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# Mechanics of ultra-thin Fiber-Reinforced Polymer (FRP) composite layers for aerospace applications

- Luca Di Stasio
- Janis Varna
- Ayadi Zoubir

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## Project log

At the end of the second decade of the XXI century, the transportation industry at large faces several challenges that will shape its evolution in the next decade and beyond. The first such challenge is the increasing public awareness and governmental action on climate change, which are increasing the pressure on the industrial sectors responsible for the greatest share of emissions, the transportation industry being one of them, to reduce their environmental footprint. The second big challenge lies instead in the renewed push towards price reduction, due to increased competition (as for example, in the market for low-Earth orbit launchers, the entry of private entities) and innovative business models (like ride-sharing and ride-hailing in the automotive sector or low-cost carriers in civil aviation). A viable and effective technical solution strategy to these challenges is the reduction of vehicles’ structural mass, while keeping the payload mass constant. By reducing consumption, a reduced weight leads to reduced emissions in fossil-fuels powered vehicles and to increased autonomy in electrical ones. By reducing the quantity of materials required in structures, a weight reduction strategy favors in general a reduction of production costs and thus lower prices. Transportation is however a sector where safety is a paramount concern, and structures must satisfy strict requirements and validation procedures to guarantee their integrity and reliability during service life. This represents a significant constraint which limits the scope of the weight reduction approach. In the last twenty years, the development of a novel type of Fiber-Reinforced Polymer Composite (FRPC) laminates, called thin-ply laminates, proposes a solution to these competing requirements (weight with respect to structural integrity) by providing at the same time weight reduction and increased strength. Several experimental investigations have shown, in fact, that thin-ply laminates are capable of delaying, and even suppress, the onset of transverse cracking. Transverse cracks are a kind of sub-critical damage in FRPC laminates and occur early in the failure process, causing the degradation of elastic properties and favoring other, often more critical, modes of damage (delaminations, fiber breaks). Delay and suppression of transverse cracks were already linked, at the end of the 1970’s, to the use of thinner plies inside a laminate. However, thin-plies available today on the market are at least 10 times thinner than those studied in the 1970’s. This characteristic changes the length scale of the problem, from millimeters to micrometers. At the microscale, transverse cracks are formed by several fiber/matrix interface cracks (or debonds) coalescing together. Understanding the mechanisms of transverse cracking delay and suppression in thin-ply laminates requires detailed knowledge regarding onset of transverse cracking at the microscale, and thus the study of the mechanisms that favor or prevent debond initiation and growth. The main objective of the present work is to investigate the influence of the microstructure on debond growth along the fiber arc direction. To this end, models of 2-dimensional Representative Volume Elements (RVEs) of Uni-Directional (UD) composites and crossply laminates are developed. The Representative Volume Elements are characterized by different configurations of fibers and different damage states. Debond initiation is studied through the analysis of the distribution of stresses at the fiber/matrix interface in the absence of damage. Debond growth on the other hand is characterized using the approach of Linear Elastic Fracture Mechanics (LEFM), specifically through the evaluation of the Mode I, Mode II and total Energy Release Rate (ERR). Displacement and stress fields are evaluated by means of the Finite Element Method (FEM) using the commercial solver Abaqus. The components of the Energy Release Rate are then evaluated using the Virtual Crack Closure Technique (VCCT), implemented in a custom Python routine. The elastic solution of the debonding problem presents two different regimes: the open crack and the closed crack behaviour. In the latter, debond faces are in contact in a region of finite size at the debond tip; in the latter, the debond is everywhere open and no contact exists between the faces. In the open crack regime, it is known that stress and displacement fields at the debond tip present an oscillating singularity. A convergence analysis of the VCCT in the context of the FEM solution is thus required to guarantee the validity of results and represents the first step of the work presented in this thesis. It is found that the total ERR does not depend on the size of elements at the debond tip, while the values of Mode I and Mode II ERR depend on element size in the open crack or mixed mode case. It is furthermore shown that Mode I and Mode II ERR do not converge, i.e. their asymptotic behavior for decreasing element size is not bounded. Thus, error reduction between successive iterations cannot be used to validate the solution and comparison with another method is required. Results obtained with the Boundary Element Method (BEM), available in the literature, are selected to this end. Debond growth under remote tensile loading is then studied in Representative Volume Elements of: UD composites of varying thickness, measured in terms of number of rows of fibers, from extremely thin (one fiber row) to thick ones; cross-ply laminates with a central 90◦ ply of varying thickness, measured as well in terms of number of rows of fibers, from extremely thin (one fiber row) to thick ones; thick UD composites (modelled as infinite along the through-the-thickness direction). Different damage configurations are also considered, corresponding to different stages of transverse crack onset: non-interacting isolated debonds; interacting debonds distributed along the loading direction; debonds on consecutive fibers along the through-the-thickness direction. Among the most relevant results, it is found that neither the 90◦ ply thickness nor the 0◦ ply thickness influences debond ERR in cross-ply laminates, differently from what is observed for transverse cracks with the so-called ply-thickness and ply-block effects. On the other hand, debond interaction along the loading direction is shown to influence significantly the Energy Release Rate, but this interaction possesses a characteristic distance (in terms of number of undamaged fibers) that defines the region of influence between debonds. Finally, an estimation of debond size at initiation and of debond maximum size is proposed based on arguments from stress analysis (for initiation) and on Griffith’s criterion from LEFM (for propagation). For a debond in a cross-ply laminate, its maximum size is estimated to lie in the range 40◦ − 60◦ , which is in strong agreement with previous results from microscopic observations available in the literature.

