@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Materials Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Ivo, Paulo Silveira"@en ; dcterms:issued "2010-04-22T22:51:35Z"@en, "1982"@en ; vivo:relatedDegree "Master of Applied Science - MASc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description "A study of the thermal stresses resulting in the Electroslag Joining Process as applied to heavy gauge forgings has been undertaken, since a survey of published reports on the process indicates that although solidification cracking ought to be a problem, apparently it is not routinely observed. Welding conditions which are known to produce solidification cracks in Electroslag Welding with wire electrodes were reported to make crack-free welds using ESJ plate electrodes. This study reports work on the thermal and stress fields developed during ESJ of 150 mm thick A36 steel plates. Conditions predicted by previous workers to form cracks with wire electrodes were established and found not to form cracks with plate electrodes. Measurements of stress and temperature during welding were made and found to agree well with a simple numerical model of the process. It is concluded that the thermal field of ESJ is sufficiently different to ESW that it can relax the stress field developed, even in a fully-constrained joint, to the point at which solidification cracking is no longer observed."@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/24079?expand=metadata"@en ; skos:note "STRESSES IN HEAVY SECTION ELECTROSLAG JOINING by PAULO SILVEIRA IVO B.A.Sc.,Universidade F e d e r a l de Minas G e r a i s , B r a s i l , l 9 7 8 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of M e t a l l u r g i c a l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October 1982 © Paulo S i l v e i r a Ivo, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree that p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of M e t a l l u r g i c a l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: October 05, 1982 i i A b s t r a c t A study of the thermal s t r e s s e s . r e s u l t i n g i n the E l e c t r o s l a g J o i n i n g Process as a p p l i e d to heavy gauge f o r g i n g s has been undertaken, s i n c e a survey of p u b l i s h e d r e p o r t s on the process i n d i c a t e s that although s o l i d i f i c a t i o n c r a c k i n g ought to be a problem, a p p a r e n t l y i t i s not r o u t i n e l y observed. Welding c o n d i t i o n s which are known to produce s o l i d i f i c a t i o n c r a c k s i n E l e c t r o s l a g Welding with wire e l e c t r o d e s were repo r t e d to make c r a c k - f r e e welds using ESJ p l a t e e l e c t r o d e s . T h i s study r e p o r t s work on the thermal and s t r e s s f i e l d s developed d u r i n g ESJ of 150 mm t h i c k A36 s t e e l p l a t e s . C o n d i t i o n s p r e d i c t e d by pre v i o u s workers to form cr a c k s with wire e l e c t r o d e s were e s t a b l i s h e d and found not to form cr a c k s with p l a t e e l e c t r o d e s . Measurements of s t r e s s and temperature durin g welding were made and found to agree w e l l with a simple numerical model of the process. I t i s concluded that the thermal f i e l d of ESJ i s s u f f i c i e n t l y d i f f e r e n t to ESW that i t can r e l a x the s t r e s s f i e l d developed, even i n a f u l l y - c o n s t r a i n e d j o i n t , to the po i n t at which s o l i d i f i c a t i o n c r a c k i n g i s no longer observed. < i i i Table of Contents A b s t r a c t , i i L i s t of Tables v L i s t of F i g u r e s v i Acknowledgement v i i i I. INTRODUCTION 1 1.1 I n t r o d u c t i o n 1 1.2 Process D e s c r i p t i o n and A p p l i c a t i o n 3 1.3 Previous Work 6 1.4 S o l i d i f i c a t i o n Cracking 9 1.5 Present O b j e c t i v e s 12 I I . MATHEMATICAL MODELING 13 2.1 Temperature D i s t r i b u t i o n C a l c u l a t i o n .14 2.1.1 Assumptions 14 2.1.2 D e r i v a t i o n Of Equations 16 2.1.3 Numerical S o l u t i o n 17 2.2 Thermal S t r e s s And S t r a i n C a l c u l a t i o n 18 2.3 Computer Production Runs 21 I I I . EXPERIMENTAL WORK 23 3.1 Furnace Design 23 3.2 C o o l i n g Shoe Design 23 3.3 E l e c t r o d e And Slag P r e p a r a t i o n 24 3.4 Weld Set-up And C o n s t r a i n i n g ....26 3.5 Sequence of Operation - Welding Procedure 28 3.6 R e s i d u a l S t r e s s 29 i v 3.7 Temperature Measurements 29 IV. DISCUSSION AND RESULTS 31 V. CONCLUSIONS 35 VI. SUGGESTIONS FOR FUTURE WORK 36 BIBLIOGRAPHY 37 APPENDIX A - BOUNDARY CONDITIONS .....68 APPENDIX B - COMPUTER PROGRAM SAMPLE 76 APPENDIX C - EFFICIENCY FACTOR AND HEAT SINK CALCULATIONS . 88 APPENDIX D - RESIDUAL STRESS EVALUATION 90 V L i s t of Tables I. Computer Model Parameters 40 I I . ESJ T y p i c a l Log Sheet 41 v i L i s t of F i g u r e s 1. Schematic Layout of ESJ Equipment 42 2. E l e c t r o s l a g T y p i c a l Weld S t r u c t u r e ( R e f . 35) 43 3. ESJ Thermal P r o f i l e - C a l c u l a t e d and Measured ........44 4. Boundary C o n d i t i o n s 45 5. Nodal Arrangement 46 6. Model Flowchart 47 7. S t r e s s A n a l y s i s Schematic Diagram 48 8. UBC E l e c t r o s l a g Unit 49 9. C o o l i n g Shoe - Water Channels 50 10. C o o l i n g Shoe Top View 51 11. Copper recess 52 12. C o o l i n g Shoes i n P o s i t i o n 53 13. C o o l i n g Shoe Close-up - Water connections 54 14. P l a t e E l e c t r o d e i n P o s i t i o n 55 15. Aluminum Feeder 56 16. E l e c t r o d e and Copper Stub 57 17. Run-in Copper Tabs 58 18. C o n s t r a i n i n g Rod with S t r a i n Gauges 59 19. S t r a i n versus Time P l o t 60 20. Boxed I-Beam 61 21. Hardened 4340 D i s c Spacer 62 22. I n f e r i o r I-beam Placement 63 23. Strain-gauge Set-up 64 v i i 24. Thermal S t r e s s Curve 65 25. Thermal S t r e s s Curve ...66 26. ESJ Thermal Gradient 67 v i i i Acknowledgement S i n c e r e thanks to Dr. A l e c M i t c h e l l f o r h i s guidance throughout the d u r a t i o n of t h i s work. Thanks are a l s o due to Dr. E. B. Hawbolt and f e l l o w graduate students f o r innumerable h e l p f u l d i s c u s s i o n s . The a s s i s t a n c e of the t e c h n i c a l s t a f f , i n p a r t i c u l a r Mr. E. Barry and Mr. G. S i d l a i s g r e a t l y a p p r e c i a t e d . The f i n a n c i a l support provided by the Canadian I n t e r n a t i o n a l Development Agency and by E l e t r o m e t a l Acos Fi n o s S . A . / M i n i s t e r i o da I n d u s t r i a e Comercio - S e c r e t a r i a de T e c n o l o g i a I n d u s t r i a l , B r a s i l i s g r a t e f u l l y acknowledged. A s p e c i a l thanks to Consuelo for her care and encouragement. 1 I. INTRODUCTION 1 .1 I n t r o d u c t i o n The manufacture of l a r g e s t e e l f o r g i n g s v i a the c o n v e n t i o n a l route r e q u i r e s s t a r t i n g i n g o t s having a low in g o t -t o - f o r g i n g y i e l d ( 3 0 to 60%) and a low equipment p o t e n t i a l u t i l i z a t i o n time due to the heavy weights i n v o l v e d . A l t e r n a t i v e p r o d u c t i o n routes have, t h e r e f o r e , to be sought. S e v e r a l techniques have been proposed in an e f f o r t to present v i a b l e s o l u t i o n s . The MHKW(Midvale-Heppenstall-Klockner-Werke) p r o c e s s 1 i s one whereby a c o n v e n t i o n a l l y c a s t ingot i s trepanned and subsequently core remelted, thus improving the q u a l i t y of the ingot c e n t r a l p a r t through enhanced i s o t r o p i c ESR p r o p e r t i e s . The B.E.S.T.(Boehler E l e c t r o s l a g Hot Topping) t e c h n i q u e 2 i s a l s o a p o t e n t i a l process f o r improving the i n g o t - t o - f o r g i n g y i e l d . A f u r t h e r promising route i s the use of E l e c t r o s l a g J o i n i n g f o r welding two or more p i e c e s of s t e e l before f o r g i n g to make a l a r g e preform or j o i n i n g a l r e a d y forged products to t h e i r f i n a l 2 shape. Russian workers have developed a method f o r j o i n i n g l a r g e s e c t i o n s used i n the manufacture of r o t o r f o r g i n g s f o r atomic power s t a t i o n t u r b o g e n e r a t o r s . \" 7 Four l a r g e s e c t i o n consumable e l e c t r o d e s were employed and the welding equipment used a b i f i l a r c o n f i g u r a t i o n which i s claimed to be very e f f i c i e n t . In t h i s i n v e s t i g a t i o n i t was concluded that the process would be a p p l i c a b l e to the production of heavy r o t o r f o r g i n g s using h i g h * a l l o y Cr-Ni-Mo-V s t e e l s and a comparative assessment was made of the f r a c t u r e r e s i s t a n c e of the weld and parent metal with good mechanical p r o p e r t i e s obtained. I t was a l s o found that p r e l i m i n a r y and concurrent h e a t i n g of the p a r t s being j o i n e d were e l i m i n a t e d . L i t t l e has been done as to the a p p l i c a t i o n of the process in the case of carbon s t e e l f o r g i n g s in the range 20-100 t , which r e p r e s e n t s the bulk of the open d i e f o r g i n g market. 9 Here the main concern i s with r e p e a t a b i l i t y , r e l i a b i l i t y , u l t r a s o n i c t e s t i n g and product q u a l i f i c a t i o n . In other words, the process behaves very s i m i l a r l y to the more c o n v e n t i o n a l welding techniques and, t h e r e f o r e , must be c a r e f u l l y c o n t r o l l e d to a v o i d d e f e c t s . The process i s c a r r i e d out with ease and r e l a t i v e l y f a s t i n one s i n g l e pass and when compared with, f o r example, submerged-arc welding, time savings are s i g n i f i c a n t . The r e s u l t a n t coarse 3 s t r u c t u r e due to long thermal c y c l e s i s l i a b l e to produce lower mechanical p r o p e r t i e s and b e t t e r equipment c o n t r o l and welding procedures are needed. 1 .2 Process D e s c r i p t i o n and A p p l i c a t i o n E l e c t r o s l a g J o i n i n g i s one of the s e v e r a l a p p l i c a t i o n s of the E l e c t r o s l a g Remelting p r i n c i p l e . I t i s a f u s i o n welding process whereby heat i s generated by Jo u l e e f f e c t when an e l e c t r i c c u r r e n t passes through an e l e c t r o r e s i s t i v e f l u x ( s l a g ) . Both the t i p of the e l e c t r o d e and the su r f a c e of the work are melted by heat coming from the s l a g -source. The e l e c t r o d e molten d r o p l e t s t r a n s f e r by g r a v i t y to the weld pool by f a l l i n g through the molten f l u x . As can be seen in F i g . 