Jérôme Rousseau
email: jerome.rousseau@u-bourgogne.fr

Noelle Edwige

Ngoufo Donkeng

Fabienne Farcas

Sébastien Chevalier

Vincent Placet

Noëlle-Edwige Ngoufo Donkeng

Thermal and hydrothermal ageing of flax/polypropylene composites and their stainless steel hybrid laminates

Keywords: A. Biocomposite, B. Environmental degradation, Impact behaviour, D. Mechanical testing

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

Introduction

Hybridization, a proven strategy to toughen composites, involves the combination of two or more types of materials or fibres. Fibre metal laminates are a good approach to overcome most limitations of metal and polymeric composites. They belong to a subfamily in which thin metal layers alternate with composite plies. When compared to single-component materials, FMLs provide added functionalities such as high bending strength, fatigue and impact resistance, damage tolerance, acoustic absorption, vibration transmissibility and damping characteristics [START_REF] Sinmazçelik | A review: Fibre metal laminates, background, bonding types and applied test methods[END_REF][START_REF] Swolfs | Fibre hybridisation in polymer composites: A review[END_REF][START_REF] Vieira | Novel fibre metal laminate sandwich composite structure with sisal woven core[END_REF]. They have been applied in the transportation sector for decades [START_REF] Roebroeks | Fibre-metal laminates: Recent developments and applications[END_REF][START_REF] Vermeeren | An Historic Overview of the Development of Fibre Metal Laminates[END_REF][START_REF] Vogelesang | ARALL: A materials challenge for the next generation of aircraft[END_REF]. FMLs with a sandwich structure have also been developed more recently for use in the construction sector. They are made of two external skins thermally bonded to a polymeric core and are referred to by the SCM acronym, which stands for Steel Composite Materials. They are used as tough materials with good energy absorption, high durability, impact resistance and aesthetic advantages. The introduction of such materials in the manufacturing of lightweight portable outdoor structures, such as urban furniture, represents an interesting opportunity.

When reviewing the history of FML developments, a strong evolution in material selection can be seen. After a first generation made of aluminium and fibre reinforced thermoset resin composites, including the most widely known examples of GLARE (glass laminate aluminium reinforced epoxy), CARALL (carbon aluminium laminate) and ARALL (aramid aluminium laminate), the second generation was characterized by the utilization of thermoplastic matrices for the composite parts, which provide shorter manufacturing cycles, reduced cost and greater flexibility in manufacturing process, recycling and repair, and more versatility in attainable shapes [START_REF] Reyes | The mechanical properties of fibre-metal laminates based on glass fibre reinforced polypropylene[END_REF]. Recently, increasing environmental concerns have encouraged researchers to develop new ranges of sustainable FMLs made of wood and plant fibre composites [START_REF] Vieira | Novel fibre metal laminate sandwich composite structure with sisal woven core[END_REF][START_REF] Kuan | The fracture properties of environmental-friendly fiber metal laminates[END_REF][START_REF] Ramakrishnan | Experimental study of adhesively bonded natural fibre compositesteel hybrid laminates[END_REF][START_REF] Santulli | Damage characterisation on PP-hemp/aluminium fibre-metal laminates using acoustic emission[END_REF][START_REF] Segovia | Life Cycle Assessment Contribution in the Product Development Process: Case Study of Wood Aluminum-Laminated Panel[END_REF][START_REF] Vasumathi | Effect of Alternate Metals for use in Natural Fibre Reinforced Fibre Metal Laminates under Bending, Impact and Axial Loadings[END_REF]. In order to maintain consistency with the naming conventions of previous solutions, new acronyms have been introduced, such as SIRAL (sisal fibre reinforced aluminium laminates) [START_REF] Vieira | Novel fibre metal laminate sandwich composite structure with sisal woven core[END_REF] and CAJRALL (carbon-jute reinforced aluminium laminate) [START_REF] Vasumathi | Effect of Alternate Metals for use in Natural Fibre Reinforced Fibre Metal Laminates under Bending, Impact and Axial Loadings[END_REF]. Plant fibre composites have many advantages related to light weight, cost, mechanical performance, and damping capacity [START_REF] Bourmaud | Towards the design of high-performance plant fibre composites[END_REF][START_REF] Liu | Damping behavior of plant fiber composites: A review[END_REF], and they are good candidates to reduce the carbon footprint of composite materials and associated FMLs. For example, the life cycle of wood-aluminium laminated (WAL) panels was recently assessed [START_REF] Segovia | Life Cycle Assessment Contribution in the Product Development Process: Case Study of Wood Aluminum-Laminated Panel[END_REF]. The results showed that the environmental impact of manufacturing was less for WAL panels than aluminium honeycomb panels. Wood-based composite manufacturing showed environmental advantages in all damage categories except in ecosystem quality, while aluminium alloy sheet manufacturing played an important role in the environmental impact for laminated panel development [START_REF] Segovia | Life Cycle Assessment Contribution in the Product Development Process: Case Study of Wood Aluminum-Laminated Panel[END_REF].

While the main advantages of this most recent generation of FMLs made of biobased composites are quite well illustrated in the recent literature, it remains necessary to investigate their long-term durability. Indeed, plant and wood fibres are very sensitive to hygrothermal and hydrothermal conditions, and the durability of PFCs is still an open question [START_REF] Chang | Studies on durability of sustainable biobased composites: a review[END_REF]. The adhesion between the metal and the PFC layers in the frames of FMLs, already identified as a critical constraint [START_REF] Ramakrishnan | Experimental study of adhesively bonded natural fibre compositesteel hybrid laminates[END_REF][START_REF] Santulli | Damage characterisation on PP-hemp/aluminium fibre-metal laminates using acoustic emission[END_REF][START_REF] Segovia | Life Cycle Assessment Contribution in the Product Development Process: Case Study of Wood Aluminum-Laminated Panel[END_REF], requires specific attention and investigation under various ageing conditions. This paper studied steel composite materials prepared from flax polypropylene and their hybrids obtained by the addition of stainless steel external skins. Their service properties for outdoor use involve variable environmental conditions, among which humidity and temperature were selected for the present study. To investigate the effects of ageing, the samples were forced to undergo oxidative degradation. Therefore, severe conditions were applied, i.e., water immersion at 70 °C and heating at 120 °C. The effects of these two accelerated ageing conditions were studied through visual examination, mass and dimension evolutions, molecular characteristics using spectroscopic analysis, and mechanical properties selected for their ability to represent the intended use (3 point bending and impact).