The effects of crack shielding, finite thickness of the composite and fiber content on fiber/matrix debond growth in thin unidirectional composites are investigated analyzing Representative Volume Elements (RVEs) of different ordered microstructures. Debond growth is characterized by estimation of the Energy Release Rates (ERRs) in Mode I and Mode II using the Virtual Crack Closure Technique (VCCT) and the J-integral. It is found that increasing fiber content, a larger distance between debonds in the loading direction and the presence of a free surface close to the debond have all a strong enhancing effect on the ERR. The presence of fully bonded fibers in the composite thickness direction has instead a constraining effect, and it is shown to be very localized. An explanation of these observations is proposed based on mechanical considerations.

The bi-material interface arc crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix interface crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix interface crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the crack tip neighborhood, while the total ERR is independent of element size.

Models of Representative Volume Elements (RVEs) of cross-ply laminates with different geometric configurations and damage states are studied. Debond growth is characterized by the estimation of the Mode I and Mode II Energy Release Rate (ERR) using the Virtual Crack Closure Technique (VCCT). It is found that the presence of the 0° /90° interface and the thickness of the 0° layer have no effect, apart from laminates with ultra-thin 90° plies where it is however modest. The present analysis supports the claim that debond growth is not affected by the ply-thickness effect.

The effects of crack shielding, finite thickness of the composite and fiber content on fiber/matrix debond growth in thin unidirectional composites are investigated analyzing Representative Volume Elements (RVEs) of different ordered microstructures. Debond growth is characterized by estimation of the Energy Release Rates (ERRs) in Mode I and Mode II using the Virtual Crack Closure Technique (VCCT) and the J-integral. It is found that increasing fiber content, a larger distance between debonds in the loading direction and the presence of a free surface close to the debond have all a strong enhancing effect on the ERR. The presence of fully bonded fibers in the composite thickness direction has instead a constraining effect, and it is shown to be very localized. An explanation of these observations is proposed based on mechanical considerations.

The growth of fiber/matrix interface cracks (debonds) located on consecutive fibers along the through-the-thickness direction is studied in glass fiber-epoxy UD composites. Two different families of Representative Volume Elements (RVEs) are developed: the first implements the classic condition of coupling of the vertical displacements to model a unit cell repeating symmetrically along the vertical (through-the-thickness) direction; the second uses a novel set of boundary conditions, proposed here by the authors, to represent a unit cell repeating anti-symmetrically along the vertical direction. The model is analyzed in the context of Linear Elastic Fracture Mechanics (LEFM) and the Mode I and Mode II Energy Release Rate are evaluated to investigate crack growth. The calculation is performed using the Virtual Crack Closure Technique (VCCT) and the evaluation of the J-Integral in the framework of the Finite Element Method (FEM). It is found that Mode I dominated propagation is favored when debonds are located on the same sides of their respective fibers, while larger debond sizes can be achieved in Mode II dominated growth when they lie on the opposite sides. No effect is present when at least two fully bonded fibers are located between the partially debonded ones.

