Delamination behaviour of composites · 2 Delamination in the context of composite structural...

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Page 1: Delamination behaviour of composites · 2 Delamination in the context of composite structural design 28 A RICCIO, C.I.R.A. (Centro Italiano Ricerche Aerospaziali – Italian Aerospace

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Multi-scale modelling of composite material systems(ISBN 978-1-85573-936-9)Predictive modelling provides the opportunity both to understand better howcomposites behave in different conditions and to develop materials with enhancedperformance for particular industrial applications. This important book focuses onthe fundamental understanding of composite materials at the microscopic scale,from designing micro-structural features, to the predictive equations of thefunctional behaviour of the structure for a specific end-application. Chaptersdiscuss stress and temperature-related behavioural phenomena based onknowledge of physics of microstructure and microstructural change over time.

Impact behaviour of fibre-reinforced composite materials and structures(ISBN 978-978-1-8573-423-4)This study covers impact response, damage tolerance and failure of fibre-reinforced composite materials and structures. Materials development, analysisand prediction of structural behaviour and cost-effective design all have a bearingon the impact response of composites and this book brings together for the firsttime the most comprehensive and up-to-date research work from leadinginternational experts.

Mechanical testing of advanced fibre composites(ISBN 978-1-85573-312-1)Testing of composite materials can present complex problems but is essential inorder to ensure the reliable, safe and cost-effective performance of anyengineering structure. Mechanical testing of advanced fibre composites describesa wide range of test methods which can be applied to various types of advancedfibre composites. The book focuses on high modulus, high strength fibre/plasticcomposites and also covers highly anisotropic materials such as carbon, aramidand glass.

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itedDelamination

behaviour ofcomposites

Edited bySrinivasan Sridharan

Published by Woodhead Publishing and Maney Publishingon behalf of

The Institute of Materials, Minerals & Mining

CRC PressBoca Raton Boston New York Washington, DC

W O O D H E A D P U B L I S H I N G L I M I T E DCambridge England

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Woodhead Publishing Limited and Maney Publishing Limited on behalf ofThe Institute of Materials, Minerals & Mining

Woodhead Publishing Limited, Abington Hall, Granta Park, Great Abington,Cambridge CB21 6AH, Englandwww.woodheadpublishing.com

Published in North America by CRC Press LLC, 6000 Broken Sound Parkway, NW,Suite 300, Boca Raton, FL 33487, USA

First published 2008, Woodhead Publishing Limited and CRC Press LLC© 2008, Woodhead Publishing LimitedThe authors have asserted their moral rights.

This book contains information obtained from authentic and highly regarded sources.Reprinted material is quoted with permission, and sources are indicated. Reasonableefforts have been made to publish reliable data and information, but the author and thepublishers cannot assume responsibility for the validity of all materials. Neither theauthor nor the publishers, nor anyone else associated with this publication, shall beliable for any loss, damage or liability directly or indirectly caused or alleged to becaused by this book.

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Contents

Contributor contact details xvii

Introduction xxiii

S SRIDHARAN, Washington University in St. Louis USA

Part I Delamination as a mode of failure andtesting of delamination resistance

1 Fracture mechanics concepts, stress fields, strainenergy release rates, delamination initiation andgrowth criteria 3

I S RAJU and T K O’BRIEN, NASA-Langley Research Center, USA

1.1 Introduction 31.2 Fracture mechanics concepts 41.3 Delaminations 101.4 Future trends 231.5 Concluding remarks 241.6 References 25

2 Delamination in the context of composite structuraldesign 28

A RICCIO, C.I.R.A. (Centro Italiano Ricerche Aerospaziali –Italian Aerospace Research Centre), Italy

2.1 Introduction 282.2 Physical phenomena behind delamination onset 302.3 Physical phenomena behind delamination growth 362.4 Introduction to delamination management in composites

design 392.5 Impact induced delamination resistance in composites

preliminary design 41

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2.7 Cost-effective delamination management 552.8 References 60

