Dr Anne Bergeret

Prof. Jörg Gilles Ausias

Dr Johnny Müssig

Beaugrand

A Abdennadher

I acknowledge my gratitude to people of "Centre des Matériaux at Ecole des Mines d'Ales" for the absolute

Extended abstract of the thesis in French

Résumé étendu de la thèse

Introduction générale

Le réchauffement climatique et l'ampleur de l'effet des déchets non-biodégradables sur l'environnement sont devenus des problématiques d'actualité sur lesquelles les industriels se sont penchés. Cela a généré la mise en place de stratégies de développement durable qui encouragent à chercher une alternative aux matériaux fossiles à la fois respectueuse de l'environnement et garante de performances similaires.

Dans ce contexte, les fibres naturelles ont reçues une grande attention au cours des deux dernières décennies pour remplacer les fibres de verre comme renfort dans les composites polymères. En plus de leur aspect écologique, les principales raisons qui incitent à l'utilisation des fibres naturelles dans les composites sont leur faible coût et le gain en poids toute en gardant des propriétés mécaniques similaires aux composites à fibres de verre. La faible densité des fibres naturelles attire particulièrement le secteur des transports (automobile, ferroviaire, aéronautique…) très sensible à la réduction de poids. Les composites à fibres naturelles sont utilisés dans les automobiles pour des pièces intérieures comme des revêtements, des garnitures de tableaux de bord, des panneaux de porte... D'autres secteurs d'application des composites à fibres naturelles sont apparus comme le sport et loisirs (ski, snowboard, vélo...) grâce à leurs bonnes propriétés d'amortissement, les instruments de musique et haut-parleurs en raison de leurs excellentes performances acoustiques, ou aussi l'ameublement (bureau, chaise...) en raison de leurs aspect lorsque les fibres sont mélangés avec une matrice translucide.

Les fibres naturelles techniques utilisées comme renfort des polymères sont soit des fibres ligno-cellulosiques, provenant de tiges de plantes comme les lin, chanvre, jute et kenaf ou de graines (coton) ou de feuilles (sisal), soit des fibres à 100 % cellulosiques filées telles que les fibres Tencel (procédé Lyocell) ou viscose. Dans ce travail, deux types de fibres naturelles ont été utilisés, le lin et Tencel avec une matrice polypropylène, avec pour objectif :  d'étudier et de comprendre l'influence des différentes compositions et morphologies de fibres :

o sur la microstructure des composites, c'est à dire la taille, l'orientation et la concentration de fibres, o sur les propriétés rhéologiques et mécaniques qui en résultent,  de vérifier si les modèles développés pour les fibres de verre peuvent prédire la pression pendant le remplissage de moule en injection et l'orientation des fibres naturelles dans des pièces moulées.

Les fibres de lin et Tencel sont différentes. Les composants principaux du lin sont la cellulose (64-81 %), l'hémicellulose (11-17 %), la lignine (2-3 %) et la pectine (2 %) tandis que Tencel est basée sur de la cellulose pure. De plus, elles présentent une morphologie différente. Tencel est une fibre élémentaire mince et flexible avec un diamètre uniforme (dû au procédé de filage), tandis que le lin est un «mélange» de fibres élémentaires semi-rigides minces et de faisceaux épais et rigides composés de fibres élémentaires assemblées. Enfin, leurs propriétés mécaniques intrinsèques sont également différentes. Il est donc supposé que ces différences de propriétés des fibres auront une influence sur la microstructure et les propriétés des composites.

En France, le lin de haute qualité est aujourd'hui cultivé dans les régions du nord (Normandie, Picardie et Nord-Pas-de-Calais) en raison des conditions climatiques modérées et du savoirfaire des liniculteurs. Avant d'être en mesure de renforcer un polymère, les fibres de lin sont soumises à un long cycle d'extraction comprenant le rouissage, la rupture, le teillage et le peignage. Plus de 80 % de la production de lin est aujourd'hui tournée vers l'industrie textile qui est leur application historique et seulement 10 % sont dédiés à un usage technique.

Le principal producteur de fibres de Tencel est la société autrichienne Lenzing qui nous a les aimablement fournies. La cellulose de base des fibres Tencel est extraite de la pulpe principalement trouvée dans les eucalyptus. La cellulose est dissoute dans du Nméthylmorpholine-N-oxyde monohydrate, puis filtrée, centrifugée, filée, coagulée et séchée.

En plus de leur utilisation principale dans l'industrie textile, les fibres Tencel sont couramment employées pour la fabrication de cordes ou des filtres automobiles.

Nous nous intéressons dans ce travail au polypropylène renforcé de fibres discontinues de lin et Tencel. Le mélange fibre/matrice se fait par extrusion bivis pour produire des granulés, qui sont ensuite transformés par injection. D'autres façons de fabriquer des composites thermoplastiques existent comme, par exemple, le moulage par compression. L'injection reste la méthode préférée pour fabriquer des pièces de géométries complexes avec une haute cadence et un faible coût de production. Le marché du moulage par injection est en pleine croissance avec l'augmentation des domaines d'application pour les composites à fibres naturelles. Le potentiel de ces matériaux combiné à la productivité du procédé d'injection satisfait au défi environnemental et à la performance industrielle. Toutefois, en raison de la complexité de choix et de la variété des fibres naturelles plusieurs questions subsistent.

Dans ce contexte, cette thèse a été lancée en octobre 2012 au Centre de Mise en Forme de Matériaux (Cemef) de Mines ParisTech, dans le cadre de la Chaire Industrielle Bioplastiques.

Cette chaire est cofinancée par Mines ParisTech et cinq entreprises: Arkema, L'Oréal, Nestlé, PSA Peugeot Citroën et Schneider Electric. C'est un grand projet de recherche de 7 ans qui comprend différents thèmes dont l'objectif est de soutenir le développement et les applications de divers matériaux bio-sourcés (bioplastiques, matériaux ligno-cellulosiques et composites polymères à fibres naturelles). Une précédente thèse s'est déroulée dans le cadre de cette chaire portant sur le comportement et la rupture de fibres cellulosiques lors de leur compoundage avec une matrice polymère. La présente thèse vient compléter ce travail et se concentre sur l'étude et la compréhension des propriétés d'un polypropylène renforcé de fibres naturelles en abordant certaines questions autours du moulage par injection.

Problématiques

Les polymères renforcés de fibres de verre discontinues ont été largement étudiés et optimisés. La question principale ici est de savoir si les résultats et approches peuvent être étendus aux fibres naturelles. Les fibres de verre sont rigides, de diamètre constant et de propriétés uniformes. Comme mentionné ci-dessus, les fibres de lin techniques sont un mélange de fibres élémentaires et de faisceaux. Pendant la mise en oeuvre, les faisceaux se dissocient en faisceaux plus minces voire même en fibres élémentaires. En fonction de leur diamètre et longueur, les fibres de lin peuvent se présenter comme semi-rigides ou rigides. En outre, les fibres de lin sont un produit d'agriculture dont les propriétés varient avec les conditions de culture et d'extraction et la variété dont elles proviennent. Tout cela fait que leur morphologie est très différente de celle des fibres de verre. L'autre type de fibres de cellulose utilisée dans ce travail est Tencel. Ces fibres sont filées à partir d'une solution de cellulose, et donc leur morphologie, composition et propriétés sont bien contrôlées. Cependant, leur morphologie est très différente non seulement du verre mais aussi du lin. La principale différence avec des fibres de verre est que les fibres Tencel sont très flexibles, ce qui, a priori, ne permet pas d'adopter les approches développées pour des fibres de verre. Considérant tout cela, les points suivants seront précisés :

1) L'effet du procédé sur les fibres naturelles (rupture, dissociation en faisceaux) est crucial pour la compréhension de la microstructure au sein des pièces moulées par injection. Quelle différence d'endommagement entre lin, Tencel et verre va en avoir lieu pendant la mise en oeuvre ? Quelle est l'ampleur de la casse des fibres pendant l'injection ? Quel est l'effet de la concentration sur la rupture des fibres ?

2) Les propriétés rhéologiques des polymères thermoplastiques renforcés de fibres naturelles à l'état fondu sont très importantes pour la simulation du procédé d'injection. Ces propriétés sont assez bien connues pour les composites à fibres de verre. Le comportement rhéologique des composites à fibres naturelles est-il similaire à celui des fibres de verre ? Quelle est l'influence du type de fibre et de leur flexibilité sur les propriétés viscoélastiques du composite à l'état fondu ?

3) Etant donné que la morphologie des fibres naturelles est différente de celle des fibres de verre, l'extrapolation aux fibres naturelles des méthodes utilisées pour caractériser la microstructure des composites à fibres de verre semble être discutable. Si elle s'avère impossible, une nouvelle méthode pour l'analyse de la distribution et de l'orientation des fibres doit être développée. 4) Comme les propriétés mécaniques des composites sont en corrélation directe avec la microstructure, les relations microstructure-propriétés devraient être étudiées pour la compréhension et pour l'amélioration des performances. 5) Dans le but d'optimiser les conditions d'injection pour les composites à fibres naturelles, il est essentiel de vérifier si les modèles d'orientation des fibres et de simulation du procédé existantes pour les thermoplastiques renforcés de fibres de verre sont adaptés aux polymères renforcés de fibres naturelles.

Pour répondre à ces questions, après l'introduction générale (Chapitre 1), la thèse se compose des parties suivantes : Chapitre 2, qui décrit les matériaux et les méthodes utilisés dans cette étude Chapitre 3, où la distribution de taille des fibres est analysée, Chapitre 4, où la microstructure (orientation, concentration, courbures) des fibres est analysée Chapitre 5, où le comportement rhéologique est mesuré Chapitre 6, consacré au comportement mécanique Chapitre 7, sur l'analyse et la simulation du procédé d'injection Dans la suite nous allons présenter l'objectif de chaque chapitre et les principaux résultats trouvés.

Chapitre 2 : Matériaux et méthodes

Ce chapitre décrit les matériaux utilisés dans ce travail ainsi que les méthodes de préparation et de caractérisation de composites. Bien que ce travail concerne principalement les polymères thermoplastiques renforcés de fibres naturelles, l'étude est étendue aux fibres de verre pour comparaison. A titre de référence, le polypropylène pur a été également étudié.

Dans la première partie de ce chapitre, les informations sur tous les matériaux utilisés dans la présente étude ont été détaillées. Ensuite, les deux étapes de mise en forme, l'extrusion bivis et l'injection, ont été présentées. Les techniques expérimentales utilisées pour évaluer la microstructure des composites (microscopie optique et électronique), leurs propriétés rhéologiques (en mode dynamique et capillaire) et leurs performances mécaniques (en tension et choc) ont été également décrites.

Chapitre 3 : Analyse de taille de fibres

Les fibres de lin, Tencel et de verre ont été mélangées avec le polypropylène par extrusion bivis en plusieurs concentrations. Les différents composites ont été injectés dans un moule en forme de boîte. La distribution de tailles des fibres a été analysée après mélange et après injection, par dissolution du polypropylène et analyse par microscopie optique, cartographie et analyse d'images. Les fibres de verre ont été fortement cassées pendant le mélange et relativement peu endommagées lors du moulage par injection. La réduction de longueur est nettement moindre pour les fibres Tencel ® . Les fibres de lin voient leur longueur et leur diamètre réduits au cours des deux étapes, les faisceaux étant dissociés. Le rapport de forme est donc constant. Quel que soit le type de fibres, la casse est plus importante lorsque la concentration augmente.

Chapitre 4 : Orientation et dispersion des fibres dans des pièces injectées

La complexité de la morphologie des fibres de lin et Tencel a nécessité une nouvelle approche de caractérisation permettant la quantification de leur orientation, distribution et courbure.

Des surfaces de coupes parallèles au plan de la boite ont été obtenues par polissage pour plusieurs niveaux dans l'épaisseur. Des images de ces sections ont été ensuite prises par microscopie optique en mode réflexion et analysées par un logiciel de traitement d'image semi automatiquement.

En fonction de leurs formes apparentes, les fibres ont été classées en quatre catégories: droites, en forme de C, en forme de S et particules ou fibres hors-plan. Nous avons démontré qu'à cause de la différence de flexibilité, les fibres Tencel peuvent se courber en deux conformations: en forme de C ou en forme de S, tandis que les fibres de lin élémentaires se courbent seulement en forme de C.

Les fibres sont généralement alignées dans la direction d'écoulement à la surface de boite et perpendiculairement à cette direction dans le plan médian. Le nombre de fibres Tencel est trois fois plus grand que celui de lin pour la même concentration en volume. Cela a été expliqué par la présence de faisceaux dans le lin qui persistent et n'arrivaient pas à se dissocier après l'injection. En outre, comme pour les fibres de verre, la concentration de lin augmente de la surface au plan milieu dans l'épaisseur, alors que la concentration Tencel est pratiquement indépendante de l'épaisseur.

Chapitre 5 : Propriétés rhéologiques des composites

Les propriétés des différents polypropylènes renforcés ont été étudiées en géométrie plan-plan en mode dynamique et en rhéométrie capillaire, pour des concentrations en fibres de 0 à 30 % en poids et des températures comprises entre 180 et 200 °C. Les mesures rhéologiques dynamiques ont montré que l'augmentation de la teneur en fibres et de la flexibilité de fibres (cas de Tencel) conduit à l'augmentation de la viscosité complexe et des modules élastique et visqueux. Une contrainte seuil apparente a été identifiée à basses fréquences lorsque la concentration volumique de fibres atteint le régime concentré. Cela est dû aux interactions entre fibres qui sont encore plus marquées lorsque la flexibilité de la fibre augmente. Pour la même concentration, les composites à fibres Tencel présentent une viscosité et une contrainte seuil apparente modérément plus élevées que celles des composites de verre et largement supérieures à celles du lin. Ceci est dû à la haute flexibilité et au plus grand nombre des fibres Tencel.

L'influence de la température sur la viscosité des composites a été analysée en utilisant la loi d'Arrhenius permettant le calcul de l'énergie d'activation. Pour les trois types de composites, l'énergie d'activation augmente quand la teneur en fibres augmente. L'ajout de fibres au polypropylène semble augmenter la "résistance" du composite à s'écouler. Les composites Tencel présentent une énergie d'activation plus élevée par rapport à celle du lin et du verre.

Nous suggérons que des restrictions supplémentaires aux mouvements de chaînes de polymères peuvent être causées par la structure en réseau de fibres extrêmement flexibles.

La superposition rhéologie capillaire/dynamique obéit à la loi de Cox-Merz. Les courbes maitresses comprenant les mesures en dynamique et capillaire ont été modélisées par l'équation de Carreau-Yasuda à seuil. Le résultat obtenu donne l'évolution de la viscosité pour une large gamme de taux de cisaillement. Ce sera une donnée d'entrée importante pour le calcul numérique de la pression et de l'orientation des fibres (Chapitre 7). L'investigation des propriétés d'impact des composites sur des éprouvettes séparément injectées a montré que les composites à fibres Tencel ont la résistance à l'impact la plus élevée par rapport au polypropylène renforcé par des fibres de verre et de lin. Cela a été interprété par la flexibilité et le nombre important de fibres à fraction volumique identique qui peuvent former un réseau qui résiste à la propagation de fissures. L'analyse de la résistance à l'impact a été réalisée en utilisant le modèle de Thomason et Vlug. Il a été démontré que les prédictions sont en accord avec les résultats expérimentaux à l'exception des composites à faible concentrations.

Chapitre 7 : Simulation de la pression et de l'orientation de fibre : comparaison avec l'expérience

Lors des campagnes d'injection, les pressions sur des capteurs situés dans la cavité ont été mesurées. Le niveau des pressions mesurées pour les différents matériaux (concentration et types de fibres) est bien corrélé aux niveaux de viscosité mesurée au Chapitre 5.

La pression a été calculée pendant la phase de remplissage avec le logiciel Rem3D. L'accord avec l'expérience est correct. Il y a un écart essentiellement au début de l'évolution de la pression qui se réduit lorsque la matière fondue progresse dans la cavité. Ceci est vrai pour le polypropylène pur et pour tous les composites étudiés. Cette constatation pourrait être expliquée par l'imprécision des paramètres thermiques requis pour la mise en place des calculs.

L'orientation des fibres de verre calculée à la fin du remplissage avec Rem3D ® est en accord avec l'expérience, sauf dans les couches à coeur où un écart est observé. Les erreurs peuvent être attribuées aux conditions aux limites thermiques, au modèle d'orientation et aux erreurs expérimentales.

La prédiction de l'orientation des fibres de lin et de Tencel dans les pièces injectées a été aussi réalisée. L'objectif était de savoir si le modèle d'orientation de fibres rigides peut être appliqué aux deux types de fibres naturelles bien que leurs structures soient très différentes de celles des fibres de verre rigides.

L'orientation calculée des fibres de lin correspond approximativement aux résultats expérimentaux. Des paramètres de calcul ajustés pourraient améliorer la précision des calculs.

Cet accord satisfaisant peut s'expliquer par le fait que les fibres sont en partie sous forme de faisceaux rigides.

L'orientation calculée des fibres Tencel est extrêmement loin de ce qui a été obtenu dans l'expérience. Les fibres Tencel sont très flexibles et leur comportement pendant l'écoulement ne peut être estimé via un modèle de fibres rigides. Par conséquent, un modèle de fibre flexible serait nécessaire pour les thermoplastiques renforcés de fibres Tencel pour obtenir des résultats d'orientation adéquats. Cependant, cela ne semble pas si évident vu que le passage du régime dilue au régime concentré des modèles fibres flexibles n'est encore pas maitrisé.

Conclusions et perspectives

Le travail réalisé a fourni une analyse en profondeur de la relation procédé-microstructurepropriétés pour l'injection du polypropylène renforcé de fibres naturelles. Ce type de composites prend progressivement de l'ampleur car il présente des avantages par rapport aux composites à fibres de verre tels que la réduction de poids, le faible coût, l'aspect environnemental toute en gardant des propriétés mécaniques similaires.

Nous avons effectué nos travaux avec deux types de fibres naturelles, Tencel et lin qui ont différentes structures intrinsèques: le lin est un mélange de fibres élémentaires semi-rigides et de faisceaux épais et rigides, alors que les fibres Tencel sont individuelles et très flexibles.

Les fibres de verre rigides ont été également utilisées pour la comparaison. Une variété de techniques expérimentales a été utilisée dont certaines ont été mises au point pour évaluer la microstructure, les propriétés mécaniques et rhéologiques des composites. Une simulation de la phase de remplissage lors de l'injection a été effectuée, ce qui a permis de comparer la pression et l'orientation des fibres calculées avec celles obtenues expérimentalement.

A la lumière de ce travail, plusieurs perspectives peuvent être envisagées. Une première est de développer une méthode automatique d'analyse de taille et d'orientation des fibres, ce qui aidera beaucoup à réduire le volume du travail expérimental. Une deuxième perspective est de tester différentes conditions d'injection, que ce soit au niveau de la forme de la cavité, de l'épaisseur et du type de seuil ou au niveau des conditions machines : débit, pression de maintien, température de moule. Une autre perspective qui parait importante est de tester d'autres fibres analogues au lin comme par exemple les fibres de chanvre ou de sisal, ou des fibres se rapprochant des fibres Tencel comme le coton pour vérifier les résultats obtenus.

Enfin, l'amélioration des modèles d'orientation de fibres en prenant compte des particularités des fibres naturelles est une piste qui mériterait d'être envisagée.

Chapter 1 General Introduction

Global warming and enormous amount of non-biodegradable waste are current problems that have to be solved. This speeds up industries to replace the fossil-based materials by alternative eco-friendly ones, which should provide similar performances together with a minimum of environmental footprint.

Within this context, natural fibres have gained a great attention over the two past decades, aiming to substitute glass fibres as reinforcement for polymer composites. In addition to their renewability, the main reasons that make natural fibres useful when applied in composites are cost and weight saving, keeping similar composite mechanical properties compared to glass fibre filled polymers. The low density of natural fibres particularly attracts the automotive industry and gives solution to the weight reduction issue. Natural fibre composites are used in automotive industry for producing interior parts as trim parts in dashboards, door panels, parcel shelves, backrests and cabin linings. In 2013, 30,000 tons of natural fibres were used in the European automotive production [START_REF] Dammer | Market Developments of and Opportunities for biobased products and chemicals[END_REF]]. For example, Mercedes-Benz used 46 kg of renewable materials including natural fibre composites in 87 components of the S-class cars (2013). For the same reasons as mentioned above, natural fibre composite were welcomed to be applied for interior cladding of railway carriages and aircraft bodies. Some other applications have also emerged for natural fibres composites such sport and leisure (ski, snowboard, bicycle…) thanks to their good damping properties, or musical instrument and loudspeakers because of their excellent acoustic performances, or furniture (desk, chair,…) due to their exceptional optical properties when mixed with translucent matrix. Natural fibres composites as a whole thus account for around 15% of the volume of composites manufactured in Europe [START_REF] Dammer | Market Developments of and Opportunities for biobased products and chemicals[END_REF]].

Natural fibres used in field of polymer composites are either lignocellulose fibres extracted from wood, from the bast of plants (flax, hemp, jute, kenaf), from seeds (cotton), from leafs (sisal) and also man-made spun cellulose fibres such as Tencel from Lyocell process and viscose.

In this work, two types of cellulosic fibres were mixed with polypropylene: flax and Tencel.

The reason was to study and to understand the influence of fibre composition, morphology and properties on composite structure and properties, starting from fibre breakage during compounding and injection moulding, to molten composite morphology, composite microstructure, composite mechanical properties and finally checking if models developed for glass fibres can predict fibre orientation in injection moulded parts with cellulosic fibres. Flax and Tencel are very different. First, they have different composition: the main component of flax is cellulose by 64-81 %, but hemi cellulose (11-17 %), lignin (2-3 %) and pectin (2 %) are also present [Baley (2002); Le Moigne (2014)], while Tencel is based on pure cellulose [START_REF] Fink | Progress in cellulose shaping: 20 years industrial case studies at Fraunhofer IAP[END_REF]]. Second, they have different morphology: Tencel is elementary thin and flexible fibre with uniform diameter (determined by spinning process) while flax is a "mixture" of thin semi-rigid elementary fibres and thick rigid bundles made of elementary fibres assembled together. Finally, their intrinsic mechanical properties are also different. It is thus supposed that these differences in fibres properties would influence composite microstructure and properties.

The use of natural fibres by humans, in particular flax (Linum usitatissimum L.), dates back the ancient Egyptian civilisation. It was imported in Europe by the Middle East Phoenician traders 2,000 years ago. The translation of its scientific name is "linen most useful", signing its importance in the world economy [Tortora and Collier (1997); [START_REF] Borland | From flower to fabric[END_REF]; [START_REF] Akin | Linen most useful: perspectives on structure, chemistry, and enzymes for retting flax[END_REF]]. In France, high-quality flax is today cultivated in the northern regions (Normandie, Picardie and Nord Pas de Calais) due to the moderate climate conditions and the developed know-how. Before being able to reinforce composite, flax fibres undergo a long cycle of extraction that includes retting, breaking, scutching and hackling (see more details in [START_REF] Bos | The potential of flax fibres as reinforcement for composite materials[END_REF] and Müssig (2010)). More than 80 % of flax production is today designated for textile industry that is their classical application, and only 10 % are dedicated for a technical use.

Tencel fibres are made via Lyocell process that was first commercialised in 1992 by Courtaulds. Today, the major producer of these fibres is the Austrian company Lenzing who kindly provided these fibres for the current study. The cellulose for Tencel fibres is extracted from the pulp of hardwood trees, mainly eucalyptus. The cellulose is dissolved in Nmethylmorpholine-N-oxide monohydrate, filtered, spun, coagulated and dried. In addition to their primary use in textile industry, Tencel fibres are commonly applied in ropes, automotive filters, abrasive materials and protecting suiting materials.

Natural fibres composites are generally manufactured under different processes either with thermoplastic or thermoset matrices. Thermoplastics are usually mixed with short natural fibres in twin-screw extruder to produce pellets that are in turn processed by injection moulding. Some other ways for producing composites are also possible such as compression moulding. Injection moulding is the preferred method to manufacture parts with a complex geometry at high production rate and low price. The market for injection moulding is constantly growing with increasing application areas for the natural fibre composites.

The potential of natural fibre composites together with the efficient productivity of injection moulding make clearly a balance between the environmental challenge and the industrial performance. However, because of the complexity and multiple choices of natural fibres some questions still need to be answered. Within this context, the present thesis was launched in Even though the understanding of natural fibre reinforced composites has recently been significantly improved, several issues related to injection moulding process remain unsolved.

The main question here is if the approaches developed for rigid glass fibre based composites can be applied to composites with cellulosic fibres. Glass fibres are rigid with a uniform diameter and defined properties. As mentioned above, technical flax fibres are a mixture of elementary fibres and bundles. During processing, bundles dissociate into thinner ones and/or into elementary fibres. Depending on their diameter and length, flax fibres and bundles can be semi-flexible or rigid. Flax fibres are agriculture based products; their properties depend on the cultivation and the extraction conditions. Flax fibres that are harvested from different varieties exhibit different properties. Their morphology is thus very different from that of glass fibres. The other type of cellulosic fibres used in this work is Tencel. They are spun cellulose fibres and thus of uniform and controlled morphology, composition and properties.

However, their morphology is very different from glass fibres and also from flax. The main difference with glass fibres is that Tencel is very flexible, which may cause problems when using approaches developed for glass fibres. Considering all said above, the following points should be clarified:

1) The effect of processing on natural fibres breakage and dissociation into bundles is crucial in terms of the understanding of composite microstructure within injection moulded parts. Are flax and Tencel breaken to the same extent? Is there a significant breakage during injection moulding? Does the fibre concentration influence the fibre breakage?

2) The rheological properties of molten composites are very important for predicting the outputs of the injection moulding process. They are reasonably well understood for glass fibre based composites. Are they similar or not to natural fibre reinforced composites? What is the influence, if any, of fibre type and flexibility on molten composite viscoelastic properties?

2) Since the morphology of natural fibres is different from glass fibres, the applicability of the methods used to characterize the microstructure of glass reinforced polymer on the microstructure characterisation of natural fibre composites is questionable. If not applicable, a new method for the analysis of fibre dispersion and orientation should be developed.

3) As the composite mechanical properties are directly correlated with the microstructure, the relationships microstructure-properties should be studied for understanding and for improving the performance of natural fibre based composites.

4)

In order to optimise the injection moulding conditions for composites with cellulosic fibres, it is important to check if the existing fibre orientation models based on glass fibre-composite are able to simulate or not the natural fibre composites.

To answer these questions, the thesis is composed of seven chapters:

Chapter 1 is the general introduction (the current chapter), in which the context, the issues and the content of the thesis are presented.

Chapter 2 sums up all details of materials and processing steps used to make the fibre reinforced polypropylene, from compounding to injection moulding. The methods used to characterize the composite microstructure (optical and scanning electron microscopy) and properties (rheology and mechanical performances) are also presented in this chapter.

The five other chapters are divided into two main parts: the first part presents a literature review on the subtopic of the ongoing chapter and the second part shows the results obtained in this work. Below is a brief presentation of each chapter.

