March 1996 Thermal Conductivity of VLS and vS Silicon Carbide Whisker-Reinforced LAS Glass-Ceramic Composites T 00 2.0 Exper Inent al Data 150 125 日 Km 15 Km iud LuLu 05 102103104105106107106109101 h(W/m2K) LOG h(W/m2K) (b) Fig. 4. Theoretical thermal conductivity curves LS SiC whisker-reinforced voI erfectly aligned whiskers calculated for a whisk er of 6 a co values compared with room-temperature values info experimental data: (a)parallel and ular to whisker axis here 0 is the angle between the direction parallel to the hot composite theory. For instance, a distribution f()= sin 0 pressing direction and any specific whisker and f(e)is a fu resulted in a value of K> Ku. Such a result is not consister tion which describes the distribution of whisker orientation with general composite theory. The most consistent values of Similarly, K, can be described by K and K were obtained from a sin 3 0 distribution and from a distribution uniform between 0=60 and 90. These results (cos 0K33+ sin AK)f(e)sin edg calculated from the experimental data at room temperature, are summarized in Table lI Comparison of these results indicates that the calculated f(e)sin 0de values of Ku and K 3 do not differ greatly for either distribution between0<0<30. For a composite consisting of a low thermal conductivity matrix and aligned whiskers with a high For a known whisker orientation distribution and known thermal conductivity, the relative magnitudes of Ki and K33 of K and K33, Eqs. ( 1)and(2)can be used to predict shown in Table ll are consistent with composite theory mal conductivity values for a given composite. Con Comparison of the K, values in Table II with the calculated the experimental thermal conductivity data and an curves for K3 shown in Figs. 4(a)and 5(a) permits establishing assumed orientation distribution function for the whiskers will a lower bound on both the whisker thermal conductivity and permit calculation of K, and K33, which is the approach taken he interfacial conductance at room temperature. For the VLs n this study whiskers, with K33 ranging from about 16.6 to 18.0 W/(mK), For instance, for a composite with a random whisker thermal e n act i d, n ic,tt aust be f east fe o wrrm -Ka As mentioned previously, however, perfect interfacial thermal Kp-”→大3+Kn contact is unlikely in these composites due to the mismatch in the elastic properties of SiC and LAS. The Similarly, for whiskers perfectly aligned normal to the hot resulting phonon-scattering at the interface can create a signif ressing direction (i.e, 6=90) thermal conductivity values reported for particulate diamond (4a) reinforced cordierite matrix composites. 2 On the other hand, if K were equal t to the maximum value K,=sK3++aKI (4b) for high-purity single-crystal SiC, 3 the lower bound on h would be inferred to be about2.5×105W/(m2·K) A similar comparison of the results for the vs whiskers For the composites and whisker distribution of this study, the nggests a lower bound on K at room temperature of the order values of K and K, are expected to lie between the values given of 40 W/(m K). This value is some 50% higher than values by eqs. (3)and estimated for vs whiskers from data for various other ceramic A numerically detailed whisker orientation distribution func- matrix composites assuming perfect thermal contact. If K, for tion for these composites was not obtained. However, as the whiskers is assumed to be 490 w/(m K), a lower bound on reported earlier, microstructural examination indicated that the h is found to be about 6x 105 w/(m2.K) whiskers were aligned within about 30 from the plane normal An estimate on the upper bound of K33 must rely on specula to the hot-pressing direction. A number of orientation distribu- tion. Investigation of data available for other co tion functions were tried over this range with the resulting hould yield information on reasonable expected values of h values for K, and K33 examined for general consistency with For instance, at room temperature and atmospheric pressure, an