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X-ray evaluation of dislocation density in ODS-Eurofer steel
Materials Science and Engineering A 534 (2012) 142–146
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
X-ray evaluation of dislocation density in ODS-Eurofer steel R.A. Renzetti a,∗ , H.R.Z. Sandim a , R.E. Bolmaro b , P.A. Suzuki a , A. Möslang c a
Escola de Engenharia de Lorena, EEL-USP, 12600-970 Lorena, Brazil Instituto de Física Rosario, CONICET-UNR, 2000 Rosario, Argentina c Karlsruher Institut für Technologie (KIT), IMF I, D-72061 Karlsruhe, Germany b
a r t i c l e
i n f o
Article history: Received 17 March 2011 Received in revised form 23 September 2011 Accepted 16 November 2011 Available online 1 December 2011 Keywords: ODS Ferritic–martensitic steels Dislocation density Recovery X-ray diffraction
a b s t r a c t The dislocation density of ferritic–martensitic oxide dispersion strengthened ODS-Eurofer steel was evaluated by using the modified Williamson–Hall method (peak broadening analysis). Measurements were performed in several metallurgical conditions (ferritic and martensitic structures). The monochromatic Xray radiation was provided by a synchrotron source. The results match qualitatively with those provided by Vickers microhardness measurements and metallographic inspection using transmission electron microscopy. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The dislocation density () is a key microstructural parameter since it is strongly related to mechanical properties of metals and alloys. The dislocation density in metals can be significantly changed during plastic straining, thermal annealing or when they undergo phase transformations such as the martensitic transformation found in Fe–C steels. In deformed metals, the stored energy provided by dislocations is the driving force for important solidstate reactions like recovery and recrystallization [1]. Furthermore, the quantitative evaluation of the dislocation density in metals is also very important in the development of theories of plastic deformation [2]. Among the several experimental techniques to evaluate the dislocation density in metals, direct and indirect methods are usually reported including Vickers hardness testing, X-ray diffraction line profile analysis, evaluation of etch pits, transmission electron microscopy (TEM), flow stress, magnetic (coercive field) and electrical resistivity measurements [3]. TEM and X-ray diffraction line profile analysis are the most recommended techniques to quantify the dislocation density, while; for instance, coercive field and resistivity are strongly affected by factors as precipitates and solutes. The choice of the method to evaluate the dislocation density by
∗ Corresponding author. Tel.: +55 12 3159 9959; fax: +55 12 3159 5000. E-mail address: [email protected] (R.A. Renzetti). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.11.051
using X-ray or TEM depends on the magnitude of dislocation density and the nature of the dislocation array. For instance, in severely deformed metals where very high dislocation densities are found in a complex substructure, TEM is less advisable since counting of individual dislocations by using quantitative metallographic methods becomes quite difficult. This difficult can be overcome by using X-ray diffraction. On the other hand, in less deformed metals or in creep-tested specimens, the TEM becomes more reliable than X-ray diffraction since the elastic distortion caused by dislocations in the lattice and consequent peak broadening is very small. Literature reports many methods to quantify the dislocation density from data provided by X-ray diffraction experiments including the modified Williamson–Hall (W–H) and Warren–Averbach (W–A) methods [4–6]. Both methods are based on the broadening analysis of the X-ray diffraction peaks. Despite the second one (W–A) is a more sophisticated and powerful method, W–H analysis is less cumbersome and powerful enough for analyzing cubic material results at the level of accuracy we are currently inspecting our material. In order to extract the sample contribution breadth, the instrumental breadth should be removed from the measured peak [7]. Another factor that must be considered is that the radiation produced in X-ray tubes is not strictly monochromatic, e.g., K␣2 contribution should be removed from the K␣1,2 doublet, by using Rachinger correction. Instead, synchrotron X-ray diffraction can be used as an alternative technique. High brilliance, tunability, and a strictly monochromatic beam are some of the characteristics of this technique.
R.A. Renzetti et al. / Materials Science and Engineering A 534 (2012) 142–146
143
Fig. 1. TEM bright field micrographs showing the microstructure of ODS-Eurofer steel deformed to 80% and annealed at: (a) 800 ◦ C for 1 h; and (b) 1100 ◦ C for 1 h.
Another important advantage over the conventional laboratory X-ray equipments is that the configuration of parallel beam optics reduces the instrumental contribution to peak broadening. In the present work, the dislocation density of 80% cold-rolled ODS-Eurofer steel was evaluated. ODS-Eurofer, an oxide dispersion strengthened reduced-activated ferritic–martensitic steel (ODSRAFM), is a promising candidate for structural applications in future nuclear fusion reactors [8–10]. The thermally stable oxide particles (Y2 O3 – about 10 nm in size) allow increasing the operating temperature [11–13]. As a result, ODS-Eurofer steel has superior creep resistance at high temperatures because nanosized particles are very effective obstacles to moving dislocations and grain boundaries [14–17]. Particle pinning exerts a considerable effect on both recovery and recrystallization processes. As a result, dislocation annihilation and dislocation rearrangement are hindered [16]. Meanwhile, the dislocations generated to compatibilize mismatches between martensite laths are of a different origin and the nature of the arrays should be investigated. A first approach will be the evaluation of dislocation densities as a contribution for further investigation. In order to evaluate the dislocation density, X-ray diffraction using a high-resolution synchrotron radiation source was performed in ODS-Eurofer steel. The modified Williamson–Hall method was applied to evaluate the dislocation density of representative specimens annealed within a wide range of temperatures. Isothermal annealing treatments were performed in both ferrite and austenite phase fields. Besides high-resolution synchrotron X-ray diffraction, TEM and Vickers hardness testing were used to characterize the microstructure.
