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Understand the electron transfer as the key to the 1 success of biredox ionic liquids 2 3

Successfully propagating electrons and storing them in the electrolyte is a significant challenge that would allow supercapacitors to exceed their current limit, especially in terms of energy density. With this objective in mind, we have synthesized new ionic liquid molecules that allowed a limited electron propagation and storage in the electrolyte. These new molecules are named as biredox ionic liquids. In the present paper, we will show how biredox ionic liquids build a new paradigm in the field of supercapacitors. Despite our encouraging results, storage of electrons in the electrolyte still has a long way to go before being mastered, given the remaining scientific and technological issues to consider. These challenges will also be outlined in this paper.

Introduction

The field of electrical energy storage is among the significant challenges of our century.

To address this challenge, it is necessary to obtain storage devices with high energy density and high power. Batteries and supercapacitors are the devices of choice to meet any of the performance criteria. [START_REF] Miller | Supercapacitors[END_REF][START_REF] Miller | Materials science -Electrochemical capacitors for energy management[END_REF] However, the dilemma is on the choice to be made between power and energy densities as a given device cannot provide both, simultaneously. For a battery, the sacrifice of power is for the benefit of energy density while for the supercapacitor it is the opposite. [START_REF] Simon | Where Do Batteries End and Supercapacitors Begin[END_REF] But the dream would be a device combining energy density without losing power.

Thus, the scientific challenge in this field is to discover electrode materials and new electrolytes that can address this dilemma.

An electrochemical double layer supercapacitor (EDLC) operates carbon electrodes with suited porosities (micropores and hierarchical porosities). [START_REF] Pandolfo | Carbon properties and their role in supercapacitors[END_REF][START_REF] Yan | Recent Advances in Design and Fabrication of Electrochemical Supercapacitors with High Energy Densities[END_REF] Electrodes are stable over time (up to 1 million charge/discharge cycles), and their synthesis is simple. The storage principle is kinetically fast; the ions are adsorbed on the surface of the electrode. However, EDLC supercapacitors store 20 times less energy than a lithium-ion battery. The increase in storage capacity then requires an increase in the surface area of carbon. [START_REF] Chmiola | Anomalous increase in carbon capacitance at pore sizes less than 1 nanometer[END_REF] However, at its maximum, the developed surface could not be greater than that of a single layer of graphene. Beyond the difficulty of synthesizing such a stable carbon, theoretical studies have shown that this graphene material would have a capacitance of 550 F/g (i.e., state of the art activated carbon capacitance is above 100 F/g). [START_REF] Huang | An Overview of the Applications of Graphene-Based Materials in Supercapacitors[END_REF][START_REF] Jiang | 3D carbon based nanostructures for advanced supercapacitors[END_REF] Note that this capacity value is not obtained by a theoretical prediction from a DFT or MD calculation, but rather from a back-of-the-envelope calculation assuming that all the surface is accessible and covered with one type of ions only, this value corresponds to a high approximation. Although attractive, 550 F/g leads to an energy density that is still lower than that of a battery (10 times lower). At this limit and it seems impossible for this supercapacitor technology to become competitive with batteries, energy wise, at least. Pseudocapacitive materials are usually considered to overcome this limit but the slower kinetics of the (sub)surface Faradaic reactions involved in the charge storage are impeding the resulting power. [START_REF] Augustyn | Pseudocapacitive oxide materials for high-rate electrochemical energy storage[END_REF][START_REF] Brousse | To Be or Not To Be Pseudocapacitive[END_REF][START_REF] Toupin | Influence of microstucture on the charge storage properties of chemically synthesized manganese dioxide[END_REF][START_REF] Toupin | Charge storage mechanism of MnO2 electrode used in aqueous electrochemical capacitor[END_REF] An innovative alternative is to consider the electrolyte for electrical charge storage (i.e., electrons and holes). Potentially, storage capacities would be increased thank to molecular Faradaic reaction while liquid state dynamics would be in favor of power. Three requirements are needed: (1) The transfer of the electron between a molecule in the electrolyte and the electrode, (2) the propagation of the electron in (a part of) the electrolyte and (3) the retention of the charge stored in the electrolyte to avoid recombination (self-discharge). The successful implementation of these three steps represents a real breakthrough in the field of supercapacitors. Associated with this new paradigm, it becomes crucial to design new molecules with the targeted properties. Ionic liquids (ILs) should thus be considered. There is an almost infinite number of possible combinations of molecules to build ILs. The organic cations and anions of ILs are obtained under specific design in regard to application. [START_REF] Davis | Task-specific ionic liquids[END_REF][START_REF] Lee | Functionalized imidazolium salts for task-specific ionic liquids and their applications[END_REF] Moreover, by controlling simple organic chemistry reactions, it is possible to build new ILs by functionalizing either the cation or the anion, or both. [START_REF] Arnaud | Theoretical study of CF3SO3Li, (CF3SO2)(2)NLi, and (CF3SO2)(2)CHLi ion pairs[END_REF][START_REF] Toulgoat | An efficient preparation of new sulfonyl fluorides and lithium sulfonates[END_REF] To use the electrolyte to propagate and store electrons, we have recently synthesized a new salt called biredox ionic liquids. [START_REF] Bodin | Biredox ionic liquids: new opportunities toward high performance supercapacitors[END_REF][START_REF] Mourad | Biredox ionic liquids: electrochemical investigation and impact of ion size on electron transfer[END_REF][START_REF] Mourad | Biredox ionic liquids with solid-like redox density in the liquid state for highenergy supercapacitors[END_REF][START_REF] Vioux | From Ionogels to Biredox Ionic Liquids: Some Emerging Opportunities for Electrochemical Energy Storage and Conversion Devices[END_REF] This molecule, soluble in a standard ionic liquid, has the advantage of conducting the ions, and, simultaneously, of being able to carry out a redox reaction at both positive electrode and negative electrode. Figure 1 illustrates this concept of storage using biredox ionic liquids. However, even if the proof of concept has been shown.

There are still many questions to be addressed. In this manuscript, we will address three of the main issues: We will present the state of the art of electrolyte electro-activity and then propose to discuss the associated electrochemical dynamics. These elements will allow us to describe the key points to be improved. For this reason, we will in particular discuss the concept of biredox ionic liquids as a new salt.

Performance of biredox ionic liquids

In this section, we will show the performance of biredox ionic liquids and compare it with other studies from the literature. Figure 2 summarizes the performance obtained for a biredox ionic liquid dissolved in BMImTFSI as electrolyte in a symmetric activated carbon as device. Electrochemical measurement of biredox ionic liquids are shown in Figure 3, a capacitance increased by two compared to a typical EDLC without observing a decrease in power. [START_REF] Mourad | Biredox ionic liquids with solid-like redox density in the liquid state for highenergy supercapacitors[END_REF] Cyclability is also high, but it depends strongly on the nature of the electrode material. [START_REF] Bodin | Biredox ionic liquids: new opportunities toward high performance supercapacitors[END_REF] Adding redox molecules to the electrolyte increasing the capacitance is not a new idea. 21- 23 Active material inside the electrolyte compensates the inert part of the electrolyte, in term of storage. The nature of redox molecule is very broad, modulated by their solubility, hydrophilicity, stability window and oxidizing or reducing environment. Currently, aqueous electrolytes are the most commonly used. However, these electrolytes offer both advantages and disadvantages. The main advantage is the low toxicity, but above all, in terms of performance, they have a high power. The disadvantage is a low cell voltage (electrochemical stability window of water is 1.23 and ∼1.5 V). This low stability window can be compensated by the capacity gain. The first reported redox molecules for aqueous media is alkali metal iodide salts, in both alkaline conditions and neutral. Other study explored hydroquinone. Many other families of redox molecules have been investigated in aqueous media, including halides, metallic cation (Cu 2+ , V 2+ , Fe 2+ , etc.), complexes (i.g., ferricyanide,), and organic molecules (i.g, viologens, quinones, etc.). In contrast to redox mediators in a water-based electrolyte, these same redox mediators in organic solvents, or even in liquid ionic media, have been very rarely studied. However, organic electrolytes offer significant advantages in terms of cell voltage over water-based electrolytes.

However, for all these results, the biredox ionic liquid stood out because it avoided two significant problems: shuttle effect and self-discharge (figure 3). In our studies on biredox ionic liquid as a redox molecule and at the same time as salt, we used BMimTFSI as a co-solvent.

BMimTFSI is an ionic liquid commonly used in the field of supercapacitors.

