Y El Khessaimi

Y El Hafiane

A Smith

Effect of fineness and citric acid addition on the hydration of ye'elimite

Keywords: Ye'elimite, Fineness, Citric acid, Ettringite, Monosulfoaluminate, Gibssite, Hydration, CSA cement. Highlights

The first purpose of this article is to investigate the effect of fineness on the hydration of highly pure ye'elimite powders prepared by solid state reaction or by a chemical route. The second purpose is to examine the role of fineness on the hydration of model calcium sulfoaluminate cements (CSA) prepared by mixing our lab-made ye'elimite with gypsum. The last part concerns the effect of citric acid addition on hydration of a model cement. The main results are the following: (i) ettringite and hydrates formation can be accelerated by the presence of very fine ye'elimite powder in a CSA cement paste; (ii) the hydration rate of CSA model cement depends mainly on the dissolution rate of ye'elimite which can be delayed by the addition of citric acid in water; (iii) the surface of ye'elimite grains presents scarce etch pits when citric acid is present in the water, while the surface seems to be totally attacked with water.

Introduction

For their shrinkage compensation and self-stressing properties, Calcium Sulfoaluminate Cements (CSA) have been developed and produced in China since the last forty years [START_REF] Glasser | High-performance cement matrices based on calcium sulfoaluminatebelite compositions[END_REF]. More recently, the interest of the international cement research community towards these cements comes not only from their expansive behaviour [START_REF] Trauchessec | Hydration of ordinary Portland cement and calcium sulfoaluminate cement blends[END_REF], but also from their environmentally friendly characteristics associated to their production, which includes a reduced CO2 footprint. However, many barriers prevent more widespread usage of this material. Despite having been used in construction for many years [START_REF] Juenger | Advances in alternative cementitious binders[END_REF] relatively little is known about effective mixture design methodology for using CSA cement in concrete infrastructure. In the absence of formalized design guidance, CSA cements are most commonly used in small-scale repairs, where their ability to set rapidly can be advantageous and long working times are not necessary. For larger scale placements, retardation of the CSA reactions is necessary, and citric acid is currently the primary set retarding carboxylic acid recommended for use with CSA cements. However, the mechanism by which citric acid solutions modify the hydration of CSA cements is still not fully understood. Effect of citric acid addition on CSA cement hydration has been well recognized, and studied by several researchers, most of the studies were either based on qualitative description of hydration curves or parameters that indirectly refer to hydration, such as set time and strength [START_REF] Burris | Influence of set retarding admixtures on calcium sulfoaluminate cement hydration and property development[END_REF][START_REF] Tinnea | Influence of Citric Acid on Reactions in the System 3CaO•Al2O3-CaSO4•2H2O-CaO-H2O[END_REF][START_REF] Winnefeld | Influence of citric acid on the hydration kinetics of calcium sulfoaluminate cement[END_REF][START_REF] Zajac | Effect of retarders on the early hydration of calcium-sulpho-aluminate (CSA) type cements[END_REF]. Organic compounds like sugars or citric, tartaric or gluconic acids and their salts are powerful retarders in CSA cements [START_REF] Zajac | Effect of retarders on the early hydration of calcium-sulpho-aluminate (CSA) type cements[END_REF]. Citrate and tartrate ions are chelating agents of Ca 2+ and Al 3+ and would be expected to influence the nucleation and growth of phases containing these ions [START_REF] Cody | The effects of chemical environment on the nucleation, growth, and stability of ettringite [Ca3Al (OH) 6] 2 (SO4) 3• 26H2O[END_REF]. Most carboxylic acids have no effect on the morphology of ettringite crystals. This probably results from the fact that the calcium ions of the crystals are buried in a sheet of negatively charged hydroxyl and water molecules and the negatively charged carboxylate groups are repelled by the negatively charged crystals [START_REF] Cody | The effects of chemical environment on the nucleation, growth, and stability of ettringite [Ca3Al (OH) 6] 2 (SO4) 3• 26H2O[END_REF]. The mechanism through which citric acid influences the hydration kinetics of the CSA systems is not fully understood. However, researchers have found that citrate will form chelates with calcium on the surface of a cement, thus hindering cement dissolution, in addition to forming chelates with calcium ions already in solution and reducing their availability for participation in hydration reactions [START_REF] Prisciandaro | The retarding effect of citric acid on calcium sulfate nucleation kinetics[END_REF]. Another inorganic retarder acid applied for CSA-type cements is boric acid, it inhibits the nucleation of ettringite, but instead it allows six-sided plates of the metastable monosulfoaluminate phase to form [START_REF] Cody | The effects of chemical environment on the nucleation, growth, and stability of ettringite [Ca3Al (OH) 6] 2 (SO4) 3• 26H2O[END_REF][START_REF] Champenois | Influence of sodium borate on the early age hydration of calcium sulfoaluminate cement[END_REF].

The first authors who worked on the influence of citric acid on hydration reactions in the 3CaO.Al2O3-CaSO4.2H2O-CaO-H2O system were Tinnea and Young [START_REF] Tinnea | Influence of Citric Acid on Reactions in the System 3CaO•Al2O3-CaSO4•2H2O-CaO-H2O[END_REF]. They found that hydration reactions are retarded by the addition of citric acid. Ettringite and monosulfoaluminate were all detected as early hydration products. The influence of citric acid as a retarder for ternary binders based on Ordinary Portland Cements (OPC), CSA and anhydrite was investigated by Winnefeld et al. [START_REF] Winnefeld | Influence of citric acid on the hydration kinetics of calcium sulfoaluminate cement[END_REF]. Their main conclusions were that the addition of citric acid retarded the early ettringite formation, lengthened the workability time, and reduced significantly the compressive strength even after 28 days. Zhang et al. [START_REF] Zhang | Effects of superplasticizers and retarders on the fluidity and strength of sulphoaluminate cement[END_REF] studied the effect of citric acid on the fluidity and strength of CSA commercial cements. They found that the initial fluidity of paste admixed with superplasticizers would be decreased by the presence of citric acid. Moreover, both early and late strengths of cement were decreased by the addition of citric acid. In a recent study about the effect of citric acid on hydration properties of commercial CSA, Burris et al. [START_REF] Burris | Influence of set retarding admixtures on calcium sulfoaluminate cement hydration and property development[END_REF] found that citric acid successfully retarded initial set by 120 min for CSA cement. Despite the reported studies about the effect of citric acid on CSA cements hydration, there is a lack of understanding about how changing retarder dosage influences cement hydrates formation. It represents a serious barrier to specification and, in particular, larger scale usage of CSA cements.

From a materials scientist point of view, one parameter which dictates the reactivity of a powder (with water for instance, or during sintering) is its fineness. Cement fineness is considered as one of the major variables influencing cement properties and concrete strength [START_REF] Sajedi | Effects of curing regimes and cement fineness on the compressive strength of ordinary Portland cement mortars[END_REF][START_REF] Kadri | Combined effect of chemical nature and fineness of mineral powders on Portland cement hydration[END_REF][START_REF] Higginson | The effect of cement fineness on concrete[END_REF][START_REF] Alexander | The relationship between strength and the composition and fineness of cement[END_REF]. It is also a dominant factor that affects cement hydration since the fineness directly controls the volume of -4-water available for hydration for each unit volume of cement particle, as well as the inter-particle spacing between them [START_REF] Hu | Influence of cement fineness and water-to-cement ratio on mortar early-age heat of hydration and set times[END_REF]. The aim of nanoparticle addition in cements is the stimulation of nucleation processes during the early cement hydration. The earlier these nuclei are formed, the earlier they can grow to larger crystals of hydration phases and thereby accelerate the cement hydration [START_REF] Land | Controlling cement hydration with nanoparticles[END_REF].

In the literature on cementitious materials and specifically Portland cements, different authors mentioned the effect of fineness on hydration [START_REF] Sajedi | Effects of curing regimes and cement fineness on the compressive strength of ordinary Portland cement mortars[END_REF][START_REF] Song | Direct synthesis and hydration of calcium aluminosulfate (Ca4Al6O16S)[END_REF][START_REF] Thomas | Kinetic mechanisms and activation energies for hydration of standard and highly reactive forms of β-dicalcium silicate (C2S)[END_REF][START_REF] Pöllmann | Cementitious Materials: Composition, Properties, Application[END_REF][START_REF] Hong | Hydration kinetics and phase stability of dicalcium silicate synthesized by the Pechini process[END_REF][START_REF] Fumo | Combustion synthesis of calcium aluminates[END_REF]. Thomas [START_REF] Thomas | Kinetic mechanisms and activation energies for hydration of standard and highly reactive forms of β-dicalcium silicate (C2S)[END_REF] examined the hydration of the β polymorph of belite (calcium di-silicate). He observed that if this polymorph had a specific surface area similar to a Portland cement, it was less reactive with water than a β-belite prepared by a chemical route (Pechini process). Pollman [START_REF] Pöllmann | Cementitious Materials: Composition, Properties, Application[END_REF] and Hong [START_REF] Hong | Hydration kinetics and phase stability of dicalcium silicate synthesized by the Pechini process[END_REF] indicated that the interest in using chemical synthesis methods was to be able to study the hydration behaviour of pure belite and in particular fine particles. The interplay between fineness and chemical composition of fillers (limestone, alumina, silica) on Portland mortars hydration was studied by Kadri et al. [START_REF] Kadri | Combined effect of chemical nature and fineness of mineral powders on Portland cement hydration[END_REF]. Whatever the type of filler, the finer it is, the more accelerated the early hydration of the mortar is. Fineness can also influence Portland concrete properties such as self-compaction, shrinkage, durability or reduction of product cost. A study is needed to accurately interpret the hydration process and quantify effects of cement fineness on CSA cement hydration and the role of ye'elimite fineness on hydration has not been studied.

Cement hydration is a complex process, because cement powder contains several inorganic phases.

A simple way to well investigate the effect, is to examine the hydration of the main reactive cementitious phase in different controlled hydration conditions. CSA cements can have highly variable compositions, but all of them contain the key-phase ye'elimite, Ca4(AlO2)6SO4 (noted C4A3S̅ in cementitious notation) [START_REF] Mehta | Mechanism of expansion associated with ettringite formation[END_REF][START_REF] Ogawa | C4A3S hydration ettringite formation, and its expansion mechanism: I. expansion; Ettringite stability[END_REF][START_REF] Khessaimi | Solid-state synthesis of pure ye'elimite[END_REF].