a monochromatic beam with an energy of 11.013 keV (wavelength, ˚ A Ge (1 1 1) single crystal was used as analyzer crystal = 1.1258 A). in order to improve the resolution to ±5 eV. The data was acquired in a Huber diffractometer equipped with an Eulerian cradle by coupling theta and 2-theta in a conventional powder diffraction configuration. A quick scan was performed for each sample in a large angular interval of 30◦ ≤ 2 ≤ 115◦ , angular steps of 0.02◦ and 1 s counting time. Following, scans on angular intervals of approximately 5◦ were performed around each peak with 0.02◦ angular steps and counting times of up to 40 s. At least 7 individual peaks for each sample were measured. The instrumental broadening was determined and corrected using a LaB6 powder (NIST certified SRM-660a standard). The X-ray diffractograms were evaluated by Profile-Fit 1.0 Program. For X-ray diffraction measurements, 20 × 20 mm2 samples were cut in the rolling plane (TD × RD plane, where TD is the transverse direction) for both rolled and annealed samples. Vacuum annealing was performed at four distinct temperatures, namely 400, 800, 1100 and 1350 ◦ C for 1 h. They were ground to half their thickness, polished and electropolished to remove surface damage. TEM observations were performed namely in RD–TD (rolling plane) sections with an accelerating voltage of 200 kV using a Philips CM30 Microscope. TEM standard 3-mm diameter thin foils were prepared by grinding down to 0.1 mm thickness followed by etching at 12 V in a TenuPol device using 20% H2 SO4 + 80% CH3 OH electrolytic solution. Following, thin foils were cleaned on both sides in an ion milling system for 3 min using a beam of 2.9 keV. 3. Results and discussion
2. Experimental
3.1. Microstructure
The nominal composition of the investigated steel was 9Cr–1W–0.08Ta–0.2V–0.07C–0.4Mn–0.3Y2 O3 (wt.%). The steel in the tempered condition (annealed at 750 ◦ C for 2 h) was cold rolled to 80% thickness reduction in multiple passes. Samples were annealed in vacuum from 300 ◦ C up to 1350 ◦ C for 1 h followed by air cooling. Vickers microhardness testing was performed in cold rolled and annealed conditions using a load of 200 g. For Vickers microhardness testing, the ND × RD plane (where ND is the normal direction and RD is the rolling direction) was mechanically ground by using SiC abrasive papers and a suspension of 0.04 m-diameter colloidal silica particles was used for final polishing. High-resolution synchrotron X-ray diffraction experiments were conducted at Brazilian Synchrotron Light Laboratory (LNLS). The measurements were carried out at D12A-XRD1 beam line using
The softening behavior of 80% cold rolled ODS-Eurofer steel was shown elsewhere [18] (see Fig. 1 in Ref. [18]). For samples annealed below 800 ◦ C the softening experienced by the material is quite small, about 7%. Results concerning the annealing behavior of ODS-Eurofer steel within the ferritic phase field were reported in a previous work [19]. The interaction between Y2 O3 particles, grain boundaries and dislocations is responsible for preventing more pronounced softening. Samples annealed above 900 ◦ C, in the austenitic field, experienced significant hardening after cooling down to room temperature. A martensitic structure was observed even after air cooling, which is known to increase dislocation density and hardness. The amount of strengthening is very small because of the low carbon content in this grade. The values of Vickers microhardness remain almost unchanged up to 1300 ◦ C.
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However, the sample annealed at 1350 ◦ C softens substantially as much as 30%. This feature suggests that pinning of grain boundaries by Y2 O3 particles becomes less effective at this temperature [18]. The high dislocation density in ODS-Eurofer steel, even when annealed at 800 ◦ C for 1 h, is confirmed by TEM observations. Fig. 1a shows the microstructure obtained for the sample annealed at 800 ◦ C for 1 h. Carbide particles, dislocation-free areas and subgrains can be distinguished in the microstructure. Dislocation-free areas are recrystallized regions nucleated at prior grain boundaries or around coarse M23 C6 particles. Contrastingly, TEM investigation of the sample annealed at 1100 ◦ C for 1 h, with subsequent air cooling, shows that the microstructure consists of martensite laths with a high dislocation density (Fig. 1b). 3.2. X-ray diffraction The dislocation density can be measured by X-ray diffraction experiments. The integral breadths of the diffraction profiles were evaluated by a modified Williamson–Hall plot in quadratic form [6]. 1 K ∼ = + d
M 2 b2 2
1/2
2¯
4¯2
(K C) + O(K C )
(1)
where K = 2 sin /, K = 2 cos /, and are the diffraction angle and the integral breadth of the diffraction peak, d is the average grain size, b = 0.25 nm is the Burgers vector and is the dislocation density. M is a constant parameter depending on the effective outer cutoff radius of dislocation and O indicates non-interpreted higher order terms. Previous profuse experience obtained on applying the current technique indicates that M is <1 for annealed materials or for very low energy dislocation arrays like the ones found in fatigued materials (e.g., persistent slip bands). In deformed materials M varies in between 1 and 2 for dislocation densities of 1.0 × 1014 m−2 and 5.0 × 1015 m−2 , respectively [20]. Despite M should be fitted together with the rest of the parameters of the model, given the level of accuracy expected and achievable by the W–H approach, we will use M = 2 for all samples. In fact, more advanced implementations like the extended Convolutional Multiple Whole Profile (eCMWP) could be applied [20]. Individual C values are the average contrast factors of dislocations for each particular reflection. The values of the average contrast factor for different diffraction vectors were defined as:
C = Ch
00
1−q
h2 k2 + h2 l2 + k2 l2 h2 + k2 + l2
(2)
where Ch 0 0 is the average contrast factor corresponding to h 0 0 reflection. Due to the low sensitivity of the analysis to small variations of Ch 0 0 we have chosen Ch 0 0 = 0.332 ± 0.015 obtained from Ungár et al. [4]. The q parameters were determined by minimizing the differences between the measured K values and the calculated ones by linear fitting in Eq. (2). A good fit for all curves was obtained for q = 2.02 ± 0.15. The modified Williamson–Hall plots corresponding to samples in both rolled and annealed conditions (400, 800, 1100 and 1350 ◦ C for 1 h) are shown in Fig. 2. There is apparently a deviation of the (4 0 0) diffraction peak of the material in the rolled condition from the general behavior. It could be due to the presence of texture and it was not taken into account in our calculations. We will get back to this issue in the discussion section. The modified Williamson–Hall plot provides two important microstructural features. The intersection at K = 0 of the linear regression of the curves gives the average grain size, 1/d, or, in an alternative interpretation, any diffraction domain size. Second, the slope of the fitted curve indicates the dislocation density given by = 2m2 /(M2 b2 ) with m is the slope of the linear fits on K2 C variable.