1, the a x i s of the j o i n t i s v e r t i c a l but the welding i s performed i n a h o r i z o n t a l p o s i t i o n . The remelted product i s surrounded by the parent m a t e r i a l and by c o o l i n g shoes e i t h e r s t a t i o n a r y or movable. The most popular v e r s i o n of the process i s the one employing f l u x - c o a t e d or bare wire e l e c t r o d e f e e d i n g as w e l l as consumable or non-consumable e l e c t r o d e guides. In t h i s case, the f i l l e r m a terial(wire+guides) and the parent metal o f t e n have d i s s i m i l a r compositions and when s e v e r a l wires are used, 4 depending on the t h i c k n e s s of the p a r t s being welded, proper monitoring of the feeding system becomes rather c r i t i c a l . The weld metal a c q u i r e s a c a s t i n g s t r u c t u r e wherein the s i z e s and o r i e n t a t i o n s of the g r a i n s are c o n t r o l l e d by heat removal. The presence of long columnar g r a i n s i s c h a r a c t e r i s t i c and four types of g r a i n s t r u c t u r e s have been d e f i n e d by P a t o n . 3 5 Because the process i n t r o d u c e s a l a r g e amount of heat i n t o the p a r t s being j o i n e d , a l a r g e heat a f f e c t e d zone can be expected. F i g . 2 i l l u s t r a t e s these m i c r o s t r u c t u r e s . Segregation along the g r a i n boundaries of these columnar g r a i n s can cause crack appearance as d i s c u s s e d below. The t y p i c a l slow c o o l i n g r a t e s i n the process when c o o l i n g from the a u s t e n i t e range form p e a r l i t e : the p r o e u t e c t o i d f e r r i t e normally forms a network along the p r i o r - a u s t e n i t e g r a i n boundaries and Widmanstatten s i d e p l a t e s that extend from the g r a i n boundaries i n t o the m a t r i x . 5 Due to f a s t c o o l i n g , r e s i d u a l s t r e s s e s are present i n the weld and heat a f f e c t e d zone but are somewhat r e l i e v e d in the l o n g i t u d i n a l d i r e c t i o n . The use of p l a t e e l e c t r o d e as f i l l e r metal has r e c e n t l y been c o n s i d e r e d and i t i s b e l i e v e d to enable more e f f i c i e n t heat t r a n s f e r . Because the el e c t r o m a g n e t i c f o r c e s do not produce as s t r a y f l u i d motions, s l a g v e l o c i t i e s are slower(2 to 4 cm/s) and the t o t a l weld heat may be reduced by as much as 30% when p l a t e e l e c t r o d e s are used i n s t e a d of wire welding. A l s o the heat f l u x 5 to the base metal from the s l a g i s more un i f o r m . 6 The hydrogen content of the s t e e l has been found t o decrease with i n c r e a s i n g c a l c i u m f l u o r i d e content i n the f l u x . A system c o n t a i n i n g CaF + A l 0 i s recommended f o r e f f e c t i v e 2 2 3 hydrogen c o n t r o l . 7 A l s o the hydrogen content has been found to be l a r g e r at the weld s t a r t than elsewhere. To le s s e n t h i s e f f e c t , as d i s c u s s e d below, proper p r e - h e a t i n g of the f l u x components was normal procedure throughout these experiments. A l i q u i d s l a g s t a r t procedure should improve the hydrogen c o n t r o l even f u r t h e r , should t h i s prove to be a problem. E l e c t r o s l a g Welding and E l e c t r o s l a g J o i n i n g have u s u a l l y been used to j o i n heavy t h i c k n e s s , l a r g e welds and a p p l i e d to the manufacture of generator r o t o r s f o r the nuclear i n d u s t r y , to the o n - s i t e welding of t h i c k v e r t i c a l j o i n t s where Arc Welding co u l d not be employed, 3 5 and to the c o n s t r u c t i o n of b r i d g e s , b u i l d i n g s and storage t a n k s . 4 High pressure v e s s e l s and heavy b o i l e r drums used i n power p l a n t s have a l s o been f a b r i c a t e d . 3 5 8 Welding of f o r g i n g presses and a n v i l s up to 2000 X 2000 mm and of r o l l i n g m i l l frames as w e l l as s h i p rudder p a r t s has been performed.\" 3 Recently, main p r o p u l s i o n s h a f t i n g and other machinery s h a f t s f o r use i n Cla s s e d Ships made by E l e c t r o s l a g J o i n i n g have been q u a l i f i e d under L l o y d ' s R e g i s t e r r equirements. 3 6 1 .3 Previous Work The theory of moving sources i n welding(Arc Welding) heat conduction presented by R o s e n t h a l 1 0 and the a n a l y t i c a l m o d e l l i n g proposed by R y k a l i n 1 1 set b a s i s f o r a l l subsequent work done in the f i e l d of weld m o d e l l i n g . L i t t l e a t t e n t i o n has been given to the thermal s t r e s s c a l c u l a t i o n s i n E l e c t r o s l a g J o i n i n g except fo r some p u b l i s h e d Czech work 2 2 2 5 done with wire e l e c t r o d e welding. The r e s u l t i n g complex equations from a n a l y t i c a l s t u d i e s on welds have always hindered a b e t t e r understanding of the d i f f e r e n t processes, e s p e c i a l l y i n studying thermal s t r e s s e s 1 7 . Gray et a l 2 0 have improved Okerblom's 1 2 theory of one-dimensional s t r e s s a n a l y s i s based on a two-dimensional heat flow treatment and a p p l i e d to t h i n gauge m a t e r i a l s . L i t t l e e xperimental i n f o r m a t i o n was given which c o u l d be used to t e s t the theory and i t made use of in-pla n e c u r v a t u r e s rather than c o n t r a c t i o n s . These authors have, however, succeeded in c a r r y i n g out experiments intended to t e s t the theory f o r l o n g i t u d i n a l c o n t r a c t i o n s . 7 With the ever i n c r e a s i n g speed of modern computers, s o l u t i o n techniques have been de v i s e d which enable more accurate and f a s t e r c a l c u l a t i o n s . The f i r s t attempt to make use of computers i n a n a l y s i n g welding s t r e s s e s dates as f a r back as 1961. 1 8 M a s u b u c h i 1 7 r e p o r t e d some e f f o r t s being made at a n a l y s i n g t r a n s i e n t l o n g i t u d i n a l s t r e s s e s d u r i n g multipass welding of a heavy p l a t e , but no r e s u l t s were g i v e n . The m a j o r i t y of experimental s t u d i e s of thermal s t r e s s e s d u r i n g welding, however, has used m a t e r i a l s i n the t h i c k n e s s range of 0.30 mm to 25.4 mm(0.0l2\" to 1\"), which were a l l done using Arc Welding w h i l s t experiments i n the present work were performed using much t h i c k e r m a t e r i a l . N i s h i d a 2 1 reviewed s e v e r a l methods for c a l c u l a t i n g thermal s t r e s s e s and compared t h e o r e t i c a l r e s u l t s with experimental data, again working with t h i n m a t e r i a l s . E r i k s s o n et a l 3 0 have developed a h o t - c r a c k i n g t e s t to assess the weld metal composition i n f l u e n c e on the h o t - c r a c k i n g tendency i n heavy E l e c t r o s l a g welds and have concluded that to avoid s o l i d i f i c a t i o n c r a c k i n g , the carbon content should be kept as low as p o s s i b l e and the Mn/S r a t i o should exceed 45. In t h i s t e s t , however, the s t r e s s f i e l d s are not known e i t h e r i n a b s o l u t e terms or i n r e l a t i o n to those present in heavy s e c t i o n welds. There e x i s t s e v e r a l other t e s t s to evaluate w e l d a b i l i t y 8 c r a c k i n g problems and two of them seem to be e s p e c i a l l y s u i t a b l e f o r s o l i d i f i c a t i o n c r a c k i n g : V a r e s t r a i n t and T r a n s v a r e s t r a i n t t e s t s . They are the same i n p r i n c i p l e and o p e r a t i o n , except f o r the d i r e c t i o n of the a p p l i e d s t r a i n with respect to the welding d i r e c t i o n . They have not been a p p l i e d to e l e c t r o s l a g welding c o n f i g u r a t i o n s . Ueda et a l 1 9 have developed a method f o r t h e o r e t i c a l a n a l y s i s of thermal s t r e s s e s , t a k i n g i n t o c o n s i d e r a t i o n e f f e c t s of changes i n modulus of e l a s t i c i t y , y i e l d s t r e s s and the c o e f f i c i e n t of l i n e a r expansion on the metal with temperature. At the i n s t a n t of welding, a l i m i t e d p o r t i o n of the p a r t s being j o i n e d such as the weld bead and the parent m a t e r i a l c l o s e to the hot face i s heated up to a very high temperature and t h e r e a f t e r c o o l e d down to room temperature. As t h i s thermal c y c l e proceeds, the temperature d i s t r i b u t i o n changes with time and the mechanical performance of the welded assembly i s a l s o a f u n c t i o n of temperature. It i s , t h e r e f o r e , imperative to assess the temperature d i s t r i b u t i o n d u r i n g welding. P e r t s o v s k i i et a l 2 6 have c a l c u l a t e d the thermal c y c l e i n the heat a f f e c t e d zone d u r i n g E l e c t r o s l a g Welding of t h i c k s t e e l p l a t e s and have r e a l i z e d that the nonuniform g e n e r a t i o n of heat in the l i q u i d pool and complex pool o u t l i n e , make i t extremely hard to study the heat flow d i s t r i b u t i o n at the boundary between s o l i d and l i q u i d phases. However, they have r e p l a c e d the above 9 mentioned complex volumes by a c o l l e c t i o n of three l i n e a r heat sources at d i f f e r e n t l e v e l s i n the pool f o r a s e m i - i n f i n i t e system. The r e s u l t s presented seem to agree w e l l with measured va l u e s and are a p p l i c a b l e to CGESW(Consumable Guide E l e c t r o s l a g Welding). More r e c e n t l y , B a c o n 2 3 s t u d i e d the heat flow i n both systems(wire and p l a t e e l e c t r o d e ) . High d e p o s i t i o n r a t e s , shallow s l a g depth requirements, smooth he a t i n g and c o o l i n g r a t e s and g r e a t e r degree of p e n e t r a t i o n are r e a l i z e d i n E l e c t r o s l a g J o i n i n g as compared to wire e l e c t r o d e welding. Temperature d i s t r i b u t i o n measurements and c a l c u l a t i o n s done f o r the present p r o j e c t followed the same trend found by B a c o n 2 3 and had s i m i l a r h e a t i n g and c o o l i n g r a t e s , r e s p e c t i v e l y 0.5 -2.0°C/s and 0.2 - 1.0°C/s.(See F i g . 