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Microstructural aspects of grain growth kinetics in non-oriented electrical steels
Materials Characterization 55 (2005) 1 – 11
Microstructural aspects of grain growth kinetics in non-oriented electrical steels Yuriy SidorT, Frantisek Kovac Institute of Materials Research of Slovak Academy of Sciences, Watsonova 47, 043 53 Kosice, Slovakia Received 3 September 2004; accepted 21 January 2005
Abstract Physically-based modeling of grain growth kinetics after primary recrystallization in different types of non-oriented electrical steel is discussed. As a first approximation, the effect of Zener drag on normal grain growth is considered. The ferrite grain growth behavior during secondary recrystallization was analyzed by applying the general equation for grain growth. The activation energy for grain boundary motion in both semi-processed and fully processed steels is calculated. An idea of anisotropic mobilities is applied to the columnar grain growth description. It is shown that the value of activation energy for columnar grain growth along the normal direction is higher than the one along the rolling direction. D 2005 Elsevier Inc. All rights reserved. Keywords: Grain growth; Recrystallization
1. Introduction Non-oriented electrical steel is a soft magnetic material produced for applications in electric machines to transform mechanical energy into electrical energy, electrical energy into electrical energy and electrical energy into mechanical energy. High permeability and low iron loss have been particularly required in recent years in order to achieve higher efficiency and hence energy saving. Therefore it is important to control the final microstructure of these T Corresponding author. Tel.: +42 155 7922448; fax: +42 155 7922408. E-mail address: [email protected] (Y. Sidor). 1044-5803/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.matchar.2005.01.015
steels in terms of grain size and texture. The grain growth kinetics significantly affects the texture evolution and consequently the final magnetic properties. Thus, modeling of grain growth is an important step in the production of electrical steels. The aim of the statistical approach is to describe the grain growth process in order to predict the evolution of the grain size distribution, which classically represents the most comprehensive and experimentally accessible microstructural set of data. Such equations represent the basis for the statistical procedure, which is aimed at describing the grain size distribution trend. The common observation in metals and alloys is that the size distributions of grain aggregates during growth become equivalent when
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the measured grain size parameter R is normalised by the time-dependent average grain size R¯ . This means that grain structures are completely characterised, in a static sense, by simple probability functions of the standard deviation of the distribution together with the time dependence of average size scale R¯ [1–3]. The general form of the equation for normal grain growth rate is given as [4]: d R¯ 1 1 ð1=nÞ1 ¼M ð1Þ dt Rc R¯ where R c is the critical radius at which grains neither shrink nor grow, M is the mobility of a grain boundary and n is the time exponent for grain growth. A general problem associated with thermal processing of steels is the instability of the matrix grain structure following coarsening or dissolution of the pinning grain boundary precipitates [5–7]. The presence of particle exerts a retarding force on grain boundaries that has an influence on grain growth. The pinning pressure is determined by size, volume fraction and distribution of particles [8–10]. The dispersion of particles reduces the rate of grain growth because the driving pressure for growth is opposed by the pinning pressure due to the presence of particles. Burke and Turnbull [4] estimated the related grain boundary driving value only from the curvature of the boundary R: ac Pd ¼ ð2Þ R¯ where c is the grain boundary free energy per unit area, a is a geometric constant. Grain growth is hindered by small inclusions that interact strongly with grain boundaries. Zener proposed that the inhibition strength against grain growth is proportional to the volume of inclusions and is also inversely proportional to their average radius [4]. Consequently, a decrease in the amount of inclusions and their coarsening are important for improving grain growth. The related grain boundary pinning value exerted by the particles on a unit area can be presented as [4]: 3Fv c ð3Þ Pz ¼ 2r where F v is a volume fraction of randomly distributed particles of radius r. Zener also showed that when the pressure on the boundary due to the particle pinning equal the driving
pressure for grain growth ( P d = P z), growth would cease and a limiting grain size is reached [4]. If the mean grain radius is taken to equal the mean radius of curvature R, then the limiting grain size D z will be: 4ar ð4Þ Dz ¼ 3Fv The existence of a limiting grain size is of great practical importance in prediction of grain growth during primary recrystallization of industrial steels. Secondary recrystallization is an abnormal grain growth process where the driving force for boundary motion is generated by the boundary energy and bcurvature effectQ of the growing grain. Abnormal grain growth occurs when a few grains rapidly coarsen by consuming smaller grains. Secondary recrystallization is possible only if the abnormal grain growth is faster than the growth of average grain assembly. The mean growth rate of grains of size R was postulated as [4]: dR 1 1 ¼ aM c ð5Þ dt R R¯ where R¯ is defined by Eq. (1). In this contribution, a theory of both normal and abnormal grain growth in different types of nonoriented electrical steels will be discussed.
2. Experimental procedure Both semi-processed (SP) and fully processed (FP1 and FP2) non-oriented electrical steels were used as the experimental material (see Table 1). SP samples were taken from the industrial process after cold and temper rolling (t.r.) processes and samples of FP— after cold rolling. The samples were laboratory annealed in dry N2 at T = 700 8C during 25 min in order to investigate normal grain growth after the primary recrystallization process. Generally, in order to obtain desired magnetic properties, non-oriented electrical steels are subjected Table 1 Chemical composition of the investigated steels, in wt.% Sample d, mm C FP1 FP2 SP
0.65 0.67 0.65
Mn
Si
P
S
Al
N
0.031 0.38 1.01 0.134 0.008 0.157 0.007 0.004 0.375 0.964 0.084 0.005 0.159 0.005 0.05 0.36 0.24 0.068 0.008 0.11 0.005
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to various annealing treatments in N2–H2–H2O gas mixtures. In the case of the semi-processed electrical steels, annealing is needed to relieve the residual stress and develop grain growth and proper texture. In the case of the fully processed electrical steels the annealing is performed to reduce the carbon content by decarburizing and to develop a microstructure with favorable texture. In the present investigation, heat treatment was conducted in dry and wet atmospheres of cracked ammonia to investigate the secondary recrystallization process. The temperature of decarburization was varied in the range of 850– 960 8C and the annealing time was changed from 1 to 45 min. During annealing, temperature was controlled within F2 8C. The microstructure of the specimens was examined in the plane parallel to the sheet surface and in longitudinal cross-section using optical microscopy. The samples were polished and subsequently etched in 3% Nital solution for 10–30 s in order to get all the grain boundaries visible. Second phase particle distribution was investigated by TEM after primary recrystallization. The carbon extraction replicas were prepared in order to isolate precipitates from the metallic matrix. The carbon film was deposited on the polished and etched surface of the sample. The film was separated from the surface of the sample by applying a current to the sample. Afterward, the pieces of the film were collected on Cu grids. The particles were examined by the electron diffraction. An average grain size was evaluated for each sample according to the procedure described in Ref. [11]. DIPS-5 image analysis software was used to make quantitative metallographic measurements. Grain size distribution was investigated by measuring the equivalent radius of approximately 1000 grains.
