@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Materials Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Mimura, Yoshihito"@en ; dcterms:issued "2010-08-30T17:46:23Z"@en, "1989"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """Sticking of the shell in the mold, which often occurs in a high-speed continuous slab casting machine, can be detected with thermocouples in the mold copper plates and prevented from developing into a breakout by reduction of the casting speed. However, a rapid reduction of the casting speed causes some quality problems and a low slab temperature. Thus, sticking-type breakouts remain a concern to the steel industry, and it is still not clear how and why the sticking initiates at the meniscus. The objectives of this study were to identify the causes of sticking at the meniscus, to elucidate the mechanism of sticking and finally to propose methods to reduce the occurrence of sticking. In order to identify the causes of sticking, it was necessary to examine a sticking-type breakout shell metallurgically, especially the dendrite structure at the shell surface. To link the metallurgical information to the casting conditions, the validity of a correlation in the literature between secondary arm spacing and local cooling rate has been examined. The secondary dendrite arm spacing in the subsurface of a slab has been measured and linked to a local cooling rate calculated from the measured mold heat-flux with this correlation. From this analysis, it was confirmed that Suzuki's correlation between secondary dendrite arm spacing and local cooling rate can be applied for a high cooling rate such as in continuous casting. A sticking-type breakout slab exhibiting five sticking events of 0.08% carbon steel, has been studied and it has been found that small holes exist at the surface in the sticking shells (most likely the site of entrapment, of solid mold flux). The shell which initially sticks exhibits a coarse dendrite structure and, in a longitudinal section, the shape of the initial sticking shell is parabolic. Moreover, with one exception, segregation lines typically 1-3 mm below the surface and almost parallel to the surface have been found in most of the sticking shell. From secondary ion mass spectroscope studies, the solutes concentrating in these segregation lines were determined to be Mn and S. Apparently, the sticking occurs at the meniscus where heat extraction is greatest and molten mold flux flows between the shell and solid mold flux rim oscillating with the mold. Therefore, to explain these meniscus phenomena, mathematical models of heat transfer at the meniscus and fluid flow in the mold flux channel have been formulated. To analyze the initial sticking event, the meniscus level has been changed in the computer simulations and the following mechanism has been proposed to explain the initiation of a sticking-type breakout. If the meniscus level rises, a deep notch forms in the shell due to the interaction between the mold flux rim and the shell. When a thick mold flux rim moves downward, it contacts the shell above the notch and the shell sticks to the mold flux rim. During the upstroke motion of the mold, tensile forces on the shell cause a rupture at the deep notch which is the hottest and weakest. The predicted solid flux rim profile agrees well with the parabolic shell shape measured in a longitudinal section of the sticking shell. Since the hot spot is the most likely point to be ruptured, conditions which minimize the hot spot were sought with the models. It was found that most of the conditions required to reduce hot-spot formation are exactly opposite to those required to minimize oscillation mark depth. Notwithstanding this, there are a few techniques to reduce the occurrence of sticking and to improve the surface quality: use a low melting point mold flux and, probably, maintain a deep mold flux pool. An interesting finding with respect to oscillation mark formation is that, if the mold flux rim is thick, the oscillation mark is caused by the interaction of the flux rim with the solidifying shell, while the fluid pressure development in the molten flux film dominates the mark formation in the case of a thin flux rim. For the analysis of the segregation line, a mass transfer model has been formulated based on a consideration of δ — γ transformation. From this analysis, it was found that the segregation observed in the sticking shell is a band of interdendric segregation enhanced by enlarged primary dendrite arm spacing which, probably, is caused by the appearance of an air gap due to the shell shrinkage."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/27941?expand=metadata"@en ; skos:note "Sticking-type Breakouts during the Continuous Casting of Steel Slabs By Yoshihito Mimura B.Eng. (Applied Physics), The University of Tokyo, Tokyo, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES METALS AND MATERIALS ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JUNE 1989 © Yoshihito Mimura, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Metals and Materials Engineering The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Sticking of the shell in the mold, which often occurs in a high-speed continuous slab casting machine, can be detected with thermocouples in the mold copper plates and prevented from developing into a breakout by reduction of the casting speed. However, a rapid reduction of the casting speed causes some quality problems and a low slab temperature. Thus, sticking-type breakouts remain a concern to the steel industry, and it is still not clear how and why the sticking initiates at the meniscus. The objectives of this study were to identify the causes of sticking at the meniscus, to elucidate the mechanism of sticking and finally to propose methods to reduce the occurrence of sticking. In order to identify the causes of sticking, it was necessary to examine a sticking-type breakout shell metallurgically, especially the dendrite structure at the shell surface. To link the metallurgical information to the casting conditions, the validity of a correlation in the literature between secondary arm spacing and local cooling rate has been examined. The secondary dendrite arm spacing in the subsurface of a slab has been measured and linked to a local cooling rate calculated from the measured mold heat-flux with this correlation. From this analysis, it was confirmed that Suzuki's correlation between secondary dendrite arm spacing and local cooling rate can be applied for a high cooling rate such as in continuous casting. A sticking-type breakout slab exhibiting five sticking events of 0.08% carbon steel, has been studied and it has been found that small holes exist at the surface in the sticking shells (most likely the site of entrapment, of solid mold flux). The shell which initially sticks ii exhibits a coarse dendrite structure and, in a longitudinal section, the shape of the initial sticking shell is parabolic. Moreover, with one exception, segregation lines typically 1-3 mm below the surface and almost parallel to the surface have been found in most of the sticking shell. From secondary ion mass spectroscope studies, the solutes concentrating in these segregation lines were determined to be Mn and S. Apparently, the sticking occurs at the meniscus where heat extraction is greatest and molten mold flux flows between the shell and solid mold flux rim oscillating with the mold. Therefore, to explain these meniscus phenomena, mathematical models of heat transfer at the meniscus and fluid flow in the mold flux channel have been formulated. To analyze the initial sticking event, the meniscus level has been changed in the computer simulations and the following mechanism has been proposed to explain the initiation of a sticking-type breakout. If the meniscus level rises, a deep notch forms in the shell due to the interaction between the mold flux rim and the shell. When a thick mold flux rim moves downward, it contacts the shell above the notch and the shell sticks to the mold flux rim. During the upstroke motion of the mold, tensile forces on the shell cause a rupture at the deep notch which is the hottest and weakest. The predicted solid flux rim profile agrees well with the parabolic shell shape measured in a longitudinal section of the sticking shell. Since the hot spot is the most likely point to be ruptured, conditions which minimize the hot spot were sought with the models. It was found that most of the conditions required to reduce hot-spot formation are exactly opposite to those required to minimize oscillation mark depth. Notwithstanding this, there are a few techniques to reduce the occurrence of iii sticking and to improve the surface quality: use a low melting point mold flux and, probably, maintain a deep mold flux pool. An interesting finding with respect to oscillation mark formation is that, if the mold flux rim is thick, the oscillation mark is caused by the interaction of the flux rim with the solidifying shell, while the fluid pressure development in the molten flux film dominates the mark formation in the case of a thin flux rim. For the analysis of the segregation line, a mass transfer model has been formulated based on a consideration of 8 — y transformation. From this analysis, it was found that the segregation observed in the sticking shell is a band of interdendric segregation enhanced by enlarged primary dendrite arm spacing which, probably, is caused by the appearance of an air gap due to the shell shrinkage. iv Abstract Table of Contents List of Tables List of Figures List of Symbols Acknowledgement 1. Introduction 2. Literature Review 2.1 Sticking-type Breakouts 2.2 Dendrite Arm Spacing Table of Contents ii v x xii xxii xxxii 1 3 3 9 v 2.3 Oscillation Mark Formation 13 2.4 Lubrication in the Mold and Behavior of Solid Flux Rim 17 2.5 Heat Transfer Models near the Meniscus 18 2.6 Segregation due to Solidification Followed by 8-y Transformation 19 3. Scope of Present Work 22 4. Secondary Dendrite Arm Spacing in Continuous Cast Slabs and Its 24 Relationship to Local Cooling Rate 4.1 Heat Flux Calculation Data and Measurement of Arm Spacing 24 4.2 Mathematical Model with Finite-Difference Method 29 4.3 Definition of Cooling Rate 31 4.4 Calculation Accuracy of Mathematical Model Based on Finite-Difference 34 Method 35 4.4.1 Effect of Time Step 35 4.4.2 Effect of Mesh Size 36 vi 4.4.3 Effect of Superheat in the Mold 4.5 Analytical Solution to Link between Secondary Dendrite Arm Spacing and 38 Mold Heat Flux 4.6 Prediction of Secondary Dendrite Arm Spacing with the Value of Heat Flux 40 5. Metallurgical Observation of Sticking-type Breakout Shells 42 5.1 General Aspects 42 5.2 Measurement of Oscillation Marks 48 5.3 Micro-Structure of Breakout Shells 51 5.4 Metallography with Secondary Ion Mass Spectroscope (S.I.M.S.) 59 6. Mathematical Model Heat Transfer near the Meniscus with Mold Flux 66 Lubrication 6.1 General Flow Sheet 66 6.2 Flow Rate of Mold Flux 71 vii '78 83 86 90 7. Model Results and Discussion 92 7.1 Response from the Initial Conditions 92 7.2 Effect of Convection on the Heat Transfer near the Meniscus 93 7.3 Heat Flux to the Mold and Heat Flux from the Slab 96 7.4 Oscillation Mark Formation 102 7.5 Mechanism of the Initiation of Sticking-type Breakout 110 7.6 Prevention of Sticking 117 8. Segregation below the Surface in a Low Carbon Steel 121 8.1 Cooling Rate Change due to Solid Flux Rim Remelting 121 6.3 Meniscus Shape 6.4 Introduction of Energy Equation 6.5 Heat Transfer in the Mold Flux Film 6.6 Slab Temperature Calculation viii 8.2 Cooling Curves for the Sticking Shells 125 8.3 Mass Transfer Model during Solidification Followed by 8 - y 129 Transformation: An Explanation for the Segregation Lines 8.4 Solute Redistribution after 8 - y Transformation 139 8.5 Segregation below the Surface in the Sticking Shell 144 8.6 Non-equilibrium Phase Diagram 146 9. Summary and Conclusions 149 Bibliography 153 ix List of Tables 2.1 Correlation between Secondary Dendrite Arm Spacing and Cooling Rate, 12 Proposed by Suzuki et al. 4.1 (a) Steel Composition, Liquidus and Solidus Temperature of Sample R 26 4.1(b) Operating Conditions of Sample R 26 4.2 Average and Standard Deviation of Secondary Dendrite Arm Spacing 27 Measurement of Sample R 5.1 (a) Steel Composition, Liquidus Temperature and Solidus Temperature of the 43 Sticking-type Breakout Slab 5.1 (b) Operating Conditions of the Sticking-type Breakout Slab 43 5.2 Average of the Mark Pitch and Depth 48 5.3 Measuring Conditions of S.I.M.S. 61 6.1 Calculation Conditions and Operating Conditions 69 6.2 Steel Properties and Pouring Temperature 70 6.3 Mold Flux Properties and Pool Depth 71 x 6.4 Estimation of Terms in Equation (6.35) 86 8.1 Boundary Conditions for Mass Transfer Model 135 8.2 Distribution Coefficient and Diffusion Coefficient Based on Ueshima et al. 137 8.3 (a) Primary and Secondary Dendrite Arm Spacing and Cooling Rate for Sample 138 IC1 8.3 (b) Primary and Secondary Dendrite Arm Spacing and Cooling Rate for Sample 139 IC7 xi List of Figures 2.1 Sticking-type Breakout Shells 4 2.2 Shell Profile on Section a - a ' i n Figure 2.1 4 2.3 Process of Sticking in the Mold 5 2.4 Prevention of Breakouts due to Reduced Casting Speed 6 2.5 Breakouts with Excessive Heat Removal or with Insufficient Heat Removal 9 2.6 Schematic Representations for Isothermal Coarsening of Dendrite 11 2.7 Schematic Diagram Showing the Longitudinal Section (Parallel to the Broad 14 Face) of a Continuous Casting Mold 2.8 Oscillation Mark Formation due to Emi's and Kawakami's Models 16 4.1 Heat Flux Data of Sample R 25 4.2 (a) Section at the Surface of Sample R, Etched with 3.5 % Picric Acid 28 4.2 (b) Section 20 mm below the Surface of Sample R, Etched with 