Journal of the American Ceramic Societ Quan et a (a)00020 0.0018 P(e)=2/(Random) 00016 P(e)(Measured 0.0014 Network Model b0.0010 <=25° <>=20°- 0.0004 0.0002 Applied Stress, E(MPa) Fig. 7. Geometry for calculating the moment because of the shear (b) 0.0050 stress on th 0.0045 =- upper bound°) ∑P(0)△02=1 (23) P(0)is the whisker orientation distribution function learnt from the fiber texture analysis and m is the 0.0015 angles covered during whisker texture measurement. a random whisker distribution, i.e. P(0)=2/I, the tot Gu et 0.0005 =0.15 Totl__6(5/6)(2/3)R3v22(1-2 Applied Stress, E(MPa) Fig 8. Computed total strain (including both the rapidly recovered where r(X)=or-le-dr elastic portion upon load drop and the time-dependent portion) because Figure 8(a)shows the total strain as a function of the whisker network. The hatched area covers the recovered strains that stress assuming R/L=0. 1. It is seen that the results ar have been measured in this study (b) for a percolative spherical particle same order of magnitude with those observed durin network and in tension(current study ). It is noted the unit cell model with a uniform misalignment angle equal to the av V. Conclusions rage misorientation predicts lower strains as compared with the ach in which the distrib In this work we first estimated the peak broadening because of considered whisker bending, which appears to be too small to be detected A similar approach can be used for a spherical partic by conventional diffraction methods. Significant anelastic strain is under compression. Figure 5(b) illustrates the ge- recovery was observed following tensile creep of the composite ometry of such particles in contact. Under the applied stress containing 20 and 30 vol% SiC whiskers and the magnitude of the average contact force, Fp, will develop around the particles the recovered strains is consistent with those measured in pre- at the loading direction, which is expressed as vious work using four-point bending creep tests. This, combi with a lack of significant strain recovery with 10 vol% SiC Fp (25) whiskers, demonstrates that the whisker network is key to hav- particles to the far-field stress and R the average particle rad the ing a high degree of anelastic strain recovery. The effect of whisker aspect ratio on the amount of recoverable strain and the Now. the total strain can be written comparable creep strain recovery observed in Sic particulate reinforced alumina composite may suggest that the local Hertz- ian contact deformation between "hard" inclusions is more likely the underlying mechanism for anelastic creep recovery. The two simple models developed for whisker and particulate networks seem to predict the magnitude of recoverable strain For randomly distributed particles, it becomes Total 3∑r(1 We gratefully acknowledge the supply of composite powders from Dr J. F. Figure 8(b)shows the calculated contact strain versus applied Rhodes of the Advanced Composite Materials Corporation, Greer, SC, and the help stress and the factor, s. The calculation indicates that the re- from Mrs. Constance Barry with composite processing is very much appreciated. coverable creep strain in Sic particulate-reinforced alumina composite, i.e. <10-3, corresponds to 5 A.25. This may suggest that the average local contact force responsible for in- Reference clusion contact deformation is small, presumably because the rons and J. K. Tien."Crex shear portion of the local stress facilitates rearrangement of the particle uch a way that the local contact str ell and K H. G. Ashbee. ""High Temperature Creep of Lithium s-Ceramics: Part 2 Compression Creep and Recovery. "J Mater. 973)and Xm i¼1 PðyiÞDyi ¼1 (23) P(yi) is the whisker orientation distribution function that can be learnt from the fiber texture analysis and m is the number of angles covered during whisker texture measurement. Assuming a random whisker distribution, i.e. P(yi) 5 2/p, the total strain is given as eTotal ¼6 7 Gð5=6ÞGð2=3Þ ffiffiffi p p R L 3 ffiffiffi 2 p Sð1
n2Þ E " #2=3 (24) where GðXÞ¼R 1 0 t X
1e
