Alexis Graux
email: alexis.graux@insa-lyon.fr

Sophie Cazottes
email: sophie.cazottes@insa-lyon.fr

David De Castro
email: david.decastro@cenim.csic.es

David San-Martín

Carlos Capdevila

Jose Maria Cabrera
email: jose.maria.cabrera@upc.edu

Sílvia Molas
email: silvia.molas@eurecat.org

Sebastian Schreiber
email: sebastian.schreiber2@thyssenkrupp.com

Djordje Mirković
email: d.mirkovic@sz.szmf.de

Frédéric Danoix
email: frederic.danoix@univ-rouen.fr

Damien Fabrègue
email: damien.fabregue@insa-lyon.fr

Michel Perez
email: michel.perez@insa-lyon.fr

Design and Development of Complex Phase Steels with Improved Combination of Strength and Stretch-Flangeability

Keywords: metallurgy, complex phase steels, microalloyed steels, hot rolling, stretch-flangeability

This study presents the design and development of a hot-rolled bainitic steel, presenting a good combination of strength and stretch-flangeability, for automotive applications. Ti, Nb, and Mo were added in the steel composition in order to control austenite grain sizes, enhance precipitation hardening, and promote the formation of bainite. This study focuses on the effect of process parameters on final microstructures and mechanical properties. These parameters are the finishing rolling temperature, which conditions the austenite microstructure before its decomposition, and the coiling temperature, which conditions the nature and morphology of the ferritic phases transformed. A preliminary study allowed to determine the austenite grain growth behavior during reheating, the recrystallization kinetics, and the continuous cooling transformation curves of the studied steel. Then, a first set of parameters was tested at a semi-industrial scale, which confirmed that the best elongation properties were obtained for homogeneous bainitic lath/granular microstructures, that can be produced by choosing a coiling temperature of 500 • C. When choosing those parameters for the final industrial trial, the microstructure obtained consisted of a homogeneous lath/granular bainite mixture that presented a Ultimate Tensile Strength of 830 MPa and a Hole Expansion Ratio exceeding 70%.

Introduction

Over the last 20 years, car designers have been facing increasing challenges concerning passenger safety, vehicle performance, and fuel economy. More specifically, two demands have raised, leading to the development by steelmakers of higher strength steel grades named Advanced High Strength Steels (AHSS). First, increasing steel strength allows to reduce the total weight of the car, therefore contributing to reduce CO 2 emissions. Second, for safety issues, increasing both yield and ultimate tensile strengths leads to enhanced crash performances. However, increasing strength generally lowers formability properties such as drawing, stretching, stretch flanging, or bending. Numerous chassis parts of the cars present complex shapes, and are manufactured by cold forming operations from steel plates, which requires good stretch-flangeability. The stretch-flangeability is indicative of the formability of the edges, and is usually evaluated by the hole expansion test [START_REF]Metallic Materials-Sheet and Strip-Hole Expanding Test[END_REF]. It is related to the local ductility of the material, which can be quite different from the "global" ductility measured from a conventional tensile test. To improve the local ductility, it is important to limit the differences in hardness between phases present in the material, or to favor single phase microstructures.

Recently, a large effort has been made to develop steels reaching a good compromise of strength and stretch-flangeability. Three main strategies can be distinguished [START_REF] Fonstein | Complex Phase Steels[END_REF]: (i) ferritic steels reinforced by nanometer-sized precipitates [START_REF] Funakawa | Development of high strength hot-rolled sheet steel consisting of ferrite and nanometer-sized carbides[END_REF][START_REF] Kamibayashi | Influence of Ti and Nb on the strength-ductility-hole expansion ratio balance of hot-rolled low-carbon high-strength steel sheets[END_REF]; (ii) reducing the hardness differences between martensite and ferrite in Dual Phase (DP) steels, either by reducing the hardness of martensite [START_REF] Fang | Effects of tempering temperature on tensile and hole expansion properties of a C-Mn steel[END_REF][START_REF] Azuma | Effect of hardness of martensite and ferrite on void formation in dual phase steel[END_REF], or by increasing the one of ferrite [START_REF] Tsipouridis | Formability of High Strength Dual-phase Steels[END_REF][START_REF] Tsai | Effect of Cr and Al additions on the development of interphase-precipitated carbides strengthened dual-phase Ti-bearing steels[END_REF]; and (iii) Complex Phase (CP) steels, which mainly present bainitic microstructures. The concept of CP steels initially emerged from the original idea of replacing martensite by bainite in DP steels [START_REF] Sudo | Niobium bearing ferrite-bainite high strength hot-rolled sheet steel with improved formability[END_REF]. CP steels present superior stretch-flangeability than DP steels with similar levels of tensile strength, which can be explained by their rather homogeneous microstructures [START_REF] Fonstein | Complex Phase Steels[END_REF].

As explained by Bhadeshia [START_REF] Bhadeshia | Bainite in Steels: Theory and Practice[END_REF] (p. 367), a successful strategy to promote bainitic transformation is to use low carbon steels with additions of boron or molybdenum. Keeping a low carbon content avoid increasing the hardenability drastically, which would lead to the formation of martensite. Addition of B or Mo suppresses allotriomorphic ferrite formation, and promote the formation of bainite [START_REF] Cizek | Effect of composition and austenite deformation on the transformation characteristics of low-carbon and ultralow-carbon microalloyed steels[END_REF][START_REF] Zhao | Continuous cooling transformation of undeformed and deformed low carbon pipeline steels[END_REF][START_REF] Kong | Effect of molybdenum on continuous cooling bainite transformation of low-carbon microalloyed steel[END_REF][START_REF] Hu | The effects of Nb and Mo addition on transformation and properties in low carbon bainitic steels[END_REF]. Ti, Nb, and V are added for their ability to form nanosized carbides, nitrides, or carbonitrides that are useful for precipitation hardening [START_REF] Hu | Effect of cooling procedure on microstructures and mechanical properties of hot-rolled Nb-Ti bainitic high strength steel[END_REF]. Moreover, those precipitates play an important role for austenite grain growth control, by limiting the grain boundaries motion [START_REF] Gladman | The Physical Metallurgy of Microalloyed Steels[END_REF].

The hot rolling process of bainitic steels is summarized in Figure 1. In hot rolling steel plants, the first step of the manufacturing process of steel sheets consists in a reheating stage, to ensure that the slab is ductile enough to be hot rolled. During this reheating, the steel is brought to a fully austenitic state. In the case of microalloyed steels, reheating ensures that primary coarse precipitates are dissolved before hot rolling, to optimize the effects of microalloying additions. After the reheating stage comes the proper hot rolling, which aims at reducing the slab thickness to get the targeted thickness of the final steel sheet. Hot rolling is divided in two stages, referred as roughing and finishing. The choice of deformation temperatures, of applied strain levels and strain rates, as well as the time between each deformation pass (interpass time) will have an influence on the phase transformation of the steel and therefore on its microstructure. The process ends with accelerated cooling on a run-out table, followed by coiling. The final microstructure will be highly influenced by the choice of the applied cooling rate and coiling temperature.

This work presents the design and development of a bainitic steel exhibiting a good compromise between strength and stretch-flangeability. The whole approach is shown, from the lab scale study of the chosen grade with the determination of Recrystallization-Precipitation-Time-Temperatures (RPTT) and the continuous cooling transformation (CCT) RPTT curves, to the industrial scale with the final microstructures and mechanical properties.

Preliminary Investigations

Preliminary investigations were first carried out, in order to gather critical information about austenite grain growth, recrystallization, precipitation, and phase transformation behavior of the chosen grade. Ti and Nb are added for their ability to form precipitates that control the austenite grain size at high temperature and enhance precipitation hardening after phase transformation, while Mo is added to promote the formation of bainite. The target composition is presented in Table 1. An ingot of approximate dimensions 140 × 150 × 50 mm 3 was produced by vacuum induction. After homogenization at 1200 • C for 2 h and hot rolling, a plate of 450 × 150 × 15 mm 3 was obtained. Table 1 provides the composition of the resulting alloy, measured by Induced Coupled Plasma-Mass Spectroscopy (ICP-MS).

