Thermo-kinetic design of retained austenite in advanced high strength steels

Accepted Manuscript Thermo-kinetic design of retained austenite in advanced high strength steels Zongbiao Dai, Ran Ding, Zhigang Yang, Chi Zhang, Hao Chen PII:

S1359-6454(18)30317-3

DOI:

10.1016/j.actamat.2018.04.040

Reference:

AM 14528

To appear in:

Acta Materialia

Received Date: 8 February 2018 Revised Date:

6 April 2018

Accepted Date: 17 April 2018

Please cite this article as: Z. Dai, R. Ding, Z. Yang, C. Zhang, H. Chen, Thermo-kinetic design of retained austenite in advanced high strength steels, Acta Materialia (2018), doi: 10.1016/ j.actamat.2018.04.040. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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ACCEPTED MANUSCRIPT

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Thermo-kinetic design of retained austenite in advanced high strength steels Zongbiao Dai, Ran Ding, Zhigang Yang, Chi Zhang, Hao Chen*

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Key Laboratory for Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing, China Email: [email protected]; Tel: 0086(0)1062788 328

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Abstract:

Design of metastable retained austenite has been one of the most key issues in the

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development of advanced high strength steels (AHSSs) as mechanical properties of AHSSs are directly linked to the amount of retained austenite and its stability. In the past decades, several approaches, e.g. isothermal bainitic transformation, quenching & partitioning, austenite reversion transformation et al. have been successfully proposed to obtain retained austenite in the AHSSs.

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However, up to now, optimization of alloy composition and processing parameters in the above approaches is primarily by “trial and error” experiments or thermodynamic calculations. In this

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study, an integrated thermo-kinetic computational model, in which thermodynamics-kinetics of phase transformations and alloying elements partitioning are carefully considered, is used to

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design multi-phase microstructure of AHSSs with an emphasis on retained austenite. The current model is benchmarked by a comparison with the available experimental data for the conventional transformation-induced plasticity and quenching & partitioning steels, and the effects of alloy composition and processing parameters on the amount of retained austenite and its composition will also be discussed. Keywords: Local equilibrium; Isothermal bainitic transformation; Quenching and partitioning; Retained austenite 1

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Nomenclature

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Q&P RA TRIP XRD 3DAP

ferrite bainitic ferrite martensite untempered martensite tempered martensite austenite pearlite bainite start temperature martensite start temperature martensite finish temperature eutectoid temperature advanced high strength steels constrain carbon equilibrium cold rolled electron probe microanalysis full equilibrium Gibbs energy balance hot rolled high energy X-ray diffraction intercritical annealing isothermal bainitic transformation local equilibrium negligible partitioning negligible partitioning local equilibrium paraequilibrium partitioning local equilibrium transition temperature between partitioning local equilibrium mode and negligible partitioning local equilibrium mode quenching and partitioning retained austenite transformation-induced plasticity X-ray diffraction three dimensional atom probe

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α αB α′ αUM αTM γ P Bs Ms Mf TE AHSSs CCE CR EPMA FE GEB HR HEXRD IA IBT LE NP NPLE PE PLE PNTT

γ cNPLE / PLE −( γ →α )

transition carbon content in austenite between partitioning local equilibrium

mode and negligible partitioning austenite-to-ferrite transformation γ cNPLE / PLE −(α →γ )

local

equilibrium

mode

for

transition carbon content in austenite between partitioning local equilibrium mode and negligible partitioning ferrite-to-austenite transformation

2

local

equilibrium

mode

for

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1. Introduction Developing advanced high strength steels (AHSSs) with excellent strength-ductility balance is of great importance for automobile industries to reduce vehicle weight and improve energy

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efficiency. However, the strength-ductility trade-off has been a long-standing dilemma, which has limited the potential of high strength steels. In the past decades, abundant efforts have been made to tune the multi-phase microstructure of steels in order to enhance strength and ductility

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simultaneously, and it was found that the metastable retained austenite (RA) is of great importance

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to the strength-ductility balance due to transformation-induced plasticity or twinning-induced plasticity effects. Therefore, it is of significant importance to tune the retained austenite phase in the AHSSs.

Austenite is usually not stable at room temperature, but it can be stabilized and retained via transformations

and

alloying

elements

partitioning.

In

the

first

generation

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phase

transformation-induced plasticity (TRIP) steels, austenite is stabilized via the austenite-to-ferrite transformation or its reverse transformations (pearlite/ferrite-to-austenite) during intercritical

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annealing (IA) and the following isothermal bainitic transformation (IBT) [1-6]. Carbon is

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redistributed into austenite during these transformations to increase the stability of austenite. It has been found that the austenite-to-ferrite transformation and its reverse transformations during IA temporarily ceases at a certain ferrite/austenite fraction lower than full equilibrium, and this deviation from equilibrium phenomenon is called as “transformation stasis” or “Incomplete Transformation” [7-15]. Transformation stasis is of great practical importance as it determines the austenite/ferrite fraction and carbon content in austenite after intercritical annealing. In [8-11], it was indicated that stasis phenomenon during intercritical annealing in the Fe-C-Mn alloys could 3

ACCEPTED MANUSCRIPT be well described by Local Equilibrium (LE) model and a so-called Gibbs energy balance (GEB) model based on solute drag theory, and interfacial Mn partitioning was found to be the reason for the presence of stasis. Transformation stasis has also been observed during isothermal bainitic

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transformation, and its mechanism has been controversial for centuries. The diffusionless school suggests that bainitic stasis is attained when carbon content in austenite reaches the T0 or T0’ limits [16, 17]. According to the diffusional school, bainitic stasis is attributed to the interaction between

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substitutional alloying elements and migrating interface [18-22]. The GEB model has been found

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to successfully describe bainitic stasis in a series of alloys, which was found to be caused by the kinetic transition from carbon diffusion to substitutional elements diffusion controlled mode [19, 20, 23, 24].

