Linda Le Roux
email: linda.le-roux@inra.fr

Serge Mejean

Raphaël Chacon
email: raphael.chacon@sill.fr

Christelle Lopez
email: cristelle.lopez@inra.fr

Didier Dupont
email: didier.dupont@inra.fr

Amélie Deglaire
email: amelie.deglaire@agrocampus-ouest.fr

Francoise Nau
email: francoise.nau@agrocampus-ouest.fr

Romain Jeantet
email: romain.jeantet@agrocampus-ouest.fr

Françoise Nau

Plant proteins partially replacing dairy proteins greatly influence infant formula functionalities

Keywords: infant formula, plant proteins, emulsion, homogenization, spray drying

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Infant formulas (IFs) can be defined as substitutes for human milk, which are mostly spray-dried to a powdered form. IFs are prepared to closely mimic the nutritional composition of the benchmark human milk, comprising of macronutrients (carbohydrates, fat and proteins) and micronutrients (minerals and vitamins), in order to provide the required nutrients for proper growth, body composition, neurodevelopment, appetite and hormonal regulation of the infants [START_REF] Michaelsen | Protein needs early in life and long-term health[END_REF]. In the absence of breastfeeding, the nutritional requirements of infants must be satisfied by supplying IF products until they become accustom to complementary food [START_REF] Agostoni | Complementary feeding: A commentary by the ESPGHAN committee on nutrition[END_REF]EU, 2016).

According to the applicable European regulation (EU, 2016), the sources of proteins allowed for 1 st age IFs (0 to 6 months) are either bovine's milk protein, goat's milk protein, soy protein isolate or hydrolysed rice protein. Furthermore, the demand for animal proteins is expected to double by 2050, driven by population growth and by the emerging middle classes in developing countries [START_REF] Egbert | Plant proteins[END_REF]FAO, 2006). Therefore, it seems essential to search for alternative protein sources that show nutritional and functional qualities close to that of breast milk or to the IFs currently on the market that include animal protein. In that respect, there is a growing interest in utilizing plant proteins as partial replacers of animal proteins in food [START_REF] Ainis | Partial replacement of whey proteins by rapeseed proteins in heat-induced gelled systems: Effect of pH[END_REF]. Due to high nutritive quality, good techno-functional properties [START_REF] Barac | Functional properties of protein hydrolysates from pea (Pisum sativum) seeds: Functional properties of pea protein isolate[END_REF] and acceptable cost, legume proteins, for instance soy, pea, chickpea, faba bean or lupine proteins, represent a potential alternative to proteins of animal origin [START_REF] Ainis | Partial replacement of whey proteins by rapeseed proteins in heat-induced gelled systems: Effect of pH[END_REF][START_REF] Alves | Mixing animal and plant proteins: Is this a way to improve protein technofunctionalities?[END_REF][START_REF] Chihi | Heat-Induced Soluble Protein Aggregates from Mixed Pea Globulins and β-Lactoglobulin[END_REF]. Especially, pea proteins (Pisum sativum) are becoming a viable alternative to soy protein products because of their high essential amino acid content [START_REF] Boye | Pulse proteins: Processing, characterization, functional properties and applications in food and feed[END_REF] and relatively good digestibility (O'Kane, [START_REF] O'kane | Gelation Behavior of Protein Isolates Extracted from 5 Cultivars of Pisum sativum L[END_REF]. Furthermore, pea protein has fat-and water-binding capabilities, emulsification and gelation properties [START_REF] Sandberg | Developing functional ingredients: a case study of pea protein[END_REF]. Faba bean (Vicia faba L.) is another source of good quality proteins, particularly rich in lysine and threonine. The most recent research is promoting its use for novel food applications, as a potential soy substitute, and as a beneficial crop having important functions for vital and sustainable agroecosystems [START_REF] Crépon | Nutritional value of faba bean (Vicia faba L.) seeds for feed and food[END_REF]. However, some functional properties of plant proteins such as the ability to stabilize emulsions are known to strongly depend on pH, ionic environment, presence of other ingredients, variation in pre-treatment processing of the proteins and thermal processing of emulsion-based foods [START_REF] Day | Proteins from land plants -Potential resources for human nutrition and food security[END_REF]Tang & Sun, 2011). Nevertheless, the interfacial properties of plant proteins are only partially known. In general, plant proteins form a relatively thicker interfacial layer at oil/water interfaces, compared with dairy proteins, due to their much larger molecular size and structural constraint by disulphide crosslinks [START_REF] Gharsallaoui | Interfacial and Emulsifying Characteristics of Acid-treated Pea Protein[END_REF]Wong et al., 2012).

Therefore, the question arises whether alternative plant proteins to soy or rice proteins could be conceivable in 1 st age IFs. Some authors studied the ability of using plant proteins in IFs, but the majority concerned follow-on formulas (6 to 12 months) using chickpea protein [START_REF] Malunga | The potential use of chickpeas in development of infant follow-on formula[END_REF]Ulloa, Valencia, & Garcia, 1988). Some others were focused on the capacity of probiotics encapsulation using plant proteins in follow-on IFs, as for example pea protein in [START_REF] Kent | Probiotic bacteria in infant formula and follow-up formula: Microencapsulation using milk and pea proteins to improve microbiological quality[END_REF] study or different legume proteins (chickpea, faba bean, lentil and pea) in [START_REF] Khan | Development of extrusion-based legume protein isolate-alginate capsules for the protection and delivery of the acid sensitive probiotic, Bifidobacterium adolescentis[END_REF] study. Recently, a process for preparing a 1 st age IF based on potato protein, naturally hypoallergenic, that is suitable for infants with cow's milk protein allergy, has been patented (WO2018 115340 A1). These relevant studies on the use of plant proteins in IFs need to be furthered with other protein sources that would be suitable to infant needs from birth, on a nutritional and functional point of view.

IFs are produced by spray drying a concentrated solution, which extends their shelf-life and aids handling [START_REF] Blanchard | Infant formula powders[END_REF]. The manufacture of powdered IFs usually includes the following unit operations: mixing, pasteurization, evaporation, homogenization and spray drying. Pasteurization aims to ensure microbiological safety and evaporation is conducted prior to drying in order to limit energy costs and increase the overall productivity. During IF homogenization, the oil phase is stabilised by proteins to form an oil-in-water emulsion [START_REF] Dickinson | Milk protein interfacial layers and the relationship to emulsion stability and rheology[END_REF]. Homogenization decreases the size of fat globules for preventing subsequent phase separation and reinforcing oil encapsulation [START_REF] Sun | Effects of Processing on Structure and Thermal Properties of Powdered Preterm Infant Formula: Properties of preterm infant formula[END_REF]. The properties of IFs, for example colour, solubility and storage stability can be affected by the component interactions [START_REF] Li | Comparative study of four physical approaches about allergenicity of soybean protein isolate for infant formula[END_REF], as well as by the unit operations. [START_REF] Sun | Effects of Processing on Structure and Thermal Properties of Powdered Preterm Infant Formula: Properties of preterm infant formula[END_REF] demonstrated that homogenization, pasteurization and spray drying steps strongly influenced the microstructure, thermal properties and structural characteristics of IFs. IF powders and the emulsions resulting from their reconstitution in water should be stable in order to avoid quality problems such as fat release, flecking, Maillard reactions, lactose crystallization (i.e., caking) and poor solubility. A greater understanding of the interactions between composition, manufacturing conditions and productprocess interactions is essential to solve the above stated problems.

In a previous study (Le Roux et al., submitted 2019a), four plant proteins have been selected for the preparation of innovative 1 st age IFs at a pilot scale. Selection was based on the following criteria: the proteins should contain an amino acid profile suited to infant needs (UE, 2016), have no known allergens or organoleptic defects, be commercially available and should be innovative alternative protein sources to animal or plant proteins already used in 1 st age IFs (EU, 2016). The aim of this study was to investigate the capability of a partial substitution (50%) of bovine milk proteins by plant proteins in IFs, considering a standard cow milk protein IF as a reference (RIF). Although these new protein sources are not yet allowed according to the applicable European regulation, the aim of the project was to investigate on it to pave the way to future innovation in this field. Physicochemical properties of these new IFs have been evaluated and in vitro static digestion assays have been performed respecting most of the infant physiological conditions. It was concluded that rice and potato proteins IFs showed limitations in terms of manufacturing (very high insolubility for rice IF and high viscosity for potato IF) as well as digestibility impairments (low proteolysis and low amino acid bioacessibility for both IFs, particularly for potato IF). On the contrary, pea and faba bean IFs (PIF and FIF) showed physicochemical properties and overall digestibility closer to the RIF.

In the present study, the semi-industrial scale-up of PIF, FIF and RIF preparation has been investigated in order to explore more representative processing conditions with regard to industrial realities and to confirm the first encouraging results previously obtained with the screening of the plant-based IFs produced at a pilot scale (Le Roux et al., submitted 2019a).

The influence of the process parameters, namely homogenization pressure and spray drying temperatures, on the physicochemical properties and the microstructure of the IFs was investigated using two different processing routes. To the best of our knowledge, this is the first time that 1 st age IFs (0 to 6 months infants) containing plant proteins other than soy, hydrolysed rice have been designed and their behaviour during processing investigated.

Materials and Methods

IF ingredients

Skim bovine milk powder (35.1 w/w% protein, 54.5 w/w% lactose) was purchased from SILL, Plouvien, France.

Maltodextrin (GLUCIDEX® Maltodextrin Premium 19, 89.0 w/w% maltodextrin) was purchased from ROQUETTE, Lestrem, France. Lactose (96.0 w/w%), whey protein concentrate (Protarmor™80, 81.4 w/w% protein), and demineralized whey protein concentrate (Lactarmor™ DM 90, 12.0 w/w% protein, 81.6 w/w% lactose) were all purchased from ARMOR PROTEINES in Loudéac, Saint-Brice-en-Coglès and Pontmain, France, respectively. Pea protein concentrate (Pisum sativum, Nutralys® XF, 71.7 w/w% protein) was purchased from ROQUETTE FRERES, Vic-sur-Aisne, France.

Faba bean protein concentrate (Vicia faba, VITESSENCE™ Pulse CT 3602, 60.9 w/w% protein) was purchased from INGREDION, Hamburg, Germany. An oil blend adapted to infant formulas (91.1 w/w% saturated fatty acids) was purchased from CARGILL REFINED OILS EUROPE, Izegem, Belgium. The composition of IFs was based on the nutritional requirements from the latest European regulation for 1 st age infant formula (EU, 2016). For 100 ml of reconstituted IFs at 13.4 ± 0.6 % DM, the nutritional composition was the following: 69.6 ± 2.0 kcal, 1.5 ± 0.1 % protein, 3.2 % ± 0.2 fat and 8.3 % ± 0.4 carbohydrates. The IFs ingredient composition is available in supplementary data (Table 3).

