Effects of Cooling Conditions and γ Grain Size on Each Behavior of Transformations, 3-Dimensional Thermal Deformation and Stress Generation during Immersion Cooling of Steel Bloom

Abstract

To optimize reverse transformation treatment, which is effective in preventing hot rolling cracking in the CC-HCR (Continuous Casting - Hot Charge Rolling) process, three-dimensional metallo-thermo-mechanical analyses were performed. The metallo-thermo-mechanics and a CCT (Continuous Cooling Transformation) diagram estimation method using JMatPro were used to obtain the required cooling time for reverse transformation in immersion cooling with water jet and to elucidate the effects of nonuniform cooling and γ grain size on thermal deformation and stress generation behaviors during cooling and the mechanisms of these events.

These analyses clarified the following. When diffusion-controlled transformation occurs during cooling, the required cooling time increases as Dγ (Diameter of γ grain) increases, and becomes substantially constant when only martensitic transformation occurs. In addition, the difference of Dγ causes a difference in the type of transformation that occurs during cooling and the temperature range where transformation occurs during cooling, and these differences produce differences in the amount of transformation expansion, which greatly affects the bloom deformation behavior during cooling. Furthermore, there is a difference in the level of the maximum generated stress during cooling depending on whether the transformation that occurs near the bloom surface layer during cooling is diffusion-controlled transformation or martensitic transformation. In addition, this difference in transformation behavior also causes a difference in the mechanism of maximum stress generation.

1. Introduction

The steel industry promotes global warming countermeasures such as development and extensive application of energy-saving processes and technologies and manufacturing energy saving eco-products.¹⁾ In this effort, it is expected to improve the hot charge rolling (HCR) ratio in the continuous casting-blooming process and expand the use of scrap. An increase in the scrap usage leads to an increase in the amount of tramp elements, such as Cu and Sn,²⁾ addition of embrittlement elements such as Nb, and an increase in the amount of N for the development for eco-products,³⁾ dramatically reducing the hot ductility. Such embrittlement increases hot rolling cracking during the HCR process.

An effective way to prevent this issue in the HCR process is to refine coarse austenite (γ) grain structure of the bloom by reverse transformation and its repetition, thereby improving the hot ductility.^4,5) However, problems such as bloom bending and quench cracking may occur in the treatment. Bloom bending causes problems in transporting and charging bloom into reheating furnace and miss rolling and imperfect shaping in blooming. Quenching cracks lead to a decrease in yield. Thus, it is necessary to identify solutions to prevent these problems while making the bloom surface more tough. Metallo-thermo-mechanical analysis is effective in examining the optimization of reverse transformation treatment. In the analysis, the cooling method, cooling conditions, steel grade and compositions are considered, and thermo-elastic-plastic analysis is performed while the behavior of transformation, bloom deformation and stress generation during cooling are estimated.^6,7)

In this analysis, transformation behavior is estimated by providing the continuous cooling transformation (CCT) diagram data that shows the start and end of each type transformation during cooling from a high temperature and at a constant rate with time on the horizontal axis and temperature on the vertical axis, thereby displaying the transformation process for each cooling rate. However, publication of CCT diagrams for the coarse γ grain structure is limited to a γ grain diameter (Dγ) of about 0.3 mm.⁸⁾ CCT diagrams when Dγ is in the order of several mm and with a structure where γ grains are as coarse as blooms have not been published. This causes a bottleneck for the estimated accuracy of the above-described analysis. When repeating reverse transformation to increase the prevention of hot rolling cracking by further refinement of the γ structure,^4,5) the optimization condition for each treatment must be examined considering the changing γ grain size.

Therefore, investigation of the optimization conditions of the reverse transformation and its repeated treatment, and improvement in the examination accuracy require CCT diagrams of the γ grain structure for each size, including its coarse structure as cast bloom. Thus, in this study, we investigated the method of obtaining the above CCT diagram, and focused on the fact that the method of calculating the CCT diagram considering the γ grain size is at a practical level. The diagrams were estimated by this calculation method.

Therefore, in this study, with the aim of optimizing reverse transformation to make the bloom surface more tough during the CC-HCR process, we selected an immersion cooled typical case quenching steel, SCr420 bloom, with water jets as the target. Further, we performed 3-dimensional (3D) metallo-thermo-mechanical analyses while considering the estimated CCT diagrams for various γ grain sizes. Then, we examined the effect of the cooling conditions, such as nonuniform cooling and the γ grain size on the required cooling time to make the bloom surface more tough, heat treatment deformation of bloom, and stress generation behavior. Previously, various behaviors were identified through 2D metallo-thermo-mechanical analyses,^9,10,11,12) but here, we performed 3D metallo-thermo-mechanical analyses to elucidate the behaviors and their mechanisms including bloom bending behavior.

2. Analytical Methods and Model

2.1. Overview of the Analytical Methods and Model

An analysis of heat treatment deformation of steel material should consider thermal shrinkage, thermal expansion, shrinkage and expansion during transformations, mutual effects among fields of deformation-stress, temperature and transformation behaviors. Therefore, this analysis requires a coupled model of heat conduction analysis and deformation analysis that considers the phase transformation.^6,7) In this study, we used heat treatment process simulation software (COSMAP v1.2 (IdeaMAP) with GiD v11.0.1 (pre-post processor, Digital Solutions Inc.), similar to the previous reports,^9,10,11,12) for the analyses.

