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Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method
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ARTICLE IN PRESS
JECS-11295; No. of Pages 4
Journal of the European Ceramic Society xxx (2017) xxx–xxx
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Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method a ˛ Agnieszka Wojteczko a,∗ , Guillaume Petaud a,b , Radosław Lach a , Zbigniew Pedzich a AGH − University of Science and Technology, Faculty of Materials Science and Ceramics, Department of Ceramics and Refractory Materials, Mickiewicza 30, 30-059 Krakow, Poland b ENSCI- Ecole Nationale Supérieure de Céramique Industrielle, University of Limoges, 12 street Atlantis, 87000 Limoges, France
a r t i c l e
i n f o
Article history: Received 21 December 2016 Received in revised form 21 May 2017 Accepted 22 May 2017 Available online xxx Keywords: Tetragonal zirconia Lifetime prediction Subcritical crack growth Constant stress rate test Biaxial loading
a b s t r a c t Subcritical crack growth is a phenomenon which limits service time of a ceramic material. It is especially prevalent for oxides, because this phenomenon is attributed to the activity of water at the crack tip of the material and can be caused even by water present as a humidity in the air (Salem and Jenkins, 2002; Michalske and Freiman, 1983). It is very important to determine its lifetime at the setting loads with high probabilities of survival. The Constant Stress Rate method gives results that are sufficient for lifetime predictions. Estimations are based on n parameter which results from the slope of the strength vs. stress rate dependence. Only a conversion from dynamic to static conditions has to be done (Wojteczko et al., 2016). The attempts were made at different stress rates on sintered samples with pre-existing flaws and in two environments − air and water. Tetragonal zirconia was the tested material. Biaxial loading method was used for strength measurements. Microstructural and fractographic observations were made using the scanning electron microscope. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction The Constant Stress Rate test [4] is an efficient method for the determination of subcritical crack growth parameters and lifetime predictions. However, strength measurements of ceramics usually lead to the results with large scattering [1–3,5–9]. This is an effect of flaw distribution. Eventually, this brings to fluctuations in lifetime estimations. To reduce this variability, the use of a larger amount of measuring points (stress rates) or more samples is required. It may cause a considerable extension of the experiment time. The Standard for the Constant Stress Rate test [4] suggests using ten samples per each stress rate and at least four stress rates. However, the tests show that using at least thirty samples at each measuring point gives satisfying statistical confidence [8,10]. What is more, it is no longer necessary to use many stress rates. Testing at only two extreme stress rates seems to be sufficient. Intermediate stress rates may be used for confirmation that the fitting has been made correctly [11]. The calculations made on the basis of the given results allowed the authors to obtain n parameter, which is crucial for the determination of the subcritical crack growth susceptibility determination.
∗ Corresponding author. E-mail address: [email protected] (A. Wojteczko).
One fitting line for strength measurements is used to designate only one value of n, while a three-step run of the crack velocity versus stress intensity factor dependence is known from the direct methods [12–15]. Nevertheless, for lifetime predictions, a simplified form of the v vs. KI run (Fig. 1) is sufficient, so only one n value is used= for calculations [9]. Many structural ceramic components are used under static loadings, while these tests are made under dynamic conditions (stress rates). The presented recalculations (1, 2) are used to estimate the lifetime (t) and strength () [3,9]: tf,static =
tf,dynamic
(1)
(n + 1)
f,static = f,dynamic ·
t
f,static
t
1n
(2)
2. Experiment The tests were conducted on tetragonal zirconia (TOSOH, TZ-3Y) sintered bodies (1 h at 1500 ◦ C). Apparent density of specimens was measured by means of the Archimedean method and related to the theoretical value dtheoretical = 6.10 g/cm3 . The mechanical treatment of the sample surface might introduce flaws which could affect a mechanical test. Testing of materials with pre-existing flaws seems to be more reasonable. Therefore, biaxial strength tests were con-
http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048 0955-2219/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
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ARTICLE IN PRESS A. Wojteczko et al. / Journal of the European Ceramic Society xxx (2017) xxx–xxx
2
Fig. 1. Simplified form of the crack velocity vs. stress intensity factor dependence.
