Nonequilibrium thermodynamic modeling of carbon ...

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plasticity (TRIP) [6,7] of the stable retained austenite results in excellent combinations of tensile strength and uniform elongation. Low alloying additions and ...

Scripta Materialia 147 (2018) 6–10

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Nonequilibrium thermodynamic modeling of carbon partitioning in quench and partition (Q&P) steel Amit K. Behera ⁎, G.B. Olson Materials Science and Engineering, Northwestern University, 2145 Sheridan road, Evanston, IL 60208, USA

a r t i c l e

i n f o

Article history: Received 23 September 2017 Received in revised form 16 December 2017 Accepted 23 December 2017 Available online xxxx Keywords: Quench and partition Para-equilibrium Thermodynamic modeling HEXRD 3DAP

a b s t r a c t The influence of partitioning temperature on carbon partitioning during the quench and partition (Q&P) cycle and the associated non-equilibrium phase transformation thermodynamics have been investigated. Lower partitioning temperatures are reported to result in higher carbon partitioning with varying austenite phase fraction. Thermodynamic simulations considering para-equilibrium conditions with an added temperature-dependent effective stored energy contribution have been shown to reasonably predict the retained austenite carbon content. The developed models have been validated with new alloy compositions, QP cycles and data from existing literature. © 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The partitioning of carbon between ferrite and the austenite phase in steels during diffusional transformations upon high temperature annealing has been well studied over the years [1,2]. However, such partitioning behavior at lower temperatures during bainite or martensite tempering transformations has been investigated to a limited extent as these possess displacive characteristics and generally result in bodycentered phases with high carbon supersaturation. In the last decade, carbon partitioning across austenite/martensite interfaces during low temperature isothermal tempering in low carbon steels has been the focus of research efforts initiated by Speer et al. [3,4]. This led to the development of quench and partition (Q&P) steels with a primarily martensite and stabilized retained austenite microstructure that are deemed the most promising alloys amongst the third generation of advanced high strength steels (AHSS) [5]. The high strength of the martensitic matrix along with the enhanced ductility due to transformation induced plasticity (TRIP) [6,7] of the stable retained austenite results in excellent combinations of tensile strength and uniform elongation. Low alloying additions and production costs make for overall lower cost of these steels compared to the second generation of AHSS. Previous modeling efforts [4,8] in Q&P steels have suggested the concept of ‘Constrained carbon equilibrium’ (CCE) that governs the carbon partitioning between martensite and austenite in absence of any other competing transformations such as carbide precipitation. The CCE concept equates the carbon chemical potential in both phases while restricting any movement of the martensite/austenite interface. However, numerous experimental results have shown evidence of this ⁎ Corresponding author. E-mail address: [email protected] (A.K. Behera). 1359-6462/© 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

interface being mobile and thus influencing the carbon partitioning behavior. Movement of the interfaces has recently been shown in low and high carbon steels with help of in-situ experiments [9,10] while interface migration in high manganese alloys has also been observed by Thomas et al. [11]. Considering these observations, the current work models carbon partitioning in these alloys using para-equilibrium (PE) simulations with the concept of an added stored energy term to the ferrite phase. The PE simulations allow for martensite/austenite interface movement and account for the dissipated energy due to interface movement in the stored energy model. The concept of stored energy has been previously applied in the case of bainitic transformation based on the concept of coupled displacive/diffusional transformations [1,12] and used to predict carbon enrichment in low alloy TRIP steels [13,14]. The formulation of the ‘effective stored energy’ model for Q&P alloys and its dependence on processing parameters, mainly partitioning temperature is further developed in this paper. In the current study, a 0.2C-2.2Mn-1.5Si-0.2Cr alloy was used to evaluate the role of partitioning temperature on carbon partitioning while minimizing effects from other process variables. As shown in Fig. 1(a), the steel was initially fully austenitized at 900 °C (above the Ac3 temperature) for 100 s and then quenched to 270 °C (quench temperature, QT) before being reheated to three different partitioning temperatures, PT (390 °C, 410 °C, 430 °C) for partitioning time, P-times of 75, 100 and 150 s respectively. The quench temperature was chosen intentionally to have about 80% of initial quenched martensite so that the final microstructure consisted predominantly of martensite and retained austenite. The different partitioning times were estimated based on DICTRA simulations [15] to determine the minimum time required to achieve homogeneous carbon distribution in the retained austenite of

