Modeling and Simulation for Material Selection and Mechanical Design Part 4 pot

Table 1 Composition (at.%) of the Fe–P and Fe–P–Mo Alloys Chemical composition, at.% C 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 S P Mo 0.002 0.003 0.002 0.003 0.002 0.002 0.005 0.014 0.017 0.10 0.15 0.093 0.033 0.14 0.09 0.074 0 0 0 3.1 3.1 3.1 0.3 0.02 bulk and on the interface As seen in Fig 14, the elastic interaction energy of the P atoms with grain boundaries in iron is equal to 0.53 eV=at and decreases significantly at molybdenum alloying to 0.24 eV=at in the alloy Fe–3.1at.% Mo Decrease of segregation energy of the impurity at its Figure 14 Change of Eseg of phosphorus with its volume concentration in Fe (1) and Fe–3.1 at.% Mo–P alloys (2) Auger electron spectroscopy of free surface segregations at 823K Copyright 2004 by Marcel Dekker, Inc All Rights Reserved volume concentration growth is caused by chemical pair interaction of the atoms in alloy Using the example of the Fe–P system, we could determine chemical interaction of elements by applying the approach proposed in Ref [34] Analyzing the solidus and liquidus equilibrium (volume and GB) on the equilibrium phase diagram at three temperatures permits the construction of a system of three equations that describe this equilibrium   100 À Xs ð17Þ ¼ X2 W0 À X2 W00 þ kqa Ta kT qa À ln s l 100 À Xl where k is the Boltzmann constant; Ta is the melting temperature of Fe; qa is melting entropy per atom divided by Boltzmann constant; W0 and W00 are the mixing energies in solid and liquid states; Xs and Xl are the impurity concentration in solid and liquid phases at the temperature T Solving these equations for the phase diagram of Fe–P binary system [35], the sign and value of mixing energy in liquid phase equal 0.425 eV=at were determined The positive value (in accordance with physical sense) means that binding force of P–P and Fe–Fe atoms is higher than for Fe–P atoms: 1 W ¼ WFeÀP À ðWFeÀFe þ WPÀP Þ 2 ð18Þ emphasizing the tendency for solid solution tendency for stratification or intercrystalline internal adsorption D Effect of Solute Interaction in Multicomponent System on the Grain Boundary Segregation Guttman has expanded the concept for synergistic co-segregation of alloying elements and harmful impurities at the grain boundaries His theory is very important for analysis of steels and alloys that contain many impurities and alloying elements In accordance with the theory, the interaction between alloying elements and the impurity atoms could be estimated from enthalpy of formation of the intermetallic compounds (NiSb, Mn2Sb, Cr3P, etc.) The alloying elements could influence on the solubility of impurities in the solid solution Only the dissolved fraction of the impurity takes part in the segregation [36] When preferential chemical interaction exists between M (metal) and I (impurity) atoms with respect to solvent, the energy of Copyright 2004 by Marcel Dekker, Inc All Rights Reserved segregation becomes functions of the intergranular concentrations of I and M: DGI ¼ DG0 þ I bb ba MI b YM À MI Xa Cb Ca M ð19Þ bb ba MI b YI À MI Xa ab aa I ð20Þ DGM ¼ DG0 þ M where Cb and ab are the fractions of sites available in the interface for I and M atoms, respectively ðab þ C b ¼ 1Þ; Yb is the partial coverage in the interface; Xa is the concentration in the solid solution a; bMI is the interaction coefficient of M and I atoms in a-solid solution (a) or on the grain boundary (b) For a preferentially attractive M–I interaction, the bMIare positive and the segregation of each element enhances that of the other If the interaction is repulsive, the bMI are negative and the segregations of both elements will be reduced For a high attractive M–I interaction in the a-solid solution, the impurity can be partially precipitated in the matrix into a carbide, or intermetallic compound The interface is then in equilibrium with an a-solution where the amount of dissolved I, XIa, may become considerably smaller than its nominal content In the ternary solid solutions, the segregation of impurity (I) could be lowered or neglected at several critical concentrations of the alloying element (M) whose value (CM) depends on surface activity of each compoa I,M nent (ESeg ) and interaction features of the dissolved atoms (bMI): CM ¼ a EI Seg bMI ðexpðEM =RTÞ À 1Þ Seg ð21Þ The critical concentration of alloying element is accessible for segregation of I;M impurity and alloying element ESeg > 0 