IF processing

The IFs were manufactured at Bionov (Rennes, France) according to the technological diagram presented in Fig. 1, which included two processing routes (1 and 2). Skim bovine milk powder, lactose, maltodextrin and the respective protein concentrates (whey protein as the reference, pea protein or faba bean protein as the plant protein sources) were solubilized in water at 20% w/w DM at 45°C under stirring at 35 Hz for 45 min. The protein concentrates represented 50 w/w% of the total protein content of the formula whereas the other 50 w/w% came from skim bovine milk; therefore, all infant powders were iso-nitrogenous. Neither additional vitamins or minerals (apart from those provided by the ingredients) were added since this study was primarily focused on protein fraction. The solution was then pasteurized at 80°C for 35 s, before concentration to approximately 48% w/w% DM in a two-stage semi-industrial scale falling film vacuum evaporator (GEA Process Engineering, St Quentin-en-Yvelines, France) with an evaporation capacity of 280 kg • h at 60 ± 4 °C. The concentrate was then cooled to 45°C and stored in a tank. The oil blend was added to the concentrate and was homogenized at 60°C and either 8/2 MPa or 14/4 MPa for the processing routes 1 and 2, respectively. Finally, the solution was spray-dried from 53 w/w% DM to 97 w/w% DM in a semi-industrial-scale Niro Atomizer (GEA-PE, Saint Quentin en Yvelines, France) spray dryer at Bionov (Rennes, France) (Bimbenet, Schuck, Brulé, Roignant & Méjean, 2002), which maximum theoretical evaporation capacity is approximately 90 kg • h . The dryer was equipped with a pressure nozzle of 0.73 mm orifice diameter and 15 MPa for RIF and PIF, 0.63 mm orifice diameter and 17 MPa for FIF, both (both providing a spray angle of around 60°). The inlet air temperatures were set at either 165°C or 150°C for the processing routes 1 and 2, respectively. The outlet air temperatures were set at either 75°C or 65°C for the processing routes 1 and 2, respectively. The concentrate homogenized flow rates were 100 ± 10 L • h and the major airflow rate was 3200 ± 100 kg • h . The resulting IF powders were finally stored in plastic bags at 20°C. Each IF, namely "formulation x processing route", was manufactured once.

Physicochemical analysis

Ash and protein content

Ash content was determined after incineration at 525 ± 25°C in a muffle furnace, according to [START_REF] Schuck | Analytical methods for food and dairy powders[END_REF].

Total nitrogen content was determined according to IDF (2001a) using the Kjeldhal method, and a conversion nitrogen factor of 6.38 for the reference bovine milk protein based IF [START_REF] Mariotti | Converting Nitrogen into Protein-Beyond 6.25 and Jones' Factors[END_REF]. For the IFs composed of 50% bovine milk proteins and 50% plant proteins, the conversion factor used was the average of the one of bovine milk proteins (6.38) and 5.4 for pea and faba bean proteins [START_REF] Mariotti | Converting Nitrogen into Protein-Beyond 6.25 and Jones' Factors[END_REF]. All measurements were carried out in duplicate.

Dry matter

Dry matter (DM; in g • 100 g ) was gravimetrically determined by drying 1 g sample mixed with sand in a forced air oven at 102 ± 2°C for 5 h. Measurements were carried out in duplicate.

Fat and free fat content

The total fat content was measured by Gerber's acid-butyrometric method after dissolution of proteins by the addition of sulfuric acid and of amyl alcohol to facilitate the separation of milk fat by centrifugation at 350g. The free fat content was obtained after extraction with petroleum ether and was determined gravimetrically after evaporation of the solvent. Total and free fat analyses were carried out in duplicate (AFNOR, 1990 ;[START_REF] Schuck | Analytical methods for food and dairy powders[END_REF]).

Water activity and glass transition temperature

Water activity ( ) was measured at 25°C ± 0.1°C using the Novasina aw-meter (Novasina, Switzerland).

The glass transition temperature (Tg) was determined on the powders after equilibration in a 20% relative humidity atmosphere using the SPSx-1µ Sorption Test System (ProUmid GmbH & Co. KG, August-Nagel-Str., Germany). Tg was determined at this constant sorption point by using a modulated temperature differential scanning calorimetry method according to [START_REF] Schuck | Analytical methods for food and dairy powders[END_REF]. Water activity and Tg measurements were carried out in triplicate.

Particle size distribution

The powder size distribution was determined using a laser scattering granulometer (Mastersizer, Malvern Instruments Ltd, Malvern, UK) with a 300-mm measurement cell (0.5-880 mm range). The refractive index of dried particles was 1.45, and 30 kPa air pressure was used. The median diameter d(0.5) was chosen to describe the particle size distribution of infant powders.

The particle size distribution of the dispersed elements present in solutions during process was determined using the same laser scattering granulometer in liquid channel. The particle size distribution was based on volume and expressed as sphere-equivalent diameter. The diameter Mode (the population of the particles the most frequent in the volume distribution) as well as and the D[4.3] (the mean volume diameter) were calculated. The refractive index used was 1.45 for blends of vegetable oils in infant formulas. The refractive index of 1.33 was used for water. The samples taken from concentration and homogenization steps were half-diluted in water prior measurement. About 0.2 mL sample was diluted in 100 mL water directly in the measurement cell of the apparatus in order to reach 10% obscuration. The experiments were performed in triplicate for each sample.

Color

The color of the powders was determined using the CIELAB color space in which the color is defined by the brightness L (from 0 to 100) and the chromaticity coordinates a* (from green to red; -60 to +60) and b* (from blue to yellow; -60 to +60). The three parameters were obtained using a chromameter (Konica Minolta Photo Imaging France SAS, Roissy, France) previously calibrated with a white reference plate. This experiment was performed in triplicate.

Rehydration properties

Dispersibility and solubility were determined according to [START_REF] Schuck | Analytical methods for food and dairy powders[END_REF]. The dispersibility index is defined as the amount of DM dispersed in water after 13 g powder have been added to 100 g water at 40°C under stirring with a spatula for 15 s. It is expressed as the w/w% of matter that can pass through a 200-mm sieve. The solubility index (SI) is defined as the v/v% of soluble particles (i.e., remaining in the supernatant after centrifugation of 160g for 5 min) after 13 g powder were added to 100 g water and two droplets of defoaming agent (octan-1-ol) at 40°C and mixed in a blender for 90 s.

These experiments were carried out in duplicate.

Viscosity

Apparent viscosity was measured using a controlled-stress rheometer (Rheometer, TA DHR2 Hybrid Instruments, Crawley, UK), equipped with a coaxial cylinder geometry and a solvent trap. Temperature was controlled by a Peltier apparatus (±0.1°C). Apparent viscosity was measured in triplicate on homogenized samples (53 w/w % DM) at 45°C, corresponding to the process temperature during the homogenization step. The shear rate was set at 1 to 1000 s -1 , under steady-state with the coaxial cylinder with a bob diameter of 28 mm and bob length of 41.98 mm. The viscosity was determined using Newton law or Power law model depending on the behaviour of the fluids measured (Newtonian or rheofluidifiant).

Confocal laser scanning microscopy

Confocal laser scanning microscopy (CLSM) observations were performed using an inverted microscope NIKON Eclipse-TE2000-C1si (NIKON, Champigny sur Marne, France). Samples collected during the process (before concentration, after concentration, after homogenization in presence of lipids) were stored at 50°C in a laboratory oven during the staining step and during the CLSM observations thanks to a temperature-regulated stage (Linkam Scientific Instruments Ltd, Tadworth Surrey, England). The powdered IFs obtained were rehydrated, stained and observed at 20°C. Fast Green FCF fluorescent probe (Sigma F7258, Sigma-Aldrich, St Louis, USA) was used for the labelling of proteins (Excitation = 632 nm). The lipid-soluble Nile Red fluorescent probe (5H-Benzo, α-phenoxazine-5-one, 9-diethylamino; Sigma -Aldrich, St Louis, USA) was used to label the lipids (Excitation laser = 543 nm). After labelling, the samples were kept for at least 30 min before microstructural analysis. A He-Ne laser operating at 543 nm wavelength excitation and emission detected between 565 nm and 615 nm, and a diode operating at 633 nm with emission detected with a long pass filter > 650 nm were used.

The observations were performed using a x40 and a x100 oil immersion objectives. The two-dimensional images had a resolution of 512 x 512 pixels and the pixel scale values were converted into micrometers using a scaling factor. In the multiple labelled samples, different colors were used to locate the fluorescent probes.

Statistical analysis

Statistical analyses were conducted with the use of R version 3.5.2 (The R Foundation, 2014).

Regarding the physicochemical composition, a one-way ANOVA ("anova.lme" function from the "nlme" package) was conducted with meal as the factor, after verifying that the residues of this model were normal with the Kolmogorov-Smirnov test ("lillie.test" from the "nortest"package) [START_REF] Fernandez | Residual Analysis and Data Transformations: Important Tools in Statistical Analysis[END_REF]. A post-hoc test ("LSD.test" of the "agricolae" package) was conducted when the differences were significant (p < 0.05). Results are expressed as means ± SDs.

Results & Discussion

In an innovation purpose, this study aimed to assess the possibility of substituting a fraction (50%) of bovine's milk proteins in IFs with alternative plant protein sources previously demonstrated to be relevant from a functional and a nutritional point of view (Le Roux et al. 2019a, submitted). Thus, pea and faba bean proteins were tested in the present study to design "plant IFs" at a semi-industrial scale and testing two different processing routes, in comparison to a reference IF including only dairy proteins. The three IFs, namely PIF, FIF and RIF were characterized for their physicochemical properties, their microstructure using confocal microscopy, as well as the stability of emulsion after reconstitution.

Physicochemical properties of IFs

The six IFs, namely PIF, FIF and RIF produced according to the processing routes 1 and 2 (Fig. 1), were equivalent in terms of dry matter (DM), ash, protein and fat contents with mean values of respectively 96.9 ± 0.6 w/w% DM, 1.6 ± 0.2 w/w% ash content, 10.9 ± 0.6 w/w% proteins and 23.3 ± 0.2 w/w% fat.

IFs generally contain a relatively large amount of unsaturated, and consequently oxidisable fatty acids. Hence, it is essential to control lipid stability and encapsulation during storage to ensure their nutritional value and flavour [START_REF] Nasirpour | Baby Foods: Formulations and Interactions (A Review)[END_REF]. The fat stability is generally considered as satisfactory when the free fat content remains below 5% in whole milk powder (Vignolles, Jeantet, Lopez, & Schuck, 2007). In the present study, free fat content was equal to 2.2 ± 0.3 w/w% of DM at T0, regardless of the IF and the process parameter sets. [START_REF] Mccarthy | Effect of protein content on the physical stability and microstructure of a model infant formula[END_REF] found similar results with a free fat level of 2.0 ± 0.2 % in dairy protein-based IF powder (with a protein: fat ratio of 0.43, i.e. a fat content a bit higher compared to IFs here tested with a protein: fat ratio of 0.47). After four months storage at 20°C (T4), free fat content increased for all IFs, with a rise between 22% and 122% for RIF1 and RIF2, respectively (Table 1).

Although all IFs contained less than 5% free fat, it is noticeable that such amount of free fat was already initially significant and increased over time, especially for RIF 2, which value (4.3 ± 0.6 w/w%) was very close to 5% after 4 months storage at 20°C. The high value of free fat measured in RIF 2 at T4 could be partly explained by the smaller particle size of this powder (d(0.5) diameter of 105.8 ± 0.6 μm) compared to the other IFs (d(0.5) diameters ranging between 111.8 ± 1.0 μm and 141.2 ± 1.6 μm), resulting in a higher surface exchange area leading to less fat retained in the particles and, consequently, more free fat released [START_REF] Buma | Particle size. Its estimation, influence of processing parameters and its relation to free-fat content. In Free fat in spray-dried whole milk[END_REF].

