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Influence of TiC particle size on the load-independent hardness of Al2O3–TiC composites
Materials Letters 57 (2003) 3439 – 3443 www.elsevier.com/locate/matlet
Influence of TiC particle size on the load-independent hardness of Al2O3 –TiC composites Yun Wan a, Jianghong Gong b,* b
a Physics Department, Northwestern University, Xi’an 710069, Shaanxi, PR China Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, PR China
Received 18 December 2002; accepted 5 January 2003
Abstract Seven samples of Al2O3 – 30 wt.% TiC composites were prepared by hot-pressing the Al2O3 powder mixed with TiC particles of different particle sizes. Knoop and Vickers hardness measurements were conducted on these samples, respectively, in the indentation load range from 1.47 to 35.77 N. The load-independent hardness numbers were then determined by analyzing the relationship between the measured indentation size and the applied indentation load. It was found that the load-independent hardness number increases with the increasing TiC particle size, and this experimental phenomenon may be attributed to the effect of the residual internal stress resulting from the mismatch between the thermal expansion of Al2O3 matrix and that of the TiC particles. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Hardness; Mechanical properties; Indentation size effect; Residual stress; Particulate-reinforced composites; Ceramics
1. Introduction It has been well known that grain size is one of the most important factors that may affect the mechanical properties of monolithic ceramics. The influence of grain size on the strength and fracture energy of monolithic ceramics has been investigated extensively [1,2]. It was usually reported that there is a particular grain size for which the strength of ceramic specimens exhibits a maximum. The influence of grain size on other mechanical properties was also studied. For example, it has been reported [3,4] that
* Corresponding author. Fax: +86-10-62771160. E-mail address: [email protected] (J. Gong).
the measured microhardness of silicon nitride-based ceramics increases as the grain size decreases. It may be expected that grain size effect is also significant in ceramic-matrix composites. However, there have been only a few studies concerning this subject and these studies were focused mainly on the effect of the size of the second phase on the toughness characteristics of the composites. In an Al2O3 – SiC nano-composites, the toughness of the composites increases as the size of the SiC submicrometer particle increases [5]. The R-curve behavior of Al2O3-dispersed 3Y-PSZ composite becomes more significant as the Al2O3 particle size increases [6]. Al2O3 is one of the most popular ceramics in the various engineering fields, owning to its excellent physical and chemical properties. However, the use of alumina ceramics in structural applications has
0167-577X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-577X(03)00096-X
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Y. Wan, J. Gong / Materials Letters 57 (2003) 3439–3443
been limited by their relatively low fracture toughness and strength. The addition of brittle particles such as TiC, TiB2, TiCN, etc., has been one approach which was usually taken to strengthen and/or toughen the Al2O3 matrix. For example, it has been shown that, if the TiC content is smaller than 30 wt.%, the density, the Young’s modulus, the bending strength and the fracture toughness of the Al2O3 – TiC composites increase nearly linear with the TiC content [7,8]. In addition, the hardness of the composites was found to be higher than that of the Al2O3 matrix and this may be attributed to the fact that TiC has a higher hardness than Al2O3 [9]. The mechanical properties degrade significantly if the TiC content increases above 30 wt.% due mainly to the difficulty of densifying the composites [7,8]. Up to now, however, little effort has been devoted to the effect of the TiC particle size on the mechanical behavior of Al2O3 – TiC composites. The objective of this paper is to evaluate the influence of the TiC particle size on the hardness of Al2O3 – TiC composites. The composition of the composite was fixed to be 70 wt.% Al2O3 + 30 wt.% TiC, which was reported [7,8] to be the optimum composition in this system.
