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Indentation fracture toughness of high purity submicron alumina
PII:
Acta mater. Vol. 46, No. 5, pp. 1683±1690, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00371-6
INDENTATION FRACTURE TOUGHNESS OF HIGH PURITY SUBMICRON ALUMINA A. MUCHTAR{1 and L. C. LIM2 Department of Mechanical and Production Engineering, and 2Institute of Materials Research and Engineering, National University of Singapore, Singapore 119260, Singapore
1
(Received 10 September 1997) AbstractÐHigh purity (99.99%) ®ne-grained alumina samples were prepared by colloidal techniques and sintered at temperatures varying from 1310 to 15508C, yielding a ®nal grain size ranging between 0.5 and 4.5 mm. Fracture toughness, KIC of the ®ne-grained alumina so prepared was determined by means of indentation test method. The KIC was found to increase with decreasing grain size. Scanning electron microscopy showed that the fracture mode in the submicron-grained samples was intergranular throughout whereas the coarser-grained samples displayed a mixture of inter- and trans-granular fracture mode. It is concluded that for brittle solids that fracture by cleavage, a way to improve its toughness is to decrease the grain size suciently to eect intergranular fracture. In the present study, a 25% increase in fracture toughness was obtained by such a technique. # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
Various techniques have been used to determine the fracture toughness (KIC) of alumina such as chevron notched beam (CVNB), single edge notched beam (SENB), double cantilever beam (DCB), single edged precracked beam (SEPB) and, more recently, the indentation method. The indentation method of fracture toughness determination is relatively easy to perform as compared to the conventional methods. It requires only a minimum area of mirror ®nish quality polishing and indentation test can be performed on a standard hardness tester, eliminating the use of heavy machinery, complex specimen geometries and experimental procedures. In excess of a critical indentation load, cracks are formed around the indentation which are indicative of the fracture properties of the material. Over the years, a number of indentation models have been reported in the literature [1±7]. The models can be divided into two groups with respect to the type of cracks they modelled. One group models the indentation fracture of Palmqvist cracks. These are initiated at the apexes of the indentation mark, radially propagating outwards whilst maintaining close contact with the surface [5]. Normally induced at low indentation loads, they are evident in materials with high toughness values such as WC±Co [8±10]. The second group is based on median cracks [5] which are initiated by the sub-surface tensile stress ®eld directly beneath the {On study leave from Universiti Kebangsaan Malaysia (The National University of Malaysia), 43600 Bangi, Malaysia.
indentation mark. The cracks may or may not propagate further and ®nally break through the surface forming what is normally called a half-penny crack shape. In both cases, the cracks are orientated perpendicular to the surface plane. The course in which a crack develops is highly dependent on both material properties and the indentation load, and as such its behaviour varies considerably from one indenter-material system to another. One must then determine the type of cracks and use the appropriate equations to calculate the fracture toughness [6±11]. More recently, Lankford [3], forwarded a revised model by Evans and Charles [2] that catered for both the Palmqvist and median cracks albeit with errors of approximately 35%. Liang et al. [7] later provided a re®ned expression which applies to both types of cracks and predicts the indentation fracture toughness more accurately. The present work aims at studying the indentation fracture toughness of ®ne-grained alumina prepared by colloidal techniques. Our prime concern is to understand how the grain size may aect the fracture behaviour of the material and its fracture toughness especially in the submicron grain range. Liang et al.'s formula was used in the present work in the evaluation of fracture toughness from indentation test data due to its universality irrespective of the type of crack produced by the indentation. 2. EXPERIMENTAL PROCEDURE
2.1. Materials and specimens The starting material was a commercially available alumina powder (TM-5D, Taimei Chemicals,
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Japan) of 99.99% purity with an average particle size of 0.25 mm. Dispersed well in an ultrasonic bath (Ney 300 Ultrasonik, U.S.A.) with pH = 2.00 distilled water (adjusted with the addition of HCl) at 20% volume, the suspension was ®rst sedimented for 24 h to remove the agglomerates. Compaction was achieved by centrifugal casting after which the green compacts were dried inside a drying chamber. They were then sintered at various temperatures from 1310 to 15508C for 1 h to yield samples of dierent grain sizes. 2.2. Indentation test In preparation for the indentation test, the specimens were mounted in hard plastics. One face of the specimen was polished successively with 6, 1 and 0.25 mm diamond pastes, succeeded by annealing at 12008C for 15 min to eliminate possible surface compressive stresses due to polishing. Then, the specimens were subjected to the indentation test using a standard Vickers microhardness indenter (Matsuzawa Microhardness Tester MXT50). The applied indentation load was in the range of 300 gf±2 kgf with the dwell time being 12 s. Crack length measurements were conducted directly in the microhardness tester with the help of an optical
instrument. Scanning Electron Microscopy, SEM (JEOL JSM-T330A Scanning Microscope) was also used to study the crack path produced by the indentation. For SEM samples, thermal etching (12008C, 3 h) was done prior to the indentation test; otherwise the heat treatment might heal the crack tips. The crack length measured by both optical means and by SEM are comparable. 2.3. Fracture toughness determination Knowing the crack length, c, and the indentation half-diagonal, a, the fracture toughness was computed using Liang et al.'s expression below. 18ac ÿ1:51 0:4 KIC F H c a 1 Ha0:5 EF a where
" # 4 ÿ 0:5 4 a 14 1 ÿ 8 1
2
a is a non-dimensional constant related to the Poisson's ratio as shown. Elastic modulus, E and Poisson's ratio, n were taken as 392 GPa and 2.7, respectively. F is a constraint factor (reported by Liang as 13) and H the hardness of the test specimen. From elementary dimensional study, the hardness was calculated in SI units using H
P 2a2
3
where P is the indentation load. 3. RESULTS
3.1. Microstructure of colloidally processed alumina
Fig. 1. Typical microstructure of the ®ne-grained highpurity alumina used in the present study: (a) grain size = 0.5 mm; (b) grain size = 4.5 mm.