Besides, pea protein isolate has been defined as a good emulsifier for preparing oil in water emulsions (Franco, Partal, Ruiz-Marquez, Conde, & Gallegos, 2000;[START_REF] Lu | Foaming and emulsifying properties of pea albumin fractions and partial characterisation of surface-active components[END_REF]. However, its emulsifying capacity, as well as solubility, has been reported to be reduced when pH is close to its isoelectric point, i.e. 5.2-6.1 [START_REF] Karaca | Emulsifying properties of chickpea, faba bean, lentil and pea proteins produced by isoelectric precipitation and salt extraction[END_REF]. Moreover, the heat treatment of pea protein resulted in emulsions in which inter-droplet hydrophobic interactions are favoured, which can increase the droplet flocculation and thus destabilize the emulsion [START_REF] Mcclements | Protein-stabilized emulsions[END_REF][START_REF] Peng | Effects of heat treatment on the emulsifying properties of pea proteins[END_REF]. In the present study, the emulsions corresponding to the different IFs were moderately stabilized regardless of the protein source, as indicated by the free fat content measured, especially after 4 months storage. This suggests that the processing parameters should be optimized to decrease free fat level, processing route 1 appearing preferable than route 2. The emulsion stability could be also improved by using emulsifiers or producing bigger powder particles.

Spray-drying behaviour and storage ability of milk powder depend very much on both glass transition temperature (Tg) and water activity ( ) [START_REF] Schuck | Keeping quality of dairy ingredients[END_REF]. The mean was 0.19 ± 0.03, i.e. close to the optimal value of 0.2 as defined by [START_REF] Efstathiou | Article[END_REF] (Table 1). Therefore, the long-term quality of the IFs should be guaranteed, these powders being free from phenomena such as lipid oxidation, caking or browning that are likely to occur when is not at its optimal value. The Tg mean value at 0.2 was 58.7 ± 4.3°C for all the powders, and was significantly higher for RIF1 and FIF1 compared to the four other IFs with 66.7 ± 0.3°C and 60.5 ± 1.8°C, respectively. Dispersibility is defined as the capacity of wet aggregates to uniformly disperse when in contact with water. A powder is considered dispersible if the dispersibility index (DI) is higher than 85% [START_REF] Schuck | Analytical methods for food and dairy powders[END_REF]. The DI of the infant formula powders prepared in this study ranged between 99.7 ± 0.9% and 97.9 ± 1.5% for the RIF1 and RIF2, respectively (Table 1). On the other hand, the solubility index (SI) represents the loss of granular structure when the powder is solubilized in water. A powder is considered soluble when the SI is above 89.5 ± 2.2% [START_REF] Schuck | Analytical methods for food and dairy powders[END_REF]. In this study, the RIFs presented a SI value of 100%, while PIFs and FIFs showed SI values of 97.5% and 97%, respectively (Table 1).

Hence, all the powders prepared in this study can be regarded as dispersible and soluble according to these methods. Even more so as the rehydration ability can be enhanced by increasing temperature or stirring speed during the reconstitution step [START_REF] Jeantet | The influence of stirring speed, temperature and solid concentration on the rehydration time of micellar casein powder[END_REF]). However, it was visually noticeable that PIF and FIF encountered dispersion impairments when powder was dissolved in water, with insoluble particles produced during manufacturing of the plant-based IF powders and that create flecking when rehydrated. This behavior has also been noticed by (P. [START_REF] Schuck | Recent advances in spray drying relevant to the dairy industry: A comprehensive critical review[END_REF][START_REF] Singh | Controlling milk protein interactions to enhance the reconstitution properties of whole milk powders -A minireview[END_REF].

The color of the three IF powders were quite similar with the same brightness (L) value. However, PIF seemed to reach out towards grey color (lower a value), FIF towards yellow color (higher b value) and RIF was quite in a middle of the two other IF powders with more beige color. These color parameters are in accordance with the one found for a whole milk powder parameters (71.9 ± 0.2, 6.0 ± 0.1 and 17.4 ± 0.4, respectively for the parameters L, a, b).

Lastly, after dispersion in water and homogenization, the viscosity of some of the IFs studied here was significantly higher than usually recommended for an effective spray-drying. The highest value was measured for PIF2 at 1.55 Pa.s (Table 1).

For an optimal spray, the viscosity of a concentrate IF should be around 60 mPa.s (Vestergaard, 2004), and should not exceed 200 mPa.s to allow subsequent spray drying. Moreover, the viscosity of a concentrate influences the quality of the powder (bulk density, solubility, etc.) by varying the size of the spray droplets (Schuck, Méjean, Dolivet, Beaucher, & Famelart, 2005). Despite this, the high viscosities measured in this study seemed to not have affected the drying characteristics, neither the physicochemical properties of the final products (Table 1). Nevertheless, it is obvious that the viscosities measured for PIF did not correspond to optimal conditions for spray drying and that process optimization would be required. Moreover, it was noticeable that the viscosity significantly increased for all the IFs between processing routes 1 and 2, which correspond to homogenization pressures of 10 MPa and 18 MPa, respectively. This observation is thus consistent with the viscosity increase when pressure increases as reported by [START_REF] Pouliot | Effect of High-Pressure Homogenization on a Sterilized Infant Formula: Microstructure and Age Gelation[END_REF] for a study on IFs. These authors suggested that high pressures homogenization result in more casein spreading on fat globules, which finally increases their ability for interactions, up to gelation. However, it is likely that the poor solubilisation obtained for PIF at the powder rehydration stage was further completed by the different processing steps, including homogenization, thus leading to additional solubilisation of plant proteins. This latter could explain by itself the higher viscosity reported for PIF.

To sum up, it seems possible to produce IFs at semi-industrial scale in which dairy proteins are partially replaced by pea or faba bean proteins with regard to the key physicochemical criteria usually considered. However, some improvements should be done, notably to enhance the dispersibility and/or solubility of plant proteins, as well as a reduction of the free fat level. The viscosity of the concentrate to be dried should be lessened too. In this way, the processing route 1 seemed to provide better physicochemical properties than processing route 2, in particular regarding the free fat release and the viscosity value prior drying.

Effect of unit process operations on the microstructure of IFs

The microstructure of the plant protein based IFs (PIF and FIF) and the reference IF (RIF) during process and after rehydration was investigated by confocal laser scanning microscopy (CLSM). This highlighted differences in size distribution, composition and architecture of lipid droplets and proteins between the three IFs and between the process steps (Fig. 2 and Table 2).

After solubilisation of the different ingredients except oil blend, the modes of the particle size were about 0.3 and 2.1 µm for RIF, whereas bigger particles could be observed in plant-base IFs, with mode values of 58.9 µm for PIF, 11.2 and 46.6 µm for FIF. The bigger particles found in PIF and FIF suggest an incomplete solubilisation of plant proteins, but protein aggregates created during the technological processes might be also involved. Indeed, heating of globular proteins above their denaturation temperature [START_REF] Amagliani | Globular plant protein aggregates for stabilization of food foams and emulsions[END_REF][START_REF] Guo | Component Distribution and Interactions in Powdered Infant Formula[END_REF][START_REF] Guo | Effect of processing on protein-protein and protein-lipid interactions and mineral distribution in infant formula[END_REF] leads to their unfolding, exposure of hydrophobic patches and irreversible aggregation by forming hydrophobic interactions, hydrogen bonds and/or disulphide bonds. Protein aggregation may be to a greater or lesser extent, depending on the protein nature and the physicochemical conditions (pH versus isoelectric point, nature and concentration of salts, etc.), but in any case it influences the solubility of the proteins [START_REF] Benjamin | Emulsifying Properties of Legume Proteins Compared to β-Lactoglobulin and Tween 20 and the Volatile Release from Oil-in-Water Emulsions: Emulsifying properties of legume proteins…[END_REF][START_REF] Corredig | A differential microcalorimetric study of whey proteins and their behaviour in oil-in-water emulsions[END_REF][START_REF] Malaki Nik | Effect of soy protein subunit composition and processing conditions on stability and particle size distribution of soymilk[END_REF]. The solubility of pea protein isolate at pH 7.0 (i.e. close to pH 6.6-6.8 applied in the present study) was measured as 59.77 ± 2.34 % or 57.94 ± 0.21 % depending on the isolate was nonheated or heated at 90°C for 3 min [START_REF] Barac | Comparative study of the functional properties of three legume seed isolates: adzuki, pea and soy bean[END_REF]. [START_REF] Karaca | Emulsifying properties of chickpea, faba bean, lentil and pea proteins produced by isoelectric precipitation and salt extraction[END_REF] obtained a similar result (61.42 ± 0.77 %) when determining the solubility of pea protein isolate at pH 7.0 and at room temperature. At the end, such low solubility values are consistent with the large protein aggregates observed for the PIF in the present study. In the same conditions (pH 7.0, room temperature), [START_REF] Karaca | Emulsifying properties of chickpea, faba bean, lentil and pea proteins produced by isoelectric precipitation and salt extraction[END_REF] measured a higher solubility for faba bean protein isolate (89.65 ± 0.24 %), which was not observed in our case where big particle size and aggregate particles were observed in FIF, even if they were smaller compared to PIF (Fig. 2). The solubility of whey protein isolate (87.67 ± 0.02 %) reported by [START_REF] Pelegrine | Whey proteins solubility as function of temperature and pH[END_REF] was pretty close to our observations for RIF where particle size was much smaller (Fig. 2). In overall, different protein structures were observed for the three IFs from the beginning of the process, indicating that plant protein based IFs should require specific processing for better solubilisation.

After the concentration step, the size distribution seemed to be quite similar in all IFs, but lactose crystals appeared (Fig. 2). Bigger particles were still observed in the concentrated PIF and FIF solutions compared to RIF. In addition, circular particles could be observed in concentrated FIF that might be fibbers. As expected, small lipid droplets (in red, Fig. 2) appeared after addition of the oil blend and homogenization. The pressure applied upon homogenization was adjusted to obtain small size droplets (i.e. mainly <1 µm) in order to ensure the physical stability of the emulsion during long storage of the powder and after rehydration in baby bottle (Vignolles et al., 2007). Using the homogenization process parameters 1, a majority of lipid droplets close to 1 µm were observed in RIF (modes of 0.6 and 2.7 µm). In the homogenized PIF, a mix of small fat droplets and protein aggregates were observed in CLSM images, with mode values of 14.5 and 66.9 µm.

Homogenized FIF also showed small fat droplets, as well as much smaller protein particles than before homogenization (modes between 0.7 and 12.7 µm compared to 11.2 and 51.8 µm after concentration). These results suggest that the protein aggregates present in PIF and FIF have been dispersed to a higher level thanks to homogenization process. Only slight differences were noticed between homogenization 1 and 2 in terms of particle size. However, heterogeneous distribution of fat and proteins were observed in PIF and FIF after homogenization 2 and might be due to protein aggregation induced by heat treatments and mechanical treatments such as homogenization [START_REF] Guo | Component Distribution and Interactions in Powdered Infant Formula[END_REF][START_REF] Guo | Effect of processing on protein-protein and protein-lipid interactions and mineral distribution in infant formula[END_REF][START_REF] Joyce | Separation of the effects of denaturation and aggregation on whey-casein protein interactions during the manufacture of a model infant formula[END_REF][START_REF] Peng | Effects of heat treatment on the emulsifying properties of pea proteins[END_REF]. Lactose crystals with the characteristic "Tomahawk shape" were observed from the concentration step, and still after the homogenization step, with no change in average size and appearance. Conversely, lactose crystals disappeared after dilution of the samples. It should be reminded that samples taken from concentration and homogenization steps were half-diluted in water prior measurement. Thus, lactose crystals were dissolved and not observed on particle size distribution graphs (Fig. 2).

