E ARELLANO. LOPEZ et aL. CREEP OF SIC-WHISKER-REINFORCED ALUMINA Table 1. Alumina nominal grain sizes(NGS)for ANL and ORNL composites Sample ANLO ANLS ANL15 ANL30 ORNLO ORNLIO ORNL20 NGS (um) 1.8 1.5 fastest path (lattice or gra 2. PREVIOUS RESULTS of which is represented by the grain size(Gs) Two important points remain unexplained In this work, we re-analyze published creep data from composites fabricated at Argonne National The creep rates are independent of the nominal Laboratory and Oak Ridge National Laboratory grain size(NGS)and only depend weakly on the The composites contained 0-30 vol. of Sic whisker volume fraction, especially for higher whiskers. The sample designations are formed by whisker content [1, 13, 15 the initials of the manufacturer, followed by a For composites containing 5-8 vol. whiskers, number representing the volume fraction of n>2 for low stress and ne l for high stress. This whiskers. The alumina grain size of each material is contrary to n a I at low stress, and n>> I at was determined by the manufacturer [10, 12, 15 high stress measured in composites containing and is included in Table 1. The same type of Sic more than 10 vol % Additionally, the acti- whiskers, of typical radius of 0.3-0.5 um, and typi- vation energies for the 5-8 vol. composites, cal aspect ratios 210, was used for all composites <700 kJ/mol, are much higher than measured Figure I shows log-log plots of the strain rates in alumina and in higher whisker-content com- of the composites (Ec), corrected by the NGs,vs posites 6, 8, 13 stress(a) for creep of ANL and ORNL composites Several models to describe the deformation of The stress exponents resulting from these exper composites are available. Wilkinson [1 proposed a iments have been previously reported [13], with rheological model for creep based on considering alues between I and 2 for the lower stresses and the composite as a creep-resistant reinforcement n>2 for higher stresses, as seen in Fig. 1. The new embedded in a plastic matrix. He acknowledges, set of experiments for the composition ORNLIO iCw/Al2O3 because of lack of knowledge of several 100 MPa. Three different groups of behavior can be parameters. Yoon and Chen [20] developed a conti- uum theory for non-Newtonian flow of a two- l. the monolithic from the two different sources phase composite containing rigid inclusions that behaves essentially the same, n=1.3. Differ- partially suppress flow. This model was applied to ences in absolute strain rates can be explained zirconia-mullite composites [20] and later to Sic- when they are corrected with d [Fig. 1(a)]. This whisker-reinforced Y-TZP [21]. However, recent correlation forms the basis of normalization by work by Parthasarathy et al. [22 on SiC-whisker d, rather than d, throughout our analysis reinforced Mg-PSZ /mullite composites showed that 2. the results for the 5 vol. composite, ANL5 the model by Yoon and Chen does not accurately can best be described by n=2.6 for lower stress, describe creep of composites containing high and n=1.3 for higher stresses. The model that aspect-ratio reinforcements. That work suggests ill explain the physical basis at a better explanation is achieved by modifi of the two-line fit: and cations to classical microscopic-based creep models. 3. samples containing more than 10 vol. of This work will apply the same microscopic-based whiskers are characterized by ns I at lower reep models as in Ref. [22] to address the questi stresses, and then n>3 at higher stress. The bove.With that purpose, a set of published data strain rates, corrected using d [Fig. I(b)]for will be re-analyzed and combined with some new the various compositions vary by approximately The nominal grain size is not a significant cr parameter. Instead, the space available between 3. EFFECTIVE GRAIN SIZE the whiskers is the significant microstructural creep parameter. When first introduced [23]. this 3.1. Development of the network of whiskers parameter was called"effective grain size"(EGS In this section we describe the determination of The results for composites having low o can be the EGS for samples containing more tha explained by means of a temperature-dependent 10 vol% whiskers. These types of composites are threshold stress. The use of a threshold stress in normally fabricated by uniaxial hot-pressing(HP). explaining the behavior of Sic-whisker-alumina so there is a preferential orientation of the whiskers composites was introduced in the past [23]. in planes perpendicular to the hP direction,within Parthasarathy et al. [22] have recently also used which the orientation of the whiskers can be con- the concept of a threshold stress. sidered random. A schematic is shown in Fig. 2fastest path (lattice or grain boundary), the length of which is represented by the grain size (GS). Two important points remain unexplained. . The creep rates are independent of the nominal grain size (NGS) and only depend weakly on the whisker volume fraction, especially for higher whisker content [1, 13, 15]. . For composites containing 5±8 vol.