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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 in the Department of METALLURGY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH January, 1972 COLUMBIA In present ing th i s thes is in pa r t i a l f u l f i lmen t o f the requirements for an advanced degree at the Un ive rs i t y of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extensive copying of th i s thes i s for s cho la r l y purposes may be granted by the Head of my Department or by h is representat ives . It is understood that copying or pub l i c a t i on of th i s thes is fo r f inanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. The Un ive rs i t y o f B r i t i s h Columbia Vancouver 8, Canada Depa rtment Date ABSTRACT St r u c t u r a l and compositional changes r e s u l t i n g from int e r r u p t i o n s i n the steady-state heat balance of an e l e c t r o s l a g remelted ingot have been investigated on a laboratory scale e l e c t r o s l a g furnace. An attempt was also made to solve some of the fundamental problems introduced by the proposed production of large commercial ingots i n a tandem electrode change furnace. The i n v e s t i g a t i o n was c a r r i e d out on three commercially a v a i l a b l e a l l o y s t e e l s : 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 st e e l s revealed only minor s t r u c t u r a l changes but did show carbon concentration banding. Carbon r i c h bands were also produced by p e r i o d i c v a r i a t i o n s i n the slag skin 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 concentrations of the major a l l o y i n g elements was detected. The mixing action i n the l i q u i d metal pool appears to be due to a slow convective motion which causes the l i q u i d to approach a state of complete mixing at the s o l i d i f i c a t i o n rates found i n the ESR process. A general heat balance was calculated f o r a 10 cm d i a . ESR ingot. The various volume f r a c t i o n s s o l i d i f i e d were calculated f o r d i f f e r e n t durations of the "power-off" mode. The r e s u l t s of the heat balance were extended to a large (61 cm dia.) commercial ingot and the volume s o l i d i f i e d during a 60 second power i n t e r r u p t i o n was estimated. A heat transfer program was written to determine the unsteady state temperature p r o f i l e s i n an electrode as a function of temperature - i i i — of the sl a g bath and time a f t e r immersion. The r e s u l t i n g p r o f i l e s indicated that i n order to avoid any major s t r u c t u r a l and/or composi-t i o n a l changes during an electrode change operation, electrode preheating i s mandatory. - i v -TABLE OF CONTENTS Page 1. INTRODUCTION . . 1 1.1 Problems Introduced by "Scale-up" 2 1.2 Objectives of the Present Work 4 1.3 Previous Work 5 2. EXPERIMENTAL TECHNIQUES 9 2.1 Introduction 9 2.2 Materials 9 2.2.1 Electrode Composition 9 2.2.2 Slag Composition 10 2.3 Ingot Production H 2.3.1 ESR Ingots H 2.3.2 VAR Ingots. H 2.4 Specimen Preparation 11 2.5 Techniques used to Analyze the E f f e c t s of Power Interruptions on the Structure and Composition of the Ingot 15 2.5.1 Etching 15 2.5.1.1 EN-25 and AISI 4340 Steels 15 2.5.1.2 AISI 630 (17-4PH) Stainless S t e e l . 15 2.5.2 Sulphur P r i n t s 16 2.5.3 Autoradiography 16 2.5.4 Micorprobe Analysis 17 2.6 Techniques Used to Determine the Extent of the Mixing i n the Li q u i d Metal Pool 18 2.6.1 Sulpur P r i n t s 1 8 - v -Page 2.6.2 Sulphur Concentration Analysis 18 2.6.3 Radio-Tin Concentration Analysis 19 2.7 Determination of the S o l i d i f i c a t i o n Rate 19 2.7.1 Melt Record 19 2.7.2 Tungsten Powder Addition 19 2.8 Determination of the Heat Transfer i n the System During the "Power-Off" Mode 20 2.9 Determination of the Volume Percent S o l i d i f i e d During a Short Power Interruption 21 3. STRUCTURAL AND COMPOSITIONAL CHANGES PRODUCED BY PERTURBATIONS IN THE GENERAL HEAT BALANCE OF THE SYSTEM. 22 3.1 An Evaluation of the Segregation and Banding i n EN-25 and AISI 4340 Produced by Interruptions i n the Power Supply to the System 22 3.1.1 Nature of the St r u c t u r a l and Compositional Changes 22 3.1.2 Or i g i n of the Carbon-Rich Bands 23 3.1.3 Alternate Techniques Employed to Investigate the Nature of the Segregation and Banding i n EN-25 and AISI 4340 Produced by Interrup-tions 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 3.2 The E f f e c t of Slag Skin Thickness on the Formation of Carbon Rich Bands i n EN-25 and AISI 4340 During Steady State Production 28 3.3 An Evaluation of the Segregation 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 Compositional Changes 3 u 3.3.3 Commercial Castings 31 - v i -Page 4. MIXING IN THE LIQUID METAL POOL... 34 4.1 Or i g i n of the Mixing Action 34 4.2 Evaluation of the Mixing Action 36 5. THERMAL PARAMETERS 39 5.1 Evaluation 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 Ingots 42 5.1.3 VAR: 10 cm Diameter Ingot 42 5.2 Heat Transfer During the "Power-Off Mode 44 5.2.1 Heat Transfer Across the L i q u i d Metal/Slag Skin Interface 45 5.2.2 Heat Transfer Across the L i q u i d Slag/Slag Skin Interface 45 5.2.3 Heat Transfer Across the L i q u i d Slag/Atmos-phere Interface 46 5.2.4 Heat Transfer Across the.Liquid Metal/Liquid Slag Interface 46 6. THE EXTENT OF SOLIDIFICATION DURING THE "POWER-OFF" MODE 49 •6.1 Determination of the volume s o l i d i f i e d i n the metal and slag pool systems i n a 10 cm diameter, EN-25 ESR Ingot 49 6.2 Volume Percent of L i q u i d Metal to S o l i d i f y Based on 5? Tungsten Powder Addition Experiments 6.3 Determination of the Volume S o l i d i f i e d i n the Metal and Slag Pool Systems i n a 61 cm Diameter Ingot During a 60 Second Power Loss 53 6.4 Determination of the Volume of the Metal Pool 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 Interruption - v i i -Page 7. ELECTRODE CHANGE OPERATIONS 58 7.1 Temperature P r o f i l e i n a Commercial Electrode 58 7.2 Heat Content of a Commercial Electrode 60 7.3 Electrode Preheating 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 . Determination of the Volume of L i q u i d Metal and L i q u i d Slag which S o l i d i f i e s i n a 10 cm Diameter Ingot During a Range of Power Interruptions 71 APPENDIX I I I . Determination of the Volume of L i q u i d Metal and L i q u i d Slag that S o l i d i f i e s i n a 10 cm Diameter Ingot During a 60 Seconds of "Power-Off Operation 81 APPENDIX IV. Heat Balance f o r a 10 cm. Diameter VAR Ingot During a 12.5 Second Power Interruption ... 81 APPENDIX V. Computer Program to Determine the Unsteady-State Temperature P r o f i l e i n an ESR Electrode 94 APPENDIX VI. Determination of the Volume of Liqu i d Metal that S o l i d i f i e s i n a 61 cm Diameter Ingot During 120 Seconds of "Power-Off Operation... 95 REFERENCES 98 - v i i i -LIST OF FIGURES Figure Page 1 Three phase, seven electrode, b i f i l a r furnace 100 2 Tandem electrode change machine 101 3 Schematic diagram of the U.B.C., ESR unit 102 4 Schematic diagram of a VAR furnace 103 5 Operating chart during a "power-off" sequence 104 6 External a d d i t i on of FeS to the melt 105 113 7 Configuration of the Sn i n the electrode 105 8 Operating chart during a Sn''""''^  experiment 9 Schematic outline of the experimental setup for heat transf e r measurements 107 10 Thermocouple for measuring slag and metal bath temperatures .. 108 11 Macrograph of ingot no. 1 showing the steady state structure of EN-25 stee l , E t c h : Oberhoffer's reagent 109 12 Macrograph of ±igot no. 3 containing three power int e r r u p t i o n s , Etch: Oberhoffer's reagent HO 13 Micrograph of the 18 sec power i n t e r r u p t i o n i n ingot no. 3 mag. 6X, Etch: Oberhoffer's reagent m 14 Macrographs of ingots etched with 3 percent n i t a l . (A) ingot no. 2 and (B) ingot no. 3 112 15 Schematic representation of the carbon band forma-tio n model 16 Pool p r o f i l e o utlined with W powder additions (ingot no. 13), Etch 3% n i t a l 114 17 Sulphur p r i n t of ingot no. 6 containing several power interruptions 115 18 Autoradiograph of a section from ingot no. 11 contain-ing a 23 second power i n t e r r u p t i o n 116 19 "Tree-ring" banding i n a high carbon a l l o y s t e e l produced by vacuum arc remelting 116 - i x -Figure Page 20 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 117 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 118 22 Schematic representation of banding due to i r r e g u l a r -i t i e s i n the slag s k i n thickness 119 23 Macrograph of ingot no. 14 containing several power in t e r r u p t i o n s , Etch 100 ml et h y l a l c o h o l , 100 ml HC1, 50 ml HN03 120 24 Location of specimens from ingot no. 14 for analysis on the electron probe 121 25 Concentration banding i n a commercial AISI 630 ingot 122 26 Arcos Corporation's continuous casting ESR process.. 122 27 Location of specimens used i n the banding a n a l y s i s . . 123 28 Micrograph of the banded structure. X 48 Etch: R a i l i n g ' s reagent 123 29 Absorbed e l e c t r o n image and X-ray images for n i c k e l and chromium i n the banded area X 1000 124 30 Pseudo-binary phase diagrams of Fe + 18% Cr + 4% Ni versus varying cabon content and Fe + 18% Cr + 8% Ni versus varying carbon content 125 31 Schaeffler f e r r i t e diagram for AISI 630 s t e e l 126 32 Standard l i n e count for percent f e r r i t e determination 127 33 Crack formation during r o l l i n g 128 34 D i f f e r e n t electromagnetic s t i r r i n g c o i l configurations 129 35 Convective motion i n the slag and metal pool produced by the f a l l i n g metal droplets 130 36 Autoradiograph of ingot no. 10 131 37 Plot of the r e l a t i v e concentrations of radioactive t i n versus 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 132 38 Pool p r o f i l e o u t l i n e d by (A) tungsten powder, (B) i r o n sulphide . 133 - x -Figure Page 39 Plot of the r e l a t i v e concentrations of sulphur versus 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 134 40 Assumed pool geometry and imposed boundary tempera-tures i n a 10 cm diameter ESR ingot 135 41 Subdivision of the metal pool 136 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 . 137 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 o n 138 44 Assumed temperature d i s t r i b u t i o n s and corresponding (AT ) values 139 S Avg 45 Assumed pool geometry and imposed boundary tempera-tures i n a 10 cm diameter VAR ingot 140 46 Assumed temperature d i s t r i b u t i o n s i n the z and r dir e c t i o n s 141 47 Regions where the rate of heat loss i s eff e c t e d by the "power-off" mode for a 7.6cm di a . ESR ingot .... 142 48 Plot of the change i n the mould w a l l temperature versus time during the "power-off"mode.. 143 49 Plot of (q/A) vs AT for (a) nonboiling and (b) surface b o i l i n g conditions 144 50 Plot of q vs time f o r (a) slag (conduction, (b) sla g ( r a d i a t i o n and (c) l i q u i d metal 145 51 Plot of temperature vs time f o r (a) the sla g and (b) the metal 146 52 Plot of q/A vs time for d i f f e r e n t values of h^ ..... 147 53 Assumed pool configurations i n a 10 cm d i a . ingot for (A) s l a g , (B) metal - 148 54 Plot of volume percent s o l i d i f i e d vs duration of the "power-off" mode 149 55 Macrograph of ingot no. 13 containing three W-powder addition experiments 150 56 Actual and approximated pool p r o f i l e s f o r a W-powder addition experiment 151 57 Schematic representation of a 61 cm dia. ESR ingot.. 152 - xi -Figure Page 58 Macrograph of ingot no. V-3 containing several power inte r r u p t i o n s ^ 3 59 Approximation of the metal pool p r o f i l e i n ingot V-3 154 60 E f f e c t of arc current and arc p o t e n t i a l on the heat f l u x to the c r u c i b l e w a l l during the VAR melting of i ^  s s t e e l electrodes X J J 61 ' Heat f l u x p r o f i l e f o r run no. 9, Figure 60 -^6 62 Approximation of the volume s o l i d i f i e d during 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 ingot. 1^7 63 Plot of temperature vs distance along the electrode for (a) T, = 1550°C, and (b) T, = 1650°C 1 5 8 b b 64 Plot of temperature vs distance along the electrode for (a) T b = 1550°C, (b) T b = 1200°C, t = 100, 500, and 1000 seconds 159 - x i i -LIST OF TABLES Table Page I Composition of the a l l o y s studied 10 II ESR melt record 12 I I I VAR melt record 14 IV Element concentrations i n the banded regions 32 V A - Volume s o l i d i f i e d i n the metal pool system during the "power-off" mode 51 B - Volume s o l i d i f i e d i n the slag pool system during the "power-off" mode 51 - x i i i -LIST OF SYMBOLS Symbol 2 A cr o s s - s e c t i o n a l area, cm B magnetic induction, gauss concentration at the S/L i n t e r f a c e , wt. % C i n i t i a l concentration, wt. % o C concentration x cm from the S/L i n t e r f a c e , wt. % x C r e l a t i v e f r a c t i o n a l concentration x cm from the S/L i n t e r f a c e x Cg concentration of the s o l i d , wt. % C concentration of the l i q u i d , wt, % C^ s p e c i f i c heat, c a l g °C ^ F Lorentz Force, nt. H height of l i q u i d metal, cm JLi -2 -1 -1 h heat transf e r c o e f f i c i e n t , c a l cm sec °C h heat t r a n s f e r c o e f f i c i e n t at the slag/metal i n t e r f a c e , n -2 -1 0--1 c a l cm sec C i current, amps K thermal conductivity, c a l cm ^sec ^ °C ^  K. area c o r r e c t i o n f a c t o r A K 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 __ k equilibrium d i s t r i b u t i o n c o e f f i c i e n t o L la t e n t heat, c a l g ^ m mass, g Q_ a v a i l a b l e heat content, kcals A heat input into the electrode, kcals Q t o t a l heat l o s s , kcals j-j Q_ t o t a l heat content, k c a l s -1 q rate of heat l o s s , k c a ls sec - x i v -Symbol q heat loss at each i n t e r f a c e , k c a l r' number of units from the c e n t e r l i n e Ar unit length i n the r' d i r e c t i o n S shape cor r e c t i o n factor slag bath temperature, ° C T Q i n i t i a l temperature, °C AT. degrees of superheat, °C V volume, cm3 AZ unit length i n the z' d i r e c t i o n p density, g cm 3 e emmisivity K 2 — 1 a —— , thermal d i f f u s i v i t y , cm sec p C p -8 _o a Stefan-Boltzmann constant, 5.67 x 10 watts, m K - XV -ACKNOWLEDGEMENT The author i s indebted to Dr. A M i t c h e l l f o r h i s advice and assistance throughout the duration of th i s work. Thanks are also due to Dr. F. Weinberg and fellow graduate students for innumerable h e l p f u l discussions. The assistance of the te c h n i c a l s t a f f during the experimental program i s greatly appreciated. The f i n a n c i a l assistance of the Consarc Corporation 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, steel ingots of considerable size and weight w i l l be required. Thus, for example, in the near future the capacity of turbogenerators in nuclear electric power stations w i l l be close to 1300 mega watts. The rotor shafts for 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 in.). To produce such rotor shafts, static cast steel ingots for forgings weighing more than 600 tons and having diameters about 5000 mm (197 in.) would be required. The problems associated with producing steel ingots exceeding even 200 tons by conventional techniques are well known. During the crystallization of such large volumes of liquid metal, mac.rosegregation and shrinkage processes become significant. The result is certain defects in the steel ingots which are irreparable even with further treatment and are inherently transferred to the forgings and to parts made from them. The existing methods for improving heavy steel ingots, such as sequentially pouring the liquid metal into the mould, vacuum treatment, heating and hot topping the head of the ingots are not efficient enough and do not guarantee a good macrostructure, 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 , therefore, i t i s not unreasonable that considerable attention i s being focussed on s c a l i n g up the e l e c t r o s l a g remelting process (ESR) to produce high q u a l i t y , large tonnage ingots. 