In recent years, much work has been devoted to the characterization of so-called thin-ply laminates, in which the central 90° ply can today achieve a thickness of the order of 4-5 fiber diameters thanks to the spread-tow technology [1]. Due to the several beneficial properties observed in this class of composites, designers are currently evaluating the feasibility of using thin-ply laminates in high-performance structural applications such as pressure vessels and even re-usable re-entry vehicles [2].
One of the most prominent capabilities observed in thin-ply laminates is their ability to delay, and even suppress, the onset and propagation of transverse cracks. This observation was not actually surprising from the perspective of composites’ damage mechanics, as it confirmed a phenomenon first reported in the 1970’s and named the ply-thickness effect. Working on [0°, 90°m]S glass fiber-epoxy laminates tested in tension, researchers observed that reducing the thickness of the central 90° layer (measured in terms of the number m of UD prepreg plies used in manufacturing) caused a delay of the onset and propagation of transverse cracks to higher levels of applied tensile strain [3].
In further studies, the same group of researchers identified the onset of fiber-matrix interface cracks (or debonds) as the first event occurring during the tensile loading of a cross-ply [4], which preludes to the onset and propagation of transverse cracks. Subsequent studies managed to provide a more detailed description of the initiation process of transverse cracks [5]. Under applied tensile strain, debonds are formed at the fiber-matrix interface and propagate at first in the arc direction of the fiber. Once a critical angular size is reached, debond propagation along the fiber arc direction stops and the crack kinks out of the interface. At this point, adjacent debonds coalesce together and a through-the-ply-thickness crack is formed, which then propagates along the fiber longitudinal direction (corresponding to the cross-ply specimen width).
Given its prominent role in the initiation and propagation of intralaminar cracks, it is reasonable to assume that it would be possible to observe the occurrence of the ply-thickness effect also for the fiber-matrix interface crack. However, microscopical observations of onset and propagation of intralaminar cracks in thin-ply and classical [0°, 90°m]S carbon fiber-epoxy laminates loaded in tension provided contrasting evidence [6]. It was observed that decreasing the 90° ply thickness resulted in the appearance of debonds at lower strains while concurrently the coalescence of debonds and thus the formation of transverse cracks were delayed to higher strains, and even suppressed for extremely thin layers.
In this work, we address this problem through the development of 2D models of Repeating Unit Cell (RUC) of UD and cross-ply glass fiber-epoxy composites. The RUCs are assumed to lie in a cross-section parallel to the loading direction and placed in the middle of the laminate. By using selected boundary conditions, each RUC represents a different microstructural configuration of partially debonded and undamaged fibers in the 90° layer. Fibers are always placed according to a square-packing configuration. In the case of cross-ply laminates, the 0° ply is modeled as a region of material with homogenized elastic properties. We apply the principles of Linear Elastic Fracture Mechanics (LEFM) and thus the main parameters used to characterize the debond are the Mode I, Mode II and total Energy Release Rate (ERR) at the crack tip calculated with the Virtual Crack Closure Technique and the J-integral method. We thus focus on the propagation of debonds in the fiber arc-direction.
The picture delineated by the results of the numerical simulations appears to be even more nuanced than expected. A significant effect of the 90° layer thickness is observed both in models of UD and cross-ply laminates and it is related to the interaction of debonds along the loading direction. The further apart debonds are along this direction, the higher is the ERR, which in turn means that lower strains are needed to propagate them. However, the presence of rows of undamaged fibers on top and below, i.e. a thicker layer, causes a reduction in this phenomenon of magnification. The presence of the stiff 0° ply in the case of a cross-ply laminate corresponds to a reduction of the magnitude of the ERR, but trends are the same as in the UD case. The numerical results seem thus to confirm the observation from microscopy: thinner plies favor the propagation of debonds at lower strains. This, in turn, means that, if a ply-thickness effect might be said to exist for the fiber-matrix interface crack, it actually points to a behavior opposite to the one observed at the laminate level for transverse cracks: thinner plies delay and might even suppress transverse cracks, but favor the propagation of debonds.
[1] H. Sasayama, S. Tomoda, New Carbon Fiber Tow-Spread Technology and Applications to Advanced Composite Materials, S.A.M.P.E. journal, 45(2), 2009, p. 6-17.
[2] A. Kopp, S. Stappert, D. Mattsson, K. Olofsson, E. Marklund, G. Kurth, E. Mooij, E. Roorda, The Aurora Space Launcher Concept, CEAS Space Journal, 2017, p. 1-21.
[3] A. Parvizi, J. E. Bailey, On multiple transverse cracking in glass fibre epoxy cross-ply laminates, Journal of Materials Science, 13(10), 1978, p. 2121-2136.
[4] J. E. Bailey, P. T. Curtis, A. Parvizi, On the Transverse Cracking and Longitudinal Splitting Behaviour of Glass and Carbon Fibre Reinforced Epoxy Cross Ply Laminates and the Effect of Poisson and Thermally Generated Strain, Proceedings of the Royal Society of London, Series A, 366(1727), 1979, p. 599-623.
[5] H. Zhang, M. L. Ericson, J. Varna, L. A. Berglund, Transverse single-fibre test for interfacial debonding in composites: 1. Experimental observations, Composites Part A: Applied Science and Manufacturing, 28(4), 1997, p. 309-315.
[6] H. Saito, H. Takeuchi, I. Kimpara, Experimental Evaluation of the Damage Growth Restraining in 90° Layer of Thin-ply CFRP Cross-ply Laminates, Advanced Composite Materials, 21, 2012, pp. 57-66.

