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Orientation relationship between austenite and bainite in a multiphased steel
Materials Characterization 58 (2007) 332 – 338
Orientation relationship between austenite and bainite in a multiphased steel C. Cabus a,b , H. Réglé a,b,⁎, B. Bacroix a a
LPMTM – CNRS, Université Paris 13, 99, Av. J.B. Clément, F-93430 Villetaneuse, France b Arcelor Research S.A., Voie Romaine BP30320 – 57283 Maizières-lès-Metz, France Received 20 March 2006; received in revised form 4 May 2006; accepted 22 May 2006
Abstract A first method is proposed to evaluate the “average” orientation relationship which may exist between two neighbouring different crystallographic phases from electron back scattering diffraction orientation cartographies. This method is applied to a multiphased steel for which the crystallographic orientation relationship between austenite and bainite can be expressed as a 44.5° rotation around a <0.13, 0.13, 0.98> axis. A second method is then proposed to determine all possible transformation products of a given austenite orientation. This statistical treatment of electron back scattering diffraction data allows to detect a possible variant selection which may occur during phase transformation. It is illustrated by the determination of the transformation products of 80 Copper oriented grains of austenite and actually reveals that some expected variants are missing experimentally. © 2006 Published by Elsevier Inc. Keywords: EBSD; Texture; Steel; Variant selection
1. Introduction The development of steel sheets, widely used for automotive or packaging industries, involves a hot-rolling step where the steel is deformed in the austenite range before transforming into ferrite at a lower temperature. When the phase transformation from the face-centered cubic structure (austenite) into the body-centered cubic structure (ferrite, bainite or martensite) occurs, an orientation relationship exists between the parent (FCC) and the produced (BCC) crystals and this gives rise to the development of ferrite textures “in relation with” the texture of the austenite [1]. Since the texture of the ferrite ⁎ Corresponding author. LPMTM – CNRS, Université Paris 13, 99, Av. J.B. Clément, F-93430 Villetaneuse, France. E-mail address: [email protected] (H. Réglé). 1044-5803/$ - see front matter © 2006 Published by Elsevier Inc. doi:10.1016/j.matchar.2006.05.016
phase has a strong impact on the final anisotropic properties of the steel sheets (like the deep-drawability for the applications cited above), the knowledge of the relation between the two textures is of prime importance in order to control the final one. In the literature, three different orientation relationships are frequently cited for this transformation, namely Bain [2], Kurdjimov–Sachs (K– S) [3] and Nishiyama–Wasserman (N–W) [4,5]. They differ from one another by only a few degrees, and a variety of intermediate orientation relationships are also frequently observed [6,7]. The reasons for this discrepancy come partly from the way these relationships are usually determined. The most common method is to look for the orientation relationships that can exist between the main orientations of the austenite and ferrite textures; as these two groups of orientations are not always associated with transformation-related crystals, this macroscopic
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method is necessarily approximate. With the help of the electron back scattering diffraction (EBSD) technique, this orientation relationship can now be directly measured on a very local scale, provided that both phases are simultaneously present within a material; this is usually performed only very locally and the characterization is incomplete in that case. It is thus important to be able to determine precisely and statistically the real local orientation relationship which may exist between both crystallographic phases, due to a transformation process. The first aim of this paper is thus to present a method to evaluate statistically this orientation relationship, from orientation cartographies acquired by EBSD in a scanning electron microscope (SEM). Another point of interest arising with the study of phase transformation textures is that the crystallographic orientation relationships observed between austenite and ferrite mathematically lead in general to several equivalent so-called variants of ferrite, from one austenite orientation (for example, the K–S relationship leads to 24 equivalent variants of ferrite and N–W to 12 variants). Experimentally, however, all these theoretically predicted ferrite variants are rarely found to be produced by one single grain of austenite. This phenomenon is called “variant selection” in the literature and its principal consequence is that the texture obtained in the ferrite can not be simply deduced from the texture of the austenite even if the crystallographic orientation relationship between the two phases is perfectly established [8]. The degree of this “variant selection” phenomena is however difficult to evaluate, again because the analysis is usually performed on the global textures obtained in ferrite, which implies a large and unknown number of ferrite variants produced by many grains of austenite with different orientations. Recently, and thanks to EBSD analysis, the “variant selection” has also been analysed in some isolated grains of austenite and physically-based assumptions have been given to explain this phenomenon [9–11]. However, the statistical treatment of the variants produced by one specific texture component of the austenite has not yet been performed. Thus the second aim of this paper is to propose a semi-automated method for extracting statistically, from EBSD orientation maps, all the experimentally formed transformation products of ideal orientations of austenite. 2. Material and experimental procedures The steel used to illustrate the presented analysis methods is a multiphased 0.6C–1.5Si–1.5Mn (wt.%) steel. This steel has already been investigated in a collaboration between NSC (Nippon Steel Corporation)
