is shown in Fig. 1. A specimen consists of a rectangular cross-section beam with dimensions b (width) by h (thickness) in y and z directions, with L (length) in x direction. The coordinate x is parallel to a material axis. For an orthotropic material twisted about an axis parallel to the material direction (x direction) with torsional moment Mt, the torsional rigidity GJ (=Mt/x) is given by [17]: GJ ¼ GxybðcÞbh3 ; bðcÞ ¼ 32c2 p4 X1 k¼1;3;5... 1 2c kp tanh kp 2c ; c ¼ b h ffiffiffiffiffiffiffi Gzx Gxy s ; ð1Þ where x is a twist angle per unit length, Gxy and Gzx are in-plane and out-of-plane shear moduli. As this equation is based on Saint–Venant torsion, so-called ‘‘warping effects’’ are neglected. Ishikawa et al. [16] investigated the effect of warpingtorsion on the torsional rigidity of a unidirectional composite beam, and revealed that torsional rigidity increases under the warping torsion. For an actual experiment, specimen grip areas shown in Fig. 1 are constrained for applying torsion moment and for fixing specimen with a fixture. Therefore, the effect of warping on torsional rigidity was preliminarily investigated by fi- nite element analysis (FEA). A commercial FEA code ABAQUS was used for the calculation. The numerical results under the condition of L/H = 26.7, and Gxy/Gzx = 2 are shown in Fig. 2 for b/h of 1, 2, 4, and 8. xn and xa are twist angles per length calculated by FEA and Lekhnitskiis torsion theory (Eq. (1)), respectively. While the grip areas are assumed to constrain the warping deformation strictly in the calculation, these boundary conditions are much stricter than those in an actual experiment. The Fig. 1. Specimen configuration and coordinate system for torsional test. 2542 T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549
T. Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 l.1 Gax by any numerical methods such as Newton-Raph- son method 3. Experimental procedure 3. 1. Materials /9, 20/ b/h=2 b/h=4 The composite under investigation contained Tyr- b/h=8 nnoTM Lox-M fibers woven into an orthogonal 3D con figuration with fiber volume fractions of 19%6, 19%, and 2% in the x, y, and z directions, respectively. Optical 0.2040.60.8 micrographs and schematic drawing in Fig 3 illustrate x/L the fiber architecture of the present composites with each fiber bundle containing 1600 fibers. The composite Fig. 2. Effect of cross-section geometry(b/h)on warping (L/H= 26.7, Gr/G2x=2, b/h= 1, 2, 4, 8).m: twist angle per preform plate(240×120×6mm) was treated at ele vated temperature in a CO atmosphere, resulting modulus ratio(G/G2x)on the numerical results. When fiber and piane i cale carbon. layer at eer surrounding calculated from FEA, @a: twist angle per length calculated from the Lekhnitski's equation(Eq(1)). the formation of a 10 nm SiOr-rich lay an inner 40 nm carbon-I iber surface between 0.3 and 0.7 of x/L. However, the effect of warp- lysis cycles, the average composite bulk density was ing becomes more significant with increase in b/h. The 2.20 g/cm. Tensile specimens were machined from the numerical result suggests that the effect of warping on composite plates such that the loading direction was torsional rigidity can be neglected under the condition parallel to the y-axis. The specimen surfaces were also ground to a flat finish such that the interlacing loops The shear moduli Gxy and Gax are determined by the shown in Fig 3 were not present in the final specimens following procedure. When the specimen width b and The unit cell size is 3 mmx3 mm hickness h are fixed, the torsional rigidity G/ is repre sented as a function of Gxy and G-x as follows: 3. 2. Tensile tests G=f(Gry, Gar) Both on-axis(0°/90°) and off-axis(±45°) tensile tests Considering two specimens, I and 2, with different rect- were conducted on a servo-hydraulic testing rig(Model angular cross-section, the following nonlinear simulta- 8501, Instron, USA)at room temperature in air using a neous equations fi and f2 are obtained specimen geometry as shown in Fig. 4(a)Cardboard f(Gr, Ga), tabs were bonded to the specimen end regions with the GJ2=f2(Gx, Ga). (3) load being applied using hydraulic wedge grips. A clip gauge-type extensometer(gauge length 25 mm; Model In Eq.(3)G, and GJ2 are obtained from torsional 632. 11C-20, MTS, USA)was used to measure the longi- experiments. The two equations are solved for Gxy and tudinal strain. Transverse strains were measured using bundle z bundle x bundle Fig. 3. Optical micrographs and schematic drawing of a SiC/SiC composite illustrating the orthogonal 3D woven fiber architecture
numerical results were almost independent on the shear modulus ratio (Gxy/Gzx) on the numerical results. When b/h 6 2, the xn/xa values are almost unity (0.999–1.000) between 0.3 and 0.7 of x/L. However, the effect of warping becomes more significant with increase in b/h. The numerical result suggests that the effect of warping on torsional rigidity can be neglected under the condition of b/h < 2 and 0.25 < x/L < 0.75. The shear moduli Gxy and Gzx are determined by the following procedure. When the specimen width b and thickness h are fixed, the torsional rigidity GJ is represented as a function of Gxy and Gzx as follows: GJ ¼ f ðGxy ; GzxÞ. ð2Þ Considering two specimens, 1 and 2, with different rectangular cross-section, the following nonlinear simultaneous equations f1 and f2 are obtained: GJ 1 ¼ f1ðGxy ; GzxÞ; GJ 2 ¼ f2ðGxy ; GzxÞ. ð3Þ In Eq. (3) GJ1 and GJ2 are obtained from torsional experiments. The two equations are solved for Gxy and Gzx by any numerical methods such as Newton–Raphson method. 