S.R. Choi et al. /Journal of the European Ceramic Sociery 25(2005)1629-1636 633 ysis from slope and intercept, respectively, when log(fracture ength)is plotted as a function of log(applied stress rate) Constant stress-rate(or called dynamic fatigue)testing based on Eq (1)has been established as ASTM Test Methods to determine slow crack growth parameters of advanced mono- Sic/CAS lithic ceramics at ambient and elevated temperatures. 0, II Notwithstanding the limited number of test specimens used, the data fit to Eq. (1) was very reasonable for the cur rent CMCs with the coefficients of correlation in regression 98 all greater than 0.930. This implies that delayed failure the composites could be described by the power-law type of slow crack growth formulation, Eq(2). With this in mind 10010110210 the apparent delayed-failure parameters n and D for the composites were determined based on Eq(1)using the ex- Applied stress rate, d[MPa/s perimental data shown in Fig. 2(with the units of of in MPa Fig 4. Ultimate tensile strength as a function of test rates determined for us determined were n= ID SiC./ CAS at 1100oC, 2D SiC /MAS-5 at 1100C, and woven SiC /Sic 13 and D= 127, n=7 and D= 188, n=13 and D= 367, ( "standard") at 1200.C in air from previous studies and n= 20 and D= 160, respectively, for Nicalon/BSAS (batch A), Hi-Nicalon/BSAS, SiCr/MAS-5, and SiCr/SiC the degree of strength degradation with respect to test rate. As The prime was used here for composites to distinguish them oxidation prevails into the material system, porosity increases from monolithic ceramic counterparts. The apparent param- and the effective number and sizes of load-bearing fibers de- eters for the Cr/sic composite were n=6 and D =196 crease. This oxidation-induced damage would be considered and n=18 and D=166, respectively, for the standard and to be equivalent to crack-like flaws growing through matri- enhanced versions. The value of n represents a measure of ces and fibers from a fracture-mechanics point of view.The susceptibility to delayed failure, and is typically categorized equivalent crack propagates under a driving force(K1)based in brittle materials such that the susceptibility is very high for on Eq (2)so that the resulting strength follows in accordance n=20, intermediate for n=30-50, and very low for n>50. with Eq(1). Note that oxidation-induced damage increases Hence, the current composites exhibited a significant suscep- with decreasing test rate since more time is available for ox- tibility to delayed failure as compared with monolithic coun- idation at lower test rate. and vice versa. In other words at terparts such as silicon nitrides and silicon carbides which are faster test rates, an equivalent crack has little time to grow. typically in the range of n>20 at temperatures >1200C. 12 resulting in higher strength; whereas at lower test rates the Similar results showing greater susceptibility of CMCs to de- crack has longer time to grow appreciably, thereby yielding layed failure at elevated temperatures were also found from lower strength. However, oxidation was not likely a unique the previous study in ID SICf/CAS, 2D SICr/MAS, and 2D source of final fracture responsible in the Cr/SiC material system, as will be discussed in Section 3.2 from n=6-18, as depicted in Fig. 4 Unlike the other CMCs, the Cr/Sic composite, as men- tioned before, was subjected to significant oxidation of car- 3.2. Preload tests results bon fibers, resulting in material loss. Therefore, strength degradation was increased, attributed to decreasing fiber vol The results of preload tests carried out at 0.005 MPa/s with ume fraction and subsequently increasing porosity, as the test an 80% preload are presented in Fig.5, where ultimate tensile rate decreased. The strength degradation due to oxidation fo strength was plotted against preload factor(a=0.8)for each the Cr/Sic composite has been described based on the results composite. The preload factor a is defined such that a preload of stress rupture through a finite difference model on oxy ensile stress(op)applied to a test specimen prior to testing is gen concentrations and carbon consumption, 13 Although this normalized with respect to the ultimate tensile strength (ae) stress-oxidation model would give a better physical explana- tion, the phenomenological power-law formulation used in this study still provides a simple, convenient way to quantify (3) A The number of test specimens used in this study, one to three at each tes For advanced monolithic ceramics whose delayed failure rate,would be insufficient to determine reliable delayed failure paramete is governed by the power-law slow crack growth formulation However, considering a small scatter in ultimate strength of (Eq(2), it has been shown that fracture strength is a func- CMCs, typically with coefficients of variation <5%, the current delayed ion of preload factor and slow crack growth parameter n as failure parameters provided will not be changed too much even with a large follows 6. 