Mohamad Al Hallak
email: alhallak@insa-toulouse.fr

Thomas Verdier
email: tverdier@insa-toulouse.fr

Alexandra Bertron
email: bertron@insa-toulouse.fr

Christine Roques
email: roques730@aol.com

Jean-Denis Bailly
email: jean-denis.bailly@envt.fr

Tio2 Photocatalytic Biocidal Activity on Escherichia Coli and On Aspergillus Niger under Different Methodological Conditions

Keywords: Bactericidal activity, Fungicidal activity, Indoor air, Aerosolization, Photocatalysis, TiO2

Biological pollution is one major cause of the degradation of indoor air quality. It was shown that microbial communities from outdoor might impact significantly the communities detected indoor. In addition, microbial contamination of the surfaces of building materials and their release into the indoor air also significantly affect indoor air quality. Preventing the growth or at least reducing the amounts of microorganisms growing on indoor building materials is essential for reducing health risks for building occupiers. Photoactive TiO2 has been widely studied as a photocatalyst that enable the inactivation of various bacterial strains. In this paper, we compare the antifungal activity of nanoparticles of TiO2 on Aspergillus niger spores and its antibacterial activity on Escherichia coli under low light irradiation, near to common indoor values. The antimicrobial activity of TiO2, expressed as log reduction, was assessed under UV irradiation in a sludge mixture of sterile water, suspension and nanoparticles of TiO2. The results showed a strong bactericidal activity of TiO2 on E. coli and a weak fungicidal activity against A. niger. Different parameters including concentration of TiO2, intensity of light, and duration of contact between TiO2 and microbial cells and spores, were investigated and significantly affected the antibacterial activity of TiO2 while poorly affected its antifungal activity. Results of this study confirmed previous investigations on antibacterial activity of TiO2 on E. coli and bring new insight on antifungal activity on the spores of A. niger. The effectiveness of the antimicrobial activity is enhanced by the duration of contact between suspension and TiO2 nanoparticles through the stirring experiments for 2H, 4H and 24H.

