M Degeiter

M Perrut

B Appolaire

Y Le Bouar

A Finel

A NEW ANALYSIS OF THE MICROSTRUCTURE OF NI-BASED SINGLE-CRYSTAL SUPERALLOYS : RELEVANT TOPOLOGICAL PARAMETERS FOR EFFICIENT MICROSTRUCTURAL MODELING

Keywords: blade superalloy, γ 1 precipitation, elasticity, modeling, pattern formation, phase diffusion

Two topological parameters derived from pattern formation theory are introduced, and their potential to accurately describe the elasticity-induced coarsening in the microstructure modeling of Ni-based singlecrystal superalloys at macroscale in 2D is investigated. For that purpose, and given the primordial role of the spatial arrangement of the precipitates on microstructure evolution, two-dimensional phasefield calculations of ideal microstructures undergoing slight topological defects have been carried out. The unstable and stable responses of the system respectively against Eckhaus and zigzag instabilites is discussed and quantitatively described by means of the developed topological parameters ψ x and ψ y .

Introduction

High pressure turbine (HPT) blades possess outstanding mechanical properties at high temperature, which stem from the microstructure of the singlecrystal nickel-base superalloy in which they are designed. This two-phase microstructure consists of cuboidal precipitates of the L1 2 -ordered phase γ 1 , coherently embedded in the disordered matrix phase γ, and globally aligned along its cubic directions. Considering the high volume fraction of γ 1 -phase in these alloys (68% at room temperature for AM1), the microstructure evolves into a cubic pattern of cuboidal precipitates, only separated by narrow channels of matrix phase.

During gas turbine operation, the size, morphology and spatial arrangement of γ 1 -precipitates continuously evolve due to the thermomechanical loading seen by the blade, which impacts its mechanical properties in return. In order to improve the service life of HPT blades, and thus enhance the stability of the microstructure, there is still a need for efficient microstructural modeling at the scale of the blade.

Single-crystal superalloys are prone to complex microstructure evolution, due to the effects of elasticity on precipitation kinetics. Without external loading, elasticity arises from the γ/γ 1 misfit, inducing coherency strains at the precipitate-matrix interfaces, and thus long-range interacting elastic fields in the alloy [START_REF] Larché | A linear theory of thermochemical equilibrium of solids under stress[END_REF][START_REF] Larché | A nonlinear theory of thermochemical equilibrium of solids under stress[END_REF][START_REF] Larché | Thermochemical equilibrium of multiphase solids under stress[END_REF][START_REF] Johnson | Interfacial conditions for thermomechanical equilibrium in two-phase crystals[END_REF][START_REF] Johnson | Phase equilibrium in two-phase coherent solids[END_REF]. During coarsening, diffusion of the alloying elements is strongly influenced by elasticity, leading to complex evolutions such as morphological changes [START_REF] Caron | High γ' solvus new generation nickelbased superalloys for single crystal turbine blade applications[END_REF][START_REF] Johnson | Precipitate shape evolution under applied stress -Thermodynamics and kinetics[END_REF][START_REF] Lund | A quantitative assessment of the three-dimensional microstructure of a γ-γ' alloy[END_REF][START_REF] Thompson | The equilibrium shape of a misfitting precipitate[END_REF][START_REF] Su | The dynamics of precipitate evolution in elastically stressed solids -I. Inverse coarsening[END_REF] and precipitate alignment [START_REF] Su | The dynamics of precipitate evolution in elastically stressed solids -II. Particle alignment[END_REF][START_REF] Yamauchi | Elastic interaction of defect clusters with arbitrary strain fields in an anisotropic continuum[END_REF][START_REF] Johnson | The coarsening kinetics of two misfitting particles in an anisotropic crystal[END_REF][START_REF] Abinandanan | Coarsening of elastically interacting coherent particles -II. Simulations of preferential coarsening and particle migrations[END_REF]. Though the involved mechanisms are well-known, the main difficulty lies in their coupling. The latter renders the understanding and modeling of this microstructure a difficult task, especially when designing at macroscale, at which precipitation is usually modeled without elastic effects [START_REF] Baldan | Review -Progress in Ostwald ripening theories and their applications to nickel-base superalloys. Part I : Ostwald ripening theories[END_REF].

The coarsening kinetics in two phase solids with elastic effects has successfully been modeled at mesoscale through sharp [START_REF] Jou | Microstructural evolution in inhomogeneous elastic media[END_REF][START_REF] Thornton | Largescale simulations of Ostwald ripening in elastically stressed solids : I. Development of microstructure[END_REF][START_REF] Thornton | Largescale simulations of Ostwald ripening in elastically stressed solids : II. Coarsening kinetics and particle size distribution[END_REF] and diffuse [START_REF] Hu | A phase-field model for evolving microstructures with strong elastic inhomogeneity[END_REF][START_REF] Cottura | Role of elastic inhomogeneity in the development of cuboidal microstructures in Ni-based superalloys[END_REF] interface approaches. The sharp interface approach is very efficient at modeling coarsening with large numbers of precipitates, and provides an exact description of the interface motion. However, it is not suitable for the modeling of high volume fraction alloys, since it does not allow for topological singularities such as precipitates merging.

The phase field, or diffuse interface approach, describes interfaces as steep variations of a continuous field. This theory allows one to catch complex topological evolution during coarsening, even at high volume fractions, though the requirement of a very fine mesh prevents the modeling of large numbers of precipitates.

Given the prominence of the spatial arrangement of precipitates on microstructure evolution in these alloys, our aim is to develop a simplified phenomenological model, based on a relevant topological parameter, to account for the influence of elasticity on coarsening at macroscale. Previous studies have been carried out so as to quantitatively describe both morphological and topological changes during microstructure evolution. A number of shape factors has been developed in the literature, among which the a R 2 coefficient has been used to obtain the bifurcation diagram of an isolated precipitate with a dilatational misfit in 2D [START_REF] Thompson | The equilibrium shape of a misfitting precipitate[END_REF]. The energy-minimizing shape has been shown to evolve from four-fold to two-fold symmetry for a specific value of the elastic-to-interfacial energy ratio. It was later used to assess the influence of elastic interactions on precipitate morphology by comparing the dispersion of its value with respect to that of the isolated particle [START_REF] Thornton | Largescale simulations of Ostwald ripening in elastically stressed solids : I. Development of microstructure[END_REF]. 2D and 3D moment invariants have also been used as a means to follow the morphological transition which the precipitates undergo during rafting [START_REF] Nguyen | Quantification of rafting of γ' precipitates in Ni-based superalloys[END_REF]. The authors were able to define the onset of rafting in microstructures with both negative and positive lattice misfits. Regarding the description of spatial arrangements, power spectra have mostly been used to qualitatively describe the development of spatial correlations, and were obtained by the Fourier transformation of the microstructure itself [START_REF] Thornton | Largescale simulations of Ostwald ripening in elastically stressed solids : I. Development of microstructure[END_REF][START_REF] Doi | Effect of elastic interaction energy on the distribution of coherent precipitate particles in nickel-base alloys[END_REF]. Radial distribution and pair correlation functions were able to provide a more quantitative description of precipitate alignment [START_REF] Thornton | Largescale simulations of Ostwald ripening in elastically stressed solids : I. Development of microstructure[END_REF]. The authors showed that the microstructure tends to evolve towards a unique configuration, regardless of the initial arrangement of precipitates, the only governing factor being the elastic-to-interfacial energy ratio.

To our knowledge, none of these topological parameters has ever been used to predict microstructural evolution. Their use has been restricted to the description of spatial correlations, since they do not seem relevant to the building of evolution laws.

The purpose of the present work is to introduce new topological parameters, derived from pattern formation theory, and evaluate their potential to account for elastic effects in the modeling of microstructure evolution. We use phase field calculations as virtual experiments of microstructures undergoing an isothermal heat treatment in the absence of mechanical loading. The initial conditions are set in simple topological situations which are then easier to analyze.

Topological parameters

Pattern formation theory focuses on systems which evolve from spatially uniform to patterned structures when driven away from equilibrium [START_REF] Cross | Pattern formation outside of equilibrium[END_REF]. Geometrical patterns emerge as a result of complex nonlinear evolution, and may be analyzed regardless of the phenomenons or of the nature of the system (e.g. Rayleigh-Bénard convection rolls [START_REF] Busse | Instabilities of convection rolls in a high Prandtl number fluid[END_REF], Faraday waves, solidification fronts, etc.).

The general idea behind pattern formation is to prescind from what the authors in [START_REF] Cross | Pattern formation outside of equilibrium[END_REF] call "microscopic" considerations (i.e. the elementary mechanisms involved) so as to investigate dynamical systems from a more general standpoint. Within this scope, this field provides theoretical tools for the phenomenological description of spatially modulated structures.

With the ambition to apply this framework to the study of microstructure evolution, we define a reference state for a 2D γ{γ' microstructure as a perfectly periodic square network of identical precipitates. We assume the following form for the Al concentration field :

c al " c 0 al `∆c 2
`cospkx `ψx q `cospky `ψy q " c 0 al `fx px, y, tq `fy px, y, tq

where k is a constant wave number, and λ " 2π{k is the wavelength of the modulated square structure (λ x " λ y " λ). ψ x and ψ y are phases, which respectively represent horizontal and vertical deviations from the reference positions in the square lattice, and are either of a topological or a morphological nature. ψ x and ψ y are the relevant parameters to be extracted, insofar as they provide valuable information on the spatial arrangement of precipitates.

We calculate ψ x and ψ y from the image of a microstructure obtained by M. Cottura et al. through phase field modeling [START_REF] Cottura | Role of elastic inhomogeneity in the development of cuboidal microstructures in Ni-based superalloys[END_REF], as shown in Figure 1.

