- Email: [email protected]
Formation of aligned two-phase microstructures by applying a magnetic field during the austenite to ferrite transformation in steels
Acta Materialia 51 (2003) 2921–2932 www.actamat-journals.com
Formation of aligned two-phase microstructures by applying a magnetic field during the austenite to ferrite transformation in steels M. Shimotomai a,∗, K. Maruta a,1, K. Mine b, M. Matsui c a
c
Technical Research Laboratories, Kawasaki Steel Corporation, 1, Kawasaki-cho, Chuo-ku, Chiba 260-0835, Japan b Kawasaki Steel Techno-Research Corporation, 1, Kawasaki-cho, Chuo-ku, Chiba 260-0835, Japan Department of Crystalline Material Science, School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 4648603, Japan Received 1 August 2002; received in revised form 27 December 2002; accepted 20 January 2003
Abstract Application of a magnetic field during the ferrite to austenite transformation in Fe–C alloys was found to yield a two-phase microstructure with the paramagnetic austenite grains aligned as chains or columns along the direction of the field in the matrix of ferromagnetic ferrite phase. The underlying mechanism of dipolar interactions suggests that similar alignment of microstructures should take place during the austenite to ferrite transformation under a magnetic field. In the present investigation, an experimental setup has been designed to study the magnetic alignment. Its concept is characterized by deforming steels prior to the austenite to ferrite transformation to introduce ample nucleation sites in addition to applying magnetic fields up to 12 T. Experiments have revealed successful conditions for aligned twophase microstructures in carbon steels. The formation mechanism of the aligned structures is discussed from the viewpoint of the nucleation and growth of ferrite grains in austenite phase under a magnetic field. Furthermore, it is shown that the shape of the aligned ferrite grains is determined by a balance of the magnetostatic and the interfacial energies. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Iron alloys; Steels; Magnetic field; Phase transformation; Microstructure; Aligned structure
1. Introduction Change in the potential energy of a phase by an applied magnetic field has been a subject of much ∗ ∗ Corresponding author. Present address: c/o Yoshikawa Laboratory, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan. E-mail address: [email protected] (M. Shimotomai). 1 Present address: Bar & Wire Research Department, Steel
interest in the study of phase transformation in steels. If two phases differing in saturation magnetization by an amount, 왕J, are placed in a magnetic field, H, the potential energy of the ferromagnetic phase is lowered by H왕J [1]. This effect has become apparent through several experiments on athermal martensitic transformation, and a mag-
Research Laboratories, JFE Corporation, Kurashiki 712-8511, Japan.
1359-6454/03/$30.00 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00106-X
2922
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
netic field is able to cause a rise in the Ms temperature by approximately 3 °C per magnetic field in the unit of T (Tesla) [2–4]. Diffusion-controlled transformations in steels are also influenced by a magnetic field. Pustovoit and Yu [5] applied a magnetic field of 1.2 T during the austenite decomposition of high carbon steels and found the amount of hypoeutectoid ferrite to increase. Palmai [6] reported that a magnetic field of 0.45 T retarded the inverse transformation in a 0.6%C (wt%) steel. Peters and Miodownik [7] observed the phase boundary between the austenite and ferrite of Fe–Co alloy to be shifted to a higher temperature. Recently, the influence of a strong magnetic field of 7.5 T on the kinetics of proeutectoid ferrite transformation in Fe–C base alloys was investigated [8], and it was clarified that a magnetic field accelerates the transformation below and also above the Curie temperature. Another aspect of applying external fields to steels has been a search for aligned microstructures as motivated by the remarkable magnetic annealing effect in alnico magnets [9–11]. The first observation of aligned microstructures in steels was made on Fe–0.1%C and Fe–0.6%C alloys undergoing α to γ transformation in a magnetic field of 8 T [12,13]. The microstructures are chains or columns of the γ phase developed along the magnetic field in the matrix of the α phase. Here, “chain” refers to a line of crystalline grains with a cross section containing only one grain, and “column” to a wide cylinder composed of grains. The explanation was that the alignment was due to anisotropic dipolar interactions between pairs of the paramagnetic γ grains, regarded as magnetic holes, in the matrix of ferromagnetic α phase. This model was derived from the phenomenon of field-induced alignment of particles in magnetorheological fluids [14]. In solid steels, however, structure formations are distinct from those in the fluids since the creation of “particles” through the transformation should precede the chain or column formation. Moreover, the shape of the particles would be determined by several factors such as magnetostatic, interfacial and elastic energies. These considerations reduce the structure formation in carbon steels under a magnetic field to a problem of nucleation and
growth during the ferrite transformation under a magnetic field. In respect of the ferrite transformation, γ to α transformation, none of the previous studies have mentioned an aligned microstructure induced by a magnetic field. The ferrite transformation and the martensitic one are similar in that they involve the nucleation and growth of ferrite phase in austenite phase. The nucleation in the latter transformation starts by faulting on planes of closest packing formed by dislocation arrays [15]. Intersection of deformation bands also serves for the nucleation [16]. In the ferrite transformation from hot-rolled austenite, dislocation cells, twin boundaries and deformation bands in addition to the grain boundaries have been nominated for preferential nucleation sites [17–19]. These nucleation characteristics imply that a large amount of pre-existing nucleation sites should be available if the ferrite grains would align during the transformation with a magnetic field. The aim of the current investigation is to establish the conditions and mechanism for magnetic alignment during the austenite to ferrite transformation in Fe–C alloy and steels, as aligned microstructures might be useful for an effective accumulation of plastic strain in the thermo-mechanical control process of steels. A preliminary report on a successful formation of an aligned microstructure during the austenite to ferrite transformation is found elsewhere [20].
2. Experimental The experimental setup designed and installed for the present study is shown in Fig. 1. It comprises an induction furnace, a pair of roller dies, a superconducting magnet with a furnace inside, a quenching bath, and a hydraulic drawing bench, all arranged in a line. Its main function is to give specimens a rolling deformation prior to the ferrite transformation in a magnetic field. The hot deformation makes it possible to introduce nucleation sites for the transformation. The superconducting magnet is capable of generating a magnetic field of up to 12 T inside the bore of 100 mm diameter. The inset of Fig. 1 depicts the details of the rol-
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
Fig. 1.
2923
Experimental setup for hot-rolling and the subsequent transformation in a superconducting magnet.
ling deformation. A typical rolling length of a specimen is 70 mm out of the total length of 1500 mm, determined by the size of the induction coil. The redundant length is necessary to draw the specimen through the magnet with the hydraulic drawing machine. The rolling dies are designed so that the thickness of specimens is reduced by up to 30%. The cross section of specimens was usually 4 mm width and 3 mm thickness. The temperature of a specimen is measured by a thermocouple spotwelded to the specimen. The rolling temperature is also monitored by a small pyrometer installed right after the roller dies. The starting materials for the specimens were prepared by vacuum induction melting. Thick steel plates cut from the ingots were hot-rolled at 1200 °C followed by homogenizing anneal at 1000– 1200 °C for 8 h. Subsequently, the specimens with the above-mentioned size were fabricated by coldrolling and machining. Two kinds of specimens were prepared. One was an Fe–0.6%C alloy, because its magnetic alignment during the inverse transformation had been well studied [12,13]. The others were carbon steels, Fe–0.2%C–0.2%Si– 1.3%Mn–0.1%Ti (Steel A, hereafter) and Fe– 0.1%C–2.0%Si–2.0%Mn (Steel B).
The experimental procedure was as follows: a specimen was first heated to a temperature above 1000 °C for austenization prior to hot-rolling. The temperature drop of the specimen during the rolling was measured to be about 100 °C. Subsequently, it was moved to a furnace inside the magnet bore. After keeping for a short time, 30– 300 s, for the partial transformation to ferrite, the specimen was pulled out of the magnet and quenched in water. Throughout this procedure, the specimen was displaced horizontally with a speed of 250 mm/s in an inert atmosphere. Metallographic studies were mostly performed on the thin edges of the rolled specimen etched with Nital. The crystallographic orientation of ferrite grains was measured by electron back scattering diffraction.