Introduction

Indoor air pollution is an important cause of serious heallth problems for occupants including respiratory diseases, allergic symptoms, cancers and cardiovascular problems [START_REF] Al Hallak | Fungal Contamination of Building Materials, Aerosolization of Particles and Toxins in the Indoor Air and Associated Risk for Health: A Review[END_REF][START_REF] Saini | A Comprehensive Review on Indoor Air Quality Monitoring Systems for Enhanced Public Health[END_REF][START_REF] Viegi | Indoor Air Pollution and Airway Disease [State of the Art[END_REF][START_REF] Tran | Indoor Air Pollution, Related Human Diseases, and Recent Trends in the Control and Improvement of Indoor Air Quality[END_REF][START_REF] Vural | Sick Building Syndrome: in Public Buildings and Workplaces[END_REF][START_REF] Turiel | Indoor Air Quality and Human Health[END_REF][START_REF] Norhidayah | Indoor Air Quality and Sick Building Syndrome in Three Selected Buildings[END_REF][START_REF] Agarwal | Indoor Air Quality Improvement in COVID-19 Pandemic: Review[END_REF][START_REF] Baudet | Indoor Air Quality in Healthcare and Care Facilities: Chemical Pollutants and Microbiological Contaminants[END_REF]. For several years now, there is an increased awareness to the effect of indoor air quality on human health and wellbeing [START_REF] Al Hallak | Fungal Contamination of Building Materials, Aerosolization of Particles and Toxins in the Indoor Air and Associated Risk for Health: A Review[END_REF][START_REF]Regional Office for Europe WHO Guidelines for Indoor Air Quality: Selected Pollutants; World Health Organization[END_REF]. Actually, people spend 80%-90% of their times indoors [START_REF] Lai | Personal Exposures and Microenvironment Concentrations of PM2.5, VOC, NO2 and CO in Oxford, UK[END_REF][START_REF] Vardoulakis | Grand Challenges in Sustainable Cities and Health[END_REF] so it's important to understand the main causes of indoor air pollution and find suitable solutions to ameliorate indoor air quality. The world health organization (WHO) reported in 2009 that biological pollution is one major cause for the degradation of indoor quality [START_REF] Alberti | Relationship between Environmental Fungal Contamination and the Incidence of Invasive Aspergillosis in Haematology Patients[END_REF][START_REF] Ayanbimpe | Relationship between Fungal Contamination of Indoor Air and Health Problems of Some Residents in Jos[END_REF]. Indoor investigations have highlighted that microbial contamination of surfaces of building materials may have a significant impact on the microbial communities present indoors. However, quantitative evaluation of such impact is only little studied. When promoting conditions (humidity and nutrient content) are available, building materials are exposed to microbial growth [START_REF] Al Hallak | Fungal Contamination of Building Materials, Aerosolization of Particles and Toxins in the Indoor Air and Associated Risk for Health: A Review[END_REF][START_REF] Verdier | A Review of Indoor Microbial Growth across Building Materials and Sampling and Analysis Methods[END_REF]. Upon their growth on surfaces, microorganisms produce aerial particles such as spores, toxins, volatile organic compounds and other metabolites that can be inhaled by occupants [START_REF] Patrick | A Review of: "Indoor Air Pollutants: Exposure and Health Effects; Euro Reports and Studies 78[END_REF][START_REF] Shariat | Acute Lung Injury after Exposure to Stachybotrys Chartarum[END_REF][START_REF] Li | Aerosolization of Fungal Spores in Indoor Environments[END_REF][START_REF] Aleksic | Aerosolization of Mycotoxins after Growth of Toxinogenic Fungi on Wallpaper[END_REF][START_REF] Kim | Airborne Bioaerosols and Their Impact on Human Health[END_REF]. To prevent or to reduce microbial contamination on surfaces, the antimicrobial activity of several chemical products has already been studied. They include semi-conductors products such as titanium dioxide (TiO2), zinc oxide (ZnO), gallium arsenide, tungsten (VI) oxide (WO3), gallium phosphide, and cadmium but also alternative products such as fatty acid and glycerol esters [START_REF] Verdier | Antibacterial Activity of TiO2 Photocatalyst Alone or in Coatings on E. Coli: The Influence of Methodological Aspects[END_REF][START_REF] Dharma | A Review of Titanium Dioxide (TiO2)-Based Photocatalyst for Oilfield-Produced Water Treatment[END_REF][START_REF] Verdier | Monoglyceride to Protect Building Materials against Microbial Proliferation[END_REF]. Titanium dioxide (TiO2) is widely recognized as one of the most efficient photocatalysts used for air purification [START_REF] Verdier | Antibacterial Activity of TiO2 Photocatalyst Alone or in Coatings on E. Coli: The Influence of Methodological Aspects[END_REF][START_REF] Dharma | A Review of Titanium Dioxide (TiO2)-Based Photocatalyst for Oilfield-Produced Water Treatment[END_REF]. It has excellent optical and electronic properties, high photocatalytic activity, high chemical stability, non-toxicity, low cost, availability, and abundance [START_REF] Dharma | A Review of Titanium Dioxide (TiO2)-Based Photocatalyst for Oilfield-Produced Water Treatment[END_REF]. Under "high" intensities of light, over >10 W/m², the photocatalysis of TiO2 nanoparticles showed strong antimicrobial activity against a wide variety of microorganisms, including algae, viruses, bacteria and fungi [START_REF] Dalrymple | A Review of the Mechanisms and Modeling of Photocatalytic Disinfection[END_REF][START_REF] Ateia | Modeling the Degradation and Disinfection of Water Pollutants by Photocatalysts and Composites: A Critical Review[END_REF][START_REF] Benabbou | Photocatalytic Inactivation of Escherischia Coli: Effect of Concentration of TiO2 and Microorganism, Nature, and Intensity of UV Irradiation[END_REF][START_REF] Foster | Photocatalytic Disinfection Using Titanium Dioxide: Spectrum and Mechanism of Antimicrobial Activity[END_REF]. Nevertheless, few studies have been carried out in the last five years investigating the effect of TiO2 on various microorganisms at lower levels of intensity (≤5W/m 2 ), closed to real-world conditions (30W/m² in sunny days and 5-10W/m² in cloudy days outdoors and 4-5 W/m² indoors) [START_REF] Verdier | Antibacterial Activity of TiO2 Photocatalyst Alone or in Coatings on E. Coli: The Influence of Methodological Aspects[END_REF][START_REF] Lux | Synthesis and gold decoration of alternative oxides to TiO2 for the photocatalytic degradation of NO and NO2 in indoor environment conditions[END_REF][START_REF] Menazea | Antibacterial Activity of TiO2 Doped ZnO Composite Synthesized via Laser Ablation Route for Antimicrobial Application[END_REF][START_REF] Falco | Antimicrobial Activity of Flame-Synthesized Nano-TiO 2 Coatings[END_REF].

The objective of this study was to investigate the effeciency of TiO2 nanoparticles on Escherichia coli and Aspergillus niger through direct contact between microbial suspension and photocatalyst TiO2 under different experimental conditions ICEPTP 154-2 (concentration of TiO2 nanoparticles, light intensity and duration of contact). Experiments were carried in dark, and under light real-life irradiation using 8W black-light bulbs at 5W/m².

Materials And Methods

Microbial cultivation and preparation of suspensions

Most frequently detected microorganisms in the indoor environment (on surfaces of building materials and airborne) are (i) Gram negative bacteria and mycobacteria [START_REF] Verdier | A Review of Indoor Microbial Growth across Building Materials and Sampling and Analysis Methods[END_REF][START_REF] Verdier | Bacterial Biofilm Characterization and Microscopic Evaluation of the Antibacterial Properties of a Photocatalytic Coating Protecting Building Material[END_REF], (ii) fungal genera such as Aspergillus, Penicillium, Cladosporium and Stachybotrys [START_REF] Verdier | Bacterial Biofilm Characterization and Microscopic Evaluation of the Antibacterial Properties of a Photocatalytic Coating Protecting Building Material[END_REF][START_REF] Borrego | Fungal Assessment on Storerooms Indoor Environment in the National Museum of Fine Arts, Cuba[END_REF][START_REF] Górny | Fungal Fragments as Indoor Air Biocontaminants[END_REF][START_REF] Hegarty | Spatial Gradients of Fungal Abundance and Ecology throughout a Damp Building[END_REF]. In this study, Escherichia coli and Aspergillus niger were chosen to evaluate TiO2 nanoparticles antimicrobial activity.

