Marc Moreno

Julien Teixeira

Jaafar Ghanbaja

Frédéric Bonnet

Sébastien Allain

Evolution of cementite composition along the processing of cold-rolled and annealed Dual-Phase steels

Keywords: steel, cementite, manganese, pearlite, ferrite

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Dual-Phase (DP) steels were developed in the 1980's and have been industrialized since the years 1990-1995 [START_REF] Speich | Formation of Austenite During Intercritical Annealing of Dual-Phase Steels[END_REF][START_REF] Kulakov | The Effect of the Initial Microstructure on Recrystallization and Austenite Formation in a DP600 Steel[END_REF]. They are still very widely used in the automotive field where they constitute the majority of the so-called first generation of advanced high strength steels [START_REF] Allam | Mechanical Properties, Formability, and Corrosion Behavior of Dual Phase Weathering Steels Developed by an Inter-Critical Annealing Treatment[END_REF]. These steels generally show high levels of Ultimate Tensile Strength (between 600 and 1200 MPa) and have excellent forming qualities (drawing or bending ability) which makes them suitable for the production of crash resistance parts [START_REF] Hofmann | Advanced Cold Rolled Steels for Automotive Applications[END_REF][START_REF] De Moor | Austenite stabilization through manganese enrichment[END_REF][START_REF] Movahed | The effect of intercritical heat treatment temperature on the tensile properties and work hardening behavior of ferrite-martensite dual phase steel sheets[END_REF]. The DP microstructures are composed mainly of soft ferrite and hard martensite [START_REF] Speich | Formation of Austenite During Intercritical Annealing of Dual-Phase Steels[END_REF]. The fraction of the latter carbon rich phase is variable (from 5% to almost 100%) depending on the targeted grades. The work-hardening rate of DPs is controlled to first order by the fraction of martensite. It is thus of prime importance for a steelmaker to tune finely and control the volume fraction of martensite in their products [START_REF] Erdogan | Effect of austenite dispersion on phase transformation in dual phase steel[END_REF][START_REF] Jacques | Enhancement of the mechanical properties of a low-carbon, low-silicon steel by formation of a multiphased microstructure containing retained Austenite[END_REF]. The sensitivity of the UTS of DP steels to the martensite fraction is in the range of 10 to 20 MPa.% -1 [START_REF] Allain | Towards the microstructure design of DP steels: A generic size-sensitive mean-field mechanical model[END_REF].

Thin gage Dual-Phase Ferrite/Martensite steels are mainly produced by intercritical annealing of coldrolled steel sheets (ie. at temperatures higher than Ac1, in the ferrite/austenite domain) [START_REF] Agren | The dissolution of cementite in a low carbon steel during isothermal annealing at 700°C[END_REF][START_REF] Martín | Effect of heating rate on reaustenitisation of low carbon niobium microalloyed steel[END_REF][START_REF] Arlazarov | Evolution of microstructure and mechanical properties of medium Mn steels during double annealing[END_REF]. Their final fractions of martensite after quenching and thus their in-use mechanical properties are closely related to their fraction of austenite at the end of annealing. These fractions of austenite are controlled by all the metallurgical mechanisms occurring during reheating and soaking of the cold-strips. Since as-hot rolled bands before cold rolling show mainly ferrite-pearlite microstructures, these mechanisms consist of recovery / recrystallization of deformed ferrite and pearlite, ripening of cementite below Ac1 and austenite transformation above Ac1 [START_REF] Humphreys | Recrystallization and related annealing phenomena[END_REF].

Below Ac1, the recovery processes occur at relatively low temperature and are followed by the recrystallization of ferrite grains. The complexity arises as the recrystallization kinetics is reduced within pearlite structures. The recovery / recrystallization are thus highly coupled phenomena and the coupling depends on the heating rates and the evolutions of pearlite islands (ripening and coarsening).

When considering the austenite transformation from these complex states above Ac1, it seems that the local recrystallization state affects the nucleation sites of austenite [START_REF] Yang | Ferrite recrystallization and austenite formation in cold-rolled intercritically annealed steel[END_REF][START_REF] Huang | Austenite formation during intercritical annealing[END_REF]. In fully recrystallized states, austenite nucleates preferentially on ferrite grain boundaries in the Mn-rich zones [START_REF] Kulakov | The Effect of the Initial Microstructure on Recrystallization and Austenite Formation in a DP600 Steel[END_REF][START_REF] Li | Effect of heating rate on ferrite recrystallization and austenite formation of cold-roll dual phase steel[END_REF][START_REF] Chbihi | Interactions between ferrite recrystallization and austenite formation in high-strength steels[END_REF][START_REF] Barbier | Microstructures resulting from the interaction between ferrite recrystallization and austenite formation in dual-phase steels[END_REF]. In the case of non-fully recrystallized states, austenite nucleates on carbides in the non-recrystallized ferrite [START_REF] Ollat | Modeling of the Recrystallization and Austenite Formation Overlapping in Cold-Rolled Dual-Phase Steels During Intercritical Treatments[END_REF]. The resulting topologies of the final microstructures are very different in both scenarios (necklace or banded structures respectively) [START_REF] Kulakov | The Effect of the Initial Microstructure on Recrystallization and Austenite Formation in a DP600 Steel[END_REF][START_REF] Yang | Ferrite recrystallization and austenite formation in cold-rolled intercritically annealed steel[END_REF][START_REF] Huang | Austenite formation during intercritical annealing[END_REF][START_REF] Li | Effect of heating rate on ferrite recrystallization and austenite formation of cold-roll dual phase steel[END_REF][START_REF] Chbihi | Interactions between ferrite recrystallization and austenite formation in high-strength steels[END_REF][START_REF] Barbier | Microstructures resulting from the interaction between ferrite recrystallization and austenite formation in dual-phase steels[END_REF].

The evolutions of the chemical compositions and morphologies of cementite, mainly inherited from pearlite domains, affect further austenitization kinetics and thus intercritical annealing conditions. The incubation time for austenite reversion from globular pearlite containing high level of manganese is higher than for non-enriched pearlite [START_REF] Garcia | Formation of austenite in 1.5 pct Mn steels[END_REF][START_REF] Caballero | An Attempt to Establish the Variables That Most Directly Influence the Austenite Formation Process in Steels[END_REF].

The composition in cementite before austenization will be affected by:

• the pearlite transformation conditions: earlier works of Razik et al. on Fe-C-Mn and Fe-C-Cr steels show that pearlite transformation occurs without partition of substitutional elements below 650°C [START_REF] Razik | An investigation of manganese partitioning during the austenite-pearlite transformation using analltical electron microscopl[END_REF][START_REF] Razik | Chromium partitioning during the austenitepearlite transformation[END_REF]. Nevertheless, experimental growth kinetics was in contradiction with this assumption. More recently, Al-Salman et al. [START_REF] Al-Salman | Pearlite growth kinetics and partitioning in a Cr-Mn eutectoid steel[END_REF], Chance and Ridley [START_REF] Chance | Chromium partitioning during isothermal transformation of a eutectoid steel[END_REF] and Hutchinson [START_REF] Hutchinson | The growth of partitioned pearlite in Fe-C-Mn steels[END_REF] obtained experimental results in contradiction with those of Razik et al. as they observed partition of alloying elements between cementite and ferrite down to 550°C.

