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Kinetics of nucleation and growth in a eutectoid plain carbon steel Kuban, Mehmet Baha 1983

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KINETICS IN  A  OF  NUCLEATION  EUTECTOID  PLAIN  AND  GROWTH  CARBON  STEEL  by  MEHMET  B . S c ,  University Institute  THESIS THE  BAHA  SUBMITTED  OF  Manchester,  o f S c i e n c e a n d T e c h n o l o g y , , : 1981  IN  REQUIREMENTS MASTER  of  KUBAN  PARTIAL  FULFILMENT  FOR  DEGREE  THE  APPLIED  OF  OF  SCIENCE  in  THE  FACULTY  Department  We  accept to  THE  of  OF  GRADUATE  Metallurgical  this  thesis  the.required  UNIVERSITY  OF  Mehmet  Bah.a  Engineering  conforming  standard  BRITISH  September  ©  as  STUDIES  COLUMBIA  1983  Kuban,  1983  DE-6  In p r e s e n t i n g  this thesis  r e q u i r e m e n t s f o r an of  British  it  freely available  agree that for  that  Library  s h a l l make  for reference  and  study.  I  for extensive copying of  h i s or  be  her  copying or  f i n a n c i a l gain  g r a n t e d by  publication  s h a l l not  be  Date  (3/81)  of  further this  Columbia  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  of  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  the  representatives.  permission.  Department  University  the  s c h o l a r l y p u r p o s e s may  understood  the  the  I agree that  permission by  f u l f i l m e n t of  advanced degree at  Columbia,  department or for  in partial  written  ABSTRACT  An  accurate  formation  prediction  (CCT)  transformation  history data  importance  Principle,  which  has In the  been this  thesis  the  principle.  As  but  the  in  many  termed  a  pearlite  range  of  temperatures. grain  size  site  tional  grain  pearlite  The austenite  new  data  which  exponent,  nucleation  and in  be  the  resulting  growth  the  of  additivity  condition,  rates  were  used  terms been  thermal  obtained  transformation  included  has  of  proposed.  and  in  of  aim  this  to in  significance  'm1,  s a t i s f i e d .  eutectoid,  with  is  been  The  sites  between  the  calculation,  growth  also  and  this  completely  sizes  isothermal  academic  satisfactory  could  equation.  using  trans-  Additivity  nucleation  and  has  and  not  saturation",  This  relationship phase  a  cooling  The  applicability  grain  size  permit  measured  austenite  transformation  measured  been  nucleation  parameter  years.  to  of  obtained  transformation  of  result,  "effective  The  have  continuous  considerable  general  kinetics  limits a  of  required  steels  clarifying  cal  for  the  steels,  been  austenite-to-pearlite  plain-carbon  for  is  defined  of  has  industrial  of  of  develop the of  a  empirithe  the  opera-  examined.  history  austenite  grain  of size  the has  i i i also  been  examined.  The  a p p l i c a b i l i t y  empirical  expression  for  predicting  size  as  function  ture  has  a  been  of  peak  confirmed.  the  temperature  of  an  available  austenite and  time  at  grain tempera-  i v TABLE  OF  CONTENTS Page  Abstract Table o f Contents; L i s t of Tables L i s t of Figures List^of..Symbols Acknowledgement  .  i i iv vi viii' xiv xvi  Chapter 1  2  AN EXAMINATION OF THE AUSTENITE DECOMPOSITION REACTION AND THE PREDICTION OF CONTINUOUS COOLING BEHAVIOUR FROM CONSTANT TEMPERATURE DATA THE INFLUENCE OF GRAIN S I Z E ON THE K I N E T I C S OF THE AUSTENITE DECOMPOSITION REACTION IN EUTECTOID CARBON STEEL  20  2.1  20  2.2  2.3  General  Introduction  2.1.1  Grain Size  2.1.2  G r a i n S i z e V e r s u s Thermal  Experimental  Versus: R e a c t i o n K i n e t i c s  Isothermal  39  2.2.2 2.2.3 2.2.4 2.2.5  ments S a l t Pot Isothermal K i n e t i c s Salt Preparation Specimen Inhomogeneity Decarburization  Kinetics  Measurements.  3.1.1 3.1.2. 3.1.3  Introduction Nucleation of Pearlite Growth, o f P e a r l i t e Additivity  Experimental  Procedures  40 44 4  4  4 5 4 9 5 0  E f f e c t o f G r a i n S i z e on T r a n s f o r m a t i o n Kinetics, G r a i n S i z e Versus; Thermal H i s t o r y  NUCLEATION AND GROWTH. K I N E T I C S AND THE PRINCIPLE  3.2  Measure-^  R e s u l t s and D i s c u s s i o n  General  20 34  Procedures  Dilatometric  2.3.2  3.1  History  2.2.1  2.3.1  3  1  5 0  61  ADDITIVITY 6 3  63 6 3 7 4 8 1  92  V  Chapter  Page  3.3  R e s u l t s , and Dlscusisaon 3.3.1 3.3.2 3.3.3 3.3.4  .  N u c l e a t i o n Rates; G r o w t h Rates. . A d d i t i v i t y and S i t e S a t u r a t i o n Effective Site Saturation  '.  95 95 106 115 121  4 4.1  Summary  ;  4.2  Recommendations  f o r F u t u r e Work  BIBLIOGRAPHY  136 138 1  4  0  APPENDICES 1  Volume  2  The E f f e c t i v e  146  Contributions Site  Saturation  Criterion  1  AO,  LIST  OF  vi  TABLES  Table 1.1  Page Composition, of  S.A.E.  Grange 1.2  2.1  Steel  4340  steel  and K i e f e r Containing  history  and g r a i n  size  used  the  by  (Ref.  30 m i n u t e s  The  the  value  of  Composition  of  study  8  1 ..1% at  grain  nucleation  in  9)  0.5% C,  Austenitized  different 2.2  thermal  Cr,  0 . 2 5 % Mo.  850°C  size  1  exponent  'm'  for  sites  eutectoid  35  plain-carbon  steel  (wt.%) 2.3  41  Austenite function  2.4  grain of  Dependence on  the  of  3.1  Approximation eutectoid  3.3  3.4  using  of  of  three  Comparison  of  different  Correction  (A.S.T.M.),  grain  size  transformed  grain of  steel.  Comparison  two  the  fraction  Comparison  by  size  as  a  2.5  3.2  6  size  rate Grain  of  size  different  4-5  ..,  obtained  by  to  determine  modules  per unit  volume  number  of  nodules  observed  on a p o l i s h e d  austenitising  75  using  the  of  Reaction  70  80  number  surface.  60  determined  methods  procedure  values  in  methods  rates  58  ' m ' ,  A.S.'T.M.  rates  51  'm'  pearlite  nucleation  nucleation  growth  exponent  exponent,  of  . . . . . . . .  temperature,  temperature  950°C  from  640°C, 94  vi i Table  Page  3.5  Pearlite  nucleation  3.6  Comparison  of  rate  d a t a . . . . . .  nucleation  rates  9 9  obtained  by 105  using  metal!ographic  3.7  Pearlite  growth  3.8  Comparison  of  growth  metal 1ographic  3.11  Initial  3.12  Cahn:  3.13  Calculated  Nucleation  rate  nucleation  Early  site  obtained  Johnson-Mehl  The  effect  reaction  of  rate  of  using  methods  112 117  in  terms  the  117 of  n  ° ^ j ^  s  .  . .  criterion  time  size  temperature  on  120 120  exponent  in  equation  grain  "Effe.ctive  by  criterion  saturation  values  the  The  rates  condition  Cahn:  . . . 109  isokinetic  3.10  methods  data  graphical  Test  3.15  graphical  and  3.9  3.14  of  rate  and  123 and  isothermal  volume  Site.Saturation"  contributions..  131  c r i t e r i o n ,  ton >  0.38,  90  values  calculated  for  experi-  the  1080  z  mental used 3.16  in  results this  Calculated  determined  for  steel  study  values  134 of  >  0.38,  the  "Effec-  c r i t e r i o n ,  for  iso-  ^90 tive  Site  thermal  Saturation"  reactions  reported  in  literature  135  vi i i LIST  OF  FIGURES  Fi gure  1.1  Page  Schematic ing  1.2  operations  using  the metal 1ographic  Typical  transformation temperatures  (Ref.  diagram,  for  the  products  representation  i n i t i a l  transformation  rate  relationship diagram  a eutectoid  Isothermal S.A.E. C C T  CCT  the  pro-  6)  3  with  formation indicated 3  cooling  on  treat-  transformation,  method  and a c i c u l a r  heat  following  pearlite  between  The  the  7)  Schematic  for  1.7  of  lamellar  cooling  1.6  early  ranges  (Ref.  1.5  isothermal  of in  of  of  1.4  involved  gress  the  1.3  representation  on  between and the steel  steel  diagram  f o r  experimental diagram from  for  the  relationship  and temperature cooling the  (Ref.  (Ref. S.A.E.  data  isothermal  9)  . . .  5  continuousdiagram  8)  5  diagram  for  9)  8  4340  (Ref.  S.A.E.  of  (Ref.  isothermal  transformation  4340  Derived  of  steel.  Based  9)  4340 data  9  steel . (Ref.  9)  1  0  i x Fi gure  1.8  Page  Comparison  of  curves  the  for  reaction 1.9.  in  Schematic  a  experimental  and  i n i t i a t i o n 4340  steel  of  calculated  the  (Ref.  representation  of  ferrite  13)  the  11  additivity  principl e 1 -1:Q  The  shape  ture 2.1  the  in  in  grain  tempera-  rating  sizes  grain  numbers for  (Ref.  caused size  in  a  28)  . . . .  0.75%  C  that  a  22  the  (Ref.  austenite  of  a  f i r s t  decomposition order  chemical  30)  grain  2 5  size  on  the  reaction  curve  30)  Schematic  2 9  diagram  of  the  space  f i l l i n g  tetra-  kaidecahedra 2.6  Schematic for  2.7  of  32  drawing  measurement  Effect  of  of  an  the  austenitising  eutectoid  apparatus  transformation  austenite-to-pearlite for  2 2  by  29)  curve  with  fracture  grain  austenite  (Ref.  of  of  size  hardenabi1ity  of  (Ref. 2.5  A.S.T.M.  Comparison  Effect  function  16  austenitic  reaction 2.4  of  Differences  steel  a  corresponding  of  changes  as  22)  Comparison  range  2.3  factor  (Ref.  with  2.2  14  time  at  employed kinetics  840°C  transformation  plain-carbon  s t e e l . . ;  on  . . .  41  the  kinetics 43  Fi gure 2.8  2.9  Different  levels  edges  the  Mn  and  content  of  transformation  middles  versus  of  salt  position  on  on  the  pot  specimens  the  salt  ..  pot  specimen 2.10  Salt  pot  after 2.11  specimen  homogenising  Effect  of  thermal  2.12  demonstrating treatment  austenite  grain  transformation  pearlite  transformation  for  each  grain  The  lnln  yl— versus  pearlite  homogeneity  size  on  kinetics; line  has  the  iso-  t h e " ; 10% been  shown  size  reaction  In  at  t  graph  640QC;  for  isothermal  austenitised  at  800°C 2.13  Fit  obtained  when  't  '  is  used  for  reaction  a v initiation 2.14  The  n ln t - j ^  graph 3.1  showing  Effect  of  thermal 3.2  time  the  for  versus a  varying  In  for  'm'  curve  of  grain  constant  (Ref.  30)  of  " sizes  0  at  to  on  the on  and  r  =  e  (Ref.  a  c  the  i  (Ref.  effect the  o  60)  n  t  Q V  iso30).. of  rate  growth  t  t  2.3  pearlite of  size  of n u c l e i volume  t  equal  nucleation  with  grain  steel  rate  representation  rates  different  d  nucleation  reaction  Number unit  C  slope  reaction  Schematic  0.82  i  of  rate  m  e  f  o  p  xi Figure  Page  3.4  Typical graph  3.5  Nodule (t)  3.6  inverted (Ref.  3.7  Nodule  73  diameter(d)  versus  transformation  time  62)  of  reaction  distribution  62)  (Ref.  Number  cumulative  73  nodules time  (Ref.  diameter  different  (EN)  per  volume  versus  62)  73  versus  grain  unit  sizes  reaction (Ref.  time  for  60)  78  3.8  Nodule  radius  versus  reaction  time  (Ref.  56)..  ^9  3.9  Nodule  radius  versus  reaction  time  (Ref.  37)..(  ^9  3.10  Effect  of  reaction 3.11  Schematic of  3.12  growth  curve.(Ref.  3.13b  3.14a  on  the  shape  of  the  19)  8 2  representation  of  the  principle  additivity  Graph  8  showing  fraction  of  grain  by  pearlite  as  a  function  fraction  transformed  in  a  Fe-9Cr-lC  for  12  hrs.  at  of  1200°C  volumealloy  (Ref.36)...  " l e s versus r e a c t i o n time mm p e a r l i t e r e a c t i o n at 640°C  for  . o d ! ^ e s versus reaction time mm p e a r l i t e r e a c t i o n at 690°C  for  Pearlite  partially  N  o  d  N  formed the  to  nodules  specimen  approximately  isothermal  Grain  in  size,  reaction  A.S.T.M.  7.3  10%  3  boundaries  occupied  austenitised 3.13a  rate  88  isothermal 96 isothermal 97 trans-  gransformation  temperature  of  Magnification  at  640°C. X160  ..  100  Fi gure  3.14b  Page  Pearlite formed the  to  size  Inverse  Inverse  Number  of  bution  3.17b  time,  size of  reaction  3.18a  (mm/s)  Reaction  time.  each  Reaction  XI60 for  graph  for  690°C versus  constructing  cumulative  d i s t r i -  temperature  640°C. 103  unit  Reaction  different  volume  versus  temperature  690°C. 104  7.3  versus  curve  reaction  gives  the  time.  growth  grain;sizes.  The rate  Reaction 107  640°C  diameter  100  7.3  A.S.T.M.  for  Largest  inverse  A.S.T.M.  temperature, 3.18b  the  640eC.  graph  volume  by  versus  temperature,  at  640°C  at  unit  obtained  diameter  of  at  distribution  nodulesper  size  Largest slope  to  of'  Magnification  per  trans-  transformation  distribution  nodules  graph.  Number  Grain  3  partially  temperature  transformation  verticals  Grain  A.S.T.M.  cumulative  reaction  10%  transformation  isothermal 3.17a  specimen  raaction  cumulative  isothermal 3.16  in  approximately  isothermal  Grain 3.15  nodules  reaction  690°C  time. 108  Fi gure  3.19a  Nodule  diameter(d)  obtained  3.19b  3.20a  3.20b  3.21  by  versus  constructing  inverse  cumulative  of  curve  each  gives  A.S.T.M.  73  diameter(d)  Reaction  temperature,  A.S.T.M.  73  Pearlite  nucleation  specimen  (A.S.T.M.  Pearlite  nucleation  specimen  (A.S.T.M.  Initial  mately  Schematic  Predicted Factor",  (mm/s).  Grain  size,  reaction  time(t).  Grain  size,  in~small  grain  size  grain  size  large  3) rate m  e  t  a  in l  l  o  terms g  r  a  p  n  partially  i  of c  a  to  l  l  y  i  n  approxi-  transformation representation  heterogeneous 3.23  Slopes  690°C.  in  transformed  15%  the  9.1)  nucleation  specimen  to  graph.  rate  640°C.  versus  n u m b e r ^ n o d u l e s l  3.22  growth  temperature,  time(t),  horizontals  distribution  Reaction  Nodule  reaction  reaction  variation ;.I,  with  of  of  homogeneous  and  kinetics the  percent  "Inhomogeneity  transformed  of  pearlite 3.24a  Experimental thermal  3.24b  reaction  Experimental thermal  variation  'I',  temperature  variation  reaction  of  of  for of  'I1,  temperature  iso-  640°C for  of  the  the  690°C  iso-  X  L I S T OF  :  Volumetric Mehl per  mm3  per  :  Growth  :  Reaction  :  Radius  :  Extended  :  True  :  Fraction  :  Temperature  SYMBOLS  nucleation  equation  rate  (Equation  in  2.4)  the  in  Johnson  number  of  and nodules  second.  rate  in  mm p e r  second  time  of  Pearlite volume  volume  Nodule  transformed  after  subtracting  transformed  equation  of  dependent  impinged  volume  pearlite  parameter  in  the  Avrami  (Equation2.5).  :  time  :  Austenite  :  time  exponent  in  grain  exponent  equation  the  high  (Equation  grain  size  :  Grain  diameter  :  Final  grain  :  Grain  diameter  Avrami  equation  diameter  for  :  nucleation  2.7).  exponent at  temperature  in  Equation  zero  time  at  2.8. temperature.(Eqn.2.16)  diameter. exponent  for  the  grain  growth  equation. Heat Grain  of  activation  growth  Diffusivity  for  equation of  Concentration Pearlite  1V  carbon gradient  spacing  the  transformation  constant in  austenite  process  Grain and  diameter  the  time  in  the  scale  shape  factor  factor  (Equation  Measured  nucleation  rate  in  per  volume  unit  time  unit  Peak t e m p e r a t u r e 2.15  per  independent  (Equation  number  initial  3.1)  3.3). of  nodules  grain size  in  equation  ACKNOWLEDGEMENTS  I the  advice  Thanks the  like  to  extended  members  of  and P r o f e s s o r  received  American  thank  Professor  and encouragement  are also  other  Group was  would  Iron  in  the  the R.  G.  form  and S t e e l  to  B.  a s my t h e s i s Professor  Phase  a  0.  Hawbolt  K,  Brimacombe,  Financial  research  Institute.  for  supervisor.  Transformations  Butters. of  E.  grant  Study assistance  from  the  Urumel i hi s a n n a Oturmusda Istanbul'un Ba§rma  da  bir  oturmus, um,  turku  tutturmusum;  mermer  ta§:lan. ;•  konuyor,  konuyor  aman  martT  Istanbul Orhan  Veil  k u s j a r t . . .  Turkusunden Kamk  1  CHAPTER  AN  EXAMINATION  REACTION  AND  THE  BEHAVIOUR  "To cold ye  in  wil  pisse, and  make  there  be n o t  the  since  i t  so  was t h e  of  then,  but  and  probing,  the  importance  farre  as ye  there  of  of  in  well  cold  and a  right  heat  water  and  this  hardning."  treating  2  that.  1  steel  Our  increasing  agonizing  directions.  fundamental  but  Also  after  has been  protracted,  our  i s  yron.  sign ,  before  hard,  i t  blue  for  men's  soone  seeme  and  together,  i t  shall  t h e wrong  furthering  in  of  forth  on y o u r i s  varuen,  glasse,  so mixe  f o r when  long  of  and p u t to  i t  mec.hanisms  not without  a  take  procedure  hardening  into  have  Steele  and probably  sometimes  of  iuyce  will  spottes or  good  i t  COOLING  DATA  the  wormes  i t s e l f ,  standard  century the  of  yron  a  take  thereof,  water  t h e edge  signifieth  CONTINUOUS  TEMPERATURE  take  see golden of  DECOMPOSITION  and strayne  harde,  coole  s o when  16th  knowledge  too  shall  water,  This  in  hardning  hardning,  in  verbana,  d i s t i l d e  ye  OF  hard,  Steele  and the  common  snow  or  any yron.,  seasoned the  yron  and l e t  AUSTENITE  PREDICTION  quenche  i t  after,  THE  FROM C O N S T A N T  l a t i n e ,  quenche  heede  OF  1  research However,  understanding  2 of  the  steel  decomposition  material  progress  research  effort  more  is  methods  of  has  human been  required.  Early  to  the  analyze  temperatures  (Fig.  processes  is  society.  An  expended studies  austenite  1.1);  the  in  clear  for  enormous  this  employed  amount  direction the  work  of  and  metal!ographic  decomposition  classical  the  at  of  constant  Davenport  and  3 Bain  is  a  leading  From ferent cal  information  temperatures,  nature  isothermal (TTT) and  example.  