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Portevin Le Chatelier Effect in a Metastable Austenitic CrMnNi Steel
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 2S (2015) S623 – S626
International Conference on Martensitic Transformations, ICOMAT-2014
Portevin Le Chatelier effect in a metastable austenitic CrMnNi steel A. Weidner*, A. Müller, H. Biermann Institute of Materials Engineering, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany
Abstract High-alloy metastable austenitic CrMnNi steels exhibit depending on the austenite stability a transformation induced plasticity at room temperature resulting in concurrently high strength and good ductility. The martensitic phase transformation is more pronounced as lower the austenite stability is. In addition, a steel variant with low austenite stability shows a macroscopically inhomogeneous deformation behavior during monotonic loading – the so-called Portevin Le Chatelier effect, which is commonly related to the interaction of moving dislocations and diffusing solute atoms. The serrated plastic flow is related to the formation of macroscopic bands with localized plastic deformation – so-called PLC bands, which was analyzed by in situ infrared thermography. © 2014 The Authors. Published by Elsevier Ltd. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations (http://creativecommons.org/licenses/by-nc-nd/4.0/). an open access under the BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). 2014. This Selection andisPeer-review underarticle responsibility of CC the chairs of the International Conference on Martensitic Transformations 2014. Keywords: PLC effect, serrated plastic flow, TRIP, thermography
1. Introduction High-alloy CrMnNi steels are a class of materials which allows depending on their chemical composition the design of excellent mechanical properties [e.g. 1,2]. By the variation of the austenite stability and the stacking fault energy it is possible to switch between the TRIP (TRransformation Induced Plasticity) effect and the TWIP (Twinning Induced Plasticity) effect [3]. The lower the austenite stability the more pronounced is the deformationinduced martensitic phase transformation, which becomes the dominating deformation mechanism as shown in
* Corresponding author. Tel.: +49-3731-39-2124; fax: +49-3731-39-3702. E-mail address: [email protected]
2214-7853 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations 2014. doi:10.1016/j.matpr.2015.07.361
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several investigations [e.g. 3–5] already in the past. In addition, a second phenomenon occurs for the TRIP steels with low austenite stability – the serrated plastic flow at higher strain values – well known as the Portevin Le Chatelier effect. The most common interpretation in the literature is the interaction of moving dislocations with diffusing solute atoms. This phenomenon was observed by several authors in different materials [e.g. 6,7], in particular also in high manganese TWIP steels. Thus, Saeed-Akbari et al. [8] used in situ infrared thermography measurements during tensile tests in order to investigate the macroscopic strain localization in so-called PLC bands. The aim of the present study was to investigate the occurrence of PLC effect in austenitic stainless TRIP steels with low austenite stability during tensile tests in dependence on the deformation temperature as well as on the strain rate. The mechanical tests were complemented by several in situ techniques (optical image recording for digital image correlation, infrared thermography and acoustic emission). However, the present paper represents only a shortened content related to the investigation of PLC band formation by infrared thermography. A more detailed presentation of all obtained results including the discussion of the origin of the PLC effect in terms of calculated activation energy is given in [9]. 2. Experimental details The high-alloy CrMnNi steel X5CrMnNi17.7.4 with 0.05 % C, 17 % Cr, 7 % Mn, 3.7 % Ni was studied in the ascast condition after solution heat treatment (0.5 h at 1050°C followed by N2 gas quenching). The initial microstructure of this steel variant consists of metastable austenite with about 10 vol. % of δ-ferrite and approx. 15 vol. % of martensite formed during cooling. The austenitic grain size was in a range between 60 μm and 500 μm. Flat tensile specimens having a rectangular cross section of 8 mm × 4 mm and a gauge length of 35 mm at a total length of 205 mm were cut from the cast plates (ACTech, Freiberg, Germany) after solution annealing. The tensile tests were performed at room temperature using an electro-mechanical testing system (Zwick, Germany). The tensile tests were carried out under crosshead displacement control with different nominal initial strain rates (10 –4 s–1, 10–3 s–1, 10–2 s–1 and 10–1 s–1, respectively). The mechanical tests were complemented by in situ thermography measurements using the infrared thermography system VarioCamhr (InfraTec, Dresden). The gauge parts of the specimens were mechanically grinded and covered by a black thermo lacquer enabling a constant thermal emission of 0.96 for the in situ measurements of the temperature evolution along the gauge length. Ferromagnetic measurements using ferritescope were performed before and after the tensile tests in order to evaluate the volume fraction of deformation-induced ’-martensite. 