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and Arcelor, and the global texture evolutions have been published by Réglé et al. [12]. The material is homogenized in the austenite region for 45 min and cooled to a temperature between 900 and 700 °C (where it is still fully within the austenite range) where it is deformed. The deformation (between 30% and 70% of thickness reduction) is performed in a laboratory rolling mill or in a channel die apparatus, that is more flexible to use and allows plane strain compression of the material, just like in rolling. After deformation, some of the specimens are maintained for 100 s at the deformation temperature so as to induce the recrystallisation of the austenite before cooling, whereas some other ones are cooled immediately after the deformation. This cooling step is performed down to 400 °C, a temperature where all the specimens are held 10 min for the bainitic transformation to occur. This transformation allows a carbon enrichment of the austenite because of the presence of silicon which hinders the carbide precipitation, and thus stops any further transformation of the austenite after the final quenching at room temperature. At the end of this treatment, a mixture of residual austenite, bainite and a small amount of martensite constitutes the microstructure. Due to the high carbon content of 0.6%, more than 20% of austenite is retained in the microstructure at room temperature. The specimens are then electropolished, and the EBSD measurements are performed on a SEM equipped with a field electron gun (FEG–SEM). 3. A method to determine statistically the orientation relationship between the austenite and the ferrite phases This first method is illustrated on EBSD orientation maps obtained with the Channel 5 analysis software (HKL technology). It consists first in extracting all the interphase boundaries present in an orientation cartography and then to determine the misorientation axis and angle between all pairs of adjacent pixels each belonging to a different crystallographic phase. The EBSD orientation cartography has been acquired with a step size of 200 nm and by assuming the presence of two possible crystallographic phases: Fe-FCC for austenite and Fe-BCC for ferrite, which is indeed mostly bainite (a few small regions containing martensite have also been indexed as BCC but they are associated with a low quality index of the diffraction patterns and can be easily distinguished from bainite). In Fig. 1a, all phases are represented: the austenite is coloured in red, bainite or martensite in yellow and grain boundaries (misorientations higher than 2°) are drawn in black. The global cartography contains a total of 166 000 pixels.
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Fig. 1. EBSD orientation maps illustrating the method used to determine statistically the orientation relationship between the FCC (in red) and the BCC (in yellow) phases: (a) initial complete data, (b) selection of all the FCC pixels and dilatation of this selection to include the first neighbouring BCC pixels, (c) selection of all the BCC pixels and dilatation of this selection to include the first neighbouring FCC pixels and (d) intersection of these two selection to obtain only the pixels in interphase position.
Fig. 5. EBSD orientation maps and {100} pole figures illustrating the method used to extract all the transformation products from a single orientation of austenite: (a) initial complete data, (b) selection from the pole figure of the austenite pixels of the desired orientation and (c) dilatation of this selection to include the first neighbouring ferrite pixels.
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Fig. 2. (a) Misorientation angle distribution for adjacent austenite and ferrite pixels, (b) the experimental distribution found in the multiphased steel plotted in a standard triangle and (c) the position of the misorientation axis in the standard triangle for the K–S and N–W relationships.
• The first step consists in selecting all the austenitic pixels of the map, i.e. all the FCC phase. An option of the software allows this image to be dilated so as to add to the austenitic pixels their first ferrite neighbours (Fig. 1b). • In a similar way, the selection of the sole BBC phase is performed from the initial EBSD map, and a dilatation procedure of this selection allows including all adjacent austenitic pixels (Fig. 1c). • Taking then the intersection (i.e. the common pixels) of both previous selections allows finally isolating all pairs of adjacent pixels of both phases (Fig. 1d). The remaining number of pixels in this intersection is
equal in the present case to 51 000, which corresponds to 30% of the total EBSD map. The misorientation angle distribution histogram corresponding to this last selection is directly calculated by the software for all pairs of neighbouring pixels (Fig. 2a). The low misorientation angles correspond to adjacent pixels belonging to the same phase and are not taken into account in the analysis. The misorientation axes are then reported in a “standard triangle” (Fig. 2b), where it is possible to identify a strong maximum which thus corresponds to the misorientation axis between the two crystallographic phases which is statistically found in this
Fig. 3. Misorientation angle distribution for adjacent austenite and ferrite pixels found in 5 different samples.
