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Yttria concentration dependence of tensile strength in yttria-stabilized zirconia
Journal of Alloys and Compounds 365 (2004) 253–258
Yttria concentration dependence of tensile strength in yttria-stabilized zirconia Junya Kondoh a,∗ , Hirohisa Shiota b , Katsuhiro Kawachi c , Toshio Nakatani c a Department of Materials Science, The University of Shiga Prefecture, 2500 Hassaka-cho, Hikone 522-8533, Japan Department of Mechanical Systems and Engineering, Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan Technical Research and Development Division, Daiichi Kigenso Kagaku Kogyo Co. Ltd., 1-6-38 Hirabayashiminami, Suminoe-Ku, Osaka 559-0025, Japan b
c
Received 6 May 2003; received in revised form 2 June 2003; accepted 2 June 2003
Abstract Tensile and bending tests were performed for ZrO2 polycrystals stabilized with 2.6–10 mol % Y2 O3 . There is no significant difference in the isothermal Young’s modulus of all the compositions. Both the tensile and bending strengths of PSZ are markedly higher than those of FSZ. This is mainly due to the fact that both strengths of PSZ reflect the increase in the resistance to crack propagation due to a stress-induced phase transformation. For both 3YSZ and 8YSZ, the tensile strengths are lower than the bending strength. The difference in the effective volume is responsible for those differences. © 2003 Elsevier B.V. All rights reserved. Keywords: Elasticity (D); Strain; High pressure (E); Scanning and transmission electron microscopy (C); Ionic conduction (D)
1. Introduction Because Yttria-stabilized Zirconia (YSZ) has excellent properties as both functional and structural ceramics, its application has been significantly promoted. In particular zirconia stabilized with 2–4 mol % of Y2 O3 has been used as a structural material due to the incomparably high fracture toughness derived from the stress-induced phase transformation (SIPT). Zirconia stabilized with 8 mol % of Y2 O3 is used as a solid electrolyte due to its high ionic conductivity. In all applications of stabilized zirconia, the mechanical properties are also an important factor, and the fracture strength is the most basic property that is indispensable to make the appropriate design of the device components. Generally, three- and four-point bending tests have been performed on ceramics, especially on YSZ, for examining the strength [1–9]. The results of the fracture strength obtained from these tests, however, is not useful for understanding the mechanisms of strengthening and deformation. For the bending specimen, the stress gradient is formed and the stress is not applied in the single-axial direction. Thus, the strength should be obtained through the tensile test. It ∗ Corresponding author. Tel.: +81-749-28-8393; fax: +81-749-28-8483. E-mail address: [email protected] (J. Kondoh).
0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00640-6
is, however, markedly difficult to perform the tensile test for ceramics because of the difficulty in aligning the specimen [10,11], and as a result, the tensile strengths and the isothermal Young’s modulus of YSZ are rarely reported [11–13]. In particular, although the adiabatic (dynamic) Young’s modulus was reported for some YSZ [14], the Y2 O3 concentration dependence of the tensile strength and the isothermal Young’s modulus over a wide dopant concentration range has not yet been established at all. In the present study, tensile test is performed using ZrO2 polycrystals stabilized with 2.6–10 mol % Y2 O3 . For the same materials, bending test, determination of isothermal (static) Young’s modulus and fracture toughness, and observation of the fracture surface have been carried out. Based on these experimental results, the Y2 O3 concentration dependence of the tensile strength and its difference from that of the bending strength are discussed.
