G.N. Morscher et al. Composites Science and Technology 67(2007)1009-1017 tion had a different, yet consistent, AE relationship with NCumAE= 1-exp(o stress on the load-bearing Sic compared to the higher vol- ume fraction Syl-iBN composites. This is similar to MI where composites [6] which were woven with different sized tows, =(gcvisic the larger tow size composites exhibiting the lower and temper stress-distribution for matrix cracking where acviSic is the stress in the load-bearing CVI SiC and The reasons for these two distributions are most likely o. the reference stress, would correspond to the average due to the effectiveness of fiber-bridging and the flaw distri- stress of the composite system for NCumAE=0.623 of the SiC matrix in the two-different orientations. The lower vol. two different distributions (285 MPa for high-density Hi ume fraction composites have not only a lower volume fraction but also would have larger unbridged tion Syl-iBN CVI SIC, and 245 MPa for low volume fraction within a matrix crack when compared to a balanced weave Syl-iBN CVI SIC). Eq. (5)was best fit for m(4 for high-den- or the high volume fraction orientation of the unbalanced sity Hi-Nicalon CVI SiC composites, 6 for high volume frac- tion Syl-iBN CVI SiC, and 9 for unbalanced low volume weave.Consequently, when a tunnel crack propagates out- fraction Syl-iBN CVI SiC) for the distributions( large circles ward from a 90 ply [12] or a microcrack forms that inter- in Fig. 6 ). Multiplying Eq (6)by the final measured matrix sects load-bearing fibers, the fiber-bridging is not sufficient crack density would then give an estimated matrix crack den- to stop the crack and through-thickness macrocracking sity distribution. Using this relationship and then transform occurs. This explains why the onset of large-energy event CaE onset stress"in Table 1)for the low volume fraction g to absolute stress for a given architecture/constituent unbalanced composite specimens correspond either with content composite Eq (5), one could then use the estimated the initial ae activity or at slightly higher stresses than behavior for each composite/orientation. Fig 8 shows the the first Ae activity for the low volume fracti predicted stress-strain behavior for some of the Hi-Nicalon ites. For the high volume fraction composite orientations, Fig 8a)and Syl-iBN Fig 8b) composites. The predicted there is a lag in stress from initial AE activity to high elastic modulus for each composite specimen from Ref [U] energy AE activity, signifying tunnel cracks or microcracks are formed at lower stresses, but higher stresses are propagate bridg racks. The st slope of the low volume fraction orientation com may also be indicative of the existence of a more prevalent HN 8 Ply(BNT lower strength flaw population to produce matrix cracks This would be due to the fact that there are more 90 tows HN 8 Ply(BN3) in the lower fiber orientation unbalanced composite speci men, sometimes aligned three abreast, compared to the 9200 higher fiber orientation composite systems(See Fig. la-c 0 150 Two important properties can be gleaned from Fig. 6. HN 8 Ply (C) The first is the stress on the load-bearing Cvi Sic for Open symbols correspond to model which significant matrix crack formation(AE onset stress) For the higher-density Hi-Nicalon composites, this stress 06 would be 140 MPa. For the Syl-iBN composites, the low volume fraction unbalanced composites the CVI SiC b 600 circles onset stress was 185 MPa: whereas for the high volume fraction composites the CvI Sic onset stress was N210 MPa. This gives a simple design parameter, more robust than a"proportional limit"since it is based on actual macrocrack formation and is a general relationship for 2D woven CVI SiC composites of different constituent contents. This CVI SiC onset stress for matrix cracking y could be used to predict the local composite stress for Syl-IBN 5.5 epcm matrix cracking if the local Ec is known [1] via Eq. (5) Second, the general AE relationships can be used to determine an estimated stress-dependent matrix crack den sity. A simple Weibull modeling approach can be employed for the two different normalized cumulative AE energy dis- tributions [7] since matrix crack saturation occurs in these Fig 8 Stress-strain predictions for: (a) Hi-Nicalon and(b)Syl-iBN high density CVI SiC matrix compositestion had a different, yet consistent, AE relationship with stress on the load-bearing SiC compared to the higher vol￾ume fraction Syl-iBN composites. This is similar to MI composites [6] which were woven with different sized tows, the larger tow size