3. Results and discussion Figure 1a shows the true stress-true strain curves obtained at different strain rates. For more clarity, the curves were shifted along the strain axis by 0.05. Figure 1b shows a magnified segment of the stress-strain curves to visualize the shape of serrated plastic flow. In addition, the maximum temperature (Tmax [K]) developed during tensile tests as well as the volume fraction of deformation-induced ’-martensite ( ’t [%]) are given. A vertical bar in the stress-strain curves marks the onset of the serrated plastic flow. A pronounced deformation-induced martensitic phase transformation becomes evident both from sigmoidal shape of the stress-strain curves as well as from the given volume fraction of ’-martensite at all strain rates tested at room temperature. Therefore, at room temperature the strain rate has only a small influence on the TRIP effect as well as on the amount of formed ’martensite varying between about 50 to 60 % from 10–1 s–1 to 10–4 s–1. In addition, a macroscopically inhomogeneous deformation behavior becomes obvious at higher strains in form of serrations in the stress-strain curve. According to the common understanding in the literature [10], these serrations can be related to the localization of plastic strain in macroscopic bands of several micrometer thickness propagating along the gauge length. It becomes evident from Fig. 1b that the type of serrations is changing with increasing strain rate. At the slow strain rate 10–4 s–1 the serrations lock very irregular (type B according to the literature). However, at higher strain rates (10–3 s–1 and 10–2 s–1) socalled type A bands were detected. Here, the stress drop can be clearly related to the formation of a macroscopic band of strain localization, whereas the smooth part, which follows, indicates the movement of the band along the gauge length, until the next stress drop occurs related to a new macroscopic band. Furthermore, it becomes evident
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that the onset of serrated plastic flow (marked by small bar in Fig. 1a) shifts to higher strain and stress values with increasing strain rate. At a strain rate of 10–1 s–1 no serrated plastic flow was observed at all. In addition, an increase of the temperature in the specimens was observed during the tensile tests, which becomes even more pronounced with an increase of the strain rate.
Fig. 1. (a) True stress-true strain curves obtained on X5CrMnNi17.7.4 steel during tensile tests at room temperature at four different strain rates. (b) Magnified segments out of (a) visualizing the different types of serrated plastic flow in dependence on the nominal strain rate.
Using in situ infrared thermography measurements during the tensile tests, it was possible to follow the development of temperature increase along the gauge length caused by the plastic deformation. Different ongoing microstructural processes lead to this temperature increase – plasticity, the martensitic phase transformation and the localization of macroscopic deformation in the PLC bands. Figure 2 shows exemplarily the results of in situ thermographic measurements at a nominal strain rate of 10-3 s–1. The true stress-true strain curve is shown in Fig. 2a in combination with temperature evolution profiles measured at three different points along the gauge length in the first part of the tensile test. It can be clearly recognized from this T-t-curves that during the first part of deformation ( < 0.15) a continuous temperature increase occurred, which can be directly correlated with the martensitic phase transformation. It is well known from previous investigations [3-5] that the martensitic phase transformation in this specific steel variant starts immediately after passing the yield point. In addition, the T-t curves indicate clearly an oscillating behavior for higher strain levels ( > 0.15), which is related to the formation and movement of PLC bands along the gauge length. The PLC bands are starting on the left side of the gauge length (green curve) and move along the gauge length (grey and red curve). The maximum of T for the three different points can be nicely followed and shows directly that one band is followed by another one. In addition to the T-t curves, Fig. 2b shows a sequence of thermograms at different subsequent strain levels nicely illustrating again the development and propagation of two individual bands along the gauge length. It becomes evident from both Figures (2a,b) that the macroscopic localization of strain in bands is related to a remarkable increase of temperature. Moreover, the period between the appearances of two bands is quite low, thus the specimen gauge length cannot cool down completely before the next band is occurring. Therefore, a continuous increase of temperature was observed over the whole test. Even if the temperature increase of only few Kelvin within one individual band is quite low, the frequency of emerging PLC bands is as high that it leads to a continuous increase of temperature. Using the in situ thermography measurements it was possible to evaluate the number of bands, the maximum temperature increase within individual bands as well as their velocity propagating along the gauge length in dependence on the nominal strain rate. It was revealed that with increasing strain rate the number of emerging bands is decreasing whereas the temperature itself is increasing. At a strain rate of 10–1 s–1 no oscillating T-t curves were measured at all. Thus, the temperature increase is only due to martensitic phase transformation and not due to additional serrated plastic flow.
