Lucía García De La Cruz

Mayerling Martinez

Clément Keller

Eric Hug

Achieving good tensile properties in ultrafine grained nickel by Spark Plasma Sintering

Keywords: nickel, ball milling, spark plasma sintering, ultrafine grained microstructure, internal stresses, mechanical properties

In this work, the tensile properties of ultrafine grain Ni samples processed by spark plasma sintering are investigated. To this aim, a high purity Ni powder was nanostructured by ball milling using different processing conditions, and consolidation of the powder was performed by spark plasma sintering. Milling parameters were varied to produce samples with different microstructures. Each sample was characterised in terms of grain size and grain boundary character distribution to study the influence of milling parameters on the microstructure. Results show that suitable ball milling and subsequent sintering can be employed to obtain specimens with grain sizes in the ultrafine grain range with a high fraction of Σ3 grain boundaries. All samples exhibit a low internal stress state, which is evaluated in terms of grain orientation spread computed from electron backscatter diffraction and dislocation observation by transmission electron microscopy. Uniaxial tensile testing shows an increase in yield strength with grain refinement with a pronounced deviation from the Hall-Petch relation, for samples with grain sizes below 1.2 µm. Heterogeneity in deformation at yielding seems responsible for the deviation due to differences in the strain hardening behaviour between ultrafine grains and conventional coarse grains. All samples display high ductility with values of elongation to fracture above 35 % as well as good toughness. The combination of ball milling with spark plasma sintering is therefore a promising tool to produce ultrafine grain Ni with good mechanical properties.

Introduction

Ultrafine grained (UFG) materials are characterised by a microstructure with a grain size typically in the 0.1-1 µm range. The current interest in UFG materials arises from their specific physical properties [START_REF] Huang | Advances in ultrafine-grained materials[END_REF][START_REF] Estrin | Extreme grain refinement by severe plastic deformation: A wealth of challenging science[END_REF][START_REF] Langdon | Twenty-five years of ultrafine-grained materials: Achieving exceptional properties through grain refinement[END_REF][START_REF] Valiev | Producing Bulk Ultrafine-Grained Materials by Severe Plastic Deformation: Ten Years Later[END_REF], superior mechanical behaviour [START_REF] Valiev | On the origin of extremely high strength of ultrafine-grained Al alloys produced by severe plastic deformation[END_REF][START_REF] Kawasaki | Interpretation of hardness evolution in metals processed by high-pressure torsion[END_REF], and the attractive combination with other functional properties, such as higher wear resistance [START_REF] Zhilyaev | Wear resistance and electroconductivity in copper processed by severe plastic deformation[END_REF] or ultrafast diffusion rates [START_REF] Straumal | Diffusion of 63Ni in severely deformed ultrafine grained Cu-based alloys[END_REF][START_REF] Prokoshkina | Persistence of ultrafast atomic diffusion paths in recrystallizing ultrafine grained Ni[END_REF]. The two main techniques to manufacture bulk UFG materials are powder metallurgy and Severe Plastic Deformation (SPD). SPD techniques are more frequently used and studied, however, they are limited by a lack of homogeneity [START_REF] Vorhauer | On the homogeneity of deformation by high pressure torsion[END_REF], a low ductility [START_REF] Krasilnikov | Tensile strength and ductility of ultra-fine-grained nickel processed by severe plastic deformation[END_REF][START_REF] Dalla Torre | Deformation behaviour and microstructure of nanocrystalline electrodeposited and high pressure torsioned nickel[END_REF], and the small dimensions of the processed specimens. In addition, the control of the grain size remains difficult with SPD due to the existence of a processing optimum, which leads to the most homogeneous microstructure [START_REF] Kawasaki | Interpretation of hardness evolution in metals processed by high-pressure torsion[END_REF][START_REF] Zhilyaev | Experimental parameters influencing grain refinement and microstructural evolution during high-pressure torsion[END_REF][START_REF] Zhilyaev | Microhardness and microstructural evolution in pure nickel during high-pressure torsion[END_REF].

Powder metallurgy can overcome some of the drawbacks of SPD by enabling the synthesis of homogeneous specimens with different microstructures in the UFG range. To this aim, the starting powder consists of either nanopowder or nanostructured powder obtained by ball milling. To preserve the refined microstructure, the precursors are sintered by means of high isostatic pressure (HIP) or spark plasma sintering (SPS). Both techniques apply pressure simultaneously to heating, achieving very fast heating rates and limiting grain growth as reported for various metals and alloys [START_REF] Ouar | Spark Plasma Sintering of Co80Ni20 nanopowders synthesized by polyol process and their magnetic and mechanical properties[END_REF][START_REF] Menapace | Spark plasma sintering behaviour of copper powders having different particle sizes and oxygen contents[END_REF][START_REF] Song | Grain growth and sintering characteristics of Ni-Cu alloy nanopowders consolidated by the spark plasma sintering method[END_REF][START_REF] Trzaska | Densification of Ni and TiAl by SPS: kinetics and microscopic mechanisms[END_REF][START_REF] Bui | Modeling of microstructure effects on the mechanical behavior of ultrafine-grained nickels processed by hot isostatic pressing[END_REF] including nickel [START_REF] Bousnina | Spark plasma sintering and hot isostatic pressing of nickel nanopowders elaborated by a modified polyol process and their microstructure, magnetic and mechanical characterization[END_REF]. For this last reference, a low relative density (86 %) and fracture occurring in the elastic regime indicates the presence of oxides, mainly due to the use of nanopowder as starting material. Indeed, sensitivity to oxidation strongly depends on the specific surface area of the powder and thus on the particle size. Such layers of oxides are formed on the surface of the nanoparticles and act as diffusion barriers, avoiding higher densification. Powder nanostructured by ball milling displays a particle size of the order of micrometres being much less susceptible to oxidation.

Varying the ball milling parameters also leads to powders with diverse characteristics, such as morphology, size, and microstructure i.e. crystallite size, microstrain and texture [START_REF] Prasad Yadav | Mechanical Milling: a Top Down Approach for the Synthesis of Nanomaterials and Nanocomposites[END_REF][START_REF] Koch | Synthesis of nanostructured materials by Mechanical Milling: problems and opportunities[END_REF][START_REF] Suryanarayana | Mechanical alloying and milling[END_REF]. The effect of some of these parameters on the resulting powder can be found for several metals and alloys: Al [START_REF] Ramezani | Mechanical milling of aluminum powder using planetary ball milling process[END_REF][START_REF] Razavi-Tousi | Effect of ball size on steady state of aluminum powder and efficiency of impacts during milling[END_REF][START_REF] Mendoza-Duarte | Study of Al composites prepared by high-energy ball milling; Effect of processing conditions[END_REF][START_REF] Khan | Effect of grain refinement on mechanical properties of ball-milled bulk aluminum[END_REF], Cu [START_REF] Boytsov | Correlation between milling parameters and microstructure characteristics of nanocrystalline copper powder prepared via a high energy planetary ball mill[END_REF], TiFe [START_REF] Neto Mendes Leal | Mechanical Alloying: An Investigation on the High-Energy Ball Milling of Iron-Titanium Powder Mixtures without Process Control Agents[END_REF] or 316L [START_REF] Keller | Influence of spark plasma sintering conditions on the sintering and functional properties of an ultra-fine grained 316L stainless steel obtained from ball-milled powder[END_REF][START_REF] Marnier | Functional properties of a spark plasma sintered ultrafinegrained 316L steel[END_REF]. Research activities concerning Ni have focused on a single parameter, milling time [START_REF] Bonetti | Magnetoelasticity and internal strains in nanocrystalline nickel[END_REF][START_REF] Daroczi | Magnetic properties of Ball Milled Nanocrystalline Ni and Fe[END_REF], or on the properties of powders after ball milling: oxidative behaviour [START_REF] Kar | Structural investigations of oxidative behavior on nanocrystalline nickel[END_REF], deformation evolution [START_REF] Garroni | Deformation conditions for Ni powders undergoing mechanical processing[END_REF], and solidstate transformations [START_REF] Bolokang | Solid-state transformation in ball milled nickel powder[END_REF]. Nevertheless, to our knowledge, the coupled effects of ball milling and SPS on the microstructure and tensile properties of bulk samples with grain sizes in the UFG regime have not been deeply investigated. This characterisation is of prime importance to ensure the development of powder metallurgy as a valuable tool for the elaboration of UFG metals and alloys.

In the present work, UFG Ni samples with variable grain size were processed by SPS.

The obtained microstructure and the initial internal stress level were investigated by means of electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM).

Afterwards, uniaxial tensile testing was performed in selected samples to evaluate their mechanical properties. The synthesis parameters were selected to produce samples with different grain sizes in the fine grained (FG)/UFG range, which can involve changes in deformation mechanisms [START_REF] Hug | Temperature dependence and size effects on strain hardening mechanisms in copper polycrystals[END_REF][START_REF] Hug | Size effects and temperature dependence on strain-hardening mechanisms in some face centered cubic materials[END_REF][START_REF] Keller | Microstructural size effects on mechanical properties of high purity nickel[END_REF]. Ductility was investigated as the major drawback in UFG metals, as well as the impact of the refined microstructure in strength (Hall-Petch relation).

Experimental procedures

Ball milling process and characterization of the powder

Nanostructured powders were prepared by high-energy ball milling from a high purity commercial nickel powder provided by Good Fellow©. The powder has a certified purity of 99.8 %, the main impurities being: Fe 100 ppm, C 200 -600 ppm, O 1000 ppm and S 10 ppm.. Ball milling (BM) was performed in a Fritsh planetary pulverisette 7 using WC vials (80 mL) and grinding balls (5 mm in diameter). Ball-to-powder ratio was fixed to 10:1. In order to modify the characteristics of powders and study their impact on the microstructure of samples after consolidation by SPS, rotation speed and milling time were varied. Time and rotation speed ranges were chosen to limit processing time and probability of contamination from the milling media. Anhydrous methanol was chosen as process control agent (PCA) for its low reaction with Ni powders [START_REF] Arias | Chemical reactions of metal powders with organic and inorganic liquids during ball milling[END_REF][START_REF] Arias | The Role of Chemical Reactions in the Mechanism of Comminution of Ductile Metals into Ultrafine Powders by grinding[END_REF] and its low boiling point, making elimination easier.

