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Solidification and heat transfer in the continuous casting of steel Lait, James Edward 1973

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/  SOLIDIFICATION AND HEAT TRANSFER IN THE CONTINUOUS CASTING OF STEEL  by  JAMES E. LAIT  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in the Department of METALLURGY  We accept this thesis as conforming to the standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE  THE UNIVERSITY OF BRITISH COLUMBIA March, 1973  In presenting  t h i s thesis in partial  fulfilment of the requirements for  an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference  and  study.  I further agree that permission for extensive copying of this thesis for scholarly purposes may by his representatives.  be granted by the Head of my  Department or  It is understood that copying or publication  of this thesis for financial gain shall not be allowed without written permission.  Department of  Metallurgy  The University of B r i t i s h Columbia Vancouver 8, Canada  Date  A p r i l 30,  1973  my  ii ABSTRACT  Radioactive gold has been added to the l i q u i d pool during the continuous casting of mild s t e e l b i l l e t s , blooms and beam blanks and of a stainless s t e e l slab.  The tests were conducted  on low-head, curved mold  and straight mold, v e r t i c a l bend type casting machines.  From autoradio-  graphs of the sections of the s t e e l , observations were made of the flow pattern i n the l i q u i d pool, of the uniformity and thickness of the s o l i d s h e l l i n the mold and sub-mold regions and of the cast structure of the strand.  Pool depths were estimated from the position of tungsten p e l l e t s  containing radioactive cobalt, dropped into the pool with the gold.  One and two-dimensional were developed ously cast.  f i n i t e difference heat transfer models  to calculate the pool p r o f i l e s i n strands being continu-  The predicted pool p r o f i l e s and pool depths have been  compared to p r o f i l e s measured from autoradiographs and pool depths measured with tungsten p e l l e t s .  The model-predicted  surface  temperatures  of low carbon s t e e l b i l l e t s at the mold bottom have been compared to measured values reported i n the l i t e r a t u r e .  The pool and surface tem^-  perature p r o f i l e s calculated with the f i n i t e difference model have been compared to p r o f i l e s predicted by an i n t e g r a l p r o f i l e model.  iii  TABLE OF CONTENTS  Page ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF FIGURES  vii  LIST OF TABLES  xi  LIST OF SYMBOLS  xii  ACKNOWLEDGEMENT  1.  2.  3.  INTRODUCTION  .  .  xv  1  1.1.  General Comments  1  1.2.  Previous Work  4  1.2.1.  F l u i d Flow and Liquid Pool . . . . . . .  4  1.2.2.  Structure  8  1.2.3.  Mathematical Models  10  1.2.4.  Objectives of Present Work  14  .  MATHEMATICAL MODEL  15  2.1.  Heat Flow Equations  15  2.2.  I n i t i a l and Boundary Conditions  18  2.3.  Method of Solution  24  METHOD  27  3.1.  Continuous Casting Operations  27  3.1.1.  General Description  27  3.1.2.  Western Canada Steel  27  3.1.3.  Manitoba Rolling M i l l s  30  iv E-age  3.2.  4.  3.1.4.  Atlas Steel  30  3.1.5.  Algoma Steel  31  3.1.6.  U.S. Steel  32  Procedure  RESULTS 4.1.  4.2.  36  Liquid Mixing, Solid Shell and Cast Structure  . . .  General Observations of the Test Results  4.1.2.  Specific Observations; Manitoba R o l l i n g M i l l s .  42  4.1.3.  Atlas Steel  46  4.1.4.  Algoma Steel  51  4.1.4.1.  Beam Blanks  51  4.1.4.2.  Blooms  58  .  65  U.S. Steel  Calculated  .  36  4.1.1.  4.1.5.  5.  33  .  and Measured Pool P r o f i l e s and Pool Depths.  36  68  4.2.1.  General Comments  68  4.2.2.  Calculated and Measured Pool P r o f i l e s i n the mold  69  4.2.3.  Calculated and Measured Pool Depths . . . .  69  DISCUSSION  79  5.1.  Liquid Mixing, Solid Shell and Cast Structures . . .  79  5.1.1.  Liquid Mixing  79  5.1.1.1.  General Comments  79  5.1.1.2.  Open Pour  79  5.1.1.3.  Submerged Shroud  81  5.1.2.  Solid Shell  . . . .  83  Page  5.1.3.  5.2.  5.1.2.1.  Near t h e Meniscus  83  5.1.2.2.  Mold Region  85  5.1.2.3.  Submold Region  86  Cast S t r u c t u r e  87  5.1.3.1.  Stainless Steel  5.1.3.2.  E f f e c t o f Tundish Teeming  5.1.3.3.  Columnar S t r u c t u r e  90  5.1.3.4.  Equiaxed  91  5.1.3.5.  S o l u t e R i c h P i p e s i n Equiaxed  5.1.3.6.  Radial Cracking  94  5.1.3.7.  Sulphide I n c l u s i o n s  95  C a l c u l a t e d and Measured P o o l P r o f i l e s and P o o l Depths .  96  5.2.1.  V a l i d i t y o f Assumptions i n M a t h e m a t i c a l Models. .  96  5.2.2.  C a l c u l a t e d and Measured P o o l P r o f i l e s i n the mold  99  5.2.2.1.  Low Carbon S t e e l  99  5.2.2.2.  S t a i n l e s s S t e e l Slab  5.2.3.  5.2.3.2.  5.2.3.3.  .  .  .  .  Structure  .  .  C a l c u l a t e d and Measured P o o l Depths 5.2.3.1.  5.2.4.  .  Zone  .  .  .  .  . .  .  . .  87 89  93  102 103  C a l c u l a t e d P o o l Depths u s i n g OneDimensional Model  103  C a l c u l a t e d P o o l Depths u s i n g TwoD i m e nsional Model  104  Comparison o f C a l c u l a t e d and Measured P o o l Depths . . . . . . . . .  105  C a l c u l a t e d and Measured S u r f a c e Temperatures  SUMMARY  .  106  110  CONCLUSIONS  114 i  vi Page SUGGESTED FUTURE WORK  116  APPENDIX  117  REFERENCES  123  PUBLICATIONS  126  vii LIST OF FIGURES Figure  Page  1  Heat transfer zones i n continuous casting  16  2  Dependence of enthalpy on temperature for the s t a i n l e s s s t e e l slab  16  Average flux of heat extracted by the mold as a function of dwell time  22  Average, o v e r a l l heat transfer c o e f f i c i e n t for the mold as a function of dwell time  22  Estimated spray heat transfer c o e f f i c i e n t as a function of spray water flux per unit area  26  3  4 5 6  7 8  9  10  11  12  13  (a) Schematic of straight mold, v e r t i c a l type casting machine with bending. (b) Schematic of low-head, curved mold casting machine  .  28  Autoradiographs of longitudinal sections of test strands Ml to M4, cast at Manitoba R o l l i n g M i l l s  43  (a) Section 2C of Figure 7, showing s h e l l and associated depressions i n surface. (b) Section 1A of Figure 7, showing above meniscus. (c) Section 2E of Figure 7, showing region with periodic bridging across large dendrites  44  thin regions of the the outer b i l l e t s o l i d s h e l l segment gold r i c h central the centreline by  Autoradiographs of transverse sections of strands at positions indicated below meniscus. (a) strand M2, (b) strand M4 . .  45  Autoradiographs of longitudinal and transverse sections of s t a i n l e s s s t e e l slab, Test A t l . The positions of the transverse sections with respect to the meniscus are indicated  47  Section 2C of Figure 10, showing discontinuity i n s h e l l thickness. Top of autoradiograph 15.7 cm. below meniscus.  49  D i s t r i b u t i o n of radioactive gold i n the s t a i n l e s s s t e e l slab p r i o r to sectioning  49  Composite of autoradiographs of beam blank A, Test A£l showing the pool p r o f i l e down the web (C) and perpendicul a r to the longitudinal axis (B and R)  50  viii Figure 14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  Page (a) Autoradiography B6 o f F i g u r e 13. (b) Sulphur p r i n t o f same s u r f a c e as i n (a)  52  (a) A u t o r a d i o g r a p h o f c e n t r a l p o r t i o n o f C l , F i g u r e 13. (b) Sulphur p r i n t o f same s u r f a c e as i n ( a ) . Note t h a t the c i r c l e i s an a r t i f a c t and i s n o t s i g n i f i c a n t . . . .  53  Composite o f a u t o r a d i o g r a p h s o f beam b l a n k E showing the p o o l p r o f i l e down t h e web (E) and p e r p e n d i c u l a r t o the l o n g i t u d i n a l a x i s (F)  55  D i s t r i b u t i o n o f r a d i o a c t i v e g o l d i n E beam b l a n k and T e s t A£4 bloom  53  Sulphur p r i n t o f s e c t i o n F4, F i g u r e 16 showing clumps o f s u l p h i d e i n c l u s i o n s and c e n t r e l i n e c r a c k i n g  56  Autoradiograph (a) and s u l p h u r p r i n t (b) o f a d j a c e n t areas o f E2, F i g u r e 16 showing clumps o f s u l p h i d e i n c l u s i o n s and s o l u t e e n r i c h e d c e n t r e l i n e c r a c k s . . .  57  Composite o f a u t o r a d i o g r a p h s o f bloom, T e s t A£3, showing the p o o l p r o f i l e down t h e s t r a n d (G) and p e r p e n d i c u l a r t o the s t r a n d a x i s (H,K)  59  S h e l l c o r n e r and average s h e l l t h i c k n e s s as a f u n c t i o n o f d i s t a n c e below meniscus  57  (a) A u t o r a d i o g r a p h G25 i n F i g u r e 20. (b) Sulphur p r i n t of same a r e a as (a)  60  Composite o f a u t o r a d i o g r a p h s o f bloom, T e s t A&4, showing the p o o l p r o f i l e down the s t r a n d (L) and p e r p e n d i c u l a r t o the s t r a n d a x i s (M,N)  61  A u t o r a d i o g r a p h (a) and s u l p h u r p r i n t (b) o f s e c t i o n N l , F i g u r e 23 showing c o r n e r c r a c k f i l l e d w i t h g o l d and sulphur r i c h m a t e r i a l at A  ^3  Sulphur p r i n t o f p a r t o f s e c t i o n L l , F i g u r e 23 showing V segregate p a t t e r n  64  Sulphur p r i n t o f s e c t i o n M5, F i g u r e 23 showing c e n t r e l i n e i n t e r g r a n u l a r cracks f i l l e d with sulphur r i c h r e s i d u a l liquid  63  Composite o f a u t o r a d i o g r a p h s o f b i l l e t , T e s t U l , showing the p o o l p r o f i l e down t h e Strand (A) and p e r p e n d i c u l a r t o the s t r a n d a x i s (B)  66  S e c t i o n B2 o f F i g u r e 27, showing s h e l l s e p a r a t i o n a t t h e corner  64  ix Figure 29  30 31  32  33 34  35 36 37 38  39  Page Measured average dendrite spacing as a function of distance from the b i l l e t surface for Test U l . . . . .  .  67  Section B5 of Figure 27, showing r a d i a l cracking i n transverse section  67  Liquid pool and surface temperature p r o f i l e s i n the mold region for the stainless s t e e l slab 0, measured inside radius; §, measured outside radius. A, calculated f i n i t e difference with equation (7). B, calculated f i n i t e difference with equation (6). C, calculated i n t e g r a l p r o f i l e with equation (7). D, calculated i n t e g r a l p r o f i l e with equation (6)  71  Liquid pool and surface temperature p r o f i l e i n the mold region for (a) Test Ml, (b) Test M2, (c) Test M3, (d) Test M4. 0 measured, average s h e l l thickness of inside and outside radius surface. Caption as for Figure 31  72  Shell thickness f o r inside and outside radius faces from Test M3  71  Liquid pool and surface temperature p r o f i l e s i n the mold region for (a) Test A£l, (b) Test A£2, (c) Test A13, (d) Test AW. Caption as for Figure 32  7  3  Liquid pool and surface temperature p r o f i l e s i n the mold region for Test U l . Caption as for Figure 32  74  Liquid pool and surface temperature p r o f i l e s f o r the stainless s t e e l slab. Caption as f o r Figure 32 . . .  75  Liquid pool and surface temperature p r o f i l e s f o r (a) Tests Ml, M2, (b) Tests M3, M4. Caption as for Figure 32 .  76  P o s i t i o n of horizontal s l i c e s i n web area, 1, and i n flange area, 2, of A and E beam blanks used i n c a l c u l a t i n g pool p r o f i l e s with the one-dimensional models. S, positions of input streams . . .  74  Liquid pool and surface temperature p r o f i l e s f o r (a) web (A) and flange (B) areas of A beam blank, Test A 1. Curves A and B calculated with f i n i t e difference using equation (7), curve C with i n t e g r a l p r o f i l e using equation (7). (b) web (A) and flange (B) areas of E beam blank Test A 2. Caption as for Figure 39(a). (c) A, Test A 3. B, Test A 4. Curves calculated with f i n i t e difference model using equation (7). S, Temperature of blooms at straightener, 900°C  77  x Figure 40  41  42  43  Liquid pool and surface temperature p r o f i l e s for Test W2a and Test W2c  78  (a) Schematic drawing of distorted s h e l l without flange rollers. (b) Shell contour after deformation by flange r o l l e r s .  88  Temperature d i s t r i b u t i o n i n A beam blank web, Test A 1, 2.5 m. bel^w meniscus. Estimated region of low ductility i s indicated as well as the observed region of r a d i a l cracking  88  Effects of method of latent heat evolution and use of k f f on calculated s h e l l thickness for the s t a i n l e s s s t e e l slab. k f f used f o r T > 1460°C, % latent heat released at solidus: 25, 50, 75%, ; 100%, — — » keff used for T > 1399°C, 100% latent heat released at solidus w Integral p r o f i l e modelr . . .  97  E f f e c t s of method of latent heat evolution and use of k f f on calculated s h e l l thickness for low carbon s t e e l . k f f used for T > 1525°C, 5-100% latent heat released at solidus, ; k f f used for T > 1492°C, 100% latent heat released at s o l i d u s , — ——. Integral P r o f i l e model,  97  e  e  44  e  e  e  45 , 46 47 48  Autoradiograph of transverse section near tungsten p e l l e t p o s i t i o n taken a f t e r tests on a 17.5 cm. b i l l e t at Laclede Steel  1 0 7  Arrangement of nodes i n horizontal s l i c e for onedimensional f i n i t e difference model  H8  Flow chart of computer program for f i n i t e difference model  H8  Arrangement of nodes i n horizontal section of b i l l e t for two-dimensional f i n i t e difference model  121  xi  LIST OF TABLES  Table  Page  I  Thermophysical Properties of Steel  21  II  Parameter Used i n Integral P r o f i l e and F i n i t e Difference Calculations  21  III  Characteristics of Heat Transfer Zones  25  IV  Casting Machine D e t a i l s  29  V  Experiment, Casting Parameters and Pool Depths  VI  Steel Compositions  37  VII  Casting Characteristics from Autoradiographs  41  VIII  Measurement of Dendrite Spacing  91  IX  Measured and Predicted Average Mold Heat Flux  X  Predicted and Measured^  . . . .  Surface Temperatures (°C) .  34  101 .  .  109  xii LIST OF SYMBOLS  a,b  constants i n equation (4)  C  s p e c i f i c heat, k c a l kg."*" °C "*"  f  view factor for radiation -2  h  heat transfer c o e f f i c i e n t , kcal m. >h^  n 0  -1 sec. °C  mold heat transfer c o e f f i c i e n t s (between the casting surface and the mold water) at and below the meniscus respectively  h^,hg  average heat transfer c o e f f i c i e n t s for the mold and sprays respectively  H  enthalpy, kcal kg."'"  H^,H^ H ,H' n' n  enthalpy of the i th node at time t and t + At respectively enthalpy of the surface node at time t and t + At respectively  H. ,,H! .  enthalpy of node ( i , i ) at time t and time t + At respectively  ^,1L k  n  enthalpy of surface nodes at y = 0 and at z = 0 respectively thermal conductivity, kcal m.^ sec.''" °C ^  k ff  e f f e c t i v e thermal conductivity f o r the l i q u i d pool  L  latent heat, kcal kg."'"  P  mold perimeter, m  ^Oy'^Oz  heat flux from the surface of the casting i n the y and z  e  d i r e c t i o n s , kcal m.^ sec.^" q  Q  average surface heat f l u x  Q  Q  measured rate of heat removal by the mold, k c a l sec."'"  t  time, sec.  xiii dwell time, sec. temperature, °C pouring temperature and temperature at the surface of the casting respectively solidus  temperature  temperature of the mold water, sprays water and surroundings respectively casting speed, m. sec."*" width of casting, m. withdrawal d i r e c t i o n , m. e f f e c t i v e mold length, m. d i r e c t i o n perpendicular to casting face thickness of s o l i d s h e l l ,  cm.  d i r e c t i o n perpendicular to x and y f r a c t i o n of metal s o l i d i f i e d constant determining rate of decrease of h^ with x, density, kg.  m.^  Stephan-Boltzman (°k)"  m."^  constant, 1.356  (10  -11  -2 -1 ) kcal m. sec.  4  Dimensionless Groups heat removal per unit length of mold perimeter Qo  xiv  X  e f f e c t i v e mold length  ^ X  upCk '  e f f e c t i v e latent heat of  solidification  X V  ACKNOWLEDGEMENT  I would l i k e to thank my research d i r e c t o r s , Dr. Fred Weinberg and Dr. Keith Brimacombe, f o r their assistance and guidance throughout the course of this research project. , I would also l i k e to thank W.A. Rachuk, the Radiation Protection O f f i c e r at U.B.C, f o r h i s assistance during the experiments.  The interest and cooperation of the management and s t a f f of Western Canada Steel, Manitoba Rolling M i l l s , Atlas Steel, Algoma Steel and U.S. Steel i s g r a t e f u l l y acknowledged.  1  1.  1.1.  INTRODUCTION  General Comments  The f i r s t commercial  facility  for the continuous casting of  s t e e l i n North America was i n s t a l l e d at the Atlas Steel Company plant i n Welland, Ontario, i n 1954. Large scale production i n North America of mild s t e e l by continuous casting started i n about 1960.  Since that time  there has been a rapidly accelerating increase i n s t e e l production, using continuous casting, throughout the world, reaching a capacity of 75 m i l l i o n tons i n 1971. A wide variety of products are produced including b i l l e t s , blooms, slabs and beam blanks, with a range of compositions varying from mild s t e e l to stainless s t e e l .  The acceptance of continuous casting over normal conventional ingot teeming i s due to a number of d i f f e r e n t factors:  1. Current s t e e l  production practices, i n which the BOF i s replacing the open hearth, results i n an e f f e c t i v e l y continuous supply of l i q u i d metal.  This  continuous supply i s therefore d i r e c t l y compatable with continuous casting. 2. Lower i n i t i a l c a p i t o l costs, e.g., large blooming m i l l s and soaking p i t s are not required. shops are eliminated.  3. Lower operating costs, e.g., molds and mold 4. Higher y i e l d .  5. Improved quality of the cast  2  product.  6. More e f f i c i e n t handling of the cast product i n subsequent  operations.  The change i n casting p r a c t i c e on going from ingot teeming to continuous casting requires s i g n i f i c a n t changes i n the steelmaking operation.  In general the control of melt temperature, homogeneity of  the melt and deoxidation practices are more c r i t i c a l i n continuous casting. Higher or lower melt temperatures can cause breakouts or plugged nozzles respectively, stopping the casting operation.  In addition the casting  undergoes much less reduction i n subsequent operations. imperfections and segregation  As a result  cracks,  i n the casting are more pronounced i n the  r o l l e d product.  The continuous casting operation i s most e f f i c i e n t , when large heats are cast (200 tons).  economically,  The heat must be cast within about  an hour since neither the ladle nor the tundish are heated during casting. In order to cast the large heat i n the time available multiple strand casting machines are employed.  In addition the casting rate per strand i s  being increased by suitable design of the machine and operating  conditions.  Both multiple strands and higher casting rates impose more stringent conditions on the casting operation.  Tundish design,  nozzle  geometry, mold design, cooling water spray configurations and alignment among other factors must be considered.  For example, the United  States  Steel Company, South Works, i s using computer controlled water sprays for submold cooling.  With this control 19 cm.  speeds up to 6 cm./sec.  square b i l l e t s can be cast at  3  The continuously cast s t e e l q u a l i t y i s a function of the defects and segregation i n the s t e e l . include:  The defects which are commonly found  1. non-metallic inclusions, which are also obtained i n normal  castings, the size and d i s t r i b u t i o n being d i r e c t l y related to the s t e e l making and casting p r a c t i c e , 2. corner and r a d i a l cracking associated with the mold design and water spray cooling practice during s o l i d i f i c a t i o n , 3. centreline or s t a r - l i k e cracks due to improper cooling of the s o l i d strand, 4. centreline porosity, 5. transverse and l o n g i t u d i n a l surface cracks due to stresses introduced i n the s o l i d strand by bending and straightening operations, 6. d i s t o r t i o n of the strand (rhomboidity) due to uneven cooling or misalignment of the withdrawal and r e t a i n i n g r o l l s , 7. V segregates and central area porosity associated with the s o l i d i f i c a t i o n process, 8. high i n c l u s i o n concentration at the surface of the strand due to segregation and entrapment of the inclusions at the meniscus and the mold w a l l .  Considerable research has been carried out to increase the e f f i c i e n c y of the continuous  casting operation and to control within  acceptable l i m i t s , the defects i n the cast s t e e l .  This work has included:  1. tundish and nozzle design to determine and control the f l u i d  flow  during casting and therefore, the reoxidation and i n c l u s i o n d i s t r i b u t i o n i n the cast s t e e l , 2. attempts to r e l a t e cast structure to the casting parameters, 3. a study of corner cracking as a function of corner radius in the mold, 4. use of heat transfer calculations to predict the pool p r o f i l e and depth during casting as a means of establishing more e f f i c i e n t operating conditions, and for machine design.  The results of some of this  4  research and development a c t i v i t y are reported below.  1.2.  