DE ARELLANO.LOPEZ et aL.: CREEP OF SIC-WHISKER-REINFORCED ALUMINA 3. 2. Corrected strain rate of the alumina matrix slower. This comparison is much more satisfactory For comparing the EGS-corrected strain rates of in light of the brief discussion on creep models that the alumina matrixes, we need to extract their was presented in the Introduction(Section 1) alues from the experimental strain rates of the which suggested a difference of about one order of different composites. Because only (I-o)of the magnitude in creep rate between a PD and a GBS system is actually plastic, we assume a relation deformation mechanism between composite strain rate, ic, and the matrix 3.3. Discussion of the"effective grain size strain rate, Emi The effective grain size is related to the onset of (σ,7,小,…)=(1-ψ)m(,T,中…)(8) the whisker network. If the volume fraction of and then we separate the dependence of the egs reinforcements is small.φ<φp, the alumina nave n d the ngs is still a em(o, T, o )=5mK(,…) (9) significant parameter. (Whiskers still affect creep However, if o>pep, a percolative network of whis from which we can calculate the EGS-corrected kers is formed. and the behavior of the individual strain rate of the matrix, Em, K(o, T,.), independent grains inside the cells of the network is linked.The of the whisker volume fraction, and that in the Pd size of these groups of grains appears to be a sig regime should be similar for all nificant parameter of the material for composites mk(Gr,)=([4m40 containing 10 vol. or more of whiskers as dis- (10) cussed above. The physical concept of the EGS lie in the increase of effective length of the diffusion K(o, T,...) is plotted in Fig. 6 for the matrix and trajectories because of the formation of those he composites. The NGs has been used for groups of grains samples containing 0 or 5 vol. of Sic while the The weak dependence of strain rates on the eGs (defr from Table 2) was used for the other whisker volume fraction for high whisker contents samples. In all cases p= 3 was used. At 30 MPa, in can be understood by considering equation (10). the low-stress regime, the monolithic alumina creeps When the whisker concentration increases between at a corrected strain rate of approximately 10 and 30 vol % two counteracting effects arise 3.5x 10 um /s, while the most creep resistant of The first is the reduction of the amount of plastic the composites, ANL30 and ORNL20, creep at material in the composite leading to slower creep approximately 2 x 10-um /s, about 17 times rates. However, at the same time the EGS 1400°C ● 2 △ ◇ORNL20 ANL30 (MPa) Fig. 6. Grain-size-corrected strain rates of the matrix, im K vs stress. For comp taining 0 and 5 vol. of whiskers the correction was made using the NGs(filled symbols) while the EGS was used for composites with higher volume percentage (open symbols). A value of p= 3 was used in all cases.3.2. Corrected strain rate of the alumina matrix For comparing the EGS-corrected strain rates of the alumina matrixes, we need to extract their values from the experimental strain rates of the di€erent composites. Because only (1 ÿ f) of the system is actually plastic, we assume a relation between composite strain rate, e_c, and the matrix strain rate, e_m: e_c…s,T,f, ...†ˆ…1 ÿ f†e_m…s,T,f, ...† …8† and then we separate the dependence of the EGS: e_m…s,T,f, ...† ˆ e_m,K…s,T, ...† deff…f† p …9† from which we can calculate the EGS-corrected strain rate of the matrix, e_m,K…s,T, ...†, independent of the whisker volume fraction, and that in the PD regime should be similar for all composites: e_m,K…s,T, ...† ˆ deff…f† p e_c…s,T,f, ...† …1 ÿ f† …10† e_m,K…s,T, ...† is plotted in Fig. 6 for the matrix and the composites. The NGS has been used for samples containing 0 or 5 vol.% of SiC while the EGS (de€ from Table 2) was used for the other samples. In all cases p = 3 was used. At 30 MPa, in the low-stress regime, the monolithic alumina creeps at a corrected strain rate of approximately 3.510ÿ5 mm3 /s, while the most creep resistant of the composites, ANL30 and ORNL20, creep at approximately 210ÿ6 mm3 /s, about 17 times slower. This comparison is much more satisfactory in light of the brief discussion on creep models that was presented in the Introduction (Section 1), which suggested a di€erence of about one order of magnitude in creep rate between a PD and a GBS deformation mechanism. 3.3. Discussion of the ``e€ective grain size'' The e€ective grain size is related to the onset of the whisker network. If the volume fraction of reinforcements is small, f < fpcp, the alumina grains behave ``normally'', and the NGS is still a signi®cant parameter. (Whiskers still a€ect creep which will be discussed in the next section.) However, if f>fpcp, a percolative network of whis￾kers is formed, and the behavior of the individual grains inside the cells of the network is linked. The size of these groups of grains appears to be a sig￾ni®cant parameter of the material for composites containing 10 vol.% or more of whiskers as dis￾cussed above. The physical concept of the EGS can lie in the increase of e€ective length of the di€usion trajectories because of the formation of those groups of grains. The weak dependence of strain rates on the whisker volume fraction for high whisker contents can be understood by considering equation (10). When the whisker concentration increases between 10 and 30 vol.%, two counteracting e€ects arise. The ®rst is the reduction of the amount of plastic material in the composite leading to slower creep rates. However, at the same time the EGS is Fig. 6. Grain-size-corrected strain rates of the matrix, e_m,K vs stress. For composites containing 0 and 5 vol.% of whiskers the correction was made using the NGS (®lled symbols) while the EGS was used for composites with higher volume percentage (open symbols). A value of p = 3 was used in all cases. 6366 DE ARELLANO-LO PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA