Philippe Serré
email: philippe.serre@supmeca.fr

Mireille Moinet

Jean-François Rameau

Decision support tool for clearance management in a conceptual design context

Keywords: Clearance, Deviation, Over-constrained mechanism, Conceptual design, Floating phenomenon

It is well known that manufactured over-constrained mechanical systems cannot operate without clearance between parts. If the clearance value is too small, parts will not fit together. Conversely, if the clearance value is too large, parts float relative to each other and the movement is imperfect. This paper presents a tool providing decision support during the conceptual design of over-constrained mechanisms. A new key characteristic of the mechanical system, named F, is defined. F quantifies the floating phenomenon of the mechanical assembly. The smaller it is, the smaller is the free movement of parts around their nominal positions. Optimizations are used to compute the minimal clearance value to guarantee the mechanism assemblability and also the corresponding F value. These values are obtained with respect to a quality level of the manufacturing process. Then, the proposed tool plots diagrams. It shows areas where the design is possible and highlights inconsistencies. We consider that it is very useful to assist users during the conceptual design step. A case study including a planar mechanism made of 6 parts and 8 joints illustrates the tool.

Introduction

An over-constrained mechanical assembly can only be assembled or mobile if shapes and dimensions of its components meet strict geometrical conditions. Due to the manufacturing process, those conditions cannot be exactly respected, as shown by Meng et al. [START_REF] Meng | Assembly problem of overconstrained and clearance-free parallel manipulators[END_REF]. To deal with this problem, clearances are generally added in the system's joints to allow tiny free movement of manufactured parts around their nominal positions. Unfortunately, consequences of this solution are not always under control. On one hand, if joint clearances are too limited with respect to manufacturing capability, the free movement of parts is too small and some manufactured parts cannot be assembled with the others. Therefore, some products will be rejected. On the other hand, if joint clearances are too large with respect to manufacturing capability, the free movement of parts is important and their actual positions can be far away of their nominal positions, as explained by Ting et al. in [START_REF] Ting | Clearance-induced output position uncertainty of planar linkages with revolute and prismatic joints[END_REF]. This generates vibrations which can affect the performances of the manufactured products. This tiny motion phenomenon is named floating phenomenon in the following.

The goal of the present work is to provide the mechanical designer with a tool to anticipate the said floating phenomenon in the assembly at conceptual design step. This tool is a diagram highlighting the relationships between joint clearances and floating phenomenon for a given manufacturing capability. This diagram is drawn at an early stage of design process, and can be used as a decision-making tool for designers.

Recent research is focused on statistical analysis during detailed design phase. For instance, in [START_REF] Idriss | Tolerance Analysis -Key Characteristics Identification by Sensitivity Methods[END_REF], a global sensitivity analysis of a mechanical system using the Sobol's method is made by Idriss et al. In [START_REF] Homri | Statistical Tolerance Analysis Technique for Over-constrained Mechanical Systems[END_REF], Homri et al. compute the probability of failure of over-constrained assemblies using quantifier based mathematical formulation. In [START_REF] Ballu | Geometrical reliability of overconstrained mechanisms with gaps[END_REF], Ballu et al.

study mechanical assemblies with clearances. Authors propose a method to compute the geometrical reliability of a product. It is applied on a completely defined mechanism composed of six parts. In several studies, mechanical motions are also taken into account as in [START_REF] Walter | Tolerance analysis of systems in motion taking into account interactions between deviations[END_REF] and [START_REF] Huang | Robust tolerance design for function generation mechanisms with joint clearances[END_REF]. Walter et al. study time-depending functional key characteristics of a crank mechanism, while X. Huang et al. evaluate the rotation deviation of the output link of a four-bar mechanism.

Goetz et al. in [START_REF] Goetz | A new approach to first tolerance evaluations in the conceptual design stage based on tolerance graphs[END_REF] propose an interesting approach to first tolerance evaluations when shapes of parts are not completely defined. Nevertheless, some effective tool is still needed for designers to predict if the manufactured products will perform as required. As demonstrated by Ebro et al. in [START_REF] Ebro | Robust design principles for reducing variation in functional performance[END_REF], this prediction is helpful during the early stages of product development.

In [START_REF] Rameau | Clearance vs. tolerance for rigid overconstrained assemblies[END_REF], [START_REF] Rameau | Clearance vs. tolerance for mobile overconstrained mechanisms[END_REF] and [START_REF] Mabire | Computing clearances and deviations in over-constrained mechanisms[END_REF] Rameau et al. and Mabire et al. present a geometrical model designed to predict, at early phase of development, the size of the minimum clearance needed to guarantee the assemblability of over-constrained mechanical assemblies in the context of mass production. Thanks to this proposal, mechanical assemblies can be characterized, at early design step, by a quantified property named clearance (noted ). If this quantity is too small, large number of manufactured parts may not fit together.

In addition to clearance , a second mechanical assembly property is defined, the so called deviation. The deviation value is a distance between the overall shape of a manufactured product and its theoretical nominal shape. The deviation value vanishes when the manufactured product and the nominal product have the same overall shape. The more different are the two shapes, the greater the deviation value is. Due to the floating phenomenon, a manufactured assembly features several configurations, each one corresponding to a particular overall shape. One of these shapes is the most distant: when the deviation is maximal. Another one is the closest: when the deviation is minimal. The difference between these two extreme values is called the floating.

Section 2 presents an algebraic representation of a nonnominal linkages. Section 3 defines four global key characteristics of non-nominal linkages. The dependency between these quantities is captured through two diagrams, as explained in section 4. Section 5 implements the solution on the assembly test case.

Algebraic representation of non-nominal assembly

A mechanical assembly is made of rigid bodies connected together by mechanical joints. Each rigid body, also called mechanical part, is manufactured by using production machines through a well-defined manufacturing process. In real life, because of unavoidable machining errors, it is impossible to get two instances of a given part featuring exactly the same dimensions. Consequently, mounting an over constrained assembly is a priori impossible and some extra work is needed. Firstly, the pairing solution is to include in the assembly one or more adjustable parts. A second solution is to allow non rigid parts that can be slightly deformed at the mounting step in order to compensate dimensional errors. The third solution is to introduce clearance in mechanical joints.

First solution is not efficient for large scale production because mounting time is substantially increased. The second solution induces parts internal strength, which can lead to poor fatigue resistance. The third solution allows tiny motions of parts in the neighborhood of their respective nominal positions, which, in turn, may induce unwanted vibrations. This paper deals with the third solution.

Closure equation of nominal assembly

Classically, a rigid assembly is modeled through a socalled closure equation. This equation is based on the closure mapping noted : × ⟶ where is the space of dimensional parameters and is the space of positional parameters. Target space of mapping is a finite dimension space. The semantic of space is closely related to the modeling of the problem, which does not need to be detailed at the level of abstraction of the present work. The dimensional parameter ∈ gathers lengths and angles that define the respective shapes of all rigid bodies of the assembly. The positional parameter ∈ gathers relative or absolute positions of the said rigid bodies of the assembly. Mathematical notation is , ⟼ , . The closure equation is then , = 0. The dimension of space is the number of scalar equations of the closure equation. The closure equation captures how rigid bodies are articulated together according to perfect mechanical joints. This generic way to deal with rigid assemblies is very efficient to set up high level concepts.