Fig. 2. The modified Williamson–Hall plot of the integral breadth of the diffraction peaks. The Miller indices are indicated in the figure.
The relation between dislocation density and the corresponding annealing behavior can be seen in Fig. 3. The results of X-ray diffraction experiments for ODS-Eurofer steel in the cold rolled condition show a high dislocation density, 8.0 × 1015 m−2 . Upon isothermal annealing in the ferritic phase field both dislocation annihilation and rearrangement become more difficult. This can be observed in the samples annealed at 400 ◦ C and 800 ◦ C where the dislocation density decreases predominantly due to static recovery reactions [18,19]. The dislocation density of the sample annealed at 800 ◦ C is about one quarter of the value obtained for the deformed sample. For samples annealed at 1100 ◦ C and 1350 ◦ C the dislocation density increases. This behavior is correlated with the martensitic transformation experienced by this steel. X-ray diffraction results of ODS-Eurofer steel annealed at 1100 ◦ C for 1 h followed by air cooling are shown in Fig. 4. The Miller indices corresponding to martensite are indicated in the figure. It is worth noticing that diffraction peaks corresponding to retained austenite are also observed in Fig. 4. The dislocation density varies significantly when steels undergo martensitic transformation [21,22]. For 9 wt.%Cr ODS RAFM steel a high density of defects is usually reported in typical martensitic lath structures [23,24]. Different heat treatment conditions are investigated in this steel and austenitization and subsequent tempering
Fig. 3. Dislocation density () as a function of annealing temperature in 80% cold rolled ODS-Eurofer. The result of Vickers microhardness is also included in the figure.
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W–H plot suggests that the real microstructures do not differ only in terms of the values of the dislocation densities but that they are of quite different nature. Because of the martensitic transformation, texture does not change very much. Dislocation storage is quite anisotropic for the rolled sample but not for the martensitic samples, if we observe the behavior of (2 0 0) and (4 0 0) diffraction peaks. They are the ones with the largest mismatch with respect to the quadratic behavior of the W–H plot in the deformed sample but they follow that behavior quite close for the martensitic samples. The peak (4 0 0) was even left out of the fitting procedure to calculate the fit for the rolled sample. The anisotropic storage in the cold-rolled sample is related not merely to the presence of texture but to the deformation process that produced such texture, which is evidenced by the fact that the same texture, persistent after heating and cooling, i.e., after the martensitic transformation, does not store anisotropic dislocation arrays after annealing.
Fig. 4. X-ray diffraction of ODS-Eurofer steel annealed at 1100 ◦ C for 1 h. Arrows mark the peaks corresponding to retained austenite. The Miller indices of martensite are also indicated in the figure.
provide an increase in tensile ductility and impact strength behavior [23]. The dislocation density as a function of carbon content in lath martensite of Fe–C alloys was evaluated by Kehoe and Kelly [22]. They found a dislocation density of about 1.0 × 1015 m−2 in asquenched 0.07 wt.%C steel, the same amount of carbon as in the ODS-Eurofer steel. This value is quite similar to that obtained for ODS-Eurofer steel annealed at 1100 ◦ C for 1 h followed by air cooling, 7.0 × 1015 m−2 . Literature reports only a few papers regarding the evaluation of dislocation density in ferritic–martensitic steels. To the best of our knowledge, dislocation densities were not yet evaluated in ODS ferritic–martensitic steels by X-ray diffraction. In a recent paper, Takebayashi and co-authors reported a value of about 2.0 × 1016 m−2 for an as-quenched 0.3 wt.% C steel with lath martensite structure using the modified Williamson–Hall method whereas a slightly lower value of 6.3 × 1015 m−2 was obtained using the modified Warren–Averbach method [25]. Peˇsiˇcka et al. reported the evolution of dislocation density in two non-ODS ferritic–martensitic steels in creep [26]. TEM and X-ray line profile analysis were used to evaluate the dislocation density. In the steel with the closest composition to ODS-Eurofer steel (7.4 wt.%Cr and 0.075 wt.%C), in the martensitic state, a value of = 4.2 × 1014 m−2 was obtained from XRD measurements. Roy and co-authors [27] reported the evolution of dislocation density in ferritic–martensitic steel (Russian EP-823 grade) containing about 12 wt.%Cr and 0.14 wt.%C during moderate cold working. TEM was used as the analytical tool to determine the dislocation density in quenched and tempered samples deformed to strains up to 11%. The value of dislocation density found for the tempered unstrained condition was 2.6 × 1015 m−2 . After moderate straining, dislocation density increased to about 6.2 × 1016 m−2 . The evolution of the dislocation density upon isothermal annealing of ODS-Eurofer steel resembles the results shown for Vickers microhardness testing [18]. The dislocation density drops during annealing in the ferritic phase field mostly due to static recovery reactions. On the other hand, martensitic transformation leads to the increase of the dislocation density above 7.0 × 1015 m−2 . These values of dislocation density have the same order of magnitude than other reported for steels in the martensitic condition. Dislocation densities are quite high for the deformed sample and for the two samples heat treated at 1100 ◦ C and 1350 ◦ C, with values differing in no more than 25%. The same similarity is revealed by the Vickers microhardness. However, a close inspection at the
4. Summary and conclusions The dislocation density of 80% cold-rolled ODS-Eurofer steel annealed within a wide range of temperatures (300–1350 ◦ C) has been evaluated by X-ray diffraction using the modified Williamson–Hall method. Based on Vickers microhardness values, X-ray profile analysis and TEM observation the following conclusions can be drawn:
1. The values of Vickers microhardness and the dislocation density obtained by the modified Williamson–Hall plot revealed similar trends, i.e., the changes in hardness due to recovery/recrystallization and martensitic transformation are mirrored by values of dislocation densities. 2. The dislocation density of 80% cold-rolled samples is 8.0 × 1015 m−2 . Further annealing within the ferritic phase field where static recovery is the predominant softening mechanism promotes a decrease in the dislocation density to values down to 2.0 × 1015 m−2 . 3. The martensitic transformation introduces a high dislocation density in ODS-Eurofer steel. In addition to the peaks corresponding to martensite, X-ray diffraction shows the presence of retained austenite. The values of the dislocation density found in samples annealed at 1100 ◦ C and 1350 ◦ C for 1 h with subsequent air cooling are, respectively, 7.0 × 1015 and 5.0 × 1015 m−2 . 4. The nature of the dislocation arrays for the cold rolled steel is revealed to be quite different from the martensitic ones. The storage of dislocations is anisotropic in the cold rolled sample, with less dislocations accumulated in crystals with the (2 0 0) direction aligned with the ND. That effect is not visible in the samples developing martensitic lath structures. Because of the many available variants, martensite variant selection and consequent build up of dislocation arrays are isotropic and not dependent on pre-existent texture.