E. coli CIP 53126 was obtained from the collection of the Pasteur Institute (CIP), Paris, France. Strains were stored at -80 °C in his Eugon medium (Biomérieux, Craponne, France) supplemented with 10% glycerol. Bacterial cells were precultured on trypticase soy agar (TSA) before each experiment (incubation 36 °C ± 1 °C for 16-24 h). A new subculture was performed (36 °C ± 1 °C for 16-20 hours) prior to testing. For testing, bacterial cells were dispersed in 1/500 broth (NB) [START_REF] Verdier | Antibacterial Activity of TiO2 Photocatalyst Alone or in Coatings on E. Coli: The Influence of Methodological Aspects[END_REF][START_REF] Verdier | Bacterial Biofilm Characterization and Microscopic Evaluation of the Antibacterial Properties of a Photocatalytic Coating Protecting Building Material[END_REF][START_REF]An Overview of Methods Used to Evaluate the Efficacy of Antibacterial Treated Surfaces and Textiles[END_REF] and the bacterial cell content of the inoculum suspension was determined using a spectrophotometer (640 nm) at approximately 10 8 cells/mL. The cell suspension was then diluted 10-fold and 1 mL of each dilution was plated incorporated in TSA to determine the number of CFU/mL.

For fungal suspension, A. niger strain CBS 733.88 was cultured in a flask, on Sabouraud agar medium (SAB) (Biomérieux) at 22.5 °C for 10 to 14 days to prepare the spore suspension [36]. Ten mL of sterilized distilled water + tween 80 with sterile glass balls were inserted into the flask of strain and the flask was shaken gently for at least 2 minutes. The suspension was then collected and filtered through sterile frit 080557-2 (40-100 µm) into a sterile pot containing sterile glass beads to prevent clustering of spores. The concentration of suspension was obtained by counting spores on Malassez cell through optical microscope. One mL of suspension adjusted to 1*107 cfu/mL was inoculated into SAB Petri dishes and then incubated at 22°C for 48 h before CFU counts.

Stirring experiment: Evaluation of antimicrobial activity of TiO2

During each experiment, 1mL was taken from each beaker at t0=0 min and every 30 minutes for 2 or 4 hours and tenfold diluted in sterile distilled water for CFU numerations (as for the suspensions). Petri dishes from E. coli experiments and A. niger experiments were incubated at 36°C ±1°C for 48 hours and at 30°C ±1°C for 48 hours respectively. The antimicrobial activity (log reduction) was then calculated using Equation 1. Where R: Log10 Reduction of TiO2 (referred as antimicrobial activity in the text), Csusp: Average concentration of suspension in control tube without TiO2, Ctest: Average concentration of suspension in test tube with TiO2 in CFU/mL. ICEPTP 154-3 Each experiment was repeated at least twice and results present the average obtained from each series of experiments with corresponding standard deviations (SD).

Results And Discussion

Effect of TiO2 in the dark

In the dark, after two hours of contact between 10g/L TiO2 and cell/spore suspension, the average log10 reduction was 0.04±0.01 for A. niger suspension and 2.27± 0.08 for E. coli (Figure 2). These results are in agreement with previous findings regarding TiO2 efficacy [START_REF] Yu | The Antifungal Efficacy of Nano-Metals Supported TiO2 and Ozone on the Resistant Aspergillus Niger Spore[END_REF]. The strong antibacterial activity may be explained by the ability of well-dispersed nano-particles of TiO2 to interact with bacterial cells absorbing them to their surfaces and leading to a remarkable decrease in their concentration [START_REF] Sohm | Insight into the Primary Mode of Action of TiO2 Nanoparticles on Escherichia Coli in the Dark[END_REF]. Regarding antifungal activity, the resistance of fungal spores to TiO2 [START_REF] Yu | The Antifungal Efficacy of Nano-Metals Supported TiO2 and Ozone on the Resistant Aspergillus Niger Spore[END_REF][START_REF] Chen | Antifungal Capability of TiO2 Coated Film on Moist Wood[END_REF] implies no interaction between nanoparticles of TiO2 and fungal spores of A. niger and thus a negligible fungicidal activity was observed after 2 hours of contact in the dark.

Effect of TiO2 under light

Under a light intensity of 5W/m 2 , both antifungal and antibacterial activity of 10g/L TiO2 were evaluated. After 2 hours of contact between suspension and TiO2, the average log10 reduction 'R' was 0.85±0.03 for A. niger spore suspension and 2.58±0.08 for E. coli. TiO2 shows a weaker activity on A. niger spores compared to its activity on E. coli cells (Figure 3). Previous findings showed a higher antifungal activity of TiO2 mixed with Ag nanoparticles on Aspergillus niger but these results were obtained using a very high light intensity of 40W/m 2 [START_REF] Rahmat | Antifungal Activity of TiO 2 /Ag Nanoparticles under Visible Light Irradiation[END_REF] or by continuous UV irradiation for 20 days [START_REF] Chen | Antifungal Capability of TiO2 Coated Film on Moist Wood[END_REF]. The ability of TiO2 to damage the cell membrane of E. coli explains its high antibacterial activity [START_REF] Dharma | A Review of Titanium Dioxide (TiO2)-Based Photocatalyst for Oilfield-Produced Water Treatment[END_REF][START_REF] Liu | The Damage of Outer Membrane of Escherichia Coli in the Presence of TiO2 Combined with UV Light[END_REF]. The differences between fungal cell membranes and bacterial ones may also contribute to the difference of TiO2 effects observed in our study [START_REF] Gao | The Membrane Proteome of Spores and Vegetative Cells of the Food-Borne Pathogen Bacillus Cereus[END_REF][START_REF] Qiu | Study on the Biological Effect of Tourmaline on the Cell Membrane of E. Coli[END_REF].

