2784 G N. Morscher, J D Cawley/ Journal of the European Ceramic Society 22(2002) 2777-2787 SYLMIb o precracked data(200 MPB) 140 Time, hours Time, Hours Fig. 6. Stress-rupture at 815C in air of BN interphase composites with(a)HN fibers and(b)SYL fibers b)above, which the single fiber failure condition would ultimate strength of the fibers in the as-produced com- predict. Therefore, rupture curves will be predicted for posite, oofcomposite) would be underestimated from the these two extremes and the switch from the kinetic- composite ultimate strength, cult [Eq. (14)], which was dependence to single fiber failure controlled rupture based on global load sharing assumptions. This would occurs at the point where single fiber failure rupture effectively reduce the estimated time-dependent fiber predicts longer times for rupture. strength and predict shorter rupture times for a given Case(a)can simply be determined by finding the time stress that satisfies the condition where Eq (20)and Eq (21) The model predicts a fiber gage-length dependence for are equal and is controlled by the time-dependent stress-rupture. This provides an opportunity to inde- embrittlement depth. Case(b) was determined by sol- pendently test model predictions. This was verified by ving for the case where Eq (23)is equal to l, i.e. the precracking composites at room temperature so that first embrittled fiber failure in a matrix crack Case(b) they possess a larger crack density than that from stress requires an accurate measure of crack-density as a rupture at an applied stress less than the precrack con- function of the stress-state. This information was avail- dition. For the HN-BN-MI specimen, some precracked able for the HN-BN-MI SiC and SYL-BN-MI SiC experiments were performed. A precrack stress of 200 systems. 4. I5 Fig. 6 shows the predictions for the two MPa was performed at room temperature and then the composite systems and the actual rupture data from specimen was subjected to stress-rupture at a lower Refs. 14, 15. Table I lists the experimentally determined stress. This precrack condition resulted in a crack den- variables that went into the model for both systems and sity of 2 cracks/mm. The increased lengths of loaded Fig. 7 shows the stress-dependent crack density as fibers resulted in significantly shorter rupture times at determined from measured crack densities from some of lower stresses than the specimens that were not pre- rupture mens cracked as the model also predicted fairly well(Fig. 6a) The two extremes predict the rupture behavior rela- The run-out stress was slightly underestimated by the tively well. The kinetic-limit seems to overestimate rup- model. However, the model effectively predicted the ture time slightly. One possible reason for this decrease in stress-rupture time with increasing crack overestimate is the presence of a possible stress-con- density centration on the outer perimeter of bridging fibers in a matrix crack. 24,25 which was not taken into account ne model. The model also slightly underestimates the rupture times for the SYL composites for the single fiber limit. One issue with SYL fiber composites in general is a relatively high t and the possibility that minor to moderate local load sharing conditions exist even for room temperature failure. o If this is the case, the SYL Composite For the model developed by Evans et aL. 25 composite system, fiber degradation was due to oxide scale growth and unbridged crack growth was due to fiber failure at the perimeter of the 100120140160180200220240260 unbridged crack. A fundamental difference with the model proposed Fig. 7. Stress-dependence for matrix crack density for SYL and HN here is that an interior strongly bonded fiber can trigger the failure of composites. The curves were based on post-test measurements of failed the entire region of strongly bonded fibers specimens.(b) above, which the single fiber failure condition would predict. Therefore, rupture curves will be predicted for these two extremes and the switch from the kinetic￾dependence to single fiber failure controlled rupture occurs at the point where single fiber failure rupture predicts longer times for rupture. Case (a) can simply be determined by finding the time that satisfies the condition where Eq. (20) and Eq. (21) are equal and is controlled by the time-dependent embrittlement depth. Case (b) was determined by sol￾ving for the case where Eq. (23) is equal to 1, i.e. the first embrittled fiber failure in a matrix crack. Case (b) requires an accurate measure of crack-density as a function of the stress-state. This information was avail￾able for the HN–BN–MI SiC and SYL–BN–MI SiC systems.14,15 Fig. 6 shows the predictions for the two composite systems and the actual rupture data from Refs. 14,15. Table 1 lists the experimentally determined variables that went into the model for both systems and Fig. 7 shows the stress-dependent crack density as determined from measured crack densities from some of the rupture specimens. The two extremes predict the rupture behavior rela￾tively well. The kinetic-limit seems to overestimate rup￾ture time slightly. One possible reason for this overestimate is the presence of a possible stress-con￾centration on the outer perimeter of bridging fibers in a matrix crack,24,25 which was not taken into account in the model.c The model also slightly underestimates the rupture times for the SYL composites for the single fiber limit. One issue with SYL fiber composites in general is a relatively high t and the possibility that minor to moderate local load sharing conditions exist even for room temperature failure.26 If this is the case, the ultimate strength of the fibers in the as-produced com￾posite, so(composite), would be underestimated from the composite ultimate strength, sult [Eq. (14)], which was based on global load sharing assumptions. This would effectively reduce the estimated time-dependent fiber strength and predict shorter rupture times for a given stress. The model predicts a fiber gage-length dependence for stress-rupture. This provides an opportunity to inde￾pendently test model predictions. This was verified by precracking composites at room temperature so that they possess a larger crack density than that from stress￾rupture at an applied stress less than the precrack con￾dition. For the HN–BN–MI specimen, some precracked experiments were performed. A precrack stress of 200 MPa was performed at room temperature and then the specimen was subjected to stress-rupture at a lower stress. This precrack condition resulted in a crack den￾sity of 2 cracks/mm. The increased lengths of loaded fibers resulted in significantly shorter rupture times at lower stresses than the specimens that were not pre￾cracked as the model also predicted fairly well (Fig. 6a). The run-out stress was slightly underestimated by the model. However, the model effectively predicted the decrease in stress-rupture time with increasing crack density. Fig. 7. Stress-dependence for matrix crack density for SYL and HN composites. The curves were based on post-test measurements of failed specimens. Fig. 6. Stress-rupture at 815
C in air of BN interphase composites with (a) HN fibers and (b) SYL fibers. c For the model developed by Evans et al. 25 of a C interphase composite system, fiber degradation was due to oxide scale growth and unbridged crack growth was due to fiber failure at the perimeter of the matrix crack due to the increased stress-concentration of the unbridged crack. A fundamental difference with the model proposed here is that an interior strongly bonded fiber can trigger the failure of the entire region of strongly bonded fibers. 2784 G.N. Morscher, J.D. Cawley / Journal of the European Ceramic Society 22 (2002) 2777–2787