3 Review of standard procedures for delaminationresistance testing 65

P DAVIES, IFREMER Centre de Brest, France

3.1 Introduction 653.2 Historical background 663.3 Mode I 673.4 Mode II 703.5 Mode III 743.6 Mixed mode I/II 763.7 Conclusion on fracture mechanics tests to measure

delamination resistance 793.8 Future trends 803.9 Conclusion 813.10 Sources of information and advice 813.11 Acknowledgements 813.12 References 81

4 Testing methods for dynamic interlaminar fracturetoughness of polymeric composites 87

C T SUN, Purdue University, USA

4.1 Introduction 874.2 Dynamic loading and crack propagation 904.3 Mode I loading with double cantilever beam (DCB) for

low crack velocity 934.4 High crack velocity with modified double cantileave

beam (DCB) and end notch flexure (ENF) 954.5 Mode I by wedge loading with hopkinson bar 1044.6 Acknowledgment 1154.7 References 115

5 Experimental characterization of interlaminar shearstrength 117

R GANESAN, Concordia University, Canada

5.1 Introduction 1175.2 Short beam shear test 1185.3 Double-notch shear test 1255.4 Arcan Test 133

Contentsvi

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ited5.5 Conclusion 134

5.6 References 1355.7 Appendix: Nomenclature 136

Part II Delamination: detection and characterization

6 Integrated and discontinuous piezoelectricsensor/actuator for delamination detection 141

P TAN and L TONG, University of Sydney, Australia

6.1 Introduction 1416.2 Typical patterns for piezoelectric (PZT) or-piezoelectric

fiber reinforced composite (PFRC) sensor/actuator 1436.3 Constitutive equations and modelling development for a

laminated beam with a single delamination andsurface-bonded with an integrated piezoelectricsensor/actuator (IPSA) 146

6.4 Parametric study 1496.5 Experimental verification 1576.6 Conclusions 1656.7 Acknowledgment 1656.8 References 1656.9 Appendix 167

7 Lamb wave-based quantitative identification ofdelamination in composite laminates 169

Z SU, The Hong Kong Polytechnic University, Hong Kong andL YE, The University of Sydney, Australia

7.1 Introduction 1697.2 Lamb waves in composite laminates 1707.3 Lamb wave scattering by delamination 1777.4 Lamb wave-based damage identification for composite

structures 1807.5 Design of a diagnostic lamb wave signal 1817.6 Digital signal processing (DSP) 1827.7 Signal pre-processing and de-noising 1867.8 Digital damage fingerprints (DDF) 1877.9 Data fusion 1937.10 Sensor network for delamination identification 1987.11 Case studies: evaluation of delamination in composite

laminates 2027.12 Conclusion 211

Contents vii

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7.14 References 212

8 Acoustic emission in delamination investigation 217

J BOHSE, BAM-Federal Institute for Materials Research and Testing,Germany and A J BRUNNER, Empa-Swiss Federal Laboratories forMaterials Testing and Research, Switzerland

8.1 Introduction 2178.2 Acoustic emission (AE) analysis 2188.3 Acoustic emission analysis applied to investigation of

delaminations in fiber-reinforced, polymer-matrix (FRP) 2228.4 Acoustic emission monitoring of delaminations in

fiber-reinforcd, polymer matrix composite specimens 2238.5 Acoustic emission investigation of delaminations in

structural elements and structures 2538.6 Advantages and limitations for acoustic emission

delamination investigations 2678.7 Related nondestructive acoustic methods for delamination

investigations 2728.8 Summary and outlook 2728.9 Acknowledgments 2738.10 References 273

Part III Analysis of delamination behaviour from tests

9 Experimental study of delamination in cross-plylaminates 281

A J BRUNNER, Empa-Swiss Federal Laboratories for MaterialsTesting and Research, Switzerland

9.1 Introduction 2819.2 Summary of current state 2829.3 Experimental methods for studying delaminations 2859.4 Fracture mechanics study of delamination in cross-ply

laminates 2869.5 Discussion and interpretation 3009.6 Structural elements or parts with

cross-ply laminates 3049.7 Summary and outlook 3059.8 Acknowledgments 3059.9 References 305

Contentsviii

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ited10 Interlaminar mode II fracture characterization 310