Influence of the concentration of TiO2 on its antibacterial activity

The antibacterial activity of TiO2 was tested at 10g/L where it showed R > 2.00 in dark and light conditions. Another series of experiments was carried at 1g/L concentration of TiO2 to investigate its activity on E. coli at a lower concentration tested previously by Verdier [START_REF] Verdier | Antibacterial Activity of TiO2 Photocatalyst Alone or in Coatings on E. Coli: The Influence of Methodological Aspects[END_REF]. In the dark, after 4 hours of contact, 1g/L of TiO2 showed a clearly weaker activity compared to that observed after 2 hours of contact to 10g/L TiO2 with only 0.61±0.01 log reduction (Figure 4). By contrast, under light, 4 hours of contact to 1g/L TiO2 showed approximately similar antibacterial activity as that of 10g/L TiO2 after 2 hours of contact. The maximum log reduction was 2.49±0.07 after 4 hours of contact for 1g/L and 2.58±0.08 after 2 hours of contact for 10g/L of TiO2 ( Figure 5). As said before, high concentration of TiO2 (10g/L) was capable to inhibit the growth and/or kill the cells of E. coli either by damaging their cell membranes under light [START_REF] Dharma | A Review of Titanium Dioxide (TiO2)-Based Photocatalyst for Oilfield-Produced Water Treatment[END_REF][START_REF] Liu | The Damage of Outer Membrane of Escherichia Coli in the Presence of TiO2 Combined with UV Light[END_REF], or by absorbing them onto their surfaces in the dark [START_REF] Sohm | Insight into the Primary Mode of Action of TiO2 Nanoparticles on Escherichia Coli in the Dark[END_REF]. At low concentration (1g/L), the number of well dispersed nano-particles of TiO2 might not be sufficient to interact directly with bacterial cells and reduce their concentrations in the dark, whereas under the light, the antibacterial activity of 1g/L of TiO2 may be explained by its capability to damage cell membrane of E.coli when photocatalyzed (Figure 4). The reduced concentration of TiO2 requires therefore a longer application time to be active. As an illustration, concentrations of TiO2 as low as 0.1g/L have shown a strong antibacterial activity but after 24 hours of contact using a light intensity range of 14-55 W/m² [START_REF] Ibáñez | Photocatalytic Bactericidal Effect of TiO2 on Enterobacter Cloacae: Comparative Study with Other Gram (-) Bacteria[END_REF].

Resistance of Aspergillus niger to TiO2 photocatalyst

To investigate the resistance of A. niger, another series of stirring experiments was carried out for 24 hours of contact between A. niger and TiO2, in light conditions. After 24 hours of contact, the resistance of A. niger against the photocatalyst TiO2 was confirmed as the maximum reduction reached was only 0.86±0.02 (Figure 6). No study has previously highlighted the resistance of A. niger to the photocatalyst TiO2 within real-life conditions. One investigation has shown the ability of TiO2 to inhibit the growth of A. niger on woods but these results were obtained at very high light intensities [START_REF] Chen | Antifungal Capability of TiO2 Coated Film on Moist Wood[END_REF]. By contrast, our results are in agreement with the resistance of A. niger against TiO2 observed after 24 hours of contact in the dark [START_REF] Yu | The Antifungal Efficacy of Nano-Metals Supported TiO2 and Ozone on the Resistant Aspergillus Niger Spore[END_REF].

Conclusion

The main objective of this study was to investigate the difference between the antibacterial effect from one side and antifungal effect on other side of TiO2 nanoparticles through stirring experiments allowing a direct contact between TiO2 and cells at low light intensity close to real-world conditions. The obtained results confirmed previous findings on the antibacterial activity of TiO2 on E. coli and highlighted the variation of its efficiency as a function of its concentration, duration of contact, light/dark conditions and especially as a function of microorganisms (Spores of A. niger vs E. coli in current study). TiO2 is an efficient photocatalyst, non-toxic and a low-cost product that is employed in most air and water purification systems using high light intensities [START_REF] Dharma | A Review of Titanium Dioxide (TiO2)-Based Photocatalyst for Oilfield-Produced Water Treatment[END_REF]. In addition, this substance is already used in coatings, paints, and in cementitious materials [START_REF] Verdier | Bacterial Biofilm Characterization and Microscopic Evaluation of the Antibacterial Properties of a Photocatalytic Coating Protecting Building Material[END_REF][START_REF] Maury-Ramirez | Titanium Dioxide Based Strategies to Prevent Algal Fouling on Cementitious Materials[END_REF]. Indeed, as the antibacterial activity of TiO2 nanoparticles is important, it is also essential to highlight the resistance of other microorganisms such as some fungal spores to this product. The inclusion of particles such as fungal spores may affect negatively the efficiency of TiO2 on vegetative cells suggesting that the application of TiO2 nanoparticles in paint [START_REF] Verdier | Antibacterial Activity of TiO2 Photocatalyst Alone or in Coatings on E. Coli: The Influence of Methodological Aspects[END_REF] is perhaps not the best way to use it. These findings suggest the limitation of photocatalytic products interest in the destruction of microorganisms under common indoor light irradiation. On the basis of new research, their applications should be aimed toward prevention through growth inhibition.

