M.B. Ruggles-Wrenn, CL. Genelin/Composites Science and Technology 69(2009)663-669 Following the procedure in 30,31, experimental data obtained in steam were plotted as log(UTS)vS log(applied stress rate). De- 25 MPa/s spite the limited number of tensile tests conducted at different 150 stress rates in steam, the fit of data to Eq. 4) was good with a coef- ficient of correlation in regression >0.980. This implies that the de- 0.0025MPa/s layed failure of N720 AM in steam at 1200C can be described by the empirical power law in Eq(1). Hence the parameters n=18 and D= 128. 13 were determined by a linear from the slope and intercept, respectively The crack growth exponent n represents a measure of suscepti- bility of the material to subcritical crack growth. Typically for brit- T=1200°c, Steam tle materials, the susceptibility is considered high for n< 20, ntermediate for30≤n≤50. and low for n>50. Thus at1200° 0.00 250.500.751001251.50 in steam the n720 AM composite exhibits significant susceptibility Strain(%) to subcritical crack growth. Similar results showing relatively high Fig. 2. Tensile stress-strain curves for N720/AM ceramic composite obtained in susceptibility to delayed failure at 1200C with n=12 were re- ests conducted with loading rates of 0.0025 and 25 MPa/s at 1200"C in steam. ported for N720/A composite [23]. In addition, Milz et al. [32] Effect of loading rate on stress-strain behavior and ultimate tensile strength is and Goering et al. 33] found that the N720 fibers exhibited consid erable susceptibility to delayed failure at temperatures >1000C, with the values of n ranging from 9 to 18. Choi et al. [24, 25] found 0.05 mm/s in air, modulus values are nearly 20% lower and failure that several non-oxide Cmcs exhibited significant susceptil stains are 53% higher than the corresponding values obtained in temperatures >1100C, with the n values ranging from 6 to 20 ir. Note that for N720/AM at 1200C, the displacement rate of 0.05 mm/s is equivalent to the stress rate of 25 MPa/s provi 3. 2. Creep-rupture elastic material behavior is assumed A change in loading rate by four orders or magnitude has a sig- Results of the creep-rupture tests for N720 /AM composite ar nificant effect on tensile stress-strain response and tensile proper presented in Table 1 and in Fig 3. Creep curves produced in all ties at 1200C in steam. As seen in Fig. 2, the tensile stress-strain tests conducted in air exhibit primary and secondary creep re- curves produced at 0.0025 MPa/s are strongly nonlinear. The gimes, but no tertiary creep Transition from primary to secondary 0.0025 MPa s stress-strain curves depart from linearity at a low creep occurs early in creep life, primary creep persists during the stress of 20 MPa. As the stress continues to increase, appreciable first w10 h of the creep test. Creep strain decreases as the applied elastic strains develop The failure strains ranging from 0.97 to stress increases from 73 to 136 MPa. Creep strains accumulate 26% are nearly two to four times those obtained at 25 MPa/s In at stresses <114 MPa considerably exceed the failure strain ob- contrast, the average UTS value of 94 MPa is 39% lower than the tained in the tension test. average strength value obtained at 25 MPa/s. The test environment appears to have little influence on the The strong dependence of tensile strength on loading rate appearance of the creep curves obtained at stresses >91 MPa exhibited by this composite at 1200C in steam is similar to that where only primary and secondary creep regimes are observed. exhibited by monolithic ceramics at elevated temperature In contrast, creep curves obtained at 73 MPa in argon and in steam [24, 25).In the case of monolithic ceramics, the time(rate)-depen- show primary, secondary and tertiary creep In argon, transition dence of strength(also known as delayed failure)has been shown from secondary to tertiary creep occurs after w70 h of creep life. to proceed by environmentally-assisted subcritical crack growth In steam, the secondary creep transitions to tertiary creep after 6-28]. The subcritical crack growth rate can be described by only x10 h. Moreover, the test environment has a significant effect the empirical power law [29-31 on creep strains accumulated at stresses <91 MPa. At 73 MPa, the creep strain produced in argon is nearly 10 times and the creep (1) strain produced in steam, four times that accumulated in air At 91 MPa, the presence of argon increases creep strain by a factor where a is the crack size, t is time, K is the mode I stress intensity factor, Kic is the critical stress intensity factor re toug ess)under mode I loading, and a and n are th parameters In the case of loading at constant st he frac Table ture strength af can be derived as a function of applied stress rate Summary of creep-rupture results for the N720/AM ceramic composite at 1200.C in o as follows [29-31: laboratory air, argon, and steam environments Cr= D(a)(n+1) (2) Test environment Creep stress(MPa) Creep strain(%) Time to rupture(h Here d is a crack growth parameter, associated with inert N720/alumina-mullite strength a, n and crack geometry, given by 04 2(n+1)o where Y is a geometry fac lated to flaw shape and its orienta tion with respect to the of applied stress. By taking loga- ste rithms of both sides Eq be expressed Steam Steam 0.11 log a t log d0.05 mm/s in air, modulus values are nearly 20% lower and failure stains are 53% higher than the corresponding values obtained in air. Note that for N720/AM at 1200 C, the displacement rate of 0.05 