The fact that partition was detected at so low temperatures in spite of the sluggish diffusivity of substitutional elements suggested for the first time that diffusion occurred not only by volume diffusion, but with an additional contribution of interfacial diffusion, which permits a local equilibrium to be maintained at interfaces. Following the original suggestion of Hillert and Coates [START_REF] Hillert | Solid-solid phase transformations[END_REF][START_REF] Coates | Diffusional growth limitation and hardenability[END_REF], Hutchinson in 2004 [START_REF] Hutchinson | The growth of partitioned pearlite in Fe-C-Mn steels[END_REF] proposed a complete framework permitting to model this partitioning process. Our results will sustain this latter development.

• the ripening occurring during coiling stage and during reheating prior austenitization in the annealing stage. Miyamoto et al. [START_REF] Miyamoto | Effect of partitioning of Mn and Si on the growth kinetics of cementite in tempered Fe-0.6 mass% C martensite[END_REF] stated that coarsening obeys to a growth without partition for temperatures inferior to 500°C, depending on the alloy composition. This observation is supported by Babu [START_REF] Babu | APFIM studies on martensite tempering of Fe-C-Si-Mn low alloy steel[END_REF] and Ghosh and Olson [START_REF] Ghosh | Precipitation of paraequilibrium cementite: Experiments, and thermodynamic and kinetic modeling[END_REF] when studying tempering process of martensitic steels. At 500°C, Song [START_REF] Song | On the Spheroidized Carbide Dissolution and Elemental Partitioning in High Carbon Bearing Steel 100Cr6[END_REF] investigated the precipitation of a cementite shell around partially dissolved cementite carbides at 500°C in a 100Cr6 and observed a growth with a weak partition of Cr and Mn but with an Mn spike located at the moving interface. These experimental observations suggest that cementite is growing under the regime of negligible partitioning with local equilibrium. At higher temperatures, the authors generally report growth process under local equilibrium with a significant partition of alloying elements (mainly Mn). For instance, Hwang et al. [START_REF] Hwang | Influence of the Initial Microstructure on the Spheroidization of SAE 52100 Bearing Steel[END_REF] observed the thickening of a cementite lamella at 710°C in 1C-1.45Cr-0.35Mn wt.% steel or Philippot et al. [START_REF] Philippot | Influence of a 2-D defect on the partitioning during the formation of a cementite particle in steels[END_REF] in an initial cold-rolled ferrite / martensite microstructure slowly heated up to 700°C in a 0.47C-2.53Mn-0.32Cr wt.% steel.

In the case of tempered martensitic microstructures, upon coarsening, carbides exhibit first non-partition but are gradually enriched with increasing annealing time as suggested by Miyamoto et al. [START_REF] Miyamoto | Effect of partitioning of Mn and Si on the growth kinetics of cementite in tempered Fe-0.6 mass% C martensite[END_REF]. Tu et al. [START_REF] Tu | Effect of Si and Mn Interactions on the Spheroidization and Coarsening Behavior of Cementite During Annealing in Severe Cold-Drawn Pearlitic Steel[END_REF] explored the concomitant effects of Mn and Si on the spheroidization behavior of severe cold-drawn pearlitic steels, S87B and S87BM (respectively 0.95C-1.15Mn-0.22Si wt.% and 0.93C-1.16Mn-0.95Si wt.%). The partition of Mn at 600°C is also progressive and the equilibrium composition of cementite is achieved after only 10h annealing.

So, enrichment processes in cementite not only depends on the annealing conditions of the ferritecementite microstructure but also on pearlite transformation conditions and heating process.

In this work, we have conducted investigations by TEM (Transmission Electronic Microscopy) in order to measure the chemical compositions at the nanoscale in cementite particles after hot-rolling and during annealing of an industrial steel. These results will be discussed in a second part at the light of thermodynamic calculations using THERMOCALC and kinetics calculations using DICTRA.

Following the suggestion of Luo et al. [START_REF] Luo | A Novel Observation on Cementite Formed During Intercritical Annealing of Medium Mn Steel[END_REF], the diffusion coefficient of Mn will be in particular reassessed to explain the composition gradient measured in cementite particles after coiling operation, i.e. when cooling down the hot-bands after hot-rolling. We will also show that in the studied steel local equilibrium seems to govern interface conditions whatever the temperature range.

The main originality of our work is to consider the mean composition enrichments and gradients in cementite particles all over the thermomechanical cycle prior to austenitization. The study reveals in particular that a strong manganese enrichment is inherited from pearlitic transformation and coiling treatments, prior to cold-rolling. Nevertheless, slow heating conditions encountered in certain industrial plants during annealing permits to reduce this inheritance effect.

Experimental methods and modeling procedures

Studied steel

The studied steel is an industrial product which serves for the production of certain DP580 grades. It has been provided by ArcelorMittal in the cold-rolled state. It has undergone a conventional hotrolling scheme (reheating of the slabs at about 1200°C, finish rolling temperature above 900°C, coiling at 550°C after a fast cooling on a run-out-table). After coiling, temperature decreases in the hot-rolled coils with a mean rate of 20°C/h (from 550°C down to room temperature). The hot-band has then been cold-rolled (reduction ratio of 60%).

Table 1 gives the composition of the studied steel. It is a low carbon steel without microalloying elements (Ti, Nb, V). The compositions are given in weight fraction and u-fraction. The u-fraction corresponds to the atomic fraction of the considered solute among substitutional species in iron sublattices. It is the natural way to present TEM composition measurements and simulation results, especially when considering interfaces between cementite and ferrite. U B the u-fraction of substitutional element B is given by:

U B = X B ∑ X n = X B 1-X C (1)
X B is the atomic fraction of element B and the sum at denominator is made on all substitutional species in the iron sublattice. The denominator is thus equal to 1-X C , with X C the atomic fraction of carbon for this particular case. The current investigation mainly focuses on manganese as it plays an important role in the austenization process of the studied steel, as highlighted in the introduction. Nonetheless, we will also discuss the evolution of silicon and chromium compositions in carbides.

Elements

Studied samples

Three samples were investigated by TEM. They correspond to key states of an industrial thermomechanical schedule.

• Sample 1: Sample obtained by heating a sample in the cold-rolled state up to 900°C during 30 min, then cooled down at 570°C at 30°C.s -1 and maintained 30s before quenching. The obtained ferrite-pearlite microstructure was thought to be representative of the state before the coiling operation. In fact, our experiments will show that composition of carbides evolve significantly during this long cooling stage. The choice of the transformation temperature (570°C), above the industrial coiling temperature, is discussed farther. • Sample 2: Sample in the as-received state, thus taken from the cold-rolled band without additional heat-treatment.

• Sample 3: Sample obtained by heating a sample in the cold-rolled state up to 700°C at a constant heating rate (3°C.s -1 ) and quenched. The obtained ferrite-pearlite microstructure was thought to be representative of the state just before the intercritical range (Ac1 = 740°C) and thus before austenite phase transformation.

