Modelling of Transformations in TRIP Steels

Transcription

1 Modelling of Transformations in TRIP Steels Antonis I. Katsamas, Gregory N. Haidemenopoulos, Nikolaos Aravas Dept. of Mechanical & Industrial Engineering, University of Thessaly, Volos/Greece Industrial processing of low-alloy Transformation Induced Plasticity (TRIP steels involves various stages of heat-treating, such as Intercritical Annealing (IA and Bainitic Isothermal Treatment (BIT, in order to produce a dispersion of retained austenite (γ R particles and bainite (α B in a ferritic matrix (α. Retained austenite then transforms to martensite (α during forming processes undergone by the steel. In the present work an effort was made to model these stages of processing, i.e. IA, BIT and the γ R α strain-induced transformation. Simulation of heat-treatment stages was implemented using computational kinetics methods. Investigation of the strain-induced γ R α transformation kinetics was performed by means of a simple analytical model. Simulation of IA and comparison with available experimental data showed that the amount of austenite (γ forming during IA reaches the values predicted by thermodynamic equilibrium only at high annealing temperatures (>825 o C. It was also observed that kinetic and thermodynamic predictions set a lower and an upper limit, respectively, within which the actual amount of austenite experimentally observed is contained. Results from the simulation of the BIT indicated considerable carbon enrichment, and thus stabilization of γ R, in agreement with recent experimental observations. As regards the strain-induced γ R α transformation, the analytical model employed in the present work was fitted to available experimental results, showing reasonably good adaptation to the kinetic behaviour of the microstructure during plastic deformation. Keywords: low-alloy TRIP steels, phase-transformations, simulation, modeling, intercritical annealing, bainitic isothermal treatment, retained austenite, strain-induced transformation. Introduction The increased demand of the automotive industry for steel grades exhibiting high strength and formability has been the main incentive for the advent of new, multi-phase steel families, such as the low-alloy DP and TRIP steels [1]. The mechanical behaviour of TRIP steels in particular is unique among the Fe-based alloys, since they manage to combine high strength (typical tensile strengths MPa and formability (typical uniform elongations 20 25% [2]. This excellent combination of mechanical properties of TRIP steels is largely attributed to their complex microstructure, consisting of dispersed retained austenite (γ R and bainite in a ferritic matrix, figure 1. Under the effect of stress and/or plastic deformation, γ R transforms to martensite (α, thus contributing to an increase in strain-hardening rate (static hardening, while simultaneously the transformation acts as a deformation mechanism (dynamic softening. The combined effect of static hardening and dynamic softening promotes the stabilization of plastic flow [3]. The γ R dispersion in the microstructure is produced by a two-stage heat-treatment, i.e. an Intercritical Annealing (IA followed by a Bainitic Isothermal Treatment (BIT, figure 2. The major factor influencing the mechanical behaviour of low-alloy TRIP steels is the stability of the γ R dispersion, which in turn is affected by chemical composition, particle size and stress-state. These parameters are usually coupled, thus making optimisation of the microstructure and properties of TRIP steels a rather complex task and creating a necessity for the application of modeling and simulation methods, in order to understand the various mechanisms involved [4,5]. The aim of the present work is to demonstrate the usefulness of simple computational models, by which the heat- Figure 2. Typical heat-treatment sequence of low-alloy TRIP steels (A: austenite, B: bainite, F: ferrite. Figure 1. Typical microstructure of a low-alloy TRIP steel. steel research int. 75 (2004 No

