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"STRESSES IN HEAVY SECTION ELECTROSLAG  JOINING  by PAULO SILVEIRA IVO B.A.Sc.,Universidade  F e d e r a l de M i n a s G e r a i s ,  Brasil,l978  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE Department  STUDIES  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 a c c e p t t h i s  thesis  to the r e q u i r e d  as conforming standard  THE UNIVERSITY OF BRITISH COLUMBIA October  \u00A9  1982  Paulo S i l v e i r a  I v o , 1982  \u000CIn  presenting  requirements  f o r an  Columbia,  I  available  for  permission  agree  for  p u r p o s e s may or  her  be  thesis  of  of  October  fulfilment  the  Library  shall  reference  and  study.  I  extensive granted  by  c o p y i n g of the It  this thesis written  for  1982  is  my  further  Engineering  gain  the  of  British  it  freely  agree for  Department  understood  financial  Columbia  make  this thesis  permission.  Metallurgical  05,  Head of  of  University  the  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  Date:  partial  that  w i t h o u t my  Department  in  advanced degree at  representatives.  publication allowed  this  that  that  scholarly  or  by  copying  shall  not  his or be  \u000Ci i  Abstract A  study  Electroslag has  Joining  the  thermal  stresses  Process as a p p l i e d  been u n d e r t a k e n ,  process be  of  since  i n d i c a t e s that  a survey  although  a problem, a p p a r e n t l y  t o heavy  solidification  Conditions  with  plate  during  ESJ p l a t e  reports ESJ  predicted  wire e l e c t r o d e s  by  were r e p o r t e d  to  make  electrodes.  work on t h e t h e r m a l  of  150 mm  thick  previous  and s t r e s s  A36  steel  fields  plates.  workers t o form c r a c k s  were e s t a b l i s h e d and f o u n d n o t  electrodes.  welding  ought t o  cracks i n  welds u s i n g  during  cracking  on t h e  a r e known t o p r o d u c e s o l i d i f i c a t i o n  Welding with wire e l e c t r o d e s  developed  reports  Welding  Electroslag  study  forgings  i t i s not r o u t i n e l y observed.  which  This  i n the  gauge  of p u b l i s h e d  conditions  crack-free  .resulting  to  form  with cracks  Measurements o f s t r e s s a n d t e m p e r a t u r e  were made and f o u n d  t o agree w e l l  with  a  simple  n u m e r i c a l model o f t h e p r o c e s s . It  is  sufficiently  concluded different  d e v e l o p e d , even  that  the  t o ESW t h a t  thermal  i t can r e l a x  in a fully-constrained joint,  which s o l i d i f i c a t i o n  cracking  field  i s no l o n g e r  &lt;  of  ESJ i s  the s t r e s s  to  the  observed.  point  field at  \u000Ciii  Table  of  Contents  Abstract  ,  List  of T a b l e s  List  of  i i v  Figures  vi  Acknowledgement  viii  I.  INTRODUCTION 1.1  Introduction  1.2  Process  1.3  Previous  1.4  Solidification  1.5  Present  II.  1 1  D e s c r i p t i o n and  Application  Work  6 Cracking  9  Objectives  12  MATHEMATICAL MODELING 2.1  13  Temperature D i s t r i b u t i o n 2.1.1  Assumptions  2.1.2  D e r i v a t i o n Of  2.1.3  Numerical  Calculation  .14 14  Equations  Solution  2.2  T h e r m a l S t r e s s And  2.3  Computer  III.  3  Production  Strain Calculation Runs  EXPERIMENTAL WORK  16 17 18 21 23  3.1  Furnace Design  23  3.2  Cooling  23  3.3  Electrode  3.4  Weld S e t - u p And  3.5  Sequence of O p e r a t i o n  3.6  Residual  Shoe D e s i g n And  Slag  Stress  Preparation  Constraining - Welding Procedure  24 ....26 28 29  \u000Civ  3.7 T e m p e r a t u r e 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 . APPENDIX D - RESIDUAL STRESS EVALUATION  88 90  \u000CV  List  of T a b l e s  I.  Computer M o d e l P a r a m e t e r s  40  II.  ESJ T y p i c a l  41  Log  Sheet  \u000Cvi  List  of  Figures  1. S c h e m a t i c L a y o u t o f E S J Equipment 2. E l e c t r o s l a g T y p i c a l Weld 3. E S J T h e r m a l P r o f i l e  Structure(Ref.  42 35)  - C a l c u l a t e d and M e a s u r e d  43 ........44  4. Boundary C o n d i t i o n s  45  5. N o d a l A r r a n g e m e n t  46  6. M o d e l F l o w c h a r t  47  7. S t r e s s A n a l y s i s S c h e m a t i c D i a g r a m  48  8. UBC  49  E l e c t r o s l a g Unit  9. C o o l i n g  Shoe  10. C o o l i n g 11. Copper  - Water  Channels  50  Shoe Top View  51  recess  12. C o o l i n g  Shoes  13. C o o l i n g  Shoe  52 in Position C l o s e - u p - Water  14. P l a t e E l e c t r o d e 15. Aluminum  53 connections  in Position  Feeder  54 55 56  16. E l e c t r o d e and Copper  Stub  57  17. R u n - i n C o p p e r T a b s  58  18. C o n s t r a i n i n g  59  Rod  w i t h S t r a i n Gauges  19. S t r a i n v e r s u s Time 20. Boxed  Plot  I-Beam  60 61  21. H a r d e n e d  4340 D i s c  Spacer  62  22. I n f e r i o r  I-beam P l a c e m e n t  63  23. S t r a i n - g a u g e  Set-up  64  \u000Cvii  24. T h e r m a l  Stress  Curve  65  25. T h e r m a l  Stress  Curve  ...66  26.  ESJ Thermal  Gradient  67  \u000Cvi i i  Acknowledgement  Sincere guidance  thanks to  Alec  throughout the d u r a t i o n  Thanks fellow  Dr.  Mitchell  of t h i s E.  for  his  work.  are  a l s o due  to Dr.  B.  Hawbolt  graduate  students  for  innumerable  the  technical  and  helpful  discussions. The  assistance  particular greatly  E.  financial International  Eletrometal  Acos F i n o s  Comercio - S e c r e t a r i a is  Barry  and  Mr.  G.  staff,  in  Sidla  is  appreciated.  The Canadian  Mr.  of  gratefully A special  encouragement.  support Development  provided Agency  S.A./Ministerio de T e c n o l o g i a  by  the  and  by  da I n d u s t r i a  Industrial,  e  Brasil  acknowledged. thanks to Consuelo  for  her  care  and  \u000C1  I.  1 .1  INTRODUCTION  Introduction  The  manufacture  conventional  route  to-forging  yield(30  utilization production  requires  routes  t o 60%)  and  t e c h n i q u e s have  is  trepanned  and  isotropic  ESR p r o p e r t i e s .  Topping)  technique  for  2  ingot-to-forging  in  potential Alternative  an  effort  to  MHKW(Midvale-Heppenstalla  conventionally core  remelted,  c e n t r a l part  through  The B . E . S . T . ( B o e h l e r  cast thus  enhanced  Electroslag  also a p o t e n t i a l process  route  two o r more p i e c e s  preform  involved.  ingot-  Hot  f o r improving  yield.  further promising  welding  large  is  equipment  proposed  subsequently  the q u a l i t y of the ingot  v i a the  h a v i n g a low  low  i s one whereby  1  forgings  t o be s o u g h t .  The  improving  A  a  been  solutions.  Klockner-Werke) p r o c e s s  the  steel  s t a r t i n g ingots  have, t h e r e f o r e ,  viable  ingot  large  t i m e due t o t h e heavy w e i g h t s  Several present  of  i s t h e use o f E l e c t r o s l a g J o i n i n g of s t e e l  or j o i n i n g a l r e a d y  forged  before  forging  products  t o make a  to their  final  \u000C2  shape.  Russian  workers  s e c t i o n s used power  bifilar this  i n t h e m a n u f a c t u r e of  station  electrodes  turbogenerators.\"  were  employed  applicable  the  and  c o n f i g u r a t i o n which  investigation  alloy  have d e v e l o p e d  it  7  a method  rotor Four  the  was  fracture  mechanical  and  rotor  obtained.  concurrent  used  efficient.  It  heating  parent  was of  was  metal  also  a In  would  forgings using  assessment  t h e w e l d and  atomic  equipment very  large  consumable  t h a t the p r o c e s s  a comparative  r e s i s t a n c e of  properties  preliminary  and  for  large section  t o be  concluded  t o t h e p r o d u c t i o n of heavy  Cr-Ni-Mo-V s t e e l s  forgings  welding  i s claimed  for joining  be  high*  made of  with  good  found  that  the p a r t s b e i n g  joined  were e l i m i n a t e d .  Little in  the  which the  has  case  been done as t o t h e a p p l i c a t i o n of  carbon  r e p r e s e n t s the bulk main c o n c e r n  testing  and  behaves  product  very  techniques  i s with  and,  steel of  the  f o r g i n g s i n the  qualification. to  t h e r e f o r e , must be  more  process 20-100 t ,  market.  reliability,  In o t h e r  the  the  range  open d i e f o r g i n g  repeatability,  similarly  of  9  Here  ultrasonic  words, t h e  process  conventional  welding  carefully  controlled  to avoid  defects.  The  process  one  single  pass  arc  welding,  is carried and  time  out  with  e a s e and  when compared w i t h ,  savings are  relatively  f o r example,  significant.  The  fast  in  submerged-  resultant  coarse  \u000C3  structure  due t o l o n g  mechanical  properties  procedures  a r e needed.  thermal c y c l e s and b e t t e r  1 .2 P r o c e s s D e s c r i p t i o n  Electroslag  heat  electric  current  passes  Both  molten  by  heat  droplets  through the  principle.  is  through  horizontal  is  is  flux  by  fusion  Joule  and t h e s u r f a c e the  .  As c a n be seen but  and  most  popular  by  welding  e f f e c t when an  of  the  the  s l a g -source.  cooling  shoes  work  The  pool  are  electrode  by  falling  i n F i g . 1, t h e a x i s o f  welding  The r e m e l t e d p r o d u c t  material  welding  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 ) .  from  vertical  position.  and  lower  a p p l i c a t i o n s of  a  t r a n s f e r by g r a v i t y t o t h e weld  the molten  joint  parent  coming  It  generated  t h e t i p of t h e e l e c t r o d e  melted  equipment c o n t r o l  i s one o f t h e s e v e r a l  the E l e c t r o s l a g Remelting whereby  t o produce  and A p p l i c a t i o n  Joining  process  is liable  is  performed  i s surrounded either  in a  by  the  s t a t i o n a r y or  movable.  The employing  flux-coated  version or bare  of  wire  filler  dissimilar  process  electrode  consumable or non-consumable e l e c t r o d e the  the  guides.  