1.1 Problems Introduced by "Scale-up" As furnace sizes increase to meet the new demands imposed by industry, so too w i l l the problems associated with t h e i r construction and operation. The f i r s t problem facing the process m e t a l l u r g i s t i s how to design an ESR machine that can economically produce large ingots (100 to 200 tons). At present the majority of the commercial ESR ingots being produced f a l l - i n t o the 5 to 20 ton range with a maximum s i z e of approximately 50 tons. As the ingot weights increase, however, the si n g l e electrode design which i s currently enjoying the greatest success becomes in c r e a s i n g l y inadequate and expensive. The main problem of s c a l i n g up a machine of t h i s design i s that i n order to . produce a 200 ton ingot a 200 ton electrode i s required. The d i f f i c u l t y of producing such large electrodes and the sophisticated equipment necessary to suspend them and control 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 exercise to investigate possible a l t e r n a t i v e s . The most obvious a l t e r n a t i v e i s a machine that uses several small electrodes to produce one large ingot. At present there are two main types of multiple electrode machines i n operation. These are the three phase, multi-electrode design (Figure 1), and the tandem electrode design (Figure 2). The three phase, seven electrode b i f i l a r - 3 -furnace has a projected capacity of 100 to 200 tons. There i s no information a v a i l a b l e , however, regarding i t s current status. Another multiple electrode machine i s the three phase, three electrode design. At present, however, t h i s design has not been used as an electrode change machine and i s l i m i t e d to producing ingots i n the 10 to 20 ton range. The p r i n c i p l e behind t h i s design i s that the electrodes are of d i f f e r e n t lengths so that whenever one requires changing there w i l l s t i l l be two electrodes operating. The advantage of this technique i s that i t provides the operator with a considerable degree of control over the system during the electrode change operation. The main drawbacks of this design, unfortunately, are i t s complexity and the cost associated with producing a large machine of t h i s type. The tandem electrode arrangement, on the other hand, i s mechanically very simple and could be modified to produce larger ingots. This design i s also much more f l e x i b l e with regard to i t s power require-ments. Its main problem i s that during the electrode change operation the power to the system must be shut o f f which could d r a s t i c a l l y a l t e r the general heat balance of the process. In order to obtain a better understanding of the effectiveness of the tandem electrode design i t i s necessary to ask the following questions: 1. To what extent i s the o v e r a l l heat balance of the system eff e c t e d by the electrode change operation? 2. To what extent do the r e s u l t i n g changes i n the heat balance a f f e c t the s t r u c t u r a l and compositional uniformity of the ingot? - 4 -The answers to these questions are of the utmost importance when considering the f e a s i b i l i t y of using the tandem electrode design. Because of the considerable investment of time and money required to produce large ESR ingots i t i s e s s e n t i a l that they contain no 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 that could e f f e c t the mechanical properties of the s t e e l . 1.2 Objectives of the Present Work Although a great deal of l i t e r a t u r e i s av a i l a b l e pertaining to normal ESR production, l i t t l e or no work has been published which concerns i t s e l f with disruptions i n the heat balance, and how they e f f e c t the structure and composition of the s t e e l being produced. I t i s the object of th i s study to analyze the e f f e c t s of a power loss to the system and also other problems r e l a t e d to electrode change machines. The present i n v e s t i g a t i o n was p r i m a r i l y concerned with f i v e major topics: 1. The s t r u c t u r a l changes that r e s u l t from a disruption i n the. power supply to the system. 2. The degree of the segregation during the power loss and the extent of any compositional banding. 3. The volume of l i q u i d metal that s o l i d i f i e d during the power l o s s . 4. The general heat balance f o r the system and how i t changed as a r e s u l t of any disruptions i n the power supply. 5. Changing electrodes and i t s e f f e c t on the o v e r a l l heat balance. - 5 -In addition to the major areas of i n v e s t i g a t i o n , work was also done r e l a t i n g v a r i a t i o n i n the slag skin thickness produced by con t r o l o s c i l l a t i o n s , to compositional banding. Also, whenever possib l e , the i n v e s t i g a t i o n was extended to include ingots produced by vacuum arc r e f i n i n g (VAR) for the purpose of comparison. Although the experiments were ca r r i e d out on a lab scale ESR unit and many assumptions had to be made about the system due to i t s complex nature i t i s believed that the r e s u l t s can be extrapolated to provide meaningful information about the questions r e l a t e d to the large scale electrode change machines. 1.3 Previous Work The fundamental p r i n c i p l e s underlying the s o l i d i f i c a t i o n of s t e e l castings have been w e l l documented i n the many books and papers 1 2 3— 8 written on the subject. ' More s p e c i f i c studies on micro- and macrosegregation i n s t e e l castings, however, have mainly pertained to s t a t i c ingots, or i d e a l i z e d systems i n which the s o l i d i f i c a t i o n 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 . Although these papers provide a great deal of information concerning s o l i d i f i c a t i o n and segregation i n s p e c i f i c systems, i t cannot be applied d i r e c t l y to the ESR process because of the large differences i n the s o l i d i f i c a t i o n mode. In the ESR process 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 within a water cooled-mould and i s maintained at a slow s o l i d i f i c a t i o n rate (0.005 to 0.03 cm sec """) against a large temperature gradient (10 to 100°C cm "'") by the system's power input. The method also d i f f e r s from other casting processes i n that fresh metal of a constant composition i s - 6 -added to the l i q u i d pool at a constant 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 casting, which i s also a c o l d - c r u c i b l e process, contribute l i t t l e information about the ESR process because of the large differences i n the casting speeds, and heat transfer between the two systems. The ESR process has often been c l a s s i f i e d as a large zone r e f i n e r , which i s generally an i n v a l i d comparison. The confusion between the two processes probably arose due 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 . I t should be noted, however, that the zone r e f i n i n g process i s usually a multi-pass operation, and that the r e l a t i o n s h i p governing the solute r e d i s t r i b u t i o n during the i n i t i a l pass i s simply the equation f o r complete mixing 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 casting assuming constant metal addition. 1 Since the extent of the mixing action i n the metal pool and 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 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 are unknown this equation, therefore, cannot be meaningfully applied to the ESR system. As far as any 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 process i n ESR ingots i s concerned there has been very l i t t l e work done. Fredricksson and Jarleborg"^ analyzed the e f f e c t s of power inte r r u p t i o n s on the structure of an 18/8 s t a i n l e s s s t e e l produced by the ESR process. Using sulphur p r i n t s and a quenching technique they determined the l i q u i d metal pool depth and microstructure of the ingots examined. On the basis of these experiments they speculated that a strong convective mixing action e x i s t s i n the metal pool. They also investigated the e f f e c t s of power in t e r r u p t i o n s , "dipping" of the electrode, and electrode changes on the ingots structure. They found that the disrup-tions i n the system resulted i n a banded structure i n the transverse - 7 -d i r e c t i o n . I t was also noted that for power interruptions shorter than 30 seconds there was no apparent sulphur segregation and for times longer than 60 seconds there was s i g n i f i c a n t detectable sulphur segregation. In an experiment using a preheated electrode, there was no improvement i n the sulphur segregation problem. The possible zone r e f i n i n g e f f e c t of the ESR process was also investigated by monitoring Cr and Ni concentrations l o n g i t u d i n a l l y i n an 18/8 ingot. They found a lower concentration of both Cr and Ni i n the f i n a l transient which they attributed to inverse segregation. An analysis of the transverse segregation of Cr and Ni was also made, and this type of segregation was found at high melt rates (13.3 g sec "*") . This was related to the much deeper metal pool found at these speeds. 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 ingots was conducted by Takada et a l . " ^ The work was performed on a 5 ton (750 mm dia.) ingot and i t was examined using dye penetration, sulphur p r i n t s as well as microstructure and segregation t e s t s . The analysis re l a t e d the temperature gradient/growth v e l o c i t y r a t i o (G/V) to the observed microstructure which became progressively coarser towards the ingot center. They also performed a chemical analysis on the ingot and found no s i g n i f i c a n t macrosegregation. 12 DeVries and Mumau examined the d e n d r i t i c formation and s o l i d i f i c a t i o n i n highly alloyed materials produced by the ESR process. They found that the microsegregation increased towards the center of the consumably melted ingots and that chromium showed inverse micro-segregation. They also demonstrated that the secondary dendrite arm spacing increased with an increase i n e i t h e r the melt rate or the ingots cross-sectional area. Firganek et a l . used radioactive isotopes to inve s t i g a t e the s o l i d i f i c a t i o n front and depth of the l i q u i d metal pool i n an ESR 185 furnace. Using W they s u c c e s s f u l l y outlined the pool p r o f i l e and ingot structure, and showed how t h i s technique could be used to determine the optimum operating conditions. Although these papers provide some general background information concerning the s o l i d i f i c a t i o n i n the ESR process, they a l l , with the exception of the Fredriksson et a l . paper, deal with the steady state condition. Despite the fac t that the Fredriksson et a l . paper deals with the e f f e c t s of power interruptions on the system, i t does not consider 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. EXPERIMENTAL 2.1 Introduction The ESR ingots used i n t h i s study were produced on the ESR unit at the University of B r i t i s h Columbia. The VAR ingots used were produced outside the u n i v e r s i t y at the Armco Steel Corporation i n Baltimore,Maryland, and the U.S. Bureau of Mines i n Albany, Oregon. The ESR process i s shown schematically i n Figure 3 and has been 14 described i n d e t a i l by Etienne. On the University unit i t was possible to produce various s i z e d ingots and to change and c o n t r o l many of the operating parameters. A l l the VAR ingots examined i n this study were manufactured externally, and the companies involved provided a complete production h i s t o r y for each ingot. A schematic diagram of a VAR furnace i s shown i n Figure 4. 2.2 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. The 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: 1) a v a i l a b i l i t y 2) cost and 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. Table I gives the composition of the a l l o y s studied. - 10 -Table I. Composition of a l l o y s studied (1) Vibrac EN-25 (supplied by the B r i t i s h Steel Corporation) Fe C Mn S i S P Ni Cr Mo Bal 0.28 0.67 0.22 0.058 0.012 .2.5 0.72 0.6 Sn Cu A l 0.028 0.27 0.01 (2) AISI 4340 (supplied by B r i t i s h Steel Corporation) Fe C Mn S i S P Ni Cr Mo Bal 0.39 0.72 0.24 0.018 0.012 1.75 0.84 .24 (3) AISI 630 (17-4PH) (supplied by the Armco Steel Company) Fe C Mn S i P S Cr Ni Co+Ta Bal 0.07 1.0 1.0 0.025 0.025 16.5 4.0 0.3 Cu Mo 4.0 0.5 2.2.2 Slag Composition The major slag constituent was prefused calcium f l u o r i d e . I t was combined with d i f f e r e n t percentages of r e c r y s t a l l i z e d alumina grain (Norton Abrazive 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) consisted of a mixture of parent metal turnings and 60 g CaF„ powder i n the r a t i o of 15 g to - 11 -25 g per cm of compact. 2.3 Ingot Production 2.3.1 ESR Ingots Table II summarizes the operating conditions f o r the ESR ingots used i n this study. The production data for several low q u a l i t y ingots analyzed was not a v a i l a b l e from the producers involved. The technique used f o r the stop-start experiments involved shutting off the main power supply to the system. During t h i s period the current recorder continued to operate. A section from the current chart during a "power-off" sequence i s shown i n Figure 5. Using the operating chart i t was possible to get an accurate estimate of the i n t e r r u p t i o n time. 2.3.2 VAR Ingots Table III summarizes the operating conditions for the VAR ingots examined. 2.4 Specimen Preparation A l l specimens to be examined under the o p t i c a l microscope or the electron microprobe were polished down to 1 micron on a diamond lap. Larger specimens and specimens where only the macrostructure was of importance were polished on No. 0 or No. 00 emergy paper. Table I I . ingot mould d i a . electrode electrode electrode atmos- slag comp. voltage current melt rate ingot no. (cm) d i a . comp. p o l a r i t y phere (volts) (amp) (g sec--*-) length (cm) 7.6 3.81 EN 25 -ve a i r CaF 2-27 23 wt.% A1.0 3 1180 3.4 23 7.6 3.81 EN 25 -ve a i r CaF 2-27 23 wt.% A l - 0 3 1170 3.7 22 7.6 3.81 EN 25 -ve a i r CaF 2-27 23 wt.% A 1 2 0 3 1160 2.8 23.5 7.6 3.81 AISI 4340 -ve a i r CaF 2-25 23 wt.% A1 20 3 1175 3.1 26 7.6 3.81 AISI 4340 -ve a i r CaF 2-25 23 wt.% A 1 2 0 3 1150 3.3 25 7.6 3.81 AISI 4340 -ve a i r CaF 2-27 23.5 wt.% A l 0 1125 2.6 25.5 7.6 3.81 EN 25 -ve argon CaF 2-27 23.5 wt.% A l 0 1200 3.1 23 7.6 3.81 EN 25 A.C. argon CaF 2-27 25 wt.% A 1 2 0 3 850 3.4 20 7.6 3.81 EN 25 A.C. argon CaF 2-27 25 wt.% A 1 2 0 3 825 3.6 11 10 7.6 3.81 EN 25 A.C. argon CaF 2-27 25 wt.% Al-0 925 3.1 24 Table I I . (Continued) 11 7.6 3.81 EN 25 -ve argon 12 10 6.3 EN 25 -ve a i r i 13 10 6.3 EN 25 -ve a i r 14 7.6 3.81 AISI -ve argon 630 15 7.6 3.81 AISI A.C. argon 630 16 7.6 3.81 AISI A.C. argon 630 17 7.6 3.81 AISI A.C. argon 630 18 7.6 3.81 AISI -ve argon 630 CaF 2-27 wt.% A 1 2 0 3 CaF 2-25 wt.% A_ 20 3 CaF 2-25 wt.% A 1 2 0 3 CaF 2-10 wt.% A 1 2 0 3 CaF 2-10 wt.% A 1 2 0 3 CaF 2-10 wt.% A 1 2 0 3 CaF 2-10 wt.% A 1 2 0 3 CaF 2-10 wt.% A 1 2 0 3 23 1275 23.5 1550 23.5 1550 22.5 1090 24.5 800 23.5 800 23.5 800 23.5 1400 2.7 23 6.4 48 6.1 51 3.4 18 3.0 21 3.09 23 3.2 20 2.8 22 Table I I I . ingot ingot ingot m a t e r i a l voltage current melt rate Producer no. dia.(cm) height(cm) (volts) (amps) (g/sec) V - l 16.5 17 AISI 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 to Analyze the E f f e c t s of Power Interruptions on the Structure and Composition of the Ingot 2.5.1 Etching 2.5.1.1 EN-25 and AISI 4340 Steels Oberhoffer's etch i n conjunction with 3 percent n i t a l were used to detect changes i n structure and composition r e s u l t i n g from power disruptions. Oberhoffer's etch consists of 1 g cupric c h l o r i d e , 0.5 g stannous chloride, 50 g f e r r i c c hloride, 30 ml hydrochloric a c i d , 500 ml water, and 500 ml eth y l alcohol."^ This etchant was p a r t i c u l a r l y u seful for examining the d e n d r i t i c structure of the two low a l l o y s t e e l s . The 3 percent n i t a l on the other hand was much more useful f o r detecting changes i n the carbon concentration i n the s t e e l as a r e s u l t of flu c t u a t i o n s i n the power. 2.5.1.2 AISI 630 (17-4PH) As there were several etchants a v a i l a b l e f o r AISI 630, they were chosen depending on the desired q u a l i t y of the etch and the s i z e of the specimen. For large specimens where only a macroetch was needed, the best technique was to immerse the specimen i n a 50 percent hydrochloric acid s o l u t i o n f o r up to 36 hours. For smaller specimens a much f a s t e r macroetch consisted of 100 ml e t h y l alcohol, 100 ml hydrochloric acid, and 50 ml of n i t r i c a c i d . The best microetch was found to be V i l e l l a ' s etch. This i s a mixture of 5 ml hydrochloric acid, 1 g p i c r i c acid and 100 ml e t h y l alcohol. This etchant was p a r t i c u l a r l y useful f o r determining the presence of the 6-ferrxte phase. Another etchant useful f o r i d e n t i f y i n g this phase - 16 -was R a i l i n g ' s reagent. This was comprised of 100 ml hydrochloric a c i d , 100 ml e t h y l alcohol and 5 g cupric c h l o r i d e . 2.5.2 Sulphur P r i n t s A convenient way to observe the e f f e c t of a d i s r u p t i o n i n the steady state condition on the structure and composition of a s t e e l , i s to make a sulphur p r i n t of the af f e c t e d region. Because of the very low sulphur contents of the three aloys studied, however, i t was necessary to ext e r n a l l y add sulphur to the system. This was done by adding approximately 4 g of i r o n sulphide between the electrode and the mould w a l l as shown i n Figure 6. A f t e r each addition the system was given several minutes to return to equilibrium before any experiments were c a r r i e d out. The s o l i d i f i e d ingot was cut a x i a l l y i n h a l f and surface-ground. Photographic bromide paper was soaked i n a 2 percent sulphuric acid s o l u t i o n for 3 to 4 minutes, then allowed to hang u n t i l the excess s o l u t i o n had drained away. The emulsion side of the paper was placed i n d i r e c t contact with the ground ingot surface for up to 5 minutes. The exposed sulphur p r i n t was then f i x e d and dried. A f t e r each p r i n t the surface of the specimen was reground to expose unreacted FeS i n c l u s i o n s . 2.5.3 Autoradiography Another technique used to detect compositional and s t r u c t u r a l changes produced by deviations from the steady state condition i s autoradiography. An experiment was devised whereby radioactive t i n could be added to the melt under a closed atmosphere. T i n was selected - 17 -because of i t s very low vapour pressure and i t s density, which i s close 113 to that of i r o n . The isotope chosen was Sn which i s an X-ray and soft gamma emitter and has a h a l f - l i f e of 112 days."