Modeling and Simulation for Material Selection and Mechanical Design Part 5 pdf

1. Phase Transformations of Undercooling Austenite At present, many computer models of evolution of structure and phase com- position of steels during quenching have been developed. Most of them are based on physical models of phase transformations [64–66]. But physical models cannot describe adequately all kinetic features of undercooled auste- nite transformations. The computer models based on regression analysis of experimental data can best predict steel phase composition changes during steel cooling. It was introduced directly by Davenport and Bain [67] and the time– temperature-transformation (TTT) diagram was the predominant tool to describe the isothermal decomposition kinetics of supercooled austenite. In most TTT diagrams, general S- or C-curves are used to represent the kinetics of a number of isothermal transformation products: ferrite, pearlite, upper bainite, lower bainite, and martensite. Conversely, many experimental results demonstrate that each type of transformation product has a separate C-curve. To build a mathematical model, all TTT diagrams published in Refs. [68–71] were analyzed. The rationalization of the kinetics of isothermal decomposition of austenite permitted the establishment of a metastable product (phase) diagram of a number of steels of different compositions with 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 to Table 7. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Most isothermal transformations take place by nucleation at the aus- tenite grain boundaries, so the original austenite grain size will affect the iso- thermal decomposition kinetics of austenite. From the total number of factors characterizing austenite matrix, the present 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] dðtÞ¼d 0 þ kt exp À Q RT  ð40Þ where d(t) is averaged grain size at moment t; d 0 is initial grain size; Q is acti- vation energy; k is a constant. The algorithm of calculating the size of austenite grains is described in Ref. [73]. The procedure for calculation of the structural proportions of ani- sothermal decomposition of austenite at engineering steel cooling is given in Tables 7 and 8 and shown in Fig. 41. The cooling curve is approximated partially by a constant function and 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 TTT diagrams [68–71] that can be digitized (see Table 8) by procedures shown in Fig. 41, using equation S ÀS 0 S N À S 0 ¼ e 1=2 U ÀU 0 U N À U 0  1=2 exp À 1 2 U ÀU 0 U N À U 0  ð41Þ where S ¼Int-time interval, s; U ¼1000=(T þ273). Since it is necessary to distinguish between the parts of the C-curves representing the formation of ferrite, pearlite, and bainite, only those diagrams having readily distinguishable component curves were used in the analysis. The calculation method includes the effect of the size of austenite grains on the kinetics of phase transformations. The main precondition is knowledge of this effect on the course of C-curves showing the start and end of transformations in the graph of isothermal decomposition of auste- nite for the relevant steel. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. The program involves the calculation of temperatures of transforma- tions of bainite and twinned, athermal and lamellar martensite [74] B S ¼ 720 À585:63ðCÞþ126:6ðCÞ 2 À 66:34ðNiÞþ6:06ðNiÞ 2 À 31:66ðCrÞþ2:17ðCrÞ 3 À 91:68ðMnÞþ7:82ðMnÞ 2 À 42:37ðMoÞþ9:16ðCoÞÀ0:125ðCoÞ 2 À 36:02ðCuÞð42Þ M TM S ¼420À208:33ðCÞÀ72:65ðNÞÀ43:36ðNÞ 2 À16 :08ðNiÞ þ0:78ðNiÞ 2 À0:025ðNiÞ 3 À2:47ðCrÞÀ33:428ðMnÞþ1:296ðMnÞ 2 þ30 :0ðMoÞþ12:86ðCoÞÀ0:2665ðCoÞ 2 À7:18ðCuÞð43Þ M LM S ¼ 540 À356:25ðCÞÀ260:64ðN À 24:65ðNiÞþ1:36ðNiÞ 2 À 17:82ðCrÞþ1:42ðCrÞ 2 À 47:59ðMnÞþ2:25ðMnÞ 2 þ 17:5ðMoÞþ21:87ðCoÞÀ16:52ðCuÞð44Þ M A S ¼ 820 À603:76ðCÞþ247:13ðCÞ 2 À 55:72ðNiÞþ3:97ðNiÞ 2 À 31:1ðCrÞþ2:348ðCrÞ 2 À 66:24ðMnÞÀ24:29ðMoÞ À 0:196ðCoÞþ0:165ðCoÞ 2 À 31:88ðCuÞð45Þ The size of ferritic grain is expressed as follows [75] d a ¼ 11:7 þ0:14d g þ 37:7V À0:5 C ð46Þ where d g is the size of austenitic grain, (mm); V C is the cooling speed, (8Cmin À1 ). The interlamellar distance of pearlite can be estimated as follows [75]: S ¼ X i 18:0DV P ðy i Þ=ð996 Ày i Þ "# =V P ð47Þ where DV P (y i ) is the volume proportion of pearlite transformed at y i tem- perature. The thickness of the ferritic and carbide lamellae of pearlite is approxi- mately l f ¼0.885S; l c ¼0.115S The size of martensitic and bainitic particles is identical with the original size of the austenite grains. The course of the anisothermal decomposition of austenite in several steels has been calculated by the Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. just-described method and by applying the digitized TTT diagrams of Table 7. 