Chapter 3 is dedicated to the study of the influence of processing (extrusion and injection) and of fibre concentration on fibre size distributions. Both types of cellulosic fibres, flax and Tencel, and also glass fibres, were investigated. For flax fibres length and diameter were analysed. This was done by dissolving polypropylene matrix and using optical microscopy, cartography and image analysis to obtain length, diameter and aspect ratio distributions for each case.

Chapter 4 studies the microstructure of injection moulded polypropylene reinforced with 20.5 vol % of flax, Tencel and glass fibres. A sample is extracted from the injected box and polished at different depths. The microstructure is analysed using optical microscope in reflection mode. The differences in the microstructural features (orientation and dispersion) between glass and natural fibres are demonstrated, showing the impossibility of using approaches developed for glass fibres to quantify their orientation in composite. To quantitatively describe the microstructure of composites with cellulosic fibres, a new approach is suggested which divides fibres in four classes according to their curvature. The distribution of the fibres along the depth of composite and fibre orientation is quantified, Chapter 5 presents the investigation of the viscoelastic properties of flax, Tencel ® and glass based polypropylene composites, focusing on the effect of fibre type, concentration and flexibility. Correlations between the dynamic and capillary viscosity of composites are also presented and discussed.

Chapter 6 exhibits a correlation between fibre microstructure in the injection moulded parts and the tensile and impact properties of composites based on flax, Tencel and glass. For the study of tensile properties, samples were cut from boxes with different orientations relative to the main flow direction: 0°, 45° and 90°. The experimentally obtained results are compared to models existing in literature.

Chapter 7 starts with the analysis of the experimental results of pressure recorded during the injection moulding of composites. Then pressure is calculated using Rem3D ® simulation software developed for glass fibre based composites and compared with the experimental results. Fibre orientation is also modelled using Rem3D

Chapter 2

Materials & Methods

This chapter describes materials used in the study, methods to prepare composites and methods to characterize them.

Although this work primarily concerns natural fibre reinforced polypropylene, glass fibre reinforced polypropylene with the same fibre volume fractions were prepared and used for comparison. As a reference, neat polypropylene was also studied. The information on all the materials used in this study are given in this chapter.

The major part of this chapter provides the details of the processing steps used to make the composites, from extrusion to injection moulding. The detailed conditions for manufacturing injection moulded parts used in this study are given. The techniques used to assess the composite microstructure, rheology and mechanical performances are also described.

Materials

Polypropylene

The polypropylene used is PPH9020 homopolymer from Total Petrochemical. Table 2.1 shows characteristics given by the supplier. Fibres with the average length of 500 µm (as given by the producer) were made from longer fibres by milling. The purpose of compounding is to enable a good dispersion of fibres throughout a polymer melt. The twin screw extruder is usually used for composite compounding. Basically, a twin screw extruder consists of two parallel screws turning within a 8-shaped housing barrel. The most industrially used one has a corotating and intermeshing screws configuration. Screws and barrel may be built up from different segments. Barrel wall is usually smooth, but it can be constructed with longitudinal or helical grooves, for particular applications requiring an intensive shear rate solicitation. The screws are designed as three main zones from the inlet to the die: melting zone, mixing zone and conveying zone ( Four concentrations of fibres were prepared for each type of fibre, flax, Tencel and glass.

Because of the difference in density  between glass and cellulosic fibres, it is the volume fraction that was chosen to be the same (Table 2.2). Clamping unit and mould 2.2.2.

The functions of the clamping unit are to open and to close the moveable platen that holds mould, and to eject components from the mould (Figure 2.8). Melts resin enters into mould from the sprue bushing which is directly connected with injection barrel by the nozzle. The sprue feeds the cavity through channels which are also referred as runners .The melt flows through the runners and arrives in the cavities by the gates. The entire design containing sprue, runners and cavities is machined out on the mould and the amount of melt needed to fill them is called "shot". Ejection is possible by a sprue puller and ejector pins, also known as knock out pins, located throughout the cavity and the runners. A cooling system is passing water through series of channels drilled and connected in the mould to form a continuous pathway. The role of water is to keep the mould at a desired temperature in order to solidify the polymer. The mould description here is primary and simple. More tools can be used for complex moulds with sophisticated design. For example, sliders enabling side-actions can be put on the mould when the part shows undercuts. The injection unit functions are to plasticise material and to inject it into the mould. These functions are handled by a three-section-screw (feed, compression and metering) (Figure 2.9).

Modern standard screws have an overall length of 20-23 D (length as a product of diameter).

The length of the feed section is generally the half-length of the screw, while compression and metering sections accounting together the residual half-length and having approximately the same length. The pitch varies between 0.8-1 D from the feed to the metering zones across the screw flights. Several pressure and temperature sensors were placed in and around the mould. Five pressure transducers are used: three transducers are located in the mould as shown in Figure 2.10, one is before the mould entrance at the nozzle and another one is placed in the hydraulic cylinder behind the screw. A temperature sensor was installed in the mould located at 2 cm from the cavity surface.

Characterisation

Fibre size analysis

Fibre length and diameter after compounding and after injection were determined as following: the composite was diluted with Decalin ® to get a fibre concentration in the mixture (polypropylene, fibres and Decalin ® ) lower than 10 %, which avoids fibre overlapping and facilitates a later fibre size measurement. As shown in Figure 2 The analysis of fibre size was then performed using cartography of ≃ 5 x5 mm² built-up from 50 elementary transmission images (830 µm x 640 µm) per composite formulation. The measurement of fibre size was done semi-automatically by Archimed (Microvision ® ), the image processing software dedicated to measurement. After selecting the fibre pattern "by hand", a numerical calliper integrated in the image acquisition software allowed the measurement of each fibre length and diameter (Figure 2.13). The statistical analysis was based on 200 fibres per sample. Each formulation was analysed at least three times, giving the difference in the size within an uncertainty interval of 10 %. The minimal size that was taken into account was 10 µm.

The non-processed (initial) fibre size was analysed in the same way by dispersing fibres on a glass slide and using the cartography approach. The preparation of the sample surface requires a great care to have a good image quality suitable for characterizing the fibre microstructure. The sample is firstly polished by abrasives, starting with coarse ones and finishing with fine ones, and secondly polished by diamond paste. At least a difference in depth of 100 µm was needed between two successive layers to avoid scratches and to get a polished surface plausible for analysing. The sample was analysed with optical microscopy in reflection mode, and 5 mm x 5 mm cartographies were recorded by assembling "elementary" images (Figure .2.14.c, see details in the section 3.1 Fibre size analysis). The obtained image was semi-automatically analysed by Archimed (Microvision ® ) software. Fully automatic measurements were not possible because of the variation of contrast within the fibres themselves and the irregularity of fibres shape. This aspect will be further discussed in Chapter 4. Viscoelastic properties of molten composites were studied using oscillatory parallel plates rheometer that imposes on the sample a shear sinusoidal deformation with frequency ω and follows the resultant stress response. The typical experiment consists of placing a sample between two plates as shown in Figure 2.15.a. While the bottom plate remains fixed, a motor rotates the top one, inducing a time dependent strain given by:

𝛾(𝑡) = 𝛾 0 sin(𝜔𝑡) [Eq.2.1]
Concurrently, the time dependent shear stress 𝜎(𝑡) = 𝜎 0 𝑠𝑖𝑛(𝜔𝑡 + 𝛿) is deduced by measuring the torque that sample imposes on the bottom plate. For an elastic material, the stress is exactly in phase with the sinusoidal strain. For a purely viscous material, the applied strain and the measured stress are out of phase, with a phase angle 𝛿 = 𝜋/2. Viscoelastic materials are in between with 0 < 𝛿 < 𝜋/2 (Figure 2.15.b). Storage modulus 𝐺′(𝜔) and loss modulus 𝐺′′(𝜔) are the solid-like and liquid-like contributions to the measured stress response, respectively. Therefore, the stress of a viscoelastic material is given by In this study, the dynamic rheological measurements (small amplitude oscillatory shear) were performed on Anton Paar MCR302 rheometer, using parallel plate geometry with plates of 25 mm as diameter and 1 mm as gap. Samples were made with Minijet Themofisher ® that is a lab scale injection moulding machine. The injection temperature, mould temperature, injection and holding pressures were respectively 190 °C, 50 °C, 500 bar and 100 bar.

𝜎(𝑡) = 𝐺 ′ (
Frequency sweep tests were performed from 100 to 0.1 rad/s at 180 °C, 190 °C and 200 °C.

The strain was fixed at 1 % for the entire series of frequency sweep tests, ensuring that all composites are in a linear visco-elastic regime. The thermal stability of composites was also checked: no viscosity variation was recorded during 30 minutes within the experimental errors, which is much longer than the duration of frequency sweep experiment.

Capillary rheology

3.3.2.
Capillary rheometer is designed to characterize polymer melts at high shear rates typically from 10 s -1 to 10 000 s -1 . Such shear rate can be reached in injection moulding process. The measurement principle consists of injecting a molten polymer into a capillary of a circular cross section and measuring the pressure drop for a given flow rate.

Pressure transducer a b

The capillary rheology measurements were performed with RheoArt rheometer at 190 °C using different extrusion speeds and die lengths (0, 4, 8 and 16 mm), constant die diameter (2 mm) and apparent shear rates ranging from 100 to 1 000 s -1 . The RheoArt is a capillary rheometer with a pre-shearing Couette chamber ( Figure 2.18 shows the average of pressure plateaus as function of the L/D of die for the different apparent wall shear rate values. The obtained plots are linear and their slopes increase when the shear rate increases, as expected. These are the Bagley plots that enable determining entrance and exit pressure losses. After these corrections, we can plot wall shear stress vs apparent shear rate, as shown in Figure 2.19 (20.5 vol % Tencel/PP was taken as an example). For all materials studied, these flow curves appear as a straight line, meaning that they follow a power law all over the shear rate range of the measurements, and then the power law index value can be determined. Tensile test set-up commonly involves fixing the sample by grips in the testing machine and extending it until failure. The elongation of the gauge section is recorded versus the applied force using a mechanical sensor. The elongational strain  is calculated using the following equation:

𝜀 = 𝐿-𝐿 0 𝐿 0 [Eq.2.5]
where 𝐿 -𝐿 0 = Δ 𝐿 is the change in gauge length, 𝐿 0 is the initial and L the final lengths, respectively. The force measurement is used to calculate the stress, σ, given by equation

𝜎 = 𝐹 𝑆 [Eq.2.6]
where 𝐹 is the tensile force and 𝑆 is the initial cross-section of the sample.

The apparent stress-strain curve can be plotted. Tensile properties can be deduced from that plot, such as Young's modulus, ultimate tensile strength and elongation at failure. Charpy impact test enables the determination of energy needed to fracture a material. The samples were moulded and designed following the ISO 179-1/1eA standard, using a mould with four cavities as drawn in Figure 2.22. The composite in granules was inserted in the same machine used to make the "boxes", DK codim NGH 110/200. Impact tests were performed on Instron Ceast 9050 under the following conditions: 1 J hammer, speed of 2.9 m.s -1 , temperature of 25 °C, with "A" notch type and a support of 60 mm.

Sample after notching

Observation of composites morphology by Scanning Electron Microscopy (SEM)

The SEM enables images by scanning sample surfaces with a focused beam of electrons. The interactions between the sample and the electron beam provide electron loss energy shaped as a teardrop and called the interaction volume (Figure 2.23). We can distinguish two types of interactions: 1) elastic interactions with energy close to the incident one. The reflected electrons are called the backscattered electrons and give information about the material composition because they reach a deep level in the sample 2) inelastic interactions with lower energy than the elastic one and their corresponding electrons are called secondary electrons.

They provide information about the topography. 3) microstructure in the moulded part. The idea is to closely observe fibres, aiming to get the information complementary to the optical microscopy observations described in Section 4.2.

Chapter 3

Fibre size analysis during processing

The mechanical properties of composites generally depend on fibres size (aspect ratio), fibre dispersion in the matrix and fibre-matrix adhesion. As glass fibres, natural fibres are broken when mixed with polymer and when injected into a mould. Studying and understanding the evolution of fibre size during processing is thus extremely important.

The first part of this chapter is dedicated to the state of the art on the fibre size evolution during processing for glass fibre-and natural fibre-reinforced thermoplastics. The second part focuses on the results of the statistical analysis of fibre size performed on all studied composites, at each processing step, from the initial fibres to their size after extrusion and finally after injection. The aim is to show the influence of each process step and also of the fibre concentration on the fibre size. A comparison between glass and natural fibre cases is discussed.

The state of the art

The technique usually used to investigate the fibre size consists of separating fibres from the polymer matrix either by burning matrix when it is possible (in the case of glass fibre, for example) or by dissolving it with an appropriate solvent. Recently, [Shen et al. (2004) [START_REF] Fu | Effects of fiber length and orientation distributions on the mechanical properties of short-fiber-reinforced polymers[END_REF] reviewed the main aspects of design and process for glass fibre reinforced thermoplastics, influencing fibre rupture during compounding and injection moulding (Table 3.1). For compounding, in addition to the aspects mentionned earlier (lower screw speed and higher feed rate), a higher barrel temperature can reduce the glass fibre breakage, due to the lower resultant viscosity and stress. For injection moulding, a higher back pressure has more dramatic effect on the fibre breakage than a higher injection moulding speed. The back pressure value is directly related to the extent of the shot plasticizing in the barrel-screw system (similar to extrusion system), before being injected into the cavity. Increasing fibre content leads also to more fibre breakage, which was explained by more intense fibre-fibre and fibre-wall interactions. In addition, [START_REF] Turkovich | Fiber fracture in reinforced thermoplastic processing[END_REF] demonstrated that longer intial fibre leads to longer fibre length in the final part for the injection moulding of glass fibre reinforced polyamide 6-6 composite. However, [START_REF] Akay | Fibre orientation and mechanical behaviour in reinforced thermoplastic injection mouldings[END_REF] showed that only a slight effect of the intial fibre length can be observed in the residual fibre length after processing for the case of glass fibre reinforced polypropylene. Reprocessing composites causes a further rupture of fibres. (2011) showed that when fibre is initially structured in bundles, it tends to be divided into elementary fibres, thus diameter decreases, while when fibre is already elementary before processing, diameter remains constant and length decreases (Figure 3.4). The mechanism of rupture of glass fibres is different and simpler than that of natural fibres. Glass fibres have a constant diameter and their rupture occurs when the surrounding stress overcomes a critical value [Tukovich and Erwin (1983)]. Beaugrand and Berzin (2012) showed that the presence of moisture in hemp fibres when added to polycaprolactone (PCL) can lead to higher bundles dissociation, which seems contrarily to what is normally expected. This was explained by the role of water for reducing the softening of fibres and for resisting against the defects induced by processing, which causes weakness points initiating fibre fracture. The authors showed also that an increase in temperature can reduce the obtained aspect ratio after extrusion, which is in disagreement with what is known for glass fibres literature [START_REF] Fu | Effects of fiber length and orientation distributions on the mechanical properties of short-fiber-reinforced polymers[END_REF]]. Beaugrand and Berzin (2012) argued this by the possible degradation of some fibre components such as lignin up to 160 °C.

These results were obtained with a particular biodegradable matrix (PCL) with low melting temperature (60 °C) and must be checked with other current thermoplastic matrices such as polypropylene or polyethylene. Berzin and Beaugrand (2012) and [START_REF] Berzin | Evolution of lignocellulosic fibre lengths along the screw profile during twin screw compounding with polycaprolactone[END_REF] showed that lower screw speed and higher flow rate during extrusion lead to lower hemp fibre breakage during compounding, which is in agreement with the glass fibre case [Yilmazer and Cansever (2002); [START_REF] Inceoglu | Correlation between processing conditions and fiber breakage during compounding of glass fiber-reinforced polyamide[END_REF][START_REF] Fu | Effects of fiber length and orientation distributions on the mechanical properties of short-fiber-reinforced polymers[END_REF]]. It was shown by [START_REF] Berzin | Evolution of lignocellulosic fibre lengths along the screw profile during twin screw compounding with polycaprolactone[END_REF] for hemp fibre reinforced polycaprolactone and LeDuc (2013) for flax fibre reinforced polypropylene that upon a critical value of Specific Mechanical Energy (SME), the fibre breakage is excessive; this is also in agreement with the results of [START_REF] Inceoglu | Correlation between processing conditions and fiber breakage during compounding of glass fiber-reinforced polyamide[END_REF] in case of glass fibre reinforced polyamide. SME is a significant parameter that can assess the fibre breakage due to the cumulative strain involved during compounding. [START_REF] Keller | Compounding and mechanical properties of biodegradable hemp fibre composites[END_REF] However, no variation of fibre diameter even after injection has been shown, which seems somewhat ambiguous. [START_REF] Berzin | Evolution of lignocellulosic fibre lengths along the screw profile during twin screw compounding with polycaprolactone[END_REF] demonstrated that the breakage of natural fibres can be partially limited by optimizing the screw profile during compounding.

Contrarily to glass fibre case, when the screw configuration was the same, [START_REF] Keller | Compounding and mechanical properties of biodegradable hemp fibre composites[END_REF] found that the length distribution of the resultant hemp fibre (type DDA) in the granules was independent on the fibre content (Figure 3.5). Using the X-ray tomography technique, Alemdar et al. (2008) investigated the fibre length and diameter of wood-reinforced polypropylene before and after processing (including compounding and injection moulding). Before processing, the length range of almost 80 % of wood fibres is between 316 µm and 600 µm. It decreases after processing, giving a length average of 238 µm and 285 µm for wood/PP with and without coupling agent, respectively.

The diameter of wood fibres was reduced by 61 % and 69 % for wood/PP with and without coupling agent, respectively [Alemdar et al. (2008)]. For the same system (wood/PP), by using SEM cross-section analysis, Soccalingame et al. (2015) showed that thick fibres/particles are more sensitive to breakdown and processing has no effect under a critical diameter. Moreover, the authors concluded that adding coupling agent does not show any influence on the fibre breaking during processing.

Conclusion

The mechanism of breakage of glass fibres in a thermoplastic matrix during twin screw compounding and injection moulding processes is rather well understood. The key parameters influencing the breakage of a glass fibre during compounding and injection moulding were investigated in details. The comparison between glass fibre and natural fibre breakage cases enables to conclude, on the one hand, some similarities under particular process conditions, such as the decrease of fibre breakage with increasing the feed rate and decreasing the screw speed at compounding step, and on the other hand, some differences such as the evolution of fibre length with increasing fibre content and the additional breakage of fibre after injection.

The main reason behind these dissimilarities is probably the difference of morphology between natural fibres and glass fibres. An adequate comparison between glass fibre and natural fibre breakage during process would have more credibility and precision under the same process conditions.

Results and discussions

The aim of this section is to show a comparative study among flax-, Tencel-and glass-fibre size distributions, after compounding and after injection moulding, in a polypropylene matrix.

All composites were processed under the same conditions and with the same polypropylene matrix, as described in Chapter 2. A statistical analysis of fibre size (length L, diameter D and aspect ratio L/D) is performed for different fibre types (Tencel, flax and glass), after compounding and injection, and for different fibre concentrations (from 3.6 vol % to 20.5 vol %). We will firstly present separately the case of each type of fibre, and then examine the effect of the fibre type on the fibre size.

Glass fibres

Effect of processing 2.1.1. Figure 3.9 shows a comparison between the length distribution of glass fibres as delivered, after compounding and after injection for the example of 20.5 vol %. The initial length distribution is bimodal with a minor peak around 1 500 µm and a sharper one around 3 000 µm. After compounding the length distribution becomes unimodal with a peak around 400 µm, indicating a strong fibre breakage. This peak is then marginally shifted to shorter lengths after injection moulding. The evolution of glass fibre length distribution during compounding and injection for 20.5 vol % glass/PP composite Table 3.2 shows that fibres are shortened by 80 % during compounding. Injection moulding causes a further fibre breakage by 20 %. In addition, after injection, L n is slightly shortened while L max is nearly two times reduced, which means that long fibres keep breaking during injection. This seems similar to the results of Yilmazer and Cansever (2002). Influence of fibre concentration 2.1.2. The length distibution in 3.1 vol % glass/PP is a large distribution, extending over a wide length range from 20 µm to 2 000 µm. The length distribution of composite with 20.5 vol % presents a sharper peak around 200 µm, and the range of sizes is reduced to 20-700 µm. We can conclude that glass fibre length decreases with the increase of fibre content, which seems in agreement with [START_REF] Fu | Effects of fiber length and orientation distributions on the mechanical properties of short-fiber-reinforced polymers[END_REF] results.

Tencel

Influence of processing 2.2.1. 3.3 shows that injection moulding did not cause an additional length reduction for Tencel fibres. The difference in length between after compounding and after injection moulding lies in the error experimental range 10 % (as mentionned in Chapter 3, Section 3.1 Fibre size anlysis). Influence of concentration 2.2.2. Table 3.3 shows that fibre length practically does not change with the increase of fibre concentration from 3.6 to 13.1 vol % after compounding. However, a considerable fibre breakage can be observed at 20.5 vol %. Figure 3.12 presents the influence of fibre content on the fibre length distribution after injection for Tencel/PP composites. The distribution peak is progressively moved to shorter length values and the distribution gets sharper with the increase of the fibre concentration. This results in L n reduction from 255 µm for 6.5 vol % concentration to 202 µm for 20.5 vol % concentration, as shown in Table 3.3. Fibre concentration has a stronger influence on fibre size than processing. As man-made fibres, the aspect ratio of Tencel is the length over a constant diameter, meaning that the aspect ratio has the same variation of the length. This is also the case of glass fibre but not that of flax fibres that will be shown in the next section.

Flax

The analysis of flax fibres size consists of studying the evolution of two variables: length and diameter. Table 3.4 regroups all these measurements.

(L/D) min 2 2 1 2 2 2 2 4 3
Influence of processing 2.3.1. Figure 3.13 a, b and c shows the length, diameter and aspect ratio distributions of flax fibres, respectively, for three states of fibres: as delivered, after compounding and after injection moulding, and this for the concentration of 20.5 vol %. The initial fibres reveal a unimodal length distribution with a sharp peak around 400 µm and an overall range between 200 µm and 1 000 µm. The distributions of fibre length after compounding and after injection are similar, exhibiting a wide peak also around 400 µm and a range of length between 50 µm and 800 µm (Figure 3.13. a). This means that fibres were broken during processing and thus L n decreases from 450 µm, as delivered, to 422 µm after compounding and 388 µm after injection moulding. 48 µm and 84 µm as delivered to 39 µm and 54 µm after compounding, and to 28 µm and 34 µm after injection, respectively. This means that not only the length is reduced during processing but also the diameter, due to the bundles' dissociation.

The distribution of the aspect ratio is similar for all steps of processing (Figure 3.13.c).

Because the extent of length decrease is nearly equal to the extent of diameter decrease (Table 3.4), (L/D) n is almost unchanged during processing. However, the initial fibres are thick and long while the final fibres are thin and short (Figure 3.14). hence L n and L w slightly decrease from 428 µm and 464 µm to 388 µm and 433 µm, respectively. However, there is almost no difference in length between 3.1 vol %, and 13.1 vol %, according to Table 3.4, which means that the major fibre breakage happens when the concentration reaches 20.5 vol %. A similar statement for diameter distribution can be concluded (Figure 3.15.b). This leads to a decrease of D n and D w from 34 µm and 46 µm to 28 and 34 µm, respectively, when increasing concentration from 3.1 vol % to 20.5 vol %.

However, the diameter remains constant between 3.6 vol % and 13.1 vol % as shown in Table 3.4. Figure 3.15.c provides the distribution of the aspect ratio that remains moderately unchanged with the increase of fibre concentration. (L/D) n and (L/D) w remain constant around 15 and 18-19, respectively, as given in Table 3.4. Frequency, % Length, µm Compounding reduces the diameter with lower extent for 13.1 and 20.5 vol % when compared to 3.6 and 6.3 vol %. However, after injection moulding, D n progressively decreases from 48 µm as delivered until 28 µm at 20.5 vol %, which corresponds on average to a bundle of two elementary fibres. This is the result of the simultaneous dissociation of bundles and the diminution of length as explained in Figure 3.17. In conclusion, the final aspect ratio after injection moulding can be organized in descendant order 1) glass 2) Tencel 3) flax. The mechanical properties of the final moulded parts depend not only on fibre length or aspect ratio but also on other microstructure features such as orientation and dispersion. This will be detailed in the next chapter.

Yilmazer, U., & Canserver, M. (2002). Effects of processing conditions on the fiber length distribution and mechanical lproperties of glass fiber reinforced nylon-6. Polymer composites, 23(1), 61.

Chapter 4

Fibre orientation and dispersion in injectionmoulded parts

Rupture of fibre during processing severely limits the mechanical properties of the injection moulded component. An unfavourable orientation and dispersion during the flow in the mould cavity can have a similar effect on composite mechanical properties. The set of fibre size, orientation and dispersion is commonly called microstructure in the field of fibre-reinforced thermoplastics. We analysed in Chapter 3 the fibre size that is one of the important microstructural features. In injection moulding process, the fibre orientation and dispersion are induced by the flow. While very little is known about the microstructure of natural fibre reinforced thermoplastic, the case of glass fibre is more mature and well-studied.

In this chapter, we begin by the state of the art in order to understand the difference between glass and natural fibres related to the flow induced orientation and dispersion. We suggest a method of characterization of natural fibres orientation, enabling to take into account some of their inherent features. A major part of the results and discussions section is concerned with the microstructure of natural fibre reinforced polypropylene; the case of glass fibre microstructure is also investigated for comparison. In order to evaluate the extent of the density variation, the experimental measurements are compared with the reference density. The latter is calculated by the mixing rule equation defined as:

State of the art

𝜌 𝑐 = 𝜌 𝑓 𝑓 + 𝜌 𝑚 (1 -𝑓) [Eq.4.1]
were 𝜌 𝑐 , 𝜌 𝑓 and 𝜌 𝑚 are the densities of composite, fibres and matrix, respectively. 𝑓 is the volume fraction of fibre.

The matrix is usually assumed to keep the same density throughout the thickness. This leads to a small error because it is expected that matrix increases in crystallinity and thus in density nearby the mid-plane of the studied part. Nevertheless, when the fibres are much denser than matrix this error can be neglected [Sphar et al. (1990)].

Orientation 1.1.2.

Glass fibres

The technique classically used to analyse the orientation of glass fibre reinforced polymers (Figure 4.1) consists of observing a cross-section in the part thickness either with optical microscope in reflected light mode or with Scanning Electron Microscope (SEM). An example of a cross-section is given in Assuming that all fibres have the same diameter, cylindrical glass fibres meet the polished surface either as circles (with diameter equal to the fibre diameter) or as ellipses (with minor axis equivalent to the fibre diameter) (Figure 4.3.b). When a fibre is perfectly perpendicular to the cross-section, the apparent shape result is circular. When a fibre makes an angle with respect to a cross-section, the minor and the major axis of ellipses determine the orientation angle  of a fibre with respect to the cross section, and the orientation of the ellipse gives the angle  (Equation. 4.2) [START_REF] Vincent | Description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics[END_REF]]. Therefore, the full 3D orientation can be determined (except indeterminacy between  and .