is  feeding In  m a t e r i a l ( w i r e + g u i d e s ) and t h e p a r e n t m e t a l compositions  and  when  several  wires  the  one  as w e l l as this often are  case, have used,  \u000C4  depending  on t h e t h i c k n e s s  monitoring  The  of the f e e d i n g  weld  metal  and  four  Because  the  process  being  Fig.  2 illustrates grain  joined,  The  typical  these  forms  a  boundaries  stresses somewhat  The  form p e a r l i t e : along side  plates 5  crack  cooling ferrite  prior-austenite that  i n t h e weld and heat  electrode  as  extend cooling,  affected  and i t i s b e l i e v e d  filler  from  grain the  residual  zone b u t a r e  slag v e l o c i t i e s  w e l d h e a t may a r e used  be r e d u c e d  instead  metal  has  recently  t o e n a b l e more e f f i c i e n t  motions,  electrodes  along  can cause  the p r o e u t e c t o i d  Due t o f a s t  stray  total  3 5  i n t o the  Segregation grains  the  Because the e l e c t r o m a g n e t i c  the  Paton.  i n t h e p r o c e s s when  transfer. fluid  by  i n the l o n g i t u d i n a l d i r e c t i o n .  use o f p l a t e  been c o n s i d e r e d  rates  i n t o the m a t r i x .  relieved  ischaracteristic  below.  network  are present  heat  zone c a n be e x p e c t e d .  microstructures.  b o u n d a r i e s and W i d m a n s t a t t e n grain  by  amount o f h e a t  of these columnar  range  wherein the  have been d e f i n e d  affected  proper  critical.  controlled  grains  a large  heat  slow c o o l i n g  from t h e a u s t e n i t e normally  structures  a large  a p p e a r a n c e as d i s c u s s e d  welded,  structure  are  columnar  introduces  boundaries  being  a casting grains  The p r e s e n c e o f l o n g  parts  the  of the  types of g r a i n  parts  s y s t e m becomes r a t h e r  acquires  s i z e s and o r i e n t a t i o n s removal.  of the  forces  heat  do n o t p r o d u c e a s  a r e s l o w e r ( 2 t o 4 cm/s) and  by a s much a s 30% when  of w i r e w e l d i n g .  Also  the heat  plate flux  \u000C5  t o t h e base The  metal  hydrogen  decrease with A  from t h e s l a g  system  content  increasing  containing  i s more u n i f o r m .  of  be  control.  larger  effect,  at  7  CaF  Also  +  Al 0  even  slag  start  further,  used  should t h i s  to  join  the manufacture  i s recommended  than elsewhere.  for effective  of  thickness,  of g e n e r a t o r r o t o r s  Joining  large  have  welds  be  and t o t h e c o n s t r u c t i o n  boiler  drums used  Welding of  of  rolling  performed.\" machinery Joining  frames  shafts have  requirements.  3  have a l s o  p r e s s e s and a n v i l s as well  Recently,  3  joints  High p r e s s u r e  i n power p l a n t s  forging  mill  4  main  as s h i p  control  qualified  usually  where  Arc  vessels been  Welding  of b r i d g e s , and  heavy  fabricated.  3 5  8  up t o 2000 X 2000 mm a n d rudder  propulsion  f o r use i n C l a s s e d been  A  f o r the nuclear industry, t o  could  b u i l d i n g s and storage t a n k s .  flux  and a p p l i e d t o  vertical  3 5  this  the  the hydrogen  welding of thick employed,  to  these experiments.  the o n - s i t e not  found  t o be a p r o b l e m .  and E l e c t r o s l a g  heavy  flux.  To l e s s e n  pre-heating  s h o u l d improve  prove  found t o  c o n t e n t h a s been  proper  procedure  been  content i n the  procedure throughout  E l e c t r o s l a g Welding been  start  has  3  t h e hydrogen  below,  components was n o r m a l liquid  2  t h e weld  as d i s c u s s e d  steel  calcium fluoride  2  hydrogen  the  6  Ships under  parts  shafting made  by  Lloyd's  has and  been other  Electroslag Register  \u000C6  1 .3 P r e v i o u s Work  The  theory  conduction  o f moving  presented  sources  by R o s e n t h a l  proposed  by R y k a l i n  the  of weld m o d e l l i n g .  field  the t h e r m a l for  some  1 1  1 0  Welding)  and t h e a n a l y t i c a l  s e t b a s i s f o r a l l subsequent Little  stress calculations published  i n welding(Arc  Czech  in  work  2 2  attention  5  modelling  work done i n  h a s been g i v e n t o  Electroslag 2  heat  done w i t h  Joining  except  wire e l e c t r o d e  welding.  The welds  resulting  have  complex  always  hindered  different  processes,  Gray  a l  et  2  have  0  dimensional  stress  treatment  and  equations  especially improved  analysis applied  a  better  analytical  studies  understanding  i n studying thermal Okerblom's  based to  from  gauge  of  materials.  i n f o r m a t i o n was g i v e n w h i c h c o u l d be u s e d  the  and  contractions. carrying  out  i t made use o f i n - p l a n e c u r v a t u r e s  These  authors  experiments  longitudinal contractions.  have,  intended  however, to  test  .  flow  Little to  rather  succeeded the  1 7  one-  heat  experimental theory  the  stresses  on a t w o - d i m e n s i o n a l  thin  of  theory  1 2  on  theory  test than in for  \u000C7  With solution and  the  techniques  faster  computers 1961.  ever  transient heavy  majority  of e x p e r i m e n t a l however,  mm  t o 25.4  Welding  whilst  for  used  with  of  far  back  being  m a t e r i a l s i n the  at  multipass  were g i v e n .  thermal  stresses  The  during  t h i c k n e s s r a n g e of  1\"), w h i c h were a l l done u s i n g i n the p r e s e n t  material.  Nishida  stresses  experimental  and  data,  work were  reviewed  2 1  Arc  performed  s e v e r a l methods  compared  again  of as  made  during  results  accurate  t o make use  efforts  no  computers, more  as  stresses  but  experiments  thermal  attempt  some  studies  mm(0.0l2\" t o  calculating  results  plate,  has  u s i n g much t h i c k e r  modern  s t r e s s e s dates  longitudinal  of  welding,  a  of  first  reported  1 7  welding  0.30  The  in a n a l y s i n g welding  analysing  speed  have been d e v i s e d w h i c h e n a b l e  calculations.  Masubuchi  1 8  increasing  theoretical  working  with  thin  materials.  Eriksson assess  the  tendency avoid as  et a l  3  weld metal  test,  composition  however, t e r m s or  the  a  hot-cracking  i n f l u e n c e on  w e l d s and  t h e Mn/S stress  ratio fields  in relation  to those  test  content  not  present  that  should  should exceed are  to  the h o t - c r a c k i n g  have c o n c l u d e d  c r a c k i n g , the carbon  as p o s s i b l e and  absolute  developed  i n heavy E l e c t r o s l a g  solidification  low  have  0  45.  known  to  be  kept  In  this  either  i n heavy  in  section  welds.  There  exist  several  other  tests  to evaluate  weldability  \u000C8  cracking for  problems  and two of them seem t o be e s p e c i a l l y  solidification  tests. the  cracking:  Varestraint  They a r e t h e same i n p r i n c i p l e  direction  direction.  of the a p p l i e d  strain  and  suitable  Transvarestraint  and o p e r a t i o n , e x c e p t f o r  with respect  They have n o t been a p p l i e d  to  t o the welding  electroslag  welding  configurations.  Ueda analysis of  et  changes  the  hot  cycle  is  hard solid  bead  heated  up  affected  al  liquid  t o study  2  6  temperature.  material  being  close  to  v e r y h i g h t e m p e r a t u r e and  temperature.  As  distribution  o f t h e welded  this  thermal  changes w i t h  assembly  time  i s also  a  imperative to assess  during welding.  have c a l c u l a t e d  the thermal c y c l e i n  that  the nonuniform  flow d i s t r i b u t i o n  of t h i c k  generation of  p o o l and complex p o o l o u t l i n e ,  phases.  and t h e  of the p a r t s  zone d u r i n g E l e c t r o s l a g W e l d i n g  the heat  and l i q u i d  a  effects  stress  with  portion  It i s , therefore,  distribution  et  yield  on t h e m e t a l  to  for theoretical  into consideration  and t h e p a r e n t  performance  of t e m p e r a t u r e .  method  elasticity,  expansion  and have r e a l i z e d  the  of  the temperature  Pertsovskii the heat  taking  c o o l e d down t o room  the temperature  a  of w e l d i n g , a l i m i t e d  the mechanical  function  in  stresses,  of l i n e a r  face  developed  modulus  proceeds,  plates  have  9  such as the weld  thereafter  and  in  the i n s t a n t  joined  1  of thermal  coefficient At  a l  make  steel heat  i t extremely  a t t h e boundary  However, t h e y have r e p l a c e d  between  the  above  \u000C9  mentioned  complex  sources at  d i f f e r e n t levels in  system.  The  v a l u e s and  volumes by  a c o l l e c t i o n of the  r e s u l t s presented  are  applicable  pool  three  for  a  linear  heat  semi-infinite  seem t o a g r e e w e l l  with  t o CGESW(Consumable G u i d e  measured  Electroslag  Welding).  More  recently,  systems(wire shallow rates  and  slag and  Bacon  plate  depth  degree  Joining  as  the  electrode).  requirements,  greater  Electroslag  studied  2 3  of  High smooth  compared  to  present  had  project  similar  heating  2.0\u00B0C/s and  1.4  followed  0.2  -  Solidification  2  8  have  b o t h by  to  welding.  The  critical  weld  been d e f i n e d  stresses  and  are  both  rates,  and  cooling  realized  wire e l e c t r o d e  in  welding.  c a l c u l a t i o n s done f o u n d by  rates,  Bacon  respectively  for and  2 3  0.5  -  3)  that  Brown e t  mainly  welding  the  2  and  7  the  should  solidification  by  al  provided  Electroslag Joining  susceptible  has  cooling  in  Cracking  indicated  applicable,  heating  same t r e n d  1.0\u00B0C/s.(See F i g .  