tes science and te 1999)833-851 From creep of Al2O3/SiC and SiC/CAS, we can con- is the activation energy(175 kJ/mol) for creep of CVD clude that creep of fiber controls the creep of the com- SiC [91 were plotted against the effective stress posite only when the matrix contributes little to creep (o-O), as shown in Fig. 21. It can be seen that all the deformation of the composite SiC/SiC does not satisfy data points can be well fitted by a single straight line the prerequisite, since the matrix cracking is not very with a slope of 5. However, if the activation energy for extensive and the creep resistance of the matrix is higher creep of Nicalon fibers is used to normalize creep than that of Nicalon fibers. The apparent stress expo- rates, the data do not fall on the same line. This means nents for creep of SiC/SiC are much higher than those that creep of the composite is controlled by creep of the of Sic fibers (1-2 [43, 46). The apparent activation matrix energies for creep of the composite at high stresses are Introducing the threshold stress, Eq.(1)becomes lower than those of the fibers (370-490 kJ/mol [43, 46) In fact, crack propagation in the matrix depends on E= A(a-Oth)exp(-Q/RT) both creep of the bridged fibers in the wake of crack and creep of the matrix in front of the crack tip. Since both where n-5 and o is the activation energy of the matri processes are intercorrelated, the slowest one is the rate- (175 kJ/mol). Combining this equation with Eq (3)and controlling process. Compression creep of CVD Sic assuming that the modulus of the matrix does not vary showed a stress exponent of 2.3 and an activation with temperature, the apparent stress exponent and energy of 175 kJ/mol [91]. The latter is very close to that apparent activation energy for creep of the composite at high stresses(Fig. 14). The stress exponent for compressive creep of CVD SiC is similar to that for flexural creep of the composite [84]. There- 0-OL cre roba trolled by creep of the matrix The apparent stress exponent and activation energy (Figs. 13 and 14). This is similar to the creep behavior of Q=g-nRT doth for creep of Sic/Sic increase with decreasing stress Sic whisker reinforced aluminum composites [94. It was explained by introducing a resisting stress(thresh- is obtained. It can be seen that both the apparent stress old stress) which may be related with the interaction of exponent and activation energy decrease with increasing whiskers with dislocations in the matrix. Following this temperature from Eqs.(8)and (9). Fig. 22 shows the approach, we phenomenologically treat the present experimentally determined apparent activation energy creep data of SiC/sic and that calculated by Eq. (9)as a function of stress. The If we plot El/n versus o, the best fit linear relation is trend predicted by Eq .(9) qualitatively agrees with that btained for n=5(Fig. 20). Defining the threshold measured in experiments. The decrease of the threshold stress as the applied stress to corresponding zero creep stress with increasing temperature causes the decrease of rate at a given temperature, the values of the threshold both the apparent stress exponent and activation energy stress(oh) can be calculated at different temperatures. The threshold stress may be related to the matrix crack Then, the creep rates normalized by exp(-OL/RT(OL ing stress which needs to be evidenced 0.1 0.08 -1300 0.06 E1028 0.04 0.02 200 50 Stress (MPa) O-Oth(MPa) Fig. 20. Relationship between a/s and o, from which the threshold Fig. 21. Creep strain rates normalized to exp(-QL/RT) versus the stress is calculated at different temperatures effective stress(o-orn)From creep of Al2O3/SiC and SiC/CAS, we can con￾clude that creep of ®ber controls the creep of the com￾posite only when the matrix contributes little to creep deformation of the composite. SiC/SiC does not satisfy the prerequisite, since the matrix cracking is not very extensive and the creep resistance of the matrix is higher than that of Nicalon ®bers. The apparent stress expo￾nents for creep of SiC/SiC are much higher than those of SiC ®bers (1±2 [43,46]). The apparent activation energies for creep of the composite at high stresses are lower than those of the ®bers (370±490 kJ/mol [43,46]). In fact, crack propagation in the matrix depends on both creep of the bridged ®bers in the wake of crack and creep of the matrix in front of the crack tip. Since both processes are intercorrelated, the slowest one is the rate￾controlling process. Compression creep of CVD SiC showed a stress exponent of 2.3 and an activation energy of 175 kJ/mol [91]. The latter is very close to that of the composite at high stresses (Fig. 14). The stress exponent for compressive creep of CVD SiC is similar to that for ¯exural creep of the composite [84]. There￾fore, creep of the SiC/SiC composite is probably con￾trolled by creep of the matrix. The apparent stress exponent and activation energy for creep of SiC/SiC increase with decreasing stress (Figs. 13 and 14). This is similar to the creep behavior of SiC whisker reinforced aluminum composites [94]. It was explained by introducing a resisting stress (thresh￾old stress) which may be related with the interaction of whiskers with dislocations in the matrix. Following this approach, we phenomenologically treat the present creep data of SiC/SiC. If we plot "_ 1=n versus , the best ®t linear relation is obtained for n=5 (Fig. 20). De®ning the threshold stress as the applied stress to corresponding zero creep rate at a given temperature, the values of the threshold stress (th) can be calculated at di€erent temperatures. Then, the creep rates normalized by exp(ÿQL=RT) (QL is the activation energy (175 kJ/mol) for creep of CVD SiC [91]) were plotted against the e€ective stress ( ÿ th), as shown in Fig. 21. It can be seen that all the data points can be well ®tted by a single straight line with a slope of 5. However, if the activation energy for creep of NicalonTM ®bers is used to normalize creep rates, the data do not fall on the same line. This means that creep of the composite is controlled by creep of the matrix. Introducing the threshold stress, Eq. (1) becomes "_ ˆ A… ÿ th† n0 exp…ÿQ0 =RT† …7† where n0 =5 and Q0 is the activation energy of the matrix (175 kJ/mol). Combining this equation with Eq. (3) and assuming that the modulus of the matrix does not vary with temperature, the apparent stress exponent and apparent activation energy for creep n ˆ 5  ÿ th …8† and Q ˆ Q0 ÿ n0 RT2  ÿ th dth dT …9† is obtained. It can be seen that both the apparent stress exponent and activation energy decrease with increasing temperature from Eqs. (8) and (9). Fig. 22 shows the experimentally determined apparent activation energy and that calculated by Eq. (9) as a function of stress. The trend predicted by Eq. (9) qualitatively agrees with that measured in experiments. The decrease of the threshold stress with increasing temperature causes the decrease of both the apparent stress exponent and activation energy. The threshold stress may be related to the matrix crack￾ing stress which needs to be evidenced. Fig. 20. Relationship between "_ 1=5 and , from which the threshold stress is calculated at di€erent temperatures. Fig. 21. Creep strain rates normalized to exp(ÿQL=RT) versus the e€ective stress ( ÿ th). S. Zhu et al. / Composites Science and Technology 59 (1999) 833±851 847