Acta mater. Vo blished by Elsevier Science Ltd. Al served Printed PI!:Sl359-6454(98)00331-0 1359-6454/98s19.00+0.00 MICROSTRUCTURAL CONSTRAINTS FOR CREEP IN SiC-WHISKER-REINFORCED Al,O3 A R. DE ARELLANO-LOPEZ DOMINGUEZ-RODRIGUEZ and L L ROUTBORTA Departamento de Fisica de la Materia Condensada, Universidad de Sevilla, 41080 Seville, Spain and Energy Technology Division, Argonne National Laboratory, Argonne, IL 60439.4838, U.S.A Received 17 July 1998; accepted 12 September 1998) a tract-New and published creep data obtained on a Sic-whisker-reinforced Al2O3 composite have been yzed in terms of an effective grain size and a threshold /critical stress. These concepts allow the for- mation of a consistent picture of the high-temperature deformation of these composites. For low volume actions of whiskers, before the formation of a point-contact percolative limit is reached, defo ceeds via grain-boundary sliding after the applied stress exceeds a temperature-dependent threshold stress. In this regime, the nominal grain size is the most important microstructural feature. For larger volume actions of whiskers, up to itical volume fraction for formation of facet-to-facet whiskers nhibit grain-boundary sliding and deformation proceeds by means of pure diffusion. In this regime, the most important microstructural feature is an effective grain size, i. e the spacing between the whiskers. De- formation proceeds until the stress reaches a temperature-dependent critical stress. At this point, damage ccurs by unaccommodated grain-boundary sliding and creep is no longer in a steady state. C 1998 Act Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved 1 INTRODUCTION Successful fabrication of SiCw/ Al2O3 composites A recent review [l] has pointed out evidence containing from 0 to 30 vol. of SiC has been three distinct volume-fraction-dependent (o) achieved by laboratories such as Argonne National regimes of mechanical behavior of rigid-particle- Laboratory(AND) [2 and Oak Ridge National regimes are separated by two critical volume frac- panies such as Advanced Ceramic Composites Inc (ARCO)[4]. In all he ed whiskers fraction is that of the formation of a point-contact which have a typical diameter of 0.6-1 um, signifi- percolative network (@pep). The second critical cantly reduced their aspect ratio during processing. volume fraction is that of the formation of a facet- from more than 50 to an average of 210, while the facet contact network(rep). The three regions of matrix grain sizes ranged between 1.2 and 3.3 um behavior are defined by oφrcp henφpep≤7%. Anelastic creep recovery exper The characteristic volume fraction for the onset iments tend to support the formation of a connect- of these networks depends on the morphology of ing whisker network over this limit[14] reinforcements In the case of the point-contact per- Several studies have reported the conditions under colation of high-aspect-ratio randomly oriented which SiCw/Al2O creeps [1, 4,, 10, 11, 13, 16).It whiskers it has been shown that [2] is well established that. the typical creep rates of the composites are (1) lower than those of the monolith: and the reduction in creep rates is due to a partial or The system SiC(whisker)/Al2O3 has been the subject complete inhibition of grain-boundary sliding numerous studies [3-15]. Whisker volume frac- because of rigid whiskers located at the Al2O ions as high as 50% have been used in some of th grain boundaries. opposites [101, but 30 vol. is a practical lim Generally, the stress exponent, n, and activation over which the whiskers are difficult to pacc energy, 2, of the composite are equal to those efficiently, forming agglomerates that inhibit full of alumina, although the complete scope of values of n≈ I and c≈400-500kJ/ mol have been d To whom all correspondence should be addressed and the parameters have been related to a diffusion-
