- Email: [email protected]
SANS investigations of pore anisotropy in superplastically deformed ceramics
ARTICLE IN PRESS
Physica B 350 (2004) e1019–e1022
SANS investigations of pore anisotropy in superplastically deformed ceramics a $ Vasyl Ryukhtina,b,*, Jan Saroun , Stefanus Harjoc, Yoshinobu Motohashic, Albrecht Wiedenmannd, Pavel Strunza,e a $ near Prague, Czech Republic Nuclear Physics Institute, 25068 Rem Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Praha 2, Czech Republic c Ibaraki University, Faculty of Engineering, Research Center for Superplasticity, Hitachi, Ibaraki 316-8511, Japan d Hahn-Meitner-Institut (HMI), Glienicker Str. 100, 14109 Berlin, Germany e Paul Scherrer Institute, 5232 Villigen PSI, Switzerland b
Abstract Superplastically deformed samples of 3 mol% yttria stabilized tetragonal zirconia polycrystals (3Y-TZP) and 3YTZP with 20 wt% of Al2O3 were studied by SANS with the aim to compare cavitation behaviours under different deformation conditions. Though the average size of cavities formed during deformation is so large that they can be measured only by high-resolution SANS techniques, conventional SANS method permitted us to measure their specific surface and aspect ratio quite effectively. Analysis of the two-dimentional SANS data clearly showed two qualitatively different cavitation regimes corresponding to the low-stress (low-strain rate and high-temperature) and high-stress conditions, respectively. In the latter case, a new type of flat pores transversal to the tension axis was observed, in addition to the usually present slightly prolate cavities. r 2004 Elsevier B.V. All rights reserved. PACS: 68.55; 61.45 Keywords: Small-angle neutron scattering; Tetragonal zirconia polycrystals; Superplastic ceramics; Cavitation
1. Introduction Evolution of cavities during superplastic deformations of ceramics is closely related to the physical mechanisms, which can control the $ near *Corresponding author. Nuclear Physics Institute, Rem Prague 25068, Czech Republic. Tel.: +420-266-173-140; fax: +420-220-940-141. E-mail address: [email protected] (V. Ryukhtin).
deformation process [1]. Measurements of these cavities (e.g. size distribution, volume fraction, etc.), therefore, help to understand these mechanisms and consequently to find the deformation conditions (temperature, strain rate), grain size or material composition, which should be optimal for plastic working. Small-angle neutron scattering (SANS) method is particularly a suitable method for this purpose and has been used in our earlier work [2] to study cavitation behaviour in 3 mol%
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.280
ARTICLE IN PRESS V. Ryukhtin et al. / Physica B 350 (2004) e1019–e1022
e1020
yttria stabilized tetragonal zirconia polycrystals (3Y-TZP) deformed under proper superplastic conditions (low-strain rate, high temperature), which lead to relatively low volume fractions of cavities, slightly elongated mostly parallel to the tension axis. In this work, we have studied the cavitation also under higher strain rate and lower temperature, where the deformation behaviour is qualitatively different. For sufficiently low applied stress, s; the strain rate e; is proportional to sn with the exponent nB3: Owen and Chokshi [3] demonstrated, that this exponent changes to nB2 if certain limits given by temperature, grain size and applied stress are exceeded. They interpreted this transition by the change in dominant deformation mechanism from a process controlled by interfacial reactions ðnB3Þ to the grain boundary sliding ðnB2Þ: SANS results presented in this paper show that these two regimes may be connected with qualitatively different cavitation behaviour.
resolution and multiple scattering effects. Nevertheless, the two-dimensional patterns of scattered intensity permitted us to study the changes in anisotropy of the cavities, which was the primary aim of this experiment. Since the scattering length density of 3Y-TZP and alumina differ by less than 2%, we could interpret all results assuming a two-phase model consisting of homogeneous matrix and cavities.
3. Results and discussion SANS data were fitted using SASPROFIT program [4] based on the indirect Fourier transform method [5] with free size distribution of ellipsoidal particles. For the samples deformed at low-stress conditions (L1, L2), a simple model of prolate ellipsoids (aspect ratio n > 1) oriented parallel to the stress direction was sufficient to describe observed anisotropy. However, scattering patterns of H1 and H2 samples were more complicated (see Fig. 1) and a second type of ellipsoidal particles with no1 had to be considered. Due to the Porod behaviour of scattering, the only relevant parameters were specific surfaces and
2. Experimental Test pieces of a 3Y-TZP and a 3Y-TZP with 20 wt% of Al2O3 were deformed in tension up to more than 100% at the both low-stress (L1, L2) and high-stress (H1, H2) conditions (see Table 1). SANS measurements were carried out at V4 instrument (HMI, Berlin) using the wavelength ( and detector distances of 16 and 4 m, l ¼ 6A covering thus the range of momentum transfers Q, from 0.05 to 0.8 nm1. Even at the highest resolution, the |Q|-dependence of the scattering functions obeyed the asymptotic (Porod) law except for minor deviations near the beam centre due to instrument
Fig. 1. SANS patterns with fitted model (dashed lines) for samples deformed under low (L1) and high stresses (H1).