The amount of methanol ranged from 16.7%wt.% to 66.7 wt.% [START_REF] Keller | Influence of spark plasma sintering conditions on the sintering and functional properties of an ultra-fine grained 316L stainless steel obtained from ball-milled powder[END_REF], and showed little impact on the corresponding microstructures. Vials were prepared and closed in a glove box with a high purity argon atmosphere in order to avoid oxidation of the powders. The milling time was divided in cycles of 5 min followed by a 1 min pause to reduce overheating which can enhance powder reactivity. Rotation direction was systematically reversed between cycles to make the process more effective and homogeneous.

Morphology and particle size of the as-received and ball milled powders were analysed by Scanning Electron Microscopy (SEM) using a Zeiss Supra 55. X-ray diffraction (XRD) measurements with a Panalytical X'Pert diffractometer using Cu Kα radiation (λ = 0.1541 nm) were employed to examine the presence of diffraction peaks corresponding to oxides.

Spark Plasma Sintering

Consolidation of the powders was performed by SPS with a FCT System GmbH, HD25 SPS apparatus. Graphite dies, punches and foils were employed in the synthesis. To limit grain growth, the sintering temperature was set to 1023 K, with a heating rate of 100 K/min by continuous current. Sintering was performed under a medium dynamic vacuum (~0.5 mbar). A thermocouple placed inside a hole in the die a few millimetres from the powder was used to monitor the temperature. A uniaxial force was applied throughout the sintering process. The maximum pressure was set to 75 MPa and a dwell time of 10 min was employed. For microstructural characterisation, disc-like specimens with a diameter of 20 mm and 2 mm in thickness were produced. In addition, 50 mm diameter samples, with a thickness of 6 mm were sintered with the same temperature and pressure cycles to produce tensile testing specimens for uniaxial tensile testing. The homogeneity of the samples was verified by hardness cartographies of the surfaces as performed previously for ceramic materials [START_REF] Bourgès | Structural analysis and thermoelectric properties of mechanically alloyed colusites[END_REF]. An additional sample with a grain size in the coarse-grained range was produced from the as received powder using the sintering conditions employed for the synthesis of UFG samples, with the exception of temperature (1273 K). The density of the bulk samples was determined using an immersion densitometry method (mass accuracy 1 mg).

Microstructure analysis and mechanical properties

The microstructure of the sintered samples was investigated by means of EBSD. For the sake of accuracy, at least 1000 grains were covered for each sample with a step size ensuring more than 4 points per grain along a given direction. For an optimal surface condition, samples were first mechanically polished with SiC paper and afterwards electropolished using a solution of perchloric acid, 2-butoxyethanol and ethanol at a voltage of 24 V. The TSL OIM® analysis software was used to estimate average grain size, grain boundary character distribution (GBCD), grain orientation spread (GOS), and to study the crystallographic microtexture of the sintered specimens from their pole figures. Brandon's criterion [START_REF] King | What does it mean to be special? The significance and application of the Brandon criterion[END_REF] was used for coincidence site lattice (CSL) fraction determinations, which were calculated on a number basis. The misorientation for determining low angle grain boundaries (LAGBs), was defined as 2°-15° [START_REF] Randle | The coincidence site lattice and the 'sigma enigma[END_REF]. Basic clean-up was performed before each analysis to eliminate artefacts. In addition, TEM observations were performed on a JEOL 2010 at an operating voltage of 200 kV. The observation of dislocation structures by TEM gave complementary indications to the overall GOS analysis related to the initial internal stress of the samples. Specimens were prepared from 3 mm discs mechanically polished down to approximately 100 µm and then electropolished using a solution of 17 % perchloric acid in ethanol by the twin jet method in a Tenupol 5.

The influence of grain size on the mechanical properties was studied using uniaxial tensile testing up to fracture. From the 50 mm discs, dog-bone tensile samples with a gauge length of 11 mm and a thickness of 1 mm were extracted by electrical discharge machining to avoid sample damage. To remove the roughness induced by the machining, the surface of the specimens were carefully polished with a diamond suspension of 6 µm. Uniaxial tensile testing was carried out at room temperature using a Zwick device with a load cell of 50 kN maximum capacity. Strain rate was fixed to 10 -3 s -1 , and deformation was recorded by measuring displacement fields using digital image correlation (DIC) with the ARAMIS® software. The results reported for each sample correspond to the average of three measurements.

Results

Synthesis and microstructural characterization of SPS processed samples

In addition to grain size, other microstructural features have a major impact on tensile properties, leading to contradictions found in scientific literature concerning the intrinsic characteristics of UFG materials. For instance, Σ3 grain boundaries have been characterised as strong barriers for dislocation motion inducing, in turn, a larger strengthening than random boundaries [START_REF] Yuan | Size effect and boundary type on the strengthening of nanoscale domains in pure nickel[END_REF][START_REF] Lu | Ultrahigh Strength and High Electrical Conductivity in Copper[END_REF][START_REF] Lu | Nano-sized twins induce high rate sensitivity of flow stress in pure copper[END_REF]. In this study, BM parameters have been modified to produce microstructures with different grain sizes and GBCD, which are investigated by EBSD.

For the synthesis of the samples, two types of powders were considered, the asreceived commercial powder and powders obtained by BM. The as-received powder is characterised by polycrystalline particles of spherical/cubic "spiky-dendritic" aspect (Fig. 1 (a)). It displays an average particle size of 3.5 µm ± 1.5 µm and a narrow particle distribution.

Ball milling powders are characterised by highly deformed particles of flattened morphology (Fig. 1 (b)). The BM powder evolves at higher milling speed and after longer milling times to a more homogeneous powder with bigger particles as reported in a previous work [START_REF] De La Cruz | Nanostructuration of metals via spark plasma sintering using activated powder obtained by ball-milling: Impact on the strain-hardening mechanisms[END_REF]. The powder displayed in Fig. 1 (b) prepared by milling for 3h at 350 rpm, displays an average particle size of 60 ± 22 µm and an approximate thickness of 1 µm. XRD was used to investigate the presence of contamination species such as oxides as well as for texture examination. Diffractograms exclusively displayed peaks that correspond to the face centred cubic (FCC) phase of nickel, irrespective of the conditions of elaboration (Fig. 2). No contamination peaks were observed for any powder, or in their corresponding sintered states. Preferred crystallographic orientation in powders was examined from the intensity ratio, I200/I111. This ratio varied between 0.37 and 0.5 depending on the milling conditions, which is close to the value of random orientation I200/I111 = 0.42 as determined from the standard diffractogram for Ni [START_REF] Valiev | Processing of nanostructured nickel by severe plastic deformation consolidation of ball-milled powder[END_REF]. No marked crystallographic texture was thus observed independently of the elaboration conditions. After sintering, bulk samples with relative densities between 96 % and 99 % were obtained, in agreement with literature [START_REF] Borkar | Influence of spark plasma sintering (SPS) processing parameters on microstructure and mechanical properties of nickel[END_REF]. The microstructures were investigated in terms of grain size and GBCD, highlighting Σ3 grain boundaries and LAGBs. The sample sintered from the as-received powder (S-PC) (Fig. 3 (a)) exhibits an average grain size of 3.4 µm in agreement with previous values reported for Ni sintered under similar conditions [START_REF] Bhattacharjee | Effect of sintering temperature on grain boundary character distribution in pure nickel[END_REF][START_REF] Dutel | Room-temperature deformation micro-mechanisms of polycrystalline nickel processed by spark plasma sintering[END_REF]. The grain size of the samples processed from BM powder (Fig. 3 (b)-(c)) correlates to the milling condition. Thus, an average grain size of 1.43 µm is obtained sintering a powder milled at 200 rpm for 3 hours (Fig. 3 (b)) and of 0.79 µm for the same milling time but higher milling speed, 350 rpm (Fig. 3 (c)). The influence of the milling parameters on the final grain size is summarised in Fig. [START_REF] Valiev | Producing Bulk Ultrafine-Grained Materials by Severe Plastic Deformation: Ten Years Later[END_REF].

An exponential decrease in grain size with milling time is shown (dashed red line), suggesting that the steady state is achieved after 12 hours, considering a rotation speed of 200 rpm. Such evolution is also observed in other methods that use high deformation for grain refinement, like equal channel angular pressing, in which the number of passes is the key parameter [START_REF] Liu | Influence of stacking fault energy and temperature on microstructures and mechanical properties of fcc pure metals processed by equal-channel angular pressing[END_REF].

