ovember 2005 Anelastic Creep Recovery 3107 (a)0006 10 vol% SIC Pa 59 MPa 1400°C (b)0.006 20 yol% si ematic illustration of Hertzian contact deformation between and (b) rods in contact. 18 MPa approximated as follows: 0.003 Total 74 MPa Li cos 0i (18) 1400° where n is the Using Eqs (c)0.006 30 voL% SiC eTotal_2=/2(2R'Esin20 2/2(1-v2)/E)1/R"sine, ∑=1Lcos 0.005 59 MP 18 MPa here 0.000 150000200000 Time( inin20)3)=∑P0)snoi20)3△9(2l) Fig 4. Tensile creep stress relaxation curve for (a) 10 vol%,(b)20 vol%, and (c)30 vol% SiC whisker-reinforced alumina composites. os)=∑P(e)cos△ Assuming∑=75MPa,〈θ)=20°,RL=0.1,v=0.127 nd e=427 Gpa the unit-cell model predicts a recoverable strain of 4. x 10. It is noteworthy that this model predicts increasing strain with a decrease in whisker aspect ratio, which is n accord with the experimental results of Gu et al. It is also E teresting that there is no explicit dependence on volume frac- tion. this follows from the stress concentration factor k which depends only on the average whisker misalignment 0. As ex- plained by wilkinson and Pompe this result applies only when the loading axis lies in the plane for which the whiskers are ∠日 nearly aligned, as we have done in the experimental work dis cussed here. If one loads the sample normal to the plane of whisker alignment. then the stress concentration factor scales For a percolating path of whiskers along the loading dire tion. the total strain because of contact deformation can Fig.6.Ⅲ lustra plies only to isotropic materials, the transversely isotropic elastic con- on constrainedAssuming S 5 75 MPa, /yS 5 201, z R/L 5 0.1,J n 5 0.127,ww and E 5 427 Gpa,ww the unit-cell model predicts a recoverable strain of B4.4 10
4 . It is noteworthy that this model predicts increasing strain with a decrease in whisker aspect ratio, which is in accord with the experimental results of Gu et al. 13 It is also interesting that there is no explicit dependence on volume frac￾tion. This follows from the stress concentration factor k which depends only on the average whisker misalignment y. As ex￾plained by Wilkinson and Pompe9 this result applies only when the loading axis lies in the plane for which the whiskers are nearly aligned, as we have done in the experimental work dis￾cussed here. If one loads the sample normal to the plane of whisker alignment, then the stress concentration factor scales as 1/f2/3, where f is the whisker volume fraction. For a percolating path of whiskers along the loading direc￾tion, the total strain because of contact deformation can be approximated as follows: eTotal ¼ Pn i¼1 P 2hi sin yi n i¼1 Li cos yi (18) where n is the number of contact points. Using Eqs. (15) and (16), it becomes eTotal ¼ Pn i¼1 2ð2R2Ssin2yiÞ 2=3 9 2 ð1
n2Þ=E  2 1=R h i1=3 sinyi Pn i¼1Lcosyi (19) Therefore, eTotal ¼2R L 3 ffiffiffi 2 p Sð1
n2Þ E " #2=3 ðsin2yiÞ 2=3 sinyi D E h i cosyi (20) where sinyiðsin2yiÞ 2=3 D E¼ Xm i¼1 PðyiÞsinyiðsin2yiÞ 2=3 Dyi (21) h i cosyi ¼ Xm i¼1 PðyiÞcosyiDyi (22) Σ Σ τ τ Σ Σ θi θi Fp Fp (a) (b) Fig. 6. Illustration of load transfer because of the far-field stress acting on constrained (a) fibers and (b) spherical particles through contact de￾formation. F F = h F ∝ h3/2 F F (a) (b) Fig. 5. Schematic illustration of Hertzian contact deformation between (a) spheres and (b) rods in contact. 0 50000 100000 150000 200000 0.000 0.001 0.002 0.003 0.004 0.005 0.006 1400°C 10 vol.% SiC 18 MPa 59 MPa Creep Strain 0.000 0.001 0.002 0.003 0.004 0.005 0.006 Creep Strain Time (s) 0 50000 100000 150000 200000 Time (s) 0 50000 100000 150000 200000 Time (s) 1400°C 1400°C 18 MPa 74 MPa 20 vol.% SiC 0.000 0.001 0.002 0.003 0.004 0.005 0.006 18 MPa 59 MPa 30 vol.% SiC Creep Strain (a) (b) (c) Fig. 4. Tensile creep stress relaxation curve for (a) 10 vol%, (b) 20 vol%, and (c) 30 vol% SiC whisker-reinforced alumina composites. z This is based on neutron diffraction measurement.14 J This corresponds to three contact points per whisker. wwAs Eq. (16) applies only to isotropic materials, the transversely isotropic elastic con￾stants of the whisker were replaced by the average isotropic elastic constants.26 November 2005 Anelastic Creep Recovery 3107