2. Determination of the Kinetics of Carbonitride Precipitation in Austenite Microalloying of steels with Ti, V, Nb, and Zr affects decomposition of supercooled austenite, its recrystallization and grain boundary segregations of harmful impurities. These changes of material properties are associated with carbonitride precipitation and changes of austenite chemical composi- tion. Based on these reasons, the modeling of the kinetics of carbonitride precipitation is important. The nucleation time t of carbonitrides per unit volume N at any tem- perature T, can be expressed as [76] t ¼ C exp Q RT  exp B T 3 ðLnK S Þ 2 ! t ¼ C exp Q RT  exp B T 3 ðLnK S Þ 2 ! ð48Þ where C ¼6  10 13 for homogeneous nucleation; activation energy of Nb diffusion Q ¼270 kJ=mol; B ¼ 16pg 3 V 2 m N 0 =3R 3 ð49Þ V m ¼1.28  10 À5 m 3 =mol; g ¼0.5 J m À2 ; N 0 are numbers of nucleus by radius R per molar volume V m ; K S is supersaturation [77] LgðK S Þ¼À A T þ B ð50Þ where thermodynamics parameters A and B for various carbides and nitrides are calculated in Ref. [78] and presented in Table 9. Thus, the cal- culation of carbonitride nucleation time necessary to reproduce the C-curves Table 9 Thermodynamics Parameters in Eq. 50 (From Ref. 77) Chemical compound Parameter AlN VC VN TiC TiN NbC NbN ZrC ZrN A 7,130 9,500 7,985 8,872 15,573 7,714 10,440 8,464 13,968 B 1.463 6.72 3.09 4.04 3.82 3.27 3.87 4.96 3.08 Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. corresponds to start or finish of this transformation in austenite under heat treatment 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 GBS develops in this case in austenite in short time and has no dependence on phase and structure transformations at steel quenching. Enrichment of grain boundaries by various impurities as well as their desorption is treated as a result of multicomponent diffusion of impurities from near-boundary volume to the boundary. Impurity binding energy with GB includes mutual 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. These experiments are basic for analysis of correlation of impurity segregation energy 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 (q i ) at steel quenching is modeled well using the equation q i ¼ q i ð0Þþ 2q 0 i ffiffiffiffiffiffi pd p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z t 0 D i ðt 0 Þdt 0 À s 1 ffiffiffiffiffiffi pd p Z t 0 C i a ðt 0 ÞD i ðt 0 Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R t t 0 D i ðt 00 Þdt 00 q dt 0 ð51Þ where d is the grain boundary thickness; D i (t 0 ) is the diffusion coefficient of impurity which depends on the temperature and phase composition (auste- nite, martensite, and ferrite); in the case of adsorption C i a ¼ C i GB 1 À P j C j GB expðÀG i =kTÞð52Þ where C GB i is the element i concentration on grain boundary; C a i is the con- centration of ith element in the adjacent bulk layer; G i is segregation energy. Desorption is determined by GB concentrations of impurities, and in this case, the parameter C a i in Eq. (51) is equivalent to GB concentration X b I in Eqs. (12) and (13). The change of temperature at cooling or isothermal exposition is described by equation TðtÞ¼½Tð0ÞÀTð/Þ expðÀrtÞþTð/Þ ð53Þ Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Table 10 presents cooling rates r for heat-treatment processes. The block diagram of multicomponent intercrystalline adsorption model is shown in Fig. 42. Adsorption of P, C, and S is determined by parameters K 1 ,K 2 , K 3 , and their desorption by parameters K 2 ,K 4 ,K 6 . The parameters C i are equivalent to GB concentration of element i. This model allows the com- putation of the condition when there is change of GB composition in steels and alloys at preselected arbitrary mode of cooling including isothermal exposition. Given below are the examples of investigation of phosphorus and sul- fur grain boundary adsorption in Cr–Ni–Mo steel (see Table 11). The components of steel mutually influence their diffusion mobility and GBS activation energy. Based on this reason, one should take into account the stochastic fluctuations of diffusion flows of various impurities on GBS kinetics. For this purpose, the random fluctuation of diffusion coefficients 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 pur- ity steels cooling that were carried out using the stochastic model. As one can see, the self-regulation of adsorption is observed which is developing despite significant short-time oscillations of impurity concentration on grain boundaries. 