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The application of the additivity principle to recrystallization Magee, Kenneth Howard 1986

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THE  APPLICATION  OF  THE  ADDITIVITY  PRINCIPLE  TO  RECRYSTALLIZATION  by KENNETH  A  THESIS THE  SUBMITTED  HOWARD  IN  REQUIREMENTS MASTER  OF  MAGEE  PARTIAL FOR  THE  APPLIED  FULFILMENT DEGREE  OF  SCIENCE  in THE  FACULTY  Department  We  of  accept to  THE  OF  Metallurgical  this  the  thesis  required  UNIVERSITY  OF  July  ©  GRADUATE  as  STUDIES Engineering  conforming  standard  BRITISH  COLUMBIA  1986  K E N N E T H HOWARD M A G E E ,  1986  OF  In  presenting  requirements  this for  an  B r i t i s h  Columbia,  freely  available  that  permission  scholarly  I  agree for  purposes or  understood  that  by  gain  in  advanced  for  Department  f i n a n c i a l  thesis  degree  that  the  reference  extensive may his  be or  copying  shall  p a r t i a l  not  be  the  and  of  Metallurgical  The U n i v e r s i t y of B r i t i s h 2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date:  July  1986  I  copying  of  this  granted  by  the  allowed  Engineering  of  make  further  Head  of It  thesis my  of it  agree  thesis  this  without  the  University  representatives.  publication  Columbia  of  shall  study.  permission.  Department  The  Library  her or  at  fulfilment  for my is for  written  ABSTRACT This  research  is  University  of  industrial  annealing  B r i t i s h  f i n a l  mechanical  after  being  progress  by  the  applying  carbon,  molten  salt  evaluation Avrami were The  a  methods.  equation.  progress  procedure resolution  formation  of  microhardness continuously Applying kinetic  data  displayed  The  using  a d d i t i v i t y  of  the  range  diamond  the  {211}  was  the  with  is  accomplished  was  of  kinetic  sheet,  was the  plane,  using  microhardness using  the  r e c r y s t a l l i z a t i o n  heated  strip  monitored  using  increased  Diamond  applied  to  t r i a l s  specimens.  experienced  material.  data  was  440°C-560°C,  characterized  heating  also  steel  to  Ka  an  doublet  during  the  pyramid the  specimens.  A d d i t i v i t y  resulted  reasonably  sheet  cycle,  applicable  pyramid  examining  r e c r y s t a l l i z e d  heated  the  isothermal  is  rolled  resistance  evaluation  predict  steel  r e c r y s t a l l i z a t i o n  cold  data  on  to  predicted  to  the  model  annealing  This  at  data.  r e c r y s t a l l i z a t i o n based  one  rolled  be  p r i n c i p l e  Continuous  out of  and  cold  annealing.  temperature  annealing  carried  x-ray peak  over  enable  must  isothermal rimmed,  To a  program  mathematically  industrial  during  whether  r e c r y s t a l l i z a t i o n ,  determined  an  kinetic  determine  low  of  a d d i t i v i t y  r e c r y s t a l l i z a t i o n  a  to  ongoing  to  processes.  r e c r y s t a l l i z a t i o n increase  for  an  Columbia  subjected  of  of  properties  temperature  To  part  in good  p r i n c i p l e  computer  the  predictions  agreement  i i  to  with  the  isothermal which kinetics  obtained  experimentally.  predicted was  related  which  is  stored the  and to  strain  recovery  computer  history  energy effect  prior  to  predictions  experimentally  r e c r y s t a l l i z a t i o n The was  found  procedure i n s i t u rates  x-ray to  w i l l  monitoring typical  of  for  degree  by  the  continuous  heating  obtained  the behaviour recovery, the  amount  r e c r y s t a l l i z a t i o n .  eliminated  displayed  of  determines  was  applying  excellent  continuous  Once  suitable  c y c l e ,  of  heat  the  correlation  with  heating  k i n e t i c s . used  effective. be  The  dependent,  available  between  r e c r y s t a l l i z a t i o n  effects.  procedure  be  difference  experimental  recovery  thermal  treatments  the  the  The  necessary of  monitor  However, to  specimens  continuous  to  r e c r y s t a l l i z a t i o n  modifications  enable  i t ' s  subjected  annealing  to  use the  for  to  the the  high  conditions.  heating  LIST  OF  TABLES  Table  Page  3.1  Steel  Composition.  3.2  Hypothesis  Testing  Determination Microhardness 4.1  Isothermal  4.2  Temperature Steel  4.3  A3.1  of  an  for  Acceptable  Response into  Parameters Conducted  Heating  Methods.  Specimen  the  62  Number  of  Indentations.  Anneals  S t r i p  Results  R e c r y s t a l l i z a t i o n  Specimen  Avrami  58  During  480°C,  Thermal  from  of  the  84 87  Salt. the  Using  Gradient.  iv  Results.  Immersion  the-Molten  Obtained at  Kinetic  Isothermal  Two  106  Different  138  LIST  OF  FIGURES  Figure 2.1  Page Schematic  representation  coalescence 2.2  Schematic  by  subgrain  (a)  Random  dislocations,  and  dislocations  to  Softening  a  as  iron.  Annealing  Softening  of  alignment  form  in  the  arrangement  (b)  6  polygonization of  edge  of  edge  7  walls.(Ref.8)  pure  of  fraction  iron  time=3h,  range=380-490°C. 2.4  of  function  recrystallized  subgrain  rotation.(Ref.8)  representation  process:  2.3  of  and  9  carburized  temperature  (Ref.12)  three  iron  a l l o y s .  Temperature  10  softening  11  range=480-650°C.(Ref.14) 2.5  The  effect  iron. 2.6  molybdenum  Temperature  as  a  for  data  for  nucleation  function  of  on  (N)  prior  of  aluminum, and  for  activation growth  15  (G)  deformation.(Ref.8)  Dislocation  density  versus  deformed  various  amounts  by  the  range=480-705°C.(Ref.15)  Recrystallization energies  2.7  of  grainsize at  in  iron  16  room  temperature.(Ref.8) 2.8  Fraction, r e c r y s t a l l i z e d  versus  temperature  anneals  Pure  iron,  iron  with  (isochronal (b)  iron  nitrogen  with  carbon  annealing of  3h).  (a)  additions,  additions.(Ref.13)  v  19  (c)  2.9  Effect  of  kinetics  temperature of  (a)  on  rimmed  the  and  r e c r y s t a l l i z a t i o n  (b)  20  aluminum-killed  steels.(Ref.16) 2.10  2.11  Typical  sigmoidal  kinetic  curve.  Schematic  shaped  r e c r y s t a l l i z a t i o n  representation  of  the  p r i n c i p l e  22  of  28  a d d i t i v i t y . 2.12  Microhardness  2.13  Effect and  2.14  of  lattice  Effect  of  Effect back  strain  charts.(Ref.37)  on  Debye-line  32  width  34  position.(Ref.25) strain  resolution 2.15  d i s t r i b u t i o n  of  in  on  the  70-30  {331}  peak  36  brass.(Ref.25)  r e c r y s t a l l i z a t i o n  reflection  doublet  pinhole  and  grain  patterns  of  growth  70-30  on  38  brass  s p e c i m e n s . ( R e f . 25) 2.16  {211} time  2.17  peak in  {211} versus  width  annealed  x-ray time  peak in  specimens.(Ref 2.18  X-ray  line  and  30-T  steel  hardness  versus  39  specimens.(Ref.26)  ratio  and  annealed  R  30-T  hardness  41  steel  .26)  broadening  r e c r y s t a l l i z e d  R  versus  and  fraction  43  temperature  in  manganese  intensities  and  steels.(Ref.29) 2.19  Integrated versus  x-ray  peak  temperature  in  steels  heating(Ref.29)  vi  during  hardness  continuous  44  2.20  E l e c t r i c a l  r e s i s t i v i t y ,  recrystallized carbon  versus  steel.  hardness annealing  and time  fraction in  46  low  Annealing  temperature=695°C.(Ref.30) 2.21  Property  changes  various 2.22  in  steel  sheet  annealed  at  47  temperatures.(Ref.27)  Schematic  drawing  of  a  batch  annealing  50  furnace.(Ref.31) 2.23  Comparison cycles  of  with  batch  the  and  continuous  iron-carbon  annealing  51  phase  diagram.(Ref.32) 2.24  Major  components  of  a  continuous  annealing  53  of  a  continuous  annealing  54  line.(Ref.34) 2.25  Furnace  sections  line.(Ref.34) 3.1  3.2  Typical  microstructure  percent  cold  Continuous  reduced,  heating  thermocouple  of  rimmed  s t r i p  attached  the  at  as  received,  steel.(X353  specimen centre  88.8 mag.)  with  of  59  65  bottom  surface. 3.3  3.4  (a)  Experimental  heating  t r i a l s ,  in  hot  open  Method  of  equation  apparatus (b)  x-ray  analysis  closeup  for  continuous  of  mounted  Ka  x-ray  66  specimen  camera. of  {211}  (3.2).  v i i  peak  using  68  3.5  Procedure  for  predicting  r e c r y s t a l l i z a t i o n kinetic  continuous  kinetics  using  heating  71  isothermal  data.  4.1  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=440°C.  74  4.2  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=460°C.  75  4.3  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=480°C.  76  4.4  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=490°C.  77  4.5  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=500°C.  78  4.6  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=520°C.  79  4.7  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=540°C.  80  4.8  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=560°C.  81  4.9  TTR  cycles,  85  diagram  showing  with  start  superimposed  and  reerystallizat  end  times  annealing  for  ion.  4.10  Temperature  dependence  of  Avrami  parameter  b.  88  4.11  Temperature  dependence  of  Avrami  parameter  k.  89  4.12  Experimental x-ray  4.13  4.14  isothermal  heating  continuous  results,  Relationship  heating  continuous  results,  Experimental x-ray  4.15  results,  Experimental x-ray  continuous  of  heating the  diagrams  heating  and  92  and  95  and  96  r a t e = 7 0 . 7 ° C / h . heating  hardness  rate=43.8°C/min. heating  hardness  rate=686°C/min.  continuous for  hardness  a  steel.(Ref.40)  v i i i  cooling  eutectoid  and  100  4.16  X-ray  results  conducted 4.17  4.18  X-ray  at  the  440°C,  results  from  recovery  for the  anneal  102  14000s. continuous  heating  annealing  cycle  conducted  at  a  6 5 . 5 ° C / h ,  after  annealing  at  440°C  for  the  s t r i p  Experimental specimen  x-ray  results  continuously  isothermally 4.19  from  Predicted  of  heated  r e c r y s t a l l i z e d  and  experimental  r e c r y s t a l l i z a t i o n  heating  at at  rate  of  14000s. 105  2 . 5 8 ° C / s ,  and  480°C.  continuous  kinetic  103  curves,  heating  108  heating  r a t e = 7 0 . 7 ° C / h . 4.20  Predicted  and  experimental  r e c r y s t a l l i z a t i o n  continuous  kinetic  curves,  heating  110  heating  rate=43.8°C/min. 4.21  Predicted  and  experimental  r e c r y s t a l l i z a t i o n  kinetic  continuous curves,  heating  111  heating  rate==686°C/min. 4.22  Additional cooling  from  heating  annealing.  cooling 4.23  r e c r y s t a l l i z a t i o n temperature  during  Heating  on  114  continuous  rate=686°C/min,  rate=63°C/s.  Predicted  and  experimental  r e c r y s t a l l i z a t i o n recovery  occuring  anneal  of  kinetics 440°C  r a t e = 6 5 . 5 ° C / h .  ix  continuous curves  for  heating  after  14000s.  a  Heating  115  A2.1  A2.2  A3.1  Microstructure  in  annealed  at  size  11.(X353  no.  70.7°C/h  Microstructure  in  annealed  at  size  8.(X353  S t r i p  no.  the  specimen for  continuously  28000s.  ASTM  131  grain  mag.) the  70.7°C/h  specimen  determining  the  specimen for  continuously  40000s.  ASTM  132  grain  mag.)  thermocouple thermal  p o s i t i o n s  gradient.  x  for  137  LIST X  rVolume  t  :time.  N  :Nucleation  rate  :Activation  energy  Q  N  fraction  OF  G  :Growth  Qg  rActivation  R  :Gas  T  rate  of  of  r e c r y s t a l l i z e d  material,  of  r e c r y s t a l l i z e d  grains.  for  nucleation.  r e c r y s t a l l i z e d  energy  for  grains.  growth.  constant.  :Temperature.  p  :Dislocation  B  :Burgers  d  :Grain  e  : P l a s t i c  D  :Dimension  T  :Incubation  v  :Volume  !3  rAssumed number  :The time  density.  vector.  size. s t r a i n .  of  nucleation  v  SYMBOLS  number  of  r e c r y s t a l l i z e d  period the  to  r e c r y s t a l l i z a t i o n .  r e c r y s t a l l i z e d of  sites of  prior  grain.  grain.  pre-existing  prior  to  preferred  r e c r y s t a l l i z a t i o n .  nucleation  sites  existing  after  r.  :Nucleation  frequency  of  each  preferred  nucleation  s i t e . n  :Number  of  nuclei  existing  of  nuclei  in  in  u n r e c r y s t a l l i z e d  matrix. n'  rNumber  unrecrystallized  both  matrix.  xi  r e c r y s t a l l i z e d  and  X  :Extended  volume  r e c r y s t a l l i z e d .  cX 6  rThickness  of  a  thin  sheet,  or  diameter  of  a  fine  wire. f  :Shape  factor  b  :Temperature  of  r e c r y s t a l l i z e d  grains,  dependent  parameter  dependent  time  in  the  Avrami  equation. k  'Temperature  exponent  in  the  Avrami  equation. t  t  'Start  , av  of  r e c r y s t a l l i z a t i o n  under  continuous  heating conditions. :Start of r e c r y s t a l l i z a t i o n  under  isothermal  J  heating d  conditions.  'Unstrained  0  'Incident  8  crystal  angle  of  lattice x-ray  spacing.  beam  with  the  crystal  surface. X  'Wavelength  of  x-ray  beam.  B  :Fractional  residual  x-ray  line  broadening  parameter. I 0  D  DPHQ  :X-ray  beam  :Bragg  angle.  -Hardness  of  intensity.  the  steel  at  the  start  of  at  the  completion  at  time  r e c r y s t a l l i z a t i o n . DPH QQ 1  -Hardness  of  the  steel  of  r e c r y s t a l l i z a t i o n . DPH  f c  'Hardness  of  the  r e c r y s t a l l i z a t i o n  steel  cycle.  x i i  t  during  the  :Estimated  time  at  which  r e c r y s t a l l i z a t i o n  during  isothermal  annealing.  : {211}  x-ray  ratio  degree  of  :P  value  :Time  at  peak  used  for  starts  evaluating  r e c r y s t a l l i z a t i o n . used  in  which  temperature. parameters  hypothesis  X=.99,  Based b  and  :Experimentally  on  testing.  for  a  given  the  best  fit  isothermal Avrami  k. determined  r e c r y s t a l l i z a t i o n  completion  x i i i  isothermal time.  the  ACKNOWLEDGEMENTS I and  would  like  guidance  like  to  their Thanks  during  thank  help are  preparation  to  the  Professor  given also of  thank  during extended  this  Dr.  course R.G. the to  E.B. of  Hawbolt  the  Butters  project. and  experimental Dana  t h e s i s .  xiv  for  Magee  Mr. part  for  his I  B. of  advice  would Chau this  helping  a l s o  for work.  with  the  Table  of  Contents  ABSTRACT  .  i i  LIST  OF  TABLES  iv  LIST  OF  FIGURES  v  LIST  OF  SYMBOLS  xi  ACKNOWLEDGEMENTS  xiv  1 .  INTRODUCTION  1  2.  L I T E R A T U R E REVIEW  3  2.1  2.2  Recovery  2.1.2  Primary  of  Annealing  ..3 3  R e c r y s t a l l i z a t i o n  12  21  2.3  Additivity  26  2.4  Methods  of  Monitoring  R e c r y s t a l l i z a t i o n  3.2  3.3  Hardness  30  2.4.2  X-ray  33  2.4.3  Miscellaneous  Industrial  Techniques Techniques  45  Processes  48  Annealing  2.5.1  Batch  Annealing  2.5.2  Continuous  49  Annealing  52 57  Isothermal R e c r y s t a l l i z a t i o n Measurements  Kinetic 57  Continuous Heating Measurements  R e c r y s t a l l i z a t i o n  Continuous Heating Predictions  R e c r y s t a l l i z a t i o n  EXPERIMENTAL RESULTS 4.1  30  2.4.1  EXPERIMENTAL PROCEDURES 3.1  4.  2.1.1  Aspects  A n a l y t i c a l M o d e l l i n g of Primary Recrystallization Kinetics  2.5  3.  Microstructural  Isothermal  Kinetic 64  AND  Kinetic 70  DISCUSSION  R e c r y s t a l l i z a t i o n  xv  Kinetic  73 Results  . . . . 7 3  4.2  4.3  4 . 4 5 .  Continuous Results  Heating  Recrystallization  Kinetic 91  Continuous Heating Predictions  Recrystallization  Kinetic 107  Discussion  116  SUMMARY  119  5.1  Conclusions  119  5.2  Recommendations  for  Future  Work  122  BIBLIOGRAPHY APPENDIX  1:  HEATING APPENDIX  2:  124 COMPUTER  PROGRAM FOR  RECRYSTALLIZATION  PREDICTING  CONTINUOUS  KINETICS  EVALUATION  OF  X-RAY  APPENDIX 3: EVALUATION GRADIENT  OF  THE  128  PROCEDURE  STRIP  SPECIMEN  130 THERMAL 136  xv i  1 . This  study  University models  of  is  part  B r i t i s h  INTRODUCTION  of  an  ongoing  Columbia  to  of  industrial  deformation,  treatment  processes.  This  mathematical properties to  an  able  of  In  order  to  predict  cycle.  in  and  as  r o l l e d ,  or  accomplish  this  the  such  as  carbide  w i l l  during  conjunction  high with  r e c r y s t a l l i z a t i o n  a  the  subjected  cycle.  model  continuous  after  must  be  with  heat  treatment  mechanical  r e c r y s t a l l i z a t i o n ,  coarsening  be  a  mechanical  being  annealing  steels'  and to  during  incorporated  as  cooling  into  the  model.  of  this  research  r e c r y s t a l l i z a t i o n  r o l l e d ,  developing  and  after  goal,  the  growth  have  at  heat  r e c r y s t a l l i z a t i o n  affecting  also  aimed  sheet  the  and  structure  batch  of  precipitation  purpose  isothermal  progress  grain  mathematical The  steel  is  at  mathematical  annealing  the  continuous  factors  overaging  f i n a l  cold  to  develop  research  predict  temperature  Other  properties  to  cold  industrial  increase  well  model  program  determine  data  steel  a d d i t i v i t y  kinetics  to  kinetic  deformability the  is  during  a  generated  sheet  p r i n c i p l e  whether  to  can  be  for used  a in  predict  continuous  heating  cycle. In  addition,  procedure specimen  that being  Similar the  an  attempt  monitors  mechanical  made  to  develop  r e c r y s t a l l i z a t i o n  subjected  approaches  is  to are  proporties  of  a  continuous  currently p l a i n  1  in  cycle.  taken  steel  insitu  steel  heating  being  carbon  a  an  to  rods  predict during  2  controlled  cooling  decomposition predicted,  processes.  kinetics  using  during  isothermal  resulting  microstructural  determine  final  mechanical  In  this  case  continuous  cooling  transformation  components  are  properties.  1  '  austenite  k i n e t i c s , then  2  is  used  and to  the  LITERATURE  2.  2.1  MICROSTRUCTURAL ASPECTS During  energy  the  w i l l  be  p l a s t i c stored  introduction  of  energy.  This  stored  the  relaxation  a  two  cold  worked  OF  REVIEW  ANNEALING  deformation  in  the  material  d i s l o c a t i o n s energy  of  and  that  metal,  recovery  can  defined  to  or  a l l o y ,  the  associated  the  d r i v i n g  occur  and  metal  due  their  provides  processes  a  strain  force  during  for  annealing  r e c r y s t a l l i z a t i o n .  