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UBC Theses and Dissertations

Study of thermal instabilities in electroslag melting. Jackson, Robert Orrin 1972

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A STUDY OF THERMAL INSTABILITIES IN ELECTROSLAG MELTING  BY  ROBERT 0. JACKSON  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of  METALLURGY  We accept this thesis as conforming  to the  required standard  THE UNIVERSITY OF BRITISH COLUMBIA January, 1972  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y I  in p a r t i a l  the U n i v e r s i t y  s h a l l make i t  freely  f u l f i l m e n t o f the of B r i t i s h  available  for  requirements  Columbia, I agree  for  that  r e f e r e n c e and s t u d y .  f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s  thesis  f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r by h i s of  this  representatives. thesis for  It  financial  i s understood that copying o r p u b l i c a t i o n gain shall  written permission.  Depa rtment The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  Date  not be allowed without my  ABSTRACT  S t r u c t u r a l and c o m p o s i t i o n a l changes  r e s u l t i n g from  interruptions  i n the s t e a d y - s t a t e heat b a l a n c e o f an e l e c t r o s l a g r e m e l t e d i n g o t been i n v e s t i g a t e d attempt was  on a l a b o r a t o r y  a l s o made to s o l v e  scale electroslag  commercial i n g o t s  in a  change f u r n a c e .  The i n v e s t i g a t i o n was alloy steels:  An  some o f the fundamental problems  i n t r o d u c e d by the proposed p r o d u c t i o n of l a r g e tandem e l e c t r o d e  furnace.  have  c a r r i e d out on t h r e e c o m m e r c i a l l y a v a i l a b l e  1) EN-25, 2) AISI 4340, and 3) AISI 630  (17-4 P.H.).  Power i n t e r r u p t i o n experiments on EN-25 and AISI 4340 s t e e l s revealed banding.  o n l y minor s t r u c t u r a l changes but d i d show carbon c o n c e n t r a t i o n Carbon r i c h bands were a l s o produced by p e r i o d i c  i n the s l a g s k i n  variations  thickness.  Power i n t e r r u p t i o n experiments on AISI 630 produced some s t r u c t u r a l changes but no change i n the c o n c e n t r a t i o n s o f the major a l l o y i n g elements was  detected.  The mixing a c t i o n i n the l i q u i d m e t a l p o o l appears to be due t o a slow c o n v e c t i v e motion which causes the l i q u i d of complete m i x i n g a t the s o l i d i f i c a t i o n A g e n e r a l heat b a l a n c e was  rates  calculated  t o approach a s t a t e  found i n the ESR p r o c e s s .  f o r a 10 cm d i a . ESR  The v a r i o u s volume f r a c t i o n s s o l i d i f i e d were c a l c u l a t e d d u r a t i o n s o f the "power-off" mode. were extended to a l a r g e  ingot.  for different  The r e s u l t s of the heat b a l a n c e  (61 cm d i a . ) commercial i n g o t  and the volume  s o l i d i f i e d d u r i n g a 60 second power i n t e r r u p t i o n was e s t i m a t e d . A heat t r a n s f e r program was w r i t t e n state  to determine the unsteady  temperature p r o f i l e s i n an e l e c t r o d e  as a f u n c t i o n  of temperature  - iii  —  of the s l a g b a t h and time a f t e r immersion. i n d i c a t e d t h a t i n order  to a v o i d any major s t r u c t u r a l  t i o n a l changes d u r i n g an e l e c t r o d e change preheating  i s mandatory.  The r e s u l t i n g  operation,  profiles  and/or  composi-  electrode  - iv-  TABLE OF CONTENTS Page 1.  2.  INTRODUCTION  .  .  1  1.1  Problems I n t r o d u c e d by " S c a l e - u p "  2  1.2  O b j e c t i v e s o f the P r e s e n t Work  4  1.3  P r e v i o u s Work  5  EXPERIMENTAL TECHNIQUES  9  2.1  Introduction  9  2.2  Materials  9  2.2.1  E l e c t r o d e Composition  9  2.2.2  S l a g Composition  2.3  10  Ingot P r o d u c t i o n  H  2.3.1  ESR Ingots  H  2.3.2  VAR Ingots.  H  2.4  Specimen P r e p a r a t i o n  11  2.5  Techniques used t o Analyze t h e E f f e c t s of Power I n t e r r u p t i o n s on the S t r u c t u r e and Composition of the Ingot  15  2.5.1  15  2.6  Etching 2.5.1.1  EN-25 and AISI 4340 S t e e l s  2.5.1.2  AISI 630 (17-4PH) S t a i n l e s s S t e e l  15 .  15  2.5.2  Sulphur P r i n t s  16  2.5.3  Autoradiography  16  2.5.4  Micorprobe A n a l y s i s  17  Techniques Used t o Determine the E x t e n t o f the M i x i n g i n the L i q u i d M e t a l P o o l 2.6.1  Sulpur P r i n t s  18 1  8  - v Page  2.7  2.8  Sulphur C o n c e n t r a t i o n A n a l y s i s  18  2.6.3  Radio-Tin Concentration Analysis  19  D e t e r m i n a t i o n of the S o l i d i f i c a t i o n  Rate  19  2.7.1  M e l t Record  19  2.7.2  Tungsten Powder A d d i t i o n  19  D e t e r m i n a t i o n o f the Heat T r a n s f e r i n the System D u r i n g the "Power-Off" Mode  20  D e t e r m i n a t i o n of the Volume P e r c e n t S o l i d i f i e d During a Short Power I n t e r r u p t i o n  21  STRUCTURAL AND COMPOSITIONAL CHANGES PRODUCED BY PERTURBATIONS IN THE GENERAL HEAT BALANCE OF THE SYSTEM.  22  2.9  3.  2.6.2  3.1  An E v a l u a t i o n o f the S e g r e g a t i o n and Banding i n EN-25 and AISI 4340 Produced by I n t e r r u p t i o n s i n the Power Supply t o the System 3.1.1  3.2  3.3  22  Nature o f the S t r u c t u r a l and C o m p o s i t i o n a l Changes  22  3.1.2  O r i g i n o f the Carbon-Rich Bands  23  3.1.3  A l t e r n a t e Techniques Employed t o I n v e s t i g a t e the Nature o f the S e g r e g a t i o n and Banding i n EN-25 and AISI 4340 Produced by I n t e r r u p t i o n s i n the Power Supply  27  3.1.3.1  Sulphur P r i n t i n g  27  3.1.3.2  Autoradiography  28  The E f f e c t of S l a g S k i n T h i c k n e s s on t h e Formation of Carbon R i c h Bands i n EN-25 and AISI 4340 D u r i n g Steady S t a t e P r o d u c t i o n  28  An E v a l u a t i o n of the S e g r e g a t i o n and Banding i n AISI 630  3  0  3.3.1  S t r u c t u r a l Changes  3  0  3.3.2  C o m p o s i t i o n a l Changes  3  u  3.3.3  Commercial  Castings  31  - viPage 4.  5.  MIXING IN THE LIQUID METAL POOL...  34  4.1  O r i g i n of the Mixing Action  34  4.2  E v a l u a t i o n of the M i x i n g A c t i o n  36  THERMAL PARAMETERS 5.1  5.2  E v a l u a t i o n of the Superheat  i n the L i q u i d Metal Pool  39  5.1.1  ESR:  10 cm Diameter  Ingot  39  5.1.2  ESR:  61 cm and 254 cm Diameter  5.1.3  VAR:  10 cm Diameter  Ingots  Ingot  5.2.2  5.2.3  5.2.4  44  Heat T r a n s f e r A c r o s s the L i q u i d M e t a l / S l a g Skin Interface  45  Heat T r a n s f e r A c r o s s the L i q u i d Skin Interface  45  Slag/Slag  Heat T r a n s f e r A c r o s s the L i q u i d Slag/Atmosphere I n t e r f a c e  46  Heat T r a n s f e r A c r o s s t h e . L i q u i d Slag Interface  46  Metal/Liquid  THE EXTENT OF SOLIDIFICATION DURING THE "POWER-OFF" MODE •6.1  6.2  42 42  Heat T r a n s f e r D u r i n g the " P o w e r - O f f Mode 5.2.1  6.  39  D e t e r m i n a t i o n o f the volume s o l i d i f i e d i n t h e m e t a l and s l a g p o o l systems i n a 10 cm diameter, EN-25 ESR Ingot Volume P e r c e n t o f L i q u i d M e t a l t o S o l i d i f y  49  49  Based on 5?  Tungsten 6.3  6.4  Powder A d d i t i o n Experiments  D e t e r m i n a t i o n of the Volume S o l i d i f i e d i n the M e t a l and S l a g P o o l Systems i n a 61 cm Diameter Ingot During a 60 Second Power Loss D e t e r m i n a t i o n of the Volume o f the M e t a l P o o l S o l i d i f i e d i n a 10 cm Diameter AISI 4340, VAR Ingot During a 12.5 Second Power I n t e r r u p t i o n  53  - viiPage 7.  ELECTRODE CHANGE OPERATIONS  58  7.1  Temperature P r o f i l e i n a Commercial E l e c t r o d e  58  7.2  Heat Content  60  7.3  Electrode Preheating  o f a Commercial E l e c t r o d e  62  8.  CONCLUSIONS  65  9.  SUGGESTIONS FOR FUTURE WORK ..  68  APPENDIX I .  Determination of Concentration P r o f i l e s  69  APPENDIX I I .  D e t e r m i n a t i o n o f the Volume o f L i q u i d M e t a l and L i q u i d S l a g which S o l i d i f i e s i n a 10 cm Diameter Ingot During a Range of Power I n t e r r u p t i o n s  71  APPENDIX I I I . D e t e r m i n a t i o n of the Volume o f L i q u i d M e t a l and L i q u i d S l a g t h a t S o l i d i f i e s i n a 10 cm Diameter Ingot D u r i n g a 60 Seconds o f "Power-Off Operation  81  APPENDIX IV.  APPENDIX V.  APPENDIX V I .  REFERENCES  Heat Balance f o r a 10 cm. Diameter VAR Ingot D u r i n g a 12.5 Second Power I n t e r r u p t i o n ...  81  Computer Program t o Determine the UnsteadyS t a t e Temperature P r o f i l e i n an ESR E l e c t r o d e  94  D e t e r m i n a t i o n o f the Volume of L i q u i d M e t a l t h a t S o l i d i f i e s i n a 61 cm Diameter Ingot During 120 Seconds o f " P o w e r - O f f O p e r a t i o n . . .  95  98  - viii  LIST OF  -  FIGURES  Figure  Page  1  Three phase, seven e l e c t r o d e , b i f i l a r f u r n a c e  100  2  Tandem e l e c t r o d e change machine  101  3  Schematic diagram of the U.B.C., ESR  4  Schematic diagram of a VAR  5  Operating  6  E x t e r n a l a d d i t i on of FeS  7  C o n f i g u r a t i o n of the Sn  8  Operating  9  Schematic o u t l i n e of the e x p e r i m e n t a l t r a n s f e r measurements  10  11  12  13  chart during  102  furnace  103  a "power-off" sequence to the melt  113  105  i n the e l e c t r o d e  105  a Sn''""''^ experiment setup f o r heat 107  Macrograph of ±igot no. 3 c o n t a i n i n g t h r e e power i n t e r r u p t i o n s , E t c h : O b e r h o f f e r ' s reagent  3 mag.  6X,  Etch: Oberhoffer's  Macrographs of i n g o t s etched w i t h (A) i n g o t no. 2 and (B) i n g o t no.  reagent  3 percent 3  109  HO  m  nital. 112  16  P o o l p r o f i l e o u t l i n e d w i t h W powder a d d i t i o n s no. 13), E t c h 3% n i t a l  19  108  M i c r o g r a p h of the 18 sec power i n t e r r u p t i o n i n  Schematic r e p r e s e n t a t i o n t i o n model  18  ..  Macrograph of i n g o t no. 1 showing the steady s t a t e s t r u c t u r e of EN-25 s t e e l , E t c h : O b e r h o f f e r ' s reagent  15  17  104  Thermocouple f o r measuring s l a g and m e t a l bath temperatures  i n g o t no. 14  chart during  unit  of the carbon band forma-  Sulphur p r i n t of i n g o t no. interruptions  (ingot 114  6 c o n t a i n i n g s e v e r a l power 115  A u t o r a d i o g r a p h of a s e c t i o n from i n g o t no. i n g a 23 second power i n t e r r u p t i o n  11  contain-  " T r e e - r i n g " banding i n a h i g h carbon a l l o y produced by vacuum a r c r e m e l t i n g  steel  116  116  - ix Figure 20  21  22  23  Page I r r e g u l a r i t i e s i n the s l a g s k i n t h i c k n e s s reproduced i n the m e t a l  117  Banding i n i n g o t no. 13 produced by i r r e g u l a r i t i e s i n the s l a g s k i n t h i c k n e s s , E t c h 3% n i t a l  118  Schematic r e p r e s e n t a t i o n o f banding due to i r r e g u l a r i t i e s i n the s l a g s k i n t h i c k n e s s  119  Macrograph of i n g o t no. 14 c o n t a i n i n g s e v e r a l power i n t e r r u p t i o n s , E t c h 100 ml e t h y l a l c o h o l , 100 ml HC1, 50 ml HN0  120  3  24  L o c a t i o n o f specimens  from i n g o t no. 14 f o r a n a l y s i s  on the e l e c t r o n probe  121  25  C o n c e n t r a t i o n banding i n a commercial AISI 630 i n g o t  122  26  Arcos C o r p o r a t i o n ' s c o n t i n u o u s c a s t i n g ESR p r o c e s s . .  122  27  L o c a t i o n o f specimens  123  28  M i c r o g r a p h of the banded s t r u c t u r e . X 48 E t c h : R a i l i n g ' s reagent Absorbed e l e c t r o n image and X-ray images f o r n i c k e l and chromium i n the banded a r e a X 1000  29  30  used i n the banding a n a l y s i s . .  123 124  Pseudo-binary phase diagrams o f Fe + 18% Cr + 4% N i v e r s u s v a r y i n g cabon content and Fe + 18% Cr + 8% N i v e r s u s v a r y i n g carbon content  125  31  Schaeffler ferrite  126  32  Standard l i n e count f o r p e r c e n t f e r r i t e  33  Crack f o r m a t i o n d u r i n g r o l l i n g  34  Different electromagnetic s t i r r i n g  35  C o n v e c t i v e motion i n the s l a g and m e t a l p o o l produced  diagram f o r AISI 630 s t e e l determination  127 128  coil  configurations  129  by the f a l l i n g m e t a l d r o p l e t s  130  36  A u t o r a d i o g r a p h o f i n g o t no. 10  131  37  P l o t of the r e l a t i v e c o n c e n t r a t i o n s of r a d i o a c t i v e t i n v e r s u s a x i a l d i s t a n c e from the o r i g i n a l i n t e r f a c e P o o l p r o f i l e o u t l i n e d by (A) t u n g s t e n powder, (B) i r o n sulphide .  38  132 133  - x Figure 39  40  Page P l o t o f the r e l a t i v e c o n c e n t r a t i o n s o f s u l p h u r a x i a l d i s t a n c e from the o r i g i n a l i n t e r f a c e Assumed p o o l geometry and imposed boundary t u r e s i n a 10 cm diameter ESR i n g o t  versus 134  tempera135  41  S u b d i v i s i o n o f the m e t a l p o o l  136  42  Assumed temperature d i s t r i b u t i o n i n t h e z d i r e c t i o n .  137  43  Assumed temperature d i s t r i b u t i o n i n t h e r d i r e c t i o n  138  44  Assumed temperature d i s t r i b u t i o n s and c o r r e s p o n d i n g (AT ) values S Avg Assumed p o o l geometry and imposed boundary temperat u r e s i n a 10 cm diameter VAR i n g o t  45  46  47  48  49  50  51  139  140  Assumed temperature d i s t r i b u t i o n s i n t h e z and r directions  141  Regions where t h e r a t e o f heat l o s s i s e f f e c t e d by the "power-off" mode f o r a 7.6cm d i a . ESR i n g o t ....  142  P l o t o f the change i n t h e mould w a l l temperature versus time d u r i n g the "power-off"mode..  143  P l o t o f (q/A) vs AT f o r (a) n o n b o i l i n g b o i l i n g conditions  144  and (b) s u r f a c e  P l o t o f q vs time f o r (a) s l a g ( c o n d u c t i o n , ( r a d i a t i o n and (c) l i q u i d m e t a l  (b) s l a g 145  P l o t o f temperature vs time f o r (a) the s l a g and (b) the metal  146  52  P l o t o f q/A vs time f o r d i f f e r e n t v a l u e s  53  Assumed p o o l c o n f i g u r a t i o n s i n a 10 cm d i a . i n g o t f o r (A) s l a g , (B) metal P l o t o f volume p e r c e n t s o l i d i f i e d v s d u r a t i o n o f the "power-off" mode  149  Macrograph o f i n g o t no. 13 c o n t a i n i n g t h r e e powder a d d i t i o n experiments  150  54  55  56  57  A c t u a l and approximated p o o l p r o f i l e s powder a d d i t i o n experiment  of h ^ .....  147  148  W-  f o r a W-  Schematic r e p r e s e n t a t i o n o f a 61 cm d i a . ESR i n g o t . .  151 152  - xi Figure 58  59  Page Macrograph of i n g o t no. V-3 power i n t e r r u p t i o n s  containing  several  Approximation of the m e t a l p o o l p r o f i l e i n i n g o t V-3  60  154  E f f e c t of a r c c u r r e n t and a r c p o t e n t i a l on the heat f l u x t o the c r u c i b l e w a l l d u r i n g the VAR m e l t i n g of  s t e e l electrodes 61 62 63 64  ^3  ' Heat  X  f l u x p r o f i l e f o r run no. 9, F i g u r e 60  A p p r o x i m a t i o n of the volume s o l i d i f i e d d u r i n g a 12.5 second power i n t e r r u p t i o n i n a 10 cm d i a . VAR i n g o t . P l o t of temperature vs d i s t a n c e along the e l e c t r o d e f o r (a) T, = 1550°C, and (b) T, = 1650°C b b P l o t o f temperature vs d i s t a n c e a l o n g the e l e c t r o d e f o r (a) T = 1550°C, (b) T = 1200°C, t = 100, 500, and 1000 seconds b  i ^s J  J  -^6  1^7 1  5  8  b  159  - xii-  LIST OF TABLES Table  Page  I  Composition o f the a l l o y s s t u d i e d  10  II  ESR melt r e c o r d  12  III  VAR melt r e c o r d  14  IV  Element c o n c e n t r a t i o n s i n the banded r e g i o n s  32  V  A - Volume s o l i d i f i e d  i n t h e m e t a l p o o l system  during  the "power-off" mode B - Volume s o l i d i f i e d i n t h e s l a g p o o l system the "power-off" mode  51 during 51  - xiii  -  LIST OF SYMBOLS Symbol 2 A  cross-sectional  B  magnetic i n d u c t i o n , gauss  C  c o n c e n t r a t i o n a t t h e S/L i n t e r f a c e , i n i t i a l c o n c e n t r a t i o n , wt. %  o  a r e a , cm  wt. %  C x  c o n c e n t r a t i o n x cm from the S/L i n t e r f a c e ,  C x  r e l a t i v e f r a c t i o n a l c o n c e n t r a t i o n x cm from the S/L  Cg  c o n c e n t r a t i o n o f the s o l i d , wt. %  C  c o n c e n t r a t i o n o f the l i q u i d , wt, %  C^  s p e c i f i c heat, c a l g  F  Lorentz Force, n t .  H  wt. % interface  °C ^  h e i g h t o f l i q u i d m e t a l , cm JLi  h  heat t r a n s f e r  h  heat t r a n s f e r c o e f f i c i e n t -2 -1 --1 c a l cm s e c C n  coefficient,  -2 -1 -1 c a l cm s e c °C a t the s l a g / m e t a l  0  i  c u r r e n t , amps  K  thermal c o n d u c t i v i t y , c a l cm ^ s e c ^°C ^  K. A  area c o r r e c t i o n  K  effective  k  __  o  distribution  equilibrium  L  latent  m  mass, g  Q_ A  available  coefficient  distribution  coefficient  heat, c a l g ^  heat c o n t e n t , k c a l s  heat i n p u t i n t o Q  factor  t o t a l heat l o s s ,  the e l e c t r o d e , kcals  j-j  Q_ q  t o t a l heat c o n t e n t , k c a l s -1 r a t e o f heat l o s s , k c a l s s e c  kcals  interface,  - xiv Symbol q  heat l o s s at each i n t e r f a c e ,  r'  number o f u n i t s  Ar  unit  S  from the  kcal  centerline  l e n g t h i n the r' d i r e c t i o n  shape c o r r e c t i o n  factor  s l a g b a t h temperature, ° C T  Q  initial  temperature, ° C  AT.  degrees o f s u p e r h e a t , ° C  V  volume,  AZ  unit  p  density,  e  emmisivity  a  K —— p  C  cm  3  l e n g t h i n the z' d i r e c t i o n g cm  3  2 1 cm sec —  , thermal d i f f u s i v i t y ,  p  -8 a  Stefan-Boltzmann  c o n s t a n t , 5.67  x 10  _o  watts, m  K  -  XV -  ACKNOWLEDGEMENT  The and  author  i s indebted  t o Dr. A M i t c h e l l f o r h i s a d v i c e  a s s i s t a n c e throughout t h e d u r a t i o n  o f t h i s work.  Thanks a r e a l s o due t o Dr. F. Weinberg and f e l l o w graduate students  f o r innumerable h e l p f u l d i s c u s s i o n s . The  assistance  of the t e c h n i c a l s t a f f d u r i n g the e x p e r i m e n t a l  program i s g r e a t l y a p p r e c i a t e d . The  f i n a n c i a l a s s i s t a n c e o f the Consarc C o r p o r a t i o n i s  g r a t e f u l l y acknowledged.  1.  INTRODUCTION  With the increasing demands of modern machine builders for large forgings that can withstand severe service conditions, s t e e l ingots of considerable s i z e and weight w i l l be required. Thus, for example, i n the near future the capacity of turbogenerators i n nuclear e l e c t r i c power stations w i l l be close to 1300 mega watts. The rotor shafts f o r such turbogenerators w i l l have b i l l e t weights of around 300 tons, with diameters greater than 3000 mm  (118 i n . ) .  To produce such rotor shafts, s t a t i c cast s t e e l ingots for forgings weighing more than 600 would be  tons and having diameters about 5000 mm  (197 in.)  required.  The problems associated with producing s t e e l ingots exceeding even 200 tons by conventional  techniques are well known.  During the  c r y s t a l l i z a t i o n of such large volumes of l i q u i d metal, mac.rosegregation and shrinkage processes become s i g n i f i c a n t .  The r e s u l t i s certain  defects i n the s t e e l ingots which are irreparable even with further treatment and are inherently transferred to the forgings and to parts made from them. The e x i s t i n g methods for improving heavy s t e e l ingots, such as sequentially pouring  the l i q u i d metal into the mould, vacuum treatment,  heating and hot topping  the head of the ingots are not  enough and do not guarantee a good macrostructure,  efficient  homogeneity,  uniformity, and isotropy of mechanical properties throughout the b i l l e t and  forgings.  - 2 -  To meet the demands of the modern machine b u i l d e r s , t h e r e f o r e , i t i s not unreasonable t h a t c o n s i d e r a b l e s c a l i n g up  the e l e c t r o s l a g r e m e l t i n g  a t t e n t i o n i s being process  (ESR)  focussed  to produce  on  high  q u a l i t y , l a r g e tonnage i n g o t s .  1.1  Problems Introduced by As  furnace  sizes increase  i n d u s t r y , so too w i l l and  operation.  how  to design  (100 being  to 200  "Scale-up"  The  the problems a s s o c i a t e d w i t h t h e i r  machine t h a t can e c o n o m i c a l l y At p r e s e n t  the m a j o r i t y  produced f a l l - i n t o the 5 to 20  approximately 50  demands imposed  tons.  As  of the  problem o f s c a l i n g up  commercial ESR  the i n g o t weights i n c r e a s e , however, the  expensive.  a machine of t h i s d e s i g n  ton i n g o t a 200  ingots ingots  ton range w i t h a maximum s i z e  success becomes i n c r e a s i n g l y inadequate and  difficulty  construction  produce l a r g e  s i n g l e e l e c t r o d e d e s i g n which i s c u r r e n t l y e n j o y i n g  produce a 200  by  f i r s t problem f a c i n g the p r o c e s s m e t a l l u r g i s t i s  an ESR  tons).  to meet the new  of p r o d u c i n g such l a r g e e l e c t r o d e s  equipment n e c e s s a r y to suspend them and  the  greatest The  main  i s t h a t i n order  ton e l e c t r o d e i s r e q u i r e d . and  the  of  to  .  The  sophisticated  c o n t r o l t h e i r v e r t i c a l motion  p r e c i s e l y makes i t a p r a c t i c a l e x e r c i s e to i n v e s t i g a t e p o s s i b l e alternatives. The most obvious a l t e r n a t i v e i s a machine t h a t uses s e v e r a l electrodes  to produce one  large ingot.  