and repulsion of different atoms M bMI > 0; or without segregation of alloying element ESeg < 0 and with attraction of different atoms bMI < 0 In this case, the dependence of EI,M on the dissolved element concentraSeg tion is not taken into account Indeed, for systems with limited solubility, the alteration of value and sign of segregation energy is possible at a definite content of alloying element The phase equilibrium diagram analysis allows the determination of mutual influence of components on their surface activity The equilibrium distribution of solute elements between solid and liquid phases in iron-base ternary system (distribution interaction coefficient K0) is known to be an important factor in relation to microsegregation during the solidification of steels As it was shown above, these analogies are useful for the prediction of GBS and for impurity segregation energy Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 15 Change of the equilibrium distribution coefficient of some elements with carbon concentration in Fe–C-based ternary systems (From Ref 37.) determination in the given solvent The K0 of some elements, especially in multicomponent systems, is considered to be different from those in binary systems because of the possible existence of solute interactions, but the mechanisms are so complicated that detailed information has not yet been obtained Therefore, it would be very useful if the effect of an addition of an alloying element on the distribution could be determined by the use of a simple parameter Equilibrium distribution coefficient K0À1 of various elements in Fe–C base ternary system is calculated from equilibrium distribution coefficient in iron-base binary systems [40–43] In Fig 15, the calculated results are compared with the measured values by various investigators The changes of the K0À1 of P and S with various alloying elements are shown in Fig 16(a, b) in Fe–P and Fe–S base ternary system, respectively These data could be applied for calculation of phosphorus segregation energy change under the alloying element influence in Fe–Me–0.1at.% P alloys (Fig 17) or for calculation of the segregation energy change of alloying elements with concentration of carbon in Fe–0.1Me–C alloys (Fig 18) For the growth of carbon volume content, the segregation energy of C and P decreases which means lowering of the segregation stimulus for these elements Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 16 (Continued) tion are developed, but rich segregations dissolve Distinguishing diffusion mobility and mutual influence of elements on their diffusion coefficients determines much of their segregation ability Amplification or suppression of adsorption could be due to a kinetic factor This peculiarity determines the fundamental factor of distinguishing adsorption from gas phase to free surface when comparing it to intercrystalline internal adsorption: GBS is controlled by diffusion during heat treatment of steels and alloys Many GBS features in multicomponent systems cannot be predicted adequately using the equilibrium segregation thermodynamic accounting basis Particularly, the thermodynamic concept of the cooperative (synergis- Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 19 Kinetics of P GBS in steel 0.3C–1.6Mn–0.8Cr–008P (1) with adds of 0.047Ti (2) or (0.07Ti and 0.026V) (3), quenched from 1273K and tempered at 923K where Xb(t) is the interfacial coverage of element, at time t; Xb(0) — is its initial value and Xb its equilibrium value as defined by Eq (7); Xia — is its volume concentration; Di is the bulk diffusivity of i and d is the interface thickness Assuming Xb=Xia ¼ const, using Laplace transformation for (22), one can obtain the approximate expression rffiffiffiffiffiffiffiffiffiffi Xb ðtÞ À Xb ð0Þ 2Xa FDti i ¼ ð23Þ Xb d p Xb À Xb ð0Þ where F ¼ 4 for grain boundaries and F ¼ 1 for free surface The kinetics of segregation dissolution could be described by these equations (22) and (23) But, in this case, the variables Xb(0) and Xb exchange places The influence of Mo, Cr, and Ni additions on kinetics of P segregation has been studied in six Fe–Me–P alloys, whose base compositions are listed in Table 1 These materials were austenitized for 1 hr at 1323K and quenched in water The tempering of foils at 773K was carried out in a work chamber of an electron spectrometer ESCALAB MK2 (VG) The kinetics of P segregation studied for Fe–Me–P alloys (Figs 20–22) show that equilibrium