Heat treatments were carried out with a homemade Rapid Cycle Dilatometer. The furnace is composed of four light bulbs of 1500 W and temperatures are measured by welded thermocouples. Quenching steps are achieved by cold helium injections.

SEM (Scanning Electronic Microscopy) sample preparation and configurations

Samples have been coated with epoxy resin (sagittal cut) and polished with silicate grid paper down to 1 µm and finished using a colloidal silica suspension solution. Before etching, an ultra-sonic cleaning bath in warm methanol (~ 30 min) permits to remove the fine colloidal silica particles and to avoid pollution of the samples. The samples are then etched with a Picral solution at 2%. Observations have been conducted on Phillips FEG-SEM XL30 microscope in Secondary Eelectron mode. Micrographs have been taken at quarter thickness in order to avoid skin effects and a possible central macrosegregated band.

TEM (Transmission Electronic Microscopy) sample preparation and configurations

Specimens for TEM investigations were ground parallel to the initial faces of the flat products down to a thickness of about 60 µm using grinding papers. Both sides of specimens were polished to remove possible decarburized layers, trying however to avoid the central segregation. After that, specimens were manually punched to obtain 3 mm diameter cylindrical samples. Finally, foils were drilled by electropolishing using perchloric-acetic acid solutions. The electrolytic solution was used at 18°C with a tension of 30V. Appropriate electropolishing parameters were sought to remove ferritic matrix while preserving cementite carbides. Before observations, foils were cleaned using a Precision Ion Polishing System (Gatan 691 PIPS). JEOL TEM microscope was operated at 200 kV (ARM FEG). Composition measurements were performed with a BRUKER XFlash EDXS Silicon Drift Detector with a chemical resolution of 127 eV and a collector plate of 30 mm². The measurements presented in the following have been obtained with a probe size of 1 nm (1000 times finer than a conventional Castaing microprobe). Accounting for the thickness of the foil and contrary to SEM, there is no enlargement of the excitation volumes within the sample. The analyzed volume is thus limited to the probe size diameter.

EDXS measurements are by nature punctual, but repeating the measurements along lines and columns permits to reconstruct composition profiles or maps. A minimum spatial step of 5 nm was chosen to provide suitable compromise between spatial resolution and X-ray counts, in order to obtain statistically meaningful results in a reasonable period of time.

Detection of light chemical species like carbon is not possible by EDXS method because of the energy resolution. For this reason, it has been carried out only for major substitutional elements for Fe like Mn, Cr and Si. The measured concentrations are given by the Desktop Spectrum Analyzer (DTSA) in relative atomic site-fraction. As carbon is not considered in the balance, the measurements correspond to the u-fractions for each element. The typical relative error for measured substitutional concentrations was calculated using standard statistical techniques and does not exceed 5% (relative value). An Electron Energy Loss Spectroscopy (EELS) detector has also been used to estimate the local thickness of the foil. For each studied state, about 5 particles have been studied in details (composition profiles). These particles were located in pearlite islands (not isolated at a ferrite grain boundary) to obtain a possible correlation with our thermodynamic prediction. However, it is not possible to tell with certainty that they are located in a microsegregated band.

Modeling procedures

The thermodynamic calculations were done with THERMOCALC and DICTRA (version 2017a). The TCFE9 database was employed for thermodynamic calculations while the MOBFE2 mobilities database was used to perform solute diffusion simulations.

Experiments

In this section, we will first describe the ferrite-pearlite microstructures in the as-received sample (sample 2) and after heating up to 700°C (sample 3) observed by SEM. Sample 1 shows a microstructure which is very similar to sample 2 except the effect of the cold-rolling strain. After these SEM observations at the micro scale, our local composition measurements in cementite by TEM will be presented.

SEM observations of the as-received and annealed states (samples 2 and 3)

Figure 1a shows a typical SEM micrograph of the studied steel in the as-cold-rolled state before annealing. The microstructure after hot-rolling and cold-rolling is made of elongated ferrite grains (dark contrast) with a typical size of 10 µm and of cementite carbides (bright contrast). Cementite is mainly located in pearlitic lamellar colonies but few isolated intergranular carbides can also be observed (about 0.44 particles.µm -2 ). A composition mapping using a Castaing microprobe (not presented here) reveals microsegregated bands inherited from continuous casting. These bands are approximatively 30 µm wide and show Mn u-fraction fluctuations between 1.78 and 2.10%.

Microsegregations of silicon and chromium are negligible on the contrary. These composition fluctuations play a role on the formation of the pearlite as they modify locally the interface conditions between austenite, ferrite and cementite during the transformation. Pearlitic islands are thus more often located in Mn microsegregated bands but it is not systematic. Figure 1b shows the microstructure obtained after slow heating at 700°C. The pearlite lamellae have undergone a severe ripening consisting mainly of a fragmentation process [START_REF] Arruabarrena | Influence of Prior Warm Deformation on Cementite Spheroidization Process in a Low-Alloy Medium Carbon Steel[END_REF]. The isolated carbides are slightly more numerous (about 2.6 particles.µm -2 ) and have grown up (higher mean diameter compared to sample 2).

TEM observations and local compositions measurements After pearlite transformation (sample 1)

Figure 2 shows a representative TEM BF (Bright Field) micrograph of the microstructure just after transformation at about 570°C in hot-rolling process. As observed in SEM in sample 2, it consists mainly of pearlitic lamellar colonies (cementite in dark contrast) surrounded by large pro-eutectoid ferrite grains (large bright areas) containing isolated cementite carbides at grain boundaries. To perform reliable EDXS measurements, the height of studied cementite lamella or particle must exceed the thickness of thin foil. In this manner, electronic beam surely goes through cementite only.

If not, the measurement can be affected by the presence of ferrite above or below the cementite particle and thus leads to underestimate manganese enrichment in cementite. In the following, such experimental artefact will be systematically avoided. Nevertheless, it is not possible to guaranty that the interfaces of cementite lamellae are always strictly parallel to the incident beam. Measurements close to the interfaces must thus be considered with care as the slightly tilted lamella can also hide the presence of ferrite under the beam. This is the reason why on the composition profiles presented below we will systematically highlight the measurement points that can be affected by such tilting issue. Figure 3a shows an example of composition measurement inside a cementite lamella. The etching depth difference between the lamella and its matrix is about 25 nm, according to the EELS signal. Investigated lamella appears in dark contrast and the surrounding ferrite in bright. An EDXS profile was obtained thanks to 10 aligned punctual measurements (10 nm step size) and is represented in Figure 3b. The composition profile within the cementite lamella is flat and reveals a significant enrichment up to U Mn = 7 %. The Mn composition in the matrix is uniform and similar to the nominal one (U Mn =1.94 %) meaning that the observed pearlite aggregate is not located inside an Mn microsegregated region.

