J. Sha et al. / Materials Characterization 57(2006)6-1/ est temperature [c] Test temperature [c] E 1 500140013001200 09▲ 三0.8 三08 0.7 0.71 1600C HT-1h 0.7 0.5 0.5 0.5 04 耍04 0.2 (b) (c) 70.80.9 Reciprocal temperature [10oc-11 Reciprocal temperature[10oC] Reciprocal temperature [10oc- Fig. 2. Temperature and time dependence of m of SiC fibers after heat treatment at elevated temperatures:(a)HNL fiber; (b)HNLS fiber; (c) TysA fiber,(HT: heat treatment). shaped curves are shifted to the right, and the shapes of In the present work, the O values were found(from these curves are slightly different at the low and high m=0.3, 0.5, 0.7, which represent the high temperature, moderate temperature and low temperature regions)to Heat treatment was seen to improve the creep be 563, 598 and 445 kJ/mol for the as-received HNL resistance of SiC fibers In Fig. 2(a), improved creep fibers; 707, 692, and 500 kJ/mol for as-received HNLS resistance was observed for the hnL fibers heat treated at fibers; 707, 774 and 525 kJ/mol for as-received TySA 1400C. The applied stress in as-received HNL fiber was nearly fully relaxed at 1300C after 1 h; however, for the Table 2 HNL fiber heat treated at 1600C, full stress relaxation Apparent activation energies for SiC-based fibers with different required 50 h at 1400C. Fig. 2(b)and(c)show the m ratios for HNLS and TySA fibers after heat treatment at Fiber condition BSR parameter In(h) t2(h) o different temperatures. The creep resistance was im- (kJ/mol) proved for both fibers after heat treatment at 1600C If we take m=0.5 as an arbitrary value for which we can compare test results, two trends are evident. First, he relaxation temperature for m=0.5 increased with an HNL1400°HTT0.7 652 increase of the HTT. Second, at the level of m=0.5 the 1 h BSR tests show a higher relaxation temperature HNL=1600°HTT0.7 than that of longer time BSR test, as would be expected 3.3. Apparent ad HNLS-as received 0.7 Since stress relaxation is a thermally activated HNLs--16000 process for ceramic materials, the apparent activation energy of creep, 0, can then be determined from the A(1/n) spacing between the curves at a constant m TySA-as received 0 value(cross-cut method) in the plots of stress relaxation parameter vs reciprocal temperature as indicated in Fig. TySA-1600C HTT 0.7 2(a)-(c). From these figures, the o for a given m value, can be calculated from the relationship TysA-1780°CHr0.7 111111111111111 50602 50774 (2)1ysA-1900c0H07 TT where R is the gas constant(8.314 J/mol K) Means no data are available for this m valueshaped curves are shifted to the right, and the shapes of these curves are slightly different at the low and high temperature regions. Heat treatment was seen to improve the creep resistance of SiC fibers. In Fig. 2 (a), improved creep resistance was observed for the HNL fibers heat treated at 1400 °C. The applied stress in as-received HNL fiber was nearly fully relaxed at 1300 °C after 1 h; however, for the HNL fiber heat treated at 1600 °C, full stress relaxation required 50 h at 1400 °C. Fig. 2 (b) and (c) show the m ratios for HNLS and TySA fibers after heat treatment at different temperatures. The creep resistance was im￾proved for both fibers after heat treatment at 1600 °C. If we take m= 0.5 as an arbitrary value for which we can compare test results, two trends are evident. First, the relaxation temperature for m= 0.5 increased with an increase of the HTT. Second, at the level of m= 0.5, the 1 h BSR tests show a higher relaxation temperature than that of longer time BSR test, as would be expected. 3.3. Apparent activation energy of creep Since stress relaxation is a thermally activated process for ceramic materials, the apparent activation energy of creep, Q, can then be determined from the Δ(1/T) spacing between the curves at a constant m value (cross-cut method) in the plots of stress relaxation parameter vs. reciprocal temperature as indicated in Fig. 2 (a)–(c). From these figures, the Q for a given m value, can be calculated from the relationship: Q ¼ Rd ln t2 t1
1 T1 − 1 T2 ð2Þ where R is the gas constant (8.314 J/mol K). In the present work, the Q values were found (from m= 0.3, 0.5, 0.7, which represent the high temperature, moderate temperature and low temperature regions) to be 563, 598 and 445 kJ/mol for the as-received HNL fibers; 707, 692, and 500 kJ/mol for as-received HNLS fibers; 707, 774 and 525 kJ/mol for as-received TySA 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 0.5 0.6 0.7 0.8 0.9 1 As received-1h As received-10h 1400C HT-1h 1400C HT-25h 1600C HT-1h 1600C HT-50h 1500 1200 1000 Test temperature [°C] Reciprocal temperature [10-3 °C-1] Stress relaxation parameter, m (1/T) (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 As received-1h As-received-50h 1600C HT-1h 1600C HT-50h Test temperature [°C] Reciprocal temperature [10-3 °C-1] Stress relaxation parameter, m (b) As received-1h As received-50h 1600C HT-1h 1600C HT-50h 1780C HT-1h 1780C HT-50h 1900C HT-1h 1900C HT-50h Test temperature [°C] Reciprocal temperature [10-3 °C-1] Stress relaxation parameter, m (c) 1400 1300 1500 1200 1000 1400 1300 1500 1200 1000 1400 1300 Fig. 2. Temperature and time dependence of m of SiC fibers after heat treatment at elevated temperatures: (a) HNL fiber; (b) HNLS fiber; (c) TySA fiber, (HT: heat treatment). Table 2 Apparent activation energies for SiC-based fibers with different conditions Fiber condition BSR parameter (m) t1 (h) t2 (h) Q (kJ/mol) HNL—as received 0.7 1 10 445 0.5 1 10 598 0.3 1 10 563 HNL—1400 °C HTT 0.7 1 25 525 0.5 1 25 622 0.3 1 25 652 HNL—1600 °C HTT 0.7 1 50 x 0.5 1 50 929 0.3 1 50 775 HNLS—as received 0.7 1 50 500 0.5 1 50 692 0.3 1 50 707 HNLS—1600 °C HTT 0.7 1 50 664 0.5 1 50 929 0.3 1 50 756 TySA—as received 0.7 1 50 525 0.5 1 50 774 0.3 1 50 707 TySA—1600 °C HTT 0.7 1 50 561 0.5 1 50 692 0.3 1 50 581 TySA—1780 °C HTT 0.7 1 50 x 0.5 1 50 602 0.3 1 50 774 TySA—1900 °C HTT 0.7 1 50 614 0.5 1 50 551 0.3 1 50 x x: Means no data are available for this m value. 8 J.J. Sha et al. / Materials Characterization 57 (2006) 6–11