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Influence of microstructure on debonding at the fiber/matrix interface in fiber-reinforced polymers under tensile loading
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Material Science. IJL, EEIGM, Université de Lorraine. (Polymeric Composite Materials)ORCID iD: 0000-0002-9261-301x
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Abstract [fr]

A la fin de la deuxi`eme d´ecennie du XXI si`ecle, l’industrie du transport fait face de nombreux d´efis qui d´etermineront son ´evolution dans la prochaine d´ecennie et au-del`a. Le premier d´efi est la sensibilisation croissante du grand public aux probl`emes environnementaux et, en cons´equence, l’intensification de l’action gouvernementale `a regard du changement climatique, fait qui d´etermine une mont´ee en pression sur tous les secteurs industriels qui sont grands ´emetteurs et dont lesquels le transport fait partie. Le deuxi`eme d´efi est repr´esent´e en revanche par la course `a la r´eduction des prix, dˆu `a une majeure concurrence (comme, par exemple, dans les secteurs des vecteurs spatiales avec l’entr´ee des acteurs priv´es dans le march´e) et `a nouveaux mod`eles commerciaux (comme le covoiturage dans l’industrie automobile ou les compagnies `a bas prix dans le transport a´erien). Une strat´egie simple mais efficace pour r´epondre `a ces d´efis est la r´eduction du poids des structures du v´ehicule, en maintenant constantes la capacit´e payante. Le premier effet de cette strat´egie est de r´eduire la consommation de carburant, fait qu’en revanche conduit `a une r´eduction des ´emissions dans les v´ehicules `a carburants fossiles et `a l’augmentation de l’autonomie des v´ehicules ´electriques. En outre, la r´eduction de la quantit´e des mat´eriaux utilis´ee dans les structures se traduit souvent en une r´eduction des coˆuts de fabrications et donc du prix pour l’utilisateur. D’autre cˆot´e le transport est un secteur dont l’attention `a la s´ecurit´e est prioritaire, avec des processus de certifications extrˆemement rigoureux. Cette exigence pose des contraintes consid´erables sur l’ampleur des interventions de r´eduction du poids des structures. Le d´eveloppement dans les derni`eres vingt ans d’un nouvel type de stratifi´e en polym`ere avec renfort en fibre, les stratifi´es thin-ply, propose une solution `a ce probl`eme en offrant des stratifies consid´erablement plus l´eg`eres avec, au mˆeme temps, des meilleures propri´et´es m´ecaniques. Nombreux essais ont en fait montr´e la capacit´e de ces stratifi´es de retarder et aussi empˆecher l’amor¸cage et la propagation des fissures transverses. Les fissures transverses repr´esentent un m´ecanisme de rupture `a l’´echelle des plis qui a lieu plutˆot tˆot dans le processus d’endommagement du stratifi´e et qui conduit `a la d´egradation des propri´et´es m´ecaniques du composite et favorise l’apparition des autres formes d’endommagement (d´elaminage, rupture des fibres) souvent plus critique pour l’int´egrit´e de la structure. Dans les ann´ees 1970, la capacit´e des stratifies composites de retarder l’amor¸cage des fissures transverses ´etait observ´ee et li´ee `a l’´epaisseur des plis. N´eanmoins, l’´epaisseur des thin-plies aujourd’hui sur le march´e est au moins 10 fois plus petit que celui des plis des ann´ees 1970. Ce fait se traduit par un changement d’´echelle du probl`eme, de millim`etres `a microm`etres. Au niveau microscopique, les fissures transxiii verses sont form´ees `a partir de nombreux d´ecollements (ou d´ecoh´esions) entre fibre et matrice connect´es entre eux. Une compr´ehension d´etaill´ee de m´ecanismes qui empˆechent les fissures transverses requiert la connaissance des ph´enom`enes d’amor¸cage des fissures transverse `a l’´echelle microm´ecanique et donc des conditions favorables `a l’amor¸cage et propagation des d´ecollements entre fibre et matrice. L’objectif principal de cette th`ese est d’´etudier l’effet de la microstructure sur l’amor¸cage et propagation de d´ecollements entre fibre et matrice. Dans ce but, des mod`eles de Volume El´ementaire Repr´esentatif (VER) des composites unidirectionnels et des stratifi´es crois´es sont d´evelopp´es, caract´eris´es par diff´erentes configurations