In the following sections, we will describe why biredox ionic liquids have distinguished itself, by comparing it to other remarkable studies. The difficulty of these measures is the choice of the right performance indicator, the right metric. Indeed, in this case, the charge is stored in the electrolyte, and the capacitances are normalized by the mass of active material. It is important in future studies to include the mass of the electrolyte. However, cells must be developed to take into account the mass of the electrolyte in a precise way. Correct evaluation is critical to realize the limitations of these technologies and target areas for further development. Interpreting performance correctly requires choosing the appropriate parameter to normalize the power and the energy density. The cells in the laboratories are not comparable to those in commercial cells. In the academic field, it is common to standardize by the mass of active material. For redox molecule including in electrolyte, the electrolyte contributes to the total mass and contains active material. In order to address this issue, the electrolyte mass (including solvent, redox couples, and supporting electrolyte) should be included, and excess electrolyte should be eliminated using volume-limiting cells. In practice, however, electrolyte mass is difficult to measure and minimize because test cells always contain some extra volume.

All these problems have been very well explained in a recent review by Evanko et al. of biredox ionic liquids at 0.5 M in BMimTFSI, (B) Stability in times, biredox ionic liquids at 0.5 M in BMimTFSI (red) and pure BMimTFSI (blue), and (C) Self-discharge measurement, red curve is biredox ionic liquids at 0.5 M in BMimTFSI and blue curve is pure BMimTFSI. [START_REF] Mourad | Biredox ionic liquids with solid-like redox density in the liquid state for highenergy supercapacitors[END_REF] We can cite the work of Frackowiak et al. In this work she used iodine as a redox shuttle to increase storage capacity, this result was remarkable, with a capacity of 1000 F/g. [START_REF] Frackowiak | Electrochemistry Serving People and Nature: High-Energy Ecocapacitors based on Redox-Active Electrolytes[END_REF][START_REF] Lota | Alkali metal iodide/carbon interface as a source of pseudocapacitance[END_REF][START_REF] Lota | Striking capacitance of carbon/iodide interface[END_REF] Here too, the question of the right metric to use in this new type of storage remains to be defined.

However, this work has opened up the significant issues of shuttle effect and self-discharge.

While the capacities were exceptional, the high shuttle effect and the high self-discharge were the limits of its approach. Strategies have been proposed to avoid it. A first strategy concerns the addition of liquid crystal molecules that inhibit self-discharge. This strategy is fascinating, but it requires adding an additive to the electrolyte and that it is at a sufficiently high concentration to have a positive effect but without disrupting storage capacity. A second strategy was used, that of Cu 2+ ions. As it reduces, the copper deposits on the electrode and thus the copper cannot diffuse into the electrolyte. The limitation of this last study is that it is necessary to work in an aqueous electrolyte. However, the influence of the concentration, temperature and even current loads are neglected in the studies. It has been proved that these factors impact the self-discharge rate remarkably.

To limit the shuttle effect and self-discharge, biredox ionic liquids represented a third alternative, inspired by the two previous phenomena. Indeed, during electron transfer, the formation of a di-cation and a tri-anion is observed. The composition of these bulky molecules disrupts the diffusion phenomenon in the pores of the electrodes. The diffusion being strongly slowed down (even inhibited) then the redox molecules remain confined in the pores. The consequence is that the shuttle effect and self-discharge are then slowed down. This particular reactivity of biredox ionic liquids is at the heart of their originality. While the large size of the solvated radius could have been seen as a limit to better stroring, this bulky property has turned into a decisive advantage, limiting the two significant storage problems by redox molecules dissolved in the electrolyte.

It is therefore essential to keep in mind that from a technological point of view, the primary challenge is to avoid self-discharge and shuttle effect. Without bypassing these two problems, then storing electrons or holes in the electrolyte will remain a dead-end academic concept.

Molecular electrochemistry in porous media.

Associated with this technological challenge, the associated redox dynamics are also an important challenge. In particular, understanding the redox reactions in pores makes it possible to better select molecules and materials. Indeed, to successfully store electrons in the electrolyte, it is necessary to transfer electrons from the electrode to the molecule successfully. Understanding this transfer between an electrode and a molecule has been very well established since Marcus' Nobel Prize in 1992. 28- 32 However, all these theories work for homogeneous electron transfers and heterogeneous electrons transfers when the electrode is ideally flat. [START_REF] Marcus | On the Theory of Electron†Transfer Reactions. VI. Unified Treatment for Homogeneous and Electrode Reactions[END_REF] This is not the case in an electrode material of a supercapacitor. The porosity of the electrode material is close to the size of a molecule. This difference changes our understanding of electron transfer theory. We are here at the frontier of the formalism of classical molecular electrochemistry.

Marcus' theory describes the speed at which an electron is transfered, this theory links, in particular, the kinetic constant to two parameters: the reorganization energy and the coupling parameter. The reorganization energy represents the energy required to reorganize the solvent close to the molecule. The coupling parameter represents the interaction between the molecule and the electrode.

= • • • • = • • • • • • (1)
Here, is the equilibrium constant for the precursor complex, is the frequency of crossing the free energy barrier (nuclear vibration), is the reorganisation energy and is the probability for electron tunnelling in the transition state. Equation 1 can be used for both heterogeneous electron transfer at an electrode and homogeneous electron transfer. For heterogeneous electron transfer the pre-exponential factor is around 10 3 to 10 4 cm•s -1 . (REF: [START_REF] Marcus | Electron transfer at electrodes and in solution: Comparison of theory and experiment[END_REF][START_REF] Savéant | Evidence for Concerted Pathways in Ion-Pairing Coupled Electron Transfers[END_REF][START_REF] Fawcett | An International Journal Devoted to all Aspects of Electrode Kinetics, Interfacial Structure, Properties of Electrolytes, Colloid and Biological ElectrochemistyOn the differences in the magnitude of the observed solvent effect in the kinetics of simple heterogeneous electron transfer reactions[END_REF][START_REF] Fawcett | Estimation of the rate constant for electron transfer in room temperature ionic liquids[END_REF] About , the question is easy to solve: the porosity being close to the size of the molecule. As the molecule is surrounded by electrode materials, the coupling between the molecule and the electrode is intense. However, it must be successfully modelled.

On the other hand, concerning the reorganization energy, the question is entirely open:

is the environment of the molecule favorable or unfavorable to electron transfer? Currently, no experimental data are available to measure the speed at which the electron transfers in such an environment. And above all, no metric can provide an equation of the reorganization energy.

In the case of a solvated molecule, the equation used to describe electron transfer is simple, it involves the dielectric constant of the solvent as well as the size of the molecule. Obtaining a formalism expressing the energy of reorganization in the pore is therefore an important issue, but the theoretical tools are missing. Thermal agitation is an important energy in solution processes. Indeed, in the context of a redox reaction in solution, the redox molecules, as well as the molecules that surround them (ions and solvents), have a thermal agitation that increases the degree of mobility of the molecule. In other words, when the molecule approaches the electrode, statistically, the redox molecule can approach with a very different orientation. This effect is even more important when the molecule is asymmetric because some areas of the molecule may be more reactive than others.

Thus, the degree of mobility of a redox molecule in solution is greater than that of a redox molecule immobilized on the surface or of an electroactive chemical element included in a crystal mesh of a lithium-ion battery material.

Another important phenomenon in the degree of mobility is the arrival of the counterion, in an electrochemical process in solution, the establishment of electro-neutrality is obtained by the approach of a counterion to compensate for the change in the degree of oxidation of the molecule. In solution, this counterion can approach with a large degree of mobility around the molecule, so in a battery material, the counterion must migrate into a crystalline mesh and position itself in the vacant cells of the mesh. This illustration of the opposition between the redox processes of an electroactive material in an electrode material and that of a free molecule in solution aims to better understand the differences in dynamics. But, above all, a molecule confined in a pore whose pore size is close to the size of the molecule loses part of its degree of mobility. Is the molecule considered as a molecule immobilized on the surface, or does the molecule still have its degree of mobility? Probably a combination of the two. This still shows the intrigue of storage using biredox ionic liquid. Finally, it is fully accepted that in a lithiumion battery material, the insertion of lithium causes a change in the crystalline mesh of the material, a mechanical deformation of the electrode is then present. The arrival of counterions to establish electro-neutrality changes contributes to the local deformation of the pore, it is a purely steric effect.

Recently, an attempt at rationalization has been made by Salanne et al., [START_REF] Li | Confinement Effects on an Electron Transfer Reaction in Nanoporous Carbon Electrodes[END_REF] using Molecular Dynamics. They have investigated how the electrochemical reactivity in such media may be impacted inside of nanoporous carbon electrodes. To this end, they have studied a simple electron transfer reaction using molecular dynamics simulations. As model molecules, they have showned show that the Fe 3+/ Fe 2+ couple dissolved in an ionic liquid exhibits a deviation with respect to Marcus theory. This behavior is rationalized by the stabilization of a solvation state of the Fe 3+ cation in the disordered nanoporous electrode that is not observed in the bulk.

