J.A. DiCarlo et al. /Appl. Math. Comput. 152(2004)473-481 peratures [20. On MG diagrams, the log-log results at various temperatures typically fall on a set of parallel straight lines that allow average rupture time t to be described by the simple equation, Here e is the steady state(or minimum)creep rate, and m and C are empirically determined parameters. Using this approach, Fig. 2 shows that the rupture behavior for the five SiC fiber types of Fig. I can indeed be best-fit to straight MG lines using data measured at 1200C in air and at 1400C in air for the Hi-Nicalon fiber. For these lines, fiber creep rate is equivalent to minimum creep rate or to the instantaneous creep rate at fiber rupture since no tertiary stages were ever observed Fig. 2 also shows that, except for the Nicalon and Hi-Nicalon fibers, the rupture lines of the different fiber types at 1200C in air do not fall on one master line as has been observed for various alumina-based fibers [21]. This can probably be attributed in part to the measured creep rates being larger than the viscoelastic creep rates due to the presence of variable anelastic creep com- ponents at fiber rupture. However, in relation to Eq (1), all the lines display approximately the same slope with an m exponent of 1. 2. The fact that the m the viscoelastic component( e t) increased with increasing rupture time or decreasing stress on the fibers. Also, by increasing test temperature from 1200 to 1400C, all fiber lines shifted upward (fivefold increase in rupture time for a given creep rate), like that of the Hi-Nicalon fiber in Fig. 2. However, the Hi Nicalon line at 1400C displayed an m value less than unity, implying reduced 1.000 Nicalon(1400C)J RUPTURE SiC/SiC Composites 1E09 1E408 1E-07 1E-06 1E05 .0001 CREEP RATE. sec Fig. 2. Monkman-Grant lines measured in air for Sic fibers, SiC matrices, and Sic/SiC com-peratures [20]. On MG diagrams, the log–log results at various temperatures typically fall on a set of parallel straight lines that allow average rupture time t to be described by the simple equation, te
m ¼ C: ð1Þ Here e
is the steady state (or minimum) creep rate, and m and C are empirically determined parameters. Using this approach, Fig. 2 shows that the rupture behavior for the five SiC fiber types of Fig. 1 can indeed be best-fit to straight MG lines using data measured at 1200
C in air and at 1400
C in air for the Hi-Nicalon fiber. For these lines, fiber creep rate is equivalent to minimum creep rate or to the instantaneous creep rate at fiber rupture since no tertiary stages were ever observed. Fig. 2 also shows that, except for the Nicalon and Hi-Nicalon fibers, the rupture lines of the different fiber types at 1200
C in air do not fall on one master line as has been observed for various alumina-based fibers [21]. This can probably be attributed in part to the measured creep rates being larger than the viscoelastic creep rates due to the presence of variable anelastic creep com￾ponents at fiber rupture. However, in relation to Eq. (1), all the lines display approximately the same slope with an m exponent of
1.2. The fact that the m value is greater than unity indicates that the average fiber rupture strain from the viscoelastic component ( e
t) increased with increasing rupture time or decreasing stress on the fibers. Also, by increasing test temperature from 1200 to 1400
C, all fiber lines shifted upward (>fivefold increase in rupture time for a given creep rate), like that of the Hi-Nicalon fiber in Fig. 2. However, the Hi￾Nicalon line at 1400
C displayed an m value less than unity, implying reduced 1E-10 1E-09 1E-08 1E-07 1E-06 1E-05 0.0001 0.01 0.1 1 10 100 1,000 RUPTURE TIME, hours CREEP RATE, sec -1 Sylramic (1200C) Ultra-SCS (1200C) Hi-Nicalon and Nicalon CVI SiC Matrix (1300C) (1200C) Hi-Nicalon (1400C) :: + + + D D SiC/SiC Composites + Zhu et al., 1997 (1300C) O Zhu et al., 1999 (1300C) D Hurst et al., 2001 (1315C) Fig. 2. Monkman–Grant lines measured in air for SiC fibers, SiC matrices, and SiC/SiC com￾posites. J.A. DiCarlo et al. / Appl. Math. Comput. 152 (2004) 473–481 477