3. Experimental procedure 3.1. Materials [9,20] The composite under investigation contained TyrannoTM Lox-M fibers woven into an orthogonal 3D con- figuration with fiber volume fractions of 19%, 19%, and 2% in the x, y, and z directions, respectively. Optical micrographs and schematic drawing in Fig. 3 illustrate the fiber architecture of the present composites with each fiber bundle containing 1600 fibers. The composite preform plate (240 · 120 · 6 mm) was treated at elevated temperature in a CO atmosphere, resulting in the formation of a 10 nm SiOx-rich layer surrounding an inner 40 nm carbon-rich layer at the fiber surface [20]. The nano-scale carbon-rich layer is believed to result in interphase with desirable properties between the fiber and matrix. Poly-titano-carbosilane was used as the matrix precursor with eight impregnation and pyrolysis cycles, the average composite bulk density was 2.20 g/cm3 . Tensile specimens were machined from the composite plates such that the loading direction was parallel to the y-axis. The specimen surfaces were also ground to a flat finish such that the interlacing loops shown in Fig. 3 were not present in the final specimens. The unit cell size is 3 mm · 3 mm. 3.2. Tensile tests Both on-axis (0/90) and off-axis (±45) tensile tests were conducted on a servo-hydraulic testing rig (Model 8501, Instron, USA) at room temperature in air using a specimen geometry as shown in Fig. 4(a) Cardboard tabs were bonded to the specimen end regions with the load being applied using hydraulic wedge grips. A clip gauge-type extensometer (gauge length 25 mm; Model 632.11C-20, MTS, USA) was used to measure the longitudinal strain. Transverse strains were measured using Fig. 3. Optical micrographs and schematic drawing of a SiC/SiC composite illustrating the orthogonal 3D woven fiber architecture. 0 0.2 0.4 0.6 0.8 1 0.5 0.6 0.7 0.8 0.9 1 1.1 x / L ωn / ωa b / h =1 b / h =2 b / h =4 b / h =8 Grip area Fig. 2. Effect of cross-section geometry (b/h) on warping torsion (L/H = 26.7, Gxy/Gzx = 2, b/h = 1, 2, 4, 8). xn: twist angle per length calculated from FEA, xa: twist angle per length calculated from the Lekhnitskiis equation (Eq. (1)). T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549 2543
T Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 110-125 Mirror a Thickness: 1=4 *:k Fixed end Mirror positio Width: b=6or 9 Thickness: t=4.5 Half mirror He-Ne laser Fig 4. Specimen configuration and dimensions used for the experi- ments:(a)tensile test, (b) torsional test. Mirror a strain gauges(gauge length 5 mm)which were bonded on both of the specimen surfaces. The displacement rate Scale a was 0.5 mm/min Matrix cracking characteristics under on-axis loading Fig. 5. Schematic configuration of a torsional test: (a)torsional test were investigated for a specimen using the replica film setting,(b)optical lever system( top view) method with surface replicas being taken under load at various stages of the loading cycle 3.3. Torsional test Pulley 1 Specimen configuration and dimensions used for tor- sional tests are shown in Fig. 4(b). Two kinds of speci- mens with different width b(b=6 and 9 mm)were Mirror prepared. The thickness, h, was 4.5 mm. Note that the pecimen width is 2 or 3 times in the size of a fabric unit cell (3 mm) Schematic drawings and photograph of torsional te configuration are shown in Figs. 5 and 6, respectively One end of a specimen was fixed to a base fixture, and Specimen a torsion arm was attached at another end. torsional moment was applied through the torsion arm to the pecimen as shown in Figs 5(a) and 6. A weight (F1) Fig. 6. Photograph showing the torsional test setting. was directly hung at one end of the torsion arm, and weight (F2, FI= F2) was subjected at another end through the pulley 1. Own weight (w)of the specimen determined by measuring the distance between the and torsion arm was cancelled using a weight (w) flected beams. The locations of the mirror points shown through the pulley 2. in Fig. 5(a) reflect the constraint of 0.25 <x/L <0.75 An optical lever system was used for measuring the obtained by the FEA simulation. Torsional rigidity GJ twist angle of the specimen. An optical lever is a conve- is defined as follows make possible an accurate measurement of the displace- G/=M:/o, O=(0A-OB)/d, ment. Two small mirrors were put at the point A and b where d is the distance between two mirrors(50 mm) on the specimen upper surface as shown in Figs. 5(a) Applied torsion moment was between 0. 2 and 0. 8 Nm. and 6 He-Ne laser beams were irradiated to the mirrors It was preliminarily confirmed that microcrack propaga as shown in Fig. 5(b), and torsion angles 0a, OB were tion never occur under the torsional moment
strain gauges (gauge length 5 mm) which were bonded on both of the specimen surfaces. The displacement rate was 0.5 mm/min. Matrix cracking characteristics under on-axis loading were investigated for a specimen using the replica film method with surface replicas being taken under load at various stages of the loading cycle. 3.3. Torsional test Specimen configuration and dimensions used for torsional tests are shown in Fig. 4(b). Two kinds of specimens with different width b (b = 6 and 9 mm) were prepared. The thickness, h, was 4.5 mm. Note that the specimen width is 2 or 3 times in the size of a fabric unit cell (3 mm). Schematic drawings and photograph of torsional test configuration are shown in Figs. 5 and 6, respectively. One end of a specimen was fixed to a base fixture, and a torsion arm was attached at another end. Torsional moment was applied through the torsion arm to the specimen as shown in Figs 5(a) and 6. A weight (F1) was directly hung at one end of the torsion arm, and a weight (F2, F1 = F2) was subjected at another end through the pulley 1. Own weight (w) of the specimen and torsion arm was cancelled using a weight (w) through the pulley 2. An optical lever system was used for measuring the twist angle of the specimen. An optical lever is a convenient device to magnify a small displacement and thus to make possible an accurate measurement of the displacement. Two small