Materials and methods

Materials

The two materials selected for the preparation of the composites and hybrid specimens were a flax/polypropylene composite and stainless steel. The composite material used in this study was Nattex (Dehondt Composites, Port-Jérôme-sur-Seine, France) constituted from a 3/1 twill fabric pre-impregnated with a polypropylene matrix (60% mass fraction, areal weight 800 g/m²). Figure 1 presents the elementary cell of the fabric. The elastic properties of the composite material are presented in Table 1. E1 and E2 are the weft and warp moduli, respectively, 12 is Poisson's ratio and G12 is the shear modulus of the composite. These properties were measured by a tensile test at a rate of 2 mm/min at room temperature using an universal tensile testing machine MTS Criterion C45 (MTS, Eden Prairie, USA). The shear modulus G13 was measured by means of a short beam shear test. The skins were made of austenitic stainless steel K41X (Aperam, Isbergues, France). Its mechanical properties, measured by a tensile test for E and , and calculated from these values for G, are also listed in Table 1.

Manufacturing

Composite plates were made from only Nattex to study the ageing behaviour of the flax/PP material. The specimens were produced using non-dry materials. As evidenced by recent research, the utilization of non-dry flax fibers in processing can improve the mechanical performances and durability of composites, particularly when utilizing matrices that are less sensitive to moisture [START_REF] Javanshour | Impact and fatigue tolerant natural fibre reinforced thermoplastic composites by using non-dry fibres[END_REF][START_REF] Lu | Improving moisture durability of flax fibre composites by using non-dry fibres[END_REF][START_REF] Lu | Long-term moisture cycling performance and unexpected strengthening of non-dry flax fibre composites[END_REF]. The Nattex material was stored in a room in which the temperature was measured between 19 and 21°C and the relative humidity between 30 and 40%. The moisture content of the material was at equilibrium under these hygrothermal conditions. Four plies were stacked with a sequence [90/0]2.

The laminate was manufactured in a Fontijne TPC 321 thermocompression press (Fontijne Presses, Delft, The Netherlands). The temperature cycle included a temperature increase at a rate of 5 °C/min to 170 °C, followed by a 5-min plateau, then cooling of the laminate at 5 °C/min to room temperature. A pressure of 3 bars was applied at the beginning of the plateau and maintained until the end of the cycle.

Samples made exclusively from polypropylene were also produced using the side regions of Nattex plies containing no fibers. The material was melted and shaped into sheets using the same temperature cycle employed in the manufacture of composite plates.

Hybrid specimens with the same dimensions (350 mm x 350 mm) were manufactured using the same temperature/pressure cycle. The only difference was that two steel skins (0.2 mm thick) were bonded to the composite with a thermoplastic ethylene/vinyl acetate copolymer adhesive film Pontacol 20.201 (Everad Adhesives, Marlenheim, France). The metal sheets were abraded with sandpaper and degreased with acetone before bonding.

The final average thickness of the plates was 3.4 mm for the composite alone and 3.8 mm for the hybrid plates. Composite and hybrid samples were cut using a ProtoMAX water jet cutting machine (Omax, Washington, USA). The dimensions of the samples were 170 mm x 25 mm for the three-point bending tests and 100 mm x 100 mm for the impact tests. The specimens were conditioned at 23 °C and 50% RH for 7 days before the initial tests.

Ageing methods

Two ageing methods were selected for this study. For hydrothermal ageing, samples were immersed in distilled water at 70 °C. For thermal ageing, samples were placed in an oven at 120 °C. In both cases, the samples were periodically removed for dimensional measurements and weighed using an electronic balance Radwag PS 1000.R1 with 0.001 g precision (Radwag, Radom, Poland). The specimen edges were not protected to allow water absorption even in the presence of the stainless steel skins.

The aged specimens used for mechanical characterization were removed from the water or the oven and placed in airtight sealed bags before testing, which was performed within 24 hours.

IR spectroscopy

Infrared spectra were obtained using a Nicolet iS20 (Thermo Fisher Scientific, Waltham, MA USA) equipped with an ID7-ATR spectrometer with a diamond crystal with a fixed incident angle of 45°. The specimens were analysed in triplicate by absorbance spectra in the region between 4000 and 400 cm -1 with 32 scans at 4 cm -1 resolution using OMNIC 9 software provided by ThermoFisher Scientific.

To monitor the ageing process of flax/polypropylene composite, the changes in the obtained spectra were analysed. Significant focus was given to two specific characteristic bands. The first, centred at approximately 1730 cm -1 , is associated with the carbonyl function (C=O) and is linked to the presence of stabilizers and to the oxidation of the polypropylene [START_REF] Huang | Thermal oxidation of poly(dicyclopentadiene) -Effect of phenolic and hindered amine stabilizers[END_REF]. The second characteristic band, centred at approximately 1640 cm -1 , is related to the conjugated carbonyl group and is representative of lignin [START_REF] Panaitescu | High flow polypropylene/SEBS composites reinforced with differently treated hemp fibers for injection molded parts[END_REF]. In order to eliminate the influence of variations in the IR beam penetration depth on the analysed quantities and given that the amount of alkyl groups remains relatively constant during ageing, the monitoring was carried out using the structural indices determined by the equations below:

I C=O = ( Area of carbonyl band centered around 1730 cm -1
Area of alkyl band between 3060cm -1 and 2760cm -1 ) × 100

(1)

I lignin = (
Area of carboxyle of lignin band centered around 1640 cm -1 Area of alkyl band between 3060cm -1 and 2760cm -1

) × 100

Scanning Electron Microscopy

A JEOL JSM-7600F SEM (Jeol, Tokyo, Japan) was utilized to investigate the surface morphology and ageing effects of specimens at a magnification ranging from x25 to x65, with a 5 kV accelerating voltage. The samples were coated with gold before analysis.

Mechanical testing

Bending test

Three-point bending tests were performed using the MTS C45 tensile testing machine, according to the ISO 14125 standard. The dimensions of the tested specimens were 170 mm in length and 25 mm in width. A span of 100 mm and a deflection rate of 2 mm/min were used for all the tests. The bending modulus, strength and strain at failure were then determined according to the standard.

Impact testing

Impact tests were performed on a Dynatup 9250 instrumented drop tower (Instron, Norwood, USA). The square specimens, 100 x 100 mm, were clamped by a pneumatic fixture, leaving a 76 mm diameter circular unclamped opening. The tup had a hemispherical head with a diameter of 20 mm. The falling mass had a weight of 5.88 kg, and the falling height was fixed at 0.35 m to obtain an impact energy of 20 J for all specimens. This impact energy was selected after conducting initial tests that demonstrated its ability to puncture unaged specimens. Data recorded by the machine were the impactor initial velocity and the impact load at a frequency of 410 kHz. Other values, such as impactor velocity, displacement, and energy evolution, were derived from the load and time data. Absorbed energies were calculated by integration of the complete load displacement curve for hybrid samples (with impactor rebound), whereas for composite samples, where perforation occurred, only the part of the curve until the maximum load was considered for this integration.

Mechanical tests after hydrothermal ageing were performed on the water-saturated specimens and at ambient temperature. In the case of thermal ageing, mechanical tests were performed on the dried material at ambient temperature.