MICROSTRUCTURAL CONSTRAINTS FOR CREEP IN SiC-WHISKER-REINFORCED Al2O3 A. R. DE ARELLANO-LOÂ PEZ1 {, A. DOMIÂ NGUEZ-RODRIÂ GUEZ1 and J. L. ROUTBORT2 1 Departamento de FõÂsica de la Materia Condensada, Universidad de Sevilla, 41080 Seville, Spain and 2 Energy Technology Division, Argonne National Laboratory, Argonne, IL 60439-4838, U.S.A. (Received 17 July 1998; accepted 12 September 1998) AbstractÐNew and published creep data obtained on a SiC-whisker-reinforced Al2O3 composite have been analyzed in terms of an eective grain size and a threshold/critical stress. These concepts allow the formation of a consistent picture of the high-temperature deformation of these composites. For low volume fractions of whiskers, before the formation of a point-contact percolative limit is reached, deformation proceeds via grain-boundary sliding after the applied stress exceeds a temperature-dependent threshold stress. In this regime, the nominal grain size is the most important microstructural feature. For larger volume fractions of whiskers, up to the critical volume fraction for formation of facet-to-facet contact, whiskers inhibit grain-boundary sliding and deformation proceeds by means of pure diusion. In this regime, the most important microstructural feature is an eective grain size, i.e. the spacing between the whiskers. Deformation proceeds until the stress reaches a temperature-dependent critical stress. At this point, damage occurs by unaccommodated grain-boundary sliding and creep is no longer in a steady state. # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION A recent review [1] has pointed out evidence of three distinct volume-fraction-dependent (f) regimes of mechanical behavior of rigid-particlereinforced ceramic-matrix composites. These three regimes are separated by two critical volume fractions. As f increases, the ®rst critical volume fraction is that of the formation of a point-contact percolative network (fpcp). The second critical volume fraction is that of the formation of a facetto-facet contact network (ffcp). The three regions of behavior are de®ned by f ffcp. The characteristic volume fraction for the onset of these networks depends on the morphology of reinforcements. In the case of the point-contact percolation of high-aspect-ratio randomly oriented whiskers it has been shown that [2] fpcp 0:7 aspect ratio 1 The system SiC(whisker)/Al2O3 has been the subject of numerous studies [3±15]. Whisker volume fractions as high as 50% have been used in some of the composites [10], but 30 vol.% is a practical limit over which the whiskers are dicult to pack eciently, forming agglomerates that inhibit full densi®cation. Successful fabrication of SiCw/Al2O3 composites containing from 0 to 30 vol.% of SiC has been achieved by laboratories such as Argonne National Laboratory (ANL) [12] and Oak Ridge National Laboratory (ORNL) [3], and commercially by companies such as Advanced Ceramic Composites Inc. (ARCO) [4]. In all cases, the as-received whiskers, which have a typical diameter of 0.6±1 mm, signi®- cantly reduced their aspect ratio during processing, from more than 50 to an average of 110, while the matrix grain sizes ranged between 1.2 and 3.3 mm. Using equation (1), the critical percolation limit is then fpcpR7%. Anelastic creep recovery experiments tend to support the formation of a connecting whisker network over this limit [14]. Several studies have reported the conditions under which SiCw/Al2O3 creeps [1, 4, 6±8, 10, 11, 13, 16]. It is well established that: . the typical creep rates of the composites are lower than those of the monolith; and . the reduction in creep rates is due to a partial or complete inhibition of grain-boundary sliding because of rigid whiskers located at the Al2O3 grain boundaries. Generally, the stress exponent, n, and activation energy, Q, of the composite are equal to those of alumina, although the complete scope of composite behavior is complex. In compression values of n11 and Q1400±500 kJ/mol have been reported for ®ne-grained polycrystalline alumina, and the parameters have been related to a diusionActa mater. Vol. 46, No. 18, pp. 6361±6373, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain PII: S1359-6454(98)00331-0 1359-6454/98 $19.00 + 0.00 {To whom all correspondence should be addressed. 6361
6362 E ARELLANO. LOPEZ et aL. CREEP OF SIC-WHISKER-REINFORCED ALUMINA accommodated grain-boundary sliding (GBS) kinetics are unchanged from GBs to PD. mechanism [16-18]. In whisker-reinforced alumina, expected, models predict that the creep rates are the whiskers impede sliding of the grain boundaries, about one order of magnitude faster if deformation so that deformation is controlled by pure diffu- proceeds via GBs compared to PD [19. For both sional(PD)creep, thus explaining partially the GBs and PD, the strain rate is controlled by the observed reduction in creep rates [13]. If diffusion diffusion of the slowest of the species along the 1400°c cp eoo oo ◇口o 1E8 O ( MPa 1400°c ◇ 口 △ ①◇ OORNL10 口ANL15 O (MPa) Fig. 1. Strain rate of the composites, ie, corrected by the nominal grain size of the matrix, d, vs stress for samples containing (a)less than 7 vol. of whiskers, and(b) more than 7 vol. of whiskers. The grain-size exponent was taken as p= 3 for all cases