2. Experimental The materials examined in this study were Al2O3 – 30 wt.% TiC composites. The basic raw materials used for preparing the composites were a commercial Al2O3 powder (purity of 99.99% and average particle size of 0.5 Am) and seven kinds of TiC particles whose average sizes are different with each other. The Al2O3 powder was mixed with one of the seven kinds of TiC particles, respectively, in proper proportion by conventional ball milling. After being dried at 70 jC in vacuum, the mixed powders were sieved, uniaxially pressed at 40 MPa, cold isostatically pressed at 400 MPa and then hot-pressed in Ar atmosphere at 1650– 1700 jC and 25 MPa for 30 min. The hot-pressed products were polished and then examined by scanning electron microscopy (SEM) with an image analyzer to measure the size of the TiC particles. The observation confirmed that the TiC particles were well dispersed in the Al2O3 matrix. The sizes evaluated as a mean value of about 200 TiC particles are listed in Table 1. The average size of the
Table 1 Some properties of the composites used in the present study Sample denotation AC1 AC2 AC3 AC4 AC5 AC6 AC7 Size of TiC particles (Am) Size of Al2O3 grain size (Am)
0.5
1.7
3.8
4.3
5.6
6.8
8.2
0.8
1.6
2.7
3.1
3.6
3.7
3.7
Al2O3 grains, determined on chemically etched samples, is also shown in Table 1. The specimens used for indentation tests were cut directly from the hot-pressed products. These specimens were mounted in bakelite, ground flat using a diamond grinding wheel and then polished carefully with successively finer diamond pastes to yield a scratch-free, mirror-like surface finish suitable for indentation. The polished surface of each specimen was perpendicular to the hot-pressing direction. A low-load hardness tester was employed to measure the Knoop hardness and the Vickers hardness, respectively, in the indentation load range from 1.47 to 35.77 N and at a constant dwell time of 15 s. At each indentation load level, at least 10 Knoop indentations and 10 Vickers indentations were made. After indentation, the lengths of the two diagonals of each Vickers indentation and the length of the long diagonal of each Knoop indentation were immediately measured by optical microscopy. The hardness number H, HK or HV, was calculated from the measured diagonal length for each indentation by H ¼k
P d2
ð1Þ
where P is the indentation load, d is the average value of the two diagonal lengths for Vickers indentation or the length of the long diagonal for Knoop indentation, k is a constant dependent on the indenter geometry, 1.8544 for Vickers indentation and 14.229 for Knoop indentation [10].
3. Results and discussion The Vickers and Knoop hardness numbers of the sample AC5 are plotted in Fig. 1 as functions of the indentation load. Each of the data points represents an average of measurements from at least 10 tests. It can be seen that, as indentation load increases, the meas-
Y. Wan, J. Gong / Materials Letters 57 (2003) 3439–3443
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correlating the measured indentation size to the applied test load, P ¼ a0 þ a1 d þ a2 d 2
Fig. 1. Knoop and Vickers hardness as functions of indentation load for the sample AC5.
ured HV and HK decrease gradually, exhibiting a significant indentation size effect (ISE). Up to now, the origin of the ISE is still a controversial subject. Two possible explanations for the ISE in ceramics have been proposed, one being the proportional specimen resistance (PSR) model [11] and the other being based on the energy balance consideration [12]. In these two models, the relationship between the indentation size, d, and the applied indentation load, P, was predicted to be P ¼ a1 þ a2 d d
ð2Þ
where a1 is a constant and a2 is suggested to be related to the load-independent hardness, H0 [11,12] H0 ¼ ka2
ð3Þ
where k is the same parameter as appeared in Eq. (1). Recently, Gong et al. re-examined the applicability of Eq. (2) to the indentation size effect observed in ceramics. It was found that Eq. (2) is insufficient for describing the experimental data measured in a relatively wide range of applied test load. By considering the effects of the machining-induced plastically deformed surface [13,14] and the experimental errors related to the smallness of the indentation on the hardness measurements [15,16], Eq. (2) was modified and the empirical equation proposed originally by Bu¨ckle [17] was proven to be more suitable for
ð4Þ
According to the previous analyses [13 – 16], the physical meaning of the parameter a2 in Eq. (4) is the same as that in Eq. (2) and a0 and a1 are constants. The applicability of Eq. (4) to describe the ISE in ceramics has been verified by examining the experimental data measured for a series of typical ceramics using both Vickers and Knoop indenters [13 – 16,18,19] and it was concluded that Eq. (4) is more suitable than Eq. (2) for the description of the indentation data measured in a relatively wide range of applied indentation load. In the present study, Eq. (4) was employed to determine the load-independent hardness for the Al2O3 –TiC composites. As an example, applications of Eq. (4) to the experimental results for samples AC3 and AC6 are shown in Fig. 2. It can be seen that Eq. (4) describes the experimental data very well. Correlations for these plots, as well as the plots for other samples tested in the present study, are very high, r2>0.99. Table 2 summarizes the best-fit values of all the three parameters, a0, a1 and a2, for all the seven samples considered. The load-independent hardness numbers, HK0 and HV0, for each sample tested were calculated with Eq. (3) and k = 14.229 for Knoop indentation and 1.8544 for Vickers indentation using the best-fit values of a2 listed in Table 2. The results are shown in Fig. 3 as functions of the average size of TiC particles in the test sample. It is of interest to note that both HK0 and HV0 increase as the TiC particle size increases. Furthermore, compared with HK0, HV0 increases much steeper. The grain-size-dependence of the measured hardness of monolithic ceramics was studied by several authors and it was generally reported that the measured hardness decreases with increasing grain size [3,4]. However, it should be pointed out that the hardness numbers quoted in these previous studies were only the apparent values, i.e., the load-dependent hardness and no effort was devoted to determine and compare the load-independent hardness numbers. So it is impossible to make a direct comparison between the experimental results obtained in the present study and those reported in the previous studies.