The Cr concentration in the matrix is close to the nominal one while an enrichment up to U Cr = 1.5 % is observed inside the lamella. On the contrary to Mn and Cr, Si shows a constant profile through the matrix and the lamella, which corresponds to the nominal composition (U Si = 0.4 % ).

Our systematic investigations on other adequate configurations confirm systematically a Mn enrichment in cementite between 6% and 8%. This result confirms that pearlitic transformation at 570°C in studied steels occurs with a partition of Mn and Cr, in accordance with the works of Al-Salman et al. [START_REF] Al-Salman | Pearlite growth kinetics and partitioning in a Cr-Mn eutectoid steel[END_REF], Chance and Ridley [START_REF] Chance | Chromium partitioning during isothermal transformation of a eutectoid steel[END_REF] or Hutchinson [START_REF] Hutchinson | The growth of partitioned pearlite in Fe-C-Mn steels[END_REF].

As-received state (sample 2)

As in sample 1, different cementite particles have been studied by TEM with the experimental limitations discussed above. Figure 4a shows for instance a fragment of cementite lamella with a suitable thickness (20 nm thicker than the foil). Therefore, the carbide (clear contrast) arises surely from the matrix. The concentration measurements measured along the blue line are reported in Figure 4b. Mn concentration in ferrite in the studied field is about U Mn = 4%. This value is significantly higher than the nominal one, meaning that this cementite particle is located in a Mn microsegregated band. In cementite, a U-shaped concentration profile of Mn is observed bringing to light a significant Mn concentration gradient at interface, extended over about 15 nm. This profile reaches a maximum Mn concentration in cementite near U Mn = 10% at interface cementite / ferrite, while a slight depletion is visible in surrounding matrix (only on the right side). A minimum value of U Mn = 6% is observed in the middle of the U-shaped profile. Cr concentration in cementite is also not uniform and shows an average value of 0.5%, which is two times higher than the nominal composition. Si seems to be rejected from cementite into the surrounding ferrite (two times higher than the nominal value) as expected from the observations of many authors [START_REF] Miyamoto | Effect of partitioning of Mn and Si on the growth kinetics of cementite in tempered Fe-0.6 mass% C martensite[END_REF][START_REF] Owen | The effect of silicon on the kinetics of tempering[END_REF][START_REF] Jang | Substitutional solution of silicon in cementite: A first-principles study[END_REF]. For these two last elements, their nominal contents and their local fluctuations prevent from determining convincing gradients from experiments. Hence, in the following, we have considered as useless to simulate the corresponding composition profiles and compare them with our experimental measurements.

Figure 5a shows a cementite lamella undergoing a ripening process as its extremity is rounded. This bulging process, as described by Tian and Kraft [START_REF] Tian | Mechanisms of Pearlite Spheroidization[END_REF], is made possible by the coiling operation after hot rolling which corresponds in fact to a long cooling stage after the pearlitic transformation. As for the previous studied cases, the compositions measured along the line in Figure 5a are plotted in Figure 5b with a step size of 17 nm. The composition profiles also reveal U-shaped concentration profiles of Mn and Cr in the straight part of the particle, with a Mn concentration at interface similar to the previous case (Figure 4), close to 10%, but with slightly more extended gradients (about 2 step sizes). At the deepest point of the Ushaped profile, the u-fraction of Mn is about 7% as in the preceding case. The u-fraction of Cr is about 1% at the ferrite / cementite interface and about 0.4% approximatively at the center of the lamella. Si is rejected into the ferritic matrix. In the rounded bulb, a significant enrichment in Mn and Cr is also measured. Mn and Cr concentrations reach 11% and 1.3% at the interface. Therefore, partitioning of substitutional elements is even higher in carbide undergoing a ripening process.

When studying other precipitates, we measured concentrations between 6 and 12%. We thus confirmed that Mn and Cr concentrations in cementite continue to increase during coiling, i.e. after pearlite transformation but at temperature lower than 550°C. Nevertheless, their repartitions are not uniform. U-shaped composition profiles are observed whose gradients are extended over few tens of nm. At the interface, the u-fractions of Mn are close to 12% whereas in the middle of particles, local compositions remain similar to those observed in sample 1. During this long cooling stage (20°C.h -1 ), cementite lamellae undergo also a ripening process (fragmentation and bulging) but this process is limited as pearlitic structures are still mainly lamellar, as shown in Figure 1a.

Interrupted annealing at 700°C (sample 3)

Next observations have been made on sample 3 after hot-rolling and cold-rolling heated slowly at 3°C.s -1 up to 700°C and quenched. As observed in Figure 1b by SEM, our TEM observations confirm that lamellar pearlitic microstructures have undergone a severe ripening. Cementite lamellae are fragmented and remnants are round-shaped.

The transversal concentration profile in a lamellar fragment has been measured and is represented in The Mn composition in the matrix is about 3% meaning that the lamella is located in a microsegregated band. In the studied particle, the Mn and Cr composition profile are almost flat (the residual gradient is about 2% over 20 nm). The average u-fractions of manganese and chromium are about 10% and 2% respectively. Mn and Cr enrichment are thus higher than in sample 2. On the contrary, Si seems to have been rejected again from the particle.

Intermediate conclusion on cementite enrichment in manganese

To conclude, the experiments reveal that pearlite transformation at 570°C in the studied steel (sample 1) occurred with a noticeable partition of Mn (u-fraction of about 7%) into cementite. In contrast, Si concentration remains constant through cementite and matrix and corresponds to the nominal values.

During coiling, i.e. the slow cooling down to room temperature (20°C.h -1 , sample 2), the Mn bulk composition of cementite does not evolve, but strong gradients, about 10-30 nm wide are found at interfaces with interfacial concentration at about 11%. The initial partition due to the transformation condition is thus reinforced during coiling by diffusion but observed composition gradients is the proof that cementite is far from being at equilibrium in the as-rolled state. This enrichment prior annealing is often neglected in most of the studies dedicated to the annealing of ferrite-cementite microstructure. After heating at 700°C (sample 3), Mn seems more homogenously distributed in cementite with an average composition of about 10%. In the following part, thermo-chemical and diffusion analysis will be thus performed to interpret the above EDXS measurements.

Discussion and modeling

This discussion will be divided into two parts. In the first part, the combined findings of Hillert and

Pandit [START_REF] Hillert | Solid-solid phase transformations[END_REF][START_REF] Panahi | Kinetic Transitions during Non-Partitioned Ferrite Growth in Fe-C-Mn Alloys[END_REF] are rationalized in order to predict thermodynamically the composition of the pearlite's constituents and thus explain the measured compositions inside cementite in the as-transformed state (Sample 1). To our knowledge, we are the first to bring experimental evidence of the validity of such a thermodynamical prediction for hypoeutectoid steels in anisothermal condition. In the second part, the composition evolution in cementite during coiling and annealing will be modeled with DICTRA software, in order to explain composition gradients in as-received and annealed states (Samples 2 and 3, respectively). This work has required reassessing Mn diffusion coefficient in the commercial MOBFE2 database. Coupling the model for phase transformation and diffusion calculations thus permits to predict the local Mn composition field in cementite particles all along steel manufacturing.

