Gorni_SFHTHandbook

STEEL FORMING ANDHEAT TREATING HANDBOOK Antonio Augusto Gorni São Vicente SP Brazil [email protected] www.gorni.eng.br This Edition: 24 July 2017 Gorni Steel Forming and Heat Treating Handbook i FOREWORD This is a compilation of some useful mathematical formulas, graphics and data in the area of forming, heat treatment and physical metallurgy of steels. The very first version arose in the early eighties, as a handwritten sheet with a few formulas. Afterwards it was converted to a digital format and eventually posted on-line, hoping that it could be also helpful worldwide. It must be noted that these formulas were compiled at random, generally in a need-to-know basis. So, this Handbook is in permanent construction and very far to be complete. Finally, the author thanks Seok-Jae Lee, Assistant Professor of the Chonbuk National University, Republic of Korea, for his contribution. DISCLAIMER The formulas and information compiled in this text are provided without warranty of any kind. Use them at your own risk! However, any help regarding the correction of eventual mistakes is appreciated. A Work in Progress First On-Line Release: 09 October 2003 Gorni Steel Forming and Heat Treating Handbook ii SUMMARY Austenite Formation Temperature ...........................................................................................................................1 Austenite Grain Size After Heating .........................................................................................................................9 Austenite No-Recrystallization Temperature ..........................................................................................................10 Austenite Solubility Products ................................................................................................................................13 Austenite Solubilization Temperature ....................................................................................................................18 Austenite Transformation Temperatures: Ar3 and Ar1 ............................................................................................20 Austenite Transformation Temperatures: Ps and Pf ................................................................................................33 Austenite Transformation Temperatures: Bs and Bf ...............................................................................................34 Austenite Transformation Temperatures: Ms and Mf ..............................................................................................44 Cooling Rate of Flat Products of Steel ....................................................................................................................60 Critical Diameter – Austenite Hardenability ...........................................................................................................61 Density of Bulk Steel at Ambient Temperature ......................................................................................................62 Density of Bulk Steel at High Temperature ............................................................................................................64 Density of Liquid Steel ..........................................................................................................................................67 Density of Microstructural Components at Ambient Temperature ..........................................................................68 Density of Microstructural Components at High Temperature ...............................................................................72 Dimensional Changes during Austenite Transformation ........................................................................................75 Equivalent Carbon – H.A.Z. Hardenability .............................................................................................................78 Equivalent Carbon – Hydrogen Assisted Cold Cracking..........................................................................................82 Equivalent Carbon – Peritectic Point ......................................................................................................................87 Fe-C Equilibrium Diagram ....................................................................................................................................92 Fe-C Equilibrium Equations in the Solidification and Eutectoid Range ..................................................................94 Ferrite Solubility Products.....................................................................................................................................96 Hardness After Austenite Cooling ..........................................................................................................................98 Hardness After Tempering ................................................................................................................................... 104 ................................................................................................................................................................................................................................... 169 Thermomechanical Processing of Steel ............................................................................................................................................................................ 172 Time-Temperature Equivalency Parameters for Heat Treating ............................. 153 Shear Modulus of Steel and its Phases .......................................................... 105 Hardness-Tensile Properties Equivalence ...................... 129 Relationships Between Chemical Composition x Process x Microstructure x Properties ....... 122 Lattice Parameters of Phases ...................................................................................................................................................................................................................................................................... 133 Schaeffler Diagram............................................................................................................................................................................................... 154 Sheet and Plate Cutting Force and Work ..................................................... 107 Hot Strength of Steel ............................................................................................ 124 Liquid Steel Solubility Products ..................... 156 Solidus Temperature of Steels ................ 161 Thermal Properties of Steel....... 174 Welding Effects ................................................................................. 127 Poisson Ratio ..................................................................................................................................................................................... 128 Precipitate Isothermal Solubilization Kinetics .............................. 179 Young Modulus ...... 109 Jominy Curves ............... 159 Specimen Orientation for Mechanical Testing ................. 189 General Statistical Formulas ......................................................................................................................................... 178 Welding Pool Phenomena ................................................................................................................................................................................................................................................................................ 126 Liquidus Temperature of Steels ............................................................................................................................................................................................................................................... 180 Appendixes Useful Data and Constants ............................................................................................................................................................................................... 182 Unit Conversions ................................... 191 ................................................................................................................................................. Gorni Steel Forming and Heat Treating Handbook iii Hardness After Welding ........................................................................................................................................................................................................................................................................................................................... 163 Thermal Properties of Steel Scale ....................................................................................................................................................................................................................................... ..................................................................... 193 .................................... Gorni Steel Forming and Heat Treating Handbook iv Trigonometry .............................................. K.1 W  30. Empirical Formulae for the Calculation of Some Transformation Temperatures.7 Si  15.7 Mn  16.W.Austenite Formation Temperatures . 721-727. . Part 7.1 Si  6.9 Cr  290 As Ae 3  910  203 C  44. Brandis Ac1  739  22 C  7 Mn  2 Si  14 Cr  13 Mo  13 Ni  20 V Ac3  902  255 C  11 Mn 19 Si  5 Cr  13 Mo  20 Ni  55 V Notation: Ae1: Lower Equilibrium Temperature Between Ferrite and Austenite [°C] Ae3: Upper Equilibrium Temperature Between Ferrite and Austenite [°C] .0 Cu  700 P  400 Al  120 As   400 Ti Notation: Ae1: Lower Equilibrium Temperature Between Ferrite and Austenite [°C] Ae3: Upper Equilibrium Temperature Between Ferrite and Austenite [°C] Alloy Content: [weight %] Observations: . July 1965.5 Mo  104 V  13. Andrews Ae1  723  16.6%C.Both formulas are valid for low alloy steels with less than 0. 203.0 Cr  20. Source: ANDREWS.9 Ni  29.2 Ni  31.38 W  10. Gorni Steel Forming and Heat Treating Handbook 1 . Journal of the Iron and Steel Institute.0 Mn  11. 1 Ni  20.Both formulas were proposed by ELDIS for low alloy steels with less than 0. Gorni Steel Forming and Heat Treating Handbook 2 Alloy Content: [weight %] Source: BRANDIS. . G. H.8 Mn  19. 270 p. Métallurgie Tome I: Métallurgie Physique.6%C. 1982. Collection Scientifique ENSAM.9 Cr  9. 8-10. Rechnerische Bestimmung der Umwandlungstemperaturen von niedriglegierten Stählen. TEW – Technische Berichte.1 Si  11.8 Mo Ae 3  871  254. Eldis Ae1  712  17.4 C  14. 1975. Band 1. Grange Ae1  1333  25 Mn  40 Si  42 Cr  26 Ni Ae3  1570  323 C  25 Mn  80 Si  3 Cr  32 Ni . Source: BARRALIS. .2 Ni  51.7 Si Notation: Ae1: Lower Equilibrium Temperature Between Ferrite and Austenite [°C] Ae3: Upper Equilibrium Temperature Between Ferrite and Austenite [°C] Alloy Content: [weight %] Observations: . & MAEDER. Heft 1. J. Gorni Steel Forming and Heat Treating Handbook 3 Notation: Ae1: Lower Equilibrium Temperature Between Ferrite and Austenite [°F] Ae3: Upper Equilibrium Temperature Between Ferrite and Austenite [°F] Alloy Content: [weight %] Source: GRANGE.46 Ni 2  28 V 2 Observations: . .5 C Si  14.95 Ni  50.8 Mo V  0. p.28 C Ni  6.10 Si Cr  57.4 C V  30.7 Si  18.P. 1984.0 Mn Si   3. Estimating Critical Ranges in Heat Treatment of Steels. 229.7 Al  3.84 Cr 2   3.A.77 Si Ni  0.1 Cr  44. Kasatkin Ac1  723  7. H. 73-75.2 Mo  8. Düsseldorf.1 V  21.18 W  297 S  830 N  11.08 Mn  37. R. Werkstoffkunde Stahl Band 1: Grundlagen.0 Mn Ni  6.46 Mo 2  0.9 C Mo  15. 70:4. Hougardy Ac1  739  22 C  7 Mn  2 Si  14 Cr  13 Mo  13 Ni Ac3  902  255 C  11 Mn  19 Si  5 Cr  13 Mo  20 Ni  55 V Notation: Ac1: Lower Temperature of the Ferrite-Austenite Field During Heating [°C] Ac3: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] Alloy Content: [weight %] Source: HOUGARDY. .80 Cr Ni  27.5 Mn Mo  5. April 1961. Metal Progress. Verlag Stahleisen GmbH. 2%.040%. Al ≤ 0. Calculation Models for Determining the Critical Points of Steel.91 Ni 2  37. 26:1-2.8 V 2 Notation: Ac1: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] Ac3: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] ΔT: Intercritical Temperature Range [°C] Alloy Content: [weight %] Observations: .0%.32 Si Cr  17.0 C Ni  4.33 Cr 2  8. ΔT) are valid within these composition limits: C ≤ 0.7 C Cr  6.0%.5 Nb  5.4 Nb  3.8 Cr  33.0%.0 Al  64. Source: KASATKIN.0%.6 Si Ni  4.8°C Ac 3  912  370 C  27. Ti ≤ 0.2 V  190 Ti  72. B ≤ 0.8 Al  87.93 Mn  26. Mo ≤ 1. Metal Science and Heat Treatment. P ≤ 0. Gorni Steel Forming and Heat Treating Handbook 4 .Multiple Correlation Coefficient r = 0.57 W  332 S  276 P  485 N   900 B  16.5%.96 . et alii.20%.35 Cr  32. Si ≤ 1.83%.5 Mo V   174 C 2  2.83 Mo 2  1. W ≤ 1. Ni ≤ 3.025%.These equations (Ac1. O. V ≤ 0. 27-31. .0 C Si   20.26 Si Cr  64.G.2 C Ni  10.8 Mn Ni  1.8°C .010%.3 C Si  15. Mn ≤ 2. S ≤ 0.4 Mn  27.15%.322 Cr 2  9.0%.Residual Mean-Square Deviation √do = 16. Ac3. N ≤ 0.2 V 2 Observations: . January-February 1984.Multiple Correlation Coefficient r = 0.5 Ni  52.2 C Mn  32.90 Mo 2  1.7 Ni  95. Cu ≤ 1.98 .5°C T  188  370 C  7.Residual Mean-Square Deviation √do = 14.5 V  194 Ti  47.0 Mo  23.3 Si Mo  18.3 Si  6.24 Ni 2  60.97 .80 Mn Ni  40.86 Si 2  0.2 C Mo  55.Residual Mean-Square Deviation √do = 10.0%. Nb ≤ 0.040%.Multiple Correlation Coefficient r = 0.0%.4 C Cr  48. Cr ≤ 2.46 Mn 2  6.82 W  266 P  53. 061 V Notation: Ac1: Lower Temperature of the Ferrite-Austenite Field During Heating [°C] Ac3: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] δ: Length Change Due to Transformation [%] Alloy Content: [weight %] Observations: . & KATOU. 1964.76 Mn  23.6 Mn  10.25%  C  0.0617  0.025 Mn  0.83  32.2%.1%. Lee Acm  224. Gorni Steel Forming and Heat Treating Handbook 5 .233 C  0.027 Cr  0.0 C Cr  6.77 Cr  24.4 C  465.75 C  14.1 Cr 2  7.6  Si  3.7 Cr  19. 0.7 Si Notation: Acm: Upper Equilibrium Temperature Between Ferrite and Cementite [°C] .49 Mo  83. 0.37 V   0.Equation valid within the following alloy range: 0.32 Si  17. 50:4. Source: KUNITAKE.62 V Ac3  920. Kunitake & Katou Ac1  754.9%.7 Cr Ni   0.25 C  17. 0.4  992. 666-668.0 Mo  6.050 Mo  0.9%. T.8 Cr Mo  6. T.1 C 2  46. .99 Si  5.45%.7 C Ni  2.9 Ni  3.7  Mn  1.4%. Effect of Various Alloying Elements on Si-Cr-Mo-V Steel.8  Cr  2. 0.049 Si  0.2  Mo  0. V  0.3 Cr  4.51 Mo  15. Tetsu-to-Hagané.21  394.8 Ni 2  16.40 Mn  54. 998837. Source: PARK.8%. 769-774. 50-128. et alii.5%. Mo  0. Development of Ductile Ultra-High Strength Hot Rolled Steels. Mn  1. Park Ac3  955  350 C  25 Mn  51 Si  106 Nb  100 Ti  68 Al  11 Cr  33 Ni  16 Cu  67 Mo Notation: Ac3: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] Alloy Content: [weight %] Observations: . Ni  2.K. Source: LEE.Equation valid within the following alloy range: 0.7%. S. precision interval:  3°C. Thermodynamic Formula for the Acm Temperature of Low Alloy Steels.Formula specifically developed for TRIP steels.6%.Regression coefficient r² = 0. . 1996. Y. Gorni Steel Forming and Heat Treating Handbook 6 Alloy Content: [weight %] Observations: . 47:5. S.5%. May 2007. Cr  1. ISIJ International. . . & LEE. Roberts Ae3  910  25 Mn  11 Cr  20 Cu  60 Si  700 P  250 Al  Fn Notation: .3%.H. Posco Technical Report.2%  C  0.J. Si  0. 2007.8 V  20 Cu Notation: Ac3: Lower Temperature of the Ferrite-Austenite Field During Heating [°C] Ac3: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] Alloy Content: [weight %] Source: TRZASKA. New York. . J. W. .7 Cr  15 Ni  6. Marcel Dekker Inc.L.25 93 0. Modelling of CCT Diagrams for Engineering and Constructional Steels.15 64 0.8 Mn  18. Trzaska (I) Ac1  739  22.40 128 Source: ROBERTS.: Flat Processing of Steel. Journal of Materials Processing Technology.05 24 0. 504-510.35 117 0.. Gorni Steel Forming and Heat Treating Handbook 7 Ae3: Upper Equilibrium Temperature Between Ferrite and Austenite [°C] Alloy Content: [weight %] Fn: value defined according to the table below: C Fn 0.2 Si  11.8 C  6.3  224.6 Mo  41. 192-193.4 Mo  5 V  28 Cu Ac3  937. et alii.10 48 0. 1988.5 C  17 Mn  34 Si  14 Ni  21.30 106 0.20 80 0. Mn + Cr + Ni  5. 0.5 . Source: TRZASKA. 2016. Cu  0. standard error:  15. Cr + Ni  5. J.04%.61.38%. Trzaska (II) Ac1  742  29 C  14 Mn  13 Si  16 Cr  17 Ni  16 Mo  45 V  36 Cu Ac3  925  219 C  7 Mn  39 Si  16 Ni  13 Mo  97 V Notation: Ac3: Lower Temperature of the Ferrite-Austenite Field During Heating [°C] Ac3: Upper Temperature of the Ferrite-Austenite Field During Heating [°C] Alloy Content: [weight %] Observations: . V  0.Equation valid within the following alloy range: 0. .Ac3 statistical parameters: regression coefficient: r² = 0. Mo  1. Gorni Steel Forming and Heat Treating Handbook 8 . Archives of Metallurgy and Materials.12  Si  1. 0.6. 61:2B.13  Mn  2. .75%. . standard error:  17.3.Additional validity limitations: Mn + Cr  3.30%.80°C.75.68%.85%.05%. Mn + Ni  4. 981-986.6.55°C. Ni  3. Calculation of Critical Temperatures by Empirical Formulae.Ac1 statistical parameters: regression coefficient: r² = 0. Cr  2.06%  C  0.38. 85. 8. 1840-1844.45%.Equation valid under the following alloy range: 0. 0.80%.K T: Austenitizing Temperature [K] t: Austenitizing Time [s] Observations: . Source: LEE.211 d  76671 exp   t  RT  Notation: d: Austenite Grain Size [μm] R: Universal Gas Constant. 29.314 J/mol.25%.: Prediction of Austenite Grain Growth During Austenitization of Low Alloy Steels. Lee & Lee  89098  3581 C  1211 Ni  1443 Cr  4031 Mo  0.20%  Si  0. . 2008.15%  C  0. Gorni Steel Forming and Heat Treating Handbook 9 . Mo  0.Austenite Grain Size After Heating . Materials and Design. Ni  1. Cr  1.73%  Mn  0. 0. et alii.45. S.J.41%. Warrendale. Alloy Content: [weight %] Observations: . p. 2011.: Development of Discrete X80 Line Pipe Plate at SSAB Americas. In: International Symposium on the Recent Developments in Plate Steels.Austenite No-Recrystallization Temperature . RST: Recrystallization Stop Temperature [°C]: austenite recrystallization stops completely below this temperature. et alii. Boratto Tnr  887  464 C  (6445 Nb  644 Nb )  (732 V  230 V )  890 Ti  363 Al  357 Si . Gorni Steel Forming and Heat Treating Handbook 10 . Bai 2001   12  RLT  174 log Nb  C  N eff   1444   14  RST  RLT  75 14 N eff  N  Ti 48 Notation: RLT: Recrystallization Limit Temperature [°C]: full austenite recrystallization between deformation steps is no longer possible below this temperature. Association for Iron and Steel Technology. D. . 13-22. Source: BAI. Proceedings.Neff ≥ 0. Ti  0. 383-390.41  Mn  1. 0. Alloy Content: [weight %] Observations: .002  Al  0.50%. . Maximum temperature at which austenite recrystallizes completetly between two deformation passes. Maximum temperature at which austenite recrystallizes completetly between two deformation passes.: Meta-Analysis of Temperature of No-Recrystallization Measurements: Determining New Empirical Models Based on Composition and Strain. M.17%. et alii. Alloy Content: [weight %]. p. Fletcher Tnr  849  349 C  676 Nb  337 V Observations: .r² = 0.: Effect of Chemical Composition on Critical Temperatures of Microalloyed Steels. Fletcher-Bai .90%.04  C  0.Equation valid under the following alloy range: 0.72 Notation: Tnr: Temperature of No-Recrystallization [°C]. 1988.45%.15  Si  0. Iron and Steel Institute of Japan. Ni  0. Proceedings. . Cr  0. Gorni Steel Forming and Heat Treating Handbook 11 Notation: Tnr: Temperature of No-Recrystallization [°C]. In: THERMEC ‘88.120%. V  0. 0. Arcelor-Mittal Internal Symposium. 