accommodated grain-boundary sliding (GBS) mechanism [16±18]. In whisker-reinforced alumina, the whiskers impede sliding of the grain boundaries, so that deformation is controlled by pure diusional (PD) creep, thus explaining partially the observed reduction in creep rates [13]. If diusion kinetics are unchanged from GBS to PD, as expected, models predict that the creep rates are about one order of magnitude faster if deformation proceeds via GBS compared to PD [19]. For both GBS and PD, the strain rate is controlled by the diusion of the slowest of the species along the Fig. 1. Strain rate of the composites, e_c, corrected by the nominal grain size of the matrix, d, vs stress, for samples containing (a) less than 7 vol.% of whiskers, and (b) more than 7 vol.% of whiskers. The grain-size exponent was taken as p = 3 for all cases. 6362 DE ARELLANO-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA
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 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. 2
fastest 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 activation energies for the 5±8 vol.% composites, 1700 kJ/mol, are much higher than measured in alumina and in higher whisker-content composites [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 diculty of applying such a model to SiCw/Al2O3 because of lack of knowledge of several parameters. Yoon and Chen [20] developed a continuum theory for non-Newtonian ¯ow of a twophase composite containing rigid inclusions that partially suppress ¯ow. This model was applied to zirconia±mullite composites [20] and later to SiCwhisker-reinforced Y-TZP [21]. However, recent work by Parthasarathy et al. [22] on SiC-whiskerreinforced Mg-PSZ/mullite composites showed that the model by Yoon and Chen does not accurately describe creep of composites containing highaspect-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 ``eective 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 typical 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 experiments 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 dierent groups of behavior can be described: 1. the monolithic from the two dierent sources behaves essentially the same, n = 1.3. Dierences 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 considered 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-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6363
E ARELLANO. LOPEZ et al.: CREEP OF SIC-WHISKER-REINFORCED ALUMINA HP Axis Table 2. Average space available between the whiskers in sections with more than 10 vol% of whiskers, and equivalent three-dimen- sional diameter(defr) Sample ANLI5 ANL30 ORNLIO ORNL20 3.5 3. 2.4 measured using an image analyzer. The average values of d and di are listed in Table 2 The equivalent three-dimensional diameters of the ellipsoidal objects are calculated by means of the geometric average referential orientation of the whiskers, perpendicularly to the hot-pressing(HP)axis values are listed in the HP axis. Reflected polarized light was used to A comparison between the values in Table 2, and obtain a clear contrast of the whiskers (white) the reported NGS in Table 1, shows some corre- on the uniform gray background of the alumina lations, except for the ORNLIO sample, for which matrIX the EGs is as much as three times larger tha In order to estimate the egs for the different the NGS. Nevertheless the egs decreases as the samples, a metallographic study has been performed volume percentage of whiskers increases, consis on both types of sections for each sample. It was tent with intuition. An analytical expression for assumed that "regular-shaped"ellipsoidal objects defr=dend, ... )can be derived by a simple two- fit into the whisker network. The diameters of dimensional model that correlates d with the these"grains"will be called dhh. if it corresponds volume fraction of whiskers, o, and the whisker to the face parallel to the hP axis, and d, if it radius, r. orresponds to the face perpendicular to the hP Figure 4 shows the location of perfectly distri- axis. The objects were subsequently digitized and buted whiskers in square cells of side e. The perp ara Fig 3. Optic graphs of polished sections parallel (para)and perpedicular (perp) to the HP axis of samples (a) ORNLIO, and (b)ANL30. Reflected polarized light was used to contrast the whiskers (white) on the uniform background of the alumina matrix