3. Results and discussion 3.1. Normal grain growth in primary recrystallized matrix The behavior of grain growth in the primary recrystallized matrix mainly depends on the dispersion of second-phase particles. The driving pressure, in the case of the normal grain growth, is governed by a reduction of the grain boundary energy.
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Second phase particle creation is occurring even during the casting process. These particles have a high melting point and they are not dissolved during further service processes. The second phases deteriorate mainly the magnetic properties of electrical steels by pinning the motion of domain walls. A classical method used by metallurgists to control both texture and microstructure is to add to the alloy a solute element with low solubility, which precipitates as second-phase particles able to pin the grain boundaries. The precipitation of AlN and MnS in the electrical steels is used to control the texture development in the material. The presence of these particles plays an important role in formation of the Goss texture in the electrical steels [12]. There is no unambiguous point in literature about the influence of precipitates on the formation of desirable cube texture in non-oriented electrical steels. In the given investigation, the sulphide, oxide and nitride precipitates were identified by electron diffraction; TiN, MnS, Fe3O4, AlN and Al2O3 were observed. Generally, each investigated material has homogeneously distributed precipitates. Table 2 presents the distribution parameters of precipitates and limiting grain size D z in the investigated materials. Both volume fraction F v and number of particles per unit area N s were determined by TEM according to the procedure described in Ref. [4]. The driving pressure P d and the grain boundary inhibition pressure P z were estimated with a condition that the volume fractions are the same for the main texture components, i.e., {110}b001N, {111}b112N and {100}b012N. In this case, the representative grain boundary energy within these orientations is c = 525 mJ/m2 [4]. Fig. 1 shows the driving pressure and Zener drag in the investigated samples. As noted, the high number N s of particles with d¯ = 35 nm invokes a strong drag effect in steel FP1. As a result, the value of limiting grain size in this sample is the lowest. Despite the small average particle size in steel FP2, Table 2 The value of limiting grain size D z and distribution parameters of precipitates in the investigated materials: volume fraction F v, number of particles N s per unit area, average particle size d Sample
F v, %
Ns 1012, m 2
d, nm
D z, Am
FP1 FP2 SP
0.208 0.142 0.140
6.50 5.00 2.65
35 33 45
11.2 15.5 21.5
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Fig. 1. Comparison between the P z and P d for respective F v in the investigated samples.
the inhibition pressure is lower than in steel FP1 because of the lower volume fraction of second phases. The volume fraction of precipitates in steel SP is comparable with the one in FP2, but the number of particles per unit area is lower than in both FP1 and FP2. Because of both the largest average particle size and the lowest volume fraction of the second phases in steel SP, the related retarding value is lower than in steels FP1 and FP2. As a consequence of low pinning intensity, the value of Zener factor D z in steel SP is the largest for the investigated steels. The different values of Zener factor strongly influence the kinetics of grain growth in the primary recrystallized matrix. As follows from Fig. 1 and Table 2, a small number of coarse precipitates do not impede the migration of grain boundary as much as a larger number of finer particles. Thus, the kinetics of grain growth after primary recrystallization has to consider the critical grain size below which growth does not occur. Maazi and Rouag derived the relation for minimal (D c1) and maximal (D c2) critical sizes of neighbouring grains [8]: 2 Dc1 ¼ ð6Þ 2 3Fv Dj 4r 2 Dc2 ¼ ð7Þ 2 3Fv þ Dj 4r
A grain with D j N D c1 will grow; a grain with D j b D c2 will shrink; when D c2 b D j b D c1 the grain boundary will be fixed. Fig. 2a presents the dependence of critical grain sizes upon the size of growing grains for steel FP1. As one can see, the grains with sizes coarser than ~ 19 Am will grow and those finer than ~ 7 Am will shrink in the microstructure with an initial average grain size of 10 Am. Growth of the remaining grains within 7 b D j b 19 Am size range will be stopped because of the high binhibition energy barrierQ. In steel FP2 with an average size of 10 Am, grains coarser than ~ 15 Am will grow and grains finer than ~ 7.5 Am will shrink (see Fig. 2b). As a consequence of the mentioned inhibition system in steel SP, in the primary recrystal¯ = 10 Am, grains coarser lized microstructure with D than ~ 13 Am will grow and finer than ~ 8 Am will shrink (see Fig. 2c). As one can see from Fig. 1, the ratio of Zener drag value to the driving pressure for both FP1 and FP2 steels is ~ 2.7. According to the Eqs. (6) and (7), the grain growth will be either stopped or grains will shrink in these steels with an average grain size of 15 Am (see Fig. 2a, b). But this fact was not proven experimentally because the average grain size in both steels after primary recrystallization was estimated as ~ 21 Am. On one hand, the driving force for grain growth increases with increasing heterogeneity of grains. As all grains are pinned homogeneously, the largest grain in the matrix will be
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unpinned first. On the other hand, the growth of the first large grains will be followed by the release of the second largest grain only when coalescence (Ostwald ripening) of the particles has progressed to a more advanced stage. The intensive precipitation range (DT = 700–850 8C [12]) of AlN particles in electrical steels is comparable with the treatment temperature T = 700 8C [12]. During the annealing a probable Ostwald ripening process produces an inhibition drop. In this case, the rate of growth is controlled by the rate of change in particle size. Then, the grains of size exceeding the critical value of D c1 will grow as a consequence of the new particle arrangement. 3.2. Secondary recrystallization Secondary recrystallization in non-oriented electrical steels, observed in the current investigation, differs from typical abnormal growth in following important aspects: 1) the initial stages of abnormal growth are not sluggish (there is no significant incubation period before grain coarsening); 2) abnormal grain growth leads to a wide grain size distribution (bimodal character of distribution was not proven); 3) secondary recrystallization occurs without a selective growth process (in bclassicalQ textured materials such as Fe–3% Si steels, the interaction between particles and grain boundaries is made in a selective way; under the present investigation, grains of different orientation start to coarsen); 4) the texture of final microstructure consists of several orientation components [13].
Fig. 2. Dependence of critical grain sizes D c1 and D c2 on the size of matrix grain D j: a) steel FP1; b) steel FP2; c) steel SP.