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A. Weidner et al. / Materials Today: Proceedings 2S (2015) S623 – S626
Detailed investigations of the critical strain for the onset of serrated plastic flow in dependence on temperature an strain rate published in [9] lead to the conclusion that the PLC effect in this type of CrMnNi steels is correlated with the interaction of carbon solute atoms with the gliding dislocations.
Fig. 2. Results of in situ infrared thermographic measurements during tensile tests of steel X5CrMnNi17.7.4 at room temperature and a nominal strain rate of 10-3 s-1. (a) True stress-true strain curve in combination with temperature evolution curves (T-t) measured at three different points along the gauge length (green, grey, red) and a sequence of infrared thermograms of the whole gauge length for low strain levels ( < 0.15). (b) Sequence of infrared thermograms of the whole gauge length for higher strain level ( > 0.15) showing the development and propagation of two individual macroscopic bands of localized plastic strain.
4. Summary The occurrence of the PLC effect was investigated on a metastable high-alloy CrMnNi cast TRIP steel (X5CrMnNi17.7.4) during tensile deformation at room temperature and different nominal strain rates. The tensile test were complemented by the measurement of local thermal fields using infrared thermography. A pronounced PLC effect was observed at room temperature in a limited field of nominal strain rates (from 10–4 s–1 up to 10–2 s–1). No PLC effect at all occurred at a strain rate of 10–1 s–1. The onset of serrated flow in the stress-strain curves depends on a critical strain, which shifts to higher strain levels with increasing of the nominal strain rate. The thermographic 0.15) and the propagation of measurements revealed a homogenous temperature increase at lower strain values ( macroscopic PLC bands along the gauge length at higher strain values ( > 0.15). Acknowledgement The authors acknowledge gratefully the German Research Foundation (DFG) for the financial support of the Collaborative Research Centre TRIP-Matrix-Composites (CRC 799). Furthermore, the authors thank Mr. G. Schade and Dr.-Ing. D. Krewerth for the support performing the tensile tests and in situ thermography measurements, respectively. References [1] A. Jahn, A. Kovalev, A. Weiß, S. Wolf, L. Krüger, P.R. Scheller, Steel Research Int. 82 (2011) 39–44. [2] L. Krüger, S. Wolf, U. Martin, S. Martin, P.R. Scheller, A. Jahn, A. Weiss, J. Phys. Conf. Ser. 240 (2010) 012098. [3] H. Biermann, J. Solarek, A. Weidner, Steel Research Int. 83 (2012) 512–520. [4] A. Vinogradov, A. Lazarev, M. Linderov, A. Weidner, H. Biermann, Acta Mater. 61 (2013) 2434–2449. [5] M. Linderov, C.Segel, A.Weidner, H.Biermann, A.Vinogradov, Mater. Sci. Eng. A 597 (2014) 183–193. [6] L.H. Almeida, I. Le May, P.R.O. Emygdio, Mater. Charac., 41 (1998) 137–150. [7] L. Bodelot, L. Sabatier, E. Charkaluk, P. Dufrénoy, Mater. Sci. Eng. A, 501 (2009) 52–60. [8] A. Saeed-Akbari, A.K. Mishra, J. Mayer, W. Bleck, Met. Mat. Trans. A, 43A (2012) 1705–1723. [9] A. Müller, C. Segel. M. Linderov, A. Vinogradov, A. Weidner, H. Biermann, Met. Mat. Trans. A (2015) in press. [10] Y. Estrin, L.P. Kubin, Acta Metall. 38 (1990) 697–708.