Acknowledgments Authors are grateful to FAPESP (Grants 07/56436-0 and 08/54064-1) for the financial support. Authors are also acknowledged to Dr. R. Lindau (KIT, Karlsruhe) for supplying the samples for this investigation. The kind assistance of Dr. M. Klimenkov (KIT, Karlsruhe) in TEM is also acknowledged. This work is partially supported by Brazilian Synchrotron Light Source Laboratory (LNLS) under Research Proposal Nr. 9761 (2010). Discussions with Prof. T. Ungár were very enlightening.
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References [1] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Elsevier, 2004. [2] G. Gottstein, Physical Foundations of Materials Science, Springer, 2004. [3] R.W. Cahn, P. Haasen, Physical Metallurgy, Elsevier, North-Holland, 1996. [4] T. Ungár, I. Dragomir, Á. Révész, A. Borbély, J. Appl. Crystallogr. 32 (1999) 992–1002. [5] E. Schafler, M. Zehetbauer, T. Ungár, Mater. Sci. Eng. A 319–321 (2001) 220–223. [6] T. Ungar, J. Gubicza, P. Hanak, I. Alexandrov, Mater. Sci. Eng. A 319–321 (2001) 274–278. [7] H.P. Klug, L.E. Alexander, X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials, John Wiley, New York, 1974. [8] R. Lindau, A. Möslang, M. Shiraa, P. Schlossmacher, M. Klimenkov, J. Nucl. Mater. 307–311 (2002) 769–772. [9] R. Lindau, A. Möslang, M. Rieth, M. Klimenkou, E. Materna-Morris, A. Alamo, A.-A.F. Tavassoli, C. Caryon, A.-M. Lancha, P. Fernandez, N. Baluc, R. Schäublin, E. Diegele, G. Filacchioni, J.W. Resman, B.v.d. Schaaf, E. Lucon, W. Dietz, Fusion Eng. Des. 75–79 (2005) 989–996. [10] M. Klimiankou, R. Lindau, A. Möslang, J. Nucl. Mater. 386 (2009) 553–556. [11] M. Klimiankou, R. Lindau, A. Möslang, Micron 36 (2005) 1–8. [12] A. Ramar, N. Baluc, R. Achäublin, J. Nucl. Mater. 367–370 (2007) 217–221.
[13] A. Möslang, C. Adelhelm, R. Heidinger, Int. J. Mater. Res. 99 (2008) 1045–1054. [14] R. Schaeublin, T. Leguey, P. Spätig, N. Baluc, M. Victoria, J. Nucl. Mater. 307–311 (2002) 778–782. [15] E. Arzt, Acta Mater. 46 (1998) 5611–5626. [16] H.K.D.H. Bhadeshia, Mater. Sci. Eng. A 223 (1997) 64–77. [17] H. Sakasegawa, M. Tamura, S. Ohtsuka, S. Ukai, H. Tanigawa, A. Kohyama, M. Fujiwara, J. Alloys Compd. 452 (2008) 2–6. [18] R.A. Renzetti, H.R.Z. Sandim, M.J.R. Sandim, A.D. Santos, A. Möslang, D. Raabe, Mater. Sci. Eng. A 528 (2011) 1442–1447. [19] H.R.Z. Sandim, R.A. Renzetti, A.F. Padilha, D. Raabe, M. Klimenkov, R. Lindau, A. Möslang, Mater. Sci. Eng. A 527 (2010) 3602–3608. [20] G. Ribárik, T. Ungár, Mater. Sci. Eng. A 528 (2010) 112–121. [21] M. Tokizane, N. Matsumura, K. Tsuzaki, T. Maki, I. Tamura, Metall. Trans. A 13A (1982) 1379–1388. [22] M. Kehoe, P.M. Kelly, Scripta Metall. 4 (1970) 473–476. [23] M. Klimiankou, R. Lindau, A. Möslang, J. Nucl. Mater. 367–370 (2007) 173–178. [24] M. Klimiankou, R. Lindau, A. Möslang, J. Cryst. Growth 249 (2003) 381–387. [25] S. Takebayashi, T. Kunieda, N. Yoshinaga, K. Ushioda, S. Ogata, ISIJ Int. 50 (2010) 875–882. [26] J. Peˇsiˇcka, R. Kuˇzel, A. Dronhofer, G. Eggeler, Acta Mater. 51 (2003) 4847–4862. [27] A.K. Roy, S. Bandyopadhyay, S.B. Suresh, D. Maitra, P. Kumar, D. Wells, L. Ma, Mater. Sci. Eng. 416A (2006) 134–138.