M F S F DE MOURA, Faculdade de Engenharia da Universidadedo Porto, Portugal

10.1 Introduction 31010.2 Static mode II fracture characterization 31110.3 Dynamic mode II fracture characterization 32110.4 Conclusions 32410.5 Acknowledgements 32410.6 References 325

11 Interaction of matrix cracking and delamination 327

M F S F DE MOURA, Faculdade de Engenharia da Universidade doPorto, Portugal

11.1 Introduction 32711.2 Mixed-mode cohesive damage model 33211.3 Continuum damage mechanics 33811.4 Conclusions 34111.5 References 342

12 Experimental studies of compression failure ofsandwich specimens with face/core debond 344

F AVILÉS, Centro de Investigación Científica de Yucatán, A C,México and L A CARLSSON, Florida Atlantic University, USA

12.1 Introduction 34412.2 Compression failure mechanism of debonded structures 34412.3 Compression failure of debonded sandwich columns 34612.4 Compression failure of debonded sandwich panels 35312.5 Acknowledgments 36212.6 References 362

Part IV Modelling delamination

13 Predicting progressive delamination via interfaceelements 367

S HALLETT, University of Bristol, UK

13.1 Introduction 36713.2 Background to the development of interface elements 36713.3 Numerical formulation of interface elements 36813.4 Applications 37313.5 Enhanced formulations 380

Contents ix

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13.7 Acknowledgements 38213.8 References 382

14 Competing cohesive layer models for prediction ofdelamination growth 387

S SRIDHARAN, Washington University in St. Louis, USAand Y LI, Intel Corporation, USA

14.1 Introduction 38714.2 UMAT (user material) model 38814.3 UEL (user supplied element) model 39114.4 Double cantilever problem 39414.5 UMAT model: details of the study and discussion of results 39414.6 UEL model: details of the study and discussion of results 40314.7 Delamination of composite laminates under impact 40714.8 Conclusion 42714.9 References 427

15 Modeling of delamination fracture in composites:a review 429

R C YU, Universidad de Castilla-La Mancha, Spain and A PANDOLFI,Politecnico di Milano Italy

15.1 Introduction 42915.2 The cohesive approach 43115.3 Delamination failure in fiber reinforced composites 43215.4 Delamination failure in layered structures 44015.5 Summary and conclusions 45015.6 Acknowledgement 45115.7 References 452

16 Delamination in adhesively bonded joints 458

B R K BLACKMAN, Imperial College London, UK

16.1 Introduction 45816.2 Adhesive bonding of composites 45816.3 Fracture of adhesively bonded composite joints 46016.4 Future trends 47916.5 Sources of further information and advice 48016.6 References 481

Contentsx

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P P CAMANHO, Universidade do Porto, Portugal and A TURON andJ COSTA, University of Girona, Spain

17.1 Introduction and motivation 48517.2 Experimental data 48617.3 Damage mechanics models 48817.4 Simulation of delamination growth under fatigue loading

using cohesive elements: cohesive zone model approach 49017.5 Numerical representation of the cohesive zone model 49117.6 Constitutive model for high-cycle fatigue 49317.7 Examples 49817.8 Mode I loading 49817.9 Mode II loading 50217.10 Mixed-mode I and II loading 50417.11 Fatigue delamination on a skin-stiffener structure 50517.12 Conclusions 51017.13 Acknowledgments 51017.14 References 511

18 Single and multiple delamination in the presence ofnonlinear crack face mechanisms 514

R MASSABÒ, University of Genova, Italy

18.1 Introduction 51418.2 The cohesive- and bridged-crack models 51518.3 Characteristic length scales in delamination fracture 52818.4 Derivation of bridging traction laws 53518.5 Single and multiple delamination fracture 53918.6 Final remarks 55318.7 Acknowledgement 55518.8 References 555

Part V Analysis of structural performance in presenceof delamination and prevention/mitigation ofdelamination

19 Determination of delamination damage incomposites under impact loads 561

A F JOHNSON and N TOSO-PENTECÔTE, German Aerospace Center(DLR), Germany

19.1 Introduction 56119.2 Composites failure modelling 563

Contents xi

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19.4 Delamination damage in high velocity impact 57619.5 Conclusions and future outlook 58319.6 References 584

