Yacine Bentaleb
email: y.bentaleb@imperial.ac.uk

R Émi Manceau
email: remi.manceau@univ-poitiers.fr

A HYBRID TEMPORAL LES/RANS FORMULATION BASED ON A TWO-EQUATION SUBFILTER MODEL

, which tends to the same RANS model in the RANS zones, but uses the Detached Eddy Simulation (DES) methodology to control the transition from RANS to LES. The paper discusses the features and capabilities of both approaches.

INTRODUCTION

Traditional Reynolds-Averaged Navier-Stokes (RANS) modelling is gradually replaced by hybrid RANS-LES methodologies for predicting complex turbulent flows in industrial practice. This trend has been encouraged by the increasing availability of high-performance computing, and the need of resolving unsteady phenomena at elevated Reynolds numbers. Especially, flows that entail separation from curved surfaces, featuring extremely high level of turbulence energy and shear stress in the separated shear layer, are still beyond the Large-Eddy Simulation (LES) capabilities. The standard compromise strategy is the use of "unsteady" RANS-based solution in the near-wall region, and resolved-scale motions in the rest of the domain. Some of these schemes may suffer from the absence of a theoretical formalism leading to unclear dividing line between the RANS and LES components [START_REF] Gatski | Current trends in modeling research for turbulent aerodynamic flows[END_REF].

In the present paper, a consistant seamless hybrid temporal LES/RANS formulation based on a two-equation sub-filter model is develpped. The SST RANS model is selected as the basis to derive the subfilter-stress model because of its capacity to account for the near-wall region, which is an essential point for such a hybrid modelling strategy, and because it proved reasonably accurate in aerodynamic flows with adverse pressure gradients and separation, and more generally in industrial applications [START_REF] Menter | Ten Years of Industrial Experience with the SST Turbulence Model[END_REF]. It is thus expected that the hybrid TLES/RANS model can be successfully incorporated into industrial and commercial codes.

A second approach is considered in this work, the DES-SST model [START_REF] Menter | Ten Years of Industrial Experience with the SST Turbulence Model[END_REF]. Recently, [START_REF] Manceau | Of the interpretation of DES as a hybrid RANS/Temporal LES method[END_REF] has argued that, under certain conditions, an equivalence between DES and TPITM can be found. Therefore, a fair comparison is aimed herein. The two formulations are implemented into the same finite volume code, and applied to the turbulent channel flow with periodic arrangement of hill constriction, at Reynolds number 10595, for which a detailed reference database is available [START_REF] Froehlich | Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions[END_REF].

In the following, the TPITM-based modelling approach is summarised; then the key features of the DES-SST formulation is briefly presented. Finally, the results are discussed in comparison with the LES reference data.

MODELLING APPROACH

The TPITM model (Fadai-Ghotbi et al., 2010b) is derived from the exact transport equation for the Eulerian temporal energy spectrum, by integrating over frequency intervals (hence the name partially integrated transport model). It is the adaptation to temporal filtering of the PITM model [START_REF] Schiestel | Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations[END_REF], and is based on the introduction of two temporal filters, in order to decompose the Eulerian temporal energy spectrum into resolved scales, energetic subfilter scales and dissipative subfilter scales. This methodology enables a continuous transition from TLES to RANS, controlled by imposed variations of the temporal filter widths. The consistency of the time filtering process with the Reynolds aver-1 age in the RANS limit and the formal similarity between the filtered and Reynolds-averaged equations has been adressed in detail in Fadai-Ghotbi et al. (2010b) and this development is not repeated herein.

The subfilter model

Let us denote the instantaneous velocity by u i , the longtime averaging operator by . and the temporal filtering operator by . . By applying the temporal filter to the Navier-Stokes equations and contracting the subfilter-scale tensor (τ i j SFS ) equation, it can be shown that, similarly to the case of spatial filtering [START_REF] Germano | Turbulence: the filtering approach[END_REF], the transport equation of the subfilter kinetic energy k SFS is formally identical to the familiar RANS equation for the total fluctuating kinetic energy k. The latter can be exactly decomposed ( (see Fadai-Ghotbi et al., 2010b)) into the sum of a modelled part k m and resolved part k r as:

k = k m + k r , k m = k SFS , k r = 1 2 u i u i -u u i (1)
In the present work, transport equations for k m and ω m = ω SFS are derived by transforming the k -ε model. Thus, the twoequation subfilter model writes:

Dk m Dt = P m -C µ ω m k m + ∂ ∂ x j (ν + σ k ν t m ) ∂ k m ∂ x j (2) Dω m Dt = γ P m ν t m -β * ω 2 m + ∂ ∂ x j (ν + σ ω ν t m ) ∂ ω m ∂ x j + 2 (1 -F 1 ) σ ω 2 ω m ∂ k m ∂ x j ∂ ω m ∂ x j ( 3
)
where

P m = τ i j m ∂ u i ∂ x j = ν t m ∂ u i ∂ x j + ∂ u j ∂ x i ∂ u i ∂ x j = ν t m S 2 (4) ν t m = a 1 k m max(a 1 ω m , S F 2 ) (5)
and the subscript m denoting the modelled part. In order to ensure the correct RANS limit of the model, the constants appearing in the "partial" turbulent viscosity, ν t m (Eq. 5), and in the transport equations (Eqs. 2 and 3) are the same as in the SST RANS model [START_REF] Menter | Ten Years of Industrial Experience with the SST Turbulence Model[END_REF], except for the β * coefficient in the ω m -equation, which is dependent on the temporal filter width, and ensures the transition from RANS to TLES. Note that F 1 and F 2 are the blending functions used in the original SST model, but the variables k and ω are replaced by their modelled (unresolved) contributions:

F 1 = tanh(arg 4 1 ) (6)
F 2 = tanh(arg 2 2 ) (7) arg 1 = min max k 1/2 m C µ ω m y , 500 ν y 2 ω m , 4 ρ σ ω 2 k m CD kω y 2 (8) arg 2 = max 2 k 1/2 m C µ ω m y , 500 ν y 2 ω m (9)
with

CD kω = max 2 ρ σ ω 2 1 ω m ∂ k m ∂ x i ∂ ω m ∂ x i
, 10 -20 and y being the distance to the nearest wall.

It is found that the function β * can be derived in a simi- lar way to what was proposed, in the spatial filtering context, by [START_REF] Schiestel | Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations[END_REF] for the variable coefficient

C * ε 2 = C ε 1 + r(C ε 2 -C ε 1 ) in the ε m -equation, which leads to β * = C µ γ + r (β -C µ γ) (10)
Alternatively, it can be deduced from a change of variables in the k-ε equations, through the relations:

γ = C ε 1 -1, β = C µ (C ε 2 -1), β * = C µ (C * ε 2 -1) (11)
In Eq. 10, the amount of long-time averaged modelled energy (and therefore, the amount of resolved energy), i.e., the transition from TLES to RANS, is driven by the value of the energy ratio

r = k m k (12)
To control effectively the energy partitioning and therefore enforce the desired behavior of the model, the above parameter has to be linked to the grid size. This issue is briefly adressed in the following section.

Dependence on the filter width

Using an equilibrium Eulerian temporal spectrum, it was shown by Fadai-Ghotbi et al. (2010b) that the energy ratio r can be related to the temporal filter width ∆ T by

r = β -1 0 ω c C µ ω -2 3 , β 0 = 2 3C K ≃ 0.44 (13)
where ω c is the cutoff frequency ω c = π/∆ T and C K the Kolmogorov constant. The sweeping hypothesis of [START_REF] Tennekes | Eulerian and Lagrangian time microscales in isotropic turbulence[END_REF] leads to using the dispersion relation ω = √ kκ to link the frequency and wavenumber domains, such that the temporal filter width is related to the grid by ∆ T = (∆x∆y∆z) 1/3 / √ k. The role of the coefficient β 0 is of importance since it is in- volved in the energy ratio r, and its effect will be investigated.

In the present study, in order to enforce the RANS mode in the near-wall region (r = 1), as well as to better control the key parameter r, the function β * is modified by introducing the blending function F 2 (Eqs. 7 and 9). The empirical formulation used in practice writes

β * = C µ γ + F 2 + (1 -F 2 ) r observed (β -C µ γ) + min α r target r observed -1 , 0 (14)
In this relation, the third term is a dynamic modification of the coefficient (Fadai-Ghotbi et al., 2010a), aiming at sustaining the correct level of resolved energy even in regions where resolved fluctuations are not promoted by the presence of a mean shear. Thus, r observed is the energy ratio k m /k, extracted from an on-the-fly averaging of the filtered fields through Eq. 1, and r target is the desired energy ratio given by Eq. 13. The constant α, set to 10 in the present calculations, is influencial in the early stages of the computation only, before the statistical sampling commence. The final result is therefore independent of this parameter.

THE DES-SST FORMULATION

A second hybrid RANS/LES model is considered in this paper, based on the widely used Detached Eddy Simulation (DES) methodology. The selected underlyind RANS model is the same as in the TPITM approach. The motivation is twofold. First, as mentioned in the introduction, the SST model has shown improved capabilities in separated shear layers, combined with its robustness and industrial applicability. Second, the resulting hybrid formulation allows consistent comparison with the above TPITM based approach. The latter reason is supported by the fact that [START_REF] Manceau | Of the interpretation of DES as a hybrid RANS/Temporal LES method[END_REF] has recently shown that an equivalence between DES and TPITM can be found provided that they give the same level of subfilter energy. However, the strict equivalence is not the aim of this paper. Rather, a separate investigation is conducted on the DES-SST model, focusing on its well known calibration constant, which is specific to the present flow configuration. Subsequently, a comparison of both the approaches will be presented. Several options for the DES-limiter may be derived [START_REF] Menter | Ten Years of Industrial Experience with the SST Turbulence Model[END_REF]. The modification in the SST model retained here is based on the blending function F 2 (Eqs. 7 and 9). Hence, the following factor

F DES = max L t C des ∆ (1 -F 2 ), 1 , L t = √ k C µ ω (15)
is introduced in the dissipation term of the k-equation, ∆ being the maximum local grid spacing. In the present work, the sensitivity to the calibration constant C des was carefully examined. A selection of values ranging from 0.1 to 0.6 was subjected to decaying isotropic turbulence study as well as to full computations of the present flow test case.