3) 1.4 S o l i d i f i c a t i o n C racking Work developed both by Brown et a l 2 7 and by P h i l l i p s et a l 2 8 have i n d i c a t e d that p rovided the same s t r e s s f i e l d i s a p p l i c a b l e , E l e c t r o s l a g J o i n i n g should not be more or l e s s s u s c e p t i b l e to s o l i d i f i c a t i o n c r a c k i n g than c o n v e n t i o n a l welding. The c r i t i c a l welding speed which w i l l ensure a sound weld has been d e f i n e d by Semenov 2 9, t a k i n g i n t o account thermal s t r e s s e s and mainly the volume change duri n g m e t a l l u r g i c a l 10 t r a n s f o r m a t i o n s . The technique c o n s i s t s i n imposing a t e n s i l e s t r e s s on the s o l i d i f y i n g r e g ion of a f u l l y - c o n s t r a i n e d weld (which r e p r e s e n t s the worst c a s e ) . According to these authors, s t a b l e welding v o l t a g e assures the c o r r e c t p e n e t r a t i o n during the weld and together with the c r i t i c a l welding speed determine the proper shape f a c t o r ( r a t i o of the weld gap to the metal pool depth) f o r a sound weld. With i n c r e a s i n g heat input the depth of the metal pool i n c r e a s e s s h a r p l y , the shape f a c t o r v a r i e s and the tendency to form c r a c k s a l s o i n c r e a s e s . A c c o r d i n g to Makara et a l \" \" , an i n c r e a s e i n the weld v o l t a g e leads to improvement of the shape of the pool p r o f i l e and r e s u l t s i n crack tendency r e d u c t i o n . B e n d i s * 3 has concluded that the most c r i t i c a l p e r i o d d u r i n g E l e c t r o s l a g Welding i s when one-quarter to one-half of the j o i n t i s welded. The parameters that c o n t r o l the r e s i s t a n c e of the weld metal to hot c r a c k i n g as r e p o r t e d by P a t o n 3 5 are: chemical composition, r i g i d i t y of the welded j o i n t and the shape f a c t o r . Brown et a l 2 7 , however, found no cracks when a p p l y i n g the suggested welding c o n d i t i o n s given by Semenov et a l 2 9 and even d e l i b e r a t e l y a l t e r e d the Mn/S r a t i o to a value lower than the recommended minimum of 4 5 which a c c o r d i n g to E r i k s s o n et a l 3 0 should have r e s u l t e d i n s o l i d i f i c a t i o n c r a c k i n g . It i s , t h e r e f o r e , c l e a r that E l e c t r o s l a g Welding(wire e l e c t r o d e ) behaves q u i t e d i f f e r e n t l y with respect to s t r e s s b u i l d - u p as compared to E l e c t r o s l a g J o i n i n g ( p l a t e e l e c t r o d e ) The high heat input observed i n E l e c t r o s l a g Welding which keeps the s l a g pool i n the molten c o n d i t i o n can be very 11 e f f e c t i v e i n a v o i d i n g the uptake of hydrogen from moisture but i t i s known to enhance c o n d i t i o n s l e a d i n g to c r a c k s i n the welds. The p o s s i b i l i t y of s o l i d i f i c a t i o n c r a c k i n g ( h o t c r a c k s ) e x i s t s both i n the weld m e t a l ( s o l i d i f i c a t i o n c r a c k i n g ) and i n the heat a f f e c t e d z o n e d i q u a t i o n c r a c k i n g ) . 3 3 S t e e l s are known to f a i l i n a b r i t t l e manner at temperatures c l o s e to the m e l t i n g p o i n t and t h i s behaviour i s a s c r i b e d t o i n c i p i e n t m e l t i n g of s o l u t e r i c h r egions i n the s t e e l which r e s u l t s from g r a i n boundary segregation or m i c r o s e g r e g a t i o n d u r i n g s o l i d i f i c a t i o n . \" 6 For continuous c a s t i n g s t e e l s with 0.25% to 1.0% C the b r i t t l e range s t a r t s at 40°C below the s o l i d u s temperature as reported by Weinberg.\" 2 When the deformations i n t h i s temperature range exceed the deformation c a p a c i t y of the metal a hot tear d e v e l o p s . 3 3 Lower me l t i n g p o i n t secondary phases such as s u l p h i d e s and oxides at the heat a f f e c t e d zone at the g r a i n boundaries fuse l o c a l l y and produce a weaker bonding that f a i l s under the e f f e c t of shrinkage s t r e s s e s c a using what i s known as l i q u a t i o n c r a c k i n g . In both cases, however, rupture of the metal occurs i n an i n t e r g r a n u l a r form, c o n t r a s t i n g with t y p i c a l lower temperature, i n t r a c r y s t a l l i n e path c o l d c r a c k s , r e s u l t i n g mainly from hydrogen e m b r i t t l e m e n t . \" 8 Rymkevich et a l 3 2 have pursued the d e t e r m i n a t i o n of the b r i t t l e temperature range i n E l e c t r o s l a g Welding of carbon s t e e l s and found i t to be 1380-1450°C. 1 2 1.5 Present O b j e c t i v e s As d e s c r i b e d above, c o n d i t i o n s i n the welds l e a d i n g to cra c k s are r e a l i z e d i n the process d e s p i t e the improvements experienced by a higher heat input and s u i t a b l e welding f l u x i n the p l a t e e l e c t r o d e technique. An understanding of the nature and extent of s o l i d i f i c a t i o n c r a c k i n g and, t h e r e f o r e , of the proper welding c o n d i t i o n s has prompted the need f o r f u r t h e r s t u d i e s of the thermal s t r e s s e s produced i n the p r o c e s s . 13 I I . MATHEMATICAL MODELING The inherent d i f f i c u l t i e s a s s o c i a t e d with performing experimental work, e s p e c i a l l y i n the case of s t r e s s d e t e r m i n a t i o n i n welds, make i t a l l the more i n t e r e s t i n g to use a model i n order to study how the process behaves. The f o l l o w i n g pages c o n t a i n the development of a computer program which was used to c a l c u l a t e the thermal s t r e s s e s r e a l i z e d d u r i n g the E l e c t r o s l a g J o i n i n g of t h i c k b l o c k s , based upon a temperature p r o f i l e i n p u t . Weld c r a c k i n g i n E l e c t r o s l a g J o i n i n g appears to be caused by thermal s t r e s s - f i e l d induced by nonuniform temperature changes. I t i s e s s e n t i a l l y a q u e s t i o n of how much heat flows through the p l a t e s being j o i n e d . Although r a d i a t i o n and conve c t i o n take p l a c e while E l e c t r o s l a g J o i n i n g , conduction i s the dominant heat t r a n s f e r mode i n the bl o c k s , except d u r i n g hot topping when r a d i a t i o n and c o n v e c t i o n s t a r t p l a y i n g a more s i g n i f i c a n t r o l e . According to L i b y et a l . 3 \" two aspects of heat flow need to be c o n s i d e r e d : heat generation i n the s l a g and heat conduction through the parent b l o c k s . The former i s assign e d a me l t i n g p o i n t temperature as the s t a r t i n g value f o r c a l c u l a t i o n s i n the f i r s t time step of the model and from the second time step on, 1 4 i t i s c a l c u l a t e d f o r every time step, t a k i n g i n t o c o n s i d e r a t i o n the e l e c t r o d e l a t e n t heat, heat c o n d u c t i v i t y and d e n s i t y . The l a t t e r w i l l c o n s t i t u t e the u n d e r l y i n g p r i n c i p l e based upon which the temperature d i s t r i b u t i o n w i l l be determined. 2.1 Temperature D i s t r i b u t i o n C a l c u l a t i o n 2.1.1 Assumpt ions The general heat conduction F o u r i e r equation i n two dimensions i s thought to d e s c r i b e the phenomena i n v o l v e d and i s used to c a l c u l a t e the thermal p r o f i l e s . In order to so l v e i t , s e v e r a l assumptions had to be made so that the boundary c o n d i t i o n s c o u l d be p r o p e r l y a p p l i e d : ( S e e F i g . 4 and F i g . 5) i ) No-flux boundary c o n d i t i o n at the top of the s l a g . According to P a t o n 3 5 only 1.3% of the t o t a l heat i s r a d i a t e d to the s u r f a c e s and 1.2% i s a c t u a l l y l o s t throught r a d i a t i o n to the atmosphere. i i ) Symmetry a x i s — because the welding process i s symmetrical, a no-f l u x boundary c o n d i t i o n i s thought to be a v a l i d assumption. i i i ) Block w a l l s -- the i n t e r n a l w a l l s were a l s o assumed a 1 5 n o - f l u x c o n d i t i o n as the heat r a d i a t i o n mentioned i n i ) i s n e g l i g i b l e . i v ) A l l the heat reaching the slag-metal i n t e r f a c e leaves i t and flows to the blocks being welded. v) P o s i t i o n s i n the block away from the hot f a c e ( f u s i o n l i n e ) are c o n s i d e r e d to be at room temperature and the temperature of the heat source (slag) to be the m e l t i n g p o i n t temperature f o r carbon steel(1520°C.) v i ) P h y s i c a l p r o p e r t i e s were c o n s i d e r e d to be constant and the e l e c t r o d e l a t e n t heat was taken i n t o c o n s i d e r a t i o n . Such an assumption i s not too f a r from r e a l i t y as the energy coming from the i d e a l i z e d heat source(slag+metal pool) a c t u a l l y reaches e l e c t r i c a l e q u i l i b r i u m i n l i g h t of the f a c t t h a t , i f the r i g h t volume of s l a g i s chosen, the welding equipment performing the weld operates i n a s t a b l e manner. Values f o r Cp, k and are l i s t e d i n Table I. v i i ) The heat s o u r c e ( s l a g + metal pool) t r a v e l s \" i n d e f i n i t e l y \" along the height of the block, although an unsteady s t a t e model was used to p r e d i c t the thermal p r o f i l e s . v i i i ) As i n the case of welding l a r g e assemblies, no heat flow in the z d i r e c t i o n i s assumed. ix) Symmetry i s invoked and the modelling i s b u i l t on one sid e of the j o i n i n g assembly as i l l u s t r a t e d i n F i g . 4. 16 2.1.2 D e r i v a t i o n Of E q u a t i o n s The two d i m e n s i o n a l heat c o n d u c t i o n e q u a t i o n 3 2T ^ 3 2T q P Cp 3_T ( 1 ) \" H ? + ~ ~ 3 ^ k k 3 t Where: T.= temperature t = time q = heat f l u x k = heat c o n d u c t i v i t y p = d e n s i t y Cp = s p e c i f i c heat L e t t i n g a =p Cp/k and knowing that t h e r e i s n e i t h e r h e a t g e n e r a t i o n nor consumption i n t h e b l o c k s ( q / k = 0 ) , e q u a t i o n (1) becomes: 3 2T f 3x' + 3 2T a 3T (2) 3y 3t 17 E q u a t i o n (2) i s s o l v e d n u m e r i c a l l y s u b j e c t e d t o d i f f e r e n t boundary c o n d i t i o n s ( S e e Appendix A ) . 2.1.3 N u m e r i c a l S o l u t i o n U s i n g a heat b a l a n c e approach f o r an i n t e r i o r node, the g o v e r n i n g e q u a t i o n was e x p r e s s e d in f i n i t e d i f f e r e n c e form as:(See F i g . 2) For 1 XX ZX S t r a i n C o m p o n e n t s : W h e r e NT i s t h e i n t e g r a l o f a E T d z f r o m - h t o +h a n d MT i s t h e i n t e g r a l o f a E T z d z f r o m - h t o +h T h e v a l u e s o f E ( Y o u n g ' s M o d u l u s ) w e r e c a l c u l a t e d a s a f u n c t i o n o f t e m p e r a t u r e a c c o r d i n g t o t h e e x p e r i m e n t a l r e s u l t s p u b l i s h e d by M i n a k a m i e t a l . 