3. Results 3.1. Fe–C alloy A specimen of the Fe–0.6%C alloy heated in the temperature range of austenite was deformed by 30% in reduction with the roller dies. The inlet temperature of the specimen was 870 °C. Then it
2924
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
was subjected to ferrite transformation in a magnetic field of 8 T for 1.8 ks at 745 °C. Finally it was quenched in water. In addition, the transformation was not completed with this treatment since the temperature was set to be in the two-phase region of the Fe–C phase diagram. The micrograph of the specimen is shown in Fig. 2(a). Both rolling and magnetic field directions are horizontal in the photograph. The light spots are due to transformed ferrite grains while the dark area represents the notyet transformed austenite which is seen, in the photograph, as martensite phase owing to the water quenching. It should be noted that the ferrite grains are connected and aligned in the direction of the field. When the specimen is inspected normal both to rolling and field directions, Fig. 2(b), the ferrite grains are randomly dispersed. However, some are present as networks marked as K and L with the respective diameters of 30 and 70 µm. They represent the ferrite grains nucleated and grown along the grain boundaries of the austenite. Therefore, the ferrite grains should have partly nucleated at the austenite grain boundaries. In search of the early stage of the ferrite transformation, optical observation of the specimen used for Fig. 2(a) was carried out with higher magnification. The result is shown in Fig. 2(c). Most of the ferrite particles are elongated along the direction of the field. However, some are polygonal, presumably dominated by the crystallographic constraint of the nucleating sites. Also, the remains of Widmansta¨ tten structure are observed. Special attention should be paid to the ferrite particles marked A and B. They are small and represent the early stage of ferrite growth. Their shape is ellipsoidal, characterized by an aspect ratio ranging 3 to 5. The crystallographic orientation of the ferrite grains measured by electron back scattering diffraction did not show any texture. In order to understand the effects of the prior rolling and applied magnetic field on the formation of the aligned microstructures, two types of experiments were carried out for comparison. One was transformation of a specimen in a magnetic field with no prior rolling. The microstructure of the transformed specimen is shown in Fig. 3(a). Coarse ferrite grains are elongated in the direction of the field. Their separations perpendicular to the field
Fig. 2. Microstructures in Fe–0.6%C alloy subjected to the ferrite transformation in a magnetic field subsequent to hot deformation: (a) the thin edge of the specimen, (b) the cross section, and (c) the thin edge observed with higher magnification. The directions of the rolling and the field are both horizontal in the micrographs. Ferrite phases are seen as light images in the background of martensitic phase with dark contrast.
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
2925
Fig. 3. Microstructures in Fe–0.6%C specimens for control experiments, observed at the thin edges: (a) transformation in 8 T with no prior rolling, and (b) transformation in 0 T with prior rolling.
direction suggest that they nucleated and grew at the grain boundaries of the austenite. This implies that nucleation of the ferrite takes place mostly at grain boundaries if a magnetic field is imposed during the ferrite transformation with no prior deformation. This is in agreement with a previous observation [8]. The other experiment was one involving a prior rolling unaccompanied by the applied field. The result is shown in Fig. 3(b). It is noted that small ferrite grains of irregular shape are distributed randomly. A comparison between Figs. 2(a) and 3(b) suggests that a prior rolling is essential to introduce many nucleation sites in the interior of the austenite grains. It is summarized that a combination of a prior rolling and transformation in an external magnetic field is essential for the Fe–0.6%C alloy to yield a two-phase microstructure with elongated ferrite grains connected along the field in the parent phase of austenite. 3.2. Carbon steels The specimens were first austenized at 1200 °C for 10 min and then cooled in situ down to 950 °C prior to rolling. The rolling reduction in thickness was varied between 0 and 30%. Subsequently, the specimens were transferred to the furnace located at the center of the magnet for the partial ferrite transformation. Then the specimens were pulled out of the magnet and quenched in water. Experiments were carried out mainly on Steel A with the austenite grain size of about 20 µm.
Fig. 4(a) shows the microstructure of a specimen subjected to transformation in 12 T for 30 s at 755 °C subsequent to 30% rolling reduction. It is noted that fine ferrite particles, seen as bright images, are extensively elongated and connected in the direction of the field in the background of martensitic phase with dark contrast which was present as remaining austenite during the transformation. In comparison, Fig. 4(b) displays the microstructure of a specimen transformed in 12 T with no prior rolling. Here, the ferrite grains are coarse and show some tendency of elongation along the magnetic field. The nucleation should have taken place mostly at the austenite grain boundaries. Fig. 4(c) shows the microstructure transformed in zero field subsequent to 30% rolling. Here, the transformation temperature was lowered to 745 °C taking into account the absence of the potential energy induced by a magnetic field. In this case, the ferrite particles are fine owing to ample intra-granular and inter-granular nucleation sites introduced by the rolling. It is important to note that the ferrite grains are not aligned here. For the sake of further comparison, an experiment with neither prior rolling nor magnetic field was carried out. The result is shown in Fig. 4(d). It is seen that coarse polygonal ferrite particles are well developed. Thus, Fig. 4(a)–(d) demonstrates that a combination of a prior rolling and subsequent partial transformation in a magnetic field is able to yield an aligned microstructure in Steel A. Since the number density of elongated and connected ferrite
2926
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
Fig. 4. Two-phase microstructures in Fe–0.2%C–0.2%Si–1.3%Mn–0.1%Ti steel, observed at the thin edge of specimens. (a) Transformation in 12 T with prior 30% rolling, (b) in 12 T with no prior rolling, (c) in 0 T with prior 30% rolling, and (d) in 0 T with no prior rolling. The directions of the rolling and the field are both horizontal in the micrographs.
grains becomes significant above 25% rolling, their origin should be the nucleation in the interior of the austenite grains. Their frequency was found to overtake that of the grain boundary nucleation at a rolling reduction of 30%. The influence of the holding temperature in the magnet on the aligned microstructure is shown in Fig. 5(a), (b) for 765 and 760 °C, respectively. Here, the other experimental conditions were equal to the case at 755 °C displayed in Fig. 4(a). The three micrographs reveal the process of the aligned microstructure developing with decreasing temperature from 765 to 755 °C. To understand the early stage of the nucleation and growth of ferrite grains, scanning electron microscopy of the 765 °C specimen was carried out. The results are shown in Fig. 6. An example of a ferrite grain nucleated and grown within the interior of an austenite grain is shown in Fig. 6(a).
Its shape is almost elliptical with the major axis parallel to the direction of the applied field. A small deviation from an ideal ellipsoidal shape might reflect the influence of habit planes at the austenite–ferrite interface. Fig. 6(b) shows a row of ferrite grains nucleated along the grain boundary of austenite. It is noted that all the grains are elongated along the applied field. However, their shape is more irregular compared to that of Fig. 6(a). For comparison, ferrite grains appearing under no magnetic field were inspected, with the result that ferrite grains nucleated inside the austenite grains were roughly polygonal. Aligned two-phase microstructures were also observed for Steel B where the austenite containing 0.1%C is stabilized with the addition of 2.0%Si and 2.0%Mn. The alignment was similar to those in Steel A. Both in Steels A and B, aligned structures were found to be produced by an applied field down to 2 T. As far as the
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
2927
Fig. 5. Evolution of aligned two-phase structure in a steel specimen with the lowering of transformation temperature: (a) the holding temperature is 765 °C, and (b) 760 °C. Refer to Fig. 4(a) for 755 °C holding. The holding time was 30 s for each case.
Fig. 6. Scanning electron micrographs of the steel specimen as used for Fig. 5(b). (a) A ferrite particle nucleated inside an austenite grain, and (b) ferrite particles nucleated at the grain boundary of austenite.
texture is concerned, a crystallographic orientation study of the ferrite grains in Fig. 4(a) revealed no particular texture. This was also the case for the Fe–0.6%C alloy.
4. Discussion The present results have revealed that aligned two-phase microstructures may be prepared through the ferrite transformation in steels by a magnetic field applied subsequent to the hot deformation prior to the ferrite transformation. This section deals with the mechanism of the alignment, the nucleation sites of ferrite grains and the grain morphology.