THE COMPUTATIONAL APPROACH

Filtered momentum and continuity equations for incompressilbe flow were solved using the finite volume based software Code Saturne [START_REF] Archambeau | Code saturne: a finite volume code for the computation of turbulent incompressible flows -industrial applications[END_REF]. The numerics relies on a SIMPLEC algorithm with a Rhie and Chow (1983) interpolation in the pressure correction step. As in the transport equations for the filtered momentum, the convective fluxes in the subfilter model transport equations (Eqs. 2 and 3) are approximated by second-order centred discretizations. The time-marching is based on a second-order, Crank-Nicolson scheme.

Simulations were performed with several grids of different streamwise and spanwise refinement. These are summarised in table 1. The streamwise variation of the cell dimensions along the bottom wall, normalized by the local friction velocity, are shown in Fig. 1. For the grid M1 (160 × 100 × 30), the distance of the first node off wall is ∆y + /2 < 0.6 (Fig. 1a) for both the approaches. The streamwise (∆x + ) and spanwise (∆z + ) cell dimensions are reported in Fig. 1b. Within the range x/h = 0 -5, ∆x + < 50 and ∆z + < 75. With the TPITM approach, three spanwise refinements were considered (see Tab. 1). In grid M3, the spanwise cell dimension is reduced such as ∆z + < 40 (Fig. 1c).

Statisical properties were gathered during 80 flowthrough times, whose convergence was increased by averaging in the spanwise direction. Finally, the results were examined in comparison with LES reference data [START_REF] Froehlich | Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions[END_REF].

RESULTS

The separation and reattachment locations of most relevant computations are reported in Tab. 1. For the DES approach, the sensitivity study to the parameter C des shows that values above 0.4 (e.g. C des = 0.5) lead to poor predictions with excessively long separation, though less than the pure SST model (Tab. 1). It is even found that the calculations degenerate into stationary mode for C des > 0.5, including then the standard value 0.6. Visual inspection of the structures present in the resolved field, through the isocontours of the Q-criterion shown in Fig. 2, reports on the too low resolution level with C des = 0.5. In comparison with 0.4, only very large scale structures are obtained. Smaller values of the C des constant, within the range 0.1 -0.3, were also considered and provided (statistically) a very good agreement with the reference data. However, observation of small globular structures (via the Q-criterion), confirmed by a decaying isotropic turbulence study revealed a wrong amount of energy dissipation, which is the indication that the fluctuations generated by decreasing the C des parameter correspond to a white noise rather to resolved turbulence. It is found, therefore, that the optimal value corresponds to C des = 0.4, and is retained herein for comparison purposes (labelled as DES-04 in the figures).

In the TPITM approach, two values of the key parameter β 0 are considered, 0.2 and 0.4. The latter, close to the the- oretical value (0.44), leads to a lower level of the modelled part of the turbulence energy, and this is found to be necessary in the present case. In fact, β 0 = 0.2 provides similar results to SST predictions. It is worth mentioning that in the present paper, the emphasis is on the TPITM approach development. The grid refinement effect is then conveyed for this model. The grid L1 appears too coarse in the streamwise direction (too late separation and long separation) and is discarded. For β 0 = 0.4, the statistics (not included for the grids M2 and M3, except the separation and reattachment positions -Tab. 1) show that the spanwise refinement is of little consequence. The grid M1 (160 × 100 × 30) is then singled out for discussions and comparisons with the DES results and reference LES data.

The overall view of the performance of the models is conveyed in Figs. 345, which show the skin-friction coefficient, the streamwise velocity and shear-stress profiles, respectively. Using the optimal constants (β 0 = 0.4 and C des = 0.4), the capability of both strategies to reproduce the main flow features is demonstrated, and it is observed that x/h (c)

Figure 1: Size of the wall-adjacent cells in wall units along the bottom wall.

the two models provide very similar results, which is an indirect confirmation of the theoretical equivalence established by [START_REF] Manceau | Of the interpretation of DES as a hybrid RANS/Temporal LES method[END_REF]. In particular, although reattachment is slightly too late, its location is much better predicted than with the TPITM-02 (i.e., with β 0 = 0.2) and SST (2D) mod- els (see table 1). Except near the reattachment region (within the range x/h = 4 -6), the shear stress shown in figure 5 is well predicted by the optimal hybrid models, which prevents the steep velocity profile observed in both SST and TPITM-02 predictions.

The "observed" energy ratio r is shown in Fig. 6. It can be seen that, at the wall, although the computation are in RANS mode, r goes to zero, because of the wrong asymptotic behaviour of the modelled turbulent energy provided by the SST model. Consequently, using r as an indicator of the energy partitioning between resolved and modelled scales is meaningful only outside of the near-wall region. Here, a significant difference between the TPITM and DES approaches can be identified: in the centre of the channel, modelled scales contribute to 30% of the total turbulent energy for the TPITM (β 0 = 0.4), and only to 10% in DES. The effective control of the amount of modelled energy through the parameter β 0 is also demonstrated. Decreasing this values to β 0 = 0.2 in- creases the modelled contribution to around 50 -60%, which degrades the model predictions.

Interestingly, the distribution of the time-averaged function β * (Eq. 14) in the TPITM approach, shown in figure 7, provides a good picture of the energy partition in the whole domain. High values correspond to the RANS mode, and low values to the LES mode. When β 0 = 0.2 is used (Fig. 7a), a substantial portion of the central domain is computed in nearly RANS mode, while β 0 = 0.4 (Fig. 7b) allows a larger part of the separated shear layer and reversed flow to be computed in LES mode. The influence of the blending function F 2 , used in both the approaches to "protect" the boundary layer from the limiters (Eqs. 14 and 15) by enforcing the RANS mode (F 2 = 1 -upper limit), deserves to be mentioned. Figure 8 shows the contours of the time-averaged functions F 1 and F 2 . These may be regarded as an a-posteriori (qualitative) indication on how the energy parameter ratio r observed in Eq. 14 is affected through the computational domain. Note that F 1 need to be viewed with caution as it is not effectively used to this purpose. In the TPITM computations (8b and 8d), it can be observed that F 2 is active in a substantial portion of the domain, even well outside the near-wall region, especially for β 0 = 0.2. This is not the case in the DES model (Fig. 8f). These observations are consistent with the predictions discussed above. Figure 8c suggests that F 1 would be a more adequate function in the TPITM approach, leading to promising capabilities.

SUMMARY

The Temporal Partially-Integrated Transport Model approach, which is based on a consistent formalism for seamless hybrid temporal LES/RANS methodologies was exploited to derive a two-equation subfilter model. The k -ω SST model was selected as the RANS underlying model due to its reasonably accurate performances in engineering practice. The resulting hybrid model was subjected to a complex flow configuration involving separation from a curved surface. The predictive capabilities of the model was demonstrated in terms of mean-flow topology, shear-stress level and flexibility in controling the amount of the modelled energy. It was also found that the model is comparable with an equivalent DES formulation, when the optimal calibration constants are used. Finally, from these developments, improved modelling proposals may be formulated, for instance, through a better control of the energy partitioning. This route is under inverstigation.

ACKNOWLEDGMENT

This work was granted access to the HPC resources of IDRIS under the allocation 2010-020912 made by GENCI (Grand Equipement National de Calcul Intensif).

  Figure 2: Isocontour Q = -1 2 ∂ u i ∂ x j ∂ u j ∂ x i = 0.2 -View from the top -Grid M1.

)Figure 3 :

 3 Figure 3: Skin-friction coefficient along the bottom wall -Grid M1.

  Figure 4: Streamwise velocity profiles -Grid M1.

Figure 6 :

 6 Figure 6: Ratio of modelled energy -Grid M1 (for legend see previous figure).

Figure 7 :

 7 Figure 7: Contours of the time-averaged function β * (see Eq. 14) in the TPITM approach -Grid M1.

  (a) Function F 1 in TPITM -β 0 = 0.2. (b) Function F 2 in TPITM -β 0 = 0.2. (c) Function F 1 in TPITM -β 0 = 0.4. (d) Function F 2 in TPITM -β 0 = 0.4. (e) Function F 1 in DES -C des = 0.4. (f) Function F 2 in DES -C des = 0.4.

Figure 8 :

 8 Figure 8: Contours of the time-averaged blending functions F 1 and F 2 (Eqs. 6 -9) -Grid M1.

Table 1 :

 1 Summary of the computations; CC: calibration constant (β 0 in TPITM -Eq. 13 and C des in DES), (.) s : separation point, (.) r : reattachment point.

									Model					Grid				CC (x/h) s (x/h) r
									SST					160 × 100 (M)		-	0.23		7.47
									TPITM				80 × 100 × 30 (L1)		0.2	0.25		7.70
									TPITM			160 × 100 × 30 (M1) 0.2	0.21		7.71
									TPITM			160 × 100 × 30 (M1) 0.4	0.19		5.25
									TPITM			160 × 100 × 45 (M2) 0.4	0.19		5.25
									TPITM			160 × 100 × 60 (M3) 0.4	0.17		5.36
									DES				160 × 100 × 30 (M1) 0.4	0.17		5.14
									DES				160 × 100 × 30 (M1) 0.5	0.21		6.01
					LES (Froehlich et al., 2005)		196 × 128 × 186		-	0.22		4.72
	0.5 0.6		∆y + /2 TPITM-04 M1 ∆y + /2 DES-04 M1					150			∆x + TPITM-04 M1 ∆x + DES-04 M1 ∆z + TPITM-04 M1 ∆z + DES-04 M1					150			∆z + TPITM-04 M1 ∆z + TPITM-04 M2 ∆z + TPITM-04 M3
	0.4
	0.3									100										100
	0.2
										50										50
	0.1
	0									0										0
	0	1	2	3	4	5	6	7	8	9	0	1	2	3	4	5	6	7	8	9	0	1	2	3	4	5	6	7	8	9
					x/h										x/h
					(a)										(b)


Guilhem Brunel
email: guilhem.brunel@cirad.fr

Philippe Borianne

Gérard Subsol

Marc Jaeger

Yves Caraglio

Defining reliability coefficients in an automated radial file identification and characterization method in microscopic images of gymnosperms

Keywords: image processing, wood microscopic images, radial file identification, a priori reliability

Highlights:

The analysis of wood anatomical sections is of great interest for understanding the growth and development of plants. We propose a novel method for automatically identifying and characterizing radial files in wood microscopic images of gymnosperms. A key point is to be able to assign a priori reliability coefficient to the results, particularly for statistical processing in large-scale analyses. We describe in this paper the principle used to establish reliability coefficients to evaluate the radial file identification process and the geometrical measurements of cells and their components.