Selection of Reheating Temperature

The evolution of austenite grain growth and precipitation state during isothermal treatments were thoroughly investigated in a recently-published study [START_REF] Graux | Precipitation and grain growth modelling in Ti-Nb microalloyed steels[END_REF]. A Bähr 805 DIL dilatometer was used to perform heat treatments consisting of a 5 • C s -1 ramp, followed by a 10 min holding at the reheating temperature and controlled cooling. For each heat treatments, austenite grain boundaries were revealed using thermal etching [START_REF] Garcıa De Andres | Revealing austenite grain boundaries by thermal etching: advantages and disadvantages[END_REF]. For isothermal annealing temperatures ranging from 900 • C to 1250 • C, the average austenite grain diameter increases from 10 µm to 400 µm. Graux et al. [START_REF] Graux | Precipitation and grain growth modelling in Ti-Nb microalloyed steels[END_REF] showed that three types of precipitates are present in the alloys in the initial state: (Ti,Nb)C, Ti 4 C 2 S 2 , and TiN precipitates. (Ti,Nb)C precipitates were the most frequently observed precipitates, and exhibit a mean diameter around 60 nm. They are the one controlling the austenite growth during soaking, as they exert a pinning pressure on austenite grain boundaries. This former study allowed to select a temperature of 1250 • C for the reheating step of the hot rolling process and for all of the following investigations. Such high reheating temperature ensures a complete dissolution of the initial (Ti,Nb)C population controlling grain growth [START_REF] Graux | Precipitation and grain growth modelling in Ti-Nb microalloyed steels[END_REF], which allows to fully benefit from microalloying additions in the next steps of the process. Although large austenite grains are obtained when reheating at 1250 • C, recrystallization could refine austenite grains during hot rolling.

Austenite Recrystallization Kinetics and Strain-Induced Precipitation

Afterwards, the microstructural evolutions of austenite after hot compression were investigated using stress relaxation in compression mode. Stress relaxation tests start with a reheating treatment of 10 min at 1250 • C. The sample is subsequently cooled down to the deformation temperature with a 5 • C s -1 cooling rate and held 30 s for homogenization before compression. After compression, the anvils remain fixed in their positions and hold the sample during a certain time period while recording the evolution of stress with time.

When both temperature and driving force are high enough, the recrystallization can be detected (Figure 2a). The curves were then processed following the method described in [START_REF] Karjalainen | Stress relaxation method for investigation of softening kinetics in hot deformed steels[END_REF]. The beginning of the curve can be accurately described by a straight line (σ 1α 1 • log(t)), corresponding to the recovery/creep behavior of the strained material. Then, the curve typically exhibits a sharp drop that is related to the rapid softening induced by the recrystallization process. The end of the curve also follows a linear trend, that corresponds mainly to the grain growth behavior of the recrystallized material (σ 2α 2 • log(t)). Assuming that a partially recrystallized material consists of a mixture of two phases (work-hardened austenite and fully recrystallized austenite), a simple mixture rule is applied. Thus, the instantaneous value of stress is derived through the following equation:

σ = (1 -X) • (σ 1 -α 1 • log(t)) + X • (σ 2 -α 2 • log(t))
where X is the recrystallized fraction. Therefore,

X = σ 1 -α 1 • log(t) -σ (σ 1 -σ -2) -(α 1 -α 2 ) • log(t) (1)
At lower temperatures or for insufficient driving forces, there is no recrystallization (Figure 2b), and a softening is observed, due to the recovery of the strained austenite. When precipitation occurs, a temporary increase in stress can be observed [START_REF] Liu | A stress relaxation method for following carbonitride precipitation in austenite at hot working temperatures[END_REF]. The beginning and end of the precipitation process are detected thanks to the deviation from the linear behavior. In this study, stress relaxations tests were conducted in compression mode, either using a Gleeble 3500 thermo-mechanical simulator on cylindrical samples of 12 mm length and 8 mm diameter or using a Bähr 805 DIL dilatometer on samples of 10 mm length and 5 mm diameter. Two different strains (0.1 and 0.3) were tested and the temperatures ranged from 900 • C to 1100 • C. Because it is not suited for long time heat treatments, the Gleeble was dedicated to high temperatures (1000 ≤ T ≤ 1100 • C), to study static recrystallization. Recrystallization kinetics are known to depend on temperature, strain, but also on strain rate [START_REF] Humphreys | Recrystallization and Related Annealing Phenomena[END_REF]. Therefore, two different strain rates (0.1 and 5 s -1 ) were applied. For lower temperatures (T ≤ 1000 • C), the dilatometer was used to conduct the same stress relaxation tests, mainly to study strain-induced precipitation. As precipitation kinetics are much less sensitive to strain rates, these phenomena were studied using only one strain rate of 0.1 s -1 . These tests were performed using the Bähr 805 DIL dilatometer, presenting a higher sensitivity, which is needed to detect strain-induced precipitation on stress relaxation curves.

The stress relaxation tests performed allowed the reconstruction of complete Recrystallization-Precipitation-Time-Temperature (RPTT) diagrams, shown in Figure 3. An applied strain of 0.1 (Figure 3a) provides enough nucleation sites for the precipitation process to occur, so that precipitation is detected between 900 and 1000 • C. Above 1000 • C, no sign of recrystallization was detected, stress relaxation curves (σ = f (log t)) exhibiting a linear decrease behavior due to recovery. When a larger deformation of ε = 0.3 is applied (Figure 3b), recrystallization is observed above 1000 • C, and precipitation at 950 and 900 • C. The increase in strain rate leads to an acceleration of the recrystallization kinetics. This is due to the fact that when higher strain rates are applied, higher stress values are reached during compression, leading to higher dislocation densities and driving energy for recrystallization.

Continuous Cooling Phase Transformation

Continuous cooling experiments were performed using a Bähr 805 DIL dilatometer on samples of 10 mm length and 5 mm diameter. After a reheating treatment of 10 min at 1250 • C, the specimens were continuously cooled down to room temperatures at rates of 0.05, 1, 5, 10, and 25 • C s -1 (Figure 4a). In order to study the effect of austenite deformation on phase transformation, a second thermal cycle was applied (Figure 4b). After reheating, the samples were cooled down to 950 • C, held for 30 s, deformed to ε = 0.3 at a rate of 10 s -1 , and subsequently cooled down to room temperature at rates of 0.05, 1, 5, 10 and 25 • C s -1 . According to the study of recrystallization presented in Section 2.2, this deformation pass is performed in the non-recrystallization domain and thus results in austenite pancaking. During continuous cooling, the longitudinal dilatation curves were used to determine the transformation temperatures. It allowed the construction of the corresponding continuous cooling transformation diagrams, either starting from undeformed austenite or from deformed austenite. Heat-treated dilatometry samples were cut in halves and the resulting microstructures were characterized by optical and scanning electron microscopy. Vickers hardness measurements were also performed using a 10 kg load. Figure 5 shows the microstructures obtained after continuous cooling from both undeformed and deformed austenite.

The cooling rate range for which bainitic microstructures were obtained is wide. Polygonal ferrite was only observed at the slowest cooling rate (0.05 • C s -1 ). Starting from 1 • C s -1 , fully bainitic microstructures were observed. When higher cooling rates are applied, the morphology of bainite gradually changed from mainly granular bainite to fully lath-like bainite/martensitic microstructures. M S is theoretically equal to 456 • C according to the MAP STEEL MUCG83 program [START_REF] Peet | Program MAP_STEEL_MUCG83[END_REF]. The martensite start temperature M S was not clearly detected by dilatometry. However, a residual amount of martensite was observed after the microstructural characterization of the steel samples using SEM, specially after cooling at 25 • C s -1 . Therefore, the high hardness values measured for the highest cooling rates (10 and 25 • C s -1 ) could be mostly attributed to the fine microstructure of the bainite, though a small additional contribution from the residual martensite cannot be fully discarded. The deformation of austenite in the non-recrystallization region significantly affected the resulting microstructures. At a cooling rate of 0.05 • C s -1 , austenite deformation at 950 • C led to refined polygonal ferrite grains, as expected. The area fraction of granular bainite (≈30%) formed at 0.05 • C s -1 was however not affected by the deformation of austenite. Despite this apparent refinement of polygonal ferrite grains, a lower hardness was obtained when austenite was deformed, which can only be explained by different precipitation hardening levels. When austenite is undeformed, it is likely that no precipitation occurs in austenite before ferrite formation. Thus, a consequent precipitation strengthening should be obtained by interphase precipitation, as reported in previous studies on steels containing combined additions of Ti, Nb, and/or Mo [START_REF] Funakawa | Development of high strength hot-rolled sheet steel consisting of ferrite and nanometer-sized carbides[END_REF][START_REF] Kamibayashi | Influence of Ti and Nb on the strength-ductility-hole expansion ratio balance of hot-rolled low-carbon high-strength steel sheets[END_REF][START_REF] Jha | Development of high strength hot-rolled steel sheet for wheel disc application[END_REF][START_REF] Jha | Development of hot-rolled steel sheet with 600 MPa UTS for automotive wheel application[END_REF][START_REF] Wang | Mechanical properties and characteristics of nanometer-sized precipitates in hot-rolled low-carbon ferritic steel[END_REF]. On the contrary, due to the low cooling rate applied after austenite deformation, there should be plenty of time for precipitates to form in austenite, coherently with the RPTT diagram shown in Figure 3. Precipitates formed in austenite being coarser than the ones formed by interphase precipitation; those hypothesis could explain the lowered precipitation strengthening contribution for the sample submitted to austenite deformation.