In fact, ye'elimite hydration proceeds through dissolution and precipitation [START_REF] Chatelier | Recherches expérimentales sur la constitution des mortiers hydrauliques[END_REF], leading to the precipitation of various hydrates. In the presence of anhydrite (calcium sulfate, CaSO4 or CS̅ ), -5-ye'elimite hydrates to form ettringite Ca6Al2(SO4) Recently, significant work has been carried out on ye'elimite single phase hydration, pioneered by Hanic et al. [START_REF] Hanic | Mechanism of hydration reactions in the system C4A3S CS CaO H2O referred to hydration of sulphoaluminate cements[END_REF]. Ye'elimite hydration was shown to occur through a two-step reaction. The reaction product in the first step was ettringite, whereas monosulfoaluminate C4AS̅ H12 was the hydration product in the second step of hydration reaction. Suspensions of synthetic ye'elimite in a saturated gypsum solution were also investigated [START_REF] Hargis | Early age hydration of calcium sulfoaluminate (synthetic ye'elimite, C4A3S) in the presence of gypsum and varying amounts of calcium hydroxide[END_REF]. The most voluminous hydration product observed was ettringite. During the hydration of orthorhombic ye'elimite in dilute suspensions with a water over binder mass ratio equal to 40 and 100, Bullerjahn et al. [START_REF] Bullerjahn | Hydration reactions and stages of clinker composed mainly of stoichiometric ye'elimite[END_REF] identified five stages of hydration: stage I (initial period), stage II (dormant period), stage III (acceleration period), stage IV (main hydration period) and stage V (final period). The duration of each stage was directly linked to the evolution of the solution concentrations and the type of hydration reaction [START_REF] Zajac | Early hydration of ye'elimite: Insights from thermodynamic modelling[END_REF]. Other authors were interested in the hydration behavior of orthorhombic and pseudo-cubic ye'elimite [START_REF] Cuesta | Hydration mechanisms of two polymorphs of synthetic ye'elimite[END_REF][START_REF] Jansen | Studies on the early hydration of two modifications of ye'elimite with gypsum[END_REF][START_REF] Bullerjahn | Factors influencing the hydration kinetics of ye'elimite; effect of mayenite[END_REF]. It was shown that in the absence of additional sulfate sources, orthorhombic-ye'elimite reacts slower than pseudo-cubicye'elimite, and monosulfoaluminate phases are the main hydrated crystalline phases (see reaction R2). However, in the presence of additional sulfates, orthorhombic-ye'elimite reacts faster than pseudo-cubic-ye'elimite, and the main hydrated crystalline phase is ettringite (see reaction R1). The published data on ye'elimite single phase hydration [START_REF] Cuesta | Hydration mechanisms of two polymorphs of synthetic ye'elimite[END_REF][START_REF] Jansen | Studies on the early hydration of two modifications of ye'elimite with gypsum[END_REF][START_REF] Bullerjahn | Factors influencing the hydration kinetics of ye'elimite; effect of mayenite[END_REF][START_REF] Hargis | Calcium sulfoaluminate (Ye'elimite) hydration in the presence of gypsum, calcite, and vaterite[END_REF] are summarized in Fig. 1, which shows show a schematic picture of the early behaviour of commercial CSA cements [START_REF] Haha | Advances in understanding ye'elimite-rich cements[END_REF]. Despite the fact that model cements do not reflect the whole complexity of commercial products, it helps to give a basic understanding of the hydration by focussing on the major hydration reactions [START_REF] Haha | Advances in understanding ye'elimite-rich cements[END_REF].

The experimental approach of the present study focuses on identifying the nature and the amount of the hydration products using Rietveld analysis coupled to TGA analysis and on monitoring the ye'elimite dissolution using continuous ionic conductivity measurement. Zeta potential measurements were also carried out to examine the mechanisms by which citric acid acts on ye'elimite-rich cement hydration.

Materials and methods

Materials

Ye'elimite C4A3S̅ powder was synthesized by solid state reactions from a 4:3:1 stoichiometric mixture of calcium carbonate (CaCO3, CAS number: 471-34-1, Sigma-Aldrich, >99.9 wt.%), alumina (Al2O3, CAS number: 1344-28-1, Acros-Organics, >99.7 wt.%) and highly pure gypsum (CaSO4.2H2O, CAS number: 10101-41-4, Sigma-Aldrich, >99.0 wt.%) powder. The raw materials were dry homogenized. The homogenized powders were then pressed into pellets (20 mm in diameter) and heated at 1300°C for 3 h. After 3 h, the samples were quenched in air. The pellets were reground with an excess of anhydrite in order to compensate sulfate volatilization during thermal treatment and then the powder was pressed again into disks before further heating. The pellets were quenched in air after this last heating and finally ground with an agate mortar. A detailed description about the synthesis protocol can be found in [START_REF] Khessaimi | Solid-state synthesis of pure ye'elimite[END_REF]. The sample was labelled: Yesol.

Ye'elimite was also synthesised by sol-gel method using the Organic Steric Entrapment route (OSE).

A stoichiometric mixture of three salts (Ca(NO3)2.4H2O, CAS number: 13477-34-4, Fisher Scientific, >99.0 wt.%), (Al(NO3)2.9H2O, CAS number: 7784-27-2, Fisher Scientific, >99.0 wt.%), and (Al2(SO4)3.16H2O, CAS number: 17927-65-0, Fisher Scientific, >98.0 wt.%) was added to a 5 wt.% aqueous solution of (PVA, CAS number: 9002-89-5, VWR Chemicals). The resulting gel was dried, then finely ground and finally calcined at 1250°C for 1 h. More details about the synthesis protocol can be found in [START_REF] Khessaimi | Ye'elimite synthesis by chemical routes[END_REF]. The sample was labelled: Ye-chem.

Since ye'elimite hydration depends on C4A3S̅ polymorphs [START_REF] Cuesta | Hydration mechanisms of two polymorphs of synthetic ye'elimite[END_REF][START_REF] Jansen | Studies on the early hydration of two modifications of ye'elimite with gypsum[END_REF], only orthorhombic ye'elimite powders were synthesised to minimize parameters affecting hydration. In this respect, Ye-sol and Ye-chem refer to orthorhombic ye'elimite phase. The synthesised ye'elimite powders were found highly pure, with the presence of some impurities such as CA and CA2. In other works, C3A and C12A7 were detected as impurities [START_REF] Khessaimi | Solid-state synthesis of pure ye'elimite[END_REF][START_REF] Khessaimi | Ye'elimite synthesis by chemical routes[END_REF][START_REF] Li | Kinetics of calcium sulfoaluminate formation from tricalcium aluminate, calcium sulfate and calcium oxide[END_REF][START_REF] Cuesta | Chemistry and mass density of aluminum hydroxide gel in eco-cements by ptychographic xray computed tomography[END_REF]. The presence of calcium aluminate impurities depends on the kinetic of solid state reactions during ye'elimite formation. It was shown that the kinetic depends mainly on alumina grain size used as a raw material for ye'elimite lab-synthesis [START_REF] Khessaimi | Examination of ye'elimite formation mechanisms[END_REF].

To prepare a CSA model cement, Ye-sol was blended with gypsum CaSO4.2H2O (CS̅ H2 in cementitious notation) (CAS number: 10101-41-4, Sigma-Aldrich, > 99.0 wt.%). In order to examine the effect of citric acid on ye'elimite hydration, commercial citric acid (HOC(CH2CO2H)2CO2H, CAS number: 77-92-9, Sigma-Aldrich) was used.

The different samples and the corresponding characterization techniques are summarized in Table 1. codes [START_REF] Cuesta | Structure, atomistic simulations, and phase transition of stoichiometric yeelimite[END_REF][START_REF] Goetz-Neunhoeffer | Refined ettringite (Ca 6 Al 2 (SO 4)[END_REF][START_REF] Allmann | Refinement of the hybrid layer structure [Ca2Al (OH) 6]+•[1/2SO4• 3H2O][END_REF][START_REF] Saalfeld | Refinement of the crystal structure of gibbsite, A1 (OH) 3[END_REF][START_REF] Angeles | Structure and microstructure of gypsum and its relevance to Rietveld quantitative phase analyses[END_REF] are given in Table 2. To check the Rietveld fitting quality between measured and calculated diffractograms, reliability factors should be given as, Rwp (weighted profile R-factor),

Characterisation methods

Rexp (expected R-factor) and GOF (Goodness Of Fit) [START_REF] Toby | R factors in Rietveld analysis: how good is good enough?[END_REF]. These reliability factors reflect the deviation between measured intensities (IiM) and calculated intensities (IiC) at any given measurement point (i) as follows:

Rwp = ∑ w i (I iM -I iC ) 2 i ∑ w i (I iM ) 2 i (E.2) Rexp = N-P ∑ w i (I iM ) 2 i (E.3) GOF = Rwp Rexp 2 (E.4)
where w i is the attributed weight, N is the number of data points and P is the number of the refined parameters.

Most of AH3 gel produced during CSA hydration (see reaction R1) is an amorphous phase [START_REF] Cuesta | Chemistry and mass density of aluminum hydroxide gel in eco-cements by ptychographic xray computed tomography[END_REF]. In the present paper only crystalline gibbsite was quantified by XRD-Rietveld analysis. Since cement pastes and set cements contain a complex mix of different crystalline and amorphous hydrates, an accurate quantification by Rietveld analysis is sometimes difficult [START_REF] Álvarez-Pinazo | Rietveld quantitative phase analysis of Yeelimite-containing cements[END_REF][START_REF] Trauchessec | Mélanges de ciments sulfoalumineux et Portland[END_REF]. Therefore, our data are considered to be semi-quantitative and absolutely not quantitative.

Scanning Electron Microscopy (SEM)

The prepared samples were examined with a LEO 1530 VP field emission scanning electron microscopy (SEM) equipped with an Energy Dispersive X-ray Spectroscopy (EDS) detector (Oxford INCA 250). The microscope was operated at a 1 kV accelerating voltage. This low voltage is necessary in order to avoid spoiling the sample. The samples were stored in desiccators filled with silica gel prior to and after examination in order to prevent hydration or carbonation. SEM observations were carried out without using a deposited conducting layer. For ye'elimite dissolution experiments, ye'elimite powder was stirred with demineralized water at 500 rpm using a magnetic agitator for the desired time. Hydration was stopped by the solvent exchange method using acetone, then filtered by vacuum aspiration and the samples could then be observed under the SEM. TGA was carried out in N2 atmosphere on 30 mg of sample using a SETARAM Labsys TG-DTA/DSC thermal analyser at 10 °C/min up to 1100°C.

Continuous ionic conductivity measurement (IC)

The ionic conductivity measurements with time of ye'elimite suspensions were performed using a CDM210 Conductivity Meter. The water over ye'elimite weight ratio, W/C, is equal to 1000 (Fig. 2).

This high dilution has been chosen to avoid the formation of hydrates and in order to have specifically information about ye'elimite dissolution. During the measurement, the suspension was stirred at 500 rpm. The volume of the measurement cell is about 150 ml. The temperature was controlled by a thermostatic bath with external water circulation at 25 °C. Similar experiments were carried out with gypsum alone.

Zeta potential measurement (ZP)

The interaction between the added citric acid and ye'elimite powder was evaluated by measuring the zeta potential of ye'elimite particles as a function of the citric acid concentration. Suspensions of 0.1 wt.% were prepared by mixing for 24 h ye'elimite powder with deionized water containing different dosages of citric acid (0 wt.%, 5 wt.% and 10 wt.% relative to the weight of ye'elimite powder). The zeta potential was measured using a Malvern ZetaSizer Nano ZS, which is based on the electrophoresis method.