mirrors were put at the point A and B on the specimen upper surface as shown in Figs. 5(a) and 6. He–Ne laser beams were irradiated to the mirrors as shown in Fig. 5(b), and torsion angles hA, hB were determined by measuring the distance between the re- flected beams. The locations of the mirror points shown in Fig. 5(a) reflect the constraint of 0.25 < x/L < 0.75 obtained by the FEA simulation. Torsional rigidity GJ is defined as follows: GJ ¼ Mt=x; x ¼ ðhA hBÞ=d; ð4Þ where d is the distance between two mirrors (50 mm). Applied torsion moment was between 0.2 and 0.8 N m. It was preliminarily confirmed that microcrack propagation never occur under the torsional moment. Mirror A Mirror B Specimen Fixed end Gxy Mt Gzx h F1 F2 b be d θ A θ B A B Half mirror He-Ne laser Mirror B Mirror A Scale B Scale A a b Fig. 5. Schematic configuration of a torsional test: (a) torsional test setting, (b) optical lever system (top view). 120 b Width: b = 6 or 9 Thickness: t = 4.5 (mm) Mirror position 35 Fiber orientation: 110 ∼ 125 10 Thickness: t = 4 (mm) Fiber orientation 0 /90 : ±45 : a b Fig. 4. Specimen configuration and dimensions used for the experiments: (a) tensile test, (b) torsional test. Fig. 6. Photograph showing the torsional test setting. 2544 T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549
T. Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 In order to investigate the effect of on-axis loading on Table I shear properties, torsional tests were carried out for the Initial elastic moduli obtained from on-axis and +45 off-axis tensile pre-loaded specimen. The specimen was loaded up to peak stress under a constant loading rate of 1 MPa/s, pecimen E(GPa)v G(GPa) and then unloaded. Consequently, a torsional rigidity umber was measured by a torsional test. The peak stress was On-axis raised step by step, for example, 40, 60, 80 MPa, and +45 off-axis tensile test I so on. When the specimen was broken, the test was 19 finished Average 118 0.20748.8 4. Results and discussion 4.2. Torsional test for pristine specimens 4. Monotonic tensile test At first. the shear modulus of aluminum alloy Typical stress-strain curves obtained from on-axis (A5052) was measured for verifying the torsional test (0°/90°)and±45°of- axis tensile tests are shown methodology. Specimens with different rectangular ig. 7. In-plane shear modulus Gxy was estimated from cross-section (thickness 4 mm, width 4 and 6 mm)were +45 off-axis stress-strain curves below 30 MPa using the following equation: width were prepared. The shear modulus measured by he torsional test was 27.0 GPa, which agreed with the 2(1+v45) (5) shear modulus(27.3 GPa) obtained from a tensile dulus 72.5 GPa. Poisson s ratio where E4s and v4s are Youngs modulus and Poisson's Data scattering(coefficient of variation; CV) for alum ratio in±45°of- axis tensile test. num specimens was less than 0.5 %. The Youngs modulus E, Poissons ratio v, and in Average torsional rigidity G] obtained from three plane shear modulus Gxy are summarized in Table 1. Ini pecimens for each specimen geometry was 4.33 Nm tial Young's modulus Ex, in on-axis(0%/90%), was 126 for a 6 mm width specimen, and 848N m for amm GPa, which is similar to that in +45 off-axis testing width specimen as summarized in Table 2 Data scatter- (118 MPa). The data scatter for three specimens is about ing(CV)for composite specimens was about 3-5% as 3-6%. However. stress-strain behavior above 30 MPa is shown in Tables I and 2, and this is much more signif- much different from each other. It is reported that the cant than that for aluminum specimens. The specimen stress-strain curves obtained from +45 off-axis tensile width was only 2 or 3 times in the size of a fabric unit ith the cell (3 mm). This suggests that the scattering in cutting shear tests(losipescu configuration)[4, 14, 15]. This im- a specimen from a plate affects the experimental results plied that the normal stress ox and o, as well as shear Therefore, several specimens are required to obtain reli stress txy affected the degradation of shear stifness Ga able results. USing Eq(1), one curve is drawn for one pecimen geometry in G2x-Gxy plane as shown in Fig 8. and the intersection of two curves gives the solution of Eq (1). The shear moduli, Gry and G-r, were deter- mined to be 45.3 and 35.6 GPa, respectively. The mea 0°/90°E 11a sured in-plane shear modulus Gry almost agreed with hat measured from the +45 off-axis tensile test (48.8 GPa) In G=x-Gxu plane, the gradient(d increases with increase of b/h, which suggests that the 100±45Er ±45°EL Initial torsional rigidity (h m,M1=0.2-0.8Nm) Specimen Width, 6 mm Width, 9 mm number b/h=4/3) (b/h=2) Strain, EL, ET(%) Fig. 7. Typical stress-strain curves obtained from on-axis(0/90%)and ±45°of- axis tensile tests. Average
In order to investigate the effect of on-axis loading on shear properties, torsional tests were carried out for the pre-loaded specimen. The specimen was loaded up to peak stress under a constant loading rate of 1 MPa/s, and then unloaded. Consequently, a torsional rigidity was measured by a torsional test. The peak stress was raised step by step, for example, 40, 60, 80 MPa, and so on. When the specimen was broken, the test was finished. 