3 7 f o r c a r b o n s t e e l . T h e i n t e g r a l s w h i c h a p p e a r i n t h e a n a l y t i c a l e x p r e s s i o n a b o v e w e r e c a l c u l a t e d n u m e r i c a l l y a n d w e r e u s e d i n e q u a t i o n s ( 8 ) a n d ( 1 0 ) t o c a l c u l a t e t h e t h e r m a l s t r e s s e s i n t h e y - d i r e c t i o n f o r e a c h c o r r e s p o n d i n g n o d a l t e m p e r a t u r e t h u s , c o v e r i n g t h e e n t i r e h e i g h t b e i n g w e l d e d . 21 A sample of the computer program used to c a l c u l a t e the s t r e s s e s and s t r a i n s i s shown in Appendix B. 2.3 Computer Production Runs The thermal s t r e s s c a l c u l a t i o n s were performed f o r s e v e r a l welding c o n d i t i o n s ( d i f f e r e n t temperature d i s t r i b u t i o n s ) , a l l of which simulated r e a l j o i n i n g s . P r o v i s i o n s were made in the program to allow f o r changes i n the furnace parameters which would a f f e c t the f i n a l welded s t r e s s s t a t e . Thus, v a r y i n g the heat input namely amperage and v o l t a g e , produced a d i f f e r e n t welding speed which, i n t u r n , caused a d i f f e r e n t s t r e s s d i s t r i b u t i o n . Since the process i s very s t a b l e e l e c t r i c a l l y , the welding v e l o c i t y was c o n s i d e r e d to be constant throughout the model. The i n i t i a l temperature c o n d i t i o n s f o r the weld region i s r e p l a c e d every subsequent time step by a new temperature c a l c u l a t e d upon a heat balance performed at the f u s i o n boundary. Only a small amount of energy r e l e a s e d by the e l e c t r o d e m e l t i n g e f f e c t i v e l y goes i n t o the j o i n i n g b l o c k s . The e f f i c i e n c y f a c t o r F used to determine how much of the a v a i l a b l e incoming energy flows through the blocks gi v e s an i n d i c a t i o n of the thermal e f f i c i e n c y of the p r o c e s s . A massive heat e x t r a c t i o n i s performed by the copper and aluminum c o o l i n g shoes. T h i s very e f f i c i e n t heat sink absorbs 22 approximately 50% of the energy a v a i l a b l e and l i t t l e i s l o s t as r a d i a t i o n energy, except u n t i l the very end of the p r o c e s s . 23 I I I . EXPERIMENTAL WORK 3.1 Furnace Design The equipment used f o r a l l runs was the U B C E l e c t r o s l a g f a c i l i t y as shown in F i g . 8. T h i s u n i t can c a s t s t e e l up to 1 t i n weight and operates on AC. The furnace power supply i s a 250 KVA step-down transformer which i s connected to a 600 V primary s i n g l e phase l i n e . T h i s dry type transformer operates with a high v o l t a g e of 600 V and a low i n the range of 25-60 V, AC c u r r e n t of up to 8000 A. The e l e c t r o d e feeding system c o n s i s t s of a) an e l e c t r o d e holder c a r r i a g e which s l i d e s on aluminum r a i l s i n s i d e the furnace framework(Fig.8 ) and i s suspended from b) an e l e c t r o d e d r i v e c a r r i a g e coupled to a v a r i a b l e speed reductor that enables speeds from 0 to 163 mm/min. The o p e r a t i o n a l parameters are r e a d i l y monitored from s e v e r a l instruments i n a c o n t r o l p a n e l . More d e t a i l e d i n f o r m a t i o n on the furnace design i s given elsewhere. 3 9 3.2 C o o l i n g Shoe Design E l e c t r o s l a g J o i n i n g i s fundamentally s i m i l a r to E l e c t r o s l a g 24 Remelting.The r e a d i l y n o t i c e a b l e d i f f e r e n c e l i e s i n the remelted product: i n the j o i n i n g process the parent m a t e r i a l i s pa r t of the heat e x t r a c t i o n system w h i l s t i n p l a i n r e m e l t i n g the product i s completely surrounded by water-cooled copper c r u c i b l e s . Heat flows by conduction through the blocks and a s u b s t a n t i a l p o r t i o n i s e x t r a c t e d v i a the c o o l i n g shoes. T h e r e f o r e , t h i s p a r t of the set-up p l a y s a s i g n i f i c a n t r o l e i n c o n t r o l l i n g the d i r e c t i o n a l s o l i d i f i c a t i o n . The design used f e a t u r e s r e c t a n g u l a r aluminum s l a b s 25.4 mm X 254 mm X 1066.8 mm(1\"X10\"X42\"), with three 11 mm deep c o o l i n g groves(channels) per shoe on the outer aluminum s e c t i o n ( S e e F i g . 9 ) copper and which was coupled to the inner copper s l a b ( F i g . 10).This recess in the copper p a r t i n c r e a s e s the su r f a c e area c o n t a c t and enables proper p o s i t i o n i n g of the e l e c t r o d e . C o n s i d e r i n g that the copper has a higher heat c o n d u c t i v i t y , i t r e s u l t e d i n a rather e f f i c i e n t heat removal, thus ensuring proper c o o l i n g and good wear r e s i s t a n c e . F i g 12 and 13 show the shoes i n p l a c e and a cl o s e - u p . The water enter s through the bottom, c i r c u l a t e s through the channels and leaves through the top. 3.3 E l e c t r o d e And Slag P r e p a r a t i o n The e l e c t r o d e ( i . e . , the f i l l e r metal) i n E l e c t r o s l a g J o i n i n g has the same composition(whenever p o s s i b l e even from the 25 same s t e e l shop run) as the parent m a t e r i a l b e i n g welded. T h i s a s s u r e s c h e m i c a l homogeneity and weld r e p e a t a b i l i t y . 8 The commercial carbon s t e e l used f o r both t h e f i l l e r and p a r e n t m a t e r i a l was ASTM A36 whose compo s i t i o n i s : C=0.29% Mn=0.90% Si=0.15% P=0.04% S=0.05% A t y p i c a l e l e c t r o d e s e c t i o n would be two 152.0 mm(6\") X 19 mm(3/ 4\") X 2930 mm(115\" ) , 3 8 mm t h i c k , as i l l u s t r a t e d i n F i g s . 14 and 15. It i s c o n n e c t e d t o a water-c o o l e d s t u b t h a t i s p e r f e c t l y a l i g n e d w i t h t h e f u r n a c e frame. ( F i g . 16) A s m a l l rod 25 mm(l\") i n d i a m e t e r and 152.4 mm(6\") long i s welded t o the bottom o f the e l e c t r o d e so as to have a f a s t e r weld s t a r t . Two 152 mm X 457 mm X 914 mm p l a t e s w e i g h i n g a p p r o x i m a t e l y 500 kg each were used i n the experiments. The w e l d i n g f l u x used was of c o m p o s i t i o n : 55F/15/15/15, i . e . , CaF 2 =55% Ca0=l5% 0.-15% S i 0 2 = l 5 % (% i n weight) and p r e - h e a t e d at a temperature of about 600°C i n o r d e r t o 26 a v o i d any moisture r e t e n t i o n . A t o t a l of 7.0 kg per weld was enough to maintain s t a b l e welding c o n d i t i o n s . 3.4 Weld Set-up And C o n s t r a i n i n g A l l the weld p r e p a r a t i o n was done on a movable c o l o r l i t h p l a t f o r m that s l i d e s on a m o n o r a i l ( F i g . 8). A p r o t e c t i v e l a y e r of asbestos i s put on top of the c o l o r l i t h where the s t a r t e r p l a t e s are p o s i t i o n e d . In order to ensure proper weld p e n e t r a t i o n s i n c e the s t a r t of the weld and a l s o to make set-up and s t r i p p i n g o p e r a t i o n s more e f f i c i e n t , r u n - i n water-cooled copper sumps, as shown i n F i g . 17 were used. At the top of the blocks c l o s e to the weld, 76.2 mm(3\") run-out sumps were tack-welded to extend the block height and thus, accommodate the s l a g volume past the j o i n i n g s e c t i o n s . The c o o l i n g shoes are h e l d i n p o s i t i o n by braces which are ti g h t e n e d on to b o l t s welded onto the b l o c k s ( F i g . 1 2 ) . The blocks were set 100 mm apart(which i s the recess length) ( F i g . 11). An a i r s e t t i n g high temperature mortar(SAIRSET) i s spread along the shoe s i d e s touching the blocks to provide a safe s e a l i n g a g a i n s t any p o s s i b l e s l a g and/or metal leakage. When t h i s was completed the assembly was ready to be pl a c e d in the welding p o s i t i o n . At t h i s stage the e l e c t r o d e was i n s e r t e d in the weld gap using the overhead crane, a l i g n e d and t i g h t e n e d 27 to the stub. When a weld i s f u l l y - c o n s t r a i n e d and no c r a c k i n g i s observed, i t may be a good i n d i c a t i o n that the weld can accommodate c o n t r a c t i o n movements and w i l l l i k e l y be a sound one. T h e r e f o r e , c o n s t r a i n e d set-ups were prepared so as to produce a weld crack. I n i t i a l l y an I-beam with I ( i n e r t i a moment) of approximately 23 i n \" was thought to be strong enough to stand up to the pressures i n the system and was p o s i t i o n e d at the top of the b l o c k s . A s t u r d i e r I-beam was needed and i t was prepared so as to have an i n e r t i a moment of 126 i n \" , as shown i n F i g . 20. The weld on the I-beam d i d f a i l as the set up became r i g i d and the s t r a i n gauges were unable to r e c o r d the a c t u a l s t r a i n undergone by the weld metal.(See F i g . 19) At t h i s stage i t was r e a l i z e d that as the weld went on the system(blocks being j o i n e d + weld region) became more r i g i d below the welding p o i n t ( m e t a l p o o l ) , to an extent that the welded I-beams c o u l d not take the pressure and, t h e r e f o r e , d i d not p r o p e r l y c o n s t r a i n the weld. I t was then thought t h a t i f the c o n s t r a i n i n g rods were p l a c e d at the bottom a lower system s t i f f n e s s would be e f f e c t e d thus, e n a b l i n g a stronger c o n s t r a i n i n g c a p a b i l i t y which would r e s u l t i n a weld c r a c k . The I-beams were arc welded on to the ends of the blocks away from the hot face, i n i t i a l l y at the top and l a t e r at the bottom. A rod 76.2 mm(3\") i n diameter, 965.2 mm(38\") i n len g t h and s l i g h t l y tapered o f f at the ends was p o s i t i o n e d i n f r e e compression r e s t r a i n i n g the p a r t s from c l o s i n g in(See F i g . 18). F i g . 20 and F i g . 21 show the boxed I-28 beam with i n c r e a s e d i n e r t i a moment and the hardened 4340 d i s c spacer to a v o i d any l o c a l i z e d deformation. The strain-gauges were set on both c o n s t r a i n i n g rods and monitored by a T r a n s d u c e r / S t r a i n I n d i c a t o r 8-channel STRAINSERT - Model TN8C. For c o r r e c t measurements a gauge f a c t o r was used and the apparatus was operated i n f u l l b ridge mode. F i g . 22 presents the same set-up d e s c r i b e d above except f o r the f a c t t h at the c o n s t r a i n i n g rods were p o s i t i o n e d at the bottom. T h i s way, the same c o n s t r a i n i n g r i g i d i t y would be experienced w h i l s t the assembly s t i f n e s s would not be as l a r g e as when the rods were pl a c e d at the top and, t h e r e f o r e , the rod s t r e n g t h would be comparable to the weld s t r e n g t h . Once the s t r a i n s are known, the s t r e s s e s can be c a l c u l a t e d as the rods remain in the e l a s t i c r e g i o n . 