10,11 number of test specimens; hence, the variation of the n and D to the number of test specimen would be expected to be minimal and statistically insignif =o(1+a+1)1(m+1)S.R. Choi et al. / Journal of the European Ceramic Society 25 (2005) 1629–1636 1633 ysis from slope and intercept, respectively, when log (fracture strength) is plotted as a function of log (applied stress rate). Constant stress-rate (or called dynamic fatigue) testing based on Eq. (1) has been established as ASTM Test Methods to determine slow crack growth parameters of advanced mono￾lithic ceramics at ambient and elevated temperatures.10,11 Notwithstanding the limited number of test specimens used, the data fit to Eq. (1) was very reasonable for the cur￾rent CMCs with the coefficients of correlation in regression all greater than 0.930. This implies that delayed failure of the composites could be described by the power-law type of slow crack growth formulation, Eq. (2). With this in mind, the apparent delayed–failure parameters n and D for the composites were determined based on Eq. (1) using the ex￾perimental data shown in Fig. 2 (with the units of σf in MPa and σ˙ in MPa/s). The parameters1 thus determined were n = 13 and D = 127, n = 7 and D = 188, n = 13 and D = 367, and n = 20 and D = 160, respectively, for Nicalon/BSAS (batch A), Hi-Nicalon/BSAS, SiCf/MAS-5, and SiCf/SiC. The prime was used here for composites to distinguish them from monolithic ceramic counterparts. The apparent param￾eters for the Cf/SiC composite were n = 6 and D = 196, and n = 18 and D = 166, respectively, for the standard and enhanced versions. The value of n represents a measure of susceptibility to delayed failure, and is typically categorized in brittle materials such that the susceptibility is very high for n ≤ 20, intermediate for n = 30–50, and very low for n > 50. Hence, the current composites exhibited a significant suscep￾tibility to delayed failure as compared with monolithic coun￾terparts such as silicon nitrides and silicon carbides which are typically in the range of n > 20 at temperatures ≥1200 ◦C.12 Similar results showing greater susceptibility of CMCs to de￾layed failure at elevated temperatures were also found from the previous study1 in 1D SiCf/CAS, 2D SiCf/MAS, and 2D woven SiCf/SiC (standard) composites with n values ranging from n = 6–18, as depicted in Fig. 4. Unlike the other CMCs, the Cf/SiC composite, as men￾tioned before, was subjected to significant oxidation of car￾bon fibers, resulting in material loss. Therefore, strength degradation was increased, attributed to decreasing fiber vol￾ume fraction and subsequently increasing porosity, as the test rate decreased. The strength degradation due to oxidation for the Cf/SiC composite has been described based on the results of stress rupture through a finite difference model on oxy￾gen concentrations and carbon consumption.13 Although this stress-oxidation model would give a better physical explana￾tion, the phenomenological power-law formulation used in this study still provides a simple, convenient way to quantify 1 The number of test specimens used in this study, one to three at each test rate, would be insufficient to determine reliable delayed failure parameters. However, considering a relatively small scatter in ultimate strength of many CMCs, typically with coefficients of variation ≤5%, the current delayed￾failure parameters provided will not be changed too much even with a large number of test specimens; hence, the variation of the n and D to the number of test specimen would be expected to be minimal and statistically insignif￾icant as well. Fig. 4. Ultimate tensile strength as a function of test rates determined for 1D SiCf/CAS at 1100 ◦C, 2D SiCf/MAS-5 at 1100 ◦C, and woven SiCf/SiC (“standard”) at 1200 ◦C in air from previous studies.1 the degree of strength degradation with respect to test rate. As oxidation prevails into the material system, porosity increases and the effective number and sizes of load-bearing fibers de￾crease. This oxidation-induced damage would be considered to be equivalent to crack-like flaws growing through matri￾ces and fibers from a fracture-mechanics point of view. The equivalent crack propagates under a driving force (KI) based on Eq. (2)so that the resulting strength follows in accordance with Eq. (1). Note that oxidation-induced damage increases with decreasing test rate since more time is available for ox￾idation at lower test rate, and vice versa.7 In other words, at faster test rates, an equivalent crack has little time to grow, resulting in higher strength; whereas, at lower test rates, the crack has longer time to grow appreciably, thereby yielding lower strength. However, oxidation was not likely a unique source of final fracture responsible in the Cf/SiC material system, as will be discussed in Section 3.2. 3.2. Preload tests results The results of preload tests carried out at 0.005 MPa/s with an 80% preload are presented in Fig. 5, where ultimate tensile strength was plotted against preload factor (α = 0.8) for each composite. The preload factor α is defined such that a preload tensile stress (σp) applied to a test specimen prior to testing is normalized with respect to the ultimate tensile strength (σf) with no preload6,10,11 α = σp σf (3) For advanced monolithic ceramics whose delayed failure is governed by the power-law slow crack growth formulation (Eq. (2)), it has been shown that fracture strength is a func￾tion of preload factor and slow crack growth parameter n as follows6,10,11 σfp = σf(1 + αn+1) 1/(n+1) (4)