J C. McNulty et al. /Composites Science and Technolog y 61(2001)1331-1338 1337 1)and the elastic stress concentration factor, times in the post-cracking regime are not likely to be ke=7. 1 [39], is significantly below the measured value, useful, because of the precipitous drop in fracture time C70-85 MPa. This difference is believed to be asso- to unacceptably low levels ciated with the steep stress gradients that exist in the The LCF threshold for center-hole specimens is simi notch tip region coupled with the intrinsic volume larly dictated by the matrix cracking limit. Once the ependence of the matrix strength. That is, the high cracking stress is exceeded locally (even over a very small stress levels exist over only small volumes ahead of the distance ahead of the hole), fracture ensues. A reasonably notch (over distances p), reducing significantly the accurate estimate of the threshold is obtained through the probability of encountering a matrix flaw to initiate elastic stress concentration factor in combination with the cracking. Finite element calculations for the center-not- matrix cracking stress [Eqn.(1)). This highly notch-sen ched geometry used in the present study (with 2a=6.35 sitive behavior suggests the need for an extremely con- mm and p=0.2 mm)reveal that the elastic stress servative design approach for CFCC structures diminishes rapidly with distance from the notch tip, by containing holes. Furthermore, it precludes the exploi- N50%at a distance of 0. 1 mm [Fig. 7(b)]. By contrast, tation of the inelastic deformation mechanisms that the reduction in elastic stress in the center-hole specimen operate in these materials and impart the requisite with a hole diameter of 6.35 mm is only A6%at the damage tolerance in non-oxidizing environments same distance from the hole edge. )It is surmised that The LCF threshold for center-notch specimens is com- even a modest volume dependence of strength might parable to that of the center hole specimens. Recognizing lead to a significant elevation in the maximum local that the stress concentration facto er in the not- stress at the onset of cracking. This elevation in the local ched geometry, the composite appears to exhibit superior cracking stress may account for the rather high threshold damage tolerance in the notched geometry. However, this of the notched specimens. If so, the beneficial effects of apparent damage tolerance may be a result of the volume inelastic straining on the stress concentration may be dependence of the matrix cracking stress, not a con- overestimated by the non-linear constitutive law used in sequence of local inelastic straining. Further experiments this study, because, in essence, the volume dependence of are needed to determine the statistical parameters asso- the cracking stress is neglected. A further implication is ciated with the matrix strength and to assess their role in that the inferred characteristic distance (dth a 0.3-0.4 the conditions for fracture ahead of a notch. Additional mm)may be anomalously high. It remains to be estab- experiments are also needed to assess the extent of lished which of these effects is dominant catter in fatigue life, for the purpose of validating the failure models presented here Appendix. Elastic stress concentrations in notched tensile The notch sensitivity of the tensile strength of the specimens SylramicTM/SiC composite at ambient temperature is consistent with the trends observed in other fccs The elastic stress concentration factors k. were cal- Typically a reduction of a25% in net-section strength is culated assuming that the composite is elastically iso- obtained for open holes of diameter 6 mm. This modest tropic. This assumption can be justified on the basis that amount of notch sensitivity can be rationalized on the the Youngs moduli measured in the 0 /90 and +450 basis of the stress redistribution that occurs as a result orientations were within 2% of one another (250 GPa) of local inelastic straining and the size-scale dependence This behavior is attributable to the fact that both the of the conditions at the onset of fracture through the matrix and the fibers are essentially pure Sic point stress fracture criterion. The notch sensitivity at For a specimen of width 2W and with a center hole of elevated temperature appears to be reduced slightly, as diameter 2a, ke is given by [37] manifest in a reduction in the inferred characteristic distance in the point stress criterion The unnotched LCF threshold for the SylramicM/ Sic ke=0=2+(1-a) (A) composite at 815C is dictated by the matrix cracking stress. Above the cracking stress, fracture occurs rapidly typically in <100 h. Moreover, the LCF life curve for where oo is the maximum longitudinal stress(at the hole stresses slightly above the threshold is extremely shallow, edge)and onet is the applied net-section stress. For the indicating a very strong sensitivity of fracture time to center hole geometry used in the present experiments applied stress. For the lifetime requirements of most gas a/w=0.2 and thus ke=2.51 turbine engine components(103-104 h), the allowable The elastic stress concentration factor for a specimen stress levels would have to remain below this threshold. of width 2W and with a center notch of length 2a and A further implication is that models to predict fracture root radius p(with a/p>>1)is given by [391Eq. (1) and the elastic