J.C. McNulty et al. /Composites Science and Technolog y 61(2001)1331-1338 Unnotched 方1 Center 100 = 50 一 Fig 8. Comparisons of the measured and predicted monotonic tensile strengths of specimens with holes and notches at 815C. The strength underestimated using the elastic stress concentration factor in com- Time to Fracture, t, (hours) bination with a critical stress fracture criterion, i.e. on=Ouke. In contrast, the model based on the inelastic stress distribution coupled with the point-stress criterion provides an adequate representation, for d0.3-0.5mm. a.250 Unnotched from comparisons of the measured and predicted not- ched strengths, assuming various values for d in the model. The comparisons are presented in Fig. 8. The 150 inferred characteristic distance is d 0.3-0.5 mm. con Center notch d=0. 3 mm erably smaller than the value obtained from the room 100 temperature tests (d N 0.75 mm). This reduction in d reflects a degradation in notch-sensitivity. It is unknown whether this degradation is intrinsic to the fracture mechanism at elevated temperature, it reflects the onset a of oxidative embrittlement or it is associated with scat Time to Fracture, t(hours) ter in the experimental data Fig. 9. Comparisons of measured and predicted thresholds at 815C 4.2. Notch sensitivity of the threshold stress for (a) center-hole and(b)center- notch specimens, based on the non- linear finite element model and the point-stress fracture criterion. An analogous stress-based fracture model has been used to rationalize the threshold stress levels in the cen in combination with the matrix cracking stress, where- ter-notch and center-hole specimens. The threshold upon the predicted threshold becomes stress was taken to be that for which the longitudinal stress,o, along the incipient fracture plane exceeds the oth=oth/ke =Omc/ke (1) unnotched threshold, ogh N 165 MPa, over a character- stic distance, duh, ahead of the hole or notch. As before This represents a lower-bound estimate of the thresh- the characteristic distance was obtained by comparing old stress For the center-hole specimen with a/W=0. 2, the calculated results with the experimental measure- ke=2.5 [37](Appendix) and thus oth N 66 MPa [also ments. Such comparisons are plotted in Fig 9. plotted on Fig. 9(a)]. This prediction is in reasonable or the center-hole specimens, the inferred distance agreement with the range obtained from the experi- spans the range dth 0-0.2 mm: the variation arising ments(60-85 MPa), reaffirming the poor notch sensi from the difference between the lowest stress at which tivity associated with LCF fracture at the test fracture had occurred, A 85 MPa, and the highest stress temperature. Furthermore, the extreme sensitivity of the at which run-out was obtained, A 60 MPa. Such low fracture time to the presence of matrix cracks is con- values of dth are indicative of extremely strong notch sen sistent with the oxidation embrittlement characteristics sitivity. Indeed, in the limit of dth=0, the threshold corre- of other Sic-based CFCCs at intermediate temperatures sponds to the case where the maximum stress(at the hole [12, 15, 17, 22, 23, 27, 38] edge)is equal to the unnotched threshold stress. Since the For the center-nlotch specimens, the inferred char- unnotched threshold is dictated by the matrix cracking acteristic distance is somewhat larger, duh A03-0.4 stress and the material response up cracking limit mm, indicating improved damage tolerance and lower is elastic, a conservative estimate of the threshold can be notch sensitivity. Furthermore, the lower bound esti obtained using the elastic stress concentration factor ke mate of the threshold stress, Oth N 23 MPa, based onfrom comparisons of the measured and predicted not￾ched strengths, assuming various values for d in the model. The comparisons are presented in Fig. 8. The inferred characteristic distance is d 0.3–0.5 mm, con￾siderably smaller than the value obtained from the room temperature tests (d 0.75 mm). This reduction in d reflects a degradation in notch-sensitivity. It is unknown whether this degradation is intrinsic to the fracture mechanism at elevated temperature, it reflects the onset of oxidative embrittlement, or it is associated with scat￾ter in the experimental data. 4.2. Notch sensitivity of the thresholdstress An analogous stress-based fracture model has been used to rationalize the threshold stress levels in the cen￾ter-notch and center-hole specimens. The threshold stress was taken to be that for which the longitudinal stress,
, along the incipient fracture plane exceeds the unnotched threshold,
o th 165 MPa, over a character￾istic distance, dth, ahead of the hole or notch. As before, the characteristic distance was obtained by comparing the calculated results with the experimental measure￾ments. Such comparisons are plotted in Fig. 9. For the center-hole specimens, the inferred distance spans the range dth 00:2 mm: the variation arising from the difference between the lowest stress at which fracture had occurred, 85 MPa, and the highest stress at which run-out was obtained, 60 MPa. Such low values of dth are indicative of extremely strong notch sen￾sitivity. Indeed, in the limit of dth=0, the threshold corre￾sponds to the case where the maximum stress (at the hole edge) is equal to the unnotched threshold stress. Since the unnotched threshold is dictated by the matrix cracking stress and the material response up to the cracking limit is elastic, a conservative estimate of the threshold can be obtained using the elastic stress concentration factor ke in combination with the matrix cracking stress, where￾upon the predicted threshold becomes
th ¼
o th=ke ¼
mc=ke ð1Þ This represents a lower-bound estimate of the thresh￾old stress. For the center-hole specimen with a=W ¼ 0:2, ke=2.5 [37] (Appendix) and thus
th 66 MPa [also plotted on Fig. 9(a)]. This prediction is in reasonable agreement with the range obtained from the experi￾ments (60–85 MPa), reaffirming the poor notch sensi￾tivity associated with LCF fracture at the test temperature. Furthermore, the extreme sensitivity of the fracture time to the presence of matrix cracks is con￾sistent with the oxidation embrittlement characteristics of other SiC-based CFCCs at intermediate temperatures [12,15,17,22,23,27,38]. For the center-notch specimens, the inferred char￾acteristic distance is somewhat larger, dth 0:30:4 mm, indicating improved damage tolerance and lower notch sensitivity. Furthermore, the lower bound esti￾mate of the threshold stress,
th 23 MPa, based on Fig. 8. Comparisons of the measured and predicted monotonic tensile strengths of specimens with holes and notches at 815
C. The strength is underestimated using the elastic stress concentration factor in com￾bination with a critical stress fracture criterion, i.e.
n ¼
u=ke. In contrast, the model based on the inelastic stress distribution coupled with the point-stress criterion provides an adequate representation, for d 0.3–0.5 mm. Fig. 9. Comparisons of measured and predicted thresholds at 815
C for (a) center-hole and (b) center-notch specimens, based on the non￾linear finite element model and the point-stress fracture criterion. 1336 J.C. McNulty et al. / Composites Science andTechnology 61 (2001) 1331–1338