Consider now a particular solution , meaning that , = 0. This solution is named the nominal solution because it perfectly fits the closure equation. When the assembly is over-constrained, it is well-known that a small perturbation of the nominal dimension , noted + , makes the problem impossible, meaning that there exists no positioning parameter such that + , = 0. In other words, feeding the closure equation with a non-nominal dimension makes the problem impossible. From the physical point of view, non-nominal components cannot be mounted together, unless some clearance is there, which is addressed in next section.

Relaxed closure equation of non-nominal assembly

A perfect mechanical joint allows a specified relative motion between two parts. For example, the spherical joint allows any rotation and prevents all translations.

Conversely, a non-perfect mechanical joint allows any relative motion between the two connected parts. Nevertheless, some degrees of freedom are expected to be as wide as the corresponding perfect joint, while remaining degrees of freedom are expected to be very small. For example, the imperfect spherical joint features wide rotation capabilities while translation capabilities feature very small magnitude. The typical example of a non-perfect spherical joint is the nunchaku, a traditional martial arts weapon consisting of two sticks connected at one end by a short chain, as illustrated in Figure 1. Any relative rotation of the sticks is possible but relative translations magnitude is limited by the chain length. So, a modeling effort must be done to add flexibility in the joints of the assembly. Formally, this is to add degrees of freedom through additional parameters, noted ∈ , which changes the closure mapping into a relaxed closure mapping : × × ⟶ , with , , ⟼ , , . The relaxed closure mapping is related to the closure mapping through , 0, = , for all , . This means that when additional degrees of freedom are inactive, the system is over constrained. The relaxed closure equation is , , = 0. In particular, , 0, is a solution of the relaxed closure equation.

The point is now that the relaxed closure equation , , = 0 is highly under constrained, meaning that given a dimensional parameter , possibly non nominal, there exists an infinity of parameters and such that , , = 0.

Deviation to nominal assembly

By nature, the nominal assembly is a ideal representation that perfectly fulfils the function of the assembly, whatever it can be. So, the deviation to nominal assembly is a reasonable way to quantify how the non-nominal assembly imperfectly fulfils the function.

The first step toward the definition of this deviation is to equip each rigid body of the assembly with characteristic points. For each rigid body, these points are chosen in such a way that a dimensional change results in a change in their relative positions. Furthermore, a dimensional change of one component should also alter the position of neighboring components. Experience shows that EGRMs of joints are good candidates. Formally, let be the number of rigid bodies.

Body number is equipped with characteristic points. So, the whole assembly is equipped with the list of characteristic points of its components, noted with = 1, ⋯ , and = ! + ⋯ + " . With this notation, points of body number are with

= ! + ⋯ + #! + 1, ⋯ , ! + ⋯ + #! + .
Of course, absolute positions of these points depend on the configuration , of the assembly. This is captured by the notation , for = 1, ⋯ , . So, points of the nominal assembly are , for = 1, ⋯ , . The deviation between the nominal assembly and the nonnominal assembly can now be written. Given a dimensional parameter value , possibly non nominal, and a positional parameter value , the deviation expression is:

$ , = %∈&' ( ! ) ∑ + , , -. , /+ ) 0 1!
To compute the value, the first step is to get the characteristic points of the non-nominal assembly, which are noted , for = 1, ⋯ , . The second step is to compute the best fitting of the non-nominal characteristic points to the nominal characteristic points. Formally, this is to find the rigid motion -∈ 23 3 such that previous expression is respected. In the current context, a closed-form solution to this problem is known and explained in [START_REF] Horn | Closed-form solution of absolute orientation using unit quaternions[END_REF].

Key characteristics

Minimal clearance

Clearance, a global quantity named , is a characteristic of the manufactured assembly. It is defined as follows:

, = ! ) ‖ ‖ )
Reader will recognize a norm expression usually used in an optimization context. Maybe other norms can be used, but we have not performed the experiments to certify it.

A first linkage configuration study is to find the positional parameter such that the additional positional parameters are as small as possible. This leads to the minimization problem:

6 0 " = 8 , 9 , , = 0
Strictly speaking, the minimal clearance 0 " is not a key characteristic but rather a design constraint, because if , is smaller than 0 " , linkage cannot be assembled and the manufactured system doesn't work. Doing so leads to an assembly featuring joints that are adjusted as much as possible. Could this be a quality criterion? The answer is no. Indeed, among the number of manufactured components of the assembly there exists a possibility that non nominal parts fit together in such a way that joints are almost perfect, despite each component is far from its nominal dimension. So, something must be done to define and quantify the "distance" from the non-nominal assembly to the nominal assembly. The previously defined deviation is chosen to represent this distance. It is the second characteristic of the manufactured assembly.

Minimal deviation

The minimum deviation between the nominal assembly and the non-nominal one is defined with respect to design or industrial constraints. Constraints are that all local joint clearances ∈ must be smaller than a constant * . For practical reasons, we consider that * values are identical for all . This quantity represents the greatest clearance value accepted by designers or imposed by the manufacturing process. In other words, this is the length of the nunchaku chain previously presented.

Minimal deviation can now be written. Given a dimensional parameter value , possibly non nominal, the minimal deviation computation is to solve the following constrained optimization problem. Minimal deviation is named $ 0 " . < $ 0 " = 8 $ , 9 , , = 0 8 ∀ ∈ , < * 9

The computed value $ 0 " depends on the dimensional parameter value and on the maximum value allowed in each joint clearance * .

Maximal deviation

The maximum distance between the nominal assembly and the non-nominal one is defined with respect to design or industrial constraints, in a similar manner than above. Given a dimensional parameter value , possibly non-nominal, the maximal deviation computation is to solve the following constrained optimization problem. Maximal deviation is named $ 0?@ . < $ 0?@ = AB 8 $ , 9 , , = 0 8 ∀ ∈ , < * 9 Like $ 0 " , $ 0?@ depends on the dimensional parameter value and on the maximum value allowed in each joint clearance * .

Floating

The fourth and last presented characteristic is floating. This quantity represents the geometrical defect of the mechanical assembly. It quantifies the possible floating phenomenon of the parts of the mechanism. The higher the value is, the more the manufactured parts can move away from their nominal positions, which may cause vibrations and be harmful for the product lifetime.

Given a dimensional parameter value , possibly nonnominal, floating computation is to subtract $ 0 " from $ 0?@ . Floating is noted C . So:

C = $ 0?@ , $ 0 "
Obviously, C depends also on the dimensional parameter value and on the maximum value allowed in each joint clearance * .

Diagrams

Therefore, we have all the bricks to draw diagrams.