Single-lap shear test

Single-lap specimens were used to evaluate the adhesion between the composite and the stainless steel. The single-lap joints were manufactured using a composite plate and a 2 mm thick steel plate of the same grade as the skins. The 300 x 150 mm plates were stacked with a 25 mm overlap length and assembled in the thermocompression press using the same procedure as for the hybrids. The assembly was then cut with a water jet into 25 mm wide specimens. Tensile tests were performed using the MTS C45 tensile testing machine equipped with offset jaws at room temperature and at 100 °C. Adhesion was characterized by the shear strength of the lap joints.

Results

Hydrothermal ageing

The evolution of the mass of the composite and hybrid specimens as a function of the immersion time in distilled water at 70 °C is presented in Figure 2.

For the composite, the evolution was similar for the bending and impact specimens, which had dissimilar geometries. After rapid water uptake during the first ten days, stabilization at approximately 8% weight gain was observed between ten and forty days.

This significant water uptake was mainly due to the hydrophilicity of the flax fibres.

The order of magnitude was consistent with that of previous studies [START_REF] El Hachem | Hygroscopic multi-scale behavior of polypropylene matrix reinforced with flax fibers[END_REF][START_REF] Cheng | Environmental durability of carbon/flax fiber hybrid composites[END_REF]. Water uptake resulted from both the diffusion of water in the composite through the main plate faces and capillary mechanisms originating from the unprotected edges. A progressive and quasi-linear mass loss was then observed from 40 to 180 days of ageing. This mass loss was attributed to the degradation and leaching of the flax fibres. Immersion in hot water is well known to induce the extraction and hydrolysis of pectins and hemicelluloses from flax and then their release and dissolution in water [START_REF] Bourmaud | Importance of fiber preparation to optimize the surface and mechanical properties of unitary flax fiber[END_REF]. These biochemical modifications could also explain the significant change in colour observed during hydrothermal ageing (Figure 3). It was observed a colour change from yellowbrown before flax was immersed to dark-grey when it was immersed and watersaturated. Similar colour transitions were previously observed for flax and hemp fibres during dew retting [START_REF] Martin | Influence of the degree of retting of flax fibers on the tensile properties of single fibers and short fiber/polypropylene composites[END_REF][START_REF] Placet | The influence of unintended field retting on the physicochemical and mechanical properties of industrial hemp bast fibres[END_REF]. This darkening in the fibres was attributed to the metabolic activities of microorganisms during retting [START_REF] Akin | Color Measurement of Flax Retted by Various Means[END_REF]. After hydrothermal ageing and drying, the fibres returned to a clear and whitish colour (Figure 3c).

When stainless steel skins were added to the composite, the sorption kinetics slowed, particularly for the square specimens (prepared for impact tests). Almost 50 days were necessary to reach equilibrium. In this case, water sorption was only possible through the specimen edges. Interestingly, with the hybrid material, equilibrium was then maintained during ageing. A slight onset in mass loss was observed after 140 days of ageing. The skins constituted protective layers that impeded the leaching of the composite and the release of hydrolysed material.

Hydrothermal ageing also induced changes in the PP matrix, as revealed by FTIR (Figure 4). For composites immersed in water, the region of the FTIR spectrum between 1500 cm -1 and 1800 cm -1 showed a decrease in the carbonyl band at 1730 cm -1 over time and an increase in a large band at approximately 1640 cm -1 .

The absorption band at 1730 cm -1 was characteristic of carbonylated stabilizers PP. Thus, this decrease showed that these components were extracted in the aqueous environment [START_REF] Minerbe | Impact of polyethylene and polypropylene geomembranes in sensitive aquatic environment[END_REF]. This phenomenon, highlighted by the evolution of IC=O in Figure 5a, appeared to be rapid from the time of immersion to 50 days, and a slower decrease was observed up to 177 days. Additionally, the increase in the absorption at approximately 1640 cm -1 , which was related to lignin, revealed loss of polymer at the surface of the composite and therefore exposure of the flax fibres. Again, the phenomenon started after 30 days and became significant at 177 days, as shown by the evolution of Ilignin in Figure 5b.

Hydrothermal ageing also induced a significant effect on the bending properties of the composite and hybrid materials (Figure 6 and Figure 7). For composites alone, a significant decrease in the bending modulus was observed from the earliest ageing days (Figures 6a and7a). It dropped from approximately 8 GPa to 1.9 GPa after ten days and then remained constant during ageing. A slight increase was observed for the last measured time (177 days). This general decrease in stiffness was mainly attributed to a reversible mechanism, the plasticization of the flax fibres by water. This was consistent with the significant increase in the strain at failure (Figure 7c). The loss of stiffness was attributed in part to damage. Indeed, the swelling of the fibres induced by water absorption in their wall also generated stresses that may have caused cracking and delamination at the fibre/matrix interface [START_REF] Duigou | In-situ evaluation of flax fibre degradation during water ageing[END_REF][START_REF] Papa | Water ageing effects on the mechanical properties of flax fibre fabric/polypropylene composite laminates[END_REF][START_REF] Hamour | Effects of MAPP Compatibilization and Acetylation Treatment Followed by Hydrothermal Aging on Polypropylene Alfa Fiber Composites[END_REF]. Such damage could explain the significant decrease in bending strength (Figure 7b).

For the hybrid material, hydrothermal ageing also induced a significant decrease in the bending properties (Figures 6b,7d, 7e and 7f). For the composite, the bending properties initially dropped and then remained substantially stable during ageing.

Decreases of approximately 55%, 65% and 70% were measured for the bending modulus (Figure 7d), strength (Figure 7e) and strain at failure (Figure 7f), respectively.

This was attributed to softening and degradation of the composite but also to degradation at the interfaces between the composite and the stainless steel skins.

Cohesive failure was observed in the buckling zone of the flexural beams tested before ageing (Figures 8a and8b), which highlighted the good efficiency of the adhesive film.

A more complex failure mode was observed after 30 days of hydrothermal ageing (Figure 8c and 8d) that combined buckling and delamination at the adhesive film (caption 1 in Figure 8e) but also cohesive failure in the composite (caption 2 in Figure 8e).

The significant effect of hybridization also deserves to be emphasized. Before ageing, the bending stiffness and strength were 6 and 3 times larger for hybrid than for composite specimens, respectively (Figure 7). After 177 days of hydrothermal ageing, the remaining bending stiffness and strength in the water-saturated state were approximately 20 GPa and 70 MPa, respectively, a performance that was still suitable with respect to most of the requirements for semi-structural applications.

The impact behaviour was also significantly affected by hydrothermal ageing for both composites and hybrids. In the case of composite specimens (Figure 9a), the initial slope of the load displacement curve decreased after 10 days of ageing and remained stable thereafter. This was consistent with the modulus drop observed in bending specimens. The maximum load slightly increased in the first period of ageing and strongly reduced after 177 days (Table 2). Observations of the impacted specimens showed that the perforation induced marked orthogonal cracks along the fibre directions in unaged specimens (Figure 10a). For specimens aged 10, 30 and 50 days, the damage was more diffuse in the affected area. At 177 days, the cracks were again very marked, but the affected area was strongly reduced in size compared to the unaged specimens.