4. Results and discussion 4.1. Monotonic tensile test Typical stress–strain curves obtained from on-axis (0/90) and ±45 off-axis tensile tests are shown in Fig. 7. In-plane shear modulus Gxy was estimated from ±45 off-axis stress–strain curves below 30 MPa using the following equation: Gxy ¼ E45 2ð1 þ m45Þ ; ð5Þ where E45 and m45 are Youngs modulus and Poissons ratio in ±45 off-axis tensile test. The Youngs modulus E, Poissons ratio m , and inplane shear modulus Gxy are summarized in Table 1. Initial Youngs modulus Ex, in on-axis (0/90), was 126 GPa, which is similar to that in ±45 off-axis testing (118 MPa). The data scatter for three specimens is about 3–6%. However, stress–strain behavior above 30 MPa is much different from each other. It is reported that the stress–strain curves obtained from ±45 off-axis tensile tests did not coincide with those obtained from pure shear tests (Iosipescu configuration) [4,14,15]. This implied that the normal stress rx and ry as well as shear stress sxy affected the degradation of shear stiffness Gxy. 4.2. Torsional test for pristine specimens At first, the shear modulus of aluminum alloy (A5052) was measured for verifying the torsional test methodology. Specimens with different rectangular cross-section (thickness 4 mm, width 4 and 6 mm) were used for the experiments. Three specimens for each width were prepared. The shear modulus measured by the torsional test was 27.0 GPa, which agreed with the shear modulus (27.3 GPa) obtained from a tensile test (Youngs modulus 72.5 GPa, Poissons ratio 0.328). Data scattering (coefficient of variation; CV) for aluminum specimens was less than 0.5 %. Average torsional rigidity GJ obtained from three specimens for each specimen geometry was 4.33 N m2 for a 6 mm width specimen, and 8.48 N m2 for a 9 mm width specimen as summarized in Table 2. Data scattering (CV) for composite specimens was about 3–5 % as shown in Tables 1 and 2, and this is much more significant than that for aluminum specimens. The specimen width was only 2 or 3 times in the size of a fabric unit cell (3 mm). This suggests that the scattering in cutting a specimen from a plate affects the experimental results. Therefore, several specimens are required to obtain reliable results. Using Eq. (1), one curve is drawn for one specimen geometry in Gzx–Gxy plane as shown in Fig. 8, and the intersection of two curves gives the solution of Eq. (1). The shear moduli, Gxy and Gzx, were determined to be 45.3 and 35.6 GPa, respectively. The measured in-plane shear modulus Gxy almost agreed with that measured from the ±45 off-axis tensile test (48.8 GPa). In Gzx–Gxy plane, the gradient (dGzx/dGxy) of a curve increases with increase of b/h, which suggests that the -1 0 1 2 0 50 100 150 200 250 300 350 Strain, ε L , ε T (%) Stress (MPa) 0˚/90˚ ε L 0˚/90˚ ε Τ ±45˚ ε L ±45˚ ε T Fig. 7. Typical stress–strain curves obtained from on-axis (0/90) and ±45 off-axis tensile tests. Table 1 Initial elastic moduli obtained from on-axis and ±45 off-axis tensile tests Specimen number E (GPa) m Gxy (GPa) On-axis tensile test 1 126 0.168 ±45 off-axis tensile test 1 114 0.223 46.6 2 119 0.188 50.1 3 120 0.210 49.6 Average 118 0.207 48.8 Table 2 Initial torsional rigidity (h = 4.5 mm, Mt = 0.2–0.8 N m) Specimen number Width, 6 mm (b/h = 4/3) Width, 9 mm (b/h = 2) Torsional rigidity GJ (N m2 ) 1 4.09 8.44 2 4.50 8.61 3 4.39 8.39 Average 4.33 8.48 T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549 2545
T Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 b±9 Dhm多mm bundle 3035404550556 Fig 8. Estimation of shear moduli Gx and G-x from the torsional test experimental error becomes more significant. Thus, pecimen geometry is important to obtain good results in this method. If the in-plane shear modulus is already measured using losipescu shear test or 45 off-axis test, the out-of-plane shear modulus can be measured more accurately by this method. If in-plane and out-of-plane shear moduli are unknown these moduli can be ob- x fiber bundle y fiber bundle tained simultaneously. This method only requires small and thin(<3 mm) specimens, and a simple equipment z fiber bundle matrix region They are important advantages of this method Shear modulus of the pristine composite was esti- Fig. 9 nt model of an orthogonal 3D woven SiC/SiC mated by finite element analysis to verify the experimen- compe region(matrix region) was assumed to be pore tal result. Optical micrograph showing x-z cross-section a)Optica howing SiC matrix in pocket regions, (b)finite of the composite is shown in Fig. 9(a). In the pocket re- element of the unit cell gion(no fiber bundle region), matrix is separated from the adjacent fiber bundles. Therefore, this region was re- garded as entire pore(porosity 10 vol %) Unit cell was modeled and divided into finite elements as shown in Fig. 9(b). A computer code based on homogenization pore= 10% method was developed and applied for the calculation Homogenization method is basically a finite element I40 method, and this is effective to deal with periodic struc e120 tures such as composite materials. Basic methodology of 100 this computer code has been presented elsewhere [21] 80 Both sic fiber and sic matrix were assumed to be iso- tropic materials with Poisson ratio of 0.2, and the a0}2=2cnQ( Youngs modulus of Sic fiber was Ef=187 GPa. 40 Youngs modulus of Sic matrix, Em, is an unknown G2=35.8GP parameter, therefore it was estimated by the parametric stud Numerical results are shown in Fig. 10. When the Fig. 10. Estimation of elastic moduli Er, Gxn and G2x of the composite Youngs modulus of SiC matrix is Em= 126 GPa, the as a function of Young's modulus of matrix Em calculated Ex of the composite agrees with the experi- mental result(126 GPa). Then the calculated shear mod uli Gxy and G=x are 49. 2 and 35.8 GPa, respectively. 4.3. Effect of on-axis tensile stress on shear properties These values are quite similar to the experimental results btained from the torsional test G= 45.3 GPa The relationship between torsional rigidity and G_=35.6 GPa on-axial maximum tensile stress is shown in Fig. 11
