January 2005 Matrix Cracking in 3D Orthogonal Melt-Infiltrated Composites in particular. With analyses of the physical factors controlling and Hi-Nicalon(Nipp Tokyo, Jap these parameters in hand, some general guidelines are offered on forced MI composites. This model would suffice for architecture approaches that can im the composite stresses ion of the y-direction-tested 3d orthogonal required for TTMC (Fig. 6). A similar approach could be used for the U based on the stress-intensity parameter(Fig. 7(b)) (1) Onset Stress For Tunnel Cracking The major factors for the superiority of rayon XPLY matrix Tunnel cracking has been discerned by the author. based on AE cracking stresses compared with T300 XPLY with ZMI XPLY 100 different esses orthogonal mini-composites oriented perpendicular to the loading direction. est composite stress for matrix cracking can be achieved in cross- ply structures with the thinnest ply widths possible in addition to may not be possible to prohibit tunnel crack formation in cross- tion. This could be taken advantage of li che loading direc- egions lower stresses for the larger 90 size Syl-iBN tows in the XPLY component structures where high matrix-cracking stresses are regions of the of ZMI and T300 composites compared with the desired thinner 90 size Sylramic tows in the XPLY regions of the Ray It is hoped that the above analyses can be used to help on composite. One possible implication of this result would be steer development of and /or t hat the 90 tow height in composites could be engineered thin property models, e.g., Cox er at o o verify fiber-architecture and Cox and McMeeking ner so as to increase the stress for crack initiation in the 90% which can be applied generally to ceramic matrix composites bundles to a stress greater than the TTMC stress. formed by textile weaving. It is also anticipated that as the un- derstanding between stress-dependent matrix cracking(as well e However, for the orthogonal Z-fiber tows in the UNI regions, as other properties, e.g., through-thickness strength and thermal nnel cracking did not occur in T300 or Rayon Z-fiber tows composites and did occur in the ZMI Z-fiber tow compos nductivity) and local architecture grows, structures will be The Z-fiber tow height was largest for ZMI. In addition, Z designed so as to incorporate the necessary local architectures for desired local properties in a given component. fiber tow mini-composite compared with the other two carbon V. Conclusions fiber Z-fiber types. This would make it ZMI tows even more prone to tunnel cracking. Matrix cracking in 3D orthogonal, melt-infiltrated SiC/SiC ma- trix composites was studied for composites with different Z-di- (2) Onset Stress For Through-Thickness Matrix Crackin rection fiber types. The stress range where matrix cracking The onset stress for TTMC is the most crucial parameter from a occurred was dependent on the Z-direction tow size and the lo- design standpoint. At this stress and above, depending on the cal architecture. The smaller the Z-direction tow size(height) temperature and environment, time-dependent strength degra the higher the composite stress range where matrix cracking dation occurs due to oxidation embrittlement and/or enhanced that w occurred. It was also found that in the region of the structure essent matrix cracks formed at higher creep of the fully loaded 0 fibers. The onset stress for TTMc stresses than in adjacent matrix-rich"unidirectional"regions can be estimated by the stress to cause significant high-energy AE activity. For XPLY regions and 2D woven composite These findings must be considered when 3D orthogonal struc- TTMC occurs at approximately the same mini-matrix stress ures are desired for elevated temperature applications where the For the UNI regions of the 3D orthogonal composites, the onset se of the 3D architecture to achieve the desired through-thick ness property could lead to strength degradation in tension due stress for TTMC appears to be entirely dependent on the size to oxidation of the interior of the composite through low-stress- (height)of the Z-fiber tow and follows a Griffith-type relation- forming matrix cracks. Understanding the effect of architecture hip (Fig. 7(a)), ie the larger the Z-fiber tow the lower the stress for matrix cracking. on matrix-cracking stress could be used advantageously to en gineer desired structures where areas of a component require high through-thickness properties and other areas of the same (3)Stress Distribution For Through-Thickness Cracking component require high-tensile matrix crack strengths. The stress distribution for through-thickness cracking dictates the nonlinear stress-strain response of the material. It is also an important parameter for intermediate temperature