ScienceDirect Materials Today: Proceedings 2S (2015) S623 – S626
International Conference on Martensitic Transformations, ICOMAT-2014
Portevin Le Chatelier effect in a metastable austenitic CrMnNi steel A. Weidner*, A. Müller, H. Biermann Institute of Materials Engineering, Technische Universität Bergakademie Freiberg, 09596 Freiberg, Germany
Abstract High-alloy metastable austenitic CrMnNi steels exhibit depending on the austenite stability a transformation induced plasticity at room temperature resulting in concurrently high strength and good ductility. The martensitic phase transformation is more pronounced as lower the austenite stability is. In addition, a steel variant with low austenite stability shows a macroscopically inhomogeneous deformation behavior during monotonic loading – the so-called Portevin Le Chatelier effect, which is commonly related to the interaction of moving dislocations and diffusing solute atoms. The serrated plastic flow is related to the formation of macroscopic bands with localized plastic deformation – so-called PLC bands, which was analyzed by in situ infrared thermography. © 2014 The Authors. Published by Elsevier Ltd. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations (http://creativecommons.org/licenses/by-nc-nd/4.0/). an open access under the BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). 2014. This Selection andisPeer-review underarticle responsibility of CC the chairs of the International Conference on Martensitic Transformations 2014. Keywords: PLC effect, serrated plastic flow, TRIP, thermography
1. Introduction High-alloy CrMnNi steels are a class of materials which allows depending on their chemical composition the design of excellent mechanical properties [e.g. 1,2]. By the variation of the austenite stability and the stacking fault energy it is possible to switch between the TRIP (TRransformation Induced Plasticity) effect and the TWIP (Twinning Induced Plasticity) effect [3]. The lower the austenite stability the more pronounced is the deformationinduced martensitic phase transformation, which becomes the dominating deformation mechanism as shown in
* Corresponding author. Tel.: +49-3731-39-2124; fax: +49-3731-39-3702. E-mail address: [email protected]
2214-7853 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations 2014. doi:10.1016/j.matpr.2015.07.361
624
A. Weidner et al. / Materials Today: Proceedings 2S (2015) S623 – S626
several investigations [e.g. 3–5] already in the past. In addition, a second phenomenon occurs for the TRIP steels with low austenite stability – the serrated plastic flow at higher strain values – well known as the Portevin Le Chatelier effect. The most common interpretation in the literature is the interaction of moving dislocations with diffusing solute atoms. This phenomenon was observed by several authors in different materials [e.g. 6,7], in particular also in high manganese TWIP steels. Thus, Saeed-Akbari et al. [8] used in situ infrared thermography measurements during tensile tests in order to investigate the macroscopic strain localization in so-called PLC bands. The aim of the present study was to investigate the occurrence of PLC effect in austenitic stainless TRIP steels with low austenite stability during tensile tests in dependence on the deformation temperature as well as on the strain rate. The mechanical tests were complemented by several in situ techniques (optical image recording for digital image correlation, infrared thermography and acoustic emission). However, the present paper represents only a shortened content related to the investigation of PLC band formation by infrared thermography. A more detailed presentation of all obtained results including the discussion of the origin of the PLC effect in terms of calculated activation energy is given in [9]. 2. Experimental details The high-alloy CrMnNi steel X5CrMnNi17.7.4 with 0.05 % C, 17 % Cr, 7 % Mn, 3.7 % Ni was studied in the ascast condition after solution heat treatment (0.5 h at 1050°C followed by N2 gas quenching). The initial microstructure of this steel variant consists of metastable austenite with about 10 vol. % of δ-ferrite and approx. 15 vol. % of martensite formed during cooling. The austenitic grain size was in a range between 60 μm and 500 μm. Flat tensile specimens having a rectangular cross section of 8 mm × 4 mm and a gauge length of 35 mm at a total length of 205 mm were cut from the cast plates (ACTech, Freiberg, Germany) after solution annealing. The tensile tests were performed at room temperature using an electro-mechanical testing system (Zwick, Germany). The tensile tests were carried out under crosshead displacement control with different nominal initial strain rates (10 –4 s–1, 10–3 s–1, 10–2 s–1 and 10–1 s–1, respectively). The mechanical tests were complemented by in situ thermography measurements using the infrared thermography system VarioCamhr (InfraTec, Dresden). The gauge parts of the specimens were mechanically grinded and covered by a black thermo lacquer enabling a constant thermal emission of 0.96 for the in situ measurements of the temperature evolution along the gauge length. Ferromagnetic measurements using ferritescope were performed before and after the tensile tests in order to evaluate the volume fraction of deformation-induced ’-martensite. 