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Fig. 3. Load-independent hardness numbers of Al2O3 – 30 wt.% TiC composites as functions of the average size of TiC particles in the test sample.
Fig. 2. Indentation size versus the applied test load for the samples AC3 (a) and AC6 (b).
The toughness characteristics of the Al2O3 – TiC composites were observed previously [20] and It was found that TiC particle size plays an important role in toughening. The composites having small TiC par-
Table 2 Best-fit values of parameters in Eq. (4) Sample Vickers indentation
AC1 AC2 AC3 AC4 AC5 AC6 AC7
Knoop indentation
a0 (N)
a1 a2 a0 (N/mm) (N/mm2) (N)
1.810 2.468 0.963 0.658 0.910 0.700 0.699
188.41 227.16 134.41 102.71 124.94 96.35 124.87
5952.5 5947.3 6119.5 6551.1 6708.9 7016.5 7395.3
0.441 0.088 0.143 0.162 0.244 0.218 0.369
a1 a2 (N/mm) (N/mm2) 23.72 14.13 18.91 11.93 7.98 8.78 6.73
919.4 912.3 930.4 968.5 979.6 976.4 986.5
ticles exhibit flat R-curve behavior and have fracture toughness similar to that of the Al2O3 matrix. Large TiC particles in Al2O3 matrix induce a rising R-curve behavior and the fracture toughness of the composite increases with increasing TiC particle size. The effect of the residual internal stress resulting from the mismatch between the thermal expansion of Al2O3 matrix and that of the TiC particles was considered to be the main source of such an experimental phenomenon. Enlightened by this study, a possible explanation for the TiC-particle-size dependence of the load-independent hardness may be provided. Because of the smaller linear coefficient of thermal expansion of the TiC particles compared to that of the Al2O3 matrix [21], residual stresses will develop in the Al2O3 matrix upon cooldown from the hot-pressing temperature. In the final products, the Al2O3 matrix would be placed in ‘‘hoop-tension’’ and the TiC particles in radial compression. When an indentation is induced onto the surface of the test specimen, the newly formed free surface of the indentation, which encounters the interfaces between TiC particles and the Al2O3 matrix, would be partially subjected to radial compression, which may ‘‘shorten’’ the indentation diagonal and result in an increase in the material’s hardness. Note that the magnitude of such residual internal stresses depends on the size of the TiC particles as well as the difference between the thermal expansion coefficient of the matrix and that of the particle [22]. As a result, the hardness increases with the increasing TiC particle size.
Y. Wan, J. Gong / Materials Letters 57 (2003) 3439–3443
For Knoop indentation, due to its elongated shape, the residual internal stresses would reduce the length of the shorter indentation diagonal significantly and affect the longer diagonal slightly. So the Knoop hardness is less sensitive to the residual internal stresses when compared to the Vickers hardness. This seems to be a possible explanation for the fact that the measured HVO increases much steeper than HK0 with increasing TiC particle size. Residual internal stresses always exist in ceramics and ceramic-matrix composites, resulting from the various sources, such as thermal expansion mismatch, thermal expansion anisotropy and phase transformation, etc. The state of residual internal stresses may be very complicated and varies from material to material. Since the effect of residual internal stresses on Knoop hardness measurement is rather different with that on Vickers hardness measurement, it is not surprising that there is generally a difference between the measured Knoop hardness and Vickers hardness for a given material. Furthermore, it seems to be unmeaning for any attempts to establish a universal expression, even empirical, to correlate the Knoop hardness to Vickers hardness.