Figure 3 presents a set of optical micrographs taken on polished sections parallel and perpendicular to the HP axis. Re¯ected polarized light was used to obtain a clear contrast of the whiskers (white) on the uniform gray background of the alumina matrix. In order to estimate the EGS for the dierent samples, a metallographic study has been performed on both types of sections for each sample. It was assumed that ``regular-shaped'' ellipsoidal objects ®t into the whisker network. The diameters of these ``grains'' will be called d6, if it corresponds to the face parallel to the HP axis, and d_, if it corresponds to the face perpendicular to the HP axis. The objects were subsequently digitized and measured using an image analyzer. The average values of d6and d_ are listed in Table 2. The equivalent three-dimensional diameters of the ellipsoidal objects are calculated by means of the geometric average: 4 3 p d? 2 2 dk 2 4 3 p deff 2 3 )deff d2 ?dk 3 q 2 The values are listed in Table 2. A comparison between the values in Table 2, and the reported NGS in Table 1, shows some correlations, except for the ORNL10 sample, for which the EGS is as much as three times larger than the NGS. Nevertheless, the EGS decreases as the volume percentage of whiskers increases, consistent with intuition. An analytical expression for de=de(f,...) can be derived by a simple twodimensional model that correlates d6 with the volume fraction of whiskers, f, and the whisker radius, r. Figure 4 shows the location of perfectly distributed whiskers in square cells of side `. The Fig. 2. Schematic of the preferential orientation of the whiskers, perpendicularly to the hot-pressing (HP) axis. Fig. 3. Optical micrographs of polished sections parallel (para) and perpedicular (perp) to the HP axis of samples (a) ORNL10, and (b) ANL30. Re¯ected polarized light was used to contrast the whiskers (white) on the uniform background of the alumina matrix. Table 2. Average space available between the whiskers in sections perpendicular (d_) and parallel (d6) to the HP direction of samples with more than 10 vol.% of whiskers, and equivalent three-dimensional diameter (de) Sample ANL15 ANL30 ORNL10 ORNL20 d_ (mm) 3.5 2.5 4.0 2.8 d6(mm) 2.4 1.6 2.9 1.8 de (mm) 3.1 2.2 3.6 2.4 6364 DE ARELLANO-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA
DE ARELLANO.LOPEZ et aL. CREEP OF SIC-WHISKER-REINFORCED ALUMINA 6365 Table 3. Measured and calculated [equation (5) dI values for samples with more than 10 vol. of whiskers using r= 0.5 um Sam ANL15 ANL30 ORNLIO ORNL20 Calculated di (um) Measured dh (um) 1.6 10vo% Schematic of the space available between perfectly uted whiskers of radius r, on a face that is paralle. To a first approximation, there is a direct propor nality between di and dh at least over the com- alumina matrix fills the space between the whiskers. Therefore, by using di=idb i. being a constant, optical micrographs in Fig. 3 is satisfactory. It is obvious that the volume fraction, is: dm=y山=2/4 A measure of the space between the whiskers is the where in this case 2x 1.5. obtained by regression of diameter of the circle that fits into this space, which the data in Fig. 5. Then using equation (5) has been denoted d We can then follow (41+2n)2 V中 and finally: S This expression allows an estimate of the effective grain size knowing only the volume fraction of whiskers and the whisker radius. It should be valid Table 3 shows a comparison between measured and over a range of compositions similar to the one calculated values of dh using r=0.5 um. Good used in this study. The value of i can be related to agreement is obtained for samples containing 10 the homogeneity of the distribution of reinforce- and 20 vol %o whiskers. For ANLI5 and ANL30, ments, and to the whisker aspect ratio. When using ne measured values are slightly higher than the the same type of whiskers and similar processing alculated ones, probably due to an imperfect dist echniques, i is expected to vary a little from the bution value reported in this study. ●ORNL10 入~1.5N15 10 du (um) Fig. 5. Correlation between d and di, assuming direct proportionality through a constant i, that is cal- culated by linear regression to be <1.5, valid for the range 10-30 vol. of whiskers
