Hassan Issa
email: hassan.issa@g2elab.grenoble-inp.fr

Vincent Debusschere

Lauric Garbuio

Philippe Lalanda

Nouredine Hadjsaid

AI-BASED CONTROLLER FOR GRID-FORMING INVERTER-BASED GENERATORS UNDER EXTREME DYNAMICS

This paper presents two artificial intelligence (AI)-based controllers for grid-forming inverter-based generators in a simplified microgrid. The supervised learning approach was considered for the AI-based controls. The training datasets were collected from an experimentally validated virtual synchronous generator controller. The first AI model is a convolutional neural network (CNN), and the second is a gated recurrent unit (GRU). These two neural network types are chosen as they handle short-term temporal sequence data, provided as a sliding window of measurements. The proposed controllers are tested under a black start, load variations, and a three-phase-to-ground short circuit at the inverter's output. Both controllers manage to achieve the black start of the inverter, supply the power demanded by the load, damp the short circuit current during a fault occurrence and recover afterward.

I.

INTRODUCTION

To reduce greenhouse gas emissions, sources of electricity production are diversified, which introduces a high penetration of distributed renewable energy resources (RES) in electrical grids [START_REF] Wang | A Review of Power Electronics Based Microgrids[END_REF] [START_REF] Li | An Accurate Power Control Strategy for Power-Electronics-Interfaced Distributed Generation Units Operating in a Low-Voltage Multibus Microgrid[END_REF]. The use of such distributed generation brings new challenges regarding grid stability due to the intermittent nature of RES [START_REF] Vandoorn | Review of primary control strategies for islanded microgrids with powerelectronic interfaces[END_REF]. Furthermore, distributed generation units are mostly inverter-based generators (IBG). As they do not provide inertia by default, their operation could weaken the stability of distribution grids. Thus, new control methods are indispensable for guaranteeing the stability of the power system under these new conditions. We are referring here notably to gridforming controllers. In that category, the main solutions are either based on model-based controllers or data-driven controllers. Concerning model-based approaches, virtual synchronous generator (VSG) controllers represent a traditional solution [START_REF] Moulichon | Observer-Based Current Controller for Virtual Synchronous Generator in Presence of Unknown and Unpredictable Loads[END_REF]. Simplified approaches exist, like virtual inertia, for instance, most of the time implementing a droop control [START_REF] Subramanian | A Cooperative Rate-Based Model Predictive Framework for Flexibility Management of DERs[END_REF], [START_REF] Tamrakar | Virtual Inertia: Current Trends and Future Directions[END_REF]. Less-traditional forms of controls are investigated in the literature as well, like virtual oscillators [START_REF] Dhople | Virtual Oscillator Control for voltage source inverters[END_REF] or matching control [START_REF] Arghir | Gridforming control for power converters based on matching of synchronous machines[END_REF]. Model-based controllers are usually restricted to operating in a predefined environment and require precise tuning. Regarding data-driven approaches, numerous methods can be found in the literature. Neural networks can be used to control a grid-connected inverter under disturbances, considering dynamic and power converter switching conditions [START_REF] Li | Artificial Neural Networks for Control of a Grid-Connected Rectifier/Inverter Under Disturbance, Dynamic and Power Converter Switching Conditions[END_REF]. The virtual inertia of grid-connected inverters can be controlled via an adaptive critic design-based reinforcement approach [START_REF] Saadatmand | Adaptive critic design-based reinforcement learning approach in controlling virtual inertia-based gridconnected inverters[END_REF]. Moreover, the inertia of a VSG can be controlled with a neural network [START_REF] Yao | RBF Neural Network Based Virtual Synchronous Generator Control With Improved Frequency Stability[END_REF]. For instance, reinforcement learning was also considered, to achieve a data-driven optimal control strategy of a VSG [START_REF] Li | Data-Driven Optimal Control Strategy for Virtual Synchronous Generator via Deep Reinforcement Learning Approach[END_REF]. The aforementioned solutions are either applied to the whole grid-following inverters or just to some parameters. In a previous study [START_REF] Issa | Artificial Intelligence-Based Controller for Grid-Forming Inverter-Based Generators[END_REF], we proposed a feedforward neural network (FFNN) to control a grid-forming inverter-based generator in a microgrid (MG). Although the FFNN has demonstrated promising capabilities of conserving the frequency and voltage at their nominal values in typical load variations, it has also shown weaknesses in capturing the extreme dynamics of the controlled system like, for instance, damping the short circuit current and recovering afterward. This is because the FFNN operates instantaneously, meaning that predictions are based on the state of the system per time step, without considering historical states. The dynamics of the system are thus lost. To avoid the complexity of model-based controllers, cover the ensemble of the grid-forming unit, and overcome the limitations of the instantaneous operation of FFNN, a short-term temporal sequence approach is considered in this work. The features are represented as short-term temporal sequences of measurements, provided via a sliding window. As a result, two data-driven models, a convolutional neural network (CNN) and a gated recurrent unit (GRU) are tested in this paper, as they both can handle short-term temporal sequence features, thus can capture the dynamics of the system during harsh events like a short-circuit. The proposed controllers have thus to achieve voltage and frequency control as a grid-forming unit, as well as be capable of damping the short circuit current in dedicated situations by capturing the temporal sequence of the controlled system. The paper is organized as follows: the second section covers the electrical models. The electrical environment, the model-based controller used for data generation, and the AI-based controllers' testing scenarios are described. The third section elaborates on the AI-related part. The CNN and GRU implementation are described as well as their interaction with the electrical environment. The obtained results and observations are presented in the fourth section. Finally, the paper is concluded and future developments are listed in the last section.

II. ELECTRICAL MODELS

The electrical aspect of the case study is elaborated in this section by explaining the electrical environment, the model-based controller used for data collection, and the testing scenarios of the proposed AI-based controllers.

A. Electrical Environment

The considered case study, from the electrical point of view, is a simplified isolated microgrid (MG), illustrated in Figure 1. It is represented by one inverter-based generator (IBG) and three loads connected one at a time during the simulation. The three loads are located at a single point of connection, downstream of the line linking them to the IBG.

Figure 1. Simplified Isolated Microgrid

The MG operates in a balanced three-phase mode at the low voltage distribution level, i.e., the nominal phase voltage is 230 V and the nominal frequency is 50 Hz. The dc bus voltage is assumed to be constant.

B. Data Generation

Knowing that the adopted data-driven approach is relying on supervised learning, the availability of labeled training data is key. Thus, data were collected by simulating the virtual synchronous generator (VSG), from [START_REF] Moulichon | Observer-Based Current Controller for Virtual Synchronous Generator in Presence of Unknown and Unpredictable Loads[END_REF], under numerous scenarios. This VSG consists of a linear quadratic regulator including an integrator and a state observer. This controller is developed to provide high robustness during harsh events such as short circuits. Each simulated scenario includes the black start of the IBG and the occurrence of a three-phase short circuit at its output during the supply of the load. The power demand, i.e., rating in kW and kVAR, and type of the load, i.e., resistive inductive and capacitive, vary from one scenario to the other, ensuring the balance of the dataset, yet the black start and the short circuit are always present. The generated dataset includes the measurements describing the state of the inverter and the MG, such as the voltages and currents of the MG and the inverter, the active and reactive powers, the frequency, and the errors between the RMS phase voltage and the nominal value. These measurements represent the features (inputs) of the AI-based controllers. Furthermore, the generated dataset also includes the control signals, meaning that the duty ratios. These control signals represent the labels (outputs) of the AI-based controllers.

