1014 G.N. Morscher et al. Composites Science and Technology 67(2007)1009-1017 E=a/Ec+ad(a)Pc/Er(o+ oth); for pc> 2 (2) Table 3 where the sliding length g. MPa 6=m(+)/2 (3) Hi- Nicalon CVI SiC composites ply(C) 35 4.1 4.1 30 and 36 ply (C o is the applied stress, oth is the residual stress, r is the fiber radius,E is elastic modulus, subscripts c, f, and m refer to Sy/-iBN CVI SiC composites omposite, fiber, and modulus, and Pe is the stress-depen- 9.epcm 4 dent matrix crack density estimated from the ae data. 5.epcm 8.9 q(2)can be best fit to the actual stress-strain curve by 7epcm(c) varying t in order to estimate a value for t(Fig. 5). This was done for most of the specimens with good fits of the a 90 minicomposite. A similar approach was attempted stress-strain curve with the exception of the Hi-Nicalon to relate matrix cracking in CVI SiC composites with less PLY and Hi-Nicalon 3PLY specimens(Table 3). The rea- success than for melt-infiltrated systems [7]. This was prob- son for this is probably that the ae data does not just rep- ably due to more non-uniformity in lower density CVi resent transverse matrix cracks. For these thin specimens, matrix systems and the variety of matrix crack sources sources of Ae at the higher stresses such as straight available in CVI SiC composites which include the out of minicomposites and longitudinal cracks"notches"that exist at the large pores as well as the inner een the 0 and 90 minicomposites which are apparent region of 90 minicomposites. The CVI SiC matrix when from polished sections. The single ply specimen was not fully-loaded is the region where through-thickness matrix modeled because the failure occurred in the grips at a cracks form and propagate. Therefore, in order to quantify low stress. Note that the relatively thick carbon interphase matrix-crack activity, the acoustic emission activity was composites had the lowest interfacial shear strength for analyzed based on the stress (or local strain) in the load- both fiber-composite systems bearing CVI SiC. This was accomplished by assuming the For nearly fully dense melt-infiltrated SiC/SiC compos- equivalence of local elastic strain (Ec=Esic) in an ites [6]it was found that the onset stress for matrix cracking uncracked region of the composite just prior to matrix and the stress-distribution for matrix cracking could be crack formation through the relationship related to the average stress on the region of the composite that excludes the load-bearing fiber-interphase-CVI SiC Sic =(a/EC)Esic minicomposite. This corresponded to the stress required where Esic=425 GPa. Note that once matrix cracks have to form and/or propagate a matrix crack emanating from formed, the average total composite strain includes the ex- tra displacement associated with matrix cracks that devi ates from elasticity. This is why the local elastic strain in the uncracked cvi SiC must be used s the normalized cumulative Ae energy plot best fit for t= 59 MPa ted versus stress in the load-bearing CVI SiC for the Hi- Nicalon(Fig. 6a) and Sylramic-iBN (Fig 6b)composites. For composites which saturate in matrix cracks, 1.e., where the normalized cumulative AE energy nearly plateaus with increasing stress, there are some definite convergences of the ae activity with stress. In particular higher-density Hi-Nicalon composites, the Sylramic-iBN stress-strain data composites when oriented in the high fiber volume direc tions, and the Sylramic-iBN composites when oriented in the lower fiber volume fraction direction each converge into distinct"distributions". The low-density Hi-Nicalon 100 composites do not converge, but also, with the exception of the epoxy-infiltrated specimen, may not all saturate in matrix cracks as was the case for low volume fraction com- posites in Ref. [6]. Therefore, the normalized cumulative AE energy was multiplied by the final matrix crack de and plotted versus the stress on the load-bearing CVI SiC Fig.5. Example of method used to determine interfacial shear stress based for the Hi-Nicalon fiber reinforced CVI SiC matrix com- on AE activity and final matrix crack density (9.4epcm(D). Dashed lines posites(Fig. 7). A good correlation exists, at least at lower represent a t value +20% of best fit value stresses, for all of the lower density composites. Also plote ¼ r=Ec þ fadðrÞqc=Efgðr þ rthÞ; for q1 c > 2d ð2Þ where the sliding length d ¼ arðr þ rthÞ=2s ð3Þ and a ¼ ð1 f ÞEm=fEc ð4Þ r is the applied stress, rth is the residual