des fibres et degr´e d’endommagement. L’amor¸cage du d´ecollement est analys´e par rapport `a la distribution des contraintes `a l’interface entre fibre et matrice. En revanche, la propagation du d´ecollement est ´etudi´ee avec l’approche de la M´ecanique Lin´eaire Elastique de la Rupture (MLER), et plus sp´ecifiquement avec l’´evaluation du taux de restitution d’´energie en Mode I et Mode II. Les champs de d´eplacement et contrainte sont calcul´es avec la M´ethode des ´el´ements finis (MEF) dans le logiciel Abaqus. La d´etermination des composants du taux de restitution d’´energie est effectu´ee avec la technique de fermeture virtuelle de fissure impl´ement´ee par l’auteur en langage Python. La solution ´elastique du probl`eme de d´ecollement entre fibre et matrice est caract´eris´ee par la pr´esence de deux r´egimes : celui de fissure ouverte et celui de fissure ferm´ee. Dans le deuxi`eme cas, il existe une zone proche de la pointe de fissure o`u les l`evres du d´ecollement sont en contact. Dans le premier cas, le d´ecollement est ouvert et il n’existe aucun contact entre les l`evres du d´ecollement. Dans le r´egime de fissure ouverte, les champs des d´eplacements et contraintes pr´esentent une singularit´e oscillatoire. Un ’´etude de convergence de la technique de fermeture virtuelle de fissure est donc requis et constitue le premier ´el´ement du travail de cette th`ese. Il est constat´e que le taux de restitution d’´energie total ne d´epend pas de la taille des ´el´ements proches de la pointe de fissure, alors que le taux en Mode I et Mode II pr´esent une d´ependance significative de la taille des ´el´ements dans le cas de fissure ouverte. Il est montr´e que le taux de restitution d’´energie en Mode I et Mode II ne converge pas, ce `a dire que le comportement asymptotique n’est pas limit´e. Par cons´equence, il n’est pas possible d’utiliser l’erreur entre it´erations successives comme mesure de la convergence de la solution et une comparaison est donc n´ecessaire avec des r´esultats obtenus avec une autre m´ethode. Le taux de restitution d’´energie calcul´e avec la m´ethode d’´el´ements de fronti`ere, disponible dans la litt´erature, est choisi comme r´ef´erence. Ensuite, la propagation de d´ecollement entre fibre et matrice est ´etudi´ee dans Volume El´ementaire Repr´esentative de : composites unidirectionnels avec ´epaisseur variable, mesur´e par le nombre des rang´ees des fibres, de ceux extrˆemement minces (une rang´ee des fibres) au plus ´epais ; stratifi´e crois´e avec un pli central `a 90◦ d’´epaisseur variable, mesur´e par le nombre des rang´ees des fibres, de ceux extrˆemement minces (une rang´ee des fibres) au plus ´epais ; composites unidirectionnels ´epais, mod´elis´es comme infinis `a travers l’´epaisseur. Configurations multiples de l’endommagement sont aussi examin´ees, qui correspondent `a diff´erentes ´etapes du processus d’amor¸cage des fissures transverses : d´ecollements isol´es ; d´ecollements interagissant distribu´es dans la direction d’application de la charge m´ecanique ; d´ecollements xiv localis´es sur fibres cons´ecutives `a travers l’´epaisseur. Entre les r´esultats plus importants, il est constat´e que ni l’´epaisseur du pli `a 90◦ ni l’´epaisseur du pli `a 0◦ influence le taux de restitution d’´energie du d´ecollement, diff´eremment de ce qu’a ´et´e observ´e pour les fissures transverses. En revanche, il est montr´e que le taux de restitution d’´energie est affect´e de mani`ere significative par l’interaction mutuelle entre d´ecollements dans la direction d’application de la charge et qu’il existe une distance caract´eristique (mesur´e par le nombre des fibres sans endommagement) d´eterminant la r´egion d’influence entre d´ecollements. Enfin, la taille du d´ecollement juste apr`es l’amor¸cage et la taille ultime du d´ecollement sont estim´ees `a partir de l’analyse de la distribution des contraintes `a l’interface entre fibre et matrice (pour l’amor¸cage) et sur la base du crit`ere de Griffith de la MLER. La taille maximale d’un d´ecollement dans un stratifi´e crois´e est estim´e dans l’intervalle 40◦ - 60◦ , r´esultat qui est en tr`es bon accord avec pr´ec´edentes observations microscopiques disponibles dans la litt´erature.