In the present coupling model, in order to consider the above mutual influence, heat conduction analysis, deformation analysis considering transformation, and analysis of various transformation behaviors are coupled. While considering the effect of the steel compositions on each property, numerical calculations were performed by the finite element method (FEM) using the basic equations discussed below.

In the deformation analysis, we performed thermo–elastic–plastic analysis while considering the thermal and transformation strains in the elastic strain. In the heat conduction analysis, we considered heat generation due to deformation and latent heat of transformation in the heat conduction equation, and calculated the temperature changes within the cross section considering bloom surface as the heat transfer boundary and providing the heat transfer coefficient. Each transformation behavior can be estimated by inputting the CCT diagram data and considering the cooling rate. Each diffusion-controlled transformation was estimated using an equation¹³⁾ that considers the hydrostatic stress p in the Johnson–Mehl equation. The martensitic transformation was estimated using modified Magee’s formula,¹³⁾ which considers stress dependence.

2.2. Basic Equation for the Model^6,7)

2.2.1. The Basic Equation for Deformation Analysis

Equations (1), (2), (3), (4), (5), (6) were used for the deformation analysis calculation. If there were multiple phases, we applied the rule of mixture and obtained properties and parameters for each calculation.

Elastic strain, plastic strain, and each strain rate were obtained using Eqs. (1), (2), (3), (4). Considering thermal expansion, thermal shrinkage, transformation expansion, and transformation shrinkage, the elastic strain for each phase was calculated using Eqs. (1) and (2). The total strain increment, defined as a sum of the elastic strain and plastic strain increment, was calculated using Eq. (4)   

$$\text{Elastic strain:}\hspace{0.5em}{\epsilon }^e=-\rho \frac{\partial {\hat{g}}^e}{\partial \sigma }={\sum }_{I=1}^N{\epsilon }_I{}^e{\xi }_I$$(1)

where,

ρ: density, ${\hat{g}}^e$: Gibbs free energy contributing to elastic deformation, σ: stress tensor, ε_I^e: elastic strain of each phase, ξ_I: internal state variable for each phase (volume fraction).   

$${\epsilon }^e{}_I=\frac{1+{\nu }_I}{E_I}\sigma -\frac{{\nu }_I}{E_I}\mathbf{1}tr\sigma +{\alpha }_I(T-T_0)\mathbf{1}+{\beta }_I\mathbf{1}$$(2)

where,

E_I: modulus of longitudinal elasticity of each phase, T: absolute temperature, T₀: reference temperature, α_I: linear thermal expansion coefficient of each phase, β_I: transformation expansion coefficient of each phase, ν_I: Poisson’s ratio of each phase, 1: unit tensor.

(2) Plastic strain increment:   

$$d{\epsilon }^P=\hat{G}\left(\frac{\partial F}{\partial \sigma }:d\sigma +\frac{\partial F}{\partial T}dT+{\sum }_{I=1}^N\frac{\partial F}{\partial {\xi }_I}d{\xi }_I\right)\frac{\partial F}{\partial \sigma }$$(3)

where, F: yield function and 1/$\hat{G}$: hardening function.,

(3) Total strain increment:   

$$\dot{\epsilon }={\dot{\epsilon }}^e+{\dot{\epsilon }}^p$$(4)

Equation (5) solved the above strain-increment equation for the stress increment and represented in matrix form, which is used to perform numerical calculations.

(4) Stress increment:   

$$\begin{array}{l}\{\dot{\sigma }\}=[D^{ep}](\{\dot{\epsilon }\}-\{\alpha \}\dot{T}-\frac{\partial {[D^e]}^{-1}}{\partial T}\{\sigma \}\dot{T}\\ \hspace{1em}\hspace{1em}-{\sum }_{I=1}^N\left(a_I(T-T_0)+{\beta }_I+\frac{\partial {[D^e]}^{-1}}{\partial {\xi }_I}\{\sigma \}\right){\dot{\xi }}_I\{1\})\\ \hspace{1em}\hspace{1em}-\frac{1}{S_0}\left\{\frac{\partial F}{\partial \sigma }\right\}\left(\frac{\partial F}{\partial \sigma }\dot{T}+{\sum }_{I=1}^N\frac{\partial F}{\partial {\xi }_I}{\dot{\xi }}_I\right)\end{array}$$(5)

  

$$S_0=\frac{1}{2G\hat{G}}+\frac{\partial F}{\partial \sigma }:\frac{\partial F}{\partial \sigma }$$(6)

where,

[D^ep]=[D^e]−[D^p], [D^e]: elastic matrix, [D^p] additional matrix, G: modulus of transverse elasticity.

2.2.2. Basic Equation for Heat Transfer Calculation

In the heat transfer calculation, we used Eqs. (7) and (8) and considered the latent heat of the phase transformation and heat generation due to deformation. By providing the heat transfer coefficient H, we estimated the temperature changes based on the sequential calculation of the heat removal rate on the bloom surface.

(1) Coupled Heat Conduction Equation   

$$\begin{array}{l}c\rho \dot{T}+\rho {\sum }_{I=1}^N{l}_I{\dot{\xi }}_I+T\frac{\partial {\epsilon }^e}{\partial T}:\dot{\sigma }\\ +\left[\rho \frac{\partial h}{\partial {\epsilon }^p}:{\dot{\epsilon }}^p+\rho \frac{\partial h}{\partial \kappa }\dot{\kappa }-\sigma :{\dot{\epsilon }}^p\right]=k\mathrm{\hspace{0.17em} } div(grad\mathrm{\hspace{0.17em} }T)\end{array}$$(7)

where, ρ: density, c: specific heat, T: absolute temperature, l: latent heat, h: enthalpy, k: thermal conductivity.