Previous studies showed that austenite deformation has contradictory effects on bainite formation temperature [START_REF] Nikravesh | Influence of hot plastic deformation and cooling rate on martensite and bainite start temperatures in 22MnB5 steel[END_REF][START_REF] Hase | Bainite formation influenced by large stress[END_REF]. In the present case, for high cooling rates (≥1 • C s -1 ), austenite deformation lowered the bainite start transformation temperature, B S . It also tended to increase the domain of granular bainite: for instance, granular bainite was observed at 5 • C s -1 when austenite was deformed whereas this type of bainite was not found when austenite was undeformed, which is coherent with [START_REF] Jun | Effects of deformation and boron on microstructure and continuous cooling transformation in low carbon HSLA steels[END_REF]. Another effect is the decreasing hardness of the lath-like microstructures, which is related to an apparent coarsening of the lath microstructures. Shorter and wider laths were obtained from pancaked austenite. This arises from the fact that dislocations hinder the growth of bainite laths, as reported by previous studies [START_REF] Yamamoto | Effects of the austenite grain size and deformation in the unrecrystallized austenite region on bainite transformation behavior and microstructure[END_REF][START_REF] Fujiwara | Effect of hot deformation on bainite structure in low carbon steels[END_REF].

Pilot Plant Hot Rolling Trials

Different hot rolling strategies were tested on a laboratory hot rolling pilot plant, aiming at evaluating process conditions on microstructures and mechanical properties. Larger quantities of material were needed for hot rolling schemes. Thus, a second 100 kg ingot of approximate dimensions 120 × 140 × 600 mm 3 was produced by induction melting (Table 1). The 100 kg ingot was sectioned into coupons of 60 × 70 × 150 mm 3 intended to be hot rolled.

Definition of Hot-Rolling Strategies

Each hot rolling scheme entails five phases:

•

Reheating at 1250 • C, ensuring a full dissolution of pre-existing (Ti,Nb)C precipitates (see Section 2.1).

•

Rough rolling or roughing.

•

Finish rolling or finishing.

•

Accelerated cooling at 20-40 • C s -1 starting from the finishing rolling temperature (FRT) down to the simulated coiling temperature.

•

Slow cooling down to room temperature once the coiling temperature is reached.

A reversing rolling mill was used to deform the plate, which resulted in rather large interpass times ranging from 11 to 18 s and deformation of about 30% for each pass. The initial thickness of the plate was 60 mm, and was reduced to 32 mm after the two roughing passes. A final thickness of 3.5 mm was reached after the five finishing passes. For such interpass times and deformation levels, the temperature of no-recrystallization (T NR ) is about 1000 • C according to the recrystallization kinetics determined by stress relaxation (Figure 3).

It was then decided to vary the temperature domain where deformation steps were applied with respect to the temperature of no-recrystallization, T NR . Two distinct deformation schemes were defined:

•

First, a recrystallization-controlled rolling strategy was tested (Figure 6a), with a finishing rolling temperature of 1050 • C. For this deformation scheme, all deformation passes were performed well above the temperature of no-recrystallization. In these conditions, austenite recrystallizes between each deformation pass, leading to grain refinement before accelerated cooling.

•

Second, a more classical thermo-mechanical control process strategy was tested (Figure 6b). For this strategy, the two roughing passes are performed above 1050 • C leading to austenite grain refinement by recrystallization. After a waiting period of 30 s, the finishing stage was performed starting from 1050 • C, with a finishing rolling temperature of 880 • C. Therefore, most of the finishing passes were performed below T NR , resulting in pancaked austenite.

After hot rolling, the plates were cooled down to the coiling temperature at a rate ranging from 20 to 40 • C s -1 . Finally, two different coiling temperatures were applied: 500 and 650 • C. After reaching the coiling temperature, the hot-rolled plates were stored into an insulated box in order to slowly cool them down to room temperature, with an estimated cooling rate of 0.5 • C min -1 , which is comparable to the cooling rates reached in industrial conditions after coiling. Thus, a total of four different hot rolling schemes were applied to generate different microstructures. Hot-rolled plates of 1050 × 160 × 3.5 mm 3 were finally obtained.

Microstructures and Mechanical Properties

Methods

For microstructural characterization, parallelepiped samples were machined from the different hot-rolled plates. Observations were performed in the plan (RD, ND) at 1/4 thickness, where RD and ND stands for rolling and normal direction, respectively. After mechanical polishing, first with SiC paper and then down to 1 µm using diamond paste polishing, the samples were etched with nital (2 %). Scanning electron microscope observations using secondary electron (SE) were carried out with an accelerating voltage of 7 kV. For EBSD characterization, an additional polishing step was performed on a cloth soaked with a Struers OP-S colloidal suspension solution. Electron backscatter diffraction (EBSD) was carried out using a ZEISS Supra 55VP Scanning Electron Microscope operating at 20 kV, equipped with an Oxford Symmetry EBSD camera. The postprocessing analysis was performed on AZtec HKL Channel 5 software.

The mechanical properties of the plates obtained after hot rolling were characterized by tensile tests and hole expansion tests. The tensile tests were performed following the DIN EN ISO 6892-1 standard. The gauge length of the tensile samples are 55 × 20× 3.5 mm 3 . The tensile properties were evaluated according to three different orientations with respect to the rolling direction: at 0 • , 45 • , and 90 • . As no clear anisotropy was observed in the sample, only the measurements made along the rolling directions are presented here. Two tensile samples were tested for each orientation, giving a total of 6 tensile samples per hot-rolling scheme. The values reported in the following are the average values (out of the six samples) for yield strength (YS), ultimate tensile strength (UTS), and total elongation.

Hole expansion tests were performed following the DIN EN ISO 16630 standard. Square specimens of 90 × 90 mm 2 were machined from the plates. Holes with 10 mm initial diameter were punched in the center of the square samples of same thickness as the plates (3.5 mm to 4 mm) and expanded with a conical punch of diameter 40 mm and angle 60 • until a crack at the edge of the expanding hole is observed. The hole expansion ratio (HER) was calculated through

HER(%) = D f -D 0 D 0 × 100 (2)
where D 0 is the initial diameter and D f is the final diameter. Three samples were tested for each hot rolling conditions. The standard error of the mean was calculated.

Microstructures

Figure 7 shows the microstructures obtained after the four different hot rolling strategies, characterized by means of SEM and EBSD. On EBSD maps, all grains are indexed as ferrite, and the phase nature identification is performed considering both the morphology and the grain/lath boundary misorientation, as explained by Zajac et al. [START_REF] Zajac | Characterisation and Quantification of Complex Bainitic Microstructures in High and Ultra-High Strength Linepipe Steels[END_REF]. The lath-like morphology of lath-bainite is usually accompanied with a high number of grain boundaries with a misorientation larger than 55 • . Ferrite presents an equiaxed morphology with a random grain boundary misorientation, while the granular bainite rounded-shape morphology with grain boundary (GB) presents both small angle GB misorientation (<15 • ) as well as high angle GB misorientation (>15 • ). Low angle GB are plotted in red on the EBSD maps while GB larger than 15 • are plotted in black. This representation allows a better visibility of the morphology of the grains.

All hot rolling strategies gave rise to microstructures mostly composed of (granular or lath-like) bainite. The main factor affecting the nature of the transformation products formed during the hot rolling process is the coiling temperature: coiling at 650 • C favors the formation of granular bainite (Figure 7a,b), whereas coiling at 500 • C favors the formation of (lath-like) upper bainite (Figure 7c,d). Hot deformation conditions, i.e., Recrystallization-Controlled Rolling (RCR) or Thermo-Mechanical Control Process (TMCP), also influences the nature and morphology of the observed phases. For the same coiling temperature of 650 • C, granular bainite was significantly refined when it formed from deformed austenite (TMCP-650 • C, see Figure 7b) compared to when it formed from recrystallized austenite (RCR-650 • C, see Figure 7a). Deformation in the non-recrystallization region also promoted the formation of slights amounts of deformed ferrite (TMCP-650 • C, which can be recognized as elongated grains formed along prior austenite grain boundaries in Figure 7b). In these conditions, the finishing rolling temperature is close to the austenite to ferrite transition equilibrium temperature, A e3 , equal to 860 • C according to Thermo-Calc [START_REF] Andersson | Thermo-Calc & DICTRA, computational tools for materials science[END_REF]. Thus the slight amount of ferrite may have formed during the last rolling pass or right after it. The lath-like microstructures obtained after coiling at 500 • C were also influenced by austenite conditioning during hot deformation. RCR-500 • C (Figure 7c) scheme gave rise to a microstructure almost exclusively composed of lath-like bainite, with fine and long laths. When lath-like bainite is formed from deformed austenite (TMCP-500 • C, see Figure 7d), the resulting lath-like microstructure is coarser, presenting shorter and wider laths.