4.1. Mechanism of alignment The formation mechanism of aligned structures during the inverse transformation was assigned to dipolar interactions based on a micrograph taken on a sample transforming inversely in a magnetic field and also under a temperature [12]. Applied to the present ferrite transformation, the law of dipolar interactions predicts the sequence of alignment for the ferrite transformation as follows: At the initial stage of the transformation, a ferromagnetic ferrite particle nucleates in the paramagnetic austenite. The particle with volume v carries a magnetic moment m = Mv, where M is the bulk magnetization of the ferrite phase induced by the external field. A collection of magnetic particles
2928
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
will thus behave as a many-body system with dipolar interactions. The interaction energy between spherical particle 1 and 2 separated by the distance r is given by Wdd ⫽ [m1·m2⫺3(m1·r)(m2·r)r⫺2] / 4πm0r3
(1)
This equation implies that pairs of particles aligned parallel to the magnetic field attract each other, while those with their lines of center perpendicular to the field repel each other. If creations of the particles in solids are involved as is the case for the ferrite transformation, they will take place at those nucleation sites which satisfy the above implication amongst many. A typical example of such incidents is seen at A in Fig. 2(c), where the three particles of ellipsoidal shape are seen to be closely aligned along the direction of the field at the interior of an austenite grain. Naturally, the growth of the aligned particles would have also been governed by the transformation thermodynamics. It should be added that aligned grains along the grain boundaries of austenite were produced owing to grain boundary nucleation activated by the rolling deformation. 4.2. Nucleation sites The problem of nucleation sites for the ferrite particles is discussed here. With regard to the alignment of ferrite grains in a magnetic field, the current results have revealed that a key for aligned two-phase microstructures is a hot rolling of specimens prior to the transformation. The alignment of grains in the regime of the dipolar interactions requires ample nucleation sites. Suggested nucleation sites for the ferrite transformation in hot-rolled austenite phase have been dislocations, their cells, and deformation bands in addition to the grain boundaries of austenite [17–19]. In the present study, where the prior rolling was 30% at most, dislocations and their cells are considered to be the most probable nucleation sites. The role of the deformation bands may be neglected since they are progressively accumulated above the deformation strain of 30% [17]. Carbides as inclusions will also work as intra-granular nucleation sites in Steel A containing Ti. By comparison, for the inverse transformation, dense dis-
locations and ample interfaces inherent to the starting martensite phase are supposed to serve as nucleation sites, and consequently, a prior deformation is unnecessary to obtain aligned microstructures during the inverse transformation. The lack of any preferred texture in the aligned ferrite grains is explained by a random distribution of crystallographic constraints on the nucleation sites. In addition, the anisotropy energy of the ferrite phase may not be so significant as to enhance preferred growth along the easy axis of magnetization. Subsequent to the nucleation, the nuclei are subject to a competition among inter-granular and intra-granular growth. The growth rate of ferrite nucleated at grain boundaries of Fe–C alloy is known to be increased by 10–15% under a magnetic field of 7.5 T [8], and this acceleration has been explained by a thermodynamic shift of austenite/ferrite phase boundaries by the magnetic field. In regard to the intra-granular ferrite growth, the influence of a magnetic field is expected to be of the same order since the lowering of the potential energy is not different for both inter- and intragranular ferrites. A part of the driving force for growth rate will also come from the strain energy, if a prior deformation is involved. In such a case, inter-granular growth will be advantageous over intra-granular growth, owing to the larger strain energy accumulated at grain boundaries. This explanation is supported by micrographs. In Fig. 5(a), taken at 765 °C, the nucleation of ferrite grains is seen to take place homogeneously, while in Fig. 5(b), at 760 °C, a preferred growth of ferrite nuclei at grain boundaries is evident. Coarse grains of irregular shape, as found in Figs. 2(c) and 4(a), are ascribed to the nucleation and growth at grain boundaries or at the triple points. Present results suggest that intra-granular ferrite grains dominate over the inter-granular ones if the prior rolling deformation is equal to or in excess of 30%. 4.3. Ferrite morphology The current results have shown that ferrite particles nucleated and grown in the interior of austenite grains under magnetic fields are mostly ellipsoidal in shape. In the following, the aspect ratio
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
of the ellipsoids is argued with a simplified model. The basic assumptions of the model are as follows. 1. A ferromagnetic ferrite particle, assumed to be ellipsoidal, is embedded in an isotropic continuum of paramagnetic austenite. A demagnetizing field is formed inside the ellipsoid if exposed to an external magnetic field. Its direction always opposes that of the applied field; the demagnetizing field therefore weakens the total field inside the ellipsoid. Minimizing the demagnetizing field favors the formation of long and thin ferrite grains. 2. Creating the surface of the ferrite particle costs interfacial energy. 3. Strain energy associated with an ellipsoidal ferrite particle embedded in the matrix of austenite is weakly dependent on its shape. This assumption is justified by the calculation that the strain energy is almost independent of the aspect ratio for a prolate ellipsoidal particle if the difference between the shear moduli of the particle and the matrix is small [21]. 4. The chemical driving force for the transformation depends only on the volume of the nuclei. 5. The interaction energy of a ferrite particle with other particles is small compared to the interaction energy with the external field or to the surface energy of the particle. The particle shape is determined by a competition between the magnetic field energy, which favors an elongated shape, and interfacial energy, which favors a spherical shape. The total energy of a ferromagnetic ellipsoid with 왕M, the bulk saturation magnetization relative to the matrix, is derived in Appendix A, and given by Et ⫽
2π 3 a (⌬M)2(kN ⫹ ASk) 3
2929
respectively. The first term of Eq. (2) represents the magnetostatic energy of a prolate ellipsoid with the radii of minor axis a and of major axis c. The second term is due to the total interfacial energy of the ellipsoid. The interfacial energy g between the ferrite and austenite was estimated to be ~200 erg/cm2 at the transformation temperature [23]. The aspect ratio of the ellipsoid is defined by k = c / a. Equations necessary to calculate the aspect ratio k vs. a for a particular value of 왕M are described in Appendix A. The relation is shown in Fig. 7 for 왕M = 30, 50, 70 and 90 emu / g. Here, 왕M is set to the saturation magnetization of the ferrite M, since the magnetization of austenite is negligibly small. We have estimated the values of M under a magnetic field at a transforming temperature by a calculation based on Weiss molecular field theory (refer to the appendix in Ref. [8]). In Fig. 8, the magnetization of iron regarded as equivalent to that of ferrite is plotted vs. temperature for various applied fields. It should be noted that a magnetic field as low as 1 T is able to induce considerable magnetization above the Curie temperature of iron. This suggests that a magnetic field of 1 T may be able to yield aligned structures. Also, an applied magnetic field is known to enhance the transformation start temperature by ~3 °C per T [2–4]. From the standpoint of controlling the transformation, a magnetic field larger than 2 T would be desirable to have a temperature margin of ~6 °C for the magnetic alignment.
(2)
Here, N is a demagnetizing factor for the major axis [22], and Sk and A stand for Sk ⫽ 1 ⫹
k2
1 arccos k 冑k ⫺1 2
and A⫽
3g , (⌬M)2a
Fig. 7. Relation between the aspect ratio of a magnetic ellipsoid and the radius of the minor axis for 왕M = 30, 50, 70 and 90 emu / g.
2930
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
Fig. 8.
The magnetization of iron under external magnetic fields calculated based on Weiss molecular field theory.
It is now possible to compare the measured aspect ratio with the calculaton. We have chosen several isolated transforming ellipsoids: the ellipsoid marked B in Fig. 2(c), and the intra-granular ellipsoid in Fig. 6(a). The ellipsoids of austenite formed during the inverse transformations in Fe– 0.1%C alloy [20] and in Fe–0.6%C alloy [12] were also analyzed. Table 1 is a list of the measured aspect ratios along with calculated values for the ellipsoids. It is stressed that the simplified model approximately accounts for the aspect ratio. Interestingly, experimental aspect ratios for the ferrite
transformation are larger than those of the theoretical values, and vice versa for the inverse transformation. This may be related to the volume expansion of 1% associated with the former or the contraction of the same order with the latter.