20 Delamination buckling of composite cylindricalshells 586

A TAFRESHI, The University of Manchester, UK

20.1 Introduction 58620.2 Finite element analysis 58820.3 Validation study 59720.4 Results and discussion: analysis of delaminated

composite cylindrical shells under different types ofloadings 597

20.5 Conclusion 61420.6 References 616

21 Delamination failure under compression ofcomposite laminates and sandwich structures 618

S SRIDHARAN, Washington University in St. Louis, USA, Y LI, IntelCorporation, USA and El-Sayed, Caterpillar Inc., USA

21.1 Introduction 61821.2 Case study (1): composite laminate under longitudinal

compression 61921.3 Case study (2): dynamic delamination of an axially

compressed sandwich column 62821.4 Case study (3): two-dimensional delamination of

laminated plates 63521.5 Results and discussion 64421.6 Conclusion 64721.7 References 648

22 Self-healing composites 650

M R KESSLER, Iowa State University, USA

22.1 Introduction 65022.2 Self-healing concept 65222.3 Healing-agent development 65722.4 Application to healing of delamination damage in FRPs 66122.5 Conclusions 67022.6 References 671

Contentsxii

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H Y LIU, The University of Sydney, Australia andW YAN, Monash University, Australia

23.1 Introduction 67423.2 Z-pin bridging law 67523.3 Effect of Z-pin bridging on composite delamination 67723.4 Z-pin bridging under high loading rate 69323.5 Fatigue degradation on Z-pin bridging force 69923.6 Future trends 70323.7 References 704

24 Delamination suppression at ply drops by plychamfering 706

M R WISNOM and B KHAN, University of Bristol, UK

24.1 Introduction 70624.2 Behaviour of tapered composites with

ply drops 70724.3 Methods of chamfering plies 71124.4 Results of ply chamfering 71124.5 Summary and conclusions 71924.6 References 720

25 Influence of resin on delamination 721

S MALL, Air Force Institute of Technology, USA

25.1 Introduction 72125.2 Resin toughness versus composite toughness 72225.3 Resin toughness effects on different modes 72525.4 Resin effects on cyclic delamination behaviour 72925.5 Temperature considerations 73325.6 Effects of interleafing and other methods 73525.7 Summary 73725.8 References 739

Index 741

Contents xiii

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Introduction

S. Sridharan*Department of Mechanical,

Aerospace and StructuralEngineering

Washington University in St. LouisSt. Louis, MO 63130USA

E-mail: [email protected]

Chapter 1

I. S. Raju* and T. K. O’BrienNASA-Langley Research Center

Hampton, VA 23861USA

E-mail: [email protected]

Chapter 2

A. RiccioC I R A (Centro Italiano Ricerche

Aerospaziali – Italian AerospaceResearch Centre)

Via Maiorise, S/N81043Capua (Caserta)Italy

E-mail: [email protected]

Chapter 3

P. DaviesMaterials and Structures Group(DOP/DCB/ERT/MS)IFREMER Centre de BrestBP7029280 PlouzanéFrance

E-mail: [email protected]

Chapter 4

C. SunSchool of Aeronautics and

AstronauticsPurdue UniversityWest Lafayette, IN 47907USA

E-mail: [email protected]

(* = main contact)

Contributor contact details

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R. GanesanConcordia Centre for CompositesDepartment of Mechanical and

Industrial EngineeringConcordia UniversityRoom EV 4 - 211, 1515 StCatherine WestMontrealQuebec H3G 2W1Canada

E-mail: [email protected]

Chapter 6

P. Tan?1 and L. Tong*School of AerospaceMechanical and Mechatronic

EngineeringUniversity of SydneyNSW 2006Australia

E-mail: [email protected]@aeromech.usyd.edu.au

Chapter 7

Z. SuThe Department of Mechanical

EngineeringThe Hong Kong Polytechnic

UniversityHung HomKowloonHong Kong

E-mail: [email protected]@aeromech.usyd.edu.au;