The adoption of the spread tow technology [1] at the industrial level in recent years has allowed the diffusion in the composite market of a novel type of material, the thin and ultra-thin ply laminates. A number of experimental and theoretical investigations over the years have shown the benefits stemming from the new laminate design. Among these, one of the most significant appears to be their ability to drastically delay, and even suppress, the onset and propagation of transverse cracks [2]. The result was not actually surprising, as early studies in the 1970s on cross-ply glass fiber/epoxy laminates reported that onset of transverse cracking was delayed to higher levels of strain in thinner 90° plies [3]. The effect was since named the ply thickness effect. Contemporary to these early observations was also the identification of microscopic cracking (debonding) at the fiber/matrix interface as the primary driver of transverse crack onset and propagation [4].
Subsequent experimental investigations determined that fiber/matrix interface cracks (or debonds) first grow in a stable manner along the arc direction of the fiber; once they reach a critical angular size debonds propagate unstably along the fiber longitudinal direction and then coalesce with debonds on adjacent fibers to form through-the-thickness (or transverse) cracks [5]. Theoretical studies have thus focused on understanding debond growth in the arc direction with the aim of predicting the critical size at which unstable longitudinal propagation and coalescence occur. Several analytical and numerical works can be found in the literature dealing with models of: a single partially debonded fiber in an infinite or effectively infinite matrix and in a homogenized 90° layer; a single partially debonded fiber with 2 or 6 neighboring, partially or fully bonded, fibers in an effectively infinite matrix and in a homogenized 90° layer. In-situ microscopic observations have nonetheless pointed to the evidence that debond onset and growth occur simultaneously on different fibers. A clear understanding of the mechanics of the fiber/matrix interface thus requires the investigation of the effect of more complex microstructural arrangements and damage states.
In the present work, we investigate a family of Repeating Unit Cells (RUCs) which represent Representative Volume Elements (RVEs) of unidirectional composites with different microstructural arrangements and different geometric configurations of debonds. This is achieved by controlling the number of fully bonded fibers appearing in the horizontal, i.e. loading, direction and in the vertical, i.e. through-the-ply-thickness, direction of the model. Application on the right and left sides of the RUC of coupling conditions on the horizontal displacement (which corresponds to the laminate in-plane transverse displacement) ensures a mirror-like repetition of the solution in the horizontal direction. Vertical displacement coupling applied to the top boundary guarantees, on the other hand, a symmetric repetition of the solution in the vertical direction. This implies that, if a debond appears on the right side of the damaged fiber in the model, the next partially debonded fiber in the vertical direction will present a debond on the right side as well. Several micrographs reported in the literature show, however, debonds often appearing on opposite sides of adjacent fibers [2]: if the debond appears on the right side of a fiber, the adjacent partially debonded fiber has it on the left side (and vice versa). In order to analyze this configuration, a set of antisymmetric coupling conditions is proposed which, to the authors’ knowledge, represents the first attempt to model such configuration in the context of numerical microstructural homogenization techniques. By applying the antisymmetric coupling conditions on the top boundary of the RUC, we investigate different configurations in which debonds appear on opposite sides of consecutive (adjacent or intercalated by undamaged fibers) partially debonded fibers along the vertical direction. The mechanics of debond growth is analyzed by evaluating the Mode I and Mode II Energy Release Rate (ERR) at the crack tip. Results for the antisymmetric and symmetric coupling conditions are compared with each other, and the likelihood of consecutive debonds to grow on the same or opposite sides in the vertical direction is assessed drawing upon energy-based arguments.
[1] Sasayama, H., and Tomoda, S., 2009. New Carbon Fiber Tow-Spread Technology and Applications to Advanced Composite Materials. S.A.M.P.E. journal, 45 (2), pp. 6-17.
[2] Saito, H., Takeuchi, H. and Kimpara, I., 2012. Experimental Evaluation of the Damage Growth Restraining in 90° Layer of Thin-ply CFRP Cross-ply Laminates. Advanced Composite Materials, 21, pp. 57-66.
[3] Parvizi, A., and Bailey, J.E., 1978. On multiple transverse cracking in glass fibre epoxy cross-ply laminates. Journal of Materials Science, 13 (10), pp. 2121-2136.
[4] Bailey, J. E., Curtis, P. T., and Parvizi, A., 1979. On the Transverse Cracking and Longitudinal Splitting Behaviour of Glass and Carbon Fibre Reinforced Epoxy Cross Ply Laminates and the Effect of Poisson and Thermally Generated Strain. Proceedings of the Royal Society of London, Series A, 366 (1727), pp. 599-623.
[5] Zhang, H., Ericson, M. L., Varna, J., and Berglund, L.A., 1997. Transverse single-fibre test for interfacial debonding in composites: 1. Experimental observations. Composites Part A: Applied Science and Manufacturing, 28 (4), pp. 309-315.