were  i t  for  (Fig.  A  the  possible  stituents^ tures  gave  of  decomposition  diagrams  transformation  duration  the  obtained.  diagrams,  making  on  of  These or  important  familiar  information  austenite  final  carried  out  Transformation  on  the  start,  reaction,  number  constructed  were  of  steels  thus  and  con-  constant  tempera-  of  isothermal  transformation  diagrams  by  Bain  of  and  Davenport,  different  and  composition  others.  5 '  A  and  grain  size  TTT  diagrams  included.  However, the  end  1.2).  large  variety  practi-  called  4 were  dif-  and  microstructure at  at  diagrams,  decomposition  predict  processes  very  Time-Temperature  valuable  to  a  reaction  heat  the  treatment  practical of  steel  application is  limited  of to  those  to  processes  3 et Hcst/np term BH rt}C In Solution  /OOHM ?S%H PStif'C 0 Fig.  1.1  Schematic involved  SO KM ?S%M SO'Af'C PSHFtC  100KF+C  Time et Tcmpensh/ne Lett/ T forTransformation t  representation in following  transformation,  the  of  the  heat t r e a t i n g  progress of  operations  isothermal  using the m e t a l l o g r a p h i c  pearlite  method ( R e f .  6).  Tnontforvnation Time flog. Soole )•  Fig.  1.2  Typical  early  temperatures products  transformation for  the  indicated  diagram,  formation of  (Ref.  7).  with  the  l a m e l l a r and  ranges  of  acicular  4 which is  are  essentially  cooled  some  rapidly  of  time,  structure occur the  in  be.  this is  addition  to  steels,  to  But  very  room  transformation with  those  Bain  fact  produced  for  a  A and  data  similar  treatments  imposed  on  for  6  isothermal  start  and  during  1.3). '  a  for  to certain the  final  treatments  processes, and  and  continu-  Bain,  in  transformations correlating  during  continuous  the  continuous-  isothermal  treatment. cooling  diagram  7  difference can  eutectoid  between  best  be  steel.  transformation  completion  a  what  region  obtained  steel  heat  Davenport  need  diagrams  for  treatment  isothermal  the  the  there  austenite  a  temperature  commercial  schematic  of  If  indicate  heat  on  out  a  continuous-cooling  reaction  the  (Fig.  demonstration  an  to  obtained  steel  0.85%e  most  characteristics  cooling in  will  few  In  pointed  nature.  held  temperature.  generating also  and  diagram  up  in  austenitising  TTT  manner. heated  cooled  the  temperature  the  will  metal  ously  in  from  intermediate  length  isothermal  times  for  isothermal  made Fig.  1.4  diagram, the  by.comparing shows,  the  altered  designated  o continuous-cooling curve  crosses  the  transformation tinuously above  for  line  for  cooled  650°C  curve.  an  six  representing isothermal  specimen the  After  total  would lapsed  seconds,  the  start  reaction have time  been of  at at  the of  cooling  the  650°C.  pearlite A  con-  temperatures  6 seconds  and  would  Time in Seconds flog. Scale).  Fig.  1.3  Schematic rate  representation  and t e m p e r a t u r e 800  of  of  I  the r e l a t i o n s h i p  initial  I  transformation  1  Eulecloid  between  1  cooling  on c o o l i n g  (Ref.9).  '  1  lemperolure  700 6 sec 600  _650'C \  """^L  /  ' i  A  i  \/ Y  ' * ' \\  /  '  •\  V  A  \ / \ \ \  500  \l  \ 400  I  ^  \  //  ^  \\  Xc  \\  —  \  \  /  \  End of peoriile tronslor— ^ • m o t i o n on continuous cooling  \  N  S i o r l of peorlite Ironsformotion on continuous c o o l i n g  \  1  X  \  ^  s  \  \  V  *. *v  \  \  v  V  v  X  v  \  \  \  N. \ s\ \ \. \ V  \ \  \  \  . \ \  200  M  90  N 1  \2  I  0 0.1  1.4  N. V.  \  100  Fig.  _ ~  \ \  V  \ N  300  s  \j  \ v  /  1  The  relationship  the  isothermal  1  10  between  100. 101 T i m e , in s e c o n d s  the  diagram f o r  1  1  10*"  10  s  5»10s  c o n t i n u o u s - c o o l i n g diagram  an e u t e c t o i d  steel.(Ref.  8).  and  6 only  have  time  to  is  reached  start  longer  specimen  at  the  65Q°C  a  process,  reaction and  characteristic over  a  range  that  results.  In mined  the  of  of  and  f i r s t  ease  ture  is  level  the  final  products,  attempt  the  each  "It  whereas;  is  over  on a  therefore  product  being  a  a  cooling lower important  transform  microstructure  (CCT),  that  any  single  at  of  deter-  diagrams,  noted  continuous  range  an  experimentally  be  formed  does  most  to  mixed  to  cooled  to  The  the  time,  continuous  allowed  the  is  than  depressed  describe  structure  proceeds  structure  to  a  time.  being is  incubation  time  in  be  longer  Since  continuously  Transformation  stated,  uniform  transformation  a  specimen  Cooling  Kiefer  isothermal  a  a  will  seconds.  the  Hence  temperatures  Continuous  Grange  start to  6  incubation  sample.  pushed  of  reaction,  longer  treated  temperature  end  temperatures,  isothermally the  the  pearlite  higher  requires  at  in  the tempera-  cooling,  temperatures,  mixture  substantially  or  a  and  series  of  indistinguishg  able  from  what  They  also  noted  derive a  a  that  isothermally i t  would  continuous-cooling  satisfactory  To  forms  allow  method  for  the  of  be  at far  diagram  derivation  experimental  the more from could  same  temperature."  convenient isothermal be  to data,  developed.  determination  of  a  if  7 continuous-^cool ing Kiefer  selected  isothermal haviour seven to  S.A.E.  diagram  (Fig.  A  seen  in  follow  and  Kiefer  for  deriving  a  cooling  The  essence  their  stage  of  which  indicates,  ture  at  the  complex  also  (Table  sluggish of  104  1.1),  whose  specimens,  rates  the  and  transformation  had  to  constructed  CCT  be-  representing be  transformation  developed  diagram  method  cooling  transformation  steel  Grange  employed during  diagram  can  1.6.  Grange  of  diagram,  cooling  experimentally  Fig.  the  total  constant  metal 1 o g r a p h i c a l l y The  4340  indicated  1.5).  different  cooling. be  a  transformation  by  a  from  point  on  its  position,  that  has  occurred  construction  an  empirical  rate.  They  procedure  on  the the  on  method  isothermal  consisted.of  by  specified  an  diagram.  respresenting  isothermal equivalent  cooling  carried  to  out  semi-log  diagram amount  that a  any  of  tempera-  f a i r l y  paper,  the  details  to  produce  the  CCT  on  several  g of  which  diagram  can in  Fig.  of  low-alloy  to  check  CCT  be  steel  One  their  1.7.  In  further  the be  paper,  experimental  s a t i s f a c t o r i l y  for can  in  steels,  diagrams.  curves  found  with  tests  determinations  empirical  of  experimental  i n i t i a t i o n  of  the  important  in  Fig.  were  determinations  Comparison  seen  grades  ferrite  and  with  the  of  calculated  reaction  in  1.8.  discrepancy  found  empirically  4340  8  C Mn Si Ni Cr Mo Comno»ilion 0.«2 0.78 0.24 1.79 0.80 0.3.1 Preliminary Treatment— llol-rollril 1H inches round, normaliied from I M O degrees 1»hr. Specimen Sir.e—1J4 incite* diameter, hull dink* inch lliick Aiislenilir.ini; Treatment—1550 desrrcs Kahr. for IS minutes Anslenile Grain Sire No. 7-8 A.S.T.M. Enitilibrmm Transformation Aci Acs Temperatures 1.100 degrees Falir. 1J75 degrees Fnhr. :  T a b ~ l e . 1..1  Composition, thermal 4340  steel  h i s t o r y and g r a i n s i z e o f  S.A.E.  used i n t h e s t u d y by Grange and K i e f e r  Trent formation Lmc, SoonJs  Fig.  1.5'  Isothermal steel  Transformation  (Ref.9).  Diagram f o r S . A . E .  4340  (Ref.9).  9  Fig.  1.6  CCT d i a g r a m f o r data  (Ref.  9).  S.A.E.  4340 s t e e l .  B a s e d on  experimental  10  Transformation Time, Second ! 1  Fig.  1.7,  CCT d i a g r a m f o r S . A . E . isothermal  data  4340 s t e e l .  (Ref.9).  Derived  from  11  • «00,  • It  /  J1  t  • ISO  EXPERIMENT «L  OF  io.'  ORAfCE I  VALUF  KIEFER  io «3 io* TIME IBCLOW A | l IN SECONDS 5  4  io*  \  Fig.  1.8  Comparison the  of experimental  and c a l c u l a t e d c u r v e s f o r  i n i t i a t i o n of the f e r r i t e  (Ref.13).  reaction  i n a 4340 s t e e l  12 determined  CCT  representing and  Kiefer  tion  of  data  for  had  be  end  this  the  be  could  of  of  by  produce  was  in  the  of to  the the  the  errors  in  plain-carbon pearlite  the  curve  reaction. the  Grange  determina(isothermal  by  study form  of  made  the  Bain  martensite bainite  would  transformation Bain's  to  argument,  diagrams.^  non-isothermal  combined by  to  adopting CCT  steel  and  temperature  incomplete  initial1y  pearlite  transformation  Kiefer,  to  of  transformation  only  higher  the  location  transformation).  that  and  in  the  eutectoid  suggestion  reactions  the  somewhat  reactions  of  because  Grange  The tion  end  produced  pearlite.  this  portion  proposed  sheltered  lay  completion  case  e a r l i e r  would  the  attributed  the  In  diagram  decomposi-  constant  S c h e i l ,  and  1 1  temperature  later  by  1 2 Steinberg. to  be  The  TTT  to  if  the  transformation  possible  rule.  If  the  additivity  non'-i so-thermal tinuous a  series  then  austenite  cooling of  reaction  constant  becomes  one  of  CCT  transformation  principle  at  any  decomposition  at  a  held  decomposition events  temperature determining  decomposition  obeyed  given  could  the  considered  an  additivity  a  specific  reaction, then  be  reactions. effect  temperature  different  for  was  upon  temperature.  as  question  partial  the In  con-  treated The  of  the  subsequent  general,  the  13 additivity any  principle  requires,  t e m p e r a t u r e be a f u n c t i o n  present  and the  i f  =  we c o n s i d e r  where  and  bxoiujgih';t t o  then  further would  by  the  require  i t  same that  the  of  transformation  the  amount  temperature,  is  a  i . e .  ...(1.1)  phase  unstable  a  second  reaction, the  at  already  Ufx,T)  temperature is  only  transformation  Fx  Hence  that  i n i t i a l l y  brought  and p a r t i a l l y  temperature the  reaction  at  the  one  transforms,  to  additivity  to  tranform principle  second  temperature 13  be  unaffected  principle  by  that  at  c a n be  seen  schematically  Experimental principle out  by  for  vestigating the  w o r k e r s .  the  additivity  i n i t i a l  investigations  different  various  the  steel  conditions rule  for  in  to  Fig.  test  for  1  These  7  additivity were  carried  included  and l i m i t a t i o n s  nucleation  This  1.9..  the  compositions,  ^ ' ^ ' ^ '  1  temperature.  and growth  of  i n applying  reactions.  1p Avrami as  defined  one w i t h i n  which  transformation a  reaction  that  Krainer  an  the  reactions is  isokinetic nucleation are  the  of  and growth  proportional.and  isokinetic  measured  range  is  time  temperatures rates  of  stated  the that  additive.  for  i n i t i a t i o n  of  the  14  Fig.:1.9  Schematic  representation  of  the a d d i t i v i t y  principle.  15 transformation  in  1.1%  Mo)  Cr,  range  59Q°C  within and  0.25% to  this  show  for  of  the  the  the  A  a  so,  change  that  at  in  be  seen  in  Table i l . 2 , is  additive  investigated.  with  is  the  temperatures  pointed  out  transformation  temperature  C,  within  transformation  Hansel^  s i m i l a r i t y  (0.5%  temperatures  can  range  l i t t l e  steel  successive  of  percent  reaction  necessarily  4150  transformation  This  the  two  results  and  for  varies  factor.  cated  Lange  SAE  single  temperature  isothermal  ture .  and His  curve  steels  at  i n i t i a t i o n  and  carbon  by  68Q°C  the  Lange^ shape  held  range.  that  throughout  specimens, of  of  that  versus  pearlite  in  of  tempera-  multiplies  shape  they  approximately  time  plain  transformation  simply  the  a l l  argued,  times indi-  isokinetic  and  additive.  22 Dorn, tested 0.92% the  the C,  de  Garmo  and  isokinetic  1.53%  pearlite  temperature  Mn,  Flanigan  condition  0.20%  with  Si.and  transformation range  620°C  to  later  added  a  on  the a  steel  0.26%Mo  was  not  710°C  other  and  of  composition  found  isokinetic  (Fig.  hand,  in  that the  1.10).  20 Cahn addi t i vi ty the  restrictive  b.a.sed Jonj s i t e s a t u r a t i o n .  pearlite  nucleation  less  reaction  becomes  at  most  irrelevant  He  observed  temperatures, and  the  condition  rate  the of  that rate growth  for for of  16  T a b l e 1 .2  S l c e l C o n t a i n i n g 0.5 P e r C e n t C , 1.1 P e r C e n t C r , 0 . 3 5 Per Cent M o . Austenitizcd 3 0 M i n u t e s at 8 5 0 * ^ . Second Temperature  Pint Temperature  Minutes llcltl  Deg. C.  0 0 0 18 0 37 0 36 • 0 3 0 4 0 6 0 8 • 0 0 0 18 0 37 0 36  6B o 660 680 660 640 640 640 640 680  CKo  O80 680  Frnctinnal Deg. C. Time  0.00 0. 35 0.50 0.75 • .00 0.00 0.35 0.50 0.75 1.00 0.00 0.35 0.50 0.75 1 .00  640 640 640 640 500 590  Sum Minof utes to Frac- FracInitiate tional tional Trans- Time Times formation 8 6 IS 4 10 I PS 38  30  590 590  •5 • 3 50 7 70  500 590  38 31  590 590  50 14 3 0 6 70  1 0 0 0 0 1 0 0 0 0 1 0 0 0 0  00 77 S> 34 00 00 73 48 38 00 OO 77 51 34 00  t  .00 I .03 1.01 0.99 1.00 1.00 0.97 0.98 1.03 1.00 .1.00 1 .03 1 .OI 0.99 1 .OO  0.6 i  i  0.6 \ 0.4  D.?\ 0  WO  Fig.  1.10  IHO  1150 IPPO IPSO Temperature, "£  BOO  The s h a p e f a c t o r a s a f u n c t i o n temperature  (Ref.  22).  of  17 dominates  the  transformation  due  to  the  early  exhaustion 21  of  available  Cahn's  nucleation  observations  In  a  recent  to  sites. be  study  Tamura  generally  conducted  et  a l . ,  found  true.  in  this  department  by  23 Agarwal ted  Brimacombe,  a  predict  the  kinetics  transformation  and  the  in  to  and  a  eutectoid,  processes used  such  isothermal  principle  was  formation, mental  1.  this  main  for  showed  the  the  describe  the  the  was  formula-  austenite-to-pearlite  during  Schloemann. assumed  distribution  continuous-cooling ':  . .  that  the  This  poor  were  agreement  believed  study  additivity  austenite-to-pearlite  continuous-cooling  that  trans-  with  experi-  kinetics.  to  be  contributing  were:  in  isothermal of  or  model  temperature  rods  and  of  inaccuracies  validity  the  relatively  factors  discrepancy  existing 2.  kinetics  determinations  The to  but  steel  Stelmor  valid  of  transient  carbon as  mathematical  the  start  and  end  transformation  using  the  incubation,  curves;  additivity nucleation  times  in and  principle and  to  growth  processes.  Hence at  the  a  more  University  extensive of  British  research  programme  Columbia.  This  was  M.A.Sc.  initiated thesis  18 was g e n e r a t e d  as  one  part  of  general  objectives  of  1.  accurately  characterize  To  austenite  the  this  programme  decomposition  controlled  research,  isothermal  were  the  to  of  under  as  The  be:  kinetics  reaction  as; w e l l  project.  the  carefully  continuous  cooling  conditions. 2.  the  To  predict  the  the  additivity  for  use  The  following  of  studies;  composition changes  in  rule  this  grain and  the  continuous-cooling while  clarifying  variables size,  section cooling  were  thermal size.  rate  to  The in  a  transformation  studies  examined  the  austenite  the  of  grain  to  pearlite  ditions the  1.  study  for  and  thermal  decomposition the  experimental  Examining  on  and  then  of  the  that  the  i n i t i a l  reaction  particular  the  rate,  specimen.  characterizing on  in  incorporates  behaviour,  This  consisted  specimens  cooling  pearlite  history  application work  to  steels.  concentrated  size  limitations  investigated  Tatter  single  the  plain-carbon  be  history,  simplify  of  the  using  principle.  To  eutectoid  behaviour  the  component effect  isothermal  investigating additivity  in  the  rule.  austenite conHence  of:  were  given  varying  thermal  19 treatment  to  sequently  reacted  tures.  comparison  A  austenite ferent 2.  to  employing 20  test  of  the  sizes  subcritical  reaction  was  made  and  sub-  tempera-  transformation  of  nucleation  specimens  transformation.  present  understanding  and  to  generate  use  in  predicting  isothermal  constant  pearlite  series  percent the  at  grain  rate  for  for  the  dif-  sizes. the  a  different  pearlite  grain  Determining  of  produce  another  kinetic  and  reacted The of  sufficient  data the  rates  to  a  is  used  maximum to  additivity  condition  continuous-cooling data.  growth  kinetics  for  rule its  from  20  CHAPTER  THE  INFLUENCE  KINETICS REACTION  2.1  GENERAL 2.1.1  OF IN  SIZE  AUSTENITE  EUTECTOID  Grain  in  THE  GRAIN  ON  THE  DECOMPOSITION  PLAIN  CARBON  STEEL  INTRODUCTION  The present  OF  2  Size  versus  Reaction  metal 1ographic  s t e e l coo.l.ed f r o m  Kinetics  features  austenite  of  were  the  constituents  observed  and  24 fairly the  well  confusion  recognized influence tion  understood in  by on  the  early  as  terminologies.  Davenport  reactions. 25  as  rates Bain  and Bain of  the  the  1890  s,  despite  Austenite  grain  as  an  having  isothermal  investigated  this  size  was  important  austenite subject  decomposi-  soon  after-  26  wards, ' and c o n t r i b u t e d to the u n d e r s t a n d i n g o f the transformation by d e v e l o p i n g an i m p r o v e d means o f revealing 2 7 28 and m e a s u r i n g a u s t e n i t e g r a i n s i z e . *  The  role  hardening French blister  of  of  austenite  steel  metallurgist steel  performance  of  a  is  grain  one o f  Reaumur  grain  growth  hardened  tool  size  ancient had i n test  in  steels  in  affecting  recognition. 