L. Ye*Centre for Advanced MaterialsTechnology (CAMT)School of AerospaceMechanical and Mechatronic

Engineering (AMME)The University of SydneyNSW 2006Australia

E-mail: [email protected]

Chapter 8

J. Bohse*BAM – Federal Institute forMaterials Research and TestingDivision V.6 Mechanical Behaviour

of PolymersUnter den Eichen 87D-12205 BerlinGermany

E-mail: [email protected]

A. J. BrunnerLaboratory for Mechanical Systems

EngineeringEmpa – Swiss Federal Laboratories

for Materials Testing andResearch

Ueberlandstrasse 129CH-8600 DuebendorfSwitzerland

E-mail: [email protected]

Contributor contact detailsxvi

1 Ping Tan is currently working as a research scientist at the Australian Defence Scienceand Technology Organisation

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itedChapter 9

A. J. BrunnerLaboratory for Mechanical Systems

EngineeringEmpa – Swiss Federal Laboratories

for Materials Testing andResearch

Ueberlandstrasse 129CH-8600 DuebendorfSwitzerland

E-mail: [email protected]

Chapters 10 and 11

Marcelo Francisco de SousaFerreira de MouraDepartamento de Engenharia

Mecânica e Gestão IndustrialFaculdade de Engenharia daUniversidade do Porto

Rua Dr. Roberto Frias s/n, 4200-465 PortoPortugal

E-mail: [email protected]

Chapter 12

F. Avilés*Centro de Investigación Científica

de Yucatán, A.C.Unidad de MaterialesCalle 43 # 103Col. Chuburná de HidalgoC.P. 97200.MéridaYucatánMéxico

L. CarlssonDepartment of Mechanical

EngineeringFlorida Atlantic UniversityBoca Raton, FL 33431USA

E-mail: [email protected]@fau.edu

Chapter 13

S. HallettAdvance Composites Centre for

Innovation and ScienceUniversity of BristolQueens BuildingUniversity WalkBristol BS8 1TRUK

E-mail: [email protected]

Chapters 14 and 21

S. Sridharan*Department of Mechanical,Aerospace and Structural

EngineeringWashington University in St. LouisSt. Louis, MO 63130USA

E-mail : [email protected]

Y. LiIntel CorporationChandler, AZ 85224USA

E-mail: [email protected]

Contributor contact details xvii

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R. Yu*E.T.S Ingenieros de Caminos,Canales y PuertosUniversidad de Castilla-La Mancha13071 Ciudad RealSpain

E-mail: [email protected]

A. PandolfiDipartimento di Ingegneria

StrutturalePolitecnico di MilanoPiazza Leonardo da Vinci 3220133 MilanoItaly

E-mail: [email protected]

Chapter 16

B. BlackmanDepartment of Mechanical

EngineeringImperial College LondonLondon SW7 2AZUK

E-mail: [email protected]

Chapter 17

P. Camanho*DEMEGIFaculdade de EngenhariaUniversidade do Porto

Rua Dr. Roberto Frias4200-465 PortoPortugal

E-mail: [email protected]

A. Turon and J. CostaAMADE

Polytechnic SchoolUniversity of Girona

Campus Montilivii s/n17071 GironaSpain

Chapter 18

Roberta MassabòDepartment of Civil,

Environmental and ArchitecturalEngineering

University of GenovaVia Montallegro, 116145, GenovaItaly

E-mail: [email protected]

Chapter 19

Alastair F. Johnson and NathalieToso-Pentecôte

German Aerospace Center (DLR)Institute of Structures and Design

Pfaffenwaldring 38-4070569 StuttgartGermany

E-mail: [email protected]

Contributor contact detailsxviii

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itedChapter 20

A. TafreshiSchool of Mechanical

Aerospace and Civil EngineeringThe University of ManchesterP.O. Box 88Sackville StreetManchester M60 1QDUK

E-mail:[email protected]

Chapter 22

M. KesslerIowa State UniversityMaterials Science and Engineering2220 Hoover HallAmes, IA 50011-2300USAE-mail: [email protected]