3. Results and discussion Figure 1a shows the true stress-true strain curves obtained at different strain rates. For more clarity, the curves were shifted along the strain axis by 0.05. Figure 1b shows a magnified segment of the stress-strain curves to visualize the shape of serrated plastic flow. In addition, the maximum temperature (Tmax [K]) developed during tensile tests as well as the volume fraction of deformation-induced ’-martensite ( ’t [%]) are given. A vertical bar in the stress-strain curves marks the onset of the serrated plastic flow. A pronounced deformation-induced martensitic phase transformation becomes evident both from sigmoidal shape of the stress-strain curves as well as from the given volume fraction of ’-martensite at all strain rates tested at room temperature. Therefore, at room temperature the strain rate has only a small influence on the TRIP effect as well as on the amount of formed ’martensite varying between about 50 to 60 % from 10–1 s–1 to 10–4 s–1. In addition, a macroscopically inhomogeneous deformation behavior becomes obvious at higher strains in form of serrations in the stress-strain curve. According to the common understanding in the literature [10], these serrations can be related to the localization of plastic strain in macroscopic bands of several micrometer thickness propagating along the gauge length. It becomes evident from Fig. 1b that the type of serrations is changing with increasing strain rate. At the slow strain rate 10–4 s–1 the serrations lock very irregular (type B according to the literature). However, at higher strain rates (10–3 s–1 and 10–2 s–1) socalled type A bands were detected. Here, the stress drop can be clearly related to the formation of a macroscopic band of strain localization, whereas the smooth part, which follows, indicates the movement of the band along the gauge length, until the next stress drop occurs related to a new macroscopic band. Furthermore, it becomes evident
A. Weidner et al. / Materials Today: Proceedings 2S (2015) S623 – S626
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that the onset of serrated plastic flow (marked by small bar in Fig. 1a) shifts to higher strain and stress values with increasing strain rate. At a strain rate of 10–1 s–1 no serrated plastic flow was observed at all. In addition, an increase of the temperature in the specimens was observed during the tensile tests, which becomes even more pronounced with an increase of the strain rate.
Fig. 1. (a) True stress-true strain curves obtained on X5CrMnNi17.7.4 steel during tensile tests at room temperature at four different strain rates. (b) Magnified segments out of (a) visualizing the different types of serrated plastic flow in dependence on the nominal strain rate.
Using in situ infrared thermography measurements during the tensile tests, it was possible to follow the development of temperature increase along the gauge length caused by the plastic deformation. Different ongoing microstructural processes lead to this temperature increase – plasticity, the martensitic phase transformation and the localization of macroscopic deformation in the PLC bands. Figure 2 shows exemplarily the results of in situ thermographic measurements at a nominal strain rate of 10-3 s–1. The true stress-true strain curve is shown in Fig. 2a in combination with temperature evolution profiles measured at three different points along the gauge length in the first part of the tensile test. It can be clearly recognized from this T-t-curves that during the first part of deformation ( < 0.15) a continuous temperature increase occurred, which can be directly correlated with the martensitic phase transformation. It is well known from previous investigations [3-5] that the martensitic phase transformation in this specific steel variant starts immediately after passing the yield point. In addition, the T-t curves indicate clearly an oscillating behavior for higher strain levels ( > 0.15), which is related to the formation and movement of PLC bands along the gauge length. The PLC bands are starting on the left side of the gauge length (green curve) and move along the gauge length (grey and red curve). The maximum of T for the three different points can be nicely followed and shows directly that one band is followed by another one. In addition to the T-t curves, Fig. 2b shows a sequence of thermograms at different subsequent strain levels nicely illustrating again the development and propagation of two individual bands along the gauge length. It becomes evident from both Figures (2a,b) that the macroscopic localization of strain in bands is related to a remarkable increase of temperature. Moreover, the period between the appearances of two bands is quite low, thus the specimen gauge length cannot cool down completely before the next band is occurring. Therefore, a continuous increase of temperature was observed over the whole test. Even if the temperature increase of only few Kelvin within one individual band is quite low, the frequency of emerging PLC bands is as high that it leads to a continuous increase of temperature. Using the in situ thermography measurements it was possible to evaluate the number of bands, the maximum temperature increase within individual bands as well as their velocity propagating along the gauge length in dependence on the nominal strain rate. It was revealed that with increasing strain rate the number of emerging bands is decreasing whereas the temperature itself is increasing. At a strain rate of 10–1 s–1 no oscillating T-t curves were measured at all. Thus, the temperature increase is only due to martensitic phase transformation and not due to additional serrated plastic flow.