C. Testing Scenarios

The AI-based controllers' capabilities are tested with the loads and the events defined in Table 1 and Table 2 respectively. The proposed controllers are expected to start the IBGs, conserve the stability of the simplified MG (i.e., fulfill the demand of the connected loads concerning their power ratings and types) by maintaining the voltage and frequency at their nominal values, and damp the short circuit current during the occurrence of a three-phase short circuit at the output of the IBG. The events in Table 2

Table 2 List of Occurring Events

The three-phase short circuit event at the output of the IBG is considered to challenge the controllers' capabilities of damping the short circuit current and recovering afterward, which is not the case with the FFNN [START_REF] Issa | Artificial Intelligence-Based Controller for Grid-Forming Inverter-Based Generators[END_REF]. In the end, the aforementioned events are designed to test the controllers' abilities to ensure the stability of the MG, by maintaining the voltage and frequency at their nominal values, during the black start and load variations. Moreover, these events are designed to test whether the controllers can physically protect the inverter, by damping the short circuit current, during the occurrence of the fault.

III. AI MODELS IMPLEMENTATION

The integrations of the proposed AI models in the electrical environment are identical. Both models communicate with the electrical environment via the same set of parameters that represent the inputs and outputs of the AI-based controllers. The outputs or the control signals provided by the AI-based controllers are the duty ratios (in the dq-frame).

The inputs expected by both AI-based controllers are the following: voltages and currents of the grid and the inverter (in the dq-frame), measured active and reactive powers, frequency of the grid, and the RMS voltage errors (difference between measured rms voltages and 230 V for the three phases).

In addition to what was implemented in [START_REF] Issa | Artificial Intelligence-Based Controller for Grid-Forming Inverter-Based Generators[END_REF], a buffer memory is added upstream of the input layer of each AI model. The purpose of this buffer is to provide short-term temporal sequences of measurements at the inputs of the Moreover, the memory buffer acts as a fixed range sliding window of inputs, such that at every time step, the oldest instantaneous measurement is dropped and the latest is added.

Figure 2 illustrates schematically the implemented control policy and the interaction with the electrical environment.

Figure 2. Implemented Control Policy

A. Convolutional Neural Network

Convolutional neural networks (CNN) are part of the various types of deep learning methods. CNNs are used in numerous fields, e.g., image classification, object tracking, and speech and natural language processing [START_REF] Gu | Recent advances in convolutional neural networks[END_REF].

The CNN provides the capacity of mapping inputs in the form of batches, i.e., a batch including a set of instantaneous measurements per feature. In our case study, the memory buffer provides batches of inputs in the following shape: {Batch, number of historical instantaneous measurements, number of features}.

The proposed sequential CNN model consists of 11 layers. The first layer represents the input layer, then is followed by a normalization layer. The third layer is a convolutional one-dimensional layer including 128 filters and followed by a one-dimensional max pooling layer. The fifth layer is also a 1-D convolutional layer, yet including 64 filters, that is followed by a 1-D max pooling layer. The seventh layer is the last 1-D convolutional layer. It consists of 32 filters. The eighth layer is a flattened layer that prepares the outputs of the previous 1-D convolutional layer to fit in the ninth layer representing a 64-units dense layer. The tenth and eleventh are as well dense layers, including 32 units and representing the outputs layer respectively.

B. Gated Recurrent Unit

The gated recurrent neural networks have proven favorable outcomes in numerous applications including sequential or temporal data [START_REF] Dey | Gate-variants of Gated Recurrent Unit (GRU) neural networks[END_REF]. As a result, the gated recurrent unit (GRU) is the second chosen approach in our case study. The addition of the memory buffer upstream of the input layer provides the temporal sequences of measurements required by the GRU.

The proposed sequential GRU model includes six layers. The first layer corresponds to the input layer. The second layer is the normalization layer. The third layer is a GRU layer that includes 160 units and returns the sequence to the following layer. The fourth layer is also a GRU layer including 64 units returning the sequence to the following layer. Finally, the fifth layer is a GRU layer with 96 units followed by the outputs layer, represented in the form of a dense layer.

IV. RESULTS AND OBSERVATIONS

The results following the testing of the CNN and the GRU models are presented in this section by considering the MG's frequency, MG's voltage, and IBG's current respectively.

A. Microgrid Frequency Profiles

The MG's frequency profiles of both the CNN and GRUbased models are illustrated in Figure 3. As shown, both controllers are capable of restoring the frequency at its nominal value (50 Hz) following the designed events. Although both plots are close, the GRU's frequency reaches a slightly higher peak than the CNN, during the black start of the IBG and following the elimination of the short circuit fault.

C. Inverter-Based Generator Current Profiles

The inverters' current profiles are presented in Figure 5. These plots aim at visualizing the CNN and GRU controllers' behaviors during the three-phase short circuit fault at the output of the IBGs. As shown, only one phase current is presented per controller. The illustrated current profiles represent the phases that undergo the highest peaks. Although the MG is a three-phase balanced system, the balance was temporarily lost, for 0.02 s, at the beginning of the fault. Moreover, it is noticed that the CNN-based controller damps the short circuit current at around 50 A, yet the GRU-based does at slightly higher value, at 60 A. It is also seen that both currents are undertaking a spike at the beginning of the fault. The spike in the CNN case reaches almost 110 A which is lower than the GRU's, with almost 160 A. This spike is to be furtherly analyzed, as it might cause physical damage to the inverter's components if not prevented, either via a software action or physical saturation for example.

Figure 5 Single-phase rms Inverter Currents of CNN vs. GRU

One of the solutions to this issue is to replace the actual AI approaches with a hybrid data-driven/model-based one, in which we will have access to the reference currents of the controllers. In the hybrid case, a saturation block would be added at the level of the reference currents.

V. CONCLUSION AND FUTURE WORK

The two AI models, CNN and GRU, presented in this paper are trained with labeled datasets collected from simulating a virtual synchronous generator (VSG). The collected datasets represent the scenarios in which the black start of the inverter-based generator (IBG), load variations, and occurrence of a three-phase short circuit at the output of the IBG take place. Both AI-based controllers are implemented to control an inverter in a simplified isolated microgrid. Testing is conducted to identify the capabilities of each AI model under scenarios including a black start, variations of load types and ratings, as well as a three-phase short circuit. Both proposed approaches can maintain the stability of the simplified microgrid, under the events of black start and load variations, by restoring the frequency and the voltage of the microgrid to their nominal values. Furthermore, both controllers cope with the three-phase short circuit fault and recover afterward, yet they are undertaking a spike in the current profiles during the occurrence of the short circuit fault. As a result, considering short-term temporal sequences of measurements, implementing a CNN or a GRU, is an adequate data-driven solution for controlling a grid-forming inverter-based generator under extreme dynamics.

