G E. Youngblood et al./Composites Science and Technology 62(2002)1127-1139 Table I The interfacial conductance, h, at 400C determined by Eqs. (2)and (4) from measured values of thermal diffusivity for a Hi-NicalonTM/PIP-SiC (amorphous Ceraset)composite in different atmospheres. Data used in Eq (4): Kr=5.72 w/(m K), Km=1.05 w/(m k),f=0.566 and a=6.9 um Atmosphere a(400°C Kr(400°C) h(400°C) ×10-6m2/s (%) by Eq (8) ( Keff/Km) Eqs. (2)and (4 1024±0.050 0.975 17.7 Helium(≈105Pa) 1435±0.049 Vacuum(≈10Pa) 1062±0.034 a lg for 10-individual measurements or each condition sample was heated to 400C and held at that tempera- 0.040 for the composite; a=6.9+0. 8 um and Kr=5.72 ture while evacuating to better than 10 Pa for 17 h using W/(m K)for Hi-Nicalon fiber; and Km-1.05 W/(m K) a mechanical roughing-pump After the diffusivity mea- for the amorphous PIP-SiC. Thus, in Eq. (4)r=K urements in vacuum were completed, the furnace was Km=5.45 at 400C. back-filled with helium and evacuated six times to a The results are presented in Table I for each atmo- pressure slightly above atmospheric while holding the spheric condition. The h-values calculated for the three temperature constant. After the measurements in separated vacuum conditions were approximately the helium were completed, the system was evacuated again same, indicating that changing the atmosphere while for 17 h and the measurements were repeated in holding the temperature constant did not affect fa and vacuum. Then the backfill/evacuation procedure was fg, the nominal fractional area coverage for the direct repeated with argon and diffusivity measurements were contact and gas conduction mechanisms, respectively. It made again. Finally, the system was evacuated once also demonstrated that the introduced gases were com- more overnight and diffusivity measurements were pletely eliminated during each 17-h evacuation proce- repeated in vacuum for the third time. Ten diffusivity dure. The average h-value for the vacuum condition was measurements were made at 400+2C for each atmos- 18.9+1.0 W/(cm- K), which represents the product fdhd sheri condition in Eq.(6). The overall h-values determined with the The Kem-values were calculated by Eq.( 8)from the argon and the helium atmospheres were 29.7 and 39.6 measured a( T)-values for each atmosphere. Then with W/(cm- K), respectively. Therefore, the difference R=Kef/Km, h-values were calculated using Eq (4). For between these overall h-values and fahd represents ghg these calculations the following data at 400oC were i. e 10.8 and 20.7 W/(cm2 K)for argon ellum gas used: p=2.08 g/cm, Cp=1. 12 J/g K) and f=0.566+ conduction in the composite, respectively In Fig 8, for the given Kr and Km-values at 400oC the analytical solutions given by Eq (I)are plotted for fiber packing fractions Vr=0. 1, 0.4, 0.5 and 0.6. Super imposed on this plot are the measured R-values at each atmospheric condition forf=0.566. The data points fall in the transition region near the homogenization point where the R-values are most sensitive to the changing h- values, but are not so sensitive to the fiber volume frac tion. Importantly, in this region Eq. (1)most accurately describes the behavior of Keff and its dependence on h Since the minimum hd value is expected to be about 100 W/(cm-K), an fahd-value of 18.9 W/(cm K)implies that f a <0. 2, so fg.8. Examination of the extensive crack structure between the fibers and matrix, as depic ted in Fig. 5, suggests that these values for fa and fg are reasonable estimates for this particular uniaxial compo Temperature (C) site structure. Then, estimating that tal um from Fig. 5 Fig. 7. The calculated thermal conductivity values from 27 to 1000 C and using Kg=0. 269 W/(m K) for helium gas at one for a Hi- fiber(upper curve)and for amorphous Ceraset TM atmosphere and 400C [28], fghgfgKg/t=21 W/(cm that simulates the PIP-Sic matrix material (lower curve) K), which closely matches the 20.7 W/(cm K) valuesample was heated to 400