Mechanical Properties

Figure 8 presents the average tensile and hole expansion properties of the hot-rolled plates. As all hot-rolled plates presented bainitic microstructures, rather high levels of strength (UTS ≥ 800 MPa) were reached (Figure 8a), considering the low carbon contents of the studied steel. High YS/UTS ratios (≥0.81) were also reached, which is a characteristic of complex phase steels. Figure 8b focuses on the ductility, evaluated by tensile tests (total elongation), and the stretch-flangeability, characterized by the HER. Plates coiled at 650 • C, with granular bainite microstructures, globally show higher ductility than the lath-like bainite plates coiled at 500 • C. The opposite tendency was observed for the HER, which is mainly governed by the local ductility of the plates. Plates coiled at 650 • C showed limited HER with a ceiling at 40%, whereas plates coiled at 500 • C showed enhanced stretch-flangeability, with HER ranging from 50 to 60%. As a consequence, the plates showing the best compromise between HER and strength are the ones coiled at a temperature of 500 • C, that contain mostly lath bainite. A better elongation is obtained with a lower FRT temperature (TMCP process) when pancaked austenite is formed before phase transformation.

Industrial Production Trial

The pilot plant hot rolling trials described in the previous section showed that lath-like bainitic microstructure obtained following a TMCP process with a coiling temperature of 500 • C provided the best compromise of strength and stretch-flangeability. The use of a FRT as high as possible is interesting industrially, as this allows lowering the forces applied during rolling, thus reducing the wear of the rolling mills and allowing a gain in productivity. The interpass times used during industrial trials were much smaller than the one used during pilot plant trials, which considerably reduced the time for recrystallization between two successive deformation passes. Thus, it was possible to increase significantly the FRT while still getting pancaked austenite before accelerated cooling. Therefore, the industrial trial was designed for a FRT of 990 • C and a coiling temperature of ~500 • C. The high FRT applied in this industrial trial is slighlty higher than the one choosen for the TMCP process presented for the pilot plant trial.

The inital slab, whose composition is presented in the Table 1, had an initial thickness of 250 mm. The roughing was performed between 1218 • C and 1126 • C, and the transfer bar thickness after this stage was 55 mm. Finishing was then conducted between 1126 • C and 991 • C, so that the final thickness was 3.8 mm. The coiling temperature achieved was 516 • C. This hot rolling scheme is close to the TMCP-500 • C one.

The microstructure of the industrial plate was characterised by means of SEM and EBSD, as shown in Figure 9. It consists of a mixture of lath and granular bainite, together with some tempered martensite (Figure 9b,c). This can be explained by the presence of retained (untransformed) austenite during coiling at 516 • C, that subsequently transforms into martensite during cooling. Some large TiN (2-4 µm) were also observed, and homogeneously distributed in the microstructure (Figure 9a). The strength obtained (UTS = 830 MPa) is comparable to the one obtained for TMCP-500 • C pilot plant trial, but a better hole expansion ratio (HER = 70%) is obtained. This result confirms that an homogeneous microstructure enhances the HER properties. The higher HER can be explained by the fact that a lower yield strength of approximately 700 MPa was obtained, compared to 800 MPa for the pilot plant one.

Discussion

The steel composition studied in this work is particularly suitable for favoring bainite transformation. As demonstrated in part Section 2.3, bainitic microstructures were obtained for a wide range of cooling rates, even from deformed austenite. With cooling rates as low as 0.05 • C s -1 , a non-negligible fraction of austenite still transforms to granular bainite. The microstructures generated by pilot plant hot rolling trials also contain a very large proportion of bainite with, in the case TMCP schemes, small fractions of ferrite. The industrial production trial demonstrates the industrial feasibility of the steel design concept, even though the use of an industrial process induces significant changes in the final microstructure compared to pilot plant trials. In particular, the interpass times used during the industrial process are much shorter than those used in pilot plant trials. As a result, despite the high finishing rolling temperature used, austenite cannot be considered as fully recrystallized before accelerated cooling, consequently leading to an increased proportion of granular bainite in the final industrial steel microstructure. Moreover, due to the high finishing temperature, the short interpass time, the fast cooling, and the low coiling temperature chosen, the interphase precipitation is suppressed.

It was experimentally observed that microstructures consisting mainly of granular bainite led to lower hole expansion ratios than those mainly consisting of lath bainite. These observations are consistent with a recent study by Weißensteiner et al. [START_REF] Weißensteiner | Effect of Morphological Differences on the Cold Formability of an Isothermally Heat-Treated Advanced High-Strength Steel[END_REF] that reported that lath bainite microstructures exhibit higher tolerance against damage during the shearing of edges, and thus higher hole expansion ratios, than granular bainite ones. This may be due to the presence of large Martensite-Austenite (MA) islands in granular bainite (see Figure 10a). MA islands are formed during cooling to room temperature, it is composed of small martensite laths and small blocks of retained austenite. As MA islands and bainite present different levels of hardness, stress concentration at interface between MA islands and bainite can induce crack nucleation. Lath bainite microstructures do not contain these large MA islands, as illustrated in Figure 10b. Thus, the formation of granular bainite should be avoided in order to achieve better HER. Two recent studies [START_REF] Pathak | Damage evolution in complex-phase and dual-phase steels during edge stretching[END_REF][START_REF] Karjalainen | The Effect of Microstructure on the Sheared Edge Quality and Hole Expansion Ratio of Hot-Rolled 700 MPa Steel[END_REF] reported that large precipitates such as micrometric TiN or cementite can act as the primary source of void nucleation in complex phase steels, which deteriorates HER. Large TiN are also known to deteriorate the toughness [START_REF] Gladman | The Physical Metallurgy of Microalloyed Steels[END_REF]. The steel studied in this work contains a significant amount of micrometric TiN particles, an example of which is presented in Figure 9a. It is known that to avoid the formation of large TiN, the presence of TiN before solidification should be avoided by maintaining Ti and N contents below the solubility product of TiN at the solidus temperature [START_REF] Yan | Effect of TiN inclusions on the impact toughness of low-carbon microalloyed steels[END_REF]. Additionally, maintaining the Ti/N ratio below 3.42 reduces the coarsening rate of TiN during reheating [START_REF] Yan | Effect of TiN inclusions on the impact toughness of low-carbon microalloyed steels[END_REF][START_REF] Chapa | N Influence of Ti and Contents on Austenite Grain Control and Precipitate Size in Structural Steels[END_REF]. In this study, the Ti/N ratio was considerably higher (Ti/N = 20 for the industrial trial), which explains the presence of coarse TiN in the microstructure. It would be interesting to try designing complex phase steels presenting lower amount of Ti to avoid forming large TiN. It should have a limited impact on the mechanical properties, as the best compromise HER and YS was achieved for process conditions that do not allow the precipitation of Ti and Nb.

Conclusions

The design and development of a bainitic steel grade presenting a combination of strength and stretch-flangeability for automotive application is presented.

After selecting a reheating temperature, experimental stress-relaxation curves were used to plot Recrystallization-Precipitation-Time-Temperature (RPTT) diagrams, which were useful for the determination of the temperature of non-recrystallization (T NR ) for the studied composition. Then, dilatometry tests, performed to estimate the effect of cooling rates on phase transformations are presented.

Those preliminary investigations allowed the selection of different hot rolling strategies that were applied in a pilot plant. Those strategies differ by the finishing rolling and coiling temperatures chosen, which strongly modify the microstructure and properties achieved. The study reveals that the coiling temperature was one of the most important parameters to adjust.

The best compromise between strength and stretch-flangeability was obtained for homogeneous microstructures developed after coiling at 500 • C. The choice of a low coiling temperature made it possible to transform austenite into lath bainite, and obtain a high final strength. The finishing rolling temperature was set to perform the last deformation passes below T NR and thus induce austenite deformation prior to phase transformation. It is worth noting that, even with such low level of carbon, a remarkable combination of properties by processing optimization was achieved, with an UTS value of 830 MPa together with a hole expansion ratio of 70%.

Figure 1 .

 1 Figure 1. Schematic representation of the elaboration process of a bainitic steel sheet.

Figure 2 .

 2 Figure 2. Illustration of the stress relaxation curves obtained at (a) 1050 • C and (b) 950 • C for = 0.3 and ˙ = 0.1 s -1 .

Figure 3 .