1.2.1.  Previous Work  F l u i d Flow and Liquid Pool A theoretical model of the f l u i d flow i n the l i q u i d pool during  casting has been proposed by Szekely and Stanek^.  In the analysis of the  model system, they examined, t h e o r e t i c a l l y , the steady state and transient dispersion of radioactive tracers added to the pool for three d i f f e r e n t flow conditions.  These conditions included eddy d i f f u s i o n , potential flow  and complete mixing.  The analysis indicated that discernably d i f f e r e n t  flow patterns would be obtained f o r the three conditions specified. However, no experimental evidence was presented to establish the v a l i d i t y of the analysis under r e a l conditions. 2  M i l l s and Barnhardt  considered the problem of high density  inclusions on the surface of cast slabs.  They constructed a water model  of the nozzle and mold systems and examined the f l u i d flow c h a r a c t e r i s t i c s as a function of the manner i n which the input stream entered the l i q u i d pool.  They c l e a r l y demonstrated that the f l u i d flow associated with  bifurcated immersed nozzles tended to keep inclusions away from the mold walls, whereas open pouring did not.  The f l u i d flow with immersed nozzles  or bifurcated nozzles produced controlled turbulence and s t i r r i n g i n the upper part of the mold preventing any second phase material from concent r a t i n g at the freezing s t e e l interface around the mold periphery. the tendency f o r subsurface entrapment of inclusions was a l l e v i a t e d .  Also The  results were applied to a f u l l scale continuous casting slab machine, and by introducing bifurcated immersed nozzles with a suitable lubricant, slabs  5 were cast with l i t t l e inclusion concentration at the outside face.  These  were then suitable f o r subsequent r o l l i n g into sheet whereas open poured cast slabs were unacceptable.  Water model studies were also undertaken by Szekely and 3  Yadoya .  In this study they measured the v e l o c i t y contours i n the mold  region for " s t r a i g h t " and r a d i a l flow nozzles.  For straight nozzles they  found the penetration of the input stream to be from 4 to 6 mold diameters. A r a d i a l flow nozzle produced a r e l a t i v e l y f l a t v e l o c i t y p r o f i l e within h to 1 mold diameter.  This investigation also confirmed the e a r l i e r  findings of M i l l s and Barnhardt that r a d i a l flow nozzles produced flow patterns more conducive to the f l o a t a t i o n of inclusions than conventional straight nozzles.  The investigation was not extended experimentally beyond  the water model. 4-10 A number of workers  have t r i e d to predict the pool p r o f i l e ,  pool depth and f l u i d flow during continuous casting through the addition of radioactive tracers during casting and subsequent autoradiography. 4 Varga and Fodor reported r e s u l t s on the d i s t r i b u t i o n of radioactive 32 60 phosphorus (P ), and tungsten p e l l e t s containing a small Co wire, i n the l i q u i d pool of continuous cast b i l l e t s . obtained pool depths of from 3.6 to 3.7  Using the tungsten p e l l e t s they m.  Similar experiments have been reported by Kohn et al."', using _184 198 32 w p e l l e t s to measure the pool depth and Au instead of P to outline the pool p r o f i l e .  Using the tungsten p e l l e t s they found the  increased with increasing casting speed. depth increased from 4.7 from  1.83  to 5.37 m.  to 2.28 m./min..  pool depth  For a 10.5 cm. b i l l e t the pool  as the casting speed increased  The position  of the tungsten  6 p e l l e t s also coincided with the bottom of the pool outlined by the radioactive gold i n d i c a t i n g that the gold mixed throughout the l i q u i d pool. Gautier et a l .  i n s i m i l a r experiments on 10.5 cm. b i l l e t s found that  the tracers did not penetrate  to the pool bottom.  From the autoradiographs  Kohn speculated that the flow pattern i n the l i q u i d pool consisted of two cells.  In the upper c e l l i n the mold, flow occurs down the centre of the  strand and up the side walls.  In the lower c e l l t h i s pattern i s reversed,  the flow occurring down the outside surface and up the centre.  Morton and Weinberg'' added radioactive gold and tungsten p e l l e t s during the continuous casting of b i l l e t s i n a Weybridge type mold. From autoradiographs of the cast strand they found that i n the mold region the s o l i d - l i q u i d interface was sharply delineated by the gold and i n the sub-mold region, p a r t i a l mixing of the gold i n the l i q u i d pool  occurred.  The amount of mixing was related to the input stream penetration.  The  depth of the pool delineated by the gold was found to be l e s s than the pool depth determined by the tungsten p e l l e t s .  The f l u i d flow i n the pool  could not be considered quantitatively i n terms of Szekely and Stanek's''" analysis since the gold was introduced below the metal surface and was released over a period of several seconds.  However, on a q u a l i t a t i v e basis  the r e s u l t s suggested that the eddy d i f f u s i o n model of Szekely and Stanek was most applicable.  The flow pattern proposed by Kohn^ was not observed  i n any of the tests.  Similar to e a r l i e r findings, the pool depth was found  to increase with increasing casting speed. 8 Gomer and Andrews on an experimental  32 added P  and tungsten p e l l e t s to the mold  continuous casting machine to estimate  solidification  7 rates and pool depths.  They found that the pool depths indicated by the  p e l l e t s were greater than that predicted by a l i n e a r extrapolation of the 32 s h e l l thickness i n the mold (obtained from autoradiographs of the P distribution  i n the mold) but was less than that predicted by assuming a  parabolic s o l i d i f i c a t i o n rate below the mold.  From autoradiographs i n  the mold they observed an uneven or wavy s o l i d i f i c a t i o n front.  The  fluctuations were usually found to be periodic corresponding to the mold oscillation. Using a radioactive tungsten p e l l e t and s c i n t i l l a t i o n counters 9  positioned down the strand, Nagaoka et a l . estimated the pool depth f o r a slab, cast with a low-head curved mold machine.  They found that f o r a slab  2 20 x 160 cm. cast at 10.8 mm./sec, a pool depth of 7.5 m. was obtained. Also with the s c i n t i l l a t i o n counters they estimated that the average rate of descent of the p e l l e t was 84.2 mm./sec. Zeder and Hestrom^ added Au^** and Ag^""^ to a slab cast with a low-head curved mold machine to define the s h e l l p r o f i l e i n the transverse sections i n the mold and submold regions.  In these tests an  immersed, bifurcated shroud and a slag powder lubricant were u t i l i z e d . They observed: definition  1. a thinning of the strand at the corners, 2. poor  of the s h e l l towards the centre of the pool along the wide faces  of the slab, 3. incomplete mixing of the gold near the pool bottom, 4. a thin s h e l l along one face when the support r o l l e r s were improperly aligned with the mold.  8 1.2.2.  Structure The structure of continuously  cast s t e e l has been examined  using radioactive tracers, sulphur p r i n t s and macroetching techniques 7 8 10-12 and has been related to d i f f e r e n t casting variables. ' ' Radio7 10 11 8 active tracers such as gold ' ' and phosphurus have been found to segregate i n a s i m i l a r fashion to sulphur, o u t l i n i n g the cast structure. Using these techniques i t was columnar zone, segregation  possible to determine the length of the  and centreline porosity i n the equiaxed zone  and the presence of r a d i a l or centreline cracking. 11 8 Both Mori et a l . and Gomer and Andrews found that with increasing casting superheat the length of the columnar zone i n the casting increased and the centreline porosity and segregation became worse. A s i m i l a r e f f e c t was  observed by Morton and Weinberg'' i n which the cast  structure of b i l l e t s cast i n a Weybridge type mold (3 b i l l e t s per strand) was  compared to the structure of a single strand cast b i l l e t .  They  observed that with the Weybridge mold, the cast structure consisted mainly of small equiaxed grains, whereas the single strand b i l l e t , cast at a s l i g h t l y lower superheat had a coarse dendritic structure with bridging across the centreline and extensive  centreline porosity.  Thus,  the size of the central equiaxed zone i s dependent on the extent of mixing in the l i q u i d pool and the casting superheat.  The n u c l e i associated with  the central equiaxed grains are believed to be generated^ i n the upper part of the l i q u i d pool by remelting of secondary dendrite branches.  A V shaped segregation  pattern has been observed on the  7 8 11 longitudinal sections of b i l l e t s i n many d i f f e r e n t investigations.' '  9  It has been suggested that the pattern r e s u l t s from the s e t t l i n g of free dendrites i n the l i q u i d pool and subsequent f l u i d flow by i n t e r d e n d r i t i c l i q u i d due to s o l i d i f i c a t i o n  shrinkage.  In tests on a slab"^ using Au^** a heavily segregated narrow central zone as well as l o c a l segregation between columnar dendrites  was  observed.  Cracks which formed during s o l i d i f i c a t i o n and which were subsequently  f i l l e d with i n t e r d e n d r i t i c l i q u i d , are often found i n the cast  structure of the strand.^'^'"^  Ushijima"^, i n tests on a v e r t i c a l  casting machine, noted that the incidence of l o n g i t u d i n a l surface cracks and i n t e r n a l cracks depended i n a complex fashion on such parameters as the casting superheat, casting speed, primary cooling i n the mold and secondary cooling i n the spray and radiant zones.  By careful control of the cooling  and s o l i d i f i c a t i o n conditions he found that the incidence of surface and i n t e r n a l cracks could be reduced.  For instance, by choosing a mold corner  radius that minimized the s h e l l separation due to bulging and shrinkage at the corner, l o n g i t u d i n a l corner cracking was incidence of i n t e r n a l cracking was  solidification  eliminated.  The  reduced by maintaining even cooling  around the strand i n the mold and submold regions, decreasing the i n t e n s i t y of cooling, reducing the stress due to the pinch r o l l s and prevention of l o c a l solute enrichment, i . e . , f i n e grained structure over coarse grained structure.  In order to t r y to further explain i n t e r n a l and external 13 cracking i n the b i l l e t , Adams measured the hot d u c t i l i t y and  strength  10 of strand-cast s t e e l to near i t s melting point.  When the strand cast  specimens were heated from room temperature and pulled, the d u c t i l i t y dropped d r a s t i c a l l y at temperatures greater than 1250°C.  This was  attributed to i n c i p i e n t l i q u i d - f i l m formation at grain boundaries. 14 Lankford  also studied t h i s problem.  Instead of re-heating  as-cast specimens, he remelted specimens and under controlled conditions cooled them to the test temperature.  Both t e n s i l e and bending tests  were performed studying the e f f e c t of composition and p r i o r thermal history.  In general he found that:  1.  Specimens that were r a p i d l y cooled from the s o l i d i f i c a t i o n  temperature exhibited a low d u c t i l i t y between 800 and 1200°C.  This i s  attributed to the p r e c i p i t a t i o n of l i q u i d FeS droplets i n planar arrays at austenite grain boundaries, producing paths of easy crack propogation. A recovery of d u c t i l i t y i n t h i s temperature range was observed when a slower cooling rate or isothermal heat treatment was applied. results from  the coalescence and growth of precipitates and the formation  of the more stable 2.  The recovery  MnS.  With increasing Mn/S  r a t i o s the loss of d u c t i l i t y becomes less  severe because of the low s o l u b i l i t y of MnS  i n the iron; also the pre-  c i p i t a t i o n of MnS i s more favorable than FeS. 3.  Under s u f f i c i e n t l y high t e n s i l e stress hot tears can occur i n  portions of the casting which are i n the low d u c t i l i t y temperature range.  1.2.3.  Mathematical Models 6 15—22 There have been a number of mathematical models '  11 formulated to calculate the heat flow and temperature d i s t r i b u t i o n i n the strand during the continuous casting of s t e e l .  These models involve the  solution of the unsteady state conduction equation using either a n a l y t i c a l (Pehlke  15  , Hills  16  Donaldson and Hess  , Fahidy  17  20  , Savage  22 6 ) or numerical (Gautier et a l . ,  18 21 , Mizikar , Kung and Pollock ) methods.  The  mathematical models d i f f e r i n the treatment of the method of removal of superheat from the l i q u i d pool and i n the surface boundary condition used to describe the heat flux from the casting to the mold. 18 Regarding the removal of superheat, Mizikar and Kung and 21 Pollock  accounted f o r convection and conduction i n the l i q u i d pool by  using an e f f e c t i v e thermal conductivity which was approximately seven times the normal l i q u i d conductivity.  Donaldson and Hess"^ and Gautier et a l . ^  assumed a stagnant l i q u i d pool and used the normal value of the thermal conductivity at that temperature.  On the other hand H i l l s ^ assumed the  pool was completely mixed, neglected conduction i n the pool, and released the superheat at the same time as the latent heat.  Szekely and Stanek^,  using the mathematical model proposed by Mizikar, varied the method of superheat removal from the pool.  They found that there was no observable  difference i n the computed solidus and liquidus l i n e s when the flow conditions or the method of superheat removal were altered.  This i s  understandable because the superheat i s only a small f r a c t i o n of the latent heat; therefore i t w i l l not have a large e f f e c t on the calculated s o l i d i f i c a t i o n rate. Many d i f f e r e n t approaches have been taken to account f o r the surface boundary condition i n the mold.  Donaldson and Hess"^ and  Gautier et a l . ^ used a two zone heat transfer model, incorporating a zone  12 of good contact between the casting and the mold and a zone of poor contact. The length of the zone of good contact was calculated by Donaldson and Hess 22 by applying a method proposed by Savage  .  In t h i s c a l c u l a t i o n the length  of contact depended upon the e l a s t i c modulus of the s t e e l at elevated temperatures, the width of the s h e l l and the casting speed.  Gautier et a l ^  calculated the zone of good contact by employing a heat balance on the mold. The t o t a l heat flux i n each zone was calculated and the r e s u l t s were compared to the measured mold heat f l u x .  The length of the zone of good  contact was then varied u n t i l the measured and the calculated heat f l u x values coincided. 21 Kung and Pollock  , i n t h e i r two-dimensional f i n i t e difference  model, compared the e f f e c t of using an average o v e r a l l heat transfer c o e f f i c i e n t i n the mold and using three d i f f e r e n t c o e f f i c i e n t s along the length of the mold to account f o r p a r t i a l contact.  From the predicted  temperature p r o f i l e s at the mold bottom they found a 2 to 6% increase i n surface temperature when using three mold c o e f f i c i e n t s .  This temperature  difference had v i r t u a l l y no effect on the calculated pool p r o f i l e or pool depth. 18 Both Mizikar  16 and H i l l s  took simpler approaches i n defining  the surface boundary condition i n the mold.  Mizikar employed the heat flux 23  relationship found experimentally by Savage and Pritchard  .  This r e l a t i o n -  ship was determined from experiments on a s t a t i c water-cooled copper mold by measuring the rate of heat removal by the mold cooling water as a function of time.  The r e s u l t s from these experiments were found to compare 2A  16  favourably with data presented by Krainer and Tarmann . H i l l s calculated an average o v e r a l l heat transfer c o e f f i c i e n t from an i n t e g r a l heat balance  i  13 19 on the mold.  Later H i l l s  modified t h i s approach by assuming a l i n e a r l y  decreasing heat transfer c o e f f i c i e n t down the mold.  Brimacombe and  25 Weinberg  calculated pool p r o f i l e s with H i l l s model using either an  average o v e r a l l or l i n e a r l y decreasing mold heat transfer c o e f f i c i e n t . These were compared to p r o f i l e s experimentally measured by Morton and Weinberg^.  They found that f o r low carbon s t e e l the predicted p r o f i l e s  using the H i l l s model with either heat transfer c o e f f i c i e n t agreed c l o s e l y with the measured p r o f i l e s .  Predictions using Mizikar's model were also  found to compare favourably to the values measured at the mold bottom. Another area i n which the models d i f f e r e d was i n their treatment of the thermophysical properties of s t e e l .  H i l l s i n solving the heat flow  equations using the i n t e g r a l p r o f i l e method, assumed the thermophysical properties were constant.  Mizikar, Kung and Pollock and Gautier et a l .  allowed the s p e c i f i c heat and thermal conductivity to vary with temperature while keeping the density constant.  Kung and Pollock found that by keeping  the thermal conductivity constant, the pool depth changed from 6-11%.  In  the f i n i t e difference models Mizikar and Kung and Pollock d i f f e r from Gautier et a l . i n their treatment of the addition of the latent heat of fusion.  Both Mizikar and Kung and Pollock assume that the latent heat can  be accounted for by adjusting the s p e c i f i c heat over the range of s o l i d i fication.  Gautier et a l . assume the s t e e l can be characterized by an  enthalpy-temperature curve which includes the latent heat of fusion. 6 17 18 21 In several of the mathematical models '  '  '  calculations  of the heat flow have been extended into the submold region.  This requires  the estimation of spray heat transfer c o e f f i c i e n t s for the secondary cooling zone.  Since l i t t l e information i s available regarding water spray  14 cooling, the procedure adopted i n most models was to allow the program to generate a spray heat transfer c o e f f i c i e n t which could be used without dropping the surface temperature of the strand below the a u s t e n i t e - f e r r i t e transformation  temperature.  Recently an investigation of water spray cooling was under26 taken by Mizikar  .  In t h i s i n v e s t i g a t i o n he determined the spray heat  transfer c o e f f i c i e n t s as a function of water flux for three d i f f e r e n t nozzle sizes and d i f f e r e n t spray pressures.  An important r e s u l t from t h i s  work was that the heat extraction e f f i c i e n c y per drop (water drop from spray) increases greatly with droplet s i z e and the corresponding increase i n drpplet momentum.  Thus by determining the heat extraction for a c e r t a i n  droplet s i z e and droplet momentum (supplied for a l l nozzles by the vendor), heat transfer c o e f f i c i e n t s for d i f f e r e n t nozzle sizes and spray configurations could be estimated. 1.2.4.  Objectives of Present Work The purpose of the present investigation i s :  1. to determine,  through the use of radioactive tracers, the l i q u i d pool p r o f i l e s , pool depths, f l u i d flow and cast structure of continuously  cast s t e e l as a  function of d i f f e r e n t casting conditions and casting s i z e s , 2. to develop a mathematical model to calculate the temperature d i s t r i b u t i o n i n s t e e l being continuously  cast; and to assess i t s r e l i a b i l i t y by comparison of  predicted and measured pool p r o f i l e s .  15  2.  2.1.  MATHEMATICAL MODEL  Heat Flow Equations  A thin horizontal section of the casting shown by the shaded area i n Figure 1 i s considered.  The section i s i n i t i a l l y located at the  meniscus and, at times greater than zero, moves downward at the same speed as the casting, successively passing through the mold, water sprays and radiant cooling zones.  Within the section heat conduction to the surface can be characterized by the unsteady state conduction equation (1),  p  9t"  =  V  (  k  V  T  )  (1)  Equation (1) may be simplified by assuming that heat conduction i n the d i r e c t i o n of withdrawal, x, i s small and can be neglected, thus giving the two-dimensional unsteady state conduction equation (2),  (2)  This assumption w i l l apply f o r analysing heat removal from blooms or b i l l e t s . In the case of slabs, (far from corners) conduction i n the z d i r e c t i o n can be ignored thus reducing equation (1) to i t s one-dimensional form,  16  y=W/2  Figure 1.  Figure 2.  y=0  Heat transfer zones i n continuous casting.  Dependence of enthalpy on temperature for the s t a i n l e s s s t e e l slab.  17  The assumptions involved i n applying equations (2) and (3) i n the models are: 1.  The density and s p e c i f i c heat are constant over the temperature range considered.  2.  The thermal conductivity can be characterized as a l i n e a r function of  temperature  k = a + bT 3.  (4)  Conduction and convection of heat i n the l i q u i d can be accounted for by adjusting the thermal conductivity. In the solutions to equations (2) and (3) the s p e c i f i c heat;  and density terms usually take the form of a product.  Since these terms  27 increase and decrease  respectively with increasing temperature, their  product does not vary s i g n i f i c a n t l y over the temperature range of interest for both stainless and low carbon s t e e l s . Conduction and convection of heat i n the l i q u i d can be described by 3H . 3T i F " ef f 7 T 3y 2  p  where k  eff  k  . , 3T e f f TI 3z 2  +  k  ( 5 )  i s an e f f e c t i v e thermal conductivity which Includes the e f f e c t s  of convective mixing.  J  18 21 Mizikar and Kung and Pollock have previously  used t h i s approach and have reported an e f f e c t i v e thermal conductivity roughly seven times greater than the l i q u i d thermal conductivity.  This  value was used i n the models over the region of the section where the  18 temperature was greater than the liquldus.  The e f f e c t of varying the  temperature range over which k £f was used was determined and i s discussed g  in a l a t e r section. In the model a procedure must be adopted f o r incorporating the latent heat evolved i n the s o l i d - l i q u i d region during s o l i d i f i c a t i o n .  Since  the evolution occurs i n a complex fashion, as a r e s u l t of the complex conf i g u r a t i o n of the s o l i d - l i q u i d interface, a s i m p l i f i e d process must be assumed. S p e c i f i c a l l y , i n the case of stainless s t e e l , the f r a c t i o n of metal s o l i d i f i e d , Y » was a r b i t r a r i l y given a value such that 75% of the g  latent heat was released i n a l i n e a r fashion between the solidus and liquidus temperatures with the remaining 25% being given o f f at the solidus.  This  a r b i t r a r y choice of latent heat removal had a n e g l i g i b l e effect on the calculated rate of s o l i d i f i c a t i o n as w i l l be shown l a t e r .  The graph of  enthalpy versus temperature f o r the stainless s t e e l along with the equations for enthalpy over each region i s given i n Figure 2. For the low carbon s t e e l s , equilibrium freezing has been assumed and Y  n a s s  been calculated from the iron-carbon phase diagram.  In this case  depending on the carbon content roughly 5 to 25% of the latent heat was released at the solidus temperature which corresponded to the p e r i t e c t i c temperature.  2.2.  I n i t i a l and Boundary Conditions  The i n i t i a l and boundary conditions used i n the solution of equation (2) are as follows:  (i)  t = 0  0 < y < |,  (ii)  t > 0  y = ^  z  (iii)  t > 0  0 < z < |,  T  19 M  -k|f = 0 9y  2  =  T =  - "aT k  =  0  y - 0  -kg =  q  z = 0  -k-^ =  D y  The i n i t i a l condition states that the temperature of the section at the meniscus i s equal to the temperature of the incoming metal stream, T^. centreline boundary condition (at y = W/2  and z = W/2)  The  assumes that the  heat flux about the centrelines of the casting i s symmetrical; therefore, only one quarter section of the casting need be considered.  To obtain the  surface boundary condition, at y = 0 and z = 0, a heat balance was formed on the surface node, q  per-  representing the surface heat flux term.  Q  It should be noted that the heat flux around the perimeter of the bloom i s assumed to be constant, term was  so that q y  i s equal to qo -  D  z  The surface heat flux  characterized i n each of the three cooling zones by the following  expressions: (i)  Mold  q  o  = 640 - 80 / t  or %  (ii)  Sprays  q  (iii)  Radiation  q  " ^M  Q  = h  g  ( T  o  -  (T  q  V  - T^)  = aF ( T - T ) o o a 4  4  These equations of the i n i t i a l and boundary conditions to the two-dimensional model and with suitable modification to the  (6) (?)  (8)  (9)  apply one-  20 dimensional f i n i t e difference and i n t e g r a l p r o f i l e models. Equation (6) i s an expression experimentally obtained by 23 Savage and Pritchard  , which describes the time dependent heat flux from  a water cooled, s t a t i c mold.  5  The time-averaged o  form of equation (6)  - 640 - 53 / t ^  (10)  predicts average mold heat fluxes which agree well with measured fluxes under a v a r i e t y of casting conditions.  In Figure 3, the average mold heat  flux i s plotted against dwell time i n the mold.  The s o l i d l i n e , calculated  from equation (10), can be seen to pass through the values obtained from commercial molds for dwell times less than 35 to 40 sec.  The v e r t i c a l bars  indicate the range i n which most of the heat fluxes f o r a given mold were 18 found.  Equation (6) has been previously used by Mizikar  boundary condition i n the mold.  for the surface  For the purposes of design equation (6)  may be used to predict with reasonable accuracy the s h e l l thickness of the strand i n the mold.  From this data, given a c e r t a i n s h e l l thickness  required to withstand the f e r r o s t a t i c head on exit from the mold, the mold length and maximum casting speed f o r the strand may be estimated. In equation (7), h^. i s the average, o v e r a l l heat transfer c o e f f i c i e n t between the casting surface and the mold water.  H i l l s ' ^ has  outlined a method for determining h^ by using an i n t e g r a l heat balance on the mold.  Tables I and II give the values used i n calculating the heat  balance on the mold and the values of h^. obtained f o r the tests. For the purposes of design, since very few values of h^ have been available i n the l i t e r a t u r e , obtained i n equation (10) giving  may be calculated from heat fluxes  Table I.  Thermophysical Properties of Steel  Low Carbon  Stainless  Property  Thermal Conductivity (kcal m ^ sec."'' °C "*" )  0.0038  Specific Heat (kcal k g "  0.16  0.16  65  65  _3 (kg m )  7400  7400  Solidus Temperature (°C)  1399  Liquidus Temperature (°C)  1460  1  0  C  _ 1  )  Latent Heat of S o l i d i f i c a t i o n (kcal kg "*") Density  +  2.75(10 )T _6  * 1492 1525  *For 0.1 to 0.2% C For 0.3% C, Solidus Temperature 1470°C.  Table I I .  Test No.  Parameters Used i n Integral P r o f i l e and F i n i t e Difference Calculations.  %  X  Q*  * X  -2  (kcal m  (kcal sec. ) 1  -1 -1 sec. C  Ml  131  0.3  0.372  0.189  0.283  M2  139  0.3  0.351  0.164  0.295  M3  142  0.3  0.459  0.325  \ 0.427  M4  159  0.3  0.484  0.375  0.499  Ati  482  0.3  0.532  0.488  0.370  A£l  352  0.308  0.474  0.354  0.283  k%2  353  0.298  0.426  0.267  0.242  A£3  170  0.304  0.430  0.273  0.252  AM  145  0.315  0.358  0.173  0.208  Ull  445  0.3  0.578  0.618  0.526  22  Figure 3.  Average flux of heat extracted by the mold as a function of dwell time.  i  1  1  1  1  1  r•00  200 f .2 100 !•=  -J  1  1  20  1  1  1—_i 1 40  Dwell  Figure 4.  1 Time  i  I  60  i  i  i  I  80  i  •  •  l0 100  (sec)  Average, o v e r a l l heat transfer c o e f f i c i e n t f o r the mold as a function of dwell time.  = .405 - 0.00386  (11)  28 This r e l a t i o n i s shown i n Figure 4 i n the mold.  , a plot of  against dwell time  Heat transfer c o e f f i c i e n t s f o r d i f f e r e n t molds and casting  conditions are also plotted i n Figure 4.  From the graph i t can be seen  that equation (11) gives values of h^. which are obtained i n practice under "average" casting conditions for dwell times less than about 35 sec. 19 Hills  also suggested using a l i n e a r l y decreasing heat  transfer c o e f f i c i e n t i n the mold, equation (12), ^  = h ( l - nx)  (12)  Q  to characterize the heat flux from the casting surface, h  Q  being equal to  25 h^ at the meniscus.  Brimacombe and Weinberg  have shown that even with  h^ decreasing to half i t s i n i t i a l value at mold bottom, the change i n the calculated s h e l l thickness compared to the constant h^ case i s small. Also i t i s d i f f i c u l t to d i s t i n g u i s h which of the two cases i s most applicable when comparing calculated s h e l l thicknesses to measured s h e l l thicknesses. Values of the spray heat transfer c o e f f i c i e n t s , h  used i n  equation (8), are presented i n Table I I I . These values were roughly estimated by obtaining the water flux per unit area i n each spray zone of a casting machine from the spray nozzle s i z e , spray configuration and 26 spray pressure.  Then using spray data obtained by Mizikar  in Figure 5, h^ f o r each spray zone was determined.  , presented  These values were  subsequently altered i n the computer solution so that the calculated surface temperature  of the strand did not f a l l below 850°C.  Mizikar's  24 data could not be used d i r e c t l y to give h  since the spray configurations  in the continuous casting machines were d i f f e r e n t than the ones used i n his investigation. Also support r o l l s pressing against the strand surface i n the spray chambers would have an unknown effect on hg.  2.3.  Method of Solution The unsteady state conduction equations (2) and  (3) with the  appropriate boundary conditions were solved by the e x p l i c i t method of f i n i t e differences.  The d e t a i l s of the solution are given i n the  Appendix.  i  Table III.  Characteristics of Heat Transfer Zones. -2 — 1 -1 Heat Transfer Coefficients, hg(kcal m sec. C )  Western Canada Steel Zone  Length  Manitoba Rolling Mills hg  Zone  (m)  Atlas Steel  Length  h„ ..g  h„ ..  (m)  (10.1cm)  (13.3cm)  g  Zone  Length  Algoma Steel  U.S. Steel h  Zone  (m)  Length  Beam Blank Length 'A' Profile 'E' Profile Length  h  (m)  (m)  1  2  1  2  Bloom Test Test  (m)  AL3  AL4  1  0.31  0.49  1  0.3  0.45  0.41  1  0.91  0.42  1  0.38  0.6  Spray P.ing 0.15  0.14  0.26  0.17  0.23  0.15  0.25  0.23  2  0.83  0.13  2  1.52  0.22  0.21  2  0.92  0.30  2A  0.49  0.31  1A Top  0.61  0.17  0.20  0.16  0.23  0.915  0.15  0.14  3  0.38  0.13  3  3.66  0.1  0.1  3  1.52  0.18  2B  0.73  0.175  1A Bottom  0.94  0.16  0.17  0.15  0.2  0.635  0.15  0.14  4  2.14  0.15  3  2.13  0.15  IB  1.925  0.13  0.13  0.12  0.12  2.18  0.11  0.105  4  2.15  0.11  2  1.925  0.10  0.10  0.10  0.10  2.13  0.08  0.08  5  5.1  0.09  3  3.05  0.07  0.07  0.07  0.07  2.68  0.07  0.07  4  3.05  0.07  0.07  0.07  0.07  2.68  0.06  0.06  26  Figure 5.  Estimated spray heat transfer c o e f f i c i e n t as a function of spray water f l u x per unit area.  27  3.  3.1.  METHOD  Continuous Casting Operations  3.1.1.  General Description  The experiments were conducted on straight mold, v e r t i c a l bend and low-head curved mold continuous casting machines.  A schematic  diagram of the two d i f f e r e n t types of casting machines i s given i n Figure 6. In Table IV the type of machine used at each s t e e l company where tests were conducted i s l i s t e d , together with a description of the cast product, mold l u b r i c a t i o n and mold dimensions. Also, i n low-head curved mold machines, the  radius of curvature of the casting i s given.  In each experiment the  withdrawal rate, water flow rate i n the mold and the water temperature drop i n the mold were recorded and are l i s t e d i n the r e s u l t s .  3.1.2.  Western Canada Steel 29 At Western Canada Steel  using a Weybridge type mold, by a thin web region.  , three b i l l e t s are cast simultaneously  the b i l l e t s being joined across the diagonal  The mold consists of two sections, s p l i t along the  diagonal and i s made of a cast copper chromium a l l o y .  Open teeming from  28  LADLE *  TUNDISH MOLD MOLD-DISCHARGE SECTION WATER SPRAY HEADERS  (a) ROLLER APRON  PINCH-ROLL CLUSTER—f=JD{gj BEND)ING CLUSTER**^ CURVED ROLLER APRON STRAIGHTENER n  n r>  D  -GANTRY CRANE  LADLL  TUNDISH c  CASTING FLOOR  v~r  MOLD T A B L E  STARTING BAR STORAGE/  (b)  EMERGENCY LADLE •///////////////  Figure 6.  (a) Schematic of straight mold, v e r t i c a l type casting machine with bending. (b) Schematic of low-head, curved mold casting machine.  Table IV.  Casting  Machines D e t a i l s .  S t e e l Company  Test No.  Machine Type  Steel  Size & D e s c r i p t i o n of C a s t i n g s (cm )  Lubrication  2  13.3x13.3 B i l l e t s  81.3  15  6.7  10.1x10.1 B i l l e t s  81.3  15  6.7  12.7x109  61  9  9.2  15  10.7  V e r t i c a l bend straight, Weybridge mold  Low and medium carbon  Rapeseed O i l  14x14  M1.M2  Manitoba Rolling Mills  Low head, curved mold  Low and medium carbon  Rapeseed O i l  Atl  Atlas  Low head, curved mold  Stainless Steel  Mold Powder  AJ.1  Algoma  Low head, curved mold  Low and medium carbon  Synthetic  Steel  Oil  +  Billets  Slab  843, A p r o f i l e Beam Blank  Mold Powder  1015, E p r o f i l e Beam Blank  A£3  Synthetic  22.9x26.7 Bloom  AM  Mold Powder**  22.9x26.7 Bloom  Rapeseed O i l  19x19  AH 2  Ul  U.S. S t e e l  V e r t i c a l Bend  Low and Medium Carbon  Oil*  Radius o f Curvature (m)  11  Western Canada S t e e l  Steel  D i s t . o f Meniscus Below Moid Top (cm)  62  W1.W2  M3.M4  Hold Length (cm)  Billet  71.2  122  20  F u s i o n Temperature 1150°C. F u s i o n Temperature 960°C. Proctor-Gamble Synthetic O i l .  N3 VO  30 the tundish into the centre section of the mold i s used.  The flow of  metal i s controlled manually using a stopper rod i n the tundish, therefore, the flow of the input stream i s intermittent.  The mold i s  o s c i l l a t e d at approximately  1 cycle/sec. during normal casting and  a stroke length of 2.5 cm.  Approximately 9.2 m. below the mold (see  Figure 6(a)), the strand i s bent through a 6.40 position.  m. radius to a horizontal  The b i l l e t s are then separated by cutting the web with torches  and mechanically  3.1.3.  has  sheared to the desired lengths.  Manitoba Rolling M i l l s 30 Manitoba R o l l i n g M i l l s  has two low-head curved mold machines  (Figure 6(b)), each machine casting two square sections from a single tundish.  Open teeming from the tundish i s used, with the l i q u i d l e v e l i n  the mold being maintained  at a constant p o s i t i o n automatically.  This i s  accomplished by using a radioactive source and detector device to determine the l i q u i d l e v e l and varying the withdrawal rate to keep the l e v e l  constant.  During the tests, the l i q u i d l e v e l was adjusted by the operator, since the radioactive tracer addition to the melt made the automatic inoperative.  instrument  Tubular chromium plated copper molds are used.  The molds are  o s c i l l a t e d at a rate proportional to the casting speed, having a stroke length of 3.8 cm.  Each strand a f t e r passing through the casting machine  i s sheared into the required lengths. 3.1.4.  Atlas Steel One test was  conducted at the Atlas Steel Company i n Tracy, 31  Quebec, on a low-head curved mold, Concast Inc. slab machine  .  The  material cast was stainless s t e e l of the composition given i n Table V, with slab dimensions of 12.7 x 109 cm.  The mold i s formed with copper  plates r i g i d l y held i n a s t e e l enclosure and i s reciprocated at 1 cycle/ sec. with an amplitude of 1.3 cm.  The l i q u i d s t e e l enters the pool from  the tundish through an immersed bifurcated tube.  The input stream from  the tube i s directed p a r a l l e l to the long face of the s t e e l slab and i n c l i n e d upwards by 20°.  The strand i s flame cut into the required  lengths after passing through the casting machine.  3.1.5.  Algoma Steel  Algoma Steel Corporation has two low-head, curved mold, continuous casting machines consisting of a four-strand bloom machine, 2 producing blooms up to 26.7 x 35.6 cm. , and a two-strand beam blank machine which casts f i v e d i f f e r e n t blank sections ranging from 843 to 2 1435 cm. .  These machines are presently being used f o r casting s t r u c t u r a l  grades of s t e e l , high-carbon s t e e l f o r the grinding media, seamless tube grades and r a i l s ; Each machine i s fed from a single tundish.  For the beam blank,  two nozzles are required f o r each strand whereas f o r the bloom, a single nozzle per strand i s used.  For the casting of aluminum k i l l e d steels, the  bloom tundish i s f i t t e d with a four-holed submerged entry shroud.  The  input streams from the shroud are directed perpendicular to the mold face and are i n c l i n e d 15° above the horizontal. powder lubricant i s used i n the mold.  When using a shroud, a slag  The l i q u i d metal l e v e l i n the mold  i s controlled manually by varying the withdrawal rate (1.5 to 1.7 cm./sec.) of the strand.  The t o t a l distance from the meniscus l e v e l i n the mold to  the tangent r o l l i n the straightener i s 16.7 m., with ari additional 15.8  m.  32  to the torch cut-off units.  The molds are o s c i l l a t e d s i n u s o i d a l l y with a stroke length of 1.9 cm.  The frequency of o s c i l l a t i o n i s matched to the casting speed.  A l l molds are hard chrome plated to improve mold l i f e and reduce mainten32 ance.  The bloom molds are of plate construction  , comprised of 3.8 cm.  copper plates, with a 0.317 cm. corner radius and a 0.152 cm. taper on the nonradial  sides. The f i r s t generation ('A  1  p r o f i l e , Test A&l) beam blank molds  consist of a s o l i d copper block s p l i t into two segments about the centrel i n e of the flange faces. bolts.  The mold halves are t i g h t l y clamped by jack-  Cooling of the mold i s accomplished by means of  3.12 cm. diameter  water-cooling channels d r i l l e d around the perimeter of the mold cavity. The second generation ('E' p r o f i l e , Test A£2) beam blank mold i s d i f f e r e n t from the first-generation i n that the flange face portion of the molds are i d e n t i c a l to plate mold sections.  The remainder of the mold i s s i m i l a r to  the first-generation mold ( i . e . , s o l i d block copper with cooling water 33 passages).  The second-generation molds are considerably  less expensive  and are easier to machine than the f i r s t - g e n e r a t i o n molds. 3.1.6.  U.S. Steel The casting machine at the United States Steel plant at South  Works, Chicago, i s a four strand, straight mold, v e r t i c a l type casting machine with bending (Figure 6(a)). b i l l e t s at speeds up to 8.5 cm./sec. speed i s usually 5.5 cm./sec.  I t was designed for casting 19 cm. During normal production the casting  Automatic mold l i q u i d - l e v e l control i s used.  This device uses thermocouples i n the top portion of the mold to determine  33 the l i q u i d l e v e l and automatically varies the withdrawal r o l l s to keep this l e v e l constant.  On exit from the casting machine the b i l l e t passes  through a system of i n - l i n e induction heating and i n - l i n e r o l l i n g , producing  3.2.  2 2 a semifinished product from 10 x 10 cm. to 15 x 15 cm. .  Procedure  The tests were conducted during normal operations i n the plant. Stable casting conditions were obtained by waiting u n t i l half of the heat had been poured before adding the radioactive materials. r a d i o a c t i v i t y used i n each test are given i n Table V.  The amounts of  In some tests the  l i q u i d temperature i n the mold was measured p r i o r to the addition of the radioactive gold. contained  Measurements were made with a Pt-Pt 13% Rh thermocouple  i n a quartz sheath. 198 Radioactive gold (Au  - B + y, h a l f - l i f e 2.7 days), i n the form  of a small cylinder 0.32 cm. i n diameter by 0.63 cm. long, was added to the l i q u i d pool i n the mold by i n s e r t i n g a 0.64 cm. diameter s t a i n l e s s s t e e l rod containing the gold into the pool d i r e c t l y below the input stream. For tests conducted on the beam blanks and the slab, two gold additions (one to each input stream) were made to each strand, whereas i n a l l other tests a single addition was made.  The s t a i n l e s s s t e e l rod, inserted into the l i q u i d  to a depth of approximately 15 cm. below the meniscus, melted within 5 sec. releasing the gold into the pool.  In some tests a tungsten p e l l e t , 1.25 cm.  i n diameter by 1.25 cm. long containing two m i l l i c u r i e s of C o ^ , was dropped Into the pool d i r e c t l y below the input stream simultaneously with the gold addition.  The p o s i t i o n of the p e l l e t i n the s t e e l was located with a geiger  counter subsequent to casting and related to the determined p o s i t i o n of the  Table V.  Test No.  Wla  Experiment, C a s t i n g Parameters and P o o l Depth.  Experiment  Total Au  Activity used (mC)  1 9 e  W-pellet  -  Tundish Teeming  Open pour  Temperature Tundish Mold  CC)  CO  -  1493  Surface Temp. Straightener  CC)  -  Cc) 5.3  Casting Speed (cm sec.')  Gold (m)  -  (VsecT^lO ) 8.2  505  2.54  3.07  8.23  1.69  2.54  4.40  1.80  3.71  2  2  1  Wlb  4.2  400  Wlc  3.5  335  1.48  419  2.37  W2a " W - p e l l e f  Open pour  W2b  -  1499  -  W2c  4.0  P o o l Depth Tungsten Calc. (m) (m)  Mold Heat Flux (kcal m~ sec, )  Mold Water Flow Rate AT  8.2  3.5  335  1.78  3.3  315  1.56  -  3.53  7.41  2.26  4.76  1.85  4.00  -  9.15  Ml  Gold  75  1513  1500  1055  4.7  2.78  358  3.5  3.0  M2  Gold + W - p e l l e t  75  1513  1500  1055  5.0  2.78  380  4.4  3.0  M3  Gold + W - p e l l e t  75  1527  1010+11  5.6  2.54  510  4.65  2.5  3.25  M4  Gold + W - p e l l e t  75  1544  6.1  2.61  572  5.5  2.5  3.7  Atl  Gold + W - p e l l e t  400  Immersed shroud  1480  -  8.5  5.68  324  1.65  2.3  2.65  All  Gold + W - p e l l e t  500  Open pour  1546  4.09  335  1.52  2.0  2.28  Gold  500  Open pour  1532  -  8.6  AJ.2  900  8.4  4.24  297  1.48  1.5  AO  Gold + W - p e l l e t  200  Open pour  1541  900  5.0  3.41  308  1.56  3.3  AM  Gold  200  Immersed shroud  1525  -  900  4.2  3.49  262  1.69  1.8  -  14.9  Ul  Gold  200  Open pour  1540  -  -  8.3  5.36  575  5.5  2.8  -  32.3  * ** t  Open pour  -  1504  -  1507  -  One-dimensional I n t e g r a l P r o f i l e and F i n i t e d i f f e r e n c e estimate o f p o o l depth. Pool depth beneath input stream. Estimated from p o s i t i o n of p e l l e t - 693 cm., below meniscus.  