Zeta potential values depend on pH value of the measured suspension. In the present experiments, when 0 wt.%, 5 wt.% and 10 wt.% of citric acid were added, the pH values of the corresponding suspensions were 11.79, 10.84 and 10.80. Therefore, pH values do not vary greatly with the addition of citric acid and the measured Zeta potential values are considered to be taken at pH from 10.8 to 11.79.

Experimental protocols

Fig. 2 and Fig. 3 summarize the experimental protocols relevant to the preparation and the characterisation of the prepared suspensions and cement pastes.

2.3.1. Preparation of suspensions for ye'elimite dissolution experiments (Fig. 2)

To gain information on the effect of ye'elimite grain fineness on the dissolution kinetics, two suspensions were compared; the first one contained ye'elimite powder synthesised by solid state reactions (Ye-sol), and the second one contained ye'elimite powder synthesised by sol-gel method (Ye-chem). All suspensions were made by adding the ye'elimite powder to the demineralized water with a water over ye'elimite weight ratio, W/C, equal to 1000. The suspension was stirred at 500 rpm. To examine the influence of citric acid on ye'elimite dissolution, three different concentrations of citric acid were first dissolved in the demineralized water prior to mixing with the powder. The quantities of citric acid were equal to 0 wt.%, 5 wt.% and 10 wt.% relative to the weight of ye'elimite powder; they are labelled Ye-Sol-0, Ye-Sol-5 and Ye-Sol-10, respectively. The chosen citric acid dosages are much higher than the common concentration ranges generally used to delay CSA hydration [START_REF] Burris | Influence of set retarding admixtures on calcium sulfoaluminate cement hydration and property development[END_REF][START_REF] Zajac | Effect of retarders on the early hydration of calcium-sulpho-aluminate (CSA) type cements[END_REF][START_REF] Zhang | Effects of superplasticizers and retarders on the fluidity and strength of sulphoaluminate cement[END_REF][START_REF] Pelletier | The ternary system Portland cement-calcium sulphoaluminate clinker-anhydrite: hydration mechanism and mortar properties[END_REF][START_REF] Hanley | Retarder for calcium sulfoaluminate cements[END_REF]. These dosages were chosen in order to allow us to highlight clearly the effect of citric acid addition on hydration.

2.3.2. CSA model cements pastes preparation (Fig. 3)

-12-
CSA model cements were prepared by dry mixing gypsum with ye'elimite powder either synthesised by solid state reaction (labelled: CSA-sol) or synthesised by sol-gel method (labelled: CSA-chem).

The cement powders were prepared with a ye'elimite to gypsum weight ratio, (Ye/Gy) of 2. The hydration was studied on cement pastes with a water to cement (cement = Ye + Gy) weight ratio, W/C of 2. Performing the hydration study at these chosen Ye/Gy and W/C ratios should allow full ettringite precipitation [START_REF] Winnefeld | Calorimetric and thermogravimetric study on the influence of calcium sulfate on the hydration of ye'elimite[END_REF]. The pastes were mixed, sealed in polyethylene containers and stored at 20°C for 3 days, 7 days and 28 days. These durations correspond to typical storage conditions for testing various properties of set cements (EN 196-1 [START_REF] En | Methods of testing cement-Part 1: Determination of strength[END_REF]).

To study the influence of citric acid on the hydration of CSA model cement, three different concentrations of citric acid were pre-dissolved in the mixing water, equivalent to 0 wt.%, 0.5 wt.% and 1 wt.% relative to ye'elimite powder weight, labelled CSA-sol-0, CSA-sol-0.5 and CSA-sol-1, respectively. The chosen citric acid dosages are within the common concentration ranges generally used to retard CSA cements [START_REF] Burris | Influence of set retarding admixtures on calcium sulfoaluminate cement hydration and property development[END_REF][START_REF] Zajac | Effect of retarders on the early hydration of calcium-sulpho-aluminate (CSA) type cements[END_REF][START_REF] Zhang | Effects of superplasticizers and retarders on the fluidity and strength of sulphoaluminate cement[END_REF][START_REF] Pelletier | The ternary system Portland cement-calcium sulphoaluminate clinker-anhydrite: hydration mechanism and mortar properties[END_REF][START_REF] Hanley | Retarder for calcium sulfoaluminate cements[END_REF]. After completion of the expected hydration durations, the hydration process was stopped, and samples were kept in a dry atmosphere (desiccator filled with silica gel) until analysis.

Hydration stoppage method

The solvent exchange method was used to stop the hydration of the hydrated pastes. To this end, the hydrated paste was smoothly ground in an agate mortar and then mixed in 150 ml of acetone for 6 min. Afterwards, the liquid was filtered from the sample by vacuum filtration.

3.

Results and discussion

PSD and BET of ye'elimite and gypsum

In our previous works concerning ye'elimite synthesis [START_REF] Khessaimi | Solid-state synthesis of pure ye'elimite[END_REF][START_REF] Khessaimi | Ye'elimite synthesis by chemical routes[END_REF], the mineralogical composition determined by XRD-quantitative Rietveld analysis, particle size distribution (PSD), powder microstructure and BET specific surface area (SSA) of the two-synthesised ye'elimite powders were studied (Table 3). The micrographs and the BET data show that Ye-chem powder presents a smaller average grain size (136 nm) and a higher specific surface area (2.2 m 2 /g), in comparison to Ye-sol powder, which has (2 µm) and (0.74 m 2 /g) as average grain size and specific surface area, respectively. On the contrary, the particle size distribution measured by laser diffraction reveals higher D50 for Ye-chem powder (27.1 µm) than for Ye-sol (14.6 µm). This is due to the agglomeration state of Ye-chem powder as shown in SEM micrographs in Table 3.

In order to prepare the CSA model cements, highly pure gypsum (> 99.0 wt.%) was used. It has the following characteristics: 4.19 m 2 /g as BET surface area, and particle size diameters equal to d10 = 9.92 µm, d50 = 23.08 µm and d90 = 45.32 µm.

Effect of fineness and citric acid on ye'elimite dissolution

The dissolution rate of anhydrous cementitious phases is proportional to the slope of the ionic conductivity versus time curves during the first minutes of dissolution. Fig. 4a shows the ionic conductivity variations of the Ye-sol-0, Ye-sol-5, Ye-sol-10 and Ye-chem suspensions (W/C=1000).

Provided the temperature remains constant, the ionic conductivity in these highly dilute situations depends mainly on two factors: concentration of ions and ionic mobility. In the present situation, as soon as the powder is in contact with water, dissolution of ye'elimite grains starts and the ions go into solution. Since the concentration of ions starts increasing, the ionic conductivity also increases immediately. It reaches a plateau with Ye-chem after 25 min. The slope value (s) of the different ionic conductivity curves (Fig. 4a) during the first minutes of dissolution (~ 5 min) are in the following order: s (Ye-chem-0) > s (Ye-sol-0) > s (Ye-sol-5) > s (Ye-sol-10). In this later case, it looks as if there is no dissolution within 50 min since the ionic conductivity level remains constant.

Thus, the corresponding dissolution rates (r) follow the following sequence as well: r (Ye-chem-0) > r (Ye-sol-0) > r (Ye-sol-5) > r (Ye-sol-10) ≈ 0. Referring to similar conductivity measurements on gypsum suspensions with different citric acid content, respectively 0 wt.% (Gy-0), 5 wt.% (Gy-5) and 10 wt.% (Gy-10) (Fig. 4b), it seems that citric acid does not delay gypsum dissolution kinetics.

The slope value of the different ionic conductivity curves (Fig. 4b) during the first minutes of dissolution (~ 5 min) are almost equal. This means that citric acid does not delay gypsum dissolution kinetic and only influences upon ye'elimite dissolution.

To investigate the morphological aspect of ye'elimite grains at early age dissolution stage, SEM micrographs of Ye-chem (Ye-chem-0) and that of Ye-sol powder immersed during 1 min in deionised water (Ye-sol-0), or in 10 wt.% citric acid solution (Ye-sol-10) are shown in Fig. 5. The water to ye'elimite ratio was 1000. After only 1 min, ye'elimite grains immersed in deionised water (Ye-sol-0, Fig. 5a, and Ye-chem-0, Fig. 5c) show a severely corroded surface with the formation of several etch-pits (holes on the micrographs). In the case of ye'elimite which has been in contact with a citric acid solution (Ye-sol-10, Fig. 5b), the ye'elimite grains surface appears smooth and much less attacked; moreover, the scarce etch-pits present characteristic geometries of crystal dissolution [START_REF] Juilland | Dissolution theory applied to the induction period in alite hydration[END_REF]. The SEM observations are in agreement with the (IC) measurements and confirm that the chemical nature of the solution in contact with ye'elimite plays an important role on its dissolution.

The formation of etch-pits during mineral dissolution has been evidenced in the literature for other cementitious anhydrous phases such as alite (tricalcium silicate, C3S) and belite (dicalcium silicate, C2S) [START_REF] Juilland | Dissolution theory applied to the induction period in alite hydration[END_REF][START_REF] Juilland | Morpho-topological investigation of the mechanisms and kinetic regimes of alite dissolution[END_REF][START_REF] Nicoleau | The di-and tricalcium silicate dissolutions[END_REF][START_REF] Barret | Filter dissolution of C3S as a function of the lime concentration in a limited amount of lime water[END_REF] and other silicates like quartz [START_REF] Lasaga | Variation of crystal dissolution rate based on a dissolution stepwave model[END_REF][START_REF] Dove | Kinetics of mineral dissolution and growth as reciprocal microscopic surface processes across chemical driving force[END_REF][START_REF] Dove | Mechanisms of classical crystal growth theory explain quartz and silicate dissolution behavior[END_REF]. In fact, the formation of such etch-pits was previously observed on the surface of alite phase grains, the major phase in ordinary Portland cements, by Juilland et al. [START_REF] Juilland | Dissolution theory applied to the induction period in alite hydration[END_REF], who stated that etch-pits formation depends on the over/under saturation state of solution, and also on the crystallographic defects density of anhydrous alite grains.

Nicoleau et al. [START_REF] Nicoleau | The di-and tricalcium silicate dissolutions[END_REF] confirmed the discussions of Juilland et al. [START_REF] Juilland | Dissolution theory applied to the induction period in alite hydration[END_REF] concerning etch-pits formation during alite dissolution, by measuring the dissolution rate of alite according to the solution saturation state. The notion of etch-pits formation during mineral dissolution was identified and theorised early by Lasaga et al. [START_REF] Lasaga | Kinetic theory in the earth sciences[END_REF] and Burch et al. [START_REF] Burch | Free energy dependence of albite dissolution kinetics at 80°C and pH 8.8[END_REF] who observed etch-pits formation during dissolution experiments of quartz and calcium carbonates.

The rapid reactivity of ye'elimite powder synthesised by sol-gel method (Ye-chem) during the early dissolution step could be explained by its microstructure. In fact, Ye-chem powder shows very small ye'elimite grains (136 ±48 nm, Table 3) compared to Ye-sol powder which contains relatively larger ye'elimite grains (2 ±1.2 µm, Table 3). This morphological difference provides ye'elimite surfaces with different reactivity to water.