𝜃 = 𝑐𝑜𝑠 -1 ( 𝑄 𝐽 ) [Eq. 4.2]
where "𝐽" is the major axis and "𝑄" is the minor of the ellipse (Figure 4.3b) Advani and Tucker (1987) defined an orientation tensor, assuming that fibres are rigid cylinders, their section is circular and their concentration is spatially uniform, given by:

𝑎 𝑖𝑗 = ∫ 𝑝 𝑖 𝑝 𝑗 𝜓(𝒑)𝑑𝒑 𝑝 [Eq. 4.3]
where 𝒑 is the unit vector associated to fibre whose component 𝑝 𝑖 are function of the angles 𝜃 and 𝜙 (Figure 4. The long fibres and the fibres oriented perpendicular to the main flow direction have a higher probability to appear in the cutting section. Furthermore, fibre oriented with (𝜃, 𝜙) and

(𝜋 -𝜃, 𝜙 + 𝜋) are undistinguishable. This must be counterbalanced by the function 𝐹(𝜃) as defined by Bay and Tucker (1992) and reported later by [START_REF] Vincent | Description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics[END_REF]:

𝐹(𝜃) 𝐹(90) = 1 𝐿 𝐷 𝑐𝑜𝑠𝜃+𝑠𝑖𝑛𝜃 [Eq. 4.4]
where 𝐹(90) is the weighting function for 𝜃 = 90°, L is the fibre length and D is the fibre diameter. The average of 𝑎 𝑖𝑗 of n fibres of orientation 𝑝 𝑖 𝑘 becomes:

𝑎 𝑖𝑗 = 1 𝑛 ∑ 𝑝 𝑖 𝑘 𝑝 𝑗 𝑘 𝐹(𝜃 𝑘 ) 𝑛 𝑘=1 ∑ 𝐹(𝜃 𝑘 ) 𝑛 𝑘=1
[Eq. 4.5] X-ray computed microtomography (µCT) is another technique that has been used to characterize the orientation of glass fibre reinforced polymer in injection moulded parts [Shen et al. (2004) The surfaces in xy planes shown in Figures 4.8,[START_REF] Fink | Progress in cellulose shaping: 20 years industrial case studies at Fraunhofer IAP[END_REF].9 and 4.10 seem suitable to quantify the orientation of natural fibres in injection-moulded parts, whatever the microscopy technique used for observations. However, the quantification of fibre orientation in xy-plane requires more experimental work because sections at different levels in thickness are needed to obtain the orientation state across thickness. By using ellipses method, only one cross section perpendicular to xy-plane is performed to characterize the orientation state of glass fibres.

Other studies have focused on the X-ray µCT as an experimental technique to assess the orientation of natural fibre-reinforced thermoplastic. However, this technique has its limitations because if high resolution is needed only small field of view is possible. Because the conservation of small details is important for the understanding of the microstructure of natural fibres (irregular shape, fibre curvature), a high resolution is required to detect the exact fibre cross section. Therefore, observations are limited to samples not large enough to establish analyses of fibre orientation in the scale of injected-moulded parts. Furthermore, the density of natural fibres (𝜌 ≈ 1.5 g/cm 3 ) is close to the one of thermoplastic matrix (𝜌 ≈ 0.9-1.2 g/cm 3 ), which makes the X-ray attenuation coefficient low and materials

Fibre orientation results

Glass fibres

1.2.1.
An example of the evolution of 𝑎 𝑥𝑥 as a function of thickness from the surface of injectionmoulded part for glass fibre reinforced PAA (polyacrylamide)) is presented in Figure 4.12. A symmetric orientation with respect to the mid-plane is typically obtained with 𝑎 𝑥𝑥 close to zero at the core (0.2 here) and 𝑎 𝑥𝑥 close to one at surface (0.8 here), concluding that orientation of fibre changes across the thickness from surface to the mid-plane. Bay and Tucker (1992) predicted by computation and observed experimentally five main layers: two skin layers (which are the thinnest and the least oriented ones), two shell layers and one core layer. Intermediate layer can exist between shell and core layers, but it is usually ignored and added to core layer as one continuous layer.

The typical fibre orientation in an edge-gated part is shown in Figure 4.13. In the shell layers fibres are oriented in the flow direction and in the core layer perpendicular to the flow direction. The shell layer is located in a zone were shear is dominant (Figure 4.13). The skin layer resulting from the fountain flow exhibits a random orientation and its thickness depends on the cooling and the filling times. Greatz number (𝐺𝑧) gives the range of the skin layer thickness:

𝐺𝑧 = 4𝑒 2 𝛼.𝑡 𝑓𝑖𝑙𝑙 [Eq.4.6]
where 2𝑒, 𝛼 and 𝑡 𝑓𝑖𝑙𝑙 are the cavity thickness, the thermal diffusivity of the melt and the mould filling time, respectively. The thickness of the skin layer increases with 𝐺𝑧 increasing, however Bay and Tucker (1992) proposed that no skin can appear if 𝐺𝑧 > 100. The entrance of the cavity that is the junction between feeding channel or sprue and the cavity itself is usually a divergent because the section of the channel is much smaller than the section of the cavity. Therefore, the flow is highly extensional at the centre, thus fibres get oriented perpendicular to the flow direction. Near the surface, a shear flow is predominant, and fibres are mostly oriented along the flow direction. 𝑎 𝑥𝑥 ≥ 0.5 when fibres are in the shell layer resulting in 𝑓 𝑝 ≥ 0 and 𝑎 𝑥𝑥 ≤ 0.5 when fibres are in the core layer resulting in 𝑓 𝑝 ≤ 0. Moreover, when fibres are strongly aligned along the flow direction (x) or along the direction perpendicular to the flow (y), 𝑓 𝑝 is close to 1 or -1, respectively. Figure 4.17 shows 𝑓 𝑝 vs the overall volume fraction for short and long fibres.

Fibres in both shell and core layers become more aligned when the fibre volume fraction increases. Short fibres are more oriented than the long ones. Based on SEM images in xz and yz cross sections, the orientation of long fibres was measured by two methods: i) personal evaluation or "by hand" (unfilled symbol) and ii) image analysis. However, short fibre orientation was only measured by "hand". Whereas the microstructure of glass fibre-reinforced thermoplastic reached a good understanding, the literature of natural fibre case is not yet mature and a lack of information still exists. The dispersion of natural fibres in injection-moulded parts was not previously studied and most of the studies dealing with fibre orientation have been limited to some qualitative observations. All the xy-plane observations shown in Chapter 4, section 1.1.2.2 Natural fibres, indicate a considerable change of orientation of fibres nearby surface compared to the core, which seems similar to the core-shell structure seen earlier for glass fibres. The main study, in which a significant quantification of flow-induced orientation was performed, is the one of Aurich and Mennig (2001). They quantified the orientation of 30 wt % flax fibre-reinforced polypropylene by optical microscopy in transmission. They observed and quantified the orientation in xy-plane for 11 cross sections with different levels across thickness and for four locations in a film-gated plaque, as shown in Figure 4.18. In each cross section, 600 fibres were characterized. Unfortunately, the method of the fibre orientation measurement was not detailed enough. Furthermore, only the average of fibre aspect ratio was provided (L/D= 13), whereas flax fibres contain bundles and their length and diameter are critical parameters to consider when analysing a composite microstructure. [Eq. 4.7] This leads to three main components of orientation

𝑎 𝑥𝑥 =< 𝑠𝑖𝑛 2 𝜃 𝑐𝑜𝑠 2 𝜙 > [Eq. 4.8] 𝑎 𝑥𝑦 =< 𝑠𝑖𝑛 2 𝜃 𝑐𝑜𝑠𝜙 𝑠𝑖𝑛𝜙 > [Eq. 4.9] 𝑎 𝑦𝑦 =< 𝑠𝑖𝑛 2 𝜃 𝑠𝑖𝑛 2 𝜙 > [Eq.4.10]
Considering that the orientation is planar, some simplifications take place as 𝜃 = 90° (Figure 4.3), so 𝑠𝑖𝑛𝜃 = 1:

𝑎 𝑥𝑥 =< 𝑐𝑜𝑠 2 𝜙 > [Eq. 4.11] 𝑎 𝑥𝑦 =< 𝑐𝑜𝑠𝜙 𝑠𝑖𝑛𝜙 > [Eq. 4.12] 𝑎 𝑦𝑦 =< 𝑠𝑖𝑛 2 𝜙 > [Eq. 4.13]
Figure 4.20.a shows that at the location A, 𝑎 𝑥𝑥 increases from 0.6 at z = 0.02 mm to 0.9 at z = 0.2 mm, indicating a strong alignment along x-direction. It then decreases until 0.2 at z = 0.9 mm and remains almost constant at the mid-plane z = 1mm, which is again a sign of strong fibres alignment but along y-direction. A similar trend was noticed for B and C locations.

However, for location D closer to the plate edge (Figure 4.20.b), at z = 0.2 mm the orientation is quite similar to that of location A, but at the mid-plane instead of decreasing till 0.2, 𝑎 𝑥𝑥 decreases only until 0.7, signifying that fibres in the core are more aligned to x-direction than to y-direction. Moreover, 𝑎 𝑥𝑦 of location D is not close to zero compared to location A, meaning that the direction of the principal orientation at location D is different to x-direction or y-axis [Tucker (1988)]. According to authors, an "uneven flow velocity" close to the edge is behind this orientation. Compared to the edge effect shown in Table 4.1, this seems in disagreement with glass fibre reinforced polypropylene studies [START_REF] Kenig | Fiber orientation development in molding of polymer composites[END_REF], [START_REF] Akay | Fibre orientation and mechanical behaviour in reinforced thermoplastic injection mouldings[END_REF]] in which, even closer to the part edges, a perpendicular core was kept with thinner thickness than at a middle part location.

Conclusions

The fibre orientation and dispersion are important factors to control the final properties of injection-moulded parts. A good understanding of these parameters has been built up for glass fibre reinforced composites. A typical orientation of core-shell structure was observed, characterized and modelled. The dispersion of fibre across thickness was correlated to fibre orientation, length and concentration. Furthermore, most factors that can influence the orientation and the dispersion of glass fibre in a thermoplastic polymer have been studied in details such as the injection conditions, the mould geometry and the rheology of melt.

Two possible techniques of fibre orientation characterization that are the microscopy (either optical or scanning electron) analysis of cross section perpendicular to xy-plane (xz or yz) and X-ray micro-tomography, were presented. Each one has its limitations when it is related to natural fibres, whereas it is going thoroughly with glass fibres. Until now, most studies on Surface Core 𝑎 𝑥𝑥 natural fibres have been limited to qualitative observations. Only few studies have been dealing with the orientation quantification of natural fibres in cross sections parallel to the part plane (xy). A core-shell structure similar to glass fibre composites has been observed for the natural fibres case. However, these studies did not take into account their specific features (flexibility, bundles structure). Moreover, the dispersion of natural fibres in injection-moulded parts is not yet investigated and correlated to fibre orientation. In the following section, we suggest a new method of microstructure characterization based on the cross section analysis, dealing with the specific features of natural fibres. This method enables to investigate the fibre dispersion, orientation and bending. We suggest then to investigate the microstructure of fibres in xy-plane, as it was done in the study of Aurich and Mennig (2001) presented in the state of art section. The reflected light technique is simpler than the transmitted one because only the surface matters, so the sample thickness is not critical. In addition, reflected light technique enables a good contrast, so that a quantitative image analysis can be performed. Hence, the optical microscopy in reflection was chosen to analyse fibres orientation. Surfaces in xy-plane at different levels across thickness are then required to quantify orientation, as mentioned in Section 1.1.2. As a representative concentration of fibres, 20.5 vol % was chosen for all composites (flax, Tencel and glass).

Results and discussion

Qualitative observations

It should be noted that three fibre orientations are possible with respect to xy-plane: i) fibres are fully "in-plane", i.e. an orientation angle  with respect to the xy-plane is 90° (see Figure 4.2), ii) fibres form a certain (large) angle with xy-plane, i.e. an orientation angle  with respect to the xy-plane between 0° and 90°, meaning that only an apparent shape of fibres can be seen in xy-plane) and iii) fibres are almost perpendicular to xy-plane (i.e. = 0°). The first two cases cannot not be distinguished when analysing the images taken in xy-plane and thus both will be considered together. We shall say that fibres are out of xy-plane when their width (or diameter) is comparable with their length on the cross section. However, the number of Tencel fibres per cartography is higher as compared to that of flax. To quantify the microstructural features in xy-plane, we suggest to approximate fibre by a rectangle. We measure its width (b), length (a) and orientation angle (ϕ) relative to x-axis (Table 4.2). We suggest four fibre categories depending on their apparent shape (Table 4.2):

straight fibres, C-shaped, S-shaped and "particles" (width is comparable to length). The latter category can be made of two classes of fibres: those which are out-of-plane (orientation angle  close to 0 °) and simply small particles that appear during fibre breakage. We suppose that when a "particle" is an "agglomerate" of smaller ones, as shown in Figure 4.22, it is a bundle of flax that is out-of-plane. However, it is difficult to distinguish between a simple small particle and an elementary fibre that is out-of-plane and gives a similar apparent shape. Here, it is again another example of the difficulty arising during the analysis of natural fibre based composites, as far as flax fibres can make a "dust" due to breakage into small pieces and fibrillation [Le Moigne et al. (2014)]. Category 4 was characterised by the equivalent diameter D a approximated by Huebscher formula [START_REF] Huebscher | Friction equivalents for round, square and rectangular ducts[END_REF]]. The bending angle β

X= Main flow direction

Y and the extended-fibre length average 𝐿 𝑐𝑛 and 𝐿 𝑠𝑛 were deduced from the rectangle dimensions by approximating fibres as a bent rod (or "C-shaped fibre") for category 2 and "Sshaped" rod for category 3. In the cartographies, the apparent objects that are represented by rectangle dimensions under 10 µm x 10 µm were not taken into account. thickness for different fibre categories, respectively. We consider that glass fibres are fully straight, and even if some particles appear at the cross section, they are usually under our critical size of measurement (10 x 10 µm²). The quantification of the number of fibres per cross section was possible because all cartographies have the same size (5 x 5 mm²). Figure 4.30.a shows that the total number of flax fibres increases twice from z = 100 µm to z = 400 µm, and it remains almost constant up to the core layer (z = 900 µm). The dominant category is the straight fibres; they make around 60 % of the total number of fibres, followed by the particles/out-of-plane category with 30 % and C-shaped category with around 10 %. S-shaped category does not appear in the case of flax fibres, which is probably due to their high stiffness and low aspect ratio. The straight fibres category keeps increasing from surface to core. Taking into account that most of straight fibres are in bundles, two assumptions are possible i) bundles are transferred toward the core, escaping high shear zones and ii) bundles are dissociated into elementary fibres or thinner bundles on high shear zone close to surface and "new" fibres are then transferred to the core. For glass fibres case (only rigid straight fibres) presented in Figure 24.c, their number is three time higher at the core (z = 900 µm) than near the surface (z = 100 µm). This is in agreement with results of [START_REF] Spahr | Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites[END_REF] showing that core layer contains more fibres than shell layer. Moreover, the number of fibres at the core compared to surface is higher for glass than for flax fibres. This can be explained by the higher aspect ratio of glass fibres as demonstrated in Chapter 3 (see the influence of a higher aspect ratio in Table 4.1, section 1.2 [START_REF] Spahr | Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites[END_REF]; [START_REF] Bailey | Fibre orientation mechanisms for injection molding of long fibre composites[END_REF]; [START_REF] Blanc | Injection molding of reinforced thermosets[END_REF]; McLelland and Gibson (1990);Truckenmuller and Fritz (1991)]. Another reason is that when flax fibres are glass fibres, respectively. We selected three representative layers corresponding to three main regions in thickness (shell, transition and core regions). The global pattern of the fibre orientation distribution is almost the same for flax and Tencel.

However, the sharpness of peaks varies with fibres type, indicating the difference in the alignment regarding the main flow direction. This difference is probably due to the difference in aspect ratio, flexibility and interactions between fibres during the flow, which leads in turn to a different melt viscosity between each fibre-type composite. It is known that a variation of aspect ratio results in a different composite rheology [START_REF] Darlington | Some features of the injection molding of short fiber reinforced thermoplastics in center sprue-gated cavities[END_REF]; Bay and Tucker (1993)]. Consequently, depending on the melt viscosity, a flatter or a sharper melt front during flow leads to a change in fibre orientation. For example, a higher fibre concentration leads to more interactions between fibres, and thus to flatter velocity profile during flow, so a different orientation in core and shell layers (see Table 4.1, section "influence of higher fibre concentration" [START_REF] Spahr | Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites[END_REF]; [START_REF] Bouti | Injection molding of glass flake reinforced polypropylene: flake orientation and stiffness[END_REF]]. A similar analogy can be considered when we compare Tencel to flax. The local concentration of fibres is higher for Tencel than for flax, leading to more interactions between Tencel fibres than between flax ones, and thus a different orientation of fibres. Moreover, according to Table 4.1, a higher aspect ratio causes a lower degree of orientation in both core and shell layers (Table 4.1). This matches well with glass fibre as far as they present a higher aspect ratio than For curved fibres, Figure 4.34 shows the case of Tencel C-shaped fibres, the result is similar to that of straight fibres (we remind here that the orientation of curved categories is represented by the orientation of the end-to-end vector).

 Influence of out-of-plane orientation

It is know that glass fibres make a small angle (angle , see Figure 4.2) regarding xy-plane [Phelps and Tucker (2009)]. In our study, this orientation can be observed in Figure 4.26 that exhibits a comparison between optical microscopy images in reflection and in transmission modes. As seen by transmission light observation, some fibres are in xy-plane but some others continue "under" the surface. Therefore, in xy-plane they appear shorter than they really are. It is thus interesting to compare how fibre length and diameter measured from the cross sections ("apparent length" and "apparent diameter", see Table 4.2) correlate with real fibre dimensions measured in Chapter 3. for the analysis of microstructure in the injected box). The "real" length of fibres seems to be twice greater than the apparent one. This seems surprising but it can be justified: according to equation 4.2 (J and Q are the apparent L and D, respectively), we plotted in Figure 4.37 a theoretical correlation between the apparent aspect ratio and the angle regarding xy-plane. Let us consider a rigid fibres with a constant diameter (case of glass), when θ= 0°, Q=J=D and θ= 90° Q=D and J=L, the real dimensions of the fibre, but 0°<θ< 90°, the apparent fibre length is smaller than L, so that the apparent L/D (J/Q) is smaller than the real L/D. For low apparent aspect ratio fibres, a deviation of small angle regarding the xy-plane, leads to a higher decrease in aspect ratio than what is expected. For example, to reduce the aspect ratio from fifteen in the real dimension to five as appearing in the cross section, the fibre must make an angle of 4~5° to the cross-section. This angle deviation is quite small but its influence on the apparent length in the cross section is great, and this is in agreement with literature in glass fibres [Phelps and Tucker (2009)]. 4.2) is ranging between 20° and 30°, remaining almost constant between 100 µm and 900 µm of depth. For C-shaped category, the "Extended fibre length average" L cn (see Table 4.2) of flax fibres are apparently longer than Tencel ones (Figure 4.39). As seen before, this can be explained by the fact that flax fibres are stiffer than Tencel ones (E flax > E Tencel, see Chapter 2, Section 1. Materials), thus flax has to be longer to recover some flexibility and to bend like Tencel. The "Extended fibre length average" L sn of S-shaped Tencel fibre is slightly higher than that of Cshaped category L cn (Figure 4.39). S-shaped fibres form different conformation while for Cshaped practically only one angle of bending was observed. Forgacs and Mason (1959) studied the motion of a flexible fibre in shear flow when they rotate. Stiff fibres rotate with orbits as predicted by Jeffry (1922). When fibres are less stiff, they rotate as springy orbits i.e. fibres slightly buckle and then become straight as they realigned along flow direction.

Increasing flexibility, fibres showed different conformations called "snake-turn", "S-turn" or other complex shape, and this seems to be similar to what we observed for C-shaped and Sshaped categories. -The distributions over the sample thickness of flax and Tencel fibres are different: as for glass fibres, the concentration of flax increased from surface to core, whereas that of Tencel was practically unchanged.

-Another difference between flax and Tencel was observed in term of fibre dispersion throughout thickness: the number of Tencel fibres was three times larger than that of flax. This difference was explained by the fact that even after injection, a lot of flax fibres remained in bundles. For glass fibres, the change of concentration per layer was important as the number of fibres was lower than that of flax at surface and become larger at core.

-The alignment of fibres with respect to the main flow direction depends on the fibre type. Flax, Tencel and glass fibres show 𝑎 𝑥𝑥 near surface-core of 0.9-0.3, 0.8-0.2 and 0.7-0.5, respectively.

-Finally, the fibre apparent length measured at the cross section is smaller than the true one obtained in Chapter 3 via matrix dissolution. This was explained by out-of-plane orientation.

Concluding, this chapter shows certain similarities and differences in the microstructure of Tencel-and flax-based composites compared to glass fibre ones. Fibre flexibility plays an important role in microstructure and has to be taken into account when predicting and modelling injection moulding process. The influence of fibre flexibility on the rheological properties of composites will be presented in the next chapter.

Chapter 5

Rheological properties of composites

The flow behaviour of molten composites is directly correlated to their microstructure. As seen in the previous chapter, the pattern of the melt front during cavity filling controls and designs the dispersion and the alignment of fibres. Therefore, assessing the composite rheology is required to correlate the microstructure with the results obtained during injection moulding process.

Moreover, rheology experiments provide input data to simulate the filling stage, which enables to optimize modelling assumptions and also to predict the mechanical properties of the moulded part.

In the following chapter, we firstly present the state of the art on dynamic and capillary rheology of glass fibre-and natural fibre-reinforced thermoplastics. Then the results of this work about the viscoelastic properties of flax, Tencel and glass based composites are provided and discussed, focusing on fibre morphology and flexibility. The effect of fibre content and aspect ratio on rheology of composites will be demonstrated. Furthermore, the correlations between the dynamic and capillary viscosity will be assessed. The influence of compatibilizer will be discussed in section 1.1.2 (Influence of compatibilizer).

State of the art

At low frequencies, compared to neat matrix showing a Newtonian plateau, the complex viscosity of 20 wt % flax/PP composites keeps increasing when decreasing the frequency. By increasing the fibre content until 50 wt %, the slope of the viscosity rise becomes sharper. At high frequencies, the complex viscosity of 20 wt % merges to the matrix one, whereas that of 50 wt % follows a similar shear thinning slope to matrix at a greater magnitude. The complex viscosity evolution is essentially related to the viscous (G'') and elastic (G') moduli. Figure 5.2 shows G' and G" versus frequency curves, for neat PP and for two concentrations of flaxreinforced polypropylene (30 wt % and 50 wt %). According to authors, viscous modulus of neat polypropylene is higher in magnitude than the elastic one, and the slopes of both elastic and viscous moduli at low frequencies are almost 1.3 and 0.8, respectively. The addition of fibres increases the magnitude of viscous and elastic moduli and reduces their slopes at low frequencies, showing plateau-like (slope≈ 0) for 50 wt % fibre content. The difference in magnitude between viscous modulus and elastic modulus becomes lower as fibre content increases. Above 20 wt %, the elastic modulus value overtakes the viscous one. Such a rheological response is similar to that of glass fibre reinforced thermoplastic. [START_REF] Greene | Steady-State and dynamic properties of concentrated fiber-filled thermoplastics[END_REF] Le Moigne et al. (2013) showed that increasing fibre content has a larger impact on complex viscosity and G' and G" moduli at concentrated regime as compared to dilute and semi dilute regimes. The transition from semi-dilute to concentrated regime occurs when volume fraction is higher than the inverse of the fibre aspect ratio (L/D) -1 . By increasing the aspect ratio, the transition semi-dilute /concentrated moves to lower concentrations. This means that the viscosity rise at low frequencies becomes greater when fibre aspect ratio increases, at the same fibre concentration. Authors concluded that the transition between semi dilute and concentrated regimes is a sign of the commencement of fibre-fibre interactions, becoming larger either by increasing fibre content or fibre aspect ratio. The fibre-fibre interactions lead to build a networklike structure at low frequencies, which lets the molten composite owning more elasticity. This is a typical solid-like behaviour indicating the presence of an apparent yield stress at low frequencies.

In order to assess the apparent yield stress, Le Moigne et al. ( 2013

𝜂 (𝜔) = 𝜎 0 𝜔 + 𝜂 0 [1 + 𝜆𝜔 𝑎 ] (𝑛-1) 𝑎 [Eq.5.1]
where 𝜎 0 is the apparent yield stress, 𝜂 0 is the zero shear viscosity, 𝜆 is the material characteristic time, a is the Yasuda parameter, 𝜔 is the frequency and 𝑛 is the power-law index.

Using an approach of suspensions of solid particles [Heymann et al. (2002); Mueller et al.

(

Influence of temperature and activation energy

1.1.3.
The determination of temperature-dependent viscoelastic properties requires applying the time-temperature superposition principle. This principle typically involves the following steps: 1) experimental determination of viscosity versus frequency curves at several temperatures and a fixed frequency range 2) selection of a reference temperature 𝑇 0 3) all viscosity vs frequency curves corresponding to different temperatures are shifted along both vertical and horizontal axis, fitting the reference viscosity curve ( 𝜂 𝑇 0 versus 𝜔 𝑇 0 ) 4) considering the temperature shift factor 𝑎 𝑇 , the obtained master curve at the reference temperature is a plot of the shifted viscosity 𝑎 𝑇 𝜂 𝑇0 as function of the shifted frequency

𝜔 𝑇 0 /𝑎 𝑇
The shift factor 𝑎 𝑇 is usually correlated to the activation energy 𝐸 𝑎 using an Arrhenius-type equation as follows

𝑎 𝑇 = 𝑒𝑥𝑝 [ 𝐸 𝑎 𝑅 ( 1 𝑇 - 1 𝑇 0 )] [Eq.5.6]
where R is the universal gas constant, T is the temperature in K and T 0 is the reference temperature.

The influence of fibre concentration on the activation energy of molten composites seems to be an opened question. In some studies E a is dependent on fibre content, while in some others, it is independent and remains constant when compared to matrix E a . [START_REF] Islam | Rheological behavior of coir-fiber-filled polypropylene composites at constant shear stress[END_REF] showed that E a of coir/PP composite increases from about 40 kJ/mol for neat PP to about 80 kJ/mol for 30 wt % concentration (Figure 5.5). According to authors, this was interpreted by the additional energy needed to drag fibres into the fluid-motion, when compared to flowing without fibres. Nevertheless, some other authors found that activation energy decreases by increasing the fibre content: this was the case for sisal fibre/poly(butylene succinate) composites (E a decreased from 35 kJ/mol for the neat polymer to 1-2 kJ/mol for 50 wt % sisal composite) [START_REF] Feng | Rheological properties of sisal fiber/poly (butylene succinate) composites[END_REF]] and for glass fibres/PP composites (from 10 kJ/mol for the neat PP to 6 kJ/mol after adding 30 wt % glass fibres) [Tiptipakorn et al. (2009)]. The reason of this decrease may be that E a was calculated within the shear thinning regime.