Work d e v e l o p e d al  and  the  flow  deposition  penetration  T e m p e r a t u r e d i s t r i b u t i o n measurements and the  heat  by  same s t r e s s  not  cracking  be  29  volume  taking  change  more  than  speed w h i c h w i l l  Semenov ,  Phillips field or  is  less  conventional  ensure  i n t o account during  et  a  sound thermal  metallurgical  \u000C10  transformations. stress  on  (which  welding  w e l d and  the  proper  depth) of  the  the et the  an  shape  reduction. during  to  increase  i n the  of  pool  Bendis*  joint  of  the  has  3  weld  composition,  factor.  Brown e t a l  the  suggested  7  ,  altered  the  minimum  al  3  recommended 0  should  have  is,therefore,  that  The keeps t h e  to E l e c t r o s l a g  high slag  heat pool  results  that  parameters  behaves q u i t e d i f f e r e n t l y compared  and  leads  welded  found  t h e Mn/S of  no  ratio  respect  Makara  joint  and when  stress  of  are:  3 5  the  shape  applying  Semenov e t a l  2  and  9  lower  than  to E r i k s s o n  et  cracking.  It  Welding(wire to  period  resistance  Paton  to a value  of  tendency  one-half  by  solidification  Electroslag with  to  cracks by  and  improvement  4 5 which a c c o r d i n g in  to  t h a t c o n t r o l the  the  depth  varies  in crack  reported  pool  the  t h e most c r i t i c a l  c r a c k i n g as of  determine  input  to  during  metal  shape f a c t o r  weld v o l t a g e  resulted  clear  the  c o n d i t i o n s given  even d e l i b e r a t e l y  t o the  i n c r e a s i n g heat  however,  welding  speed  also increases.According  rigidity 2  welding  weld  authors,  penetration  w e l d gap  sharply,  tensile  to these  i s when o n e - q u a r t e r  to hot  chemical  the  concluded  The  metal  correct  profile  Welding  i s welded.  of  a  fully-constrained  critical  With  form c r a c k s  a  According  the  the  increases  Electroslag  the  with  factor(ratio  the  of  case).  assures  a sound w e l d .  tendency  c o n s i s t s i n imposing  region  worst  together  metal pool  al\"\",  the  voltage  shape  for  technique  solidifying  represents  stable the  the  The  electrode)  build-up  as  Joining(plate electrode)  input in  observed the  in E l e c t r o s l a g  molten  condition  Welding can  be  which very  \u000C11  effective it  avoiding  the uptake  i s known t o enhance  welds.  The  exists the to  in  both  heat fail  point solute  i n the weld  this  rich  0.25%  1.0%  solidus  capacity  in this  phases  temperature a hot  zone a t t h e g r a i n  what  i s known as  rupture  contrasting  fails  with  cold  boundaries under  Rymkevich  determination  of  the  Welding  of c a r b o n  steels  brittle and  In  3  2  i t t o be  When  the  deformation  at the and  heat  produce  a  stresses  both  cases,  intergranular  form,  intracrystalline  mainly al  the  2  the  with  below  of s h r i n k a g e  cracking.  temperature  found  40\u00B0C  fuse l o c a l l y  temperature,  et  grain during  oxides  o c c u r s i n an  of  Lower m e l t i n g p o i n t  3 3  and  resulting  8  from  steels  Weinberg.\"  the e f f e c t  lower  embrittlement.\"  melting  results  exceed  sulphides  of t h e m e t a l  cracks,  by  develops.  liquation  typical  to the m e l t i n g  incipient  at  in  S t e e l s a r e known  casting  range  tear  as  3 3  close  starts  reported  the  and  microsegregation  range  as  in  cracking)  which  continuous  such  that  to  steel  or  C the b r i t t l e  weaker b o n d i n g  path  the  For  6  of t h e m e t a l  secondary  however,  in  temperature  deformations  causing  i s ascribed  cracks  but  cracking(hot cracks)  metal(solidification  segregation  to  affected  of s o l i d i f i c a t i o n  behaviour  solidification.\"  from m o i s t u r e  to  manner a t t e m p e r a t u r e s  regions  boundary  leading  zonediquation cracking).  in a b r i t t l e  and  conditions  possibility  affected  of hydrogen  have range  from  hydrogen  pursued  the  in Electroslag  1380-1450\u00B0C.  \u000C12  1.5  Present  Objectives  As d e s c r i b e d above, c o n d i t i o n s cracks  are  realized  in  the  experienced  by a h i g h e r  the  electrode technique.  plate  and e x t e n t  heat  of s o l i d i f i c a t i o n  proper  welding  conditions  studies  of the thermal  in  process  the  welds  d e s p i t e the  i n p u t and s u i t a b l e  has  and,  prompted  to  improvements  welding  An u n d e r s t a n d i n g  cracking  leading  flux  of the  therefore, t h e need  in  nature of  the  for further  s t r e s s e s produced i n the p r o c e s s .  \u000C13  II.  The  inherent  experimental  MATHEMATICAL MODELING  difficulties  work,  especially  determination  i n w e l d s , make  a  order  model  in  following  to  temperature  Weld c r a c k i n g thermal  stress-field  the  dominant when  point first  of  process  of  a  to  use  behaves.  computer  The  program  stresses realized blocks,  stress  based  during upon  a  by  to  nonuniform o f how  be  caused  temperature  much  heat  flows  joined.  Although  radiation  Electroslag  Joining,  conduction  mode and  i n the b l o c k s , except convection  start  and is  d u r i n g hot  p l a y i n g a more  role.  to Liby et a l . heat parent  temperature time  transfer  radiation  considered: the  case  J o i n i n g appears  a question  being  place while  heat  According  through  plates  take  significant  be  the  thick  induced  through  topping  of  in Electroslag  It i s essentially  convection  the  performing  input.  changes.  the  how  the thermal  Joining  profile  with  i t a l l t h e more i n t e r e s t i n g  study  to calculate  Electroslag  by  in  pages c o n t a i n the development  w h i c h was u s e d the  associated  generation blocks.  3  \" two a s p e c t s i n the slag The f o r m e r  as the s t a r t i n g  value  of heat and  flow  heat  conduction  i s assigned  a melting  for calculations  s t e p o f t h e model a n d from t h e s e c o n d  need t o  time  i n the s t e p on,  \u000C1 4  it  is calculated  the  electrode  latter  will  f o r every time  step,  taking  l a t e n t heat, heat c o n d u c t i v i t y  constitute  the u n d e r l y i n g  temperature  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  general  dimensions  The which  determined.  heat  i s thought  conduction to describe  Fourier  assumptions  conditions  could  i) No-flux According  to  be p r o p e r l y  be  and  3 5  1.2%  only  made  so  at  the  of  heat  throught  solve  the  the  two  and i s i t ,  boundary  4 and F i g .  top  1.3% of t h e t o t a l  i s actually lost  to  that  Fig.  in  involved  In o r d e r  applied:(See  boundary c o n d i t i o n  to P a t o n  surfaces  had  equation  t h e phenomena  t o c a l c u l a t e the thermal p r o f i l e s .  several  the  be  and d e n s i t y .  Assumpt i o n s  The  used  distribution will  consideration  p r i n c i p l e b a s e d upon  the  2.1.1  into  5)  slag.  i s radiated to  r a d i a t i o n to the  atmosphere. ii)  Symmetry  symmetrical, valid  a  axis no-flux  \u2014  because boundary  the  welding  condition  process  i s thought  is  t o be a  assumption.  iii)  Block  walls  -- t h e i n t e r n a l w a l l s  were  also  assumed  a  \u000C1 5  no-flux  condition  as  the  heat  radiation  mentioned  in i) i s  negligible. i v ) A l l the heat and  r e a c h i n g the  flows to the b l o c k s b e i n g v)  Positions  line)  considered  temperature  of the heat  temperature  f o r carbon  Physical  the  i s not  idealized  electrical  be  source  heat  was  taken  in light  weld  i n a s t a b l e manner.  vii)  The  \"indefinitely\" unsteady viii) in  heat along  i n the case  the z d i r e c t i o n i x ) Symmetry  side  of t h e  the  face(fusion and  melting  the point  constant  into consideration. as the energy pool)  of t h e  the welding  fact  equipment  Values  Such  coming  actually that,  and  from  reaches  i f the  right  performing  f o r Cp,  an  the  k and  are  I. source(slag the  s t a t e model was As  temperature  reality  i s chosen,  in Table  hot  were c o n s i d e r e d t o be  volume o f s l a g  listed  room  source(slag+metal  equilibrium  operates  the  ( s l a g ) t o be  t o o f a r from  heat  at  from  steel(1520\u00B0C.)  properties  the e l e c t r o d e l a t e n t assumption  to  leaves i t  welded.  i n t h e b l o c k away  are  vi)  slag-metal interface  height  used  of  to p r e d i c t  of w e l d i n g  large  pool)  the  block,  the t h e r m a l  travels although  an  profiles.  a s s e m b l i e s , no  heat  flow  on  one  i s assumed.  i s i n v o k e d and  joining  + metal  assembly  as  the m o d e l l i n g illustrated  is  built  i n F i g . 4.  \u000C16  2.1.2  Derivation  The  Of  Equations  two d i m e n s i o n a l h e a t  3T  ^  2  \" H ?  conduction  3T ~~3^  q  2  +  Where:  P Cp  k  k  T.=  temperature  t  =  time  q  = heat  k = heat  p =  Letting generation  a  =p  nor  Cp/k  equation  3_T 3 t  flux  conductivity  density  Cp = s p e c i f i c  heat  knowing t h a t  there  and  consumption  (1 )  is  neither  in the blocks(q/k=0),  heat  equation  (1)  becomes:  3 T  3 T 2  2  f  3x'  +  3y  a 3T 3t  (2)  \u000C17  Equation boundary  2.1.3  (2) i s s o l v e d  conditions(See  Numerical  Using governing as:(See  a  numerically  subjected  to  different  Appendix A ) .  Solution  heat  balance  equation  was  approach  expressed  f o r an i n t e r i o r  in  finite  node, t h e  difference  form  F i g . 2) For  1&lt;i&lt;IM-1 1&lt;j&lt;IN  For  the f i r s t  T. . . ,  -a Ax^  (  2  half  time  . 2a,*  Ac  Axz  _a  i,i+l 1,1 Ay.(Ay. + Ay. ) 3 3 J+l  Similarly  -2a Ayj(Ayj+Ayj_1)  T  .  Ax^  1,2  2 a I , ., - T. . +  step:  1  ,  3  X  i , i Ay.(Ay. + 3 3  ^ At  m  J  i , i - l Ay  time  V j  (Ay.+Ay  )  step:  2 a A  /  J-1  o  , _2_ +  n  2 a ( T . .- T. . .)  _  o  T. ._.  At  J  f o r the second h a l f  m\"+l  2 T  1  . j + 1  )  2  a  T  n+1 T.  Ay (Ay +Ay _ ) j  j  j  *  1  2 T. . )  '  J  (4)  \u000C18  and ection  solved  Finite  determined  numerically Difference  similarly(See  conditions,  typical  distribution  i n the blocks)  the  of  by u s i n g  an I m p l i c i t  method  i n 2-D.  Appendix  A).  Electroslag calls  The o t h e r The  Joining(mainly  f o r an i m p l i c i t  This  technique  approach  in  half  s t e p and a g a i n  time  (implicit system  by  of  direction(implicit  rows)  equations  restrictions presents  one  as  t h e main  to  a 1-D  o f any  spatial  flowchart  s u c h as  stability  using  s o l u t i o n f o r the other  simultaneously  the  heat  a  1-D  by c o l u m n s ) f o r t h e f i r s t  and s e c o n d h a l f t i m e is  state  the  method  s o l v e s a 2-D p r o b l e m by  Dir  nodes were  unsteady  I.A.D.F.D., making t h e s o l u t i o n i n d e p e n d e n t  criteria.  Alternate  step.  3 6  solved  and time  direction  A tridiagonal without  increments.  any Fig.  f o r the model.  2.2 T h e r m a l S t r e s s And S t r a i n C a l c u l a t i o n  Stresses elements  of  plate  joining  but,  as  rather and  the  a p p e a r as a r e s u l t a body w h i c h c a n n o t the heating process  of nonuniform expand  a  long  are  one, t h e t o t a l  l a r g e a n d , t h e r e f o r e , bound t o  strains.  freely.  and c o o l i n g r a t e s  is  heating  create  of  the  In E l e c t r o s l a g typically heat  thermal  low  input i s stresses  6  \u000C19  Considering and  length  other  a  rectangular  L(See F i g . 7),  dimensions(See  simple  model  was  used  of  assuming  Appendix  C)  depth  L t o be  and  the  beam i s c o n s i d e r e d  a  s t r e s s assumption  2h,  thickness  TH  much l a r g e r t h a n  knowing  to c a l c u l a t e thermal  Because plane  beam  that  T  = T(x),  s t r e s s e s and  thin(mid-section  plane  the a  strains.  in F i g .  4)  i s made:  zz  xy  yz  a  XX  =  a  =  a  zx  = 0  (6)  and  a  For  the  dimensional  yy  analytical  problem  which  by  solution applying  one-dimensional  problem(equation  free  except  of  traction  following conditions  equations 3 8  the  end  satisfy  (7))  of  the  equation  equilibrium  Components:  resulting (6)  a l l bounding  f a c e s y=+L/2 and  :  Stress  (7)  (x)  yy  and  becomes surfaces  y = - L / 2 and  twoa are the  compatibility  \u000C20  \u00B0yy  c  = a XX  the  NT  integral  The function  of  by  appear  nodal  aETzdz  from  thermal  and  the were  -h  a  to  et  a l .  3  used  thus,  in  in the  ETdz  from  &lt;9&gt;  to  for  7  +h  and  MT  steel. above and  (8)  y-direction  calculated  experimental  carbon  equations  the  were  the  expression  covering  to  -h  is  +h  Modulus)  according  analytical  stresses  temperature  of  E(Young's  Minakami in  .  0  integral  of  (8)  Components:  temperature  numerically the  of  the  values  published which  is  =  KT-H-f^MT  ZX  Strain  Where  + - ^  =\"^1  for  entire  The  were (10)  each  height  as  a  results integrals  calculated to  calculate  corresponding being  welded.  \u000C21  A  sample o f t h e computer program  and  strains  2.3  Computer P r o d u c t i o n Runs  The welding which  simulated  would  real  affect input  the  distribution.  the model.  temperature  incoming  replaced calculated  energy  A massive  several  stress  state.  were made i n t h e parameters Thus,  produced  caused  a  very  a l l of  which  varying a  different  different  stable  the  stress  electrically,  c o n s i d e r e d t o be c o n s t a n t t h r o u g h o u t  every  conditions  subsequent  upon a  heat  a small  F used  distributions),  furnace  voltage,  time  balance  into  to determine  for step  by  released  the j o i n i n g  how  the  performed  amount o f e n e r g y  goes  weld a  new  at  the  by  blocks.  much o f t h e  f l o w s t h r o u g h t h e b l o c k s g i v e s an  the The  available  indication  of  of the p r o c e s s .  heat e x t r a c t i o n  cooling  for  the  turn,  melting e f f e c t i v e l y factor  were p e r f o r m e d  temperature  Only  the thermal e f f i c i e n c y  aluminum  was  initial  boundary.  efficiency  in  velocity The  is  electrode  welded  which,  stresses  Provisions  S i n c e the p r o c e s s i s  welding  fusion  in  namely amperage and speed  region  final  the  temperature  joinings.  to a l l o w f o r changes  welding  the  (different  to c a l c u l a t e  B.  thermal s t r e s s c a l c u l a t i o n s conditions  program  heat  i s shown i n A p p e n d i x  used  shoes.  This  i s performed  by  the  very e f f i c i e n t  heat  copper sink  and  absorbs  \u000C22  approximately radiation  50%  energy,  of t h e e n e r g y except  until  available the v e r y  and  end  little  of t h e  is lost  process.  as  \u000C23  III.  3.1  Furnace  The  in  as  weight  250  KVA  primary  Design  equipment  facility  shown  and  phase  line.  60 V,  AC  c u r r e n t of up  voltage  of  T h i s dry 600  t o 8000  carriage  furnace  framework(Fig.8)  carriage  which  V  from  readily  monitored  0 to  detailed 3  and  type  mm/min.  from  several on  cast  Electroslag  steel  power  up  to  supply  connected  i n the  1 t  is  a  t o a 600  V  transformer  a low  operates  range  of  25-  A.  consists on  The  speed  from  an  rails  electrode inside  b) an  enables  parameters  in a control  furnace  design  the  electrode  reductor that  operational  instruments the  of a)  aluminum  i s suspended  163  information  can  is  and  coupled to a v a r i a b l e  speeds  elsewhere.  slides  the U B C  furnace  which  e l e c t r o d e f e e d i n g system  holder  3.2  The  transformer  high  More  This unit  o p e r a t e s on AC.  a  drive  f o r a l l r u n s was  i n F i g . 8.  step-down single  used  with  The  EXPERIMENTAL WORK  are  panel. is  given  9  C o o l i n g Shoe  Design  Electroslag  Joining  i s fundamentally  similar  to  Electroslag  \u000C24  Remelting.The  readily  noticeable difference lies  product:  i n the j o i n i n g  the  e x t r a c t i o n system w h i l s t  is  heat  completely  flows is  process  surrounded  by c o n d u c t i o n  the parent  through the blocks  e x t r a c t e d v i a the c o o l i n g shoes.  set-up  plays  a significant  role  material  in plain  by w a t e r - c o o l e d  i n the remelted is  remelting  copper  part  of  the product  crucibles.  Heat  and a s u b s t a n t i a l p o r t i o n  Therefore,  this  in controlling  part  of the  the d i r e c t i o n a l  solidification.  The slabs 11  design  25.4 mm  mm  deep  aluminum inner  used  X  254 mm  cooling  section(See  copper  increases  X  F i g . 9 ) copper  surface  rectangular  aluminum  1066.8 mm(1\"X10\"X42\"),  groves(channels)  slab(Fig.  the  features  10).This area  per  shoe  on  with  three  the  outer  and w h i c h was c o u p l e d recess  contact  in and  enables  higher  conductivity, i t resulted in a rather e f f i c i e n t  Fig  thus  ensuring  proper  12 and 13 show t h e s h o e s  enters leaves  through through  Joining  t h e copper has a heat  c o o l i n g and good wear r e s i s t a n c e . i n p l a c e and a c l o s e - u p .  the bottom, c i r c u l a t e s  The water  through  the channels  metal)  in  and  the t o p .  3.3 E l e c t r o d e And S l a g  The  part proper  of the e l e c t r o d e .  removal,  that  copper  positioning heat  Considering  the  to the  Preparation  electrode(i.e.,  the  filler  h a s t h e same c o m p o s i t i o n ( w h e n e v e r  Electroslag  p o s s i b l e even  from t h e  \u000C25  same s t e e l assures  shop r u n ) a s t h e p a r e n t chemical  commercial material  carbon  homogeneity steel  used  was ASTM A36 whose  material being  and  weld  f o r both  welded.  This  repeatability.  the  filler  and  8  The  parent  composition i s :  C=0.29% Mn=0.90% Si=0.15% P=0.04% S=0.05%  A 152.0  typical  cooled  stub  in  frame. ( F i g .  have a f a s t e r  152 mm  500  kg e a c h  The  14 a n d 15.  is  16)  152.4 mm(6\") l o n g  Two  Figs.  that  A  perfectly small  i s welded weld  welding  would  aligned  rod  be  mm  with  25 mm(l\")  in  two  thick,  It i s connected  t o t h e bottom  as  t o a water-  the  furnace  diameter  and  o f the e l e c t r o d e so as  start.  X 457 mm X 914 mm were u s e d  section  4\") X 2930 m m ( 1 1 5 \" ) , 3 8  mm(6\") X 19 mm(3/  illustrated  to  electrode  plates  weighing  approximately  i n the experiments.  flux  used  was o f c o m p o s i t i o n :  55F/15/15/15,  i.e.,  C a F =55% 2  and  Ca0=l5%  pre-heated  0.-15%  a t a temperature  Si0 =l5% 2  of a b o u t  (% i n w e i g h t )  600\u00B0C  i n order t o  \u000C26  avoid  any  moisture  enough t o m a i n t a i n  retention.  A total  stable welding  o f 7.0 kg p e r w e l d was  conditions.  3.4 Weld S e t - u p And C o n s t r a i n i n g  All  the weld p r e p a r a t i o n  platform of  that  asbestos  plates  are  since  welded  (Fig.  safe  were  along sealing  When t h i s  in  on  11).  spread  8).  to  A protective where  starter  t o make  weld set-up  water-cooled  At the t o p of  76.2 mm(3\") r u n - o u t and t h u s ,  layer  proper  run-in  17 were u s e d .  height  the  ensure  efficient,  colorlith  sumps were  accommodate  the tack-  the s l a g  the j o i n i n g s e c t i o n s .  cooling  tightened  movable  of the weld and a l s o  in Fig.  the block  a  colorlith order  more  t o the weld,  t o extend  The  blocks  operations  close  volume p a s t  In  the s t a r t  sumps, a s shown  blocks  the  positioned.  stripping  copper  on a m o n o r a i l ( F i g .  