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2019.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords [en]
Fiber/matrix interface, Debonding, Polymer-Matrix Composites (PMC), Finite Element Method (FEM), Linear Elastic Fracture Mechanics (LEFM)
National Category
Composite Science and Engineering
Research subject
Polymeric Composite Materials
Identifiers
URN: urn:nbn:se:ltu:diva-76646ISBN: 978-91-7790-496-0 (print)ISBN: 978-91-7790-497-7 (electronic)OAI: oai:DiVA.org:ltu-76646DiVA, id: diva2:1368667
Public defence
2019-12-13, E632, E-Huset, Luleå University of Technology, Luleå, 08:30 (English)
Opponent
Supervisors
Available from: 2019-11-08 Created: 2019-11-08 Last updated: 2019-11-19Bibliographically approved
List of papers
1. Finite Element solution of the fiber/matrix interface crack problem: Convergence properties and mode mixity of the Virtual Crack Closure Technique
Open this publication in new window or tab >>Finite Element solution of the fiber/matrix interface crack problem: Convergence properties and mode mixity of the Virtual Crack Closure Technique
2019 (English)In: Finite elements in analysis and design (Print), ISSN 0168-874X, E-ISSN 1872-6925, Vol. 167, article id 103332Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Fiber/matrix interface crack, Bi-material interface arc crack, Linear Elastic Fracture Mechanics (LEFM), Virtual Crack Closure Technique (VCCT), Mode separation, Convergence
National Category
Composite Science and Engineering
Research subject
Polymeric Composite Materials
Identifiers
urn:nbn:se:ltu:diva-76252 (URN)10.1016/j.finel.2019.103332 (DOI)000493951600005 ()2-s2.0-85072852081 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-10-07 (johcin)

Available from: 2019-10-05 Created: 2019-10-05 Last updated: 2019-11-21Bibliographically approved
2. Energy release rate of the fiber/matrix interface crack in UD composites under transverse loading: Effect of the fiber volume fraction and of the distance to the free surface and to non-adjacent debonds
Open this publication in new window or tab >>Energy release rate of the fiber/matrix interface crack in UD composites under transverse loading: Effect of the fiber volume fraction and of the distance to the free surface and to non-adjacent debonds
2019 (English)In: Theoretical and applied fracture mechanics (Print), ISSN 0167-8442, E-ISSN 1872-7638, Vol. 103, article id 102251Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Polymer-matrix Composites (PMCs), Thin-ply, Energy Release Rate, Debonding, Finite Element Analysis (FEA)
National Category
Composite Science and Engineering
Research subject
Polymeric Composite Materials
Identifiers
urn:nbn:se:ltu:diva-75072 (URN)10.1016/j.tafmec.2019.102251 (DOI)000489191500024 ()2-s2.0-85066800172 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-06-27 (johcin)

Available from: 2019-06-27 Created: 2019-06-27 Last updated: 2019-11-08Bibliographically approved
3. Effect of the proximity to the 0°/90° interface on Energy Release Rate of fiber/matrix interface crack growth in the 90°-ply of a cross-ply laminate under tensile loading
Open this publication in new window or tab >>Effect of the proximity to the 0°/90° interface on Energy Release Rate of fiber/matrix interface crack growth in the 90°-ply of a cross-ply laminate under tensile loading
2019 (English)In: Journal of composite materials, ISSN 0021-9983, E-ISSN 1530-793XArticle in journal (Refereed) Submitted
Abstract [en]

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 support the claim that debond growth is not affected by the plythickness effect.

