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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. 11experimental 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