The simulation results have fitted with a recently proposed two solvation state model, which allows them to estimate the effect of such a deviation on the kinetics of electron transfer inside of nanoporous electrodes. Regardless of the effect of porosity, we studied the impact of the chemical structure of biredox ionic liquids on electron transfer efficiency. [START_REF] Mourad | Biredox ionic liquids: electrochemical investigation and impact of ion size on electron transfer[END_REF][START_REF] Fontaine | Mass transport and heterogeneous electron transfer of a ferrocene derivative in a room-temperature ionic liquid[END_REF] Indeed, by revisiting Marcus' theory, we have shown that biredox ionic liquids orient itself to the surface of the electrode to have a fast electron transfer. To do this, we split the expression of the velocity constant in two. We assumed a constant pseudo-kinetic representing the assumption that only reorganization energy limits electron transfer and then we assumed a constant pseudo-kinetic representing the assumption that only electrode/molecule interaction limits electron transfer. We pull out the part of Eq. 1 that describes the contribution from reorganization energy and denote it as Eq. 2:

! = " Λ # $%&' • ( Λ ) $%&' (2)
Analogously, we denote the part that describes the contribution of tunneling as Eq. (3):

* +, = (-•# $%&' (3)
Overall Eq. 1 is then rewritten as Eq. ( 4):

. = / • ! • * +, (4)
Where A is

/ = 0 √2•3•4•5 (5)
With Q being

6 = . • • 7 8 (9 (6)
This formalism allowed us to identify that in the case of biredox molecules, the limiting step was the coupling between the electrode and the molecule ( ). However, these models are not applicable to a porous electrode at all. There is, therefore, a lot of conceptualization work to be done to understand the dynamics within a porous electrode better.

Concerning the dynamics of diffusion in pores, the theories and our experimental results are more convincing. Indeed, there is a multitude of formalisms to include porosity in the diffusion coefficient. Recently, we have shown that depending on the nature of the nanostructuring of the electrode, the diffusion of the molecule is modified entirely. Above all, we have shown that in the case of activated carbon, the molecules remain confined in the pores and thus the diffusion phenomenon is almost absent. [START_REF] Bodin | Biredox ionic liquids: new opportunities toward high performance supercapacitors[END_REF] Improving the concept of biredox ionic liquids requires a better understanding of the redox reactions that occur in porous electrodes. So much for mass transfer dynamics, the challenges seem solvable. However, regarding electron transfer in the porous medium, the problem seems almost impossible concerning existing models. It then becomes essential to bring together models such as Molecular Dynamics or DFT to understand these redox reactions better. From an experimental point of view, succeeding in extracting information from the electrochemical signal is also complicated. Indeed, classical molecular electrochemistry is based on two essential criteria. The first criterion is a counter electrode with a surface more significant than the surface of the working electrode. The second criterion is that all electrochemical measurements can be made when the characteristic time of the measured phenomenon is less than the time constant. [START_REF] Amatore | When voltammetry reaches nanoseconds[END_REF][START_REF] Amatore | Ohmic drop compensation in cyclic voltammetry at scan rates in the megavolt per second range: access to nanometric diffusion layers via transient electrochemistry[END_REF] These two missing points are the experimental limit to characterize the redox reactions inside the pores correctly. It is therefore also necessary to successfully develop instrumentation to describe these redox reactions better.

Overpass current limitation of biredox ionic liquids

We have shown that biredox stores electrons in the electrolyte. However, the energy density is not competitive with the density of a lithium-ion battery. To make it competitive, electrons would have to be successfully propagated beyond the first layers of EDLC ions.

Depending on the propagation area, the challenges will be different. If the charge only spreads through the pores or if the charge spreads through the entire volume of the electrolyte, then the phenomena will encounter different limits.

Consider the first propagation zone, i.e., the charge only spreads through the pores. The scientific question will be to understand the dynamics of electron transfer and to understand which molecular structure is favorable to electron transfer. However, we have just shown that there is a knowledge gap between the mastery of the theory of electron transfer on a flat electrode vs. electron transfer in a pore.

Let's consider the second propagation zone, i.e., the charge propagates from the volume of the electrolyte. The challenge here will be to produce molecules that will successfully coexist in the electrolyte without reacting with each other. Again, electron transfer theories are constructive. Indeed, the recombination between an electron donor and an electron acceptor, in a homogeneous phase has been very well studied (always through the formalism of Marcus' theory). [START_REF] Heckmann | Neutral Organic Mixed-Valence Compounds: Synthesis and All-Optical Evaluation of Electron-Transfer Parameters[END_REF][START_REF] Heckmann | Organic Mixed-Valence Compounds: A Playground for Electrons and Holes[END_REF][START_REF] Kaupp | Computational and spectroscopic studies of organic mixed-valence compounds: where is the charge[END_REF] However, the self-discharge resulting from the encounter between the oxidant and the reduction is typically a homogeneous phase electron transfer reaction, i.e., a redox reaction between two molecules.

In this formalism of electron transfer in homogeneous phase, as for electron transfer in heterogeneous phase, three criteria explained before select the efficiency of electron transfer:

The ∆< . , , and .

Thus, succeeding in making electrons and holes cohabit in the same zone is reaching in shaping molecules that will modulate these three parameters. The strategy is, therefore, to build molecular buildings to promote electron transfer to the electrodes but above all to hinder the redox reaction in a homogeneous phase.

About ∆< . , it is evident that the energy difference must be negative, the reaction must be thermodymically possible. Thus, it must be made kinetically impossible. For this purpose,

, and parameters will be the choice parameters.

The reorganization energy, , depends on the solvent but also on the size of the molecule. In an ionic liquid medium, from the reorganization energy, it has been shown that it is close to a solvent such as dichloromethane. Thus, reducing the reorganization energy seems complicated given this information. The other parameter, indirectly associated with the reorganization energy, is the movement of the counter-ion to establish electroneutrality. [START_REF] Wang | Electron Transport and Counterion Relaxation Dynamics in Neat Ferrocenated Imidazolium Ionic Liquids[END_REF] Again, decreasing the mobility of the counterion would be equivalent to increasing the resistance of the solution, and therefore reducing the power. This last point is then impossible.

Where electron transfer theory can help us is to make the encounter between the electron donor and the electron acceptor difficult or even impossible. That is to say, reduce the . To do this, there are different possibilities, obtaining redox molecules with a significant steric clutter can prevent recombination between the donor and the electron acceptor.

Conclusions

In this race for high energy density, the supercapacitor is limited to the surface of the electrodes.

Succeeding in storing more charges is a major scientific and technological challenge. Using part of the electrolyte to store electrical charges is then a considerable opportunity. However, the two significant problems are crossover effect and self-discharge. So, for this opportunity to become a reality, it is essential to succeed in finding a strategy to avoid these two problems.

Biredox ionic liquids are one of the possible options. By playing on the nature of cations and anions, through molecular design, it is possible to find molecules that will store part of the electrons but avoid crossover and self-discharge. From a scientific point of view, using redox molecules to store charges in the electrolyte is at the frontier of classical molecular electrochemistry. Indeed, the porosity of the electrode means that there is currently no model to understand the dynamics of electron transfer. This is the most important scientific challenge:

to succeed in understanding the electrochemical signal.

Figure 1 │

 1 Figure 1 │ New paradigm is the electrochemical energy storage. (a) the Faradaic bulk storage

Figure 2 │

 2 Figure 2 │ Electrochemical reaction involved biredox ionic liquids. (A) Redox reaction at negative

24

 24

Figure 3 │

 3 Figure 3 │ Performance of biredox ionic liquids as electrolyte in symmetric carbon/carbon

Figure 4 │

 4 Figure 4 │ Electron transfer at flat electrode vs. in microporous media. (A) diagrams

Figure 5 │

 5 Figure 5 │ Schematic representation of likely preferential orientation of the TEMPO bearing species A,

Acknowledgements

We would sincerely like to thank the French National network "Réseau sur le Stockage Electrochimique de l'Energie" (RS2E) for the financial support. The authors thank the French National Research Agency (STORE-EX Labex Project ANR-10-LABX-76-01) Olivier Fontaine thanks in particular Fréderic Favier for his reading, corrections and discussions.


Salima Bouvier
email: salima.bouvier@utc.fr

Marion Risbet
email: marion.risbet@utc.fr

Dorick Ballat-Durand
email: dorick.ballat-durand@utc.fr

treatment to the micro-tensile behavior of two mono-material Linear Friction Welded joints using: the β-metastable Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17

à la 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 interest in using Ti-alloys for structural applications within the aerospace industry has constantly risen for the past three decades. This increase is related to the advantageous specific strength of these alloys associated with favorable thermal and electro-chemical compatibility with Carbon-Fiber Reinforced Plastics (CFRP).

Furthermore the objectives of costs and weight reduction led the manufacturers to increase the number of functions handled by each part as well as to favor welding at the expense of mechanical assemblies. Such a strategy resulted in an escalation in the shape complexity of the structural parts and ultimately in the development of machining preshapes to limit the machining costs and to improve the buy-to-fly ratio. Additive manufacturing and welding techniques appeared promising to produce these pre-shapes.