alumina matrix ®lls the space between the whiskers. A comparison of the proposed distribution with the optical micrographs in Fig. 3 is satisfactory. It is obvious that the volume fraction, f, is: f pr2 `2 3 A measure of the space between the whiskers is the diameter of the circle that ®ts into this space, which has been denoted d6. We can then follow: ÿ dk 2r 2 2`2 4 and ®nally: dk r 2p f s ÿ 2 5 Table 3 shows a comparison between measured and calculated values of d6, using r = 0.5 mm. Good agreement is obtained for samples containing 10 and 20 vol.% whiskers. For ANL15 and ANL30, the measured values are slightly higher than the calculated ones, probably due to an imperfect distribution of whiskers. To a ®rst approximation, there is a direct proportionality between d_ and d6, at least over the composition range in this study, as shown in Fig. 5. Therefore, by using d_=ld6, l being a constant, and equation (2), the following is obtained: deff d2 ?dk 3 q l2=3 dk 6 where in this case l11.5, obtained by regression of the data in Fig. 5. Then using equation (5): deff l2=3 r 2p f s ÿ 2 7 This expression allows an estimate of the eective grain size knowing only the volume fraction of whiskers and the whisker radius. It should be valid over a range of compositions similar to the one used in this study. The value of l can be related to the homogeneity of the distribution of reinforcements, and to the whisker aspect ratio. When using the same type of whiskers and similar processing techniques, l is expected to vary a little from the value reported in this study. Fig. 5. Correlation between d6and d_, assuming direct proportionality through a constant l, that is calculated by linear regression to be 11.5, valid for the range 10±30 vol.% of whiskers. Fig. 4. Schematic of the space available between perfectly distributed whiskers of radius r, on a face that is parallel to the HP axis. Table 3. Measured and calculated [equation (5)] d6values for samples with more than 10 vol.% of whiskers using r = 0.5 mm Sample ANL15 ANL30 ORNL10 ORNL20 Calculated d6(mm) 2.2 1.3 3.0 1.8 Measured d6(mm) 2.4 1.6 2.9 1.8 DE ARELLANO-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6365
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.φpep, 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 dierent 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, ... 1 ÿ fe_m s,T,f, ... 8 and then we separate the dependence of the EGS: e_m s,T,f, ... 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, ... 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 dierence of about one order of magnitude in creep rate between a PD and a GBS deformation mechanism. 3.3. Discussion of the ``eective grain size'' The eective grain size is related to the onset of the whisker network. If the volume fraction of reinforcements is small, f fpcp, a percolative network of whiskers 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 signi®cant parameter of the material for composites containing 10 vol.% or more of whiskers as discussed above. The physical concept of the EGS can lie in the increase of eective length of the diusion 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 eects 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-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA
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 in
reduced 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 discussion. The use of an eective 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 boundaries and alumina/whisker interfaces because diusion in the matrix is not fast enough to accommodate 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 satisfactorily to the higher-stress NGS-corrected creep rates of ANL5 (Fig. 6). The high-stress exponent for ANL5 does not result from microstructural degradation because insigni®cant microstructural damage was found in these specimens after deformation. The creep rates for ANL5 correspond to steadystate creep. Under the conditions of this study, monolithic polycrystalline alumina creeps by diusionaccommodated 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 BGBSÿ s ÿ s0 ODeff kTd2 11 where BGBS is a constant, O is the atomic volume, De is an eective diusion coecient, 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-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6367