0. Tokyo.110%. Nb  0.650%. Source: FLETCHER. F.060%. Source: BORATTO.67%. In: Austenite Processing Symposium. 2008. 1-14. : Modelling of Microstructure Evolution and Properties of Low-Carbon Steels. Alloy Content: [weight %]. 574-580. . 2008. M.36  Notation: Tnr: Temperature of No-Recrystallization [°C]. : True Strain. April 2000. Source: MILITZER. M. Maximum temperature at which austenite recrystallizes completetly between two deformation passes.: Meta-Analysis of Temperature of No-Recrystallization Measurements: Determining New Empirical Models Based on Composition and Strain. 13:2. Maximum temperature at which austenite recrystallizes completetly between two deformation passes. In: Austenite Processing Symposium. 1-14. Gorni Steel Forming and Heat Treating Handbook 12 Tnr  203  310 C  657 Nb  149 V  683 e 0.020%  Nb  0. Alloy Content: [weight %] Observations: .Equation valid for 0.090%. Acta Metallurgica Sinica (English Letters). Arcelor-Mittal Internal Symposium. . Militzer Tnr  893  910 Nb Notation: Tnr: Temperature of No-Recrystallization [°C]. Source: FLETCHER. 55 Narita AlN 6770 1. given in the table below: Precipitate A B Source 7060 1.00 Ashby 9290 4.37 Johansen NbC 7290 3. B: Constants of the Solubility Product.80 Ashby BN 13970 5. Gorni Steel Forming and Heat Treating Handbook 13 . X: Alloy Contents [weight %] T: Temperature [K] C: Constant A.04 Meyer 7900 3.303 RT  2.42 Narita .03 Irvine 7750 1.24 Fountain Cr23C6 7375 5.36 Ashby Mo2C 7375 5.Austenite Solubility Products . General Formula (a M ) m (a X ) n [M ]m [ X ]n  Q  C A log10 k s  log10  log10      B aM m X n [ MX ]  2.303 T Notation: MmXn: Precipitate Considered for Calculation Ai: Activity M. 04 Smith 10800 3.87 7700 3.11 Ashby NbC0. .80 Narita NbN 10230 4.27 Irvine ZrC 8464 4.75 Irvine 15020 3. ks) defines the graphical boundary of solubilization in a graph [M] x [X].26 Ashby 7520 3.36 Ashby 8330 3.The product [M]m[X]n (that is.32 Ashby VC 9500 6.46 Irvine VN 7070 2.96 Nordberg 5860 1.54 Meyer NbCN 6770 2.70 Ashby TiC 7000 2.72 Narita V4C3 8000 5. Gorni Steel Forming and Heat Treating Handbook 14 7510 2.82 Narita TiN 8000 0.18 Mori 8500 2.26 Narita Observations: .aAmBn is equal to one if the precipitate is pure.26 Narita ZrN 16007 4.aAmBn  1 if there is co-precipitation with another element. . Sources: . H. 205:2. . K. 1982. . & ARONSSON. The Solubility of Niobium (Columbium) Nitride in Gamma Iron.Values compiled by Rajindra Clement Ratnapuli and Fúlvio Siciliano from assorted references when not specified above. Dec. 1651-1654. Irvine . B.SMITH. 145-151. Acta Metallurgica.E. T. Physical Chemistry of the Groups IVa (Ti/Zr). 1962. et alii.G.F. Transactions of the Metallurgical Society of AIME. K. Journal of the Iron and Steel Institute. 30.IRVINE. T.JOHANSEN. 239:10. Journal of the Iron and Steel Institute. 1263-1266. 1958.NORDBERG.et alii. M. The Physical Metallurgy of Microalloyed Steels. 1967. Transactions of the ISIJ. 15:5. A First Report on Diagrams for Grain Growth in Welds. . et alii. & CHIPMAN. 363 p. February 1968. .ASHBY. . . R. Solubility and Precipitation of Vanadium Nitride in Alpha and Gamma Iron. . R.J. Transactions of the Metallurgical Society of AIME. 1997. 224:2. Solubility of Niobium Carbide in Austenite.P. May 1975. The Institute of Materials.FOUNTAIN. 737-739 .NARITA.GLADMAN.Gorni Steel Forming and Heat Treating Handbook 15 . Transactions of the AIME. & EASTERLING. 1969-1978. October 1967. London. Feb. Grain-Refined C-Mn Steels. K. 161-182. J. The Solubility of Niobium (Columbium) Carbide in Gamma Iron. Va (V/Nb/Ta) and the Rare Elements in Steel. . 190-191. Journal of the Iron and Steel Institute. Feb.24  4. .26   14  T Notation: T: Temperature [K] .: Thermodynamic Behaviors of Niobium-Carbide-Nitride and Sulfide in Steel.65 [C ]0.J. Mori 10400 log [ Nb ] [ N ]0. Siciliano  12  838 [ Mn]0. 2031-2011. 1965. K. 1967. T. et alii. Grain-Refined C-Mn Steels. 205:2. 161-182. Gorni Steel Forming and Heat Treating Handbook 16  12  6770 log[ Nb] C  N   2.09  T Notation: T: Temperature [K] Alloy Content: [weight %] Source: MORI.26   14  T Notation: T: Temperature [K] Alloy Content: [weight %] Source: IRVINE.594  6440 log[ Nb] C  N   2. . Tetsu-to-Hagané.246  1730 [ Si ]0. 51:11. et alii. 1982. K. 30. Gorni Steel Forming and Heat Treating Handbook 17 Alloy Content: [weight %] Source: SICILIANO JR. F. June 2000. Ph. . 40:6.91 [ Mn]   14  T Notation: T: Temperature [K] Alloy Content: [weight %] Source: DONG.. et alii.N) Precipitation during the Hot Working of Nb-bearing Steels.D.: Effect of Silicon on the Kinetics of Nb(C. & EASTERLING.14  0.X. Thesis.E.F. . McGill University. Acta Metallurgica. M. 165 p. J. Irvine log [V ]  N   3. February 1999.: Mathematical Modeling of the Hot Strip Rolling of Nb Microalloyed Steels. . Dong  12  1371 [ Mn]  923 [ Si]  8049 log [ Nb ] C  N   3.12 Mn  8330 T Notation: T: Temperature [K] Alloy Content: [weight %] Source: ASHBY. ISIJ International. 1969-1978.46  0. A First Report on Diagrams for Grain Growth in Welds. 613-618..35 [ Si]  0. 6 [ Nb ] 231. November 2015.61   1657 [N ] Notation: Td: Dissolution temperature of NbCN [°C] Alloy Content: [weight %] Source: CHASTUKHIN. .73 [Cr ]  17. A. 581-589. B: Constants of the solubility product. General Formula A Td ( 0 C )   273 B  log10 (a A ) m (a B ) n Notation: AmBn: Precipitate considered for calculation Td: Solubilization temperature [°C] ax: Alloy content [weight %] A.V. Formation of Austenitic Structure During Heating of Slabs of Pipe Steels Microalloyed with Niobium.Austenite Solubilization Temperature . et alii.1 3. 59:7-8.6 )  33. given in the table at the topic Austenite Solubilization Products. Chastukhin (Nb Solubilization) [Ti ] Td  log10 ([C ] 203. Uranga (Nb Solubilization) . Gorni Steel Forming and Heat Treating Handbook 18 .48 [ Mn]  2. . Metallurgist.86 [ Si]  1. 0116 C  1.0176  0. Private Communication.0176  0.9122 Nb  ln   60030   20587.3     T  273  Nb sol  0. Gorni Steel Forming and Heat Treating Handbook 19  20587. 2016. Source: URANGA.Neff ≥ 0. . et alii. P.3 Td   273   0.172 N eff  0.08878 Nb  60030 e 12 N eff  N  Ti 48 Notation: Td: Dissolution temperature of NbCN [°C] Alloy Content: [weight %] Observations: .116 [C ]  1.172 N eff  0. This formula was determined using temperature data got from samples cooled directly from hot rolling experiments. Choquet Ar3  902  527 C  62 Mn  60 Si Notation: Ar3: Ferrite Start Temperature [°C] Alloy Amount: [weight %] .0072% N.024-0.004-0.068% C.G. 1. Outubro 1989.Useful range: 0. vol.094% Nb.27-0.Austenite Transformation Temperatures: Ar3 and Ar1 . .0019-0.r = 0. 1.934. . Root Mean Square Deviation = 5°C Source: BLÁS. ABM.054% Al.909 v Notation: Ar3: Ferrite Start Temperature [°C] Alloy Amount: [weight %] v: Cooling Rate [°C/s] Observations: . et alii.0- 35°C/s . Blás Ar3  903  328 C  102 Mn  116 Nb  0. Thus it includes the effects of hot forming over austenite decomposition.000-0. 0. Gorni Steel Forming and Heat Treating Handbook 20 .39% Mn. 0. J.: Influência da Composição Química e da Velocidade de Resfriamento sobre o Ponto Ar 3 em Aços de Baixo C Microligados ao Nb. 0. São Paulo. 0. In: 44° Congresso Anual da Associação Brasileira de Metais. p 11-29. P.This formula was determined using data got from samples cooled directly from hot rolling experiments. Austenitization: 1150°C.: Mathematical Model for Predictions of Austenite and Ferrite Microstructures in Hot Rolling Processes.This formula was determined using data got from samples submitted to a normalizing rolling simulation in a dilatometer.8  251 C  103. Thus it includes the effects of hot forming over austenite decomposition. 7 p. Source: CHOQUET. Kariya Ar3  910  203 C  30 Mn  44. Germain-en-Laye.2 Ni Notation: Ar3: Ferrite Start Temperature [°C] Alloy Amount: [weight %] Source: KARIYA.7 Si  11 Cr  31.5 Nb  202 Ti  9.103. 23.5 Mo  15. 5 min. Thus it includes the effects of hot forming over austenite decomposition. 15 p. 20% strain @975°C. . final cooling.7 Cr  105. Lotter Ar3  834. .697.A1. 10 s holding. European Patent Application EP 2. 1985.5 Mo  204. 10 s holding. Root Mean Square Deviation = 21°C . .r = 0. St. IRSID Report.86 sinh 1 t 8 / 5  Observations: .2 Mn  60.0 B  11. N.5 Si  69.2009. et alii. 20% strain @950°C. Gorni Steel Forming and Heat Treating Handbook 21 Observations: .92.09. High Carbon Hot-Rolled Steel Sheet and Method for Production Thereof. 09 Mn  16. 10 s holding. U. Thyssen Stahl.26 Si  11.13 C  46. 136 p.6 Mn  110. Aufstellung von Regressionsgleichungen zur Beschreibung des Umwandlungsverhaltens beim thermomechanischen Walzen.2  331 C  98. Lutsenko Ar3  913. 20% strain @975°C. Root Mean Square Deviation = 23°C Notation: Ar3: Ferrite Start Temperature [°C] Alloy Amount: [weight %] t8/5: Time Between 800°C and 500°C [s] Source: LOTTER. .7 Mn  65. Technische Bericht. 5 min.7  7.7  207. 10 s holding.2 Si  75.28 sinh 1 t 8 / 5  Observations: . Duisburg.69 Ni Notation: Ar3: Ferrite Start Temperature [°C] Ar1: Ferrite Finish Temperature [°C] Alloy Amount: [weight %] . final cooling.6 Nb  158 Ti  290 V  9.54 Cr  49.4 Cu  76. 20% strain @950°C. Austenitization: 1150°C.54 Cr  108.r = 0. Gorni Steel Forming and Heat Treating Handbook 22 Ar3  884.88. Thus it includes the effects of hot forming over austenite decomposition. 35% @800°C.9 Cr  97. 1988.13 C  14.7 Mo  322.1 N Ar1  741. .This formula was determined using data got from samples submitted to a thermomechanical rolling simulation in a dilatometer. The Definition and Use of Technological Reserves – An Effective Way to Improve the Production Technology of Rolled Metal. The coefficients for Nti (82.004-0. 0. Kommission der Europäischen Gemeischaften. et alii. d: 0.8%) were not significant for a 95% minimum confidence level.949. 0.085% Al.2%). Second Proposal: .6 C  67.4 Mn  1522 S  2296 N ti  1532 Nb  7.9°C.30-1.070-0.4%) and CR (92. d (87.008% N. Abschluβbericht. Luxembourg.The unexpected positive effect of S can be associated to the enhanced nucleation of ferrite at sulphides. . CR: 25-200°C/min . 0.014-0.Useful range: 0.6  190.02-0.91 d 1 / 2  0.49% Si.04-0. Mintz First Proposal: Ar3  833.032% S. 1991.5 Notation: Ar3: Ferrite Start Temperature [°C] Alloy Amount: [weight %] Nt: Total Nitrogen Content [weight %] d = Austenite Grain Diameter [mm] CR = Cooling Rate [°C/min] Observations: . . 0.This formula was determined using temperature data got from non-hot deformed samples. 136 p.r = 0. 0.00-0.003-0.31% Nb. A.75% C. 0.950 mm. Root Mean Square Deviation = 15. Gorni Steel Forming and Heat Treating Handbook 23 Source: LUTSENKO.117 CR Ti N ti  N t  3. .60% Mn. Useful range: 0. 197-203.52% Mn. .55% Al. et alii.0012-0.0 mm.032% S.1-1. Gorni Steel Forming and Heat Treating Handbook 24 Ar3  868  181 C  75. 0.r = 0. B. 0.31-2.1°C. Root Mean Square Deviation = 18. Regression Equation for Ar3 Temperature for Coarse Grained as Cast Steels.014% N. Source: MINTZ.04-0. 0. CR: 10-200°C/min . 0.35 (h  8) Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] h: Plate Thickness [mm] .00-1.75% C. Ironmaking and Steelmaking.22% Si.01-1. Ouchi Ar3  910  310 C  80 Mn  20 Cu  15 Cr  55 Ni  80 Mo  0. 0.042% Nb.0933 CR Ti N ti  N t  3. .5 Notation: Ar3: Ferrite Start Temperature [°C] Alloy Amount: [weight %] Nt: Total Nitrogen Content [weight %] CR = Cooling Rate [°C/min] Observations: .002-0. March 2011.110% P.This formula was determined using temperature data got from non-hot deformed samples and includes TRIP steels. d: 0. 0.001-0.000-0.8 Mn  1086 S  3799 N ti  1767 Nb  0. 38:3. 0.939. 4  516.: Steels: Metallurgical Principles. Gorni Steel Forming and Heat Treating Handbook 25 Observations: .0 Si  274. The Effect of Hot Rolling Condition and Chemical Composition on the Onset Temperature of Gamma-Alpha Transformation After Hot Rolling.Applicable to Plain C Steels.B. C. . et alii. . 22:3. The MIT Press. Source: PICKERING.7 P Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] .1 C  65. 6. Source: OUCHI. F. Proprietary #1 Ar3  879. March 1982. Transactions of the ISIJ. Cambridge. In: Encyclopedia of Materials Science and Engineering. 1986. vol.This formula was determined using temperature data got from samples of Nb microalloyed steels cooled directly from hot rolling experiments. Thus it includes the effects of hot forming over austenite decomposition. 214-222. Pickering Ar3  910  230 C  21 Mn  15 Ni  32 Mo  45 Si  13 W  104 V Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] Observations: .7 Mn  38. . Proprietary #3 Ar1  706.The previous conditioning of the steel samples that supplied data for the deduction of this formula is unknown. Source: Unknown. . Proprietary #2 Ar3  901  325 C  92 Mn  33 Si  287 P  40 Al  20 Cr Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] Observations: . . Gorni Steel Forming and Heat Treating Handbook 26 Source: Unknown.Samples cooled at 20°C/s.The previous conditioning of the steel samples that supplied data for the deduction of this formula is unknown.2 Mn Notation: Ar1: Ferrite Finish Temperature [°C] Alloy Content: [weight %] Observations: .4  350. Source: Unknown.4 C  118. . Santos Ar3  874. Joinville. In: 41° Seminário de Laminação – Processos e Produtos Laminados e Revestidos. Source: SANTOS.915 Mn  23.334 lnCR   0.Applicable to plain C Steels.A.44  512.148 A  1. 10 p. 2004. Associação Brasileira de Metalurgia e Materiais.002 d   A   2 ln   ln2  Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] A: Austenite Grain Size [ASTM units] CR: Continuous Cooling Rate [°C/s] dγ: Austenite Grain Size [μm] Observations: . r² = 0.Equation fitted with data from 94 points. A. .797 C Si  4.551 C Mn  265.: Previsão das Temperaturas Críticas de Decomposição da Austenita em Ferrita e Perlita Durante Resfriamento Contínuo. Gorni Steel Forming and Heat Treating Handbook 27 .075 Si  567.9888 .03 CR  11.0465 C  40.126 C ²  199. Schacht Ar3'  811  255 C  7 Mn  19 Si . 042 d   7. Source: SCHACHT.9888 .7402 3 r Ar1  739  22 C  7 Mn  2 Si Notation: Ar3’: Ferrite Start Temperature without Undercooling [°C] Ar3: Ferrite Start Temperature with Undercooling [°C] Alloy Content: [weight %] vr: Continuous Cooling Rate [°C/s] dγ: Austenite Grain Size [μm] Observations: . 2016. Sekine Ar3  868  396 C  68. K. 174-182.6 Si  36.1 Ni  24.8 Cr  20. 854.: Material Models and their Capability for Process and Materials Properties Design in Different Forming Processes.Equation fitted with data from 94 points. . Gorni Steel Forming and Heat Treating Handbook 28  0.481 2. .This formula was determined using temperature data got from samples cooled directly from hot rolling experiments.Applicable to plain C Steels.8      Ar3  Ar  19 v  0.5 e   ' 0. et alii. Materials Science Forum.1 Mn  24. r² = 0. Thus it includes the effects of hot forming over austenite decomposition.7 Cu Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] Observations: . This formula was determined using temperature data got from samples cooled directly from hot rolling experiments.07 TA  17 vR0. et alii.Precision: ±13°C. et alii.25 Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] TA: Austenitizing Temperature [°C] vR: Cooling Rate [°C/min] . London. .: Thermomechanical Processing of High-Strength Low-Alloy Steels. Kawasaki Steel Technical Report. 1988. Source: SHIGA. December 1981. I. . Shiga Ar3  910  273 C  74 Mn  56 Ni  16 Cr  9 Mo  5 Cu Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] Observations: . Butterworths. 248 p. Thus it includes the effects of hot forming over austenite decomposition. Gorni Steel Forming and Heat Treating Handbook 29 . 97-109. C. Trzaska Ar3  857  257 C  69 Mn  23 Si  38 Ni  20 Cr  20 Mo  34 V  26 Cu  0.: Development of Large Diameter High Strength Line Pipes for Low Temperature Use. Source: TAMURA. : Empirical Formulae for the Calculation of Austenite Supercooled Transformation Temperatures.90%. Gorni Steel Forming and Heat Treating Handbook 30 Observations: . 0.5°C.This formula was determined using temperature data got from non-hot deformed samples. Yuan Non-Deformed Austenite:  D  Ar3  370 exp    325 CR 0. Archives of Metallurgy and Materials.28%  Mn  2.20% Si.38%. 2015. CR: 0.5%.68%.00%. 181-185.038% Nb.000-0.11% C.13%  Si  1.85%. .005% N. V  0. . .21%  C  0.20% Mn. r = 0. Deformed Austenite: .Error = 19. Cr  2. 0.38% and Cu  0. 1.1  5649 Nb  78194 Nb 2  1019  6. Mo  1. Useful range: 0. J.7    Notation: Ar3: Ferrite Start Temperature [°C] CR: Continuous Cooling Rate [°C/s] Nb: Niobium content [weight %] Observations: .5-30°C/s. Ni  3.05%.Formula valid within the following range: 0. 60:1.Base steel: 0. 0. Source: TRZASKA.86. 0. 20% Mn. 0. et alii.000-0.005% N.165 Co 2  0.10 Cr  2.29 Mo  31.05 and Δ.72 Ni  3.151 Ni 3  31.Base steel: 0. CR: 0. See reference for details about the calculation of t0.038% Nb.24 Mn  55.88 Cu  0. Apr.05    Notation: Ar3: Ferrite Start Temperature [°C] CR: Continuous Cooling Rate [°C/s] Nb: Niobium content [weight %] t0.05: Nb(CN) Precipitation Start Time [s] Δ: Residual Strain in Austenite Observations: .196 Co   0.00255 Co 3  28.20% Si. 579-585. 2006.This formula was determined using temperature data got from samples cooled directly from hot rolling experiments.1  6646 Nb  2327 Nb 2  66  1     830 D Ar3  370 exp  t   6. Gorni Steel Forming and Heat Treating Handbook 31     198 CR 0. ISIJ International.348 Cr 2  24.7   0.01 Ru Notation: Ma: Massive Ferrite Start Temperature [°C] Alloy Content: [weight %] . .76 C  247. Source: YUAN. which requires external models.13 C 2  66.11% C. 1.97 Ni 2  0. Useful range: 0. .5-30°C/s.: The Onset Temperatures of  to -Phase Transformation in Hot Deformed and Non-Deformed Nb Micro-Alloyed Steels. Thus it includes the effects of hot forming over austenite decomposition. 46:4. Zhao M a  820  603.Q. 0. X. November 1992. Gorni Steel Forming and Heat Treating Handbook 32 Source: ZHAO.: Continuous Cooling Transformations in Steels. 8:11. Materials Science and Technology. 997-1002. J. . 0. 60:1.4°C. 0. Source: TRZASKA.: Empirical Formulae for the Calculation of Austenite Supercooled Transformation Temperatures.05%.21%  C  0. Cr  2. .00%. Mo  1.25 Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] vR: Cooling Rate [°C/min] Observations: .Austenite Transformation Temperatures: Ps and Pf . r = 0. 2015. .Formula valid within the following range: 0.80.13%  Si  1. 181-185.Error = 19.38% and Cu  0.5%.28%  Mn  2. Gorni Steel Forming and Heat Treating Handbook 33 . Archives of Metallurgy and Materials.68%. Ni  3.90%. Trzaska Ps  780  30 C  65 Mn  24 Si  29 Ni  26 Mo  21 Cu  17 vR0.85%. V  0. J.38%. L.25Cr-1Mo Bainitic Alloy Steel. Si and Purity on the Design of 3. In: Superclean Rotor Steels. 1445-1460. Kang .5NiCrMoV. Metallurgical Transactions A. .Austenite Transformation Temperatures: Bs and Bf . Effects of Mn. Bodnar #1 Bs  844  597 C  63 Mn  16 Ni  78 Cr Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Source: BODNAR. 20A. R.Equation developed using data got from continuous cooled samples. 1991.L. 1989. Source: BODNAR. Bodnar #2 Bs  719  127 C  50 Mn  31 Ni  27 Cr  61 Mo Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Observations: . 1CrMoV and 2. The Design of an Improved High-Temperature 1%Cr-Mo-V Rotor Steel. R. . Pergamon Press. Gorni Steel Forming and Heat Treating Handbook 34 . 331-401. et alii. et alii. 8  193.Reliable chemical composition range: 0. Prediction of Bainite Start Temperature in Alloy Steels with Different Grain Sizes.6 Mo  10. Prediction of Microstructure and Hardenability in Low Alloy Steels. ISIJ International. 125-148. 54:4. Gorni Steel Forming and Heat Treating Handbook 35 Bs  634.62 microns Source: KANG. S.96% Mo max.6 Ni  32. et alii. 1983. et alii.7-1.40% Si max. 0. 