^ The radioactive isotope was introduced i n t o the system by embedding i t i n the electrode and melting i t into the system. Figure 7 shows how the t i n was situated i n the electrode. The purpose of the aluminum was to ensure that there was no oxidation of the t i n while i t was melting and a l l o y i n g . As i t was important to know the exact moment the t i n entered the system, a series of preliminary experiments were performed to determine the minimum quantity of t i n plus aluminum required to produce a perturba-t i o n i n the operating chart. It was found that approximately 2 g produced a noticeable change i n the operating current. The e f f e c t on the current when they enter the system i s shown i n Figure 9. The drop i n the operating current occurs because the t i n and the aluminum enter the system as one or two large drops thereby increasing the electrode-ingot gap. Once produced, the radioactive ingots were cut a x i a l l y i n h a l f and surface ground. They were then autoradiographed using exposure times ranging from 24 to 72 hours. 2.5.4 Microprobe Analysis The best technique for determining compositional v a r i a t i o n s i n elements such as n i c k e l , chromium, and copper i s to use the electron probe. The microanalysis was performed on a JE0L-JXA-3A microprobe using a voltage of 25 KeV and a beam current of 0.08 ua. A quartz - 18 -c r y s t a l was used i n the spectrometer and K a r a d i a t i o n was measured f o r a l l specimens. Due to the low X-ray take-off angle (9 = 20°), etched specimens could not be e f f e c t i v e l y examined. I t was necessary, therefore, to l i g h t l y etch the specimens and mark the areas of i n t e r e s t with indentation on a microhardness t e s t e r . Microphotographs were then taken of the specimens before they were highly repolished on the 1 micron diamond lap. Measurements with the microprobe were made by point counting f o r periods of 10 sec, at 20 micron i n t e r v a l s . The r e s u l t s were then printed out both numerically and g r a p h i c a l l y . A l l r e s u l t s were 18 corrected using the MAGIC program. S p e c i f i c areas which showed concentration anomalies were q u a n t i t a t i v e l y analyzed using t h e i r adsorbed electron and X-ray images. 2.6 Techniques Used to Determine the Extent of the Mixing i n the  Metal Pool 2.6.1 Sulphur P r i n t s A mixture of i r o n sulphide and tungsten powder was added to the melt using the technique described i n Section 2.5.2. The pool p r o f i l e outlined by the sulphur r i c h metal on the sulphur p r i n t was then compared with the p r o f i l e outlined i n the metal by the tungsten powder. 2.6.2 Sulphur Concentration Analysis A co n t r o l l e d amount of i r o n sulphide was added to a melt i n which s o l i d i f i c a t i o n was allowed to proceed under steady-state conditions. - 19 -The ingot was subsequently sulphur printed and the exact p o s i t i o n of the sulphur r i c h i n t e r f a c e located. The change of sulphur concentration moving up the ingot was then determined by a chemical analysis of d r i l l i n g s taken at f i n i t e i n t e r v a l s along the ce n t e r l i n e . 2.6.3 Radioactive Tin Concentration Analysis Radioactive t i n was introduced into the melt using the same technique outlined i n Section 2.5.3. Thermal s t a b i l i t y was maintained and the r e s u l t i n g autoradiograph was used to locate the t i n r i c h i n t e r f a c e . D r i l l i n g s taken at f i n i t e i n t e r v a l s along the centerline were then monitored to give a concentration p r o f i l e for the t i n . 2.7 Determination of the S o l i d i f i c a t i o n Rate 2.7.1 Melt Record The average s o l i d i f i c a t i o n rate for 100 to 200 second i n t e r v a l s can be determined from the melt record. The parameters involved i n th i s determination are the r a t i o of electrode to ingot diameters and the rate of electrode t r a v e l . 2.7.2 Tungsten Powder Addition An alternate method f o r determining the s o l i d i f i c a t i o n rate was the external addition of tungsten powder. The powder was added i n the same manner as outlined f o r the addition of the i r o n sulphide to the melt. The additions were made at s p e c i f i c time i n t e r v a l s . Surface grinding the r e s u l t i n g ingot c l e a r l y shows up the tungsten bands and hence an average s o l i d i f i c a t i o n rate can be determined. - 20 -2.8 Determination of the Heat Transfer i n the System during the  "Power-Off" Mode Most of the a v a i l a b l e heat t r a n s f e r data concerning the ESR u n i t p e r t a i n s p r i m a r i l y to the steady s t a t e c o n d i t i o n . I t was necessary, t h e r e f o r e , to i n v e s t i g a t e the rat e s of heat t r a n s f e r from the m e t a l , the slag,and across the slag/metal i n t e r f a c e during the "power-off" mode. The rates of heat l o s s from the s l a g and the metal to the mould c o o l i n g water were obtained by performing a s e r i e s of "power-off" experiments i n a mould which had thermocouples attached along i t s l e n g t h . 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 Figure 9. Copper/constantan i n t e g r a l thermocouples were used to measure the change i n the mould w a l l temperature under "power-off" c o n d i t i o n s . Constantan wires (0.0254 cm d i a . ) were embedded i n 0.1 cm diameter x 0.125 cm deep holes i n the copper mould, and were plugged by 0.1 cm diameter copper w i r e . The copper mould was the p o s i t i v e t e r m i n a l and c o l d j u n c t i o n s were maintained at 0°C by immersing them i n i c e cooled gl a s s tubes c o n t a i n i n g mercury. The experimental problems a s s o c i a t e d w i t h temperature measurements i n s i d e an operating ESR u n i t are enormous. The high temperatures, intense magnetic f i e l d s , and high p o t e n t i a l s present combined w i t h the co r r o s i v e 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 of t r i a l and e r r o r experiments l e d to the thermocouple design shown i n Fi g u r e 10. The boron n i t r i d e provided good p r o t e c t i o n as i t was compatible w i t h the W-3Re/W-25Re (0.092 cm dia.) thermocouple w i r e , and acted as an e l e c t r i c a l i n s u l a t o r at the temperatures experienced. The boron 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 the ESR s l a g - 21 -for a considerable time. The thermocouple t i p was immersed i n powdered graphite to prevent any oxidation of the thermocouple wires, and to provide some e l e c t r i c a l conduction i n the event of a wire break at the t i p . The temperatures were read out to a Sargentmodel SR-4 recorder. The procedure used to obtain the change i n the slag and metal temperatures at the slag/metal i n t e r f a c e r e s u l t i n g from a loss i n power, was a t r i a l and error immersion of the thermocouple i n t o the system. The thermocouple was slowly lowered i n t o the slag u n t i l a r e a l i s t i c temperature was being detected then the power was switched o f f , and the r e s u l t i n g temperature changes recorded. Once the power was terminated the termocouple became trapped i n the slag cap or the ingot, so that i t s exact p o s i t i o n could be determined. 2.9 Determination of the Volume S o l i d i f i e d during a Short Power  Interruption This experiment involved the external addition of approximately 15 g of tungsten powder between the electrode and the mould w a l l i n a 10 cm diameter mould. At the same instant the powder was added to the system, the power was turned o f f . A f t e r a time i n t e r v a l ranging from 10 to 15 seconds a s i m i l a r quantity of powder was added and simultaneously the machine was turned back on. 3. STRUCTURAL AND COMPOSITIONAL CHANGES PRODUCED BY PERBURBATIONS IN THE GENERAL HEAT BALANCE OF THE SYSTEM 3.1 An Evaluation of the Segregation and Banding i n EN-25 and AISI 4340 Produced by Interruptions i n the Power Supply to the System The e f f e c t s of the "power-off" condition on the structure and composition of EN-25 and AISI 4340 were investigated using various techniques. Although most of the experiments were performed using EN-25 as the electrode material, i t was necessary to use AISI 4340 when EN-25 was not a v a i l a b l e . I t should be noted, however, that the compositions of these two al l o y s are very s i m i l a r . 3.1.1 The Nature of the S t r u c t u r a l and Compositional Changes The f i r s t step i n the i n v e s t i g a t i o n was to determine the e f f e c t s that power interruptions have on the ingot structure. To get a better understanding of these e f f e c t s , however, the steady state structure was determined f o r the purpose of comparison. Ingot no. 1 was produced under steady state conditions and i s shown i n Figure 11. The structure i s very uniform and has a w e l l defined a x i a l growth d i r e c t i o n . Having determined the steady state structure ingots no. 2 and no. 3 were produced containing deliberate power inte r r u p t i o n s ranging i n duration from 8 seconds to 65 seconds. Figure 12 shows ingot no. 3 etched with Oberhoffer's reagent. The e f f e c t e d regions are c l e a r l y marked by the l i g h t coloured bands. A micrograph of the 18 second power i n t e r r u p t i o n region was examined to see i f the l i g h t bands could be accounted for by a change i n the ingot structure (Figure 13). The center of the banded region appears to show some refinement i n the structure, but nearer the edges the dendrites have continued to grow with l i t t l e or no change i n t h e i r primary arm spacing. Another p o s s i b i l i t y was that the l i g h t l y etched bands were associated with compositional changes i n the e f f e c t e d regions. Considering the a l l o y i n g elements present i n tie two s t e e l s , and t h e i r maximum concentrations i n the l i q u i d (Co/k o) the three elements most l i k e l y to show any detectable change i n concentration were carbon, n i c k e l , and chromium. To check the p o s s i b i l i t y that the bands were produced by changes i n the carbon concentration ingots no. 2 and no. 3 were etched with 3 percent n i t a l which i s used to i n d i c a t e decarburiza-t i o n i n steels (Figure 14). Comparing Figures 12 and 14 i t can be seen that the previously l i g h t coloured bands etched up dark i n the 3 percent n i t a l . This indicated that the bands are probably regions of carbon enriched s t e e l . The banded regions were also analyzed f o r f l u c t u a t i o n s i n the concentration of both n i c k e l and chromium on the electron probe. Step-scanning specimens from ingots no. 2 and no. 3, however, revealed no s i g n i f i c a n t v a r i a t i o n s i n the concentration of e i t h e r element. 3.1.2 The O r i g i n of the Carbon-Rich Bands A possible explanation for the o r i g i n of the carbon r i c h regions has been proposed. For convenience the proposed model has been - 24 -divided into three stages: 1) turning the power o f f , 2) turning the power back on, and 3) re - e s t a b l i s h i n g equilibrium conditions. The three stages are shown schematically i n Figure 15. Stage I In the i n i t i a l seconds of the "power o f f " mode, s o l i d i f i c a t i o n i n the metal pool would proceed normally, with the possible exception of the l i q u i d metal i n contact with the sla g skin adjacent to the mould. Due to the high heat trans f e r i n th i s region, t h i s metal could begin to s o l i d i f y . A general delay i n the metal system's response to the "power-off" condition would probably occur, however, because the steady state heat supply to the metal pool would be i n part maintained. As t h i s flow of heat diminished with time the s o l i d i f i c a t i o n rate i n the system would gradually increase. As the l i q u i d metal continued to s o l i d i f y the r e l a t i v e concentration of carbon i n the l i q u i d would increase since the volume of l i q u i d metal would be s t e a d i l y diminishing. The l i q u i d s l a g , on the other hand, would cool r a p i d l y because of i t s much higher rate of heat l o s s , and because i t s heat supply i s pri m a r i l y due to resistance heating. I t would, therefore, begin to s o l i d i f y ; i n i t i a l l y at the edges and top, and then around the electrode t i p . As the slag skin at the edges and the top thickened the rate of heat loss from the system would decrease, reducing the s o l i d i f i c a t i o n rate. Stage II When the power supply to the system i s turned back on the electrode melt rate would be higher than i t s equilibrium value. The reason for this higher melt rate i s that the heat generation i n the molten slag would be increased for a given power input, because of the - 25 -l i q u i d slag's reduced volume. The increased melt rate would have two main e f f e c t s on the metal pool system. F i r s t l y , there would be a large f l u x of heat i n t o the remaining l i q u i d metal pool. This heat would cause the s o l i d i f i c a t i o n rate to decrease, and i n cases where the l i q u i d pool was completely or almost completely s o l i d i f i e d i t could r e s u l t i n some remelting of the i n t e r f a c e . Secondly, the increased volume of l i q u i d metal would r e s u l t i n a height of l i q u i d metal (H-^ ) being established at the edge of the ingot. The net 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 metal pool p r o f i l e than the equilibrium configuration. Another e f f e c t of the increased heat generation i n the slag during t h i s stage would be the remelting of some of the slag that s o l i d i f i e d during the "power-off" mode. Stage I II As the volume of molten s l a g returns to i t s equilibrium value, the electrode melt rate would be decreased, reducing the heat supply to the metal system. Therefore, with the system returning to i t s thermodynamic steady state, the deep metal pool would become progressively less stable. In order for the pool to re-achieve i t s equilibrium configuration, the s o l i d i f i c a t i o n rate i n the center region of the ingot must increase. The r e s u l t of the increased s o l i d i f i c a t i o n rate i s 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 (K ) for carbon i n the system would approach unity. As flie value of K increases the concentration of carbon i n the s o l i d i f y i n g metal would be increased. This proposed explanation f o r the o r i g i n of the carbon r i c h bands has been substantiated by several experimental r e s u l t s . F i r s t l y , the f a c t that l i q u i d metal enrichment by carbon does occur during the "power-off" mode i s supported by the carbon rich patches, which represent the f i n a l volume of liquid metal to freeze at the top of a l l the AISI 4340 and EN-25 ingots examined. These patches are clearly shown at the top of ingot no. 1 in Figure 11. Secondly, the possibility that the carbon rich bands were produced by an increase in the sol i d i f i c a t i o n rate when the power was turned off, was disproved by the fact that no transverse banding was observed in the f i n a l liquid pool of any of the ingots produced. This implied, therefore, that the carbon rich regions were associated with the power being re-established. Thirdly, 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 profile was very deep in the center part of the ingot (Figure 16). Particles of tungsten powder can be seen at the bottom of the carbon rich band. In this case there was undoubtedly some remelting of the equiaxed zone when the power was turned on. Finally, 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 in terms of the temperature gradient that exists in the liquid metal at this stage. Because the heat content of the metal pool would not have been completely re-established the temperature gradient in the liquid would be lower than i t s equilibrium value. This would make the solidification rate much more sensitive to any change in the thermal conditions. Therefore, the fluctuations in the power input while the system was re-establishing i t s equilibrium thermal conditions would be - 27 -sufficient to produce the "step-like" banded structure. On the basis of this experimental evidence, therefore, i t appears that the proposed model is a r e a l i s t i c explanation of how the carbon rich bands are formed. 3.1.3 Alternative Techniques Employed to Investigate the Nature of  the Segregation and Banding in EN-25 and AISI 4340 Produced  by Interruption in the Power Supply Two alternative techniques were used to investigate the effects of an interruption in the power supply on the ingots structure and composition. The two techniques employed were sulphur printing and autoradiography. 3.1.3.1 Sulphur Printing Iron sulphide pellets were added to the melt as outlined in Section 2.5.2. Because the solubility of sulphur in solid iron i s very 19 low, iron sulphide inclusions are formed when the sulphur rich metal s o l i d i f i e s . When a sulphur print is made of the sulphide rich zone, the iron sulphide inclusions evolve R^S which reacts with the photo-graphic paper turning i t brown. Figure 17 shows a sulphur print made from ingot no. 6 which contains several power interruption experiments. The dendritic structure of the ingot and the pool profiles at the time of each addition have been clearly outlined. The effects of the power inter-ruptions on the composition of the ingot, however, are not - 28 -c l e a r l y represented on the sulphur p r i n t . There appears to be very l i t t l e solute enrichment even i n the longer"power-off" experiments. 