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. AverageIn 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 Young
s modulus and Poisson
s ratio in ±45
off-axis tensile test. The Young
s modulus E, Poisson
s ratio m , and in￾plane shear modulus Gxy are summarized in Table 1. Ini￾tial Young
s 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 im￾plied 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 (Young
s modulus 72.5 GPa, Poisson
s ratio 0.328). Data scattering (coefficient of variation; CV) for alumi￾num 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 scatter￾ing (CV) for composite specimens was about 3–5 % as shown in Tables 1 and 2, and this is much more signif￾icant 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 reli￾able 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 deter￾mined to be 45.3 and 35.6 GPa, respectively. The mea￾sured 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