5. Summary In search of the formation of two-phase microstructures aligned with the direction of a magnetic field applied during the ferrite transformation in
Table 1 Analysis of morphology of transforming ellipsoids Specimen for ferrite Transformation temperature Applied ellipsoid (°C) magnetic field (kOe)
Magnetization (왕M) (emu/g)
Radius of minor axis a (µm)
Aspect ratio (k) Aspect ratio (measured) (k) (calculated)
Fe–0.6%C alloya Steelb (Fe–0.2C– 2Si–1.3Mn–0.1Ti) Fe–0.1%C alloyc Fe–0.6%C alloyd
75 72
1.25 0.5
4.0 2.5
2.3 1.7
38 69
7.5 8.7
2.0 3.5
2.7 4.9
a b c d
An An An An
Ferrite transformation 745 Ferrite transformation 760
80 120
Inverse transformation 800 80 Inverse transformation 742 40
ellipsoid marked as B in Fig. 2(c). intra-granular ellipsoid in Fig. 6(a). ellipsoid appearing during the inverse transformation of Fe–0.1%C alloy [20]. ellipsoid appearing during the inverse transformation of Fe–0.6%C alloy [12].
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
carbon steels, an experimental setup was designed and installed. It features a combination of rollerdies for hot deformation and a superconducting magnet for applying a magnetic field during the transformation. Successful conditions for aligned two-phase microstructures in carbon steels have been established. The carbon content necessary for the aligned structures is determined by the Fe–C phase diagram. Experimentally, it was between 0.1 and 0.6 wt%C. The steels have to undergo rolling deformation of more than 30% in the temperature range, where the recrystallization of the austenite does not take place. This condition is necessary to secure ample intra-granular nucleation sites for aligned nucleation. A magnetic field of more than 2 T should be applied during the ferrite transformation at a temperature in the two-phase region of the steel. Formation of the aligned structure is analyzed and discussed from the standpoint of nucleation and growth of the transforming ferrite grains under the law of dipolar interactions. The aligned ferrite grains were found to show no particular preferred crystallographic orientations. The advantage of the aligned microstructures may be found in the field of fine-grained steels since an efficient accumulation of plastic strain is expected with the deformation of elastically heterogeneous two-phase steels. Currently, finite element calculations coupled with grain refining experiments through rolling and subsequent recrystallization are underway. Acknowledgements The authors are indebted to Mr. Y. Yonehana for his valuable technical assistance. The present investigation was carried out as a part of the research activities of the Ferrous Super Metal Consortium of Japan under the auspices of the New Energy Development Organization of Japan, NEDO. Appendix A. Aspect ratio of ferromagnetic ellipsoid embedded in a paramagnetic matrix The magnetostatic energy of a prolate ellipsoidal particle embedded in matrix magnetized parallel to the major axis is given by the following equation:
2931
1 2π Emag ⫽ N(⌬M)2V ⫽ a2cN(⌬M)2 2 3
(A.1)
Here, a is the radius of the two equal minor axes, and c the radius of major axis. V denotes the particle volume. 왕M stands for the difference of the saturation magnetization between the particle and the matrix. Since the magnetic susceptibility of the austenite c is the order of ~10–6 emu/g Oe, its magnetization at 120 kOe (equivalent to 12 T) amounts to only ~0.12 emu/g, negligibly small compared to that of ferrite, 220 emu/g at room temperature. N in Eq. (A.1) represents a demagnetizing factor for the major axis, and is given by [22] N ⫽
冋冑
4π k ⫺1 2
冉
冊 册
ln k ⫹ 冑k2⫺1 ⫺1 k ⫺1 k
2
(A.2)
Here, k is defined as the ratio of major axis to minor axis c/a, and called aspect ratio. Since the particle has interfacial energy g in addition to the magnetostatic energy, the total interfacial energy for an ellipsoid Esur is expressed as
再
Esur ⫽ 2πga2 1 ⫹
k2
冎
1 arccos k 冑k ⫺1 2
(A.3)
The total energyEt of a ferrite particle is given by adding Eqs. (A.1) and (A.3), Et ⫽
2π 3 a (⌬M)2(kN ⫹ ASk) 3
(A.4)
This expression already appeared as Eq. (2) in the text, and Sk and A were given as Sk ⫽ 1 ⫹
k2
1 arccos k 冑k ⫺1
(A.5)
2
and A⫽
3g , (⌬M)2a
(A.6)
respectively. Differentiation of Eq. (A.4) with respect to k and a determines the most stable shape of the ellipsoid:
冉
∂N ∂Sk ∂Et 2 3 ⫽ πa (⌬M)2 k ⫹ N ⫹ A ∂k 3 ∂k ∂k ⫽0
冊
(A.7)
2932
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
and ∂Et ⫽ 2πa2(⌬M)2(kN ⫹ ASk) ⫽ 0 ∂a
(A.8)
Furthermore, auxiliary conditions for the minimum are given as follows:
冉
∂2N ∂N ∂2Et 2 3 2 πa ⫽ (⌬M) k ⫹2 2 2 ∂k 3 ∂k ∂k
冊
(A.9)
∂2 S k ⫹A 2 ⬎0 ∂k and ∂2Et ⫽ 4πa(⌬M)2(kN ⫹ ASk) ⬎ 0 ∂a2
(A.10)
Combining (A.7) with (A.8), one can compute a relation between k and a for a particular value of 왕M. Fig. 7 shows the results for 왕M = 30, 50, 70 and 90 emu / g. Finally, it is added that both (A.7) and (A.8) are automatically satisfied if a = 0. This trivial solution exists because the chemical free energy change involved in the generation of the particles through the ferrite transformation has been neglected in Eq. (A.4) for the sake of simplicity.
References [1] Saunders N, Miodownik AP. In: CALPHAD. Oxford: Elsevier Science; 1998. p. 253–8.
[2] Sadovskiy VD, Rodigin L, Smirnov LV, Filonchik GM, Fakidov IG. Phys Met Metallogr 1961;12:131. [3] Satyanarayan KR, Eliasz W, Miodownik AP. Acta Metall 1968;16:877. [4] Fields R, Graham CD. Metall Trans 1976;7A:719. [5] Pustovoit VN, Dombrovskii YuM, Grishin SA. Metalloved Term Obrab Met 1979:22. [6] Palmai Z. Gepgyartastechnologia [in Hungarian] 1982;22:463. [7] Peters CT, Miodownik AP. Scr Met 1973;7:955. [8] Enomoto M, Guo H, Tazuke Y, Abe YR, Shimotomai M. Metall Mater Trans 2001;32A:445. [9] Jones B, von Emden HJM. Philips Tech Rev 1941;6:8. [10] Cahn JW. J Appl Phys 1963;34:3581. [11] Iwama Y, Takeuchi M. Trans Jpn Inst Met 1974;15:371. [12] Shimotomai M, Maruta K. Scr Mater 2000;42:499. [13] Maruta K, Shimotomai M. Mater Trans JIM 2000;41:902. [14] Skjeltorp AT. J Appl Phys 1985;57:3285. [15] Olson GB, Cohen M. Metall Trans 1976;7:A 1897, 1905, 1915. [16] Lecroisey F, Pineau A. Metall Trans 1972;3:387. [17] Ouchi C, Sampei T, Kozasu I. Trans ISIJ 1982;22:214. [18] Tanaka T. In: Korchynsky M, DeArdo AJ, Repas P, Tither G, editors. Microalloying 95, ISS, Pittsburgh. 1995. p. 165. [19] Bengochea R, Lo´ pez B, Gutierrez I. In: Rodriguez-Ibabe JM, Gutie´ rrez I, Lo´ pez B, editors. Proceedings of the International Conference on Microalloying in Steels. Zuerich: Trans Tech Publications; 1998. p. 201–8. [20] Maruta K, Shimotomai M. Proceedings of the 13th International Conference on Crystal Growth, July 2001, Kyoto. J Cryst Growth 2002;237-239:1802. [21] Barnett DM, Lee JK, Aaronson HI, Russell KC. Scr Met 1974;8:1447. [22] Bozoroth RM. Ferromagnetism. New York: IEEE Press; 1951. p. 849 [re-issued in 1993]. [23] Radcliffe SV, Cohen M. In: Zackay VF, Aaronson HI, editors. Decomposition of austenite by diffusional processes. New York: Interscience Publishers; 1962. p. 34-0.