3.5 Sequence of Operation - Welding Procedure A f t e r the e l e c t r o d e i s p r o p e r l y a l i g n e d , a mixture of c a l c i u m f l u o r i d e and s t e e l shavings(the 'compact') i s p o s i t i o n e d on top of the s t a r t e r p l a t e and under the e l e c t r o d e t i p ; the 29 c o o l i n g system i s checked f o r leaks and the pre-heated f l u x i s poured i n t o the gap. I n i t i a l l y an arc i s s t r u c k and the small 25 mm diameter rod i s r e a d i l y melted. At t h i s stage,some of the f l u x s t a r t s to melt and soon the volume of s l a g i s such that no more a r c i n g occurs and heat i s generated by s l a g r e s i s t a n c e o n l y . Table II shows the furnace parameters f o r a t y p i c a l E l e c t r o s l a g J o i n i n g experimental run. Aluminum d e o x i d a t i o n was e f f e c t e d throughout a l l the runs at a r a t e of 1 g/min.(See F i g . 15) 3.6 R e s i d u a l S t r e s s A f t e r the weld was. c o o l e d down to room temperature, r e s i d u a l s t r e s s measurements were performed at the top of the assembly i n the parent metal, i n the heat a f f e c t e d zone and i n the weld. The equipment used was s u p p l i e d by P h o t o l a s t i c Inc., and the r e s u l t s were a r r i v e d at by using the B l i n d Hole D r i l l i n g M ethod.\" 5Fig. 23 shows the schematic s t r a i n gauge set-up. 3.7 Temperature Measurements Chromel-alumel thermocouples were p l a c e d i n the block to measure temperatures i n order to compare them with the 30 model.(Fig. 3) The r e s u l t s obtained as w e l l as the p e n e t r a t i o n depth p r e d i c t e d agreed w e l l with the observed v a l u e s . 31 IV. DISCUSSION AND RESULTS The Russian and Czech work developed i n E l e c t r o s l a g Welding(wire e l e c t r o d e ) had i n d i c a t e d that hot cra c k s were, a s s o c i a t e d mostly with the weld chemical composition l e a d i n g to t r a n s f o r m a t i o n a l volume changes which would cause d e f e c t s and tha t there e x i s t e d a c r i t i c a l height range wherein c r a c k s were more prone to appear. In t h e i r work i t was never made c l e a r whether the thermal s t r e s s f i e l d had been f u l l y understood or even i n v e s t i g a t e d . The magnitude of the s t r e s s f i e l d s i n ESJ was not d e f i n e d and even i n a q u a l i t a t i v e sense was not known. The f i r s t attempts to study thermal s t r e s s e s d u r i n g p l a t e e l e c t r o d e welding in t h i s work, r e v e a l e d that a great amount of the s t r e s s was being r e l a x e d as the heat source t r a v e l l e d along the weld h e i g h t . The l a r g e heat input(1.7 kW/cm), t y p i c a l of t h i s process, c r e a t e s a ra t h e r broad temperature f i e l d ( h e a t a f f e c t e d zone) capable of absorbing the high s t r e s s e s that develop. F u r t h e r experimentation confirmed the i n a b i l i t y of the I-beams and rods to e f f e c t i v e l y c o n s t r a i n the bl o c k s at the top and the f a c t that the thermal f i e l d was accommodating the deformations. A much s h o r t e r weld was made with the c o n s t r a i n i n g rods p o s i t i o n e d a t the bottom. The p r o p o s a l was t h a t , as mentioned above, the weld s t r e n g t h at a smal l e r height i n terms of weld 3 2 c r o s s - s e c t i o n a l area would be comparable to the area of the rods and, t h e r e f o r e , the l a t t e r would be able to take up the weld s t r e s s e s . I t was found that even a f t e r that procedure the weld d i d not present any c r a c k s , the thermal f i e l d having presumably r e l a x e d them even i n a true f u l l y - c o n s t r a i n e d weld. Both w e l d s ( c o n s t r a i n e d at the top and at the bottom) were thoroughly t e s t e d u l t r a s o n i c a l l y and no cr a c k s were found. A f t e r that they were sent out to be i n s p e c t e d by radiography. The p i e c e s were exposed to Co-60 r a d i a t i o n f o r approximately 15 hours and again no i n d i c a t i o n of c r a c k s was found. The thermal s t r e s s e s p r e d i c t e d by the model and c a l c u l a t e d fo r s e v e r a l welding c o n d i t i o n s were c o n s i s t e n t with experimental o b s e r v a t i o n . In F i g . 24 the c o n d i t i o n s set f o r the computer run were the same as the ones undergone by the a c t u a l j o i n i n g experiment. I t i s noted that d u r i n g most part of the weld the r e s u l t i n g thermal s t r e s s e s f o r d i f f e r e n t d i s t a n c e s away from the block hot face are t e n s i l e i n nature. When the l i q u i d pool approached the end, new boundary c o n d i t i o n s were imposed to account for r a d i a t i o n and c o n v e c t i o n whereupon compressive s t r e s s e s s t a r t to appear, subsequently, i n d u c i n g t e n s i l e s t r e s s e s underneath the l i q u i d pool where metal i s s o l i d i f y i n g . I f those compressive s t r e s s e s are higher than the m a t e r i a l y i e l d s t r e n g t h , then they should induce the high t e n s i l e s t r e s s e s that would l e a d to c r a c k s . 33 In order to i n v e s t i g a t e f u r t h e r the r e s u l t s above, a run with i d e n t i c a l welding c o n d i t i o n s ( e x c e p t f o r the weld height which was doubled up) was t r i e d and the same t r e n d was again observed.(See F i g . 25). In other words, should the computed values f o r the s t r e s s e s at the end of of the weld be exc e e d i n g l y high f o r a p a r t i c u l a r set of welding c o n d i t i o n s then, by a d j u s t i n g the l a t t e r a l e s s severe s t r e s s f i e l d would r e s u l t which, i n t u r n , provided enough p e n e t r a t i o n i s e f f e c t e d , c o u l d in p r i n c i p l e i n d i c a t e the optimum welding c o n d i t i o n s to produce a c r a c k - f r e e weld. The r e s i d u a l s t r e s s e s remaining i n the system a f t e r c o o l i n g to room temperature were measured and found to show t e n s i l e s t r e s s e s develop during or a f t e r welding. The r e s i d u a l s t r e s s e s in a l l three p o s i t i o n s ( p a r e n t metal, heat a f f e c t e d zone and weld metal) were t e n s i l e and below the m a t e r i a l y i e l d p o i n t . See Appendix D. Based on the modelling r e s u l t s and on the a c t u a l experiments performed, i t i s p o s s i b l e to say that the c h a r a c t e r i s t i c broad thermal f i e l d of E l e c t r o s l a g J o i n i n g i n the p a r t s being j o i n e d enhances thermal s t r e s s e s i n the weld(as w e l l as i n the heat a f f e c t e d zone) which are r e l a x e d by the thermal f i e l d to a c o n s i d e r a b l e extent as the weld p r o g r e s s e s . 34 These f i n d i n g s seem to c o n t r a d i c t the r e s u l t s presented by the Czech l i t e r a t u r e on E l e c t r o s l a g Welding c r a c k s . I t has been observed and p r e d i c t e d that the c r a c k s i n E l e c t r o s l a g J o i n i n g , i f at a l l present, w i l l always occur at the top of the j o i n t when compressive s t r e s s e s s t a r t mounting due to thermal c o n t r a c t i o n , wherever the top may be. If the Czech/Russian approach to p r e d i c t i n g hot c r a c k i n g were to be followed, then a s t e e l which transforms at high temperatures would have c r a c k s when a s t e e l of low tr a n s f o r m a t i o n temperature would not. These workers have p r e d i c t e d that h i g h a l l o y grades such as Ni-Cr-Mo-V f o r g i n g s do not crack when carbon s t e e l s do. I f so, the s t e e l used f o r the present study should have r e s u l t e d i n s o l i d i f i c a t i o n c r a c k i n g once i t i s a l r e a d y a 'good' crack-former i n terms of tr a n s f o r m a t i o n volume changes. 35 V. CONCLUSIONS 1) C o n s i d e r i n g the t h e o r e t i c a l c a l c u l a t i o n s and experimental evidence, i t can be s a i d that E l e c t r o s l a g Welding and E l e c t r o s l a g J o i n i n g d i f f e r q u i t e s i g n i f i c a n t l y as to the thermal s t r e s s b u i l d - u p and hot cracky tendency. I t i s c l e a r that the d i s s i m i l a r thermal p r o f i l e s experienced i n each of these processes r e s u l t in d i f f e r e n t s t r e s s f i e l d s . The r e s u l t i n g crack formation tendency i s t h e r e f o r e q u i t e d i f f e r e n t . 2 ) The r e s i d u a l s t r e s s measurement confirms the r e s u l t s p r e d i c t e d by the model and observed e x p e r i m e n t a l l y . The r e s i d u a l s t r e s s values are below the weld y i e l d s t r e n g t h l e v e l and, t h e r e f o r e , no c r a c k s were d e t e c t e d i n ESJ under c o n d i t i o n s which would have produced c r a c k s i n ESW. 3) E l e c t r o s l a g J o i n i n g i s more a p p l i c a b l e to the welding of heavy gauge f o r g i n g s than E l e c t r o s l a g Welding due to i t s i n t r i n s i c f e a t u r e s . I t should probably be regarded more as a shop f a b r i c a t i o n technique than as a f i e l d welding process. 4 ) A simple mathematical model was developed which enables the s e m i - q u a n t i t a t i v e v i s u a l i s a t i o n of the thermal and s t r e s s trends r e a l i z e d d u r i n g welding 5) The t h e o r e t i c a l p r e d i c t i o n s can be used when a s s e s s i n g the a p p l i c a t i o n of t h i s heavy t h i c k n e s s j o i n i n g method. 36 VI. SUGGESTIONS FOR FUTURE WORK 1) Produce a weld having a narrow thermal f i e l d , i . e . , a narrow weld gap, using wire e l e c t r o d e with narrow consumable guide i n order to v e r i f y the thermal s t r e s s f i e l d approach to e x p l a i n i n g hot c r a c k s i n t h i s kind of weld. 2) Use higher a l l o y s t e e l s having d i f f e r e n t lower t r a n s f o r m a t i o n temperatures under the same c o n d i t i o n s c i t e d i n 1) t o check on the i n f l u e n c e of volume change i n crack forming tendency. 3) Develop a more s o p h i s t i c a t e d mathematical model i n order to be able to a r r i v e at more accurate values when e v a l u a t i n g s t r e s s e s . Such.an approach would i n v o l v e a lengthy and complex f i n i t e element thermal s t r e s s a n a l y s i s coupled with experimental support i n r e l a t i o n to the boundary c o n d i t i o n s . 37 BIBLIOGRAPHY 1. 