Since phase values range from 0 to 2π (0 and 2π being the same phase value), ψ x and ψ y phase maps in Figure 1 are represented in periodic gray-scale for easier readability. ψ x (resp. ψ y ) is spatially uniform for horizontally (resp. vertically) regular patterns, and varies as the horizontal (resp. vertical) regularity is lost near topological defects. Thus, topological and morphological imperfections in the precipitate arrangement are highlighted by phase

ψ x Microstructure [20] ψ y f x f x `fy f y Figure 1:
Phase-based approach of microstructural analysis : example of calculated phases and associated 1D-periodic functions of a microstructure.

variations.

With the knowledge of k, ψ x and ψ y , the concentration field can be decomposed into two contributions f x and f y , which physically correspond to its horizontal and vertical modulations. These 1D-periodic functions make the quantitative analysis of period modulations, channel branches or terminations an easier task. Since most of the topological defects are "forks" or "dislocations" in the pattern (as clearly visible on f x and f y ), the question as to why they are present in the microstructure will be discussed in the following sections. Eventually, the microstructure can be reconstructed simply by adding f x and f y .

Even if ψ x and ψ y have been shown to hold great potential with regards to the topological description of 2D microstructures, the question of their evolution through time still needs to be addressed in order to build a phase-based model for microstructure evolution. In pattern formation, phase evolution is commonly described by a diffusion equation [START_REF] Cross | Pattern formation outside of equilibrium[END_REF]. The phase equation, or phase diffusion equation, was first introduced by Pomeau and Manneville to phenomenologically investigate the consequences of long-wavelength distortions on a spatially periodic convective flow [START_REF] Pomeau | Stability and fluctuations of a spatially periodic convective flow[END_REF]. By analogy, we postulate the following low-order diffusion equations for ψ x and ψ y :

Bψ x Bt " D xx B 2 ψ x Bx 2 `Dxy B 2 ψ x By 2 Bψ y Bt " D yx B 2 ψ y Bx 2 `Dyy B 2 ψ y By 2 (2)
where D xx and D xy (resp. D yx and D yy ) are the phase diffusion coefficents associated to ψ x (resp. ψ y ), and depend on the physical parameters of the system. Their signs govern the stability of the pattern respectively against horizontal and vertical perturbations of ψ x and ψ y . If the system is unstable (i.e. negative phase diffusion coefficient) against a specific phase perturbation, higher-order terms must be added in the phase equations to properly control the system evolution [START_REF] Cross | Pattern formation outside of equilibrium[END_REF].

This formalism has recently been used in the case of 1D-periodic patterns, to investigate the stability of lamellar eutectic growth [START_REF] Akamatsu | Overstability of Lamellar Eutectic Growth below the Minimum-Undercooling Spacing[END_REF].

The variations of ψ x and ψ y are slow in space and time, as compared to that of the concentration field. Therefore, a phase-based calculation would require a smaller number of meshing points, possibly allowing the transition of microstructural modeling to macroscale. Investigating the relevance of the phase equations (2) to the modeling of microstructure evolution in Ni-based single-crystal superalloys is a work still in progress.

Phase field model

To better understand how elasticity affects coarsening kinetics through the spatial arrangement of precipitates, we conduct a perturbative analysis on the 2D reference state defined above, by using phase field calculations as virtual experiments.

The superalloy is modeled as an effective binary alloy, and the local concentration field cpr, tq ensures the description of the microstructure. The four translational variants of the γ' phase, usually described by three non-conservative structural fields, have not been implemented. Consequently, the ordered crystal structure of the precipitates is not taken into account in our calculations, restricting their relevance to the instant preceding coalescence.

The mesoscopic free energy functional F is decomposed into a chemical F ch and an elastic F el contribution :

F " F ch pcq `Fel pc, ε ε ε el q (3)
where ε ε ε el is the elastic strain tensor. The evolution of the conserved concentration field with time is governed by the Cahn-Hilliard equation which, assuming a linear constitutive relationship, is written :

Bc Bt pr, tq " M ∇ 2 δF δcpr, tq (4)
where the kinetic coefficient M is such as to recover the interdiffusion coefficent D Al{N i in γ, and assumed constant. The chemical free energy of the system is written as :

F ch pcq " ż V ´fhom pcq `α 2 |∇c| 2 ¯dV ( 5
)
where V is the volume, f hom is the homogeneous free energy density and the gradient term accounts for the energy cost of the interfaces. α is the gradient energy coefficient related to the value of the interface energy, which was chosen isotropic. Since the value of the non-dimensional gradient energy coefficient α governs the discretization of the diffuse interfaces, α was chosen to ascertain their sufficient width.

The homogeneous free energy density f hom is taken as a conventional double-well function of the following form :

f hom pcq " 4 « ´1 2 pc ´cm q 2 `pc ´cm q 4 pc 0 γ 1 ´c0 γ q 2 ff ( 6
)
where c is the concentration field, c 0 γ " 0.15 and c 0 γ 1 " 0.231 are the equilibrium concentrations identified on the Ni-Al phase diagram at 950 0 C, and c m " pc 0 γ 1 `c0 γ q{2.

In the framework of linear elasticity, and assuming small strains, the elastic energy is written :

F el pc, ε ε ε el q " 1 2 ż V C C Cpcq : ε ε ε el : ε ε ε el dV (7)
where C C C is the local elastic tensor, assumed to linearly depend on cprq. The local elastic strain ε ε ε el prq can be decomposed into :

ε ε ε el prq " ε ε εprq ´ε ε ε 0 prq (8)
where ε ε εprq is the total strain, and ε ε ε 0 prq is the eigenstrain which is related to the misfit δ " 2pa γ 1 ´aγ q{pa γ 1 `aγ q, and thus accounts for the lattice parameter change during the γ Ñ γ 1 transformation. Moreover, the elastic constants of γ' were chosen to provide a specific value of elastic inhomogeneity in the coherent mixture (∆C 1 " 50%) [START_REF] Cottura | Role of elastic inhomogeneity in the development of cuboidal microstructures in Ni-based superalloys[END_REF]. Further details on the computation of the mechanical equilibrium are available at [START_REF] Cottura | Role of elastic inhomogeneity in the development of cuboidal microstructures in Ni-based superalloys[END_REF][START_REF] Boussinot | Phase-field simulations with inhomogeneous elasticity: Comparison with an atomic-scale method and application to superalloys[END_REF].

With the aim of modeling an alloy close to AM1, we set the volume fraction of precipitates in our calculations at 70%. This choice compelled us to implement a very fine mesh so as to avoid spurious coalescence, which might have resulted from poorly descretized matrix channels with respect to interface width.

To conduct perturbative analysis on a microstructure during coarsening, we considered the reference state as the starting point of our calculations, thus ignoring the nucleation and growth stages. This was achieved by modeling perfectly periodic arrays of precipitates, whose shapes were set to be four-fold in order to approach their equilibrium morphology. This "relaxation" stage lasted until the energy levels in the system were stabilized, at which time these ideal microstructures had remained stable and perfectly regular.

We then proceeded to drive the system away from equilibrium by applying slight topological defects in the precipitate arrangements, and monitored the elasticity-driven evolution. We focused on two specific topological perturbations, namely the Eckhaus and zigzag instabilities.

By means of combined attractive and repulsive elastic interactions, we expected the simulated topological perturbations to relax over time, and the microstructure to stabilize itself in order to evolve back towards the reference arrangement.

Results and Discussions

In this section, the consequences of Eckhaus and zigzag instabilities on the stability of a micrsotructure during isothermal heat treatment at T " 950 0 C and without external loading are investigated. In view of our hypothesis, the evolution of the microstructure is followed until the instant preceding coalescence, and compared to the variation of ψ x and ψ y .

For both topological defects, the size of the simulations is 9.6 ˆ0.6 µm 2 , descretized with 2048 ˆ128 nodes (grid spacing d " 4.7 nm).

If the phase maps in Figure 1 are in periodic grayscale for clearer representation, the following phase maps are designed in regular gray-scale. Therefore, extreme phase values (0 and 2π for ψ i"x,y P r0 ; 2πs, ´π and π for ψ i"x,y P r´π ; πs) will respectively appear black and white, though representing the same phase value.

Eckhaus instability

An Eckhaus instability corresponds to a horizontal modulation of the precipitate positions by a sine, resulting in axial variations of the precipitate spacing λ x , and thus of the γ 1 volume fraction. The Eckhaus instability applied on the reference microstructure at the initial time is written as the following phase perturbation :

ψ x px, t " 0q " A E cos ´KE px ´x0 q ¯(9)
where the dimensionless amplitude A E " 0.47, and the wave number K E " 2π{Λ E was taken so that the wavelength Λ E " 9.6 µm. The Eckhaus amplitude A E was chosen with great care in order to avoid overlapping of the diffuse interfaces of neighboring precipitates, which could have led to spurious coalescence.

The resulting evolution of the reference microstructure is presented in Figure 2, and compared to that of ψ x and ψ y . At t " 0 h, the very slight variation in precipitate spacing λ x resulting from the Eckhaus instability is difficult to visualize on the microstructure alone, but it can be followed more easily as a modulation of ψ x of moderate amplitude along x axis. ψ y is uniform throughout space at this instant. The variations of λ x amplify with time, and the precipitates gather in groups of two and three. Simulatneously, additional fluctuations of ψ x gradually emerge along x axis, and ψ y remains steady during the simulation.

t " 0 h c al ψ x ψ y t " 1.6 h c al ψ x ψ y t " 3.2 h c al ψ x ψ y
As clearly visible in Figure 2, the microstructure is unstable against the Eckhaus instability. Contrary to what was initially expected, a horizontal modulation of precipitate positions does not relax over time. Rather, the Eckhaus instability amplifies, disturbing the regularity of the arrangement further until precipitates coalesce. This progressive loss of horizontal regularity of the pattern is traced by additional fluctuations of ψ x , locally arising along x axis. The vertical regularity of the arrangement is conserved during the simulation, and thus ψ y remains uniform in space through time.

t " 0 h c al ψ x t " 3.2 h c al ψ x ψ x
x pµmq The use of ψ x as a means to witness the amplification of the Eckhaus instability is completed by the study of its profile over time, as shown in Figure 3. The red curve corresponds to the initial profile of ψ x along x, while the blue curves are the same profile but taken at subsequent times.