Ea, kJ/mol

Fibre content, wt% [START_REF] Laun | Orientation effects and rheology of short glass fiber-reinforced thermoplastics[END_REF] Influence of fibre flexibility 1.1.4.

To interpret the rheological properties of a suspension of flexible fibres, [START_REF] Switzer | Rheology of sheared flexible fiber suspensions via fiber-level simulations[END_REF] used the criterion of flexibility F that couples fibre Young's modulus and aspect ratio with the shear stress  𝑚 γ ̇ surrounding fibres:

𝐹 = 64 π ( 𝐿 𝐷 ) 4  𝑚 γ Ė𝑓 [Eq.5.7]
 m is the matrix viscosity. When F → ∞, fibres are perfectly flexible threads; when F → 0, fibres become rigid. Keshtkar et al. (2008) applied this criterion to study the dynamic rheology of model synthetic (Polyacrylate and Nylon) fibres dispersed in silicone oil. Figure 5.6.a shows that higher complex viscosity and elastic modulus were obtained at the same fibre concentration (6.5 vol %) either for fibres with lower Young's modulus at the same the same fibre aspect ratio or for fibres with higher aspect ratio at the same Young's modulus. This means that complex viscosity and elastic modulus of suspensions are larger as fibre flexibility increases (lower Young's modulus and higher aspect ratio). The difference in complex viscosity and elastic modulus between suspensions becomes progressively smaller as the frequency increases. This trend was more pronounced for composites with higher fibre concentrations. They concluded that with more flexible fibres a "stronger structure" is formed due to larger number of fibre-fibre interactions. The authors outlined that the complex viscosity does not depend on the fibre stiffness (fibre Young's modulus) after a high preshearing of 5 s -1 (results presented in Figure 5.6 were made after a pre-shear of 0.1 s -1 ).

Capillary rheology and comparison with dynamic

The capillary rheology of natural fibre composite was investigated by [START_REF] Basu | Comparative rheological studies on jute-fiberand glass-fiber-filled polypropylene composite melts[END_REF], comparing jute fibre-to glass fibre-reinforced polypropylene. The initial fibre length of glass and jute fibres is 4.7 mm and 1-5mm, respectively. Figure 5.7 shows that the viscosity of both composite systems increases as fibre content increases, for a shear rate ranging from 60 s -1 to 4000 s -1 . The increase of viscosity becomes smaller when the shear rate gets higher.

Considering that jute and glass fibres do not possess the same density, the comparison at the same weight fraction (so different volume fraction) between jute and glass fibre composites is difficult. The same volume fraction is needed to obtain a plausible comparison. Viscosity versus shear for high density polyethylene melt without fibres and with 30 wt % glass fibres [START_REF] Laun | Orientation effects and rheology of short glass fiber-reinforced thermoplastics[END_REF]]

Conclusions

A brief review of literature on the rheological properties of fibres suspended in a fluid under simple shear showed that viscoelastic properties depend on fibre concentration, aspect ratio, flexibility and also on the presence of compatibilizer. Natural fibres have much complex morphology compared to glass fibres; they can be rigid or flexible (or semi-rigid) and can consist of elementary fibres and/or bundles in which fibres are "glued" together. The rheology of such composites is more complex and strongly depends on fibre type, in addition to all other "classical" parameters. In the next section, we describe the results obtained for flax and Tencel-based polypropylene composites and compare them with the viscoelastic properties of glass fibre based composites, all obtained in the same conditions.

Results and discussion

Dynamic rheology results

We remind that no compatibilizer was used in this study in order not to modify matrix viscoelastic properties. The correlation between volume and weight concentrations is presented in Chapter 2, Table 2.3. The tangent of phase angle  represents to what extent the system is more viscous or more elastic. For all studied systems, tan is greater than 1 overall studied frequencies, which is expected for the case of neat PP (Figure 5.11). The lower the frequency, the higher tan. The increase of fibre concentration leads to a decrease of tan, indicating a greater elasticity of the system that is particularly pronounced at low frequencies. For 20.5 vol % concentration of Tencel/PP and flax/PP composites, tanis around 2 at low frequencies and around 1 at high frequencies. tanwas also obtained for glass fibre based composites, as already reported in literature [START_REF] Kitano | Shear flow rheological properties of vinylon-and glass-fiber reinforced polyethylene melts[END_REF] The apparent yield stress s 0 for each composite at each temperature was determined by the following steps: 1) plotting the s (the shear stress) versus frequency in a conventional plot (not log-log plot) 2) fitting the low frequency-end of curve by a linear model (s= a ω +b) 3) "b" gives the shear stress at zero frequency "s 0 " that corresponds to the apparent yield stress. The higher the concentration is, the higher the s 0 is, being higher for Tencel-based composites and glass and lower for flax. Moreover, increasing temperature leads to decrease s 0 . Measured flax and Tencel yield stress-concentration dependences were fitted with power law, shown as solid lines in Figure 5.14. In all cases studied the yield stress is proportional to fibre volume fraction to the power 3 within 20 % of deviation, as predicted at [START_REF] Bennington | The yield stress of fibre suspensions[END_REF] study. It is difficult to predict the other exponents in Eq. 5.5 as far as there are too many variables and the influence of temperature on fibre Young's modulus is not known. (1)

Influence of fibre concentration on composite viscoelastic properties

(2)

(3) (4)

Figure 5.18 shows Ln (𝑎 𝑇 ) versus (1/T)-(1/T 0 ) of neat PP and Tencel/PP composite. Similar results were obtained for flax and glass based composites (not shown here). The shift factor 𝑎 𝑇 seems to obey to Arrhenius law (Eq. 5.4). The slope of the curve enables to assess E a . [START_REF] Islam | Rheological behavior of coir-fiber-filled polypropylene composites at constant shear stress[END_REF] and [START_REF] Herrera | Development of natural fiber reinforced polylactide-based biocomposites[END_REF] showing that an increase of fibre concentration in composites leads to enhance the activation energy. We suppose that fibres prevent polymer chains to move as they would do without them. The increase of fibre concentration also leads to increase interactions between fibres (friction, overlapping, etc.)

and between fibres and matrix, requiring an additional energy to flow. A quantitative All results presented above demonstrate that composites with Tencel fibres show higher viscosity, elasticity, apparent yield stress and activation energy as compared to glass-and flax-based composites at the same fibre concentration. Several reasons can be given to explain this finding. The first one is related to the number of fibres N i per 1 mm 3 of 30 wt % flax and Tencel ® composites, calculated as follows:

𝑁 𝑖 = 4𝑓 𝜋𝐿 𝑖 𝐷 𝑖 2 [Eq.5.9]
where subscript "i" is "n" or "w" corresponding to length and diameter weighted either in number or in weight.

For example, for 20.5 vol % fibre concentration, the number of Tencel fibres N n and N w is almost 10 times higher than the corresponding numbers for flax and 1.5-2 times higher than for glass fibres. 5.2). High dispersion in fibre dimensions (See Chapter 4, Section 2) and wide L/D distribution do not enable to calculate the exact value of this concentration. However, Figure 5.10 shows that for the concentration of 6.3 vol % a yield-like stress occurs at low frequency in case of Tencel and glass, signing that fibre-fibre interactions get already larger and a concentrated regime is well established. However, at the same concentration, the flax curve viscosity looks similar to that of polypropylene with a slight increase of viscosity at low frequencies, which means that fibre-fibre interactions just started to take place and the f(s-d/c) may be not reached. This is in agreement with the estimation of f(s-d/c) presented in Table 5.2.

It should also be taken into account that glass fibre aspect ratio strongly decreases when fibre concentration increases. If fibre aspect ratio was the only parameter controlling composite viscosity and yield stress (at a given fibre concentration), it would be glass fibre based composite and not Tencel-based that should have the highest values. However, the number of glass fibres is lower than that of Tencel, and thus the third fact, which is the fibre flexibility, has to be taken into account, as discussed below.

To illustrate the influence of fibre flexibility, we calculated the flexibility F (Eq.5.7) for fibre concentration of 20.5 vol % and frequency of ω = 0.1 rad/s. Moreover, we used both aspect ratios, (L/D) n and (L/D) w , to give the interval of flexibility values that we call F n and F w , respectively. The results are presented in Table 5.2. We approximate that the shear stress surrounding fibres is the same applied to the melt composite at a given frequency. Because it is impossible to prepare glass, flax and Tencel-based composites with the same fibre aspect ratio keeping the same processing conditions, the flexibility F reflects the influence of both fibre aspect ratio and Young's modulus. The flexibility of Tencel fibres is slightly higher than that of glass fibres and more than two orders of magnitude higher than for flax fibres.

As discussed in the state of the art section, flexible fibres (here the most flexible is Tencel) flow in a different way compared to the rigid ones (here glass fibres and flax bundles).

Flexibility makes fibres turning under shear as S-turn or C-turn, which leads to shorter effective aspect ratio [Forgacs and Mason (1959)]. This will induce quicker rotation compared to rigid fibres, increasing the probability of fibre-fibre interactions, creating a larger normal stresses and longer time not aligned in the flow direction. All these factors contribute to the additional dissipation of viscous energy, higher yield stress, viscosity and elasticity of Tencelbased composites.

Although, glass fibres have higher aspect ratio, Tencel based composites show higher viscosity, elasticity and higher yield stress (at a given fibre concentration). The specificity of cellulosic fibres has thus to be taken into account: if comparing Tencel and flax based composites, the number of fibres per volume unit is much higher for Tencel than for flax. The reason is that a major part of flax fibres are in bundles, and in addition Tencel is more flexible than flax. The understanding of fibre morphology and the adequate analysis of the distributions of both fibre length and diameter in natural fibre based composite are thus the key points for the interpretation of composite rheological properties. and of  0 (that is zero shear rate viscosity) have to be taken with care as far as these composites show apparent yield stress and no Newtonian plateau is detectable. To set up the fitting of the experimental curves by Carreau-Yasuda model we have dealt with parameters as follows -The apparent yield stress s 0 we used the method described in Section 2.1.1.

Capillary rheology and comparison with dynamic

-"𝑛" was determined by fitting the end (high shear rate) of viscosity-shear rate curve, respectively -"𝑎" is calculated from the neat PP curve and fixed for all composites. This parameter defines the shear rate length of the transition between the Newtonian plateau (without considering the yield stress) and the power law region at high shear rate. According to Figure 5.21, the shear thinning part of Tencel composites curves is connected to the Newtonian plateau in the same shear rate range as the one of the neat PP. This is also true for glass and flax composites that are not presented in Figure 5.21. This approach was already used by [START_REF] Lertwimolnun | Réalisation de nanocomposites polypropylene/argile par extrusion bivis[END_REF] for nanocomposites of clay reinforced polypropylene with similar rheological behaviour.

-"" and " 0 " were calculated using Microsoft Solver © in Excel © . Tencel fibres seem to be perpendicular which is unexpected. The number of flax fibres seems to be much lower than that of the two other composites. This is in agreement with the number of fibres per unit volume given in Table 5.2. Glass fibres appear as straight rods, whereas and Tencel are curved. Flax fibres appear as elementary semi-rigid fibres and as thick bundles. For dynamic rheology, we showed that complex viscosity, viscous and elastic moduli increase especially at low frequencies, when the fibre aspect ratio, flexibility and concentration

increase. An apparent yield stress at low frequencies was evaluated and correlated with the fibre content. We interpreted the apparent yield stress by the enhancement of fibre-fibre interactions, which leads to network-like structure when volume fraction reaches the concentrated regime. The influence of temperature was modelled by Arrhenius law enabling to evaluate the composite activation energy. The latter increases as fibre content gets higher.

Tencel composites showed higher activation energy as compared to flax and glass ones. This was explained by reducing the polymer chains mobility when fibres are added to polymer.

The fibre-fibre and fibre-matrix interactions increase when fibre content is greater, which needs more energy to let polymer chains flow.

The superposition dynamic/capillary rheology obeyed the Cox-Merz approximation. The overall curves including dynamic and capillary measurement were fitted with the modified Carreau-Yasuda model. The obtained results are plausible to be as inputs rheological data for further injection moulding process simulation. This will be the aim of Chapter 7. Finally, the increase in viscosity due to the concentration enhancement is evaluated by a concentration shift factor following an exponential evolution as a function of fibre concentration.

Tiptipakorn, S., Rimdusit, S., Kitano, T., & Damrongsukkul, S. (2009). Thermomechanical and rheological behaviours of waste glass fibre-filled polypropylene composites. Engineering Journal, 13(3), 45-59.

Twite-Kabamba, E., Mechraoui, A., & Rodrigue, D. (2009). Rheological properties of polypropylene/hemp fiber composites. Polymer Composites, 30(10), 1401-1407.

Chapter 6

Mechanical properties of composites

Mechanical properties of short fibre reinforced thermoplastics strongly depend on the microstructure established during processing. As seen in the previous chapters, the flowinduced microstructure in injection moulded parts leads to a multilayer-structure in which fibres are usually oriented parallel to the flow direction near the surface and perpendicular to the flow direction at the mid-plane. Therefore, injection moulded parts can be considered as anisotropic materials. The mechanical behaviour of such materials is dependent on the dispersion, size and orientation of fibres and the reinforcement is expected from the fibres aligned along the load direction.

The aim of this chapter is to correlate fibre microstructure in the injection moulded parts with the tensile and impact properties of composites. First, we present the state of the art related i)

to the mechanical properties of natural fibre-and glass fibre-reinforced thermoplastics, focusing on the correlations with composite microstructure and ii) to the existing models classically used to predict their mechanical properties. We present then the experimental results of tensile tests performed on samples that were cut out from the moulded "box" along three different directions with respect to the main flow direction. The correlation with the microstructure was possible since tensile samples have been cut from the same location as the samples used for the microstructure analysis. The data that were obtained from the quantification of orientation in Chapter 4 and from fibre size analysis in chapter 3 will be used to model the tensile properties of composites. Moreover, an investigation of the impact properties made with impact bars injected separately will be presented and analysed. A comparison between experimental and theoretical results predicted by models will be discussed.

State of the art 1.Tensile properties

Experimental results 1.1.1.

Many studies report on the mechanical properties of natural fibre reinforced thermoplastics, but only few studies correlate them with the microstructure in injection moulded parts. Aurich and Mennig (2001) studied the stiffness of 30 wt % flax reinforced polypropylene with fibre aspect ratio being 13 and with 2 wt % of MAPP added to improve adhesion. Tensile specimens were taken in parallel and in perpendicular directions to the main flow direction; the obtained elastic moduli were 3020 MPa and 2200 MPa, respectively. The authors explained the difference between elastic moduli in the parallel and the perpendicular directions by the different fibre alignment in the core and shell regions. The orientation component 𝑎 𝑥𝑥 (with respect to the main flow direction) was 0.9 at the sample surface and 0.2 at the core in the central area of the plaque, and 0.6-0.9 close to the lateral border. The fibres are more aligned close to surface as compared to core. Similar results were found by Neves et al. (1998) for glass fibre-reinforced polycarbonate. The main factors influencing fibre alignment, and shell and core layers thickness were pointed out at Chapter 3 (State of the art section). Bourmaud et al. (2013) investigated the stiffness of 13.7 vol % flax-reinforced polypropylene.

To understand the difference in tensile properties between core and shell layers, a dog-bone sample with thickness of 4 mm was cut into 3 samples of the same shape such as the thickness of each was 1 mm (Figure 6.1). The samples from the shell layer were taken at a distance of 0.1 mm from the surface and the core sample was taken from the mid-plane. The tensile test was performed on the entire 4 mm thick sample and for the core and the shell samples of 1 mm thick each. 2013) observed also the breakage of the core sample during testing by a SEM micrograph. During the extension of the sample, the crack is initiated at the bundles, which make angle to the cross section plane (Figure 6.3). The authors considered that these bundles should present weakness areas that affect the composite properties. Therefore, improving bundles' dissociation could result in better tensile properties. at the same volume fraction 13.7 vol % [Bourmaud et al. (2013)]. With the same volume fraction, the weight fractions are different because of the difference in fibre density. In addition, 4 wt % of MAPP was added in the case of natural fibre composite. A considerable difference in stiffness and strength at break is observed between shell and core specimens, for each type of composite. The shell samples show a much higher Young's modulus as compared to core ones, by +69 % and +24 % for glass and flax based composites, respectively. The shell samples exhibit also a larger strength at break as compared to the core ones, by +81 % and +21 %, for glass and flax based composites, respectively. The glass fibre based composites reveal more important stiffness and strength at core and shell samples as compared to the flax based. The authors explained this by the higher stiffness of glass fibres, in addition to the bundle structure of flax that limits their dispersion in matrix and orientation in the tensile direction. Moreover, in a previous study of Bourmaud and Baley (2010), nanoindentation measurements demonstrated that the mechanical properties of the cell wall of flax fibres decrease after compounding and injection moulding, which changes their structure, composition, cohesion and water content. Bourmaud et al. (2013) did not focus on the influence of the fibre size on the tensile properties. The difference of properties between glass and flax based composites can be related to the difference of fibre size in composites, in addition to the other reasons (fibre properties and orientation). It is known that fibre size decreases by processing and the mechanism of rupture of flax fibre is dissimilar to the glass one. Therefore, a difference of size of flax fibres compared to glass ones is expected after the injection moulding of composites (See Chapter 3, Section 2.4. Comparison between fibre types). The elongation at break is about 2.2-3.4 % for both types of composites. The neat polypropylene has an elongation at break of 3.4 % at the core and 11.2 % at the shell (not shown in Figure 6.4). Whereas, the elongation at break of composites considerably decreases at the shell samples compared to the neat PP, it remains almost constant at the core samples. Many authors studied the influence of various parameters, else than fibre orientation and dispersion, on the mechanical properties of composites. By analysing the influence of length and concentration on the stiffness of glass/PP composites [Thamason and Vlug (1996,a,b)] and flax/PP composites [START_REF] Nechwatal | The Dependence between the Process Technologies and the Effect of MAH-PP-Adhesives in Natural Fibre Reinforced Thermoplastic Composites[END_REF]], it was shown that the fibre length needed to reach the maximum stiffness is much lower than that needed to reach the maximum strength.

For glass/PP, a fibre length higher than 0.8 mm is enough to make the stiffness of a short fibre composite equivalent to 90 % of the stiffness of a continuous fibre composite, whereas 90 % of strength requires at least a fibre length of 13 mm [Thamason and Vlug (1996,a)]. For flax/PP composites the equivalent length enabling a maximum stiffness is 1 mm, which is 8 times shorter than the length needed for a maximum strength [START_REF] Nechwatal | The Dependence between the Process Technologies and the Effect of MAH-PP-Adhesives in Natural Fibre Reinforced Thermoplastic Composites[END_REF]]. Peijis et al. (1998), [START_REF] Van Den Oever | Influence of the physical structure of flax fibres on the mechanical properties of flax fibre reinforced polypropylene composites[END_REF], Gharkhail et al. (2000), Karmaker et al. (1996) and Barkoula et al. (2010) showed that MAPP improves the composite strength but has almost no effect on the stiffness for flax fibres based systems. [START_REF] Ganster | Novel cellulose fibre reinforced thermoplastic materials[END_REF] focused on the mechanical properties of composite reinforced with man-made cellulose fibres.

 Tensile stiffness

The prediction of tensile stiffness of natural fibre-reinforced thermoplastics uses models already developed for discontinuous (short) glass or synthetic fibre composites. The model of Cox and Krenchel [Cox (1952), [START_REF] Krenchel | Fibre reinforcement[END_REF]] (Eq.6.1) is commonly used to predict the stiffness 𝐸 𝑐 for oriented short fibre composite, which is the case of injection moulded parts.

𝐸 𝑐 = 𝜉 0 𝜉 1 𝑓𝐸 𝑓 + (1 -𝑓)𝐸 𝑚 [Eq.6.1]
where 𝐸 𝑓 , 𝐸 𝑚 and 𝑓 are the fibre Young's modulus, matrix Young's modulus and the fibre volume fraction, respectively. 𝜉 0 and 𝜉 1 are the orientation and the efficiency factors, respectively.

𝜉 1 = [1 - tanh ( 𝜅𝐿 2 ) 𝛽𝐿 2 ] [Eq.6.2] 𝜅 = 2 𝐷 [ 2𝐺 𝑚 𝐸 𝑓 𝑙𝑛(√ 𝑟 𝑅 ) ]
1 2

[Eq. 6.3] where 𝐿 is the fibre length, 𝐺 𝑚 is the shear modulus of the matrix, 𝜒 𝑖 is a factor depending on the geometrical packing arrangement of fibres, 𝑟 is the fibre radius and 𝑅 is the centre to centre spacing of fibres. The 𝜉 0 is actually the theoretical orientation factor of [START_REF] Krenchel | Fibre reinforcement[END_REF]] that takes into account fibre orientation as follows:

𝜉 0 = ∑ 𝑓 𝑛 𝑛 𝑐𝑜𝑠 4 𝜙 𝑛 [Eq.6.5]
where 𝑓 𝑛 is the fraction of fibres with the orientation angle 𝜙 𝑛 with respect to the tensile direction axis. It was shown by [START_REF] Krenchel | Fibre reinforcement[END_REF] and Folkes (1985) that 𝜉 0 = 3/8 for random planar orientation and 𝜉 0 = 1/5 for three dimensional random fibre orientation, and 1 for all fibres oriented in the direction of traction. Gharkhail et al. (2000) discussed these values and suggested that deviations may likely occur for flax fibres due to the out-of-plane oriented fibres and the bending of fibres.

 Tensile strength [START_REF] Kelly | Tensile properties of fibre-reinforced metals: copper/tungsten and copper/molybdenum[END_REF] extended the rule of mixture to predict strength 𝜎 𝑐 of unidirectional fibre-reinforced polymer composites as follows:

𝜎 𝑐 = 𝜁 𝐿 𝑓𝜎 𝑓 + (1 -𝑓)𝜎 𝑚 [Eq.6.6] where 𝜎 𝑓 is the fibre tensile strength, 𝜎 𝑚 is the matrix strength. 𝜁 𝐿 is the fibre length efficiency factor:

𝜁 𝐿 = 1 𝑓 [∑ 𝐿 𝑖 𝑓 𝑖 2𝐿 𝑐 + ∑ 𝑓 𝑗 (1 - 𝐿 𝑐 2𝐿 𝑗
)] [Eq.6.7] Equation 6.7 contains two parts depending on if fibre length is subcritical 𝐿 𝑖 < 𝐿 𝑐 (first summation) or supercritical 𝐿 𝑗 > 𝐿 𝑐 (second summation), where 𝐿 𝑐 is the critical length:

𝐿 𝑐 = 𝜎 𝑓 𝐷 2𝜏 [Eq.6.8]
where 𝐷 is the fibre diameter and 𝜏 is the fibre-matrix interfacial shear strength.

The critical length 𝐿 𝑐 = 𝜎 𝑓 ( 𝐷 2𝜏

) can be determined either experimentally as a single fibre fragmentation test [START_REF] Beckermann | Engineering and evaluation of hemp fibre reinforced polypropylene composites: Micro-mechanics and strength prediction modelling[END_REF]] or calculated knowing the strength of the fibre 𝜎 𝑓 . The interfacial shear strength 𝜏 are usually assessed by micromechanical tests. [START_REF] Bowyer | On the re-inforcement of thermoplastics by imperfectly aligned discontinuous fibres[END_REF] suggested a modified Kelly and Tyson model by adding an orientation factor to take into account the fibre orientation. Applied on sisal fibre composite, this model provides results that fit well the experimentally obtained tensile strengths [START_REF] Li | Sisal fibre and its composites: a review of recent developments[END_REF]; Kalaprasard et al. (1997)]. Thomason et al. (1996) used an empirical orientation factor equal to 0.2 to fit the experimental measurements of glass/PP composites

Impact properties

Experimental results

1.2.1.

Most studies related to impact properties of natural fibre-reinforced thermoplastics were not associated with injection moulding process, except those of [START_REF] Paunikallio | Influence of maleated polypropylene on mechanical properties of composite made of viscose fiber and polypropylene[END_REF][START_REF] Paunikallio | Composition, tensile properties, and dispersion of polypropylene composites reinforced with viscose fibers[END_REF] and [START_REF] Ganster | Novel cellulose fibre reinforced thermoplastic materials[END_REF]. [START_REF] Ganster | Novel cellulose fibre reinforced thermoplastic materials[END_REF] focused on the composites with manmade cellulosic fibres; they showed that Tencel/PP exhibits better impact strength over jute/PP and viscose/PP but lower than Cordenka/PP at the same fibre concentration (25 wt %) (Figure 6.6). However, no correlation among composite microstructure, fibre concentration and impact properties was performed. For processes else than injection moulding, [START_REF] Wambua | Natural fibres: can they replace glass in fibre reinforced plastics?[END_REF] made a comparison among Charpy impact properties of compressed randomly oriented kenaf, coir, sisal, hemp and jute fibre reinforced polypropylene. It turned out that hemp and sisal composites have better impact properties over others. Moreover, it was shown that impact strength increases with the fibre content. [START_REF] Van Den Oever | Influence of the physical structure of flax fibres on the mechanical properties of flax fibre reinforced polypropylene composites[END_REF] investigated mechanical properties of flax mat reinforced polypropylene and showed that while impact strength increases with increasing fibre content and fibre length, it decreases with increasing fibre-matrix adhesion. This was explained by the fact that higher adhesion results in shorter average pull-out length. Similar results were found by Gharkhail et al. (2000) for a random non-woven flax fibre mats/polypropylene and [START_REF] Gironès | Biocomposites from Musa textilis and polypropylene: evaluation of flexural properties and impact strength[END_REF] for abaca/polypropylene composites. This statement was even more confirmed by Bax and Müssig (2009) for flax/PLA and [START_REF] Plackett | Biodegradable composites based on L-polylactide and jute fibres[END_REF] for jute/PLA, where fibre-matrix adhesion is naturally good and adding fibre can unexpectedly decrease the impact strength. [START_REF] Clemons | Impact toughness of cellulose-fiber reinforced polypropylene: influence of microstructure in laminates and injection molded composites[END_REF] studied the injection moulded pulp-reinforced polypropylene and demonstrated that dynamic fracture toughness during impact test increased when fibres are oriented perpendicular to the crack direction. For the injection moulding of glass fibrereinforced polypropylene, [START_REF] Thomason | Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: Part 4. Impact properties[END_REF] demonstrated that impact strength increases when the length and the concentration of fibres get higher. Furthermore, an improved fibre-matrix interaction decreases impact strength, as found for the natural fibre case.

A small enhancement in impact strength can be obtained with a temperature decrease. Various mechanisms of energy dissipation may operate during impact test. Wells and Beaumont (1985) revealed that composite containing short fibres randomly dispersed and aligned follows a fibre pull-out, as energy dissipation mechanism preceding a fast fracture. [START_REF] Thomason | Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: Part 4. Impact properties[END_REF] considered that fibre fracture is the dominant energy dissipation mechanism.

The identification of the fracture mechanism is classically possible by a microscopy observation.

