476.A.DiCarloetal./Appl.Mat.Comput.152(2004)473-481 reduce rather than enhance creep. Therefore, at the present time, it would appear that the most likely species for volatilization is silicon from the Sic grains, which in turn can reduce grain size and enhance fiber creep rate. Indeed this effect should be especially observable in the Sylramic fiber, which has the smallest diameter(10 um)and therefore the largest surface to volume ratio of all the Fig. I fibers. Thus, from a technical point-of-view, one might expect differences in fiber creep behavior within a SiC/SiC composite, depending on whether the fiber surfaces are exposed to inert or to oxidizing environments However, for most high-temperature applications of current interest, the typ- ical service environments for the composites are oxidizing; so that even with porous interfacial zones, silica protective layers should eventually form on the Sic/SiC outer surfaces and effectively inhibit further volatilization of gaseous species from the fiber. It follows then that for mechanistic modeling of Sic/SiC creep-rupture behavior, the fiber in situ environment should be considered; but for most applications, the single fiber data in air should be appropriate A final point of interest for Fig. I is the rupture life behavior of the various SiC fiber types. In this regard, some important general observations have been made in previous studies [8, 18]. These include: (1) the activation energy con- trolling high-temperature rupture of the SiC fibers is nearly constant and equal to the activation energy controlling fiber creep;(2)fiber rupture strains for a given test temperature and test environment are fairly independent of the minimum creep rate at rupture, but are dependent on fiber type; (3)when the minimum creep rate is enhanced by argon testing, rupture times are shorter rupture strains are typically 100% higher in air than in argon; and(5)some of the fiber types rupture before clear attainment of steady-state creep behavior (see Fig. 1). The activation energy observation confirms that the most im- portant mechanism controlling the high-temperature fracture of SiC fibers(and monolithic ceramics)is creep-induced micro-crack growth. The observa of rupture strain independence on creep rate and shorter rupture times higher creep rates in argon indicate that for each fiber type, a certain amount of micro-crack growth is required to create the critical flaw size. Thus lower creep rates are conducive to longer fiber rupture lives. The observation of an approximate doubling of fiber rupture strain in air suggests that the con trolling micro-crack growth is primarily on the fiber surface, where silica for mation can blunt the stress concentration arising from this micro-crack growth. Finally, the observation of rupture before obvious steady-state creep behavior indicates that viscoelastic creep and micro-crack growth are on going The high-temperature creep curves of monolithic Si-based ceramics, such as pressureless sintered Si3N3[19], are very similar to those of the Sic fibers. For the monolithic materials, a convenient empirical approach for modeling rup- ture time is by use of Monkman-Grant(MG) diagrams that plot the log of average rupture time versus the log of minimum creep rate at various tem-reduce rather than enhance creep. Therefore, at the present time, it would appear that the most likely species for volatilization is silicon from the SiC grains, which in turn can reduce grain size and enhance fiber creep rate. Indeed, this effect should be especially observable in the Sylramic fiber, which has the smallest diameter (
10 lm) and therefore the largest surface to volume ratio of all the Fig. 1 fibers. Thus, from a technical point-of-view, one might expect differences in fiber creep behavior within a SiC/SiC composite, depending on whether the fiber surfaces are exposed to inert or to oxidizing environments. However, for most high-temperature applications of current interest, the typ￾ical service environments for the composites are oxidizing; so that even with porous interfacial zones, silica protective layers should eventually form on the SiC/SiC outer surfaces and effectively inhibit further volatilization of gaseous species from the fiber. It follows then that for mechanistic modeling of SiC/SiC creep-rupture behavior, the fiber in situ environment should be considered; but for most applications, the single fiber data in air should be appropriate. A final point of interest for Fig. 1 is the rupture life behavior of the various SiC fiber types. In this regard, some important general observations have been made in previous studies [8,18]. These include: (1) the activation energy con￾trolling high-temperature rupture of the SiC fibers is nearly constant and equal to the activation energy controlling fiber creep; (2) fiber rupture strains for a given test temperature and test environment are fairly independent of the minimum creep rate at rupture, but are dependent on fiber type; (3) when the minimum creep rate is enhanced by argon testing, rupture times are shorter; (4) rupture strains are typically 100% higher in air than in argon; and (5) some of the fiber types rupture before clear attainment of steady-state creep behavior (see Fig. 1). The activation energy observation confirms that the most im￾portant mechanism controlling the high-temperature fracture of SiC fibers (and SiC monolithic ceramics) is creep-induced micro-crack growth. The observa￾tions of rupture strain independence on creep rate and shorter rupture times under higher creep rates in argon indicate that for each fiber type, a certain amount of micro-crack growth is required to create the critical flaw size. Thus lower creep rates are conducive to longer fiber rupture lives. The observation of an approximate doubling of fiber rupture strain in air suggests that the con￾trolling micro-crack growth is primarily on the fiber surface, where silica for￾mation can blunt the stress concentration arising from this micro-crack growth. Finally, the observation of rupture before obvious steady-state creep behavior indicates that viscoelastic creep and micro-crack growth are on going during the transient stage. The high-temperature creep curves of monolithic Si-based ceramics, such as pressureless sintered Si3N3 [19], are very similar to those of the SiC fibers. For the monolithic materials, a convenient empirical approach for modeling rup￾ture time is by use of Monkman–Grant (MG) diagrams that plot the log of average rupture time versus the log of minimum creep rate at various tem- 476 J.A. DiCarlo et al. / Appl. Math. Comput. 152 (2004) 473–481