experimental error becomes more significant. Thus, specimen geometry is important to obtain good results in this method. If the in-plane shear modulus is already measured using Iosipescu shear test or 45 off-axis test, the out-of-plane shear modulus can be measured more accurately by this method. If in-plane and out-of-plane shear moduli are unknown, these moduli can be obtained simultaneously. This method only requires small and thin (<3 mm) specimens, and a simple equipment. They are important advantages of this method. Shear modulus of the pristine composite was estimated by finite element analysis to verify the experimental result. Optical micrograph showing x–z cross-section of the composite is shown in Fig. 9(a). In the pocket region (no fiber bundle region), matrix is separated from the adjacent fiber bundles. Therefore, this region was regarded as entire pore (porosity 10 vol.%). Unit cell was modeled and divided into finite elements as shown in Fig. 9(b). A computer code based on homogenization method was developed and applied for the calculation. Homogenization method is basically a finite element method, and this is effective to deal with periodic structures such as composite materials. Basic methodology of this computer code has been presented elsewhere [21]. Both SiC fiber and SiC matrix were assumed to be isotropic materials with Poisson ratio of 0.2, and the Youngs modulus of SiC fiber was Ef = 187 GPa. Youngs modulus of SiC matrix, Em, is an unknown parameter, therefore it was estimated by the parametric study. Numerical results are shown in Fig. 10. When the Youngs modulus of SiC matrix is Em = 126 GPa, the calculated Ex of the composite agrees with the experimental result (126 GPa). Then the calculated shear moduli Gxy and Gzx are 49.2 and 35.8 GPa, respectively. These values are quite similar to the experimental results obtained from the torsional test, Gxy = 45.3 GPa, Gzx = 35.6 GPa. 4.3. Effect of on-axis tensile stress on shear properties The relationship between torsional rigidity and on-axial maximum tensile stress is shown in Fig. 11. Fig. 9. Finite element model of an orthogonal 3D woven SiC/SiC composite. The pocket region (matrix region) was assumed to be pore. (a) Optical micrograph showing SiC matrix in pocket regions, (b) finite element model of the unit cell. 80 100 120 140 160 0 20 40 60 80 100 120 140 160 180 Elastic modulus, Ex, Gxy, Gzx (GPa) Ex Gxy Gzx Ex=126GPa Em=126GPa Gxy=49.2GPa Gzx=35.8GPa Vpore = 10% Fig. 10. Estimation of elastic moduli Ex, Gxy, and Gzx of the composite as a function of Youngs modulus of matrix Em. 30 35 40 45 50 55 60 20 25 30 35 40 45 50 Shear modulus, Gxy (GPa) Shear modulus, Gzx (GPa) b =9 mm b =6 mm Fig. 8. Estimation of shear moduli Gxy and Gzx from the torsional test results. 2546 T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549
T. Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 ●b=6 o b=9 mm 冒06 0 0.4 0100150200250300350 0.1mm Fig. 11. Effect of on-axis tensile stress on torsional rigidity G. The Loading direction torsional rigidity was normalized by the initial values of GJo Fig. 13. Optical micrograph of the replica films, illustrating matrix cracking within the transverse (90 )fiber bundles at 320 MPa The torsional rigidity GJ is normalized by the initial for a 6 mm width specimen, and 428 MPa for a 9 mm 320 MPa, is shown in Fig. 13. Beyerle et al. [4] reported width specimen, respectively. The torsional rigidity that the shear stiffness decreased under pure shear stres values were measured up to on-axis stress levels of (losipescu shear test). The experimental results suggest 320 MPa. Because the torsion moment versus twist that the shear stiffness degradation is caused by on-axis angle relation was linear, it is suggested that any crack tensile stress as well as shear stress, and this is due to propagation did not occur during the torsional tests transverse cracking in 90 fiber bundles and matrix The torsional rigidity finally decreased by 60%of the cracking in the 0o fiber bundles initial value at 320 MPa as shown in Fig. 11 The relationship between the transverse crack density Degradation of the torsional rigidity indicates that and maximum tensile stress is represented in Fig. 14 shear moduli Gx and Gex vary due to on-axis tensile The onset of transverse crack propagation is approxl- mately 40 MPa. The transverse crack initiation stress I-axis tensile stress is shown in Fig. 12, which repre- corresponds to the onset of decrease in GJ( see Fi sents the decrease of both Gry and G=r. As reported in I1), and the crack density reaches 11-12 mmat the previous study [91, SiC/SiC woven composites suffer 320 MPa. From Fig. 12, it is seen that the tensile stress from two major damage modes under tensile stress: (1) at the onset of decrease of Gxy coincides with the trans transverse cracking in the transverse(90%)fiber bundles, verse crack initiation stress (40 MPa), whereas almost and(2)matrix cracking in the longitudinal(0%) fiber no degradation of Ger is recognized until the tensile bundles.An optical micrograph of the replica films, stress of 100 MPa. In laminated composites, it is well illustrating transverse cracking within the 90o fiber known that in-plane shear modulus degrades due to bundles and matrix cracking in the 0 fiber bundles at 10 100150200250300350 Maximum tensile stress(MPa) Fig. 12. The relationship between shear moduli(Gxv, Gex) and on-axi Fig 14. Transverse crack density in the 90 fiber bundles as a function of the on-axis maximum tensile stress