Fig. 2. A plot presenting the influence of the stress rate on the flexural strength of tetragonal zironia in air [17].
ducted on as sintered (not polished) samples. The experiment was carried out using the piston-on-three-balls method [16] in two environments- experiment in water, which was an extension of tests conducted in air (40–50% of humidity) [17]. The temperature of both environments was 20 ◦ C. Four different stress rates of 0.1, 1, 10 and 200 MPa/s were used in air and for water two stress rates of the highest range (0.1 and 200 MPa/s) were used and one stress rate in between (10 MPa/s) for the confirmation. Fracture toughness was obtained in three-point bending of beams with notches, according to the Standard [18]. To ensure that slow and fast cracking takes place in the same manner, two samples were prepared and observed with Nova Nano SEM 200 scanning electron microscope. In the case of the first sample, the crack was introduced only by Vickers indentation (3 kg of loading). In the second one, the crack was extended using static loading. It was calculated that during this experiment the crack grew with the velocity of ∼10−9 m/s, which could be recognized as a slow cracking. Fig. 3. A plot presenting the influence of the stress rate on the flexural strength of tetragonal zironia in water.
3. Results The sintered samples were highly densified to the level of 99.96 ± 0.1%. Fracture toughness of the presented material was 6.01 ± 1.14 MPa·m1/2 . To describe the subcritical crack growth phenomenon determination of the inert strength is unavoidable. Inert strength is considered to be free of corrosive factor influence. In this case, the higher stress rate for the air conditions was recognized as fast enough to prevent water migration to the crack tip. The mean value of this strength was used for calculations. The obtained disc-shaped samples were of a diameter of about 12 mm and thickness of 1.2 mm. As it was mentioned before, the specimens strength was tested under several stress rates and in two environments. The results were presented in Figs. 2 and 3. In both presented environments the increase of strength for the increasing stress rate was distinct. Moreover, there was a strength reduction for the material tested in water in comparison to the one tested in air. It means that the amount of water from the air (air humidity) was clearly not as harmful as it was in the case of immersion in water. The slope of the fitting lines in Figs. 2 and 3 was used for determination of the n parameter for both environments (Table 1) using Eq. (3). The differences between the obtained values are negligible.
Table 1 Values of n parameter for air and water environment. Environment
n parameter [−]
Air Water
28.30 (23.88–34.66) 30.15 (26.04–35.74)
This indicates that n parameter, which is a measure of subcritical crack growth susceptibility, is not environmentally dependent. log f =
1 log ˙ + log D n+1
(3)
Two SEM images, presenting cracks obtained during fast growth (Fig. 4) and slow growth (Fig. 5), were compared. It allowed the authors to get confidence that both types of cracking run with the same manner and even in the case of slow propagation, grain boundaries (where the presence of the glassy phase could be expected) did not represent the only way for a crack to extend. The strength − probability − time diagrams were made on the basis of the obtained strength results and n parameters, assuming that crack is under stage I (Fig. 1). These parameters do not differ significantly, so in both environments, the change of the predicted strength between very short loading (1 s) and longer ones (1 day,
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
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Fig. 6. Strength − probability − time diagram for zirconia loaded in air.
Fig. 4. SEM image of a crack obtained in fast cracking.
Fig. 7. Strength − probability − time diagram for zirconia loaded in water.
Fig. 5. SEM image of a crack obtained in slow cracking (∼10−9 m/s).
month, year) is similar. However, the decrease of strength in water is significant in comparison to air (Figs. 6 and 7). 4. Conclusions The presented experiment was performed on the assumption that the lifetime estimation, based on the simplified form of the v vs. KI run, is possible and sufficient. Using different stress rates allowed the authors to evaluate weakening of the tested material by the phenomenon of the subcritical crack propagation. The tests showed that the n parameter was not distinctly dependent upon the environment. However, a significant strength decrease of zirconia tested in water was noticed. This decrease could be also explained by the low temperature degradation (LTD) phenomenon, but its designation, by checking the crystalline phases before and after the strength tests, would not give unambiguous results due to the phase transformation during stress occurrence while material is
cracking. Results lead to the assumption that it did not affected the n parameter significantly. The observations of cracks evoked in a different manner, imitating conditions of a fast and slow cracking indicated that in both cases crack paths went in a similar way. Two crack observations were compared to assess the nature of fast and slow propagation. It could be expected for a slow crack propagation that the crack path went along the grain boundaries. Microscopic observations showed that there was no difference in the manner of cracking for both cases. Cracking occurred across grains as well as along grains boundaries. The strength − probability − time diagrams seem to give useful information about structural ceramic components that are vulnerable to the subcritical crack propagation. Most of them are used in a long-time service, so the estimation of strength under given conditions is important. Even though this method is used to obtain results for dynamic loading, using the presented calculations (1, 2) allows us to predict material behaviour under static conditions.
