Journal of the American Ceramic Society-Parthasarathy and Kerans Vol. 80. No 8 目E 2010 4000 6000 20004000 6000 Fiber Stress (MPa Fiber Stress (MPa) Fig. 11. Piecewise linear approximation, suggested for the relationship(a) between the debond length and the fiber stress for the case of progressive debonding along a rough and(b) for the case of a post-debond fiber sliding relative to the matrix. 1800 s1200 h=20 nm 600 h=o nm <l> 0 0010.020.03 Strain 1800 I(MPu) 1400,3(9 60 l200 077(18 Amm(d) 600 9(127 Peak I oad: =40-140 MPa Sliding Load: t=25-40 MPa) 0.0l 0.02 0.03 Strai ig. 12. Composite stress-strain predicted the model along with the slip length, ( ), at the ultimate stress. In Fig. 12(a), the ecewise linear approximation of Fig. ll(b) strength, whereas in Fig. 12(b), the constant shear stress approximation used. In the inset shown in Fig. 12(b), the range of T value tha measured using different methods is shown (from Fig. 10), all estimates T will overpredict the ultimate strength of the h= 20 nm of Fig. 12(a)Fig. 11. Piecewise linear approximation, suggested for the relationship (a) between the debond length and the fiber stress for the case of progressive debonding along a rough interface and (b) for the case of a post-debond fiber sliding relative to the matrix. Fig. 12. Composite stress–strain predicted using the model of Curtin,1 along with the slip length, 〈l〉, at the ultimate stress. In Fig. 12(a), the piecewise linear approximation of Fig. 11(b) is used to predict the ultimate strength, whereas in Fig. 12(b), the constant shear stress approximation is used. In the inset shown in Fig. 12(b), the range of
value that would be measured using different methods is shown (from Fig. 10); all estimates of
will overpredict the ultimate strength of the h 20 nm prediction of Fig. 12(a). 2052 Journal of the American Ceramic Society—Parthasarathy and Kerans Vol. 80, No. 8