19 Because sulphur 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 (k Q = 0.1) more sulphur enrichment was expected. Due to the crude nature of the sulphur p r i n t i n g technique, however, the changes i n sulphur concentration were probably too small to be detected. 3.1.3.2 Autoradiography Radioactive t i n was introduced into the metal pool as outlined i n Section 2.5.3. and several power i n t e r r u p t i o n experiments were performed. Figure 18 shows the autoradiograph f o r a section of ingot no. 11 i n which the power was shut o f f for 23 seconds. The power was shut o ff approximately 5 seconds a f t e r the radioactive t i n entered the metal pool. The autoradiograph shows no change i n the d e n d r i t i c structure as a r e s u l t of the power being turned o f f . There i s , however, a t i n r i c h band which i s very s i m i l a r to the carbon r i c h bands found by etching. This t i n r i c h region was probably formed i n the same manner as outlined i n Section 3.1.2 for the formation of the carbon r i c h bands. 3.2 The E f f e c t of the Slag Skin on the Formation of Carbon Rich Bands  i n EN-25 and AISI 4340 during Steady State Production Banding during the steady state production of high carbon a l l o y s t e e ls (e.g. AISI 51100) i s common. This " t r e e - r i n g " banding i s c l e a r l y shown i n Figure 19 which i s a high carbon a l l o y s t e e l produced by vacuum arc remelting. This type of banding can occur i n s t e e l s with a - 29 -much lower carbon content, however, i f there are significant irregularities in the slag skin thickness. Such irregularities in the slag skin thickness are produced by discontinuous changes in the electrode movement, or in the power settings. Since the slag skin forms on the edge of the copper mould before the metal freezes, any irregularities in i t s thickness replicate themselves on the ingot surface. This effect can be clearly seen i n Figure 20. Because the rate of heat removal radially from the metal pool is inversely proportional to the slag skin thickness, any irregularities in the thickness w i l l effect the thermal s t a b i l i t y of the system. The result of such thermal i n s t a b i l i t i e s can be seen i n Figure 21. This is a photograph of the top of ingot no. 13 and shows a series of carbon rich bands near the edge of the ingot. The way these bands are formed can be explained in terms of the schematic diagram shown in Figure 22. At point A the liquid metal would be solidifying at a rate which would be in part governed by the slag skin thickness ( A X ) . Assuming that A X at point A i s greater than the normal value, the solffication 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 in the system would decrease and a thicker solute rich band would develop in front of the interface at point A. As the profile continued to advance towards point B, the so 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 in producing a small concentration band. With the continued advance of the interface to point C the sequence would repeat i t s e l f . - 30 -3.3 An Evaluation of the Segregation arid Banding i n AISI 630 The e f f e c t s of the "power-off" condition on the structure and composition of AISI 630 were investigated. 3.3.1 S t r u c t u r a l Changes The s t r u c t u r a l changes that resulted from the "power-off" condition were c l e a r l y revealed by a standard macro-etchant (Figure 23). The macrograph shows that there was 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 ingot where the maximum rate of heat loss occurs. I t was also observed the growth d i r e c t i o n of the grains near the centerline of the ingot became more r a d i a l l y i n c l i n e d . A possible cause of t h i s r e o r i e n t a t i o n i s that when the power was restored the s o l i d i f i c a t i o n rate near the center of the ingot was suppressed r e s u l t i n g i n a deeper pool p r o f i l e . This would occur i n the same manner as discussed i n Section 3.1.2. Because of the low c r y s t a l growth anisotropy exhibited by AISI 630, the re-nucleated grains would tend to grow perpendicular to 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 Compositional Changes In order to determine whether or not the "power-off" condition produced any anomalies i n the steady state composition of AISI 630, specimens were q u a n t i t a t i v e l y analyzed on the electron probe. Specimens taken from ingot no. 14 (Figure 24) were scanned f o r n i c k e l , chromium and copper. The microprobe survey of specimens A-1, A-2, B - l , and B-2 revealed no s i g n i f i c a n t v a r i a t i o n i n the concentrations of the - 31 -three elements when compared with the steady state concentrations found i n specimens C-1 and C-2. 3.3.3 Commercial Castings Stainless s t e e l ingots have been produced commercially, however, which do exhibit s i g n i f i c a n t concentration banding (Figure 25). This i s an AISI 630 grade s t a i n l e s s s t e e l ingot which was produced by the Arcos Corporations continuous casting ESR process (Figure 26). The o r i g i n a l section was cast i n an 8 inch square mould and was subsequently hot r o l l e d down to a 5.5 inch by 3.5 inch b i l l e t . During normal operation on the above furnace, ingots are removed from an open-bbttomed copper mould at a constant rate. The banded structure (Figure 25) probably resulted from a non-uniform withdrawal rate caused by the casting s t i c k i n g i n the mould. In order to determine the exact nature of the banded stru c t u r e , specimens were taken from both the banded and uniform regions of the ingot (Figure 27). An i n i t i a l examination was done by etching the specimens with V i l e l l a ' s and R a i l i n g ' s reagents. The r e s u l t s showed that the dark bands contained a high percentage of the 6 - f e r r i t e phase (Figure 28). The next step was to determine the concentrations of the main a l l o y i n g elements i n the banded regions. Using the electron probe, the 6 - f e r r i t e p a r t i c l e s were found to be high i n chromium and low i n both n i c k e l and copper. Figure 29 shows the X-ray images f o r chromium and n i c k e l i n a banded region. The actual concentrations of chromium, n i c k e l and copper i n the areas of i n t e r e s t are shown i n Table IV. - 32 -Table IV. Element concentrations i n the banded regions. Area Ni Cr Cu wt.% wt.% wt.% Steady-state region 4.58 15.51 3.40 6-Ferrite p a r t i c l e 2.44 17.69 2.32 I n t e r - f e r r i t i c region 4.54 13.70 3.83 Non-ferrite band 4.05 11.28 3.48 In order to understand how the 6 - f e r r i t e bands formed and t h e i r e f f e c t on the mechanical properties of the s t e e l , i t was necesaary to examine the thermal h i s t o r y of an AISI 630 s t a i n l e s s s t e e l . The 630 grade of 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 martensitic, precipitation-hardening s t e e l . At the s o l u t i o n treating temperature of 1038°C the metal i s a u s t e n i t i c and undergoes the transformation to martensite on cooling to room temperature. This transformation s t a r t s at approximately 132°C but i s not complete u n t i l the temperature drops to around 32°C. The p r e c i p i t a t i o n hardening compounds remain i n s o l u t i o n as the metal cools. Subsequent heating to temperatures around 500 to 625°C for one to four hours p r e c i p i t a t e s the small p a r t i c l e s that increase the s t e e l s strength and 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 that the solution treatment i s c a r r i e d out i n the s i n g l e phase a u s t e n i t i c region. Since the s i z e and p o s i t i o n of the d i f f e r e n t phase regions - 33 -are strongly dependent on the concentration of the a l l o y i n g elements present, the composition of the s t e e l must be c a r e f u l l y c o n t r o l l e d . Figure 30 shows how the s i z e of the two phase region i s increased as the n i c k e l concentration i s decreased. The 6 - f e r r i t e bands, therefore, probably formed because the s t e e l composition i n these areas was outside the s p e c i f i c a t i o n range causing the s o l u t i o n treatment to occur i n the two phase region. During the subsequent heat treatments the 6 - f e r r i t e phase was retained throughout, r e s u l t i n g i n a mixture of austenite, martensite, and bands of 6 - f e r r i t e . Since the copper i s less soluble 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 to the same extent as the matrix metal. The r e s u l t , therefore, would be bands of weaker material that could deform at a lower stress l e v e l . The s p e c i f i c a t i o n s on AISI 630 allow f o r a maximum of 5 to 7 percent 20 f e r r i t e i n the matrix. The Schaeffler f e r r i t e diagram shown i n Figure 31 demonstrates how c l o s e l y the composition of the s t e e l must be co n t r o l l e d i n order to keep the f e r r i t e content within the s p e c i f i e d range. Using t h i s diagram the f e r r i t e content of the unhanded regions was approximately 4 percent. In order to determine the f e r r i t e content of the banded regions a standard l i n e count was employed (Figure 32). The r e s u l t s indicated that the bands contained approximately 19 percent f e r r i t e and therefore were w e l l outside the s p e c i f i e d range. The r e s u l t of t h i s increased f e r r i t e content can be seen i n Figure 33. This shows a section from the casting which has cracked along the banded structure during r o l l i n g . 4. MIXING IN THE LIQUID METAL POOL In order to get a better understanding of the mixing i n the metal pool i t was important to examine both the o r i g i n and the extent of t h i s mixing action. 4.1 O r i g i n of the Mixing Action With regard to the o r i g i n of the mixing action there are three main p o s s i b i l i t e s to consider: 1) thermal convection, 2) e l e c t r o -magnetic s t i r r i n g , and 3) momentum and heat transfer from the f a l l i n g drops. Generally the degree of thermal convection i n the l i q u i d metal would be n e g l i g i b l e as the regions of highest temperature e x i s t at the top of the molten pool. The degree of thermal convection could become s i g n i f i c a n t only i f the pool p r o f i l e became deeply curved causing the isotherms i n the l i q u i d metal to have a pronounced curvature. It i s u n l i k e l y that t h i s s i t u a t i o n would a r i s e i n a commercial ingot, however, as the pool depth i s generally proportional to the ingot radius and therefore, r e l a t i v e l y quite shallow. The second possible cause of mixing i n the l i q u i d pool i s electromagnetic s t i r r i n g . I n i t i a t i n g t h i s type of mixing are the Lorentz forces created around an e l e c t r i c a l l y a ctive conductor. These produce a magnetic f i e l d with which the current can i n t e r a c t . - 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 e s s e n t i a l l y a f u n c t i o n of the f u r n a c e ' s e l e c t r i c a l c o n f i g u r a t i o n and, as s u c h , are v e r y u n p r e d i c t a b l e . E l e c t r o m a g n e t i c s t i r r i n g can be d e l i b e r a t e l y c r e a t e d , however, by imposing a magnetic f i e l d on the l i q u i d p o o l . T h i s technique i s f r e q u e n t l y employed i n VAR furnaces where the f i e l d c rea ted by the r a d i a l c o i l s ( F i g u r e 34-A) i n t e r a c t s 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 to produce a f o r c e on the l i q u i d m e t a l . T h i s f o r c e causes the l i q u i d meta l to p i l e up a g a i n s t the mould w a l l i n the f o r c e d i r e c t i o n . By c y c l i n g the c u r r e n t i n the c o i l s at a low frequency (approximate ly 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 m i x i n g e f f e c t i s a l s o produced due to the s l i g h t asymmetry of the r a d i a l c o i l s . I n a normal ESR u n i t ( F i g u r e 34-B) the main c u r r e n t component i s p a r a l l e l to the induced magnetic f i e l d ; consequent ly there are no L o r e n t z f o r c e s c r e a t e d . The o n l y except ions are ESR machines o p e r a t i n g w i t h a l i v e mould connec t ion such as those conver ted from VAR u n i t s . T h i s type of mould connec t ion has a l a r g e h o r i z o n t a l current component, but i t i s p r i m a r i l y c o n f i n e d to the top of the s l a g . The r e s u l t i s a h i g h degree of 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 l a g . T h e r e f o r e , 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 cou ld be induced i n a normal ESR u n i t would be to produce a magnetic f i e l d w i t h a h o r i z o n t a l component ( F i g u r e 34 - C ) . However, i n order to produce a f i e l d of s u f f i c i e n t 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 t h i s type of c o i l , , a v e r y l a r g e power i n p u t i s r e q u i r e d . T h i s f a c t makes - 36 -the technique d i f f i c u l t to achieve i n a mechanical sense, p a r t i c u l a r l y as the ingot sizes increase. The foregoing discussion applies to di r e c t current furnaces only. In furnaces employing a l t e r n a t i n g current, the in t e r a c t i o n s are much more complex, but the net e f f e c t i s to produce only small forces. The t h i r d and most l i k e l y cause of mixing i n the l i q u i d pool i s momentum and heat transfer to the l i q u i d metal by the f a l l i n g droplets. The type of convective motion set up i n the system by the f a l l i n g drops i s shown schematically i n Figure 35. The momentum of the f a l l i n g drops c a r r i e s them down int o the pool entraining l i q u i d behind them. Then, because of t h e i r higher temperature they tend to spread out and r i s e . At i n d u s t r i a l melt rates (1200 to 1500 lbs hr ^ ) s u f f i c i e n t momentum would be transfered to the metal pool to produce a continuous mixing action. • 4.2 Evaluation of the Mixing Action In order to evaluate the mixing action experimentally, 0.26 g of radioactive t i n was added to the metal pool using the technique outlined i n Section 2.5.2. Adding the t i n i n t h i s manner would simulate the behaviour of the f a l l i n g metal droplets, and i f mixing was p r i m a r i l y due to heat and momentum transfe r the following r e s u l t s would be expected. 1) The mixing action would be s u f f i c i e n t to allow the radi o a c t i v e t i n to outline the shape of the pool p r o f i l e . 2) The mixing action would be s u f f i c i e n t to approach a state of complete mixing at the s o l i d i f i c a t i o n rates used for ESR production - 37 -(0:005 to'0.03 cm s e c " 1 ) ; 3) Due to the d e n d r i t i c nature of the s o l i d i f y i n g i n t e r f a c e , The r e s u l t s of the radioactive t i n experiment x^ere consistent with the predicted r e s u l t s . Figure 36 i s an autoradiograph of the metal pool which c l e a r l y outlines the pool p r o f i l e . The rate of depletion of the t i n with 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 was experimentally determined by monitoring d r i l l i n g s taken at f i n i t e i n t e r v a l s along the centerline of the ingot. Figure 37 shows a p l o t of the normalized concentrations of radioactive t i n versus 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 (Appendix I-A). A t h e o r e t i c a l curve was then p l o t t e d based on the assumptions that there was complete mixing i n the l i q u i d pool, and 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 f o r the t i n was unity (Appendix I-B). The r e s u l t i n g p r o f i l e showed very good agreement with the experimental curve i n d i c a t i n g the predictions were e s s e n t i a l l y correct. The small deviation near the i n t e r f a c e could ind i c a t e that there was some solute enrichment of the l i q u i d metal. A s i m i l a r set of experiments were ca r r i e d out using sulphur to determine the extent of the mixing i n the l i q u i d pool under steady state conditions. Iron sulphide mixed with tungsten powder was externally added to the system and the pool p r o f i l e outlined by a sulphur p r i n t was compared with the p r o f i l e o u t l i n e d by the tungsten powder. The two p r o f i l e s are shown i n Figure 38. Since the two p r o f i l e s are i d e n t i c a l t h i s implies that s u l f u r p r i n t i n g accurately 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 would approach 22 - 38 -outlines the pool p r o f i l e . The rate of depletion of sulphur from the o r i g i n a l i n t e r f a c e was also determined. D r i l l i n g s were taken from ingots no. 4 and no. 5 and were analyzed f o r t h e i r sulphur concentration. The r e s u l t i n g concentration p r o f i l e for ingot no. 4 i s shown i n Figure 39. Because sulphur has a much lower k value than t i n ((k )„ = 0.1), i t s O O o concentration p r o f i l e was expected to show more macrosegregation. Examining the p r o f i l e s i t can be seen that the concentration of sulphur does i n i t i a l l y drop below the t h e o r e t i c a l p r o f i l e , but maintains a higher concentration at larger distances from the o r i g i n a l i n t e r f a c e . On the basis of t h i s information, therefore, several proposals can be made concerning the extent of the mixing action i n the metal pool system. F i r s t l y , the mixing i s probably produced by a slow convective motion, which at the very slow s o l i d i f i c a t i o n rates used i n ESR production approaches a state of complete mixing. Secondly elements with k Q values between 0.5 and 1.0 (eg.Cr,Ni,Sn ) would probably have very l i t t l e macrosegregation associated with them, and t h e i r concentration would be r e l a t i v e l y uneffected by a d i s r u p t i o n i n the power supply to the system. T h i r d l y , elements with k Q values below 0.5 (eg.C,S,P) could show some macrosegregation and t h e i r l o c a l concentration could be effected by an i n t e r r u p t i o n i n the power supply. 