At p r e s e n t  there  are two  types of m u l t i p l e e l e c t r o d e machines i n o p e r a t i o n .  These are  three phase, m u l t i - e l e c t r o d e  the  electrode design  (Figure 2).  design The  ( F i g u r e 1 ) , and  small main  the  tandem  three phase, seven e l e c t r o d e  bifilar  - 3 -  f u r n a c e has  a p r o j e c t e d c a p a c i t y of 100  to 200  tons.  There i s no  i n f o r m a t i o n a v a i l a b l e , however, r e g a r d i n g i t s c u r r e n t s t a t u s .  Another  m u l t i p l e e l e c t r o d e machine i s the t h r e e phase, t h r e e e l e c t r o d e d e s i g n . At p r e s e n t , however, t h i s d e s i g n has not been used as an e l e c t r o d e change machine and  i s limited  The p r i n c i p l e b e h i n d different be  two  to p r o d u c i n g  ingots i n  the 10 to 20 ton range.  t h i s d e s i g n i s that the e l e c t r o d e s are of  l e n g t h s so t h a t whenever one  electrodes operating.  The  r e q u i r e s changing  there w i l l  advantage of t h i s technique  i s that  i t p r o v i d e s the o p e r a t o r w i t h a c o n s i d e r a b l e degree of c o n t r o l the system d u r i n g the e l e c t r o d e change o p e r a t i o n . of  t h i s d e s i g n , u n f o r t u n a t e l y , are i t s complexity  associated with producing The  a l a r g e machine of t h i s  still  over  The main drawbacks and  the c o s t  type.  tandem e l e c t r o d e arrangement, on the o t h e r hand, i s m e c h a n i c a l l y  very simple  and  c o u l d be m o d i f i e d  to produce l a r g e r i n g o t s .  This  d e s i g n i s a l s o much more f l e x i b l e w i t h r e g a r d to i t s power r e q u i r e ments.  I t s main problem i s t h a t d u r i n g the e l e c t r o d e change o p e r a t i o n  the power to the system must be shut o f f which c o u l d d r a s t i c a l l y  alter  the g e n e r a l heat b a l a n c e o f the p r o c e s s . In order to o b t a i n a b e t t e r u n d e r s t a n d i n g of  the tandem e l e c t r o d e d e s i g n i t i s n e c e s s a r y  of the e f f e c t i v e n e s s to ask  the f o l l o w i n g  questions: 1.  To what e x t e n t i s the o v e r a l l heat b a l a n c e  e f f e c t e d by 2.  of the system  the e l e c t r o d e change o p e r a t i o n ?  To what e x t e n t do the r e s u l t i n g  a f f e c t the s t r u c t u r a l  and  changes i n the heat  balance  c o m p o s i t i o n a l u n i f o r m i t y of the i n g o t ?  - 4 -  The  answers t o these q u e s t i o n s  are o f the utmost importance when  c o n s i d e r i n g the f e a s i b i l i t y o f u s i n g the tandem e l e c t r o d e Because o f the c o n s i d e r a b l e investment  design.  of time and money r e q u i r e d t o  produce l a r g e ESR i n g o t s i t i s e s s e n t i a l t h a t they s t r u c t u r a l or compositional i r r e g u l a r i t i e s  c o n t a i n no  t h a t c o u l d e f f e c t the  m e c h a n i c a l p r o p e r t i e s of the s t e e l .  1.2  O b j e c t i v e s of t h e P r e s e n t Work Although  a g r e a t d e a l of l i t e r a t u r e i s a v a i l a b l e p e r t a i n i n g t o  normal ESR p r o d u c t i o n , l i t t l e  o r no work has been p u b l i s h e d which  concerns i t s e l f w i t h d i s r u p t i o n s i n t h e heat b a l a n c e , e f f e c t the s t r u c t u r e and composition is  the o b j e c t o f t h i s study  and how  they  of the s t e e l b e i n g produced.  to a n a l y z e  It  the e f f e c t s o f a power l o s s t o  the system and a l s o other problems r e l a t e d t o e l e c t r o d e change machines. The p r e s e n t major  i n v e s t i g a t i o n was p r i m a r i l y concerned w i t h  five  topics: 1.  The s t r u c t u r a l changes t h a t r e s u l t  from a d i s r u p t i o n i n the.  power supply t o the system. 2.  The degree o f the s e g r e g a t i o n d u r i n g the power l o s s and the  e x t e n t o f any c o m p o s i t i o n a l 3.  banding.  The volume of l i q u i d m e t a l t h a t s o l i d i f i e d  d u r i n g the  power l o s s . 4.  The g e n e r a l heat b a l a n c e  f o r the system and how i t changed  as a r e s u l t of any d i s r u p t i o n s i n the power s u p p l y . 5.  Changing e l e c t r o d e s and i t s e f f e c t on t h e o v e r a l l heat  balance.  - 5 -  In a d d i t i o n t o the major areas o f i n v e s t i g a t i o n , work was a l s o done r e l a t i n g v a r i a t i o n i n the s l a g s k i n t h i c k n e s s oscillations,  to compositional  banding.  produced by c o n t r o l  A l s o , whenever p o s s i b l e ,  the i n v e s t i g a t i o n was extended t o i n c l u d e i n g o t s produced by vacuum arc r e f i n i n g  (VAR) f o r the purpose o f comparison.  Although the experiments were c a r r i e d out on a l a b s c a l e ESR u n i t and many assumptions had t o be made about the system due t o i t s complex n a t u r e i t i s b e l i e v e d t h a t the r e s u l t s can be e x t r a p o l a t e d to provide  meaningful information  large scale electrode  1.3  Previous The  about the q u e s t i o n s  r e l a t e d t o the  change machines.  Work  fundamental p r i n c i p l e s u n d e r l y i n g  the s o l i d i f i c a t i o n of s t e e l  c a s t i n g s have been w e l l documented i n the many books and papers w r i t t e n on the s u b j e c t .  1 2 '  More s p e c i f i c s t u d i e s  3— 8  on m i c r o - and  m a c r o s e g r e g a t i o n i n s t e e l c a s t i n g s , however, have m a i n l y p e r t a i n e d t o s t a t i c i n g o t s , or i d e a l i z e d systems i n which v a r i a b l e s have been p a r t i a l l y c o n t r o l l e d . provide  a great  segregation ESR  deal of information  the s o l i d i f i c a t i o n  Although these papers  concerning  s o l i d i f i c a t i o n and  i n s p e c i f i c systems, i t cannot be a p p l i e d d i r e c t l y  t o the  process because of the l a r g e d i f f e r e n c e s i n the s o l i d i f i c a t i o n mode.  In the ESR p r o c e s s the s o l i d i f i c a t i o n i s d i r e c t i o n a l w i t h i n a water cooled-mould and i s m a i n t a i n e d a t a slow s o l i d i f i c a t i o n r a t e 0.03 by  cm s e c """) a g a i n s t  a l a r g e temperature g r a d i e n t  the system's power i n p u t .  (10 t o 100°C cm "'")  The method a l s o d i f f e r s  casting processes i n that f r e s h metal of a constant  (0.005 t o  from  other  composition i s  - 6 -  added to the  l i q u i d p o o l at a c o n s t a n t slow (3 to 120  g sec  "S  rate.  9 S o l i d i f i c a t i o n studies  on continuous c a s t i n g ,  cold-crucible process, contribute  little  information  p r o c e s s because of the l a r g e d i f f e r e n c e s i n the heat t r a n s f e r between the The  ESR  p r o c e s s has  which i s g e n e r a l l y two  two  ESR  c a s t i n g speeds,  and  systems.  comparison.  p r o c e s s e s p r o b a b l y arose due  between  the  to t h e i r p h y s i c a l s i m i l a r i t i e s .  It  s h o u l d be noted, however, t h a t the  r e d i s t r i b u t i o n during  about the  a  o f t e n been c l a s s i f i e d as a l a r g e zone r e f i n e r ,  an i n v a l i d  a multi-pass operation,  which i s a l s o  and  the  The  confusion  zone r e f i n i n g p r o c e s s i s u s u a l l y  t h a t the r e l a t i o n s h i p g o v e r n i n g the  solute  i n i t i a l pass i s s i m p l y the e q u a t i o n f o r  complete m i x i n g i n a d i r e c t i o n a l l y s o l i d i f i e d c a s t i n g assuming c o n s t a n t metal a d d i t i o n . and  1  S i n c e the e x t e n t of the m i x i n g a c t i o n i n the m e t a l  the e f f e c t of the d e n d r i t i c i n t e r f a c e on  are unknown t h i s e q u a t i o n , t h e r e f o r e , the ESR As in  ESR  the  the d i s t r i b u t i o n c o e f f i c i e n t s  cannot be m e a n i n g f u l l y a p p l i e d  to  system. f a r as any ingots  Fredricksson on  pool  d e t a i l e d examinations of the s o l i d i f i c a t i o n p r o c e s s  i s concerned there has and  Jarleborg"^  s t r u c t u r e of an  18/8  Using s u l p h u r p r i n t s and  been v e r y l i t t l e work done.  a n a l y z e d the e f f e c t s of power i n t e r r u p t i o n s s t a i n l e s s s t e e l produced by  the ESR  a quenching t e c h n i q u e they determined  l i q u i d m e t a l p o o l depth and m i c r o s t r u c t u r e  that a strong  changes on the i n g o t s  structure.  the  and  They found t h a t the  t i o n s i n the system r e s u l t e d i n a banded s t r u c t u r e i n the  On  convective  They a l s o i n v e s t i g a t e d  e f f e c t s of power i n t e r r u p t i o n s , " d i p p i n g " of the e l e c t r o d e , electrode  the  o f the i n g o t s examined.  the b a s i s of these experiments they s p e c u l a t e d mixing a c t i o n e x i s t s i n the m e t a l p o o l .  process.  disrup-  transverse  - 7 -  direction.  I t was  a l s o noted  than 30 seconds there was  t h a t f o r power i n t e r r u p t i o n s s h o r t e r  no apparent s u l p h u r s e g r e g a t i o n and  l o n g e r than 60 seconds t h e r e was segregation. was  significant  detectable  In an experiment u s i n g a preheated  p r o c e s s was  monitoring  Cr and N i c o n c e n t r a t i o n s  They found  a lower c o n c e n t r a t i o n of both  t r a n s i e n t which they a t t r i b u t e d  was  e l e c t r o d e , there  related  found  l o n g i t u d i n a l l y i n an 18/8 Cr and N i i n the  to i n v e r s e s e g r e g a t i o n .  at h i g h melt r a t e s (13.3  (750 mm  d i a . ) i n g o t and  i t was  and  g sec "*") . speeds. ingots  tests.  velocity ratio  The (G/V)  m i c r o s t r u c t u r e which became p r o g r e s s i v e l y c o a r s e r They a l s o performed a c h e m i c a l  found no s i g n i f i c a n t  This  was  performed on a 5 ton  segregation  r e l a t e d the temperature gradient/growth  the i n g o t c e n t e r .  this  examined u s i n g dye p e n e t r a t i o n ,  p r i n t s as w e l l as m i c r o s t r u c t u r e and  observed  final An a n a l y s i s  at these  Another i n v e s t i g a t i o n of the s o l i d i f i c a t i o n i n ESR The work was  ingot.  a l s o made, and  to the much deeper m e t a l p o o l found  conducted by Takada e t a l . " ^  The p o s s i b l e  a l s o i n v e s t i g a t e d by  of the t r a n s v e r s e s e g r e g a t i o n of Cr and N i was type of s e g r e g a t i o n was  times  sulphur  no improvement i n the s u l p h u r s e g r e g a t i o n problem.  zone r e f i n i n g e f f e c t of the ESR  for  sulphur  analysis to  the  towards  a n a l y s i s on the i n g o t  macrosegregation.  12 DeVries  and Mumau  examined the d e n d r i t i c f o r m a t i o n  s o l i d i f i c a t i o n i n h i g h l y a l l o y e d m a t e r i a l s produced by They found  that the m i c r o s e g r e g a t i o n  the consumably m e l t e d i n g o t s and segregation.  and  the ESR  process.  i n c r e a s e d towards the c e n t e r of  t h a t chromium showed i n v e r s e  micro-  They a l s o demonstrated t h a t the secondary d e n d r i t e  s p a c i n g i n c r e a s e d w i t h an i n c r e a s e i n e i t h e r the melt r a t e o r i n g o t s c r o s s - s e c t i o n a l area.  the  arm  Firganek solidification  et a l .  used r a d i o a c t i v e i s o t o p e s to i n v e s t i g a t e the  f r o n t and depth o f the l i q u i d  m e t a l p o o l i n an ESR  185 furnace.  Using W  they s u c c e s s f u l l y o u t l i n e d the p o o l p r o f i l e and  i n g o t s t r u c t u r e , and showed how t h i s technique  c o u l d be used to  determine the optimum o p e r a t i n g c o n d i t i o n s . Although these papers p r o v i d e concerning exception condition. with  some g e n e r a l background  the s o l i d i f i c a t i o n i n the ESR p r o c e s s ,  information  they a l l , w i t h the  of the F r e d r i k s s o n e t a l . paper, d e a l w i t h the steady Despite  the f a c t t h a t the F r e d r i k s s o n e t a l .  paper  state deals  the e f f e c t s o f power i n t e r r u p t i o n s on the system, i t does not  c o n s i d e r the problem i n enough d e t a i l to answer the fundamental questions  asked i n t h i s  presentation.  2.  2.1  EXPERIMENTAL  Introduction The  ESR  i n g o t s used i n t h i s study were produced on the ESR  at the U n i v e r s i t y of B r i t i s h Columbia.  The  VAR  i n g o t s used were  produced o u t s i d e the u n i v e r s i t y a t the Armco S t e e l C o r p o r a t i o n Baltimore,Maryland, The  ESR  and  process  the U.S.  unit  in  Bureau o f Mines i n Albany, Oregon.  i s shown s c h e m a t i c a l l y i n F i g u r e 3 and has  been  14 d e s c r i b e d i n d e t a i l by E t i e n n e .  On  the U n i v e r s i t y u n i t i t was  p o s s i b l e to produce v a r i o u s s i z e d i n g o t s and many of the o p e r a t i n g All  the VAR  e x t e r n a l l y , and  2.2  control  parameters.  i n g o t s examined i n t h i s study were manufactured the  companies i n v o l v e d p r o v i d e d  h i s t o r y f o r each i n g o t . shown i n F i g u r e  to change and  a complete  A schematic diagram of a VAR  production  furnace i s  4.  Materials  2.2.1  Electrode  Composition  For t h i s i n v e s t i g a t i o n three commercial a l l o y s were used. c r i t e r i a f o r s e l e c t i n g these p a r t i c u l a r s t e e l s were: 2) c o s t and  availability  3) the presence of a l l o y i n g elements that would show  s i g n i f i c a n t segregation. alloys  1)  studied.  T a b l e I g i v e s the composition  The  of  the  - 10 -  Table I. (1)  Composition o f a l l o y s  studied  V i b r a c EN-25 ( s u p p l i e d by the B r i t i s h S t e e l C o r p o r a t i o n ) Fe  C  Mn  Bal  0.28  Sn  Cu  Al  0.27  0.01  0.028  (2)  0.67  Si 0.22  S  P  Ni  Cr  0.058  0.012  .2.5  0.72  Mo 0.6  AISI 4340 ( s u p p l i e d by B r i t i s h S t e e l C o r p o r a t i o n ) Fe Bal  (3)  C  Mn  0.39  0.72  Si 0.24  S  P  Ni  Cr  0.018  0.012  1.75  0.84  Mo .24  AISI 630 (17-4PH) ( s u p p l i e d by the Armco S t e e l Company) Fe  C  Bal  0.07  Cu  Mo  4.0  2.2.2  Mn 1.0  Si 1.0  P 0.025  S  Cr  Ni  Co+Ta  0.025  16.5  4.0  0.3  0.5  Slag  Composition  The major s l a g c o n s t i t u e n t was p r e f u s e d c a l c i u m f l u o r i d e . combined w i t h d i f f e r e n t percentages o f r e c r y s t a l l i z e d alumina  I t was grain  (Norton A b r a z i v e 99.9% p u r i t y ) . The s t a r t i n g compact  (used i n a l l cases) c o n s i s t e d of a mixture  of p a r e n t m e t a l t u r n i n g s and 60 g CaF„ powder i n the r a t i o  of 15 g t o  - 11 -  25 g per cm of compact.  2.3  Ingot  2.3.1  Production ESR  Table  Ingots  I I summarizes the o p e r a t i n g  used i n t h i s study. analyzed was The  The  production  c o n d i t i o n s f o r the ESR  data f o r s e v e r a l low  q u a l i t y ingots  not a v a i l a b l e from the producers i n v o l v e d .  technique  used f o r the s t o p - s t a r t experiments i n v o l v e d  s h u t t i n g o f f the main power s u p p l y the c u r r e n t r e c o r d e r continued  to the system.  to o p e r a t e .  During  o p e r a t i n g c h a r t i t was  2.3.2  VAR Table  this period  A s e c t i o n from the  c h a r t during a "power-off" sequence i s shown i n F i g u r e 5.  interruption  ingots  current  Using  p o s s i b l e to get an a c c u r a t e e s t i m a t e  of  the  the  time.  Ingots  I I I summarizes the o p e r a t i n g c o n d i t i o n s f o r the VAR  ingots  examined.  2.4  Specimen P r e p a r a t i o n All  specimens to be examined under the o p t i c a l microscope or  the  e l e c t r o n microprobe were p o l i s h e d down to 1 micron on a diamond l a p . L a r g e r specimens and  specimens where o n l y the m a c r o s t r u c t u r e  importance were p o l i s h e d on  No.  0 or No.  00 emergy paper.  was  of  Table I I .  ingot no.  mould d i a . (cm)  electrode dia. (cm)  7.6  3.81  7.6  7.6  3.81  3.81  electrode comp.  EN 25  EN 25  EN 25  electrode polarity  -ve  -ve  -ve  atmosphere  s l a g comp.  air  CaF -27 wt.% A 1 . 0  3  CaF -27 wt.% A l - 0  3  CaF -27 wt.% A 1 0  3  CaF -25 wt.% A 1 0  3  CaF -25 wt.% A 1 0  3  air  air  2  2  2  2  7.6  7.6  3.81  3.81  AISI 4340  -ve  AISI 4340  -ve  air  2  2  air  2  2  current (amp)  melt rate (g sec -*-) -  ingot length  23  1180  3.4  23  23  1170  3.7  22  23  1160  2.8  23.5  23  1175  3.1  26  23  1150  3.3  25  7.6  3.81  AISI 4340  -ve  air  CaF -27 wt.% A l 0  23.5  1125  2.6  25.5  7.6  3.81  EN 25  -ve  argon  CaF -27 wt.% A l 0  23.5  1200  3.1  23  7.6  3.81  EN 25  A.C.  argon  CaF -27 wt.% A 1 0  25  850  3.4  20  3  CaF -27 wt.% A 1 0  25  825  3.6  11  3  25  925  3.1  24  2  2  2  2  7.6  3.81  EN 25  A.C.  argon  2  2  10  voltage (volts)  7.6  3.81  EN 25  A.C.  argon  CaF -27 wt.% A l - 0 2  Table I I .  11  (Continued)  7.6  3.81  EN 25  -ve  argon  CaF -27 wt.% A 1 0  3  CaF -25 wt.% A _ 0  3  CaF -25 wt.% A 1 0  3  CaF -10 wt.% A 1 0  3  CaF -10 wt.% A 1 0  3  CaF -10 wt.% A 1 0  3  CaF -10 wt.% A 1 0  3  CaF -10 wt.% A 1 0  3  2  2  12  10  6.3  EN 25  -ve  air  2  i  13  10  2  6.3  EN 25  -ve  air  2  2  14  15  16  17  18  7.6  7.6  7.6  7.6  7.6  3.81  3.81  3.81  3.81  3.81  AISI 630  -ve  AISI 630  A.C.  AISI 630  A.C.  AISI 630  A.C.  AISI 630  -ve  argon  2  2  argon  2  2  argon  2  2  argon  2  2  argon  2  2  23  1275  2.7  23  23.5  1550  6.4  48  23.5  1550  6.1  51  22.5  1090  3.4  18  24.5  800  3.0  21  23.5  800  3.09  23  23.5  800  3.2  20  23.5  1400  2.8  22  Table I I I .  ingot no.  ingot dia.(cm)  ingot height(cm)  material  voltage (volts)  current (amps)  melt r a t e (g/sec)  Producer  V-l  16.5  17  A I S I 630  23  4000  16.2  Armco  V-2  16.5  11  AISI 630  23  4000  14.6  Armco  V-3  10.0  25  AISI 4340  26  2900  --  Bureau of Mines  V-4  7.6  25  AISI 630  23  2000  9.1  Armco  - 15 -  2.5  Techniques Used t o A n a l y z e the E f f e c t s o f Power on the S t r u c t u r e  2.5.1  Interruptions  and Composition o f the Ingot  Etching  2.5.1.1  EN-25 and AISI 4340  Oberhoffer's etch to d e t e c t  Steels  i n conjunction  changes i n s t r u c t u r e  disruptions.  and c o m p o s i t i o n r e s u l t i n g from power  Oberhoffer's etch  stannous c h l o r i d e , 50 g f e r r i c  w i t h 3 p e r c e n t n i t a l were used  c o n s i s t s o f 1 g c u p r i c c h l o r i d e , 0.5 g c h l o r i d e , 30 ml h y d r o c h l o r i c  500 ml water, and 500 ml e t h y l a l c o h o l . " ^  This  e t c h a n t was  p a r t i c u l a r l y u s e f u l f o r examining the d e n d r i t i c s t r u c t u r e low  alloy steels.  The 3 p e r c e n t n i t a l  more u s e f u l f o r d e t e c t i n g  acid,  o f the two  on the o t h e r hand was much  changes i n the carbon c o n c e n t r a t i o n  i n the  s t e e l as a r e s u l t o f f l u c t u a t i o n s i n t h e power.  2.5.1.2 As  AISI 630 (17-4PH) there were s e v e r a l e t c h a n t s a v a i l a b l e f o r AISI 630, they  were chosen depending on the d e s i r e d of the specimen.  q u a l i t y o f the e t c h  F o r l a r g e specimens where only  and the s i z e  a macroetch was  needed, the b e s t technique was t o immerse the specimen i n a 50 p e r c e n t hydrochloric  a c i d s o l u t i o n f o r up t o 36 hours.  specimens a much f a s t e r macroetch c o n s i s t e d 100 ml h y d r o c h l o r i c  o f 100 ml e t h y l  a c i d , and 50 ml o f n i t r i c a c i d .  m i c r o e t c h was found t o be V i l e l l a ' s hydrochloric  For smaller  acid, 1 g p i c r i c  etch.  This  alcohol,  The b e s t  i s a mixture o f 5 ml  a c i d and 100 ml e t h y l a l c o h o l .  This  etchant was p a r t i c u l a r l y u s e f u l f o r d e t e r m i n i n g the p r e s e n c e o f the 6-ferrxte  phase.  Another e t c h a n t u s e f u l f o r i d e n t i f y i n g t h i s phase  - 16 -  was  R a i l i n g ' s reagent.  T h i s was  comprised  100 ml e t h y l a l c o h o l and 5 g c u p r i c  2.5.2  Sulphur  o f 100 ml h y d r o c h l o r i c a c i d ,  chloride.  Prints  A convenient way  to observe  the e f f e c t o f a d i s r u p t i o n i n the  steady s t a t e c o n d i t i o n on the s t r u c t u r e and c o m p o s i t i o n of a s t e e l , is  to make a s u l p h u r p r i n t o f the a f f e c t e d r e g i o n .  Because o f the v e r y  low s u l p h u r contents o f the t h r e e a l o y s s t u d i e d , however, i t was n e c e s s a r y to e x t e r n a l l y add s u l p h u r to the system.  T h i s was  done  by adding approximately 4 g o f i r o n s u l p h i d e between the e l e c t r o d e and the mould w a l l as shown i n F i g u r e 6. system was  were c a r r i e d  solidified  i n g o t was  s o l u t i o n f o r 3 to 4 minutes, s o l u t i o n had d r a i n e d away. placed i n direct  cut a x i a l l y i n h a l f and soaked  surface-ground.  i n a 2 percent s u l p h u r i c  then allowed t o hang u n t i l  the  The emulsion s i d e o f the paper  acid  excess was  c o n t a c t w i t h the ground i n g o t s u r f a c e f o r up t o  5 minutes.  The exposed s u l p h u r p r i n t was  each p r i n t  the s u r f a c e of the specimen was  2.5.3  any  out.  P h o t o g r a p h i c bromide paper was  FeS  the  g i v e n s e v e r a l minutes to r e t u r n t o e q u i l i b r i u m b e f o r e  experiments The  A f t e r each a d d i t i o n  then f i x e d and d r i e d . reground  After  to expose u n r e a c t e d  inclusions.  