is reached within several hours Based on the starting position of adsorption isotherms, the phosphorus diffusion coefficients in these alloys were calculated using Eq (22) The data are presented in Table 2 Molybdenum reduces significantly P surface activity and decelerates its diffusion Nickel is not a surface-active element in carbonless alloys, Fe– P–Ni It increases sharply P thermodynamic activity and equilibrium GB concentration, and accelerates its diffusion Chromium segregates poorly Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 23 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mo steel (see Table 3) Auger electron spectroscopy of free surface segregations time at increasing temperature With temperature increase, the solubility of impurity in solid solution increases, and its GB concentration reduces It follows that the probability to form the segregation with high impurity content reduces, and time for such segregation increases extensively The upper branch of isodose curves corresponds to dissolution of rich segregations and access to new equilibrium with lower impurity concentration The Figure 24 The isodose C-curves of multicomponent interface segregation in 0.2C– Cr–Mn–Ni–Si steel (see Table 3) under its tempering Auger electron spectroscopy of free surface segregations Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 25 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–Nb steel (see Table 3) under its tempering Auger electron spectroscopy of free surface segregations adsorption patterns for engineering steels have common as well as individual features As a rule, carbon segregates at temperatures lower than 523K, nitrogen—in 523–623K range, phosphorus—in 523–823K range, sulfur segregates at temperatures higher than 723K The substitual and interstitial element concurrence promotes blocking of adsorption centers by mobile impurities and impedes P segregation at Figure 26 The isodose C-curves of multicomponent interface segregation in 0.3C– Cr–Mn–V steel (see Table 3) under its tempering Auger electron spectroscopy of free surface segregations Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 28 Influence of alloying on the kinetics isotherms of P free surface segregation at 723K The following steels were investigated (see Table 3): 1, 3C–Cr– Mn–Nb; 2, 3C–Cr–Mn–Si–Ti; 3, 2C–Cr–Mn–Ni–Si; 4, 3C–Cr–Mo; 5, 3C–Cr– Mn–V the thermokinetic diagrams for ternary Fe–Me–P alloys based on Eqs (23) and (6), the mutual influence of elements on their binding energy to GB was determined [36] EP ¼ 20:6 þ 183CP À 4:8CAl À 7:2CMo À 3:4CNi À 7141CB seg a a a a a þ 4:9CCr À 444CS À 183EMo À 87EN a a seg seg ð24Þ ES ¼ 6:9 À 151CS À 1:5CAl þ 14:5CP À 39ESn seg a a a seg ð25Þ EN ¼ 16 À 2:6CAl þ 3CMo þ 4:2CCr À 2625CTi þ 175EMo seg a a a a seg ð26Þ Copyright 2004 by Marcel Dekker, Inc All Rights Reserved EC ¼ 7:9 À 1:4CAl þ 5CMo þ 676CB þ 1:2CCr À 130EN þ 116EP seg a a a a seg seg ð27Þ EMo ¼ À0:7 þ 32EN À 28EP seg seg seg ð28Þ ETi ¼ 17 þ 3CC À EP seg a seg ð29Þ EAl ¼ 1:4CAl seg a ð30Þ ESn ¼ 21; ENi ¼ 14; EB ¼ 54; ECu ¼ 20 kJ/mol seg seg seg seg where EI is segregation energy of the I element, Caj is bulk concentration of seg j impurity F Stability of the Segregation The equilibrium GBS dissolves as temperature increases Analysis of the kinetic development of the equilibrium segregation level of P shown in Fig 29 gives the T–t plot of segregation directly Obviously that segregation level close to the maximum exists only within a specific temperature range This range is characterized by a maximum temperature stability Tmax, over which the intensive dissolution of the segregates is observed This temperature can be calculated by computer analysis of Eq (7) at dCbmax=dT ¼ 0 The temperature Tmax depends on Eseg and temperature dependencies of solubility limits, which can be determined from analysis of phase equilibrium diagrams [43] Using these dependencies as a generalizing criterion, it is possible to simplify the analysis of data on element segregation kinetics in iron alloys The interrelationship of maximum temperature of stability (Tmax) of rich equilibrium segregations and segregation energies of different elements is presented in Fig 30 The common features of kinetics show the following groups: enriching grain boundaries at low- and medium-tempering temperatures—B, C, N, and Cu; 2 co-segregating with P at high tempering—P, Sn, Ti, and Mo; 3 segregating at high temperatures—S and Al 1 Phosphorus in Fe