Research on scaling laws of damage in materials and structures has absorbed the attention of the Fracture Mechanics community since the inception of the field itself. The attractiveness of such relationships resides in their simplicity and predictive power, which would allow a more cost-effective design of structures. Building on early works in dimensional analysis by Buckingham [1], several results have been derived for metals and concrete [2]. Despite the considerable effort spent, Fiber Reinforced Polymer Composites (FRPCs) have proved themselves elusive to such simple analytical description and have even shown to possess counterintuitive thermo-mechanical behaviors, such as the thin-ply effect [3] in the context of transverse crack onset. At the microscopic level, the first appearance of transverse cracks is defined by the growth of fiber-matrix interface cracks (or debonds). Characterization of this damage mechanism has been focused on the evaluation of the Energy Release Rate (ERR) under different local and global configurations. Different expressions of a reference ERR have been proposed over the years since the publication of the first analytical solution by Toya [4], but the topic of scaling laws has been left largely unexplored. The aim of this work is to bridge this gap and, if not provide an exhaustive treatment, at least propose a framework to analyze the issue.
[1] E. Buckingham, On physically similar systems; illustrations of the use of empirical equations, Phys. Rev. 4 (1914) 345-376.
[2] Z. P. Bažant, Scaling Laws in Mechanics of Failure, J. Eng. Mech. 119 (1993) 1828-1844.
[3] D.L. Flaggs and M.H. Kural, Experimental Determination of the In Situ Transverse Lamina Strength in Graphite/Epoxy Laminates, J. Compos. Mater., 16 (1982) 103-116.
[4] M. Toya, A crack along the interface of a circular inclusion embedded in an infinite solid, J.Mech. Phys. .Solids, 22 (1974) 325-348.

