R H. Jones, C.H. Henager: /Journal of the European Ceramic Sociery 25(2005)1717-1722 energies under these conditions and they match quite well the fiber thermal limits. There is a need for additional stress with activation energies for fiber about 500-600 rupture data as a function of oxygen concentration. kJ/mol. Our dynamic crack growth model agrees reasonably While thermal creep of polymer derived ceramic fibers is well with measured crack growth rates and these activation often non-linear, or viscous-like, in time and stress, irradia- tion creep of these same fibers appears to be linear in both When oxygen is introduced during the crack growth test- time(dose)and applied stress. The fiber thermal creep has an ing the deformation rates increase and the activation energy activation energy of about 600 kJ/mol. The irradiation creep decreases to about 50 kJ/mol, in agreement with carbon ox- equation assumes a temperature independent regime below idation processes. Significantly, the crack growth kinetics 1173K(900C)and an activation energy of 50 kJ/mol for change from non-linear to linear since now the bridge compli- temperatures greater than 1173 K. The creep rate is linear in ance is dominated by the linear portion as lfree lox approach dose rate and stress. We observe that irradiation creep of the and exceed deb, Fig. 2. Again, our model agrees well with fibers dominates the fiber deformation process for tempera- these changes in both kinetics and activation energies. The tures below 1273 K(1000C)but thermal creep dominates at transition between the FR and Ir mechanisms is defined as higher test temperatures, Fig 4. This implies that we will need the locus of points where the crack growth rates of each mech- to further understand and model irradiation creep processes anism are roughly equal. This was determined by choosing an in SiC-based fibers since apparently that process is important oxygen concentration where the crack velocity doubled com- in applications that operate at or below 1000C. There is little pared to the velocity without any oxygen. This curve is steep understanding of the mechanisms of irradiation creep in these as shown in Fig. 2 due in part to the high activation energy fibers, whereas the thermal creep data can be understood by of the fiber creep process. It is bounded at high temperatures analogy to creep in viscous solids. The creep mechanisms in by fiber stress rupture mechanisms the fibers may be distinct from those that operate in the crys- Transitions from IR to either OE or VS/OE mechanisms talline SiC-matrix just by virtue of the nanocrystalline nature are shown. We find that there is a competition between of the fibers, even the stoichiometric fibers. The linear creep specimen failure due to Ir relative to the time for pinch-off response suggests that a Nabarro-Herring creep mechanism and oe to occur. The dynamics are handled by removing may be operating but this remains to be shown conclusively those fibers from the bridging zone that have an oxide thick ness greater than some critical value, such as the interphase thickness. However, this transition is crack length(specimen 4. Conclusion size) and interphase thickness dependent. The size effect occurs since Oe depends on total fiber exposure time, which a dynamic crack growth model with the following fea- is dependent on crack length. Interphase thickness effects tures has been developed: (1) it is based on the weight arise due to our criterion that pinch-off occurs prior to the function method using discrete fiber bridges, (2)it contains onset of oE. The computations shown here are for an inter- non-linear bridge extension laws based on fiber-creep kinet- phase thickness of 150 nm. Other plausible OE mechanisms ics for Nicalon-CG and Hi-Nicalon fibers, (3)it contains only require a critical oxide thickness that is not interphase bridge extension laws for the case of interphase removal, thickness dependent, 39. However, such mechanisms will and(4)it provides fully dynamic crack tracking using a still exhibit a specimen size effect or history effect. Transi- critical-stress-intensity propagation criterion. The model re- tions from OE (pinch-off with brittle glass phase)to VS/oE produces the time-dependent crack growth kinetics observed (non-brittle, viscous glass phase) depend on the viscosity of experimentally in specimens of Nicalon-CG and Hi-Nicalon the glass which is strongly dependent on glass composition. 0/90 woven composites. The transition from non-linear crack Thus, these transitions are not rigorously defined here growth kinetics to linear growth kinetics is also reproduced and will have to wait for future work. By incorporating by the model by comparing crack growth rates under FR or existing models of viscous interphase mechanics, we will IR domination. Using the activation energy for the oxidation be able to understand the effects of viscosity on fiber stress of carbon in the model it correctly predicted this change from concentrations non-linear to linear crack growth kinetics By implementing The database for fiber stress rupture is mainly limited to a simple"fiber removal"algorithm, where the criterion for tests in air so dependence on oxygen concentration is lack- removal is based either on a critical oxide thickness or stress ing. SR competes with OE and IR at temperatures higher rupture threshold, we can also map out transitions between than about 1373 K for oxygen concentrations near 0. 