The long wavelength modulation of ψ x along x is centered around the mean phase value, which corresponds to that of the undisturbed pattern. This moderate variation ranges over the entire simulated microstructure, and is consistent with the definition of the Eckhaus instability. The amplification of this instability is traced by additional modulations of ψ x , whose growth over the already disturbed topology accelerates with time.

The initial phase modulation owing to the Eckhaus instability is conserved until the last instant, and the developing fluctuations highlight the existence of pattern-destabilizing phase modes, which activate with time. In this situation, the following form for ψ x may be assumed :

ψ x px, tq " N ÿ i"1 A i pK i qe Ωit cos ´Ki px ´x0 i q ¯( 10
)
where A i , Ω i and K i are the amplitude, growth rate and wave number of the i th phase mode. The expression of ψ x in Eq. ( 10) unveils the involvement of various wavelengths in phase evolution and may allow for the definition of phase modes related to the coalescence of precipitates. The modes which are most threatening for the reference microstructure are expected to be those of lowest wavelength and highest growth rate, since they lead to local and fast fluctuations in the regularity of the pattern.

Eventually, the precipitates which had gathered coalesce, leaving the microstructure as an irregular structure of two-fold-shaped precipitates, and bringing forward the question of a potential stabilization of the pattern at a new λ 1 x ą λ x . Considering the postulated diffusion equation ( 2) for the temporal evolution of ψ x and ψ y , we may assert that D xx ă 0 (and by symmetry, D yy ă 0) since the system is unstable against Eckhaus-type distortions of its pattern, revealing the probable need for higher-order phase diffusion equations to appropriately describe phase evolution [START_REF] Cross | Pattern formation outside of equilibrium[END_REF].

Eckhaus instabilities have been reported to be responsible for the existence of topological defects in a number of modulated systems [START_REF] Cross | Pattern formation outside of equilibrium[END_REF][START_REF] Sakaguchi | Defect Creation by the Eckhaus Instability[END_REF][START_REF] Millán-Rodríguez | Defect Motion in Rotating Fluids[END_REF], be it for their creation, drift or annihilation. In convectionroll patterns, forks and dislocations in the structure are a direct result of Eckhaus instabilities, which brings forward the question of their involvement in the presence of those visible in f x and f y in Figure 1.

Zigzag instability

A zigzag instability consists in a transverse modulation of the precipitate positions by a sine, which leads to a wavy configuration of the microstructure. The zigzag instability initially applied to the reference state is written as the following phase perturbation :

ψ y px, t " 0q " A ZZ cos ´KZZ px ´x0 q ¯(11)
where the dimensionless amplitude A ZZ " 1.5, and the wave number K ZZ " 2π{Λ ZZ is such that the wavelength Λ ZZ " 9.6 µm in our simulations. The evolution of the microstructure subjected to this topological defect is presented in Figure 4, along with the corresponding phase maps.

At t " 0 h, the applied zigzag instability causes the vertical regularity of the microstructure to strongly vary along x axis. At subsequent time, the wavy configurations of precipitates has decreased in amplitude, and the zigzag is almost completely realigned, proving the perfect alignment of the precipitates to be an energetically-favorable configuration of the microstructure in the first instance. At the final instant, the relaxation of this instability is complete and the horizontal periodicity of the square structure has begun to fluctuate along x. Simultaneously, while initially modulated along x, ψ y is almost uniform in space at t " 3.8 h and horizontal variations in ψ x arise, though it was uniform at the early stages of the simulation.

The elasticity-driven realignment of the instability proves that the microstructure is stable against zigzag-type distortions of its regularity. Fluctuations in λ x appear once the vertical periodicity is found again, highlighting the development of an Eckhaus instability subsequent to the zigzag relaxation. The combined use of ψ x and ψ y allows for a precise tracking of the topological evolution of the microstructure undergoing this defect in the arrangement of its precipitates.

Since the precipitates alignment is traced by the temporal variations of ψ y along x, we study the evolution of its profile over time in Figure 5, prior to the development of the Eckhaus instability (which could also have been followed by analyzing ψ x along x). The red and blue curves respectively correspond to the initial profile of ψ y along x, and to the same profile at subsequent times. In Figure 5, the zigzag relaxation is traced by the decreasing amplitude of the phase modulation, whose decay decelerates over time. Contrary to what was observed for the Eckhaus instability, this result reveals the zigzag phase mode to be patternstabilizing, since its decay corresponds to the evolution of the wavy microstructure back towards the regular state. We write ψ y in the following form :

ψ y px, tq " A ZZ e Ω ZZ t cos ´KZZ px ´x0 q ¯(12)
where the amplitude A ZZ and wave number K ZZ are known, and Ω ZZ is the decay rate.

We show in Figure 6 the evolution of the zigzag amplitude A ZZ with time, and the fitted data to a decreasing exponential, from which we are able to extract the decay rate Ω ZZ " ´1{τ ZZ .

Substituting Eq. ( 12) in Eq. ( 2) for ψ y , we obtain the following dispersion relation in the case of the zigzag instability :

A ZZ t phq
Ω ZZ " ´Dyx K 2 ZZ ( 13
)
We have confirmed the quadratic dependence of Ω ZZ on K ZZ in ( 11) by means of additional simulations of zigzag instabilities of various wavelengths, thus supporting further the hypothesis of the diffusion equations ( 2) for the temporal evolution of ψ x and ψ y .

Eq. ( 11) allows for the phase diffusion coefficient D yx to be numerically evaluated in our calculations, and the values obtained for zigzag instabilities of various wavelengths are within the range of 150 nm 2 {s to 350 nm 2 {s. These values are close to that of the interdiffusion coefficient taken in our calculations (D Al{N i " 217 nm 2 {s). Though the comparison of the interdiffusion coefficient D Al{N i with the phase diffusion coefficient D yx may seem premature, it appears to hold some significance since the alignment of precipitates during the zigzag relaxation can only occur by elasticity-induced diffusion of Al atoms, resulting in the simultaneous dissolution and growth of precipitates disposed at energetically-unfavorable positions in the pattern.

Conclusions and Prospects

The phase-based analysis has been shown to be both relevant and efficient as a means to topologically describe microstructure evolution during elasticity-induced coarsening. The response of a perfectly regular microstructure undergoing Eckhaus and zigzag instabilities has been investigated, and measured with ψ x and ψ y . The system has revealed itself to be respectively unstable and stable against Eckhaus-type and zigzag-type distorsions of its regularity. The amplification of the Eckhaus instability leads to additional fluctuations of λ x which are traced by growing phase modes of various wavelengths, until precipitates coalesce. The zigzag instability relaxes at first, but the alignment process brings about the development of an Eckhaus instability whose growth becomes faster than the zigzag decay, eventually leading to precipitates coalescence before the complete relaxation of the initial instability.

In this work, we presented the perturbative analysis which we carried out on regular patterns with 1D topological defects. Aside from the latters, we also focused on 2D topological defects ("vacancy" and "dislocation" in the precipitates network, etc.) whose complex evolution may be quantitatively described using ψ x and ψ y as well. The transition from 2D to 3D topological analysis of microstructures will require the introduction of a third phase ψ z and of the corresponding equation for its dynamic. Therefore, three diffusion equations will be needed for the temporal evolution of ψ x , ψ y and ψ z , which, if taken at low-order, will each possess one Eckhaustype and two zigzag-type terms. The relevance of the phase-diffusion equations must be ascertained beforehand.

We intend to further develop this work by investigating the influence of the physical parameters of the system (i.e. temperature, misfit, volume fraction, elastic inhomogeneity, translational variants, external loading, etc.) and of the features of the topological defects (i.e. wavelength, amplitude, position in the pattern, interactions with other defects, etc.) on phases dynamics, in order to either confirm or overturn the relevance of phase equations for their temporal evolution.

In light of the results we have exposed in the present work, the phase-based analysis of microstructures appears promising, and seems to open new prospects for the modeling of microstructural evolution in these alloys at macroscale.

Figure 2 :

 2 Figure 2: Evolution with time of the Eckhaus instability imposed on an ideal microstructure and associated ψ x and ψ y maps.

Figure 3 :

 3 Figure 3: Profile of ψ x along x : amplification of the Eckhaus instability over 3.2 h.

Figure 4 :

 4 Figure 4: Evolution with time of the zigzag instability imposed on an ideal microstructure and associated ψ x and ψ y maps.

Figure 5 :Figure 6 :

 56 Figure 5: Profile of ψ x along x : growth of the Eckhaus instability over 3.8 h.

Figure 7 :

 7 Figure 7: Evolution of A ZZ with time : relaxation of the zigzag amplitude over 3.8 h, fitted by an exponential law A ZZ " e ´t{τ (time constant τ ZZ " 4.37 h).