A few manufacturers in the world, among them NTPT (USA-CH), Oxeon (SE), Chomarat (FR), Hexcel (USA) and Technomax (JP), offer today ultra-thin fiber reinforced composite plies with thicknesses of around 2-4 times the reinforcement’s diameter.
Values of the ratio of thickness to reinforcement diameter as small as those found in thin plies test the limits of classical homogenization methods. In the spirit of Saint Venant, the heterogeneity effect of adjacent plies can be neglected for a sufficiently thick ply as perturbation stress fields decrease exponentially along the thickness. Thus, ply mechanics can be studied by using Repeating Volume Elements (RVE) with periodic boundary conditions. The actual stress and strain distribution will differ from those calculated with the RVE only in a small region close to the boundary. As ply boundaries in thin plies are much closer to fibers in the bulk than in classical plies, their presence will have a measurable effect on the stress and strain fields at the fiber-matrix interface. Given the presence of a flaw, the effect of the boundary on crack initiation will not be negligible.
To evaluate the effect of boundary conditions on fiber/matrix debonding in thin ply laminates, a square element of ply with a single fiber and a single debond at the fiber-matrix interface is studied using FEM. Crack initiation is characterized through the evaluation of mode I, mode II and total energy release rates with the VCCT and the J-integral method. Validation is performed for the case of a single fiber in an infinite matrix, of which there exist an analytical and a numerical solution, the latter developed with use of the Boundary Element Method (BEM). The model is used to investigate the extreme case of a ply with a single layer of fibers subjected to transverse loading under different combinations of boundary conditions on its lower and upper surface. Thus, the element can possess one or two free surfaces, be bounded by a 0° layer from one or two sides, be symmetric with respect to the lower or upper side, or in general possess any combination of these conditions. The analysis is performed for different material systems and interaction effects are investigated by parametric studies over several parameters, namely fiber volume fraction, debond size and position, applied strain magnitude.

Introduit il y a environ 20 ans, la technologie dite en anglais spread tow technology a permis la production au niveau industriel des composites stratifiés avec couches extrêmement minces. Les producteurs de ce type de composite, comme North Thin Ply Technology en Suisse et Oxeon en Suède, sont aujourd’hui capables d’offrir des plis pré-imprégnés avec épaisseurs entre 2 et 4 fois le diamètre du renfort, dans les cas des fibres de carbone ou verre E à haut performance.
L’utilisation de couches minces dans stratifiés pour applications structurales a été prouvé bénéfique en raison de l’amélioration du comportement mécanique avec au même temps une réduction significative du poids. Le facteur clé de ce succès est un phénomène découvert expérimentalement il y a 40 ans, appelé thin ply effect dans la communauté des composites polymériques stratifiés. L’observation principale est que la contrainte maximale transversale à rupture mesuré dans un stratifié unidirectionnel n’est pas applicable à une couche très mince dans une stratifié générique. De toute façon, la contrainte maximale réel, connu comme in-situ strength, est beaucoup plus grande par rapport aux stratifié unidirectionnel.
La propagation du dommage dans stratifies avec couches minces et épais a été largement étudié à travers moyens expérimentales, analytique et numériques. Un grand nombre des recherches a montré l’utilité des simulations par éléments finis pour la modélisation des processus de fissuration transversale à l’échelle micromécanique. Plusieurs travaux proposent une reformulation de la complexité du phénomène avec une extension du nombre des paramètres caractérisants le matériau. Malheureusement, la plupart d’entre eux ne sont souvent pas accessibles à l’expérimentateur et il n’est donc pas possible de les mesurer avec un degré suffisant de confiance. Méthodes indirectes d’estimation ont été proposées, mais la possibilité d’une application fiable en dehors du domaine d’entraînement reste toujours une question ouverte.
Par contre, les mécanismes d’initiation des fissures dans couches minces a été négligé et ils représentent un domaine riche pour l’investigation. Il manque encore une connaissance approfondi de la dépendance du taux de restitution d’énergie par rapport à la position et dimension du décollement initial, l’orientation des plis contigus et leur épaisseur. De plus, pour une pleine description de ce mécanisme, il est important d’étudier les effets dû à la fraction volumique des fibres, les matériaux choisis, les conditions au bord, les caractéristiques de la charge appliquée et sa distribution spatiale. Deux buts principaux peuvent être envisagés : du point de vue du concepteur-projeteur, la production des principes et recommandations pour le projet optimal du stratifié ; du point de vue du numéricien, la définition des meilleures stratégies pour la modélisation de l’initiation des fissures. Pour adresser ces enjeux, plusieurs modèles bidimensionnels de Volume élémentaire représentatif (VER) ont été développés en combinant différents éléments : solveur, conditions au bord, charge appliquée, qualité du maillage. Diverses grandeurs de sortie sont calculés et analysés : les taux de restitution d’énergie, les contraintes et les déplacements à l’interface entre fibre et matrice, l’état de contrainte et de déformation sur sections radiales et circonférentielles.