Autoradiography Another  t e c h n i q u e used to d e t e c t c o m p o s i t i o n a l and  changes produced autoradiography.  structural  by d e v i a t i o n s from the steady s t a t e c o n d i t i o n i s An experiment  was  d e v i s e d whereby r a d i o a c t i v e t i n  could be added to the melt under a c l o s e d atmosphere.  T i n was  selected  - 17  because of i t s v e r y  -  low vapour p r e s s u r e  and  i t s d e n s i t y , which i s c l o s e 113  to t h a t of i r o n .  The  s o f t gamma e m i t t e r The  i s o t o p e chosen was  and has  Sn  a h a l f - l i f e of 112  r a d i o a c t i v e i s o t o p e was  introduced  embedding i t i n the e l e c t r o d e and m e l t i n g 7 shows how  the t i n was  the aluminum was while  i t was As  i t was  and  important  and  days."^  i n t o the system by  i t i n t o the system.  s i t u a t e d i n the e l e c t r o d e .  to ensure t h a t t h e r e was  melting  which i s an X-ray  no  The  Figure  purpose of  o x i d a t i o n of  the t i n  alloying. to know the exact  moment the  t i n entered  the  system, a s e r i e s of p r e l i m i n a r y experiments were performed to determine the minimum q u a n t i t y of t i n p l u s aluminum r e q u i r e d to produce a t i o n i n the o p e r a t i n g  c h a r t . I t was  a n o t i c e a b l e change i n the o p e r a t i n g when  they  operating  found t h a t a p p r o x i m a t e l y 2 g produced c u r r e n t . The  e f f e c t on the  the system i s shown i n F i g u r e 9.  c u r r e n t occurs  system as one ingot  enter  or two  perturba-  because the t i n and  The  drop i n the  the aluminum e n t e r  l a r g e drops thereby i n c r e a s i n g the  current  the  electrode-  gap. Once produced, the r a d i o a c t i v e i n g o t s were cut a x i a l l y i n h a l f  and  s u r f a c e ground.  times ranging  2.5.4  from 24  They were then a u t o r a d i o g r a p h e d u s i n g to 72 hours.  Microprobe A n a l y s i s The b e s t t e c h n i q u e f o r determining  elements such as n i c k e l , chromium, and probe. using  exposure  The m i c r o a n a l y s i s was a v o l t a g e of 25 KeV  and  compositional  variations in  copper i s to use  the e l e c t r o n  performed on a JE0L-JXA-3A microprobe a beam c u r r e n t of 0.08  ua.  A  quartz  - 18 -  c r y s t a l was used i n the spectrometer and K all  a  r a d i a t i o n was measured f o r  specimens. Due t o the low X-ray t a k e - o f f angle (9 = 2 0 ° ) , e t c h e d specimens  could not be e f f e c t i v e l y examined.  I t was n e c e s s a r y , t h e r e f o r e , t o  l i g h t l y e t c h the specimens and mark t h e areas o f i n t e r e s t w i t h i n d e n t a t i o n on a microhardness  tester.  Microphotographs  were then taken  of the specimens b e f o r e they were h i g h l y r e p o l i s h e d on the 1 micron diamond l a p . Measurements w i t h the microprobe were made by p o i n t c o u n t i n g f o r p e r i o d s o f 10 s e c , a t 20 m i c r o n i n t e r v a l s .  The r e s u l t s were then  p r i n t e d out both n u m e r i c a l l y and g r a p h i c a l l y .  A l l r e s u l t s were  18 c o r r e c t e d u s i n g the MAGIC  program.  S p e c i f i c areas which showed  c o n c e n t r a t i o n anomalies were q u a n t i t a t i v e l y a n a l y z e d u s i n g t h e i r adsorbed e l e c t r o n and X-ray  2.6  images.  Techniques Used t o Determine  the Extent o f the M i x i n g i n the  Metal Pool 2.6.1  Sulphur P r i n t s A m i x t u r e o f i r o n s u l p h i d e and t u n g s t e n powder was added to the  melt u s i n g the t e c h n i q u e d e s c r i b e d i n S e c t i o n 2.5.2.  The p o o l p r o f i l e  o u t l i n e d by the s u l p h u r r i c h m e t a l on the s u l p h u r p r i n t was then compared w i t h the p r o f i l e o u t l i n e d i n the metal by the t u n g s t e n powder.  2.6.2  Sulphur C o n c e n t r a t i o n A n a l y s i s A c o n t r o l l e d amount o f i r o n s u l p h i d e was added t o a melt i n which  s o l i d i f i c a t i o n was allowed t o proceed under s t e a d y - s t a t e c o n d i t i o n s .  -  The  19  -  i n g o t was subsequently s u l p h u r p r i n t e d and the e x a c t p o s i t i o n of  the s u l p h u r r i c h i n t e r f a c e l o c a t e d .  The change of s u l p h u r c o n c e n t r a t i o n  moving up the i n g o t was then determined by  a  c h e m i c a l a n a l y s i s of  drillings  taken at f i n i t e i n t e r v a l s a l o n g the c e n t e r l i n e .  2.6.3  Radioactive T i n Concentration Analysis R a d i o a c t i v e t i n was i n t r o d u c e d i n t o the melt u s i n g the same  t e c h n i q u e o u t l i n e d i n S e c t i o n 2.5.3.  Thermal  and the r e s u l t i n g a u t o r a d i o g r a p h was used interface.  Drillings  were then monitored  2.7 2.7.1  t o l o c a t e the t i n r i c h  taken a t f i n i t e i n t e r v a l s a l o n g the c e n t e r l i n e  to g i v e a c o n c e n t r a t i o n p r o f i l e  D e t e r m i n a t i o n of the S o l i d i f i c a t i o n Melt  s t a b i l i t y was m a i n t a i n e d  f o r the t i n .  Rate  Record  The average can be determined  s o l i d i f i c a t i o n r a t e f o r 100 to 200 second from the melt r e c o r d .  The parameters  intervals  involved i n  t h i s d e t e r m i n a t i o n are the r a t i o of e l e c t r o d e t o i n g o t diameters and the r a t e o f e l e c t r o d e t r a v e l .  2.7.2  Tungsten Powder A d d i t i o n An a l t e r n a t e method f o r d e t e r m i n i n g the s o l i d i f i c a t i o n r a t e was  the e x t e r n a l a d d i t i o n o f tungsten powder.  The powder was added i n the  same manner as o u t l i n e d f o r the a d d i t i o n o f the i r o n s u l p h i d e to the melt.  The a d d i t i o n s were made a t s p e c i f i c time i n t e r v a l s .  Surface  g r i n d i n g the r e s u l t i n g i n g o t c l e a r l y shows up the t u n g s t e n bands and hence an average s o l i d i f i c a t i o n r a t e can be  determined.  - 20 -  2.8  D e t e r m i n a t i o n o f t h e Heat T r a n s f e r i n t h e System d u r i n g t h e "Power-Off" Mode Most o f t h e a v a i l a b l e heat t r a n s f e r d a t a c o n c e r n i n g t h e ESR u n i t  p e r t a i n s p r i m a r i l y t o the steady s t a t e c o n d i t i o n .  I t was n e c e s s a r y ,  t h e r e f o r e , t o i n v e s t i g a t e t h e r a t e s o f heat t r a n s f e r from t h e m e t a l , the s l a g , a n d a c r o s s t h e s l a g / m e t a l i n t e r f a c e d u r i n g t h e " p o w e r - o f f " mode.  The r a t e s o f h e a t l o s s from t h e s l a g and t h e m e t a l t o t h e  mould c o o l i n g w a t e r were o b t a i n e d by p e r f o r m i n g a s e r i e s o f " p o w e r - o f f " experiments i n a mould w h i c h had thermocouples a t t a c h e d a l o n g i t s length.  The c o n f i g u r a t i o n i s shown s c h e m a t i c a l l y i n F i g u r e 9 .  Copper/constantan i n t e g r a l thermocouples were used t o measure t h e change i n t h e mould w a l l temperature under " p o w e r - o f f " c o n d i t i o n s . Constantan w i r e s (0.0254 cm d i a . ) were embedded i n 0.1 cm d i a m e t e r x 0.125 cm deep h o l e s i n t h e copper m o u l d , and were p l u g g e d by 0.1 cm diameter copper w i r e .  The copper mould was t h e p o s i t i v e  terminal  and c o l d j u n c t i o n s were m a i n t a i n e d a t 0°C by immersing them i n i c e c o o l e d g l a s s tubes c o n t a i n i n g mercury. The e x p e r i m e n t a l problems a s s o c i a t e d w i t h temperature measurements i n s i d e an o p e r a t i n g ESR u n i t a r e enormous.  The h i g h t e m p e r a t u r e s ,  i n t e n s e magnetic f i e l d s , and h i g h p o t e n t i a l s p r e s e n t combined w i t h t h e corrosive nature of the s l a g provide a formidable b a r r i e r to p r e c i s e temperature measurements. A s e r i e s o f t r i a l and e r r o r experiments l e d t o t h e thermocouple d e s i g n shown i n F i g u r e 1 0 . The b o r o n n i t r i d e p r o v i d e d good p r o t e c t i o n as i t was c o m p a t i b l e w i t h t h e W-3Re/W-25Re (0.092 cm d i a . ) thermocouple w i r e , and a c t e d as an e l e c t r i c a l i n s u l a t o r a t t h e temperatures experienced.  The b o r o n n i t r i d e a l s o r e s i s t e d a t t a c k by t h e ESR s l a g  - 21 -  f o r a c o n s i d e r a b l e time.  The thermocouple  t i p was  immersed i n powdered  g r a p h i t e to p r e v e n t any o x i d a t i o n of the thermocouple w i r e s , and t o p r o v i d e some e l e c t r i c a l c o n d u c t i o n i n the event of a w i r e break a t the  t i p . The temperatures were r e a d out t o a Sargentmodel  SR-4  recorder. The procedure used  to o b t a i n the change i n the s l a g and m e t a l  temperatures at the s l a g / m e t a l i n t e r f a c e r e s u l t i n g from a l o s s i n power, was system.  a trial  and e r r o r immersion o f the thermocouple i n t o the  The thermocouple was  s l o w l y lowered i n t o the s l a g u n t i l a  r e a l i s t i c temperature was b e i n g d e t e c t e d then the power was off, was  and the r e s u l t i n g  temperature changes  recorded.  switched  Once the power  t e r m i n a t e d the termocouple became t r a p p e d i n the s l a g cap o r the  i n g o t , so t h a t i t s exact p o s i t i o n c o u l d be determined.  2.9  D e t e r m i n a t i o n of the Volume S o l i d i f i e d  d u r i n g a Short Power  Interruption T h i s experiment i n v o l v e d the e x t e r n a l a d d i t i o n of a p p r o x i m a t e l y 15 g o f tungsten powder between the e l e c t r o d e and the mould w a l l i n a 10 cm diameter mould. the  system, the power was  At the same i n s t a n t the powder was turned o f f .  A f t e r a time i n t e r v a l r a n g i n g  from 10 to 15 seconds a s i m i l a r q u a n t i t y o f powder was s i m u l t a n e o u s l y the machine was  added to  t u r n e d back  on.  added  and  3.  STRUCTURAL AND COMPOSITIONAL CHANGES PRODUCED BY PERBURBATIONS IN THE  3.1  GENERAL HEAT BALANCE OF THE SYSTEM  An E v a l u a t i o n  o f the S e g r e g a t i o n and Banding i n EN-25 and A I S I  4340 Produced by I n t e r r u p t i o n s The  i n the Power Supply to the System  e f f e c t s o f the "power-off" c o n d i t i o n on the s t r u c t u r e and  composition of EN-25 and A I S I 4340 were i n v e s t i g a t e d u s i n g techniques.  various  A l t h o u g h most o f the experiments were performed  EN-25 as the e l e c t r o d e  using  m a t e r i a l , i t was n e c e s s a r y t o use AISI 4340  when EN-25 was n o t a v a i l a b l e . I t should be n o t e d , however, that the compositions o f these two a l l o y s a r e v e r y s i m i l a r .  3.1.1 The  The Nature o f the S t r u c t u r a l and C o m p o s i t i o n a l Changes first  step  i n the i n v e s t i g a t i o n was t o determine the e f f e c t s  that power i n t e r r u p t i o n s have on the i n g o t  structure.  To get a b e t t e r  understanding o f these e f f e c t s , however, the steady s t a t e was determined f o r the purpose o f comparison. produced under steady s t a t e c o n d i t i o n s  structure  Ingot no. 1 was  and i s shown i n F i g u r e  s t r u c t u r e i s v e r y u n i f o r m and has a w e l l d e f i n e d  11.  The  a x i a l growth  direction. Having determined the steady s t a t e s t r u c t u r e 3 were produced c o n t a i n i n g duration  i n g o t s no. 2 and no.  d e l i b e r a t e power i n t e r r u p t i o n s r a n g i n g i n  from 8 seconds to 65 seconds.  Figure  12 shows i n g o t no. 3  etched w i t h O b e r h o f f e r ' s marked by  the l i g h t  reagent.  c o l o u r e d bands.  power i n t e r r u p t i o n r e g i o n was c o u l d be The  The e f f e c t e d r e g i o n s are  clearly  A micrograph of the 18 second  examined to see i f the l i g h t bands  accounted f o r by a change i n the i n g o t s t r u c t u r e ( F i g u r e  c e n t e r of the banded r e g i o n appears to show some refinement  s t r u c t u r e , but n e a r e r w i t h l i t t l e or no  the edges the d e n d r i t e s have c o n t i n u e d  change i n t h e i r primary  Another p o s s i b i l i t y was associated with Considering  compositional  n i c k e l , and  spacing.  tie  two  s t e e l s , and  o  To check the p o s s i b i l i t y  tion i n steels  2 and no.  ( F i g u r e 14).  3 percent n i t a l . of carbon e n r i c h e d  Comparing F i g u r e s 12 and  14 i t can  c o l o u r e d bands etched up  be  dark i n the  T h i s i n d i c a t e d t h a t the bands are p r o b a b l y  regions  steel.  The banded r e g i o n s were a l s o a n a l y z e d c o n c e n t r a t i o n of both n i c k e l and  f o r f l u c t u a t i o n s i n the  chromium on the e l e c t r o n probe.  specimens from i n g o t s no.  2 and no.  3, however, r e v e a l e d  Stepno  s i g n i f i c a n t v a r i a t i o n s i n the c o n c e n t r a t i o n of e i t h e r element.  3.1.2  The  3  3 p e r c e n t n i t a l which i s used to i n d i c a t e d e c a r b u r i z a -  seen t h a t the p r e v i o u s l y l i g h t  scanning  carbon,  t h a t the bands were  produced by changes i n the carbon c o n c e n t r a t i o n i n g o t s no. were etched w i t h  their  (Co/k ) the t h r e e elements most  d e t e c t a b l e change i n c o n c e n t r a t i o n were  chromium.  to grow  changes i n the e f f e c t e d r e g i o n s .  the a l l o y i n g elements p r e s e n t i n  to show any  i n the  t h a t the l i g h t l y etched bands were  maximum c o n c e n t r a t i o n s i n the l i q u i d likely  arm  13).  O r i g i n of the Carbon-Rich Bands  A p o s s i b l e e x p l a n a t i o n f o r the o r i g i n of the carbon r i c h has been proposed.  For convenience the proposed model has  regions  been  - 24 -  d i v i d e d i n t o three s t a g e s :  1) t u r n i n g the power o f f , 2) t u r n i n g the  power back on, and 3) r e - e s t a b l i s h i n g e q u i l i b r i u m c o n d i t i o n s .  The  t h r e e stages are shown s c h e m a t i c a l l y i n F i g u r e 15. Stage I In  the i n i t i a l seconds o f the "power o f f " mode, s o l i d i f i c a t i o n i n  the metal p o o l would proceed n o r m a l l y , w i t h the p o s s i b l e e x c e p t i o n o f the l i q u i d metal i n c o n t a c t w i t h the s l a g s k i n a d j a c e n t t o the mould. Due  t o the h i g h heat  to s o l i d i f y . "power-off"  t r a n s f e r i n t h i s r e g i o n , t h i s metal  could begin  A g e n e r a l d e l a y i n the m e t a l system's response  t o the  c o n d i t i o n would p r o b a b l y o c c u r , however, because the  steady s t a t e heat supply t o the m e t a l p o o l would be i n p a r t As t h i s flow o f heat  d i m i n i s h e d w i t h time the s o l i d i f i c a t i o n  the system would g r a d u a l l y i n c r e a s e .  As the l i q u i d metal  maintained. rate i n  continued to  s o l i d i f y the r e l a t i v e c o n c e n t r a t i o n of carbon i n the l i q u i d would i n c r e a s e s i n c e the volume o f l i q u i d metal would be s t e a d i l y d i m i n i s h i n g . The of  l i q u i d s l a g , on the other hand, would c o o l r a p i d l y because  i t s much h i g h e r r a t e of heat  l o s s , and because i t s heat supply i s  p r i m a r i l y due to r e s i s t a n c e h e a t i n g . solidify; initially tip.  I t would, t h e r e f o r e , b e g i n t o  a t the edges and top, and then around the e l e c t r o d e  As the s l a g s k i n a t the edges and the top t h i c k e n e d the r a t e  heat l o s s  from the system would decrease,  of  r e d u c i n g the s o l i d i f i c a t i o n  rate. Stage I I When the power supply t o the system i s turned back on the e l e c t r o d e melt for  r a t e would be h i g h e r than i t s e q u i l i b r i u m v a l u e .  The reason  t h i s h i g h e r melt r a t e i s t h a t the heat g e n e r a t i o n i n the molten  s l a g would be i n c r e a s e d f o r a g i v e n power i n p u t , because of the  - 25 -  l i q u i d s l a g ' s reduced volume.  The i n c r e a s e d m e l t r a t e would have two  main e f f e c t s on the m e t a l p o o l system.  Firstly,  t h e r e would be a  l a r g e f l u x of heat i n t o the remaining l i q u i d metal p o o l .  T h i s heat  would cause the s o l i d i f i c a t i o n r a t e t o d e c r e a s e , and i n cases where the l i q u i d p o o l was completely  o r almost completely  c o u l d r e s u l t i n some r e m e l t i n g  of the i n t e r f a c e .  solidified i t  Secondly, the  i n c r e a s e d volume o f l i q u i d metal would r e s u l t i n a h e i g h t metal (H-^) b e i n g  e s t a b l i s h e d a t the edge o f the i n g o t .  of l i q u i d  The n e t r e s u l t  of these two e f f e c t s would be a much deeper l i q u i d m e t a l p o o l than the e q u i l i b r i u m c o n f i g u r a t i o n . heat g e n e r a t i o n  i n the s l a g d u r i n g  profile  Another e f f e c t of the i n c r e a s e d t h i s stage would be the r e m e l t i n g  of some of the s l a g t h a t s o l i d i f i e d d u r i n g  the "power-off" mode.  Stage I I I As  the volume o f molten s l a g r e t u r n s t o i t s e q u i l i b r i u m v a l u e ,  the e l e c t r o d e melt r a t e would be decreased, r e d u c i n g to the m e t a l system.  Therefore, with  the heat  supply  the system r e t u r n i n g t o i t s  thermodynamic steady s t a t e , the deep m e t a l p o o l would become p r o g r e s s i v e l y less stable.  In order  f o r the pool to re-achieve  i t s equilibrium  c o n f i g u r a t i o n , the s o l i d i f i c a t i o n r a t e i n the c e n t e r r e g i o n o f the i n g o t must i n c r e a s e . is  The r e s u l t o f the i n c r e a s e d s o l i d i f i c a t i o n  that the e f f e c t i v e d i s t r i b u t i o n c o e f f i c i e n t  the system would approach u n i t y . concentration  As flie v a l u e  rate  (K ) f o r carbon i n of K  i n c r e a s e s the  o f carbon i n the s o l i d i f y i n g m e t a l would be i n c r e a s e d .  T h i s proposed e x p l a n a t i o n  f o r t h e o r i g i n o f the carbon  bands has been s u b s t a n t i a t e d by s e v e r a l e x p e r i m e n t a l  rich  results.  the f a c t t h a t l i q u i d m e t a l enrichment by carbon does occur  Firstly,  d u r i n g the  "power-off" mode i s supported by the carbon r i c h patches, which represent the f i n a l volume of l i q u i d metal to freeze at the top of a l l the AISI 4340 and EN-25 ingots examined.  These patches are  c l e a r l y shown at the top of ingot no. 1 i n Figure 11.  Secondly, the  p o s s i b i l i t y that the carbon r i c h bands were produced by an increase i n the s o l i d i f i c a t i o n rate when the power was  turned o f f , was  disproved by the fact that no transverse banding was f i n a l l i q u i d pool of any of the ingots produced.  observed i n the  This implied,  therefore, that the carbon r i c h regions were associated with the power being  re-established.  T h i r d l y , i t was  shown with the use of  tungsten  powder additions during a long "power-off" experiment, that when the power was  turned back on the resulting pool p r o f i l e was very deep i n  the center part of the ingot (Figure 16).  P a r t i c l e s of  tungsten  powder can be seen at the bottom of the carbon r i c h band.  In this  case there was undoubtedly some remelting of the equiaxed zone when the power was  turned on.  F i n a l l y , the photographs of ingots no. 2 and  no. 3 (Figure 14) show that most of the banded regions are composed of many smaller bands which extend for some distance after the power has been turned back on.  This phenomenon can readily be explained i n  terms of the temperature gradient that exists i n the l i q u i d metal at this stage.  Because the heat content of the metal pool would not have  been completely re-established the temperature gradient i n the l i q u i d would be lower than i t s equilibrium value.  This would make the  s o l i d i f i c a t i o n rate much more s e n s i t i v e to any change i n the thermal conditions. system was  Therefore, the fluctuations i n the power input  while the  re-establishing i t s equilibrium thermal conditions would be  - 27 -  s u f f i c i e n t to produce the " s t e p - l i k e " banded structure. On the basis of this experimental evidence, therefore, i t appears that the proposed model i s a r e a l i s t i c explanation of how  the carbon  r i c h bands are formed.  3.1.3  Alternative Techniques Employed to Investigate the Nature of the Segregation and Banding i n EN-25 and AISI 4340 Produced by Interruption i n the Power Supply Two  alternative techniques were used to investigate the effects  of an interruption i n the power supply on the ingots structure and composition.  The two techniques employed were sulphur p r i n t i n g and  autoradiography.  3.1.3.1  Sulphur Printing  Iron sulphide p e l l e t s were added to the melt as outlined i n Section 2.5.2.  Because the s o l u b i l i t y of sulphur i n s o l i d iron i s very  19 low,  iron sulphide inclusions are formed when the sulphur r i c h metal  solidifies.  When a sulphur p r i n t i s made of the sulphide r i c h zone,  the iron sulphide inclusions evolve R^S which reacts with the photographic paper turning i t brown. Figure 17 shows a sulphur p r i n t made from ingot no. 6 which contains several power interruption experiments.  The dendritic  structure of the ingot and the pool p r o f i l e s at the time of each addition have been c l e a r l y outlined.  