6.0  -  1060'  12.54 7.35 9.52 3.72-5.36* 7.3** 7.1** 12.9  35 meniscus.  The position of the p e l l e t i n r e l a t i o n to the central axis  of the strand was found by flame cutting through the strand to expose the  pellet. After the strand had cooled, i t was flame cut into sections,  along planes both p a r a l l e l and transverse to the longitudinal central axis.  The cuts p a r a l l e l to the central axis were perpendicular to the  plane of curvature.  After cutting, the exposed surfaces were milled and  then autpradiographed by placing the milled surface on X-Ray f i l m . Exposure times varied from 1 hour to 4 days, depending on the a c t i v i t y of the p a r t i c u l a r section.  The outer edge of the section being auto-  radiographed was delineated by the section to l i g h t .  on the f i l m by exposing the f i l m not covered  36  4.  4.1.  RESULTS  Liquid Mixing, Solid Shell and Cast Structures  4.1.1.  General Observations of the Test Results In Tables V and VI, the s t e e l composition, type of experiment,  casting parameters and pool depths are given for a l l of the tests. Composite photographs of the autoradiographs  showing the d i s t r i b u t i o n of  gold i n the l i q u i d pool for the tests are presented i n Figure 7 for Manitoba R o l l i n g M i l l s , Figure 10 for Atlas Steel, Figures 13, 16, 20 and 23 for Algoma Steel and Figure 27 for U.S. autoradiographs  Steel.  In a l l cases the  of the longitudinal and transverse sections from each  strand have been positioned to conform with the curvature of the strand in and below the mold, and have been separated by a distance equivalent to the thickness of metal removed i n the cutting process.  A l l of the  longitudinal sections have been sectioned perpendicular to the plane of curvature.  The s o l i d s h e l l at the time radioactive gold was  added to  the l i q u i d i s c l e a r l y delineated i n each strand as a white band on either side of each section.  Between the two s o l i d s h e l l s , the dark region  results from the presence of radioactive gold i n the b i l l e t .  The dark  regions surrounding each section are caused by exposing the f i l m to l i g h t . The start of the s o l i d s h e l l i n the longitudinal sections indicates the  Table VI.  Test No.  Heat No.  Wl  Steel  Compositions  Steel C  Mn  18084  0.31  1.11  0.05  W2  18140  0.35  0.67  M1,M2  62737  0.11-0.16  M3  52603  M4  S  Rati<  Si  Cu  Cr  0.04  0.15  0.35  0.17  0.21  22  0.025  0.02  0.10  0.24  0.13  0.17  27  0.60-0.75  0.05  0.04  0.2-0.3  0.037  13  0.13-0.18  0.60-0.75  0.05  0.04  0.2-0.3  0.037  13  52604  0.33-0.37  0.90-1.05  0.05  0.04  0.22-0.32  0.037  20  Ati  26018  0.065  1.77  0.016  0.029  0.47  Ail  8 7 52A  0.21  1.17  0.032  0.018  0.24  37  AJ12  6257D  0.22  1.03  0.017  0.013  0.25  61  AM  8756A  0.20  0.92  0.028  0.013  0.34  33  AM  6256D  0.30  1.32  0.023  0.013  0.30  57  Ul  KD3252  0.015  0.03  0.21-0.24  0.65-0.80  P  Composition  0.17-0.27  0.23  0.15  18.31  0.20  Mo  0.33  0.02  Ni  8.75  0.10  Pb  0.003  Mn/S  -  48  LO  38 position of the meniscus when the gold was  added to the l i q u i d pool.  Using t h i s p o s i t i o n as a reference, the top and the bottom of the mold are shown by h o r i z o n t a l l i n e s . marked IR, the outside  The inside radius of the strand i s  OR.  In the composite photographs the s o l i d s h e l l i s observed to be sharply delineated at the s o l i d - l i q u i d interface i n the mold i n d i cating the mold l i q u i d region i s w e l l mixed.  Below the mold the s h e l l  becomes less d i s t i n c t , accompanied by a marked increase i n the apparent s h e l l thickness due to incomplete mixing i n the l i q u i d pool.  In the upper part of the strands the middle of each section i s depleted i n gold.  This i s attributed to the d i l u t i o n of the gold by  the input stream, i n agreement with previous observations ^.  The central  depleted region usually extends to near the bottom of the mold.  Also i n  the upper part of the strands i n some tests, alternate l i g h t and dark bands (banding) i n d i c a t i n g gold r i c h and gold depleted regions can be observed i n the transverse section  autoradiographs.  Below the mold the autoradiographs show the gold to be distributed i n the form of an inverted cone.  In most of the strands cast  using a curved mold, more gold has deposited on the outside radius  inter-  face of the casting than on the inside radius interface (compare Test M3 i n Figure 7 to test Ul i n Figure 27).  This behaviour i s usually  associated with buoyancy e f f e c t s i n the l i q u i d , the high density gold f a l l i n g further before being mixed i n the l i q u i d pool.  The depth of penetration of the radioactive gold i s less than the pool depth indicated by the p o s i t i o n of the tungsten p e l l e t .  The  depths of penetration of the p e l l e t and the gold are given i n Table V. In some t e s t s , fluctuations i n s h e l l thickness i n the longitudinal sections i n the upper mold region are observed (Figure 8(a) and (b)).  A closer examination of the fluctuations reveals that usually  there i s a depression  (or r i p p l e mark) i n the surface of the b i l l e t  wherever there i s a decrease i n s h e l l thickness.  In addition a small  amount of s o l i d s h e l l can be observed above the p o s i t i o n of the meniscus i n Figure 8(b).  This indicates that a small segment of the s h e l l has  stuck to the mold wall and been torn from the s h e l l when the mold moves upward.  These fluctuations have been observed i n tests using a flux  lubricant and on tests using rapeseed o i l lubricant i n the mold.  In  general, the fluctuations are small and tend to disappear by the time the strand leaves the mold.  The autoradiographs  of the transverse sections indicate that  there i s no s i g n i f i c a n t difference i n average s h e l l thickness along the face centres i n the molds i n any of the tests.  However, i n several of  the tests on the blooms and b i l l e t s , appreciable thinning of the s o l i d s h e l l at the corners (re-entrant corners) was observed. The average s h e l l thickness i n the mold has been measured f o r a l l the tests and compared to calculations of s h e l l thickness based on : heat transfer considerations.  These r e s u l t s are reported i n a l a t e r  section.  The cast structure i n most of the strands consists of columnar grains growing from the outside surface i n a d i r e c t i o n perpendicular to the outside faces and an equiaxed d e n d r i t i c structure i n the central  region of the casting.  A displacement of the casting centreline from the  geometric centre of the strand i s observed i n strands cast using curved molds.  In these strands the equiaxed zone i s displaced toward the  outside radius, r e s u l t i n g i n the zone adjacent to the inside radius being nearly e n t i r e l y columnar and a shortened columnar zone adjacent to the , outside radius.  In strands cast using v e r t i c a l molds no s h i f t i n the  centreline of the casting was observed.  In equiaxed zones of the castings some dendritic bridging of the central region with solute r i c h l i q u i d f i l l i n g the c a v i t i e s below the bridging points i s observed.  Macrosegregation, taking the form of V  shaped segregation,is also evident i n some cases. Extensive i n t e r d e n d r i t i c r a d i a l cracking i s observed i n strands which have a Mn/S r a t i o less than 50 (see Table VI).  The cracks are f i l l e d  with l i q u i d enriched with gold and sulphur (since they appear as dark l i n e s in the autoradiographs and sulphur p r i n t s ) , and are not observed on the machined surfaces.  A l l the a l l o y i n g elements which have a segregation co-  e f f i c i e n t less than unity i n iron (sulphur, phosphorus, carbon, etc.) w i l l also be enriched i n the l i q u i d f i l l i n g the cracks, producing compositional inhomogenieties i n the strand which can only be reduced by s o l i d state diffusion.  Intergranular centreline cracking, the cracks being f i l l e d with  solute r i c h l i q u i d , was also observed i n some strands.  Small dark spots can be observed i n a number of the autoradiographs; many of the spots can be d i r e c t l y related to sulphur r i c h spots i n ^ sulphur print of the same surface.  These spots have been found to be  clumps of manganese sulphide inclusions, approximately 100 to 500u i n diameter, by electron probe m i c r o a n a l y s i s ^ .  The small dark areas tend to  Table VII.  Test No.  Casting Characteristics from  Autoradiographs.  Banding  Shell Tearing at Meniscus  13.3x13.3  X  X  X  13  13.3x13.3  X  X  X  70  13  10.1x10.1  X  X  70  20  10.1x10.1  X  X  -  12.7x109  X  Depth of Penetration by Input Stream (cm)  Mn/S Ratio  Ml  90  13  M2  90  M3 M4  Casting Size  Re-entrant Corners  Centreline Cracking  (cm ) 2  X  Ati  100  AA1  90  37  843  X  A£2  50  61  1015  X  A£3  120  33  22.9x26.7  X  A£4  50  57  22.9x26.7  X  X  X  110  48  19x19  X  X  X  Ul  Radial Cracking  X X  X X X X X  42 be concentrated i n a band p a r a l l e l to the inside radius surface i n the curved castings, Table VII gives a summary of the tests i n which some of these defects iii the casting were observed.  4.1.2.  Specific Observations; Manitoba Rolling M i l l s In a l l four tests the s h e l l thickness i n the l o n g i t u d i n a l  sections i n the mold were observed to fluctuate appreciably.  Note i n  sectipn D of Test M2 (IR)(Figure 7) the s h e l l i s about half the average $he11l thickness just before the b i l l e t leaves the mold.  The frequency of  the fluctuations do not appear to be periodic and cannot be d i r e c t l y related to mold o s c i l l a t i o n s .  In Figure 8(a)  a depression at the  surface  of t;he b i l l e t i s shown wherever there i s a decrease i n s h e l l thickness. In addition i n section 1A, Figure 8(b), a small segment of the s o l i d s h e l l can be observed above the meniscus. Variations i n s h e l l thickness across the b i l l e t i n Tests M2 and M4, are shown i n Figures 9(a) and 9(b) respectively.  Also i n Figure 9(b),  Test M4, an appreciable thinning of the lower corners i s observed. In Tests Ml and M2 the centrelines of the castings are displaced towards the lower radius surface by 0.3 cm. from the geometric centre.  The  columnar structure extends 4.4 cm. i n from the inside radius and 2.5 cm. i n from the outside radius  surface.  Some centreline porosity was observed on the machined surface of the b i l l e t s for Tests Ml and M2, and i n the autoradiographs Figure 7, section 2G).  (see  Gold r i c h central regions with periodic bridging  44  F i g u r e 8.  (a) S e c t i o n 2C of F i g u r e 7, showing s h e l l and a s s o c i a t e d d e p r e s s i o n s i n surface. (b) S e c t i o n 1A of F i g u r e 7, showing above meniscus. (c) S e c t i o n 2E of F i g u r e 7, showing region with p e r i o d i c b r i d g i n g across laree dendrites.  t h i n r e g i o n s of the the o u t e r b i l l e t solid shell  segment  gold r i c h c e n t r a l the c e n t r e l i n e by  45  F i g u r e 9.  A u t o r a d i o g r a p h s of t r a n s v e r s e s e c t i o n s of s t r a n d s at p o s i t i o n s i n d i c a t e d below meniscus. (a) s t r a n d M2, (b) s t r a n d M4.  46 across the centreline by large dendrites i s shown i n Figure 8(c). In Tests M3 and M4 (10.1 cm. b i l l e t s ) the bulk of the cast structure consists of small d e n d r i t i c grains.  There i s no apparent  columnar region or centreline s h i f t .  Extensive r a d i a l cracking was observed i n the inside radius half, of the b i l l e t s i n Tests Ml and M2 (see Figure 8 ( c ) ) .  Clumps of  sulphide inclusions i n the inside radius half were also observed.  4.1,3.  Atlas Steel  The s o l i d - l i q u i d i n t e r f a c e i n the mold i s smooth and regular with no s i g n i f i c a n t  thickness f l u c t u a t i o n s . A closer examination of the  s h e l l i n section C2, Figure 11, indicates the interface breaks down to a dark l i n e separated  from the general dark area by a thin gold free region.  Moving down the slab, the dark l i n e terminates, r e s u l t i n g i n a l o c a l apparent increase i n the s h e l l thickness. the flow pattern i n the l i q u i d pool.  This e f f e c t i s attributed to  Some thinning of the s o l i d s h e l l i s  observed near the outside corner of series L (Figure 10).  The round clear  region i n the lower l e f t corner of section 3L i s the outline of the corner marker placed i n t h i s p o s i t i o n when the gold was added to the l i q u i d pool.  The f l u i d flow pattern i n the l i q u i d pool, based on the gold d i s t r i b u t i o n shown In Figure 10 i s complex.  (a) A dark l i n e i s observed  to be present around part or a l l of the periphery of the sections i n series L and R, associated with the f i r s t stream of gold r i c h l i q u i d which washes the solldr-liquid interface and was frozen i n .  In series L, section 1, 2,  and 3 have a dark band around the entire periphery of the section. Sections 4 to 7 have a dark l i n e around the end of the slab and p a r t l y up  47  c  F i g u r e 10.  A u t o r a d i o g r a p h s of l o n g i t u d i n a l and t r a n s v e r s e s e c t i o n s of s t a i n l e s s s t e e l s l a b , T e s t A t l . The p o s i t i o n s of the t r a n s v e r s e s e c t i o n s w i t h r e s p e c t to the meniscus are indicated.  48 the side, extending further toward the middle on the top side.  In  section 9 and below, there i s no dark l i n e at the slab ends; dark l i n e s are present i n section 9 on the large faces i n the central part of the slab.  (b) Adjacent to the s o l i d - l i q u i d interface i n the l i q u i d pool,  gold i s d i s t r i b u t e d i n a series of bands, approximately 0.4  the  cm. wide.  The  edge pf each ban,d appears to correspond to the trace of the s o l i d - l i q u i d interfape.  The bands are most c l e a r l y delineated i n sections L2 to L7,  02 and 03.  (c) The a c t i v i t y i n the slab, both above and below the meniscus  at the time of addition of the gQld, was measured with a geiger counter before the slab was  sectioned.  The r e s u l t s are shown i n Figure 12, i n  which the a c t i v i t y r e l a t i v e to the a c t i v i t y at the meniscus at the edge, i s plotted as a function of p o s i t i o n along the slab for the edge, 15 from the edge  ?  and along the middle of the slab face.  cm,  The figure shows  that the d i s t r i b u t i o n of gold above the meniscus i s very s i m i l a r to that below the meniscus, even though the mode of d i s t r i b u t i o n of the gold must be markedly d i f f e r e n t i n both regions.  At the meniscus the a c t i v i t y i s  higher at the edge; below the meniscus the three sets of measurements e s s e n t i a l l y coincide; above the. meniscus the a c t i v i t y i s highest at the centre.  Tfte cast structure In t;he slab consists of columnar grains with a r e l a t i v e l y narrow band of equiaxed grains i n the centre. sections (L8 to L10)  In some  small gold free spots with an apparent dendritic;  st;ruci;ure were observed i n the central part of the slab.  R e l a t i v e l y dark  structureless spots were alsp observed.  The c e n t ^ r l i n e of the strand consists of a coarse dendritic structure separated by gold r i c h regions. the centreline of the transverse  The dendritic structure along  sections becomes less d i s t i n c t and then  Figure  11.  S e c t i o n 2C of F i g u r e 10, showing d i s c o n t i n u i t y i n s h e l l thickness. Top of a u t o r a d i o g r a p h 15.7 cm. below meniscus.  Direction of Withdrawal  150 •  100 «A D  \ .  50  Meniscus •A" J <  I  50  100  a 150  t  •  Edge  A  15 cm  From  D  Center  of  Edqe  Slab  200  04 Relative  Figure  12.  08 Intensity  D i s t r i b u t i o n of r a d i o a c t i v e gold slab p r i o r to sectioning.  i n the s t a i n l e s s s t e e l  51 dijLsappearp, moving from the middle t o t h e end f a c e of the s l a b .  4.1.4.  4.1.4.1.  Algoma S t e e l  Beam Blanks  The  r a d i o a c t i v e g o l d was w e l l mixed i n the l i q u i d p o o l i n t h e  A p r o f i l e beam blank,  o u t l i n i n g the s o l i d  s h e l l t o about 107 cm. below  tbje meniscus ( F i g u r e 1 3 ) . At t h e meniscus i n s e c t i o n C l , s m a l l s e c t i o n s of the s h e l l were observed t o be p r e s e n t tinuous s h e l l .  2.5 t o 3.2 cm. above the con-  Below t h e meniscus the s h e l l t h i c k n e s s f l u c t u a t e s  p e r i o d i c a l l y , t h e d i s t a n c e between f l u c t u a t i o n s b e i n g 3.2 cm.  Note t h a t  the break i n t h e s h e l l i n s e c t i o n C2 i s an a r t i f a c t a s s o c i a t e d w i t h t h e flame c u t t i n g o p e r a t i o n .  F u r t h e r below t h e meniscus ( C l , C2, C3) t h e r e  a r e f l u c t u a t i o n s i n s h e l l t h i c k n e s s o f much g r e a t e r magnitude than associated with t e a r i n g .  These f l u c t u a t i o n s correspond  those  to a thinning of  the s h e l l i n the web a r e a o f t h e t r a n s v e r s e s e c t i o n s B3, B6, and B8.  In s e c t i o n s B l t o B5, l o c a l i z e d t h i n n i n g o f the s h e l l can be observed near the c e n t r e o f the f l a n g e f a c e .  T h i s i s a t t r i b u t e d t o a 1.5  cm. spacer p l a c e d between t h e two mold h a l v e s r e s u l t i n g i n poor thermal c o n t a c t between the s t r a n d and t h e mold.  Note the dark a r e a i n the c o r n e r  of B l i s an a r t i f a c t due t o l o c a l overexposure o f the f i l m t o l i g h t .  Deformation of t h e s o l i d s h e l l i n t h e web f i l l e t f a c e and f l a n g e t i p p f t h e beam b l a n k i s seen i n F i g u r e  The  area,  flange  14(a).  c e n t r a l l i n e o f t h e c a s t s t r u c t u r e i s observed t o be  d i s p l a c e d 0.2 cm. from the geometric c e n t r e o f t h e beam b l a n k t o t h e o u t s i d e r a d i u s , the columnar zone extending  i n t h e web 3.3.cm. i n from  F i g u r e 14.  (a) A u t o r a d i o g r a p h B6 of F i g u r e 13. (b) Sulphur p r i n t of same s u r f a c e as i n ( a ) .  F i g u r e 15.  (b) (a) (a) A u t o r a d i o g r a p h o f c e n t r a l p o r t i o n o f C l , F i g u r e 13. (b) Sulphur p r i n t of same s u r f a c e as i n ( a ) . . Note t h a t the c i r c l e i s an a r t i f a c t and i s not s i g n i f i c a n t .  Direction of  150  100  o A  o  200  Test  4  Inside Test Center Test * Center  Radius Foce 2 Beam Blank of Sooth Flange 2 Beam Blank ot Web  04 Relative  F i g u r e 17.  Bloom  06  Face  08  intensity  D i s t r i b u t i o n o f r a d i o a c t i v e gold i n E beam blank and Test A U bloom.  54 the outside radius and 4,8  cm.  i n from the inside radius.  ^mall r a d i a l clacks (Figures 14 and 15) were observed i n a l l the specimens autoradipgraphed, 3.6 cm  T  They tended to be i n a region (a) 2.6  from the outside radius surface i n the web  from the outside radius surface i n the web  (b) 1.7  f i l l e t and  tp  to 3.6 cm. i n  (c) 1.9  to 3.3  cm.  fn frpra the flange surface; near the inside radius of the flange t i p . centreline porosity pr cracking was  No  observed i n the strand.  Chumps of inclusions forming a band p a r a l l e l to the inside radius surface can be seen i n Figure 14(a) and  Evident throughout  the web  (Figures 15(a) and  (b).  Also inclusions are  (b)), some at positions  r e l a t i v e l y close to the outer surface where l i t t l e solute segregation between the f i n e columnar dendrites would, occur. In the E p r o f i l e beam blank (Figure 16) the s o l i d s h e l l i s sharply delineated to about 65' cm. below the meniscus.  Less mixing of  the gold i n the l i q u i d pool occurred i n t h i s test than i n the A beam blank. Pripr to sectioning, the. d i s t r i b u t i o n of gold i n the casting was measured with a geiger counter along the web  and flange faces.  The  results pf which are shown l n Figure 17. Shell thickness variations accompanied by surface r i p p l e marks and tearing at the meniscus were observed i n the l o n g i t u d i n a l sections i n series E, Figure 1^,  The fluctuations and r i p p l e marks were spaced at  approximately 3,1 cm,  intervals.  In the transverse sections of the strand, i t i s evident that  F i g u r e 16.  Composite o f a u t o r a d i o g r a p h s of beam blank E showing the p o o l p r o f i l e down the web (E) and p e r p e n d i c u l a r to the longitudinal axis (F).  56  F i g u r e 18.  Sulphur p r i n t o f s e c t i o n F4, F i g u r e 16 showing clumps of s u l p h i d e i n c l u s i o n s and c e n t r e l i n e c r a c k i n g .  if  l • T i f  i  #•  F i g u r e 19.  (a) Aucorad i o g r a p h (a) and s u l p h u r p r i n t (b) o f a d j a c e n t areas of E2, F i g u r e 16 showing clumps o f s u l p h i d e i n c l u s i o n s and solute enriched c e n t r e l i n e cracks. 0 0|—g  0 4 1  n  1  Shell Thickness  (cm)  0 8 1  16  2  1  o  1——i  1  1  20 1  1  24  jo  o average shell thickness A Minimum shell t^.xkness (reentranl corners)  0 I  0.5  02 °0 o  0 3  a 04-  S 03  |  I 5  5  20  S  05 Mold Bottom 06  a 07  • 25 08  09.  F i g u r e 21.  02  04  06  0.8  Shell Thickness (in)  S h e l l c o r n e r and average s h e l l t h i c k n e s s as a f u n c t i o n o f d i s t a n c e below meniscus.  58 the s h e l l thickness i s highly uniform around the periphery of the beam. Note that the s h e l l sections missing i n the flange of F3 and F4 are a r t i f a c t s due to cutting.  '  Although there was no evidence of r a d i a l cracking i n the beam blank, extensive intergranular cracking occurred along the central plane of the web i n a l l of the sections examined.  The cracking i s evident i n  the web i n Figure 18 and i n the autoradiograph and sulphur p r i n t i n Figure 19.  In Figure 18 the sulphur p r i n t of the transverse section shows a much higher density of inclusions than observed previously, most oi; which are uniformly d i s t r i b u t e d throughout the beam.  4.1.4.2.  Blooms The extent of mixing of the radioactive gold i n the two tests  done on the blooms i s markedly d i f f e r e n t .  In the f i r s t test, A£3  (Figure 20), open teeming was used between the tundish and the mold resulting i n a sharply outlined interface for a distance of 180 and 135 cm. below the meniscus f o r the outside radius and the inside radius interfaces respectively.  In the second test, A£4 (Figure 23), a submerged entry  shroud was used i n the tundish r e s u l t i n g i n a penetration of gold i n the l i q u i d pool half that i n Test A£3.  The graph i n Figure 17 shows that with  the shroud, there was an equal d i s t r i b u t i o n of gold above and below the meniscus, with a decrease i n i n t e n s i t y at the meniscus.  Also very l i t t l e  mjLxin^ of the gold occurred i n the lower parts of the pool.  Preferential  flow down the outside radius i s evident i n sections L5, 6, and 7.  Figure  20.  Composite  of  the  pool  the  strand  autoradiographs  profile axis  down (H,K).  the  of  strand  bloom, (G)  Test  and  A5-3,  showing  perpendicular  to  60  R  F i g u r e 22.  (a) A u t o r a d i o g r a p h G25 i n F i g u r e 20. (b) Sulphur p r i n t of same a r e a as ( a ) .  Figure 23.  Composite of a u t o r a d i o g r a p h s of bloom, Test A2.4, showing the p o o l p r o f i l e down the s t r a n d (L) and p e r p e n d i c u l a r t o the s t r a n d a x i s (M,N).  62 In Test A&3,  the s o l i d s h e l l i n the v e r t i c a l sections appear  to be even and regular with no s i g n i f i c a n t fluctuations i n thickness.  In  the transverse sections re-entrant corners can be observed on the inside radius, the corners remaining  thin at about half the s h e l l thickness at  the centre (Figure 21).  In Test A&4, meniscus (section L l ) .  there i s evidence of tearing occurring at the Surface r i p p l e marks at 3.5 cm.  intervals  correspond to s h e l l fluctuations i n longitudinal sections.  In the mold  region the s h e l l i s reasonably uniform i n thickness (irregular shape i n L3 and L4 due to incomplete mixing of gold i n the l i q u i d pool)•  In this  test i t was noted that the submerged shroud was off centre, tending to point to the south-outside radius corner.  The misalignment of the shroud  had no observable e f f e c t on the s h e l l thickness around the periphery of the bloom. observed  Re-entrant  corners with corresponding corner cracking were  on the inside radius corners, the corner crack being f i l l e d with  gold and sulphur r i c h material (Figure 24(a) and (b)). In the open pour bloom the columnar structure extended 10 and 6.3  cm.  cm. i n from the inside and outside radius surface r e s p e c t f u l l y .  Macrosegregation, not marked.  taking the form of V shaped segregation, i s evident, but  No r a d i a l or centreline cracking was observed  sections, nor was  there any centreline porosity.  i n any of the  Large clumps of sulphide  inclusions are concentrated i n a band 2.3 cm. from the inside radius surface as shown i n Figure 22(b).  Sulphur r i c h areas are also present i n  the centre of the bloom which can be d i r e c t l y related to gold r i c h areas in Figure 22(a).  61  F i g u r e 24.  F i g u r e 26.  A u t o r a d i o g r a p h (a) and s u l p h u r p r i n t (b) of s e c t i o n N l , F i g u r e 23 showing c o r n e r c r a c k f i l l e d w i t h g o l d and s u l p h u r r i c h m a t e r i a l a t A.  Sulphur p r i n t of s e c t i o n M5, F i g u r e 23 showing c e n t r e l i n e i n t e r g r a n u l a r c r a c k s f i J L l e d w i t h sulphur r i c h r e s i d u a l l i q u i d .  64  OR  Figure  25.  Sulphur p r i n t of p a r t of s e c t i o n L l , F i g u r e V segregate p a t t e r n .  23 showing  65 In the test using the submerged shroud the major part of the bloom consisted of cored, d e n d r i t i c , equiaxed grains with no resolvable columnar zone. particularly  Macrosegregation of the gold and sulphur were observed,  i n sections L l (Figure 25) and M5 (Figure 26), i n the form  of V shaped pipes.  Again no evidence of r a d i a l cracking was observed  but some centreline cracking did occur, as shown i n the sulphur print of M5.  The centreline cracks are intergranular and intermittent, occurring  i n some sections and not others.  No s i g n i f i c a n t numbers of large  sulphide inclusions were observed.  4.1.5.  U.S. Steel  In section A2, Figure 27, i t i s evident that the s o l i d s h e l l starts much lower on the South side than on the North side.  The trans-  verse section, B2, also shows a s o l i d s h e l l on the North side and a p a r t i a l s h e l l on the South.  Note that i n the Southwest corner of B2,  Figure 28, some radioactive gold has entered behind the s o l i d s h e l l f o r about 2 cm. from the corner suggesting already  s h e l l separation at the corner has  occurred. Variations i n s h e l l thickness i n the l o n g i t u d i n a l sections A2  and A3 and re-entrant corners i n the transverse sections B3 to B6 were observed.  The fluctuations i n the l o n g i t u d i n a l sections are small and  are comparable to those that occur i n Test A£4.  The cast structure consists of a highly regular columnar zone, to about 5.5 cm. from the outside surface, and a cored d e n d r i t i c equiaxed zone.  In the columnar zone the primary dendrite spacing was measured as  a function of distance from the outside surface.  The r e s u l t s of these  F i g u r e 27.  Composite of a u t o r a d i o g r a p h s o f b i l l e t , Test U l , showing the p o o l p r o f i l e down the s t r a n d (A) and p e r p e n d i c u l a r to the s t r a n d a x i s (B).  67  Figure 30.  Section B5 of Figure 27, showing radial cracking in transverse section.  measurements a r e g i v e n i n F i g u r e 29. r i c h p i p e s can be observed  ( s e c t i o n A9)  Radial cracking occurred  c o r n e r s , 1.5  the N o r t h f a c e ;  to 2.5  2. 3.0  cm.  to 3.5  cm.  forming  i n s e c t i o n B5,  Some evidence In s e c t i o n A10,  Figure  a V pattern.  a r e : 1. near the Southwest  and  from the o u t s i d e s u r f a c e p a r a l l e l from the East f a c e and  from the West f a c e p a r a l l e l to the N o r t h f a c e . observed  68  zone, s o l u t e  i n most of the s e c t i o n s examined.  Areas where r a d i a l c r a c k s were found Southeast  In the equiaxed  2.5  to  to 4.0  These c r a c k s can  cm.  be  30.  of c e n t r e l i n e p o r o s i t y was  observed  i n the  billets.  the dark r e g i o n s i n the upper p a r t of the s e c t i o n c o r r e -  spond to h o l e s .  4.2.  4.2.1.  C a l c u l a t e d and Measured P o o l P r o f i l e s and P o o l Depths  General  Comments  In T a b l e V the v a l u e s of the c a s t i n g parameters measured d u r i n g the t e s t s , the measured mold heat p o o l depths are l i s t e d .  The  f l u x e s and  l e n g t h s and heat  the measured and c a l c u l a t e d t r a n s f e r c o e f f i c i e n t s of  s u c c e s s i v e spray zones are g i v e n i n T a b l e I I I .  In T a b l e I the thermo-  p h y s i c a l p r o p e r t i e s of s t e e l used i n the models and the mold heat  t r a n s f e r c o e f f i c i e n t , h^  pool p r o f i l e s  i n the mold and  were c a l c u l a t e d .  i n the c a l c u l a t i o n of  (Table I I ) , are p r e s e n t e d .  these v a l u e s i n the f i n i t e d i f f e r e n c e and  the  Using  i n t e g r a l p r o f i l e models, the  submold r e g i o n s and  s t r a n d s u r f a c e temperatures  The r e s u l t s a r e p l o t t e d i n F i g u r e s 31 to  40.  69 4.2.2.  C a l c u l a t e d and Measured P o o l P r o f i l e s i n t h e Mold  In the f i g u r e s showing t h e p o o l p r o f i l e i n the mold r e g i o n , ( F i g u r e s 31 t o 3 5 ) , curves A and B were c a l c u l a t e d u s i n g the onedimensional  f i n i t e d i f f e r e n c e model w i t h e q u a t i o n s  i v e l y t o d e s c r i b e t h e s u r f a c e heat f l u x . and  32(b),  (7) and (6) r e s p e c t -  F o r comparison, i n F i g u r e s 31  the i n t e g r a l p r o f i l e model was used t o c a l c u l a t e the p o o l  p r o f i l e g i v i n g curves  C and D w i t h e q u a t i o n s  (7) and (6) r e s p e c t i v e l y t o  define q . o The  s h e l l t h i c k n e s s o f the c a s t i n g as a f u n c t i o n o f d i s t a n c e  below the meniscus was measured from t h e a u t o r a d i o g r a p h s .  These  measurements were made on the l o n g i t u d i n a l s e c t i o n s , i . e . , a t the midp o i n t o f the o u t s i d e and i n s i d e r a d i u s f a c e s .  F i g u r e s 31 and 33 show the  v a r i a t i o n i n s h e l l t h i c k n e s s between the o u t s i d e and i n s i d e r a d i u s f o r the s t a i n l e s s s t e e l s l a b and a 10.1 cm. b i l l e t  (Test M3).  In a l l other  f i g u r e s , the average o f t h e s h e l l t h i c k n e s s from t h e two s i d e s i s p l o t t e d along w i t h the c a l c u l a t e d s h e l l  4.2.3.  thickness.  C a l c u l a t e d and Measured P o o l Depths  The  p o o l depths f o r the s t a i n l e s s s t e e l s l a b ( F i g u r e 36) and f o r  the web and f l a n g e areas (Tests A£l and All, dimensional  (shaded areas  i n F i g u r e 38) o f the beam  blanks  F i g u r e s 39(a) and (b)) were c a l c u l a t e d w i t h the one-  f i n i t e d i f f e r e n c e model.  In F i g u r e 36, Test A t i , the p o o l  p r o f i l e s have been c a l c u l a t e d w i t h b o t h t h e f i n i t e d i f f e r e n c e model (curves A and B) and the i n t e g r a l p r o f i l e model (curve C ) . b l a n k s , curves A and B, f o r t h e web and f l a n g e areas  F o r the beam  r e s p e c t i v e l y , were  calculated with the f i n i t e difference model and curve C with the i n t e g r a l p r o f i l e model.  For the tests on the blooms and b i l l e t s  (Table V) the pool  depths were calculated with the two-dimensional f i n i t e difference model. The p o s i t i o n of tungsten p e l l e t with respect to the calculated s h e l l thickness i s shown f o r Tests A t i (Figure 36), M2 (Figure 37(a)), M3 and M4 (Figure 37(b)), A U (Figure 40).  and Ail3 (Figure 39(a) and (c)) and W2a and W2c  71  Shell  Thickness  0.4  0.2  Slob  1.2  1.6  0.4  Shell  Figure 31.  (cm)  08  0.6  Thickness  (in)  Surface  Temp. (°C)  900  1100  1300  1600  2000  2400  Slab  Surface  1500 0  Temp. (°F)  Liquid pool and surface temperature profiles in the mold region for the stainless steel slab 0, measured inside radius; 9, measured outside radius. A, calculated finite difference with equation (7). B, calculated finite difference with equation (6). C, calculated integral profile with equation (7). D, calculated integral profile with equation (6).  Shell Thickness 0.5  1  1  OA  (cm) 2.5  1  1  1  3.0  AO  0.1 _ A O  _  Ot AO  ;  0.2  I  -  I  5  A A  0  o inside  °*0 CA A 0 A O OA  i 0.3  A O  0.4  05  AO OA O A AO AO O A A  A  A  O  1  Mold Bottom  O O  Figure 33.  -  0  0  -  Radius  » Outside Radius  0  1 -  A  1  '  -  Shell thickness for inside and outside radius faces from Test M3.  72  Shell  (c)  Figure 32.  Thickness  1cm)  Billet  Surface  Temperature  TO  (d)  Liquid pool and surface temperature p r o f i l e i n the mold region for (a) Test Ml, (b) Test M2, (c) Test M3, (d) Test 0 measured, average s h e l l thickness of inside and outside radius surface. Caption as f o r Figure 31.  M4.  73  Shell Thickness  Shell Thickness  (cm)  Surface  (in)  Temperature  (°C)  Surface Temperoture  (°F)  Shell Thickness  Shell Thickness  (cm)  Surface  Temperature  (°C)  (in)  Surface  Temperature  (°F)  (b)  (a)  Shell Thickness  Shell Thickness  (cm)  Surface  Temperoture  TO  (inl  Surface Temperature  (°F)  (c)  Figure 34.  Shell Thickness  (cm)  Surface  Temperature  Shell Thickness  (in)  Surface  Temperoture PF)  (d)  Liquid pool and surface temperature p r o f i l e s i n the mold region for (a) Test AA1, (b) Test A£2, (c) Test A£3, (d) Test A l b . Caption as for Figure 32.  TO  Shell  Shell  Figure 35.  Thickness  (cm)  Thickness (in)  Surface  Surface  Temperalure CC)  Temperature (°F)  Liquid pool and surface temperature p r o f i l e s i n the mold region f o r Test U l . Caption as f o r Figure 32.  OUTSIDE RADIUS  WEB -i762cm  ^508 cm S FLANGE FACE INSIDE  Figure 38.  RADIUS  P o s i t i o n of horizontal s l i c e s i n web area, 1, and i n flange area, 2, of A and E beam blanks used i n c a l c u l a t i n g pool p r o f i l e s with the one-dimensional models. S, positions of input streams.  75  .0  6.0 0  F i g u r e 36.  Shell Thickness 20 4.0  (cm) 6.0  Slab Surface Temp 500 IQQQ  (°C) 1500  End of Zone 4 Spravs J I L__l_ 1.0 2.0 800 1600 2400 Shell Thickness (in Slab Surface Temp CF)  L i q u i d p o o l and s u r f a c e temperature p r o f i l e s f o r the stainless steel slab. C a p t i o n as f o r F i g u r e 32.  76  i  (a)  F i g u r e 37.  L i q u i d p o o l and s u r f a c e temperature p r o f i l e s f o r (a) T e s t s M l , M2, (b) T e s t s M3, M4. C a p t i o n as f o r F i g u r e 32.  77 Shell  Shell  Figure 39.  Thickness  (in)  Surface  Temp.  Thickness  (cm)  Surface  Temp.  (°C1  CF)  Liquid pool and surface temperature p r o f i l e s f o r (a) web (A) and flange (B) areas of A beam blank, Test A&l. Curves A and B calculated with f i n i t e difference using equation (7), curve C with i n t e g r a l p r o f i l e using equation (7). (b) web (A) and flange (B) areas of E beam blank Test A£2. Caption as for Figure 39(a). (c) A, Test A13. B, Test A£4. Curves calculated with f i n i t e difference model using equation (7). S, temperature of blooms at straightener, 900°C.  78  F i g u r e 40.  L i q u i d p o o l and s u r f a c e temperature p r o f i l e s f o r T e s t W2a T e s t W2c.  and  79  5.  5.1.  DISCUSSION  Liquid Mixing, Solid Shell and Cast Structures  5.1.1.  Liquid Mixing  5.1.1.1.  General Comments The present results indicate that the f l u i d flow pattern i n  the l i q u i d pool i s complex.  The d i s t r i b u t i o n of radioactive gold i n the  pool depends to a great degree on the method of tundish teeming, i . e . open pour or submerged shroud, and the method of tracer addition to the pool.  Since the method of tracer addition was  the same i n a l l tests,  variations i n mixing c h a r a c t e r i s t i c s are mainly a result of tundish teeming practice.  5.1.1.2.  Open Pour When open pouring between the tundish and mold i s used ( a l l  tests except A t i and AM) sub-mold regions.  extensive mixing occurs i n the mold and upper  Most of the gold mixes below the meniscus sharply  o u t l i n i n g the s o l i d - l i q u i d interface i n the mold.  In the sub-mold region,  the interface becomes less d i s t i n c t due to incomplete mixing.  The gold  80 never mixes t o the p o o l depth measured w i t h the tungsten  pellet.  This  i n d i c a t e s t h a t the g o l d r i c h r e g i o n i n the lower p o o l i s surrounded l i q u i d m e t a l w i t h no d i s c e r n a b l e m i x i n g between the two some t e s t s the g o l d p e n e t r a t e d Figure 7).  The  p e n e t r a t i o n may  the g o l d e n t e r e d  liquid  by  zones.  to near the p e l l e t p o s i t i o n (see T e s t  In M3,  be a s s o c i a t e d w i t h the manner i n which  the l i q u i d p o o l , the h i g h d e n s i t y g o l d f a l l i n g f u r t h e r  b e f o r e b e i n g mixed i n the p o o l , o u t l i n i n g the o u t s i d e r a d i u s  solid-liquid  interface.  In the a u t o r a d i o g r a p h s t r a n s v e r s e s e c t i o n s and  l i g h t and  a l t e r n a t e l i g h t and  dark bands i n the  dark cones i n the l o n g i t u d i n a l s e c t i o n s  were observed.  S i m i l a r bands have been observed i n o t h e r t r a c e r work on  b o t h continuous  and  s t a t i c castings  35 36 ' .  According  to the  literature  the bands can a l s o be  seen i n s u l p h u r p r i n t s , a l t h o u g h  i n any  The presence of the bands cannot be accounted f o r  of the t e s t s .  at p r e s e n t . and  They may  r e s u l t from f l u i d  flow due  thermal c o n t r a c t i o n as the s t r a n d s o l i d i f i e s .  t h i s was  not  36  to s o l i d i f i c a t i o n The  temperature  i n the l i q u i d p o o l i n t h i s r e g i o n must be v e r y s m a l l , making any of the buoyancy f o r c e s due  to d e n s i t y v a r i a t i o n s i n the l i q u i d  In the E p r o f i l e beam b l a n k (Test A12, l e s s m i x i n g of the g o l d than i n any why  t h i s occurred.  F i g u r e 16)  o t h e r open pour t e s t .  From F i g u r e 17,  observed  shrinkage gradients  estimate  difficult.  there  was  I t i s not c l e a r  i t i s apparent t h a t as much or  s l i g h t l y more g o l d mixed i n the l i q u i d p o o l above the meniscus than below it.  S i m i l a r h i g h a c t i v i t y d i s t r i b u t i o n s above the meniscus were observed  i n Test A&4  and A t l where submerged shrouds were used.  However, i n t e s t s  i n v o l v i n g open teeming, the a c t i v i t y u s u a l l y dropped o f f s h a r p l y above meniscus.  The  a c t i v i t y d i s t r i b u t i o n i n T e s t All  may  be  tentatively  the  81 explained by assuming that a part of the gold addition was  picked up  d i r e c t l y by the input stream and, despite mixing, was maintained as a region of high gold concentration, while i t moved rapidly down through the pool into the lower region of the mold where the stream momentum i s small.  This gold r i c h region would then produce the peak i n a c t i v i t y  seen 13 to 25 cm, below the meniscus.  At the same time, the rest of the  gold added to the pool would have been distributed  quickly throughout  most of the mold region to delineate the s o l i d s h e l l observed i n the autoradiographs.  Near the bottom of the mold, a portion of the gold r i c h l i q u i d could be caught by a r e c i r c u l a t i n g walls or up the centre of the web.  stream flowing up the side  The r i s e v e l o c i t y ,  from model measure-  3 ments of Szekely and Yadoya sec. \  , appears to be low, probably less than 5  cm.  The return of the gold r i c h s t e e l to the surface of the l i q u i d  pool would then take roughly 12 sec. or more.  In the meantime the strand,  with the meniscus i n i t i a l l y outlined by the gold, would have descended a distance of 18 cm.  Thus, the gold r i c h l i q u i d would move above the  o r i g i n a l meniscus and eventually come into contact again with the input stream near the top of the pool.  The reappearence of gold i n the region  above the o r i g i n a l meniscus would give r i s e to the second peak i n a c t i v i t y 18 to 32 cm. above the meniscus l i n e i n Figure 17.  The dip i n a c t i v i t y  between the peaks would be due to the successive d i l u t i o n of gold i n the pool by the input stream after the gold addition. 5.1.1.3.  Submerged Shroud  Use of a submerged entry shroud markedly changes the flow pattern and d i s t r i b u t i o n  of gold i n the l i q u i d pool.  The exit ports from  the shrouds used i n Tests A£4 and A t l were angled 20 and 15° above the horizontal.  From the autoradiographs and the a c t i v i t y d i s t r i b u t i o n s  (Figures 12 and 17) i t was  observed that the flow patterns and mixing  c h a r a c t e r i s t i c s i n the two tests were s i m i l a r .  The r e s u l t s i n Test A£4 indicate that flow from the r a d i a l input stream divides e s s e n t i a l l y into two parts, possibly equally.  One  part mixes into the small l i q u i d region above the input stream, and subsequently mixes upward and becomes d i l u t e d as the slab i s withdrawn and the i n i t i a l point of introduction moves downward.  The other part  flows across the pool, down the end wall to about 100 cm. below the meniscus, and then back to the centre of the slab. the side w a l l , adjacent side of the slab.  Flow also occurs down  to the end, more extensively on the outer radius  Much of the gold i s therefore d i s t r i b u t e d around the  periphery of the slab by the momentum of the input stream.  