-15-

To highlight the interaction between the added citric acid and ye'elimite powder, zeta potential measurements were carried out on the ye'elimite suspensions, Ye-sol-0, Ye-sol-5 and Ye-sol-10. The pH values of the corresponding acidic suspensions were 11.79, 10.84 and 10.80, respectively. Citric acid is normally considered to be a tri acid, with pKa values at 25 °C, extrapolated to zero ionic strength, of 2.92, 4.28, and 5.21 [START_REF] Goldberg | Thermodynamic quantities for the ionization reactions of buffers[END_REF]. Thereby, citrate is the dominant form of citric acid present in our suspensions. The results of zeta potential measurements are shown in Table 4. An increase in the citric acid concentration from 0 to 5 wt. % leads to a shift of the zeta potential from 7.7 ± 0.3 mV to -0.2 ± 0.1 mV, and the zeta potential turns to lower negative values (-10.9 ± 2.8 mV) for Ye-sol-10.

The adsorption of citrate molecules at the surface of ye'elimite grains could explain this change of zeta potential values. In citrate, the distances between two oxygen atoms in two neighbouring carboxylate groups, are between 2.7 and 4.0 Å (Fig. 6a) [START_REF] Emmert | The European bioinformatics institute (EBI) databases[END_REF]. For ye'elimite, the (131 ) plane is a possible face for a ye'elimite crystal [START_REF] Cuesta | Structure, Atomistic Simulations, and Phase Transition of Stoichiometric Yeelimite[END_REF]; the distances between two calcium atoms are between 3.0 and 4.0 Å (Fig. 6b). Therefore, the citrate molecules can adsorb on the (131 ) faces via the oxygen of the carboxylate groups to form a chelate. The remaining carboxylate functions of the adsorbed citrate molecules are negatively charged and can be responsible for the negative values of the zeta potential.

This citrate adsorption can inhibit ye'elimite grains dissolution. In solution, calcium and citrate can form chelates too [START_REF] Boisvert | Hydration of calcium sulfate hemihydrate (CaSO4• 12H2O) into gypsum (CaSO4• 2H2O). The influence of the sodium poly (acrylate)/surface interaction and molecular weight[END_REF]. Consequently, two events can explain the slow setting of cement paste containing ye'elimite: the adsorption of citrate at the surface of ye'elimite grains can delay ye'elimite dissolution, and the formation of chelates between calcium and citrate in the solution can prevents calcium ions to participate in hydrates formation. The concept of citrate adsorption on gypsum crystals was adopted by different authors [START_REF] Boisvert | Hydration of calcium sulfate hemihydrate (CaSO4• 12H2O) into gypsum (CaSO4• 2H2O). The influence of the sodium poly (acrylate)/surface interaction and molecular weight[END_REF][START_REF] Ersen | Effect of malic and citric acid on the crystallisation of gypsum investigated by coupled acoustic emission and electrical conductivity techniques[END_REF][START_REF] Badens | Crystallization of gypsum from hemihydrate in presence of additives[END_REF] to the explain the retarding effect on plaster crystallisation.

Another possible way to explain the effect of citric acid addition in the shifting of the zeta potential from positive values to negative values, is to use Bombled's approach [START_REF] Bombled | Rhéologie des mortiers et des bétons frais, influence du facteur ciment[END_REF]. This author estimated the surface charge of alite (C3S) particles, and he showed that there are three times fewer positive sites than negative sites. Similarly, Smith et al. [START_REF] Smith | Role of a small addition of acetic acid on the setting behavior and on the microstructure of a calcium aluminate cement[END_REF] applied Bombled's approach to estimate the surface charge of krotite particles (calcium aluminate, CA) and they found that the negative sites are dominant. The approach is based on a statistical representation of the charges on the surface of grains. It can be expressed as follows:

σ + σ -is proportional to ∑ r + 2 positive ions ∑ r - 2 negative ions (E.5)
where σ + σ -is the positive to negative surface charge ratio, r+ is the ionic radius associated to positive ions and r-is the ionic radius associated to negative ions.

The application of this approach to ye'elimite starts by knowing the ionic radius of each element:

1.35 Å for oxygen, 1.05 Å for calcium, 0.5 Å for aluminium and 0.43 Å for sulphur.

σ + σ -can be calculated and it is proportional to 0.2. This means that the negative sites are dominant and that the surface of the anhydrous C4A3S̅ (Ca4Al6O16S) particles is consequently negatively charged.

Assuming that all of the calcium ions of the surface form chelates molecules when citrate is present, the σ + σ -ratio becomes equal to 0.05. This means that negative sites become more dominant. Since zeta potential of a cement suspension is proportional to the surface charge of the cement grains present in this solution [START_REF] Smith | Role of a small addition of acetic acid on the setting behavior and on the microstructure of a calcium aluminate cement[END_REF], the shift of (ζ) from positive to negative values could be explained by the high dominance of negative sites in the C4A3S̅ particle surface in contact with citrate. Even though Bombled's approach is somewhat simplistic because it assumes that all the surfaces have the same atomic arrangement and that the surface of the grains has the same chemical composition as the bulk, it gives an interesting insight into the variations of the surface charge with the addition of citric acid.

Hydration of CSA model cements containing ye'elimite with two different grain sizes

The results of XRD analysis of the hydrated CSA model cements CSA-sol and CSA-chem at t0 = 0 day, and after curing for 3 days, 7 days and 28 days are shown in Fig. 7a. The corresponding Rietveld analysis results are given in Table 5. Since we consider that Rietveld analysis gives an approximate picture of the quantities of remaining reactants (ye'elimite and gypsum) and formed hydrates, we will focus for clarity on the amount of remaining ye'elimite and on the total quantities of formed hydrates (ettringite, the most abundant hydrate, monosulfoaluminate and gibbsite). The nature of the formed hydrate phases is in accordance with experimental results previously published about ye'elimite-calcium sulfate system hydration [START_REF] Bullerjahn | Hydration reactions and stages of clinker composed mainly of stoichiometric ye'elimite[END_REF][START_REF] Cuesta | Hydration mechanisms of two polymorphs of synthetic ye'elimite[END_REF][START_REF] Jansen | Studies on the early hydration of two modifications of ye'elimite with gypsum[END_REF][START_REF] Bullerjahn | Factors influencing the hydration kinetics of ye'elimite; effect of mayenite[END_REF]. First of all, Fig. 7b displays the calculated hydration degree, α given by equation (E.1), of CSA-sol and CSA-chem pastes. After 3 days, CSA-chem paste reaches more than 96.3 % while it is almost 72.4 % for the CSA-sol paste.

After 7 days, the degree of reaction reached 97.6 % and 79.9 % for CSA-chem and CSA-sol, respectively. Finally, it was observed that at 28 days, the hydration of Ye-chem was nearly complete reaching almost 98 % hydration degree, while Ye-sol hydration degree attains only 88.7 %.

Concerning the hydrates, the quantities are higher at any time in CSA-chem than in CSA-sol.

TGA curves are presented in Fig. 7c. Weight loss between 80 and 150°C can be assigned to ettringite decomposition (Zone II, Fig. 7c) [START_REF] Winnefeld | Calorimetric and thermogravimetric study on the influence of calcium sulfate on the hydration of ye'elimite[END_REF][START_REF] Bullerjahn | Factors influencing the hydration kinetics of ye'elimite; effect of mayenite[END_REF]. Gypsum can decompose between 150 and 220°C (Zone III, Fig. 7c) [START_REF] Winnefeld | Calorimetric and thermogravimetric study on the influence of calcium sulfate on the hydration of ye'elimite[END_REF][START_REF] Bullerjahn | Factors influencing the hydration kinetics of ye'elimite; effect of mayenite[END_REF]. Weight loss between 100 and 800°C can originate from the decomposition of monosulfoaluminate (Zones II, III, and IV, Fig. 7c), with a maximum decomposition at 200°C [START_REF] Winnefeld | Calorimetric and thermogravimetric study on the influence of calcium sulfate on the hydration of ye'elimite[END_REF][START_REF] Cuesta | Hydration mechanisms of two polymorphs of synthetic ye'elimite[END_REF]. Lastly, between 200 and 300°C, the weight loss associated to the decomposition of gibbsite can be detected (Zone IV, Fig. 7c) [START_REF] Winnefeld | Calorimetric and thermogravimetric study on the influence of calcium sulfate on the hydration of ye'elimite[END_REF][START_REF] Bullerjahn | Factors influencing the hydration kinetics of ye'elimite; effect of mayenite[END_REF]. Despite an overlap between the decomposition of the different products with temperature, TGA results (Fig. 7c) show higher total weight loss for CSAchem compared to CSA-sol, at all hydration durations, which comes mainly from the decomposition of hydrates. In conclusion, TGA and XRD results give similar trends: the finer the ye'elimite powder, the faster the cement containing this powder hydrates. The presence of nano-grains of ye'elimite stimulates nucleation processes during the early cement hydration. The earlier these nuclei are formed, the earlier they can grow to larger crystals of hydrated phases and thereby accelerates the cement hydration [START_REF] Land | Controlling cement hydration with nanoparticles[END_REF]. Moreover, the high dissolution rate of nano-grains of ye'elimite probably leads to higher saturation index with respect to the different hydrates during the first days of hydration [START_REF] Winnefeld | Hydration of calcium sulfoaluminate cements-experimental findings and thermodynamic modelling[END_REF].

Influence of citric acid on CSA model cements hydration

The evolution of phases of the CSA-sol pastes, in the presence of different citric acid dosages (0 wt.%, 0.5 wt.% and 1 wt.%) and for different curing ages (3 days, 7 days and 28 days), were followed by XRD (Fig. 8a) with the corresponding Rietveld results (Table 6). Again, we will focus for clarity on the amount of remaining ye'elimite and on the total quantities of formed hydrates (ettringite, the most abundant hydrate, monosulfoaluminate and gibbsite). The nature of the formed hydrate phases is in accordance with experimental results previously published about CSA cement hydration in the presence citric acid [START_REF] Tinnea | Influence of Citric Acid on Reactions in the System 3CaO•Al2O3-CaSO4•2H2O-CaO-H2O[END_REF][START_REF] Winnefeld | Influence of citric acid on the hydration kinetics of calcium sulfoaluminate cement[END_REF]. The variations of the calculated hydration degree, α given by equation (E.1), of CSA-sol pastes containing different citric acid dosages are presented in Fig. 8b.

