Y. Gowayed et aL/ Composites Science and Technology 70(2010)435-441 numerical solutions. Most of these models lack the detailed geom- stability study was conducted and a mesh of three hexahedra brick etry that can represent the composites internal fabric architecture elements per yarn in each direction was chosen. This resulted in a hich may have a strong impact on the mechanical behavior of the 225 eight-noded hexahedra brick elements per unit cell of the fab- textile composites. Quantification of elastic properties requires an ric architecture as shown in Fig. 6. Results of the calculations are understanding of the spatial location of yarns and the contribution listed in Table 2 for composites with and without voids. Since no of each composite constituent to the composite overall respon information is available on the exact location of the voids the To this end, a geometric model previously developed was used to upper bound values are for the case when all the voids exist in a evaluate the spatial location of yarns [10 for the composite under spherical form in the matrix away from the fibers, while the lower consideration. The knowledge of yarn location and matrix distribu- bound values are when all the voids are within yarns and at yarn tion provide basis for application of numerical mechanical models, cross-over points [15]. It can be seen from the table that estimates such as traditional finite element analysis(FEA), to evaluate the for in-plane tensile moduli (Ex and Ey), shear modulus( Gxy) and omposite properties. Nevertheless, the use of traditional FEA is Poissons ratio(vxy)using properties of constituent materials are limited by the complexity of the fabric geometry and associated very close to the experimental data hing problems, and requires a large number of elements. a typ- The value for the through-thickness modulus calculated by the ical plain weave fabric would require a few thousands elements to numerical model is approximately 50% higher than the experimen- model [7]. It is expected that other complex fabrics, such as 3D fab- tal value as shown in Table 2. But it can also be observed that the rics, would require hundreds of thousands of elements. To solve experimental value of the compressive modulus is lower than the this problem a hybrid FEa was used [11 where a unit cell of the uli of major composite constituents listed in Table 1 which is fabric architecture is identified and divided into hexahedra brick not a typical result. The effect of the compressive stress on the elements with fiber and matrix around each integration point. modulus value, in the stacked disks experiment, is evident from Material homogenization was carried out around each integration Fig. 5. The modulus showed a linear increase with the increase in oint to define the anisotropic material response 12. The bound compressive stress until it reached a plateau at a stresses higher ary conditions of the unit cell, dictated by the assumptions of than 300 MPa. This can be due to the existence of asperities be- repeatability and continuity, helped reduce the size of the stiffness tween the disks being flattened by the stress or the existence of latrix. A virtual work technique was used to calculate the elastic voids inside the yarns, or both. Micrographic images of yarns properties of the unit cell. Both geometric and mechanical FEa cross-sections showed intra-yarn voids between fibers of approxi- odels were combined and integrated using a visual C++ computer algorithm 5. Correlation of in situ properties of constituent phases to mposite properties Properties of constituent materials obtained from nano-inden- tation and information on fabric architecture. obtained from the weaver, were used as input in the numerical model presented above to calculate the elastic properties of the composites Calcu lated values of elastic properties of the composite were compared to experimental data to examine the consistency of the relation- ship between constituent properties and the composite properties. Such comparison would also present, if any, the impact of internal features like voids on the relationship. Material properties of ents are listed in Table 1 along with their relative volume fractions. the poisson 's ratios of constit uents were obtained from[13 and the shear moduli were calcu- lated using the elasticity equation E=2G(1+v), assuming all constituent phases are locally isotropic; where e is the elastic mod ulus. g is the shear modulus and y is the poisson's ratio To reduce the complexity of the problem imposed by the large number of constituents, an initial step was carried out by dividing the composite into two parts - coated fibers comprised of iBN-Syl- ramic fibers coated with Si-doped BN, and a matrix formed from Fig. 6. Geometric model and FE mesh of 5-hamess satin woven MI SIC/SiC SiC-CVI, SiC-SC and Si Properties of the coated fibers were calcu lated using the micromechanics model developed in [14 The micrographic images shown in Fig. 1 reveal a shiny material (Si) mixed with another grayish color material Sic-SC)in the place be- Table 2 ween the yarns with some dark areas that are most probably Experimental data and results of numerical model for elastic properties at room voids. Based on this micrograph, an in-series model was used to temperature (GPal calculate the combined properties of Sic-SC and si(iso-stress mod Property Without voids With 2.6% void el)and an in-parallel model (iso-strain model)was used to com- Upper bound bine these properties with the properties of Sic-CVl. Utilizing this approach the matrix properties were calculated as Em=329.3 GPa. Ex Ey 2748±1034 2138 1300±3.39 Gm=139.1 GPa, and Vm=0. 