This behaviour could have been related to evolution of the plasticity of the material, which would have been consistent with the evolution of the failure strain observed in bending. In the case of hybrid specimens, a decrease in initial stiffness was also observed with ageing but only after 30 days (Figure 7b and Table 2). It was possible that after 10 days of ageing, the composite material in the centre of the specimen was not yet saturated with water because the weight gain was not stabilized for impact specimens after 10 days (Figure 2). As observed in bending specimens, there was no real performance loss between 30 and 177 days, and the absorbed energy even increased.

The observations of the impacted specimens (Figure 10b) made it possible to formulate some explanations for this behaviour. For unaged specimens, the area deformed by impact was small, and cracks were present in the skin at the back. With ageing, this area increased significantly due to the more widely distributed plastic deformation in the skins, which were less constrained by the composite core. It is interesting to note that the skins were not cracked during impact after 30 days.

Thermal ageing

To better understand and model the long-term behaviour of such hybrid materials, it is necessary to decouple the effects of water absorption and temperature. Therefore, in this study, thermal ageing was also investigated. For the targeted applications (street furniture and construction), the materials must withstand variable temperatures, which can reach maximum values of approximately 70 °C. The temperature of materials during atmospheric exposure depends on a number of factors related to the material properties but also to the conditions of exposure to solar radiation and the geographical location. The maximum daily temperature of material under solar radiation was estimated and measured at approximately 75 °C for composite materials [START_REF] Tompkins | Prediction of Moisture and Temperature Changes in Composites During Atmospheric Exposure[END_REF] and metal [START_REF] Russell | The temperature of various surfaces exposed to solar radiation: An experiment[END_REF]. To reproduce long-term ageing (several years or decades) from short trials (several weeks or months), a classical strategy is to accelerate ageing using degradation factors at levels exceeding the service range. This allows the material to reach the same state as a naturally aged material but in a shorter time. The risk in such an approach is, however, to induce mechanisms that do not occur in real ageing. This is almost exactly what has been observed when the hybrid material has been exposed to an accelerated ageing temperature of 120 °C. The adhesive film degraded, and delamination between the stainless steel skins and the composite occurred. This was expected since the melting temperature of the adhesive was approximately 100 °C. The measured shear strength dropped from 4.3 MPa to 0.6 MPa when the temperature was varied from 21 °C to 100 °C using a single-lap shear test. Therefore, the investigation of accelerated thermal ageing was restricted to the scale of the composite material, the component most likely to be altered after the adhesive layer.

Figure 11 shows the evolution of the mass loss as a function of the thermal ageing time.

During the first hours, a rapid decrease in mass was observed; afterwards, the mass loss rate slowed over the next days to reach a value of approximately 2.8% after 40 days.

This mass loss was attributed to the drying of the sample and, more precisely, to the release of the water remaining in the plant fibres after composite manufacturing.

Unexpectedly, after 50 days, a second stage with a significant mass loss was observed with a sharp drop until 120 days, reaching a value of 8.5%. Then the rate of mass loss slowed but remained significant. After 252 days of ageing, a mass loss of approximately 11.5% was finally recorded. This mass loss observed after material dried was attributed to the degradation of the polypropylene. Indeed, a significant change in colour was observed along with many cracks in the PP matrix of the composite when exposed to thermal ageing (Figure 12). These phenomena were also observed in the neat polymer (Figure 13) and were attributed to the thermal oxidation of polypropylene.

Indeed, in certain circumstances, the thermal oxidation of polypropylene appeared at moderate temperatures (typically below 150 °C) and was heterogeneous at a macroscopic level [START_REF] Fayolle | Macroscopic heterogeneity in stabilized polypropylene thermal oxidation[END_REF]. This was observed for PP fibres at 110 °C in air at atmospheric pressure [START_REF] Fayolle | Embrittlement of polypropylene fibre during thermal oxidation[END_REF] and for thin PP films in air at 90 °C [START_REF] Fayolle | Oxidation induced embrittlement in polypropylenea tensile testing study[END_REF]. The results showed the presence of predominant chain scission, chemicrystallization and embrittlement. This was attributed to stabilizer consumption. George et al. [START_REF]Homogeneous and heterogeneous oxidation of polypropylene[END_REF] demonstrated that an infectious spreading kinetic model could simulate the observed behaviour well. The heterogeneous features of the oxidation of polypropylene in the amorphous region were consistent with infectious spreading from a small number of sites, such as catalyst residues. A stochastic model was developed to demonstrate the spatial and temporal development of oxidation at these sites [START_REF] Goss | Modelling of infectious spreading in heterogeneous polymer oxidation I. Development of a stochastic model[END_REF].

In the present study, FTIR analyses were performed in the aged materials in the region where degradation was observed (Figures 14 and15). The region of the FTIR spectrum between 1500 cm -1 and 1900 cm -1 of the composite aged at 120 °C showed a decrease until a disappearance of the carbonyl band at 1730 cm -1 after 50 days. After 252 days of exposure, a broad band with three shoulders at 1775 cm -1 , 1730 cm -1 and 1715 cm -1 , as well as a slight increase in a large band at approximately 1640 cm -1 , appeared in the spectrum.

The depletion of the absorption at 1730 cm -1 observed during the first 50 days could be attributed to the loss of stabilizer ester groups due to a physical evaporation phenomenon [START_REF] Moisan | Diffusion des additifs du polyethylene-V: Influence sur le vieillissement du polymère[END_REF][START_REF] Richaud | Kinetic modelling of stabilization coupled with stabilizer loss by evaporation. Case of dithioester stabilized polyethylene[END_REF]. After 255 days of thermal exposure, the FTIR spectrum of the composite showed a sharp increase in carbonyl functions at 1730 cm -1 with the appearance of ketones at 1715 cm -1 and peresters or lactones at 1775 cm -1 that may have formed during PP degradation [START_REF] Niemczyk | Accelerated laboratory weathering of polypropylene composites filled with synthetic silicon-based compounds[END_REF]. The increase in the absorption at approximately 1640 cm -1 revealed a very slight exposure of flax fibres due to a moderate loss of polymer matrix at the composite surface.

From a mechanical point of view, thermal ageing also had significant effects on the composite material. After 10 days of exposure, a slight increase in the bending modulus was measured (Figure 16a and Table 3) that was associated with a significant decrease in stress and strain at failure. This was attributed to the drying of the material. The removal of water molecules led to stiffer but also more brittle behaviour. This effect was exacerbated with ageing time and particularly marked after 252 days. The stress and strain at failure were then divided by factors of 2.6 and 4.6, respectively, when compared to the unaged conditions. This was attributed to the embrittlement of PP due to thermal oxidation and induced fibre/matrix debonding in the infected region.