At the electrical environment level, the proposed AI models will be tested in a more complex and realistic representation of a microgrid, in which multiple AIcontrolled IBGs will be installed supplying multiple loads. This will help investigate the limitations and the capabilities of the proposed solutions in a more realistic manner.

  are chosen to ensure the capability of the proposed AI-based controllers in terms of black start and load variations, similar to the FFNN in [13]. Time (s) Event 0 Black start and connection of Load 1 (A) 0.5 Occurrence of a three-phase short circuit on the output of the IBG (B) 0.7 End of the short circuit faulty event (C) 1 Disconnection of Load 1 and connection of Load 2 (D) 2 Disconnection of Load 2 and connection of Load 3 (E)

  controllers. This temporal sequence of measurements adds extra stability to the controller, during operation, by compensating for any faulty instantaneous measurement by the other instants present in the sequence.

Figure 3 FrequencyFigure 4

 34 Figure 3 Frequency Profiles of CNN vs. GRUB. Microgrid Voltage ProfilesThe MG's voltage profiles of both the CNN and GRUbased models are illustrated in Figure4. Since the considered simplified MG is a balanced three-phase system, only one phase voltage is presented. As shown, both controllers are capable of keeping the RMS voltage within the acceptable range following the designed events. However, the CNN requires extra time to stabilize the voltage at the beginning of the event (D).

Table 1

 1 describes the three designed loads by including their power ratings and types. Load 1 is set to be highly capacitive, Load 2 is resistive with small rated power, and Load 3 is designed to be highly inductive.

	Load	Active	Inductive	Capacitive
		Power	Reactive	Reactive
		(kW)	Power	Power
			(kVAR)	(kVAR)
	Load 1	15	0	7
	Load 2	1	0	0
	Load 3	15	7	0

Table 1

 1 Characteristics of the Connected Loads

ACKNOWLEDGMENTS

This work has been partially supported by MIAI@Grenoble Alpes, (ANR-19-P3IA-0003).


Benoît Ter-Ovanessian
email: benoit.terovanessian@ensiacet.fr

Julien Deleume
email: bjulien.deleume@areva.com

Jean-Marc Cloué
email: cjean-marc.cloue@areva.com

Eric Andrieu
email: deric.andrieu@ensiacet.fr

Influence of interstitials content on the sensitivity of alloy 718 to oxidation assisted intergranular fracture

Keywords: Nickel alloys, Dynamic Strain Ageing (DSA), Environmental induced embrittlement

Alloy 718 is known to be sensitive to oxidation assisted intergranular cracking. It is also demonstrated that the occurrence of jerky flow (also called Portevin-Le Châtelier effect) stops the intergranular damaging mechanism. As dynamic strain ageing is known to be linked with the alloy content of interstitial species, the aim of the present work is to study the effect of carbon, nitrogen and oxygen concentrations on the mechanical behaviour of thin tensile specimens tested under oxidation conditions close to those encountered industrially for turbo machine disks. Thanks to heat treatments performed under reducing atmosphere, the content of interstitial species in tested alloy 718 samples is gradually curbed. Tensile specimens were then tested between 550 and 700°C for the strain rate range [10 -5 , 10 -1 ] s -1 . The key point of this work is that, for a given testing temperature, the tensile tests clearly demonstrated that the transition from an intergranular fragile fracture mode to a transgranular ductile one was always linked with the occurrence of Portevin-Le Châtelier phenomenon but for slower strain rates in comparison with what was observed on the as received aged material tested in the same conditions. This shift of the transition of fracture mode through the lower strain rates remained true until a threshold value of the heat treatment time under reducing atmosphere. Specimens heat treated over this value systematically exhibited a fully transgranular ductile fracture mode, whatever the plastic flow regime was. Implication of such a finding on the intergranular embrittlement of alloy 718 by high temperature oxidation is then discussed.

Introduction

Alloy 718 is well-known to be sensitive to intergranular stress corrosion crack growth at temperatures close to those encountered industrially for turbo machine disks (650°C -air). Recent works proposed for this domain of temperatures some mechanisms of oxidation assisted intergranular cracking on alloy 718, based on the effect of oxygen penetration in the material [1][2][3]. Exploring the detrimental effect of oxidation on the mechanical behaviour of alloy 718, Fournier et al. [4], noted that, during tensile tests under air at temperature range 400°C-600°C and at a strain rate of 5.10 -7 s -1 , the disappearance of the intergranular brittle area on the fracture surface corresponded systematically to the occurrence of Portevin-Le Châtelier (PLC) phenomenon. The same tests under inert atmosphere systematically exhibited a fully transgranular ductile fracture mode, whatever the plastic flow regime was. For Fournier et al. [4], this correlation is connected to the strong localization of the strain in the PLC bands which confers a ductile character to the fracture and stops the growth of cracks induced by oxidation. During tensile tests realized under air for temperatures higher than 400°C and in a larger strain rate range, Garat et al. [5] found the same results. Thanks to the establishment of experimental DSA-fracture mode-PLC map, they represented and completed the results previously obtained. Moreover, they suggested that the occurrence of stress instabilities during the plastic flow, which characterized the PLC phenomenon after a critical strain level has been reached, decreases the local stress in grain boundaries or in front of the defect, so preventing the development of a fragile intergranular crack.

The effects of plastic instabilities, also called jerky flow or Portevin-Le Châtelier phenomenon [6][7][8][9][10][11][START_REF] Weaver | 706 and various derivatives[END_REF][13][14], are known in nickel based alloys, more particularly for dilute metallic alloys [6][7][8][9][10][11]. The principal actors of this phenomenon are the dislocations and the interstitial species. As PLC phenomenon is connected to interstitial species and as PLC occurrence has an influence on the rupture mode, the objective of the present work was to investigate the effect of carbon, nitrogen and oxygen concentrations on the mechanical behaviour of thin tensile specimens tested under oxidation conditions.

Material and experimental procedures

The material used in this study was obtained through a double melting process: vacuum induction melting plus vacuum arc remelting. The nominal composition of the alloy is given in Table 1. The cast ingot was hot and cold rolled down to the thickness of 4 -5 mm, followed by a solution annealing heat treatment at 1000°C for one hour ended by air quenching. 1 mm thick tensile specimens were machined by milling from the plate and could then be thinned to the thickness of 0.3 mm along the gage length. Tensile specimens (dimension are given in Fig. 1) were first heat treated under hydrogenated argon at 980°C for 0h (HT 1), 15h (HT 2), 30h (HT 3) and then heat treated under argon atmosphere following the conventional aeronautical route: hold 720°C-8h, cooling 50°C/h down to 620°C, hold 620°C-8h and final air cooling to room temperature. The heat treatment under reducing atmosphere aims at gradually curbs the content of interstitial species. Chemical analyses by glow discharge mass spectrometry (GDMS) for each heat treatment were realized. Finally, sample were mechanically polished using SiC paper and diamond paste to the grade 1 µm in order to remove the heat affected zone and/or the oxide scale formed during the treatments.