However, welding Ti-alloys is known to be challenging using common fusion techniques as solidification defects [START_REF] Huang | On the mechanism of porosity formation during welding of titanium alloys[END_REF], [START_REF] Donachie | Titanium A Technical Guide Second Edition[END_REF], and embrittling oxygen/nitrogen pollution could occur within the joint if the protective environment is deficient [START_REF] Liu | Effects of oxygen and heat treatment on the mechanical properties of alpha and beta titanium alloys[END_REF], [START_REF] Ando | Microstructure and mechanical properties of a high nitrogen titanium alloy[END_REF]. Thus solid-state joining processes are considered as encouraging alternative techniques for joining Ti-alloys since they are believed to prevent these issues [START_REF] Mcandrew | Modelling of the workpiece geometry effects on Ti-6Al-4V linear friction welds[END_REF], [START_REF] Mcandrew | A literature review of Ti-6Al-4V linear friction welding[END_REF].

Linear Friction Welding (LFW) belongs to these so-called solid-state joining processes. Yet, contrary to Friction Stir Welding (FSW), the heat and joining in LFW is solely achieved by the friction between the two work-pieces to be assembled (i.e. no welding tool is involved in the joint): one forging part is pressed against a second work piece describing an oscillating linear motion (oscillating part), the contact friction generates heat and wear which leads ultimately to joining. Four distinct process stages, schematized in Figure 1, were identified during LFW by the authors in [START_REF] Mcandrew | A literature review of Ti-6Al-4V linear friction welding[END_REF]- [START_REF] Li | Linear and rotary friction welding review[END_REF] as:



The contact stage 1: The two parts are brought into contact initially resting on surface asperities followed by an increase in the contact area due to asperity flattening.



The initial stage 2: The large particles are expelled from the interface and the friction on the asperities leads to a local heating; the latter forming hot spots which initiates material joining and the axial shortening.



The friction stage 3: The heat and joining extends up to the entire contact interface leading to severe local shear deformation and a subsequent heating; the joint is no longer able to handle the axial load which results in an extensive material extrusion.



The forging stage 4: Once the axial shortening condition is fulfilled, the oscillating motion stops and the weld is consolidated by holding the axial pressure; fast cooling of the joint is ensured by heat diffusion into each work pieces.

Figure 1 : Schematic representation of the four process stages involved in LFW Tialloys

Generally Ti-alloys have been found to be excellent candidates for LFW due to their following properties: 1) a fairly low thermal conductivity that limits the energy dissipation to the bulk resulting in a fast and localized material heating; 2) the α→β phase transformation happening during the process [START_REF] Li | Linear and rotary friction welding review[END_REF]- [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF] that allows strong metal/metal bonds between the body-centered cubic (BCC) β lattices [11]; 3) The propensity of the β phase to accommodate large plastic deformations in the β-domain [START_REF] Lütjering | Titanium[END_REF], [START_REF] Weiss | Thermomechanical processing of beta titanium alloys-an overview[END_REF] which enables the use of large amplitudes (2-3 mm) for a consistent heat generation. Numerous studies investigated the weldability, microstructures and the mechanical behavior of the widely used α+β Ti64 [START_REF] Vairis | High frequency linear friction welding of a titanium alloy[END_REF], [START_REF] Karadge | Texture development in Ti-6Al-4V linear friction welds[END_REF]- [START_REF] Stinville | High and low cycle fatigue behavior of linear friction welded Ti-6Al-4V[END_REF] and showed that a thin hard joint is formed characterized by a significant microstructure refinement and a subsequent weld overmatch. The monotonic tensile tests and fatigue tests resulted mostly in failure in the parent material (i.e. far from the weld). Yet, the growing interest on alternative Ti-alloys for specific uses (in place of the multi-purpose α+β Ti64) has brought few authors into investigating β\β-metastable [START_REF] Ballat-Durand | Multi-scale and multi-technic microstructure analysis of a linear friction weld of the metastable-β titanium alloy Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) towards a new Post-Weld Heat Treatment[END_REF], [START_REF] Ji | Linear friction welding of Ti-5Al-2Sn-2Zr-4Mo-4Cr alloy with dissimilar microstructure[END_REF]- [START_REF] Dalgaard | Linear friction welding of a near-β titanium alloy[END_REF] or near-α [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF], [START_REF] Baeslack | Characterization of Solid-Phase Welds Between Ti-6A1-2Sn-4Zr-2Mo-0.1Si and Ti-13.5A1-21.5Nb Titanium Aluminide[END_REF]- [START_REF] Frankel | Comparison of residual stresses in Ti-6Al-4V and Ti-6Al-2Sn-4Zr-2Mo linear friction welds[END_REF] LFW joints. These studies showed that the results obtained on the α+β Ti64 are not transposable to every Ti-alloys as: the as-welded microstructures are highly related to the intrinsic properties of each alloys as well as to the initial microstructures.

Thus, subjecting the as-welded microstructures to improper Post-Weld Heat Treatments (PWHT) resulted in undesirable effects: an embrittlement of the β\β-metastable joints [START_REF] Tao | Effects of post-weld heat treatment on fracture toughness of linear friction welded joint for dissimilar titanium alloys[END_REF], [START_REF] Zhang | Effects of heat treatment on microstructure and microhardness of linear friction welded dissimilar Ti alloys[END_REF] and a drop in toughness of the near-α joints [START_REF] Meshram | Influence of matrix microstructure on aging response of near alpha titanium alloy (IMI834) parent metal and welds on toughness[END_REF].

Preceding studies performed by the authors were focused on mono-material assemblies of the β-metastable Ti17 and the near-α Ti6242 in [START_REF] Ballat-Durand | Multi-scale and multi-technic microstructure analysis of a linear friction weld of the metastable-β titanium alloy Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) towards a new Post-Weld Heat Treatment[END_REF], [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF] respectively.

These papers were endeavored to advanced microstructural characterizations, and to the identification of the transformation mechanisms involved during the process. The following major findings were drawn: 1) remarkable gradients of thermo-mechanical loads were present within the welds during the process, this resulted in deep microstructure changes through phase transformations and the activation of recrystallization/recovery mechanisms; 2) the joints were characterized by significant microstructure heterogeneities, local metastable states (martensitic α' or mechanically unstable β m ), and consistent discontinuous hardness properties. These particular microstructures and mechanical properties drove the authors to develop a specific heat treatment which permitted to reduce/resorb the microstructure gradients as well as obtaining stable hardness properties across the assemblies. This PWHT consisted of an annealing at 910 °C for 2 h followed by furnace cooling to 635 °C in 2 h, then ageing was performed at 635 °C for 8 h followed by air cooling. However, hardness tests could not provide enough information to identify the local mechanical viability of the aswelded joints and the contributions of a PWHT to it.

In this paper, the authors aimed at identifying the relationship between the mechanical properties and the local microstructures, before and after this PWHT, across two mono-material LFW joints using: the β-metastable Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) and the near-α Ti-6Al-2Sn-4Zr-2Mo (Ti6242) Ti-alloys. A detailed analysis combining full-field measurements and microstructural investigations will be proposed to characterize in depth the mechanisms affecting the local responses to monotonic tensile tests. Such a study will demonstrate the beneficial effects of this PWHT on the macroscopic mechanical behaviors compared to the metastable AW configurations.

Information on the joints durability to high cycle fatigue tests can be found elsewhere in [START_REF] Garcia | Strength and fatigue strength of a similar Ti-6Al-2Sn-4Zr-2Mo-0.1Si linear friction welded joint[END_REF] and [START_REF] Garcia | Effect of a thermal treatment on the tensile and fatigue properties of similar Ti17 Linear Friction Welding joints and Ti17 parent material[END_REF] for the Ti6242 and the Ti17 respectively.