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
X-ray evaluation of dislocation density in ODS-Eurofer steel R.A. Renzetti a,∗ , H.R.Z. Sandim a , R.E. Bolmaro b , P.A. Suzuki a , A. Möslang c a
Escola de Engenharia de Lorena, EEL-USP, 12600-970 Lorena, Brazil Instituto de Física Rosario, CONICET-UNR, 2000 Rosario, Argentina c Karlsruher Institut für Technologie (KIT), IMF I, D-72061 Karlsruhe, Germany b
a r t i c l e
i n f o
Article history: Received 17 March 2011 Received in revised form 23 September 2011 Accepted 16 November 2011 Available online 1 December 2011 Keywords: ODS Ferritic–martensitic steels Dislocation density Recovery X-ray diffraction
a b s t r a c t The dislocation density of ferritic–martensitic oxide dispersion strengthened ODS-Eurofer steel was evaluated by using the modified Williamson–Hall method (peak broadening analysis). Measurements were performed in several metallurgical conditions (ferritic and martensitic structures). The monochromatic Xray radiation was provided by a synchrotron source. The results match qualitatively with those provided by Vickers microhardness measurements and metallographic inspection using transmission electron microscopy. © 2011 Elsevier B.V. All rights reserved.
1. Introduction The dislocation density () is a key microstructural parameter since it is strongly related to mechanical properties of metals and alloys. The dislocation density in metals can be significantly changed during plastic straining, thermal annealing or when they undergo phase transformations such as the martensitic transformation found in Fe–C steels. In deformed metals, the stored energy provided by dislocations is the driving force for important solidstate reactions like recovery and recrystallization [1]. Furthermore, the quantitative evaluation of the dislocation density in metals is also very important in the development of theories of plastic deformation [2]. Among the several experimental techniques to evaluate the dislocation density in metals, direct and indirect methods are usually reported including Vickers hardness testing, X-ray diffraction line profile analysis, evaluation of etch pits, transmission electron microscopy (TEM), flow stress, magnetic (coercive field) and electrical resistivity measurements [3]. TEM and X-ray diffraction line profile analysis are the most recommended techniques to quantify the dislocation density, while; for instance, coercive field and resistivity are strongly affected by factors as precipitates and solutes. The choice of the method to evaluate the dislocation density by
∗ Corresponding author. Tel.: +55 12 3159 9959; fax: +55 12 3159 5000. E-mail address: [email protected] (R.A. Renzetti). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.11.051
using X-ray or TEM depends on the magnitude of dislocation density and the nature of the dislocation array. For instance, in severely deformed metals where very high dislocation densities are found in a complex substructure, TEM is less advisable since counting of individual dislocations by using quantitative metallographic methods becomes quite difficult. This difficult can be overcome by using X-ray diffraction. On the other hand, in less deformed metals or in creep-tested specimens, the TEM becomes more reliable than X-ray diffraction since the elastic distortion caused by dislocations in the lattice and consequent peak broadening is very small. Literature reports many methods to quantify the dislocation density from data provided by X-ray diffraction experiments including the modified Williamson–Hall (W–H) and Warren–Averbach (W–A) methods [4–6]. Both methods are based on the broadening analysis of the X-ray diffraction peaks. Despite the second one (W–A) is a more sophisticated and powerful method, W–H analysis is less cumbersome and powerful enough for analyzing cubic material results at the level of accuracy we are currently inspecting our material. In order to extract the sample contribution breadth, the instrumental breadth should be removed from the measured peak [7]. Another factor that must be considered is that the radiation produced in X-ray tubes is not strictly monochromatic, e.g., K␣2 contribution should be removed from the K␣1,2 doublet, by using Rachinger correction. Instead, synchrotron X-ray diffraction can be used as an alternative technique. High brilliance, tunability, and a strictly monochromatic beam are some of the characteristics of this technique.
R.A. Renzetti et al. / Materials Science and Engineering A 534 (2012) 142–146
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Fig. 1. TEM bright field micrographs showing the microstructure of ODS-Eurofer steel deformed to 80% and annealed at: (a) 800 ◦ C for 1 h; and (b) 1100 ◦ C for 1 h.
Another important advantage over the conventional laboratory X-ray equipments is that the configuration of parallel beam optics reduces the instrumental contribution to peak broadening. In the present work, the dislocation density of 80% cold-rolled ODS-Eurofer steel was evaluated. ODS-Eurofer, an oxide dispersion strengthened reduced-activated ferritic–martensitic steel (ODSRAFM), is a promising candidate for structural applications in future nuclear fusion reactors [8–10]. The thermally stable oxide particles (Y2 O3 – about 10 nm in size) allow increasing the operating temperature [11–13]. As a result, ODS-Eurofer steel has superior creep resistance at high temperatures because nanosized particles are very effective obstacles to moving dislocations and grain boundaries [14–17]. Particle pinning exerts a considerable effect on both recovery and recrystallization processes. As a result, dislocation annihilation and dislocation rearrangement are hindered [16]. Meanwhile, the dislocations generated to compatibilize mismatches between martensite laths are of a different origin and the nature of the arrays should be investigated. A first approach will be the evaluation of dislocation densities as a contribution for further investigation. In order to evaluate the dislocation density, X-ray diffraction using a high-resolution synchrotron radiation source was performed in ODS-Eurofer steel. The modified Williamson–Hall method was applied to evaluate the dislocation density of representative specimens annealed within a wide range of temperatures. Isothermal annealing treatments were performed in both ferrite and austenite phase fields. Besides high-resolution synchrotron X-ray diffraction, TEM and Vickers hardness testing were used to characterize the microstructure.