INTRODUCTION

Wood structure reflects the physiological and molecular regulation of cambium activity [START_REF] Cato | Wood formation from the base to the crown in Pinus radiata: gradients of tracheid wall thickness, wood density, radial growth rate and gene expression[END_REF] and also registers environmental conditions [START_REF] Barlow | Predicting the environmental thresholds for cambial and secondary vascular tissue development in stems of hybrid aspen[END_REF]. Understanding cambium growth mechanisms calls for a study of cell pattern regularity, and of cell disruption or modification in space and time [START_REF] Liang | Wood structure of biotically and climatically induced light rings in eastern larch (Larix laricina)[END_REF]. Two types of organizations are considered: the growth ring representing cell production at a given time, and the radial file representing the activity of an initial cell over time [START_REF] Rozenberg | Clonal variation of indirect cambium reaction to within-growing season temperature changes in Douglas-fir[END_REF]); radial files help in understanding the development, differentiation and temporal changes of cells.

Morphological fluctuations of successive cells along a radial file and the influence of external factors have been investigated for a long time [START_REF] Ford | Influence of environmental factors on cell production and differentiation in the early wood of Picea sitchensis[END_REF]), but those investigations were greatly restricted by a limited number of radial file comparisons and a restrictive number of successive cell descriptions. Those studies, concerning secondary growth and its relationships with primary growth, were based on fragmentary studies, due to high acquisition and processing costs. Large-scale studies for understanding wood growth and disturbance are available nowadays thanks to automated radial file identification and cell characterization [START_REF] Brunel | Automatic characterization of the cell organization in light microscopic images of wood: application to the identification of the cell files[END_REF], Kennel et al. 2011). In fact, wood continuously records changes in the development of the tree. Such new methodologies and approaches offer real new opportunities for more in-depth investigations of tree biology and climate change [START_REF] Fonti | Studying global change through investigation of the plastic responses of xylem anatomy in tree rings[END_REF]. The size and shape fluctuations observed along radial files are usually considered to be the result of external constraints [START_REF] Frankenstein | The onset of cambium activity -A matter of agreement?[END_REF]. This is a restrictive and simplified viewpoint: these fluctuations are probably due to a combination of external and internal factors. We aim to promote an objective quantification of these measurements, on the basis of statistics based on numerous image datasets.

This paper focuses on the reliability of such data from statistical studies, i.e. produced by automated radial file identification [START_REF] Brunel | Automatic characterization of the cell organization in light microscopic images of wood: application to the identification of the cell files[END_REF]. For large-scale data analyses, it is necessary to ensure a posteriori that the measurements are valid in order to find invariants or validate hypotheses. This is a classic line taken in statistics [START_REF] Bruton | Reliability: What is it, and how is it measured?[END_REF] and experimental approaches.

MATERIALS

We processed histological sections of several gymnosperm species: Pinus caramanica, Pinus nigra and Abies alba. Wood cross-sections with a thickness of 20 μm were produced with a vibratome. The sections were stained to increase the contrast between the lumen and cell walls. They were then digitized with an Olympus DP71 LCD camera on an Olympus BX51 microscope. The square color images produced had a resolution of 4 million pixels.

OVERVIEW OF THE METHOD

Radial files are alignments of substantially similar cells in terms of color dynamics, shapes and sizes. Intuitively, the notion of cell alignment implies the existence of cellular organization based on the neighborhood relationships between cells. Those properties are used to identify radial files.

Our approach, described in [START_REF] Brunel | Automatic characterization of the cell organization in light microscopic images of wood: application to the identification of the cell files[END_REF]) was divided into three steps: cell identification which specified single cells, cell organization which detected radial files, and cell classification which gave the biological and qualitative typing of cells and radial files.

The incremental construction of radial files was based on two assumptions: (i) such a file is independent from image orientation; (ii) two consecutive cells of a file are very similar. From a methodological point of view, cell individualization was derived from a watershed algorithm [START_REF] Vincent | Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations[END_REF], and the cell pattern was described by an adjacency graph created from the watershed crest lines. Radial files were then built by finding a reversible path in the under spatial constraints (maintaining a specific direction) and similarity constraints (two consecutive cells should show close geometric characteristics). Our method produced several layers of results, respectively corresponding to different observation levels: (i) radial files were classified according to their length, their fractionation and their cell self-similarity, (ii) cells were characterized by geometric parameters (such as size, diameter, shape, etc.) and topological parameters (number of neighbors), (iii) cell component elements (wall, lumen) were characterized by geometric parameters (size, thickness, diameter, etc.).

DEFINITION OF A PRIORI RELIABILITY COEFFICIENTS

Quality assessment of these results depends on many factors. It concerns the data set itself (image noise, biological configuration complexity, etc.), the process (algorithm approximations, computation costs, stability, etc.), and the geometrical scale (related to the observation level). Each result should be qualified using different indicators, notably to keep the significant outcome while processing high volume data. It is thus relevant to assign an estimated reliability coefficient to each result. We illustrate cases on file and cell scales.

Radial file construction reliability. We propose defining this radial file reliability coefficient R f from three criteria: length, fractionation and similarity. The first criterion derives from the file length, L f , compared to the threshold value T. T is set by 2means and defines the minimum significant length. Fractionation is evaluated from the file construction algorithmic cost. It involves the total number of cells L fm stacked to build the file, the length L f of the file, and the number of sections N f . The similarity criterion is built from the product of the n-1 consecutive cell surface variations. The final reliability coefficient R f of the file f is then defined by a product of normalized terms ranging between 0 and 1. When this coefficient tends to 1, the reliability of the radial file increases.

𝑅 𝑓 = �1 -𝑚𝑎𝑥 � 𝑇 -𝐿 𝑓 𝑇 , 0�� �1 - 𝐿 𝑓𝑚 -𝐿 𝑓 𝑁 𝑓 * 𝐿 𝑓𝑚 � �(1 - �𝑆𝑓 𝑗 -𝑆𝑓 𝑗+1 � 𝑆𝑓 𝑗 + 𝑆𝑓 𝑗+1 ) 𝑛-1 𝑗=0
Lumen area estimation reliability. The reliability coefficient of the lumen surface is defined on a similar principle, by a product of two normalized terms, based on the cell size and an image local blur estimation. In fact, the watershed algorithm is known as a robust method for extracting cell boundaries, since it is based on intensity discontinuities which are less sensitive to blurring, whereas the lumen area shows high sensitivity to local blur. The cell area definition involves a two-class clustering split, corresponding to the lower and the higher intensity classes. The local blur estimator is derived from [START_REF] Ladjal | Blur estimation in Natural Images, 15 e congrès francophone AFRIF-AFIA Reconnaissance des Formes et Intelligence Artificielle[END_REF], based on the relationship between local dynamics and intensity differences.

EXPERIMENTS, CONLUSION AND WORK IN PROGRESS

Experiments were performed on ten colored sections of different species of gymnosperms, representative of biological variability. The color quantifies the reliability results, both on a global (Fig. 1) and local (Fig. 2) scale. On a global scale, we can see in Fig. 1 that the reliability estimator properly qualifies the cell files: green colors are assigned to straight and regular cell lines whereas red colors correspond to incomplete cells on the side of the image or incrusted cells. Such a color map alerts the expert to potential unsure classifications and emphasizes the ambiguous biological status of a file or cells. On a local scale, for lumen area computation, the estimator also retrieves obvious cases. The reliability factor also ensures areas showing lower intensity variations (areas in green in Fig. 2, right).

Several points were studied. (i) in angiosperms, the vessel morphology is different and calls for a different evaluation of cell similarity which defines the third term of the file reliability coefficient, by taking into account the larger diameter instead of its surface. (ii) other blur estimators were studied, such as estimators based on multi-scale filtering in order to assess the independence of the reliability coefficient with respect to the blur estimation method. (iii) how the local reliability coefficient could be used to correct the measured values according to the local blur estimator relationship (Fig 2 . Left).

To conclude, we introduced some reliability coefficients for image processing related to cell organization identification and illustrated the cases of radial file detection and of lumen area computation. The reliability coefficients were essentielly used to filter the input data of statistical studies conducted by botanists or to draw attention to special biological configurations.

Fig. 1 .

 1 Fig. 1. Left: cross-section of Abies alba. Right: automated identification of radial files. Color value qualifies the reliability coefficient: weakly reliable files appear in red tones and highly reliable files are in green tones.

Fig. 2 .

 2 Fig.2. Left: relationship between a Gaussian blur applied to a cell image and the local blur estimator. The estimator emphasizes the blur tendency; red crosses stand for five microscopic optical blurs, matched from their area variance. Right: the five corresponding lumen areas from the optical blurs: the color qualifies the reliability coefficient, from green for the real lumen area to orange for the reduced lumen area.

The authors acknowledge NUMEV Labex and SIBAGHE Graduate School of the University of Montpellier 2 for their support.

LITERATURE CITED


Thomas Forgione
email: thomas.forgione@irit.fr

Axel Carlier
email: axel.carlier@enseeiht.fr

Géraldine Morin
email: morin@enseeiht.fr

Wei Tsang Ooi

Vincent Charvillat

Praveen Kumar
email: praveen@comp.nus.edu.sg

An Implementation of a DASH Client for Browsing Networked Virtual Environment

We demonstrate the use of DASH, a widely-deployed standard for streaming video content, for streaming 3D content in an NVE (Networked Virtual Environment) consisting of 3D geometry and associated textures. We have developed a DASH client for NVE to show how NVE benefits from the advantages of DASH: it offers a scalable, easy-to-deploy 3D streaming framework. In our system, the 3D content is first statically partitioned into compliant DASH data, and metadata is provided in order for the client to manage which data to download. Based on a proposed utility metric for geometry and texture at the different resolution, the client can choose the content to request depending on its viewpoint. We effectively provide a Web-based client to navigate through our sample 3D scene, while deriving the streaming requests from its computation of the necessary online parameters, in a receiverdriven manner.

INTRODUCTION

Dynamic Adaptive Streaming over HTTP (DASH), or MPEG-DASH, is now a widely deployed international standard for streaming adaptive video content on the Web. The merit of DASH is its simplicity and its scalability. DASH uses the existing World Wide Web infrastructure and protocols, and so provides a scalable, easy to deploy video streaming framework in an HTTP supported network. In this technical demonstration, we demonstrate how DASH can be used for another application and media type -a freely navigable, https://doi.org/10.1145/3240508.3241398 networked virtual environment (NVE) consisting of 3D meshes with textures.