The results show that citrate retards the hydration: CSA-sol-0 reacts at a faster pace after 3 days since the degree of hydration of ye'elimite is 72.4 %, while CSA-sol-0.5 and CSA-sol-1 pastes reach only 66.6 % and 17.0 %, respectively. After 7 days, CSA-sol-0, CSA-sol-0.5 and CSA-sol-1 reach more than 79.9 %, almost 73.2 % and 26.4 % degree of hydration, respectively. Lastly, after 28 days of hydration, the figures are 88.7 %, almost 75.6 % and 65.2 % for CSA-sol-0, CSA-sol-0.5 and CSA-sol-1 respectively. Therefore, the major effect of citric acid addition on ye'elimite hydration is the slowing down of the hydration kinetics of the cement paste, suggesting an adsorption of citrate molecules on ye'elimite grains. In (section 3-2), it was explained how citric acid can delay ye'elimite dissolution by the possible citrate adsorption on ye'elimite grains. An analysis of TGA results (Fig. 8c) shows the same trend, i.e. a marked decrease of weight loss with the addition of citric acid, especially with 1 wt.%. The delay induced by citric acid on the reactivity of CSA-sol-0.5 and CSAsol-1 can be explained by the fact that citrate molecules will bond with calcium on the surface of ye'elimite to give a chelate and interfere with ye'elimite dissolution, in addition to forming chelates with calcium ions already in solution, thus lowering their availability for participating in hydration reactions as it was already shown for OPC cement [START_REF] Prisciandaro | The retarding effect of citric acid on calcium sulfate nucleation kinetics[END_REF]. Citric acid addition lowers ettringite quantities (Table 6). In fact, some amounts of calcium and aluminium ions produced from ye'elimite and gypsum dissolution could form chelates with citrate, leading to the decease of the saturation index with respect to ettringite [START_REF] Winnefeld | Hydration of calcium sulfoaluminate cements-experimental findings and thermodynamic modelling[END_REF]. The absence of interaction between citrate and ettringite was proven in literature and it can be confirmed in the present case [START_REF] Cody | The effects of chemical environment on the nucleation, growth, and stability of ettringite [Ca3Al (OH) 6] 2 (SO4) 3• 26H2O[END_REF].

-19-

Conclusion

In order to contribute to the understanding of CSA concrete characteristics, this work has examined the effect of fineness on hydration of ye'elimite powder, which is one component of CSA cements.

Ye'elimite of two different finesses was prepared either by a solid state method or by a chemical route. The role of fineness on the hydration of two model CSA cements and the effect of citric acid addition on the hydration of a CSA model cement were examined. The main conclusions of the present work can be summarized as follows.

The main difference found between the dissolution of ye'elimite powders prepared by chemical or solid state routes is related to the reaction rate. The presence of fine grains (100 to 200 nm) of ye'elimite accelerates the dissolution. From an industrial point of view, the presence of a fine fraction of ye'elimite grains (of the order of 100 -200 nm) formed after grinding a commercial CSA clinker can considerably accelerate the hydration and therefore the expansion behavior. The presence of nano-grains of ye'elimite stimulates nucleation processes during the early cement hydration. The earlier these nuclei are formed, the earlier they can develop into large crystals of hydrated phases and thereby accelerate the cement hydration. Moreover, the high dissolution rate of nano-grains of ye'elimite probably leads to higher saturation index with respect to the different hydrates during the first days of hydration.

The addition of citric acid to the mixing water leads to a retarding effect on the dissolution of ye'elimite grains. Also, the surface of the grains presents scarce etch pits when citric acid is present in the water, while the surface seems to be totally attacked with water. These results indicate that the hydration of CSA model cements prepared from the mixing of ye'elimite powder -prepared by solid state reaction -and gypsum is retarded in the presence of citric acid at concentrations of 0.5 wt.% and 1 wt.% with respect to ye'elimite. Citric acid may work efficiently as a retarding additive for CSA cements since it slows down the initial ye'elimite dissolution. In the present work, it was also shown that the addition of citric acid with CSA model cements delays the formation of hydrates, especially ettringite. The delay effect of citric acid can be explained by the fact that citrate molecules form chelates with calcium on the surface of ye'elimite and interfere with ye'elimite dissolution, in addition to forming chelates with calcium ions already in solution, thus lowering their availability for participating in hydration reactions.

Expansion behavior of commercial CSA cements could be controlled by the addition of citric acid, because it is well known that the fresh CSA concrete properties depend mainly on ettringite quantities in the hydrated cement pastes.

In conclusion, powder fineness and citric acid addition are two levers that could be helpful for industrial CSA cement producers, because they constitute a practical way to control the amount of formed ettringite, and hence the expansion behaviour of CSA cements. The influence of ye'elimite powder fineness and citric acid addition on the dimensional stability, workability, mechanical properties and durability performances of CSA cements and concretes could be the subject of further studies.

Figure captions

Sample name Preparation method Characterizations

For the study of

2. 2 . 1 .

 21 XRD-Quantitative Rietveld analysis X-Ray Diffraction (XRD) data were collected at room temperature in the Bragg-Brentano geometry using a Bruker D8 Advance X-ray diffractometer with CuKα radiation (λCu = 1.54056 Å, without monochromator; operating voltage of 40 kV and electric current 40 mA). The step scan was 0.02° with a time counting per step of 0.45 seconds. The sample was rotated during data collection at 15 rpm in order to increase particle statistics. The diffractometer was equipped with an energydispersive LYNXEYE XE-T detector for filtration of fluorescence and Kβ radiation. Mineral phases of the synthesised samples were quantified by using the Rietveld method as implemented in the TOPAS 4.2 software. The fitting parameters were the background coefficients, the phase scales, the zero-shift error, the cell parameters, and the phase shape parameters. The peak shapes were fitted using the pseudo-Voigt function. The Rietveld refinement strategy and the criteria for selecting the best crystal structure data were based on the recent methods concerning diffraction and crystallography applied to anhydrous cements published by De la Torre et al.[START_REF] De La Torre | Diffraction and crystallography applied to anhydrous cements[END_REF]. The structures used for fitting the crystalline phases and the respective ICSD (Inorganic Crystal Structure Database)

Figure ( a )

 a Figure (a) Calculated ye'elimite hydration degree (α%); Formed hydrates quantities relevant

Figure

  FigurePreparation protocol for hydration study of CSA model cement pastes, (a) based on

Figure

  Figure (a)Ionic conductivity evolution of ye'elimite suspensions Ye-sol-0, Ye-chem, Ye-

Figure SEM micrographs of

  Figure SEM micrographs of Ye-sol-0 (a), Ye-sol-10 (b) and Ye-chem (c) suspensions.

Figure ( a )

 a Figure (a) Citric acid structure (CHEBI:30769) from the European Bioinformatics Institute

Figure 7

 7 Figure 7 XRD patterns (a), calculated hydration degree (α) (b), for CSA model cements (CSA-

Figure 8

 8 Figure 8 XRD patterns (a), calculated hydration degree (α) (b), for CSA model cements (CSA-

Figure 1 -

 1 Figure 1-(a)

Figure 5 Figure 6 -

 56 Figure 4a

  † IC: continuous ionic conductivity measurement, SEM: scanning electron microscopy, XRD: X-ray diffraction, TGA: thermogravimetric analysis, DTG: Derivative thermogravimetry.

  3(OH)12.26H2O or (C6AS̅ 3H32 * ) as well as gibbsite

	Al(OH)3 or (AH3) (Reaction 1) [2,27-29]:
	C4A3S̅	+	2 CS̅	+	38 H	→	C6AS̅ 3H32	+	2 AH3	(R1)
	Ye'elimite		Anhydrite		Water		Ettringite		Gibbsite
	In the absence of calcium sulfate, the hydration of ye'elimite can lead to the formation of
	monosulfoaluminate (Ca4Al2(SO4)(OH)12.6H2O or C4AS̅ H12) and gibbsite (Reaction 2) [2,27-29]:
	C4A3S̅	+	38 H	→	C4AS̅ H12	+	2 AH3	(R2)
	Ye'elimite	Water	Monosulfoaluminate	Gibbsite

Table

  Presentation of all prepared samples the corresponding performed characterizations techniques. Table ICSD collection codes used for XRD-Rietveld quantitative analysis. Table Physical and chemical characteristics of the ye'elimite powders (Ye-sol and Ye-chem). Table Zeta potential measurements of the prepared ye'elimite suspensions. Table Results of Rietveld phase analysis (wt.%) for model cements (CSA-sol) and (CSA-Chem) at different hydration ages. Rietveld agreement factors are also given. Table Results of Rietveld phase analysis (wt.%) for model cements (CSA-sol-0), (CSA-sol-0.5) and (CSA-sol-1) at different hydration ages. Rietveld agreement factors are also given.

Table 1

 1

Table 3 Ye-sol powder Ye-chem powder

 3

	Synthesis method	Solid-state reactions	Sol-gel chemical route
	Synthesis protocol details	Ref. [25]	Ref. [39]
	Synthesis temperature (°C)	1300	1250
		d10 (µm)	3.1	8.6
	PSD	d50 (µm)	14.6	27.1
		d90 (µm)	51.1	68.0
	SSABET (m 2 /g)	0.74	2.2
		C4A3S̅ (wt.%)	99.2	98.3
	Rietveld	CA (wt.%)	-	1.7
	analysis	CA2 (wt.%)	0.8	-
	Microstructure (SEM)
	Ye'elimite average grain size	2 ±1.2 (µm)	136 ±48 (nm)

Table 4

 4 Ye'elimite suspensionζ (mV)

	Ye-sol-0	7.7 ± 0.3
	Ye-sol-5	-0.2 ± 0.1
	Ye-sol-10	-10.9 ± 2.8


Jie Wang

Peng Wang

Nahiene Hamila

Philippe Boisse
email: philippe.boisse@insa-lyon.fr

Mesoscopic analyses of the draping of 3D woven composite reinforcements based on macroscopic simulations

Keywords: Meso-macro analyses, Forming, Hyperelasticity, 3D textile reinforcement, RVE

diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The analysis and simulation of the draping of textile composite reinforcements has given rise to a great deal of research work over the past decades. Most approaches are carried out on a macroscopic scale and consider the woven fabric as a continuous medium [START_REF] Gereke | Experimental and computational composite textile reinforcement forming: A review[END_REF][START_REF] Bussetta | Numerical forming of continuous fibre reinforced composite material: A review[END_REF]. The mechanical behaviour of this continuous medium must reflect the specificities textile reinforcement during draping. These macroscopic approaches can predict the global wrinkling of the woven fabric, which is the major defect that can occur during draping [START_REF] Skordos | A simplified rate dependent model of forming and wrinkling of pre-impregnated woven composites[END_REF][START_REF] Boisse | Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses[END_REF][START_REF] Dangora | Predictive model for the detection of outof-plane defects formed during textile-composite manufacture[END_REF][START_REF] Sjölander | Forming induced wrinkling of composite laminates: a numerical study on wrinkling mechanisms[END_REF]. Nevertheless, some important phenomena take place on a smaller scale during the draping process. On a mesoscopic scale, the woven fabric is considered as a set of yarns in contact with their neighbours. Defects such as gaping (gap between two yarns) [START_REF] Gatouillat | Meso modelling for composite preform shaping-simulation of the loss of cohesion of the woven fibre network[END_REF][START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Schirmaier | A macroscopic approach to simulate the forming behaviour of stitched unidirectional non-crimp fabrics (UD-NCF)[END_REF][START_REF] Schirmaier | Characterisation of the draping behaviour of unidirectional non-crimp fabrics (UD-NCF)[END_REF], local buckling of yarns [START_REF] Allaoui | Experimental preforming of highly double curved shapes with a case corner using an interlock reinforcement[END_REF][START_REF] Tephany | Development of an experimental bench to reproduce the tow buckling defect appearing during the complex shape forming of structural flax based woven composite reinforcements[END_REF][START_REF] Salem | Experimental, analytical and numerical investigation to prevent the tow buckling defect during fabric forming[END_REF] can be analyzed at the mesoscopic scale. Beyond the defects, the architecture of yarns on a mesoscopic scale makes it possible to calculate the permeability of the textile reinforcement by simulating a flow of resin in the fabric [START_REF] Bréard | Analysis of dynamic flows through porous media. Part I: Comparison between saturated and unsaturated flows in fibrous reinforcements[END_REF][START_REF] Loix | Woven fabric permeability: From textile deformation to fluid flow mesoscale simulations[END_REF][START_REF] Tran | Unified microporomechanical approach for mechanical behavior and permeability of misaligned unidirectional fiber reinforcement[END_REF][START_REF] Gangloff | A process model for the compaction and saturation of partially impregnated thermoset prepreg tapes[END_REF][START_REF] Zeng | Numerical prediction of in-plane permeability for multilayer woven fabrics with manufacture-induced deformation[END_REF]. The mesoscopic analysis provides the direction and the volume fraction of the fibres in the yarns that conditions the mechanical properties of the cured 2 composite [START_REF] Whitcomb | Evaluation of homogenization for global/local stress analysis of textile composites[END_REF][START_REF] Carvelli | A homogenization procedure for the numerical analysis of woven fabric composites[END_REF][START_REF] Lomov | Meso-FE modelling of textile composites: Road map, data flow and algorithms[END_REF][START_REF] Obert | Micro and meso modeling of woven composites: Transverse cracking kinetics and homogenization[END_REF][START_REF] El Said | Multiscale surrogate modelling of the elastic response of thick composite structures with embedded defects and features[END_REF][START_REF] Liang | Multi-scale modeling of mechanical behavior of cured woven textile composites accounting for the influence of yarn angle variation[END_REF]. Simulations of the entire preform draping using mesoscopic models have been developed [START_REF] Gatouillat | Meso modelling for composite preform shaping-simulation of the loss of cohesion of the woven fibre network[END_REF][START_REF] Creech | Meso-modelling of non-crimp fabric composites for coupled drape and failure analysis[END_REF][START_REF] Pickett | Braiding simulation and prediction of mechanical properties[END_REF][START_REF] Bayraktar | Forming and performance analysis of a 3D-woven composite curved beam using meso-scale FEA[END_REF][START_REF] Daelemans | Finite element simulation of the woven geometry and mechanical behaviour of a 3D woven dry fabric under tensile and shear loading using the digital element method[END_REF][START_REF] Thompson | Modelling process induced deformations in 0/90 non-crimp fabrics at the meso-scale[END_REF][START_REF] Iwata | Coupled meso-macro simulation of woven fabric local deformation during draping[END_REF]. These meso-models of the entire preform require very large computing power because of the high number of yarns and their contacts.

The objective of this paper is to propose a simulation approach on the mesoscopic scale with low numerical cost based on macroscopic simulation. Approach of the same nature have been proposed in a more general framework of solid mechanics [START_REF] Whitcomb | Iterative global/local finite element analysis[END_REF][START_REF] Dureisseix | A numerically scalable domain decomposition method for the solution of frictionless contact problems[END_REF][START_REF] Dhia | The Arlequin method as a flexible engineering design tool[END_REF][START_REF] Amini | Multi-scale domain decomposition method for large-scale structural analysis with a zooming technique: Application to plate assembly[END_REF][START_REF] Gendre | A two-scale approximation of the Schur complement and its use for non-intrusive coupling[END_REF] and for the analyses of composite structures [START_REF] Llorca | Multiscale modeling of composite materials: a roadmap towards virtual testing[END_REF].

In the present article, the embedded mesoscopic geometry is derived from the macroscopic deformation.

This may be sufficient for some mesocopic scale analyses (e.g. permeability calculations). Nevertheless, as will be shown, it generally has drawbacks, in particular excessive yarn extensions. A local mesoscopic analysis avoids these problems. This local analysis is performed from the embedded mescopic geometry and only in areas where mesocopic simulation is required. As a result, the numerical cost is moderate.

Two examples are presented: three-point bending and hemispherical forming of a 3D non crimp woven fabric. Experimental analyses, macroscopic, embedded mesoscopic and local mesoscopic simulations are presented and compared.

The mesoscopic analyses are performed locally as downstream simulations after the macroscopic analysis. The aim is to obtain a local solution on a mesoscopic scale. The accuracy of the macroscopic simulation is essential for the quality of the analyses.

After a macroscopic simulation, the presented mesoscopic analyses are done, in two steps. An embedded mesoscopic analysis (without mechanical resolution), then a local mesoscopic analysis which aims to avoid some of the defects of the previous calculation, in particular excessive extensions. The two mesoscopic steps can be considered as two approaches and the results compared.

Macroscopic simulation of the forming with a hyperelastic constitutive law

Because of possible slippage between constituting fibers and yarns, the mechanical behavior of textile reinforcements is very specific compared with traditional materials, such as metals. It leads to a strong tensile stiffness in the fiber directions in comparison to the other rigidities. In the case of thick textile reinforcement, 3D constitutive law is needed. To model the large deformations of these textile reinforcements, hyperelastic constitutive laws for orthotropic materials have been proposed [START_REF] Criscione | Physically based strain invariant set for materials exhibiting transversely isotropic behavior[END_REF][START_REF] Itskov | A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function[END_REF][START_REF] Balzani | A polyconvex framework for soft biological tissues. Adjustment to experimental data[END_REF][START_REF] Ten Thije | Large deformation simulation of anisotropic material using an updated Lagrangian finite element method[END_REF][START_REF] Aimène | A hyperelastic approach for composite reinforcement large deformation analysis[END_REF]. In particular the model developed in [START_REF] Charmetant | Hyperelastic model for large deformation analyses of 3D interlock composite preforms[END_REF] is adapted for the analysis of the deformation of 3D textile reinforcements. Nevertheless, when using this type of model, some discrepancies can be identified because of the limitation of the standard continuum mechanics of Cauchy framework in which these models are formulated. Such models are not able to simultaneously take into account the low transverse shear property (due to possible slippage between the fibres) and the local bending stiffness of the fibres [START_REF] Boisse | The difficulties in modeling the mechanical behavior of textile composite reinforcements with standard continuum mechanics of Cauchy. Some possible remedies[END_REF]. Afterwards, Mathieu et al. [START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF] has improved the 3D hyperelastic model by taking into account the local curvature in 3D hexahedral finite elements. This approach has proven to be effective as shown by the comparison between simulations and experimental results. For the same objective, other models have been developed using second gradient approaches [START_REF] Dell'isola | A two-dimensional gradient-elasticity theory for woven fabrics[END_REF][START_REF] Madeo | Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks[END_REF][START_REF] Agostino | Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements[END_REF]. In this paper, the enhanced hyperelastic model [START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF] is used to carry out the macroscopic simulations. The material parameters of this constitutive model are identified by different experiments using direct or inverse methods.

Studied textile reinforcement

The fabric analyzed in this paper is an E-glass 3D non-crimp orthogonal woven fabric (Fig. 1).

Tab.1 shows the geometric and physical characteristics of the woven reinforcement. The warp and weft yarns are not interlaced. The binder yarns are present through the thickness of the reinforcement. Thus, mechanical properties in the transverse direction are improved, particularly for the resistance to delamination. Fig. 1 shows the structure of this 3D orthogonal woven reinforcement and its architecture obtained by X-ray tomography. This reinforcement is taken as an example to show the different steps of the proposed multi-scale method. The considered hyperelastic constitutive law models the deformation of thick 3D composites reinforcements. Six deformation modes are considered (Fig. 2). Thick textile reinforcements have three privileged directions: the warp direction 1 M ; the weft direction 2 M and the direction of thickness 3

M

that is perpendicular to the plane ( )

1 2
, M M . According to the representation theorems [START_REF] Boehler | Applications of tensor functions in solid mechanics[END_REF], the strain energy density function of an orthotropic material can be written as:

( ) (2)

1
and the mixed invariants are defined by the direction vectors i M (i=1,3): , and

= ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ i i i j i i i ij i I M C M I M C M I M C M (3)
For each deformation mode of Fig. 2, a corresponding physical invariant is defined in Equation ( 4) by combination of the invariants defined in Equation ( 2) and (3) [START_REF] Charmetant | Hyperelastic model for large deformation analyses of 3D interlock composite preforms[END_REF]. been shown [START_REF] Mitchell | Investigation into the changes in bending stiffness of a textile reinforced composite due to in-plane fabric shear: Part 2-Numerical analysis[END_REF][START_REF] Yao | Influence of tension-shear coupling on draping of plain weave fabrics[END_REF][START_REF] Alshahrani | Characterization and finite element modeling of coupled properties during polymer composites forming processes[END_REF], it is assumed, for the purpose of simplicity, that the contribution to the strain energy potential of each deformation mode is independent from the others. Therefore, the strain energy density is the sum of 6 terms:

  = = =     -   = = = = (4)
1 1 2 2 1 1 2 2 ( ) ( ) ( ) ( ) ( ) ( ) elong elong elong elong comp comp cp cp ct ct ct ct w w I w I w I w I w I w I = + + + + + (5)
The form of each strain energy density can be written in polynomial form [START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF]:

6 1 6 6 1 if 0 if 0 i i i i i i k I I w k I I = + =  >   =   ≤   ∑ ∑ (6)
where I is the physical invariant related to the concerning strain energy. The coefficients i k need to be determined by appropriate experiments. Then, the second Piola-Kirchhoff stress tensor S and Cauchy stress tensor σ can be calculated by derivation:

2 2 k k k w I w S C I C ∂ ∂ ∂ = = ∂ ∂ ∂ (7) 1 2 T T w J F S F F F J C σ - ∂ = ⋅ ⋅ = ⋅ ⋅ ∂ (8)

Taking into account the curvature of the fibers

The presented anisotropic hyperelastic model used in hexahedral finite element is based on the standard continuum mechanics of Cauchy. It has been shown that beyond this approach, the fiber bending stiffness associated to the curvature is significant to depict correctly the mechanical behavior of fabrics [START_REF] Boisse | The difficulties in modeling the mechanical behavior of textile composite reinforcements with standard continuum mechanics of Cauchy. Some possible remedies[END_REF][START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF]. An independent bending stiffness of fibers has been added into the 3D hexahedral finite element [START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF]. The curvature in the hexahedral element is calculated from the geometrical position of neighboring elements (Fig. 3) [START_REF] Onate | Rotation-free triangular plate and shell elements[END_REF]. Then, a nonlinear constitutive law is defined by Equation ( 9) and this fiber bending stiffness is added to the others. Mbend is the bending moment, χ is the curvature and D0 and D1 are parameters determined by inverse identification:

( ) 0 0 1 1 0 if 2 if not 2 bend D D D D M D χ χ χ χ  - <   =     (

Identifications of material parameters

The identification of material parameters i k of Eq. ( 6) were carried out by the following tests:

tensile tests in the warp and weft directions, transverse compaction test, in-plane shear test, and transverse shear tests. In addition, the two parameters 0 D and 1 D were determined by a bending test.