Michael Hamwi
email: m.hamwi@estia.fr

Iban Lizarralde

Business model innovation for energy transition in household sector

Keywords: Business model, energy transition, prosumer, energy value chain, PSS

This paper focuses on Business Model (BM) innovation practices within a specific field: the household sector energy transition. In recent years, the value chain between the stakeholders involved in this field has been modified due to recent technological changes, which poses a threat for current companies and an opportunity for insiders. This research work is carried out within the Greenplay project, which is an EU funded Horizon H2020 project. This project aims to develop new business models that reduce energy consumption in the household sector and can be successfully implemented. In this study, a systematic literature review is conducted related to energy business models. Furthermore, the proposed framework is a crossing classification based on criteria concerning innovation targets and various energy production, distribution and consumption BMs. In the second phase of the Greenplay project the authors will apply the proposed framework to the use cases identified in the project.

Introduction:

Last decades, there has been a great pressure on the different sectors in order to reduce CO² emissions aiming to mitigate the climate change effects [START_REF] Manabe | On the distribution of climate change resulting from an increase in CO2 content of the atmosphere[END_REF]. Energy sector's contribution to CO² emissions is one of the highest [START_REF] Davis | Future CO2 Emissions and Climate Change from Existing Energy Infrastructure[END_REF], thus more worth efforts have to be put towards more sustainable energy sources rather than the carbon based energy system. As a response to this call, energy utilities are redirecting their attention to more sustainable Business Models (BM). For example, most of the energy utilities in the U.S. have estimated a stagnant energy demand in the next few years and some of them expected a negative load growth (Utility Dive, 2015). This expected decline of energy demand is coupled with the expansion of renewable energy (RE) and distributed energy (DE). Moreover, European energy Utility Companies (EUCos) face up a threat regarding their stable deep-rooted traditional BM (Boston Consulting Group, 2010;[START_REF] Forrester | Utility Tariff Bonds: New and Refined Applications for Proven Stranded Cost Securitization Technology[END_REF]. While the preliminary reaction of utilities to the upcoming changes is to develop new BMs and invest in distributed generation, the question is how and what are the mechanisms to overcome this challenge (Hellström et This paper was presented at The XXVII ISPIM Innovation Conference -Blending Tomorrow's Innovation Vintage, Porto, Portugal on 19-22 June 2016. The publication is available to ISPIM members at www.ispim.org. [START_REF] Sioshansi | Electricity utility business not as usual[END_REF][START_REF] Helms | Asset transformation and the challenges to servitize a utility business model[END_REF]. This sector is facing an uncertain period due to the changing roles of current utilities and the arriving insiders in energy market.

2

Actions for CO² reduction in energy sector require changes in the energy utility BM that has been used by energy utilities for over a decades. There are two types of approaches regarding energy transition. On the one hand, top-down approaches where policy and regulations are pushing utilities and business stakeholders to take part on the energy transition. The emergence of Energy Service Companies (ESCos) is one of the results of this approach [START_REF] Hannon | Demand pull" government policies to support Product-Service System activity: the case of Energy Service Companies (ESCos) in the UK[END_REF]. On the other hand, the bottom-up approaches, where social initiative cooperatives enable citizen and community to get involved in distributed energy market. In Germany, for example, the social cooperatives have raised from 136 utilities in 2008 to 888 in 2013 [START_REF] Morris | German Energy Transition[END_REF]. In addition there are new marketing opportunities, where economic and financial benefits also drive the transition towards renewables and more efficient consumption [START_REF] Johnson | Lessons learned from the field: key strategies for implementing successful on-the-bill financing programs[END_REF].

Based on a study lead by (Utility Dive, 2015) the shape of the energy service BMs, in the next few years could be based on: 1) Energy efficiency and demand response (71%); 2) consumer information services (51%); 3) distributed generation (48%). Yet the business model for energy services is vague and unclear; however, there are some characteristics that can be a cornerstone for researchers and practitioners to build their own energy service BM.

The paper is structured as follows. Section 2 reviews sustainable and collaborative business models. Besides, this section introduces the Greenplay project. Section 3 introduces a framework based on innovation targets classification and energy value chain. This framework is used to map the review of the literature about the energy transition BMs along the energy value chain .In section 4, in addition to the discussion, it poses the scope and the research questions of the PhD work of the main author. Finally, section 5 draws the conclusions.

2 Theoretical background and scope:

Sustainable and collaborative BMs:

The concept of BM has many definitions that vary according to the context of use: it refers to the logic of the firm and how it operates and creates value for its stakeholders. Moreover it reflects the realized strategy which is the base to come back when making critical decisions [START_REF] Casadesus-Masanell | From Strategy to Business Models and onto Tactics[END_REF]. BM can be viewed as a strategy transition into a logical framework for economic value creation [START_REF] Osterwalder | The business model ontology: A proposition in a design science approach[END_REF]. The same technology can be developed through different business models, affecting the economic value created. Thus there are often conflicts between current BM and the desired one due to the deployment of emerging technologies [START_REF] Chesbrough | Business Model Innovation: Opportunities and Barriers[END_REF].

Sustainable business models (SBMs) have been discussed recently as a way of balancing the ecological, social and economic needs through value proposition, stakeholders involvement and taking the responsibility of ecological burdens rather than displacing them to customer or suppliers [START_REF] Boons | Business models for sustainable innovation: stateof-the-art and steps towards a research agenda[END_REF]. SBMs are the framework where sustainability is integrated in the activities of the organization and it is embedded into the business purpose and process. The scope in the deployment of SBMs often considers the firm level as well as the socioeconomic systems [START_REF] Stubbs | Conceptualizing a "Sustainability Business Model[END_REF]. Choosing the right SBM could be confusing for firms and start-up companies. In order to overcome this problem eight archetypes have been introduced by [START_REF] Bocken | A literature and practice review to develop sustainable business model archetypes[END_REF] to categorize different practices and facilitate the adoption of new BMs.

These new BMs are often conceived between several organizations and developed within a scope that surpass the firm level. As a result of this fact, Collaborative Business Models (CBMs) have been pointed as an interesting approach to co-develop BMs that are deployed jointly in the same value chain.

CBM has been defined as "an activity where multiple organizations that might differ in type (industry, public research and non-profit), their position in the value chain (manufacturing, service, etc.) and industry (energy, ICT, etc.) work together to create a value creation system. In some cases, they will also attempt jointly to create the value capture system" [START_REF] Rohrbeck | Collaborative business modelling for systemic and sustainability innovations[END_REF]. [START_REF] Laudien | Antecedents and Outcomes of Collaborative Business Model Innovation[END_REF] proposes four levels of collaborations: no collaboration, slight operational changes to BM, open the BM for the integration of consumer and external partners where internal adjustment of BM occurs, and finally to reach BM innovation and network partner-driven or customer-driven BM.

Greenplay Project:

The household sector represents 28% of the energy consumption in the EU. Households alone have a limited capability to change their consumption patterns, thus there is a need to include other actors who could support households toward sustainability [START_REF] Sanne | Willing consumers-or locked-in? Policies for sustainable consumption[END_REF][START_REF] Roy | Sustainable product-service systems[END_REF]. However, energy efficiency organizations like ESCo haven't manage to reach this sector [START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF]. There is lack of awareness concerning energy efficiency specifically in the household sector. Moreover, energy efficiency is not a priority for consumers, it could be perceived as disruption and hassle to households and the fear of long-term commitment. All these factors made household unreachable for ESCos [START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF].

This research work is developed in the framework of a European Union's Horizon 2020 project called GreenPlay. This project seeks to reduce by 30% the electricity consumption in the household sector and will be validated through a large-scale experiment based on 200 households situated in France and Spain.

The Greenplay system is composed by sensors, a smart monitoring platform and a game.

The sensors installed at the user's home are linked to GreenPlay system, and measure global electricity, heating, water heating and temperature. The core of this system is a pervasive game i.e. eco-gestures in real life and thus electricity consumption reduction allows to earn points and evolve in the game.

The system allows to monitor real behaviour and possible long-term changes in the context of the participation of the customer in the load management (Apajalahti et al., 2015) and energy efficiency [START_REF] Helms | Asset transformation and the challenges to servitize a utility business model[END_REF].

The use of game principles or "gamification" is an efficient tool to deal with behavioural modifications (Nieuwdrop, 2007), (Germaud, 2013). (Abi Akle et al., 2016) have identified nine projects working on pervasive and persuasive gaming for energy conservation.

The main research objective of the Greenplay project is to study the potential of combining game elements and instructional advices for modifying energy consumption. The combination of these two elements within a serious games offers some possibilities to encourage the immersion in context, the empowerment and the learning appetence of users.

Through this approach, the system identifies the use of energy and users' behavior in the private sphere. This information can be used to identify decision variable for product design processes (building, home appliances, etc.), as well as an input for the During the first phase of the Greenplay project, a review of existing BMs in the energy sector has been performed aiming to have a thorough picture related to energy transition. This paper presents some of the results of this review. Then, during the second phase of the project, the goal is to study the potential of joining the new household behavior patterns and energy consumption routines to innovative BMs that are being shaped in the energy sector.

The current impact of the household sector in the global energy consumption and the emerging technologies related to decentralized energy systems, set the basis for new BMs development that involve the household as a key stakeholder. Indeed, The household sector represents 28% of the energy consumption in the EU Besides, rapid changes in the technologies, including small scale renewable energy, energy storage and smart grid provoke upcoming changes in the consumption and production model of energy. However these technologies alone are not enough to change the current patterns, thus exploiting them within appropriate BM seems to be the key factor for the emergence of new practices that create economic, social and environmental value. [START_REF] Chesbrough | Business Model Innovation: Opportunities and Barriers[END_REF] postulates that "a mediocre technology pursued within a great business model may be more valuable that a great technology exploited via a mediocre business model" (P.355).