1722  devised  association and. even  the The  for with  had a  his the  crude  21 scale the  for  designating  following  the  austenite  grain  size.  29  Bain  made  comment:  I t s e e m s i n e s c a p a b l e , t h a t t h e a n c i e n t s who hardened s t e e l m u s t h a v e made two i m p o r t a n t observations: 1.  That s t e e l w h i c h , a f t e r coarse fracture surface than that having a f i n e  2.  That s t e e l which broke e a s i l y a f t e r hardening had a c o a r s e r f r a c t u r e s u r f a c e than t h a t which broke only with the a p p l i c a t i o n of heavier blows.  In  Sweden,  of  the  ly  employed  the  fracture  actual  dard  of  a  Fig. to  or  1926,  surfaces  of  hardened  quantitative  rating  being  surfaces;  was  size  influence section,  2.2.  Since  be  enhance  fineness  by  tool  steel  of  certain  comparison  distributed  over  Shortly  afterwards,  a  well  as  with  can  the  be  coarseness  was  with  evenly  and  or  regular-  q u a l i t i e s , five  the  stan-  ful 1  range  ten-step  seen  standard  in ASTM  Fig.  2.1,  austenite  scale.  steel  can  the  measure  made  adopted  exceedingly  transform  size  as  a  scale  agreed  The  early  encountered.  standard  grain  as  fracture  usually  it  as  hardening revealed a h a r d e n e d more deeply texture.  to  1  austenite inch  in  hardenabi1ity martensite,  seen the  of  to  retard  formation  of  grain  size  diameter is  the  is  the  formation  martensite.  the  hardness  demonstrated  capacity  increasing the  on  of  of  a  in  steel  austenite  grain  pearlite,  Bain  correctly  22  Fracture  Fig.  2.1  Comparison  of A . S . T . M .  corresponding austenitic  fracture  grain  sizes  Oram  grain rating (Ref.  St}e-  size  numbers  with  for  a range  the  of  28).  3 Temp.  (Mean)  1800 °/T p 380 °C. jB I700"F=.  ,  3Z5°C. Ci 1575 °F 3-5 855 °C. JD  785°C. E_  7-4-5 °C  ^  "So Carbon O •74 Manganese O-^l Silicon 0\4-  Fig.  2.2  Differences austenite  in hardenability  grain  size  c a u s e d by c h a n g e s  i n a 0.75%. C s t e e l  (Ref.  in 29).  suggests  that  the  real  hardenability  was  the  relative unit  number  volume  nucleation number  of  of  of  equally  compared  by  many  nuclei  Bain  with  workmen  pearlite  than  nucleation  austenite vast  to  the  grain  the  g r a i n s , the  greater numerous  of  Based  on  istics  the  of  the  is  The  the  time, effect  comparable  scattered wall  is  of  to  a  over  a  painted  great wall  sooner  that  both  rate  the  size  affected  and  grain  transformation  of  the per  confirmed  pearlite the  was  rate",  nuclei  austenite. the  grain  area  available S-curves)  austenite  per  and  were Thus  unit  the  that  the in  located the  boundary  the  f i r s t  S-curve  and  effect  austenite  isothermal and  the  a at  smaller  area;  volume,  attempt of  at  data  known  decomposition  made  The  unit  i . e .  few."  boundary  the  called  Davenport  "It  rate,  the  the more  nuclei.  sometimes of  controlling  evidence  greater  grain  the  a  per  describing  few.  by  in  nucleation  painters  steels,  boundaries  the  a  pearlite  majority  In  states,  only  work  appearing  skilled  Metal 1ographic  at  pearlite  austenite.  rate  as  factor  major  explaining  curve,  grain  being  diagrams, character-  reaction,  austenite  decomposition  (TTT  Bain the  and shape  size.  a  rate  curve,  24 was  f i r s t  compared  reactions ference ning  and  on  a  end a  chemical line  sets  the  transformation  order  The the  a  the  end  chemical  of  reaction of  the  the  mined  a  by  were  two  rate  S-curve  at  the  S-curve  begin-  started  not.  100%  dif-  2.3).  curve  transformation  the  major  (Fig.  did  the  chemical  The  noted  plots  the  readily  In  addition,  curve,  the  transformed  appeared  of  by  activated  arising  from  typical  and  The  determined  of  to  growth  in  f i r s t  assuming  molecules  an  collision reaction  austenite  process,  the  had  homogeneous of  terms  order  favourable a  decomposition  nucleation  explainable  reactions.  was  system;  whereas  was  approached  formation  process,  liquids.  reaction  the  for  time.  redistribution  throughout  and  Whereas  discrepancies  probability energy  of  obtained  curves  the  curve  finite  nature  of  velocity,  reaction  in  gases  chemical  asymptotically,  finish  of  two  f i r s t  approaching  curves  in  of  maximum  rate  occur  between  Whereas with  that  to  is  occurring  deterat  .inter-  30 faces,  i . e . ;  Since pearlite  a  heterogeneous  metal 1ographic  formation,  controlled,  Mehl  the  pointed  reaction  evidence reaction out  the;  process.  established  was  that  nucleation  need  to  derive  and a  for growth  25  Time Theoretical Curve Hours  I  0 2  4  6  8 10 12 14 16 Id 20 22 24 26 26  1 — i — i — i — i — i — i — i — i — i — i — i — i — i — r —  Log Scale  Fig.  2.3  Comparison o f t h e a u s t e n i t e decomposition curve that of a f i r s t order chemical reaction  with  (Ref. 30).  26 quantitative  expression  in  terms:  of  the  real  physical  para-  31 meters,  the  nucleation  rate  the  familiar  Johnson  and  the  reaction  rate  terms,  cesses  in  e m e r g e d . In  transformation  Mehl  and  the  growth  equation  of  deriving  Johnson  and  rate.  which  nucleation  this:  kinetic  Mehl  made  characterizes  and  growth  equation  the  Thus  pro-  for  the  following  assumpti ons: 1.  The  reaction  2.  The  rate  of  nuclei  and of  3.  of  the  proceeds  nucleation, per  rate  length  by  unit  of  per  radial  unit  throughout  the  Nucleation  is  of  of  nucleation Nv,  and  expressed  time,  per  growth, time  unit  6,  are  growth.  in  number  of  volume,  expressed  both  in  units  constant  reaction. random,  without  regard  form  spheres  for  matrix  structure. 4.  The  reaction  impingement  They versus proach;  actual  in  the  arbitrary  occurs  derived  time  an  terms  rate  time  nodule  products  is of  of  during  of  Ny  growth  pearlite  -  for  the  and  G  using  of  a  sphere  the  rate  calculated; a  and  thus  is  no  fraction  the  rate  of  growth  except  when  growth.  expression  impingement of  as  sphere  longer of  extent the  reaction  following  nucleated of  that  growth has  spherical the  of  -  sphere;  at of  apsome an  suffered is  a  this  fraction  27 is  equal  to  the  fraction  determines  the  multiplied  by  same  time,  gives  ated  at  gives  this  an  rate the  the  arbitrary  of  of  rate  for  untransformed  growth,  number  equation  function  of  of  one  nodules  of  time; the  of  nodule,  of  a l l  integrating  This  which  nucleated  growth  volume  matrix.  at  when  the  nodules  this  nucle-  expression  transformed  as. a  time;  .  t t=  N  £TT R3dt  . . . (2.1 )  / 3 t=o where  for  the  austenite  of  the  pearlite  radius  R where  G  is  This Avrami, which and in  the  arises  the  following  where  V  ex  integral  is  true the  given  nodule  reaction,R  is  the  and  ...(212)  rate  of  give  the  Avrami  pearlite  what  volume,  impingement  and l a t e r  V  will  extended from  pearlite  Gt  growth  equation the  Mehl  =  to  was  and of  later  includes  nodules.  calculated  the  sphere.  termed that Both  true  by  volume Johnson  volume  fraction  way;  '  l - » x p ( - V „ >  extended  above.  volume  ...12.3) as  determined  b yJ  the  28 Hence  the  Johnson  X  This  =  equation  transformed  versus  and Mehl  equation  l-exp(-|NvG  as  stated  time  for  t  3  4  becomes;;  )  . . . ( 2 . 4 )  previously, random  defines  nucleation.  fraction To 19  characterize to  make  the  boundary  the  pearlite  following  reaction  additional  Johnson  and Mehl  assumptions  fior  had  grain  nucleation:,  1.  Nucleation  occurs  2.  The  is  matrix  exclusively  composed  of  at  grain  boundaries.  spherical  grains  the  in  of  equal  size. 3.  The  nuclei  originate 4.  The of  rate  grow and  of  growing  only  do  into  not  cross  grain  transformation nodules  and  grain  is  to  they  boundaries.  retarded  growth  which  the  by  impingement  adjacent  grain  boundaries.  Including  these  additional  assumptions  enables  19 Johnson of  grain  and Mehl size  transformation The  increased  nucleation  on  to the  curve grain  sites  per  quantitatively shape of  and  the  size unit  determine  position  pearlite  produces volume  the  reaction  fewer and  of  grain  requires  the  effect  isothermal (Fig.  2.4).  boundary longer  Fig.  2.4  E f f e c t of (Ref.30).  grain  size  on t h e  reaction  curve  30 growth  times  grain,  i . e .  This a  for  the  increasing  primarily  transformation  and  time  process  given  makes  the  assumption  preferred  the  sites;  X,  X where  general  and  =  problem  growth  relationship  n  nucleation  occurs  Avrami only  at  exhausted.  process,  between  /reaction  reaction.  Avrami.  gradually  and  isothermal  l-exp(-bt  by  nucleation  the  characterizing  both  treatment  are  austenite  of  of  includes  that  which  the  completion  nucleation  more  transformed,  for  a general  three-dimensional  developed  traverse  which  was  certain  to  geometrical  growth,  also  a  nodules;  For  he  fraction  time,  t:  )  . . .  (2.5)  3 <_.n <_ 4 and  b  is  a  constant.  32 Christian, suggests  that  the  formed  remains  growth  with  The ferent any  grain  Avrami  in  a  his  2. <_.n<_3  for  the  as  the  expression  Avrami  equation,  for  the  volume  two-dimensional  and  one-dimensional  does  varies the  volumetric  variation  equation.  of  trans-  respectively.  equation  size in  analysis  general  valid  Avrami  changes  result  in  of  the  in  the  Johnson  same and  nucleation empirical  way  Mehl rate,  constant  with  dif-  equation; Ny, 'b'  will in  the  31 One  of  the  Mehl  was  that  only  into  important  nodules,  the  grain  assumptions,  of  in  the  made  reaction  which  they  by  Johnson  and  p r o d u c t v.woul d  nucleated.'  grow  Rothenau  and  33 Boas  .in  their  microscope, for  the  They  pearlite  that  the  reaction  that  work  with  reverse  in  pearlite  reaction growth  also rate  attempted but  s i b i l i t y  of  or  Using  being  grain  the  s  terms  offer the  of  the  the  emission true  carbon  steels.  - cross  austenite  rate  equation  no  resistance  i t e s ,  nucleation  workers,  such  and as  Parcel  at  '  of  included  grain  the  of  pos-  surfaces,  Assuming  corners, Cahn  that  the  growing  for  derived grain  and a  Lyman  grain  surfaces  transforma-  boundaries Cahn,  measurements  Mehl,  a  (Fig..2.5)  edges  nodule.  kinetics  and  boundary  analysis  tetrakaidecahedron  assuming  growth  grain  35  diameter,  a  of  he  3 4  localized  numbers  to  isothermal  and.Fisher's  corners.  grain  an  effects  Clemm  o f a s p a c e - f i 11 i n g  determining  tion  was  plain  readily  calculate  o f p;ar.t;i-'cjj;l-a;r  nuclei  edges  shape, t h a t  in  electron  this  eutectoid  20  and  of  nodules  to  excluded  restraints.  energetics  grain  the  boundaries.  Cahn  the  showed  observed  grain  exhaustive  and  analysing of  several  Triano  and  37 Hull,  Colton  steels, site  and  pearlite  saturation  Mehl,  came  nucleation (this  to was.  concept  is  the fast to  conclusion enough be  to  examined  that  in  cause in  most  early  more  32  edge  Fig.  2.5  Schematic  diagram of  t e t r a k a i decahedra.  the  space  filling  33 detail which to  in  the  3rd  resulted  the  in  to  the  f  Hence, a  Cahn formation  In  a  however, at  a  on  and  t  Using  by  being  temperatures unimportant  "finish  the  decreasing duration  where  time"  grain  was  diameter,  d,  an  site  the of  grain the  expression  size  would  reaction.  for  trans-  where  low  nucleation  saturation  may  type  expression  not  in  occur.  which  the  rate,  k  t  : :  n  i  . . . ( 2 . 7 )  constants reaction  time  20  Cahn  Cahn's  and  termperatures  = nj  event  high  . . . ( 2 . 6 )  Johnson-Mehl  k,  fairly  ^  derive  nucleation  d e r i ved  G,  the  high  Nv  was  or  did  very  case  volumetric  °' Q  effect  at  reaction  rate,  ".  predominate  such  The  increasing  direct  even  nucleation  growth  z  rates  the  transformation.  related  have  chapter)  analysis  and  the  dependence  of  reaction 40  and  nucleation  developed  a  empirical  rate  rates  on  relationship equation  the  grain  which the  size,  Tamura  incorporated  austenite  grain  et  into size,  a l . , Avrami's d:  'i  X  =  l-exp[-b^-] d"  . . . ( 2 . 8 )  It  is  important  t i o n 2J8YLS n o t equation size  the  to  note  same  (EquAtidn).2.5)  as due  their  studies 39  tions,  Tamura  signifies cess  as  and  gate  the  to  in  a  means  to  'b'  contained  contained  the  in  the  introduction  in  equa-  Avrami  of  the  grain  of  the  2.1..  1  Size  It  is  industrial  heat  materials.  It  resulting temperature  grain  to  Versus  exponent  nucleation  objective  determine  carbon  of  and  observation  the  'm' pro-  this  the  steel  Thermal  grain  size  history  exponents to  investi-  s i g n i f i -  prior  zone  therefore  size  of  a  and  any  steel  factors  duration  important  thermal  cooling  History of  and  therefore  affected is  the  the  one  peak.temperature  not  predicting  plain  thermal  between  for  transforma-  m 1 . • •'  prior  etc.  bainite  that  in  is  analysis,  relationship only  It  austenite  composition,  treatment,  active  metal 1ographic  to  and  suggested  site  Table  Grain  of  of  pearlite  40 '  their  The result  of  eutectoid  attached 2.1.2  a l .  type  test  m for  by  cance  et  shown  project  the  that  the  factor.  From  n,  that  to  history  processes,  and but  microstructures  necessary  material  a n d - h o l d i n g timeatppealk  in  to  is  a  such of  as  heat  establish grain also in  size, for  weld  characterize  terms  of  temperature.  a  the  the  peak  35  TABLE  2.1  The  Value  Nucleation  of  'm'  for  Different  Surface  Nucleation  Edge  Sites  Corner  Site  m  1  2  3  36 The  uniform  coarsening  material  held  an  growth.  One  grain  on  of  a  by  the  a  at can  elevated  microscope.  temperature  However, the  of  grains  follow  surface, in. situ,  surface  characteristic  the  experimentally  polished  free  of  and  that  so of  is  the  on  a  resulting  the  grain  a  stress  free  known  as  grain  growth  of  a  heated growth  phenomena  bulk  in  may  single  stage is  not  inhibited be  growth.  41 Carpenter a  1.5%  and  antimony,  Elam,  tin  investigated  alloy  with  the  grain  following  growth  in  results  being  noted; 1.  2.  Growth  occurs  not  coalescence  by  Boundary  of  A  given  and  be  The  boundary  migration  of  neighbouring  is  discontinuous;  boundary  may  grain  is  periods  and  not  grains. the  constant  the  may  frequently  in  direction  grow  into  a  neighbour  consumed  by  a  of  subof  on  one  neighbour  more  of  a  rapid  grain  by  its  neighbours  just  as  the  grain  di sappear.  the  rate  side on  side.  consumption  Using  and  change.  simultaneously  another 4.  a  heating  migration 3.  grain  migration  migration sequent  by  same  material,  Sutoki  added;  is  is  about  to  37 5.  A  curved  its  grain  centre  boundary  of  usually  migrates  towards  curvature. 43  In  addition,  6.  Where  Harker  boundaries  angles  by  Different  Parker  in  different  included  driving  and  a  more  of  grain  120  phase  metal  degrees,  acute  mechanisms  force  single  from  the  observed:  and  growth  angle  the  will  meet grain  be  consumed.  different  sources  have  proposed.  been  at  for  the Exten44  sive  reviews  have  been  published  by  Burke  and  Turnbull  ,  45 and  Nielsen.  completely  It  is  recrystal1ized  for  grain  growth  the  grain  boundaries.  volume dary  surface  per  of  metals  that in  cells  a  boundaries grain  is  authors  growth  are  the  and  unit  energy  Many  cells  is  decreases  area  generally  in  reduction the  their  volume  the  of  number  size  that  driving  the of  grains  less,  the  and  the  a  force  surface  increases,  becomes  in  energy  per  of  unit  grain  boun-  overall  lowered. have a  pointed  froth  of  out  the  similarities  between  soap  and  grain  in  recrystal!ized. foam,  as  driving  growth  material,  As  soap a  recognized  kinetics  using  the  force,  can  be  For  the  surface a  simple  growth  simple energy  model of  formulation o established;  of  the of  38 D2  -  =  K't  . ..  (2.9)  where D  Although of  cells  in  confirm  activation  cell  D  =  f i nal  K1  =  constant  t  =  time  it  has  a -soap  experimental to  =  o  an  been  froth  studies  of  extension  energy  for  D?  -  size eel 1  =  o  s i ze  of  proportionality  that  the  agrees  well  with  metallic of  =  t  shown  this  grain  D2  at  A  grain  kinetics this  growth  equation  of  growth  expression, have  based  boundary  migration,  exp  t  on  failed the  . . .  (2.10)  R - T  0  where Q  Instead, metallic the  :  empirical the  process constant  R  :  gas  T  :  degrees  A  :  most  systems  heat  of  activation  for  Kelvin  constant  of  the  isothermal  corresponds,  to  an  grain  growth,  empirical  data  equation  in of  form;  Dn" -  Dl]"  =  K't  . . . (2.11  )  4  39 where  i s  K',  a material  Hannerz austenite that  and Kazinczy  in  steels  carbides  duced  the  refined coarse  to  with  a  rate  value  varying  steels. grained  of of  They  proportionality  studied  and n i t r i d e s  growth  responded  dependent  of  the the  also  grain  alloy  Nb,  V,  constant.  growth  contents,  Ti  austenite  in and  drastically grains  found  re-  and t h i s  exponent!;.  n"=~ 2 0 ,  in  determined  n"? 5,6  for  cor-  grain as-cast  steels.  48 Hu  and Roth,  reported  a  variety  of  n"  values  between  4Q 2  and 4 ,  Alberry,  their  0.5  Cr,  n" -  for  a  4  studies grain  In  carbon  in  steel  2.2  grain  the  heat  grain  purity to  between size  for  Ni  same  zones  used  temperature,  eutectoid  2.73  for  these  austenite  welds.  has been  to  of  prior  of  in  be  determined Most  the  method  'n;'" t o 50  a l .  steel.  kinetics  c a n be  peak  et  determine  affected  growth  and hence  found  and Ikawa  t h e s i s , t h i s  the  relationship final  Mo-V s t e e l  undertaken  this  determine  and Jones  commercial  were  size  Chew  oar  used  to  eutectoid  establish heating  plain  the  time  and  steel.  E X P E R I M E N T A L PROCEDURES Experiments  reaction  kinetics  were  performed  to  investigate  for  different  grain  sizes  the  and f o r  isothermal different  40 reaction  temperatures.  2.2.1  Pi 1atometric For  precise tus  an  tinuous  on  Fig.  cooling  composition  was  Diametral"  rather  to  a  the  plane  voltage  the  extensometer  the  tubular  length All  =  100  samples  steel  rod,  axial  test  was  preselect  common  steel  Q.D:  machined  having  by  the  were The  used and a  in  to  1080,  composition  prevent  gradients^  and  the  controlled spot on  welded  the  same  dilatometer.  thermocouple Signals  continuously  overall  wall  were  diametral  this  de-  extensometer.  specimen  to  con-  dilatometer  specimen  the  dimensions  apparatus  eutectoid in  from  re-  Table  of  were;  t h i c k n e s s ; =• 0 . 8  shown  a  appara-  and  changes  temperatures.  base.  from  a  tipped  attached  test  = 8 mm.,  with  tubular  was  specimens  .mm, were  the  the  austenite  thermocouple  thermocouple time  the  monitored  intrinsic  system  and  of  temperature  measured  to  a  the  and  isothermal  dimensional  as  that  temperature  a l l  quartz  of  was  with  of  Measurements  k i n e t i c s ,  continuously  temperature  feedback  used  for  surface  and  corded  with  of  progress  axial  middle  chromel-alumel outside  used  cooled,  than  specimen  diameter A  the  control  The  water  assoe-iated  The using  in  was  measured  a  Ki n e t i c s  transformation  tests.  of  monitored  of  2.6  consisting  errors  accurate  measurement  shown  Isothermal  mm.  carbon 2.2.  Si PHASE SH 1FTER TEMPERATURE CONTROL  TEMPERATURE 8 DIAMETER RECORDER A B C D E F  2.6  Diometrol Dilotomeler Inlet for internol gos -flow Outlet for internol gos flow Inlet for externol gos flow Thermocouple on somple Support Structure  Schematic drawing o f the apparatus measurement  Table  of transformation  2.2  COMPOSITION PLAIN-CARBON  c 0.79 Cu 0.049  Mn 0.91  . Cr  0.062  OF  employed f o r  kinetics.  EUTECTOID  STEEL  (ut%)  Si  S  P  0.49  0.029  0.018  Sn 0.003  Ni 0.014  Al 0.084 Mo 0.002  42 The were  austenitising  preselected  and  treatment,  the  i . e .  resultant  time  and  austenite  temperature  grain  size  51 measured  metal  transformed ing  condition,  of time at pearlite time for  samples.  at  kinetic  5  kinetics  and for  the  the  cooling second  rate TTT  range  pearlite  in to  austenite 740°C  sample.  minutes  Fig.  ensure  nucleation  and  and  64Q°C  growth  the  isothermal  to  minutes  decarburization  were the  identical  600°C.  conditions  5  cooling  maximum  with  high  A  sizes, to  above  reflect  .2.2.  grain  r e s t r i c t e d ' v a l i d  to  kinetics  temperatures  6Q0QC,  690°C  austenitising  structure.  prior  The  to  faster  minimize  at  Two  effect  slightly  austenite  to  the  austenite  combined  selected, growth  chosen  temperature test  15  and  shown  to  austenitis-  specific  transformation  austenitising  returned  a  The  5 and  treatments  of  partially  investigate  similar  as  quenched,  108°C/sec  nose  temperatures  and  a  each of  1,  homogeneous  always  in  for  was  different  to  temperature.  minute,  transformation  conditions  were  a  produce was  1  treatment  Although  sample  minute  water  selecting  decided  demonstrated  ensuring  to  was  results  15  austenitising  used  Before  austenitising  840°C,  the  while  it  on  conditions.  to  cooling  available approximate  TTT  tests  test  Tow  1  to  temperatures  temperature  depict  test  nucleation  temperature  43  l  1  1  -  -  •  700  0  —  -  o  -  o  i  -  o  OA  -  -  -  O OJ  Austenitising f  E 650 -  M  .OJ  -  /  *  ( 0 OA  A  O f  V'O  111§  -  f i  - .  i i 1i  2.7  AV  •  o  -  1 %  •  A  -  #  O  -  f  9 9 %  1000  100  Effect of austenitising to-pearlite plain-carbon  time  transformation steel.  (s)  a t 8 4 0 ° C on t h e  kinetics  f o r an  min  -  i  Time  Fig.  5 , 15  1  it  i  600  —  Treatment  min  8 4 0 °C  y^ y  .  iction Tran sforrru  o  austenite-  eutectoid  44 2.2.2  Salt  Pot  Isothermal  Traditional were  also  performed  transformation traditional samples after  from  one  salt  increments  of  sample  area  rates.  This  method  and  growth  specimens  The were to  test  quenched  and  holding of  to  thin  quenching  time  suitable  the  samples  provides  nucleation  more  due  The  relatively  another  much  data.  and  for  large  a growth  nuclea-  number  of  tests  10 5  mm  diameter  minutes  with  condition.  the The  from  at  x  mm  temperatures  exception grain  partially  1-2  size  of  thickness identical  the  was  1100°C determined  transformed,  water  specimens.^  2.2.3  was  Salt  to  640°C.  lowest  temperature  be  640°C.  A  60.0°C  The  salt had  Preparation  The  approximately  and  also  tests  metal!ographic  dilatometric  examination  is  for  metal 1 o g r a p h i c a l l y  NaCl  to  isothermal for  measured  transferring  pot  samples,  austenitised  neutral  of  transformation  the  the  Measurements  required.  austenitising  of  with,  measurements,  dilatometric  tests  compare  results  larger  tion  isothermal  to  procedure  Kinetics  1550}  melting  having  required  available  (L.H. a  was  salt  high,  for  of  for  a  melting  a  working  temperature  which, point  selected  contained  salt 85%  approximately  isothermal point  of  temperature was  BaCl  2  a ,  640°C  15% which  45 was of  not KC1  suitable. and  desired  NaCl  tion 20%  of NaCl.  L.H.  melting  After were  1 550 ,  component This  the  used.  conditions  10.0  the  lower  were  melting  composition;  To  15  had  a  several  NaCl,  melting  using  40  was,  additions  t r i a l s ,  obtained  c h l o r i des  salt  point,  KC1 .  55%  a  salt  The  BaCl^.  point  the  of  of  composi-  25%  KC1  ,  approximately  590°C.  The mately than  temperature  control  2°C  transfer  +  one  and  After-heat  treatment  transferring  5  minutes,  for  1  minute,then  maintained  at  specimen  the was  desired quenched  and  etched  pearlite  was  measured  high  contrast  that  a  each  field  2.2.4  using  between  valid  area  of  salt  from  pots  pot  to  was  approxi-  pot  was  less  the  the  involved sample the  to  water,  cold  2%  Nital.  The  of  the  test  in  using  pearlite  austenitising  specimen  isothermal  directly  fraction  S p e c i. m e n  the  which,  a  and  pearlite  to  740°C  salt  the  salt  temperature, mounted  in  fraction  Quantimet  of 720.  martensite was  bakelite,  The  ensured  measured  for  view.  Initial in  time  transferring  polished  ducted  all  second.  for  the  the  for  salt  I n h o mo ge n e i t y isothermal  pots  yielded  transformation the  result  tests,  shown  in  conFig.  2.8.  Fig.  2.8  Different  l e v e l s of  the middles of The  figure  transformation  s a l t pot specimens.  i n the middle i s the  s p e c i m e n g r o u n d down t o of  the  half  specimen t h e r e f o r e ,  c e n t e r l i n e of  the wire  rod.  on t h e e d g e s Mag.  photograph  i t s diameter.  corresponds to  X  7.  of  a  The the  and  disc middle  47  Wt % Mn  v.s  Position  EDGE  MIDDLE  EDGE  POSITION of SPECIMEN Fig.  2.9  Mn c o n t e n t N.B.  It  versus  must  seen i n F i g . that  p o s i t i o n on t h e  be n o t e d 2.9,  that  i s lower  s a l t pot  specimen.  t h e a v e r a g e Mn c o n t e n t t h a n t h e Mn c o n t e n t  shows t h e c o m p o s i t i o n o f  this  steel .  as can  on T a b l e  be  2.2  48  Fig.  2.10 S a l t p o t after  specimen demonstrating  homogenising treatment.  Specimens of disc  homogeneity Mag.  X  7.  shown c o r r e s p o n d t o t h e d i a m e t r a l c r o s s - s e c t i o n  specimens.  49 The  disc  rate  at  center  specimens the  of  edges,  the  center!ine  the  and  a  slower  specimen.  of  the  transformation in  demonstrated  rod  The  used  kinetics  original  steel  s e g r e g a t i n g .element,'  the  Mn  A  content  did  homogenising  not  the  were  literature  sealed  for  15  not  show  in  '  (Fig.  was  a l l  2.2.5  to  specimens in  the  from  the  followed  minute  containing and  the  salts  by  the the  depth,  probe  then  variation  thought  in  to  be  examination  of  suspicion as  (Fig.  .2.9).  recommended  performed.  under  noted  of  from was  were at  resulting  vacuum  after  Specimens  and  such  a  This  kept  at  1200°C  treatment  inhomogeneity  of  did  pearlite  homogeni s i n g  decarburization the  austenitising  also  determined.  treated  740°C,  a  layer  d e c a r b u r i z a t i on  total  was was  on  treatment  the  heat  of  then  disc treatment  Specimens  5 minutes  d e c a r b u r i z a t i on .  decarburized of  the  zation  extent  rod  determine  to  the  specimens.  108Q 1  was  specimen  at  macrosegregation  electron  2.10).  resulting  neutral  to  Mn  performed  Decarburi The  The  Although  the  tubes  previously  transformation applied  of  was  Tests  the  corresponds  study.  this  rate  CO  quartz  hours.  the  confirm  treatment CO  in  an  transformation  transformation  attributed  rod.  the  enhanced  center  in  was  an  at  850°C,  6 minutes The  cut  to  mi.crostructure  photographed  determined.  Using  50 a  maximum  men  a l 1 owable  thickness,  decarbur.ized  the  layer  austenitising  of  10%  of  the  at  850°C  was  found  on  Transformation  specito  be  acceptable.  2.3  RESULTS 2.3.1  AND  Effect The  tising tests  DISCUSSION of  Grain  Size  grain  sizes  obtained  conditions are  given  isothermal  for  in  included  on  from  the  pot,  pot  salt  this  higher  to  reaction  kinetics  c a n be  for well  the  that  temperature 5 0  i s  that  bulk  due  in  to  Fig.  .38,55  3 1  seen  using  of  n  d  c  the  The  and the  salt data.  decrease and  underlying and  be•summarized  n  obtained  in  nucleation  on 2.1:1.  dilatometric  nucleation a  Fig.  nucleation treated  pot  size  on  data  temperatures  2.IT.  a  grain  kinetic  slower  dependence '  c a n , be  the  austeni-  and s a l t  of  specimens  reaction  given  effect  the  obtained  rate  seen  researched,  The  kinetics  from  the  dilatometric  2.3.  figure  isothermal  pearlite  the  confirming  measurements  correspond  That  Table  transformation  Also  growth  both  with  Kinetics  the  growth reasons  growth  is  as  follows: The  nucleation  overcoming  of  can  grow  cal  particle  nuclei  with  is  usually  thermodynamical steadily size  decreases  temperature,  event  i . e .  with the  barriers  decreasing  beyond  concerned  which  free  the  a  energy.  particles  undercoolingffram lower  before  with  become  the  isothermal  new The  the phase c r i t i -  growth  equilibrium transformation  TABLE  2.3  Austenite  Grain  Austenitising Temperature  °c  Size  A..S.T.M. Grai n Size  10.8  740  800  .  9.1  840  7.8  900  7.4  950  7.3  1100  3.0  52  Fig.  2.11  Effect of  austenite  g r a i n s i z e on t h e  formationrknne'tlcs;  the  has b e e n shown f o r  each g r a i n  isothermal  10% p e a r l i t e t r a n s f o r m a t i o n size.  transline  53 temperature,  The  the  temperature  complicated (the  higher  and  diffusion  is  the  nucleation  dependence  determined  of  by  rate  the  of  growth  rate  t h e  d i s t a n c e ) , the d i f f u s i o n  rate  fi 1  pearlite.  is;  more  spacing  and the  Concentra-  te  tion in  difference.  the  diffusion  creasing  pearlite  gradient.  The  maximum  a  fusion  at rate  For  As  the  rate  is  growth  becomes  and  rate  than  increasing  therefore  small,  reaction  and at  then  a  increase  the  incubation•time  time  to  complete  the  transformation.  essentially  of  transformation  a of  rate  drop  in  this  equation thermal (Fig.  the  temperature,  increasing nucleation  the  grain rate,  and  is  a  dif-  a  isothermal size  can  the  the  growth  function in  by  rate  only  transforma-  accountable  confirmed  be  increase  difference  size as  to  Since  insensitive  the  to  the  only  by  measurement  quantity.  Work pearlite  with  structure  de-  decreases.  grain and  the  rapidly  which  specific  to  reduction  by  increases  temperature,increasing  is  the  concentration  below  seen  tion  f a l l s ,  compensated  temperature,  very  pearlite  transformation  more  spacing  particular  the  temperature  done  earlier  reaction  can  (Equation test  2.12).  was The  on be  this well  2.5).  plotted exact  The in  material  has  characterized kinetic  terms  i n i t i a t i o n  of  In  time  data In for  shown by for y^-— the  the  that  the  Avrami  each versus  isoIn  t  transformation  54  1.0  0.0  t =3,0€s  t = 0 ot  A V  n= 2,143 In b = - 3 , 0 3 0 5  x  i  n'= 4 , 2 5 2 1.0  In b'= - 8 , 4 3 0 4  Austenitising Temperature • 8 0 0 ° C Reaction Temperature  -2.Oh  '  •  640  °C  L  2.0  1.5  In t Fig.  2.12  The  Inln y ^ - versus  reaction at  640QC;  In  t  graph  for'isothermal  austenitised at  8009C.  pearlite  55 was  d i f f i c u l t  to  determine  was  estimated  by  f i r s t  mum  of  eight  points  t  o,  based  on  =  transformation increment This for  and  data  termed  on  again was  t  i . e .  excluding a  =  o  at  t  Although pearlite  reaction  does  not  include  done  by  a  Tamura  and  more  Thus the  at the  the  by  In  plotting  grain  best  n'  and  be  t  m In  =  Int  a  was  was  f i t  deterobtained  i n i t i a t i o n  be  seen  the  obtained  were  good  with  performed.  time  b'  mini-  small  line  'In  a  Then  was  i n i t i a t i o n  in  characterizes  subcritieal as  a  time  Fig.  2.13  d  +  versus  exponent  a  grain  transformation equation  re-written  In  'm'  the  in  it  This  was  size  para-  terms  (Equation  of 2.8).  as;  In  Ind  well  temperatures  parameter.  incorporated  pearlite  can  to  steel.  size  who  by  f i t  start  plot  analysis  time, can  transformation  n'  size  1  Int  increased  a  equation  grain  studied  2.8  versus  line  temperature.  resultant  constant  a l .  n'  until  r e s u l t i n g3  Avrami  generalized  squares  squares  incubation  et  Equation  was  plain-carbon  the  transformation  t , „ . The e x t r e m e l y a v used as the r e a c t i o n  is  the  y-^-  start  time  The  the  least  In  least  The  .. a v  eutectoid  meter  In  repeated  b a s i s o f  when  for  the  points.  the  a  approximate  ' t„wv,„ . ' . avrami  mined  the  i n i t i a t i o n  procedure the  f i t t i n g  on  an  because  I n k  :  the  can  value be  (2.12)  of  determined.  56  F i g3 .  2.13  Fit time  obtained for  0.82  when C  't  av steel.  is  used f o r  reaction  initiation  57 To  determine  formed, the n'ln  t  found The  Q  be  plot  value  Tamura  a l ' s  on  calculated  a w  the ,  of  the  'm'  be  from  of  t  Q  'm'  was  values  for  fraction £g v e r s u s  Q  Ind;  in  Ind,  i t  transformed given  trans-  was  (Table  Fig.  2.4).  2.14;.,  A  determined.  values  eutectoid  t  versus  fraction  2.2  the  n ' In  7 5  is  on  determined  by  using  plain-carbon  steels  the  reaction  pearlite  two  with can  2.5.  noted  however  t  at  pearlite start  n'ln  as  transformation  Table  must  dependent  plotted  and  approximately  et  It  t  50%  composition  seen  for  also  Ind  comparison  similar  be  was  is  'm.'  independent  for  of  A  data versus  5  to  whether  =  0  T  „ and  Fig.  measurable  Tamura  found  A]  reaction.  of  that  2.14  et  the  is  a l .  value  based  transformation.  used  times  ofm=  1.8  on If  t  =  the  9  time  a V  was  calculated  based  on  t  obtained  is  approximately  obtained  in  the  study  Tamura  et  a l .  this  number  as  a  tion  sites  later  in  the  nucleation is  more  as  by  =  3.0  summarized  seem  important,,  to  et  is  in  be  the  higher  significance  Table  value  of  2.J.  to  dominant with  than  '  m  '  that  As  and  m =  the  value  pearlite  studies,corner  consistent  of  a l .  