The main interest of the physical invariants used in the strain energy densities (Eq. ( 5)) is that they correspond to the deformations of the elementary tests and make possible a simple identification of the potentials, and thus of the ki of equation [START_REF] Sjölander | Forming induced wrinkling of composite laminates: a numerical study on wrinkling mechanisms[END_REF]. Each test contributes to a specific energy density.

These tests are briefly described below and the identified parameters are given in Tab.A1 in Appendix A.

Elongations in warp and weft directions

Textile materials have a high stiffness in tension with respect to other stiffnesses. This results in small tensile strains in the yarns (a few percent before rupture). The hyperelastic tensile potential parameters are given in Tab. A1 in the case of the studied textile reinforcement. The specimen with dimensions of 70 × 20 mm 2 is fixed on the jaw surfaces (Fig. 6). This studied reinforcement is not balanced and the transverse shear behaviour in the direction warp and weft is different and transverse shear potentials are identified in the warp and weft directions.

Additional bending behaviour of fibres

The aim here is to complete the 3D hyperelastic behaviour with an additional stiffness linked to the curvature of the fibres [START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF]. A three-point bending test is carried out for this identification analysis. A

Levenberg-Marquardt algorithm is used for an inverse identification of the coefficients D0 and D1 of Equation ( 9).

Macroscopic textile reinforcement forming simulations

The macroscopic simulations (i.e. the simulations at the scale of the textile preform) carried out in this paper use the in-house software PlasFib [START_REF]Inter Deposit Certification[END_REF][START_REF] Hamila | A meso-macro three node finite element for draping of textile composite preforms[END_REF][START_REF] Hamila | A semi-discrete shell finite element for textile composite reinforcement forming simulation[END_REF]. This finite element code uses an explicit dynamic scheme as is the case with most software for forming simulation. Macroscopic simulations of three points bending and hemispherical stamping of are carried out using the above hyperelastic behavior and the parameters identified for the 3D non-crimp orthogonal woven fabric. The macroscopic results serve as a basis for mesoscopic modelling in the macro-meso method developed.

Three point bending

A 200×30 mm 2 strip of 3D non-crimp woven fabric is loaded in three point bending with a 30 mm deflection imposed at a speed of 10 mm/min (Fig. 7). The paper focuses on the bending in the warp direction with which the binder yarns are aligned (Fig. 8). Fig. 9 shows the comparison of the deformed middle line obtained by simulation and experiment.

They are in correct agreement.

Mesoscopic analyses based on macroscopic simulations (embedded mesoscopic geometries)

Mesoscopic analyses consider the deformation of each yarn in contact with their neighbours..

Analyses of the entire preform at the mesoscopic scale have been carried out [START_REF] Gatouillat | Meso modelling for composite preform shaping-simulation of the loss of cohesion of the woven fibre network[END_REF][START_REF] Creech | Meso-modelling of non-crimp fabric composites for coupled drape and failure analysis[END_REF][START_REF] Pickett | Braiding simulation and prediction of mechanical properties[END_REF][START_REF] Bayraktar | Forming and performance analysis of a 3D-woven composite curved beam using meso-scale FEA[END_REF][START_REF] Daelemans | Finite element simulation of the woven geometry and mechanical behaviour of a 3D woven dry fabric under tensile and shear loading using the digital element method[END_REF][START_REF] Thompson | Modelling process induced deformations in 0/90 non-crimp fabrics at the meso-scale[END_REF][START_REF] Iwata | Coupled meso-macro simulation of woven fabric local deformation during draping[END_REF], but the size of the numerical model and the computation time are very important. In this paper, with the aim of analyzing mesoscopic deformations of the woven reinforcement during the forming process, the developed macro-meso method proposes to carry out mesoscopic analyses by using, as a first step, the information obtained at the macroscopic scale. If macroscopic information is pertinent, it should be able to provide certain basic elements at the mesoscopic scale. In a first step, the embedded mesoscopic geometry is determined from the macroscopic simulation.

Mesoscopic geometry of the undeformed RVE

In this work the 3D textile reinforcement in its initial configuration is considered to be periodic. In a mesoscopic modelling, the Representative Volume Element (RVE) is the smallest elementary pattern, which allows reconstituting the entire fabric by repetitions and translations [START_REF] Miehe | A framework for micro-macro transitions in periodic particle aggregates of granular materials[END_REF]. The geometry of the RVE of the 3D non-crimp woven fabric studied in the present paper is obtained using X-ray micro tomography (Fig. 12) [START_REF] Naouar | 3D composite reinforcement meso FE analyses based on X-ray computed tomography[END_REF]. A mesh composed of prismatic elements is generated from this geometry.

The finite element model constructed has no interpenetrations as can occur using software packages for 3D modelling of textiles [START_REF] Long | Modelling the geometry of textile reinforcements for composites: TexGen[END_REF]. To obtain a first mesoscopic model, the woven elementary cells (RVE) embedded in the macroscopic reinforcement are considered. The initial configuration of the RVE is given by the X-ray tomography analysis and the associated mesh (Fig. 13).

Fig. 13 Initial state: mesoscopic RVEs embedded in a macroscopic mesh of the fabric

Deformed geometry of the embedded mesoscopic model

Each node of the mesoscopic model can be located (embedded) in a macroscopic element (Fig. 14).

An embedded mesoscopic element is deformed together with the macroscopic element and its nodes have constant coordinates in the macroscopic reference element. In the initial and deformed configuration, the naturel coordinates ( , , ) ξ η ζ of a mesoscopic node in the corresponding macroscopic element remain constant and the position of a mesoscopic embedded element remains constant within the macroscopic element. Consequently, the deformation obtained by the macroscopic simulation can provide a first deformed geometry of the RVEs at the mesoscopic scale in the deformed configuration that is called embedded meso model.

Analysis of deformations on a mesoscopic scale

To analyze the deformations of the meso-FE model, strain invariants corresponding to deformation modes at the mesoscopic scale are calculated from the initial and deformed geometries of the yarns (Fig. 15). The yarns are assumed to be transversely isotropic. For this type of material, a hyperelastic strain energy potential in the following form can be defined [START_REF] Boehler | Applications of tensor functions in solid mechanics[END_REF]:

= ⋅ ⋅ = ⋅ ⋅ II M C M II M C M ( 12
)
The physical invariants that correspond to the deformation modes are introduced [67] (Fig. 15).

They are linked to the above invariants and are used to quantify the deformation at the mesoscopic scale.

= =     - -   = + - = -             (13)
where elong I is the stretch invariant in the fiber direction; comp I is the transverse compression invariant; dis I is the transverse distortion invariant and sh I is the longitudinal shear invariants of the yarn.

Embedded mesoscopic analyses: three points bending

The geometry of the reinforcement at mesocopic scale (Fig. 12), positioned in the undeformed (flat) configuration of the bending specimen defines the embedded mescoscopic elements (Fig. 16a). They are fixed in the macroscopic model and follow it in its deformation (Fig. 16b and17). From the macroscopic simulation presented in section 2.5.1, the embedded mesoscopic analysis of three points bending provides the deformations of the yarns, their final orientations and then the voids in the unit 13 cell. These results can be used for the calculation of permeability in the following resin injection stage.

Fig. 16 presents the initial and deformed geometries of the textile reinforcement in three point bending.

Embedded mesoscopic analyses: hemispherical stamping

This embedded mesoscopic analysis is based on the macroscopic simulation of the hemispherical forming presented in section 2.5.2. The mesoscopic embedded elements are defined from the mesoscopic geometry of the reinforcement (Fig. 12) positioned in the initial macroscopic reinforcement. These mesoscopic embedded mesoscopic elements deform with the macroscopic model. The embedded mesoscopic analysis of the hemispherical stamping provides the orientations and deformation of each (c) yarn (Fig. 18). This deformed preform with a double curved shape can be achieved thanks to in-plane shear.

Local mesoscopic simulations from the embedded analyses

The macro-meso embedded analysis described in section 3 can provide a solution at the mesoscopic scale in forming analysis. It is very fast and may be enough to determine some quantities such as permeability. However, the equations of mechanics at the mesoscopic scale are not strictly verified. The deformed mesocopic embedded configuration is not obtained by solving a mechanical problem but is directly deduced from the macroscopic analysis, itself approximated given the assumptions on the continuous medium and the finite element approach. The embedded mesoscopic analysis provides displacements and deformations in the yarns. Given the constitutive law, the stresses do not check the local equilibrium. In particular, this approach can lead to excessive elongations of yarns because it does not take into account the local slippage between the yarns. This point is first highlighted. To overcome this difficulty, a local mesoscopic simulation based on the macroscopic analysis and the embedded mesoscopic analysis is proposed. Finally, the mesoscopic numerical results are compared with the experiment.

Excessive elongations

In the results obtained by the macro-meso embedded analysis, some excessive elongation may occur. For instance in Fig. 17c, the elongations of the binder yarn reach 11%, which is excessive. This ??=41°

is because the approach is based on the macroscopic analysis and does not take into account the local slippage between the yarns. For intermediate yarns such as those considered in Fig. 19, the elongation is important and much larger than effective stretching of yarns in the fabric. In particular, the elongations of the binder yarns are large (Fig. 17c).

Local mesoscopic simulation

The macro-meso embedded analysis avoids having to carry out a mesoscopic scale simulation for the entire textile reinforcement that is numerically very expensive and it is not always possible to carry out. In order to use this method and avoid the spurious yarn elongations highlighted in the previous section, a mesoscopic simulation is carried out on a local zone (for example a RVE) from the results of the macro-meso embedded simulations. The deformed configuration obtained by the embedded mesoscopic simulation constitutes the initial state of the local mesoscopic calculation.This configuration has some drawbacks, in particular excessive yarn elongations, but nevertheless it constitutes an initial state close to the solution and interesting for the local mesoscopic simulation.

Mesoscopic simulation

A hyperelastic transverse isotropic (Neo-Hookean) constitutive law is used to describe the mechanical behaviors of yarns. The strain energy potential is divided into two parts [START_REF] Bonet | A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations[END_REF]:

The isotropic potential iso w describes the longitudinal behaviour of a yarn, and the potential trans w corresponds to the deformations of a yarn in the transverse plane. Table B2 in Appendix B shows the four material parameters used in the mesoscopic simulation [START_REF] Florimond | Contribution à la modélisation mécanique du comportement de mèches de renforts tissés à l'aide d'un schéma éléments finis implicite[END_REF]. This hyperelastic law is implemented in Abaqus/Explicit, by a VUMAT user subroutine. Contact with friction between yarns is controlled by a penalty method and a Coulomb friction model with a coefficient of 0.21 [START_REF] Hivet | Design and potentiality of an apparatus for measuring yarn/yarn and fabric/fabric friction[END_REF]. During hemispherical stamping, in-plane shear is the main deformation mode because it is necessary to obtain the spherical geometry which is double curved. A RVE in the high-shear zone is analyzed (Fig. 22). A macro-meso embedded analysis of the entire textile reinforcement is first carried out. It leads to spurious elongations of the yarns (Fig. 22a). In the local mesoscopic calculation, all the displacements of the macro-meso embedded analysis inside the cell are relaxed. On the edges, the displacements in the plane of the cell are retained for the yarns oriented by the edge. For the other yarns the displacements in the cell plane are retained in the center of the yarn. Relative slippage between the yarns in contact is possible. The comparison before and after this simulation (Fig. 22) shows the excessive elongation phenomenon have been avoided. Because this RVE is subjected to a high shear stress, the sections of the ends of yarns no longer remain parallel with the yarns in the other direction.