Parameters u are fixed

The J-D diagram, shown in Figure 2, is sketched for an instance of manufactured mechanical assembly, that is to say where dimensional parameters are fixed.

This figure illustrates the dependence between the clearance , and the deviation $ , as defined above. Four areas are reported. , is less than the 0 " value. • Zone 2: The system can be assembled. The deviation value $ , cannot be less than the $ 0 " value represented by the (C1) curve. • Zone 3: The system can be assembled. The deviation value $ , cannot be greater than the $ 0?@ value represented by the (C2) curve. • Zone 4: This is the area of existence of the system under study. The area represents the allowable floating of the manufactured parts connected together by imperfect joints. As the reader can appreciate, the $ 0?@ quantity increases when the clearance , increases, while the $ 0 " quantity decreases. This behavior is consistent, since the parts can move more freely when imperfect joints allow greater ranges of motion.

Parameters u vary between two limits

The diagram shown in Figure 5 is sketched for a series of assemblies. This means that dimensions of parts vary between two limits imposed by the manufacturing process. The allowed tolerance of the parts are noted * . Therefore the dimensional parameters is such that | , | < * . For practical reasons, we consider that * values are the same for all . It is noticeable that for each value of , the (C3) curve slightly changes, and that the vertical line 0 " is shifted a little. The union of all curves defines the gray and pink areas in Figure 5. Curve (C4) is the right limit of this pink area. Curve (C5) is the upper limit of the gray area. Analysis of this figure indicates that in order to ensure assemblability and interchangeability of all manufactured parts, the smallest value of 0 " must be outside of the pink area.

Thanks to this diagram, designers team knows that the floating value of the whole set of manufactured products, will be always under (C5) curve.

Case study

In this section, we applied the presented approach to one case study: a planar mechanism made of six parts and eight joints.

Presentation

This 2D-assembly is includes six bars linked together by six spherical joints as described in Figure 6.

Floating diagrams F(J) when | , | < *

By varying lengths of parts, a random set of 1000 articulated systems is generated. Then, by using a Maple® prototype program, clearance values and the floating values are computed for each system.

Figure 8 illustrates the resulting curves with tolerance * = 0.05 mm. Figure 9 illustrates the resulting curves with * = 0.1 mm. Using a standard Macbook Pro computer, each test requires a computing time of 4362s. We notice that:

• The maximum value of 0 " is 0.031mm for an allowed variation of the part dimensions less than 0.05mm.

• The maximum value of 0 " is 0.058mm for an allowed variation of the part dimensions less than 0.1 mm Results are consistent. As dimensional uncertainty increases, the largest minimum clearance, insuring assemblability, increases also. Moreover, HAB 0 " value doubles by doubling * . Take a particular value of , named * , for example at * = 0.15 mm, the floating value is 2.71 for | , | < 0.05 mm while it is 3.54 for | , | < 0.1 mm. When the dimensional uncertainty increases, the floating value also increases but not in the same proportions as the allowed tolerances. The minimum floating value is 0.826 in the first case while it is 1.91 in the second one. Thus, even if we allow tolerances of 0.05 mm, we can never have a floating value lower than 0.826.

Global measures of the mechanical assembly provided by this diagram allow designers to compare different tolerancing solutions. They can predict the floating phenomenon of parts with respect to the manufacturing tolerances of parts.

Conclusion

Presented tools allow engineers to study clearances and deviations during the conceptual design phase. Three characteristics of manufactured mechanical assembly are used: clearance, deviation and floating. The last two are new. They are defined and their algebraic expressions are given.

Two diagrams are drawn. The J-D diagram highlights four zones. Three of them are prohibited, the other represents the existence zone of the assembly under study. The floating diagram highlights the dependency between the floating phenomenon and the clearance allowed into the imperfect joints.

All these features provide genuine arguments for selecting the correct level of quality for manufacturing process. They provide also fruitful inputs to compare different architectural solutions of a same product with an equal manufacturing capability level.

The number of input data of the proposed tool is very small: connectivity matrix of the assembly structure, coordinates of the characteristics points, manufacturing precision class of the parts and range precision of the joint clearance. First simulation results are quickly obtained but the degree of confidence is questionable. Nevertheless, the longer the simulation is, the more reliable it is. For these reasons, our proposal is dedicated to assist designer's team during early phase of development products.

Perspectives of this work are being considered. The first one is to develop a new prototype to experiment other cases. Actually, our platform is implemented with Maple® language for some cases and with the standard optimization command "Minimize". An improvement would be using casADi, an open-source tool for non-linear optimization. A second perspective is a fundamental investigation about how to systematically introduce clearance parameters into perfect joints for standard kinematic 2D and 3D joints. A third perspective is related to deviation local severity. Clearly, not all deviations are equally severe. A concept can be robust to some deviations and sensitive to other deviations, and the present work does not address this point.

Figure 1 :

 1 Figure 1: Non-perfect spherical joint in a "nunchaku"

Figure 2 :

 2 Figure 2: J-D diagram when is fixed • Zone 1: The system cannot be assembled because the actual clearance value, is less than the 0 " value. • Zone 2: The system can be assembled. The deviation value $ , cannot be less than the $ 0 " value represented by the (C1) curve. • Zone 3: The system can be assembled. The deviation value $ , cannot be greater than the $ 0?@ value represented by the (C2) curve. • Zone 4: This is the area of existence of the system under

Figure 3 :

 3 Figure 3: C * is the floating value for * when is fixed

Figure 3

 3 Figure 3 highlights the construction to obtain the floating value. Given a maximum value * for clearance, draw the vertical line (D). Line D and curve (C1) intersect at point A and line D intersects curve (C2) at point B. Distance between A and B is the floating value for * . The Figure 4 shows the floating diagram. The (C3) curve sketched illustrates the floating evolution of the mechanical assembly versus clearance in the imperfect joints. The zone

Figure 4 :

 4 Figure 4: Floating diagram when is fixed

Figure 5 :

 5 Figure 5: Areas swept by curves C3 and 0 " , when | , | < *

Figure 6 : 6 -

 66 Figure 6: 6-bars structure studied The nominal length of each horizontal bar is 300 mm. Points A, B, C and D (resp. E, F, G and H) are aligned and equidistant in bar (1) (resp. bar (2)). The nominal length of each crossbar (numbered from 3 to 6) is 141,4 mm. This mechanical assembly is over-constrained.

Figure 7 : 6 -

 76 Figure 7: 6-bars structure studied Classically, conceptual design involves geometry through a skeleton made of points and line segments. Thicknesses of parts are not taken into account. As illustrated in Figure 7, connections are characterized by a point and parts by straight lines.