The impact resistance of the composite was also strongly affected by thermal ageing (Figure 16b and Table 3). The maximum force, energy absorbed and displacement at perforation decreased slightly and progressively for ageing times up to 50 days. This was mainly attributed to the drying of the material. For the bending properties, a significant drop in impact properties was observed after 252 days. The failure mode (Figure 17) was completely different with complete perforation of the plate, without tearing around the hole. This could again be attributed to the embrittlement of the PP matrix induced by thermal oxidation.

This effect of temperature on this polypropylene-reinforced composite was unexpected.

Indeed, thermal oxidation in air for these ranges of exposure times and temperatures has mainly been observed in the literature for fibres and films but not for bulk materials.

The question of the effect of flax fibres on PP stabilizers could be raised and deserves to be thoroughly analysed in further studies. Even if quite severe temperatures were applied in this study to accelerate ageing, these temperatures could also be encountered under certain service conditions where they could limit the safe use of such composites over long times.

Conclusion

Studying the durability of FMLs made of PFCs is of primary importance for their safe and reliable introduction in many application sectors, such as outdoor structures. This study investigated the hydrothermal and thermal ageing of a flax/polypropylene composite and its stainless steel hybrid laminates. The results showed that before ageing, the bending stiffness increased by a factor of 6 and the bending strength and impact force by a factor of 3 when the flax/polypropylene composite was hybridized with thin stainless steel sheets. After 177 days of hydrothermal ageing, the remaining bending stiffness and strength in the water-saturated state were approximately 20 GPa and 70 MPa, respectively, and the skins were no longer cracked during impact. The hydrothermal ageing involved reversible mechanisms such as plasticization of flax fibres by water and the activation of viscoelastic properties but also irreversible mechanisms such as the degradation of interfacial adhesion between steel and composite and between flax fibres and PP and the hydrolysis of flax fibres.

During thermal ageing, the critical points were the shear strength and adhesion between stainless steel sheets and PFC and the thermal oxidation of PP, which induced a drop in the bending and impact properties of flax/PP composites for long exposure This was mainly due to the embrittlement of PP attributed to the consumption of PP stabilizers. Loss of stabilizers was also observed during water immersion.

Despite the degradation mechanisms observed for the accelerated ageing protocols used in this study, it was concluded that this new generation of FMLs made of PFCs is suitable for outdoor applications. In real applications, the composite material should be fully protected by stainless steel (including lateral faces) to limit risks of contact between the composite and liquid water, and polypropylene stabilizers suitable with plant fibres also should be used.

Figure 1 :

 1 Figure 1: Schematic diagrams and photographs of the hybrid material

Figure 2 :Figure 3 :

 23 Figure 2: Evolution of the composite (a.) and hybrid (b.) specimen weight as functions of

Figure 4 :

 4 Figure 4: FTIR spectra (vertically shifted for clarity) of the composite during hydrothermal

Figure 5 :

 5 Figure 5: Evolution of the IC=O (a) and Ilignin (b) of the composite as functions of exposure time to water at 70 °C according to the alkyl band between 3060 cm -1 and 2760 cm -1 .

Figure 6 :

 6 Figure 6: Three-point bending behaviour of composite (a.) and hybrid (b.) materials for

Figure 7 :

 7 Figure 7: Evolution of the bending modulus, strength and strain at failure for composite (a., b.,

Figure 8 :

 8 Figure 8: Photographs and scanning electron microscopy observations of hybrid specimens

Figure 9 : 29 Figure 10 :

 92910 Figure 9: Load vs. displacement curves recorded during impact tests on composite (a.) and

Figure 11 :

 11 Figure 11: Mass loss as a function of thermal ageing time for composite specimens.

Figure 12 :

 12 Figure 12: Optical and SEM observations of the composite before and during thermal ageing.

Figure 13 :

 13 Figure 13: Optical images of polypropylene samples before ageing (a) and after 11 days (b), 40

Figure 14 :

 14 Figure 14: FTIR spectra (vertically shifted for clarity) of the composite under thermal ageing at

Figure 15 : 32 Figure 16 :

 153216 Figure 15: Evolution of the I C=O (a) and I lignin (b) of the composite as functions of the thermal ageing time at 120 °C according to the alkyl band between 3060 cm -1 and 2760 cm -1 .

Figure 17 :

 17 Figure 17: Back surfaces of the composite specimens after impact tests after different thermal

Table 1 :

 1 Mechanical properties of the Nattex composite and the K41X austenitic stainless steel.

		E1 (GPa)	E2 (GPa)	12 (-)	G12 (GPa)	G13 (GPa)
	Nattex	9.3	11.1	0.09	0.85	0.54
		E (GPa)	 (-)	G (GPa)
	Stainless
			220	0.34	82
	steel

Table 2 :

 2 Impact properties (maximum force, absorbed energy, displacement) for the different tested hydrothermal ageing times (mean values and (standard deviation)).

			Unaged	10 days	30 days	50 days	177 days
		Maximum force (N)	1650 (92) 1919 (183) 1789 (47) 1432 (55) 798 (49)
		Energy absorbed at	9.3 (0.7)	6.6 (0.5)	7.1 (1.8)	4.7 (1.4) 3.6 (0.5)
	Composite	perforation (J)
		Displacement at	7.7 (0.4)	6.7 (0.2)	7.3 (1.6)	5.9 (0.9) 6.7 (0.8)
		perforation (mm)
			5270 (172) 5520 (19) 5530 (39)	-	4963
		Maximum force (N)
							(209)
	Hybrid	Energy absorbed (J)	15.8 (0.3)	16 (0.2)	16 (0.1)	-	17.4 (0.1)
		Maximum	5.8 (0.1)	6.1 (0.2)	7.4 (0.0)	-	7.9 (0.1)
		displacement (mm)

Table 3 :

 3 Three-point bending and impact properties of the composite for the different tested thermal ageing times (mean values and (standard deviation)).

			Unaged	10 days	30 days	50 days	252 days
		Modulus (GPa)	8.2 (0.3)	8.3 (0.4)	7.7 (0.5)	8.8 (0.4)	6.3 (0.4)
	3-point
		Strength (MPa)	80.0 (1.4) 70.3 (1.6) 68.2 (1.8) 70.3 (2.1) 30.1 (1.5)
	bending
		Strain at failure (%) 2.8 (0.1)	1.5 (0.1)	1.3 (0.1)	1.2 (0.1)	0.6 (0.0)
		Maximum force (N) 1650 (92) 1369 (54) 1313 (14) 1165 (51) 275 (14)
		Energy absorbed at
			9.3 (0.7)	7.0 (1.0)	6.0 (0.6)	4.7 (0.2)	0.4 (0.1)
	Impact	perforation (J)
		Displacement at
			7.7 (0.4)	7.0 (0.6)	6.5 (0.5)	5.9 (0.4)	2.2 (0.3)
		perforation (mm)
			34

Acknowledgments:

The authors acknowledge the Conseil Régional of Bourgogne Franche-Comté (BFC) and the French Agency for Ecological Transition (ADEME) for the granting of a PhD thesis scholarship to N.E. Ngoufo Donkeng. This work has also been supported by the EIPHI Graduate School (contract "ANR-17-EURE-0002").