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L., \"Modeling of C a s t i n g and Welding Processes\", Conference Proceedings, The Met. Soc. of AIME, Rindge, NH, Aug. 1980, p. 161-196 39 35. Paton, B. E., \" E l e c t r o s l a g Welding\", A W S, N. Y., 1962 36. Carnahan, B.; Luther, H. A. and Wilkes, J . 0., \" A p p l i e d Numerical Methods\", John Wiley & Sons, 1969 37. Minakami, H. et al.,Tetsu-to-Hagane, v o l . 63, 1973, s562 38. Boley, A. and Weiner, J . H., \"Theory of Thermal S t r e s s e s \" , John Wiley & sons, Inc., 1960 39. S i d l a , G. and M i t c h e l l , A., \"The Design, C o n s t r u c t i o n and Operation of an ESC I n s t a l l a t i o n \" , S p e c i a l Report to DREP/DSS, Vancouver, BC, June 1980 40. F r o s t , R. H. et a l . , Weld. J . , Jan. 1981, p. 1s-6s 41. Mosny, J . and Slabon, I., Proceedings of an I n t e r n a t i o n a l Conference on Welding Research r e l a t e d to Power P l a n t , U. of Southampton, England, Sept. 1972, p. 456-463 42. Weinberg, F., Met.- Trans. B, v o l . 10B, June 1979, p. 219-227 43. Bendis, A., Zvaranie, v o l . 16, (10), 1967, p. 365-370 44. Makara, A. M.; G o t a l ' s k i i , Yu. and Nuvikov, I. V., Avt. Svarka, v o l . 8, (4), 1955, p. 3-12 45. Redner, S., \"Measurement of R e s i d u a l S t r e s s e s by B l i n d Hole D r i l l i n g Method\", B u l l e t i n TDG-5, P h o t o l a s t i c Inc., May 1974 46. Weinberg, F., Met. Trans. B, v o l . 10B, Dec. 1979, p. 513-522 47. Paton, B. E. et al.., Proceedings of a Conference on ESR, The ISI , U. of S h e f f i e l d , Jan. 1973, p. 105-112 48. G r a v i l l e , B. A., \"The P r i n c i p l e s of Cold C r a c k i n g C o n t r o l i n Welds\", Dominion Bridge Company, L t d . , Montreal, 1975 40 T a b l e I - C o m p u t e r M o d e l P a r a m e t e r s T M P * 1 5 2 0 . 0 ( D e g C ) I N I T I A L T E M P - 2 5 . 0 ( D e g C) T I M E S T E P = 3 0 . 0 ( s ) S P E C I F I C H E A T = 0 . 1 0 7 0 ( c a l / g . C ) D E N S I T Y - 7 . 8 6 0 ( g / c m * * 3 ) C O N D U C T I V I T Y * 0 . 0 7 4 0 ( c a l / c m . s . C ) D X = 2 . 0 ( c m ) H E A T F A C T O R * 0 . 1 4 2 H E A T S O U R C E D E P T H = 1 2 . 0 0 0 ( c m ) P R I N T C Y C L E - 6 0 0 . 0 ( s ) E N D O F C A L C U L A T I O N * 4 2 0 0 . 0 ( s ) D Y = 0 . 5 1 . 0 1 . 0 1 . 0 1 . 0 1 . 0 3 . 0 3 . 0 3 . 0 3 . 0 D Y = 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 D Y = 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 3 . 0 N U M B E R O F D I V I S I O N S I N X - D I R E C T I O N = 5 0 N U M B E R O F D I V I S I O N S I N Y - D I R E C T I O N = 3 0 W E L D I N G P A R A M E T E R S : W E L D G A P * 9 . 5 c m T H I C K N E S S = 1 5 . 0 c m C U R R E N T * 5 0 0 0 . 0 A V O L T A G E * 3 3 . 0 V E L E C T R O D E S U R F A C E A R E A * 5 7 . 9 ( c m * * 2 ) W E L D G A P A R E A * 1 5 4 . 8 ( c m * * 2 ) L A T E N T H E A T * 6 5 . 0 ( c a l / g ) H O T T O P P I N G T I M E = 3 9 9 0 . 0 ( S ) A I R T E M P E R A T U R E = 3 0 . 0 ( D E G C ) H O T T O P C U R R E N T * 5 0 0 0 . O A H O T T O P V O L T A G E * 3 3 . 0 V W E L D I N G V E L O C I T Y * 0 . 0 2 3 ( c m / s ) 41 Table I I - ESJ T y p i c a l Log Sheet Time NMT Prim Sec V o l t MS WT (s) \" (A) (A) (V) (rps) (Deg. ' 300 1468 320 4800 34 19 1 1 .0 500 2118 330 5000 34 19 11.5 700 2881 330 5000 34 20 11 .5 1 000 4042 330 5000 34 21 11.5 1 400 5631 330 5000 34 21 11.5 1700 6839 340 5100 33 21 12.0 2200 • 8847 340 5000 34 21 13.0 2400 9672 330 4900 33 21 13.0 2700 1 0987 340 5000 33 21 13.0 3000 1 2275 340 5000 33 21 13.0 3400 1 4058 330 4900 33 21 13.0 3700 1 5451 330 4900 33 21 13.0 4000 16805 310 4700 34 21 13.0 NMT = Number of Motor Turns MS = Motor Speed WT = Water Temperature \\ 42 movement water-cooled shoes B 250 KVA F i g u r e 1 - Schematic Layout of ESJ Equipment 43 fusion line zone 2 fusion line Type I Type II zone 1 zone 2 zone 3 fusion line zone 1 fusion line Type Type IV F i g u r e 2 - E l e c t r o s l a g T y p i c a l Weld S t r u c t u r e ( R e f . 35) \\ 44 F i g u r e 3 - ESJ Thermal P r o f i l e - C a l c u l a t e d and Measured 45 run-in t a b ^ ^ F i g u r e 4 - B o u n d a r y C o n d i t i o n s 46 Boundary III Boundary V Boundary II-Heat Source, (slag) x (i) y(j) Boundary VIII IM. IN • \\ \\ \\ \\ \\ W \\ \\ \\ \\ • '//////; V/////-//////> • '/////* • • V////S • •Ti +1 •j • '/////> T.,j-1 .Ti.j •Ti.j+1 '/////A • •THj '////// • •TAX VMM Arf AYj« V////A //////, \\ ^ \\ \\ \\ ^ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ V Boundary I U N Boundary VI Boundary IV F i g u r e 5 - Nodal Arrangement 47 f S T A R T ) SUB ROUTINE 0 INPUT SUBROUTINE INITL SUBROUTINE V E L SUBROUTINE CONST t = t + A t SUBROUTINE S N D S SUBROUTINE HEAT SUBROUTINE PRINT TB(I.J) =T(I.J) SUBROUTME] S T R E S S SUBROUTINE F S T S ^ R E S U L T S ^ / SUBROUTINE S N D S Q E N D ) F i g u r e 6 - Model Flowchart 48 L 2 x L. 2 I 1 TH F i g u r e 7 - S t r e s s A n a l y s i s Schematic Diagram 4 9 F i g u r e 8 - UBC E l e c t r o s l a g U n i t 50 86.5 mm. F i g u r e 9 - C o o l i n g Shoe - Water Channels 51 Copper A l u m i n u m F i g u r e 10 - C o o l i n g S h o e T o p V i e w 77 mm. 100mm. 25.£mm. BnomV - N 0 5 2 3 * / 77 mm. 86.5 mm. 81 mm. 86.5 mm. 254 mm. F i g u r e 11 - Copper r e c e s s F i g u r e 12 - C o o l i n g Shoes in P o s i t i o n F i g u r e 13 - C o o l i n g Shoe Close-up - Water connections 5 5 F i g u r e 14 - P l a t e E l e c t r o d e i n P o s i t i o n F i g u r e 15 - Aluminum Feeder 5 7 F i g u r e 16 - E l e c t r o d e and Copper Stub Figure 17 - Run-in Copper Tabs 59 60 0 60.8 121.6 1324 243.2 304 364.8 TIME , min. F i g u r e 19 - S t r a i n versus Time P l o t 61 Fi g u r e 20 - Boxed I-Beam 62 F i g u r e 21 - Hardened 4340 Disc Spacer 6 3 F i g u r e 2 2 - I n f e r i o r I-beam Placement 64 strain gauge 914 mm F i g u r e 2 3 - S t r a i n - g a u g e S e t - u p 6 5 300 240 nG 180 r : 120 Q. 60 CO LU rr 0 175 -60 rr x -120 -180 -240 h -300 1 1 1 1 1 1 1 1 — ELECTROSLAG JOINING Time = 4200 s Distance from hot face = 0.5 / 1.5 / 3.5 cm. Voltage = 33 V Current = 5000 A 0 . 5 1 . 5 3 . 5 J 1 1 i_ J 1 • 0 33.6 672 100.8 134.4 168 201.6 2352 268.8 3024 336 369.6 403.2 TIME . s ( 1 x io1) F i g u r e 24 - Thermal S t r e s s Curve 66 300 240 180 00 •_ 120 o X 60 CO 0 CO LU rr . t— -60 CO _ l < -120 cc LU X -180 1— -240 -300 ~l 1 1 I ELECTROSLAG JOINING Time = 8400 s Distance from hot face =0.5 cm. Voltage = 33 V Current = 5000 A Weld height = 193 cm. 0.5 0 672 134.4 201.6 268B 336 403.2 470.4 5376 604.8 672 739.2 806-4 TIME , s (1 x 10 1) F i g u r e 25 - Thermal S t r e s s Curve 6 7 ELECTROSLAG JOINING weld height = 96 cm. Welding conditions : voltage = 33 v current = 5000 A welding speed = 0.023 c m / s 64 128 192 256 320 384 448 512 576 640 704 768 DISTANCE FROM HOT FACE (mm.) F i g u r e 2 6 - E S J T h e r m a l G r a d i e n t 4 6 8 APPENDIX.A - BOUNDARY CONDITIONS BOUNDARY I ( i = l , j = l ) i ) I f e l e m e n t I c o n t a c t s t h e h e a t s o u r c e : 1 S t ^ T 1 , 1 = TMI 2 n d - A | i i ) I f e l e m e n t I d o e s n o t c o n t a c t t h e h e a t s o u r c e , t h e f o l l o w i n g e q u a t i o n c a n b e o b t a i n e d b y a p p l y i n g a h e a t b a l a n c e : * n 1 s t A t A y A x C p p ^ l , ! \" T l , l ) _ k A y _ l ( T * - T* ) + 2 2 A t ~ x Z , X i ' i 2 k A x + 2 2 \" T* ) o r / 2 2 . * 2ou T* 2 Tlf: a _ n n ( A T + A x ^ ) T l , r ^ ' A t 1 , 1 + A y i(A y ; L+Ap ) t T l , 2 ~ T l , l } n+1 * CT - T ^ kAv * * 2nd A t Ay A x C p p v 1 , 1 1,1 yl (T - T ) + 2 1 2 A t \" A x Z y ± 1 , 1 k A x . i j_i + ~ 2 ( T n + 1 - T D + 1 ) 1 2 1 l ' Ay +Ay2 X \" L 2 o r a T n + 1 2 ) T n + 1 _ 1 » 2 - 2 * 2 a * * ^At + A y i ( A y i + A y 2 ) ; A l , l ^ ( A y ^ A y p A t ^ . l & 2 U 2 , r i , l J 69 BOTNDARY_II ( i=2-IM-l, j=1) i ) I f element I I c o n t a c t s the heat source: 1st At T * ) 1 = 2 n d ^ T t l = T M F i i ) I f element I I does not contact the heat source, the f o l l o w i n g equation can be obtained by a p p l y i n g a heat balanc e : ( T l r T i , i } k A y i , * * * 1st A^ Ay^xpCp • ^ = - - ( T . ^ ^ ^ ^ ^ ^ T . ^ ) 2 • kAx n n . y l y 2 1 , 2 1 ' 1 * 2 2 * a T* 2 T n + ^—2\" 1-1,1 At A x z / i , l Ax^ ' At ( T ? , - T ° ) + A y ^ A y ^ A y ^ 1 ' i n+1 * 9 ( T i l ~ T i 1> k A y l * •2nd At Ay A x p C p — ± * ± — — = A (T..,+,T. , r 2 T . . ) — Jl r At Ax x+1,1 1-1,1 i , j 2 A y l + A y 2 or , 2 a \\ T n + 1 2 r n + 1 = 2 T * + g „ f T * 4.T* 9T*S 1 At +' A y i ( A y i + A y 2 ) ; T i , l \" Ay 1 ( A y 1 + A y 2 ) \" , 1 l , 2 \" S P i , ! 1 \" A ^ T i 4 a , l ^ i ^ i ; i 2 T i J l 7 0 BOUNDARY I I I ( i = I M , j = l ) i ) I f e l e m e n t I I I c o n t a c t s t h e h e a t s o u r c e : 1 S t ^ V l = T M P 2 2 n d A t T m ; i = T M i i i ) I f e l e m e n t I I I d o e s n o t c o n t a c t t h e h e a t s o u r c e , t h e f o l l o w i n g e q u a t i o n c a n b e o b t a i n e d b y a p p l y i n g a h e a t b a l a n c e : 1st A | ^ P ^ ^ ' V - ^ ( T ; ; 1 - + k A x n * 2 + 2 I M , 2 I M . r o r ( A y l + % ) 2 2 \" T * . + r _ 2 _ . + 2 a = _2_rn a n n , Ax2 I M - 1 , 1 v A t A x ^ ' I M , 1 A t I M , 1 A y ^ ( A y ^ + A y ^ ) I M , 2 \" I M , 1 n+1 * I M 1~ IM 1 k A y - i * * 2 n d ^ | x p C P ( ^ M' 1)- - - ^ T m > 1 - T ^ ^ ) + 2 k A x f T n + l n+1 . + 2 v I M . 2 I M , 1 ; o r A y l + A y 2 + A t A y 1 ( A y 1 + A y 2 ) •)T n+1 I M , 1 A y 1 ( A y 1 + A y 2 ) T n + 1 = 2 T * -- I M , 2 - V l ^ f T * T * ^ A x 2 v I M , 1 I M - 1 U 71 BOUNDARY I V ( i = l , j = 2 - I N - l ) * n * * T . - T , . k A y . ( T . - T . ) 1st A t A x A y .pCpC-^^ i t l ) = 3 7^ ± - a J -—x 3 A t ' A x ^ 2 k A x ( T ? . - T n . ) k A x ( T ? . - T ? . , ) -r- l , j + l i , j — l , j 1 , J -1 ' + z \" * • A y . + Ay A y . + Ay 1 -1+1 .1 .1-1 o r 2 a ( T n - T n ) 2 a ( T l i ~ T l 1-1> ( -2- + - = ~ r i T * - - ^ T * - - 2 - T n + l>.r ~ Av (Ay +Av ) ( A t + ^ T l , j ^ 2 , j A t T l , j + Ay ( A y +Ay ) ( A y j + t * i - l > n+1 * * * . . _ T \" T - T . . k A y . ( T „ . - T ^ . ) . 2 n d A t -AxAy pCp l t , i l t i 1 y i a 2 ? , 1 1?,T + — 2 J A t A x k A x n+1 _ n+1 k A x . n+1 n+1 . + 2 U l , j + 1 1 l , . j J _ 2 U l , j ; A y . + A y . . . A y . + Ay *1 1+1 _ J .1-1 2 2 o r -2 a -n+1 A y . ( A y . +Avi_j_^) l , j - l + (\" 2 2 a A t A y ( A y +Ay ^ 2 a A y . ( A y . + A y . J 3 3\" - ) T n + 1 \" 2 a n+1 2 * 2a * * T , 4 + 7 3 Z ( T o 4 - T , 4 ) Ay ( A y +Ay ^ X j + l A t to? V A 2 , j 72 BOUNDARY Y(i=IM,j =IN-1) -1st At AxAy.pCpf-TIM,i \" ^ M,j,= T (.. 3M,j ~ TIM-l,j) + 2 2 3 • At - Ax 2 A y j + A yj+1 ' 4 y 1 +Ayj-1. 2 \" 2 \" or &x^ n t AxZ flC Ay4 (Ay. + Ay' ) 2n Cm,A - ^ . j - i) Ay.. (Ay.. +Ay.._1) n+1 * * * 2nd At AxAy.p Cp(TIM,.i-TIM,j) = - KAyj (TIM,3-TIM-1,j) 2 2 3 At Ax kAxd^.^-T^ 1.) kAxCT^.-T?: 1. n) -J IM,j+l IM,j' — IM.,2 IMo-l' + Ay. +Ay... Ay. + Ay. 1 -1+1 -1 -I-* or -2 a ^n+1 . , 2 . 