Material and methods

The joints were obtained using a MDS-30 within the facilities of the company ACB, Nantes, France. The assemblies were welded with the following LFW process parameters: a forging pressure of 90 MPa, an amplitude of 2 mm, a frequency of 50 Hz, and an axial shortening of 3 mm. The assemblies consisted of two blocks of 15*80*70 mm 3 of similar materials butt welded with: the 15*80 mm 2 surface as the initial contact surface, the 80 mm edge as the oscillating direction, and the 70 mm edge as the forging direction (Figure 2). Each blocks were obtained by electrical discharge machining (EDM) from forged billets of TIMETAL®6-2-4-2 and TIMETAL®17. The complete chemical compositions of each alloys are detailed in Table 1; the parent materials were received in the solution treated then aged configuration (STA) from TIMET Savoie S.A., France. The PWHTs were performed on the whole assemblies using a Nabertherm P330 oven under an Argon protective atmosphere. The tensile test specimens were cut to the dimensions detailed in Figure 3 by precutting 1 mm plates using a cut-off machine followed by water jet machining at Microjet, Herrlisheim, France. The samples tested for each LFW configurations were cut at the very center of the assemblies, one of their {xz} surface was polished and etched to precisely identify the position of the weld and the crack path. The microstructure observations were performed using specific samples on the {yz} surface;

both {xz} and {yz} cuts exhibit analogous microstructure changes. The surface preparation consisted of: 1) coarse polishing using grid papers at 100 rpm, P80, P220, P1200, P2400 and P4000; 2) semi-finishing using polyester cloth polishing, first with a A specific space-time approach will be used in this study to highlight the inhomogeneous deformation behaviors within the assemblies. The full-field measurements will be presented as spatio-temporal graphs [START_REF] Garcia | Strength and fatigue strength of a similar Ti-6Al-2Sn-4Zr-2Mo-0.1Si linear friction welded joint[END_REF], [START_REF] Besnard | A space-time approach in digital image correlation: Movie-DIC[END_REF] depicting the evolution of the mean elongation profile across the weld while loading. The three stages to obtain such spatio-temporal graphs are schematized in Figure 5 as: 1) the local elongations within the ROI are obtained for each DIC frame; 2) the corresponding average elongation profiles are calculated for the three applied strains (ε 1 <ε 2 <<ε 3 ); 3) each profile is normalized by its maximum value and plotted as an intensity map in dependence on the <z> position and the applied macroscopic strain. ; ε 2 ; ε 3 ).

Local numerical gauges will be used in this study to investigate and compare the mechanical behaviors of the macro-zones constituting the tested joints before and after the PWHT. The data obtained from the full-field measurements and the force sensor will be used to determine the local engineering and true stress/strain curves (restricted by the macroscopic necking onset). Several indicators of the mechanical behavior will be extracted from the latter such as: the stiffness, the yield strength, and the work hardening exponent (ranging from the yield point at 0.5% offset to the onset of necking σ necking ). A schematic representation of this protocol is shown in Figure 6. However, since the microstructures are heterogeneous and that the micro-tensile samples do not fulfill the representative elementary volume (REV) conditions, the subsequent provided data will solely be considered for comparison purposes.

Results and discussions

3.1. Ti17 LFW joint

Microstructure

Preceding work performed by the authors aimed at characterizing the microstructural changes resulting from LFW the β-metastable Ti17 with a Widmanstätten α+β starting microstructure [START_REF] Ballat-Durand | Multi-scale and multi-technic microstructure analysis of a linear friction weld of the metastable-β titanium alloy Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) towards a new Post-Weld Heat Treatment[END_REF]. The microstructures and hardness properties of the joint before and after the PWHT are displayed in Figure 7.

The gradients of thermo-mechanical loads experienced by the material during the process resulted in significant microstructural changes affecting the crystallographic phases and/or the grain morphologies; both having remarkable effects on the local mechanical properties. Three distinct macro-zones can be identified from these changes: phase upon cooling in place of the high temperature β t . Such Ti17 (α)+β m microstructures could be prone to a stress-induced martensitic (SIM) transformation that precipitates orthorhombic α‖ laths within BCC β m parent grains [START_REF] Aeby-Gautier | Influence of microstructure on tensile properties of β-metastable Ti 17 alloy[END_REF], [START_REF] Aeby-Gautier | Isothermal α″ formation in β metastable titanium alloys[END_REF]. The triggering stress for this SIM transformation depends on the local chemical compositions, the parent β grain size and the dislocation density [START_REF] Grosdidier | Effect of Microstructure Variations on the Formation of Deformation-Induced Martensite and Associated Tensile Properties in a Beta-Metastable Ti-Alloy[END_REF]. Furthermore this transformation and pure elastic deformation of the β m phase could occur simultaneously thus affecting the apparent stiffness of the sample [START_REF] Lee | Elastic moduli and tensile and physical properties of heattreated and quenched powder metallurgical Ti-6Al-4V alloy[END_REF], [START_REF] Castany | In situ synchrotron Xray diffraction study of the martensitic transformation in superelastic Ti-24Nb-0.5N and Ti-24Nb-0.5O alloys[END_REF]. The PWHT transformed the local (α)+β m microstructure in favor of a Widmanstätten α+β mixture ensuring microstructural features (i.e. phase ratio, prior-β grain diameter, α lath size and hardness properties) similar to the ones of the as-received base material. Yet the prior-β grains in the former WL remained two times smaller (D=500 μm) than the ones in the rest of the material (D=1 mm) and traces of the initial {110}<111> texture of the β phase were still measurable after grain growth.

Micro-tensile test response

Monotonic micro-tensile tests were conducted up to failure on each configurations: the as-welded (AW) and the heat treated (PWHT). The PAZ and the WL+TMAZs constitute respectively 50% and 25% of the total gauge length L 0 (L 0 ≈10 mm). The tests outcomes are plotted in Figure 8 in the form of: 1) macroscopic engineering stress/strain curves (solid white); 2) intensity maps of the spatio-temporal graphs depicting the local ε zz strain in dependence on the <z> position and the applied macroscopic longitudinal strain (see section 4.2), each profiles are normalized by their maximum value to emphasize potential heterogeneous behaviors and strain localizations. The approximate <z> positions of the WL (black solid line) and the final crack paths (black dashed line) are also provided along with the limits of the joint (white dots) and the PAZ (white dash-dot lines).

The following major features could be noted for AW: 1) worsened properties were obtained compared to the ones of the as-received BM (see Table 1) characterized by a remarkably shortened elongation at break (3.6%), an apparent lower stiffness (78 GPa), and a seemingly early plastic behavior (731 MPa); 2) the β m joint core (WL+TMAZs) appeared more prone to deform than the neighboring α+β m microstructures (HAZs); 3) significant strain heterogeneities existed within the β m joint core in the initial linear stage; 4) a shift in the position of the maximum strain from the forging to the oscillating TMAZ occurred around 0.8% of macroscopic strain which corresponds to the end of the A similar analysis conducted on PWHT revealed the following main features: 1)

forming back the Widmanstätten α+β microstructure across the weld permitted to recover an elongation at break (9.2%), a stiffness (100 GPa) and a yield stress at 0.2% offset (884 MPa) in the order of magnitude of the ones specified for the as-received BM; 2) a rather homogeneous response was found across the assembly in the linear stage up to 1% of macroscopic elongation; 3) plastic deformation occurred in the whole structure including the transformed WL; 4) plastic strain localized in two preeminent zones with one sitting in the former oscillating HAZ leading ultimately to failure in the latter.

The previously depicted evolution of the tensile behavior across AW showed that the gradients of microstructure affected considerably the local mechanical behavior.

Hence the use of local sub-analysis was proposed in this study to eventually identify the inherent differences in the tensile responses (see protocol in section 4.2). To do so numerical gauges were symmetrically set on either side of the weld center line obtained by determining the α orientations of one cluster of three self-accommodating intragranular α laths that obey the burgers orientation relationship with the parent β matrix [START_REF] Lee | Selection of α variants during microstructural evolution in α/β titanium alloys[END_REF]; a phase volume fraction similar to the one of as-received BM was set (80% α ; 20% β). The elastic tensor components used for this analysis are listed in Table 2.