6368 E ARELLANO. LOPEZ et aL. CREEP OF SIC-WHISKER-REINFORCED ALUMINA superplastic deformation of monolithic Y-PSZ [25]. and the first two extrapolate to ao<6 MPa, while f o do. then the sliding of the grains is not poss- the third extrapolates to o<33 MPa. Additionally Ale and the creep mechanism has to change to ful- Fig 8 tends to substantiate that the creep mechan- this constraint. At high temperatures and low ism of anL5 is the same as monolithic alumina, stress, purely diffusional creep becomes the domi- difiusion-accommodated GBs, but with an nant controlling mechanism, for which classical increased threshold stress models predict [19] If diffusional kinetics are unchanged the slope of BPDonDelt a pd mechanism is about ten times smaller than kTdA ( 12) that of GBS. The PD slope has been represented by the solid line in Fig. 8, as a reference, and shows where BpD is a constant, which is about one order fair agreement with the EgS-corrected creep rates of magnitude smaller than BGBs. Additionally, in the low-stress regime for composites having more when the sliding of the grains is not possible, it has than 10 vol. whiskers. In the linear-linear plot of been shown [26 that monoliths as 3Y-TZP tend to Fig. 8, acceleration of creep rates is evident over a accommodate deformation forming large cavities certain value of the stress that corresponds to the (as large as five times the nominal grain size). This critical stress mentioned above. feature has not been found in the present micro- The critical stress for each of the compositions structural analysis. It is possible that the network of can be estimated by extrapolation of the high-stress whiskers also prevents the formation of cavities as regime of EGS-corrected creep rates to zero, using an accommodating mechanism, and the defor- the same slopes calculated for monolithic ation can be completely accommodated by trans- alumina and anl5. Such critical stresses must be port of matter. In this case a small contribution of distinguished from threshold stresses [24. Above the liding is needed but it seems to be slow enough to critical stress, creep rates do not correspond to true be born by the whisker network steady states because the production of damage is In light of equations(11) and (12), it is suggested significant. Critical and threshold stresses are hat the creep data in Fig. 6 can be represented in a plotted in Fig. 9. Although the estimate of the criti- linear-linear plot(Fig 8)to estimate the threshold cal stress is only approximate, the tendency for the stress as defined in equation(11). The slopes of the stress to increase as the whisker volume fraction plots for ANLO, ORNLO and ANL5 are similar, increases is evident. 3.0E-4 1400°C 2.0E4 O(MPa) Fig.8. Linear-linear plot of the data in Fig. 6, used for calculating the threshold stresses(filled sym- bols)and estimating the critical stresses(open symbols). The monoliths (ORNO and ANLO) creep by diffusion-accommodated GBS, characterized by a slope(dashed line) which is about one order of mag nitude higher than that of a purely diffusional(PD)mechanism, with the same diffusional kinetics (solid line, as reference)
superplastic deformation of monolithic Y-PSZ [25]. If s < s0, then the sliding of the grains is not possible, and the creep mechanism has to change to ful- ®ll this constraint. At high temperatures and low stress, purely diusional creep becomes the dominant controlling mechanism, for which classical models predict [19]: e_PD BPDsODeff kTd2 12 where BPD is a constant, which is about one order of magnitude smaller than BGBS. Additionally, when the sliding of the grains is not possible, it has been shown [26] that monoliths as 3Y-TZP tend to accommodate deformation forming large cavities (as large as ®ve times the nominal grain size). This feature has not been found in the present microstructural analysis. It is possible that the network of whiskers also prevents the formation of cavities as an accommodating mechanism, and the deformation can be completely accommodated by transport of matter. In this case a small contribution of sliding is needed, but it seems to be slow enough to be born by the whisker network. In light of equations (11) and (12), it is suggested that the creep data in Fig. 6 can be represented in a linear±linear plot (Fig. 8) to estimate the threshold stress as de®ned in equation (11). The slopes of the plots for ANL0, ORNL0 and ANL5 are similar, and the ®rst two extrapolate to s016 MPa, while the third extrapolates to s0133 MPa. Additionally, Fig. 8 tends to substantiate that the creep mechanism of ANL5 is the same as monolithic alumina, diusion-accommodated GBS, but with an increased threshold stress. If diusional kinetics are unchanged, the slope of a PD mechanism is about ten times smaller than that of GBS. The PD slope has been represented by the solid line in Fig. 8, as a reference, and shows fair agreement with the EGS-corrected creep rates in the low-stress regime for composites having more than 10 vol.