The colloidal sedimentation process was found to be eective in the elimination of agglomerates in the starting powder material. This yielded a high green density of 65.8% th. The ®nal sintered density of our alumina samples, obtained by Archimedes Immersion Technique were between 96 and 99.4% th for the range of sintering temperatures attempted in the present work. SEM micrographs indicated fairly equiaxed grains of uniform size. Porosity was low with voids being scarce and were homogeneously distributed throughout the specimens. As expected, the elimination of the agglomerates resulted in a narrow grain size distribution. The average ®nal grain size, measured using the linear intercept technique, was about 0.5 mm for the lowest temperature and about 4.5 mm for the highest temperature used. Figure 1 shows the microstructures of two samples produced by the two extreme sintering temperatures used. Figure 2 shows the grain growth curve versus 1/ T, d and d0 being the ®nal and initial grain size, respectively; the latter was taken to be 0.25 mm. A straight line was obtained giving a corresponding
MUCHTAR and LIN: INDENTATION FRACTURE TOUGHNESS
Fig. 2. Grain growth of high-purity alumina with initial particle size of 0.25 mm. Activation energy is found to be 643 kJ/mol. Data label indicates grain size in m m.
activation energy of 643 kJ/mol, which compares well with values obtained by previous researchers [12, 13]. 3.2. Indentation fracture toughness To facilitate computations of fracture toughness values that obligated the use of hardness data, the hardness of the alumina specimens was computed using equation (3). The values were found to lie within a range of 18.5±20.0 GPa. The scatter was considered normal for ceramics. The above hardness values were obtained under valid load ranges determined by carrying out a series of hardness tests over a suciently large load range. In general, loads less than 100 gf might have contributed to what is normally referred to as the indentation size eect (ISE) whereby the apparent hardness increases rapidly with decreasing loads [14, 15]. Too high a load was a nuisance too as the induced cracks would aect the data. Figure 3 gives the indentation fracture toughness of alumina (average of at least 6 indentations for each test load) against the grain size. It shows that within the range of grain sizes investigated, the fracture toughness increases continuously with decreasing grain size. For instance, at 2 kgf load, an average toughness value of 3.9 MPaZm was registered at a grain size of 0.5 mm while samples with a grain size of 3±5 mm registered a lower toughness value of 3.3 MPaZm. In the case of the microngrained samples, the toughness value was also observed to increase with increasing indentation load for a given grain size. These values compare well to those reported by other workers using conventional methods [16]. 3.3. Indentation cracks Generally, the ratio, c/a, c being the crack length and a the indentation half diagonal, is found to be greater than 2.0, suggesting that the type of crack
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Fig. 3. Grain size eect on the indentation fracture toughness.
produced by the indentation is more a median or half-penny type. Similar results were also reported by Liang et al. [7] although their results showed that the cracks formed by indentation of ®negrained alumina were of Palmqvist type at low loads which evolved into median type at high loads. The fracture mode was predominantly intergranular for the submicron-grained specimens. Figure 4 is a SEM picture of a 0.5 mm grain size specimen indented with a 1 kgf load. Intergranular cracking was evident throughout the length of the crack which was on one arm of the indenter impression. For the micron-grained samples, the tendency for intergranular fracture was also evident albeit less frequently. A sample micrograph for this behaviour is given in Fig. 5. In this case, the apex landed in the vicinity of a grain boundary and thus the crack found an easy propagation mode by following the boundary. At one point however (A), the crack opted to traverse transgranularly rather than be de¯ected and continue intergranularly. After traversing two grains, the crack seemed to have been arrested at a grain boundary (B). Note also that the fracture mode of micron-grained alumina is load dependent. In general, the percentage of intergranular fracture increases with increasing indentation load, as vividly shown in Fig. 6.
4. DISCUSSION
4.1. Colloidal alumina
processing
for
submicron-grained
As recently reviewed by Lange [17], colloidal processing serves as an eective means to produce reliable and improved engineering ceramics. Removal of heterogeneities from the initial starting material has yielded a well dispersed particle distribution in the green compact. In this research, sedimentation at pH = 2.0 successfully stabilised the suspension and separated it from the unwanted agglomerates.
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Fig. 4. SEM micrograph showing one arm of an indented 0.5 mm grain size alumina sample. Intergranular fracture is evident all throughout the length of the crack.
A dense homogeneous microstructure was achieved with a uniform, ®ne grain size generated at low sintering temperatures. Abnormal grain growth was not apparent in any of the micrographs taken under SEM even with the absence of sintering additives like those required in other works [18]. The smallest grain size attained with a density of greater than 96% was 0.5 mm at a sintering temperature of 13108C. 4.2. Grain size and indentation load dependent fracture toughness of alumina The present work showed that submicron-grained alumina exhibited a high fracture toughness value of about 3.9 MPaZm while that of a grain size of 3±5 mm was consistently lower averaging about 3.3 MPaZm. This corresponds to about 25% increase in fracture toughness. Another interesting ®nding of the present work is that the fracture toughness values of the submicron-grained alumina were relatively independent of the indentation load used, while that of the coarser grained samples increased with the indentation load used. It is further noted that the submicron-grained specimens fracture intergranularly. On the other hand, for the micron-grained specimens, there is a
mixture of trans- and intergranular fracture, with the proportion of transgranular fracture increasing with the grain size. In other words, when the grain size is suciently ®ne, alumina is more resistant to cleavage and fracture occurs by grain boundary cracking. Since little evidence of grain bridging nor microcracking was observed nor were there any extrinsic ¯aws present, the higher toughness of the submicron-grained alumina specimens must be a result of the true intergranular fracture in these specimens. Note that the fracture mode remained unchanged as the indentation load was increased. This explains why the indentation fracture toughness of submicron-grained alumina is relatively load independent, as observed in the present work. On the other hand, the picture is quite dierent for the coarser grained specimens. As the grain size increases, alumina becomes more prone to cleavage fracture. This transition from a preference to intergranular fracture to cleavage fracture is gradual, with the fraction of transgranular cleavage facets increasing with decreasing indentation load. Associated with this transition in fracture mode is a decrease in the fracture toughness of the alumina specimen.