A linear decrease in the average grain size is observed for increasing rotation speed (Fig. 4 (blue line)). Higher speed triggers more energetic collisions [START_REF] Razavi-Tousi | Effect of ball size on steady state of aluminum powder and efficiency of impacts during milling[END_REF][START_REF] Schaffer | On the kinetics of mechanical alloying[END_REF] which, in turn, accelerates plastic strain reducing grain size faster. For instance, the sample processed from the powder obtained after milling for 3 hours at 350 rpm has an average grain size in the same range as the specimen milled for 12 hours at 200 rpm. The determination of GBCD for all processed samples revealed a correlation between the fractions of each type of grain boundaries and grain size (Fig. 6). The fraction of Σ3 grain boundaries decreases significantly with grain size, especially for values below 1 µm, whereas the fractions of LAGBs and random high angle grain boundaries (HAGBs) increase. The fraction of other CSL (Σ5-Σ29) grain boundaries displays no significant variations. These evolutions can be related to the processing techniques. On the one hand, microstructures obtained by BM are characterised by a high fraction of LAGBs [START_REF] Zhu | Microstructure and mechanical strength of near-and submicrometre grain size copper prepared by spark plasma sintering[END_REF][START_REF] Wang | Microstructural evolution in ultrafine-grained titanium processed by high-pressure torsion under different pressures[END_REF]. The fast sintering process ensured by SPS hinders the evolution of these boundaries into HAGB, due to the lower mobility of LAGBs as reported for Cu [START_REF] Liang | Influence of microstructure on thermal stability of ultrafine-grained Cu processed by equal channel angular pressing[END_REF] and Al [START_REF] Huang | Subgrain growth and low angle boundary mobility in aluminium crystals of orientation {110}〈001〉[END_REF]. Consequently, sample S-P0, prepared with the powder obtained under the most severe milling conditions, displays the highest fraction of LAGBs. Regarding Σ3 boundaries, the high fraction emerges from the intermediate stacking fault energy of nickel [START_REF] Rosengaard | Calculated stacking-fault energies of elemental metals[END_REF], which enables the formation of annealing twin boundaries upon sintering. With the exception of the sample with the smallest grain size, in all samples, a high fraction of 75 -87 % of the Σ3 grain boundaries corresponds to twin boundaries (TB). Deformation and consequent annealing to increase the density of TB has been studied and reported by many authors [START_REF] Horton | Aspects of twinning and grain growth in high purity and commercially pure nickel[END_REF][START_REF] Jin | Annealing twin development during recrystallization and grain growth in pure nickel[END_REF][START_REF] Mahajan | Formation of annealing twins in fcc crystals[END_REF][START_REF] Gleiter | The formation of annealing twins[END_REF][START_REF] Randle | Grain growth and twinning in nickel[END_REF]. It explains the elevated fraction of this type of boundaries in the sintered specimens from BM powders, compared to the fractions found in SPD processed UFG nickel (less than 5 %) [START_REF] Raju | Grain size and grain boundary character distribution in ultra-fine grained (ECAP) nickel[END_REF]. In addition, the decrease of the TB density with grain size is in agreement with studies by C.S. Pande et al. [START_REF] Pande | Study of annealing twins in FCC metals and alloys[END_REF]. The initial internal stress state was investigated by grain orientation spread (GOS) obtained from EBSD analyses and the observation of dislocation structures by TEM imaging 1 .

GOS represents a statistical measurement of the local weak crystallographic misorientations existing inside grains and can be related to local internal stress fluctuations. A mean value below 1° corresponds to the stress free internal state displayed by recrystallized samples [START_REF] Sitarama Raju | Microstructure evolution and hardness variation during annealing of equal channel angular pressed ultra-fine grained nickel subjected to 12 passes[END_REF].

Fig. 7 (left) displays GOS cartographies for two different grain sizes. In these samples, 88 % (Fig. 7 (a)) and 74 % (Fig. 7 (b)) of grains display an average misorientation below 1°. GOS histograms (inset to GOS cartographies in Fig. 7) verify a statistical distribution centred around 0.5°. More generally, the average GOS determined for all samples is in the range 0.5°-0.8°.

These crystallographic misorientations inside the grains can result from dislocation configurations as evidenced by TEM observations. Sample S-PC (processed from the asreceived powder) exhibits mostly defect free grains. Nevertheless, a few grains display some straight dislocation arrangements, as evidenced in the grain displayed in Fig. 7 (a) right, which was observed using a diffraction vector = [202 ], or pile-ups. Sample S-P0, with smaller grain size and observed using a diffraction vector = [111 ], also displays mainly straight dislocation segments (Fig. 7 (b) right) even if small tangles can be scarcely found in some grains. The absence of dislocation cells, together with the existence of straight dislocation segments, few in number, are representative of the weak internal stress level inside UFG specimens, in agreement with GOS results.

Mechanical properties of UFG Ni processed by SPS

In order to study the influence of grain size in the FG/UFG regime on strength and ductility, five samples were prepared, two from the as-received powder and three from BM powders (Table 1). To hinder the influence of GBCD, BM parameters were chosen taking into account the aforementioned results to process samples with different grain sizes and grossly the same fraction of Σ3 grain boundaries. A relative density over 97 % was obtained for all samples. The microstructural characteristics of the five samples are collected in Table 2. Grain size ranges from 0.8 µm to 25 µm. Low GOS is displayed by all samples and a high fraction of Σ3 grain boundaries (above 45 %) can be observed. The density of geometrically necessary dislocations (GNDs) determined from kernel misorientations by EBSD analysis is also collected in Table 2. The measurement of GNDs by EBSD is gaining popularity as a useful tool for dislocation quantification to analyse big surfaces of the microstructure, as compared to TEM observations [START_REF] Fressengeas | On the evaluation of dislocation densities in pure tantalum from EBSD orientation data[END_REF][START_REF] Moussa | Statistical analysis of dislocations and dislocation boundaries from EBSD data[END_REF]. It enables a minimum GND density of about 2x10 12 m -2 to be measured with a better sensitivity at low plastic strain levels [START_REF] Muransky | On the measurement of dislocations and dislocation substructures using EBSD and HRSD techniques[END_REF]. GND densities are calculated from the local misorientations inside a grain and using the algorithm already implemented in OIM 8 software. In the present study, a higher density of GNDs is observed in samples prepared from BM powders. ρGND is also higher for sample 5 than for bulk specimens obtained by casting and careful annealing that display the same grain size (ρGND = 3-4x10 12 m -2 ) [START_REF] Muransky | On the measurement of dislocations and dislocation substructures using EBSD and HRSD techniques[END_REF]. A plastic deformation in tension of 0.08 is needed in cast nickel to obtain the same range of GND density as sample 5, indicating some residual deformation from the applied pressure during sintering. The value of ρGND obtained for sample 1, the most refined microstructure, is in agreement with results obtained for UFG Ni processed by SPS from nanopowders, ρGND = 5.1x10 14 m -2 [START_REF] Gubicza | Microstructure and mechanical behavior of ultrafine-grained Ni processed by different powder metallurgy methods[END_REF]. Corresponding engineering stress-strain curves are provided in Fig. 8, showing two distinct tensile behaviours. Samples 3-5 (d > 1.2 µm) exhibit homogeneous plastic deformation. Samples with grain sizes below 1.2 µm display a "Lüders-type" strain at the beginning of the plastic domain, larger in sample 1 than in sample 2, and followed by homogeneous deformation at higher strain. SPD + heat treatment [START_REF] Krasilnikov | Tensile strength and ductility of ultra-fine-grained nickel processed by severe plastic deformation[END_REF] 890 835 12 ---10020

Table 3 collects the mechanical characteristics in tension of the samples. High yield strength (σ(0.2%)) and ultimate tensile strength (UTS) are observed for the UFG samples. The smaller difference between yield strength and the UTS for UFG samples indicates their lower strain-hardening capacity as reported by other authors [START_REF] Dalla Torre | Deformation behaviour and microstructure of nanocrystalline electrodeposited and high pressure torsioned nickel[END_REF]. Good ductility is displayed by all samples in terms of elongation to fracture (εf) and uniform elongation (εu). It is noteworthy that for sample 1, εf = 39 %, and uniform elongation εu = 30 %, which is far above what is reported for UFG Ni processed by SPD [START_REF] Krasilnikov | Tensile strength and ductility of ultra-fine-grained nickel processed by severe plastic deformation[END_REF]. The high fraction of Σ3 grain boundaries in the SPS processed samples may be responsible for the high ductility as reported for Cu [START_REF] Lu | Ultrahigh Strength and High Electrical Conductivity in Copper[END_REF] and other metals [START_REF] Meyers | Mechanical properties of nanocrystalline materials[END_REF].

The product of σ(0.2%) and εf is included in Table 3 as an indicator of toughness. For comparison, the value of this product for a SPD processed sample and a sample produced by SPD and subsequent annealing are added. A value three times higher is observed for sample 1 compared to sample 5 and 2.5 times higher than the value obtained for the SPD sample. The specific microstructure obtained by BM and SPS, which combines a reduced grain size with a high fraction of Σ3 grain boundaries, enables the good combination of strength and ductility, especially in specimens with grain sizes in the UFG range.

To investigate the influence of grain size on yield strength, its evolution as a function of d -1/2 is plotted (Fig. 9). The Hall-Petch (HP) [START_REF] Hall | The deformation and ageing of mild steel: III discussion of results[END_REF] relation provides an expression that relates the two parameters as follows:

. = + • 1 √ (1)
where σ0 is the friction stress and kHP the HP constant. As a reference, the linear HP fit for nanostructured (NsM)/UFG Ni samples processed by electrodeposition is included in Fig. 9 [START_REF] Bui | On the strengthening behavior of ultrafine-grained nickel processed from nanopowders[END_REF]. Such linear fit corresponds to a friction stress of 37 MPa and a HP constant of 175 MPa/µm 1/2 . These values are very close to those previously determined [START_REF] Keller | Hall-Petch behaviour of Ni polycrystals with a few grains per thickness[END_REF] for coarse grained Ni, σ0 = 14.23 MPa and kHP = 180 MPa/µm 1/2 . A good agreement with the expected values of yield strength is observed for samples 3-5, whereas UFG samples 1-2 strongly deviate from the expected values.

Discussion

The results in the previous section show that the synthesis of samples from BM powders and SPS consolidation produces grain sizes in the UFG range with a GBCD characterised by a high fraction of Σ3 grain boundaries and low internal stresses. The sintered samples exhibit good tensile properties despite, especially in the UFG regime, with an improved toughness, a small percentage of porosities.

The grain size dependence on yield strength exhibits a deviation from the expected value from the HP relation in the UFG samples. Such deviation has been reported for UFG Ni processed by other means including SPS sintering of nanopowders [START_REF] Bui | On the strengthening behavior of ultrafine-grained nickel processed from nanopowders[END_REF]. The higher density of dislocations in UFG samples could be at the origin of this deviation as flow stress is related to the total density of dislocations (ρ) following Eq. ( 2) [START_REF] Kocks | Physics and phenomenology of strain hardening: the FCC case[END_REF][START_REF] Mecking | Kinetics of flow and strain-hardening[END_REF][START_REF] Kuhlmann-Wilsdorf | Theory of plastic deformation:-properties of low energy dislocation structures[END_REF]:

= ( 2
)
where α is an interaction coefficient that depends on the type of interaction between dislocations as well as their configuration, M is the Taylor factor, μ is the shear modulus, and b is the norm of the Burgers vector. The total dislocation density includes GNDs and statistically stored dislocations (SSD). Thus, the higher density of GNDs collected in Table 2 for the UFG samples obtained from BM could account for the extra-strengthening. Assuming, in first approximation, additive effects of the crystalline defects on the tensile strength [START_REF] Krasilnikov | Tensile strength and ductility of ultra-fine-grained nickel processed by severe plastic deformation[END_REF][START_REF] Bui | On the strengthening behavior of ultrafine-grained nickel processed from nanopowders[END_REF], characterized by Eq. ( 3), the contribution to strength from GNDs (σGND) can be evaluated using Eq. ( 2) considering only the density of GNDs (ρGND).

