相变温度计算经验公式

1 STEEL FORMING AND HEAT TREATING HANDBOOK Antonio Augusto Gorni São Vicente, Brazil www.gorni.eng.br Release #12 – 12 April 2005 USEFUL METALLURGICAL FORMULAS - Austenite Formation Temperatures . Grange Ae Mn Si Cr Ni1 1333 25 40 42 26= − + + − Notation: Ae1: Equilibrium Temperature for Austenitization Start [°F] Alloy Content: [weight %] Ae C Mn Si Cr Ni3 1570 323 25 80 3 32= − − + − − Notation: Ae3: Equilibrium Temperature for End of Austenitization [°F] 2 Alloy Content: [weight %] Source: GRANGE, R.A. Metal Progress, April 1961, 73. Ae Mn Si Cr Ni As W1 723 10 7 29 1 16 9 16 9 290 6 38= − + + − + +, , , , , Notation: Ae1: Equilibrium Temperature of Austenitization Start [°C] Alloy Content: [weight %] . Andrews Ae C Si Ni Mo V W Mn Cr Cu P Al As Ti 3 910 203 44 7 15 2 315 104 13 1 30 0 11 0 20 0 700 400 120 400 = − + − + + + − + + − − − − − , , , , , , , Notation: Ae3: Equilibrium Temperature for End of Austenitization [°C] Alloy Content: [weight %] Notes: - Both formulas are valid for low alloy steels with less than 0,6%C. Source: ANDREWS, K.W. Empirical Formulae for the Calculation of Some Transformation Temperatures. Journal of the Iron and Steel Institute, 203, Part 7, July 1965, 721-727. . Roberts 3 Ae Mn Cr Cu Si P Al Fn3 910 25 11 20 60 700 250= − − − + + − − Notation: Ae3: Equilibrium Temperature for End of Austenitization [°C] Alloy Content: [weight %] Fn: value defined according to the table below: C Fn 0,05 24 0,10 48 0,15 64 0,20 80 0,25 93 0,30 106 0,35 117 0,40 128 Source: ROBERTS, W.L.: Flat Processing of Steel; Marcel Dekker Inc., New York, 1988. . Eldis Ae Mn Ni Si Cr Mo1 712 17 8 19 1 20 1 11 9 9 8= − − + + +, , , , , Notation: Ae1: Equilibrium Temperature of Austenitization Start [°C] Alloy Content: [weight %] Ae C Ni Si3 871 254 4 14 2 51 7= − − +, , , 4 Notation: Ac3: Equilibrium Temperature for End of Austenitization [°C] Alloy Content: [weight %] Notes: - Both formulas were proposed by ELDIS for low alloy steels with less than 0,6%C. Source: BARRALIS, J. & MAEDER, G. Métallurgie Tome I: Métallurgie Physique. Collection Scientifique ENSAM, 1982, 270 p. - Austenite Transformation Temperatures . Boratto T C Nb Nb V V Ti Al Sinr = + + − + − + + −887 464 6445 644 732 230 890 363 357( ) ( ) Notation: Tnr: Temperatura of No-Recrystallization [°C] Alloy Content: [weight %] Source: BORATTO, F. et al.: In: THERMEC ‘88. Proceedings. Iron and Steel Institute of Japan, Tokyo, 1988, p. 383-390. . Ouchi Ar C Mn Cu Cr Ni Mo h3 910 310 80 20 15 55 80 0 35 8= − − − − − − + −, ( ) Notation: 5 Ar3: Start Temperature of the Transformation Austenite → Ferrite [°C] Alloy Content: [weight %] h: Plate Thickness [mm] Notes: - This formula was determined using data got from samples cooled directly from hot rolling experiments. Thus it includes the effects of hot forming over austenite decomposition. Source: OUCHI, C. et al.: Transactions of the ISIJ, March 1982, 214-222. . Choquet Ar C Mn Si3 902 527 62 