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Fig. 6. Eect of the indentation load on the fracture mode of micron-grained specimen.
Fig. 5. SEM micrograph showing one arm of an indented 4.5 mm grain size alumina sample showing a mixture of intergranular and transgranular fracture mode. Transgranular fracture commenced at (A) until crack was ®nally arrested at grain boundary (B).
Another point to note is that the percentage of intergranular fracture increased with indentation load (Fig. 6). This would account for the indentation load dependence of fracture toughness of the coarser grained alumina, i.e. at a given grain size, the fracture toughness was higher when a higher indentation load was used (Fig. 3). The above-mentioned load-dependence of fracture toughness of alumina should be distinguished from the R-curve eect reported by other researchers [19±21]. In the latter case, a higher fracture toughness was observed for specimens containing a larger initial ¯aw which had been observed in alumina of 20±80 mm in grain size. Grain bridging behind the crack was identi®ed to be the contributing factor to the improved fracture toughness in this case. Most of the works reported were also carried out at relatively low loading rates during which slow crack growth might occur especially when the environment was corrosive. In the present work, the cracks observed were fast growing cracks which were formed immediately upon initiation at the apexes of the indentation mark with little evidence of grain bridging nor microcracking. 4.3. Cleavage vs intergranular fracture in alumina In explaining the grain size and load dependent indentation fracture toughness of alumina, one may have to examine the various factors aecting both cleavage and intergranular fracture of brittle solids such as alumina. It is well known that in intrinsically brittle materials, cleavage fracture is controlled by the crack nucleation event [22±26]. When such happens, the
fracture strength of a solid follows a Hall±Petch relationship with grain size. This is because in brittle solids, pile-ups of dislocation are a means in nucleating crack and the strength of a dislocation pile-up generally scales with its length, which in turn is determined by the grain size. One may thus agree that when cleavage fracture predominates, a Hall± Petch like relationship is to be expected between the indentation fracture toughness and grain size of brittle solids. In other words, a high cleavage fracture toughness is to be expected for extremely ®ne grained solids free of major ¯aws, because very high stresses are required to nucleate cleavage cracks in the material. On the other hand, grain boundaries can be viewed as internal defects and sources of stress raisers in the material. One may assume that the energy associated with intergranular fracture is dominated by crack propagation along the interface. Thus, when fracture occurs intergranularly, the fracture energy is expected to scale approximately linearly with the grain size, being more tortuous for a larger grained material. Another reason for the lower intergranular fracture toughness of ®ne grained material is the ease with which the ®ner grains in the material could rotate to eect intergranular fracture, as suggested by Gobran et al. [27]. The fracture energies for brittle solids vs grain size associated with cleavage and intergranular fracture are shown schematically in Fig. 7. It can be seen that when the grain size is large, cleavage cracks can nucleate readily in brittle solids and fracture is dominated by cleavage with a low fracture energy or toughness. On the other hand, for small grain material, cleavage fracture is dicult as a high nucleation stress is required. In this case, intergranular fracture becomes feasible. Note also that the fracture energy or toughness associated with an intergranular fracture near the transition is higher than that of a total cleavage fracture, as observed in the present work.
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Fig. 7. Schematic representation of the fracture energies for brittle solid vs grain size.
One question arises as to how the above fracture phenomenon would be aected by the indentation load. On one hand, the intergranular fracture energy or toughness should be relatively independent of the indentation load. On the other hand, a higher load is expected to aect cleavage crack nucleation. However, unlike tensile stressing in which a higher load helps to promote cleavage crack nucleation, in an indentation test, a higher load generates a larger compressive stressed region which would promote plastic deformation by multiple slip. This would help delay cleavage crack nucleation as the latter is promoted by pile-ups of dislocations by single glide, which in turn are favoured should the stress state in the material be predominantly tensile. In other words, the eect of increasing indentation load can be viewed as shifting the cleavage fracture energy at ®ne grain sizes to the right while not aecting the other parts of the energy curves, as shown in Fig. 7. It can also be seen from Fig. 7 that the indentation fracture energy or toughness should be relatively independent of indentation load at very small grain size when the fracture energy or toughness is controlled by intergranular fracture. A similar conclusion is reached at large grain sizes when cleavage fracture is the dominating mechanism. However, at intermediate grain size where transition from intergranular to cleavage fracture occurs, a higher indentation load is expected to delay cleavage fracture while promoting intergranular fracture. When such happens, the indentation fracture toughness of the materials should increase with indentation load, as observed in the present work. 4.4. Intrinsic fracture toughness of alumina It is evident from the present work that under proper control conditions indentation fracture toughness test yields valid fracture toughness values of brittle solids such as alumina. More importantly, the present work shows that when major sintering defects are eliminated, the fracture mode of alumina depends on the grain size and so does its intrinsic fracture toughness value. The lowest fracture value was obtained when the fracture mode is predomi-
nantly transgranular, which occurred at low indentation loads for samples of a few microns or larger in grain size. This value is less than that obtained using conventional bend tests with notched bars which often registered a higher toughness value. Note also that under the said test conditions, the initial slow fracture path is largely intergranular. In other words, the fracture toughness values for cleavage fracture and intergranular fracture in alumina obtained in the present work for micron-grained and submicron-grained materials, respectively, can be taken as the intrinsic cleavage and intergranular fracture toughness values of alumina. This is because, ®rstly, unlike conventional bend tests, the loading rate is comparatively fast in an indentation test hence the eect of slow crack growth can be avoided should the crack length measurements be taken immediately after the test. Secondly, due to the small indentation size, it is possible that cleavage fracture can be initiated within a grain so that its propagation in the material and the associated fracture behaviour can be studied. Such is not possible in a conventional fracture toughness test as intergranular slow crack growth predominates during the