Table 2 : Elastic stiffness components C ij in [GPa] in Voigt matrix representation at room temperature for the equilibrium Ti17 β lattice, LCB Ti-alloy β m lattice and commercially pure (CP) Ti-alloy α lattice determined in [START_REF] Fréour | Determining Ti-17 β-Phase Single-Crystal Elasticity Constants through X-Ray Diffraction and Inverse Scale Transition Model[END_REF], [START_REF] Nejezchlebová | The effect of athermal and isothermal ω phase particles on elasticity of β -Ti single crystals[END_REF], [START_REF] Tane | Elastic properties of single-crystalline ω phase in titanium[END_REF] respectively; E iso is the isotropic Young's modulus determined from the Voigt-Reuss-Hill approximation. The lattice data (see Table 2) highlighted the fact that a loss in volume fraction of the α phase would necessarily lead to a decrease in the isotropic elastic modulus. Such a dissolution of the cluster of α laths would also result in enhanced local stiffness variations inherited from the anisotropic behavior of the β phase. Furthermore, the growth of the β matrix at the expense of the α phase at high temperatures (T°>700 °C) causes a decrease in fraction of the β stabilizing elements [START_REF] Grosdidier | Effect of Microstructure Variations on the Formation of Deformation-Induced Martensite and Associated Tensile Properties in a Beta-Metastable Ti-Alloy[END_REF] which was shown to remarkably affect the components of the elastic tensor of the Ti BCC lattice [START_REF] Ikehata | First-principles calculations for development of low elastic modulus Ti alloys[END_REF]. These findings as well as the elastic properties of the retained β m lattice measured in [START_REF] Nejezchlebová | The effect of athermal and isothermal ω phase particles on elasticity of β -Ti single crystals[END_REF] for the LCB Ti-alloy are corroborating the global decrease and the remarkable local variations in stiffness identified in the as-welded sample. Yet, given the preferred orientation of the β crystallites in the WL aligning one <112> direction with the forging axis <z> during LFW [START_REF] Ballat-Durand | Multi-scale and multi-technic microstructure analysis of a linear friction weld of the metastable-β titanium alloy Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) towards a new Post-Weld Heat Treatment[END_REF], [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF], the elastic stiffness components of this β m phase would imply to have an estimated longitudinal stiffness in the WL about 88 GPa. This value is 45% higher than the one measured here (60 GPa in Figure 9) which could be imputed to the differences in chemical compositions of the β m phases of the Ti17 and the LCB Tialloys. In addition to the local variations in stiffness that could be attributed to the anisotropic elastic properties of the BCC β m phase, a remarkable asymmetry was also noted in the tensile behavior of the as-welded sample on either side of the weld center line. Indeed, the forging part appeared to be more affected by LFW than the oscillating part through lower stiffness and yield strength but higher hardening capacity in the former compared to the latter (see Figure 9). Such differences could be imputed to the presence of asymmetrical thermo-mechanical loads during the process as shown in Figure 13. This might have affected differently both welded parts in terms of fraction of remaining α phase and/or the local triggering stress for the SIM transformation. In fact, the latter was found to be responsible for: 1) lowering the apparent yield strength when forming below the true yield strength of the parent phase; 2) resulting in a significant work-hardening by slip-length reduction and α‖ reorientation [START_REF] Grosdidier | Effect of Microstructure Variations on the Formation of Deformation-Induced Martensite and Associated Tensile Properties in a Beta-Metastable Ti-Alloy[END_REF], [START_REF] Duerig | Formation and reversion of stress induced martensite in Ti-10V-2Fe-3Al[END_REF]- [START_REF] Elmay | Texture evolution of orthorhombic α″ titanium alloy investigated by in situ X-ray diffraction[END_REF]. Thus, the forging side may have experienced an early and gradual SIM transformation that worsened both the local stiffness and the yield stress but resulted in a significant α‖ precipitation (see marker  in Figure 10) hardening the microstructure. The probably lower α‖ precipitation in the oscillating TMAZ might have favored strain localization in this macro-zone which ultimately cracked. In addition to that the grain refinement in the WL might have resulted in hindering the SIM transformation in the refined crystallites compared to the neighboring TMAZs as: 1) fine grains impede the shape change accommodation of the martensitic plate [START_REF] Paradkar | Effect of Al and Nb on the trigger stress for stress-induced martensitic transformation during tensile loading in Ti-Al-Nb alloys[END_REF]; 2) the formation of subgrains with low dislocation densities [START_REF] Ji | Linear friction welding of Ti-5Al-2Sn-2Zr-4Mo-4Cr alloy with dissimilar microstructure[END_REF] limits the presence of nucleation sites [START_REF] Tokizane | The effect of tensile pre-straining on nucleation of martensite in an Fe-Ni-C alloy[END_REF]; 3) the migrating boundaries enhanced the diffusion and chemical homogenization [START_REF] Smidoda | Diffusion in migrating interfaces[END_REF], thus reducing the martensitic start temperature [START_REF] Grosdidier | Effect of Microstructure Variations on the Formation of Deformation-Induced Martensite and Associated Tensile Properties in a Beta-Metastable Ti-Alloy[END_REF]. These microstructural features directly affect the triggering stress for the SIM transformations which was probably limited in the refined WL in favor of the rest of the joint resulting in slightly higher stiffness and yield strength in the former. The strain localization in the oscillating TMAZ led ultimately to failure characterized by quasi-cleavage features consisting of a mixture of micro-voids and facets. The formation of dimples could be imputed to crack nucleation at the β/α‖ boundaries and/or at the intersections of intense slip bands [START_REF] Gysler | Deformation behavior of age-hardened Ti-Mo alloys[END_REF]. The heterogeneous deformation induced by the sharp microstructure refinement at the WL/TMAZ border might be responsible for cleavage and/or intergranular fracture. Similar fracture features were observed for an as-welded LFW Ti17 joint [START_REF] Li | Microstructure Evolution and Mechanical Properties of Linear Friction Welded Ti-5Al-2Sn-2Zr-4Mo-4Cr (Ti17) Titanium Alloy Joints[END_REF], however the authors in [START_REF] Dalgaard | Linear friction welding of a near-β titanium alloy[END_REF] reported solely a ductile transgranular fracture in the as-welded LFW Ti5553 joint.

Phase

Higher density of ω athermal particles forming in the latter might have deflected the crack from the WL/TMAZ border in favor of a regular transgranular fracture [START_REF] Joshi | Titanium alloys: an atlas of structures and fracture features[END_REF].

The investigations conducted on the samples after PWHT showed that a rather homogeneous elastic behavior was recovered in the whole assembly. Such an improvement from the as-welded properties are directly related to the reprecipitation of the hardening α phase in the form of self-accommodating α WI clusters as shown in Figure 12. However the former oscillating HAZ still appeared as a weak point after PWHT due to a significant plastic strain localization ultimately leading to failure.

Indeed the coarser prior-β grains in this macro-zone (see Figure 7) might have resulted in a local weakening due to large α plates at the prior-β grain boundaries [START_REF] Lütjering | Titanium[END_REF]. Moreover the activation of restoration mechanisms in the joint during the PWHT might have lowered the density of intragranular dislocations; the latter being desirable for a precipitation of fine entangled α WI laths [START_REF] Lütjering | Titanium[END_REF]. The slight decrease in stiffness from the as-received material might be due to a probable higher fraction of β matrix. The heat treated samples exhibited mixed fracture modes of ductile intragranular and intergranular crack propagations mainly consisting of large dimples and cleavage rivers on grain facets. This fracture mode is typical of β annealed lamellar microstructures [START_REF] Lütjering | Titanium[END_REF], [START_REF] Joshi | Titanium alloys: an atlas of structures and fracture features[END_REF]- [START_REF] Shi | The effects of lamellar features on the fracture toughness of Ti-17 titanium alloy[END_REF]; to the authors knowledge no similar transformed β-metastable Ti-alloys LFW joints was found in the literature for comparison purposes. The difference of approximately ten percent (-10%) in the stiffness and/or the yield stresses measured in the base material compared to the ones provided by the manufacturer could be imputed to a sample size effect.

Ti6242 LFW joint

Microstructure

Previous investigations focused on identifying the mechanisms responsible for the microstructural changes in a near-α Ti6242 LFW joint with a starting fully-equiaxed microstructure [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF]. The microstructures and hardness properties of the joint before and after the PWHT are displayed in Figure 14. This significant microstructure refinement from the initial fully-equiaxed α+β mixture by phase transformations and/or continuous dynamic recrystallization resulted in a notable hardening and a consistent weld overmatch effect. Such microstructural changes might have affected considerably the local mechanical behavior and durability of the joint. Indeed the authors in [START_REF] Lee | Elastic moduli and tensile and physical properties of heattreated and quenched powder metallurgical Ti-6Al-4V alloy[END_REF] showed, through an extensive study, that the mechanical behavior of the α+β Ti64 (10 v% β) is remarkably dependent on the Heat Treatment and Quenching (HTQ) temperature impacting at least: the stiffness, the tensile strength and the work-hardening capacity. This was mostly attributed to the α→β t phase transformation which leads to a decrease in the fraction of β stabilizing elements in the β t matrix (β lean in place of β rich ) ultimately transforming upon quenching either in: hexagonal α', orthorhombic α‖, metastable β m , and/or cubic β depending on the volume fraction of β t [START_REF] Lee | Young's Modulus and Damping of Ti-6Al-4V Alloy as a Function of Heat Treatment and Oxygen Concentration[END_REF]. The α' and/or α‖ precipitation from the β t matrix was shown to considerably increase the tensile strength as well as the work-hardening capacity while slightly lowering the tensile stiffness. Yet retaining a 15 v% β m matrix by HTQ from 800 °C leads to a significant decrease in the apparent yield stress and stiffness due to a SIM transformation occurring during loading; the latter being also identifiable by an enhanced work-hardening capacity. The PWHT consisting of an α+β annealing followed by ageing resulted in: 1) homogenizing the β phase fractions and micro-hardness values across the assembly; 2) a gradual microstructure refinement from the HAZ to the WL; 3) maintaining a fully-equiaxed microstructure in the rest of the assembly.

Micro-tensile test response

Monotonic micro-tensile tests were performed in the same manner than on the TI17 on the as-welded (AW) and the heat treated (PWHT) assemblies. The PAZ and the WL+TMAZs constitute respectively 30% and 15% of the total gauge length L 0 (L 0 ≈10 mm). The macroscopic engineering stress/strain curves (solid white) and the normalized spatio-temporal graphs of the local ε zz strain during the tests are plotted in Figure 15.