Zampoglou et al. have been the rst to propose using DASH to stream 3D content [START_REF] Zampoglou | Adaptive streaming of complex Web 3D scenes based on the MPEG-DASH standard[END_REF]. The authors organize the content, following DASH terminology, into a scene graph containing multiple resolutions for each model of the scene. Their approach targets several objects but does not handle the case of large NVEs, for which view-dependent streaming is desirable.

In [START_REF] Forgione | Impact of 3D Bookmarks on Navigation and Streaming in a Networked Virtual Environment[END_REF], view-dependent 3D streaming has been investigated and uses frustum and back-face culling by the server to decide the set of polygons to be streamed to a client. The drawback of this method is its lack of scalability.

Using the DASH methodology, we are able to reorganize the 3D data into DASH compliant segments and provide metadata, so that the client computes the necessary parameters to determine which parts of the content it should download. The server is only used to store data segments and related information.

CONTENT PREPARATION

This section details the DASH compliant organization of the 3D data modeling the NVE, that is, a polygon soup and texture les, and the associated metadata. This corresponds to the o ine computation of the 3D content stored in the server.

The MPD le. The Media Presentation Description (MPD) le is an XML le de ned in DASH to provide global information about the content storage and access. In our 3D NVE use case, this information is based on spatial location, content resolution, or size. In the next paragraphs, we describe the organization of the 3D data to be streamed, and the corresponding MPD.

Geometry management. We spatially partition the faces of the scene using a k-d tree and further divide each cell into segments of a xed number of faces, grouping faces of comparable area. Each segment is stored in a .obj le. We encode in the MPD the coordinates of each cell's bounding box, as well as the total 3D area of their constituting polygons and the size (in bytes) of their associated OBJ les.

The uncommonly large faces are stored in a separate segment (e.g., the water in gure 1), since they are essential to the model and do not t into cells.

Texture management. Each texture of the model is stored in multiple PNG les at di erent resolutions. The MPD contains the size in bytes of each image le, the number of faces that use this texture, as well as the average color of each texture so that a client can render the corresponding faces with a uniform color when the texture has not been loaded yet. We also encode the MSE between the texture and its highest available resolution, so that a client is able to tell how important it is.

DASH 3D CLIENT

Once the 3D content is organized as described in the last section, we simply put all this data on a regular static HTTP server. In this section, we describe the implemented greedy DASH NVE client that exploits the preparation of the 3D content in an NVE for streaming.

Implementation of the client

We propose a Web-based client that uses XML HTTP requests to download content. The client takes into account some known parameters (e.g., position, the eld of view, etc.) to decide which segment to request next. When a segment is received, it is added to a scene that is rendered using Three.js, and another one is queried. Since we run the server locally, in order to have realistic results, we con gure the local network to limit the bandwidth to 5 Mbps.

Streaming policy

The rst data fetched by our client is the MPD le. Once this le is retrieved, the client is able to identify the segment containing the large faces (mentioned in Section 2) and to understand the k-d tree structure of the scene. It downloads the outlying faces as well as the corresponding textures. Based on its current viewpoint, the client computes a utility for each segment, in order to decide whether it should download geometry or texture, and which resolution to download. The segment s * to be downloaded is the one that optimizes the criterion:

s * = argmax s ∈S utility(s) size (s)
.

The client computes the intersection between the k-d tree BB (bounding boxes), its frustum, and sets the utility of a BB outside the frustum to 0. Otherwise, utility is proportional to the total 3D area of the faces that it contains (MPD information) and inversely proportional to the squared distance between the camera and the center of the corresponding bounding box (computed online by the client). The client weight the utility of a texture based on the utilities of the received geometry segments that refer to it. More information is available in [START_REF] Thomas Forgione | DASH for 3D Networked Virtual Environment[END_REF].

User interface

For browsing through the scene, we implemented classical interactions in 3D navigation. First, the pointer lock API allows the user to turn the camera just like in a rst-person view video game. The user moves the camera with the keys W, A, S and D. Unlike in video games, this interface o ers no physical simulation so the user can y around the scene. The height also increases or decreases using the mouse wheel. Pressing the space key increases the speed of the camera, which is useful to move quickly to another part of the scene; releasing this key allows more precise motion.

Rendering optimization

For rendering, we limit the number of WebGL calls: we keep faces that share the same texture in the same vertex bu er. The MPD indicates how many faces are needed for each texture; thus the client can allocate the exact size for the vertex bu ers. When more faces are received, the preallocated vertex bu er corresponding to the right texture is just lled. Thus the client bene ts from the MPD information to avoid successive memory allocation and copy and to keep only one face bu er per texture. The textures are initialized by an image containing a single pixel of the average color, and whenever a higher resolution image arrives, the client updates the texture.

Figure 1 :

 1 Figure1: The sample 3D scene and an arbitrary viewport, with partitioning bounding boxes delimited with red edges. In white, the regions that fall outside the eld of view of the camera; in blue, the regions inside the eld of view of the camera.

DEMONSTRATION

The demonstration will display our DASH client, described in Section 3, and allow users to navigate in a 3D model of the Marina Bay area in Singapore (552K faces stored on 67MB, 161.6MB of textures). In particular, it will demonstrate streaming dependency to the viewpoint, e.g., the e ect of camera motion, such as heavy rotation. A video presenting this demonstration can be seen at the following address: https://youtu.be/tGruvbs_H0g


Magali Brunet

Audrey Cochard

Christophe Deshayes

Chantal Brouca-Cabarrecq

Luc Robbiola

Jean-Marc Olivier

Philippe Sciau

Study of post-World War II French aeronautical aluminium alloy and coatings: historical and materials science approach

Keywords: aluminium alloys, aeronautical heritage, aeroplanes, coatings, conservation

In many countries, collections of ancient aircraft, conserved in Air and Space museums or local associations, reflect the importance of a national or local history. Mostly parked outdoor, aircraft suffer from important corrosion requiring conservation operations. During renovation, metallic parts are often replaced by association members. This can lead to a major loss of information since industrial archives dealing with materials and processes were not necessarily conserved. However, if these elements can be considered, they could be a fundamental source of information on the materials originally used and of the technical history of aeronautics. This work reports a thorough study of aluminium-based alloys parts collected on a Breguet aeroplane dating from the 1950s, during its recent renovation. Thanks to an approach coupling multi-scale material characterisation and researches in archives, information on the industrial know-hows are revealed. Several historic grades of aluminium-based alloys were found, namely A-U4G, A-U4G1 and A-U3G, depending on the role of the part. Similarly, different protective coatings were identified (anodic oxidation, primers and paintings), depending on the role of the metallic part and its location in the plane. The knowledge of the materials from bulk to the coated surface is necessary for a good conservation practice of the aeronautics heritage artefacts. Related documents and archives also help fundamentally the understanding of such complex cultural heritage systems.

Introduction

Amongst markers of the industrialisation process, which started at the end of the 19 th century and carried out throughout the 20 th century, aeroplanes are one of the most emblematic. Motorized aeroplanes at the very beginning of the 20 th century were the symbol of human adventure as for instance in the United States, the flight of the Wright brothers in 1903 (Orville Wright and Wilbur Wright September 1908, n°5) and in Western Europe, the flight over the Channel by Louis Blériot in 1909 [START_REF] Fontaine | Un grand français, Blériot, franchit la Manche en aéroplane[END_REF]. But soon, aeronautics revolutionised transport of human and goods, armies, international trades and exchanges of all sorts [START_REF] Chadeau | De Blériot à Dassault. L'industrie aéronautique en France[END_REF][START_REF] Olivier | Histoire de l'armée de l'air et des forces aériennes françaises du XVIIIème siècle à nos jours[END_REF][START_REF] Pattillo | Pushing the Envelope : The American Aircraft Industry[END_REF]. Preserving this history covers the preservation of aeronautical artefacts (aeroplanes, helicopters, flying machines …etc) and also intangible dimensions such as memories, social aspects and industrial manufacturing know-hows [START_REF] Ticcih | Principles for the Conservation of Industrial Heritage Sites, Structures, Areas and Landscapes[END_REF]. On both aspects, tangible and intangible, the conservation of aeronautical heritage presents many challenges. Although Air and Space museums exist in most countries around the world, with dedicated covered sheds and with specific aircraft restoration procedures [START_REF] Mikesh | Restoring Museum Aircraft[END_REF], there is a large part of collections managed by local associations. And in most cases, aircraft are conserved outdoors, because of their size and their numbers. Some old aircraft consequently undergo severe corrosion. For ensuring security, major intervention on the aircraft can be required such as the replacement of corroded or mechanically damaged structural parts. Repainting the overall aircraft is most of the time, carried out at the end of the structural restoration. This is performed firstly, in order to protect the parts newly replaced and the original parts whose coating lost probably efficiency and secondly, because the association members want to exhibit a like-new appearance. During the parts removal and the repainting step, we assist in the major loss of historical information concerning materials and indirectly to industrial know-hows. Archives related to the manufacturing of the aircraft, where such information could be found, are most of the time difficult to find and fragmentary. Technical documents could be spread on different sites and thrown away when considered out of date or during the merging between two companies.

Considering all these factors, this highly specific cultural heritage is in danger. Information on raw materials used and processes has to be retrieved and contextualised in the same way it is done for works of art. The interests are manifold: for conservation purposes, the materials parts of old aircraft should be studied or at least identified well in advance to propose appropriate restoration protocols [START_REF] Adams | Finishes on Aluminium -a Conservation Perspective[END_REF][START_REF] Gayle | Precipitation Hardening in the First Aerospace Aluminum Alloy: The Wright Flyer Crankcase[END_REF][START_REF] Guilminot | Etude des alliages aluminium pour la mise au point des traitements de conservation des avions[END_REF][START_REF] Rocca | Long Term Corrosion of Aluminium Materials of Heritage: Analysis and Diagnosis of Aeronautic Collection[END_REF]; for historical purposes then, historic materials reveal the technicity of a country and indirectly the historical context in which they were produced. Specifically for aeroplanes, the technology is relatively recent and it experienced a tremendous development throughout the 20 th century leading to fast evolution in terms of materials and processes. In particular, aluminium alloys enabled the development of lighter-than-air vehicles: Zeppelins and aeroplanes [START_REF] Duparc | Alfred Wilm et les débuts du Duralumin[END_REF][START_REF] Starke | Application of Modern Aluminum Alloys to Aircraft[END_REF]. Correlating the evolution of materials with the historical context should highlight the synergy which existed in this field.