crack nucleation and initial growth stage, leading to a higher fracture toughness value. Therefore, we may conclude that, when executed properly, the indentation fracture toughness technique is a valid technique for obtaining the intrinsic fracture toughness of brittle solids. Another important ®nding of the present work is that for brittle solids which fracture by cleavage, one way of improving fracture toughness is to decrease the grain size suciently to eect intergranular fracture. As shown in the present work, for pure alumina, a 25% increase in fracture toughness can be eected by such a technique. However, it should also be cautioned that in intergranular fracture mode, a continuous decrease in grain size would yield the opposite eect in that the fracture toughness value would decrease with decreasing grain size as then the fracture path will be less tortuous with decreasing grain size. This would be the case should the grain boundary character distribution in a material be independent of grain size. Should this be the case, then, there should exist an optimum ®ne grain size at which the intrinsic fracture toughness of brittle solids is a maximum. Similar observation has in fact been made by Rice et al. [28]. 4.5. Other observations It is interesting to note that the debris generated by indentation are dierent depending on the grain size of the alumina specimen under study. In general, for specimens with a grain size larger than 3 mm, the debris consisted of crushed grains of alumina at the bottom faces of the impression and signs of spallation of grains were detectable at the top faces of the impression and surrounding ma-
MUCHTAR and LIN: INDENTATION FRACTURE TOUGHNESS
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ing of the specimens, as evidenced by the spalled grains at the top faces of the impression and surrounding material in Fig. 8(b). Note also the spalled grain which was not crushed and still retained its shape in this ®gure (arrowed). Spontaneous micro-fracture of individual grains has been reported and modelled by Cho et al. [29]. In their case, the driving force is the anisotropic thermal expansion associated with the fast temperature rise generated by sliding wear. The present work con®rms the possibility of spontaneous microfracture of alumina grains during indentation loading and elastic unloading. Furthermore, the smaller the grain size, the higher the resistance to spontaneous micro-spallation of the material both during indentation loading and elastic unloading. The lower resistance to grain spallation of the coarser grained samples is probably promoted by the higher tendency to cleavage fracture of the coarser grained alumina, which also accounts for their lower fracture toughness. 5. CONCLUSION
Fig. 8. SEM micrograph showing the fracture surface appearance inside the indented samples: (a) grain size = 4.5 mm; (b) grain size = 0.5 mm. Notice the spallated grain (arrow) and its socket.
terial [Fig. 8(a)]. For the submicron-grained samples, the impression had smooth surfaces and was almost free of crushed debris although signs of spallation of grains remained apparent near the top faces and the surrounding material [Fig. 8(b)]. Our explanation for the above is as follows: Due to the lower fracture resistance of the coarser grains in the micro-grained alumina, spallation of these grains occurred during loading in the indentation test, which probably occurred at the periphery of the indenter due to the high bending stress there. As the indenter continued to penetrate into the material, the spalled grains were dragged along and crushed in the process, producing the ®ne debris of crushed material near the bottom of the impression. The intact, spalled grains near the top faces of the impression are the likely result of spontaneous micro-fracture of grains produced by the elastic unloading associated with the retraction of the indenter due to the anisotropy eect in elastic constants of alumina. Since no crushed debris could be detected at the bottom faces of the impression in the submicrongrained specimens, spallation of grains probably did not occur during indentation loading of the submicron-grained specimens. Nevertheless, spontaneous spallation of grains did occur upon elastic unload-
1. Colloidal processing was successfully employed to produce dense ultra purity (99.99%) alumina samples at relatively lower sintering temperatures compared to other processing techniques. Submicron-grained alumina of about 0.5 mm in grain size was produced by such a technique. 2. The fracture toughness, KIC of the alumina samples determined by the indentation method was found to decrease with increasing grain size, being about 3.9 MPaZm for the submicrongrained samples and about 3.3 MPaZm for specimens with a grain size of 3±5 mm. 3. The fracture toughness of submicron-grained alumina was independent of the indentation load applied but that of the micron-grained samples increased with the indentation load. 4. One way to improve the toughness of materials displaying ``intrinsic'' cleavage fracture is to minimise the grain size (submicron) to induce total intergranular fracture. For the high-purity alumina used in this research, the fracture toughness improvement is about 20±25% via such a mechanism. 5. The KIC value registered of between 3 and 4 MPaZm in the present work compares well with those measured using conventional fracture toughness tests. This suggests that despite its simplicity, the indentation method is a viable technique for fracture toughness determination of brittle materials provided that proper specimen preparation and test procedures were observed. 6. Spontaneous spallation of individual grains occurred during elastic unloading of the indenta-
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tion test of the submicron-grained alumina. For the micron-grained alumina, spontaneous spallation was also observed to occur during loading, producing a lot of crushed debris at the bottom of the impression produced by the indenter.
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13. Bae, S. I. and Baik, S., J. Mater. Sci., 1993, 28, 4197. 14. Bull, S. J., Page, T. F. and Yoe, E. H., Philosophical Magazine Letters, 1989, 59, 281. 15. Farges, G. and Degout, D., Thin Solid Films, 1989, 181, 365. 16. Miyahara, N., Mutoh, Y., Yamaishi, K., Uematsu, K. and Inoue, M., in Grain Boundary Controlled Properties of Fine Ceramics, JFCC Workshop Series: Materials Processing and Design, ed. K. Ishizaki, K. Niihara, M. Isotani, and R. G. Ford, Elsevier Science, Amsterdam, 1992. 17. Lange, F. F., J. Am. Ceram. Soc., 1989, 72, 3. 18. Bae, S. I. and Baik, S., J. Am. Ceram. Soc., 1994, 77, 2499. 19. Swanson, P. L., Fairbanks, C. J., Lawn, B. R., Mai, Y-W. and Hockey, B. J., J. Am. Ceram. Soc., 1987, 70, 279. 20. Wieninger, H., Kromp, K. and Pabst, R. F., J. Mater. Sci., 1986, 21, 411. 21. Swain, M. V., J. Mater. Sci. Lett., 1986, 5, 313. 22. Zener, C., Trans. ASM, 1948, 40A, 3. 23. Cottrell, A. H., Trans. TMS-AIME, 1958, 212, 192. 24. McMahon, C. J. Jr and Cohen, M., Acta metall., 1965, 13, 591. 25. Smith, E., Acta metall., 1966, 14, 985. 26. Curry, D. A., King, J. E. and Knott, J. F., Met. Sci., 1978, 12, 247. 27. Gobran, N. K., Mansy, F. M., Mohsen, F. A. and Kamel, R., Mat. Sci. Eng., 1982, 54, 17. 28. Rice, R. W., Freiman, S. W. and Becher, P. F., J. Am. Ceram. Soc., 1981, 64, 345. 29. Cho, S-J., Hockey, B. J., Lawn, B. R. and Bennison, S. J., J. Am. Ceram. Soc., 1989, 72, 1249.