of  3  RECOVERY  2.1.1  Recovery properties  of  a  be  cold  annealing  prior  and  mechanical  other  recovery. increase during  to  worked  as  metal  the  properties  decrease recovery  There  is  no  which  generally  with  t i m e , i e . ,  modification  that  r e c r y s t a l l i z a t i o n .  However," depending or  any  in  the  the  during  Generally,  change  on  these  occurs  to  hardness  very  l i t t l e  during  a l l o y ,  either  an  properties  can  be  observed  period.  incubation proceeds  in  period an  observed  exponential  during decay  recovery,  pattern  ...(2.1)  Z=K,exp(-kt) where  Z  is  the  instantaneous  value  of  some  property  of  the  3 material, The during the  t  is  time,  stored  energy  recovery.  activation  and  It  of  K,  cold  combines  energy  and  k  are  work  with  serves  thermal  requirements, 3  constants.  and  a  dual  energy  provides  purpose to the  satisfy driving  4  force  for  the  mechanisms be  various  may  annealed  occur  out  are  activation  energy.  the  input  energy  recovery during  point As  be  recovery.  defects,  the  w i l l  processes.  s u f f i c i e n t  activation  energy  requirements  F i n a l l y  higher  temperatures,  at  movements act  as  can  the  The  occur,  nucleation  i n i t i a l  deformation  as  occurs  cold  tangled  dislocation  worked)  dislocations  in  of  the  recovery,  towards  the  variety  of  centers  structure  percent  walls  creating  in  c o n s i s t s  c e l l  and  overcome  scale  movement.  d i s l o c a t i o n  grains  which  may  r e c r y s t a l l i z a t i o n . after  sheet  c e l l s  very  high  defined,  steels  the  tend in  are  with  some  f i r s t  to  stages  migrate  numbers  addition,  with  (60-80  walls  density,  During  In  heavy  whose  reduced  processes.  c l e a r l y  lowest  the  rolled  also  the  to  to  exists  of  of  increases,  d i s l o c a t i o n s  are  annihilation more  of  have  variety defects  dislocation  i n t e r i o r s .  interior  walls,  become  cold  f i r s t  strain-free for  wide  temperature  large  that  arrays  the  for  The  which  annealing  A  due  the  higher  to  a  c e l l  dislocation  3 density,  higher  energy,  and  greater  misorientation.  4 Hu  examined  annealing  of  rolled  percent.  70  a  the  i r o n - s i l i c o n  of  annealing  the  He  suggested  this  described subgrain  as  the  boundary  surrounding  microstructural  them.  He  found  subgrain to  be  between A  that  to  schematic  size  subgrain  moving two  that  during  boundary  due  gradual  c r y s t a l  changes  of  had the  during been  recovery  increased  to  the  representation  stage  s l i g h t l y .  coalescence  d i s l o c a t i o n s  c e l l s ,  cold  out  which of  he  the  boundaries of  this  process  5  is  shown  in  Figure  eliminated, same  and  atom  boundaries  as  from  o r i g i n a l l y  the  is  must  take  rearrangement to  to  CH  occurs  rotated  along  unshaded to  being  subgrain.  place  the  is  being  neighboring  shaded  connected  boundary  CDEFGH  i t ' s  diffusion  geometrical  Here  subgrain  orientation  occur,  2.1.  the  into  For  the  the  this  to  subgrain  areas.  F i n a l l y ,  a  boundaries  CH. 5  Another thought  to  structure theory form  occur with  states  at  active The  recovery  an  the  energy  from  deformed  a  in  polygonization Although mechanism  experimental  for the  to  there  d i s l o c a t i o n s  recovery,  the  glide  planes  that  polygonized  is  occurs some  during  as  of  which  the  occurs  at  high  dispute  as  of  indicate  a  type.  This  d i s l o c a t i o n s  shown  is  is  creates  one  had  in  been  Figure  reduction  during  structure.  recovery  observations  of  walls  bending,  material  a  polygonization  deformation  polygonization  reaction  active  of  during to  c a l l e d  applied  o r i g i n a l  force  strain  the  excess  angles  during  driving  when  that  right  process,  2.2. in  conversion  The  temperatures. to  iron that  the  exact  based both  a l l o y s ,  subgrain  o  coalescence The and of  427-871°C a  and  k i l l e d  correlation and  the  steels  the  area.  Large  occur.  annealed was  between  cold  do  r e c r y s t a l l i z a t i o n  (800-1600°F)  present, same  polygonization  recovery  aluminum  noted  and  worked  in  examined  the  type  of  structure  subgrains  with  low  behaviour the by  of  rimmed  temperature Goodenow.  subgrain previously angle  6  range He  structure occupying  grain  6  F i g .  2.1  Schematic by  representation  subgrain  rotation.  of  subgrain  (Ref.8)  coalescence  (a)  F i g .  2.2  Schematic process:  (b)  representation (a)  d i s l o c a t i o n s , dislocations  Random and to  the  arrangement  (b)  form  of  alignment walls.  polygonization of  edge  of  edge  (Ref.8)  8 boundaries cold to  existed  worked  the  in  grains.  low  These  mobility  consisted  of  elongated  cold  determined  of  small  to  areas  grains  their  exhibited  which  grains.  the  occupied  boundaries.  subgrains  rolled be  previously  nuclei  l i t t l e  Other  formed  These  for  large growth  due  areas  from  subgrains  responsible  by  small, were  subsequent  nucleation. The operate high a  ease  with  depend  stacking  large  fault  in  Pure during  energy,  motion  can  occur.  atoms  iron  by  occur  as  exerting  in  is  annealing  Figure  with  to  Pure  iron,  reduce  usually  ease  the  a t t r a c t i v e The  systems  to having  a  experience  during with  which  dislocation forces  ease is  able  metals  recovery  relative  drag.  alloy  found than  to  .  on  with  which  greatly  reduced  due  in  Figure  found  to  display effect  the 2.3.  be  much  more  attributed  increase  processes Carbon  to  softening r e c r y s t a l l i z a t i o n  in  softening  occuring  additions  at  w i l l  can  the  be  same  decrease  time the  recovery Both  similar on  display  .  This  recovery  which  to  can  2  2.3.  shown  combined  in  as  are  drag.  r e c r y s t a l l i z a t i o n .  ease  the  generally  resulting  iron  a t t r i b u t e d  due  processes  purity.  such  softening  1 alone,  metal  to  can  impurity  on  due  d i s l o c a t i o n s , recovery  recovery  is  Impurity mobility  of  This  d i s l o c a t i o n  to  largely  amount  annealing.  which  processes are able to occur, as 14 15 manganese and molybdenum were  e f f e c t s .  softening  of  Figures  alloying  2.4  and  additions  2.5. in  The  9  F i g .  2.3  Softening in  pure  time=3h,  as  iron  a  function  and  of  carburized  temperature  fraction iron.  r e c r y s t a l l i z e d  Annealing  range=380-490°C.(Ref.12)  10  %  Fig  2.4  Softening  of  RECRYSTALLIZED  three  iron  range=480-650°C.(Ref.14)  a l l o y s .  Temperature  l—L 0  F i g .  2.5  The  I  20  effect  Temperature  L_J  |  I . I . I  40 60 % RECRYSTALLIZED  of  molybdenum  80  on  the  100  softening  range=480-705°C.(Ref.15)  of  iron.  12  amounts Al)  is  t y p i c a l shown  reduced, of  in  low  can  with  PRIMARY Primary  2.4.  be  time  the  cold  by  an  of  during  is  cold  recovery.  common  to  of  activation  place  by  both  The the  growth  the  the  of  majority  the  nucleation  rate,  amount  slope N,  is  free  high  as  grains  growth  angle  matrix  is  temperature  the in  S i m i l a r i l y , is  obtained  of  the at  is  grain and  the  boundaries  the  nuclei  is  r e c r y s t a l l i z a t i o n  Since  activation  being  defined  The  growth  grains  the  related  processes, are  present  by  plotting  rate.  time  °K,  R  the  the  energy  gas  growth  by: ...(2.2)  experimentally  for  constant, rate  by  of  The  N  activation  takes  determined.  versus  temperature  in  both  determined  nucleation to  data  r e c r y s t a l l i z a t i o n  energies  usually  0  N  low  cycle.  N=N exp(-Q /RT) Q  of  '  r e c r y s t a l l i z e d  annealing,  where  is  8  and  rate  be  worked  energies.  nucleation  number  of  characterize  nucleation  and  can  strain  movement the  terms  nucleation  0.005  recovery  for  studying  matrix.  3  It  by  C,  R e c r y s t a l l i z a t i o n  annealing  new  worked  the  between  form  since  0.06  RECRYSTALLIZATION  expense  that  Mn,  responsible  r e c r y s t a l l i z a t i o n  accomplished  (0.52  steels.  during  growth  exist  is  quantified  and  of  steel  Therefore,  carbon  nucleation  that  carbon  Figure  in  steel  softening  2.1.2  low  r e c r y s t a l l i z a t i o n  softening  carbon  of  of  a  plotting  nucleation, and  N  0  a  T  is  constant.  r e c r y s t a l l i z e d the  the  diameter  grain of  the  13  largest slope  unimpinged  being  the  temperature  grain  growth  against  rate,  the  G.  As  annealing  before,  G  time,  is  the  related  by: G=G exp( Q /RT)  ...(2.3)  1  0  where  QQ  to  is  the  G  activation  energy  for  growth,  and  G  is  0  a  constant. If for  a  can  be  growth range  of  versus  -Q  G  or  the - Q  There  N  and  nucleation  temperatures,  determined  N  /R  rate  by  inverse / R ,  the  plotting of  rate  data  values  the  of  natural  temperature,  are  Q^,  obtained  Q_ ,  G  N  logarithm  the  slope  and  0  of  w i l l  G  N  0  or  equal  respectively.  has  been  extensive  research  into  the  factors 7  which  affect  formulated these 1.  A  r e c r y s t a l l i z a t i o n .  the  following  minimum  amount  The  smaller  Increasing necessary  4.  of  laws  Turnbull  concerning  many  of  The  of  amount  required the  to  of  to  cause  time  needed  to  i n i t i a t e  the  higher  is  the  r e c r y s t a l l i z a t i o n . decreases  the  temperature  r e c r y s t a l l i z a t i o n . grain  size  of  deformation,  and  annealing  temperature,  being  degree  deformation  of  is  deformation,  cause  annealing  r e c r y s t a l l i z e d  degree  deformation  ion.  the  temperature 3.  series  and  effects:  r e c r y s t a l l i z a t 2.  Burke  and  to  depends a  c h i e f l y  lesser  smaller  extent  the  the  lower  the  grain  size,  the  upon on  the  the  greater  the  annealing  temperature. 5.  The  larger  the  o r i g i n a l  greater  is  the  1  amount  6.  7.  of  deformation  required  equivalent  r e c r y s t a l l i z a t i o n  The  of  amount  cold  work  deformation  hardening  temperature  of  Continued causes The  since the  cold  grain  extent  the  of  strain  d r i v i n g  minimum  amount  for  migration  the  size  required  to  give  with  an  and  time.  equivalent  increasing  r e c r y s t a l l i z a t i o n  to  of  affects  resulting  nucleation  strain  energy  high  is  complete  increase.  deformation  for  of  temperature  increases  after  energy  force  give  working.  heating  the  to  4  from and  is  angle  r e c r y s t a l l i z a t i o n cold  work  growth  needed  grain  provides  processes.  for  A  nucleation  boundaries  and  during  growth. The cold  activation  work,  as  greater  than  towards  0_  finer w i l l  the  shown Q^,  result  in  while  i n i t i a l  is  at  in  higher  N  grain  to  affected  2.6.  large  easier  and  and  grain  G  p  is  the  density,  B  by  low  s t r a i n s ,  the  for  can  a  Q_  given  d i s t r i b u t i o n .  the  N  amount Q  of is  N  decreases  and  a  activation  contribute  size  the  s t r a i n s ,  nucleation  resulting energies  temperature. to The  variation  in  d i s l o c a t i o n  by:  p=e/akEd where  At  Lowering  size  density  related  are  Figure  structure.  d i s l o c a t i o n  density  in  resulting  G  grained  The  energies  n  ...(2.4)  burgers  vector,  d  the  grain g  s i z e ,  e  the  effect  of  Figure  2.7.  p l a s t i c  grainsize At  s t r a i n , on  higher  a,k  and  d i s l o c a t i o n s t r a i n s ,  the  n  are  density  constants. is  d i s l o c a t i o n  shown  The in  density  15  15  J  i  10 G\  "55 c  2  N  5  a* a  50  60  70  80  Q, kcal/g atom  F i g .  2.6  Recrystallization energies a  for  function  of  data  nucleation prior  for (N)  aluminum, and  for  activation growth  deformation.(Ref.8)  (G)  as  16  Fig.  2.7  Dislocation  density  versus  deformed  various  amounts  by  temperature.(Ref.8)  grainsize at  room  in  iron  17  becomes  less  sensitive  Dislocations w i l l  since have  Q  changing metal cold  w i l l  H i g g i n s  0.74  ym  is  1  also  noted  c r i t i c a l joint  a l l o y i n g  p a r t i c l e s  in  if  particle  effect  the  phase  a  stimulated  that  to  the  a  0.4  sites  as  Goodenow  r e c r y s t a l l i z a t i o n d i s l o c a t i o n s than  matrix  to  p a r t i c l e s .  rather the  decrease  main  than  the  total  s i z e .  Gawne  on  particle  is  due  greater  to  occur.  spacing  matrix,  appears  percent  to  a  the  of  steel  However,  the  in  size  carbon  small,  to  be  it  additions  the  formation  both on  i n t e r s t i t i a l  recovery  and  and  has  found  that  percent)  been  investigated  small  added  to  r e c r y s t a l l i z a t i o n  of  substitutional  r e c r y s t a l l i z a t i o n  of  12  x  steel  was  zones.  of  amounts  of  at  length.  carbon  high  purity  rate.  They  6  by  in  the  The  particle  c r i t i c a l  nucleation  w i l l  these  well  harder  the  weight  p a r t i c l e  size  at  in  preferential  p a r t i c l e s  upon  that  strain  results  as  of  are  deform  depends  9  affect  d i s t r i b u t i o n  determined  1  a l .  that  d i s l o c a t i o n s ,  however  This  of  boundaries.  can  adjacent  of  application  occuring  et.  grain  second  deformation The  and  necessary  p a r t i c l e  at  the  hard  This  Rosen,  p l a s t i c a l l y  d i s t r i b u t i o n  number.  for  If  immediately of  the  boundaries.  p a r t i c l e s  number 1  influence  and  occur  matrix. ^  extent  by  generally  lower.  phase  the  work  grain  s i z e .  metallographically  does  Second  the  be  v a r i f i e d  nucleation  at  nucleation  w i l l  N  grain  generated  concentrate  preferential  to  iron  (up  Venturello to  0.0086  s l i g h t l y  speculated  that  et.  weight  affected any  a l .  the  reduction  18  in  grain  would  boundary  be  system  compensated  due  It  mobility  to  was  less  also  noted  increased  (Fe C)  the  and  Nitrogen retarding 2 . 8 .  1  was  effect  found on  14  affect  rolled  of  carbon  p a r t i c l e a  carbon  energy  in  the  previously.  formation  have  levels  of  iron  carbide  stimulated  s l i g h t l y as  more  shown  steel  found  to  Unlike  show  the  exhibited  has  nucleation. pronounced  in  Figure  2.9(b).  ^  aluminum  k i l l e d  This  type  precipitation  an  to  occur,  i n i t i a l  to  a  on  r e c r y s t a l l i z a t i o n of  of  many  occur than  in  is  of off  period  of  very  complete longer  for  steels.  has  been  (AlN)  attributed  to  during  .  precipitates  impeding  k i l l e d  r e c r y s t a l l i z a t i o n ,  for  nitride  curve  steels  period  rimmed  response  sometimes  r e c r y s t a l l i z a t i o n .  2.9(a),  rapid  for  .  therely  were  s i g n i f i c a n t l y  aluminum  the  steels  leveling  necessary  sluggish of  by  off  time  17 r e c r y s t a l l i z a t i o n ;  both  k i n e t i c s .  during  Figure  followed  steels of  to  r e c r y s t a l l i z a t i o n  s t e e l s ,  The  r e c r y s t a l l i z a t i o n  found  subject  response  finishing 1  the  shaped  displayed  r e c r y s t a l l i z a t i o n ,  Figure  been  sluggish  rimmed  kinetics,  practice  Aluminum-killed  a  aluminum  were  1 8  —  sigmoidal by  15  r e c r y s t a l l i z a t i o n  k i l l i n g  investigations.  drag  the  of  to  higher  molybdenum  the  1 6  the  to  stored  explained  r e c r y s t a l l i z a t i o n  and  decrease  The  slow  due  i n t e r s t i t i a l  greater  as at  by  3  s l i g h t l y  with  the  that  occurrence  Manganese  cold  by  recovery,  nucleation  3  for  caused  the  cause  mobility  grain of  boundary  the  high  19  350  F i g .  2.8  400  Fraction  with  (b)  500  r e c r y s t a l l i z e d  temperature iron,  450  (isochronal  iron  nitrogen  with  550 600 Ann Temp, *C  versus  annealing  anneals  carbon  of  3  additions,  additions.(Ref.13)  h). (c)  (a)  Pure  iron  «Wr-i  2.9  ;  Effect  J  1  of  kinetics  1  1  temperature of  (a)  steels.(Ref.16)  rimmed  1  1  on  1  the  and  (b)  1  1  r  r e c r y s t a l l i z a t i o n aluminum-killed  21  angle  grain  which  is  necessary  However, of  the  boundaries.  it  would  aluminum  sluggish  cause  appear  and  exact this  that  size  of  effect  the  is  precipitate  not  known.  pre-precipitation  nitrogen  might  be  c l u s t e r i n g  responsible  for  the  kinetics. ** 1  Any  heat  treatment  r e c r y s t a l l i z a t i o n subsequent  2.2  to  The  can  which  be  precipitates  used  to  prevent  AlN  the  prior  delay  to during  r e c r y s t a l l i z a t i o n .  ANALYTICAL MODELLING  OF  PRIMARY  RECRYSTALLIZATION  KINETICS T y p i c a l l y , sigmoidal  pattern  incubation processes  primary with  period are  active,  near  of  worked  r e c r y s t a l l i z e d  is  rate,  decelerates cold  time,  during  r e c r y s t a l l i z a t i o n  the  r e c r y s t a l l i z a t i o n as  which  shown the  followed which  completion  then  of  structure  the  w i l l  in  follows Figure  various by  an  2.10.  An  recovery  i n i t i a l l y  accelerates, reaction. be  a  slow  and  f i n a l l y  Eventually,  consumed  a l l  by  grains. 7  Burke  and  describing and  Turnbull  presented  r e c r y s t a l l i z a t i o n  a  formal  kinetics  in  theory  terms  of  nucleation  growth. If  growth  D  describes  isothermally  described  by  the  the  dimension  into  a  cold  of  a  worked  grain  experiencing  matrix,  it  can  relation: D=G(t T)  ...