Models of impact strength

1.2.2. [START_REF] Cottrell | Strong solids[END_REF] developed a model for composites containing unidirectional fibres, including three possible mechanisms of energy dissipation: 1) matrix fracture, 2) fibre fracture and 3) fibre pull-out. The predicted impact energy increases with fibre length up to a critical fibre length 𝐿 𝑐 in a similar way to [START_REF] Kelly | Tensile properties of fibre-reinforced metals: copper/tungsten and copper/molybdenum[END_REF] model prediction for the composite strength. The maximum of impact energy was correlated with the change in the mode of fracture: from fibre pull-out for length < 𝐿 𝑐 to fibre fracture for length > 𝐿 𝑐 . Since this model has been considered only for the unidirectional reinforcement, it is somewhat questionable to apply it for randomly oriented fibres or multi-layer oriented structure as the case of injection moulding of short fibre-reinforced composite. Therefore, [START_REF] Thomason | Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: Part 4. Impact properties[END_REF] developed a simpler fibre strain energy model based on the rule of mixture as follows:

𝑈 𝑐 = 𝑓 ( 𝜎 𝑓 2 𝐿 𝑑 2𝐸 𝑓 ) ( 𝐿 𝐿+𝐿 𝑐 ) + (1 -𝑓)𝑈 𝑚 [Eq.6.9]
where 𝑈 𝑐 is composite impact strength, 𝑓 is the fibre volume fraction, 𝐸 𝑓 is the fibre Young's modulus, 𝐿 is the fibre length, 𝑈 𝑚 is the matrix impact strength, 𝐿 𝑑 is the length of the debonding fibre, 𝜎 𝑓 is the fibre strength and 𝐸 𝑓 is the fibre Young's modulus. The term

( 𝜎 𝑓 2 𝐿 𝑑 2𝐸 𝑓
) corresponds to the total energy for the fracture of a single fibre. According to [START_REF] Thomason | Influence of fibre length and concentration on the properties of glass fibre-reinforced polypropylene: Part 4. Impact properties[END_REF], 𝐿 𝑑 increases when 𝐿 𝑐 increases. However the effect of fibre orientation is not taken into account.

Conclusions

The mechanical performances of natural fibres reinforced thermoplastic are directly related to fibre aspect ratio and length, concentration, orientation and dispersion. The flow-induced microstructure formed in composite leads to a material with anisotropic properties. This anisotropy is directly reflected by tensile stiffness and strength. In most cases, the Young's modulus and the tensile strength are higher when specimen tensile bar is parallel to the main direction of flow than perpendicular. This stems from a different fibre alignment at the shell layer compared to the core layer. Higher fibre aspect ratio and concentration lead to better tensile and impact properties. While adding compatibilizer increases the tensile strength, it has almost no effect on the tensile stiffness and decreases the impact strength.

Models predicting the mechanical properties of composites were developed for glass fibre reinforced plastics and the same models are presently extended to the case of natural fibres.

The models of the tensile properties are associated to fibre critical length; below it the contribution of fibres in composite performance is less important than above it. The value of the critical length varies from one study to other and depends on the use of compatibilizer or not. This must be one of the main reasons of the deviation of the estimated mechanical properties for natural fibre-reinforced thermoplastics. Some recent modifications of the models dedicated to tensile stiffness and strength enable to take into account fibre orientation, which makes the predicted results closer to the experimental ones. However, the existing models of prediction of the impact properties do not yet include the orientation effect.

Results and discussion

Tensile Properties

Experimental results: influence of fibre orientation 2.1.1.

The location of dog-bone samples is identical to the sample used to characterize the fibre orientation, dispersion and length. This enables to correlate the tensile properties to the microstructure in the injection moulded box. All testing conditions were described in Chapter 2. we found 𝑎 𝑥𝑥 is 0.8-0.9 at the shell, meaning that fibres are well oriented along the flow direction. In the core, 𝑎 𝑥𝑥 is around 0.3-0.4. This corresponds to a slight orientation perpendicular to the flow direction (0 would be perfect orientation, and 0.5 means random inplane orientation). Therefore, there is a qualitative agreement between the measured orientation and the mechanical response. Similar stress-strain curves were obtained for glass/PP and Tencel/PP (not shown). Stress-strain dependences of 20.5 vol % flax/PP for α= 0 °,45 ° and 90 ° Figures 6.9, 6.10 and 6.11 show the fracture surface after the tensile test of 20.5 vol % flax, Tencel and glass composites, respectively. For each type of composite, zy-plane and zx-plane are shown, corresponding to the traction of samples along x-direction (α = 0 °) and y-direction (α = 90 °), respectively. Two observations can be pointed out: 1) the shell layers are thicker than the core ones especially for flax and glass fibres 2) only fibres oriented in the extension direction are broken or/and pulled out. This means that fibres aligned in the tensile direction contribute marginally to the resistance against the sample extension. Moreover, thicker shell layers enable to explain more the higher tensile properties when samples are extended in xdirection than perpendicular. This seems reasonable because shell layers are almost aligned in the x-direction. The flax fibres that are pulled-out from matrix or broken during tensile testing can be elementary fibres or structured in bundles (Figure 6.9). This means that the mechanism of rupture is not dependent on the fibre morphology. Experimental results: influence of fibre type 2.1.2. Figure 6.12 shows Young's moduli of 20.5 vol % composites for different fibre types and different angles α (with respect to x-direction). The glass composite shows the highest Young's modulus as compared to flax and Tencel ones overall angles α. As compared to the neat PP, Young's modulus of glass-reinforced composites is 116 % higher, while it is only 66 % and 43 % higher for flax and Tencel based composites, respectively. One of the reasons is that the aspect ratio of glass fibres is twice higher than that of flax and 1.5 higher than that of Tencel (see Chapter 3). Moreover, glass fibre Young's modulus is 73 GPa, whereas that of Tencel is 10-15 GPa and that of flax varies between 50 and 110 GPa depending on flax fibre diameter [Charlet et al. (2010)]. In our case, most of flax fibres are in bundles and thus their moduli should be close to 50 GPa.

The obtained moduli of composites decrease with α increasing from 0 ° to 45 ° and then remain almost constant for α from 45 ° to 90 ° overall fibre types. Moreover, when α increases, the difference in modulus between Tencel and flax composites becomes smaller.

This can be explained by the fact that when the traction direction is perpendicular to the flow direction (α= 90 °), the core fibres are more effective than the shell ones, and according to results obtained in Chapter 4, Tencel fibres are more aligned than flax fibres at core (𝑎 𝑥𝑥 (flax) = 0.33 at 𝑎 𝑥𝑥 (Tencel) = 0.17) Figure 6.12 Young's modulus of 20.5 vol % composites for different types of fibres (flax, Tencel and glass) and for different loading directions (α= 0 °, α= 45 °, α= 90 °) Figure 6.13 shows the ultimate tensile strength for composites of 20. 5 vol % for different fibre types and different angles α. Tensile strength decreases when α increases for all fibre types. The glass composite strength is higher than that of flax and Tencel. Nevertheless, the difference in strength between glass and flax is relatively small compared to the difference in Young's modulus seen in Figure 6.11. The improvement in tensile strength relative to the neat PP is lower than the one of Young's modulus. For example at α= 0 °, the addition of fibres to PP increases strength of composite by 45 % with glass, by 40 % with and by Tencel.

According to Peijis et al. (1998), [START_REF] Van Den Oever | Influence of the physical structure of flax fibres on the mechanical properties of flax fibre reinforced polypropylene composites[END_REF], Gharkhail et al. (2000) and Barkoula et al. (2010) compatibilizer effect is more pronounced on the tensile strength than on tensile stiffness. Therefore, the lower improvement of tensile strength of composites relative to the neat PP is due to the absence of compatibilizer.

Ultimate strength, MPa

Tencel based composite does not depend on how the sample is positioned (and extended) with respect to the main flow direction. The most probable reason is that Tencel fibres are curved and extremely flexible so that they can be stretched under tensile force whatever the direction.

Predictions of composite tensile properties and comparison with experimental results

2.1.3.

 Stiffness

In this study we assume that fibre orientation is planar and symmetric with respect to the mid thickness plane. Considering that the orientation measurements were carried out for many layers at different depths across sample thickness from surface to core (Chapter 4), we approximate that 𝑎 𝑥𝑥 between two successive layers does not vary and thus thickness "e" can be divided into smaller sub-thicknesses 'e n ' each with different orientation components 𝑎 𝑥𝑥 .

We approximate also that the orientation coefficient 𝜉 0 (see Eq6.5) can be calculated by a quadratic assumption such as 𝑐𝑜𝑠 4 𝜑 𝑛 = 𝑎 𝑥𝑥𝑥𝑥 = (𝑎 𝑥𝑥 ) 2 when sample main axis (and thus extension direction) is parallel to the flow direction (α= 0 °), and 𝑐𝑜𝑠 4 𝜑 𝑛 = 𝑎 𝑥𝑥𝑥𝑥 = (𝑎 𝑦𝑦 ) 2 when sample main axis direction is perpendicular to the flow direction (α= 90 °). 𝑎 𝑦𝑦 is calculated with 𝑎 𝑥𝑥 + 𝑎 𝑦𝑦 = 1, the normalization approach of the components in the orientation tensor (see chapter 4), assuming that 𝑎 𝑧𝑧 is small when compared to 𝑎 𝑥𝑥 and 𝑎 𝑦𝑦 . This enables to describe the core-shell orientation induced by injection moulding flow and We suppose that these factors remain constant with concentration variation. Table 6.1 presents the results of this approximation.

𝝃 𝟎𝒚 0.2 0.3 0.18
The efficiency factor 𝜉 1 [Eq.6.2] varies with fibre size that in turn varies with fibre content and fibre type. The results of fibre size during processing presented previously in Chapter 3

were used to estimate the efficiency factor 𝜉 1 . Table 6.2 presents all calculated values. The moduli are 20 % overestimated. The same range of deviation was found by Aurich and Mennig (2001) for 30 wt % flax/PP (which is the same fibre concentration in weight).

For Tencel based composites, the model predicts a nearly isotropic behaviour, despite a skincore structure. The evolution with the fibre concentration is quite well predicted, but the model underestimates the measured values. Both predicted moduli of Tencel merge together towards high concentrations. Their two respective orientation factors are close, as seen in Table 6.1. Therefore, the only considerable difference to move them apart is the difference between Young's modulus of matrix in x and y directions, and this effect decreases progressively by adding fibres.

For glass composites, the y-direction modulus is well fitted with Cox-Krenchel prediction, whereas in the x-direction the modulus is overestimated and the difference between the measured and the modelled modulus gets larger with increasing the fibre content.The measurement of orientation provided in Chapter 4 showed that 𝑎 𝑥𝑥 = 0.7-0.4, which means that the average of 𝑎 𝑥𝑥 give almost a random orientation. This is reflected in the experimental stiffness by close moduli in x and y directions, and a quite isotropic material. However, the orientation factors obtained by the quadratic assumption we adopted in Eq.6.10 and Eq. 6.11 predict a considerable anisotropy (Table 6.1), which is not in agreement with experiments.

We can conclude that all y-direction moduli are fitted well the measured ones. To take into account the orientation effect for predicting tensile strength with Kelly and Tyson model [Eq. 6.6], we suggest considering the orientation coefficient in the same way as it was done for Young's modulus prediction. This results in 𝜎 𝑐 as follows:

𝜎 𝑐 = 𝜁 0 𝜁 𝐿 𝑓𝜎 𝑓 + (1 -𝑓)𝜎 𝑚 [Eq.6.12]
where 𝜁 0 is the orientation factor either denoted 𝜉 0𝑥 (Eq. 6.10) when sample is oriented along

x (α= 0 °) or denoted 𝜉 0𝑦 (Eq. 6.10) when sample is oriented along y (α= 90 °). To predict the critical length, we used the results obtained on fibre size analysis and for flax The calculated critical length (Table 6.3) is far higher than the fibre length in composites for the three fibre types, thus the second summation in equation 6.7 is not considered in our study.

Figure 6.16 a, b and c shows comparisons between the predicted and the measured tensile strengths as a function of fibre content for flax/PP, Tencel/PP and glass/PP, respectively. The tensile strength increases when the fibre content increases, and it is higher when sample axis (and stretching direction) is parallel to the main flow direction (x-direction) compared to the perpendicular (y-direction). The difference in strength between both directions x and y gets higher for glass composite over the other composites. For flax composites, while the predicted strength curve fits well the measured strength along x-direction with a small deviation at high fibre concentration, it is underestimated at α= 90 °, along y-direction. For Tencel composite, the predicted strength is underestimated for both x and y directions. One of the possible explanations is that Tencel fibres are flexible and can be curved, such as they can be easily interlocked and build network-like structure. A part of energy was probably dissipated to make them straight or to break this structure before rupture or pulling-out, which is not taken into account in the model of Kelly and Tyson. The effective fibre length can be shorter than it is really, which affects the predicted strength. For glass composites, strength in y-direction is well predicted by the Kelly and Tyson model. However, a deviation occurs at high concentration values such as the predicted strength is higher than the measured one. The most important reasons for the deviation in strength is the incertitude in the measured 𝜎 𝑓 that can widely vary as a function of fibre diameter, matrix properties and the presence or not of a compatibilizer. Since we have not used any compatibilizer in this study, adding MAPP to the formulation of composite can improve the obtained tensile strength.

Impact properties

Experimental results 2.2.1. Figure 6.17 shows the impact strength 𝑈 𝑐 as a function of fibre volume fraction, for the neat PP and flax, Tencel and glass composites. The impact strength slightly decreases for 3.6 and 6.3 vol % of fibres compared to the neat PP, and then increases from 13.1 to 20.5 vol %, for all types of fibres used. This increase rate and the values at the highest fibre concentration is the highest for Tencel followed by glass and then by flax based composites. The decrease of reinforced polypropylene impact strength for 3.6 and 6.3 vol % can be explained by a large spacing among fibres, which probably causes an easy crack propagation. Lhymn and Schultz (1982) studied the crack morphology in injection moulded glass/PET (Polyethylene terephthalate) and demonstrated that crack path takes an irregular zig-zag shape propagating along the easiest and the weakest way around the main crack direction. Moreover, the crack tip progresses within composite by the connectivity between several discrete micro-cracks at the ends of fibres. As mentioned in Chapter 4, up to 6.3 vol % Chapter 5 fibre-fibre interactions become larger and a network-like structure starts to take place, and thus may push cooperative obstacles against the crack propagation, leading to higher impact strength. This is the main plausible reason explaining that Tencel composite shows the highest impact strength at high concentration over glass and flax composites (Figure 6.17).

Figure 6.17

Impact strength of flax/PP, Tencel/PP and glass/PP, as a function of the fibre content. Lines are given to guide the eye This impact strength depends also on the fibre orientation in the tested bar. [START_REF] Clemons | Impact toughness of cellulose-fiber reinforced polypropylene: influence of microstructure in laminates and injection molded composites[END_REF] showed that fibres perpendicular to the crack direction enable higher impact strength.

In our case, the impact samples were moulded separately and not cut from the moulded box as the way for tensile samples. The sample dimensions required for testing in agreement with the standard norms were not compatible with the dimensions of the box. The flow direction in the impact bar is perpendicular to the notch direction. By analogy to the microstructure in the box, a considerable part of fibres should be aligned along the flow direction, and thus perpendicular to the crack direction.

Basically, three rupture modes are possible, matrix fracture, fibre pull-out or debonding and fibre fracture, according to [START_REF] Cottrell | Strong solids[END_REF]. The pull-out turned out the dominant rupture mechanism for short fibre reinforced polymer [START_REF] Cottrell | Strong solids[END_REF], [START_REF] Cooper | The fracture toughness of composites reinforced with weakened fibres[END_REF], Lhymn and Schultz (1982)]. To have a better understanding of the impact strength results, the rupture surfaces of 20.5 vol % composites were observed by SEM. Figure 6.18. a and c shows that the flax and glass fibres were debonded at the matrix-fibre interface (marks of fibres' tearing in the matrix), while some fibres were pulled out (black voids and empty space) and some others remain glued to the matrix. Figure 6.18.b shows that fracture can occur in the unsupported length of fibre. According to Lhymn and Schultz (1982), this is characteristically the result of fibre fatigue. 6.3). The debonding length 𝐿 𝑑 was determined by varying 𝐿 𝑑 in equation 6.9 to get the best fitting of the experimental curve. This results in 𝐿 𝑑 of 2.8 mm for flax, 6 mm for Tencel and 14 mm for glass fibre. According to Thomason and Vlug (1996), the debonding length obtained by fitting glass/PP composites varies between 8.7-18.2 mm to give a good agreement with experimental data. Moreover, it turned out that 𝐿 𝑑 increases as the critical length 𝐿 𝑐 increases. However, this fitting lost its physical signification, since 𝐿 𝑑 is much higher the possible fibre length in injection moulding process. Therefore the obtained results must be interpreted as a quantitative manner. The The predicted values increase with the fibre concentration, as experimentally. The predicted tensile stiffness and strength fit well the experimental ones in y-direction. The prediction overestimates the tensile properties in x-direction (main flow direction). The highest deviation (about 20 %) was particularly obtained for the tensile and strength at high concentration, when tensile direction is parallel to the flow. The main reasons are that no compatibilizer was used to improve fibre-matrix adhesion, the incertitude in the measurement of the fibre strength 𝜎 𝑓 (particularly for flax fibres), the out-of-plane fibre orientation, the fibre bending and the skin fibre-free-layers. Most of these reasons were discussed in Chapter 4.

The investigation of composites' impact properties showed that Tencel based composites have the highest impact strength as compared to glass and flax reinforced composites. This was interpreted by the well-developed network structure of Tencel fibres due to their large number and flexibility that supposed to limit the crack propagation during failure. The experimental results were compared to the impact strength calculated according to Thomason and Vlug model as a function of fibre content. A considerable deviation occurs at low fibre content and becomes smaller by increasing fibre concentration; this is true overall studied composites.

As already mentioned in the previous chapters, flax based composites are the most complex ones to be analysed. The complexity is related to the flax fibre morphology (bundles or fibres, various composition, flexibility, length and diameter) that leads to deviations between the theoretically predicted values and those experimentally obtained. Filling stage is the most comprehensively studied stage of injection moulding process [Papathanasiou and Guel (1997)]. The relevant feature of the mould filling is the existence of an advancing front. The filling stage has a great influence on the final properties of moulded fibrereinforced thermoplastics because, as seen in Chapter 4, fibre orientation is dependent on the flow within the cavity.

Computation of injection moulding

The use of computational techniques for analysing the flow during mould filling started in the 1970s with Kamal and Kenig (1972 a,b) and [START_REF] Kuo | The fluid mechanics and heat transfer of injection mold filling of thermoplastic materials[END_REF]. The level of sophistication increased in 1980s [START_REF] Hieber | A finite-element/finite-difference simulation of the injection-molding filling process[END_REF][START_REF] Hieber | Filling thin cavities of variable gap thickness: A numerical and experimental investigation[END_REF]] with the incorporation of the finite element method to solve the Hele Shaw equations for thin gap geometry with a viscous non-Newtonian behaviour law. [START_REF] Shen | Simulation of polymeric flows in the injection moulding process[END_REF] introduced the energy equation to compute the heat transfer in the mould cavity. The consideration of viscoelasticity and fountain flow were introduced by [START_REF] Kamal | Computer simulation of injection mold filling for viscoelastic melts with fountain flow[END_REF] and [START_REF] Mavridis | The effect of fountain flow on molecular orientation in injection molding[END_REF]. The coupling between filling and Further studies were performed in the two past decades to optimise the computation time by implementing sophisticated techniques. Most of today's simulation software are founded on the Hele-Shaw approach [Papathanasiou and Guell (1997)]. The reason is that injection moulded parts classically present a thickness smaller than other dimensions and there are no sudden variations of thickness, which is in agreement with Hele-Shaw assumptions. The approach of Hele-Shaw mainly consists of coupling a pressure equation to an energy equation through a temperature-dependent viscosity that can be the Arrhenius or the Williams-Landel-Ferry functions. The energy equation represents the heat convection due to the melt advancement, the heat conduction (due to the difference of temperature between cavity walls and the melt) and viscous dissipation. [START_REF] Manzione | Applications of computer aided engineering in injection molding[END_REF] coupled the flow and heat transfer analysis in the cavity, the heat transfer in the mould and included the cooling channels influence. If such coupling is not possible, the boundary condition at the polymer-mould surface can be either a constant wall temperature or a heat transfer coefficient.

Experimental pressure and comparison with simulation

Few works in literature have dealt with the pressure evolution in the mould cavity. Moreover, most of the studied cases used an unreinforced polymer material. In the following, we will focus on the results that concern the neat polypropylene, because it is the polymer matrix used in the present study. Two examples of polypropylene studies, Chiang et al. (1991) and [START_REF] Han | Compressible flow analysis of filling and postfilling in injection molding with phase-change effect[END_REF], will be presented. All conditions of injection moulding are regrouped in Table 7.1. The filling phase simulation of the sprue-centre gated-box (the moulded part in this study) was performed by [START_REF] Agassant | La mise en forme des matières plastiques[END_REF]. Figure 7.7 shows the pressure isovalues in the box filling. The top side fills to some extent the big lateral sides and then the smaller lateral ones. Isovalues of pressure at different filling times (t 1 , t 2 , t 3 and t 4 ) of the sprue-centre gated-box [START_REF] Agassant | La mise en forme des matières plastiques[END_REF]] , Ω and 𝜺̇ are vorticity and rate of deformation tensors, respectively.

Jeffery's analysis is only valid for rigid fibres in a dilute regime. To take into account fibrefibre interactions, [START_REF] Folgar | Orientation behavior of fibers in concentrated suspensions[END_REF] [START_REF] Doi | Molecular-dynamics and rheological properties of concentrated-solutions of rodlike polymers in isotropic and liquid-crystalline phases[END_REF], hybrid closure [START_REF] References Advani | The use of tensors to describe and predict fiber orientation in short fiber composites[END_REF] and Orthotropic closure approximation [START_REF] Cintra | Orthotropic closure approximations for flowinduced fiber orientation[END_REF]. More sophisticated approximations appeared after the latter one, and they are still a research area. New equations for the time evolution of a ij have appeared, bringing a better precision for the orientation field by a strain reduction factor and/or anisotropic fibre-fibre interactions [START_REF] Huynh | Improved fiber orientation predictions for injection-molded composites Jeffery[END_REF]; Chung and Kwon (2002 a,b); Sepehr et al. (2004 a,b,c); [START_REF] Wang | An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence[END_REF]; [START_REF] Férec | Modeling fiber interactions in semiconcentrated fiber suspensions[END_REF]]

Flexible fibres' models 1.4.2.

The individual flexible fibre is considered as an assembly of multiple rigid parts linked to each other. The most relevant models are the bead-chain model, needle-chain model and rodchain model. Yamamoto and Masyoka (1993;[START_REF] Yamamoto | Viscosity of dilute suspensions of rodlike particles: A numerical simulation method[END_REF] developed a bead-chain model for flexible fibre in dilute regime without hydrodynamic interactions. The flexible fibre is represented by a series of spheres lined up and bonded to each other (Figure 7.9). Yamamoto and Masyoka (1995;1996) modified their first model to take into account the hydrodynamic interactions. and Forgacs and Mason (1959) experimental results for flexible fibres. However, this model did not take into account the hydrodynamic interactions, and it is limited to the dilute regime. [START_REF] Schmid | Simulations of fiber flocculation: Effects of fiber properties and interfiber friction[END_REF] introduced the notions of the irregular fibre equilibrium and the frictional fibre interactions into the needle chain model to develop a model called the particle-level model. Further improvements in this model were carried out by Switzer (2002) to well describe the relationship between fibre properties, fibre interactions and rheological properties under a simple shear flow.

Examples of simulation and comparison with experiment

The modelling of flexible fibre suspensions has not reached the level of rigid fibre suspensions. Most of the results related to flexible fibres' models have dealt with a dilute regime system. The prediction of the orientation of rigid fibres has been well developed, considering the important progress in modelling and the wide experimental studies of glass fibre-based composites. First, we will focus on Bay and Tucker (1992) study, using a modified Jeffry model, taking into account the coefficient of interaction of Folgar and Tucker (Eqs.7.2 and 7.3), without any optimisation for slowing the kinetics of fibre orientation or fibres interactions; this is the same model used in Rem3D ® software used in this study.

Second, we will present three main results using improved models that slow down the fibre orientation to closely match the experimental orientation: 1) strain reduction factor (SRF) [START_REF] Huynh | Improved fiber orientation predictions for injection-molded composites Jeffery[END_REF], Wang (2007)] 2) reducing strain closure (RSC) [START_REF] Wang | An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence[END_REF]], and 3) anisotropic rotary diffusion (ARD) [Phelps and Tucker (2009)]. Bay and Tucker (1992) investigated the fibre orientation in two different injection-moulded parts (film gated strip and a centre gated disk). The composite material was 43 wt % glass/Nylon 6-6. The authors performed a comparison between the measured fibre orientation using the ellipses method (See Chapter 4) and the simulation results. Figure 7.12.a represents the predicted and the experimental orientation components (𝑎 𝑥𝑥 and 𝑎 𝑧𝑧 ) of the film-gated strip. x is the main flow direction and z is the direction perpendicular to the plaque plane. The value of 𝐶 𝐼 = 0.01 was chosen to fit the measurement. Γ was taken as 1[Eq. 7.1], meaning that the aspect ratio was considered as infinite. The inlet orientation (𝑎 𝑥𝑥 = 0.5, 𝑎 𝑦𝑦 = 0.2, 𝑎 𝑧𝑧 = 0.3 and 𝑎 𝑥𝑦 = 𝑎 𝑥𝑦 = 𝑎 𝑥𝑦 = 0) that is the initial condition for the fibre orientation equation resolution was determined by experimental measurements near the gate. The computed orientation shows a typical core-shell structure that fits the experimental ones. According to the authors, the surprising rise in the predicted 𝑎 𝑥𝑥 at the surface is an artefact of the calculation related to the fountain flow calculation. For a further position from the gate (40.4 times the disk thickness), a considerable deviation turned out between the predicted and the experimental orientation. The predicted 𝑎 𝑥𝑥 at the core is much lower than the experimental one. The core, measured in experiment, gets larger compared to the position near the gate and there is preferred orientation somewhere between the shell and the core layers, which is also not well predicted by simulation. According to the authors, this is due to the circumferential stretching dominating the flow in the disk. Bay and Tucker (1992) examined the sensitivity to the processing conditions for the same glass fibre-reinforced polyamide 6-6 in the disk mould. The obtained results showed that varying the wall temperature from 337 to 357 K and the inlet temperature from 540 to 560 K has a slight influence on the fibre orientation. The variation of the filling time controls to some extent the thickness and the orientation of each layer across the disk thickness. For example, a short filling time prevents the appearance of a skin layer (layer between shell layer and wall) and a long filling time enables a more aligned core.