Formation of aligned two-phase microstructures by applying a magnetic field during the austenite to ferrite transformation in steels M. Shimotomai a,∗, K. Maruta a,1, K. Mine b, M. Matsui c a
c
Technical Research Laboratories, Kawasaki Steel Corporation, 1, Kawasaki-cho, Chuo-ku, Chiba 260-0835, Japan b Kawasaki Steel Techno-Research Corporation, 1, Kawasaki-cho, Chuo-ku, Chiba 260-0835, Japan Department of Crystalline Material Science, School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 4648603, Japan Received 1 August 2002; received in revised form 27 December 2002; accepted 20 January 2003
Abstract Application of a magnetic field during the ferrite to austenite transformation in Fe–C alloys was found to yield a two-phase microstructure with the paramagnetic austenite grains aligned as chains or columns along the direction of the field in the matrix of ferromagnetic ferrite phase. The underlying mechanism of dipolar interactions suggests that similar alignment of microstructures should take place during the austenite to ferrite transformation under a magnetic field. In the present investigation, an experimental setup has been designed to study the magnetic alignment. Its concept is characterized by deforming steels prior to the austenite to ferrite transformation to introduce ample nucleation sites in addition to applying magnetic fields up to 12 T. Experiments have revealed successful conditions for aligned twophase microstructures in carbon steels. The formation mechanism of the aligned structures is discussed from the viewpoint of the nucleation and growth of ferrite grains in austenite phase under a magnetic field. Furthermore, it is shown that the shape of the aligned ferrite grains is determined by a balance of the magnetostatic and the interfacial energies. 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Iron alloys; Steels; Magnetic field; Phase transformation; Microstructure; Aligned structure
1. Introduction Change in the potential energy of a phase by an applied magnetic field has been a subject of much ∗ ∗ Corresponding author. Present address: c/o Yoshikawa Laboratory, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan. E-mail address: [email protected] (M. Shimotomai). 1 Present address: Bar & Wire Research Department, Steel
interest in the study of phase transformation in steels. If two phases differing in saturation magnetization by an amount, 왕J, are placed in a magnetic field, H, the potential energy of the ferromagnetic phase is lowered by H왕J [1]. This effect has become apparent through several experiments on athermal martensitic transformation, and a mag-
Research Laboratories, JFE Corporation, Kurashiki 712-8511, Japan.
1359-6454/03/$30.00 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved. doi:10.1016/S1359-6454(03)00106-X
2922
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
netic field is able to cause a rise in the Ms temperature by approximately 3 °C per magnetic field in the unit of T (Tesla) [2–4]. Diffusion-controlled transformations in steels are also influenced by a magnetic field. Pustovoit and Yu [5] applied a magnetic field of 1.2 T during the austenite decomposition of high carbon steels and found the amount of hypoeutectoid ferrite to increase. Palmai [6] reported that a magnetic field of 0.45 T retarded the inverse transformation in a 0.6%C (wt%) steel. Peters and Miodownik [7] observed the phase boundary between the austenite and ferrite of Fe–Co alloy to be shifted to a higher temperature. Recently, the influence of a strong magnetic field of 7.5 T on the kinetics of proeutectoid ferrite transformation in Fe–C base alloys was investigated [8], and it was clarified that a magnetic field accelerates the transformation below and also above the Curie temperature. Another aspect of applying external fields to steels has been a search for aligned microstructures as motivated by the remarkable magnetic annealing effect in alnico magnets [9–11]. The first observation of aligned microstructures in steels was made on Fe–0.1%C and Fe–0.6%C alloys undergoing α to γ transformation in a magnetic field of 8 T [12,13]. The microstructures are chains or columns of the γ phase developed along the magnetic field in the matrix of the α phase. Here, “chain” refers to a line of crystalline grains with a cross section containing only one grain, and “column” to a wide cylinder composed of grains. The explanation was that the alignment was due to anisotropic dipolar interactions between pairs of the paramagnetic γ grains, regarded as magnetic holes, in the matrix of ferromagnetic α phase. This model was derived from the phenomenon of field-induced alignment of particles in magnetorheological fluids [14]. In solid steels, however, structure formations are distinct from those in the fluids since the creation of “particles” through the transformation should precede the chain or column formation. Moreover, the shape of the particles would be determined by several factors such as magnetostatic, interfacial and elastic energies. These considerations reduce the structure formation in carbon steels under a magnetic field to a problem of nucleation and
growth during the ferrite transformation under a magnetic field. In respect of the ferrite transformation, γ to α transformation, none of the previous studies have mentioned an aligned microstructure induced by a magnetic field. The ferrite transformation and the martensitic one are similar in that they involve the nucleation and growth of ferrite phase in austenite phase. The nucleation in the latter transformation starts by faulting on planes of closest packing formed by dislocation arrays [15]. Intersection of deformation bands also serves for the nucleation [16]. In the ferrite transformation from hot-rolled austenite, dislocation cells, twin boundaries and deformation bands in addition to the grain boundaries have been nominated for preferential nucleation sites [17–19]. These nucleation characteristics imply that a large amount of pre-existing nucleation sites should be available if the ferrite grains would align during the transformation with a magnetic field. The aim of the current investigation is to establish the conditions and mechanism for magnetic alignment during the austenite to ferrite transformation in Fe–C alloy and steels, as aligned microstructures might be useful for an effective accumulation of plastic strain in the thermo-mechanical control process of steels. A preliminary report on a successful formation of an aligned microstructure during the austenite to ferrite transformation is found elsewhere [20].
2. Experimental The experimental setup designed and installed for the present study is shown in Fig. 1. It comprises an induction furnace, a pair of roller dies, a superconducting magnet with a furnace inside, a quenching bath, and a hydraulic drawing bench, all arranged in a line. Its main function is to give specimens a rolling deformation prior to the ferrite transformation in a magnetic field. The hot deformation makes it possible to introduce nucleation sites for the transformation. The superconducting magnet is capable of generating a magnetic field of up to 12 T inside the bore of 100 mm diameter. The inset of Fig. 1 depicts the details of the rol-
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
Fig. 1.
2923
Experimental setup for hot-rolling and the subsequent transformation in a superconducting magnet.
ling deformation. A typical rolling length of a specimen is 70 mm out of the total length of 1500 mm, determined by the size of the induction coil. The redundant length is necessary to draw the specimen through the magnet with the hydraulic drawing machine. The rolling dies are designed so that the thickness of specimens is reduced by up to 30%. The cross section of specimens was usually 4 mm width and 3 mm thickness. The temperature of a specimen is measured by a thermocouple spotwelded to the specimen. The rolling temperature is also monitored by a small pyrometer installed right after the roller dies. The starting materials for the specimens were prepared by vacuum induction melting. Thick steel plates cut from the ingots were hot-rolled at 1200 °C followed by homogenizing anneal at 1000– 1200 °C for 8 h. Subsequently, the specimens with the above-mentioned size were fabricated by coldrolling and machining. Two kinds of specimens were prepared. One was an Fe–0.6%C alloy, because its magnetic alignment during the inverse transformation had been well studied [12,13]. The others were carbon steels, Fe–0.2%C–0.2%Si– 1.3%Mn–0.1%Ti (Steel A, hereafter) and Fe– 0.1%C–2.0%Si–2.0%Mn (Steel B).
The experimental procedure was as follows: a specimen was first heated to a temperature above 1000 °C for austenization prior to hot-rolling. The temperature drop of the specimen during the rolling was measured to be about 100 °C. Subsequently, it was moved to a furnace inside the magnet bore. After keeping for a short time, 30– 300 s, for the partial transformation to ferrite, the specimen was pulled out of the magnet and quenched in water. Throughout this procedure, the specimen was displaced horizontally with a speed of 250 mm/s in an inert atmosphere. Metallographic studies were mostly performed on the thin edges of the rolled specimen etched with Nital. The crystallographic orientation of ferrite grains was measured by electron back scattering diffraction.