Figure 1 :

 1 Figure 1: A schema illustrating the stirring experiment: Magnetic stirrer at 300 rpm; Beaker containing suspension: (E. coli or A. niger), TiO2 in test tubes or distilled water in control tubes; Light irradiation of 5 W/m 2 in light conditions; Pyrex lid. 𝑅𝑅 = 𝐿𝐿𝐿𝐿𝐿𝐿(Csusp) -𝐿𝐿𝐿𝐿𝐿𝐿(𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶) = 𝐿𝐿𝐿𝐿𝐿𝐿( 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 )

Figure 2 :

 2 Figure 2: Average ±SD of log reduction of 10g/L TiO2 in dark conditions on A. niger suspension (a) vs on E. coli (b).

Figure 3 :

 3 Figure 3: Average ± SD of log reduction of 10g/L TiO2 in light conditions on A. niger suspension (a) vs on E. coli (b).

Figure 4 :

 4 Figure 4: Variation with time of average concentration of E. coli suspension (log CFU) in the dark in: control tube; test tube containing 10g/L of TiO2; test tube containing 1g/L of TiO2.

Figure 5 :

 5 Figure 5: Variation with time of average concentration of E. coli cell suspension (log CFU) under light conditions in: control tube; test tube containing 10g/L of TiO2; test tube containing 1g/L of TiO2.

Figure 6 :

 6 Figure 6: Variation with time of average concentration of A. niger spore suspension (log CFU) in control tube and in test tube during contact with TiO2 nanoparticles for 24 hours in light conditions

  Average concentration of test tube in log 10Average concentration of control tube in log 10

Acknowledgements

The authors would like to thank Université Paul Sabatier Toulouse III and the Région Occitanie (Project SoBio2QAI) for their financial support.


Ch Hochard

J Payan

O Montagnier

Design and computation of laminated composite structures

Keywords: A. Textile composites, B. Mechanical properties, B. Fracture, C. Damage mechanics, C. Laminates. -0.15 -0.1 -0.05

The design and computation of laminated composite structures in terms of their strength is a complex task because many different mechanisms are involved in the damage and rupture to which these materials are subject. The great diversity of the damage mechanisms and their patterns of evolution make it extremely difficult to estimate the strength margins. In the case of woven plies laminates, the number of damage mechanisms is fairly small (no transverse rupture occurs and the material has a greater resistance to delamination) and the behaviour of the material is fairly simple to model up to rupture. The strategy adopted in this study on designing laminated composite structures is based on the choice of materials (woven or unidirectional plies) and the use of simple models (focusing on the rupture of the first ply) with which industrial structure analyses can be carried out. The choice of materials does not depend only on mechanical criteria but also on the simplicity of the corresponding modelling procedures.

Introduction

The qualities for which laminated composites are mainly chosen are their specific rigidity and strength. Although designing structures according to rigidity does not raise any particular problems, designing with respect to strength is much more complicated. When these materials are subjected to severe loading up to rupture, the many mechanisms responsible for the damage and rupture occur on different scales: matrix micro-cracking, fibre/matrix debonding, transverse rupture, fibre rupture, delamination, rupture of the plies and the laminate [START_REF] Reifsnider | Durability and damage tolerance of fibrous composite systems[END_REF]. The great diversity of the damage mechanisms and their patterns of evolution make it extremely difficult to estimate the strength margins.

When transverse rupture and delamination occur in the edge zones of unidirectional (UD) ply laminates, they will extend inside the structure and it is therefore not yet possible (by performing 3-D modelling) to simulate the damage processes occurring in complex industrial structures. In the case of woven plies laminates, the number of damage mechanisms is fairly small (no transverse rupture occurs and the material has a greater resistance to delamination) and the behaviour of the material is fairly simple to model up to rupture [START_REF] Hochard | Modelling of the mechanical behaviour of woven-fabric CFRP laminates up to failure[END_REF]. Moreover, in the case of woven ply laminates, the rupture of a ply is associated to fiber rupture and is very close to the rupture of the laminate and the structure. This observation noted in experiments, at least for static loadings, simplifies simulation until rupture since it is not necessary to simulate propagations of cracks in the plies. A finite element calculation in terms of plane stresses until the rupture of the first ply and which includes the elastic plastic damage behaviour of the woven ply enables to describe the rupture of a structure [START_REF] Bordreuil | Finite element computation of woven ply laminated composite structures up to rupture[END_REF].

As we already specified, the principal difficulties in the case of the laminated composites relate to the modelling and the simulation of propagations of cracks in the plies and interfaces (delaminations). For studying UD ply laminates under static and fatigue loading, a first ply failure model was previously proposed for structures not subject to delamination [START_REF] Payan | Damage modelling of carbon/epoxy laminated composites under static and fatigue loads[END_REF]. Within this restricted framework, a model based on plane stresses accounting for the elastic plastic damage behaviour of the ply again turned out to be sufficient. This type of model can be used for dealing with tubes, for example, in contexts where a high level of safety is required.

Obviously, the use of UD plies is optimal when rigidity plays a dominating part. Due to the reduction in the costs of new high-modulus fibres (pitch fibre), it seems logical to use this type of fibre for applications where rigidity is of particular importance (in the case of structures subjected to dynamic and buckling loading, for instance). For these applications, it suffices to use the elastic behaviour to be able to predict the rigidity. However, these fibres have very weak characteristics in compression and particular precautions are to be taken in order to know them as well as possible.