Fig. 3 presents the development of microstructure in cold rolled steel SP. It can be pointed out that the grain boundaries mostly move along the decarburization front (Fig. 3a, b). The level of carbon after the 15 min annealing in wet NH3 is ultra low and the grain propagation occurs also in the plane of the rolling direction (Fig. 3c). This kinetic experiment indicates that there is no incubation period during this type of recrystallization. Also, the rate of grain growth is highest initially and decreases with time of
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[4,14–16] lead to the parabolic grain growth kinetics: d2 ~ tm
ð8Þ
where m = 1. The Monte Carlo simulation in Ref. [16] gives a grain growth exponent m close to 0.84. The fulfillment of this law was taken as one criterion in order to determine whether a simulation procedure is able to describe normal grain growth or not. Under the given investigation, the kinetics of grain growth is well described by the law of growth d 2 ~ t n , with n c 0.5. The estimated values of exponent n presented in Table 3 are in disagreement with the ones presented for both normal and abnormal grain growth simulations [1–4,14–16]. In Ref. [17] authors confirm that coefficient n in Eq. (8) strongly depends on the annealing temperature. Under the present investigations these facts were not proven. The mentioned coefficient behaves as a constant value in the investigated temperature range. The slight variation can be explained as an experimental error. The bclassicalQ abnormal grain growth rate increases with temperature according to the exponential relationship: 1 kf d exp ð9Þ T
Fig. 3. Microstructure development in semi-processed steel SP during annealing in wet atmosphere of cracked ammonia at 790 8C: a) 5 min; b) 15 min; c) 45 min.
annealing. Similar grain growth behavior was observed in other studied samples. This fact suggests that grain growth in this type of steel is rather bintensive normalQ than abnormal. Many efforts have been made to simulate grain growth, either to confirm well-known theoretical assumptions or to compare simulation results with experimental data. Most of the grain growth theories
where k = 1. As will be shown below, the grain growth rate during secondary recrystallization in non-oriented electrical steels is described by an exponential temperature dependence with k = 2 in Eq. (9). In order to make the interpretation of the results compatible, with an adequate accuracy in describing the main characteristic of abnormal grain growth process in non-oriented electrical steels, the ferrite
Table 3 The grain growth exponent for the investigated steels according to Eq. (10) Sample
n
Temperature range, 8C
FP1 FP2 SP after t.r. SP without t.r.
0.48 0.49 0.45 0.46
890 – 950 780 – 960 780 – 880 780 – 880
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grain growth behavior during secondary recrystallization was analyzed by applying the equation: Q d 2 d02 ¼ Ct n exp ð10Þ RT where d is the grain size at a given annealing time, d 0 is the initial grain size, t denotes annealing time, Q is the activation energy of grain growth and T is annealing temperature. The values of the coefficients C and n depend on the type of material. Using Eq. (10), the value of activation energy Q can be found from the dependence of (d 2 d 02) on the (1 / T) in semi-logarithmic scale for the fixed annealing time. In spite of the fact that complete and exact modeling of grain growth phenomena is complicated by a number of different factors, the simulation with some simple assumptions may lead to profound insight into the mechanism of processes. The development of this semi-empirical approach is based on the experimental observations and above mentioned principles of grain growth in non-oriented electrical steels. The activation energy of secondary recrystallization for grain boundary motion was calculated in the semi-processed steel SP (Fig. 4a). Because of low concentration of alloying elements, the value of Q = 145 kJ/mol (Fig. 4a, line 2) is comparable with the activation energy for grain boundary mobility in pure iron (see Table 4). The activation energy Q = 91 kJ/mol for the grain growth of the temper rolled steel (Fig. 4a, line 1) is lower than the activation energies
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Table 4 The values of activation energies connected with ferrite grain growth [4] Process
Q, kJ/mol
Volume diffusion of Fe in a iron Grain boundary diffusion of Fe in a iron Grain boundary mobility of pure iron
280 164 147
for processes associated with ferrite grain growth. Comparing the value of Q in temper rolled material to the corresponding value of the same material without temper rolling (see Fig. 4a), it is possible to claim that temper rolling means an additional driving force for ferrite grain growth. The observation that a small prior plastic strain may promote anomalous grain growth is widely known [4] and interpreted as strain-induced grain boundary migration. Deformation leads to two contributions in microstructure changes, i.e., an increase in dislocation density and grain elongation with an associated increase in grain boundary area. The difference in stored energy provides the driving force for grain boundary motion that also leads to a reduction in internal energy of material. These facts support the suggestion that non-equilibrium grain boundary motion is induced by plastic deformation, i.e., by temper rolling, and as a result, the material shows higher mobility of grains in comparison with non-deformed material. The polygonal microstructure formation (Fig. 5a) in ultra low carbon steel FP2 is connected with the
Fig. 4. Plot of ln (d 2 d 20) as a function of 1 / T for ferrite grain growth in: a) steel SP; b) steels FP2 (line 1) and FP1 (line 2).
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Fig. 5. Microstructures of the investigated samples annealed for 5 min at 875 8C in wet NH3 atmosphere: a) steel FP2; b) steel FP1.