mm/s is equivalent to the stress rate of 25 MPa/s provided elastic material behavior is assumed. A change in loading rate by four orders or magnitude has a sig￾nificant effect on tensile stress–strain response and tensile proper￾ties at 1200 C in steam. As seen in Fig. 2, the tensile stress–strain curves produced at 0.0025 MPa/s are strongly nonlinear. The 0.0025 MPa/s stress–strain curves depart from linearity at a low stress of 20 MPa. As the stress continues to increase, appreciable inelastic strains develop. The failure strains ranging from 0.97 to 1.26% are nearly two to four times those obtained at 25 MPa/s. In contrast, the average UTS value of 94 MPa is 39% lower than the average strength value obtained at 25 MPa/s. The strong dependence of tensile strength on loading rate exhibited by this composite at 1200 C in steam is similar to that exhibited by monolithic ceramics at elevated temperatures [24,25]. In the case of monolithic ceramics, the time (rate)-depen￾dence of strength (also known as delayed failure) has been shown to proceed by environmentally-assisted subcritical crack growth [26–28]. The subcritical crack growth rate can be described by the empirical power law [29–31]: da dt ¼ A KI KIC n ð1Þ where a is the crack size, t is time, KI is the mode I stress intensity factor, KIC is the critical stress intensity factor (or fracture tough￾ness) under mode I loading, and A and n are the slow crack growth parameters. In the case of loading at constant stress rate, the frac￾ture strength rf can be derived as a function of applied stress rate r_ as follows [29–31]: rf ¼ Dðr_ Þ 1=ðnþ1Þ ð2Þ Here D is a crack growth parameter, associated with inert strength ri, n and crack geometry, given by: D ¼ 2ðn þ 1ÞK2 IC rn2 i AY2 ðn 2Þ " #1=ðnþ1Þ ð3Þ where Y is a geometry factor related to flaw shape and its orienta￾tion with respect to the direction of applied stress. By taking loga￾rithms of both sides Eq. (2) can be expressed as: logrf ¼ 1 n þ 1 logr_ þ logD ð4Þ Following the procedure in [30,31], experimental data obtained in steam were plotted as log (UTS) vs. log (applied stress rate). De￾spite the limited number of tensile tests conducted at different stress rates in steam, the fit of data to Eq. (4) was good with a coef- ficient of correlation in regression >0.980. This implies that the de￾layed failure of N720/AM in steam at 1200 C can be described by the empirical power law in Eq. (1). Hence the parameters n = 18 and D = 128.13 were determined by a linear regression analysis from the slope and intercept, respectively. The crack growth exponent n represents a measure of suscepti￾bility of the material to subcritical crack growth. Typically for brit￾tle materials, the susceptibility is considered high for n 6 20, intermediate for 30 6 n 6 50, and low for n > 50. Thus at 1200 C in steam the N720/AM composite exhibits significant susceptibility to subcritical crack growth. Similar results showing relatively high susceptibility to delayed failure at 1200 C with n = 12 were re￾ported for N720/A composite [23]. In addition, Milz et al. [32] and Goering et al. [33] found that the N720 fibers exhibited consid￾erable susceptibility to delayed failure at temperatures P1000 C, with the values of n ranging from 9 to 18. Choi et al. [24,25] found that several non-oxide CMCs exhibited significant susceptibility at temperatures P1100 C, with the n values ranging from 6 to 20. 3.2. Creep–rupture Results of the creep–rupture tests for N720/AM composite are presented in Table 1 and in Fig. 3. Creep curves produced in all tests conducted in air exhibit primary and secondary creep re￾gimes, but no tertiary creep. Transition from primary to secondary creep occurs early in creep life, primary creep persists during the first 10 h of the creep test. Creep strain decreases as the applied stress increases from 73 to 136 MPa. Creep strains accumulated at stresses 6114 MPa considerably exceed the failure strain ob￾tained in the tension test. The test environment appears to have little influence on the appearance of the creep curves obtained at stresses P91 MPa, where only primary and secondary creep regimes are observed. In contrast, creep curves obtained at 73 MPa in argon and in steam show primary, secondary and tertiary creep. In argon, transition from secondary to tertiary creep occurs after 70 h of creep life. In steam, the secondary creep transitions to tertiary creep after only 10 h. Moreover, the test environment has a significant effect on creep strains accumulated at stresses 691 MPa. At 73 MPa, the creep strain produced in argon is nearly 10 times and the creep strain produced in steam, four times that accumulated in air. At 91 MPa, the presence of argon increases creep strain by a factor Fig. 2. Tensile stress–strain curves for N720/AM ceramic composite obtained in tests conducted with loading rates of 0.0025 and 25 MPa/s at 1200 C in steam. Effect of loading rate on stress–strain behavior and ultimate tensile strength is evident. Table 1 Summary of creep–rupture results for the N720/AM ceramic composite at 1200 C in laboratory air, argon, and steam environments. Test environment Creep stress (MPa) Creep strain (%) Time to rupture (h) N720/alumina–mullite Air 73 0.60 >100a Air 91 0.59 >100a Air 114 0.47 22.3 Air 136 0.28 0.59 Argon 73 5.86 92.8 Argon 91 2.99 18.8 Argon 114 0.66 0.45 Argon 136 0.62 0.07 Steam 73 2.49 37.0 Steam 91 1.57 4.18 Steam 114 0.48 0.38 Steam 136 0.11 0.01 a Run-out. M.B. Ruggles-Wrenn, C.L. Genelin / Composites Science and Technology 69 (2009) 663–669 665