DE ARELLANO.LOPEZ et aL. CREEP OF SIC-WHISKER-REINFORCED ALUMINA 6365 Table 3. Measured and calculated [equation (5) dI values for samples with more than 10 vol. of whiskers using r= 0.5 um Sam ANL15 ANL30 ORNLIO ORNL20 Calculated di (um) Measured dh (um) 1.6 10vo% Schematic of the space available between perfectly uted whiskers of radius r, on a face that is paralle. To a first approximation, there is a direct propor nality between di and dh at least over the com- alumina matrix fills the space between the whiskers. Therefore, by using di=idb i. being a constant, optical micrographs in Fig. 3 is satisfactory. It is obvious that the volume fraction, is: dm=y山=2/4 A measure of the space between the whiskers is the where in this case 2x 1.5. obtained by regression of diameter of the circle that fits into this space, which the data in Fig. 5. Then using equation (5) has been denoted d We can then follow (41+2n)2 V中 and finally: S This expression allows an estimate of the effective grain size knowing only the volume fraction of whiskers and the whisker radius. It should be valid Table 3 shows a comparison between measured and over a range of compositions similar to the one calculated values of dh using r=0.5 um. Good used in this study. The value of i can be related to agreement is obtained for samples containing 10 the homogeneity of the distribution of reinforce- and 20 vol %o whiskers. For ANLI5 and ANL30, ments, and to the whisker aspect ratio. When using ne measured values are slightly higher than the the same type of whiskers and similar processing alculated ones, probably due to an imperfect dist echniques, i is expected to vary a little from the bution value reported in this study. ●ORNL10 入~1.5N15 10 du (um) Fig. 5. Correlation between d and di, assuming direct proportionality through a constant i, that is cal- culated by linear regression to be <1.5, valid for the range 10-30 vol. of whiskersalumina matrix ®lls the space between the whiskers. A comparison of the proposed distribution with the optical micrographs in Fig. 3 is satisfactory. It is obvious that the volume fraction, f, is: f ˆ pr2 `2 …3† A measure of the space between the whiskers is the diameter of the circle that ®ts into this space, which has been denoted d6. We can then follow: ÿ dk ‡ 2r
2 ˆ 2`2 …4† and ®nally: dk ˆ r   2p f s ÿ 2  …5† Table 3 shows a comparison between measured and calculated values of d6, using r = 0.5 mm. Good agreement is obtained for samples containing 10 and 20 vol.% whiskers. For ANL15 and ANL30, the measured values are slightly higher than the calculated ones, probably due to an imperfect distri￾bution of whiskers. To a ®rst approximation, there is a direct propor￾tionality between d_ and d6, at least over the com￾position range in this study, as shown in Fig. 5. Therefore, by using d_=ld6, l being a constant, and equation (2), the following is obtained: deff ˆ  d2 ?dk 3 q ˆ l2=3 dk …6† where in this case l11.5, obtained by regression of the data in Fig. 5. Then using equation (5): deff ˆ l2=3 r   2p f s ÿ 2  …7† This expression allows an estimate of the e€ective grain size knowing only the volume fraction of whiskers and the whisker radius. It should be valid over a range of compositions similar to the one used in this study. The value of l can be related to the homogeneity of the distribution of reinforce￾ments, and to the whisker aspect ratio. When using the same type of whiskers and similar processing techniques, l is expected to vary a little from the value reported in this study. Fig. 5. Correlation between d6and d_, assuming direct proportionality through a constant l, that is cal￾culated by linear regression to be 11.5, valid for the range 10±30 vol.% of whiskers. Fig. 4. Schematic of the space available between perfectly distributed whiskers of radius r, on a face that is parallel to the HP axis. Table 3. Measured and calculated [equation (5)] d6values for samples with more than 10 vol.% of whiskers using r = 0.5 mm Sample ANL15 ANL30 ORNL10 ORNL20 Calculated d6(mm) 2.2 1.3 3.0 1.8 Measured d6(mm) 2.4 1.6 2.9 1.8 DE ARELLANO-LO PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6365