Retained austenite has been introduced into the microstructure of all the recently developed

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third generation AHSSs including carbide-free bainitic steels, medium Mn TRIP steels and quenching & partitioning (Q&P) steels. The carbide-free bainitic steels including bainitic ferrite and retained austenite is produced through the isothermal bainitic transformation process [25]. The

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microstructure of medium Mn steels consisting of tempered martensite and retained austenite is

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obtained via the martensite-to-austenite reversion, during which both C and Mn are partitioned into austenite to increase its chemical stability [12-14, 26]. In the Q&P steels, the steel is first quenched to a temperature between martensite start temperature and martensite finish temperature to obtain the martensite-austenite mixture and then reheated to partitioning temperature to allow carbon diffusion from martensite into austenite [27, 28]. The stability of austenite is increased after the step of carbon partitioning, which will allow more austenite to be retained at room temperature. Alloying elements partitioning and transformation behavior during the Q&P process 4

ACCEPTED MANUSCRIPT is quite complicated, and has been discussed extensively [29-35]. Recently, a so-called QP-LE model based on LE assumption has been proposed to predict the kinetics of carbon partitioning and phase transformations during the Q&P process [36]. It has been suggested by the QP-LE

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model that, similar with the IBT process, a stasis state will be also reached during the Q&P process, and the fraction of austenite and carbon content in austenite at the stasis is affected by interfacial Mn partitioning significantly. Recently, interfacial partitioning of Mn has been detected

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directly by three dimensional atom probe (3DAP) at bainitic ferrite/austenite interface after the

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IBT process [37, 38] and martensite/austenite interface after the Q&P process [39, 40]. Until now, mechanism of the above mentioned transformations have been widely but separately studied in the literatures, while microstructure design of AHSSs, e.g. optimization of alloy composition and processing parameters, is still strongly relied on “trial and error”

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experiments or some basic thermodynamic calculations. In this study, an integrated thermo-kinetic model based on local equilibrium assumption, in which thermodynamics/kinetics of phase transformations and alloying elements partitioning are carefully considered, is proposed to design

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the multi-phase microstructure of the TRIP and Q&P steels with an emphasis on retained austenite.

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The effects of alloy composition and processing parameters on the amount of retained austenite and its composition will also be discussed in details.

2. Thermodynamics and kinetics of phase transformations in AHSSs Fig. 1a-c illustrate the key phase transformations and the resultant microstructure evolution

during the processing of cold rolled TRIP (denoted as CR-TRIP) steels, hot rolled TRIP (denoted as HR-TRIP) steels and cold rolled Q&P (denoted as CR-Q&P) steels, respectively. The multi-phase microstructure of the TRIP steels usually contains ferrite, bainitic ferrite and a 5

ACCEPTED MANUSCRIPT considerable amount of retained austenite, which is obtained via phase transformations during intercritical annealing and the following isothermal bainitic transformation. The microstructure of the Q&P steels is obtained via martensite transformation upon quenching and the following

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transformations during partitioning. In order to design the multi-phase microstructure of the TRIP and Q&P steels, an integrated thermo-kinetic model, which could describe all transformations during the processing and their interactions, is required. The chemical composition of the

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investigated TRIP and Q&P steels is listed in Table 1. It is shown that the composition of these

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two types of steels is quite similar, and the key elements are C, Mn and Si. Si is added to suppress carbide precipitation, while C and Mn are both austenite stabilizers.

2.1 Transformations during intercritical annealing

Fig. 1a-b show that both the pearlite/ferrite-to-austenite transformation and the

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austenite-to-ferrite transformation during intercritical annealing are the key transformations for the TRIP steels. It is known that pearlite/ferrite-to-austenite transformation occurs in two stages [4, 41, 42]: (i) pearlite dissolves rapidly during heating to the IA temperature, which results in the

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formation of carbon supersaturated austenite; (ii) subsequently ferrite-to-austenite transformation

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occurs during holding at IA temperature. As the first stage is very fast and does not affect the stasis state,

the

analysis

of

pearlite/ferrite-to-austenite

transformation

is

focused

on

the

ferrite-to-austenite transformation here. According to LE assumption, each element for the Fe-C-M (M is substitutional alloying element) system has equal chemical potential at the interface:

µiα /γ = µiγ /α

(1)

Where µiα /γ and µiγ /α represent chemical potential of element i at the interface in ferrite and 6

ACCEPTED MANUSCRIPT austenite phase, respectively. In addition, mass balance for both carbon and M should be satisfied simultaneously:

v=

J iα /γ − J iγ /α xiα /γ − xiγ /α

(2)

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Where v represents the interface velocity, J iα /γ and J iγ /α represent the flux of element i at the interface in ferrite and austenite phase, respectively, xiα /γ and xiγ /α represent the mole fractions

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of element i at the interface in ferrite and austenite phase, respectively.