5. THERMAL PARAMETERS During the const ruct ion of a simple heat balance fo r the s lag and metal pool systems during the "power-off" mode, i t became apparent that a bet te r understanding of the l i q u i d meta l ' s superheat and the heat losses from the system during the "power-off" mode were necessary. 5.1 Eva luat ion of the Superheat i n the L iqu id Metal Pool In order to get a be t te r understanding of th i s parameter a se r ies of ca l cu l a t i ons were ca r r i ed out us ing d i f f e r en t assumed temperature conf igurat ions i n the metal poo l . Since the l i q u i d meta l 's superheat i s d i r e c t l y p ropor t iona l to AT (ATQ = T-T ) th i s parameter w i l l be used to represent the heat content. 5.1.1 ESR: 10 cm d i a . ingot To s imp l i f y the c a l c u l a t i o n , the pool geometry was assumed to be c y l i n d r i c a l . The height of the c y l i n d r i c a l poo l was ca l cu la ted so that i t contained the same volume of l i q u i d metal as the ac tua l p o o l . Based on known temperatures i n the system the l i m i t i n g values for 23 the temperature d i s t r i b u t i o n were chosen. The assumed pool geometry and the imposed boundary temperatures are shown i n F igure 40. - 40 -The c y l i n d r i c a l metal pool was divided i n t o segments having an arc of 1 radian (Figure 41). Suitable Az and Ar values were chosen based on the dimensions of the c y l i n d r i c a l pool. z' d i r e c t i o n : 4 elements with Az = 0.5 cm 1 element with Az = 0.25 cm r' d i r e c t i o n : 5 elements with Ar = 1 cm. The volume of each element was calculated using the general formula volume = base x height V = l / 2 [ ( r ' A r + | ^ ) 2 - (r'Ar - |^ ) 2 ] A z (5.1.1) where Ar = the unit length r" = the number of units away from the c e n t e r l i n e . Therefore for a l l the units with r' > 0 ( V ) r , > ( ) = r'Ar 2Az (5.1.2) Ar And for the t r i a n g u l a r unit at the center where r' = 0 and Ar = W^»_n = A r 2 Az (5.1.3) 8 Knowning the volume of each element i t was possible to c a l c u l a t e the amount of superheat associated with each one of them for a given temperature d i s t r i b u t i o n i n the metal pool. For the purpose of t h i s c a l c u l a t i o n i t was assumed that 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 a l i n e a r function 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 Figure 42. From Figure 42 the maximum and minimum temperatures for each layer of cubes i n the z' d i r e c t i o n could be determined. These became the end points 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 rate of heat trans f e r near the edges of the ingot would be much higher than the rate at the center, 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 could not be approximated by a l i n e a r function of r ' . To compensate f o r t h i s a series 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 towards the center (Figure 43). Using Figure 43 could be determined f o r each element. Having determined the volume and temperature of each element i t was then possible to c a l c u l a t e the amount of superheat associated with each one. Q_ = mCp AT g = (Cpp)VAT g (5.1.4) where AT s = T. , - 1500°C (r',z') Therefore, the average superheat for the e n t i r e c y l i n d e r can be determined as follows: (5.1.5) 42 -10.40 x 10' 178 = 58.4°C In order to get some estimate of the range of ( A T g ) ^ , t* i e same c a l c u l a t i o n was done for two d i f f e r e n t temperature configurations. The d i s t r i b u t i o n s investigated and the r e s u l t i n g (AT_)^ v a-'- u e s are shown i n Figures 44-A and 44-B. The r e s u l t s show that i n a 10 cm diameter ingot of EN-25 or AISI 4340 the upper l i m i t of ( A T g ) A v g i s approximately 86°C and the lower l i m i t of (^T g)^ v^ i s approximately 47°C. 5.1.2 ESR: 61 cm diameter and 254 cm diameter Approximate values of (AT_)^ f ° r i n d u s t r i a l s i z e d ingots were evaluated using the same technique demonstrated above. Two ingot sizes were examined: 1) 61 cm diameter and 2) 254 cm diameter. In both cases a c y l i n d r i c a l approximation for the pool shape was used. 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 ( A T ^ ^ ^ values are shown i n Figures 44-D and 44-E. Based on these r e s u l t s i t appears that the magnitude of ( A T g ) ^ increases very slowly with increasing ingot diameters. 5.1.3 VAR: 10 cm diameter For the purpose of comparison, (AT_,) A v_ was calculated f o r a 10 cm diameter VAR ingot. Since the pool p r o f i l e f o r t h i s s i z e of VAR ingot i s V-shaped the pool was sectioned i n t o a series of cones. - 43 -Figure 45 shows the pool geometry and assumed limiting temperatures. Although no direct measurement of the metal temperature below the electrode has been made, i t is generally agreed that i t f a l l s in the 24 range of 1800°C to 1900°C. Therefore, the temperature in 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 liquid metal at the ingot surface i s zero. For the purpose of simplifying the calculation the temperature distribution in the z direction was assumed to be a linear function of z (Figure 46-A). The temperature distribution in the r direction however, was assumed to rise near the edge and taper off towards the center (Figure 46-B). The volume of each conical element was calculated as follows: where n = the number of the element being considered. The particular 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_ for the entire metal pool. The average superheat ((AT ) ) for the metal pool was then calculated. Volume = (Volume) - (Volume) n n-1 TT 2 2 = -5- [ (r ) z - ( r - ) z -] 3 n n n-1 n-1 (5.1.6) VAT (AT ) s (5.1.7) s Avg V = 121°C - 44 -The r e s u l t s of t h i s comparison show that the metal pool during VAR production contains much more e f f e c t i v e superheat than the metal pool during the ESR production of the same diameter ingot. This a d d i t i o n a l superheat produces the very deep metal pools associated with VAR ingots. As a r e s u l t of the differences i n pool depth between the two processes, several differences i n the structure and q u a l i t y of the f i n a l product can be seen; 1) VAR ingots have a much more r a d i a l l y oriented growth d i r e c t i o n than those found i n s i m i l a r ESR ingots. 2) VAR ingots contain more shrinkage porosity and piping than s i m i l a r ESR ingots. 5.2 Heat Transfer during the "Power-Off" Mode Recently, there has been a great deal of information a v a i l a b l e concerning the rate of heat trans f e r from the slag and metal pool 25 systems during the steady state. This data could not be applied to the "power-off" condition, however, as many of the heat trans f e r parameters are changed during t h i s period. There are four main areas affected by the loss of heat input into the system (Figure 47). 1) The l i q u i d metal/slag skin i n t e r f a c e : Heat trans f e r i n t h i s region would be reduced by s o l i d i f i c a t i o n of the metal at t h i s i n t e r f a c e and contraction of the ingot away from the water-cooled mould. 2) The l i q u i d s l a g / s l a g skin i n t e r f a c e : Heat transfer i n t h i s region would be reduced by s o l i d i f i c a t i o n of the sl a g at th 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 transfer i n - 45 -thi s region would be reduced as the surface temperature of the slag 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 region would change as the 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 nature of this i n t e r f a c e changed. To calculate the heat transfer p r o f i l e s across the various interfaces during the "power-off" mode, a serie s of experiments were performed as outlined i n Section 2.8. The apparatus and general 9 5 procedure used have been discussed i n d e t a i l by Jo s h i . 5.2.1 Heat Transfer Across the Li q u i d Metal/Slag Skin Interface Thermocouples i n the mould recorded the change i n the cooling water temperature with time during the "power-off" mode (Figure 48). This data was then converted to a rate of heat flow per unit area (q/ using Figure 49. Lines 1 and 3 on Figure 49 were used to determine q./A as they most accurately described t h i s system. Knowing the surf a area of each i n t e r f a c e i t was then possible to p l o t the t o t a l heat loss across each one against the duration of the "power-off" condition (Figure 50). 5.2.2 Heat Transfer Across the Li q u i d Slag/Slag Skin Interface Employing the same technique i l l u s t r a t e d above a rate of heat loss versus time curve f o r the "power-off" condition was calculated for the l i q u i d s l a g / s l a g skin i n t e r f a c e (Figure 50). - 46 -5.2.3 Heat Transfer Across the Li q u i d Slag/Atmosphere Interface Employing the same technique i l l u s t r a t e d above a rate of heat loss versus time curve f o r the "power-off" condition was calculated for the l i q u i d slag/atmosphere i n t e r f a c e (Figure 50). 5.2.4 Heat Transfer Across the Liqu i d Metal/Liquid Slag Interface In order to determine the nature of the heat transfer across the slag/metal i n t e r f a c e during the "power-off" mode, i t was necessary 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 side of the i n t e r f a c e . Because of the experimental d i f f i c u l t y involved, however, only the p r o f i l e for the slag was obtained. I t was necessary,therefore, to approximate the metal temperature p r o f i l e i n order to get some estimate of the heat transfer across the slag/metal i n t e r f a c e . The equilibrium metal temperature, d i r e c t l y below where the sla g p r o f i l e was obtained was estimated from the temperature p r o f i l e s used i n Section 5.1.1. Also, the time required f o r the metal i n th i s area to begin s o l i d i f y i n g was estimated to be approximately 15 seconds on the basis of the "power-off" experiments discussed i n Section 3.1. Using t h i s information an approximate temperature p r o f i l e was constructed for the metal at the slag/metal i n t e r f a c e . Figure 51 shows the two temperature p r o f i l e s superimposed on one another. From Figure 51 the temperature difference across the in t e r f a c e (AT = T . -T ,) slag metal could be determined f o r any duration of the "power-off"condition. To calculate the rate of heat tr a n s f e r , however, i t was necessary to know the heat transfer c o e f f i c i e n t at the in t e r f a c e (h_.). The actual value of th i s c o e f f i c i e n t has never been accurately measured, although - 47 -most .authors have used values ranging from 0.1 to 1.0 c a l cm °C sec . ' Figure 52 shows the rate of heat trans f e r per unit area across the slag metal i n t e r f a c e during the "power-off" mode, f o r three assumed values of h_. These p r o f i l e s show that within t h i s assumed range of the heat transfer c o e f f i c i e n t s there are large v a r i a t i o n s i n the magnitude of the heat flow across the i n t e r f a c e . To get a cl e a r e r understanding of what probably does occur at the i n t e r f a c e , therefore, there were three points that must be considered. F i r s t l y , assuming that h_ remains constant during the "power-off" mode, and that the assumed metal temperature p r o f i l e i s a reasonable approximation of the actu a l p r o f i l e , then the net heat flow across the i n t e r f a c e i s approximately zero regardless of the value of h_ chosen. This conclusion i s dependent to some extent on the shape of the assumed temperature p r o f i l e . Reasonable v a r i a t i o n s i n i t s shape, however, d i d not change the net heat flow s i g n i f i c a n t l y . Secondly, since the heat transfer across the i n t e r f a c e i s dependent on the degree of mixing, and since the degree of mixing could only decrease during the "power-off" mode, therefore h_. could only decrease i n value. The t h i r d and most important point i s concerned with the changes i n the surface area to volume r a t i o as the ingot s i z e increases. As the size of the ingot increases, the heat flow at the slag/metal i n t e r f a c e would become in 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 with the large heat contents i n the metal and slag pools. I t was f e l t on the basis of these considerations, and despite the shortage of data concerning the slag/metal i n t e r f a c e , that the heat trans f e r across t h i s i n t e r f a c e during the "power-off" mode could be considered n e g l i g i b l e . I t was also f e l t that the v a l i d i t y of thi s assumption increased with the ingot s i z e . - 48 -The r e s u l t i n g p r o f i l e s revealed several i n t e r e s t i n g features about the rate of heat transfer from the slag and metal systems during the "power-off" mode. F i r s t l y i t can be seen i n Figure 50 that the rate of heat loss (q) from these i n t e r f a c e s drops ,off very r a p i d l y and that they respond instantaneously to the "power-off" condition. Secondly, Figure 52 shows that the heat transfer across the s l a g / metal i n t e r f a c e i s very dependent on the value of the heat transfer c o e f f i c i e n t due to the small temperature gradient across t h i s i n t e r f a c e . The effectiveness of a u x i l i a r y electrodes to heat the s l a g and metal pool systems during an electrode change operation, therefore, w i l l be very dependent on the exact value of t h i s c o e f f i c i e n t . I f i t s value -2 -1 -1 i s close to 1.0 c a l cm sec °C there w i l l be a considerable amount of heat transfer from the s l a g to the metal i f the o r i g i n a l slag temperature i s maintained. This heat supply would reduce the extent of the s o l i d i f i c a t i o n i n the metal pool during the electrode change operation and thereby reduce any s t r u c t u r a l and compositional e f f e c t s . On the -2 other 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 close to 0.1 c a l cm sec l o C 1 the heat trans f e r across the slag/metal i n t e r f a c e would be greatly reduced. The e f f e c t of the a u x i l l i a r y electrodes, therefore, i would be mainly confined to maintaining the slag systems temperature, thereby reducing the requirement f o r s l a g heating on power resumption. 6. THE EXTENT OF SOLIDIFICATION DURING THE "POWER-OFF" CONDITION Heat balances were calculated f or a small and a large scale ESR ingot as w e l l as a small scale VAR ingot, i n order to obtain some estimate of the volume of l i q u i d metal and l i q u i d slag that would s o l i d i f y during a r e l a t i v e l y short 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 contained several assumptions and can only be considered as approximations, they do provide a good i n d i c a t i o n of how the two systems react to the "power-off" condition. To circumvent the complex problems of pool shape change and temperature gradient changes during the "power-off" mode, the c a l c u l a t i o n s were li m i t e d to a determination of the volume s o l i d i f i e d i n a given period of time. 6.1 Determination of the Volume S o l i d i f i e d i n the Metal and Slag Pool  Systems i n a 10 cm dia. EN-25, ESR Ingot The slag and metal pool configurations used i n t h i s c a l c u l a t i o n are shown i n Figure 53. The f i r s t step i n t h i s c a l c u l a t i o n was to determine the a v a i l a b l e heat contents (Q ) of the two systems at the beginning of the "power-o f f " condition (t = 0). This i s shown i n Appendix I I - l . For s i m p l i c i t y i t was assumed that both systems retained t h e i r sensible heat during the"power-off 1 1 mode. Therefore: - 50 -= mC AT P + mi- ce. 1) and from Appendix I I - l 79 kcals = 98 kcals Having calculated the av a i l a b l e heat content of both systems, the next step was to cal c u l a t e the t o t a l heat loss (Q ) from each for JL d i f f e r e n t durations of the "power-off" mode (Appendix II-2). The res u l t s of these cal c u l a t i o n s are shown i n Tables V-A and V-B. Knowing Q and Q i t was then possible to calculate the volume /_ JL percent s o l i d i f i e d (P.S.) for the d i f f e r e n t lengths of "power-off" operation. The r e s u l t s are shown i n Tables V-A and V-B. P l o t t i n g the r e s u l t s of Tables V-A and V-B points out several i n t e r e s t i n g features about each system during the "power-off" mode (Figure 54). I t can be seen that the volume percent s o l i d i f i e d i n the metal pool increases very uniformly with time which indicates that there are no gross changes i n the s o l i d i f i c a t i o n rate associated with the early stages of a power i n t e r r u p t i o n . As the duration of the "power-off" condition increases, the heat loss from the system i s prim a r i l y due to conduction down the ingot, and r a d i a l l y to the mould P.S. (6.2) - 51 -Table V. A. Volume s o l i d i f i e d i n the metal pool system Time (sec) Heat «1 loss q2 (kcals) q3 To t a l heat loss (kcals) Available heat at t=0 (kcals) Volume % s o l i d i f i e d 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. Volume s o l i d i f i e d i n the slag pool system Time Heat loss (kcals) T o t a l heat Available Volume % (sec) loss (kcals) heat at t=o s o l i d i f i e d q4 q5 (kcals) 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 -w a l l . I t i s poss i b l e , however, that i n addition there could be some heat transfer from the metal to the slag across the slag/metal i n t e r f a c e . Photographs of the f i n a l pool volume show that some s o l i d i f i c a t i o n does take place s t a r t i n g at the slag/metal i n t e r f a c e (Figure 21). This phenomenon could supply a d d i t i o n a l heat to the slag at the expense of the metal pool. Unlike the l i q u i d metal, the slag 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 the s o l i d i f c a t i o n rate de-creased quickly with time. The rapid drop i n the s o l i d i f i c a t i o n rate i s p r i m a r i l y due to the low thermal conductivity of the s o l i d i f i e d s l a g . When the power i s turned o f f , the slag freezes i n from the mould walls and the top, and theieby becomes insulated from i t s major sources of heat loss. Because the slag remains l i q u i d f o r a much longer time than does the metal i t i s possible to r e - r e s t a b l i s h e l e c t r i c a l continuity even though the metal pool might have completely s o l i d i f i e d . These r e s u l t s are consistent with the experimental observations and with the model f o r the formation of carbon concentration bands proposed i n Section 3.1.2. 