60= − − + Notation: Ar3: Start Temperature of the Transformation Austenite → Ferrite [°C] Alloy Amount: [weight %] Notes: - This formula was determined using data got from samples cooled directly from hot rolling experiments. Thus it includes the effects of hot forming over austenite decomposition. Source: CHOQUET, P. et al.: Mathematical Model for Predictions of Austenite and Ferrite Microstructures in Hot Rolling Processes. IRSID Report, St. Germain-en-Laye, 1985. 7 p. . Nippon Steel 1 Ar C Mn Si P3 879 4 516 1 65 7 38 0 274 7= − − + +, , , , , 6 Notation: Ar3: Start Temperature of the Transformation Austenite → Ferrite [°C] Alloy Content: [weight %] Ar C Mn1 706 4 350 4 118 2= − −, , , Notation: Ar1: Final Temperature of the Transformation Austenite → Ferrite [°C] Alloy Content: [weight %] Notes: - It is unknown the previous conditioning of the steel samples that supplied data for the deduction of this formula. - Samples cooled at 20°C/s. Source: R&D Team of the Kimitsu Steelworks of Nippon Steel, 2003. . Nippon Steel 2 CrAlPSiMnCAr 204028733923259013 −+++−−= Notation: Ar3: Start Temperature of the Transformation Austenite → Ferrite [°C] Alloy Content: [weight %] Notes: - It is unknown the previous conditioning of the steel samples that supplied data for the deduction of this formula. Source: R&D Team of the Kimitsu Steelworks of Nippon Steel, 2003. 7 . Steven B C Mn Cr Ni Mos = − − − − −1526 486 162 126 67 149 B Bs50 108= − B Bs100 216= − Notation: Bs: Start Temperature of the Bainitic Transformation [°F] Alloy Amount: [% em peso] Bx: Temperature Required for the Formation of x% of Bainite [°F] Source: STEVEN, W. et al. Journal of the Iron and Steel Institute, 183, 1956, 349. . Suehiro B C Mns = − −718 425 42 5. Notation: Bs: Start Temperature of the Bainitic Transformation [°F] Alloy Amount: [weight %] Source: SUEHIRO, M. et al. Tetsu-to-Hagané, 73 (1987), p. 1026-1033. . Rowland 8 M C Mn Si Cr Ni Mo Ws = − − − − − − −930 600 60 20 50 30 20 20 Notation: Ms: Start Temperature of the Martensitic Transformation [°F] Alloy Amount: [% em peso] Source: ROWLAND, E.S. et al. Transactions ASM, 37, 1946, 27. . Steven M Ms10 18= − M Ms50 85= − M Ms90 185= − M Ms100 387= − Notation: Mx: Temperature Required for the Formation of x% of Martensite [°F] Source: STEVEN, W. et al. Journal of the Iron and Steel Institute, 183, 1956, 349. . Andrews M C Mn Ni Cr Si Mos = − − − − − −539 423 30 4 17 7 12 1 11 0 7 0, , , , , 9 Notation: Ms: Start Temperature of the Martensitic Transformation [°C] Alloy Content: [weight %] Notes: - Formula valid for low alloy steels with less than 0,6%C. Source: ANDREWS, K.W. Empirical Formulae for the Calculation of Some Transformation Temperatures. Journal of the Iron and Steel Institute, 203, Part 7, July 1965, 721-727. . Eldis M C Mn Ni Crs = − − − −531 391 2 43 3 21 8 16 2, , , , Notation: Ms: Start Temperature of the Martensitic Transformation [°C] Alloy Content: [weight %] Notes: - Equation developed