(2.5)  -  where  G  is  the  be  linear  growth  rate,  t  is  the  time  of  the  22  Time  F i g .  2.10  Typical curve.  sigmoidal  shaped  r e c r y s t a l l i z a t i o n  kinetic  23  reaction,  and T  the  of  start  volume  given  the  length  of  the  incubation  period  at  r e c r y s t a l l i z a t i o n .  Assuming the  i s  the  (v)  grain  of  the  to  be  grain  growing  at  any  in  three  particular  dimensions, time  c a n be  by: v = f G G A  where  G  and  d i r e c t i o n s ,  z  ,  G  and G  -According number  of  matrix  during  and  to  the  f  i s  Johnson  n u c l e i , a  are  G ( t - r ) y *c*  dn,  time  . . . ( 2 . 6 )  3  linear a  growth  shape  interval,  in  the  x,  y  factor.  and Mehl,  originating  rates  19  in  d r ,  and Avrami, the  20  the  u n r e c r y s t a l l i z e d  c a n be  expressed  by  the  relation: dn=N(1-X)dr where the  N  i s  the  volume The  nucleation  fraction  number  interval  in  structure,  of  both  . . . ( 2 . 7 )  frequency  per  unit  volume  and X  r e c r y s t a l l i z e d . nuclei  the  originating  r e c r y s t a l l i z e d  d n ' , c a n be  given  during  and  the  same  "ghost" it  nuclei  had not  grains  nuclei  i s  which  grow given  c a n be  originating  already  transformed, the  NXdr  by: . . . ( 2 . 8 )  considered in  the  disregards  to  be  transformed  r e c r y s t a l l i z e d .  through  time  u n r e c r y s t a l l i z e d  dn'=dn+NXdr=Ndr Therefore,  i s  This  grain  one a n o t h e r ) ,  the  number  material,  extended  impingement  of if  volume ( i e .  and includes  assumes  the  ghost  by:  X=/J ex  v d n '  . . . ( 2 . 9 )  24  Substituting yields  the  Avrami  e x  =  f  G  x  y V  G  o  and Johnson-Mehl  the  extended  r e c r y s t a l l i z e d ,  X,  Substituting  and  (2.8)  into  (2.9)  t  ~  T  )  have X  g  x  3  N  ...(2.10)  T  d  written  an  equation  and the  actual  volume  a s :  g  x  equation  the  =l-X  that  growth  obtain  Johnson-Mehl  into  =fG G G /Q x  necessary  assumption  ...(2.11)  (2.11)  f*dX/(1-X)=-ln(1-X) Performing  (  volume,  dX/dX  the  (2.6)  relationship: X  relating  equations  z  are  obtain: ...(2.12)  3  equal  equation  we  (t-T) Ndr  integration  rates 19  y  (2.10)  for  and making  in  a l l  the  directions,  three  we  dimensional  r e c r y s t a l l i z a t i o n : X=1-exp(-fG Nt 3  so  If  growth  occurs  that  growth  in  (2.6)  c a n be  in  a  f l  very  ...(2.13)  thin  one d i r e c t i o n  modified  /4)  i s  sheet  of  thickness  negligible,  6,  equation  to: v = f G  2  8 ( t - r )  ...(2.14)  2  19 The  Johnson-Mehl  equation  for  two  dimensional  growth  is: X=1-exp(-fG 6Nt /3) 2  S i m i l a r l y , diameter G =G = 0 . x y  for  ...(2.15)  3  r e c r y s t a l l i z a t i o n  6, growth w i l l o c c u r Equation (2.13) then ^  in  a  thin  in one dimension becomes:  wire only,  X=1-exp(-fG6 Nt /2) 2  of with  ...(2.16)  2  19 The N  to  be  Johnson-Mehl constant,  equation  and determined  assumes by  the  nucleation  experimentation.  rate  25  . 20 Avrami assumed preferred certain sites  there  nucleation  nucleation  existing  to  be  sites  a  in  the v.  frequency,  after  time  r  number  is  of  pre-existing  matrix,  N",  The number  given  each of  having  nucleation  by:  N =Sexp(-^r)  ...(2.17)  T  Therefore, expressed  the  nucleation  rate  at  T  time  c a n be  by: N=N>exp(-*<7-)  Substituting growth the  in  a l l  equation  directions  necessary  ...(2.18)  (2.18)  to  be  integration,  we  into  equal  (2.12),  to  G,  assuming  and  performing  obtain:  X=1-exp(-fG R"t ) 3  for  approaching  VT  (2.19)  i n f i n i t e .  ...(2.19)  3  If  VT  approaches  zero,  equation  becomes: X=1-exp(-fG N"z/tV4)  ...(2.20)  3  If  N  (2.18)  i s  assumed  to  be  independent  of  time,  equation  becomes: N=N>  and  a  equation  (2.20)  w i l l  be  ...(2.21) the  same  as  that  obtained  by  19 Johnson-Mehl given  in  for  equation  three  dimensional  r e c r y s t a l l i z a t i o n ,  (2.13).  20 Avrami equation  to  proposed  the  general  r e c r y s t a l l i z a t i o n  be: X=1-exp(-bt )  ...(2.22)  k  with for  3^k<4 two  for  three  dimensional  dimensional  dimensional  r e c r y s t a l l i z a t i o n ,  r e c r y s t a l l i z a t i o n ,  r e c r y s t a l l i z a t i o n .  and  1^k<2  for  2<k^3 one  26  2.3  ADDITIVITY Due  growth  to  the  rates  with  nonisothermal However,  i f  shown  be a  to  independent  temperature,  reactions  function  already  reaction  i s  only  nucleation  the transformation  rate  present,  additive  of  are d i f f i c u l t  the reaction  material  variation  at  of  to  and of  rate  of  characterize.  any instant  t h e amount  and  in  of  time  c a n be  transformed  the temperature,  a n d c a n be m a t h e m a t i c a l l y  the  described.  21 Christian simple  explained  non-isothermal  treatments.  If  temperature  T , ,  t  1  r  and then  lower  where  i s  Therefore, amount  of  f T ( t , ) =f  2  T  (in  2  t  i s  2  volume  2  i f  ) ,  by c o n s i d e r i n g  combining reaction  kinetic  law  i s  two  of  X=t,(t),  continues  h a d been  the time  taken  at  transformed  as f,  ( t , ) ,  and the whole  to  occurs for a  a  at  time  s l i g h t l y  r e c r y s t a l l i z a t i o n ) ,  the reaction f ^ t , )  a  isothermal  p a r t i a l l y  instantaneously  the case  transformed  i f  ( 1  the  transferred  i s additive  fraction  reaction  transformation  temperature  reaction the  a  additivity  T  reaction  2  at  t  as  2  transformed to  at  produce  the  the i f T  2  .  same  then  can be  written:  X=f,(t),(t<t,) = f The fraction  f i r s t  ( t + t  equation  transformed  the  transformation  the  time  spent  transformed v i r t u a l  2  time  at  at  T ^  T  with  terms  }  - t , ) , ( t > t , )  in the  depends  at  2  2  the above i n i t i a l only  The second f ^ t , )  set  refers  temperature  on t h e r e a c t i o n equation  already  are contained  ...(2.23)  in  gives  present.  this  to the T , ,  where  kinetics the Both  expression.  and  fraction real  and  Since  27  ti  has already  T  must  2  the  be  been  ( t - t , ) .  component  must  be h e l d  must  held  temperature  transformed 2.11.  be added  during  The time  time  given  spent  at  at  T, ,  for a  this  time  i s  2  above, both  time  at  T,  T  the additional  T  t  for  2  time  t  t  a  2  applies  to  cause  given  a  time  temperatures,  if  ( t - t , ) / t  small,  the difference  the kinetics  temperature spent  at  w i l l  each  of  3  is  obtained  temperature additivity  X  a  by adding until  ,  2  under the  + ( t  s  t  2  X  a  ,  amount  Figure of stage  be t h e sum o f  a  the  1  at  i s  each increments  zero, / t  a  )  2  / t  a  ...(2.26) we  obtain:  , ) = 1  reach  a  unity.  (T)=1  ...(2.27) specified  heating  time  by the  a  by  ...(2.25)  As the time  continuous  d t / t  Dividing  ) = 1  2  (2.25)  to  t h e sum r e a c h e s  J \  a  becomes:  isothermal  c a n be g e n e r a l i z e d  i s  ...(2.24)  other.  time  be X  t h e two temperatures  into  a  time  of  2  / t  2  ) = ( t  (2.26)  the total  transformation,  1  at  fraction  t h e two  w i l l  approach  ( t - t , ) / t  of  + ( t  each  temperature  Therefore,  In  the transformation  approach  equation  w i l l  (2.24)  2  the  component  i s additive.  between  ( t i / t Substituting  a  i s  time  o r :  the reaction equation  a  the  .  2  real  formation  i f  , ,  a  which  t h e same  by t  the total  and rearranging,  When  ,  the  interval  t=t,+ta2-t This  2  i n . For example,  necessary  transformation example  at  The v i r t u a l  f 1 ( t ! ), at  spent  or  fractions  amount cooling at  each  Therefore,  equation: ...(2.28)  28  Time  F i g .  2.11  Schematic  representation  a d d i t i v i t y .  of  the  p r i n c i p l e  of  29  where is  t  the  (T)  i s  the  time  at  which  a  continuous X  a  i s  time  heating  formed  the  or  under  to  transform  X  at  a  transformation  cooling,  begins  and txa  non-isothermal  temperature  is  the  T,  t  s  during time  at  which  conditions.  22 Scheil incubation event.  proposed period  Assuming  temperature this  to  temperature that  If  successive  the  up,  the  one,  is  a  incubation  be  t^,  exhausted  period by  the  w i l l  at  to  t^  any  of  c a n be  nucleation  start  once  determine  the  transformation  and the  fraction  during  "fractional  transformation  equation  non-isothermal  represented to  period  similar  during  the be  a  p a r t i c u l a r time  the  at  incubation  given times"  the  spent  by  t^/r^.  are  *  summed  sum e q u a l s  or:  Therefore,  the  .£ t./r.=1 i=1 i i t o t a l nucleation s  ...(2.29) time  is  given  by:  fc  / where is  t  the  s  i s  the  incubation  Equations describe  the  equation  i s  a d d i t i v i t y *  In  quite  approach  Avrami  which  period  (2.28)  temperatures  kinetics  at  at  and  20  the  (2.30)  addition,  and the  r e s t r i c t i v e T^  and T  one  The S c h e i l equation linear function with  ...(2.30)  reaction  differ  in  that  it  so close  r(T)  they  events  development that  and  T.  incubation  in  are  s t a r t s ,  of  only  the  Scheil  applies  together  when  that  the  another.  examined  p r i n c i p l e  2  '  temperature  transformation  respectively.  the  time  dt/r(T)=1  the  and  . . p o s s i b i l i t y  isothermal  assumes time.  the  of  applying  kinetic  incubation  data event  the  to to  predict be  a  30  austenite believed  decomposition that  this  approach  i s o k i n e t i c  range  of  and  rates  remain  If  growth this  addi  during  condition  continuous  would  temperatures  then  v a l i d  exist  constant  e x i s t s ,  be  He  providing  where  with  the  cooling.  the  respect  reaction  that  an  nucleation  to  each  would  other.  be  tive. 23 Cahn  suggested  r e s t r i c t i v e , site at  and  saturation  the  by  Kuban  et.  in  the  contribute 2.4  2.4.1  METHODS OF  the  case,  on  the  w i l l  nuclei  l i t t l e  to  MONITORING  be  and  is  two  s a t i s f i e d  if  early  the  is  complete  reaction  is  material.  that  "effective  site  the  a d d i t i v i t y  requirement.  idea  that  dominate formed the  condition  nucleation  transformed  s a t i s f y  based  while  very  of  also  is  could  this  suggested  reaction  transformed,  In  growth 2  would  isokinetic  transformation,  a l .  condition  early  of  the  a d d i t i v i t y  occurs.  the  saturation" This  that  beginning  governed  that  the  later  total  the  nuclei  volume in  fraction  the  volume  formed  reaction  transformed.  RECRYSTALLIZATION  HARDNESS Probably  the  most  common  progress  of  r e c r y s t a l l i z a t i o n  its  of  use,  ease  s i t u a t i o n s . content,  and  its  However,  softening  r e c r y s t a l l i z t i o n  on  method is  does a  not  one  to  on  in  This  such  correspond  basis.  the  is  due  industrial  factors  always one  measuring  hardness.  s i g n i f i c a n c e  depending  for  If  a  as with  metal  alloy  to  31  experiences give  a  recovery  false  during  estimate  of  r e c r y s t a l l i z a t i o n ,  the  amount  of  hardness  w i l l  r e c r y s t a l l i z e d  g structure  actually  present.  Macrohardness r e c r y s t a l l i z a t i o n 12-15 '  the  using  For  indentation  studies  using  hardness  have  of  not  is  of  cold  to  been  of  reduce  p a r t i c u l a r l y  at  microhardness  in  each  the  ensure  least 3 6  ten  times  for  metals,  grains have  yet  correct the a  w i l l to  indentation  depth  regions  be  of  which  are  r e c r y s t a l l i z e .  number  of  or  of  readings  This  located  in  must  be  is  microhardness is  A  s i g n i f i c a n t l y  inaccuracies. of  thickness.  d i s t r i b u t i o n  large  the  t e s t i n g .  r e c r y s t a l l i z e d  case  indentations  the  hardness  limited  being  that  specimen  s t a t i s t i c a l in  to  is  sheet  the  which the  steel  by  regions,  true  where  r o l l e d  r e c r y s t a l l i z e d  located  macrohardness  necessary  affected  obtain  unrecrystallized  of  material, are  regions  indentations  methods,  the  use  recrystallized  than  to  the  recommended  p a r t i a l l y  Therefore,  taken  most  thickness  composed softer  which  loads is  penetration In  by  thinner  lighter  specimen  means  However,  thickness  studied.  the  24  done. by  is  evaluation a  very  small  area. A applied by of  microhardness  population  count  technique  has  been  the study of copper r e c r y s t a l l i z a t i o n 37 . • Gordon. This technique i n v o l v e s making a l a r g e number indentations, (typically 200-400) in each specimen in a  series  to  of  samples  annealed  for  varying  lengths  of  time,  at  a  32  VICKERS HARDNESS NUMBER 90 70 50 40 35 UNRECRYSTALLIZED  ANMEALING PER CENT TIME, HOURS RECRYSTALLIZED 94.5  100.0  8.96  70.0  6.74  56.6  5.33  42.6  4.25  30.0  2.87  12.5  RECOVERY ANNEAL I HOUR 190° C AS DEFORMED  0.0  0.0  i—r 18 20 22 24 26 28 DIAMETER OF HARDNESS INDENTATION ARBITRARY UNITS  F i g .  2.12  Microhardness  d i s t r i b u t i o n  c h a r t s . ( R e f . 3 7 )  33  s p e c i f i e d are  temperature.  determined  2.12.  In  for  each  specimens  typical  clustered  the  size  cold  around  the  softer  2.4.2  specimens,  is  of  populations  the  both  made.  by  When  change, grains  curves  by  For  p a r t i a l l y  by  comparing  number  found  this  hardness  present.  total was  a  of  to  method,  exist and  those  means.  TECHNIQUES metal  the  interact  compression,  is  metal  becoming  The  obtained  are  Figure  present,  determined  correlation  calorimetric  a  in  Good  to  at  is  value.  values  r e c r y s t a l l i z e d  X-RAY  grains  structure  in  any  d i s t r i b u t i o n  hardness  both  diagrams  i l l u s t r a t e d  experienced  percent  kinetic  obtained  not  worked  d i s t r i b u t i o n  as  population  the  indentations between  one  have  of  r e c r y s t a l l i z e d The  specimen,  which  r e c r y s t a l l i z a t i o n , value  Microhardness  workpiece  elongated during  and  effect  p l a s t i c a l l y  other of  deformed  w i l l  in  the  r o l l i n g  varying  of  r o l l i n g ,  experience  deformation, regions  by  a  shape  d i r e c t i o n .  resulting  the  The  in  regions  of  l a t t i c e  spacing  and  tension.  strain  on  the  25 x-ray  line  position Braggs  position  of  the  and  shape  diffracted  is  peak  shown can  be  in  Figure  determined  X  is  incident  0  is  from  ...(2.31)  o  d  The  law: X=2d sin0  where  2.13.  the  the  angle  wavelength the  beam  unstrained  of  makes  l a t t i c e  the  x-ray  with  the  spacing.  beam,  6  crystal  is  the  surface,  and  34  CKYSTAL LATTICK  DIKFIiACTION LINK  dn  NO STHAIN (a)  UNII"OHM STHAIN il.)  anil?  NO.NI'Ml'OHM STHAIN It)  F i g . 2.13 E f f e c t  of l a t t i c e s t r a i n on D e b y e - l i n e width and  position.(Ref.25)  35  If right  the  angles  w i l l  to  increase If  as  c r y s t a l  in  a  d  +  0  w i l l  spacings.  The d  a  enable  peak and  2  produce metal  is  a  one  the  d  -  0  of  a  must  combine, broad  a  introduced  into  inspection  of  these can  two then  be  in  the  a  l a t t i c e  wide  variety  of  A to  varying  peak  such  in  assumed  be  plane  c h a r a c t e r i s t i c  greater  figure  broadened  a  of  d i f f r a c t i o n by  be  a  extremes.  regions  single amount  that be  at  peak.  better a  the  of  by  number  of  dotted  curves.  d i f f r a c t i o n  line  is  d i f f r a c t i o n  line  as  is  Figure  by  However,  degrees  peaks of  in  annealed  2.14.  cold  doublet.  work  w i l l  the  work  of  be  amount can  f u l l y  two  c o l d a  be  cold  Ka  cold doublet  peaks work,  Ka, to  worked  resolved. of  a  metal,  the  the  When  a  and  if  examined,  higher  both  cold  the  estimation  metal Ka  of  peak  known.  metal  annealed,  a  between,  p o s i t i o n .  c r y s t a l ,  with  w i l l  spacing  peak  the  tension  side  In  replaced  the  worked  Therefore,  in  in  at  2.13(c).  widths,  f u l l y  be  to  strain  l a t t i c e  shift  given  small  large  a  is  Ad.  c r y s t a l of  in  other  between  be  use  cold  w i l l  w i l l  curves,  specimens  of Ka  while  determine peak  strain  represented  Figure  worked  resulting  side  w i l l  0  produced,  standard  the  single  these  to  planes,  number  Combining  means  reflecting  exist  peaks,  To  tensile  deformed  of  spacing  one  Ad,  comprised  smaller  uniform  spacing  p l a s t i c a l l y  of  a  Ad,  given  non-uniform  compression, spacings  the  by  bending,  spacing  is  strain  obtained  by  36  F i g .  2.14  Effect  of  resolution  strain in  on  70-30  the  {331}  doublet  brass.(Ref.25)  peak  37  Since a of  recovery  microscopic a  cold  worked  recovery. peaks  and  When  w i l l  Grain pinhole  grain  using growth  with  a  broad  occurs,  resolved,  the  with  r e c r y s t a l l i z a t i o n  growth  after  can  detected  The  fine  sharply  grained,  on  x-ray  both  peaks  during Ka  doublet  sharper  proceeds.  r e c r y s t a l l i z a t i o n  diffractometry.  be  r e l i e f ,  sharpen  x-ray  photographs.  associated  as  the  p a r t i a l l y  p a r t i a l l y  occuring  detected  will  stress  l e v e l ,  r e c r y s t a l l i z a t i o n  Unfortunately, be  p a r t i a l  macroscopic metal  become  resolution  involves  using  back  cannot  reflection  defined  Debye  annealed  metal  lines w i l l  become  25 spotty  as  i n i t i a l  the  peak  grain  size  increases,  the  cold  rolled  been  some  research  of  Figure  metal  is  2.15.  very  The  broad  and  d i f f u s e . There  has  degree  of  peak  resolution  during  annealing  of  cold  on  done  various  worked  to  characterize  x-ray  s t e e l s .  