2. Experimental procedure 2.1. Materials Y2 O3 stabilized ZrO2 polycrystals with the following compositions were used in the present study: 2.6 mol % Y2 O3 –97.4 mol % ZrO2 (called 2.6YSZ hereinafter,
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J. Kondoh et al. / Journal of Alloys and Compounds 365 (2004) 253–258
Table 1 Details of sintered specimens Sample (Supplier)
Supplier ID
Grain size (m)
Sintering temperature (K)
Sintered density (g/cm3 )
2.6YSZ (Daiichi Kigenso) 3YSZ (Daiichi Kigenso) 4YSZ (Daiichi Kigenso) 8YSZ (Daiichi Kigenso) 10YSZ (Daiichi Kigenso)
HSY-2.6 HSY-3 HSY-4 HSY-8 HSY-10
0.40 0.42 0.46 5.0 5.0
1723 1723 1723 1723 1723
6.02 6.04 6.02 5.94 5.96
HSY-2.6 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), 3 mol % Y2 O3 –97 mol % ZrO2 (3YSZ, HSY-3 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), 4 mol % Y2 O3 –96 mol % ZrO2 (4YSZ, HSY-4 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), 8 mol % Y2 O3 –92 mol % ZrO2 (8YSZ, HSY-8 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), and 10 mol % Y2 O3 –90 mol % ZrO2 (10YSZ, HSY-10 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.). Table 1 shows sintering temperature, density, and grain size of each material. 2.2. Evaluation of mechanical properties Fig. 1 shows the shape and dimensions of the tensile specimens used in the present study. A closed-loop-type hydraulic system was employed for loading in the tensile test. The tensile test was carried out under atmospheric pressure in air at room temperature, and the stress rate was 2 GPa/s. In all tests, strain gauges were directly attached to both sides of the specimen in order to measure the strain during the tensile test and to examine the bending component of the strain accompanying the tensile loading. The bending component was always below 5% of the average strain. Based on the results of the tensile test, isothermal (static) Young’s modulus was determined by analyzing the relationship between the nominal stress and strain. The four-point bending test was conducted by employing test fixtures with an inner span of 10 mm and an outer span of 30 mm at the loading rate of about 1.3 kN/s using the closed-loop-type hydraulic system. The bending specimen is a prismatic beam, 4 and 3 mm in width and height, respectively.
Fig. 1. The shape and dimensions of the tensile specimen.
The tensile and bending fracture strengths of 3YSZ and 8YSZ were plotted on Weibull probability paper. The cumulative probabilities of fracture, F, were calculated by the median-rank method [15]. The fracture toughness was determined using two methods; one is the micro-indentation method through equations developed by Niihara et al. [16], and the other is the analytical solution calculated from the size of preexistent defect and the tensile fracture stress [17]. The fracture surfaces of the specimens after tensile test were examined by scanning electron microscopy (SEM: JSM-T20, JEOL Co. Ltd., Akishima, Japan).
3. Results In the present study, all the stress–strain relationships obtained from the tensile test indicated the linear relationship till fracture. Some literature sources reported that the inelastic deformation occurred in stabilized zirconia under tensile loading at room temperature [18–20]. This difference is attributed to the difference in internal friction due to the difference in the stress rate. Fig. 2 shows the Y2 O3 concentration dependence of isothermal (static) Young’s modulus determined from the stress–strain response. There was no significant difference in Young’s modulus for all the specimens. Fig. 3 shows the tensile strength versus Y2 O3 concentration. The tensile strengths of the partially stabilized zirconia (PSZ) (2.6YSZ, 3YSZ, and 4YSZ) were significantly higher than those of the fully stabilized zirconia (FSZ) (8YSZ and 10YSZ). As shown in Fig. 4, the bending strength of 3YSZ was also higher than that of 8YSZ. As is generally recognized, the tensile strength was lower than the bending strength in both 3YSZ and 8YSZ. For 3YSZ, the bending strength was about 1.5 times as high as the tensile strength, though the difference was very small for 8YSZ. The tensile and bending strengths of 3YSZ and 8YSZ plotted on a Weibull probability paper are shown in Fig. 5. Distributions of both strengths in both materials were expressed by the two-parameter Weibull distribution. The shape parameters for the bending strengths of 3YSZ and 8YSZ obtained from the regression method are 6.8 and 8.2, respectively. Those for the tensile strengths of 3YSZ and 8YSZ are 6.8 and 9.8, respectively. Because the difference in the strength between the two kinds of tests can be explained through the con-
J. Kondoh et al. / Journal of Alloys and Compounds 365 (2004) 253–258
Fig. 2. The Y2 O3 concentration dependence of isothermal (static) Young’s modulus.
cept of the effective volume [21,22], the tensile strength can be deduced from the bending strength using the following equation: m σt 2 = ; (1) σb 3 (m + 1) where σ t and σ b are the tensile and bending strengths, respectively, and m is the shape parameter of the Weibull distribution. σ b and m obtained from the bending tests are
Fig. 3. The Y2 O3 concentration dependence of the tensile strength.
255
Fig. 4. The tensile and bending strengths of 3YSZ and 8YSZ.
substituted into Eq. (1) so that σ t is obtained relative to each σ b . The cumulative probability of fracture (F) and m for the deduced tensile strength are necessarily the same as those for the bending strength. As indicated in Fig. 5, in both 3YSZ and 8YSZ, all of the tensile strengths deduced from the bending strength almost coincide with experimental results of the tensile strength.