= + ! + "#$%&"&'('$) +. .. (3)
A new value of strength, can thus be computed by the subtraction of σGND from the yield strength, σ(0.2%) -σGND, to investigate the origin of the HP deviation. Fig. 10 illustrates the evolution of σ(0.2%) -σGND as a function of d -1/2 , for fine and coarse grained samples. In samples 3-5 the effect of grain size in the strength at ε = 0.002 is erased by subtracting the contribution of GNDs as these dislocations are mainly responsible for the grain size strengthening [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF]. Nevertheless, an additional strength is always observed in the case of UFG samples, which reveals that another mechanism is linked to this phenomenon.

The origin of such additional stress may be related to the unusual "Lüders-type" strain displayed by the two samples in the UFG regime. This Lüders-type strain has already been reported for other UFG FCC metals such as Cu [START_REF] Zhu | Microstructure and mechanical strength of near-and submicrometre grain size copper prepared by spark plasma sintering[END_REF][START_REF] Tian | Remarkable transitions of yield behavior and Lüders deformation in pure Cu by changing grain sizes[END_REF], Al [START_REF] Yu | Transition of tensile deformation behaviors in ultrafine-grained aluminum[END_REF] and austenitic stainless steel [START_REF] Gao | Mechanism of huge Lüders-type deformation in ultrafine grained austenitic stainless steel[END_REF], indicating the occurrence of heterogeneous deformation at the beginning of the plastic domain. In such cases, the average strain measured across the gauge length is not representative of the strain in the deformed zone. Heterogeneity in deformation can be observed in sample 1 from strain cartographies obtained by DIC (Fig. 11). In addition, during tensile testing deformation bands in the centre of the gauge length at approximately 45° from the tensile axis were depicted at low strain. C.Y. Yu et al. [START_REF] Yu | Transition of tensile deformation behaviors in ultrafine-grained aluminum[END_REF] suggest that the origin of such behaviour lies on a microstructure that contains grains with very variable grain sizes that display different deformation behaviours. Yielding is easier in bigger grains, which undergo a pre-yielding microstrain that then percolates to smaller grains, generating homogeneous yielding and deformation. The lower strain hardening reported for small size grains delays the homogenization of deformation, triggering a Lüders-type deformation. To eliminate the "heterogeneous yielding factor", C.Y. Yu et al. suggest extrapolating the stress at ε = 0.002 using a strain-hardening model capable of describing the deformation behaviour of the investigated samples. In the present case, the true stress-true strain curves can be correctly modelled for coarse-grained samples using the Hollomon model:

= * • + , (4)
where σ is the true stress, ε the true strain, K the Hollomon strain-hardening coefficient and n the strain hardening exponent. In Fig. 12 (a), the modelled stress and the true stress determined from the experimental data of sample 4 show good agreement. On the other hand, Fig. 12 (b) shows that for the UFG sample 1, the model correctly describes the experimental results only for ε values above 0.05.

If the yield strengths for samples 1 and 2 are extrapolated from the modelled curves, the obtained values correspond to the one expected by the HP relation (Fig. 12 (c)).

To verify if heterogeneous yielding is the only factor leading to higher stress, true stresses at higher deformation levels were determined and plotted against d -1/2 (Fig. 13). The HP relation holds for higher levels of deformation [START_REF] Feaugas | Grain-size effects on tensile behavior of nickel and AISI 316L stainless steel[END_REF], thus the persistence of the deviation indicates that other factors should account for the supplementary strengthening. Despite a lower deviation at higher strain, the additional strength that persists through strain hardening could indicate modified plasticity mechanisms specific to the UFG range. In the case of UFG metals obtained by SPD, a deviation from the expected HP relation has also been reported for pure nickel, justified by the presence of dislocation substructures and "non-equilibrium" grain boundaries [START_REF] Valiev | Superior strength in ultrafine-grained materials produced by SPD processing[END_REF]. Due to the highly deformed nature of BM powders, the existence of such grain boundaries in the UFG samples of this study is possible. Thus, to verify their presence, grain boundary diffusion measurements [START_REF] Divinski | Ultra-fast diffusion channels in pure Ni severely deformed by equal-channel angular pressing[END_REF] or high resolution TEM observations [START_REF] Sauvage | Grain boundaries in ultrafine grained materials processed by severe plastic deformation and related phenomena[END_REF] of the grain boundaries should be performed.

Conclusion

UFG Ni samples were successfully produced by nanostructuration of powders via ball milling and subsequent SPS consolidation resulting into highly dense samples with homogeneous microstructures and good tensile properties. The main results obtained in this study can be summarised as follows:

-The synthesis of highly dense samples (relative density > 96 %) with grain sizes in the FG/UFG range can be achieved combining BM and SPS.

-Varying milling conditions enable the synthesis of samples in the FG/UFG range with average grain sizes ranging from 0.6 µm to 3 µm and a GBCD dependent on grain size. A large fraction of Σ3 grain boundaries is depicted, which decreases with grain size.

-GOS analysis and TEM observations illustrate the low internal stress level after SPS processing regardless the final grain size.

-Sintered samples display a good combination of strength and ductility, especially for samples in the UFG regime, with εf > 35 % and σ0.2% > 300 MPa.

-A deviation from the HP relation is depicted for samples in the UFG range, which is explained by heterogeneous yielding at yield strength. The persistence of the deviation at higher deformation levels suggests a change in plasticity mechanisms characteristic for UFG samples.

Fig. 1 -

 1 Fig. 1 -SEM image of the as-received powder (a) and BM powder (350 rpm, 3 h) (b), and corresponding particle distribution.

Fig. 2 -

 2 Fig. 2 -XRD diffractograms of the as-received and the BM powder (350 rpm, 3 h) (solid lines), and results of the corresponding sintered specimens (dashed lines).

Fig. 3 -

 3 Fig. 3 -EBSD inverse pole figure (IPF) and corresponding grain size distribution for SPS samples with different grain sizes: d = 3.4 µm ± 2.4 (2) µm (S-PC) (a), d = 1.43 µm ± 1.01 (5) µm, prepared from milled powder (3 hours at 200 rpm) (b) and d = 0.79 µm ± 0.47 (6) µm, prepared from milled powder (3 hours at 350 rpm) (c). IPF reference, normal direction to the surface of the sample.

Fig. 4 -Fig. 5 -

 45 Fig. 4 -Effect of milling time (rotation speed of 200 rpm) and rotation speed (milling time of 3 h) on the final grain size of SPS sintered Ni.

Fig. 6 -

 6 Fig. 6 -Evolution with grain size of the fraction of the different types of grain boundaries in UFG sintered Ni.

Fig. 7 -

 7 Fig. 7 -GOS maps processed from EBSD data obtained for the initial state of samples, d = 3.5 µm (S-PC) (a) and d = 686 nm (S-P0) (b) (left). Bright field TEM images corresponding to the same samples (right).

Fig. 8 -

 8 Fig. 8 -Engineering tensile curves corresponding to samples processed by SPS with different grain sizes.

Fig. 9 -

 9 Fig. 9 -Grain size dependence of yield strength for Ni samples, in which the dashed line represents a linear fit for UFG Ni processed by electrodeposition [75].

Fig. 10 -

 10 Fig. 10 -Grain size dependence of yield strength (red circles) and computed stress σ(0.2%) -σGND (blue stars).

Fig. 11 -

 11 Fig. 11 -Deformation cartographies obtained from DIC at different strain levels: ε = 0.003 (a), ε = 0.009 (b) and ε = 0.02 (c), for sample 1 (d = 0.82 µm).

Fig. 12 -

 12 Fig. 12 -Computed stress superposed to experimental true stress vs true strain curves for samples 4 (a) and 1 (b). Grain size vs measured yield strength (red circles) and extrapolated yield strength (green stars) for samples 1 and 2 (c).

Fig. 13 -

 13 Fig. 13 -Effect of grain size on stress at different deformation levels.

Table 1

 1 Relative density and synthesis parameters of samples processed for tensile testing.

	Sample	ρrel (%)	Precursor powder BM time (h) BM speed (rpm)
	1	98.5	BM	10	350
	2	99.5	BM	3	350
	3	99.3	BM	3	300

Table 2

 2 Microstructural features of tensile specimens.

	Sample Grain size (µm) GOS (°) LAGB	Σ3	CSL	HAB	ρGND (m -2 )
	1	0.82 ± 0.67	0.7	0.036	0.495	0.056	0.587	3.5x10 14
	2	1.11 ± 0.84	0.6	0.04	0.456	0.044	0.54	2.1x10 14
	3	1.39 ± 1.11	0.7	0.023	0.535	0.057	0.385	2.1x10 14
	4	4.5 ± 3.3	0.6	0.02	0.526	0.046	0.592	5.1x10 13
	5	25 ± 17	0.7	0.02	0.616	0.037	0.327	1.4x10 13

Table 3

 3 Tensile characteristics of Ni samples processed by SPS.

	Sample	UTS (MPa)	σ(0.2%) (MPa)	εf (%)	εu (%)	σ(0.02%) x εf
	1	625 ± 4	441 ± 7	39 ± 3	30 ± 5	17199 ± 21
	2	582 ± 6	325 ± 7	43 ± 1	37 ± 1	13975 ± 7
	3	506 ± 8	183 ± 9	46 ± 4	38 ± 4	8418 ± 36
	4	443 ± 2	130 ± 2	49 ± 3	41 ± 2	6370 ± 6
	5	408 ± 1	87 ± 4	58 ± 3	44 ± 5	5046 ± 12
	ECAP + Cold rolling [11]	1050	990	7	---	6930

Black spots in GOS cartographies correspond to badly indexed zones that match the presence of pores, which become larger by electropolishing. Likewise, pores appear as white spots in TEM images. Porosity structures are displayed at grain boundaries as well as in the bulk of the samples, as confirmed by focused ion beam observations.