the  d i f f r a c t i o n 2 6  Hawbolt  peaks  and  27 DiCello  both  examined  r e c r y s t a l l i z a t i o n Ka  and  that  Cr  an  and  on  same  point  r e c r y s t a l l i z a t i o n with  {211}  x-ray  of  time  by  the  recovery 1/2  peak  The  followed  characteristic  of  the  12s, a  width  occurred 2 6  using  hardness  at  sigmoidal  r e c r y s t a l l i z a t i o n .  found  the  results  results which  Fe  during  compares  hardness  by  and  researchers  2.16  with  approximately  starts,  peak  Both  Figure  Hawbolt  specimens. at  of  respectively.  resolution  obtained  the  i n f l e c t i o n  drop  effect  r e c r y s t a l l i z a t i o n .  results  obtained  the  radiation,  considerable  recovery x-ray  KB  on  the  display  point hardness The  1/2  A N N E A L I N G T E M P E R A T U R E ("(') (a) H a r d n e s s curve  F i g .  2.15  Effect back  of  (d) 1 hour at 45()°C  r e c r y s t a l l i z a t i o n  r e f l e c t i o n  pinhole  specimens.(Ref.25)  and  patterns  grain of  growth  70-30  on  brass  39  Effect of 627*C Itothermol Anneal on X-Roy ond Hordnett Propertiei of IMRI Sheet Steel # I  .  (*254mmAl»2e) 25  6  80  ro  50 Isothermol  C h-0'°~ ~0~O 0  75 Annealing Time  100  600  (s)  70 f  O-jj-O-  60 As Cold Rolled  Fig.  2.16  {211} time  1/2 in  peak  width  annealed  and  steel  R  30-T  hardness  specimens.(Ref.26)  versus  40  peak  width  point,  readings  or  the  also  metallographic during  appear than  that  to  both  recovery  the  inflection  r e c r y s t a l l i z a t i o n  the  K a  hardness  recovery  either  2  / K a , peak  measurements  Although  a  curve.  height and  ratio  change  and r e c r y s t a l l i z a t i o n ,  affected for  the  the  r a t i o  to  a  particular  ratio,  was  it  would  greater  steel  extent  tested,  2.17.  The peak  shaped  observations.  r e c r y s t a l l i z a t i o n ,  Figure  display  examined  was c o r r e l a t e d  noted  not  sigmoidal  Hawbolt^ which  do  main  r a t i o  counting  disadvantage  x-ray  heating  required  This  rates  1/2  measurements  interval  d e f i n i t i o n .  of  limits  to  their  encountered  peak  width  appear  to  obtain  the  be  the  Ka /Ka! 2  large  required  usefulness  during  and  during  continuous  peak  the  high  annealing.  28 Hu  a n d Goodman  carbon  steels  parameter defined  of  examined  different  c a l l e d  the  B  i s  T  recovered  the  (and  broadening  cold  r o l l e d  defined  peaks  / ( B  recovery  contents  residual  using  line  in  low  a  broadening",  cr- rex» B  broadening  parameters  specimen  ...(2.32)  parameter  recrystallized)  of  specimen,  for  a  f u l l y  respectively.  the B  r  p a r t i a l l y e  x  and B  are  r e c r y s t a l l i z e d  The variable  and  B c a n be  a s : B  where  of  a s : B  the  degree  manganese  "fractional  <V rex where  the  1 m  ^  n  using  ^  s  the  =  (  I  m i n -  I  b  )  /  intensity  Mo K a r a d i a t i o n ,  (  I  m a x -  b  I  minimum I  m  a  x  i s  ...(2.33)  )  between the  the  Ka,  intensity  and K a of  the  2  41  Effect  of  627*C liothermol Anneol  on X-Roy ond Hordnati Proper tie»  05  % rr  of  IMRI Sheet Steel  #1  o, 01 0  ,U -cv> -0-2 U^O -0-1  -  25  8 or  oo  80  50 Isothermal  75 Annealing Time (s)  w O  Fig.2.17  600  70  •o  X  100  -O—i?-o  60  {211} time  x-ray in  peak  ratio  annealed  steel  and  R  30-T  hardness  specimens.(Ref.26)  versus  42  Ka,  peak, The  a n d 1^ results  r e f l e c t i o n s ,  in  r e c r y s t a l l i z e d appears by  that  recovery  i n f l e c t i o n roughly  When a  addition i s  shown  to in  {200},  the  actual  Figure  parameter  i s  {222}  and  2.18.  affected  Once to  a  r e c r y s t a l l i z a t i o n .  point  appears  to  with  exist  the  onset  metallographically, narrow the  the  s a t i s f i e d , of  beam  known  deviate  of  the  the  the  Bragg  beam  w i l l  from  0_.  of  be If  greater  it extent  However,  curve  an  which  2.18(c). x-rays  reflected  Bragg  law,  angle,  f a i r l y a l l  again,  r e c r y s t a l l i z a t i o n  Figure  where  as  each  monochromatic  intensity  angle  the  of  in  {112}  percent  primary  at  s l i g h t l y  for  intensity.  than  a  intensity  background  obtained  the  c r y s t a l ,  greatest is  the  corresponds  determined  on  i s  are  beam  incident  w i l l  equation  (2.31),  t9g. H o w e v e r ,  large  at  the  angles  the diffracted  be  which  beams  are  JD  measured  around  intensity"  of  0g,  the  the  t o t a l  refracted  energy,  beam  is  termed obtained.  the  "integrated  25  29 Ono cold the  e t .  rolled {222},  Figure  is  {200}  using  well  c l e a r l y  in  the  r e c r y s t a l l i z a t i o n  integrated peaks.  changes  in  hardness  changes  during  i s  apparent  kinetics  of  the  dependent  cases upon  factors  values  of  i n t e n s i t i e s  texture  texture a s A1N  of  shown  r e c r y s t a l l i z a t i o n  that  the  texture  are  r e c r y s t a l l i z a t i o n  although such  results  integrated  It  some  intensity  Their  the  development. the  the  a n d {110}  where  with  reproduces f a i r l y  examined  steel  2.19,  compared texture  a l .  in are  and  development process development  p r e c i p i t a t i o n .  F i g .  2.18  X-ray versus  line  broadening  temperature  in  and  fraction  manganese  r e c r y s t a l l i z e d  steels.(Ref.29)  44  os 500 550 600 650 TOO ^ Temperature ( t )  O , A : Steel 1 • , A : Steel 4 A , A- Specimens with A1N precipitation treatment in hot bands  os 500 550 600 650 700 Temperature ( t )  O , A : Steel 1 A- Steel 4 A i A- Speciemens with A1N precipitation treatment in hot bands  Fig.  2.19  Integrated versus  x-ray  peak  temperature  heating.(Ref.29)  in  i n t e n s i t i e s steels  and  during  hardness  continuous  45  2.4.3  MISCELLANEOUS  TECHNIQUES 30  Abe  and  e l e c t r i c a l to  the  monitored  conductivity  various  r e s i s t i v i t y during  Suzuki  and  microstructural  phenomena  that  in  are  a  cold  shown  hardness are  noticed  annealing.  recovery  stage,  dislocations  a  also  the  in  annealing  DiCello show  a  changes  width  the  is  a  the not  and  correlated occur.  For  it  The  steel  comparison  fraction d i s t i n c t  f i r s t  to  stages  stage, is  any  third  other  noted  were  the  observed  as  v i s i b l e  stages  factors  in  that  magnetic  low  exhibit  an  unrelated  to  steel  hardness  Obviously  width  process.  temperature c l e a r l y  In at  sheet  during  and  which  {211}  x-ray  both  substantial of  to  1/2  causes  however  case  compared property  display  the  metals  the  annealing  properties,  peak  worked  permeability  carbon  a l l  cold  i l l u s t r a t e s  magnetic,  x-ray  recovery  prior  to  2.21  values.  and  permeability, i n i t i a t e s  by  the  s t e e l ' s  phenomena. 27  Figure  changes  permeability  due  2.20.  the  a  carbon  r e s i s t i v i t y  second  their  comparing  substantial  during  in  exhibited  line  in  low  Three  During  C u l l i t y  metals.  annealing, peak  and  decrease  annealed  The  and  plotted.  r e s i s t i v i t y  various  Figure  annihilated  r e c r y s t a l l i z a t i o n . increase  in  decrease  were  r o l l e d ,  changes  r e c r y s t a l l i z e d during  of  annealing  changes  the  changes  during  annealing  purposes,  the  magnetic change  magnetic  r e c r y s t a l l i z a t i o n  evident.  2 6 Hawbolt permeability  also for  examined  measuring  the  use  primary  of  magnetic  r e c r y s t a l l i z a t i o n  of  an  46  6000  1  2.20  2 4 6 10 20 40 Isothermal annealing time (sec)  E l e c t r i c a l  r e s i s t i v i t y ,  r e c r y s t a l l i z e d s t e e l .  versus  (Annealing  hardness  annealing  temperature,  and time  fraction in  low  carbon  6 9 5 ° C . ) ( R e f . 3 0 )  47  F i g .  2.21  Property various  changes  in  steel  sheet  temperatures.(Ref.27)  annealed  at  48  80  percent  similar  cold  to  worked  DiCello  r e p r o d u c i b i l i t y that  specimen  device, gave  as  rise Other  and  position as  using  C u l l i t y .  resulted  well to  steel  the  respect  temperature  large  experimental  However,  during  with  an  set-up  poor  tests,  and  to  Hall  the  gradients  in  it  was  noted  effect  the  specimen  e r r o r s .  methods  that  have  been  used  to  study  the  cold  3 worked These  and  include  impact  to  In  the  energy  2.5  INDUSTRIAL  reduced to  be  must  be  of  the  in  in  industry  properties  and  subequent  in  of is  cold  increased  strength,  e l a s t i c  work,  rolled  and  this  (CA).  steel  have  been  and  compare  operations, heat  sheet,  resulting  hardness.  appropriate  currently  annealing  .  r e c r y s t a l l i z a t i o n .  exhausted,  forming  through  and  Byrne  y i e l d the  cold  by  PROCESSES  accomplishing  continuous  energy recovery  r e c r y s t a l l i z a t i o n  for  changes  as  of  during  are  such  total  material  processes  and  summarized  measurements  manufacture  restored  Two  and  the  been  calorimetric  ANNEALING  formability,  used  result  the  released  During  have  density,  addition,  determine  p l a s t i c i t y  states  mechanical  resistance,  modulus. used  annealed  If the  the  in  the  sheet  d u c t i l i t y  treatments  which  softening  of  the  s t e e l .  employed  by  the  steel  task,  batch  annealing  (BA)  is  49  2.5.1  BATCH Batch  gas  fired  inert  ANNEALING annealing  furnace  gas.  A  involves  containing  schematic  heating a  tight-wound  r e c i r c u l a t i n g  diagram  of  such  a  c o i l s  in  atmosphere  of  furnace  is  given  a  in  31 Figure which  The  enable  edges. then  2.22.  The  whole by  material  which  protects  the  by for  over  burners.  a  confines  the  from  on  cover inert  the  furnace  annealing  recirculation  of  the  inert  heating  and  representation  batch  of  annealing  usually  generally The  in  temperatures,  the  rates  a  r e l a t i v e l y cycle  of  2 0 - l 0 0 ° C / h .  coarse  formability  During  carbon  precipitate  thereby  to  the  by  w i l l  during  slow  eliminating  accomplished means  thermal  mass,  slow.  A  typical  during  Heating  The  entire  during At  form,  the  rates  process  time  quench  which  c y c l e , ambient and  soak  cycle  higher  subsequent  cooling the  then  complete.  700-730°C.  carbides  is  the  2.23(A).  obtained  approximately  is  experienced 3 2  order  temperature  furnace  provides  large  the  operations.  occuring.  in  Figure  to  reached,  f i r i n g  in  detrimental  w i l l  result  days  A  and  atmosphere.  annealing  several  and  resistant  gases.  base  c o i l  base,  atmosphere,  shown  maximum to  cooling  plates  the  annealing  is  takes  limited  c o i l s  over  heat  and  the  tight-wound  an  gas  cover,  convector  gas  of  the  protective  on  inert  placed  protective  c o i l s  A  is  the  in  making  is  stack  of  stacked  fan  The  are  are  c i r c u l a t i o n  covered  placed  c o i l s  are  manufacturing  nearly  a l l  the  temperature  strain  aging  is  from  50  ALL DIMENSIONS M mm  F i g .  2.22  Schematic  drawing  furnace.(Ref.31)  of  a  batch  annealing  51  A.  B.  BOX ANNEALING  Fe F e C EQUILIBRIUM DIAGRAM  C. 3  1600  Ai  TEMP, 800 400  I  A  i  Fig.  y.  1  1  2  1  •  Q  \  .  1  1  High Temo  p —:  7  Q +  1  \  800 600  Rapid Cooling 400  /  «  Fe  +  /T \ /  C 3  Overaging "  200  3  Comparison cycles  ,  /  1  1  1  L.  .01  .02  .03  .04  TIME, days  2.23  •  CONTINUOUS ANNEALING  with  C  of  f  •  21  wt%  batch  the  0  and  4»  6  8  TIME, min  continuous  iron-carbon  phase  annealing diagram.(Ref.32)  TEMP,  52  2.5.2  CONTINUOUS Typical  CA  ANNEALING lines  combine  including  e l e c t r o l y t i c  sometimes  temper  several  cleaning,  r o l l i n g .  t y p i c a l in  in  CA  Figure  annealing The  the  2.24. and  A  annealing  preheat,  heat,  improves  exhaust  gases  temperature  from  use  heat  maintain  and  temperature. then  The  using  section  where  bring  the  gas  Reheating  s t r i p  the  cooling  of  the  which  the  down  jets  to  are  are  Chicago)  Figure  the  heat  fired  followed  of  the  s t r i p  fans  by  preheat by  using  s t r i p soak  natural  gas  common. by  Cooling  water  by  overage  area  where  into  the  convective  the  required  overaging  then  employed  in  media  used  during  CA  processes  the  cooling  from  differ the  and  multipass  fast  overage cooling  cool  s t r i p .  main  to  annealing  passes  provide  The  the  reheat,  accomplished  the  2.25.  and  required are  shown  of  section  raise  the  a  sections,  heat  to  of  is  drawing  four  8 - 1 2 ° C / s  jets,  is  r e c i r c u l a t i n g  zone  The  rates  to  c o n s i s t s  Gas  cool  steel  and  drawing  sections.  tubes  furnace  temperature. to  Both  nozzles.  after  cool of  in  of  section  radiant  by  Steel,  shown  jet  quench  zones.  tubes,  is  heating.  the  Heating  aging  cool  heat  lines  schematic  c o n s i s t s  gas  overaging  CA  schematic  e f f i c i e n c y  multipass  radiant  to  to  accomplished  quenching  fast  and  the  prior  sections  detailed  furnace  the  A  Inland  furnaces  soak  section  is  more  aging  '  (at  of  processes  34  l i t e r a t u r e .  i n s t a l l a t i o n  annealing,  Descriptions 33  available  different  are  in  annealing  the  53  ENTRY  ANNEALING  LOOP  FURNACE  AGEING FURNACE  ENTRY ENO PROCESSING  F i g .  2.24  Major  WATER QUENCH  components  l i n e . ( R e f . 3 4 )  LOOP TOWER  TOWER  STRIP CLEANING  EXIT  of  STRIP PICKLING  a  DELIVERY ENO PROCESSING  continuous  annealing  54  -ANNEALING FURNACE-  -AGEING FURNACE-  o o  o o  •r© STRIP TRAVEL  Fig.  2.25  «3  Furnace  sections  line.(Ref.34)  of  '^PICKLING  a  continuous  annealing  55  temperature. mixture  Gas  which  passes  sheet.  Using  can  obtained.  be  rates  in  jet  this  the  cooling  employs  through  jets  which  impinge  cooling  rates  of  method, Gas/water  order  of  cooling  8 0 - 3 0 0 ° C / s  a  is  nitrogen/hydrogen  about  used  during  on  to  the  the  gas steel  5 - 3 0 ° C / s  obtain  cooling  manufacture  of  35 high  strength  rates  in  excess  The  in  to  be  eliminating necessary The on  the  the  of  aging  water  exact  depending  on  the  their  product  l i t t l e  Figure  maximum  complete  from  carbide  grain  necessary.  The  are  finer  which  in  The  shorter  and  aids  to  aging  w i l l  that  vary  application. company  at  is  depending  Therefore,  to  maximum  company  are can  considerably be  used  growth,  resultant  not  carbides  due as  deep to  well  the as  is  occur. the A  for  ,  faster  The  2 . 2 3 ( C ) .  does  of  to  above  allow  f e r r i t e ,  formability  temperatures,  to  Figure  from  times  temperature  coarsening  temperature  processing  annealing  the  temperature,  used  carbide  precipitation  overaging  rates  time  for  2.23(B),  cooling  enables  used.  from  which  and  heating  l i n e .  the  time  is  its  vary  r e c r y s t a l l i z a t i o n rate  cooling  the  cooling  prior  procedure and  w i l l  jet  affect  overaging  quenching  temperatures  temperature,  provides  w i l l  Gas  reheating  process,  C A  giving  Therefore,  the  composition  processes  short,  at  processing  annealing  media  furnace.  arrested  when  quenching  cooling  subsequent  steel  In  Water  1000°C/S.  of  selection  procedure cooling  steels.  allow  fast  for  making in  products  C A  drawn  parts.  higher the  heating  fast  56  cooling in  a  rates  matter  improved in  that  to  the  of  y i e l d a  wide  wide  a v a i l a b l e .  enables  processing  minutes over range  range  of  (usually  of 4-8  BA p r o c e s s e s . of  steel  the  min),  CA  grades  temperatures  steel  and  is can  s t r i p  to  resulting  also be  more  occur  in  v e r s a t i l e  manufactured  cooling  rates  due  3. A l l r o l l e d , 0. 213 3.1.  experimentation rimmed,  mm A  EXPERIMENTAL  low  carbon  (0.0084").  rimmed  problems  steel  related  was  to  PROCEDURES  performed  steel  sheet  The  steel  was  choosen  AlN  precipitation  on  88.8  of  gauge  chemistry to  is  avoid  percent  cold  thickness  l i s t e d  in  Table  r e c r y s t a l l i z a t i o n  t y p i c a l  of  aluminum  1 6— 1 8 k i l l e d  s t e e l s .  present, kinetic r o l l e d  this  is  below  response. sheet  The 1.  Although  the  is  A  the  level  typical  shown  in  experiments  were  determination  of  r e c r y s t a l l i z a t i o n  some  acid  soluble  required  to  microstructure  Figure  test  kinetics  cause  of  the  is  delayed cold  3.1.  divided the  aluminum  into  three  s t e e l ' s  over  an  d i s t i n c t  areas:  isothermal  appropriate  range  of  temperatures, 2.  the  determination  kinetics 3.  a  check  for  during on  the  predicting  kinetics  using  of  the  selected  s t e e l ' s  r e c r y s t a l l i z a t i o n  continuous  a p p l i c a b i l i t y  of  heating  the  the  continuous  the  experimentally  cycles,  a d d i t i v i t y  heating  and  p r i n c i p l e  r e c r y s t a l l i z a t i o n  determined  isothermal  data.  3.1  ISOTHERMAL RECRYSTALLIZATION KINETIC Molten  steel 430, by  to a  the  salt  annealing  required  commercially  Houghton,  was  was  isothermal  available  used  used  for  to  57  subject  temperatures.  tempering  this  MEASUREMENTS  purpose.  s a l t ,  the Draw  test Temp  manufactured  Table  3.1  Steel  Element  * acid  Composition.  Weight P e r c e n t  C  0.071  Mn  0.350  P  0.005  S  0.018  Si  0.002  Cu  0.011  Ni  0.010  Cr  0.032  Mo  0.002  V  0.002  Cb  0.002  Al  0.011  s o l u b l e aluminum  (0.002)*  F i g .  3.1  Typical  microstructure  percent  cold  reduced,  of  the  rimmed  as  received,  steel.