(2) Heat Influx From Fluid   

$$-k(grad\mathrm{\hspace{0.17em} }T)\cdot n=H(T-T_g)$$(8)

where, H: heat transfer coefficient, T_g: coolant temperature (water temperature), n: outward unit normal vector of the boundary.

2.2.3. Analysis of Transformation Behaviors

In the analysis of phase transformation behavior, we used the following equation,¹³⁾ which included the effect of hydrostatic stress p to the Johnson–Mehl equation.   

$${\xi }_p(t)=1-\text{exp(}-v_e\text{)}$$(9)

  

$$v_e={\int }_0^{t}f(T,{\sigma }_m){(t-\tau )}^{3}d\tau$$(10)

  

$$f(T,{\sigma }_m)=f(T,0)\text{exp(}A{\sigma }_m\text{)}$$(11)

where,

ξ_p(t): volume fraction of p phase at time t from the start of transformation, T: absolute temperature, σ_m: mean stress, f(T,0): parameter determined from transformation behavior under no stress, τ: incubation time, A: parameters of the material (f(T,0), τ and A are determined in COSMAP from the data of CCT diagram under no stress).

As for martensitic transformation, the following equation¹³⁾ that derived from Magee’s kinetics considering the stress dependence was employed.   

$${\xi }_M=1-\text{exp}\left[\varphi (M_s-T)+\psi \text{:}\sigma \right]$$(12)

where,

ξ_M: volume fraction of martensite, ϕ: material parameters derived from Gibbs free energy, M_s: martensitic transformation start temperature under no load, σ: stress tensor, ψ: material parameters determined in an experiment based on the stress dependence of martensitic transformation start conditions.

In the diffusion-controlled transformation analysis with COSMAP, the progress of transformation after the start of transformation was calculated with Eqs. (9), (10), (11); however, to determine the parameters used in this calculation and transformation start time, data for the start line of each transformation must be provided separately from the CCT diagram under no stress. This data can be prepared from the CCT diagram the actual measurement. However, a CCT diagram for coarse γ grain structures with D_γ that exceeds several 100 μm has not been published, hence, it was estimated using a CCT diagram calculation model, whose result provided the start line data.

Various methods and models have been proposed for the calculation model and transformation prediction model for the Time Temperature Transformation (TTT) diagram and CCT diagram, which are roughly classified as follows.

One of the methods is a semi-empirical approach that uses the equation of Avrami (or Johnson–Mehl (JM), or Kolmogorov–Johnson–Mehl–Avrami.¹⁴⁾ X = 1 − exp(−ktⁿ), X: volume fraction, t: time). In this method, the prediction of each diagram was made in consideration of the steel composition and D_γ, using the parameters of the equation (k,n) and the composition and D_γ dependence of each parameter, clarified from the actually measured TTT diagram and transformation behavior data.^15,16)

The other method is a semi-empirical approach that uses a function other than JM that allows for the description of the transformation rate. It is a method that can predict TTT and CCT diagrams considering the dependence of the transformation rate on the composition and D_γ by determining the coefficients and various parameters in the equation from the results of actual measurements.^17,18,19) Furthermore, various models are proposed based on thermodynamics, nucleation theory, and diffusion theory for nucleation/growth and interface moving speed.^{20,21,22,23,24,25,26,27,28,29,30,31,32)} Once the TTT diagram is obtained, the CCT diagram can also be obtained using the additivity rule from the TTT diagram.^{15,16,17,18,22,31)}

Theoretical models of transformation become more complex and difficult to handle as they are refined. Nucleation sites could be the grain boundary surface, grain boundary edge, and grain boundary corner. Handling partitioning local equilibrium (PLE)/non-partitioning local equilibrium (NPLE), para-/ortho-equilibrium^{21,24,25,26,27,30,31)} varies between models and are not specified. In addition, the consideration of solute drag and interaction of coexisting elements^{15,17,18,21,24)} is insufficient and verification of the effectiveness of the models might be limited to specific types of steel. Furthermore, to explain measurement results using a theoretical model, unknown parameters must be estimated from experimental results or parameters must be determined through fitting the measurement data. However, the evaluation of the dependence of the parameters on steel grade and γ grain size is still insufficient. Therefore, in this study, we examined each model to determine whether it is possible to estimate the behavior of diffusion-controlled transformation considering the composition of a wide range of steel grades and the D_γ dependency, and whether or not the verification of the results is sufficient. After the examination, we chose the model proposed by J. S. Kirkaldy^17,21) to estimate the CCT diagram. This model is employed in JMatPro,^18,33,34,35) which is calculation and database software for material properties from Sente Software Ltd. In this study, we used the JMatPro v12.4 and General Steel database to estimate CCT diagrams.