relatively high value of activation energy Q ~ 178 kJ/ mol (Fig. 4b). The latter is comparable with the activation energy for grain boundary diffusion of Fe in ferrite (see Table 4). The activation energy for normal grain growth in fully processed steel FP1 (Fig. 5b) was estimated as ~ 245 kJ/mol (Fig. 4b). The calculated value is comparable with self-diffusion of Fe in ferrite (see Table 4). The chemical compositions of both FP1 and FP2 steels are similar, apart from carbon content. Carbon addition to laminate steels decreases the a to ac transformation temperature. The temperature A c1 was calculated by bThermo-calcQ software for FP1 and FP2 as 880 and 962 8C, respectively. It is obvious that phase transformation does not occur in steel FP2 in the investigated temperature range. By comparing the activation energy of steel FP1 for normal grain growth with the corresponding activation energy of steel FP2 (see Fig. 4b), one can conclude that the ferrite grain growth in a steel without a phase transformation needs a lower activation energy than the one with phase transformation. This phenomenon is because the difference in chemical composition leads to distinct mechanisms of grain boundary motion, as a consequence of different phase composition at elevated temperature. The existence of a second phase (austenite) acts as an inhibitor for ferrite grain growth. Furthermore, carbon in solid solution, which is preferentially enriched at the moving grain boundary, reduces grain boundary mobility of the growing grain due to a solute drag effect. Recently, a significant amount of experimental work has been carried out on steels to tailor the
properties. A common difficulty in many cases is the inhomogeneity of the microstructure and the texture of steel as a result of the production process. This is of particular importance in electrical steels. For low carbon steels, it is possible to apply a decarburizing annealing in the intercritical region that leads to the columnar-grained microstructure with a specific type of the texture [13]. The columnar grain growth of fully processed steel FP1 is driven by diffusioncontrolled grain boundary motion mechanism. The moisture of the gas mixture, temperature and heating rate are the main parameters that influence the directional grain growth [13]. Carbon diffusion along the grain boundary produces an elastic stress on the boundary that causes motion of latter. A discontinuous concentration profile of carbon through the thickness of steel is observed during decarburization [12]. The latter is caused by the difference in carbon solubility in ferrite and austenite. The carbon content increases from zero at the surface to a quasiequilibrium value at the a / (a + c) interface. Thus, decarburization proceeds through bdiffusion pipesQ that are aligned with normal direction (ND) to the sheet-plane. The blocking of carbon in the bdiffusion pipeQ decreases the rate of carbon removal and, thus, decreases the elastic stress along the grain boundary. For optimal columnar grain growth during the decarburization, the carbon removal should have a sequential character. It is well known that the boundary velocity is proportional to the frequency of atoms bjumpingQ across the grain boundary plane. On the other hand, the intensive decarburization should accelerate the bjumping processQ of matrix atoms along the normal direction. Hence, intensive
Y. Sidor, F. Kovac / Materials Characterization 55 (2005) 1–11
decarburization causes a small pinning effect on the grain boundary that leads to directional grain boundary motion. As the microstructure is non-equiaxed the activation energy of grain growth may be considered as a dependent value on growth direction. In the field of grain growth simulation, the Monte Carlo algorithm is widely used to model anisotropic grain growth [4]. In the present work, the idea of anisotropic mobilities is applied to the columnar grain growth description. The activation energy was calculated for two growth directions, i.e., the rolling direction (RD) and the normal direction. When material is heated at a proper rate, at temperatures lower than A c1, primary recrystallization occurs simultaneously with intensive decarburization of the surface material layers. After the material is heated up to temperatures above A c1, a phase transformation, which refines primary recrys-
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tallized matrix, occurs in the inner region. At the same time, surface layers are not subjected to the phase transformation because of the low local concentration of carbon. First, the small c phase grains are transformed into a ones and as a result the material has a fine primary recrystallized microstructure and the thin decarburized a-region on the sheet surface (Fig. 6a). These created grains act as the bnucleiQ for columnar grains (see Fig. 6b). Fig. 6c describes the formation process of the columnar microstructure from the point of view of activation energy. From this figure, the values of Q for grain growth were estimated as 240 and 404 kJ/mol for the RD and the ND, respectively. The activation energy for columnar grain growth in the plane of the RD is comparable with activation energy of self-diffusion of Fe in ferrite. The high value of Q for grain boundary motion with the ND (404 kJ/mol) confirms
Fig. 6. a) Columnar-nuclei creation at the commencement of decarburization process in steel FP1; b) scheme of columnar microstructure formation; c) plot of ln (d 2 d 20) as function of 1 / T for columnar-nuclei creation with the normal direction (line 1) and with the rolling direction (line 2) in steel FP1; d) columnar grains propagation towards mid-plane of the sheet.
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Fig. 7. a) Microstructure of steel FP1 after annealing when the activation energy of columnar-nuclei creation is Q ~ 400 kJ/mol; b) microstructure of steel FP1 after annealing when the activation energy of grain growth at the beginning of decarburization is Q ~ 280 kJ/mol.
that columnar grain growth needs a high energy to start the directional abnormal growth, and this can be explained by the energy demand for phase transformation during heating and subsequent growth of formed a grains on the surface. At later stages of this process, the size advantage of surface ferritic grains in comparison with fine-grained inner material is high and sufficient for continuation of directional abnormal grain growth of the surface layer towards mid-plane (Fig. 6d). As shown, coarsening of grains in the mid-plane is very slow because of the high bactivation energy barrierQ. After finishing the decarburization process, the microstructure is fully ferritic and grains have a columnar shape (Fig. 7a). As the parameters of decarburization process do not satisfy the optimal condition for columnar nuclei creation, then the inhomogeneous microstructure development takes place (Fig. 7b).
linked with either the grain boundary diffusion or the self-diffusion of Fe in ferrite. A model of anisotropic mobilities is applied to columnar grain growth description. For the early stage of columnar microstructure development, the value of the activation energy of grain growth with normal direction is higher than the one with rolling direction. The high value of activation energy for grains propagation with a normal direction towards the sheet mid-plane ( Q ~ 404 kJ/mol) confirms that columnar grains need a high energy to start and continue the directional abnormal growth. Acknowledgement This work was supported by the Slovak Grant Agency VEGA (project No. 2/4175/04). References
4. Summary The Zener factor strongly influences the kinetics of grain growth in a primary recrystallized matrix. The modeling of grain growth process in the matrix is complicated by both coalescence and dissolution of the precipitates. Plastic deformation induces non-equilibrium grain boundary motion. As a consequence the material shows higher grain boundary mobility in comparison with non-deformed material. Depending upon the chemical composition of the steels under investigation, polygonal grain growth is
[1] Grong O, Shercliff HR. Microstructural modelling in metals processing. Prog Mater Sci 2002;47:163 – 282. [2] Yamazaki Y, Watanabe T. Physical aspects of grain growth phenomena. Mat Sci Forum 1996;204–206:257 – 66. [3] Bate P. The effect of deformation on grain growth in Zener pinned system. Acta Mater 2001;49:1453 – 61. [4] Humphreys FJ, Hatherly M. Recrystallization and related annealing phenomena. Oxford7 Pergamon; 1996. 497 p. [5] Abbruzzese G, Campopiano A. A general theory of secondary recrystallization in grain oriented Fe–Si: metallurgical parameters controlling the microstructural evolution. JMMM 1994; 133:123 – 35. [6] Rajmohan N, Szpunar JA, Hayakawa Y. A role of fractions of mobile grain boundaries in secondary recrystallization of Fe– Si steels. Acta Mater 1999;47:2999 – 3008.
Y. Sidor, F. Kovac / Materials Characterization 55 (2005) 1–11 [7] Smith DA. On the mechanisms of grain boundary migration. Mat Sci Forum 1992;94–96:221 – 32. [8] Maazi N, Rouag N. Consideration of Zener drag effect by introducing a limiting radius for neighbourhood in grain growth simulation. J Cryst Growth 2003;243:361 – 9. [9] Fortunati S, Matera S, Ban G, Abbruzzese G. Influence of Zener-drag and related primary recrystallization on grain growth kinetics in N.O. 3.2% silicon–iron. Mat Sci Forum 1992;94–96:619 – 26. [10] Novikov VY. On Zener pinning in 3-D polycrystals. Scr Mater 2000;42:439 – 43. [11] Sidor Y, Dzubinsky M, Kovac F. New approach for the quantification of microstructures in nonoriented electrical steels. Mater Charact 2003;51:109 – 16. [12] Dzubinsky M. Modeling of oriented structure development in Fe–3% Si electrical steels, Ph.D. Thesis, Institute of Materials Research, Kosice, Slovakia; 2002.