Figure 8 :

 8 Figure 8: 1 st case -Results for | , | < 0.05 mm

Figure 9 :

 9 Figure 9: 2 nd case -Results for | , | < 0.1 mm


Bernard Normand
email: bernard.normand@insa-lyon.fr

Nicolas Bererd

Philippe Martinet

Sabrina Marcelin

Moustapha Moine

José Feirrera

Dominique Baux

Thierry Sauvage

Nathalie Moncoffre

Electrochemical behaviour of austenitic stainless steel under tribological stresses and irradiation

Keywords: Stainless steel, B: Polarisation, Electrochemical Impedance Spectroscopy, C: Passive film, Tribocorrosion, Irradiation. Highlights

An experiment was developed to characterise the behaviour of 316L stainless steel under the combined effects of corrosion, tribology, and irradiation. This original experiment shows that radiolysis, through the production of free radicals and H2O2, leads to an oxidising medium.

The electrochemical behaviour of the material from the recorded polarisation curves and electrochemical impedance spectroscopy measurements indicates that the passive film under irradiation is a Cr oxi-hydroxide layer. The layer has more formative thickness under irradiation. When the irradiation is interrupted, the passive film is identical to that observed before irradiation. The repassivation is faster during irradiation and friction.

2

Austenitic stainless steel materials are often used in structural applications, where they have to undergo mechanical stresses. Thus, they must possess relatively good mechanical as well as corrosion resistance properties in the environment where they are used. Moreover, their reactivity has to be taken into account. Numerous studies exist on stress corrosion [START_REF] Scott | General corrosion and stress corrosion cracking of Alloy 600 in light water reactor primary coolants[END_REF], fatigue corrosion [START_REF] Andresen | A brief history of environmental cracking in hot water[END_REF], and hydrogen embrittlement [START_REF] Dwivedi | Hydrogen embrittlement in different materials: A review[END_REF] of these materials. More recently, some studies related to superficial stresses on stainless steel materials have also been reported [START_REF] Hertz | Approach to analysis of wear mechanisms in the case of RCCAs and CRDM latch arms: From observation to understanding[END_REF]. The concept related to the effect of a combination of tribology and corrosion (known as tribocorrosion) has also been explored [START_REF] Ponthiaux | Tribocorrosion: a new approach of the problems related to combined friction and wear in a corrosive surrounding[END_REF].

However, nuclear field is one of the areas in which the occurrence of tribocorrosion can be very risky. Indeed, several tribosystems, cited in [START_REF] Chitty | Tribocorrosion in Pressurized Water Reactors, 3 rd International Symposium on Tribo-Corrosion: Research, Testing, and Applications[END_REF], have been identified where large displacements and fretting phenomena have occurred. For example, the power developed by a nuclear reactor is controlled by managing the rod cluster control assemblies (RCCAs) that contain neutron-absorbing elements. This arrangement is controlled by the control rod drive mechanism (CRDM), guided by control rod guidance assemblies (CRGAs), as presented in All these devices are immersed in the reactor and are subject to vibrations. As shown in Figure 2, the 304L rod is guided by a 316L plate hardened with ion nitriding [START_REF] Hertz | Approach to analysis of wear mechanisms in the case of RCCAs and CRDM latch arms: From observation to understanding[END_REF]. This treatment comprises a superficial diffusion of nitrogen into the stainless steel to limit the wear.

In this study, the development of this device was first studied from a tribological viewpoint, which involves the hardening of the surface to limit the wear. Then, in the second step, a corrosionist point of view was considered that takes into account the effect of nitrogen on the maintenance of the passive properties of the austenitic stainless steel. Further, for optimising the process, this previous work guided the quantity of nitrogen content to be introduced to avoid the formation of nitride, which is very critical to corrosion resistance [START_REF] Normand | Electrochemical and surface studies of the passive layers grown on sputter-deposited nitrogen-stainless steel alloys in 1M H 2 SO 4 solution[END_REF]. However, the cited study considered a mechanical approach and followed it with a physico-chemical approach, which is sub-optimal for studying the multifunctional behaviour of materials.

Simultaneously considering the mechanical and physico-chemical stresses is important to assess their synergistic effects. Consequently, scale 1 simulators (MAGALY and AURORE) were developed by Framatome that allow the material to be loaded under conditions more representative of reactor operations [START_REF] Chitty | Tribocorrosion in Pressurized Water Reactors, 3 rd International Symposium on Tribo-Corrosion: Research, Testing, and Applications[END_REF]. These simulators are remarkable and can handle great complexities, besides facilitating the simulation of real-world contact conditions in terms of load, kinetics, and environment. However, as these simulators do not allow a combination of electrochemical measurements and irradiation effect testing, all the constraints involved in nuclear energy production are not completely represented. Electrochemical measurements are essential to study the evolution of the reactivity of the material exposed in the aqueous medium and subjected to superficial stresses. These measurements, associated with the characteristics of wear, can provide more holistic information on the synergistic effects of wear and corrosion [START_REF] Landolt | Electrochemical and materials aspects of tribocorrosion systems[END_REF], and the objective of such fields of study is to quantify the wear accelerated by corrosion and vice versa [START_REF] López-Ortega | Tribocorrosion of passive materials: A review on test procedures and standards[END_REF]. Notably, this type of damage is mainly observed on materials that can reach a passive state, such as stainless steel [START_REF] Cao | Modeling tribocorrosion of passive metals -A review[END_REF].

Austenitic stainless steel is protected by a thin film of a few nanometers thickness that develops on its surface [START_REF] Sato | An overview on the passivity of metals[END_REF]. The passive film is initially air-formed and can be modified in terms of composition and thickness depending on the nature of the electrolyte in which the stainless steel is immersed. When the stainless steel substrate is subjected to sliding contact or impact, the passive film can get damaged leading to the exposure of the underlying material, which can dissolve in the solution. The dynamics of the contact compete with the reconstruction kinetics of the passive film, also called the repassivation phenomenon [START_REF] Frankel | Repassivation Transients Measured with Thin Film Breaking Electrodes[END_REF][START_REF] Itagaki | Quantitative Analysis of Iron Dissolution during Repassivation of Freshly Generated Metallic Surfaces[END_REF].

To this, one must add the fact that the load causes microstructural modifications in the rubbed/impacted surface, resulting in a tribologically transformed surface [START_REF] Chunga | An experimental study on fretting wear behavior of crosscontacting Inconel 690 tubes[END_REF][START_REF] Laribi | Study of mechanical behavior of molybdenum coating using sliding wear and impact tests[END_REF].

Consequently, this worn surface has a different reactivity than the unaffected surface of the material, which is the whole issue of tribocorrosion in general. The importance of this issue deserves particular attention and motivates this work.

Although, as mentioned above, earlier works have also tried to identify the risk factors associated with damage due to tribocorrosion [START_REF] Chitty | Tribocorrosion in Pressurized Water Reactors, 3 rd International Symposium on Tribo-Corrosion: Research, Testing, and Applications[END_REF], the present work aims to introduce electrochemical measurements of the friction device to quantify the observations already made. Moreover, for an even wider representation, irradiation effects have also been added to the considerations.