2 treatment stages (IA and BIT can be simulated, and also to present an analytical model, which can be used to estimate the kinetics of γ R α transformation during uniaxial tension of TRIP steels. Intercritical Annealing (IA Figure 3. Schematic representation of the one-dimensional moving boundary diffusion model for IA simulation [7]. (a (b (c Figure 4. Experimental, equilibrium and kinetic model results of vol.% austenite as a function of IA temperature for the low-alloy TRIP steels of Table 1. a Steel 1, b Steel 2 and c Steel 3. The starting microstructure of low-alloy TRIP steels consists of proeutectoid ferrite and pearlite. It is well established that austenite (γ formation during heating of ferrite/pearlite microstructures proceeds in two steps [6]. The first step is relatively rapid and involves the formation of high-c γ from pearlite. The second step is substantially slower and involves the growth of γ in expense of proeutectoid ferrite (α. Therefore, in the simple IA model employed here, the assumption was that pearlite transformation to austenite is completed in a negligible amount of time. The conditions at the end of the first step (i.e. vol. fractions and compositions of phases were considered as initial conditions for the second step. Consequently, the system was considered to initially consist of a high-c γ region (formed from pearlite with width L γ, and a proeutectoid α region with width L α, figure 3. Under these conditions, simulation of γ formation within the intercritical range (α+γ can be performed by solving the coupled diffusion equations in the two phases involved. Details on the mathematical formulation of the model can be found in [7]. The resulting 1-D moving-boundary diffusion problem can be solved by a numerical method for the solution of coupled diffusion equations developed by Ågren, which is incorporated in the DICTRA computational kinetics software [8]. Determination of various necessary thermodynamic quantities for the simulation was implemented with the use of CALPHAD methodology, through Thermo-Calc computational alloy thermodynamics software [9]. Simulations of IA were performed for the three laboratory-produced low-alloy TRIP steels shown in table 1, for which experimental measurements of vol.% γ as a function of annealing temperature and time were available [10]. Annealing temperatures tested ranged between C. Figures 4a-c depict a comparison between calculated by the model (full lines, experimentally measured (square symbols and equilibrium values as calculated by Thermo- Calc (dotted lines, of vol.% γ as a function of annealing temperature, for an annealing time of 90 sec. Despite the simplicity of the model, a reasonable agreement can be observed. At low annealing temperatures ( C experimental and model results agree quite well, whereas at higher annealing temperatures the amount of γ is slightly underestimated by the model. This could be attributed to the activation of high-diffusivity paths, such as grain-boundaries, which accelerate the rate of transformation at higher temperatures, but cannot be taken into account by the model. It is also interesting to compare model and experimental results with the ones predicted by thermodynamic equilibrium. As regards the kinetically calculated and equilibrium values, it seems that for all the steels and annealing temper- 740 steel research int. 75 (2004 No. 11

3 atures considered, kinetics predict significantly less γ than thermodynamics. It can be observed that the experimentally measured vol.% γ lies between the kinetically and thermodynamically calculated curves. Thus, kinetics and thermodynamics set a lower and an upper limit, respectively, within which the experimental results are contained. In fact, equilibration has proven to require substantially greater annealing times in order to be achieved [7]. Table 1. Chemical composition (in mass% of TRIP steels employed in IA simulations. Material C Mn Si Steel Steel Steel Bainitic Isothermal Treatment (BIT The stage of BIT is of great importance for the formation of a stable γ R dispersion in the microstructure. Bainite growth is accompanied by the rejection of C in austenite, thus increasing the stability of the final γ R dispersion. Recent measurements of C-content within individual γ R particles in various low-alloy TRIP steels, using sophisticated techniques such as PEELS, have shown considerable C enrichment of γ R after the BIT stage, with concentrations reaching as high as mass % C [11,12]. In order to investigate C enrichment of γ R a simple kinetic model was employed, which was based on an idea originally developed by Hillert et al. [13]. To adapt this idea for the case of low-alloy TRIP steels, some initial considerations had to be made: i Austenite (γ enters the BIT stage with an initial composition determined by thermodynamic equilibrium at the IA temperature. ii High Si or Si+Al content