The strategy adopted in this study on designing laminated composite structures is based on the choice of materials (woven or UD plies, high modulus fibres) and the use of simple models (focusing on the rupture of the first ply) with which industrial structure analyses can be carried out. It is proposed here to study the following three cases, using this strategy: (i)

In the case of woven plies laminates, the behaviour of the material is fairly simple to model and the reliability of the simulation up to rupture is improved. The woven ply model is recalled and finite element computations are compared with experiments in the case of a laminated composites plate containing an open hole subjected to tensile loadings. (ii)

In the case of UD ply laminates not subject to delamination under static and fatigue loading, a first ply failure model turned out to be sufficient. The main features of the model are pointed out and some experimental results are presented. (iii)

High modulus fibres are suitable for applications where rigidity is of particular importance (dynamic and buckling). However, these fibres are not very resistant to compression and their response to high compression conditions therefore needs to be precisely determined. A pure bending test is described and some experimental results showing the nonlinear behaviour in the fibre direction are presented.

Woven ply laminates

Woven ply laminates have weaker mechanical characteristics and are more expensive than UD ply laminates. However, they are used in industry (to make helicopter blade skins, for example). The explanation often given by companies for this choice of woven ply laminates is that they are not subject to transverse rupture, which can be catastrophic in the case of UD plies. Moreover, these materials are more resistant to delamination. The number of damage mechanisms liable to occur is thus reduced and the behaviour of the material is simpler to model up to rupture. The behaviour of materials of this type and the modelling procedure used were previously described in Ref. [START_REF] Hochard | Modelling of the mechanical behaviour of woven-fabric CFRP laminates up to failure[END_REF]. The material is reinforced with a carbon fabric of the four-harness satin type, with balanced warp and fill yarns. In the fibre directions, the woven ply shows a brittle linear elastic behaviour when subjected to tension (see Fig. 1(a)). The damage occurring in these directions does not affect the behaviour of the ply under traction loading. When shear loading was applied (from a tensile test on a [45] n

Damage behaviour of woven plies

 x  x (Pa) + : Model -: Test  x (a) (b)  x (Pa)
laminate), a decrease in the shear modulus as well as inelastic strains were observed (see Fig. 1(b)). The decrease in the modulus was due to the ply shear stress, which generated some fibre/matrix decohesion and matrix micro-cracks within the warp and fill yarns. The inelastic strains and the loading-unloading hysteresis observed (Figure 1(b)) were mainly due to the slipping/friction processes occurring between the fibres and matrix as the result of the damage. With a view to modelling the behaviour of laminates with a woven reinforcement, we have adapted the "meso-scale" model developed for unidirectional plies proposed by Ladevèze [START_REF] Ladevèze | A damage computational method for composite structures[END_REF][START_REF] Ladevèze | Damage modelling of the elementary ply for laminates composites[END_REF]. This model was designed for dealing with woven plies with balanced or non-balanced warp and fill yarns. The damage kinematics adopted was based on the following three internal damage variables (d 1 , d 2 , d 12 ): the brittle fracture of fibres in the warp and fill directions and the decreasing stiffness under shear loading, respectively. The gradual development of the damage d 12 depends on the shear load as well as on the traction load, which generates micro-cracks in both the fill and the warp components. These micro-cracks, which are mainly located at the fibre/matrix interfaces, are assumed to run parallel to the fill and warp directions. Under the assumption of plane stresses and small perturbations, we can write the strain energy of the woven ply in the following form:

                         12 0 12 2 12 0 2 2 2 2 0 2 2 2 2 1 0 1 0 12 0 1 2 1 1 0 1 2 1 1 1 2 ) 1 ( 2 1 d G E d E E E d E E ps D         (1)
where < . > + is the positive part and < . > -is the negative part. The tension energy and compression energy are split in order to describe the unilateral feature due to the opening and closing of the micro-defects. From this potential, thermodynamic forces associated with the tension and shear internal variables d i (i=1 and 2) and d 12 are defined:

    2 12 0 12 2 12 12 2 0 2 1 2 ; 1 2 12 d G d E Y d E d E Y ps D d i i i i ps D d i              (2)
The development of the internal variables depends on these thermodynamic forces and more precisely on their maximum values during the history of the loading. In traction, the development of d 1 and d 2 is brutal in order to represent the brittle behaviours according to the warp and fill directions. To take into account the traction/shear coupling during the development of d 12 , we define the equivalent thermodynamic force and the maximum value of this force during the history of the loading:

)) ( ( sup ) ( 12 2 1 2 1     Y t Y and Y Y Y Y t d d d      (3)
where  1 and  2 are the tension/shear coupling coefficients. It should be noted that this equivalent force, which govern the development of the progressive damage variable d 12 , does not depend on the compression stresses in the warp and fill directions. As for the unidirectional plies [START_REF] Ladevèze | Damage modelling of the elementary ply for laminates composites[END_REF], a linear law with respect to the square root of Y is chosen to describe the damage variable development:

    O c O Y Y Y Y d 12 , d 1 =d 2 =0 if (d 12 1 and Y d1 Y 1f and Y d2 Y 2f ) else d 12 = d 1 = d 2 =1 (4)
where the constant parameters Y o and Y c correspond to the threshold and the critical value of the development of d 12 (which varies from 0 to 1). Y 1f and Y 2f are the parameters, which define the ultimate forces in the warp and fill directions. After loading on a laminate [45] 8 (Fig. 1(b)), inelastic strains are observed. These strains can be linked to the slipping/friction phenomena between the fibres and matrix as a consequence of the damage. Because of the warp and fill fibre directions, which prevent traction inelastic strains, only the shear inelastic strains are significant. We shall describe these strains by a plastic hardening model [START_REF] Hochard | Modelling of the mechanical behaviour of woven-fabric CFRP laminates up to failure[END_REF]. The loading-unloading hysteresis, which is mainly due to the slipping/friction phenomena between the fibres and matrix, is not modelled. The high resistance of woven ply laminates to delamination, in addition to the fact that they are not subject to transverse rupture, allows to simulate the behaviour up to rupture of complex structures made of these materials. For this purpose, a simple finite element model of the shell type, based on plane stresses and accounting for the inelastic damage behaviour of the woven ply, can be used. This relatively simple modelling procedure is not suitable in the case of UD plies, in which transverse rupture and delamination processes resulting from the 3-D effects mentioned above are factors responsible for the rupture of the laminate.