Table 1 Samples description, e denotes initial strain rate in 104 s1, d is the mean grain size in mm, r is density in g cm3 Label
T (K)
d
r
e
Composition
L1 L2 H1 H2
1723 1723 1623 1723
0.39 0.77 0.39 0.39
6.05 5.47 6.05 6.05
3.3 3.3 3.3 67
3Y-TZP 3Y-TZP+20 wt%Al2O3 3Y-TZP 3Y-TZP
ARTICLE IN PRESS V. Ryukhtin et al. / Physica B 350 (2004) e1019–e1022
Fig. 2. Specific surface of cavities obtained from SANS.
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elongated 3Y-TZP by Wang et al. [6]. Model calculations show that SANS is very sensitive to such cracks and can reveal their presence even at initial stages of deformation, although they are difficult to be observed by SEM due to low-volume fraction and/or their sizes being too fine to be identified. The different cavitation behaviour is probably related to the transition in eBsn dependence [3,7] mentioned in the Introduction. Mass fraction of cubic phase in the 3Y-TZP varies from (9–10)% (H1, H2) to 12% (L1, L2) due to different sintering temperatures. However, the mean grain size of the cubic phase is only slightly higher than that of the tetragonal one. Therefore the cubic-tetragonal transformation has a negligible effect on the cavitation.
4. Conclusions
Fig. 3. Aspect ratios of ellipsoids determined by data fitting.
aspect ratios, which were fitted as free parameters in both models. The specific surfaces of cavities obtained by SANS are summarized in Fig. 2. Obviously, they increase much faster with applied strain for samples H1 and H2, whereas the samples deformed under low-stress conditions (L1 and L2) behave similarly in spite of different compositions and grain sizes. The different cavitation behaviour of the material deformed under high-stress conditions (H1 and H2) is underlined by higher aspect ratios of the prolate cavities and by the presence of transverse oblate cavities as seen in Fig. 3. The aspect ratios seem to saturate at about 1.2 for very large strains. The oblate particles ðno1Þ were observed only in the samples H1 and H2 and appear even at low deformations (e>20%). They might correspond to the transverse intergranular cracks observed on scanning electron micrographs (SEM) of highly
The SANS measurements show that the cavities in superplastically deformed 3Y-TZP evolve in qualitatively different ways under low-stress and high-stress conditions. In the latter case, a new type of flat pores normal to the tension axis was observed in addition to the usually observed slightly prolate cavities with aspect ratio no1:2: This difference is possibly related to the transition between nB2 and 3 regions of the eBsn dependence [3,7] and corresponding change in deformation mechanism. SANS method has proved to be very sensitive to the detection of such flat pores and permits their observation even at eo20%.
Acknowledgements This work was supported by the Grant Agency of the Czech Republic (No. 202/03/0891) and by the EC IHP Programme No. 445, Access to Research Infrastructures activity.
References [1] Y. Motohashi, N. Sugeno, S. Koyama, T. Sakuma, Mater. Sci. Forum 243–245 (1997) 399.
ARTICLE IN PRESS e1022
V. Ryukhtin et al. / Physica B 350 (2004) e1019–e1022
[2] S. Harjo, N. Kojima, Y. Motohashi, J. Saroun, V. Ryukhtin, P. Strunz, M. Baron, R. Loidl, Mater. Trans. 43 (2002) 2480. [3] D.M. Owen, A.H. Chokshi, Acta Mater. 46 (1998) 667. [4] http://omega.ujf.cas.cz/Bsaroun/SAS/ [5] O. Glatter, Acta Phys. Austral. 47 (1977) 83.
[6] Z.C. Wang, N. Ridley, T.J. Davis, J. Mater. Sci. 34 (1999) 2695. [7] A. Dominguez-Rodriguez, F. Gutierrez-Mora, M. JimenesMelendo, J.L. Routbort, R. Chaim, Mater. Sci. Eng. A 302 (2001) 154.