by Eldis - Equation valid for steels with chemical composition between the following limits: 0.1~0.8% C; 0.35~1.80% Mn; <1.50% Si; <0.90% Mo; <1.50% Cr; <4.50% Ni . Source: BARRALIS, J. & MAEDER, G. Métallurgie Tome I: Métallurgie Physique. Collection Scientifique ENSAM, 1982, 270 p. . Krauss M C Mn Cr Ni Mos = − − − − −561 474 33 17 17 21 10 Notation: Ms: Start Temperature of the Martensitic Transformation [°C] Alloy Amount: [% em peso] Source: KRAUSS, G. Principles of Heat Treatment and Processing of Steels, ASM International, 1990, p. 43-87. - Austenitization Time-Temperature Equivalency Parameter . Isothermal Austenitizing P T R H t a a a a = −⎡ ⎣⎢ ⎤ ⎦⎥ 1 1 2 3, log∆ Notation: Pa: Austenitization Time-Temperature Equivalence Parameter in Terms of Grain Size [K] Ta: Austenitization Temperature [K] R: Molar Gas Constant, 8.314 JK-1mol-1 ta: Soaking time under Ta ∆Ha: Activation Energy of Austenitic Grain Coarsening, 460 kJmol-1 for low alloy steels . Anisothermal Austenitizing In this case Pa is the period of heating/cooling time between Tmax and Tmin, where Tmax: maximum temperature during the austenitizing treatment; 11 Tmin: temperature calculated according to the following equation: T T R T Hmin max max a = − 2 ∆ Source: BARRALIS, J. & MAEDER, G. Métallurgie Tome I: Métallurgie Physique. Collection Scientifique ENSAM, 1982, 270 p. - Equivalent Carbon – H.A.Z. Hardenability . Dearden & O’Neill (1940) 21513546_ PNiCuVCrMoMnCC DeardenEQ +++++++= 2001200 _max −= DeardenEQCHV Notation: CEQ_Dearden: Equivalent Carbon (Dearden) [%] Alloy Content: [weight %] HVmax = Dureza Máxima [Vickers] Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . IIW - International Institute of Welding 12 1556_ NiCuVMoCrMnCC IIWEQ ++++++= Notation: CEQ_IIW: Equivalent Carbon (IIW) [%] Alloy Content: [weight %] Source: HEISTERKAMP, F. et al.: Metallurgical Concept And Full-Scale Testing of High Toughness, H2S Resistant 0.03%C - 0.10%Nb Steel. C.B.M.M. Report, São Paulo, February 1993. . Bastien 3,104,157,74,4_ NiCrMoMnCC BastienEQ ++++= BastienEQm CCR _6,109,13)ln( −= Notation: CEQ_Bastien: Equivalent Carbon (Bastien) [%] Alloy Content: [weight %] CRm: Critical Cooling Rate at 700°C [°C/s] (that is, minimum cooling rate that produces a fully martensitic structure) Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . Yurioka et al. 13 152412846_ CuSiNiCrMoMnCC YuriokaEQ ++++++= 8,46,10)log( _ −= YuriokaEQm Ct Notation: CEQ_Yurioka: Equivalent Carbon (Yurioka) [%] Alloy Content: [weight %] tm: Critical Cooling Time from 800 to 500°C [s] (that is, maximum cooling time that produces a fully martensitic structure) Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . Kihara et al. 244014546_ SiNiVCrMoMnCC KiharaEQ ++++++= Notation: CEQ_Kihara: Equivalent Carbon (Kihara) [%] Alloy Content: [weight %] Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. - Equivalent Carbon – Hydrogen Assisted Cold Cracking . DNV 14 4105402410_ MoVCrCuNiSiMnCC