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 cooling velocity from 0.001 to 1000K s À1 decreases the non-equilibrium GBS of P and S. Formation of non-equilibrium rich GBS of harmful impurities at small cooling times could be established only by using computer modeling methods. The experimental verification of such phenomena needs special techniques which allow to open grain boundaries: hydrogenation of quenched samples or delayed fracture tests. Since these techniques are conducted in air and could not be applied in the vacuum chamber of electron spectrometer; for most of engineering steels, the regularities of non-equilibrium GBS formation at quenching could only be estimated by a computer experiment. Table 10 Cooling Rates for Some Metallurgical Technologies Name of the treatment Cooling rates r (K sec À1 ) Quenching 100–10 Controlled cooling 10 Air cooling of hot-rolled metal 10–0.1 Cooling with furnace 0.01 Controlled cooling of large-size forging 0.001 Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Figure 44 The change of GBS during quenching of Cr–Ni–Mo steel containing 0.01S and 0.006P (mass%). Computer simulation of fast (a) and slow (b) cooling. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Figure 45 Chemical composition of GB in Cr–Ni–Mo steel containing 0.027S and 0.054P (mass%) after austenitization at 1373K (30 min), interim cooling up to 873K and quenching in water (a) and in furnace (b). Auger electron spectroscopy of intergranular fracture. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. Figure 46 Chemical composition of GB in Cr–Ni–Mo steel containing 0.01S and 0.006P (mass%) after austenitization at 1373K (30 min), interim cooling up to 873K and quenching in water (a) and in furnace (b). Auger electron spectroscopy of intergranular fracture. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. The validation of calculation reliability was done for steel composition 82 and 83 (see Table 10) by Auger spectroscopy. The samples after austeni- tization at 1373K (30 min) were in the interim cooled to 873K with further cooling in water or with furnace cooling. The undercooled austenite in this steel has high stability and does not transform in ferrite region for 2 hr. After cooling the samples had martensite–baintite structure. To investigate the chemical composition of grain boundaries by Auger spectroscopy, spe- cial samples were crushed in the electron spectrometer ESCALAB MK2 at vacuum at about 10 À8 Pa at temperature 83K. The fields with intercrystal- line fracture type were investigated on the fracture surface. The variation of phosphorus and sulfur content in GBS in Cr–Ni–Mo steel of several melts after heat treatment is shown in Figs. 45 and 46. At accelerated cooling the GB are significantly enriched by carbon. The P concentration in GB increases only at slow cooling of samples, and P segregation is strongly sup- pressed in pure steel. A good correspondence of calculated and experimental results is observed for all cases to be analyzed. The results of numerical modeling give information about the equili- brium and non-equilibrium character of a GB adsorption processes, which are frequently unavailable from experiments. Moreover, these simulation methods explain the phenomenon of reverse temper embrittlement as the result of non-equilibrium concurrent GBS of carbon and phosphorus. These results explain many questions in the multicomponent GB adsorption kinetics in engineering steels that were dynamically developed in the last 10 years. Further investigations in this direction are required especially for competitive internal adsorption in engineering steels treated by using newest schemes of heat treatment. REFERENCES 1. Briant, C.L.; Banerji, S.K. Intergranular failure in steel. Int. Met. Rev. 1978, 4, 164–196. 2. Arharov, V.I.; Ivanovskaya, S.I.; Kolesnikova, K.M.; Farafonova, T.A. The nature of phosphorous influence on temper embrittlement. Fiz. Met. Metallioved. 1956, 2, 57–65. 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 temper embrittlement. Surf. Sci. 1975, 53, 213–227. 6. Kaminskii, E.Z.; Stelletskaya, T.I. Kinetic of martensite dissolution in carbon steel. Problems of Fisical Metallurgy; Metallurgy: Moscow, 1949, 192–210. 7. Bokshtein, S.Z. Structure and Mechanical Properties of Alloyed Steel; Metallurgy: Moscow 1954. Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved. [...]