2 a 2a et 1. + A Y j(A y j +Ay j_ 1) iIM,j-l v At A 7 j (A y j+Ay j + 1) y.. (Ay^ .+Ay.._^ ) IM,j 2_a n+1 2 * 2a * * Ay j(Ay j+Ay j + 1) TIM,j+l = At TTM,j\" Ax? CTTM,j \" T I M - l , j ) •BOUNDARY V I ( i = l , j = I N ) 1st j& j g A v T L I P C » F T 1. I N- T1, I N : - J^S T2,IH-T1,IN 2 A t ' Ax ' 2 _ R ^ ( T l > IN-^1 > ' A y I N + A 5 ? I N -1 o r ;_2 + 2 k A t ) T 1 , IN - ^ T 2 , I N = f ^ T l . I N A x Ax a r i . I N - 1,IN-1) A y l N ( A y I N ^ I N - l ) n+1 * * 2nd A t A x A Y I N p C p , T l , I N - l . I N . = ^ I M , T 2 , I N - T 1 , I N 2 2 ^ A t ; A k A x n+1 „ n + l K 2C1 .IN - l . I K -1) A y I N + Ay I N - l o r r n + l l . I N - l + _2 +.. r n + l 1 , IN A y l N ( A y I N + A y I N - l ) A t A y I N A y I N + A y I N - l , * * *, _2 T 1 , I N + 2o_ ( T2 , IN - T 1 , I N ) A t Ax 74 •BOUNDARY V I I ( i = 2 - I M - l , j = I N ) * * 1 s t A t AxAy pCp * T l t I N - T l , H p = 2 i N j& 2 & A tk jx xi K A y I N ( T i + l , I N + T i - 1 , I N - 2 T 1 , I N ) - K A x ( T i , I N - T i , I N - 1 ^ A y I N + A y I N - l o r * * * n -a T i - 1 , I N + , _ 2 + 2a v T i , I N - _ a _ T i + 1 , I N = 2 _ T 1 , I N + A 2 V A t . 2} . 2 A t Ax Ax Ax ( T n T n ) - a 1 , I N - i , I N - r A y i N ( A y I N + A y l N - l } ( T n + 1 T * ) ( T n + 1 T n + 1 ) 2 n d A t AxAy p C p v i , I N - 1 , I N ; = - K A x v i , I N - i . I N - r * 2 f- A ? I N + A y ! N - l 2 * + K A y l N ( T i + l , I N + T i - 1 , I N - 2 T i , I N ) Ax o r T n + 1 T n + 1 i , I N - l + ; ( _ 2 + a ) A i , I N A y i N ( A y i N + ^ I N - l 5 A t A y i N ( A y l N + A y l N - l } * * * * _ 2 T i , I N + _ a _ ( T I , I N + T i - I , I N - 2 T i , I N ) A t ... 2 Ax 'BOUNDARY VIII(i=IM,1=IN) * n (T - T ) •1st At AxAy pCp ^ IM,IN IM,nr = 2 2 N t * * K A x C T n - T n 1 ^ I N (TTM,IN \" TIM-1,IN> - \"2 m ^ ** A y I N + A y I N - l Or T * + - 2a IM-1,IN Ax 2' • i.2. At + Ax 2a) 2 K n C = 2 T I M , I N 7 - I M , I N + _.At (T n T n ) v I M , I N - I M , I N - r A y I N ( A y I N A y I N - l > n+1 * (T - T ) 2nd At AxAy pCp v T M , I N I M . I N ^ = 2 2 ' At K A Y I N (TIM,IN ~ TIM-1,IN ) Ax K Ax . n + 1 _ n+1 . IM.IN IM,IN-r W + A v y I N y I N - l o r A y I N ( A y l N + A y l N - l ) Tn+1 I N , I n - l ( 2 + Tn+1 a . I M , I N A t A y I N ( A W y I N - l > * * A _2 T I M , I N \" _2a ( T I M , I N ~ ^ I M - l . I N * At Ax' 7 6 APPENDIX B ~ COMPUTER PROGRAM SAMPLE C CALCULATION OF THERMAL STRESSES IN HEAVY SECTION C ELECTROSLAG JOINING C C C C PAULO SILVEIRA IVO C C C C MAIN PROGRAM C DIMENSION T(100,100),TS(100,100),TB(100,100),DY(100),ID(100) CALL DlNPUT(DY,DX,TMP,TBO,DT,CP,RO,AK,DPH,PRNT,TLAST,IM, *IN,XI,VO,TH,F,G,SE,SWG,AL,FR,CPW,DELT,ROW,HEB) C C C C C C C C c c CALL INITL(T,TS,TB,TBO,DPH,DX,ID,IM,IN,PRNT,PRNTO) CALL VEL(V,F,XI,VO,Q1,IM,DT,DX,TH,T,DY,DPH,AK,IN,TBO,TMP,ID) TIME=0.0 1 TIME=TIME+DT CALL HSPOS(DPH,V,TIME,DX,ID,IM) CALL CONST(DT,DX,CP,RO,AK,ALPHA,A 1 ,A2,A3) CALL FSTS(TB,TS,DY,DX,DT,ALPHA,IN,IM,TMP,ID,A1,A2,A3) CALL SNDS(TS,T,DY,DX,DT,ALPHA,IN,IM,TMP,ID,A1,A2,A3) CALL HEAT(XI,VO,AK,CP,RO,DX,DPH,TH,T,TMP,ID,G,F,IM,IN,TBO,DY, *DT,V,TIME,SE,SWG,AL,FR,CPW,DELT,ROW,HEB) CALL PRINT(T,TIME,IN,IM,IP,PRNT,PRNTO,TLAST,ID) IFdP.EQ. 1 ) GO TO 2 DO 10 I = 1 ,1M DO 20 J=1,IN TB ( I , J ) = T ( I , J ) 20 CONTINUE 10 CONTINUE GO TO 1 2 CALL STRESS(T,TT,TTT,IT,IM,IN,ALFA,H) STOP END C C READ DATA AND PRINT HEADINGS C SUBROUTINE DlNPUT(DY,DX,TMP,TBO,DT,CP,RO,AK,DPH,PRNT,TLAST,IM, *IN,XI,VO,TH,F,G,SE,SWG,AL,FR,CPW,DELT,ROW,HEB) C DIMENSION DY(100) READ(5,100) TMP,TBO,DT,CP,RO,AK,DX,F,DPH,PRNT,TLAST 100 FORMAT(F6.1,9F6.3,F10.0) READ(5,110) IM.IN 110 FORMAT(2I3) 7 7 READ(5,120) DY(1),DY(2),DY(3),DY(4),DY(5),DY(6),DY(7) 120 FORMAT(7F5.0) DO 10 I=8,IN DY(I)=DY(7) 10 CONTINUE READ(5,130) G,TH,XI,VO,SE,SWG,AL 130 FORMAT(7F6.1) READ(5,140) FR,CPW,DELT,ROW,HEB 140 FORMAT(4F6.3,F7.4) WRITE(6,200) 200 FORMAT(1H ,///,5X,' ESW THERMAL PROFILE *,3X, *'PAULO S. IVO',/,6X,l9('*'),///) WRITE(6,210) TMP,TBO,DT,CP,RO,AK,DX,F,DPH,PRNT,TLAST 210 FORMAT(1H ,IX,'TMP=',F6.1,1X,'(Deg C)',/,2X,'INITIAL TEMP=', *F6.1,1X,*(Deg C)',/,2X, *'TIME STEP=',F6.1,IX,'(s)',/,2X,'SPECIFIC HEAT*',F6.4,IX, * ' ( c a l / g . C ) ' *,/,2X,'DENSITY=',F6.3,IX,'(g/cm**3)',/,2X, *'CONDUCTIVITY=\",F6.4,1X,'(cal/cm.s.C)',/,2X,'DX=', *F6.1,IX,'(cm)',/,2X,'HEAT FACTOR=',F6.3,IX, */,2X,'HEAT SOURCE DEPTH*',F6.3,IX,'(cm)',/, *2X,'PRINT CYCLE=',F7.1,1X,'(S)',/,2X,'END OF CALCULATION' * , F l 0 . 1 , 1 X , ' ( s ) ' ) WRITE(6,220) (DY(I),1=1,IN) 220 FORMATOH , 1X, 'DY= ' , 1 0F6. 1 ) WRITE(6,230) IM,IN 230 FORMATOH ,IX,'NUMBER OF DIVISIONS IN X-DIRECTION =',13,//, *2X,'NUMBER OF DIVISIONS IN Y-DIRECTION =',I3) WRITE(6,240) G,TH,XI,VO,SE,SWG,AL 240 FORMAT(1H ,///,2X,'WELDING PARAMETERS',///,2X, *'WELD GAP=',F5.1,IX,'cm',2X,'THICKNESS=',F5.1,1X,'cm',// *2X,'CURRENT=',F7.1,1X,'A',2X,'VOLTAGE=',F5.1,IX,'V,//, *2X,'ELECTRODE SURFACE AREA=',F5.1,IX,'(cm**2)',2X, *'WELD GAP AREA =',F6.1,IX,'(cm**2)',2X,//,2X,'LATENT HEAT=*, *F 5 . 1 , I X , * ( c a l / g ) ' , / / ) WRITE(6,250) FR,CPW,DELT,ROW,HEB 250 FORMAT (\"IH , IX,'WATER FLOW RATE= ' , F6 . 1 , 1X, ' (cm** 3/s ) * , */,2X,'WATER SPECIFIC HEAT=',F6.1,1X,'(cal/g.C)',/, *2X,'TEMP. DIFF. IN MOULD=' ,F6.1,1X,' (C) ' ,/,2X, *'WATER DENSITY=',F6.1,1X,'(g/cm**3)',/,2X, *'HEAT EFF. TO THE BLOCKS'',F7.4,1X,/) RETURN END C C C C C c SUBROUTINE INITL(T,TS,TB,TBO,DPH,DX,ID,IM,IN,PRNT,PRNTO) C DIMENSION T(100,100),TS(100,100),TB(100,100),ID(100) DO 10 1=1,IM DO 20 J=1,IN T(I , J)=TBO TS(I,J)=TBO TB(I,J)=TBO 20 CONTINUE 10 CONTINUE NO=IFIX(DPH/DX+0.49)+1 78 DO 30 1=1,NO 30 ID(I)=1 NP=NO+1 DO 40 I=NP,IM 40 ID(I)=0 PRNTO=PRNT RETURN END C C C CALCULATION OF THE WELDING SPEED C C C SUBROUTINE VEL(V,F,XI,VO,Q1,IM,DT, DX, TH, T, DY,DPH,AK,IN,TBO, *TMP,ID) DIMENSION ID(100),T(100,100),DY(100) CALL HEAT 1 (AK,DX,TH,T,DY,ID,Q1,1M,DPH,DT,IN,TBO,TMP) FACTOR=0.24*0.95*0.35*XI*VO/(.023*Q1) V=((.35*XI*VO*0.24*.95)/(FACTOR*Q1)) WRITE(6,88B) V,FACTOR 888 FORMAT(1H ,/,'WELDING VELOCITY*',F6.3,2X,'(cm/s)',F7.2,/) RETURN END DECISION ON WHETHER THE HEAT SOURCE IS CONTACTING THE BLOCK SUBROUTINE HSPOS(DPH,V,TIME,DX,ID,IM) DIMENSION ID(100) NO=IFIX(V*TIME/DX+0.51) + 1 NS=IFIX((DPH+V*TIME)/DX+0.49)+l NN=NO-1 IF(N0-1) 1,1,2 2 DO 10 I=1,NN ID(I)=0 10 CONTINUE 1 DO 20 I=NO,NS ID(I)=1 20 CONTINUE NNS=NS+1 DO 30 I=NNS,IM ID(I)=0 30 CONTINUE RETURN END C C C C C C SUBROUTINE CONST(DT,DX,CP,RO,AK,ALPHA,A1,A2,A3) ALPHA=AK/(CP*RO) A1=2.0*(1.0/DT+ALPHA/(DX**2)) A2=2.0*ALPHA/(DX**2) A3=2.0/DT RETURN END C C C 79 c C CALCULATION OF THE FIRST HALF-TIME STEP C C C c SUBROUTINE FSTS(TB,TS,DY,DX,DT,ALPHA,IN,IM,TMP,ID,Al,A2,A3) C DIMENSION TB(100,100),TS(100,100),DY(100),ID(100) DIMENSION A(100),B(100),C(100),D(100),TPRIME(100) C I F ( I D ( 1 ) - 1 ) 1,2,2 2 CALL S0URCE(A(1),B(1),C(1),D(1),TMP) GO TO 3 1 A(1)=0.0 B(1)=A1 C(1)=-A2 D(1)=A3*TB(1,1)+ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) **(TB(1,2)-TB(1,1)) 3 CONTINUE IJ=IM-1 IK=IN-1 DO 10 I=2,IJ I F ( I D ( I ) - 1 ) 4,5,5 5 CALL•SOURCE(A(I),B(l),C(I),D(l),TMP) GO TO 10 C 4 A(I)=-0.5*A2 B(I)=A1 C(I)=-0.5*A2 C D(I)=A3*TB(I,1)+(ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) * * ( T B ( I , 2 ) - T B ( I , 1 ) ) ) C 10 CONTINUE C IF(ID(IM)-1) 6,7,7 7 CALL SOURCE(A(IM),B(IM),C(IM),D(IM),TMP) GO TO 8 C 6 A(IM)=-A2 B(IM)=A1 C(IM)=0.0 C D(IM)=A3*TB(IM,1)+(ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) **(TB(IM,2)-TB(IM,1))) C 8 CALL TRIDAGd , IM, A, B ,C ,D,TPRIME) C DO 15 1 = 1 ,IM 15 TS(I,1)=TPRIME(I) DO 20 J=2,IK C A(1)=0.0 B(1)=A1 C(1)=-A2 D(1)=A3*TB(1,J)+(2.0*ALPHA/(DY(J)*(DY(J)+DY(J+1)))) **(TB(1,J+1)-TB(1,J))-(2.0*ALPHA/(DY(j)*(DY(j) *+DY(J-1))))*(TB(1,J)-TB(1,J-1)) 80 c DO 25 1=2,IJ C A(I)=-0.5*A2 B(I)=A1 C(I)=A(I) C D(I)=A3*TB(I,J)+(2.0*ALPHA*(TB(I,J+1)-TB(I,3))/ *(DY(J)*(DY(J)+DY(J+1 ).) )) *-(2.0* A L P H A * ( T B ( I , J ) - T B ( I , J - 1 ) ) / ( D Y ( J ) * ( D Y ( J ) + D Y ( J - 1 ) ) ) ) C 25 CONTINUE C C A(IM)=-A2 B(IM)=A1 C(IM)=0.0 C D(IM)=A3*TB(IM,J)+(2.0*ALPHA*(TB(IM,J+1)-TB(IM,J)) */(DY(J)*(DY(J)+DY(J+1))))-(2.0*ALPHA*(TB(IM,J) * - T B ( l M , J - 1 ) ) / ( D Y ( J ) * ( D Y ( J ) + D Y ( J - 1 ) ) ) ) C CALL TRIDAG(1,IM,A,B,C,D,TPRIME) C DO 30 1=1,IM 30 TS(l', J)=TPRIME(I) 20 CONTINUE C A(1)=0.0 B(1)=A1 C(1)=-A2 C D(1)=A3*TB(1,IN)-(ALPHA*(TB(1,IN)-TB(1,IN-1)) */(DY(IN)*(DY(IN)+0.5*DY(IN-1)))) C DO 35 1=2,IJ A(I)=-0.5*A2 B(I)=A1 C(I)=-0.5*A2 C D(I)=A3*TB(I,IN)-(ALPHA*(TB(I,IN)-TB(I,IN-1)) */(DY(IN)*(DY(IN)+0.5*DY(IN-1)))) C 35 CONTINUE C A(IM)=-A2 B(IM)=A1 C(IM)=0.0 C • D(IM)=A3*TB(IM,IN)-(ALPHA*(TB(IM,IN)-TB(IM,IN-1)) */(DY(IN)*(DY(IN)+0.5*DY(IN-1)))) C CALL TRIDAG(1,IM,A,B,C,D,TPRIME) DO 40 1 = 1 ,IM 40 TS(I,IN)=TPRIME(I) RETURN END C C c 81 SUBROUTINE SNDS(TS,T,DY,DX,DT,ALPHA,IN,IM,TMP,ID,A1,A2,A3) C DIMENSION TS(100,100),T(100,100),DY(100),ID(100) DIMENSION A(100),B(100),C(100),D(100),TPRIME(100) I F ( I D O ) - I ) 1,2,2 2 CALL SOURCE(A(1),B(1),C(1),D(1),TMP) GOTO 3 1 A(1)=0.0 B(1)=A3+ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) CO)=-ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) C D(1)=A3*TS(1,1)+A2*(TS(2,1)-TS(1,1)) 3 CONTINUE C IJ=IM-1 IK=IN-1 DO 10 J=2,IK C A(J)=-2.0*7\\LPHA/(DY(J)*(DY(J)+DY(J-1))) C B(J)=A3+(2.0*ALPHA/(DY(J)*(DY(J)+DY(J+1)))) *+(2.0*ALPHA/(DY(J)*(DY(J)+DY{J-1)))) C C(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J+1))) C D(J)=A3*TS(1,J)+A2*(TS(2,J)-TS(1, J ) ) 10 CONTINUE C A(IN)=-ALPHA/(DY(IN)*(DY(IN)+0.5*DY(IN-1))) C B(IN)=A3+ALPHA/(DY(IN)*(DY(IN)+0.5*DY(IN-1))) C C(IN)=0.0 C D(IN)=A3*TS(1,IN)+A2*(TS(2,IN)-TS(1,IN)) C C C CALL TRIDAG(1,IN,A,B,C,D,TPRIME) C DO 15 J=1,IN 15 T(1,J)=TPRIME(J) C DO 20 1=2,IJ I F ( I D ( I ) - 1 ) 4,5,5 5 CALL S0URCE(A(1),B(1),C(1),D(1),TMP) GO TO 6 C 4 A(1)=0.0 B(1)=A3+ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) C C(1)=-ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) C D(1)=A3*TS(I,1)+0.5*A2*(TS(I+1,1)+TS(1-1,1)-*2.0*TS(I,1)) 6 CONTINUE C DO 30 J=2,IK C A(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J-1))) 8 2 B(J)=A3+2.0*ALPHA/(DY(J)*(DY(,3)+DY(J+1 )))+ *2.0*ALPHA/(DY(J)*(DY(J)+DY(J-1))) C(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J+1))) D(J)=A3*TS(I,J)+(0.5*A2*((TS(I+1,J)+TS(I-1,J))-*2.0*TS(I,J))) 30 CONTINUE A(IN)=-ALPHA/(DY(IN)*(DY(IN)+0.5*DY(IN-1))) B(IN)=A3-A(IN) C(IN)=0.0 D(IN)=A3*TS(I,IN)+0.5*A2*(TS(I+1,IN)+TS(I-1, IN)-*2.0*TS(I,IN)) CALL TRIDAG(1,IN,A,B,C,D,TPRIME) DO 40 J=1 ,IN T(I,J)=TPRIME(J) 40 CONTINUE 20 CONTINUE IF(ID(IM)-1) 7,8,8 8 CALL SOURCE(A(1),B(1),C(1),D(1),TMP) GO TO 9 7 A(1)=0.0 B(1)=A3+ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) C(1)=-ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) D(1)=A3*TS(IM,1)-A2*(TS(IM,1)-TS(IM-1,1)) 9 CONTINUE DO 50 J=2,IK A(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J-1))) C(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J+1))) B(J)=A3-A(J)-C(J) D(J)=A3*TS(IM,J)-A2*(TS(IM,J)-TS(IM-1,J)) 50 CONTINUE A(IN)=-ALPHA/(DY(IN)*(DY(IN)+0.5*DY(IN-1))) B(IN)=A3-A(IN) C(IN)=0.0 D(rN)=A3*TS(IM,IN)-A2*(TS(IM,IN)-TS(lM-1,IN)) CALL TRIDAG(1,IN,A,B,C,D,TPRIME) DO 60 J=1,IN 83 60 T(IM,J)=TPRIME(J) RETURN END C C C SUBROUTINE SOURCE(A,B,C,D,T) C A=0.0 B=1 .0 C=0.0 D=T RETURN END C C C SUBROUTINE PRI NT (T, T l ME, IN , IM, IP,PRNT,PRNTO,TLAST, ID) C C c DIMENSION T(100,100),ID(100) IP=0 IF(TIME.GT.TLAST) GO TO 1 C IF(TlME.LT.PRNT) GO TO 2 C C WRITE(8,100) TIME C 100 FORMAT(1H ,21X,'TIME=' ,F10 . 