Data Availability Statement

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.


Elena Mazzon

Pascal Guigues

ICGM Jean-Pierre Habas
email: jean-pierre.habas@umontpellier.fr

Biobased Structural Epoxy Foams Derived from Plant-Oil: Formulation, Manufacturing and Characterization

Keywords: Plant-oil derivates, biobased epoxy foam, rheology, anhydride hardener, foaming agent, thermal techniques

This paper is devoted to the description of the scientific method used for developing biobased structural foams derived from highly reactive epoxy resins. The chemical formulations were obtained from the mixing of two epoxidized plant oil-derivates (epoxidized linseed oil ELO and glycerol triglycidyl ether commonly named epoxidized glycerol EG) with an anhydride hardener and a non-toxic foaming agent. The optimization of the composition was achieved by studying the influence of many parameters such as the proportion of each epoxy molecule in

INTRODUCTION

Polymer foams define a large range of lightweight materials with very different chemical and physical characteristics that are influenced by the matrix properties, the proportion of the inner cells but also the possible presence of filler in the initial formulation. Polymer foams can be classified into several categories. For instance, they can be separated into either thermoset or thermoplastic materials depending on the nature of the matrix. Each family can be further divided into rigid or flexible substrates. If one considers the spatial repartition of the cells, isolated gas bubbles are specific of closed-cell foams whereas open-cell structures are based on gas tunnels [START_REF] Bjork | Properties of thermal insulation materials during extreme environment changes[END_REF]. Due to all these characteristics, polymer foams can behave as shape memory materials or inversely are able to fulfil structural functions [START_REF] Lavoie | Structural foam in transportation industry[END_REF]. Their atypical morphologies provide them outstanding aptitudes for thermal or acoustic insulation. Not surprisingly, given all these properties, these lightweight materials are used in a large range of applications such as building construction [START_REF] Bogdan | Meeting the insulation requirements of the building envelope with polyurethane and polyisocyanurate foam[END_REF][START_REF] Kallaos | Long-Term Performance of Rigid Plastic Foam Building Insulation[END_REF][START_REF] Richardson | FOAMS IN THE BUILDING-INDUSTRY[END_REF], transportation [START_REF] Farkas | Automotive, molded viscoelastic foams[END_REF][START_REF] Sakly | Experimental and modelling study of low velocity impacts on composite sandwich structures for railway applications[END_REF][START_REF] Schmitt | Evaluation of a new visco-elastic foam for automotive applications[END_REF][START_REF] Zheng | Crashworthiness design of transport aircraft subfloor using polymer foams[END_REF], food packaging [START_REF] Ingrao | Foamy polystyrene trays for fresh-meat packaging: Life-cycle inventory data collection and environmental impact assessment[END_REF][START_REF] Paraskevopoulou | Migration of styrene from plastic packaging based on polystyrene into food simulants[END_REF] furniture [START_REF] Barker | Combustion modified molded polyurethane flexible foam for the furniture industry[END_REF][START_REF] Smardzewski | Nonlinear mechanics of hyper elastic polyurethane furniture foams[END_REF] or sports [START_REF] Chiu | Effects of insoles and additional shock absorption foam on the cushioning properties of sport shoes[END_REF][START_REF] Duncan | Quasi-static characterisation and impact testing of auxetic foam for sports safety applications[END_REF].

A general survey shows that most of commercial polymeric foams are derived from petrochemistry. However, for some decades, different elements support the development of biobased foams. First, such materials are really interesting in the framework of a sustainability policy. Indeed, by definition, biomass is renewable whereas crude oil is a fossil resource and so with limited reserves. Secondly, the fluctuating prices of chemicals issued from petroleum is another tangible reason because this makes difficult the choice of long-term technical or scientific solutions [START_REF] Dvir | Demand effects and speculation in oil markets: Theory and evidence[END_REF]. The toxicity of many chemical compounds derived from petroleum chemistry also provides motivation for the identification and use of harmless products. Such situation is found with many conventional types of foams such as polyurethane formulations that are based on isocyanate-functionalised molecules [START_REF] Avashia | Effects of prolonged low exposure to methyl isocyanate[END_REF][START_REF] Ganguly | Spectrum of health condition in methyl isocyanate (MIC)-exposed survivors measured after 30 years of disaster[END_REF][START_REF] Lee | Pulmonary toxicity of polymeric hexamethylene diisocyanate aerosols in mice[END_REF][START_REF] Pauluhn | Short-term inhalation toxicity of polyisocyanate aerosols in rats: Comparative assessment of irritant-threshold concentrations by bronchoalveolar lavage[END_REF]. It is also encountered with epoxy foams derived from DiGlycidyl Ether of Bisphenol A (DGEBA). Indeed, Bisphenol A (BPA) was recently suspected to present endocrine disruptor properties but this topic is still subject to controversy [START_REF] Chen | Acute toxicity, mutagenicity, and estrogenicity of bisphenol-A and other bisphenols[END_REF][START_REF] Resnik | Bisphenol A and risk management ethics[END_REF][START_REF] Ruan | Evaluation of the in vitro estrogenicity of emerging bisphenol analogs and their respective estrogenic contributions in municipal sewage sludge in China[END_REF]. The use of other aromatic prepolymers derived from crude-oil is a possible approach to avoid BPA toxicity but it cannot be considered as a sustainable solution [START_REF] El Gazzani | High Temperature Epoxy Foam: Optimization of Process Parameters[END_REF].

In response to this situation, various studies were undertaken by several teams of researchers to develop epoxy foams from less toxic precursor compounds, in particular through the use of molecules derived from biomass. For instance, Brown et al. explored the interest of a commercial formulation (under trade name Super Sap 100 from Entropy Resins) comprised by epoxidized pine oil and DGEBA and (Brown et al., 2017). Using polymethylhydrosiloxane (PMHS) as a foaming agent in combination with a polyamine hardener, they obtained foams with bulk densities between 0.263 and 0.600 g/cm 3 after curing for 24 hours at ambient temperature. To develop resins with a higher biobased content, Agnihotri used this chemical formulation with variable proportions of epoxidized soya oil ESO [START_REF] Agnihotri | Biobased thermosetting cellular blends: Exploiting the ecological advantage of epoxidized soybean oil in structural foams[END_REF]. But, an increase of the ESO content had detrimental impact on both mechanical properties and glass transition temperature of the polymeric foam. Altuna et al. observed similar trend with foams derived from the mixture of DGEBA and ESO [START_REF] Altuna | Syntactic foams from copolymers based on epoxidized soybean oil[END_REF]. This evolution is likely a consequence of the higher molecular flexibility of aliphatic fatty chains compared to rigid aromatic structures present in DGEBA. Generally speaking, epoxidized vegetable oils are known as being characterized by low reactivity due to the poor steric position of oxirane rings in the fatty chains with respect to the hardener [START_REF] Alam | Vegetable oil based eco-friendly coating materials: A review article[END_REF][START_REF] Biermann | New syntheses with oils and fats as renewable raw materials for the chemical industry[END_REF]Khot et al., 2001). The time required to produce polymer foams derived from this class of compounds is often several hours and can even be made worse by the choice of the hardener. For instance, Dogan et al. proposed to use malonic acid to cure ESO and act as a blowing agent at the same time. But, they described a slow process and the derived foams were characterized by low performances [START_REF] Dogan | Synthesis and in situ foaming of biodegradable malonic acid ESO polymers[END_REF]. Nevertheless, in a recent work, we showed that it was possible to produce biobased epoxy foams (i.e. without BPA) within short processing times by using plant-oil derivates and a cycloaliphatic diamine as hardener [START_REF] Mazzon | Lightweight rigid foams from highly reactive epoxy resins derived from vegetable oil for automotive applications[END_REF].

However, due to the excessive exothermicity of the curing reaction, this curing agent also required the addition of other chemicals in the reactive mixture to act as "heat reducer" that is say for preventing thermal runaway. The use of heat reducer made it possible the production of foams. However, the physical characteristics of these foams such low thermomechanical properties (Tg close to 50°C) and excessive density (≈ 0.17 g/cm 3 ) were judged perfectible considering their possible application in transportation. Then, in this paper, we decided to explore another scientific pathway by the use of cyclic anhydrides that are known to release less heat during their reaction with epoxy molecules (Kumar et al., 2017b). The choice of this kind of hardener was also motivated by the intent to produce foams with higher mechanical properties to fulfil structural applications, in particular for transportation field [START_REF] Altuna | Biobased Thermosetting Epoxy Foams: Mechanical and Thermal Characterization[END_REF]. More precisely, the minimal wished Tg value is about 70 °C whereas the density must be lower than 0.1 g/cm 3 . It is important to keep in mind that in this latter sector, the final choice is also oriented towards the formulation able to combine high reactivity during curing and good performances after transformation.

EXPERIMENTAL SECTION

Materials

All raw materials are commercially available and they were used as received, i.e. without further purification. Epoxidized linseed oil (ELO) with 5.8 epoxy groups per triglyceride and molecular weight of 974 g mol -1 was kindly offered by ARD (France). Glycerol triglycidyl ether named also epoxidized glycerol (EG) with 3 epoxy groups per molecule and a molecular weight of 260 g mol -1 was purchased from Nagase ChemteX (Japan). The chemical structures of these epoxy molecules are drawn in Figure 1.

Insert Figure 1

Different cyclic anhydrides were preselected keeping in mind the wish to get cured materials with good mechanical properties. The different curing agents used in this study are reported in Table 1. All were purchased from Acros Organics and used as received. It is well established by now that the epoxy-anhydride reaction must be catalysed to achieve a full consumption of the reagents and consequently get a material with higher performances. Then, 2-methyl imidazole (2MI) was used as catalyst and was supplied by Sigma Aldrich. NaHCO3 (sodium bicarbonate, "SB") and KHCO3 (potassium bicarbonate, "PB"), purchased from Sigma Aldrich, were used as foaming agent.