Behaviour of a perforated plate subjected to tension

In order to test the model, comparisons were made between the results of an experimental test and those of a simulation involving a perforated plate under traction loading. The perforated plate (Figure 2) was a [45] 4 laminate made of woven plies. Figure 3 makes it possible to compare the measured strain (gauges g1, g2 and g3, Figure 2) with the simulated strain (the mean strain on the surface of the gauge). It can be seen here that the model accurately predicted the breaking force and the strongly non-linear behaviour. The simulation predicted very high levels of damage (more than 0.5). A further study is now being carried out in order to measure the damage levels involved [START_REF] Bois | Measurements and modelling for the monitoring of damage in laminated composites structures[END_REF]. Comparisons with other stacking sequences are shown Figure 4. For the quasi-isotropic laminate ([22.5°,-22.5°] s ) it was observed that the simulation under predicted the experimental result (rupture in the fibre direction). Currently, we are looking to introducing an internal length in order to better predict the fibre direction rupture in the case of structures with high gradient stresses.

Fatigue behaviour

For dealing with UD ply laminates, it was proposed to model the material up to rupture of the first ply in the case of structures or laminates which are not subject to delamination, under static and fatigue loading conditions [START_REF] Payan | Damage modelling of carbon/epoxy laminated composites under static and fatigue loads[END_REF]. Within this restricted framework, a model based on plane stresses accounting for the elastic plastic damage behaviour of the ply again turned out to be sufficient.

Behaviour of a unidirectional ply under static and fatigue loading.

The model previously presented [START_REF] Payan | Damage modelling of carbon/epoxy laminated composites under static and fatigue loads[END_REF] is a non-linear cumulative damage model, enables to describe the development of damage under both static and fatigue loading conditions. The delamination processes are not accounted for in this model, which is therefore relevant only to some particular structures and laminates that are not subject to delamination (those which have no edges, as in the case of tubes, for example). The validity scope of the model described here depends on the 'diffuse damage' phase (which is associated with micro-cracks) up to the first intra-laminar macro-crack only. In this respect, the modelling procedure adopted differs from the approaches that describe the macro-crack density [START_REF] Akshantala | A micromechanics based model for predicting fatigue life of composite materials[END_REF][START_REF] Mc | Matrix cracking induced by cyclic ply stresses in composite laminates[END_REF]. This type of model can be used in contexts where a high level of safety is required.

The material is assumed to be brittle and non-sensitive to the cyclic loading occurring in the direction of the fibres. The in-plane transversal and shear moduli are modified under the assumption that a gradual damage process is involved, via the micro-cracks running parallel to the fibres. The development of the damage depends on the maximum static and cyclic loads and their amplitude as well as on the level of damage involved. Furthermore, it uses the cumulative damage where damage variables (for shear and transverse tension) are obtained by addition of two terms: one part is due to static loading and the other one is governed by fatigue loading. The static damage evolution is linear versus associated equivalent force. For fatigue damage evolution, experiments have shown its double dependency on maximun load and amplitude load; so a law which respects this observation has been built:

    ) ( sup ) ( ) Y ( inf sup Y * * ) ( max ) ( ) ( 0 max Y t Y Y Y Y c N d t cycle t cycle t cycle f f                         (5)
where the constant parameter Y of corresponds to the threshold in fatigue. Fig. 6. Fatigue behaviour on [45] ns laminates; the notation "exp V" corresponds to specimens which did not break (tests from Petermann [START_REF] Petermann | Strain based service time estimation for angle-ply laminates[END_REF]).

An example of the evolution of the damage process in the case of a tension/ tension fatigue test on a [45°] ns laminate is shown in Figure 5. The first level of damage (d=0.3) was found to occur during the first cycle. The damage then increases slowly at each cycle, and the speed of evolution gradually increases until rupture occurs. In the simulation, the rupture of a [45°] ns laminate was obtained by introducing a structure instability condition. Under static loading, this condition corresponds to a damage value d=0.5, although this value can be greater under fatigue loading. This result is in line with what was observed experimentally. After a loading process has taken place in a laminate, residual strains can be observed. These strains can be due to the friction occurring between the fibres and the matrix as a result of the damage. To describe them, a kinematical hardening model is under development. This type of anelastic damage behaviour was studied by performing traction tests and 4 point bending tests. The samples used in the bending tests were sandwich structures (a laminate with the ply studied, a honeycomb, and a woven ply laminate at 0°). With this sandwich structure, it is possible to create an almost uniform state of strain in the ply studied, and the [0°] woven plies are assumed to undergo almost no degradation. One of the advantages of the four point bending test is that it makes it possible to prescribe a compression load on the ply under investigation.

SN curve and residual strength.