1 ) C DO 10 1 = 1 ,IM K=I IF(ID(K)-1) 10,20,20 20 WRITE(8,200) (T(I,J),J=1,8),K 200 FORMAT(8(F6.1,IX),13) 10 CONTINUE PRNT= PRNT+ PRNTO GO TO 2 1 IP=1 2 RETURN END C C c c C SUBROUTINE \"TRIDAG\" FROM 'APPLIED NUMERICAL METHODS' BY C CARNAHAN, LUTHER AND WILKES C C C SUBROUTINE FOR SOLVING A SYSTEM OF LINEAR SIMULTANEOUS C EQUATIONS HAVING A TRIDIAGONAL COEFFICIENT MATRIX. C THE EQUATIONS ARE NUMBERED IF THROUGH L AND THEIR C SUB-DIAGONAL, DIAGONAL AND SUPER-DIAGONAL COEFFICIENTS C ARE STORED IN THE ARRAYS A, B AND C. THE COMPUTED C SOLUTION VECTOR IS STORED IN THE ARRAY V. C C C C SUBROUTINE TRIDAG(IF,L,A,B,C,D,V) 84 DIMENSION A(100),B(100),C(100),D(100),V(100) DIMENSION BETA(101),GAMMA(101) C C c C#### COMPUTE INTERMEDIATE ARRAYS BETA AND GAMMA... C BETA(IF)=B(IF) GAMMA(IF)=D(IF)/BETA(IF) IFP1=IF+1 DO 10 I=IFP1,L BETA(I)=B(I)-A(I)*C(I-1)/BETA(I-1) GAMMA(I)=(D(I)-A(I)*GAMMA(1-1))/BETA(I) 10 CONTINUE C C*##« COMPUTE FINAL SOLUTION VECTOR V... C V(L)=GAMMA(L) LAST=L-IF DO 20 K=1,LAST I=L-K V(I)=GAMMA(I)-C(I)*V(I+1)/BETA(I) 20 CONTINUE RETURN END C C C C C C HEAT. BALANCE USED TO CALCULATE THE NEW BOUNDARY TEMPERATURE C AT EVERY TIME STEP C SUBROUTINE HEAT(XI,VO,AK,CP,RO,DX,DPH,TH,T,TMP,ID,G,F,IM,IN, *TBO,DY,DT,V,TlME,SE,SWG,AL,FR,CPW,DELT,ROW,HEB,BF) DIMENSION ID(100),T(100,100),DY(100) Q1=0.0 NO=IFIX(V*TIME/DX+0.51)+1 NS=IFIX((DPH+V*TIME)/DX+0.49)+1 NN=NO-1 IF(N0-1) 1,1,2 2 DO 15 K= 1,NN ID(K)=0 15 CONTINUE 1 DO 25 M=NO,NS ID(M)=1 25 CONTINUE NNS=NS+1 DO 35 J=NNS,IM ID(J)=0 35 CONTINUE BETA=((SE/SWG)/(1.-(SE/SWG))) DO 10 1=1,IM IF(ID(I)-1) 10,20,20 20 Q1=Q1-((AK*DX*TH)*((4*T(I,2)-T( I ,3)-3*TMP)/ *(DY(1)+DY(2)))) 10 CONTINUE WRITE(6,990) Q1,BETA 990 FORMAT(1H ,'HEAT INPUT=',1X,F15.2,/,F8.5,IX,/) CE=CP*RO*DPH*TH*G 85 TS=TMP-(((Q1*DT*HEB)/(CE))-((XI*VO*F*DT*.228)/(CE)) *+((AL*(1,/BETA)*V*DT)/(CP*DPH))) TMP=TS WRITE(6,999) TMP,V 999 FORMAT(1H ,'TMP=',1X,F7.2,/,F7.2) RETURN END C C C SUBROUTINE HEAT1(AK,DX,TH,T,DY,ID,Q1,IM,DPH,DT,IN,TBO,TMP) DIMENSION ID(100),T(100,100),DY(100) DO 4 I=1,IM DO 6 J=1,IN . T(I,J)=TBO 6 CONTINUE 4 CONTINUE Q1=0.0 TIME=DT NO=IFIX(0.05*TIME/DX+0.51)+1 NS=IFIX((DPH+0.05*TIME)/DX+0.49)+1 NN=NO-1 IF(NO-I) 1,1,2 2 DO 10 K=1,NN ID(K)=0 10 CONTINUE 1 DO 20 M=NO,NS ID(M)=1 20 CONTINUE NNS=NS+1 DO 30 J=NNS,IM iD(J)=0 30 CONTINUE DO 5 1=1,IM I F ( I D ( I ) - 1 ) 5,50,50 50 Q1=Q1-((AK*DX*TH)*((4*T(I,2)-T(I,3)-3*TMP)/ *(DY(1)+DY(2)))) 5 CONTINUE WRITE(6,897) Q1 897 FORMAT(1H ,IX,'HEAT INPUT=',F15.1) RETURN END C C THERMAL STRESS CALCULATION PERFORMED FOR EACH NODAL C TEMPERATURE C SUBROUTINE STRESS(T,TT,TTT,IT,IM,IN,ALFA,H) DIMENSION T(500,20),TT(500),TTT(500) DO 10 1=1,IT READ(5,100) (T(IT,IN),IN=1,8) 100 FORMAT(8(F6.1,1X)) • 10 CONTINUE C CALCULATION OF E(YOUNG*S MODULUS) AS A FUNCTION OF TEMPERATURE C DO 11 L=1,IM DO 12 J=1,8 DO 14 1=1,IT TT(I ) = T ( I , J ) TTT(I)=TT(I)*L I F ( T T ( I ) .LT. 1000.) GO TO 1 86 E=0.000012 1 I F ( T T ( I ) .GE. 1000. .AND. TT(I) .LE. 1400.) GOTO 2 E=(2000.-(1.875*(TT(I)-l000.)*100000.)) 2 IF(TT(I) .GE. 1400. .AND. TT(I) .LE. 1475.) GO TO 3 E=((1250.*(l475.-TT(l))/75.)*10000.) 3 IF(TT(I) .GT. 1475.) GO TO 14 E=0.0 AREA1=QINT4P(I tTT(I),465,1,465) AREA2=QINT4P(I,TTT(I),465,1,465) SIGMA=(-ALFA*E*TT(I)+((0.5*H)*(ALFA*E*AREA1)) *+(((1.5*L)/(H**3.))*(ALFA*E*AREA2))) WRITE(7,200) SIGMA 200 FORMAT(1H ,2X,'THERMAL STRESS=',FB.3) 14 CONTINUE 12 CONTINUE 11 CONTINUE RETURN END C C C C C C LIST OF SYMBOLS USED IN THE MODEL C C C C C C TMP = Melti n g p o i n t temperature(Deg. C) C C TBO = Parent metal i n i t i a l temperature(Deg. C) C C DT = Time step(s) C C CP = S p e c i f i c heat of steeKcal/g.deg.C) C C RO = Density of steel(g/cm**3) C C AK = Thermal c o n d u c t i v i t y of steel(cal/cm.s.deg C C DX = Space increment i n X-direction(cm) C C DY = Space increment i n Y-direction(cm) C C V = Welding v e l o c i t y ( c m / s ) C C DPH = Slag + l i q u i d metal depth(cm) C • C PRNT = P r i n t c y c l e ( s ) C C TLAST = End of c a l c u l a t i o n ( s ) C C IM = # of d i v i s i o n s in the X - d i r e c t i o n C C IN = # of d i v i s i o n s i n the Y - d i r e c t i o n C C T = Temperature(deg. C) C C XI = Current(A) 8 7 c C VO = Vo l t a g e ( V ) C C TH = Thickness(cm) C C G = Weld gap(cm) C C F = E f f i c i e n c y f a c t o r C C SE = E l e c t r o d e area(cm**2) C C SWG = Weld gap area(cm**2) C C AL = Latent h e a t ( c a l / g ) C C FR = F i l l r a t i o C C ALFA = C o e f f i c i e n t of expansion(/deg. C) C C H = Weld height(cm) C C ID = Heat source c o n t a c t index 88 A P P E N D I X C - E F F I C I E N C Y F A C T O R A N D H E A T S I N K C A L C U L A T I O N S P a t o n 3 5 r e p o r t s t h a t a b o u t 5 8 . 6 % o f t h e a v a i l a b l e h e a t g o e s i n t o t h e b l o c k s w h e n E l e c t r o s l a g W e l d i n g ( w i r e e l e c t r o d e ) . D u e t o t h e d i f f e r e n t t h e r m a l c h a r a c t e r i s t i c s a l r e a d y d i s c u s s e d , f o r E l e c t r o s l a g J o i n i n g t h a t n u m b e r w o u l d n o t a p p l y . T h e r e f o r e , new c a l c u l a t i o n s h a d t o b e p e r f o r m e d b a s e d o n some m e a s u r e m e n t s : T h e c o o l i n g s h o e w a t e r f l o w r a t e w a s m e a s u r e d a n d f o u n d t o b e 3 6 9 8 c m 3 / s . The e l e c t r o d e m e l t r a t e c a n b e c a l c u l a t e d a s f o l l o w s : M e l t R a t e = E l e c t r o d e F e e d R a t e x A r e a x D e n s i t y T h e e l e c t r o d e f e e d r a t e c a n b e a s c e r t a i n e d u s i n g t h e f o l l o w -i n g e x p r e s s i o n g i v e n b y F r o s t e t a l . 1 * 1 : w h e r e : E F R = e l e c t r o d e f e e d r a t e F R = f i l l r a t i o ( e l e c t r o d e a r e a / w e l d a r e a ) V = w e l d i n g v e l o c i t y F o r t h e m a t e r i a l d i m e n s i o n s u s e d i n m o s t e x p e r i m e n t s - 1 . 6 7 3 5 F o r a n e x p e r i m e n t a l w e l d i n g v e l o c i t y o f 0 . 0 2 3 c m / s , t h e EFR was f o u n d t o b e : E F R = 1 . 6 7 3 5 x 0 . 0 2 3 = 0 . 0 3 8 5 c m / s T h e r e f o r e , M e l t R a t e = 0 . 0 3 8 5 c m / s x 5 7 . 9 1 2 c m 2 x 7 . 8 6 g / c m 3 = 1 7 . 5 2 g / s I f a p p r o x i m a t e l y 4 0 0 KWH a r e n e e d e d t o m e l t 1 0 0 0 k g o r 1 x 1 0 ^ g o f s t e e l , t h e n t h e p o w e r f o r m e l t i n g w o u l d b e : T>_ 1 7 . 5 2 g / s x 4 0 0 KWH x 3 6 0 0 s _ . . . . 1 x 10o g 89 The h e a t f l u x p e r m o u l d w o u l d t h e n b e : 1 ^ = F l o w r a t e x C p y x AT x p y x ^ Q Q Q 8 = 8 5 . 1 6 K W T h e r e f o r e , 2 5 . 2 3 = 1 6 . 1 % = 5 4 . 3 % \\ \" 3 3 x 5 0 0 0 x . 9 5 8 5 . 1 6 1 5 6 . 7 5 H R = - 1 % • ^ l o c k \" 1 0 0 \" Z ( H M + H W + V \" b l o c k * 1 5 % A n d , t h e r e f o r e , o n l y a b o u t 15 % o f t h e a v a i l a b l e e n e r g y f l o w s t h r o u g h t h e b l o c k s a n d i s a c c u m u l a t e d t h e r e . T h i s i s t h e f a c t o r u s e d i n t h e m o d e l w h e n c a l c u l a t i n g t h e h e a t f l o w . ***************** THE BLOCK AS A HEAT S I N K The a m o u n t o f h e a t l o s t t h r o u g h t h e b l o c k c o l d f a c e i s v e r y s m a l l w h e n c o m p a r e d w i t h t h e h e a t a v a i l a b l e f r o m t h e e l e c t r o d e t h a t i s e n t e r i n g t h e b l o c k v i a t h e o p p o s i t e f a c e . I n o r d e r t o s e e how t h a t i s e f f e c t e d a p l o t o f t e m p e r a t u r e v e r s u s d i s t a n c e f r o m t h e h o t f a c e h a s b e e n g e n e r a t e d a n d i l l u s t r a t e d i n F i g . 26 T h e p o i n t a t w h i c h t h e t e m p e r a t u r e d r o p s t o r o o m t e m p e r a t u r e h a s b e e n f o u n d t o b e 61 cm away f r o m t h e h o t f a c e . ( A p p r o x i m a t e l y 2 f e e t ) 9 0 A P P E N D I X D - R E S I D U A L S T R E S S E V A L U A T I O N . (A + B c o s 2 g ) e a - (A - B c o s 2 g ) e c 0 1 4 A B c o s 23 (A + B c o s 20) e c - (A - B c o s 20) e a ° 2 4 A B c o s 20 ca - 2 e b + e c t a n 20 = -e a - e c P o s i t i o n 1 - P a r e n t m e t a l D e p t h = 120 t h o u e a = - 3 5 u e eb = - 6 2 u e e c = - 1 4 3 y e 2 - 5 5 4 A - - 1 . 3 5 * 1 0 \" * 4 B = - 3 . 5 5 x 10 ( A f t e r R e d n e r ) T h e r e f o r e , A = - 3 . 3 7 5 x 1 0 ~ 9 a n d B = - 8 . 8 6 8 x 1 0 ~ 9 a i = + 9 7 8 1 p s i a 2 = +16589 p s i P o s i t i o n 2 - H e a t a f f e c t e d z o n e D e p t h = 120 t h o u e a = +67ue eb = +51ue e c = - 2 2 5 u e 0 . 2 0 4 5 0 , . i n/o i n - 8 r 2 = Q Q 7 1 = 2 . 8 7 4 A = - 1 . 1 1 4 2 x 10 4 B = - 2 . 9 9 2 0 x 1 0 ~ 8 T h e r e f o r e , A = - 2 , 7 8 5 5 x 1 0 ~ 9 a n d B = - 7 . 4 8 x 1 0 ~ 9 01 = + 1113 p s i 0 2 = + 2 7 2 4 8 p s i 91 P o s i t i o n 3 - W e l d m e t a l D e p t h = 1 2 0 t h o u £ a = - 1 5 2 y e eb = - 1 5 7 u e e c = - 1 0 7 y e \" n'lfS5 = 2 ' 8 4 A = - 1 . 1 ^ 2 x 1 0 \" 8 3 U . u o / 4 B = - 3 . 0 x 1 0 ~ 8 T h e r e f o r e , A - - 2 . 7 8 5 4 x 1 0 ~ 9 a n d B = - 7 . 5 x 1 0 ~ 9 oi = + 2 5 6 1 5 p s i a 2 = + 2 0 8 7 7 p s i T h e r e s i d u a l s t r e s s m e a s u r e m e n t w a s c a r r i e d o u t u s i n g t h e B l i n d 45 H o l e D r i l l i n g t e c h n i q u e w h i c h i s a s e m i - d e s t r u c t i v e m e t h o d w h e r e b y a s m a l l h o l e , 3 . 1 7 5 m m ( l / 8 \" ) i n d i a m e t e r i s d r i l l e d t o a d e p t h a p p r o x i m a t e l y e q u a l t o i t s d i a m e t e r . T h e r e l a x e d s t r a i n s a r e t h e n m e a s u r e d a r o u n d t h e h o l e . 02' i s t h e l o n g i t u d i n a l s t r e s s r e m a i n i n g i n t h e w e l d e d a s s e m b l y a n d a j i s a t a 90 d e g r e e a n g l e t o 02- T h e y w e r e m e a s u r e d i n t h e p a r e n t m a t e r i a l , h e a t a f f e c t e d z o n e a n d w e l d m e t a l . "@en ; edm:hasType "Thesis/Dissertation"@en ; edm:isShownAt "10.14288/1.0078665"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Metals and Materials Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Stresses in heavy section electroslag joining"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/24079"@en .