i s p u t on t o p o f t h e  penetration and  slides  was done on  shoes a r e h e l d  to set  An  bolts  welded  100 mm  onto  apart(which  a i r s e t t i n g high  t h e shoe s i d e s against  position.  t h e w e l d gap u s i n g  the b l o c k s ( F i g . 1 2 ) . is  the  temperature  touching  the  recess  the assembly  blocks  At t h i s  stage  was r e a d y  to  t o be  the electrode  the overhead crane,  are The  length)  mortar(SAIRSET) i s  any p o s s i b l e s l a g a n d / o r m e t a l  was c o m p l e t e d  welding  i n p o s i t i o n by b r a c e s w h i c h  provide  a  leakage. placed  in  was i n s e r t e d  a l i g n e d and  tightened  \u000C27  to the stub.  When  a  observed,  weld  i t may  accommodate one.  a  be  fully-constrained a  good  contraction  Therefore,  produce  is  weld  crack.  the  t o p of the b l o c k s .  Fig.  set-ups  point(metal not  take  the  were p l a c e d effected would the  gauges were u n a b l e  It  was  result  became  more  in(See  up  to record  below  welded  enough  became  the a c t u a l  the  away  I-beams  could  constrain  stiffness  rods  would  constraining capability  be  which  The I-beams were a r c w e l d e d on t o from t h e h o t f a c e , A  compression  F i g . 18).  welding  i f the c o n s t r a i n i n g  system  rod  965.2 mm(38\") i n l e n g t h and s l i g h t l y  closing  the  that  lower  a stronger  a t the bottom.  free  rigid  that  then thought  enabling  in  t o be s t r o n g  and, t h e r e f o r e , d i d not p r o p e r l y  ends o f t h e b l o c k s  positioned  I(inertia  being  i n a weld c r a c k .  top and l a t e r  to  as t h e w e l d went on t h e s y s t e m ( b l o c k s  a t t h e bottom a  thus,  with  as  stage  p o o l ) , t o an e x t e n t  weld.  so  19) A t t h i s  region)  the pressure  be a sound  as the s e t  u n d e r g o n e by t h e weld m e t a l . ( S e e F i g .  + weld  can  moment o f 126 i n \" , a s shown i n  strain  joined  strain  that  weld  is  A s t u r d i e r I-beam was needed a n d i t was  and  was r e a l i z e d  likely  prepared  rigid  it  the  I-beam  The w e l d on t h e I-beam d i d f a i l the  cracking  i n t h e s y s t e m and was p o s i t i o n e d a t  so a s t o have an i n e r t i a  20.  will  were an  no  that  23 i n \" was t h o u g h t  up t o t h e p r e s s u r e s  prepared  and  Initially  moment) o f a p p r o x i m a t e l y to stand  indication  movements  constrained  and  initially  76.2 mm(3\") tapered  in  at the  diameter,  o f f a t t h e ends was  restraining  the  parts  from  F i g . 20 a n d F i g . 21 show t h e boxed I -  \u000C28  beam w i t h spacer  increased  to a v o i d  The  inertia  any  localized  strain-gauges  monitored  by  moment and  a  was  set  on  the  4340  both c o n s t r a i n i n g  Transducer/Strain  u s e d and  hardened  disc  deformation.  were  STRAINSERT - M o d e l TN8C. factor  the  For  Indicator  correct  a p p a r a t u s was  rods  8-channel  measurements  operated  and  in  a  gauge  full  bridge  above  except  mode.  Fig. for  the  22  fact  bottom.  that  This  experienced as  presents  would be  strains  are  3.5  i n the  calcium on  top  assembly  the  comparable the  elastic  region.  Operation  electrode  fluoride of  the  same  known,  Sequence of  After  the  r o d s were p l a c e d  strength  the  and  same s e t - u p d e s c r i b e d  constraining  way,  whilst  when the  remain  the  the  steel  starter  at  constraining stifness the  t o the  stresses  - Welding  is  r o d s were p o s i t i o n e d  shavings(the and  be  be  would as  therefore,  strength. c a l c u l a t e d as  the be  large the  rod  Once  the  the  rods  Procedure  properly  plate  and,  weld can  rigidity  would not  top  at  aligned,  a  'compact') i s  under  the  mixture  of  positioned  electrode  t i p ; the  \u000C29  cooling  system  poured  into  25 mm flux  t h e gap.  diameter starts  more  3.6  Joining  throughout  At  this  parameters  experimental run. runs  at  the s m a l l the  i s such that  no  i s g e n e r a t e d by  furnace  slag  resistance  for  a  typical  Aluminum d e o x i d a t i o n a  rate  is  stage,some of  t h e volume of s l a g  a l l the  flux  an a r c i s s t r u c k and  melted.  heat  the  the p r e - h e a t e d  was  of  1 g/min.(See  room  temperature,  15)  Residual Stress  After residual  the  weld  in  the  weld.  and  the  cooled  the p a r e n t m e t a l ,  The  results  Method.\" Fig. 5  Temperature  equipment  used  were a r r i v e d 23  down  to  at the  i n the heat  was a t by  supplied  top  affected by  strain  of  gauge  the  zone and  Photolastic  u s i n g the B l i n d  shows t h e s c h e m a t i c  Hole  in  Inc.,  Drilling  set-up.  Measurements  Chromel-alumel measure  was.  s t r e s s measurements were p e r f o r m e d  assembly  3.7  soon  and  T a b l e I I shows  effected  Initially  and  occurs  Electroslag  f o r l e a k s and  rod i s r e a d i l y  to melt  arcing  only.  Fig.  i s checked  temperatures  thermocouples in  order  were to  p l a c e d i n the b l o c k t o  compare  them  with  the  \u000C30  model.(Fig.  3)  The  results  obtained  depth p r e d i c t e d agreed well with  the  as  w e l l as  observed  the  values.  penetration  \u000C31  IV.  The  Russian  Welding(wire  DISCUSSION AND RESULTS  and  Czech  electrode)  a s s o c i a t e d mostly  with  transformational  volume  that  there existed  more  prone  whether even was  to  indicated  changes  The  attempts  height  field  work  in a qualitative  t o study  in this  thermal  stress  was b e i n g  r e l a x e d as the heat  the  weld  height.  The l a r g e h e a t  this  process,  a  rather  develop.  Further experimentation  of  absorbing  to e f f e c t i v e l y that  leading  cracks  i t was n e v e r fully  sense  to  were  made  clear  understood fields  or  i n ESJ  was n o t known.  stresses  the  source  input(1.7  broad  zone)  fact  capable  were,  during  plate  work, r e v e a l e d t h a t a g r e a t amount o f  affected  the  cracks  magnitude of t h e s t r e s s  the  and  hot  composition  had been  welding  I-beams a n d r o d s  Electroslag  range wherein  electrode  creates  that  in  w h i c h would c a u s e d e f e c t s and  In t h e i r  stress  n o t d e f i n e d and even  first  developed  t h e weld c h e m i c a l  appear.  investigated.  The  had  a critical  the thermal  work  travelled  kW/cm), t y p i c a l o f  temperature the  confirmed  along  high  field(heat stresses that  the i n a b i l i t y  of the  c o n s t r a i n the blocks a t the top  thermal  field  was accommodating t h e  deformations.  A much s h o r t e r w e l d was made positioned above,  at  the weld  t h e bottom.  with  the  constraining  rods  The p r o p o s a l was t h a t , a s m e n t i o n e d  strength at a smaller height  in  terms  of  weld  \u000C32  cross-sectional and,  therefore,  stresses. did  that  would be a b l e t o t a k e  up t h e weld  even a f t e r  that  they  ultrasonically  field  thermal  and  no  t o Co-60 r a d i a t i o n  In  resulting  found.  with  calculated experimental  the  actual  joining  thermal  stresses  for different  d i s t a n c e s away from t h e  in  When  the  end,  underneath  If  compressive then  new  radiation  stresses  lead  15  that  start  would  radiography.  i s noted  for  strength,  found.  It  stresses  those  by  were  24 t h e c o n d i t i o n s s e t f o r t h e computer  hot face are t e n s i l e  approached  bottom)  for approximately  o f c r a c k s was  run were t h e same a s t h e ones u n d e r g o n e by experiment.  weld  presumably  c r a c k s were  c o n d i t i o n s were c o n s i s t e n t Fig.  the  weld.  s t r e s s e s p r e d i c t e d by t h e model and  welding  observation.  account  having  were s e n t o u t t o be i n s p e c t e d  a n d a g a i n no i n d i c a t i o n  several  block  procedure  in a true f u l l y - c o n s t r a i n e d  tested  that  The  of the rods  any c r a c k s , t h e t h e r m a l  p i e c e s were e x p o s e d  hours  to the area  w e l d s ( c o n s t r a i n e d a t t h e t o p and a t t h e  thoroughly  The  latter  found  them even  Both  After  the  I t was  not p r e s e n t  relaxed  for  a r e a would be c o m p a r a b l e  they  to  d u r i n g most p a r t of t h e weld  nature.  boundary  and appear,  the l i q u i d  convection  to cracks.  whereupon  subsequently,  than  pool  imposed t o compressive  inducing  p o o l where m e t a l  induce  liquid  c o n d i t i o n s were  stresses are higher should  the  the  tensile  is solidifying.  the m a t e r i a l y i e l d  the high t e n s i l e  stresses  that  \u000C33  In with  order to i n v e s t i g a t e  identical  welding  w h i c h was d o u b l e d observed.(See values high  a  adjusting  in  the  principle  In  set  latter  metal)  indicate  a  less  a  same  trend  run  height  was  again  words, s h o u l d t h e computed  welding severe  be e x c e e d i n g l y  conditions  stress  field  t h e optimum w e l d i n g  then,  by  would  result  effected,  could  c o n d i t i o n s t o produce  weld.  residual  stresses  remaining  were measured  d e v e l o p d u r i n g or a f t e r  were  Appendix  tensile  and  i n the system  and  cooling  show  tensile  The r e s i d u a l  stresses  found  welding.  metal,  after  heat  to  affected  below t h e m a t e r i a l  zone and w e l d  yield  point.  See  D.  Based  on  experiments  being  the  modelling  performed,  characteristic  broad  joined  i n the heat  field  other  of  a l l three positions(parent  parts  and t h e  above,  f o r t h e weld  p r o v i d e d enough p e n e t r a t i o n i s  room t e m p e r a t u r e  stresses  as  up) was t r i e d  particular  in turn,  The  in  conditions(except  F i g . 25).  