composites exhibiting the lower and steeper stress-distribution for matrix cracking. The reasons for these two distributions are most likely due to the effectiveness of fiber-bridging and the flaw distri￾bution or nature of local stress-concentrations on the CVI SiC matrix in the two-different orientations. The lower vol￾ume fraction composites have not only a lower volume fraction but also would have larger unbridged regions within a matrix crack when compared to a balanced weave or the high volume fraction orientation of the unbalanced weave. Consequently, when a tunnel crack propagates out￾ward from a 90 ply [12] or a microcrack forms that inter￾sects load-bearing fibers, the fiber-bridging is not sufficient to stop the crack and through-thickness macrocracking occurs. This explains why the onset of large-energy events (‘‘AE onset stress’’ in Table 1) for the low volume fraction unbalanced composite specimens correspond either with the initial AE activity or at slightly higher stresses than the first AE activity for the low volume fraction compos￾ites. For the high volume fraction composite orientations, there is a lag in stress from initial AE activity to high energy AE activity, signifying tunnel cracks or microcracks are formed at lower stresses, but higher stresses are required to propagate bridged macrocracks. The steeper slope of the low volume fraction orientation composites may also be indicative of the existence of a more prevalent lower strength flaw population to produce matrix cracks. This would be due to the fact that there are more 90 tows in the lower fiber orientation unbalanced composite speci￾men, sometimes aligned three abreast, compared to the higher fiber orientation composite systems (See Fig. 1a–c in Ref. [1]). Two important properties can be gleaned from Fig. 6. The first is the stress on the load-bearing CVI SiC for which significant matrix crack formation (AE onset stress). For the higher-density Hi-Nicalon composites, this stress would be 140 MPa. For the Syl-iBN composites, the low volume fraction unbalanced composites the CVI SiC onset stress was 185 MPa; whereas, for the high volume fraction composites the CVI SiC onset stress was 210 MPa. This gives a simple design parameter, more robust than a ‘‘proportional limit’’ since it is based on actual macrocrack formation and is a general relationship for 2D woven CVI SiC composites of different constituent contents. This CVI SiC onset stress for matrix cracking could be used to predict the local composite stress for matrix cracking if the local Ec is known [1] via Eq. (5). Second, the general AE relationships can be used to determine an estimated stress-dependent matrix crack den￾sity. A simple Weibull modeling approach can be employed for the two different normalized cumulative AE energy dis￾tributions [7] since matrix crack saturation occurs in these systems: NCumAE ¼ 1 expð/Þ ð6Þ where / ¼ rCVISiC ro m ð7Þ where rCVI SiC is the stress in the load-bearing CVI SiC and ro, the reference stress, would correspond to the average stress of the composite system for NCumAE = 0.623 of the two different distributions (285 MPa for high-density Hi￾Nicalon CVI SiC composites, 345 MPa for high volume frac￾tion Syl-iBN CVI SiC, and 245 MPa for low volume fraction Syl-iBN CVI SiC). Eq. (5) was best fit for m (4 for high-den￾sity Hi-Nicalon CVI SiC composites, 6 for high volume frac￾tion Syl-iBN CVI SiC, and 9 for unbalanced low volume fraction Syl-iBN CVI SiC) for the distributions (large circles in Fig. 6). Multiplying Eq. (6) by the final measured matrix crack density would then give an estimated matrix crack den￾sity distribution. Using this relationship and then transform￾ing to absolute stress for a given architecture/constituent content composite Eq. (5), one could then use the estimated matrix crack density in Eq. (2) to determine the stress–strain behavior for each composite/orientation. Fig. 8 shows the predicted stress–strain behavior for some of the Hi-Nicalon (Fig. 8a) and Syl-iBN (Fig. 8b) composites. The predicted elastic modulus for each composite specimen from Ref. [1] 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 Strain, % Stress, MPa Syl-iBN 5.5 epcm Syl-iBN 9.4epcm Syl-iBN 7.9epcm Syl-iBN C￾interphase circles correspond to model 0 50 100 150 200 250 300 350 400 450 0 0.2 0.4 0.6 0.8 1 Strain, % Stress, MPa HN 36 Ply HN 8 Ply (BN3) HN 8 Ply (C) HN 8 Ply (BN1) Open symbols correspond to model a b Fig. 8. Stress–strain predictions for: (a) Hi-Nicalon and (b) Syl-iBN high￾density CVI SiC matrix composites. 1016 G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017