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
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ARTICLE IN PRESS A. Wojteczko et al. / Journal of the European Ceramic Society xxx (2017) xxx–xxx
4
Acknowledgements The work was supported by the Polish State Ministry of Science and Higher Education under AGH University work no. 11.11.160.617 and the Polish Ceramic Society. References [1] J.A. Salem, M.G. Jenkins, The effect of stress rate on slow crack growth parameter estimates, in: Fracture Resistance Testing of Monolithic and Composite Brittle Materials, ASTM STP 1409, American Society for Testing and Materials, 2002, pp. 213–227. [2] T.A. Michalske, S.W. Freiman, A molecular mechanism for stress corrosion in vitreous silica, J. Am. Ceram. Soc. 66 (4) (1983) 284–288. ˛ [3] A. Wojteczko, R. Lach, K. Wojteczko, Z. Pedzich, Investigations of the subcritical crack growth phenomenon and the estimation of lifetime of alumina and alumina-zirconia composites with different phase arrangements, Ceramics Int. 42 (2016) 9438–9442. [4] ASTM Standard, C1368-06, Standard Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Flexural Testing at Ambient Temperature. [5] J.A. Griggs, S.M. Alaqeel, Y. Zhang, A.W. Miller, Z. Cai, Effects of stress rate and calculation method on subcritical crack growth parameters deduced from constant stress-rate flexural testing, Dental Mater. 27 (2011) 364–370. [6] B. Taskonak, J.A. Griggs, J.J. Mecholsky, J.H. Yan, Analysis of subcritical crack growth in dental ceramics using fracture mechanics and fractography, Dental Mater. 24 (2008) 700–707. [7] R. Bermejo, P. Supancic, C. Krautgasser, R. Morrell, R. Danzer, Subcritical crack growth in low temperature co-fired ceramics under biaxial loading, Eng. Fract. Mech. 100 (2013) 108–121.
[8] M. Cheng, W. Chen, Measurement and determination of dynamic biaxial flexural strength of thin ceramic substrates under high stress-rate loading, Int. J. Mech. Sci. 47 (2005) 1212–1223. [9] J.B. Wachtman, W.R. Cannon, M.J. Matthewson, Subcritical Crack Propagation, Mechanical Properties of Ceramics, second edition, John Wiley & Sons, 2009. [10] ASTM C1161-02c, Standard Test Method for Flexural Strength of Advances Ceramics at Ambient Temperature, 2017. [11] J.I. McCool, Statistical error in crack growth parameters deduced from dynamic fatigue tests, Int. J. Fatigue 26 (2004) 1207–1215. [12] S.M. Wiederhorn, Subcritical crack growth of ceramics, Fract. Mech. Ceram. 2 (1974) 613–646. [13] A.H. DeAza, J. Chevalier, G. Fantozzi, M. Schehl, R. Torrecillas, Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses, Biomaterials 23 (2002) 937–945. [14] M.E. Ebrahimi, J. Chevalier, G. Fantozzi, Slow crack growth behavior of alumina ceramics, J. Mater. Res. 15 (2000) 142–147. ˛ [15] Z. Pedzich, Sub-critical crack propagation in particulate composites with Y-TZP matrix, Compos. Theory Pract. 5 (2005) 86–90. [16] ASTM F394-78, Test Method for Biaxial Flexure Strength (Modulus of Rupture) of Ceramic Substrates, 1996. ˛ [17] A. Wojteczko, R. Lach, K. Wojteczko, P. Rutkowski, D. Zientara, Z. Pedzich, Subcritical crack growth in oxide and non-oxide ceramics using the Constant Stress Rate Test, Process. Appl. Ceram. 9 (4) (2015) 187–191. [18] ASTM Standard, C1421-16 Standard Test Methods for Determination of Fracture Toughness of Advanced Ceramics at Ambient Temperature, 2017.