To do so, the restoration of an aircraft is a good opportunity to study thoroughly a representative industrial artefact, to understand its materiality and the manufacturing processes involved in its fabrication. It is the time when the structure of the aircraft is apparent and when materials are exposed, which allows to document an important part of the materials constitutive of the primary and secondary structures. On parts that are being removed (for replacement), scientific analysis can be carried out. A thorough research in all related documents such as industrial archives, when accessible, completes the understanding and the knowledge on the object.

In this article, through an interdisciplinary approach coupling material investigation and archives analysis, we will show and discuss the extent of information which can be revealed from parts collected on an old aeroplane, information useful for the conservation of a specific industrial heritage and for history of techniques. We will illustrate our approach with the case of a French aeroplane built in the 1950s: the double-decker Breguet 765 Sahara n°504 65-PH. This aeroplane is nowadays being renovated at the association Les Ailes Anciennes Toulouse. The case of the Breguet 765 Sahara is a good example of the incomplete and dispersed archives due to politics and economics. Breguet enterprise was one of the most important aeronautical companies which developed, during the first middle of the 20 th century, numerous aeroplane models in Western Europe. After the merging of Breguet Company with Dassault Aviation group in 1971, some documents disappeared: either lost or destroyed (Audrey Cochard 2016). In this context, the analysis of the materials collected directly on the aeroplane allows to complete the understanding of the construction techniques as well as the context enlightening a part of the history of Breguet company. This study follows previous studies made on this aircraft: one focused on rivets (A. [START_REF] Cochard | Benefits of the Complementary Use of Archaeometry Investigations and Historical Research in the Study of Ancient Airplanes: The Breguet Sahara's Rivets[END_REF]) and one comparing two aluminium alloys (A. Cochard et al.;[START_REF] Cochard | Natural Aging on Al-Cu-Mg Structural Hardening Alloys -Investigation of Two Historical Duralumins for Aeronautics[END_REF]. Here, the methodology is extended to different parts collected on strategic areas of the aircraft: on the primary and secondary structures, exposed either inside or outside, on which a precise investigation is carried out covering the analysis of aluminium alloys but also the protective coatings, which haven't been reported before. The purpose is to extend and define the common knowledge on French aeronautical alloys and protective coatings of the 1950s. Moreover, since standardisation in aeronautics industries started during and after World War II, first in each country and then internationally, the results obtained in this specific case are believed to be useful for a more global view on historic aeronautical materials.

Sampling strategy and experimental methods

Sampling strategy

Since several years, we are following the renovation of a big carrier airliner Breguet 765 Sahara n°504 64-PH, which is part of the aircraft collection exposed and conserved by the association Les Ailes Anciennes de Toulouse (France). The principal goal of this association is to conserve and to highlight the aeronautical memory of the region: visitors are allowed to enter and admire the aircraft interior during the cockpit days organised several times a year. This collection reflects the aeronautic adventure and the local industrial history. The Breguet 765, a double-decker built in 1958 by the local industrial Louis Breguet for military usage (Audrey Cochard 2016), is one of the most valuable aeroplane of the collection. Due to budget drastic reduction, the purchase orders were reduced down to four aircraft by the French state in 1959 (Archive 1957). This aeroplane is thus a rare specimen. During the renovation of the Breguet 765, some partly corroded parts are removed by members of the association for replacement. For this study, representative parts were collected inside or outside the aircraft as shown in Figure 1 (Breguet n.d.):

 Three plates (L2, L8, L20) with different roles and locations: L2 is from the primary structure, a reinforcement plate underneath the bottom floor inside; L8 is a cladding plate near the engine used as a flame shield and L20 is a plate from the upper surface of the wing centre section also called skin (thus an outside part);  Two structural parts: L9 is a lock bracket from inside the landing gear and L15 is a profile1 from the trailing edge of the wing centre section. Both these parts are very much stressed during the aircraft lifetime;  Rivets previously studied (A. [START_REF] Cochard | Benefits of the Complementary Use of Archaeometry Investigations and Historical Research in the Study of Ancient Airplanes: The Breguet Sahara's Rivets[END_REF] are included in the corpus for comparison purposes between the different selected metallic parts. RL1, from a stringer (called L1) has a diameter of 4 mm and RL2 from the plate L2 has a diameter of 5 mm.

Material analysis

After this collection step, multi-scale characterisation were conducted to determine the nature of the original alloys together with their coatings taking into account their alterations. Practically for each collected part, this was carried out to cover all aspects: the composition and the microstructure of the bulk material (aluminium alloy), and the nature and stratigraphy of the surface (protection coating). The observation by optical microscopy (OM) of cross sections allowed a more in-depth study of the bulk alloy as well as the coating stratigraphy on both sides of each metallic selected part. Scanning Electron Microscopy (SEM) on a FEI Helios Nanolab 600i operating at 20 kV coupled with Energy Dispersive X-Ray Spectroscopy (EDS), an Oxford X-Max N 150 spectrometer, was used for alloy elemental composition, intermetallic precipitates composition and coatings composition at the microscale.

Compared with our previous results in articles [START_REF] Cochard | Benefits of the Complementary Use of Archaeometry Investigations and Historical Research in the Study of Ancient Airplanes: The Breguet Sahara's Rivets[END_REF]A. Cochard et al.;[START_REF] Cochard | Natural Aging on Al-Cu-Mg Structural Hardening Alloys -Investigation of Two Historical Duralumins for Aeronautics[END_REF] where inductively coupled plasma optical emission spectroscopy (OES) and wavelength dispersive X-ray spectroscopy (WDS) were used to determine alloys elemental composition, we favoured here SEM-EDS which is accurate enough for differentiating alloys grades. For each alloy, EDS acquisition was performed on four areas of 500x500 µm² with a minimum of 100 000 counts on each spectrum. Before each measurement, the optimisation of the beam intensity was carried out on pure Co standard. Quantitative analysis was performed with internal standards (pure K-line Al, Si and Fe standards). Results were normalised to 100 wt.%. Both observation techniques (OM and SEM) required a sample preparation which consists in cutting the parts according to the three principal orientations, giving rise to three principle planes: expected rolling plane, transverse plane and normal plane; then in embedding the specimen in an epoxy resin and mechanically polishing it on water-lubricated abrasive papers (silicon carbide) of decreasing granulometry: from 600 to 1200 paper grades. Samples were eventually polished on cloths with diamond abrasive pastes with 3 µm particle size and 1 µm particle size, to obtain a mirror aspect. A Keller's solution (HF 1 ml, HNO3 2.5 ml, HCl 1.5 ml in demineralized H2O 95 ml) was used to reveal the microstructure of the alloys.

As aluminium alloys are structural hardening alloys here, transmission electronic microscopy observations with elemental analysis (TEM-EDS) were carried out to study the microstructure at the nanoscale, i.e. identify dispersoïds and hardening precipitates. In this case, specimen preparation was the following: after mechanical polishing up to 2400 SiC paper grade, in order to obtain a thickness of 25 µm, the specimens were then electrochemically thinned using a Tenupol-5 Struers apparatus operating at 60V in a solution of methanol and nitric acid (3:1) at -15°C. The nanostructure was observed using a Transmission Electron Microscopy (TEM) JEOL 2010 operating at 200kV. As regards the identification of protective coating constituents, XRD was performed with a Bruker D8 Discover equipped with a microsource Co and a 2D detector.

Archives research and analysis

In parallel, research was performed in the archives of Breguet enterprise which were dispersed in the 1970s and are now partly conserved in different sites: at the Institute for History of Aluminium (IHA, Paris), at the archives centre of the Historical Service for Defence (SHD, Châtellerault), at the documentation centre of the Air and Space museum Paris-Le Bourget and at the association Les Ailes Anciennes Toulouse. Other sources were employed such as metallurgical journals of that time: la Revue de l'Aluminium or l'Aluminium Français, as well as private archives2 . Even though archives may be lacunar, it allows to collect some information on the materials, the manufacturing processes and on the aircraft itself and to relate them to the measured data on materials. Two documents belonging to Breguet company provided very useful information on aeronautical materials: the standard from the factory of Vélizy (Breguet 1946(Breguet -1954)), containing forms edited from 1946 up to December 1954, and the standard from the factory of Anglet (Breguet 1951(Breguet -1959) ) with forms edited from 1951 up to 1959. This latter document concerns exclusively the Breguet 761 to 765, Breguet 960 and 1050. It is important to mention that not all the pages of the standards were recovered.