Manganese partition during pearlite transformation Prior pro-eutectoid transformation and criterion for pearlite transformation start

The ferrite-pearlite microstructure obtained after hot-rolling is the product of a two-step decomposition of austenite. The pro-eutectoid ferrite transformation occurs first in recrystallized austenite. The pro-eutectoid transformation temperature in the studied steel has been measured using a dilatometer around 685°C for the studied cooling condition (20°C.s -1 ) (neglecting possible interactions with austenite deformation). This temperature is far below the NPLE (negligible partitioning local equilibrium)/PE (Para Equilibrium) transition temperature determined by Zurob around 825°C [START_REF] Pandit | Diffusion-controlled growth of pearlite in ternary steels[END_REF][START_REF] Zurob | A transition from local equilibrium to paraequilibrium kinetics for ferrite growth in Fe-C-Mn: A possible role of interfacial segregation[END_REF] (for an alloy Fe-0.57C-0.94Mn). Ferrite transformation in the studied steel occurs thus under NPLE conditions, in accordance also with the work of Chen et al. [START_REF] Chen | The Effect of Interfacial Element Partitioning on Ferrite and Bainite Formation[END_REF]. It thus means that the substitutional solute composition of untransformed austenite remains constant during ferritic pro-eutectoid transformation. Only its carbon concentration increases progressively. It is generally admitted that the pearlitic transformation then occurs when the carbon concentration is high enough, i.e. when the local composition in untransformed austenite reaches the extrapolated Acm boundary below the eutectoid point. This criterion is called Hultgren criterion.

In house software TACSI developed by ArcelorMittal has been used to calculate this transformation condition in industrial conditions.

TACSI software is a simulation tool for intelligent manufacturing able to simulate the phase transformations occurring during hot-rolling of conventional high strength steels, considering complex thermomechanical schedules. The predicted microstructures (phases, size, precipitation state…) then serve to predict the mechanical properties of the steels using micromechanical approaches. When linked to sensors on industrial plants, TACSI is used to drive the industrial production and is able to predict the local mechanical properties on coils. The model is thus calibrated on large industrial and laboratory databases. The module used to calculate the ferrite/pearlite transformations from austenite (deformed or not) has been extensively described in previous papers [START_REF] Perlade | Application of microstructural modelling for quality control and process improvement in hot rolled steels[END_REF][START_REF] Iung | Physical modelling of phase transformations in high strength steels[END_REF].

In this model, the Classical Nucleation Theory (CNT) developed by Aaronson et al. [START_REF] Enomoto | The kinetics of ferrite nucleation at austenite grain edges in Fe-C and Fe-C-X alloys[END_REF][START_REF] Enomoto | On the critical nucleus composition of ferrite in an Fe-C-Mn alloy[END_REF][START_REF] Tanaka | Nucleation kinetics of grain boundary allotriomorphs of proeutectoid ferrite in Fe-C-Mn-X2 alloys[END_REF][START_REF] Enomoto | Nucleation kinetics of proeutectoid ferrite at austenite grain boundaries in Fe-C-X alloys[END_REF] is applied.

Ferrite growth is modeled by a mixed-mode approach. Pearlite transformation is triggered according to a modified Hultgren criterion calibrated on a large database. For studied steels and cooling conditions, it has been established that pearlite transformation starts at 570°C. For studied steels and cooling conditions, it has been established with the TACSI software that pearlite transformation starts at 570°C.

This value has been confirmed by analyzing the interlamellar spacing in the as-received state (cf.

Figure 1a). The mean interlamellar spacing, measured in cold-rolled pearlite by the planar intercept method is 48 nm. The stereological correction proposed by Ridley [START_REF] Ridley | A Review of the Data on the Interlamellar Spacing of Pearlite[END_REF] for pearlite was applied. The true interlamellar spacing before cold-rolling is thus calculated using equation ( 2) [START_REF] Embury | The structure and properties of drawn pearlite[END_REF]:

= . exp ( -) (2)
where is the interlamellar spacing after cold-rolling. ε is the plastic equivalent deformation by rolling and can be calculated with Equation (3) [START_REF] Freshwater | Simplified theories of flat rolling-I. The calculation of roll pressure, roll force and roll torque[END_REF]:

= √ . ln( ) (3)
where R is the cold rolling ratio.

The empirical law of Marder [START_REF] Marder | Effect of continuous cooling on the morphology and kinetics of pearlite[END_REF] gives the interlamellar spacing as function of the difference between A e1 and the transformation temperature for continuous cooling according to the equation ( 4):

= ∆ (4)
where is the interlamellar spacing in µm and ∆T the temperature shift with respect to A e1 in °C.

The upper Ae1 temperature of the studied steel is 682°C according to THERMOCALC. Inverting Marder's relationship [START_REF] Marder | Effect of continuous cooling on the morphology and kinetics of pearlite[END_REF] gives then a transformation temperature of 585°C, very close to the predicted one by TACSI.

At 570°C (from TACSI), the empirical Acm formula of Lee [START_REF] Yoon | Improved Thermodynamic Formula for Austenite/(Austenite+Cementite) Phase Boundary in Low Alloy Steels[END_REF] predicts a carbon concentration in austenite of 0.39%wt. The lever rule then gives a volume fraction of pearlite of 25%, which is close to our experimental observations (16% considering only well delimited pearlite islands). As qualitative explanation, the difference between measured and expected pearlite fraction is given by the presence of the isolated cementite carbides which represent the carbon missing to achieve the complete pearlite volume fraction. Lee et al. [START_REF] Lee | The interaction between proeutectoid ferrite and austenite during the isothermal transformation of two low-carbon steels ? a new model for the decomposition of austenite[END_REF] elegantly depicted the formation of such particles which occurs concomitantly to the growth of the pro-eutectoïd ferrite grains.

Finally, it should be highlighted that an error of +/-10°C on the transformation temperature leads to a difference of 2% on the pearlite fraction in the studied range (around 570°C) using the empirical. Thus, a high degree of precision on this transformation temperature is not necessary to set the proposed simulation chain of the paper.

Interface conditions for pearlite transformation

The pearlite transformation from carbon rich austenite involves two phases growing in a cooperative manner and sharing a common front with the remaining austenite. Since the substitutional species diffuse far slower than carbon, the growth mode of pearlite could induce or not a partition of alloying elements between ferrite and cementite.