𝒂 𝒙𝒙 𝒂 𝒛𝒛 𝒂 𝒙𝒙 -predicted 𝒂 𝒛𝒛 -predicted

Surface

Core Surface b found that increasing this coefficient leads to move orientation towards random-in-space and to increase the thickness of the shell layer. Decreasing 𝐶 𝐼 makes the fibres in core more aligned perpendicular to the flow and in the shell more aligned parallel to the flow direction.

Finally the authors highlighted that the deviation in the prediction occurs at the transition between core and shell. They argued this deviation by the closure approximation used in the model. The effect of the closure approximation is to overestimate the out-of-plane orientation (greater 𝑎 𝑧𝑧 and 𝑎 𝑥𝑧 than expected), which results in thinner core and thicker shell as compared to experiment. In their study, Bay and Tucker (1992) used a hybrid closure approximation. A closure approximation that provides a smaller out-of-plane-orientation would give a better agreement between simulation and experiments.

Wang ( 2007) investigated the fibre orientation as the same geometries to Bay and Tucker (1992) (film gated strip and a centre gated disk) for 30 wt % glass/PBT (polybutylene terephtalate). Figure 7.13 shows that the improved Folgar and Tucker model including the strain reduction factor [START_REF] Huynh | Improved fiber orientation predictions for injection-molded composites Jeffery[END_REF]] fits better the experimental orientation than the original Folgar and Tucker model. However, a deviation is still remained at the core. According to Phelps and Tucker (2009), these errors could mainly come from differences of the melt temperature.

Conclusions

The state of the art presented in this section copes with the simulation of the pressure during injection moulding and the orientation of fibres in the cavity. Some studies that handled the 𝒂 𝒙𝒙

Surface Core

Surface computation of the pressure in the filling and the post filling stages were presented. While the predicted pressure in the filling stage is close to experimental results, some deviations were noted in the post filling stages. Moreover, the investigations were limited to unfilled thermoplastics and no studies have yet emerged in literature to assess the pressure for fibrereinforced thermoplastics. The main models classically used to compute the rigid and the flexible fibre orientation were briefly presented. Rigid fibres' models are well optimized, but more works must be done to improve the flexible fibres models. This is due to the complexity of the equations that describe the flexible fibres' orientation and calculation issues when moved from dilute regime to semi-dilute and concentrated regimes (fibre bending, fibre interactions…). Natural fibres contain elementary flexible fibres and rigid bundles. Therefore, computing the flexible fibres orientation is in our interest, but no further investigation is performed in this study, considering the lack of today's numerical tools to simulate such complex materials. The optimization of flexible fibres' models must be separately studied.

We thus focused on the literature of the rigid fibres' models, which provides glass fibres orientation results in injection moulded parts, and they can be compared with experiments.

The predicted results give a shell-core structure similar to the experimental one. Many factors can influence the computed orientation such as rheological and heat transfer data, the closure approximation and the interaction coefficient. Inaccuracies of these factors can probably cause some errors in the prediction.

Results and discussions

Experimental Pressures

The aim of this section is to understand the effect of fibre concentration and fibre type on the measured pressures. Neat PP and all the studied composites were moulded in the same conditions (summarized in Chapter 2). The experiments were repeated until reaching a stable thermal regime. The three last trials were then recorded. The range of variation in the measured pressure is around +/-10 %. We filtered the parasitic signals and averaged the measurements to get smooth pressure curves suitable for investigations.

Influence of the location of pressure measurement 2.1.1.

The mould is equipped with three transducers located at different sites within the cavity.

Transducer 1 is close to the gate, transducers 2 and 3 are placed at the end of the box top-side and at the small lateral side, respectively (Figure 7.15). At the switch-over point, (from filling with speed control to packing with pressure control, around 0.7 s) there is a sharp increase of pressure. After the pressure overshoot, the transducer 1 shows a plateau-like curve between 1.6 and 4.2 s. Then, the pressure falls rapidly down. In fact, around 4.2 s, the polymer is solidified somewhere between the cavity entrance and the transducer. The polymer around the transducer does not feel anymore the pressure imposed by the machine; and as it cools down, it shrinks and applies less stress on the transducer. The solidification will occur first around the thinnest area of the cavity that is located on the top box side. An order of magnitude of the cooling time is generally given by e 2 /a, where "e" is the half thickness (here 0.9 mm) and "a" the thermal diffusivity (of the order of 10 -7 m 2 /s for a polymer), leading to an estimate of 8 s.

After the switch-over point, the P2 presents a "decreasing plateau-like" answer and falls down 1 s earlier than P1. P3 shows a direct pressure drop 3 s earlier than P2. The reason is that the melt solidification occurs earlier as far as the entrance is (more polymer cooling due to a longer path and less influence of new hot material coming up during the packing stage).

While an important pressure drop occurs from P1 to P2, only a slight loss of pressure can be noted between P2 and P3. for 13.1 vol % and 4 s for 20.5 vol %. We can conclude that solidification occurs earlier when the fibre concentration increases.

Figure 7.17 The effect of the fibre type on the pressure will be interpreted in the next section. The level of the plateau during the packing stage (Fig. 7.19a) for the different composites is higher for 20.5 than 3.6 vol %. For each concentration, the composites rank as follows:

-at 3.6 vol % : Tencel < glass < flax -at 20.5 vol % : flax < glass < Tencel There is no direct correlation with the viscosity, which means that the packing pressure is not only proportional to the viscosity. The simulation was performed with the Rem3D ® package, using a classical mixed finite element method with a decoupled approach. Three problems were solved: and the specific heat "𝐶 𝑝 " of polypropylene used to set up the simulation are 0.25 W.m -1 .°C -1 and 1500 J.kg -1 .K -1 [START_REF] Weidenfeller | Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene[END_REF]], respectively. The thermal conductivity of composites was calculated with mixture law-type equations as follows:

𝑘 𝑐 = 𝑓𝑘 𝑓 + (1 -𝑓)𝑘 𝑚 [Eq. 7.4]
where 𝑓 is the fibre volume fraction, and 𝑘 𝑐 , 𝑘 𝑓 and 𝑘 𝑚 are the thermal conductivity of composite, fibres and matrix, respectively. Other models for 𝑘 𝑐 that contain factors taking into account the fibre orientation were presented in the literature [START_REF] Landel | Mechanical properties of polymers and composites[END_REF], Sanou et al. (1985), [START_REF] Papathanasiou | Stiffness enhancement in aligned, short-fibre composites: a computational and experimental investigation[END_REF]]. Since fibre orientation varies across the moulded part thickness, the investigation of the influence of each model on the predicted results seems extremely complicated.

The specific heat of composites "(𝐶 𝑝 ) 𝑐 " and the density "𝜌 𝑐 " were also calculated by a mixture law-type, as the same manner of 𝑘 𝑐 , considering that (𝐶 𝑝 ) 𝑓 and 𝜌 𝑓 are the specific heat and the density of fibres, respectively and "(𝐶 𝑝 ) 𝑚 and 𝜌 𝑚 are those of the matrix. The thermal conductivity 𝑘 𝑓 and the specific heat 𝐻 𝑓 of glass fibres are 1.2 W.m -1 .K -1 and 800 J.kg -1 .K -1 , respectively according to [START_REF] Weidenfeller | Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene[END_REF], and those of flax fibres are 1.2 W.m -1 .K -1 and 800 J.kg -1 .K -1 respectively according to [START_REF] Li | Thermal diffusivity, thermal conductivity, and specific heat of flax fiber-HDPE biocomposites at processing temperatures[END_REF]. We assume that Tencel fibres present nearly the same properties as flax fibres, considering Tencel as a regenerated cellulose mainly based on cellulose and flax based on more than circa 70 % of cellulose. We assume also that all studied materials are incompressible, thus the density remains constant during the filling stage.

The fibres aspect ratios experimentally calculated after injection for each fibre concentration (Chapter 3) were used for the filling stage simulation. The inlet orientation was random in space, meaning that ((𝑎 𝑥𝑥 = 𝑎 𝑦𝑦 = 𝑎 𝑧𝑧 = 1/3 and 𝑎 𝑥𝑦 = 𝑎 𝑥𝑦 = 𝑎 𝑥𝑦 = 0). We used an injection temperature of 190 °C (temperature of the last barrel heating rings) and a flow rate of 92.3 cm 3 /s, as in experiment. In order to estimate the wall temperature, a sensor was located at 2 cm from the cavity wall. The measured temperaturevaries between 40 and 60 °C. Considering the distance separating the cavity from the measurement point, the temperature at the cavity wall should be higher than that measured by sensor. We decided to use a wall temperature of 70 °C. This temperature is may be not accurate enough; therefore additional tests were performed concerning the effect of the wall temperature together with the composite thermal conductivity on the predicted pressure and fibre orientation. This will be shown throughout the predicted results obtained on the following.Table 7.2 summarises all the material input parameters used for simulating the filling stage In this section, we will primarily analyse the pressure during the filling stage for the neat polypropylene and compare with the experimental results. Second, we will present the filling stage pressure and the induced fibre orientation in composites. A comparison with the experimental results will be also discussed. We are going to focus on the pressure (P1) to analyse the predicted results and to compare with experiment. Figure 7.23 shows a comparison between the predicted and the experimental pressure P1 during the filling stage. Considering the error due to the experiment repeatability (20 %), the prediction fits the experimental pressure except in the filling start-up where a deviation can be noticed. The overshoot in the experimental curve is due to the packing coming after the filling stage.

The neat polypropylene

 Cavity filling

 Thermal sensitivity

Studying the thermal sensitivity can indicate errors in the input data, which might be responsible for the disagreement between predictions and experiments. The value of the thermal conductivity of polypropylene used in Rem3D ® was taken from literature [START_REF] Weidenfeller | Thermal conductivity, thermal diffusivity, and specific heat capacity of particle filled polypropylene[END_REF]] and no characterization was performed to assess its accurate value. Moreover, assuming that the cavity-wall temperature is constant (70 °C) overall the cavity is may be not precise enough to reach a well agreement with experiment. Therefore, the influence of the thermal conductivity and the wall temperature must be examined. Figures 7.24 and 7.25 show the influence of the thermal conductivity "k" and the wall temperature "T wall " on the pressure of transducer P1 for the neat polypropylene, respectively. All other variables were left unchanged as in Table 7.2. The predicted pressure is higher as "k" The influence of wall temperature "T wall " on the predicted pressure (P1) for a k= 0.25 W/m.°C and comparison with the experimental pressure

Composites

 Pressure Figures 7.26,7.27 and 7.28 show comparisons between the experimental and the predicted pressures (P1) during the filling stage, for different concentrations of Tencel, flax and glass based composites, respectively. For flax composites and to a lesser extent for glass composites the agreement is correct. Numerical results overestimate the pressure for Tencel composites especially at 20.5 vol %. For most cases, the computation overestimates the pressure at the beginning, as was observed for the neat polypropylene. The pressure at the end is correctly predicted. The increase of pressure with the fibre content is in agreement with the measurements.

The prediction of pressure is more complicated for composites than for unreinforced polymers. Flow induced microstructure affects the thermal conductivity and the rheology.

This microstructure changes through time, but it is usually accounted on average (rheology for a given orientation in the rheometers, mixing law for the thermal conductivity). Concerning moulding experiments, there are some difficulties such as material expulsion when the nozzle of the injection unit is not in contact with the mould and even if all precautions have been taken, some material thermal degradation cannot be avoided.  Fibre orientation Orientation model in Rem3D ® is basically made to predict the orientation of rigid fibres.

Therefore, we are going first to focus on the case of glass fibres (rigid fibres) to analyse the fibre orientation in the box after filling. We will secondly compare with the experimental results and investigate those predicted for flax and Tencel based composites. Considering the lack of orientation models taking into account the properties of natural fibres, the aim here is to estimate the precision that can be expected from a rigid fibre model. unchanged by increasing the fibre content. The core orientation for 3.6 to 13.1 vol % is mostly along the flow direction (𝑎 𝑥𝑥 around 0.7-0.8), whereas for 20.5 vol %, it becomes strongly perpendicular to the flow direction (𝑎 𝑥𝑥 around 0.2). Some studies in the literature [START_REF] Spahr | Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites[END_REF]; [START_REF] Bouti | Injection molding of glass flake reinforced polypropylene: flake orientation and stiffness[END_REF]] concluded that increasing fibre content results in a thicker core that is highly oriented perpendicular to the main flow direction, which is in agreement with our results. We have seen earlier that the thermal boundary condition has a great influence on the pressure involved during filling. We also checked its influence on the fibre orientation state across thickness. Figures 7.33 and 7.34 show the experimental and the predicted 𝑎 𝑥𝑥 for 20.5 vol % glass/PP obtained by different thermal conductivities "k" and wall temperatures T wall , respectively. All other variables left unchanged with respect to standard conditions in Table 7.2. We can conclude that increasing k and decreasing T wall lead to move the core orientation from well aligned perpendicular to x-direction to randomly oriented in xy-plane. This is probably related to the respective sizes of the fluid core and solidified layer near the mould walls (although there is no real solidification criteria in Rem3D, the velocity is almost zero near the walls because of the low temperature and high viscosity, mimicking the solidified layer). The shear rate (responsible for the flow direction orientation at the surface) and the elongational rate (due to the central position of the sprue, responsible for the orientation perpendicular to the flow direction in the core) repartitions are dependent on the solidified layers. Other factors can explain the differences between experiments and computation. The first one concerns the interaction coefficient 𝐶 𝐼 (Eq.7.2). According to [START_REF] Folgar | Orientation behavior of fibers in concentrated suspensions[END_REF] and Bay and Tucker (1992), 𝐶 𝐼 is usually found by fitting predictions to experiments. However, varying only 𝐶 𝐼 would not enable to fit our experimental results. Generally, decreasing 𝐶 𝐼 leads to higher fibre alignment in both shell and core layers [Bay and Tucker (1992)]. The second factor that may explain the prediction error is the closure approximation used in the simulation. The effect of an inappropriate closure approximation is to overestimate the out-ofplane fibres (fibres that make angle to xy-plane), leading to a shell layer too thick and a core too thin. Rem3D ® uses the simple quadratic closure approximation. A better closure approximation such as the hybrid one [START_REF] References Advani | The use of tensors to describe and predict fiber orientation in short fiber composites[END_REF]] could improve the precision of the prediction. Nevertheless, by using improved models of orientation (RSC and ARD, see section 1.5), Phelps and Tucker (2009) found that the core alignment is not well The material data for the simulation are that presented in Table 7.2. The orientation state predicted for Tencel composite is extremely different from the experimental one. This was expected due to the high flexibility of Tencel fibres, considering that Rem3D ® is basically dedicated to rigid fibres. The experimental error can also be an important reason behind this deviation, since we have approximated fibre orientation by the end-to-end vector. We can thus conclude that Rem3D ® does not represent the real behaviour of Tencel fibres. For flax (almost rigid fibres) based composites, the predicted 𝑎 𝑥𝑥 is broadly consistent with the major trends of the shell-core structure. Some experimental points were closely predicted (z= 100 µm and z= 800 µm), but for some other deviations exist, particularly in the shell/core transition. By adjusting the simulation with accurate thermal parameters, the prediction could closely fit experiment. Moreover, considering that flax fibres contain bundles, the number of fibres is smaller as compared to glass fibres (individual fibres) for the same aspect ratio and concentration, which limits the fibre-fibre interactions. Therefore a better evaluation of the interaction coefficient 𝐶 𝐼 can bring more accuracy to the predicted orientation for flax fibre composites.

Conclusions

In this chapter we have investigated the pressure and the fibre orientation predicted by simulation of the injection moulding of glass, flax and Tencel reinforced polypropylene and compared with those experimentally obtained. We found a strong correlation between the rheology of composite and the experimental pressure. The increase of viscosity, due to either the fibre concentration or the fibre aspect ratio/flexibility increase, leads to enhance the pressure in cavity. It turned out that pressure increase is of the same magnitude to the viscosity increase. The simulation of the filling stage overestimates the experimental pressure around the start-up of the pressure evolution. The difference reduces when the melt progresses into the cavity. This is for the neat polypropylene and overall the studied composites. Thermal boundary conditions parameters have a large influence on the predicted pressure.

Since the software Rem3D ® uses a computational model adapted to rigid fibres, we have

1-Influence of compounding and injection on fibre size distribution

The influences of compounding and injection moulding have revealed the dissimilarities in fibre breakage between glass, flax and Tencel fibres. Glass fibres, which are rigid rods, are submitted to large breakage during compounding and an additional slight breakage during injection moulding. For Tencel fibres, which are individual and flexible, their length after processing is shortened by 30 % and fibres break more with the increase of fibre content. For flax fibres, both length and diameter are reduced during processing, but the resulting aspect ratio remains almost unchanged when compared to its initial value. Some bundles persist even after injection moulding, giving an aspect ratio lower than those of glass and Tencel fibres, despite that the length of flax fibres is higher than that of Tencel. This bundle's structure is a specific feature of a typical natural fibre, which leads to a different rupture mechanism during processing compared to glass fibres.

2-Microstructure of Tencel and flax composites

A novel experimental approach has been developed to study in details the microstructure of the injection moulded flax and Tencel reinforced polypropylene. Cross-sections parallel to the part plane (xy-plane) were analysed by optical microscopy in reflection mode and image analysis for several levels in the thickness.

Depending on their apparent shapes, fibres were classified into four categories: straight, Cshaped, S-shaped and short particles or out-of-plane fibres. We demonstrated that because of flexibility difference between flax and Tencel (flexibility being proportional to aspect ratio over Young's modulus), Tencel fibres can be bent in two conformations: C-shaped and Sshaped, whereas elementary flax fibres are bent only in C-shaped conformation. We showed that as in glass fibres based composites, flax and Tencel composites generally show a coreshell structure where fibres are aligned along the main flow direction near the surface and perpendicular to it in the core.

Some differences between flax and Tencel fibres in terms of the spatial distribution and bending conformation were identified. The number of Tencel fibres is three times larger than that of flax for the same volume concentration. This was explained by the presence of bundles in flax containing several elementary fibres "glued together" that remained after processing.

Moreover, as for glass fibres, the concentration of flax increases from surface to core, while

Tencel concentration is practically independent on thickness.

3-Composite rheological properties

The dynamic rheological measurements have shown that the increase of fibre content and flexibility (case of Tencel) lead to enhanced complex viscosity and viscous and elastic

moduli. An apparent yield stress was recorded at low frequencies when fibre volume fraction reaches the concentrated regime. This is due to fibre-fibre interactions which become more pronounced as the fibre content increases, and they are further increased when fibre flexibility increases. For the same volume fraction, because of the larger number of fibres and their high flexibility, Tencel-based composites show a viscosity and an apparent yield stress that are moderately higher than those of the glass based composites and further higher than of the flax ones.

The influence of temperature on composite viscosity was analysed using Arrhenius law, enabling the calculation of composite activation energy. For the three types of composites, the activation energy increases as the fibre content increases. Adding fibres to polypropylene seems to increase composite "resistance" to flow. Tencel composites exhibit higher activation energy compared to flax and glass ones. We suggest that additional restrictions of polymer chains motion may be caused by the strong network-like structure of flexible fibres. The superposition dynamic/capillary rheology obeyed the Cox-Merz approximation. The overall curves including dynamic and capillary measurement were fitted with the yield stress Carreau-Yasuda model. The obtained data, which give the viscosity evolution throughout a large range of shear rate, are important input for the simulation of the pressure during injection and of the fibre orientation within the filling stage.

4-Composite tensile properties

The influence of the microstructure on composite tensile properties was investigated by testing specimen cut-out in the moulded part at different angles with respect to the main flow direction. Samples aligned with the main flow direction exhibit larger tensile performance compared to those oriented at 45° and 90°, for all studied composites. All glass-based composites with different fibre concentrations are stiffer and stronger compared to flax and Tencel composites. Tencel composites show higher elongation at break compared to glass and flax. Cox-Krenchel and Kelly-Tyson models were used to analyse composites tensile stiffness and strength using orientation factors that were calculated on the basis of experimentally obtained fibre orientation. Some deviations occurs when predicting the tensile properties along the main flow direction, which were associated to the inaccuracy of the fibre strength values, the out-of-plane fibre orientation, the fibre bending and the skin fibre-free-layers.

5-Composite impact properties

The investigation of composites' impact properties showed that Tencel based composites have the highest impact strength compared to glass and flax reinforced composites. This was interpreted by the well-developed network of Tencel fibres because of their largest number and flexibility. The analysis of the impact strength was performed using Thomason and Vlug model; it was demonstrated that the predicted impact strength fits well the experimental and high concentration but deviation occurs at low concentrations.

6-Analysis of pressure during injection: experiment vs model prediction

Pressure evolution during injection was measured and calculated using Rem3D ® software.

The experimental analysis of the pressure involved during the injection moulding cycle showed that higher melt viscosity (due to the increase in either fibre concentration or fibre aspect ratio or flexibility) increased the pressure in the cavity. The range of the pressure increase is close to that of viscosity when fibre content gets larger. The pressure during the filling stage, predicted with Rem3D ® software, matches experimental pressure with a deviation mostly at the start-up of the pressure evolution, for neat polypropylene and over all studied composites. This error is reduced when the melt progresses into the cavity for the neat polypropylene and for all the studied composites. The deviation was explained by the inaccuracy of the thermal parameters required for setting-up the calculations.

7-Fibre orientation: theoretical prediction vs experiment

The prediction of glass fibre orientation after filling performed with Rem3D ® fits well the experimental one, except in the core layer where the fibre alignment is overestimated. The errors were related to thermal conditions set-up in the model, but the orientation model itself may be questionable.

The prediction of the orientation of flax and Tencel fibres in the moulded part was carried out.

The goal was to examine if rigid fibres' model can predict the orientation of both types of

Prospects

Because this work is one of the first investigations of the microstructure of natural fibre reinforced composites and its correlation with composite processing and properties, a lot of points still need clarifications.

1. In our study a semi-automated method was used to quantify the microstructure across the thickness of the injection moulded part. Development of a fully automated image analysis of fibre size and orientation would enormously help in reducing this time-consuming experimental work. X-ray microtomography will be also a possibility, if applicable to fibres whose contrast regarding the matrix is low.

2. We demonstrated that cellulosic fibres are broken during compounding and injection moulding. Despite some progress in the understanding of the mechanisms of fibres breakage during processing (work in Cemef using rheo-optics), some questions remain opened. For example, till now, there is no clear answer on what is the main parameter controlling fibre rupture: is it specific mechanical energy, or cumulated strain, or a combination of both? Does it depend on fibre type and flexibility? These answers are needed to predict fibre sizes in the final composite. 4. The experiments that we conducted were with unique injection moulding conditions.

Nothing is known about their influence (flow rate, mould temperature, packing parameters) on the microstructure of natural fibre reinforced composites. These studies would open-up discussions and comparison with the results known for glass fibre based composites.

5. We performed the analysis of composites microstructure and structure-properties correlations for two types of fibres, flax and Tencel. This work should be extended to other types of cellulosic fibres. For example, the results obtained on Tencel should be checked on cotton fibres that are also based on pure cellulose and are flexible elementary fibres. The results obtained on flax should be checked on hemp or sisal that are similar to flax with semi-rigid elementary fibres and bundles.

6. To predict the orientation of natural fibres within an injected part we used Rem3D ® software that is developed for rigid fibres. We demonstrated that it does not work for Tencel fibres. Thus numerical modelling of microstructure during injection of composites based on fibres with different flexibility and different diameters is strongly needed, if willing to further develop natural fibre reinforced composites. This is not an easy task that should be undertaken step by step from simple to complex cases. Key-words: Natural fibres, composites, rheology, injection, microstructure, modelling.

Chapitre 6 :

 6 Propriétés mécaniques des composites L'influence de la microstructure sur les propriétés en traction des composites a été étudiée dans des éprouvettes prélevées dans les boites injectées, à différents angles par rapport à la direction principale d'écoulement. Les échantillons alignés avec cette direction présentent de meilleures propriétés en traction que ceux orientés à 45 ° et 90 ° pour tous les composites étudiés. Les composites à base de verre présentent un module d'Young et une résistance à la traction supérieurs aux composites à fibres de lin et de Tencel, et ce quel que soit la concentration en fibres. Les composites Tencel montrent un plus grand allongement à la rupture par rapport aux composites de verre et de lin. Les modèles de Cox-Krenchel et Kelly-Tyson ont été utilisés pour analyser la rigidité et la résistance à la traction, en utilisant des facteurs d'orientation améliorés et déterminés à partir des observations au Chapitre 4. Certains écarts se sont produits au niveau de la prédiction des propriétés de traction dans la direction principale d'écoulement. Ces écarts ont été associés à l'imprécision des valeurs de module de la fibre, à l'orientation des fibres hors plan, aux courbures des fibres et à la possibilité de présence d'une couche appauvrie en fibres vers la surface.

  October 2012 at the Centre for Material Forming (Cemef) of Mines ParisTech, in the frame of the Industrial Chair in Bioplastics. This Chair is co-financed by Mines ParisTech and five companies: Arkema, L'Oréal, Nestlé, PSA Peugeot Citroën and Schneider Electric. It is a 7years large research project that includes different research topics, supporting the development and applications of various materials based on biomass polymer (bioplastics, lignocellulose, polymer composites with natural fibres). A previous thesis on natural fibre based composites in the frame of this Chair investigated the behaviour and rupture mechanisms of cellulosic fibres during their compounding with a polymer matrix [Le Duc (2013)]. The present thesis continues this topic and focuses on studying and understanding of the properties of natural fibre based composites particularly when processed by injection moulding.

Flax

  fibres were supplied by Dehondt Technologies (France) as NATTEX roving which were harvested in 2010 from Drakkar variety (France). These rovings were cut to a length of 0.5 mm by the company Apply Carbon (France). After these transformations, fibres appear as a mixture of thin and rather flexible elementary fibres and thick rigid bundles composed of elementary fibres "glued" together (Figure2.1a). Bundles were partially separated during compounding (Figure2.1 b).

Figure

  Figure 2.1

Figure 2. 2

 2 Figure 2.2

Figure 2. 3

 3 Figure 2.3

  Figure 2.4.a). The screws can be adjustable depending on the particular configuration of each zone. Conveying elements are used in melting and conveying zones (Figure 2.4.b). They may have different pitches and spacing between flights. Mixing zone contains reverse flight screw elements or kneading elements for more intensive mixing (Figure 2.4.c and d).

  Figure 2.4

  Figure 2.5

Figure

  Figure 2.6

Figure

  Figure 2.7

Figure

  Figure 2.8

Figure

  Figure 2.9

Figure

  Figure 2.10 Injection molded box, all dimensions are in mm

  .11, the mixture is placed in a ball-flask immersed in an oil bath and gently stirred during 2h under 170 °C (see more details in ref. LeMoigne et al. (2011); LeDuc et al. (2011); Soccalingame et al. (2015)).

Figure

  Figure 2.11

  Figure 2.13

Figure

  Figure 2.14 A schematic representation of a sample cut from the injected box and polished as 6 layers in the flow xy-plane

Figure

  Figure 2.15

  Figure 2.16.a). After feeding (Figure 2.16.b), the material is first pre-sheared at a shear rate of 10 s -1 for 60 seconds (Figure 2.16.c). Then it is transferred in the bottom chamber and the central piston injects the polymer through the die (Figure 2.16.d, e and f).