indication  metal 1ographic  would  T^,  and  Tamura  attached  probable  0 at  be  and  edge  probably 2.2.  of  nuclea-  will  at .  seen  corner  58  TABLE  2.4  Dependence on  the  of  the  Fraction  Pearlite Transprmation  Grain  Size  Transformed  [%)  'm'  25  2.2  50  2.3  75  2.2  Exponent of  'm'  Pearlite.  14  •  i  ~m=2-6l  •  12  t = 0 at t Reaction at 640°C O 650°C O II II 670°C A H II 690°C • ov  10  8 m= 2l7  40  Fig.  2.14  The  nTnt-^  versus  l n d f o r .t = 0 at  t  graph showing  a slope  'm'  equal  to  2.3.  TABLE  2.5  Comparison  of  'm'  Source  This w  o  r  k  ( (  1080  (  0.77  Values  'm'  steel  C  Tamura  steel  et  (Eutectoid carbon  2.2  2.0  a l . plain  steel )  1.8  61 2.3.2  Grain The  Size  Versus;  Thermal  determination  of  History  the  grain  size  versus 49  thermal based in  history  on  an  heat  relationship  examination  affected  of  zones  developed  of  welds.  for  different  holding  ture  and  using  relationship  D"  where  and  D  N  n'"  a  using  a  maximum  The  r  series  of  D  1  - t  II  N  peak  a l . ,  was  growth grain tempera-  )  ...(2.12)  squares  after  They  i . e .  holding  they  plots,  coefficient.  4 7  grain  constant  respecti vely,  least  - Do  2  et  determining  obtained  relationship  N  at  sizes  andtt2  correlationJ  original  K ( t  grain  e  2  After  times  =  D£  for-time&i^  temperature |!  a  D  -  Alberry  the prior a u s t e n i t e  size  the  by  determined  selected found  Equation  at  using  n" =  2.73.  2.11;  II  =  Kt  where K^= A  and  Dq  is  the  Assuming peak is  grain  that  temperature  similar  for  exp(-C-|r),  size  the is  all  at  time  t  «  for  negligible, temperatures;  ...(2.13)  0,  the  can  be  also  specimen  i . e . then,  grain  to size  used,  however.  reach  the  6Q  t  at  =  0  62  D^"  Using  -  -the  D""  =  A exp(.-Q/R(T1-T2))t  ...(.2.14a)  =  A  ...(2.14b)  activation  exp(-Q/R(T3-T4))t  energy  of  austenite  grain  growth  53 as  Q =  460,000  diameter  in  equations of  The  'A'  l ;  be  n!";  3.57  =  A  =  D  2.73  determined  .  D  by  et  time, to  t  al . , =  5  and' g ' r a i n minutes,the  determine  the  value  i s :  3.57 2.98  grain  =  Bastien  numerically  result  n"  steel,  from;.•.  appropriate  solved  _.*3.57 0  t h i s 1080  •  the  the  specific  Z  For  mm a n d  can  and  J/mol/K,  x  growth  2  >  9  8  10  m i n  1 2  equation  ^ ^ i e x p T  x  3 , 5 7  / s  therefore  4  6  '  0  0  0  ; /  becomes;  1  0  0  ° ) ] t  ..(2.15)  Kl  compared  2.73  =  K  4  Alberry  with  1  x  et  1 0  a l .  13  [ e x p (  for  -460,00R0  a  0.11  C  +  alloy  33 , 0 0 0  )  ^  } t  ( 2 <  steel.  * N.B.  It  must  equation  be n o t e d 2.15  that  D  Q  b e c a u s e DQ  in equation  2.15  is different  i s not a f u n c t i o n of  peak  from  D  Q  temperature.  in  ]  fi)  63  CHAPTER  NUCLEATION, AND  3.1  THE  3  GROWTH  ADDITIVITY  KINETICS PRINCIPLE  INTRODUCTION  75 The  pearly  and  later  has  been  existed toid rate,  named  pearlite  studied in  i n *most  fine,  logical  as  vestigated The examined  i s  used.  detail.  the  bearded,  t r o o s t i t i c This  nature  a n d became-  nucleation as e a r l y ' 5 5 -.- •-.  Benedics  the  'and i d e s c r i b e d  by  metal  great  Sorby  structure  deal  of  defining  Globular,  rod-like  massive,  banded,  pearlites  of  that  confusion the  eutec-  degene-  reefy,  a n d many  gradually  formation  better  1905 by  the  1864  terminology  other  became  terms  more  pearlite  was i n -  understood  and growth  as  A  situation of  in  probably  products.  coarse,  s o r b i t i c ,  often  observed  the morphological  transformation  blocky, were  constituent  character  Arnold clearly  of  pearlite  was  and M c W i l l i a m  54 •-) ( a n d ,-by  in  of  the works  Bain  3 and  Davenport.  3.1.1  Nucleation A  was  necessary  correct i f  of  Pearlite  theory  quantitative  for  the  formation  relationships  of for  pearlite harden-  64 ability.;  in  formation stituent  An  steels  were  to  be  of  pearlite  existed  was  observed  under  excellent  review  determined. almost  as  Theories:  soon  the  microscope.  the  theories  of  as  for  for  the  the  con-  formation  of  56 pearlite  is  given  evidence  accumulated  summarized of  the  pearlite  austenite of  pearlite  sidewise ferrite pearli  then  as  by  by  a  Hull up  to  follows: of as  and  cementite  From  time  of  understanding  nucleation a  result  growth.  of  review,  of  the  forms and  edgewise  may  genesis  and  from colonies  growth  cementite serve  to  and or  both  nucleate  te."  The nucleus  question of  of  pearlite  which  constituent  remained  a  served  controversial 56  somewhat was  they  directly  growth  Ferrite,  simultaneously  experimental  their  " . . . P e a r l i t e  process  nucleation  Mehl.  the  current  originate  and  and  contradictory  generally  relationships  available  accepted, with  based  on  pro-eutectoid  evidence. studies  as  the  active  one  due  to  the  However  it  57 '  of  orientation  cementite,  that  cementite 30  was  the  most  This fied  in  Hultgren  probable  generally  the and  light  active  accepted  of  Ohlin.^'4  new  nucleus  for  pearlite.  interpretation  evidence  Through,  provided  some  had by  cr.itical  to  be  H i l l e r t ,  modi5 8  experiments,  they  65 found  that  ferrite  nucleating place by  not  the  was  pearlite by  and  repeated  branching  an  of  equal  that  partner  the  sidewise  existing  with  growth  of  nucleation  ferrite  cementite  colonies and  and/or  in  took  growth  but  cementite  plates.  Hence occur  in  point, main  during  the  structurally  barrier,  i . e .  force  to  of  the  size  c r i t i c a l  size  favouring his  the  the for  the  only  and  Depending larity  on  was of  which  In preted  such as  ferrite  or  they  the  a  of  a  were  1evel  this  the  of  become  through "level  energy  there  nucleation  fluctuate  these to  The  acts  dominates. the  a  a  driving  that  as  proportional  exists  force Based  ferrite  with  and  each  developed. degree  that  a l l  spheroidal, of  a  return.  competing  argued  that  is  inversely  cooperation, the  of  no  cooperation  with, which  stable.  is  phase,  i n i t i a l l y  lamellar  cementite  and  there  thermodynamic  Hillert  concept  of  surface  envisioned  si-.tua.tion, the rate  of  new  was  fluctuations  austenite,  Therefore  Hillert  determined.  by  creation  gradually:  the  of  particle.  pearlite  pearlite,  explained  body  nucleation  observations,  other  composition  energetically,  formation  of  which  and  beyond  cementite  forms  random  metastable  restraining  on  the  of the  lamelobserved  could  be  cooperation".  rate,  can  'embryo1,  of  c r i t i c a l  be  inter-  either  size,beyond  66 Pearlite faces due  such  nucleation  as  grain  uses  corners,  to  the  contribution  faces,  and  is  to  therefore  essentially grain  the  edges  driving  pre-existing and  grain  force  of  sur-  boundaries,  such  sur-  heterogeneous..  19 Johnson nucleation  and  rate  Mehl using  analyzed the  tions  summarized  in  shape  factor  where:  By ' a  selecting 1  ,  the  be 1  N,  seen and  different  grain  determined rate,  'X'  in  °°,  size  the  on  the  the Fig.  values  of  3.1  where  interesting  result  the  reaction  changed  on and  1  to  the  grain  cally  as  To  is  °°.  rate  different  the  The  of  effect  an  this  only of  by low  extreme  and  the  pearlite  reaction  size  are  constant  can  test  in  their  Fig.  be  that  when  N  of  this  tn the  N. time  changes rates rate  schemati-  3.2.  equations,  real  nucleation  can  between  growth  demonstrated  they  nucleation  nucleation the  a  keeping  varies  although high  by  result  is  assump-  defined  the  variation  analysis  of  shown  The  the  constant  tin  factor  60%,  on  constant  values  shape  changing  They  rate,  reaction.  representing  this  this  growth  of  based  chapter.  for  the  isothermal  The  from  G,  effect  equation  previous  and  effect  J.M  the  rates  were  of  Fig.  3.2  Schematic r e p r e s e n t a t i o n of of  the e f f e c t  n u c l e a t i o n on t h e r a t e o f  and growth  rate  constant  (Ref.  of varying  reaction with 30).  grain  rates size  68 needed;  in  fact  measurements  austenite-to-pearlite Mehl  formulated  The tion  of  a  occurs  to  detected  l i t t l e  hope  as  they  of  the  are  on  of  that,  to  direct  created We  can  the  Johnson  in  the  both  on  to  the  ascertain examine  predicted rate  of  the  and  the  i n i t i a -  nucleation  space  Hence,  measurements  whose  the  and  there  is  nuclei  exact  nature  details  behaviour  nucleation  time  of  seems  and  to  its  parameters,  nucleation  Blanter,  scale  best  observed  known  earliest  or  at  models the  for  observe  invariably  techniques.  with  and  trying  available  agree  Mirkin  is  in  with  making  rate  before  a  using  The  d i f f i c u l t y  being  on  made  localized  nucleation  dependence  were  too  process.  well  nucleation  equation.  transformation  event be  reaction  their  inherent  of  5 9  a  .!  measurements  Scheil  and  are  reported  L a n g e - W e i se.f  0  by  and o f t a t e r 37  a  more  There  systematic are  two  investigation  accepted  methods  by for  Hull,  Col tori..arid  measuring  Mehl.  nucleation  rate; 1.  Determining  the  observing  the  volume  a  times  in at  number  series  one  nucleation  nucleation of  of  is  the  pearlite  specimens  isothermal  rate  rate  reaction time  by  metal!ographical ly  nodules reacted  per for  temperature.  derivative  of  the  unit different The number  69 of  nodules;.  the.  Th.e.  nodules;  assumption  are  of  in  spherical  this,  approach,  shape.  is;  Scheil  and  Lange-  60 Wei s e new  nodules,  i . e . 2.  using  this  reached  measured  Determining  the  the  distribution In  addition  also  In  from  their  measured  a measurable  nucleation  nucleation  of  pearlite  to  assumes  uniform  method,  that  G  nodule  review  of  size  rate  by  a  in  at  the  which  specimen,  nodule.  the  various  a  the  single  nodules,  constant  to  measuring  in  spherical  is  rate  rate.  nodules  assuming  th.e.  with  methods  sample.  this  time  of  size  method  and  is  measuning  61 the  nucleation  tions not  necessary  valid  suited  and  for  The  and Fig.  the  nucleation  suffer  time of  from  therefore  are  and  Hagel  simple multi  the rate  specimen  specimen  method  nucleation  is  to  known  temperature,  the  austenite. lack  of  d i f f i c u l t  be the  Early  interpret  the  to  is  assump-  work  the  are  best  rate.  influenced grain  by  size,  nucleation  specification  to  that  method  pearlite  and  the  stated  of  (Table  the  and measure-  information 3.1  and  3.3).  As tion  the  examining  homogeneity  ments  Cahn  for  that  austenitising the  rate  can  rate  is  be  seen  usually  in  Table.  reported  3.1 as  and  Fig.  3 . 3 , the.  the  number  of  nuclea-  nodules;  per  70  TABLE  3.1  Approxijnation „ Grann  P  Size  of c  N u c l e a t i on  in  Eutect oi d  Steel,  60  4-5.  Temperature of Formation  No.  of N u c l e i cm3  per  sec  °e  717  5xl0  704  7x10  662  2xl0  620  6x1  580  3xl0  per  No,, o f N u c l e i :per cm2, of grain surface area per s e c .  1.6  2  4  6  0  8  7  2.  2xl0  2  6.3xl0  3  1.9x10  5  9.4xl0  6  71  Fig.  3.3  Number o f n u c l e i v e r s u s R e a c t i o n u n i t volume grain  sizes  (Ref.  60).  Time f o r  different  72 mm  3  .st  The  .  main  volume  and  sometimes  variables  can  be  the  driving  the  more  edges  The  sites  and  to  for  of  ried  until  is  transformed,  n o d u l e s makes  the  Recently,  size  and  and  rate  approximately which  per  rate  mm  per  isothermal  2  . s :  unit reaction  the  larger  the  the  grains,  smaller at  grain  of  the  is  that  dZ0%.t  impingement  corners,  metal it  1ographic  can  be  car-  6f<% t h e  . i ;  of  pearlite  the  sample  inaccurate.  measurements  of  the  nucleation  rate  on  a 62  number They all  of  steels  determined employing  curve  (Fig.  (Fig.  3.5)  of  the  d  time  data  from  the  Their  versus  t  £ N  V  value  cumulative Johnson-Mehl  d  time «  curve  Ridley.  number  the  3.4). E N  d  V  (total  at  (Fig. 2.4)  which  The  t  the  plot inverse  extrapolating number  of  intercepts there  verticals  is  methods,  distribution'  to  second  3.6).  63 '  of  versus  By  positive  o.  (Equation  a  and  horizontals  (Fig.  the  by  uses  constructing  distribution equation  the  Brown  cumulative  different  at  by  (!)  drawing  zero,  gives  generated  inverse  curve  to  by  rates  method  by  for  volume) axis  out  nucleation  distribution  corresponding uses  data  carried  constructed  nodules/unit with  the  3.4).  cumulative graphs  were  ..  temperature,  nucleation  shortcoming  method  nodules  nucleation  nucleation  after  of  reaction  for  One  the  this  the  nucleation  surfaces.  only  number  grain  available  determination out  be  lower  force  the  affecting  seen  temperature.  as  is  method,2[2) on  the  Finally, used  a  to  inverse the  determine  73 Tr on 1 fO fin o r ion remperorurr 645 C  Troniformotion tcmperotuft 643  io  0 /  i  X  <  /  a  Q  ///  \  \  My.  \ *\  10"  20  time, mm  \  -  /A  s s  JO  40  • o • » •  IN, 10 50 10' , 5 " KT K) J  1  —L  1  50  60  70  TIME t,  \* \ \ \  • 55 • 65 i  i_  NODULE  3.4  \ \  \•  * 35 o <5  z  3  / /  TRANSFORMATION  TrontformoTion  Fig.  //  ///  z  o  //  Typical  DIAMETER  d«IO,mm  Inverted Cumulative  Distribution  graph  Fig.  3.5  (Ref.62).  Nodule Diameter (d) versus T r a n s f o r m a t i o n Time (Ref.62)  ~  T  Steel 60  1  i  i  1  i  -  AjO-SiC  Tronsformotion  temperoture, 720*C  60  -  40  -  A  20  -  -  dx lo'mm 1  0  40  50  60  70  TIME  Fig.  3.6  Number o f n o d u l e s  90  (t), s  (&N) p e r u n i t v o l u m e  v e r s u s R e a c t i o n Time ( R e f . 6 2 ) .  (t)  74 nucleation seen ing  Table  The  3.2  and  results  the  nucleation  isothermal  3.1.2  Any structures structure  had of  pendence  of  pearlite  to  the  of  a l l  to  good  seems  to  to  the  exhibit  temperature  explain  into  carbide the  procedures  agreement.  increase  the  account:  cementite-ferrite  2)  three  can  Increas-  nucleation  a  time  (Fig.  be  rate.;  dependence 3.6).  Pearlite  take  colonies  temperatures;  rate  theory  the  temperature;  seen  transformation  Growth  of  demonstrate  u n d e r c o d l be  Also at  on  rates.  spacing  magnitude  and  the  3)  the  kinetics  of  pearlite  the  the  pearlite  lamellar and  growth  rate  in  growth  rate  inhibition  of  the  de-  transformation  the  increase  and  1)  of  aggregate  on  of  growth  growth  of at  with  lower  alloy  additions.  The  theoretically cant  6 9  logical  ,  Zener  lamellar  be  have  7 0  importance,  The can  experimentally  calculations  Brandt,  the  and  main  growth  and  factors by  carried  H i l l e r t .  the  structure  demonstrated  been  by  been  the  many out  and  an  influencing using  been  by  and  S c h e i l ,  from  its  both s i g n i f i -  6 8  techno-  reprodueabi1ity  area  the  examined  workers  Apart  7 1  uniformity has  has  of  interest.  pearlite  approximate  growth  growth,  rate equation  5 that  was  derived  by  Mehl  and  Hagel  based  of  on  diffusion  75  TABLE  3.2  Comparison Using  Temperature  3  of  Nucleation  Different  Methods.  Nucleation Method  1  Rates  Determined  6 2 , 6 3  - 3 -1 [ n u c l e i , mm s ) Johnson-Mehl 2 Equation  Rates Method  °C  720  2.7xl0  _ 1  9.4xl0"  712  4.2xl0  _ 1  5.0xl0  2  _ 1  -2  5.0xl0"  1.8xl0  702  5.0  1.0  685  33  18  2.8  20  9  667  110  by  2  _ 1  76 geometry, across  diffusion  the  of  pearlite  At.any  given  carbon  and  concentration  gradients  interface.  temperature,  D — S  a  6  AC . . . ( 3 . 2 ) P  where the  S  is  the  interlamellar  concentration  carbon with  in  austenite.  experimental  experimental  data  deductions.  The  is  not  dependent  factor. side one  of  Since  expect  dependent  gradient  term  and  AC  but  produces  the  therefore rate  grain  size  the  can or  any  temperature  the  growth  rate  With  increases  of  decreases  relatively  very  same  shape  as  D  the  3.2  right-hand  pearlite  S  Equation  structural  dependent,  and  well  certain  from  other  c Dc  agree  decreasing  and  of  not  seen  on  is  AC  diffusivity  possible  be  quantities  are  well.  makes  as  pearlite,  the does  3.2  as  is  equation  growth on  a n d -D  of  This  data  a 1.1. o f  Equation  would  ture  gradient-  spacing  to  clearly be  tempera-  temperature  the  decreases.  But  p  rapidly  and  tends  to  measuring  the  growth  dominate  the  growth.  The has on  been  usual to  specimens  temperature.  way  of  metallographically reacted The  for  time  a  rate  measure  series of  of  change  the  times of  rate  of  largest at  the  pearlite nodules  constant nodule  size  77 is  taken  as  the  growth  until  mately  20%  and  growth,  rate.  impingement  This  occurs,  transformation. 60  Lange-Weise  (Fig.  method  which  Growth,  can  is  rates  only  measure  usually  at  approxi-  measured  by  Scheil  56  3.7),  Hull  and  Mehl  (Fig.  (Fig.  3.9)  a l l  demonstrate  3.8)  and  37 Hull,  Colton  and  Mehl  stant  growth  rate  at  an  isothermal  a  transformation  con-  tempera-  ture . Growth inverse  rate  cumulative  the  same  ing  horizontals  graph  curvegrowth, the  time  mined  in  can  be  in  tion  d  to  versus the  determined  t  can of  curves  (Fig.  inverse also  indirectly (Fig.  3.5)  obtained  plots.  by  ( 1 );, a g a i n  the  traditional  maximum  nodule  Table  However  an  in  graphical of  nodules  of  3.3.  of  effect  growth  can  be  seen  by  rate  will,  influence  constant  rate  examining  ). a n d . t h e t i m e s e a l e  well  determination  on the  both  factor,  Z  by  construct-  size  determining rates  with  growth size  that  can  be  where  (2),  paradox the  determined.  isothermal  shape  rates  method  only  Johnson-Mehl  the  deter-  apparent  such  the  From  distribution  Growth  compare  from  3.4).  drawn  cumulative  be  these  The  growth 3.1  rate  be  way  seen  e x i s t s ti.n t h e growth  of  rates  this  also  distribution  derivative  determined, as  can  factor  transformacurves.  The  (Equation  78  Fig.  3.7  Nodule grain  Diameter sizes  (Ref.  v e r s u s R e a c t i o n Time f o r 60).  different  79  C  /  t  it  TlMC IU  Fig.  3.8  Nodule  Radius  3.9  Nodule  Radius  te  v e r s u s R e a c t i o n Time ( R e f . 5 6 ) .  25  Fig.  i*  HCONDS  SO  75 100 SECONDS  versus' Reaction  125  150  Time ( R e f . 3 7 ) .  80  TABLE  3.3  Comparison Two  of  Different  Temperature °C  Growth  Rates  Methods.  '  6 2  Obtained  1  Using  6 3  Growth Method  by  Rates  (mm/s)  Method  2  l.OxlO"  4  5.0xl0"  4  2.2xl0"  3  712  l . l x l O "  702  4. 3 x l 0 ~  685  1.6x10"  675  2. 2x10"3'  3.8xl0"  3  667  2.5xl0"  3  5.4xl0"  3  655  2.7xT0~3  8.5xl0"  3  648  3.3xl0"  1.lxlO"  2  4  4  3  3  81 A shape  change factor  of  the  be  seen  has  a  as  in  from  reaction from  over  a  a  00  3.3 on  result be  seen  'c'  to  'a'  that  the  size.  range  a  variation  to  change  (Fig.  increasing  overall In  important  greater  in  can  from  grain  more  will  to  curve  the  far  much  0.3  effect  decreasing is  that  Equation  similar  rate  G  the  the  reality  grain  the  shape  3.10).  It  growth  transformation  variable,  than  of  can rate  kinetics  though,the  for  it  can  size,  by  alloy  growth  be  varied addi-  tions.  3.1.3  Additivity Due  and  growth  reactions reaction tion is  rates, it  is  rate  product  the  to  the to  independent  mathematically  necessary  is  only  present  additivity  variation  a and  to  show  function the  describe  that of  of  the  the  reaction  nucleation  non-isothermal  instantaneous  amount  of  transforma-  temperature.  This  requirement.  32 To siders  define the  is  obtained  in  Fig.  T1  where  f  is  the  concept  simplest by  3.11. the  additive,  type  combining The  to  law  of  of  is  additivity  Christian.  non-isothermal  two  assembly  kinetic  fraction  transferred is  the  isothermal is f  transformed.  for  It  then  second  temperature  the  course  of  is  T^.  that  treatments,as  f^ ( t )  a  the  reaction  transformed -  con-  at a  If  temperature  time very the  transformation  shown  at  t-j,  where  quickly reaction 1  0  will  be  83  100  j  0  R E A C T I O N T I M E  Fig.  3.11  Schematic r e p r e s e n t a t i o n  100  * 501o2  of  the  p r i n c i p l e of  ( s e c )  additivity.  84 exactly had  the  same  a l l been  taken  i f  the  transformed  at  to  produced  as  in  produce  time  t^  fraction  at  the  at  the  course  f  For  example,  amount  of  =  f ^ t )  =  f  time  then  to  at  T2,  in  is  the  of  transformation  t > t  'f  a  '  = t  a 2  time  transformation  as  the  ,  . . . ( 3 . 5 )  ]  taken  at  composite  will  t  the  ...(3.4).  time  produce  the  is  2  f-, (t»j )  reaction  - t ] )  2  transformation  responding  T-| ,  t><<t ]  ( t + t  ta-|  of  t  fz(tz)  =  the whole  i f  amount  i f  at  ,  of  2  Therefore  same  W and  T,,.  transformed  to  produce  and t ^  same  amount  process in  a  -  i f  the  + t  2  1  of  the  fixed cor-  transformation  above,  be p r o d u c e d  t  is  2  a  an  amount  'f  '  time,  reaction  is  additive If  t  1  / t  . . . ( 3 . 6 )  2  *a2  !JL t  An  additive  to  reach  by  adding  a  +  al  -  t  thus  amount  fractions  !  . . . ( 3 . 7 )  a2  reaction  specified the  ^hl  of  of the  implies  that  the  transformation time  to  reach  total  is this  time  obtained stage  i sothermal ly tion  of  the  until last  the  sum  equation  reaches: to  any  unity.  time  The  generaliza-  temperature  path  is:;  t dt  where the  t ( T )  time  equation this  is  to  the  'fa'  can  relationship  dependent  only  be  the  time  to  stage  non-isothermal  derived  will  . . . ( 3 . 8 )  hold  if  if  the  ,  and  reaction.  Equation  only  'fa'  3.6  is  1.  Fraction  2.  Temperature  rate  that  reaction  any  rate  transformation may  be  for  a  is  function  expected  Both  a  function  only  to  be  the  written:  of  of  volume  (3  temperature  fraction  only  and  transformed,  g(f) can  can  be  be  additive.  Avrami  shown  Consider  9)  is  equation  and  the  Johnson-Mehl  equa-  72 tion  is  which  41 = H±X dt g(TT h(T)  and  transformed  suggests  instantaneous  where  is  This  true  reaction  t  upon:  Christian the  isothermal  for  only  1  to  be  the Avrami  X  =  of  this  type.  equation,  l-exp(-bt  n  )  .Equation  2.5  86 where  n  ~  constant  b  =.  function  of  temperature  only  R e a r r a n g i ng log  (1-x)  =•  =  t  Differentiating  with  -bt  n  n / ' ° g p ^  respect  to  't'  ( i . e .  Equation  2.5)  n -  v- n b . t  e  J n-1  (l-x)c-bn)  [ gn- )] " lQ  x  1/n (l-x)(n).(-b) .[log(l-x)] n : ( - b )  n  "  1  rt  1 / n  (3.10)  n-1 ^1-x)  =  hog(l-x)^  MT) g(x):.  In  the  Johnson-Mehl  X = 1  -  equation:  exp(-|  NG3t4)  where n  =  4  b  = - | NG  and  to  be  additive  if  N  , and  ;hence G  are  the  J  M. e q u a t i o n  functions  of  is  expected  temperature  alone  87 1 8 Avrami kinetics  suggested  could  be  that  predicted  non-isothermal using  transformation  isothermal  kinetic  data  N if  the  ratio  of  remained  a  reaction  (i.e.  tion).  the  nucleation  constant  This  that  over  the  they  have  condition  was.  rate  to  the  temperature the  same  termed  the  growth  range  rate,  of  g,  the  temperature  varia-  "isokinetic  condi-'  tion".  pp Early that ing  the  nucleation  isokinetic  that  this  and  growth  condition  condition  was  observations  did  too  not  hold.  OC  '  showed  Cahn  restrictive  recogniz-r  proposed  the  35 concept  of  pearlite  reaction the  grain  site  reaction,*,  exhausted  and  early  the  saturation; exclusively  available  (Fig.  3.12).  boundary  function  of  function  only  transformed  slabs  temperature of  and  that,  grain  boundary  nucleation  sites  very  was  consisted  of  observed  a  Growth  transformation  He  thus  temperature therefore  Growth  that  and  the  early  of  being  the  in  the  factor  widening only  reaction  instantaneous  satisfied  reaction,"!  dominant  essentially  pearlite. ensured  the  the  of  a  was  a  fraction  additivity  c r i t e r -  ion . Cahn test  the  suggested  went site that  on  to  propose  saturation with  .a  a  series;  condition.  partially  of  c r i t e r i a  that  Metal, 1 o g r a p h i c a l l y  transformed"•specimen,":  iif  would he i t  .is  88  o o s  'i 0  Fig.  3.12  Graph showing  I  I  •  L_  0.2  0.4  0.6  0.B  VOLUME-FRACTION  TRANSFORMED  fraction  of grain  by p e a r l i t e  as a f u n c t i o n  transformed  in a Fe-9Cr-lC alloy  12 h r s . a t 1 2 0 0 ° C  of  (Ref. 36).  boundaries  occupied  volume-fraction austenitised  for  89  possible  to  tion  beginning  per  was;  grain,  see  one  pearlite to  occur.  t  is  the  is  the  time  implies  a  ±  grain  to  second  of  rates  for  basis  grain  shape  sites  as  a  nucleation  grains  equally  large  space.  A  array  and  so  diameter  of  volume, of  follows:  site  at^least';one~nodul e ; ,  for  model  that  the  site  and  the  by  Cahn,  grain  edges  and  § This  a  faces  are is  the  area  on  the  number of  grain  on  on the  available  34 Fisher.  assumed  to  so  they  that  be f i l l  centered-cubic are  on  (111)  designated 3215).  of  and  were  body  based  calculated  arranged  (.Fig.  calculated  was  Clemm  square  faces  austenite  and  saturation,  energetics  austenite  faces  square  rate  transformation.  sites  developed  parent  the  growth  )  saturation.  specific  hexagonal  between  length  of  the  tetrakaidecahedra  distance  unit  of  50%  is  tetrakaidecah.edra-i.-s  oriented  planes,,  satura-  . . . (3.11  G  c r i t e r i a  nucleation  The  on  site  Q.5  size,  complete  condition  Cahn's  of  Based  grain,  ,-  n  ^ d d  per  if  G  where  nodule  On of  the  (100)  planes. D,  the  the  grain  basis  grain  surfaces  The  of  corners, as  a  90 c [  number  of  grain  corners]  ,  mm  L [  length  of  D grain  edges,-,  R  mm-  c r  surface  S|_  l|/mm  ...(3.12)  3  J  8 ^  m/mm  3  . . .  (  3  .  1  3  )  D  area  3-  3.35 2 3 " —g—mm /mm  _  n  J  M  /- , ...(3.14)  / M M  mm  The  site  saturation  N  >  2.5  c  for  corner is i t e "  N  for  edge  site  N  for  surface  After  >  the  active  >  laws  growth  X  specific  sites  \ D  become  ...(3.15)  saturation.  10  3  6 4 D  6xl0  3  ...(3.16)  ,=  _G_ 4 D  . . . (3.1  7)  saturation.  establishing  kinetic:  for  saturation  site  the  c r i t e r i a  were sites,  that  the  easily are  obtained  grain  l-exp(.-2SGt)  reaction  was  site  depending  boundary  saturated,  on  whether  surfaces,  . (3.18)  91 or  grain  edges,  X >  or  grain  ...(3.19)  l-exp(.-TrLG2t2)  corners, ..  Cahn tions  did derive  with  tures,  very  based  on  a  reaction  low n u c l e a t i o n Johnson  equation rates,  and M e h l ' s  for  e.g.  transforma-  at  analysis  .(3.20)  high  of  tempera-  time  depen-  19 dent  nucleation  condition  there  Thus tion  and  the  behaviour 1)  The  general the  of  the  in  the  state  of  stated  the  a b i l i t y  (N/6  phenomenon., of  thereby  of  even  local  for  site on  to  =  2)  as  constant) For  steels,  is  the  site  permitting  saturation.  to  predict  data  this  the  relationship  temperature  majority  that  understanding  their  condition  nucleathe  continuous follows:  is  not  pearlite  saturation  the  a  is  a  application  of  undertaken  to  principle.  thesis the  and  constant  phenomenon,  this  h,e  pearlite,  observed  investigate pearlite  possibility  isokinetic  additivity  In  was  principle from  generally reaction  but  current  growth  additivity  rates,  metal 1 ograpb.i c work  nucleation  reaction  for  a  and  growth,  eutectoid  was  aspects  plain  carbon  of  the  steel  and  92 to  test  the  ability  of  various  criteria  the a d d i t i v i t y  for establishing  principle  for  the  the  applic-  pearlite  reaction.  3.2  and  PROCEDURES  Experimental  determination  growth  pots as  EXPERIMENTAL  using  the  previously  diameter, constant of  rates  was: d o n e  same  1-2  mm t h i c k ,  temperatures  specimens  pearlite.  These  graphically  in  Chapter  2.  samples  of  then  these  Hull,  reaction  flat  driving  Tfie  reaction  nucleation  nose  to, the of  The  high  of  1 0 mm  reacted  obtain  range  up  a  at  number  t o 20%  metallo-  employed  by  S c h e i l and  and the  CO  and R i d l e y N,  and the  and 690°C  temperature,  t h e TTT  diagram  was 5 m i n u t e s  resulting  range  Brown  growth  rate  low  (690°C),  temperatures,  and  were  diagram  treatment  austenitising  temperatures  rate  640°C  th.e TTT  portion  austenitising  temperature.  of  be e x a m i n e d  and Mehl  temperatures  portion  force.,  Colton  the  corresponding  force,  to  salt  procedure  series  times  in  O "7  establishing  Two  A  the method  rn  for  treated  samples were  different  could  nucleation  treatment  th.e t r a n s f o r m a t i o n  and u s e made  Lange-Weise,  pearlite  heat  and heat  disc-shaped for  covering  the  on s a m p l e s  equipment  described  of  used,  driving and  high  (640°C).  at  peak  isothermal of  grain  G  93 sizes,  obtained  A ing  nital  2%  the  can  be  etching  the  following  prefetching  prior  being  solution  of  15  minutes.  to  reveal  A  2  g A  the  kinetics treatment  grain  mounted,  the  picric swab  manually  on  specimen  using  size  acid,  etch  with  distribution  unit  area,  and,  Zeiss was  these  Schwartz  for  reveal-  same  as  that  described  in  Chapter  was  required  and  the  g  2%  counting  representative  size  the  employed  for  used  to  2.  The  revealing  pearlite.  After  were  treated  in  a  NaOH  and  100  ml  water  for  was  then  carried  out  nital  boiling  nodules.  nodule  the  25  2.3.  was-  specimens  pearlite  pearlite  Table  details;,  reaction  austenite  cold  in  procedure  microstructural  determine  both  seen  was  photo-micrographs, optical  carried were  procedure  .of  microscope.  out  for  corrected  procedure,  performed  to  each  using obtain  A  ; .each particle  specimen the the  per  Sch.eil.-and number  of  3 nodules/mm seen  on  .  Table  austenitising  An  example  3.4 at  for  the  950°C.  of  the  correction  reaction  procedure  temperature  Corresponding  64;Q°C  nucleation  can and  rates 3  were  obtained  versus  from  reaction  N  graphs  of  the  number  of  nodules/mm  t i m e . n o Td huel e ss l o p eCsA v eorfa g et h se lsoep e cwas u r v et as k e ng a vf oer reactions with increasing 3 mm . s c ; nucleation rate.)  be  T A B L E 3.4  Correction  P r o c e d u r e t o D e t e r m i n e Number o f N o d u l e s P e r U n i t  Number o f N o d u l e s O b s e r v e d on P o l i s h e d 640°C, A u s t e n i t i s i n g Diameter(mm)  12.5xl0"  Number o f p a r t i c l e s per mm2 Number o f p a r t i c l e s with actual d = 62;$xlO mm  135  Corrected no.  135  2  Temperature 25xl0" 110  2  Surface.  Reaction  Volume  From  Temperature  950°C. 37.7xl0"  2  95  50xl0" 55  2  62.5xl0"  2  15 25  9  108  91  Number of p a r t i c l e s with actual d = 50x10~ mm  50 75  z  133  Corrected no.  101  Number of p a r t i c l e s with actual d = 37.5x10"^ mm  76 102  127  Corrected no.  81  Number of p a r t i c l e s with actual d = 25x10"^ mm Corrected no.  115  Measured d i s t r i b u t i o n  135  110  95  55  15  Corrected d i s t r i b u t i o n  . 115  93  102  75  25  Number o f p a r t i c l e s per unit volume Total number o f , p a r t i c l e s per mm  9200  3720  2720  1500  400  93  1 7 , 5 4 0 1  U3  -1^  95  salt  The  pearlite  pot  heat  times  of  up  growth  treated  to  rate  was: d e t e r m i n e d  specimens  approximately  that  from  had been  20-30%  of  the  similar  reacted  total  for  trans-  37 formation. of  the  The  largest  isothermal The  standard  method  individual  transformation  alternative  of  measuring  pearlite  nodule  time  used.  was  measuring  procedures  as  a  two  rates  check  used  on  the  techniques.  cumulative  by  This  reaction.  struction  of time  reaction  3.3  3.3.1  AND  nucleation  '  nodule  each were  function  of  and  were  also  obtained of  by  diameter  of nodules mm  v  for  r  s  u  s  trans-  the  versus e  the  inverse  isothermal used  examined,  con-  isothermal i  s  o  t  h  e  r  m  a  l  DISCUSSION  Nucleation The  plots  formation  o  f  main  number  time  individual  method  nodules — mm . s.  of  reaction  ^  of  obtaining  of^oduTes  isothermal  of  Rates  mm c a n be s e e n  number im-i^.— the  of  values  for  curves  number  a  time.  RESULTS  from  the  of  the  as  construction  curves  These  plots  and  of  involved  distribution  the  and R i d l e y  magnitudes  formation  reaction  Brown  diameter  CO  C p  growth  the  . i . e .  on  v  e  r  s  Fig.  u  s  temperature  nucleation  hermal The  curves  , nucleation and the  i s : o t  3.13.  transformation ... the  the  , rate.  grain  t  r  a  slope  n  s  of  rate . the  gives T  L  The size  . influence on  the  96  10*  oo  o  ICf  Reaction Temperature: 640°C Austenitising O 800°C O 840°C A 950°C • II00°C  A  O A  Treatment  °8A to. 1  to  ,o  5  X) o  •  10'  • • •  10  ±  10 Time  Fig.  3.13a 1  Nodul e - ran t , reation  versus at  Reaction  640°C.  30  20 (s)  Time f o r  isothermal  pearlite  t±  I0 h 5  o o  Number of Nodules  v.s  Time  mm 10  REACTION TEMPERATURE  : 690°C  AUSTENITISING TREATMENT O 800 U 840 A 900 O 950  IO  E E  io  10  °C *C  °C °C  z  10  •  10  200  400  J . U D  Nodules mm  versus  Reaction'Time  800  600 TIME  rig.  A  1000  ( Sec )  f o r isothermal  pearlite  reaction  a t 690°C  1200  98 resulting  nucleation  Increasing tion  rate  the  on  the  where  the  i n i t i a l  small  and  large  The  alternative  tive  distribution  constant for  t h  e  The  time  number  of  can  the  of  approach  the  size also  derivative e  be  Table  the  in  metallo-  Fig.  are  3.5.  nuclea-  observed  shown  lines  on  3.15,  yields  3.14  compared  of  for  >  t  graph  h  e  n  u  l  e  t  cumula-  values  be  on i  o  n  seen  Fig. r  a  t  e  of  time  distribution  can  a  at  reaction  line c  nucleation  inverse  3.16)  size  each  the  the  the  equivalent  |  reduces  determining  resultant  nodules^  examining  specimens.  (Figs.  an  by  reaction  vertical  curves  This  size;  of  method  obtaining  grain  seen  grain  This  size  drawing  ' d ' .  be  photomicrographs  grain  requires  3.17.  pearlite  stages  rate  given  can  dramatically.  graphically  quired  rate  for  on  T  a  Fig.  3.17 .  re-  gives n  e  mm comparison  of  be  Table  seen  in  With A.S.T.M. length  nucleation  increasing 3,  and  the the  and  grain  dramatically  the  nucleation  obtained  agree  reasonably  grain  number  are  greater  3.6  rates  of  grain  surface  reduced.  rate.  undercooling  size  and  it  A.S.T.M.  a  the unit  explains  can  larger  on  be  both  the  seen  driving  methods  can  well.  corners,  area,  This  Also  from  by  9.1 grain  edge  volume decrease  that  force  to  with for  basis, in  99  TABLE  3.5  Austenitising Temperature °C  Pearlite  Nucleation  A.S.T.M. Grain Size  Average Grain Diameter (mm)  Rate  Data  Nucleation Rate 640°C  = 1  Nodules 3, mm / s 690°C  800  9.1  15  10,400  995  840  7.8  27  18,000  382  900  7.4  30  —  950  7.3  32  1100  3.0  200  7xl0"2  3,800  16xl0"2  6  -  Fig.  3.14a  Pearlite  nodules  to approximately reaction 7.3  Fig.  3.14b  nodules  to approximately reaction  10% t r a n s f o r m a t i o n  temperature  Magnification  Pearlite  i n specimen p a r t i a l l y  Grain  at the size,  isothermal A.S.T.M.  X160.  i n specimen p a r t i a l l y 10% t r a n s f o r m a t i o n  temperature  3 Magnification  of 640°C.  transformed  X160.  of 640°C.  Grain  transformed  at the size  isothermal A.S.T.M.  101  Fig.  3.15  Inverse  Cumulative  transformation  at  Distribution 640°C.  graph f o r  isothermal  Fig.  3.16  Inverse  Cumulative  transformation  at  Distribution 690°C.  graph f o r  isothermal  i  1  i  1  1  •  •  A  —  • • TD A  A  O  O  o  A  ,3  10  O  O  A O  Austenitising  10'  - O  Reoction  A 2xio"  O i  10  i  Number o f n o d u l e s obtained  640°C,  3XI0~  2  O  4XI0"  2  H  »  II  M  Distribution  Grain  Size  ASTM 7 . 3 .  H  1  9  10  (s)  volume  graph.  H  1  versus  by c o n s t r u c t i n g v e r t i c a l s t o t h e  Cumulative  Dia. n  1  per unit  nodule  2  O  8 Time  -  Temp:950°C  Temp:640°C  -2 1X10 mm  •  3.17a  —  Reaction  Reaction  Time  Inverse temperature  i  60  to a>  40  O  2 XI0 mm  O  4XlO~ mm  A  8XlO~ mm  •  l2XI0 mm  O  2  2  II  II  2  o  -2  l6XI0" mm  II  2  o  30  A Z W  20  -  H  \J  T3  -  nodules diameter  •i  O  O -  Austenitising Temperature : 950°C Reaction Temperature : 6 9 0 ° C  50 E  i  1  o" o  o  10  A  o  A A  0  A A  i 300  n  n » D  LL—=u 500  i 400  ^ 600  0  •  o 1  700  Time (s) 3.17b  Number o f 690°C,  nodules per u n i t  Grain  S i z e ASTM  7.3.  volume  versus  Reaction  time.  Reaction  temperature  T A B L E 3.6  Comparison o f N u c l e a t i o n Rates O b t a i n e d U s i n g and M e t a l l o g r a p h i c M e t h o d s  A.S.T.M. Grain S i z e  Isothermal Reaction Temperature °C  Nucleation Rate -nodulesx mm 3.s K  Graphical  Method  Source  ;  7.3  640  3800  7.3  690  16xl0"  7.3  640  3000  7.3  690  8xl0~  Metallographic Metallographic  2  1080 s t e e l Graphical used i n (For the s m a l l e s t s i z e d i s t r i b u t i o n ) t h i s work Graphical  2  L i t e r a t u r e Values 5%  640  47  5Js  690  5.9xl0"  650  36  4Ji  689  6.2xl0"  0-1  685  18  Metallographic 2  Metallographic Metallographic  2  Metallographic Graphical  0.78 C Plain Carbon Steel  3 7  0.80 C Plain Carbon Steel  3 7  0.81CPlain Carbon Steel 3 7  o  nucleation,the order  of  nucleation  magnitude  larger  isothermal  reaction  results  of  nucleation  workers  using  3.3.2  largest  the  size can  and be  seen  rates  pearlite  The rate  i s  to  f  number  at  least  obtained  Also  on  an  at  the  690°C  Table  3.6  are  made  by  different  methods.  determined  from  nodule  diameter  versus  3.18).  The  on  plots  the  isothermal  influence  the  of  pearlite  of  grain  growth  rate  3.7.  way  construct  of  is  were  (Fig.  Table  curve,  640°C  measurements  temperature  alternate  distribution Q  time  in  that  different  Growth  reaction  than  rate  Rates.  transformation  at  temperature.  Growth  single  rate  of  determining  horizontals (Figs.  nodules;  T  h  f  to  3.15, s  y  i  e  l  the  the  inverse  3.16), d  s  &  r  e  pearlite  at 1  a  t  i  growth  cumulative  constant o  n  S  :  h  i  p  values  b e t  ween  mm reaction  time  and  distributions; curves rates  give are  the  more  measurement seen  in  growth methods  of  Table rates of  (Fig.  nodule  3.19).  pearlite scattered the  3.8;  diameter  growth than  largest this;  measured  by  measurement.  The  for  time  specific derivative  rate.  The  nodule of  size  these  resulting  growth  those  obtained  by  direct  pearlite  diameter  as  can  table  also  various;  contains  other  the  workers  be  pearlite using  both  28  24  1  1  Reaction Temperature.- 6 4 0 ° C Austenitising Treatment  — h  20  I  16  2  •  1  O  800°C  O  840°C  A  950°C  •  II00°C  -  •  -  CM I  8  - 12  •  -  -  CP  0  —  °  A A  A  o 1  0  I  1 10  40  Time (s) Fig.  318a  Largest  Diameter  versus Reaction Time.  (mm/s) f o r d i f f e r e n t  grain sizes. 1  o  The s l o p e o f e a c h c u r v e g i v e s t h e g r o w t h  Reaction temperature,  640°C.  rate  25 Reaction  Temperature-. 690°C  Austenitising O A • •  _ 20 6 E  CM  o  X Q  I  Treatment  •  800°C 840°C 900°C 950°C  J  15  •  CD  10  A  o  b  to  o  cn  o _l  O 0  Fig.  A  o  o  &  •  A  1000  100 Time (s)  10  3.18b  A  Largest Diameter versus Reaction Time.  Reaction  temperature,  690°C.  o co  109  TABLE  3.7  Pearlite  Growth  Austenitising Temperature °C  Rate  A.S.T.M. Grain Size  Data  Pearlite Growth Rate(mm/s) 640°C 690°C  800  9.1  10.6xl0"3  5.4xl0"4  840  7.8  8xl0"3  9.8xl0"4  900  7.4  950  7.3  6.7xl0"3  3.0  10.7xl0"3  1100  2.9xl0~4  3.3xl0~4  no  Austenitising Temp: 9 5 0 ° C Reoction T e m p : 6 4 0 ° C O I 0 4 nodules/mm 3 ^N>d O  I03  A  500  •  I02  • •  E E CM  «  O X  A o  • A o  4 A o  •o .A  O  o  o 0  O  0  10.  8  7  (s)  Time Fig.  3.19a  Nodule  diameter(d)  versus  Reaction  by c o n s t r u c t i n g h o r i z o n t a l s Distribution  graph.  rate  Reaction  (mm/s).  A.S.T.M.  7.3.  to  Slopes of  the  time  Inverse  each curve  temperature,  (t),obtained  640°C.  Cumulative  gives Grain  growth Size,  Austenitising  • 1  Temperature:950°C  Reaction Temperature : 69Q°C O  5 0 nodules/mm 10  •  2  3  O A 5  |  £N>d  A ~  • • A A  •  O  O  A O  O 400  300  Nodule diameter(d) Grain S i z e ,  versus  A.S.T.M.  7.3.  Reaction  i  500 Time (s) time  o  O _L  3.19b  O  (t).  Reaction  7(  600  temperature,  690°C.  TABLE 3.8  Comparison o f Growth Rates Obtained by Using M e t a l l o g r a p h i c and Graphical A.S.T.M.:. " .Grain..::. Size  Methods. Reaction Temperature  °c  Growth Rate (mm/s)  Source  Method  3  Largest Diameter  3.3xl0~  4  Largest Diameter  640  8.0xl0"  3  Largest Diameter  1080 steel used  690  9.8xl0"  Largest Diameter  in this work  7.3 & 7.8  640  5-45x10"  Graphical  7.3 & 7.8  690  l-20xl0"  Graphical  7.3  640  6.7xl0"  7.3  690  7.8 7.8  4  3  4  Literature Values 3  Largest Diameter  0.78 C Plain Carbon  8.5xl0~  4  Largest Diameter  Steel  650  3.6xl0~  3  Largest Diameter  0.80 C Plain Carbon  4  689  4x10"  4  Largest Diameter  Steel  0-1  685  1.6xl0"  3  Largest Diameter  0.81 C Plain Carbon  OTI  685  2.2xl0"  3  Graphical  5  640  6.2xl0~  5  690  4  3 7  3 7  c*  SteelT62  ro  113 An ments  important  is  the  austenite grain growth  relative  grain  sizes  of  size.  by  the the  from  the  growth  rate  measure-  of  growth  rate  cfrom  independence For  the  exaroi n e d , l i t t l e  rate  determined  conclusion  large  if  pearlite.  any  effect  The  isothermal  range  growth  reaction  of  austenite  is  seen  rate  is  on  the  largely  temperature.  This 2  result Hull,  i s et  The  consistent al .  1.  7  size  of  Pearlite be  located  an  approximately  at  therefore  to  be  Pearlite  the 4  can  in  the to  have  be  made  after  of  the  as;  grain  grain  intersections  grain  nucleate  into  1  of  at the  these  size  et  and  large  2  and  size  3.20a). sample  grain  grains  (Fig.  growth  have  inter-  adjacent  different  have  (spherical),  (Fig.  shapes  tend  nucleate  grain-sized  material. unit  at  the  available  Fewer volume  of are  in  these  high the  morphologies  energy, small  high  avai1able  and  3.20b).  f o l 1 ows: will  a l . ,  an  sample  growth  grains  large  intersections  per  small  small  non-spherical  for  Dorn,  3.20:  surrounding  only  nodules  sites  of  6 0  Fig.  multi-grain  energy  .  work  equi-directional  reasons  summarized  in  or  tendency grow  can  3  all  sections,  possible  in  nodules  greater  The  1.  shown  to  a  al  photomicrographs  nodules  Pearlite  et  previous  observations  the  into  the  Sch.eil  samples  growing 2.  and  following  examination grain  3  with,  in  the  Fig.  3.20b  Pearlite (A.S.T.M.  nucleation 3).  Mag.  in large X  230.  grain  size  specimen  115  coarse grained sample, requiring the nodules to nucleate at two grain intersections in the large grained material. 2.  T h e one-sided Chemi-spherical) growth of pearlite nodules nucleating on the grain boundaries that could be due to lower interface mobility in one direction, suggests the existence of a special orientation relationship*as observed for nodules on the flat grain boundaries of the larger grain size  (Fig.  3.20b).  On the other hand for nodules nucleating at multi-grain intersections (i.e. either corner or edge) in the smaller grain-sized sample, a special orientation relationship would be highly unlikely, resulting in predominantly spherical growth ( F i g . 3 . 2 0 a ) . ' ' 5 8  6 4  7 4  T h e effect this difference in nucleation and growth morphologies would have on the kinetics of the isothermal pearlite reaction for small and large grain sizes cannot be separated from the effect of differing nucleation rates for the two reactions. R o t h , the lower nucleation rate and the non-spherical nature of growth in the large grained samples will result in a slower isothermal reaction rate. 3.3.3  Additiyity It  Has  been  and  Si te  Saturation  demonstrated  consistently  that  the  116 Avrami'.;  equation  isothermal  is  pearlite  able  to  express  transformations, 38  vity  principle  data  the  to  be  isokinetic  v a l i d .  the  assuming  39 49 72 » > • > . ,  condition  kinetics the  of  non-  adch'ti-  73 p  as' d e f i n e d  by  thiS'Same  Q r  Avrami,  i . e .  N the  proportionality  range,  has  been  3.9,  consistent  This  is  a  with  rate  with  the  smaller  The  site  20 Cahn of  found  over not  to  earlier  consequence  nucleation with  of  of  a  given  reaction  be  valid  as  more  increasing  change  in  saturation  shown  observations  the  the  rapid  concept  as  in  (Fig.  Table  1.11).  increase  temperature growth  temperature  as  in  the  compared  rate.  described  by  J.  W.  35 '  the  was  also  additivity  examined  to  p r i n c i p l e .  explain The  the  number  a p p l i c a b i l i t y  of  available  3 nucleation  sites/mm  determined  using  space  f i l l i n g  An derived sites  can  Since  i t  rates  for  was  made  seen,  Cahn's  the  Cahn, be  is  any  austenite  austenite  grain  grain  size  shape  can  model  of  be a  tetrakaidecahedra.  assessment by  for  of  the  based  seen  in  site  on  the  Table  experimentally  each using  saturation, nucleation  3.10  for  c r i t e r i a rate  corner  impossible  to  for  site  nucleation  s i t e ,  the  the  nucleation  rate.  As  corner  experimentally  determined  total  saturation.  measure  individual  specific  nucleation comparison  can  be  nucleation  rate,  117  TABLE 3.9  Test of I s o k i n e t i c  Condition N - Constant £ -  Austenitising Temperature °c  TABLE 3.10  A.S.T.M. Grain Size  3 Nodules/mm mm/s 690°C  N  E  640°C  800  9.1  98xl0  840  7.8  225X10  950  7.3  57xl0  184xl0  4  4  39xl0  4  4  0.05X10  4  4  Cahn : N u c l e a t i o n Rate C r i t e r i a N N N  s  > 6xl0 > 10 > 2.5 3  e  c  3  G/D' G/D G/D  Austenitising Temperature °c  Reaction Temperature °c  2.5  G/D  4  o  (1/mm .s)  Total Nucleation  /nodules \ mm 3 . s 1  690  26,675  995  640  528,000  10,400  690  4,610  382  640  37,500  18,000  900  690  895  0.07  950  690  787  0.2  640  15,900  640  16.7  800  840  1100  Rate  3,800 5.6  118  2n which  is  those  required  much  N  lower  for  was  is  firmed  by  a  site  the  per  unit  for  determination  on  a  consideration  grain.  be  for  specimens  per  to  In  that  reacted  transformation without  is  far  based  unit  The  a  on  volume  measured results  of  partially  given  on  exception,  Table  for  a l l  one  take  one  consideration  nodule,  to  consume  this up  early  to  of  This  l i k e l y  can  the  one  time  of  nodules done  be  15% seen  examined,  never  expression  con-  diameter  approximately  cases  of  per  number  pearlite  of  on  speci-  was  the  grain  It  is  of  calculation  the  site  one  nodule  3.11.  based half  the  number  mathematical  metal 1ographic  of  transformation  true.  from  Cahn  the  15%  determining  per  derived  nucleation.  attaining  pearlite  from  c o n d i t i o n o f one n o d u l e also  grain  boundary  of  than  therefore  photomicrograph  approximately  seen  experimentally  or  lower  and  criterion  can  volume.  saturation edge  calculation  and  consistently  for  per  grains  is  required  reacted  i t  '  metal 1 o g r a p h i c a l l y  austenite  that,  '  s  corner  is  nodule  (Fig.3.21),  N  based  partially  grain  +  e  other  saturation  mens  N  than  Cahn's  pearlite  +  c  3 Rfil  the  attained.  for  this  i t  would  grain:  ^ - 2 . <_ 0 . 5  . . .(3.11)  d This  would  results  of  hold  if  site  saturation  this  calculation  can  be  was seen  taking to  place.  suggest  The that  3.21  Initial  nucleation  metallographically to  approximately  rate  i n terms  of  n u m b e r  i n specimen t r a n s f o r m e d  15%  transformation.  °f  n o d u 1 e  grain  Mag.  s>  partially X  600.  120 TA B L E  3.11  Initial  Nu c l e a t i o n  Rate  in  Terms  of  Nodules;/Grain  Austenitizing Temperature °C C.5 m i n )  I.s,oth.e.rmal Transformation Temperature  8Q0  840  950  1100  TABLE  3.12  Cahn  A.S.T.M. Grain Size  Initial Nucleation Rate 3 (no/mm )  Initial Number Nodules, Grain 1/0-88  640  9.1  10,400  690  9.1  995  1/141  640  7.8  18,000  1/32  690  7.8  382  1/44  640  7.3  3,800  1/19  640  3  : Early  Site  Austenitizing Temperature °C C5 m i n )  1/6  6  Saturation  G t  Criterion  0.5 d  640°C  690°C  800  4.5  3.0  840  2.5  5.4  9Q0.  -  11.0  950,  2.1  12.4  2.4  -  11Q0.  121 this  condition  for  site  saturation  is  not  realized  (Table  3.12).  In  the  light  of  conclude  that  and  saturation  site  principle evidence  these  s i n c e the  should that  the  isokinetic  has  not  calculations  not  be  taken  would  condition place,  applicable.  additivity  one  principle  does not  the  Yet  to hold  additivity  there  can  have  be  is  direct  applied  38 39 4 0 72 successfully It  is  to  a  sufficient  work  but  "effective  were for  measure  formation sites,  would if  not  as  and  a  the  rate  appear.  coming  centres  The  total of  thus  '  '  model"  principle  An  alternative  principle,  termed  investigated.  determined  which  new  long  sites  to i s ;  fraction If  as  an  of  rate  trans-  there are a v a i 1 a b l e  rate  be  nucleation  centres  approaches  question  growth?  additivity  '  Avrami's  saturation  condition.  nucleation  volume  both  '  Saturation  As  available  exhausted.  "site  the  was  transformation  the  the  at  that  additivity  experimentally  the  to  the  Site  experimental  bution  for  cooling behaviour.  fact  necessary  saturation"  of  expect  the  Cahn's  condition not  product  this  However,  recognize  Effective An  continuous  applying  site  3.3.4  a  to  condition"  requirement  is  predict  important  "isokinetic were  to  need  not  completion,  decreasing  what  decrease.  is  the  transformed  overwhelming  in  one numbers,  contriof  the  fraction  lateof  122 the  transformed  early  nuclei,  tion  rate  very  l i t t l e  To  be  to  calculate at  formation  in  Johnson-Mehl quantities  Mehl  was  The  time  volume times  was; c a r r i e d  growth  2.4),  rates  the  the  appropriate  determination  of  results 640°C  for and  values  the  can  determined  the  reaction  for  its the  the  isothermal  690°C  with  in  n  -  be  10%  the  re-  equation)  reaction  seen  does  isothermal  determined  and  J.M  confirm 4,  and  isothermal  A  4  these  Johnson  transformed.  (originally  The  transformation.  5  equation  examined.  includes  experimentally  the  trans-  rates.  approximately  Johnson-Mehl  tures  the  the  the  to  exponent  pearlite  of  growth  2.4)  using  and  nodules  course  and  of  out  and  from  corresponding  exponent  of  progress  nuclea-  place.  characterize  (Equation  very  transformed  the  nucleation  the  the  contribute  taken  during  equation  (Equation  nuclei  have  to  of  measured  contribution  (J.M)  express  late  will  the  The  temperatures  the  growth  fraction  of  times  made.  volume  terms  and  time  the  necessary  fraction  sulting  constant, total  of  experimentally  is  equation  volume  result  it  calculation  reaction  the  different  to  nucleation  the  saturation"  transformation,  A  a  the  site  nucleating  is  although  may  "effective  phase  on  Table  that not  3.13.  