6.2 Volume Percent of L i q u i d Metal to S o l i d i f y Based on Tungsten Powder  Addition Experiments The volume s o l i d i f i e d f o r a given "power-off" period was determined experimentally,; for the purpose of checking the v a l i d i t y of the t h e o r e t i c a l values obtained i n Section 6.1. Tungsten powder was externally added to the system the moment the power supply was shut down and then again approximately 13 seconds (+ 2 second) l a t e r . - 53 -Figure 55 shows a section of ingot no. 13 which contains three such experiments. The r e s u l t i n g pool p r o f i l e s f o r experiment no. 2 are shown i n Figure 56-A, and an approximation of these i s shown i n Figure 56-B. The volume s o l i d i f i e d was estimated by using c y l i n d r i c a l elements to calculate the volume encompassed by each p r o f i l e . The re s u l t of th i s c a l c u l a t i o n showed that approximately 18.3 percent of the metal pool had s o l i d i f i e d i n the "power-off" i n t e r v a l . The r e s u l t s of the other tungsten addition experiments a l l agreed to within 10 percent of th i s value. Although the experimental values were s l i g h t l y higher than the calculated percentages, the agreement i s s t i l l good considering the assumptions that were made. Tungsten addition experiments f o r longer durations were not possible as the top of the slag cap became s o l i d a f t e r approximately 15 to 20 seconds of "power-off" operation. 6.3 Determination of the Volume S o l i d i f i e d i n the Metal and Slag Pool  Systems i n a 61 cm di a . Ingot during a 60 Second Power Loss In an e f f o r t to get a better understanding of the "power-off" mode and how i t e f f e c t s the larger commercial furnaces an attempt was made to calculate the approximate volumes of ingot and sla g which s o l i d i f i e d during a 60 second power i n t e r r u p t i o n . The 60 second time i n t e r v a l was chosen as t h i s i s the approximate maximum length of time required to change an electrode i n an i n d u s t r i a l u n i t . Due to the lack of information a v a i l a b l e on the rates of heat trans f e r i n commercial sized ingots, however, i t was necessary to include i n the analysis several major assumptions. Therefore, the r e s u l t s can only be interpre - 54 -as order of magnitude values. The system i s shown schematically i n Figure 57. The f i r s t step i n the c a l c u l a t i o n once again, was to determine the av a i l a b l e heat content of both the metal and s l a g pool systems (Appendix I I I - l ) . In order to determine the rate of heat loss during the "power-off" period (Appendix III-2) i t was necessary to use the data for a 7.6 cm diameter ingot and assume that the heat loss was proportional to the surface area. Joshi used t h i s technique to calculate a steady state heat balance for a 61 cm diameter ingot which 25 was i n reasonable agreement with commercially observed r e s u l t s . The r e s u l t s of the heat balance showed that approximately 10 percent of the metal pool and 10.3 percent of the s l a g pool would have s o l i d i f i e d during a 60 second i n t e r r u p t i o n i n the power supply (Appendix III- 3 ) . I t i s u n l i k e l y , therefore, that any s t r u c t u r a l or compositional changes would be produced i n the ingot as a r e s u l t of the power lo s s . These r e s u l t s are reasonable considering the f a c t that i s proportional 3 to the volume of l i q u i d (r ) and Q i s proportional to i t s surface Li 2 area (r ). Therefore, as the ingot radius increases, the e f f e c t s of power disruptions on the system are reduced, f o r a given period of "power-off" operation. 6.4 Determination of the Volume of the Metal Pool 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  Interruption Because of a growing i n t e r e s t i n the more subtle differences between the ESR and VAR processes, i t was s i g n i f i c a n t to i n v e s t i g a t e how the two - 55 -processes d i f f e r during the "power-off" mode. T r a d i t i o n a l l y , i t has been f e l t that the VAR process would be much more s e n s i t i v e to changes i n the operating conditions as there i s no hot slag layer to act as a thermal buffer.. In order to make th i s comparison a heat balance was done f o r ingot no. V-3 which contains two power interruptions of approximately 12.5 seconds (Figure 58). An approximation of the metal pool p r o f i l e i s shown i n Figure 59. The available heat content of the metal pool was calculated based on the same assumptions used for the 10 cm diameter ESR ingot (Appendix IV-1). Determination of the heat loss from the system during the"power-off" period was complicated by the lack of heat flow data pertaining to t h i s mode of operation i n a VAR Ingot. Because of t h i s lack of relevant information i t was necessary to use the steady state 28 heat loss p r o f i l e s shown i n Figure 60. Using these curves and other a v a i l a b l e information (Section 5.1) i t was possible to obtain an upper l i m i t f o r the heat loss from the metal pool i n 12.5 seconds (Appendix IV-2). Once having determined and the volume percent of l i q u i d metal s o l i d i f i e d during the "power-off" mode was calculated (Appendix IV-3). The r e s u l t showed that the maximum amount of l i q u i d metal which could freeze, based on the assumed data, was approximately 32.2 percent. In order to determine whether or not the heat flow values used i n the c a l c u l a t i o n were at a l l reasonable, the t h e o r e t i c a l volume s o l i d i f i e d was compared with the experimentally observed value. The two power interruptions and the f i n a l pool volume for ingot no. V-3 are c l e a r l y outlined i n Figure 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 Figure 62 by two parabolas. The volume s o l i d i f i e d was determined as follows: Volume percent s o l i d i f i e d = y dx -0 11 TT y dx] = 18.5% It can be seen that the calculated value was approximately 1.7 times higher than the experimentally observed r e s u l t . The error i n the calculated value probably arose by using the r a d i a l heat f l u x p r o f i l e s for the steady-state condition. I t appears, therefore, that the r a d i a l heat f l u x i s reduced during the "power-off" conditon and that the steady state p r o f i l e s cannot be applied to t h i s mode of operation. I t should be noted, however, that despite the fact that the volume fractio n s s o l i d i f i e d i n 12.5 seconds were approximately the same f o r the two processes, the much larger volume of l i q u i d metal i n the VAR pool (V T r A_/V_ C T ) = 3.4) means that more metal s o l i d i f i e d . I t should also be noted i n Figure 58 that the two power interruptions and the f i n a l pool volume have a l l etched up darker than the steady-state sections of the ingot using 3 percent n i t a l . This indicates some increase i n the carbon concentration. The probable cause of the increased carbon concentration i s an increase i n the system's s o l i d i f i c a -t i o n rate. Based on the l i m i t e d information a v a i l a b l e , therefore, i t - 57 -appears that interruptions i n the VAR power supply produce a greater e f f e c t on the ingot's composition 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 ESR unit. 7. ELECTRODE CHANGE OPERATIONS In the previous section i t was shown that i n the time required to change the electrode i n a 61 cm diameter tandem electrode machine only about 10 percent of the l i q u i d metal and l i q u i d s l a g would be s o l i d i f i e d . However, th i s c a l c u l a t i o n did not take into account the addition of the new electrode i n t o the system. In order to determine the o v e r a l l e f f e c t of an electrode change on the heat balance, therefore, i t was necessary to obtain an estimate of how the new electrode would influence the system. 7.1 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 experimentally determined for lab scale electrodes, no p r a c t i c a l measurements have been c a r r i e d out on the much larger commercial electrodes. To estimate the temperature d i s t r i b u t i o n i n these electrodes, therefore, p r o f i l e s were calculated using the unsteady-state heat conduction equation. To si m p l i f y the c a l c u l a t i o n the electrode was approximated by a semi-i n f i n i t e slab i n which there was no heat loss i n the r a d i a l d i r e c t i o n . This 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 that the r a d i a l heat flow component i n the lab scale electrodes was very small. I t was also assumed that the electrode t i p was f l a t and that there was 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 industrial ESR production. The general form of the unsteady-state heat conduction equation 32 i s : 2 a = f t o < y <.» C 7 . D 3y The boundary conditions for the addition of a new electrode into the system are: 1. T = T a t t = 0 y > 0 o J 2. T ->• T as y -> o J 3. h(T,-T ) = -K at y = 0 b o 3y -where T^ is the i n i t i a l temperature of the new electrode T^ is the slag temperature. Using these boundary conditions the solution to equation (7.1) has the form: h'y+h,2at T(y,t) = (T.-T ) [ e r f c - ^ - e e r f c ( - ^ — + h y^t) ] (7.2) ° 2/at 2/at where h = the heat transfer coefficient 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 electrode at any p o s i t i o n along i t s length (y) at any time ( t ) , with the assumption that remains constant. A general computer program was written f or equation (7.2) and i s shown i n Appendix V. 7.2 Heat Content of a Commercial Electrode In commercial ESR operations the minimum p r a c t i c a l electrode to ingot diameter r a t i o i s approximately 0.75. Therefore, f o r a 61 cm diameter ingot a 45.6 cm diameter electrode would be used. Having established the electrode s i z e to be considered i n the c a l c u l a t i o n the next step was a determination of the constants i n equation (7.2). Average values of p , Cp , and K for i r o n i n the temperature range s s s from 25°C to 1500°C of 7.8 g per cm3, 0.16 c a l per g °C, and 0.071 c a l per cm sec °C, res 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 . 27 26 Based on the r e s u l t s of Mitchell et a l . , and E l l i o t et a l . the heat transf e r c o e f f i c i e n t (h) at the electrode t i p was assumed to be 0.04 2 c a l per cm sec °C.. I t was l a t e r shown, however, that the c a l c u l a t i o n was i n s e n s i t i v e to the value of h i n the accepted range of values f o r 2 the electrode t i p (0.01 to 0.1 c a l per cm sec °C). The reason for th i s i n s e n s i t i v i t y i s that for t h i s range of heat trans f e r c o e f f i c i e n t s the rate c o n t r o l l i n g step i s conduction i n the electrode and not the rate of heat supply to the electrode base. Using the above information and assuming the i n i t i a l temperature (T q) was 25°C temperature p r o f i l e s were calculated as a function of time f o r two assumed values of the slag bath temperature (T^). The r e s u l t i n g p r o f i l e s are shown i n Figure 63. These p r o f i l e s represent - 61 -the temperature d i s t r i b u t i o n i n the electrode at the instant the temperature of the metal 1.0 mm above the slag/electrode i n t e r f a c e reached the melting point. The increased heat content of the electrode for both slag bath temperatures was then calculated using graphical i n t e g r a t i o n . Since Qj = mC_AT (7.3) = VpC pAT 2 = irr hpC pAT = Trr 2 pC p_ hAT therefore 2 1 5 C Q l ) T = 1 5 5 0 = * r C R[ E yAT - (15) ( T Q ) ] (7.4) y=0 = 11962 kcals and 2 1 2 W T = 1 6 5 0 = * r C P S P s [ E n ^ A T " <12>(V1 ( 7' 5 ) y=0 = 9892 kcals There c a l c u l a t i o n s , however, assume that the l i q u i d slag system i s an i n f i n i t e heat source capable of maintaining T^ constant. Comparing these heat contents with the av a i l a b l e heat content of the slag 3 ((.Q ) = 8 x 10 kcals) , calculated i n Appendix I I L l . 3 , c l e a r l y indicates A S - 62 -that the slag system is not an i n f i n i t e heat source and that, in fact, the heat loss from the slag to the electrode i s sufficient to completely freeze the slag. Therefore, in order to get the tip 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 interface. This would result in the accelerated sol i d i f i c a t i o n of the metal pool producing irreversible structural and compositional changes. On the basis of these calculations, therefore, i t is 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 potential for the production of large ingots. 7.3 Electrode Preheating A possible solution suggested to alleviate the thermal burden problem is to preheat the electrode tip 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 liquid slag, several temperature profiles were calculated assuming that the electrode was being heated in a slag bath at 1200°C. Figure 64 shows the resulting profiles superimposed on the electrode profile for T, equals 1550°C. On the basis of these profiles a b preheating time of approximately 500 seconds at 1200°C provides the - 63 -best compromise between heat content i n the t i p r e g i o n of the e l e c t r o d e and the thermal energy r e q u i r e d t o achieve i t . Us ing t h i s p r o f i l e i t was p o s s i b l e to c a l c u l a t 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 to get the e l e c t r o d e 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 s l a g temperature of 1550°C. T h i s heat i n p u t Q_ was determined as f o l l o w s : Q I = p s Z y A T ( 7 ' 4 ) s = 950 k c a l s where _ yAT i s the hatched area between the two p r o f i l e s . T h i s represents on ly 11.2 percent of the o r i g i n a l a v a i l a b l e heat content of the l i q u i d s l a g . 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 the e l e c t r o d e 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 at 1650°C w i t h the use of a u x i l l i a r y e l e c t r o d e s . 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 preheated e l e c t r o d e would be approximate ly 60 sec . I t has been shown ( S e c t i o n 5 . 2 ) , however, that the heat supply to the meta l p o o l i s p r i m a r i l y from the molten 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 these c o n d i t i o n s , t h e r e f o r e , i t would take approximate ly 120 seconds be fore the heat supply to the meta l p o o l was r e - e s t a b l i s h e d . I t s h o u l d be n o t e d , however, tha t t h i s represents a maximum time i n t e r v a l as the time r e q u i r e d to change e l e c t r o d e s c o u l d be reduced from 60 seconds down to 20 to 30 seconds w i t h more s o p h i s t i c a t e d equipment. - 64 -Assuming that i t was 120 seconds before the new electrode began melt the maximum amount of liquid metal that would freeze would be 18.6 percent (Appendix VI). On the basis of the results from Section (3.2) this would result in minimal concentration banding particularly in alloys with low carbon, sulphur, and phosphorous concentrations. The tandem electrode process, therefore, appears to be a feasible technique for producing large commercial ingots i f preheated electrodes are used. 8. CONCLUSIONS 1. 