% whiskers, n>2 for low stress and n11 for high stress. This is contrary to n11 at low stress, and n >> 1 at high stress measured in composites containing more than 10 vol.%. Additionally, the acti￾vation energies for the 5±8 vol.% composites, 1700 kJ/mol, are much higher than measured in alumina and in higher whisker-content com￾posites [6, 8, 13]. Several models to describe the deformation of composites are available. Wilkinson [1] proposed a rheological model for creep based on considering the composite as a creep-resistant reinforcement embedded in a plastic matrix. He acknowledges, however, the diculty of applying such a model to SiCw/Al2O3 because of lack of knowledge of several parameters. Yoon and Chen [20] developed a conti￾nuum theory for non-Newtonian ¯ow of a two￾phase composite containing rigid inclusions that partially suppress ¯ow. This model was applied to zirconia±mullite composites [20] and later to SiC￾whisker-reinforced Y-TZP [21]. However, recent work by Parthasarathy et al. [22] on SiC-whisker￾reinforced Mg-PSZ/mullite composites showed that the model by Yoon and Chen does not accurately describe creep of composites containing high￾aspect-ratio reinforcements. That work suggests that a better explanation is achieved by modi®- cations to classical microscopic-based creep models. This work will apply the same microscopic-based creep models as in Ref. [22] to address the questions above. With that purpose, a set of published data will be re-analyzed and combined with some new data, making two assumptions. . The nominal grain size is not a signi®cant creep parameter. Instead, the space available between the whiskers is the signi®cant microstructural creep parameter. When ®rst introduced [23], this parameter was called ``e€ective grain size'' (EGS). . The results for composites having low f can be explained by means of a temperature-dependent threshold stress. The use of a threshold stress in explaining the behavior of SiC-whisker±alumina composites was introduced in the past [23]. Parthasarathy et al. [22] have recently also used the concept of a threshold stress. 2. PREVIOUS RESULTS In this work, we re-analyze published creep data from composites fabricated at Argonne National Laboratory and Oak Ridge National Laboratory. The composites contained 0±30 vol.% of SiC whiskers. The sample designations are formed by the initials of the manufacturer, followed by a number representing the volume fraction of whiskers. The alumina grain size of each material was determined by the manufacturer [10, 12, 15], and is included in Table 1. The same type of SiC whiskers, of typical radius of 0.3±0.5 mm, and typi￾cal aspect ratios r10, was used for all composites. Figure 1 shows log±log plots of the strain rates of the composites (e_c), corrected by the NGS, vs stress (s) for creep of ANL and ORNL composites. The stress exponents resulting from these exper￾iments have been previously reported [13], with values between 1 and 2 for the lower stresses, and n>2 for higher stresses, as seen in Fig. 1. The new set of experiments for the composition ORNL10, resulted in n = 1.620.2 for stresses below 100 MPa. Three di€erent groups of behavior can be described: 1. the monolithic from the two di€erent sources behaves essentially the same, n = 1.3. Di€er￾ences in absolute strain rates can be explained when they are corrected with dÿ3 [Fig. 1(a)]. This correlation forms the basis of normalization by dÿ3 , rather than dÿ2 , throughout our analysis; 2. the results for the 5 vol.% composite, ANL5, can best be described by n = 2.6 for lower stress, and n = 1.3 for higher stresses. The model that will be developed will explain the physical basis of the two-line ®t; and 3. samples containing more than 10 vol.% of whiskers are characterized by n11 at lower stresses, and then n>3 at higher stress. The strain rates, corrected using dÿ3 [Fig. 1(b)] for the various compositions vary by approximately 100. 3. EFFECTIVE GRAIN SIZE 3.1. Development of the network of whiskers In this section, we describe the determination of the EGS for samples containing more than 10 vol.% whiskers. These types of composites are normally fabricated by uniaxial hot-pressing (HP), so there is a preferential orientation of the whiskers in planes perpendicular to the HP direction, within which the orientation of the whiskers can be con￾sidered random. A schematic is shown in Fig. 2. Table 1. Alumina nominal grain sizes (NGS) for ANL and ORNL composites Sample ANL0 ANL5 ANL15 ANL30 ORNL0 ORNL10 ORNL20 NGS (mm) 1.8 2.8 3.3 1.5 1.5 1.2 2.0 DE ARELLANO-LO PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6363