Aluminium alloys

Results of material analysis

The alloy composition of the different collected parts, measured by SEM-EDS, is given Table 1. All alloys are Al-Cu-Mg belonging to the Duralumin family. Duralumin, discovered by Alfred Wilm in 1906[START_REF] Duparc | Alfred Wilm et les débuts du Duralumin[END_REF] and produced industrially in Germany from 1910, is an aluminium alloy containing originally copper, manganese, to which magnesium was added. Thanks to alloying with copper, magnesium and thanks to appropriate thermomechanical and ageing treatments inducing nanoprecipitation of specific Alphases, high strength materials were obtained [START_REF] Hornbogen | Hundred Years of Precipitation Hardening[END_REF]. Different alloy grades were quickly developed by nations for aircraft and zeppelins construction at the beginning of the 20 th century and produced under specific corrosion from Aérospatial, SNCAN and Dassault Aviations just after merging with Breguet company in 1971. classification. In France, they were named A-U4G, A-U4G1, A-G3… etc according to the alphanumeric classification3 adopted at the beginning of the 1940s [START_REF] Lebouteux | La symbolisation de l'aluminium et de ses alliages en France et dans quelques pays étrangers[END_REF]) and followed by the AIR 3350/C aeronautical standard of 1957 (AIR3350/C 1957): From Table 1, two alloys are identified: A-U4G1 for L2, L9, L15 and L20 parts, A-U4G for L8 and RL2. The main difference between A-U4G and A-U4G1 concerns the magnesium and silicon concentrations: a higher concentration of magnesium for A-U4G1 (Mg around 1.5 wt.%) than for A-U4G (Mg less than 1 wt.%) and silicon (about 0.6 wt.%) intentionally added in A-U4G. One of the rivet alloy (RL1) was found with a different composition: less Cu (around 3 wt.% compared with the 4 wt.% for A-U4G and A-U4G1) and less magnesium and manganese. It was identified as an A-U3G. The precise elemental composition of this ancient alloy was found in an article from Tournaire and Renouard4 published in 1956 [START_REF] Tournaire | Alliages pour rivets de la famille du Duralumin[END_REF]. Micro-alloying and thermomechanical treatments control the mechanical properties of aluminium alloys (Polmear 2005a). Observing the microstructural features, i.e. grain size and shape, intermetallic precipitations at all scales, can reveal important information on the alloys mechanical and chemical behaviour. In particular, according to the Hall-Petch law [START_REF] Hall | The Deformation and Ageing of Mild Steel: Discussion of Results[END_REF], the grain size contributes partly to the hardening of the alloy: the smaller the grain size is, the higher the yield strength of the alloy. Figure 2 shows metallographic structure of the studied parts, from optical microscopy performed after a Keller metallographic attack. Grains of the different alloys are this way revealed. Full report of metallographic structures for L2 (Figure 2a) and L8 (Figure 2b) can be found in previous publication (A. [START_REF] Cochard | Natural Aging on Al-Cu-Mg Structural Hardening Alloys -Investigation of Two Historical Duralumins for Aeronautics[END_REF]. Here, only one orientation (normal plane) is shown and commented. L2, L8 and L20 plates (Figures 2.a.b.c) show grains with a preferential orientation (anisotropy in shape). The size and the shape of the grain depends mainly on the manufacturing process, in particular the thermomechanical treatments applied. For the plates, the preferential orientation is the signature of a rolling process followed by recrystallization steps. L20 (Figure 2.c) exhibits longer grains (average length equal to 117 ± 19 µm) than L2 (69 ± 35 µm) and L8 (46 ± 15 µm). As the three plates don't have the same thickness (3 mm, 2 mm and 1.6 mm respectively), they probably received different number of rolling passes and/or different recrystallization treatments leading to different grain size and shape. Bracket L9 (Figure 2.d) and profile L15 (Figure 2.e) have also a microstructure with preferential orientation but grains are very long, thin and crushed. This specific microstructure is produced during extrusion generating severe plastic deformation [START_REF] Hérenguel | Un mécanisme métallurgique particulier à l'extrusion : L'hypercorroyage[END_REF]. For rivets RL1 (Figure 2.f) and RL2 (Figure 2.g), grains are equiaxed. Rivets were also fabricated by extrusion but a heat treatment for recrystallization generally was done before the formation of the head [START_REF] Penel | Fiche H -Octobre 1950: Le traitement thermique des alliages légers. Première partie: trempe et revenu[END_REF]) which transformed the grains shape. Furthermore, it is observed that A-U3G rivets have larger grains (average diameter equal to 47 ± 25 µm) than A-U4G rivets (average diameter equal to 29 ± 15 µm) (A. [START_REF] Cochard | Benefits of the Complementary Use of Archaeometry Investigations and Historical Research in the Study of Ancient Airplanes: The Breguet Sahara's Rivets[END_REF]. This particular point will be discussed below after a deeper look at the precipitation at the nanoscale. Overall, the microstructures of the two rivets are comparable with those reported in 1955 for similar rivets [START_REF] Tournaire | Alliages pour rivets de la famille du Duralumin[END_REF]. In all the collected parts (plates, bracket, profile and rivets), particles in the micron range are observed (See Figure 2). These coarse particles (> 1µm) are intermetallic phases generally encountered in this type of Al-alloys [START_REF] Hughes | A Consistent Description of Intermetallic Particle Composition: An Analysis of Ten Batches of AA2024-T3[END_REF] [START_REF] Mondolfo | Aluminum Alloys, Structure and Properties[END_REF]). Analysed with EDS, particles in A-U4G and A-U4G1 alloys are composed of Al-Cu-Mn-Fe-Si, Al-Cu, Al-Cu-Mg and/or Al-Mg-Si. For the A-U3G alloy, only Al-Cu-Fe particles were found. Such coarse intermetallic particles are normally deleterious for mechanical properties: they can cause cracks as well as corrosion. It is thus, important to document them in terms of size and density for understanding the possible alteration of historic alloys.

At a higher scale, Figure 3 shows TEM images (Bright field) of the concerned alloys. One can see dispersoids, particles of about ten nanometres to a few hundred nanometres and homogeneously distributed. Formed during the homogenisation heat treatment and always containing manganese in Duralumin, the dispersoids are partly responsible for the hardness of the material by limiting the size of the grains in the alloy. In A-U4G1, the dispersoids are rod-shaped (Figure 3.a L2 plate) and their composition is AlCuMn, whereas in A-U4G, their forms are ovoid (Figure 3.b L8 plate and 3.d RL2 rivet) with AlMnSi composition. In A-U3G, there is hardly any dispersoids (Figure 3.c RL1 rivet) due to the absence of manganese in the alloy composition. This explains the larger grain size in this rivet observed in Figure 2.f.

Figure 2. Optical microscopy images after Keller etching of collected parts in the plane normal to the rolling direction. a) L2 (A-U4G1), b) L8 (A-U4G), c) L20 (A-U4G1), d) L9 (A-U4G1), e) L15 (A-U4G1), f) RL1 (A-U3G), g) RL2 (A-U4G

). For the rivets, the images were acquired in the shank. ND: normal direction / RD: rolling direction.

) plate L8 (A-U4G), c) rivet RL1 (A-U3G) and d) rivet RL2 (A-U4G).

Above all, the particularity of these aluminium alloys is to induce nanoprecipitation during the ageing step after solution heat treatment and quenching, which markedly enhance their strength by preventing the movement of the dislocations [START_REF] Starink | The Origins of Room Temperature Hardening of Al-Cu-Mg Alloys[END_REF]) [START_REF] Silcock | Structural Ageing Characteristics of Binary Aluminium-Copper Alloys[END_REF]. As demonstrated in our previous work (A. [START_REF] Cochard | Natural Aging on Al-Cu-Mg Structural Hardening Alloys -Investigation of Two Historical Duralumins for Aeronautics[END_REF] for two alloys, A-U4G and A-U4G1, the microstructures revealed by TEM in conventional mode are typical of an ageing at room temperature corresponding to a treatment T4 (Polmear 2005b).

5 "Fiche Standard Br. 201, feuille 1, 1956from Standard Forms, Anglet Factory (Breguet. 1951(Breguet. -1959)).

Results of archives analysis

Information on materials is scattered in several documents of the Breguet Company. In the Anglet standard (Breguet 1951(Breguet -1959) ) 5 , amongst other alloys, are listed all the aluminium alloys employed for the fabrication of plates, profiles, rivets together with some information on thermomechanical treatments and minimum required mechanical properties. For plates in A-U4G and A-U4G1, a heat treatment at 495°C was applied on the metallic element and was followed by ageing at room temperature for 4 days, corresponding to a treatment T4. In terms of mechanical properties, A-U4G1 shows an

1 µm 1 µm 1 µm 1 µm a) b) c) d)
ultimate strength of 50.5 kg/mm² (495 MPa), a yield strength of 32 kg/mm² (314 MPa)) and a hardness of 110 HB significantly higher than the values for A-U4G (respectively 45 kg/mm² (441 MPa), 27 kg/mm² (265 MPa) and 100 HB).

In another document, the technical clauses for Breguet 765 aircraft [START_REF] Breguet | Technical Clauses for Breguet 765: Service Technique de l'Aéronautique -Section Avions[END_REF]), the typical usage of each of these two alloys in the aircraft is specified: A-U4G constitutes the fuselage with its reinforcement frame, stringers and all non-structural parts whereas A-U4G1 is employed for high resistance profiles. Particularly for the Breguet 765, as the aircraft was dedicated to the transport of heavy loads, an adaptation was made: the skin and stringers of the wings originally in A-U4G were changed to A-U4G1.

About rivets, in the standard of Vélizy (Breguet 1946(Breguet -1954) ) 6 , a hand-written note mentions the fact that all rivets A-U4G should be replaced by rivets A-U3G. In the more recent standard of Anglet (Breguet 1951(Breguet -1959) ) a new recommendation was done by the constructor7 : A-U3G was to be used only for rivets with diameters ≤ 5 mm until stocks were exhausted and only if cutting resistance was at least 25 kgf/mm² (245 MPa).

Discussion : Laboratory analysis and archives

Cross-referencing Breguet's archives, scientific knowledge in the 1950s and laboratory analysis was necessary to understand and verify the choices of the constructor on this specific aircraft. The choice of the aluminium alloy to be employed for the fuselage, the stringers or the rivets was driven by the required mechanical properties but, as seen in the Breguet standards, evolution in the decision of using such or such alloy could intervene.

At the time of the Breguet Sahara construction, the role of magnesium in hardening had been evaluated empirically [START_REF] Chevigny | L'aluminium et ses alliages[END_REF]. It was known that addition of Mg up to 1.5 wt% was beneficial for the mechanical properties. That is why A-U4G1 was introduced in the aeronautical industries for high resistance parts. Analysis of the collected parts confirms the usage of A-U4G1 for the airfoil (L20) as well as parts requiring a high resistance (bracket L9 and profile L15). On the other hand, A-U4G was used in cladding parts (such as L8). However, analysis showed that L2, a vertical reinforcement plate placed underneath the floor is actually made out of A-U4G1 which contradicts the clauses specifying that the frame of the fuselage and the floor should be in A-U4G. Although not mentioned in the technical clauses, the plates reinforcing the floor may have been changed to A-U4G1 because of heavy loads to be carried on this aircraft, similarly to the wings case.