4. Conclusions Seven samples of Al2O3 – 30 wt.% TiC composites, in which the TiC particle sizes are different with each other, were prepared. Both Knoop and Vickers indentation tests were conducted on these samples and the load-independent hardness numbers were determined by analyzing the relationship between the measured indentation size and the applied indentation load. It was found that the load-independent hardness increases with increasing TiC particle sizes. Such an increasing tendency in hardness may be attributed to the effect of residual internal stresses, which result from the mismatch between the thermal expansion of the TiC particles and that of the Al2O3 matrix. It was deduced that any attempt to establish a universal expression to correlate the Knoop hardness to Vickers hardness are
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unmeaning, since the microstructural effects on both hardness tests are rather different from each other.
Acknowledgements The financial support from the High-Tech Research and Development Program of China under grant 2001-AA-339010 is appreciated.
References [1] R.W. Rice, S.W. Freiman, J.J. Mecholsky, J. Am. Ceram. Soc. 63 (1980) 129. [2] R.W. Rice, S.W. Freiman, P.F. Becher, J. Am. Ceram. Soc. 64 (1981) 345. [3] G.N. Babini, A. Bellosi, C. Galassi, J. Mater. Sci. 22 (1987) 1687. [4] A.K. Mokhopadhyay, S.K. Datta, D. Chakraborty, J. Eur. Ceram. Soc. 6 (1990) 303. [5] I. Levin, W.D. Kaplan, D.G. Brandon, J. Am. Ceram. Soc. 78 (1995) 254. [6] J.F. Li, R. Watanabe, J. Mater. Sci. Lett. 15 (1996) 1264. [7] R.P. Whai, B. Ilschner, J. Mater. Sci. 15 (1980) 875. [8] M. Furukawa, O. Nakano, Y. Takashima, Int. J. Refract. Met. Hard Mater. 7 (1988) 37. [9] K.F. Cai, D.S. McLachlan, N. Axen, R. Manyatsa, Ceram. Int. 28 (2002) 217. [10] D.J. Clinton, R. Morrell, Mater. Chem. Phys. 17 (1987) 461. [11] H. Li, R.C. Bradt, J. Mater. Sci. 28 (1993) 917. [12] J.B. Quinn, G.D. Quinn, J. Mater. Sci. 32 (1997) 4331. [13] J.H. Gong, J.J. Wu, Z.D. Guan, Mater. Lett. 35 (1998) 58. [14] J.H. Gong, J.J. Wu, Z.D. Guan, J. Eur. Ceram. Soc. 19 (1999) 2625. [15] J.H. Gong, Y. Li, J. Mater. Sci. 35 (2000) 209. [16] J.H. Gong, Z.D. Guan, J.J. Wu, Mater. Lett. 38 (1999) 197. [17] H. Bu¨ckle, Mikroha¨rtepru¨fung, Berliner Union Verlag, Stuttgart, 1965. [18] J.H. Gong, H.Z. Miao, Z. Zhao, Z.D. Guan, Mater. Sci. Eng., A 303 (2001) 179. [19] J.H. Gong, Z.D. Guan, Mater. Lett. 47 (2001) 140. [20] J.H. Gong, Z. Zhao, H.Z. Miao, Z.D. Guan, Scr. Mater. 43 (2000) 27. [21] R. Morrell, Handbook of Properties of Technical and Engineering Ceramics: Part 1. An Introduction to the Engineer and Designer, Her Majesty’s Stationary Office, London, 1987. [22] B.R. Lawn, Fracture of Brittle Solids, Cambridge Univ. Press, New York, 1993.