Lately, there are increasing trends in the energy sector towards decentralized energy system especially in the household and city precinct [START_REF] Daley | Financing and Managing Urban Energy Systems[END_REF]. Furthermore, Rocky Mountin Institute has included the distributed generation (DG), zero-net buildings and energy metering as a major issues in the development of the 21 st century energy business models [START_REF] Lacy | Net Energy Metering, Zero Net Energy And The Distributed Energy Resource Future: Adapting Electricity Utility Business Models For The 21st Century[END_REF]. [START_REF] Skinner | Technology: Net-Zero Buildings and Distributed Generation Forcing New Business Models[END_REF] highlights the fact that utilities have started not only to invest in renewable energy but also in distributed energy systems, providing services to users willing to be more independent of the centralized energy system.

In the next chapter, these disruptive energy systems are reviewed through the analysis of the associated BMs.

3 New business models for energy transition:

Energy business models framework:

In order to classify the different BMs, a framework based on two criteria was defined. On the one hand the BM category centred on the innovation focus. On the other hand the specific value chain related to the energy sector (Table 1).

Existing classifications concerning changes in business models as well as the degree of these changes is often related to the scope and the nature of the innovation. According to (Oslo manual, 2005) innovation is a system that targets not just the product and process but also the organizational structure of the firm, marketing strategies, institution and society. [START_REF] Boons | Business models for sustainable innovation: stateof-the-art and steps towards a research agenda[END_REF] have defined three streams with regard to SBM: technological, organisational, and social innovation and stressed that these streams don't stand for separated phenomena and there is kind of dependency among them.

Concerning the energy value chain, segments of the energy market differ depending on the typology of the energy commodity. In the upstream phases there is the extraction or the generation of the energy commodity; then, there are different distribution and storage phases before the consumption stage. This division can be more detailed by including trading and retailing segments. Moreover, in specific energy value chain like the electricity, some operator can have a key role maintaining the system generation and load balance.

Consequently, the framework utilised in the next chapter includes two criteria:

 BM category is defined as follows:

 Technology: focus on product, services or methods of production or procedures.

 Organization: the responsibilities and the organizational structure of management.  System: goes beyond the organizations and targeting issue linked to the society or community (e.g. institutional arrangements, social norms and cultural values, etc.).  And the energy value chain includes the production, distribution and consumption phases.

Technology level:

Recent advances in energy technologies allow the deployment of new BMs. This is the case of more efficient appliances, smart grid solutions, metering systems, smart devices or decentralized renewable energy means. Nevertheless, the technological oriented BMs [START_REF] Mizobuchi | Replacement or additional purchase: The impact of energy-efficient appliances on household electricity saving under public pressures[END_REF] are often subject to consumer behavior [START_REF] Chen | What can we learn from high-frequency appliance-level energy metering? Results from a field experiment[END_REF][START_REF] Khazzoom | Energy Saving Resulting from the Adoption of More Efficient Appliances[END_REF], or other modifications within the scope of the new energy system. For this reason, some reviewed technologies have been discussed in the "system level" chapter. In this chapter, technologies that allow a transition to a service or function oriented BM have been reviewed.

Table 1 Mapping energy business models along the energy value chain

BM target Production Distribution Consumption

Technology [START_REF] Sorrell | The contribution of energy service contracting to a low carbon economy[END_REF]) [START_REF] Kobus | A real-life assessment on the effect of smart appliances for shifting households' electricity demand[END_REF], [START_REF] Laicane | Reducing Household Electricity Consumption through Demand Side Management: The Role of Home Appliance Scheduling and Peak Load Reduction[END_REF], [START_REF] Valencia | The Design of Smart Product-Service Systems (PSSs): An Exploration of Design Characteristics[END_REF], [START_REF] Tan | Modelling and analysis of a business model to offer energysaving technologies as a service[END_REF] Organization [START_REF] Loock | Going beyond best technology and lowest price: on renewable energy investors' preference for service-driven business models[END_REF], [START_REF] Liu | Purchasing vs. leasing: A benefitcost analysis of residential solar PV panel use in California[END_REF], [START_REF] Kroposki | Renewable systems interconnection: Executive summary[END_REF], [START_REF] Schoettl | Photovoltaic business models: threat or opportunity for utilities[END_REF], [START_REF] Richter | Utilities' business models for renewable energy: A review[END_REF], [START_REF] Gsodam | The renewable energy debate: how Austrian electric utilities are changing their business models[END_REF], (Hannon et Servicizing has been discussed as a way of reducing natural resource dependency. The goal is to deliver a function instead of a physical product, decoupling the consumption from the used material [START_REF] Heiskanen | Can services lead to radical eco-efficiency improvements?-a review of the debate and evidence[END_REF].

In general, supplying a function or a final service is a process where the tangible product is replaced by integration of a product and a services, known as a Product-Service System (PSS), which is usually coupled with economic and environmental advantages [START_REF] Tukker | Product-services as a research field: past, present and future. Reflections from a decade of research[END_REF]). Yet little work has been done into the energy field to tackle energy as a service and scrutinizing the related business model (Apajalahti et al., 2015;[START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF][START_REF] Hannon | The co-evolutionary relationship between Energy Service Companies and the UK energy system: Implications for a lowcarbon transition[END_REF][START_REF] Helms | Asset transformation and the challenges to servitize a utility business model[END_REF][START_REF] Shomali | The consequences of smart grids for the business model of electricity firms[END_REF].

Servicizing energy is providing what people really need; for example, people need light and accurate constant temperature rather than electricity, lamps or heating systems. It is a shift from energy commodity transaction to providing function. [START_REF] Sorrell | The contribution of energy service contracting to a low carbon economy[END_REF] proposed two concepts: the "useful energy" and the "final energy services" while the former is driven by primary conversion equipment such as boilers and CHP (Combined Heat and Power) which provide steam, hot water and coolant, the latter is driven by secondary conversion equipment such as radiators and fluorescent lighting which converts the useful energy to final energy services like heating and light.

In the distribution part of the value chain, Demand Response (DR) is a mechanism to reduce environmental impact of electricity's use and production cost, it includes timeshifting or load reduction or both in response to price signals or other incentives. The DR is a mechanism that allows the deployment of innovative BMs supported by emerging technologies such as smart devices. Nevertheless, DR in the residential sector depends on the user perception for the need to shift consumption, trust in utility or energy service provider, incentives and transition cost [START_REF] Darby | Social implications of residential demand response in cool temperate climates[END_REF]. [START_REF] Laicane | Reducing Household Electricity Consumption through Demand Side Management: The Role of Home Appliance Scheduling and Peak Load Reduction[END_REF] indicates that smart meters provide useful information about appliance's consumption in households, and can lead to significant changes in load consumption, thus the load peak could be avoided. The emerging of smart devices enables a higher level of automation of appliances and reducing behavioral effects.

Integrating smart appliances with dynamic electricity tariff and energy management systems resulted in significant shift in energy consumption towards sunny days when the solar panel power is maximum [START_REF] Kobus | A real-life assessment on the effect of smart appliances for shifting households' electricity demand[END_REF]. Furthermore, adding e-service for the smart devices through web portal enables more functions to be activated such as following consumption charts, comparing consumption and communicating with other consumers. This BM has been identified as Smart Product-Services System [START_REF] Valencia | The Design of Smart Product-Service Systems (PSSs): An Exploration of Design Characteristics[END_REF]. Offering energy saving technologies as a service would bring economic benefits for both the customer and the supplier as fluctuation of energy consumption, uncertainty in energy prices and carbon offset are considered, in addition to the environmental benefits [START_REF] Tan | Modelling and analysis of a business model to offer energysaving technologies as a service[END_REF].

Organization level:

Even if technological aspects are often the source of many new BMs in the energy sector, innovative BMs can arise in fields where technology is mature and are mainly related to modifications in the practices within the organization. Existing energy companies for example have include within their activities, new energy service BMs. Some utilities addressed this need as a reaction to the de-growth of energy demand in U.S, where most of energy utilities are trying to face the energy reduction demand by identifying new BMs (Utility Dive, 2014). Innovative energy service BMs include Distributed Generation based on micro-generation in the consumer site supported by the necessary services (Richter, 2013a). Furthermore, energy services have been outlined as Demand Side Management which related to energy end-user efficiency and conservation (Apajalahti et al., 2015). Energy Service Companies ESCos have also developed original energy service BMs that aims to reduce the customer consumption by either supplying energy from micro-generation or by providing efficiency measures that cut energy consumption [START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF][START_REF] Hannon | The co-evolutionary relationship between Energy Service Companies and the UK energy system: Implications for a lowcarbon transition[END_REF][START_REF] Sorrell | The contribution of energy service contracting to a low carbon economy[END_REF]. In an attempt to define the role of energy utilities in the transition towards renewable energy, package of services has been suggested, starting from simple consulting services that include financing, ownership, operation and maintenance [START_REF] Gsodam | The renewable energy debate: how Austrian electric utilities are changing their business models[END_REF][START_REF] Richter | Utilities' business models for renewable energy: A review[END_REF].

Investors in the renewable energy sector prefer "customer intimacy" as a servicecentralised business model rather than the upstream production-oriented model based on technology and lowest price [START_REF] Loock | Going beyond best technology and lowest price: on renewable energy investors' preference for service-driven business models[END_REF]. Likewise, leasing solar photovoltaic cells has been presented as a successful alternative to the purchasing one because it allows to get around of up-front payment and it offers supplement services like the regular maintenance. In addition [START_REF] Liu | Purchasing vs. leasing: A benefitcost analysis of residential solar PV panel use in California[END_REF]. As changing to service-oriented BM is more complex than product-oriented BM and to reach broader markets concerning renewable energy, there is a need to include a third party who could manage the process. "1 st Generation business model" is a BM driven by third party rather that the utility or the consumer. The advantages of such model are reducing the hassle and complexity for consumers [START_REF] Kroposki | Renewable systems interconnection: Executive summary[END_REF]. This BM is preferable for consumer who doesn't want to be bothered by selecting and installing their PV, and just need reliable sources of energy, competitive prices and assurance of rapid-response service and supporting maintenance [START_REF] Schoettl | Photovoltaic business models: threat or opportunity for utilities[END_REF].