Acta mater. Vol. 46, No. 5, pp. 1683±1690, 1998 # 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/98 $19.00 + 0.00 S1359-6454(97)00371-6
INDENTATION FRACTURE TOUGHNESS OF HIGH PURITY SUBMICRON ALUMINA A. MUCHTAR{1 and L. C. LIM2 Department of Mechanical and Production Engineering, and 2Institute of Materials Research and Engineering, National University of Singapore, Singapore 119260, Singapore
1
(Received 10 September 1997) AbstractÐHigh purity (99.99%) ®ne-grained alumina samples were prepared by colloidal techniques and sintered at temperatures varying from 1310 to 15508C, yielding a ®nal grain size ranging between 0.5 and 4.5 mm. Fracture toughness, KIC of the ®ne-grained alumina so prepared was determined by means of indentation test method. The KIC was found to increase with decreasing grain size. Scanning electron microscopy showed that the fracture mode in the submicron-grained samples was intergranular throughout whereas the coarser-grained samples displayed a mixture of inter- and trans-granular fracture mode. It is concluded that for brittle solids that fracture by cleavage, a way to improve its toughness is to decrease the grain size suciently to eect intergranular fracture. In the present study, a 25% increase in fracture toughness was obtained by such a technique. # 1998 Acta Metallurgica Inc.
1. INTRODUCTION
Various techniques have been used to determine the fracture toughness (KIC) of alumina such as chevron notched beam (CVNB), single edge notched beam (SENB), double cantilever beam (DCB), single edged precracked beam (SEPB) and, more recently, the indentation method. The indentation method of fracture toughness determination is relatively easy to perform as compared to the conventional methods. It requires only a minimum area of mirror ®nish quality polishing and indentation test can be performed on a standard hardness tester, eliminating the use of heavy machinery, complex specimen geometries and experimental procedures. In excess of a critical indentation load, cracks are formed around the indentation which are indicative of the fracture properties of the material. Over the years, a number of indentation models have been reported in the literature [1±7]. The models can be divided into two groups with respect to the type of cracks they modelled. One group models the indentation fracture of Palmqvist cracks. These are initiated at the apexes of the indentation mark, radially propagating outwards whilst maintaining close contact with the surface [5]. Normally induced at low indentation loads, they are evident in materials with high toughness values such as WC±Co [8±10]. The second group is based on median cracks [5] which are initiated by the sub-surface tensile stress ®eld directly beneath the {On study leave from Universiti Kebangsaan Malaysia (The National University of Malaysia), 43600 Bangi, Malaysia.
indentation mark. The cracks may or may not propagate further and ®nally break through the surface forming what is normally called a half-penny crack shape. In both cases, the cracks are orientated perpendicular to the surface plane. The course in which a crack develops is highly dependent on both material properties and the indentation load, and as such its behaviour varies considerably from one indenter-material system to another. One must then determine the type of cracks and use the appropriate equations to calculate the fracture toughness [6±11]. More recently, Lankford [3], forwarded a revised model by Evans and Charles [2] that catered for both the Palmqvist and median cracks albeit with errors of approximately 35%. Liang et al. [7] later provided a re®ned expression which applies to both types of cracks and predicts the indentation fracture toughness more accurately. The present work aims at studying the indentation fracture toughness of ®ne-grained alumina prepared by colloidal techniques. Our prime concern is to understand how the grain size may aect the fracture behaviour of the material and its fracture toughness especially in the submicron grain range. Liang et al.'s formula was used in the present work in the evaluation of fracture toughness from indentation test data due to its universality irrespective of the type of crack produced by the indentation. 2. EXPERIMENTAL PROCEDURE
2.1. Materials and specimens The starting material was a commercially available alumina powder (TM-5D, Taimei Chemicals,
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Japan) of 99.99% purity with an average particle size of 0.25 mm. Dispersed well in an ultrasonic bath (Ney 300 Ultrasonik, U.S.A.) with pH = 2.00 distilled water (adjusted with the addition of HCl) at 20% volume, the suspension was ®rst sedimented for 24 h to remove the agglomerates. Compaction was achieved by centrifugal casting after which the green compacts were dried inside a drying chamber. They were then sintered at various temperatures from 1310 to 15508C for 1 h to yield samples of dierent grain sizes. 2.2. Indentation test In preparation for the indentation test, the specimens were mounted in hard plastics. One face of the specimen was polished successively with 6, 1 and 0.25 mm diamond pastes, succeeded by annealing at 12008C for 15 min to eliminate possible surface compressive stresses due to polishing. Then, the specimens were subjected to the indentation test using a standard Vickers microhardness indenter (Matsuzawa Microhardness Tester MXT50). The applied indentation load was in the range of 300 gf±2 kgf with the dwell time being 12 s. Crack length measurements were conducted directly in the microhardness tester with the help of an optical
instrument. Scanning Electron Microscopy, SEM (JEOL JSM-T330A Scanning Microscope) was also used to study the crack path produced by the indentation. For SEM samples, thermal etching (12008C, 3 h) was done prior to the indentation test; otherwise the heat treatment might heal the crack tips. The crack length measured by both optical means and by SEM are comparable. 2.3. Fracture toughness determination Knowing the crack length, c, and the indentation half-diagonal, a, the fracture toughness was computed using Liang et al.'s expression below. 18ac ÿ1:51 0:4 KIC F H c a 1 Ha0:5 EF a where
" # 4 ÿ 0:5 4 a 14 1 ÿ 8 1
2
a is a non-dimensional constant related to the Poisson's ratio as shown. Elastic modulus, E and Poisson's ratio, n were taken as 392 GPa and 2.7, respectively. F is a constraint factor (reported by Liang as 13) and H the hardness of the test specimen. From elementary dimensional study, the hardness was calculated in SI units using H
P 2a2
3
where P is the indentation load. 3. RESULTS
3.1. Microstructure of colloidally processed alumina
Fig. 1. Typical microstructure of the ®ne-grained highpurity alumina used in the present study: (a) grain size = 0.5 mm; (b) grain size = 4.5 mm.