alloys has abnormally weak dependence of Tmax on Eseg in reversible temper embrittlement temperature range In other Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 31 Thermo-kinetics diagrams of multicomponent segregation on free surface in steel 0.35C–1.58Mn–0.1P–0.6Al Figure 31 presents the thermokinetic diagram of element segregation in 0.35C–1.5Mn–0.1P–0.6Al steel The chemical composition of free surface segregations was determined by AES for a set of isothermal conditions in the spectrometer ESCALAB MK2 (VG) The temperature–time interval of preferential segregation of chemical elements is the result of different diffusion mobility and binding energy of elements with GB The temperature interval of P preferential segregation is caused by concurrence of this impurity with mobile interstitial elements C and N This process determines temperature and exposition necessary for RTE development Direct investigation of grain boundary composition by AES confirms the conclusion about the prevailing role of concurrent segregation in RTE The composition of several grain boundaries on brittle intercrystalline fracture of 0.35C–Mn–Al steel after heat treatment: quenching from 1223K, tempering at 923K for 1 hr with rapid (a) and slow (b) cooling is presented in Fig 32 [47] These data are in good correspondence with those in Fig 31 Accelerated cooling of steel, does not provide enough time for the development of segregations with high P content, and GB are enriched by C During slow cooling, phosphorus has enough time to enrich the grain boundaries In this case, the carbon concentration on GB is sufficiently lower than at rapid cooling of steel Carbon segregations are unstable at temperatures higher than 500–673K, and they are dissolved At slow cooling, P segregates to grain boundaries, decreasing the GB redundant energy This circumstance lessens the thermodynamic stimulus for carbon segregation as the temperature decreases Carbon and phosphorus in steels are responsible for RTE development They have high surface activity and diffusion mobility that Copyright 2004 by Marcel Dekker, Inc All Rights Reserved enrichment of GB by carbon at rapid cooling [48] Undoubtedly, carbide transformation, internal stresses, substructure transformations are very important for RTE One should take into account such circumstances where kinetics of C and P segregation are dependent significantly on steel alloying IV DYNAMIC SIMULATION OF GRAIN BOUNDARY SEGREGATION A Interface Adsorption During Tempering of Steel 1 Decomposition of Martensite The common laws of multicomponent GBS and analysis of experimental diagrams on elements segregation kinetics in iron alloys are used to develop the computer models of these processes The exact solution of McLean’s diffusion Eq (21) accounting for temperature dependant of diffusion and element solubility is a complex problem In low-alloyed steels, the concentration of surface-active impurities (S, P, and N) is rather small, and based on this reason, it is possible to analyze the diffusion of each element separately The model takes into account mutual influence of bulk and surface concentration of elements with respect to segregation energies Carbon in solid solution has maximum influence on phosphorus GBS kinetics Concentration of C in martensite changes significantly during quenched steel tempering and mainly depends on alloying element content Based on this reason, one should take into account the solid solution composition altering segregation processes modeling during tempering Investigations of martensite tetragonality at alloyed steel tempering [6,7] are the basis for calculations of mutual influence of alloying elements on martensite decomposition kinetics and carbon content in solid solution The carbon content change in solid solution during tempering of engineering steels is well described by equation   ! DXC Q n a ¼ 1 À exp ÀKDo t exp À XC ð0Þ RT a ð31Þ where DXC ¼ XC ð0Þ À XC ðtÞ a a a C Xa (0) C Xa (t) ð32Þ and are the carbon content in quenched steel and after a time t; Do is the carbon diffusion coefficient; Q is the activation energy associated with the interstitial diffusion of carbon atoms; K is the constant associated Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Table 4 Coefficient A in Eq (28) for Low-Alloying Engineering Steels Alloying element Coefficient A Ni Si Mn Cr Mo 433.56 1,432.54 À726.35 À2,898.91 À971.51 with the nucleation; n is the constant independent of both temperature and C Xa (0); R is the gas constant and T is the temperature Influence of C and alloying elements on parameters Q, K, and n in Eq (31) is determined for various steels The activation energy Q in lowalloyed steel depends on the concentration of carbon and alloying elements in solid solution: Qðcal=molÞ ¼ 8571:5XC þ A XMe þ 18; 000 a a ð33Þ where XaC and XaMe are concentrations of C and alloying elements, mass%; A is a constant depending on alloying element The values of coefficients in Eq (31) are presented in Tables 4 and 5 The diffusion activation energy of Table 5 Influence of Carbon and Alloying Elements on Parameters Q, K, and n in Eq (31) Steel, wt.