36 G E. Youngblood et al./Composites Science and Technology 62(2002)1127-1139 K,=572WmK) 2"r3a38E奖 K=1.05W/(mK "r 20 W/(m K) Fiber Interfacial thermal conductance, h [W/(cm K) Fig 8. Analytical solution of the Hasselman-Johnson Eq (1) for fiber Fig 9. Analytical solutions of the Hasselman-Johnson Eq (1)at 27C volume fractions up to 0.6. The selected Kr and Km-valt lues corres. for fiber volume fractions up to 0.6. The selected values for a. Kr, and pond to constituent values at 400C for the Hi-Nicalon/PIP-Sic Km correspond to constituent values at 27C for a hypothetical composite shown in Fig. 5. The three superimposed data points were 2D- Tyranno SATM/CVI-SiC composite. The determined for this composite(with f=0.566)in vacuum, argon or analytical solution at 1000C for f=0.4 only calculated using Eq.(6). However, using the same tion environment since each component consists mostly method for the argon gas case with Kg=0.0478 W/m of crystalline p-SiC. However, at the time of this study K),fgKgt 3.8 W/(cm- K)rather than 10.8 W/(cm=K) such a composite was not available for actual testing calculated using Eq (6) from data given in Table 1 predicted analytic solutions for such a The reasonable agreement and the correct hypothetical Tyranno SA/CVI-Sic composite are shown by these rough estimates suggest that the shown as a function of h for f-values up to 0.6 when thermal barrier model together with the H-J model using representative data: Kr=65 w/(m k)and Km=20 describe the behavior of Keff and its dependence on h W/(m K)at 27C and a=5 um. The dependence of R for the uniaxial Hi-Nicalon/PIP-SiC composite fairly onf and h is similar to the case examined in Fig. 1(a) and has a crossover at R=l for h=578 W/(cmK).At 1000C, for f=0.4 the h-value for crossover actually 4.2. Hypothetical 2D-Tyranno M/CVI-SiC composite increases to 910 W/(cmK), as indicated in Fig 9 by the (unirradiated and irradiated) bold dashed line. For hx104 W/(cm2 K)or greater, R becomes relatively independent of further increases in h For 2D-woven configurations, an increasing number Importantly, any degradation of an interface with such of fiber-fiber interactions within tightly packed tows are a high value of h would drop Keff into the transition expected to cause an under-estimate of Keff by Eq (1). zone where Kef would significantly decrease as h Furthermore, the degree of the under-estimate will be decreases further larger the further the fiber-matrix thermal conductivity The temperature dependence as well as the irradiation ratio Kr/Km departs from unity and for larger f-values, effects can be included in the analysis by expressing Ke as discussed in Section 3. With these limitations in and Km as a function of temperature and dose in the mind, the H-J model will be used in this section to pre- following manner. For many ceramics, the reciprocal of dict Kefr and assess degradation effects for a hypothe- the thermal conductivity can be fit to a linear function tical 2D-SiCeSiC composite designed to have a desired of temperature for the temperature range near and high Keff as well as dimensional stability in a radiation above the Debye temperature [34]. However, for SiC environment where the Debye temperature is relatively high(807C) The selected fiber, Tyranno SA(Tyranno SA is a [35], a good linear fit is not obtained immediately above trademark used by the Ube Industries, Ltd, Ube City 27C because of the steep temperature dependence of 755, Japan), has a crystalline, near-stoichiometric Sic the Sic heat capacity. However, by using reciprocal microstructure and a relatively high thermal con- thermal diffusivity data the influence of the heat capa- ductivity(65 W/(m K) at RT)[33]. Both the Tyranno city temperature dependence below the Debye tempera SA fiber and a chemical vapor infiltrated(CVI)-Sic ture is removed from Eq.( 8), and a good linear fit matrix should exhibit dimensional stability in a radia- generally icalculated using Eq. (6). However,using the same method for the argon gas case with Kg=0.0478 W/(m K), fgKg/t 3.8 W/(cm2 K) rather than 10.8 W/(cm2 K) calculated using Eq. (6) from data given in Table 1. The reasonable agreement and the correct trends shown by these rough estimates suggest that the simple thermal barrier model together with the H–J model describe the behavior of Keff and its dependence on h for the uniaxial Hi-Nicalon/PIP-SiC composite fairly well. 4.2. Hypothetical 2D-Tyranno TM/CVI-SiC composite (unirradiated and irradiated) For 2D-woven configurations,an increasing number of fiber–fiber interactions within tightly packed tows are expected to cause an under-estimate of Keff by Eq. (1). Furthermore,the degree of the under-estimate will be larger the further the fiber-matrix thermal conductivity ratio Kf/Km departs from unity and for larger f-values, as discussed in Section 3. With these limitations in mind,the H–J model will be used in this section to pre￾dict Keff and assess degradation effects for a hypothe￾tical 2D-SiCf/SiC composite designed to have a desired high Keff as well as dimensional stability in a radiation environment. The selected fiber,Tyranno SATM (Tyranno SA is a trademark used by the Ube Industries,Ltd.,Ube City 755,Japan),has a crystalline,near-stoichiometric SiC microstructure and a relatively high thermal con￾ductivity (65 W/(m K) at RT) [33]. Both the Tyranno SA fiber and a chemical vapor infiltrated (CVI)-SiC matrix should exhibit dimensional stability in a radia￾tion environment since each component consists mostly of crystalline b-SiC. However,at the time of this study such a composite was not available for actual testing. In Fig. 9,predicted analytic solutions for such a hypothetical Tyranno SA/CVI-SiC composite are shown as a function of h for f-values up to 0.6 when using representative data: Kf=65 W/(m K) and Km=20 W/(m K) at 27
C and a=5 mm. The dependence of R on f and h is similar to the case examined in Fig. 1(a) and has a crossover at R=1 for h=578 W/(cm2 K). At 1000
C,for f=0.4 the h-value for crossover actually increases to 910 W/(cm2 K),as indicated in Fig. 9 by the bold dashed line. For h 104 W/(cm2 K) or greater, R becomes relatively independent of further increases in h. Importantly,any degradation of an interface with such a high value of h would drop Keff into the transition zone where Keff would significantly decrease as h decreases further. The temperature dependence as well as the irradiation effects can be included in the analysis by expressing Kf and Km as a function of temperature and dose in the following manner. For many ceramics,the reciprocal of the thermal conductivity can be fit to a linear function of temperature for the temperature range near and above the Debye temperature [34]. However,for SiC where the Debye temperature is relatively high (807
C) [35],a good linear fit is not obtained immediately above 27
C because of the steep temperature dependence of the SiC heat capacity. However,by using reciprocal thermal diffusivity data the influence of the heat capa￾city temperature dependence below the Debye tempera￾ture is removed from Eq. (8),and a good linear fit generally is obtained. Fig. 9. Analytical solutions of the Hasselman–Johnson Eq. (1) at 27
C for fiber volume fractions up to 0.6. The selected values for a, Kf,and Km correspond to constituent values at 27
C for a hypothetical 2D-Tyranno SATM/CVI-SiC composite. The solid line represents the analytical solution at 1000
C for f=0.4 only. Fig. 8. Analytical solution of the Hasselman–Johnson Eq. (1) for fiber volume fractions up to 0.6. The selected Kf- and Kmvalues corres￾pond to constituent values at 400
C for the Hi-NicalonTM/PIP-SiC composite shown in Fig. 5. The three superimposed data points were determined for this composite (with f=0.566) in vacuum,argon or helium atmospheres. 1136 G.E. Youngbloodet al. / Composites Science andTechnology 62 (2002) 1127–1139