Introduced around 20 years ago, the so-called spread tow technology has allowed the production on the industrial scale of extremely thin fiber-reinforced prepreg plies. The few manufacturers of this kind of composite material, such as North Thin Ply Technology in Switzerland and Oxeon in Sweden, are nowadays capable of providing prepregs with thicknesses up to 2/4 times the reinforcement's diameter for high-performance carbon and glass E fibers.
The employment of thin plies in laminates for structural applications has been proven beneficial in terms of increased mechanical performance and improved tolerance to damage with concurrent savings in weights, particularly in cross- and angle-ply stacking configurations. The key factor underpinning the success of this technology is a phenomenon first experimentally observed around 40 years ago. This is known as the thin ply effect in the composite community and made its appearance on the research stage thanks to a seminal paper by Parvizi and Bailey. The main observation is that the transverse strength at failure measured for unidirectional composites (UD) is not applicable to a thin layer inside a laminate. Its real strength, known as the in-situ strength, is in fact much higher.
Damage propagation in thin and thick plies has been extensively studied experimentally and modeled by analytical and numerical techniques. Simulations with the Finite Elements Method has been proven to be a valuable tool to model transverse fracture processes at the micromechanical level. Many models of damage propagation recast the complexity of the phenomenon into a greater set of material parameters; unfortunately, several of them are inaccessible by means of mechanical tests and thus cannot be reliably measured. Indirect methods of estimation have been proposed, but the applicability of such parameters outside the domain of training is still an open question.
On the other hand, crack initiation in thin plies has been mostly neglected and still represents a field ripe for investigation. Understanding is still lacking about the dependence of energy release rate with respect to debond size and position, the effect of adjacent plies, their thickness, and relative orientation. Furthermore, the influence of fiber volume fraction, material selection, boundary conditions, load type and distribution should be considered to grasp the inner workings of this phenomenon. Detailed knowledge of the mechanisms underlying the initiation of fracture processes inside a single ply is useful in a twofold way: from the designer’s perspective, by providing guidelines on optimal laminate design; from the modeler perspective, by highlighting the best strategies to simulate crack initiation in terms of solver selection, mesh quality, boundary’s conditions, load type and distribution. To address these issues, several 2-dimensional models of Representative Volume Element (RVEs) have been developed by combining together different variations of the aforementioned elements. Energy release rates are computed for different debond position and size, as well as contact stresses and displacements at fiber/matrix interface and elastic strains and stresses along selected radial and circumferential sections.