The effects of irradiation on corrosion are collectively known as irradiation assisted stress corrosion cracking (IASCC), which is considered as a special case of corrosion under stresses assisted by irradiation, and is characterised by intergranular cracking on one hand and a loss of ductility on the other [START_REF] Scott | A review of irradiation assisted stress corrosion cracking[END_REF]. The damage is attributed to a microstructural and chemical evolution of the solid material (irradiation effect) and the radiolysis of the liquid medium (chemical effect) [START_REF] Shoji | Current status and future of IASCC research[END_REF]. The work of Bruemmer et al. illustrated the effects of a neutron beam fluence on the microstructural modifications in a 304 steel sample and the consequences of the modifications on IASCC behaviour [START_REF] Bruemmer | Radiation-induced material changes and susceptibility to intergranular failure of lightwater-reactor core internals[END_REF]. The microstructural evolution of materials is due to the displacement of atoms, and each displacement produces a combination of an interstitial atom and a vacancy, together called a Frenkel pair. It is mainly the displacement of these point defects that gives rise to dislocation loops, precipitation, segregation, and local chemical evolutions (inverse Kirkendall segregation, interstitial association segregation) that characterise the irradiation damages. The latter processes also lead to a local enrichment or depletion of alloying elements (including chromium), which contributes to the weakening of the passive film that protects the stainless steel and to a loss of the steel's mechanical properties [START_REF] Bruemmer | Grain boundary modification during neutron irradiation at intermediate temperatures[END_REF].

At this stage of knowledge, the analyses of passive films under irradiation, or only exposed to a fluid having undergone radiolysis phenomena, practised on a 316L, exposed to conditions representative of the nuclear environment (320°C, 3 wppm H2, neutral pH), show significant modifications of the passive film. This work indicates a chromium depletion in the internal part of the passive film of spinel oxides type and the presence of hematite on the surface of the oxide, which indicates the oxidizing power of the solution during or after irradiation [START_REF] Raiman | Radiolysis driven changes to oxide stability during irradiationcorrosion of 316L stainless steel in high temperature water[END_REF].

This phenomenon is less marked when the material is passivated before radiolysis. Physicochemical analyses indicate that passive films are thinner and more porous under the effect of proton irradiation, which gives them poorer corrosion resistance properties [START_REF] Raiman | Accelerated corrosion and oxide dissolution in 316L stainless steel irradiated in situ in high temperature water[END_REF].

In our work, the results obtained do not show such variations in the passive film. In these references the exposures of materials to irradiation are carried out over periods of 24 to 72 hours, in our case we expose our systems over a very short period, the time of an impedance or friction measurement, that is to say between 20 and 35 minutes maximum.

Radiolysis, on the other hand, leads to a modification in the redox potential of the medium due to the production of free radicals (H , O , OH , e -aq, etc.) and their recombination under H2 and H2O2 [START_REF] Caër | Water Radiolysis: Influence of Oxide Surfaces on H2 Production under Ionizing Radiation[END_REF], which can lead to an evolution of the passive film [START_REF] Wang | Electrochemical behaviour of 316L stainless steel exposed to representative chemistry in pressurised water reactors under proton radiation[END_REF]. Hence, an H2 overpressure is added in the Pressurised Water Reactor (PWR) to maintain a potential lower than -230 mV vs NHE (Normal Hydrogen Electrode), to prevent the production of oxidising radicals and the associated increase in potential and thereby the occurrence of SCC in stainless steel materials [START_REF]Shreir's corrosion, Fourth Ed[END_REF][START_REF] Was | Irradiation-assisted stress corrosion cracking[END_REF].

Figure 3 illustrates the different themes to be considered for achieving synergy among the different possible demands of the nuclear field. It demonstrates the interactions between [START_REF] Scott | General corrosion and stress corrosion cracking of Alloy 600 in light water reactor primary coolants[END_REF] tribology and corrosion, (2) corrosion and irradiation, and (3) tribology and irradiation. The fourth and final interaction represents tribocorrosion under irradiation, which is addressed in this paper.

To summarise, in this study we present an original experiment to jointly characterise the interactions between tribology and corrosion under irradiation and then discuss the resultant modifications in the properties of the passive film under the irradiation and its ability to reform after a tribological event. This paper is divided into two parts: the first presents the experiments and related activities performed in this study; the second presents the results obtained from the experiments. This work can be considered as a preliminary study to prove the feasibility of such complex research that focuses on a systemic approach to quantifying the multifunctionality of nuclear materials. It is of course aimed at nuclear applications, but the subject being so complex, we first chose to validate in this paper the feasibility of our study by working on a more conventional solution, for which we have a great deal of data concerning passive materials.

Material and methods

Material

A commercial austenitic steel material (316L type) supplied by GoodFellow, and composed of C (0.02 wt%), Si (0.49 wt%), S (0.001 wt%), P (0.035 wt%), Mn (1.79 wt%), Ni (10.1 wt%), Cr (16.7 wt%), Mo (2.03 wt%), balanced with Fe, was used in this study.

A 500 µm thick sheet of the selected steel type was chosen as the study sample. The particular thickness was chosen to allow the irradiating proton beam to pass through the sample and stop close to the metal/solution interface.

Electrochemical measurements

Electrochemical technics were employed in this work because they enable us accurately capture the evolution of the 316L stainless steel/electrolyte interface properties. For example, electrochemical impedance spectroscopy is an especially sensitive technic which allows us to access the properties of the passive film over potential, particularly in terms of thickness.

All electrochemical measurements were recorded in an aerated 0.02 mol/L Na2SO4 solution (50 mL), maintained at 20°C without stirring. The electrochemical cell comprised three electrodes: the working electrode, which included the 316L thin sheet fixed in the tribocorrosimeter, with an exposed surface of 12.5 cm²; the counter electrode, which was a porous carbon stick (26 cm²); and the reference electrode, a mercury sulphate electrode (MSE). This conventional three-electrode device was controlled with a Ref600 type potentiostat distributed by Gamry.

To ensure the reproducibility of the electrochemical measurements, the surface of the material was subjected to a preliminary electrochemical protocol to reduce the air-formed passive film that may have developed during sample storage. The preparatory protocol included an Open Circuit Potential (OCP) measurement for 600 s, followed by a applied potential of -1.5

V/MSE for 600 s to reduce the passive film formed in the air. This was followed by an OCP measurement for 600 s to relax the cathodically polarised surface and finally a polarisation of -330 mV/MSE for 3600 s. After this conditioning, the sample was left at OCP for one hour.

The polarisation value of -330 mV/MSE was chosen because it corresponds to the potential achieved by the material when immersed in the solution for 48 h. Thus, this value corresponds to the corrosion potential of the material in the passivated state, immersed in the neutral and aerated sulphate solution used in this study.