The effects of the power i n t e r -  ruptions on the composition of the ingot, however, are not  - 28 -  c l e a r l y r e p r e s e n t e d on the s u l p h u r p r i n t . little  s o l u t e enrichment  There appears  even i n the l o n g e r " p o w e r - o f f "  to be v e r y experiments. 19  Because s u l p h u r has a low d i s t r i b u t i o n c o e f f i c i e n t s u l p h u r enrichment  was expected.  (k  Q  = 0.1)  more  Due t o the crude n a t u r e o f the s u l p h u r  p r i n t i n g t e c h n i q u e , however, the changes i n s u l p h u r c o n c e n t r a t i o n were p r o b a b l y too s m a l l t o be d e t e c t e d . 3.1.3.2  Autoradiography  R a d i o a c t i v e t i n was i n t r o d u c e d i n t o the m e t a l p o o l as o u t l i n e d i n S e c t i o n 2.5.3. and s e v e r a l power i n t e r r u p t i o n experiments performed. no.  were  F i g u r e 18 shows t h e a u t o r a d i o g r a p h f o r a s e c t i o n o f i n g o t  11 i n which the power was shut o f f f o r 23 seconds.  shut o f f approximately  The power was  5 seconds a f t e r the r a d i o a c t i v e t i n e n t e r e d the  metal p o o l . The a result  autoradiograph  shows no change i n the d e n d r i t i c s t r u c t u r e as  o f the power b e i n g turned o f f .  There i s , however, a t i n  r i c h band which i s v e r y s i m i l a r t o t h e carbon r i c h bands found by etching.  T h i s t i n r i c h r e g i o n was p r o b a b l y formed i n the same manner  as o u t l i n e d i n S e c t i o n 3.1.2 f o r the f o r m a t i o n o f the carbon  rich  bands.  3.2  The E f f e c t o f the S l a g S k i n on the Formation i n EN-25 and AISI 4340 d u r i n g Steady  of Carbon R i c h Bands  State Production  Banding d u r i n g the steady s t a t e p r o d u c t i o n o f h i g h carbon steels  (e.g. AISI 51100) i s common. T h i s " t r e e - r i n g " banding  i s clearly  shown i n F i g u r e 19 which i s a h i g h carbon a l l o y s t e e l produced vacuum a r c r e m e l t i n g .  T h i s type o f banding  alloy  by  can o c c u r i n s t e e l s w i t h a  - 29 -  much lower carbon content, however, i f there are s i g n i f i c a n t i r r e g u l a r i t i e s i n the slag skin thickness.  Such i r r e g u l a r i t i e s i n the  slag skin thickness are produced by discontinuous  changes i n the  electrode movement, or i n the power settings. Since the slag skin forms on the edge of the copper mould before the metal freezes, any i r r e g u l a r i t i e s i n i t s thickness r e p l i c a t e themselves on the ingot surface. Figure 20.  This e f f e c t can be c l e a r l y seen i n  Because the rate of heat removal r a d i a l l y from the metal  pool i s inversely proportional to the slag skin thickness, any i r r e g u l a r i t i e s i n the thickness w i l l e f f e c t the thermal s t a b i l i t y of the system. Figure 21.  The r e s u l t of such thermal i n s t a b i l i t i e s can be seen i n This i s a photograph of the top of ingot no. 13 and shows  a series of carbon r i c h bands near the edge of the ingot.  The way  these bands are formed can be explained i n terms of the schematic diagram shown i n Figure 22.  At point A the l i q u i d metal would be  s o l i d i f y i n g at a rate which would be i n part governed by the slag skin thickness  ( A X ) . Assuming that A X at point A i s greater than the  normal value, the s o l f f i c a t i o n rate at this point would be slower than the equilibrium rate.  Because of the decreased s o l i d i f i c a t i o n rate,  the K-, value for carbon i n the system would decrease and a thicker solute r i c h band would develop i n front of the interface at point A. As the p r o f i l e continued  to advance towards point B, the s o l i d i f i c a t i o n  rate would increase due to the decreasing value of A X . As the rate increased, K_ would move towards unity and some of the carbon.rich metal ahead of the interface would be s o l i d i f i e d i n producing a small concentration band.  With the continued  point C the sequence would repeat  advance of the interface to  itself.  - 30  3.3  -  An E v a l u a t i o n o f the S e g r e g a t i o n arid Banding i n AISI The  630  e f f e c t s of the "power-off" c o n d i t i o n on the s t r u c t u r e  composition o f AISI 630  3.3.1  and  were i n v e s t i g a t e d .  S t r u c t u r a l Changes The  s t r u c t u r a l changes t h a t r e s u l t e d from the  were c l e a r l y r e v e a l e d by  a standard  macrograph shows t h a t there was  macro-etchant  "power-off" c o n d i t i o n ( F i g u r e 23).  The  a marked change i n the steady  state  growth d i r e c t i o n , p a r t i c u l a r l y at the edges of the i n g o t where maximum r a t e of heat l o s s o c c u r s .  I t was  a l s o observed the  the  growth  d i r e c t i o n of the g r a i n s near the c e n t e r l i n e of the i n g o t became more radially inclined. when the power was of the i n g o t was  A p o s s i b l e cause of t h i s r e o r i e n t a t i o n i s t h a t restored  the  s o l i d i f i c a t i o n r a t e near the  suppressed r e s u l t i n g i n a deeper p o o l p r o f i l e .  would o c c u r i n the same manner as d i s c u s s e d of the  low  c r y s t a l growth  re-nucleated  center  anisotropy  i n Section  3.1.2. Because  e x h i b i t e d by AISI 630,  g r a i n s would tend to grow p e r p e n d i c u l a r  This  to the  the new  p r o f i l e r e s u l t i n g i n the more r a d i a l l y i n c l i n e d o r i e n t a t i o n .  3.3.2  C o m p o s i t i o n a l Changes In order  produced any  to determine whether or not  anomalies i n the steady s t a t e c o m p o s i t i o n of AISI  specimens were q u a n t i t a t i v e l y analyzed Specimens taken from i n g o t no. chromium and and  B-2  the "power-off" c o n d i t i o n  copper.  r e v e a l e d no  The  14  630,  on the e l e c t r o n probe.  ( F i g u r e 24) were scanned f o r n i c k e l ,  microprobe survey of specimens A-1,  significant variation in  A-2,  the c o n c e n t r a t i o n s  of  B-l, the  - 31 -  three elements when compared w i t h the steady s t a t e c o n c e n t r a t i o n s found i n specimens C-1  3.3.3  and  C-2.  Commercial C a s t i n g s S t a i n l e s s s t e e l i n g o t s have been produced  which do e x h i b i t s i g n i f i c a n t  commercially, however,  c o n c e n t r a t i o n banding  ( F i g u r e 25).  i s an AISI 630 grade s t a i n l e s s s t e e l i n g o t which was  produced  Arcos C o r p o r a t i o n s continuous c a s t i n g ESR p r o c e s s ( F i g u r e 26). o r i g i n a l s e c t i o n was  cast i n an 8 i n c h square mould and was  hot r o l l e d down to a 5.5  i n c h by 3.5  inch  This  by  the The  subsequently  billet.  D u r i n g normal o p e r a t i o n on the above f u r n a c e , i n g o t s are removed from an open-bbttomed copper mould a t a c o n s t a n t r a t e . banded s t r u c t u r e  ( F i g u r e 25) p r o b a b l y r e s u l t e d from a  w i t h d r a w a l r a t e caused by the c a s t i n g s t i c k i n g In o r d e r to determine  The  non-uniform  i n the mould.  the exact n a t u r e o f the banded  structure,  specimens were taken from b o t h the banded and u n i f o r m r e g i o n s o f the ingot  ( F i g u r e 27).  An i n i t i a l examination was  done by e t c h i n g the  specimens w i t h V i l e l l a ' s and R a i l i n g ' s r e a g e n t s .  The r e s u l t s showed  t h a t the dark bands c o n t a i n e d a h i g h percentage of the 6 - f e r r i t e phase ( F i g u r e 28).  The next s t e p was  main a l l o y i n g elements  t o determine  the c o n c e n t r a t i o n s o f the  i n the banded r e g i o n s .  probe, the 6 - f e r r i t e p a r t i c l e s were found t o be low i n b o t h n i c k e l and copper.  T a b l e IV.  copper i n  h i g h i n chromium and  F i g u r e 29 shows the X-ray images f o r  chromium and n i c k e l i n a banded r e g i o n . chromium, n i c k e l and  U s i n g the e l e c t r o n  The a c t u a l c o n c e n t r a t i o n s o f  the areas of i n t e r e s t are shown i n  - 32 -  T a b l e IV. Element  c o n c e n t r a t i o n s i n the banded r e g i o n s .  Area  Steady-state 6-Ferrite  region  particle  Inter-ferritic  region  N o n - f e r r i t e band  In o r d e r to understand how  Ni wt.%  Cr wt.%  Cu wt.%  4.58  15.51  3.40  2.44  17.69  2.32  4.54  13.70  3.83  4.05  11.28  3.48  the 6 - f e r r i t e bands formed  e f f e c t on the m e c h a n i c a l p r o p e r t i e s of the s t e e l , i t was examine the thermal h i s t o r y grade of s t a i n l e s s  o f an AISI 630 s t a i n l e s s  s t e e l has been c l a s s i f i e d as a  precipitation-hardening steel.  At the s o l u t i o n  of 1038°C the m e t a l i s a u s t e n i t i c m a r t e n s i t e on c o o l i n g  and undergoes  to room temperature.  This  and  necesaary to  steel.  in solution around 500  32°C.  treating  Subsequent  the t r a n s f o r m a t i o n t o transformation  h e a t i n g to  to 625°C f o r one t o f o u r hours p r e c i p i t a t e s  p a r t i c l e s that  i n c r e a s e the s t e e l s  s t r e n g t h and  630  temperature  The p r e c i p i t a t i o n h a r d e n i n g compounds  as the m e t a l c o o l s .  The  martensitic,  s t a r t s a t a p p r o x i m a t e l y 132°C but i s not complete u n t i l the drops to around  their  temperature remain  temperatures the s m a l l  hardness.  The key to t h i s p r e c i p i t a t i o n hardening mechanism i s t h a t solution  treatment i s c a r r i e d out i n the s i n g l e phase  region.  Since the s i z e and p o s i t i o n  the  austenitic  o f the d i f f e r e n t phase r e g i o n s  - 33 are s t r o n g l y dependent on the c o n c e n t r a t i o n of the a l l o y i n g p r e s e n t , the composition F i g u r e 30 shows how  of the s t e e l must be  carefully  elements  controlled.  the s i z e of the two phase r e g i o n i s i n c r e a s e d as  the n i c k e l c o n c e n t r a t i o n i s decreased. The  6 - f e r r i t e bands, t h e r e f o r e , p r o b a b l y  composition  i n these areas was  the s o l u t i o n treatment  formed because the  o u t s i d e the s p e c i f i c a t i o n range c a u s i n g  t o o c c u r i n the two phase r e g i o n .  subsequent heat treatments  steel  the 6 - f e r r i t e phase was  During  retained  the  throughout,  r e s u l t i n g i n a mixture of a u s t e n i t e , m a r t e n s i t e , and bands of 6-ferrite.  S i n c e the copper i s l e s s s o l u b l e i n the 6 - f e r r i t e phase,  the f e r r i t e p a r t i c l e s would not harden t o the same e x t e n t as the m a t r i x metal.  The r e s u l t , t h e r e f o r e , would be bands of weaker m a t e r i a l  t h a t c o u l d deform at a lower s t r e s s The  s p e c i f i c a t i o n s on AISI 630  level. a l l o w f o r a maximum of 5 t o 7 p e r c e n t  20 f e r r i t e i n the m a t r i x .  The  F i g u r e 31 demonstrates how  S c h a e f f l e r f e r r i t e diagram shown i n  c l o s e l y the composition of the s t e e l must  be c o n t r o l l e d i n o r d e r to keep the f e r r i t e range. was  content w i t h i n the  specified  Using t h i s diagram the f e r r i t e content of the unhanded r e g i o n s  approximately  4 percent.  In o r d e r t o determine  the  content of the banded r e g i o n s a s t a n d a r d l i n e count was ( F i g u r e 32).  The  ferrite employed  r e s u l t s i n d i c a t e d t h a t the bands c o n t a i n e d  approximately  19 p e r c e n t f e r r i t e and t h e r e f o r e were w e l l o u t s i d e the s p e c i f i e d The  r e s u l t of t h i s i n c r e a s e d f e r r i t e content  can be seen i n F i g u r e  T h i s shows a s e c t i o n from the c a s t i n g which has banded s t r u c t u r e d u r i n g  rolling.  range.  cracked along  the  33.  4.  MIXING IN THE  LIQUID METAL POOL  In order to get a b e t t e r u n d e r s t a n d i n g m e t a l p o o l i t was  important  extent of t h i s m i x i n g  4.1  of the mixing  to examine both  the o r i g i n and  Action  With r e g a r d to the o r i g i n of the m i x i n g to c o n s i d e r :  magnetic s t i r r i n g , and drops.  the  action.  O r i g i n of the M i x i n g  main p o s s i b i l i t e s  i n the  1) thermal  3) momentum and heat  G e n e r a l l y the degree of thermal  a c t i o n t h e r e are  c o n v e c t i o n , 2)  electro-  t r a n s f e r from the  c o n v e c t i o n i n the  three  falling  liquid  m e t a l would be n e g l i g i b l e as the r e g i o n s of h i g h e s t temperature at the top of the molten p o o l .  The  degree of thermal  convection  could become s i g n i f i c a n t o n l y i f the p o o l p r o f i l e became curved  c a u s i n g the isotherms  curvature.  exist  deeply  i n the l i q u i d m e t a l to have a pronounced  I t i s u n l i k e l y t h a t t h i s s i t u a t i o n would a r i s e i n a  commercial i n g o t , however, as the p o o l depth i s g e n e r a l l y p r o p o r t i o n a l to the i n g o t r a d i u s and The  therefore, r e l a t i v e l y quite  second p o s s i b l e cause o f m i x i n g  electromagnetic  stirring.  Initiating  shallow.  i n the l i q u i d p o o l i s  t h i s type of m i x i n g  are  L o r e n t z f o r c e s c r e a t e d around an e l e c t r i c a l l y a c t i v e conductor. produce a magnetic f i e l d w i t h which the c u r r e n t can  interact.  the These  - 35 -  However, such i n t e r a c t i o n s w i t h c u r r e n t p a t h f i e l d s are a f u n c t i o n o f the f u r n a c e ' s  electrical  essentially  c o n f i g u r a t i o n a n d , as s u c h ,  are v e r y u n p r e d i c t a b l e . Electromagnetic  s t i r r i n g can be d e l i b e r a t e l y  by i m p o s i n g a magnetic f i e l d on the l i q u i d p o o l .  created,  however,  This technique  f r e q u e n t l y employed i n VAR f u r n a c e s where the f i e l d c r e a t e d by radial coils  ( F i g u r e 34-A) i n t e r a c t s  causes the l i q u i d m e t a l t o p i l e up a g a i n s t  frequency  the  w i t h the l a r g e h o r i z o n t a l  c u r r e n t component t o produce a f o r c e on the l i q u i d m e t a l .  force d i r e c t i o n .  is  This  force  the mould w a l l i n the  By c y c l i n g the c u r r e n t i n the c o i l s a t a low  ( a p p r o x i m a t e l y 0.1 c p s ) ,  the f o r c e d i r e c t i o n changes and  produces an o s c i l l a t i o n of the l i q u i d m e t a l .  A r o t a t i o n a l mixing  e f f e c t i s a l s o produced due t o the s l i g h t asymmetry of the r a d i a l coils. I n a n o r m a l ESR u n i t ( F i g u r e 34-B) the main c u r r e n t i s p a r a l l e l t o the i n d u c e d m a g n e t i c f i e l d ; no L o r e n t z f o r c e s c r e a t e d .  consequently  The o n l y e x c e p t i o n s  component there  are  a r e ESR machines  o p e r a t i n g w i t h a l i v e mould c o n n e c t i o n such as those c o n v e r t e d from VAR u n i t s . current  T h i s type o f mould c o n n e c t i o n has a l a r g e h o r i z o n t a l  component, b u t i t i s p r i m a r i l y c o n f i n e d t o  the top of  slag.  The r e s u l t i s a h i g h degree o f e l e c t r o m a g n e t i c  slag.  Therefore,  the o n l y way e l e c t r o m a g n e t i c  s t i r r i n g i n the  s t i r r i n g c o u l d be  i n d u c e d i n a normal ESR u n i t would be t o produce a magnetic w i t h a h o r i z o n t a l component  (Figure 34-C).  produce a f i e l d of s u f f i c i e n t type of c o i l , , a v e r y l a r g e  the  field  However, i n o r d e r  to  s t r e n g t h i n the l i q u i d m e t a l w i t h  power i n p u t i s r e q u i r e d .  this  T h i s f a c t makes  - 36 -  the technique d i f f i c u l t  t o a c h i e v e i n a m e c h a n i c a l sense,  as the i n g o t s i z e s i n c r e a s e . direct  particularly  The f o r e g o i n g d i s c u s s i o n a p p l i e s t o  current furnaces only.  I n f u r n a c e s employing  alternating  c u r r e n t , t h e i n t e r a c t i o n s a r e much more complex, but t h e n e t e f f e c t is  t o produce The  only small forces.  t h i r d and most l i k e l y cause o f m i x i n g i n t h e l i q u i d p o o l i s  momentum and heat t r a n s f e r t o t h e l i q u i d metal by t h e f a l l i n g The type o f c o n v e c t i v e motion  droplets.  s e t up i n the system by t h e f a l l i n g  drops i s shown s c h e m a t i c a l l y i n F i g u r e 35.  The momentum o f t h e f a l l i n g  drops c a r r i e s them down i n t o the p o o l e n t r a i n i n g l i q u i d behind them. Then, because rise.  o f t h e i r h i g h e r temperature  At i n d u s t r i a l m e l t r a t e s  they tend t o spread out and  (1200 t o 1500 l b s h r ^) s u f f i c i e n t  momentum would be t r a n s f e r e d t o the m e t a l p o o l t o produce  a continuous  mixing a c t i o n . •  4.2  E v a l u a t i o n o f the M i x i n g A c t i o n In o r d e r t o e v a l u a t e the m i x i n g a c t i o n e x p e r i m e n t a l l y , 0.26 g o f  r a d i o a c t i v e t i n was added t o the m e t a l p o o l u s i n g t h e t e c h n i q u e o u t l i n e d i n S e c t i o n 2.5.2.  Adding  the t i n i n t h i s manner would  s i m u l a t e t h e b e h a v i o u r o f t h e f a l l i n g metal d r o p l e t s , and i f m i x i n g was  p r i m a r i l y due t o heat and momentum t r a n s f e r t h e f o l l o w i n g  results  would be expected. 1)  The mixing a c t i o n would be s u f f i c i e n t  to a l l o w t h e r a d i o a c t i v e  t i n t o o u t l i n e t h e shape o f t h e p o o l p r o f i l e . 2)  The m i x i n g a c t i o n would be s u f f i c i e n t  t o approach  a state  of complete m i x i n g at the s o l i d i f i c a t i o n r a t e s used f o r ESR p r o d u c t i o n  - 37 (0:005 to'0.03 cm 3)  Due  sec" ); 1  t o the d e n d r i t i c n a t u r e o f the s o l i d i f y i n g  the e f f e c t i v e d i s t r i b u t i o n  interface, would approach  coefficient  22 The r e s u l t s of the r a d i o a c t i v e t i n experiment consistent  w i t h the p r e d i c t e d r e s u l t s .  x^ere  F i g u r e 36 i s an  autoradiograph  of the m e t a l p o o l which c l e a r l y o u t l i n e s the p o o l p r o f i l e . of d e p l e t i o n o f the t i n w i t h a x i a l d i s t a n c e from i n t e r f a c e was  e x p e r i m e n t a l l y determined  the  by m o n i t o r i n g d r i l l i n g s  t h e r e was  then p l o t t e d based  complete mixing  F i g u r e 37  (Appendix  I-A).  on the assumptions t h a t  i n the l i q u i d p o o l , and  d i s t r i b u t i o n c o e f f i c i e n t f o r the t i n was  t h a t the  u n i t y (Appendix  r e s u l t i n g p r o f i l e showed v e r y good agreement w i t h the  effective  I-B).  d e v i a t i o n near the i n t e r f a c e c o u l d i n d i c a t e t h a t t h e r e was of the l i q u i d  the e x t e n t of the mixing  state conditions.  The  small  some s o l u t e  metal.  A s i m i l a r s e t of experiments determine  The  experimental  curve i n d i c a t i n g the p r e d i c t i o n s were e s s e n t i a l l y c o r r e c t .  enrichment  taken  c o n c e n t r a t i o n s of r a d i o a c t i v e t i n  versus a x i a l d i s t a n c e from the o r i g i n a l i n t e r f a c e A t h e o r e t i c a l curve was  rate  original  at f i n i t e i n t e r v a l s a l o n g the c e n t e r l i n e of the i n g o t . shows a p l o t of the n o r m a l i z e d  The  were c a r r i e d out u s i n g s u l p h u r t o i n the l i q u i d p o o l under  I r o n s u l p h i d e mixed w i t h tungsten powder  steady was  e x t e r n a l l y added t o the system and the p o o l p r o f i l e o u t l i n e d by a s u l p h u r p r i n t was powder.  The  two  compared w i t h the p r o f i l e o u t l i n e d by the p r o f i l e s are shown i n F i g u r e 38.  S i n c e the  tungsten two  p r o f i l e s are i d e n t i c a l t h i s i m p l i e s t h a t s u l f u r p r i n t i n g a c c u r a t e l y  - 38 o u t l i n e s the p o o l The was  -  profile.  r a t e of d e p l e t i o n of s u l p h u r  a l s o determined.  and were analyzed  D r i l l i n g s were taken from i n g o t s no.  f o r t h e i r sulphur  c o n c e n t r a t i o n p r o f i l e f o r i n g o t no. sulphur has  from the o r i g i n a l i n t e r f a c e  a much lower k  value  concentration.  Because  than t i n ((k )„ = 0.1), i t s O  o  expected to show more m a c r o s e g r e g a t i o n .  Examining the p r o f i l e s i t can be seen t h a t the c o n c e n t r a t i o n sulphur  does i n i t i a l l y  a higher On  the e x t e n t  maintains  the o r i g i n a l i n t e r f a c e .  the b a s i s of t h i s i n f o r m a t i o n , t h e r e f o r e , s e v e r a l  p o o l system.  of  drop below the t h e o r e t i c a l p r o f i l e , but  c o n c e n t r a t i o n at l a r g e r d i s t a n c e s from  can be made c o n c e r n i n g  5  resulting  4 i s shown i n F i g u r e 39.  O  c o n c e n t r a t i o n p r o f i l e was  The  4 and no.  proposals  of the m i x i n g a c t i o n i n the m e t a l  F i r s t l y , the m i x i n g i s p r o b a b l y  produced by  a slow  c o n v e c t i v e motion, which at the v e r y slow s o l i d i f i c a t i o n r a t e s used i n ESR  p r o d u c t i o n approaches a s t a t e of complete m i x i n g .  elements w i t h k  Q  v a l u e s between 0.5  and  1.0  (eg.Cr,Ni,Sn ) would  have v e r y l i t t l e m a c r o s e g r e g a t i o n a s s o c i a t e d w i t h c o n c e n t r a t i o n would be power supply 0.5  them, and  probably  their  r e l a t i v e l y u n e f f e c t e d by a d i s r u p t i o n i n the  to the system.  