The approximate <z> positions of the WL (black solid line) and the final crack paths (black dashed line) are also provided along with the limits of the joint (white dots) and the PAZ (white dash-dot lines).

The main outcomes of the tensile behavior of Ti6242 AW are listed as followed:

1) the stiffness and yield stress at 0.2% offset (101 GPa and 784 MPa respectively) were in the order of magnitude of the as-received BM (see Table 1), however a clear drop in the elongation at break could be noted (65%); 2) a slightly higher displacement was observable within the joint during the macroscopic linear stage compared to the unaffected material; 3) the hard joint (WL+TMAZs) appeared to not contribute significantly to the macroscopic deformation past the apparent yield point compared to the seemingly plasticized HAZs and BM; 4) a remarkable strain localization was identified in the oscillating HAZ which ultimately cracked. The transposable investigations conducted on the heat treated Ti6242 assembly revealed that: 1) the decomposition of the α'+(α‖) martensitic laths into an equilibrium α+β microstructures resulted in a remarkable improvement of the macroscopic elongation at break (14%) and yield stress at 0.2% offset (829 MPa); 2) the stiffness was slightly increased (105 GPa) compared to the AW configuration; 3) homogeneous displacement were recorded across the assembly during the linear stage; 4) the plastic deformation seemed to solely occur outside of the transformed joint (i.e. in the unaffected material); 5) no particular strain localization was noted any longer; 6) failure ultimately occurred in the unaffected material (i.e. far from the joint).

Given the discrepancies in the local displacements during loading, a complementary analysis was conducted to account with the gradients of microstructures across the assemblies (see Figure 16). A procedure similar to the one performed on the Ti17 was proposed here: the stiffness, the yield stress and the work-hardening capacity were determined (when applicable) from the local true stress/strain curves truncated at the onset of macroscopic necking (see protocol in section 4.2). The numerical gauges were symmetrically set on either side of the weld center line corresponding to the positions of the following macro-zones: the WL (│z│≤ 100 μm), the NTMAZs (100 ≤│z│≤ 350 μm), the FTMAZs (350 ≤│z│≤ 800 μm), and the HAZs (800 ≤│z│≤ 1600 μm). Since the REV conditions were not fulfilled, these mechanical behavior indicators would solely be used for comparison purposes between the AW and PWHT samples.

The original true stress/strain curves are provided in Appendix B.

One could observe from the data gathered in Figure 16 that, besides exhibiting a significant overmatch, the AW joint (WL+TMAZs) is characterized by a ten percent decrease in stiffness compared to the as-received unaffected material. This loss appeared not to be dependent on the local microstructure nor the weld side. However, a noteworthy asymmetry was identified between the forging and the oscillating parts regarding the yielding of their respective FTMAZs and HAZs. Indeed these macrozones seemingly plasticized solely in the oscillating work-piece. In addition to that the HAZ of the latter was characterized by decreases in stiffness and in yield strength (10% and 5% respectively) compared to the adjacent unaffected material (UAZ) despite exhibiting supposedly similar microstructures.

The analogous studies conducted on the PWHT sample showed that the overmatching effect in the joint was drastically lowered after the heat treatment through an apparent plastic behavior in the latter as well as in the rest of the assembly; yet slightly higher strengths were locally noted in the initially refined zones. The stiffness was also homogenized across the assembly to a value similar to the one of the as- The micro-tensile tests performed in this study confirmed that the remarkable microstructural changes experienced within the LFW Ti6242 joint led to consistent discrepancies in the local mechanical behaviors. These discrepancies are directly linked to the gradients of thermo-mechanical loads experienced across the weld during the process resulting in logical gradients of microstructural changes and refinements.

received
Indeed previous investigations detailed in [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF] showed that the microstructure refinement in the joint was due to an extensive α→β t transformation in this zone. Such a transformation led to different local reprecipitation from the β t zones upon cooling depending on their local chemical composition: 1) β t →α' in the WL due to the high temperatures and migrating boundaries that enhanced the diffusion and chemical homogenization; 2) β t →α s +β+(β m ) in the FTMAZ caused by a limited diffusion of the β stabilizing elements from the initial β matrix to the whole β t area; 3) a mix of the previously depicted transformations in the NTMAZ with a probable presence of α‖ martensitic plates within the retained -Ghost‖ β. In the preliminary microstructural investigations no microstructural changes were identified in the HAZ compared to the as-received BM. However recent SEM micrographs shown in Figure 19 revealed that the β matrix in the BM was actually initially hardened by fine α s platelets; the latter were absent in the HAZ. The apparent dissolution of these α s platelets in the HAZ caused an increase (+40%) in the area fraction of the β matrix by contrast distinction from eight percent in the BM to eleven percent in the HAZ. The authors in [START_REF] Mei | Martensitic transformation from β to α′ and α″ phases in Ti-V alloys: A first-principles study[END_REF] showed that quenching a Ti-alloys from the β-domain would result in a significant loss of stiffness depending on the fraction of β stabilizing elements dissolved in the bulk (see Figure 20). As a result, retaining an α' martensitic microstructure in place of an equilibrium α phase would inevitably lead to a noteworthy not provide evidence of any asymmetrical heat flux that would corroborate the difference in mechanical behavior observed here between both work-pieces. However, the microstructural investigations detailed in [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF] showed that the oscillating part actually experienced an enhanced recrystallization compared to the forging part. This might have resulted in slightly higher local temperatures and an enhanced chemical diffusion which caused the differences in mechanical behavior identified here in the AW configuration.

Despite showing a fifty percent decrease in grain size compared to the as-received fully-equiaxed microstructure and no weakening texture [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF], the as-welded oscillating FTMAZ exhibited a rather low yield strength combined with a noteworthy workhardening capacity. Such a behavior was identified in metastable Ti64 microstructures as resulting from the occurrence of a SIM transformation within a β m matrix [START_REF] Lee | Elastic moduli and tensile and physical properties of heattreated and quenched powder metallurgical Ti-6Al-4V alloy[END_REF], [START_REF] Lee | Young's Modulus and Damping of Ti-6Al-4V Alloy as a Function of Heat Treatment and Oxygen Concentration[END_REF].

The dissolution of the α s platelets in favor of the β matrix in the oscillating HAZ combined with a local altered strength and a notable work-hardening capacity would indicate that this macro-zone also experienced the β m →α‖ transformation. Yet the extensive strain localization in the HAZ and the consistent limited macroscopic elongation might be most likely due to an increase in slip length resulting from the local dissolution of incoherent (Ti,Zr) 5 Si 3 and coherent Ti 3 Al particles. These two precipitation hardening mechanisms, initially present in the as-received BM, are known to effectively prevent the occurrence of easy slip over long distances through former α colonies [START_REF] Lütjering | Titanium[END_REF], [START_REF] Banerjee | Microstructure and Slip Character in Titanium Alloys[END_REF]; their dissolution would inevitably lead to an early strain localization and a limited macroscopic elongation. The dislocation pile-up at the boundaries of these α colonies in the HAZ may have resulted in multiple early crack nucleation sites causing the subsequent quasi-cleavage fracture. The anisotropic thermal expansion of the α colonies [START_REF] Malinov | Synchrotron X-ray diffraction study of the phase transformations in titanium alloys[END_REF] could have also led to internal damage resulting from the thermal shock experienced in the HAZ, thus weakening the latter.

In addition to a homogenized stiffness, subjecting the assembly to a PWHT led to a smooth microstructure refinement across the joint with lamellar α+β in the WL and gradually refined α nodules in the TMAZ; the fully-equiaxed microstructure of the BM was preserved. These gradients of microstructure are visible in the form of a remaining slight weld overmatch. However one could still note a significant asymmetrical behavior as TMAZ of the oscillating side appeared to be softer than the one of the forging side. This might be resulting from the presence of finer microstructures in the latter. Furthermore ageing at 635 °C for 8h might have favored an enhanced precipitation of Ti 3 Al particles responsible for the slight hardening of the BM after the PWHT. These microstructural changes resulted in a homogeneous slip and in an extensive plastic deformation within the heat treated base material (UAZ); ductile fracture ultimately occurred by internal necking which is typical of equiaxed near-α Tialloys [START_REF] Joshi | Titanium alloys: an atlas of structures and fracture features[END_REF].

Investigations corroborating a weakening in the vicinity of an as-welded Ti6242 LFW joint were reported by the authors in [START_REF] Garcia | Strength and fatigue strength of a similar Ti-6Al-2Sn-4Zr-2Mo-0.1Si linear friction welded joint[END_REF] during High-Cycle Fatigue (HCF) tests.