The colloidal sedimentation process was found to be eective in the elimination of agglomerates in the starting powder material. This yielded a high green density of 65.8% th. The ®nal sintered density of our alumina samples, obtained by Archimedes Immersion Technique were between 96 and 99.4% th for the range of sintering temperatures attempted in the present work. SEM micrographs indicated fairly equiaxed grains of uniform size. Porosity was low with voids being scarce and were homogeneously distributed throughout the specimens. As expected, the elimination of the agglomerates resulted in a narrow grain size distribution. The average ®nal grain size, measured using the linear intercept technique, was about 0.5 mm for the lowest temperature and about 4.5 mm for the highest temperature used. Figure 1 shows the microstructures of two samples produced by the two extreme sintering temperatures used. Figure 2 shows the grain growth curve versus 1/ T, d and d0 being the ®nal and initial grain size, respectively; the latter was taken to be 0.25 mm. A straight line was obtained giving a corresponding
MUCHTAR and LIN: INDENTATION FRACTURE TOUGHNESS
Fig. 2. Grain growth of high-purity alumina with initial particle size of 0.25 mm. Activation energy is found to be 643 kJ/mol. Data label indicates grain size in m m.
activation energy of 643 kJ/mol, which compares well with values obtained by previous researchers [12, 13]. 3.2. Indentation fracture toughness To facilitate computations of fracture toughness values that obligated the use of hardness data, the hardness of the alumina specimens was computed using equation (3). The values were found to lie within a range of 18.5±20.0 GPa. The scatter was considered normal for ceramics. The above hardness values were obtained under valid load ranges determined by carrying out a series of hardness tests over a suciently large load range. In general, loads less than 100 gf might have contributed to what is normally referred to as the indentation size eect (ISE) whereby the apparent hardness increases rapidly with decreasing loads [14, 15]. Too high a load was a nuisance too as the induced cracks would aect the data. Figure 3 gives the indentation fracture toughness of alumina (average of at least 6 indentations for each test load) against the grain size. It shows that within the range of grain sizes investigated, the fracture toughness increases continuously with decreasing grain size. For instance, at 2 kgf load, an average toughness value of 3.9 MPaZm was registered at a grain size of 0.5 mm while samples with a grain size of 3±5 mm registered a lower toughness value of 3.3 MPaZm. In the case of the microngrained samples, the toughness value was also observed to increase with increasing indentation load for a given grain size. These values compare well to those reported by other workers using conventional methods [16]. 3.3. Indentation cracks Generally, the ratio, c/a, c being the crack length and a the indentation half diagonal, is found to be greater than 2.0, suggesting that the type of crack
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Fig. 3. Grain size eect on the indentation fracture toughness.
produced by the indentation is more a median or half-penny type. Similar results were also reported by Liang et al. [7] although their results showed that the cracks formed by indentation of ®negrained alumina were of Palmqvist type at low loads which evolved into median type at high loads. The fracture mode was predominantly intergranular for the submicron-grained specimens. Figure 4 is a SEM picture of a 0.5 mm grain size specimen indented with a 1 kgf load. Intergranular cracking was evident throughout the length of the crack which was on one arm of the indenter impression. For the micron-grained samples, the tendency for intergranular fracture was also evident albeit less frequently. A sample micrograph for this behaviour is given in Fig. 5. In this case, the apex landed in the vicinity of a grain boundary and thus the crack found an easy propagation mode by following the boundary. At one point however (A), the crack opted to traverse transgranularly rather than be de¯ected and continue intergranularly. After traversing two grains, the crack seemed to have been arrested at a grain boundary (B). Note also that the fracture mode of micron-grained alumina is load dependent. In general, the percentage of intergranular fracture increases with increasing indentation load, as vividly shown in Fig. 6.
4. DISCUSSION
4.1. Colloidal alumina
processing
for
submicron-grained
As recently reviewed by Lange [17], colloidal processing serves as an eective means to produce reliable and improved engineering ceramics. Removal of heterogeneities from the initial starting material has yielded a well dispersed particle distribution in the green compact. In this research, sedimentation at pH = 2.0 successfully stabilised the suspension and separated it from the unwanted agglomerates.
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Fig. 4. SEM micrograph showing one arm of an indented 0.5 mm grain size alumina sample. Intergranular fracture is evident all throughout the length of the crack.