Insert Table 1 2.2 Preparation of biobased epoxy resins

All epoxy reactive formulations were prepared with an anhydride groups/epoxy groups ratio R of 0.8 [START_REF] Boquillon | Polymer networks derived from curing of epoxidised linseed oil: influence of different catalysts and anhydride hardeners[END_REF][START_REF] Gupta | Development of Novel Bio-Based Soybean Oil Epoxy Resins as a Function of Hardener Stoichiometry[END_REF]. A quantity of 1% wt 2-MI catalyst based on anhydride weight was added to the reactive mixture. For instance, binary mixtures ELO -MTHPA (MTHPA for methyl tetrahydrophthalic anhydride) were characterized by 4.64 mol of hardener for 1 mol of ELO. Ternary formulations are identified under the code "xELO -(100-x)EG -hardener", where x is the percentage of epoxy groups brought by epoxidized linseed oil. Since ELO and EG have a different reactivity with a hardener, these ternary formulations provide the ability to tune the properties of the reactive mixture and the derived material (Habas et al., 2013). Reactive mixtures were prepared in a one-stage process by mixing all chemicals at room temperature under mechanical stirring during 3 minutes until apparent homogeneity. Optimal curing conditions (i.e. time and temperature) were determined by differential scanning calorimetry and rheological analysis.

Preparation of foams

The epoxy prepolymers were first mixed together in varying proportions but by keeping constant the total number of epoxy groups in order to ensure a complete reaction with the hardener units whatever the formulation studied. Then, the foaming agent was added. Its quantity was fixed between 10 and 50 parts for 100 parts of epoxy formulation corresponding to a weight percentage between 9.1 and 33.3% wt. Finally, the curing agent and the catalyst were also added. All components were mixed at room temperature for about 2-3 minutes. The final blend was poured in an aluminium open mould previously heated at T = 180 °C. The curing/foaming time was set at 3 minutes in order to identify and retain the only formulations compliant with an industrial productivity found in automotive sector.

Methods

The temperature domains and heat enthalpies attached to the different reactions (i.e. curing of epoxy formulations and decomposition of foaming agents…) were evaluated by differential scanning calorimetry (DSC StarOne from Mettler Toledo ® ). The dynamic scans were performed with a heating rate of 5 °C min -1 under inert atmosphere (N2) using a 40 µl perforated aluminium capsules and an empty crucible as reference. Kinetic rheological experiments were performed on crude reactive mixtures (i.e. without foaming agent) to determine from the evolution of the complex shear modulus G* = G' + j G" their respective gel and vitrification times. The real component G', called storage modulus, is related to the elastic contribution of the sample. The imaginary part G'', named loss modulus, is specific of the dissipated mechanical energy. These analyses were registered at constant temperature using a dynamic rheometer (MCR 102 from Anton Paar ® ) equipped with cup-plate geometry. The diameter of the upper plate was 25 mm and the inner diameter of the cup was 40 mm in order to prevent parasitic side effects. After geometry preheating in the testing chamber up to the desired temperature, the freshly prepared reactive mixture was poured in the measurement cup. Then, the upper plate was lowered until contact with the sample surface. Storage modulus (G') and loss modulus (G'') were recorded at constant strain (5 %) and fixed angular frequency (ω = 1 rad s -1 ). The gel time was evaluated by taking the time where the divergence of both moduli was observed. The thermomechanical properties of the cured polymer were characterized using a stress-controlled dynamic rheometer (AR2000Ex from TA Instruments ® ) equipped with rectangular torsion geometry. Analyses were performed from -50 °C to 150 °C with a heating rate of 3 °C min -1 and at a constant shearing angular frequency (ω = 1 rad s -1 ).

Glass transition temperature (Tg) was evaluated by taking the temperature Tα at the maximum of G'' peak that is characteristic of the main mechanical relaxation. Due to the value of the shearing angular frequency used, Tg ≈ Tα. Dynamic thermogravimetric analyses were performed from room temperature to 300 °C under air flow with the heating rate of 5 °C min -1 using a Q50 thermogravimetric analyser (TGA) from TA Instruments ® . In isothermal experiments, the weight loss of sample was registered during 60 minutes at a fixed temperature comprised between 100 °C and 180 °C. The density of the foams (ρ) was obtained as the ratio between the weight and the volume of cubes of 25 mm of side. Reported results were the average of measurements taken on three different samples issued from the same chemical formulation. Dynamic mechanical analyses (DMA) of the foams were performed with a 50N model from ACOEM-Metravib® using parallel plate geometry in compressive mode at a constant frequency (1 Hz). The temperature ranged from -50 °C and 130 °C with a heating rate of 2° C min -1 . Glass transition temperature (Tg) of the foam was evaluated by taking the temperature at the maximum of peak on E'' curve. This temperature also corresponds to the beginning of the drop of the Young's modulus plot that is characteristic of the mechanical rigidity. The compressive performances of the foam were also evaluated at room temperature on cubic samples (20 mm x 20 mm x 20 mm) using a 5533 Universal Testing Machine from Instron ® with a crosshead speed of 5 mm min -1 . The compressive modulus was determined from the slope of stress -strain curve in linear region associated with the elastic behaviour. The compressive strength was taken at a strain of 10 %. Reported results were the average of at least eight measurements on specific samples.

RESULTS AND DISCUSSION

Choice of anhydride hardener

The reactivity of ELO with each kind of anhydride hardener was first investigated with dynamic DSC. The crosslinking thermal domain was detected by the presence of an exothermic peak (Figure 2). Its position and respective area were observed to be slightly different form one anhydride to other. The peak characteristic of the reaction between ELO and MHHPA (methyl hexahydrophthalic anhydride) units presented a maximum centred at the lowest temperature (i.e. T = 150 °C) and was judged as specific of the most reactive mixture. The reverse situation (i.e. lowest reactivity) was observed with the use of METH (nadic methyl anhydride) hardener.

Such hierarchy was found consistent with literature data [START_REF] Boquillon | Polymer networks derived from curing of epoxidised linseed oil: influence of different catalysts and anhydride hardeners[END_REF].

Insert Figure 2

Then, kinetic rheological analyses could be recorded for each reaction mixture at different constant curing temperatures taken in the thermal crosslinking range defined above. In particular, the divergence of both viscoelastic moduli was used to evaluate the gel time. Figure 3 shows the gel times characteristic of the four couples "ELO-anhydride" registered at T = 80 °C and 140 °C, respectively. At the lowest curing temperature, the mixtures based on THPA (tetrahydrophthalic anhydride), MTHPA and MHHPA have similar reactivity with gel times close to 200 minutes. In contrast, epoxy formulation based on METH is considerably less reactive since its gel time close to 350 minutes. The same hierarchy is observed at high temperature (T = 140 °C). The lower reactivity of METH is likely a consequence of its bulky nadic structure synonym of reduced molecular mobility (Table 1).

Insert Figure 3

The thermomechanical properties of "ELO -anhydride" cured materials were evaluated by dynamic rheology. Figure 4 resumes glass transition temperature values after curing at T = 80 °C during 24 hours or at T = 140 °C during 10 hours. After curing at T = 80 °C, the formulations with the highest Tg are ELO -MHHPA and ELO -MTHPA (75 °C and 73 °C respectively). This result is not surprising since MTHPA and MHHPA show very similar chemical structures and reactivity. In contrast, the lowest value (30 °C) is obtained with the ELO -METH formulation. Such result can be once more related to the lower reactivity of this system. In this latter case, a curing time of 24 hours seems insufficient for the total consumption of reactive compounds. A temperature increase to T = 140 °C provides a higher crosslinking rate. Then, the Tg of ELO -METH formulation is close to that registered with ELO -MHHPA and ELO -MTHPA cured materials. It is to note that the cured material based on ELO -THPA displays the lowest Tg values for both curing temperatures used. Considering that THPA anhydride is under solid state up to 102 °C, its use is less practical than liquid anhydrides such as MHHPA and MTHPA. As the latter offer the best combination between reactivity and ultimate performances, they will be the only anhydrides retained in the pursuing of our work.

In fact, only results related to formulations derived from anhydride MTHPA are presented because those registered with MHHPA are very little different.

Insert Figure 4 3.2 Study of ternary formulations

Dynamic DSC analyses were performed on several "xELO -(100-x)EG -MTHPA" ternary formulations in order to evaluate the temperature domains attached to the curing reaction. The corresponding thermograms are presented in Figure 5. The binary ELO -MTHPA and EG -MTHPA formulations exhibit specific exothermic reactions peaks attributed to the epoxy -anhydride curing reaction. In case of reactive mixture based on ELO, the crosslinking reaction starts at high temperature (T ≈ 80 °C) and ends at 250 °C. The use of EG in place of ELO shifts the reaction domain to lower temperature. Indeed, the reaction between EG and MTHPA produces itself from 25 °C to 160 °C. This evolution is ascribed to higher accessibility of oxirane groups to anhydride functions [START_REF] Alam | Vegetable oil based eco-friendly coating materials: A review article[END_REF][START_REF] Biermann | New syntheses with oils and fats as renewable raw materials for the chemical industry[END_REF]Habas et al., 2013;Khot et al., 2001). The calorimetric response of ternary mixtures is characterized by the presence of two partially overlapped exothermic peaks, the intensities of which are more or less pronounced according to the initial composition of the formulation. They are easily attributable to EG -MTHPA reactions for the lowest temperatures and to ELO -MTHPA for the highest. A similar behaviour was already observed in the literature for systems based on "DGEBA -epoxidized soybean oil -MTHPA" with increasing amounts of DGEBA [START_REF] Altuna | Thermal and Mechanical Properties of Anhydride-Cured Epoxy Resins with Different Contents of Biobased Epoxidized Soybean Oil[END_REF].