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Fig. 4. ODF (φ2 = 45° Euler space sections) of the transformation products of ideal orientations of austenite (Copper, Brass, Goss and Cube) calculated with the K–S orientation relationship and with the OR relationship (44.5° < 0.13, 0.13, 0.98 > (iso-levels 2, 4, 6, …).
material. The position of the misorientation axes corresponding to the ideal orientation relationships K–S and N– W is also shown in Fig. 2c. It is seen that the maximum of the experimental distribution lies between the two K–S and N–W positions. This method has then been applied to several other specimens and EBSD misorientation angle distributions are reported in the Fig. 3. The total number of considered pairs of pixels is between 10 000 and 40 000 depending on the size of the map. From these distributions, the average local crystallographic orientation relationship between the FCC and BCC phases of the investigated steel can be expressed as a 44.5° rotation around a <0.13, 0.13, 0.98> axis (this orientation relationship will be designed below by OR). It is obvious, from the measured shapes of the various histograms, that some scatter remains around this value. Apart from some limited bad indexing of a few orientations which may occur, some other reasons can be proposed to explain this remaining discrepancy: for example, the transformation process could be perturbed very locally; also, some of considered adjacent pixels may not be transformation related. Thus the characterized orientation relationship is valid only in a statistical sense and we can expect that the greater the considered number of pairs of pixels, the better the precision on this value.
Since the K–S and N–W relationships correspond respectively to a 42.8° rotation around a <0.18, 0.18, 0.97> axis and a 46° rotation around a <0.08, 0.20, 0.98> axis, it is easy to show that the variants associated with OR are misoriented 3.4° and 4° from K–S and N–W, respectively. It can be noted that OR produces 24 variants due to the 24 equivalent axes related to the associated axis type, just like the K–S relationship. Practically, OR corresponds preferentially to the orientation relationship between austenite and bainite rather than between austenite and martensite. Indeed, it is clear from the microstructure of Fig. 1a that austenite lies between the laths of bainite, whereas the regions without austenite correspond to martensite regions. As already mentioned, the martensite and the bainite can actually be distinguished by the determination of the quality index. The sharpness of the diffraction patterns of martensite are lower, probably due to their higher dislocation content and which then induce a lower quality index of pattern recognition by the automatic system. Given the method used to determine OR and these microstructural considerations, the BCC phase selected by this method corresponds essentially to bainite. It is now of interest to determine, for some ideal austenite orientations, all possible transformation products
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created with OR or with a more classical transformation rule such as K–S for example. The selected orientations for the initial austenite are the one which are the most frequent after plane strain deformation of an FCC steel (the orientations called Copper {112}<111>, Brass {110} <112> and Goss {110}<001>) or after recrystallisation (orientation Cube {001}<100>). For one particular austenite orientation, a BCC ODF is calculated with the harmonic method (truncation limit lmax = 22) as the sum of individual Gaussian peaks (with a spread of 5°) around each of the 24 transformation products. All calculated ODFs are presented in Fig. 4 for the two relationships OR and K–S. It is clear from these figures that these two are quite close and that all variants produced by one single austenite orientation are located in the same regions. However, it can be noted that the intensities obtained on the ODF are slightly higher when the experimental OR is used (intensity level of 22 or 32 for the highly symmetric orientation Goss and Cube, instead of 18 for the K–S relationship). 4. A method to extract all the transformation products of one single austenite orientation It is possible now to compare these theoretical transformation products to the ones identified within the experimental ferrite textures as the transformation products of one given austenite orientation (Copper, Brass, Goss or Cube). In order to do so, the following procedure is applied, again illustrated on the same EBSD map replotted in Fig. 5 using the same color code – the austenite is in red, the bainite and martensite in yellow and the grain boundaries (misorientations higher than 2°) are drawn in black: • The first step consists in selecting, within one global EBSD map (Fig. 5a), all pixels of austenite associated with the selected orientation – here the Copper {112} <111> orientation. This can be done directly on the pole figure of the austenite phase (here with a tolerance of 15°), or on the orientation map by defining a subset corresponding to the desired texture component. As a consequence, all the austenitic pixels of the map corresponding to the Copper orientation are selected (see Fig. 5b); this selection usually includes several fragments of previously existing large grains of austenite. • A dilatation of this selection allows again including the first neighbouring ferrite pixels, which are assumed to derive from the previously selected austenitic ones by phase transformation (Ferrite 5c). • The austenite is then eliminated from the selection so that the final selection contains only the bcc pixels adjacent to the desired austenite orientation, which