3. Results 3.1. Fe–C alloy A specimen of the Fe–0.6%C alloy heated in the temperature range of austenite was deformed by 30% in reduction with the roller dies. The inlet temperature of the specimen was 870 °C. Then it
2924
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
was subjected to ferrite transformation in a magnetic field of 8 T for 1.8 ks at 745 °C. Finally it was quenched in water. In addition, the transformation was not completed with this treatment since the temperature was set to be in the two-phase region of the Fe–C phase diagram. The micrograph of the specimen is shown in Fig. 2(a). Both rolling and magnetic field directions are horizontal in the photograph. The light spots are due to transformed ferrite grains while the dark area represents the notyet transformed austenite which is seen, in the photograph, as martensite phase owing to the water quenching. It should be noted that the ferrite grains are connected and aligned in the direction of the field. When the specimen is inspected normal both to rolling and field directions, Fig. 2(b), the ferrite grains are randomly dispersed. However, some are present as networks marked as K and L with the respective diameters of 30 and 70 µm. They represent the ferrite grains nucleated and grown along the grain boundaries of the austenite. Therefore, the ferrite grains should have partly nucleated at the austenite grain boundaries. In search of the early stage of the ferrite transformation, optical observation of the specimen used for Fig. 2(a) was carried out with higher magnification. The result is shown in Fig. 2(c). Most of the ferrite particles are elongated along the direction of the field. However, some are polygonal, presumably dominated by the crystallographic constraint of the nucleating sites. Also, the remains of Widmansta¨ tten structure are observed. Special attention should be paid to the ferrite particles marked A and B. They are small and represent the early stage of ferrite growth. Their shape is ellipsoidal, characterized by an aspect ratio ranging 3 to 5. The crystallographic orientation of the ferrite grains measured by electron back scattering diffraction did not show any texture. In order to understand the effects of the prior rolling and applied magnetic field on the formation of the aligned microstructures, two types of experiments were carried out for comparison. One was transformation of a specimen in a magnetic field with no prior rolling. The microstructure of the transformed specimen is shown in Fig. 3(a). Coarse ferrite grains are elongated in the direction of the field. Their separations perpendicular to the field
Fig. 2. Microstructures in Fe–0.6%C alloy subjected to the ferrite transformation in a magnetic field subsequent to hot deformation: (a) the thin edge of the specimen, (b) the cross section, and (c) the thin edge observed with higher magnification. The directions of the rolling and the field are both horizontal in the micrographs. Ferrite phases are seen as light images in the background of martensitic phase with dark contrast.
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
2925
Fig. 3. Microstructures in Fe–0.6%C specimens for control experiments, observed at the thin edges: (a) transformation in 8 T with no prior rolling, and (b) transformation in 0 T with prior rolling.
direction suggest that they nucleated and grew at the grain boundaries of the austenite. This implies that nucleation of the ferrite takes place mostly at grain boundaries if a magnetic field is imposed during the ferrite transformation with no prior deformation. This is in agreement with a previous observation [8]. The other experiment was one involving a prior rolling unaccompanied by the applied field. The result is shown in Fig. 3(b). It is noted that small ferrite grains of irregular shape are distributed randomly. A comparison between Figs. 2(a) and 3(b) suggests that a prior rolling is essential to introduce many nucleation sites in the interior of the austenite grains. It is summarized that a combination of a prior rolling and transformation in an external magnetic field is essential for the Fe–0.6%C alloy to yield a two-phase microstructure with elongated ferrite grains connected along the field in the parent phase of austenite. 3.2. Carbon steels The specimens were first austenized at 1200 °C for 10 min and then cooled in situ down to 950 °C prior to rolling. The rolling reduction in thickness was varied between 0 and 30%. Subsequently, the specimens were transferred to the furnace located at the center of the magnet for the partial ferrite transformation. Then the specimens were pulled out of the magnet and quenched in water. Experiments were carried out mainly on Steel A with the austenite grain size of about 20 µm.
Fig. 4(a) shows the microstructure of a specimen subjected to transformation in 12 T for 30 s at 755 °C subsequent to 30% rolling reduction. It is noted that fine ferrite particles, seen as bright images, are extensively elongated and connected in the direction of the field in the background of martensitic phase with dark contrast which was present as remaining austenite during the transformation. In comparison, Fig. 4(b) displays the microstructure of a specimen transformed in 12 T with no prior rolling. Here, the ferrite grains are coarse and show some tendency of elongation along the magnetic field. The nucleation should have taken place mostly at the austenite grain boundaries. Fig. 4(c) shows the microstructure transformed in zero field subsequent to 30% rolling. Here, the transformation temperature was lowered to 745 °C taking into account the absence of the potential energy induced by a magnetic field. In this case, the ferrite particles are fine owing to ample intra-granular and inter-granular nucleation sites introduced by the rolling. It is important to note that the ferrite grains are not aligned here. For the sake of further comparison, an experiment with neither prior rolling nor magnetic field was carried out. The result is shown in Fig. 4(d). It is seen that coarse polygonal ferrite particles are well developed. Thus, Fig. 4(a)–(d) demonstrates that a combination of a prior rolling and subsequent partial transformation in a magnetic field is able to yield an aligned microstructure in Steel A. Since the number density of elongated and connected ferrite
2926
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
Fig. 4. Two-phase microstructures in Fe–0.2%C–0.2%Si–1.3%Mn–0.1%Ti steel, observed at the thin edge of specimens. (a) Transformation in 12 T with prior 30% rolling, (b) in 12 T with no prior rolling, (c) in 0 T with prior 30% rolling, and (d) in 0 T with no prior rolling. The directions of the rolling and the field are both horizontal in the micrographs.
grains becomes significant above 25% rolling, their origin should be the nucleation in the interior of the austenite grains. Their frequency was found to overtake that of the grain boundary nucleation at a rolling reduction of 30%. The influence of the holding temperature in the magnet on the aligned microstructure is shown in Fig. 5(a), (b) for 765 and 760 °C, respectively. Here, the other experimental conditions were equal to the case at 755 °C displayed in Fig. 4(a). The three micrographs reveal the process of the aligned microstructure developing with decreasing temperature from 765 to 755 °C. To understand the early stage of the nucleation and growth of ferrite grains, scanning electron microscopy of the 765 °C specimen was carried out. The results are shown in Fig. 6. An example of a ferrite grain nucleated and grown within the interior of an austenite grain is shown in Fig. 6(a).
Its shape is almost elliptical with the major axis parallel to the direction of the applied field. A small deviation from an ideal ellipsoidal shape might reflect the influence of habit planes at the austenite–ferrite interface. Fig. 6(b) shows a row of ferrite grains nucleated along the grain boundary of austenite. It is noted that all the grains are elongated along the applied field. However, their shape is more irregular compared to that of Fig. 6(a). For comparison, ferrite grains appearing under no magnetic field were inspected, with the result that ferrite grains nucleated inside the austenite grains were roughly polygonal. Aligned two-phase microstructures were also observed for Steel B where the austenite containing 0.1%C is stabilized with the addition of 2.0%Si and 2.0%Mn. The alignment was similar to those in Steel A. Both in Steels A and B, aligned structures were found to be produced by an applied field down to 2 T. As far as the
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
2927
Fig. 5. Evolution of aligned two-phase structure in a steel specimen with the lowering of transformation temperature: (a) the holding temperature is 765 °C, and (b) 760 °C. Refer to Fig. 4(a) for 755 °C holding. The holding time was 30 s for each case.
Fig. 6. Scanning electron micrographs of the steel specimen as used for Fig. 5(b). (a) A ferrite particle nucleated inside an austenite grain, and (b) ferrite particles nucleated at the grain boundary of austenite.
texture is concerned, a crystallographic orientation study of the ferrite grains in Fig. 4(a) revealed no particular texture. This was also the case for the Fe–0.6%C alloy.
4. Discussion The present results have revealed that aligned two-phase microstructures may be prepared through the ferrite transformation in steels by a magnetic field applied subsequent to the hot deformation prior to the ferrite transformation. This section deals with the mechanism of the alignment, the nucleation sites of ferrite grains and the grain morphology.