Fig. 1. Geometry of tensile thin specimens (thickness = 0.27mm). Specimen dimensions are given in mm.

Mechanical tests were performed in air with a hard electro-mechanical tensile machine with controlled displacement rate in the temperature range [550°C-700°C]. Different imposed strain rates were tested in the range [10 -5 s -1 , 10 -1 s -1 ]. A laser extensometer was used to measure the deformation of the specimen and the heating was ensured by a radiation furnace. The critical strain rate triggering flow instabilities was collected after each test.

After mechanical testing, the fracture surfaces of the samples were examined in a LEO 435VP scanning electron microscope.

Results

Characterisation of PLC types. In the light of recent modelling of PLC mechanism, Weaver et al. on conventional alloy 718 [START_REF] Weaver | 706 and various derivatives[END_REF] as well as on alloy 718SPF [13]. For the conventional alloy 718, they studied the occurrence of PLC on three different metallurgical states: just solutionised state, underaged state and overaged state. They noticed that for the underaged material, the alloy had normal / inverse strain rate sensitivity as a function of the testing temperature. They also observed that, for low temperatures, the PLC effect gave rise to load drops above the general level of the stress-strain curve (oscillations of type A or B) and, for high temperatures, to load drops below that level (oscillations of type C), according to Rodriguez's definitions of PLC types [9]. This transition of regimes seems to correspond to the transition from a normal to an inverse mechanical behaviour. For the overaged material, in the investigated experimental conditions, the behaviour is always inverse and the oscillations are always of type C. Finally, for the material just solutionised, there are no oscillations in the field of temperature and strain rate studied. As an example, Fig. 2 shows the type of serrations on the stress-strain curve for a tensile test performed at 650°C under laboratory air with a strain rate of 5.10 -3 s -1 . The facts that serrations produce load drops below the general level of the stress-strain curve and their amplitude is rather regular correspond to type C PLC. This type is associated with an audible emission and with the random nucleation of deformation bands all along the specimen. Evolution of the critical strain triggering flow instabilities. In the temperature range of this study, the critical strain for the onset of PLC instabilities slightly increases when temperature increases (or strain rate decreases). This critical plastic strain ranges from 2.4% to 3.1%, which is in fair agreement with the results of former studies on the same kind of materials [5]. For the HT 1 and HT 2 conditions, a fully transgranular ductile mode of rupture is observed when the plastic flow shows PLC instabilities, whereas in the other case, the fracture surface presented intergranular brittle areas. So a double frontier can be systematically drawn which separates on the strain rate-temperature diagram, both nature of the plastic flow and mode of rupture (Fig. 3 and Fig. 4). The main difference between HT 1 and HT 2 is the shift of the borderline DSA-fracture mode-PLC. Compared to HT 1, the frontier of HT 2 moves for almost a decade on lower strain rates (or higher temperatures). Samples treated following the HT 3 conditions systematically exhibit a fully transgranular ductile fracture mode, whatever the plastic flow regime was (Fig. 5). Only a single DSA-PLC frontier can be drawn. Compared to HT 2, this frontier moves also on lower strain rates.

Fig. 5. Rupture modes and plastic flow modes map for the HT 3 heat treating conditions.

Discussion

The phenomenon of dynamic strain ageing, of which the PLC instabilities are a particular demonstration, is strictly connected and controlled by the concentration of interstitial content of alloys such as the carbon, the nitrogen or the oxygen [6][7][8][9][10][11][START_REF] Weaver | 706 and various derivatives[END_REF][13]. The Table 2 sums up the concentration of interstitial species in each heat treating conditions. Excluding the concentration of sulphur, it seems that the contents in carbon, nitrogen and oxygen are significantly reduced between HT 1, HT 2 and HT 3. The contents of carbon and nitrogen for HT 1 are more than two times that of the HT 3 and the content of oxygen more than three times. Influence of the concentrations of interstitial species on PLC. All of the HTs 1, 2 and 3, present PLC plastic instabilities in the range of temperatures and macroscopic strain rates investigated, even if the frontier of the occurrence of PLC change for each HT. The shift of this borderline to lower strain rates (or higher temperatures) is concomitant with the reduction of the concentration of interstitial species. Moreover, the amplitude of the PLC oscillation is also affected. Indeed, the are 75 MPa for HT 1, 52 MPa for HT 2 and 31 MPa for HT 3.

Studying the circumventing of obstacles during the PLC phenomenon on the alloy 718 in various microstructural states, Chen et al. [14] propose, according to the size of precipitates, two mechanisms of PLC and validate them by the correspondence between these mechanisms and the normal / inverse behaviour of the alloy. The PLC mechanism, connected with the precipitates and the interstitials content, is complex.

The results of the present work show that the interstitial content has two effects on the PLC mechanism in alloy 718. Firstly, lower the concentrations of interstitials species are, lower the amplitudes of plastic instabilities are. In fact, the pined dislocations need less strain to liberate them from there atmosphere. Secondly, the frontier of the occurrence of PLC is more shifted with lower concentrations of interstitials species. This fact may be explained thank to McCormick works [15][16]. In one of his numerical model, McCormick expresses the solute concentration at arrested mobile dislocations C s as:

)) ) ( exp( 1 ( 0 m n a m s C KDt C C C - - = . ( 1
)
where C m is the saturation value of C s , C 0 is the solute composition of the alloy, D is the solute diffusion coefficient, t a the effective ageing time, and K and n are two constants. If steady state conditions are considered, t are supposed to be equal to the waiting time of dislocations, as given by the Orowan equation:

ε ρ & Lb t a = . ( 2
)
Where ρ is the mobile dislocation density, L is the effective obstacle spacing and b is the Burgers vector. For each heat treated material some parameters of the equations Eq. 1 and Eq. 2 are the same, like C m , D, ρ, L, b. Moreover a threshold value of the solute concentration at arrested mobile dislocations C sc , when the critical strain rate triggering flow instabilities c ε& is reached, is considered constant for a cast. It may be expressed as:

))

) ( exp( 1 ( 0 m n c m sc C Lb KD C C C ε ρ & - - = . (3)
Therefore, if the concentration of interstitial content of alloy decreases for each HT, it seems to be logical that the critical strain rate of the occurrence of PLC decreases in order to get constant the critical solute concentration at arrested mobile dislocation.

Influence of the concentrations of interstitial species on rupture mode. For having a, it is necessary that firstly the level of strain in front of the defect is constant or positive and that secondly the local strain rate is slower than the kinetics of damage linked to the environment. As content acts on PLC mechanism and PLC bands, by decreasing the local load, act on the rupture mode [4,5], it logically plays a role on the rupture mode. Effectively, for lower concentrations of interstitials species the transition from an intergranular fragile fracture mode to a transgranular ductile one, shifts to lower strain rates, as the frontier of the occurrence of PLC shifts. Meanwhile, this shift of the transition of fracture mode through the lower strain rates remained true until a threshold concentration of interstitials species. Indeed, specimens of HT 3 systematically exhibit a fully transgranular ductile fracture mode, whatever the plastic flow regime was.