After the in situ electrochemical surface preparation of the 316L sample, the evolution of the corrosion potential (with OCP measurements) and the polarisation curves (I = f(E)) were recorded. The OCP measurement provides information on the oxidation-reduction potential between the material and the solution and identifies the evolutionary cycles of the stainless steel surface. The measured values tend toward passivation when the potential increases, or toward corrosion when the potential decreases significantly. The polarisation curve supplied informations regarding the involved reaction mechanisms and their kinetics, and the current densities involved and their range of existence from the potentials [START_REF] Ouerd | Reactivity of titanium in physiological medium[END_REF]. The potential scanning rate for the polarisation curve plotting was set as 1 mV.s -1 to ensure the reversibility of the measurement, and the potential scan limits were set as -0.5 V/OCP in the cathodic range and +1.5 V/OCP in the anodic range.

As the 316L austenitic stainless steel is a passive material, studying the evolution of the passive film and its resistivity at the 316L/passive film/electrolyte interfaces in situ and in the presence of irradiation is also of interest. These observations could only be obtained thanks to electrochemical impedance spectroscopy. This technic is based on the power-law model, which has proved its relevance in characterising the properties of passive films [27,28,[START_REF] Orazem | Dielectric properties of material showing Constant-Phase-Element (CPE) impedance response[END_REF][START_REF] Tribollet | EIS Technique in Passivity Studies: Determination of the Dielectric Properties of Passive Films, EIS Technics[END_REF]. However, the material must be under stationary state for successfully obtaining the electrochemical behaviour measurements; therefore, they were performed without any friction. The electrochemical impedance measurements were acquired at the corrosion potential with an amplitude of 25 mV, respecting the linearity condition of the signal. The impedance diagrams were obtained over a frequency range of 100 kHz to 5 mHz with 8 pts per decade.

Thereafter, the measurements were retaken during friction, when the metal/solution interface is considered to be in a non-stationary state. The displacement of the pin depassivated the surface of the material, resulting in potential and current transients, which

were measured with the electrochemical noise (EN) technic under ZRA mode monitored by using a Ref 600 potentiostat. The EN data were acquired sequentially with 100 Hz as the sampling frequency, filtered at 1% with the ESA 410 software. The analysis of these transients provided information on the repassivation time constants extracted from the model.

Irradiation conditions

Irradiation was applied to a CEMHTI UPR 3079 CNRS cyclotron with a 16 MeV proton It must be noted that all results presented in this paper do not come from the same cyclotron run which explains differences in the corrosion potential values under irradiation. For each run, the corrosion potential value has been measured as a blank.

Tribological procedure

To apply the frictional stresses, the required tribocorrosimeter that could be adapted for installation on one beam line of the CEMHTI cyclotron was first developed. Figure 5 shows the functional diagram of the developed apparatus along with the specifications of its various components. The on-site tribocorrosion device installed on the cyclotron is presented in Figure 6. Friction was provided with a chemically inert alumina pin of 12 mm diameter, which ensured a reciprocating displacement of 8 mm (+/-4 mm). Sample is immersed during 14h before sliding. An idle time of 6 s was ensured after each pin displacement to allow time for the material to repassivate. The displacement rate of the pin was 8 mm.s -1 . The number of performed cycles was between 600 and 1000. According to Hertzian considerations, the maximum shear stress was 450 MPa and the maximum shear depth was 20 µm.

Results and discussion

Irradiation effect on the passive film

Figure 7 shows the evolutionary stages of the potential of 316L stainless steel immersed in Na2SO4 solution. After undergoing the preparation protocol, the material quickly reaches a stable potential close to -430 mV/MSE. The polarisation curves later confirmed that this is the potential that characterises the passivated state of the austenitic stainless steel. When the corrosion potential reaches a steady state, the proton irradiation beam is switched on, which causes an instant increase in the potential to a more anodic value close to -320 mV/MSE. This potential remains constant for the duration the beam remains active. When the irradiation is interrupted, the potential further ennobles to attain a value close to -290 mV/MSE and then slowly drops after 5 min of latency to reach a corrosion potential close to the one recorded during the application of the beam. At this stage, two assumptions can be made: either the passive film has changed, or the oxido-reduction potential of the solution has modified toward more noble values. Notably, such behaviour has been observed in other works also [START_REF] Wang | Electrochemical behaviour of 316L stainless steel exposed to representative chemistry in pressurised water reactors under proton radiation[END_REF][START_REF] Tribollet | EIS Technique in Passivity Studies: Determination of the Dielectric Properties of Passive Films, EIS Technics[END_REF][START_REF] Muzeau | Electrochemical behaviour of stainless steel in PWR primary coolant conditions: Effects of radiolysis[END_REF] and is generally associated with the presence of radiolysis-induced radicals. The phenomenon can be described as follows: there is a rapid potential change (either toward oxidising or reducing values) at the beginning of irradiation followed by a steady state potential throughout the irradiation, and finally, after the stoppage of the irradiation, a transient phase is followed by a slower evolution toward a new potential.

The modifications that the medium undergoes during the irradiation is due to the production of free radicals [START_REF] Ziegler | SRIM -The stopping and range of ions in matter[END_REF]. Most radiolytic free radicals and excited species are created near the end of the proton range known as the Bragg peak. These free radicals are known to recombine with dissolved oxygen and lead to the formation of H2O2 [START_REF] Caër | Water Radiolysis: Influence of Oxide Surfaces on H2 Production under Ionizing Radiation[END_REF][START_REF] Orazem | Dielectric properties of material showing Constant-Phase-Element (CPE) impedance response[END_REF]. Consequently, the passive layer/solution interface remains in contact with the radical species (H , O , OH , etc.) as well as the recombination products (e.g., H2O2). The red curve depicted in Figure 8 shows the evolution of the corrosion potential during irradiation. This evolution follows the variations described in Figure 7 during the irradiation beam application. The blue curve shows the evolution of the potential before irradiation when H2O2 is added after 7 min of immersion.

The potential increases and reaches a value observed under irradiation, and the shapes of both the curves are similar.

The results presented in Figure 8 present a powerful argument to prove the effect of the radiolysis in the solution on the corrosion potential evolution. Anodic polarisation curves were drawn to identify whether a change in passive behaviour could explain the potential ennoblement, as shown in Figure 9.

The anodic curve obtained for the 316L stainless steel sample in the sodium sulphate solution before irradiation (black curve) indicates a corrosion potential close to -280 mV/MSE and shows for more anodic potential that the electrochemical behaviour of the substrate is characterised by a passive state. The current density i in the anodic portion is low (less than 10 µA/cm²), as also reported in [START_REF] Tranchida | Electronic properties and corrosion resistance of passive films on austenitic and duplex stainless steels[END_REF]. The polarisation curve obtained for the sample under irradiation (red curve) exhibits a maximum corrosion potential of approximately 0 mV/MSE.