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correspond to several different orientations (see the corresponding pole figure in Fig. 5). In order to get statistical data, this procedure has been repeated for several specimens. Two experimental states were distinguished, i.e. whether the austenite was recrystallised or deformed at the end of the thermo-mechanical cycle preceding the bainite transformation. This analysis has then been performed on a significant number of investigated specimens and grains: 20 EBSD maps including 41 different austenite grains have been considered in the case where the austenite was recrystallised and 15 EBSD maps including 43 austenite grains in the case where it was in a deformed state. The two ODFs are calculated directly by Channel 5 from all the extracted ferrite orientations, Fig. 6a and b. The theoretical transformation products, obtained with the OR relationship from the Copper orientation is again reported also in Fig. 6c, to underline the differences between theoretical and experimental transformation products of the Copper oriented grains. Please note that, in order to make the comparison easier in term of intensity levels, the ODF of the theoretical products has been recalculated with a Gaussian spread of 15° (instead of 5° in Fig. 4), to reflect the fact that the “ideal Copper orientation” has been selected within the experimental texture with a tolerance of 15°.1 It is clear from the comparison between the experimental and theoretical ODF that the rotated Goss orientation {011}<011> is less intense experimentally than expected from the calculation of all possible variants and even less when the austenite was deformed. Since this result has been obtained from the analysis of a large number of grains (80), we can reasonably be confident that it actually reflects a “variant selection” phenomenon. 5. Conclusion Two methods have been proposed in the present paper to extract statistical data from EBSD orientation cartographies in multiphased steels. The first one aims at characterizing the local orientation relationship between the austenite and the produced ferrite and consists in the 1 Please note that, when a texture can be considered to be composed of one single orientation with some spread, to describe this texture as a set orientations scattered around a peak with a tolerance of 15° or to consider a complete and perfect Gaussian peak with a spread angle of 15° are not strictly equivalent; indeed, 85% only of the total peak is comprised at ±15° from the center of the peak. In the present case, however, as the texture is either composed of several peaks which can overlap on the theoretical side or of a great number of orientations widely spread in the whole Euler space on the experimental one, to take the same value on both sides for the description of the spread seems to a satisfactory solution.
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Fig. 6. ODFs (φ2 = 45° Euler space sections) of the transformation products of the Copper oriented austenitic grains (a) experimentally found from all samples where the austenite is recrystallised, (b) experimentally found from all samples where the austenite is deformed and (c) calculated with the OR relationship with a Gaussian spread of 15° (iso-levels 1, 2, 3,..).
extraction of all the pixels of both phases which form interphase boundaries. The local orientation relationship between austenite and bainite has been identified as a 44.5° rotation around a <0.13, 0.13, 0.98> axis. The knowledge of this orientation relation allows calculating the theoretical texture of the transformation products of any austenite orientation. The second method aims at determining the experimental transformation products of all the grains present in a cartography with a defined austenite orientation. This method is useful to identify a possible “variant selection” which may occur during phase transformation from austenite to ferrite. The method has been applied on a large number of Copper oriented austenitic grains. The experimental ferrite texture produced from these grains differs slightly from the one which can be theoretically predicted with the orientation relationship identified by the first method, in the sense that some theoretical variants are experimentally missing. This “variant selection” is found to be more intense when the austenite is deformed before the phase transformation rather than recrystallised. References [1] Ray RK, Jonas JJ, Butron-Guillen P, Savoie J. Transformation textures in steels. ISIJ Int 1994;34:927–42. [2] Bain EC, Dunkirk NY. The nature of martensite. Trans AIME 1924;70:25–46.
[3] Kurdjumow G, Sachs G. Über den Mechanismus der Stahlhärtung. Z Phys 1930;64:325–43. [4] Nishiyama Z. X-ray investigation of the mechanism of the transformation from face-centred cubic lattice to body-centred cubic. Sci. Rep. Tohoku Imp. Univ. 1934/1935;23:637. [5] Wasserman G. Arch Eisenhüttenwes 1933;16:647. [6] Verlinden B, Bocher P, Girault E, Aernoudt E. Austenite texture and bainite/austenite orientation relationships in TRIP steel. Scr Mater 2001;45(8):909–16. [7] Suh D-W, Kang J-H, Hwan Oh K, Lee H-C. Evaluation of the deviation angle of ferrite from the Kudjumov–Sachs relationship in a low carbon steel by EBSD. Scr Mater 2002;46(5):375–8. [8] Wittridge NJ, Jonas JJ, Root JH. A dislocation-based model for variant selection during the g-to-a′ transformation. Metall Mater Trans A 2001;32A:889–901. [9] Bruckner G, Pospiech J, Seidl I, Gottstein G. Orientation correlation during diffusional a–g phase transformation in a ferritic low carbon steel. Scr Mater 2001;44(11):2635–40. [10] Godet S, Glez JC, He Y, Jonas JJ, Jacques PJ. Grain-scale characterization of transformation textures. J Appl Crystallogr 2004;37:417–25. [11] He Y, Godet S, Jacques PJ, Jonas JJ. Crystallographic relations between face- and body-centred cubic crystals formed under near-equilibrium conditions: observations from the Gibeon meteorite. Acta Mater 2006;54(5):1323–34. [12] Réglé H, Maruyama N, Yoshinaga N. Texture of multiphased steel sheets. In: AIST Editor. International Conference on Advanced High Strength Sheet Steels for Automotive Applications. Margaret A. Baker, Ronald E. Ashburn, Winter Park, USA, 2004;239–246.