Bricknell and Woodford [17][18][START_REF] Woodford | Interstitials Content on the Sensitivity of Alloy 718 to Oxidation Assisted Intergranular Fracture[END_REF] listed the different mechanisms of high temperature oxidation for nickel and nickel base alloys. The first one is the trapped of oxygen in grain boundary and other one is the internal oxidation assisted by the formation of gases bubbles (CO-CO 2 ) close to carbides. The fact that direct strain ageing drains interstitial carbons through grains boundaries while PLC let them where they pin dislocations is well-known. So when DSA occurs, oxygen may react with interstitial carbons bringing by dislocations on grains boundaries in order to form the weakening gases bubbles while the occurrence of PLC not allows this kind of oxidation mechanism. Thus, for HTs 1 and 2, this explanation well-expresses the perfect concomitance between rupture mode and PLC phenomenon. For HT 3 the low concentration of interstitials species may be insufficient for activate the oxidation assisted by gases bubbles mechanism even if DSA occurs. So whatever the plastic flow regime was, the rupture mode of HT 3 is systematically transgranular ductile.

Conclusions

The effect of carbon, oxygen and nitrogen concentrations on the sensitivity of alloy 718 to oxidation assisted intergranular fracture are clearly shown. For HTs 1 and 2, the influence of interstitials content on rupture mode is perfectly connected to the influence of interstitials content on PLC mechanism and for HT 3 another role is proposed. As a result, this study proves the three different roles played by the interstitials content in such alloy: on the occurrence of PLC phenomenon, on the amplitude of the stress oscillations, on the resistance to oxidation assisted intergranular cracking.

Fig. 2 .

 2 Fig. 2. Stress-strain curve at 650 °C under laboratory air with an imposed strain rate dε/dt equal to 5.10 -3 s -1 .

Fig. 3 .Fig. 4 .

 34 Fig. 3. Rupture and plastic flow modes map for HT 1 heat treating conditions.

Table . 1

 . Chemical composition of as-received alloy 718 [weight %]

	Al	C	Co	Cr Cu Mn Mo	Ni	Nb+Ta Si	Ti
	0.54 0.056 0.040 18.1 0.03 0.11 2.88 53.71	5.15	0.12 1.04

Table . 2

 . Carbon, nitrogen, oxygen and sulphur nominal content for the three tested heat treating conditions as determined by GDMS [weight ppm]

	Heat treatment conditions	Carbon Nitrogen Oxygen Sulfur
	HT 1	581	87	39	3.3
	HT 2	340	69	24	2.4
	HT 3	261	42	12	2.6


Benoît Ter-Ovanessian
email: benoit.terovanessian@ensiacet.fr

Julien Deleume
email: julien.deleume@areva.com

Jean-Marc Cloué
email: jean-marc.cloue@areva.com

Eric Andrieu
email: eric.andrieu@ensiacet.fr

Kinetic study of the low temperature internal oxidation of nickel based model alloys exposed to PWR primary water

Keywords: Corrosion, Nickel alloys, STEM, SIMS, Grain boundary embrittlement

Two Ni-Fe-Cr ternary alloys have been oxidized in simulated pressurized water reactor primary water at 360°C for 1000 h. The chemical composition of those alloys were chosen in order to be representative of the one of chromium depleted areas under the oxide scale of industrial alloys (e.g. alloy 600) exposed in the same conditions. The resulting oxidized structures (corrosion scale and underlying metal) were characterized using complementary analytical methods (FEG-SEM, TEM, SIMS, optical microscopy). On the one hand, the characterized external oxide layer is very close to the one observed on industrial nickel-base alloys, hence validating the use of such model alloys. On the other hand, both free oxygen and oxides have been detected at grain boundaries several micrometers under the metal/oxide interface. Implications of such a finding on the involved transport mechanisms for oxygen and the intergranular stress corrosion cracking resistance of nickel-base alloys are then discussed.

Introduction

Environmentally-induced intergranular stress corrosion cracking (IGSCC) is known to be a damaging mode in number of nickel-base alloys used in pressurized water reactors (PWR) of nuclear power plants [1][START_REF] Jones | Proceedings of the 1 st International Conference on Environment-Induced Cracking of Metals[END_REF][START_REF] Was | [END_REF][START_REF] Speidel | Proceedings of the 6 th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems -Water Reactors[END_REF][START_REF] Scott | [END_REF]. Alloy 600 has been studied intensively because of the widespread problems encountered with steam generators tubing and other components [START_REF] Jones | Proceedings of the 1 st International Conference on Environment-Induced Cracking of Metals[END_REF][START_REF] Was | [END_REF][START_REF] Scott | [END_REF]. In spite of numerous studies, the mechanism that controls IGSCC in nickel-base alloys is still controversial [START_REF] Magnin | Proceedings of the 9 th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems -Water Reactors[END_REF][START_REF] Scott | Proceedings of the 9 th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems -Water Reactors[END_REF][START_REF] Andrieu | Proceedings of the 2 nd International Conference on Corrosion-Deformation Interactions CDI'96[END_REF][START_REF] Was | Proceedings of the 2 nd International Conference on Corrosion-Deformation Interactions CDI'96[END_REF]. However, evidence for an internal and/or intergranular embrittlement of polycrystalline Nialloys by oxygen already exists [START_REF] Delabrouille | Proceedings of the 6 th International Conference on the Microscopy of oxidation[END_REF]. It has also been shown that alloys 600 and 690 both exhibit an inner chromium rich oxide layer (Cr rich spinel/Cr 2 O 3 ) and a chromium depleted underlying metal layer after exposure to PWR primary water [START_REF] Delabrouille | Proceedings of the 6 th International Conference on the Microscopy of oxidation[END_REF][START_REF] Panter | [END_REF].

The continuous character of that inner chromium rich oxide scale is also known to depend directly upon the experimental parameters, such as surface preparation, temperature, pressure and chemical composition of the aqueous solution, as well as the chemical composition of the alloy. Indeed, as oxidation/dissolution phenomena occur during the growth of oxide scales, all under-layers (e.g. chromium depleted area, base metal) could then be exposed to a corrosive medium if the chromium rich oxide layer is discontinuous. It would be then relevant to study the behavior of such layers exposed to PWR primary water at 360°C. In addition, in order to ensure the development of a continuous protective Cr rich spinel/Cr 2 O 3 oxide scale, hence lowering IGSCC sensitivity, the chromium content of nickel-base alloys has been increased; this has led to the industrial replacement of alloy 600 (which contains ~15 wt% Cr) by the alloy 690 (~30 wt% Cr).

In addition, it is worthy to notice that the chromium gradient induced by oxidation has also a mechanical impact on the alloy grains. Indeed, the migration of chromium atoms towards the surface throughout the lattice generates a contraction of alloy grains, hence stressed grain boundaries. As the characterizations are made at room temperature after exposure to primary media, one should also take into account the difference of thermal expansion coefficient between the oxide scale and the underneath layers. Those last points are not investigated in the present work.