Fig. 5. The Weibull plots of the tensile and bending strengths (䊊䊉: 3YSZ, 䉱: 8YSZ). The open symbols indicate the bending strengths, and the closed symbols the tensile strengths. ——— indicates the fitted lines for the experimental results, — — — and – • – • – indicate the tensile strengths deduced from the bending strengths of 3YSZ and 8YSZ, respectively.
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Fig. 7. The Y2 O3 concentration dependence of the fracture toughness. The open and closed symbols show the fracture toughness obtained by the microindentation method and calculated from the diameter of the void and the tensile strength, respectively.
Fig. 6. SEM micrographs of the fracture origins on the fracture surfaces: (a) 3YSZ; and (b) 10YSZ.
Fig. 6a, b indicates typical fractographs after the tensile tests. For about 70% of the tensile specimens, it was observed that the fracture was initiated from the voids inside specimens. However, for the rest of the specimens, mainly for 4YSZ and 8YSZ, the origin of the crack was difficult to identify. The average diameters of the voids, which were observed as the fracture origin in respective specimens, were 65 m for 2YSZ, 85 m for 3YSZ, and 87 m for 10YSZ. The diameter was determined by the following method; first by assuming that the void was an ellipse, then the area was determined, and next the diameter of a circle that has the same area as the ellipse was determined. Fig. 7 shows the fracture toughness plotted versus the Y2 O3 concentration. Fracture toughness of PSZ was much higher than that of FSZ, which was independent of the method.
4. Discussion There was no significant difference in isothermal Young’s modulus between all the specimens. The size of the fracture origin, or voids, was not so dependent on the yttria concentration. Because the stress–strain relationships preserved the linear relationship until fracture in all specimens, the plastic deformation did not macroscopically occur till fracture. Ac-
cording to Griffith’s theoretical interpretation of the fracture strength, the stress under which the crack begins to propagate must be proportional and inversely proportional to the square root of Young’s modulus and the square root of the diameter of the void, respectively, based on the assumption that the surface energy is independent of the composition [23]. Therefore, if the surface energy of YSZ does not depend on the yttria concentration, for YSZ, the stress under which the crack begins to propagate must be almost constant in the yttria concentration range of 2.6–10 mol %. Therefore, in brittle materials, without the mechanism of the increase in the resistance to the crack propagation, the fracture strength of YSZ must be almost independent of the yttria concentration. Generally, the surface energies of polycrystalline materials at high temperatures are determined using the multi-phase equilibration technique and some experimental results for stabilized zirconia at high temperatures have already been reported [24,25]. The contact angle, the groove angle, and the dihedral angle must be measured for determining the surface energy [24,25]. Though this method is sensitive to the values of the groove and dihedral angles [24,25], these angles can be considered to be almost constant in the dopant concentration range of the present study, also at room temperature. This is due to the fact that the differences in these angles of stabilized zirconia with the changes in the temperature and the compositions are very small and these angles are necessarily the average values subjected to a statistical processing in polycrystals. On the
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other hand, in general, the contact angle shows significant difference with the change in the temperature and the composition [24–26]. However, it is reported that of YSZ is almost constant at a high temperature regardless of the crystal structure and the composition [26]. In fact, even at room temperature, it can be considered that the surface energy of YSZ is almost constant between 2.4 and 10 mol % Y2 O3 in comparison with the other factors. Thus, the intrinsic fracture strength should almost be the same in all the compositions in the present study. Nevertheless, PSZ showed a much higher experimental tensile strength than FSZ. Because isothermal Young’s modulus does not depend on the yttria concentration, the difference in the tensile strength means the difference in the strain at fracture. Larger strain, in other words higher ductility, in PSZ is partially attributed to the fact that PSZ consists of finer grains. According to a review by Rice [27], we can estimate that the fracture strength of YSZ whose grain size is 0.5 m is 20% higher that that of YSZ whose grain size is 4 