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
ARTICLE IN PRESS
JECS-11295; No. of Pages 4
Journal of the European Ceramic Society xxx (2017) xxx–xxx
Contents lists available at www.sciencedirect.com
Journal of the European Ceramic Society journal homepage: www.elsevier.com/locate/jeurceramsoc
Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method a ˛ Agnieszka Wojteczko a,∗ , Guillaume Petaud a,b , Radosław Lach a , Zbigniew Pedzich a AGH − University of Science and Technology, Faculty of Materials Science and Ceramics, Department of Ceramics and Refractory Materials, Mickiewicza 30, 30-059 Krakow, Poland b ENSCI- Ecole Nationale Supérieure de Céramique Industrielle, University of Limoges, 12 street Atlantis, 87000 Limoges, France
a r t i c l e
i n f o
Article history: Received 21 December 2016 Received in revised form 21 May 2017 Accepted 22 May 2017 Available online xxx Keywords: Tetragonal zirconia Lifetime prediction Subcritical crack growth Constant stress rate test Biaxial loading
a b s t r a c t Subcritical crack growth is a phenomenon which limits service time of a ceramic material. It is especially prevalent for oxides, because this phenomenon is attributed to the activity of water at the crack tip of the material and can be caused even by water present as a humidity in the air (Salem and Jenkins, 2002; Michalske and Freiman, 1983). It is very important to determine its lifetime at the setting loads with high probabilities of survival. The Constant Stress Rate method gives results that are sufficient for lifetime predictions. Estimations are based on n parameter which results from the slope of the strength vs. stress rate dependence. Only a conversion from dynamic to static conditions has to be done (Wojteczko et al., 2016). The attempts were made at different stress rates on sintered samples with pre-existing flaws and in two environments − air and water. Tetragonal zirconia was the tested material. Biaxial loading method was used for strength measurements. Microstructural and fractographic observations were made using the scanning electron microscope. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction The Constant Stress Rate test [4] is an efficient method for the determination of subcritical crack growth parameters and lifetime predictions. However, strength measurements of ceramics usually lead to the results with large scattering [1–3,5–9]. This is an effect of flaw distribution. Eventually, this brings to fluctuations in lifetime estimations. To reduce this variability, the use of a larger amount of measuring points (stress rates) or more samples is required. It may cause a considerable extension of the experiment time. The Standard for the Constant Stress Rate test [4] suggests using ten samples per each stress rate and at least four stress rates. However, the tests show that using at least thirty samples at each measuring point gives satisfying statistical confidence [8,10]. What is more, it is no longer necessary to use many stress rates. Testing at only two extreme stress rates seems to be sufficient. Intermediate stress rates may be used for confirmation that the fitting has been made correctly [11]. The calculations made on the basis of the given results allowed the authors to obtain n parameter, which is crucial for the determination of the subcritical crack growth susceptibility determination.
∗ Corresponding author. E-mail address: [email protected] (A. Wojteczko).
One fitting line for strength measurements is used to designate only one value of n, while a three-step run of the crack velocity versus stress intensity factor dependence is known from the direct methods [12–15]. Nevertheless, for lifetime predictions, a simplified form of the v vs. KI run (Fig. 1) is sufficient, so only one n value is used= for calculations [9]. Many structural ceramic components are used under static loadings, while these tests are made under dynamic conditions (stress rates). The presented recalculations (1, 2) are used to estimate the lifetime (t) and strength () [3,9]: tf,static =
tf,dynamic
(1)
(n + 1)
f,static = f,dynamic ·
t
f,static
t
1n
(2)
2. Experiment The tests were conducted on tetragonal zirconia (TOSOH, TZ-3Y) sintered bodies (1 h at 1500 ◦ C). Apparent density of specimens was measured by means of the Archimedean method and related to the theoretical value dtheoretical = 6.10 g/cm3 . The mechanical treatment of the sample surface might introduce flaws which could affect a mechanical test. Testing of materials with pre-existing flaws seems to be more reasonable. Therefore, biaxial strength tests were con-
http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048 0955-2219/© 2017 Elsevier Ltd. All rights reserved.
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
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ARTICLE IN PRESS A. Wojteczko et al. / Journal of the European Ceramic Society xxx (2017) xxx–xxx
2
Fig. 1. Simplified form of the crack velocity vs. stress intensity factor dependence.