For the rivets of the Breguet 765, two types of alloys were identified by the scientific analysis: A-U4G and A-U3G. The diameters of these rivets were measured to be 4 mm for RL1 (A-U3G) and 5 mm for RL2 (A-U4G) in accordance to the recommendation made by Breguet Company. Now, to understand why this specific alloy composition had been applied here, it is necessary to explore the historical context. To start with, rivets play a strategic role in aircraft construction, as they constitute the basis of the aircraft assembly and insure its good mounting. Highly demanding properties are thus required for rivets and aluminium alloys were specifically developed to meet the requirements. In their article from 1956 [START_REF] Tournaire | Alliages pour rivets de la famille du Duralumin[END_REF], Tournaire and Renouard talked about the necessity of simplifying riveting. A-U4G traditionally used for rivets, because of its good cutting resistance (26 kgf/mm² minimum), had a limited period (about 8 hours) after quenching for being placed, after which it became too hard. When rivets became too hard, they had to be heat treated again (solution treatment followed by quenching into water). To avoid this problem, A-U2G alloy, containing only 2 wt.% of copper and less than 1wt.% of Mg was developed. Although this new alloy didn't suffer from premature ageing, the cutting resistance was reduced down to 22-24 kgf/mm². Eventually, A-U3G with 3 wt.% of copper and less than 1 wt.% of magnesium was developed in 1943. This alloy, only studied in 1954 consists in a compromise between A-U4G and A-U2G: it didn't have a limited period for riveting and it exhibited a guaranteed cutting resistance of 24 kgf/mm², with the possibility to reach 26 kgf/mm² after 3 months at 25°C. Hopes for a better cutting resistance were strong in the industry and this new alloy was authorized by the French Aeronautics Industry. Breguet Company followed the development of this new alloy and decided to implement it in December 1954 in the Breguet 765 as the standard from Vélizy testifies. However, due to the limit in cutting resistance of this new alloy, the constructor decided eventually to limit its use to rivets with a diameter less than 5 mm in diameter. Laboratory analysis prove here that the standard of 1957 (Anglet) is the one which was applied to this particular aircraft.

Protective coatings

From the early stages of the development of aluminium alloys, corrosion of aeronautical parts has been an issue [START_REF] Pubellier | La protection des alliages légers contre la corrosion[END_REF]. Protective coatings of all sorts were developed throughout the 20 th century up to now. Generally constituted of several layers with different chemical nature (mineral or organic), the choice of the protective coating applied on a 8 Aluminum Company of America part depends on its role, its location (inside or outside, accessible or not for future maintenance operations) and the type of environment the aeroplane would experience (marine or land). Cost issues intervene as well in the choices. Previous work identifying coatings thanks to analysis on WWII aeroplanes (American, German and Japanese) and thanks to a thorough research of historical documents was carried out by [START_REF] Adams | Finishes on Aluminium -a Conservation Perspective[END_REF]. This work as well as technico-scientific documents produced in the 1950s in France (Meynis de Paulin Novembre 1947; Octobre 1947; Rousset-Bert 1958) helped understanding the several options that constructors had in hand for the protection of structures in light metals in aeronautical construction. These main protective treatments were :

 Cladding with a more electronegative metal to prevent electrolyte from reaching the bulk alloy and to insure cathodic protection. Alclad where high purity aluminium is cladded on the alloy, was developed by AlCoA 8 in 1927 in the USA [START_REF] Dix | Alclad": A New Corrosion Resistant Aluminum Product[END_REF]. The product was known in France under the name Vedal [START_REF] Bailly | Construction en Vedal pour hydraviation[END_REF].  Anodic oxidation where alumina between 5 and 25 µm thick is formed electrochemically. As reported by [START_REF] Adams | Finishes on Aluminium -a Conservation Perspective[END_REF], different processes were developed worldwide as soon as 1927 based on: chromic acid baths (in Great Britain, the well-known "Bengough-Stuart" process, in the USA), sulphuric acid baths (GB, USA) and oxalic acid baths (mainly in Japan and Germany). In France, the most employed electrolytic baths in the 1950s were the ones with chromic acid, sulfuric acid or BF4 process [START_REF] Rousset-Bert | La protection des structures en métal léger dans la construction aéronautique[END_REF]. The BF4 process was a mixture of chromic, oxalic and boric acids.

 Chemical oxidation where an oxide layer is grown in boiling water or in an alkaline bath containing chromates and/or phosphates. The first process was developed by Bauer-Vogel in Germany in 1916 andmodified in 1923 (Modified Bauer-Vogel process): it is based on boiling bath of potassium carbonate, sodium bicarbonate and potassium bichromate. Many other processes were developed between the 1930 and 1945.  Chemical conversion coatings in acid baths. In this category, a particular process developed in 1945 in the USA called Alocrom [START_REF] Spruance | Composition for and Method of Coating Aluminum[END_REF] was soon employed in France under the name Alodine [START_REF] Hess | Le procédé Alodine, protection galvanique de l'aluminium[END_REF]. It consists in a mixture of mineral acids, phosphoric acid mainly, with metallic salts containing chromium cations and fluoride anions. The resulting coating is essentially composed of amorphous metallic phosphates.  Primers: a layer usually in contact with the naked metal, whose role is to be anodic thanks to the use of pigments inhibitors of corrosion [START_REF] Raison | Revêtements des métaux par peinture[END_REF]) and to provide adhesion properties for the paint layers. Different types of primers were developed in most countries: primers using zinc chromates and later phosphate primers. In France, widely used in the 1940s was a complex zincchromate and potassium chromate written under the formula (K2O, 4ZnO, 4 CrO3, 3 H2O) (Meynis de Paulin Novembre 1947).

Based on this knowledge, the objective here was to understand the applied protective coatings on the Breguet Sahara and to confront the material analysis to the recommendations defined by the constructor's standards.

Results of materials analysis

For each selected metallic part, the two surface sides were observed and analysed: the front side and the back side. The front side is defined here as the accessible or visible side when the part is still assembled on the aircraft, while the back side is in contact with another part when assembled, therefore non-accessible. Representative sections for all the coatings are reported in Figure 4 with possible identification. The nature of each layer was determined thanks to SEM-EDS analysis and XRD. On the bracket L9, the front side is too much altered by corrosion to detect any protective coating left. As seen in Figure 4, the protective coatings are quite different between the collected parts and between sometimes the front side and the back side for a same part. Nevertheless, some similarities exist. The transparent layer directly on the surface of the aluminium, detected on both sides of L8, L20 and on the backside of L9 and L15, is identified as an aluminium oxide with traces of sulphur. This oxidation layer is between 6 and 9 µm thick depending on the investigated part. On the plate L2 and on the rivets RL1 and RL2, no oxide layer is detected. Then, the light green layer on top of the oxide, seen on L9, L2, L8, L20, RL1, RL2 and on the backside of L15 is an organic layer containing chromium, zinc and phosphorous. XRD pattern collected on the light green layer (on L2 and L8 samples) allowed us to identify a zinc chromium oxide hydrate of formulae Zn2CrO5, H2O (PDF 11-0277) mixed with ZnO (PDF 89-0510) and TiO2 rutile (PDF 89-0554). On the profile L15, the front side appears very different from the back side and to the other parts (see Figure 4.e). On the front side indeed, no oxide is found (as opposed to the back side) and the primer is composed of two layers of different colours: a darker green layer at the surface of the aluminium and a light green layer on top as revealed from the EDS maps in Figure 5. This double-layer, thicker and more resistant than the primer found on the other collected parts seems to have a similar nature but with a different composition. As shown in Table 2, it has a much higher phosphorus content (about 9 wt.% in the dark green) compared with 1 to 2 wt.% for the other primer L9 and it also contains some potassium (about 2.5 wt.%). XRD patterns on the dark green layer of L15 indicated clearly the presence of an aluminium phosphate AlPO4 (PDF 03-0446) and in the light green a potassium zinc chromium oxide hydrate of Back side Front side g) Paint formulae 4ZnCrO4, K2O, 3H2O (PDF 08-0202 XRD reference). This is in good agreement with the formulae reported in (Meynis de Paulin Novembre 1947). This chemical compound had proved to be an excellent inhibitor as well as resistant to humidity. Applied in a polybutyral vinyl solution mixed with an alcoholic solution containing phosphoric acid, a microcrystalline layer very adherent containing metallic phosphates was formed at the surface of the aluminium covered with a polybutyral vinyl [START_REF] Raison | Revêtements des métaux par peinture[END_REF]. Eventually, on top of the primers, one or several paint layers (beige) containing carbon, oxygen, barium, titanium, zinc and sulphur were applied. The nature of some pigments was revealed by XRD: ZnO, TiO2 (rutile) were found as well as

Protective coating recommended by Breguet Company

The standard of Anglet (Breguet 1951(Breguet -1959)), exclusively reserved to aeroplanes 761 to 765, 960 and 1050 and gliders, details 9 for each type of alloy and for each part, taking into account their role and location (inside or outside), the protective coating recommended (based on the AIR 7251 standard) and this, both for land and marine planes. For anodic oxidation first, workshops for aeronautical constructions in France and for Air Force maintenance possessed industrial installations for anodic oxidation using the sulfuric acid process [START_REF] Rousset-Bert | La protection des structures en métal léger dans la construction aéronautique[END_REF]. In particular, the installation in Louis Breguet factories of Anglet and Toulouse (France) allowed treating very large parts with tanks of 10 m long and 1 to 2 m deep. It is expected thus that the anodic oxidation applied by the company for the Breguet 765 was produced in such installation.

Chemical oxidation on the other hand was considered as a rapid process obtained at low temperature and without electrical current. It was thus quickly adopted in the aeronautical industry since 1945, in particular the Alodine 1200 process [START_REF] Hess | Le procédé Alodine, protection galvanique de l'aluminium[END_REF] (Breguet. 1951(Breguet. -1959)).

mentioned in the standard of Breguet. It is also mentioned that the only chemical oxidation employed so far is the "Alodine 1200" provided by the C.F.P.I10 . At last, the full normalised P.50 painting set, specifically mentioned in the Breguet standard of 1956 should contain, according to the literature [START_REF] Rousset-Bert | La protection des structures en métal léger dans la construction aéronautique[END_REF], several stages: degreasing, alkaline cleaning, a phosphate primer, a levelling and a nitrosynthetic finish. This painting set was chosen after a competition decided by the Service technique de l'Aéronautique and thus authorised in aeronautical applications. It replaced the P.42 set, selected from a competition which took place in 1942, which contained a primer based on alkyd resins but without chromates (Meynis de Paulin Novembre 1947). In the new painting set P.50, a phosphate primer was introduced.