The isothermal section of the Fe-C-M system shown in Fig. 2a illustrates the

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ferrite-to-austenite transformation occurs under LE condition at an IA temperature. After fully dissolution of pearlite, carbon content in austenite, Point o, is assumed to be the eutectoid carbon concentration (~0.7 wt. %). Since the diffusivity of M is much lower than that of carbon, the newly formed austenite could inherit M content of parent α phase. Hence, the interfacial

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composition of γ phase is determined by the intersection between carbon component ray bc and γ/(α+γ) phase boundary, Point b. Under such condition, carbon activity in austenite is larger than

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that at the interface, i.e. aCγ (o) > aCγ (b) , which causes large carbon activity gradient in austenite. The diffusion flux in austenite can be given by:

DCγ xCγ ∇ µ Cγ = − DCγ xCγ ∇ ln aCγ RT

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J Cγ = −

(3)

Where DCγ is the carbon diffusivity in austenite, xCγ is the mole fraction of carbon in austenite,

µCγ is chemical potential of carbon in austenite, R is the universal gas constant and T is absolute temperature. In order to satisfy LE condition, Eq. (1), a negative spike of M content, which is determined by the end of tie-line ab connecting with the α/(α+γ) phase boundary, will appear ahead of the interface in α phase. Assuming that carbon activity in α phase is not affected by the 7

ACCEPTED MANUSCRIPT thin M spike, the composition at the interface in α phase will be determined by the intersection between carbon isoactivity line ac and carbon component ray bc, Point c. Neglecting the contribution of xiα /γ and J iα /γ , interface velocity described in Eq.(2) can be estimated by:

J Cα /γ − J Cγ /α J Cγ /α v = α /γ ≅ γ /α ≅ − DCγ ∇ ln aCγ γ /α xC − xC xC

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(4)

Under such circumstance, kinetics of the ferrite-to-austenite transformation is controlled by carbon

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diffusion in austenite while a spike of M exists ahead of the interface. This is termed as Negligible Partitioning Local Equilibrium (NPLE) mode. As the transformation proceeds, carbon content in

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austenite gradually decreases to Point b and thus carbon activity gradient in austenite disappears. According to Eq. (4), the interface velocity becomes fairly sluggish, which allows the redistribution of M across the interface. Therefore, kinetics of the ferrite-to-austenite transformation switches into M diffusion controlled Partitioning Local Equilibrium (PLE) mode.

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Fig. 2b shows the austenite-to-ferrite transformation occurs under the NPLE mode. The growing α phase inherits M content of parent γ phase. Hence, the composition of newly formed α phase,

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point P, is determined by the intersection between carbon component ray PR and α/(α+γ) phase boundary. Different from the ferrite-to-austenite transformation, a positive spike of M, point Q,

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appears ahead of the interface in γ phase. Correspondingly, carbon content at the interface in γ phase is given by the intersection between carbon isoactivity line QR and carbon component ray PR, Point R. Hence, the carbon activity at the interface in γ phase is larger than that at the austenite matrix, i.e. aCγ (R) > aCγ (O) . Similar with the ferrite-to-austenite transformation, large carbon activity gradient exists in austenite, and thus kinetics of the austenite-to-ferrite transformation is still controlled by carbon diffusion in austenite. With ferrite precipitation proceeding, carbon content in austenite will gradually reach point R, which reduces carbon 8

ACCEPTED MANUSCRIPT activity gradient in austenite. Subsequently, kinetics of the austenite-to-ferrite transformation switches from NPLE into PLE mode. The NPLE/PLE transition points, i.e. Point b and R, for both the ferrite-to-austenite and

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austenite-to-ferrite transformations are calculated based on Thermo-Calc with TCFE7 database. Details about NPLE/PLE calculations can also be found in [36]. Transformation stasis will be achieved when carbon content in austenite reaches the NPLE/PLE transition. Carbon content in

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austenite at the stasis state along with that in full equilibrium state as a function of temperature for

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the 0.2C-1.5Mn-1.5Si (all in wt.%) steel is shown in Fig. 2c. It shows that, compared with the ferrite-to-austenite, carbon content in austenite at the stasis for the austenite-to-ferrite transformation deviates from the full equilibrium significantly. In the current study, it is assumed that the duration of intercritical annealing is long enough for both the ferrite-to-austenite and

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austenite-to-ferrite transformations to reach the stasis state. Therefore, carbon content in austenite γ after intercritical annealing cIA is given as follows:

for α→γ transformation

(5A)

γ cIA = cγNPLE / PLE −(γ →α )

for γ→α transformation

(5B)

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γ cIA = cγNPLE / PLE −(α →γ )

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Correspondingly, the fraction of austenite f IAγ can be estimated using lever rule: γ

f IA = γ

f IA =

γ cNPLE / PLE −(α →γ ) − c0

γ α cNPLE / PLE −(α →γ ) − c NPLE / PLE −(α →γ ) γ cNPLE / PLE −( γ →α ) − c0

γ α cNPLE / PLE −( γ →α ) − c NPLE / PLE −( γ →α )

for α→γ transformation

(6A)

for γ→α transformation

(6B)

Where c0 is the initial bulk carbon content.

2.2 Isothermal bainitic transformation According to Gibbs Energy Balance model [19, 20, 23], the kinetics of isothermal bainitic 9

ACCEPTED MANUSCRIPT transformation in general can be divided into three stages. In the first stage, the lengthening of bainitic ferrite is under paraequilibrium (PE) condition, and substitutional alloying element M does not redistribute across the interface. In this stage, the fraction of bainitic ferrite and carbon

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content in untransformed austenite increase pronouncedly. When the driving force for bainitic ferrite formation decreases to some extent, the growth of newly nucleated bainitic ferrite is accompanied with a spike of M in front of the bainitic ferrite/austenite interface, e.g. the growth of

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bainitic ferrite switches from PE into NP (Negligible partitioning) mode. Since the lengthening

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rate of bainitic ferrite in the NP mode is controlled by M diffusion inside the austenite/bainitic ferrite interface, and the overall kinetics of bainitic transformation becomes sluggish and the stasis state is assumed to be reached. In the steel processing, the transition from PE to NP mode is practically important, as it determines the fraction of bainitic ferrite that can be obtained in the

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limited transformation time. In [20, 23], it was interestingly found that the transition from PE to NP predicted by the GEB model is comparable with the NPLE/PLE transition for the Fe-C-Mn-Si alloys, and both GEB and NPLE model can predict the effect of Mn on stasis phenomenon. The

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NPLE concept is a specific case of the GEB model [11, 23], while it was found that it did not work