Orientation relationship between austenite and bainite in a multiphased steel C. Cabus a,b , H. Réglé a,b,⁎, B. Bacroix a a
LPMTM – CNRS, Université Paris 13, 99, Av. J.B. Clément, F-93430 Villetaneuse, France b Arcelor Research S.A., Voie Romaine BP30320 – 57283 Maizières-lès-Metz, France Received 20 March 2006; received in revised form 4 May 2006; accepted 22 May 2006
Abstract A first method is proposed to evaluate the “average” orientation relationship which may exist between two neighbouring different crystallographic phases from electron back scattering diffraction orientation cartographies. This method is applied to a multiphased steel for which the crystallographic orientation relationship between austenite and bainite can be expressed as a 44.5° rotation around a <0.13, 0.13, 0.98> axis. A second method is then proposed to determine all possible transformation products of a given austenite orientation. This statistical treatment of electron back scattering diffraction data allows to detect a possible variant selection which may occur during phase transformation. It is illustrated by the determination of the transformation products of 80 Copper oriented grains of austenite and actually reveals that some expected variants are missing experimentally. © 2006 Published by Elsevier Inc. Keywords: EBSD; Texture; Steel; Variant selection
1. Introduction The development of steel sheets, widely used for automotive or packaging industries, involves a hot-rolling step where the steel is deformed in the austenite range before transforming into ferrite at a lower temperature. When the phase transformation from the face-centered cubic structure (austenite) into the body-centered cubic structure (ferrite, bainite or martensite) occurs, an orientation relationship exists between the parent (FCC) and the produced (BCC) crystals and this gives rise to the development of ferrite textures “in relation with” the texture of the austenite [1]. Since the texture of the ferrite ⁎ Corresponding author. LPMTM – CNRS, Université Paris 13, 99, Av. J.B. Clément, F-93430 Villetaneuse, France. E-mail address: [email protected] (H. Réglé). 1044-5803/$ - see front matter © 2006 Published by Elsevier Inc. doi:10.1016/j.matchar.2006.05.016
phase has a strong impact on the final anisotropic properties of the steel sheets (like the deep-drawability for the applications cited above), the knowledge of the relation between the two textures is of prime importance in order to control the final one. In the literature, three different orientation relationships are frequently cited for this transformation, namely Bain [2], Kurdjimov–Sachs (K– S) [3] and Nishiyama–Wasserman (N–W) [4,5]. They differ from one another by only a few degrees, and a variety of intermediate orientation relationships are also frequently observed [6,7]. The reasons for this discrepancy come partly from the way these relationships are usually determined. The most common method is to look for the orientation relationships that can exist between the main orientations of the austenite and ferrite textures; as these two groups of orientations are not always associated with transformation-related crystals, this macroscopic
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method is necessarily approximate. With the help of the electron back scattering diffraction (EBSD) technique, this orientation relationship can now be directly measured on a very local scale, provided that both phases are simultaneously present within a material; this is usually performed only very locally and the characterization is incomplete in that case. It is thus important to be able to determine precisely and statistically the real local orientation relationship which may exist between both crystallographic phases, due to a transformation process. The first aim of this paper is thus to present a method to evaluate statistically this orientation relationship, from orientation cartographies acquired by EBSD in a scanning electron microscope (SEM). Another point of interest arising with the study of phase transformation textures is that the crystallographic orientation relationships observed between austenite and ferrite mathematically lead in general to several equivalent so-called variants of ferrite, from one austenite orientation (for example, the K–S relationship leads to 24 equivalent variants of ferrite and N–W to 12 variants). Experimentally, however, all these theoretically predicted ferrite variants are rarely found to be produced by one single grain of austenite. This phenomenon is called “variant selection” in the literature and its principal consequence is that the texture obtained in the ferrite can not be simply deduced from the texture of the austenite even if the crystallographic orientation relationship between the two phases is perfectly established [8]. The degree of this “variant selection” phenomena is however difficult to evaluate, again because the analysis is usually performed on the global textures obtained in ferrite, which implies a large and unknown number of ferrite variants produced by many grains of austenite with different orientations. Recently, and thanks to EBSD analysis, the “variant selection” has also been analysed in some isolated grains of austenite and physically-based assumptions have been given to explain this phenomenon [9–11]. However, the statistical treatment of the variants produced by one specific texture component of the austenite has not yet been performed. Thus the second aim of this paper is to propose a semi-automated method for extracting statistically, from EBSD orientation maps, all the experimentally formed transformation products of ideal orientations of austenite. 2. Material and experimental procedures The steel used to illustrate the presented analysis methods is a multiphased 0.6C–1.5Si–1.5Mn (wt.%) steel. This steel has already been investigated in a collaboration between NSC (Nippon Steel Corporation)