In JMatPro, using the model proposed by J. S. Kirkaldy^17,21) that uses Zener–Hillert type Eqs. (13), (14), (15), (16), (17), (18), (19) shown below, equations parameters are determined for a wide range of steel grade compositions and D_γ by fitting of estimated diagrams with measured data. In this manner, estimating CTT diagram for a wide range of steel grades and D_γ becomes possible.¹⁸⁾

In the above model, rapid site saturation is assumed for the generation of each transformation phase in order to avoid argument about complex nucleation and make it simple. The time required for γ phase to transform to a certain volume faction τ is assumed to be proportional to the reciprocal of the 1/4 power of D_γ; i.e., if the ASTM grain size number is N, it is proportional to the reciprocal of 2^(N/8). Though theoretically, the value of power for the degree of supercooling ΔT is 2 or 3,²¹⁾ in bainite transformation (Eq. (15)), the value of 2 was empirically employed. In Eq. (13) (ferrite transformation), the value of 3 was empirically employed. The exponent q of ΔT in Eq. (14) (pearlite transformation) gradually decreases from 3 as Cr, Mo, and W concentrations increase.¹⁸⁾ Furthermore, the effective diffusion coefficient in a system including various alloying elements is approximated with the linear function of the elemental concentration. The coefficient that multiplies each elemental concentration and activation energy of each diffusion coefficient, D_{iff, F}, D_{iff, P}, D_{iff, B} Q_eff, were determined through fitting with measured data published in the U. S. Steel Atlas.¹⁸⁾

The chemical compositions of steel materials and N were provided to obtain the TTT diagram using Eqs. (13), (14), (15), (16), (17), (18), (19). When this diagram is converted with the additivity rule as defined in Eq. (20), the CCT diagram is obtained.   

$${\tau }_F=\frac{60\%Mn+2\%Ni+68\%Cr+244\%Mo}{6\times 2^{(N/8)}\mathrm{\Delta }{T}^3{D}_{iff,\mathrm{\hspace{0.17em} }F}}I$$(13)

  

$${\tau }_P=\frac{1.8+5.4(\%Cr+\%Mo+4\%Mo\cdot \%Ni)}{6\times 2^{(N/8)}\mathrm{\Delta }{T}^q{D}_{iff,\mathrm{\hspace{0.17em} }P}}I$$(14)

  

$${\tau }_B=\frac{(2.3+10\%C+4\%Cr+19\%Mo)}{6\times 2^{(N/8)}\mathrm{\Delta }{T}^2{D}_{iff,\mathrm{\hspace{0.17em} }B}}I$$(15)

  

$$D_{iff,\mathrm{\hspace{0.17em} }F}=exp(-23\mathrm{\hspace{0.17em} }500/RT)$$(16)

  

$$\frac{1}{D_{iff,\mathrm{\hspace{0.17em} }P}}=\frac{1}{exp(-27\mathrm{\hspace{0.17em} }500/RT)}+\frac{0.5\%Mo}{exp(-37\mathrm{\hspace{0.17em} }000/RT)}$$(17)

  

$$D_{iff,\mathrm{\hspace{0.17em} }B}=exp(-27\mathrm{\hspace{0.17em} }500/RT)$$(18)

  

$$I={\int }_0^x\frac{dx}{x^{2(1-x)/3}{(1-x)}^{2x/3}}$$(19)

  

$${\int }_{T_{Ae3}}^{T_{CCT}}\frac{dt}{{\tau }_{IT}}= {\int }_{T_{Ae3}}^{T_{CCT}}\frac{dT}{{\tau }_{IT}\dot{T}}=1$$(20)

where, x: the transformation ratio (volume fraction) of γ phase transformed at temperature T, τ_j: time for the transformation rate to reach x at temperature T, N: ASTM grain size No., ΔT: degree of supercooling for each transformation, D_iff,j: effective diffusion coefficient for each transformation, R: gas constant.

2.3. 3D-analysis Model and Analytical Conditions

In metallo–thermo–mechanical analyses, analyses were performed using the 3D FEM with the goal of elucidating the 3D behavior of heat treatment deformation during immersion cooling of a bloom. However, within the limit range of element division number of software (COSMAP v1.2 with GiD v11.0.1) introduced, the division number was increased as much as possible to ensure calculation accuracy. Considering the symmetry conditions, the range of analytical target was narrowed, where the analytical target was having a 1/2 length of a square bloom cross section of 100 mm × 1000 mm, dividing at the center of the bloom thickness (1/2 cross section). This range was divided into 10, 20, and 25 for the bloom thickness, width, and length directions, respectively. Then, in the element division, weighting was applied, and the surface layer where variables such as temperature, strain, stress and volume fraction of the transformation phase changed greatly was subdivided (Fig. 1). In transformation behavior calculation in COSMAP, only the volume faction of each phase is calculated and it is not necessary to consider the γ grain size for element division.

Fig. 1.

Element division of FEM model and boundary conditions of heat transfer during non-uniform cooling. (Online version in color.)

In the examination of prevention conditions of cracking in the blooming of the HCR process, which directly connects mid cross-section bloom CC and blooming,³⁶⁾ the γ grain within the range of the 10 mm from the surface layer must be refined to prevent cracking in the blooming of difficult-to-manufacture steel grades in reverse transformation.¹¹⁾ Thus, in this analysis, the γ refinement target range in bloom was set to 10 mm from the bloom surface, and the time taken for the volume fraction of γ phase to reach within the range of 0.1 or less was defined as the required cooling time. While this time was estimated, the temperature, volume fraction of each phase, and time transition of the generated stress were estimated at each cross-sectional position in numerical calculations using the FEM.