 3 Figure 3. (a,b) Recrystallization-Precipitation-Time-Temperature (RPTT) diagram determined by stress relaxation method.

Figure 4 .Figure 5 .

 45 Figure 4. Thermal cycles applied and continuous cooling transformation diagrams with (a) undeformed austenite and (b) after austenite deformation at 950 • C with ε = 0.3 and ε =10 s -1 .

Figure 6 .

 6 Figure 6. Schematic hot rolling schemes performed on pilot plant : (a) Recrystallization-controlled rolling (RCR) and (b) Thermo-Mechanical Control Process (TMCP). For each hot deformation scheme, two different coiling temperatures of 500 and 650 • C were applied, giving a total of four different hot rolling strategies.

Figure 7 .

 7 Figure 7. Microstructures of (a) RCR-650 • C, (b) TMCP-650 • C, (c) RCR-500 • C, and (d) TMCP-500 • C characterized by SEM and EBSD. Grain boundary maps showing grain boundaries between 4 • and 15 • in red and above 15 • in black are displayed.

Figure 8 .

 8 Figure 8. Mechanical properties of pilot plant hot-rolled plates, measured along the rolling direction. (a) Yield and ultimate tensile strengths. (b) Ductility properties : Total and uniform elongation determined by tensile tests, and hole expansion ratios.

Figure 9 .

 9 Figure 9. Microstructure of the industrial plate observed by SEM (a-c) and corresponding EBSD grain boundary map (d), consisting of a mixture of lath and granular bainite. Panel (e) shows the resulting tensile and hole expansion properties of this industrial plate.

Figure 10 .

 10 Figure 10. SEM observations of the microstructures of (a) RCR-650 • C and (b) RCR-500 • C hot-rolled plates. Nital etching.

Table 1 .

 1 Bulk composition of the steel used for preliminary investigations (Lab scale), for pilot plant trials, and for industrial trials, determined by ICP-MS.

	Element (wt%)	C	Mn	Si	Ti	Nb	V	Mo	Al	Cr	N
	Target	0.06	1.9	0.5	0.1	0.04	0	0.2	0.05	0	0.005
	Lab-scale	0.062 1.91 0.50 0.085 0.039	0.002	0.212 0.065 0.013	0.006
	Pilot Plant trials 0.062 1.90 0.50 0.097 0.041 <0.001 0.208 0.053 0.093 0.0039
	Industrial slabs 0.061 1.91 0.50	0.1	0.040	0.008	0.191 0.067 0.034	0.005

Acknowledgments:

The authors gratefully acknowledge Florian Mercier (INSA Lyon) for his help and expertise with the Gleeble tests.

Funding:

The authors gratefully acknowledge the funding received from the European Commission, Research Fund for Coal and Steel, under grant agreement 709803 (NANOFORM).

Conflicts of Interest:

The authors declare no conflict of interest.


Anne L'hôte

Eric Jeangirard

Using Elasticsearch for entity recognition in affiliation disambiguation

Keywords: Elasticsearch, affiliation disambiguation, entity recognition, open science

Automatic recognition of affiliations in the metadata of scholarly publications is a key point for monitoring and analyzing trends in scientific production, especially in an open science context. We propose an automatic alignment method on registries, based on Elasticsearch. The proposed method is modular and leaves the choice of the alignment criteria to the user, allowing him to keep control over the precision and recall of the method. An implementation is proposed for an automatic alignment on three registries: countries, GRID.ac and RNSR (research laboratory directory in France) on the Github https://github.com/dataesr/matcher and the performances are analyzed in this paper.

Introduction

The precise identification of the affiliations found in the bibliographic databases is a crucial point in various aspects and in particular to follow the production of one or a group of laboratories or institutions, and thus be able to observe trends related to publications at the institutional level.

Unfortunately, this exercise remains a complex task, giving part of the value of commercial bibliographic databases. Nevertheless, [START_REF] Donner | Comparing Institutional-Level Bibliometric Research Performance Indicator Values Based on Different Affiliation Disambiguation Systems[END_REF] have shown that relying solely on commercial databases is insufficient for any use with policy implications and that a specific cleanup effort is needed. Some techniques have been proposed, based on supervised or semi-supervised approaches with clustering [START_REF] Cuxac | Efficient Supervised and Semi-Supervised Approaches for Affiliations Disambiguation[END_REF]. However, there are few, if any, labeled databases with an open license. These difficulties have led us, for the French Open Science Monitoring [START_REF] Jeangirard | Monitoring Open Access at a National Level: French Case Study[END_REF], to build our own methodology to detect publications with French affiliations.

1

This document aims at detailing a new methodology for linking affiliations to entities listed in international or national registries, in particular:

• Country list • GRID ("GRID, Global Research Identifier Database" 2021)

• RoR ("RoR, Research Organization Registry" 2021) • RNSR in France ("RNSR, Répertoire National Des Structures de Recherche" 2021)

• Sirene in France ("Sirene, Système National d'identification et Du Répertoire Des Entreprises et de Leurs établissements" 2021)

We propose a new approach, using the Elasticsearch search engine, based only on open data. This approach is built to be modular and easily adaptable to other international or local registries.

Method

Our matching framework

The problem we are looking for can be summarized as follows: let q be a string, describing an affiliation, and let be a set C { (condition_i, value_i ) } (potentially empty) of additional conditions, giving structured information about the affiliation described by query. To fix the ideas, we can sometimes have extra informations, like the country of the affiliation, or the name of a supervisor. These informations should help the matcher to narrow down the possibilities. For example, in the case in which we know in advance the affiliation is in France, the set C will contain an element like (country, F rance).

On the other hand, let R be a registry of entities (laboratories, institutions, even countries, cities etc). R is a set of objects with characteristics, such as, for example, in the case of a laboratory, one, or more name, acronym, address, supervisor, etc. The problem of affiliation recognition is to find the (potentially empty) set of elements of R that correspond to the query q and the conditions C.

Let's give an example. With q="French Ministry of Higher Education, Research and Innovation, Paris, France", and no condition set, using the the GRID repository, the expected result is https://grid.ac/institutes/grid.425729.f. This task seems relatively simple to the human mind, but it is actually not so simple to automate. Rather than using a black-box technique, we propose a simple and modular approach where the user of the algorithm can keep control over the risk of error.

There are two types of errors in reality, precision (the proportion of false positives, i.e. how many times the algorithm gives a result that is a wrong match), and recall (the proportion of false negatives, i.e. how many times the algorithm does not give a match when a good one does exist).

Let us now introduce two concepts: criterion and strategy.

A criterion is a metadata describing the elements of the registry R (basically a field in the database). For example the entity name or the city is a criterion for the GRID registry. That is to say that this repository contains information about the names and cities of the entities that are in the registry. To take the previous example, the entity grid.425729.f has the following grid_country, grid_name and grid_city criteria (values of these criteria in the GRID registry):

• grid_city :

-Paris • grid_country :

-France • grid_name :

-Ministry of Higher Education and Research -Ministère de l'Enseignement Supérieur et de la Recherche -Ministeri d'Educació Superior i Recerca francès

A strategy is a combination of one or multiple criterion. Thus, applying the strategy ['grid_city', 'grid_country', 'grid_name'], consists in returning all the elements of the registry R for which there is, at the same time, a match on the name, on the city and on the country with respect to the query received in input q and C. Using the same example, a single match is appropriate, giving the expected result:

Criteria and strategies

Direct criteria

Depending on the registry R and the nature of the registered objects, many criteria are possible. For example, a country repository could contain criteria like:

• the official name and the usual name of the country in different languages and their possible abbreviations (iso 3166 alpha-2, iso 3166 alpha-3) • its subdivisions (regions, provinces. . . ) • its cities • its street names, etc • its institutions, universities, hospitals, etc • its rivers, mountains, etc • its Point of Interests All of these are direct criteria, meaning they are direct characteristics that can be found as such in an affiliation text. For a research unit, think about an affiliation like "Institut des Géosciences de l'Environnement CNRS Saint Martin d'Hères". That string is actually a concatenation of:

• the research unit name: ""Institut des Géosciences de l'Environnement"

• the acronym of one the supervisors of the unit : "CNRS"

• the city of the unit : "Saint Martin d'Hères" As explained above, the strategy combining the 3 criteria: name, supervisor acronym and city will match the correct entry in the RNSR registry.