Distributed and small-scale electric power generation is defined as Distributed Generation. The combination of the DG and renewable energy sources is known as the Distributed Renewable Energy (DRE). In the last years new BMs have arisen in the field of the DRE. Two main stakeholders are concerned by these BMs: On one hand, utilities as the main actors in energy market. However, utilities do not see in distributed generation neither a threat nor an opportunity and many barriers hinder utilities from developing new BM for exploiting renewables such as lack of competencies, lack of consumer demand, lack of products and services and lack of profitability (Richter, 2013b). On the other hand, consumers are directly concerned by this approach as they have the opportunity to empower themselves by obtaining cheap clean sources of energy and become prosumer (producer and consumer). In this case the utility role would be confined to back-up source of power [START_REF] Sioshansi | Electricity utility business not as usual[END_REF]. The environmental impact of distributed generation has been examined compared with the traditional utility model. The environmental impacts can be mitigated in four areas; reduction in greenhouse gases emissions, reduce damage to health, higher energy efficiency and conservation of resources for additional use (Akorede et al., 2010).

Demand Side Management (DSM) has been introduced as a way of flatten the load curve of consumption. Two main services have become the major elements of the DSM (Behrangrad, 2015) Energy efficiency and Demand response. The former is a model for incentivize customers to change their consumption pattern in order to reduce the electricity consumption and the peak of the consumption in the load curve. "Business model involving load" includes both price incentives and consumption awareness in order to reduce the cost of the load. This BM can be based on an infrastructure for the consumer in order to receive price information at a suitable time and format (Behrangrad, 2015).

This paper was presented at The XXVII ISPIM Innovation Conference -Blending Tomorrow's Innovation Vintage, Porto, Portugal on 19-22 June 2016. The publication is available to ISPIM members at www.ispim.org.

Implementing energy efficiency measures and installing micro-generation in households seems a promising approach but it is blocked by many factors like low energy cost, long term engagement, weak recognition for energy services, less motivation as no show off, in addition to the disruption and hassle for the households [START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF]. Moreover there is a weak relationship between big utilities and its customers, and some authors have identified a distrust surrounding energy utilities to deliver efficiency measures (Apajalahti et al., 2015;[START_REF] Helms | Asset transformation and the challenges to servitize a utility business model[END_REF]. As a solution to this fact, [START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF] presents Mini-ESCos as a business model that can propose energy efficiency measures to households as alternative for big ESCos and services proposed by big utilities. Mini-ESCo could be small facilities that are used to provide maintenances and breakdown repair for households. The reasons are behind this proposal are the lack of awareness of ESCo business, the cost comparing with savings (Pätäri et al., 2016) and the lack of trust towards large energy utilities [START_REF] Holt | The Treatment of Renewable Energy Certificates, Emissions Allowances, and Green Power Programs in State Renewables Portfolio Standards[END_REF][START_REF] Richter | Utilities' business models for renewable energy: A review[END_REF] and scepticism about the real motivation for utility to engage in households energy efficiency (Apajalahti et al., 2015).

System level:

Going from the organization level to system level requires more collaboration between the stakeholders in the energy ecosystem. This collaboration comes out from the inability of one business model alone to deliver competitive and sustainable value in renewable business, which requires a broader system perspective. Furthermore, in complex and heterogeneous field like energy service, collaborative BM is needed to create in each stakeholder motivation for contributing towards the innovative system [START_REF] Ericson | Commercial Space Tourism -A Case of Applied Product-Service Systems Networks[END_REF]. Thus, it is important to determine the factors that drive business models of the collaborating firms to facilitate system transition where the value creation is a holistic process. Sharing common BM elements and developing inter-dependencies between companies can create sustainable value that can't be captured by one business model [START_REF] Hellström | Collaboration mechanisms for business models in distributed energy ecosystems[END_REF].

Even if efficient measures and renewable energy means already exist in the market, some barriers like landlord and tenant split incentives as well as the up-front payment are blocking the diffusion of these technologies. Designing innovative business models can overcome these barriers. For example, on-the-bill financing is a financial model to overcome the previous barriers and encourage households to participate in renewable and efficiency programs [START_REF] Johnson | Lessons learned from the field: key strategies for implementing successful on-the-bill financing programs[END_REF]. As a result, some utilities have changed their BM to integrate loans management, to provide maintenance and to work with contractors. This case study indicates that BM innovation can exploit technologies and bring out some changes like collaboration with municipalities and contractors who have a closer relationship with customers.

On-bill financing is an innovative financing method that allows consumers to overcome up-front payment of implementing energy efficiency measures by providing the necessary loan and dividing it to small monthly payments that are cut from the amount of monthly bill savings. This BM can lead to win-win situations and permit the energy companies to diffuse efficiency measures and renewable energy technologies [START_REF] Johnson | Lessons learned from the field: key strategies for implementing successful on-the-bill financing programs[END_REF]. This solution is a financial product served by utilities that work closely with energy efficiency services providers (Bell et al., 2011).

Similarly, White Certificates have been considered as a market mechanism for stimulating energy efficiency actions, it confirms that a specific amount of energy savings have been achieved by market actor as a results of energy efficiency improvement measures [START_REF] Bertoldi | Tradable white certificate schemes: fundamental concepts[END_REF]. White certificates are tradable in the market, so that it is considered as a cost recovery mechanism. A positive relationship between providing energy services and white certificate in France has been noticed and tested (Duplessis et al., 2012). Renewable energy certificate (REC) is an instrument proves that the supplier has generated and fed in the grid 1 megawatt-hour of electricity (in the U.S). RECs can be bought and sold separately from electricity and can facilitate the diffusion of renewables as their trading is easier than renewable electricity [START_REF] Holt | The Treatment of Renewable Energy Certificates, Emissions Allowances, and Green Power Programs in State Renewables Portfolio Standards[END_REF].

The Renewable Energy cooperative BM represents a bottom-up approach where citizens set up their own socio-economic organisation aiming to exploit the benefits of renewable energy. RE cooperatives appeared after the liberalisation of energy markets as a reaction of local consumer desiring to control their source of energy. In some cases cooperatives offers lower prices, are more transparent, and have simpler pricing mechanisms. They diffuse democratic way of taking decisions and social acceptance of green consumption that leads to positive environmental and social effects for the community. Cooperatives have also implemented "demand side management" practices that provides advices about consumption and conservation [START_REF] Huybrechts | The relevance of the cooperative model in the field of renewable energy[END_REF].

Lastly, some technological approaches can be part of a systemic modification that involves several stakeholders of the energy value chain. For example, Smart grids have been described as a disruptive technology as it holds fundamental changes for current energy BM by allowing flow of energy and information in two-directions and by providing a real-time access to usage data. Moreover, it encourages people to move towards distributed generation, promotes energy saving, enables the implementation of new energy services and induces consumer's demand response [START_REF] Shomali | The consequences of smart grids for the business model of electricity firms[END_REF], Consequently the distinction between the role of the supplier and the consumer might be blurred. Smart grids offer more tailored energy services that match with consumer's need, extend the relationship with customer to be more continuous and bring new players to the market [START_REF] Giordano | A business case for Smart Grid technologies: A systemic perspective[END_REF].

Gamification is powerful way to educate people and influence the energy consumption.

EnerCities is serious game that has some preliminary results that led to increase user's awareness and stimulate more positive attitude towards some every-day energy related behaviours [START_REF] Knol | EnerCities-A serious game to stimulate sustainability and energy conservation: Preliminary results[END_REF]. In gamification many factors affect energy conservation such as metering level, feedback visibility, financial incentives, competition as motivation, use social media and educate audience [START_REF] Playgen ; Richter | Business model innovation for sustainable energy: German utilities and renewable energy[END_REF].

The virtual enterprise/virtual organizations has examined in energy service as a platform that facilitates the flow and exchange of energy information among different partners (Allan and Menzel, 2009).

Discussion:

The Greenplay project focuses on electricity consumption of households and the electricity's consumer is a critical factor in our research as it moves away from traditional one-way relationship pattern to a more interactive system. The Greenplay project is seeking to better understand electricity consumers' behavior, their expectation and their capacity and ability to be engaged in new more dynamic business models. Going beyond the-meter-market and find the business opportunities beyond the two-side flow of information and energy, will change consumer preferences and rise energy diversity. Thus a bundle of energy services and products, such as home energy audit, consultation and devices or services to automate home energy can be developed as there is an emerging trends to overcome price issue and consume green energy. Taking into account these critical changes, this paper focuses on different energy BMs. It emphasizes the BMs that create sustainable value and outlines the role that the consumer can play within these new BMs.

Indeed the dominant role of utilities is fading while the share of sustainable distributed energy resources are expanding. The risk surrounding the existence of their BM "Spiral death" is widening [START_REF] Costello | Electric Utilities' "Death Spiral": Hyperbole or Reality?[END_REF]. Consequently, the more and more utilities focus on the creation of innovative services that utilities can provide to consumer. Nevertheless, even if utilities have decades of experience related to energy production, distribution and consumption; they suffer from consumer lack of trust concerning of their role in energy efficiency and renewable energy.