A dense homogeneous microstructure was achieved with a uniform, ®ne grain size generated at low sintering temperatures. Abnormal grain growth was not apparent in any of the micrographs taken under SEM even with the absence of sintering additives like those required in other works [18]. The smallest grain size attained with a density of greater than 96% was 0.5 mm at a sintering temperature of 13108C. 4.2. Grain size and indentation load dependent fracture toughness of alumina The present work showed that submicron-grained alumina exhibited a high fracture toughness value of about 3.9 MPaZm while that of a grain size of 3±5 mm was consistently lower averaging about 3.3 MPaZm. This corresponds to about 25% increase in fracture toughness. Another interesting ®nding of the present work is that the fracture toughness values of the submicron-grained alumina were relatively independent of the indentation load used, while that of the coarser grained samples increased with the indentation load used. It is further noted that the submicron-grained specimens fracture intergranularly. On the other hand, for the micron-grained specimens, there is a
mixture of trans- and intergranular fracture, with the proportion of transgranular fracture increasing with the grain size. In other words, when the grain size is suciently ®ne, alumina is more resistant to cleavage and fracture occurs by grain boundary cracking. Since little evidence of grain bridging nor microcracking was observed nor were there any extrinsic ¯aws present, the higher toughness of the submicron-grained alumina specimens must be a result of the true intergranular fracture in these specimens. Note that the fracture mode remained unchanged as the indentation load was increased. This explains why the indentation fracture toughness of submicron-grained alumina is relatively load independent, as observed in the present work. On the other hand, the picture is quite dierent for the coarser grained specimens. As the grain size increases, alumina becomes more prone to cleavage fracture. This transition from a preference to intergranular fracture to cleavage fracture is gradual, with the fraction of transgranular cleavage facets increasing with decreasing indentation load. Associated with this transition in fracture mode is a decrease in the fracture toughness of the alumina specimen.
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Fig. 6. Eect of the indentation load on the fracture mode of micron-grained specimen.
Fig. 5. SEM micrograph showing one arm of an indented 4.5 mm grain size alumina sample showing a mixture of intergranular and transgranular fracture mode. Transgranular fracture commenced at (A) until crack was ®nally arrested at grain boundary (B).
Another point to note is that the percentage of intergranular fracture increased with indentation load (Fig. 6). This would account for the indentation load dependence of fracture toughness of the coarser grained alumina, i.e. at a given grain size, the fracture toughness was higher when a higher indentation load was used (Fig. 3). The above-mentioned load-dependence of fracture toughness of alumina should be distinguished from the R-curve eect reported by other researchers [19±21]. In the latter case, a higher fracture toughness was observed for specimens containing a larger initial ¯aw which had been observed in alumina of 20±80 mm in grain size. Grain bridging behind the crack was identi®ed to be the contributing factor to the improved fracture toughness in this case. Most of the works reported were also carried out at relatively low loading rates during which slow crack growth might occur especially when the environment was corrosive. In the present work, the cracks observed were fast growing cracks which were formed immediately upon initiation at the apexes of the indentation mark with little evidence of grain bridging nor microcracking. 4.3. Cleavage vs intergranular fracture in alumina In explaining the grain size and load dependent indentation fracture toughness of alumina, one may have to examine the various factors aecting both cleavage and intergranular fracture of brittle solids such as alumina. It is well known that in intrinsically brittle materials, cleavage fracture is controlled by the crack nucleation event [22±26]. When such happens, the
fracture strength of a solid follows a Hall±Petch relationship with grain size. This is because in brittle solids, pile-ups of dislocation are a means in nucleating crack and the strength of a dislocation pile-up generally scales with its length, which in turn is determined by the grain size. One may thus agree that when cleavage fracture predominates, a Hall± Petch like relationship is to be expected between the indentation fracture toughness and grain size of brittle solids. In other words, a high cleavage fracture toughness is to be expected for extremely ®ne grained solids free of major ¯aws, because very high stresses are required to nucleate cleavage cracks in the material. On the other hand, grain boundaries can be viewed as internal defects and sources of stress raisers in the material. One may assume that the energy associated with intergranular fracture is dominated by crack propagation along the interface. Thus, when fracture occurs intergranularly, the fracture energy is expected to scale approximately linearly with the grain size, being more tortuous for a larger grained material. Another reason for the lower intergranular fracture toughness of ®ne grained material is the ease with which the ®ner grains in the material could rotate to eect intergranular fracture, as suggested by Gobran et al. [27]. The fracture energies for brittle solids vs grain size associated with cleavage and intergranular fracture are shown schematically in Fig. 7. It can be seen that when the grain size is large, cleavage cracks can nucleate readily in brittle solids and fracture is dominated by cleavage with a low fracture energy or toughness. On the other hand, for small grain material, cleavage fracture is dicult as a high nucleation stress is required. In this case, intergranular fracture becomes feasible. Note also that the fracture energy or toughness associated with an intergranular fracture near the transition is higher than that of a total cleavage fracture, as observed in the present work.
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Fig. 7. Schematic representation of the fracture energies for brittle solid vs grain size.