a monochromatic beam with an energy of 11.013 keV (wavelength, ˚ A Ge (1 1 1) single crystal was used as analyzer crystal = 1.1258 A). in order to improve the resolution to ±5 eV. The data was acquired in a Huber diffractometer equipped with an Eulerian cradle by coupling theta and 2-theta in a conventional powder diffraction configuration. A quick scan was performed for each sample in a large angular interval of 30◦ ≤ 2 ≤ 115◦ , angular steps of 0.02◦ and 1 s counting time. Following, scans on angular intervals of approximately 5◦ were performed around each peak with 0.02◦ angular steps and counting times of up to 40 s. At least 7 individual peaks for each sample were measured. The instrumental broadening was determined and corrected using a LaB6 powder (NIST certified SRM-660a standard). The X-ray diffractograms were evaluated by Profile-Fit 1.0 Program. For X-ray diffraction measurements, 20 × 20 mm2 samples were cut in the rolling plane (TD × RD plane, where TD is the transverse direction) for both rolled and annealed samples. Vacuum annealing was performed at four distinct temperatures, namely 400, 800, 1100 and 1350 ◦ C for 1 h. They were ground to half their thickness, polished and electropolished to remove surface damage. TEM observations were performed namely in RD–TD (rolling plane) sections with an accelerating voltage of 200 kV using a Philips CM30 Microscope. TEM standard 3-mm diameter thin foils were prepared by grinding down to 0.1 mm thickness followed by etching at 12 V in a TenuPol device using 20% H2 SO4 + 80% CH3 OH electrolytic solution. Following, thin foils were cleaned on both sides in an ion milling system for 3 min using a beam of 2.9 keV. 3. Results and discussion
2. Experimental
3.1. Microstructure
The nominal composition of the investigated steel was 9Cr–1W–0.08Ta–0.2V–0.07C–0.4Mn–0.3Y2 O3 (wt.%). The steel in the tempered condition (annealed at 750 ◦ C for 2 h) was cold rolled to 80% thickness reduction in multiple passes. Samples were annealed in vacuum from 300 ◦ C up to 1350 ◦ C for 1 h followed by air cooling. Vickers microhardness testing was performed in cold rolled and annealed conditions using a load of 200 g. For Vickers microhardness testing, the ND × RD plane (where ND is the normal direction and RD is the rolling direction) was mechanically ground by using SiC abrasive papers and a suspension of 0.04 m-diameter colloidal silica particles was used for final polishing. High-resolution synchrotron X-ray diffraction experiments were conducted at Brazilian Synchrotron Light Laboratory (LNLS). The measurements were carried out at D12A-XRD1 beam line using
The softening behavior of 80% cold rolled ODS-Eurofer steel was shown elsewhere [18] (see Fig. 1 in Ref. [18]). For samples annealed below 800 ◦ C the softening experienced by the material is quite small, about 7%. Results concerning the annealing behavior of ODS-Eurofer steel within the ferritic phase field were reported in a previous work [19]. The interaction between Y2 O3 particles, grain boundaries and dislocations is responsible for preventing more pronounced softening. Samples annealed above 900 ◦ C, in the austenitic field, experienced significant hardening after cooling down to room temperature. A martensitic structure was observed even after air cooling, which is known to increase dislocation density and hardness. The amount of strengthening is very small because of the low carbon content in this grade. The values of Vickers microhardness remain almost unchanged up to 1300 ◦ C.
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However, the sample annealed at 1350 ◦ C softens substantially as much as 30%. This feature suggests that pinning of grain boundaries by Y2 O3 particles becomes less effective at this temperature [18]. The high dislocation density in ODS-Eurofer steel, even when annealed at 800 ◦ C for 1 h, is confirmed by TEM observations. Fig. 1a shows the microstructure obtained for the sample annealed at 800 ◦ C for 1 h. Carbide particles, dislocation-free areas and subgrains can be distinguished in the microstructure. Dislocation-free areas are recrystallized regions nucleated at prior grain boundaries or around coarse M23 C6 particles. Contrastingly, TEM investigation of the sample annealed at 1100 ◦ C for 1 h, with subsequent air cooling, shows that the microstructure consists of martensite laths with a high dislocation density (Fig. 1b). 3.2. X-ray diffraction The dislocation density can be measured by X-ray diffraction experiments. The integral breadths of the diffraction profiles were evaluated by a modified Williamson–Hall plot in quadratic form [6]. 1 K ∼ = + d
M 2 b2 2
1/2
2¯
4¯2
(K C) + O(K C )
(1)
where K = 2 sin /, K = 2 cos /, and are the diffraction angle and the integral breadth of the diffraction peak, d is the average grain size, b = 0.25 nm is the Burgers vector and is the dislocation density. M is a constant parameter depending on the effective outer cutoff radius of dislocation and O indicates non-interpreted higher order terms. Previous profuse experience obtained on applying the current technique indicates that M is <1 for annealed materials or for very low energy dislocation arrays like the ones found in fatigued materials (e.g., persistent slip bands). In deformed materials M varies in between 1 and 2 for dislocation densities of 1.0 × 1014 m−2 and 5.0 × 1015 m−2 , respectively [20]. Despite M should be fitted together with the rest of the parameters of the model, given the level of accuracy expected and achievable by the W–H approach, we will use M = 2 for all samples. In fact, more advanced implementations like the extended Convolutional Multiple Whole Profile (eCMWP) could be applied [20]. Individual C values are the average contrast factors of dislocations for each particular reflection. The values of the average contrast factor for different diffraction vectors were defined as:
C = Ch
00
1−q
h2 k2 + h2 l2 + k2 l2 h2 + k2 + l2
(2)
where Ch 0 0 is the average contrast factor corresponding to h 0 0 reflection. Due to the low sensitivity of the analysis to small variations of Ch 0 0 we have chosen Ch 0 0 = 0.332 ± 0.015 obtained from Ungár et al. [4]. The q parameters were determined by minimizing the differences between the measured K values and the calculated ones by linear fitting in Eq. (2). A good fit for all curves was obtained for q = 2.02 ± 0.15. The modified Williamson–Hall plots corresponding to samples in both rolled and annealed conditions (400, 800, 1100 and 1350 ◦ C for 1 h) are shown in Fig. 2. There is apparently a deviation of the (4 0 0) diffraction peak of the material in the rolled condition from the general behavior. It could be due to the presence of texture and it was not taken into account in our calculations. We will get back to this issue in the discussion section. The modified Williamson–Hall plot provides two important microstructural features. The intersection at K = 0 of the linear regression of the curves gives the average grain size, 1/d, or, in an alternative interpretation, any diffraction domain size. Second, the slope of the fitted curve indicates the dislocation density given by = 2m2 /(M2 b2 ) with m is the slope of the linear fits on K2 C variable.