of low-alloy TRIP steels suppresses carbide precipitation. Thus only bainitic ferrite (α B forms during the BIT stage. iii α B grows in parabolic cylinder plates, figure 5, in an edge-wise manner [14]. iv Growth rate is rapid enough, so that solute species (C, Mn, Si initially become entrapped inside α B. Thus, α B initially inherits the chemical composition of γ. v The initial supersaturation of α B is then eliminated by side-wise diffusion of the solute species out of the α B plate and into the adjacent γ R, figure 6. The purpose of the proposed kinetic model is to simulate the side-wise rejection of solute species out of the α B plates and not their growth rate. In order to do so, a two-cells approach was employed for the geometry of the model. Two cells, separated by an immobile interface allowing the diffusional exchange of mass, were used; one assigned to α B and the other to γ R. The width of the α B cell is associated to the half-thickness of the plate (W/2, whereas the width of the γ cell is associated to the austenite grain size. The initial chemical composition of the γ R cell is determined by thermodynamic equilibrium at the IA temperature and, as explained above, this is also the initial composition for the α B cell. The model was then applied for simulating the BIT treatment of a 0.20C-1.65Mn-1.60Si (mass % industrially produced low-alloy TRIP steel. The initial composition of γ R was calculated by Thermo-Calc at 775 C (i.e. at the IA temperature corresponding to a 50%-50% γ /α mixture, and was found to be 0.38C-2.30Mn-1.42Si (mass %. Various cell sizes (0.2-5 µm, as well as BIT temperatures ( o C and holding times (up to 600 sec were examined in Figure 5. Parabolic cylinder model for the bainitic ferrite plates. Figure 6. Edge-wise growth and side-wise rejection of C from a bainitic ferrite plate. the simulations, which were performed by using the DIC- TRA computational alloy kinetics software. A series of interesting results can be drawn from the simulations. Figure 7 depicts the variation of C concentration profiles within a γ R particle at various BIT holding times, for treatment at 300 C and 400 C. As shown, significant C- enrichment of γ R occurs, which is more pronounced at the interface with α B (right-hand end of the diagram. Increasing BIT temperature seems to have an effect on the rate of C migration and homogenisation of the particle, but not on the total amount of C entering the particle. This is better illustrated in figure 8, which depicts the total C-concentration of the γ R particle of figure 7 as a function of the square root of BIT time. It should also be observed in figure 8 that at the end of BIT, the C-content of the γ R particle has increased by a factor of 2 with respect to the initial value. steel research int. 75 (2004 No

4 Figure 7. C-concentration profiles in a γ R particle as a function of BIT time at 300 o C and 400 o C. Figure 8. Total C-content in a γ R particle (cell size 1µm as a function of BIT time at 300 o C and 400 o C. It should however be noted that the levels of C-enrichment calculated by the model are solely dependent on the cell sizes, which were selected arbitrarily for the sake of the simulations. In order to get more realistic results, the cell sizes have to be related to the actual α B plate thickness and γ grain size. Additionally, the limitations imposed by the T o line have to be taken into account, in order to determine the maximum amount of C that can be accommodated by γ R. The T o line can be readily determined by thermodynamics. For the alloy examined here the T o line was calculated by Thermo-Calc and is presented in figure 9. The dotted vertical line represents the chemical composition of γ at the end of the IA stage. Simulation results were quite different for the substitutional species of the alloy (Mn, Si, for which no significant mass transfer between the two phases was calculated. This is illustrated in figure 10, which depicts the total Mn-content of a γ R particle as a function of square root BIT time for treatment at 300 C and 400 C. There seems to be a net flow of Mn out of the γ R particle towards α B during the treatment, but in very small quantities. The same outcome was also valid for Si. These results indicate that the process possibly takes place under paraequilibrium conditions with respect to C. The usefulness of such a relatively simple kinetic model for the BIT lies in the information it can provide regarding γ R