Indirect criteria

In some cases, direct criteria such as these may be insufficient. Think about the example above, but with a slight modification : "Institut des Géosciences de l'Environnement CNRS Grenoble". Saint Martin d'Hères and Grenoble are two neighboring municipalities. Grenoble being much larger is sometimes used in the affiliation signature, even though the official address of the unit is with Saint Martin d'Hères. In that case, the above strategy combining name, supervisor acronym and city will give no match. A workaround is to use an indirect criterion, based on geographic proximity or influence. That could be a criteria like 'all cities within a radius of x kilometers'. Better, for France, INSEE has developed in the COG (French Official Geographic Code) ("Code Officiel Géographique (COG)" 2021) with several divisions, such as urban unit or employment zones (an employment zone is a geographic area within which most people reside and work). In itself, an employment zone has an identifier, but it is actually a list of all the cities that belong to the employment zone. That way, we can affect a criterion with the employment zone identifier to all the cities that belong to this employment zone. The employment zone identifier itself will generally not appear in the affiliation description, but still can be used as an (indirect) criterion.

If we take back the example above, during indexing, "Saint Martin d'Hères" will be catched as being part of employment zone 8409. At search time, with the query "Institut des Géosciences de l'Environnement CNRS Grenoble", "Grenoble" will also be catched with the criteria employment zone 8409, and so the strategy combining name, supervisor acronym and employment zone will return the correct match from the registry.

Strategies

The possible strategies are simply all the combinations of the criteria. A risk level can be associated to each strategy, depending on the risk of false positives.

A strategy combining many criteria will give a high precision but a low recall.

Thus, in the case of a country matcher, the strategy composed of the only criterion 'name of the country' can be risky. For example, for an affiliation like "Hotel Dieu de France, Beirut, Lebanon", this strategy would propose two matchings: France and Lebanon. In this case, France is a false positive. A more demanding strategy, searching for both the country name and a city, can avoid this pitfall in this case.

We therefore propose to test several strategies, more or less demanding, starting with the safest (in terms of risk of false positives). That way, the user of the matching algorithm keeps the control on the risks it accepts, choosing himself the balance between precision and recall through the choice of the strategies that can be used.

Filtering sub-matching results

Some fine-tuning can be applied to the results. The main one we developed is a post-filtering to remove sub-matching results. Let us give an example to show what a sub-matching result is. Think about an input affiliation description like "Columbia University Medical Center, New York, USA". The strategy combining name, city and country for the GRID registry naturally matches two entries : For each criterion, the second result (grid.21729.3f) has either the same match as the first result or a match that is contained in the first result match for the same criteria. Namely, "Columbia University" is contained in "Columbia University Medical Center" for the name criterion, and the other matches ("New York" for the city criterion and "USA" for the country criterion are the same. The second result is then a sub-match compared to the first result, and can be filtered.

Strategy groups

As explained above, different strategies should be tested, from the most demanding (meaning with many matching criteria) to the least demanding (few matching criteria). If a strategy give one or more result, the loop over the strategies can be stopped. However, it does not always make sense to have a strict order between the strategies. That would have no impact if only one registry entry (at most) could be matched, but, in some cases, the affiliation signature in input should be matched with multiple registry entries. In that case, stopping at the first result of the most demanding strategy may impact the recall, especially if all the entries to be matched are not described with the same amount of details in the affiliation signature. So, instead of having an ordered list of strategies, we implemented an ordered list of strategy groups. A strategy group is itself a set of strategies, all the strategies within the group being tested for the matching.

Implementation with Elasticsearch

Elasticsearch is a very powerful and modular search engine technology. We used the 7.8.0 Elasticsearch version, with the analysis-icu plugin. The implementation of our method is done in two main steps:

• index construction: loading the criteria, each corresponding to an index in Elasticsearch • search: the actual matching, by applying a list of strategy groups.

The choice of strategies to apply is made at the matching level and not at the loading level. The user of the matcher can therefore control himself his level of risk of false positives (or in other words his precision / recall balance).

The matching leverage on the diversity of features offered by Elasticsearch, in particular queries of type

• match_phrase (all terms, consecutively and in the same order) for short criteria where we want an exact match (like city names, or acronyms). • match with a minimum_should_match parameter. For example, with a minimum_should_match at -20%, meaning that at most 20% (rounded down) of the terms can be missing, the order and the consecutive character not being taken into account : for longer criteria like the names of laboratories or supervisors.

Percolation in Elasticsearch

One feature of Elasticsearch that is critical for the implementation of our matching method is percolation. Usually, Elasticsearch allows to store documents in an index, and then to perform a query on this index. A typical example would be to perform a search query "InstitutionXYZ" against an indexed containing documents like "InstitutenXYZ Paris France". The searched term is actually contained in some of the indexed documents, that are then retrieved by Elasticsearch, with a computed score. However, in our use case, we face queries that look like "Hotel Dieu de France Beirut Lebanon". With the regular Elasticsearch behaviour, the document "Hotel Dieu de France" is matched, but the document "CHU Fort de France" is also retrieved, because all of them have in common the token 'France'. One could try to get around this issue using the Elasticsearch computed score, but it can quickly become cumbersome.

Actually, the desired behaviour is to reverse the role of the search query and the indexed document. Percolation allows us to do this, i.e. to store queries in an index, and then to search for a document in this index. With percolation, "Hotel Dieu de France Beirut Lebanon" will match "Hotel Dieu de France" but not "CHU Fort de France".

All other implementation details can be read directly in the open source code made available.

Elasticsearch index building

The first step of the matching algorithm is a one-shot process (to be done once), building all the indexes in Elasticsearch, each index corresponding to the criteria that will be used during the second step (the matching itself).

Each index is built using a datasource, namely:

• pycountry python module ("Pycountry" 2021) for country iso-codes, name and subdivisions

• GRID for country name and code, cities, and institutions names / acronyms

• RNSR for French research units names, acronyms, codes, supervisors and cities / employment zone A document in a given index encapsulates two elements :

• 1. a matching query (using percolation) for the criterion (with the Elasticsearch match or match_phrase)

• 2. a list of matching entries from the source registry.

For example, in the matcher_grid_acronym index, the indexed document corresponding to the acronym "IUN" looks like the following: { "_index": "matcher_grid_acronym", ... "_source": { "ids": [ "grid.257418.d", "grid.489012.6" ], "query": { "match_phrase": { "content": { "query": "IUN", "analyzer": "acronym_analyzer", } } } } }

In particular, we observe two entries in the GRID registry share the same acronym "IUN". Overall, the count of elements in each index is in the next

Elasticsearch matching

The matching implementation itself is rather straightforward and relies and the Elasticsearch percolate queries.

Evaluation

For a given repository R, we fix the strategies to apply, allowing us to set up an automatic matching. We will apply this method in the following section for 3 types of matcher: at the country level, for the GRID registry and for the French laboratory repository RNSR.

Results

Gold standard

In order to test our methodology and our strategies, we use a set of 4,705 data. The set of data and the affiliation of each data is collected from the Pubmed API. Each data has 5 attributes : the affiliation name itself and RNSR, siren, grid, country. The affiliation name is a string but it can contain multiple affiliations.

The other attributes (rnsr, siren, grid and country) are manually collected. This dataset let us compute the precision and recall of each matcher by measuring the difference between the expected result and the computed one.

Current matchers results

For the country matcher, we used multiple strategies, combining:

• institution name (from GRID)

• institution acronym (from GRID)

• city name (from GRID)

• country name (from pycountry)

• country iso-code (from pycountry)

• country subdivisions (from pycountry)

For the RNSR matcher, the tested strategies combines the following criteria (all coming from RNSR):

• code number

Discussion and conclusion

Findings

The first take-away of this work is that Elasticsearch is a great tool not only for search (of course) but also for matching purposes. A lot of text treatment features are already in place (there are plenty of built-in tokenizers and analyzers) and the percolate queries fit well the matching use case. On top of that, the highlights features (that highlight the matching terms in the input context) are really useful.

Besides, it is also clear that the quality of the matching result really depend on the affiliation signature fed as input into the matcher: is there enough information ? but not too much noise ? That is why we thina matcher should be able to adapt to different situations and that we implemened a modular approach where the strategies and the underlying criteria can be chosen at the search time without having to re-initialze all the indexes.

The result we get for country matcher and the RNSR registry, on the corpus we tested are very promising.

Limitations and future research

The first limitation is that this matcher, and in particular the chosen criteria and strategies should be tested against more data. That would probably highlights new issues to solve. We also plan to develop more matchers for the international registry ROR and the French registry Sirene.

•

  'grid_city': ['Ministry of Higher Education, Research and Innovation, Paris, France'] • 'grid_country': ['Higher Education, Research and Innovation, Paris, France'] • 'grid_name': ['French Ministry of Higher Education, Research and Innovation, Paris, France']

  On the gold standard dataset we compiled, the results (precision and recall) are detailed for 3 matchers (country, RNSR and GRID) in the next table:

	• name
	• acronym
	• city
	• employment zone (deducted from the city)
	• supervisor name
	• supervisor acronym
	And for the GRID matcher, the criteria used are (all coming from GRID):
	• name
	• acronym
	• country
	• country code
	• city
	matcher precision recall
	country 0.999	0.97
	RNSR	0.987	0.757
	GRID	0.773	0.678

Software and code availability

The source code is released under an MIT license in the GitHub repository https://github.com/dataesr/matcher.