To date, the origin of the positive effect of chromium content on IGSCC sensitivity is not very well understood. Thus, the aim of this study was to perform a fine characterization of the oxide scales (nature, protective aspect, brittleness …) developed in simulated primary water on Ni-Fe-Cr ternary alloys representative of the chemical composition of chromium depleted layers observed on industrial alloys. The objective was to experimentally validate internal and/or intergranular oxidation by using different characterization techniques, from optical and electron microscopy observations to secondary ion mass spectrometry (SIMS) and help to improve understanding of both embrittlement mechanisms and the positive chromium effect.

Materials and Experimental Procedures

Model Ni-Fe-Cr ternary alloys used in this study were prepared by the research centre of Imphy Alloys with a strictly controlled processing route. Two different alloys were obtained by vacuum induction melting. Their nominal composition is given in Table 1. In order to keep the compositions as close as possible to industrial alloys, the concentrations of alloying elements, such as Al, Cu, Mn or Ti for example, were maintained within the specifications of alloys 600 and 690. The cast ingot was hot rolled down to the thickness of 5 -6 mm. The microstructure of the model alloys was characterized by equiaxed small grains (ASTM grain size number = 8 -9) and very few carbides (Fig. 1). For each heat, coupons were machined from the plates by milling in the form of rectangular bars 30 mm long, 20 mm width and 5 mm thick. The standard surface preparation of coupons consisted of grinding their surface down to SiC paper grade 1200. During and after these preparation steps, the coupons were ultrasonically cleaned in acetone, ethanol and pure water.

Exposures of the alloys to simulated PWR primary water were carried out in a static autoclave at 360°C for 50h, 300h and 1000h. PWR primary water was simulated by deionized and deaerated water to which was added 1200 ppm of boric acid and 2 ppm of lithium hydroxide. The partial pressure of hydrogen was set to 0.3 bar using a Pd-Ag membrane.

The morphology and microstructure of the corrosion products were characterized using a field emission gun scanning electron microscope (FEG-SEM) LEO 1530 operating at voltages from 100V to 30kV. Chemical analyses were performed in the SEM with an energy dispersive X-ray spectroscopy (EDX) system (Oxford Inca Energy). Transmission electron microscope (TEM) characterization and EDX analyses were performed on cross-sections using the conventional preparation method (sandwich slices, dimpler, ion milling). A JEOL JEM 2010 microscope operating at 200 kV from the TEMSCAN service of the Paul Sabatier University, Toulouse was used. Note that, due to the difficulties in quantifying oxygen using EDX methods, the oxygen signal was not used for determining the composition of oxides (the percentages given in oxides correspond to the ratio of metallic cations). Local determinations of chemical composition by SIMS were performed using a CAMECA IMS 4F/6F instrument. Resistive Anode Encoder (RAE) mode was selected on the SIMS with an analyzed zone diameter of 30 µm. However, the total area of the abrasion zone was 150 x 150 µm².

The RAE mode enables 2D-basic maps of oxygen and the main constitutive metallic elements of the alloy (Ni, Fe, Cr …) to be collected throughout the abrasion of the specimen. Cs + ions were used in order to reduce the "matrix effect". If M is the considered metallic element, the intensity of the collected M + secondary ions signal is strongly influenced by all other metallic cations with frequent aberration phenomena. It is no longer a problem if CsM+ metallic cation are collected; hence the use of the Cs+ ions source. The calibration of the abrasion rate for the specific material and operating conditions has been previously performed [START_REF] Delabrouille | Proceedings of the 6 th International Conference on the Microscopy of oxidation[END_REF] by measuring the depth of different cavities using optical interferometry. Consequently, the collected data for the basic elemental maps can be both plotted versus time and/or depth.

In order to avoid roughness of the oxide scale influencing the definition of the location of the metal/oxide interface and to ensure highest sensitivity for crucial elements, particularly oxygen, SIMS analyses were also performed by abrading the metal from the underside of the oxide scale (so-called "Reverse mode"). For this purpose, specific specimens were prepared by mechanical polishing according to a procedure published previously [START_REF] Delabrouille | Proceedings of the 6 th International Conference on the Microscopy of oxidation[END_REF].

In order to assess the accuracy of such a SIMS specimen preparation for both preventing roughness effects from affecting the SIMS analyses and determining precisely the thickness of the different layers and/or the length of intergranular oxide penetrations, complementary optical microscope characterizations were made as shown in Fig. 2.

A coupon of each model Ni-Fe-Cr alloy was cut into two parts after exposure to simulated primary water. One of them was analyzed by SIMS using the "Direct mode" (e.g. the abrasion of the specimen started from the outer surface of the oxide layer) whereas the second one was observed by optical microscopy (OM) after several polishing steps using a colloidal silica suspension (OP-S Suspension TM Struers). The polishing depth of each step was determined by the reduction of the diagonal length of four HV 1000/15s hardness indentations arranged in a square of 1cm width. The comparison of depths given by the two methods shows conclusively that the SIMS data is reliable and has good accuracy for determining the depth of oxidation affected scale (e.g. external oxide layers, underlying scale and base metal affected by intergranular oxide penetrations).

Fig. 2. Comparison between SIMS data and OM micrographs to compare and validate the calibration of ionic abrasion depth (SIMS) by a mechanical polishing depth (oxide penetration depth given by Vickers hardness indentation as shown above).

Results

Ten coupons of each model ternary alloy were characterized by STEM and SIMS after exposure to PWR primary medium at 360°C for 50h, 300h and 1000h. Two extra coupons of both the asreceived heats were analyzed by SIMS in order to determine the average response of the technique for each element in the studied materials before the corrosion tests. This percentage corresponds to the fraction of chromium among all the metallic cations excluding oxygen which was not quantified.

Structure of the oxide layer. The microstructure of the external oxide scale developed in simulated primary water on coupons was first examined by SEM. Both Ni-Fe-Cr ternary alloys exhibited a distribution of small crystallites as illustrated in Fig. 3. The size of these small crystallites was very similar for the two synthetic alloys of about 1 µm. EDX analyses showed two types of crystallites (Table 2), some nickel rich and also probably NiFe 2 O 4 spinels (indicated by white arrows in Fig. 3). The oxide scales were observed in cross-section by TEM in order to examine the different layers that composed the scale and also to analyze the composition of those layers more accurately than in the SEM. Fig. 4 shows an example of the whole structure of the oxide on the two studied alloys. The two kinds of crystallites observed by SEM were seen at the outer surface. The average thickness was about 100 nm. The layer appears not to have been a compact continuous one but instead was formed of discrete separated grains. Crystallite size was about 50 nm for the smallest ones whereas it ranged from 300 to 700 nm for the biggest ones, which corroborates the SEM observations. Another layer of very small oxide grains can also be distinguished underneath the crystallites. The thickness of this layer was around 10 nm and seemed to be quite constant. The layer appeared to be compact and continuous. The external oxide crystallites seemed to be embedded in this layer. EDX analyses showed that this inner oxide was chromium rich whereas the zone under the metal/oxide interface was chromium depleted over a distance of a few tens of nanometers (Fig. 5). Note that the level reached by chromium in the inner layer differed with the chromium content of studied alloys: 24 wt% for the 5% chromium model alloy and 70 wt% for the 10% chromium alloy. Furthermore, the tested times of exposure to simulated PWR primary medium led to the same oxide layers with no noticeable difference in terms of dimensions and/or chemical composition. However, although the SEM and TEM data were in very good agreement, there was no evidence of intergranular oxidation and/or oxygen penetration in the underlying metal.