The present calculation targeted case hardening steel SCr420 (representative chemical composition (mass%): 0.22%C–0.2%Si–0.64%Mn–0.97%Cr–0.03%Al) for the analysis. For this steel grade, the CCT diagrams of D_γ of 22.1, 250, 1000, 3000, and 5000 μm were obtained by JMatPro using the General Steel database. Each transformation start line of this CCT diagram was provided as the COSMAP input data to perform metallo–thermo–mechanical analyses. The data set of SCr420 in COSMAP reported by Okamura^37,38) was used to determine the properties of this steel grade, which is needed for calculation. In the heat transfer calculation, bloom that was heated to 850°C was cooled by immersing in a water bath at 20°C stirred with a water jet. The relationship between the surface temperature and heat transfer coefficient H³⁹⁾ in this case was applied to the entire surface in uniform cooling. In the nonuniform cooling, the value of H at the same temperature was halved for the right side of the bloom, for the analyses (Fig. 1).

3. Analytical Results

3.1. CCT Diagram Estimation

We estimated the CCT diagram of SCr420 when the γ grain diameter (D_γ) was 22.1, 250, 1000, 3000, and 5000 μm with JMatPro using the General Steel database. Figure 2 shows CCT diagrams when D_γ was 250 or 5000 μm. In these diagrams, the 1% volume fraction line of ferrite (α), pearlite (P), bainite (B), and residual austenite (γ) phases was used to indicate the start or end lines of diffusion-controlled transformation. For martensite (M), the starting temperature and the lines for the volume fraction of 50% and 90% are shown. In COSMAP with GiD, the 1% volume fraction line of each transformation phase was considered as the transformation start line to analyze transformation behavior.

Fig. 2.

Estimated CCT diagrams of SCr420 by JMatPro. (Online version in color.)

From the obtained CCT diagrams, it was confirmed that the start line and end line of each diffusion-controlled transformation moved to the right with increasing D_γ. As D_γ increased from 22.1, 250, 1000, 3000 to 5000 μm, the shortest time to initiate α transformation was estimated to increase by about 2, 23, 102, 280, and 489 s.

The CCT diagrams estimated for a D_γ of 22.1 μm and 250 μm were consistent with the CCT diagram measured under the condition of the austenitizing temperature of 870°C and D_γ of 20–30 μm,⁴⁰⁾ and the CCT diagram that was measured when D_γ was 200–400 μm.⁸⁾ These results confirm that JMatPro can roughly predict the CCT diagrams of SCr420 at various D_γ.

3.2. Cooling Time Required for Reverse Transformation and Transformation Behavior during Immersion Cooling

When the 850°C heated SCr420 bloom was immersion cooled using a water jet with a temperature of 20°C, we estimated the cooling time required for the reverse transformation (Fig. 3). This diagram shows that the required cooling time for reverse transformation increases during nonuniform cooling compared to uniform cooling, because of decreasing of the transformation rate with the lower cooling intensity on the right side during nonuniform cooling.

Fig. 3.

Relation between diameter of γ grain and required cooling time for reverse transformation. (Online version in color.)

In the present study, during the immersion cooling with a water jet, the required cooling time increased as D_γ increased regardless of uniform or nonuniform cooling, until D_γ was about 1000 μm, and when D_γ was about 1000 μm or higher, it remained constant at 90 s or 120 s. Therefore, for an actual bloom with 100 mm × 100 mm coarse γ structure cooled using immersion cooling with a water jet, cooling times of 90 s to 120 s were sufficient for reverse transformation. The time required to cool an actual 220 mm × 200 mm bloom³⁶⁾ is about 2 minutes. In the present case, the difference in the cross-section size can reduce the time up to 30 s. Figure 3 also indicates that if D_γ can be less than 1000 μm in the previous treatment when reverse transformation is repeated, the treatment time can be shortened compared to the previous treatment.

To refine the γ grain with this treatment, the γ phase in the target refinement range must be transformed to a low-temperature phase through cooling. Then, a new γ phase must be generated by heating to the γ single phase range, while limiting the heating temperature simultaneously to regulate the growth of the γ grain.^4,5) Therefore, transforming the γ phase to a low-temperature phase temporarily is necessary but not sufficient to refine the γ grain.

The authors consider that the reason for the hot ductility improvement by γ grain refinement is the reduction in D_γ, increasing the boundary surface area of the γ grain. Increased boundary surface area alleviates the intragranular strengthening due to multiplication of dislocation by hot working, the accumulation of dislocations to the grain boundaries and stress concentration on the grain boundaries, thereby regulating the occurrence of grain boundary cracking. Furthermore, there is an almost inversely proportional correlation between the γ grain boundary area per unit volume and D_γ. Considering the above points, D_γ must be reduced to 500 μm or lower to significantly increase the grain boundary surface area for bloom in the order of mm and improve hot workability. In the range where D_γ is 300 μm or less, improvement in hot ductility with a decrease in D_γ is confirmed in a laboratory experiment.^4,5) The refinement goal for the γ grain in actual operation changes based on the steel grade and hot rolling conditions; thus, the target value should be determined based on the actual operation data. In this paper, we conclude the discussion on the refinement goal of γ grain at this point.

For the transformation phase that appears during the present cooling conditions, a contour diagram of the volume fraction for each transformation phase was delineated at 1/2 cross-sectional thickness of bloom for examination. In the present contour diagram, the α phase, P phase and B phase were not differentiated, but instead, the sum of the volume fraction of α, P, and B phases is displayed as the volume fraction of the B/P phase.