T h i r d l y , elements w i t h k  (eg.C,S,P) c o u l d show some m a c r o s e g r e g a t i o n and  concentration  Secondly  Q  values  their  below  local  c o u l d be e f f e c t e d by an i n t e r r u p t i o n i n the power  supply.  5.  THERMAL PARAMETERS  During the c o n s t r u c t i o n of a s i m p l e heat b a l a n c e f o r the s l a g and m e t a l p o o l systems d u r i n g the " p o w e r - o f f " mode, i t  became apparent  that a b e t t e r u n d e r s t a n d i n g of the l i q u i d m e t a l ' s superheat and the heat l o s s e s from the system d u r i n g the " p o w e r - o f f " mode were necessary.  5.1  E v a l u a t i o n o f the Superheat i n the L i q u i d M e t a l P o o l In o r d e r to get a b e t t e r u n d e r s t a n d i n g of t h i s parameter a  s e r i e s o f c a l c u l a t i o n s were c a r r i e d out u s i n g d i f f e r e n t assumed temperature c o n f i g u r a t i o n s i n the m e t a l p o o l .  S i n c e the l i q u i d  m e t a l ' s superheat i s d i r e c t l y p r o p o r t i o n a l to AT parameter w i l l be used to r e p r e s e n t the heat  5.1.1  ESR:  10 cm d i a .  (AT  Q  = T-T  )  this  content.  ingot  To s i m p l i f y the c a l c u l a t i o n , the p o o l geometry was assumed to be cylindrical. that i t  The h e i g h t of the c y l i n d r i c a l p o o l was c a l c u l a t e d so  c o n t a i n e d the same volume o f l i q u i d m e t a l as the a c t u a l  Based on known temperatures i n the system the l i m i t i n g v a l u e s  pool.  for  23 the temperature d i s t r i b u t i o n were chosen.  The assumed p o o l geometry  and the imposed boundary temperatures are shown i n F i g u r e 40.  - 40 -  The c y l i n d r i c a l m e t a l p o o l was arc o f 1 r a d i a n  ( F i g u r e 41).  d i v i d e d i n t o segments h a v i n g an  S u i t a b l e Az and Ar v a l u e s were chosen  based on the dimensions o f the c y l i n d r i c a l z' d i r e c t i o n :  4 elements w i t h Az = 0.5 1 element w i t h  r' d i r e c t i o n :  volume  =  =  cm  cm.  c a l c u l a t e d u s i n g the g e n e r a l f o r m u l a  base x h e i g h t  l/2[(r'Ar +  where Ar = the u n i t  cm  Az = 0.25  5 elements w i t h Ar = 1  The volume of each element was  V  pool.  |^ )  2  - (r'Ar - |^ ) ] A z  (5.1.1)  2  length  r" = the number of u n i t s away from the c e n t e r l i n e . T h e r e f o r e f o r a l l the u n i t s w i t h r ' > 0  (V) , r  =  > ( )  r'Ar Az  (5.1.2)  2  And f o r the t r i a n g u l a r u n i t at the c e n t e r where r ' = 0 and Ar =  W^»_n  =  Ar  2  Az 8  Ar  (5.1.3)  Knowning the volume of each element i t was  p o s s i b l e to c a l c u l a t e  the amount of superheat a s s o c i a t e d w i t h each one of them f o r a g i v e n temperature d i s t r i b u t i o n i n the metal p o o l . c a l c u l a t i o n i t was z d i r e c t i o n was  F o r the purpose o f t h i s  assumed t h a t the temperature d i s t r i b u t i o n i n the  a l i n e a r f u n c t i o n of z.  The assumed  temperature  - 41 -  d i s t r i b u t i o n i n the z d i r e c t i o n i s shown i n F i g u r e 42.  From F i g u r e  42  the maximum and minimum temperatures f o r each l a y e r o f cubes i n the z' d i r e c t i o n c o u l d be determined.  These became the end p o i n t s f o r the  temperature d i s t r i b u t i o n s i n the r ' d i r e c t i o n .  Because  the r a t e of  heat t r a n s f e r near the edges o f the i n g o t would be much h i g h e r than the r a t e at the c e n t e r , the temperature d i s t r i b u t i o n i n the r ' d i r e c t i o n c o u l d not be approximated by a l i n e a r f u n c t i o n o f r ' .  To  compensate f o r t h i s a s e r i e s of temperature d i s t r i b u t i o n curves were drawn which climbed r a p i d l y near the edges and f l a t t e n e d out the c e n t e r ( F i g u r e 43). each  U s i n g F i g u r e 43  c o u l d be determined f o r  element. Having determined  was  towards  the volume and temperature of each element i t  then p o s s i b l e t o c a l c u l a t e the amount of superheat a s s o c i a t e d  w i t h each  one.  Q_  = mCp  AT  g  = (Cpp)VAT  (5.1.4)  g  where AT  s  = T. , (r',z')  1500°C  T h e r e f o r e , the average superheat f o r the e n t i r e c y l i n d e r can be determined as f o l l o w s :  (5.1.5)  42 10.40 x 10' 178  =  58.4°C  In o r d e r t o get some e s t i m a t e o f the range of ( A T ) ^  , * t  g  same c a l c u l a t i o n was  done f o r two d i f f e r e n t temperature  The d i s t r i b u t i o n s i n v e s t i g a t e d and the r e s u l t i n g are shown i n F i g u r e s 44-A  and 44-B.  i e  configurations.  (AT_)^  va  -'-  ues  The r e s u l t s show t h a t i n a 10  diameter i n g o t of EN-25 o r AISI 4340 the upper l i m i t of ( A  T g  )  i  cm s  A v g  approximately 86°C and the lower l i m i t of ( ^ T ) ^ ^ i s a p p r o x i m a t e l y g  v  47°C.  5.1.2  ESR: Approximate  61 cm diameter and 254 cm diameter v a l u e s of ( A T _ ) ^  f°  r  i n d u s t r i a l s i z e d i n g o t s were  e v a l u a t e d u s i n g the same t e c h n i q u e demonstrated s i z e s were examined:  above.  Two  ingot  1) 61 cm diameter and 2) 254 cm diameter.  both cases a c y l i n d r i c a l a p p r o x i m a t i o n f o r the p o o l shape was The assumed temperature d i s t r i b u t i o n and the r e s u l t i n g are shown i n F i g u r e s 44-D  and  Based on t h e s e r e s u l t s  In  used.  (AT^^^  values  44-E.  i t appears t h a t the magnitude of ( A T ) ^ g  increases very slowly with i n c r e a s i n g ingot diameters.  5.1.3  VAR:  10 cm  diameter  For the purpose of comparison, 10 cm diameter VAR VAR  ingot.  i n g o t i s V-shaped  (AT_,) _ was Av  calculated  for a  S i n c e the p o o l p r o f i l e f o r t h i s s i z e o f  the p o o l was  s e c t i o n e d i n t o a s e r i e s of cones.  - 43 Figure 45 shows the pool geometry and assumed l i m i t i n g temperatures. Although no direct measurement of the metal temperature below the electrode has been made, i t i s generally agreed that i t f a l l s i n the 24 range of 1800°C to 1900°C.  Therefore, the temperature i n this  region was assumed to be 1850°C.  The top edge temperature was  assumed to be at the melting point, as during normal VAR  operation  the height of l i q u i d metal at the ingot surface i s zero. For the purpose of simplifying the c a l c u l a t i o n the temperature d i s t r i b u t i o n i n the z d i r e c t i o n was assumed to be a l i n e a r function of z (Figure 46-A).  The temperature d i s t r i b u t i o n i n the r d i r e c t i o n  however, was assumed to r i s e near the edge and taper o f f towards the center (Figure 46-B). The volume of each conical element was calculated as follows: Volume = (Volume) - (Volume) n-1 n 2  TT  = -5- [ (r ) z 3  n  n  2 - ( r - ) z -] n-1 n-1  (5.1.6)  where n = the number of the element being considered.  The p a r t i c u l a r  values of r and z for each element were determined from Figures 46-A and 46-B using temperature increments of 50°C.  Knowing the average  temperature of each element and i t s volume, i t was then possible to determine the value of VAT_ superheat ((AT )  s Avg  The average  ) for the metal pool was then calculated. VAT  (AT )  for the entire metal pool.  V  s  = 121°C  (5.1.7)  - 44 -  The  r e s u l t s o f t h i s comparison show t h a t the m e t a l p o o l  VAR p r o d u c t i o n pool during  during  c o n t a i n s much more e f f e c t i v e superheat than the m e t a l  the ESR p r o d u c t i o n  o f t h e same diameter i n g o t .  a d d i t i o n a l superheat produces the v e r y w i t h VAR i n g o t s .  deep m e t a l p o o l s  This  associated  As a r e s u l t of the d i f f e r e n c e s i n p o o l depth between  the two p r o c e s s e s ,  s e v e r a l d i f f e r e n c e s i n the s t r u c t u r e and q u a l i t y  of the f i n a l product can be seen; 1)  VAR i n g o t s have a much more r a d i a l l y o r i e n t e d growth d i r e c t i o n  than those found i n s i m i l a r ESR i n g o t s . 2)  VAR i n g o t s c o n t a i n more shrinkage  p o r o s i t y and p i p i n g than  s i m i l a r ESR i n g o t s .  5.2  Heat T r a n s f e r d u r i n g Recently,  concerning  the "Power-Off" Mode  t h e r e has been a g r e a t  d e a l of i n f o r m a t i o n a v a i l a b l e  t h e r a t e of heat t r a n s f e r from the s l a g and m e t a l  pool  25 systems d u r i n g  the steady s t a t e .  T h i s data  c o u l d not be a p p l i e d  to the "power-off" c o n d i t i o n , however, as many o f the heat t r a n s f e r parameters a r e changed d u r i n g  this  period.  There are f o u r main areas a f f e c t e d by t h e l o s s o f heat  input  i n t o the system ( F i g u r e 47). 1)  The l i q u i d m e t a l / s l a g  skin interface:  Heat t r a n s f e r i n t h i s  r e g i o n would be reduced by s o l i d i f i c a t i o n o f the m e t a l a t t h i s i n t e r f a c e and  c o n t r a c t i o n o f t h e i n g o t away from the w a t e r - c o o l e d mould. 2)  The l i q u i d s l a g / s l a g s k i n i n t e r f a c e :  Heat t r a n s f e r i n t h i s  r e g i o n would be reduced by s o l i d i f i c a t i o n of the s l a g a t t h i s i n t e r f a c e . 3)  The l i q u i d  slag/atmosphere i n t e r f a c e :  The heat t r a n s f e r i n  - 45 -  t h i s r e g i o n would be reduced as t h e s u r f a c e temperature o f the s l a g decreased. 4)  The l i q u i d m e t a l / l i q u i d s l a g i n t e r f a c e :  The heat  transfer  i n t h i s r e g i o n would change as t h e r e l a t i v e temperature between the two l i q u i d s changed and as p h y s i c a l n a t u r e o f this i n t e r f a c e  changed.  To c a l c u l a t e the heat t r a n s f e r p r o f i l e s a c r o s s the v a r i o u s i n t e r f a c e s d u r i n g the "power-off" mode, a s e r i e s of experiments were performed as o u t l i n e d i n S e c t i o n 2.8.  The apparatus and g e n e r a l  procedure used have been d i s c u s s e d i n d e t a i l by J o s h i .  5.2.1  95  Heat T r a n s f e r A c r o s s the L i q u i d M e t a l / S l a g S k i n I n t e r f a c e Thermocouples  water  i n the mould r e c o r d e d the change i n the c o o l i n g  temperature w i t h time d u r i n g the "power-off" mode ( F i g u r e 48).  T h i s d a t a was then converted t o a r a t e o f heat f l o w p e r u n i t a r e a ( q / u s i n g F i g u r e 49.  L i n e s 1 and 3 on F i g u r e 49 were used t o determine  q./A as they most a c c u r a t e l y d e s c r i b e d t h i s system.  Knowing the s u r f a  a r e a o f each i n t e r f a c e i t was then p o s s i b l e t o p l o t  t h e t o t a l heat  l o s s a c r o s s each one a g a i n s t t h e d u r a t i o n o f the "power-off" condition  (Figure 50).  5.2.2  Heat T r a n s f e r A c r o s s the L i q u i d S l a g / S l a g S k i n I n t e r f a c e  Employing  the same t e c h n i q u e i l l u s t r a t e d above a r a t e of heat  l o s s v e r s u s time curve f o r the "power-off" c o n d i t i o n was c a l c u l a t e d f o r the l i q u i d s l a g / s l a g s k i n i n t e r f a c e  (Figure 50).  - 46 -  5.2.3  Heat T r a n s f e r A c r o s s t h e L i q u i d Slag/Atmosphere  Employing  Interface  the same t e c h n i q u e i l l u s t r a t e d above a r a t e o f heat  l o s s v e r s u s time curve f o r t h e "power-off" c o n d i t i o n was c a l c u l a t e d f o r the l i q u i d slag/atmosphere i n t e r f a c e  5.2.4  (Figure 50).  Heat T r a n s f e r A c r o s s the L i q u i d M e t a l / L i q u i d S l a g  Interface  In o r d e r t o determine the n a t u r e o f t h e heat t r a n s f e r a c r o s s the s l a g / m e t a l i n t e r f a c e d u r i n g the "power-off" mode, i t was n e c e s s a r y to e s t a b l i s h the temperature p r o f i l e s on e i t h e r s i d e o f the i n t e r f a c e . Because o f the e x p e r i m e n t a l d i f f i c u l t y i n v o l v e d , however, o n l y the p r o f i l e f o r the s l a g was o b t a i n e d .  I t was n e c e s s a r y , t h e r e f o r e , t o  approximate the metal temperature p r o f i l e i n o r d e r t o get some e s t i m a t e o f the heat t r a n s f e r a c r o s s t h e s l a g / m e t a l i n t e r f a c e .  The  e q u i l i b r i u m m e t a l temperature, d i r e c t l y below where the s l a g p r o f i l e was obtained  was e s t i m a t e d from the temperature p r o f i l e s used i n  S e c t i o n 5.1.1.  A l s o , the time r e q u i r e d f o r t h e m e t a l i n t h i s a r e a  to b e g i n s o l i d i f y i n g was e s t i m a t e d t o be a p p r o x i m a t e l y 15 seconds on the b a s i s o f the "power-off" experiments d i s c u s s e d i n S e c t i o n 3.1. Using t h i s i n f o r m a t i o n an approximate  temperature p r o f i l e was c o n s t r u c t e d  f o r the m e t a l a t the s l a g / m e t a l i n t e r f a c e . temperature p r o f i l e s superimposed  F i g u r e 51 shows the two  on one another.  temperature d i f f e r e n c e a c r o s s the i n t e r f a c e  From F i g u r e 51 the  (AT = T . -T ,) slag metal  c o u l d be determined f o r any d u r a t i o n o f the " p o w e r - o f f " c o n d i t i o n .  To  c a l c u l a t e the r a t e o f heat t r a n s f e r , however, i t was n e c e s s a r y t o know the heat t r a n s f e r c o e f f i c i e n t  a t the i n t e r f a c e  (h_.).  The a c t u a l  v a l u e o f t h i s c o e f f i c i e n t has never been a c c u r a t e l y measured, a l t h o u g h  - 47 most .authors have used v a l u e s r a n g i n g from 0.1 to 1.0 c a l cm F i g u r e 52 shows the r a t e o f heat  h_.  sec  .  t r a n s f e r p e r u n i t a r e a a c r o s s the s l a g  m e t a l i n t e r f a c e d u r i n g the "power-off" mode, of  °C  f o r t h r e e assumed v a l u e s  These p r o f i l e s show t h a t w i t h i n t h i s assumed range o f the heat  t r a n s f e r c o e f f i c i e n t s t h e r e a r e l a r g e v a r i a t i o n s i n the magnitude o f the heat f l o w a c r o s s the i n t e r f a c e . what  To get a c l e a r e r u n d e r s t a n d i n g o f  probably does o c c u r a t the i n t e r f a c e , t h e r e f o r e , t h e r e were  three p o i n t s t h a t must be c o n s i d e r e d .  F i r s t l y , assuming t h a t h_  remains constant d u r i n g the "power-off" metal  temperature  mode, and t h a t the assumed  p r o f i l e i s a reasonable approximation  o f the a c t u a l  p r o f i l e , then the n e t heat f l o w a c r o s s the i n t e r f a c e i s a p p r o x i m a t e l y zero r e g a r d l e s s of the v a l u e o f h_ chosen.  This conclusion i s  dependent t o some e x t e n t on the shape o f the assumed profile.  temperature  Reasonable v a r i a t i o n s i n i t s shape, however, d i d n o t change  the n e t heat  flow s i g n i f i c a n t l y .  Secondly,  s i n c e the heat  transfer  a c r o s s the i n t e r f a c e i s dependent on the degree of m i x i n g , and s i n c e the degree o f m i x i n g  c o u l d o n l y decrease  d u r i n g the "power-off"  t h e r e f o r e h_. c o u l d o n l y decrease i n v a l u e .  The t h i r d and most  mode, important  p o i n t i s concerned w i t h the changes i n the s u r f a c e a r e a to volume r a t i o as the i n g o t s i z e i n c r e a s e s .  As the size of the i n g o t i n c r e a s e s ,  the heat f l o w at the s l a g / m e t a l i n t e r f a c e would become i n c r e a s i n g l y i n s i g n i f i c a n t when compared w i t h the l a r g e heat and s l a g p o o l s .  I t was f e l t  contents i n the m e t a l  on the b a s i s of these c o n s i d e r a t i o n s , and  d e s p i t e the shortage o f d a t a c o n c e r n i n g the s l a g / m e t a l i n t e r f a c e , t h a t the heat t r a n s f e r a c r o s s t h i s i n t e r f a c e d u r i n g the "power-off" c o u l d be c o n s i d e r e d n e g l i g i b l e . t h i s assumption  I t was a l s o f e l t  i n c r e a s e d w i t h the i n g o t s i z e .  mode  t h a t the v a l i d i t y of  '  - 48 -  The r e s u l t i n g p r o f i l e s r e v e a l e d s e v e r a l i n t e r e s t i n g about the r a t e of heat t r a n s f e r from the s l a g and m e t a l d u r i n g the "power-off" mode. t h a t the r a t e of heat l o s s  Firstly  features  systems  i t can be seen i n F i g u r e 50  (q) from these i n t e r f a c e s drops ,off v e r y  and t h a t they respond i n s t a n t a n e o u s l y t o the "power-off"  rapidly  condition.  Secondly, F i g u r e 52 shows t h a t the heat t r a n s f e r a c r o s s the s l a g / metal i n t e r f a c e i s v e r y dependent c o e f f i c i e n t due  on the v a l u e o f the heat  transfer  t o the s m a l l temperature g r a d i e n t a c r o s s t h i s  interface.  The e f f e c t i v e n e s s of a u x i l i a r y e l e c t r o d e s to heat the s l a g and p o o l systems  d u r i n g an e l e c t r o d e change o p e r a t i o n , t h e r e f o r e , w i l l  v e r y dependent  on the e x a c t v a l u e of t h i s c o e f f i c i e n t . -2  i s c l o s e to 1.0  c a l cm  -1 sec  i s maintained.  be  I f i t s value  -1 °C  t h e r e w i l l be a c o n s i d e r a b l e amount  of heat t r a n s f e r from the s l a g to the m e t a l i f the o r i g i n a l temperature  metal  slag  T h i s heat s u p p l y would reduce the e x t e n t of  the s o l i d i f i c a t i o n i n the m e t a l p o o l d u r i n g the e l e c t r o d e change o p e r a t i o n and thereby reduce any s t r u c t u r a l and c o m p o s i t i o n a l e f f e c t s .  o t h e r hand, i f the heat t r a n s f e r c o e f f i c i e n t i s c l o s e to 0.1 sec  l o  C  1  On  the -2  c a l cm  the heat t r a n s f e r a c r o s s the s l a g / m e t a l i n t e r f a c e would be  g r e a t l y reduced.  The e f f e c t o f the a u x i l l i a r y e l e c t r o d e s ,  therefore,  i  would be mainly c o n f i n e d t o m a i n t a i n i n g the s l a g systems  temperature,  thereby r e d u c i n g the requirement f o r s l a g h e a t i n g on power resumption.  6.  THE  EXTENT OF SOLIDIFICATION DURING THE  "POWER-OFF" CONDITION  Heat b a l a n c e s were c a l c u l a t e d f o r a s m a l l and a l a r g e s c a l e i n g o t as w e l l as a s m a l l s c a l e VAR  ESR  i n g o t , i n o r d e r to o b t a i n some  e s t i m a t e of the volume of l i q u i d m e t a l and l i q u i d s l a g t h a t would s o l i d i f y d u r i n g a r e l a t i v e l y s h o r t i n t e r r u p t i o n i n the systems power supply.  Although these c a l c u l a t i o n s c o n t a i n e d s e v e r a l assumptions  and  can o n l y be c o n s i d e r e d as a p p r o x i m a t i o n s , they do p r o v i d e a good i n d i c a t i o n o f how To circumvent  the two systems r e a c t  to the "power-off"  condition.  the complex problems of p o o l shape change and  temperature  g r a d i e n t changes d u r i n g the "power-off" mode, the c a l c u l a t i o n s were l i m i t e d to a d e t e r m i n a t i o n of the volume s o l i d i f i e d i n a g i v e n p e r i o d of time.  6.1  D e t e r m i n a t i o n o f the Volume S o l i d i f i e d i n the M e t a l and S l a g P o o l Systems i n a 10 cm d i a . EN-25, ESR  Ingot  The s l a g and m e t a l p o o l c o n f i g u r a t i o n s used i n t h i s  calculation  are shown i n F i g u r e 53. The  first  step i n t h i s c a l c u l a t i o n was  to determine  the  available  heat c o n t e n t s (Q ) o f the two systems a t the b e g i n n i n g of the "powero f f " condition simplicity  (t = 0 ) .  i t was  T h i s i s shown i n Appendix I I - l .  assumed that both systems r e t a i n e d t h e i r  heat d u r i n g the"power-off  11  mode.  Therefore:  For sensible  - 50 -  =  mC AT P  and from Appendix  +  ce. 1)  mi-  II-l  79 k c a l s  =  98 k c a l s  Having c a l c u l a t e d  the a v a i l a b l e heat content o f both systems, the  next step was to c a l c u l a t e the t o t a l heat l o s s  (Q ) from  each f o r  JL d i f f e r e n t d u r a t i o n s o f the "power-off" mode (Appendix I I - 2 ) .  The  r e s u l t s o f these c a l c u l a t i o n s a r e shown i n T a b l e s V-A and V-B. Knowing Q  and Q  /_ percent s o l i d i f i e d  i t was then p o s s i b l e t o c a l c u l a t e the volume  JL (P.S.) f o r the d i f f e r e n t l e n g t h s of "power-off"  operation. (6.2)  P.S.  The r e s u l t s a r e shown i n T a b l e s V-A and V-B. Plotting  the r e s u l t s of T a b l e s V-A and V-B p o i n t s out s e v e r a l  i n t e r e s t i n g f e a t u r e s about each system d u r i n g the "power-off" mode ( F i g u r e 54).  I t can be seen t h a t the volume p e r c e n t s o l i d i f i e d i n the  m e t a l p o o l i n c r e a s e s v e r y u n i f o r m l y w i t h time which  indicates  that  there a r e no gross changes i n the s o l i d i f i c a t i o n r a t e a s s o c i a t e d w i t h the e a r l y stages o f a power i n t e r r u p t i o n .  As t h e d u r a t i o n o f the  "power-off" c o n d i t i o n i n c r e a s e s , the heat l o s s from the system i s p r i m a r i l y due t o c o n d u c t i o n down the i n g o t , and r a d i a l l y  to the mould  - 51 -  T a b l e V. A. Time (sec)  Volume s o l i d i f i e d Heat l o s s  (kcals)  2  i n the m e t a l p o o l T o t a l heat loss (kcals)  3  system Available heat a t t=0 (kcals)  Volume % solidified  «1  q  2.5  1.6  1.3  0.3  3.2  79  4.0  5.0  2.8  2.6  0.6  5.9  79  7.5  7.5  3.6  3.8  1.0  8.4  79  10.6  10.0  4.4  5.1  1.3  10.8  79  13.7  12.5  4.9  6.4  1.6  12.9  79  16.4  15.0  5.5  7.7  1.9  15.1  79  19.1  20  6.1  10.2  2.7  19.0  79  24.1  30  6.3  15.3  3.8  25.4  79  32.1  B.  