3.5 % Picric 28 Acid 4.3 (a) Enthalpy as a Function of Temperature 31 xii 4.3 (b) Modified Temperature as a Function of Temperature 31 4.4 (a) Temperature Calculated with Time 32 4.4 (b) Cooling Rate Calculated with Time 32 4.5 Secondary Dendrite Arm Spacing Prediction and Measurement (Average and 33 Standard Deviation) with Distance from the Slab Surface 4.6 Effect of Time Step on the Predicted Cooling Rate 35 4.7 Effect of Mesh Size on the Predicted Cooling Rate 36 4.8 Effect of Super Heat on the Predicted Cooling Rate 37 4.9 Variation of Non-dimensional Temperature with rj 40 4.10 Secondary Dendrite Arm Spacing Prediction 41 5.1 Casting Speed Variation after the Nozzle Change 43 5.2 Photograph of Broadface (Outside Radius) of Sticking-type Breakout Slab 44 5.3 Slab with Sticking Shell and Sample Locations 45 5.4 Appearance of Sound Area IC5 in the Breakout Slab 46 5.5 Appearance of Initial Sticking Area OC2 in the Breakout Slab 47 xiii 5.6 Appearance of Rupture Zone OC3 in the Breakout Slab 47 5.7 Mark Depth vs. Mark Pitch in Sound Shell 49 5.8 Mark Depth vs. Mark Pitch in Sticking Shell 50 5.9 Mark Depth vs. Mark Pitch in Ruptured Shell 50 5.10 Cast Structure in IC5, Sound Shell, Etched with 2.5 % Picric Acid 52 5.11 Cast Structure in OC2, Sticking Zone, Etched with 2.5 % Picric Acid 52 5.12 Cast Structure in OC3, Rupture Zone, Etched with 2.5 % Picric Acid 53 5.13 Cast Structure without Segregation Line in Sample IC7 Etched with 2.5 % 53 Picric Acid 5.14 Locations in the Breakout Shell Exhibiting Segregation Lines 54 5.15 (a) Sketch of a Cross Section Including the Initial Sticking Region 55 5.15 (b) Photograph of Cast Structure in the Initial Sticking Area 55 5.16 Parabolic Shape of the Initial Sticking Shell 56 5.17 Change of Secondary Dendrite Arm Spacing with Distance from the Surface 57 in Sound Shell IC3 xiv 5.18 Change of Secondary Dendrite Arm Spacing with Distance from the Surface 58 in Ruptured Shell with the Segregation Line IC1 5.19 Change of Secondary Dendrite Arm Spacing with Distance from the Surface 58 in Ruptured Shell without the Segregation Line IC7 5.20 Change of Secondary Dendrite Arm Spacing with Distance from the Surface 59 in Initial Sticking Shell OC2 5.21 Cast Structure Examined with S.I.M.S., Sample IC1 61 5.22 Carbon Distribution in the Area Shown in Figure 5.21 62 5.23 Manganese Distribution in the Area Shown in Figure 5.21 62 5.24 Sulphur Distribution in the Area Shown in Figure 5.21 63 5.25 Phosphorus Distribution in the Area Shown in Figure 5.21 63 5.26 Distribution of Pearlite in Sample IC1 64 5.27 Manganese and Sulphur Distribution with Line Analysis 65 6.1 Relationship among Four Parts of Heat Transfer Model at the Meniscus 67 6.2 General Flow Chart of Heat Transfer Model at the Meniscus 68 6.3 Physical System of Mold Flux Row 73 xv 6.4 Physical System in the Calculation by Takeuchi and Brimacombe or Anzai et 75 al. 6.5 Channel between Solid Mold Flux Rim and Shell with Oscillation Marks 78 6.6 Physical System at the Meniscus 80 6.7 Meniscus Shape Calculated by Analytical Solution and Numerical Method 82 6.8 Physical System of Heat Transfer in the Mold Flux 87 6.9 Tracking System of the Slab Temperature Distribution 91 7.1 Response of the Average of the Heat Flux to the Mold and the Average of 93 the Heat Flux from the Slab in the Region 0 ~ 1 cm below the Meniscus from the Initial State 7.2 Profile of Heat Flux to the Mold 94 7.3 Profile of Heat Flux from the Slab 94 7.4 Comparison of the Heat Flux to the Mold with or without Convection 95 7.5 Comparisons of the Heat Flux from the Slab with or without Convection 95 7.6 Heat Balance in the Region 0 ~ 1 cm below the Meniscus 96 xvi 7.7 Effect of Flux Viscosity on the Heat Fluxes near the Meniscus 97 7.8 Effect of Casting Speed on the Heat Fluxes near the Meniscus 97 7.9 Effect of Mold Oscillation Frequency on the Heat Fluxes near the Meniscus 98 7.10 Effect of Mold Oscillation Half Stroke on the Heat Fluxes near the Meniscus 98 7.11 Effect of Flux Melting Point on the Heat Fluxes near the Meniscus 98 7.12 Effect of Flux Viscosity on the Heat Balance near the Meniscus 100 7.13 Effect of Casting Speed on the Heat Balance near the Meniscus 100 7.14 Effect of Mold Oscillation Frequency on the Heat Balance near the Meniscus 100 7.15 Effect of Mold Oscillation Half Stroke on the Heat Balance near the 100 Meniscus 7.16 Flux Velocity Distribution with a Low or High Mold Flux Viscosity 101 7.17 Flux Velocity Distribution with a Low or High Casting Speed 101 7.18 Shape of Oscillation Mark Calculated in the Model 103 7.19 Effect of Flux Pool Depth on Predicted Oscillation Mark Depth 104 7.20 Effect of Flux Viscosity on Predicted Oscillation Mark Depth 104 xvii 7.21 Effect of Casting Speed on Predicted Oscillation Mark Depth 104 7.22 Effect of Mold Oscillation Frequency on Predicted Oscillation Mark Depth 104 7.23 Effect of Mold Oscillation Half Stroke on Predicted Oscillation Mark Depth 105 7.24 Effect of Flux Melting Point on Predicted Oscillation Mark Depth 105 7.25 Effect of Flux Viscosity on Average Distance of the Shell from the Mold 106 Wall 7.26 Effect of Casting Speed on Average Distance of the Shell from the Mold 106 Wall 7.27 Schematic Change of Oscillation Mark Shape from Kawakami-type to 109 Emi-type Mark 7.28 Effect of Mold Oscillation Frequency on Emi-type Oscillation Mark Depth 110 7.29 Meniscus Level Change in the Computer Simulation 111 7.30 Shell Profile and Solid Flux Rim Profile with a Constant Meniscus Level 112 7.31 Slab Surface Temperature Profile with a Constant Meniscus Level 112 7.32 Shell Profile and Solid Flux Rim Profile after a Rise in the Meniscus 113 7.33 Slab Surface Temperature Profile after a Rise in the Meniscus 113 xviii 7.34 Comparison between the Real Sticking Shell and the Shell Profile or the 114 Solid Flux Profile 7.35 Comparison between the Real Sticking Shell and the Meniscus Shape 114 without Solid Flux Rim and Liquid Flux Film 7.36 Mechanism of the Occurrence for the Initial Sticking of the Shell 115 7.37 Shell Profile and Solid Flux Profile after a Fall in the Meniscus 117 7.38 Slab Surface Temperature Profile after a Fall in the Meniscus 117 7.39 Effect of Flux Viscosity on the Predicted Hot Spot Temperature 119 7.40 Effect of Casting Speed on the Predicted Hot Spot Temperature 119 7.41 Effect of Mold Oscillation Frequency on the Predicted Hot Spot Temperature 120 7.42 Effect of Flux Melting Point on the Predicted Hot Spot Temperature 120 7.43 Effect of Mold Oscillation Half Stroke on the Predicted Hot Spot 120 Temperature 7.44 Effect of Flux Pool Depth on the Predicted Average of Solid Flux Rim 120 Thickness above the Meniscus 8.1 Schematic Diagram of the Rupture in the Sticking Shell 123 xix 8.2 Comparison of the Secondary Dendrite Arm Spacing between Measurement 125 and Calculations Incorporating Solid Flux Rim Remelting 8.3 Heat Flux Pattern for Sample IC1 126 8.4 Heat Flux Pattern for Sample IC7 127 8.5 Comparison of Measured Secondary Dendrite Arm Spacing for Sample IC1 127 to Values Calcualted by the Trial-and-Error Method 8.6 Comparison of Measured Secondary Dendrite Arm Spacing for Sample IC7 128 to Values Calculated by the Trial-and-Error Method 8.7 Cooling Curves Calculated for Sample IC1 128 8.8 Cooling Curves Calculated for Sample IC7 129 8.9 Solidification Model Used (a) Position of Volume Element in Mushy Zone 130 (b) Magnified Volume Element with Concentration Profile 8.10 Control Volume in Primary Arm Spacing for Mass Transfer Model 133 8.11 General Flow Chart for Mass Transfer Model Based on the Model of 134 Ueshima et al. 8.12 Solute Concentrations after Solidification for Sample IC1 141 xx 8.13 Solute Concentrations after 8 - YTransformation for Sample IC1 (at 1300 °C) 142 8.14 Solute Concentrations after 8 - YTransformation for Sample IC7 (1300 °C) 143 8.15 Mechanism for Appearance of Air Gap during the Sticking 145 8.16 Non-equilibrium Transformation Temperature Calculated for IC1 147 8.17 Equilibrium and Non-equilibrium Phase Diagram (a) with Different Cooling 148 Rate (b) Different Primary Arm Spacing xxi List of Symbols a2 the capillary constant (-) as mold oscillation half stroke (cm) C solute concentration (wt%) C° initial solute concentration (wf %) C7 solute concentration in liquid far from solid interface (wt%) C,r°, C\\x solute concentration at the interface of dendrite with radius r 0 and rx, respectively (wt%) C* solute distribution at liquid-solid interface (wt%) CL solute concentration in liquid (wt%) C 5 solute concentration in 5-phase (yvt%) C Y solute concentration in y-phase (wr%) xxii CR local cooling rate (°C/s) CpFe specific heat of steel (Jlg°C) CpP specific heat of mold flux (Jig °C) Ds diffusion coefficient in solid (cm2Is) D& diffusion coefficient in 5-phase (cm2Is) Dy diffusion coefficient in y-phase (cm2Is) Dslab slab thickness (cm) dCu mold copper plate thickness (cm) dp mold flux film thickness (cm) Ft friction stress between shell and mold (dyne I cm2) f mold oscillation frequency (cycleIs) fs fraction of solid (-) xxiii g gravitation constant (cm/s2) HF, enthalpy of steel (Jig) h thickness of molten flux film (cm) h{ ~ /z3 meniscus dimension in the through thickness direction defined in Figure 6.4 (cm) hh hN distance of the shell from the mold wall defined in Figure 6.5 (cm) hB the largest distance of shell from the mold wall defined in Figure 6.5 (cm) hT the smallest distance of shell from the mold wall defined in Figure 6.5 (cm) hc a constant heat-transfer coefficient (between steel and mold cooling water) (W/cm2oC) h^ average heat-transfer coefficient between mold hot face and cooling water (W/cm2oC) hPM heat-transfer coefficient between solid flux rim and mold (W/cm2°C) xxiv hw heat-transfer coefficient between mold cold face and cooling water (Wlm2°C) k distribution coefficient (-) k*11 distribution coefficient between liquid steel and 5-phase (-) krL distribution coefficient between liquid steel and y-phase (-) kih distribution coefficient between 5-phase and y-phase (-) kCu thermal conductivity of mold copper plate (kW/m°C) kF, thermal conductivity of steel (W/cm2oC) kP thermal conductivity of mold flux (W/cm°C) kw thermal conductivity of mold cooling water (W/m°C) L characteristic length for heat transfer (cm) LH latent heat (Jig) LFe latent heat of steel (Jig) xxv Lp latent heat of mold flux (Jig) lP mold flux pool depth (cm) lx ~ / 2 meniscus dimension in the casting direction defined in Figure 6.4 (cm) lh lN distance of points on the shell surface from the meniscus defined in Figure 6.5 (cm) M the number of control volume at the liquid-solid interface in mass transfer model (-) Mc the number of the outer control volume (middle point between two primary dendrites) in mass transfer model defined in Figure 8.10 (-) m liquidus slope (°C/wt%) N the number of control volume at the 8 - y interface in mass transfer model (-) P or PP pressure in the mold flux film (dyne I cm2) P^ pressure in the air (dyne I cm2) xxvi AP pressure difference between steel and mold flux (dyne I cm2) Ptw the Prandd number of the mold cooling water (-) Q mold flux flow rate (cm}Is) qL heat generation (Jig) qu heat flux to mold (W/cm2) qs heat flux from slab (W/cm2) Rew the Reynolds number of mold cooling water (-) r0, rx radius dendrite defined in Chapter 2 (cm) rx distance of the meniscus from the top of mold defined in Chapter 6 (cm) r2 distance of mold flux pool from the top of mold defined in Chapter 6 (cm) s distance along the meniscus (cm) S0 thickness of solid mold flux rim (cm) xxvii T A 4 o r T A 4 l temperature at which the 8 - y transformation starts (°C) TAAe temperature at which the 8 - y transformation completes (°C) TF, temperature in steel slab (°C) T°Fe poring temperature of steel in mold (°C) T, equilibrium liquidus temperature (°C) TM mold hot face temperature (°C) TP temperature in mold flux (°C) TPM melting point of mold flux (°C) T, equilibrium solidus temperature (°C) Tslab slab surface temperature (°C) TSJ- slab surface temperature at the meniscus (°C) Tw mold cooling water temperature (°C) xxviii t time (s) t* non-dimensionalized time defined in Equation (6.40) (s) ti time when the temperature decreases to liquidus temperature (s) tN negative strip time of mold oscillation (s) ts time when the temperature decreases to solidus temperature (s) u mold flux velocity in the fixed system (cmIs) ii mold flux velocity in the moving system (cmls) u* non-dimensionalized mold flux velocity defined as Equation (6.37) (-) VM mold oscillation velocity (cmls) Vz casting speed (cmls) Vw velocity of mold cooling water (m/s) x distance in the casting direction (cm) xxix x* non-dimensionalized distance in the casting direction defined in Equation (6.39) H y distance in the through thickness direction (cm) y\" non-dimensionalized distance in the through thickness direction defined in Equation (6.38) (-) Z 0 distance from the top of mold to carbon-enrich flux layer (cm) Zj system length concerned in the heat transfer model at the meniscus (cm) contact angle (radian) y ¥ F e modified temperature defined in Equation (4.3) (°C) co angular velocity of mold oscillation (s~l) xxxi Acknowledgement I would like to express my sincere gratitude to my supervisor, Professor J.K. Brimacombe for his continuous assistance and guidance during the course of this research. The assistance of Associate Professor I.V. Samarasekera is gratefully acknowledged. I wish to thank Nippon Steel Corporation and the Natural Science and Engineering Research Council of Canada for the provision of a graduate scholarship and research support, respectively. Without the help of LTV Steel Company, this study would not be possible. I want to express my gratitude to Dr. P.H. Dauby and Mr. W.H. Emling of LTV Steel Company for their permission and support. It