Discussion: Laboratory analysis and archives study

Although the types of protective coatings that were employed by Breguet in his factories could be listed, and some information could be found in the literature on the characteristics and nature of these coatings, investigation performed on the collected parts allowed a more precise knowledge of the chemistry of the protective coatings. Confronting the identified protective coatings with the information collected on the Breguet standards was then attempted to highlight the true manufacturing and industrial use. This is summarised in Table 3 for each collected part and in parallel for recommended coatings as defined in the Breguet standard of Anglet from 1956 (Breguet 1951(Breguet -1959) ) for marine and land planes. Thus, from Table 3, it can be distinguished similarities but also some differences between real cases and recommended standards. For plates, L2 has only a primer protection, which is consistent with the case of inside plates for land aeroplanes, such as the Breguet 765. Conversely for plates L8 and L20 and for bracket L9 and profile L15, an anodic oxidation was applied prior the primer, which is the protection recommended only for marine aeroplanes. This is not coherent with the case of Breguet 765, a land aeroplane. At the moment, there is no logical explanation on why a protective coating specific to marine environment was applied to this aeroplane. Furthermore, plate L20 (outside skinwing) which is an external part, should have received a chemical oxidation based on chromium salts (O.C.H.C.) corresponding to the Alodine 1200 product. However, in the materials analysis carried out on L20 and all other collected parts, no trace of Alodine 1200 was found. One explanation could be the following: the introduction of this new protection technique was mentioned in the standards of the Breguet Company, however, anodic oxidation was still used because it was considered by Breguet as the most efficient protection, even though more expensive. The case of brackets in landing gear trap (L9) is not specifically mentioned in the standard. But the landing gear is a particularly severe environment as it is exposed to impacts of all sorts (in air and during take-off and landing), which could explain why an anodic oxidation was applied.

For rivets on land aeroplanes, anodic oxidation (O.A.F.I.C.) should have been applied. However, a note is given later in the document rectifying this recommendation, saying that rivets A-U3G are less sensitive to corrosion compared to A-U4G ones and they don't react well to anodic oxidation. Breguet decided thus, to abandon this protection. Rivets, whether in A-U3G or in A-U4G were only covered, after assembling, by the primer and the finition coating (i.e. a painting) in good accordance with the descriptions in the Breguet standard of Anglet (Breguet 1951(Breguet -1959)).

Considering now the primers, as mentioned earlier, two types of primers were identified in the collected parts: one type, for most of the parts and another type, for the front side of part L15. In the first case, zinc chromate is the active pigment and it is mixed with titanium white (TiO2). A widespread technique was indeed to mix zinc chromate with other pigments (Meynis de Paulin Novembre 1947) to decrease the price and increase the coating power. Final content was usually 40 parts of zinc chromate for 100 parts of other pigments. On the other hand, the primer detected in L15 contains another pigment: a potassium zinc chromium oxide hydrate which produces, when mixed with a phosphorus acid contained in a polybutyral vinyl resin, a very adherent metallic phosphate layer at the surface of the aluminium. At this stage, it is difficult to determine which primer corresponds to the protection "P50.I. (impression)" depicted in the standard of Anglet and recommended (Table 3). However, the primer detected on the front side of L15 is maybe not representative and could correspond to a local repairing operation. One reason to think this is that the back side of L15 exhibits the same type of primer as the other parts with the presence of an oxide as well. An hypothesis can be formulated: on the accessible side, due to alteration during usage (such as corrosion for instance), L15 was probably de-oxidized in-situ, maybe by mechanical polishing, as the surface of this part seems rougher than for the rest of the other parts. Then the surface may have been treated with a new formulation of primer. All these differences lead to the conclusion that for the Breguet Sahara 765, although built in 1958, the standard of Anglet from 1956 (Breguet 1951(Breguet -1959) ) which concerns the protective coatings was not fully applied and adaptation was performed. Confronting materials analysis to archives is important as differences can exist between the real materials used and the technical expected recommendation. The history for an aircraft construction is not linear. It is to be remembered that there were only 4 Breguet 765 built: this aeroplane is close to a prototype. Modifications may have been decided during manufacturing. Furthermore, repairing of some parts most probably occurred during the lifetime of the aeroplane and solutions for protection were changing in this period (new paint set P.50 for instance). All these factors are possible explanations for the differences found in primers.

Materials laboratory analysis

Archives :

Conclusion

This work carried out on different parts collected on an aeroplane from the 1950s revealed a number of information on aluminium alloys and protective coatings employed in the French aeronautical industry. Different alloys, namely A-U4G, A-U4G1 and A-U3G, were identified depending on their role in the aeroplane, in coherence with the Breguet standard: A-U4G1, with a higher concentration of magnesium and high mechanical characteristics, was used for structural parts, whereas A-U4G for cladding parts. Rivets were made out of A-U3G and A-U4G depending on their diameter. The microstructure of the different studied parts revealed some differences mainly due to the manufacturing process (rolling or extrusion) and/or postmanufacturing treatments. In terms of protective coatings, we could highlight the use of anodization and primers and identify the nature of the anticorrosive pigments within the primers by cross-checking analysis from different techniques: optical microscopy, SEM-EDS and XRD. Raman and Infra-Red spectroscopies, Gas-Chromatography-Mass Spectrometry are complementary techniques which would help identifying the organic binders.

As regards to the usefulness of all the information retrieved, several points can be made. Firstly, even if historical research is a basic fundamental approach, archives are sometimes difficult to localise and not complete. On the other hand, changes for particular aircraft could be decided by the constructors, as it was demonstrated here for the alloys and for the protection coatings. Therefore, archives alone are not sufficient for full reconstitution of reality on a specific aircraft. Furthermore, in technical archives, materials are most of the time mentioned under commercial names that sometimes no longer exist, which make the identifying task difficult: for instance, the exact nature of the protective coating P.50 employed by Breguet in 1958 yet remains to be found. The investigation of ancient aeroplane materials by direct characterisation helps, thus, correlating the historical archives with the effectively applied industrial process, for an improvement of the history of techniques and science. It also helps preserving and transmitting aeronautic testimony. In fact, documenting thoroughly materials should be considered whenever possible as aircraft conserved outdoor are threatened of destruction: corrosion attacks push people in charge of the conservation to replace parts.

Secondly, there is no doubt that the information on aeronautical materials will help improving conservation practices. For defining the conservation state of aircraft metallic elements, the full characterisation of both the metallic bulk material (especially its microstructure at different scales) and the applied protection remains fundamental, as often for cultural metallic artefacts. Understanding alterations (in this case corrosion) will consist in looking for influencing factors: nature of the alloy, alteration of the coating, and for industrial cultural heritage, such here for aeronautics, it is also mandatory to take into consideration their location and role on the aircraft as well as possible environmental conditions, during and after usage, to establish an appropriate diagnosis of the conservation state. This particular point will constitute the heart of our future work.

Eventually, this study can help the understanding of the materials involved in other aircraft's construction in the same period. A mid-term perspective will be to implement a database specific for these cultural heritage filing all these information. This would allow complete and crossed researches on aluminium aeronautic alloys from an historical and materials point of view, also providing an aid to curators willing to confront their own observations to references.

Figure 1 .

 1 Figure 1. Photographs of collected parts (front and back side) from Breguet 765 airplane with localization on original plans (Breguet n.d.); a) Plate L2 (2 mm thick) with RL2 rivets (5 mm diameter) and profile L1 with RL1 rivets (4 mm diameter), b) Plate L20 (3 mm thick) and profile L15 (4 mm thick); c) Plate L8 (1.6 mm thick) and bracket L9 (5 mm thick).

Figure 3 .

 3 Figure 3. Observations by TEM of dispersoids in top row (bright field observation): a) plate L2 (A-U4G1), b) plate L8 (A-U4G), c) rivet RL1 (A-U3G) and d) rivet RL2 (A-U4G).

Figure 4 .

 4 Figure 4. Optical microscope images (dark field mode) of protective coatings for both sides: a) L2, b) L8, c) L20, d): L9, e) L15, f) RL1, g) RL2. For L9, the front side was completely corroded and the coating no longer existed

  BaSO4 and ZnS corresponding to the white pigment lithopone, a mixture of barium sulphate and zinc sulphide[START_REF] O'brien | A Study of Lithopone[END_REF]. Elemental composition (wt%) of the primers on L9 (back side) and L15 (front side), analysis by SEM-EDS: average on 3 areas.

Figure 1 .

 1 Figure 1. Coating detected in L9 (back side) and L15 (front side) with SEM: backscattering image and EDS maps. Only Zn, P, Cr and Al are shown. In blue: Al-alloy, green: zinc, yellow: chrome and red: phosphorus.

  The chemical nature of the protective coatings is however not detailed in the Company's standards. Only acronyms and brand names are used: O.A.F.I.C. for anodic oxidation with chromic finishing, O.C.H.C. for chemical oxidation with chromium, and P50.I and P50.F for Impression and Finishing respectively of the P.50 set. To understand what stands behind these appellations, literature published in the 1950s was of great help.

Table 3 .

 3 Protective coatings detected on the collected parts and information extracted from Anglet standard. For comparison, underline is used for oxides and corresponding industrial names (OAFIC and OCHC), italic for primers and corresponding industrial name (P50), bold italic for paints.

A long part with a constant section other than bars, rod, strip or sheet.

Studies in Conservation -https://doi.org/10.1080/00393630.2019.1610846 -Article accepted: April 2019

André Sunez, a member of Les Ailes Anciennes, former trainer at the Air Army school in Rochefort, provided us with documents on coatings and protection against

A for aluminium, U for copper and G for magnesium followed by the nominal content in wt.%.

Respectively head of Researches and Laboratories and head of Researches of the factory Issoire, General Company of Duralumin and Copper.

Adjonctions et modifications au standard Breguet, Br 411 « Rivets en AU4G et 35NC6f », Décembre 1954 from Standard Forms, Vélizy Factory(Breguet. 1946(Breguet. -1954)).

Form « Rivets AU3G et 35 NC6f », Br 411/416, Juin 1957from Standard Forms, Anglet Factory (Breguet. 1951-1959).

Compagnie Française des Produits Industriels, 177 quai du docteur Dervaux, Asnières (Seine)from article C.Hess, RA 1951, n°174.

Acknowledgements

The authors would like to thank the volunteers of the association Les Ailes Anciennes Toulouse, especially the team 'Breguet-2 ponts': Patrick Goutoule, Michel Frostin, Laurent Malric, Albert-Franz Van Dew Bussche, Daniel Hartmann, Yves Martin as well as André Sunez, André Suzon, Jacques Leborgne for their availability, their help in sampling, archives research and histories around the aircraft.

This study has been partially supported through the grant NanoX n° ANR-17-EURE-0009 in the framework of the « Programme des Investissements d'Avenir".