The model allows to predict SN curves. A comparison between simulations and tests (Petermann [START_REF] Petermann | Strain based service time estimation for angle-ply laminates[END_REF]) on [45°] ns laminates under fatigue loading showed the possibilities of the model (Figure 6). The results of the simulations carried out with different stresses and stress ratios (minimum stress over maximum stress) were in good agreement with the experimental results. The endurance limits were found to vary with respect to the stress ratios in the case of both the model and the experiments. Finally, it was observed that the residual strength does not decrease with respect to the fatigue loading. The performances of high rotation frequency tubes (such as drive shafts and centrifugal machines) can be improved by using high rigidity carbon fibres. A high effective modulus enables to delay the onset of the vibration modes. The buckling strength under torsion, which is one of the main criteria used in designing hollow laminated composite drive shafts, can also be greatly improved by using these fibres. For these applications, it suffices to model the material in terms of its elastic behaviour according to dynamic and buckling design. It is worth noting that materials of this kind with a very high modulus have a very low breaking strain in the fibre direction, which is even lower than that observed in the transverse direction. In laminates where the plies do not undergo shearing and compression stresses in the fibre direction, elastic criteria can be used to describe the rupture of the laminate under static loading conditions. In the case of compression stresses, the strength of these fibres is very low and their behaviour under high compression conditions therefore needs to be precisely determined. Rupture behaviour under compression loading in the fibre direction is difficult to predict. The standard tests consisting in applying pure compression (Celanese tests) lead to premature rupture because of the edge effects and the buckling of the specimen. Compression tests on [+60 2 ,0,-60 2 ] s laminates [START_REF] Welsh | Testing of angle-ply laminates to obtain unidirectional composite compression strengths[END_REF] allows to decrease the risk of buckling of the specimen. In these compression tests, the calculation of the stresses in the 0° plies is rather complex, however, due to the non-linear behaviour of the 60° plies. Buckling/bending tests [START_REF] Wisnom | On the high compressive strains achieved in bending tests on unidirectional carbonfibre/epoxy[END_REF] and four point bending tests [START_REF] Vittecoq | Comparison between compression and tension behaviours of composite laminates[END_REF] also make it possible to determine the rupture strain under compression loading. However, these buckling/bending tests do not yield any direct information about the stresses in the beam (the inverse calculations are complex, due to the large displacements and rotations involved).

High modulus fibres

A pure bending test has been proposed (Figure 7) for determining the compression behaviour more precisely. This test, which consists in applying two bending couples at the two free ends and letting one of the ends translate freely, enables to determine the forces at work (constant moment) throughout the sections. In addition, it is possible here to use machined specimens (Figure 7) in order to rule out the occurrence of edge effects at the level of the tabs. The specimens were instrumented on each face with strain gauges. The behaviour of pitch fibres Dialead K63712 was tested. The behaviour is elastic and nonlinear (the rigidity decreases, see Figure 8). The rupture mode observed is original. After point A is reached (Figure 8), the strains increased slowly for a constant moment. Indeed, the compressive strain evolved from 0.18% to 0.40%, in parallel, the tensile strain evolved from 0.16% to 0.27%, and the neutral fibre moved towards the tension zone. We think that point A corresponds locally to the top of the compressive stress/strain curve. From this loading, where the maximum compressive stress was reached, the compressive strains increased but the compressive stresses decreased (Figure 9). We suppose that the equilibrium was relatively stable due to viscous phenomena of the matrix.

Non-linear behaviour in compression

To model this non-linear behaviour, the rigidity was chosen to decrease under compression (and to increase under tension) depending on the strain. A first model was a linear law between the modulus and the strain [START_REF] Ladevèze | A damage computational method for composite structures[END_REF]. This model was not sufficient here to describe the fast decrease of the compressive modulus. The model used was a power law between the modulus and the strain. The constitutive law, if we add the rigidifying behaviour in tension, is written:

tension compression A 2 1                  n E (6)
The identification of the parameters E and  was realized on tensile tests. The parameters  and n were identified by a minimization method [START_REF] Vittecoq | Comparison between compression and tension behaviours of composite laminates[END_REF] and an additional constraint relative to the rupture associated to the instability process (Figure 9). Fig. 9. K63712 constitutive law in the fiber direction.

Conclusion

In conclusion, simple rules emerge from the results of this study as far as the technological design of laminated composite structures is concerned:  It is recommended to use woven plies to design structures according to strength;  It is recommended to use high-modulus UD plies to design structures according to rigidity  UD plies can be used to design structures according to strength, but only up to failure of the first ply and for structures which are not subject to delamination The choice of type of ply (woven or unidirectional plies) does not depend only on mechanical criteria but also on the simplicity of the corresponding modelling procedures.

Fig. 1 .

 1 Fig. 1. Tensile tests on a [0] 8 (a) and [45] 8 (b) woven ply laminates.

Fig. 2 .

 2 Fig. 2. Traction test on a perforated plate made of [45] 4 woven ply laminate.

Fig. 3 .

 3 Fig.3. Measured and simulated strains (see Figure2).

Fig. 4 .

 4 Fig. 4. Testing and simulation for perforated plates in traction.

Fig. 5 .

 5 Fig. 5. Testing and simulation of damage evolution (fatigue loading, max=120MPa, stress ratio R=0.5).

Fig. 7 .

 7 Fig. 7. Diagram and specimen for pure bending test.

Fig. 8 .

 8 Fig. 8. Pure bending test on unidirectional Dialead K63712 ( c : compression face;  t : traction face).