is my obligation and pleasure to note here that many friends in the Department of Metals and Materials Engineering help this study. xxxii 1 1. Introduction In the last fifteen years, the productivity of continuous casting machines has increased substantially. The production of a slab casting machine has changed from one hundred thousand tons per month to two hundred thousand tons per month largely by increasing the casting speed [1]. More recently, as a result of directly connecting the continuous casting process and the hot strip mill, maintenance of high casting speed has become an important technology not only for an increase in productivity but also for energy reduction in the reheating furnace [2]. Unfortunately, breakouts, especially sticking-type breakouts, occur more often in a high casting speed machine [1]. Breakouts, in which liquid steel flows out below the mold, result in significant repair costs and disturbance of production. Many researchers and engineers have investigated the prevention of sticking-type breakouts. As a result of this work, sticking-type breakouts can be detected with thermocouples in the mold copper plate [3]~[6] or by measurements of the friction force during mold oscillation [3][6]. Moreover, through these studies, lubrication in the mold as a function of mold flux properties is becoming understood. With the development of detection systems for sticking-type breakouts, the steel industry has succeeded in minimizing the breakout itself; however, this success does not mean the elimination of the sticking. For the prevention of these breakouts, the casting speed must be reduced [4]~[6], which causes some quality problems and a low slab temperature. Thus, the sticking-type breakouts remain a concern to the steel industry and it is still not clear how and why sticking-type breakouts initiate at the meniscus in the mold. For an analysis of initial sticking, information about events near the meniscus is important. Measurements of the mold copper plate temperature and the mold friction force, 2 however, do not always fully reflect meniscus phenomena. Other information that is invaluable in elucidating the causes of sticking is the dendrite structure at the sticking shell surface. However, previous studies of dendrite structure have been usually done on a laboratory scale and, therefore, it is difficult to apply the information gained from such studies to actual continuous casting operations. For example, correlations between secondary dendrite arm spacing and cooling rate have been found under conditions of a uniform temperature gradient and a low cooling rate. Therefore, it should be investigated whether or not information on secondary dendrite arm spacing in the literature could be employed for analyzing the meniscus phenomena in a continuous casting mold, where the temperature gradient is not uniform and the cooling rate is high. Moreover, in this region, there are mechanical interactions between the solidified shell and oscillating mold. Many previous studies have been done solely from the viewpoint of heat transfer or simply by considering mechanical aspects, but not both. In the region near the meniscus, these phenomena are related and, consequently, the study of meniscus phenomena should involve both a heat transfer analysis and a mechanical investigation. The primary purpose of this study is to identify the causes of sticking at the meniscus, particularly by examining the dendrite structure at the surface of a sticking-type breakout shell and relating it to casting conditions. The applicability of correlations in the literature between secondary dendrite arm spacing and cooling rate to continuous casting has been examined. Links have been established between mold heat flux and dendrite structure at the slab surface. Mathematical models of fluid flow in the mold flux channel and heat flow at the meniscus have been employed to elucidate the mechanism of sticking. The final objective of the work is to propose methods to eliminate sticking-type breakouts from a fundamental understanding of how they initiate. 3 2. Literature Review 2.1 Sticking-type Breakouts Sticking-type breakouts are induced by shell sticking which starts at the meniscus with the resulting shell rupture moving successively down the mold. Shells of sticking-type breakouts have a characteristic appearance as shown in Figure 2.1 (based on the figure by Itoyama et al. [3]). The shell that underwent sticking, which usually remains in the mold after the breakout, can be seen as (A) in Figure 2.1, while (B) is a sound shell which is withdrawn with the strand. The ruptured part (C) usually moves with the sound shell (B). Between the sticking part (A) and the ruptured part (C), there is a distinct line (D) which has an inclination of 30-45 ° from the horizontal which is the site of maximum shear stress. An actual breakout occurs at the bottom of the line (D) when the line moves down below the mold. The sound shell (B) has oscillation marks which are horizontal, while the sticking part (A) and the ruptured part (C) exhibit marks which are not horizontal but V-shaped [4]. The marks in the sticking and ruptured parts are described frequendy as psuedo-oscillation marks [4] or ripple marks [3]. The pitch of the marks both in parts (A) and (C) are smaller than that in part (B). If the shell profiles are examined at the longitudinal section a - a' in Figure 2.1, the section would appear as shown in Figure 2.2. The sound shell (B) has a profile in which the thickness increases with increasing distance downward in the casting direction. On the other hand, the sticking part (A) has the opposite shell profile, in which the 4 thickness increases towards the top of the mold (towards the meniscus). Thus, it can be concluded that the shell near the meniscus has stuck initially because it has a thicker shell. a Figure 2.1 Sticking-type Breakout Shells Figure 2.2 Shell Profile in Section a - a'in Figure 2.1 Based on the above observations of the sticking shells, Itoyama et al. [3] and Tsuneoka et al. [4] have explained how the rupture proceeds in the mold, which is illustrated in Figure 2.3. Initially, the shell near the meniscus has stuck for reasons undetermined and the shell rupture occurs a little below the initial sticking point. Thus, liquid steel flows into this area and forms the new shell. Part (A) remains stuck and moves up during the upward stroke of the mold oscillation, while part (C) is withdrawn with the strand. As a result, the shell is placed in tension which causes another rupture 5 at the weakest point where the shell is newly forming. These processes continue in each oscillation cycle and, finally, when the rupture line reaches the bottom of the mold, liquid steel flows out to create a breakout. Figure 2.3 Process of Sticking in the Mold [3] If the mold temperature is measured at several positions in the casting direction, when the sticking occurs, first, in the top of the mold, the temperature increases and gradually decreases. Because the newly formed thin shell has a high temperature, the hot spot moves down according to the movement of the rupture. Usually, the velocity of the hot spot is lower than the casting speed [4]. Thus, sticking in the mold can be detected by mold temperature measurements [3]~[6]. In order to release the sticking, the operator reduces the casting speed quickly and as shown in Figure 2.4, if the casting speed is reduced to below 1.0 m/min, the sticking breakouts can be prevented in this particular machine [4]. From a consideration of the sticking process and release of sticking due to reduced casting speed, Tsuneoka et al.[4] 6 and Itoyama et al.[6] have proposed a mechanism for preventing the rupture from progressing. In both proposed mechanisms, it is suggested that an increase in the shell thickness during the negative-strip time stops the rupture. During the negative-strip time, the rupture does not occur owing to the compressive force exerted on the shell by the downward motion of the mold. Thus, if the shell solidifies to sufficient thickness during the negative-strip time, the sticking part can be removed from the mold without rupture, when the mold begins to move upward and tensile forces begin to act on the shell. 0.6 0.5 ^) 0.3 0.2 0.1 a = 3 = 0.75 L = 450 L = 400 L = 350 / 1 1 ' 111 i HI/I a if -V 1 III 1 i, , , L = 300 'I'II ^•^Shel V 1 recovery curve Ac tua cor.di 1 oscilati tion curve on L: Distance from meniscus to quasi-meniscus j • Occurrence of breakout Q Prevention of breakout by reducing casting speed ! 0.5 1.0 2.0 Casting Speed ( m / m i n ) Figure 2.4 Prevention of Breakouts due to Reduced Casting Speed [4] Although the sticking movement or the sticking release is relatively well understood, it is not clear why and how the initial sticking occurs near the meniscus. Many previous studies of initial sticking have been based on analyses of friction force 7 between the shell and the mold [3],[6]~[10]. The equation often used for the friction force analysis is: VM-VZ F > = T \\ - ^ (2.D aP where F, : friction stress between the shell and the mold rj : mold flux viscosity VM : mold oscillation velocity Vz : casting speed dP : mold flux film thickness These studies have indicated that a large friction force brings about a shell rupture near the meniscus and the ruptured shell is stuck to the mold. Therefore it has been concluded that, for prevention of the sticking, the friction force should be reduced with a low viscosity of mold flux [3], or an increase of flux film thickness (an increase of flux consumption) [7]. The effect of Al203 [11] or gas bubbles [9] on the flux viscosity also have been discussed. It has been reported that fluxes containing Li and Mg [12], mold flux with a low melting point [12] and non-sinusoidal mold oscillation [7] improves the flux consumption and reduces the friction force. Another approach for the prevention of sticking is the elimination of disturbance to the shell near the meniscus. The importance of mold level control [14] and of an adequate mold flux pool depth [15] has been emphasized. However, these studies cannot explain what the shell is stuck to and what causes the initial sticking. Considering the strength of steel at high temperature, the initial rupture must occur at the hottest part of the shell, which means that a hot spot must exist below the sticking point before the initial sticking occurs. No mechanism for appearance of the hot spot has been proposed. In the previous studies, the causes of the initial sticking have not been determined, but the findings can be classified into two categories. The first is related to the direct 8 contact of liquid steel to the mold plate since Itoyama et al.[3] and Tsuneoka et al.[4] have found copper or coating material on the sticking shell. In the second case, metal is not found on the sticking shell but, instead, there is a carbon-rich region in the vicinity of the initial sticking [4] [16]. Data which is useful in considering these two categories regarding the initial sticking are reported by Ogibayashi et al.[16], as shown in Figure 2.5. When the breakout occurs, the mold heat-transfer coefficient calculated is excessively large or small, relative to normal operation. Because the mold flux represents the largest thermal resistance, it is considered that more heat transfer is caused by a thin mold flux film while less heat transfer implies a thicker flux film. The first cause (direct contact of liquid steel to the mold plate) is, then, related to the smaller flux film thickness. It can be said that poor lubrication causes the sticking, because liquid steel easily contacts and sticks to the mold plate. On the other hand, it can be regarded that the rich carbon in the vicinity of the initial sticking comes from the mold flux [17]. Therefore, the second cause may be explained by phenomena involving a thicker flux film. However, the actual causes of the initial sticking, especially in the second case (less heat transfer), are still unknown. 9 • Breakout slab O Normal slab —i 1 : i i I 0.8 1.0 1.2 1.4 1.6 1.8 Casting speed (m/min) Figure 25 Breakouts with Excessive Heat Removal or with Insufficient Heat Removal or with Insufficient Heat Removal [16] 2.2 Dendrite A rm Spacing Measurements of the dendrite arm spacing are useful for understanding the thermal history of metal during solidification. Many correlations between the primary or secondary dendrite arm spacings and the thermal conditions have been proposed theoretically and empirically [18]~[31]. For the analysis of the thermal history of continuously cast steel, the measurements of secondary dendrite arm spacings are more often made than those of primary arm spacings, because the latter is affected by convection which is always present in the continuous casting mold [28]. Consequently, in this study, secondary dendrite arm spacings have been investigated. 10 The secondary dendrite arm spacing can be determined by the coarsening and coalesence processes, which essentially are Ostwald ripening [33]. Kattamis et al. have proposed two models for dendrite arm coarsening, as shown in Figure 2.6 [22]. From the Gibbs-Thomson relationship, for part \"0\" of dendrites with radius r0: T-T=—— (2.2) 'v-'h where T,>T>TS Tt : equilibrium liquidus temperature Ts : equilibrium solidus temperature T : a constant temperature (i.e. isothermal field is assumed) 0.67, Cs(fs = 1) < C°. Thus, Equations (2.8) and (2.9) indicate incorrectly that the solute is redistributed less than the initial alloy composition in the whole region. Therefore, the application of these equations is limited to slow diffusion, i.e. small a. To improve Brody's equations (2.8) and (2.9), Clyne and Kurz [54] and Ohnaka [55] have proposed other models. However, these analytical solutions cannot be applied for the case of 8 - y transformation following solute redistribution after solidification. With a numerical method, Chuang et al. have calculated the carbon redistribution due to 8 - y transformation for a 0.39 % carbon steel [56]. For steel with multiple alloy elements, Ueshima et al.