0.2 Mn  4.3 Ni  34 Cr  41.7 C  35 Mn  75 Si  15. AIME.91% Mn.Reliable prior austenite grain size range: 6. p.S. Philadelphia. April 2014. In: Phase Transformations in Ferrous Alloys.4 Cr  15.00% C. Steel.4 C 2  31.10-1.36 lnd   Notation: Bs: Bainite Start Temperature [°C] dγ: Austenite Grain Size [microns] Alloy Amount: [weight %] Observations: . 997-999.2 Mo Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Observations: .1 C  102. 1. .6 Si  18.16% Cr max.This is a modification of Steven & Haynes’ formula using isothermal transformation diagrams determined for low and high alloy steels produced by U. .10% Ni max.S. Source: KIRKALDY. Kirkaldy Bs  656  57.17-1. . 2. J. 2. Gorni Steel Forming and Heat Treating Handbook 36 . 84:2. T. Y.56% C.14~4. Correlation Coefficient r² = 0. Tetsu-to-Hagané.14~0. .3 Mn  43.49% Mn.97.These authors concluded that the measured Bs temperature for steels with a greater Ni or Cr content is much higher than that predicted by Steven & Haynes. 0.5°C.9 C 2  28. Lee #1 Bs  984. .Formula specifically developed for TRIP steels.80% Cr.9 C  261. 0. .11~0.7 Si Notation: Bs: Bainite Start Temperature [K] Alloy Amount: [weight %] Observations: . Source: KUNITAKE. & OKADA. February 1998. . 0.23~4.33% Ni. 137-141. Kunitake & Okada Bs  732  202 C  85 Mn  216 Si  37 Ni  47 Cr  39 Mo Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Observations: .34~1. 0.99% Mo.Reliable chemical composition range: 0.4  361. The Estimation of Bainite Transformation Temperatures in Steels by Empirical Formulas.07~1. 0.40% Si.Error = 10. 5%. in 1991. .F. Gorni Steel Forming and Heat Treating Handbook 37 Source: LEE.48% Cr. 2002. 0. .00-4. J. et alii.96% Mo. Lee #2 Bs  745  110 C  59 Mn  39 Ni  68 Cr  106 Mo  17 Mn Ni  6 Cr 2  29 Mo 2 Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Observations: .This formula is based in the equations of Steven & Haynes. Metals Park. . 0. Li Bs  637  58 C  35 Mn  15 Ni  34 Cr  41 Mo Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] .Reliable chemical composition range: 0. 0. including low alloy steels and steels with Ni and Cr contents up to 4.80% C. 1999.K. Journal of Materials Science Letters. Pohang. as well data from many time-temperature diagrams for several steels. which were published in the Atlas of Time-Temperature Diagrams for Iron and Steels by G.10-0.00-1. Posco Technical Research Laboratories Report.26-1. 21:16.63% Mn.67% Si. Vander Voort through ASM International. Empirical Formula of Isothermal Bainite Start Temperature of Steels. et alii. 0. Prediction of Tensile Deformation Behaviour of Formable Hot Rolled Steels.K. Y. Kirkaldy and Kunitake & Okada.34% Ni. 1253-122. Source: LEE.00- 4.13-0. 0. 10 s holding.72.05-0.00-0.4 Mn  38.96 sinh 1 t 8 / 5  Observations: .0 Mo  248 V  3. 661-672.25%.This formula was determined using data got from samples submitted to a thermomechanical rolling simulation in a dilatometer. 20% strain @975°C. Thus it includes the effects of hot forming over austenite decomposition. Thus it includes the effects of hot forming over austenite decomposition. M. June 1998. Root Mean Square Deviation = 27°C Notation: .28% Si. 20% strain @975°C. .02- 0.20-0. 0.8  558 C  96. 10 s holding.1 Cr  76. 29:6. . Austenitization: 1150°C.r = 0. Austenitization: 1150°C.3 Mo  723.12 sinh 1 t 8 / 5  Observations: .8 Mn  26. 35% @800°C.41% C.01% Mn.10-0. 5 min. as most low alloy steels exhibit a content of this alloy element in this order of magnitude. 0.02-3. A Computational Model for the Prediction of Steel Hardenability. 20% strain @950°C.This formula was determined using data got from samples submitted to a normalizing rolling simulation in a dilatometer.98% Cr. . 0. et alii. Source: LI. . 0. final cooling.44% Mo.2 Nb  530 Ti  6. 5 min.7 Si  111. 10 s holding. final cooling.04% Ni.2  180 C  53.9 Cr  72.11% Cu.Reliable chemical composition range: 0. Root Mean Square Deviation = 29°C Bs  705. Gorni Steel Forming and Heat Treating Handbook 38 Observations: .64.9 Si  92. Lotter BS  809. 0. 10 s holding.31-1.r = 0. Metallurgical and Materials Transactions B.This formula is a modification of Kirkaldy’s Bs equation. 0. .It assumes that Si amount is constant and equal to 0. 20% strain @950°C. 1988.Equation determined using data from isothermal transformation diagrams. W.0-5. & HAYNES.0-1. 0. . 136 p.7% Mn. Thyssen Stahl. Aufstellung von Regressionsgleichungen zur Beschreibung des Umwandlungsverhaltens beim thermomechanischen Walzen. Technische Bericht.10-0. 183. Suehiro . 0.0-3. 0.0% Ni. The Temperature of Formation of Martensite and Bainite in Low Alloy Steels. 349-359.Reliable chemical composition range: 0. . 0. Source: STEVEN.2-1. Duisburg.55% C. . U. Gorni Steel Forming and Heat Treating Handbook 39 Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] t8/5: Time Between 800°C and 500°C [s] Source: LOTTER. Steven & Haynes Bs  830  270 C  90 Mn  37 Ni  70 Cr  83 Mo B50  Bs  50 B100  Bs  120 Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Bx: Temperature Required for the Formation of x% of Bainite [°C] Observations: . 1956.5% Cr.0% Mo.G. Journal of the Iron and Steel Institute. A. 0.40% C. 73:8.96% Cr. . September 2002. Tetsu-to-Hagané.11-0.5 Mn Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Source: SUEHIRO.20-1.5 Mo Notation: Bs: Bainite Start Temperature [K] Alloy Amount: [weight %] Observations: . M. Source: TAKADA.3 Mn  36.056 TA  1. Alloy Designing of High Strength Bainite Steels for Hot Forging. Trzaska #1 BS  675  212 C  57 Mn  17 Si  29 Ni  49 Cr  60 Mo  94 V  0.25 . 88:9. Takada Bs  1336  1446 C  62.Reliable chemical composition range: 0. 534-538.6 vR0.31-1. et alii. Gorni Steel Forming and Heat Treating Handbook 40 Bs  718  425 C  42.26% Si. 1026-1033. 0. Tetsu-to-Hagané.Formula developed specifically for forging steels. . June 1987.5 Si  47. 0.50-2. A Kinetic Model for Phase Transformation of Low C Steels during Continuous Cooling.52% Mn.8 Cr  160 V  77. . H. 06%  C  0.Equation valid within the following alloy range: 0. Gorni Steel Forming and Heat Treating Handbook 41 Notation: Ar3: Ferrite Start Temperature [°C] Alloy Content: [weight %] TA: Austenitizing Temperature [°C] vR: Cooling Rate [°C/min] Observations: .85%.6.3.13%  Si  1.00%.13  Mn  2.6°C.12  Si  1. 0.75. J. Source: TRZASKA.38.05%.05%. standard error:  27.5 Cr  31 Ni  55 Mo  41V Notation: Bs: Bainite Start Temperature [°C] Alloy Content: [weight %] Observations: . Source: TRZASKA. 2015.Additional validity limitations: Mn + Cr  3.Regression coefficient r² = 0. Calculation of Critical Temperatures by Empirical Formulae. Ni  3.: Empirical Formulae for the Calculation of Austenite Supercooled Transformation Temperatures.68%.38%. Cu  0. Cr  2.Formula valid within the following range: 0. Mn + Ni  4. 0.28%  Mn  2. Archives of Metallurgy and Materials.5%.53°C.75%. Archives of Metallurgy and Materials. 0. V  0. r = 0.Error = 30.6. Trzaska #2 Bs  771  231. Mo  1. 981-986. Mn + Cr + Ni  5. 60:1. J. Cr  2. . Mo  1.5 .38%. 2016. Ni  3. .04%. 61:2B. .72.68%. V  0.90%.85%. 0.5 C  69 Mn  23 Si  58.38% and Cu  0. 181-185.30%.21%  C  0. . Cr + Ni  5. The Effect of Alloying Elements on the Structure and Mechanical Properties of ULCB Steels. 1993. April 2012. & KAO. 28. van Bohemen Bs  839  86 Mn  23 Si  67 Cr  33 Ni  75 Mo  270 1  exp( 1.C. Materials Science and Technology. Standard Error of Estimate σ = 13°C. Source: van Bohemen. 487-495. Bainite and Martensite Start Temperature Calculated with Exponential Carbon Dependence.M.56 Ni Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Source: WANG.Factors multiplying substitutional elements are less than 10% different from the factors found by Steven and Haynes. Gorni Steel Forming and Heat Treating Handbook 42 . 28:4. Wang & Cao Bs   36.43 Mo  0.Correlation Coefficient R² = 0. P. J. . . 5169-75. S.97. S.6 Mneq Mneq  Mn  3.33 C) Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] Observation: . of Materials Science. . 2001. Z.60 C 2  91. 1992. Zhao #1 Bs  720  585. et alii.1255 Co ²  0.15 Ru Source: ZHAO.: Continuous Cooling Transformations in Steels.000284 Co ³  36.68 Mn  7.02 Cu  46.82 Mn²  0. .37 Mo  9. Nov.34 Ni  6.16 Co  0. 997-1002. J. 5045-5056. Materials Science and Technology. Gorni Steel Forming and Heat Treating Handbook 43 .17 Cr ²   42.06 Ni ²  0. 36. A New Empirical Formula for the Bainite Upper Temperature Limit of Steel. Notation: Bs: Bainite Start Temperature [°C] Alloy Amount: [weight %] . Zhao #2 Bs  630  45 Mn  40 V  35 Si  30 Cr  25 Mo  20 Ni  15 W Source: ZHAO. 8:11. Journal of Materials Science.66 Cr  2.3378 Mn³  66.232 Ni ³  31.63 C  126. 6 Mn  16. K.0010. Ni ≤ 27. .2  302.40. Co ≤ 30.0% Ni and 5.4 Mn  17. Gorni Steel Forming and Heat Treating Handbook 44 . Source: ANDREWS.0 Si  7.W.65.10.6 C Cr Notation: Ms: Martensite Start Temperature [°C] Alloy Content: [weight %] Observations: .Austenite Transformation Temperatures: MS and Mf .4 W  14. Cr ≤ 17.55. Cu ≤ 0. Nb ≤ 0. Si ≤ 3. Mn ≤ 3.98. Mo ≤ 5.5 Mo M s  512  453 C  16.5 Si Notation: Ms: Martensite Start Temperature [K] Alloy Content: [weight %] Observations: .5 C Mn  15 Cr  67.6 Ni  8. 203.3 Cu  8. 721-727.76. V ≤ 4.5 Mo  217 C 2  71.9 Cr  2.10.1 Cr  11. 0.58 Co  7.Formula valid for low alloy steels with less than 0.9.7 Ni  12. Capdevila M s  764. 5. Empirical Formulae for the Calculation of Some Transformation Temperatures.6%C.Equation valid for steels with chemical composition between the following limits: 0.0.0001 ≤ N ≤ 0.9 Ni  9.9. 4.060. July 1965.6 C  30.4 Mo  11. B ≤ 0.0% Cr. Al ≤ 1. Journal of the Iron and Steel Institute.9% Mn.2. Andrews M s  539  423 C  30. W ≤ 12.23. 5. .001 ≤ C ≤ 1. Part 7.4% Mo. F. . 1944. Eichelman & Hull M s  41. et alii. 894-902.067 Co) Notation: Ms: Start Temperature of the Martensitic Transformation [°C] Alloy Amount: [weight %] Source: CARAPELLA.068  C  N   17.C.039 Cr ) (1  0. 1953. Determination of Ms Temperature in Steels: A Bayesian Neural Network Model. .8 (0.9  Ni )  33.6  Cr )  5. 77-104.3 (1. 108. Source: EICHELMAN. G.344 C) (1  0. . Metal Progress. 42:8. August 2002. 45. p.47  Si)  1666.6 8.051 Mn) (1  0.Equation valid for 18-8 stainless steels. L.7 (14. Computing A11 or Ms (Transformation Temperature on Quenching). C. Gorni Steel Forming and Heat Treating Handbook 45 Source: CAPDEVILA.010 W ) (1  0. & HULL.33  Mn)  27.1 (1  0. ISIJ International.016 Mo) (1  0.H.A. 46.018 Si) (1  0.025 Ni ) (1  0. Transactions of the American Society for Metals.8 Notation: Ms: Martensite Start Temperature [°C] Alloy Content: [weight %] Observations: . The Effects of Composition on the Temperature of Spontaneous Transformation of Austenite to Martensite in 18-8 Stainless Steels.7 (0. Carapella M s  496. < 1. Steel Research. < 1.15 ( Nb  Zr )  0. . Source: FINKLER.0 to 14% Cr. Transformation Behavior of High Temperature Martensitic Steels with 8 to 14% Chromium.80% Mn.90% Mo. H.066 (Ta  Hf )  33 Mn  17 Cr  17 Ni  21 Mo  39 V  11W  Notation: Ms: Martensite Start Temperature [°C] Alloy Content: [weight %] Observations: . .2 C  43.Equation valid for steels with chemical composition between the following limits: 0.50% Ni.86 N  0. & MAEDER. 270 p. G.80% C.50% Si. Finkler & Schirra M s  635  474 C  0. 328-336. p.3 Mn  21. Collection Scientifique ENSAM.35~1. August 1986. J. 67:8. Métallurgie Tome I: Métallurgie Physique. Eldis M s  531  391.2 Cr Notation: Ms: Martensite Start Temperature [°C] Alloy Content: [weight %] Observations: . Source: BARRALIS. & SCHIRRA. < 4. Gorni Steel Forming and Heat Treating Handbook 46 .10~0.50% Cr. M. < 0. 1982.8 Ni  16.Equation valid for high temperature martensitic steels with 8. 0. .36  103  0.495 M sjh  0. H.Correction of Jaffe & Hollomon equation considering several other similar equations already published.1 C  38.32  108 M s3  0.8 Mo Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: GRANGE. 467-490.52  1011 M s4 . Gorni Steel Forming and Heat Treating Handbook 47 . R.34  106 M s2  0. Hougardy M s  0. 1946.8  361.M.  VM  1  exp  k ( M s  T ) q  k  0.A.9 (Mn  Cr )  19.10  104 M s  0. & STEWART. Transactions of the AIME. 167. Grange & Stewart M s  537.00095 M sjh 2  40 Notation: Ms: Corrected Martensite Start Temperature [°C] Msjh: Martensite Temperature Start According to Jaffe & Hollomon [°C] Alloy Amount: [weight %] Observation: .4 Ni  27. The Temperature Range of Martensite Formation. CAMP-ISIJ. Gorni Steel Forming and Heat Treating Handbook 48 q  2.16  104 M s2  0. Berlin.4 Mn  7. Springer-Verlag. Steel: A Handbook for Materials Research and Engineering – Volume 1: Fundamentals. et alii.5 Si  30 Al Notation: Ms: Start Temperature of the Martensitic Transformation [°C] Alloy Amount: [weight %] Observation: . Source: IMAI. 1995.90  108 M s3 Notation: VM: Volume Fraction of Martensite Ms: Temperature at Which 1% Martensite Forms [ºC] T: Temperature [ºC] Source: HOUGARDY.08  0. H.76  102 M s  0. 572-575. N.Formula specific for CMnAl TRIP steels. Description and Control of Transformations in Technical Applications. 1992. . Jaffe & Hollomon M S  550  350 C  40 Mn  35 V  20 Cr  17 Ni  10 Cu  10 Mo  8 W  15 Co  30 Al . . 8. 167-200.P. Imai M S  539  423 C  30. Effect of Alloying Element and Microstructure on Mechanical Properties of Low Alloy TRIP Steels. 8 Mn  14.5 Mo  7. . 167.67 lnd   Notation: Ms: Martensite Start Temperature [°C] dγ: Austenite Grain Size [microns] Alloy Amount: [weight %] . & STEWART. Journal of the Japan Society for Heat Treatment.Hougardy proposed a correction to this formula. T. 617-646. Transactions of the AIME. 41. 1946. Kunitake M s  560.8 Cr  19.5 Ni  13.5 Cu Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: KUNITAKE. 164-169. 2001.3 Si  15.1 Cr  10.5  407.A.6 Cu  11. Lee & Park M s  475.7 Mo  9.3 Si  20. Source: GRANGE. Gorni Steel Forming and Heat Treating Handbook 49 Notation: Ms: Start Temperature of the Martensitic Transformation [°C] Alloy Amount: [weight %] Observation: .M. Prediction of Ac1. Ac3 and Ms Temperatures by Empirical Formulas.5 Ni  4.5 Mn  1.9  335.3 C  37. R. H.1 C  34. . Hardenability and Quench Cracking. S. S.5 Si  10. Li M s  540  420 C  35 Mn  12 Cr  20 Ni  21 Mo  10. 423-427.S. K.1836 C  0.J. Metallurgical and Materials Transactions A.J.0017 Ni  0. Prediction of Martensite Start Temperature in Alloy Steels with Different Grain Sizes. 3423-3427. 44A:8. February 2012.0193 Mo nLV  1. C.0231 0. Gorni Steel Forming and Heat Treating Handbook 50 Source: LEE.Start Temperature of Martensitic Transformation Calculated According to Capdevila. A Kinetics Model for Martensite Transformation in Plain C and Low-Alloyed Steels. 43A:12. Metallurgical and Materials Transactions A. .0258 Ni  0.J. & VAN TYNE.0074 Cr  0. .5 W  20 Al  140 V .3108 Mo Notation: VM: Volume Fraction of Martensite Ms: Martensite Start Temperature [K] T: Temperature [K] Alloy Amount: [weight %] Observation: . Lee & Van Tyne  VM  1  exp  K LV ( M s  T ) nLV  K LV  0. Source: LEE.7527 C 2  0. August 2013.0105 C  0. p.4304  1.0739 Cr  0. & PARK. et alii. Gorni Steel Forming and Heat Treating Handbook 51 Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: LI. . Liu .05)  45 Mn  30 Cr  20 Ni  16 Mo  5 Si  8 W  6 Co  15 Al  35 (V  Nb  Zr  Ti ) Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: LIU.0 Mn  24. C. . 293-298. C > 0.05% M s  550  350 C  45 Mn  30 Cr  20 Ni  16 Mo  5 Si  8 W  6 Co  15 Al  35 (V  Nb  Zr  Ti ) . Journal of Materials Processing Technology. Lotter M S  558. Computation of Ms Temperature in Carbon Equivalence Method. 113:1-3.9 Cr  649 Ti . Journal of Liaoning Technology University. 2001. 1998. 556-562. C. A New Empirical Formula for Ms Temperature in Pure Iron and Ultra Low Carbon Alloy Steels.3  312 C  49. et alii.05% M s  525  350 (C  0. 17. C < 0. r = 0. 5 min. Gorni Steel Forming and Heat Treating Handbook 52 Observations: .r = 1. Thyssen Stahl.4 Mn  7. Duisburg. 10 s holding. Austenitization: 1150°C. 5 min.94. 10 s holding. 1988. 20% strain @950°C. Standard Error of Deviation = 1. Mahieu M s  539  423 C  30. Standard Error of Deviation = 9. final cooling. 10 s holding. 20% strain @950°C.5 Si  30.1 Mn  36.7 Cr  71.1°C M s  452. Thus it includes the effects of hot forming over austenite decomposition. Technische Bericht. 20% strain @975°C. 10 s holding. Aufstellung von Regressionsgleichungen zur Beschreibung des Umwandlungsverhaltens beim thermomechanischen Walzen. Austenitization: 1150°C. . U.00.7 Mo  120V Observations: . final cooling. .8 Cu  146. Thus it includes the effects of hot forming over austenite decomposition.6  245 C  8. 35% @800°C.5°C Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] t8/5: Time Between 800°C and 500°C [s] Source: LOTTER.This formula was determined using data got from samples submitted to a normalizing rolling simulation in a dilatometer. 20% strain @975°C. 136 p.This formula was determined using data got from samples submitted to a thermomechanical rolling simulation in a dilatometer.0 Al Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] . . 603 V  420. Apparently it is a development of the Andrews formula.9  300 C  33.7 Ni  11. August 2002.967 Si  18. . Source: MAHIEU. Phase Transformation and Mechanical Properties of Si-free CMnAl Transformation-Induced Plasticity-Aided Steel. Nehrenberg M s  498. 18:1-2. Mikula & Wojnar M s  635. et alii. A.07 Cr  30. 2573-2580.82 C  85.26 Nb  553. September-October 2006.E. Journal of Achievements in Materials and Manufacturing Engineering. Gorni Steel Forming and Heat Treating Handbook 53 Observation: . In: Contribution to Discussion on Grange and Stewart.1 (Si  Mo) Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: NEHRENBERG. Metallurgical and Materials Transactions A. . J.8 Ti  1746.301 Mo  6. 37-42.K. A. .441 Mn  68. 33A:8.73%. 167. & LIS. High Strength Hot Rolled and Aged Microalloyed 5% Ni Steel. J.Equation valid for TRIP steels with 0.5 B Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: LIS.02  549.965 Ni  69.2 Cr  16. 1946. 494-498.91  Al  1.3 Mn  22. Transactions of the AIME. 8 Cr  16. Transactions A.M.8 Cr  16. .S. & SAVAGE.H.1 (Si  Mo  W ) Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: PAYSON. Gorni Steel Forming and Heat Treating Handbook 54 .9  333. Rowland & Lyle M s [C]  498.7 Ni  11.7 Ni  11. Payson & Savage M s  498.. 33. Martensite Reactions in Alloy Steels.3 Mn  27.3 C  33.7 C  33. P.1 (Si  Mo  W ) M s [F ]  930  600 C  60 Mn  50 Cr  30 Ni  20 (Si  Mo  W ) M10 [F ]  M s  18 M 50 [F ]  M s  85 M 90 [F ]  M s  185 M100 [F ]  M s  387 Notation: Ms: Martensite Start Temperature Mx: Temperature Required for the Formation of x% of Martensite Alloy Amount: [weight %] .3 Mn  27. C.9  316. 1944. 261-280. V. Gorni Steel Forming and Heat Treating Handbook 55 Source: ROWLAND.7 (Cr  Ni )  21.1  473. 1956.G. p. 183. & HAYNES..M. 37. W. A. E.R. 1946. S. 1997.1 Mo Notation: Ms: Martensite Start Temperature [°C] Source: STEVEN. Sverdlin-Ness M s  520  320 C  50 Mn  30 Cr  20 ( Ni  Mo)  5 (Cu  Si) Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: SVERDLIN.9 C  33 Mn  16. 349-359. 45-91. A. Journal of the Iron and Steel Institute. The Effects of Alloying Elements on the Heat Treatment of Steel. Steven & Haynes M s  561. Marcel Dekker.R. Tamura M s  550  361 C  39 Mn  20 Cr  17 V  17 Ni  10 Cu  5 (Mo  W )  15 Co  30 Al . In: Steel Heat Treatment Handbook. Transactions A. & NESS. The Application of Ms Points to Case Depth Measurement. A. The Temperature of Formation of Martensite and Bainite in Low Alloy Steels. . .S. & LYLE.S. New York. 27-47. . 85%.5 Si  14 Cr  18 Ni  17 Mo Notation: .: Empirical Formulae for the Calculation of Austenite Supercooled Transformation Temperatures. r = 0.28%  Mn  2. 0.Formula valid within the following range: 0.00%. 