C and held at that tempera￾ture while evacuating to better than 10 Pa for 17 h using a mechanical roughing-pump. After the diffusivity mea￾surements in vacuum were completed,the furnace was back-filled with helium and evacuated six times to a pressure slightly above atmospheric while holding the temperature constant. After the measurements in helium were completed,the system was evacuated again for 17 h and the measurements were repeated in vacuum. Then the backfill/evacuation procedure was repeated with argon and diffusivity measurements were made again. Finally,the system was evacuated once more overnight and diffusivity measurements were repeated in vacuum for the third time. Ten diffusivity measurements were made at 4002
C for each atmos￾pheric condition. The Keff-values were calculated by Eq. (8) from the measured a(T)-values for each atmosphere. Then with R=Keff/Km, h-values were calculated using Eq. (4). For these calculations the following data at 400
C were used: =2.08 g/cm3 , Cp=1.12 J/(g K) and f=0.566 0.040 for the composite; a=6.90.8 mm and Kf=5.72 W/(m K) for Hi-Nicalon fiber; and Km=1.05 W/(m K) for the amorphous PIP-SiC. Thus,in Eq. (4) r=Kf/ Km=5.45 at 400
C. The results are presented in Table 1 for each atmo￾spheric condition. The h-values calculated for the three separated vacuum conditions were approximately the same,indicating that changing the atmosphere while holding the temperature constant did not affect fd and fg,the nominal fractional area coverage for the direct contact and gas conduction mechanisms,respectively. It also demonstrated that the introduced gases were com￾pletely eliminated during each 17-h evacuation proce￾dure. The average h-value for the vacuum condition was 18.91.0 W/(cm2 K),which represents the product fdhd in Eq. (6). The overall h-values determined with the argon and the helium atmospheres were 29.7 and 39.6 W/(cm2 K),respectively. Therefore,the difference between these overall h-values and fdhd represents fghg, i.e. 10.8 and 20.7 W/(cm2 K) for argon and helium gas conduction in the composite,respectively. In Fig. 8,for the given Kf- and Km-values at 400
C the analytical solutions given by Eq. (1) are plotted for fiber packing fractions Vf=0.1,0.4,0.5 and 0.6. Super￾imposed on this plot are the measured R-values at each atmospheric condition for f=0.566. The data points fall in the transition region near the homogenization point where the R-values are most sensitive to the changing h￾values,but are not so sensitive to the fiber volume frac￾tion. Importantly,in this region Eq. (1) most accurately describes the behavior of Keff and its dependence on h. Since the minimum hd-value is expected to be about 100 W/(cm2 K),an fdhd-value of 18.9 W/(cm2 K) implies that fd40.2,so fg 0.8. Examination of the extensive crack structure between the fibers and matrix,as depic￾ted in Fig. 5,suggests that these values for fd and fg are reasonable estimates for this particular uniaxial compo￾site structure. Then,estimating that t 1 mm from Fig. 5 and using Kg=0.269 W/(m K) for helium gas at one atmosphere and 400
C [28], fghg fgKg/t=21 W/(cm2 K),which closely matches the 20.7 W/(cm2 K) value Table 1 The interfacial conductance, h,at 400
C determined by Eqs. (2) and (4) from measured values of thermal diffusivity for a Hi-NicalonTM/PIP-SiC (amorphous CerasetTM) composite in different atmospheres. Data used in Eq. (4): Kf=5.72 W/(m K), Km=1.05 W/(m K), f=0.566 and a=6.9 mm Atmosphere  (400
C) [ 106 m2 /s] 1sa (%) Keff (400
C) by Eq. (8) [W/(m K)] R (400
C) (=Keff/Km) h (400
C) Eqs. (2) and (4) [W/(cm2 K)] Vacuum ( 10 Pa) 0.442 4.9 1.0240.050 0.975 17.7 Helium ( 105 Pa) 0.619 3.4 1.4350.049 1.367 39.6 Vacuum ( 10 Pa) 0.464 4.0 1.0750.043 1.023 19.7 Argon ( 105 Pa) 0.554 4.6 1.2840.059 1.223 29.7 Vacuum ( 10 Pa) 0.458 2.6 1.0620.034 1.011 19.2 a 1s For 10-individual measurements or each condition. Fig. 7. The calculated thermal conductivity values from 27 to 1000
C for a Hi-NicalonTM fiber (upper curve) and for amorphous CerasetTM that simulates the PIP-SiC matrix material (lower curve). G.E. Youngbloodet al. / Composites Science andTechnology 62 (2002) 1127–1139 1135