In comparison with the curve plotted for the sample without irradiation, the difference between the corrosion potentials is approximately 280 mV. The same shift is observed when H2O2 is added to the neutral aerated sodium sulphate electrolyte. That confirms the importance of the modifications that the medium undergoes when under irradiation, which involves modifications in the chemistry of the medium due to the formation of free radicals and then H2O2 observed previously by several authors, as Wang et al. [START_REF] Wang | Electrochemical behaviour of 316L stainless steel exposed to representative chemistry in pressurised water reactors under proton radiation[END_REF] and more recently by Y. Wada et al. [START_REF] Wada | Radiolytic hydrogen evolution in a closed vessel[END_REF]. The potentials for which the reactions are involved correspond to the domain of existence of Cr2O3 growing. They are the same whatever the state of the medium: with or without irradiation, which indicates that the nature of the passive films remains the same. We assume that the film is made of oxy-hydroxide, mainly a mixture of Cr2O3 and Cr(OH)3 as the inner layer and iron oxide and hydroxide as the outer layer, as it was previously identified by Z. Wang et al. [START_REF] Wang | Chloride-induced alterations of the passive film on 316L stainless steel and blocking effect of pre-passivation[END_REF]. This is obviously a global description, and the exact demarcation between each layer is difficult to identify.

If the potential ranges are identical, the current densities differ in the passive range, and are slightly higher under irradiation conditions. In general, when the current densities are higher, it is because more dissolution of the material is required to maintain the passive film and the and is represented by the green curve. It should be noted that it was not possible to remove oxygen completely since it is continuously produced by water radiolysis. The higher current density recorded in the cathodic part of the green curve is due to the production of higher quantities of reducing species during irradiation. These curves provide information about the reaction potential and its kinetics from the current densities. To understand the evolution of the passive film and quantify some of its properties, electrochemical impedance measurements were obtained.

Electrochemical impedance measurements were obtained before, during, and after the irradiation. Figure 11 shows the impedance (IZI) and phases (ϕ) observed for these three conditions. They were adjusted from the ohmic drop and are represented in Bode coordinates.

All impedance diagrams were characterised by two time constants. The time constant for the low frequency range was not well defined in the result obtained during irradiation (blue curve). The high-frequency part of the phase angle was defined by a plateau for a phase less than -90°, which is attributed to the constant-phase-element response due to the presence of the passive film. It should be underlined that in the impedance diagram, the plateau is not very well defined, probably due to the difficulty in calculating the electrolyte resistance correctly.

Thus, the high-frequency time constant is attributed to the passive film response and the time constant at the low frequency is attributed to the charge transfer at the passive film/electrolyte interfaces. The impedance analysis performed in our study is based on the graphical method reported in [START_REF] Sato | An overview on the passivity of metals[END_REF] and the CPE behaviour is analysed with the help of the power-law model, largely employed to attribute a physical meaning to the CPE obtained for passive films [START_REF] Orazem | Dielectric properties of material showing Constant-Phase-Element (CPE) impedance response[END_REF].

The graphical or fitted parameters corresponding to the high-frequency time constants and the corrosion potential values are reported in Table 1. The table shows that some values deviate from the mean. These values are distributed over a range to provide information on the dispersion of the results.

The potential values for the three irradiation conditions confirm the trends described above with a demonstrated ennoblement of potential related to the chemistry of the environment.

This evolution may also explain the significant changes in the resistance of the electrolyte, which tends to decrease during and after irradiation. Moreover, this evolution cannot be attributed to corrosion phenomena because the material remains passive in all the cases. The dissolution of the material is insufficient for modifying the resistance of the electrolyte.

Whatever the condition, the CPE parameter α remains close to 0.8, which is an intermediate value between a resistive (0.5) and an ideal capacitive (1) behaviour. The capacitance of the passive film is associated with that of the space charge and is graphically identified on a Cole-Cole diagram representing the imaginary part of the capacitance as a function of its real part, according to the relation:

= Eq. 1
As shown in the Table 1, the capacitance value decreases under irradiation and returns to a value close to its initial value after irradiation. The behaviour of the passive film can therefore be considered as reversible between the before and after irradiation periods.

From the space charge capacitance, it is possible to define the thickness of the passive film, as

given by: = Eq. 2

Here, Csc corresponds to the space charge capacitance, A to the exposed area, ε to the permittivity of the passive film (12 for Cr2O3), ε0 to the permittivity of the vacuum, and δsc to the thickness of the passive film. The film thickness was estimated at 6 nm before irradiation, 12 nm during irradiation, and 4 nm after irradiation. Therefore, the thickness variation seems reversible. The thinner the film, the more protective it is [START_REF] Sato | An overview on the passivity of metals[END_REF]38]. It is possible that under irradiation, the passive film may be less protective since it is more defective.

The power-law model was specifically used for analysing the CPE behaviour in the high frequency ranges of the electrochemical impedance diagrams because it allows the evaluation of the resistivity distribution through the passive film [START_REF] Marcelin | Electronic properties of passive films from the multi-frequency Mott-Schottky and power-law coupled approach[END_REF]. This distribution is established by the equation:

= Eq. 3 Here, = 1 + 2.88 $ % & '.()*
, + is the thickness of the passive film, and , and , -are the resistivities at the passive film/electrolyte and 316L stainless steel/passive film interfaces, respectively.

The resistivity , decreases significantly under irradiation (Table 1). , -is remains constant before and during irradiation, but increases by one order of magnitude after irradiation.

Figure 12 shows the resistivity distributions through the passives film for the three irradiation conditions, based on a dimensionless representation of the thickness (0 corresponds to the 316L/passive film interface (, -and 1 corresponds to the passive film/sodium sulphate solution interface (, ). These results support the assumption made during the passive film analysis that a thicker film presents a weaker barrier. In our case, the metal oxide interface did not change before and during the irradiation. The polarisation curves indicated that the potentials were the same, which indicates the similar nature of the film. Thus, the oxide/solution interface is less resistive under irradiation either because of the more significant contribution of the hydroxide under irradiation (due to the presence of radiolytic species of the solution), or because of creation of defects in the passive film due the beam output. Further analyses are underway to identify the exact type of contribution. The argument leans more in favour of the formation of a more significant hydroxide because once the irradiation is interrupted, , -reaches the maximum value and , is substantially similar to the initial value without irradiation. A higher resistivity at the metal/oxide interface characterises a more significant passive film maturity in terms of the hydroxide/oxide ratio, with more Cr2O3. It is therefore likely that the overvoltage applied to the system during irradiation contributed to the promotion of deprotonation, as described in Okamoto's model for passive film formation [START_REF] Sato | An overview on the passivity of metals[END_REF].

Irradiation effect on the tribo-electrochemical behaviour of 316L

Friction tests were conducted after immersion during 14h. This period insure a reproducibility of the passive state. Eq. 4

Here, J1 and J2 correspond to the two components of current which contribute to the fit of current fall and τ1 and τ2 correspond to the adsorption time constants of the 2D layer and the growth of the 3D film, respectively. These parameter have been introduced by Beck [START_REF] Beck | Electrochemistry of freshly-generated titanium surfaces-II. Rapid fracture experiments[END_REF] and illustrated by Dalbert et al [START_REF] Dalbert | In situ determinations of the wear surfaces, volumes and kinetics of repassivation: Contribution in the understanding of the tribocorrosion behaviour of a ferritic stainless steel in various pH[END_REF].