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for the alloys containing Mo [20-22, 24, 43]. As the TRIP grades are mostly Fe-C-Mn-Si alloys, NPLE model is utilized here for simplicity. γ In this study, carbon content in austenite at the stasis state cIBT for the Fe-C-Mn-Si steels is

expected to reach the NPLE/PLE transition point for γ→α transformation: γ γ cIBT = cNPLE / PLE −( γ →α )

(7)

γ Correspondingly, austenite fraction at the stasis state f IBT is given by:

γ

f IBT =

γ c γNPLE / PLE −( γ →α ) − c IA

(8)

c γNPLE / PLE − ( γ →α ) − cαNPLE / PLE − ( γ →α ) 10

ACCEPTED MANUSCRIPT Where c γIA is carbon content in austenite after intercritical annealing. For the isothermal bainitic transformation process, it usually takes less than five minutes to reach the stasis state. Therefore, it is reasonably assumed that during the processing of TRIP steels isothermal bainitic transformation

2.3 Complex transformations during the Q&P process

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can reach the stasis state.

Different from the IBT process, the Q&P process is proposed to obtain retained austenite via

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carbon partitioning to austenite from martensite instead of bainitic ferrite. As shown in Fig. 1c, the

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Q&P process involves athermal martensite transformation during quenching and complex transformations during the partitioning process.

γ

It has been found that the untransformed austenite fraction f QT at a certain quenching temperature TQ can be estimated well by the Koistinen–Marburger (K-M) equation:

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γ fQT = Exp[−α ( M S − TQ )]

Where MS is the martensite start temperature and

(9)

α is a fitting kinetic parameter. The

thermodynamic and kinetic basis of K-M equation has been discussed in details in Refs [44, 45].

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Ms can predicted quantitatively well by the following empirical equation [46]:

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M S (K) = 764.2 − 302.6wC − 30.6wMn − 14.5wSi − 8.9wCr Where wi is the content of element i in wt. %.

(10)

α as an exponential function of carbon

concentration is adopted [47]:

α (10−3 K −1 ) = 27.2 − (0.14 wMn + 0.21wSi + 0.11wCr ) − 19.8 [1 − exp( −1.56 wC )]

(11)

It has been validated theoretically and experimentally that carbon partitioning from martensite into austenite and martensite/austenite interface migration could occur simultaneously during the partitioning process [32, 34]. The stasis state after the partitioning process has been 11

ACCEPTED MANUSCRIPT successfully predicted by the QP-LE model for the Fe-C-Mn-Si steels [36]. It is predicted by the QP-LE model that there are complex kinetic transitions during the Q&P process. When the martensite/austenite interface migrates in the sequence of NPLE-(α′→γ)→PLE-(α′→γ), carbon

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content in austenite at the stasis after the partitioning process is predicted to be located between the NPLE/PLE transitions for γ→α and α→γ transformation, which depends on the quenching/partitioning temperatures and alloying composition significantly. When the migrates

in

the

sequence

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martensite/austenite

of

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NPLE-(α′→γ)→PLE-(α′→γ)→NPLE-(γ→α′)→PLE-(γ→α′), carbon content in austenite at the stasis is determined by the NPLE/PLE transition for γ→α transformation, which is similar with that for isothermal bainitic transformation. In this study, the QP-LE model is coupled into the current model to predict retained austenite fraction and its carbon content. More details about the

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QP-LE model can be found in [36].

For a comparison, Constrain Carbon Equilibrium (CCE) model proposed by Speer et.al [27, 28] is also used to predict the dependence of phase constitutes on processing parameters and

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composition for the Q&P steels. CCE model assumed that the martensite/austenite interface is

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immobile while carbon has equal chemical potential across the martensite/austenite interface. The CCE condition can be described as:

µ Cα '/γ = µ Cγ /α '

(12A)

γ γ f CCE (1 − xCCE ) = f 0γ (1 − x0 )

(12B)

α' α' γ γ f CCE xCCE + f CCE xCCE = x0

(12C)

α' γ f CCE + f CCE =1

(12D)

Where µ Cα '/ γ and µ Cγ /α ' represent chemical potential of carbon at the interface in martensite 12

ACCEPTED MANUSCRIPT and austenite, respectively, x0 represents the initial mole fraction of carbon,

α' γ xCCE and xCCE

represent the mole fractions of carbon in martensite and austenite after partitioning, respectively, α' γ f0γ represents the phase fraction of austenite before partitioning, f CCE and f CCE represent the

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phase fractions of martensite and austenite after partitioning, respectively.

3. Results and discussion 3.1 The 1st generation TRIP steels by design

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3.1.1 Model Validations

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Before our thermo-kinetic model is applied to design the multi-phase microstructure of TRIP steels, it is firstly benchmarked by a comparison with the available experiments for several conventional TRIP steels. Fig. 3 shows a comparison between the measured and predicted phase constitutions

as

a

function

of

IA

temperature

for

the

several

conventional

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(0.12~0.4)C-1.2Mn-1.2Si CR-TRIP steels when IBT temperature is fixed at 400°C [48]. It shows that phase constitutions predicted by the current model are in reasonable agreement with experiments. It is interestingly predicted that retained austenite fraction is almost not affected by

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IA temperature, which is also verified by experiments. Both experiments and simulations indicated

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that the fraction of retained austenite can be effectively increased via enhancing C content. In addition to retained austenite fraction, its carbon content is also significantly important to mechanical properties of TRIP steels. So far, carbon content in retained austenite are usually measured by XRD, electron probe microanalysis (EPMA) and 3DAP. To some extent, XRD and EPMA provides an average carbon content in retained austenite, while 3DAP gives a very local and nanoscale carbon distribution at austenite/martensite(bainite) interfaces in an individual austenite grain. Carbon content in retained austenite predicted by the current model is also an 13

ACCEPTED MANUSCRIPT average value.