[57] and Kobayashi et al.[51] have proposed models concerning solute redistribution. They have indicated that interdendric segregation is enhanced by 8 - y transformation, if the solute has a diffusion coefficient above unity. Moreover, their models imply that solidification and the 8 - y transformation are affected by cooling rate, as discussed further in Section 8.6. (2.10) 22 3. Scope of Present Work From the previous work, development of the rupture due to shell sticking in the mold is reasonably well understood and moreover the sticking can be detected with thermocouples in the mold copper plate or by measurements of the frictional forces on the mold during its oscillation cycle. A reduction in casting speed can prevent the sticking from developing to create a breakout. Still unknown, however, is the mechanism of initial sticking, especially in the case in which a carbon-rich region is found in the vicinity of the initial sticking, and which may be related to a thicker mold flux film. The primary objective of the present work is: (1) to find the causes of initial sticking. Apparently, causes of the initial sticking are related to phenomena in the meniscus region. The most dependable source of information on meniscus phenomena is the dendrite structure near the slab surface. To accomplish this, the following methodology was followed: (i) sticking-type breakout shells were examined metallurgically and links have been established between the characteristics of these shells and casting conditions. (ii) relationships between secondary dendrite arm spacing and mold heat flux have been established and compared to those measured in the subsurface of a slab. (iii) to elucidate the mechanism of initial sticking, mathematical modeling of heat transfer and lubrication at the meniscus have been conducted. 23 With the value of heat flux calculated from the secondary dendrite arm spacing at the surface of initial sticking shell, the mathematical models of heat transfer and lubrication at the meniscus has been evaluated. In the meniscus region, a large heat extraction from the liquid steel to the mold occurs and the oscillating mold interacts mechanically with the solidified shell. Therefore, in the present work, heat transfer phenomena and lubrication in the mold have been studied and link between both phenomena has been established in these mathematical models. Additionally, other meniscus phenomena such as oscillation mark formation which is related to slab defects (transverse cracks and pin holes) have been explained consistently. Without slab quality, there is no reason for continuous casting operation. Therefore, the other objectives are: (2) to clarify the effects of mold flux properties and operating conditions on oscillation mark depth. (3) to propose methods for both the elimination of sticking-type breakouts and improvement of slab surface quality. 24 4. Secondary Dendrite Arm Spacing in Continuous Cast Slabs and Its Relationship to Local Cooling Rate 4.1 Heat Flux Calculation Data and Measurement of Arm Spacing Examination of the dendrite structure at the slab surface is a technique that provides insight on meniscus phenomena. For plain carbon steels, Suzuki's equations relating secondary dendrite arm spacings and cooling rates [27] have often been referred to, but application of these equations to continuous casting is beset by two problems. First, it is not clear whether these equations can represent such a high cooling rate and, second, because the cooling rate is not easily measured in the production process, particularly during a sticking-type breakout, it has to be determined indirectly through other related process data such as mold heat flux. As has already been discussed in Section 2.2, the correlation between shell thickness and secondary dendrite arm spacing may be applicable inside slabs, but it often gives incorrect information near the surface region. For the prediction of the secondary dendrite arm spacing near the surface, the heat flux is relatively easily measured and can be translated to local cooling rate with a mathematical model. Therefore, in this study, it has been necessary to establish whether secondary dendrite arm spacing can be predicted from the heat flux data. In plant trials on an operating caster, Mahapatra [58] has measured mold copper plate temperature with thermocouples and calculated heat flux from the slab with a three-dimensional heat-transfer model of the mold plate, as shown in Figure 4.1. Figure 4.2 (a) and (b) show sections of Sample R, etched with 3.5 % picric acid in a hot water 25 bath, near the surface and 20 mm below the surface, respectively at precisely the location corresponding to the heat flux in Figure 4.1. The steel composition and the operating conditions are listed in Table 4.1 (a) and (b). Measurements of secondary dendrite arm spacing (Xj were made by counting the number of arms over a given length of primary arm. All measurements contained at least 5 arms and were recorded as a function of distance from the surface. The average and the standard deviations of the measurements are given in Table 4.2. 3 0 0 c ? 2 0 0 -u-100-2 E o X 3 (0 I 0 6 0 0 2 0 4 0 Time (s) Figure 4.1 Heat Flux Data of Sample R 26 Table 4.1 (a) Steel Composition (wt%), Liquidus and Solidus Temperature (°C) of Sample R c Mn Si P S Al T, T. 0.29 1.25 0.19 0.016 0.005 0.041 1506.8 1446.9 Table 4.1 (b) Operating Conditions of Sample R Slab Width (mm) Tundish Temperature (°C) Casting Speed (cm/min) 1530 1550 80.0 27 Table 42 Average and Standard Deviation of Secondary Dendrite Arm Spacing Measurement of Sample R Distance from the Surface (mm) Secondary Arm Spacing (\\vn) Deviation (\\\\m) 0 ~ 1 50 21.8 1-2 68 21.4 2 - 3 63 18.9 3 - 4 77 16.3 4 - 6 82 14.2 6 - 8 85 19.8 8-11 97 7.5 11 - 14 98 15.8 14- 17 101 22.0 17 - 20 119 13.3 28 I mm Figure 42 (a) Section at the Surface of Sample R, Etched with 35 % Picric Acid (x!6) I mm Figure 42 (b) Section 20 mm below the Surface of Sample R, Etched with 35 % Picric Acid (x!6) 29 4.2 Mathematical Model with Finite-Difference Method Except for the corner, a one-dimensional heat transfer calculation is adequate to estimate the slab temperature distribution, as will be discussed further in Section 6.4. However, the release of latent heat and the temperature dependence of the thermal conductivity of steel complicate the temperature calculation. To minimize the complexity, enthalpy and modified temperature have been adopted in the governing equation as follows. The governing equation is: (4.1) The definitions of enthalpy and modified temperature are: (4.2) (4.3) where kpe = thermal conductivity atT = T0 Equation (4.1) is integrated with respect to temperature: (4.4) Therefore, the governing equation becomes: 30 — K, Fa dt ay2 (4.5) using: 9 9 — = V —-dt The enthalpy and the modified temperature for a 0.29 % carbon steel are shown as a function of temperature in Figure 4.2. The boundary conditions are: 9T <*ty=0 -kFe-^- = qs(x) (4.7) 9T aty=yDltabl2 ^ f = 0 (4.8) and: atx=0,0 CO Distance from the Surface (mm) Figure 5.17 Change of Secondary Dendrite Arm Spacing with Distance from the Surface in Sound Shell IC3 58 1 5 0 2 o ^ 1 0 0 o a s a . C O E < a> a •o C O 5 0 Segregation Line 1 0 Distance from the Surface (mm) Figure 5.18 Change of Secondary Dendrite Arm Spacing with Distance from the Surface in Ruptured Shell with the Segregation Line IC1 Figure 5.19 Change of Secondary Dendrite Arm Spacing with Distance from the Surface in Ruptured Shell without the Segregation Line IC7 59 150 co Distance from the Surface (mm) Figure 520 Change of Secondary Dendrite Arm Spacing with Distance from the Surface in Initial Sticking Shell OC2 5.4 Metallography with Secondary Ion Mass Spectroscope (S.I.M.S.) The segregation line found in almost all the sticking and rupture zones except for sample IC7 is accompanied by an enlarged dendrite structure. This means that, when solute segregated below the surface, the cooling rate was extremely low. Generally speaking, when the solidification rate is reduced by fluid flow such as due to electro magnetic stirring, the solute (with distribution coefficients under unity during solidification) negatively distributes and forms a \"white band\" [64]. This concept suggested that the segregation found in this study might be caused not by redistribution during solidification but during 8 - y transformation, because carbon and manganese have distribution coefficients over unity for 8 - y transformation. The sample studied is a 0.08 % carbon steel and the solidification is followed immediately by the 5-y transformation. 60 Thus, it was expected that, even though solute negatively distributed during the solidification with a low solidification rate, the following 8 - y transformation might make the solute segregates positively. With the S.I.M.S., the solute in the segregation line was determined under the conditions listed in Table 5.3 for the sample cut from section IC1. Figure 5.21 shows the segregation line and the area which was examined by S.I.M.S.. Figure 5.22 ~ 5.25 show the distributions of carbon, manganese, sulphur, and phosphorus, respectively. Carbon, manganese and sulphur appear to correspond to the segregation line whereas phosphorus has an almost uniform distribution. Because carbon easily diffuses at a relatively low temperature, it seemed strange that the carbon rich area existed inside the shell. Therefore, with 2 % nital, the locations of pearlite in the sample were identified, as shown in Figure 5.26. It is thus evidence that the carbon concentrates in the pearlite phase, whose distribution is almost uniform, and it is concluded that the carbon does not relate to the segregation line. The distribution of sulphur corresponds to that of manganese. This is also confirmed with line-analysis by S.I.M.S., as shown in Figure 5.27. Therefore, it can be concluded that the solute in the segregation is manganese accompanied by sulphur. From these considerations and the results, it was expected that the mechanism of manganese segregation was attributed to the redistribution by 8 - y transformation following the solidification. The mechanism of the segregation will be discussed in Chapter 8. 61 Table 5-3 Measuring Conditions of SI.M.S. Size of Analysis Spot 20 \\un Electron Beam Irradiation Time 40-2580 sec Acceleration Voltage 8 KV Probe Current 20 nA Vacuum Condition \\0-wmbar Figure 521 Cast Structure Examined with SJ.M.S. Sample IC1 (xl6) (rectangle in photograph is the area examined with SJ.M.S. and arrow indicates the segregation line) Figure 5.23 Manganese Distribution in the Area Shown in Figure 5.21 (xl6) Figure 524 Sulphur Distribution in the Area Shown in Figure 521 (xl6) Figure 525 Phosphorus Distribution in the Area Shown in Figure 521 (x!6) Figure 5.26 Distribution of Pearlite in Sample ICl (x!6) (parallel lines (center of photograph) are sites ofSJM.S. and pin-link spots are marks to indicate the location of segregation line) 65 Manganese k — Segregation Line ^ Sulphur ! 100 Am I 1 Figure 527 Manganese and Sulphur Distribution with Line Analysis 66 6 Mathematical Model of Heat Transfer near the Meniscus with Mold Flux Lubrication 6.1 General Flow Sheet As discussed in Sections 2.3 and 2.5, the meniscus phenomena include not only heat transfer but also mechanical movement of the mold flux. Therefore, to examine the effects of mold oscillation and mold flux properties on meniscus phenomena, a mathematical model of heat transfer in which the mold flux movement is considered must be formulated. It is difficult, however, to consider the heat-transfer problem and the mechanical movement simultaneously. Thus, the model is divided into parts and, in each part, only a single phenomenon is considered and the results from each part are subsequently combined. As shown in Figure 6.1, the mathematical model is actually divided into four parts: mold flux velocity calculation (A), meniscus shape calculation (B), heat transfer analysis in the mold flux film (C) and slab temperature calculation (D). Each part can be combined with the others by common process data. For example, pressure gradient in the mold flux (dPPldx) which is calculated from flux flow rate (Q) is related to both part (A) and part (B). The result from part (B), thickness of molten mold flux film (h), is in turn used as the boundary conditions in part (A) and part (C). In part (C), using mold flux velocity (u) from part (A), slab surface temperature (Tslah) from part (D) and other process data, the mold flux temperature is calculated and heat flux from the slab (hs) and thickness of the solid flux rim (50) can be introduced. The general flow chart for the model is shown in Figure 6.2. Cyclical steady state is assumed and is achieved 67 computationally by an interative technique in which initial conditions are given a priori to start the calculation. The conditions employed in the calculation are listed in Tables 6.1 - 6.3. h d P / d x ^ Mold Flux Velocity in Liquid Film q s Lab Slab Temperature ® T il 1 Vz Figure 6.1 Relationship among Four Parts of Heat Transfer Model at the Meniscus 68 Start Initial Data Set t = 0 Geometrical Shape I Mold Flux Velocity f Mold Flux Film Temperature T Slab Temperature t=t+ A t Figure 6.2 General Flow Chart of Heat Transfer Model at the Meniscus Table 6.1 Calculation Conditions and Operating Conditions Symbol Condition Initial Value Units dt calculation time step i 12/ s f mold oscillation frequency 1 cycle/s a, mold oscillation half stroke 0.4 cm casting speed 1.267 cm/s meniscus position from the top of the mold (in fixed coordinate system) 10 cm hpM heat-transfer coefficient between the solid flux rim and the mold 0.702 Wlcrn^C mold hot face temperature 300 °C Table 6.2 Steel Properties and Pouring Temperature Symbol property / condition Initial Value Units pouring temperature of liquid steel in the mold 1536 °C T, liquidus temperature 1531 °C Ts solidus temperature 1498 °C kFe thermal conductivity of steel 0.514 W/cm°C PF, density of steel 7 g/cm2 CpFt specific heat of steel 0.6 Jlg°C 71 Table 6.3 Mold Flux Properties and Pool Depth symbol property / condition Initial Value Units melting point of the mold flux 1125 °C kp thermal conductivity of the mold flux 0.0072 W/cm°C PP density of the mold flux 2.6 gi'cm3 CpP specific heat of the mold flux 0.9 Jig°c IF mold flux pool depth 0.45 cm mold flux viscosity 1.7 poise a interfacial tension between the liquid steel and the molten mold flux 1200 [65] dyne/cm 6.2 Flow Rate of Mold Flux In this section, to calculate the velocity of molten mold flux in the flux channel, the Navier-Stokes equation has been employed and solved analytically, but the analytical solution includes two undetermined values: thickness of the flux film which is obtained in the meniscus shape calculation (in the next section) and pressure gradient in the flux 72 film. To calculate the pressure gradient, the mold flux flow rate (Q), which is introduced by integration of the velocity distribution in the flux film, has been estimated from the process data reported in the literature. The density of the mold flux is 2.6 g/cm3 while its viscosity at operating temperatures is at least 0.5 poise. The velocity of the molten mold flux in the flux channel can be estimated to be up to 3 cm/s (~ casting speed) and the characteristic length of the mold flux flow is the mold flux film thickness of about 0.1 cm (~ estimated from mold flux consumption). Therefore, the Reynolds number for the powder flow is: „ 2.6x3x0.1 t Re= — =1.56 (6.1) Usually, turbulent flow occurs if the Reynolds number is larger than 1000, and von Karman's vortex street appears in the flow with the Reynolds number over 50 [66]. Consequendy, the flow of molten mold flux is laminar without a vortex. Under these conditions, the Navier-Stokes equation can be reduced to a simple form based on the following assumptions: (1) constant properties of the fluid (2) one-dimensional flow However, the geometry near the meniscus is two-dimensional, so that the second assumption may not be valid. This problem is taken up again in Section 6.5. Subject to the above assumptions, the Navier-Stokes equation is: du d 2u f dPP^ PPS-V dx (6.2) The details of the coordinate system in Figure 6.3 and the meaning of \" ~ \" are discussed in the next section. 73 V vz * Figure 6.3 Physical System of the Mold Flux Flow If the left hand side of Equation (6.2) (pPr:) and the first term in the right hand d 2* side C n are compared, the left hand side can be neglected. In other words, the inertial term is small, compared to the viscous term as follows: pP-—160 < rj—;~500gcm/s2 at dy i „ , , i du 2 , where pP = 2.6 glcm , — < a.u) , T) = 1 poise at dy2 dp Therefore, the governing equation is: , as = 0.4cm, co = 47t, dp-0Acm d2u dPp (6.3) 74 The time dependency of the mold oscillation can be incorporated into the boundary conditions, which are (refer to Figure 6.3): u(y=0) = VM-Vz (6.4) The solution is: u(y=h) = 0 u = 2 n dPP ~dx ~PP8 J iy2-hy) + ^(Vz-VM)(y-h) (6-5) (6.6) With the equation of continuity, the mold flux flow rate Q can be defined as: r* 1 dPP ~dx ~PP8 M (6.7) Takeuchi and Brimacombe [43] or Anzai et al. [44] have calculated the mold flux pressure PP from Equation (6.7) assuming a fixed meniscus shape as shown in Figure 6.4. The mold flux pressure gradient — can be solved with the equation of continuity subject to the following boundary conditions: Pp(x=0) = Pair (6.8) Pp(x=l2)=Pair (6.9) It should be noted that implicit in Equation (6-9) is that the air gap appears at x = l2. In reality, the meniscus shape during the mold oscillation is not fixed. Therefore, the mold flux pressure cannot be determined explicitly from Equation (6.7). The pressure gradient — or the mold flux flow rate Q really needs to be predicted from another equation or from process data. 75 Figure 6.4 Physical System in the Calculation by Takeuchi and Brimacombe [43] or Anzai et al. [44] The factors which have an effect on the mold flux flow rate are considered next. As shown in Figure 6.5, the mold flux channel between the mold and the solid steel shell is assumed to consist of a series of notches corresponding to the oscillation marks. Similar to the method of Takeuchi and Brimacombe [43] or Anzai et al. [44], the mold flux pressure (P, at JC = A _ i) can be calculated as follows: 6T\\(YM-VZ) 6r\\Q hi + \\hi hi + 1ht where l AP * ~ T <6-22) where <]) is the contact angle as shown in Figure 6.6, s is the distance along the meniscus, AP, pressure difference between the steel and the mold flux, is defined as: u = a + vz (6.21) AP = pFegx-Pp(x) (6.23) 80 Figure 6.6 Physical System at the Meniscus From geometry, dx ds = sin<|) dh ds = -cos<(> Therefore, and d<]>_dcos<|> ds dx dh 1 dx tan Combining Equations (6.20) and (6.23) dAP l2r\\Q 6T](VM-VZ) dx h' + (pFe-pP)8 (6.24) (6.25) (6.26) (6.27) (6.28) 81 With the above equations, the meniscus shape (=h(x)) can be calculated numerically. In finite-difference form, from Equation (6.28) and the definition of the pressure gradient, AP' = AP+^-Ax (6.29) ax From Equations (6.22) and (6.26), AP cos (6.310 (6.35) where 7> = temperature of the molten mold flux film u = velocity of the mold flux in the x-direction aP = thermal diffusivity of the mold flux CpP = specific heat of the mold flux v = kinematic viscosity of the mold flux Equation (6.35) can be non-dimensionalized as follows: Tp —TST 6 = TPM — TST I* = — Vz v* = — y dp x*=-L LIVZ where = slab surface temperature at the meniscus (=1500 °C) TPM = melting point of the mold flux (=1000 °C) Vz = casting speed (=2 cm/s) dp = molten mold flux film thickness (=0.1 cm) L = characteristic length for heat transfer ( cm ) The energy equation with these dimensionless variables is LaP\\dt* + U dx*\\ CppL2aPAT %\\2 y e dx*2' where AT = TST-TPM 85 With consideration of the system size and the temperature difference in the system, the characteristic length L in the x direction should be chosen so that the order of —, is unity. For example, if the overall mold is focused on, the length L should be derived from the slab surface temperature profile. (Note that the mold flux temperature adjacent to the shell is assumed to be the same as that of the shell surface.) Usually, the slab surface temperature at the bottom of the mold is approximately 1200 °C; consequently, 6 changes from 0 to 0.6 in the mold. The mold length is 80 cm and, if — is unity, the dx length L may be 80/0.6 = 133 cm. This estimation is changed by the definition of 0. If 9 is defined as 6 = f \" (TSB = slab temperature at the bottom of the mold), the 'SB~'ST characteristic length L will be the mold length, but, in this case, the system concerned is only slab surface, not including the mold flux film. With these values, the order of each term in Equation (6.35) can be estimated and the results are listed in Table 6.4. From Table 6.4, if the thermal field in the overall mold is of concern, the energy equation can be reduced to a one-dimensional steady-state heat-conduction equation. 0 = aP—i (6.42) Therefore, a simple mathematical model can give reasonable results for the macroscopic heat-transfer from the slab surface. However, if the meniscus region is of interest, the length L can be determined with the derivation involving the cooling rate which can be calculated based on the secondary dendrite arm spacing at the slab surface. As shown in Chapter 4, the cooling rate of slabs near the meniscus is approximately 100 °Cls and, divided by the casting speed Vz, 86 *L is 50 °Clcm. In the channel at the meniscus (length 1 cm), AT = 50 °C and A0 is 0.1. Ax Therefore, the typical length L may be 1/0.1 = 10 cm. The order of each term in Equation (6.35), in this case, are also listed in Table 6.4. Then, the energy equation is: dTP dTP 2 + a7, (6.44) The velocity of the molten mold flux (u) can be provided from Equation (6.6) and (6.21). Equation (6.44) can be applied both in the solid mold flux rim and in the molten flux pool as well as in the liquid mold flux film. The physical system and the coordinate system are shown in Figure 6.8. The domain of the molten mold flux channel is determined by the meniscus shape calculation, as shown in Section 6.3, and the thickness of the solid mold flux rim (S0) which can be obtained from the locus of calculated melting point temperatures (TPM) in the mold flux film. I f -Z 1 Mold Figure 6.8 Physical System of Heat Transfer in the Mold Flux 88 The boundary conditions are: ftp aty=0, kP — = hPU(TP - TM) (6.45) where Tu = mold hot face temperature (= 300 °C) hPM = heat transfer coefficient between the mold flux rim and the mold hot face (0.702 W/cm2oC) forZ0M = 1125°C 7.3 Heat Flux to the Mold and Heat Flux from the Slab Not only for the prediction of sticking in the mold but also for judging slab quality, measurements of the heat flux or the mold copper plate temperature are useful. Especially the magnitude of the heat flux near the meniscus where almost all surface defects of slabs are initiated will be important. Therefore, the effects of the flux properties and the operating conditions on the heat flux near the meniscus have been 97 analyzed with the mathematical model, which include the calculation of mold flux velocity, meniscus shape, mold flux temperature and slab temperature, as described in Chapter 6. Figures 7.7 ~ 7.11 show the effects on the heat flux to the mold (qM) and the heat flux from the slab (qs). Here, the heat flux is the time average in the region 0 ~ 1 cm below the meniscus, the same as in the previous discussion. The primary conditions in the calculation are noted in the figures and the remaining conditions are given in Tables 6.1 ~ 6.3. It has been found that the average heat flux to the mold and the average heat flux from the slab responds similarly with changes to operating conditions and mold flux properties. An increase of the flux viscosity (in Figure 7.7), the casting speed (in Figure 7.8) and the flux melting point (in Figure 7.11) decreases the heat flux. A high oscillation frequency (in Figure 7.9) and a long mold oscillation stroke (in Figure 7.10) enhance the heat flux. 0 2 4 Mold Flux Viscosity (poise) Figure 7.7 Effect of Flux Viscosity on the Heat Fluxes near the Meniscus Vz = 1.27cmls f=\\cyclels a, =4mm 7>M = 1125°C O H — i — i — i — i — i — t — i — i — i — i — i — i — i — i — i — i — i — i — r -1.5 2 2.5 3 Casing Speed (cm/s) Figure 7.8 Effect of Casting Speed on the Heat Fluxes near the Meniscus n = 1.7poise f=\\cyclels a, = 4mm TPM=U25°C 120 OH i 1 1 1 1 1 1 3 5 7 Mold Oscillation Frequency (cycle/s) Figure 7.9 Effect of Mold Oscillation Frequency on the Heat Fluxes near the Meniscus 11 = 1.7poise Vz = 2.54cmls a, = 4mm TPM=U25°C Figure 7.11 Effect of Flux Melting Point on the Heat Fluxes near the Meniscus T) = 1.7 poise V z=1.26 cmls f - Icy dels a, = 4 mm Q-i 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1 1 2 3 4 Mold Oscillation Half Stroke (mm) Figure 7.10 Effect of Mold Oscillation Half Stroke on the Heat Fluxes near the Meniscus T| = 1.7poise VZ = Z54 c/s f = 6.67cycle/s TPU=\\\\2S°C 120 0 | 750 850 950 1050 1150 Mold Flux Melting Point (C) The effect of casting speed as shown in Figure 7.8 is different from that on the overall mold heat transfer. In the overall mold, an increase in the casting speed increases the slab surface temperature and, therefore, the heat flux from the slab is enhanced. However, a few millimeter below the meniscus, the slab temperature is not significantly 99 changed because of the large latent heat and is less affected by the casting speed. Thus, the value of the heat flux near the meniscus depends on the thermal resistance (i.e. flux film thickness) and the convection in the molten flux, not the slab surface temperature. The effect of the flux melting point is easily understood. A high melting point of the flux enhances the solid flux rim thickness and a thicker solid flux rim pushes the shell away from the mold. Therefore, an increase of the flux melting point results in reduced cooling near the meniscus. As discussed in the previous section, convection in the liquid flux film has an effect on the heat transfer near the meniscus. Figures 7.12-7.15 show the heat balance changes with the flux viscosity, the casting speed, the oscillation frequency and the oscillation stroke respectively. Although the heat flux to the mold and from the slab have the same tendency with respect to the above conditions, the mechanisms are not always the same, as shown in Figure 7.12 and Figure 7.13. The average heat flux from the slab is largely changed by the effect of the convection in the liquid flux film with changes of the flux viscosity and the casting speed. In the stagnant case, the heat flux from the slab is almost constant with these changes. On the other hand, the average heat flux to the mold is almost independent of the convection. Therefore, the heat flux to the mold is mainly affected by conduction. In other words, the meniscus shape, which changes the thermal resistance in the liquid flux, causes a change of the solid flux rim thickness. The change of the meniscus shape will be discussed in the next section. 