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 warp￾ing 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 repre￾sented as a function of Gxy and Gzx as follows: GJ ¼ f ðGxy ; GzxÞ. ð2Þ Considering two specimens, 1 and 2, with different rect￾angular cross-section, the following nonlinear simulta￾neous 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–Raph￾son method. 3. Experimental procedure 3.1. Materials [9,20] The composite under investigation contained Tyr￾annoTM 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 ele￾vated 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 re￾sult in interphase with desirable properties between the fiber and matrix. Poly-titano-carbosilane was used as the matrix precursor with eight impregnation and pyro￾lysis 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 longi￾tudinal 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 Lekhnitskii
s equation (Eq. (1)). T. Ogasawara et al. / Composites Science and Technology 65 (2005) 2541–2549 2543