Fig. 2. The modified Williamson–Hall plot of the integral breadth of the diffraction peaks. The Miller indices are indicated in the figure.
The relation between dislocation density and the corresponding annealing behavior can be seen in Fig. 3. The results of X-ray diffraction experiments for ODS-Eurofer steel in the cold rolled condition show a high dislocation density, 8.0 × 1015 m−2 . Upon isothermal annealing in the ferritic phase field both dislocation annihilation and rearrangement become more difficult. This can be observed in the samples annealed at 400 ◦ C and 800 ◦ C where the dislocation density decreases predominantly due to static recovery reactions [18,19]. The dislocation density of the sample annealed at 800 ◦ C is about one quarter of the value obtained for the deformed sample. For samples annealed at 1100 ◦ C and 1350 ◦ C the dislocation density increases. This behavior is correlated with the martensitic transformation experienced by this steel. X-ray diffraction results of ODS-Eurofer steel annealed at 1100 ◦ C for 1 h followed by air cooling are shown in Fig. 4. The Miller indices corresponding to martensite are indicated in the figure. It is worth noticing that diffraction peaks corresponding to retained austenite are also observed in Fig. 4. The dislocation density varies significantly when steels undergo martensitic transformation [21,22]. For 9 wt.%Cr ODS RAFM steel a high density of defects is usually reported in typical martensitic lath structures [23,24]. Different heat treatment conditions are investigated in this steel and austenitization and subsequent tempering
Fig. 3. Dislocation density () as a function of annealing temperature in 80% cold rolled ODS-Eurofer. The result of Vickers microhardness is also included in the figure.
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W–H plot suggests that the real microstructures do not differ only in terms of the values of the dislocation densities but that they are of quite different nature. Because of the martensitic transformation, texture does not change very much. Dislocation storage is quite anisotropic for the rolled sample but not for the martensitic samples, if we observe the behavior of (2 0 0) and (4 0 0) diffraction peaks. They are the ones with the largest mismatch with respect to the quadratic behavior of the W–H plot in the deformed sample but they follow that behavior quite close for the martensitic samples. The peak (4 0 0) was even left out of the fitting procedure to calculate the fit for the rolled sample. The anisotropic storage in the cold-rolled sample is related not merely to the presence of texture but to the deformation process that produced such texture, which is evidenced by the fact that the same texture, persistent after heating and cooling, i.e., after the martensitic transformation, does not store anisotropic dislocation arrays after annealing.
Fig. 4. X-ray diffraction of ODS-Eurofer steel annealed at 1100 ◦ C for 1 h. Arrows mark the peaks corresponding to retained austenite. The Miller indices of martensite are also indicated in the figure.
provide an increase in tensile ductility and impact strength behavior [23]. The dislocation density as a function of carbon content in lath martensite of Fe–C alloys was evaluated by Kehoe and Kelly [22]. They found a dislocation density of about 1.0 × 1015 m−2 in asquenched 0.07 wt.%C steel, the same amount of carbon as in the ODS-Eurofer steel. This value is quite similar to that obtained for ODS-Eurofer steel annealed at 1100 ◦ C for 1 h followed by air cooling, 7.0 × 1015 m−2 . Literature reports only a few papers regarding the evaluation of dislocation density in ferritic–martensitic steels. To the best of our knowledge, dislocation densities were not yet evaluated in ODS ferritic–martensitic steels by X-ray diffraction. In a recent paper, Takebayashi and co-authors reported a value of about 2.0 × 1016 m−2 for an as-quenched 0.3 wt.% C steel with lath martensite structure using the modified Williamson–Hall method whereas a slightly lower value of 6.3 × 1015 m−2 was obtained using the modified Warren–Averbach method [25]. Peˇsiˇcka et al. reported the evolution of dislocation density in two non-ODS ferritic–martensitic steels in creep [26]. TEM and X-ray line profile analysis were used to evaluate the dislocation density. In the steel with the closest composition to ODS-Eurofer steel (7.4 wt.%Cr and 0.075 wt.%C), in the martensitic state, a value of = 4.2 × 1014 m−2 was obtained from XRD measurements. Roy and co-authors [27] reported the evolution of dislocation density in ferritic–martensitic steel (Russian EP-823 grade) containing about 12 wt.%Cr and 0.14 wt.%C during moderate cold working. TEM was used as the analytical tool to determine the dislocation density in quenched and tempered samples deformed to strains up to 11%. The value of dislocation density found for the tempered unstrained condition was 2.6 × 1015 m−2 . After moderate straining, dislocation density increased to about 6.2 × 1016 m−2 . The evolution of the dislocation density upon isothermal annealing of ODS-Eurofer steel resembles the results shown for Vickers microhardness testing [18]. The dislocation density drops during annealing in the ferritic phase field mostly due to static recovery reactions. On the other hand, martensitic transformation leads to the increase of the dislocation density above 7.0 × 1015 m−2 . These values of dislocation density have the same order of magnitude than other reported for steels in the martensitic condition. Dislocation densities are quite high for the deformed sample and for the two samples heat treated at 1100 ◦ C and 1350 ◦ C, with values differing in no more than 25%. The same similarity is revealed by the Vickers microhardness. However, a close inspection at the
4. Summary and conclusions The dislocation density of 80% cold-rolled ODS-Eurofer steel annealed within a wide range of temperatures (300–1350 ◦ C) has been evaluated by X-ray diffraction using the modified Williamson–Hall method. Based on Vickers microhardness values, X-ray profile analysis and TEM observation the following conclusions can be drawn:
1. The values of Vickers microhardness and the dislocation density obtained by the modified Williamson–Hall plot revealed similar trends, i.e., the changes in hardness due to recovery/recrystallization and martensitic transformation are mirrored by values of dislocation densities. 2. The dislocation density of 80% cold-rolled samples is 8.0 × 1015 m−2 . Further annealing within the ferritic phase field where static recovery is the predominant softening mechanism promotes a decrease in the dislocation density to values down to 2.0 × 1015 m−2 . 3. The martensitic transformation introduces a high dislocation density in ODS-Eurofer steel. In addition to the peaks corresponding to martensite, X-ray diffraction shows the presence of retained austenite. The values of the dislocation density found in samples annealed at 1100 ◦ C and 1350 ◦ C for 1 h with subsequent air cooling are, respectively, 7.0 × 1015 and 5.0 × 1015 m−2 . 4. The nature of the dislocation arrays for the cold rolled steel is revealed to be quite different from the martensitic ones. The storage of dislocations is anisotropic in the cold rolled sample, with less dislocations accumulated in crystals with the (2 0 0) direction aligned with the ND. That effect is not visible in the samples developing martensitic lath structures. Because of the many available variants, martensite variant selection and consequent build up of dislocation arrays are isotropic and not dependent on pre-existent texture.