References:


Riadh Ben Jelili
email: riadh@dhaman.org

A New Composite Measure of FDI Attractiveness: Global FDI Country Attractiveness (GFICA) Index 1

Drawing out the main conclusions from the theoretical and empirical literatures, the aim of our modest contribution is to provide an explanation of why some countries are more attractive for foreign investors than others and what underlies the relative attractiveness failure of some countries. Therefore, a composite index that adequately describes a host country's attraction for FDI is constructed. This index, henceforth referred to as "GFICA Index", considers all identified foremost, measurable and comparable aspects that affect FDI decision. The index, ranking a set of 111 countries, representing 92% and 95% of the world inward FDI flows and stocks respectively, according to their attractiveness for receiving inward FDI, is structured so as to provide the possibility of conducting detailed strength and weakness analyses for countries in general and Arab countries in particular> Indeed, 18 Arab countries are part of the sample representing more than 95% and 98% of the total inward FDI flows and stocks into the Arab region respectively. These analyses can be used by policy-makers to draw conclusions on how to improve the country's attraction for inward FDI.

Introduction

Along with the deepening international economic and financial integration over the last two decades, the 2000s saw a significant increase in foreign direct investment (FDI) to developing countries. The upward trend has been reversed in 2008, following the global economic slowdown that started in the end of 2007. However, developing and transition economies, which proved relatively immune to this global turmoil, did better than developed countries and continued to absorb nearly half and 6 per cent of global FDI flows respectively. In these countries FDI continue to be the most important source of foreign financing, by far surpassing inflows of official development assistance, and other types of private capital inflows. In comparison, the record of FDI in Arab countries is poor. Indeed, the region attracted only 2.8% of global inward FDI flows and 6.3% of the FDI flows to developing countries according to the latest World Investment Report from UNCTAD (WIR, 2012) in spite of the adoption and implementation of substantial reform programs in most of the Arab countries covering stock market modernization and liberalization, state owned firms' privatization, regulatory and legal improvements. It is, therefore, quite legitimate to ask whether or not Arab countries might be missing out and should include financial and others incentives to attract FDI as part of a development strategy.

A review of the empirical literature on FDI determinants suggests that expected positive externalities of FDI depends on a multitude of factors, such as the level of technology used in domestic production in the host country, the level of education of the host country workforce, the level of financial sector and institutional development, etc. All these factors and more contribute to whether the host country in question can attract and hence benefit from FDI. Obviously this multitude of factors is impossible to capture in a single economic model or regression analysis. Drawing out the main conclusions from this empirical literature, the aim of this modest contribution is to provide an explanation of why some countries are more attractive for foreign investors than others and what underlies the relative attractiveness failure of the Arab countries. Therefore, a composite index that adequately describes a host country's attraction for FDI is constructed. This index, henceforth referred to as "GFICA Index", considers all identified foremost, measurable and comparable aspects that affect FDI decision. The index, ranking a set of 111 countries, representing 92% and 95% of the world inward FDI flows and stocks respectively, according to their attractiveness for receiving inward FDI, is structured so as to provide the possibility of conducting detailed strength and weakness analyses for countries in general and Arab countries in particular. Indeed, 18 Arab countries are part of the sample representing 95% and 98% of the total inward FDI flows and stocks into the Arab region respectively. These analyses can be used by policy-makers to draw conclusions on how to improve the country's attraction for inward FDI.

The data series selection process does not depend only on the question of what is necessary and most adequate to assess FDI attractiveness, data availability is also considered as a constraint in order to maximize our country sample. We detect 60 different indicators as adequate proxies for the FDI key drivers categorized according to three major axes or pillars: To smooth fluctuation most series or factors are averaged over a period of the last three years. The index structure is based on three levels (See Figure 1): the first is the level of the three pillars (prerequisites, underlying factors, and differentiation and agglomeration economies); the second level consists of data series or sub-factors, which are aggregated from the level three data series.

The index calculation methodology used follows the approach of Nardo et al, (2005) and can be divided into four steps: consistency analysis, normalization, weighting and aggregation3 .

GFICA Index Structure

Without being familiar with the socioeconomic environment in various host countries, an investor cannot make rational FDI allocation decisions. Investors overcome potential knowledge deficits and gather data to analyze the determinants they consider important before allocating to a particular country. However, this country due diligence is timeconsuming and costly. Additionally, the pace of economic development of many emerging and developing countries makes the selection of those that support foreign direct investment activity more and more cumbersome. GFICA index could be considered as a guide for foreign investors to solve the problem of where to allocate their capital. The aim of the index is also to point out the leverage factors to improve FDI attractiveness of Arab countries and constitutes as such a valuable policy tool available for economic policy makers in the region4 .

The purpose of GFICA index is to measure and study, in an ongoing manner, 8 world regions' attraction as FDI destinations by means of quantitative indicators, while at the same time comparing each group performance with an extended group of different countries and relevant geographical areas. This study shall be carried out on a yearly basis, thus enabling the monitoring of each country's development with respect to different categories considered to cover the most important axes that MNEs bear in mind when making investment decisions. The index aggregates and provides the requisite information for FDI allocation decisions. Of course, this information should not be considered as a substitute for investors' own efforts to build up country knowledge and experience; it can only facilitate this process and support the initial due diligence stage.

The results shall obviously serve as a support tool in assessing the reasons boosting or slowing down foreign investment in a considered region of the world.

The attractiveness analysis benchmarks the attractiveness of 111 countries to receive FDI allocations representing more than 95% of the world inward FDI stocks and covers a total of 60 indicators structured around 11 FDI key drivers covering three pillars which aim to group together the main sources of competitive advantage that internationalization offers to MNEs: Prerequisites indicators, Underlying Indicators and Externalities Indicators. The three pillars, shown in figure 1, are described below. The ranking provides the evidence for which factors a considered region/country stands behind and has to improve them in order to become more attractive.