Several questions arise related to the role of each stakeholder within the competitive and sustainable energy BMs, as well as the capacities related to intangible service, consumer relationship, regulations and the organizational structure. With this in mind, it is also necessary to analyze the arrival of some new actors, like ESCos, who have penetrated the energy market where they go beyond the energy retail and provide services that create win-win situations. .Yet ESCos are remaining far away from households. This gap is due to some barriers such as the lack of awareness about energy services, the low prices of energy commodities, as well as the hassle of being engaged in long term financial commitment. However [START_REF] Bertoldi | Liberating the power of energy services and ESCOs in a liberalised energy market[END_REF] suggests new business model based on "Mini-ESCo" which could be small enterprises that have long term close relationship with consumer based on trust.

Consumers' role is not anymore passive, they see in renewable energy an independent and more secure source of energy and become a key stakeholder in the load management. Therefore, it is necessary to engage them along the whole process of designing the new services and products considering their roles within the future BMs. The flow of energy and information in the two-directions thanks to the Smart Grid brings new opportunities manifested in various services that include from simple advices for energy analysis charts, to actions, to build interconnected home networks.

Finally, between the two sides, the consumer and the provider, many business model have arisen either related to the energy efficiency or to the demand response approach. Such BMs can target load control, electricity transaction and renewable energy correlation. In addition as retailer dealing with consumers, they have various BMs that can targets different segments of energy market rather than production or transmission units (Behrangrad, 2015). A promising role of Information and communication technology ICT in this part has been described as virtual organizations that mange the flow of information and energy which could be bought and sold through the smart grid. All on all, organizing the previous issues stimulate us to raise few questions related to energy business model. Wondering how energy can satisfy the final need of consumer, could the integration of energy and smart technologies creates new demand for specific needs, can appliance's manufacturers take parts in the energy value chain, what kind of capacities required from the consumer and what is the role of utilities and new insiders.

Conclusion:

In this paper, we scrutinize some BMs in the energy sector in order to have deep understanding of what could be the value proposition that new BM would deliver either by new version of current utility or by new insiders who would find their own way in the liberalized energy market. From the review, we notice that exploiting technology by good business model is better than exploiting good technology by trivial BM. So that, the importance of this study comes from the fact that there is a lot of confusion about the future business in the energy sector and the shape of its BM. We discussed different issues such as the role of utilities and ESCOs, the new concepts that deal with energy as product-service rather that a commodity the prosumers emergence and their role in the new value chain, the increasing importance of demand side management and smart grids.

This paper could be considered as the cornerstone of the PhD launched within the Greenplay project which aims to define energy business models that respond to the changes in the energy value chain. It poses questions related to the degree of servicizing, interested stakeholders, the user expectations, the capability of utilities to take major role, as well as the possibility of new players to move into the energy value chain. In addition, it tackles the role of incentives factors and barriers such as dynamic prices and hampering factors like regulations and lack of trust on utilities. Lastly it addresses the issues related to up-front cost and the role of citizens and cooperatives.

The blurring picture of energy BMs that comes out of the recent technological advancements in energy sector can be better handled by deep understanding of its BM components and its value proposition. Sustainable business models contribution can be adopted to energy sector and add green value by innovating in energy efficiency and distributed generation. Moreover, collaboration business models could enable the different actors in energy sector to find their way to work together as energy sector is becoming the more and more complex system by emerging such concepts "Servicizing energy". In addition to the increasingly active role of consumer, which brings the need for a better management of the two-side energy and information flow.

Acknowledgement

Authors would like to thank the GreenPlay project (www.greenplay-project.eu) that has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 649621.

7 References:

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  Akorede, M.F.,Hizam, H., Pouresmaeil, E., 2010. Distributed energy resources and benefits to the environment. Renew. Sustain. Energy Rev. 14, 724-734. doi:10.1016/j.rser.2009.10.025 Allan, L., Menzel, K., 2009. Virtual Enterprises for Integrated Energy Service Provision, in: Leveraging Knowledge for Innovation in Collaborative Networks. Springer, pp. 659-666. Apajalahti, E.-L., Lovio, R., Heiskanen, E., 2015. From demand side management (DSM) to energy efficiency services: A Finnish case study. Energy Policy 81, 76-85. doi:10.1016/j.enpol.2015.02.013 Behrangrad, M., 2015. A review of demand side management business models in the electricity market. Renew. Sustain. Energy Rev. 47, 270-283. doi:10.1016/j.rser.2015.03.033 Bell, C.J., Nadel, S., Hayes, S., 2011. On-Bill Financing for Energy Efficiency Improvements: A Review of Current Program Challenges, Opportunities, and This paper was presented at The XXVII ISPIM Innovation Conference -Blending Tomorrow's Innovation Vintage, Porto, Portugal on 19-22 June 2016. The publication is available to ISPIM members at www.ispim.org. This paper was presented at The XXVII ISPIM Innovation Conference -Blending Tomorrow's Innovation Vintage, Porto, Portugal on 19-22 June 2016. The publication is available to ISPIM members at www.ispim.org.


Sébastien Mercier
email: sebastien.mercier@onera.fr

Romain Agogue
email: romain.agogue@onera.fr

Anne Mavel
email: anne.mavel@onera.fr

Philippe Nunez
email: philippe.nunez@onera.fr

Céline Le Sinq
email: celine.le_sinq@onera.fr

Study of the galvanic corrosion in Al/CFRP co-cured hybrid materials

Keywords: Galvanic corrosion, Aluminium/CFRP hybrid material, Salt spray aging, Mechanical strength

The use of hybrid structures where the right material is used at the right place for its best properties is of great interest for structures optimisation, particularly when mass reduction is required. In such hybrid structures, where metal and composite are closely in contact, the strength of the interface between the metal and the composite can be altered by the galvanic corrosion between the aluminium and the composite when Carbon Fibres Reinforced Plastic (CFRP) is used. This paper is related to the corrosion and mechanical properties of an Aluminium/CFRP co-cured hybrid structure. The influence of the aluminium surface treatment on the interface properties obtained after a one step co-curing manufacturing process has been assessed. Al-2024 aluminium alloy treated by either tartaric-sulphuric anodizing (TSA), chromic acid anodizing (CAA) or silane pre-treatment (γ-GPS) has been used and co-cured with CFRP. The galvanic corrosion behaviour of the Al/CFRP hybrid system has been determined with the Evans diagram method and the mechanical strength of the interface has been characterized with a single-lap joint tensile test before and after exposure of the samples in a salt spray chamber. The different surface treatments of the aluminium alloy have been compared in term of both galvanic corrosion and adhesion properties before and after corrosive environment exposure in order to find the best compromise for Al/CFRP structure applications.

Introduction

Hybrid composite/metal structures already exist for aerospace applications. These hybrid structures are mainly made of composite materials for their good performance to weight ratio. Metal inserts are generally used so as to fill the lack of composite performances, such as conductivity or joining capabilities.

The classical industrial process used for hybrid structure is to manufacture the composite and metal components separately, prepare them before performing the assembly step to get the final hybrid structure. This process is time consuming and some operations, such as drilling of the composite material, could drastically reduce its performances. To overcome this situation, this study focuses on Aluminium/CFRP (Carbon Fibres Reinforced Plastic) hybrid structures made by a one step co-curing process.

In such hybrid structures, where metal and CFRP are closely in contact, the strength and durability of the interface between metal and composite are fundamental to ensure the load introduction from metal to composite. It is well known that metal pre-treatments like chromate conversion or anodizing is beneficial to the adherence and corrosion resistance of polymers on aluminium [1,[START_REF] Petrie | Metal Finishing[END_REF][START_REF] Zhang | [END_REF]. These processes are for example commonly used in painted aluminium structures or aluminium adhesive bonding in aerospace industry [START_REF] Petrie | Metal Finishing[END_REF].

Because of high corrosion potential gap between aluminium and carbon, strong galvanic corrosion can occur. It is therefore of great interest to study the influence of the aluminium treatments on interface corrosion properties in such couple of materials and to assess the durability of the joint after exposure to corrosive environment.

The dichromate etching and chromic acid anodizing are well known to improve corrosion resistance and adhesion between aluminium and polymers in adhesive joining or painting systems. But, due to its CrVI compounds content, these treatments have to be substituted. In this study, other treatments without CrVI compounds, and identified as potential substitutes in aerospace industry have been used and compared to chromic acid anodizing in co-cured Al/CFRP applications. Chromic Acid Anodizing (CAA), Tartaric Sulphuric Anodizing (TSA) and γglycidoxypropyltrimethoxysilane silanization (γ-GPS) treatments have been applied to Al-2024 and characterised in term of galvanic corrosion face to CFRP, and in term of mechanical properties of the interface before and after salt spray exposure. The galvanic corrosion rate has been determined with untreated and treated Al-2024 by the Evans diagram method. The mechanical strength of the interface between Al-2024 and CFRP has been determined with co-cured Al/CFRP single lap joints (SLJ) tensile test in order to asses the mechanical properties of the Al/CFRP interfaces in mode II (in-plane shear).

Experimental

The materials selected for this study are a Al-2024 aluminium alloy (composition in wt.%: 4.4% Cu, 1.50% Mg, 0.6% Mn, Al bal.), and a CFRP quasi-isotropic UD laminate (T700GC/M21, Hexcel Composites) made from prepreg.

For galvanic corrosion measurements, 10 x 10 x 4 mm coupons were cut into a 4 mm thick Al-2024 sheet. 10 x 10 x 4 mm coupons were cut in a CFRP in order to expose the face in contact of the aluminium alloy in the co-cured material as shown on Figure 1. In order to asses the direct galvanic coupling between Al and carbon fibres, a carbon fibres yarn was embedded in isolating resin and polished, to be used as electrode. The surface of the carbon fibres was determined with the number of fibres in the yarn and the diameter of the carbon fibres.