2015. 40. Archives of Metallurgy and Materials.5%. Source: TRZASKA. Nikkan Kogyo Shinbun Ltd.21%  C  0.Error = 20. Trzaska (I) M s  411  328 C  13 Mn  9 Ni  3 Cr  16 Mo  34 Cu  6. 0. .38% and Cu  0.88.90%. 60:1. 181-185.38%.68%. Trzaska (II) M s  541  401C  36 Mn  10. Steel Material Study on the Strength. . 1970. V  0.25 Notation: Ms: Martensite Start Temperature [°C] Alloy Content: [weight %] vR: Cooling Rate [°C/min] Observations: . Mo  1. .13%  Si  1.5°C.05%. J. Gorni Steel Forming and Heat Treating Handbook 56 Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Source: TAMURA.. Ni  3. Cr  2.7 vR0. Tokyo. I. V  0. standard error =  19.75%. 2016. Source: TRZASKA.30%.38%.6.79. Mn + Ni  4.0014 K-1.13  Mn  2. Calculation of Critical Temperatures by Empirical Formulae. correlation coefficient R² = 0. J. 981-986.06%  C  0.05%.12  Si  1.Additional validity limitations: Mn + Cr  3.68%. Mn + Cr + Ni  5.3. 61:2B. . . van Bohemen f  1  exp  m (TKM  T ) TKM  462  273 C  26 Mn  13 Cr  16 Ni  30 Mo  m  0. . Mo  1.Formula based from Koistinen and Marburger equation.00005 Ni  0.0224  0. . Cr  2. Gorni Steel Forming and Heat Treating Handbook 57 Ms: Martensite Start Temperature [°C] Alloy Content: [weight %] Observations: .85%. 0.Regression coefficient r² = 0.6. Cr + Ni  5.0001 Mo Notation: f: Volume Fraction of Martensite as a Function of Undercooling Below TKM Temperature (TKM – T) T: Temperature [°C] TKM: Theoretical Martensite Start Temperature [°C] Alloy Amount: [weight %] Observation: .0107 C  0.Equation valid within the following alloy range: 0.04%. 0.87.0007Mn  0.αm: Standard error of estimate σ = 0. Ni  3. Archives of Metallurgy and Materials.00012 Cr  0.5 .38. Cu  0.99°C. 25:8.2  0. S. 487-495. Gorni Steel Forming and Heat Treating Handbook 58 Source: VAN BOHEMEN.21 Si  0. . f  1  exp  m (M s  T )  m  27. Effect of Composition on Kinetics of Athermal Martensite Formation in Plain Carbon Steels.08 Ni  0. 28:4. 1009-1012.97.05 Mo  19.Standard error of estimate σ = 13°C.C. correlation coefficient r² = 0. April 2012. August 2009. M s  565  31 Mn  13 Si  10 Cr  18 Ni  12 Mo  600 1  exp( 0. J.8 1  exp( 1.M. S.αm: Standard error of estimate σ = 0. Bainite and Martensite Start Temperature Calculated with Exponential Carbon Dependence. Materials Science and Technology.96 C) Notation: Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Observation: . Materials Science and Technology.95. correlation coefficient r² = 0.M.11 Cr  0. Source: VAN BOHEMEN.Formula based from Koistinen and Marburger equation.C and SIETSMA.56 C) Notation: f: Volume Fraction of Martensite as a Function of Undercooling Below Ms Temperature (Ms – T) T: Temperature [°C] Ms: Martensite Start Temperature [°C] Alloy Amount: [weight %] Observation: .005 K-1. .14 Mn  0. 7817 Ni ²  0.36 Ni ²  0. Nov. 997-1002. both lath martensite and twinned martensite can be present in steel. J.25 C  47.If MsLM is higher than MsTM.However.08 Ni  0.02464Ni ³  2. only twinned martensite can exist.00296 Co ³  16.64 N  17.428 Mn  1. if MsLM is lower than MsTM. 1992.50 Mo   21.00 Mo  12.2654 Co ²  0.87 Co  0.36 N 2  16.001547 Co ³  7.59 Mn  2.56 Ni  1. This condition is fulfilled for some steels above a critical composition. . 8:11.25 Mn ²  0.33 C  33.18 Cu  72.82 Cr  1.28 Ru  1.52 Cu  260. .65 N  43.66 Ru Notation: MsTM: Twinned Martensite Start Temperature [°C] MsLM: Lath Martensite Start Temperature [°C] Alloy Amount: [weight %] Observation: . Zhao M sTM  420  208.0384 Ni ³  17. Gorni Steel Forming and Heat Treating Handbook 59 . Materials Science and Technology.296 Mn²  0.72 Ru 2  0.468 Co ²  0.08117 Ru 3 M sLM  540  356. which can be determined setting MsLM = MsTM.: Continuous Cooling Transformations in Steels.473 Cr  30.0415 Mn ³  24.02167 Mn³  16. Source: ZHAO.86 Co   0.42 Cr 2  17. Bodnar t8 / 5  946 t 1.Temperature evolution was measured at plate quarter-thickness. 2004. R. In: Materials Science & Technology. Gorni Steel Forming and Heat Treating Handbook 60 . et alii: Erfahrungen mit des beschleunigten Abkühlung von Grobblech aus der Walthitze. Source: DEGENKOLBE. Degenkolbe CR8 / 5  4. vol. 1.74694 Notation: CR8/5: Cooling Rate of in the Core of a Steel Plate in Air Between 800°C and 500°C [°C/s] t: Plate Thickness [mm] Observation: . New Orleans. . 1987. Source: BODNAR. 1. J. . et alii: The Physical Metallurgy of Normalized Plate Steels. 41-55.032 Notation: t8/5: Average Cooling Rate of Steel Plate in Air Between 800°C and 500°C [°C/min] t: Plate Thickness [mm] Observation: . AIST. Thyssen Technische Berichte.52762 t 0.Equation fitted by the author of this review using data available in the figure 2 of the reference below. 89-109.Cooling Rate of Flat Products of Steel .L. 203-214. Oct. 3. Gorni Steel Forming and Heat Treating Handbook 61 .Critical Diameter .Austenite Hardenability . Transactions of the Institute of Welding.28 18 15   Notation: Di: Critical Diameter [mm] Alloy Content: [weight %] Source: DEARDEN. Dearden & O’Neill   Mn Mo Cr Si Ni   Di  6  exp 7.: A Guide to the Selection and Welding of Low Alloy Structural Steels. . 1940.13 6. J & O’NEIL.1   C         5.87 3. H. .307 Mn  2.046 S ) . all C has gone to cementite).178 C sol  1. March 2000.Density calculated at 20°C. 10 6 Notation: : Ferrite Density [kg/m³] Alloy Content: [weight %] Observations: .The solubilities of the other alloy elements in cementite are zero. U.436 Si  1.8477 Cu  1.018 Mo  1. 71:3.890 Ti  1.032 TiC ) . .C is considered insoluble in ferrite (that is. .012 V  4. 88-93.270 Fe  1.Density of Bulk Steel at Ambient Temperature .381 Si  1. .384 Cr  0.Csol is the content of this element not bound in TiC. et alii.370 Ni  2. Steel Research.111 Co  2. Ferritic Steels 1   (1.380 C  1.186 N  2.Density calculated at 20°C. Source: BOHNENKAMP.205 Cu  1.231 Fe  3.524 Mn  2.: Evaluation of the Density of Steels.076 Mo  1. Gorni Steel Forming and Heat Treating Handbook 62 . .431 Cr  1. Austenitic Steels 1   (1. 10 6 Notation: : Austenite Density [kg/m³] Alloy/TiC Content: [weight %] Observations: .137 Ni  1. 88-93. A.. September 1991. . 71:3.: Evaluation of the Density of Steels. Steel Research. et alii. . Density of Fe-C Alloys in Heterogeneous Phase Mixtures 1 f1 f2 f3 fn     . March 2000. 62:1.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction.   Steel 1 2 3 n Notation: Steel: Steel Density [kg/m³] fi: Fraction of the phase i in the microstructure ρi: Density of the phase i Source: JABLONKA.. U. Gorni Steel Forming and Heat Treating Handbook 63 Source: BOHNENKAMP. 24-33. Steel Research. Gorni Steel Forming and Heat Treating Handbook 64 .Density of Bulk Steel at High Temperature . BISRA ρ T 1008 1023 1040 1524 0 7861 7863 7858 7854 15 7856 7859 7854 7849 50 7847 7849 7845 7840 100 7832 7834 7832 7826 150 7816 7819 7817 7811 200 7800 7803 7801 7794 250 7783 7787 7784 7777 300 7765 7770 7766 7760 350 7748 7753 7748 7742 400 7730 7736 7730 7723 450 7711 7718 7711 7704 500 7792 7699 7692 7685 550 7673 7679 7672 7666 600 7653 7659 7652 7646 650 7632 7635 7628 7622 700 7613 7617 7613 7605 750 7594 7620 7624 7615 800 7582 7624 7643 7641 850 7589 7625 7617 7614 900 7600 7600 7590 7590 . 11 0.037 0.Chemical composition of the steels [wt %]: Steel C Mn Si P S Cu 1008 0.13 1040 0. 1953.029 0.62  105 T 2 (T ≤ Ar3)   8099.64 0.08 0. Gorni Steel Forming and Heat Treating Handbook 65 950 7572 7574 7564 7561 1000 7543 7548 7538 7532 1050 7515 7522 7512 7503 1100 7488 7496 7486 7474 Notation: ρ: Density of steel [kg/m³] T: Temperature [°C] Observations: .050 - 1023 0.029 0. London.31 0.297 T  5.11 Source: Physical Constants of Some Commercial Steels at Elevated Temperatures.034 0. Picquè   7875.031 0.96  0.034 0. .23 1.11 0.08 0.51 0. BISRA/Butterworths Scientific Publications.12 1524 0.42 0.64 0.79  0.23 0. 1-38.12 0.506 T (T > Ar3) Notation: .038 0. . Doctor Thesis. p. 0. 247.Formulas specific for a 0.5% Mn steel Source: PICQUÉ. Experimental Study and Numerical Simulation of Iron Oxide Scales Behavior in Hot Rolling. 2004. Gorni Steel Forming and Heat Treating Handbook 66 ρ: Density of steel [kg/m³] T: Temperature [°C] Observation: . École de Mines de Paris. B.16% C. 01 C) Notation: Liquid Iron: Liquid Iron Density [kg/m³] T: Temperature. [°C] C: Carbon content [weight %] Source: JABLONKA. Gorni Steel Forming and Heat Treating Handbook 67 . Chemical Engineering. 44-46. C. A. September 1991. November 2007. Yaws  T  0. [K] Source: YAWS.835 T ) (1  0. . 24-33.49  0.Density of Liquid Steel . .7  1    Liquid Iron  1.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction. Jablonka  Steel  (8319.L. 62:1.9946  0. Steel Research.: Liquid Density of the Elements.22457  9340  Notation: Liquid Iron: Liquid Iron Density [g/ml] T: Absolute Temperature. 001  Carbide 8.4387 4 8.00 0.00 ~ 2.1271 + 0.00 0. 1981.130  0.00 ~ 2.1212 + 0. Common Phases and Constituents Phase/Constituent C Specific Volume [weight %] [cm³/g] at 20°C Austenite 0.4118 4 6.: Steel and its Heat Treatment – Bofors Handbook.Density of Microstructural Constituents at Ambient Temperature .0015 (C – 0.00 ~ 2.00 0. London. Density and Molar Volume of Microalloy Carbides and Nitrides Compound Structure Molecular Lattice Molecules per Density Molar Volume Mass Parameter Unit Cell [g/cm³] [cm³/mol] [nm] NbC FCC 105 0.002 Graphite 100 0.1271 + 0.83 10.140  0.18 10.1277 + 0.02 0.25 ~ 2.00 0.39 NbN FCC 107 0.451 Ferrite + Cementite 0.52 .0015 C Notation: C: Carbon Content [weight %] Source: THELNING.4154 4 5. .84 13. 570 p.0005 C Low C Martensite +  Carbide 0.4462 4 7.0033 C Martensite 0.25) Ferrite +  Carbide 0.00 ~ 2.00 0. Butterworths.1271 + 0.5  0.2 0.E.0025 C Ferrite 0.41 12.81 VN FCC 65 0.7 0.7  0.1271 Cementite (Fe3C) 6.72 VC FCC 63 0. K.00 ~ 0. Gorni Steel Forming and Heat Treating Handbook 68 . 357 4 8.Data based on room temperature lattice parameters.4313 4 4. Density and Molar Volume of Precipitates and Metals Compound Density Molar Volume [kg/m³] [cm³/mol] NbCN 9291 12.11 Observations: .Data based on room temperature lattice parameters. The Institute of Materials.4965 AlN CPH 41 6 3.29 N .80 ZrC 6. 363 p. The Physical Metallurgy of Microalloyed Steels. Gorni Steel Forming and Heat Treating Handbook 69 TiC FCC 60 0. .4233 4 5.89 12. T. Source: GLADMAN.35 Si 2330 12.85 7.311 -Fe FCC 56 0. . 13.54 Steel 7850 7.00 Observations: .286 2 7.23 Cu 8920 7.85 -Fe BCC 56 0.42 11.30 - Mn 7470 7.54 a = 0.27 TiN FCC 62 0.572 - ZrN 7. 1997.44 c = 0.15 6. London.27 12.06 Cr 7140 7.11 C 2267 5. Gorni Steel Forming and Heat Treating Handbook 70 Sources: - SAN MARTIN, D. et alii. Estudio y Modelización de la Influencia de las Partículas de Segunda Fase sobre el Crecimiento de Grano Austenítico en um Acero Microaleado com Niobio. Revista de Metalurgia – Madrid, 42:2, Marzo-Abril 2006, 128-137. - Web Elements (www.webelements.com) - NISHIZAWA, T. Thermodynamics of Microstructure Control by Particle Dispersion. ISIJ International, 40:12, December 2000, 1269-1274. - ADRIAN, H. Thermodynamical Model for Precipitation of Carbonitrides in HSLA Steels Containing Up to Three Microalloying Elements with or without Additions of Aluminum. Materials Science and Tecnology, 8:5, May 1992, 406-420. . Relationship Between Lattice Parameter and Density nM  (a 10 10 ) 3 N Notation: : Density [kg/m³] n: Number of atoms per unit cell (depends on crystalline structure): . Cubic body-centered: 2 . Cubic face-centered: 4 M: Molecular mass [kg/mol]: . Pure Fe: 0.055847 . Cementite: 0.179552 a: Lattice Parameter [Å] N: Avogrado’s number: 6.023 . 1023 Gorni Steel Forming and Heat Treating Handbook 71 Source: JABLONKA, A.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction, Steel Research, 62:1, September 1991, 24-33. Gorni Steel Forming and Heat Treating Handbook 72 - Density of Microstructural Constituents at High Temperature . Fink  T   20C  0.47 T T  20C  0.33 T Notation: T: Austenite Density at Temperature T [kg/m³] 20°C: Austenite Density at 20°C [kg/m³] T: Ferrite Density at Temperature T [kg/m³] 20°C: Ferrite Density at 20°C [kg/m³] T: Temperature[°C] Source: FINK, K. et alii.: Physikalische Eigenschaften von Stählen, insbesondere von warmfesten Stählen. Thyssenforschung, 2:2, 1970, 65-80. . Jablonka  T  7875.96  0.297 T  5.62  10 5 T 2  (1  2.62  10 2 C )  T  8099.79  0.506 T  (1  1.46  10 2 C )  T  7875.96  0.297 T  5.62  10 5 T 2  (1  2.62  10 2 C )  Fe 3C  7686.45  6.63  10 T  3.12  10 4 T 2  T 2 Gorni Steel Forming and Heat Treating Handbook 73 Notation: T: Delta Ferrite Density at Temperature T [kg/m³] T: Austenite Density at Temperature T [kg/m³] T: Ferrite Density at Temperature T [kg/m³] Fe3CT: Cementite Density at Temperature T [kg/m³] T: Temperature[°C] C: Carbon content [weight %] Observations: - Carbon content in ferrite is limited to 0.02% maximum. Source: JABLONKA, A.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction, Steel Research, 62:1, September 1991, 24-33. . Molar Volume of Austenite as Function of Temperature  VM  6.688726 106 exp 7.3097  105 T  Notation: VM: Molar Volume of Austenite, [m³/mol] T: Temperature [K] Source: FERNÁNDEZ, D.M.S.M. Modelización de la Cinética de Austenización y Crecimiento de Grano Austenítico en Aceros Ferrítico-Perlíticos. Tesis Doctoral, Centro Nacional de Investigaciones Metalúrgicas, Madrid, Julio 2003, 258 p. . Relationship Between Density and Thermal Expansion Gorni Steel Forming and Heat Treating Handbook 74  (T0 )  th  3 1  (T ) Notation: th: Thermal Expansion/Contraction ρ(T0): Density at lower/higher T0 ρ(T): Densotu at temperature T T0: Reference temperature Source: JABLONKA, A.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction, Steel Research, 62:1, September 1991, 24-33. Gorni Steel Forming and Heat Treating Handbook 75 - Dimensional Changes during Austenite Transformation . During Cooling L   1.232  10  2  1.347  10 5 T  6.544  10 3 C   5.829  10 3 C 2  9.766  10 6 C  T  2.379  10 9 T 2 L C 0 (1  X A ) C tr C  XA Notation: ΔLγ→α: Specimen Length Change During Austenite Transformation [μm]; L: Specimen Original Length [μm] T: Temperature [°C] Cγ: Carbon Content in Austenite [wt %] C0: Initial Carbon Content [wt %] Ctr: Carbon Content of Transformed Phases [wt %] XA: Untransformed Austenite Volume Fraction Source: PARK, S.H. Microstructural Evolution of Hot Rolled TRIP Steels During Cooling Control. In: 40th Mechanical Working and Steel Processing Conference, ISS/AIME, Pittsburgh, October 1998, 283-291. . After General Heat Treating Transformation V l [%] [mm/mm] THELNING.64 – 0.0056 C Austenite  Lower Bainite 4. Gorni Steel Forming and Heat Treating Handbook 76 Spheroidized Pearlite  Austenite -4. . After Quenching V  100  VC  V A  V   1.V/V: Volumetric Change after Quenching [%] .0155 – 0. 2005.78 C 0.43 C 0. G. K.0155 + 0.100 – VC – VA: Martensite Volumetric Fraction [%] .64 – 1. .0026 C Austenite  Upper Bainite 4.68 C 0. 420 p. Structure and Performance.CM: Carbon Content Solubilized in Martensite [weight %] .0048 C Spheroidized Pearlite  Lower Bainite 0. KRAUSS.: Steel and its Heat Treatment – Bofors Handbook. 1981.C: Carbon Content [weight %].21 C A ) V  100  100 Notation: . Metals Park.53 C 0.14 – 2. 570 p.64  2. Sources: .VA: Austenite Volumetric Fraction [%] .0074 C Spheroidized Pearlite  Upper Bainite 0 (Zero) 0 Notation: .E. London. Butterworths.0018 C Spheroidized Pearlite  Martensite 1.21 C 0.0155 – 0.VC: Non-solubilized Cementite Volumetric Fraction [%] .64 + 2.0074 C Austenite  Martensite 4.68 C M  A (4. Steel: Processing.0155 – 0. ASM International.21 C -0. E. CA: Carbon Content Solubilized in Austenite [weight %] Source: THELNING. Butterworths. K. London. Gorni Steel Forming and Heat Treating Handbook 77 . 570 p. 1981. .: Steel and its Heat Treatment – Bofors Handbook. 4 10. Dearden & O’Neill Mn Mo Cr  V Cu Ni P C EQ _ Dearden  C       6 4 5 13 15 2 Notation: CEQ_Dearden: Equivalent Carbon (Dearden) [%] Alloy Content: [weight %] Source: DEARDEN.: Metal Construction and British Welding Journal.7 15.Equivalent Carbon – H. .4 7.3 ln(CRm )  13. Hardenability . . Bastien Mn Mo Cr Ni C EQ _ Bastien  C     4. 1970. minimum cooling rate that produces a fully martensitic structure) Source: BASTIEN.Z. 9.9  10. October 1940. H.: A Guide to the Selection and Welding of Low Alloy Structural Steels.6 C EQ _ Bastien Notation: CEQ_Bastien: Equivalent Carbon (Bastien) [%] Alloy Content: [weight %] CRm: Critical Cooling Rate at 700°C [°C/s]. 3.A. that is. 203-214.G. Transactions of the Institute of Welding. P. 49. Gorni Steel Forming and Heat Treating Handbook 78 . J & O’NEIL. F.: Metallurgical Concept And Full-Scale Testing of High Toughness. . H2S Resistant 0.0. Report.B. Kihara Mn Mo Cr V Ni Si C EQ _ Kihara  C       6 4 5 14 40 24 Notation: CEQ_Kihara: Equivalent Carbon (Kihara) [%] Alloy Content: [weight %] Source: KIHARA. São Paulo. et alii.10%Nb Steel. February 1993. 1. H. Gorni Steel Forming and Heat Treating Handbook 79 . C.M. et alii. 93. 1959. Technical Report of JRIM.3 Ti (1  5 C )   29 B (11 C  1) 5 15 9 3 2 Notation: .M. Shinozaki Mn Si Cr V (50 C  1) Mo (1  6 C ) C EQ _ FBW  C     7 Nb (1  10C )   1. .03%C . IIW .International Institute of Welding Mn Cr  Mo  V Cu  Ni C EQ _ IIW  C    6 5 15 Notation: CEQ_IIW: Equivalent Carbon (IIW) [%] Alloy Content: [weight %] Source: HEISTERKAMP. 8 Notation: CEQ_Yurioka: Equivalent Carbon (Yurioka) [%] Alloy Content: [weight %] tm: Critical Cooling Time from 800 to 500°C [s] (that is. 6. 1976.D. 55. 1982. .: Effects of Chemical Composition and Structure of Hot Rolled High Strength Steel Sheets on the Formability of Flash Butt Welded Joints. Gorni Steel Forming and Heat Treating Handbook 80 CEQ_FBW: Equivalent Carbon Designed Specifically for Flash Butt Welding [%] Alloy Content: [weight %] Source: SHINOZAKI. Stout  Mn Cr  Mo Ni Cu  C EQ _ Stout  1000 C       6 10 20 40  Notation: CEQ_Stout: Equivalent Carbon (Kihara) [%] Alloy Content: [weight %] Source: STOUT. et alii. M. Kawasaki Steel Technical Report. R. 89s-94s. .6 C EQ _ Yurioka  4. Sept. Welding Journal Research Supplement. et alii. 21-30. maximum cooling time that produces a fully martensitic structure) . Yurioka Mn Mo Cr Ni Si Cu C EQ _ Yurioka  C       6 4 8 12 24 15 log(t m )  10. et alii. N. Gorni Steel Forming and Heat Treating Handbook 81 Source: YURIOKA. 1987.: Metal Construction. 19. 217R. . 3R International. . (CD Edition).: Casti Metals Blue Book: Welding Filler Metals. Weldability of Pipe Steels for Low Operating Temperatures. 1. B. Edmonton. February 1993.PATCHETT.BERSCH.Equivalent Carbon – Hydrogen Assisted Cold Cracking .M.Formula deduced for pipeline steels Source: .. et alii. Bersch & Koch (Hoesch) Mn  Si  Cr  Mo  V  Cu  Ni C EQ _ Bersch  C  20 Notation: CEQ_Bersch: Equivalent Carbon for Pipeline Steels [%] Alloy Content: [weight %] Observations: . 1977. et alii. Gorni Steel Forming and Heat Treating Handbook 82 . DNV Mn Si Ni  Cu Cr V Mo C EQ _ DNV  C       10 24 40 5 10 4 Notation: CEQ_DNV: Equivalent Carbon (DNV) [%] Alloy Content: [weight %] . 608 p. Casti Publishing Corp. . B. Formula deduced for pipeline steels with C < 0. .Formula deduced for pipeline steels Source: GRAVILLE. Conf. Gorni Steel Forming and Heat Treating Handbook 83 Source: HANNERZ.A.: In: Proc. Materials Park. 1980. 1976. . Ito & Bessyo (I) Si Mn  Cu  Cr Ni Mo V Pcm  C      5B 30 20 60 15 10 Notation: Pcm: Cracking Parameter [%] Alloy Content: [weight %] Observations: . IIW Document IX-1169-80. . on Welding of HSLA Structural Steels.This is the most popular formula for this kind of material. B.E.15% . N.: The Influence of Si on the Weldability of Mild and High Tensile Structural Steels. Graville Mn Ni Cr Mo Nb V C EQ _ HSLA  C       16 50 23 7 5 9 Notation: CEQ_HSLA: Equivalent Carbon (Uwer & Graville) [%] Alloy Content: [weight %] Observations: . ASM. Y.22%. Y. except H: Hydrogen amount in the weld metal.20%. 