Early studies of Razik et al. on Fe-C-Mn and Fe-C-Cr [START_REF] Razik | An investigation of manganese partitioning during the austenite-pearlite transformation using analltical electron microscopl[END_REF][START_REF] Razik | Chromium partitioning during the austenitepearlite transformation[END_REF] steels announce that below about 650°C, no partition is observed. However, the comparisons of experimental growth kinetics with those calculated from the former assumption are in complete disagreement. Al-Salman et al. [START_REF] Al-Salman | Pearlite growth kinetics and partitioning in a Cr-Mn eutectoid steel[END_REF] observed manganese partitioning in Fe-C-Mn-Cr steel at temperatures down to 600°C, but were unable to identity a threshold temperature between growth modes with or without partition. Chance and Ridley [START_REF] Chance | Chromium partitioning during isothermal transformation of a eutectoid steel[END_REF] extended this finding by observing partition for temperatures as low as 550°C. The fact that partition was detected at such low temperatures despite of the weak diffusivity of substitutional elements suggested for the first time that diffusion occurred not only by bulk diffusion. An interfacial diffusion must in fact be considered to maintain a local equilibrium at the interface. More recently, Hutchinson [START_REF] Hutchinson | The growth of partitioned pearlite in Fe-C-Mn steels[END_REF] reported again a manganese partitioning in strongly alloyed steels (up to U Mn = 6.8% at 625°C). The experimental results to date from the literature lead to conclude that substitutional elements do partition at any temperature where pearlite is known to grow [START_REF] Pandit | Diffusion-controlled growth of pearlite in ternary steels[END_REF]. Hillert [START_REF] Hillert | Solid-solid phase transformations[END_REF] developed an interesting framework to estimate the composition of growing cementite and ferrite in ternary alloys, successfully applied by Hutchinson et al. [START_REF] Hutchinson | The growth of partitioned pearlite in Fe-C-Mn steels[END_REF]. The approach is based on two important assumptions:

(1) Local Equilibrium (LE) conditions prevail at both γ / α and γ / θ interfaces (2) Carbon diffuses much faster than Mn. Therefore, the carbon activity is assumed uniform in the vicinity of the growing fronts as well as in the bulk austenite.

Consistently, it involves that a single carbon iso-activity line passes through the bulk composition and intercepts both γ / α+γ and γ+θ / θ phase boundaries. In the following, thermodynamic calculations only take into account Mn. Indeed, accounting of Cr or Si did not modify significantly the simulation results. Moreover, as explained above, experimental measurements regarding Cr and Mn are not relevant enough to be compared to simulations (only mean trends can be observed). Figure 7 shows the carbon iso-activity line of the austenite bulk composition in an isothermal section of the Fe-C-Mn ternary diagram at 570°C calculated with THERMOCALC. This black dotted-dashed line passes through the blue dot representing the initial bulk composition. The red and black continuous lines represent respectively the α+γ and γ+θ two-phase field boundaries. These lines were mapped separately by considering the metastable equilibrium between either α / γ or γ / θ. In Figure 7, these two calculations are superposed. The interception of the carbon iso-activity line with the phase boundaries indicates the compositions prevailing at the γ side at the γ / α and the γ / θ interfaces respectively. The corresponding LE tie-lines can then be calculated to deduce the compositions of the growing ferrite and cementite.

For the current study, THERMOCALC calculations give in austenite U Mn = 13.3 % at the α / γ interface and U Mn = 1.6 % at the θ / γ interface. The two corresponding configurations are represented separately in Figures 8a and8b (for θ and α respectively). In both cases, the dotted-dashed line still represents the carbon iso-activity line and the dashed lines represent the operative tie-lines at θ / γ and α / γ interface respectively. For the studied configuration, the Mn compositions predicted in cementite and ferrite are U Mn = 6.05 and 2.33 % respectively. The predicted Mn compositions of cementite and ferrite (respectively U Mn = 6.05 and 2.33%) are in excellent agreement with TEM measurements of sample 1 (U Mn = 6.6 and 1.90 %), supporting the assumption of a partitioned growth of pearlite with local specific equilibria at γ/α and γ/θ interfaces.

One emphasizes that the composition in cementite would be significantly different if an equilibrium α / θ had been considered at 570°C (U Mn θ = 19 %). 20

However, the previous thermodynamic prediction does not satisfy a priori the Mn solute molar balance, such that:

f M θ . X Mn θ + f M α . X Mn α =X Mn 0 (6)
where X Mn 0 is the nominal atomic Mn composition of γ. X Mn θ and X Mn α are the atomic Mn compositions of cementite and ferrite respectively, determinated with the latter approach. f M θ , f M α are the molar fractions of cementite and ferrite respectively. At 570°C, assuming a nominal atomic carbon composition X c = 1.78 % (0.39%wt) in austenite at the beginning of the transformation and a negligible content in ferrite, the lever rule imposes a molar fraction of cementite of 7.1 % in pearlite.

Therefore, assuming that the Mn compositions inside cementite and ferrite are those determined by the thermodynamic approach, the overall manganese atomic composition (2.46 %) should have been higher than the nominal atomic composition (1.94 % expected from Table 1). This purely thermodynamic approach thus does not permit to verify a correct molar balance in the studied case.

This unsatisfactory situation has been avoided by Pandit and Bhadeshia [START_REF] Pandit | Diffusion-controlled growth of pearlite in ternary steels[END_REF] who in fact recommend first to calculate the γ / θ tie-line from the uniform carbon activity assumption. Once the Mn composition inside cementite is determined, they establish a new tie-line starting from this composition and passing through the bulk composition. (It is not an equilibrium tie-line). The corresponding Mn composition inside the growing ferrite is then deduced by extending this tie-line to the α / α + γ phase boundary. Figure 9 shows the approximation of Pandit and Bhadeshia for the current steel. Mn composition in ferrite determined under this approximation is U Mn = 1.80 % which is even closer to our TEM measurement in ferrite. In that case, the solute molar balance is verified. The thermodynamic approach using the carbon iso-activity is thus a convenient tool for the prediction of the solute composition within pearlite constituents (ferrite and cementite). However, this kind of approach is seldom used, even in the most recent investigations on pearlite. To our knowledge, only Pandit and Bhadeshia [START_REF] Pandit | Diffusion-controlled growth of pearlite in ternary steels[END_REF] have attempted to apply this reasoning to explain successfully the experimental results of Razik and Ridley. These investigations have been carried out on eutectoid steels in frame of isothermal treatments only. The present work seems to be the first to date to investigate with this model the pearlite transformation conditions after a pro-eutectoid transformation and thus at very low temperature.

Ripening process of cementite during coiling and annealing

Basic thermodynamic and diffusion analysis

We have seen in the previous sections that the phase compositions inherited from the transformation conditions are far from the local equilibrium conditions (considering the local carbon composition in pearlite 1.78 %at). The differences are even higher at room temperature (even if the results of thermodynamic at such low temperatures should be considered carefully). The equilibrium composition in Mn and Cr at room temperature in cementite are U Mn = 36 and U Cr = 4%. The measurements of sample 2 are far lower revealing that the diffusivities of substitutional solutes are too low below coiling temperature range to obtain a uniform equilibrium composition profile through cementite. As central composition of cementite has not evolved, it means that substitutional solutes had even not the time to diffuse from the interfaces to the middle of cementite particles. Composition gradients from interfaces are thus observed over a limited distance (about 15-30 nm).