As a result of this investigation, as can be seen from the contour diagram of Fig. 6, Figs. 12 and 13 later mentioned, the following facts were found. Figure 6 shows the occurrence condition of transformation phase by the contour diagram and Figs. 12 and 13 show transition diagrams in volume fraction of the transformation phase. M transformation did not occur during cooling, but instead only B/P transformation occurred when D_γ was 22.1 μm in both uniform and nonuniform cooling. At 250 μm, M transformation was dominant on the surface side, while B/P transformation was dominant inside. When D_γ was 1000 μm or more, only M transformation occurred. The contour diagram such as Fig. 6 showed that the required cooling time depends only on D_γ for a diffusion-controlled transformation in which the transformation rate changes by D_γ. When only M transformation occurs, where the transformation rate does not depend on D_γ, the required cooling time was not dependent on D_γ. In the case of the latter, even if D_γ is further increased, diffusion-controlled transformation is further delayed, where M transformation stipulates the required cooling time, indicating that the required cooling time also do not depend on D_γ.

Fig. 6.

Distributions of volume fraction of martensite or bainite/pearlite and temperature when deformation amount in positive x-direction is maximum. (Online version in color.)

Fig. 12.

Time transitions of Sxx, volume fraction of martensite, bainite/pearlite and temperature (Dγ: 22.1 μm). (Online version in color.)

Fig. 13.

Time transitions of Sxx, volume fraction of martensite, bainite/pearlite and temperature (Dγ: 5000 μm). (Online version in color.)

For the same water temperature, cooling by immersing in static water, agitated water with air, or water or mist spray cooling where water and air are mixed and sprayed through a nozzle have lower heat transfer coefficient and cooling rate compared to the immersion cooling with a water jet,^10,11,12) thus, increasing the required cooling time.^11,12) In cooling methods and conditions where the cooling rate is lower than that of water jet immersion cooling, diffusion-controlled transformation is more likely to occur, thus, the range of D_γ in which diffusion-controlled transformation occurs at this cooling rate and the required cooling time changes, expands toward larger D_γ.

3.3. Bloom Deformation Behavior during Nonuniform Immersion Cooling

In this study, for a case hardening steel SCr420 bloom cooled with water jet immersion cooling, we used the CCT diagram estimated for various γ grain sizes; moreover, we examined the effects of nonuniform cooling and γ grain size on the heat treatment deformation through 3D deformation analysis that used the metallo–thermo–mechanics model and found the following.

Figure 4 shows the maximum amount of deformation in the negative and positive x directions during the cooling process. The amount of deformation in the negative and positive x directions was understood by the difference in the amount of displacement in these directions between the positions of the bloom center position in the longitudinal direction and the peak on the edge of the right and left sides at the 1/2 cross section of the bloom (Fig. 4). Figure 4 and FEM post processing video observation show the following regarding the deformation behavior of each case.

Fig. 4.

Relation between diameter of γ grain and maximum amount of deformation in x-direction. (Online version in color.)

Bloom bending during nonuniform cooling is not dependent on D_γ in the initial stage. During the stage of cooling, the amount of thermal shrinkage was large on the left side with a higher cooling intensity, leading to notable bending in the negative x direction. The maximum amount of deformation (ΔX_L) was 1.81 mm when D_γ was 22.1 μm. When D_γ was 250 μm or higher, ΔX_L was about 1.55 mm, showing that it does not depend on D_γ (Fig. 4). If cooling continues after the maximum deformation in the negative x direction, the amount of deformation of bloom in the negative x direction begins to decrease.

When D_γ was 22.1 μm, the amount of deformation in the negative x direction decreased but was not resolved until the end of cooling. The amount of deformation (ΔX_R) on the right side of the bloom was −1.83 mm, when D_γ was 22.1 μm (Fig. 4). Meanwhile, when D_γ was 250 μm or higher, if the cooling continued after the maximum deformation occurred in the negative x direction, the amount of expansion due to M transformation and B/P transformation on the left side and the increase in the amount of thermal shrinkage on the right side led to a notable distortion in the positive x direction, where the maximum ΔX_R became approximately +2.24 mm (Fig. 4). Before the end of subsequent cooling, expansion due to M transformation and B/P transformation on the right side slightly reduced the amount of deformation in the positive x direction. Thus, we found that when D_γ was 22.1 μm and 250 μm or higher, deformation behavior during cooling was dramatically different. When D_γ was 22.1 μm, more time was required for the deformation in the negative x direction to reach its maximum amount of displacement compared to when D_γ was 250 μm or higher; thus, the amount of temperature drop and thermal shrinkage increase on the left side, as seen in Fig. 5 described later. In turn, the maximum amount of displacement in the negative x direction also increases. Furthermore, since the time until the end of subsequent cooling is short, the above distortion would not to be resolved. The presently estimated distortion with a maximum of 2.24 mm per 500 mm length became a distortion of about 27 mm in the actual bloom with a length of 6 m, where the bloom transport becomes unstable.

Fig. 5.

Distributions of volume fraction of martensite or bainite/pearlite and temperature when deformation amount in negative x-direction is maximum. (Online version in color.)

The bloom cross-section shape, distributions of volume fraction of each transformation phase, and temperature within a longitudinal section are shown as contour diagrams for the position of 1/2 bloom thickness when the negative or positive x direction deformation of the bloom attains its maximum due to continuous cooling (Figs. 5, 6). Each contour diagram in this paper shows a higher value of variables with the higher color on the color bar. The cross-sectional shape shown in the contour diagrams are enlarged by 40 times for each displacement in the x, y, and z directions so that it is easier to understand the deformation behavior.