Insert Figure 5

The total specific enthalpy of reaction (∆H, in J g -1 ) can be evaluated by direct integration of the exothermic peaks. Then, it clearly appears that the progressive substitution of ELO by EG in the reaction mixture provokes a slight increase of the released heat (Figure 6). Indeed, the discrepancy between the extreme values corresponding respectively to ELO -MTHPA and EG -MTHPA formulations remains limited (about 30 J g -1 ) while the maximal value of enthalpy does not exceed 350 J g -1 . In that sense, this behaviour is quite different from that observed in the case of epoxy ternary formations based on ELO, EG and an amine hardener [START_REF] Mazzon | Lightweight rigid foams from highly reactive epoxy resins derived from vegetable oil for automotive applications[END_REF]. Indeed, in this latter case, the crosslinking enthalpy was observed to strongly increase with the EG content in the formulation. This evolution has been explained and related to the parasitic consumption of amine functions by ester functions only present in ELO. Such unwished reaction named "amidation" and described in other papers is not possible here due to the nature of the hardener [START_REF] Del Rio | Analysing the Temperature Effect on the Competitiveness of the Amine Addition versus the Amidation Reaction in the Epoxidized Oil/Amine System by MCR-ALS of FTIR Data[END_REF][START_REF] Lee | Modification of soybean oil for intermediates by epoxidation, alcoholysis and amidation[END_REF][START_REF] Liu | Preparation, characterization and mechanical properties of epoxidized soybean oil/clay nanocomposites[END_REF].

It is important to keep in mind that in the present study, the highest enthalpy value is well below the minimal value above which the self-combustion of the sample cured with the diamine was observed. In other words, anhydride-based formulations offer more comfortable and safe manufacturing conditions.

Insert Figure 6

Kinetic rheological experiments were performed at different constant temperatures to evaluate the gel time of each formulation but also the minimum time required for the complete consumption of all reactive components. Figure 7a shows the evolution of complex shear modulus G* = G' + j G'' of 80ELO -20EG -MTHPA formulation as a function of time and at two constant temperatures T = 80 °C and 140 °C. At the beginning of both analyses, moduli G' and G'' have low values with G'' > G'. This means that the reactive mixture is still in the liquid state and the reaction advancement remains limited. Then, the formation of a percolating network induces the gelation of the system revealed by a sudden increase of both moduli. The time related to this strong evolution is used to evaluate the gel time of the medium. As showed before with calorimetry, a temperature increase boosts reactivity and a reduction of gel time.

After the gel point, the densification of the polymeric network provokes the pursuing of both moduli increase. Then, the viscoelastic curves tend to a limit allowing the definition of the minimal period required to achieve the curing reaction at the temperature used during the experiment. Figure 7b presents the different gel times registered at T = 80 °C and 140 °C for several ternary formulations. Whatever the curing temperature is, the progressive replacement of ELO by EG induces a reduction in gel time. Similar tendency is observed with the vitrification time. These evolutions agree with the conclusions proposed after examination of the DSC experiments. Compared to ELO molecules, EG units are more reactive with MTHPA because they combine more accessible epoxy groups with higher molecular mobility. As mentioned in introduction of this research, epoxy resins with high reactivity are often good candidates for possible application in industry. Seen from this perspective, the most interesting formulations are undeniably those with high amounts of EG because they present a gel time significantly lower than 3 minutes as required for the wished industrial application.

Insert Figure 7

The thermomechanical properties of cured materials were investigated by dynamic rheology.

The analysis characteristic of the 10ELO -90EG -MTHPA formulation after complete curing is presented as example in Figure 8a. At low temperatures, the cured material is in the glassy state. It is rigid and the storage modulus G' displays high values (G' > 1 GPa). Then, in the "transition zone" the value of G' sharply decreases in a limited temperature range.

Simultaneously in the same area, the loss modulus G'' describes a peak commonly called "α peak" that is characteristic of the mechanical relaxation of polymeric network during the glass transition. Taken at its maximum, the Tα temperature is evaluated close to 70 °C. Above the glassy transition, the sample is in rubbery state. The storage modulus G' is still predominant but its values are two decades lower than in the glassy state. Figure 8b resumes the Tg values for several cured materials based on "xELO -(100-x)EG -MTHPA" reactive mixtures. These data reveal that the glass transition temperature of the cured material is poorly dependent on the respective proportions of ELO and EG in the initial reactive mixture.

Insert Figure 8 A possible explanation for this behavior can be found by examining the structure of the network formed during curing. The smaller size of EG compared to ELO would suggest higher crosslinking density, so higher final properties for cured materials with high amount of EG. But in ELO, oxirane functions derived from epoxidation of native double bonds are much close to each other. Each epoxy cycle is able to establish two covalent bonds with anhydride units. So the distance between crosslinking points in cured network based on ELO is potentially lower than in those based on EG. Figure 9a shows a schematic representation of an "ELO -anhydride (A)" crosslinked structure, with different mesh sizes: 1) based on close epoxy groups and 2) including "glycerol" core.

Insert Figure 9

The introduction of an increasing proportion of EG in the reactive formulation should increase the density of the network due to the smaller size of the epoxy prepolymer. But mesh size could be larger (Figure 9b). In conclusion mesh average sizes in "ELO -anhydride" and "EG -anhydride" are likely to be equivalent what could justify that the initial composition has slight influence on glass transition temperatures. Such hypothesis seems to be supported by the direct comparison of the thermomechanical profiles of two cured materials (Figure 8a), the former being rich in ELO, the latter in EG. In the rubbery plateau, both cured formulations present almost the same value of the storage modulus. According to the law of rubber elasticity, this means that the crosslink densities of these materials are quite close [START_REF] Everaers | TEST OF THE FOUNDATIONS OF CLASSICAL RUBBER ELASTICITY[END_REF][START_REF] Treloar | The physics of rubber elasticity[END_REF].

Characterization of foaming agents

In order to produce polymeric thermosetting foams within short period, a polymeric formulation rich in EG must be retained. Then, the formulation 10ELO -90EG -MTHPA characterized by very short gel times (i.e. close to 1 minute at T = 140 °C) and good thermomechanical properties after curing (Tg > 70 °C), was selected. According to the method proposed by Pan [START_REF] Pan | High Biobased Content Epoxy-Anhydride Thermosets from Epoxidized Sucrose Esters of Fatty Acids[END_REF] the biobased content of this reactive mixture is about 38.6 %. A foam production from a polymer matrix requires the addition of a blowing agent but its choice is not trivial since a good equilibrium between the gas emission and the crosslinking reaction is indispensable (M. O. [START_REF] Okoroafor | Introduction to foams and foam formation[END_REF][START_REF] Mazzon | Lightweight rigid foams from highly reactive epoxy resins derived from vegetable oil for automotive applications[END_REF][START_REF] Mcelhanon | Removable foams based on an epoxy resin incorporating reversible Diels-Alder adducts[END_REF][START_REF] Takiguchi | Effect of rheological behavior of epoxy during precuring on foaming[END_REF]. Among the different possible chemical agents, we decided to investigate the interest of sodium bicarbonate (NaHCO3, SB) and potassium bicarbonate (KHCO3, PB). Indeed, upon heating, these non-toxic compounds decompose producing carbon dioxide and water in gaseous state (Scheme 1).

Insert Scheme 1

The range associated with the thermal decomposition of both bicarbonates was investigated by thermogravimetric analysis in dynamic mode. Sodium bicarbonate decomposes between 80 °C and 190 °C while the thermal decomposition of potassium bicarbonate is observed at higher temperature between 100 °C and 195 °C (Figure 10).

Insert Figure 10

In both cases, a significant residual weight is observed, the value of which (63 % for SB and 69% for PB) agrees with the reaction scheme (i.e. production of Na2CO3 and K2CO3). To evaluate which blowing agent is the most adequate with the reactive polymeric formulation, we reported in Figure 11 the calorimetric behaviours of the reactive formulation 10ELO -90EG -MTHPA and those of SB and PB. All these experiments were recorded in the same conditions.

The crosslinking reaction is detected through the presence of an exothermic peak while the respective decompositions of the blowing agents appear as endothermic phenomena. At first sight, the use of SB seems to be preferable instead of PB because its decomposition thermal range overlaps in a better way with that specific of the resin curing.

Insert Figure 11

But, other aspects must be considered such as the evolution of the resin viscosity with temperature confronted with the gas generation. Figure 12 shows the viscosimetric profile of the pure reactive mixture superimposed with the derivative of weight loss curve of each foaming agent registered with the same heating ramp. The gelation of the only resin detected by the divergence of the viscosity occurs in a temperature range for which SB start to decompose. At first sight, this situation may appear ideal for the foaming process since the bubbles are likely to be trapped [START_REF] Hwang | A Chemorheological Study on the Curing of Thermosetting Resins[END_REF][START_REF] Mcelhanon | Removable foams based on an epoxy resin incorporating reversible Diels-Alder adducts[END_REF][START_REF] Tungare | Chemorheological characterization of thermoset cure[END_REF]. Nevertheless, practical trials revealed that the crosslinking process is delayed when SB is added to the initial resin. An apparent lack of curing is even observed since the resin is still sticky. These unwished characteristics are likely provoked by the heat consumption during SB decomposition and so, a reduction of the real curing temperature. Further possible factor is the production of water molecules that consume anhydride molecules what affects the wished epoxy-hardener reaction.

Then, it appears that the blowing agent decomposition should take place in the last part of the thermal domain characteristic of the resin curing so as to limit the parasitic influence of the endothermic gas production on the temperature-activated crosslinking reaction.

Insert Figure 12

Both Figures 11 and12 show that such situation is encountered with the use of potassium bicarbonate. Then, this latter compound was finally retained as foaming agent in order to produce lightweight rigid foams.

In order to evaluate the kinetics of PB decomposition, different isothermal thermogravimetric analyses of this compound were registered for temperatures comprised between 80 °C and 180 °C. The corresponding data presented in Figure 13 demonstrate that the decomposition rate increase with temperature. A process temperature of 180 °C seems adequate for the complete gas production in very short delays.