Figure1: GFICA Index Structure

Prerequisites

The prerequisites or required prior conditions axe includes those basic features that enable investors to identify and exploit the sources of competitive advantage of the other two axes. It consists of 23 indicators grouped into the following categories:

A. Uncertainty and Macroeconomic Stability:

Uncertainty Factors:

In macroeconomic applications, the term uncertainty is used mainly in two senses: there is the statistical meaning of uncertainty in a measurement or value due to the dispersion of repeated occurrences in the face of the same prediction, and then there is the epistemological meaning of uncertainty in the opposite sense from likelihood or from strength of belief. Used in the second sense, uncertainty is a measure of doubt about a single event being true or real (von Furstenberg, 1988 5 ). More precisely, in the context of attractiveness analysis, uncertainty limits and casts doubt on what stabilization policies and defense mechanisms of an economy can accomplish. Given the irreversible nature of FDI, macroeconomic uncertainty also causes an increase in uncertainty about future profits, raising the value of waiting and thus delaying investment decision. It's approximated by 4 indicators:

1. Real GDP growth volatility;

2. Inflation Rate;

3. Real effective exchange rate volatility;

4. Number of exchange rate crisis, crisis being defined as in Frankel and Rose (1996): a depreciation of the (average) nominal exchange rate that exceeds 25 percent, and exceeds the preceding year's rate of nominal depreciation by at least 10 percent.

Macroeconomic Stability:

Macroeconomic stability basically means a mix of external and internal balance approximated by the following indicators:

5. Current account deficit to GDP ratio;

6. Fiscal balance to GDP ratio;

7. General government gross debt to GDP ratio.

B. Financial Structure and Development:

The evaluation of financial structure and development covers the following indicators of financial size and depth:

1. Ratio of broad money to GDP (M2 to GDP); 2. Domestic credit to private sector (% of GDP);

3. Market capitalization of listed companies to GDP.

C. Public Governance:

The quality of public governance is evaluated by using the Worldwide Governance Indicators Database produced by Daniel Kaufmann, Aart Kraay and Massimo Mastruzzi6 . These indicators combine the views of a large number of enterprise, citizen and expert survey respondents in industrial and developing countries.

F. Human and Natural Resources

Natural resources:

1. Total natural resources rents (% of GDP)

Human resources:

1. Labor Productivity Average Growth, 2. Mean years of schooling (adults),

Expected Years of Schooling (of children)

4. Human Development Index (HDI) value

Agglomeration Economies and Differentiation

The term "agglomeration economies" is used, as in urban economics, to describe the benefits that MNEs obtain when locating near each other (agglomerating). This concept relates to the idea of economies of scale and network effects. While the differentiation axe refers to the factors that provide MNEs access to scarce resources enabling them to differentiate their products, strategies or process from the competition and, , as a result, to develop or sustain a competitive advantage in the markets in which they operate.

Normalization and Consistency Analysis

Normalization

In order to make the cross-sectional data series comparable and to realize index aggregation, the raw data has to be converted into a common range. The rescaling method is used to normalize sub-indicators to such a range by the following linear transformation:

 if the concerned sub-indicator influence positively the attractiveness for investors:

 if the concerned sub-indicator influence negatively the attractiveness for investors:

: normalized value of category c and country i : raw data value of category c and country i : minimum raw data value of category c within the sample : maximum raw data value of category c within the sample For every individual sub-indicator, 100 represents the best score and 1 represents the worst.

Consistency Analysis

High quality tests are important to evaluate the reliability of data supplied in a research study as a first step of consistency analysis of the indices prior to computing composite variables and fitting explanatory models. Cronbach's alpha is a commonly employed statistic used to determine the internal consistency, so the considered statistic increases as the inter-correlations among a set of sub-indicators included in the analysis increase. A high Cronbach's alpha (greater or equal to the acceptable threshold value 0.7) is an indication that the considered set of indices proxy the desired key variable well.

The other two measures commonly used for consistency purpose are related to factor analyses or data reduction and summarization: the Haiser-Meyer-Olkin measure of sampling adequacy (MSA), based on the partial correlations among the input variables, and the Bartlett's test of sphericity used to test the hypothesis that the correlation matrix is an identity matrix (the indices are correlated in the population). The first measure should be greater or equal to 0.5 to proceed with factor analysis, and the test value of the second measure should be below the 0.05 significance level. When using factor analysis, each component is assigned a weight according to its contribution to the total variance in the data to insure that the resulting summary indicators account for a large part of the cross-country variance of the considered subindicators.

Cronbach's  over the considered three axes is 0.91 and consequently underlines the quality of data selection for all the countries. The MSA value is 0.708 and Bartlett's Test of sphericity is significant at 0.000. Table 3 presents the results of the Principal Component Analysis (PCA). One single component is extracted (only one eigenvalue greater than 1) representing more than 89% of the total variance of the considered indicators. The high Cronbach's and MSA value, and extracting only one factor explaining such a large part of the data variance, mean that the key axes are adequate joint proxies for a single latent factor. They are unidimensional and express only one characteristic. This is an indication of an appropriate choice of key drivers to assess FDI attractiveness for the considered countries. The FDI attractiveness is excellently measured by using the three criteria -prerequisites, underlying factors and agglomeration-differentiation factors-as proxies.

The PCA analysis also generates the communalities or the total influence on a single observed item from all the factors associated with it (in this case only one factor is generated). It's equal to the squared factor loading related to the observed indicator and is the same as R 2 in multiple regression. These communalities, described in Table 4, are used to calculate the weights for the three key drivers (the square of the factor loading represents the proportion of the variance of the indicator explained by the factors): The results exposed in Table 4 illustrate that the underlying factors receive the highest weight and constitutes the strongest determinant of FDI activity followed by the prerequisites factors. They also show a small difference with respect to an equal weighting scheme (0.333 for each key driver).

Aggregation

Additive methods, geometric aggregation and non-compensatory multi-criteria analysis constitute the main three classes of aggregation methods. We focus on the linear and geometric methods as the most adequate for the purpose of FDI attractiveness analysis.

Linear aggregation assigns base indicators proportionally to the weights. It's useful when all sub-indicators have the same measurement unit, which is our case:

, where and Index value i : index value of country i : normalized value of category q and country i : weight of category q However, geometric aggregation rewards those countries or those sub-indicators with higher scores. A shortcoming in the value of one indicator can be compensated by a surplus in another. Compensability is constant in linear aggregation, while it is smaller in geometric aggregation for the sub-indicators with low values. It means that countries with low scores in some sub-indicators would benefit from linear aggregation:

, where and

Statistical Validation of the Results

This section compares the explanatory power of all the combinations presented in the previous section. By explanatory power we mean the strength and directionality of the linear relation between the proposed FDI attractiveness index and the actual FDI activity in the particular countries measured either by inward FDI flows or stocks. The Pearson correlations for each index calculation method are presented in Table 5: Considering these findings, the most adequate method for measuring the attractiveness of a country for FDI activity is method 1.