stability. For example, the simplest expression of austenite stability is the M s temperature, which can be calculated by using simple empirical laws, such as the well-known Andrews equation [15]. For the steel analysed with the present model, Andrews equation yields an M s temperature of 308 C for γ R at the beginning of the BIT, while after the treatment this reduces to 152 C. Furthermore, as a result of the formation of a C concentration gradient within the γ R particles (figure 7, it would be reasonable to expect that a stability gradient should also exist inside each γ R particle. Such an example is presented in the diagram of figure 11, which shows the calculated Ms σ temperature, using an analytical model proposed by Haidemenopoulos et al. [16], as a function of distance from the centre of the particle. It should be reminded at this point that the characteristic Ms σ is a measure of the stability of γ R dispersions against mechanically induced transformation. As expected, Ms σ in figure 11 is low in the vicinity of the γ R /α B interface (i.e. retained austenite is very stable there and increases towards the centre of the particle. On straining of the steel, this could lead to the formation of martensitic cores surrounded by very stable retained austenite rims. Actually, a similar though reverse morphology (martensitic rims surrounding austenite particles has been observed by Speich et al. [17], in intercritically annealed and then slowly cooled DP steels. Strain-Induced Transformation of Retained Austenite to Martensite Figure 9. Calculated T o line for the Fe C 2.30Mn 1.42Si alloy system. Transformation induced plasticity can occur by two distinct mechanisms, i.e. stress-assisted and strain-induced γ R α transformation. In the stress-assisted regime α 742 steel research int. 75 (2004 No. 11

5 forms on pre-existing nucleation sites. In contrast, in the strain-induced regime, new and more potent nucleation sites are created by plastic deformation of the parent phase. As the steel is stressed and deformed, γ R will transform to α by the simultaneous operation of both mechanisms. The stress-assisted mechanism dominates at stresses lower than the yield-strength of γ R, whereas the strain-induced mechanism prevails after the yield-strength has been surpassed. The total volume fraction of γ R transforming to martensite, f, could then be expressed in the following form: f = f (σ stress + f (σ, ε strain (1 where f(σ stress and f(σ,ε strain denote the contributions of the stress-assisted and strain-induced mechanisms, respectively. According to the mechanism for heterogeneous martensitic nucleation proposed by Olson et al. [18,19], formation of a martensitic nucleus can occur by the dissociation of an existing defect, which serves as a nucleation site for the transformation. Dissociation of such a defect creates a faulted structure or martensitic embryo, the growth of which is determined by the energy change accompanying the dissociation. The energy per unit area of an embryo with thickness of n crystal planes, γ f (n, is given by equation: Figure 10. Total Mn-content of a γ R particle (cell size 1µm as a function of BIT time at 300 o C and 400 o C. γ f (n = n d ( g ch + g el + w f + 2γs (2 in which g ch is the chemical driving force for the transformation, g el the elastic strain energy, associated with distortions in the embryo/matrix interface, w f the frictional work of interfacial motion, γ s the specific embryo/matrix interfacial energy and d the close-packed interplanar spacing in the martensitic embryo. The potency of a nucleation site (defect can be expressed in terms of the thickness n (expressed in number of crystal planes of the nucleus, which can be formed from barrierless dissociation of the defect. The critical value of n, for nucleation at a given chemical driving force per unit volume, is then given by: 2γ s n = (3 ( ch + g el + w f d Based on this theory, the cumulative defect-potency distribution has been derived [20], using results from the wellknown Cech and Turnbull small-particle experiments in Fe- 30Ni alloys [21]: N v = Nv o exp( α n [ ] N v = Nv o exp 2α γ s ( g ch + g el + w f d where N v denotes the number density of nucleation sites randomly distributed throughout the volume, Nv o the total number density of nucleation sites of all potencies and α is a constant. (4 Figure 11. Variation of temperature in a γ R particle of size 0.5 µm, after BIT at 400 o C for 60 sec. In the case of