Finally, the rehydration in baby bottles of the IF powders obtained after either processing routes 1 or 2 showed a homogeneous and unimodal distribution of the fat droplets and the proteins in RIF with modes of 0.5 µm (i.e. < 1 µm). In PIF and FIF baby bottles, a bimodal particle size distribution was still observed with on the one hand, the proteins and the fat droplets < 1 µm and on the other hand, the protein aggregates (modes of 0.8-0.9 and 39-56 for PIF ; 0.6 and 9-10 for FIF). It could be noticed that the particle size decreased more than 3 times from the beginning to the end of the process, meaning that the process had probably an impact on the plant protein structure and re-dispersion of the aggregate particles.

These observations were in accordance with previous studies [START_REF] Guo | Component Distribution and Interactions in Powdered Infant Formula[END_REF][START_REF] Sun | Effects of Processing on Structure and Thermal Properties of Powdered Preterm Infant Formula: Properties of preterm infant formula[END_REF] in which it was highlighted that the homogenization and the thermal process steps had a key role on the microstructure of the infant milk formulas. In the present study, although particle size in the two plant-based IFs seemed to have decreased thanks to the process, it is clear that such an effect could be observed because plant proteins were initially not completely dispersed. Therefore, it is not possible to conclude which of the protein effect and the process effect has the major impact on the microstructure of PIF and FIF. In any case, additional analysis as well as replication of the manufacturing should be conducted further in order to clearly elucidate why the particle size of the plant protein-based IFs is so high and how it can be possible to decrease it. Especially, homogenization prior concentration step should be tested for improvement of the plant protein solubilisation.

Critical concentration of protein to stabilize emulsion in IFs

The oil-water interface has to be stabilized by surface-active molecules which can form a coat surrounding fat droplets of less than 1 μm in diameter. It ensures a good emulsion stability and a subsequent protection of fat droplets during drying and storage [START_REF] Dalgleish | Adsorption of protein and the stability of emulsions[END_REF]Turchiuli et al., 2005). Proteins are surface-active elements that play an important role in oilwater interfaces during the homogenization step, and then in air-liquid interfaces during drying. For instance, adsorbed proteins in homogenized milk result in steric repulsions, which allow emulsion stability (Vignolles et al., 2007). In fact, instability during emulsion formation occurs if there is insufficient surfactant to cover the entire oil-water interface created by the homogenizer. Adsorbed protein spread out to cover the maximum area, but if there are gaps in the interfacial layer, fat droplets may coalesce, decreasing the total surface area, until it is totally covered by the available surfactant [START_REF] Fang | Dimensions of the adsorbed layers in oil-in-water emuslions stabilized by caseins[END_REF]. The concentration of proteins in RIF after homogenization had thus been determined in order to verify whether it was sufficient to stabilize the emulsion. The critical protein concentration, namely the minimum protein concentration needed for encapsulating the fat content, was estimated as follows.

First, the fat droplet number (kg ) was determined according to:

= (1)
in which the total volume of fat droplet was calculated according to:

= ! ! " ! # ! " $ ! = %.'( )%% = 1.3 '% * + • ,-' (2)
given that the fat content in the IFs after homogenization was 12 w/w % and the density of the fat blend was )%% ,-• + .

The mean fat droplet diameter d chosen was 1 µm (close to D[4.3] values obtained after homogenization for RIF, Table 2).

The fat droplet volume (m / ) was calculated as:

= 0 ³ 2 = 3. ( '% ') ³ (3)
Equations 1, 2 and 3 came with a number of fat droplets equal to 2.5 '% '* ,-' .

Then, the area of the fat droplet interface ( ( • ,-' ) was obtained from the number of fat droplets and the fat droplet surface, given by: = 0d ( = 3.1 '% '( ( (4)

5 6 "! = N • = 7%% ( • ,-' (5)
Last, the minimum protein concentration (w/w %) was determined on the basis of area of the fat droplet interface and the droplet coverage by the proteins. Bovine milk proteins are well-known to widely spread on oil-water interface in emulsions [START_REF] Courthaudon | Influence of Emulsifier on the Competitive Adsorption of Whey Proteins in Emulsions[END_REF][START_REF] Hunt | Adsorption behaviour of whey protein isolate and caseinate in soya oil-in-water emulsions[END_REF], and authors generally consider that the amount of milk proteins absorbed at the surface of fat droplets is around 1.5 to 3.0 • 10 < kg of proteins • m D surface after homogenization [START_REF] Mccarthy | Effect of protein content on emulsion stability of a model infant formula[END_REF][START_REF] Pelan | The Stability of Aerated Milk Protein Emulsions in the Presence of Small Molecule Surfactants[END_REF]Ye, Singh, Taylor, & Anema, 2002):

E"!" "! ! ! " ! = F "! 6 "! • 5 6 "! = '. ( (. * '% + ,- "! • ,-' 6 -!"G ! ! (6)
In conclusion, 1.2 to 2.4 g of proteins per kg of emulsion were necessary to cover the fat droplets in the IFs. Then, the protein concentration in the IFs after homogenization (30 g.kg -1 ) was ten times higher than the critical concentration calculated. This probably explained why the stability of the emulsion did not significantly differ (structure and free fat release) regardless of the protein source, as the protein content was in excess in all IFs and thus enough to stabilize all the fat droplets. In other words, even in the plant-based IFs, soluble proteins might be in sufficient concentration to stabilize the emulsion, despite insoluble fraction was noticed.

Conclusion

This study handled the feasibility of producing, at a semi-industrial scale, plant protein-based IFs close to a reference dairy IF in terms of physicochemical and functional properties. It was seen that pea and faba bean proteins were hardly dispersed all along the manufacturing of the plant-based IFs, resulting in bigger particles, as well as flecking in the reconstituted powder compared to the milk reference IF.

It seemed that particle size in the two plant-based IFs have decreased thanks to the process, but it is clear that plant proteins were still in part aggregated, and contributed to high particle size values observed for PIF and FIF. Therefore, additional analysis as well as replication of the manufacturing should be conducted further in order to clearly elucidate why the particle size of the plant protein based IFs is so high and how it can be possible to decrease it. Especially, homogenization prior concentration step should be tested for increasing the plant protein solubilisation.

Moreover, the calculation of the theoretical quantity of proteins required to cover the lipid-water interface let to think that dairy proteins would have been in sufficient concentration to stabilize the emulsion, including in the plant based IFs. This likely explains the similar results between the three IFs in terms of emulsion stability with equivalent free fat release regarding the conditions applied in the present study.

In addition, high viscosity was reported for the concentrate to be dried for some of the IFs, in particular PIF using processing route 2. Despite this high viscosity seemed to not have affected the drying characteristics (Table 1, physicochemical properties of PIF 1 and PIF 2), the viscosity measured for PIF does not correspond to optimal conditions for spray drying and process optimization would be required.

Moreover, no major differences were noticed between processing routes 1 and 2 except slightly lower free fat (after 4 months storage) and higher dispersibility for RIF1 compared to RIF2; and lower viscosity for RIF1 and PIF1 compared to processing route 2. Thus, the choice would fell for processing route 1 if a decision should be taken.

In overall, it was seen that protein source had a great impact on IFs properties. That means process parameters should be adapted for each formulation in order to provide satisfactory IFs quality. Nevertheless, we have to remember that the results of this exploratory study needs validation. And beyond this, this study will further be extended through process optimization and industrial development as well as in vivo studies for nutritional assessment. Table 1. Physicochemical properties of the three powdered IFs (RIF: reference infant formula ; PIF: pea infant formula ; FIF: faba bean infant formula) and tested for the two processing routes: (1) 8/2 MPa homogenization and 165°C to 75°C drying temperatures; (2) 14/4

MPa homogenization and 150°C to 65°C drying temperatures. T0: measurement immediately after process; T4: measurement after 4 months storage at 20°C. Data are expressed as mean ± SD. For a given characteristic, values with a different superscript letter are significantly different (p < 0.05). Supplementary data. Table 3. Infant formulas ingredient composition for a liquid formula at 24 % DM. (RIF: reference infant formula;

PIF: pea infant formula; FIF: faba bean infant formula). Tg (°C) 66.7 ± 0.3 ᵃ 56.9 ± 5.5 ᵇ 60.5 ± 1.8 ᵃᵇ 55.9 ± 1.4 ᵇ 55.9 ± 4.7 ᵇ 55.9 ± 0.8 ᵇ Solubility index (SI; %) 100.0 ± 0.1ᵃ 97.5 ± 0.5 ᵇ 97.0 ± 0.5 ᶜ 100.0 ± 0.1ᵃ 97.5 ± 0.5 ᵇ 97.0 ± 0.5 ᶜ Dispersibility index (DI; %) 99.7 ± 0.9 ᵃ 99.5 ± 0.6 ᵃᵇ 98.7 ± 0.4 ᵃᵇ 97.9 ± 1.5 ᵇ 99.0 ± 0.9 ᵃᵇ 98.6 ± 0.5 ᵃᵇ Viscosity (Pa.s) 0.03 ± 0.01ᵉ 0.80 ± 0.04ᵇ 0.06 ± 0.02ᵈᵉ 0.24 ± 0.02ᶜ 1.55 ± 0.01ᵃ 0.09 ± 0.01ᵈ

Color parameters L a b 69.6 ± 1.0 ᵃ -4.4 ± 0.1 ᶠ 12.4 ± 1.9 ᵃᵇ 69.6 ± 1.0 ᵃ -1.9 ± 0.1 ᵃ 14.7 ± 1.6 ᵃᵇ 69.6 ± 1.0 ᵃ -4.0 ± 1.4 ᵈ 16.5 ± 0.8 ᵃ 70.5 ± 0.8 ᵃ -3.7 ± 0.1 ᶜ 10.7 ± 2.1 ᵇ 69.5 ± 1.0 ᵃ -2.2 ± 0.1 ᵇ 15.9 ± 1.3 ᵃ 70.9 ± 0.9 ᵃ -4.2 ± 1.2 ᵉ 16.5 ± 1.9 ᵃ

  Tham, Yeoh, & Zhou (2017) found comparable Tg values for IFs compared to the present study and showed a good storage stability at 25°C. McCarthy et al. (2013) reported a Tg value of 55.5 +/-1.01 °C for a dairy protein based IF powder ( = 0.23), also in accordance with our results.

CaptionsFig. 1 .

 1 Fig. 1. Semi-industrial process flow diagram for infant formulas (IFs) production including processing routes (1) or (2) (DM: dry matter; w/w: weight/weight).

Fig. 2 .