a crack-free  to  the r e s u l t s  f o r t h e s t r e s s e s a t t h e end o f o f t h e w e l d  for  which,  further  it  thermal  results is  field  enhances thermal  affected  and  possible  on to  of E l e c t r o s l a g stresses  say  actual  that  Joining  the  progresses.  the  i n the  i n the weld(as  z o n e ) w h i c h a r e r e l a x e d by  t o a c o n s i d e r a b l e e x t e n t a s t h e weld  the  well  thermal  \u000C34  These the Czech  findings literature  seem t o c o n t r a d i c t on E l e c t r o s l a g  the r e s u l t s  Welding  o b s e r v e d and p r e d i c t e d  that  the c r a c k s i n  if  will  always  stresses  start  when  at  a l l present,  compressive  contraction,  If  wherever  the  were t o be f o l l o w e d , t h e n would  predicted  high alloy  present once  i t  study is  transformation  volume  due  Joining,  to  would grades  have a  do.  thermal  not.  changes.  hot c r a c k i n g  transforms  when  a  at  steel  These  of  workers  s u c h a s Ni-Cr-Mo-V I f so, the s t e e l  resulted  'good'  to predicting which  cracks  steels  should already  Electroslag  mounting  steel  have  temperature  not c r a c k when c a r b o n  I t has been  occur at the t o p of the j o i n t  approach a  transformation that  cracks.  t h e t o p may b e .  Czech/Russian  temperatures  p r e s e n t e d by  high low have  f o r g i n g s do  used  f o r the  in solidification  cracking  crack-former  in  terms  of  \u000C35  V.  1)  Considering  experimental and  evidence,  Electroslag  thermal that  stress  the  these  2) predicted residual and,  i t can  crack  result  stress  intrinsic  the  quite significantly  profiles  features.  5)  The  cracks  in  Electroslag  than  mathematical  of t h i s  clear  i n e a c h of The  different. the  results  experimentally.  i n ESJ  The  strength  under  the  level  conditions  ESW.  I t should probably  during  is  i s more a p p l i c a b l e t o t h e w e l d i n g  than  Welding  be  as a f i e l d  model was  due  regarded welding  more  its as  a  process.  developed  of t h e  to  of  thermal  which  enables  and  stress  welding  theoretical  the a p p l i c a t i o n  is therefore quite  observed  to  fields.  measurement c o n f i r m s  and  Joining  technique  A simple  realized  stress  and  Welding as  It  experienced  different  semi-quantitative visualisation  trends  tendency.  c r a c k s were d e t e c t e d  forgings  shop f a b r i c a t i o n  4)  Electroslag  v a l u e s a r e below t h e weld y i e l d  Electroslag gauge  calculations  that  cracky  stress  w h i c h would have p r o d u c e d  heavy  said  tendency  model  t h e r e f o r e , no  3)  hot  in  formation  the  be  thermal  residual  by  theoretical  differ  b u i l d - u p and  dissimilar  The  the  Joining  processes  resulting  CONCLUSIONS  p r e d i c t i o n s can  heavy  be  used  thickness joining  when a s s e s s i n g  method.  \u000C36  VI.  SUGGESTIONS FOR FUTURE WORK  1) P r o d u c e a w e l d h a v i n g narrow guide  weld  gap,  i n order  explaining  2)  to  to verify  hot c r a c k s  Use  transformation 1)  using  wire  alloy  temperatures  thermal  field,  e l e c t r o d e w i t h narrow  the thermal  in this  higher  a narrow  stress  field  i.e.,a consumable  approach  to  kind of weld.  steels  under  having  different  t h e same c o n d i t i o n s  c h e c k on t h e i n f l u e n c e o f volume change  lower  cited  i n crack  in  forming  tendency.  3) D e v e l o p a more s o p h i s t i c a t e d to  be a b l e  stresses. finite support  to a r r i v e  a t more  accurate  Such.an a p p r o a c h would  element  thermal  in relation  mathematical  i n order  when  evaluating  involve a lengthy  and complex  stress analysis  values  model  coupled  t o the boundary c o n d i t i o n s .  with  experimental  \u000C37  BIBLIOGRAPHY 1.  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Mosny, J . and S l a b o n , I . , P r o c e e d i n g s of an I n t e r n a t i o n a l C o n f e r e n c e on W e l d i n g R e s e a r c h r e l a t e d t o Power P l a n t , U. of Southampton, E n g l a n d , S e p t . 1972, p. 456-463  42.  W e i n b e r g , F., Met.219-227  43.  B e n d i s , A.,  Zvaranie, v o l .  16,  44.  M a k a r a , A. M.; G o t a l ' s k i i , S v a r k a , v o l . 8, ( 4 ) , 1955,  Yu. p.  45.  R e d n e r , S., \"Measurement o f R e s i d u a l S t r e s s e s by B l i n d H o l e 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 I n c . , May 1974  46.  W e i n b e r g , F., 513-522  47.  P a t o n , B. E. e t a l . . , P r o c e e d i n g s of a C o n f e r e n c e on The ISI , U. of S h e f f i e l d , J a n . 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 o f C o l d C r a c k i n g C o n t r o l i n W e l d s \" , D o m i n i o n B r i d g e Company, L t d . , M o n t r e a l , 1975  R.  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ESR,  \u000C40  Table  I  -  Computer  Model  TMP*1520.0 (Deg C) INITIAL TEMP2 5 . 0 ( D e g C) TIME STEP= 3 0 . 0 (s) SPECIFIC HEAT=0.1070 (cal/g.C) DENSITY- 7.860 (g/cm**3) CONDUCTIVITY*0.0740 (cal/cm.s.C) DX= 2 . 0 (cm) HEAT FACTOR* 0 . 1 4 2 HEAT SOURCE D E P T H = 1 2 . 0 0 0 (cm) PRINT CYCLE600.0 (s) E N D OF C A L C U L A T I O N * 4200.0 (s) DY= 0 . 5 1.0 1 .0 1.0 1.0 DY= 3.0 3.0 3.0 3.0 3.0 DY= 3.0 3.0 3.0 3.0 3.0 NUMBER OF D I V I S I O N S I N X - D I R E C T I O N  1 .0 3.0 3.0 = 50  NUMBER  OF D I V I S I O N S  =  WELDING  PARAMETERS:  WELD  GAP*  CURRENT*  5000.0  ELECTRODE LATENT  9 . 5 cm  HEAT*  TOPPING  HOT  TOP  THICKNESS=  AREA*  65.0 TIME  Y-DIRECTION  VOLTAGE*  SURFACE  HOT  WELDING  A  IN  =  Parameters  3 .0 3 .0 3 .0  3 .0 3 .0 3 .0  3. 3. 3.  0 0 0  3. 3. 3.  0 0 0  30  1 5 . 0 cm  33.0 V  57.9  (cm**2)  WELD  GAP AREA*  154.8  (cm**2)  (cal/g) 3990.0(S)  CURRENT*  5000.OA  VELOCITY*  0.023  HOT  AIR TOP  (cm/s)  TEMPERATURE VOLTAGE*  =  33.0V  30.0(DEG  C)  \u000C41  T a b l e I I - E S J T y p i c a l Log Sheet Time (s)  NMT  Prim \" (A)  Sec (A)  Volt (V)  MS (rps)  WT (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  \u2022 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 MS WT  = Number of M o t o r T u r n s = Motor Speed = Water Temperature  \\  \u000C42  movement  water-cooled shoes B  Figure  250 KVA  1 - S c h e m a t i c L a y o u t of E S J E q u i p m e n t  \u000C43  fusion line  zone 1 zone 2 zone 3 fusion line  Type II  Type I  zone 1  zone 2 fusion line  Figure  fusion line Type IV  Type  2 - Electroslag  Typical  Weld S t r u c t u r e ( R e f .  \\  35)  \u000C44  Figure  3  - ESJ Thermal  Profile - Calculated  and  Measured  \u000C45  run-in  tab^^  Figure  4 -  Boundary  Conditions  \u000C46  Boundary III  Boundary V  \u2022 \u2022 \u2022 \u2022  Heat Source, (slag)  T.,j-1  \u2022 \u2022 x (i) y(j)  IM. IN  \\ \\ \\ \\ \\ W \\ \\ \\ \\  \u2022 \u2022  Boundary II-  Boundary VIII  '//////;  V///////////&gt;  '/////*  &lt;/////&gt; \u2022Ti +1\u2022j .Ti.j  \u2022 \u2022Ti.j+1  \u2022THj  \u2022TAX  Arf  AYj\u00AB  \\^\\  \\ \\ ^ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ V  V////S  '/////&gt; '/////A  '//////  VMM V////A //////,  UN Boundary VI  Boundary I Boundary IV  Figure  5 - Nodal  Arrangement  \u000C47  fSTART  ) SUBROUTINE  SUB ROUTINE  SNDS  0 INPUT SUBROUTINE HEAT  SUBROUTINE INITL  SUBROUTINE VEL  SUBROUTINE PRINT  SUBROUTINE CONST t = t + At  SUBROUTME] TB(I.J) =T(I.J)  STRESS  SUBROUTINE FSTS  ^RESULTS^/  Q  SUBROUTINE SNDS  Figure  6 - Model  Flowchart  END  )  \u000C48  x  L 2 Figure  L. 2 7 - Stress  Analysis  Schematic  I  Diagram  TH  1  \u000C49  Figure  8 - UBC  Electroslag  Unit  \u000C50  86.5 mm.  Figure  9 - Cooling  Shoe - Water  Channels  \u000C51  Copper  Aluminum  Figure  10  -  Cooling  Shoe  Top  View  \u000C100mm.  77 mm. BnomV-N0523*  25.\u00A3mm.  81 mm.  86.5 mm.  254 mm.  Figure  11 - C o p p e r  recess  /  77 mm.  86.5 mm.  \u000CFigure  12  - Cooling  Shoes  in  Position  \u000CFigure  13 - C o o l i n g  Shoe C l o s e - u p - Water  connections  \u000C55  Figure  14 - P l a t e E l e c t r o d e  in Position  \u000CFigure  15 - Aluminum  Feeder  \u000C57  Figure  16 - E l e c t r o d e  and Copper  Stub  \u000CFigure  17 - R u n - i n Copper  Tabs  \u000C59  \u000C60  0  60.8 Figure  121.6 1324 243.2 TIME , min.  19 - S t r a i n  v e r s u s Time  Plot  304  364.8  \u000C61  Figure  20 - Boxed  I-Beam  \u000C62  Figure  21  - Hardened  4340 D i s c  Spacer  \u000C63  Figure  22 - Inferior  I-beam  Placement  \u000C64  strain gauge  914 mm  Figure  23  -  Strain-gauge  Set-up  \u000C65  300  1  G  180  r:  120  Q.  CO LU  1  1  1  ELECTROSLAG  240 n  1  1  1  1 \u2014  JOINING  Time = 4200 s Distance from hot face = 0.5 / 1.5 / 3.5 cm. Voltage = 33 V Current  = 5000 A 0.5  60  1.5  3 . 5  0  rr  175 -60 -120  rr x -180 -240 h -300  J  0  1  1  i_  J  1  \u2022  33.6 672 100.8 134.4 168 201.6 2352 268.8 3024 336 369.6 403.2 TIME . s  Figure  24 - T h e r m a l  ( 1 x io) 1  Stress  Curve  \u000C66  300  ~l  ELECTROSLAG  240  Time 180 00 \u2022_  o X  CO CO LU  rr  =  1  1  I  JOINING  8400 s  Distance from hot face = 0 . 5 cm.  120 60  Voltage  =  33 V  Current  =  5000 A  Weld height  =  193 cm.  0.5  0 -60  . CO t\u2014  _l &lt;  cc LU X  -120 -180  1\u2014  -240 -300 0  672 134.4 201.6 268B 336 403.2 470.4 5376 604.8 672 739.2 806-4  TIME , s Figure  (1 x 10 )  25 - T h e r m a l S t r e s s  1  Curve  \u000C67  ELECTROSLAG weld height Welding  JOINING = 96 cm.  conditions :  voltage  = 33 v  current = 5000  A  welding speed = 0.023 c m / s  64  128  192 256 320 384 448  DISTANCE Figure  26 -  ESJ  FROM HOT Thermal  512 576 640 704 768  FACE  Gradient  (mm.)  \u000C68  4  APPENDIX.A  - BOUNDARY CONDITIONS I(i=l,j=l)  BOUNDARY  i)  I f element  I contacts the heat  ^  1 S t  T  1,1  = T  source:  MI  2nd-A|  ii)  If  element  equation  I does n o t c o n t a c t  t h e heat  source,  c a n be o b t a i n e d by a p p l y i n g a h e a t  1st  At 2  * n AyAxCpp^l,!