SIMS characterization of the metal/oxide interface and the underlying metal. In order to investigate if oxidation was present deeper inside the alloys than revealed by optical and electron microscopy, chemical analyses of the coupons were performed by SIMS both in the "Direct mode" and the "Reverse mode", as explained on Fig. 6. 2D-basic oxygen maps collected in both abrasion modes and clearly demonstrated that oxygen penetrated distances into the metal (~ 10 µm). It is also interesting to note that this penetration of oxygen was not uniform but localized at grain boundary triple lines. Furthermore, the exposure time slightly modified the affected depth (9 µm after 50h and 12 µm after 1000h).

Fig. 4. TEM cross-section of the oxide scale developed after exposure to simulated primary water 1000h at 360°C on the 5% chromium alloy and example of EDX analyses. A M16O curve (with M=52Cr or 56Fe) corresponds to the signal intensity evolution of the oxidized form of the considered M metallic cation plotted versus abrasion depth. Fig. 8. Evidence of oxygen penetration under the oxide scale for the 10% chromium model alloy after exposure to simulated primary water for 1000h at 360°C. SIMS chemical analyses were also made each ternary alloy before and after exposure to simulated primary water in the "Reverse mode" in order to measure more precisely oxygen and oxide distribution at the vicinity of the metal/oxide interface. The comparison of SIMS profiles in Fig. 7 conclusively demonstrates that the oxygen already detected on the 2D-basic maps presented in Fig. 6 was not linked to the preparation of the model ternary alloys but directly linked with the exposure of the coupons to simulated PWR primary water. The signal intensities of each element remained quite constant for the non exposed coupons. The carbon signal intensity is given in order to assess whether the detected increase of the oxygen signal intensity for the oxidized coupons (Fig. 7(b)) was due to the reaction of oxygen with carbides; no oxidation of carbides was highlighted. Profiles in Fig. 7(b) confirmed the thickness and the chemical composition of the oxidation affected layer, as determined by optical and electronic microscopy. The average thickness of the oxidation affected scale was about 10 µm. The outer oxide layer was made of mixed oxides (mainly Ni-rich oxides) whereas the inner layer was chromium rich oxide. However in the "Reverse" scans, the first ionic signal to increase was surprisingly identified as oxygen alone without any correlation with other elemental signals. The extent of this zone where oxygen penetrated beneath the oxide reached 200 nm. Small "islands" of oxygen were detected up to 12 µm below the metal/oxide interface with a width of less than a micrometer.

The SIMS data are summarized in Fig. 8(a) showing 3D reprocessed RAE maps to "rebuild" the analyzed volume of the coupon. Contrary to STEM observations which remain local and/or 2D representations of the polycrystal, SIMS analyses provide more volumetric data, with an average analyzed volume of about 30x30x10 µm 3 . In addition, it is possible to generate SIMS profiles corresponding to selected 2D areas of the 3D reconstruction illustrated in Fig. 8(b). The obtained results are consistent with those of Fig. 7. Profile N°1 clearly shows that the exposure to simulated primary water had no consequence for the average signal intensities of each matrix element. However, if a quite small area around an oxygen penetration along the grain boundaries/triple lines is considered, a second kind of small "island" of oxygen can be observed in the underlying metal. This oxygen is not "free" but associated with the metallic elements (Cr and Fe). Another kind of "island" could be observed: oxygen associated with silicon and magnesium.

Discussion

The structure of the oxide layer developed from the examination of the model ternary alloys after exposure to simulated primary water is summarized in the sketch of Fig. 9. The outer scale was composed of two families of oxide grains, one in the form of discrete large crystallites (NiFe 2 O 4 spinel oxides) and the other, which apparently covered the whole surface, made of smaller grains of a mixed oxide of nickel, chromium and iron of average thickness of 50 nm. The oxide scale was not compact and was judged to be non-protective. Such an observed oxide structure is in good agreement with previous studies [START_REF] Delabrouille | Proceedings of the 6 th International Conference on the Microscopy of oxidation[END_REF][START_REF] Panter | [END_REF][START_REF] Soustelle | Proceedings of the 9 th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems -Water Reactors[END_REF][START_REF] Machet | [END_REF].

The different models developed to describe the corrosion behavior of such alloys in pressurized pure water at high temperature can be considered in the light of these results. All of them are based on an original one proposed by Evans [14] for the corrosion of iron in caustic solution that assumes a duplex microstructure for the growing oxide scale. That duplex structure was observed in the present work. A mechanism of growth involving dissolution and precipitation can be supported to explain such an observed oxide structure [14,15]. In addition, another thin, compact and continuous inner layer made of Cr rich spinel/Cr 2 O 3 oxide was identified at the metal/oxide interface. This layer is assumed to be the first to be able to act as a barrier to further oxidation. This modifies the usual description of oxide scales. However, such a structure has already been observed on a similar alloy [16]. Furthermore, it should also be kept in mind that exposure to PWR primary water at 360°C affects the underlying metal; a chromium depleted layer is present over a few tens nanometers under the inner chromium rich oxide scale. This phenomenon could be linked with what is well known at higher temperatures (800°C -1200°C): nickel-chromium alloys exhibit sensitivity to intergranular and internal oxidation for chromium contents lower than 10% [17]. Moreover, the formation of the chromium depleted zone in the metal is related to that of the chromium rich inner oxide layer. As a gradient of chromium concentration is observed, it is commonly assumed that a chromium rich oxide layer is formed by the diffusion and selective oxidation of chromium atoms. Such a mechanism has been studied [15,18] and implies the injection of vacancies into the material beneath the oxide scale [18]. Up to now, the oxide layers grown on nickel-base alloys after exposure to PWR primary medium have been described as having a duplex structure formed by an Cr-rich layer and an outer layer consisting of two well-defined families of crystallites. A third area can be identified as a consequence of the corrosion phenomena, namely the chromium depleted layer beneath the oxide. On average, the overall thickness of the corrosion scales was about a micrometer. Fig. 9. Sketch summarizing the oxide film structure on model Ni-Fe-Cr ternary alloys and intergranular penetrations after exposure to simulated primary water for 1000h at 360°C. One of the striking results of the present work is the observation of the presence of oxygen in the alloys to several micrometers under the oxide layer. Preferential oxygen penetration along the grain boundaries/triple lines was observed, which is consistent with an intergranular/internal oxidation phenomenon. Indeed, two types of small "islands" of oxygen were detected on both ternary model alloys, independent of their chromium content is. In one case, the small "islands" were related to the formation of oxides of the metals/impurities present in the matrix (e.g. mainly chromium oxide or silicon/magnesium oxide). "Free" oxygen atoms dissolved in the metal matrix were also observed upstream to the intergranular oxide penetration along grain boundaries/triple lines. The affected depths reached more than 10 µm into the alloy suggesting an oxygen transport mechanism applying over large distances. An outstanding question remains as to whether oxygen penetrates along grain boundaries before or while the continuous protective rich spinel/Cr 2 O 3 oxide layer is forming. For the three tested times of exposure to PWR primary medium, the affected depth remains quite important and a kinetic study for shorter (< 50 has to be performed to collect data so as to describe precisely the very first steps of the corrosion phenomenon.