 2 Fig.2. Spatial organization of lipids (in red) and proteins (in green) as evidenced by confocal laser scanning microscopy (CLSM) in the three IFs (RIF: reference infant formula; PIF: pea infant formula; FIF: faba bean infant formula) after the different process steps, from solubilisation of the ingredients to the rehydration of the IF powders in baby bottle. Homogenization 1: 8/2 MPa, homogenization 2: 14/4 MPa. Baby bottle 1 and 2 were obtained after the rehydration of the IFs obtained with the process parameters 1 and 2 (homogenization and drying described in Section 2.2). Size distributions of processed IFs were determined by laser light scattering; The diameter Mode is the population of the particles the most frequent in the volume distribution and the D[4.3] is the mean volume diameter, these results are summarized in the Table2.

Fig. 1

 1 Fig. 1

Fig. 2

 2 Fig. 2

Table . 1

 .

			Process parameters 1			Process parameters 2
		RIF 1	PIF 1	FIF 1	RIF 2	PIF 2	FIF 2
	Free fat T0	1.9 ± 0.3 ᵃ	2.6 ± 0.6 ᵃ	2.1 ± 0.1 ᵃ	1.9 ± 0.3 ᵃ	2.6 ± 0.1 ᵃ	2.2 ± 0.2 ᵃ
	(w/w% total fat)
	Free fat T4	2.4 ± 0.2 ᵇ	3.2 ± 0.3 ᵃᵇᶜ	2.9 ± 0.7 ᵃᵇᶜ	4.3 ± 0.6 ᶜ	3.4 ± 1.2 ᵃᵇ	2.8 ± 0.3 ᵇᶜ
	(w/w% total fat)
	d(0.5) (μm)	133.7 ± 0.6 ᵇ	129.6 ± 1.2ᶜ	141.2 ± 1.6 ᵃ	105.8 ± 0.6 ᶠ	123.2 ± 0.2 ᵈ	111.8 ± 1.0 ᵉ
	𝑎 𝑤	0.14 ± 0.02ᵈ	0.18 ± 0.02ᶜ	0.18 ± 0.01ᶜ	0.21 ± 0.01ᵃᵇ	0.19 ± 0.01ᵇᶜ	0.22 ± 0.01ᵃ

Table 2

 2

	.
			D[4.3] (µm)	Mode 1 (µm) Mode 2 (µm) Mode 3 (µm)
		Solubilization	0.8 ± 0.4	0.3	2.1
		Concentration	4.6 ± 1.9	0.4	2.8
	RIF	Homogenization 1 Homogenization 2	0.8 ± 0.1 0.9 ± 0.3	0.5 0.6	2.8 2.4
		Baby bottle 1	0.4 ± 0.1	0.5
		Baby bottle 2	0.4 ± 0.4	0.4
		Solubilization	48.3 ± 0.1	58.9
		Concentration	45.4 ± 0.3	58.9
	PIF	Homogenization 1 Homogenization 2	34.0 ± 0.2 31.6 ± 1.4	14.5 58.9	66.9
		Baby bottle 1	18.9 ± 0.4	0.8	56.4
		Baby bottle 2	15.3 ± 2.0	0.9	39.7
		Solubilization	20.9 ± 0.1	11.2	46.6
		Concentration	18.9 ± 0.1	11.2	51.8
	FIF	Homogenization 1 Homogenization 2	9.9 ± 1.7 7.6 ± 0.3	0.7 0.7	2.4 6.7	12.7
		Baby bottle 1	6.2 ± 0.4	0.6	8.9
		Baby bottle 2	5.6 ± 0.2	0.6	10.0

Acknowledgements

The authors thank Pierre Schuck for his involvement in the experimental design and Anne Dolivet for her technical support for biochemical analysis. This work was part of a PhD project supported by the company Sill Dairy International.

Tang, C.-H., & Sun, X. (2011). A comparative study of physicochemical and conformational properties in three vicilins from Phaseolus legumes: Implications for the structure-function relationship. Food Hydrocolloids, 25(3), 315-324. https://doi.org/10.1016/j.foodhyd.2010.06.009 Tham, T. W. Y., Yeoh, A. T. H., & Zhou, W. (2017). Characterisation of aged infant formulas and physicochemical changes. Food Chemistry, 219, 117-125. https://doi.org/10.1016/j.foodchem.2016.09.107

The R Foundation. (2014). The R Foundation. R: a language and environment for statistical computing (Version 3.5.2).

Vienna (Austria).


S Bardy

B Aubert

T Bergara

L Berthe

P Combis

D Hébert

E Lescoute

Y Rouchausse

L Videau

Development of a numerical code for laser-induced shock waves applications

The recent development of LAser Shock Adhesion Test (LASAT) as quantitative Non-Destructive Testing (NDT) process for evaluation of structural bonded assemblies brings new challenges. Applicative assemblies composed of complex materials with poor transverse mechanical properties and highly resistant bonded joints require laser parameters optimization and a more accurate control on the whole process. The development of a numerical tool is then necessary to ensure laser parameters specification to evaluate the bond mechanical strength for a given assembly. In this document, the ability of ESTHER code for the description of laser-matter interaction on aluminum and ablation pressure prediction is exposed. The influence of the target initial reflectivity on ablation pressure is investigated. In this paper, validation of the code in both direct (1 -500

∕ 2 ) and water-confined (0, 2 -7 ∕ 2 ) irradiation regimes is achieved with comparison to suitable sets of experimental data. Experiments were led on two laser facilities: the transportable laser shock generator (GCLT) at the CEA/DAM/DIF and the Hephaïstos facility at the Processes and Engineering in Mechanics and Materials laboratory (PIMM lab). Numerical models developed in this work are compared to previous experimental data and to reference models. Ablation pressures defined by our predictive models can then be coupled to other codes which are able to describe 2D/3D shock propagation, in order to model the entire LASAT process on complex assemblies. Characterization of a 6061 Aluminum / Epoxy / 6061 Aluminum assembly is achieved using ESTHER, showing its ability to master the phenomena involved in the LASAT process. For the first time, results open the full numerical design of laser adhesion test with the same code.

INTRODUCTION

Transportation sector is currently facing a major challenge: the need to reduce greenhouse gas emissions in a context of significant growth, in particular in civil aeronautics [1,2,3]. One way to meet this challenge is to reduce structures' weight [START_REF] Cregger | Breaking the development cost curve by using analysis[END_REF]. Since the 1970's, civil aircraft structures lightening has been achieved by incorporating composite materials, which exhibit higher specific properties than metallic materials [START_REF] Mangalgiri | [END_REF]. Composites part has thus increased in such structures from 1 -2 .% to more than 50 .%. It is however unlikely that future programs involve even more composites in aircraft structures. Bonding technology appears then as a very promising way to achieve structural lightening. In fact, replacing mechanical fasteners such as bolts and rivets by bonded joints should enable a direct reduction of 12 to 15 % of a civil aircraft structural weight [6]. Nevertheless, bonded joints generalization and their application to critical components implies a need of certification. Nowadays, none of the conventional non-destructive testing (NDT) techniques is able to evaluate mechanical strength. There is therefore a crucial need to develop a NDT technology capable of bonded assemblies quantitative evaluation. The development of the LAser Shock Adhesion Test (LASAT) on bonded assemblies with NDT concerns must answer this challenge [7].

LASAT process is based on both shock generation by laser-matter interaction and shock propagation within multimaterials stacks. Focusing a pulsed laser beam of several to several tens of during some on a spot of some 2 of a metallic target enables heating the matter from solid to plasma state [8]. The rapid ejection of vapor from the extracted from models developed here, in both direct interaction configuration and WCR -temporal Gaussian pulse -= 7

FWHM -= 532 -Identification of the LASAT working range and water breakdown range target front face implies the application of a reaction force on the illuminated surface [9,10,11]. The resulting ablation pressure (

) exhibits roughly the same properties as the laser pulse: a fast loading ramp (1-2 ) combined to a high amplitude (maximal ablation pressure ( , ) of several ), typical of a shock wave. Two different interaction regimes are identified for laser-induced shock wave generation: the direct illumination regime, performed in vacuum conditions as presented in Figure 1 (a), and the Water-Confined Regime (WCR) (Figure 1 (b)) [12].

In the last case, the confining medium prevents plasma expansion and hence maximizes ablation pressure amplitude and duration [12,13,14]. As exposed on Figure 2, WCR requires then lower intensities (0

∕ 2 < < 7
∕ 2 ) than the one used in direct interaction regime (0 ∕ 2 < < 500 ∕ 2 ) to cover the typical LASAT ablation pressure range (0, 5 -6

). WCR is also employed for Laser Shock Peening (LSP) applications in the same range of laser pulse duration and intensities. WCR is thus preferred for industrial applications since it enables the use of compact laser facilities and is easily integrable to production or maintenance environments. Previous studies have highlighted the existence of plasma breakdown threshold at higher intensities ( > 7 ∕ 2 ) which limits shock generation in these conditions [15,[START_REF] Berthe | Processus de claquage des milieux transparents sous irradiation laser. application au choc laser en regime de confinement par eau[END_REF][START_REF] Sollier | Etude des plasmas generes par interaction laser-matiere en regime confine. application au traitement des materiaux par choc laser[END_REF]. In this study, all investigations were led under this threshold.

The second part of LASAT process lies on the propagation, transmission, reflection and attenuation of the front face-generated shock wave within the considered multi-materials stack. In acoustic propagation hypothesis, matter is subjected to compression stresses after a shock wave passes through it. Stresses diminishes then with release waves which follows the shock wave front. The incident shock wave is reflected in release wave at the free surface, on the target back face. Recombination of both incident and reflected release waves induces tensile stresses, which can lead to target spallation, and enables thus to test an interface [START_REF] Antoun | Spall fracture[END_REF]. It is therefore possible to steer tensile stresses amplitude and position with laser parameters.

In the case of bonded assemblies implying thick substrates (>> 0, 1

) of complex materials such as stratified composite, typical -laser pulse induces preferentially an intra-substrate failure, as shown on Figure 3 (a). Indeed, in this case, the recombination zone is located in the back face substrate which exhibits intra-laminar mechanical strength very close to bond mechanical strength. Previous studies have demonstrated the interest of laser parameters optimization to localize tensile stresses on the bonded joint [START_REF] Gay | [END_REF][START_REF] Ecault | Etude experimentale et numerique du comportement dynamique de composites aeronautiques[END_REF]. The double frontal pulse configuration has been identified as the ideal configuration, easier to use with access to one face only, as exposed on Figure 3 (b). Taking into account the complexity of composites' behavior under shock loading and the requirement for weak bond discrimination with just-below-tolerance mechanical strength (about 80 % of the correct mechanical strength), optimizing laser parameters in double-pulse configuration and mastering more accurately the whole LASAT process are two essential requirements. In the frame of an industrial exploitation of the process, an automatic numerical tool, integrating predictive models, is the unique solution for laser parameters optimizing, regarding a given application. No existing numerical laser-matter interaction models have proven to be predictive in the here-above mentioned configuration of interest. A previous numerical model, developed for mono-pulse ablation pressure prediction, produced results in good accordance with experimental results [START_REF] Wu | [END_REF]22,23]. However, it doesn't describe shock waves propagation on -thick samples and was never evaluated in double-pulse configuration. It is thus inappropriate for the here-above described application. The development of such numerical models for both direct interaction regime and WCR is shown here. The numerical tool used in this study for model development is ESTHER code. It is a Lagrangian mono-dimensional code able to describe radiation-matter interaction and shocks propagation in targets. It was initially developed at the CEA/DAM/DIF for femtosecond laser-matter interaction modeling [24,25,26]. It has also been used to simulate nanosecond laser-matter interaction in a high intensity range [27]. In our intensity range, a previous study was led with this code to highlight the influence of material properties on the ablation pressure determination process based on rear Free Surface Velocity (FSV) measurements [28]. This previous study also enabled to demonstrate ESTHER capacity of ablation pressure prediction on aluminum in the 50 -500 ∕ 2 range, identified as the typical range used in laser-induced shock wave experiments. This paper presents Esther code validation at even lower intensities to cover the 0 -500 ∕ 2 range in direct regime and the 0 -7 ∕ 2 in WCR on aluminum. The influence of physical phenomena on the ablation pressure is exposed and comparison of laser-matter interaction models with previous results is also achieved in both direct and WCR regimes. Finally, they are coupled to appropriate materials models and used for characterization of a 6061 Aluminum / Epoxy / 6061 Aluminum assembly. So, ESTHER has already been widely used to study the matter laser interaction in many conditions. This paper aims to demonstrate for the first time its ability to simulate all phenomena related to adhesion test techniques including material laser interaction, propagation in assemblies and damage to interface opening tools to design adhestion laser shock testing.