Physica B 350 (2004) e1019–e1022
SANS investigations of pore anisotropy in superplastically deformed ceramics a $ Vasyl Ryukhtina,b,*, Jan Saroun , Stefanus Harjoc, Yoshinobu Motohashic, Albrecht Wiedenmannd, Pavel Strunza,e a $ near Prague, Czech Republic Nuclear Physics Institute, 25068 Rem Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Praha 2, Czech Republic c Ibaraki University, Faculty of Engineering, Research Center for Superplasticity, Hitachi, Ibaraki 316-8511, Japan d Hahn-Meitner-Institut (HMI), Glienicker Str. 100, 14109 Berlin, Germany e Paul Scherrer Institute, 5232 Villigen PSI, Switzerland b
Abstract Superplastically deformed samples of 3 mol% yttria stabilized tetragonal zirconia polycrystals (3Y-TZP) and 3YTZP with 20 wt% of Al2O3 were studied by SANS with the aim to compare cavitation behaviours under different deformation conditions. Though the average size of cavities formed during deformation is so large that they can be measured only by high-resolution SANS techniques, conventional SANS method permitted us to measure their specific surface and aspect ratio quite effectively. Analysis of the two-dimentional SANS data clearly showed two qualitatively different cavitation regimes corresponding to the low-stress (low-strain rate and high-temperature) and high-stress conditions, respectively. In the latter case, a new type of flat pores transversal to the tension axis was observed, in addition to the usually present slightly prolate cavities. r 2004 Elsevier B.V. All rights reserved. PACS: 68.55; 61.45 Keywords: Small-angle neutron scattering; Tetragonal zirconia polycrystals; Superplastic ceramics; Cavitation
1. Introduction Evolution of cavities during superplastic deformations of ceramics is closely related to the physical mechanisms, which can control the $ near *Corresponding author. Nuclear Physics Institute, Rem Prague 25068, Czech Republic. Tel.: +420-266-173-140; fax: +420-220-940-141. E-mail address: [email protected] (V. Ryukhtin).
deformation process [1]. Measurements of these cavities (e.g. size distribution, volume fraction, etc.), therefore, help to understand these mechanisms and consequently to find the deformation conditions (temperature, strain rate), grain size or material composition, which should be optimal for plastic working. Small-angle neutron scattering (SANS) method is particularly a suitable method for this purpose and has been used in our earlier work [2] to study cavitation behaviour in 3 mol%
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.03.280
ARTICLE IN PRESS V. Ryukhtin et al. / Physica B 350 (2004) e1019–e1022
e1020
yttria stabilized tetragonal zirconia polycrystals (3Y-TZP) deformed under proper superplastic conditions (low-strain rate, high temperature), which lead to relatively low volume fractions of cavities, slightly elongated mostly parallel to the tension axis. In this work, we have studied the cavitation also under higher strain rate and lower temperature, where the deformation behaviour is qualitatively different. For sufficiently low applied stress, s; the strain rate e; is proportional to sn with the exponent nB3: Owen and Chokshi [3] demonstrated, that this exponent changes to nB2 if certain limits given by temperature, grain size and applied stress are exceeded. They interpreted this transition by the change in dominant deformation mechanism from a process controlled by interfacial reactions ðnB3Þ to the grain boundary sliding ðnB2Þ: SANS results presented in this paper show that these two regimes may be connected with qualitatively different cavitation behaviour.
resolution and multiple scattering effects. Nevertheless, the two-dimensional patterns of scattered intensity permitted us to study the changes in anisotropy of the cavities, which was the primary aim of this experiment. Since the scattering length density of 3Y-TZP and alumina differ by less than 2%, we could interpret all results assuming a two-phase model consisting of homogeneous matrix and cavities.
3. Results and discussion SANS data were fitted using SASPROFIT program [4] based on the indirect Fourier transform method [5] with free size distribution of ellipsoidal particles. For the samples deformed at low-stress conditions (L1, L2), a simple model of prolate ellipsoids (aspect ratio n > 1) oriented parallel to the stress direction was sufficient to describe observed anisotropy. However, scattering patterns of H1 and H2 samples were more complicated (see Fig. 1) and a second type of ellipsoidal particles with no1 had to be considered. Due to the Porod behaviour of scattering, the only relevant parameters were specific surfaces and
2. Experimental Test pieces of a 3Y-TZP and a 3Y-TZP with 20 wt% of Al2O3 were deformed in tension up to more than 100% at the both low-stress (L1, L2) and high-stress (H1, H2) conditions (see Table 1). SANS measurements were carried out at V4 instrument (HMI, Berlin) using the wavelength ( and detector distances of 16 and 4 m, l ¼ 6A covering thus the range of momentum transfers Q, from 0.05 to 0.8 nm1. Even at the highest resolution, the |Q|-dependence of the scattering functions obeyed the asymptotic (Porod) law except for minor deviations near the beam centre due to instrument
Fig. 1. SANS patterns with fitted model (dashed lines) for samples deformed under low (L1) and high stresses (H1).