(X353  88.8 mag.)  60  Specimens the  steel  then  s t r i p  cleaned  o i l  and  approximately  in  other  Upon  using  sheet  denatured  foreign  90  specimens  were  immersed  for  more  than  four  specimens  The  salt  bath  setpoint  Upon  removal  quenching The mount  and  1n  The  and  two  using  Tukon  further  sided  determination was  s t a t i s t i c a l l y  immersed was  of  600  grit  the to  was  to  volume  tester,  and  indentations  was  bath  from  a  by  water  cooling.  f l a t  p l a s t i c  preparation  of  paper, the  5M  and  polished  etchant.  r e c r y s t a l l i z e d  in  examination, (DPH)  using  a  load.  necessary  result  at  on  testing  I00g  salt  performed  microscopic  a  No  n i t a l  fraction  microhardness  interval.  deviate  grinding  percent  eliminate  investigated.  microstructures 2  were  surfaces.  temperatures  using  s i g n i f i c a n t  in  fixed  of  specimens  time  found  cooling  out  temperature,  required  a c c o m p l i s h e d by  pyramid  number  and  of  their  bath  cut  to  Metallographic  The  revealed  from  were  tape.  400  A l l  r e c r y s t a l l i z a t i o n  specimens  microhardness The  a l l  were  ethanol  salt  the  were  for  powder.  diamond  the  specimen,  320,  were  specimen by  the  annealed  percent  temperature  ±3°C  avoid  alumina  specimens  each  of  to  using  followed  by  square shears.  substances of  i t ' s  mm  metal  s t a b i l i z a t i o n  once.  20  to  give  determined  a  using  3 8 s t a t i s t i c a l  hypothesis  annealed  600°C  subjected  at to  microhardness 6,  8  and  12.  24  for  5  and  indentations  values For  testing.  each  were  9  seconds each.  divided  group,  Two  the  For into  mean  specimens  were  respectively, each  specimen,  random and  and  groups  standard  the of  4,  deviation  61  was  calculated,  indentations. group, level equal,  This  which at  and  can  which  can  be  compared  with  comparison  be  the  defined  yielded  as  the  hypothesis  rejected.  that  for a  a l l  "P  value"  smallest  that  the  Therefore,  as  for  each  s i g n i f i c a n c e  two P  24  group  gets  means  higher,  are  the  38 less  evidence Values  to  be  of  8  P  and  12  in  of  to  reject than  can in  be  P  the  best  P  however,  indentations  indentations  was  seen  would  s i g n i f i c a n t  are in  t y p i c a l l y  Table  less  results.  Twelve  with  was  the  considered as  considered only  0.20. to  4  Therefore,  y i e l d  indentations smallest  involved  choosen  3.2,  than  appear  time  f i n a l l y  hypothesis.  a l l  values, the  the  0.2  values  indentations  v a r i a b i l i t y , number  As  result  s t a t i s t i c a l l y resulted  is  greater  acceptable.  indentations 6,  there  in  to  making  be  being  this  excessive.  an  Eight  acceptable  compromi s e . The from  isothermal  hardness  evaluation  r e c r y s t a l l i z e d and to  f i n i s h be  used. was  of  relationship  was  the  shape  isothermal  of  the  hardness  (2.22).  exists  between 14-1624  fraction  '  process  the  equation  X  was  data  obtained  fraction  of  using  v a r i a t i o n ,  to  hardnesses  r e c r y s t a l l i z a t i o n  regardless  kinetic  converted  determining  sigmoidal  analyzed  hardness  by the  constant The  r e c r y s t a l l i z a t i o n  at and  the  start  assuming  it  temperature  versus  Assuming  a  time linear  r e c r y s t a l l i z e d ,  determined  curve  using  X,  and  the  relationship: X=(DPH -DPH )/(DPH -DPH 0  t  n  1  0  0  )  . . . ( 3 . 1 )  62  Table  3.2  Hypothesis of  an  // I n d e n t a t  Testing  Acceptable  Results  Number  ions/Group  for  of  the  Determination  Microhardness  P  Value  Mean  Range  4  0.54  0 04-0.98  6  0.42  0 26-0.84  8  0.61  0 30-0.97  12  0.73  0 62-0.84  Indentations.  63 where  DPHQ  start  and completion  event,  and DPH  a n d DPH^  i s  are the hardnesses  1 Q 0  of  the  the  isothermal  hardness  at  of  the  steel  at  the  r e c r y s t a l l i z a t i o n  time  t,  during  r e c r y s t a l l i z a t i o n . The  r e c r y s t a l l i z a t i o n  isothermal  temperature,  estimating  the  i n i t i a t e s  times,  through  examination  of  hardness  the  equation line ln  t  _  e  s  t ^ '  estimated  procedure  s  av  fc  ln  a  plot  of  was  then  best  repeated  f i t until  was d e t e r m i n e d ;  this  The  the  and  the  ln(1/1-X)  versus  a  best  time  determined  once  maximum time  f i t  recorded.  small  start  shape  using  a n a l y s i s ,  by  line  v i s u a l l y  sigmoidal  c o e f f i c i e n t  varied  by  examination,  was a n a l y z e d  ln  each  r e c r y s t a l l i z a t i o n  data.  squares  correlation  and the was  curve  for  determined  which  hardness  ,  The  again.  correlation was  taken  * The  then  i t ' s  t  metallographic  least  for  time  A t ,  c o e f f i c i e n t a  ^  n  start  increment, The  a  at  time  Using  time,  i n i t i a l l y ,  t  the  versus  (2.22).  t  t  of  was d e t e r m i n e d  ^  was  use of  visual  start  Avrami  determined  In(1/1-X)  parameters by  plot  taking at  b  and  the  (t-t  k,  equation  intercept  )=1s,  of  and the  (2.22),  the  line  were  l n ( t ~ t  a  v  )  vs  slope  3 V  respectively. The for  a  experimental  range  of  mathematical dependence  of  isothermal  temperatures  expressions the  kinetic  were  r e c r y s t a l l i z a t i o n then  describing parameters  described  the b  by  temperature and  k.  kinetics  64  3.2  CONTINUOUS  HEATING  RECRYSTALLIZATION  KINETIC  MEASUREMENTS Two  methods  were  r e c r y s t a l l i z a t i o n continuous  heating  determined  by  For  monitored  heated  by  bottom  the  rate.  means  of  specimen  camera  the  conditions.  a  was in  and  and a  inert,  are  shape was  of  set  seconds.  the at  {211}  time  the  valley  between  12  seconds,  which  of  70°C/hr,  making  The fraction  method  of  in  was  The  in  the  annealing  with  FeKa  with  Ka,  a  to and  Ka  scan  was  on  in  the  the  results hot  by  are x-ray  recording The  interval  e s s e n t i a l l y  based  to  3.3.  the  0.23°C  to  monitored  p o s i t i o n  peaks  2  resistance  welded  heated  from  to  used  and  radiation.  scan  x-ray  examination  insitu  count  was  required  spot  The  Figure  hot  were  the  x-ray  monitored  using  analysis  r e c r y s t a l l i z e d  at  resistance  equivalent  each  3.2,  controlled  variation  required  is  batch  thermocouple  beneath  was  peak  the  Figure  experimentally.  1 / 2 ° ( 2 0 ) / m i n ,  The  simulate  atmosphere  shown  R e c r y s t a l l i z a t i o n  was  temperature  temperature  3.  employed  controlled  chromel-alumel  sample  method  during  r e c r y s t a l l i z a t i o n  temperature  Appendix  steel  6 5 . 5 ° C / h ) ,  helium  determined  test  The  to  shown  d i r e c t l y  the  rate.  meant  using  The  The  contained  of  specimens  surface,  p o s i t i o n .  kinetics  (70.7°C/h  S t r i p  heating  determine  rates  insitu  in  to  heating  heating  conditions  camera.  the  used  Ka,  was at  scan  rate  1  2  or  peak  through  approximately a  heating  rate  isothermal.  determine the  of  the  the  volume  resolution  of  the  65  F i g .  3.2  Continuous  heating  thermocouple  s t r i p  attached  at  specimen centre  of  with bottom  surface.  66  F i g .  3.3  (a)  Experimental  t r i a l s , hot  (b)  x-ray  apparatus  closeup camera.  of  for  mounted  continuous specimen  in  heating open  67  p c p f. valley The  in  Ka  the  parameter  . most  doublet  which  e f f e c t i v e l y  is R  where  I ^  is  intensity and  1^  of  the  For  the the  to  too  slow  would  successive  the  BA  and  off  atmosphere; cooled  of  for  K a " b  I  I  1  r e c r y s t a l l i z a t i o n  ...(3.2)  )  Ka,  {211}, doublet  than  available use  the  were  of  those  peak, the  I  ^  m  {211}  the  n  peak,  encountered  x-ray  scan  the  i n s i t u  of  This  high  is  method  heated  up  rates  at  rates. was  the  were  by  686°C/min, which  accomplished  cooling  the  specimen enhanced  resistance  approximately  heating  63°C/s  by of  is  by  rate  the  to  to  which between  shutting  the  the  were  where  cooling  was  was  Therefore,  required  in  found  of  devised  43.8°C/min  in  non-isothermal  Cooling  rate  were  method  followed  used  and  rates  because  heating  temperatures,  cooling  used  '  furnace  *  water specimen.  realized  using  procedure.  series  *  (  Ka  greater  Heating  air  3.4.  equation:  the  the  conditions,  and  rates  After  Ka  CA  the  grips  Cooling this  higher  power  /  Figure  i n t e n s i t y . *  from  CA c o n d i t i o n s .  the  in  )  of  monitoring.  specimens  of  the  1  in  monitor  heating-quenching  temperature.  t y p i c a l  I  shown  to  K a r « i n  enable  result  progressively  is  I  rates  to  interrupted  room  (  by  intensity  r e c r y s t a l l i z a t i o n  an  =  valley  heating  annealing,  scans  I  as  found  given  background  batch be  was  peak,  of  valley  C u l l i t y fraction  the four  specimens x-ray  resolution  were  scans as  cooled  were  2  room  performed  described  suggested use of the r e c r y s t a l l i z e d . ^  to  by  ratio  temperature,  and  equation I  m  ;  n  / l  analyzed (3.2) f °  K K  a  '  r  a  for  above.  A  describing  68  R  F i g .  3.4  Method  I  of  equation  =  ( I  Ka - ^n>/( Kar b I  I  I  {211}  Ka  )  1  analysis (3.2).  of  x-ray  peak  using  69  small  section  specimen, examined  to  to  were the  made  of  start  obtained The  by  shape  x-ray  effect  for  was  14,000  Eight  each  on  and  of  and  of  a  were  the  prior  kinetics  subjected  Ka  to  the  method of  r e c r y s t a l l i z a t i o n at  a  r e c r y s t a l l i z e d  the  used  BA  The  a  recovery  were  was  to  treatment  curves  Here,  cool  to  to  then  being  of  a 440°C  room  treatment,  was  on  treatment  performed  heating  o s c i l l a t i n g  monitor heated  monitored  the  at  a  using  rate the  on  response,  was  examined  2 . 5 8 ° C / s ,  isothermally.  r e c r y s t a l l i z a t i o n  kinetic  above.  recovery  of  v i s u a l l y  heating  heat  specimen  continuous  rate  by  heat  allowed  described  kinetics  r e c r y s t a l l i z a t i o n  investigated.  r e c r y s t a l l i z a t i o n  p r e - r e c y s t a l l i z a t i o n  specimen,  peak  recovery.  effect  also  t e s t i n g .  also  {211}  The  to  was  scans  x-ray  was  heat  recovery  i n s i t u  immediately  recovery  the  6 5 . 5 ° C / h ,  of  microhardness  During  of  method  subjected  continuous  temperature.  of  specimen  determined  then  progress  each  microhardness  temperatures  and  the  of  p o s i t i o n .  seconds,  of  portion  m i c r o s c o p i c a l l y  polished  specimens  heating  r e c r y s t a l l i z a t i o n specimen  and  heating-quenching  times  the  in  centre  7 0 . 7 ° C / h .  continuous  examining  the  etched  thermocouple  hardness  rate  The during  polished,  interrupted  determine  heating  from  r e c r y s t a l l i z a t i o n .  indentations  The  removed  mounted, for  adjacent  was  The  monitored  to  and by  480°C,  progress i n s i t u  by  the  subsequent  heating where  it  a  s t r i p was  of using  o s c i l l a t i n g  70  x-ray  scans  kinetic best  3.3  the  {211}  Fe  parameters  were  then  fit  of  Avrami  line  CONTINUOUS HEATING The  heating  experimentally  a d d i t i v i t y .  A  The  were  the  kinetics  on  Figure  described  by  isothermal  The  steps,  r e c r y s t a l l i z e d  r e c r y s t a l l i z a t i o n  and  is  was  can  be  made  3.5(a).  At  i.e.  the  and  already  during  the  isothermal  p r i n c i p l e to  Appendix the  r e c r y s t a l l i z a t i o n  cycle of  each  on  a  with  the  aid  employed  can  be  series  step t  of  after ,  the  the  fraction  isothermal of  fraction  present,  the  1.  explained  up  of  perform  temperature  the  PREDICTIONS  the  ,  after  based  at  step,  be  heating  calculated  material  in  predicting  to  kinetics  t  the  the  a n a l y s i s .  written  l i s t e d  started,  isothermal  r e c r y s t a l l i z e d  data,  heating  Figure  was  Avrami  determining  u t i l i z i n g  times,  for  it  has  The  obtained  start  continuous  assuming  r e c r y s t a l l i z a t i o n  particular  used  continuous  3.5.  by  squares  kinetics  program  program  procedure  calculated  predicted  kinetic  computer  c a l c u l a t i o n s ;  peak.  RECRYSTALLIZATION KINETIC  determined  r e c r y s t a l l i z a t i o n  doublet  least  r e c r y s t a l l i z a t i o n  continuous  of  using  Ka  the  of  i e . ,  assuming  that  21 r e c r y s t a l l i z a t i o n  is  an  additive  i l l u s t r a t e d  schematically  temperature  at  during  the  time  transforming, kinetic  which  equation  at  Figure  transformation  interval  AXT,,  in  structure  is T , .  At/2,  the  determined At  T  2  the  change.  3.5(b). starts  is  volume using  the T , ,  then  fraction  the  v i r t u a l  If  This  isothermal  time  required  to  is  F i g .  3.5  Procedure  for  predicting  r e c r y s t a l l i z a t i o n kinetic  data.  continuous  kinetics  using  heating  isothermal  72  produce and  a  AXT,  new  isothermal a l l  the  fraction  at  T  2  is  c a l c u l a t e d .  fraction  is  calculated  kinetic  cold  worked  equation. matrix  r e c r y s t a l l i z e d  This  To for  this T  2  based  process  has  been  equals  one.  time,  is  consumed,  At  on  is the  continued and  added,  the  u n t i l volume  4.  4. 1  EXPERIMENTAL RESULTS  ISOTHERMAL  440-560°C, the  curve  bars  r e c r y s t a l l i z a t i o n  versus  are is  the  during  the  percent  16  was  After to  to  the  the  Three  of  r e l a t i v e l y this  f l a t  region  product,  of  were  to  the  be  based  prior  on  to  of  return  of  short  deviations hardness sheet  of  based The  indentations.  hardness a  decreased  f i r s t  i n i t i a t i o n , was  and  assumed  to  be  temperature. isothermal in  mentioned,  over  error  250.0±16.9.  occurred  already  on  r e c r y s t a l l i z a t i o n  As  the  the  Recovery  point  The  25  the  of  two  steel  of  annealing  increased  the  DPH  onset  complete,  typical  As  Each  specimens.  to  of  range  standard  r e c r y s t a l l i z a t i o n  portion.  the  4.8.  indentations.  curves.  generally  due  14  to  as-received  isothermal  regions  r e c r y s t a l l i z a t i o n  the  to  hardness  the  4.1  determined  on  temperature  minimum  2 5 2 . 2 ± 4 . 2 ,  completion  independent  of  was  results  indentations,  and  prior  be  8  r o l l e d ,  was  based  approximation, after  cold  r e c r y s t a l l i z a t i o n  127.3±2.3,  of  RESULTS  kinetic  the  Figures  evaluation  immediately  determined  for  maximum  indentations  hardness  in  average  the  observed  on  time,  shown  represent  88.8  DISCUSSION  RECRYSTALLIZATION KINETIC  Isothermal microhardness  AND  that range  of  the  i n i t i a l ,  hardnesses  the  order  as  in  received  associated  3 with  the  formation  instances,  for  hardnesses  as  softening  to  subgrain  instance high  a  of  as  at  DPH  hardness  boundaries.  500°C, 268  were  typical 73  of  shown  in  In  some  Figure  encountered, the  recovered  4.5,  followed  by  structure.  280  260  —  • °  o  1  —  1  I  1  —  o o  240  o»  O 2  •  220  X CL °.200 in in  XN  0  •  x  a> c  ? X  X  X  \  N  \  s \  '80  \ \  X  160  X  X  X  X X.  X,  sX X  X  140  120 Ix IO  •  IxlO^  3  ,  IxlO"  1  1x10°  « — —  IxlO'  1  — -  1x10  s  Time (s)  Fig.  4.1  Isothermal  recrystallization  kinetics,  T=440°C.  IX 109  280  Time (s)  F  l  9 .  4.2  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=460°C.  270  0  o  ~t>^  \ o  o \ s  'o Ixio'  1x10°  IxKT  ixio-  1x10°  Time (s)  4.3  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=480  Ix 10  IxlO'  IxlO  3  IxlO  I x 10-  Time (s)  Fig.  4.4  . Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T-490  Hardness, DPH (lOOg) in  cn O  nD' ft) >-i  3 0)  a> n ^< cn rr OJ  N  O 3  ro  n cn -3 II  c n  o o  o  n  8£  IxlO  1  IxlO  Time  Fig.  4.6  Isothermal  IxlO"  |x 10"  I  x 10 -  (s)  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=520°  270 i  •o-o-cu. o  250  C\0  230 CP O O — 210  ^o  I  a a  \ \  cP  190  in </> OJ  c  170  o  T.  150  I 30  -o—  110  ixio  1  IxlO  1  IxlO^  1x10-  I x 10^  Time (s)  CO o  Fig.  4.7  Isothermal  r e c r y s t a l l i z a t i o n  k i n e t i c s ,  T=540°C.  260  I  ..a  240  O O  220  a. 2 0 0  Q  £ 0)  180  c  •a O  |60  140  120 LJIIO'-  1x10'  Ix 10'  Time (s)  co  Fig.  4.8  Isothermal  r e c r y s t a l l i z a t i o n  kinetics,  T=560°C.  82  This  large  hardness  been  observed  by  increase  other  prior  to  researchers,  r e c r y s t a l l i z a t i o n  and  attributed  to  has the  39 occurance in  the  of  cold  resulting and no  strain rolled  in  higher longer  the  be  in  the  the  recovered  while  return  the  hardness  of  the  more  DPH  cold  matrix  r o l l e d  third  s t a b i l i z a t i o n curve.  during  of  by  the  region, of  Very  the  isothermal  In  grain  to  it  more  slight  to  w i l l  aging, typical  of  hardness  recovery  increase  processes,  of  strain  aging.  isothermal  a  sigmoidal  this  due  high  region,  to  angle  the  hardness  drop  the  consumption  boundaries  of  of  the  the  grains. representing  hardness  l i t t l e  the  the  displayed  strength,  strain  those  a t t r i b u t e d  reduced  r e c r y s t a l l i z e d  The  the  is  to  hardness  typical  higher  causing  return  r e c r y s t a l l i z a t i o n . density  of  present  pinning,  p r e c i p i t a t e s ,  attributed  be  curves  point,  carbon  Therefore, be  carbon  d i s l o c a t i o n  y i e l d  capable  can  stage  d i s l o c a t i o n  growing  the  w i l l  can  18  d i s s o c i a t e d  cause  the  substantial  second  of  Once  values  r e c r y s t a l l i z a t i o n typical  of  form  2-5  Any  may  structure.  