One question arises as to how the above fracture phenomenon would be aected by the indentation load. On one hand, the intergranular fracture energy or toughness should be relatively independent of the indentation load. On the other hand, a higher load is expected to aect cleavage crack nucleation. However, unlike tensile stressing in which a higher load helps to promote cleavage crack nucleation, in an indentation test, a higher load generates a larger compressive stressed region which would promote plastic deformation by multiple slip. This would help delay cleavage crack nucleation as the latter is promoted by pile-ups of dislocations by single glide, which in turn are favoured should the stress state in the material be predominantly tensile. In other words, the eect of increasing indentation load can be viewed as shifting the cleavage fracture energy at ®ne grain sizes to the right while not aecting the other parts of the energy curves, as shown in Fig. 7. It can also be seen from Fig. 7 that the indentation fracture energy or toughness should be relatively independent of indentation load at very small grain size when the fracture energy or toughness is controlled by intergranular fracture. A similar conclusion is reached at large grain sizes when cleavage fracture is the dominating mechanism. However, at intermediate grain size where transition from intergranular to cleavage fracture occurs, a higher indentation load is expected to delay cleavage fracture while promoting intergranular fracture. When such happens, the indentation fracture toughness of the materials should increase with indentation load, as observed in the present work. 4.4. Intrinsic fracture toughness of alumina It is evident from the present work that under proper control conditions indentation fracture toughness test yields valid fracture toughness values of brittle solids such as alumina. More importantly, the present work shows that when major sintering defects are eliminated, the fracture mode of alumina depends on the grain size and so does its intrinsic fracture toughness value. The lowest fracture value was obtained when the fracture mode is predomi-
nantly transgranular, which occurred at low indentation loads for samples of a few microns or larger in grain size. This value is less than that obtained using conventional bend tests with notched bars which often registered a higher toughness value. Note also that under the said test conditions, the initial slow fracture path is largely intergranular. In other words, the fracture toughness values for cleavage fracture and intergranular fracture in alumina obtained in the present work for micron-grained and submicron-grained materials, respectively, can be taken as the intrinsic cleavage and intergranular fracture toughness values of alumina. This is because, ®rstly, unlike conventional bend tests, the loading rate is comparatively fast in an indentation test hence the eect of slow crack growth can be avoided should the crack length measurements be taken immediately after the test. Secondly, due to the small indentation size, it is possible that cleavage fracture can be initiated within a grain so that its propagation in the material and the associated fracture behaviour can be studied. Such is not possible in a conventional fracture toughness test as intergranular slow crack growth predominates during the crack nucleation and initial growth stage, leading to a higher fracture toughness value. Therefore, we may conclude that, when executed properly, the indentation fracture toughness technique is a valid technique for obtaining the intrinsic fracture toughness of brittle solids. Another important ®nding of the present work is that for brittle solids which fracture by cleavage, one way of improving fracture toughness is to decrease the grain size suciently to eect intergranular fracture. As shown in the present work, for pure alumina, a 25% increase in fracture toughness can be eected by such a technique. However, it should also be cautioned that in intergranular fracture mode, a continuous decrease in grain size would yield the opposite eect in that the fracture toughness value would decrease with decreasing grain size as then the fracture path will be less tortuous with decreasing grain size. This would be the case should the grain boundary character distribution in a material be independent of grain size. Should this be the case, then, there should exist an optimum ®ne grain size at which the intrinsic fracture toughness of brittle solids is a maximum. Similar observation has in fact been made by Rice et al. [28]. 4.5. Other observations It is interesting to note that the debris generated by indentation are dierent depending on the grain size of the alumina specimen under study. In general, for specimens with a grain size larger than 3 mm, the debris consisted of crushed grains of alumina at the bottom faces of the impression and signs of spallation of grains were detectable at the top faces of the impression and surrounding ma-
MUCHTAR and LIN: INDENTATION FRACTURE TOUGHNESS
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ing of the specimens, as evidenced by the spalled grains at the top faces of the impression and surrounding material in Fig. 8(b). Note also the spalled grain which was not crushed and still retained its shape in this ®gure (arrowed). Spontaneous micro-fracture of individual grains has been reported and modelled by Cho et al. [29]. In their case, the driving force is the anisotropic thermal expansion associated with the fast temperature rise generated by sliding wear. The present work con®rms the possibility of spontaneous microfracture of alumina grains during indentation loading and elastic unloading. Furthermore, the smaller the grain size, the higher the resistance to spontaneous micro-spallation of the material both during indentation loading and elastic unloading. The lower resistance to grain spallation of the coarser grained samples is probably promoted by the higher tendency to cleavage fracture of the coarser grained alumina, which also accounts for their lower fracture toughness. 5. CONCLUSION
Fig. 8. SEM micrograph showing the fracture surface appearance inside the indented samples: (a) grain size = 4.5 mm; (b) grain size = 0.5 mm. Notice the spallated grain (arrow) and its socket.
terial [Fig. 8(a)]. For the submicron-grained samples, the impression had smooth surfaces and was almost free of crushed debris although signs of spallation of grains remained apparent near the top faces and the surrounding material [Fig. 8(b)]. Our explanation for the above is as follows: Due to the lower fracture resistance of the coarser grains in the micro-grained alumina, spallation of these grains occurred during loading in the indentation test, which probably occurred at the periphery of the indenter due to the high bending stress there. As the indenter continued to penetrate into the material, the spalled grains were dragged along and crushed in the process, producing the ®ne debris of crushed material near the bottom of the impression. The intact, spalled grains near the top faces of the impression are the likely result of spontaneous micro-fracture of grains produced by the elastic unloading associated with the retraction of the indenter due to the anisotropy eect in elastic constants of alumina. Since no crushed debris could be detected at the bottom faces of the impression in the submicrongrained specimens, spallation of grains probably did not occur during indentation loading of the submicron-grained specimens. Nevertheless, spontaneous spallation of grains did occur upon elastic unload-
1. Colloidal processing was successfully employed to produce dense ultra purity (99.99%) alumina samples at relatively lower sintering temperatures compared to other processing techniques. Submicron-grained alumina of about 0.5 mm in grain size was produced by such a technique. 2. The fracture toughness, KIC of the alumina samples determined by the indentation method was found to decrease with increasing grain size, being about 3.9 MPaZm for the submicrongrained samples and about 3.3 MPaZm for specimens with a grain size of 3±5 mm. 3. The fracture toughness of submicron-grained alumina was independent of the indentation load applied but that of the micron-grained samples increased with the indentation load. 4. One way to improve the toughness of materials displaying ``intrinsic'' cleavage fracture is to minimise the grain size (submicron) to induce total intergranular fracture. For the high-purity alumina used in this research, the fracture toughness improvement is about 20±25% via such a mechanism. 5. The KIC value registered of between 3 and 4 MPaZm in the present work compares well with those measured using conventional fracture toughness tests. This suggests that despite its simplicity, the indentation method is a viable technique for fracture toughness determination of brittle materials provided that proper specimen preparation and test procedures were observed. 6. Spontaneous spallation of individual grains occurred during elastic unloading of the indenta-
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tion test of the submicron-grained alumina. For the micron-grained alumina, spontaneous spallation was also observed to occur during loading, producing a lot of crushed debris at the bottom of the impression produced by the indenter.
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