Keywords
Polymer-matrix Composites (PMCs), Fibre/matrix bond, Debonding, Finite Element Analysis (FEA)
National Category
Composite Science and Engineering
Research subject
Polymeric Composite Materials
Identifiers
urn:nbn:se:ltu:diva-76253 (URN)
Available from: 2019-10-05 Created: 2019-10-05 Last updated: 2019-11-08
4. Growth of interface cracks on consecutive fibers: on the same or on the opposite sides?
Open this publication in new window or tab >>Growth of interface cracks on consecutive fibers: on the same or on the opposite sides?
2019 (English)Conference paper (Refereed)
Abstract [en]

The growth of fiber/matrix interface cracks (debonds) locatedon consecutive fibers along the through-the-thickness (vertical)direction is studied in glass fiber-epoxy UD composites. Debonds couldappear, along the vertical direction, on the same or on opposite sides oftheir respective fibers. Determining which configuration is the mostenergetically favorable to debond growth is the objective of this paper.To this end, two different families of Representative Volume Elements(RVEs) are developed: the first implements the classic condition ofcoupling of the vertical displacements to model a unit cell repeating symmetrically along the vertical direction; the second uses a novel setof boundary conditions, proposed here by the authors, to represent a unitcell repeating anti-symmetrically along the vertical direction. The modelis analyzed in the context of Linear Elastic Fracture Mechanics (LEFM)and the Mode I and Mode II Energy Release Rate are evaluated toinvestigate crack growth. The calculation is performed using the VirtualCrack Closure Technique (VCCT) in the framework of the Finite ElementMethod (FEM). It is found that Mode I dominated propagation is favoredwhen debonds are located on the same sides of their respective fibers;while for larger (Mode II-dominated) debonds, Mode II ERR is higher whenthey lie on the opposite sides. No interaction effect is present when atleast two fully bonded fibers are located between the partially debonded ones.

Keywords
Polymer Matrix Composite (PMC), Fracture mechanics, Debonding, Debond Interaction
National Category
Composite Science and Engineering
Research subject
Polymeric Composite Materials
Identifiers
urn:nbn:se:ltu:diva-76255 (URN)
Conference
12th International Conference on Composite Science and Technology (ICCST 12)
Available from: 2019-10-05 Created: 2019-10-05 Last updated: 2019-12-10
5. Estimating the average size of fiber/matrix interface cracks in UD and cross-ply laminates
Open this publication in new window or tab >>Estimating the average size of fiber/matrix interface cracks in UD and cross-ply laminates
2019 (English)In: / [ed] A. Turon, P. Maimi, M. Fagerström, 2019Conference paper, Published paper (Refereed)
Abstract [en]

Initiation and propagation of fiber/matrix interface cracks are analyzed in Representative Volume Elements (RVEs) of UD and cross-ply laminates. By studying the distribution of stresses at the fiber/matrix interface in the undamaged case, an estimate of the initial flaw size is derived. By adopting a 2-parameters energy-based criterion for propagation [1], we then proceed to the estimation of the expected debond size in different microstructural arrangements. Finally, the results are compared with microscopic observations available in the literature [2].

Keywords
Fiber Reinforced Polymer (FRP), Debonding, Linear Elastic Fracture Mechanics (LEFM)
National Category
Composite Science and Engineering
Research subject
Polymeric Composite Materials; Polymeric Composite Materials; Polymeric Composite Materials; Polymeric Composite Materials
Identifiers
urn:nbn:se:ltu:diva-76254 (URN)
Conference
7th ECCOMAS Conference of the Mechanical Response of Composites (COMPOSITES 2019)
Available from: 2019-10-05 Created: 2019-10-05 Last updated: 2019-11-08

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