Comparisons of numerical and experimental results at the mesoscale

To demonstrate the correctness of the proposed approach, the numerical and experimental results are compared in the case of three points bending. The bending experiment is performed under the same condition as described in section 2.5.1. After the bending, a resin is injected into the deformed fabric.

Then, the fabric fixed by the resin is cut on the section of binder yarn. This makes it possible to observe the deformed geometry of the yarns (Fig. 24).

Conclusion

Analyses on a mesoscopic scale give the internal geometry and therefore the deformations and internal defects of textile reinforcements during forming. Draping of woven fabrics can be simulated by mesoscopic analysis of the entire preform, but these simulations lead to generally prohibitive computation times. An approach based on the macroscopic simulation of the forming process and the embedded mesoscopic model was presented. It provides a solution at the mesoscopic scale by a local analysis based on the embedded geometry. The local mesoscopic model is linked to the macroscopic model at its edges, but is relaxed enough to avoid spurious extensions. This local mesoscopic calculation is only carried out in areas where this analysis is necessary, e.g. maximum shear zones or regions of high curvature. It has been shown that the approach achieves the mesoscopic deformation of a woven cell in the case of three-point bending of the textile reinforcement and in the case of a hemispherical forming. In the latter case, local deformation of a sheared woven cell was obtained.

The deformed geometries obtained by the mesoscopic analysis can be used to determine the change in fibre volume fraction of the yarns during draping and their consequences on the mechanical properties of the cured composite. In addition, the voids obtained between the deformed yarns can change the permeability of the textile reinforcement.

Appendix B. Hyperelastic transverse isotropic constitutive law for the mesoscopic simulation

The hyperelastic transverse isotropic (Neo-Hookean) constitutive law is made up of a sum of two potentials [START_REF] Bonet | A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations[END_REF]: the isotropic potential iso w describes the longitudinal behaviour of a yarn, and the potential trans w corresponds to the deformations of a yarn in the transverse plane.

[ ]

  = +   = -- + -    = + + - -- -   (B1)
The parameters λ , µ , α , β and γ are defined in Equation (B2) according to the four material parameters: transverse modulus of elasticity E, longitudinal modulus of elasticity A E , Poisson's ratio ν and longitudinal shear modulus A G . Then the material parameters used in the mesoscopic simulation are given in Table B2 [START_REF] Florimond | Contribution à la modélisation mécanique du comportement de mèches de renforts tissés à l'aide d'un schéma éléments finis implicite[END_REF].

Fig. 1 2

 12 Fig.1Structure of the 3D non-crimp orthogonal woven fabric and its 3D architecture by X-ray tomography Tab.1 Geometric characteristics of the woven reinforcement[START_REF] Vilfayeau | Modélisation numérique du procédé de tissage des renforts fibreux pour matériaux composites[END_REF] Linear mass, ±6% (g/km)

  In-plane shear (e) Transverse shear_warp (f) Transverse shear_weft

Fig. 2

 2 Fig.2Six deformation modes of a 3D woven reinforcement[START_REF] Charmetant | Hyperelastic model for large deformation analyses of 3D interlock composite preforms[END_REF]

  are the classical invariants of the right Cauchy-green tensor

  are the stretch invariants in warp and weft directions; comp I is the compression invariant in the thickness direction; cp I is the in-plane shear invariant and ct I α are the transverse shear invariants in warp and weft directions. In this hyperelastic model, a strain energy potential is a function of the right Cauchy Green physical invariants. Although couplings between the different properties have

Fig. 3 a

 3 Fig.3 a) Integration areas in the hexahedral element b) Computation of curvatures from neighbouring elements[START_REF] Mathieu | Enhanced modeling of 3D composite preform deformations taking into account local fiber bending stiffness[END_REF]

2. 4 . 2

 42 Fig.4 a) Experimental device and b) experimental and numerical identification curves 2.4.3 In-plane shearThe Bias Extension Test (BET) is used to realize the identification of material parameters of inplane shear mode[START_REF] Lebrun | Evaluation of bias-extension and picture-frame test methods for the measurement of intraply shear properties of PP/glass commingled fabrics[END_REF][START_REF] Cao | Characterization of mechanical behavior of woven fabrics: experimental methods and benchmark results[END_REF][START_REF] Na | Shear behavior of a shear thickening fluid-impregnated aramid fabrics at high shear rate[END_REF][START_REF] Boisse | The bias-extension test for the analysis of in-plane shear properties of textile composite reinforcements and prepregs: a review[END_REF]. In order to obtain an in-plane shear deformation, the yarns of a specimen with dimensions 210×70 mm are oriented at 45° with respect to the direction of traction.

Fig. 6 a

 6 Fig. 6 a) Experimental device and identification curves for transverse shear in the b) warp and c) weft directions

Fig. 7

 7 Fig. 7 Three points bending

Fig. 8 Fig. 9

 89 Fig. 8 Transverse shear angle of the initial and deformed preform in bending

Fig. 11

 11 Fig.11 Top view of the deformed preform: simulation (left) and experiment (right)

Fig. 12 a

 12 Fig.12 a) Geometry obtained by X-ray tomography of the 3D non-crimp woven reinforcement, b) Corresponding prism mesh

  are the reference coordinates in the macro element, meso X and macro X the spatial coordinates of the mesoscopic and macroscopic node.

Fig. 14

 14 Fig.14 Embedded meso model in a macro element. Real and reference frames.

Fig. 15

 15 Fig.15 Deformation modes of a yarn: (a) elongation compaction (c) distortion (d) longitudinal shear

5 ,

 5 are classic invariants defined in Equation (2), and 4 II II are mixed invariants defined by the direction of the fibers M :

Fig. 17

 17 Fig.17 displays the mesoscopic elongation and transverse compaction invariants of yarns in the bending test.

Fig. 16 .Fig. 17 .

 1617 Fig.16. Three point bending: Transverse sections of the initial (a) and deformed (b) geometries

Fig. 18 .

 18 Fig. 18. Hemispherical forming. Embedded mesoscopic analysis. Deformations of yarns in compaction (Invariant Icomp).

Fig. 19 considers 1 M diag and 2 M

 1912 Fig.19considers the case of a shear deformation of a macroscopic finite element. This deformation is frequent in the forming of textile materials. The two blue lines represent two yarns in the undeformed macroscopic element. Besides, the two red lines represent the same two yarns in the deformed macroscopic element. In this element, the diagonals

Fig. 19 .

 19 Fig.19. Elongation of yarns in a sheared macroscopic element

4. 2 . 2

 22 Three points bending: local mesoscopic simulation The local mesoscopic simulation must be linked to the macroscopic simulation. In the case of threepoint bending, the displacements of all nodes of the meso embedded analysis are relaxed except for the nodes of the right and left sections of the RVE for which the components of displacement in the direction of the beam are set equal to those of the macroscopic calculation. The results of the extensions obtained by the embedded mesoscopic analysis and by the local mesoscopic analysis are shown in Fig.20.

Fig. 20 .

 20 Fig. 20. Three points bending: mesoscopic simulations of a RVE. a) Elongation in macro-meso embedded analysis b) Elongation in local mesoscopic simulation analysisThe elongation of ten elements located in different areas of this RVE are displayed in Fig.21. Thisshows that the spurious elongations obtained in the macro-meso embedded analysis are mostly removed by the local mesoscopic simulation.

Fig. 21

 21 Fig.21 Elongation at different points obtained by the macro-meso embedded analysis and the local mesoscopic simulation in a RVE of the reinforcement in three points bending 4.2.3 Hemispherical forming: local mesoscopic simulation

Fig. 22

 22 Fig.22 Hemispherical stamping: mesoscopic simulations of a RVE. a) Elongation in macro-meso embedded analysis b) Elongation in local mesoscopic simulation analysis

Fig. 23 .

 23 Fig.23. Elongation at different points obtained by the macro-meso embedded analysis and the local mesoscopic simulation in a RVE in hemispherical stamping

Fig. 24 .

 24 Fig. 24. Observation of mesoscopic geometry of the deformed reinforcement by microscope A comparison between the experimental and simulated geometry of a deformed RVE is presented in Fig. 25. They are in good agreement. In both cases, slippage occurs between the yarns during the bending deformation of the reinforcement.

Fig. 25 .

 25 Fig. 25. Woven unit cells in the same position obtained by: a) Local mesoscopique simulation b) experiment c) comparison

Table A1 .

 A1 Material parameters used for macroscopic simulations (ki in MPa, D0 in Nmm, D1 in Nmm2)

		k1	k2	k3	k4	k5	k6
	welong1/2	8.692 k7	4.816e3 k8	-1.002e6 k9	8.275e7 k10	-2.419e9 k11	2.442e10 k12
		8.692	-5.056e2	1.073e5	-2.687e6	0	0
	wcomp	k1/ k7 9.69e-2	k2/ k8 7.009e-1	k3/ k9 6.426e-2	k4/ k10 -1.339e0	k5/ k11 8.777e-1	k6/ k12 2.855e-2
	wsh	k1/ k7 3.441e-1	k2/ k8 -2.019e0	k3/ k9 7.416e0	k4/ k10 -1.401e1	k5/ k11 1.401e1	k6/ k12 -5.444e0
	wshT1	k1/ k7 3.721e-2	k2/ k8 3.844e-2	k3/ k9 -5.21e-1	k4/ k10 1.877e0	k5/ k11 -2.78e0	k6/ k12 1.572e0
	wshT2	k1/ k7 3.473e2	k2/ k8 -5.674e-2	k3/ k9 -1.46e-2	k4/ k10 5.835e-1	k5/ k11 -1.201e0	k6/ k12 8.084e-1
			D0 (warp)	D1 (warp)	D0 (weft)	D1 (weft)
			3.6	117.9	3.748	123.6

Table B2 .

 B2 Material parameters used in Neo-Hookean constitutive law

				E (MPa)	EA (MPa) elongation		EA (MPa) compression		ν				GA ( MPa)
								3200	45516				100		0					1600
	λ	=	2 (1 ) + + n ν ν ( m E ν	)	µ	=	2(1 ) + E ν	= -α µ	G	A	β	=	2 4 (1 ) (1 ) -+ E n m ν ν	γ	=	E	A	(1 ) 8 -m ν	-	2 8 + λ µ α 2 + -	β	(B2)
	m	1 = --ν	2	n ν	2	/ n E E = A

Acknowledgment

This work was supported by the ANR, (French Research Agency), grant aap-rmnp-2013-INTERLOCK and by the China Scholarship Council (CSC) (J. Wang).

The objective of this paper was to show the feasibility of this meso-macro approach. Validation work, determination of the precision will be a next step in particular by extending the comparisons to different cases of forming and different unit cells in the reinforcement.

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.