Acknowledgments Authors are grateful to FAPESP (Grants 07/56436-0 and 08/54064-1) for the financial support. Authors are also acknowledged to Dr. R. Lindau (KIT, Karlsruhe) for supplying the samples for this investigation. The kind assistance of Dr. M. Klimenkov (KIT, Karlsruhe) in TEM is also acknowledged. This work is partially supported by Brazilian Synchrotron Light Source Laboratory (LNLS) under Research Proposal Nr. 9761 (2010). Discussions with Prof. T. Ungár were very enlightening.
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References [1] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Elsevier, 2004. [2] G. Gottstein, Physical Foundations of Materials Science, Springer, 2004. [3] R.W. Cahn, P. Haasen, Physical Metallurgy, Elsevier, North-Holland, 1996. [4] T. Ungár, I. Dragomir, Á. Révész, A. Borbély, J. Appl. Crystallogr. 32 (1999) 992–1002. [5] E. Schafler, M. Zehetbauer, T. Ungár, Mater. Sci. Eng. A 319–321 (2001) 220–223. [6] T. Ungar, J. Gubicza, P. Hanak, I. Alexandrov, Mater. Sci. Eng. A 319–321 (2001) 274–278. [7] H.P. Klug, L.E. Alexander, X-ray Diffraction Procedures for Polycrystalline and Amorphous Materials, John Wiley, New York, 1974. [8] R. Lindau, A. Möslang, M. Shiraa, P. Schlossmacher, M. Klimenkov, J. Nucl. Mater. 307–311 (2002) 769–772. [9] R. Lindau, A. Möslang, M. Rieth, M. Klimenkou, E. Materna-Morris, A. Alamo, A.-A.F. Tavassoli, C. Caryon, A.-M. Lancha, P. Fernandez, N. Baluc, R. Schäublin, E. Diegele, G. Filacchioni, J.W. Resman, B.v.d. Schaaf, E. Lucon, W. Dietz, Fusion Eng. Des. 75–79 (2005) 989–996. [10] M. Klimiankou, R. Lindau, A. Möslang, J. Nucl. Mater. 386 (2009) 553–556. [11] M. Klimiankou, R. Lindau, A. Möslang, Micron 36 (2005) 1–8. [12] A. Ramar, N. Baluc, R. Achäublin, J. Nucl. Mater. 367–370 (2007) 217–221.
[13] A. Möslang, C. Adelhelm, R. Heidinger, Int. J. Mater. Res. 99 (2008) 1045–1054. [14] R. Schaeublin, T. Leguey, P. Spätig, N. Baluc, M. Victoria, J. Nucl. Mater. 307–311 (2002) 778–782. [15] E. Arzt, Acta Mater. 46 (1998) 5611–5626. [16] H.K.D.H. Bhadeshia, Mater. Sci. Eng. A 223 (1997) 64–77. [17] H. Sakasegawa, M. Tamura, S. Ohtsuka, S. Ukai, H. Tanigawa, A. Kohyama, M. Fujiwara, J. Alloys Compd. 452 (2008) 2–6. [18] R.A. Renzetti, H.R.Z. Sandim, M.J.R. Sandim, A.D. Santos, A. Möslang, D. Raabe, Mater. Sci. Eng. A 528 (2011) 1442–1447. [19] H.R.Z. Sandim, R.A. Renzetti, A.F. Padilha, D. Raabe, M. Klimenkov, R. Lindau, A. Möslang, Mater. Sci. Eng. A 527 (2010) 3602–3608. [20] G. Ribárik, T. Ungár, Mater. Sci. Eng. A 528 (2010) 112–121. [21] M. Tokizane, N. Matsumura, K. Tsuzaki, T. Maki, I. Tamura, Metall. Trans. A 13A (1982) 1379–1388. [22] M. Kehoe, P.M. Kelly, Scripta Metall. 4 (1970) 473–476. [23] M. Klimiankou, R. Lindau, A. Möslang, J. Nucl. Mater. 367–370 (2007) 173–178. [24] M. Klimiankou, R. Lindau, A. Möslang, J. Cryst. Growth 249 (2003) 381–387. [25] S. Takebayashi, T. Kunieda, N. Yoshinaga, K. Ushioda, S. Ogata, ISIJ Int. 50 (2010) 875–882. [26] J. Peˇsiˇcka, R. Kuˇzel, A. Dronhofer, G. Eggeler, Acta Mater. 51 (2003) 4847–4862. [27] A.K. Roy, S. Bandyopadhyay, S.B. Suresh, D. Maitra, P. Kumar, D. Wells, L. Ma, Mater. Sci. Eng. 416A (2006) 134–138.