1968. Equation valid under the following conditions: 0. B  0. . [cm³/100 g] d: Plate Thickness.20%.40%. 59-70.50%. .W.I. Mo  0.. 1. et alii. Weldability Formula of High Strength Steels Related to Heat-Affected-Zone Cracking.005%.12%. Mannesmann Si Mn  Cu Cr Ni Mo V C EQ _ PLS  C       25 16 20 60 40 15 Notation: . & BESSYO. Document IX-576-68. Sources: .07%  C  0.60%. 983. Si  0.: Weldability Formula of High Strength Steels. Ito & Bessyo (II) Si Mn  Cu  Cr Mo V d H Pc  C       30 20 15 10 600 60 Notation: Pc: Cracking Parameter [%] Alloy Content: [weight %]. K. I. & BESSYO. V  0. Ni  1.: Journal of the Japan Welding Society. . 0.40%  Mn  1. K. Gorni Steel Forming and Heat Treating Handbook 84 . [mm] Source: ITO. The Sumitomo Search.7%.ITO. Cu  0. 1969. Y. Cr  1.ITO. 37. C. São Paulo.0. H2S Resistant 0.M. & NIEDEROFF. Uwer & Hohne Mn Cu Ni Cr Mo C EQ _ Uwer  C      10 20 40 20 10 Notation: CEQ_Uwer: Equivalent Carbon (Uwer & Hohne) [%] Alloy Content: [weight %] Source: UWER. C. Gorni Steel Forming and Heat Treating Handbook 85 CEQ_PLS: Equivalent Carbon for Pipeline Steels [%] Alloy Content: [weight %] Observations: .M. London. on Welding and Performance of Pipeline. HEISTERKAMP. IIW Document IX-1631-91. Yurioka .B.: Metallurgical Concept And Full-Scale Testing of High Toughness. .A version of this formula divides V by 10 Sources: . & HOHNE. Report.10%Nb Steel. February 1993. D. et alii. 1991. TWI. H.03%C . .Formula deduced for pipeline steels . DUREN. F.: Determination of Suitable Minimum Preheating Temperature for the Cold-Crack-Free Welding of Steels. .: In: Proc. 1986. K. February 1993. 608 p.PATCHETT.Formula for C-Mn and microalloyed pipeline steels . .. 566-570. Edmonton. et alii.12) Notation: CEQ_Yurioka: Equivalent Carbon for Pipeline Steels [%] Alloy Content: [weight %] Observations: . B.M.: Casti Metals Blue Book: Welding Filler Metals.This formula combines Carbon Equivalent equations from IIW and Pcm Sources: . .75  0. N. ISIJ International. 41:6.25 tanh 20 (C  0. (CD Edition). June 2001. Gorni Steel Forming and Heat Treating Handbook 86  Mn Si Cr  Mo  V Cu Ni Nb  C EQ _ Yurioka  C  A(C )        5 B  6 24 5 15 20 5  A(C )  0. Casti Publishing Corp.: Physical Metallurgy of Steel Weldability.YURIOKA. 1%.0458 Al  0.04 Cr  0.03%.0896  0. CB: Peritectic composition of the Fe-C phase diagram [%].2%.Formula valid within the following ranges: Al  2. Blazek CA  0. Mn  2. . Mo  2.08%.075% and W  0.1%.0205 Mn  0. Ti  0.CB: r² = 0.1 Mo . RMS Error = 0. Iron and Steel Technology.02 Mn  0. Gorni Steel Forming and Heat Treating Handbook 87 . Si  2.5%.0197 W C B  0.1 Si  0. Alloy Content: [weight %] Observations: . V  1.0106 Mo  0. July 2008.22%.03255 Mo  0.0316 Mn  0.35%.CA: r² = 0. .0239 Ni  0.Equivalent Carbon – Peritectic Point . S  0. Nb  0.05 Al Si  0.This model fitted data generated by the Thermocalc software. et alii.036 Al  0.0266 W Notation: CA: Maximum Carbon Solubility of the δ-Ferrite Phase [%]. Mills C P _ Mills  C  0.E.0103 Si  0.00059 Cr 2  0.0032 Cr  0. Calculation of the Peritectic Range for Steel Alloys.1967  0.1411 Al 2  0.0077 Si  0.05%. .00059 Cr Ni  0. P  0.0126%. Ni  10. RMS Error = 0.3%. K.0053%. Cr  18.00142 Cr 2   0.0134 V  0.99.0603 V  0.0024 Cr  0.0401 Ni  0.98.15%. .3%.0223 Al 2  0. 80-85. Cu  1. Sn  0.0%.04 Ni  0. Source: BLAZEK. Gorni Steel Forming and Heat Treating Handbook 88 Notation: CP_Mills: Equivalent Carbon for Peritectic Point [%] Alloy Content: [weight %] Source: XU, J. et alii. Effect of Elements on Peritectic Reaction in Molten Steel Based on Thermodynamic Analysis. ISIJ International, 52:12, October 2012, 1856-1861. . Miyake C P _ Inf  f1  0.10 C P _ Sup  f 2  0.05 f1  0.0828 Si  0.0195 Mn  0.07398 Al  0.04614 Ni  0.02447 Cr  0.01851 Mo  0.090 f 2  0.2187 Si  0.03291Mn  0.2017 Al  0.06715 Ni  0.04776 Cr  0.04601Mo  0.173 Notation: CP_Inf: Lower Bound of Carbon Peritectic Content Range [%] CP_Sup: Upper Bound of Carbon Peritectic Content Range [%] Alloy Content: [weight %] Observations: - Alloy elements contents are assumed to be 4.0% or less, excluding 0%. Source: MIYAKE, T. et alii. Method of Continuous Casting of High-Aluminum Steel and Mold Powder. U.S. Patent n° US 8,146,649 B2, April 3, 2012, 13 p. Gorni Steel Forming and Heat Treating Handbook 89 . Shepherd C'  0.0927 – 0.0151 Mn  0.00776 Si 2  0.0565 Al  0.0143 Al 2  0.00338 Al 3 – 0.0170 Mn Si – 0.0148 Mn Al – 0.0574 Si Al – – 0.00848 Mn Si Al – 0.00900 (Si Al) 2 – 0.0121 (Si  Al) – 0.000775 Si 4  0.00128 (Mn Si) 3  0.00119 (Mn  Si  Al) 3   0.000913 (Mn Al) 4 – 0.00193 (Mn Si Al) 4 – 0.000341 (Mn  Si  Al) 4 – 0.0425 P 2  0.0549 P  0.1369 S – 0.0135 Cu – – 0.4694 N  0.0036 Sn 2 – 0.014 Sn – 0.0256 Nb – 0.0357 Ti  0.0113 V – 0.0009 Mo 2  0.0062 Mo – 0.0016 Cr – – 0.0195 Ni C'  0.249  0.0673 Si 2  0.177 Al 2 – 0.0232 Mn Si – 0.0116 Mn Al  0.140 Al 5 – 0.105 Si Al  0.0214 Mn Si Al   0.0104 (Mn Si) 2 – 0.0429 (Si Al) 2 – 0.195 Al 4  0.0441 Mn 4 – 0.0269 Mn 5 – 0.0242 e Mn – 0.0437 e Si  0.0233 (Si Al) 4   0.0152 (Mn Si Al) 4 – 0.000721 (Mn  Si  Al) 4  0.2651 P  0.5573 S – 0.0174 Cu – 0.585 N  0.0094 Sn 2 – 0.0211 Sn – – 0.027 Nb  0.0377 Ti 2 – 0.0463 Ti  0.042 V – 0.0015 Mo 2  0.0238 Mo  0.0024 Cr 2 – 0.002 Cr – 0.0349 Ni ' Cliq  0.746 – 0.0469 Mn  0.0305 Si – 0.0265 Si 2  0.0236 Si 3  1.37 Al – 1.21 Al 2  1.70 Al 3 – 0.771 Al   0.0745 log10 (Al) – 0.0351 Mn Si – 0.0560 Mn Al – 0.249 Si Al  0.00571 Mn Si Al – 0.00973 (Mn·Al) 2 – 1.07 Al 4   0.321 Al 5  0.00544 (Mn  Al) 2 – 0.0338 (Si Al) 3  0.1065 P  1.239 S – 0.0621 Cu – 0.8642 N  0.001 Sn 2 – – 0.0191 Sn  0.0051 Ti 2  0.0386 Ti  0.0043 V 2  0.0896 V  0.046 Mo  0.0056 Cr 2 – 0.0178 Cr – – 0.0047 Ni 2 – 0.0763 Ni Notation: C’δ: Maximum Carbon Solubility of the δ-Ferrite Phase [%] C’δ: Peritectic Composition [%] C’liq: Maximum Carbon Solubility of the Liquid Phase [%] Alloy Content: [weight %] Gorni Steel Forming and Heat Treating Handbook 90 Observations: - Range of Validity: Mn  2.0%, P  0.192%, S  0.070%, Si  1.5%, Cu  1.0%, Al  2.0%, N  0.1%, Sn  1.0%, Nb  0.5%, Ti  0.44%, V  1.0%, Mo  1.0%, Cr  0.5% and Ni  0.5%. - Standard Deviation: C’δ = 0.0002, C’δ = 0.0011, C’liq = 0.0023. - This model fitted data generated by the FactSage software. Source: SHEPERD, R. et alii. Improved Determination of the Effect of Alloying Elements on the Peritectic Range in Low- Alloyed Cast Steel. Iron and Steel Technology, October 2012, 77-85. . Wolf C P _ Wolf  C  0.04 Mn  0.1 Ni  0.7 N  0.14 Si  0.04 Cr  0.1 Mo  0.4 Ti Notation: CP_Wolf: Equivalent Carbon for Peritectic Point [%] Alloy Content: [weight %] Source: WOLF, M.M. Estimation of Crack Susceptibility for New Steel Grades. In: 1st European Conference on Continuous Casting, Florence, 1991, 2489-2499. . Xu C P _ Xu  0.1763  0.0616 Al  2.5275 S  0.2652 P  0.0023 Si  0.0344 Mn  1.5250 S Mn  0.0210 Si Mn Notation: CP_Xu: Equivalent Carbon for Peritectic Point [%] Alloy Content: [weight %] Observations: 06%. et alii. Effects of Elements on Peritectic Reaction in Molten Steel Based on Thermodynamic Analysis.5%. J. . Source: XU.015%.Fitting data generated by FactSage software. 52:10.978 . Gorni Steel Forming and Heat Treating Handbook 91 . Al  0. October 2012.Formula valid within the following ranges: Si  0. S  0.05%. P  0. . Mn  1. 1856-1861.5%.r² = 0. ISIJ International. Gorni Steel Forming and Heat Treating Handbook 92 .Fe-C Equilibrium Diagram . asminternational. http://www. Gorni Steel Forming and Heat Treating Handbook 93 Source: ASM’s Heat Treating One-Minute Mentor.org/pdf/HTSRefCharts/Vol4p4Fig1.pdf. . 0198 56.Fe-C Equilibrium Equations in the Solidification and Eutectoid Range . Solidus of -iron 1525  T %C  185 . Gorni Steel Forming and Heat Treating Handbook 94 . Liquidus of -iron 1525  T 1. Liquidus of -iron 1536  T %C  79 .0198 Notation: %C: coordinate in the Fe-C diagram [%] T: Temperature [°C] .1284  10 3 (T  1525) 2 %C   56. Solidus of -iron 1536  T %C  460 . A. Steel Research.7137 Source: JABLONKA.7917  10 4 (T  723) 2 %C  0. 62:1. Acm Line T  723 7. Start of transformation of -iron (on cooling) T  1392 %C  1140 .785 484. .8574  10 5 (T  911) 3 %C    484.8   453. End of transformation of -iron (on cooling) T  1392 %C  624.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction.785 484.7137 453. Gorni Steel Forming and Heat Treating Handbook 95 .3749 .818  10 4 (T  911) 2 2. September 1991. A3 Line 911  T 2. 24-33.785 . 45 Froberg VN 8120 2.Ferrite Solubility Products .53 Fountain & Chipman MnS 8400 2.62 Kunze NbN 10650 3.87 Kunze TiN 17640 6. B: Constants of the Solubility Product. Gorni Steel Forming and Heat Treating Handbook 96 .17 Kunze VC 12265 8. given in the table below: Precipitate A B Source AlN 9595 2.05 Taylor VN 7830 2.48 Roberts & Sandbert ZrN 18160 5.24 Kunze Observations: . General (a A ) m (a B ) n A log10  B a Am Bn T Notation: AmBn: Precipitate Considered for Calculation ax: Alloy Content [weight %] T: Temperature [K] A.77 Ivanov NbC 10990 4.65 Kunze & Reichert BN 13560 4. J.A.FOUNTAIN. Stockholm. B. Sources: . Stahl. A. . .IVANOV. aAmBn is equal to one if the precipitate is pure. 539. 1981. Gorni Steel Forming and Heat Treating Handbook 97 . In: Transactions of the Metallurgical Society of AIME. & REICHERT. 192. Stahl und Eisen. et alii. M. 224. & SANDBERG. R.S. W. .KUNZE. . J. 32. & GRAF. 1996. 26. 1964.ROBERTS. 1991. 599. . . 80. K. . & CHIPMAN. Neue Hütte. 1990. 1995.KUNZE. et alii. Report IM 1489. Scripta Metallurgica.W. H. .G. Akademie Verlag. Nitrogen and Carbon in Iron and Steels – Thermodynamics. p.FROBERG. Berlin. 1960. J. 7. 23. J.TAYLOR. Institute for Metallurgical Research. aAmBn  1 if there is co-precipitation with another element. 52. 8. Gorni Steel Forming and Heat Treating Handbook 98 .6 Ni  (10  19 Si  8 Cr  4 Ni  130 V ) logvr  HVB   323  185 C  330 Si  153 Mn  144 Cr  191 Mo  65 Ni  (89  53 C  55 Si  22 Mn  20 Cr  33 Mo  10 Ni ) logvr  HVM  127  949 C  27 Si  11 Mn  16 Cr  8 Ni  21 logvr  log(v1 )  9.57 Cr  1.78 Ni  0.70 Ni  0.62 C  1.80 C  1.36  0.66 Mo  0.81  4.00183 PA log(v2 )  10.43 C  0.27 Cr  0.58 Mo  0.54 Ni  0.5 Cr  0.38 Mo  2 Mo  0.58 log(t )  PA    T H  Notation: HV: Global Hardness [Vickers] fFP: Fraction of Ferrite-Pearlite in Microstructure fB: Fraction of Bainite in Microstructure fM: Fraction of Martensite in Microstructure HVFP: Hardness of Ferrite-Pearlite [Vickers] HVB: Hardness of Bainite [Vickers] .07 Mn  0.0032 PA log(v3 )  6.05 Mn  0.0019 PA 1  1 4.Hardness After Austenite Cooling .49 Mn  0.17  3. Blondeau HV  f FP HVFP  f B HVB  f M HVM HVFP  42  223 C  53 Si  30 Mn  7 Cr  19 Mo  12. 0. 1976. Ni ≤ 4. . Lorenz   Si Mn Cu Cr Ni Mo V  HV  2019  C (1  0.: Mathematical Model for the Calculation of Mechanical Properties of Low-Alloy Steel Products: A Few Examples of its Application. Mo < 1. Source: BLONDEAU.50%.10% < C < 0. 189-200.Limits for Austenitization: 1073 K (800°C) ≤ T ≤ 1373 K (1100°C) and t ≤ 1 h. Si < 1. In: 16th International Heat Treatment Conference – Heat Treating ‘76. R.5 log t 8 / 5 )  0. The Metals Society Stratford-upon-Avon.010% < Al < 0.0%.5%.2%. Gorni Steel Forming and Heat Treating Handbook 99 HVM: Hardness of Martensite [Vickers] Alloy Content: [weight %] vr: Applied Cooling Rate at 700°C [°C/h] v1: Critical Cooling Rate at 700°C for Martensitic Quenching [°C/h] v2: Critical Cooling Rate at 700°C for Bainitic Quenching [°C/h] v3: Critical Cooling Rate at 700°C for Annealing [°C/h] PA: Austenitization Parameter [K] T: Austenitization Temperature [K] t: Austenitization Soaking Time [h] H: Austenitization Activation Energy: 240 kJ/mol for C Steels.3          66 (1  0. Cu < 0.8 log t 8 / 5 )   11 8 9 5 17 6 3  Notation: HV: Maximum Hardness for a Martensitic-Bainitic HAZ Microstructure [Vickers.0%. 418 kJ/mol if Mo  0.050% and Mn + Ni + Cr + Mo < 5. Mn < 2. .0%.Equations Valid for the Following Chemical Composition Range: 0.04% Observations: . V < 0. Cr < 3. 10 kg Load] Alloy Content: [weight %] t8/5: Cooling Time Between 800°C and 500°C [s] .0%. et alii.0%.0%. 03 0. et alii.35  ln     t M    1 t M  t 0 12 n 3.6 U t 0n  HV  HVmax  HVmax  HV0  exp  n  n   t  t 0    0.1  C  p       exp 2. London.04  t 0  C exp 2. In: International Conference on Steels for Linepipe and Fittings. Murry  0.: Evaluation of Large Diameter Pipe Steel Weldability by Means of the Carbon Equivalent.3  0    i Ci    0 t  HV0  HVmin  0.3   0     i Ci    d    0.43    d C    t   2 U  1  p exp  0. K.09  n  C exp 2. . 322-332. Gorni Steel Forming and Heat Treating Handbook 100 Source: LORENZ.055 HVmax  300 9  log t 300 700  . Oct. Metals Society. 1981.3   0      i Ci0. 00 Observations: .27 22.22 0.40 0.75 i Notation: HVmax: Maximum Hardness for a Martensitic Structure C: Carbon [weight %] Ci: Alloy Content [weight %] d: Mean Austenite Grain Size [mm] t700300: Cooling Time Between 700°C and 300°C [s] HVmin: Minimum Hardness at Equilibrium Calculated According to the Substitution Solid Solution Hardening Effect Proposed by Lacy and Gensamer Zi: Concentration of the Element i in solid solution with ferrite at equilibrium [at %] μi: Action Coefficient of the Element i.39 0.82 Constants: αi.20 0.12 Cr 067 0. γ0 = 1. βi and γi according to the alloy element: Element i αi βi γi Mn 0.50 0.84 19.42 61.57 8.15 22.40 Si 0.15 0.16 12.40 Mo 0.17 0.94 1.40 1. Gorni Steel Forming and Heat Treating Handbook 101 HVmin  63    i Z i0.89. as described in the following table: Element Mn Si P Ni Cr Mo V W μi 14.90 Nb 0.80 Ni 0.44 2.20 1.09 2.22.20 0.79 V 0.72 0.42 General Constants: α0 = 0. β0 = 1. 05% ≤ C ≤ 0. G.5%.5%.13 4 vc .50% ≤ Mn ≤ 2. Nb ≤ 0. 1985.5 Wb  72 Wm 0 if S X  N Wx   1 if S X  N e Kx Sx  1  e Kx .1%. .5%. V ≤ 0.040%.Equations Valid Within the Following Chemical Composition Range: 0. Techniques de l'Ingénieur. 0.5 4 vc HVm  200  824 C  44 Mn  14 Cr  9 Ni  171V  78. Cr ≤ 1.0%. Mo ≤ 0. Gorni Steel Forming and Heat Treating Handbook 102 .09 TA  3.5 Mo  147 V  71 Cu  0.: Transformations Dans les Aciers. Paris. Source: MURRY.5 Cu  4. Trzaska .15% ≤ Si ≤ 0.11 TA  12.7  225 C  82 Mn  28 Si  55 Cr  28 Ni  53. General equation: HV  3. Ni ≤ 1.80%. 0. Specific equations: HVp   73  253 C  52 Mn  10 Si  36 Cr  8 Ni  20 Mo  80 V  0. Document M 1 115.8 4 vc  68 C 4 vc  42 W f  69 W p   32. 54 p.35%. 4 Cu  0.9 Mn  0. standard error = 62.5  4. 0. Observations: . . .85%.3 HV.13%  Mn  2. 2016.6%.4 HV.5 Ni  4. Ni  3.6%. mean absolute error = 19. mean absolute error = 48.743.Additional conditions: Mn+Cr  3.45 Mn  0.HV: r² = 0.5 Cr  1.18 Ni  1.4 V  1.7 C  0.05%.1 4 vc Notation: HVαp: Ferrite-Pearlite Hardness [Vickers] HVm: Martensite Hardness [Vickers] HV: General Hardness [Vickers] Alloy Content: [weight %] vc: Cooling Rate [°C/min] x: f (ferrite).17 4 vc  0. Archives of Metallurgy and Materials. standard error = 39. p (pearlite).HVm: r² = 0.3  3.75%. pearlite (p) and martensite (m).6 Mn  0.68%.35  4 vc ) 2 K m   16. Mn+Ni  4.4  15.4 HV.8 Cu  0.8 Mo  2.38% and Cu  0.9 HV. V  0.847.4 C  1.30%.4 Ni  6 Mo  3.HVαp: r² = 0.: Empirical Formulae for the Calculation of the Hardness of Steels Cooled from the Austenitizing Temperature.5 HV.9 Mo  0.5%.3 Cr  1.7 Si  2.12%  Si  1.Formula valid within the following range: 0.006 TA  1. Cr+Ni  5. .06%  C  0. 0.004 TA  4 vc K p  12  1.4 for bainite (b). 61:3.57 (4. .2 Ni  1.2 4 vc K b  1.9 Mo  4.9 V  0. .6 Si  2. Mn+Cr+Ni  5.5 for ferrite (f). J.3%.38%. 0. Cr  2. mean absolute error = 30.3 Mn  2.5 HV. b (bainite) or m (martensite) N: 0.7 C  2.04%. Source: TRZASKA.855.002 TA  1. Gorni Steel Forming and Heat Treating Handbook 103 K f  18. 1297-1302.2 Cr  0.4 C  2.4 Cr  1. Mo  1. standard error = 24. Gorni Steel Forming and Heat Treating Handbook 104 - Hardness After Tempering . Spies HB  2.84 HRC  75 C  0.78 Si  14.24 Mn  14.77 Cr  128.22 Mo  54.0 V  0.55 T  435.66 Notation: HB: Brinell Hardness After Hardening and Tempering HRC: Rockwell Hardness (C Scale) After Hardening Alloy Content: [weight %] T: Tempering Temperature [°C] Observations: - This equation is valid within the following ranges: HRC: 20~65; C: 0.20~0.54%; Mn: 0.50~1,90%; Si: 0.17~1.40%; Cr: 0.03~1.20%; T: 500~650°C. Source: SPIES, H.J. et alii.: Möglichkeiten der Optimierung der Auswahl vergütbarer Baustähle durch Berechnung der Härt-und-vergütbarkeit. Neue Hütte, 8:22, 1977, 443-445. Gorni Steel Forming and Heat Treating Handbook 105 - Hardness After Welding . Dearden & O’Neill HVmax  1200 C EQ _ Dearden  200 Mn Mo Cr V Cu Ni P C EQ _ Dearden  C       6 4 5 13 15 2 Notation: CEQ_Dearden: Equivalent Carbon (Dearden) [%] Alloy Content: [weight %] HVmax = Maximum Hardness [Vickers] Observations: - This equation calculates maximum hardness after welding. Source: DEARDEN, J & O’NEIL, H.: A Guide to the Selection and Welding of Low Alloy Structural Steels. Transactions of the Institute of Welding, 3, 1940, 203-214. . Khan HV  188  630 C EQ _ Yurioka Notation: CEQ_Yurioka: Equivalent Carbon for Pipeline Steels [%]  Mn Si Cr  Mo  V Cu Ni Nb  C EQ _ Yurioka  C  A(C )        5 B  6 24 5 15 20 5  Gorni Steel Forming and Heat Treating Handbook 106 A(C )  0.75  0.25 tanh 20 (C  0.12) Alloy Content: [weight %] Observations: - HV is the fusion zone hardness for a single pulse resistance spot weld with a 5 cycle hold time, calculated with r = 0.961. Source: KHAN, M.I. et alii.: Microstructure and Mechanical Properties of Resistance Spot Welded Advanced High Strength Steels. Materials Transactions, 49:7, 2008, 1629-1637. . Shinozaki HV  78  331 C EQ _ FBW Mn Si Cr V (50 C  1) Mo (1  6 C ) C EQ _ FBW  C     7 Nb (1  10C )   1.3 Ti (1  5 C )   29 B (11 C  1) 5 15 9 3 2 Notation: CEQ_FBW: Equivalent Carbon Designed Specifically for Flash Butt Welding [%] Alloy Content: [weight %] HV: Hardness at the Welding Interface [Vickers] Source: SHINOZAKI, M. et alii.: Effects of Chemical Composition and Structure of Hot Rolled High Strength Steel Sheets on the Formability of Flash Butt Welded Joints. Kawasaki Steel Technical Report, 6, Sept. 1982, 21-30. Hardness-Tensile Properties Equivalence . Gorni Steel Forming and Heat Treating Handbook 107 . Gorni Steel Forming and Heat Treating Handbook 108 Source: ASM Handbook – Mechanical Testing and Evaluation. 8. vol. Metals Park. 275. ASM International. . 2000. Alloy Elements Effect .Hot Strength of Steel . Gorni Steel Forming and Heat Treating Handbook 109 . 52 Cr 0. et alii.76 Observations: .Plot generated from data available in the original source.9838 2. . Butterworths. Gorni Steel Forming and Heat Treating Handbook 110 ∆𝝈𝟎.𝟑 [%/% atomic] [%/% weight] Mn 0. I.13 Si 0.6527 127.000 Ni 0.5054 7. London.9317 1.8584 59.9130 31.31 Cu 0. Misaka    exp 0.13    2  T   dt  Notation: : Steel Mean Flow Stress [kgf/mm²] .000 0.126  1.𝟑 𝝈𝟎.70061 12.06 V 0.𝟑 Alloy Element 𝝈𝟎.000 0.000 Nb 1.𝟑 ∆𝝈𝟎. 248 p.93 Mo 1. 1988.594 C  2851  2968 C  1120 C 2  0.75 C  0.: Thermomechanical Processing of High Strength Low Alloy Steels.76 Ti 0. Source: TAMURA. 21  d  0 . The mean flow stress calculated by this equation is given in effective (von Mises) units. .65 C Ar1  876.7893  0.76  734.75 C  0. Formulatization of Mean Resistance to Deformation of Plain C Steels at Elevated Temperature. Source: MISAKA.13    2  T   dt  f  0. 1967-1968.769 C Ar3  974. 750  έ  1200°C.126  1. Otherwise g is equal to unity. 21  d  0 .389 V  0.20%. et alii.004 Ni If T.916  0. 8:79. Misaka Reloaded    f g exp 0.594 C  2851  2968 C  1120 C 2  0. Gorni Steel Forming and Heat Treating Handbook 111 C: C content [weight %] T: Absolute Temperature [K] : True Strain έ: Strain Rate [s-1] Observations: . Journal of the Japan Society for the Technology of Plasticity. then g must be calculated according to the formula below.191 Mo  0. as it was determined under plane strain conditions. 