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A. Weidner et al. / Materials Today: Proceedings 2S (2015) S623 – S626
Detailed investigations of the critical strain for the onset of serrated plastic flow in dependence on temperature an strain rate published in [9] lead to the conclusion that the PLC effect in this type of CrMnNi steels is correlated with the interaction of carbon solute atoms with the gliding dislocations.
Fig. 2. Results of in situ infrared thermographic measurements during tensile tests of steel X5CrMnNi17.7.4 at room temperature and a nominal strain rate of 10-3 s-1. (a) True stress-true strain curve in combination with temperature evolution curves (T-t) measured at three different points along the gauge length (green, grey, red) and a sequence of infrared thermograms of the whole gauge length for low strain levels ( < 0.15). (b) Sequence of infrared thermograms of the whole gauge length for higher strain level ( > 0.15) showing the development and propagation of two individual macroscopic bands of localized plastic strain.
4. Summary The occurrence of the PLC effect was investigated on a metastable high-alloy CrMnNi cast TRIP steel (X5CrMnNi17.7.4) during tensile deformation at room temperature and different nominal strain rates. The tensile test were complemented by the measurement of local thermal fields using infrared thermography. A pronounced PLC effect was observed at room temperature in a limited field of nominal strain rates (from 10–4 s–1 up to 10–2 s–1). No PLC effect at all occurred at a strain rate of 10–1 s–1. The onset of serrated flow in the stress-strain curves depends on a critical strain, which shifts to higher strain levels with increasing of the nominal strain rate. The thermographic 0.15) and the propagation of measurements revealed a homogenous temperature increase at lower strain values ( macroscopic PLC bands along the gauge length at higher strain values ( > 0.15). Acknowledgement The authors acknowledge gratefully the German Research Foundation (DFG) for the financial support of the Collaborative Research Centre TRIP-Matrix-Composites (CRC 799). Furthermore, the authors thank Mr. G. Schade and Dr.-Ing. D. Krewerth for the support performing the tensile tests and in situ thermography measurements, respectively. References [1] A. Jahn, A. Kovalev, A. Weiß, S. Wolf, L. Krüger, P.R. Scheller, Steel Research Int. 82 (2011) 39–44. [2] L. Krüger, S. Wolf, U. Martin, S. Martin, P.R. Scheller, A. Jahn, A. Weiss, J. Phys. Conf. Ser. 240 (2010) 012098. [3] H. Biermann, J. Solarek, A. Weidner, Steel Research Int. 83 (2012) 512–520. [4] A. Vinogradov, A. Lazarev, M. Linderov, A. Weidner, H. Biermann, Acta Mater. 61 (2013) 2434–2449. [5] M. Linderov, C.Segel, A.Weidner, H.Biermann, A.Vinogradov, Mater. Sci. Eng. A 597 (2014) 183–193. [6] L.H. Almeida, I. Le May, P.R.O. Emygdio, Mater. Charac., 41 (1998) 137–150. [7] L. Bodelot, L. Sabatier, E. Charkaluk, P. Dufrénoy, Mater. Sci. Eng. A, 501 (2009) 52–60. [8] A. Saeed-Akbari, A.K. Mishra, J. Mayer, W. Bleck, Met. Mat. Trans. A, 43A (2012) 1705–1723. [9] A. Müller, C. Segel. M. Linderov, A. Vinogradov, A. Weidner, H. Biermann, Met. Mat. Trans. A (2015) in press. [10] Y. Estrin, L.P. Kubin, Acta Metall. 38 (1990) 697–708.