4.1. Mechanism of alignment The formation mechanism of aligned structures during the inverse transformation was assigned to dipolar interactions based on a micrograph taken on a sample transforming inversely in a magnetic field and also under a temperature [12]. Applied to the present ferrite transformation, the law of dipolar interactions predicts the sequence of alignment for the ferrite transformation as follows: At the initial stage of the transformation, a ferromagnetic ferrite particle nucleates in the paramagnetic austenite. The particle with volume v carries a magnetic moment m = Mv, where M is the bulk magnetization of the ferrite phase induced by the external field. A collection of magnetic particles
2928
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
will thus behave as a many-body system with dipolar interactions. The interaction energy between spherical particle 1 and 2 separated by the distance r is given by Wdd ⫽ [m1·m2⫺3(m1·r)(m2·r)r⫺2] / 4πm0r3
(1)
This equation implies that pairs of particles aligned parallel to the magnetic field attract each other, while those with their lines of center perpendicular to the field repel each other. If creations of the particles in solids are involved as is the case for the ferrite transformation, they will take place at those nucleation sites which satisfy the above implication amongst many. A typical example of such incidents is seen at A in Fig. 2(c), where the three particles of ellipsoidal shape are seen to be closely aligned along the direction of the field at the interior of an austenite grain. Naturally, the growth of the aligned particles would have also been governed by the transformation thermodynamics. It should be added that aligned grains along the grain boundaries of austenite were produced owing to grain boundary nucleation activated by the rolling deformation. 4.2. Nucleation sites The problem of nucleation sites for the ferrite particles is discussed here. With regard to the alignment of ferrite grains in a magnetic field, the current results have revealed that a key for aligned two-phase microstructures is a hot rolling of specimens prior to the transformation. The alignment of grains in the regime of the dipolar interactions requires ample nucleation sites. Suggested nucleation sites for the ferrite transformation in hot-rolled austenite phase have been dislocations, their cells, and deformation bands in addition to the grain boundaries of austenite [17–19]. In the present study, where the prior rolling was 30% at most, dislocations and their cells are considered to be the most probable nucleation sites. The role of the deformation bands may be neglected since they are progressively accumulated above the deformation strain of 30% [17]. Carbides as inclusions will also work as intra-granular nucleation sites in Steel A containing Ti. By comparison, for the inverse transformation, dense dis-
locations and ample interfaces inherent to the starting martensite phase are supposed to serve as nucleation sites, and consequently, a prior deformation is unnecessary to obtain aligned microstructures during the inverse transformation. The lack of any preferred texture in the aligned ferrite grains is explained by a random distribution of crystallographic constraints on the nucleation sites. In addition, the anisotropy energy of the ferrite phase may not be so significant as to enhance preferred growth along the easy axis of magnetization. Subsequent to the nucleation, the nuclei are subject to a competition among inter-granular and intra-granular growth. The growth rate of ferrite nucleated at grain boundaries of Fe–C alloy is known to be increased by 10–15% under a magnetic field of 7.5 T [8], and this acceleration has been explained by a thermodynamic shift of austenite/ferrite phase boundaries by the magnetic field. In regard to the intra-granular ferrite growth, the influence of a magnetic field is expected to be of the same order since the lowering of the potential energy is not different for both inter- and intragranular ferrites. A part of the driving force for growth rate will also come from the strain energy, if a prior deformation is involved. In such a case, inter-granular growth will be advantageous over intra-granular growth, owing to the larger strain energy accumulated at grain boundaries. This explanation is supported by micrographs. In Fig. 5(a), taken at 765 °C, the nucleation of ferrite grains is seen to take place homogeneously, while in Fig. 5(b), at 760 °C, a preferred growth of ferrite nuclei at grain boundaries is evident. Coarse grains of irregular shape, as found in Figs. 2(c) and 4(a), are ascribed to the nucleation and growth at grain boundaries or at the triple points. Present results suggest that intra-granular ferrite grains dominate over the inter-granular ones if the prior rolling deformation is equal to or in excess of 30%. 4.3. Ferrite morphology The current results have shown that ferrite particles nucleated and grown in the interior of austenite grains under magnetic fields are mostly ellipsoidal in shape. In the following, the aspect ratio
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
of the ellipsoids is argued with a simplified model. The basic assumptions of the model are as follows. 1. A ferromagnetic ferrite particle, assumed to be ellipsoidal, is embedded in an isotropic continuum of paramagnetic austenite. A demagnetizing field is formed inside the ellipsoid if exposed to an external magnetic field. Its direction always opposes that of the applied field; the demagnetizing field therefore weakens the total field inside the ellipsoid. Minimizing the demagnetizing field favors the formation of long and thin ferrite grains. 2. Creating the surface of the ferrite particle costs interfacial energy. 3. Strain energy associated with an ellipsoidal ferrite particle embedded in the matrix of austenite is weakly dependent on its shape. This assumption is justified by the calculation that the strain energy is almost independent of the aspect ratio for a prolate ellipsoidal particle if the difference between the shear moduli of the particle and the matrix is small [21]. 4. The chemical driving force for the transformation depends only on the volume of the nuclei. 5. The interaction energy of a ferrite particle with other particles is small compared to the interaction energy with the external field or to the surface energy of the particle. The particle shape is determined by a competition between the magnetic field energy, which favors an elongated shape, and interfacial energy, which favors a spherical shape. The total energy of a ferromagnetic ellipsoid with 왕M, the bulk saturation magnetization relative to the matrix, is derived in Appendix A, and given by Et ⫽
2π 3 a (⌬M)2(kN ⫹ ASk) 3
2929
respectively. The first term of Eq. (2) represents the magnetostatic energy of a prolate ellipsoid with the radii of minor axis a and of major axis c. The second term is due to the total interfacial energy of the ellipsoid. The interfacial energy g between the ferrite and austenite was estimated to be ~200 erg/cm2 at the transformation temperature [23]. The aspect ratio of the ellipsoid is defined by k = c / a. Equations necessary to calculate the aspect ratio k vs. a for a particular value of 왕M are described in Appendix A. The relation is shown in Fig. 7 for 왕M = 30, 50, 70 and 90 emu / g. Here, 왕M is set to the saturation magnetization of the ferrite M, since the magnetization of austenite is negligibly small. We have estimated the values of M under a magnetic field at a transforming temperature by a calculation based on Weiss molecular field theory (refer to the appendix in Ref. [8]). In Fig. 8, the magnetization of iron regarded as equivalent to that of ferrite is plotted vs. temperature for various applied fields. It should be noted that a magnetic field as low as 1 T is able to induce considerable magnetization above the Curie temperature of iron. This suggests that a magnetic field of 1 T may be able to yield aligned structures. Also, an applied magnetic field is known to enhance the transformation start temperature by ~3 °C per T [2–4]. From the standpoint of controlling the transformation, a magnetic field larger than 2 T would be desirable to have a temperature margin of ~6 °C for the magnetic alignment.
(2)
Here, N is a demagnetizing factor for the major axis [22], and Sk and A stand for Sk ⫽ 1 ⫹
k2
1 arccos k 冑k ⫺1 2
and A⫽
3g , (⌬M)2a
Fig. 7. Relation between the aspect ratio of a magnetic ellipsoid and the radius of the minor axis for 왕M = 30, 50, 70 and 90 emu / g.
2930
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
Fig. 8.
The magnetization of iron under external magnetic fields calculated based on Weiss molecular field theory.
It is now possible to compare the measured aspect ratio with the calculaton. We have chosen several isolated transforming ellipsoids: the ellipsoid marked B in Fig. 2(c), and the intra-granular ellipsoid in Fig. 6(a). The ellipsoids of austenite formed during the inverse transformations in Fe– 0.1%C alloy [20] and in Fe–0.6%C alloy [12] were also analyzed. Table 1 is a list of the measured aspect ratios along with calculated values for the ellipsoids. It is stressed that the simplified model approximately accounts for the aspect ratio. Interestingly, experimental aspect ratios for the ferrite
transformation are larger than those of the theoretical values, and vice versa for the inverse transformation. This may be related to the volume expansion of 1% associated with the former or the contraction of the same order with the latter.