414-422. expressed in Celsius degrees. Y. g  0.81  336.18 Mn  0. .Equation valid for the following parameter range: C  1. is between Ar3 and Ar1.26 C . 20  έ  200 s-1.5.   0. 1981. g: Softening Factor Due to Intercritical Deformation C: Carbon Content [weight %] T: Absolute Temperature [K] : True Strain t: Time [s] Mn: Manganese Content [weight %] V: Vanadium Content [weight %] Mo: Molybdenum Content [weight %] Ni: Nickel Content [weight %] Ar3: Temperature of Start Austenite Transformation in Proeutectoid Ferrite [°C] Ar1: Temperature of Finish Austenite Transformation in Proeutectoid Ferrite [°C] Observations: . Y. A53-A56. Gorni Steel Forming and Heat Treating Handbook 112 Notation: : Steel Mean Flow Stress [kgf/mm²] f: Effect of alloy elements on Mean Flow Stress. Source: MISAKA. Tetsu-to-Hagané. Estimation of Rolling Force in Computer Controlled Hot Rolling of Plates and Strip . as it was determined under plane strain conditions. . 67:2. et alii.Theme III: Mathematical Model for Estimating Deformation Resistance in Hot Rolling of Steels.The mean flow stress calculated by this equation is given in effective (von Mises) units. Senuma & Yada  a     n (1  X dyn )   s X dyn . 05 e  T  (Wang & Tseng 1996) If ε  εc:   (   C )   2   0.0  1011 (Senuma 1984)  1  c  8.315 e  T  (Senuma 1984)  7500    b  6227   0. Gorni Steel Forming and Heat Treating Handbook 113 c (1  e b  ) n    0 e b  b  8000    b  9850  0.5  1010 1   D0  (Yada & Senuma)   8000     c  4.76  10 e 4  T  (Senuma)  2500     c  0.28 e  T  (Wang & Tseng) c  1.693         X dyn  1  e 0.5 . 05 e T  . According to Yada & Senuma:   8000    295  0. According to Senuma (1984):  6420     0.1 e  T    Dp  Ddyn  ( Dpd  Ddyn ) 1  e t    . According to Wang & Tseng:  2650     0.5  1.144  10 D0 5 0.95: .Gorni Steel Forming and Heat Treating Handbook 114  (1613  T )  2  s  3.03 e  T   8670    Ddyn  22600  0.5  1.28  0.8242  109  0.07  10 2 D0 0.2   290  .28  0.27 e  T  If Xdyn > 0. 6 24 (0.155 e   0.5   X st  1  e . Gorni Steel Forming and Heat Treating Handbook 115 .693      t0. According to Senuma (1984):  18000  0.2 2   t0.286  107 0.5    e T  Sv .1433 e 3 ) SV   D0   ( t  t s )   2  0.1 e T  t   D p  Ddyn  1. According to Wang & Tseng:   8000     295  0.1 ( D pd  Ddyn ) 1  e     6840    Dpd  5380 e T  If ε < εc: 5 Dst   SV  0.4914 e   0. 322 t0. According to Senuma (1984):  63800    Dg  Dst  1. According to Wang & Tseng:  32100    Dg  Dst  1.95 and tip  t0.5    0.44  1012 t g e  T  2 .2  0. According to Wang & Tseng:  30000  2.44  1012 t g e  T  2 .e.95: .8 X st ) If Xst  0.5 If Xst < 0.2  10 12   t 0.2  2 e  T  Sv t0.95 (i.Gorni Steel Forming and Heat Treating Handbook 116 .95): Du  Dst (0.95  4. tip < t0.. 5: Strain Required for 50% Dynamic Recrystallization εr: Residual Strain After One Pass of Hot Rolling .95 In case of multipass hot rolling: ( Dpd  Dp )  R  t (1  X dyn ) (1  X st )   s X dyn ( Dpd  Ddyn )   8000      90 e  T  t 0. Gorni Steel Forming and Heat Treating Handbook 117 t g  tip  t0.7   a  t   n e    (  b  c)  ln  0 (  b  c)  r   r b Notation: : Steel Mean Flow Stress [kgf/mm²] ρ: Dislocation Density [cm-²] ρ0: Initial Dislocation Density [cm-²] ρn: Dislocation Density in the Dynamically Recovered Region [cm-²] ρs: Dislocation Density in the Dynamically Recristallized Region [cm-²] ρr: Dislocation Density After Deformation/Static Recovery [cm-²] ρt: Remaining Dislocation Density in the Dynamically Recovered Region [cm-²] Xdyn: Fraction of Dynamic Recrystallization Xst: Fraction of Static Recrystallization T: Absolute Temperature [K] : True Strain εc: Critical Strain for the Onset of Dynamic Recrystallization ε0. 00-1.00-0.Suggested value for ρ0: 1 x 10-8 cm-2 (Wang & Tseng) .The mean flow stress calculated by this equation is given in effective (von Mises) units.20-1. 0.24% Si) . 0. 0.62-1.If εr from the former pass is greater than 0.95: Time Required for 95% Static Recrystallization [s] tip: Time Interval Between Successive Rolling Passes [s] tg: Time Available for Grain Growth [s] ta: Time After Deformation [s] Observations: .40% C.00175 MN/m² (Senuma 1984: 0. 0. .01-0. For instance: .00% Mn. Gorni Steel Forming and Heat Treating Handbook 118 𝜺̇ : Strain Rate [s-1] D0: Grain Size Before Deformation [μm] Ddyn: Dynamically Recrystallized Grain Size [μm] Dp: Transition Grain Size from Ddyn to Dpd at a time t after deformation [μm] Dpd: Grain Size resulted from driving force due to the decrease of dislocation density [μm] Dst: Statically Recrystallized Grain Size [μm] Du: Mixed Grain Size Due to Incomplete Static Recrystallization [μm] Dg: Grain Size After Complete Static Recrystallization Plus Growth [μm] Sv: Nucleation Site Area [μm-1] t: Time [s] ts: Incubation Time for Static Recrystallization [s] t0. 0. 0. .50% Si) .08-0. 0.The value of constant a depends on steel composition.00165 MN/m² (Yada & Senuma: 0. 0. Sources: .81% C. then it must be added to value of ε of the next pass.05-0.81% C.05-0.50% Mn.5: Time Required for 50% Static Recrystallization [s] t0.20-0.14% Mn.ts can be assumed as being zero as it is negligibly short for the deformation conditions of hot flat rolling (Wang & Tseng).50% Si) . as it was determined under plane strain conditions. 0.00180 MN/m² (Wang & Tseng: 0.This model is very interesting as it links hot strength with microstructural evolution. . . September 1996.and Micro-Modeling of Hot Rolling of Steel Coupled by a Micro Constitutive Relationship.SENUMA. 39:2. S. T. Journal of the Japan Society for Technology of Plasticity.32) T = (T + 273) / 1000 If T >= Td Then g=1 Tx = T mShida = (-0. 34-9. Microstructure Evolution of Plain Carbon Steels. mShida. 1986. Structure of Austenite of Carbon Steels in High Speed Hot Working Process. November 1984.SENUMA.07 * C Td = 0.WANG. & LIU. J. Td.41) / (C + 0.YANAGIMOTO. g. 2112-2119. et alii. H. & SENUMA. February 1999.41 – 0.019 * C + 0.126) * T + (0. J. ISIJ International. Tx. . Incremental Formulation for the Prediction of Microstructural Change in Multi-Pass Hot Forming. Def. p.A. . 70:15. 27:300.R. Tetsu-to- Hagané.075 * C – 0. A. Gorni Steel Forming and Heat Treating Handbook 119 . 49-61. 1986.05) Else . H. T. Resistance to Hot Deformation of Steels. 7th Riso International Symposium on Metallurgy and Materials Science. & TSENG. SigF As Single nShida = 0. 171-175. T. Riso National Laboratory. Macro.95 * (C + 0. VelDef) Dim nShida.YADA. Roskilde. 547-552. . T. & YADA. Iron and Steelmaker. . Shida Calculation algorithm expressed in Visual Basic: Function Shida(C. The mean flow stress calculated is this algorithm is already expressed in effective (von Mises) units.49) / (C + 0. as it is multiplied by 2/√3. 0.   0.081 * C – 0. 700  έ  1200°C. Gorni Steel Forming and Heat Treating Handbook 120 g = 30 * (C + 0.95 * (C + 0. Cr is the chromium content.05)) Shida = 2 / Sqr(3) * SigF * (1. all expressed as weight percent. Sources: . .2) ^ nShida – 0. which formula is described below: Mn Cr  V  Nb C eq  C   6 12 where Mn is the manganese content.32) End If SigF = 0. . that is.019 * C + 0.3 * (Def / 0.2)) * _ (VelDef / 10) ^ mShida End Function Notation: Shida: Steel Mean Flow Stress [kgf/mm²] C: C content [weight %] T: Temperature [°C] Def: True Strain VelDef: Strain Rate [s-1] Observation: .9) * (T – 0.7. V is the vanadium content and Nb is the niobium content.3 * (Def / 0.027 / (C + 0.42)) ^ 2 + (C + 0.28 * g * Exp(5 / Tx – 0.09) Tx = Td mShida = (0.154) * T + (-0.01 / (C + 0. corrected for plane strain conditions.20%.The effect of some alloy elements over hot strength can be considered by Shida equation.1  έ  100 s-1.207) + 0.06) / (C + 0. In this case carbon content must be replaced by an equivalent carbon (Ceq) content.Equation valid for the following parameter range: C  1. 610-7. . Elsevier. et alii. 1969. .G.Resistance to Deformation of C Steels at Elevated Temperature. Journal of the Japan Society for Technology of Plasticity. : Mathematical and Physical Simulation of the Properties of Hot Rolled Products. S. Amsterdam. J. SHIDA. 10:103.Gorni Steel Forming and Heat Treating Handbook 121 . LENARD. Empirical Formula of Flow Stress of C Steels . 248 p. 1999. 0%.45% ≤ Mn ≤ 1. Ni ≤ 5. Just .4 mm J d  60 C  20 . Cr ≤ 1.7 mm J d  78 C  22 Cr  6.Jominy Curves .Equations valid for the following chemical composition range: 0.4 Ni  19 Mn  34 Mo  28 V  19.29% and 6.4 mm ≤ d < 39. Mo ≤ 0. 0.52% and V ≤ 0.3 Ni  16 Mn  29 Mo  16.00992 d 2 C  20 Cr  6.15% ≤ Si ≤ 1.7 mm J d  87 C  14 Cr  5.17 d  18 Observation: . Gorni Steel Forming and Heat Treating Handbook 122 .1 d  1.55%.95%.d < 6.Equation Considering the Effect of Austenite Grain Size .4 mm ≤ d < 39.05 d  1. 0.28% and 6.39 d  22 .80 d  7 .C > 0.60%.4 ≤ d < 39.7 mm J d  98 C  0.C < 0.2%.9 Ni  21 Mn  33 Mo  16.6.75%.10% ≤ C ≤ 0. .8 d  1. Ni ≤ 8.3 Ni  16 Mn  35 Mo  5 Si  0.5 ≤ Gγ ≤ 11.97. 96. Gorni Steel Forming and Heat Treating Handbook 123 J d  88 C  0. Si ≤ 3.94%. Cr ≤ 1. November 1969.00553 C  19 Cr  6. Mo ≤ 0. 0.33 d  2 Observation: . .53 and 1.82 G  15. Metal Progress. New Formulas for Calculating Hardenability.Equation valid for the following conditions: 0.08% ≤ C ≤ 0.20% ≤ Mn ≤ 1.56%. Notation: Jd: Hardness [Rockwell C] Alloy Content: [weight %] d: Distance from the Cooled End [mm] Gγ: Austenite Grain Size Index [mm] Source: JUST. E.9 d  1.88. 87-88.80. 8863 [1  17.0006 Cr  0.78  ) [1  (24.1000 K < T < 1250 K .5  106 (T  800)] Notation: aα: Ferrite Lattice Parameter [Ǻ] T: Temperature [K] Observations: .0002 Ni  0.0031 Mo  0.0. Austenite a 0  3.800 K < T < 1200 K .033 C  0.Lattice Parameters of Phases . Gorni Steel Forming and Heat Treating Handbook 124 . Ferrite a  2.0005 < ξ < 0.573  0.0018 V Notation: aγ: Austenite Lattice Parameter [Ǻ] T: Temperature [K] ξ: C [Atomic Fraction] Observations: .00095 Mn  0.0365 a  (3.9  50  )  10 6 (T  1000)] .6306  0. 5234 [1  (5. bθ.311  106  1.300 K < T < 1000 K Source: CABALLERO. F. . Modelling of Kinetics and Dilatometric Behaviour of Austenite Formation in a Low- carbon Steel with a Ferrite Plus Pearlite Inicial Microstructure.311  106  1. Cementite a  4. cθ: Cementite Lattice Parameter [Ǻ] T: Temperature [K] Observations: .655  1012 T 2 ) (T  293)] b  5. 2002. Gorni Steel Forming and Heat Treating Handbook 125 Notation: aγ: Austenite Lattice Parameter [Ǻ] Alloy Content: [Weight Percent] Observations: . 3533- 3540.0883 [1  (5.1000 K < T < 1250 K .G.655  1012 T 2 ) (T  293)] c  6.942  109 T  9.655  1012 T 2 ) (T  293)] Notation: aθ.311  106  1.7426 [1  (5. et alii. Journal of Materials Science.942  109 T  9. 37.942  109 T  9. Source: Values compiled by Rajindra Clement Ratnapuli from assorted references. given in the table below: Precipitate A B MnS 8236 5.aAmBn is equal to one if the precipitate is pure.90 TiS 8000 4. B: Constants of the Solubility Product.00 ZrN 17000 6. .aAmBn  1 if there is co-precipitation with another element.38 Observations: . General (a A ) m (a B ) n A log  B a Am Bn T Notation: AmBn: Precipitate Considered for Calculation ax: Alloy Content [weight %] T: Temperature [K] A. . Gorni Steel Forming and Heat Treating Handbook 126 .03 TiN 16586 5.Liquid Steel Solubility Products . und Stahlschmelzen.6 Si  4. 399-402. K. Gorni Steel Forming and Heat Treating Handbook 127 .3 Cr  3. _ . Günstige Giesstemperatur im Vergleich zum Erstarrungspunkt von Eisen.Liquidus Temperature of Steels TLiq  1536  78 C  7.1 Ni  1. 71: 8. Stahl und Eisen. 1951.9 Mn  34 P  30 S  5 Cu  3.6 Al  2 Mo  2 V  18 Ti Notation: TLíq: Steel Melting Temperature [°C] Alloy Content: [weight %] Source: GUTHMANN. 327 700 0. 2000. Plastic Range: 0. 243. Fletcher Temperature  [°C] 600 0. 2004. Burns Harbor. Gorni Steel Forming and Heat Treating Handbook 128 . Definition : Poisson Ratio . .352 1000 0. Guidelines for Fabricating and Processing Plate Steel.360 Source: PICQUÉ. p. A. B.5 Source: WILSON. . Bethlehem-Lukens Plate Report.344 900 0. Elastic Range: 0.Poisson Ratio . Doctor Thesis.3 .D. 97 p. Experimental Study and Numerical Simulation of Iron Oxide Scales Behavior in Hot Rolling.335 800 0. École de Mines de Paris. Precipitate Isothermal Solubilization Kinetics r02 t 2cD Notation: AmBn: Spheric precipitate considered for calculation t: Time for solubilization of the precipitate [s] r0: Radius of the precipitate [m]. [cm] or [mm] Ci  C m Ci c  C p  Ci C p Cm: Solute concentration in the bulk metal [%] Ci: Solute concentration in the precipitate/matrix interface [%]  A    B  T  10 Ci  aB T: Temperature [K] A. aB: Alloy content [weight percent] Cp: Solute content in the precipitate [%] m MA Cp  m MA  n MB Mx : Atomic mass of the element [g] . given in the table at the topic Austenite Solubilization Products. Gorni Steel Forming and Heat Treating Handbook 129 . B: Constants of the Solubility Product. cm²/s or mm²/s].49 * 10-4 * Exp(-284100/R’ T) Austenite D [m2/s] = 2. 1.52 * Exp(-59900/RT) Cr .30 * 10-2 * Exp(-234500/R’ T) Pickering Al Austenite D [m2/s] = 0.314 J/mol.10 *10-4 * Exp(-135700/R’ T) Ferrite D [cm2/s] = 8.K R’: Universal Gas Constant.02 * Exp(-20100/RT) C Ferrite D [m2/s] = 0.K Element Phase Equation Source Ferrite D [m2/s] = 0.981 cal/mol.62 * 10-6 * Exp(-80400/R’ T) Pickering Austenite D [m2/s] = 0. 8. Gorni Steel Forming and Heat Treating Handbook 130 Cm: Solute content in a position far away from the precipitate [%] D: Solute Diffusion Coefficient [m²/s. calculated according to the general equation below: Q D  D0 exp   RT  D0: Constant Q: Activation Energy for Diffusion [J] or [cal] R: Universal Gas Constant.10 * 10-3 * Exp(-286000/R’ T) Borggren B Austenite D [m2/s] = 2 * 10-4 * Exp(-87864/R’ T) Ferrite D [cm2/s] = 0. 90 * 10-4 * Exp(-343000/R’ T) Andersen Nb Austenite D [m2/s] = 5.67 * 10-4 * Exp(-256700/R’ T) Pickering Fe Austenite D [m2/s] = 0.80 * Exp(-69700/RT) Ferrite D [m2/s] = 1.30 * 10-2 * Exp(-344600/R’ T) Pickering Austenite D [m2/s] = 5.65 * Exp(-276000/R’ T) Austenite D [m2/s] = 1.78 * 10-5 * Exp(-264000/R’ T) Borggren Ferrite D [cm2/s] = 6.90 * Exp(-55000/RT) .00 * 10-5 * Exp(-28600/R’ T) Borggren Austenite D [mm2/s] = 140 * Exp(-286000/R’ T) Mn Austenite D [cm2/s] = 0.91 * 10-4 * Exp(-168600/R’ T) Pickering Austenite D [mm2/s] = 5.Gorni Steel Forming and Heat Treating Handbook 131 Austenite D [cm2/s] = 10.50 * 10-6 * Exp(-77000/R’ T) Pickering Austenite D [m2/s] = 0.6 * 10-3 * Exp(-18600/RT) N Ferrite D [m2/s] = 0.49 * 10-4 * Exp(-284100/R’ T) Pickering Austenite D [m2/s] = 7.60 * 10-4 * Exp(-286000/R’ T) Borggren Austenite D [mm2/s] = 51 * Exp(-230120/R’ T) P Austenite D [cm2/s] = 2. 1997. 2673-2688. Acta Metallurgica and Materialia. I. Advanced Materials Research.Information compiled by Rajindra Clement Ratnapuli from assorted references. T.25 * 10-4 * Exp(-264200/R’ T) Pickering Sources: .25 * Exp(-63100/RT) Austenite D [m2/s] = 0. 43:7. e al. 2007. 1995.00 * 10-4 * Exp(-286000/R’ T) Borggren Ti Austenite D [m2/s] =1.61 * 10-4 * Exp(-267100/R’ T) Pickering Austenite D [cm2/s] = 0. 714-719. BORGGREN. & GRONG.50 * 10-5 * Exp(-251000/R’ T) Borggren Ferrite D [cm2/s] = 3. O. A Model for Particle Dissolution and Precipitation in HSLA Steels.GLADMAN. . Analytical Modelling of Grain Growth in Metals and Alloys in the Presence of Growing and Dissolving Precipitates – I. The Physical Metallurgy of Microalloyed Steels. London. . Normal Grain Growth. The Institute of Materials. Gorni Steel Forming and Heat Treating Handbook 132 Si Austenite D [m2/s] = 7. 15-17. U. .ANDERSEN. 363 p. .92 * Exp(-57600/RT) V Ferrite D [m2/s] = 0. 26 ( disc   ppt )  d Notation: YS: Yield Strength at 0.9 f  x   ppt  ln   4  x  2.Relationships Between Chemical Composition x Process x Microstructure x Properties .1 YS  88  37 Mn  83 Si  2900 N sol    disc   ppt dL TS  246  1900 C  230 (Mn  Cr )  185 Mo  90 W  125 Ni  65 Cu  385 (V  Ti ) 11. Acicular Ferrite/Low Carbon Bainite Steels 15.2  10 3  ( PICKERING ) or 8  10 4  ( KEH ) 5. Gorni Steel Forming and Heat Treating Handbook 133 .5 ITT   19  44 Si  700 N sol  0.5  10  .2% Real Strain [MPa] TS: Tensile Strength [MPa] ITT: Impact Transition Temperature for 50% Tough Fracture [°C] Alloy Content: [weight %] Nsol: Solubilized (Free) Nitrogen [%] dL: BainiteFerrite Lath Size [mm] disc: Strength Due to Dislocations [MPa] ppt: Precipitation Strengthening According to the Ashby-Orowan Model [MPa] Nsol: Solubilized (Free) Nitrogen [%] d: Mean Spacing between High Angle Boundaries (“Packet” or Prior Austenite Grain Boundaries)  disc    b   1. KEH.1  27.2 N sol  d 7. Jan-Oct 1980.2 Si  2. TISCO. C-Mn Mild Steels (Pickering) 17.7 Mn  83. .S.85 Pearl  d d 15.B.9  32.3 Mn  83.4 YS  53. 1965.2 Si  354. Silver Jubilee Volume.2 N sol . PICKERING.25 Mn  0.1 Mn  116 Si  554 P  143 Sn  1509 N sol  d d  unif  0.28  0. F. Some Aspects of the Relationships between the Mechanical Properties of Steels and their Microstructures. A. . 12:115.039 Sn  1.044 Si  0.. 9-30. Work Hardening and Deformation Sub-Structure in Iron Single Crystals in Tension at 298K.4  370  120 C  23.20 C  0. 105-132. Philosophical Magazine.7 TS  294. Gorni Steel Forming and Heat Treating Handbook 134 Notation: : Empirical Constant : Shear Modulus [MPa] b: Burger’s Vector [cm] : Dislocation Density [lines/cm²] f: Volume Fraction of the Precipitate x: Mean Planar Intercept Diameter of the Precipitate [m] Sources: . F. Expressed as Real (Logarithmic) Strain tot: Total Elongation.5 50% ITT   19  44 Si  700 N sol  2.4  30 C  6.: Physical Metallurgy and the Design of Steels.20 Mn  0. C-Mn Mild Steels (Choquet)  15.2 S  3.32  19250 N sol  162 Mn  462 O Notation: YS: Yield Strength at 0.40  2. . 1978.094    F  0.017  tot  1. Allied Science Publishers.25 Sn  d 11.2% Real Strain [1/MPa] unif: Uniform Elongation.2 Pearl  d Y  12.9 P  0.90 C  0.2% Real Strain [MPa] TS: Tensile Strength [MPa] d/d: Strain Hardening Coefficient at 0.B. Expressed as Real (Logarithmic) Strain Pearl: Pearlite Fraction in Microstructure [%] 50% ITT: Impact Transition Temperature for 50% Tough Fracture [°C] Y: Strain Ageing After 10 Days at Room Temperature [MPa] Alloy Content: [weight %] d: Grain Size [mm] Source: PICKERING. Gorni Steel Forming and Heat Treating Handbook 135 0. 275 p.8  Mn   (360  2600 C 2 ) (1  F ) YS  63  23 Mn  53 Si  700 P  d . London.16 Si  2. Proceedings.: Modelling of Forces. Structure and Final Properties during the Hot Rolling Process on the Hot Strip Mill. P. et alii. .5 Mn  43 Si  114 P  45 S  31 N sol   0. In: Mathematical Modelling of Hot Rolling of Steels.01 (723  Tcoil )  0.02 T fin ) S0 d . Montreal.08 (38.002 T fin  100 N sol ) Ceq  0.01 etot  0.06 Pearl   100 0. 1990.016 Pearl 12.2 (6 C  Mn  30 P  35 S  23 Al  0. 34-43.2   5.6 YS  99. C-Mn Steels Processed at a Hot Strip Mill d  11.1 S0  723  Tcoil 0. Gorni Steel Forming and Heat Treating Handbook 136 7.2% Real Strain [MPa] TS: Tensile Strength [MPa] Alloy Content: [weight %] F: Ferrite Fraction d: Ferritic Grain Size [mm] Source: CHOQUET.78 0 .5  2.24 F TS  237  29 Mn  79 Si  700 P   500 (1  F ) d Notation: YS: Yield Strength at 0. The Metallurgical Society of CIM. 004 Pearl 11.8~4.03 Mn  41.23 P  4.000096 Pearl S 0  0. S < 0.030%.0 mm.05 Mn  4. . Tfin: 850~880°C.36 S  2.These equations are valid under the following conditions: Slab Reheating Temperature: 1250°C.18%. Gorni Steel Forming and Heat Treating Handbook 137 0.4 Si  57.8   8. Mn: 0.47 (19.40~1.5 TS  130.2% Real Strain [MPa] TS: Tensile Strength [MPa] : Total Elongation [%] d: Ferrite Grain Size [m] Alloy Content: [weight %] Tcoil: Coiling Temperature [°C] etot: Total Hot Rolling Conventional Strain [%] Tfin: Finishing Temperature [°C] Nsol: Solubilized (Free) Nitrogen [%] Pearl: Pearlite Fraction Present in Microstructure [%] S0: Pearlite Lamelar Spacing [mm] Mn Si Ceq  C   S 6 24 T fin  Tcoil  T fin Observations: . Al: 0.0090%.020~0. N: 0. Tcoil: 615~650°C.16 N sol   0.0030~0.00%.020%.12   100 (0.37 Sn  1. Si < 0.08~0.0006 T fin ) d Notation: YS: Yield Strength at 0.050%.7 P  69 S  262 N sol  ) S0 d 0. C: 0.020%. P < 0. Final Thickness: 1. N: 0. .27  78. et alii.5 d CR 0.10%. P < 0.005~0. Al: < 0.37  YS  28.28 d HR (after 60% cold rolling and annealing) d CR  0. Gorni Steel Forming and Heat Treating Handbook 138 Source: ARTIGAS.29 d HR (after 70% cold rolling and annealing) 2.040%. 