Subsequently  flow occurs at a much lower rate into the lower part of the l i q u i d pool, due to volume shrinkage, and solute and thermal gradients, from the central regions of the upper part of the pool.  This r e s u l t s i n a r e l a t i v e l y dark  region i n the central lower part of the pool and a gold depleted  region  i n the c e n t r a l part of the upper region of the pool, as i s observed. 3 These r e s u l t s d i f f e r markedly from those predicted by Szekely and Yadoya on the basis of a water model study of f l u i d flow associated with r a d i a l input streams.  They concluded that penetration with r a d i a l nozzles i s  small and i s much less than with straight nozzles.  The present r e s u l t s  indicate appreciable penetration of the l i q u i d pool by the input stream with r a d i a l inputs. The difference between these r e s u l t s and the r e s u l t s  presented by Szekely and Yadoya may  be due to the difference i n the  head of l i q u i d metal feeding the mold.  Since the tundish nozzle feeding  the shroud i s smaller than the shroud exit ports, the shroud w i l l not be e n t i r e l y f u l l of l i q u i d metal.  Thus, the head of l i q u i d metal feeding  the mold w i l l be the height of the l i q u i d surface i n the shroud above the meniscus.  If the head of l i q u i d i n the shroud decreases, the input  stream momentum would d r a s t i c a l l y decrease r e s u l t i n g i n a reduction i n mixing i n the l i q u i d pool.  This effect i s observed i n Tests A£4 and A t i .  In the Atlas case a bifurcated shroud i s used with extensive mixing occurring, whereas at Algoma, a four-holed shroud i s used giving less mixing i n the pool since the head of metal i n the shroud i s lower due to the increased cross sectional area of the shroud exit ports. In the test at Algoma, Figure 23, the flow pattern can be inferred to r e s u l t from the input stream s p l i t t i n g into two parts similar to the Atlas case.  The lower portion of the stream formed a c e l l flowing  down the outside of the casting, across to the centre and then up the central axis.  5.1.2.  5.1.2.1.  Solid Shell  Near the Meniscus A possible mechanism leading to the fluctuations of s h e l l  thickness observed i n the l o n g i t u d i n a l sections i n some experiments i s that a small segment of the s h e l l , attached to the mold at the meniscus, i s torn from the continuous  s o l i d s h e l l and moves above the l i q u i d surface  on the upward stroke of the mold.  On the downward stroke, the lower end  of the segment i s pushed away from the mold by the thin s o l i d s h e l l i t encounters.  This r e s u l t s i n poor l o c a l thermal contact with the mold  and therefore, a l o c a l l y thin s h e l l .  This mechanism accounts for r i p p l e  marks being present on the strand surface wherever there i s a l o c a l i z e d thinning of the s o l i d s h e l l and the presence of s h e l l segments above the meniscus.  I t appears that the s h e l l thickness v a r i a t i o n s are dependent  i n a complex fashion on the l u b r i c a t i o n and mold configuration.  Tearing  of the s h e l l might occur at the corners of the mold and then propogate across the faces.  In this case, the detailed mold f i n i s h at corners as  well as the l u b r i c a t i o n practices might be c r i t i c a l l y related to the fluctuations.  When casting at low speeds, the r i p p l e marks and s h e l l fluctuations can be d i r e c t l y related to the mold o s c i l l a t i o n .  At Algoma  Steel, i n Test A i l , A12 and A£4, the s h e l l fluctuations and r i p p l e marks occur at 3.2, 3.1 and 3.5 cm. i n t e r v a l s respectively.  Assuming the s h e l l  tears uniformly on every upstroke of the mold, the distance between fluctuations i s calculated to be 3.4 cm., based on an average casting rate of 1.5 cm./sec. and a mold o s c i l l a t i o n stroke length of 1.9 cm.  When casting at high speeds, Tests Ml to M4 and U l , no apparent p e r i o d i c i t y i n s h e l l fluctuations i s observed.  This i s  reasonable since at these high casting speeds, s h e l l tearing at the meniscus i s probably i r r e g u l a r and intermittent.  Thus no d i r e c t r e l a t i o n -  ship between mold o s c i l l a t i o n and s h e l l tearing can be made. The i r r e g u l a r tearing of the s h e l l at the meniscus i s a possible  explanation  for the difference i n the position of the meniscus on either side of the b i l l e t i n Test U l , Sections A2 and B2 (Figure 27).  85 5.1.2.2.  Mold Region  The s o l i d s h e l l progressively thickens with distance down from the meniscus.  In a l l of the tests the s h e l l s formed were r e l a t i v e l y  uniform around the periphery of the mold.  In Tests A£l and A£2 (Figures 13 and 16) i t i s evident that the second generation mold (E p r o f i l e ) i s as s a t i s f a c t o r y as the f i r s t generation mold (A p r o f i l e ) i n producing a uniform s h e l l around the entire mold.  Also A and E beam blank have the same s h e l l thickness on leaving  the mold indicating that the heat flux from both molds i s i d e n t i c a l .  The  flange corners of the E beam blank (Figure 16) are more uniform than the corners i n the A beam blank (Figure 13, compare F3 to B6), which suggests that less d i s t o r t i o n of the E beam blank occurs during s o l i d i f i c a t i o n i n the mold.  I t i s not apparent why less d i s t o r t i o n occurs, nor whether  this difference i s consistent since only one test was carried out for each mold.  The reasons f o r the large fluctuations i n s h e l l thickness observed i n the web area of A beam blank (Figure 16, sections C l to C3) are not clear.  Since the f i r s t large f l u c t u a t i o n occurs at about the centre  of the mold, the event causing the fluctuation l i k e l y occurs i n the mold. In tests conducted on both curved and straight molds r e entrant corners have been observed  (see Table VII).  I t i s speculated that  the formation of these corners i s due to the strand shrinking during s o l i d i f i c a t i o n and losing contact with the mold w a l l .  The f e r r o s t a t i c  pressure on the s o l i d s h e l l increases with distance below the meniscus eventually causing the strand to bulge.  This r e s u l t s i n the centre of the  86 f a c e of the s t r a n d making good c o n t a c t w i t h the mold and l o s i n g contact. c o r n e r s and  the  corners  Consequently, the s o l i d i f i c a t i o n r a t e d e c r e a s e s i n the  the s o l i d s h e l l i s t h i n  locally.  12 Ushijima  has  shown t h a t r e - e n t r a n t c o r n e r s observed i n  pour out t e s t s at c o r n e r s o f s t e e l s e c t i o n s can be a s s o c i a t e d w i t h cracking.  The  c r a c k i n g i n the s h e l l r e s u l t s from h i g h t e n s i l e s t r e s s e s  a t the c o r n e r due  to the b u l g i n g of the s h e l l near the c o r n e r s .  a s s o c i a t e d c o r n e r c r a c k i n g w i t h the c o r n e r c u r v a t u r e  He  of the mold,  and  d e f i n e d a range of c o r n e r r a d i i i n which c o r n e r c r a c k i n g would not Unfortunately,  corner  occur.  the r a d i i he proposed a r e u s u a l l y too l a r g e f o r commercial  castings since with  i n c r e a s e i n c o r n e r r a d i u s , mold d r e s s i n g becomes a  problem. A corner and  (b).  The  crack i n a re-entrant corner  crack occurred  crack healed  From the s u l p h u r p r i n t  i t can be seen t h a t the c r a c k was  l i q u i d which was  i n the mold, s i n c e t h e r e was  and  f i l l e d by s o l u t e r i c h  immediately ahead o f the s o l i d - l i q u i d  of weakness below the mold.  24(a)  i n t h e mold, c l o s e to the meniscus,  presumably as a r e s u l t of l o c a l s t r a i n s . autoradiograph  i s shown i n F i g u r e  interface.  The  no breakout, but would be a p o i n t  T h i s c o u l d l e a d to the l o n g i t u d i n a l  corner-  c r a c k i n g , observed on the o u t s i d e s u r f a c e of the bloom.  5.1.2.3.  Submold Region  G e n e r a l l y the s h e l l t h i c k n e s s below the mold i s not o u t l i n e d i n d i c a t i n g l i t t l e mixing o c c u r r i n g i n t h i s region.  clearly  87 In Test A l l deformation  of the s o l i d s h e l l by support  i n the spray region i s seen i n Figure 14(a).  One or more of the  rolls web  r o l l e r s were misaligned on one side causing d i s t o r t i o n of the s h e l l i n the web  f i l l e t area.  Also the wavy contour of the s o l i d - l i q u i d interface  along the wide flange face i n Figure 14(a) may  be due to deformation  by  33 the support r o l l e r s . the web,  As described by Lucenti  r o l l e r s are used against  flange face and flange t i p s i n the spray zones to maintain  mold contour of the beam blank.  the  Without the constraining r o l l s on the  flange, the flange deformed to the shape shown i n Figure 41(a).  The wide  face of the flange bulged out, r e s u l t i n g i n a d i s t o r t i o n of the inside radius flange edge, as shown, which could lead to l o n g i t u d i n a l flange t i p cracks.  The presence of the r o l l e r s reshapes the beam blank by deforming  the s o l i d s h e l l .  The deformation  does not s h i f t the s o l i d - l i q u i d i n t e r f a c e  i n the flange edge, accounting for the divergence of the plane of the interface i n the autoradiographs 5.1.3.  from the flange edge surface.  Cast Structure  5.1.3.1.  Stainless Steel In the test involving the casting of stainless s t e e l , the cast  structure consisted of a large columnar zone and a r e l a t i v e l y narrow equiaxed zone.  The small gold free spots observed i n some sections  (L8 to L10, Figure 10) are probably small dendrites which have formed i n a gold free part of the l i q u i d pool, and f a l l e n down the pool to the positions observed i n the autoradiographs.  It i s not clear to what the  dark structureless spots (also observed i n the autoradiographs) ascribed.  can be  88  Figure 42.  Temperature d i s t r i b u t i o n i n A beam blank web, Test A£l, 2.5 m. below meniscus. Estimated region of low d u c t i l i t y ^ i s indicated as well as the observed region of r a d i a l cracking.  89 ' In some sections (C3, C6, and L12)  the s o l i d - l i q u i d i n t e r -  face delineated by the gold had a series of small regular bumps.  These  appeared to be associated with dendrite t i p s at the advancing interface. Since only the dendrite t i p s are outlined, i t would appear that l i t t l e l i q u i d has penetrated 1.9 mm.  into the s o l i d - l i q u i d zone.  were measured at a s h e l l thickness of 1.6  Tip spacings of about cm.  i n section C3.  The d e n d r i t i c structure i n the centreline of the slab  may  be due to both d e n d r i t i c debris f a l l i n g from the upper part of the pool and, since the casting i s mainly columnar, dendritic bridging of the centre by columnar grains.  The difference i n the dendritic structure along  the centreline of the transverse sections suggests more debris drops from the middle of the slab, closer to the point of introduction of the input stream, than at the slab ends.  In using electron probe microanalysis of the concentration of n i c k e l and chromium i n a 304 slab, cast at Atlas Steels i n a s i m i l a r manner 37 to the present segregation  has shown that no s i g n i f i c a n t macro-  occurs at the slab centreline.  microsegregation 5.1.3.2.  t e s t , R. Dickens  The r e s u l t s also indicated that  between the primary dendrites did occur, as was  anticipated.  E f f e c t of Tundish Teeming In most of the tests where open teeming from the tundish  used, the cast structure consisted of a columnar region around the of the casting and a central equiaxed region. used (Test A&4,  was  periphery  Where a submerged shroud  was  Figure 23) the cast structure consisted of cored, d e n d r i t i c ,  equiaxed grains with no resolvable columnar region. equiaxed grains i n this casting may  The larger volume of  r e s u l t from the r a d i a l input streams  90 d i r e c t l y impinging on the s o l i d - l i q u i d interface. This could cause extensive l o c a l remelting of fine dendrites to occur, appreciable increasing the number of n u c l e i i n the l i q u i d pool. i n this test may  The number of n u c l e i  have been further increased by the addition of aluminum  to the melt i n the l a d l e .  Only i n Tests M3 and M4 did the cast structure, when using open pouring, d i f f e r from the normal.  In these tests the bulk of the  cast structure consisted of small dendritic grains with no apparent columnar region.  The structure indicates that copious nucleation occurs i n  the upper part of the l i q u i d pool.  The n u c l e i f a l l and f i l l the r e l a t i v e l y  short pool preventing columnar growth. billet  (10.1 cm.)  Because of the small size of the  and high casting speeds (5 cm./sec), the r e l a t i v e l y  large input stream causes a high degree of turbulence i n the mold.  This  could result i n extensive l o c a l dendrite remelting, thus increasing the number of n u c l e i i n a similar manner as i n Test A£4.  5.1.3.3.  Columnar Structure The columnar grains were s u f f i c i e n t l y c l e a r l y resolved i n the  autoradiographs  i n some of the tests that the primary dendrite spacing  could be measured as a function of distance from the outside surface.  The  results of these measurements are shown i n Figure 29 (for Test Ul) and in Table VIII.  Also i n Table VIII, the range of primary dendrite spacings  with distance from the surface i n AISI 4340 s t e e l cast u n i d i r e c t i o n a l l y 38 against a water cooled copper block i s given  .  These r e s u l t s indicate  that the heat transfer between the strand and the mold i n the present experiments i s less e f f i c i e n t than i n the case of s t e e l cast s t a t i c a l l y  Table VIII.  Measurements of Dendrite  Test No.  D i s t . from Surface  91  Spacing  Meas. Primary Dendrite  (cm)  (mm)  Ail  3.0  1.0  A£3  4.5  1.0  Ul  1.5  Atl Weinberg & Buhr  to  5.0  0.4  1.6 1.6  to  to  Spacing  0.8  1.9 5.0  0.2  to  0.4  against a cold block, and therefore, the freezing conditions and r e s u l t i n g structure are not comparable.  It i s also i n t e r e s t i n g to note that the  dendrite spacing i n the stainless s t e e l slab i s much larger than i n low carbon s t e e l castings, probably due to the greater freezing range i n stainless s t e e l .  5.1.3.4.  Equiaxed Structure The equiaxed grains i n the centre of the strands are l i k e l y  formed near the lower l i m i t of penetration of the input stream, where s i g n i f i c a n t temperature fluctuations can be expected, and where larger dendrites have had a chance to develop at the s o l i d - l i q u i d interface. n u c l e i are secondary dendrite branches separated by l o c a l remelting.  The  from the primary branches  The n u c l e i f a l l i n the pool, due to their s l i g h t l y  higher density, and grow, i n the absence of s i g n i f i c a n t temperature gradients i n the l i q u i d , i n areas of progressive solute enrichment due to  c o n s t i t u t i o n a l supercooling.  This suggests that the number, s i z e and  d i s t r i b u t i o n of the equiaxed grains i s related to the penetration of the input stream, the flow pattern i n the l i q u i d and the a l l o y  composition.  The e f f e c t of d i f f e r e n t flow patterns on the equiaxed zone was discussed in an e a r l i e r section.  When the strand i s cast using a curved mold, because of the curvature of the casting, the grains w i l l tend to f a l l and form a loosely packed agglomerate on the outside radius s o l i d - l i q u i d i n t e r f a c e . As a r e s u l t columnar growth on the outside radius i s halted and columnar growth on the inside radius i s allowed to proceed to near the casting centreline. This accounts for the observed displacement  of the casting centreline and  the presence of an equiaxed structure i n the outside radius half of the strand.  When a straight mold i s used, there i s no observable s h i f t i n the  equiaxed zone from the casting centreline (see Test U l , B6, Figure 27).  In Test U l , section B6, i t can be seen that the columnar structure terminates abruptly at the columnar-equiaxed t r a n s i t i o n l i n e . At this t r a n s i t i o n there i s no s i g n i f i c a n t concentration of gold ahead of the columnar structure.  This indicates that there i s no s i g n i f i c a n t macro-  segregation ahead of the advancing columnar grains.  At this l e v e l , the  l i q u i d adjacent to the interface i n Figure 27 i s not mixed with the centre l i q u i d , indicating that there i s l i t t l e f l u i d flow to reduce concentrations of gold ahead of the i n t e r f a c e , i f such concentrations existed.  In Tests Ml and M2 (Figure 7) the centreline porosity i s a r e s u l t of inadequate feeding of l i q u i d at the bottom of the pool, due to periodic bridging across the pool by d e n d r i t i c debris or r a d i a l dendrites. Along the centreline of the castings a band of gold r i c h material i s  93 observed.  This band may be caused by the l a s t l i q u i d to s o l i d i f y , r i c h  i n solute material, flowing into the shrinkage c a v i t i e s created as a result of bridging at the bottom of the pool and freezing r a p i d l y without s i g n i f i c a n t segregation. occurs p e r i o d i c a l l y .  I t i s not clear why bridging across the pool  This e f f e c t i s also observed  to a lesser degree i n  Tests A£3 and A t l .  5.1.3.5.  Solute Rich Pipes i n Equiaxed Zone  In Test A£4 (sections L l and M5, Figure 23 and sulphur p r i n t of L l i n Figure 25) and i n Test U l (section A9 and B series, Figure 27) gold and sulphur r i c h pipes forming a V pattern were observed.  In the l o n g i -  tudinal sections (A9 and L l ) the pipes appear as long dark l i n e s .  The l i n e s  are not as steeply i n c l i n e d as the s o l i d - l i q u i d interface, tending to form a larger angle with the v e r t i c a l axis toward the centre of the strand. In the transverse sections (B series) the pipes tend to be small and round, becoming larger and more i r r e g u l a r near the centre of the strand.  The  presence of these pipes i s probably due to l i q u i d flowing down through the s o l i d - l i q u i d mass to feed volume shrinkage associated with s o l i d i f i c a t i o n . The pipes are l i k e l y a r e f l e c t i o n of the packing of d e n d r i t i c debris as i t f a l l s down the l i q u i d pool.  Some debris w i l l attach i t s e l f to the  s o l i d - l i q u i d interface with greater frequency towards the bottom of the pool as the debris becomes larger i n size.  ;  As a r e s u l t , the e f f e c t i v e  s o l i d - l i q u i d interface w i l l become more i n c l i n e d away from the v e r t i c a l lower i n the pool. The solute r i c h l i q u i d w i l l search for pipes of poor packing and flow down these pipes, melting small b a r r i e r s , i f they e x i s t , to form the observed V segregate pattern.  5.1.3.6.  Radial Cracking The d u c t i l i t y of continuously cast mild s t e e l at high 14  temperatures has been related by Lankford steel.  r a t i o i n the  At low r a t i o s , 20, the s t e e l has poor d u c t i l i t y while at high  r a t i o s , 60, i t has good d u c t i l i t y . r a d i a l or centreline cracking was ratio.  to the Mn/S  Table VII gives the tests i n which observed and the corresponding  Generally, r a d i a l cracking was  intermediate Mn/S  ratio.  observed  Mn/S  i n tests having a low to  A l l cracking i s i n t e r d e n d r i t i c i n agreement with  the Lankford model since unfavourable Mn/S  r a t i o s would occur i n i n t e r -  dendritic areas, due to sulphur segregation during freezing, leading to poor d u c t i l i t y . Radial cracking caused by deformation of the p a r t i a l l y s o l i d i f i e d strand can be observed  i n Test A l l , Figures 14 and 15.  Deformation  of the s h e l l by the corner of a r o l l e r would cause high t e n s i l e stresses i n the i n t e r i o r of the s h e l l .  This leads to i n t e r d e n d r i t i c cracking  which would extend to the interface, the crack then being f i l l e d with solute r i c h l i q u i d .  Most of the r a d i a l cracks terminate about 3.6  from the outside surface of the beam blank.  cm.  If t h i s i s assumed to be the  position of the interface when the cracks formed, then from the heat analysis described e a r l i e r , this s h e l l thickness would occur at about 2.5 m. below the meniscus.  The temperature p r o f i l e across the s h e l l at  this depth can be calculated, and i s shown i n Figure 42.  Using the 14  temperature range over which the s t e e l i s b r i t t l e , from Lankford  , the  probable range of r a d i a l cracking i s indicated as a function of distance from the beam blank surface.  The observed  range of r a d i a l cracking i s  shown to be a l i t t l e further from the beam blank surface than that estimated.  However, considering the assumptions made, the estimated  and  observed range of r a d i a l cracking are not too divergent.  