Influence of TiC particle size on the load-independent hardness of Al2O3 –TiC composites Yun Wan a, Jianghong Gong b,* b
a Physics Department, Northwestern University, Xi’an 710069, Shaanxi, PR China Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, PR China
Received 18 December 2002; accepted 5 January 2003
Abstract Seven samples of Al2O3 – 30 wt.% TiC composites were prepared by hot-pressing the Al2O3 powder mixed with TiC particles of different particle sizes. Knoop and Vickers hardness measurements were conducted on these samples, respectively, in the indentation load range from 1.47 to 35.77 N. The load-independent hardness numbers were then determined by analyzing the relationship between the measured indentation size and the applied indentation load. It was found that the load-independent hardness number increases with the increasing TiC particle size, and this experimental phenomenon may be attributed to the effect of the residual internal stress resulting from the mismatch between the thermal expansion of Al2O3 matrix and that of the TiC particles. D 2003 Elsevier Science B.V. All rights reserved. Keywords: Hardness; Mechanical properties; Indentation size effect; Residual stress; Particulate-reinforced composites; Ceramics
1. Introduction It has been well known that grain size is one of the most important factors that may affect the mechanical properties of monolithic ceramics. The influence of grain size on the strength and fracture energy of monolithic ceramics has been investigated extensively [1,2]. It was usually reported that there is a particular grain size for which the strength of ceramic specimens exhibits a maximum. The influence of grain size on other mechanical properties was also studied. For example, it has been reported [3,4] that
* Corresponding author. Fax: +86-10-62771160. E-mail address: [email protected] (J. Gong).
the measured microhardness of silicon nitride-based ceramics increases as the grain size decreases. It may be expected that grain size effect is also significant in ceramic-matrix composites. However, there have been only a few studies concerning this subject and these studies were focused mainly on the effect of the size of the second phase on the toughness characteristics of the composites. In an Al2O3 – SiC nano-composites, the toughness of the composites increases as the size of the SiC submicrometer particle increases [5]. The R-curve behavior of Al2O3-dispersed 3Y-PSZ composite becomes more significant as the Al2O3 particle size increases [6]. Al2O3 is one of the most popular ceramics in the various engineering fields, owning to its excellent physical and chemical properties. However, the use of alumina ceramics in structural applications has
0167-577X/03/$ - see front matter D 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-577X(03)00096-X
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been limited by their relatively low fracture toughness and strength. The addition of brittle particles such as TiC, TiB2, TiCN, etc., has been one approach which was usually taken to strengthen and/or toughen the Al2O3 matrix. For example, it has been shown that, if the TiC content is smaller than 30 wt.%, the density, the Young’s modulus, the bending strength and the fracture toughness of the Al2O3 – TiC composites increase nearly linear with the TiC content [7,8]. In addition, the hardness of the composites was found to be higher than that of the Al2O3 matrix and this may be attributed to the fact that TiC has a higher hardness than Al2O3 [9]. The mechanical properties degrade significantly if the TiC content increases above 30 wt.% due mainly to the difficulty of densifying the composites [7,8]. Up to now, however, little effort has been devoted to the effect of the TiC particle size on the mechanical behavior of Al2O3 – TiC composites. The objective of this paper is to evaluate the influence of the TiC particle size on the hardness of Al2O3 – TiC composites. The composition of the composite was fixed to be 70 wt.% Al2O3 + 30 wt.% TiC, which was reported [7,8] to be the optimum composition in this system.
2. Experimental The materials examined in this study were Al2O3 – 30 wt.% TiC composites. The basic raw materials used for preparing the composites were a commercial Al2O3 powder (purity of 99.99% and average particle size of 0.5 Am) and seven kinds of TiC particles whose average sizes are different with each other. The Al2O3 powder was mixed with one of the seven kinds of TiC particles, respectively, in proper proportion by conventional ball milling. After being dried at 70 jC in vacuum, the mixed powders were sieved, uniaxially pressed at 40 MPa, cold isostatically pressed at 400 MPa and then hot-pressed in Ar atmosphere at 1650– 1700 jC and 25 MPa for 30 min. The hot-pressed products were polished and then examined by scanning electron microscopy (SEM) with an image analyzer to measure the size of the TiC particles. The observation confirmed that the TiC particles were well dispersed in the Al2O3 matrix. The sizes evaluated as a mean value of about 200 TiC particles are listed in Table 1. The average size of the
Table 1 Some properties of the composites used in the present study Sample denotation AC1 AC2 AC3 AC4 AC5 AC6 AC7 Size of TiC particles (Am) Size of Al2O3 grain size (Am)
0.5
1.7
3.8
4.3
5.6
6.8
8.2
0.8
1.6
2.7
3.1
3.6
3.7
3.7
Al2O3 grains, determined on chemically etched samples, is also shown in Table 1. The specimens used for indentation tests were cut directly from the hot-pressed products. These specimens were mounted in bakelite, ground flat using a diamond grinding wheel and then polished carefully with successively finer diamond pastes to yield a scratch-free, mirror-like surface finish suitable for indentation. The polished surface of each specimen was perpendicular to the hot-pressing direction. A low-load hardness tester was employed to measure the Knoop hardness and the Vickers hardness, respectively, in the indentation load range from 1.47 to 35.77 N and at a constant dwell time of 15 s. At each indentation load level, at least 10 Knoop indentations and 10 Vickers indentations were made. After indentation, the lengths of the two diagonals of each Vickers indentation and the length of the long diagonal of each Knoop indentation were immediately measured by optical microscopy. The hardness number H, HK or HV, was calculated from the measured diagonal length for each indentation by H ¼k
P d2
ð1Þ
where P is the indentation load, d is the average value of the two diagonal lengths for Vickers indentation or the length of the long diagonal for Knoop indentation, k is a constant dependent on the indenter geometry, 1.8544 for Vickers indentation and 14.229 for Knoop indentation [10].