In Fig. 4, carbon content in retained austenite of several TRIP steels is calculated

and compared with various experimental measurements [10, 38, 49-53]. It shows that average carbon content in retained austenite measured by electron probe microanalysis (EPMA) and XRD

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in general is quite comparable with model predictions. However, there is a quite large scatter for 3DAP data, and some of them deviate a lot from model predictions. Carbon content in individual retained austenite is affected by its morphology and neighboring phases [38, 51], which means

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that carbon content of different austenite grains in the same sample could be different. Therefore,

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carbon content in a specific austenite grain measured by 3DAP could be different from the average value predicted by the current model. It is also worth noting that, when IBT temperature is selected to be 400ºC or 450ºC, carbon content in retained austenite for the typical conventional 0.2-1.5Mn-1.5Si TRIP steels measured by 3DAP deviates significantly from the T0 or T0’ limits

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[38, 52].

3.1.2 Microstructure Design

It was empirically considered that the product of strength and ductility of TRIP steels is

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proportional to retained austenite fraction, and thus much effort has been made to optimize it via

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tuning composition or processing parameters, i.e. IA temperature and IBT temperature. For a given steel composition it is very interesting to find the optimized IA temperature and IBT temperature combination to obtain the maximum amount of retained austenite. Alternatively, it can be thermodynamically expected that the fraction of retained austenite can be enhanced via increasing C or Mn content due to their nature of austenite stabilizers, but this needs to be further verified via our thermos-kinetic model. In this section, systematic calculations have been made to search the optimized processing parameters for several Fe-C-Mn-Si steels with different C and Mn 14

ACCEPTED MANUSCRIPT content. Fig. 5 shows the calculated contour plots of retained austenite fraction and its carbon content as a function of IA temperature and IBT temperature for the 0.2C-1.5Mn-1.5Si (Fig. 5a-b),

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0.3C-1.5Mn-1.5Si (Fig. 5c-d) and 0.2C-3.0Mn-1.5Si (Fig. 5e-f) CR-TRIP steels. IA temperature is selected to be above the eutectoid temperature for cementite dissolution. It is predicted for all steels that at a given IBT temperature the fraction of retained austenite and its carbon content for

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three CR-TRIP steels are almost independent on IA temperature. Fig. 5a shows the maximum

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amount of retained austenite (13~15%) can be obtained for the 0.2C-1.5Mn-1.5Si CR-TRIP steel when IBT temperature is in the range of 350~450°C, which means there is a very large process window (red zone) of IBT temperature to obtain maximum amount of retained austenite. Fig. 5b shows that carbon content in austenite after the IBT process increases from ~1.3 wt. % to ~1.6 wt. %

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when IBT temperature decreases from 450°C to 350°C. The critical carbon content in austenite to avoid the noticeable fresh martensite formation (>2%) at room temperature for the 0.2C-1.5Mn-1.5Si steel is estimated by the K-M equation to be around 1.3 wt. %. Therefore, there

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should be no brittle fresh martensitic phase formation in the final microstructure of the

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0.2C-1.5Mn-1.5Si CR-TRIP steel if IBT temperature is selected to be in the optimized range. Compared with the 0.2C-1.5Mn-1.5Si CR-steel, Fig. 5c shows that the maximum faction of retained austenite increases by about 8% while the corresponding process window of IBT temperature is almost unchanged for the 0.3C-1.5Mn-1.5Si CR-TRIP steel. Fig. 5d shows that, in the optimized process window, carbon content in austenite after the IBT process for the 0.3C-1.5Mn-1.5Si CR-TRIP steel is also above the critical value for the formation of fresh martensite. However, compared with that for 0.2C-1.5Mn-1.5Si CR-TRIP steel, Fig. 5e shows the 15

ACCEPTED MANUSCRIPT maximum fraction of retained austenite in the 0.2C-3.0Mn-1.5Si CR-TRIP steel decreases to ~10% even though Mn content is increased. Furthermore, the process window to obtain the maximum amount of retained austenite shrinks significantly and shifts to fairly lower IA temperature and

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IBT temperature regions. Fig. 5f shows carbon content in austenite after the IBT process for the 0.2C-3.0Mn-1.5Si CR-TRIP steel is less than ~1.0 wt. %, which means a considerable amount of fresh martensite will be formed during final quenching. Based on the above calculations, it is

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concluded that increasing carbon content instead of Mn content is more effective to enhance the

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fraction of retained austenite in the CR-TRIP steels without significantly reduce the process window, which could be one of the reasons that Mn content in the commercialized TRIP steels is usually less than 2.wt.%.

In addition to retained austenite, the ratio between soft ferrite phase and hard bainitic ferrite

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is also very important for ductility and formability of TRIP steels. Fig. 6 shows the phase constitutions as a function of IA temperature for the 0.2/0.3C-1.5Mn-1.5Si CR-TRIP steels. IBT temperature is fixed at 400ºC to obtain maximum amount of retained austenite. Although more

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retained austenite can be obtained in the 0.3C-1.5Mn-1.5Si CR-TRIP steel, the process window of

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IA temperature shrinks from 740~850ºC for the 0.2C-1.5Mn-1.5Si CR-TRIP steel to 740~820ºC for the 0.3C-1.5Mn-1.5Si CR-TRIP steel. In addition, the maximum fraction of ferrite decreases from ~70% to ~55% with an increase of 0.1 wt.% C. As shown in Fig. 5e, the process window to obtain the maximum fraction of retained austenite is extremely narrow for the 0.2C-3.0Mn-1.5Si CR-TRIP steel, in which it is almost impossible to tune ferrite fraction. In [41, 54-56], the maximum fraction of retained austenite and IBT temperatures for a series of conventional TRIP steels (0.12~0.55wt.% C, 0.2~2.5wt.% Mn and 0.4~1.8wt.% Si) have been experimentally 16