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[13] Kovac F, Dzubinsky M, Sidor Y. Columnar grain growth in non-oriented electrical steels. JMMM 2004;269:333 – 40. [14] Rollet A, Srolovitz D, Anderson M. Simulation and theory of abnormal grain growth—anisotropic grain boundary energies and mobilities. Acta Metall 1989;37:1227 – 40. [15] Weygand D, Brechet Y, Lepinoux J. Zener pinning and grain growth: a two-dimensional vertex computer simulation. Acta Mater 1999;47:961 – 70. [16] Lucke K, Brandt R, Abbruzzese G. Development of the statistical theory of grain growth for the general case of nonuniform grain boundaries and textures. Mat Sci Forum 1998; 273–275:41 – 54. [17] Jiao S, Penning J, Leysen F, Houbaert Y, Aernoudt E. The modeling of the grain growth in a continuous reheating process of a low carbon Si–Mn bearing trip steel. ISIJ Int 2000;40:1035 – 40.
Microstructural aspects of grain growth kinetics in non-oriented electrical steels Yuriy SidorT, Frantisek Kovac Institute of Materials Research of Slovak Academy of Sciences, Watsonova 47, 043 53 Kosice, Slovakia Received 3 September 2004; accepted 21 January 2005
Abstract Physically-based modeling of grain growth kinetics after primary recrystallization in different types of non-oriented electrical steel is discussed. As a first approximation, the effect of Zener drag on normal grain growth is considered. The ferrite grain growth behavior during secondary recrystallization was analyzed by applying the general equation for grain growth. The activation energy for grain boundary motion in both semi-processed and fully processed steels is calculated. An idea of anisotropic mobilities is applied to the columnar grain growth description. It is shown that the value of activation energy for columnar grain growth along the normal direction is higher than the one along the rolling direction. D 2005 Elsevier Inc. All rights reserved. Keywords: Grain growth; Recrystallization
1. Introduction Non-oriented electrical steel is a soft magnetic material produced for applications in electric machines to transform mechanical energy into electrical energy, electrical energy into electrical energy and electrical energy into mechanical energy. High permeability and low iron loss have been particularly required in recent years in order to achieve higher efficiency and hence energy saving. Therefore it is important to control the final microstructure of these T Corresponding author. Tel.: +42 155 7922448; fax: +42 155 7922408. E-mail address: [email protected] (Y. Sidor). 1044-5803/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.matchar.2005.01.015
steels in terms of grain size and texture. The grain growth kinetics significantly affects the texture evolution and consequently the final magnetic properties. Thus, modeling of grain growth is an important step in the production of electrical steels. The aim of the statistical approach is to describe the grain growth process in order to predict the evolution of the grain size distribution, which classically represents the most comprehensive and experimentally accessible microstructural set of data. Such equations represent the basis for the statistical procedure, which is aimed at describing the grain size distribution trend. The common observation in metals and alloys is that the size distributions of grain aggregates during growth become equivalent when
2
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the measured grain size parameter R is normalised by the time-dependent average grain size R¯ . This means that grain structures are completely characterised, in a static sense, by simple probability functions of the standard deviation of the distribution together with the time dependence of average size scale R¯ [1–3]. The general form of the equation for normal grain growth rate is given as [4]: d R¯ 1 1 ð1=nÞ1 ¼M ð1Þ dt Rc R¯ where R c is the critical radius at which grains neither shrink nor grow, M is the mobility of a grain boundary and n is the time exponent for grain growth. A general problem associated with thermal processing of steels is the instability of the matrix grain structure following coarsening or dissolution of the pinning grain boundary precipitates [5–7]. The presence of particle exerts a retarding force on grain boundaries that has an influence on grain growth. The pinning pressure is determined by size, volume fraction and distribution of particles [8–10]. The dispersion of particles reduces the rate of grain growth because the driving pressure for growth is opposed by the pinning pressure due to the presence of particles. Burke and Turnbull [4] estimated the related grain boundary driving value only from the curvature of the boundary R: ac Pd ¼ ð2Þ R¯ where c is the grain boundary free energy per unit area, a is a geometric constant. Grain growth is hindered by small inclusions that interact strongly with grain boundaries. Zener proposed that the inhibition strength against grain growth is proportional to the volume of inclusions and is also inversely proportional to their average radius [4]. Consequently, a decrease in the amount of inclusions and their coarsening are important for improving grain growth. The related grain boundary pinning value exerted by the particles on a unit area can be presented as [4]: 3Fv c ð3Þ Pz ¼ 2r where F v is a volume fraction of randomly distributed particles of radius r. Zener also showed that when the pressure on the boundary due to the particle pinning equal the driving
pressure for grain growth ( P d = P z), growth would cease and a limiting grain size is reached [4]. If the mean grain radius is taken to equal the mean radius of curvature R, then the limiting grain size D z will be: 4ar ð4Þ Dz ¼ 3Fv The existence of a limiting grain size is of great practical importance in prediction of grain growth during primary recrystallization of industrial steels. Secondary recrystallization is an abnormal grain growth process where the driving force for boundary motion is generated by the boundary energy and bcurvature effectQ of the growing grain. Abnormal grain growth occurs when a few grains rapidly coarsen by consuming smaller grains. Secondary recrystallization is possible only if the abnormal grain growth is faster than the growth of average grain assembly. The mean growth rate of grains of size R was postulated as [4]: dR 1 1 ¼ aM c ð5Þ dt R R¯ where R¯ is defined by Eq. (1). In this contribution, a theory of both normal and abnormal grain growth in different types of nonoriented electrical steels will be discussed.