100 120 Mold Flux Viscosity (poise) Figure 7.12 Effect of Flux Viscosity on the Heat Balance near the Meniscus Vz = \\.21cmls f=\\cyclels a,=4mm r w = 1125°C Mold Oscilation Frequency (cycle/s) Figure 7.14 Effect of Mold Oscillation Frequency on the Heat Balance near the Meniscus T| = 1 . 7 poise Vz = 2 . 5 4 cmls a, = 4 mm TP„=U250C 120 1.27 2.54 Casting Speed (cm/s) Figure 7.13 Effect of Casting Speed on the Heat Balance near the Meniscus i\\-1.7poise f=\\cyclels a, = 4mm TPU=\\\\25°C 1 4 Mold Oscilation Half Stroke (mm) Figure 7.15 Effect of Mold Oscillation Half Stroke on the Heat Balance near the Meniscus T| = 1.7powe Vz = Z54c/s /=6.67cyclels TPU=W25°C 101 The effect of the flux viscosity or the casting speed on the heat flux from the slab is, therefore, related to the flux velocity distribution. Figures 7.16 and 7.17 schematically show the flux velocity distributions with changes in mold flux viscosity and casting speed. With a high flux viscosity or with a high casting speed, the flux velocity in the vicinity of the slab is almost the same as the casting speed and, therefore, the heat transfer situation is similar to the stagnant case. Figure 7.16 Flux Velocity Distribution with a Low or High Mold Flux Viscosity LOUJ VZ High V-Figure 7.17 Flux Velocity Distribution with a Low or High Casting Speed 102 With a change in mold oscillation frequency, it is apparent that a change in heat flux is caused by a change in meniscus shape, because the heat flux from the slab in the stagnant case increases with an increase in mold oscillation frequency. In this case, the effect of convection reduces the change. If the oscillation stroke is reduced, the heat carried by the solid flux, as well as the change in the meniscus shape, affects the heat balance near the meniscus. In the region 0 ~ 1 cm below the meniscus, the solid flux rim usually receives heat from the slab through the liquid flux film and, above the meniscus, it transfers the heat to the mold wall. As a result, above the meniscus, the solid flux rim become thicker. However, with short-stroke oscillation, the molten flux pool in the region affected by the movement of the solid flux rim has a high temperature, because it is close to the meniscus. Therefore, the heat in the solid flux rim is not significantly reduced above the meniscus and is carried again into the meniscus channel region. 7.4 Oscillation Mark Formation As described in Section 2.3, there are two mechanisms for oscillation mark formation. One of them, termed Emi's model [39], links oscillation mark formation to flux pressure change. Kawakami [38] associates the change of the solid flux rim thickness near the meniscus with oscillation mark formation. In this study, with a mathematical model based on the Kawakami's concept, the meniscus shape is calculated with consideration of the solid flux rim as mentioned in Section 6.3. One result of a calculated oscillation mark is shown in Figure 7.18. The bottom of oscillation mark (\"2\" in Figure 7.18) is formed at the lower point of the mold oscillation displacement, and the top of the oscillation mark (\"4\" in Figure 7.18) corresponds to the 103 upper point of the mold oscillation displacement. If this deformation of the shell near the meniscus corresponds to the oscillation mark formation, the predicted depth is larger than the measured values. -c3 o 8 °< \"Co 4 3 * ^ - « ^ 1 \\ \\ 2 — Cast ing Direction I I I I 3.8 -0.3 -0.1 i i i i i i i i 0.1 0.3 0.8 0.7 0.9 1.1 1.3 Distance on the Slab Surface (cm) Figure 7.18 Shape of Oscillation Mark Calculated in the Model rj = 1.7poise Vz = 1.27cmls f=\\cyclels a, = 4mm TPM=ll25°C The effects of the flux properties and of the operating conditions on the oscillation mark depth near the meniscus are shown in Figures 7.19 ~ 7.24. A high viscosity of the flux, a high casting speed, a high frequency and a short stroke of the mold oscillation decrease the oscillation mark depth. These tendencies agree with data reported in previous works [16][36]~[39]. Although no data has been reported, it is understandable that an increase in flux pool depth or reduction in melting point of the flux would reduce the oscillation mark depth. 104 0.3 O H 1 1 1 1 1 1 1 1 4.5 6.5 8.5 Mold Flux Pool Depth (mm) Figure 7.19 Effect of Flux Pool Depth on Predicted Oscillation Mark Depth r\\ = 1.7poise Vz-\\.27cmls / = 1 cyclels a, = Amm 7>M = 1125°C 0.3 T 1 | 0.! • 1 I ; O-l , , , 1 1 1 1 1 1 • 1 . . , . • 1 1 r 1.5 2 2.5 3 Casting Speed (cnVs) Figure 721 Effect of Casting Speed on Predicted Oscillation Mark Depth lP = 4.5mm TJ = 1.7 poise f = 1 cyclels as = 4mm T m = 1125°C 0.3 •• fo,; o . M = 1125°C 105 0.3 Mold Oscillation Half Stroke (mm) Figure 7.23 Effect of Mold Oscillation Half Stroke on Predicted Oscillation Mark Depth lP = 4.5 mm r\\ = 1.7 poise Vz = 2.54 cmls f= 6.67 cycle/s TPM = 1125 °C 0.3 0-1 , , , 1 , , , 1 750 850 950 1050 1150 Mold Flux Melting Point (C) Figure 724 Effect of Flux Melting Point on Predicted Oscillation Mark Depth lP = 4.5 mm TJ = 1.7 poise Vz=l .27 cmls /= 1 cycle Is as = 4mm The effect of the oscillation frequency or of the oscillation stroke on the mark depth can be explained by a heat balance on the solid flux, as mentioned in the previous section. If the period or the distance of exposure of heated solid flux to a cooler flux pool is reduced, the solid flux rim thickness is reduced and the oscillation mark depth become shallow. In contrast to the above thermal analysis, the effects of the flux viscosity and the casting speed on the oscillation mark depth are mechanical in origin. Figures 7.25 and 7.26 show the average distance of the shell from the mold wall in the region 0 ~ 1 cm below the meniscus. A high mold flux viscosity or a high casting speed moves the shell farther from the mold and, therefore, the shell is less affected by the movement of the solid flux rim. As mentioned in the previous section, the conductive heat transfer near the meniscus is affected by these meniscus shape changes. In the case of a high oscillation frequency the convection heat transfer is much larger because the shell is 106 closer to the mold than in the case with a low oscillation frequency. In spite of that, a small change of the solid flux rim thickness during the oscillation, because of heat remaining in the flux rim, makes the oscillation mark shallow, as mentioned previously. 0.25 \" \" ' 0 2 4 Mold Flux Viscosity (poise) Figure 7.25 Effect of Flux Viscosity on Average Distance of the Shell from the Mold Wall lP = 4.5mm Vz = \\.21cmls f= 1 cycle/s as = 4mm 7>M = 1125°C 0.25 | | 0 . 2 0 o 2 I E°-15 .2 o 0.1 I i — i I I I — r - i — I — I I I — i — r — i — i — i — r 1.5 2 2.5 3 Casting Speed (cm/s) Figure 726 Effect of Casting Speed on Average Distance of the Shell from the Mold Wall lP = 4.5mm rj = 1.7 poise / = 1 cycle/s as = 4mm TPM = U25°C Here, it should be noted how the meniscus behaves during mold oscillation. Takeuchi and Brimacombe [43] have indicated, based on Emi's model, that, at the maximum downward velocity of the mold oscillation, the shell is pushed away farther than at the maximum upward velocity of the mold oscillation, as shown in Figure 2.6. However, the calculation results in this study show that the shell is located close to the mold at the maximum downward velocity of the mold oscillation, if the solid flux rim does not exist. For the meniscus shape calculation, Equation (6.22) is used in the same way as in the study of Takeuchi and Brimacombe. Only one difference exists, in the boundary condition, Equation (6.34). In this calculation, the condition ( = j at y =0) is achieved only when the flux is stagnant, as shown in Figure 6.7. In other words, Takeuchi and Brimacombe have calculated the meniscus shape from the contact point 107 between the shell and the mold toward the meniscus, while, in this study, the calculation starts from the meniscus. This difference in the calculation step, however, brings about opposite results in the distances of the shell from the meniscus and from the mold wall. For example, a large radius of the meniscus shape means a large capillary length in Takeuchi and Brimacombe's study, but, in this study, it results in a small displacement (of the contact point between the shell and the mold) from the meniscus. In Takeuchi and Brimacombe's study, the change of the meniscus shape is explained by the capillary theory: that is a small pressure difference and a large interfacial tension between the steel and molten flux make the meniscus shape radius large and push the shell far from the mold. Although the wave equation is not used in this model, the result is closer to the surface wave phenomena than to the capillary phenomena. In other words, a small pressure difference and a large interfacial tension reduce the displacement from a flat meniscus. Matsushita et al. [71] have succeeded directly in observing the meniscus shape in the mold. Although they did not explicitly indicate the wave phenomena at the meniscus, their figures of the meniscus shape show that the meniscus is closer to the mold during downward movement than during upward movement. Therefore, it is a reasonable result that, at high frequency mold oscillation which introduces a high pressure in the liquid flux, the shell is closer to the mold and a large heat transfer occurs. The effects of the flux viscosity and casting speed on the heat transfer near the meniscus can be explained by the same mechanism. A high viscosity of the flux brings about a low internal flux pressure because of a small flow rate, as suggested in Equation (6.17). If the casting speed increases, the mold flux flow near the slab surface 108 increases, then, the pressure is reduced (Bernoulli's theorem). Therefore, with a high viscosity mold flux and a high casting speed, the shell is farther from the mold wall and the heat flux decreases. Under normal casting conditions, oscillation marks are formed by the movement of the solid flux rim at the meniscus. However, it is interesting that, if the flux rim thickness is reduced and its taper value becomes small, the mechanism of the oscillation mark formation changes from Kawakami's concept to that of Emi. For example, in the case of 1 mm mold osculation stroke in Figure 7.23, the bottom of the oscillation mark is formed at the maximum upward velocity of the mold oscillation and the top of the oscillation mark corresponds to the downward motion. The above finding permits prediction of the shape of the oscillation mark. If the solid flux rim is thicker, the oscillation mark is deep and its shape has a steep slope from the top to the bottom and a relatively mild slope from the bottom to the top in the casting direction, as shown in Figure 7.27. In the transient state from Kawakami's to Emi's concept, because the top of the oscillation mark will correspond to the downward velocity, its shape has a relatively steep slope from the bottom to the top in the casting direction. If the mechanism of the mark formation is changed completely to Emi's model, the mark shape becomes a sine curve. Therefore, if the solid flux rim thickness is largely reduced, the effect of the flux properties or the operating conditions on the oscillation mark depth is not always consistently explained by Kawakami's concept. Figure 7.28 shows, for example, the effect of the mold oscillation frequency on the mark depth for TPM = 919°C. A low 109 frequency causes a shallow oscillation mark, contrary to the tendency in Figure 7.22. This result indicates that the oscillation mark formation, in the case of a thin flux rim, is based on Emi's mechanism. Time Casting Direction c o ) Kamakami-type \\///////////////////////////////, CP) Transient- type V////////////////////////////// (C) Emi - type Figure 727 Schematic Change of Oscillation Mark Shape from Kawakami-type Mark to Emi-type Mark 110 3 5 Mold Oscillation Frequency (cyde/s) Figure 7.28 Effect of Mold Oscillation Frequency on Emi-type Oscillation Mark Depth lP = 4.5 mm T\\ = 1.5 poise Vz = 2.54 cm/s as = 4mm TPM = 914°C 7.5 Mechanism of the Initiation of Sticking-type Breakout Even in a high casting speed machine, the rare occurrence of breakouts makes the analysis of sticking-type breakouts difficult. The same conditions under which sticking-type breakouts occur do not always bring about sticking. Rather, analysis of the sticking-type breakouts is a study which elucidates the possibility of sticking. Therefore, in the computer simulation, there is a need to enhance the possibility of sticking. In other words, in the computer simulation, another factor - noise, disturbance - should be included. At the meniscus, this noise is usually caused by meniscus level fluctuation. In this simulation, the meniscus level is allowed to rise and to fall during the mold oscillation, as shown in Figure 7.29. In the case in which the meniscus level remains constant, the predicted solid flux rim profile and the shell profile are shown in Figure 7.30, while the surface temperature profile is exhibited in Figure 7.31. It can be seen that, at the bottom of the oscillation I l l mark, the surface temperature of the slab is higher than in the other area, but the increase is not significant. Although the meniscus shape is affected by the solid flux profile, in this case, there is a wide meniscus channel for the liquid flux and it reduces the friction force between the solid flux and the shell. i a) o 6 9.6 § 10.0 > Case-l Meniscus leuel rises o c o <5 0 rr 2n 3 n 4n c o Case-2 Meniscus leuel fails Figure 729 Meniscus Level Change in the Computer Simulation 112 Distance from the Mold Wall (cm) Figure 7.30 Shell Profile and Solid Flux Rim Profile with a Constant Meniscus Level Slab Surface Temperature (C) 1500 1520 1540 4^-1 1 1 1 — - J - — i 1 1 1 S2J0-0 Figure 731 Slab Surface Temperature Profile with a Constant Meniscus Level Figure 7.32 shows the solid flux rim profile and the shell profiles after the meniscus level rises. Over a long region from the meniscus, the channel is squeezed and it may cause a large friction force on the shell. It should be noted that, as shown in Figure 7.33, below this interaction area between the solid flux and the shell a remarkable hot spot exists, corresponding to a deep notch on the shell (as shown in Figure 7.32), which forms due to the interaction of a thicker flux rim when the meniscus rises. At such high temperatures, the solidified steel is easily ruptured by friction between the oscillating mold and descending strand. 