% whiskers. In the linear±linear plot of Fig. 8, acceleration of creep rates is evident over a certain value of the stress that corresponds to the critical stress mentioned above. The critical stress for each of the compositions can be estimated by extrapolation of the high-stress regime of EGS-corrected creep rates to zero, using the same slopes as calculated for monolithic alumina and ANL5. Such critical stresses must be distinguished from threshold stresses [24]. Above the critical stress, creep rates do not correspond to true steady states because the production of damage is signi®cant. Critical and threshold stresses are plotted in Fig. 9. Although the estimate of the critical stress is only approximate, the tendency for the stress to increase as the whisker volume fraction increases is evident. Fig. 8. Linear±linear plot of the data in Fig. 6, used for calculating the threshold stresses (®lled symbols) and estimating the critical stresses (open symbols). The monoliths (ORNL0 and ANL0) creep by diusion-accommodated GBS, characterized by a slope (dashed line) which is about one order of magnitude higher than that of a purely diusional (PD) mechanism, with the same diusional kinetics (solid line, as reference). 6368 DE ARELLANO-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA
E ARELLANO. LOPEZ et al.: CREEP OF SIC-WHISKER-REINFORCED ALUMINA +210 MPa -115 MPa o-90 MPa 33 MPa Threshold Stress Critical Stress φ(% Fig. 9. Regression-calculated threshold stresses(filled symbols) and estimated critical stresses(open symbols) plotted vs the volume percentage of whiskers. 4.2. Discussion of creep mechanisms between the low- and high-stress regimes, as seen in A threshold/critical stress has been used to Fig. 6. The estimated critical stress appears to be inde- alumina in previous publications (23, 27). The same pendent of creep technique, as expected. Figure 10 ideas were also applied to SiC-whisker-reinforced presents the results of the ORNL20 composite ZTA [28]. Parthasarathy et al. [22] have used a tested in compression [13] and in four-point temperature-dependent"threshold stress"to ration- bending [loj alize a set of results on sic-whisker-reinforced com- The creep activation energies must be reexamined posites with high whisker volume fraction. Other considering a temperature-dependent threshold examples of the use of threshold stress are found in stress. Activation-energy studies are available for the study of SiC-whisker-reinforced aluminum alumina-matrix composites fabricated by ARCO, [29, 30]. Creep in these metal-matrix composites was containing 0, 6, 18 and 30 vol. of SiC whiskers [6] controlled by the movement of dislocations and the Temperatures ranged between 1300 and 1450oC threshold stresses were interpreted in terms of and all the tests were conducted on single samples Orowan, back, and detachment stresses using temperature changes, under compressive stres- of alumina col ses of 60 MPa for composites and 40 MPa for the of undeformable whiskers to the alumina monolithic matrix. These stresses correspond to the inhibits the sliding of the grains below a low-stress regime for ARCO18 and ARCO30, but value of the stress. For stresses over that value. slid.- are over the threshold stress for ARCOO(5 MPa) ing is possible, but as the transport of matter in the and ARCO (2I MPa). The results are included in plastic alumina is not fast enough to accommodate Table 4. Similar values of the activation energies the microstructural constraints of the whisker net- were reported by Nutt et al. [7 and Liu et al.[8] work, damage is subsequently formed. The network The values of 2 for ARCOO, ARCOI8 and of whiskers is apparently set forφ>中pwp.Fo volume fraction of whiskers below that limit, defor- mation under high stresses can proceed at a steady 1300-1450-C under 40 MPa(arco)and 60 MP: state. For larger whisker volume fractions, the criti om Ref [6 cal stress increases as the number of whiskers increases. However, the formation of damage is ARCOO ARCO6 ARCOI8 ARCO30 more significant as less plastic material is available Q(k/mol) 511 556 in the composite. This results in a sharper change