Introduced around 20 years ago, the so-called spread tow technology has allowed the production on the industrial scale of extremely thin fiber-reinforced prepreg plies. The few manufacturers of this kind of composite material, such as North Thin Ply Technology in Switzerland and Oxeon in Sweden, are nowadays capable of providing prepregs with thicknesses up to 2-4 times the reinforcement's diameter for high-performance carbon and glass E fibers.
The employment of thin plies in laminates for structural applications has been proven beneficial in terms of increased mechanical performance and improved tolerance to damage with concurrent savings in weights, particularly in cross- and angle-ply stacking configurations. The key factor underpinning the success of this technology is a phenomenon first experimentally observed around 40 years ago, known as the thin ply effect in the composite community. The main observation is that the transverse strength at failure measured for unidirectional composites (UD) is not applicable to a thin layer inside a laminate. Its real strength, known as the in-situ strength, is in fact much higher.
Damage propagation in thin and thick plies has been extensively studied experimentally and modeled by analytical and numerical techniques. Simulations with the Finite Elements Method have been proven to be valuable tools to model transverse fracture processes at the micromechanical level. Many models of damage propagation recast the complexity of the phenomenon into a greater set of material parameters; unfortunately, several of them are inaccessible to the experimenter and thus cannot be reliably measured. Indirect methods of estimation have been proposed, but the applicability of such parameters outside the domain of training is still an open question.
On the other hand, crack initiation in thin plies has been mostly neglected and still represents a field ripe for investigation. Understanding is still lacking about the dependence of energy release rate with respect to debond size and position, adjacent plies’ orientation and thickness. Furthermore, the influence of fiber volume fraction, material selection, boundary conditions, load type and distribution should be considered in order to grasp the inner workings of this phenomenon. Detailed knowledge of the mechanisms underlying the initiation of fracture inside a single ply is useful in a twofold way: from the designer’s perspective, by providing guidelines on optimal laminate design; from the modeler’s perspective, by highlighting the best strategies to simulate crack initiation in terms of solver selection, mesh quality, boundary conditions, load type and distribution.

Introduced around 20 years ago, the so-called spread tow technology has allowed the production on industrial scale of extremely thin fiber-reinforced prepreg plies. The few manufacturers of this kind of composite material, such as North Thin Ply Technology in Switzerland and Oxeon in Sweden, are nowadays capable of providing prepregs with thicknesses up to 2-4 times the reinforcement's diameter for high performance carbon and glass E fibers.
The employment of thin plies in laminates for structural applications has been proven beneficial in terms of increased mechanical performance and improved tolerance to damage with concurrent savings in weights, particularly in cross- and angle-ply stacking configurations. The key factor underpinning the success of this technology is a phenomenon first experimentally observed around 40 years ago, known as the thin ply effect in the composite community. The main observation is that the transverse strength at failure measured for unidirectional composites (UD) is not applicable to a thin layer inside a laminate. Its real strength, known as the in-situ strength, is in fact much higher.
Damage propagation in thin and thick plies has been extensively studied experimentally and modeled by analytical and numerical techniques. Simulations with the Finite Elements Method have been proven to be valuable tools to model transverse fracture processes at the micromechanical level. Many models of damage propagation recast the complexity of the phenomenon into a greater set of material parameters; unfortunately, several of them are inaccessible to the experimenter and thus cannot be reliably measured. Indirect methods of estimation have been proposed, but the applicability of such parameters outside the domain of training is still an open question.
On the other hand, crack initiation in thin plies has been mostly neglected and still represents a field ripe for investigation. Understanding is still lacking about the dependence of energy release rate with respect to debond size and position, adjacent plies’ orientation and thickness. Furthermore, the influence of fiber volume fraction, material selection, boundary conditions, load type and distribution should be considered in order to grasp the inner workings of this phenomenon. Detailed knowledge of the mechanisms underlying the initiation of fracture inside a single ply is useful in a twofold way: from the designer’s perspective, by providing guidelines on optimal laminate design; from the modeler’s perspective, by highlighting the best strategies to simulate crack initiation in terms of solver selection, mesh quality, boundary conditions, load type and distribution. To address these issues, several 2-D models of Representative Volume Elements (RVEs) have been developed by combining together different variations of the aforementioned elements. Energy release rates are computed for different debond position and size, as well as contact stresses and displacements at fiber/matrix interface and elastic strains and stresses along selected radial and circumferential sections.