113 Distance from the Mold Wall (cm) Slab Surface Temperature (C) 1500 1520 »2.0 0 Figure 7.32 Shell Profile and Solid Flux Rim Profile after a Rise in the Meniscus Figure 7.33 Slab Surface Temperature Profile after a Rise in the Meniscus Figure 7.34 indicates that the real sticking shell profile, as previously shown in Figure 5.16, is close to the solid flux rim profile calculated below the meniscus. If the solid flux rim and the molten flux film do not exist, the shell profile is precisely the same as the static meniscus which can be calculated using surface tension (1900 dyne/cm) [65] instead of the interfacial tension between the flux and the steel. The result in the case without flux is shown in Figure 7.35. At the meniscus, its shape is close to the sticking shell but below the meniscus it is completely different from the sticking shell profile. Therefore, this sticking does not occur to the mold wall when liquid and solid mold fluxes are not present. The above finding indicates that the shell sticks to the solid flux rim. 114 Distance from the Mold Wail (cm) Figure 7.34 Comparison between the Real Sticking Shell and the Shell Profile or the Solid Flux Profile Detance from the Mold Wall (cm) Figure 7.35 Comparison between the Real Sticking Shell and the Meniscus Shape without Solid Flux Rim and Liquid Flux Film With consideration to the above finding, a mechanism for initial sticking can be proposed, as schematically shown in Figure 7.36. During casting, if the meniscus level rises, the meniscus shape (shell profile) has a deep notch due to the interaction of a thicker flux rim (b). During the upward motion of the mold oscillation, the thicker flux rim moves away from the meniscus, then, the meniscus moves toward the mold (c). The shell close to the mold becomes cooler than the deep notch area. This is accompanied by the appearance of a hot spot below the meniscus (d). During the downward motion of the mold oscillation, the thicker flux rim moves down and interacts with the shell (e) 115 and the shell sticks to the flux rim. When the mold begins to move upward again, tensile friction force acts on the shell and a rupture occurs at the weakest (hottest) point of the shell. Hot Spot Figure 7.36 Mechanism of the Occurrence for the Initial Sticking of the Shell In the case in which the meniscus level falls, there is no interaction between the solid flux and the shell and no hot spot exist below the meniscus, as shown in Figures 116 7.37 and 7.38. So, the sticking is not likely to occur after the meniscus level falls. It is interestingly seen in Figure 7.37 that an oscillation mark does not form, because the interaction of the mold flux rim with the newly forming shell is reduced after the fall of the meniscus level. As mentioned in Section 5.1, it was found in the pre-rupture area of the sticking-type breakout shell that the oscillation mark was lost or deeply notched at the same shell surface. These appearances of the shell surface, therefore, are considered as an evidence of the mold level fluctuation, which means that, if the meniscus level rises, the shell is deeply notched (even though sticking does not occur) and, in the case of the meniscus level fall, the oscillation mark is shallow or lost. It also can be predicted from Figure 7.32 and 7.37 that, if the meniscus level rises (not significantly), the pitch and depth of the oscillation mark increase and a relatively small fall of the meniscus level brings about a short and shallow oscillation mark; this is the relationship between the mark pitch and depth found by oscillation mark measurement for the sound shell, as mentioned in Section 5.2. 117 Figure 7.37 Shell Profile and Solid Flux Figure 7.38 Slab Surface Temperature Profile after a Fall in the Meniscus Profile after a Fall in the Meniscus 7.6 Prevention of Sticking It is worthwhile to analyze the friction force when sticking occurs, because it is responsible for rupture of the shell. However, this analysis must be conducted along the strand, because the rupture does not occur at the sticking point. In other words, the initial sticking point is different from the initial rupture point. Therefore, the likelihood of the occurrence of sticking depends on the likelihood of rupture below the sticking point. Without a complicated stress-strain analysis of the sticking shell, the best manifestation of the rupture is the hot spot temperature. Figures 7.39 ~ 7.41 show the hot spot temperature after the meniscus level rises as a function of the viscosity of the flux, the casting speed and the frequency of the mold 118 oscillation. The likelihood of rupture as indicated by the hot spot temperature agrees with the result of the friction force analysis. A high viscosity flux, a high casting speed and a high cycle mold oscillation is likely to cause the sticking. Because a high viscosity flux and a high casting speed reduce the heat flux from the slab as mentioned in the previous section, the hot spot temperature increases. In the meanwhile, in the case of high mold oscillation frequency, the period from the rise of the meniscus level to the sticking of the shell significantly affects on the hot spot temperature. In a short period (high frequency), the temperature of the hot spot scarcely decrease. In addition to the above conclusions, the notch depth of the shell, when the meniscus level rises, is related to the hot spot temperature. Figure 7.42 shows the effect of the flux melting point on the hot spot temperature. A low melting point flux reduces the solid flux rim thickness and makes the notch shallow. As shown in Figure 7.43, the effect of the oscillation stroke on the hot spot temperature is not clear. Although a short stroke brings about a thin solid flux rim in the meniscus channel region (below the meniscus) as mentioned in the previous section, the solid flux rim far from the meniscus (above the meniscus) is thicker than in the case of long stroke of the mold oscillation. This is because the heat near the meniscus which is carried by the solid flux rim is small at the location far from the meniscus, if the mold oscillation stroke is short. Therefore, a short stroke mold oscillation is not always adequate for a large meniscus level fluctuation. The effect of the flux pool depth on the hot spot was not analyzed, because the control system in this mathematical model has a limited length above the meniscus for the calculation of a case of large flux pool depth accompanying a meniscus level rise. 119 Instead of that, the average solid flux rim thickness above the meniscus shows in Figure 7.44. A deep flux pool reduces the occurrence of the sticking, because the solid flux rim above the meniscus is thin. Almost all methods to reduce the hot spot temperature are opposite to those for adopted shallow oscillation marks which minimize pin holes and transverse cracks. Only possible methods to improve both the occurrence of the sticking and the surface quality of slabs are to use a low melting point flux and probably to keep a deep flux pool. However, it should be noted that too low a melting point flux may cause the first type of sticking with an excess heat removal as mentioned in Section 2.1. 1 5 3 0 1 5 2 0 Mold Flux Viscosity (poise) Figure 7.39 Effect of Flux Viscosity on the Predicted Hot Spot Temperature lP = 4.5 mm Vz = 1.27 cmls f= 1 cyclels a, = 4 mm TPM = 974°C 1 5 3 0 O CD Casting Speed (cm*) Figure 7.40 Effect of Casting Speed on the Predicted Hot Spot Temperature lp = 4.5 mm TJ = 1.5 poise / = 1 cyclels a, = 4 mm 7>M = 974°C 120 1530 1530 3 5 7 Mold Oscillation Frequency (cycle/s) Figure 7.41 Effect of Mold Oscillation Frequency on the Predicted Hot Spot Temperature lP = 4.5 mm Tj = 1.5 poise Vz = 2.54 cmls o 3 1525 a CO 1520 750 850 950 1050 1150 Mold Flux Melting Temperature (C) Figure 7.42 Effect of Flux Melting Point on the Predicted Hot Spot Temperature lP = 4.5 mm T) = 1.5 poise Vz = l.27 cmls f=\\cyclels a, = 4mm a, = 4mm 7>M = 974°C 1530 O s i 1525 -1520 1 1 i 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 Mold Oscillation Half Stroke (mm) Figure 7.43 Effect of Mold Oscillation Half Stroke on the Predicted Hot Spot Temperature lP = 4.5 mm r\\ = 1.5 poise Vz = 2.54 cmls f= 6.67 cycle/s TPM = 914°C 0H 1 1 1 1 1 1 1 1 4.5 5.5 6.5 7.5 8.5 Mold Flux Pool Depth (mm) Figure 7.44 Effect of Flux Pool Depth on the Predicted Average of Solid Flux Rim Thickness above the Meniscus rj = 1.7 poise Vz - 1.27 cmls f= 1 cyclels a, = 4 mm 7>M = 1125°C 121 Segregation below the Surface in a Low Carbon Steel 8.1 Cooling Rate Change due to Solid Flux Rim Remelting Although the mechanism of initial sticking has been clarified, as discussed in Chapter 7, the segregation line with enlarged dendrite arm spacing found in almost all the samples from the sticking-type breakout shell (with one exception) has not been explained. In this chapter, the causes of the segregation, which probably is a characteristic of the sampled slab because it has not been reported previously, have been investigated. It was proposed that a low cooling rate which was equivalent to enlarged dendrite structure could bring about negative segregation if the distribution coefficient was under unity; and therefore the segregation found in the sticking-type breakout shell (0.08 % carbon steel) was not caused by solute redistribution during solidification but possibly due to the 8 - y transformation in which some elements had a distribution coefficient over unity. Before the calculation of solute redistribution in the dendrite, it was necessary to determine the thermal history of the dendrite in the sticking-type breakout shell, which can be related to the diffusion time of solute. Therefore, first, the mechanism of the discontinuous change of secondary dendrite arm spacing at the segregation line has been considered in an attempt to link it to characteristic phenomena of sticking below the meniscus. It is reasonable to suppose that, when the sticking occurs and the rupture is proceeding in the mold, liquid steel flows into the gap created by the rupture, as described in Section 2.1, and it comes into contact directly with the solid flux rim as shown schematically in Figure 8.1. A large heat transfer from the liquid steel to the solid flux rim occurs in the moment after the contact, and the heat conducted through the mold 122 flux subsequently decreases if the thermal field become steady. Therefore, it is expected that the cooling rate for the sticking shell is reduced discontinuously after the contact of the liquid steel. To estimate the cooling rate, a mathematical model of heat transfer in the flux rim and the steel, as shown in Figure 8.1, has been formulated. The governing equations are: For the mold flux rim, = a ? — f ; (8.1) For the steel, the same as Equation (4.5), The boundary conditions are: aty=0, qu = -kP |,. 0 = -h (TPy _ Q - TM) (8.3) aty=dP, TP=TF, (8.4) dTp dHp4 top, dy pt <*y=dF q, = -kp-^\\y=dp = —— (8.5) aty=DsJl 0 = — ( 8 - 6 ) The initial condition is: 2 Tpt = Tt, dP) (8.12) fr(C) = 1392 +1122(%C), C < 0.09% /r(C) = 1495, 0.09% 3 N = 2 C/ + 2 { l + ^ i - 2 S c 3 ' « C 1 + 2C a i = 1 M = 4 N = 3 Cl' + 2C2' = Cl+2C2 i = 1 others or for y { ^ 2 ^ - 2 ^ = 0, 2 < i ^ N - 2 , N>4 i = N - 1, M = 4 N = 3 C ' - — c 136 i = N - 1, others ( N > 3 ) {i+^ lc +°Z£L\\C ' - ^ L r ' — r '-r + r i = N, N = M - 1 ( N > 2 ) CN' = k**Cu i = N, others ( N > 2 ) N+l < i < M-2 (M < Mc) i = M - 1 for 6 CH.