E ARELLANO. LOPEZ et aL. CREEP OF SIC-WHISKER-REINFORCED ALUMINA 1E 1400°C 日 Experimental Data ⊙ Equation10 -30 MPa φ(%) Fig. 7. Experimental strain rates(squares)of the composites under 30 MPa of stress, and calculated values(circles) using the strain rate of ANL30 as a reference and using equation (10) educed which results in an increase in the creep 10 vol. of whiskers. For materials containing rates. The net result is a weak dependence of fewer whiskers, higher stress exponents were found Em x(o, T, ...)on whisker concentration. at lower stresses. and was nal for stresses over Considering equation (10), the values of defr in 70 MPa [6, 8, 13]. In the present study, this is alse Table 2. and taking the strain rate value of anl30 the case for anl. as a reference, Fig. 7 has been plotted of the raw The NGS-corrected creep rates of the monolithic creep rates and the expected absolute values for aluminas(ANLO and ORNLO) extrapolate satisfa ORNLIO, ANLI5, ORNL20 and ANL30 at torily to the higher-stress NGS-corrected creep rates 30 MPa. The observation that the composite that of ANL5(Fig. 6). The high-stress exponent for contains the fewest whiskers creeps slower than ANLS does not result from microstructural degra the composite that contains the most whiskers dation because insignificant microstructural damage (except for ANLI5)is consistent with the above dis- was found in these specimens after deformation cussion. The use of an effective grain size provides The creep rates for ANL5 correspond to steady an explanation to the first of the two points that state creep were raised in Section 1, namely, the strain rates do Under the conditions of this study, mono- not depend on NGS and that the creep rate of the lithic polycrystalline alumina creeps by diffusion- composite is only a weak function of the whisker accommodated grain-boundary sliding. A reported concentration model [24 proposed a linear dependence of the strain rate on the stress corrected by a threshold 4. CREEP MECHANISMS stress(Go) 4. Critic EGEs= BGBs(@-Oo)2Def kTo (11) Previous analyses have established the exist of a critical stress over which the stress expor where BGBs is a constant, Q is the atomic volum increases sharply to values larger than Dett is an effective diffusion coefficient, and d is [6,7, 10, 13]. This feature has been correlated with the grain size. If the accommodating transport of the formation of damage at alumina gra matter is through the grain boundaries rather than through the bulk, Deft has an additional dependence diffusion in the matrix is not fast enough to on 1/d. According to equation(11), apparent stress modate deformation during grain-boundary exponents greater than one can be measured if the Whiskers provide creep resistance only if the applied stress is slightly higher than go, while n& l is prevented. This conclusion has been shown to results if a > 0o. Apparent stress exponents, due be valid for materials containing more than to a threshold stress, have been also reported inreduced which results in an increase in the creep rates. The net result is a weak dependence of e_m,K…s,T, ...† on whisker concentration. Considering equation (10), the values of de€ in Table 2, and taking the strain rate value of ANL30 as a reference, Fig. 7 has been plotted of the raw creep rates and the expected absolute values for ORNL10, ANL15, ORNL20 and ANL30 at 30 MPa. The observation that the composite that contains the fewest whiskers creeps slower than the composite that contains the most whiskers (except for ANL15) is consistent with the above dis￾cussion. The use of an e€ective grain size provides an explanation to the ®rst of the two points that were raised in Section 1, namely, the strain rates do not depend on NGS and that the creep rate of the composite is only a weak function of the whisker concentration. 4. CREEP MECHANISMS 4.1. Critical stress and threshold stress Previous analyses have established the existence of a critical stress over which the stress exponent increases sharply to values larger than two [6, 7, 10, 13]. This feature has been correlated with the formation of damage at alumina grain bound￾aries and alumina/whisker interfaces because di€usion in the matrix is not fast enough to accom￾modate deformation during grain-boundary sliding. Whiskers provide creep resistance only if the sliding is prevented. This conclusion has been shown to be valid for materials containing more than 10 vol.% of whiskers. For materials containing fewer whiskers, higher stress exponents were found at lower stresses, and was n11 for stresses over 70 MPa [6, 8, 13]. In the present study, this is also the case for ANL5. The NGS-corrected creep rates of the monolithic aluminas (ANL0 and ORNL0) extrapolate satisfac￾torily to the higher-stress NGS-corrected creep rates of ANL5 (Fig. 6). The high-stress exponent for ANL5 does not result from microstructural degra￾dation because insigni®cant microstructural damage was found in these specimens after deformation. The creep rates for ANL5 correspond to steady￾state creep. Under the conditions of this study, mono￾lithic polycrystalline alumina creeps by di€usion￾accommodated grain-boundary sliding. A reported model [24] proposed a linear dependence of the strain rate on the stress corrected by a threshold stress (s0): e_GBS ˆ BGBSÿ s ÿ s0
ODeff kTd2 …11† where BGBS is a constant, O is the atomic volume, De€ is an e€ective di€usion coecient, and d is the grain size. If the accommodating transport of matter is through the grain boundaries rather than through the bulk, De€ has an additional dependence on 1/d. According to equation (11), apparent stress exponents greater than one can be measured if the applied stress is slightly higher than s0, while n11 results if s >> s0. Apparent stress exponents, due to a threshold stress, have been also reported in Fig. 7. Experimental strain rates (squares) of the composites under 30 MPa of stress, and calculated values (circles) using the strain rate of ANL30 as a reference and using equation (10). DE ARELLANO-LO PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6367