m. Because the tensile strength of 3YSZ is 2.3 times as high as that of 8YSZ, the effect of grain size on the difference in the tensile strength is comparably slight. As recognized from the results of the fracture toughness in Fig. 7, PSZ has a higher resistance to the crack propagation than FSZ. It is generally accepted that the expansion in front and around the neighborhood of the crack tip due to SIPT from the tetragonal phase to the monoclinic phase takes place in PSZ [28–31]. On the other hand, such a transformation does not occur in FSZ. In principle, because the stress gradient does not exist in the tensile specimen and the stress is constant at any point on the fracture surface, the entire fracture surface must be almost instantaneously formed. Actually, as shown in Fig. 6, even in the tensile test, the crack originates in the void and is propagated to the surface of the specimen, resulting in the fracture. The fracture toughness of 3YSZ, determined by the latter method, is about 2.3 times as high as that of 10YSZ, while the tensile strength of 3YSZ is about 2.6 times as high as that of 10YSZ. Therefore, the increase in the resistance to the crack propagation due to SIPT is responsible mainly for the higher tensile strength of PSZ. Therefore, when isothermal Young’s modulus, the diameter of the void, and the surface energy are independent of the yttria concentration, the higher the resistance to the crack propagation, the higher the tensile strength. Because the phases after the occurrence of SIPT are different from those before loading, the tensile strength of PSZ does not express the inherent fracture strength before applying the stress to the specimen. The bending strength of PSZ is also much higher than that of FSZ, which is due to the same reason as the tensile strength. However, as shown in Fig. 4, the bending strength has a much larger difference between PSZ and FSZ than the tensile strength. According to Fig. 5, in both 3YSZ and 8YSZ, the difference in fracture strength between tensile and bending strengths is attributed to the fact that the effective
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volume of the tensile specimen is larger than that of the bending specimen.
5. Summary The tensile and bending tests were performed using ZrO2 polycrystals stabilized with 2.6–10 mol % Y2 O3 . For the same materials, the determination of isothermal (static) Young’s modulus and the fracture toughness utilizing the results of the tensile test and observation of the fracture surface were carried out. The fracture toughness was also determined by the micro-indentation method. The tensile strengths of PSZ (2.6YSZ, 3YSZ, and 4YSZ) are markedly higher than those of FSZ (8YSZ and 10YSZ). The bending strength of PSZ (3YSZ) is also much higher than that of FSZ (8YSZ). The tensile strength is lower than the bending strength in both 3YSZ and 8YSZ, and the difference between the two kinds of strengths is much larger in 3YSZ than in 8YSZ. In both 3YSZ and 8YSZ, the difference in the effective volume is responsible for the difference between tensile and bending strengths. The size of the fracture origin is not so dependent on the yttria concentration. There is no significant difference in the Young’s modulus of all the specimens. Therefore, the difference in the tensile strength means the difference in the strain at fracture. Larger strain in PSZ is partially attributed to the fact that PSZ consists of finer grains. The fracture toughness of PSZ is much higher than that of FSZ and independent of the method. It is concluded that the higher tensile strength of PSZ is mainly due to the fact that the tensile strength of PSZ reflects the increase in the resistance to the crack propagation due to SIPT.
Acknowledgements The authors gratefully acknowledge the experimental support and fruitful suggestions for the tensile test by Professor Shiomi Kikuchi of the University of Shiga Prefecture.
References [1] K. Kobayashi, H. Kuwajima, T. Masaki, Solid State Ionics 3–4 (1981) 489. [2] K. Tsukuma, K. Ueda, M. Shimada, J. Am. Ceram. Soc. 68 (1) (1985) C4. [3] K. Tsukuma, M. Shimada, Am. Ceram. Bull. 64 (2) (1985) 310. [4] K. Tsukuma, Y. Kubota, K. Nobugai, Yogyo-Kyokai-Shi 92 (5) (1984) 11. [5] T. Masaki, J. Am. Ceram. Soc. 69 (8) (1986) 638. [6] T. Masaki, K. Sinjo, Ceram. Int. 13 (1987) 109. [7] K. Tsukuma, T. Takahata, M. Shiomi, in: S. Somiya, N. Yamamoto, H. Yanagida (Eds.), Science and Technology of Zirconia III, Advances in Ceramics, Vol. 24, The American Ceramics Society, Columbus, OH, 1988, pp. 721–728. [8] T. Masaki, K. Shinjo, S. Somiya N. Yamamoto H. Yanagida (Eds.), Science and Technology of Zirconia III, Advances in Ceramics