... depends on the plastic deformation of solid materials due to rapid non-uniform cooling And, the strain and deformation due to phase transformation and change of microstructure are the sources of the micro-type residual stresses We also know that the distortion due to thermal and elastic–plastic deformation and strain as well as change of phase transformation and texture in manufactured materials are important... H.J Surface and grain boundary segregation on and in iron Steel Res 1986, 57 , 4178–41 85 21 Grabke, H.J Surface and Grain Boundary segregation on and in Iron and Steels ISIJ Int 1989, 29, 7 ,52 9–7 ,53 8 22 Kovalev, A.I.; Mishina, V.P.; Stsherbedinsky, G.V.; Wainstein, D.L EELFS method for investigation of equilibrium segregation on surfaces in steel and alloys Vacuum 1990, 41 (7–9), 1794–17 95 23 Bruver,... combined: it employs a fixed finite volume mesh for tracking material deformation and an automatically refined facet surface (material surface) to accurately trace the free surface of Copyright 2004 by Marcel Dekker, Inc All Rights Reserved the deforming material This is particularly suitable for large three-dimensional material deformation such as forging since remeshing techniques are not required... metallo-thermo -mechanical theory, numerical modeling and simulation technology considered with coupling of temperature and phase transformation or solidification as well as inelastic behavior involved with elastic–plastic, viscoplastic and creep deformation will be introduced The theory and simulation technology also are used in metallurgical process, such as heat treatment, continuous casting, and thermal... residual stress Therefore, one of the many important problems is how to control and utilize residual stresses and distortion due to variations of macro- and microstructure in materials for increasing and ensuring strength and quality of products after metallurgical process To improve the mechanical properties of materials, it is important to know how to raise compressive residual stress and reduce tension... transformation, latent heat, transformation stress, and strain are included This approach has been implemented in the commercial computer program MSC.SuperForge [62] III DESIGNING OF HEAT TREATMENT PROCESS FOR CONTROL OF RESIDUAL STRESS AND DISTORTION The purpose of the quenching and carburizing quenching of steel parts is to get desired metallurgical structures, hardness and strength of steel parts... were carried out for the quenching process [66–71] The simulation of quenching process is so complicated that most of the current research focused on the validity of numerical modeling for designing steel parts On the other hand, to obtain improved mechanical properties and fatigue strength of machine components, such as gears, and shafts carburizing–quenching process is often used for surface hardening... temperature, residual stresses and distortion in various metallurgical processes In the final part of the chapter, some conclusions and remarks which are used in the designing of metallurgical process for control of residual stress and distortion are presented From these conclusions, we summarize many, yet expected problems and subjects in future metallurgical process and material industry for reference of research... temperature, and stress=strain in the forging process associated with strain-induced phase transformation has been developed The material is considered as elastic–plastic and takes into account the phase transformation effects on the yield stress The temperature increase due to plastic deformation, heat conduction in the workpiece and dies, heat transfer between workpiece= die and ambient and thermal... alloys with 0– 15% Cr and their a=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 Science and Physical Metallurgy; Metallurgy: Moscow 1 958 ; 327–3 65 61 Militzer, . :0ðMoÞþ12:86ðCoÞÀ0:26 65 CoÞ 2 À7:18ðCuÞð43Þ M LM S ¼ 54 0 À 356 : 25 CÞÀ260:64ðN À 24: 65 NiÞþ1:36ðNiÞ 2 À 17:82ðCrÞþ1:42ðCrÞ 2 À 47 :59 ðMnÞþ2: 25 MnÞ 2 þ 17 :5 MoÞþ21:87ðCoÞÀ16 :52 ðCuÞð44Þ M A S ¼ 820 À603:76ðCÞþ247:13ðCÞ 2 À 55 :72ðNiÞþ3:97ðNiÞ 2 À. stresses and micro-residual stresses [1,2]. The macro-type depends on the plastic deformation of solid materials due to rapid non-uniform cooling. And, the strain and deformation due to phase transformation. stresses and distortion due to variations of macro- and microstruc- ture in materials for increasing and ensuring strength and quality of pro- ducts after metallurgical process. To improve the mechanical