% 0.4C–0.24Ni 0.39C–3.0Ni 0.37C–5.6Ni 0.4C–0.32Mn 0.4C–1.32Mn 0.4C–2.43Mn 0.4C–0.2Cr 0.4C–2.1Cr 0.4C–3.6Cr 0.4C–6.7Cr 0.4C–0.37Si 0.38C–1.75Si 0.4C–2.75Si 0.4C 1.4C 1.2C–2.0Mo Q, cal=mol Ln K n 21,532 22,643 23,599 21,196 20,298 19,406 20,848 15,348 10,992 2,005 21,929 23,764 25,368 21,429 30,000 26,343 15.364 17.481 18,575 15.737 14.241 13.713 15.366 10.076 5.481 1.698 16.351 15.234 10.050 16.72 40.881 29.768 0.26 0.22 0.24 0.24 0.22 0.24 0.21 0.24 0.42 2.32 0.19 0.22 0.15 0.24 0.07 0.08 Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 33 Change of carbon concentration in solid solution with temperature and time of tempering Steel 0.43C–2.43 Mn (mass%) Isodose curves for: 1, 1 at.% C; 2, 0.5 at.% C; 3, 0.1 at.% C; 4, 0.05 at.% C; 5, 0.03 at.% C carbon decreases on the growth of carbide-forming element (Mn, Cr, and Mo) concentration The contrary effect is observed for Ni and Si Obviously, it is associated with the different influence of these elements on thermodynamic activity of carbon in ferrite These dependencies are basic for calculations of segregation kinetics of C since carbon is the element that influences on P segregation highly The kinetics of carbon content in solid solution change during tempering of quenched steel 0.43C–2.43Mn (mass%) are shown in Fig 33 These data are obtained by computer modeling using Eqs (31–33) and those from Tables 4 and 5 This model provides the possibility of calculating the influence of alloying on cementite formation temperature interval, growth rate of its particles, and many other parameters of martensite decomposition at tempering [49] Fig 34 presents the calculation results of effective growth rate of Fe3C nucleus at tempering of engineering alloyed steels The calculations were carried out using expression [49]: Vmax R ¼ ð27D=256pÞN ð34Þ where R is the cementite particle radius; N is the right part of Eq (30) Manganese decreases martensite stability significantly promoting its decomposition at low temperatures Silicon, at a concentration greater than 1%, activates martensite decomposition at 700–800K and inhibits it at lower Copyright 2004 by Marcel Dekker, Inc All Rights Reserved i Figure 35 Calculation scheme of equilibrium impurity GBS Xa(0) is the initial C concentration of ith element in the steel; Xa (T,t) is the running carbon concentration i in martensite during its tempering; Xb(T) is the maximal equilibrium GBS of ith i element; Eseg Fe–i is the segregation energy of ith element in two-component Fe–I i alloy; Eseg Fe–i–j is the segregation energy of ith element in multicomponent alloy; Di(T) is the diffusion coefficient of ith element in austenite, martensite, and ferrite of treatment This factor influences on thermodynamic activity of all steel components and on their energy of GB segregation The second important stage of GBS modeling includes calculation of C volume concentration in martensite XaC(T), depending on steel i chemical composition Xa(0) and parameters of tempering New segregation energy values of each element at changing of treatment temperature or time and new equilibrium GBS level have been calculated in this way (see Fig 35) The final stage of modeling includes a set of independent calculations of various element diffusion to GB zone, and their desorption The limited capacity of boundary and its effective width (about 0.5 nm) are shown It is assumed that interstitial and substitial impurities occupy different positions on GB Time t of reaching the definite concentration of impurity in segregation Xb(t) at given temper temperature T is calculated by (22), and it is controlled by diffusion Di(T) Adsorption in multicomponent system is accompanied by concurrence: arrival of some surface-active impurity decreases GB energy and, in this way, the thermodynamic stimulus for segregation