The constant τ1 was successfully analysed in this study; however, τ2 could not be analysed in this preliminary study, probably because the repassivation time was insufficient to allow the stable growth of the passive film. Figure 16 shows the evolution of the adsorption time constant of the species prior to repassivation under different conditions. The red curve indicates a time constant value of 0.3 s under friction without irradiation. When irradiation is applied after 800 current transients, the time constant (red curve) drops drastically to 0.25 s.

The time constant then decreases, implying a faster adsorption step. The black curve confirms this decrease in the time constant for the irradiation applied before the pin was moved. The time constant remains 0.25 throughout the transients. In an attempt to confirm the representativeness of the effects of the H2O2 produced by radiolysis mentioned in the first part of this work, friction tests were performed, with H2O2 added after 1250 transients. After this addition (blue curve), the time constant dropped significantly under the effect of radiation.

The extent of this decrease varied for different H2O2 concentrations. Work is still in the progress to confirm this observation.

Conclusions

The objective of this study was to develop an experiment to characterise the behaviour of a 316L stainless steel sample subjected to tribocorrosion under irradiation. Such an experiment required a tribocorrosimeter design that could be installed on the cyclotron of the CEMHTI laboratory to allow in situ proton irradiation. This original design enabled us to perform superficial mechanical stresses on the stainless steel while recording the electrochemical measurements.

The obtained measurements indicated a significant increase in the corrosion potential during The resistivity of the passive film at the steel/oxide interface remained the same before and after the irradiation. The oxide/solution resistivity dropped significantly during irradiation.

Further analyses are being considered to identify whether this is an effect of the solution caused by the production of more hydroxide at the oxide solution interface due to the presence of H2O2 or an effect of the presence of irradiation defects at the interface, which may have promoted the formation of a degraded passive film structure. Considering the changes in the oxidising power of the solution, the various phenomena involved during tribocorrosion were studied. This preliminary work was based on the study of repassivation time constants after depassivation under friction, and it was observed that adsorption, a preliminary step before the growth of the passive film, was faster under irradiation. At this point, the growth stage could not be characterised fully. As a final observation, the behaviour of the passive film under the irradiation was found to be reversible.

Figure 1 .

 1 Figure 1.

  beam (H + ). During their path to reach the electrochemical cell, the protons loses energy passing through two titanium foils (27 µm each) of the ionization chamber, the titanium exit foil (27 µm) at the beam line end and the 316L stainless steel sample. The energy loss in air between the Ti exit foil and the sample is considered as negligible. The energy at the entrance side of the sample is 15,2 MeV. Its thickness is reduced to 500 µm to ensure a total transmission of the incident protons through the sample. An energy of 2.9 ±0.5 MeV was transferred to the solution. The energy can be calculated to such near precision in these conditions thanks to the SRIM code[START_REF] Ziegler | SRIM -The stopping and range of ions in matter[END_REF], which postulates that protons stop at a distance equal to approximately 140 ±40 µm above the interface (Figure4). During all of the experiments, the protons flux impinging the sample is monitored by the ionization chamber to obtain a constant dose rate in the solution. The ionization chamber current is calibrated by a Faraday cup and its calibration verified before and after the irradiation. The beam size was 8 mm in diameter, providing a scanning area of 50 mm². The beam current was fixed to 10 or 40 nA, giving rise to a flux of 1.2x10 11 ion.cm -2 .s -1 or 5x10 11 ions.cm -2 .s -1 , respectively. These low values of current are mandatory to minimize the activation of steel samples induced by protons. The duration of irradiation varied according to the electrochemical measurements, considered cyclical or not. It was between 20 min and 10 hours, resulting in doses deposited in the solution (50mL) ranging from 1.3 kGy to 167 kGy. The equivalent dose rate, due to sample activation after 30 min of irradiation is about 100 µSv/h, making rapid ex situ and post mortem surface analysis difficult.

  barrier function of the passive film is less prominent. These observations were confirmed with experiments performed in a deaerated environment, as shown in Figure10. The potentiodynamic curves exhibited an increase in both potential and current density in irradiation conditions. For reasons of clarity, the cathodic part of the polarisation curve under irradiation is not shown. The polarisation curve obtained for the stainless steel sample in an aerated solution is represented by the black curve. As demonstrated by the blue curve, obtained with the deaerated solution, the electrochemical behaviour of stainless steel shifts to a more cathodic domain due to oxygen removal, which is oxidising. The corrosion potential shifts toward cathodic values, driven by proton reduction. Under irradiation also, the trends are the same as described previously. The shift toward a nobler potential due to the radiolysis effect is represented by the red curve. Under irradiation, the dissolved oxygen removed performed by N2 bubbling results in a slight shift of the corrosion towards cathodic values,

Figure 13 .

 13 figure shows the corresponding curve in red. When the friction was interrupted, the potential

Figure 14 Figure 15 .

 1415 Figure 14 presents a focused view of the potential and current transients. Both the current and

  irradiation. Experiments by adding hydrogen peroxide to the solution in the absence of irradiation demonstrated that this potential evolution was mainly caused by a change in the oxidative power of the solution due to the presence of radiolytic species in the solution. Of course this experiment simulates the effects of radiolysis without taking into account the defects created in the passive film by the irradiation beam. The time scale investigations performed in this work indicated that the characteristics of the passive film remained identical before and after the application of irradiation. The PLM was used to obtain the impedance measurement parameters. The results showed a thickening of the passive film during irradiation, with the other parameters remaining unchanged. These are preliminary results that do not correspond to those obtained by other authors for longer irradiations under more representative nuclear conditions. More detailed studies will be envisaged in the near future to complement the thickness measurements with other techniques.

Table 1 :

 1 Graphically extracted or fitted parameters obtained from impedance diagrams presented in Figure11for the three-irradiation conditions.

	Irradiations conditions	Potential (V vs MSE)	Re (Ω.cm²)	α	Q (Ω -1 .cm².s α )	Csc (F.cm -²)	δsc (nm)	ρ0 (Ω.cm)	ρδ (Ω.cm)
	Without	-0.530	918	0.78	1.14 10 -5	0.8 -1.8 10 -6	6-12	3.67 10 11	6 -140 10 6
	During	-0.315	885	0.79	7.84 10 -6	3.2 -8.7 10 -7	12-33	4.04 10 11	0.1 -20 10 6
	After	-0.190	844	0.78	1.67 10 -5	1.1 -3.6 10 -6	3-9	2.69 10 12	4 -577 10 6

Acknowledgements

This project received financial support from the CNRS through the NEEDS program and, more recently, through the MITI interdisciplinary programs. The authors also thank P. Sireira, C. Déhée, A. Guichon, and C. Panetier for their fruitful contributions during their Master Project and O. Farid from Nuclear Research Center, Cairo, Egypt during his scientist internship at MATEIS UMR 5510 CNRS, INSA Lyon.