ACCEPTED MANUSCRIPT determined, which are comparable with our predictions. Fig. 7a-b show the contour plots of retained austenite fraction and its carbon content for the 0.2C-1.5Mn-1.5Si HR-TRIP steel. Similar as the CR-TRIP steel (see Fig. 5a-b), the predicted

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maximum amount of retained austenite for the 0.2C-1.5Mn-1.5Si HR-TRIP steel is about 13%, and carbon content in austenite is in the range of 1.3~1.5 wt. %. In Ref [38], a HR-TRIP steel (0.17C-1.6Mn-1.5Si-0.2Cr) with a similar composition as the 0.2C-1.5Mn-1.5Si steel has been

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studied, and IBT temperature was selected to be 400ºC. It was experimentally found that carbon

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content in retained austenite is about 1.4 wt.%, which is in good agreement with our model predictions.

The main difference between the CR and HR-TRIP steels is that the process window of IA temperature for the 0.2C-1.5Mn-1.5Si HR-TRIP steel shifts into relatively lower temperatures,

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which is attributed to the different phase transformations during intercritical annealing (see Fig. 1a-b). Fig. 3 shows the NPLE/PLE transition lines for α→γ transformation and γ→α transformation for the 0.2C-1.5Mn-1.5Si steel. It shows that the NPLE/PLE transition line for

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γ→α transformation shifts to the low carbon region as compared with that for α→γ transformation.

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The transformation temperature for the 0.2C-1.5Mn-1.5Si HR-TRIP steel must be below PNTT-(γ→α), which is the transition temperature between NPLE and PLE mode, to allow ferrite formation. In addition, the transformation temperature should also be above Ae1 to avoid the formation of pearlite. The fraction of ferrite as a function of IA temperature for the 0.2C-1.5Mn-1.5Si HR and CR-TRIP is shown in Fig. 8. It shows that the obtainable maximum fraction of ferrite for the 0.2C-1.5Mn-1.5Si HR-TRIP steel is 55%, which is less than 70% for the CR-TRIP steel. 17

ACCEPTED MANUSCRIPT 3.2 The 3rd generation Q&P steels by design 3.2.1 Model Validations In this section, the current integrated Q&P model is firstly benchmarked via a comparison

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between model predictions and the available Q&P experiments in the literatures. The effects of processing parameters and composition on the fraction of retained austenite and its carbon content are validated using three representative Q&P steels − low C and low Mn (0.2C-2.3Mn-1.4Si-0.2Cr

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[40, 57]), low C and medium Mn (0.2C-4.0Mn-1.6Si-1.0Cr [39]), medium C and medium Mn

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(0.3C-4.0Mn-1.6Si-1.0Cr [39]). The fraction of retained austenite (Fig. 9a) and its carbon content (Fig. 9b) after partitioning at 400°C predicted by the current model as a function of quenching temperature are compared with those measured by XRD for the 0.2C-2.3Mn-1.4Si-0.2Cr Q&P steels [57]. The corresponding Carbon Constrain Equilibrium (CCE) calculations have also been

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made for a comparison. Fig. 9a-b shows the dependence of retained austenite fraction and its carbon content on quenching temperature predicted by the current model can be generally divided into three regions. It was also predicted by the QP-LE model that the martensite/austenite interface

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migration behavior is different in these three regions [36]. In region A at relatively low quenching

AC C

temperatures, it is predicted by the current model that the martensite/austenite interface would be mobile and retained austenite fraction is not dependent on quenching temperature, while the CCE model predicts that the austenite/martensite interface should be immobile and the fraction of retained austenite decreases with decreasing quenching temperature. The current model predicts that retained austenite fraction and its carbon content are determined by the NPLE/PLE transition point for the α→γ transformation, which could explain their independence on quenching temperature. Although the dependence of retained austenite fraction on quenching temperature 18

ACCEPTED MANUSCRIPT predicted by the current model and CCE model is different, the difference is too marginal to be identified by the experiments. In region B, similar as CCE model predictions, the martensite/austenite interface migration during the partitioning process is predicted to be

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negligible by the current model, and thus the retained austenite fraction and its carbon content after the partitioning process predicted by these two models are the same. In region C, the discrepancy between the current model and the CCE model predictions becomes pronounced with

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increasing quenching temperature, which is because interface migration and/or bainite

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transformation is not considered by the CCE model. Fig. 9b shows carbon content in retained austenite after the partitioning process in region C is about 1.1 wt.%, which is insufficient to avoid the formation of fresh martensite [57]. As shown in Fig. 9a-b, the dependence of retained austenite fraction and its carbon content on quenching temperature measured by XRD for the

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0.2C-2.3Mn-1.4Si-0.2Cr steels is in reasonable agreement with the current model predictions. For the case that QT is 280ºC, the measured carbon content in retained austenite deviates significantly from both the current and CCE model predictions, which could be attributed to transition carbide

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precipitation during the partitioning process [57]. Fig. 9c shows the dependence of carbon content

AC C

in retained austenite on partitioning temperature predicted by the current model for the 0.2C-2.2Mn-1.5Si-0.2Cr Q&P steels is also quite comparable with those measured by high energy XRD and 3DAP [40]. The effects of C and Mn content on retained austenite fraction and its carbon content are shown in Fig. 9d-f. Compared with the 0.2C-2.3Mn-1.4Si-0.2Cr Q&P steel (see Fig. 9a), Fig. 9d-f show the region C disappears when Mn/Cr content increases. For the 0.2/0.3C-4.0Mn-1.6Si-1.0Cr Q&P steels, the current model predictions are quite comparable with those of CCE model, which is because the martensite/austenite interface should not move during 19

ACCEPTED MANUSCRIPT the partitioning process in a very large range of quenching temperature. It is also predicted that the maximum fraction of retained austenite can be increased via enhancing C/Mn content, while retained austenite fraction and its carbon content for the Q&P medium Mn steels content are very

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sensitive to quenching temperature.