Mn composition profile measured in cementite after heating up to 700°C are almost flat and the constant value (about U Mn = 10.0% in sample 3) is approaching the equilibrium composition (U Mn = 14.3%). It leads to the conclusion that, during heating, above a certain temperature, the Mn diffusivity is sufficient to permit the homogenization of Mn close to the equilibrium composition within a short period of time. Cr equilibrium composition (U Cr = 2.7%) is nevertheless not reached, as 1.7% is measured in the cementite in sample 3 owing to a lower diffusivity. Similar observations were reported by Baltazar et al. [START_REF] Hernandez | Tempering of Martensite in Dual-Phase Steels and Its Effects on Softening Behavior[END_REF] or by Phillipot et al. [START_REF] Philippot | Influence of a 2-D defect on the partitioning during the formation of a cementite particle in steels[END_REF] who studied the Mn enrichment in cementite after heating up to 700°C at 1°C.s -1 of a 0.37C-2.53Mn wt.% steel (Mn content close to the studied steel). They measured Mn concentration in cementite by atom probe tomography close to 11 %wt (U Mn = 12%) in very good agreement with our own observations. As in the studied case, Cr does not reach equilibrium after heating.

Mn diffusion lengths in cementite for both cooling from 570°C down to room temperature at 20°C h -1 and heating up to 700°C at 3°C.s -1 were estimated using the sole diffusion coefficient of Mn in cementite found in literature. D Mn θ has been extracted the MOBFE2 database of DICTRA (with TCFE9). For the sake of simplicity, isothermal holdings at 570°C and 700°C, during t = 24 h and t= 200 s were considered to estimate an upper value of √Dt. In both cases, diffusion lengths did not exceed 2 nm. This is far lower than our observations (about 15-30 nm in the first case and larger than cementite half width in the second case).

Since D Mn θ provided by DICTRA software is obviously too weak, it must be reassessed, as did e.g. by Song [31]. This author proposes to multiply D Mn θ by 5 in order to better calibrate its own experiments.

More recently, Luo [START_REF] Luo | A Novel Observation on Cementite Formed During Intercritical Annealing of Medium Mn Steel[END_REF] needed to multiply it by 72 to make its DICTRA simulations consistent with their own experimental data. He noticed that this coefficient is still too low. In the present study, we propose to reassess this diffusion coefficient D Mn θ on the basis of our own experimental results. As done by Luo, simulations of Mn diffusion in pearlite will be conducted using the DICTRA software.

DICTRA Simulations

A model ternary Fe-C-Mn system is considered for the phase transformation calculations with DICTRA software (2017a version), using TCFE9 and MOBFE2 databases. Our equilibrium calculations have shown that other alloying element (Si and Cr) do not affect significantly the chemical compositions of the phases and transformation temperatures. For this reason, the following DICTRA simulations do not deal with the latter species.

A planar configuration representing a lamellar pearlite structure (half ferrite lamella in contact with a half cementite lamella) has been considered for the sake of simplicity, even if our observations are not all obtained in such simple geometrical configurations. Half-lamellar spacing and lamella thickness have been set respectively to 340 and 20 nm in accordance with our observations. The considered volumes are consistent with equilibrium calculations at 570°C (94.2 and 5.8 % vol of ferrite and cementite respectively).

Two successive thermal treatments have been simulated. The first one corresponds to the coiling treatment (between sample 1 and 2) and the second one to the interrupted annealing at 700°C (between sample 2 and 3). Initial Mn concentrations profiles in cementite and ferrite have been considered

uniform and set to U Mn = 6.25% in cementite and U Mn = 1.70% in ferrite as observed experimentally in sample 1 (cf. Figure 3b). Phase and composition fields resulting from the first simulated treatment are used as initial conditions for the second simulations (by a field transfer).

Modeling space is discretized using unidimensional grids. 30 grid nodes have been distributed in both ferrite and cementite following a geometrical progression in both phases with ratio 0.8 and 1.02 respectively, in order to get a finer mesh near α/θ interface. Both time and spatial discretization have to be optimized in order to reduce computation time without losing accuracy. Inappropriate simulation parameters could induce a significant decrease of the overall Mn concentration in the system. One points out that of curvature effects (Gibbs Thompson), morphological evolutions or interaction between particles (coarsening) were disregarded in our simulations. These contributions could be nonetheless taken into account to explain the significantly higher compositions measured inside the spheroidized extremity of the lamella shown in Figure 5. However, such a deeper investigation lies beyond the scope of this article.

The activation energies and the pre-exponential factors calculated with DICTRA for ferrite and cementite are summarized in Table 2. To obtain these values, the composition of the austenite grains have been considered (X c = 1.78% at , U MN = 1.94%). In the case of ferrite, both parameters vary significantly with the temperature. An Arrhenius plot was drawn to deduce the values shown in Table 2.

Pre-exponential factor Q (kJ.mol - Mn diffusion coefficient in cementite has been tuned to best reproduce our experimental observations.

In this procedure, only pre-exponential term has been modified so far (not the activation energy) and multiplied by 2000. This value is consistent with the respective remarks of Song and Luo [START_REF] Song | On the Spheroidized Carbide Dissolution and Elemental Partitioning in High Carbon Bearing Steel 100Cr6[END_REF][START_REF] Luo | A Novel Observation on Cementite Formed During Intercritical Annealing of Medium Mn Steel[END_REF]. Mn diffusion coefficient in ferrite has been taken from the database and has not been modified, since it is considered well validated.

Simulation results

Figure 11a shows the composition profiles calculated in cementite considering a slow cooling representative of the coiling operation (from sample 1 to sample 2) and Figure 11b the composition profiles after heating from room temperature (25°C) to 700°C at 3°C.s -1 (from sample 2 to sample 3).

For the sake of comparison, calculated composition profiles have been compared to experimental measurements in cementite. In the second simulation, the expected equilibrium composition at 700°C is represented by a dotted line. It corresponds to the partition expected in the sole pearlite sub-system.

It should first be noticed that in both cases, interface remains fixed during the inter-diffusion process as carbon solubility in ferrite and in pearlite does not vary much with temperature. In Figure 11a, the composition profile shows a steep gradient in cementite at the interface (extended over about 15 nm) whereas the middle of the cementite particle is not enriched (still at 6.25%). Mn interfacial composition predicted by DICTRA is U Mn = 12.7 %, that is far lower than that equilibrium composition expected at room temperature (U Mn ≈ 36%) consistently with the low Mn diffusivity in this temperature range (T < 570°C). The Mn composition profile inside ferrite shows a depletion over 40 nm from the interface, similarly to the TEM measurements, except that particle studied in sample 2 is located in a Mn microsegregated band, involving a Mn concentration twice higher (U Mn ≈ 4%). It is the reason why the experimental Mn profile is higher than the simulated one in the ferrite matrix.

Hence, calibrating Mn diffusion coefficient in cementite has permitted to reproduce consistently our experimental observations. The reliability of our reassessment was confirmed by simulating the composition evolution in cementite during reheating to 700°C. Figure 11b shows that the calculated profile after heating is far flatter than after coiling. Low calculated composition gradients are in excellent agreement with our experimental observations. Only interface compositions are slightly lower than observed experimental values. The presence of a microsegregation could explain this difference.

Our DICTRA simulations show that it is possible to explain and predict experimental Mn concentration profiles inside cementite during coiling and heating by simple diffusion calculations with local equilibrium at ferrite/cementite interface. When using MOBFE2 database, Mn diffusion coefficient in cementite has to be multiplied by a factor 2000 to obtain consistent composition profiles and gradients.