Data availability

The gold standard dataset we have compiled is available here.


Alexander Dahlström
email: adahlstr@kth.se

Frederic Danoix

Peter Hedström

Joakim Odqvist

Helena Zapolsky

Nanostructure in Fe0.65Cr0.35 close to the upper limit of the miscibility gap

Keywords:

The nanostructure of an Fe0.65Cr0.35 alloy has been investigated by atom probe tomography after highprecision thermal treatments close to the upper limit of the miscibility gap (MG). It is found that the wavelength of the decomposed ferrite between Cr-and Fe-rich regions grows exponentially when approaching the upper limit of the MG. Furthermore, the nanostructure change is gradual with temperature indicating a narrow metastable region and a diffuse transition out of the spinodal regime. Atomistic modelling near the limit of instability further supports the experimental observations. The findings are discussed in relation to the Cahn-Hilliard theory.

Stainless steels are versatile alloys used in, for example, energy industry [1 , 2] . Their attractive properties include a combination of high strength and excellent resistance towards corrosion. FeCr is the base alloy system for stainless steels, where Cr contributes to the "stainlessness". However, demixing of Fe and Cr is known to cause significant degradation of the toughness [3][4][START_REF] Pineau | Duplex Stainless Steels[END_REF] . This is a potential issue for all FeCr based alloys that contain either the BCC or the BCT phase. Hence, phase separation when α decompose into α (Fe-rich) + α (Cr-rich) is important to consider in technical applications [START_REF] Capdevila | [END_REF][7][8][9] . The mechanism through which phase separation occurs is, at an early kinetic stage, either nucleation and growth (NG) or spinodal decomposition (SD). Whereas the later stage of kinetics in both cases can be described by coarsening theory [10] . The limit of the unstable spinodal regime is often defined by the concentration ( C ) dependant Gibbs energy ( G ) locus at: ∂ 2 G/∂ C 2 = 0 . However, it is known from experiments that a gradual transition zone may better describe the spinodal limit [11 , 12] . This aspect has also been treated theoretically [13 , 14] . The Cahn-Hilliard (CH) equation is frequently used to model SD in FeCr by the temporal evolution of Cr compositional fluctuations [3 , 15-17] . In the FeCr case, the CH equation can be described by G and a gradient energy term ( K ), i.e. neglecting the α/ α coherency strain. The maximum amplification factor in the CH theory relates to the maximum velocity wavelength ( λ m ) of the developing structure. λ m can be related to the critical wavelength ( λ c ) by λ m = √ 2 λ c , where the critical wavelength is given by [18] . In the early stages of phase separation before α/ α equilibrium volume fraction has been established α coarsening is here neglected. It is also assumed in this work that the measured mean wavelength, λ, in the early stages has been developed at maximum velocity (i.e. λ m ). When the spinodal limit is approached, the wavelength λ c is predicted to go towards infinity because ∂ 2 G / ∂C 2 → 0 [19] . Therefore, λ c of SD varies across the MG depending on ∂ 2 G / ∂C 2 [11] . However, it is cumbersome to accurately model SD and its periodic length-scale in the FeCr system using CH, in part due to the complexity of the concentration dependant gradient energy term K [20 , 21] and the effect of the initial nanostructure on the kinetics of SD [22 , 23] . To further explore the varying nanostructure at different tem peratures within the MG we here study the nanostructural changes as the critical upper temperature limit ( T c ) of the MG is approached in an Fe 0.65 Cr 0.35 alloy. The experiments are conducted by highly precise thermal treatments and atom probe tomography (APT) analyses. To supplement the experimental observations Khachaturyan's atomic density function theory is used [START_REF] Khachaturyan | Theory of Structural Transformations in Solids[END_REF] . Based on this theory, the temporal evolution of the system is modelled through minimisation of the free energy given by the difference in chemical potential without explicitly stating K in the energy function.

λ c = 2 K/ ( -∂ 2 G/∂ C 2 )
The Fe 0.65 Cr 0.35 alloy was supplied by the company OCAS N.V. with the realised composition Fe-34.61Cr-0.04Al-0.0016C in at %.

Table 1

The HV (i.e. HV change after ageing relative to the solution treated state), variation V, and wavelength λ (from APT) all after 120 hrs of ageing.

Temperature HV V λ[nm]

as-quenched 0.0 ± 3. The following solution treatment of 0.3 ×10 ×15 mm sheets was conducted: 2 h at 1100 °C before water quenching and subsequent thermal ageing in a JOFRA 601 calibration furnace, with a temperature accuracy of ±0.9 °C. APT needles were prepared using the classical two-step electro-polishing method using a microloop [START_REF] Miller | Atom-Probe Tomography[END_REF] . A local electrode APT system LEAP 40 0 0HR from CAME-CA® was used, with the operating parameters: 50 K, pulse fraction 20% and detection rate 0.2%. The reconstruction parameters were optimised in IVAS 3.6.8 using spatial distribution maps [26 , 27] .

The LEAP system allows for a large field-of-view which means a higher probability of detecting crystallographic features such as the < 011 > -Fe pole with low impact density [28] . Using such crystallographic features the interatomic plane distance was corrected in accordance with the reconstruction procedure as suggested by Moody et al. [START_REF] Moody | [END_REF] . Quantification of the mean wavelength was based on autocorrelation function along the analysis axis for optimal resolution. The autocorrelation analysis in this work allowed for a maximum λ of 120 nm. Statistical frequency distribution (Freq. Dist.) analyses were performed in representative volumes of ~1million ions excluding the low index pole regions, as in Moody et al. [29] . In this work, the Freq.Dist. bin volume was 50 ions collected at a detection efficiency of 36%. In addition, the variation parameter (V) defined by Blavette et al. [30] utilising Freq.Dist. was used to quantify the extent of demixing based on relative Cr amplitudes.

The results from Vickers micro-hardness (HV 0.2 ) measurements of these samples are presented in Table 1 . 15 measurements were conducted in accordance with the ISO 6507-1 standard. The reported value is the mean out of 11 measurements after excluding the four extreme values, the uncertainty is given by the standard deviation. The samples were aged 120 h at temperatures from 550 °C and higher. The 120 h was selected after prior kinetic HV investigation at 525 °C that showed a steady HV evolution after 120 h [START_REF] Dahlström | Influence of a Mechanical Load on the Ageing of Fe-Cr Alloys Ph[END_REF] .

Table 1 shows larger HV at lower temperatures, i.e. at greater driving force by deeper undercooling from the limit of the MG which favour SD. It should be noted that HV is known to be related to the amplitude of Cr fluctuations in the sample through V [START_REF] Danoix | [END_REF] . In the range 563-568 °C, HV is lower but fairly constant, while at higher temperatures HV is negative. The negative values may be an effect of some recovery of the alloys. Based on these hardness results, samples aged at 550, 560, 563, 568 and 570 °C were selected for further APT analyses. APT 2D Cr composition cross sections obtained with the gpm3Dsoft software developed at the University of Rouen, are displayed in Fig. 1 [START_REF] Lefebvre-Ulrikson | Atom Probe Tomography Put Theory Into Practice[END_REF] .

Considering the minor temperature difference (i.e. negligible effects on Cr diffusion), the evolution of nanostructure is most likely a thermodynamic effect of approaching the spinodal and/or the limit of the MG. Since the driving force of α formation should decrease at higher temperature, this can be seen quantitatively by the decrease of V. The Cr composition distribution maps are shown in volumes of 10 ×30 ×90 nm, for direct visual comparison of λ. Furthermore, the influence of temperature on nanostructure can be observed in 3D by evaluating α/ α Cr composition fluctuations based on proxigrams in the normal direction of the nominal composition iso -surface [START_REF] Hellman | [END_REF] . An interconnected SD structure associated with Fe/Cr phase separation can easily be detected at 560 °C, 563 °C and 568 °C. But there is no interconnected SD structure nor α precipitates at 570 °C. Nevertheless, there exist small Cr fluctuations around the nominal composition which are quantitatively significant relative to the as-quenched state (i.e. V = 0.19 versus V = 0.02 in Table 1 ). For the Fe 0.65 Cr 0.35 alloys no distinction could be made between the metastable binodal and the unstable spinodal regimes within the MG. This supports the view of a very narrow metastable region near T c (if it exists), and consequently the transition zone over T c appears "diffuse". It should be emphasised that whether the spinodal curve coexists with the limits of the MG at Fe 0.65 Cr 0.35 is not concluded here. The abrupt change in morphology is thus an effect of driving force and hence indicative of approaching the MG limit. The result is shown in Fig. 3 and presented in Table 1 .