Time (sec)  q  Volume s o l i d i f i e d  Heat l o s s q  4  (kcals) q  i n the s l a g p o o l  T o t a l heat loss (kcals)  5  system  Available heat a t t=o (kcals)  Volume % solidified  2.0  1.0  4.2  5.2  98  5.3  5.0  2.2  9.6  11.8  98  12  10.0  3-4  14.3  17.7  98  18  15.0  4.3  16.0  20.3  98  20.7  30  5.8  17.5  23.3  98  24  - 52  wall. heat  -  I t i s p o s s i b l e , however, t h a t i n a d d i t i o n t h e r e c o u l d be some t r a n s f e r from the metal t o the s l a g a c r o s s the s l a g / m e t a l  interface.  Photographs o f the f i n a l p o o l volume show t h a t some  solidification ( F i g u r e 21).  does take p l a c e s t a r t i n g a t the s l a g / m e t a l i n t e r f a c e T h i s phenomenon c o u l d supply a d d i t i o n a l heat  to the  s l a g at the expense of the m e t a l p o o l . U n l i k e the l i q u i d m e t a l , the s l a g system s o l i d i f i e d r a p i d l y i n the i n i t i a l stages of the power i n t e r r u p t i o n but creased quickly w i t h time. i s p r i m a r i l y due  the s o l i d i f c a t i o n  The r a p i d drop i n the s o l i d i f i c a t i o n  r a t e de-  rate  t o the low thermal c o n d u c t i v i t y of the s o l i d i f i e d  slag.  When the power i s turned o f f , the s l a g f r e e z e s i n from the mould w a l l s and the top, and theieby becomes i n s u l a t e d from i t s major sources of heat loss.  Because the s l a g remains l i q u i d  f o r a much l o n g e r time  does the metal i t i s p o s s i b l e to r e - r e s t a b l i s h e l e c t r i c a l even though the metal p o o l might have completely  than  continuity  solidified.  These r e s u l t s are c o n s i s t e n t w i t h the e x p e r i m e n t a l o b s e r v a t i o n s and w i t h the model f o r the f o r m a t i o n of carbon proposed  6.2  c o n c e n t r a t i o n bands  i n S e c t i o n 3.1.2.  Volume P e r c e n t of L i q u i d M e t a l t o S o l i d i f y Addition  Based on Tungsten Powder  Experiments  The volume s o l i d i f i e d  f o r a g i v e n "power-off"  p e r i o d was  experimentally,; f o r the purpose of checking the v a l i d i t y t h e o r e t i c a l v a l u e s o b t a i n e d i n S e c t i o n 6.1.  of the  Tungsten powder  e x t e r n a l l y added t o the system the moment the power supply was down and then a g a i n approximately  13 seconds (+ 2 second)  determined  was shut  later.  - 53 -  F i g u r e 55 shows a s e c t i o n o f i n g o t no. 13 which experiments.  The r e s u l t i n g p o o l p r o f i l e s  c o n t a i n s t h r e e such  f o r experiment no. 2 a r e  shown i n F i g u r e 56-A, and an a p p r o x i m a t i o n o f these i s shown i n F i g u r e 56-B. elements  The volume s o l i d i f i e d was e s t i m a t e d by u s i n g c y l i n d r i c a l  t o c a l c u l a t e the volume encompassed by each p r o f i l e .  The  r e s u l t o f t h i s c a l c u l a t i o n showed that a p p r o x i m a t e l y 18.3 p e r c e n t o f the m e t a l p o o l had s o l i d i f i e d i n the "power-off" i n t e r v a l . of the o t h e r tungsten a d d i t i o n experiments percent of t h i s value.  The r e s u l t s  a l l agreed t o w i t h i n 10  Although the e x p e r i m e n t a l v a l u e s were  s l i g h t l y h i g h e r than the c a l c u l a t e d p e r c e n t a g e s , the agreement i s s t i l l good c o n s i d e r i n g  the assumptions  Tungsten a d d i t i o n experiments  t h a t were made.  f o r l o n g e r d u r a t i o n s were n o t  p o s s i b l e as the top o f the s l a g cap became s o l i d a f t e r a p p r o x i m a t e l y 15 t o 20 seconds  6.3  o f "power-off" o p e r a t i o n .  D e t e r m i n a t i o n o f the Volume S o l i d i f i e d i n the M e t a l and S l a g P o o l Systems i n a 61 cm d i a . Ingot d u r i n g a 60 Second Power Loss In an e f f o r t  t o get a b e t t e r u n d e r s t a n d i n g o f the "power-off" mode  and how i t e f f e c t s the l a r g e r commercial  f u r n a c e s an attempt was made  to c a l c u l a t e the approximate volumes o f i n g o t and s l a g which d u r i n g a 60 second power i n t e r r u p t i o n . was  The 60 second  time  interval  chosen as t h i s i s t h e approximate maximum l e n g t h o f time  to change an e l e c t r o d e i n an i n d u s t r i a l u n i t .  solidified  required  Due t o the l a c k o f  i n f o r m a t i o n a v a i l a b l e on the r a t e s o f heat t r a n s f e r i n commercial s i z e d i n g o t s , however, i t was n e c e s s a r y to i n c l u d e i n t h e a n a l y s i s s e v e r a l major assumptions.  T h e r e f o r e , the r e s u l t s  can o n l y be i n t e r p r e  - 54  as order of magnitude v a l u e s . Figure  -  The  system i s shown s c h e m a t i c a l l y i n  57.  The  f i r s t s t e p i n the c a l c u l a t i o n once a g a i n , was  a v a i l a b l e heat  content  (Appendix I I I - l ) . the "power-off" data f o r a 7.6  of both  the m e t a l  p e r i o d (Appendix I I I - 2 ) i t was cm diameter  c a l c u l a t e a steady i n reasonable The  J o s h i used t h i s  to use  r e s u l t s of the heat b a l a n c e 10.3  loss  was  observed  i n g o t which  25 results.  showed t h a t approximately  percent  the  t e c h n i q u e to  f o r a 61 cm diameter  agreement w i t h commercially  percent of the m e t a l p o o l and  10  of the s l a g p o o l would have  s o l i d i f i e d d u r i n g a 60 second i n t e r r u p t i o n i n III-3).  necessary  loss during  i n g o t and assume t h a t the heat  s t a t e heat b a l a n c e  the  s l a g p o o l systems  In o r d e r to determine the r a t e of heat  p r o p o r t i o n a l to the s u r f a c e a r e a .  was  and  to determine  I t i s u n l i k e l y , t h e r e f o r e , t h a t any  the power s u p p l y s t r u c t u r a l or  (Appendix  compositional  changes would be produced i n the i n g o t as a r e s u l t of the power l o s s . These r e s u l t s are reasonable to the volume of l i q u i d  c o n s i d e r i n g the f a c t t h a t  3 ( r ) and Q  Li  i s proportional  i s p r o p o r t i o n a l to i t s s u r f a c e  2 area  (r ).  T h e r e f o r e , as the i n g o t r a d i u s i n c r e a s e s , the e f f e c t s  power d i s r u p t i o n s on the system are reduced, "power-off"  6.4  of  f o r a g i v e n p e r i o d of  operation.  Determination  of the Volume of the M e t a l P o o l S o l i d i f i e d i n a  10 cm Diameter AISI 4340, VAR  Ingot d u r i n g a 12.5  Second Power  Interruption Because of a growing i n t e r e s t i n the more s u b t l e d i f f e r e n c e s between the ESR  and VAR  p r o c e s s e s , i t was  significant  to i n v e s t i g a t e how  the  two  - 55  -  p r o c e s s e s d i f f e r d u r i n g the "power-off" mode. been f e l t  that the VAR  T r a d i t i o n a l l y , i t has  p r o c e s s would be much more s e n s i t i v e  to  changes i n the operating c o n d i t i o n s as t h e r e i s no hot s l a g l a y e r t o a c t as a thermal b u f f e r . . In o r d e r to make t h i s comparison  a heat b a l a n c e was  done f o r  i n g o t no. V-3 which c o n t a i n s two power i n t e r r u p t i o n s of a p p r o x i m a t e l y 12.5  seconds  ( F i g u r e 58).  An approximation of the metal p o o l p r o f i l e  i s shown i n F i g u r e 59. The a v a i l a b l e heat content of the m e t a l p o o l was on the same assumptions (Appendix  IV-1).  calculated  used f o r the 10 cm diameter ESR  based  ingot  D e t e r m i n a t i o n of the heat l o s s from the system d u r i n g  the"power-off" p e r i o d was  c o m p l i c a t e d by the l a c k o f heat f l o w d a t a  p e r t a i n i n g to t h i s mode of o p e r a t i o n i n a VAR l a c k of r e l e v a n t i n f o r m a t i o n i t was  Ingot.  Because o f  n e c e s s a r y t o use the steady  this state  28 heat l o s s p r o f i l e s  shown i n F i g u r e 60.  a v a i l a b l e i n f o r m a t i o n ( S e c t i o n 5.1)  i t was  U s i n g these curves and o t h e r p o s s i b l e t o o b t a i n an  upper l i m i t f o r the heat l o s s from the m e t a l p o o l i n 12.5 (Appendix  IV-2).  Once having determined  of l i q u i d metal s o l i d i f i e d (Appendix  IV-3).  and  the volume p e r c e n t  d u r i n g the "power-off" mode was  calculated  The r e s u l t showed t h a t the maximum amount of l i q u i d  metal which c o u l d f r e e z e , based on the assumed d a t a , was 32.2  seconds  approximately  percent. In o r d e r to determine whether or not the h e a t flow v a l u e s used i n  the c a l c u l a t i o n were a t a l l r e a s o n a b l e , the t h e o r e t i c a l volume was  compared w i t h the e x p e r i m e n t a l l y observed v a l u e .  The  i n t e r r u p t i o n s and the f i n a l p o o l volume f o r i n g o t no. V-3  solidified  two power are  clearly  o u t l i n e d i n F i g u r e 58.  The dark band produced by the second power  i n t e r r u p t i o n has been approximated i n F i g u r e 62 by two  parabolas.  The volume s o l i d i f i e d was determined as f o l l o w s :  11 y Volume p e r c e n t  dx 0  solidified = y  TT  dx]  = 18.5% I t can be seen t h a t the c a l c u l a t e d v a l u e was approximately h i g h e r than the e x p e r i m e n t a l l y c a l c u l a t e d value probably for  observed r e s u l t .  and t h a t the  cannot be a p p l i e d to t h i s mode o f o p e r a t i o n .  I t s h o u l d be noted, however, t h a t d e s p i t e the f a c t  t h a t the volume  f r a c t i o n s s o l i d i f i e d i n 12.5 seconds were approximately two p r o c e s s e s , pool  (V  TrA  _/V_  profiles  I t appears, t h e r e f o r e , t h a t the r a d i a l  heat f l u x i s reduced d u r i n g the "power-off" c o n d i t o n state profiles  times  The e r r o r i n the  arose by u s i n g the r a d i a l heat f l u x  the s t e a d y - s t a t e c o n d i t i o n .  steady  1.7  the same f o r the  the much l a r g e r volume of l i q u i d m e t a l i n the VAR CT)  = 3.4) means t h a t more m e t a l s o l i d i f i e d .  I t should  a l s o be noted i n F i g u r e 58 t h a t the two power i n t e r r u p t i o n s and the f i n a l p o o l volume have a l l etched  up darker  s e c t i o n s of the i n g o t u s i n g 3 p e r c e n t n i t a l . i n c r e a s e i n the carbon c o n c e n t r a t i o n .  than the s t e a d y - s t a t e T h i s i n d i c a t e s some  The p r o b a b l e  cause of the  i n c r e a s e d carbon c o n c e n t r a t i o n i s an i n c r e a s e i n the system's s o l i d i f i c a tion rate.  Based on the l i m i t e d i n f o r m a t i o n a v a i l a b l e , t h e r e f o r e , i t  - 57  -  appears t h a t i n t e r r u p t i o n s i n the VAR e f f e c t on ESR  unit.  the i n g o t ' s  power s u p p l y produce a  greater  c o m p o s i t i o n than do s i m i l a r i n t e r r u p t i o n s i n an  7.  ELECTRODE CHANGE OPERATIONS  In the p r e v i o u s  s e c t i o n i t was  to change the e l e c t r o d e i n a 61 cm o n l y about 10 percent solidified.  shown t h a t i n the time r e q u i r e d diameter tandem e l e c t r o d e machine  of the l i q u i d m e t a l and  However, t h i s c a l c u l a t i o n d i d not  a d d i t i o n of the new  e l e c t r o d e i n t o the system.  l i q u i d s l a g would take i n t o account In o r d e r  n e c e s s a r y to o b t a i n an e s t i m a t e  i n f l u e n c e the  7.1  of how  the new  the  to determine  the o v e r a l l e f f e c t of an e l e c t r o d e change on the heat b a l a n c e , i t was  be  therefore,  e l e c t r o d e would  system.  Temperature P r o f i l e i n a Commercial  Electrode  Although temperature p r o f i l e s have been e x p e r i m e n t a l l y  determined  f o r lab s c a l e e l e c t r o d e s , no p r a c t i c a l measurements have been c a r r i e d out on the much l a r g e r commercial e l e c t r o d e s .  To e s t i m a t e  the  temperature d i s t r i b u t i o n i n these e l e c t r o d e s , t h e r e f o r e , p r o f i l e s were c a l c u l a t e d u s i n g the u n s t e a d y - s t a t e simplify  heat c o n d u c t i o n  the c a l c u l a t i o n the e l e c t r o d e was  i n f i n i t e s l a b i n which  there was  equation.  approximated by  no heat l o s s i n the r a d i a l  To  a semidirection.  T h i s assumption i s j u s t i f i e d based on the r e s u l t s of M i t c h e l l and 27 Szekely  who  found t h a t the r a d i a l heat flow component i n the  s c a l e e l e c t r o d e s was e l e c t r o d e t i p was  very small.  flat  and  I t was  that t h e r e was  a l s o assumed t h a t  lab  the  n e g l i g i b l e immersion i n t o the  - 59 -  slag bath.  This i s a reasonable assumption based on the observations  made during i n d u s t r i a l ESR production. The general form of the unsteady-state heat conduction  equation  32 is: 2 a  =  o<  f t  <.»  y  C7.D  3y The boundary conditions f o r the addition of a new electrode into the system are:  1.  T = T  att=0  y>0  o  J  2.  T ->• T o  3.  h(T,-T ) = -K b o 3y  as y -> J  at y = 0 -  where T^ i s the i n i t i a l temperature of the new electrode T^ i s the slag temperature.  Using these boundary conditions the solution to equation (7.1) has the form:  h'y+h at e ,2  T(y,t) = (T.-T ) [ e r f c - ^ -  °  2/at  erfc(-^—  2/at  +  h y^t) ]  (7.2)  where h = the heat transfer c o e f f i c i e n t across the base of the new electrode h' =  ^ K  Using equation (7.2), therefore, i t was possible to calculate the  - 60 -  temperature i n the e l e c t r o d e a t any p o s i t i o n along i t s l e n g t h any time ( t ) , w i t h the assumption t h a t g e n e r a l computer program was i n Appendix  7.2  remains c o n s t a n t .  (y) a t A  w r i t t e n f o r e q u a t i o n (7.2) and i s shown  V.  Heat Content o f a Commercial In commercial ESR  Electrode  o p e r a t i o n s the minimum p r a c t i c a l e l e c t r o d e t o  i n g o t diameter r a t i o i s a p p r o x i m a t e l y 0.75. 61 cm diameter i n g o t a 45.6 Having e s t a b l i s h e d the next step was  Therefore, f o r a  cm diameter e l e c t r o d e would be  used.  the e l e c t r o d e s i z e to be c o n s i d e r e d i n the  calculation  a d e t e r m i n a t i o n of the c o n s t a n t s i n e q u a t i o n (7.2).  Average v a l u e s of p , Cp , and K f o r i r o n i n the temperature s s s from 25°C to 1500°C of 7.8 g per cm , 0.16 c a l p e r g °C, and  range  3  0.071  c a l p e r cm sec °C, r e s p e c t i v e l y were used i n the c a l c u l a t i o n s .  Based on the r e s u l t s o f M i t c h e l l e t a l . , transfer coefficient  insensitive  and E l l i o t  (h) a t the e l e c t r o d e t i p was  2 c a l per cm sec °C.. I t was was  27  26 et a l . the heat  assumed t o be  l a t e r shown, however, t h a t the  0.04  calculation  to the v a l u e of h i n the a c c e p t e d range o f v a l u e s f o r 2  the e l e c t r o d e t i p (0.01 t o 0.1  c a l p e r cm sec ° C ) .  The reason f o r  t h i s i n s e n s i t i v i t y i s t h a t f o r t h i s range of heat t r a n s f e r  coefficients  the r a t e c o n t r o l l i n g step i s c o n d u c t i o n i n the e l e c t r o d e and n o t the r a t e of heat supply to the e l e c t r o d e base. Using the above i n f o r m a t i o n and assuming ( T ) was q  the i n i t i a l  temperature  25°C temperature p r o f i l e s were c a l c u l a t e d as a f u n c t i o n of  time f o r two assumed v a l u e s of the s l a g b a t h temperature r e s u l t i n g p r o f i l e s are shown i n F i g u r e 63.  (T^).  The  These p r o f i l e s r e p r e s e n t  - 61 -  the temperature temperature  d i s t r i b u t i o n i n the e l e c t r o d e a t the i n s t a n t the  o f the m e t a l 1.0 mm  reached the m e l t i n g p o i n t .  above the s l a g / e l e c t r o d e  The i n c r e a s e d heat c o n t e n t o f the  e l e c t r o d e f o r both s l a g b a t h temperatures graphical  integration.  Since  Qj =  interface  was then c a l c u l a t e d u s i n g  (7.3)  mC_AT  =  VpC AT p  2 =  irr hpC AT  =  Trr C _  p  hAT  2  p  p  therefore 2  CQl)  = *rC  T = 1 5 5 0  1  5  yAT - (15) ( T Q ) ]  R[ E  (7.4)  y=0  =  11962 k c a l s  and 2 W =1650  *  =  T  =  r  C P S  1  Ps  [  E  2  ^ y=0 n  A  T  "  < >(V1 12  (7  '  5)  9892 k c a l s  There c a l c u l a t i o n s , however, assume t h a t the l i q u i d  s l a g system i s an  i n f i n i t e heat s o u r c e capable o f m a i n t a i n i n g T^ c o n s t a n t .  Comparing  these heat contents w i t h the a v a i l a b l e heat content o f the s l a g 3 ((.Q A  ) = 8 x 10 S  k c a l s ) , c a l c u l a t e d i n Appendix I I L l . 3 , c l e a r l y  indicates  - 62 -  that the slag system i s not an i n f i n i t e heat source and that, i n f a c t , the heat loss from the slag to the electrode i s s u f f i c i e n t to completely  freeze the slag.  Therefore, i n order to get the t i p of  the electrode to i t s melting point a very large power input into the system would be required, and the time to achieve this state would be considerably lengthened.  Another probable consequence of the  large thermal burden on the slag would be an increased rate of heat loss from the metal, across the slag/metal i n t e r f a c e . This would result i n the accelerated s o l i d i f i c a t i o n of the metal pool producing s t r u c t u r a l and compositional  changes.  irreversible  On the basis of these calculations,  therefore, i t i s clear that unless the problems associated with  the  thermal burden of the electrode on the slag system are solved,- the electrode change process holds very l i t t l e p o t e n t i a l for the  production  of large ingots.  7.3  Electrode  Preheating  A possible solution suggested to a l l e v i a t e the thermal burden problem i s to preheat the electrode t i p to within 200°C to 300°C of i t s melting point.  This would eliminate a large portion of the  heat necessary to begin melting the electrode and reduce the time necessary to re-achieve steady-state conditions.  In order to obtain  an estimate as to the extent that preheating reduces the thermal burden on the l i q u i d slag, several temperature p r o f i l e s were calculated assuming that the electrode was  being heated i n a slag bath at 1200°C.  Figure 64 shows the r e s u l t i n g p r o f i l e s superimposed on the electrode p r o f i l e for T, equals 1550°C. b preheating  On the basis of these p r o f i l e s a  time of approximately 500 seconds at 1200°C provides  the  - 63 -  b e s t compromise between heat c o n t e n t  i n t h e t i p r e g i o n of the  and the t h e r m a l energy r e q u i r e d t o a c h i e v e i t . i t was p o s s i b l e t o c a l c u l a t e  of 1550°C.  Using t h i s p r o f i l e  an approximate v a l u e f o r the heat i n p u t  r e q u i r e d t o get the e l e c t r o d e s l a g temperature  electrode  t i p to i t s m e l t i n g p o i n t w i t h a l i q u i d T h i s h e a t i n p u t Q_ was d e t e r m i n e d as  follows:  Q  I  =  s =  where  _  yAT  represents  p  950  Z  y A T  of the l i q u i d s l a g .  '  4 )  kcals  percent  of the  o r i g i n a l a v a i l a b l e heat  This content  Q_ c o u l d be s t i l l f u r t h e r reduced by p r e h e a t i n g  t i p to w i t h i n 100 to 200°C below i t s m e l t i n g p o i n t and  by m a i n t a i n i n g the s l a g temperature auxilliary  ( 7  i s the h a t c h e d a r e a between the two p r o f i l e s .  o n l y 11.2  the e l e c t r o d e  s  a t 1650°C w i t h the use of  electrodes.  U s i n g the c o n d i t i o n s d e s c r i b e d i n F i g u r e 63 the time r e q u i r e d t o s t a r t m e l t i n g w i t h the p r e h e a t e d e l e c t r o d e would be a p p r o x i m a t e l y 60 s e c .  I t has been shown ( S e c t i o n  5.2),  however, t h a t the h e a t  s u p p l y to the m e t a l p o o l i s p r i m a r i l y from the m o l t e n d r o p l e t s d u r i n g the m e l t i n g o p e r a t i o n .  Under t h e s e c o n d i t i o n s , t h e r e f o r e ,  i t would  take a p p r o x i m a t e l y 120 seconds b e f o r e the heat s u p p l y to the m e t a l p o o l was r e - e s t a b l i s h e d .  It  s h o u l d be n o t e d , however, t h a t  represents  a maximum time i n t e r v a l as the time r e q u i r e d t o  electrodes  c o u l d be reduced from 60 seconds  w i t h more s o p h i s t i c a t e d  equipment.  this change  down to 20 to 30  seconds  - 64 -  Assuming that i t was  120 seconds before the new  electrode began  melt the maximum amount of l i q u i d metal that would freeze would be 18.6  percent  (Appendix VI).  On the basis of the results from Section  (3.2) this would result i n minimal concentration banding p a r t i c u l a r l y i n alloys with low carbon, sulphur, and phosphorous concentrations. The tandem electrode process, therefore, appears to be a feasible technique for producing electrodes are used.  large commercial ingots i f preheated  8.  1.  CONCLUSIONS  Power i n t e r r u p t i o n experiments on AISI 4340 and EN-25 s t e e l s ,  produced only minor changes i n the i n g o t s t r u c t u r e s . c o m p o s i t i o n a l banding was elements p r e s e n t .  observed f o r carbon but not f o r the o t h e r  A p o s s i b l e model f o r the f o r m a t i o n of the carbon  c o n c e n t r a t i o n banding d u r i n g the "power-on-off" proposed.  Significant  sequence  was  F l u c t u a t i o n s I n the s l a g s k i n t h i c k n e s s were found to  produce carbon c o n c e n t r a t i o n bands at the edge o f the i n g o t .  