A.K. Behera, G.B. Olson / Scripta Materialia 147 (2018) 6–10


chemically thinned using a solution of HF + H2O2 + distilled water to remove any possible surface deformation effects. Lattice parameter was calculated using the (111), (200), (220), (311) austenite peaks. The lattice parameter measurements were used to estimate the austenite carbon content using the following empirical equation [16] and are summarized in Table 1.   aγ in Å ¼ 3:572 þ 0:033  XC þ 0:0012  XMn þ 0:00157  XSi þ 0:0056  XAl …ðin wt%Þ

Fig. 1. (a) Q&P cycles with varying PT, (b) SEM micrographs showing the final microstructure for PT of 410C, (c) EBSD image quality map with superimposed austenite phase IPF color map for PT 410C.

observed average thickness 0.2 μm, and thereby minimize undesired carbide precipitation at each partitioning temperature. The final microstructure consisted mainly of martensite phase with retained austenite as seen in the SEM images for sample with PT of 410C in Fig. 1(b). An image quality map from electron backscattered diffraction (EBSD) experiments with superimposed inverse pole figure (IPF) color maps for the austenite phase is shown in Fig. 1(c). The retained austenite within the same parent austenite grain can be seen to have similar crystallographic orientation. The retained austenite is found to be in the form of blocks and fine inter lath films, the latter mostly undetected by EBSD. Samples from the three different Q&P cycles were analyzed using synchrotron based high energy x-ray diffraction (HEXRD) measurements to determine the individual phase fractions and austenite lattice parameters. Prior to the experiments the samples were polished and

In addition to HEXRD studies, three-dimensional local electrode atom probe tomography (3D-LEAP) was also used to accurately determine composition of the individual phases. Needle shaped specimens were prepared via electropolishing method using a solution of 2butoxyethanol and perchloric acid in methanol. The experiments were carried out in a LEAP 4000X Si instrument used in laser mode with laser energy at 25pJ and specimen temperature of 40 K. The laser frequency was set at 500 kHz and evaporation rate was set at 0.5%. Fig. 2 shows tip reconstructions for each sample highlighting the austenite/ martensite interfaces of fine interlath austenite films. Proximity histograms shown alongside the tip reconstructions plot the composition profiles across the interface averaged along the entire interface. Carbon atoms (marked as red dots) are seen to be clearly enriched in the austenite phase. The average austenite carbon content for each partitioning temperature is measured from the proximity histograms away from the interface and is listed in Table 1. In case of austenite content measured by APT, the error bars noted represent the average statistical error for the total ions collected in the austenite region. For HEXRD measurements the error noted is between the lattice parameter calculated from the 4 different austenite peaks. The measured carbon content from HEXRD and LEAP experiments are found to match quite closely. The results indicate that the austenite carbon content decreases with increase in partitioning temperature. The LEAP experiments also establish that no long-range diffusion of substitutional alloying elements occurs during partitioning step although manganese is starting to diffuse within a few nanometers of the interface. Para-equilibrium conditions define that only the interstitial carbon atoms can undergo long range diffusion while the substitutional elements remain fixed. Simulations under these conditions were performed using ThermoCalc software and the recent thermodynamic database for iron based alloys, TCFE9. Based on the framework of coupled diffusional/displacive transformation as proposed by OlsonBhadeshia-Cohen [12,17], an additional resistive energy (GR) termed ‘Effective stored energy’ is added to ferrite to represent the net driving force available to form the product phase. The effective stored energy term includes the stored elastic strain energy (Gel) along with the frictional work dissipated for interface movement against solid solution D hardening (WSS F ) and forest dislocations (WF ). In the representation of martensite interface mobility in martensite nucleation theory [18,19], the net critical driving force for interface motion is derived to be a function of the elastic strain energy (Gel), solid solution frictional work (WSS F ) and the frictional work due to forest dislocations (WD F ). A thorough analysis of the solid solution friction in steels by Ghosh-Olson [19] has shown that the solution hardening (WSS F ) is athermal in nature for displacive interfacial motion above room temperature and can be predicted from elemental contributions, Table 1 Phase composition and volume fraction for different QP cycles. QT (°C)