mechanical Appendix A: Estimation of Local Elastic Modulus for properties because the greater the number of matrix cracks, the Y-Direction 3D Orthogonal Composites greater the degradation in time-dependent strength In order to determine the stress on the matrix outside of the For stresses above the TTMC stress, matrix cracks originate fiber, BN, CVI SiC mini-composite, the elastic moduli of the in the 90 and or Z-fiber tows and propagate or link up with one another through the thickness of the composite. For 2D com- The approach taken was to estimate EUNI from rule-of-mixtures posites with a 90 orthogonal tow, a simple empirical Weibull- ROM) based on the volume fractions that made up the UNI model has been developed for matrix cracking in 2D MI com- egion. Then, the contribution of Exply could be estimated or backed out"from the measured Ec, assuming a serial link-up (Reuss estimate) of the UNI and XPLY regions" Pe(omini-matrix)=pe1-es Omini-mat The fraction of fibers in the X- and y-directions was dete mined from the fiber area in the loading direction divided by the neasured tensile specimen area from the simple relationship where Pe(omini-matris) is the estimated crack density at a given (note that specimen width would be in the numerator and stress, Pc is the final crack density measured after the tensile tes denominator and therefore cancels itself out) Oo would be the reference stress and correspond to the average ix where the normalized cumulative ae energy equals 0.623, and m is the Weibul modulus. m was the only unknown fror -Ply NYTRr(epmm) variable. For the 2D MI matrix systems assuming an average Pe=9.5 cracks/mm, it was determined that oo= 150 MPa and where Ply is the number of plies or layers of woven fiber, Nr is m=5. The scatter in the normalized cumulative ae with mber of fibers in a tow(800 for Sylramic), Rr is the fiber mini-matrix was only +12 MPa for composites with Sylrami epmm is ends per mm converted from epcm, and t is thein particular. With analyses of the physical factors controlling these parameters in hand, some general guidelines are offered on architecture approaches that can improve the composite stresses required for TTMC. (1) Onset Stress For Tunnel Cracking Tunnel cracking has been discerned by the author, based on AE, to some degree prior to TTMC in every Syl-MI composite (over 100 different composite panels tested) that possesses orthogonal mini-composites oriented perpendicular to the loading direction, i.e., 2D woven and 3D orthogonal in the cross-ply regions. It may not be possible to prohibit tunnel crack formation in cross￾ply composites. Also, it appears that tunnel cracking occurred at lower stresses for the larger 901 size Syl-iBN tows in the XPLY regions of the of ZMI and T300 composites compared with the thinner 901 size Sylramic tows in the XPLY regions of the Ray￾on composite. One possible implication of this result would be that the 901 tow height in composites could be engineered thin￾ner so as to increase the stress for crack initiation in the 901 bundles to a stress greater than the TTMC stress. However, for the orthogonal Z-fiber tows in the UNI regions, tunnel cracking did not occur in T300 or Rayon Z-fiber tows composites and did occur in the ZMI Z-fiber tow composite. The Z-fiber tow height was largest for ZMI. In addition, ZMI fibers are expected to decompose (shrink) to some extent during MI fabrication that would result in weaker bonding in the Z- fiber tow mini-composite compared with the other two carbon fiber Z-fiber types. This would make it ZMI tows even more prone to tunnel cracking. (2) Onset Stress For Through-Thickness Matrix Cracking The onset stress for TTMC is the most crucial parameter from a design standpoint. At this stress and above, depending on the temperature and environment, time-dependent strength degra￾dation occurs due to oxidation embrittlement and/or enhanced creep of the fully loaded 01 fibers.6 The onset stress for TTMC can be estimated by the stress to cause significant high-energy AE activity.7 For XPLY regions and 2D woven composites, TTMC occurs at approximately the same mini-matrix stress. For the UNI regions of the 3D orthogonal composites, the onset stress for TTMC appears to be entirely dependent on the size (height) of the Z-fiber tow and follows a Griffith-type relation￾ship (Fig. 7(a)), i.e., the larger the Z-fiber tow size, the lower the stress for matrix cracking. (3) Stress Distribution For Through-Thickness Cracking The stress distribution for through-thickness cracking dictates the nonlinear stress–strain response of the material. It is also an important parameter for intermediate temperature mechanical properties because the greater the number of matrix cracks, the greater the degradation in time-dependent strength. For stresses above the TTMC stress, matrix cracks originate in the 901 and/or Z-fiber tows and propagate or link up with one another through the thickness of the composite. For 2D com￾posites with a 901 orthogonal tow, a simple empirical Weibull￾model has been developed for matrix cracking in 2D MI com￾posites8 as follows: rcð Þ¼ smini-matrix rc 1 exp smini-matrix s0 

