3190 Journal of the American Ceramic Society-Morscher et al. VoL. 90. No. 10 2D-woven 0/90 composites oriented in one of the orthogonal directions Assuming the applicability of Eq (1), there is a question as to model for [0/90] single-tow 2D woven data(ref. 14) how to approximate Emini because the fibers are oriented at an angle to the loading axis. One limit would be to assume that the ould act as if they were in parallel, si 3.95 epcm [o/9o there was the same fraction of minicomposites +23 as there are 8 uble-tow woven 7.9 epcm[o/90]single- 23 from the tensile axis The other extreme would be to as- sume that the modulus of a minicomposite at an angle to the 3 loading axis would behave similar to a unidirectional ply ori- 8.7 epcm [o/9o] single- ented at an angle and could therefore be estimated from the properties of an anisotropic lamina cos"(e)( 1-22)si2()cs() Braid Upper Bound +-sin4(0)(2) where subscript I refers to the 0 orientation of a minicomposite, subscript 2 refers to the transverse direction or to the 90orien- tation of a minicomposite, and 0 refers to the orientation of the 0 loading direction off the 0 fiber axis. G1 is the bulk modulu 200 and v12 is Poissons ratio. Minimatrix stress, MPa To determine the effect of orientation, ea was determined for the 23 fiber orientation case relative to the value of E,(360 GPa Fig 9. Estimated matrix crack density versus minimatrix stress for the braided composite ) E, is unknown for these minicom- posites, but a conservative estimate would be 100 GPa, which portant to discuss the response of the different types of CMCs to would be on the low -end of elastic moduli estimated for 90o off-axis loading CMC mechanical behavior has been defined as matrix dom- minicomposites in CVI SiC matrix composites. V12 was as- inated(Class ID)and fiber dominated( Class lID). 2.17 For matrix- umed to be 0. 15 and G1 was estimated from the simple iso tropic relationship E1/2(1+v12). Based on these simple dominated composites(.g, SiC fiber-reinforced glass ceramic ssumptions Ee/E1=0.943, a minor effect. Figure 9 shows the or Sic matrix composites), initial loads are shared by an un- timated matrix crack density versus minimatrix stress(Eq (D)) cracked matrix and by the fibers. Therefore, elastic properties for both the cases in comparison with the 2D composites. The lower bound"assumes that the minicomposites behave in the same way as parallel minicomposites and Emini is determined from the rule of mixtures based on the fractional content of fi- ber, BN, and CVI SiC. The"upper bound"refers to a reduced Emini from Eq. (2). There is only a small difference in minimatrix ess for the two extremes and they compare well with the composites loaded in the orthogonal direction. From this i would appear that matrix cracking in the braided composites is controlled by the stress acting on the axial minicomposites ori- ented perpendicular to the loading axis in the same manner a the 2D-woven 0/90 composites with single tows. However, in order to increase fiber volume fraction, the 0+67 braided com- sites were braided with two(double) tows woven together for both the axial and bias fibers. But there were a smaller fraction of minicomposites oriented perpendicular to the loading axis for the braided composites compared with the 2D-woven 0/90 com- osites. Also, the minicomposites oriented perpendicular to the loading direction of the braided composites do not contact one another(Fig. 10)and do not form back-to-back minicomposites as is the case for the 2D-woven 0/90 double-tow composites These two factors are probably the reason for the cracking be- havior of the braided composite being more in line with that of tow woven composites and not the double-tow woven composites. Figure 7 compares the effect of effective fiber frac- tion bridges a transverse matrix crack in the loadi tion on AE onset stress for all the MI SiC/SiC composites studied with 2D-woven and braided architectures, which possess minicomposites oriented perpendicular to the loading direction i.e., the likely source for the initiation of matrix cracks. (4) Ultimate Strength for Off-Axis Panels The ultimate strengths of the panels loaded off-axis were gen- erally less than those for panels tested in a primary fiber direc tion. This result is to be expected since the fibers were not aligned in the direction of applied stress and are subject to local bending and shear within a matrix crack. At this point, it is im- The fractional content of fiber BN. and CvI SiC We ere very similar to the data already re- ported in Morscher'fmini for the bias fibers of the braided composites was 0.54 compared Fig 10. Micrograph of a 0/+67 braid composite after roor with 0.36 for the orthogonal composit temperature tensile failur2D-woven 0/90 composites oriented in one of the orthogonal directions. Assuming the applicability of Eq. (1), there is a question as to how to approximate Emini because the fibers are oriented at an angle to the loading axis. One limit would be to assume that the bias minicomposites would act as if they were in parallel, since there was the same fraction of minicomposites 1231 as there are 231 from the tensile axis. The other extreme would be to as￾sume that the modulus of a minicomposite at an angle to the loading axis would behave similar to a unidirectional ply ori￾ented at an angle, and could therefore be estimated from the properties of an anisotropic lamina15 1 Ey ¼ 1 E1 cos4 ðyÞ 1 G12 2n12 E1