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and Arcelor, and the global texture evolutions have been published by Réglé et al. [12]. The material is homogenized in the austenite region for 45 min and cooled to a temperature between 900 and 700 °C (where it is still fully within the austenite range) where it is deformed. The deformation (between 30% and 70% of thickness reduction) is performed in a laboratory rolling mill or in a channel die apparatus, that is more flexible to use and allows plane strain compression of the material, just like in rolling. After deformation, some of the specimens are maintained for 100 s at the deformation temperature so as to induce the recrystallisation of the austenite before cooling, whereas some other ones are cooled immediately after the deformation. This cooling step is performed down to 400 °C, a temperature where all the specimens are held 10 min for the bainitic transformation to occur. This transformation allows a carbon enrichment of the austenite because of the presence of silicon which hinders the carbide precipitation, and thus stops any further transformation of the austenite after the final quenching at room temperature. At the end of this treatment, a mixture of residual austenite, bainite and a small amount of martensite constitutes the microstructure. Due to the high carbon content of 0.6%, more than 20% of austenite is retained in the microstructure at room temperature. The specimens are then electropolished, and the EBSD measurements are performed on a SEM equipped with a field electron gun (FEG–SEM). 3. A method to determine statistically the orientation relationship between the austenite and the ferrite phases This first method is illustrated on EBSD orientation maps obtained with the Channel 5 analysis software (HKL technology). It consists first in extracting all the interphase boundaries present in an orientation cartography and then to determine the misorientation axis and angle between all pairs of adjacent pixels each belonging to a different crystallographic phase. The EBSD orientation cartography has been acquired with a step size of 200 nm and by assuming the presence of two possible crystallographic phases: Fe-FCC for austenite and Fe-BCC for ferrite, which is indeed mostly bainite (a few small regions containing martensite have also been indexed as BCC but they are associated with a low quality index of the diffraction patterns and can be easily distinguished from bainite). In Fig. 1a, all phases are represented: the austenite is coloured in red, bainite or martensite in yellow and grain boundaries (misorientations higher than 2°) are drawn in black. The global cartography contains a total of 166 000 pixels.
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Fig. 1. EBSD orientation maps illustrating the method used to determine statistically the orientation relationship between the FCC (in red) and the BCC (in yellow) phases: (a) initial complete data, (b) selection of all the FCC pixels and dilatation of this selection to include the first neighbouring BCC pixels, (c) selection of all the BCC pixels and dilatation of this selection to include the first neighbouring FCC pixels and (d) intersection of these two selection to obtain only the pixels in interphase position.
Fig. 5. EBSD orientation maps and {100} pole figures illustrating the method used to extract all the transformation products from a single orientation of austenite: (a) initial complete data, (b) selection from the pole figure of the austenite pixels of the desired orientation and (c) dilatation of this selection to include the first neighbouring ferrite pixels.
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Fig. 2. (a) Misorientation angle distribution for adjacent austenite and ferrite pixels, (b) the experimental distribution found in the multiphased steel plotted in a standard triangle and (c) the position of the misorientation axis in the standard triangle for the K–S and N–W relationships.
• The first step consists in selecting all the austenitic pixels of the map, i.e. all the FCC phase. An option of the software allows this image to be dilated so as to add to the austenitic pixels their first ferrite neighbours (Fig. 1b). • In a similar way, the selection of the sole BBC phase is performed from the initial EBSD map, and a dilatation procedure of this selection allows including all adjacent austenitic pixels (Fig. 1c). • Taking then the intersection (i.e. the common pixels) of both previous selections allows finally isolating all pairs of adjacent pixels of both phases (Fig. 1d). The remaining number of pixels in this intersection is
equal in the present case to 51 000, which corresponds to 30% of the total EBSD map. The misorientation angle distribution histogram corresponding to this last selection is directly calculated by the software for all pairs of neighbouring pixels (Fig. 2a). The low misorientation angles correspond to adjacent pixels belonging to the same phase and are not taken into account in the analysis. The misorientation axes are then reported in a “standard triangle” (Fig. 2b), where it is possible to identify a strong maximum which thus corresponds to the misorientation axis between the two crystallographic phases which is statistically found in this
Fig. 3. Misorientation angle distribution for adjacent austenite and ferrite pixels found in 5 different samples.