DNVEQ +++++++= Notation: CEQ_DNV: Equivalent Carbon (DNV) [%] Alloy Content: [weight %] Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . Uwer & Hohne 1020402010_ MoCrNiCuMnCC UwerEQ +++++= Notation: CEQ_Uwer: Equivalent Carbon (Uwer & Hohne) [%] Alloy Content: [weight %] Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . Mannesmann 104060201625_ VMoNiCrCuMnSiCC PLSEQ +++++++= Notation: 15 CEQ_PLS: Equivalent Carbon for Pipeline Steels [%] Alloy Content: [weight %] Notes: - Formula deduced for pipeline steels - A version of this formula divides V by 15 Source: HEISTERKAMP, F. e outros: Metallurgical Concept And Full-Scale Testing of High Toughness, H2S Resistant 0.03%C - 0.10%Nb Steel. C.B.M.M. Report, São Paulo, February 1993. . Graville 957235016_ VNbMoCrNiMnCC HSLAEQ ++++−+= Notation: CEQ_HSLA: Equivalent Carbon (Uwer & Graville) [%] Alloy Content: [weight %] Notes: - Formula deduced for pipeline steels Source: YURIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . Bersch & Koch 20_ NiCuVMoCrSiMnCC BerschEQ +++++++= 16 Notation: CEQ_Bersh: Equivalent Carbon for Pipeline Steels [%] Alloy Content: [weight %] Notes: - Formula deduced for pipeline steels Source: PATCHETT, B.M. et al.: Casti Metals Blue Book: Welding Filler Metals. Casti Publishing Corp., Edmonton, February 1993, 608 p. (CD Edition). . Ito & Bessyo (I) P C Si Mn Cu Cr Ni Mo V Bcm = + + + + + + + +30 20 60 15 10 5 Notation: Pcm: Cracking Parameter [%] Alloy Content: [weight %] Notes: - Formula deduced for pipeline steels with C < 0,15% - This is the most popular formula for this kind of material. Source: HEISTERKAMP, F. e outros: Metallurgical Concept And Full-Scale Testing of High Toughness, H2S Resistant 0.03%C - 0.10%Nb Steel. C.B.M.M. Report, São Paulo, February 1993. . Ito & Bessyo (II) 17 P C Si Mn Cu Cr Mo V d H c = + + + + + + + +30 20 15 10 600 60 Notation: Pc: Cracking Parameter [%] Alloy Content: [weight %], except H: Hydrogen amount in the weld metal, [cm³/100 g] d: Plate Thickness, [mm] Source: ITO, Y. e outros: Weldability Formula of High Strength Steels. I.I.W. Document IX-576-68. . Yurioka ⎟⎠ ⎞⎜⎝ ⎛ +++++++++= BNbNiCuVMoCrSiMnCACC YuriokaEQ 5520155246)(_ [ ]A C C( ) , , tanh ( , )= + −0 75 0 25 20 0 12 Notation: CEQ_Yurioka: Equivalent Carbon for Pipeline Steels [%] Alloy Content: [weight %] Notes: - Formula for C-Mn and microalloyed pipeline steels - This formula combines Carbon Equivalent equations from IIW and Pcm Source: PATCHETT, B.M. et al.: Casti Metals Blue Book: Welding Filler Metals. Casti Publishing Corp., Edmonton, February 1993, 608 p. (CD Edition). 