These results showed that, despite failing in the base material under monotonic tensile test, the plastic activity initiated at 1.5 mm from the weld center line (i.e. in the oscillating HAZ). However the authors in [START_REF] Garcia | Strength and fatigue strength of a similar Ti-6Al-2Sn-4Zr-2Mo-0.1Si linear friction welded joint[END_REF] attributed this early plastic activity solely to the probable presence of residual stresses as reported in [START_REF] Romero | Effect of the forging pressure on the microstructure and residual stress development in Ti-6Al-4V linear friction welds[END_REF] in Ti64 LFW assemblies. Four among five of these HCF failures occurred in this early plasticized macro-zone; the crack was mostly composed of α grain facets. However, to the author's knowledge, no comparable fractographies of the as-welded Ti6242 LFW joint nor mechanical characterization of the weld after PWHT was found in the literature for comparison purposes. The difference of approximately ten percent (-10%) in the stiffness and/or the yield stresses measured in the base material compared to the ones provided by the manufacturer could be imputed to a sample size effect.

Conclusion

The tensile responses of both Ti17 and Ti6242 LFW joints were investigated before and after a heat treatment, the following conclusions on the contributions of this postweld heat treatment to the improvement of the local mechanical behaviors can be drawn:

1)

The soft and mechanically unstable as-welded Ti17 joint was characterized by significantly heterogeneous properties both in the elastic and plastic domain mostly related to the dissolution of the hardening α precipitates in favor of an anisotropic β metastable phase. The latter was subjected to intense slip and different extent of stressinduced martensitic transformations in the joint core depending on the local microstructural features (i.e. grain size, dislocation density and chemical composition).

This behavior resulted in worsened macroscopic mechanical properties compared to the ones of the as-received base material (i.e. stiffness, yield strength, and elongation at break). Heat treating the Ti17 joint permitted to recover an equilibrium α+β Widmanstätten microstructure across the whole assembly leading to both homogenized stiffness values and plastic behavior.

2)

In the Ti6242, the extensive α→β transformation during LFW in the joint core and the subsequent α' or α s reprecipitation upon cooling resulted in a remarkable microstructure refinement and a consistent weld overmatch. An early plastic activity was detected at the vicinity of the refined joint due to the local dissolution of α s platelets (initially hardening the β phase) in favor of a β m matrix combined with a probable resorption of the (Ti,Zr) 5 Si 3 and Ti 3 Al particles. This changes led to a slight loss of stiffness in the joint core and to a major strain localization at the weakened vicinity of the latter. Subjecting the Ti6242 assembly to the heat treatment permitted to decompose the metastable phases into equilibrium α+β microstructures (homogenizing the stiffness) and to harden back the macro-zones initially softened by the process. A gradual microstructure refinement was preserved in the weld ensuring a remaining slight weld overmatch.

Figure 2

 2 Figure 2 : a) sketch of the assembly detailing the dimensions of the welded parts and

Figure 3

 3 Figure 3 : a) Dimensions in [mm] of the specimens dedicated to micro-tensile testing;

Figure 4 :

 4 Figure 4 : Position of the region of interest (ROI) on the micro-tensile test samples

Figure 5 :

 5 Figure 5 : Schematic representation of the spatio-temporal graphs (marker )

Figure 6 :

 6 Figure 6 : Schematic representation of the protocol used for determining the stiffness C,

theFigure 7 :

 7 Figure 7 : Combined data from OM bright-field observations and the corresponding

Figure 8 :

 8 Figure 8 : Intensity maps of the spatio-temporal graphs depicting the evolution of the ε zz

  corresponding to the positions of the WL (│z│≤ 200 μm), the TMAZs (200 ≤│z│≤ 1200 μm), and the HAZs (1200 ≤│z│≤ 2600 μm). The resulting local true stress/strain curves (truncated at the onset of macroscopic necking) were then compared to each other in Figure9using the following indicators: the longitudinal stiffness, the yield stress at 0.2% offset and the work-hardening exponent (ranging from the yield point at 0.5% offset to the onset of necking). Such data were used here in a qualitative way for identifying the eventual contributions of the gradients of microstructure, SIM transformations and/or micro-mechanical effects to the local tensile behavior. Thus these data should not be assimilated as intrinsic mechanical properties of the assemblies for Representative Elementary Volume (REV) conditions are not verified and combined complex mechanisms were part of the tensile responses. The original true stress/strain curves are provided in Appendix A.

Figure 9 :Figure 10 :Figure 11 :

 91011 Figure 9 : Local main tensile properties of each joint macro-zones (i.e. the WL, TMAZs,

Figure 12 :

 12 Figure 12 : Variation of the elastic modulus depending on the crystallographic

Figure 13 :

 13 Figure 13 : Local temperature maxima measured by the thermocouples (black dots) in

29 Figure 14 :

 2914 Figure 14 : Combined data from OM observations under polarized light and the

Figure 15 :

 15 Figure 15 : Intensity maps of the spatio-temporal graphs depicting the evolution of the

  base material after ageing in the α+β domain. Moreover the forging HAZ did not constitute a particular soft point any longer since the yield strength and the workhardening capacity were henceforth comparable with the adjacent heat treated base material (UAZ). Yet the asymmetry in yield strength between the TMAZs of the forging and the oscillating part was still present and the PWHT seemed to have caused a slight hardening of the base material (+3%). Due to the position of the weld center line within the sample, no data were acquired in the forging HAZ.

Figure 16 :Figure 17 .Figure 17 :Figure 18 :

 16171718 Figure 16 : Local main tensile properties of each joint macro-zones (i.e. the WL,

Figure 19 :

 19 Figure 19 : SEM observations of the β matrix in the as-received Base Material (left)

Table 1 :

 1

				Alloying elements (w%)			Tensile properties
	Alloy	Al Sn Zr Mo	Cr	Si	Ti	E (GPa)	σ 0.2% (MPa)	UTS (MPa)	A%
	Ti17	5	2	2	4	4	N/A Bal.	110	1019	1110	15%
	Ti6242	6	2	4	2	N/A	0.1	Bal.	115	895	1000	12%

Chemical compositions in mass (Ti being the balance) and the tensile properties provided by the manufacturer for the two investigated Ti-alloys; E is the Young's modulus, σ 0.2% is the yield strength at 0.2% offset, UTS is the ultimate tensile strength, and A% the elongation at break.

DATA AVAILABILITY

The raw/processed data required to reproduce these findings can be shared on request.

decrease in Young's modulus. Such a mechanism was thought to be responsible for the lower stiffness measured in the WL compared to the as-received BM.

Figure 20 : Evolution of the isotropic Young's modulus of the martensitic phases retained by quenching from the β-domain for different contents of β stabilizing element in

Ti-(0-20 at.%)V alloys [START_REF] Mei | Martensitic transformation from β to α′ and α″ phases in Ti-V alloys: A first-principles study[END_REF].

The apparent lower chemical homogenization further from the WL probably led to the presence of soft α‖ and/or β m phases in the rest of the joint (i.e. NTMAZs, FTMAZs, and HAZs), this might have lowered as well the local stiffness. Consequently, repartitioning the β stabilizing elements during the PWHT into equilibrium α+β microstructures permitted to homogenize the stiffness across the assembly back to values similar to the one of the as-received BM. In both AW and PWHT cases, the presence of multiple α variants prevented the joint core (i.e. WL, NTMAZs and FTMAZs) from exhibiting significant stiffness variations from one macro-zone to the other.

The microstructure refinement caused a noteworthy weld overmatch, yet solely the oscillating side appeared to be prone to reach an apparent yielding point. Unlike in the Ti17, the temperature measurements conducted during welding and reported in [START_REF] Ballat-Durand | Through analysis of the microstructure changes during linear friction welding of the near-α titanium alloy Ti-6Al-2Sn-4Zr-2Mo (Ti6242) towards microstructure optimization[END_REF] did

ACKNOWLEDGEMENT

The authors acknowledge the financial support from the French National Research Agency (ANR) through the OPTIMUM ANR-14-CE27-0017 project as well as the Spatial and Aeronautic Research Foundation, the Hauts-de-France Region and the European Regional Development Fund (ERDF) 2014/2020 for the funding of this work.

The authors are also grateful to Dr A. El Bartali and A. Dos Santos for performing the micro-tensile tests at Centrale Lille as well as to ACB for providing LFW welded samples and Airbus for both their technical support.

APPENDIX A

True stress/strain curves (truncated at the onset of macroscopic necking) in the joint macro-zones of the Ti17 LFW assemblies before and after the PWHT; the vertical and horizontal axis represent the true stress and true strain respectively; the graph scales and units are provided at the left-bottom plot; macroscopic necking occurred at 3.1% and 4.22% of macroscopic engineering strain for the AW and PWHT respectively.

APPENDIX B

True stress/strain curves (truncated at the onset of macroscopic necking) in the joint macro-zones of the Ti6242 LFW assemblies before and after the PWHT; the vertical and horizontal axis represent the true stress and true strain respectively; the graph scales and units are provided at the left-bottom plot; macroscopic necking occurred at 2.78% and 7.92% of macroscopic engineering strain for the AW and PWHT respectively.