the characterize  reaction  tempera-  123  TABLE  3.13  C a l c u l a t e d Values* of in  the  A u s t e n i t i s i ng Temperature °C  Johnson-Mehl  the  Time  Exponent  Equation.  Time Exponent for 640°C Isothermal Reaction Temperature  Time Exponent for 69Q°C Isothermal Reaction Temperature  800  1.4  3.2  840  1.4  2.2  900  -  3.9  950  2.4  3.5  2.8  -  1100  C a l c u l a t i o n s  based  on  t  =  0  at  t  124 The volume  • i n a b i 1 i.ty  fraction  satisfactory derivation 1.  The  " , of.-  the  transformed  assumptions.  of  the  rate  of  J.M.  • J.M  was The  due  to  and  to  predict  certain  assumptions  equation  nucleation  equation  the  non-  made  in  the  growth  are  are: the  rate  of  constant. 2.  The  growth  of  pearlite  nodules  is  spherical  and  constant. 3.  The  nucleation  Although last  assumption,  definitely grain is  the  therefore  be  nucleation actual  a  able and  random  f i r s t in  the  incorrect.  corners,  To  is  grain  two  assumptions  ease  of  Pearlite edges  use  growth  transformation,  the  nucleation).  are  pearlite  nucleates .grain  and  preferentially  at  that  better  "inhomogeneity  the is  boundaries  equation to  reasonable, nucleation,  transformation  J.M  rates an  the  and/or  heterogeneous  to  (homogeneous  and  product.  includes  simulate factor"  the defined  as:  T  has eous  been  calculated.  versus  ^homogeneous V heterogeneous The  schematic  comparison  of  heterogeneous  reactions  is  Fig.  made  in  homogen3.22.  125  HOMOGENEOUS ( Unit  HETEROGENEOUS  NUCLEATION  ( Unit  Volume )  ° o o  After  1  After  2 sec.  ^real  =  ®»  <S  o  ^ex  Fig.  3.22  =  ^real  Schematic r e p r e s e n t a t i o n of reaction  Volume )  sec.  ^ex  o ° o°°  NUCLEATION  kinetics.  homogeneous  and  heterogeneous  126 As  can  will  be  be  seen,  slower  greater  the  rate  of  the  than  that  of  a  impingement  The  time  reaction  in  the  dependent  would  be  inhomogeneous  homogeneous  expected  to  of  have  the  Because  extensive  'impingement  at  e a r l i e r  stages  the  the  homogeneous  not  be  of  very  the  slow  and  and.where for  between  would  determined  with  the  salt  tion  and  growth  and  The  rates  of  (Equation 'b'  was  (i.e.  2.5),  used  real)  to  in  would  much to  volume take  in  Fig.  take  the  rates  place  rates  of  should  completion be  very  untrans-  place and  i n . :  The  heterogen-  with  rate terms  follow  r e a c t i on .  used n  in =  the 4,  the  the  Johnson  (As The  of  generated nuclea-  and  determine  the  Mehl the  assumed  Avrami  empirical  kinetics  kinetics  determined  to  reaction.  equation.) of  reaction  k i n e t i c , data  experimentally  homogeneous  their  not  reactions  inhomogeneous  were  progress  deriving  would  homogeneous  isothermal  (Equation .2.4),  when  of  isothermal  shown  the  growth  rates  equation  the  be  to  diminish.  using  pot.  not  and/or  homogeneous  were  an  towards  reaction  would  the  form  heterogeneous  the  there  reactions  Both  where  for  transformation,  Similarly  nucleation  difference eous  the  different.  reaction  formed  of  due  reaction.  'I'  3.23. the  reaction  inhomogeneous  variation  reaction  by  J.M  equation  constants  'n'  inhomogeneous  and  Fig.  3.23  Predicted variation with  of  the  percent transformed  of  "Inhomogeneity pearlite.  Factor",  I,  128 The  effect  at  different  in  Fig.  The  could  ' The  grain  be  due  the  located  intersections  .i  :  2.  of  these  in  turn  tion the  the  overall  the  haviour.  to  in  are  will  large far  nodules  from  competing  (Fig. deviate  could  a),  the  be  nodules (as  that  explained  may  seen  more  where  nuclea-  impingement  rise  to  of  relatively  growth.  be on  used Fig.  largest  from by  proxi-  specimens,  impinging  samples  give  explained  of  This  relative  Greater  significantly  availability  grained  spherical  behaviour 3.24  the  small  effects  nodules  20).  grained  will  of  grain  material.  growth  start  apart.  of  multi-grain  number  Duetto in  seen  predicted  greater  grained  F i g . , 3.  sites  nodules  abnormal  This  to  as  the  spherical  effect:  deviations  two  graph  seen  than  pearlite  These of  r e l a t i oh  nucleation  sites  larger  are  increases  be  range  number  such  fine  the  total  to  can  factor"  considerations;  larger  the  pearlite  rapidly  a  in  impingement  the  of  the  due  in  of  For  increases  earl i er  from  possible  sites  sites  "inhomogeneity  temperatures  energy  approximately  mity  640°C  twq  exhibit  The  some  to  effect;  high  the  departures  possibility  at  on  reaction  observed  nucleation  sizes  size  isothermal  3.24.  behaviour 1.  of  to  explain  3.24.  In  grain the  the  size  expected  nucleation  the  samples be^ effect  0  Volume Fig.  3.24a  Experimental reaction  Fraction  variation of  temperature of  Transformed T ,  reaction  f o r the isothermal  1 0 0  5 0  Volume 3.24b Experimental  (%)  640°C.  0  Fig.  100  5 0  Froction  Transformed  variation of-,'I.1,  temperature of  690°C.  for  (%)  the isothermal  130 which  would  increase  the  The nodules  rise  to  non-spherical  inhomogeneity  contribution nucleating  calculated this  give  by  in  using  equation  see  V  o/20  to  the  total  f i r s t  Z  volume  201  of  equation;  Appendix  _  4 90  that  would  factor.  the  the  growth  transformed  the  (For  the  reaction  of  was  derivation  of  1.)  ^ -  9 0  U  *  ...3.12  W  Zf V  90  t  90  where ^o/20  :=  Volume  nucleating 90% Vgg  .=  in  the  nodules  f i r s t  20%  at  transformation.  Total  volume  transformed  at  90%  transformation.  By  using  tion total  was  the  time  carried  volume  isothermal  of  to out  on  pearl i te  Table  isothermal  to  nodules  transformation). seen  90%  reaction  determine  the  nucleating  in  transformation  The  3.14.  transformation  results  for  the  of  range  temperatures  a  calcula  contribution the  ( i . e .  this of  for,V'gQ„  f i r s t t^Q  -  20%  sizes  investigated.  can and  the  of  time  calculation grain  to  the to be  131 TABLE  3.14  The  Influence  Temperature  (C o n t r i b u t i o n t o t h e T o t a l 1/ o l u m e T r a n s f o r m e d , by [M o d u l e s w h i c h N u c l e a t e d i n t h e F i r s t 20% o f t h e . " r a n s f o r m a t i o n , a t 9Q% r o t a l Volume T r a n s f o r m e d (%)  on  of  Grain  Volume  Size  and  Isothermal  Contributions.  Austenitising  Reaction  Temperature  Temperature  f°C).  (°C)  85  950  690  93  840  690  94  800  690  88  900  690  97  11QQ  640  %  950  640  82  840  640  86  800  640  Reaction  132 In 20%  of  a l l the  volume  instances reaction  transformed  clearly  support  haviour  as  the  to  percent the  reduce growing should  sites  develop  using  In  the  the be  adjacent  to  85%  in  the  f i r s t  80%  of  the  The  results  experimental This  process  total  be-  means  dominates  that, the  structure  minimize in  case,  to  to  the  reduce existing  also  encourage  test  its  the  an  areas the  phase  with  positive  increasing states  effect,  increased  to  nodules.  pressure thereby  saturation" for  site  to t o t a l  nucleation this  con-  saturation".  criterion other  The  of  Therefore  "effective  to the  temperatures.  effectiveness  that  i . e .  adjacent  temperature,  contribution  process.  a  principle  this  lower  validity  important  transformation  Chatelie'r.'s  austenite  with  pearlite  transformation  to  for  to  the  the  the  Le  this  "effective-site  formulated  in  of  transformed  nodules.  An  By  volume  of  amount  would  the  coupled  move  would  dition  be  should  reduce  result  least  saturation".  consideration  greater  stabilizing  of  growth  can  transformation.  the  at  transformation.  site  dependent  would  system  to  description  observation  the  pressure  90%  nucleating  event.  thermodynamic Due  at  "effective  transformation  nodules  contribute  the  temperature  This  the  can  be  grades  of  volume  at  steel. 90%  133 transformation, the  of  nodules  transformation  ship  can  be  in  obtained  nucleating  in  e q u a t i o n 3.12 t h e (Appendix  the  f i r s t  following  20%  of  relation-  A2):  1 2 0 — 0 •' 3 8- t g Q •  . . . 3 . 1 3  where  This tested 3.15)  all for  literature The  a  to  20%  transformation  t  g 0  :  time  to  90%  transformation  site  saturation"  isothermal different that  reaction the  sufficient  additivity  time  show  investigated, is  ..  experimental  for  results  isothermal  2 Q  "effective  for and  t  for  results  kinetic grades the  condition  principle.  for  site the  this  and  has  study  reported  steel  total  temperatures  "effective  of  data of  criterion  in  been (Table the  ( J a ' b l . e 33.; 1 6')..  range steel  of  grain  sizes,  compositions  saturation"  criterion  applicability  of  the  134 TABLE  3.15  The  "Effective  Site  Saturation"  Criterion,  t?n • • x ^ J : r 90  Reaction Temperature °C  0  -  3  '  8  Values  Results  Determined  in  Study.  this  Grain Size A.S.T.M.  *20  Calculated  for  t  the  90  for  1080  *20 t  Experimental  Steel  Used  Source  90  640  9.1  3.22  8.38  0.38  640  7.8  3.08  8.93  0.34  640  7.3  6.8  640  3  31 . 7 6  690  9.1  51  690  7.8  119.0  690  7.4  690  7.3  12.7  0 . 53  55.14  0.58  1080  1 01 . 4  0 . 51  Steel  243.0  0.49  918  2275  0.40  847  2301  0 . 37  .1  135  TABLE 3.16  Calculated values of ^ >_ 0.38, t h e " E f f e c t i v e t S i t e S a t u r a t i o n : C r i t e r i o n , f o r Isothermal g  o  R e a c t i o n s Reported i n L i t e r a t u r e . Reaction Temperature °c  Grain Size A.S.T.M.  t  20  t  9Q  t  20  t  90  Source  500  51s  4.2  5.5  0.76  0.78XC plain  540  5%  4.8  6.5  0.74  carbon s t e e l  600  5k  6.4  10  0.64  630  5k  8  20  0.40  650  4%  23  42  0.54  660  B,k  70  92  0.76  690  4*s  700  1100  0.63  662  5  4.7  691  5  80  689  1  715  3 7  0.80%C plain carbon steel  37  0.72  1.10XC s t e e l  3 7  200  0.40  0.57%C s t e e l  3 7  35  46  0.75  0.932X s t e e l  3 7  -  95  200  0.48  SKD-6 s t e e l  670  -  34Q  830  0.41  615  5-7  3.25  5^4  0.62  0.82XC plain  630  5r7  5.6  9*8  0.57  carbon steel  660  5-7  32.4  72  0.45  670  5-7  58  163  0.36  6.5  3 8  72  136  Chapter  4.1  SUMMARY The  examine in  1.  and  the  sizes  this  conclusions  interpretation  kinetics  eutectoid  grain in  ;  following  discussion  4  of  of  steels;  transformation  the  resultsj  experiments  nucleation  plain-carbon and  summarize  and a  performed  growth  wide  of  range  temperatures  of  were  to  pearlite austenite included  study:  The  Avrami  equation 39  Tamura  et  can  used  be  a l ,  2.5),  as  modified  by  40 '  to  (Equation  to  include  characterize  a  the  grain  size  pearlite  parameter, transforma-  tion X 2.  =  1  The  measured  'm'  in  of  tion  tion  magnitude  site it  sites  2.8,  should  confirm  edges;  exp(-b  Equation  pearlite  tions  -  tn ——) dm  that  of  ...Equation.2.8 the  indicates  dominate. the  size  exponent  that  edge  nucleation  Metal 1ographic  predominant  is  austenite  grain  is  d i f f i c u l t  to  by  grain  corners  separate  metallographic  pearlite and/or  these  observation,  two  observanucleagrain nuclea-  137 The  austenite  can  be  grain  growth  characterized  by  kinetics  using  the  of  this  1080.  steel  relationship  49 developed  by  Alberry  et  a l . ,  structure  in  the  of  weldmentsv  This  expresses  peak  temperature D3'  the  -  5 7  HAZ  and  I)3/  -460,000 ( -^j  +  existing  which  the  grain  holding =  5 7  /  The  final  to  c r i t e r i a  additivity  N  micro-  (Equation  size  time  2.98xl0  1000  predict  in  at  2.16).  terms  peak  of  temperature.  exp  1 2  ^ ;t  c „ l i a + 4„„ ...Equation  that  define  principle  the  the  is  o ic 2.15  conditions  applicable,  under  an 1 9  isokinetic and  temperature  saturation  pearlite,  as  of  transformati An  in  of  tinuous  cooling  has  "effective growth  defined  Cahn,  explaining  the  '  by  Avrami  sites  '  of  were  shown  to  be  austenite-to-pearlite  on.  ability  the  by  alternative,sufficient  data  as  aval 1ablelhucleation  outlined  ;tnsufficient  range,  the  been  additivity data  proposed.  site  dominated  relative  from  condition  for  principle  to  isothermal This  saturation" nature  of  insignificance  to the of  the  predict  con-  transformation  condition express pearlite the  applic-  was  the  termed  essentially  reaction  pearlite  and  nucleation  138 event  after  the  Calculations tion  early  based  and growth  rates  contribution  of  f i r s t  the  20% o f  transformed very  at  high;  at  on  stages  of  the  the measured have  pearlite  shown  least  pearlite  that  nodules  nuclea-  the  relative  nucleating  transformation the  transformation.  to  the  in  the  total  end of  the  transformation  80% o f  the  total  volume  volume is trans-  formed.  The  "effective  site  saturation"  has  been  t o be  .a  mitting range  shown the  of  use of  grain  temperatures as  for  principle,  isothermal grades.  ( E q u a t i o n 3.13)  condition  additivity  and s t e e l  per-  for  transformation It  c a n be  a i  summarized  follows:  > 0.38 t  t^Q  4.2  RECOMMENDATIONS  1.  Although able  salt  number  of  cooling  obtained  for  on  very rates  g  have the  specimens a  n  ...Equation  FUTURE  and growth  provide  slow  FOR  pots  equipment  nucleation  to  sufficient,  the  sizes,  criterion  WORK  been  kinetics  involved,  (in  used  accurate  limited  transferring  a  as  the  most  determination due to  they  cooling  the  3.13  order  the  have  of  specimen  25-30 from  of  large  been  rate.  suit-  The Q  shown very  C/s),  one  salt  139 pot  to  another  the  nose  salt  of t h e  formation  initiates  temperature. relation  a  whole  the  and  data  near  which  rates  can  is  could  a  water  could  jets  The  upper  and  the  additivity  studying  the  pearlite  in  in  very  more  lower  small  large  extensive  grained  of  n u c l e a t i o n at" m u l t i - g r a i n  the  curved  grain  pearlite  phenomena pearlite  of  grain  surfaces nodules  departure  nodules•  by  using  spraying  better  of  defined  kinetics  by  of  (A.S.T.M.  (A.S.T.M.'.]).  study  of  and  growth  better  spherical  or  rates.  specimens  the  flat  electrical  the the  intersections,  could from  the  higher  water  boundaries  on  of  nose  applicability  growth  metallographic  TTT  Idisc-shaped  specimens  flat  and  be  grained  of  of  and  could  with  the  cooling  the  cor-  experimental  If  to  and  isothermal  significantly  rapidly  limits  nucleation very  below  an  faster  principle  the  near  trans-  kinetics  two-directional  achieve  the  understanding  achieve  heated  heating,  edges  and  necessity.  be  to  tests  satisfactory  growth  transformation,  resistance  A  cooling  range  specimens  3.  during  fundamental,  cooling  and  impossible;  complete of  isothermal  curve,  nucleation kinetic  technique  2.  makes  Therefore,for  of  isothermal and  TTT  pot  effect effect  grain  morphology  c l a r i f y growth  the of  12),  140 BIBLIOGRAPHY  1.  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Trans. 1983.  Appendix 1  VOLUME CONTRIBUTIONS  147 APPENDIX  1  dx  -i  •  t = o  — — i —  t =• x  Number  of  during  a  —-—'  nuclei  t =  . w h e r e - ! .'• N i s The at  t  N  dx  dx  volume  =  a.^  2  t h e . ; v o l u m e t r i e onti»e l e a t i o n , r a t e .  extended time  t  nucleating *  time  i  t = t-j  of  growth  of  these  nuclei  i s :  Ndx  .  G  3  (t  2  -x)  3  where a  =  shape  factor  4 = y G = Therefore nuclei  f °  r  growth the  nucleating  spherical  growth  rate  (mm/s)  extended  volume  between  t  = o  (V_v)  and t  =  of t-j  growth at  time  of t  =  i s: *1  t, Vp2 e x  = o/t  la '  1  .  G3(t?-x)3Ndx L  o  ^  lx\ -  ( t  2  -  t l  )  4  ]  . . . A l . l  148  The  total  extended  t V  The  3 =  2  ex  N G 1  fractional  nucleating total t  volume  4 *2  ( i . e .  from  t  -  o  to  '  t  transformed  -  ..,AT  volume  between  t  contributed ~  o  volume  and at  t t  « =  by  the  t^, t  2  to i s ;  t  ) ,  2  . 2  nuclei, the  1  2  V e x  o/t  —z  t? — — :  1  -  =  2 V ex  z  2  (t?-t  )4 ...AT. 3  4 (Ref  72)  *2 It  must  be n o t e d t h a t  transformed at of  t=t|,  V  i s not  rather  it  the extended  i s the extended  p e a r l i t e n o d u l e s n u c l e a t i n g between t  g r o w i n g up t o t  = t2.  volume  volume a t t  = 0 and t  =  t2  = 1 and  Thus  t2 V  t0 e > < 0 / t  v since  l  i s considered to  t 2  ex both extended  be e q u i v a l e n t t o  V  t  r u e  ft ) ^ 1'  ,  t v/ 2  true  volumes a r e c o r r e c t e d to t r u e volume a t  t2.  Appendix 2  THE E F F E C T I V E  S I T E SATURATION CRITERION  150  APPENDIX  ex o/t-  t\  2  -  ( t  2  - t  T  )  4  A2.1  'ex  when *1  2  z  "  t  20  =  t  90  and  V  *2 ex^,. o/t  1  0.85  *2 V ex  The  ^effective  site  '90  90.  •t  saturation"  2 Q  )  >  0.85  criterion  is  A 2.2  •90 Therefore ^ 0  ° -  3  8  %  . A 2, 3  


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