The torsional rigidity GJ is normalized by the initial value GJ0. The ultimate tensile strength was 414 MPa for a 6 mm width specimen, and 428 MPa for a 9 mm width specimen, respectively. The torsional rigidity values were measured up to on-axis stress levels of 320 MPa. Because the torsion moment versus twist angle relation was linear, it is suggested that any crack propagation did not occur during the torsional tests. The torsional rigidity finally decreased by 60% of the initial value at 320 MPa as shown in Fig. 11. Degradation of the torsional rigidity indicates that shear moduli Gxy and Gzx vary due to on-axis tensile stress. The relationship between shear moduli and on-axis tensile stress is shown in Fig. 12, which represents the decrease of both Gxy and Gzx. As reported in the previous study [9], SiC/SiC woven composites suffer from two major damage modes under tensile stress: (1) transverse cracking in the transverse (90) fiber bundles, and (2) matrix cracking in the longitudinal (0) fiber bundles. An optical micrograph of the replica films, illustrating transverse cracking within the 90 fiber bundles and matrix cracking in the 0 fiber bundles at 320 MPa, is shown in Fig. 13. Beyerle et al. [4] reported that the shear stiffness decreased under pure shear stress (Iosipescu shear test). The experimental results suggest that the shear stiffness degradation is caused by on-axis tensile stress as well as shear stress, and this is due to transverse cracking in 90 fiber bundles and matrix cracking in the 0 fiber bundles. The relationship between the transverse crack density and maximum tensile stress is represented in Fig. 14. The onset of transverse crack propagation is approximately 40 MPa. The transverse crack initiation stress corresponds to the onset of decrease in GJ (see Fig. 11), and the crack density reaches 11–12 mm1 at 320 MPa. From Fig. 12, it is seen that the tensile stress at the onset of decrease of Gxy coincides with the transverse crack initiation stress (40 MPa), whereas almost no degradation of Gzx is recognized until the tensile stress of 100 MPa. In laminated composites, it is well known that in-plane shear modulus degrades due to 0 50 100 150 200 250 300 350 0 10 20 30 40 50 Shear modulus, Gxy, Gzx (GPa) Gxy Gzx Fig. 12. The relationship between shear moduli (Gxy,Gzx) and on-axis tensile stress. Fig. 13. Optical micrograph of the replica films, illustrating matrix cracking within the transverse (90) fiber bundles at 320 MPa. 0 100 200 300 0 2 4 6 8 10 12 14 Maximum tensile stress (MPa) Transverse crack density (mm-1) Fig. 14. Transverse crack density in the 90 fiber bundles as a function of the on-axis maximum tensile stress. 0 50 100 150 200 250 300 350 0.2 0.4 0.6 0.8 1 Normalized torsional rigidity, GJ /G J 0 b =6 mm b =9 mm Fig. 11. Effect of on-axis tensile stress on torsional rigidity GJ. The torsional rigidity was normalized by the initial values of GJ0. T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549 2547
T. Ogasawara et al. Composites Science and Technology 65(2005)2541-2549 transverse cracking. However, Whitney [22] reported that out-of-plane shear modulus transverse cracking in 90 layers. These results indicate that Gry decreases due to the accumulation of transverse cracks in the 90 fiber bundles and matrix cracks in the 0o fiber bundles, while Gex is affected only by matrix cracks in o fiber bundles Finally, the degradation of in-plane shear stiffness of the orthogonal 3 D woven CMC as a function of trans- verse crack density is predicted using the shear-lag model. It is assumed that: (1)z-bundles are neglected here because of their low volume fraction, and orthog 2468 onal 3D woven composites are treated as laminates with multiple0°/90° ply blocks (i.e.,([09/90°1) lami nsity(mm nates), and(2)analysis of [0 /90] laminates can be Fig. 16. Relationship between the shear modulus (Grr) and the matic drawing of the shear-lag model of a cross-ply corresponding initial value (Gmg/ar modulus is normalized by the applied to([0%/90%1) laminates. Fig. 15 shows sche transverse crack density. Each sh laminated composite. The relationship between the shear stresses and the through-the-thickness average in-plane displacements of each layer is written by the laminate as a function of transverse crack density p is gi- following equation ven by H1u01「a2-l 1+ t? 2p tanh G10 where u; and v; are average in-plane displacements of the B2(1+) 0(=l)and 90(i= 2)layers in the x and y directions GLt It2 HI parameters are often dealt with as empirical parameters. When Eq (7)is used for the shear-lag parameter, Eq ( 8) The parameters are also determined by assuming the predicts the lower limit of the shear stiffness reduction fur nction l;, Ui) in each [2] example, Tsai and Daniel [ll], Nuismer and Tan [23] Using Eqs. (7) and( 8)the in-plane shear modulus proposed the following equations as the shear-lag was calculated as a function of transverse crack den- sity. The numerical result is plotted by the solid line in Fig. 16. The parameters used for the calculation HIL 3GLT GTT BGLT GI H ) were GLT=453 GPa, GTT=29.3 GPa and 11=t2 t?GLT+hI GTT t, GLT t ?G 0. 16 mm, respectively. The shear moduli, GLT, GTT, where GLt and Grr are longitudinal and transverse of a lamina were assumed by the reuss type approxi- shear stifness of unidirectional composites(or fiber bun- mation based on the experimental results. The effect dles), respectively, and I, and f2 are thickness of 0 and of the 3D woven architecture including voids(pocket 90 layers. The in-plane shear modulus of the whole region) was not explicitly considered as described re, and incorporated into these shear modulus values. Although it is known that Eq(8)predicts the lower limit, the numerical curve almost agreed with the experimental data. This result also suggests that the in- plane shear stifness is degraded by matrix crack (i,+1) ing in 0 fiber bundles as well as transverse cracking in 90° fiber bundles. i" ply T +1+2) 5. Conclusion i+1ply=(+1+2) Shear moduli c、 and G=r of an orthogonal 3D x woven SiC/SiC composite were estimated by torsional tests of rectangular cross-section specimens. In-plane shear modulus Gxy from the torsional test agreed with laminated composite that measured from +45 off-axis tensile test. FEM