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J. Kondoh et al. / Journal of Alloys and Compounds 365 (2004) 253–258 Vol. 24 (1988) 709–720The American Ceramics SocietyColumbus, OH. K. Tsukuma, Y. Kubota, T. Tsukidate, in: N. Claussen, M. Ruhle (Eds.), Science and Technology of Zirconia II, Advances in Ceramics, Vol. 12, The American Ceramics Society, Columbus, OH, 1984, pp. 382–390. L.W. Stephens, M.V. Swain, in: R.C. Bradt, A.G. Evans, D.B.H. Hasselman, F.F. Lange (Eds.), Fracture Mechanics of Ceramics, Vol. 8, Plenum Press, New York, 1986, pp. 163–173. K. Noguchi, M. Fujita, T. Masaki, M. Mizushina, J. Am. Ceram. Soc. 72 (7) (1989) 1305. K. Matsusue, Y. Fujisawa, K. Takahara, Yogyo-Kyokai-Shi 91 (1) (1983) 59. K. Noguchi, Y. Matsuda, M. Oishi, T. Masaki, S. Nakayama, M. Mizushina, J. Am. Ceram. Soc. 73 (9) (1990) 2667. M. Shimada, K. Matsushita, S. Kuratani, T. Okamoto, K. Tsukuma, T. Tsukidate, J. Am. Ceram. Soc. 67 (2) (1984) C23. J.D. Sullivan, P.H. Lauzon, J. Mater. Sci. Lett. 5 (1986) 1245. K. Niihara, R. Morena, D.P.H. Hasselman, J. Mater. Sci. Lett. 1 (1) (1982) 13.
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Yttria concentration dependence of tensile strength in yttria-stabilized zirconia Junya Kondoh a,∗ , Hirohisa Shiota b , Katsuhiro Kawachi c , Toshio Nakatani c a Department of Materials Science, The University of Shiga Prefecture, 2500 Hassaka-cho, Hikone 522-8533, Japan Department of Mechanical Systems and Engineering, Faculty of Engineering, Gifu University, 1-1 Yanagido, Gifu 501-1193, Japan Technical Research and Development Division, Daiichi Kigenso Kagaku Kogyo Co. Ltd., 1-6-38 Hirabayashiminami, Suminoe-Ku, Osaka 559-0025, Japan b
c
Received 6 May 2003; received in revised form 2 June 2003; accepted 2 June 2003
Abstract Tensile and bending tests were performed for ZrO2 polycrystals stabilized with 2.6–10 mol % Y2 O3 . There is no significant difference in the isothermal Young’s modulus of all the compositions. Both the tensile and bending strengths of PSZ are markedly higher than those of FSZ. This is mainly due to the fact that both strengths of PSZ reflect the increase in the resistance to crack propagation due to a stress-induced phase transformation. For both 3YSZ and 8YSZ, the tensile strengths are lower than the bending strength. The difference in the effective volume is responsible for those differences. © 2003 Elsevier B.V. All rights reserved. Keywords: Elasticity (D); Strain; High pressure (E); Scanning and transmission electron microscopy (C); Ionic conduction (D)
1. Introduction Because Yttria-stabilized Zirconia (YSZ) has excellent properties as both functional and structural ceramics, its application has been significantly promoted. In particular zirconia stabilized with 2–4 mol % of Y2 O3 has been used as a structural material due to the incomparably high fracture toughness derived from the stress-induced phase transformation (SIPT). Zirconia stabilized with 8 mol % of Y2 O3 is used as a solid electrolyte due to its high ionic conductivity. In all applications of stabilized zirconia, the mechanical properties are also an important factor, and the fracture strength is the most basic property that is indispensable to make the appropriate design of the device components. Generally, three- and four-point bending tests have been performed on ceramics, especially on YSZ, for examining the strength [1–9]. The results of the fracture strength obtained from these tests, however, is not useful for understanding the mechanisms of strengthening and deformation. For the bending specimen, the stress gradient is formed and the stress is not applied in the single-axial direction. Thus, the strength should be obtained through the tensile test. It ∗ Corresponding author. Tel.: +81-749-28-8393; fax: +81-749-28-8483. E-mail address: [email protected] (J. Kondoh).
0925-8388/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-8388(03)00640-6
is, however, markedly difficult to perform the tensile test for ceramics because of the difficulty in aligning the specimen [10,11], and as a result, the tensile strengths and the isothermal Young’s modulus of YSZ are rarely reported [11–13]. In particular, although the adiabatic (dynamic) Young’s modulus was reported for some YSZ [14], the Y2 O3 concentration dependence of the tensile strength and the isothermal Young’s modulus over a wide dopant concentration range has not yet been established at all. In the present study, tensile test is performed using ZrO2 polycrystals stabilized with 2.6–10 mol % Y2 O3 . For the same materials, bending test, determination of isothermal (static) Young’s modulus and fracture toughness, and observation of the fracture surface have been carried out. Based on these experimental results, the Y2 O3 concentration dependence of the tensile strength and its difference from that of the bending strength are discussed.