3. Results and discussion The Vickers and Knoop hardness numbers of the sample AC5 are plotted in Fig. 1 as functions of the indentation load. Each of the data points represents an average of measurements from at least 10 tests. It can be seen that, as indentation load increases, the meas-
Y. Wan, J. Gong / Materials Letters 57 (2003) 3439–3443
3441
correlating the measured indentation size to the applied test load, P ¼ a0 þ a1 d þ a2 d 2
Fig. 1. Knoop and Vickers hardness as functions of indentation load for the sample AC5.
ured HV and HK decrease gradually, exhibiting a significant indentation size effect (ISE). Up to now, the origin of the ISE is still a controversial subject. Two possible explanations for the ISE in ceramics have been proposed, one being the proportional specimen resistance (PSR) model [11] and the other being based on the energy balance consideration [12]. In these two models, the relationship between the indentation size, d, and the applied indentation load, P, was predicted to be P ¼ a1 þ a2 d d
ð2Þ
where a1 is a constant and a2 is suggested to be related to the load-independent hardness, H0 [11,12] H0 ¼ ka2
ð3Þ
where k is the same parameter as appeared in Eq. (1). Recently, Gong et al. re-examined the applicability of Eq. (2) to the indentation size effect observed in ceramics. It was found that Eq. (2) is insufficient for describing the experimental data measured in a relatively wide range of applied test load. By considering the effects of the machining-induced plastically deformed surface [13,14] and the experimental errors related to the smallness of the indentation on the hardness measurements [15,16], Eq. (2) was modified and the empirical equation proposed originally by Bu¨ckle [17] was proven to be more suitable for
ð4Þ
According to the previous analyses [13 – 16], the physical meaning of the parameter a2 in Eq. (4) is the same as that in Eq. (2) and a0 and a1 are constants. The applicability of Eq. (4) to describe the ISE in ceramics has been verified by examining the experimental data measured for a series of typical ceramics using both Vickers and Knoop indenters [13 – 16,18,19] and it was concluded that Eq. (4) is more suitable than Eq. (2) for the description of the indentation data measured in a relatively wide range of applied indentation load. In the present study, Eq. (4) was employed to determine the load-independent hardness for the Al2O3 –TiC composites. As an example, applications of Eq. (4) to the experimental results for samples AC3 and AC6 are shown in Fig. 2. It can be seen that Eq. (4) describes the experimental data very well. Correlations for these plots, as well as the plots for other samples tested in the present study, are very high, r2>0.99. Table 2 summarizes the best-fit values of all the three parameters, a0, a1 and a2, for all the seven samples considered. The load-independent hardness numbers, HK0 and HV0, for each sample tested were calculated with Eq. (3) and k = 14.229 for Knoop indentation and 1.8544 for Vickers indentation using the best-fit values of a2 listed in Table 2. The results are shown in Fig. 3 as functions of the average size of TiC particles in the test sample. It is of interest to note that both HK0 and HV0 increase as the TiC particle size increases. Furthermore, compared with HK0, HV0 increases much steeper. The grain-size-dependence of the measured hardness of monolithic ceramics was studied by several authors and it was generally reported that the measured hardness decreases with increasing grain size [3,4]. However, it should be pointed out that the hardness numbers quoted in these previous studies were only the apparent values, i.e., the load-dependent hardness and no effort was devoted to determine and compare the load-independent hardness numbers. So it is impossible to make a direct comparison between the experimental results obtained in the present study and those reported in the previous studies.