transverse cracking. However, Whitney [22] reported that out-of-plane shear modulus Gzx is insensitive to transverse cracking in 90 layers. These results indicate that Gxy decreases due to the accumulation of transverse cracks in the 90 fiber bundles and matrix cracks in the 0 fiber bundles, while Gzx is affected only by matrix cracks in 0 fiber bundles. Finally, the degradation of in-plane shear stiffness of the orthogonal 3 D woven CMC as a function of transverse crack density is predicted using the shear-lag model. It is assumed that: (1) z-bundles are neglected here because of their low volume fraction, and orthogonal 3D woven composites are treated as laminates with multiple 0/90 ply blocks (i.e., ([0/90]s)n laminates), and (2) analysis of [0/90]s laminates can be applied to ([0/90]s)n laminates. Fig. 15 shows schematic drawing of the shear-lag model of a cross-ply laminated composite. The relationship between the shear stresses and the through-the-thickness average in-plane displacements of each layer is written by the following equation: sxz syz ¼ H11 0 0 H22 u2 u1 v2 v1 ; ð6Þ where ui and vi are average in-plane displacements of the 0 (i = 1) and 90 (i = 2) layers in the x and y directions. H11 and H22 are the shear-lag parameters. The shear-lag parameters are often dealt with as empirical parameters. The parameters are also determined by assuming the function of displacement (ui, vi) in each layer. For example, Tsai and Daniel [11], Nuismer and Tan [23] proposed the following equations as the shear-lag parameters: H11 ¼ 3GLTGTT t2GLT þ t1GTT ; H22 ¼ 3GLTGTT t1GLT þ t2GTT ; ð7Þ where GLT and GTT are longitudinal and transverse shear stiffness of unidirectional composites (or fiber bundles), respectively, and t1 and t2 are thickness of 0 and 90 layers. The in-plane shear modulus of the whole laminate as a function of transverse crack density q is given by: Gxy ðqÞ Gxy0 ¼ 1 þ t2 t1 2q a tanh a 2q 1 ; a ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi H22 GLT 1 t1 þ 1 t2 s . ð8Þ When Eq. (7) is used for the shear-lag parameter, Eq. (8) predicts the lower limit of the shear stiffness reduction [12]. Using Eqs. (7) and (8) the in-plane shear modulus was calculated as a function of transverse crack density. The numerical result is plotted by the solid line in Fig. 16. The parameters used for the calculation were GLT = 45.3 GPa, GTT = 29.3 GPa and t1 = t2 = 0.16 mm, respectively. The shear moduli, GLT, GTT, of a lamina were assumed by the Reuss type approximation based on the experimental results. The effect of the 3D woven architecture including voids (pocket region) was not explicitly considered as described above, and incorporated into these shear modulus values. Although it is known that Eq. (8) predicts the lower limit, the numerical curve almost agreed with the experimental data. This result also suggests that the in-plane shear stiffness is degraded by matrix cracking in 0 fiber bundles as well as transverse cracking in 90 fiber bundles. 5. Conclusion Shear moduli Gxy and Gzx of an orthogonal 3D woven SiC/SiC composite were estimated by torsional tests of rectangular cross-section specimens. In-plane shear modulus Gxy from the torsional test agreed with that measured from ±45 off-axis tensile test. FEM Fig. 15. Schematic drawing of a shear-lag model of a cross-ply laminated composite. 0 2 4 6 8 10 0 0. 2 0. 4 0. 6 0. 8 1 Transverse crack density (mm-1) Gxy /Gxy0 Fig. 16. Relationship between the shear modulus (Gxy) and the transverse crack density. Each shear modulus is normalized by the corresponding initial value (Gxy0). 2548 T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549
T. Ogasawara et al./ Composites Science and Technology 65(2005)2541-2549 analysis based on homogenization method was also con- 18 Park CH, McManus HL. Thermally induced damage in compos- ducted for verifying the experimental results. A good ite laminates: predictive methodology and experimental investi- orrespondence between the analytical and the experi tion. Comp Sci Technol 1996: 56: 1209-19 mental results was obtained. the effect of on-axis tensile 9] Ogasawara T, Ishikawa T, Ito H, Watanabe N, Davies D. Multiple cracking and tensile behavior for an orthogonal 3-D stress on shear properties was also investigated. Both in woven Si-Ti-C-O fiber/Si-Ti-C-O matrix composite. J Am plane and out-of-plane shear moduli decreased witl Ceram Soc2001;84(7):1565-74 creasing maximum tensile stress. It was confirmed that [10]Kobayashi S, Kawamoto H, Wakayama S Evaluation of shear in-plane shear stiffness degrades due to transverse crack modulus of te laminates containing microscopic damages in 90 fiber bundles and matrix cracking in 0o fiber Mater Syst 2002: 20: 125-30 [ in Japa [11] Tsai CL, Daniel IM. The behavior of cracked le out-of-plane shear stiffness is affected laminates under shear loading. Int J Solids by matrix cracking in 00 fiber bundles. The degradation 3251-67 of in-plane shear modulus was predicted based on the [2] Hashin Z. Analysis of cracked laminates: a variational approach shear- lag model for a cross-ply laminated composite [13] Gudmundson P, Zang w. An analysis model for thermoelastic and compared with experimental results roperties of composite laminates containing transverse matrix It was demonstrated that the torsional test is an effec- cracks. Int j Solids struct 1993: 30- 3211-31 ive method to estimate out-of-plane shear modulus of [14] Cady C, Heredia FE, Evans AG. In-plane mechanical properties ceramic matrix composites, because a thick specimen is not required 1995:78(8):2065-78 [15] Genin GM, Hutchinson JW. Composite laminates in plane stress: constitutive modeling and stress redistribution due to matrix cracking. J Am Ceram Soc 1997: 80(5): 1245-55 References [16] Ishikawa T, Koyama K, Kobayashi S. Elastic moduli of carbon epoxy composites and carbon fibers. J Compos Mater [1 Evans AG, Zok Fw. The physics and mechanics of fibre 1977:11:332-4. reinforced brittle matrix c tes. J Mater Sci 1994: 29: 3857-9 [7] Lekhnitskii SG. Theory of elasticity of an anisotropic elastic 2 Hutchinson JW, Jensen HM. Models of fiber debonding and body. San Francisco: Holden-Day, Inc; 