506 M.B. Ruggles-Wrenn et al. International Journal of Fatigue 30 (2008)502-516 Evolution of the hysteresis response of N720/A with Fig 4 reveal that ratcheting, defined as progressive increase fatigue cycles is typified in Fig. 4, which shows hysteresis in accumulated strain with increasing number of cycles stress-strain loops for tests conducted in steam at various continues throughout the test. Effects of loading frequency loading frequencies In all tests, regardless of the frequency, and test environment on hysteresis response are illustrated the most extensive damage occurs on the first cycle, where in Figs. 5a and b, respectively. It is seen that the permanent considerable permanent strain is seen upon unloading. strain produced during the first cycle decreases with Afterwards hysteresis loops stabilize quickly. Results in increasing frequency. It is also seen that larger permanent strain is produced in steam than in air Of importance in cyclic fatigue is the reduction in stifl- ness(hysteresis modulus determined from the maximum T=1200C, Steam and minimum stress-strain data points during a loa Omax= 125 MPa f=0.1 Hz cycle), reflecting the damage development during fatigue cycling. Change in modulus is shown in Fig. 6, where nor malized modulus (i.e. modulus normalized by the modulus obtained in the second cycle) is plotted vs. fatigue cycles. The first cycle was not used for normalization because of Cycle 1 the large permanent strain offset upon unloading. It is note- 00 ycle 50 worthy that although all in-air tests achieved run-out, a decrease in normalized modulus with cycling was still observed(Fig 6a) Modulus loss increased with increasing fatigue stress level. In air at the frequency of 1.0 Hz, the 1251.50 Strain(%) a200 1.0 Hz. Ruggles-Wrenn, 2006 T=1200C, Steam Cycle Omax= 125 MPa Cycle 2 Cycle 1025 T=1200 C, Steam 0250.500.751.00125 0.50 00 Strain (%) Strain(%) 1200℃c, Steam Cycle 1 T=1200"c Cycle 1000 gma=170 MPa 1.001.25150 0.25 0.75 1.00 Strain (%) Strain(%) Fig 4. Typical evolution of stress-strain hysteresis response of N720/A Fig. 5. The stress-strain response of N720/A ceramic composite at with fatigue cycles at 1200C in steam:(a)at 0. I Hz and 125 MPa, (b)at 1200C: (a)in steam environment at three different loading frequencies 1.0 Hz and 125 MPa, data from Ruggles-Wrenn et al. [44](c) at 10 Hz and (b) at 0. I Hz in air and in steam environments. Curves shifted by O1% and 170 MPa for clarity. Data at 1.0 Hz from Ruggles- Wrenn et al. [44]Evolution of the hysteresis response of N720/A with fatigue cycles is typified in Fig. 4, which shows hysteresis stress–strain loops for tests conducted in steam at various loading frequencies. In all tests, regardless of the frequency, the most extensive damage occurs on the first cycle, where considerable permanent strain is seen upon unloading. Afterwards hysteresis loops stabilize quickly. Results in Fig. 4 reveal that ratcheting, defined as progressive increase in accumulated strain with increasing number of cycles, continues throughout the test. Effects of loading frequency and test environment on hysteresis response are illustrated in Figs. 5a and b, respectively. It is seen that the permanent strain produced during the first cycle decreases with increasing frequency. It is also seen that larger permanent strain is produced in steam than in air. Of importance in cyclic fatigue is the reduction in stiff- ness (hysteresis modulus determined from the maximum and minimum stress–strain data points during a load cycle), reflecting the damage development during fatigue cycling. Change in modulus is shown in Fig. 6, where nor￾malized modulus (i.e. modulus normalized by the modulus obtained in the second cycle) is plotted vs. fatigue cycles. The first cycle was not used for normalization because of the large permanent strain offset upon unloading. It is note￾worthy that although all in-air tests achieved run-out, a decrease in normalized modulus with cycling was still observed (Fig. 6a). Modulus loss increased with increasing fatigue stress level. In air at the frequency of 1.0 Hz, the 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Strain (%) T = 1200 ˚C, Steam max = 125 MPa f = 0.1 Hz Cycle 1000 Cycle 1 Cycle 50 Cycle 1820 0 50 100 150 0.00 0.25 0.50 0.75 1.00 1.25 1.50 ) aP M( ssert S ) aP M( ssert S 0 50 100 150 ) aP M( ssert S T = 1200 ˚C, Steam max = 125 MPa f = 1.0 Hz Cycle 100000 Cycle 10000 Cycle 1025 Cycle 25 Cycle 2 Cycle 1 a b c 0 50 100 150 200 0.00 0.25 0.50 0.75 1.00 1.25 1.50 Strain (%) Strain (%) T = 1200 ˚C, Steam σmax = 170 MPa f = 10 Hz Cycle 1 Cycle 10000 Cycle 1000 Cycle 50 Cycle 10 Fig. 4. Typical evolution of stress–strain hysteresis response of N720/A with fatigue cycles at 1200 C in steam: (a) at 0.1 Hz and 125 MPa, (b) at 1.0 Hz and 125 MPa, data from Ruggles-Wrenn et al. [44], (c) at 10 Hz and 170 MPa. 0 50 100 150 200 0.00 0.25 0.50 0.75 1.00 Strain (%) ) aP M( ssert S T = 1200 ˚C, Steam σmax = 170 MPa 0.1 Hz 10 Hz 1.0 Hz, Ruggles-Wrenn, 2006 0.00 0.25 0.50 0.75 1.00 Strain (%) T = 1200 ˚C σmax = 170 MPa f = 0.1 Hz Air Steam a 0 50 100 150 200 ) aP M( ssert S b Fig. 5. The stress–strain response of N720/A ceramic composite at 1200 C: (a) in steam environment at three different loading frequencies and (b) at 0.1 Hz in air and in steam environments. Curves shifted by 0.1% for clarity. Data at 1.0 Hz from Ruggles-Wrenn et al. [44]. 506 M.B. Ruggles-Wrenn et al. / International Journal of Fatigue 30 (2008) 502–516