182: where the subscript m denotes the 9584±0 m temperature elastic properties of the composite were cal- 0.14 0.127±0003 0.188 using the numerical model described above. A numericalnumerical solutions. Most of these models lack the detailed geom￾etry that can represent the composites internal fabric architecture which may have a strong impact on the mechanical behavior of the textile composites. Quantification of elastic properties requires an understanding of the spatial location of yarns and the contribution of each composite constituent to the composite overall response. To this end, a geometric model previously developed was used to evaluate the spatial location of yarns [10] for the composite under consideration. The knowledge of yarn location and matrix distribu￾tion provide basis for application of numerical mechanical models, such as traditional finite element analysis (FEA), to evaluate the composite properties. Nevertheless, the use of traditional FEA is limited by the complexity of the fabric geometry and associated meshing problems, and requires a large number of elements. A typ￾ical plain weave fabric would require a few thousands elements to model [7]. It is expected that other complex fabrics, such as 3D fab￾rics, would require hundreds of thousands of elements. To solve this problem a hybrid FEA was used [11] where a unit cell of the fabric architecture is identified and divided into hexahedra brick elements with fiber and matrix around each integration point. Material homogenization was carried out around each integration point to define the anisotropic material response [12]. The bound￾ary conditions of the unit cell, dictated by the assumptions of repeatability and continuity, helped reduce the size of the stiffness matrix. A virtual work technique was used to calculate the elastic properties of the unit cell. Both geometric and mechanical FEA models were combined and integrated using a visual C++ computer algorithm. 5. Correlation of in situ properties of constituent phases to composite properties Properties of constituent materials obtained from nano-inden￾tation and information on fabric architecture, obtained from the weaver, were used as input in the numerical model presented above to calculate the elastic properties of the composites. Calcu￾lated values of elastic properties of the composite were compared to experimental data to examine the consistency of the relation￾ship between constituent properties and the composite properties. Such comparison would also present, if any, the impact of internal features like voids on the relationship. Material properties of constituents are listed in Table 1 along with their relative volume fractions. The Poisson’s ratios of constit￾uents were obtained from [13] and the shear moduli were calcu￾lated using the elasticity equation {E = 2G (1 + m)}, assuming all constituent phases are locally isotropic; where E is the elastic mod￾ulus, G is the shear modulus and m is the Poisson’s ratio. To reduce the complexity of the problem imposed by the large number of constituents, an initial step was carried out by dividing the composite into two parts – coated fibers comprised of iBN-Syl￾ramic fibers coated with Si-doped BN, and a matrix formed from SiC-CVI, SiC-SC and Si. Properties of the coated fibers were calcu￾lated using the micromechanics model developed in [14]. The micrographic images shown in Fig. 1 reveal a shiny material (Si) mixed with another grayish color material (SiC-SC) in the place be￾tween the yarns with some dark areas that are most probably voids. Based on this micrograph, an in-series model was used to calculate the combined properties of SiC-SC and Si (iso-stress mod￾el) and an in-parallel model (iso-strain model) was used to com￾bine these properties with the properties of SiC-CVI. Utilizing this approach the matrix properties were calculated as Em = 329.3 GPa, Gm = 139.1 GPa, and mm = 0.182; where the subscript m denotes the matrix. Room temperature elastic properties of the composite were cal￾culated using the numerical model described above. A numerical stability study was conducted and a mesh of three hexahedra brick elements per yarn in each direction was chosen. This resulted in a 225 eight-noded hexahedra brick elements per unit cell of the fab￾ric architecture as shown in Fig. 6. Results of the calculations are listed in Table 2 for composites with and without voids. Since no information is available on the exact location of the voids, the upper bound values are for the case when all the voids exist in a spherical form in the matrix away from the fibers, while the lower bound values are when all the voids are within yarns and at yarn cross-over points [15]. It can be seen from the table that estimates for in-plane tensile moduli (Ex and Ey), shear modulus (Gxy) and Poisson’s ratio (mxy) using properties of constituent materials are very close to the experimental data. The value for the through-thickness modulus calculated by the numerical model is approximately 50% higher than the experimen￾tal value as shown in Table 2. But it can also be observed that the experimental value of the compressive modulus is lower than the moduli of major composite constituents listed in Table 1 which is not a typical result. The effect of the compressive stress on the modulus value, in the stacked disks experiment, is evident from Fig. 5. The modulus showed a linear increase with the increase in compressive stress until it reached a plateau at a stresses higher than 300 MPa. This can be due to the existence of asperities be￾tween the disks being flattened by the stress or the existence of voids inside the yarns, or both. Micrographic images of yarns cross-sections showed intra-yarn voids between fibers of approxi￾Fig. 6. Geometric model and FE mesh of 5-harness satin woven MI SiC/SiC composite. Table 2 Experimental data and results of numerical model for elastic properties at room temperature (GPa). Property Without voids With 2.6% voids Experiment Lower bound Upper bound Ex, Ey 269.5 224.3 263.0 274.8 ± 10.34 Ez 213.8 203.0 209.0 130.0 ± 3.39 Gxy 92.39 88.46 90.39 95.84 ± 0.6 Gxz, Gyz 90.12 86.46 87.77 – mxy 0.14 0.161 0.146 0.127 ± 0.003 mxz, myz 0.195 0.188 0.204 – Y. Gowayed et al. / Composites Science and Technology 70 (2010) 435–441 439