1963. p. 197-205 allout in brittle composites with friction. Mech Mater 1990: 9: [18] Tsai C-L, Daniel IM, Yaniv G. Torsional response of rectangular omposite laminates. J Appl Mech 1990: 57: 383-7 3] Karandikar P, Chou T-W. Characterization and modeling of [19] Swanson SR. Torsion of laminated rectangular rods. Comput cocracking and elastic modulo changes in Nicalon/CAS Struct1998:42:23-31 tes Comp Sci Technol 1993: 46: 253-63 20 Ishikawa T, Bansaku K, Watanabe N, Nomura Y, Shibuya [4 Beyerle DS, Spearing SM, Evans AG. Damage mechanisms and M, Hirokawa T. Experimental stress/strain behavior of SiC. the mechanical properties of laminated 0/90 ceramic/matrix matrix composites reinforced with Si-Ti-C-O fibers and omposite. J Am Ceram Soc 1992: 75(12): 3321-30 estimation of matrix elastic modulus. Comp Sci Technol [Okabe T, Komotori J, Shimizu M, Takeda N. Mechanical 998:58:51-63 behavior of sic fiber reinforced brittle-matrix composites J Mater [21] Watanabe N, Teranishi K. Thermal stress analysis for Al Scil99934:3405-12 honeycomb sandwich plates with very thin CFRP faces. AIAA- [6 Kuo W-s, Chou T-W. Multiple cracking of unidirectional and 5-1394:1995 22] Whitney JM. Effective elastic constants of bidirectional lami- ates containing transverse ply cracks. J Comp Mater 2000:3 [7 Xia ZC, Carr RR, Hutchinson JW. Transverse cracking in fiber- 54-78 einforced brittle matrix ly laminates. Acta Metall Mater [23] Nuismer RJ, Tan SC. Constitutive relations of a cracked composite lamina. J Comp Mater 1989: 22: 306-21
analysis based on homogenization method was also conducted for verifying the experimental results. A good correspondence between the analytical and the experimental results was obtained. The effect of on-axis tensile stress on shear properties was also investigated. Both inplane and out-of-plane shear moduli decreased with increasing maximum tensile stress. It was confirmed that in-plane shear stiffness degrades due to transverse cracking in 90 fiber bundles and matrix cracking in 0 fiber bundles, while out-of-plane shear stiffness is affected by matrix cracking in 0 fiber bundles. The degradation of in-plane shear modulus was predicted based on the shear-lag model for a cross-ply laminated composite, and compared with experimental results. It was demonstrated that the torsional test is an effective method to estimate out-of-plane shear modulus of ceramic matrix composites, because a thick specimen is not required. References [1] Evans AG, Zok FW. The physics and mechanics of fibrereinforced brittle matrix composites. J Mater Sci 1994;29:3857–96. [2] Hutchinson JW, Jensen HM. Models of fiber debonding and pullout in brittle composites with friction. Mech Mater 1990;9: 139–63. [3] Karandikar P, Chou T-W. Characterization and modeling of microcracking and elastic modulo changes in Nicalon/CAS composites. Comp Sci Technol 1993;46:253–63. [4] Beyerle DS, Spearing SM, Evans AG. Damage mechanisms and the mechanical properties of laminated 0/90 ceramic/matrix composite. J Am Ceram Soc 1992;75(12):3321–30. [5] Okabe T, Komotori J, Shimizu M, Takeda N. Mechanical behavior of sic fiber reinforced brittle-matrix composites. J Mater Sci 1999;34:3405–12. [6] Kuo W-S, Chou T-W. Multiple cracking of unidirectional and cross-ply ceramic matrix composites. J Am Ceram Soc 1995;78(3): 745–55. [7] Xia ZC, Carr RR, Hutchinson JW. Transverse cracking in fiberreinforced brittle matrix, cross-ply laminates. Acta Metall Mater 1993;41(8):2365–76. [8] Park CH, McManus HL. Thermally induced damage in composite laminates: predictive methodology and experimental investigation. Comp Sci Technol 1996;56:1209–19. [9] Ogasawara T, Ishikawa T, Ito H, Watanabe N, Davies IJ. Multiple cracking and tensile behavior for an orthogonal 3-D woven Si–Ti–C–O fiber/Si–Ti–C–O matrix composite. J Am Ceram Soc 2001;84(7):1565–74. [10] Kobayashi S, Kawamoto H, Wakayama S. Evaluation of shear modulus of composite laminates containing microscopic damages. Mater Syst 2002;20:125–30 [in Japanese]. [11] Tsai CL, Daniel IM. The behavior of cracked cross-ply composite laminates under shear loading. Int J Solids Struct 1992;29(24): 3251–67. [12] Hashin Z. Analysis of cracked laminates: a variational approach. Mech Mater 1985;4:121–36. [13] Gudmundson P, Zang W. An analysis model for thermoelastic properties of composite laminates containing transverse matrix cracks. Int J Solids Struct 1993;30:3211–31. [14] Cady C, Heredia FE, Evans AG. In-plane mechanical properties of several ceramic-matrix composites. J Am Ceram Soc 1995;78(8):2065–78. [15] Genin GM, Hutchinson JW. Composite laminates in plane stress: constitutive modeling and stress redistribution due to matrix cracking. J Am Ceram Soc 1997;80(5):1245–55. [16] Ishikawa T, Koyama K, Kobayashi S. Elastic moduli of carbonepoxy composites and carbon fibers. J Compos Mater 1977;11:332–44. [17] Lekhnitskii SG. Theory of elasticity of an anisotropic elastic body. San Francisco: Holden-Day, Inc.; 1963. p. 197–205. [18] Tsai C-L, Daniel IM, Yaniv G. Torsional response of rectangular composite laminates. J Appl Mech 1990;57:383–7. [19] Swanson SR. Torsion of laminated rectangular rods. Comput Struct 1998;42:23–31. [20] Ishikawa T, Bansaku K, Watanabe N, Nomura Y, Shibuya M, Hirokawa T. Experimental stress/strain behavior of SiCmatrix composites reinforced with Si–Ti–C–O fibers and estimation of matrix elastic modulus. Comp Sci Technol 1998;58:51–63. [21] Watanabe N, Teranishi K. Thermal stress analysis for Al honeycomb sandwich plates with very thin CFRP faces. AIAA- 95-1394; 1995. [22] Whitney JM. Effective elastic constants of bidirectional laminates containing transverse ply cracks. J Comp Mater 2000;34: 954–78. [23] Nuismer RJ, Tan SC. Constitutive relations of a cracked composite lamina. J Comp Mater 1989;22:306–21. T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549 2549