NUMERICAL TOOL

Modeled physical phenomena in ESTHER 2.1.1. Laser propagation and energy deposition

Laser propagation through matter is modeled by solving Helmoltz equation on each cell. Equation 1 represents Helmholtz relation which determines the absorbed part of the incident amount of energy entering in each cell. ⃖⃖⃖⃖ ⃗ 0 is the laser field, 0 the pulsation associated to the laser field, the light velocity and ̃ the complex index. ̃ is defined by Equation 2 with 1 the real index and 2 the imaginary index.

Δ ⃖⃖⃖⃖ ⃗ 0 + ( 0 ̃ ) 2 ⃖⃖⃖⃖ ⃗ 0 = 0 (1) ̃ = 1 + . 2 (2)
In ESTHER, 1 and 2 can be determined in a large range of matter states. Solid indexes are defined using E.D. Palik tables [START_REF] Palik | Handbook of Optical Constants[END_REF]. Plasma indexes are determined using Equation 3 and Equation 4, where is the electronic density, the critical electronic density and the electron-ion collision frequency.

1 = √ 1 - ( ) (3) 2
= 1 2 ∕ ( ) √ 1 -∕ ( ) (4)
These two last terms are calculated by the code with Equation 5 and Equation 6, typical of the Lorenz plasma model [START_REF] Spitzer | Physics of fully ionized gas[END_REF]. In these expressions, is the electron mass, the atomic number of the considered material, the electronic charge, Λ the electron-ion Coulomb logarithm, Boltzmann constant and the cell temperature. (5)

= 4∕3 √ 2 4 Λ (4 0 ) 2 √ ( ) 3∕2 (6)
In the Warm Dense Matter (WDM) field between solid and plasma state, indexes are determined by interpolation. Absorption of laser light is therefore calculated in a wide range of conditions. In addition, the method described here permits also to take into account reflection phenomenon at interfaces, defining the reflectivity (R) at normal incidence of each cell using Equation 7 [START_REF] Born | Principles of Optics[END_REF].

= ( 1 -1) 2 + 2 2 ( 1 + 1) 2 + 2 2 ) (7)
The ability to describe matter state evolution from solid to plasma state and reflection phenomena enables to model laser propagation on the whole range of states concerned by our application: from laser-metal to laser-plasma interaction. Continuities relationships are applied at cell interfaces and permit then to describe laser propagation through a stack of cells, defining reflection, absorption and transmission of laser light in each cell, as shown on Figure 4.

Hydrodynamics

In ESTHER, hydrodynamics is described by solving the equation of cell position evolution (Equation 8) and conservation equations for mass (Equation 9), momentum (Equation 10) and energy (Equation 11) on finite volumes in planar mono-dimensional hypothesis. In these equations, is the cell position, the time, the material velocity, is the density, the pressure, the pseudo-viscosity, the deviatoric stresses and the internal energy.

= (8) + ( ) = 0 (9)
+ 1 ( + -) = 0 (10)
+ + - ( ) = 0 (11)
These conservation equations are coupled to Equations Of State, solved on finite volumes, permitting to describe hydrodynamics in the cell stacking. Three types of EOS are available in ESTHER: perfect gas EOS, Puff-Mie-Grüneisen (PMG) EOS and tabulated EOS. PMG EOS enable to describe matter state close to ambient conditions ( 0 = 10 5 , 0 = 300 ). Tabulated EOS establish relationships between density, pressure, temperature and internal energy. Associated data are representative of matter state in conditions far from ambient ones, typical of lasermatter interaction-generated plasmas. These tabulated EOS take also into account solid/liquid and liquid/vapor state transitions. Bushman-Lomonosov-Fortrov EOS (BLF) and Sesame EOS transmitted by the Los Alamos National Laboratory (LANL) are very close to each other in the case of aluminum. Minor divergences exist around state transitions but the effects of such differences are negligible in the considered regime of intensities. These two EOS can thus be employed to model hydrodynamics in matter subjected to significant changes due to laser illumination on the target front face.

Energy transfer

In ESTHER, two types of energy transfer phenomena are implemented: thermal conduction and radiative transfer. Thermal conduction is driven by conductivity, calculated at interfaces as an harmonic mean, following Equation 12, where ℎ , + 1 2 is the mean conductivity at the considered interface, ℎ , the conductivity of one cell and ℎ , +1 of the cell on the other side of the considered interface. Thermal conductivity ( ℎ ) is determined in each cell, taking into account matter state. In solid state, data are extracted from Y.S. Touloukian tables [START_REF] Touloukian | Thermophysical properties of matter[END_REF]. In plasma state, data are determined from tabulated data, generated by the atomic physics SCAALP code [START_REF] Faussurier | [END_REF], [34]. Thermal conductivity can thus be calculated for a wide range of matter states, enabling the description of thermal conduction in the plasma and beyond, in the ablation zone.

ℎ , + 1 2 = 2 ℎ , ℎ , +1 ℎ , + ℎ , +1 (12)
Radiative transfer model in ESTHER is based on the so-called "SN" method [START_REF] Modest | Radiative heat transfer[END_REF]. Opacities and emissivities are calculated by using the Nohel code, developed at the CEA/DAM/DIF [START_REF] Decoster | Rapport des activités laser, Comissariat à l'Energie Atomique[END_REF]. Radiative transfer is activated as soon as at least one cell reaches a threshold temperature (typically 2eV).

Influence of initial reflectivity 2.2.1. Reflectivity-Roughness dependance -Implementation in ESTHER

Initialization of the target front face reflectivity is achieved using E.D. Palik tables. These tables determine optical indexes 1 and 2 for a given material and a given wavelength ( ). As precised before, these data consider a light beam with normal incidence on a perfectly flat surface. However, a previous study has highlighted how the surface state, e.g. roughness, can affect the apparent reflectivity [START_REF] Bergstrom | [END_REF]. This study demonstrates that a rough surface induce multiple reflections/absorptions of a single laser beam, due to local incident angle modification. Absorptivity is then enhanced, traducing a decrease of the apparent reflectivity. In order to take into account the initial surface state of the target in our model, solid reflectivity is directly steered by the modification of 2 . On Figure 5 (a), both 1 and 2 evolutions with wavelength are exposed for the case of a pure aluminum target, according to E.D. Palik tables. For the same material, Figure 5 (b) shows the evolution of the reflectivity ( ) with 2 variations, according to Equation 7and keeping 1 as defined by E.D. Palik tables, for the two wavelengths usually employed in laser-induced shock experiments ( = 532 and = 1064 ). We notice that = 0, 92 for = 532 with 2 = 6, 4 (Palik value) and = 0, 95 for = 1064 with 2 = 10, 0 (Palik value). Decreasing 2 enables to steer easily from the above-mentioned value to 0. Using this method permits to take indirectly into account the initial reflectivity state of the target in ESTHER simulations.

Reflectivity influence on ablation pressure

The influence of initial reflectivity on the ablation pressure process has been investigated by performing simulations in direct irradiation regime with = 1064 at various maximal intensities ( = 1,10 and 100 ∕ 2 ) for temporal top-hat pulses of duration = 10 . Intensity ramp from = 0 to = has a voluntarily-fixed duration at 10 , in order to minimize intensity ramp-induced effects. The decrease slope at the end of the pulse is linear with Table 1 Theoretical (Palik-based [START_REF] Palik | Handbook of Optical Constants[END_REF]) and experimental results of aluminum initial reflectivity = 532 = 1064 Theoretical 0,92 0,96 Experimental 0,4 (+/-0,1 mm) 0,52 (+/-0,1 mm) a duration of 1 , which is typical of experimental temporal top-hat pulses. In each configuration, a variation of is applied ( = 0, 5, 0, 65, 0, 8, 0, 95) and resulting ablation pressures are extracted from simulations and compared to each other. At low intensities ( = 1 ∕ 2 ), the initial reflectivity has a significant influence on ablation pressure. We notice on Figure 6 that lowering initial reflectivity implies more laser absorption and hence more energy deposition in aluminum at the beginning of the laser pulse. This phenomenon finally participates to a faster matter heating, state changes and plasma generation, in particular between = 0, 95 and = 0, 8 since absorption at solid state varies of a factor 4 between those two values. The resulting ablation pressures durations are consequently longer for lower reflectivities since the shock front corresponding to plasma generation appears sooner.

RESULTS AND DISCUSSION

Initial reflectivity definition

Reflectivity measurements were achieved at the two wavelengths of interest for the present work ( = 532 and = 1064 ) on aluminum targets by two previous studies [START_REF] Sollier | Etude des plasmas generes par interaction laser-matiere en regime confine. application au traitement des materiaux par choc laser[END_REF][START_REF] Courapied | Interaction laser-matière en régime de confinement par eau avec deux impulsions laser -application au test d'adhérence par choc laser[END_REF]. A synthesis of these measurements at solid state is exposed in the Table 1. These results confirm the difference existing between theoretical results and experimental results and highlight the need to consider lower-than-theoretical initial reflectivity to correctly reproduce low-intensity laser-matter interaction. = 0, 5 was used in ESTHER for = 532

WCR experiments and = 0, 6 was employed to reproduce = 1064 direct interaction experiments. The corresponding results are presented in the two following subsections.

Direct interaction regime

Experimental facility

The experimental facility used to perform direct irradiation experiments is the transportable laser shock generator (GCLT) of the CEA (Alternative Energies and Atomic Energy Commission). The Nd:YAG source of this facility delivers 1064 -laser pulses up to 40 with on-demand pulse durations from 5-to 100 -. The laser-pulse temporal profile can be designed in order to produce Gaussian-like, triangle or top-hat pulses. A vacuum chamber is employed to ensure direct interaction of the laser beam with the target. In this study, phase plates adapted to spot diameters ( ) from 1 to 3, 2 and CCD cameras were used to master and control the on-target spatial energy distribution. Phase-plates are placed as close as possible to the focusing lens. An anti-sparks plate, located between the target and the focusing lens as shown on Figure 7 (a), prevent any degradation from front-face particles ejection. Figure 7 (b) shows a typical spatial top-hat focal spot obtained by CCD imaging. A 532-nm VISAR system enables Free Surface Velocity (FSV) measurements of the aluminum target along time [START_REF] Barker | [END_REF]. Uncertainty on the intensity ( ) ( ) deposited in the axis of the VISAR spot is calculated for each laser shot by convolution of uncertainty on measured energy ( ), temporal profile, spatial distribution and uncertainty on GCLT focal spot -VISAR spot alinement. A large set of experiments was realized in these conditions, within the 0, 5 -500 ∕ 2 range and pulse durations from = 5 to 40 . It enabled to provide reliable experimental data for this study.