Fig. 2. A plot presenting the influence of the stress rate on the flexural strength of tetragonal zironia in air [17].
ducted on as sintered (not polished) samples. The experiment was carried out using the piston-on-three-balls method [16] in two environments- experiment in water, which was an extension of tests conducted in air (40–50% of humidity) [17]. The temperature of both environments was 20 ◦ C. Four different stress rates of 0.1, 1, 10 and 200 MPa/s were used in air and for water two stress rates of the highest range (0.1 and 200 MPa/s) were used and one stress rate in between (10 MPa/s) for the confirmation. Fracture toughness was obtained in three-point bending of beams with notches, according to the Standard [18]. To ensure that slow and fast cracking takes place in the same manner, two samples were prepared and observed with Nova Nano SEM 200 scanning electron microscope. In the case of the first sample, the crack was introduced only by Vickers indentation (3 kg of loading). In the second one, the crack was extended using static loading. It was calculated that during this experiment the crack grew with the velocity of ∼10−9 m/s, which could be recognized as a slow cracking. Fig. 3. A plot presenting the influence of the stress rate on the flexural strength of tetragonal zironia in water.
3. Results The sintered samples were highly densified to the level of 99.96 ± 0.1%. Fracture toughness of the presented material was 6.01 ± 1.14 MPa·m1/2 . To describe the subcritical crack growth phenomenon determination of the inert strength is unavoidable. Inert strength is considered to be free of corrosive factor influence. In this case, the higher stress rate for the air conditions was recognized as fast enough to prevent water migration to the crack tip. The mean value of this strength was used for calculations. The obtained disc-shaped samples were of a diameter of about 12 mm and thickness of 1.2 mm. As it was mentioned before, the specimens strength was tested under several stress rates and in two environments. The results were presented in Figs. 2 and 3. In both presented environments the increase of strength for the increasing stress rate was distinct. Moreover, there was a strength reduction for the material tested in water in comparison to the one tested in air. It means that the amount of water from the air (air humidity) was clearly not as harmful as it was in the case of immersion in water. The slope of the fitting lines in Figs. 2 and 3 was used for determination of the n parameter for both environments (Table 1) using Eq. (3). The differences between the obtained values are negligible.
Table 1 Values of n parameter for air and water environment. Environment
n parameter [−]
Air Water
28.30 (23.88–34.66) 30.15 (26.04–35.74)
This indicates that n parameter, which is a measure of subcritical crack growth susceptibility, is not environmentally dependent. log f =
1 log ˙ + log D n+1
(3)
Two SEM images, presenting cracks obtained during fast growth (Fig. 4) and slow growth (Fig. 5), were compared. It allowed the authors to get confidence that both types of cracking run with the same manner and even in the case of slow propagation, grain boundaries (where the presence of the glassy phase could be expected) did not represent the only way for a crack to extend. The strength − probability − time diagrams were made on the basis of the obtained strength results and n parameters, assuming that crack is under stage I (Fig. 1). These parameters do not differ significantly, so in both environments, the change of the predicted strength between very short loading (1 s) and longer ones (1 day,
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
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Fig. 6. Strength − probability − time diagram for zirconia loaded in air.
Fig. 4. SEM image of a crack obtained in fast cracking.
Fig. 7. Strength − probability − time diagram for zirconia loaded in water.
Fig. 5. SEM image of a crack obtained in slow cracking (∼10−9 m/s).
month, year) is similar. However, the decrease of strength in water is significant in comparison to air (Figs. 6 and 7). 4. Conclusions The presented experiment was performed on the assumption that the lifetime estimation, based on the simplified form of the v vs. KI run, is possible and sufficient. Using different stress rates allowed the authors to evaluate weakening of the tested material by the phenomenon of the subcritical crack propagation. The tests showed that the n parameter was not distinctly dependent upon the environment. However, a significant strength decrease of zirconia tested in water was noticed. This decrease could be also explained by the low temperature degradation (LTD) phenomenon, but its designation, by checking the crystalline phases before and after the strength tests, would not give unambiguous results due to the phase transformation during stress occurrence while material is
cracking. Results lead to the assumption that it did not affected the n parameter significantly. The observations of cracks evoked in a different manner, imitating conditions of a fast and slow cracking indicated that in both cases crack paths went in a similar way. Two crack observations were compared to assess the nature of fast and slow propagation. It could be expected for a slow crack propagation that the crack path went along the grain boundaries. Microscopic observations showed that there was no difference in the manner of cracking for both cases. Cracking occurred across grains as well as along grains boundaries. The strength − probability − time diagrams seem to give useful information about structural ceramic components that are vulnerable to the subcritical crack propagation. Most of them are used in a long-time service, so the estimation of strength under given conditions is important. Even though this method is used to obtain results for dynamic loading, using the presented calculations (1, 2) allows us to predict material behaviour under static conditions.