To supplement the experimental results, atomistic modelling was performed using a quasiparticle approach proposed by Lavrskyi et al. [36] , which is based on Khachaturyan's theory [START_REF] Khachaturyan | Theory of Structural Transformations in Solids[END_REF] . In the quasiparticle approach, the size of the simulation grid is smaller than the interatomic distance. Thus, atoms will occupy a spherical volume containing some number of simulation grid points. Hence, simulation grid points inside of atomic spheres are regarded as atomic fragments and referred to as Fratons. The main variable of the simulation is the occupation probability function ρ A ( r ) which is the probability that a Fraton of the sort A, situated at point r , is inside of any atomic sphere at moment t . The proper choice of a model Hamiltonian requires describing the interaction of Fratons that should result in both their "condensation" into atomic spheres and the movement of the spheres into the desired atomic equilibrium configuration, all driven by the spontaneous minimisation of the free energy. The model potential of this Hamiltonian contains short-range and long-range interactions. The short-range interaction is chosen as a step function where the negative part defines the atomic radius, and the positive part assures the repulsion of atomic spheres at short distance. For the BCC structure, the long-range AA and BB Fraton interactions are fitted by a one mode potential chosen as a Gaussian function with the minima centred at the first neighbour distance of the BCC lattice. The width of the Gaussian functions defines the elastic properties of the system, and in this case, the BCC-Fe elastic constants were fitted to the DFT calculations by Mendelev et al. [35] . The Helmholtz energy of the system F = U -TS is written in mean-field approximation, where the first term describes the internal energy of the system and the second term is related to entropy. The temporal evolution of the density function of Fratons ρ A ( r ) can be written using the kinetic Landau-Khalatnikov equation [START_REF] Dahlström | Influence of a Mechanical Load on the Ageing of Fe-Cr Alloys Ph[END_REF] governed by the minimisation of Helmoltz energy:

d ρ A ( r , t ) dt = r B = m B =1 L AB ( r -r ) k B T δF δρ B ( r , t )
Where, m is the number of components, k B is the Boltzmann constant, T is temperature and L AB ( r ) is a matrix of kinetic coefficients related to the probabilities of elemental diffusional jumps from lattice site r to r on a Bravais lattice during a time unit. The ρ A ( r ) is a conserved variable and in the case of a binary system to describe the atomic configuration only one ρ A ( r ) function is needed. In this work, we simulate the BCC-Fe equilibrium structure (i.e. ρA ) and then introduce a second substitutional component ρB . To describe phase separation kinetics, the long-range AB potential is chosen as a Gaussian function centred at k = 0 :

V AB = -μ • exp ( -k 2 / 2 σ 2 ) .
Here, a dimension coefficient μ defines the strength of the interaction A / B . Thus, μ impacts the driving force of separation kinetics, and, consequently, the simulation time to observe the wavelength λ. In this work, a good compromise between simulation and real-time was found with μ= 0.08, SD has been modelled by quasiparticles using the same reduced system variables as by Lavrskyi et al. [36] . Spinodal decomposition is simulated as isothermal "ageing" below the spinodal line with an initially homogeneous but disordered solid solution. The driving force of phase separation, i.e. temperature is adjusted by the negative depth of the long-range potential. Thus, zero driving force (i.e. ∂ 2 G/∂ C 2 = 0) is set as equivalent to T c to serve as a reference point for the experimental comparison [31 , 36] .The as-quenched state of the system is determined by an initial condition:

ρ i ( r, t = 0 ) = ρi + δρ i (r) ( i = A or B)
where ρi is the average density of the component i and δρ i ( r ) are small perturbations generated by a random number generator. To perform the simulations a semi-implicit Fourier spectral method was used to solve the kinetic equation in reciprocal space [37] . Thus, the matrix of kinetic coefficients in reciprocal space can be written as: L AB (k ) = -L 0 AB k 2 where L 0 AB is the jump probability between A and B Fratons at nearest-neighbour sites at a time unit. In particular, we chose L 0 AA = L 0 BB = 1 and L 0 BA = L 0 AB = -0 . 5 . Fig. 2 shows the simulated microstructure of the A-35B alloy at time t * = 2 ·10 6 , aged at different temperatures. In our simulations, the critical temperature of instability was defined as the limit observed in the experiments as T c . Hence, at temperatures T / T c < 1 the decomposed microstructure is observed.

To evaluate the spinodal structure from modelling results at different tem peratures, the structure factor S ( k ) was calculated directly from the atomic distributions in reciprocal space. The evolution of the calculated S ( k ) as a function of temperature is presented in Fig. 3 b). In the simulations S ( k ) decrease rapidly approaching the limit of instability, as S ( k ) is calculated in reciprocal space, the inverse trend is true for λ in real space. Thus, this trend agrees well with our APT observations. Our experiments and simulations suggest a rapid increase of λ as T c and the spinodal is approached. The decrease in the extent of Cr compositional fluctuations given by V suggests that there is no distinct difference in mechanism of phase separation and that the spinodal limit is close to the limit of the MG. However, quantitatively at 570 °C, the Fe-35Cr sample is far from homogeneous. Short-range clustering due to the high Cr-Cr affinity has previously been seen to be temperature-dependant even at high temperature in Fe-Cr [23] , with increasing intensity closer to the limit of the MG [22] .

The point to highlight from the APT analyses in Fig. 3 a) is that even though it is not possible to measure a characteristic wavelength at 570 °C, the decreasing trend of the V parameter continues. However, the value V = 0.19 obtained at 570 °C is almost 10 times greater than in the solution treated state (see Table 1 ). This might be a short-range clustering effect due to the proximity to the MG. It is possible to observe an exponential increase of λ in FeCr when the driving force goes towards zero, this rapid evolution of the structure is in agreement with CH, but it should be kept in mind that the theory only considers SD. In this work, the rapidly increasing trend starts very close to the suggested T c at approximately T / T c = 0.98 (i.e. ~560 °C), which is why the high precision thermal treatments have been key to this study.

The periodicity of the spinodal structure is highly temperaturedependant within the MG, where λ classically decreases linearly with increasing driving force [13] . Prior works have questioned the formation of a λ c near the spinodal curve, and thus the existence of an exact boundary near the instability locus [11 , 14] . Furthermore, the SD regime is more accurately defined as a region where the activation energy for phase separation becomes smaller than for thermal fluctuations [11] . Cr-Cr clustering may also exist to quantifiable extent due to short-range order effects outside of the MG in α without forming α [38] . Considering low temperature composition dependant transition from SD to NG, a percolated α structure makes discrimination between NG/SD experimentally cumbersome [39] . In addition during long-term heat treatment, linear approximation is generally deemed non-sufficient to describe later stages of low-temperature phase separation [40] . Instead, the LBM method which considers nonlinear diffusion is often used to describe the later stages of SD near-equilibrium [41] . This is all in support of a gradual/diffuse transition out of the SD regime where we can experimentally measure an exponential increase of λ in the range 0.98-0.998 T / T c (i.e. up until 1 °C below T c ). In summary, these direct observations of the λ evolution close to the limit of the Fe-35Cr MG in 3D by APT, confirmed by simulation results, are novel of their kind. Considering the incremental temperature differences, this effect is most likely due to the difference in driving force when undercooling below the limit of the MG.

Fig. 1 .Fig. 2 .

 12 Fig. 1. APT results of the nanostructure at increasing temperatures close to the limit of the MG, 2D Cr composition maps from 10 ×30 ×90 nm, wavelengths from autocorrelation. 1.) 560 °C, λ = 11 nm, 2.) 563 °C, λ = 12 nm, 3.) 568 °C, λ = 20 nm, 4.) 570 °C no λ can be evaluated. The suggested limit of the MG (i.e. T c ) lies in-between 3. and 4. indicated by the dotted red line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig.3. a) The V-parameter from APT Freq.Dist analysis and λ from autocorrelation. When T c is approached λ increase exponentially, the opposite trend is observed for V. b)The maximum of the calculated structure factor S ( k ) from simulation results showing a rapid decrease in reciprocal space.

Acknowledgement

The financial support from Centre National de la Recherche Scientifique (CNRS), Region-Normandie and Carl Tryggers Research Foundation is gratefully acknowledged. Supercomputing capability at Centre Régional Informatique et d'Applications Numériques de Normandie (CRIANN) is also acknowledged. This work was partly carried out owing to the experimental GENESIS platform. GENESIS is supported by the region Haute Normandie, the Metropole Rouen Normandie, the CNRS via LABEX EMC and the French National Research Agency as part of the program "Investissement d'avenir" ARN-11-EQPX-0020 .

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.