2.  Power i n t e r r u p t i o n experiments on AISI 630  (17-4PH) s t a i n l e s s  s t e e l produced s i g n i f i c a n t s t r u c t u r a l changes due growth  anisotropy.  t o the s t e e l s low  crystal  No changes i n the c o n c e n t r a t i o n of N i , Cr, and  Cu were observed as a r e s u l t of the "power-off" experiment i n the i n g o t s produced on the U.B.C. ESR u n i t .  The n a t u r e o f the banded  s t r u c t u r e found i n some commercial i n g o t s was of  3.  i d e n t i f i e d as r e g i o n s  high 6 - f e r r i t e content.  The most p r o b a b l e cause of the m i x i n g a c t i o n i n the ESR  p o o l i s momentum and heat t r a n s f e r from the f a l l i n g m e t a l The r e s u l t i n g m i x i n g a c t i o n i s a slow c o n v e c t i v e motion approaches  metal  droplets.  which  a s t a t e o f complete m i x i n g at the slow s o l i d i f i c a t i o n  found i n the ESR p r o c e s s .  During a "power-off-on" s i t u a t i o n ,  rates  elements  - 66 with k  o  v a l u e between 0.5 and 1.0 w i l l have minimal c o n c e n t r a t i o n  banding a s s o c i a t e d w i t h them.  Elements  on t h e o t h e r hand, w i t h k  v a l u e s lower than 0.5 c o u l d show s i g n i f i c a n t  Q  c o n c e n t r a t i o n banding  and m a c r o s e g r e g a t i o n .  4.  The average superheat of the l i q u i d m e t a l p o o l f o r a 10 cm  diameter ESR i n g o t was e s t i m a t e d t o be 58°C.  The o u t s i d e l i m i t s o f  t h i s superheat were found t o be 47°C and 87°C.  The average  superheat  of the l i q u i d m e t a l p o o l i n a 61 cm diameter and 254 cm diameter ESR i n g o t were e s t i m a t e d t o be 70°C and 80°C r e s p e c t i v e l y .  The average  s u p e r h e a t . o f . t h e l i q u i d m e t a l p o o l f o r a 10 cm diameter VAR i n g o t was e s t i m a t e d t o be 121°C.  T h i s i s much h i g h e r than t h a t found i n a  s i m i l a r s i z e d ESR i n g o t and c o u l d account f o r the much deeper p o o l p r o f i l e s observed i n VAR i n g o t s .  5.  The r a t e o f heat t r a n s f e r a t the l i q u i d m e t a l / s l a g s k i n ,  s l a g / s l a g s k i n , and l i q u i d  slag/atmosphere  as a f u n c t i o n o f the "power-off" mode. and showed an immediate  i n t e r f a c e s were determined  They a l l decreased r a p i d l y  response t o the "power-off" c o n d i t i o n .  r a t e o f heat t r a n s f e r a c r o s s t h e l i q u i d i s c r i t i c a l l y dependent  liquid  s l a g / l i q u i d metal  on the heat t r a n s f e r , c o e f f i c i e n t  i n t e r f a c e due to the s m a l l temperature  gradient.  The  interface across  the  The n e t flow o f  heat a c r o s s t h i s i n t e r f a c e f o r l o n g e r d u r a t i o n s ( t > 15 s e c ) o f the "power-off" mode i s a p p r o x i m a t e l y z e r o .  6.  The l i q u i d m e t a l s o l i d i f i e s a t an a p p r o x i m a t e l y u n i f o r m r a t e d u r i n g  the e a r l y stages o f the "power-off" mode. r a p i d l y at f i r s t loss.  insulating i t s e l f  The l i q u i d  slag  solidifies  from i t s major sources o f heat  T h i s causes i t s s o l i d i f i c a t i o n  r a t e to d e c r e a s e .  The c a l c u l a t e d  v a l u e s o f t h e volume p e r c e n t s s o l i d i f i e d based on a heat b a l a n c e d u r i n g the "power-off" mode were v e r i f i e d additions.  e x p e r i m e n t a l l y by tungsten powder  I n a 61 cm diameter ESR i n g o t i t was e s t i m a t e d t h a t a  maximum of 10 p e r c e n t o f the l i q u i d m e t a l and 10.3 p e r c e n t o f the liquid  s l a g would s o l i d i f y  VAR p r o c e s s appears  d u r i n g a 60 second power i n t e r r u p t i o n .  The  t o be more s e n s i t i v e than the ESR p r o c e s s t o any  d i s r u p t i o n s i n the systems power s u p p l y .  7.  A g e n e r a l u n s t e a d y - s t a t e heat t r a n s f e r program was w r i t t e n to  c a l c u l a t e temperature s l a g bath.  p r o f i l e s i n an e l e c t r o d e t h a t i s immersed i n a  Preheated e l e c t r o d e s must be used i n the tandem e l e c t r o d e  change machine i f s t r u c t u r a l and c o m p o s i t i o n a l changes a r e t o be avoided.  The use o f a preheated e l e c t r o d e and a u x i l i a r y e l e c t r o d e s  to m a i n t a i n the s l a g temperature would ensure minimal s t r u c t u r a l and c o m p o s i t i o n a l changes i n the i n g o t d u r i n g an e l e c t r o d e change o p e r a t i o n .  - 68 -  9.  1.  SUGGESTIONS FOR FUTURE WORK  S i n c e i t has been shown t h a t  the c o m p o s i t i o n a l i r r e g u l a r i t i e s  are produced when the power was r e - e s t a b l i s h e d , p r a c t i c a l exercise stage.  t o c a r r y out a more d e t a i l e d e x a m i n a t i o n o f t h i s  By c a r e f u l l y c o n t r o l l i n g the power i n p u t  re-establishing  the e q u i l i b r i u m  to completely e l i m i n a t e  i n t o the system when  thermal conditions  i t may be p o s s i b l e  the f o r m a t i o n o f any c o m p o s i t i o n a l  i r r e g u l a r i t i e s d u r i n g the e l e c t r o d e  2.  i t would be a  change o p e r a t i o n .  Although some i n f o r m a t i o n was o b t a i n e d c o n c e r n i n g the heat  t r a n s f e r across the s l a g / m e t a l i n t e r f a c e i t would be o f i n t e r e s t t o c a r r y out a more d e t a i l e d examination o f the heat t r a n s f e r i n t h i s region.  T h i s would e n t a i l a d e t e r m i n a t i o n o f the heat  c o e f f i c i e n t a t t h i s i n t e r f a c e , as w e l l as a b e t t e r  transfer  understanding o f  how the m e t a l and s l a g temperatures change d u r i n g the "power-off" mode. The  r e s u l t s o f t h i s i n v e s t i g a t i o n would a l s o p r o v i d e some e s t i m a t e  as t o the e f f e c t i v e n e s s and  metal p o o l s d u r i n g the e l e c t r o d e  3.  on  i n h e a t i n g the s l a g  change o p e r a t i o n .  A s e r i e s o f power i n t e r r u p t i o n experiments on a l a r g e  ingot had  of a u x i l l i a r y e l e c t r o d e s  could  commercial  be used t o check the v a l i d i t y o f the many assumptions  to be made i n o r d e r t o s c a l e up the e x p e r i m e n t a l r e s u l t s the l a b - s c a l e ESR u n i t .  that  obtained  - 69 -  APPENDIX I DETERMINATION OF CONCENTRATION PROFILES  1.1  Determination  of  the normalized concentration of radioactive  t i n and sulphur  'X  = -  (C'-C ) x o (C.-C.)  C_  =  the equilibrium concentration  C. l  =  the concentration at the interface  C^  =  the concentration at any point x from the interface  C„  =  the r e l a t i v e  C  x  (A.I-1.1)  0  where:  fractional  concentration at any point x  from the i n t e r f a c e .  1.2  Determination  of the t h e o r e t i c a l p r o f i l e for k = 1 and complete  mixing To circumvent  the pool shape problem the l i q u i d pool was considered  to be c y l i n d r i c a l .  Because the geometry of the s o l i d i f i c a t i o n front  was assumed to be f l a t the volume of l i q u i d metal s o l i d i f i e d i s proportional to the  change i n height (Ah).  Volume s o l i d i f i e d  where:  h  Q  «  ^ h  (A.1-2.1) o  i s the o r i g i n a l height of the cylinder.  Since the l i q u i d i s assumed to be of uniform composition  (C ) and k  - 70 e q u a l t o u n i t y , the c o n c e n t r a t i o n of the s o l i d  %  - «_>_ r 1  o  However, s i n c e  the volume of l i q u i d m e t a l d u r i n g ESR  remain constant a new  T h e r e f o r e the new  composition  the l i q u i d i s  (C  =  L2 )  'Wl  When another equal increment of  p r o c e s s i n g must  volume of pure m e t a l must be i n t r o d u c e d which  i s e q u a l to the volume s o l i d i f i e d . of  (Cg) i s :  the s o l i d  (  ((  V2  c s  ) )  i  of volume s o l i d i f i e s the c o n c e n t r a t i o n  s  2  -  ic  i?2 i r o  o  A g e n e r a l form of t h i s e q u a t i o n can be w r i t t e n as f o l l o w s assuming Ah , h o  i s constant  o Using e q u a t i o n profile  A.1-2.2  All  and assuming  for solute dilution  was  = 1 and ^— = 0.1 o calculated.  a theoretical  - 71 -  APPENDIX II DETERMINATION OF THE VOLUME OF LIQUID METAL AND LIQUID SLAG WHICH SOLIDIFIES IN A 10 cm DIAMETER INGOT DURING A RANGE OF POWER INTERRUPTIONS  I I . 1 Heat content of the metal pool system and the slag pool system at the start of the "power-off" mode II.1.1  Assumed Data (a) the metal pool system: (i)  T m.p.  (ii)  (  (iii)  L  (iv)  P  Avg  (v)  p  £  •• 1500°C  v » •••  0.18 cal/g/°C  > 65.5 cal/g 7.5 g/cm  3  7.0 g/cm  3  (vi)  A  =  T  s  ==  58°C  the slag pool system: (i)  T m. p.  (ii)  Avg  1450°C  •  1660°C  29  30  •• 0.3 cal/g/°C  (iii)  II.1.2  -  (iv)  L  46.6 cal/g  (v)  P  Avg  2.6 g/cm  3  Available heat content of the metal pool system.  Figure 53-B shows a schematic diagram of the metal pool system. The t o t a l heat content ( ( Q ) ) was calculated as follows: T  M  - 72 -  VM  (  =  mC AT + mL P  E  V p C A T + Vp C_AT A  p  p  =  284 k c a l s  +  =  363 k c a l s  A  10 k c a l s  The a v a i l a b l e heat content o f  (A.II-1.1)  + Vp L  s  +  69 k c a l s  the m e t a l p o o l system  ((Q^)^) i -  s  the sum o f the l a t e n t heat and superheat terms i n e q u a t i o n A . I I - 1 . 1 ) . This implies  that the s o l i d metal r e t a i n s i t s s e n s i b l e heat  until  the m e t a l p o o l has c o m p l e t e l y s o l i d i f i e d .  ( Q  A M }  =  V P  =  II.1.3  L p C  A T  +  V P  S  A  (A.II-1.2)  L  79 k c a l s  A v a i l a b l e heat c o n t e n t o f the s l a g p o o l system:  F i g u r e 53-A shows a schematic diagram o f the s l a g p o o l system. The t o t a l heat content  CQ_)S  =  ((Q,-,)g)  I mC AT p  =  VP GpAT  =  402 k c a l s  =  500 k c a l s  L  was c a l c u l a t e d as f o l l o w s :  + mL  +  VP C AT L  +  p  g  + VP L  54 k c a l s  (A.II-1.3)  L  +  44 k c a l s  - 73 The a v a i l a b l e heat content of the s l a g p o o l system the  sum  s l a g p o o l has c o m p l e t e l y  ( Q  A S }  =  V p  =  II.2  s  L p C  A T  S  +  s l a g r e t a i n s i t s s e n s i b l e heat  until  solidified.  V  P  L  (A.II-1.4)  L  98 k c a l s  Rate of heat l o s s from the s l a g and m e t a l p o o l systems. For  the purpose o f t h i s c a l c u l a t i o n i t was  of heat l o s s to  i  A  o f the l a t e n t heat and superheat terms i n e q u a t i o n A.II-1.3.  T h i s i m p l i e s that the s o l i d i f i e d the  ((Q )g)  (q) from any p a r t o f the system was  i t s surface area.  I t was  Heat of  directly  a l s o assumed t h a t the heat  a c r o s s the s l a g / m e t a l i n t e r f a c e II.2.1  assumed t h a t the r a t e  (q^) was  proportional  transfer  negligible.  l o s s from the m e t a l p o o l system f o r d i f f e r e n t d u r a t i o n s  the "pbwer-bff" mode  F i g u r e 53-B  shows the main r e g i o n s o f heat l o s s from the  liquid  metal pool. II.2.1.1  Heat  l o s s a c r o s s the l i q u i d m e t a l / s l a g s k i n i n t e r f a c e  Using F i g u r e 50 and an a r e a c o r r e c t i o n f a c t o r l o s s from t h i s r e g i o n f o r any time  =  K. A  . W  h  e  r  e  „ A  "  ( t ) was  E q t=l  (4.7) (1.5) (4.45X1.5)  (Q])  (K^) the heat  c a l c u l a t e d as  follows:  (A.II-2.1)  -I =  - 1  n  0 6  ,  - 74 -  (a)  t  =  2.5 q  (b)  t  =  t  =  1.06  =  1.6  =  =  1.06  =  2.8  7.5 q  = =  (d)  t  =  t  =  t  0.27)kcals  kcals  2 [ E + 1(0.53 + 0.48 + t=l kcals  0.43)]kcals  seconds 5 1.06[ E + E(0.38 + 0.33 + 0 . 1 5 ) ] k c a l s t=l 3.6  kcals  =  1.06[  =  4.4  12.5  q  (f)  +  10 seconds q  (e)  E(0.63 + 0.60  5 seconds q  (c)  seconds  =  7 E + E(0.29 + 0.26 + t=l  0.23)]kcals  kcals  seconds  =  1.06[  =  4.9  10 E t=l  + E(0.20 + 0.18 +  0.08)]kcals  kcals  15 seconds q  =  1.06[  =  5.5  10 E t=l  kcals  + E(0.20 + 0.18  + 0.16  + 0.14  + 0.12)]kcals  - 75 -  (g)  t  =  20 seconds  q  (h)  t  =  15 S t=l  =  1.06  +  =  6.1 k c a l s .  1.06(5)(0.1)  30 seconds  q  II.2.1.2  =  6.1 k c a l +  =  6.3 k c a l s  1.06(10)(0.1)  Heat l o s s by c o n d u c t i o n down the s o l i d i f i e d i n g o t (q^)  Using the r a t e o f heat l o s s down a 7.6 cm diameter i n g o t determined by J o s h i  (q = 0.3 k c a l s / s e c )  the heat l o s s a c r o s s  q  =  t h i s i n t e r f a c e f o r any time ( t ) was c a l c u l a t e d .  K qt  (A.II-2.2)  A  (10) -—= (7.6)  , 1.7  2  where  K  =  A  (a)  t  =  (b)  t  =  t  =  1.3 k c a l s  5 seconds q  (c)  Z  2.5 seconds q  =  =  2.5 k c a l s  7.5 seconds q  =  and the a r e a c o r r e c t i o n f a c t o r ( K ^ ) ,  3.8 k c a l s  - 76 -  (d)  10 seconds  t q  (e)  t  =  12.5 q  (f)  t  =  t  =  t  kcals  seconds 6.0  kcals  =  7.5  kcals  20 seconds q  (h)  =  5.0  15 seconds q  (g)  =  =  =  10.0  kcals  30 seconds q  II.2.1.3  =  15.0  kcals  Heat l o s s a c r o s s the s o l i d m e t a l / s l a g s k i n  interface  U s i n g the minimum r a t e of heat l o s s f o r c o n d u c t i o n from the metal i n f i g u r e  (q = 0.1 k c a l / s e c ) and the a r e a c o r r e c t i o n  factor  CK.), the heat l o s s a c r o s s t h i s i n t e r f a c e a t any time ( t ) was calculated.  q  where K  =  (A.II-2.3)  K qt A  (10)L (7.6)L  =  1.3  (a)  t  =  2.5 q  (b)  t  =  =  t  =  =  7.5 q  (d)  t  =  =  t  =  =  t  =  t  =  t  seconds 1.0  kcals  1.3  kcals  =  1.6  kcals  =  1.9  kcals  20 seconds q  (h)  kcals  15 seconds q  (g)  0.6  12.5 seconds q  (f)  kcals  10 seconds q  (e)  0.3  5 seconds q  (c)  seconds  =  =  2.7  kcals  30 seconds q  =  3.8  kcals  - 78 -  II.2.2  Heat  l o s s from the s l a g p o o l system f o r d i f f e r e n t d u r a t i o n s  of the "power-off" mode F i g u r e 53-A slag  shows the main r e g i o n s o f heat l o s s from the  liquid  pool.  II.2.2.1  Heat  l o s s a c r o s s the s l a g - a i r i n t e r f a c e  Using F i g u r e 50 and an a r e a c o r r e c t i o n across t h i s i n t e r f a c e  =  K  f o r any time ( t ) was  factor  (q^)  (K^) the heat  calculated  loss  as f o l l o w s :  E q. t=l  (A.II-2.4)  C  2 where K  =  (  t  =  t  =  t  =  )  1.16  =  1.16  =  1.0  E(0.47 +  0.41)  5 seconds q  (c)  8  2 seconds q  (b)  ,  (4.45r  A  (a)  4  =  =  1.16  =  2.2  10 q  E(0.47 + 0.41 + 0.35  + 0.34  + 0.28)kcals  kcals  seconds =  1.16[  =  3.4  5 E + E(0.25 + 0.23 + 0.21 t=l  kcals  + 0.20  + 0.19)]kcals  - 79 -  (d)  t  =  15 seconds q  =  10 1.16[ £ t=l  + E ( 0 . 1 8 + 0.17 + 0.16 + 0.15 + 0 . 1 4 ) ] k c a l s  = 4.3 k c a l s  (e)  t  =  30 seconds q  =  15 1.16[ E t=l  + £(0.13 + 0.12 + 0.12 + 0.11 + 0.10 + 0.10 + 0.09 + 0.08 + 0.07 + 2(0.06) + 4 ( 0 . 0 5 ) ) ] k c a l s  =  II.2.2.2  5.8 k c a l s  Heat l o s s a c r o s s t h e l i q u i d s l a g - s l a g s k i n i n t e r f a c e (q<_)  U s i n g F i g u r e 50 and an a r e a c o r r e c t i o n f a c t o r  (K ) t h e h e a t l o s s  a c r o s s t h i s i n t e r f a c e f o r any time ( t ) was c a l c u l a t e d as f o l l o w s :  q  =  K A  ,  .  W h e r e  (a)  =  2 q  (b)  t  =  1 =  X  '  0 2  seconds E(1.89 + 1 . 7 5 ) k c a l s  =  1.2  =  4.2 k c a l s  5 q  (A.II-2.5)  C  (4.8)(5.0) (4.45K4.5)  =  t  E q t=l  seconds =  1.2 E(1.89 + 1.75 + 1.60 + 1.45 + 1 . 3 0 ) k c a l s  =  9.6 k c a l s  - 80 -  (c)  t  =  10 seconds q  =  5 1.2[ E  + £(1.25 + 1.0 + 0.85  + 0.7 + 0 . 5 2 ) ] k c a l s  t=l = 14.3 k c a l s  (d)  t  =  15 seconds q  (e)  t  =  10 E t=l  =  1.2[  + E(0.4 + 0.33 + 0.28 + 0.23 +  =  16.0 k c a l s  0.20)]kcals  30 seconds q  =  15 1.2[ E t=l  + E(0.17 + 0.14  + 0.12 0.07  =  17.5 k c a l s  + 0.11 + 0.09  + 0.08  +  + 0.06 + 7 ( 0 . 0 5 ) ) ] k c a l s  - 81 -  APPENDIX I I I DETERMINATION OF THE VOLUME OF LIQUID METAL AND LIQUID SLAG THAT SOLIDIFIES IN A 61.0 cm DIAMETER INGOT DURING 60 SECONDS OF "POWER-OFF" OPERATION  II 1.1 The available heat content of the m e t a l and s l a g p o o l systems a t the III.1.1 (a)  s t a r t of the "power-off" mode Assumed d a t a the metal p o o l system (i)  T m. p.  =  1500°C  (ii)  (C )„  =  0.18 cal/g/°C  (iii)  L  a  P  (  l  v  )  (v) (vi)  (b)  p  p  Avg  =65.5 =  ^  7  '  5  g  =  T m.p.  (ii)  (C )  (iii)  L  (iv)  p  (v)  AT_  A  m  3  g/cm  70°C  the s l a g p o o l system (i)  c  3  =7.0  AT  /  cal/g  (CaF  2  + 25 wt.% A1-.0-)  =  1450°C  =  0.3 cal/g/°C  =  46.6 c a l / g  =  2.6  =  210°C  3  III.1.2 The follows:  A  v  g  g/cm  The a v a i l a b l e heat content o f the m e t a l p o o l system t o t a l heat content o f the system  ((Q-J^) was c a l c u l a t e d as  - 82 -  (Q ) T  =  M  EmCpAT + mL  Vp.C AT + V p C AT  + Vp L  T  A P  Li P  (58.1 x I O 75 x 1 0  3  XJ  O  + 2.6 x I O  3  (A.III-1.1)  T  + 14.3 x 1 0 ) k c a l s  3  3  kcals  The t o t a l a v a i l a b l e h e a t c o n t e n t (Q.)», i s assumed t o be the sum A  M  of t h e l a t e n t heat and s u p e r h e a t terms i n e q u a t i o n ( A . I I I - 1 . 1 ) .  (Q ) A  III.1.3  M  -  VpC AT  =  17 x 1 0  p  + Vp L  s  (A.III-1.2)  A  kcals  3  The a v a i l a b l e heat c o n t e n t o f t h e s l a g p o o l system  The t o t a l heat c o n t e n t ( ( Q ) g ) " w a s c a l c u l a t e d as f o l l o w s : T  (QJ l b C  =  EmC P  AT. + mL b  (A.III-1.3)  Vp C AT + Vp C AT A  p  A  (33.6 x 1 0  42 x 1 0  3  3  p  s  + Vp L A  + 4.8 x 1 0  3  + 3.5 x 1 0 ) k c a l s 3  kcals  The t o t a l a v a i l a b l e heat c o n t e n t (Q )p i s assumed t o be the sum A  of t h e l a t e n t h e a t and superheat terms i n e q u a t i o n A . I I I - 1 . 3 .  - 83 -  (  Vs  =  V p  =  III.2  A p C  A T  S  8 x 10  +  3  V p  A  (A. I I I - l . 4)  L  kcals  Rate o f the heat l o s s from the s l a g p o o l and m e t a l p o o l systems d u r i n g the "power-off" mode F o r the purpose o f t h i s c a l c u l a t i o n i t was assumed t h a t the r a t e  of heat l o s s  (q) from any p a r t o f the system was d i r e c t l y  to t h e s u r f a c e areas i n v o l v e d .  proportional  T h i s assumption made i t p o s s i b l e t o  use the heat t r a n s f e r p r o f i l e s e x p e r i m e n t a l l y determined f o r the 7.6  cm diameter i n g o t s .  I t was a l s o assumed f o r s i m p l i c i t y  the n e t heat f l o w a c r o s s the s l a g / m e t a l i n t e r f a c e  that  ( q ) was z e r o . £  6  III.2.1  Heat  l o s s from the m e t a l p o o l system d u r i n g the 60 seconds  of "power-off" o p e r a t i o n III.2.1.1  Heat  l o s s from the m e t a l p o o l a c r o s s the l i q u i d m e t a l / s l a g  skin interface  (q^) i n 60 seconds  Using F i g u r e 50 and an a r e a c o r r e c t i o n f a c t o r a c r o s s t h i s boundary  q'• =  K A  ,  „  where K  A  T  =  r  l l  f o r any time  .  (A.III-2.1)  t  =  (30.5)(10.0) „ -( (4.45)(1.5)  =  ._ _ 45.7  I t was a l s o assumed t h a t the minimum v a l u e f o r t h e r a t e o f heat a c r o s s t h i s i n t e r f a c e was 0.1 k c a l s / s e c . 60 seconds was  loss  ( t ) was c a l c u l a t e d as f o l l o w s :  t E q t=l  i  — - — 2 2  (K ) the heat  loss  T h e r e f o r e the heat l o s s i n  - 84 -  q  III.2.1.2  60 _ t=l  =  45.7  q  =  490 k c a l s  Heat l o s s from the m e t a l p o o l a c r o s s  the l i q u i d  metal/solid  m e t a l i n t e r f a c e (q^) The  r a t e of heat l o s s a c r o s s  t h i s i n t e r f a c e f o r the 7.56 cm diameter  i n g o t s was a p p r o x i m a t e l y 0.3 k c a l s / s e c ,  q  2  =  K  ( A  ~°' ' 3  t  k c  therefore:  *ls  Cr ) 2 (30.5)^ r- = — (r.) (3.78)  (A.III-2.2)  2  u where K v  1  =  Z  hence q  =  ,65  Z  =  (65)(0.3)(60)  =  1172 k c a l s  I t should be noted, however, t h a t t h i s r e p r e s e n t s flow p o s s i b l e i n t h i s d i r e c t i o n .  the maximum heat  Because the heat l o s s down the  i n g o t i s i n v e r s e l y p r o p o r t i o n a l to the i n g o t h e i g h t be  t h i s v a l u e would  only  a p p l i c a b l e near the bottom o f the i n g o t and would decrease w i t h  the i n g o t h e i g h t .  The a c t u a l v a l u e ,  t h e r e f o r e , e o u l d be between 30 t o  50 percent  smaller  than the c a l c u l a t e d  III.2.1.3  Heat l o s s from the m e t a l p o o l across  value.  the s o l i d  metal/slag  skin interface The  r a t e o f heat l o s s across  t h i s i n t e r f a c e f o r the 7.6 cm  diameter i n g o t s was approximately 0.1 k c a l s / s e c ,  therefore:  - 85 q  , where K,  =  hence  q  v  A  III.2.1.4  =  3  K  61. OL -, — 7.8L O T  3  (O.i)t kcals  (A.III-2.3)  Q  =  7.8  =  (7.8)(0.1)(60)  =  47 k c a l s  The t o t a l heat l o s s  ( q ^ ) ^ from the m e t a l p o o l d u r i n g the  60 seconds o f "power-off" o p e r a t i o n  (q ) L  M  =  q-L + q  =  (490 + 1172 +  =  1709  2  + q  (A.III-2.4)  3  47)kcals  kcals  T h i s r e p r e s e n t s a maximum v a l u e  f o r the amount of h e a t l o s t  from  the m e t a l p o o l i n 60 seconds.  III.2.2  Heat l o s s from the s l a g p o o l system d u r i n g the 60  seconds  of "power-off" o p e r a t i o n III.2.2.1  Heat  Using across  l o s s a c r o s s the s l a g / a i r i n t e r f a c e  F i g u r e 50 and the area c o r r e c t i o n f a c t o r  t h i s i n t e r f a c e at any time ( t ) was  q.  =  K.  4  where K  = A  '(30.5)  (4.45r  E q t-1  =  fc t  47  (q^) (K^) the heat  loss  c a l c u l a t e d as f o l l o w s :  (A.III-2.5)  - 86 -  therefore  q. 4  III.2.2.2  =  (47)(8.4) k c a l s  =  394 k c a l s  Heat l o s s a c r o s s t h e l i q u i d s l a g / s l a g s k i n i n t e r f a c e (q,.)  