2%. The crack growth due to OE and Sr. This model is being used to onset of Sr occurs at 1373 K in air during dynamic crack predict the effects of fiber stress rupture and neutron irradia- growth according to our model and this onset is predict tion, where there is no data on composite material. A map of to shift to 1423 K for lower oxygen concentrations. Without the crack growth mechanism as a function of environmental detailed data as a function of oxygen concentration, we can oxygen concentration and temperature was developed with not be more quantitative. The map suggests that SR shifts to assumption about the transition between mechanisms and this higher temperatures as the oxygen concentration decreases. has been very effective in identifying optimum environmen- The boundary between FR and Sr is suggested to occur at tal regimes for using these materials. The model and resultingR.H. Jones, C.H. Henager Jr. / Journal of the European Ceramic Society 25 (2005) 1717–1722 1721 energies under these conditions and they match quite well with activation energies for fiber creep, about 500–600 kJ/mol. Our dynamic crack growth model agrees reasonably well with measured crack growth rates and these activation energies. When oxygen is introduced during the crack growth test￾ing the deformation rates increase and the activation energy decreases to about 50 kJ/mol, in agreement with carbon ox￾idation processes. Significantly, the crack growth kinetics change from non-linear to linear since now the bridge compli￾ance is dominated by the linear portion as lfree + lox approach and exceed ldeb, Fig. 2. Again, our model agrees well with these changes in both kinetics and activation energies. The transition between the FR and IR mechanisms is defined as the locus of points where the crack growth rates of each mech￾anism are roughly equal. This was determined by choosing an oxygen concentration where the crack velocity doubled com￾pared to the velocity without any oxygen. This curve is steep as shown in Fig. 2 due in part to the high activation energy of the fiber creep process. It is bounded at high temperatures by fiber stress rupture mechanisms. Transitions from IR to either OE or VS/OE mechanisms are shown. We find that there is a competition between specimen failure due to IR relative to the time for pinch-off and OE to occur. The dynamics are handled by removing those fibers from the bridging zone that have an oxide thick￾ness greater than some critical value, such as the interphase thickness. However, this transition is crack length (specimen size) and interphase thickness dependent. The size effect occurs since OE depends on total fiber exposure time, which is dependent on crack length. Interphase thickness effects arise due to our criterion that pinch-off occurs prior to the onset of OE. The computations shown here are for an inter￾phase thickness of 150 nm. Other plausible OE mechanisms only require a critical oxide thickness that is not interphase thickness dependent38,39. However, such mechanisms will still exhibit a specimen size effect or history effect. Transi￾tions from OE (pinch-off with brittle glass phase) to VS/OE (non-brittle, viscous glass phase) depend on the viscosity of the glass which is strongly dependent on glass composition. Thus, these transitions are not rigorously defined here and will have to wait for future work. By incorporating existing models of viscous interphase mechanics, we will be able to understand the effects of viscosity on fiber stress concentrations. The database for fiber stress rupture is mainly limited to tests in air so dependence on oxygen concentration is lack￾ing. SR competes with OE and IR at temperatures higher than about 1373 K for oxygen concentrations near 0.2%. The onset of SR occurs at 1373 K in air during dynamic crack growth according to our model and this onset is predicted to shift to 1423 K for lower oxygen concentrations. Without detailed data as a function of oxygen concentration, we can￾not be more quantitative. The map suggests that SR shifts to higher temperatures as the oxygen concentration decreases. The boundary between FR and SR is suggested to occur at the fiber thermal limits. There is a need for additional stress rupture data as a function of oxygen concentration. While thermal creep of polymer derived ceramic fibers is often non-linear, or viscous-like, in time and stress, irradia￾tion creep of these same fibers appears to be linear in both time (dose) and applied stress. The fiber thermal creep has an activation energy of about 600 kJ/mol. The irradiation creep equation assumes a temperature independent regime below 1173 K (900 ◦C) and an activation energy of 50 kJ/mol for temperatures greater than 1173 K. The creep rate is linear in dose rate and stress. We observe that irradiation creep of the fibers dominates the fiber deformation process for tempera￾tures below 1273 K (1000 ◦C) but thermal creep dominates at higher test temperatures, Fig. 4. This implies that we will need to further understand and model irradiation creep processes in SiC-based fibers since apparently that process is important in applications that operate at or below 1000 ◦C. There is little understanding of the mechanisms of irradiation creep in these fibers, whereas the thermal creep data can be understood by analogy to creep in viscous solids. The creep mechanisms in the fibers may be distinct from those that operate in the crys￾talline SiC-matrix just by virtue of the nanocrystalline nature of the fibers, even the stoichiometric fibers. The linear creep response suggests that a Nabarro-Herring creep mechanism may be operating but this remains to be shown conclusively. 4. Conclusion A dynamic crack growth model with the following fea￾tures has been developed: (1) it is based on the weight￾function method using discrete fiber bridges, (2) it contains non-linear bridge extension laws based on fiber-creep kinet￾ics for Nicalon-CG and Hi-Nicalon fibers, (3) it contains bridge extension laws for the case of interphase removal, and (4) it provides fully dynamic crack tracking using a critical-stress-intensity propagation criterion. The model re￾produces the time-dependent crack growth kinetics observed experimentally in specimens of Nicalon-CG and Hi-Nicalon 0/90 woven composites. The transition from non-linear crack growth kinetics to linear growth kinetics is also reproduced by the model by comparing crack growth rates under FR or IR domination. Using the activation energy for the oxidation of carbon in the model it correctly predicted this change from non-linear to linear crack growth kinetics. By implementing a simple “fiber removal” algorithm, where the criterion for removal is based either on a critical oxide thickness or stress rupture threshold, we can also map out transitions between crack growth due to OE and SR. This model is being used to predict the effects of fiber stress rupture and neutron irradia￾tion, where there is no data on composite material. A map of the crack growth mechanism as a function of environmental oxygen concentration and temperature was developed with assumption about the transition between mechanisms and this has been very effective in identifying optimum environmen￾tal regimes for using these materials. The model and resulting