Furthermore, for a D_γ of 22.1 μm and 5000 μm, distributions of volume fraction of each transformation phase and temperature in the bloom width direction (x direction) from the center position in the longitudinal direction at the 1/2 thickness cross section of the bloom are shown, when the amount of deformation of the bloom in the negative and positive x direction was at their maximum, and at the end of cooling (Figs. 7, 8). Figures 5, 6, 7, 8 show the following regarding the deformation behavior and mechanism during immersion cooling.

Fig. 7.

Relation between relative distance in bloom width direction and volume fraction of bainite/pearlite or martensite. (Online version in color.)

Fig. 8.

Relation between relative distance in bloom width direction and temperature. (Online version in color.)

Figures 5, 7(a), and 8(a) show that when D_γ is 22.1 μm, the B/P phase appears more on the left side of the bloom than on the right side. However, the bloom bent into the negative x direction. Therefore, the amount of thermal shrinkage exceeds the amount of expansion due to the B/P transformation on the left side, and the substantive amount of shrinkage (the amount of shrinkage obtained by subtracting the amount of transformation expansion from the amount of thermal shrinkage) is greater on the left side than on the right side. For these reasons, it turned out to bend in the negative direction once after cooling started.

D_γ of 250, 1000, and 3000 μm, we drew a diagram similar to the case where D_γ was 5000 μm, as shown in Figs. 5, 7(b), and 8(b), and found that when D_γ was 250 μm and higher, only a small portion of the edge and corner went through M transformation without any other transformation when the negative x direction deformation reached the maximum. Since the amount of thermal shrinkage was higher on the left side than on the right side, the bloom bent once in the negative x direction after the start of cooling.

When D_γ was 22.1 μm, deformation shifts to the positive x direction following the maximum deformation in the negative x direction; however, despite the amount of B/P transformation during this time and the amount of transformation expansion being larger on the right side than the left side (Fig. 7(a)), deformation occurs in the positive x direction. On the other hand, the temperature drop is larger on the right side than on the left side (Fig. 8(a)). From the above, it was presumed that the deformation in the positive x direction was not caused by transformation expansion, but because the amount of thermal shrinkage was greater on the right side than on the left side.

In cases where D_γ was 250 μm or higher, the diagram was similar to Figs. 5, 6, 7(b), and 8(b) of D_γ of 5000 μm showed the following regarding the deformation mechanism during cooling.

During the transition from the maximum amount of deformation in the −x direction to the maximum amount of deformation in the +x direction, the amount of M and B/P transformations increased more on the right than left, when D_γ was 250 μm. Furthermore, during the transition, the amount of M transformation increased more on the left side than the right side, when D_γ was 1000 μm or higher (Fig. 7(b)). For any D_γ, the amount of temperature drop was higher on the right than the left side (Fig. 8(b)); hence, in addition to the amount of transformation expansion being higher on the left than the right, the amount of thermal shrinkage also increased more on the right than the left, thereby bending the bloom in the positive x direction.

In the deformation behavior during the nonuniform cooling of a bloom through immersion cooling with water jet, the difference in D_γ between 22.1 μm and 250 μm or higher, made notable difference in the deformation behavior due to the difference in the transformation behavior. Until transformation occurs, the deformation behavior is stipulated by the distribution of the amount of thermal shrinkage; however, when diffusion-controlled transformation occurs at a high temperature, such as when D_γ is 22.1 μm (Figs. 5, 6, 7(a), and 8(a)), the deformation behavior is strongly dependent on the distribution of the amount of thermal shrinkage due to limited amount of transformation expansion.⁴¹⁾ Meanwhile, when D_γ was about 250 μm and both diffusion-controlled transformation and M transformation occurred at a low-temperature (Figs. 5, 6), and when D_γ was 1000 μm or higher and only M transformation occurred (Figs. 5, 6, 7(b), and 8(b)), the deformation behavior depended on both the cross-sectional amount distributions of thermal shrinkage and transformation expansion since the amount of transformation expansion was large.⁴¹⁾

As discussed above, bloom deformation behavior during cooling varies according to D_γ, but the effect of variations in the cooling intensity against the bloom bending during cooling is large regardless of D_γ, necessitating a reduction in cooling intensity and its variations.

3.4. Stress Generation Behavior during Immersion Cooling

From the viewpoint of quenching crack prevention, the effect of D_γ on the normal stress that occurs during nonuniform immersion cooling was analyzed using the metallo–thermo–mechanics (Fig. 9). We also performed similar analyses in uniform cooling. Here, the stress distribution in the cross section was different from the nonuniform cooling, but the value of the maximum stress was similar to the nonuniform cooling. The maximum generated stress was larger for the normal stress in the width and thickness directions (S_xx, S_yy) than normal stress in the bloom axial direction (S_zz) for the uniform and nonuniform cooling. Due to the symmetry of the square cross-section bloom, the maximum value of S_xx and S_yy showed little differences. Furthermore, the maximum value of S_xx and S_yy were the highest at approximately 800 MPa when D_γ was 22.1 μm, and were almost constant at 600 MPa at 250 μm or higher D_γ.

Fig. 9.

Relation between diameter of γ grain and maximum stress. (Online version in color.)