38. 2002.0020~0.011  0. . S < 0. Mn: 0.2% Real Strain [MPa] yield: Yield Elongation [%] n: Strain Hardening Coefficient Measured during Tension Test Observations: . 339-347.16  154 d HR d CR  yield  6.01 n  0.013  0.016%.: Prediction de Propiedades Mecánicas y Microestructurales em Aceros Laminados en Caliente. A.026%. C-Mn Mild Steel: Hot/Cold Rolled and Annealed d CR  0. Revista Metalurgica CENIM. Si < 0.72 YS  3.33  d CR Notation: dCR: Grain Size of Cold Rolled Strip [mm] dHR: Grain Size of Hot Rolled Strip [mm] YS: Yield Strength at 0.0040%.40%.These equations are valid under the following conditions: C: 0.010%. Cold rolled steel was box annealed at 700°C. was equal to 32 hours.68 Mn  70. . 1966. 824-845.: Untersuchungen über den Einflu der Korngröe des Warmbandes auf die Kaltbandeigenschaften. C-Mn Steels with Ferrite-Pearlite Structure (Grozier & Bucher) 3. 2. et alii. 59. C-Mn Mild Steel.97 Si  4.84  40. including heating of the samples. W.517 Pearl  d 2.40 Si  1.344 TS  223. being followed by furnace cooling.74 Mn  101. Source: LANGENSCHEID. . 64-70.: The Effect of Grain Size on the Stress-Strain-Relationship in Low-Carbon Steel.323 Pearl  d Notation: . G. Gorni Steel Forming and Heat Treating Handbook 139 . 1971.11  56. Transactions of the ASM. Full Annealed 5 n 1 10  d Notation: n: Strain Hardening Coefficient Measured during Tension Test d: Grain Size [mm] Source: MORRISON. Hoesch Berichte aus Forschung und Entwicklung unserer Werke. the time of treatment.282 YS  95. 89. J.H. correlation coefficient r is equal to 0. 0.00~0. d: 0.6 TS  492  3.Useful range: Mn: 0. Its 95% confidence limit is 7%. Source: GROZIER. tensile strength.25% Si and 0~40% Pearl.: Influence du Niobium et de l’Azote sur la Résistance des Aciers a Structure Ferrite-Perlite.9 C  11. .00~1. .4 Si which was fitted used 32 points of date of ferritic-pearlitic hot rolled.002770 cm. Novembre 1966.30% C.00~0.3 Mn  48. 939-941. C-Mn Steels with Ferrite-Pearlite Structure (Pickering) 14. Si 0. 52 MPa.These equations were fitted using at least 50 points of data.7  110.38 Pearl  246 Mn  277 Si  2616 S  723 P  246 Cr  6616 N sol  d . . . Its useful range is 0.000252 ~ 0. Gorni Steel Forming and Heat Treating Handbook 140 YS: Yield Strength [MPa] TS: Tensile Strength [MPa] Pearl: Pearlite Fraction in Microstructure [%] Alloy Content: [weight %] d: Grain Size [mm] Observations: .D.60%.80% Mn.00 ~ 0. 26MPa.00 ~ 1.9 YS  246  4. 0.15 Pearl  44. air cooled and normalized steel . J. Pearl: 0 ~ 80%.6 Mn  138 Si  923 P  169 Sn  3754 N sol  d 44.Eventually pearlite fraction can be calculated with the equation below: Pearl  10. & BUCHER. 63:11. cooled in air with a mean cooling rate of 1°C/s at 760°C.95% confidence limits: yield strength. Revue de Métallurgie.80%. 20 Si  3. Tokyo.043 Sn  1. p.4 S  4.30 Mn  0.29 Sn  d 6.2% Real Strain [MPa] TS: Tensile Strength [MPa] d/d: Strain Hardening Coefficient at 0. in: Towards Improved Ductility and Toughness.39 Pearl  111 Si  462 P  152 Sn  1369 N sol  d d  unif  0.2 Ttrans  43  1.: The Effect of Composition and Microstructure on Ductility and Toughness.4 P  0.0 N sol 0. Expressed as Real (Logarithmic) Strain tot: Total Elongation.5 Pearl  37 Mn  d Notation: YS: Yield Strength at 0.2% Real Strain [1/MPa] unif: Uniform Elongation. F.015 Mn  0.015  tot  1.040 Si  0.30  0.016 Pearl  0. Climax Molybdenum Company. 9-32 .B. Dual Phase Steels .020 Pearl  0.27  0. 1971. Expressed as Real (Logarithmic) Strain Pearl: Pearlite Fraction in Microstructure [%] Ttrans: Fracture Appearance Transition Temperature [°C] Alloy Content: [weight %] d: Grain Size [mm] Source: PICKERING. Gorni Steel Forming and Heat Treating Handbook 141 d 15.4  385  1. . 1992. O.A. & BRANCHINI. Análise da Evolução do Encruamento de um Aço Bifásico. Nov. A.A.L. 127-145. Relações Microestrutura-Propriedades Mecânicas em um Aço Bifásico Laminado a Quente. Set.L. Gorni Steel Forming and Heat Treating Handbook 142 1 YS  203  855 L 1 f TS  266  548  1741 L d d 1 f  266  548  1741 d L d 1  unif  32  64 L Notation: LE: Yield Strength [MPa] LR: Tensile Strength [MPa] d/d: Strain Hardening Coefficient at Uniform Elongation [1/MPa] aunif: Uniform Elongation [%] L: Mean Ferritic Free Path [m] d: Mean Diameter of Martensite Islands [m] Sources: .G.G. São Paulo. A. EPUSP/UNICAMP/ABAL. & BRANCHINI. In: 4° Simpósio de Conformação Mecânica. O. .GORNI. ABM/AEA. 23-42. In: 1º Seminário sobre Chapas Metálicas para a Indústria Automobilística. São Paulo. 1990.GORNI. 4    1   3  f  178   3.5  S 0   97 Si  d    11. Gorni Steel Forming and Heat Treating Handbook 143 .7 Si  762 N sol  d   S0 p  Notation: YS: Yield Strength at 0.48  106 t   48.6 13. Medium C Steels    YS  3 f   35  58 Mn  17.5      1  f   5.2    1  3 f     720  3.8   63 Si  42 N sol   d   S0   TS  3 f   246  1140 N sol  18.2% Real Strain [MPa] TS: Tensile Strength [MPa] ITT: Impact Transition Temperature for 50% Tough Fracture [°C] f: Volume Fraction of Ferrite d: Ferrite Grain Size [mm] Alloy Content: [weight %] Nsol: Solubilized (Free) Nitrogen [%] S0: Pearlite Lamelar Spacing [mm] p: Pearlite Colony Size [mm] t: Pearlitic Carbide Lamellar Thickness [mm] Sources: .3 ITT  f    46   335    3. December 1992. Some Aspects of the Relationships between the Mechanical Properties of Steels and their Microstructures.6  26.0 TS  164.2% Real Strain [MPa] TS: Tensile Strength [MPa] Alloy Content: [weight %] d: Grain Size [mm] pptNb: Precipitation Strengthening [MPa]. only for steels with V [MPa] CR: Cooling Rate [°C/s] Source: HODGSON. 210.7 YS  62.0 P  212. e outros.6 Ni  3339. GLADMAN.7 Si  651. 32:12.9  634.B. & GIBBS.9 Cu  3286. .6 Mn  99. Gorni Steel Forming and Heat Treating Handbook 144 . . Dec. only for steels with Nb [MPa] pptV: Precipitation Strengthening [MPa]. TISCO. PICKERING.0 N sol    ppt d 11.2 Si  759. 105-132. Some Aspects of the Structure-Property Relationships in High Carbon Ferrite-Pearlite Steels. 1972. Silver Jubilee Volume. F. .4 N sol    ppt d  ppt Nb  2500 Nb  Vppt  57 log CR  700 V  7800 N sol  19 Notation: YS: Yield Strength at 0. P. ISIJ International. Jan-Oct 1980. 916-930. A Mathematical Model to Predict the Mechanical Properties of Hot Rolled C-Mn and Microalloyed Steels.7 C  53. T. Journal of the Iron and Steel Institute. R.1 Mn  60.9 P  472.D. Microalloyed Steels (Hodgson) 19. 1329-1338.K. Observations: . defined by the formula below [MPa]. using the following linear coefficients: Element MPa/weight % Ni 33 Cr -30 . for steels with Nb. Gorni Steel Forming and Heat Treating Handbook 145 . Ti and/or V.2% Real Strain [MPa] 0: Friction Stress [MPa] Alloy Content: [weight %] d: Grain Size [mm] ppt: Precipitation Strengthening [MPa].1 YS   0  37 Mn  83 Si  2918 N sol    ppt d Notation: YS: Yield Strength at 0. The effect of solid solution strengthening from another alloy elements solubilized in ferrite can be included in this equation.The Friction Stress 0 value depends on the previous treatment of the material and can be found in the table below: Condition 0 [MPa] Mean 70 Air Cooled 88 Overaged 62 . Microalloyed Steels (Pickering) 15. 00 ~ 0.Relationship adequate for the calculation of the precipitation strengthening of quench-aged carbides and precipitate carbonitrides in Nb.05 Ti as TiC 3000 1500 0.5  10  Notation: ppt: Precipitation Strengthening According to the Ashby-Orowan Model [MPa] f: Volume Fraction of the Precipitate x: Mean Planar Intercept Diameter of the Precipitate [m] Observations: .18 . V and Ti steels.ppt can be calculated using a more simplified approach.06 Nb as Nb(CN) 3000 1500 0.00 ~ 0. multiplying the total content of the precipitating alloy by the factor B shown in the table below: Alloy and Bmax Bmin Alloy Range Precipitate [MPa/weight %] [MPa/weight %] [weight %] V as V4C3 1000 500 0.03 ~ 0. 5. .9 f  x   ppt  ln   4  x  2.15 V as VN 3000 1500 0. The precipitation strengthening contribution is calculated according to the Ashby-Orowan model. Gorni Steel Forming and Heat Treating Handbook 146 P 680 Cu 38 Mo 11 Sn 120 C 5000 N 5000 .00 ~ 0. Silver Jubilee Volume. .20 C eq  (27401 N ef  2) V  hf 181.Precision of the Formulas:  40 MPa.35%. Gorni Steel Forming and Heat Treating Handbook 147 Source: PICKERING.B. F. .42 Observations: . 105-132. Jan-Oct 1980.5 TS  74.1 Ceq  (31125 N ef  39) V  hf Notation: YS: Yield Strength at 0.Formula Derived for Steels with Al Content over 0.2% Real Strain [MPa] TS: Tensile Strength [MPa] Alloy Content: [weight %] hf: Plate Thickness [mm] Mn Cr  Mo Ni  Cu Ceq  C    6 5 15 Ti N ef  N tot  3. Microalloyed VTiN Steels Processed by Recrystallization Controlled Rolling 419. TISCO. . Some Aspects of the Relationships between the Mechanical Properties of Steels and their Microstructures.5 YS  41.1  985.25 and 0.4  575.010% and Si Content between 0. -50~-120°C. 7~26 μm. Structural Steels: Impact Transition Temperature (Mintz 1979) 8. Proceedings. American Society for Metals/The Metallurgical Society. .1  ppt ITT 54J  192 t   d 2 .S. et alii. Oct. et alii.2% Proof Stress [MPa] Observations: . 2015. Campinas. CBMM.: Effect of Niobium and Boron on the Strength and Toughness of Abrasive Wear Resistant Direct-Quenched Low-Carbon Steel. Pittsburgh.3 ITT 27 J  173 t   0. Structural Steels: Ductile-Brittle Transition Temperature (Hannula 2015) 1038  0. International Symposium on Wear Resistant Alloys for the Mining and Processing Industry. Source: HANNULA. P.341  YS d 90  d   90  Notation: DBTT 34 J/cm²: Ductile-Brittle Transition Temperature for Charpy Specific Energy of 34 J/cm² [°C] d90: 90th Percentile of Grain Size (Equivalent Circle Diameter) Distribution [μm] YS: 0.: Effect of Vanadium on Mechanical Properties and Weldability of Structural Steels. 910~1070 MPa. Proceedings. 1993. Gorni Steel Forming and Heat Treating Handbook 148 Source: MITCHELL. YS.Useful range: DBTT 34 J/cm². J. In: Low Carbon Steels for the 90’s.37  ppt d 10. d90.047  DBTT 34 J / cm 2  42    0. . 0.7 CR  57.021%. Source: MINTZ. Δσppt. July 1979.49%.11~0.63~1.97 CR  70. t.2 Si  1224 S  1360 P  3.08 . .65 ITT 54J  84.7 50% FATT  131 t   0.1   1.67 p  53.8 Mn d 5.5 μm.4 p  57. Alsol.Useful range: C. Ntotal. 252-260.003~0.02~0. et alii. 4.950.9~38. 0.72 μm. s = 8. 0. 0. Gorni Steel Forming and Heat Treating Handbook 149 12. Timax. 0. Vmax. Nbmax. Structural Steels: Impact Transition Temperature (Mintz 1994) 7. Metals Technology. Si.20%. d. 0. B.1 Si  1490 S  1379 P  4.: Influence of Carbide Thickness on Impact Transition Temperature of Ferritic Steels. 0. up to 225 MPa.41 ITT 27 J  80.071%.20%.45  ppt  46 d Notation: ITT 27 J: Impact Transition Temperature for Charpy Energy of 27 J [°C] ITT 54 J: Impact Transition Temperature for Charpy Energy of 54 J [°C] 50% FATT: 50% Fibrous Fracture Appearance Transition Temperature [°C] t: Carbide Thickness as Measured by Scanning Electron Microscopy [μm] d: Grain Size [μm] Δσppt: Precipitation Hardening [MPa] Observations: .56%.8   1.12%.16~0.16%. up to 0. Mn. 0.1 Mn d Notation: ITT 27 J: Impact Transition Temperature for Charpy Energy of 27 J [°C] – r² = 0. : Structure-Property Relationships in Ferrite-Pearlite Steels. Si. 0.43%. 0. . Source: MINTZ.0412 YR  0.030%.067~0.170 Al d Notation: YS: Lower Yield Strength [MPa] TS: Tensile Strength [MPa] YR: Yield Ratio d: Ferrite Grain Size [mm] . Nbmax.8 Al  2450 B d 0. Gorni Steel Forming and Heat Treating Handbook 150 ITT 54 J: Impact Transition Temperature for Charpy Energy of 54 J [°C] – r² = 0. et alii. B.2 TS  183   506 P  48. 21:3.0 YS  34. s = 7.8 Si d 11. Almax.Useful range: C. 215-222. 1994. Mn.041%.0025~0. Non-Oriented Si Electrical Steels 22. Ntotal.56~1.Recommended only for normalised steels with ferrite-pearlite microstructure.80 d: Grain Size [μm] p: Pearlite Fraction [%] CR: Cooling Rate [°C/min] Observations: .3   258 P  34.078 Si  0. 0.010%.424   0. 0. 0.220%. 0.955. .51%. Ironmaking and Steelmaking.7 Mn  109 Si  48.2 Mn  52.02~0. Al: < 0.0020%.474 Si  2.003~0.311 Al  25. Gorni Steel Forming and Heat Treating Handbook 151 Alloy Content: [weight %] Observations: . S: 0. N: 0.432%.040%. Influence of Composition and Hot Rolling Parameters on the Magnetic and Mechanical Properties of Fully Processed Non-Oriented Low-Si Electrical Steels.0030%.0282 GBI  16.0014~0.51 C  123.4 C  0. B < 0. .5 N  5. .015%. . 8. 1998.99 O  12.075~0. Mn: 0. Residual Mean Square: 0. the time of treatment. J. P < 0.004~0.004%. Pr2-487/Pr2-490. Si < 0.002~0.658  0. IV France.Adjusted Squared Multiple Correlation: 0.007%.These equations are valid under the following conditions: ULC Steel. including heating of the samples. Phys.082 W²/kg² h2 PT  4. PT  0.Negative effects of O and N are in direct contradiction with specific experimental results.29  66.266 h Notation: PT: Core Loss [W/kg] Alloy Content: [weight %] h: Thickness [mm] Observations: . Source: PINOY.2 r Notation: PT: Total Core Loss at 15 KG [W/kg] .003~0.Cold rolled steel was box annealed at 700°C.823.7 Sinit  130. N: 0.578%.This equation ise valid under the following conditions: C: 0. being followed by furnace cooling.2 S  137. L et alii.34%. S: 0. was equal to 32 hours.109%. Journal of Metals. G. Non-Oriented Electrical Steels. 18-26.mm] Source: LYUDKOVSKY. Gorni Steel Forming and Heat Treating Handbook 152 Alloy Content: [weight %] GBI: Number of Grain Boundary Intercepts per mm h: Thickness [mm] : Density [g/mm³] r: Resistivity [. et alii. January 1986. . html). .com/maxx/software/UK/WeldingFaultFinder/wff22413. Gorni Steel Forming and Heat Treating Handbook 153 .airproducts.Schaeffler Diagram Source: Air Products Web Site (http://www. Gorni Steel Forming and Heat Treating Handbook 154 .032 (T  573) 2  0. Ferrite  (T  300)    64000 1  (-273°C < T < 300°C)  2235   (T  300)    64000 1   0. Austenite  (T  300)    81000 1  (911°C  T < 1392°C)  1989  . Delta Ferrite  (T  300)    39000 1  (1392°C  T < 1537°C)  2514  Notation: .032 (T  573) 2 (300°C  T < 700°C)  2235   (T  300)    64000 1   0.Shear Modulus of Steel and its Phases .024 (T  923) 2 (700°C  T < 770°C)  2235   (T  300)    69200 1  (770°C  T < 911°C)  1382  . Gorni Steel Forming and Heat Treating Handbook 155 : Shear Modulus [MPa] T: Temperature [K] Source: FROST.: Pure Iron and Ferrous Alloys.J. H. & ASHBY. 1982. M. . Cambridge. In: Deformation-Mechanism Maps. Pergamon Press. The Plasticity and Creep of Metals and Ceramics.F. 88 TS Fc  t P K c Notation: Kc: Cutting Specific Pressure or Shear Stress [MPa] TS: Tensile Strength [MPa] Fc: Cutting Force [N] t: Thickness [mm] P: Cutting Perimeter [mm] Source: MESQUITA. E. Gorni Steel Forming and Heat Treating Handbook 156 . Conformação dos Aços Inoxidáveis.L.A. . 39 p. Dezembro 1997.Sheet and Plate Cutting Force and Work . Manual da Acesita. Mesquita K c  0. Tschaetsch F W tB aFt W  1000 Fv P  Notation: F: Cutting Force [N] . 988.10 max 0. Hot rolled or annealed steel (soft) – r² = 0. These equations were fitted using the τB data available below.10 max 0.7) τB: Shear Stress [MPa].50 max . 250 320 .mm] a: Mean Force/Maximum Force Ratio (≈ 0. Standard Error of Deviation = 9 MPa:  B  249  786 C .992. Observations: .50 max .40 max . Standard Error of Deviation = 13 MPa:  B  223  550 C .6 for shearing) P: Cutting Power [W] v: Shear Speed [m/s] η: Machine Efficiency (≈ 0. Cold rolled steel (hard) – r² = 0. as defined by the table or formulas described in the observation below. 240 300 St 13 0. where C is the carbon weight content of steel: . expressed in N/mm²: Steel C Mn Si Soft Hard St 12 0.The value of τB can be calculated from the following equations.08 max 0. 240 300 St 14 0. Gorni Steel Forming and Heat Treating Handbook 157 W: Width [mm] t: Thickness [mm] W: Cutting Work [N. Tools.Processes.80 0. H.30-0.30-0.25 max 1. 2006. Machines.57-0.34 0.40 400 500 C60 0. Berlin. Springer-Verlag.25 max 400 - C10 0. .08-0.15-0.23 0. Gorni Steel Forming and Heat Treating Handbook 158 St 37 0. 218-40.20 max 1.30 max 280 340 C20 0.70 0.27-0.65 0.60 0. Metal Forming Practice . Shearing.30 max 320 380 C30 0.25 max 310 - St 42 0.35 550 720 Source: TSCHAETSCH.25 max 0.13 0.10-0.50-0.18-0.90 0.25 max 0.60-0. H.5 C  33. . .5 ( S  P)  3.8 Mn  124. . 184.9 S  4.5 Cr  3 Ni Ce  80. for Ce > 0.5 P  183.1 ≤ Ce ≤ 0.4 Cr  4.1 ≤ Ce ≤ 0. Effect of the Non-Equilibrium Solidus Temperature on Length of Soft Reduction Zone. for Ce < 0.5 Notation: TSol: Steel Solidus Temperature [°C] a: Constant equal to .2%. Advanced Materials Research.2%. 1493.5 C  12.1% or Ce > 0.4 Co  3. for 0. b: Constant equal to . 2012. Gorni Steel Forming and Heat Treating Handbook 159 . 476-478. 410.3 Si  6.2%. for 0. et alii. .3 Ni  1.8 Si  3.8 Al  1. Alloy Content: [weight %] Source: QIAN. Takeuchi TSol  1536  415.Solidus Temperature of Steels . 139-143. for Ce < 0.75 Mn  17.2%.1%. Qian TSol  a  b Ce 80. 0. 1534.1 Al  Notation: TSol: Steel Solidus Temperature [°C] Alloy Content: [weight %] . Metallurgical Transactions B. . J. Effect of Oscillation-Mark Formation on the Surface Quality of Continuously Cast Steel Slabs. 605-625. E.K. 16B. & BRIMACOMBE. 1985. Gorni Steel Forming and Heat Treating Handbook 160 Source: TAKEUCHI. 9. Gorni Steel Forming and Heat Treating Handbook 161 .Specimen Orientation for Mechanical Testing . Gorni Steel Forming and Heat Treating Handbook 162 The first letter denotes the direction of the applied main tensile stress. Source: ASTM Standard E399-06. 2006. 32 p. ASTM International. West Conshohocken. . Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIC of Metallic Materials. The second letter denotes the direction of crack propagation. 30 537.16 615.83 648.41 598.39 661.37 544.25 690.43 740.46 825 866.36 775 958.92 625 753.83 648.83 632.20 648.29 707.59 1431.78 820.48 875 648.83 525 694.20 725 1138.74 611.69 694. Gorni Steel Forming and Heat Treating Handbook 163 .55 753.48 569.39 485.23 425 623.74 556.22 602.83 623.85 925 648.74 548.23 975 657.44 527.25 519.32 506.71 623.71 598.18 325 569.58 485.44 275 556.83 648.22 837.60 1025 657.Thermal Properties of Steel .16 514.71 590.95 175 523.71 611.88 510.39 648.16 573.57 770.50 736.92 749.48 675 858.48 78697 732. BISRA k T 1008 1023 1040 1524 75 481.51 502.69 225 544.31 1448.20 125 502.32 493.13 845.83 623.61 1582.34 581.97 .18 531.59 950.88 575 740.30 565.88 703.09 606.34 475 661.04 590.62 527.83 615.11 375 594.58 477.20 648.60 586. 16 573.50 736.29 707.48 786.50 686.39 661.39 657.18 531.41 598.59 1431.60 586.18 325 569.58 477.32 493.83 615.32 506.61 1582.71 1175 665.88 703.09 615.39 648.88 510.44 527.83 648.23 690.20 125 502.88 575 740.25 519.51 502.23 425 623.59 950.22 602.27 1275 665.71 623.31 1448.57 653.02 632.48 675 858.83 632.48 875 648.22 837.34 1125 661.34 581.74 611.78 820.57 686.92 749.71 611.30 565.04 590.95 175 523.50 644.97 732.13 845.46 825 866.76 636.92 527.30 573.20 640.83 525 694.34 475 661.36 775 958.57 770.39 648.20 725 1138.44 275 556.57 665.46 623.37 544.74 556.16 615.85 .55 753.43 740.39 485.69 225 544.64 c T 1008 1023 1040 1524 75 481.Gorni Steel Forming and Heat Treating Handbook 164 1075 661.74 548.48 569.83 648.13 669.58 485.11 375 594.92 625 753.69 694.57 678.06 514.09 1225 665. 