2. Experimental procedure Both semi-processed (SP) and fully processed (FP1 and FP2) non-oriented electrical steels were used as the experimental material (see Table 1). SP samples were taken from the industrial process after cold and temper rolling (t.r.) processes and samples of FP— after cold rolling. The samples were laboratory annealed in dry N2 at T = 700 8C during 25 min in order to investigate normal grain growth after the primary recrystallization process. Generally, in order to obtain desired magnetic properties, non-oriented electrical steels are subjected Table 1 Chemical composition of the investigated steels, in wt.% Sample d, mm C FP1 FP2 SP
0.65 0.67 0.65
Mn
Si
P
S
Al
N
0.031 0.38 1.01 0.134 0.008 0.157 0.007 0.004 0.375 0.964 0.084 0.005 0.159 0.005 0.05 0.36 0.24 0.068 0.008 0.11 0.005
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to various annealing treatments in N2–H2–H2O gas mixtures. In the case of the semi-processed electrical steels, annealing is needed to relieve the residual stress and develop grain growth and proper texture. In the case of the fully processed electrical steels the annealing is performed to reduce the carbon content by decarburizing and to develop a microstructure with favorable texture. In the present investigation, heat treatment was conducted in dry and wet atmospheres of cracked ammonia to investigate the secondary recrystallization process. The temperature of decarburization was varied in the range of 850– 960 8C and the annealing time was changed from 1 to 45 min. During annealing, temperature was controlled within F2 8C. The microstructure of the specimens was examined in the plane parallel to the sheet surface and in longitudinal cross-section using optical microscopy. The samples were polished and subsequently etched in 3% Nital solution for 10–30 s in order to get all the grain boundaries visible. Second phase particle distribution was investigated by TEM after primary recrystallization. The carbon extraction replicas were prepared in order to isolate precipitates from the metallic matrix. The carbon film was deposited on the polished and etched surface of the sample. The film was separated from the surface of the sample by applying a current to the sample. Afterward, the pieces of the film were collected on Cu grids. The particles were examined by the electron diffraction. An average grain size was evaluated for each sample according to the procedure described in Ref. [11]. DIPS-5 image analysis software was used to make quantitative metallographic measurements. Grain size distribution was investigated by measuring the equivalent radius of approximately 1000 grains.
3. Results and discussion 3.1. Normal grain growth in primary recrystallized matrix The behavior of grain growth in the primary recrystallized matrix mainly depends on the dispersion of second-phase particles. The driving pressure, in the case of the normal grain growth, is governed by a reduction of the grain boundary energy.
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Second phase particle creation is occurring even during the casting process. These particles have a high melting point and they are not dissolved during further service processes. The second phases deteriorate mainly the magnetic properties of electrical steels by pinning the motion of domain walls. A classical method used by metallurgists to control both texture and microstructure is to add to the alloy a solute element with low solubility, which precipitates as second-phase particles able to pin the grain boundaries. The precipitation of AlN and MnS in the electrical steels is used to control the texture development in the material. The presence of these particles plays an important role in formation of the Goss texture in the electrical steels [12]. There is no unambiguous point in literature about the influence of precipitates on the formation of desirable cube texture in non-oriented electrical steels. In the given investigation, the sulphide, oxide and nitride precipitates were identified by electron diffraction; TiN, MnS, Fe3O4, AlN and Al2O3 were observed. Generally, each investigated material has homogeneously distributed precipitates. Table 2 presents the distribution parameters of precipitates and limiting grain size D z in the investigated materials. Both volume fraction F v and number of particles per unit area N s were determined by TEM according to the procedure described in Ref. [4]. The driving pressure P d and the grain boundary inhibition pressure P z were estimated with a condition that the volume fractions are the same for the main texture components, i.e., {110}b001N, {111}b112N and {100}b012N. In this case, the representative grain boundary energy within these orientations is c = 525 mJ/m2 [4]. Fig. 1 shows the driving pressure and Zener drag in the investigated samples. As noted, the high number N s of particles with d¯ = 35 nm invokes a strong drag effect in steel FP1. As a result, the value of limiting grain size in this sample is the lowest. Despite the small average particle size in steel FP2, Table 2 The value of limiting grain size D z and distribution parameters of precipitates in the investigated materials: volume fraction F v, number of particles N s per unit area, average particle size d Sample
F v, %
Ns 1012, m 2
d, nm
D z, Am
FP1 FP2 SP
0.208 0.142 0.140
6.50 5.00 2.65
35 33 45
11.2 15.5 21.5
4
Y. Sidor, F. Kovac / Materials Characterization 55 (2005) 1–11
Fig. 1. Comparison between the P z and P d for respective F v in the investigated samples.
the inhibition pressure is lower than in steel FP1 because of the lower volume fraction of second phases. The volume fraction of precipitates in steel SP is comparable with the one in FP2, but the number of particles per unit area is lower than in both FP1 and FP2. Because of both the largest average particle size and the lowest volume fraction of the second phases in steel SP, the related retarding value is lower than in steels FP1 and FP2. As a consequence of low pinning intensity, the value of Zener factor D z in steel SP is the largest for the investigated steels. The different values of Zener factor strongly influence the kinetics of grain growth in the primary recrystallized matrix. As follows from Fig. 1 and Table 2, a small number of coarse precipitates do not impede the migration of grain boundary as much as a larger number of finer particles. Thus, the kinetics of grain growth after primary recrystallization has to consider the critical grain size below which growth does not occur. Maazi and Rouag derived the relation for minimal (D c1) and maximal (D c2) critical sizes of neighbouring grains [8]: 2 Dc1 ¼ ð6Þ 2 3Fv Dj 4r 2 Dc2 ¼ ð7Þ 2 3Fv þ Dj 4r
A grain with D j N D c1 will grow; a grain with D j b D c2 will shrink; when D c2 b D j b D c1 the grain boundary will be fixed. Fig. 2a presents the dependence of critical grain sizes upon the size of growing grains for steel FP1. As one can see, the grains with sizes coarser than ~ 19 Am will grow and those finer than ~ 7 Am will shrink in the microstructure with an initial average grain size of 10 Am. Growth of the remaining grains within 7 b D j b 19 Am size range will be stopped because of the high binhibition energy barrierQ. In steel FP2 with an average size of 10 Am, grains coarser than ~ 15 Am will grow and grains finer than ~ 7.5 Am will shrink (see Fig. 2b). As a consequence of the mentioned inhibition system in steel SP, in the primary recrystal¯ = 10 Am, grains coarser lized microstructure with D than ~ 13 Am will grow and finer than ~ 8 Am will shrink (see Fig. 2c). As one can see from Fig. 1, the ratio of Zener drag value to the driving pressure for both FP1 and FP2 steels is ~ 2.7. According to the Eqs. (6) and (7), the grain growth will be either stopped or grains will shrink in these steels with an average grain size of 15 Am (see Fig. 2a, b). But this fact was not proven experimentally because the average grain size in both steels after primary recrystallization was estimated as ~ 21 Am. On one hand, the driving force for grain growth increases with increasing heterogeneity of grains. As all grains are pinned homogeneously, the largest grain in the matrix will be
Y. Sidor, F. Kovac / Materials Characterization 55 (2005) 1–11
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unpinned first. On the other hand, the growth of the first large grains will be followed by the release of the second largest grain only when coalescence (Ostwald ripening) of the particles has progressed to a more advanced stage. The intensive precipitation range (DT = 700–850 8C [12]) of AlN particles in electrical steels is comparable with the treatment temperature T = 700 8C [12]. During the annealing a probable Ostwald ripening process produces an inhibition drop. In this case, the rate of growth is controlled by the rate of change in particle size. Then, the grains of size exceeding the critical value of D c1 will grow as a consequence of the new particle arrangement. 3.2. Secondary recrystallization Secondary recrystallization in non-oriented electrical steels, observed in the current investigation, differs from typical abnormal growth in following important aspects: 1) the initial stages of abnormal growth are not sluggish (there is no significant incubation period before grain coarsening); 2) abnormal grain growth leads to a wide grain size distribution (bimodal character of distribution was not proven); 3) secondary recrystallization occurs without a selective growth process (in bclassicalQ textured materials such as Fe–3% Si steels, the interaction between particles and grain boundaries is made in a selective way; under the present investigation, grains of different orientation start to coarsen); 4) the texture of final microstructure consists of several orientation components [13].