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 ingot structures. S i g n i f i c a n t compositional banding was observed f o r carbon but not for the other elements present. A possible model for the formation of the carbon concentration banding during the "power-on-off" sequence was proposed. Fluctuations In the slag skin thickness were found to produce carbon concentration bands at the edge of the ingot. 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 to the steels low c r y s t a l growth anisotropy. No changes i n the concentration of Ni, Cr, and Cu were observed as a r e s u l t of the "power-off" experiment i n the ingots produced on the U.B.C. ESR un i t . The nature of the banded structure found i n some commercial ingots was i d e n t i f i e d as regions of high 6 - f e r r i t e content. 3. The most probable cause of the mixing action i n the ESR metal pool i s momentum and heat trans f e r from the f a l l i n g metal droplets. The r e s u l t i n g mixing action i s a slow convective motion which approaches a state of complete mixing at the slow s o l i d i f i c a t i o n rates found i n the ESR process. During a "power-off-on" s i t u a t i o n , elements - 66 -with k value between 0.5 and 1.0 w i l l have minimal concentration o banding associated with them. Elements on the other hand, with k Q values lower than 0.5 could show s i g n i f i c a n t concentration banding and macrosegregation. 4. The average superheat of the l i q u i d metal pool f o r a 10 cm diameter ESR ingot was estimated to be 58°C. The outside l i m i t s of this superheat were found to be 47°C and 87°C. The average superheat of the l i q u i d metal pool i n a 61 cm diameter and 254 cm diameter ESR ingot were estimated to be 70°C and 80°C r e s p e c t i v e l y . The average superheat.of.the l i q u i d metal pool f o r a 10 cm diameter VAR ingot was estimated to be 121°C. This i s much higher than that found i n a si m i l a r sized ESR ingot and could account f o r the much deeper pool p r o f i l e s observed i n VAR ingots. 5. The rate of heat transfer at the l i q u i d metal/slag skin , l i q u i d s lag/slag skin, and l i q u i d slag/atmosphere i n t e r f a c e s were determined as a function of the "power-off" mode. They a l l decreased r a p i d l y and showed an immediate response to the "power-off" condition. The rate of heat transfer across the l i q u i d s l a g / l i q u i d metal i n t e r f a c e i s c r i t i c a l l y dependent on the heat transfer, c o e f f i c i e n t across the in t e r f a c e due to the small temperature gradient. The net flow of heat across t h i s i n t e r f a c e f o r longer durations (t > 15 sec) of the "power-off" mode i s approximately zero. 6. The l i q u i d metal s o l i d i f i e s at an approximately uniform rate during the e a r l y stages of the "power-off" mode. The l i q u i d slag s o l i d i f i e s r a p i d l y at f i r s t i n s u l a t i n g i t s e l f from i t s major sources of heat lo s s . This causes i t s s o l i d i f i c a t i o n rate to decrease. The calculated values of the volume percents s o l i d i f i e d based on a heat balance during the "power-off" mode were v e r i f i e d experimentally by tungsten powder additions. In a 61 cm diameter ESR ingot i t was estimated that a maximum of 10 percent of the l i q u i d metal and 10.3 percent of the l i q u i d slag would s o l i d i f y during a 60 second power i n t e r r u p t i o n . The VAR process appears to be more s e n s i t i v e than the ESR process to any disruptions i n the systems power supply. 7. A general unsteady-state heat transfer program was wri t t e n to calc u l a t e temperature p r o f i l e s i n an electrode that i s immersed i n a slag bath. Preheated electrodes must be used i n the tandem electrode change machine i f s t r u c t u r a l and compositional changes are to be avoided. The use of a preheated electrode and a u x i l i a r y electrodes to maintain the slag temperature would ensure minimal s t r u c t u r a l and compositional changes i n the ingot during an electrode change operation. - 68 -9. SUGGESTIONS FOR FUTURE WORK 1. Since i t has been shown that the compositional i r r e g u l a r i t i e s are produced when the power was re-established, i t would be a p r a c t i c a l exercise to carry out a more d e t a i l e d examination of t h i s stage. By c a r e f u l l y c o n t r o l l i n g the power input i n t o the system when re-es t a b l i s h i n g the equilibrium thermal conditions i t may be possible to completely eliminate the formation of any compositional i r r e g u l a r i t i e s during the electrode change operation. 2. Although some information was obtained concerning the heat transfer across the slag/metal i n t e r f a c e i t would be of i n t e r e s t to carry out a more d e t a i l e d examination of the heat transfer i n t h i s region. This would e n t a i l a determination of the heat transfer c o e f f i c i e n t at t h i s i n t e r f a c e , as w e l l as a bett e r understanding of how the metal and sla g temperatures change during the "power-off" mode. The r e s u l t s of t h i s i n v e s t i g a t i o n would also provide some estimate as to the effectiveness of a u x i l l i a r y electrodes i n heating the slag and metal pools during the electrode change operation. 3. A serie s of power i n t e r r u p t i o n experiments on a large commercial ingot could be used to check the v a l i d i t y of the many assumptions that had to be made i n order to scale up the experimental r e s u l t s obtained on the lab-scale ESR uni t . - 69 -APPENDIX I DETERMINATION OF CONCENTRATION PROFILES 1.1 Determination of the normalized concentration of radioactive ti n and sulphur (C'-C ) x o 'X - (C.-C.) C = x 0 (A.I-1.1) where: C_ = the equilibrium concentration C. = the concentration at the interface l C^ = the concentration at any point x from the interface C„ = the relative fractional concentration at any point x from the interface. 1.2 Determination of the theoretical profile for k = 1 and complete  mixing To circumvent the pool shape problem the liquid pool was considered to be cylindrical. Because the geometry of the so l i d i f i c a t i o n front was assumed to be f l a t the volume of liquid metal s o l i d i f i e d i s proportional to the change in height (Ah). Volume s o l i d i f i e d « ^ (A.1-2.1) h o where: h Q is the original height of the cylinder. Since the liquid is assumed to be of uniform composition (C ) and k - 70 -equal to unity, the concentration of the s o l i d (Cg) i s : % - «_>_ r 1 o However, since the volume of l i q u i d metal during ESR processing must remain constant a new volume of pure metal must be introduced which i s equal to the volume s o l i d i f i e d . Therefore the new composition of the l i q u i d i s ( CL ) 2 = ' W l When another equal increment of volume s o l i d i f i e s the concentration of the s o l i d ( ( c s ) 2 ) i s ( V 2 - ici?2 i r o o A general form of t h i s equation can be written as follows assuming Ah o , i s constant h o All Using equation A.1-2.2 and assuming = 1 and ^— = 0.1 a t h e o r e t i c a l o p r o f i l e f o r solute d i l u t i o n was calculated. - 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 II. 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. • 1500°C ( i i ) ( v » • • 0.18 cal/g/°C ( i i i ) L > 65.5 cal/g (iv) (v) PAvg p£ = 7.5 g/cm3 7.0 g/cm3 (vi) A T s = = 58°C the slag pool system: (i) T m. p. - 1450°C 2 9 ( i i ) Avg • 1660°C3 0 ( i i i ) • 0.3 cal/g/°C (iv) L 46.6 cal/g (v) PAvg 3 2.6 g/cm II.1.2 Available heat content of the metal pool system. Figure 53-B shows a schematic diagram of the metal pool system. The total heat content ((Q T) M) was calculated as follows: - 72 -(VM = E mC AT + mL P Vp AC pAT + Vp pC_AT s + Vp AL (A.II-1.1) = 284 kcals + 10 kcals + 69 kcals = 363 kcals The a v a i l a b l e heat content of the metal pool system ((Q^)^) i - s the sum of the lat e n t heat and superheat terms i n equation A.II-1.1). This implies that the s o l i d metal retains i t s sensible heat u n t i l the metal pool has completely s o l i d i f i e d . ( QA }M = V P L C p A T S + V P A L (A.II-1.2) = 79 kcals II.1.3 Available heat content of the slag pool system: Figure 53-A shows a schematic diagram of the slag pool system. The t o t a l heat content ((Q,-,)g) was calculated as follows: CQ_)S = I mCpAT + mL = VPLGpAT + VP LC pAT g + VP LL (A.II-1.3) = 402 kcals + 54 kcals + 44 kcals = 500 kcals - 73 -The a v a i l a b l e heat content of the slag pool system ((Q A)g) i s the sum of the latent heat and superheat terms i n equation A.II-1.3. This implies that the s o l i d i f i e d slag retains i t s sensible heat u n t i l the slag pool has completely s o l i d i f i e d . ( QA }S = V p L C p A T S + V P L L (A.II-1.4) = 98 kcals II.2 Rate of heat loss from the s l a g and metal pool systems. For the purpose of t h i s c a l c u l a t i o n i t was assumed that the rate of heat loss (q) from any part of the system was d i r e c t l y p roportional to i t s surface area. I t was also assumed that the heat trans f e r across the slag/metal i n t e r f a c e (q^) was n e g l i g i b l e . II.2.1 Heat loss from the metal pool system f o r d i f f e r e n t durations  of the "pbwer-bff" mode Figure 53-B shows the main regions of heat loss from the l i q u i d metal pool. II.2.1.1 Heat loss across the l i q u i d metal/slag skin i n t e r f a c e (Q]) Using Figure 50 and an area co r r e c t i o n f a c t o r (K^) the heat loss from t h i s region f or any time (t) was calculated as follows: = K. E q (A.II-2.1) A t=l . „ (4.7) (1.5) -I n , W h e r e A " (4 . 4 5 X 1.5) = - 1- 0 6 - 74 -(a) t = 2.5 seconds q = 1.06 E(0.63 + 0.60 + 0.27)kcals = 1.6 kcals (b) t = 5 seconds 2 q = 1.06 [ E + 1(0.53 + 0.48 + 0.43)]kcals t=l = 2.8 kcals (c) t = 7.5 seconds 5 q = 1.06[ E + E(0.38 + 0.33 + 0.15)]kcals t=l = 3.6 kcals (d) t = 10 seconds 7 q = 1.06[ E + E(0.29 + 0.26 + 0.23)]kcals t=l = 4.4 kcals (e) t = 12.5 seconds 10 q = 1.06[ E + E(0.20 + 0.18 + 0.08)]kcals t=l = 4.9 kcals (f) t = 15 seconds 10 q = 1.06[ E + E(0.20 + 0.18 + 0.16 + 0.14 + 0.12)]kcals t=l = 5.5 kcals - 75 -(g) t = 20 seconds 15 q = 1.06 S + 1.06(5)(0.1) t=l = 6.1 kcals . (h) t = 30 seconds q = 6.1 k c a l + 1.06(10)(0.1) = 6.3 kcals II.2.1.2 Heat loss by conduction down the s o l i d i f i e d ingot (q^) Using the rate of heat loss down a 7.6 cm diameter ingot determined by Joshi (q = 0.3 kcals/sec) and the area correction factor (K^), the heat loss across t h i s i n t e r f a c e for any time (t) was calcu l a t e d . q = K Aqt (A.II-2.2) (10) 2 , where K = - — = 1.7 A (7.6) Z (a) t = 2.5 seconds q = 1.3 kcals (b) t = 5 seconds q = 2.5 kcals (c) t = 7.5 seconds q = 3.8 kcals - 76 -(d) t 10 seconds q = 5.0 kcals (e) t = 12.5 seconds q = 6.0 kcals (f) t = 15 seconds q = 7.5 kcals (g) t = 20 seconds q = 10.0 kcals (h) t = 30 seconds q = 15.0 kcals II.2.1.3 Heat loss across the s o l i d metal/slag skin i n t e r f a c e Using the minimum rate of heat loss f o r conduction from the metal i n figure (q = 0.1 kcal/sec) and the area correction factor CK.), the heat loss across t h i s i n t e r f a c e at any time (t) was calculated. q = K Aqt (A.II-2.3) where K (10)L (7.6)L = 1.3 (a) t = 2.5 seconds q = 0.3 kca ls (b) t = 5 seconds q = 0.6 kca ls (c) t = 7.5 seconds q = 1.0 kca ls (d) t = 10 seconds q = 1.3 kca ls (e) t = 12.5 seconds q = 1.6 kca l s (f) t = 15 seconds q = 1.9 kca ls (g) t = 20 seconds q = 2.7 kca ls (h) t = 30 seconds q = 3.8 kca ls - 78 -II.2.2 Heat loss from the slag pool system f o r d i f f e r e n t durations  of the "power-off" mode Figure 53-A shows the main regions of heat loss from the l i q u i d slag pool. II.2.2.1 Heat loss across the s l a g - a i r i n t e r f a c e (q^) Using Figure 50 and an area correction factor (K^) the heat loss across t h i s i n t e r f a c e for any time (t) was calculated as follows: = K E q. (A.II-2.4) t=l C 2 where K = ( 4 , 8 ) = 1.16 A (4.45r (a) t = 2 seconds q = 1.16 E(0.47 + 0.41) = 1.0 (b) t = 5 seconds q = 1.16 E(0.47 + 0.41 + 0.35 + 0.34 + 0.28)kcals = 2.2 kcals (c) t = 10 seconds 5 q = 1.16[ E + E(0.25 + 0.23 + 0.21 + 0.20 + 0.19)]kcals t=l = 3.4 kcals - 79 -(d) t = 15 seconds 10 q = 1.16[ £ + E(0.18 + 0.17 + 0.16 + 0.15 + 0.14)]kcals t = l = 4.3 k c a l s (e) t = 30 seconds 15 q = 1.16[ E + £(0.13 + 0.12 + 0.12 + 0.11 + 0.10 + 0.10 + t = l 0.09 + 0.08 + 0.07 + 2(0.06) + 4(0.05))]kcals = 5.8 k c a l s II.2.2.2 Heat l o s s across 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 (q<_) Using Figure 50 and an area c o r r e c t i o n f a c t o r (K ) the heat l o s s across 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 E q (A.II-2.5) A t = l C , . (4.8)(5.0) 1 0 W h e r e = (4.45K4.5) = X' 2 (a) t = 2 seconds q = 1.2 E(1.89 + 1.75)kcals = 4.2 k c a l s (b) t = 5 seconds q = 1.2 E(1.89 + 1.75 + 1.60 + 1.45 + 1.30)kcals = 9.6 k c a l s - 80 -(c) t = 10 seconds 5 q = 1.2[ E + £(1.25 + 1.0 + 0.85 + 0.7 + 0.52)]kcals t=l = 14.3 kcals (d) t = 15 seconds 10 q = 1.2[ E + E(0.4 + 0.33 + 0.28 + 0.23 + 0.20)]kcals t=l = 16.0 kcals (e) t = 30 seconds 15 q = 1.2[ E + E(0.17 + 0.14 + 0.12 + 0.11 + 0.09 + 0.08 + t=l 0.07 + 0.06 + 7(0.05))]kcals = 17.5 kcals - 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 metal and slag pool systems at the s t a r t of the "power-off" mode III.1.1 Assumed data (a) the metal pool system (i) T = 1500°C m. p. ( i i ) (C )„ = 0.18 cal/g/°C P a ( i i i ) L = 6 5 . 5 cal/g ( l v ) pAvg = 7 ' 5 g / c m 3 3 (v) p ^ = 7 . 0 g/cm (vi) AT = 70°C (b) the slag pool system (CaF 2 + 25 wt.% A1-.0-) (i) T = 1450°C m.p. ( i i ) (C ) A = 0.3 cal/g/°C ( i i i ) L = 46.6 cal/g 3 (iv) p A v g = 2.6 g/cm (v) AT_ = 210°C III.1.2 The av a i l a b l e heat content of the metal pool system The t o t a l heat content of the system ((Q-J^) was calculated as follows: - 82 -( Q T ) M = EmCpAT + mL Vp.C AT + Vp TC AT + Vp TL (A.III-1.1) A P Li P O XJ (58.1 x I O 3 + 2.6 x I O 3 + 14.3 x 1 0 3 ) k c a l s 75 x 1 0 3 k c a l s The t o t a l a v a i l a b l e heat content (Q.)», i s assumed to be the sum A M of the l a t e n t heat and superheat terms i n equation ( A . I I I - 1 . 1 ) . ( Q A ) M - VpC pAT s + Vp AL (A.III-1.2) = 17 x 10 3 k c a l s I I I . 1 . 3 The a v a i l a b l e heat content of the s l a g pool system The t o t a l heat content ((Q T)g)"was c a l c u l a t e d as f o l l o w s : ( Q J C = EmC AT. + mL (A.III-1.3) l b P b Vp AC pAT + Vp AC pAT s + Vp AL (33.6 x 10 3 + 4.8 x 1 0 3 + 3.5 x 1 0 3 ) k c a l s 42 x 1 0 3 k c a l s The t o t a l a v a i l a b l e heat content (QA)p i s assumed to be the sum of the l a t e n t heat and superheat terms i n equation A . I I I - 1 . 3 . - 83 -(Vs = V p A C p A T S + V p A L (A. I I I - l . 4) = 8 x 10 3 kcals III.2 Rate of the heat loss from the slag pool and metal pool systems during the "power-off" mode For the purpose of th i s c a l c u l a t i o n i t was assumed that the rate of heat loss (q) from any part of the system was d i r e c t l y p roportional to the surface areas involved. This assumption made i t possible to use the heat transfer p r o f i l e s experimentally determined for the 7.6 cm diameter ingots. I t was also assumed f o r s i m p l i c i t y that the net heat flow across the slag/metal i n t e r f a c e (q £) was zero. 6 III.2.1 Heat loss from the metal pool system during the 60 seconds of "power-off" operation III.2.1.1 Heat loss from the metal pool across the l i q u i d metal/slag  skin i n t e r f a c e (q^) i n 60 seconds Using Figure 50 and an area correction f a c t o r (K ) the heat loss across this boundary for any time (t) was calculated as follows: t q'• = K E q . (A.III-2.1) A t=l t , „ T l i l (30.5)(10.0) ._ _ where K = — - — = „ -( = 45.7 A r2 2 (4.45)(1.5) It was also assumed that the minimum value f o r the rate of heat loss across t h i s i n t e r f a c e was 0.1 kcals/sec. Therefore the heat loss i n 60 seconds was - 84 -60 q = 45.7 _ q t=l = 490 kcals III.2.1.2 Heat loss from the metal pool across the l i q u i d metal/solid  metal i n t e r f a c e (q^) The rate of heat loss across t h i s i n t e r f a c e f o r the 7.56 cm diameter ingots was approximately 0.3 kcals/sec, therefore: q2 = K A ( ~ ° ' 3 ' t k c * l s (A.III-2.2) Cr )2 2 u v 1 (30.5)^ ,-where K = r- = — = 65 ( r . ) Z (3.78) Z hence q = (65)(0.3)(60) = 1172 kcals It should be noted, however, that t h i s represents the maximum heat flow possible i n t h i s d i r e c t i o n . Because the heat loss down the ingot i s inversely proportional to the ingot height t h i s value would only be applicable near the bottom of the ingot and would decrease with the ingot height. The act u a l value, therefore, eould be between 30 to 50 percent smaller than the calculated value. III.2.1.3 Heat loss from the metal pool across the s o l i d metal/slag  skin i n t e r f a c e The rate of heat loss across t h i s i n t e r f a c e f o r the 7.6 cm diameter ingots was approximately 0.1 kcals/sec, therefore: - 85 -q 3 = K (O.i)t kcals (A.III-2.3) , v 61. OL Q where K, = -, O T — = 7.8 A 7.8L hence q 3 = (7.8)(0.1)(60) = 47 kcals III.2.1.4 The t o t a l heat loss ( q ^ ) ^ from the metal pool during the  60 seconds of "power-off" operation ( q L ) M = q-L + q 2 + q 3 (A.III-2.4) = (490 + 1172 + 47)kcals = 1709 kcals This represents a maximum value f or the amount of heat l o s t from the metal pool i n 60 seconds. III.2.2 Heat loss from the slag pool system during the 60 seconds of "power-off" operation III.2.2.1 Heat loss across the s l a g / a i r i n t e r f a c e (q^) Using Figure 50 and the area correction f a c t o r (K^) the heat loss across t h i s i n t e r f a c e at any time (t) was calculated as follows: q. = K. E q f c (A.III-2.5) 4 t-1 t where K = '(30.5) = 47 A (4.45r - 86 -therefore q. = (47)(8.4) kcals 4 = 394 kcals III.2.2.2 Heat loss across the l i q u i d s l a g / s l a g skin i n t e r f a c e (q,.) Using Figure 50 and the area correction factor the heat loss across t h i s i n t e r f a c e f o r any time (t) was calculated as follows: q = K E q (A.III-2.6) J A t = 1 t , (30.5)(10) _ W h e r e K A = (4.45)(5) = 1 3 ' 8 therefore q 5 = (13.8)(27.8) kcals = 384 kcals III.2.2.3 The t o t a l heat loss ( q T ) n from the l i q u i d slag during the 60 seconds of "power-off" operation ( q L ) s = q 4 + q 5 (A.III-2.7) = (394 + 384) kcals = 778 kcals This represents a maximum value for the amount of heat l o s t from the slag pool i n 60 seconds. - 87 -I I I . 