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Fig. 4. ODF (φ2 = 45° Euler space sections) of the transformation products of ideal orientations of austenite (Copper, Brass, Goss and Cube) calculated with the K–S orientation relationship and with the OR relationship (44.5° < 0.13, 0.13, 0.98 > (iso-levels 2, 4, 6, …).
material. The position of the misorientation axes corresponding to the ideal orientation relationships K–S and N– W is also shown in Fig. 2c. It is seen that the maximum of the experimental distribution lies between the two K–S and N–W positions. This method has then been applied to several other specimens and EBSD misorientation angle distributions are reported in the Fig. 3. The total number of considered pairs of pixels is between 10 000 and 40 000 depending on the size of the map. From these distributions, the average local crystallographic orientation relationship between the FCC and BCC phases of the investigated steel can be expressed as a 44.5° rotation around a <0.13, 0.13, 0.98> axis (this orientation relationship will be designed below by OR). It is obvious, from the measured shapes of the various histograms, that some scatter remains around this value. Apart from some limited bad indexing of a few orientations which may occur, some other reasons can be proposed to explain this remaining discrepancy: for example, the transformation process could be perturbed very locally; also, some of considered adjacent pixels may not be transformation related. Thus the characterized orientation relationship is valid only in a statistical sense and we can expect that the greater the considered number of pairs of pixels, the better the precision on this value.
Since the K–S and N–W relationships correspond respectively to a 42.8° rotation around a <0.18, 0.18, 0.97> axis and a 46° rotation around a <0.08, 0.20, 0.98> axis, it is easy to show that the variants associated with OR are misoriented 3.4° and 4° from K–S and N–W, respectively. It can be noted that OR produces 24 variants due to the 24 equivalent axes related to the associated axis type, just like the K–S relationship. Practically, OR corresponds preferentially to the orientation relationship between austenite and bainite rather than between austenite and martensite. Indeed, it is clear from the microstructure of Fig. 1a that austenite lies between the laths of bainite, whereas the regions without austenite correspond to martensite regions. As already mentioned, the martensite and the bainite can actually be distinguished by the determination of the quality index. The sharpness of the diffraction patterns of martensite are lower, probably due to their higher dislocation content and which then induce a lower quality index of pattern recognition by the automatic system. Given the method used to determine OR and these microstructural considerations, the BCC phase selected by this method corresponds essentially to bainite. It is now of interest to determine, for some ideal austenite orientations, all possible transformation products
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created with OR or with a more classical transformation rule such as K–S for example. The selected orientations for the initial austenite are the one which are the most frequent after plane strain deformation of an FCC steel (the orientations called Copper {112}<111>, Brass {110} <112> and Goss {110}<001>) or after recrystallisation (orientation Cube {001}<100>). For one particular austenite orientation, a BCC ODF is calculated with the harmonic method (truncation limit lmax = 22) as the sum of individual Gaussian peaks (with a spread of 5°) around each of the 24 transformation products. All calculated ODFs are presented in Fig. 4 for the two relationships OR and K–S. It is clear from these figures that these two are quite close and that all variants produced by one single austenite orientation are located in the same regions. However, it can be noted that the intensities obtained on the ODF are slightly higher when the experimental OR is used (intensity level of 22 or 32 for the highly symmetric orientation Goss and Cube, instead of 18 for the K–S relationship). 4. A method to extract all the transformation products of one single austenite orientation It is possible now to compare these theoretical transformation products to the ones identified within the experimental ferrite textures as the transformation products of one given austenite orientation (Copper, Brass, Goss or Cube). In order to do so, the following procedure is applied, again illustrated on the same EBSD map replotted in Fig. 5 using the same color code – the austenite is in red, the bainite and martensite in yellow and the grain boundaries (misorientations higher than 2°) are drawn in black: • The first step consists in selecting, within one global EBSD map (Fig. 5a), all pixels of austenite associated with the selected orientation – here the Copper {112} <111> orientation. This can be done directly on the pole figure of the austenite phase (here with a tolerance of 15°), or on the orientation map by defining a subset corresponding to the desired texture component. As a consequence, all the austenitic pixels of the map corresponding to the Copper orientation are selected (see Fig. 5b); this selection usually includes several fragments of previously existing large grains of austenite. • A dilatation of this selection allows again including the first neighbouring ferrite pixels, which are assumed to derive from the previously selected austenitic ones by phase transformation (Ferrite 5c). • The austenite is then eliminated from the selection so that the final selection contains only the bcc pixels adjacent to the desired austenite orientation, which
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correspond to several different orientations (see the corresponding pole figure in Fig. 5). In order to get statistical data, this procedure has been repeated for several specimens. Two experimental states were distinguished, i.e. whether the austenite was recrystallised or deformed at the end of the thermo-mechanical cycle preceding the bainite transformation. This analysis has then been performed on a significant number of investigated specimens and grains: 20 EBSD maps including 41 different austenite grains have been considered in the case where the austenite was recrystallised and 15 EBSD maps including 43 austenite grains in the case where it was in a deformed state. The two ODFs are calculated directly by Channel 5 from all the extracted ferrite orientations, Fig. 6a and b. The theoretical transformation products, obtained with the OR relationship from the Copper orientation is again reported also in Fig. 6c, to underline the differences between theoretical and experimental transformation products of the Copper oriented grains. Please note that, in order to make the comparison easier in term of intensity levels, the ODF of the theoretical products has been recalculated with a Gaussian spread of 15° (instead of 5° in Fig. 4), to reflect the fact that the “ideal Copper orientation” has been selected within the experimental texture with a tolerance of 15°.1 It is clear from the comparison between the experimental and theoretical ODF that the rotated Goss orientation {011}<011> is less intense experimentally than expected from the calculation of all possible variants and even less when the austenite was deformed. Since this result has been obtained from the analysis of a large number of grains (80), we can reasonably be confident that it actually reflects a “variant selection” phenomenon. 5. Conclusion Two methods have been proposed in the present paper to extract statistical data from EBSD orientation cartographies in multiphased steels. The first one aims at characterizing the local orientation relationship between the austenite and the produced ferrite and consists in the 1 Please note that, when a texture can be considered to be composed of one single orientation with some spread, to describe this texture as a set orientations scattered around a peak with a tolerance of 15° or to consider a complete and perfect Gaussian peak with a spread angle of 15° are not strictly equivalent; indeed, 85% only of the total peak is comprised at ±15° from the center of the peak. In the present case, however, as the texture is either composed of several peaks which can overlap on the theoretical side or of a great number of orientations widely spread in the whole Euler space on the experimental one, to take the same value on both sides for the description of the spread seems to a satisfactory solution.