Fig. 2. Dependence of critical grain sizes D c1 and D c2 on the size of matrix grain D j: a) steel FP1; b) steel FP2; c) steel SP.
Fig. 3 presents the development of microstructure in cold rolled steel SP. It can be pointed out that the grain boundaries mostly move along the decarburization front (Fig. 3a, b). The level of carbon after the 15 min annealing in wet NH3 is ultra low and the grain propagation occurs also in the plane of the rolling direction (Fig. 3c). This kinetic experiment indicates that there is no incubation period during this type of recrystallization. Also, the rate of grain growth is highest initially and decreases with time of
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[4,14–16] lead to the parabolic grain growth kinetics: d2 ~ tm
ð8Þ
where m = 1. The Monte Carlo simulation in Ref. [16] gives a grain growth exponent m close to 0.84. The fulfillment of this law was taken as one criterion in order to determine whether a simulation procedure is able to describe normal grain growth or not. Under the given investigation, the kinetics of grain growth is well described by the law of growth d 2 ~ t n , with n c 0.5. The estimated values of exponent n presented in Table 3 are in disagreement with the ones presented for both normal and abnormal grain growth simulations [1–4,14–16]. In Ref. [17] authors confirm that coefficient n in Eq. (8) strongly depends on the annealing temperature. Under the present investigations these facts were not proven. The mentioned coefficient behaves as a constant value in the investigated temperature range. The slight variation can be explained as an experimental error. The bclassicalQ abnormal grain growth rate increases with temperature according to the exponential relationship: 1 kf d exp ð9Þ T
Fig. 3. Microstructure development in semi-processed steel SP during annealing in wet atmosphere of cracked ammonia at 790 8C: a) 5 min; b) 15 min; c) 45 min.
annealing. Similar grain growth behavior was observed in other studied samples. This fact suggests that grain growth in this type of steel is rather bintensive normalQ than abnormal. Many efforts have been made to simulate grain growth, either to confirm well-known theoretical assumptions or to compare simulation results with experimental data. Most of the grain growth theories
where k = 1. As will be shown below, the grain growth rate during secondary recrystallization in non-oriented electrical steels is described by an exponential temperature dependence with k = 2 in Eq. (9). In order to make the interpretation of the results compatible, with an adequate accuracy in describing the main characteristic of abnormal grain growth process in non-oriented electrical steels, the ferrite
Table 3 The grain growth exponent for the investigated steels according to Eq. (10) Sample
n
Temperature range, 8C
FP1 FP2 SP after t.r. SP without t.r.
0.48 0.49 0.45 0.46
890 – 950 780 – 960 780 – 880 780 – 880
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grain growth behavior during secondary recrystallization was analyzed by applying the equation: Q d 2 d02 ¼ Ct n exp ð10Þ RT where d is the grain size at a given annealing time, d 0 is the initial grain size, t denotes annealing time, Q is the activation energy of grain growth and T is annealing temperature. The values of the coefficients C and n depend on the type of material. Using Eq. (10), the value of activation energy Q can be found from the dependence of (d 2 d 02) on the (1 / T) in semi-logarithmic scale for the fixed annealing time. In spite of the fact that complete and exact modeling of grain growth phenomena is complicated by a number of different factors, the simulation with some simple assumptions may lead to profound insight into the mechanism of processes. The development of this semi-empirical approach is based on the experimental observations and above mentioned principles of grain growth in non-oriented electrical steels. The activation energy of secondary recrystallization for grain boundary motion was calculated in the semi-processed steel SP (Fig. 4a). Because of low concentration of alloying elements, the value of Q = 145 kJ/mol (Fig. 4a, line 2) is comparable with the activation energy for grain boundary mobility in pure iron (see Table 4). The activation energy Q = 91 kJ/mol for the grain growth of the temper rolled steel (Fig. 4a, line 1) is lower than the activation energies
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Table 4 The values of activation energies connected with ferrite grain growth [4] Process
Q, kJ/mol
Volume diffusion of Fe in a iron Grain boundary diffusion of Fe in a iron Grain boundary mobility of pure iron
280 164 147
for processes associated with ferrite grain growth. Comparing the value of Q in temper rolled material to the corresponding value of the same material without temper rolling (see Fig. 4a), it is possible to claim that temper rolling means an additional driving force for ferrite grain growth. The observation that a small prior plastic strain may promote anomalous grain growth is widely known [4] and interpreted as strain-induced grain boundary migration. Deformation leads to two contributions in microstructure changes, i.e., an increase in dislocation density and grain elongation with an associated increase in grain boundary area. The difference in stored energy provides the driving force for grain boundary motion that also leads to a reduction in internal energy of material. These facts support the suggestion that non-equilibrium grain boundary motion is induced by plastic deformation, i.e., by temper rolling, and as a result, the material shows higher mobility of grains in comparison with non-deformed material. The polygonal microstructure formation (Fig. 5a) in ultra low carbon steel FP2 is connected with the
Fig. 4. Plot of ln (d 2 d 20) as a function of 1 / T for ferrite grain growth in: a) steel SP; b) steels FP2 (line 1) and FP1 (line 2).