of other impurities Dissolution of segregations is observed at increasing temperature Impurity desorption to grain bulk is analogous to adsorption, however it is tied not with concentration Xi(0) but with Xb(t), and it is also controlled by diffusion Di(t) Copyright 2004 by Marcel Dekker, Inc All Rights Reserved The model is restricted to initially homogeneous bulk concentrations Xib ð0Þ ¼ Xia ð35Þ The kinetics of segregation to surfaces or grain boundaries from the bulk are determined by volume diffusion of impurities with bulk concentrations Xia(t) which can be treated as a one-dimensional problem Since both bulk concentrations are very small, Arrhenius type diffusion coefficients: Di ¼ Di0   Qi exp À RT ð36Þ can be used which are independent of Xia(t) In the case of site competition, the GB impurities concentration is qi ¼ 1À Xi P   Ei exp À KT J Xj ð37Þ The equations describing the time evolution of segregation for homogeneous initial condition [60] are sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z t Z t X0 1 qi ðt0 ÞDi ðt0 Þ i qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Di ðt0 Þ dt0 À pffiffiffi Xi ðtÞ ¼ Xi ð0Þ þ 2 pffiffiffi ð38Þ R t0 pd 0 pd 0 Di ðt00 Þ dt00 t In the case of constant temperature (i.e Di ¼ const), Eq (38) can be simplified: pffiffiffiffi pffiffi 2 D 0 Xi ðtÞ ¼ Xi ð0Þ þ pffiffiffi ½Xi À qi ðtފ t pd ð39Þ Diffusion coefficient for impurities in Fe and Fe-base alloys in ferrite interval is present in Table 6 The calculated diagrams of multicomponent adsorption in steels 0.3C– Cr–Mo, 0.3C–Cr–Mn–V, 0.3C–Cr–Mn–Si–Ti (see Table 3) are presented in Figs 36–38 Comparing these diagrams with the experimental ones (Figs 24, 26, and 27), a good correlation of segregation kinetic features for various elements is observed, that confirms the basic principles of the proposed model of GBS in steels According to this model, the main role of carbide precipitation in GBS consists of changing solid solution Copyright 2004 by Marcel Dekker, Inc All Rights Reserved Figure 40 Dependence of time of 6 at.% GBS of phosphorus and sulfur as a function of sulfur concentration in 0.3C–Cr–Mn–Si–Ti steel during its tempering at 700K Computer simulation The results of mathematical modeling provide backgrounds for reasonable planning of full-scale experiments when seeking for the optimum technological procedures and steel composition and they enable the extrapolation of the consequences of variations in the technological conditions even outside the boundary of the empirical experience we have available Interaction of GB segregation enrichment and phase transformations during heat treatment of steels in the austenitic region is hard to imagine Nb and V carbonitride precipitation in microalloyed austenite, precipitation of free ferrite, change chemical composition of austenite, and influence on GBS kinetics to a large extent The experiments show that nonequilibrium grain boundary phenomena occur for a rather short time up to 100 sec The minimum time of 5% volume fraction of Nb and V carbonitride precipitation is about 1000 sec [62,63] Precipitation of free ferrite needs from several seconds to several minutes depending on steel chemical composition Therefore, the non-equilibrium GBS in steels with a wide region of undercooled austenite stability independently from phase transformations This computer model has some limitations but redistribution of harmful impurities between grain bulk and boundaries permits the analysis of steel quenching The modeling of non-equilibrium GB phenomena allows during investigation of such short-time changes of chemical composition that could not be measured experimentally and that has an extreme importance for modern heat-treatment processes with high heating and cooling velocities in controlled media Copyright 2004 by Marcel Dekker, Inc All Rights Reserved  ... 23,7 64 25,368 21 ,42 9 30,000 26, 343 15.3 64 17 .48 1 18,575 15.737 14. 241 13.713 15.366 10.076 5 .48 1 1.698 16.351 15.2 34 10.050 16.72 40 .881 29.768 0.26 0.22 0. 24 0. 24 0.22 0. 24 0.21 0. 24 0 .42 2.32... 0.4C–1.32Mn 0.4C–2 .43 Mn 0.4C–0.2Cr 0.4C–2.1Cr 0.4C–3.6Cr 0.4C–6.7Cr 0.4C–0.37Si 0.38C–1.75Si 0.4C–2.75Si 0.4C 1.4C 1.2C–2.0Mo Q, cal=mol Ln K n 21,532 22, 643 23,599 21,196 20,298 19 ,40 6 20, 848 15, 348 10,992... 183CP 4: 8CAl 7:2CMo À 3:4CNi À 7 141 CB seg a a a a a ỵ 4: 9CCr 44 4CS 183EMo 87EN a a seg seg 24? ?? ES ẳ 6:9 151CS 1:5CAl ỵ 14: 5CP 39ESn seg a a a seg 25ị EN ẳ 16 2:6CAl ỵ 3CMo ỵ 4: 2CCr