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Fig. 6. ODFs (φ2 = 45° Euler space sections) of the transformation products of the Copper oriented austenitic grains (a) experimentally found from all samples where the austenite is recrystallised, (b) experimentally found from all samples where the austenite is deformed and (c) calculated with the OR relationship with a Gaussian spread of 15° (iso-levels 1, 2, 3,..).
extraction of all the pixels of both phases which form interphase boundaries. The local orientation relationship between austenite and bainite has been identified as a 44.5° rotation around a <0.13, 0.13, 0.98> axis. The knowledge of this orientation relation allows calculating the theoretical texture of the transformation products of any austenite orientation. The second method aims at determining the experimental transformation products of all the grains present in a cartography with a defined austenite orientation. This method is useful to identify a possible “variant selection” which may occur during phase transformation from austenite to ferrite. The method has been applied on a large number of Copper oriented austenitic grains. The experimental ferrite texture produced from these grains differs slightly from the one which can be theoretically predicted with the orientation relationship identified by the first method, in the sense that some theoretical variants are experimentally missing. This “variant selection” is found to be more intense when the austenite is deformed before the phase transformation rather than recrystallised. References [1] Ray RK, Jonas JJ, Butron-Guillen P, Savoie J. Transformation textures in steels. ISIJ Int 1994;34:927–42. [2] Bain EC, Dunkirk NY. The nature of martensite. Trans AIME 1924;70:25–46.
[3] Kurdjumow G, Sachs G. Über den Mechanismus der Stahlhärtung. Z Phys 1930;64:325–43. [4] Nishiyama Z. X-ray investigation of the mechanism of the transformation from face-centred cubic lattice to body-centred cubic. Sci. Rep. Tohoku Imp. Univ. 1934/1935;23:637. [5] Wasserman G. Arch Eisenhüttenwes 1933;16:647. [6] Verlinden B, Bocher P, Girault E, Aernoudt E. Austenite texture and bainite/austenite orientation relationships in TRIP steel. Scr Mater 2001;45(8):909–16. [7] Suh D-W, Kang J-H, Hwan Oh K, Lee H-C. Evaluation of the deviation angle of ferrite from the Kudjumov–Sachs relationship in a low carbon steel by EBSD. Scr Mater 2002;46(5):375–8. [8] Wittridge NJ, Jonas JJ, Root JH. A dislocation-based model for variant selection during the g-to-a′ transformation. Metall Mater Trans A 2001;32A:889–901. [9] Bruckner G, Pospiech J, Seidl I, Gottstein G. Orientation correlation during diffusional a–g phase transformation in a ferritic low carbon steel. Scr Mater 2001;44(11):2635–40. [10] Godet S, Glez JC, He Y, Jonas JJ, Jacques PJ. Grain-scale characterization of transformation textures. J Appl Crystallogr 2004;37:417–25. [11] He Y, Godet S, Jacques PJ, Jonas JJ. Crystallographic relations between face- and body-centred cubic crystals formed under near-equilibrium conditions: observations from the Gibeon meteorite. Acta Mater 2006;54(5):1323–34. [12] Réglé H, Maruyama N, Yoshinaga N. Texture of multiphased steel sheets. In: AIST Editor. International Conference on Advanced High Strength Sheet Steels for Automotive Applications. Margaret A. Baker, Ronald E. Ashburn, Winter Park, USA, 2004;239–246.