Figure

  Figure. 2.16

Figure

  Figure 2.17

  Typical pressure curves for different speeds and different die length, example of 20.% vol % Tencel/PP composite.

  Figure 2.18

  Tensile trials were performed with Erichsen machine equipped by 2 kN transducer. The tensile specimens were cut out from the moulded box at the location (x = 70 mm, y = 0 mm) (0°, 45°, 90°) with respect to the flow direction x (Figure2.21). The aim is to investigate the influence of fibre orientation on tensile properties. The dimensions of "dog bone" samples were according NF ISO527-25B standard: 30 mm x 4 mm x 1.8 mm. The tests were performed on three samples of each formulation.

Figure

  Figure 2.21

Figure

  Figure 2.23

  [START_REF] Lafranche | Processingdependent microstructure of long glass fibre reinforced polyamide 6-6 injection moulding and related mechanical properties[END_REF] measured the evolution of glass fibre length along the injection molding screw, the non-return valve, nozzle and cavity. Almost 70 % of fibre breakage happens at the compression section of the screw. polystyrene) matrix for three extrusion-screw designs, and for different locations in the injection-moulded part (A, B and C) (Figure. 3.1.a). The composite was moulded with zero back pressure and low injection molding speed to avoid fibre breakage.

Figure 3 .

 3 1.b shows that whatever the screw design, L n decreases from the sprue to the end of the cavity.

Figure 3

 3 Figure 3.1

Figure 3 . 3 Rheo

 33 Figure 3.3

Figure 3 . 4

 34 Figure 3.4

  investigated the size of hemp fibres in PEA (co-polyesteramide) and PHBV (poly(3-hydroxybutyrate-co3hydroxyvalerate)) matrices after compounding and after injection moulding. Two types of hemp fibres differently extracted from the plants were studied: BIA (fibre degummed by the biological separation process) and DDA (fibres separated by the steam explosion process) with two different initial number-average lengths L n = 8 mm and L n = 15.2 mm and number-average diameters D n = 23 ± 6 µm and D n = 25 ± 8 µm, respectively. A particular screw configuration was used for each system and the moulded parts were shaped as tensile bars. The fibre length dramatically decreased: the residual L n in the moulded tensile bar was 530 µm for PEA/DDA hemp and 100 µm for PEA/BIA hemp.

Figure 3

 3 Figure 3.5

Figure 3 . 6

 36 Figure 3.6

Figure 3 . 7

 37 Figure 3.7

Figure 3 . 8

 38 Figure 3.8

Figure 3

 3 Figure 3.9

Figure 3 .

 3 Figure 3.10 shows the influence of fibre content on fibre length distribution after injection.

Figure 3 .

 3 Figure 3.10 Glass/PP composite: influence of fibre content on the fibre length distribution after injection

Figure 3 .

 3 Figure 3.11 shows a comparison between the length distribution of Tencel fibres as delivered, after compounding and after injection, for the volume fraction of 20.5 vol %. The length distributions after compounding and after injection are similar and no significant difference can be distinguished. Both distributions are slightly shifted to shorter lengths compared to the distribution of the initial fibres.

Figure 3 .

 3 Figure 3.11 The evolution of Tencel fibre length distribution at different processing steps in the composite for 20.5 vol % Tencel/PP

Figure 3 .

 3 Figure 3.12 Influence of fibre content on Tencel fibre length distribution after injection moulding

  Figure 3.13 The evolution of distributions of (a) fibre length, (b) fibre diameter and (c) aspect ratio, along processing for 20.5 vol % flax/PP

Figure 3 .

 3 Figure 3.14 Schematic representation of the degradation of flax fibres during processing

Figure 3 .

 3 Figure 3.15 a, b and c shows a comparison between length, diameter and aspect ratio distributions in composites with 20.5 vol % and 3.1 vol % of flax, respectively. Some long fibres (L n ≥ 740 µm) with low frequencies ~ 1 % disappear and the frequency of some short fibres (L n ≤ 300 µm) increases when concentration increases from 3.1 % vol. to 20.1 vol % ,

FlaxFigure 3 .

 3 Figure 3.15 Influence of fibre content on flax fibre (a) length (b) diameter and(c) fibre aspect ratio distributions after injection

Figure 3 .

 3 Figure 3.17 Evolution of flax D n with the fibre content; zero volume fraction corresponds to the initial fibres (unprocessed)

  Figure 3.18 a) (L/D) n evolution with the fibre content; zero volume fraction corresponds to the initial fibres (unprocessed) b) zoom of the figure (a) within the dashed rectangle

  fibres consists of investigating the volume fraction distribution in the injection-moulded part. The most used technique is to determine the density of composite across the thickness by grinding sample to an appropriate thickness. Reproducing this experiment in several locations in the injection-moulded part enables to map out the distribution of the fibre volume fraction all over this part.

Figure 4

 4

Figure 4 . 1

 41 Figure 4.1

Figure 4

 4 Figure 4.2

Figure 4 . 3 (

 43 Figure 4.3 (a) fibre cross-section perpendicular to xy-plane and (b) ellipses method for quantification of fibre orientation [Neves et al. (1998)]

  Figure 4.4

;Figure 4

 4 Figure 4.5

Figure 4

 4 Figure 4.8

Figure 4

 4 Figure 4.9

  , many researchers work on improving this technique and recently some progress have been made in the determination of the fibre length distribution[Alemdar et al. (2008),[START_REF] Joffre | X-ray micro-computed tomography investigation of fibre length degradation during the processing steps of shortfibre composites[END_REF]], but fibre orientation distribution in a wide region of observation with high resolution and 3D reconstruction, such as the glass fibre case, is not yet reached. Figure 4.11 presents two examples of a 3D reconstruction in µCT of wood fibre-and hemp fibre-reinforced polypropylene. Only qualitative observations were carried out and a statistical analysis of fibre orientation was not possible.

Figure 4

 4 Figure 4.11

  Figure 4.12

Figure 4

 4 Figure 4.13

  Fibres located very close to the surface (skin region) were submitted to the fountain flow ([Tadmor 1974], Figure 4.14). The complex flow with extensional deformations (but not only) leads to a random or slight orientation at the flow direction. This orientation state is rapidly frozen very close to the cold mould walls.

Figure 4

 4 Figure 4.14

Figure 4 .

 4 15 shows the ratio core thickness/part thickness that is plotted as a function of the volume fraction. The core thickness increases by increasing the fibre concentration and the fibre length.

Figure 4 .

 4 Figure 4.15

Figure 4 .

 4 Figure 4.16 shows the local volume fraction of glass fibres in shell and core layers as a function of the overall volume fraction. The core layer is denser than the shell one by increasing the fibre concentration. The difference in the local concentration induced by long and short fibres is higher at the core as compared to the shell, when the overall concentration increases.

Figure 4 .

 4 Figure 4.16

Figure 4

 4 Figure 4.17

  𝑓 𝑝 as function of overall volume fraction of long and short fibres[START_REF] Spahr | Microstructure and fracture behaviour of short and long fibre-reinforced polypropylene composites[END_REF]] Understanding which factors can influence dispersion and orientation of fibres is important to control the mechanical properties of the moulded part. The main key factors are the injection conditions such as the injection speed, the packing holding and cooling time, the geometry of cavity and the melt rheology. Many studies have investigated the influence of these factors on the alignment of fibres or the thickness of skin, shell and core layers. The results are summarized in Table4.1.ShellCoreTable 4.1 Factors influencing the orientation and dispersion of glass fibre in thermoplastic composites, GF means glass fibres

Figure 4

 4 Figure 4.18 Injection moulded plaque with locations of orientation; all dimensions are in mm [Aurich and Mennig (2001)]

Figure. 4

 4 Figure.4.19

Figure. 4

 4 Figure. 4.20

Figure 4 .

 4 21 shows 𝑎 𝑥𝑥 evolution across the thickness for different volume fractions. Starting from 10 % in depth from the surface, fibres become quite aligned in the main direction of flow ( 𝑎 𝑥𝑥 = 0.9) and keep the same orientation toward the core, except the highest fibre concentration of 22 vol % for which fibres are less aligned near the surface ( 𝑎 𝑥𝑥 = 0.6-0.7) and are rather randomly oriented ( 𝑎 𝑥𝑥 the moulding conditions and the shape of the gate, as mentioned in Table4.1.[START_REF] Lafranche | Prediction of tensile properties of injection moulding flax fibre reinforced polypropylene from morphology analysis[END_REF] investigated the orientation state with increasing fibre concentration, providing results from large number of analysed layers. Nevertheless, neither details about the method of fibre orientation measurement nor images of the cut surfaces were provided.

Figure 4 .

 4 Figure 4.21

Figure 4 .

 4 Figure 4.22 shows two cross sections in xz-plane and yz-plane of 20.5 vol % flax/PP. The location of both sections in injection-moulded box is presented in the same figure. The orientation of fibre changes across the thickness from surface to core. A core-shell structure similar to that observed for glass fibre composites is obtained. While fibres are aligned along x-direction close to surface in xz-plane, they are aligned along y-direction around the core in yz-plane. The magnified image shown in Figure 4.22 confirms that the cross section of flax fibre is irregular. The reason is that the majority of flax fibres consist of bundles in which elementary fibres are "glued" together in an asymmetrical way. The number of elementary fibres in a bundle varies from few to several tens, giving 3-4 elementary fibres per bundle on average (as measured in Chapter 3, section 2.3. Flax) and they are assembled in different ways.

Figure 4 .Figure 4 .

 44 Figure 4.22 Two cross sections in xz-and zy-planes and their positions in the injection-moulded box.

Figure 4

 4 Figure 4.23

Figure 4 .

 4 Figure 4.24

  Figure 4.21 but different observation plane).

Figure 4 .ZFigure 4

 44 Figure 4.25

Figure 4 .

 4 Figure 4.27 provides the flax fibre orientation state in xy-plane (at location shown in Figure 4.25: x = 70 mm, y = 0 mm) at six different levels across the thickness from z = 100 µm (~shell) to z= 900 µm (core). We remind here that observed surfaces have dimension of 5 x 5 mm², made by bringing 50 reflected optical microscopy images together into one cartography (see Chapter 2). Whereas fibres show a parallel orientation to x-axis in the shell region at z =

Figure 4 .

 4 28 shows a similar orientation state for Tencel fibres.

  Figure 4.27

Table 4 . 2 Figure 4 .

 424 Figure 4.30.a, b and c represents the distribution of flax, Tencel and glass fibres across the

  Figure 4.30 Distribution of the different categories of fibres (straight, C-shaped, S-shaped and particles/out-of-plane) for (a) flax, (b) Tencel and (c) glass across the thickness of sample. For glass fibres only one category (straight) is considered

  leave away more "dust" or small particles that decrease the amount of straight fibres obtained after breakage.The total number of Tencel fibres is almost three times greater than that of flax fibres(compare Figure 4.30.a and 4.30.b). This is also illustrated in Figure4.30 that compares two cross sections of flax and Tencel composites taken at the same position from sample surface, z = 400 µm.

Figure 4 .

 4 31 demonstrates that this difference is caused by the effect of bundles that are present in flax fibres even after processing. Furthermore, the total number of Tencel fibre remains almost constant across composite thickness, which seems different from glass case for which core contains more fibres. Tencel fibres may disobey the dispersion trends in the cavity because of their higher flexibility compared to flax and glass fibres. While around 50 % of Tencel fibres are straight (most of them have short aspect ratio), 30 % are particles/outof-plane and the rest are curved in which less than 4 % are S-shaped fibres. The latter category appears only in Tencel, which may be also caused by the high flexibility of these fibres. The number of C-shaped category of Tencel decreases almost twice from surface to core. The most probable reason is that a lower shear is produced at core as compared to surface, leading to less curved fibre at core.

Figure 4 . 3 .

 43 Figure 4.31 Comparison between flax (a) and Tencel (b) fibres dispersion (at the same location and position in thickness, z = 400 µm), number of Tencel fibres is much higher than that of flax which are partially structured in bundles

Figure 4 .

 4 Figure 4.32

  fibres(Figure 4.32.c). More details on the correlation between the morphology of fibres and composite viscosity will be provided in the next chapter.

Figure 4 .

 4 Figure 4.34

Figure 4 .

 4 Figure 4.34.a presents the evolution of 𝑎 𝑥𝑥 for straight and C-shaped flax fibres across thickness from surface to core. Both categories are well aligned along x-direction from z= 100µm to z= 200 µm (the shell layer) with 0.8 < 𝑎 𝑥𝑥 < 0.9, whereas their orientation from z= 400 µm to z= 900 µm is almost isotropic, showing 0.3 < 𝑎 𝑥𝑥 < 0.6.

Figure 4 .

 4 Figure 4.34.b shows the evolution of 𝑎 𝑥𝑥 of straight, C-shaped and S-shaped Tencel fibres across thickness from surface to core. The three categories are aligned to x-direction in the

Figure 4 .

 4 Figure 4.34

Figure 4 .

 4 Figure 4.35

Chapter 4 :Figure 4 .

 44 Figure 4.36 shows the number average of the apparent length and diameter of the straight fibres category of flax across the thickness. Flax apparent average length is almost constant (180-200 µm) along sample thickness. The apparent average diameter increases from 26 at z = 100 µm to 40 at z= 900 µm. Hence, the resultant aspect ratio decreases from 8.6 to 5.3 (not shown in Figure 4.36).

Figure 4 .

 4 Figure 4.36

Figure 4 .Figure 4 .

 44 Figure 4.37

Figure 4

 4 Figure 4.38

Figure 4 .

 4 Figure 4.39

  considerable studies of dynamic rheology of natural fibre-reinforced thermoplastics have emerged in literature. Twite-Kamamba et al. (2009) studied hempreinforced polypropylene, Le Moigne et al. (2013) flax-and sisal-reinforced polypropylene and Sojoudiasli et al. (2014) flax -reinforced polypropylene. All these studies showed that increasing fibre content leads to an important change in the rheological behaviour of composites. We are going to focus on the study of Le Moigne et al. (2013) to describe this change. Figure 5.1 shows the evolution of complex viscosity η* versus frequency 𝜔 for neat matrix with or without compatibilizer and two concentrations 20 wt % and 50 wt % of flax-reinforced polypropylene.

  ;[START_REF] Thomasset | Rheological properties of long glass fiber filled polypropylene[END_REF];[START_REF] Eberle | Rheology of non-Newtonian fluids containing glass fibers: A review of experimental literature[END_REF]].

Figure

  Figure 5.1

  ) and previously Twite-Kamamba et al. (2009) fitted the experimental curves with the modified Carreau-Yusuda model described by:

Figure 5

 5 Figure 5.3 shows that 𝜎 0 keeps gradually increasing with fibre content up to a critical concentration above which the increase becomes very steep. This critical concentration

Figure 5. 3

 3 Figure 5.3

Figure 5 .

 5 Figure 5.4 shows the log-log plot of apparent yield stress versus fibre volume fraction for three types of pulp fibre suspension (Semi-Bleached Kraft: SBK, Stone Ground Wood: SGW

Figure 5. 5 E

 5 Figure5.5 E a of coir/PP as function of fibre content[START_REF] Islam | Rheological behavior of coir-fiber-filled polypropylene composites at constant shear stress[END_REF]

Figure

  Figure 5.6

Polyacrylate,

  Figure 5.7

  Figures 5.10 and 5.11 show complex viscosity 𝜂 * and tan𝛿 = G"/G' as a function of frequency 𝜔 at 190 °C for the neat polypropylene and composites with 6.3 and 20.5 vol % of flax, Tencel and glass. The results obtained for other fibre concentration (3.1 vol % and 13.1 vol %) are not shown in order not to overload the graphs. Polypropylene shows a classical rheological behaviour with a Newtonian plateau at low frequencies and shear thinning at higher frequencies. The increase of fibre concentration leads to a viscosity rise and the disappearance of the Newtonian plateau, which is in agreement with literature Le Moigne et al. (2013)[START_REF] Sojoudiasli | Rheological, morphological and mechanical properties of flax fiber polypropylene composites: influence of compatibilizers[END_REF]

;

  [START_REF] Drozdov | The viscoelastic and viscoplastic behavior of polymer composites: polycarbonate reinforced with short glass fibers[END_REF];[START_REF] Mobuchon | Shear and extensional properties of short glass fiber reinforced polypropylene[END_REF];[START_REF] Guo | Rheology of fiber filled polymer melts: Role of fiber-fiber interactions and polymer-fiber coupling[END_REF]].

Figure

  Figure 5.11

Figure

  Figure 5.12 Elastic G' (a) and viscous (G") (b) moduli vs frequency at 190 °C for the neat PP and 6.3 and 20.5 vol % of fibres for Tencel/PP, flax/PP and glass/PP composites

Figure 5 .

 5 Figure 5.13 shows shear stress-frequency dependence of Tencel/PP, glass/PP and flax/PP at 190 °C for two fibre concentrations, 6.3 and 20.5 vol %. The shear stress is defined by s = G* × γ, where G* = × is the norm of complex modulus and γ is the strain. At the same fibre concentration, Tencel-based composites have higher shear stress than glass and flax based composites at low frequencies; however at high frequencies all curves merge together.

Figure 5

 5 Figure 5.13 Stress shear vs frequency of flax/PP and Tencel/PP composites with 6.3 and 20.5 vol % of fibres at 190 °C

Figure 5 .

 5 Figure 5.14 gives examples of calculation of s 0 of 20.5 vol % of Tencel, flax and glass composites, respectively

  Figure 5.15 Apparent yield stress evolution with fibre volume fraction for Tencel/PP,flax/PP and glass/PP composites at 180 and 200 °C; lines are power law approximations

Figure 5 .

 5 Figure 5.16 shows an example of complex viscosity-frequency dependence for the case of the neat polypropylene and 20.5 vol % flax and Tencel composite at different temperatures (180, 190 and 200 °C). Similar results were obtained for other fibre concentrations and for glass fibre based composite (not shown). As expected, viscosity decreases as temperature gets higher, for all studied systems. Master plots were built using time-temperature superposition principle and shift factors 𝑎 𝑇 for each composite were determined, as explained in Section 1.1.3 (Influence of temperature and activation energy). The examples for the neat PP and 20.5 vol % composites with flax/PP, Tencel/PP and glass/PP are shown in Figures 5.15 and 5.16.

Figure

  Figure 5.18

Figure 5 .

 5 Figure 5.19 shows the activation energy for all composites studied as a function of fibre concentration. E a increases with fibre content for all types of fibres. Below 5 vol %, the composites with different types of fibres show very similar activation energy. From 5 vol % to 13 vol % Tencel and flax based composites have similar evolutions, while E a of glass fibre composites shows a smaller increase. A steep increase in the activation energy for Tencel based composites occurs between 13 and 20.5 vol % while flax and glass based composites' activation energies are almost constant and very close. Our results are in agreement with the studies of[START_REF] Islam | Rheological behavior of coir-fiber-filled polypropylene composites at constant shear stress[END_REF] and[START_REF] Herrera | Development of natural fiber reinforced polylactide-based biocomposites[END_REF] showing that an increase of fibre

  D: fibre aspect ratio (L/D) w averaged in weight, (L/D) n : averaged in number -E f: fibre Young's modulus -N = Number of fibres per unit volume,: N w average in weight, N n : average in number -f(s-d/c) = volume fraction of the transition semi-dilute/concentrated regime -F: Flexibility [Eq 5.7], F n average in number, F w average in weight The second reason is that the transition from the semi-dilute to concentrated regime f(s-d/c) occurs at different concentrations depending on the type of fibre: f(s-d/c) (glass) < f(s-d/c) (Tencel) < f(s-d/c) (flax), due to the difference in (L/D) values (Table

Figure 5 .

 5 Figure5.20 shows a superposition of viscosity values obtained with capillary and dynamic rheology for neat PP and Tencel/PP composites for all studied concentrations,3.6, 6.3, 13.1

Figure 5 .

 5 Figure 5.22 shows SEM images of cross sections of Tencel, glass and flax fibre based composites with 20.5 vol %. Most glass fibres appear aligned in the flow direction. Most

Figure

  Figure 5.22

  Tencel/PP a f = 12,25 e-12,25f glass/PP a f = 10,89 e-11,89f flax/PP a f = 9,34 e -11

Figure

  Figure 6.2

  Figure 6.3

Figure

  Figure 6.4

  30 wt% Glass/PP CG: Core 30 wt% Glass/PP SF: Shell 21 wt% Flax/PP CF: Core 21 wt% Flax/PP

  Figure 6.5 shows a comparison among composites with several types of man-made fibres and jute; all of them were made with 25 wt % of fibres and 1 wt % of MAPP. Tencel/PP composites show the highest Young's modulus. All composites show reduced elongations at break compared to the neat polypropylene.

Figure

  Figure 6.5

  related to the fibre volume fraction 𝑓 as follows: . (1996) suggested 𝜒 𝑖 = 4 for glass fibre-reinforced polypropylene.

Figure

  Figure 6.6

Figure

  Figure 6.7

  Figure 6.8

  Figure 6.9

Figure

  Figure 6.13

Figure

  Figure 6.14

  provides orientation factors 𝜉 0𝑥 and 𝜉 0𝑦 in x-direction and y-direction,

Figure 6 .

 6 Figure 6.15. a, b and c shows a comparison between experimental and predicted Young's modulus with Cox and Krenchel model as a function of fibre content for flax/PP, Tencel/PP and glass/PP, respectively. For flax composites, while the predicted moduli in x-and ydirections matche well the measured ones until 13.1 vol %, a deviation occurs at 20.5 vol %.

  Figure 6.15

  /PP system without MAPP 𝜎 𝑓 = 980 MPa and 𝜏 =13 MPa [Van Den Oever and Bos (1998)]; for Tencel 𝜎 𝑓 = 570 MPa given by the manufacturer and 𝜏= 5 Pa measured by Adusumalli et al. (2006 a, b), and for glass 𝜎 𝑓 = 1818 MPa and 𝜏= 13 MPa according to Thomason and Vlug (1997). The calculated critical length L c , the fibre strength, the fibre-matrix interfacial shear strength τ and dimensions of fibres are shown at

  Figure 6.16

  get a longer way to progress prior the composite breakdown. Tencel composites exhibit a much larger number of flexible fibres as compared to glass and flax fibres, as demonstrated in Chapter 4 and 5. A more developed network of Tencel fibres creates

  Figure 6.18

  Figure 6.19

  injection moulding is an important tool for analysing the process parameters and optimizing the final properties of parts. The main outputs of simulation software that can be experimentally evaluated are the pressure in the mould cavity and the fibre orientation. In this chapter, we will first present a brief literature review about the common computational techniques used in simulation of injection moulding, some results known from literature related to the cavity pressure and the fibre orientation models of rigid and flexible fibres. Second, we will present the experimental pressure results obtained during the injection moulding for the neat and fibre-reinforced polypropylene. The effect of viscosity variation due to the fibre type and fibre concentration will be correlated with pressure results and discussed. Third, we will compare the experimental pressure and the fibre orientation results to those numerically obtained with Rem3D ® , the simulation software used in this study.Injection moulding is an intermittent cyclic process with three main stages: (1) filling, (2) packing and holding (3) cooling (Figure7.1). These stages can be observed by following the pressure in the cavity. Filling is the stage when the melt flows into an empty cavity whose walls are held at a temperature below the solidification one. Once the cavity is full, additional material is packed into the mould to counterbalance the shrinkage caused by cooling, and thus pressure increases sharply to a plateau maintained for some time. After holding/packing step, cooling stage occurs, enabling the ejection of the component and the decrease of pressure.

Figure 7. 1

 1 Figure 7.1 Pressure curve in the mould cavity showing the stages of a typical injection moulding cycle

  Chiang et al. (1991,b) investigated the filling and the post-filling pressure of polypropylene in a sprue-gated plaque. The pressure measurement was carried out by three transducers located in the cavity as shown in Figure7.2.

Figure 7. 2

 2 Figure 7.2

Figure 7. 3 aFigure 7 . 4 Filling

 374 Figure 7.3

Figure

  Figure 7.5

Figure

  Figure 7.7

  fibre orientation began with Jeffrey equation[START_REF] Jeffery | The motion of ellipsoidal particles immersed in a viscous fluid[END_REF]], considering a single ellipsoid of aspect ratio L/D (in fact Jeffery considered ellipsoids with three different axes, but we will restrain here the analysis to two different axes) immersed in a Newtonian fluid. The unit vector p is parallel to the major axis, as shown in Figure7.8. The orientation of 𝑝 is a function of two angles θ and ϕ.

Figure

  Figure 7.8

Figure

  Figure 7.9

Figure

  Figure 7.10

Figure

  Figure 7.11

  Figure 7.12

Figure 7. 13 Fibre

 13 Figure 7.13

Figure

  Figure 7.14

Figure

  Figure 7.15

Figure

  Figure 7.16

Figure 7 .

 7 Figure 7.17.a and b shows the evolution of the pressure (P1) throughout time for the neat polypropylene and Tencel composites with different concentrations. During the filling stage, the pressure increases as the fibre content gets larger (Fig. 7.17b). This is because of the viscosity increase when adding fibres, as discussed in Chapter 5. The level of the plateaus during the packing stage for the different composites is also correlated to the fibre content.The end of the plateau is around 5.7 s for the neat PP and 3.6 vol %, 5.3 s for 6.3 vol %, 4.7 s

  a) The overall injection pressure P1 vs time obtained (filling and post-filling stages) for different concentrations of Tencel/PP composite and the neat polypropylene b) Zoom on the pressure during the filling stage for the same materials of figure a. Similar trends were obtained for P2 and P3 with lower values of pressure and shorter time ranges of measurement with respect to P1, because of the pressure losses in between transducers. An example of P2 curve for Tencel composite is plotted in Figure 7.18. The based composites present a similar schematic fall of pressure (not shown).

Figure

  Figure 7.18

Figure 7 .

 7 Figure 7.19 shows a comparison between the pressure P1 for Tencel, glass and flax based composites with two different concentrations 3.6 vol % and 20.5 vol %. During the filling stage, the neat PP pressure is the lowest as compared to composites (Fig. 7.19.b). At 3.6 %, up to 0.6 s, the pressure of flax composite gets higher, but around the switch-over point, Tencel pressure becomes equivalent. At 20.5 vol %, flax composite pressure becomes the lowest and those of Tencel and glass composites are similar. Around the switch-over, Tencel composite pressure shows a sharper overshoot as compared to glass composite.

Figure

  Figure 7.19

Figure

  Figure 7.20

-

  Mechanical equations (velocity, stress…), assuming a Carreau-Yasuda behaviour law and incompressible material. The flow rate is imposed at the cavity entrance and a sticking contact is used along the mould cavity walls.-The energy equation, taking into account conduction, convection and viscous dissipation. The enthalpy of crystallization is neglected. The inlet temperature is given and the mould temperature is imposed at the wall.-Position of the flow front: the whole cavity domain (polymer and air during the filling stage) is meshed and the position of the flow front is represented with a level set method. The latter is used to evaluate the material characteristics to be considered (polymer or air).Additionally, the Folgar and Tucker equation (Eq. 7.3) is solved with a quadratic closure approximation. Rem3D ® software is developed for a fixed interaction coefficient 𝐶 𝐼 = 0.01.The geometry of the moulded box is symmetric with respect to both xz and yz planes. This enables to simulate the quarter of the box, leading to a considerable CPU time and memory reduction (Figure7.21). To compare with the experimental pressures three numerical transducers were placed throughout the box, as shown in Figure7.15.