PT (°C)

P-time (s)

Ret. Aust (%)

270 270 270

430 410 390

75 100 150

8.2 6.9 7.2

Cγ in wt% (HEXRD)


1.00 ± 0.03 1.05 ± 0.03 1.10 ± 0.03

1.03 ± 0.05 1.054 ± 0.03 1.094 ± 0.05

SE WD F (J/mol) (J/mol) 1305 1440 1575

710 834 969


A.K. Behera, G.B. Olson / Scripta Materialia 147 (2018) 6–10

where μ is the shear modulus of austenite obtained from Ghosh et al. [21] and Aμ ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2 0:5 ∑i K iμ X 0:5 þ ∑ j K iμ X 0:5 þ K Co i j μ X Co

where i = Al, C, N, Cr, Mn, Mo, Nb, Si, Ti, V, W and j = Cu, Ni.

Fig. 2. 3D-LEAP reconstructions showing austenite/martensite interfaces and the composition proximity histograms across them for alloys with (a) PT = 430 °C, (b) PT = 410 °C, (c) PT = 390 °C. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

giving the following set of equations. effective Stored Energy or GR ðcomp; TÞ ¼ Gel þ WDF þ WSS F D where Gel – elastic strain energy, WSS F - solid solution frictional work,WF -frictional work dissipated due to interface movement across forest dislocations [20]

WSS F ¼ Aμ  μ ðXi Þ

Fig. 3. (a) Schematic free energy diagram showing effect of stored energy on the paraequilibrium austenite carbon content, (b) WFD vs partitioning temperature for the different QP samples, (c) austenite carbon content vs partitioning temperature with dotted lines denoting PE model calculated values with and without using effective stored energy contribution.