m ð2Þ where rc(smini-matrix) is the estimated crack density at a given stress, rc is the final crack density measured after the tensile test, s0 would be the reference stress and correspond to the average smini-matrix where the normalized cumulative AE energy equals 0.623, and m is the Weibul modulus. m was the only unknown variable. For the 2D MI matrix systems assuming an average rc 5 9.5 cracks/mm, it was determined that s0 5 150 MPa and m 5 5. The scatter in the normalized cumulative AE with smini-matrix was only 712 MPa8 for composites with Sylramic and Hi-Nicalont (Nippon Carbon, Tokyo, Japan) fiber-rein￾forced MI composites. This model would suffice for the XPLY region of the Y-direction-tested 3D orthogonal composites (Fig. 6). A similar approach could be used for the UNI regions based on the stress-intensity parameter (Fig. 7(b)). The major factors for the superiority of rayon XPLY matrix cracking stresses compared with T300 XPLY with ZMI XPLY (Figs. 4 and 6) appear to be straighter load-bearing fibers with thinner 901 bundles in the rayon composite. Therefore, the high￾est composite stress for matrix cracking can be achieved in cross￾ply structures with the thinnest ply widths possible in addition to the highest fiber volume fraction possible in the loading direc￾tion. This could be taken advantage of in local regions of component structures where high matrix-cracking stresses are desired. It is hoped that the above analyses can be used to help steer development of and/or to verify fiber-architecture property models, e.g., Cox et al. 20 and Cox and McMeeking,21 which can be applied generally to ceramic matrix composites formed by textile weaving. It is also anticipated that as the un￾derstanding between stress-dependent matrix cracking (as well as other properties, e.g., through-thickness strength and thermal conductivity) and local architecture grows, structures will be designed so as to incorporate the necessary local architectures for desired local properties in a given component. V. Conclusions Matrix cracking in 3D orthogonal, melt-infiltrated SiC/SiC ma￾trix composites was studied for composites with different Z-di￾rection fiber types. The stress range where matrix cracking occurred was dependent on the Z-direction tow size and the lo￾cal architecture. The smaller the Z-direction tow size (height), the higher the composite stress range where matrix cracking occurred. It was also found that in the region of the structure that was essentially ‘‘cross-ply,’’ matrix cracks formed at higher stresses than in adjacent matrix-rich ‘‘unidirectional’’ regions. These findings must be considered when 3D orthogonal struc￾tures are desired for elevated temperature applications where the use of the 3D architecture to achieve the desired through-thick￾ness property could lead to strength degradation in tension due to oxidation of the interior of the composite through low-stress￾forming matrix cracks. Understanding the effect of architecture on matrix-cracking stress could be used advantageously to en￾gineer desired structures where areas of a component require high through-thickness properties and other areas of the same component require high-tensile matrix crack strengths. Appendix A: Estimation of Local Elastic Modulus for Y-Direction 3D Orthogonal Composites In order to determine the stress on the matrix outside of the fiber, BN, CVI SiC mini-composite, the elastic moduli of the UNI (EUNI), and XPLY (EXPLY) regions had to be estimated. The approach taken was to estimate EUNI from rule-of-mixtures (ROM) based on the volume fractions that made up the UNI region. Then, the contribution of EXPLY could be estimated or ‘‘backed out’’ from the measured Ec, assuming a serial link-up (Reuss estimate) of the UNI and XPLY regions.22 The fraction of fibers in the X- and Y-directions was deter￾mined from the fiber area in the loading direction divided by the measured tensile specimen area from the simple relationship (note that specimen width would be in the numerator and denominator and therefore cancels itself out): fX or Y ¼ NplyNfpR2 fð Þ epmm t ðA-1Þ where Nply is the number of plies or layers of woven fiber, Nf is the number of fibers in a tow (800 for Sylramic), Rf is the fiber radius, epmm is ends per mm converted from epcm, and t is the January 2005 Matrix Cracking in 3D Orthogonal Melt-Infiltrated Composites 151