18 - Equivalent Carbon – Bake Hardenability Capability . Melco C C Si Mn Cr Nb C V C Ti C Mo C B Ceq bh_ ( ) , ( ) ( )= + + + + + − + − + − + − + −15 5 9 7 1 10 50 1 3 1 3 1 5 1 6 2 29 11 1 Notation: Ceq_bh: Equivalent Carbon Expressed As Bake Hardenability [%] Alloy Content: [weight %] Source: Mitsubishi Electric Co., 1998. - Hot Strength of Steel . Tselikov 22 01379,06,2251740001200052892052514400042924308250 TTSPMnSiCCE +−+−−+−+= 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 %] 19 T: Temperature [°C] Note: - Valid for carbon, alloy and stainless steels between 20 and 900°C. Source: ROYZMAN, S.E. Thermal Stresses in Slab Solidification. Asia Steel, 1996, 158-162. . Misaka ( ) 13,021,022 112029682851594.075.1126.0exp ⎟⎠⎞⎜⎝⎛⎥⎦ ⎤⎢⎣ ⎡ −+++−= dt d T CCCC εεσ Notation: σ: Steel Hot Strength [kgf/mm²] C: C content [weight %] T: Absolute Temperature [K] ε: True Strain t: Time [s] Source: MISAKA, Y. et al. Formulatization of Mean Resistance to Deformation of Plain C Steels at Elevated Temperature. Journal of the Japan Society for the Technology of Plasticity, 8, 79, 1967-1968, 414-422. . Shida Calculation algorithm expressed in Visual Basic: Function Shida(C, T, Def, VelDef) 20 Dim nShida, Td, g, Tx, mShida, SigF As Single nShida = 0.41 – 0.07 * C Td = 0.95 * (C + 0.41) / (C + 0.32) T = (T + 273) / 1000 If T >= Td Then g = 1 Tx = T mShida = (-0.019 * C + 0.126) * T + (0.075 * C – 0.05) Else g = 30 * (C + 0.9) * (T – 0.95 * (C + 0.49) / (C + 0.42)) ^ 2 + (C + 0.06) / (C + 0.09) Tx = Td mShida = (0.081 * C – 0.154) * T + (-0.019 * C + 0.207) + 0.027 / (C + 0.32) End If SigF = 0.28 * g * Exp(5 / Tx – 0.01 / (C + 0.05)) Shida = 2 / Sqr(3) * SigF * (1.3 * (Def / 0.2) ^ nShida – 0.3 * (Def / 0.2)) * _ (VelDef / 10) ^ mShida End Function Notation: σ: Steel Hot Strength [kgf/mm²] C: C content [weight %] T: Temperature [°C] Def: True Strain VelDef: Strain Rate [s-1] Source: SHIDA, S. Effect of Carbon Content, Temperature and Strain Rate on Flow Stress of Carbon Steels. Hitachi Technical Report, 1974, 14 p. 21 - Liquidus Temperature of Steels [ ]T C Si Mn P S Cu Ni Cr Al Mo V TiLiq = − + + + + + + + + + + +1536 78 7 6 4 9 34 30 5 31 1 3 3 6 2 2 18, , , , , Notation: TLíq: Steel Melting Temperature [°C] Alloy Content: [weight %] Source: GUTHMANN, K. Stahl und Eisen, 71(1951), 8, 399-402. - Niobium Solubilization in Microalloyed Steels . Irvine log[ ] .Nb C N T +⎡⎣⎢ ⎤ ⎦⎥ = − 12 14 2 26 6770 Notation: T: Temperature [°C] Alloy Content: [weight %] Source: IRVINE, K.J. et al.: Journal of the Iron and Steel Institute, 205, 1967, 161. 22 . Siciliano log[ ] . [ ] [ ]. .Nb C N Mn Si T +⎡⎣⎢ ⎤ ⎦⎥ = + − −12 14 2 26 838 1730 64400 246 0 594 Notation: T: Temperature [°C] Alloy Content: [weight %] Source: SICILIANO JR., F..: Mathematical Modeling of the Hot Strip Rolling of Nb Microalloyed Steels Ph.D. Thesis, McGill University, February 1999, 165 p. - Relationships Between Chemical Composition x Microstructure x Mechanical Properties . C-Mn Steels LE Perl Mn Si P Sn N dsol = + + + + + + +246 4 15 44 6 138 923 169 3754 14 9, , , LR Perl Mn Si S P Cr N dsol = − + + − + + + +492 3 38 246 277 2616 723 246 6616 44 6, , d d Perl Si P Sn N dsol σ ε = + + + + + +385 1 39 111 462 152 1369 15 4, , ε unif solPerl Mn Si Sn N= − − − − −0 27 0 016 0 015 0 040 0 043 1 0, , , , , , 23 ε tot Perl Mn Si S P Sn d= − + + − − + +1 