2. Experimental procedure 2.1. Materials Y2 O3 stabilized ZrO2 polycrystals with the following compositions were used in the present study: 2.6 mol % Y2 O3 –97.4 mol % ZrO2 (called 2.6YSZ hereinafter,
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J. Kondoh et al. / Journal of Alloys and Compounds 365 (2004) 253–258
Table 1 Details of sintered specimens Sample (Supplier)
Supplier ID
Grain size (m)
Sintering temperature (K)
Sintered density (g/cm3 )
2.6YSZ (Daiichi Kigenso) 3YSZ (Daiichi Kigenso) 4YSZ (Daiichi Kigenso) 8YSZ (Daiichi Kigenso) 10YSZ (Daiichi Kigenso)
HSY-2.6 HSY-3 HSY-4 HSY-8 HSY-10
0.40 0.42 0.46 5.0 5.0
1723 1723 1723 1723 1723
6.02 6.04 6.02 5.94 5.96
HSY-2.6 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), 3 mol % Y2 O3 –97 mol % ZrO2 (3YSZ, HSY-3 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), 4 mol % Y2 O3 –96 mol % ZrO2 (4YSZ, HSY-4 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), 8 mol % Y2 O3 –92 mol % ZrO2 (8YSZ, HSY-8 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.), and 10 mol % Y2 O3 –90 mol % ZrO2 (10YSZ, HSY-10 made by Diichi Kigenso Kagaku Kogyo Co. Ltd.). Table 1 shows sintering temperature, density, and grain size of each material. 2.2. Evaluation of mechanical properties Fig. 1 shows the shape and dimensions of the tensile specimens used in the present study. A closed-loop-type hydraulic system was employed for loading in the tensile test. The tensile test was carried out under atmospheric pressure in air at room temperature, and the stress rate was 2 GPa/s. In all tests, strain gauges were directly attached to both sides of the specimen in order to measure the strain during the tensile test and to examine the bending component of the strain accompanying the tensile loading. The bending component was always below 5% of the average strain. Based on the results of the tensile test, isothermal (static) Young’s modulus was determined by analyzing the relationship between the nominal stress and strain. The four-point bending test was conducted by employing test fixtures with an inner span of 10 mm and an outer span of 30 mm at the loading rate of about 1.3 kN/s using the closed-loop-type hydraulic system. The bending specimen is a prismatic beam, 4 and 3 mm in width and height, respectively.
Fig. 1. The shape and dimensions of the tensile specimen.
The tensile and bending fracture strengths of 3YSZ and 8YSZ were plotted on Weibull probability paper. The cumulative probabilities of fracture, F, were calculated by the median-rank method [15]. The fracture toughness was determined using two methods; one is the micro-indentation method through equations developed by Niihara et al. [16], and the other is the analytical solution calculated from the size of preexistent defect and the tensile fracture stress [17]. The fracture surfaces of the specimens after tensile test were examined by scanning electron microscopy (SEM: JSM-T20, JEOL Co. Ltd., Akishima, Japan).
3. Results In the present study, all the stress–strain relationships obtained from the tensile test indicated the linear relationship till fracture. Some literature sources reported that the inelastic deformation occurred in stabilized zirconia under tensile loading at room temperature [18–20]. This difference is attributed to the difference in internal friction due to the difference in the stress rate. Fig. 2 shows the Y2 O3 concentration dependence of isothermal (static) Young’s modulus determined from the stress–strain response. There was no significant difference in Young’s modulus for all the specimens. Fig. 3 shows the tensile strength versus Y2 O3 concentration. The tensile strengths of the partially stabilized zirconia (PSZ) (2.6YSZ, 3YSZ, and 4YSZ) were significantly higher than those of the fully stabilized zirconia (FSZ) (8YSZ and 10YSZ). As shown in Fig. 4, the bending strength of 3YSZ was also higher than that of 8YSZ. As is generally recognized, the tensile strength was lower than the bending strength in both 3YSZ and 8YSZ. For 3YSZ, the bending strength was about 1.5 times as high as the tensile strength, though the difference was very small for 8YSZ. The tensile and bending strengths of 3YSZ and 8YSZ plotted on a Weibull probability paper are shown in Fig. 5. Distributions of both strengths in both materials were expressed by the two-parameter Weibull distribution. The shape parameters for the bending strengths of 3YSZ and 8YSZ obtained from the regression method are 6.8 and 8.2, respectively. Those for the tensile strengths of 3YSZ and 8YSZ are 6.8 and 9.8, respectively. Because the difference in the strength between the two kinds of tests can be explained through the con-
J. Kondoh et al. / Journal of Alloys and Compounds 365 (2004) 253–258
Fig. 2. The Y2 O3 concentration dependence of isothermal (static) Young’s modulus.