3 Volume of l i q u i d metal and l i q u i d slag to freeze during the 60 second "power-off" mode I I I . 3 . 1 The percentage of the l i q u i d metal pool that would s o l i d i f y  i n 60 seconds under the assumed conditions The t o t a l a v a i l a b l e heat content ( 1 .2 ) (q.)_ = 17 x 1 0 3 kcals A M The t o t a l heat loss i n 60 seconds ( 2 . 1 . 4 ) ( q T ) _ = 1709 kcals N L M Therefore the percentage of the metal pool that would be s o l i d i f i e d i n 60 seconds ( Q L } M Volume percent s o l i d i f i e d = x 100 = 10% (A . I I I -3 .1 ) ^VM I I I . 3 . 2 The percentage by volume of the l i q u i d slag that would  s o l i d i f y i n 60 seconds under the assumed conditions The t o t a l a v a i l a b l e heat content ( 1 .3 ) (q ) = 8 x 1 0 3 kcals The t o t a l heat loss i n 60 seconds ( 2 . 2 . 3 ) ( q L ) g = 778 kcals - 88 -Therefore the percentage of the slag pool that would be so l i d i f i e d in 60 seconds ( Q L } S Volume percent s o l i d i f i e d = . 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 = 1500°C (b) C - 0.18 cal/g/°C p (c) L =65.5 cal g" 1 ( d ) pAvg = 7 , 5 g C m ~ 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_ = VpAC AT + Vp C AT. + VpAL (A.IV-1.1) T ^A p rp p S A = 936 kcal + 71 kcals + 231 kcals = 1238 kcals IV.1.3 Total available heat content of the metal pool system (Q ) Q. = Vp C AT + Vp.L (A.IV-1.2) A p p o A = 302 kcals - 90 -This value assumes that the metal pool retains i t s sensible heat until both the superheat and the latent heat are removed. IV.2 Determination of the heat loss from the pool in 12.5 seconds There are three main sources of heat loss in 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 liquid metal (q-^ ) (a) Assumed data (i) The average temperature of the metal at the surface was 1650°C. ( i i ) The electrode was removed. ( i i i ) The shape factor (S) for the system was 1.0. (iv) The emisivity (e) for the metal was 0.37. (b) The amount of heat loss from the metal due to radiation in 12.5 seconds was: q-L = SAea[T 1 4-T 2 4]t (A.IV-2.1) = 6.72 kcals IV.2.2 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 profile which showed the change in 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 profiles are - 9 1 -given for s t e e l electrodes melted at d i f f e r e n t rates of power input (Figure 60). I t was assumed that the power input was proportional to the c r o s s - s e c t i o n a l area of the ingot so that the 10 cm diameter ingot could be scaled up to f i t the p r o f i l e s . The power input i n t o ingot no. V-3 was calculated on the basis of i t s operating conditions. i . e . power input (KW) = (volts)(amps) A.IV-2.2) = (25)(2900) = 72.5 KW This corresponds to a power input of approximately 300 kilowatts for a 20.32 cm diameter ingot. Although this i s a higher power input than run no. 9 i n Figure 60, the p r o f i l e s t i l l provides a good approximation of the rate of heat t r a n s f e r during steady-state conditions. Because the rate of heat transfer w i l l decrease during the "power-off" mode th i s p r o f i l e w i l l provide a maximum value f o r the r a d i a l heat loss during the "power-off" mode. Figure 61 shows the heat flux p r o f i l e for run no. 9 i n metric u n i t s , (a) Assumed data (1) The heat conduction above the ingot top during the "power-off" condition was assumed to be n e g l i g i b l e . This was reasonable since the high f l u x values i n t h i s area represented arc i n s t a b i l i t i e s , and hot metal splashing on the cr u c i b l e walls, and therefore, would not occur during the "'power-off" mode. (2) The r a d i a l heat f l u x lower than 12 cm below the ingot surface was considered n e g l i g i b l e . - 92 -(b) C a l c u l a t i o n of the r a d i a l heat loss from the ingot (q,.) 12 q 2 = A( E hAT)t (A.IV-2.3) n=l where the average f l u x (hAT) i s determined at 1 cm i n t e r v a l s . Therefore, q- = TT(10) (1) (0.214) (12.5) kcals = 84 kcals IV.2.3 Heat loss by conduction down the ingot(q^) (a) Assumed data: (1) The rate of heat loss was proportional to the rate for a s i m i l a r s i z e d ESR machine. (2) The rate of heat loss was proportional to the surface area. Using the rate of heat loss down a 7.6 cm diameter ESR ingot as determined by Joshi (q = 0.3 kcal/sec) and the area correction factor (K^), the heat loss down the ingot was determined. q 3 = K A ( 0 , 3 ) ( 1 2 ' 5 ) k c a l s (A.IV-2.4) , „ (10) 2 . 7 where K = - — — = 1.7 A (7.6) 2 Therefore q„ = 6.4 kcals . - 93 -IV.2.4 T o t a l heat loss from the l i q u i d pool i n 12.5 seconds (QL> Q L = q± + q 2 + q 3 (A.IV-2.5 = (6.7 + 84.0 + 6.4) kcals = 97.1 kcals This represents the maximum heat loss from the system during the 12.5 second power i n t e r r u p t i o n . IV.3 Percentage of the metal pool that s o l i d i f i e d i n 12.5 seconds of  "power-off" operation Q L Volume percent s o l i d i f i e d = — x 100 (A.IV-3.1) = 32.2% s o l i d i f i e d APPENDIX V. COMPUTER PROGRAM TO DETERMINE THE UNSTEADY-STATE TEMPERATURE PROFILE IN AN ESR ELECTRODE. FORTRAN IV G CUMPILtK MAIN 12-13-71 10:43:33 PAGE 0001 OOU 1 ALPHA = .Ot>7 0002 HP = . t>64 O00 3 H = .OA TP=130. 000 TIMt = TP 000 6 TP = b. 000 7 Tu = 2b. 000 8 Tb = l 6t>0 . 000 9 Tr- = TB-TU 0010 OU 2 N = l , lA 0011 WKlTfc (6.9) 0012 Y = .1 001 3 B = SURT(ALPHA*TI M t ) 00 IA OU 1 M = l,3t> 001 b C = Y / ( 2 . * B ) 0016 TEWP =TF* 111. "FRF t e n »FXP (*HP* t Y+HP«ALPHA^rtME rT* t r.-^RFrc-m*BrrT 0017 T tMP = T tMP + TU 0018 WKlTt (6,10) TIME,Y,TEMP 0019 It- (Y.Gfc.l'J. ) Y=Y+S. 00 20 It- (Y.LT.lt>..ANL).Y.GB.l. ) Y=Y + 1. 0021 I M Y . L T . l . ) Y=Y+.l 0022 1 CUNT INUE 0023 WKlTb (6,11) 002A 2 T l M t = TIMt • TP 002*3 9 (-UKMAT ( 8X ' T IME ' « 12X , ' n I STANCE ' , 7X , ' TtMP' / ) 00 2 6 10 r-UKMAT ( IX,3( l P t l S . T f ' j X ) ) 0027 11 tUKMAT (1H1) 0028 5T0P ~ " - ' 0029 tNU - 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.)„ = 17 x 10 3 kcals AM VI.2 Rate of heat loss from the metal pool system during the "power-off"  mode This calculation contains the same assumptions found in Appendix III.2. VI.2.1 Heat loss from the metal pool across the liquid metal/slag  skin interface in 120 seconds Using Figure 50 and an area correction factor (K^) the heat loss across this boundary was calculated as follows: q = K £ q A t=0 1 where K. = — — = 45.7 A x2l2 Therefore the heat loss in 120 seconds was 60 120 q = £ q + £ q (A.VI-2.1) t=l Z t=60 - 96 -= 490 kcals + (45. 7)(O.D(60) 764 kcals VI.2.2 Heat loss from the metal pool across the l i q u i d metal/solid metal i n t e r f a c e The rate of heat loss across t h i s i n t e r f a c e f o r the 7.56 cm diameter ingots was approximately 0.3 kcals/sec, therefore, hence = 2344 kcals VI.2.3 Heat loss from the metal pool across the s o l i d metal/slag  skin i n t e r f a c e The rate of heat loss across t h i s i n t e r f a c e f o r the 7.6 cm diameter ingot was approximately 0.1 kcals/sec, therefore, = K A(0.3)t (A.VI-2.2) where K = 65 q 3 = K A(0.1)t (A.VI-2.3) where K. = 7.8 hence q = 94 kcals - 97 -VI.2.4 Total heat loss (Q^) M from the metal pool during the 120 seconds  of "power-off" operation (Q L ) M = (764 + 2344 + 94 ) kcals . (A.VI-2.4) = 3202 kcals VI.3 The percentage of the metal pool that would sol i d i f y in 120 seconds of "power-off" operation The total available heat content (7.1.1) Q. = 17 x 10 3 kcals A The total heat loss in 120 seconds (7.1.4) Q L = 3202 kcal Therefore Q L Volume percent so l i d i f i e d = -f- x 100 = 18.8% (A.VI-3.1) QA It should be noted that this represents the maximum amount of liquid metal that would so l i d i f y in 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 Wiley (1964). 2. Chalmers B., and King R. , ( E d i t o r s ) , Pergamon Press (1959), 8, 203. 3. Turkdogan E.T., and Grange R.A., J.I.S.I. (1970), 208, 482. 4. Jatczak C.F., G i r a d i D.J., and Rowland E.S., Trans. A.S.M. (1956) 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 Metals", Iron and Steel Inst., (1967) 295. 6. Thresh H., Bergeron M., Weinberg F., and Buhr R.K., Trans A.I.M.E. (1968) , 48, 279. 7. Flemings M.C., P o i r i e r D.R., Barone R.V., and Brody H.D., J.I.S.I. (1970) 208, 371. 8. Kattamis T.S., and Flemings M.C., Trans A.I.M.E. (1956) 233, 992. 9. Morton S.K., M.A.Sc. Thesis, University of B r i t i s h Columbia (1971). 10. Fredriksson H. , and Jarleborg 0., J. Metals (1971) 23_, (9) , 32. 11. Takada H., Fukuhara Y., and Miura M., i n t e r n a l report, Kobe Steel Ltd., Japan. 12. De Vries R.P., and Mumau G.R., J . Metals (1968), 20, (11), 33. 13. Firganek H., J e z i e r s k i K., and Siewierski J . , Pace Inst. Huts, (1969) 21 (3), 141. 14. Etienne M., Ph.D. Thesis, University of B r i t i s h Columbia, (1970). 15. Buhr R.K., and Weinberg F., J.I.S.I. (1967) 205, 1161. 16. Kehl G.L., "The P r i n c i p l e s of Metallographlc Laboratory P r a c t i c e " , McGraw-Hill (1949), 186. 17. L i l l i e W.D., and Ward F.R. ( E d i t o r s ) , "Radioisotope Applications Engineering,"D. Van Nostrand Co., Inc. (1961). 18. Microprobe Analysis General Intensity Correction, Fortran Program adapted by O'Brien T.E., Department of Metallurgy, U.B.C. 19. Hansen M., and Anderko K., "Constitution of Binary A l l o y s " , McGraw-Hill (1958) 705. - 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. Mitchell A., and Joshi S., University of British Columbia, private communication (1971). 24. Beall R.A., Bureau of Mines, Albany Oregon, private communication (1971). 25. Joshi S., Ph.D. Thesis, University of British Columbia (1971). 26. Maulvault A., and E l l i o t J.F., Electric Furnace Proceedings (1970) 28, 13. 27. Mendrykowski J., Poveromo J.J., Szekely J., and Mitchell A., Met. Trans., to be published. 28. Clites P.G., and Beall R.A., (Washington) U.S. Dept. of the Interior, Bureau of Mines (1967), R.I. 7035. 29. Burel B.C., M.A.Sc. Thesis, University of British Columbia (1969) 33. 30. Joshi S.J., op. Cit., 13. 31. Joshi S.J., University of British Columbia, private communication (1971). 32. Szekely and Themelis, "Rate Phenomena in Process Metallurgy", Wiley, (1971), 188. 33. Swoboda K., and Kleinhagauer 0, German Pat., 1,903,843, 10 December (1970). 100 ingot line slag line Figure 1. Three phase, seven electrode, b i f i l a r furnace. 101 Figure 2. Tandem electrode change machine. 102 Figure 3. Schematic diagram of the U.B.C, ESR un i t . Figure 4. Schematic diagram of a VAR furnace. Figure 5 Operating chart during a "power-off" sequence. 105 FeS addition slag Figure 6. External addition of FeS to the melt. 3,81 cm •• | * — 2 , 5 2 cm - 1 ' TI3' ' , I Sn ;AI iMetal 0 95 Figure 7. Configuration of the Sn in the electrode. 106 900 Ingot no. 17 0.32 g Sn added 0 Figure 8. Operating chart during a S n 1 1 3 experiment. 107 50 mV shunt I—thermocouples recorder cooling water Hobart 750 i ".ower supplies Figure 9. Schematic outline of the experimental setup for heat transfer measurements. 108 recorder Yi 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.) graphite powder F i g u r e 10. Thermocouple f o r m e a s u r i n g s l a g and m e t a l b a t h t e m p e r a t u r e s . 109 Figure 11. Macrograph of ingot no. 1 showing the steady state structure of EN-25 s t e e l Etch:Oberhoffer's reagent. 110 9.5 sec. 18 sec. 75 sec. F i g u r e 12. Mac rograph o f i n g o t n o . 3 c o n t a i n i n g t h r ee power i n t e r r u p t i o n s , E tch:0berhof fe r ' s r e a g e n t . Figure 13. Micrograph of the 18 sec power interruption i n ingot no. 3 mag. 6X, EtchrOberhoffer's reagent. 112 Figure 14. Macrographs of ingots etched with 3 percent n i t a l . (A) ingot no. 2 and (B) ingot no. 3. 113 Figure 16. Pool profile outlined with W powder additions (ingot no. 13) Etch 3% Nital. 115 S"rich band power-off FeS addition Figure 17. Sulphur p r i n t of ingot no. 6 containing several interruptions. 116 Figure 19. "Tree-ring" banding i n a high carbon a l l o y s t e e l produced by vacuum arc remelting. 117 Figure 2 0 . Irregularities in the slag skin thickness reproduced in the metal. 118 Figure 21. Banding in ingot no. 13 produced by irregularities in the slag skin thickness, Etch 3% Nital. 119 Figure 22. Schematic representation of banding due to i r r e g u l a r i t i i n the slag skin thickness. 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 Figure 26. Arcos Corporation's continuous c a s t i n g ESR process. 123 Figure 28. Micrograph of the banded structure. X 48 Etch: Railing's reagent. 124 Absorbed electron image Ni X-ray image Cr X- ray image Figure 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 area X 1000. 125 Fe, 18Cr, 4Ni wt 56 C F e' 1 8 C r ' 8 N i Figure 30. Pesudo-binary phase diagrams of Fe + 18% Cr + 4% Ni versus varying carbon content and Fe + 18% Cr + 8% Ni versus varying carbon content. 127 total 78 average particle width = 0.2 cm Figure 32. Standard line count for percent ferrite determination. 128 Figure 33. Crack formation during rolling. 129 F i g u r e 34. D i f f e r e n t e l e c t r o m a g n e t i c s t i r r i n g c o i l c o n f i g u r a t i o n s . 130 CONSUMABLE ELECTRODE: \ MOLD LIQUID SLAG LIQUID METAL SOLIDIFICATION FRONT INGOT ASBESTOS SEAL GRAPHITE CHILL WATER COOLED COPPER BASE Figure 35. Convective motion i n the s l a g and metal pool produced by the f a l l i n g metal d r o p l e t s . 131 132 Figure 37. Plot of the r e l a t i v e concentrations of radioactive t i n versus 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 . 133 Figure 38. Pool p r o f i l e outlined by (A) tungsten powder, (B) i r o n sulphide. 134 Figure 39. Plot 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 interface. 135 -> 5 cm • 2,2 1 • 1,5 cm • 5 cm 3 .8 r 1550 C 1700 C 15£S0 C 1500 C 1500 C 1500 C z r Figure 40. Assumed pool geometry and imposed boundary temperatures i n a 10 cm d i a . ESR ingot. 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 1500 1500 1750 1500 1650 B 10 cm. dia. T S =86°C io cm. dia. T s =47 C 1500 1550 1500 1700 1500 10 cm. dia. T s = 58 C 1550 1500 D 1700 1500 61 cm. dia. T s =70C 1550 1500 1700 2 5 4 cm. d ia . T s = 80 C 1500 Figure 44. Assumed temperature d i s t r i b u t i o n s and corresponding (ATs) values. ' g 140 Figure 45. Assumed pool geometry and imposed boundary temperatures m a 10 cm dia. VAR ingot. 141 A Temperature Profile in the Z Direction B Temperature Profile in the R Direction Figure 46. Assumed temperature d i s t r i b u t i o n s i n the z and r d i r e c t i o n s . 142 •4 4 5 cm Figure 47. Regions where the rate of heat loss i s effected by the "power-off" mode for a 10 cm d i a . ESR ingot. 143 Figure 48. \ Plot of the change i n the mould w a l l temperature versus time during the "power-off" mode. 144 10 20 40 60 100 20 0 AT = Tmold - Twa t e r r T m o l d - 5 0 ( ° C ) Figure 4 9 . Plot of (q/A) vs. AT for (a) non-boiling and (b) surface b o i l i n e conditions. 145 0 1 —I 1 1 1— 0 4 8 12 16 Time (sec) Figure 50. Plot of q vs time for (a) slag (conduction), Cb) slag (radiation) and (c) liquid metal. 1700 » o - ^ E I I 1 — — — r — o 1600 a •«» N. s >v N \ s X . N ^ ^ ^ ^ pypprimpntal rpmppratnrP profile in the slag assumed temperature profile in the metal rature 1500 cu Q. E ,cu X 1400 1300 I I I 1 1 0 5 10 15 20 25 Duration of the Power-off Mode (sec.) Figure 51. Plot of temperature vs time for (a) the slag and (b) the metal. 1 5 7 9 n 13 15 Time (sec) Figure 52. Plot of q/A vs time for different values of h . 148 (A) -5,0 cm--4,8 cm 5,0 cm Figure 53. Assumed pool configurations i n a 10 cm d i a . ingot for (A) s l a g , (B) metal. T 1 1 1 1 r Duration of the Power-off Mode (sec") Figure 54. 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 Actual and approximated pool p r o f i l e s f o r addition experiment. 152 -<—30.5 cm % 1 1< cr  3 n slag • % 1 c 0 m metal % Figure 57. Schematic representation of a 61 cm d i a . ESR ingot. 153 Figure 58. Macrograph of ingot no. V-3 containing several power interruptions. 154 Figure 5 9 . Approximation of the metal pool profile in ingot V - 3 . 155 + 8 T 1 1 •O— Run No. 7 6,600 amps - 2 7 v •A— Run No. 8 steel 4 i - i n c h electrode, 6,500 omps-31 v Run No 9 steel 4 8,000 amps- 33 v - • — . g - inch electrode, steel 4g- inch electrode, </> o 8-inch-diam crucible -8 0.i> 0.4 0.6 HEAT FLUX, IO6 Btu/ft2 hr F i g u r e 60. 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 the 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 s t e e l e l e c t r o d e s . 0 I 1 I I I i i i 0 2 4 6 8 10 12 14 Distance Below the Ingot Top (cm) Figure 61. Heat flux profile 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 interruption in a 10 cm dia. 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 for (a) T = 1550°C, (D) T = 1200°C, t = 100, 500 and 1000 seconds. 

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