\" T l , l ) 2 At 2 kAx + 2 \" T* )  the following  balance:  _ kAy_l(T* Z ~ x  ,  X  - T* i '  )  +  i  2  or  /2 AT (  2nd  2 . * Ax^)Tl,r  +  2ou T* ^ '  2 Tlf At 1 ,  a  :  1+  A  y i  (A  y ; L  _n +Ap)tTl,2~  n+1 * CT - T ^ kAv * * Ay A x C p p v 1 , 1 1,1 l (T - T ) 1 Z y \u00B1 1 , 1 2 At \" A x  At 2  y  +  .i  kAx ~2 Ay +Ay2 2  T  n l , l  }  +  j_i  (T - T ) 1 2 1 lL ' X \" n + 1  D + 1  or a T _ 1\u00BB2 l , l ^ ( A y ^ A y p n + 1  ^At  +  2 ) Ayi(Ayi+Ay2);  T A  n  +  1  2 * At ^ .  l  2a &amp;  2  U  * * 2 , r i , l  J  \u000C69  BOTNDARY_II ( i = 2 - I M - l , j=1)  i)  ii)  I f element I I c o n t a c t s t h e heat  1st  At  2 n d  ^  T*  T  source:  ) 1 =  tl  MF  = T  I f element I I does n o t c o n t a c t t h e heat 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 be o b t a i n e d by a p p l y i n g a h e a t b a l a n c e :  (  1st  A^  l r  T  i , i  T  }  k  Ay^xpCp \u2022 ^  A  i  y  =  , *  *  *  - - ( T . ^ ^ ^ ^ ^ ^ T . ^ )  2 \u2022  kAx l  y  * ^\u20142\"  y  2  1-1,1 A t  n 2  1  2  *  Ax  z /  ,  n  2  1  '  1  a  i , l  2 T ' At  T*  Ax^  *  n+1  +  n  (T?,-T\u00B0 '  Ay^Ay^Ay^  +  1  ) i  9  i l ~ i 1&gt; l * Ay AxpCp\u2014\u00B1*\u00B1\u2014\u2014 = (T..,+,T. , r 2 T . . ) J l At Ax x+1,1 1-1,1 i , j (  \u20222nd  .  At 2  \u2014  T  T  k  y  l  + A y  y  A  r  A  A  2  or  ,  2  1  a  At ' A +  y i  (A  y i  \\  +Ay ) 2  ; T  n  +  2  1  T  r  n  +  1  i , l \" Ay (Ay +Ay )\" l,2 , 1  1  1  2  =  2 T  *  +  \"SPi,! \" 1  g  \u201Ef  T  *  4.T*  9T*S  A^ i4a,l^i^i;i T  2  T  iJl  \u000C70  BOUNDARY  i)  If  element  ii)  If  n  contacts  ^  1 S t  2  III  d  A  t  V  1st  III  2 n d  ^  A|  P  M i  T  ^  _2_. At  +  v  ^  2a Ax^'  Ay1(Ay1+Ay2)  A  l  y  =  IM,1  |xpCP(  \u2022)T  n+1 IM,1  ^  n IM,2  the heat  kAx 2  '  f T v  l  V  source,  the following  balance:  -^ ( T ;  * 2 IM.r  ;  1  -  +  or  % ) 2  +  _2_ n At IM,1 r  n+1 IM 1~ ^  A y  +  MP  T  c a n be o b t a i n e d by a p p l y i n g a h e a t  +  At  =  source:  does not c o n t a c t  (  + r  l  =  kAx + 2  2\" T * . Ax2 I M - 1 , 1  the heat  m ; i  T  2  element  equation  III(i=IM,j=l)  * kA IM 1 y-i M' )- - - ^ T  +  *  1  2 n+l IM.2 A y  n n , IM,2 \" IM,1  a Ay^(Ay^+Ay^)  m  &gt;  n+1 . IM,1;  1  -  * T ^ ^ )  +  or  2  Ay1(Ay1+Ay2)  Tn+1 -IM,2  = 2T* - V  l  T* ^ - ^ f Tv * Ax2 IM,1 IM-1U  \u000C71  BOUNDARY  * n T . - T, . AxAy.pCpC-^^ )= 3 At '  At  1st  IV(i=l,j=2-IN-l)  i t l  \u2014x  ^  * * kAy.(T . - T 7^ Ax 3  \u00B1  a J  .) -  2  kAx(T? . -r- l , j + l +  z  Ay.  1  + Ay  Tn .) i , j  kAx(T? . \u2014 l , j \"  *  T? . , ) 1,J-1'  \u2022  A y . + Ay .1 .1-1  -1+1  or 2a(Tn  ( -2- + - = ~ r i T * (  At  +  ^  T  - -^T* ^ 2 , j  l , j  2 n d  - - 2 -T T At l , j  +  n  +  Ay ( A y  n+1 * . . _ T\" T - T . -AxAy pCp l t , i l 2 J At  A t  \u2014  kAx  1  +Ay  t  i  )  l&gt;.r )  2  ~  a  i ~ T l 1-1&gt; Av ( A(Ay ) + t +Av y j *i-l&gt; (  T  l  * * k Ay y . ( T2 \u201E . - T ^ . i a ?,1 1?,T Ax  . 1  n+1 _ n+1 2 l,j+1 l,.j _ Ay. + Ay... *1 1+1 2 U  +  - Tn  J  k A x . n+1 n+1 2 l , j Ay. + Ay _J .1-1 2 U  )  . +  . ;  or  -2 a Ay.(Ay.  +Avi_j_^)  -n+1 l,j-l  + (\"  2 At  2 a A y ( A y +Ay  2 a Ay  ( A y +Ay  ^  2 a -)T Ay.(Ay.+Ay. J 3 3\"  ^  n+1  2  Xj+l  At  * T,  n + 1  \"  2a * * + 7 3 Z ( T o 4 T , to? 2,j  4  V A  4  )  \u000C72  BOUNDARY Y(i=IM,j =IN-1)  -1st At AxAy.pCp - IM,i \" ^M,j,= 2 2 \u2022 At 2  T (.. 3M,j ~ I M - l , j ) +  T  T  f  Ax  3  A y  4 +A j-1. \" 2 \"  j + j+1 ' 2 Ay  y  y  1  or  &amp;x^  Ax  n t  Z  Ay  flC  2  Cm,A - ^ . j  n  4  (Ay. + Ay'  )  - i)  Ay.. (Ay.. +Ay.._) 1  n+1 * AxAy.p Cp( IM,.i- IM,j) = 2 At  2nd At 2  T  T  3  kAxd^.^-T^ .) -J IM,j+l IM,j' 1  +  - KA j Ax y  * * ( IM,3- IM-1,j) T  T  kAxCT^.-T?: . ) \u2014 IM.,2 I M o - l ' 1  n  Ay. +Ay... 1 -1+1  Ay. + Ay. -1 -I-*  or  -2 a ^n+1 ., 2 A (A +Ay _ ) IM,j-l At i  Y j  y j  j  . A  v  1  7j  2a (A +Ay  2_a n+1 Ay (Ay +Ay ) IM,j+l T  j  j  j+1  yj  =  j+1  )  et . +  2a 1 y.. (Ay^.+Ay.._^) IM,j  2 * 2a * * At TM,j\" Ax? TM,j \" I M - l , j T  CT  T  )  \u000C\u2022BOUNDARY V I ( i = l , j = I N )  1st j&amp;  jgAv  T L I P  C\u00BB  T  2  _  '  R  ^ (  T  A y  IN  +  J^S  1.IN- 1,IN: At ' 2  T  F  Ax  T  2,IH- 1,IN T  l &gt; IN-^1 &gt; A5?  IN-1  or  ;_2 + 2 k  At  ) 1,IN - ^ T  Ax  T  2,IN  a r i . I N - 1,IN-1)  f^Tl.IN  =  A y  Ax  2nd  lN(  A y  I N^ I N - l )  *  n+1 At  2  Ax  INpCp,Tl,IN^ At  A Y  2  Ax K  n+1  IN  +  Ay  *  , 2,IN- 1,IN T  T  \u201En+l  2C1.IN -  A y  l.IN. = ^ I M ; Ak  l.IK-1)  IN-l  or  r  A y  lN  (  A y  IN+  A y  IN-l  n+l l.IN-l  r  + _2 A t  )  _2 At  T  1,IN  +.. A y  IN  A y  IN+  * * 1 , I N + 2o_ ( 2 , I N T  Ax  n+l  A y  T  IN-l,  *, 1,IN)  '  \u000C74  \u2022BOUNDARY V I I  (i=2-IM-l,j=IN)  * 1st  At 2  AxAy  pCp * l t I N - l , H p j&amp; 2  i N  &amp; K A y  *  T  =  T  tk  A  IN(Ti+l,IN+Ti-1,IN  -  jx  2T1,IN)  -  xi  KAx(Ti,IN-Ti,IN-1^ A y  IN  +  A y  IN-l  or * -a A  Ax  T  2  *  i-1,IN  + ,_2 V At  + 2a v i , I N . 2 Ax  a A y  At  - _ a _ i + 1 , I N = 2_ 1 , I N . 2 At Ax  (Tn  ( Tn+1 pCpv i,IN  AxAy  ( A y  -  IN  +  A y  )  i,IN-r  lN-l  }  T* ) (Tn+1 1 , I N ; = - KAxv i , I N  f-  2  +  T  Tn  1,IN -  iN  n  T  }  -  2nd  *  T  A  ?IN  +  Tn+1 ) i.IN-r*  -  A y  !N-l 2  * +  K A y  lN  ( T  i+l,IN +  T  i-1,IN  -  2  T  i,IN  )  Ax  or T  A y  iN  ( A y  iN  +  ^IN-l  n+1 i,IN-l+;(_2+  5  A t  * _2 At  T  i,IN +  T  a A y  iN  *  ( A y  lN  *  ) +  A y  lN-l  }  *  _a_(TI,IN+Ti-I,IN-2Ti,IN) ... 2 Ax  A  n+1 i,IN  \u000C'BOUNDARY VIII(i=IM,1=IN)  \u20221st A t 2  AxAy 2  * n (T - T ) pCp ^ IM,IN IM,nr = t  N  *  ^ I N  (T  *  KAxCTn  - Tn  TM,IN \" IM-1,IN&gt; - \"2 T  **  A y  m  IN  +  A y  IN-l  Or  - 2a  T*  Ax '  IM-1,IN  +  i.2. + At  \u2022  2  2a) 2 Ax  ( T v  K  C = 2 IM,IN 7-  T  T  )  _.At  n  IM,IN -  A y  2nd  At  AxAy  2  2 '  IN(AyIN  n+1 TM,IN  (T  pCp  v  IN Ax  T  n+1  (T  ( A y  IM,IN-r  IN-l&gt;  * ) IM.IN^ =  IM,IN ~ IM-1,IN  lN+ lN-l)  T  T (  2  _2  At  a  + A y  * T  v  or  A t  A y  K Ax.n+1 _ IM.IN Wy + Ay  )  IN  IN,In-l  IN  - T  +  At  K A Y  A y  A y  n  n IM,IN  IN  *  I M , I N \" _2a  Ax'  ( T  IM,IN  (  A  . W  y  I N - l &gt;  A  ~^IM-l.IN*  n+1 . IM,IN-r  IN-l  n+1 IM,IN  1  ^  \u000C76  APPENDIX B ~ COMPUTER PROGRAM C C C C C C C C C C C  C C C C C C C C  c c  C C C C  SAMPLE  CALCULATION OF THERMAL STRESSES I N HEAVY SECTION ELECTROSLAG JOINING  PAULO SILVEIRA IVO  MAIN PROGRAM DIMENSION T ( 1 0 0 , 1 0 0 ) , T S ( 1 0 0 , 1 0 0 ) , T B ( 1 0 0 , 1 0 0 ) , D Y ( 1 0 0 ) , I D ( 1 0 0 ) 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) 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) I F d P . E Q . 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 READ DATA AND PRINT HEADINGS 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)  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)  \u000C77  READ(5,120) D Y ( 1 ) , D Y ( 2 ) , D Y ( 3 ) , D Y ( 4 ) , D Y ( 5 ) , D Y ( 6 ) , D Y ( 7 ) FORMAT(7F5.0) DO 10 I = 8 , I N 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 ) ' , / , 2 X , ' I N I T I A L TEMP=', *F6.1,1X,*(Deg C ) ' , / , 2 X , *'TIME S T E P = ' , F 6 . 1 , I X , ' ( s ) ' , / , 2 X , ' S P E C I F I C HEAT*',F6.4,IX, *'(cal/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 C A L C U L A T I O N ' *,Fl0.1,1X,'(s)') WRITE(6,220) ( D Y ( I ) , 1 = 1 , I N ) 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=*, *F5.1,IX,*(cal/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 H E A T = ' , F 6 . 1 , 1 X , ' ( c a l / g . C ) ' , / , *2X,'TEMP. D I F F . I N MOULD=' ,F6.1,1X,' (C) ' ,/,2X, *'WATER DENSITY=',F6.1,1X,'(g/cm**3)',/,2X, *'HEAT E F F . TO THE BLOCKS'',F7.4,1X,/) RETURN END 120  C C C C C  c SUBROUTINE  INITL(T,TS,TB,TBO,DPH,DX,ID,IM,IN,PRNT,PRNTO)  C DIMENSION T ( 1 0 0 , 1 0 0 ) , T S ( 1 0 0 , 1 0 0 ) , T B ( 1 0 0 , 1 0 0 ) , I D ( 1 0 0 ) 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  \u000C78  C C C C C C  C C C  DO 30 1=1,NO 30 I D ( I ) = 1 NP=NO+1 DO 40 I=NP,IM 40 I D ( I ) = 0 PRNTO=PRNT RETURN END CALCULATION OF THE WELDING SPEED  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 I S CONTACTING THE BLOCK SUBROUTINE HSPOS(DPH,V,TIME,DX,ID,IM)  2 10 1 20  30 C C C  DIMENSION ID(100) NO=IFIX(V*TIME/DX+0.51) + 1 NS=IFIX((DPH+V*TIME)/DX+0.49)+l NN=NO-1 I F ( N 0 - 1 ) 1,1,2 DO 10 I=1,NN ID(I)=0 CONTINUE DO 20 I=NO,NS ID(I)=1 CONTINUE NNS=NS+1 DO 30 I=NNS,IM ID(I)=0 CONTINUE RETURN END  SUBROUTINE CONST(DT,DX,CP,RO,AK,ALPHA,A1,A2,A3)  C C C  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  \u000C79  c  C C C C  CALCULATION OF THE FIRST HALF-TIME STEP  c  SUBROUTINE FSTS(TB,TS,DY,DX,DT,ALPHA,IN,IM,TMP,ID,Al,A2,A3)  C C  C  C C C  C  C C C  C  DIMENSION T B ( 1 0 0 , 1 0 0 ) , T S ( 1 0 0 , 1 0 0 ) , D Y ( 1 0 0 ) , I D ( 1 0 0 ) DIMENSION A ( 1 0 0 ) , B ( 1 0 0 ) , C ( 1 0 0 ) , D ( 1 0 0 ) , T P R I M E ( 1 0 0 ) I F ( I D ( 1 ) - 1 ) 1,2,2 2 CALL S 0 U R C E ( A ( 1 ) , B ( 1 ) , C ( 1 ) , D ( 1 ) , T M P ) 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 , I J I F ( I D ( I ) - 1 ) 4,5,5 5 CALL\u2022SOURCE(A(I),B(l),C(I),D(l),TMP) GO TO 10 4  A(I)=-0.5*A2 B(I)=A1 C(I)=-0.5*A2 D(I)=A3*TB(I,1)+(ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) **(TB(I,2)-TB(I,1)))  10 CONTINUE I F ( I D ( I M ) - 1 ) 6,7,7 7 CALL SOURCE(A(IM),B(IM),C(IM),D(IM),TMP) GO TO 8 6 A(IM)=-A2 B(IM)=A1 C(IM)=0.0 D(IM)=A3*TB(IM,1)+(ALPHA/(DY(1)*(DY(1)+0.5*DY(2))) **(TB(IM,2)-TB(IM,1))) 8 CALL T R I D A G d , IM, A, B ,C ,D,TPRIME) DO 15 1 = 1 ,IM 15 T S ( I , 1 ) = T P R I M E ( I ) DO 20 J=2,IK 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))  \u000C80  c  DO 25 1=2,IJ  C  A(I)=-0.5*A2 B(I)=A1 C(I)=A(I)  C  C C C  D(I)=A3*TB(I,J)+(2.0*ALPHA*(TB(I,J+1)-TB(I,3))/ * ( D Y ( J ) * ( D Y ( J ) + D Y ( J + 1 ).) )) *-(2.0*ALPHA*(TB(I,J)-TB(I,J-1))/(DY(J)*(DY(J)+DY(J-1)))) 25 CONTINUE 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) *-TB(lM,J-1))/(DY(J)*(DY(J)+DY(J-1))))  C C  C  CALL TRIDAG(1,IM,A,B,C,D,TPRIME) DO 30 1=1,IM 30 TS(l', J ) = T P R I M E ( I ) 20 CONTINUE 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 C C  D(I)=A3*TB(I,IN)-(ALPHA*(TB(I,IN)-TB(I,IN-1)) */(DY(IN)*(DY(IN)+0.5*DY(IN-1)))) 35 CONTINUE A(IM)=-A2 B(IM)=A1 C(IM)=0.0  C \u2022 C  C C  c  D(IM)=A3*TB(IM,IN)-(ALPHA*(TB(IM,IN)-TB(IM,IN-1)) */(DY(IN)*(DY(IN)+0.5*DY(IN-1))))  CALL TRIDAG(1,IM,A,B,C,D,TPRIME) DO 40 1 = 1 ,IM 40 T S ( I , I N ) = T P R I M E ( I ) RETURN END  \u000C81  SUBROUTINE C  C C  DIMENSION T S ( 1 0 0 , 1 0 0 ) , T ( 1 0 0 , 1 0 0 ) , D Y ( 1 0 0 ) , I D ( 1 0 0 ) DIMENSION A ( 1 0 0 ) , B ( 1 0 0 ) , C ( 1 0 0 ) , D ( 1 0 0 ) , T P R I M E ( 1 0 0 ) 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))) D(1)=A3*TS(1,1)+A2*(TS(2,1)-TS(1,1)) 3 CONTINUE 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 C  C(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J+1))) D(J)=A3*TS(1,J)+A2*(TS(2,J)-TS(1,J)) 10 CONTINUE 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 C  C C C  C C  SNDS(TS,T,DY,DX,DT,ALPHA,IN,IM,TMP,ID,A1,A2,A3)  15  DO 15 J=1,IN T(1,J)=TPRIME(J)  DO 20 1=2,IJ I F ( I D ( I ) - 1 ) 4,5,5 5 CALL S 0 U R C E ( A ( 1 ) , B ( 1 ) , C ( 1 ) , D ( 1 ) , T M P ) GO TO 6 4  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(I,1)+0.5*A2*(TS(I+1,1)+TS(1-1,1)*2.0*TS(I,1)) 6 CONTINUE DO 30 J=2,IK A(J)=-2.0*ALPHA/(DY(J)*(DY(J)+DY(J-1)))  \u000C82  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, I N ) *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 I F ( I D ( I M ) - 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  \u000C83  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 ( 1 0 0 , 1 0 0 ) , I D ( 1 0 0 ) 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 I F ( I D ( 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 C C C C C C C C C C C C C  SUBROUTINE \"TRIDAG\" FROM 'APPLIED NUMERICAL METHODS' BY CARNAHAN, LUTHER AND WILKES SUBROUTINE FOR SOLVING A SYSTEM OF LINEAR SIMULTANEOUS EQUATIONS HAVING A TRIDIAGONAL COEFFICIENT MATRIX. THE EQUATIONS ARE NUMBERED I F THROUGH L AND THEIR SUB-DIAGONAL, DIAGONAL AND SUPER-DIAGONAL COEFFICIENTS ARE STORED IN THE ARRAYS A, B AND C. THE COMPUTED SOLUTION VECTOR IS STORED IN THE ARRAY V.  SUBROUTINE TRIDAG(IF,L,A,B,C,D,V)  \u000C84  C C  DIMENSION A ( 1 0 0 ) , B ( 1 0 0 ) , C ( 1 0 0 ) , D ( 1 0 0 ) , V ( 1 0 0 ) DIMENSION BETA(101),GAMMA(101)  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*##\u00AB 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 I D ( 1 0 0 ) , T ( 1 0 0 , 1 0 0 ) , D Y ( 1 0 0 ) 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 I F ( I D ( 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  \u000C85  C C C  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  SUBROUTINE HEAT1(AK,DX,TH,T,DY,ID,Q1,IM,DPH,DT,IN,TBO,TMP) DIMENSION I D ( 1 0 0 ) , T ( 1 0 0 , 1 0 0 ) , D Y ( 1 0 0 ) 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 I F ( N O - 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 D(J)=0 30 CONTINUE DO 5 1=1,IM I F ( I D ( I ) - 1 ) 5,50,50 50 Q 1 = Q 1 - ( ( A K * D X * T H ) * ( ( 4 * T ( I , 2 ) - T ( I , 3 ) - 3 * T M P ) / *(DY(1)+DY(2)))) 5 CONTINUE WRITE(6,897) Q1 897 FORMAT(1H ,IX,'HEAT INPUT=',F15.1) RETURN END i  C C C C  THERMAL STRESS CALCULATION PERFORMED FOR EACH NODAL TEMPERATURE  SUBROUTINE STRESS(T,TT,TTT,IT,IM,IN,ALFA,H) DIMENSION T ( 5 0 0 , 2 0 ) , T T ( 5 0 0 ) , T T T ( 5 0 0 ) DO 10 1=1,IT READ(5,100) ( T ( I T , I N ) , I N = 1 , 8 ) 100 FORMAT(8(F6.1,1X)) \u2022 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  \u000C86  E=0.000012 1 I F ( T T ( I ) .GE. 1000. .AND. T T ( I ) .LE. 1400.) G O T O 2 E=(2000.-(1.875*(TT(I)-l000.)*100000.)) 2 I F ( T T ( I ) .GE. 1400. .AND. T T ( I ) .LE. 1475.) GO TO 3 E=((1250.*(l475.-TT(l))/75.)*10000.) 3 I F ( T T ( I ) .GT. 1475.) GO TO 14 E=0.0 AREA1=QINT4P(I TT(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 t  C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C \u2022 C C C C C C C C C C C  L I S T OF SYMBOLS USED IN THE MODEL  TMP = M e l t i n g p o i n t TBO = P a r e n t m e t a l DT = Time  t e m p e r a t u r e ( D e g . C) initial  temperature(Deg.  C)  step(s)  CP = S p e c i f i c  h e a t of s t e e K c a l / g . d e g . C )  RO = D e n s i t y o f s t e e l ( g / c m * * 3 ) AK = T h e r m a l  conductivity  of s t e e l ( c a l / c m . s . d e g  DX = Space  increment i n X - d i r e c t i o n ( c m )  DY = Space  increment i n Y - d i r e c t i o n ( c m )  V  = Welding  DPH = S l a g  velocity(cm/s)  + liquid  PRNT = P r i n t  metal  depth(cm)  cycle(s)  TLAST = End o f c a l c u l a t i o n ( s ) IM = # o f d i v i s i o n s  i n the X - d i r e c t i o n  IN = # o f d i v i s i o n s  i n the Y-direction  T = Temperature(deg. XI = C u r r e n t ( A )  C)  \u000C87  c  C C C C C C C C C C C C C C C C C C C C C  VO = V o l t a g e ( V ) TH =  Thickness(cm)  G = Weld  gap(cm)  F = Efficiency  factor  SE = E l e c t r o d e a r e a ( c m * * 2 ) SWG  = Weld gap a r e a ( c m * * 2 )  AL = L a t e n t h e a t ( c a l / g ) FR = F i l l  ratio  ALFA = C o e f f i c i e n t o f e x p a n s i o n ( / d e g . H = Weld  height(cm)  ID = Heat s o u r c e c o n t a c t i n d e x  C)  \u000C88  APPENDIX  C -  EFFICIENCY  Paton35 into  FACTOR  reports  AND  that  HEAT  about  would n o t a p p l y .  Therefore,  CALCULATIONS  58.6% of the a v a i l a b l e heat  t h e b l o c k s when E l e c t r o s l a g W e l d i n g ( w i r e  thermal c h a r a c t e r i s t i c s already discussed,  SINK  e l e c t r o d e ) . Due t o t h e  for Electroslag Joining  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  goes  different  that  number  b a s e d o n some  measurements:  The 3698 c m / s . 3  c o o l i n g shoe water  The e l e c t r o d e m e l t Melt The  ing  rate  f l o w r a t e was m e a s u r e d a n d f o u n d  can be c a l c u l a t e d as f o l l o w s :  Rate = E l e c t r o d e  Feed Rate x Area x  electrode feed r a t e  e x p r e s s i o n g i v e n by F r o s t  where:  et  can be a s c e r t a i n e d u s i n g the  E F R = electrode feed  area)  velocity  t h e m a t e r i a l d i m e n s i o n s used i n most -  was f o u n d  follow-  rate  ratio(electrode area/weld  V = welding  For  Density  al.1*1:  F R = f i l l  For  t o be  experiments  1.6735  an experimental welding v e l o c i t y of 0.023  cm/s, the  EFR  t o be : E F R = 1.6735 x 0.023  = 0 . 0 3 8 5 cm/s  Therefore, M e l t Rate = 0.0385cm/s x 57.912cm2 x 7.86g/cm3 If of  steel,  approximately  4 0 0 KWH a r e n e e d e d t o m e l t  = 17.52 g/s  1000 k g o r 1x10^  t h e n t h e power f o r m e l t i n g would b e :  T&gt;_  17.52  g / s x 4 0 0 KWH x 3 6 0 0 s 1 x 10o g  _  ....  g  \u000C89 The h e a t  flux  p e r mould would then b e :  1 ^ = F l o w r a t e x C p y x AT x p y x  ^QQQ  8  = 8 5 . 1 6 KW  Therefore,  \\  \"  25.23 33x5000x.95  =  85.16 156.75  H  \u2022  R=  \"block *  through  = 54.3%  - 1 %  ^ l o c k \"  And,  16.1%  1  0  0  \"  Z ( H  M  +  H  W  V  +  1 5 %  therefore,  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  t h e b l o c k s and i s a c c u m u l a t e d t h e r e .  m o d e l when c a l c u l a t i n g t h e h e a t  This  flows  i s the f a c t o r used i n the  flow.  *****************  THE  BLOCK AS A HEAT  The amount o f h e a t s m a l l when compared w i t h  the heat  the b l o c k v i a the opposite f a c e .  lost  SINK through the b l o c k c o l d  face i s  a v a i l a b l e from the e l e c t r o d e that In order  t o s e e how t h a t  is  very entering  i s effected a plot  of  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 been g e n e r a t e d and i l l u s t r a t e d i n F i g . 26 been found  The p o i n t  at which the temperature  d r o p s t o room t e m p e r a t u r e h a s  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  feet)  \u000C90  APPENDIX  D  -  .  (A + B c o s 2 g ) e a - (A - B c o s 4 A B c o s 23  0 1  \u00B0  RESIDUAL  STRESS  EVALUATION  2g)ec  (A + B c o s 20) e c - (A - B c o s 20) e a 4 A B c o s 20  2  ca - 2eb + ec t a n 20 = ea ec  Position  1  D e p t h = 120  -  Parent  metal  thou  ea = - 3 5 u e  eb = - 6 2 u e 2  -  ec = - 1 4 3 y e 4 A -  5 5  -1.35  *  4 B = -3.55 x Therefore,  A = -3.375  ai  =  + 9781  a2  =  +16589 p s i  Position  2  D e p t h = 120  2  -  and B = - 8 . 8 6 8 x  Heat  affected  eb = +51ue 0  2.87  0  A = -2,7855  1  = +  1113  psi  2  = +  27248  psi  0  10~9  zone  ec =  -225ue  , . i n/o i n 4 A = - 1 . 1 1 4 2 x 10 4 B = -2.9920 x  Therefore,  ( A f t e r Redner  thou  0.2045 Q Q 7 1 =  =  10  psi  ea = +67ue r  x 10~9  10\"*  x 10~9  and  -  8  10~8  B = -7.48  x  10~9  )  \u000C91  Position  3  -  D e p t h = 120  Weld  thou  \u00A3a = - 1 5 2 y e  \"  3  n'lfS U.uo/  5  metal  eb = - 1 5 7 u e =  2  '  8  4  ec = - 1 0 7 y e  = -1.1^2  A  4 B = -3.0 x Therefore,  A -  - 2 . 7 8 5 4 x 10~9  oi =  + 25615  psi  a2  + 20877  psi  The  =  r e s i d u a l s t r e s s measurement 45  Hole D r i l l i n g technique hole,  3.175  mm(l/8\")  to i t s diameter.  The  02' i s t h e aj  affected  10\"8  10~8 B = -7.5  x  10~9  was c a r r i e d o u t  u s i n g the  Blind  w h i c h i s a s e m i - d e s t r u c t i v e method whereby  i n diameter relaxed  is drilled  s t r a i n s are  to  a depth  approximately  then measured around  the  a  angle  z o n e and w e l d  to  02- T h e y w e r e m e a s u r e d  metal.  i n the parent  small  equal  hole.  l o n g i t u d i n a l s t r e s s remaining i n the welded assembly  i s a t a 90 d e g r e e  heat  and  x  and  material,  "@en
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