30 0 020 0 30 0 20 3 4 4 4 0 29 0 015, , , , , , , , T Perl Mn dtrans = + − −43 1 5 37 6 2, , Notation: LE: Yield Strength at 0,2% Real Strain [MPa] LR: Tensile Strength [MPa] dσ/dε: Strain Hardening Coefficient at 0,2% Real Strain [1/MPa] εunif: Uniform Elongation, Expressed as Real (Logarithmic) Strain εtot: Total Elongation, Expressed as Real (Logarithmic) Strain Perl: Pearlite Fraction in Microstructure [%] Ttrans: Fracture Appearance Transition Temperature [°C] Alloy Content: [weight %] d: Grain Size [µm] Source: PICKERING, F.B.: The Effect of Composition and Microstructure on Ductility and Toughness; in: Towards Improved Ductility and Toughness, Climax Molybdenum Company, Tokyo, 1971, p. 9-32 LE Mn Si N dsol = + + + +53 9 32 3 83 2 354 2 17 4, , , , , LR Mn Si Perl d = + + + +294 1 27 7 83 2 2 85 7 7, , , , , Notation: 24 LE: Yield Strength at 0,2% Real Strain [MPa] LR: Tensile Strength [MPa] Perl: Pearlite Fraction Present in Microstructure [%] Alloy Contents: [weight %] d: Grain Size [µm] Source: PICKERING, F.B.: Physical Metallurgy and the Design of Steels. Allied Science Publishers, London, 1978, 275 p. 50% 19 44 700 2 2 115ITT Si N Perl dsol = − + + + −, , Notation: 50% ITT: Impact Transition Temperature for 50% Tough Fracture [°C] Perl: Pearlite Fraction Present in Microstructure [%] Alloy Contents: [weight %] d: Grain Size [µm] Source: PICKERING, F.B. & GLADMAN, T.: In Metallurgical Developments in Carbon Steels. The iron and Steel Institute, London, 1961, 10-20 . V-Ti-N Steels Processed by Recrystallization Controlled Rolling LE C N V heq ef f = + + − +41 4 575 20 27401 2 419 5, , ( ) , 25 LR C N V heq ef f = + + − +74 1 985 1 31125 39 181 5, , ( ) , Notation: LE: Yield Strength at 0,2% Real Strain [MPa] LR: Tensile Strength [MPa] Alloy Content: [weight %] hf: Plate Thickness [mm] C C Mn Cr Mo Ni Cueq = + + + + +6 5 15 N N Tief tot= + 3 42, Notes: - Formula Derived for Steels with Al Content over 0,010% and Si Content between 0,25 and 0,35%. - Precision of the formulas: ± 40 MPa. Source: MITCHELL, P.S. et al.: In: Low Carbon Steels for the 90’s. Proceedings. American Society for Metals/The Metallurgical Society, Pittsburgh, Oct. 1993. . Dual Phase Steels LE L = +203 855 1 αα 26 LR L f d = + +266 548 1 1741 αα β β d d L f d σ ε αα β β = + +266 548 1 1741 a Lunif = −32 64 1 αα Source: GORNI, A.A.: Efeito da Temperatura de Acabamento e Velocidade de Resfriamento na Microestrutura e Propriedades Mecânicas de um Aço Bifásico ao Mn-Si-Cr-Mo; Dissertação de Mestrado, Departamento de Engenharia Metalúrgica e de Materiais da Escola Politécnica da Universidade de São Paulo, São Paulo, 1989, 184 p. Notation LE: Yield Strength [MPa] LR: Tensile Strength [MPa] dσ/dε: Strain Hardening Coefficient at Uniform Elongation [1/MPa] aunif: Uniform Elongation [%] Lαα: Mean Ferritic Free Path [µm] dβ: Mean Diameter of Martensite Islands [µm] - Solidus Temperature of Steels 27 [ ]AlCrNiSPMnSiCTSol 1,44,13,49,1835,1248,6