Model validation

Data extracted from the experiments are used as inputs or comparative outputs for numerical model validation. The pulse temporal profile ( ( )) and the laser wavelength ( ) are entered in the cell stacking of ESTHER as a solicitation on the external cell. Both internal and external cells are free to move. The velocity of the internal cell is recorded as nominal numerical FSV. Different simulations are run with ( ) -and ( ) + as input data, in order to generate numerical FSV curves representative of the energy source term uncertainty. For each shot, numerical and experimental FSV curves are then plotted together and compared. The shock generated by laser-matter interaction propagates through the target thickness and generates a fast increase of the FSV, followed by a slower decrease which characterizes the release wave coming out onto the target free surface. Validation of laser-matter interaction model must then be achieved using thin targets of thickness in the 100 -200 range in order to minimize material properties influence on the FSV curves [START_REF] Bardy | Contrôle et optimisation du test d'adhérence par choc laser sur assemblages collés[END_REF]. For each shot of the above-described set of experiments in the 1-500 ∕ 2 range, a good correlation between numerical and experimental curves was observed, as shown on Figure 8. Taking into account, maximal values of numerical FSV curves correspond to experimental ones. In addition, shapes and durations of FSV numerical peaks are very similar to what is observed in experiments. These observations account for a good reproduction of the laser-generated ablation pressure ( ( )) by the code, whatever the pulse duration and the temporal pulse shape. The laser-matter interaction model integrated to ESTHER is then validated as predictive tool with +∕ -15 % of accuracy on ( ), regarding ≤ 20% and the , -dependency expressed in the following part. Below 1 ∕ 2 , FSV peaks are of much smaller amplitude (< 20 ∕ ). FSV measurement uncertainty is evaluated in this work as ≈ 5 ∕ , based on a previous study [START_REF] Dolan | [END_REF]. Taking into account and , there is no possibility of valuable comparison in these conditions.

Pressure laws

Ablation pressures profiles ( ( )) can be extracted from ESTHER simulations. It is therefore possible to compare numerical results obtained with the above-described direct irradiation regime model to other models or experimental results. On Figure 9, maximal values of ablation pressures ( , ) are plotted against maximal values of the temporal [42] and experimental points determined by inverse methodology [START_REF] Tollier | Caractérisation de chocs-laser a éclairements modérés par interférometrie doppler visar. application a l étude de l'endommagement par écaillage de matériaux métalliques[END_REF]. Pressure-intensity dependency is the same in the three exposed cases and can be expressed as follows: , ∝ 0,75 . ESTHER results are similar to experimental ones, taking into account . They differ significantly from the semi-analytical model's results. However, taking into account the estimated accuracy on , of this last model, ESTHER seems in accordance with this model. Similar studies have been led with ESTHER to identify pressureduration and pressure-wavelength dependencies. The results of these studies enable to determine a scaling law for Gaussian pulses (Equation 13), comparable to the one of the semi-analytical model.

, [ ] = 1, 2.10 -3 . [ ∕ 2 ] 0,75 . [ ] -0,125 . [ ] 0,25 (13)

Water Confined Regime

Experimental facility

All water-confined experiments of this study are realized on the Hephaïstos laser facility of the PIMM laboratory (Laboratoire Procédés et Ingénierie en Mécanique et Matériaux). This table-top Nd-YAG source is composed of two independant laser beams (respectively A and B). These two laser beams follow the same optical path from the laser to 532 . Each beam is able to generate 7 -FWHM Gaussian laser pulses up to 7 . Perfect synchronization of A and B beams enable then to deposit energies up to 14 on the target front face. Significant improvement of the on-target spatial distribution of energy has been achieved through phase plates use. Figure 10 shows an example of energy spatial distribution. It has to be noticed that local extrema within the focal spot are significantly smoothed, lowering then . The experimental configuration used on this facility is similar to the one presented previously, unless experiments are led in air-free conditions and a thin layer of water is applied on the target front face. FSV measurements are also achieved with a 532-nm VISAR system. Single-pulse experiments were realized in these conditions within the 0, 1-7 ∕ 2 range and double-pulse experiments in the 0, 3-1, 2 ∕ 2 range, with associated delays such as 100 < Δ < 400 .

Adaptation of the numerical model to WCR conditions

The numerical model previously exposed and validated in direct interaction regime is slightly modified for WCR calculations. Water cells are added on the the external side of the aluminum cell stacking. The behavior of water must be described in a large range of states, from liquid to plasma state and even in the WDM field. However, very few experimental data refer to water in the WDM regime and, contrarily to aluminium, reconstruction by interpolation of optical constants and conductivity in WDM field is complicated because of the two-atoms specificity of water. Optical constants of water cells are thus fixed at ambient conditions for = 532

( 1 = 1, 33 and 2 = 0) [START_REF] Palik | Handbook of Optical Constants[END_REF]. These values enable to take into account incident laser beam reflection at air-water interface ( = 0, 04) and no absorption is permitted through the water layer. This hypothesis ensures complete absorption of the laser beam within the aluminum target. The WCR model is therefore based on the same absorption phenomena than the one aboveexposed for direct interaction regime. Thermal and hydrodynamic exchange is allowed at the water-aluminum interface. Hydrodynamic behavior of water is described by a tabulated EOS, inspired from Zamyshlyaev and Menzhulin model [START_REF] Zamyshlyaev | [END_REF]. Electronic contribution to ionization is taken into account by a typical Zel'dovich-Raizer formulation [START_REF] Zel | Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena[END_REF]. This EOS enables to describe the evolution of water state ( , , ) in each concerned cell and to take into account the acoustic confining action of the water layer on plasma. The overall water layer thickness must be higher than 500 to prevent perturbations of plasma behavior by water-front face release waves.

Model validation

The validation of the WCR model is realized using the same procedure than the one employed for direct interaction regime and exposed here-above. Taking into account , numerical and experimental FSV curves exhibit a good correlation in the 0, 2 -7 ∕ 2 range, as exposed on Figure 11. Numerical FSV peaks show the same shape, dependency exposed in the following part. Below 0, 2 ∕ 2 , higher discrepancy was found between numerical and experimental results. The thermal conduction model employed in ESTHER might be insufficient in these cases. In addition, the relevance of water conductivities in the WDM field, typical of these low intensities, must be questioned. Further works on thermal conduction data and modeling should be led if a major interest arises for laser-mater interaction in these very specific conditions.

Pressure law

Similarly to direct irradiation regime, numerical results obtained with ESTHER WCR model are compared on Figure 12 to experimental and analytical results. Experimental results were obtained recently in the same conditions than the ones used for this study ( = 7

FWHM -Gaussian single-pulses at = 532 on Hephaïstos) [START_REF] Courapied | Interaction laser-matière en régime de confinement par eau avec deux impulsions laser -application au test d'adhérence par choc laser[END_REF]. The comparative analytical model has been specifically designed for WCR and has been since then considered as a reference for ( , ) predictions in water-confined experiments [14]. However, this analytical tool contains a physical parameter ( ) that has to be calibrated using experiments. Based on experimental points exposed on Figure 12, = 0, 6 has been identified as the optimal value [START_REF] Courapied | Interaction laser-matière en régime de confinement par eau avec deux impulsions laser -application au test d'adhérence par choc laser[END_REF][START_REF] Berthe | [END_REF]. ESTHER results are very closed to experimental ones, taking into account and uncertainties on experimental points determined by inverse methodology (Figure 12). Pressure-intensity dependency is the same for both analytical and numerical models. It can be expressed as follows: , ∝ 0,5 . The adaptation of ESTHER to WCR conditions is good enough for pressure predictions, regarding the mentioned field of application. Scaling laws for , predictions can be defined using ESTHER. The Equation 14enables to determine maximal values of , for = 532 7 FWHM Gaussian pulses.

,

[ ] = 2, 4. [ ∕ 2 ] 0,5 (14)

Double-Pulse configuration

The relevance of ESTHER WCR model for double-pulse configuration is evaluated by comparing FSV outputs to experimental ones that have been generated on Hephaïstos facility. All double-pulse experiments were realized using phase plates, enabling a significantly lower uncertainty on the source term ( = 11%). Numerical FSV curves reproduce quite accurately experimental ones in the range of interest (0, 3 -1, 2 ∕ 2 with 100 < Δ < 400 ), as shown on Figure 13 (a). Synchronization of second pulse-generated peak (2) is excellent. FSV increment due to the second pulse is well reproduced and discrepancy between numerical and experimental signals is not higher for the second pulse peak than for the first one (1). Peak shapes are also quite similar, despite higher amplitude modulations on the numerical curve. The numerical model developed for WCR single-pulse configurations gener- = 2, ) exhibit a lower peak associated to the second pulse than the first one. This observation has already been reported in a previous work [START_REF] Berthe | [END_REF]. It implies a decrease in the laser matter-interaction ( 2, , < 1, , ), whatever and Δ . The diagram on Figure 13 b) corroborates this observation and shows also that the interaction intensity decreases with higher laser intensities and delays. Double-pulse configurations design for LASAT application should then be achieved by taking these limitations into account. In particular, higher intensity should be used on second pulse in order to generate double-pulse irradiation configuration with equal pressure on both pulses. It shows also that there is a very limited interest for delays higher than 400 for LASAT application, due to pressure decay with Δ .

Shock propagation in multi-materials stacks

Modeling multi-materials stacks behavior under shock loading implies to characterize each constitutive material independently, in order to choose, adapt and validate appropriate material models with a suitable set of experiments. An assembly model is then built by adding all layers successively with their corresponding material models. Validation of the assembly model is then achieved by comparing numerical FSV curves to experimental ones generated by laser pulse experiments without damaging. Another suitable set of experimental data generated at higher intensities should finally enable identification of inter-layer mechanical strengths. The application of such methodology is here exposed in the case of a 6061 Aluminum ( 800) / Epoxy (150 ) / 6061 Aluminum (600 ) assembly subjected to singlepulse laser-induced shock loading. Numerical results are achieved with ESTHER and compared to the ones given by a 2D-code.

Materials behavior under shock loadings

As previously exposed, ESTHER is able to accurately describe hydrodynamic behavior of materials subjected to shock loadings. However, reproduction of laser-shock experiments at moderate intensities requires also to take their mechanical behavior into account [28]. In addition, LASAT application modeling imply damaging properties implementation. Shock wave experiments have then been led in various intensity regimes in order to generate a sufficient set of experimental data for highlighting hydrodynamic, mechanical and damaging behavior of 6061 Aluminum. Epoxy behavior is supposed to be largely dependent of conditions of use, whether it is shocked as bulk material or employed as thin bonding layer within a multi-materials stack. No specific model is therefore developed in this work for epoxy as mono-material. An existing model is used and adapted to reproduce epoxy behavior in the assembly model [START_REF] Laporte | Analyse de la réponse d'assemblages collés sous des sollicitations en dynamique rapide[END_REF].