( = kVLCL' or for y CM_( = k^LCL' M < i < Mc c:=cL' where CL'= „ 1 ' ' ( V, is the volume of the control volume i) | 137 Table 82 Distribution Coefficient and Diffusion Coefficient based on Ueshima et al. [57] Element k*L k~*L D\\cm2ls) 1400-1500 °C D\\cm2ls) 1300-1400 °C D\\cm2ls) 1400-1500 °C D\\cm2ls) 1300-1400 °C C 0.19 0.34 1.79 4.368 xlO\"5 2.799 x 10\"5 0.6489 x 10-5 0.309 x 10\"5 Si 0.77 052 0.68 2.459 x 10-7 0.588 x 10-7 0.0775 x 10-7 0.019 x 10'7 Mn 0.76 0.78 1.03 1.275 xlO\"7 0.364 x 10-7 0.0164 x lO - 7 0.0041 x 10~7 P 023 0.13 057 3.28 x 10~7 0.907 x 10~7 0.2991 x 10-7 0.108 xlO\"7 S 0.05 0.035 0.70 1.506x10\"* 0.4545 x 10-6 0.4314x10^ 0.1249x10^ 138 Table 8.3 (a) Primary and Secondary Dendrite Arm Spacings and Cooling Rate for Sample IC1 Distance from the Surface (mm) Kim) Cooling Rate CCIs) 0-1 76.6 44.9 32.7 1-2 118.2 46.4 29.9 2-3 132.3 53.5 20.1 3-4 170.9 71.9 8.8 4-5 191.7 75.6 7.7 5-7 196.1 86.8 5.2 7-9 200.4 101 3.4 9-11 230.5 101.6 3.4 139 Table 8.3 (b) Primary and Secondary Dendrite Arm Spacing and Cooling Rate for Sample IC7 Distance from the Surface (mm) K (m) Kim) Cooling Rate CCIs) 0-1 78.1 49.2 25.4 1-2 104.2 70.2 9.45 2-3 164.1 74.3 8.07 3-4 167.2 72.2 8.74 4-5 175.0 85.9 5.40 5-7 181.3 93.4 4.28 8.4 Solute Redistribution after 8 - y Transformation The solute concentrations in the interdendric area with a fixed size (20 |i) after solidification for Sample IC1 are shown in Figure 8.12 and those after the 8-y transformation (at 1350 °C) are presented in Figure 8.13. The latter shows that the maximum concentration of all the solute increases in the region corresponding to the segregation line. As manganese hardly diffuses at lower temperature, these results imply that manganese and sulphur (probably associated together with as MnS) cause the segregation lines. However, the solute increase (especially manganese) 3 - 4 mm below 140 the surface can be seen also in the solute concentration distribution after solidification (in Figure 8.13), which means that solute does not redistribute significantiy during 5-y transformation. During and after solidification solute hardly diffuses in the enlarged primary dendrite arm spacing (diffusion length is enlarged) due to the mild cooling and the solute remaining in the interdendric region after solidification causes the segregation. For Sample IC7, the solute concentrations after 5 - y transformation are shown in Figure 8.14. Except for the region near the surface, there is no significant change in the solute distributions. Not only in Sample IC7 but also in Sample IC1, large changes in the solute distribution are calculated at the surface. These indicate that segregation should exist just below the surface. In other words, a negative segregation should be observed at the surface. From the photographs in this study, negative segregation (i.e. white bands) was not found at the surface. Perhaps, surface segregation caused by carbon sintering from the mold flux [16] [17] and positive segregation at the surface reported by Takeuchi and Brimacombe [35] may compensate for the white bands. Although the existence of negative segregation near the surface is not clear, the segregation line in Figures 5.8 or 5.9 can be explained by interdendric segregation. In the etched photograph, these interdendric regions with rich solute form a band and they are observed as a segregation line. However, contrary to the initial hypothesis, the interdendric segregation is not strongly affected by solute redistribution due to the 8 - y transformation. 141 Distance from the Surface (mm) Distance from the Surface (mm) Figure 8.12 Solute Concentrations after Solidification for Sample IC1 142 Distance from the Surface (mm) Distance from the Surface (mm) Figure 8.13 Solute Concentrations after 6-y Transformation for Sample IC1 (at 1350 °C) 143 Figure 8.14 Solute Concentrations after 8-y Transformation for Sample IC7 (at 1350 °C) 144 8.5 Segregation below the Surface in the Sticking Shell From the preceding sections, it seems clear that segregation lines below the surface in the sticking shell are related to redistribution of solute due to solidification, and it appears that enlarged primary dendrite arm spacing enhance the solute segregation. This tendency is expected from Equations (2.4) and (2.5) of Brody and Hearings [53]. The equations show that a low cooling rate reduces interdendric segregation, if the primary dendrite arm spacing is constant. However, explicitly, the effect of the primary arm spacing on the interdendric segregation is larger than that of the cooling rate. Although the segregation lines are formed by interdendric segregation, not due to the cooling rate change, but due to the primary arm spacing change, it is also true that the primary arm spacing is strongly related to the cooling rate. From the discussion in Section 8.1, the cooling rate change in the sticking shell is not caused by mold flux remelting phenomena. The discontinuous cooling rate change must be caused by a mechanical change of the boundary conditions of the sticking shell, perhaps due to the appearance of an air gap between the sticking shell and the solid mold flux. If the transverse section of the sticking shell in the mold is considered, except for the vicinity of the initial sticking area at the meniscus, there is a thin shell in the ruptured area surrounded by a thicker sound shell, as shown in Figure 8.15. The sound shells are cooler and shrink faster than the ruptured part. Therefore, the ruptured part is put into tension and a depression occurs, similar to the mechanism of the depression with longitudinal surface crack which is a result of \"necking\" [73]. In contrast, during the casting of the shell corresponding to Sample IC7 which experienced the discontinuous change in the cooling curve only at the surface (as shown in Figure 8.8), perhaps an air gap appeared independently of the shell shrinkage because of the mechanical disturbance of the other sticking A-4 which created the breakout, as shown in Figure 5.3. 145 Ruptured Tension Shell Air Gap ///////////// Figure 8.15 Mechanism for Appearance of Air Gap during the Sticking If this mechanism for the appearance of an air gap is true, all sticking-type breakout shells would have a segregation line below the surface. However, these segregation lines have never been reported in the previous studies of sticking-type breakouts. Probably because, in steels in which the 5 - y transformation does not occur immediately after solidification, the deformation of the sticking shell is not large enough to cause an air gap. It can be said that these segregation lines may appear only in the steel with 8-y transformation at a higher temperature because of the shell shrinkage enhanced by the transformation but not solute redistribution. 146 8.6 Non-equilibrium Phase Diagram Experimentally, it has already been confirmed that the 8 - y transformation of steel is not based on the equilibrium diagram [74] [75]. Therefore, previous work on crack formation accompanied by the 8 - y transformation should be reconsidered from a viewpoint based on the non-equilibrium diagram. As a result of the mass transfer model, the non-equilibrium solidus temperature, the initial temperature of the 8 - y transformation (TMi) and the completed temperature of the 8 - y transformation (TA4c) can be predicted. Figure 8.16 shows the calculated non-equilibrium temperatures for Sample IC1. The solidus temperature changes from 1498 °C (the equilibrium temperature) to 1460 °C. The initial temperature and the completed temperature also shift from the equilibrium temperature. It should be noted, therefore, that the cooling curves, as shown in Figure 8.7 and 8.8, will be slightly different from the cooling curves based on the heat transfer calculation with the equilibrium temperatures. Figure 8.17 demonstrates non-equilibrium temperatures in the Fe-C phase diagram with different primary arm spacing and different cooling rate. Apparently, an increase in cooling rate and an increase in primary arm spacing enhance the deviation from the equilibrium temperature. However, because the primary arm spacing itself is affected by the cooling rate in reality, the deviation is not always increased with an increase in the cooling rate. Although some theoretical or empirical correlations between the primary arm spacing and the cooling rate have been proposed, they cannot be easily applied for the case of continuously cast steel, because the effect of convection in the liquid on the primary arm spacing cannot be ignored. Therefore, for the prediction of the 147 non-equilibrium transformation in continuously cast steel, it will be necessary to obtain the correlation between the primary arm spacing and the thermal conditions accompanying liquid flow. Time (s) Figure 8.16 Non-equilibrium Transformation Temperature Calculated for IC1 148 - - e q u i l i b r i u m X 10C/S A 450 C /s 1240 1 1 1 1 1 1 1 1 1 1 1 1 1 1 — 0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 Carbon wt % (a) Effect of Cooling Rate ( Xx = 50 \\im ) 0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 Carbon wt % (b) Effect of Primary Arm Spacing ( Cooling Rate = 10 °Cls ) Figure 8.17 Equilibrium and Non-equilibrium Phase Diagram (a) with Different Cooling Rate (b) Different Primary Arm Spacing 149 9 Summary and Conclusions Sticking of the shell in the mold, which often occurs in a high speed continuous slab casting machine, can be detected with thermocouples in the mold copper plate and prevented from developing to create a breakout by reduction of the casting speed; However previous work has not revealed why and how the sticking initiated at the meniscus. The objectives of this study were to identify the causes of sticking by examining the dendrite structure in a sticking-type breakout shell and to elucidate the mechanism of sticking with mathematical models of fluid flow in the mold flux channel and heat transfer at the meniscus. First of all, to link information from dendrite structure at a slab surface to casting conditions, the application of correlation in the literature between secondary dendrite arm spacing and local cooling rate has been examined. The secondary dendrite arm spacing in the subsurface of a slab has been measured and correlated against local cooling rate calculated with measured mold heat-flux. Based on this correlation, the following can be stated: (1) The experimental correlation of Suzuki between secondary dendrite arm spacing and cooling rate can be applied for high cooling rates experienced during continuous casting. (2) For the application of this experimental correlation to a continuous casting slab, the definition of cooling rate should be the average cooling rate between the liquidus and solidus temperature. However, the accuracy of the cooling rate at the slab surface calculated with a computer model depends on the finite-difference mesh size. Therefore, an analytical solution has been introduced to correlate the secondary dendrite arm spacing to the heat flux at the slab 150 surface. A sticking breakout slab exhibiting five sticking events was studied. Small holes were observed at the surface in the sticking shells and were most likely the site of entrapment of solid mold flux which subsequently was scoured out during sand blasting. From a metallographic examination of the sticking-type breakout shell, it has been found that: (1) A shell which initially sticks has a coarse dendrite structure. (2) The geometrical shape of the initial sticking shell in a longitudinal cross section is parabolic and resembles the meniscus shape. (3) With one exception, segregation lines are found in the sticking shell typically 1 ~ 3 mm below and almost parallel to the surface. From secondary ion mass spectroscope analysis, the solutes concentrating in these segregation lines were determined to be Mn and S. For the analysis of meniscus phenomena such as the initiation of sticking, a mathematical model based on heat transfer in the mold flux was formulated. The following results were obtained: (1) The average heat flux from the slab calculated with this model is almost the same as the heat flux predicted from the dendrite arm spacing with the analytical solution. (2) In the region near the meniscus, the heat flux from the slab is different from the heat 151 flux to the mold, because an amount of heat from the slab is carried by mold flux in the casting direction. (3) Convection in the liquid mold flux has a significant influence on the heat flux from the slab, but it has little influence on the heat flux to the mold. (4) The heat flux to the mold is strongly related to the solid mold flux thickness. With respect to oscillation mark formation: (1) The mathematical model, based on the mechanism of oscillation mark formation due to the movement of the mold flux rim proposed by Kawakami et al. can explain the effects of the mold flux properties and the operating conditions on the oscillation mark depth reported in previous work. (2) If the solid mold flux film thickness is reduced, the mechanism of the oscillation mark formation is better explained by Emi's model, concerning the change of the pressure in the mold flux channel. To analyze the initial sticking event, the meniscus level has been changed in the computer simulation and it has been found that: (1) A rapid rise in the meniscus level enhances the interaction between the shell and the solid mold flux rim and creates a hot spot below the interaction point. (2) The solid flux rim profile calculated after a rise of the meniscus agrees with the measured profile of the initial sticking shell in a longitudinal cross section. (3) A fall in the meniscus level does not have a significant effect on the interaction between the shell and the solid mold flux rim. 152 Therefore, the mechanism of the initiation of a sticking-type breakout can be proposed as follows: If the meniscus level rises, the shell has a deep notch due to the interaction between the mold flux rim and the shell. When a thicker mold flux rim moves downward, it contacts the shell above the notch and the shell sticks to the mold flux rim. During the upstroke motion of the mold, tensile forces on the shell cause a rupture at the deep notch which is the hottest and weakest. Since the hot spot is the most likely point to be ruptured, conditions which minimize temperature of the hot spot were sought with the model. Most of the conditions required to reduce hot-spot formation are exactly opposite to those required to minimize oscillation mark depth. Notwithstanding this, there are a few technique to reduce the occurrence of sticking and to improve the surface quality and they are to use a low melting point powder and, probably, to maintain a deep mold flux pool. To analyze the segregation line, a mass transfer model has been formulated based on a consideration of 8 - y transformation. From this analysis: (1) The segregation observed in the sticking shell appears to be a band of interdendric segregation enhanced by enlarged primary dendrite arm spacings. 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Gunzi : Tetsu-to-Hagane, 1987, vol.73, pp. 1738-45 "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0078470"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Materials Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Sticking-type breakouts during the continuous casting of steel slabs"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/27941"@en .