stress concentration factor, ke=7.1 [39], is significantly below the measured value, 70–85 MPa. This difference is believed to be asso￾ciated with the steep stress gradients that exist in the notch tip region coupled with the intrinsic volume dependence of the matrix strength. That is, the high stress levels exist over only small volumes ahead of the notch (over distances ), reducing significantly the probability of encountering a matrix flaw to initiate cracking. Finite element calculations for the center-not￾ched geometry used in the present study (with 2a=6.35 mm and =0.2 mm) reveal that the elastic stress diminishes rapidly with distance from the notch tip, by 50% at a distance of 0.1 mm [Fig. 7(b)]. (By contrast, the reduction in elastic stress in the center-hole specimen with a hole diameter of 6.35 mm is only 6% at the same distance from the hole edge.) It is surmised that even a modest volume dependence of strength might lead to a significant elevation in the maximum local stress at the onset of cracking. This elevation in the local cracking stress may account for the rather high threshold of the notched specimens. If so, the beneficial effects of inelastic straining on the stress concentration may be overestimated by the non-linear constitutive law used in this study, because, in essence, the volume dependence of the cracking stress is neglected. A further implication is that the inferred characteristic distance (dth 0.3–0.4 mm) may be anomalously high. It remains to be estab￾lished which of these effects is dominant. 5. Summary The notch sensitivity of the tensile strength of the SylramicTM/SiC composite at ambient temperature is consistent with the trends observed in other CFCCs. Typically a reduction of 25% in net-section strength is obtained for open holes of diameter 6 mm. This modest amount of notch sensitivity can be rationalized on the basis of the stress redistribution that occurs as a result of local inelastic straining and the size-scale dependence of the conditions at the onset of fracture through the point stress fracture criterion. The notch sensitivity at elevated temperature appears to be reduced slightly, as manifest in a reduction in the inferred characteristic distance in the point stress criterion. The unnotched LCF threshold for the SylramicTM/SiC composite at 815
C is dictated by the matrix cracking stress. Above the cracking stress, fracture occurs rapidly, typically in 4100 h. Moreover, the LCF life curve for stresses slightly above the threshold is extremely shallow, indicating a very strong sensitivity of fracture time to applied stress. For the lifetime requirements of most gas turbine engine components (103 –104 h), the allowable stress levels would have to remain below this threshold. A further implication is that models to predict fracture times in the post-cracking regime are not likely to be useful, because of the precipitous drop in fracture time to unacceptably low levels. The LCF threshold for center-hole specimens is simi￾larly dictated by the matrix cracking limit. Once the cracking stress is exceeded locally (even over a very small distance ahead of the hole), fracture ensues. A reasonably accurate estimate of the threshold is obtained through the elastic stress concentration factor in combination with the matrix cracking stress [Eqn. (1)]. This highly notch-sen￾sitive behavior suggests the need for an extremely con￾servative design approach for CFCC structures containing holes. Furthermore, it precludes the exploi￾tation of the inelastic deformation mechanisms that operate in these materials and impart the requisite damage tolerance in non-oxidizing environments. The LCF threshold for center-notch specimens is com￾parable to that of the center hole specimens. Recognizing that the stress concentration factor is higher in the not￾ched geometry, the composite appears to exhibit superior damage tolerance in the notched geometry. However, this apparent damage tolerance may be a result of the volume￾dependence of the matrix cracking stress, not a con￾sequence of local inelastic straining. Further experiments are needed to determine the statistical parameters asso￾ciated with the matrix strength and to assess their role in the conditions for fracture ahead of a notch. Additional experiments are also needed to assess the extent of scatter in fatigue life, for the purpose of validating the failure models presented here. Appendix. Elastic stress concentrations in notched tensile specimens The elastic stress concentration factors, ke; were cal￾culated assuming that the composite is elastically iso￾tropic. This assumption can be justified on the basis that the Young’s moduli measured in the 0
/90
and 45
orientations were within 2% of one another (250 GPa). This behavior is attributable to the fact that both the matrix and the fibers are essentially pure SiC. For a specimen of width 2W and with a center hole of diameter 2a, ke is given by [37]: ke
o
net ¼ 2 þ 1  a W
3 ðA1Þ where
o is the maximum longitudinal stress (at the hole edge) and
net is the applied net-section stress. For the center hole geometry used in the present experiments, a=W ¼ 0:2 and thus ke=2.51. The elastic stress concentration factor for a specimen of width 2W and with a center notch of length 2a and root radius  (with a=1) is given by [39]: J.C. McNulty et al. / Composites Science andTechnology 61 (2001) 1331–1338 1337