Intergranular oxide penetrations remain difficult to explain by diffusional mechanisms, even those already observed at higher temperatures [START_REF] Delabrouille | Proceedings of the 6 th International Conference on the Microscopy of oxidation[END_REF][START_REF] Panter | [END_REF][START_REF] Newman | Proceedings of the 9 th International Symposium on Environmental Degradation of Materials in Nuclear Power Systems -Water Reactors[END_REF]. For example, by extrapolating to 300°C the results of Bricknell and Woodford [START_REF] Bricknell | [END_REF] for high-temperature diffusion of oxygen in nickel, the required time for oxygen to penetrate as far as 10 nm is several years. However, intergranular embrittlement of grain boundaries by oxygen has been attributed to a possible accelerated "transport" of free oxygen as compared to the normal bulk diffusion coefficients [START_REF] Scott | Proceedings of the 2 nd Conference on Corrosion-Deformation Interactions CDI'96[END_REF][START_REF] Bricknell | [END_REF][23]. According to Scott [START_REF] Scott | Proceedings of the 2 nd Conference on Corrosion-Deformation Interactions CDI'96[END_REF], the applied mechanical loading and/or the porous structure of crack oxide can increase oxygen diffusion rates significantly at grain boundaries. This embrittlement can also be attributed to the accelerated transport of oxygen by vacancy injection at grain boundaries [23]. This phenomenon allows the formation of oxides in the grain boundaries and so contributes to their embrittlement. Such an assumption is in agreement with SIMS profiles presented in Fig. 8b. up, evidence of both intergranular and internal oxidation of synthetic ternary alloys has been observed, including the presence of small "islands" of oxides deep under the metal/oxide interface. As a continuous protective Cr rich spinel/Cr 2 O 3 oxide layer forms on both alloys, the "free" oxygen observed along grain boundaries/triple lines in the vicinity of IOP may result from a massive penetration of oxygen during the very first steps of oxidation (e.g. as long as the chromium rich layer is not continuous and thick enough). The detected small "islands" of chromium/iron and silicon/magnesium oxides may have been formed subsequently, so as to reduce the amount of free oxygen in the alloy to reach a pseudo-equilibrium state. Finally, whatever the involved mechanisms could be for the formation of small oxide "islands", they have to be considered as "damaging spots", in good agreement with what was already known in term of interface embrittlement mechanisms [START_REF] Carpenter | 706 and various derivatives[END_REF][25][26][27][28]. Consequently, it would be then better to consider an "oxidation affected layer" rather than the classical "oxide scale thickness" to evaluate the depth of alloy affected by the corrosion/oxidation processes. This is all the more true since it has been established that the metal/oxide scale can no longer be described as a planar interface parallel to the initial surface because both oxide and oxygen penetrations are deeper along grain boundaries/triple lines. Finally, the complete set of observations of the present study can be easily conciliated by considering transport phenomena based on bonding effects between vacancies and oxygen atoms [18]. Such a binding effect has been observed recently in a study of the high-temperature oxidation of pure nickel [23,29]. The selective oxidation of chromium produces vacancies close to the metal/oxide interface which are able to diffuse along grains boundaries toward the bulk material driven by the concentration gradient. This migration accelerates the diffusion of chromium in the opposite direction, hence accelerating chromium depletion. Transport of interstitial species, including oxygen, is expected due to a binding effect between atoms of small size and vacancies. Moreover, the vacancy concentration is gradually reduced as a compact and continuous Cr rich spinel/Cr 2 O 3 layer grows until it becomes zero. This mechanism is all the more probable as the oxidation took place at 360°C and the mobility of the couple vacancy-oxygen atom should be much higher than the one of oxygen alone and similar to the one of a vacancy alone [29,30]. Indeed, in the of a vacancy, the activation energy for oxygen diffusion is very small. As a consequence, all the results obtained in this study, after comparison with former proposed models, tend to plead for an oxidation mechanism based on internal and intergranular oxidation [START_REF] Scott | Proceedings of the 2 nd Conference on Corrosion-Deformation Interactions CDI'96[END_REF][START_REF] Gendron | Proceedings of the 3 rd International Steam Generator and Heat Exchanger Conference[END_REF], leading to an embrittlement of grain boundaries.

Conclusion

The corrosion on synthetic ternary Ni-Fe-Cr alloys were characterized by electron microscopy (SEM and TEM) and chemical analysis (EDX and SIMS) after exposure to simulated PWR primary water at 360°C 300h and 1000h. It was shown that the oxide scale is to be described as a triple layer and that only a thin chromium oxide layer is continuous and could be considered as a protective layer. Indeed, it was also shown that there exists a chromium depleted zone in the metal and that penetrations of oxygen under the oxide scale are evidenced by SIMS imaging. Oxygen was observed in solution and associated with chromium or silicon/magnesium along triple lines as far as 12 µm from the oxidized surface. All those facts are in good agreement with previously established experimental facts on industrial alloys, such as alloy 600 or alloy 690. As a consequence, using such coupled characterizations (e.g. STEM and SIMS) of model and/or industrial alloys after exposure to oxidizing environments seems to be of relevant interest to study the mechanisms involved in intergranular oxidation and oxygen enhanced crack growth.

Fig. 1 .

 1 Fig. 1. Microstructure observed by SEM of studied model Ni-Fe-Cr ternary alloys after etching: (a) the 5% and (b) the 10% chromium alloys.

Fig. 3 .

 3 Fig. 3. SEM observation of the oxide scale developed after exposure to simulated primary water after 1000h at 360°C on (a) the 5% and (b) the 10% chromium model alloys. White arrows indicate Ni/Fe spinels.

Fig. 5 .1Fig. 6 .

 56 Fig.5. TEM cross-section of the oxide scale developed after exposure to simulated primary water for 1000h at 360°C on the 10% chromium alloy and characterization of the chromium gradient by EDX analyses.

Table . 1

 . Chemical composition of Ni-Fe-Cr ternary alloys [weight %]

	Heat	C	Cr	Fe	Ni
	NiFe15Cr5 0.025 5.15 15.13 Bal.
	NiFe10Cr10 0.027 10.2 10.39 Bal.

Table . 2

 . Characteristics of the oxide layers appearing on Ni-Fe-Cr ternary alloys.

	Heat	Maximum size of big crystallites	Composition of big crystallites	Maximum % of chromium in the inner layer 1
			2 types:
	NiFe15Cr5	Less than a µm	NiFe 2 O 4 and Ni rich	24
			(78% Ni, 16% Fe, 6%Cr)
	NiFe10Cr10	Less than a µm	35% Ni, 25% Fe, 40% Cr	70
	1