57 678.20 648.613 11.492 167.432 368.467 34.09 606.57 665.459 11.596 290.23 975 657.71 1175 665.719 375 196.652 110.923 112.446 139.834 625 366.848 125 59.802 255.242 362.742 475 259.372 193.46 623.407 75 35.270 259.177 293.072 329.316 361.83 623.302 223.127 175 85.352 225.028 111.39 648.83 632.13 669.196 275 139.32 1125 661.237 85.06 632.319 35.794 195.243 225 111.547 136.909 325.987 325 167.564 11.57 653.960 196.60 1025 657.27 1275 665.237 138.71 598.603 425 227.121 60.597 167.83 632.76 636.71 590.005 35.143 227.20 640.194 .489 164.290 288.Gorni Steel Forming and Heat Treating Handbook 165 925 648.83 648.20 648.50 686.598 60.164 59.57 686.83 623.346 525 293.50 644.480 256.39 657.761 85.97 1075 661.64 H T 1008 1023 1040 1524 0 0 0 0 0 25 11.09 615.09 1225 665.594 84.243 324.939 575 329. 643 1225 823.425 699.779 542.11 0.551 825.533 699.418 573.722 409.375 Notation: k: Thermal Conductivity [W/(m.050 - 1023 0.601 550.644 793.741 797.238 730.64 0.961 725 456.271 1125 756.029 0.668 875 592.°C)] c: Specific Heat Capacity [J/(kg.034 0.42 0.859 604.904 762.020 831.625 459.13 1040 0.425 638.835 730.263 579.08 0.820 825 554. Gorni Steel Forming and Heat Treating Handbook 166 675 406.697 567.574 1025 690.673 667.498 732.ºC)] H: Enthalpy [J/kg] T: Temperature [°C] Observations: .022 634.552 925 625.034 0.497 795.742 666.12 .129 398.605 512.352 1275 856.640 466.581 602.31 0.070 525.23 0.854 975 657.575 761.100 775 509.820 668.64 0.248 1175 789.252 515.Chemical composition of the steels [wt %]: Steel C Mn Si P S Cu 1008 0.059 457.029 0.031 0.714 1075 723.240 608.299 865.812 401.567 764.307 635.11 0.184 698.08 0.612 829. 217657 10 9 c   10068.21  32. BISRA/Butterworths Scientific Publications. Gorni Steel Forming and Heat Treating Handbook 167 1524 0.313  103 T (T > Ar3) 1. .11 Source: Physical Constants of Some Commercial Steels at Elevated Temperatures. Chou k  80.K] T: Temperature [K] . 1953.109483 10 9 c   4720.02658T (1042K < T < 1060K) 5.98686 T  (1060K < T < 1184K) T2 c  429.18  5.s] c: Specific Heat Capacity [J/kg.038 0.8495  0.07  12.23 1. 1-38.613  10 5 T 2 (T ≤ Ar3) k  20.51 0.037 0.9269  10 2 T  4.324  4.K.91  9.12 0.14  9. London.1497802T (1084K < T < 1665K) Notation: k: Thermal Conductivity [J/m.583364T  (800K < T < 1000K) T2 c   11501.476362T (1000K < T < 1042K) c  34871. M. Seredynski k   58. Gorni Steel Forming and Heat Treating Handbook 168 Source: SEREDYNSKI.084   (T > 700°C)  1000    23.6  103 T  72. .319  10 5 T  (T ≤ 700°C) 24.°C] T: Temperature [°C] λ: Thermal Conductivity [J/m.16  51. 15:10.7  48.66 exp 0.: Finite Element Model of Steel oxide Failure During Tensile Testing Under Hot Rolling Conditions. Materials Science and Technology. .0  0.: Performance Analysis and Optimization of the Plate-Rolling Process. October 1999. F. Proceedings. Krzyzanowski  c p  422. Iron and Steel Institute.96 exp 2.02519  103 T  7850  1  0.°C. Amsterdam.5 (T < 810°C) . 6  T  c p  657.004  10 6 T2  3 Notation: cp: Specific Heat [J/kg.s] ρ: Density [kg/m³] Source: KRZYZANOWSKI. 1191-1198. et alii. In: Mathematical Process Models in Iron and Steelmaking. 1973. s] D: Thermal Diffusivity [m²/s] : Emissivity T: Temperature [°C] Observation: . In: Mathematical Process Models in Iron and Steelmaking.0948 1000  1000  Notation: k: Thermal Conductivity [J/m.12491  0.90% Mn Source: SEREDYNSKI. Iron and Steel Institute. 0.60-0.17-0.Formulas specific for BS En 3 or SAE 1021 steel: 0.68  0. .0115 ] Notation: : Emissivity .02682 Tsup ) 0.07825 104 (700°C < T < 875°C) D  0.85  [1  exp( 42.75  103 T  16. Touloukian 0.23% C.15  107 T  0.°C.02966  104 (T > 875°C) T  T    0. Proceedings.: Performance Analysis and Optimization of the Plate-Rolling Process.8 (T > 810°C) D  0. Gorni Steel Forming and Heat Treating Handbook 169 k  10.02667  107 T  0. 1973. F.38012  1. Amsterdam. : A Transient Simulation and Dynamic Spray Cooling Control Model for Continuous Steel Casting. et alii. 297-306. Metallurgical and Materials Transactions B.A. Gorni Steel Forming and Heat Treating Handbook 170 Tsup: Superficial Temperature [K] Source: HARDIN. R. June 2003. 34B:6. . Gorni Steel Forming and Heat Treating Handbook 171 . M.: Finite Element Model of Steel oxide Failure During Tensile Testing Under Hot Rolling Conditions.K] c: Specific Heat Capacity [J/kg.297 T  4. et alii.°C] E: Young’s Modulus [GPa] T: Temperature [°C] Source: KRZYZANOWSKI.Thermal Properties of Steel Scale . October 1999.7  104 T  25 Notation: k: Conductivity [W/m.367  105 T (600°C < T < 1100°C)   E  240 1  4. . Krzyzanowski k  1  7.969  0. 15:10. 1191-1198. Materials Science and Technology.833  104 T (873K < T < 1473K) c  674. Gorni Steel Forming and Heat Treating Handbook 172 .Thermomechanical Processing of Steel . Revision 2. IACS – International Association of Classification Societies Requirement 1975. . 228 p. Gorni Steel Forming and Heat Treating Handbook 173 Source: Requirements Concerning Materials and Welding. 2004. . where Tmax: Maximum Temperature during the Austenitizing Treatment [°C]. 270 p.3 R    log t a   Ta H a  Notation: Pa: Austenitization Time-Temperature Equivalence Parameter in Terms of Grain Size [K] . & MAEDER. 1982.314 JK-1mol-1 Ha: Activation Energy of Austenitic Grain Coarsening. Collection Scientifique ENSAM. Anisothermal Austenitizing In this case the Austenitization Time-Temperature Equivalence Parameter in Terms of Grain Size. 8. is the period of heating/cooling time between Tmax and Tmin. 460 kJmol-1 for low alloy steels Source: BARRALIS. Métallurgie Tome I: Métallurgie Physique. Isothermal Austenitizing 1 Pa   1 2. G. J. Gorni Steel Forming and Heat Treating Handbook 174 .Time-Temperature Equivalency Parameters for Heat Treating . Tmin: Temperature Calculated According to the Following Equation [°C]: 2 R Tmax Tmin  Tmax  H a Notation: R: Molar Gas Constant. Pa. 457-470. 20.05: Treatment Time Necessary to Achieve 5% Microstructure Banding [min] l: Mean Spacing between Bands [mm] Do: Diffusion Constant for the Alloy Element being Considered [cm²/s]: . Métallurgie Tome I: Métallurgie Physique.16 cm²/s Q: Activation Energy for the Alloy Element Being Considered [cal/mol]: .987 JK-1mol-1 T: Austenitization Temperature [K] Source: YIMING.P: 0. 8. & MAEDER. Gorni Steel Forming and Heat Treating Handbook 175 Ta: Austenitization Temperature [K] R: Molar Gas Constant.P: 43700 cal/mol .01 cm²/s . 1.3 l 2 t 0. 460 kJmol-1 for low alloy steels Source: BARRALIS. .Mn: 0. 1982.Mn: 62500 cal/mol R: Molar Gas Constant. G. Collection Scientifique ENSAM.05  Q D0 e RT Notation: t0.: A Metallographic Investigation of Banding and Diffusion of Phosphorus in Steels. . 270 p.314 JK-1mol-1 ta: Soaking time under Ta Ha: Activation Energy of Austenitic Grain Coarsening. Microstructural Science. 1993. J. X. et alii. Microstructural Banding Homogeneization 0. Transactions of the American Society of Mechanical Engineers. . Tempering (Hollomon-Jaffe) P  T (c  log t ) c  21. Sources: . & MILLER. 162. J.HOLLOMON. Such relationship was also used for the study of hydrogen resistance and HAZ hardness of steels.8 C Notation: P: Hollomon-Jaffe Parameter [K] T: Tempering Temperature [K] c: Constant Characteristic of the Steel Being Tempered t: Soaking time under T [h] C: Carbon Content [wt%] Observations: .D. microalloyed and low alloy steels: .This expression was also deduced by Larson & Miller. Thelning) .R. Transactions of the AIME. 20 (Larson & Miller.Other values for the constant c were proposed by several authors for carbon. Time-Temperature Relations in Tempering Steel. & JAFFE. .. 765-775.53  5. 18 (Grange & Baughman) .H. 223-249. Irvine et alii. A Time-Temperature Relationship for Rupture and Creep Stresses.LARSON. In that case c is equal to 20 and P is divided by 1000. which applied it to the study of metal creep. L. F. Gorni Steel Forming and Heat Treating Handbook 176 . 1945. 74. 1952. J. Journal of the Iron and Steel Institute.: Steel and its Heat Treatment – Bofors Handbook. .Gorni Steel Forming and Heat Treating Handbook 177 . 570 p. 1981. . 1956. 161-182. 165-197. Feb. Transactions of the American Society for Metals. & BAUGHMAN. R. Grain-Refined C-Mn Steels. . Butterworths.J.A. K.IRVINE. et alii. K.GRANGE.E. R. London. Hardness of Tempered Martensite in Carbon and Low Alloy Steels. 68. 1967.THELNING.W. et alii. . June 1984. Nippon Steel Technical Report.Welding Effects . M. Gorni Steel Forming and Heat Treating Handbook 178 .03) Si     (4 Al )   2     10   2   Notation: Feq: Weld Interface Cracking Susceptibility during Flash Butt Welding (No Crack = Zero) Alloy Content: [weight %] Source: MIZUI. Nippon Steel Technical Report. Weld Interface Cracking Susceptibility during Flash Butt Welding  2  Mn  2  3 Cr   2 Feq  (C  0. et alii. 23. 23. June 1984.: Application of High-Strength Steel Sheets to Automotive Wheels. 19-30. Tensile Strength after Flash Butt Welding  Mn Si Cr V  TS eq  52  C       30  5 7 9 2 Notation: TSeq: Tensile Strength After Flash Butt Welding [kgf/mm²] Alloy Content: [weight %] Source: MIZUI. M. 19-30.: Application of High-Strength Steel Sheets to Automotive Wheels. . 55-58.Welding Pool Phenomena Source: ROGER. F. Comsol News. 2010. . Gorni Steel Forming and Heat Treating Handbook 179 . p. Modeling Finds the Minimum Energy for the Best Weld. 3 . A. Guidelines for Fabricating and Processing Plate Steel. Definition E  2 G (1   ) Notation: E: Young Modulus G: Shear Modulus : Poisson Ratio .48466    6.5 Source: WILSON. High Temperature: Pietrzyk   T   T  2  T  3  T  4  5 E  2.87438    10. Gorni Steel Forming and Heat Treating Handbook 180 .0906    14. Burns Harbor. .D.Valid for steel.07  0. Steel. Bethlehem-Lukens Plate Report.20767    10   1000   1000   1000   1000   Notation: E: Young Modulus [MPa] T: Temperature [°C] Observation: . 97 p. . 2000.Young Modulus . Plastic Range: 0. No information available about the range of valid temperatures. Elastic Range: 0. p. B. 158-162. .01379 T 2 Notation: E: Young Modulus [kgf/cm²] C: C content [weight %] Mn: Mn content [weight %] Si: Si content [weight %] P: P content [weight %] S: S content [weight %] T: Temperature [°C] Observation: . Gorni Steel Forming and Heat Treating Handbook 181 Source: PICQUÉ.E. Asia Steel. Experimental Study and Numerical Simulation of Iron Oxide Scales Behavior in Hot Rolling. . Doctor Thesis. Steel. Thermal Stresses in Slab Solidification. S. 2004. École de Mines de Paris. Source: ROYZMAN. High Temperature: Tselikov E  308250  42924 C  144000 C 2  20525 Si  5289 Mn  12000 P  174000 S  225.6 T  0. alloy and stainless steels between 20 and 900°C.Valid for carbon. 243. 1996. 000022 CO2 0. Air: 1. Propane: 1.000090 .81 kg/Nm³ . Natural Gas: 0.871 0. Values of a and b for some gases are seen below: Gas a b C2H6 0. Heat Capacity in Function of Temperature .54 kg/Nm³ .000540 C3H8 0. Gorni Steel Forming and Heat Treating Handbook 182 APENDIXES USEFUL DATA AND CONSTANTS Fuels and Combustion Gases: .29 kg/Nm³ .00 kg/Nm³ .406 0. Propane: 0.001226 CH4 0. Liquified Petroleum Gas (LPG): 0. Butane: 2.44 kg/Nm³ . Water: 1.000210 CO 0.85 kg/Nm³ . Density (Gas) . Liquified Petroleum Gas (LPG): 2.27 kg/Nm³ .600 0.58 kg/l .51 kg/l .302 0. Butane: 0.380 0. Density (Liquid) . Heat Capacity [kcal/°C m³] = a + bT [°C]. 132 Kcal/Nm³ .301 0. Benzene (C6H6): 33. Basic Oxygen Steelmaking Off-Gas (OG Gas): 770 kcal/Nm³ . Charcoal: 6.823 Kcal/Nm³ . Propene/Propylene (C3H6): 20. i-Butane (C4H10): 28.550 Kcal/Nm³ . Toluene (C7H8): 40.000 ~ 9.116 Kcal/Nm³ .600 ~ 10. Hydrogen (H): 2. Hydrogen Sulfide (H2S): 5. Ethene/Ethylene (C2H4): 14. Fuel Oil: 8.000022 O2 0.200 kcal/kg . Acetylene (C2H2): 13412 Kcal/Nm³ .300 ~ 27. Diesel Oil: 10.Gorni Steel Forming and Heat Treating Handbook 183 H2 0.900 Kcal/Nm³ .582 Kcal/Nm³ .640~9. Pentane (C5H12): 34. Carbon Monoxide (CO): 3. Natural Gas: 9.300 kcal/Nm³ .794 Kcal/Nm³ . Butane (C4H10): 29.943 Kcal/Nm³ .400 Kcal/Nm³ .000200 N2 0. Propane (C3H8): 21.000 kcal/kg .019 Kcal/Nm³ . Liquified Petroleum Gas (LPG): 25. Hexane (C6H14): 41.000 kcal/l or 9.000059 .400 Kcal/Nm³ . Methane (CH4): 8. Butene/Buthylene (C4H8): 27. Blast Furnace Gas: 770 Kcal/Nm³ .236 Kcal/Nm³ .317 Kcal/Nm³ .733 Kcal/Nm³ .302 0. Ethane (C2H6): 15. Electricity: 860 kcal/kW . Coke Oven Gas: 4. Net Heating Value .320 0.182 Kcal/Nm³ .557 Kcal/Nm³ .560 Kcal/Nm³ .809 Kcal/Nm³ . i-Pentane (C5H12): 34.800 kcal/kg .527 Kcal/Nm³ . Xylene (C8H10): 46. Avogrado: NA = 6.056 cm³ atm/(K.082056 l atm/(K.500 kcal/kg .54 0.04 0.00 0.09 61.022 x 1023 1/mol .31433 x 107 erg/(K.38065 x 10-23 J/K . Wood: 2. Gorni Steel Forming and Heat Treating Handbook 184 .55 24. e: 2. Boltzmann: k = 1.87. Pi: 3.31433 J/(K. Typical Chemical Compositions [% vol] N2 H2 CH4 C2H6 C3H8 CO CO2 O2 Coke Oven Gas 3.6704 x 10-8 W/(m² K4) or J/(s m² K4) Physical Properties of Scale (Iron Oxide) .26 Natural Gas 1.805 m/s² . Thermal Conductivity: .83 ---. 82.98717 cal/(K mol) . 8.mol) . Stefan-Boltzmann: σ = 5. 8.mol) .59 0. Acceleration of gravity: g = 9.718281828 .00 Mathematical Constants .141592654 Physical Constants . 0.91 ---.0.06 8.mol) .mol) .91 7.42 0.08 1. 1. Ideal Gas Constant R: . Wustite: 14 x 10-6 m/°C . Thermal Expansion Coefficient: .K) .K) (600°C) .Stowage Factor: 0.00 g/cm³ (Picqué) .SiO2): 1177°C . Hematite (Fe2O3): 1. Specific Heat: .4. Magnetite (Fe3O4): 320 ~ 500 HV . Magnetite (Fe3O4): 5. Wustite (FeO): 3. Wustite (FeO): 5. Bulk. Ferrite (0 ~ 900°C): 15.90 g/cm³ .2 W/(m. Industrial Scale: 3.70 g/cm³ (Krzyzanowski) .5. Hematite (Fe2O3): 4. Magnetite (Fe3O4): 870 J/(kg.00 g/cm³ . Industrial Scale: . Magnetite (Fe3O4): 1.70 g/cm³ .40~2. Wustite (FeO): 725 J/(kg.K) . Fe: 19 x 10-6 m/°C . Wustite (FeO): 270 ~ 350 HV . Melting Point: .3 x 10-6 K-1 .89 t/m³ . Porous Scale as Raw Material. Iron Content in Scale: 74.K) . Room Temperature: . Fayalite (2FeO.5 W/(m.K) .K) .38 m³/t .6% (Stoichiometric) .K) .2 W/(m.2.Gorni Steel Forming and Heat Treating Handbook 185 . Hematite (Fe2O3): 1000 HV . Linear Coefficient of Thermal Contraction: .0 W/(m. Hematite (Fe2O3): 980 J/(kg. Industrial Scale: 766 J/(kg.5.86 g/cm³ (Combustol) . Hardness: .K) . Density: . Jablonka: 7870 kg/m³ (20°C) .9 x 10-6 K-1 .400 ~ 800°C: 13. 0.K) . Hematite (Fe2O3): . 0. Densities: .5 W/(m.0 x 10-6 K-1 Physical Properties of Steel and its Microstructural Constituents . Emissivity of Polished Metal Surface: .2 x 10-6 K-1 . Gorni Steel Forming and Heat Treating Handbook 186 .Jablonka: 7685 kg/m³ (20°C) .0 x 10-6 K-1 . VC: 5700 kg/m³ . Electrical Resistivity at 15. Emissivity of Oxidized Steel Plate at 15.Caballero: 7687 kg/m³ .10 @ 260°C .20 ~ 900°C: 14.14 @ 540°C .2 x 10-6 K-1 .m .100 ~ 1000°C: 12.Caballero: 7882 kg/m³ . Magnetite (Fe3O4): 1.80 .400°C: 14.100 ~ 1000°C: 12. Ferrite (Fe ): .07 @ 38°C .0 x 10-6 K-1 .0 x 10-6 K-1 . NbC: 7790 kg/m³ . Wustite (FeO): .6°C: 17 x 10-8 Ω.400 ~ 800°C: 15.8 x 10-6 K-1 . Cementite (Fe3C): . Bulk Steel: 7850 kg/m³ .100 ~ 300°C: 10.0 x 10-6 K-1 .25°C: 11.6°C: 0. 0.550°C: 27. Specific Heat: 0.9 W/m. Recycling Steel Mill Scale as Fine Aggregate in Cement Mortars.5246 Ǻ. Heat Transfer Coefficient at Scale/Steel Interface: 30.490 m/s .000 MPa . 24:3. Linear Coefficient of Thermal Expansion: . Gorni Steel Forming and Heat Treating Handbook 187 . Bulk: 11.000 MPa . The Timken Company. b = 5.K . . c = 6. Shear: 83. Plastic Range: 0.1 x 10-6 °C-1 Sources: . 2008.7423 Ǻ . Thermal Conductivity at 15.5 . Volumetric Coefficient of Thermal Expansion: 35. Ferrite (pure Fe): 2. Lattice Parameters (Ambient Temperature): .K . Austenite: 2. 332-338. .000 MPa .ANON. 130 p. Poisson’s Ratio: . S.065 x 10-5 l°C-1 . Elastic Range: 0. European Journal of Scientific Research.12 cal/g. Modulus: .000 W/m². September 2006. Melting Point: 1300 ~ 1450°C . Speed of Sound through Steel: 5. Bulk: 159. Ferrite: 1.AL-OTAIBI.0885 Ǻ. Young: 207. Canton.: Practical Data for Metallurgists.6°C: 58.244 x 10-5 °C-1 .°C . Cementite: a = 4.7 x 10-6 °C-1 .3 .866 Ǻ . Experimental Study and Numerical Simulation of Iron Oxide Scales Behavior in Hot Rolling. Saint-Germain-en-Laye. Chichester. 2000. Comparing CO2 Emissions and Energy Demands for Alternative Ironmaking Routes.D. .Établissement de Bilans Thermiques Globaux et Étages dans les Temps. September 1991.JABLONKA. Juillet 1976. Bethlehem-Lukens Plate Report. 2002. B.: Finite Element Model of Steel oxide Failure During Tensile Testing Under Hot Rolling Conditions.G. 37. October 1999.PICQUÉ. . M.HEIDEMANN.WILSON. 97 p.: Thermomechanical Properties of Iron and Iron-Carbon Alloys: Density and Thermal Contraction. Guidelines for Fabricating and Processing Plate Steel. John Wiley & Sons-The Institute of Corrosion. .SCHÜTZE. et alii. KRZYZANOWSKI. A. . Doctor Thesis. École de Mines de Paris. F. 184 p.E. March 2006. M. 1191-1198. Materials Science and Technology. 15:10. p. Fours Pits . 32-36. Rapport IRSID 77-02. . Journal of Materials Science. 2004. 1997.CABALLERO. 248. . A. . 24-33. M. Protective Scales and Their Breakdown. 3533- 3540. et alii. Burns Harbor. .METNUS. Steel Times International. et alii. 62:1.Gorni Steel Forming and Heat Treating Handbook 188 . Modelling of Kinetics and Dilatometric Behaviour of Austenite Formation in a Low- Carbon Steel with a Ferrite Plus Pearlite Initial Microstructure. Steel Research. 15 p. G. 78541178 liters kW 0.102040816 t ft.√m ft³ 0.389 x 10-7 th bar 1.lb 1.71 x 10 3 lbf/ft ft.80665 N ft 12 inch kgf.6 x 105 cal in² 645.016020506 g/cm³ J 9.7456999 kW kW.163 W/m² °C cal 4.lbf 1.√in 1.1129815 J ou N.90 x 10 -3 m² ksi.356 J ou N.4535924 kg in³ 16387.h 8.860 th/h HP 0.h 3.412 x 103 BTU in 25.80665 J ft 0.m ksi 6.355818 J or N.lb 0.184 J Kg 2.064 mm³ lb.019716 kg/cm² J 1 W.205 lb F 5/9 (°F-32) °C kgf 9.lbf 0.s BTU 1058.lb/s 1.098901099 MPa.000175127 J/mm² lb/ft³ 0.h 3.45 x 10-4 BTU lb/in³ 27.7121551 W kW.355380862 W kN/mm 5.lb lbf/in² 1 psi .777 x 10 -9 kWh BTU 251.341022 HP gallon 3.Gorni Steel Forming and Heat Treating Handbook 189 UNIT CONVERSIONS From Multiply by To From Multiply by To A 10-10 m J 2.30485126 m kgf/mm² 9.2390 cal lbf 4.6 x 106 J HP 745.448222 N J 0.lb 1.80665 MPa ft.2 mm² lb 0.894757 MPa ft.m 9.7376 ft.324 cal kN 224.02831685 m³ kW 1.4 mm kW.201058 J J 2.in 0.8 lbf ft.9958 cal Kcal/m² h °C 1.m Kip 1000 lbf ft.355748373 J kN 0.m in-lb/in² 0.1382 kg ksi 1000 psi ft² 92.67783006 g/cm³ J 0. 000.186 x 106 J N.145 ksi Short Ton 907.8 kN MPa.047 kg Pa 1.m 910.06 psi.m 0.0068947573 MPa mm² 1.000 BTU Psi in 0.920 Ksi.000 BTU psi 0.m 1 J th/h 1.028352707 kg W 0.001098829 MPa m MPa 1 N/mm² Rad 57.001 ksi mm 0.020 x 10 -7 Kg/mm² M 3.000.76 ft² ppm 0.0394 in psi 0.1847 Kg MPa 145 lbf/in² t 9.281 ft pct (%) 10000 ppm m² 10.0001 % MBTU 1.550 x 10³ in² psi 0.2958 ° MPa 0.163 kW nm 10-9 m W 1 J/s oz 0.in Th 1 Mcal MPa.449 x 10 -4 psi M 1010 A Pa 1.001341 HP Pa 1 N/m² .Gorni Steel Forming and Heat Treating Handbook 190 From Multiply by To From Multiply by To long ton 1016.in Th 4.0007030697 kgf/mm² MMBTU 1. 580 p.. Editora McGraw-Hill do Brasil Ltda. Estatística.Correlation Coefficient _  (Yest  Y ) 2 r _  (Y  Y ) 2 Notation: r: Correlation Coefficient Y: Raw Data Yest: Estimated Data Calculated by the Fitted Equation _ Y : Mean of the Raw Data Source: SPIEGEL. 1976. . São Paulo. M.Root Mean Square Deviation (Yest Y real ) 2   n Notation: : Root Mean Square Deviation Yest: Estimated Data Calculated by the Fitted Equation Yreal: Real Data .R. Gorni Steel Forming and Heat Treating Handbook 191 GENERAL STATISTICAL FORMULAS . 1976..R. Gorni Steel Forming and Heat Treating Handbook 192 n: Number of Points of Data Source: SPIEGEL. . M. Editora McGraw-Hill do Brasil Ltda. 580 p. São Paulo. Estatística. Gorni Steel Forming and Heat Treating Handbook 193 TRIGONOMETRY .Trigonometrical Relations .