5. Summary In search of the formation of two-phase microstructures aligned with the direction of a magnetic field applied during the ferrite transformation in
Table 1 Analysis of morphology of transforming ellipsoids Specimen for ferrite Transformation temperature Applied ellipsoid (°C) magnetic field (kOe)
Magnetization (왕M) (emu/g)
Radius of minor axis a (µm)
Aspect ratio (k) Aspect ratio (measured) (k) (calculated)
Fe–0.6%C alloya Steelb (Fe–0.2C– 2Si–1.3Mn–0.1Ti) Fe–0.1%C alloyc Fe–0.6%C alloyd
75 72
1.25 0.5
4.0 2.5
2.3 1.7
38 69
7.5 8.7
2.0 3.5
2.7 4.9
a b c d
An An An An
Ferrite transformation 745 Ferrite transformation 760
80 120
Inverse transformation 800 80 Inverse transformation 742 40
ellipsoid marked as B in Fig. 2(c). intra-granular ellipsoid in Fig. 6(a). ellipsoid appearing during the inverse transformation of Fe–0.1%C alloy [20]. ellipsoid appearing during the inverse transformation of Fe–0.6%C alloy [12].
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
carbon steels, an experimental setup was designed and installed. It features a combination of rollerdies for hot deformation and a superconducting magnet for applying a magnetic field during the transformation. Successful conditions for aligned two-phase microstructures in carbon steels have been established. The carbon content necessary for the aligned structures is determined by the Fe–C phase diagram. Experimentally, it was between 0.1 and 0.6 wt%C. The steels have to undergo rolling deformation of more than 30% in the temperature range, where the recrystallization of the austenite does not take place. This condition is necessary to secure ample intra-granular nucleation sites for aligned nucleation. A magnetic field of more than 2 T should be applied during the ferrite transformation at a temperature in the two-phase region of the steel. Formation of the aligned structure is analyzed and discussed from the standpoint of nucleation and growth of the transforming ferrite grains under the law of dipolar interactions. The aligned ferrite grains were found to show no particular preferred crystallographic orientations. The advantage of the aligned microstructures may be found in the field of fine-grained steels since an efficient accumulation of plastic strain is expected with the deformation of elastically heterogeneous two-phase steels. Currently, finite element calculations coupled with grain refining experiments through rolling and subsequent recrystallization are underway. Acknowledgements The authors are indebted to Mr. Y. Yonehana for his valuable technical assistance. The present investigation was carried out as a part of the research activities of the Ferrous Super Metal Consortium of Japan under the auspices of the New Energy Development Organization of Japan, NEDO. Appendix A. Aspect ratio of ferromagnetic ellipsoid embedded in a paramagnetic matrix The magnetostatic energy of a prolate ellipsoidal particle embedded in matrix magnetized parallel to the major axis is given by the following equation:
2931
1 2π Emag ⫽ N(⌬M)2V ⫽ a2cN(⌬M)2 2 3
(A.1)
Here, a is the radius of the two equal minor axes, and c the radius of major axis. V denotes the particle volume. 왕M stands for the difference of the saturation magnetization between the particle and the matrix. Since the magnetic susceptibility of the austenite c is the order of ~10–6 emu/g Oe, its magnetization at 120 kOe (equivalent to 12 T) amounts to only ~0.12 emu/g, negligibly small compared to that of ferrite, 220 emu/g at room temperature. N in Eq. (A.1) represents a demagnetizing factor for the major axis, and is given by [22] N ⫽
冋冑
4π k ⫺1 2
冉
冊 册
ln k ⫹ 冑k2⫺1 ⫺1 k ⫺1 k
2
(A.2)
Here, k is defined as the ratio of major axis to minor axis c/a, and called aspect ratio. Since the particle has interfacial energy g in addition to the magnetostatic energy, the total interfacial energy for an ellipsoid Esur is expressed as
再
Esur ⫽ 2πga2 1 ⫹
k2
冎
1 arccos k 冑k ⫺1 2
(A.3)
The total energyEt of a ferrite particle is given by adding Eqs. (A.1) and (A.3), Et ⫽
2π 3 a (⌬M)2(kN ⫹ ASk) 3
(A.4)
This expression already appeared as Eq. (2) in the text, and Sk and A were given as Sk ⫽ 1 ⫹
k2
1 arccos k 冑k ⫺1
(A.5)
2
and A⫽
3g , (⌬M)2a
(A.6)
respectively. Differentiation of Eq. (A.4) with respect to k and a determines the most stable shape of the ellipsoid:
冉
∂N ∂Sk ∂Et 2 3 ⫽ πa (⌬M)2 k ⫹ N ⫹ A ∂k 3 ∂k ∂k ⫽0
冊
(A.7)
2932
M. Shimotomai et al. / Acta Materialia 51 (2003) 2921–2932
and ∂Et ⫽ 2πa2(⌬M)2(kN ⫹ ASk) ⫽ 0 ∂a
(A.8)
Furthermore, auxiliary conditions for the minimum are given as follows:
冉
∂2N ∂N ∂2Et 2 3 2 πa ⫽ (⌬M) k ⫹2 2 2 ∂k 3 ∂k ∂k
冊
(A.9)
∂2 S k ⫹A 2 ⬎0 ∂k and ∂2Et ⫽ 4πa(⌬M)2(kN ⫹ ASk) ⬎ 0 ∂a2
(A.10)
Combining (A.7) with (A.8), one can compute a relation between k and a for a particular value of 왕M. Fig. 7 shows the results for 왕M = 30, 50, 70 and 90 emu / g. Finally, it is added that both (A.7) and (A.8) are automatically satisfied if a = 0. This trivial solution exists because the chemical free energy change involved in the generation of the particles through the ferrite transformation has been neglected in Eq. (A.4) for the sake of simplicity.
References [1] Saunders N, Miodownik AP. In: CALPHAD. Oxford: Elsevier Science; 1998. p. 253–8.
[2] Sadovskiy VD, Rodigin L, Smirnov LV, Filonchik GM, Fakidov IG. Phys Met Metallogr 1961;12:131. [3] Satyanarayan KR, Eliasz W, Miodownik AP. Acta Metall 1968;16:877. [4] Fields R, Graham CD. Metall Trans 1976;7A:719. [5] Pustovoit VN, Dombrovskii YuM, Grishin SA. Metalloved Term Obrab Met 1979:22. [6] Palmai Z. Gepgyartastechnologia [in Hungarian] 1982;22:463. [7] Peters CT, Miodownik AP. Scr Met 1973;7:955. [8] Enomoto M, Guo H, Tazuke Y, Abe YR, Shimotomai M. Metall Mater Trans 2001;32A:445. [9] Jones B, von Emden HJM. Philips Tech Rev 1941;6:8. [10] Cahn JW. J Appl Phys 1963;34:3581. [11] Iwama Y, Takeuchi M. Trans Jpn Inst Met 1974;15:371. [12] Shimotomai M, Maruta K. Scr Mater 2000;42:499. [13] Maruta K, Shimotomai M. Mater Trans JIM 2000;41:902. [14] Skjeltorp AT. J Appl Phys 1985;57:3285. [15] Olson GB, Cohen M. Metall Trans 1976;7:A 1897, 1905, 1915. [16] Lecroisey F, Pineau A. Metall Trans 1972;3:387. [17] Ouchi C, Sampei T, Kozasu I. Trans ISIJ 1982;22:214. [18] Tanaka T. In: Korchynsky M, DeArdo AJ, Repas P, Tither G, editors. Microalloying 95, ISS, Pittsburgh. 1995. p. 165. [19] Bengochea R, Lo´ pez B, Gutierrez I. In: Rodriguez-Ibabe JM, Gutie´ rrez I, Lo´ pez B, editors. Proceedings of the International Conference on Microalloying in Steels. Zuerich: Trans Tech Publications; 1998. p. 201–8. [20] Maruta K, Shimotomai M. Proceedings of the 13th International Conference on Crystal Growth, July 2001, Kyoto. J Cryst Growth 2002;237-239:1802. [21] Barnett DM, Lee JK, Aaronson HI, Russell KC. Scr Met 1974;8:1447. [22] Bozoroth RM. Ferromagnetism. New York: IEEE Press; 1951. p. 849 [re-issued in 1993]. [23] Radcliffe SV, Cohen M. In: Zackay VF, Aaronson HI, editors. Decomposition of austenite by diffusional processes. New York: Interscience Publishers; 1962. p. 34-0.