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Fig. 3. Load-independent hardness numbers of Al2O3 – 30 wt.% TiC composites as functions of the average size of TiC particles in the test sample.
Fig. 2. Indentation size versus the applied test load for the samples AC3 (a) and AC6 (b).
The toughness characteristics of the Al2O3 – TiC composites were observed previously [20] and It was found that TiC particle size plays an important role in toughening. The composites having small TiC par-
Table 2 Best-fit values of parameters in Eq. (4) Sample Vickers indentation
AC1 AC2 AC3 AC4 AC5 AC6 AC7
Knoop indentation
a0 (N)
a1 a2 a0 (N/mm) (N/mm2) (N)
1.810 2.468 0.963 0.658 0.910 0.700 0.699
188.41 227.16 134.41 102.71 124.94 96.35 124.87
5952.5 5947.3 6119.5 6551.1 6708.9 7016.5 7395.3
0.441 0.088 0.143 0.162 0.244 0.218 0.369
a1 a2 (N/mm) (N/mm2) 23.72 14.13 18.91 11.93 7.98 8.78 6.73
919.4 912.3 930.4 968.5 979.6 976.4 986.5
ticles exhibit flat R-curve behavior and have fracture toughness similar to that of the Al2O3 matrix. Large TiC particles in Al2O3 matrix induce a rising R-curve behavior and the fracture toughness of the composite increases with increasing TiC particle size. The effect of the residual internal stress resulting from the mismatch between the thermal expansion of Al2O3 matrix and that of the TiC particles was considered to be the main source of such an experimental phenomenon. Enlightened by this study, a possible explanation for the TiC-particle-size dependence of the load-independent hardness may be provided. Because of the smaller linear coefficient of thermal expansion of the TiC particles compared to that of the Al2O3 matrix [21], residual stresses will develop in the Al2O3 matrix upon cooldown from the hot-pressing temperature. In the final products, the Al2O3 matrix would be placed in ‘‘hoop-tension’’ and the TiC particles in radial compression. When an indentation is induced onto the surface of the test specimen, the newly formed free surface of the indentation, which encounters the interfaces between TiC particles and the Al2O3 matrix, would be partially subjected to radial compression, which may ‘‘shorten’’ the indentation diagonal and result in an increase in the material’s hardness. Note that the magnitude of such residual internal stresses depends on the size of the TiC particles as well as the difference between the thermal expansion coefficient of the matrix and that of the particle [22]. As a result, the hardness increases with the increasing TiC particle size.
Y. Wan, J. Gong / Materials Letters 57 (2003) 3439–3443
For Knoop indentation, due to its elongated shape, the residual internal stresses would reduce the length of the shorter indentation diagonal significantly and affect the longer diagonal slightly. So the Knoop hardness is less sensitive to the residual internal stresses when compared to the Vickers hardness. This seems to be a possible explanation for the fact that the measured HVO increases much steeper than HK0 with increasing TiC particle size. Residual internal stresses always exist in ceramics and ceramic-matrix composites, resulting from the various sources, such as thermal expansion mismatch, thermal expansion anisotropy and phase transformation, etc. The state of residual internal stresses may be very complicated and varies from material to material. Since the effect of residual internal stresses on Knoop hardness measurement is rather different with that on Vickers hardness measurement, it is not surprising that there is generally a difference between the measured Knoop hardness and Vickers hardness for a given material. Furthermore, it seems to be unmeaning for any attempts to establish a universal expression, even empirical, to correlate the Knoop hardness to Vickers hardness.
4. Conclusions Seven samples of Al2O3 – 30 wt.% TiC composites, in which the TiC particle sizes are different with each other, were prepared. Both Knoop and Vickers indentation tests were conducted on these samples and the load-independent hardness numbers were determined by analyzing the relationship between the measured indentation size and the applied indentation load. It was found that the load-independent hardness increases with increasing TiC particle sizes. Such an increasing tendency in hardness may be attributed to the effect of residual internal stresses, which result from the mismatch between the thermal expansion of the TiC particles and that of the Al2O3 matrix. It was deduced that any attempt to establish a universal expression to correlate the Knoop hardness to Vickers hardness are
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unmeaning, since the microstructural effects on both hardness tests are rather different from each other.
Acknowledgements The financial support from the High-Tech Research and Development Program of China under grant 2001-AA-339010 is appreciated.
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