A.K. Behera, G.B. Olson / Scripta Materialia 147 (2018) 6–10

The importance of the WD F term in displacive transformations has been clarified by study of nonthermoelastic-thermoelastic transition of martensitic transformation with ordering in the Fe3Pt system [22]. A dramatic reduction in the critical driving force for transformation with the elimination of accommodation slip by order strengthening indicates the contribution of Gel is negligible compared to WD F . The magnitude of WD F as a function of dislocation density has been quantified by measuring the effect of pre-strain on the rate of isothermal martensitic transformation at cryogenic temperatures [19]. This dependence on dislocation density accounts for a strong correlation of the temperature dependence of the critical driving force for displacive transformation with the temperature dependence of the dislocation density associated with displacive transformations, ascribed to dynamic recovery [23,24]. Forest hardening with dynamic recovery thus provides a mechanistic explanation for the empirical linear temperature dependence of bainite critical driving force first identified by Bhadeshia [25–27]. Accordingly, in our application of coupled displacive/diffusional transformation to interfacial motion in Q&P heat treatment, we neglect the contribution of Gel and identify the form of WD F (T) that accounts for the measured phase compositions under para-equilibrium constraint. Fig. 3(a) shows a schematic plot of the free energy of individual phases with carbon content at a fixed temperature. The common tangent marks the para-equilibrium carbon content in the two phases. Addition of effective stored energy to the BCC phase shifts the curve upwards thus reducing para-equilibrium carbon content of austenite phase at that temperature. The value for the GR, effective stored energy at each partitioning temperature was calculated such that the predicted carbon content matched the experimental measurements. The WD F for the current samples along with those from that previous reported for the same alloy [28] is plotted in Fig. 3(b). The plot supports the linear D dependence of WD F with partitioning temperature (WF = − 6.25 ∗ PT + 3403 J/mol, where PT is in degree Celsius) which is used to calibrate the stored energy model. The WD F (T) measured for TRIP steels undergoing bainitic transformation in earlier research [13,14] are also plotted. An average estimate of the uncertainty for these estimates is shown based on the experimental measurement errors. The WD F is found to be slightly lower for case of bainite. The calculated carbon content of austenite from PE calculations with and without the effective stored energy is shown by dashed lines in Fig. 3(c). Experimentally measured austenite carbon content for the different samples is also shown in the figure. The PE simulations with temperature-dependent WD F (T) accurately account for the austenite carbon content. To further validate the developed model, six different TRIP alloy compositions were cast, rolled and given optimized Q&P cycles. The QT in each case was chosen to have approximately 80% of initial quenched martensite. The PT and P-time were chosen to have optimal austenite stability with minimal carbide precipitation. The experimentally measured and model predicted values for austenite fraction and its carbon content are listed in Table 2. The austenite carbon content measured from HEXRD experiments is compared against the model predicted values in Fig. 4. A few other measurements obtained from existing literature [29] are also plotted alongside in the figure. The plot shows quite reasonable agreement between the predicted and measured values. The results indicate that para-


Fig. 4. Predicted carbon in austenite versus measured carbon in austenite for different alloys.

equilibrium simulations with a stored energy model addition can be used to reasonably predict austenite carbon content. Carbide precipitation could also influence austenite carbon content by reducing the activity of carbon in the matrix and thus lowering the experimentally measured austenite carbon content. An accurate model is critical as the austenite carbon content determines the retained austenite stability which strongly influences the final mechanical properties via the TRIP effect. In summary, the present study used advanced characterization techniques (3DAPT, HEXRD) to determine the influence of partitioning temperature on the carbon partitioning between austenite and martensite phases. Higher partitioning temperatures were shown to produce lower austenite carbon content. CALPHAD based para-equilibrium simulations with an added temperature-dependent effective stored energy model based on the framework of coupled displacive/diffusional transformations were shown to be able to accurately predict the austenite carbon content for various alloys with varying QP cycles. The current developed PE models can be used with austenite stability models in future work to design optimal alloy compositions and Q&P cycles for optimal mechanical performance. The authors would like to acknowledge ArcelorMittal Global R&D, East Chicago, Indiana for providing the financial support and raw materials for the study. HEXRD experiments were performed at the DuPontNorthwestern-Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by Northwestern University, E.I. DuPont de Nemours & Co., and The Dow Chemical Company. The Advanced Photon Source is a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.

Table 2 List of new casted alloys with their QP cycles and measured phase fraction and composition. Alloy

QT (°C)

PT (°C)

Ptime (s)

Aust frac. (%)

CAust, HEXRD (wt%)

Model CAust (wt%)

0.18C 2Mn 1.55Si 0.15Mo 0.18C 2Mn 1.55Si 0.15Mo 0.2C 1.8Mn 1.5Si 0.2Mo (B,Ti) 0.2C 1Mn 1.5Si 0.2Mo (B,Ti) 0.3C 1Mn 1.5Si 0.2Mo (B,Ti) 0.25C 1.5Mn 2Si 0.2Mo

290 290 310 325 300 275

420 440 420 450 430 410

75 60 75 60 75 100

5.3 6.9 6.5 1.1 5.6 7.5

1.11 1.08 1.17 1.36 1.44 1.23

1.18 1.15 1.25 1.52 1.41 1.3


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