4.2. Discussion of creep mechanisms A threshold/critical stress has been used to explain the behavior of SiC-whisker-reinforced alumina in previous publications [23, 27]. The same ideas were also applied to SiC-whisker-reinforced ZTA [28]. Parthasarathy et al. [22] have used a temperature-dependent ``threshold stress'' to rationalize a set of results on SiC-whisker-reinforced composites with high whisker volume fraction. Other examples of the use of threshold stress are found in the study of SiC-whisker-reinforced aluminum [29, 30]. Creep in these metal-matrix composites was controlled by the movement of dislocations, and the threshold stresses were interpreted in terms of Orowan, back, and detachment stresses. In the case of alumina composites, the addition of undeformable whiskers to the alumina matrix inhibits the sliding of the grains below a certain value of the stress. For stresses over that value, sliding is possible, but as the transport of matter in the plastic alumina is not fast enough to accommodate the microstructural constraints of the whisker network, damage is subsequently formed. The network of whiskers is apparently set for f>fpcp. For a volume fraction of whiskers below that limit, deformation under high stresses can proceed at a steady state. For larger whisker volume fractions, the critical stress increases as the number of whiskers increases. However, the formation of damage is more signi®cant as less plastic material is available in the composite. This results in a sharper change between the low- and high-stress regimes, as seen in Fig. 6. The estimated critical stress appears to be independent of creep technique, as expected. Figure 10 presents the results of the ORNL20 composite tested in compression [13] and in four-point bending [10]. The creep activation energies must be reexamined considering a temperature-dependent threshold stress. Activation-energy studies are available for alumina-matrix composites fabricated by ARCO, containing 0, 6, 18 and 30 vol.% of SiC whiskers [6]. Temperatures ranged between 1300 and 14508C, and all the tests were conducted on single samples using temperature changes, under compressive stresses of 60 MPa for composites and 40 MPa for the monolithic matrix. These stresses correspond to the low-stress regime for ARCO18 and ARCO30, but are over the threshold stress for ARCO0 (15 MPa) and ARCO6 (121 MPa). The results are included in Table 4. Similar values of the activation energies were reported by Nutt et al. [7] and Liu et al. [8]. The values of Q for ARCO0, ARCO18 and Fig. 9. Regression-calculated threshold stresses (®lled symbols) and estimated critical stresses (open symbols) plotted vs the volume percentage of whiskers. Table 4. Activation energies for ARCO composites in the range 1300±14508C, under 40 MPa (ARCO0) and 60 MPa (composites), from Ref. [6] ARCO0 ARCO6 ARCO18 ARCO30 Q (kJ/mol) 511 691 556 610 DE ARELLANO-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA 6369
6370 DE ARELLANO.LOPEZ et aL.: CREEP OF SIC-WHISKER-REINFORCED ALUMINA 13E5 1400° ORNL20 ● Compression ○4 pt-Bending 75E6 25E6 00E+01 O (MPa) Fig. 10. Linear-linear plot of the creep rates obtained on ORNL20 by compression(filled symbols) and nt bending (open symbols, Lin et al. [10). The critical stress appears to be independent of ARCO30 were considered to correspond to the tivity of the diffusivities in AlO3 to impurities is ame diffusional kinetics, although ArCO deforms very high. It was concluded, however, that the rate- by gBs and the composites by PD. In a previous controlling diffusion in the monolith was Al publication [13]. details were discussed of the through the grain boundaries, and that this fact diffusion kinetics, which is complex as the sensi- was essentially unchanged in the composites with ARCO6 1500°C 2.0E5 1400° G-21 MPa 50E6 a~38M"Pa1300 00E+0 o(MPa) Fig. ll. Linear-linear plot of the creep rates of ARCO6 composites [6] showing the dependence of the threshold stress with the temperature. As seen, Go decreases as T increases
ARCO30 were considered to correspond to the same diusional kinetics, although ARCO0 deforms by GBS and the composites by PD. In a previous publication [13], details were discussed of the diusion kinetics, which is complex as the sensitivity of the diusivities in Al2O3 to impurities is very high. It was concluded, however, that the ratecontrolling diusion in the monolith was Al3+ through the grain boundaries, and that this fact was essentially unchanged in the composites with Fig. 10. Linear±linear plot of the creep rates obtained on ORNL20 by compression (®lled symbols) and by four-point bending (open symbols, Lin et al. [10]). The critical stress appears to be independent of the testing technique. Fig. 11. Linear±linear plot of the creep rates of ARCO6 composites [6] showing the dependence of the threshold stress with the temperature. As seen, s0 decreases as T increases. 6370 DE ARELLANO-LOÂ PEZ et al.: CREEP OF SiC-WHISKER-REINFORCED ALUMINA