For D_γ of 22.1 μm or 5000 μm, distributions at the 1/2 cross section of the bloom of S_xx and S_zz, and volume fraction of the M phase or B/P phase and temperature when the S_xx is maximum, are shown as contour diagrams (Figs. 10, 11). In the figures, the occurrence position of the maximum S_xx and S_zz are shown with oval symbol. Time transitions of maximum S_xx and the volume fraction of M and B/P phase and temperature at the occurrence position of the maximum S_xx are shown in Fig. 12 (D_γ: 22.1 μm) and Fig. 13 (D_γ: 5000 μm). We performed the same analysis when D_γ was 250, 1000, and 3000 μm, and arrived at the following findings:

Fig. 10.

Distributions of Sxx, Szz, volume fraction of bainite/pearlite and temperature, when Sxx is maximum (D_γ: 22.1 μm). (Online version in color.)

Fig. 11.

Distributions of Sxx, Szz, volume fraction of martensite and temperature, when Sxx is maximum (D_γ: 5000 μm). (Online version in color.)

When D_γ was 22.1 μm, at the maximum S_xx occurrence position within the B/P transformation layer at the edge of the bloom, shown with oval symbol in Fig. 10(a), the maximum S_xx occurred after B/P transformation at the position (Fig. 12). Therefore, it is presumed that when the B/P transformation occurs inside the cross section from the maximum S_xx position, the expansion due to the transformation pulls that position in the bloom width direction, causing the maximum S_xx to occur. Before reaching the maximum S_xx, temperature drop was confirmed at the position of the maximum S_xx; thus, an increase in the thermal stress of tension caused by restraining of the thermal shrinkage by the surrounding was also involved in the occurrence of the maximum S_xx.

When D_γ was 250 μm or higher, just before M transformation occurred at the position of the maximum S_xx, maximum stress occurred at the edge of the bloom, as shown by oval symbol in Fig. 11(a). Then, S_xx dropped dramatically after M Transformation began, and the temperature drop rate is also large when the maximum S_xx occurs at the position (Fig. 13). Therefore, when the peripheral portion of the surface layer undergoes M transformation and expands, the portion of the γ phase immediately below the M layer is pulled in the bloom width direction, and the tensile thermal stress acting on that position increases, causing the maximum S_xx occurs.

When D_γ was 250 μm or higher, since the γ phase was in the low-temperature range and γ grain structure was coarse, the above-described maximum stress worked on the γ phase with low hot ductility. Therefore, the risk of quenching a crack was higher.

When D_γ is 250 μm or more, if the maximum stress acts on the coarse γ phase at low temperature, it is presumed that the risk of quench cracking is high due to the low hot ductility of the γ phase. If quenching cracks is an issue during the cooling in reverse transformation, a reduction in the amount of transformation expansion and thermal shrinkage per unit time is effective in reducing the stress. Thus, cooling methods and conditions that allow further reduction in the cooling intensity^10,11,12) must be selected.

4. Conclusion

With the aim of optimizing reverse transformation that is effective in preventing hot rolling cracks during the CC-HCR process, we used the metallo–thermo–mechanics method and the transformation prediction model to perform 3D metallo–thermo–mechanical analyses. We discovered the following on the effects and mechanism of nonuniform cooling and γ grain size on the required cooling time for reverse transformation, deformation behavior and stress generation behavior during immersion cooling of small section bloom of case hardening steel with water jet.

(1) Under the currently examined cooling conditions, the required cooling time to refine γ grains within 10 mm of the bloom surface in reverse transformation was estimated to be as high as approximately 90–120 s. The time increases as Dγ increases in the range where diffusion-controlled transformation occurs when Dγ is less than 1000 μm, and becomes almost constant when Dγ is 1000 μm or higher where only non-diffusion martensitic transformation occurs.

(2) As such, when reverse transformation is applied multiple times, if D_γ can become 1000 μm or below in the previous treatment, treatment time in the current state can be shortened.

(3) The maximum amount of bending deformation in nonuniform cooling that was examined in this study was about 2.2 mm per 500 mm length. Since the amount of expansion due to diffusion-controlled transformation that occurs at high temperatures was small at Dγ of about 22.1 μm, deformation behavior during nonuniform cooling is strongly dependent on the distribution of thermal shrinkage amount in the bloom cross section. When Dγ was 250 μm or higher, expansion associated with the diffusion-controlled transformation that occurred at a low temperature and M transformation was large; hence, distributions of the amount of thermal shrinkage and transformation expansion have an effect on the deformation behavior.

(4) The maximum stress during cooling was approximately 800 MPa when D_γ was 22.1 μm and remained constant at about 600 MPa for a D_γ of 250 μm or higher.

(5) The mechanism of the maximum stress generation depends on D_γ. In addition to thermal stress, expansion caused by B/P transformation in the inner area from the position of the maximum stress or M transformation near the surface layer pulled the position to cause the maximum stress.

(6) In the range where D_γ was 22.1–250 μm, the nucleation site of diffusion-controlled transformation is reduced as D_γ increased, delaying the diffusion-controlled transformation. In the CCT diagram, diffusion-controlled transformation shifts toward a longer time; thus, the temperature range of the transformation decreases. Furthermore, M transformation began from the bloom surface and the amount of M transformation increased; thus, the required cooling time, bloom deformation, and stress generation behavior gradually approaches those of a D_γ value of 250 μm.

Acknowledgments

This research was supported by the 29th ISIJ Research Promotion Grant. We sincerely thank this research grant.

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