DPH  approximately The  steel  hardness.  and  increase  aging.  grain  resulting  hardness growth  in  variation at  the  growth a  displayed  l e v e l i n g  was  found  off  to  of  exist  temperatures  investigated. Using  the  procedures  r e c r y s t a l l i z a t i o n the  isothermal  constants  k  and  kinetics  start b,  described  times,  and  the  have t  „ a v  e a r l i e r ,  been ,  the  described  the  correlation  in  associated  terms Avrami  c o e f f i c i e n t s ;  the  of  83  results  are  shown  correlation  t  e  n  Table  c o e f f i c i e n t s  experimentally times,  in  £  were  determined  are  also  4.1.  For  a l l  found  to  l i s t e d  and  compared  times,  tgg  ,  equations.  cases,  the  predicted  are  greater  quite  a l l  than  those  d i f f i c u l t ,  if  r e e r y s t a l l i z a t i o n The for  the  shown fit  TTR  t  on  f a i r l y  to  good.  the  the  best  times  99  r e c r y s t a l l i z a t i o n  4.9.  values,  percent  fit  Avrami  for  completion  It  was  found  detect  the  end  (time-temperature-recrystallization)  Figure  The  completion  with  observed.  impossible  the  to  be  of  metallographically.  isothermal  in  based  actually  not  be  r e c r y s t a l l i z a t i o n  r e c r y s t a l l i z a t i o n In  curves,  The  while  "start  the  "end  of  time"  the  is  time"  is  diagram  test  based based  steel  is  the  best  on on  the  3 V  v i s u a l l y dashed  estimated  lines  temperature  r e c r y s t a l l i z a t i o n  represent for  the  the  formation  r e c r y s t a l l i z e d  structure.  fit  k  t,  .  b  and  time  values.  necessary  of  These The  completion  the  at  were  discrepancy  The  each  s p e c i f i e d  times  times.  percent  based  that  on  of  the  exists  best  between  3 V  the by  observed the  and  predicted  completion  d i f f i c u l t y  in  pinpointing  r e c r y s t a l l i z a t i o n  is  complete  the  using  times exact  could time  be  at  caused  which  metallographic  procedures. The the  specimens  required this  TTR  diagram exposed  temperature  assumption  introduced  by  is  this  was to  constructed the  molten  immediately f a l s e .  To  on salt  upon  determine  assumption,  a  the  assumption  reached  immersion. the  amount  chromel-alumel  that  the Obviously, of  error  thermocouple  Table  Temp.  ( C)  4.1  Isothermal  Recrystallization  Avrami Parameters k b  Corr.  av  Kinetic  Coeff.  Results.  'end^  t  9 9  440  .463  6.88xl0~  4  1.9xl0  460  .432  2.12xl0~  3  2600  0.985  480  .690  4.47xl0~  4  700  0.982  .3xl0  490  .540  4.70xl0~  3  280  0.943  8x10  500  .690  1.78xl0~  3  270  0.975  4x10  520  .736  3.78xl0"  3  69  0.977  9xl0  540  .830  5.31xl0"  3  16  0.980  1200  3480  560  1.030  11  0.944  360  527  7.4xl0"  3  4  0.957  5  4 4 3  (s)  1.83xl0  8  5.30xl0  7  6.55xl0  5  3.46xl0  5  8.86xl0  4  1.56xl0  4  ,4  Time Fig.  4.9  io5  (s)  TTR diagram with superimposed a n n e a l i n g  showing s t a r t  i „  and end times f o r r e c r y s t a l l i z a t i o n .  cycles,  86  was  spot  welded  was  immersed  to  in  a  the  standard molten  temperatures.  The  recorded,  the  results  necessary  to  ranged the  from  required The  is  a  to  one  only  period  example,  a  4s  percent,  6  percent  to and  values the  at  of at  determined  the  above  temperatures  to  the  2.0s  to  in  percent  The  and  percent  where  in  is  short.  the  kinetics  the  values  predicted  experimental  range  Thus  due  attaining  at  were of  For  0.6  with  times  response  the  respectively.  associated  of  s.  approximately  560°C  Instead,  95  2.2  time  temperature  temperature  errors  which  k  high not and  were  b  at  determined  extrapolation. It  should  also  be  noted  that  the  Avrami  obtained  for  the  r e c r y s t a l l i z a t i o n  at  based  on  p a r t i a l  r e c r y s t a l l i z a t i o n  data,  times  in  excess  complete  The k  are  of  one  million  r e c r y s t a l l i z a t i o n  unreasonably  and  4.2.  r e c r y s t a l l i z a t i o n  r e c r y s t a l l i z a t i o n  the  was  reach  r e c r y s t a l l i z a t i o n  560°C.  time  required  temperatures,  d i f f i c u l t i e s  outside  Table  specimens  results  36  specimen, isothermal  with  instantaneous  520°C  accurate  in  to  only  higher  and  experimental  measuring  an  delay  480°C,  response  The  bath  different  l i s t e d  in  prior  time  temperatures,  by  5.6s.  salt  at  specimen  temperature  incubation  t  being  the  assumption  poor  salt  temperature  raise 3.8s  size  long  in  seconds occur,  experimental  temperature shown  to  dependence  Figures  460°C  4.10  constants and  since  were  440°C  annealing  necessary  resulting  were  for  in  times. of and  the  Avrami  4.11.  The  parameters  b  constant  was  k  87  Table  4.2  Temperature Steel  Saltbath  Temp.  Response  Specimen  Specimen  into  Temp.  During the  % of  Immersion  Molten  Max.  Temp. Time  to  ( c)  432  412  95.0  2.2  432  100.0  5.6  462  95.2  2.0  484  100.0  3.8  490  94.5  2.0  517  100.0  4.2  527  95.0  2.2  553  100.0  5.4  517  553  the  S a l t .  ( C)  484  of  (s)  Temp.  88  IxlO  IxlO "2  I  IxlO"  r  3  IxlO -4  IxlO -5 420  440  460  480  500  520  540  560  Temperature (°C)  F i g .  4.10  Temperature  dependence  of  Avrami  parameter  b.  580  0.2 0.1 I0.0 420 440 460 4 8 0 500 520 540 560 580 Temperature (°C)  4.11  Temperature  dependence  of  Avrami  parameter  90 found  to  f i t  the  linear  relationship:  k = -1 . 6 3 + 4 . 6 3 X 1 0 ~ while  b  was  found  to  vary  with  T  3  temperature  lnb=-15.56+1.90x10~ where  T  is  The  the  temperature  variation  examined  by  depending  Rosen  on  the  of  k  et.  in  with  a l .  9  progress  ....(4.1) to:  T  2  ...(4.2)  °C. temperature  They of  according  said  was  that  recovery  k  previously w i l l  vary  processes p r i o r  to  the  20 onset  of  r e c r y s t a l l i z a t i o n .  nucleation (2.18),  rate  varies  According  with  time  to  Avrami  according  to  the  equation  or: H-^pexpi-t/r)  When so  recovery  that  early  potential PT a l l in  i s  times  is  extensively  saturation occupied  and equation  after  case  expression by  site  site  large  the  occurs  of  the  equation  by  a  to the  nuclei  (2.18)  site  prior  occurs,  formation  early  relating  ...(2.18)  i s  becomes  p r o b a b i l i t y large,  equal  a l l  the  saturation  the  fraction  of  r e c r y s t a l l i z a t i o n ,  to  n u c l e i .  zero  Therefore,  to  time  the  given  no  recovery that  VT  is  w i l l  a  occurs  site  small,  is  prior  occupied  and the  ...(2.19)  3  to  r e c r y s t a l l i z a t i o n ,  by  equation  a  nuclei  i s  the  small,  d e s c r i b i n g  become: N=N"y  and  is  (2.19):  p r o b a b i l i t y  nucleation  for  mathematical  r e c r y s t a l l i z e d  3  therefore  a  therefore  X=1-exp(-fG N"t ) When  that  corresponding  r e c r y s t a l l i z a t i o n  ...(2.21) equation  w i l l  be  91  X=1-exp(-fG R^tV4)  ...(2.20)  3  Therefore, degree  0.43 at  of  recovery  In  this  at  460°C  higher  able  to  factors nuclei  value that  study, and  the  1.03  isothermal  occur  The  the  prior  value such  ( i e .  of  as  k  can vary  occurs value at  prior of  560°C.  annealing to  the  the  of  the  o n e , two  exponent  or  k  shape  three  to  was  found  Therefore,  of  on  the  r e c r y s t a l l i z a t i o n . to it  temperatures  onset  growth  k  depending  vary  between  appears  less  that  recovery  is  r e c r y s t a l l i z a t i o n .  w i l l of  also  the  be  affected  by  r e c r y s t a l l i z e d  dimensional  growth),  a n d how  21 the  growth  rate  the  Avrami  and Johnson-Mehl  considered  4.2  to  be  CONTINUOUS The  HEATING  heating  recovery  with  time.  In  equations,  the the  development growth  rate  of i s  constant.  experimental  continuous prior  changes  RECRYSTALLIZATION KINETIC x-ray  and hardness  annealing  heat  results  experiments  treatments,  are  RESULTS of  performed  shown  in  the without  Figures  4.12  to  4.14. The  results  of  annealing  rate  x-ray  run  was p e r f o r m e d  {211}  Ka peak.  which  the  course  of  obtained  of  the  70.7  on  ° C / h are insitu  The dashed  individual the  run conducted  scans  annealing  specimens  heating-cooling  lines were  c y c l e .  subjected  procedure  at  the  in  Figure  4.12.  This  o s c i l l a t i n g  scans  of  shown with  simulated  indicate  the  found  vary  to  The hardness to  described  the  range  over  during  results  interrupted  previously.  batch  the were  the  92  O  Hordn«»$  X-Ray  o  o  o  o  i.o 0.9 0.8 i  i  o;  0.7  ;6  i0.6  g l  \0&  *  0.4 0.3  '.2  .1  IxlO  2xl0  4  3xl0  4  Time  F i g .  4.12  Experimental r e s u l t s ,  4*io  4  5x10  4  (s)  continuous  heating  4  heating  r a t e = 7 0 . 7 ° C / h .  hardness  and  x-ray  93  The stages  x-ray  of  x-ray  annealing.  ratio  indicating due  to  begins then  to  some  At  of  peak  rate.  once  more  of  ratio  This  negligble The  indicate  equivalent at  no  28000s,  relief  occurs  probably  responsible  hardness  was  approximately  this be  approximately  until  then  found  the  occuring  to  ratio slowly,  and  indicate  scale,  the  rapid  occurs. the  grain Very  x-ray  with  time.  growth  l i t t l e  period,  ratio This  after  the  change  in  the  indicating  occuring. results  show  16000s.  Since  this  in  the  DPH  254  the  the  shape  of  r e c r y s t a l l i z a t i o n  would  appear  off time  a  marked x-ray  rate  18000s,  hardness  level  during  appears  time  increase  to  f i r s t  linear  approximately for  be  time,  large  with  hardness  substantial  to  x-ray  (557°C),  becomes  to  18000s,  fashion,  the  energy  r e c r y s t a l l i z a t i o n .  strain  hardness  with  where  strain  during  linear  (345°C),  .region  corresponds  occurs  three  f i r s t  resolution  rapidly  and  the  the  recovery.  18000s,  residual  apparently  relief  r e l a t i v e l y  during  approximately  completion  in  a  r e c r y s t a l l i z a t i o n ,  off  x-ray  in  more  between  approximately  doublet  relief  greater  d i s s i p a t i o n  stage  Ka  increase  a  of  levels  For  approximately  at  onset  differentiate  increases  stress  At  results  at  analysis which  strain  a  value  interval  strain  aging  increase.  at  increase  is  The of  of  18000s  to  22000s. Based  region  of  on  18000s  (345°C)  to  the  hardness  curve,  to  somewhere  22000s  start  (440°C).  These  in  the  times  are  94  approximately predicted  the  by  x-rays.  rapid  decrease  value  of  further  same,  DPH  is  Once  noted  117.5  hardness  or  at  s l i g h t l y  longer  than  r e c r y s t a l l i z a t i o n  until  it  28000s.  reduction  begins  DPH  76.8  i n i t i a t e s ,  leveling  Continued  to  that  heating  off  a at  a  results  caused  by  at  two  in  a  grain  growth. The heating  kinetics rates,  interrupted rapidly were  43.8°C/min,  heating  room  conducted  at  room  4.13  those  shows  at  in  the  X-rays  show  a  ratio  while  the  701s,  (449°C).  Both  to  complete  at  be  f i r s t  microscopic Figure t r i a l  which  employed  s t r i p  X-ray  the  specimens  and  were  hardness  tests  the  results  hardness, time  increase  appreciable  the  Comparing  start  at  a  of  continuous  the  x-ray  This  once  again  r e c r y s t a l l i z a t i o n .  decrease  predicted  (640°C).  heating  results  discrepency  approximately  hardness  techniques  866s,  of  605s,  (449°C),  occurs  after  r e c r y s t a l l i z a t i o n  was  v e r i f i e d  using  the  continuous  examination. 4.14  conducted  shows at  the  results  686°C/min.  apparent  r e c r y s t a l l i z a t i o n  (450°C),  compared  with  In  both  complete  approximately  metallographically.  cases  Once  start  43s,  evaluation. at  in  higher  temperature.  using  apparent  the  686°C/min,  temperature.  43.8°C/min.  obtained  exists  and  procedure  to  conducted  with  r e c r y s t a l l i z a t i o n  cooled  Figure run  of  of  again,  time  (500°C),  of  x-rays  obtained  (660°C),  suggest  approximately  r e c r y s t a l l i z a t i o n 57s,  heating  using  appears  which  was  an  38s,  hardness to  be  v a r i f i e d  95  2  O O I Q_ Q  8  0  2  6  0  2  4  0  2  2  0  O  O OOO  o  0  9  .  8  0 . 7  o  0  0 . 6  X I  ZD  A 2  0  0  0 . 5  A  in  8  0  A £  <V c  "O D X  A  .  6  a >•<  O  0  .  4  O  0 0 . 3  1  4  0 0 . 2  1  1  2  0  0  O  Hardness  A  X-Ray  O O  1  2  6  2  6  3  4  0  0  5  Time  4.13  O,  0  0  F i g .  0 . 1  Experimental results,  3  7  6  4  8 1 1  9  4  8  1  0  8  5  (s)  continuous  heating  7  heating  hardness  rate=43,8°C/min.  and  x-ray  96  280  0.9  260  O  240  O O  220  ?  200  in c  O  0.8  o o o  AA  A  O O O  0.6  X  O  0.5  X  04 160  A  140  100  o  Hardness  A  X-Ray 8  16.8  Experimental results,  O  A  0.2  CP 25.5  343  Time  4.14  9  0.3  20  F i g .  %  3D  I 80  0)  "D i_ D  0.7  continuous  heating  43.0  5IB  60.5  0.1  69.3  (s)  heating  rate=686°C/min.  hardness  and  x-ray  97  At  a l l  heating  rates  employed,  predicted  r e c r y s t a l l i z a t i o n  predicted  by  examination the  failed  findings  instances be  microhardness  which  were  based  on  the  during  f a i l  area  at  cold  see  by  involves  to at  in  that  to  support  some  grains  boundaries  appeared  to  of  specimens  r e c r y s t a l l i z e d  material,  These  the  evidence  although  no  their  to  grains  were  extremely  high  very  small  size,  magnifications  include  since  cause  in  the  and  used  the  be  covers  only  r e c r y s t a l l i z e d  of  i n i t i a l  larger  seems  than  more  that  l i k e l y  As  discussed  during  large  formation  of  scale of  l a t t i c e  d i s l o c a t i o n  strain  in  free  the observed  the  e a r l i e r ,  i n i t i a l to  strain  recovery  defects. movement  nuclei  in  material  actually that  larger  grains  predominantly  various  small  much  increases  e f f e c t s .  rearrangement  a  r e c y s t a l l i z e d  due  occurs  very  small  is  temperatures,  a  the  amount  w i l l  r e c r y s t a l l i z e d  analyzes  ratio  higher  of  beam  observed  it  patches  x-ray  much  x-ray  the  small  indentations  The  the  the  recovery  microhardness  indentation  specimen.  w i l l  the  isolated,  metallographically,  relief  due  that  each  w i l l  ratio  increase  contain  obtained  these  However, required  concrete  grain  predictions.  possible  each  scan.  to  discern  since  each  worked  before  examination.  to  x-ray  the  predicted  is  and  any  r e c r y s t a l l i z e d  It  area,  y i e l d  technique  Metallographic  small  the  of  evaluation.  extremely  image  material  well  r e s u l t s ,  to  poor  i n i t i a t e  x-ray  hardness  d i f f i c u l t  x-ray  the  present  of  to  to  the  At that  capable  of  growth,  can  involves  a  processes c y c l e , this  take  place.  gradual w i l l  when  in  consistent  be  is  with  the  temperature,  to  occur  reaches  strain  r e s u l t s .  noted  effects  In of  in  This  to  a d d i t i o n , recovery  annealing l e v e l .  the  Once  and  mechanism  other  on  the  form,  .observations  cycle  nucleation  required  begin  occurs.  heating  these  later the  nuclei  metallographic  microhardness  continuous  in  reached,  l a t t i c e  similar  able  temperature  temperature  reduction  increase  only  the  Since  a  is  and  researchers various  have  x-ray  26 — 28 parameters The for  the  used  i n i t i a t i o n  technique  Figure  indicate  a  with  shift  686°C/min.  A  to  4.9.  by the  is  s l i g h t l y  intersection  of  the  A  heating  longer  times  continuous The  heating  r e c r y s t a l l i z a t i o n  TTR  rate  past  observed  For  of  the  of  well  analysis  a l l  to  curve.  of  The only  curve  or  and  of  of  for  times  the  at  results heated  in  18000s  in  heating a  shift  of  the  TTR  time  for  intersection  and  the  continuous  resulted  x-ray  continuous  resulted  at  the  shorter  the  between  as  on  the  specimens  roughly  43.8°C/min  point  rates,  hardness  7 0 . 7 ° C / h  somewhere  before  the  plotted  start  TTR  rate  are  heating  intersection  times  as  r e c r y s t a l l i z a t i o n ,  the  i n i t i a t i o n  which  curve.  x-ray  shorter  heating  r e c r y s t a l l i z a t i o n 22000s  and  as  r e c r y s t a l l i z a t i o n  predicted  curves  rates,  completion  hardness  in  r e c r y s t a l l i z a t i o n .  heating  and  predicts  than  heating  at  by  diagram  times  monitor  experimental  determined TTR  to  to and  curves. s h i f t during  of  the  i n i t i a t i o n  continuous  heating,  obtained  from  99 x-ray  examination  austenite  a  (CCT),  shift  continuous higher  opposite  decomposition  transformation case,  is  to  during  as  longer  cooling  that  which  continuous  shown  in  where  the the  sample  occurs  4 . 1 5 .  start  4  ^  In  times  spends  incubation  during  cooling  Figure  transformation  because  temperatures  to  this occurs  on  times  at  longer  period  is  longer.  22 Thus  using  incubation  S c h e i l ' s time  as  transformation, shifted  to  If  a  a  the  longer  transformation  suggested c r i t e r i o n  than  diagram  under  continuous  shift  to  argument  times  material.  precede  r e c r y s t a l l i z a t i o n  realized heating  much during  to  o r i g i n a l  a  strain  r e c r y s t a l l i z a t i o n energy  is  required  r e c r y s t a l l i z e d during  The heating, the  expected with  is  in  the  be  isothermal  is  for one  r e c r y s t a l l i z a t i o n might  expect  a  of  cold  recovery  processes  which  thermally  activated,  and  at  lower  heating.  and  Thus, a  retained,  temperatures on  larger the  continuous fraction  driving  therefore  less  i n i t i a t e  r e c r y s t a l l i z a t i o n .  