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048
G Model JECS-11295; No. of Pages 4
ARTICLE IN PRESS A. Wojteczko et al. / Journal of the European Ceramic Society xxx (2017) xxx–xxx
4
Acknowledgements The work was supported by the Polish State Ministry of Science and Higher Education under AGH University work no. 11.11.160.617 and the Polish Ceramic Society. References [1] J.A. Salem, M.G. Jenkins, The effect of stress rate on slow crack growth parameter estimates, in: Fracture Resistance Testing of Monolithic and Composite Brittle Materials, ASTM STP 1409, American Society for Testing and Materials, 2002, pp. 213–227. [2] T.A. Michalske, S.W. Freiman, A molecular mechanism for stress corrosion in vitreous silica, J. Am. Ceram. Soc. 66 (4) (1983) 284–288. ˛ [3] A. Wojteczko, R. Lach, K. Wojteczko, Z. Pedzich, Investigations of the subcritical crack growth phenomenon and the estimation of lifetime of alumina and alumina-zirconia composites with different phase arrangements, Ceramics Int. 42 (2016) 9438–9442. [4] ASTM Standard, C1368-06, Standard Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Flexural Testing at Ambient Temperature. [5] J.A. Griggs, S.M. Alaqeel, Y. Zhang, A.W. Miller, Z. Cai, Effects of stress rate and calculation method on subcritical crack growth parameters deduced from constant stress-rate flexural testing, Dental Mater. 27 (2011) 364–370. [6] B. Taskonak, J.A. Griggs, J.J. Mecholsky, J.H. Yan, Analysis of subcritical crack growth in dental ceramics using fracture mechanics and fractography, Dental Mater. 24 (2008) 700–707. [7] R. Bermejo, P. Supancic, C. Krautgasser, R. Morrell, R. Danzer, Subcritical crack growth in low temperature co-fired ceramics under biaxial loading, Eng. Fract. Mech. 100 (2013) 108–121.
[8] M. Cheng, W. Chen, Measurement and determination of dynamic biaxial flexural strength of thin ceramic substrates under high stress-rate loading, Int. J. Mech. Sci. 47 (2005) 1212–1223. [9] J.B. Wachtman, W.R. Cannon, M.J. Matthewson, Subcritical Crack Propagation, Mechanical Properties of Ceramics, second edition, John Wiley & Sons, 2009. [10] ASTM C1161-02c, Standard Test Method for Flexural Strength of Advances Ceramics at Ambient Temperature, 2017. [11] J.I. McCool, Statistical error in crack growth parameters deduced from dynamic fatigue tests, Int. J. Fatigue 26 (2004) 1207–1215. [12] S.M. Wiederhorn, Subcritical crack growth of ceramics, Fract. Mech. Ceram. 2 (1974) 613–646. [13] A.H. DeAza, J. Chevalier, G. Fantozzi, M. Schehl, R. Torrecillas, Crack growth resistance of alumina, zirconia and zirconia toughened alumina ceramics for joint prostheses, Biomaterials 23 (2002) 937–945. [14] M.E. Ebrahimi, J. Chevalier, G. Fantozzi, Slow crack growth behavior of alumina ceramics, J. Mater. Res. 15 (2000) 142–147. ˛ [15] Z. Pedzich, Sub-critical crack propagation in particulate composites with Y-TZP matrix, Compos. Theory Pract. 5 (2005) 86–90. [16] ASTM F394-78, Test Method for Biaxial Flexure Strength (Modulus of Rupture) of Ceramic Substrates, 1996. ˛ [17] A. Wojteczko, R. Lach, K. Wojteczko, P. Rutkowski, D. Zientara, Z. Pedzich, Subcritical crack growth in oxide and non-oxide ceramics using the Constant Stress Rate Test, Process. Appl. Ceram. 9 (4) (2015) 187–191. [18] ASTM Standard, C1421-16 Standard Test Methods for Determination of Fracture Toughness of Advanced Ceramics at Ambient Temperature, 2017.
Please cite this article in press as: A. Wojteczko, et al., Lifetime determination of tetragonal zirconia under static loading using the Constant Stress Rate method, J Eur Ceram Soc (2017), http://dx.doi.org/10.1016/j.jeurceramsoc.2017.05.048