3.2.2 Microstructure design

Fig. 10 shows the contour plots of retained austenite fraction and its carbon content as a

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function of quenching temperature and partitioning temperature for the 0.2C-1.5Mn-1.5Si,

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0.3C-1.5Mn-1.5Si and 0.2C-3.0Mn-1.5Si Q&P steels with full austenitization. As shown in Fig. 10a, there is a large “L” shape process windows (red zone) of quenching temperature and partitioning temperature to obtain the maximum amount of retained austenite for the 0.2C-1.5Mn-1.5Si Q&P steel. Compared with the 0.2C-1.5Mn-1.5Si Q&P steel, Fig. 10c shows

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that the maximum fraction of retained austenite is increased while the corresponding optimized process window for the 0.3C-1.5Mn-1.5Si Q&P steel is almost unchanged. Fig. 10b and d indicate for the 0.2/0.3C-1.5Mn-1.5Si Q&P steels processed in the optimized process window, carbon

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content in austenite after the partitioning process is high enough to avoid the formation of fresh

AC C

martensite during the final quenching. Based on the above results, it is also interestingly found that the obtained maximum fraction of retained austenite for the 0.2/0.3C-1.5Mn-1.5Si steels produced via Q&P process are quite comparable with those produced via the IA+IBT process. Fig. 10e shows the maximum amount of retained austenite that can be obtained from the 0.2C-3.0Mn-1.5Si Q&P steel is slightly higher than the 0.2-1.5Mn-1.5Si Q&P steel. However, the optimized process window (red zone) for the 0.2C-3.0Mn-1.5Si Q&P steel shrinks significantly and changed into “I” shape. Fig. 10f shows that the critical carbon content in austenite for the 0.2C-3.0Mn-1.5Si Q&P 20

ACCEPTED MANUSCRIPT steel to avoid the noticeable fresh martensite formation (>2%) is around 1.2 wt. %. Therefore, a certain amount of fresh martensite will be formed at room temperature for the 0.2C-3.0Mn-1.5Si Q&P steel when quenching temperature is above the optimized value (~230ºC). However,

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compared with that processed via IA+IBT (see Fig. 5e), a considerable amount of retained austenite can still be obtained in the 0.2C-3.0Mn-1.5Si steel processed via Q&P in the optimized process window.

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The hard martensite and bainitic ferrite phases increase the strength at the expense of

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formability and ductility of AHSSs, which is usually compensated by introducing a considerable fraction of soft ferrite phase via intercritical annealing [1, 58, 59]. Carbon content in austenite is increased during intercritical annealing, which is supposed to retard the kinetics of the following transformations and affect the process windows of the Q&P process. Fig. 11 shows the contour

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plots of retained austenite fraction as a function of quenching temperature and partitioning temperature for the 0.2C-1.5Mn-1.5Si CR-Q&P steels with different ferrite fractions. It shows that the maximum fraction of retained austenite is not affected by ferrite fraction, while the optimized

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process window of quenching temperature shifts into lower temperature region when ferrite

AC C

fraction increases. It is worth noting that the typical microstructure of commercial Q&P980 steels (0.2C-1.8Mn-1.5Si), which has a similar composition with the 0.2C-1.5Mn-1.5Si steel, usually contains ~37% ferrite, ~52% tempered martensite and ~12% retained austenite [60]. According to the current model predictions, there is a quite large process window to obtain the typical microstructure of commercial Q&P980 steels in the 0.2C-1.5Mn-1.5Si CR-Q&P steel.

4. Conclusion An integrated thermo-kinetic model based on local equilibrium theory has been proposed to 21

ACCEPTED MANUSCRIPT systematically explore the dependence of phase constitutions on processing parameters and alloy compositions for the Fe-C-Mn-Si steels processed via IA+IBT (the 1st generation TRIP steels) and Q&P (the 3rd generation Q&P steels) methods, respectively. For the conventional TRIP and Q&P

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steels with low Mn content (0.2C-1.5Mn-1.5Si, in wt.%), the maximum amount of retained austenite obtained via the Q&P process is predicted to be the same as that by the IA+IBT process, and both process windows are quite large. It is also interestingly predicted that fraction of retained

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austenite is almost not dependent on IA temperature during the IA+IBT process. The model

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predictions are in good agreement with the available experimental results for a series of conventional TRIP and Q&P steels. Our model also predicts that increasing Mn content (e.g. to 3 wt.%) is not a proper solution to enhance retained austenite fraction in both TRIP and Q&P steels, while C addition is effective in retaining austenite.

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Acknowledgements

H. Chen acknowledges financial support from the National Natural Science Foundation of China (Grant 51501099), Beijing Natural Science Foundation （2182024）, National Key R&D

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program of China (2016YFB0300104) and National Young 1000-Talents Program (D1101073). R.

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Ding acknowledges financial support from China Postdoctoral Science Foundation (Grant 2017M610082). C. Zhang acknowledges financial support from the National Natural Science Foundation of China (Grant 2015CB654802), the National Magnetic Confinement Fusion Energy Research Project of China (Grant 2015GB118001) and Fund of Key Laboratory of Advanced Materials of Ministry of Education (Grant 2017AML09). Z G. Yang acknowledges financial support from the National Natural Science Foundation of China (Grant 51471094).

22

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QP980 steel from a combined synchrotron X-ray diffraction and crystal plasticity approach, Acta Mater 132 (2017) 230-244.