are  to  able  grow  at  as  lower  of  force  the for  thermal Therefore, temperatures  heating. peak  respect  microhardness  the  higher,  to  shown  would  r e c r y s t a l l i z a t i o n  temperature,  nuclei  continuous  the  are  continuous  energy  fractional  of  time  applied  effective  s p e c i f i c  onset  start  conditions,  However,  less  those  is  during  reduced  therefore  the  of  (TTT).  heating  longer  for  transformation  times  similar  consumption  shift to  results  the of  to  longer  times  on  continuous  was  only  observed  TTR  curve,  the  continuous  heating  rate  in of  100  8ooi  1  ol 0.1  F i g .  4.15  1  I  I  1  10  Relationship isothermal  of  • — i  1  I  I  100 IO Time, in seconds  the  diagrams  1  3  I  1  10*  10  continuous for  a  r  1 5  5x10  cooling  eutectoid  5  and  steel.(Ref.40)  101  4 3 . 8 ° C / m i n . shift  of  the  recovery at  a  To  start  anneal  heating  designed  to  of  rate make  continuously the  further  are  the  shown  recovery  a  440°C  for  of  heated  in  effect  The  1.4000s, The  and  specimen  and  results  and  displayed  a  4.17,  treatment  those  prior of  to the  in  to  a  was  the  existing  the  in  onset  {211}  heat  of  Ka  peak  treatments  respectively.  typical  the  r e c r y s t a l l i z e d  conditions to  on  subjected  then  r e c r y s t a l l i z a t i o n  4.16  recovery  was  recovery  similar  x-ray  of  specimen  microstructural  Figures  anneal  s t r i p  specimen  recovery  the  6 5 . 5 ° C / h .  annealed  r e c r y s t a l l i z a t i o n . during  time,  the  isothermally  varify  exponential  The decay 3  pattern x-ray  with  ratio  l i t t l e  time, during  change  isothermal  is  the  prior  R e c r y s t a l l i z a t i o n the  as  the  was  onset  found l i n e ,  its  corresponding  start  the and  driving  recovery  are  4.9.  r e c r y s t a l l i z a t i o n  The  shifted  start to  occuring  approximately  at  This  roughly  shift  incubation for  of  roughly  can  period  the  an  TTR was  with  force  specimen  with  for  diagram found  (465°C),  in  to  Figure  have  the  completion  (570°C).  explained  during  19000s.  25100s  31000s be  on  times  above  quicker  annealed  completion  plotted  considerably  thermal  r e c r y s t a l l i z a t i o n  very  r e c r y s t a l l i z a t i o n .  high  temperatures.  The  shows  much  at  of  of  cycle  display  present  rate  heating  k i n e t i c s .  to  due  heating  the  recovery  i n i t i a t e  and  response,  The  to  to  kinetic  these  of  continuous  to  start  typical  by  considering  isothermal  Annealing  for  anneal  14000s  does  that  at not  the  440°C allow  lasts time  102  0.5  i  M A X I M U M LIMIT-  0.4  0.3  MINIMUM L I M I T -  D  or >> o or i X  0.2  •  6  6  Time  F i g . at  4.16  440°C,  X-ray  results  for~i4000s.  from  10  12  14  (xl0 s) 3  the  recovery  anneal  conducted  103  0.9 0.8  0.7 0.6  cr  MAXIMUM LIMIT-  0.5  /  /  D  o:  0.4  O  *  0.3  r  i  MINIMUM L I M I T -  X 0.2 • 0. I  8  12  16  20  4.17  annealing after  X-ray cycle  annealing  results  conducted at  440°C  28  32  36  40  (x\Cps)  Time  F i g .  24  from  the  at  heating  for  a  continuous  14000s.  rate  of  heating 6 5 . 5 ° C / h ,  1 04  for  the  required  microstructural  r e c r y s t a l l i z a t i o n on  subsequent  required,  the be  recovery w i l l was  be  time  found  to  that  to  is  additional  recovery  1400s  the to  440°C  was  additional temperatures  required  and  for  would  Experimentally,  temperature  occur,  necessary  at  higher  exceeded.  be  the  time  less  since  w i l l  u n t i l  isothermally  for  Therefore,  recovery  occur  heating,  required  once  more  additional  occur  440°C  temperature.  w i l l  The  necessary  during  exceeded  for  it  440°C,  for  r e c r y s t a l l i z a t i o n  i n i t i a t e .  of  evidence  recovery  subsequent  experimental  which  results  of  are  Table  of  the  insitu  shown  and  4.3.  at  continuous  to  in  specimen  kinetic the  x-ray  to  a  of  comparison  table.  The  increased  by  the  continuous  also shown  the in  was  temperature  performed  the  data  yielded  Avrami  purposes,  isothermally  the  that  is  the  of  480°C, The  on  the  4.18.  corresponding  in  and  r e c r y s t a l l i z e d .  analysis  Figure  shown  affects  response,  specimen  isothermally  analysis  the  For  of  heating  r e c r y s t a l l i z a t i o n ,  2 . 5 8 ° C / s  was  squares  time,  in  results  it  the  Least start  prior  heated  point  specimen  that  r e c r y s t a l l i z a t i o n  continuously  are  an  additional  amount  at  once  heating,  Further  the  440°C.  be  this  which  continuous  will  reached  at  heating,  of  recovery  During  continuous the  l i t t l e  reaches  remaining 5000s.  occur  continuous  very  temperature  to  modifications  parameter  heating  best  parameters  the  r e c r y s t a l l i z e d k  a  was  Avrami in  treatment,  l i s t e d parameters  molten  found  fit  to  salt be  indicating  0.8 ^  0.7 A  0.6 ^  0.5  o cr  A A A / A A  0.4  A  , _ _ A - A A - A - -  o cr  x  &  A  <A A  o  DPH 119.6  A  A  ' ^  A  0.3 0.2  0.1  Ixio  lxl0  1x10^  2  4.18  continuously  Experimental heated  r e c r y s t a l l i z e d  at  at  x-ray  r e s u l t s  2 . 5 8 ° C / s ,  480°C.  IxlO  6  (s)  Time  Fig.  1x10*  H  and  of  the  s t r i p  isothermally  specimen o  106  Table  4.3  Avrami  Parameters  Anneals  Conducted  Obtained at  480°C,  from  the  Using  Isothermal  Two  Different  Methods.  Heating  Method  Avrami k  Parameters b  Corr.  Continuous heating at 2.58 C/s  0.791  2.74xl0~  Molten  0.690  4.47x10  4  Coeff.  0.933  -4 salt  anneal  0.982  Heating  107  that  recovery  thermal during  occurs  driving  force  continuous  shown to  in  the  for  a l l  Each  time  heat  also  contains  limits to  p r e d i c t i o n s . times  The show  assumed  isothermal  start kinetic  c y c l e ,  as  found  can  be  resulting  continuous  performed in  predicted rate  the  time at  range on  the  attributed  from  the  heating.  PREDICTIONS  kinetic  without  Figure  curves  prior  4.19  to  4.21.  observed  response  experimental The  predictions  or  which  hardness  22000s,  curves  isothermal were  r e c r y s t a l l i z a t i o n  18000s in  and  7 0 . 7 ° C / h .  for  kinetic  l i t t l e  can  of  computer  which  based during were  r e c r y s t a l l i z a t i o n and  curves  was  x-ray based  on  those  two  difference.  i n s e n s i t i v i t y time  be  experimentally  predicted  observed  to  the  based  very  was  shown  set  the  start,  for  are  start  was  of  neccesary  r e c r y s t a l l i z a t i o n runs,  the  which  heating  energy  smaller  encountered  heating  This  4.9.  during  heating  assumed  the  techniques.  shows  on  to  RECRYSTALLIZATION KINETIC  analysis  4.19  The  outer  The  HEATING  completed  Figure  recovery  continuous  considered  the  of  time  continuous  strain  treatments,  x-ray  10s.  start  diagram,  due  temperatures  total  be  the  heating  continuous the  to  continuous  increment  was  by  extent  low  The  predicted  Figure the  the  computer  figure  kinetic  lesser  process  residual  CONTINUOUS  recovery  for  TTR  amount  The  at  reduced  higher  reduced  4.3  the  a  heating.  r e c r y s t a l l i z a t i o n s u b s t a n t i a l l y  to  be in  of  the  explained the  predicted by  the  temperature  kinetics  slow range  to  108  1.0 Exparimtntol  N  0.9  X-Roy Doto  0.8  Predicted Hardn*i»  0.7 0.6  A  Kintfics  Kinetic* Data  t » 18000 s g  0 t,« 2 2 0 0 0 i  </)  >»  i_  O  0.5  OJ  or  c o o o  0.4 0.3 0.2  0. I 0  20  22  24  26  28  30  32  34  36  Time (xl0 s) 3  Fig.  4.19  Predicted  and  experimental  r e c r y s t a l l i z a t i o n r a t e = 7 0 . 7 ° C / h .  kinetic  continuous curves,  heating  heating  109  associated  with  the  Therefore,  very  l i t t l e  occur  during  considered time, the  the  same  to  be  at  Good curve  if  the  the  time  two  using  was  found  hardness,  to and  curve.  between  results  and  x-ray  experimental  r e c r y s t a l l i z a t i o n rate  of  time  increment  of  data).  the  after  material best  The the  present  4.21  curves  be  start  e s s e n t i a l l y during  v i r t u a l l y  exist  between  on  in  x-ray  the  after  existed  based  shows  the  on  exists  p r e d i c t i o n s .  continuous  4.20.  The  predictions based  analysis)  of to  carried  a  increment  of  isothermal 0.2s. start  Once time  (based  found  Once  hardness start  obtained out  0.015s  heating  to  on be  r e c r y s t a l l i z e d  hardness  results  a  701s  were  0.15.  the  was  on  or  curves  treatment  time  the  were  between  predicted  correlation  Figure  0.10  kinetic  predicted  fraction  roughly  the  computer  computer  predicted  volume  was  the  r e c r y s t a l l i z a t i o n isothermal  are  to  is  either  combine  for  computer  two  predictions  Figure  time  on  w i l l  Less  the  predictions  (based  correlation  computer  start  to  computer  shown  for  computer  hardness same  are  used  605s  and  kinetic  43.8°C/min  either  predicted  r e c r y s t a l l i z i n g  curves  kinetic  the  22,000s.  conditions  increments  kinetic  is  based  fraction  r e c r y s t a l l i z a t i o n  again,  to  22,000s.  obtained  The  the  Therefore,  and  correlation  the  18,000s  microstructual  isothermal  approximately  interval  18000s.  22,000s,  enabling  interval  r e c r y s t a l l i z a t i o n  time  i n i t i a l  subsequent same,  this  time  at  for  again,  data  and  the the  time. for  the  686°C/min, computer  using  1 10  F i g .  4.20  Predicted  and  experimental  r e c r y s t a l l i z a t i o n r a t e = 4 3 . 8 ° C / m i n .  kinetic  continuous curves,  heating  heating  111  F i g .  4.21  Predicted  and  experimental  r e c r y s t a l l i z a t i o n rate=686°C/min.  kinetic  continuous curves,  heating  heating  1 12  p r e d i c t i o n s . l i t t l e  Varying  effect  on  the  the  predicted  response.  Considerable  predicted  and  the  time  the  of  The  the  similar  in  The  shorter  terms  that  recovery  to  predicted  the  due  heating,  time  to  43s  curves, of  a  with  curves  similar  are  fraction  of  the respect  given  However,  had  kinetic  between  structure.  response  might  present  to  volume the  shape  of  once  r e c r y s t a l l i z e d  be  of  additional  to  the  k i n e t i c s ,  isothermal  data,  incubation  period,  slower  predicted  during result  on  which  to  the  by  by  the  the  strain  the  in  continuous  heating  w i l l  in  k i n e t i c s ,  less  was  can  The  be  being  present  recovery  i n i t i a t e also  heating. are  during  based  be  actually  a  computer  on during  energy  annealing  at  suggests  The  recovery  strain  therefore  greater.  r e c r y s t a l l i z a t i o n .  to  more  less  higher  as  is  curve  hand,  response  computer  of  TTR  is  kinetic  energy  of  onset  experiences  resulting  curves  force  appears  other  A  experimentation.  in  continuous  k i n e t i c s .  similar  faster  occurrance  predicted  hindered  a  two  experimentally  r e c r y s t a l l i z a t i o n than  the  driving  observed  prior  of  expect  thermal  response  l a t t i c e  fact  one  since  in  continuous  existed  formation  temperatures  kinetic  the  kinetic  since  higher  explained  volume  38s  present.  predictions, rapid  0.10  is  surprising, at  the  experimental  approximately structure  for  from  r e c r y s t a l l i z a t i o n  kinetic  r e c r y s t a l l i z e d  predicted  time  variation  experimental  necessary  fraction  start  the  and  temperature  necessary observed  to during  1 13  It  was  thought  between  the  experimental  continuous further during  that  heating  the  interrupted  were  depending  common, the  assumption  interrupted  heating  c a l c u l a t i n g  the  cooling,  a  of  the  4.22.  accounted  has  the the  for  a l l  cooling  recovery  it  can  be  to  appears  predicted  more  This  in  fact  subjected  to  the  by  with  using  of  the  c l e a r l y on  the  that  the  as  the  and  on in  the  shown  error  during  the  rate,  curve  noted,  the  63°C/s  to  this  predicted  some  which  can  in be  c o o l i n g  recovery  effect  experimental  to  isothermal  more  data.  c l o s e l y  annealing,  process  of  recovery  r e c r y s t a l l i z a t i o n  r e c r y s t a l l i z a t i o n  made  isothermal  subjected at  on  obtained.  r e c r y s t a l l i z e d  was  to  k i n e t i c s .  accuracy  prior  curve  Based  temperature  cooled  the  temperature,  approximately  r e c r y s t a l l i z a t i o n  influence  predicted  the  although  further  of  at  attributed  tests.  specimens  of  be  exists curves  c o o l i n g  fraction  shift  kinetic  from  tests  dominating  can  followed  that  -  that  could  maximum  temperature,  the  be  the  required  affect  during  on  error  c o o l i n g  rates  experimental  by  Therefore,  heating  during  cooling  Therefore,  the  predicted  heating  slight  r e c r y s t a l l i z a t i o n  be  -  of  686°C/min  additional  only  d i r e c t i o n  from  of  r e c r y s t a l l i z a t i o n  r e s u l t s ,  Figure  and  rate  experimental  Making  some  the  If  the  during  kinetics  amount  of  continuous  simulate  kinetics  can  that  should  present be  able  to  accurately. was  what  recovery  continuous  was  found  anneal  heating  of  to  occur  440°C  annealing  for of  in  specimens  14,000s,  6 5 . 5 ° C / h ,  as  11 4  F i g .  4.22  Additional from  r e c r y s t a l l i z a t i o n  temperature  annealing.  during  Heating  r a t e = 6 3 ° C / s .  occuring  continuous  r a t e = 6 8 6 ° C / m i n ,  on  cooling  heating cooling  1 15  i i  i  &s  j  i  1  1  1  i  i  22 23 24 25 26 27 28 29 30 31 32 Time (x(0 s) 3  F i g .  4.23  Predicted  and  experimental  r e c r y s t a l l i z a t i o n anneal  of  440°C  kinetic  for  continuous curves  14000s.  after  Heating  heating a  recovery  r a t e = 6 5 . 5 ° C / h .  1 16  shown  in  Figure  exist  between  r e s u l t s .  The  e s s e n t i a l l y  4.23.  the  computer  recovery the  same  r e c r y s t a l l i z a t i o n continuous recovery  heating  and  anneal  are  of  found  in  the  occurrence  annealed  isothermally,  the  can  can  of  to or  by  p r e - r e c r y s t a l l i z a t i o n much  be  be  to  experimental  p r i o r  Once  predictions  was  recovery  duplicated,  r e c r y s t a l l i z a t i o n  and  resulted  specimens  methods.  conditions  correlation  predicted  amount  in  r e c r y s t a l l i z a t i o n data,  Excellent  better  made  using  considered  isothermal  to  be  additive.  4.4  DISCUSSION The  following  v a r i a b i l i t y  in  the  r e c r y s t a l l i z a t i o n 1.  The  increase  isothermal 2.  The  The  slow  observed  during in  the  to  The  faster  kinetic  r e c r y s t a l l i z e d employing  the  prior  to  k  with  increase  in  temperature. of  the  required  during  continuous  to  heating  r e c r y s t a l l i z a t i o n the  continuous  response  specimens  temperature  in  annealing.  preceeding  during  continuous  to  occurring  constant  predicted  immediately  a t t r i b u t e d  recovery  Avrami  isothermal  computer  were  annealing:  lowering  r e c r y s t a l l i z a t i o n 4.  of  r e c r y s t a l l i z a t i o n  comparison 3.  extent  annealing  apparent  i n i t i a t e  observations  to  of  heating.  observed  brought  heating  start  kinetics  in  isothermally  temperature  methods.  by  117  The  idea  of  recovery  r e c r y s t a l l i z a t i o n noticed  that  is  not  recovery  having a  can  new  a  marked  one.  markedly  Other  effect  on  investigators  affect  have  the 42  r e c r y s t a l l i z a t i o n that  the  f e r r i t e  length  of  specimen  annealing They  of  had  noted  a  was  when  immediately  after  present  unit  r e c r y s t a l l i z e d attributed time  to  left  which at  a  room  cold  on  working,  four  than  if  t h i r t y  days  after  recovery  the  worked  was  prior  iron  worked  nucleation.  nuclei  material  was.  working. place  This  that  the  during  crystal  matrix  had  growth  of  r e c r y s t a l l i z e d  depended  on  the  recovered  In  structure,  r e c r y s t a l l i z e d  experience  any  a  poorly  to  less  found  growth,  developed  recovery,  to  proceed  These recovery nuclei  specimens  at  of  f a i r l y  that  high  the  by  In  very  pure  were  lowering  extent,  that  softening  iron,  to  this  .  .  grains which  in the  polygonized  were  polygonized present  annealing  structure  did  not  temperatures.  was  r e c r y s t a l l i z e d  present, nuclei  due  was  rapidly.  driving  growth  a  well-defined  polygonized  growth  the  a  nuclei  even  observations  reduces  with  into  degree  were  was  .  structure.  If  to  performed more  taking  noted  s i l i c o n  times  cold  processes  Mehl  subsequent  r e c r y s t a l l i z a t i o n  cold  and  temperature  affect  area  noted  s i l i c o n  cold  at  Stanley  interval. 43 Hu  a  time  a l l o y s .  s i g n i f i c a n t  that  per  iron  the  attributed force  can  be  the  available  stored  recovery  to  can  strain occur  completed  fact  for  that  subsequent  energy. to  such  without  a  large  118  r e c r y s t a l l i z a t i o n fault  energy  of  i n t e r s t i t i a l  occuring. iron.  This  However,  impurities  reduce  is  both the  due  to  the  high  substitutional ease  by  which  stacking and  recovery  12-15 can it the  proceed, would  appear  various  proof  of  specimen anneal  due  to  impurity  that  recovery  experimental  this  argument  to  e f f e c t s .  