Insert Figure 13 3.5 Characterization of final materials Trials for production of macroscopic epoxy foams were undertaken at T = 180 °C with a fixed time of 3 minutes. The amount of foaming agent ranged from 10 to 70 parts for 100 parts of epoxy formulation, corresponding to a weight percentage comprised between 9.1 and 41.1% wt. Figure 14a clearly shows that the introduction of 10 parts of BP produces compact samples due to a quite reduced foaming process. Then, it is observed that that the final volume of the foam increases with the initial quantity of PB. But, please note that for PB amounts higher than 50 parts, the foam is made with big inner bubbles and is even quite brittle. Our trials lead to the conclusion that the highest value of PB amount is 50 parts. In this case, the gas production selfstops after 3 minutes at T = 180 °C and the expansion is quite acceptable.

Insert Figure 14

Figure 14b resumes apparent density of prism-shaped samples cut in the core of each foam for an initial PB comprised 20 and 50 parts. All registered values are lower than 0.10 g/cm 3 . However, a big dispersion of density values is observed with the materials containing 20 parts of PB and is probably a consequence of the samples heterogeneity before cutting process. The apparent density decreases with an increasing amount of foaming agent and a better reproducibility is obtained for the foams produced with the higher PB amounts.

The same foams were also characterized by dynamic mechanical analysis in compressive mode and as a function of temperature. Above a critical temperature, the E' curve decreases faster due the material transition from the glassy state to the rubbery state. This critical temperature provides a good evaluation of the Tg of the polymer matrix due to the value of the compressive frequency used for this thermomechanical analysis (f = 1 Hz) [START_REF] Chen | Effect of SiO2 on Rheology, Morphology, Thermal, and Mechanical Properties of High Thermal Stable Epoxy Foam[END_REF][START_REF] Mcelhanon | Removable foams based on an epoxy resin incorporating reversible Diels-Alder adducts[END_REF][START_REF] Sankaran | Characterization of epoxy syntactic foams by dynamic mechanical analysis[END_REF]. The exploitation of DMA results is resumed in Figure 15. The Tg of the different foams is comprised between 80 and 87 °C. Then, it seems not to be dependent on the amount of PB present in the initial mixture as found by Stefani with another kind of epoxy foam [START_REF] Stefani | Characterization of epoxy foams[END_REF]. Please note that this Tg value is higher than the minimal value required for the wished application for all formulations studied.

Insert Figure 15

This point is particularly important because the first tests conducted with sodium bicarbonate revealed that this blowing agent significantly affected the foam thermomechanical properties by consuming heat at the expense of the resin crosslinking degree. In other words, by decomposing at higher temperature PB seems once more a better choice with our epoxy formulation.

To complete the mechanical characterisation section, compressive tests were also performed with the different foams produced with a PB content comprised between 20 and 50 parts Figure 16a depicts as example a typically stress-strain curve registered on a sample obtained with 30 parts of PB. This curve can be roughly divided into three different zones. The first one is characterized by a linear evolution of stress with strain. It corresponds to the linear elastic domain. It allows the evaluation of the "apparent" Young's modulus of the foam, mainly related to the mechanical rigidity of cells walls. In the second zone, the collapse of cells walls induces the formation of a plateau-like region in the stress-strain curve. The compressive strength (σc) is measured at 10 % strain for further comparison between all samples. Finally, at higher strain, opposed cell walls touch each other what induces a strong increase of the curve. This last step is usually named "densification" [START_REF] Avalle | Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram[END_REF][START_REF] Deschanel | Mechanical response and fracture dynamics of polymeric foams[END_REF][START_REF] Gibson | The mechanics of three-dimensional cellular materials[END_REF][START_REF] Greco | The Influence of the Stress Relaxation and Creep Recovery Times on the Viscoelastic Properties of Open Cell Foams[END_REF][START_REF] Pampolini | Les propriétés mécaniques des mousses polymériques à cellules ouvertes : expériences, modèle théorique et simulations numériques[END_REF]. Figure 16b summarizes the results of all compressive tests. These data reveal that the compression modulus value decreases with the amount of foaming agent. The same trend is also observed for the compressive strength.

However, the foams produced with 20 parts of PB are characterized by a big dispersion of their mechanical compressive properties, probably due to their poor homogeneity. These results perfectly agree with density data presented above. Indeed, the gradual transition from a solid material to a cellular structure induces a classical reduction in compressive mechanical properties. The same evolution was observed by Altuna [START_REF] Altuna | Biobased Thermosetting Epoxy Foams: Mechanical and Thermal Characterization[END_REF] in case of polymeric foams based on epoxidized soybean oil and MTHPA hardener. According to the classification proposed in literature [START_REF] Basso | Green, formaldehyde-free, foams for thermal insulation[END_REF][START_REF] Guo | Rigid polyurethane foams based on soybean oil[END_REF] foams with 20 and 30 parts of PB are defined as "rigid" while those obtained with 40 and 50 parts of foaming agent are "semi-rigid".

Insert Figure 16

Compared to the previous materials derived from the same epoxy compounds but using isophorone diamine as hardener and SB as blowing agent [START_REF] Mazzon | Lightweight rigid foams from highly reactive epoxy resins derived from vegetable oil for automotive applications[END_REF], this new family of foams offers real added value. In particular, due to the reduced exothermicity of the crosslinking reaction, it does not require the use of any additive acting as heat absorber on the opposite of the first generation. Moreover, the ultimate properties of the foams described here are significantly superior to those previously described. For instance, the final Tg is 30°C higher while the mechanical rigidity is increased by nearly 60%. It is important to note that these improvements were not obtained at the expense of the density since in this research, it was comprised between 0.05 and 0.08 g/cm 3 against 0.17 g/cm 3 for the best candidate developed in our previous study. Considering biobased epoxy foams produced from other resources, it is worthy to note that the Tg of our materials are significantly higher than that obtained by with foams synthesized from various mixtures of epoxidized soybean oil (ESO) and epoxidized mangosteen tannin cured with the same hardener (MTHPA) used in our research [START_REF] Khundamri | Bio-based flexible epoxy foam synthesized from epoxidized soybean oil and epoxidized mangosteen tannin[END_REF]. In this latter case, the absence of catalyst in the reactive formulation but also the lower functionality of ESO (Kumar et al., 2017a) are likely at the origin of this discrepancy. The macroscopic properties of our optimal foam are also significantly higher than those recently described by Agnihotri et al. with a foam produced from the mixture of ESO, epoxidized pine oil and DGEBA with polyamines as hardener. Indeed, in this study the maximal Tg is close to 56 °C while the minimal density is 0.53 g/cm 3 [START_REF] Agnihotri | Biobased thermosetting cellular blends: Exploiting the ecological advantage of epoxidized soybean oil in structural foams[END_REF]. The elimination of ESO in the formulation to the benefit of DGEBA is a good way for increasing the thermomechanical properties since the Tg rises up to 97 °C. But, the time required for the curing (24 h) remains much higher than that described here. In our study, the controlled addition of EG to ELO made it possible the reduction of the process time to 3 minutes. This approach offers a real implementation of the solution explored by Altuna et al. from the mixture of ESO, MTHPA and SB since in this last case, gel times higher than 20 minutes are reported [START_REF] Altuna | Biobased Thermosetting Epoxy Foams: Mechanical and Thermal Characterization[END_REF].

CONCLUSIONS

This work shows that it is possible to produce epoxy foams for a structural purpose in a few minutes using different chemical compounds derived from plant-oil and an inert blowing agent.

The proposed methodology emphasizes that several factors must be considered such as the thermal domains associated with the crosslinking of the polymer formulation and the decomposition of the blowing agent respectively. Based on our results, it is preferable to choose a blowing agent the action of which occurs when the crosslinking has already reached an advanced stage. Indeed, it is possible to trap the gas produced in the gelled polymer matrix without affecting its cross-linking degree. In addition, the kinetics associated with each of these phenomena must be carefully determined. In our study, the low reactivity of an epoxidized vegetable oil is compensated by the use of epoxidized glycerol that presents oxirane groups more accessible to the hardener units. This study also underlines that the use of several experimental techniques is of first importance to identify the most performing formulation. The best one is based upon the 10ELO -90EG -MTHPA reactive mixture and ideally contains 30 parts of PB for 100 parts of resin ( 23.1% w/w). After 3 min of curing at T = 180 °C, the foam derived from this formulation combines good mechanical performances (Tg > 80 °C, high mechanical rigidity) with a quite low density (0.065 g/cm 3 ). Such mixture allows the description of short processing times thus meeting the requirements of an industrial production line. All these scientific elements but also the raw materials prices and their factual availability make it realistic a possible valorisation of this plant-oil based formulation for producing foams at larger scale. Table 1. Anhydride hardeners retained in this work.

Figure 1 .

 1 Figure 1. Epoxy prepolymers used in this study.

Figure 2 .Figure 3 .

 23 Figure 2. Dynamic DSC scans of several "ELO -anhydride" reactive mixtures performed

Figure 4 .

 4 Figure 4. Glass transition temperatures of cured materials based on "ELO -anhydride"

Figure 5 .

 5 Figure 5. Dynamic DSC scans of several binary and ternary epoxy reactive mixtures

Figure 6 .

 6 Figure 6. Influence of initial respective proportion of EG and ELO on enthalpy of

Figure 7 .

 7 Figure 7. (a): Kinetic rheological analyses of 80ELO -20EG -MTHPA reactive mixture and

Figure 8 .

 8 Figure 8. (a): Thermomechanical analyses of cured materials based on ELO-MTHPA (open

Figure 9 .

 9 Figure 9. (a) : Representation of ELO -anhydride (A) and (b) : EG -anhydride networks

Figure 10 .

 10 Figure 10. TGA (solid line) and DTG (dashed line) of sodium bicarbonate (left) and potassium bicarbonate (right) under air at the heating rate of 5 °C min -1 .

Figure 11 .Figure 12 .Figure 13 .

 111213 Figure 11. Dynamic DSC scans of epoxy reactive mixture and foaming agents (SB and PB)

Figure 14 .

 14 Figure 14. Overview of foams produced (during 3 minutes at T = 180 °C) with an increasing

Figure 15 .

 15 Figure 15. Tg values of foams produced during 3 minutes at T = 180 °C with an increasing

Figure 16 .

 16 Figure 16. (a) : Compressive stress -strain curve of foam obtained in 3 minutes at