cept of the effective volume [21,22], the tensile strength can be deduced from the bending strength using the following equation: m σt 2 = ; (1) σb 3 (m + 1) where σ t and σ b are the tensile and bending strengths, respectively, and m is the shape parameter of the Weibull distribution. σ b and m obtained from the bending tests are
Fig. 3. The Y2 O3 concentration dependence of the tensile strength.
255
Fig. 4. The tensile and bending strengths of 3YSZ and 8YSZ.
substituted into Eq. (1) so that σ t is obtained relative to each σ b . The cumulative probability of fracture (F) and m for the deduced tensile strength are necessarily the same as those for the bending strength. As indicated in Fig. 5, in both 3YSZ and 8YSZ, all of the tensile strengths deduced from the bending strength almost coincide with experimental results of the tensile strength.
Fig. 5. The Weibull plots of the tensile and bending strengths (䊊䊉: 3YSZ, 䉱: 8YSZ). The open symbols indicate the bending strengths, and the closed symbols the tensile strengths. ——— indicates the fitted lines for the experimental results, — — — and – • – • – indicate the tensile strengths deduced from the bending strengths of 3YSZ and 8YSZ, respectively.
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Fig. 7. The Y2 O3 concentration dependence of the fracture toughness. The open and closed symbols show the fracture toughness obtained by the microindentation method and calculated from the diameter of the void and the tensile strength, respectively.
Fig. 6. SEM micrographs of the fracture origins on the fracture surfaces: (a) 3YSZ; and (b) 10YSZ.
Fig. 6a, b indicates typical fractographs after the tensile tests. For about 70% of the tensile specimens, it was observed that the fracture was initiated from the voids inside specimens. However, for the rest of the specimens, mainly for 4YSZ and 8YSZ, the origin of the crack was difficult to identify. The average diameters of the voids, which were observed as the fracture origin in respective specimens, were 65 m for 2YSZ, 85 m for 3YSZ, and 87 m for 10YSZ. The diameter was determined by the following method; first by assuming that the void was an ellipse, then the area was determined, and next the diameter of a circle that has the same area as the ellipse was determined. Fig. 7 shows the fracture toughness plotted versus the Y2 O3 concentration. Fracture toughness of PSZ was much higher than that of FSZ, which was independent of the method.
4. Discussion There was no significant difference in isothermal Young’s modulus between all the specimens. The size of the fracture origin, or voids, was not so dependent on the yttria concentration. Because the stress–strain relationships preserved the linear relationship until fracture in all specimens, the plastic deformation did not macroscopically occur till fracture. Ac-
cording to Griffith’s theoretical interpretation of the fracture strength, the stress under which the crack begins to propagate must be proportional and inversely proportional to the square root of Young’s modulus and the square root of the diameter of the void, respectively, based on the assumption that the surface energy is independent of the composition [23]. Therefore, if the surface energy of YSZ does not depend on the yttria concentration, for YSZ, the stress under which the crack begins to propagate must be almost constant in the yttria concentration range of 2.6–10 mol %. Therefore, in brittle materials, without the mechanism of the increase in the resistance to the crack propagation, the fracture strength of YSZ must be almost independent of the yttria concentration. Generally, the surface energies of polycrystalline materials at high temperatures are determined using the multi-phase equilibration technique and some experimental results for stabilized zirconia at high temperatures have already been reported [24,25]. The contact angle, the groove angle, and the dihedral angle must be measured for determining the surface energy [24,25]. Though this method is sensitive to the values of the groove and dihedral angles [24,25], these angles can be considered to be almost constant in the dopant concentration range of the present study, also at room temperature. This is due to the fact that the differences in these angles of stabilized zirconia with the changes in the temperature and the compositions are very small and these angles are necessarily the average values subjected to a statistical processing in polycrystals. On the