Table 1 Samples description, e denotes initial strain rate in 104 s1, d is the mean grain size in mm, r is density in g cm3 Label
T (K)
d
r
e
Composition
L1 L2 H1 H2
1723 1723 1623 1723
0.39 0.77 0.39 0.39
6.05 5.47 6.05 6.05
3.3 3.3 3.3 67
3Y-TZP 3Y-TZP+20 wt%Al2O3 3Y-TZP 3Y-TZP
ARTICLE IN PRESS V. Ryukhtin et al. / Physica B 350 (2004) e1019–e1022
Fig. 2. Specific surface of cavities obtained from SANS.
e1021
elongated 3Y-TZP by Wang et al. [6]. Model calculations show that SANS is very sensitive to such cracks and can reveal their presence even at initial stages of deformation, although they are difficult to be observed by SEM due to low-volume fraction and/or their sizes being too fine to be identified. The different cavitation behaviour is probably related to the transition in eBsn dependence [3,7] mentioned in the Introduction. Mass fraction of cubic phase in the 3Y-TZP varies from (9–10)% (H1, H2) to 12% (L1, L2) due to different sintering temperatures. However, the mean grain size of the cubic phase is only slightly higher than that of the tetragonal one. Therefore the cubic-tetragonal transformation has a negligible effect on the cavitation.
4. Conclusions
Fig. 3. Aspect ratios of ellipsoids determined by data fitting.
aspect ratios, which were fitted as free parameters in both models. The specific surfaces of cavities obtained by SANS are summarized in Fig. 2. Obviously, they increase much faster with applied strain for samples H1 and H2, whereas the samples deformed under low-stress conditions (L1 and L2) behave similarly in spite of different compositions and grain sizes. The different cavitation behaviour of the material deformed under high-stress conditions (H1 and H2) is underlined by higher aspect ratios of the prolate cavities and by the presence of transverse oblate cavities as seen in Fig. 3. The aspect ratios seem to saturate at about 1.2 for very large strains. The oblate particles ðno1Þ were observed only in the samples H1 and H2 and appear even at low deformations (e>20%). They might correspond to the transverse intergranular cracks observed on scanning electron micrographs (SEM) of highly
The SANS measurements show that the cavities in superplastically deformed 3Y-TZP evolve in qualitatively different ways under low-stress and high-stress conditions. In the latter case, a new type of flat pores normal to the tension axis was observed in addition to the usually observed slightly prolate cavities with aspect ratio no1:2: This difference is possibly related to the transition between nB2 and 3 regions of the eBsn dependence [3,7] and corresponding change in deformation mechanism. SANS method has proved to be very sensitive to the detection of such flat pores and permits their observation even at eo20%.
Acknowledgements This work was supported by the Grant Agency of the Czech Republic (No. 202/03/0891) and by the EC IHP Programme No. 445, Access to Research Infrastructures activity.
References [1] Y. Motohashi, N. Sugeno, S. Koyama, T. Sakuma, Mater. Sci. Forum 243–245 (1997) 399.
ARTICLE IN PRESS e1022
V. Ryukhtin et al. / Physica B 350 (2004) e1019–e1022
[2] S. Harjo, N. Kojima, Y. Motohashi, J. Saroun, V. Ryukhtin, P. Strunz, M. Baron, R. Loidl, Mater. Trans. 43 (2002) 2480. [3] D.M. Owen, A.H. Chokshi, Acta Mater. 46 (1998) 667. [4] http://omega.ujf.cas.cz/Bsaroun/SAS/ [5] O. Glatter, Acta Phys. Austral. 47 (1977) 83.
[6] Z.C. Wang, N. Ridley, T.J. Davis, J. Mater. Sci. 34 (1999) 2695. [7] A. Dominguez-Rodriguez, F. Gutierrez-Mora, M. JimenesMelendo, J.L. Routbort, R. Chaim, Mater. Sci. Eng. A 302 (2001) 154.