Figure 2 :

 2 Figure 2: Equal Weights Aggregation Scheme

1. Prerequisites or initial conditions: including

  23 different sub-indicators covering macroeconomic stability, financial structure and development, public governance and business environment;

2. Underlying factors or factors motivating FDI: 27

	factors are detected as
	adequate proxies to explore the FDI key decisions of multinational enterprises
	(MNEs) and covering the following considerations: market access and market
	potential, human and natural resources, cost components and physical
	infrastructures.
	3. Differentiation and Agglomeration economies: The term agglomeration
	economies' is used in urban economics to describe the benefits that firms obtain
	when locating near each other. This concept relates to the idea of economies of
	scale and network effects. These effects are considered by detecting 10 different
	factors as proxies to the differentiation and agglomeration economies affects.
	Several databases are used with annual data ranging generally from 1980 to 2012
	including fundamentally but not exclusively GeoDist database of CEPII, WDI database
	of the World Bank, Institutional Profiles Database of the DGTPE-France, Worldwide
	Governance Indicators of the World Bank, The Conference Board Total Economy
	Database, WIPO database, UNCTAD STAT database, WTO database, ILO database,
	World Federation of Exchange database, CDIS, DOTS, FAS, IFS and WEO databases of
	the IMF.

Table 1 :

 1 Countries covered Angola, Benin, Botswana, Burkina Faso, Cameroon, Central African Republic, Chad, Cote d'Ivoire, Ethiopia, Gabon, Ghana, Kenya, Madagascar, Mali, Mauritius, Mozambique, Namibia, Nigeria, Senegal, South Africa, Tanzania, Togo, Uganda

	Africa (23)
	Arab Region (18)	Algeria, Bahrain, Egypt, Iraq, Jordan, Kuwait, Lebanon, Libya, Mauritania,
		Morocco, Oman, Qatar, Saudi Arabia, Sudan, Syria, Tunisia, United Arab
		Emirates, Yemen
	Asia (18)	Azerbaijan, Cambodia, China, Hong Kong, India, Indonesia, Iran, Israel,
		Japan, Kazakhstan, Korea Rep., Malaysia, Nepal, Pakistan, Philippines,
		Singapore, Thailand, Vietnam
	Australasia (2)	Australia, Australasia

Eastern Europe (14) Bulgaria, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Russia, Serbia, Slovakia, Slovenia, Turkey, Ukraine Latin America (16) Argentina, Bolivia, Brazil, Chile, Colombia, Dominican Republic, Ecuador, Guatemala, Honduras, Mexico, Nicaragua, Panama, Paraguay, Peru, Uruguay, Venezuela North America (2) Canada, United States Western Europe (18) Austria, Belgium, Cyprus, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom

  This axe includes the key aspects that MNEs take into account when making investment decision conditional upon fulfilling the prerequisites factors. These aspects have been grouped in 4 categories: Market access and potential, Human and natural resources, costs components and physical infrastructures.E. Market Access, Size and PotentialOne of the reasons behind FDI is access to new markets that enables the increase of MNEs' turnovers. Investments in a particular country can represent an attempt to gain access to its internal market, or to facilitate access to other markets of other countries. These are the factors shown by means of the following indicators:

	5. Rule of Law 2.2. The Underlying Factors
	6. Control of Corruption
	D. Business Environment:
	The business environment is covered by the following set of 7 indicators:
	1. Starting a Business
	1.1.	Number of Start-up procedures
	1.2.	Time required to start a business
	2. Dealing with Construction Permits
	2.1. 1. Real per capita domestic demand, Number of procedures to have the permits
	2.2. 2. Domestic demand volatility, Time required to have the permits
	3. Registering Property 3. Trade performance Index
	3.1.	Number of registration procedures
	3.2. 4. Trade to GDP ratio, Time required for registering property
	4. Getting Electricity 5. Applied Tariff
	4.1. 6. Trading Across Borders Index Number of procedures to get electricity
	4.2. 6.1.	Time required for getting electricity Documents to export (number)
	5. Getting Credit 6.2.	Time to export (days)
	5.1. 6.3.	Strength of legal rights Documents to import (number)
	5.2. 6.4.	Depth of credit information Time to import (days)
	6. Protecting Investors
	6.1.	Extent of disclosure index	They
	are based on 31 individual data sources produced by a variety of survey institutes, think tanks, non-governmental organizations, international organizations, and 6.2. Extent of director liability index
	private sector firms. Six dimensions of governance are covered: 6.3. Ease of shareholder suits index
	1. Voice and Accountability 6.4. Strength of investor protection index
	2. Political Stability and Absence of Violence 7. Enforcing Contracts
	6.1.	Number of procedures
	3. Government Effectiveness 6.2. Time required
	4. Regulatory Quality

Table 3 :

 3 Total Variance Explained

			Initial Eigenvalues		Extraction Sums of Squared Loadings
	Component
		Total	% of Variance Cumulative %	Total	% of Variance Cumulative %
	1	2.677	89.241	89.241	2.677	89.241	89.241
	2	.227	7.561	96.802
	3	.096	3.198	100.000
	Extraction Method: Principal Component Analysis.

Table 4 :

 4 Weights for the three key axes

	Component	Communalities	Weight

Table 5 :

 5 Pearson Correlations with Inward FDI Stocks

Index Calculation Method Correlation with Log FDI Inward Stocks (Two-tailed significance level) Method 1: Proportional weight and geometric aggregation

		0.776 (0.000)
	Method 2: Equal weight and geometric aggregation	0.747 (0.000)
	Method 3: Equal weight and arithmetic aggregation	0.747 (0.000)

Nardo, Saisana, Saltelli, Tarantola, Hoffman and Giovannini (2005): Handbook on constructing composite indicators: Methodology and user guide, OECD Statistics Working Paper STD/DOC2005

Dhaman Index is derived from GFICA Index with the permission of its author Riadh Ben Jelili who is the sole copyright holder.

von Furstenberg G, M., 1988, "Uncertainty in Macroeconomics: A Survey of its Treatment", The Geneva Papers onRisk and Insurance, 13,

See http://info.worldbank.org/governance/wgi/index.aspx#doc for more information regarding the adopted methodology.

GFICA Index

The reliability test statistics for the sub-indicators used to assemble the ten key drivers are all above the Nunally's cut-off value of 0.7 except the two key drivers Financial Structure/Development and Cost Components. In addition to the limited number of subindicators available for the concerned key drivers, detailed analyses of the inter-item correlation matrix reveal relatively low correlations between the items. It's well known that a decrease in the number of indicators and a low average inter-item correlation are associated with a decrease in α. Furthermore, good values for all key drivers for the MSA and Bartlett's Test are obtained (MSA values greater than 0.5 and p-values for Bartlett's Test less than 0.05). Accordingly, from the above results it's possible to perform a valid factor analysis.

Weighting and Aggregation

Weighting

After calculating the performance scores for each sub-items on the lowest level, and before the aggregation can be conducted, the weightings of the index items have to be determined. Two schemes are followed:

1. On the lowest level, index items are aggregated with equal weights, i.e. the weights are derived from the number of components that are aggregated. At the key drivers level (10 key drivers), weights are attributed according to the number of items and so are the weights attributed to the three axes as exposed in Figure 2: