Most isothermal transformations take place by nucleation at the tenite grain boundaries, so the original austenite grain size will affect the iso-thermal decomposition kinetics of austen
Trang 11 Phase Transformations of Undercooling Austenite
At present, many computer models of evolution of structure and phase position of steels during quenching have been developed Most of them arebased on physical models of phase transformations [64–66] But physicalmodels cannot describe adequately all kinetic features of undercooled auste-nite transformations The computer models based on regression analysis ofexperimental data can best predict steel phase composition changes duringsteel cooling
com-It was introduced directly by Davenport and Bain [67] and the time–temperature-transformation (TTT) diagram was the predominant tool todescribe the isothermal decomposition kinetics of supercooled austenite
In most TTT diagrams, general S- or C-curves are used to represent thekinetics of a number of isothermal transformation products: ferrite, pearlite,upper bainite, lower bainite, and martensite Conversely, many experimentalresults demonstrate that each type of transformation product has a separateC-curve
To build a mathematical model, all TTT diagrams published in Refs.[68–71] were analyzed The rationalization of the kinetics of isothermaldecomposition of austenite permitted the establishment of a metastableproduct (phase) diagram of a number of steels of different compositionswith 6% of total content of all alloying elements
Figure 41 The presentation of C-curve on simulating TTT diagrams (Scheme.)Parameters U and S correspond toTable 7
Trang 2Most isothermal transformations take place by nucleation at the tenite grain boundaries, so the original austenite grain size will affect the iso-thermal decomposition kinetics of austenite.
aus-From the total number of factors characterizing austenite matrix, thepresent day experimental knowledge allows only an approximate examina-tion of the statistically recrystallized proportion and estimation of the size
of deformed austenite grains
The grain growth kinetics satisfy the law [73]
ani-inTables 7and8and shown inFig 41
The cooling curve is approximated partially by a constant functionand at the individual time intervals Dt and the rate of decomposition is cal-culated as isothermal transformation corresponding to the mean tempera-ture of that interval The required kinetic data are available from the TTTdiagrams [68–71] that can be digitized (see Table 8) by procedures shown
in Fig 41, using equation
U U0
UN U0
ð41Þ
where S¼ Int-time interval, s; U ¼ 1000=(T þ 273)
Since it is necessary to distinguish between the parts of the C-curvesrepresenting the formation of ferrite, pearlite, and bainite, only thosediagrams having readily distinguishable component curves were used inthe analysis
The calculation method includes the effect of the size of austenitegrains on the kinetics of phase transformations The main precondition isknowledge of this effect on the course of C-curves showing the start andend of transformations in the graph of isothermal decomposition of auste-nite for the relevant steel
Trang 3The program involves the calculation of temperatures of tions of bainite and twinned, athermal and lamellar martensite [74]
Trang 4just-described method and by applying the digitized TTT diagrams of
The nucleation time t of carbonitrides per unit volume N at any perature T, can be expressed as [76]
for homogeneous nucleation; activation energy of Nbdiffusion Q¼ 270 kJ=mol;
Table 9 Thermodynamics Parameters in Eq 50 (From Ref 77)
Chemical compound
A 7,130 9,500 7,985 8,872 15,573 7,714 10,440 8,464 13,968
Trang 5corresponds to start or finish of this transformation in austenite under heattreatment of steel.
3 Calculation of Thermokinetic Diagrams of Impurity
Segregation During Quenching of Steel
Computation of grain boundary multicomponent adsorption kinetics could
be simplified for steels with high undercooled austenite stability The GBSdevelops in this case in austenite in short time and has no dependence onphase and structure transformations at steel quenching Enrichment of grainboundaries by various impurities as well as their desorption is treated as aresult of multicomponent diffusion of impurities from near-boundaryvolume to the boundary Impurity binding energy with GB includesmutual influence of elements in grain bulk and on the boundary in accor-dance with Guttmann’s theory [Eqs (18) and (19)] Auger electron spectro-scopy is the technique for experimental investigation of GBS kinetics Theseexperiments are basic for analysis of correlation of impurity segregationenergy with the content of other elements in the bulk and on boundaries(see Section 2.5, Eqs (23)–(29)
Adsorption and desorption of impurities on GB (qi) at steel quenching
is modeled well using the equation
qi¼ qið0Þ þ 2qffiffiffiffiffiffi0i
pdp
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Z t 0
Diðt 0Þ dt0
s
1ffiffiffiffiffiffipdp
Zt
0
Ci
aðt0ÞDiðt0Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
con-I
inEqs (12) and (13)
The change of temperature at cooling or isothermal exposition isdescribed by equation
Trang 6Table 10 presents cooling rates r for heat-treatment processes The blockdiagram of multicomponent intercrystalline adsorption model is shown in
Fig 42 Adsorption of P, C, and S is determined by parameters K1, K2,
K3, and their desorption by parameters K2, K4, K6 The parameters Ci
are equivalent to GB concentration of element i This model allows the putation of the condition when there is change of GB composition in steelsand alloys at preselected arbitrary mode of cooling including isothermalexposition
com-Given below are the examples of investigation of phosphorus and fur grain boundary adsorption in Cr–Ni–Mo steel (seeTable11)
sul-The components of steel mutually influence their diffusion mobilityand GBS activation energy Based on this reason, one should take intoaccount the stochastic fluctuations of diffusion flows of various impurities
on GBS kinetics For this purpose, the random fluctuation of diffusioncoefficients up to 30% of its mean value was used in the model.Figures 43
and 44 present the GBS kinetics calculation results at cooling of various ity steels cooling that were carried out using the stochastic model As onecan see, the self-regulation of adsorption is observed which is developingdespite significant short-time oscillations of impurity concentration on grainboundaries The significant non-equilibrium enrichment of GB by impuri-ties is observed at initial stage of the heat treatment This effect is deter-mined by cooling velocity as well as impurities content Increasing coolingvelocity from 0.001 to 1000K s1decreases the non-equilibrium GBS of Pand S Formation of non-equilibrium rich GBS of harmful impurities atsmall cooling times could be established only by using computer modelingmethods The experimental verification of such phenomena needs specialtechniques which allow to open grain boundaries: hydrogenation ofquenched samples or delayed fracture tests Since these techniques areconducted in air and could not be applied in the vacuum chamber ofelectron spectrometer; for most of engineering steels, the regularities ofnon-equilibrium GBS formation at quenching could only be estimated by acomputer experiment
pur-Table 10 Cooling Rates for Some Metallurgical Technologies
Name of the treatment Cooling rates r (K sec1)
Controlled cooling of large-size forging 0.001
Trang 7Figure 44 The change of GBS during quenching of Cr–Ni–Mo steel containing0.01S and 0.006P (mass%) Computer simulation of fast (a) and slow (b) cooling.
Trang 8Figure 45 Chemical composition of GB in Cr–Ni–Mo steel containing 0.027S and0.054P (mass%) after austenitization at 1373K (30 min), interim cooling up to 873Kand quenching in water (a) and in furnace (b) Auger electron spectroscopy ofintergranular fracture.
Trang 9Figure 46 Chemical composition of GB in Cr–Ni–Mo steel containing 0.01S and0.006P (mass%) after austenitization at 1373K (30 min), interim cooling up to 873Kand quenching in water (a) and in furnace (b) Auger electron spectroscopy ofintergranular fracture.
Trang 10The validation of calculation reliability was done for steel composition
82 and 83 (seeTable 10)by Auger spectroscopy The samples after tization at 1373K (30 min) were in the interim cooled to 873K with furthercooling in water or with furnace cooling The undercooled austenite in thissteel has high stability and does not transform in ferrite region for 2 hr.After cooling the samples had martensite–baintite structure To investigatethe chemical composition of grain boundaries by Auger spectroscopy, spe-cial samples were crushed in the electron spectrometer ESCALAB MK2 atvacuum at about 108Pa at temperature 83K The fields with intercrystal-line fracture type were investigated on the fracture surface The variation
austeni-of phosphorus and sulfur content in GBS in Cr–Ni–Mo steel austeni-of several meltsafter heat treatment is shown inFigs 45and46.At accelerated cooling the
GB are significantly enriched by carbon The P concentration in GBincreases only at slow cooling of samples, and P segregation is strongly sup-pressed in pure steel A good correspondence of calculated and experimentalresults is observed for all cases to be analyzed
The results of numerical modeling give information about the brium and non-equilibrium character of a GB adsorption processes, whichare frequently unavailable from experiments Moreover, these simulationmethods explain the phenomenon of reverse temper embrittlement as theresult of non-equilibrium concurrent GBS of carbon and phosphorus Theseresults explain many questions in the multicomponent GB adsorptionkinetics in engineering steels that were dynamically developed in the last
equili-10 years Further investigations in this direction are required especiallyfor competitive internal adsorption in engineering steels treated by usingnewest schemes of heat treatment
3 Hondros, E.D.; Seah, M.P Segregation to interfaces Int Met Rev 1977, 22,12,261–12,303
4 Seah, M.P Grain boundary segregation J Phys F 1980, 10 (6), 1043–1064
5 Guttmann, M Equilibrium segregation in ternary solution: a model for temperembrittlement Surf Sci 1975, 53, 213–227
6 Kaminskii, E.Z.; Stelletskaya, T.I Kinetic of martensite dissolution in carbonsteel Problems of Fisical Metallurgy; Metallurgy: Moscow, 1949, 192–210
7 Bokshtein, S.Z Structure and Mechanical Properties of Alloyed Steel;Metallurgy: Moscow 1954
Trang 118 Briant, C.L.; Banerji, C.K Intergranular failure of ferrum alloys in inagressiveenvironment In Treatise on Materials Science and Technology, Vol 25;Embrittlement of Engineering Alloys; Briant, C.L., Banerji, S.K., Eds.;Academic Press: 1983; 29–59.
9 Erhart, H.; Paju, M Phosphorus segregation in austenite Scripta Met 1983,
17, 171–174
10 Kovalev, A.I Influence of grain boundaries phosphorus segregation and steelmicrostructure on fracture after quenching and middle tempering Fiz Met.Metalloved 1980, 49, 818–826
11 Glikman, E.; Cherpakov, Ju.; Bruver, R Dependence of fracture toughness andsurface energy of grain boundaries on grain size of Si-steel under reversibletemper embrittlement Fiz Met Metalloved 1978, 42, 864–870
12 Howe, H.M Proc Inst Mech Eng 1919, Jan–May, 405
13 Carr, F.L.; Goldman, M.; Jaffe, L.D.; Buffin, D.C Trans AIME 1953, 197,998
14 McLean, D Grain Boundaries in Metals; Oxford University Press: London1957
15 Hondros, E.D.; Seah, M.P The theory of grain boundary segregation in terms
of surface adsorption analogues Met Trans A 1977, 8, 1363
16 Abraham, F.F.; Brundle, C.R Surface segregation in binary solid solutions: atheoretical and experimental perspective J Vac Sci Technol 1981, 18 (2),506–519
17 Abraham, F.F Bond and strain energy effects in surface segregation ScriptaMet 1979, 13 (5), 307–311
18 Fowler, R.H.; Guggenheim, E.A Statistical Thermodynamics; University Press:Cambridge 1939
19 Grabke, H.J Adsorption, segregation and reactions of non-metal atoms oniron surfaces Mat Sci Eng 1980, 42, 91–99
20 Grabke, H.J Surface and grain boundary segregation on and in iron Steel Res
23 Bruver, R.E Investigation of impurities influence on intergranular lowtemperature failure of metallic solid solution Ph.D Dissertation, Tomsk, 1970
24 Chelikowsky, J.R Predictions for surface segregation in intermetallic alloys.Surf Sci 1984, 139, L197–L203
25 Miedema, A.R.; Boer, F.R et al Enthalpy of formation of transition metalalloys Calphad 1977, 1, 4341–4359
26 Miedema, A.R On the heat of formation of plutonium alloys In Plutonium andOther Actinides; Blank, H.; Linder, R., Eds.; North-Holland Publ.: Amsterdam,1976; 3–20
27 Bennett, L.H.; Watson, R.A A database for enthalpies of formation of binarytransition metal alloys Calphad 1980, 5 (1), 19–23
Trang 1228 Watson, R.E Optimized prediction for heats of formation of transition metalalloys Calphad 1981, 5 (1), 25–60.
29 Birnie, D.; Machlin, E.S.; Kaufman, C.; Taylor, K Comparison of pairpotential and thermochemical models of the heat of formation of BCC andFCC alloys Calphad 1982, 6 (2), 93–126
30 Machlin, E.S Correlation terms to pair potential model values of the energy offormation for transition element–polyvalent element phases Calphad 1980, 5(1), 1–17
31 Zadumkin, S.N Modern theory of surface energy of pure metals In SurfacePhenomena in Liquid metals and Solid Phases; Kabardino-Balkarskoe Publ.Press: Nalchik 1965; 12–28
32 Zadumkin, S.N Surface energy on the interface of metals In SurfacePhenomena in Liquid metals and Solid Phases; Kabardino-Balkarskoe Publ.Press: Nalchik, 1965; 79–88
33 Morita, Z.; Tanaka, T Effect of solute-interaction on the equilibriumdistribution of solute between solid and liquid phases in iron base Trans.ISIJ 1984, 24, 206–211
34 Kamenetskaya, D.S Influence of molecular interaction on phase diagrams.Problems of Physical Metallurgy and Metal Science; Metallurgia: Moscow 1949;113–131
35 Toshihiro, T Equilibrium distribution coefficient of P in Fe-base alloys J IronSteel Inst Jpn 1984, 70 (4), 220
36 Guttmann, M.; Dumolin, Ph.; Wayman, M The thermodynamics of interactiveco-segregation of phosphorous and alloying elements in iron and temper-brittlesteels Met Trans A 1982, 13, 1693–1711
37 Morito, Z.-I.; Tanaka, T Effect of solute-interaction on the equilibriumdistribution of solute between solid and liquid phases in iron base ternarysystem Trans ISIJ 1984, 24, 206–211
38 Morito, Z.-I.; Tanaka, T Equilibrium distribution coefficient of phosphorus iniron alloys Trans ISIJ 1986, 26, 114–120
39 Okamoto, T.; Morito, Z.; Kagawa, A.; Tanaka, T Partition of carbonbetween solid and liquid in Fe–C binary system Trans ISIJ 1983, 23,266–271
40 Yamada, K.; Kato, E Effect of dilute concentrations of Si, Al, Ti, V, Cr, Co,
Ni, Nb and Mo on the activity coefficient of P in liquid iron Trans ISIJ 1983,
Trang 13embrittle-45 Otani, H.; Feng, H.C.; McMahon, C.J New information on the mechanism
of temper embrittlement of alloy steels Met Trans 1974, 5 (2), 516–518
46 Lei, T.C.; Tang, C.H.; Su, M Temper brittleness of 0.3C–Cr–Mn7–Si–2Ni steelwith various initial microstructures Metal Sci 1983, 17, 75–79
47 Kovalev, A.I.; Michina, V.P Role of grain boundary segregation in RTE ofsteels Physical basis of construct of physical and mechanical properties of steelsand alloys In Proceedings of CNIICHERMET; Bardin, I.P., Ed., Metallurgia:Moscow, 1990, 43–46
48 Kovalev, A.I.; Mishina, V.P.; Stsherbedinsky, G.V Features of intergranularadsorption of carbon and phosphorus in Fe-alloys Fiz Met Metalloved 1986,
53 Grabke, H.J.; Hennesen, K.; Moller, R.; Wei, W Effect Mn on the grainboundary segregation, bulk and grain boundary diffusitivity of P in ferrite.Scr Met 1987, 21 (10), 1329–1334
54 Yongbin, I.M.; Daniluk, St A surface segregation study in P and S-doped type
304 stainless steel Met Trans A 1987, 18 (1), 19–26
55 Mastsuyama, T.; Hosokawa, H.; Suto, H Tracer diffusion of P in iron alloys.Trans JIM 1983, 24 (8), 589–594
56 Gruzin, P.L.; Mural, V.V S -diffusion in 3%Si–Fe alloy Fiz Met Metalloved
1971, 32 (1), 208–212
57 Treheus, D.; Marchive, D.; Delagrange, J Determination of the coefficient ofdiffusion of Sn of infinite dilution in a-Fe Compt Rend Acad Sci C 1972, 274(13), 1260–1262
58 Huntz, A.M.; Guiraldeng, P.; Aucouturier, M.; Lacombe, P Relation betweenthe diffusion of radioactive Fe and Cr in Fe–Cr alloys with 0–15% Cr and theira=g transformation Mem Sci Rev Met 1969, 66, 85–104
59 Hirano, K.; Cohen, M Diffusion of Co in Fe–Co alloys Trans JIM 1972, 13(2), 96–102
60 Gruzin, P.L.; Babikova, Yu.F.; Borisov, E.B.; Zimskii, S.V., et al Investigation
of diffusion of C in steel and alloys by C14 isotope Problems of Metals Scienceand Physical Metallurgy; Metallurgy: Moscow 1958; 327–365
61 Militzer, M.; Wieting, J Theory of segregation kinetics in ternary systems ActaMet 1986, 34 (7), 1229–1236
62 Dutto, B.; Sellars, C.M Effect of composition and process variables onNb(CN) precipitation in niobium microalloyed austenite Mat Sci Technol
1987, 3 (3), 197–206