stress, r is the fiber radius, E is elastic modulus, subscripts c, f, and m refer to composite, fiber, and modulus, and qc is the stress-depen￾dent matrix crack density estimated from the AE data. Eq. (2) can be best fit to the actual stress–strain curve by varying s in order to estimate a value for s (Fig. 5). This was done for most of the specimens with good fits of the stress–strain curve with the exception of the Hi-Nicalon 2PLY and Hi-Nicalon 3PLY specimens (Table 3). The rea￾son for this is probably that the AE data does not just rep￾resent transverse matrix cracks. For these thin specimens, other sources of AE at the higher stresses such as straight￾ening out of minicomposites and longitudinal cracks between the 0 and 90 minicomposites which are apparent from polished sections. The single ply specimen was not modeled because the failure occurred in the grips at a low stress. Note that the relatively thick carbon interphase composites had the lowest interfacial shear strength for both fiber-composite systems. For nearly fully dense melt-infiltrated SiC/SiC compos￾ites [6] it was found that the onset stress for matrix cracking and the stress-distribution for matrix cracking could be related to the average stress on the region of the composite that excludes the load-bearing fiber-interphase-CVI SiC minicomposite. This corresponded to the stress required to form and/or propagate a matrix crack emanating from a 90 minicomposite. A similar approach was attempted to relate matrix cracking in CVI SiC composites with less success than for melt-infiltrated systems [7]. This was prob￾ably due to more non-uniformity in lower density CVI matrix systems and the variety of matrix crack sources available in CVI SiC composites which include the ‘‘notches’’ that exist at the large pores as well as the inner region of 90 minicomposites. The CVI SiC matrix when fully-loaded is the region where through-thickness matrix cracks form and propagate. Therefore, in order to quantify matrix-crack activity, the acoustic emission activity was analyzed based on the stress (or local strain) in the load￾bearing CVI SiC. This was accomplished by assuming the equivalence of local elastic strain (ec = eSiC) in an uncracked region of the composite just prior to matrix crack formation through the relationship rSiC ¼ ðr=EcÞESiC ð5Þ where ESiC = 425 GPa. Note that once matrix cracks have formed, the average total composite strain includes the ex￾tra displacement associated with matrix cracks that devi￾ates from elasticity. This is why the local elastic strain in the uncracked CVI SiC must be used. Fig. 6 shows the normalized cumulative AE energy plot￾ted versus stress in the load-bearing CVI SiC for the Hi￾Nicalon (Fig. 6a) and Sylramic-iBN (Fig. 6b) composites. For composites which saturate in matrix cracks, i.e., where the normalized cumulative AE energy nearly plateaus with increasing stress, there are some definite convergences of the AE activity with stress. In particular, all of the higher-density Hi-Nicalon composites, the Sylramic-iBN composites when oriented in the high fiber volume direc￾tions, and the Sylramic-iBN composites when oriented in the lower fiber volume fraction direction each converge into distinct ‘‘distributions’’. The low-density Hi-Nicalon composites do not converge, but also, with the exception of the epoxy-infiltrated specimen, may not all saturate in matrix cracks as was the case for low volume fraction com￾posites in Ref. [6]. Therefore, the normalized cumulative AE energy was multiplied by the final matrix crack density and plotted versus the stress on the load-bearing CVI SiC for the Hi-Nicalon fiber reinforced CVI SiC matrix com￾posites (Fig. 7). A good correlation exists, at least at lower stresses, for all of the lower density composites. Also plot- 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 Strain, % Stress, MPa stress-strain data best fit for τ= 59 MPa Fig. 5. Example of method used to determine interfacial shear stress based on AE activity and final matrix crack density (9.4epcm(1)). Dashed lines represent a s value ±20% of best fit value. Table 3 Model parameters Specimen s, MPa rth, MPa qc, mm1 Hi-Nicalon CVI SiC composites 8 ply (C) 14 10 2.2 8 ply BN1 35 0 4.1 8 ply BN3 20 0 4.1 30 and 36 ply (C) 26 0 3.5 Syl-iBN CVI SiC composites 7.9epcm 45 30 9.0 9.4epcm 60 42 10.4 5.5epcm 60 30 8.9 7.9epcm(C) 28 30 6.7 1014 G.N. Morscher et al. / Composites Science and Technology 67 (2007) 1009–1017