transformation induced plasticity, the potency distribution of pre-existing nucleation sites in the stress-assisted region, is given by: N stress v = N o v exp ( 2α γs where A = g ch +(1/3 g σ,max +g el +w f. Here, Nv stress is the number density of pre-existing nucleation sites and Nv 0 the number density of pre-existing nucleation sites of all potencies. Comparing equation (5 to equation (4, the former contains an extra term, g σ,max, which stands for the mechanical contribution to the driving force. The mechanical driving force contribution term has been determined by Patel and Cohen [22]: g σ,max = 1 ( σ γo ε2 o + σ ε o (6 where γ o and ε o are the transformation shear and normal strains, respectively. (5 steel research int. 75 (2004 No

6 A similar expression can be used to describe the potency distribution of the new, strain-induced nucleation sites: N strain v [ ] 2α = Nv o (ε exp γs in which B = g ch + g σ,max +g el +w f. All parameters in equation (7 represent the same physical quantities as explained for equation (5. It should, however, be emphasized that in contrast to equation (5, the total strain-induced nucleation sites density up to plastic strain ε, Nv 0 (ε, is in this case a function of plastic strain ε. The number density of all nucleation sites is equal to the sum of equations (5 and (7: N v = Nv stress + Nv strain N v = Nv o exp( α stress n stress Nv o (ε exp( α strain n strain (7 (8 f = 1 exp ( N v V p (11 where V p is the particle volume. Combined with equations (8, (9 and (10, equation (11 gives: { [ ( f = 1 exp V p Nv o exp 2γs α stress +... ( ]} ( Nv o (ε exp 2γs α strain An expression for the total strain-induced nucleation sites density up to a specific plastic strain ε, Nv 0 (ε, has been proposed by Kuroda [23]: N o v (ε = N [1 exp ( k ε n] (13 Parameters n stress and n strain are given by: ( 2γs n stress = (9 where N represents the overall number density of nucleation sites that is possible to be induced by plastic strain, while k and n are dimensionless constants. Introducing equation (13 into (12 the later becomes: for the stress-assisted and ( 2γs n strain = (10 for the strained-induced regime of the transformation, respectively. Assuming that the nucleating defects are randomly distributed, the vol. fraction γ R transforming to α is given by: Table 2. Chemical composition (in mass% of the low-alloy TRIP steels with available f ε kinetics experimental data. Steel C Mn Si Al Nb TRIP TRIP Figure 12. Experimental and model f - ε results for steels TRIP 1 and TRIP 2 of table 2. f = 1 exp{ V p [Nv o exp(2γ s α stress N [1 exp( k ε n ] exp( 2γ s α strain ]} (14 Equation (14 establishes a relation between vol. fraction γ R transformed to α, f, and true plastic strain, ε. It is, therefore, possible to predict the kinetics of the transformation at certain amounts of plastic strain, provided that some values for the rest of the parameters in equation (14 are given. The analytical kinetics model described above was used in order to calculate the f-ε behaviour in uniaxial tension of two laboratory-produced low-alloy TRIP steels, for which experimental f-ε kinetic data where available in literature [2]. Table 2 presents the chemical composition of these steels. Appropriate values for the parameters employed in equation (14 were found in literature [1,2,23]. Equation (14 was then subjected to a non-linear curve fitting procedure, in order to best fit the experimental results. This was accomplished by varying parameters NV 0 and N. Figure 12 depicts experimental (symbols and calculated (lines f-ε results for the two steels examined. The diagrams also show the BIT conditions applied to the steels. As shown, the model manages to describe fairly well the sigmoidal variation of the transformation product with respect to plastic strain. One should also note the substantial fraction of the transformation, which occurs in the elastic region (ε = 0, under the operation of solely the stress-assisted nucleation mechanism. Comparing the f-ε behaviour of the two steels, the existence of Nb in steel TRIP 2 does not seem to produce any significant differences in the kinetics of the strain-induced part of the transformation. However, Nb seems to promote the stress-assisted transformation of γ R, since a greater fraction of γ R has transformed in the elastic region for the Nb containing steel (TRIP steel research int. 75 (2004 No. 11