Using F i g u r e 50 and the a r e a c o r r e c t i o n f a c t o r a c r o s s t h i s i n t e r f a c e f o r any time  q  =  E  K  J  , h  e  r  e  K  A  =  III.2.2.3  =  1  (30.5)(10) (4.45)(5)  therefore  q  5  (A.III-2.6)  t t  W  _ =  1  3  '  8  =  (13.8)(27.8)  =  384 k c a l s  The t o t a l heat l o s s 60 seconds  (q ) L  s  loss  ( t ) was c a l c u l a t e d as f o l l o w s :  q  A  the heat  kcals  ( q ) from t h e l i q u i d s l a g d u r i n g the T  n  of "power-off" o p e r a t i o n  =  q  =  (394 + 384) k c a l s  =  778 k c a l s  4  + q  5  (A.III-2.7)  T h i s r e p r e s e n t s a maximum v a l u e f o r the amount of heat l o s t the s l a g p o o l i n 60 seconds.  from  -  III.3  87 -  Volume o f l i q u i d m e t a l and l i q u i d 60  III.3.1  second "power-off" mode The percentage o f t h e l i q u i d m e t a l p o o l t h a t would i n 60 seconds under  The  =  AM  (q )_ L T  conditions  17 x 1 0 k c a l s 3  heat l o s s i n 60 seconds  total  N  the assumed  solidify  a v a i l a b l e heat content ( 1 . 2 )  total  (q.)_  The  s l a g to freeze during the  M  =  (2.1.4)  1709 k c a l s  T h e r e f o r e the percentage o f the m e t a l p o o l t h a t would be s o l i d i f i e d i n 6 0 seconds  ( Q  Volume p e r c e n t s o l i d i f i e d  L M }  =  x 100 =  10%  (A.III-3.1)  ^VM III.3.2  The percentage by volume o f the l i q u i d  i n 60 seconds under the assumed c o n d i t i o n s  solidify  a v a i l a b l e heat c o n t e n t ( 1 . 3 )  The t o t a l  (q )  The  =  8 x 1 0 kcals 3  t o t a l heat l o s s i n 60 seconds  (q ) L  g  s l a g t h a t would  =  778 k c a l s  (2.2.3)  - 88 -  Therefore the percentage of the slag pool that would be s o l i d i f i e d i n 60 seconds  ( Q  Volume percent s o l i d i f i e d  =  L S }  .  x 100  =  10.3%  (A.III-3.2)  - 89 -  APPENDIX IV HEAT BALANCE FOR A 10 cm DIAMETER VAR INGOT DURING A 12.5 SECOND POWER INTERRUPTION  IV.1  Determination of the heat content of the system  IV.1.1  Thermal data  (a) , Melting point (b)  C p L  (c) ( d )  p  Avg  -  =  1500°C  0.18 cal/g/°C  =65.5 =  7 , 5  g  cal g" C m  ~  1  3  _3 (e)  p  L  =  7.0 g cm  (f)  AT_  =  120°C  IV. 1.2  Total heat content of the metal pool system (Q_.)  Q_ T  IV.1.3  =  Vp C AT + Vp C AT. + Vp L ^A p p p S A  =  936 k c a l + 71 kcals + 231 kcals  =  1238 kcals  A  r  A  (A.IV-1.1)  Total available heat content of the metal pool system (Q )  Q.  =  Vp C AT + Vp.L p p o A  =  302 kcals  A  (A.IV-1.2)  - 90 This value assumes that the metal pool retains i t s sensible heat u n t i l both the superheat and the latent heat are removed.  IV.2  Determination of the heat loss from the pool i n 12.5 seconds There are three main sources of heat loss i n the VAR system:  1) radiation from the surface of the metal, 2) conduction through the sides of the ingot, and 3) conduction down the ingot.  IV.2.1  Heat loss by radiation from the surface of the l i q u i d metal (q-^)  (a)  Assumed data (i)  The average temperature of the metal at the surface was 1650°C.  (b)  (ii)  The electrode was removed.  (iii)  The shape factor (S) f o r the system was 1.0.  (iv)  The emisivity (e) for the metal was 0.37.  The amount of heat loss from the metal due to radiation i n 12.5 seconds was:  q-L  = SAea[T -T ]t 4  1  =  IV.2.2  4  2  (A.IV-2.1)  6.72 kcals  Heat loss through the sides of the ingot  In order to obtain some estimate of the rate of heat flow through the sides of the ingot i t was necessary to have a p r o f i l e which showed the change i n the heat flux with distance below the top of the ingot.  In a paper published by the Bureau of Mines s e v e r a l p r o f i l e s are  -  given  91 -  f o r s t e e l e l e c t r o d e s melted a t d i f f e r e n t r a t e s of power i n p u t  ( F i g u r e 60).  I t was assumed t h a t the power i n p u t was p r o p o r t i o n a l t o  the c r o s s - s e c t i o n a l a r e a o f the i n g o t so t h a t the 10 cm diameter i n g o t c o u l d be s c a l e d up t o f i t the p r o f i l e s . The  power i n p u t i n t o i n g o t no. V-3 was c a l c u l a t e d on the b a s i s o f  i t s operating  i.e.  conditions.  power i n p u t  (KW) = ( v o l t s ) ( a m p s )  A.IV-2.2)  = (25)(2900) =  72.5 KW  T h i s corresponds to a power i n p u t o f a p p r o x i m a t e l y 300 k i l o w a t t s for  a 20.32 cm diameter i n g o t .  Although t h i s i s a h i g h e r  power  i n p u t than r u n no. 9 i n F i g u r e 60, the p r o f i l e s t i l l p r o v i d e s approximation of the r a t e of heat t r a n s f e r d u r i n g conditions.  a good  steady-state  Because the r a t e o f heat t r a n s f e r w i l l decrease d u r i n g the  "power-off" mode t h i s p r o f i l e w i l l p r o v i d e r a d i a l heat l o s s d u r i n g  a maximum v a l u e  the "power-off" mode.  f o r the  F i g u r e 61 shows the  heat f l u x p r o f i l e f o r r u n no. 9 i n m e t r i c u n i t s , (a)  Assumed (1)  data  The heat conduction  above the i n g o t top d u r i n g the  "power-off" c o n d i t i o n was assumed t o be n e g l i g i b l e . s i n c e the h i g h and  f l u x values  i n t h i s area represented  T h i s was  reasonable  arc i n s t a b i l i t i e s ,  h o t metal s p l a s h i n g on the c r u c i b l e w a l l s , and t h e r e f o r e , would  not occur  during (2)  the "'power-off" mode.  The r a d i a l heat f l u x lower than 12 cm below the i n g o t  s u r f a c e was c o n s i d e r e d n e g l i g i b l e .  - 92 -  (b)  C a l c u l a t i o n o f t h e r a d i a l heat l o s s from the i n g o t (q,.)  12 q  =  2  A( E n=l  hAT)t  (A.IV-2.3)  where the average f l u x (hAT) i s determined a t 1 cm i n t e r v a l s . Therefore,  q-  = TT(10) (1) (0.214) (12.5) k c a l s =  IV.2.3  84 k c a l s  Heat l o s s by c o n d u c t i o n down the i n g o t ( q ^ )  (a)  Assumed (1)  data:  The r a t e o f heat l o s s was p r o p o r t i o n a l t o the r a t e  f o r a s i m i l a r s i z e d ESR machine. (2)  The r a t e o f heat l o s s was p r o p o r t i o n a l t o the s u r f a c e  area. U s i n g the r a t e o f heat l o s s down a 7.6 cm diameter ESR i n g o t as determined by J o s h i factor  (q = 0.3 k c a l / s e c )  and t h e a r e a  correction  ( K ^ ) , t h e heat l o s s down t h e i n g o t was determined.  q  , „ where K  3  =  A  K  =  A  ( 0 , 3 ) ( 1 2  (10) - — — (7.6)  2  =  '  5 )  . 1.7 7  2  Therefore q„  =  6.4 k c a l s .  k  c  a  l  s  (A.IV-2.4)  - 93 -  IV.2.4  T o t a l heat l o s s from the l i q u i d p o o l i n 12.5 seconds  Q  L  =  q± + q  =  (6.7 + 84.0 + 6.4) k c a l s  =  97.1 k c a l s  2  + q  (Q > L  (A.IV-2.5  3  T h i s r e p r e s e n t s the maximum heat l o s s from t h e system d u r i n g the 12.5 second power i n t e r r u p t i o n .  IV.3  Percentage o f the m e t a l p o o l t h a t s o l i d i f i e d i n 12.5 seconds of "power-off"  operation  Volume percent  solidified  =  Q —  =  32.2% s o l i d i f i e d  L  x 100  (A.IV-3.1)  APPENDIX V. COMPUTER PROGRAM TO DETERMINE THE UNSTEADY-STATE TEMPERATURE PROFILE IN AN ESR ELECTRODE.  FORTRAN IV G CUMPILtK OOU 1 0002 O00 3 000 000 6 000 7 000 8 000 9 0010 0011 0012 001 3 00 IA 001 b 0016 0017 0018 0019 00 20 0021 0022 0023 002A 002*3 00 2 6 0027 0028 0029  MAIN  12-13-71  2 9 10  11  PAGE 0001  ALPHA = .Ot>7 HP = . t>64 H = .OA TP=130. T I M t = TP TP = b. Tu = 2 b . Tb = l 6t>0 . Tr- = TB-TU OU 2 N = l , l A WKlTfc ( 6 . 9 ) Y = .1 B = SURT(ALPHA*TI t ) OU 1 M = l,3t> C = Y/ ( 2 .* B ) TEWP =TF* 111. "FRF t e n »FXP (*HP* t Y+HP«ALPHA^rtME r T * t r . - ^ R F r c - m * B r r T T tMP = T tMP + TU W K l T t (6,10) TIME,Y,TEMP It- ( Y . G f c . l ' J . ) Y=Y+S. It- (Y.LT.lt>..ANL).Y.GB.l. ) Y=Y + 1. I M Y . L T . l . ) Y=Y+.l CUNT INUE WKlTb ( 6 , 1 1 ) TlMt = TIMt • TP (-UKMAT ( 8X ' T IME ' « 12X , ' n I STANCE ' , 7X , ' T t M P ' / ) r-UKMAT ( IX,3( l P t l S . T f ' j X ) ) tUKMAT (1H1) 5T0P ~ "- ' tNU M  1  10:43:33  - 95 -  APPENDIX VI DETERMINATION OF THE VOLUME OF LIQUID METAL THAT SOLIDIFIES IN A 61.0 cm DIAMETER INGOT DURING 120 SECONDS OF "POWER-OFF" OPERATION  VI.1  Available heat content of  the metal pool system at the start  of the "power-off" mode From Appendix III.1.2.  (Q.)„ AM  VI.2  =  17 x 10  3  kcals  Rate of heat loss from the metal pool system during the "power-off" mode This c a l c u l a t i o n contains the same assumptions found i n Appendix  III.2.  VI.2.1  Heat loss from the metal pool across the l i q u i d metal/slag skin interface i n 120 seconds  Using Figure 50 and an area correction factor (K^) the heat loss across this boundary was calculated as follows:  q  =  K A  where K. A  =  — — xl 2  £ q t=0  1  =  45.7  2  Therefore the heat loss i n 120 seconds was  q  =  60 £ t=l  q Z  120 + £ t=60  q  (A.VI-2.1)  - 96 -  =  490 k c a l s + (45. 7)(O.D(60) 764 k c a l s  VI.2.2  Heat l o s s from the m e t a l p o o l a c r o s s  the l i q u i d  metal/solid  metal i n t e r f a c e The r a t e of heat l o s s a c r o s s  t h i s i n t e r f a c e f o r the 7.56 cm  diameter i n g o t s was approximately 0.3 k c a l s / s e c ,  =  A  =  =  VI.2.3  (A.VI-2.2)  K (0.3)t  where K  hence  therefore,  65  2344 k c a l s  Heat l o s s from the m e t a l p o o l a c r o s s  the s o l i d  metal/slag  skin interface The r a t e of heat l o s s a c r o s s  t h i s i n t e r f a c e f o r the 7.6 cm  diameter i n g o t was approximately 0.1 k c a l s / s e c ,  q  3  where K.  hence  q  =  K (0.1)t A  =  =  94 k c a l s  7.8  therefore,  (A.VI-2.3)  - 97 -  VI.2.4  Total heat loss ( Q ^ ) from the metal pool during the 120 seconds M  of "power-off" operation  (Q ) L  VI.3  M  =  (764 + 2344 + 94 ) kcals  =  3202 kcals  .  (A.VI-2.4)  The percentage of the metal pool that would s o l i d i f y i n 120 seconds of "power-off" operation  The t o t a l available heat content (7.1.1)  Q. A  =  17 x 10  3  kcals  The t o t a l heat loss i n 120 seconds (7.1.4)  Q  L  = 3202 k c a l  Therefore L -f- x 100 A Q  Volume percent s o l i d i f i e d =  =  18.8%  (A.VI-3.1)  Q  It should be noted that this represents the maximum amount of l i q u i d metal that would s o l i d i f y i n this time period.  - 98 -  REFERENCES  1.  Chalmers  B.,  " P r i n c i p l e s of S o l i d i f i c a t i o n " , John W i l e y  2.  Chalmers  B.,  and K i n g R. , ( E d i t o r s ) , Pergamon P r e s s (1959), 8,  3.  Turkdogan  4.  J a t c z a k C.F., 48, 279.  5.  Weinberg F., and Buhr R.K., "The S o l i d i f i c a t i o n of M e t a l s " , I r o n and S t e e l I n s t . , (1967) 295.  6.  Thresh H., Bergeron M., (1968) , 48, 279.  7.  Flemings M.C., P o i r i e r D.R., (1970) 208, 371.  8.  Kattamis T.S.,  9.  Morton  E.T.,  S.K.,  and Grange R.A.,  J.I.S.I.  (1970), 208,  G i r a d i D.J., and Rowland E.S.,  and Flemings M.C.,  482.  Trans A.I.M.E.  and Brody H.D.,  J.I.S.I.  Trans A.I.M.E. (1956) 233,  M.A.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia  10.  F r e d r i k s s o n H. , and J a r l e b o r g 0.,  11.  Takada H., Fukuhara Y., S t e e l L t d . , Japan.  12.  De V r i e s R.P.,  13.  F i r g a n e k H.,  J . Metals  and M i u r a M.,  and Mumau G.R.,  J e z i e r s k i K.,  203.  Trans. A.S.M. (1956)  Weinberg F., and Buhr R.K.,  Barone R.V.,  (1964).  992. (1971).  (1971) 23_, (9) , 32.  i n t e r n a l r e p o r t , Kobe  J . Metals  (1968), 20,  (11), 33.  and S i e w i e r s k i J . , Pace I n s t .  Huts,  (1969) 21 ( 3 ) , 141. 14.  E t i e n n e M.,  Ph.D.  T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia,  and Weinberg F., J . I . S . I .  (1967) 205,  (1970).  15.  Buhr R.K.,  16.  K e h l G.L., "The P r i n c i p l e s o f M e t a l l o g r a p h l c L a b o r a t o r y P r a c t i c e " , McGraw-Hill (1949), 186.  1161.  17.  L i l l i e W.D., and Ward F.R. ( E d i t o r s ) , " R a d i o i s o t o p e A p p l i c a t i o n s E n g i n e e r i n g , " D . Van Nostrand Co., I n c . (1961).  18.  Microprobe A n a l y s i s G e n e r a l I n t e n s i t y C o r r e c t i o n , F o r t r a n Program adapted by O'Brien T.E., Department of M e t a l l u r g y , U.B.C.  19.  Hansen M., and Anderko K., McGraw-Hill (1958) 705.  " C o n s t i t u t i o n of B i n a r y A l l o y s " ,  - 99 -  20.  Rein D.M.,  Armco Steel Corporation, private communication (1971).  21.  Campbell J . , J . Metals (1970)'22 (7) 23.  22.  Hansen M., and Anderko K., op c i t , 718-719.  23.  M i t c h e l l A., and Joshi S., University of B r i t i s h Columbia, private communication (1971).  24.  B e a l l R.A., (1971).  25.  Joshi S., Ph.D. Thesis, University of B r i t i s h Columbia (1971).  26.  Maulvault A., and E l l i o t J.F., E l e c t r i c Furnace Proceedings (1970) 28, 13.  27.  Mendrykowski J . , Poveromo J . J . , Szekely J . , and M i t c h e l l A., Met. Trans., to be published.  28.  C l i t e s P.G., and B e a l l R.A., (Washington) U.S. Dept. of the I n t e r i o r , Bureau of Mines (1967), R.I. 7035.  29.  Burel B.C., M.A.Sc. Thesis, University of B r i t i s h Columbia (1969) 33.  30.  Joshi S.J., op. C i t . , 13.  31.  Joshi S.J., University of B r i t i s h Columbia, private communication (1971).  32.  Szekely and Themelis, "Rate Phenomena i n Process Metallurgy", Wiley, (1971), 188.  33.  Swoboda K., and Kleinhagauer 0, German Pat., 1,903,843, 10 December (1970).  Bureau of Mines, Albany Oregon,  private communication  100  ingot line  F i g u r e 1.  Three phase, seven e l e c t r o d e , b i f i l a r  slag line  furnace.  101  F i g u r e 2.  Tandem e l e c t r o d e change machine.  102  F i g u r e 3.  Schematic diagram of the U.B.C, ESR  unit.  Figure 4.  Schematic diagram of a VAR  furnace.  Figure 5  Operating  chart d u r i n g a "power-off"  sequence.  105  FeS  addition  slag  Figure 6.  External addition of FeS to the melt.  3,81  cm ••  | * — 2 , 5 2 cm '  TI3'  I Sn  Figure 7.  '  ,  ;AI iMetal  Configuration of the Sn  1 0 95  i n the electrode.  106  900 Ingot no. 17  0.32 g Sn added  0  F i g u r e 8.  O p e r a t i n g c h a r t during a S n  1 1 3  experiment.  107  50  mV  shunt  I—thermocouples  recorder  cooling water  Figure 9.  Hobart  750  i ".ower supplies  Schematic outline of the experimental setup for heat transfer measurements.  108  recorder  W3Re W25Re thermocouple wire (o,o92 cm dia )  mullite tube (ojo cm O. D.)  2-holed silica tube (0,035 cm O.D.)  boron nitride (o.65 cm O.D.)  Yi  F i g u r e 10.  Thermocouple f o r measuring  graphite  powder  s l a g and m e t a l b a t h  temperatures.  109  Figure 11.  Macrograph of i n g o t no. 1 showing the steady s t a t e s t r u c t u r e of EN-25 s t e e l E t c h : O b e r h o f f e r ' s reagent.  110  9.5 sec.  18 sec.  75 sec.  Figure  12.  Macrograph of interruptions,  ingot  no.  3 containing  Etch:0berhoffer's  three  reagent.  power  F i g u r e 13.  Micrograph of the 18 sec power i n t e r r u p t i o n i n i n g o t no. mag. 6X, E t c h r O b e r h o f f e r ' s reagent.  3  112  Figure 14.  Macrographs of ingots etched with 3 percent (A) ingot no. 2 and (B) ingot no. 3.  nital.  113  Figure 16.  Pool p r o f i l e outlined with W powder additions Etch 3% N i t a l .  (ingot no.  13)  115  S"rich band power-off FeS addition  F i g u r e 17.  Sulphur p r i n t of i n g o t no. 6 c o n t a i n i n g interruptions.  several  116  Figure 19.  " T r e e - r i n g " banding i n a h i g h carbon a l l o y by vacuum a r c r e m e l t i n g .  steel  produced  117  Figure 2 0 .  I r r e g u l a r i t i e s i n the slag skin thickness reproduced i n the metal.  118  Figure 21.  Banding i n ingot no. 13 produced by i r r e g u l a r i t i e s i n the slag skin thickness, Etch 3% N i t a l .  119  F i g u r e 22.  Schematic r e p r e s e n t a t i o n of banding due to i n the s l a g s k i n t h i c k n e s s .  irregulariti  120  17 sec.  11 sec.  6  sec.  Macrograph of ingot no. 14 containing several power interruptions, Etch 100 ml ethyl alcohol, 100 ml HCl, 50 ml HNO_.  121  Figure 24.  Location of specimens from ingot no. 14 for analysis the electron probe.  122  F i g u r e 26.  Arcos C o r p o r a t i o n ' s c o n t i n u o u s  c a s t i n g ESR  process.  123  Figure 28.  Micrograph of the banded structure. Etch: Railing's reagent.  X 48  124  Absorbed electron image  Ni  X-ray image  Cr X- ray image  F i g u r e 29.  Absorbed e l e c t r o n image and X-ray images f o r n i c k e l and chromium i n the banded a r e a X 1000.  125  Fe, 18Cr, 4Ni  Figure  30.  wt 56 C  Fe  '  1 8 C r  '  8 N i  Pesudo-binary phase diagrams of Fe + 18% Cr + 4% N i v e r s u s v a r y i n g carbon content and Fe + 18% Cr + 8% N i v e r s u s v a r y i n g carbon c o n t e n t .  127  total  78  average particle width = 0.2 cm  Figure 32.  Standard l i n e count for percent f e r r i t e determination.  128  Figure 33.  Crack formation during r o l l i n g .  129  F i g u r e 34.  Different  electromagnetic s t i r r i n g c o i l  configurat  ions.  130  CONSUMABLE ELECTRODE: \  MOLD  LIQUID  SLAG  LIQUID  METAL  SOLIDIFICATION FRONT INGOT  ASBESTOS  GRAPHITE WATER  F i g u r e 35.  COOLED  SEAL  CHILL COPPER  BASE  C o n v e c t i v e motion i n t h e s l a g and m e t a l p o o l produced by the f a l l i n g m e t a l d r o p l e t s .  131  132  F i g u r e 37.  P l o t of the r e l a t i v e c o n c e n t r a t i o n s of r a d i o a c t i v e t i n v e r s u s a x i a l d i s t a n c e from the o r i g i n a l i n t e r f a c e .  133  F i g u r e 38.  P o o l p r o f i l e o u t l i n e d by sulphide.  (A) tungsten powder, (B)  iron  134  Figure 39.  P l o t of the r e l a t i v e concentrations of sulphur vers a x i a l distance from the o r i g i n a l i n t e r f a c e .  135  ->  5 cm  •  •  1,5 cm • 2,2 5 cm  3 .8  1  r  1550 C  1700 C  15£S0 C  1500 C  1500 C  1500 C  z r  F i g u r e 40.  Assumed p o o l geometry and imposed boundary temperatures i n a 10 cm d i a . ESR i n g o t .  136  Figure 41.  Subdivision of the metal pool.  137  ure  42.  Assumed temperature d i s t r i b u t i o n i n the z d i r e c t i o n .  138  gure 43.  Assumed temperature d i s t r i b u t i o n i n the r d i r e c t i  139  1600  1750  10 c m .  dia.  T =86°C S  1500  1500  1500  1650  B i o cm.  T  dia.  =47 C  s  1500  1550  1700  10 cm. T 1500  1500  1550  1700  dia.  = 58 C  s  D 61 cm.  T 1500  1500  1550  1700 254  F i g u r e 44.  =70C  s  cm.  T 1500  dia.  s  dia.  = 80 C  1500  Assumed temperature d i s t r i b u t i o n s values.  and c o r r e s p o n d i n g '  (ATs) g  140  F i g u r e 45.  Assumed p o o l geometry and imposed boundary temperatures m a 10 cm d i a . VAR i n g o t .  141  A Temperature  Profile  in  the Z  Direction  B Temperature  F i g u r e 46.  Profile  in  the  R  Direction  Assumed temperature d i s t r i b u t i o n s i n directions.  the z and r  142  •4 4 5  F i g u r e 47.  cm  Regions where the r a t e of heat l o s s i s e f f e c t e d by the "power-off" mode f o r a 10 cm d i a . ESR i n g o t .  143  F i g u r e 48. \ P l o t of the change i n the mould w a l l temperature v e r s u s time d u r i n g the "power-off" mode.  144  10 Figure  20 49.  40  60  100  20 0  AT = T m o l d - T w a t e r r T m o l d - 5 0 (°C)  P l o t of (q/A) v s . AT boiline conditions.  f o r (a) n o n - b o i l i n g and  (b)  surface  145  0  1 0  —I  4 Time  Figure 50.  1  1  1—  8  12  16  (sec)  Plot of q vs time for (a) slag (conduction), Cb) (radiation) and (c) l i q u i d metal.  slag  E  1700 »  I  I  1  —  —  —  —  r  o - ^ a  pypprimpntal rpmppratnrP  •«»  N.  1600  profile in the slag  s N  >v  \  X.  s  assumed temperature  N  profile in the metal  o  rature  ^^^^ 1500  cu Q.  X  E ,cu  1400  1300 0  I  I  I  1  1  5  10  15  20  25  Duration Figure 51.  of  the  Power-off  Mode  (sec.)  Plot of temperature vs time f o r (a) the slag and (b) the metal.  1  5  9  7  Time  Figure 52.  n  13  (sec)  Plot of q/A vs time for d i f f e r e n t values of h .  15  148  (A) -5,0 -4,8  5,0  F i g u r e 53.  cm-  cm  cm  Assumed p o o l c o n f i g u r a t i o n s i n a 10 cm d i a . i n g o t f o r (A) s l a g , (B) m e t a l .  T  1  1  1  Duration of the Power-off Mode  Figure 54.  1  r  (sec")  Plot of volume percent s o l i d i f i e d vs duration of the "power-off" mode.  150  Figure 55.  Macrograph of ingot no. 13 containing three w powder addition experiments.  151  A c t u a l and approximated p o o l p r o f i l e s f o r a d d i t i o n experiment.  152  -<—30.5 cm  1  1  1<3n  •  slag  cr  %  %  10 c  m  metal  %  F i g u r e 57.  Schematic r e p r e s e n t a t i o n o f a 61 cm d i a . ESR i n g o t .  153  F i g u r e 58.  Macrograph of i n g o t no. interruptions.  V-3  containing  s e v e r a l power  154  Figure 5 9 .  Approximation of the metal pool p r o f i l e i n ingot V - 3 .  155  + 8  1 •O— •A— -•—  </> o -8  T 1 Run No. 7 steel 4 g - i n c h electrode, 6,600 amps - 2 7 v Run No. 8 steel 4 i - i n c h electrode, 6 , 5 0 0 omps-31 v No. 9 steel 4 g - i n c h electrode, Run No 8,000 amps- 33 v  8-inch-diam crucible  0.i>  0.6  0.4  HEAT FLUX, IO Btu/ft hr 6  Figure 60.  2  E f f e c t o f a r c c u r r e n t and a r c p o t e n t i a l on the h e a t f l u x t o t h e c r u c i b l e w a l l d u r i n g t h e VAR m e l t i n g o f steel electrodes.  0  I 0  1 2  I 4  Distance Below the  Figure 61.  I  I  i  i  i  6  8  10  12  14  Ingot Top  (cm)  Heat flux p r o f i l e for run no. 9, Figure  60.  157  Figure 62.  Approximation of the volume s o l i f i e d during a 12.5 power i n t e r r u p t i o n i n a 10 cm d i a . VAR ingot.  158  Figure 5 3 ,  Plot of temperature vs distance along the electrode for (a) T, = 1550°C, and (b) T, = 1650°C. D  b  159  Distance along the Electrode (cm)  Figure 64. Plot of temperature vs distance along the electrode f o r (a) T = 1550°C, (D) T = 1200°C, t = 100, 500 and 1000 seconds.  

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