29

ACCEPTED MANUSCRIPT Table 1. Chemical composition of the investigated steels (all in wt.%). C

Mn

Si

Cr

Ref

TRIP1

0.08

3.0

−

−

[49]

TRIP2

0.05/0.14

2.0

−

−

[10]

TRIP3

0.15

1.5

0.2

−

[53]

TRIP4

0.22

2.5

1.5

−

[51]

TRIP5

0.29

2.4

1.8

−

[50]

CR-TRIP

0.12~0.4

1.2

1.2

−

[48]

HR-TRIP1

0.17

1.6

1.5

0.2

[38]

HR-TRIP2

0.2

1.5

1.5

−

[52]

QP1

0.2

2.2

1.5

0.2

[40]

QP2

0.2

2.3

1.4

0.2

[57]

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TE D QP3

0.2

4.0

1.6

1.0

[39]

QP4

0.3

4.0

1.6

1.0

[39]

M1

0.2

1.5

1.5

−

−

M2

0.3

1.5

1.5

−

−

M3

0.2

3.0

1.5

−

−

EP AC C

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Steels

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Figure captions Fig. 1 Sketches of the microstructure evolution during processing for (a) cold rolled TRIP steels,(b) hot rolled TRIP steels and (c) cold rolled Q&P steels. Abbreviations: α, ferrite; γ, austenite;

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αB, bainitic ferrite; αUM, untempered martensite; αTM, tempered martensite; P, pearlite; Bs: Bainite start temperature; Ms: Martensite start temperature; Mf: Martensite finish temperature; TE: eutectoid temperature; IBT: Isothermal bainitic transformation; Q&P:

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Quenching & Partitioning.

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Fig. 2 Schematic isothermal sections of the Fe-C-M (M is austenite stabilizing element) system to illustrate both the (a) ferrite-to-austenite and (b) austenite-to-ferrite transformations occur under the NPLE mode. Point X in (a, b) indicates the composition of austenite at the full equilibrium (FE) state. (c) The NPLE/PLE transition lines are plotted on the partial vertical

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section of the Fe-xC-1.5Mn-1.5Si steel. Full equilibrium line (short dot) for the Fe-0.2C-1.5Mn-1.5Si steel is also plotted in (c) for a comparison. Fig. 3 Comparison between the predicted and measured phase constitutions for (a)

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0.12C-1.2Mn-1.2Si, (b) 0.2C-1.2Mn-1.2Si; (c) 0.3C-1.2Mn-1.2Si and (d) 0.4C-1.2Mn-1.2Si

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cold rolled TRIP steels [48]. The isothermal bainitic transformation temperature is 400°C. Fig. 4 Comparison between the predicted and measured carbon content in retained austenite of TRIP steels [10, 38, 49-53]. Open square/circle symbols indicate carbon content in film-like retained austenite; Solid square/circle symbols indicate carbon content in blocky-like retained austenite. EPMA: Electron probe microanalysis; XRD: X-ray diffraction; 3DAP: Three-dimensional atom probe.

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ACCEPTED MANUSCRIPT Fig. 5 (a, c, e) Fraction of retained austenite and (b, d, f) carbon content in retained austenite after the isothermal bainitic transformation process as a function of intercritical annealing temperature and isothermal bainitic transformation temperature for the (a, b)

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0.2C-1.5Mn-1.5Si, (c, d) 0.3C-1.5Mn-1.5Si and (e, f) 0.2C-3.0Mn-1.5Si cold rolled TRIP steels. The red dash lines in (b, d) indicate the critical carbon content in austenite to avoid noticeable (>2%) fresh martensite formation at room temperature.

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bainitic transformation temperature is 400°C.

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Fig. 6 Phase constitutions for the 0.2/0.3C-1.5Mn-1.5Si cold rolled TRIP steels. The isothermal

Fig. 7 (a) Fraction of retained austenite and (b) carbon content in retained austenite after the isothermal bainitic transformation process as a function of intercritical annealing temperature and isothermal bainitic transformation temperature for the 0.2C-1.5Mn-1.5Si

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hot rolled TRIP steel. The dash lines in (b) indicates the critical carbon content in austenite to avoid noticeable (>2%) fresh martensite formation at room temperature. PNTT-(γ→α): transition temperature between NPLE and PLE mode.

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Fig. 8 The ferrite fraction as a function of intercritical annealing temperature for the

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0.2C-1.5Mn-1.5Si hot rolled and cold rolled TRIP steels. PNTT-(γ→α): transition temperature between NPLE and PLE mode; TE: eutectoid temperature.

Fig. 9 Comparisons between the predicted and measured (a, d, f) retained austenite fraction and (b, c, e) carbon content in retained austenite as a function of processing parameters for different Q&P steels. (a, b) 0.2C-2.3Mn-1.4Si-0.2Cr [57], (c) 0.2C-2.2Mn-1.5Si-0.2Cr [40], (d, e) 0.2C-4.0Mn-1.6Si-1.0Cr [39], (f) 0.3C-4.0Mn-1.6Si-1.0Cr [39]. Pt: Partitioning time; HEXRD: High energy X-ray diffraction; 3DAP: Three-dimensional atom probe. 32

ACCEPTED MANUSCRIPT Fig. 10 (a, c, e) Fraction of retained austenite and (b, d, f) carbon content in retained austenite after the partitioning process as a function of quenching temperature and partitioning temperature for the (a, b) 0.2C-1.5Mn-1.5Si, (c, d) 0.3C-1.5Mn-1.5Si and (e, f)

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0.2C-3.0Mn-1.5Si Q&P steels. The dash lines in (b, d, e) indicate the critical carbon content in austenite for three Q&P steels to avoid noticeable (>2%) fresh martensite formation.

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Fig. 11 Fraction of retained austenite as a function of quenching and partitioning temperatures for

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the 0.2C-1.5Mn-1.5Si cold rolled Q&P steels with (a) 30%, (b) 40% and (c) 50% ferrite.

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