Figure

  Figure 7.21

Figure 7 .

 7 Figure 7.22 shows the sequence of the box filling for the neat PP. The time needed to fill the entire box is 0.717 s. As the sprue is located in the centre of the box top-side (xy), the initial flow around the sprue is circumferential (Figure 7.22.a and b).The top side (xy) fills to some extent the large lateral side (zx) (Figure 7.22.c,d and f) that in turn feeds the small lateral side (yz) (Figure 7.22.h, g and i).

  Figure 7.23

  increases and "T wall "decreases, meaning that the prediction of the pressure during the filling stage is sensitive to the thermal boundary condition. While the range of deviation related to k and T wall change is closely equal to the experimental error range at the filling end, it is slight and has almost no effect on the filling start-up where the predicted results overestimate experiments. This error can be associated to the assumption that the melt temperature at the cavity entrance is constant and equal to the temperature imposed in the barrel surrounding the plasticisation unit. Viscous heating takes place due to the high shear rate in the nozzle of the injection moulding machine. Some other inaccuracies in the prediction by Rem3D ® software can also be caused by the ignorance of the kinetics of the crystallinity (which is also the case of most similar software).[START_REF] Pantani | Modeling of morphology evolution in the injection molding process of thermoplastic polymers[END_REF] demonstrated the important influence of crystallinity on the interpretation of pressure during the injection moulding of an isostatic polypropylene. According to the authors, an increase in crystallization during flow leads to a greater pressure involved. Many studies in literature have dealt with the prediction of the development of crystallinity during injection moulding process[START_REF] Manzione | Applications of computer aided engineering in injection molding[END_REF]; Lafleur and[START_REF] Kamal | Computer simulation of injection mold filling for viscoelastic melts with fountain flow[END_REF];[START_REF] Papathanasiou | Stiffness enhancement in aligned, short-fibre composites: a computational and experimental investigation[END_REF][START_REF] Hieber | Modeling/simulating the injection molding of isotactic polypropylene[END_REF]].

Figure

  Figure 7.24

Figure

  Figure 7.26

  Figure 7.29 maps out the predicted orientation component 𝑎 𝑥𝑥 in several cross sections in yzplane and xz-plane for the 20.5 vol % glass/PP. The xz-cross-section at y= 0 mm shows a core-shell structure. The core exhibits fibres well aligned to y-direction (blue area). They become progressively less aligned near the sprue. For xz-cross-section performed at y= 17.75 mm, in the core, fibres are aligned to x-direction, whereas near the surface fibres are randomly aligned (yellow and green areas). The yz-cross sections show that fibre alignment is different for y between 17.75 and y= 35.5 mm compared to y between 0 and y= 17.75 mm. compared to y between 0 and y= 17.75 mm.

Figure 7

 7 Figure 7.29

Figure 7. 30 Predicted

 30 Figure 7.30

  Figure 7.32

-

  Comparison with experimental resultsAs mentioned in Chapter 4, the characterization of the fibre orientation was conducted for 20.5 vol % composites at the location (x= 70 mm, y= 0 mm) for six different levels across thickness from z= 100 µm (near surface) to z= 900 µm (the mid-plane). The experimental characterization along z= 0-100 µm was not possible because the cross-section is obtained by polishing. At least a distance of 100 µm from surface is required to achieve a smooth surface of sample suitable for image processing investigation. We assume that fibre orientation is symmetric with respect to the mid-plane, thus the fibre orientation was not investigated from 900 µm to 1800 µm. Characterisation of the orientation state is essentially focused on flax and Tencel fibres. Only three levels across thickness were investigated for the glass based composite to reduce the extent of the experimental work. The predicted 𝑎 𝑥𝑥 for k= 0.7 W/m.°C (Figure7.33) or for T wall = 30 °C (Figure7.34) closely fit the experimental 𝑎 𝑥𝑥 carried out at (y= 0 mm, x= 70 mm). The standard boundary conditions used for simulation in Table7.2 (k= 0.444 W/m.°C and T wall = 70 °C) overestimates the core alignment (at z= 900 µm) with respect to experiment. This reveals again the influence of the thermal boundary conditions on the pressure and the fibre orientation state, and partially clarifies the causes of the deviation between simulation and experimental results.

Figure

  Figure 7.33

  Figure 7.35 shows the experimental and the predicted 𝑎 𝑥𝑥 across thickness carried out at the same location (x= 70 mm, y= 0 mm), for 20 vol % Tencel, flax and glass based composites.

Figure

  Figure 7.35

  conducted a detailed investigation of glass fibres orientation in the moulded box. A core-shell structure across the thickness dominates the moulded part. The evolution of the orientation tensor component a xx across the thickness is nearly the same for concentrations between 3.6 and 13.1 vol %. It turned out that the core layer with fibres oriented perpendicular to the flow direction appears only for 20.5 vol %. According experimental data performed for glass fibre reinforced polypropylene, only partial conclusions can be drawn concerning the accuracy of the simulation. The simulation predicts well the experimental orientation except in the core layer in which the simulation overestimates the degree of alignment perpendicular to the flow direction. The thermal boundary conditions can be modified to get a good agreement. The simulation of orientation of flax and Tencel fibre cases were carried out. The purpose is to test to what extent a rigid fibres' model can simulate both types of natural fibres. It turned out that the predicted flax fibres' orientation matches correctly the experimental results, while that of Tencel fibre is extremely far from experiment. The flax fibres contain partially rigid bundles. An accurate set-up of the thermal conditions input could clearly improve the obtained results. However, Tencel fibres are very flexible and their behaviour during the flow cannot be modelled by a rigid fibres model. A specific flexible fibre model is required to get more promising results. Our work is one of the first investigations about the prediction of the orientation of natural fibres based composites. This could be a contribution to the ongoing has provided an in-depth analysis of processing-microstructureproperties relationships in injection moulding of natural fibre-reinforced polypropylene. This type of composites are quickly developing and have several advantages compared to glass fibre based composites such as lower density, reduced environmental foot print and low cost. We have conducted our work with two types of cellulose-based fibres, Tencel and flax which have different intrinsic structures: flax is a mixture of semi-rigid thin elementary fibres and thick rigid bundles and Tencel is thin elementary flexible fibre. Classical rigid glass fibres were also used for comparison. A variety of experimental techniques has been used and some were developed to assess the microstructure and mechanical and rheological properties of composites. A simulation of the filling stage during injection moulding has been performed, enabling to compare the predicted pressure and fibre orientation with those experimentally obtained. A summary of the main results obtained is presented below.

  natural fibres which have very different structure compared to rigid glass fibres. Considering that flax fibres contain rigid bundles, we found that their predicted orientation approximately matches the experimental results; an accurate set-up of the calculation parameters would bring improvements to the obtained orientation. The predicted orientation of Tencel fibres is extremely far from what was obtained in experiment. Tencel fibres are very flexible and their behaviour during the flow cannot be modelled by a typical rigid fibres model. Therefore, a flexible fibre model is required for Tencel based composites to reach adequate orientation results.

3 .

 3 A simple sprue-gated box was used in this work for the analysis of the microstructure of Tencel and flax based composites. Other mould and gate geometries need to be used to confirm (or not) the results obtained and to reach further advance in the understanding of natural fibre composite microstructure.

  Les fibres naturelles sont une alternative aux fibres de verre pour renforcer les polymères. Lors de la mise en oeuvre par injection, la taille, l'orientation et la distribution de fibres évoluent en fonction de l'écoulement, et cela conditionne les propriétés des pièces injectées. L'objectif de cette thèse est de caractériser la microstructure de composites à base de deux types de fibres, le lin et Tencel, et d'établir une corrélation avec leurs propriétés.Les fibres et matrice ont été mélangés en extrusion bivis et les composites obtenus injectés. La rupture de fibres est plus importante lorsque leur concentration augmente. La casse est principalement pendant la phase de mélange. Une nouvelle approche de caractérisation permettant la quantification des orientation, distribution et courbure de fibres a été développée. Les composites présentent une structure coeur-peau dans l'épaisseur de la pièce injectée. Les propriétés rhéologiques des composites ont été étudiées en modes dynamique et capillaire. Les fibres Tencel, qui sont les plus flexibles, conduisent à une augmentation plus grande des viscosités, modules et seuil d'écoulement. Les propriétés mécaniques en traction et au choc ont été déterminées dans des éprouvettes prélevées dans des boites injectées avec différentes orientation par rapport à l'axe d'écoulement. Les propriétés d'impact des composites à fibres Tencel sont supérieures à celles à base de lin et de verre. Des modèles ont été testés en prenant en compte l'orientation de fibres. Lors des campagnes d'injection, les pressions sur des capteurs situés dans la cavité ont été mesurées. Les pressions calculées avec le logiciel Rem3D ® sont en assez bon accord avec la mesure. Le modèle d'orientation de fibre rigide utilisé dans Rem3D ® donne des résultats corrects pour les fibres de lin, mais il s'est avéré inapproprié pour prédire l'orientation des fibres Tencel extrêmement flexibles. Ce travail est réalisé dans le cadre de la Chaire Industrielle Bioplastiques financée par Mines ParisTech et Arkema, l'Oréal, Nestlé, PSA et Schneider Electric. Mots clefs : fibres naturelles, composites, rhéologie, injection, microstructure, modélisation Injection Moulding of Natural Fibre Reinforced Polypropylene: Process, Microstructure and Properties Abstract. Natural fibres are an alternative to glass fibres for reinforcing polymers. During injection, fibre size, orientation and distribution evolve as a function of flow and determine composite properties. The goal of this thesis is to characterize the microstructure of composites based on two types of fibres, flax and Tencel, and to correlate with composite properties. The composites were prepared by extrusion and injection. Fibre rupture was higher at higher fibre concentrations. There was practically no breakage during injection. A new approach allowing quantification of fibre orientation, distribution and curvature was developed. The composites with cellulosic fibres have core-skin structure along the part thickness. The rheological properties of composites were studied in dynamic and capillary modes. Tencel fibres, which are the most flexible, showed the highest viscosity, moduli and yield stress. Tension and impact were measured for samples cut from the moulded part at different orientations towards the main flow direction. Impact properties of Tencel-based composites were the highest compared to flax and glass fibre composites. Models taking into account fibre orientation were tested. Pressure in the mould during injection was recorded. Pressure calculated with Rem3D ® software showed a reasonable agreement with the experiment. Modelling of fibre orientation with Rem3D ® gave results comparable with experiment for flax but turned out to be not applicable for Tencel which are flexible. The work was performed within the Industrial Chair in Bioplastics supported by MINES ParisTech and Arkema, L'Oréal, Nestlé, PSA and Schneider Electric.

  ® , and compared to the experimental orientation shown in Chapter 4. The applicability of this simulation tool to natural fibres is discussed in this chapter. Müssig, J. (Editor) (2010). Industrial Applications of Natural Fibres -Structure, Properties and Technical Applications. Chichester, John Wiley & Sons, United Kingdom. Tortora, P. G., & Collier, B. J. (1997). Understanding textiles. Prentice-Hall, Englewood Cliffs, New Jersey, United States.

Table 2 .

 2 1 Characteristics of the polypropylene used in this study

				Method	Unit	Value
	Melt	Flow	Index	ISO 1133	g/10 min	25
	230°C/2.16 kg
	Melting point		ISO 3146	° C	165
	Density		ISO 1183	g/cm 3	0.905
	Tensile Strength at Yield ISO 527-2	MPa	37
	Elongation at Yield		ISO 527-2	%	8
	Tensile Modulus		ISO 527-2	MPa	1700
	Flexural Modulus		ISO 178	MPa	1600
	Izod Impact Strength	ISO 180	kJ/m²	4
	(notched) at 23°C
	Charpy Impact Strength	ISO 179	kJ/m²	4.5
	(notched) at 23°C
	1.2. Fibres
	1.2.1.	Flax

Table 2 .2 Composite formulations Volume fraction, % Weight fraction, %

 2

	Melting zone		Mixing zone	Convoying zone
	a
	b
		Flax	Tencel	Glass
	3.6	5	5	9.3
	6.3	10	10	15.6
	13.1	20	20	29.4
	20.5	30	30	41.6

Table 2 .

 2 3 regroups the injection moulding conditions.

Table 2 .

 2

		3 Injection moulding conditions
	Injection temperature, °C	190	Cooling time, s	10
	Mold temperature, °C	30	Holding time, s	10
	Flow rate, cm 3 /s	92.4	Holding pressure, bar	600
	Shot length, mm	115	Back pressure, bar	0
	Clamping force, KN	1100	Screw speed, RPM	120

Table 2

 2

	.4 gives details of

Table 2 .4 Injection moulding conditions for making impact bars Injection temperature, °C 190 Cooling time, s 10 Mold temperature, °C 30 Holding time, s

 2

	10

1.1. Glass fibre reinforced thermoplastic

  𝑛 𝑖 is the number of fibres and 𝑃 𝑖 can be 𝐿 𝑖 as fibre length or 𝐷 𝑖 as fibre diameter or (𝐿/𝐷) 𝑖 as fibre aspect ratio.

			,
	Bernasconi et al. (2012); Tausif et al. (2014); Thi et al. (2015)] a non-destructive technique
	that is X-ray µCT (Micro Computed Tomography) has been used to analyse the
	microstructure of composites, in particular the fibre size. The statistical analysis of fibre
	dimensions are based on the number-average of fibre length L n , diameter D n and aspect ratio
	(L/D) n , and weight-average fibre length L w , diameter D w and aspect ratio (L/D) w defined as
	follows:
	𝑃 𝑛 =	∑ 𝑛 𝑖 𝑃 𝑖 𝑖 ∑ 𝑛 𝑖 𝑖	[Eq 3.1]
	𝑃 𝑤 =	∑ 𝑛 𝑖 𝑃 𝑖 𝑖 ∑ 𝑛 𝑖 𝑖 𝑃 𝑖 2	[Eq 3.2]
	Yilmazer and Cansever (2002) investigated the breakage of glass fibre in polyamide-6 based
	composites and demonstrated that compounding highly reduces the fibre length and additional
	fibre breakage can be caused by injection moulding. The initial glass fibre length was 4 500
	µm. This value decreased to L n = 122-195 µm and L w = 406-496 µm after extrusion and
	further decreased to L n = 104-141 µm and L w = 206-302 µm after injection moulding. The
	extent of decrease in L w is larger that of L n , meaning that long fibres remained after extrusion
	are broken during injection moulding. L w was reduced by 90 % in twin screw extruder and it
	was further reduced by 37 % after injection molding. The extent of fibre breakage after
	compounding decreased with the increase of the screw speed and slightly increased with the
	feed rate. Inceoglu et al. (2011) reported similar findings in what concerns compounding of

Table 3

 3

	.1 Influence of design/fabrication factors on final fibre length in short fibre reinforced
	polymer composite [Fu et al. (1999)]
	Design /fabrication factors	Average
			fibre length
	Compounding	Lower screw speed	Higher
		Higher barrel temperature
		Lower mixing times
	Injection Molding	Lower back pressure	Higher
		Lower injection speed
		More generous gate &
		runners dimensions
	Lower fibre content		Higher
	Larger original fibre		Higher
	Reprocessing		Lower

Table 3 .

 3 2 Glass fibre sizes as delivered, after compounding and after injection

		As
		delivered	After compounding		After injection moulding
	Wt %	-	9.4	15.6	29.4	41.6	9.4	15.6	29.4	41.6
	Vol %	-	3.6	6.3	13.1	20.5	3.6	6.3	13.1	20.5
	L n	2512	618	498	391	330	495	379	302	286
	L w	2941	858	607	571	438	719	502	412	361
	L max	6475	2550	2498	2353	1659	2066	1170	1035	715
	L min	317	87	64	43	49	30	39	30	44
	(L/D) n	251	62	50	39	33	49	38	30	29
	(L/D) w	294	86	61	57	44	72	50	41	36

Table 3 .

 3 3 Sizes of Tencel fibres: as delivered, after compounding and after injection moulding

		As
		delivered		After compounding		After injection moulding
	Wt %	-	5	10	20	30	5	10	20	30
	Vol %	-	3.6	6.3	13.1	20.5	3.6	6.3	13.1	20.5
	L n	300	240	242	237	195	262	255	230	202
	L w	338	294	318	306	264	342	277	290	287
	L max	714	680	793	656	820	738	627	562	688
	L min	113	53	30	29	34	50	50	46	21
	(L/D) n	30	24	24.2	23.7	19.5	26.2	25.5	23	20.2
	(L/D) w	33.8	29.4	31.8	30.6	26.4	34.2	27.7	29	28.7

Table 3 .

 3 [START_REF] Fink | Progress in cellulose shaping: 20 years industrial case studies at Fraunhofer IAP[END_REF] Flax fibre sizes as delivered, after compounding and after injection moulding

		As
		delivered		After compounding		After injection moulding
	Wt %	-	5	10	20	30	5	10	20	30
	Vol %	-	3.6	6.3	13.1	20.5	3.6	6.3	13.1	20.5
	L n	450	433	415	434	422	428	407	420	388
	L w	458	478	472	469	477	464	446	458	433
	L max	1020	1028	1150	874	1116	855	827	922	863
	L min	211	53	64	60	74	98	85	71	81
	D n	48	35	34	39	39	34	36	32	28
	D w	84	46	49	60	54	46	54	43	34

  studied the activation energy of 30 wt % glass fibre-reinforced for different matrices (PP, HDPE, LDPE, and PA6) in steady state mode. 𝐸 𝑎 of 30 wt % glass/PP (82± 3.2

	kJ/mol) and 30 wt % glass/HDPE (34.9± 1.4 kJ/mol), are slightly higher than that of neat PP
	(44 kJ/mol) and neat HDPE (28 kJ/mol). Whereas, 𝐸 𝑎 is not affected by fibres in case of
	LDPE (51 kJ/mol for neat LDPE versus 48.7± 3.6 for 30 wt % glass/LDPE) and PA6 (80
	kJ/mol for neat PA6 versus 82± 3.2 kJ/mol).

Table 5

 5

	.1 G' and G" power-law exponents, x and y, respectively, at low frequencies
		vol %	u	v
	Neat PP	0	1.59	0.98
	Tencel/PP	6.3	0.84	0.73
	flax/PP	6.3	0.86	0.92
	glass/PP	6.3	0.38	0.64
	Tencel/PP	20.5	0.32	0.29
	flax/PP	20.5	0.53	0.56
	glass/PP	20.5	0.02	0.15

Table 5 .

 5 Table 5.3.

	1000000	, Pa.s
		20 vol % Tencel/PP
	100000	20 vol % glass/PP
		20 vol % flax/PP
	10000
			Neat PP
	1000
	100
								, (rad.s -1 ) and 𝛾 ̇ (s -1 )
	10
	0.001	0.01	0.1	1	10	100	1000	10000

3

shows that s 0 increases with the fibre content whereas n decreases. At low concentration (3.6 and 6.3 vol % for Tencel and glass, 3.6 vol % for flax) n is larger for the composite than for the PP. For the highest concentration, the values of  (that is the characteristic time corresponding to the transition from Newtonian plateau to shear thinning)

Table 6

 6

	.1 Orientation factors for different composite types
		flax/PP	Tencel/PP	glass/PP
	𝝃 𝟎𝒙	0.38	0.28	0.34

Table 6 .

 6 2 Efficiency factor variation with fibre type and fibre content

		Fibre content (vol %)	𝝃 𝟏
	flax	3.6	0.39
		6.3	0.39
		13.1	0.53
		20.5	0.61
	Tencel	3.6	0.82
		6.3	0.84
		13.11	0.85
		20.5	0.86
	Glass	3.6	0.79
		6.3	0.76
		13.1	0.75
		20.5	0.77

  Table 6.3.

		Table 6.3 Parameters used for tensile strength modelling
		vol %	6		E, GPa L c, ( µm)	σ f, (MPa)	τ (MPa)	c L n (µm)	D n (µm)
		3.6			1278		980		13			428	34
	Flax	6.3	5		1368		980		13			407	36
		13.11	4		1206		980		13			420	32
		20.05	3		1067		980		13			388	28
		3.6			570		570		5			262	10
	Tencel	6.3	2		570		570	Experiment, x-direction Experiment, y-direction 5 255	10
		13.11	1		570		570	C_K model, x-direction 5	229	10
		20.05			570		570	C_K model, y-direction 5	211	10
		3.6	0	0	6992	0.05	0.1 1818	0.15	13	0.2		0.25 494	10
	Glass	6.3			6992		1818	Fibre volume fraction 13 379	10
		13.11			6692		1818		13			301	10
		20.05			6692		1818		13			286	10

Table 7 .

 7 1 Conditions of the injection moulding of polypropylene inChiang et al. (1991) and

		Han and Im (1997) studies
		Chiang et al. (1991,b)	Han and Im (1997)
	Cavity thickness (mm)	2.54	2
	Melt temperature (°C)	200	180
	Flow rate (cm 3 /s)	26.8	7.4
	Fill time (s)	0.69	1.5
	Hydraulic hold pressure (MPa)	6.9	-
	Holding duration (s)	>15	6
	Coolant temperature (°C)	32	40

  introduced the orientation tensor evolution and added a diffusion term 𝐷 𝑟 (see Eq. 7.3) such as:𝛾̇ is the generalized shear rate and 𝐶 𝐼 is the interaction coefficient, a dimensionless number usually taken lower than 10 -² to enable a good fit with experimental fibre orientation data. The evolution of the second order orientation tensor a ij (Eq. 7.3) requires the knowledge of the 𝑝 fourth order orientation tensor a ijkl . To cope with this, dedicated approximations are suggested in the literature for representing the fourth order orientation tensor as a function of the second order one. The simplest closure approximations are: linear closure[START_REF] Hand | A theory of anisotropic fluids[END_REF], quadratic closure

		Z	θ
			Y
			𝜙
			X
	𝐷 𝑟 = 𝐶 𝐼 𝛾̇		[Eq. 7.2]
	𝐷𝑎 𝑖𝑗 𝐷𝑡	= Ω. 𝑎 𝑖𝑗 + Γ[𝜺̇. 𝑎 𝑖𝑗 -2𝜺̇: 𝑎 𝑖𝑗𝑘𝑙 ] + 2 𝐷 𝑟 (𝐼 -2 𝑎 𝑖𝑗 )	[Eq. 7.3]

Table 7

 7

				.2 The input material parameters used for simulation
			Vol %	𝜌	k		𝐶 𝑝		E a		L/D	𝜂 0	𝜆	n	a
				(kg.m -3 )	(W.m -1 .°C	-1 )	(J.kg -1 .°C	-1 )	(J.mol	-1 )		(Pa.s)	(s)
	Neat PP	-	905	0.25		1377		45501		-	1201	0.04	0.38	0.85
			3.6	926	0.284		1496		52354		26	2003	0.2	0.53	0.85
	Tencel/PP	6.3	942	0.31		1492		61284		25	2702	0.19	0.48	0.85
			13.1	983	0.374		1483		74458		23	3457	0.04	0.23	0.85
			20.5	1026	0.444		1474		140000	20	12025 0.15	0.23	0.85
			3.6	926	0.284		1496		48969		15	1500	0.05	0.4	0.85
	Flax/PP	6.3	942	0.31		1492		61284		15	1515	0.05	0.35	0.85
			13.1	983	0.374		1483		67904		14	3055	0.07	0.3	0.85
			20.5	1026	0.444		1474		69089		15	6173	0.09	0.21	0.85
			3.6	962	0.284		1475		42334		49	1597	0.2	0.55	0.85
	Glass/PP	6.3	1005	0.310		1456		45500		38	2000	0.2	0.53	0.85
			13.1	1114	0.374		1408		55617		30.2 3492	0.14	0.39	0.85
			20.5	1232	0.444		1354		55617		29	3968	0.02	0.118 0.85
	*Conditions for all materials:
	-Flow rate = 92.3 cm 3 /s
	-Injection temperature = 190 °C
	-Wall temperature = 70 °C
	2.2.2.	Filling stage analysis and comparison with experiment

post-filling stages (packing, holding and cooling) was performed byChiang et al. (1991,a,b).

Acknowledgements

This work was performed within the Industrial Chair in Bioplastics supported by MINES ParisTech and Arkema, L'Oréal, Nestlé, PSA and project for helping in experiments. I am also thankful to Prof. Jean-Marc Haudin, Dr. Edith Peuvrelgrateful to Thierry Collin for his technical support and to Marie-Francoise Guenegan for her administrative support. Deep thanks go to Dr. Rudy Valette for his precious advices on research as well as on my career. I must also thank Dr. Olivia Levingston and Dr. Sian support to the thesis. Special thanks to Benjamin Gallard for helping in experiments and Nicolas LeMoigne for his advices. I am grateful also to Dr. Mohamed Jaziri from the National School of Engineers of Sfax for his support and advices before and during my thesis.

injection molded polyamide. Polymer composites, 14(2), 116-125. Truckenmüller, F., & Fritz, H. G. (1991). Injection molding of long fiber-reinforced thermoplastics: A comparison of extruded and pultruded materials with direct addition of roving strands. Polymer Engineering & Science, 31(18), 1316-1329. Tucker III, C. L. (1988). Predicting Fiber Orientation in Short Fiber Composites. The Manufacturing Science of Composites, TG Gutowski, ed., ASME, New York. Vincent, M., & Agassant, J. F. (1986). Experimental study and calculations of short glass fiber orientation in a center gated molded disc. Polymer composites, 7(2), 76-83. [START_REF] Vincent | Description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics[END_REF]. Description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics. Polymer,46(17), 6719-6725. their corresponding scans showing the presence of fibre aggregates (white areas). Three samples were tested for each core and shell regions. All samples were scanned before and after testing, using a scan micrograph. The purpose is to show the influence of fibre dispersion on the tensile properties. According to authors, the bundles' concentration is greater at the core than at the shell. For the core stress-strain curves (a), authors concluded that samples 3 and 2 contain larger bundles' size than the sample 1. The breakage occurs earlier as the bundles' size is larger, leading to a lower elongation at break. The strength also decreases as the bundles size is greater. For the shell stress-strain curves (b), the cross-sections show a lower bundles amount than at the core sample, explained by the higher shear close to the dogbone surface. Only sample 1 in Figure 6.2.b has a bundle in the effective cross-section, which led to a premature breaking compared to the shell samples 2 and 3. In addition, whatever the sample is cut from shell or core, the presence of bundles does not affect the Young's modulus.

The authors observed also cross sections of samples (parallel to the dog-bone plane) by SEM and showed that flax fibres are more aligned in the shell than in the core, the reason explaining the difference in term of strength and stiffness between core and shell samples. However, the microstructure investigation was limited to a qualitative observation and no quantitative analysis of fibre orientation was performed.

discussions about which models are suitable to predict the microstructure of natural fibres in injection moulded parts.