Radial cracks  on the inside radius flange t i p can also be attributed to t e n s i l e stresses introduced i n the i n t e r i o r of the s h e l l , when the s h e l l i s being deformed, by the flange and flange t i p r o l l e r s .  These cracks extend over a similar  range as those described previously, 1.9 to 3.6 cm. from the outside surface. the  This suggests that the flange t i p cracks occur at approximately  same distance below the meniscus as the web r a d i a l cracks, and are  due to deformation.  It i s d i f f i c u l t to determine the cause of r a d i a l cracking i n the other tests.  Cracking may be related to thermal stresses set up i n  the strand i n the water sprays, deformation  by misaligned support  rollers  and l o c a l t e n s i l e stresses r e s u l t i n g from compression of the strand by the withdrawal or straightening r o l l e r s .  The intergranular centreline  cracking observed i n some tests i s probably a result of thermal stresses set up i n the strand i n the spray and radiant cooling regions.  These  stresses cause cracking at the solute enriched grain boundaries at a time when some r e s i d u a l l i q u i d was s t i l l present to f i l l the crack.  5.1.3.7.  Sulphide Inclusions In Tests A l l , A&3, Ml and M2, clumps of sulphide inclusions  were found i n the inside radius of half the strands.  Since the clumps are  enriched i n gold and sulphur, they must have formed i n the s o l i d - l i q u i d region of the s o l i d i f y i n g front, at a point different than their f i n a l position (see Figures 14 and 15).  The f l u i d flow r e s u l t s suggest that  l i t t l e flow occurs i n the lower part of the pool.  Accordingly, the  evidence indicates that the clumps of inclusions, after t h e i r  formation,  floated up i n the l i q u i d pool due to their low density, u n t i l they met the s o l i d i f y i n g front advancing  from the inside radius surface.  Thus,  they can be seen to form a band p a r a l l e l to the inside radius surface (see Figures 14(a) and  (b)).  The inclusions present near the outer  surface of the strand(see Figures 15(a) and  (b)) are also consistent with  the hypothesis that clumps of inclusions f l o a t up i n the l i q u i d from the s o l i d i f y i n g front i n the lower pool regions since l i t t l e segregation between the f i n e columnar dendrites would occur.  The r i s i n g v e l o c i t y 39  for a 500u i n c l u s i o n i s 14 cm./sec, from Stokes Law  .  Therefore, there  i s ample time for the i n c l u s i o n to f l o a t up through large distances i n the pool. The d i s t r i b u t i o n of inclusions seems to be dependent on the Mn/S  r a t i o i n the s t e e l .  With a low r a t i o , clumps of MnS  found i n a band near the inside radius surface.  inclusions are  With a high Mn/S  ratio,  the clumps of inclusions are uniformly dispersed throughout the casting (compare Figures 14, 15,and 22 to Figures 18, 19, and 26).  5.2.  Calculated and Measured Pool P r o f i l e s and Pool Depths  5.2.1.  V a l i d i t y of Assumptions i n Mathematical Models The assumptions i n the models regarding the release of latent  heat and the use of an e f f e c t i v e thermal conductivity should be examined before comparing the predicted and measured pool p r o f i l e s for the tests. For the stainless s t e e l slab (Test A t l ) the effect of changing the method of latent heat removal on the s o l i d i f i c a t i o n rate was evaluated by altering y  (see Figure 2).  This i n effect changes the quantity of latent  97  Figure 43.  Shell Thickness  (cm)  Sheil JThir.kness  (in)  E f f e c t s of method of latent heat evolution and use of k f f on calculated s h e l l thickness f o r the stainless s t e e l slab. k f f used f o r T > 1460°C, % latent heat released at solidus: 25, 50, 75%, — ' ; 100%, . k f f used f o r T > 1399°C, 100% latent heat released at solidus . Integral p r o f i l e model,—-—--- . e  e  e  Shell Thickness (cm)  Shell Thickness (in)  Figure 44.  E f f e c t s of method of latent heat evolution and use of k f f on calculated s h e l l thickness f o r low carbon s t e e l . k f f used for T > 1525°C, 5-100% latent heat released at solidus, ; keff used f o r T > 1492°C, 100% latent heat released at soludus, . , Integral P r o f i l e model, . e  e  98  heat released per unit mass of s t e e l at the solidus temperature.  The  results of varying the amounts of latent heat released at the solidus ( Y ) on the calculated pool p r o f i l e i n the mold i s shown i n Figure 43. G  From these calculations i t was  found that there was no difference i n  s h e l l thickness i f from 25 to 75% of the latent heat was released at the solidus.  If a l l the latent heat was released at the solidus (Y<, = 0)  a 1 to 2% increase i n s h e l l thickness was  observed.  This resulted i n a  decrease i n the calculated pool depth of approximately  5%.  Equation  (7)  has been used for the surface heat flux i n c a l c u l a t i n g these p r o f i l e s .  For the case of low carbon s t e e l s , as shown i n Figure 44 there i s no difference between the pool p r o f i l e which has been calculated using the phase diagram to determine y expected  and that for which Y  = C  0.  This i s as  since the freezing range i n low carbon steels (,1%C) i s small.  For high carbon steels there should be an increase i n the calculated s h e l l thickness similar to that observed  for the stainless s t e e l .  In Figure 44  the curves were calculated using equation (6) as the surface boundary condition i n the mold.  Pool p r o f i l e s have been calculated using the e f f e c t i v e thermal conductivity (equation (5)) for both regions of the l i q u i d pool where the temperature was  greater than the liquidus temperature and for regions where  the temperature was  greater than the solidus temperature.  are shown i n Figures 43 and 44.  When using  These p r o f i l e s  through the s o l i d - l i q u i d  region, the pool p r o f i l e s are s l i g h t l y thicker, approximately  6% for the  stainless s t e e l and 3% for the low carbon s t e e l , then the previously calculated p r o f i l e s .  This procedure brings the pool p r o f i l e s closer to  those calculated using the i n t e g r a l p r o f i l e model (also shown  in  99 Figures 43 and 44).  In the i n t e g r a l p r o f i l e model conduction i n the  l i q u i d i s ignored and superheat  i s released at the same time as the  latent heat, i . e . , at the solidus. model the use of  Thus, with the f i n i t e difference  results i n considerably more superheat  removed from the l i q u i d i n the mold region.  being  This may explain why the  f i n i t e difference s h e l l s are marginally thinner than the i n t e g r a l p r o f i l e shells.  5.2.2.  Calculated and Measured Pool P r o f i l e s i n the Mold  5.2.2.1.  Low Carbon Steel  In Tests Ml, M2 (Figures 32(a) and (b)) and A£l to A£3 (Figures 34(a) to (c)) there i s excellent agreement between the measured p r o f i l e s and the calculated p r o f i l e s (curve B) using the f i n i t e difference model with equation (6) f o r the surface boundary condition.  Using the f i n i t e  difference model and equation (6), the s h e l l thickness of low carbon s t e e l i n the mold can be expressed as a function of time giving  y  = 0.118t°'  75  (cm.,sec.)  (13)  In Test A£4 (Figure 34(d)) the agreement i s good down to 0.32 m. below the meniscus beyond which the measured s h e l l i s appreciable thicker than B.  However, the measured s h e l l i n the lower regions of the mold may be  thicker than the actual s h e l l , since the autoradiographs  show the s o l i d -  l i q u i d interface to be less d i s t i n c t there than further up the mold. This i s l i k e l y a consequence of inadequate mixing of the gold nearer the mold bottom.  100  It can be seen from the graphs that curves A ( f i n i t e difference) and C (integral p r o f i l e ) calculated using equation (7) f o r the surface boundary condition agree c l o s e l y f o r the mold; the same i s true of curves B and D computed with equation (6).  From Table IX and Figure 3, i t i s apparent that the measured mold heat fluxes f o r Tests Ml, M2 and A£l to A£3 d i f f e r by less than 20% . from the respective values predicted by equation (10). I t i s this difference that causes curve A, calculated using the measured heat flux, to d i f f e r to the extent observed from curve B, computed with the Savage and Pritchard heat f l u x .  The largest difference between the measured  and calculated heat fluxes i s seen f o r Test A£4.  That the measured heat  flux was low i n t h i s test may be due to inaccurate measurement of the mold water temperature  rise.  In Tests M3, M4 (Figures 32)c) and (d)) and U l (Figure 35) there i s better agreement between the measured s h e l l thickness and the s h e l l thickness calculated using equation (7) (curve A) than equation (6) (curve B).  This i s as expected since i n these tests the measured  heat fluxes are greater than the predicted heat fluxes (Table IX). There i s excellent agreement between the measured and predicted p r o f i l e s i n Test U l , but i n Test M3 the difference between the two p r o f i l e s i s approximately 30%. billet  From Figure 3 the measured heat flux f o r the 10.1 cm.  (Test M3) appears to be reasonable reducing the p o s s i b i l i t y that  the heat flux measurements were grossly incorrect.  An  101 Table IX.  Measured and Predicted Average Mold Heat Flux  Test  Average Mold Heat Flux (kcal m.^ sec.^")  No.  Measured  Predicted  Ml  358  405  M2  380  430  M3  510  437  M4  572  452  AU  335  320  A£2  297  315  AJ13  308  323  AM  262  335  Ul  575  415  Ati  324  345  assumption that has been made i n the model that may not apply i n this case i s that the s h e l l thickness i s uniform around the periphery of the mold.  An examination of the autoradiograph  of a transverse section  from Test M4 (Figure 9(b), 10.1 cm. b i l l e t ) reveals that i n the mold, the centres of the faces of the b i l l e t are considerably thicker than the corners.  I f this i s also true i n Test M3, the measured s h e l l thickness  taken from the centre of the faces would be greater than the calculated value.  There i s a p o s s i b i l i t y that errors have been made i n the  102  measurement of the heat f l o w d a t a , e.g. of 4 to 8°C. from F i g u r e  However i t does not  seem t h a t such e r r o r s are l a r g e  3 the c a l c u l a t e d heat f l u x e s f o r a l l of the  seen to be w i t h i n  5.2.2.2.  the mold water temperature  the average range of heat  rise since  t e s t s can  be  fluxes.  S t a i n l e s s S t e e l Slab  In F i g u r e  31  the measured and  s t a i n l e s s s t e e l s l a b are p r e s e n t e d .  predicted  From the  pool p r o f i l e s for  graph i t can be  seen  the p r o f i l e s c a l c u l a t e d w i t h the f i n i t e d i f f e r e n c e model f o r the d i f f e r e n t surface  boundary c o n d i t i o n s  are  similar.  that  two  This i s understandable  s i n c e the measured mold heat f l u x , used to c a l c u l a t e h ^ i n e q u a t i o n  (7),  i s v e r y s i m i l a r to the time averaged, Savage and  P r i t c h a r d heat f l u x  r e l a t i o n , equation  3).  (10)  (see T a b l e IX and  Figure  mold bottom, the c a l c u l a t e d p r o f i l e i s 20 t o 30% measured p r o f i l e . o u t l i n i n g the from the  This  s l a b , the s h e l l can be  In F i g u r e  presence of r a d i o a c t i v e g o l d distance  11,  seen to t h i c k e n  f a s h i o n a t 15.7 cm.below the meniscus.  s h e l l f o r a short  However, near  thinner  have been r e p o r t e d  For  the  by  gold  i n a discontinuous  i s observed a p p a r e n t l y i n s i d e the  below the d i s c o n t i n u i t y .  of the  r a d i o a c t i v e t r a c e r s and Zeder and  not  section  A t h i n dark l i n e , i n d i c a t i n g  o b s e r v a t i o n s of d i s c o n t i n u o u s t h i c k e n i n g  the  the  a longitudinal  This  t h e r e i s l i t t l e m i x i n g i n t h i s a r e a of the l i q u i d p o o l .  of a s l a b when u s i n g  than  d i f f e r e n c e i s p r o b a b l y a r e s u l t of the  true s o l i d s h e l l .  the  the  solid  suggests  that  Similar  s h e l l i n the wide  immersed b i f u r c a t e d  face shrouds  Hedstrom"'"^.  s t a i n l e s s s t e e l s l a b , the d i f f e r e n c e between  p o o l p r o f i l e s c a l c u l a t e d w i t h the  i n t e g r a l p r o f i l e model and  the  with  the  103 f i n i t e difference model was l e s s than 10%.  5.2.3.  Calculated and Measured Pool Depths  5.2.3.1.  Calculated Pool Depths using One-Dimensional Model  Figures 39(a)  and (b) show the pool p r o f i l e s calculated  using  the one-dimensional f i n i t e difference model i n the web and flange areas of the beam blanks.  The pool depths for Tests All and A12 are, i n the  web, 3.75 and 3.9 m., while i n the flange, 7.3 and 7.1 m. respectively. The s l i g h t difference i n pool depths between the two tests i s mainly due to variations i n spray heat transfer c o e f f i c i e n t s used i n the model (Table I I I ) .  In Test All, the i n t e g r a l p r o f i l e model was also used to  predict the pool depth i n the flange area, giving a depth about 30% l e s s than the f i n i t e difference value.  The difference i n the calculated pool  depths between the two models i s a r e s u l t of the constant thermal conductivity, used i n the i n t e g r a l p r o f i l e model (0.0071 kcal m."*" sec."'" °C "*"), being greater than the temperature dependent conductivity, used i n the f i n i t e difference model, f o r temperatures under 1200°C.  Thus, i n the  i n t e g r a l p r o f i l e model the calculated surface temperature i s higher (as seen i n Figure 39(a)), r e s u l t i n g i n a greater predicted rate of heat extraction from the s t e e l according to equation (8) than i n the f i n i t e difference model.  For the stainless s t e e l slab (Figure 36), the one-dimensional f i n i t e difference model predicts a pool depth of 5.2 to 5.36 m., depending on the surface boundary condition employed i n the mold.  The  horizontal bar i n Figure 36 gives the p o s i t i o n as well as the width of the tungsten p e l l e t .  A pool depth of 3.72 m. was calculated using the  104 i n t e g r a l p r o f i l e model, also shown i n Figure 36.  5.2.3.2.  Calculated Pool Depths using Two-Dimensional  Model.  The two-dimensional f i n i t e difference model was used to calculate pool p r o f i l e s f o r the tests on b i l l e t s  and blooms.  The pool  p r o f i l e s and the p e l l e t positions f o r the four tests conducted at Manitoba R o l l i n g M i l l s are presented i n Figures 37(a) and (b).  These  p r o f i l e s show how changing casting speed and b i l l e t size (10.1 cm. and 13.3 cm.) a f f e c t s the calculated and measured pool depths.  The e f f e c t of changing casting speed on pool depth was also tested at Western Canada Steel (Test Wl and W2, Figure 40 and Table V). In tests conducted during the same cast, i t was found that the calculated pool depth increased i n Test Wl from 3.7 to 8.2 m. as the casting speed increased from 1.48 to 2.54 cm./sec, and i n Test W2 from 4.0 to 7.4 m. with casting speed increase from 1.56 to 2.37 cm./sec.  In Figure 40,  the pool p r o f i l e and p e l l e t positions f o r Test W2a and W2c are presented.  Pool depths calculated f o r Tests A U and A£4 (Figure 39(c)) are 12.9 and 14.9 m. respectively. The larger pool depth f o r Test A£4 i s a r e s u l t of the higher withdrawal rate and lower spray c o e f f i c i e n t s . In Test U l , the pool depth of the 19 cm. b i l l e t , cast at 5.5 cm./sec, was calculated to be 32.3 m.  Although the calculated  depth seems exceptionally long, i t i s thought to be reasonable since at the plant bulging of the strand has been reported 30. m. below the mold.  105  5.2.3.3.  Comparison of Calculated and Measured Pool Depths From Figures 36 to 40 and Table V i t can be seen that i n a l l  tests except Test A&3, the calculated pool depths are much greater than the pool depths obtained using the p e l l e t .  There are several possible  reasons f o r the discrepancy between the pool depths.  In strands cast  using low-head curved mold machines, i t i s l i k e l y that the p e l l e t did not f a l l f r e e l y through the l i q u i d s t e e l , but intercepted the outside radius interface shortly a f t e r entry into the pool.  Then the p e l l e t could  roll  down the interface u n t i l i t became lodged against the s h e l l or contacted s o l i d debris i n the pool.  For example, i n Test A£3, the tungsten p e l l e t  was found displaced toward the outside radius surface of the casting, as shown i n Figure 39(c).  The f i n a l p e l l e t position was i n f a i r l y good  agreement with the calculated s h e l l thickness at this point. position of the p e l l e t the pool depth was estimated  From the  (Figure 39(c)) to be  1060 cm., using a l i n e a r extrapolation of the p e l l e t position and correcting for f a l l i n g time.  Since a l i n e a r extrapolation of the p e l l e t  position would give a minimum pool depth, i t i s highly probable that the actual pool depth i s below t h i s point and the pool depth calculated by the model i s reasonable.  For Tests Wl and W2 where a straight mold, v e r t i c a l type casting machine was used, the p e l l e t should f a l l f r e e l y through the l i q u i d pool (estimated f a l l i n g v e l o c i t y of the p e l l e t i s 70 cm./sec), stopping only when i t contacted s o l i d debris at the pool bottom.  From the r e s u l t s  shown i n Table V and Figure 40 the calculated pool depth i s about twice the pool depth measured with the p e l l e t .  Therefore, for v e r t i c a l  castings the f i n a l p e l l e t p o s i t i o n must indicate the point i n the casting where loosely packed dendritic debris or bridging has stopped the descent  106  of the p e l l e t .  Recently, evidence supporting this statement has been  obtained from tests on a v e r t i c a l casting (17.5 cm. b i l l e t ) at Laclede 40 Steel  .  In these t e s t s , radioactive gold contained i n the tungsten  p e l l e t was released a f t e r the p e l l e t had f a l l e n to the "pool bottom". The gold was drawn down i n the casting by f l u i d flow due to s o l i d i f i c a t i o n shrinkage.  The p e l l e t was found near the centreline of the casting  and the e f f e c t i v e width of the l i q u i d pool, outlined by the gold, at the p e l l e t position can be seen i n a transverse section autoradiograph, Figure 45, taken a f t e r the test.  This shows that the e f f e c t i v e pool  width i s greater than the width of the p e l l e t and l i q u i d metal i s present far below the f i n a l p e l l e t p o s i t i o n .  Therefore, the calculated pool  depth which indicates the point at which the l a s t l i q u i d metal has s o l i d i f i e d may be reasonable. 5.2.4.  Calculated and Measured Surface Temperatures From Figures 31 to 35 i t i s obvious that the choice of either  equation (6) or (7) to describe the surface heat flux has a s i g n i f i c a n t effect on the surface temperature i n the mold region.  For the case of a  constant heat transfer c o e f f i c i e n t (equation (7) curve A) the temperature decreases uniformly while use of the assumed heat flux (equation (6) curve B) results i n a s l i g h t reheating of the surface.  Despite the  difference between the two temperature p r o f i l e s at the bottom of the mold, the temperatures  are i d e n t i c a l by the end of the zone 1 sprays.  Similar  21  findings have been reported by Kung and Pollock The surface temperatures  .  predicted by the f i n i t e difference and  i n t e g r a l p r o f i l e models (Figures 31 and 32(b)) when using the same  107  F i g u r e 45.  A u t o r a d i o g r a p h of t r a n s v e r s e s e c t i o n near t u n g s t e n p e l l e t p o s i t i o n t a k e n a f t e r t e s t s on a 17.5 cm. b i l l e t a t L a c l e d e S t e e l .  108 surface boundary condition i n the mold agree to within  4%.  The surface temperatures at the mold bottom, calculated using the Savage and Pritchard surface boundary condition (equation (6)), are thought to be reasonable.  This i s based on a comparison of calculated  surface temperatures to values measured by Gautier et al. ^ at the mold exit.  These workers measured the surface temperature of s t e e l b i l l e t s  at the mold bottom by using l i g h t pipes positioned at the b i l l e t face to channel l i g h t to a two color pyrometer.  They found through laboratory  t r i a l s that the accuracy of this system was  about ± 30°C.  and predicted surface temperatures (using equation  The measured  (6)) are presented  in  Table X.  The surface temperature calculated with the f i n i t e difference model are within 2 to 5% of the measured values, with one  exception.  With the i n t e g r a l p r o f i l e model the calculated temperatures are within 2 to 8% of the measured values. The calculated surface temperatures i n the sub-mold regions (shown i n Figures 36 to 40) are only approximate because of the lack of adequate data to properly calculate the spray heat transfer c o e f f i c i e n t s . However these temperatures also appear to be reasonable  since, for  example, with Test A t i (Figure 36) the calculated surface temperature of 600 to 700°C was very low; i n agreement with t h i s , the surface of the slab emerging from the casting machine was radiate noticeable l i g h t .  observed to be too cool to  In Table V surface temperature measurements  taken at the straightener with an o p t i c a l pyrometer for Tests Ml to M3 and A£2 to A£4 are l i s t e d .  For Tests A£3 and A£4, as seen i n Figure 39(c),  109  T a b l e X.  P r e d i c t e d and Measured  Cast No.  Surface  Temperatures (°C)  D w e l l Time (sec.)  Measured  Calculated Finite Difference  Calculated Integral Profile  42771  13.3  1237  1170  1188  13440  12.8  1234  1174  1190  13401  11.0  1228  1193  1200  13402  12.8  1210  1174  1190  13855  19.7  1084  1136  1176  13756  15.5  1099  1154  1180  13757  18.6  1091  1140  1176  13761  18.6  1093  1140  1176  13762  19.7  1089  1136  1176  13763  19.7  1089  1136  1176  42803  21.7  1100  1132  1178  13427  24.1  1106  1129  1184  13428  20.2  1054  1135  1177  8.5 x 8.5 cm  10.5 x 10.5 cm  12.0 x 12.0 cm  the c a l c u l a t e d s u r f a c e  temperatures a t the s t r a i g h t e n e r a r e r e a s o n a b l e .  For T e s t s Ml t o M3 the c a l c u l a t e d s u r f a c e was u s u a l l y h i g h e r it  than the measured.  temperatures a t the s t r a i g h t e n e r  In F i g u r e 40, T e s t s W2a and W2c,  i s i n t e r e s t i n g t o note the decrease i n s u r f a c e temperature t h a t o c c u r s  when the c a s t i n g speed i s lowered and the spray p r e s s u r e s accordingly. cracking.  The i n c r e a s e d  a r e not a d j u s t e d  c o o l i n g o f the s t r a n d may r e s u l t  i n internal  110  SUMMARY  1.  In the l i q u i d pool, the f l u i d flow pattern i s complex.  Extensive mixing occurs i n the mold region, due to the momentum of the input stream; l i t t l e mixing occurs i n the lower regions of the l i q u i d pool.  The depth of penetration of the input stream i s greater for open  pouring than for pouring through an immersed shroud, and correspondingly mixing i n the pool extends to a much lower l e v e l for open pouring.  The  input stream mixes equally above and below the point of entry with immersed shrouds. 2.  Some solute banding can occur i n the l i q u i d pool.  In the present tests the s o l i d - l i q u i d interface was c l e a r l y  delineated i n the upper mold region, and i n some tests i n the lower mold and sub-mold regions as well. ness around the mold.  In general, the s h e l l i s uniform i n t h i c k -  No major difference i n s h e l l uniformity was noted  using either o i l lubricant or slag powder lubricant. Tearing of the s h e l l at the meniscus, surface r i p p l e marks, and small f l u c t u a t i o n s i n s h e l l thickness were observed, which are related to mold o s c i l l a t i o n , l u b r i c a t i n g practise and condition of mold surface.  3.  The flanges of the beam blanks  (Tests A l l and A£2) were r e -  shaped by the support r o l l e r s when p a r t i a l l y s o l i d i f i e d , r e s u l t i n g i n d i s t o r t i o n of the s o l i d i f y i n g front.  D i s t o r t i o n of the s h e l l was also  observed due to misaligned web support r o l l e r s .  Ill 4.  Misalignment of the submerged shroud i n Test A£4 had  no  observable effect on the thickness of the s o l i d s h e l l i n the mold. 5.  Thinning of the s o l i d s h e l l at the corners of the strand  observed i n some cases.  was  In Test A£4, a corner crack, f i l l e d with material  enriched i n gold and sulphur, was  observed i n the bloom corner.  The  re-entrant corners are associated with poor thermal contact between the strand and the mold as a result of s o l i d i f i c a t i o n shrinkage and subsequent bowing out of the c e n t r a l part of the strand face due to the f e r r o s t a t i c pressure. 6.  The cast structure of the open poured strands was  columnar  adjacent to the outside surface and coarse equiaxed d e n d r i t i c i n the centre.  For strands cast using a curved mold the as-cast centreline of  the strand was  displaced toward the outer radius surface.  The equiaxed  grains are considered to r e s u l t from the remelting of dendrite arms due to the input stream near the bottom of the mold, the dendrite segments f a l l i n g to the lower regions of the l i q u i d pool. dendritic debris at the pool bottom may  The c o l l e c t i o n of  result i n the periodic bridging  and centreline porosity observed i n some tests.  The cast structure of the bloom using an immersed nozzle (Test A£4) consisted primarily of cored, d e n d r i t i c , equiaxed grains with l i t t l e evidence of a columnar structure.  In this bloom and i n the  equiaxed zone i n Test U l , marked solute r i c h pipes, aligned i n V formation, were observed.  The pipes are attributed to downward flow of residual  solute r i c h l i q u i d resulting from s o l i d i f i c a t i o n shrinkage, along " f a u l t paths" i n the d e n d r i t i c debris.  7.  The primary dendrite spacing i n continuously cast s t e e l  was  larger than that observed i n high strength s t e e l cast d i r e c t i o n a l l y against a copper c h i l l .  8.  No macrosegregation was  observed to be present i n the s t a i n -  less s t e e l slab at the centreline, where columnar grains from each of the large slab faces  9.  met.  Radial i n t e r d e n d r i t i c cracking was observed i n strands with  a low to intermediate Mn/S  ratio.  A l l the cracks were f i l l e d with solute  r i c h material.  10-  Intergranular centreline cracking occurred extensively down  the centre of the web  i n the E beam blank, and to a lesser extent i n the  centre of one bloom (Test A£4). r i c h material.  The cracks are mostly f i l l e d with solute  They are attributed to overcooling of the strand i n the  sprays. 11.  In strands cast using a curved mold the d i s t r i b u t i o n of  sulphide inclusions appears to be related to the Mn/S  r a t i o of the s t e e l .  With a low r a t i o , clumps of sulphide inclusions are found i n a band near the inside radius surface of the strand.  The clumps of inclusions c l e a r l y  form i n the s o l i d - l i q u i d region and f l o a t up to the advancing inner radius s o l i d i f y i n g front where they are trapped.  With a high Mn/S  r a t i o , the  clumps of inclusions are more uniformly dispersed throughout the casting.  12.  There i s excellent agreement between the observed pool p r o f i l e s  i n the mold and the p r o f i l e s calculated, using the Savage and Pritchard equation for the heat flux between the strand and the mold.  113  13.  The calculated surface temperature of low carbon b i l l e t s at  the bottom of the mold agreed to within 2 to 5% of measured values reported i n the l i t e r a t u r e .  14.  The pool and surface temperature p r o f i l e s i n the mold,  calculated using the f i n i t e difference model, have been found to agree closely with p r o f i l e s calculated with an i n t e g r a l p r o f i l e model.  15.  The calculated values of the pool depth based on a heat  transfer analysis of the strand along the entire l i q u i d pool are thought to be reasonable.  This i s supported by the good agreement between the  estimated pool depth i n Test A£3, determined with the tungsten p e l l e t , and the calculated value. 16.  Recent evidence indicates that i n most of the tests the  tungsten p e l l e t , used to estimate the pool depth, was obstructed from reaching the pool bottom by s o l i d debris.  This accounts for the difference  between the measured and calculated pool depths.  114  CONCLUSIONS  The r e s u l t s of the present investigation c l e a r l y demonstrate that important information  can be obtained concerning the operating  c h a r a c t e r i s t i c s of continuously  cast b i l l e t s , blooms, beam blanks and  slabs, using radioactive tracer techniques.  Observations of the thickness  and uniformity of the s o l i d s h e l l i n the casting (a) can be related to the l u b r i c a t i n g practice by the incidence of tearing at the meniscus, and fluctuations i n s h e l l thickness,  (b) can indicate a tendency for corner  cracking associated with t h i n corners,  (c) demonstrate d i s t o r t i o n s of the  casting due to non-uniform cooling, normally not observable due to r e shaping of the s t e e l i n the spray cages or withdrawal r o l l s , (d) r e l a t e r a d i a l cracking to s h e l l d i s t o r t i o n s and determine when the cracking occurs.  The cast structure of the s t e e l i s normally resolved i n the autoradiographs and can be examined to determine (a) the size and d i s t r i b u tion of equiaxed grains, (b) the presence of corner, r a d i a l and centreline cracks f i l l e d with residual l i q u i d during f i n a l s o l i d i f i c a t i o n , (c) the d i s t r i b u t i o n of clumps of inclusions i n the s t e e l , distinguishing those which formed i n s i t u from those which moved, through the l i q u i d pool to t h e i r f i n a l positions, (d) the relationship of solute r i c h pipes and the cast structure.  The extent of f l u i d flow i n the l i q u i d pool can be  established, p a r t i c u l a r l y as i t relates to pouring with an open stream or using immersed nozzles.  The heat flow analysis, by coupling calculations with d i r e c t observations and measurements, establishes that the boundary conditions  115  adopted i n the calculations do apply to the r e a l continuous casting situation.  Pool depths and surface temperatures  can be  realistically  calculated and the e f f e c t of changing casting conditions or mold design can be predicted with reasonable confidence.  116  SUGGESTED FUTURE WORK  1.  I t i s recommended that further tracer experiments be  conducted t o : a)  e s t a b l i s h the f l u i d flow pattern i n the l i q u i d pool by varying the p o s i t i o n and time of tracer addition.  b)  determine the relationship between mold corner radius and corner cracking by examining the e f f e c t of radius on l o c a l shell  c)  thickness.  investigate the e f f e c t s of tundish teeming practice and pouring temperature on the cast structure.  2.  Temperature measurements i n the mold should be made to determine  d i r e c t l y the heat flux from the casting to the mold cooling water as a function of distance both below the meniscus and around the mold perimeter. 3.  The relationship between i n t e r n a l cracking and stress concen-  trations i n the b i l l e t due to improper cooling conditions should be investigated using a simple stress analysis and the temperature d i s t r i bution i n the s o l i d s h e l l determined from the heat flow analysis. 4.  Measurements of the surface temperature of the strand i n the  sub-mold regions should be made to check the temperatures predicted by the mathematical models. 5.  The spray heat transfer c o e f f i c i e n t s should be determined as a  function of spray water flux.  droplet s i z e , momentum, impingement angle and  Also the e f f e c t of r o l l e r s i n the spray chamber on the heat transfer  c o e f f i c i e n t should be evaluated.  117  APPENDIX  Derivation of Formulae f o r the F i n i t e Difference Models  In the f i n i t e difference formulation of equation (3), a thin horizontal s l i c e of the section being cast was subdivided into a number of equally spaced elements with nodal points being located at their centres (Figure 4 ° ) .  The node corresponding to the centre l i n e of the  casting was designated as 1 and successive nodes as 2, 3, 4, etc., with the surface node being designated as n.  Each nodal point f o r nodes 1  through (n-1) represents a volume of metal of unit area and width, Ay, the width of the n th node being Ay/2.  In order to solve the unsteady one dimensional conduction equation (3) an e x p l i c i t method of f i n i t e differences was used.  This  method involves c a l c u l a t i o n of the t o t a l enthalpy of a node at time t + At, (H') from the known node enthalpies calculated at time t,(H). The t o t a l enthalpy of a node f o r nodes 2 through (n-1) was calculated by substituting into equation (3) f i r s t - o r d e r forward and central difference approximations f o r the time and distance p a r t i a l derivatives.  Then, solving f o r H i , equation (14) was obtained.  118  n  n-1  2  i - l  i  + 1  I dx = u • A t  •Ay r~-  Ay/2  Figure 46.  Arrangement of nodes i n horizontal s l i c e f o r one-dimensional f i n i t e difference model.  C  INPUT  START  DATA ,  )  PHYSICAL  P R O P E R T I E S , INITIAL BOUNDARY  COND,  CONDITIONS  t = t + Al  CALC.  Hn  CALC.  Hn  CALC.  U .M  [20). [6.7]  SIMPSON  Hn'  [2 2] . [9]  S  INTEGRATION OF Q.  CALC.  T'  2 Ion  Figure 47.  FOR FROM  NODES H'  Flow chart of computer program f o r f i n i t e difference model.  119  Ii  H =H  +  i i l " i i-1>  [(a+ b T  )(T  2T  + T  +  +  p(Ay)  ! <W  - i+i2 T  The temperature a second-order boundary  +  i - i  T  2  )  ]  (  1  4  )  of the c e n t e r node was c a l c u l a t e d by w r i t i n g  forward d i f f e r e n c e a p p r o x i m a t i o n f o r the c e n t r e l i n e  condition.  t £ 0  Solving  i - i  T  y = 0  ay  = 0  (15)  f o r T^ then g i v e s  T  i  I 2  =  T  " I  T  3  (  1  6  )  The s u r f a c e temperature was computed from a heat b a l a n c e on node n , 3T  -  ^  Ay  -  %  2  P  3H  K  ( 1 7 )  U s i n g a f i r s t - o r d e r forward and backward f i n i t e d i f f e r e n c e expansion f o r the time and d i s t a n c e p a r t i a l d e r i v a t i v e s , e q u a t i o n (17) can be  rewritten  as  Kn  =  H  r, n +  2At  o t ( a + b T ) (T v2 n P (Ay)  - T ) - Ay • q ] n-1 n o  Having c a l c u l a t e d the e n t h a l p y o f a g i v e n node a t time t + A t , the  (18)  120  temperature was then computed using the enthalpy-temperature relationships presented i n Figure 2 .  The distance between nodes, Ay, was f i r s t taken to be 1/20 of the half width of the casting.  Using t h i s value of Ay, the time i n t e r v a l  between i t e r a t i o n s , At, was determined from the s t a b i l i t y c r i t e r i o n (equation (19)).  k  P  A  C  < 1/6  t  (Ay)  (19)  2  The values of both Ay and At were varied i n subsequent computer runs and i t was found that the temperature f i e l d was not appreciably affected. A flowchart of the computer program i s given i n Figure 47. In the f i n i t e difference formulation of equation (2), the nodal arrangement used i n the transverse quarter section of the casting i s shown i n Figure 48.  In order to simplify the computation, i t was assumed that  the blooms and b i l l e t s were square so that nodes i n the y and z directions i  are equal i n size. This assumption was true i n a l l cases except on the blooms at 2 Algoma Steel (22.9 x 26.7 cm.).  In this case the dimensions pf the blooms 2 were taken to be 24.8 x 24.8 cm. . The method of solution of the two-dimensional conduction equation i s similar to the one-dimensional case.  By solving equation (2)  to determine the t o t a l enthalpy at time t + At f o r the central nodes, H^_., equation (20) was obtained.  121  Figure 48.  Arrangement of nodes i n horizontal section of b i l l e t f o r two-dimensional f i n i t e difference model.  122  f  ( I  i,J«  "  "  2  2  T  i,  [(a + b l ,  ,  — (T  2 _ 2T  4 i+l,j  3  +  l  T  )(I  i+l,j  U  • i,i-i  +  +  - 2T,  • T ±-l,3  + T  2) 1  + T i-l,j  l  )+  ; J  Determining the enthalpy at time t + At f o r the surface nodes, (i,n) at y = 0, from the heat balance on the node, gives  H!  i,n  = H,  i,n  + p  2  A  (  A y  t  . [(a + bT,  )2  )(T,  i,n  . - T.  i,n-l  ) - Ay * q  i,n  J  n  °  D  ]  (21)  y  and f o r the surface nodes, (n,j) at z = 0, gives  H' = H + - [(a + bT n,j n,j p(Az)  , J  )(T - . - T .) - Az ' q ' J » J °z n  _  1  ]  (22)  n  Since i t i s assumed that Ay = Az, the temperature d i s t r i b u t i o n in  the cross section should be symmetric about the diagonal.  Therefore,  the heat flux from only one face need be considered.  The same s t a b i l i t y c r i t e r i o n was used i n t h i s solution as i n the one-dimensional case.  123  REFERENCES  1.  S z e k e l y , J . and Stanek, V., Met. T r a n s . , V o l . 1 , 1970, pp.119-126.  2.  M i l l s , N.T. and B a r n h a r d t , L.F., J . M e t a l s , V o l . 2 3 , 1971, pp.37-43.  3.  S z e k e l y , J . and Yadoya, R.T., Met. T r a n s . , V o l . 3 , 1972, pp.2673-2680.  4.  Varga, C. and Fodor, J . , P r o c e e d i n g s of the Second I n t e r n a t i o n a l Conference on the P e a c e f u l Uses of Atomic Energy, U n i t e d N a t i o n s , 1959, pp.235-236.  5.  A r n o u l t , J . , Kohn, A. and Plumensi, J.P., Revue de M e t a l l u r g i e , V o l . 6 6 , pp.585.  6.  G a u t i e r , J . J . , M o r i l l o n , V. and D u m o n t - F i l l o n , J . , J . I r o n S t e e l Vol.208, pp.1053-1059.  7.  Morton, S.K. and Weinberg, F., J . I r o n S t e e l I n s t . , Vol.211,  1973.  8.  Gomer, C R . pp.26-35.  1969,  9.  Nagaoka, N., Inamoto, K. and Nemoto, H., T r a n s . I S I J , Vol.12, 1972, pp.317-319.  and Andrews, K.W.,  J . I r o n S t e e l I n s t . , Vol.207,  Inst.,  10.  Zeder, V.H. and Hedstrom, J . , Radex-Rundschau, V o l . 2 , 1971, pp.407-417.  11.  M o r i , H., Tanaka, N., Sato, N. and H i r a i , M., 1972, pp.102-111.  12.  U s h i j i m a , K., Continuous C a s t i n g of S t e e l , I r o n and S t e e l S p e c i a l Report 89, 1965, pp.59-71.  13.  Adams, C.J., P r o c . Nat. Open H e a r t h B a s i c Oxygen S t e e l Conf., pp.290-302.  14.  L a n k f o r d , W.T.  15.  Pehlke, R.D.,  16.  H i l l s , A.W.D., J . I r o n S t e e l I n s t . , Vol.203,  17.  Donaldson, J.W. and Hess, M., i n Continuous P r o c e s s i n g and P r o c e s s C o n t r o l , ed., T.R. Ingraham, Met. Soc. AIME Conf., V o l . 4 9 , 1966, pp.299-319.  18.  M i z i k a r , E.A., T r a n s . Met. Soc. AIME, Vol.239,  Trans. I S I J ,  Vol.12,  Inst.  Vol.54,  J r . , Met. T r a n s . , V o l . 3 , 1972, pp.1331-1357. ASM Met. Eng. Quart., V o l . 4 , 1964, pp.42-47. 1965, pp.18-26.  1967, pp.1747-1753.  124  19.  H i l l s , A.W.D., Trans. Met. Soc. AIME, Vol.245, 1969, pp.1471-1479.  20.  Fahidy, T.Z., J . Iron Steel Inst., Vol.207, 1969, pp.1373-1376.  21.  Kung, E.Y. and Pollock, J . C , i n Instrumentation f o r the Iron and Steel Industry, ISA Proceedings, Vol.17, 1967, pp.8-1 - 8-2.  22.  Savage, J . , J . Iron Steel Inst., Vol.200, 1962, pp.41-47.  23.  Savage, J . and Pritchard, W.H., pp.267-277.  24.  Krainer, H. and Tarmann, B., Stahl Eisen, Vol.69, 1949, pp.813-819.  25.  Brimacombe, J.K. and Weinberg, F., J . Iron Steel Inst., Vol.211, 1973.  26.  Mizikar, E.A., Iron Steel Eng., Vol.47, No.6, 1970, pp.53-60.  27.  BISRA, Physical Constants of Some Commercial Steels at Elevated Temperatures, 1952, Butterworths, London.  28.  Brimacombe, J.K., L a i t , J.E. and Weinberg, F., Proceedings Mathematical Process Models i n Iron and Steelmaking, Amsterdam, February, 1973.  29.  Andrew, D.J., Open Hearth Proceedings, 1969, pp.143-148.  30.  Hester, K.D., Mulligan, E.H., Rohatynski, E. and Woodhouse, CH., Can. Met. Quart.,, Vol.7(2), 1968, pp.97-107.  31.  Wagstaff, R.S., Stock, G.E. and Layne, CN., Iron Steel Eng., Vol.43, 1966, pp.71-76.  32.  M u t t i t t , F . C , Iron Steel Eng. , Vol.46, No.l, 1969, pp.83-91.  33.  Lucenti, G.S., Iron Steel Eng., Vol.46, No.7, 1969, pp.83-100.  34.  Vandrunen, G., The Univ. of B r i t , Col., private communication (1973).  35.  Gomer, C-R. and Andrews, K.W., P.110, 1968, pp.363-369.  36.  Kohn, A., Discussion Four, The S o l i d i f i c a t i o n of Metals ISI, p.110, 1968, p.416.  37.  Dickens, R., The Univ. of B r i t . Col., private communication (1972).  J . Iron Steel Inst., Vol.178, 1954,  The S o l i d i f i c a t i o n of Metals ISI,  125  38.  Weinberg, F. and Buhr, R.K., 1968, pp.295-304.  The S o l i d i f i c a t i o n of M e t a l s I S I , P.110,  39.  Sims, C.E. and Forgeng, W.D., E l e c t r i c Furnace Steelmaking, V o l . 2 , Sims, C.E., ed., pp.373, I n t e r s c i e n c e P u b l i s h e r s , New York, 1967.  40.  Weinberg, F. and Vandrunen, G., communication (1973).  The U n i v . o f B r i t . C o l . , p r i v a t e  126 PUBLICATIONS  J.K. Brimacombe, J.E. L a i t and F. Weinberg, The Application of Mathematical Models to Predict Pool P r o f i l e s i n Continuously Cast Steel, Paper presented to the Second ISI Conference on Mathematical Process Models Applied i n Iron and Steelmaking, Amsterdam, Netherlands, 19-21, February, 1973, to be published by the ISI. J.E. L a i t , J.K. Brimacombe, and F. Weinberg, Pool P r o f i l e , Liquid Mixing and Cast Structure i n Steel, Continuously Cast i n Curved Molds, Paper to be presented and published at the Conference on Continuous Casting, February, 1973, AIME Annual Meeting, Chicago, I l l i n o i s .  J.K. Brimacombe, J.E. L a i t , and F. Weinberg, A Comparison of Calculated and Observed Liquid Pool P r o f i l e s and Pool Depths i n Continuous Casting of Steel, Paper to be presented and published at the Conference on Continuous Casting, February, 1973, AIME Annual Meeting, Chicago, I l l i n o i s . J.E. L a i t , J.K. Brimacombe, F. Weinberg, and F.C. Muttitt, The Liquid Pool Geometry and Cast Structure i n Continuously Cast Blooms and Beam Blanks at the Algoma Steel Corporation, Paper to be presented at the National Open Hearth and Basic Oxygen Steel Conference, AIME, A p r i l , 1973, Cleveland, Ohio.  

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