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