processes  observations is  r e c r y s t a l l i z e d  designed  drag  provided  after  reduce  being  recovery  p r e - r e c r y s t a l l i z e d ,  microstructual  recovery)  to  were  made  during  isothermal  during  the  using  a d d i t i v i t y  can  be  r e c r y s t a l l i z a t i o n .  c l o s e l y  annealing,  continuous  accurately  more  the  heating  isothermal applied  to  are  responsible  l i s t e d the  above.  results  subjected e f f e c t s .  to  a  Once  conditions duplicate  kinetic  was  data.  process  the recovery  the  (ie.  degree  those  predicted  of  obtained kinetics  very  Therefore, of  for  Further  of  r e c r y s t a l l i z a t i o n  cycle  the  by  Therefore,  5.  5.1  CONCLUSIONS The  following  obtained  from  a p p l i c a b i l i t y continuous r o l l e d , the  the of  to  carbon  steel  after  steel  determine  pyramid  an  In  r e c r y s t a l l i z a t i o n  in  data  found  3.  to  analysis  kinetic  data  The  at  the  according  affect  the  the  salt. such  cold results  of  to  100g  loads in  However,  as  hardness  grain  growth  s i g n i f i c a n t l y .  b  and  )  k  fit  the  performed  each  on  isothermal  isothermal  start  time  t  event.  the  . av  ,  as  hardness  Least  r e c r y s t a l l i z a t i o n  temperature well  to  determine  as  the  k.  constant  k  was  found  to  vary  with  temperature  to: k=-1.63+4.63x10~  for  of  using  r e c r y s t a l l i z a t i o n  was  transformation  Aurami  predicting  r e c r y s t a l l i z a t i o n  phenomena  s a t i s f a c t o r i l y  describing  constants  the  equation:  squares  the  for  parameter  (DPH),  molten  X=1-exp(-bt was  determine  summarized.  isothermal  microstructural  to  kinetics  x-ray  microhardness  annealed  out  results  addition,  effective are  the  p r i n c i p l e  sheet.  monitored  Avrami  c a r r i e d  r e c r y s t a l l i z a t i o n  specimens  various  summarize  additivity  r e c r y s t a l l i z a t i o n  Diamond  The  experiments the  e f f e c t i v e l y  2.  conclusions  heating  low  work  monitor 1.  SUMMARY  experimental  temperature 119  3  T  range  440°C  to  560°C.  120  The  increase  temperature the  onset  in  k  with  indicates of  higher that  isothermal  less  r e c r y s t a l l i z a t i o n  annealing  recovery at  occurs  these  prior  to  higher  temperatures. The  Avrami  according  constant to  the  b  was  found  to  A  the  experimental  using  microscopically completion,  temperature  and  the  Avrami  ^  lines  exceeds  are  99  the  x-ray  effective  grain  as  strain  fit  range  t  each  predicted  reasonable  curve and  by  The the  agreement  r e c r y s t a l l i z a t i o n  t  was the  e  ^  values, fit  although  time,  determined  n  best  the  tgg,  completion  was  measure  the  progress  aging  of  heating.  and to  and  other a  was  It  was  to of  be  a  always of  found  found  degree.  to  experimentally  and  be  than  method  of  monitoring  state  such  generally to  start  those  metallographic  the  affected  processes  However,  temperatures  microhardness  f a i r l y  r e c r y s t a l l i z a t i o n  microstructural  small  lower  found  observations. insitu  560°C.  ion.  r e c r y s t a l l i z a t i o n  The  to  r e c r y s t a l l i z a t i o n  temperature.  Rj,  by  (TTR)  for  parameter,  times,  440°C  values,  times  microscopically  growth  predicted  best  times  in  continuous  by  shorter  at  percent  r e c r y s t a l l i z a t  during  ,  completion  predicted  The  the  determined  t  temperature  T  2  time-temperature-recrystallization  constructed  with  equation:  lnb=-15.56+1.90x10~ for  vary  of  at  121  r e c r y s t a l l i z a t i o n x-ray  peak  was  rates  typical  by  found of  to  batch  be  r e c r y s t a l l i z a t i o n  and  addition,  in  At  heating-quenching specimens scanned  were  at  data The  heated  room  consuming  and  points  f a i r l y  batch  used  less  good  heating  heating  slow,  were  interrupted successive  cooled,  method  due  Ka  heating  scans  to  was  fewer  r e c r y s t a l l i z a t i o n  isothermal  correlation  p a r t i c u l a r l y  annealing,  kinetic  with at  the  the  7 0 . 7 ° C / h ,  and  and  then  more  time  number  43.8°C/min.  simulating  continuous  annealing,  experimental  kinetic  of  experimentally  At  rates  results  in observed  simulating to  heating  686°C/min,  kinetic  curves  resulted  intermediate  annealing,  and  data  heating  continuous  predicted  an  temperature,  accurate  low  r e l a t i v e l y  where  This  at  {211}  obtained.  using  k i n e t i c s ,  was  to  are  rates,  the  these  isothermal  temperature.  far  continuous  predicted  heating  of  only  At  kinetics  method  shape  effective  e s s e n t i a l l y  higher  the  annealing.  rates,  obtained.  8.  recording  batch  and  rates the  show  less  c o r r e l a t i o n . 9.  The  predicted  kinetic  curves  temperature  at  continuous are  heating  affected  which  very  r e c r y s t a l l i z a t i o n l i t t l e  r e c r y s t a l l i z a t i o n  by is  the  time  assumed  and  to  s t a r t . 10.  If  a  prior  specimen  recovery  prior  to  r e c r y s t a l l i z a t i o n  anneal  the  is  given  continuous  anneal,  the  to  the  steel  heating  predicted  and  experimental  122  r e c r y s t a l l i z a t i o n once  the  onset are  i n i t i a l  of  kinetics  r e c r y s t a l l i z a t i o n ,  made  to  be  The  test  are  affected  similar  s t e e l ' s  specimen heating  to a  more  to  heating  required to  faster  1.  In  the  to  improve  r e c r y s t a l l i z a t i o n extent  of  prior  This  might  change  time  the and  i n i t i a t i o n , more  comparing 2.  An  {211}  the  Ka  to  method  peak  i t ' s  the  the  less l a t t i c e ,  heating,  must  amount  the  on  be  of  determined. x-ray  ratio  recovery,  amounts  of  and  recovery  on  r e c r y s t a l l i z a t i o n transformation  might  released  involve during  values  k i n e t i c s .  calorimetric  recovery,  and  k i n e t i c s .  instantaneously  intensity  in  in  effect  r e c r y s t a l l i z a t i o n of  Continuously  correlating  resultant  energy  the  predict  response  of  approach  bring  continuous  different  and  of  to  effect  of  to  kinetics  response.  to  temperature  this  improved  and  kinetic  isothermally,  results  recovery,  fundamental  examination  on  a c c o m p l i s h e d by  during  examining the  be  used  energy  a b i l i t y  recovery,  the  WORK  kinetics  r e c r y s t a l l i z a t i o n  rate  kinetic  FUTURE  to  heating,  r e c r y s t a l l i z a t i o n  strain  RECOMMENDATIONS FOR  prior  additive.  temperature.  5.2  Therefore,  continuous  obtained  temperature  retained  subsequently  order  be  s i m i l a r .  conditions  during  those  isothermal the  the  to  seems  specimen  recovery, and  by  very  microstructural  r e c r y s t a l l i z a t i o n 11.  are  during  c o l l e c t i n g annealing  the must  be  A  1 23  determined higher  heating  the  rates process  to  the  shift  follow  continuous  employed  peak The  to  use  of  as The  a  ratio x-ray  c l o s e l y  with  I  m  should  by  High  time  viable CA  more  peak  for  with  energy  the  processes.  f u l l y  In  automated  temperature  x-rays  necessary  i n t e n s i t i e s  j  or  n  to  I  the  material be  r e c r y s t a l l i z a t i o n annealing  the  ,  during  made  {211}  d i r e c t l y  calibrated  e f f o r t  the  using  made  during  (for ,  R  microhardness  r e c r y s t a l l i z e d An  be  Rj  for  should  c o l l e c t i n g  data.  either  and  ratio  annealing.  integrated  monitoring,  must  of  reduce  intensity  x-ray  encountered  the  be  4.  make  a d d i t i o n ,  during  3.  to  be  techniques  using  formation),  should  the or  microscopic  be  fraction  metallographic  pinpoint  or  investigated.  volume  continuous  electron  r e c r y s t a l l i z a t i o n  texture  should  actual  to  for  start  more of  techniques. times  isothermal techniques.  of  BIBLIOGRAPHY  I.  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AIME,  1959,  v o l . 1 :  vol.215,  Properties  Soc.  and  AIME,  pp.320-326.  1942,  127  APPENDIX 1  APPENDIX 1; COMPUTER PROGRAM FOR PREDICTING CONTINUOUS HEATING RECRYSTALLIZATION KINETICS C C C C C C C C C  THE FUNCTION OF THIS PROGRAM IS TO PREDICT THE RECRYSTALLIZATION KINETICS OF A LOW CARBON, COLD ROLLED STEEL SHEET DURING A CONTINUOUS HEATING ANNEALING CYCLE, USING THE PRINCIPLE OF ADDITIVITY, AND EXPERIMENTALLY DETERMINED ISOTHERMAL RECRYSTALLIZATION KINETIC DATA. ISOTHERMAL KINETIC DATA IS DESCRIBED BY THE AVRAMI EQUATION, X=1-EXP(-B*T**K). REAL TINCR,HR,XINCR(5000),XPRE,XNEW,B,Z,G, Q TEMP(5000),X(5000),N,K,Q INTEGER L I S T d ) / ' * ' / C ENTER THE DESIRED ISOTHERMAL TIME INCREMENT. TINCR=10. C ENTER THE PARAMETERS WHICH DESCRIBE HOW THE AVRAMI C CONSTANTS (K AND B) VARY WITH TEMPERATURE. N=-1.63 Q=0.00463 G=0.019 Z=1.747E-7 DO 99 1=1,5000 X(I ) = 0.0 XINCRd)=0. 99 TEMP(I)=0. 1=1 C THE TEMPERATURE AT WHICH RECRYSTALLIZATION IS ASSUMED C TO INITIATE IS USED TO CALCULATE THE AVRAMI KINETIC C CONSTANTS, AND THE SUBSEQUENT VOLUME FRACTION OF C RECRYSTALLIZED MATERIAL FORMED DURING THE INITIAL C TIME INCREMENT. TEMPCl)=465.0 HR=.0182 K=N+Q*TEMP(I) B=Z*EXP(G*TEMP(I)) XINCRd)=1.-EXP(-B*(0.5*TINCR)**K) X(I)=XINCR(I) XPRE=X(I) 1=1+ 1 J=I-1 C CALCULATE THE TEMPERATURE AT THE NEXT ISOTHERMAL TIME C INCREMENT. 44 TEMP(I)=(HR*TINCR)+TEMP(J) B=Z*EXP(G*TEMP(I)) K=N+Q*TEMP(I) C FIND THE VIRTUAL TIME REQUIRED AT THE NEW TEMPERATURE C TO HAVE FORMED THE FRACTION ALREADY RECRYSTALLIZED. TEQ=(ALOG(1.-XPRE)/(-B))**(1/K) TNEW=TEQ+TINCR XNEW=1.-EXP(-B*(TNEW)**K) C FRACTION TRANSFORMED DURING NEW TIME INCREMENT. XINCR(I)=XNEW-XPRE C TOTAL FRACTION TRANSFORMED UP TO THIS POINT. X(I)=XNEW C CHECK TO SEE WHETHER THE STEEL HAS TOTALLY C RECRYSTALLIZED. IF(X(I).GE.1,0)GO TO 7 XPRE=X(I) 1=1+ 1 J = I-1 GO TO 4 4 C PRINT OUT RESULTS OF TEMP VS FRACTION TRANS. 7 WRITEC5,1900) 1900 FORMATC ','TEMP',9X,'XINCR',9X,'XTOTAL') DO 456 1=1,5000 WRITE (5,700) TEMP (I ) , XINCRd ) ,X(I ) 700 FORMAT(' ',F9.4,4X,F8.6,6X,F8.6) 456 CONTINUE STOP END  128  129  APPENDIX  2  APPENDIX  The study  for  The  monitoring the  3.  of  by  The  a b i l i t y  x-ray  and  completion  The  a p p l i c a b i l i t y  for  that  hardness  (attributed the  a  of  the  increase  ratio.  In  was  the  found  to  have ASTM  totally  Rj,  other  determine  to  by  is  than  the  start  different  No.  11,  be  displayed  an  increase  117.5. in  reveals  time  during  very  interval. this  The  result  grain  study  The  size of  l i t t l e  is  seems 130  to  4.12,  shows  any  ratio  affected  a  resulting  No.  76.8. in  was grain  value  for 8,  40,000s Figure  Examination the  x-ray  affected  ratio ratio to  a  much  28,000s  ASTM  the  to  for  annealed  change  effect  after  microhardness  DPH  be  x-ray  with  to  Therefore,  in  growth  the  specimen  value  Figure  annealed  A2.1.  grain  microhardness  data  not  affect  specimen  results  r e c r y s t a l l i z a t i o n  microhardness  Figure  to  a  DPH  to  does  to  kinetic  r e c r y s t a l l i z e d ,  found  employed  this  determined  r a t i o ,  method  addition,  found  instance,  this  in  annealing.  7 0 . 7 ° C / h ,  prior  x-ray  For  during  of  aging),  more.  x-ray  to  x-ray  strain  with  x-ray  during  ratio  to  while  A2.2,  be  processes,  occur  the  rate  extent,  of  the  experimental  small  size  can  used  r e c r y s t a l l i z a t i o n .  heating  r e c r y s t a l l i z a t i o n very  of  of  obtained  upon  procedure  rates.  Examination  the  which  that  the  PROCEDURE  factors.  r e c r y s t a l l i z a t i o n ,  the  x-ray  microstructural  of  X-RAY  r e c r y s t a l l i z a t i o n  amount  by  heating  was  the  following  relative  affected  2.  E V A L U A T I O N OF  effectiveness  considering 1.  2:  a  of  131  F i g . A2.1  Microstructure  i n the specimen  continuously  a n n e a l e d a t 70.7°C/h f o r 28000s. ASTM g r a i n no.  11.(X353  mag.)  size  132  Fig.  A2.2  Microstructure annealed no.  i n the specimen  a t 70.7°C/h  8.(X353  mag.)  continuously  f o r 40000s.  ASTM g r a i n  size  133  lesser  extent  by  microhardness Based  various  measurements.  on  the  procedure  which  r e c r y s t a l l i z a t i o n  heating  prior  rates  recovery  quicker  does  start"  heat  r e c r y s t a l l i z a t i o n ,  analysis, times  starts  and  and  as  obtained  x-ray  to  predicted  this  affect  the  analysis  the  existed  of  At  a  predicted for  completion  and  at  heating.  predicted  with  the  time  temperatures  accurately  microhardness  study,  application  those  However,  agreement  from  that  continuous  the  start  compared  was  good  (without  lower  of  determine  during  treatment),  evaluation.  r e c r y s t a l l i z a t i o n  results  accurately  employed  times  microhardness  not  processes  *  experimental  x-ray  a l l  metallurgical  by  by times  for  x-ray  the  completion  metallographic  evaluation. The  a p p l i c a b i l i t y  o s c i l l a t i n g the  long  peak,  would  time  and  energy  scans  the  source  required  the  limited  interval  achieve  x-ray be  is  of  to  desired a  insitu  to  peak  more  x-ray  slow  necessary  with  for  i n s i t u  method  heating scan  rates,  the  Ka  resolution.  rapid  scan  monitoring  due  to  doublet A  very  rate  of  involving  high  capability  continuous  annealing. Another for  the  heating  monitoring is  According  *Back  the to  of  x-ray  Bragg's  reflection  d i f f r a c t i o n sizes  problem  lines  encountered  Laue had in  that  complicates  the  r e c r y s t a l l i z a t i o n peak  shift  with  law,  given  in  tests this  work.  of  during  x-ray  that  continuous  change.  (2.31),  the for  data  continuous  temperature  equation  indicated  remained  use  the  {211} a l l  grain  134  position spacing linear s t e e l ,  of of  the the  crystal  thermal 4  the  1  degrees  is  d i f f r a c t e d  planes  expansion  position  related  peak  of  is  the  the  dependent  interest,  c o e f f i c i e n t s  of  to  x-ray  {211}  of  FeKa  temperature,  d  an  0  Based  in  26,  describing  the  it  was  peak  ...(A2.1)  determined  shift  with  that  the  equation  temperature  increase  was:  (26)°=109.30-0.0026^T Although  the  considerably  determined  different  the  caused  by  improper  s h i f t s  for  a  lines)  are  f a i r l y  During monitoring for  by  the  angular  ...(A2.2)  experimentally  given  than  of  temperature  change  continuously  heating  adjusting of  the  monitoring  devised,  then  the  position  w i l l  have  p o s i t i o n  the  value  (probably  specimen),  the  (ie.  of  slope  is  peak the  s i m i l a r .  r e c r y s t a l l i z a t i o n ,  range  peak  theoretical  positioning  continuous  manually  in  by:  (26)°=111.72-0.00249T Experimentally,  1008  peak,  °C,  the  on  AISI-SAE  x-ray T  .  upon  the 26  the  be  the  limit  peak  the  peak  scan.  temperature to  using  shift  switches  If  an  and  for.  was  of  method  of  compensated  which  improved  valley  dependence  accounted  i n s i t u  control  method  of  i n t e n s i t i e s  is  the  peak  135  APPENDIX  3  APPENDIX  3;  E V A L U A T I O N OF  THE  STRIP  SPECIMEN  THERMAL  GRADIENT  To the  determine  resistance  were  welded  indicated  The at  at  difference the  then  of  29°C  to  the  specimen  of  at  a  range  positions then  of  held  200°C  temperature  by  the  in  thermocouples  the was  position  to  600°C.  maintained  control  the  three  measuring  in  Table  A3.1  thermocouples,  A  maintained  d i f f e r  the  from  Here  This  a  the  glass  was  difference  specimen  The  glass  lowering  the  largest found  centreline  temperature  large  p o s i t i o n .  thereby  thermal and  at  C.  the  6°C.  gradients  The  at  substantially In  the  the  of  were  difference  centreline  Only  temperature. width  5mm  temperature  The  to  occur  across  difference can  holders holders  be  the of  up  attributed  immediately appear  temperature  of  to  act  the  metal.  positions  than  of  this  Smaller  A  over  with  four  specimen  setpoint  setpoint  e x i s t .  sinks,  adjacent  more  The  shown  located  presence to  are  specimen.  could  heat  specimens, specimen,  the  the  that  the  B,  the  adjacent as  of  and  from  position  to  A3.1.  between  results  deviation  width  typical  variation  determined.  The  at  s t r i p  temperatures  centreline  thermocouple, was  a  Figure  isothermally  temperature  heated  onto  in  the  600°C from  addition, specimen  found  from  the  was  generally  did  the  that  of  to  exist  temperature found  temperature the  control  to  be  at  postion  temperature  gradient  was  found  greater  136  be  no  thermocouple  the  to  at  across than  that  137  -•-WIDTH-*-  I3.0  C/L  ALL  DIMENSIONS  C.T. = C O N T R O L C/L=  F i g .  A3.1  Strip  specimen  determining  the  IN  mm  THERMOCOUPLE  CENTRELINE  thermocouple thermal  positions  gradient.  for  1 38  Table  A3.1  S t r i p  Specimen  Temperature at C o n t r o l Thermocouple (°c)  Thermal  Gradient.  Temperature at Measuring Thermocouple (°C) A  B  C  200  197  198  199  300  295  289  300  1+00  39^  385  398  500  1+97  kn  1+95  600  586  571  596  139 experienced Of within for  the the  volume  thermal  gradient.  x-ray  three  positions  area  small,  x-ray s l i t  of  monitored, the  any  source,  x-ray  in  this of  error area  thereby  the  only  beam  r e c r y s t a l l i z e d  reduction  reduced  s i z e .  by  existing  reduce  This  length.  covered  fraction  further  energy  the  gradient  r e l a t i v e l y w i l l  along  be  during  material.  area  appears  area  by  obtained  enabling  the  use  f e l l  analysis  to  the  be  by  the by  A  Although  covered  introduced  can  position  the  beam  thermal using  of  a  a  high  smaller  


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