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other hand, in general, the contact angle shows significant difference with the change in the temperature and the composition [24–26]. However, it is reported that of YSZ is almost constant at a high temperature regardless of the crystal structure and the composition [26]. In fact, even at room temperature, it can be considered that the surface energy of YSZ is almost constant between 2.4 and 10 mol % Y2 O3 in comparison with the other factors. Thus, the intrinsic fracture strength should almost be the same in all the compositions in the present study. Nevertheless, PSZ showed a much higher experimental tensile strength than FSZ. Because isothermal Young’s modulus does not depend on the yttria concentration, the difference in the tensile strength means the difference in the strain at fracture. Larger strain, in other words higher ductility, in PSZ is partially attributed to the fact that PSZ consists of finer grains. According to a review by Rice [27], we can estimate that the fracture strength of YSZ whose grain size is 0.5 m is 20% higher that that of YSZ whose grain size is 4 m. Because the tensile strength of 3YSZ is 2.3 times as high as that of 8YSZ, the effect of grain size on the difference in the tensile strength is comparably slight. As recognized from the results of the fracture toughness in Fig. 7, PSZ has a higher resistance to the crack propagation than FSZ. It is generally accepted that the expansion in front and around the neighborhood of the crack tip due to SIPT from the tetragonal phase to the monoclinic phase takes place in PSZ [28–31]. On the other hand, such a transformation does not occur in FSZ. In principle, because the stress gradient does not exist in the tensile specimen and the stress is constant at any point on the fracture surface, the entire fracture surface must be almost instantaneously formed. Actually, as shown in Fig. 6, even in the tensile test, the crack originates in the void and is propagated to the surface of the specimen, resulting in the fracture. The fracture toughness of 3YSZ, determined by the latter method, is about 2.3 times as high as that of 10YSZ, while the tensile strength of 3YSZ is about 2.6 times as high as that of 10YSZ. Therefore, the increase in the resistance to the crack propagation due to SIPT is responsible mainly for the higher tensile strength of PSZ. Therefore, when isothermal Young’s modulus, the diameter of the void, and the surface energy are independent of the yttria concentration, the higher the resistance to the crack propagation, the higher the tensile strength. Because the phases after the occurrence of SIPT are different from those before loading, the tensile strength of PSZ does not express the inherent fracture strength before applying the stress to the specimen. The bending strength of PSZ is also much higher than that of FSZ, which is due to the same reason as the tensile strength. However, as shown in Fig. 4, the bending strength has a much larger difference between PSZ and FSZ than the tensile strength. According to Fig. 5, in both 3YSZ and 8YSZ, the difference in fracture strength between tensile and bending strengths is attributed to the fact that the effective
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volume of the tensile specimen is larger than that of the bending specimen.
5. Summary The tensile and bending tests were performed using ZrO2 polycrystals stabilized with 2.6–10 mol % Y2 O3 . For the same materials, the determination of isothermal (static) Young’s modulus and the fracture toughness utilizing the results of the tensile test and observation of the fracture surface were carried out. The fracture toughness was also determined by the micro-indentation method. The tensile strengths of PSZ (2.6YSZ, 3YSZ, and 4YSZ) are markedly higher than those of FSZ (8YSZ and 10YSZ). The bending strength of PSZ (3YSZ) is also much higher than that of FSZ (8YSZ). The tensile strength is lower than the bending strength in both 3YSZ and 8YSZ, and the difference between the two kinds of strengths is much larger in 3YSZ than in 8YSZ. In both 3YSZ and 8YSZ, the difference in the effective volume is responsible for the difference between tensile and bending strengths. The size of the fracture origin is not so dependent on the yttria concentration. There is no significant difference in the Young’s modulus of all the specimens. Therefore, the difference in the tensile strength means the difference in the strain at fracture. Larger strain in PSZ is partially attributed to the fact that PSZ consists of finer grains. The fracture toughness of PSZ is much higher than that of FSZ and independent of the method. It is concluded that the higher tensile strength of PSZ is mainly due to the fact that the tensile strength of PSZ reflects the increase in the resistance to the crack propagation due to SIPT.
Acknowledgements The authors gratefully acknowledge the experimental support and fruitful suggestions for the tensile test by Professor Shiomi Kikuchi of the University of Shiga Prefecture.
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