t dt Figure 8(a) shows the total strain as a function of the applied stress assuming R/L 5 0.1. It is seen that the results are in the same order of magnitude with those observed during creep in bending10–13 and in tension (current study). It is noted the unit￾cell model with a uniform misalignment angle equal to the av￾erage misorientation predicts lower strains as compared with the approach in which the distribution of whisker orientation is considered. A similar approach can be used for a spherical particle net￾work that is under compression. Figure 5(b) illustrates the ge￾ometry of such particles in contact. Under the applied stress S, the average contact force, Fp, will develop around the particles at the loading direction, which is expressed as Fp ¼ SzpR2 (25) where z is a factor relating the average local contact force on the particles to the far-field stress and R the average particle radius. Now, the total strain can be written as eTotal ¼ 1 2 3Szpð1
n2Þ ffiffiffi 2 p E  2=3 ðcos yiÞ 5=3 D E h i cos yi (26) For randomly distributed particles, it becomes eTotal ¼ ffiffiffi 3 p p3=2 15Gð2=3ÞGð5=6Þ 3Szpð1
n2Þ ffiffiffi 2 p E  2=3 (27) Figure 8(b) shows the calculated contact strain versus applied stress and the factor, z. The calculation indicates that the re￾coverable creep strain in SiC particulate-reinforced alumina composite,13 i.e. B10
3 , corresponds to z 0.25. This may suggest that the average local contact force responsible for in￾clusion contact deformation is small, presumably because the shear portion of the local stress facilitates rearrangement of the particle network in such a way that the local contact strain is minimized. V. Conclusions In this work we first estimated the peak broadening because of whisker bending, which appears to be too small to be detected by conventional diffraction methods. Significant anelastic strain recovery was observed following tensile creep of the composite containing 20 and 30 vol% SiC whiskers, and the magnitude of the recovered strains is consistent with those measured in pre￾vious work using four-point bending creep tests. This, combined with a lack of significant strain recovery with 10 vol% SiC whiskers, demonstrates that the whisker network is key to hav￾ing a high degree of anelastic strain recovery. The effect of whisker aspect ratio on the amount of recoverable strain and the comparable creep strain recovery observed in SiC particulate reinforced alumina composite may suggest that the local Hertz￾ian contact deformation between ‘‘hard’’ inclusions is more likely the underlying mechanism for anelastic creep recovery. The two simple models developed for whisker and particulate networks seem to predict the magnitude of recoverable strain reasonably well. Acknowledgments We gratefully acknowledge the supply of composite powders from Dr. J. F. Rhodes of the Advanced Composite Materials Corporation, Greer, SC, and the help from Mrs. Constance Barry with composite processing is very much appreciated. References 1 R. M. Arons and J. K. Tien, ‘‘Creep and Strain Recovery in Hot-Pressed Sil￾icon Nitride,’’ J. Mater. Sci., 15, 2046–58 (1980). 2 R. Morrell and K. H. G. Ashbee, ‘‘High Temperature Creep of Lithium Zinc Silicate Glass–Ceramics: Part 2 Compression Creep and Recovery,’’ J. Mater. Sci., 8, 1271–7 (1973). τ τ ω dω Fig. 7. Geometry for calculating the moment because of the shear stress on the whisker surface. 0 25 50 75 100 125 150 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 Network Model Unit Cell Model P(θ)=2/π (Random) P(θ) (Measured ) Contact Strain Applied Stress, Σ (MPa) 0 25 50 75 100 125 150 Applied Stress, Σ (MPa) 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 0.0050 ζ = φ (upper bound ) φ = 0.15 φ = 0.3 Gu et al. φ = 0.15 Contact Strain ζ= 0.4 ζ= 0.3 ζ= 0.2 (a) (b) <θ>=25° <θ>=20° Fig. 8. Computed total strain (including both the rapidly recovered elastic portion upon load drop and the time-dependent portion) because of local contact deformation as a function of applied stress for (a) whisker network. The hatched area covers the recovered strains that have been measured in this study (b) for a percolative spherical particle network. 3108 Journal of the American Ceramic Society—Quan et al. Vol. 88, No. 11