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Y. Sidor, F. Kovac / Materials Characterization 55 (2005) 1–11
Fig. 5. Microstructures of the investigated samples annealed for 5 min at 875 8C in wet NH3 atmosphere: a) steel FP2; b) steel FP1.
relatively high value of activation energy Q ~ 178 kJ/ mol (Fig. 4b). The latter is comparable with the activation energy for grain boundary diffusion of Fe in ferrite (see Table 4). The activation energy for normal grain growth in fully processed steel FP1 (Fig. 5b) was estimated as ~ 245 kJ/mol (Fig. 4b). The calculated value is comparable with self-diffusion of Fe in ferrite (see Table 4). The chemical compositions of both FP1 and FP2 steels are similar, apart from carbon content. Carbon addition to laminate steels decreases the a to ac transformation temperature. The temperature A c1 was calculated by bThermo-calcQ software for FP1 and FP2 as 880 and 962 8C, respectively. It is obvious that phase transformation does not occur in steel FP2 in the investigated temperature range. By comparing the activation energy of steel FP1 for normal grain growth with the corresponding activation energy of steel FP2 (see Fig. 4b), one can conclude that the ferrite grain growth in a steel without a phase transformation needs a lower activation energy than the one with phase transformation. This phenomenon is because the difference in chemical composition leads to distinct mechanisms of grain boundary motion, as a consequence of different phase composition at elevated temperature. The existence of a second phase (austenite) acts as an inhibitor for ferrite grain growth. Furthermore, carbon in solid solution, which is preferentially enriched at the moving grain boundary, reduces grain boundary mobility of the growing grain due to a solute drag effect. Recently, a significant amount of experimental work has been carried out on steels to tailor the
properties. A common difficulty in many cases is the inhomogeneity of the microstructure and the texture of steel as a result of the production process. This is of particular importance in electrical steels. For low carbon steels, it is possible to apply a decarburizing annealing in the intercritical region that leads to the columnar-grained microstructure with a specific type of the texture [13]. The columnar grain growth of fully processed steel FP1 is driven by diffusioncontrolled grain boundary motion mechanism. The moisture of the gas mixture, temperature and heating rate are the main parameters that influence the directional grain growth [13]. Carbon diffusion along the grain boundary produces an elastic stress on the boundary that causes motion of latter. A discontinuous concentration profile of carbon through the thickness of steel is observed during decarburization [12]. The latter is caused by the difference in carbon solubility in ferrite and austenite. The carbon content increases from zero at the surface to a quasiequilibrium value at the a / (a + c) interface. Thus, decarburization proceeds through bdiffusion pipesQ that are aligned with normal direction (ND) to the sheet-plane. The blocking of carbon in the bdiffusion pipeQ decreases the rate of carbon removal and, thus, decreases the elastic stress along the grain boundary. For optimal columnar grain growth during the decarburization, the carbon removal should have a sequential character. It is well known that the boundary velocity is proportional to the frequency of atoms bjumpingQ across the grain boundary plane. On the other hand, the intensive decarburization should accelerate the bjumping processQ of matrix atoms along the normal direction. Hence, intensive
Y. Sidor, F. Kovac / Materials Characterization 55 (2005) 1–11
decarburization causes a small pinning effect on the grain boundary that leads to directional grain boundary motion. As the microstructure is non-equiaxed the activation energy of grain growth may be considered as a dependent value on growth direction. In the field of grain growth simulation, the Monte Carlo algorithm is widely used to model anisotropic grain growth [4]. In the present work, the idea of anisotropic mobilities is applied to the columnar grain growth description. The activation energy was calculated for two growth directions, i.e., the rolling direction (RD) and the normal direction. When material is heated at a proper rate, at temperatures lower than A c1, primary recrystallization occurs simultaneously with intensive decarburization of the surface material layers. After the material is heated up to temperatures above A c1, a phase transformation, which refines primary recrys-
9
tallized matrix, occurs in the inner region. At the same time, surface layers are not subjected to the phase transformation because of the low local concentration of carbon. First, the small c phase grains are transformed into a ones and as a result the material has a fine primary recrystallized microstructure and the thin decarburized a-region on the sheet surface (Fig. 6a). These created grains act as the bnucleiQ for columnar grains (see Fig. 6b). Fig. 6c describes the formation process of the columnar microstructure from the point of view of activation energy. From this figure, the values of Q for grain growth were estimated as 240 and 404 kJ/mol for the RD and the ND, respectively. The activation energy for columnar grain growth in the plane of the RD is comparable with activation energy of self-diffusion of Fe in ferrite. The high value of Q for grain boundary motion with the ND (404 kJ/mol) confirms
Fig. 6. a) Columnar-nuclei creation at the commencement of decarburization process in steel FP1; b) scheme of columnar microstructure formation; c) plot of ln (d 2 d 20) as function of 1 / T for columnar-nuclei creation with the normal direction (line 1) and with the rolling direction (line 2) in steel FP1; d) columnar grains propagation towards mid-plane of the sheet.
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Fig. 7. a) Microstructure of steel FP1 after annealing when the activation energy of columnar-nuclei creation is Q ~ 400 kJ/mol; b) microstructure of steel FP1 after annealing when the activation energy of grain growth at the beginning of decarburization is Q ~ 280 kJ/mol.
that columnar grain growth needs a high energy to start the directional abnormal growth, and this can be explained by the energy demand for phase transformation during heating and subsequent growth of formed a grains on the surface. At later stages of this process, the size advantage of surface ferritic grains in comparison with fine-grained inner material is high and sufficient for continuation of directional abnormal grain growth of the surface layer towards mid-plane (Fig. 6d). As shown, coarsening of grains in the mid-plane is very slow because of the high bactivation energy barrierQ. After finishing the decarburization process, the microstructure is fully ferritic and grains have a columnar shape (Fig. 7a). As the parameters of decarburization process do not satisfy the optimal condition for columnar nuclei creation, then the inhomogeneous microstructure development takes place (Fig. 7b).
linked with either the grain boundary diffusion or the self-diffusion of Fe in ferrite. A model of anisotropic mobilities is applied to columnar grain growth description. For the early stage of columnar microstructure development, the value of the activation energy of grain growth with normal direction is higher than the one with rolling direction. The high value of activation energy for grains propagation with a normal direction towards the sheet mid-plane ( Q ~ 404 kJ/mol) confirms that columnar grains need a high energy to start and continue the directional abnormal growth. Acknowledgement This work was supported by the Slovak Grant Agency VEGA (project No. 2/4175/04). References
4. Summary The Zener factor strongly influences the kinetics of grain growth in a primary recrystallized matrix. The modeling of grain growth process in the matrix is complicated by both coalescence and dissolution of the precipitates. Plastic deformation induces non-equilibrium grain boundary motion. As a consequence the material shows higher grain boundary mobility in comparison with non-deformed material. Depending upon the chemical composition of the steels under investigation, polygonal grain growth is
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