sin2 ðyÞ cos2 ðyÞ þ 1 E2 sin4 ðyÞ (2) where subscript 1 refers to the 01 orientation of a minicomposite, subscript 2 refers to the transverse direction or to the 901orien￾tation of a minicomposite, and y refers to the orientation of the loading direction off the 01 fiber axis. G12 is the bulk modulus and n12 is Poissons ratio. To determine the effect of orientation, Ey was determined for the 231 fiber orientation case relative to the value of E1 (360 GPa for the braided compositez ). E2 is unknown for these minicom￾posites, but a conservative estimate would be 100 GPa, which would be on the low-end of elastic moduli estimated for 901 minicomposites in CVI SiC matrix composites.16 n12 was as￾sumed to be 0.15 and G12 was estimated from the simple iso￾tropic relationship E1/2 (11n12). Based on these simple assumptions Ey/E1 5 0.943, a minor effect. Figure 9 shows the estimated matrix crack density versus minimatrix stress (Eq. (1)) for both the cases in comparison with the 2D composites. The ‘‘lower bound’’ assumes that the minicomposites behave in the same way as parallel minicomposites and Emini is determined from the rule of mixtures based on the fractional content of fi- ber, BN, and CVI SiC. The ‘‘upper bound’’ refers to a reduced Emini from Eq. (2). There is only a small difference in minimatrix stress for the two extremes and they compare well with the composites loaded in the orthogonal direction. From this it would appear that matrix cracking in the braided composites is controlled by the stress acting on the axial minicomposites ori￾ented perpendicular to the loading axis in the same manner as the 2D-woven 0/90 composites with single tows. However, in order to increase fiber volume fraction, the 0767 braided com￾posites were braided with two (double) tows woven together for both the axial and bias fibers. But there were a smaller fraction of minicomposites oriented perpendicular to the loading axis for the braided composites compared with the 2D-woven 0/90 com￾posites. Also, the minicomposites oriented perpendicular to the loading direction of the braided composites do not contact one another (Fig. 10) and do not form back-to-back minicomposites as is the case for the 2D-woven 0/90 double-tow composites.7 These two factors are probably the reason for the cracking be￾havior of the braided composite being more in line with that of the single-tow woven composites and not the double-tow woven composites. Figure 7 compares the effect of effective fiber frac￾tion that bridges a transverse matrix crack in the loading direc￾tion on AE onset stress for all the MI SiC/SiC composites studied with 2D-woven and braided architectures, which possess minicomposites oriented perpendicular to the loading direction, i.e., the likely source for the initiation of matrix cracks. (4) Ultimate Strength for Off-Axis Panels The ultimate strengths of the panels loaded off-axis were gen￾erally less than those for panels tested in a primary fiber direc￾tion. This result is to be expected since the fibers were not aligned in the direction of applied stress and are subject to local bending and shear within a matrix crack. At this point, it is im￾portant to discuss the response of the different types of CMCs to off-axis loading. CMC mechanical behavior has been defined as matrix dom￾inated (Class II) and fiber dominated (Class III).2,17 For matrix￾dominated composites (e.g., SiC fiber-reinforced glass ceramic or SiC matrix composites), initial loads are shared by an un￾cracked matrix and by the fibers. Therefore, elastic properties 0 2 4 6 8 10 12 0 50 100 150 200 250 300 Minimatrix stress, MPa Estimated Crack Density, #/mm model for [0/90] single-tow 2D woven data (ref. 14) 7.9 epcm [0/90] single￾tow woven (this study) 8.7 epcm [0/90] single￾tow woven (this study) 3.95 epcm [0/90] double-tow woven - this study - ref. 7 Braid Lower Bound Braid Upper Bound Fig. 9. Estimated matrix crack density versus minimatrix stress. Fig. 10. Micrograph of a [0/767] braid composite after room temperature tensile failure. z The fractional content of fiber, BN, and CVI SiC was 0.32, 0.07, and 0.25, respectively. The fractional contents of the other composites were very similar to the data already re￾ported in Morscher7 fmini for the bias fibers of the braided composites was 0.54 compared with B0.36 for the orthogonal composites. 3190 Journal of the American Ceramic Society—Morscher et al. Vol. 90, No. 10