7 Conclusions Modern metallurgical methods, such as computational alloy thermodynamics and kinetics, can be used in order to simulate the phase transformations involved during the heat-treatment stages of low-alloy TRIP steels, i.e. intercritical annealing and bainitic isothermal transformation. The use of relatively simple models allows for the simulation of these heat-treatments, which in turn can provide useful information regarding microstructural characteristics such as volume fraction and stability of the γ R dispersion in TRIP steels. In addition, prediction of the evolution of the microstructure during plastic deformation of TRIP steels, by employing a suitable analytical model, can be used in order to optimise the final microstructure of the steel and, thus, its mechanical behaviour. The main concluding remarks of the present work can be summarized in the following points: i Simulation of IA annealing and comparison to available experimental results showed good agreement at lower annealing temperatures (<825 C. At higher IA temperatures the experimental results reach better agreement with predictions obtained by equilibrium calculations. In any case, kinetics and thermodynamics set a lower and upper limit, respectively, within which the experimental results are obtained. ii Considerable C-enrichment and, thus, stabilisation of γ R particles was calculated by the simulation of the BIT treatment. In contrast, negligible exchange of substitutional elements, such as Mn and Si, seems to take place between γ R and α B during the BIT. As a consequence of a C-concentration gradient within γ R particles a stability gradient should also exist. iii The analytical model used for the analysis of the γ R α deformation induced transformation kinetics displayed good adaptation to available experimental data. Acknowledgement This work has been partly supported by the European Coal and Steel Community (ECSC through the 7210-PR- 370 project Control and exploitation of the bake-hardening effect in multi-phase high-strength steels. (A Contact: Prof. Dr.-Ing. G. N. Haidemenopoulos Department of Mechanical and Industrial Engineering University of Thessaly Volos, Greece References [1] A.N. Vasilakos: Transformation-Induced Plasticity of Retained Austenite in Low-Alloy Steels, PhD. Thesis, Dept. of Mechanical & Industrial Engineering, University of Thessaly, Volos, Greece, [2] J. Öhlert: Einfluss von chemischer Zusammensetzung und Herstellungsverlauf auf Mikrostruktur und mechanische Eigenschaften von TRIP-Stählen, Ph.D. Thesis, Institute of Ferrous Metallurgy, RWTH Aachen, Germany, [3] G.B. Olson, M. Cohen: Metal. Trans. A, 13A (1982, [4] G.N. Haidemenopoulos: Dispersed-Phase Transformation Toughening in Ultra High-Strength Steels, Ph.D. Thesis, Dept. of Materials Science & Engineering, M.I.T., Boston, MA, U.S.A, [5] A. Perlade, O. Bouaziz, Q. Furnémont: Materials Science Engineering A, 356 (2003, 145. [6] G.R. Speich, V.A. Demarest, R.L. Miller: Metal. Trans. A, 12A (1981, [7] A.I. Katsamas, A.N. Vasilakos, G.N. Haidemenopoulos: Steel Research, 71 (2000, 351. [8] J. Ågren: ISIJ intern., 32 (1992, 291. [9] B. Sundman, B. Jansson, J.-O. Andersson: CALPHAD, 9 (1985, 153. [10]K. Papamantellos: Umwandlungsverhalten und mechanisch-technologische Eigenschaften von niedriglegierten TRIP-Stählen, Ph.D. Thesis, Institute of Ferrous Metallurgy, RWTH Aachen, Germany, [11] C. Scott, J. Drillet: Quantitative analysis of local carbon concentrations in TRIP steels, Proc. Intern. Conf. on TRIP-Aided High Strength Ferrous Alloys, 2002, Ghent, Belgium, p. 97. [12] ECSC-project 4488: Control and Exploitation of the Bake-Hardening Effect in Multi-Phase High-Strength Steels, interim report no. 2, June [13] M. Hillert, L. Höglund, J. Ågren: Acta Metal. Mater., 41 (1993, [14] R. Trivedi: Metallurgical Transactions, 1 (1970, 921. [15]K.W. Andrews: JISI, 203 (1965, 721. [16] G.N. Haidemenopoulos, A.N. Vasilakos: Steel Research, 67 (1996, 513. [17] G.R. Speich: 110th AIME Annual Meeting Proc., 1981, p. 3. [18] G.B. Olson and M. Cohen: Metal. Trans. A, 7A (1976, [19] G.B. Olson, M. Cohen: Metallurgical transactions A, 7A (1976, [20] M. Cohen, G.B. Olson: Jpn. Suppl. Trans., 17 (1976, 93. [21] R.E. Cech, D. Turnbull: Trans. AIME, 206 (1956, 124. [22]J.R. Patel, M. Cohen: Acta Metal., 1 (1953, 531. [23] Y. Kuroda: Kinetics of Deformation-Induced Transformation of Dispersed Austenite in two Alloy Systems, M.Sc. Thesis, Dept. of Materials Science & Engineering, M.I.T., Boston, Massachusetts, U.S.A, steel research int. 75 (2004 No