Face in contact with the aluminium alloy For single lap joint tensile tests, 125 x 156 x 8 mm hybrid plates, made of two overlapped foils of Al/CFRP were prepared by a co-curing process (Figure 2). The first foil was made of composite whereas the second one was made of aluminium. Each layer had the same size of 125 x 90 x 4 mm. The overlapping distance was set to 24 mm. The following step were followed for the co-curing process: (i) aluminium sheet was put into the mould, after being prepared; (ii) The plies were deposited according to the stacking sequence; (iii) A two hours dwell at 180°C was performed to consolidate the composite. In addition, a pressure of 6 bars was applied to composite during curing. The Al/CFRP interface was generated before gelation of the polymer when the resin flows from prepreg to the interface; (iv) Finally, four 156 x 24 x 8 mm SJL specimens were machined in the co-cured specimen. Before manufacturing of hybrid materials, the aluminium samples were prepared as follows:

The surface of the alloy samples was cleaned with ethanol and deionised water. Alkaline cleaning of the samples was carried out in a 10% NaOH solution for 2 min at 60 °C. The samples were then rinsed in deionised water and etched in a 30% nitric acid solution for 10 min at room temperature. The samples were then cleaned with deionised water and dried for 30 min at 80°C. Finally, Chromic Acid Anodizing (CAA), Tartaric Sulphuric Anodizing (TSA) or γ-glycidoxypropyltrimethoxysilane silanization (γ-GPS) were used as shown in Table 1. The pre-treated samples were tested in corrosion tests or co-cured with the CFRP before one hour after the pre-treatment.

Process

The galvanic corrosion was evaluated by the Evans method using polarisation curves of aluminium alloy and CFRP specimens separately. The polarisation curves were measured using a model 273A potentiostat in a neutral 3.5% NaCl solution at room temperature (20 °C). The potential scanning rate was 1 mV. s -1 . A saturated Ag/AgCl electrode was used as the reference electrode, and the counter electrode was a platinum wire. The specimens were embedded with epoxy resin to isolate the rear face of the sample and the electric connection, leaving only one face exposed to the solution during the electrochemical measurement. The surface of each specimen was measured before testing and the current densities presented in this paper were normalized to this measured surface.

The durability test of the specimens was conducted during 240h at 35°C in neutral 5% NaCl salt spray according to ASTM B117 with a S120T Salt Spray Chamber from Ascott.

The SLJ mechanical test was carried out with a MTS DY-37 tensile test machine.

Results and discussion

The galvanic current density and potential determination was carried out using the Evans method. This method consists in measuring the polarisation curve of the two constitutive materials in the aggressive media separately and in constructing the galvanic coupling in representing on the same graph, the anodic part of the aluminium polarisation curve and the absolute value of the cathodic part of the composite curve.

The Figure 3 shows the obtained Evans diagrams for unprotected and protected Al-2024 coupled with either the CFRP or the single non-impregnated carbon fibres yarn. For each Aluminium/CFRP or Aluminium/CF yarn configuration the coupling potential and coupling current density was determined by intercept of the anodic part of aluminium curve and the cathodic part of CFRP or carbon fibers yarn curves. An example of the determination of the coupling potential and current density is presented for the unprotected Al-2024/Carbon fibres yarn configuration in the Figure 3. The results obtained for each coupling configuration are summarised in the Table 2. It can be seen that whatever the treatment, a decrease of the galvanic corrosion current can be observed compared to untreated alloy showing the protective effect of either CAA, TSA or γ-GPS treatment. However, the efficiency of the treatment is different depending on whether the coupling has been measured with the CFRP sample or the carbon fibres yarn.

In the case of galvanic coupling with a CFRP sample, the best treatment is γ-GPS with a galvanic current density divided by 2.4 compared with the unprotect Al-2024 alloy, followed by CAA with a galvanic current density divided by 1.9 and TSA with a galvanic current divided by 1.5.

In the case of coupling with a carbon fibres yarn, the best treatment is CAA with a galvanic current divided by 5 compared to the unprotected Al-2024 alloy, followed by γ-GPS with a galvanic current density divided by 3.1 and TSA with a galvanic current density divided by 2.1.

This difference can be explained by the fact that CAA, TSA and γ-GPS don't show the same behaviour on the polarisation curves (Figure 3). It can be seen that TSA and γ-GPS lead to a significant positive potential shift of the Al-2024 polarization curve with only a weak current density reduction at high potential, whereas a very weak positive potential shift of the polarization curve and a strong current density reduction are obtained with CAA Treatment. This difference in behaviour leads to the fact that the efficiency of the CAA treatment compared to TSA or γ-GPS strongly depends on the cathodic part behaviour of the galvanic couple (Al-2024 part). When the galvanic coupling is weak (low zero current potential gap and/or low current density), γ-GPS is better than CAA because of its positive potential shift effect, whereas CAA becomes better than γ-GPS when galvanic coupling is strong (high zero current potential gap and/or high current density) because of its resistive effect inducing current density reduction at high potentials. The Evans diagrams can also compare the effect of carbon fibres themselves on the galvanic coupling between the aluminium alloy and the CFRP. It can be seen from Table 2 that the galvanic current density is about 8 to 25 times higher in the case of direct coupling with a carbon fibres yarn than in the case of coupling with the CFRP. This result shows the fundamental effect of the conductive carbon fibres in the galvanic corrosion behaviour of metal/CFRP structures.

The presence of the epoxy resin between carbon fibres in the CFRP increases the electrical resistance of the interface, and thus reduces the apparent galvanic current density compared to the case of direct coupling of carbon fibres with aluminium alloy. However, it has to be noticed that the galvanic current density measured in this case is obtained by dividing the measured current by the total surface of the CFRP specimen which is constituted of conducting carbon fibres and isolating epoxy resin. Actually, the local current density can probably be as high as the current density measured in the case of direct coupling between aluminium alloy and the carbon fibres yarn, suggesting that if the apparent corrosion rate appears to be low, the local corrosion rate can be very high and damage the interface anyway.

In order to evaluate the damage of the galvanic corrosion on the Al/CFRP interface strength and assess the durability of CAA, TSA and γ-GPS in corrosive environment, SLJ tensile tests were carried out on co-cured specimens before and after aging in a neutral salt spray chamber during 240h at 35°C. Tensile tests were carried out at a constant strain velocity of 1 mm/s until the ultimate load was reached. In order characterize the experimental dispersion, four samples of each configuration were tested. The lap-shear failure stress of the samples are presented on Figure 4. The results are normalized by the failure strength of the CAA specimens before ageing. On this figure, error bars represent the standard deviation of the four measurements. It can be seen from the tensile tests results that the ultimate load is approximately similar before salt spray exposure whatever the treatment of the aluminum foil, showing that TSA and γ-GPS can provide a similar adhesion between aluminum and CFRP compared to CAA treatment. However, it can be seen from the results obtained after salt spray exposure that a strength reduction of about 20% occurs with TSA and γ-GPS, whereas no reduction is observed with CAA treatment. The reduction of strength is lower with TSA and γ-GPS than without any treatment, showing an anticorrosive effect of TSA and γ-GPS, but the protection is not as efficient as CAA treatment.

This result confirms the excellent durability of the CAA treatment in corrosive environment but also confirms the issue of substituting CAA with a REACh compliant treatment providing similar performances.

Conclusion and perspectives

A process of co-curing Al/CFRP structures was presented. Several surface treatments of the aluminium alloy were used to improve the interface properties between the polymer matrix of the composite and the aluminium substrate. These surface treatments were characterized in terms of galvanic corrosion resistance and residual properties of the interface after ageing. The galvanic corrosion behaviour was measured by the Evans diagram method, and the interface properties were assessed using the SLJ tensile test before and after neutral salt spray exposure.

According to the Evans diagrams, it appeared that the γ-GPS and TSA can give a better corrosion protection than CAA in weak coupling case, but that CAA is still the best treatment in case of strong coupling. In our Al-2024/CFRP case, where the galvanic coupling was measured to be weak, it was shown that γ-GPS gave the best protection in 3.5% NaCl solution.

According to the results of the SLJ tests, the three tested treatments of the aluminium alloy gave a similar interface strength of the interface just after co-curing, showing that TSA or γ-GPS can provide a good adhesion of the interface.

However, as it has been shown that a 20% reduction of the interface strength was obtained after 240h salt spray exposure with TSA and γ-GPS whereas no reduction is observed with CAA. This result highlight the very good durability of CAA treatment compared to the TSA and γ-GPS one.

It therefore appears from this study that TSA and γ-GPS appear to be suitable candidates for the substitution of CAA treatments in terms of adhesion and initial mechanical properties, but the long term anti-corrosion properties of TSA and γ-GPS is not durable enough, inducing mechanical strength reduction after corrosive environment exposure, which is detrimental for aerospace applications.

It thus appears important to work on alternative solutions like surface treatment improvement or electrical isolation between the CFRP and the alloy without degrading the adhesion in order to isolate aluminium from CFRP and prevent galvanic corrosion in Al/CFRP hybrid structures.

Figure 1 :

 1 Figure 1: Description of the CFRP used in the study and identification of the face tested in galvanic corrosion measurements.

Figure 2 :

 2 Figure 2: Al/composite specimen preparation for SLJ tensile tests.

Figure 3 :

 3 Figure 3: Evans diagrams obtained for untreated and treated Al-2024 alloy coupled with a CFRP specimen and a carbon fibers yarn.

Figure 4 :

 4 Figure 4: Effect of aluminium pre-treatments on the tensile strength of Al-2024/CFRP interface before and after 240h salt spray test on co-cured single lap joint specimens.

Table 1 :

 1 Surface treatments of the aluminium samples before corrosion tests or co-curing of hybrid material specimens.

Table 2 :

 2 Potential and coupling current density for coupling between untreated and treatedAl-2024/CFRP, and between untreated and treated Al-2024/carbon fiber yarn.