Conclusions

Cementite composition in a ferrite-pearlite steel dedicated to the production of DP steels has been investigated along the manufacturing process, i.e. after hot-rolling and during annealing. By coupling TEM investigations and Thermocalc / DICTRA modeling, we have explained how cementite is progressively enriched in manganese.

This enrichment begins at the pearlite transformation stage. The uniform enrichment we have measured in our cementite particle (about 7 %) can be well explained and thus predicted by the model proposed by Hutchinson [START_REF] Hutchinson | The growth of partitioned pearlite in Fe-C-Mn steels[END_REF] considering the simultaneous local equilibria between ferrite and austenite and cementite and austenite during the pearlite transformation. To the best knowledge of the authors, this work is the first to validate the model for a pearlite transformation after a pro-eutectoid transformation and thus at very low temperature. Nevertheless, we have shown that in the studied case the strict application of transformation conditions does not lead to a satisfactory mass balance. As suggested by Pandit et al. [START_REF] Pandit | Diffusion-controlled growth of pearlite in ternary steels[END_REF], a simplified version is shown to overcome this difficulty. This enrichment stage is rarely taken into account when addressing cementite composition in ferrite-pearlite steels.

Compositions inherited from phase transformation are far from equilibrium. During subsequent coiling operation and annealing, cementite enrichment in manganese will continue. Our DICTRA calculations

show that observed composition profile can be nicely understood and reproduced considering simple diffusion calculations with local equilibrium at ferrite/cementite interface. Nevertheless, the known diffusion coefficient of manganese in cementite must be revised to explain composition gradients observed after coiling and after interrupted annealing. The simulations have also enabled a better understanding of operative interface conditions between ferrite and cementite during the thermal treatments.

We have finally showed that both thermodynamic approach of pearlite phase transformation and diffusion calculation must be coupled to follow seamlessly manganese composition gradients in cementite all along the manufacturing process. Knowing the exact composition profile is a prerequisite to predict accurately austenite transformation kinetics and thus final DP microstructures. One should however admit that in the studied slow annealing conditions, cementite composition is close to the equilibrium at 700°C reducing possible inheritance effects. It is likely that this conclusion does not hold anymore in the case of fast annealing conditions.

Figure 1 :

 1 Figure 1: SEM in Secondary Electron mode of studied microstructures after Picral etching (a) sample 2 and (b) sample 3 respectively.

Figure 2 :

 2 Figure 2: TEM BF (Bright Field) of a lamellar pearlite island formed at 570°C. The latter is surrounded by large pro-eutectoid ferrite grains. Intergranular carbides are found along the grain boundaries.

Figure 3 :

 3 Figure 3: (a) TEM BF micrograph of cementite lamella (dark contrast) emerging from the thin foil and its surrounding matrix (bright contrast) in sample 1. The aligned blue points correspond to the positions of EDXS measurements to establish a composition profile across the carbide and its surrounding matrix. (b) Mn (black), Cr (red) and Si (blue) u-fraction profiles. The areas bounded by the dashed lines indicate spots where the TEM beam could cross simultaneously ferrite and cementite at interface due to a possible tilting issue.

Figure 4 :

 4 Figure 4: (a) TEM BF micrograph of cementite lamella (object with the brightest contrast) emerging from the thin foil and its surrounding matrix in sample 1. The aligned blue points (step size = 5 nm) correspond to the positions of EDXS measurements to establish a composition profile across the carbide and its surrounding matrix. (b) Mn (black), Cr (red) and Si (blue) u-fraction profiles. The areas bounded by the dashed lines indicate spots where the TEM beam could cross simultaneously ferrite and cementite at interface due to a possible tilting issue.

Figure 5 :

 5 Figure 5: (a) TEM BF micrograph of second cementite lamella (dark contrast) emerging from the thin foil and its surrounding matrix (bright contrast) in sample 1. The aligned blue points (step size = 17 nm) correspond to the positions of EDXS measurements to establish a composition profile across the carbide and its surrounding matrix. (b) Mn (black), Cr (red) and Si (blue) u-fraction profiles. The dashed line indicates the position of the sub-grain separating the straight and the bulged part of the particle. The areas bounded by the dot-dashed lines indicate spots where the TEM beam could cross simultaneously ferrite and cementite at interface due to a possible tilting issue.

Figure 6 .Figure 6 :

 66 Figure 6. The studied carbide is suspended into vacuum by one extremity avoiding a possible dilution effect.

Figure 7 :

 7 Figure 7: Isothermal section of the Fe-C-Mn diagram at 570°C. The dotted-dashed line represents the carbon iso-activity determined from the austenite bulk composition. The two domains delimited by the red and black boundaries represent respectively the α + γ and θ + γ two-phase fields.

Figure 8 :

 8 Figure 8: Isothermal section of Fe-C-Mn ternary diagram for (a) θ / γ and (b) α / γ metastable equilibrium. The dotted dashed line is the carbon iso-activity line that is used to find the composition of austenite, cementite and ferrite at the θ / γ and α / γ interfaces. It enables the calculation of the effective tie-lines relative to each equilibrium and thus to deduce the Mn compositions of the growing phases.

Figure 9 :

 9 Figure 9: Isothermal section of the Fe-C-Mn ternary diagram at 570°C. Red line represents the α / α+γ boundary. Black line represents the γ+θ / θ boundary. The initial austenite composition is representedby the blue dot (input from TACSI simulation). The black dotted line represents the tie-line approximated according to Pandit and Bhadeshia [41]. It goes through the points representative of cementite composition and bulk austenite composition. Intersection with α/α+γ boundary provides the estimated ferrite composition.

Figure 11 :

 11 Figure 11: Results of DICTRA simulations (a) Mn concentration profiles in ferrite and cementite after cooling from 570°C down to room temperature at 20°C.h -1 (continuous red line); (b) Mn concentration profiles in ferrite and cementite at 700°C after slow heating (3°C.s -1 ) from room temperature (continuous blue line). The continuous red line corresponds to the initial composition profile considered for the reheating simulation. Dashed line represents the equilibrium composition expected in the pearlite sub-system at 700°C. Symbols indicate in both cases TEM composition measurements in cementite obtained in sample 2 and sample 3 for the sake of comparison.

Table 1 :

 1 Composition of the studied steel in weight percents and in u-fractions.

		C	Mn	Si	Cr
	weight fraction (%)	0.10	1.91	0.20	0.20
	u-fraction (%)	n.a.	1.94	0.41	0.21

Table 2 :

 2 pre-exponential factor and activation energies of the Mn diffusion coefficient in cementite and ferrite, respectively.

	1 )

Acknowledgements

This research was funded by Centre National de la Recherche Scientifique (CNRS) and by ArcelorMittal Maizières les Metz (Product Research Centre). The Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures (Labex DAMAS) from Université de Lorraine (France) is also fully acknowledged for its support.

Conflicts of Interest

The authors declare no conflict of interest.