The tabulated Sesame EOS used for laser-matter interaction modeling on aluminum has already been used to model shock propagation in 6061 Aluminum [28]. In the present study, a more discriminating experimental configuration has been used to verify the relevance of such EOS for this specific alloy. In order to maximize the hydrodynamic component and minimize mechanical properties influence on FSV curves, thin 6061 Aluminum targets (50 -100 ) are subjected to high-pressure laser-generated shocks ( , > 10 ). Comparison of FSV curves reveals a satisfying reproduction of experimental results by the numerical model, as shown on Figure 14 (a). The first peak amplitude is accurately determined, as well as its shape and duration when is taken into account. The slight chemical composition discrepancy between pure and 6061 Aluminum seems to not interfere too much in the hydrodynamic behavior. The tabulated EOS used here is therefore able to describe both laser-matter interaction and hydrodynamic component of shocks in 6061 Aluminum. In this study, the same EOS is then used in the whole cell stack, preventing any perturbations due to EOS change through the target thickness.

The mechanical behavior of 6061 Aluminum under laser-generated shock waves has already been characterized in a previous study [START_REF] Jodar | [END_REF]. The same Steinberg-Cochran-Guinan (SCG) model has been choosen here [START_REF] Steinberg | [END_REF]. Specific experiments have been realized on thicker targets (250 -500 ) at lower pressures (0

> , > 3
), in order to highlight the elastic precursor and the elasto-plastic shock response. Modeling these experiments enables to evaluate the relevance of this model in the case of 6061 Aluminum subjected to moderate shocks. Small modifications of SCG parameters were necessary to describe more accurately the mechanical behavior of 6061 Aluminum, as exposed on Figure 14 b). For all experiments realized in similar conditions, elastic precursor amplitude is very well reproduced, implying a good identification of the material yield strength. In addition, the second peak synchronization is very good, which highlights a good reproduction of the whole elasto-plastic field. The final set of S-C-G parameters, given in Table 2, is then validated for 6061 Aluminum mechanical behavior modeling.

The damaging behavior of 6061 Aluminum was previously characterized in very near conditions than the ones considered in this study [START_REF] Jodar | [END_REF]. We used here the same Johnson model to fit spall experiments realized on both Hephaïstos and GCLT facilities [50]. High-pressure shocks ( , > 10

) have been employed in order to initiate damaging and generate spallation. Two minor modifications were brought on the previously defined set of parameters in order to increase the accuracy of the numerical model. 0 was slightly increased from 1, 0003 to 1, 0004 and lowered from 180 to 130 . 0 modification enables to reduce the evolution range of porosity. Decreasing of induces a lower stress to initiate damaging. The new set of parameters facilitates material failure, hence quicker spallation and higher ballistic velocity, as shown on Figure 15 (a) and (b). On this Figure, laser-matter interaction model generates a quite longer pressure profile than the experimental one. However, the new set of parameters enhances the correlation with the experimental FSV curve. Both changes are then required. The newly defined set of parameters is exposed on Table 3.

Assembly model validation

A set of single-pulse experiments has been led on GCLT facility on the assembly of interest for this study (6061 Aluminum ( 800) / Epoxy (150 ) / 6061 Aluminum (600 )). Laser illumination ( = 3, 2

) is applied on the thicker substrate and VISAR diagnostics is employed on the free surface. For a given pulse shape, pulse duration and focal spot diameter, variation of energy is applied to generate a large range of pulse intensities. Non-destructive testing (NDT) and post-shock micrographs of the post-shock sample enables to detect defects within the assembly. A disbond threshold has been identified using this technique but no damage has been found in 6061 Aluminum substrates. The experimental FSV curve exposed on Figure 16 (b) is taken out from the set of undamaged assemblies results and it is considered as the reference for numerical-experimental comparison. A first observation is that the signal is hardly understandable, contrarily to mono-material FSV curves. The assembly model is built using the 6061 Aluminum material model, coupled to the laser-matter interaction introduced in this document. Between both 6061 Aluminum substrates, a layer of epoxy is introduced. The epoxy behavior under shock loading is realized using a Puff-Mie-Grüneisen (PMG) EOS, coupled to an Elastic-Perfectly-Plastic (EPP) mechanical model, identified in a previous study [START_REF] Laporte | Analyse de la réponse d'assemblages collés sous des sollicitations en dynamique rapide[END_REF]. Using this assembly model enables to reproduce the experimental results with an overall good agreement. The origin of each shock breaking out on the free surface can thus be determined using a time-position diagram generated with ESTHER outputs, such as the one employed on Figure 16 (a). This tool shows that most of FSV increments are due to impedance mismatches between the epoxy layer and both substrates. An other numerical FSV curve has been generated with a 2D-axis-symmetrical simulation led with the same material models and the ablation pressure profile generated with ESTHER, introduced as source term. Despite some small discrepancies induced by focal spot edges-effects (i.e. for 350 < < 400 ), numerical FSV curves are very similar. Larger difference is observed for > 1000 , when 2D effects become dominants. ESTHER code with the associated numerical models is then validated for shock propagation modeling in the assembly presented here.

Identification of bond mechanical strength

Determination of the epoxy layer mechanical strength is determined using a FSV signal of a disbonded assembly. Numerical calculation of this experiment is realized using the validated assembly model. A cut-off model is then added to the epoxy material model and calculations are run with different cut-off strength values ( ℎ ℎ ). Comparison of numerical outputs with the reference experimental is then realized and the best numerical-experimental correlation is determined. The corresponding numerical signal defines the epoxy layer bond mechanical strength. In the case exposed on Figure 17 , whereas a significant discrepancy is visible between the numerical signal without damaging model and the experimental one. The stress history at both substrate/epoxy interfaces generated with ESTHER and exposed on Figure 17 (a) enables to determine the disbonding time ( = 730 ) and localization (interface 1). Disbonding generates free surfaces at the first interface, which modify the shock propagation pattern and thus the FSV curve exposed on Figure 17 (b). The same procedure has been applied on a higher bond quality and ℎ ℎ = 350 was found. The methodology here exposed has then allowed to discriminate two different bonding qualities on the considered assembly by determination of respective mechanical strengths. Table 4 exposes results obtained on both assembly qualities at high (laser-induced shock) and very low (pull-out quasi-static test) strain rates. These results show an obvious correlation between high and very low strain rates mechanical strength. One order of magnitude separates results obtained with both techniques, whatever the bond quality.

CONCLUSION

ESTHER code has proven to be a reliable code for ablation pressure predictions in both WCR and direct irradiation regime. Validation of the corresponding laser-matter interaction numerical models has been achieved respectively in the 0, 2 -7 ∕ 2 and 1 -500 ∕ 2 intensity ranges, considering appropriate experimental uncertainty

Figure 1 :

 1 Figure 1: Schematic view of the generation of a shock wave induced by laser (a) in direct interaction regime, (b) in water-confined regime

Figure 2 :

 2 Figure 2: Typical pressure laws

Figure 3 :

 3 Figure 3: Schematic Time-Position diagrams showing shock and release waves travels in a multi-materials target (a) in a typical ns-pulse configuration with the pulse duration, (b) in double frontal pulse configuration, with Δ the delay separating the two ns-pulses

Figure 4 :

 4 Figure 4: Schematic view of the propagation of an incident laser pulse through a stack of n cells, with optical indexes 1, and 2, determined for each cell (1 ≤ ≤ )

Figure 5 :

 5 Figure 5: (a) Evolution of optical real ( 1 ) and imaginary ( 2 ) indexes with the wavelength ( ) for pure aluminum according to E.D. Palik tables [29] and (b) Evolution of reflectivity ( ) with the imaginary index ( 2 ) for = 532 and = 1064 for pure aluminum with 1 determined by E.D. Palik tables [29]

Figure 6 :

 6 Figure 6: Influence of initial reflectivity on (a) laser deposition and (b) ablation pressure on pure aluminum target -= 1064 -= 1 ∕ 2 -= 10 -= 0, 5, 0, 65, 0, 80, 0, 95

Figure 7 :

 7 Figure 7: (a) Schematic view of the experimental set-up used on GCLT (b) Typical CCD image of a = 3, 2 focal spot

Figure 8 : 2 Figure 9 :

 829 Figure 8: Experimental and numerical FSV curves of 100 -aluminum target under direct laser irradiation -25 ∕ 2 -Temporal top-hat -= 10 -= 2, 2

Figure 10 :

 10 Figure 10: Typical CCD image of a = 6

Figure 11 :

 11 Figure 11: Experimental and numerical FSV curves of 500 -aluminum target under WCR irradiation -3, 0 ∕ 2 -Temporal Gaussian -= 7 FWHM-= 4, 0

Figure 12 :Figure 13 : 2 -

 12132 Figure 12: Evolution of

Figure 14 :Figure 15 :

 1415 Figure 14: Experimental and numerical FSV curves of 6061 Aluminum targets under laser irradiation (a) 100 -thick target exposed to GCLT -300 ∕ 2 -Temporal top-hat -= 10 -= 1 -= 11% in direct irradiation regime (b) 250 -thick target exposed to Hephaïstos -1, 1 ∕ 2 -Gaussian -= 7 FWHM -= 4 -= 30% in WCR

  (b), FSV oscillations of the experimental curve for > 880 are well reproduced by the numerical model with ℎ ℎ = 165

Figure 16 :

 16 Figure 16: Experimental and numerical results of 6061 Aluminum (800 ) / Epoxy (150 ) / 6061 Aluminum (600 ) under direct laser irradiation -GCLT -2, 9 ∕ 2 -Temporal top-hat -= 20 -= 3, 2 -Deduction of 20% on corresponding to -(a) Time-position numerical diagram generated with ESTHER (x=0 corresponds to front face position at t=0) (b) Experimental and numerical FSV curves with ESTHER (1D) and with a 2D code

Figure 17 :

 17 Figure 17: Experimental and numerical results of 6061 Aluminum (800 ) / Epoxy (150 ) / 6061 Aluminum (600 ) under direct laser irradiation -GCLT -16, 6 ∕ 2 -Temporal top-hat -= 20 -= 3, 2 -Deduction of 20% on corresponding to -(a) Numerical stresses in the shock propagation direction at both substrate/epoxy interfaces, generated with ESTHER (b) Experimental and numerical FSV curves with ESTHER (1D) with ℎ ℎ = 165

Table 2

 2 Optimal SCG parameters defined for 6061 Aluminum

	0 (MPa)		0 (GPa)	′	′ (GPa/K)	(MPa)
	400	5500 0, 10 0	27, 6	1, 79952 -1, 70016.10 -2	500

Table 3

 3 Optimal Johnson parameters defined for 6061 Aluminum

Table 4

 4

	Mechanical tensile strengths of two different bonding qualities on 6061 Aluminum (800	) / Epoxy (150	) / 6061 Alu-
	minum (600	) assembly
		ℎ ℎ ,	(MPa)	ℎ ℎ ,	(MPa)
		Quality 1 175		15,8 +/-3,3
		Quality 2 350		36 +/-3,6

ACKNOWLEDGMENTS

We gratefully acknowledge the support of BPI France, Ile de France, Nouvelle Aquitaine regions, and competitiveness clusters ASTECH, Route des Laser and Aerospace Valley through the CompoChoc project for this work. We also wish to thank L. Dinand for samples realization.