Chapter 23

H. Liu*Centre for Advanced Materials

TechnologySchool of AerospaceMechanical and Mechatronic

EngineeringThe University of SydneySydneyNSW 2006Australia

E-mail: [email protected]

Contributor contact details xix

W. YanDepartment of Mechanical

EngineeringMonash UniversityMelbourneVictoria 3800Australia

E-mail:[email protected]

Chapter 24

M. R. WisnomUniversity of BristolAdvanced Composites Centre for

Innovation and ScienceQueens BuildingUniversity WalkBristol BS8 1TRUK

E-mail: M. [email protected]

Chapter 25

S. MallAir Force Institute of TechnologyAFIT/ENYBldg. 6402950 Hobson WayWright-Patterson AFB, OH 45433USA

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S S R I D H A R A N, Washington University in St. Louis, USA

E-mail: [email protected]

Introduction

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Introductionxxii

Laminated composites are becoming the preferred material system in a varietyof industrial applications, such as aeronautical and aerospace structures, shiphulls in naval engineering, automotive structural parts, micro-electro-mechanical systems as also civil structures for strengthening concrete members.The increased strength and stiffness for a given weight, increased toughness,increased mechanical damping, increased chemical and corrosion resistancein comparison to conventional metallic materials and potential for structuraltailoring are some of the factors that have contributed to the advancement oflaminated composites. Their increased use has underlined the need forunderstanding their modes of failure and evolving technologies for the continualenhancement of their performance.

The principal mode of failure of layered composites is the separationalong the interfaces of the layers, viz. delamination. This type of failure isinduced by interlaminar tension and shear that develop due to a variety offactors such as: Free edge effects, structural discontinuities, localizeddisturbances during manufacture and in working condition, such as impactof falling objects, drilling during manufacture, moisture and temperaturevariations and internal failure mechanisms such as matrix cracking. Hiddenfrom superficial visual inspection, delamination lies often buried betweenthe layers, and can begin to grow in response to an appropriate mode ofloading, drastically reducing the stiffness of the structure and thus the life ofthe structure. The delamination growth often occurs in conjunction withother modes of failure, particularly matrix cracking.

A study of composite delamination, as does any technological discipline,has two complementary aspects: An in depth understanding of the phenomenonby analysis and experimentation and the development of strategies foreffectively dealing with the problem. These in turn lead to a number ofspecific topics that we need to consider in the present context. These compriseof:

1. An understanding of the basic principles that govern the initiation ofdelamination, its growth and its potential interaction with other modesof failure of composites. This is the theme of the first chapter, but severalauthors return to this theme in their own respective contributions.

2. The determination of material parameters that govern delaminationinitiation and growth by appropriate testing. These must necessarily beinterfacial strength parameters which govern interlaminar fracture initiationand interlaminar fracture toughness parameters, viz. critical strain energyrelease rates that must govern interlaminar crack growth. The book containsseveral valuable contributions from leading international authorities inthe field of testing of composites.

3. Development of analytical tools : What are the methodologies one mayemploy to assess the possibility of delamination onset and growth under

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Introduction xxiii

typical loading scenarios? This may be approached from the points ofview of fracture mechanics, damage mechanics, cohesive modelingapproach and approaches which draw from and combine these. In particular,the cohesive modeling approach has proven to be a powerful and versatiletool in that when embedded in a nonlinear finite element analysis, it cantrace the two-dimensional delamination growth without user interference,is robust from the point of view of numerical convergence, and canpotentially account for a variety of interfacial failure mechanisms. Thissubject is discussed thoroughly in several authoritative contributions.

4. Detection of delamination: Ability to diagnose the presence of delaminationand to be able to capture in graphical terms the extent of delaminationdamage is a desideratum towards which the composite industry iscontinuing to make progress. Several nondestructive evaluation toolsare available and have been used with varying degrees of success. Acousticemission, Lamb-wave and Piezo-electric technologies are discussed inthe context of delamination detection in the present work.

5. Prevention of delamination: Several techniques of either inhibitingdelamination or altogether suppressing it are available. The book containsa section treating the following techniques of delamination prevention/inhibition: ‘Self-healing’ composites which internally exude adhesivematerial as soon as crack advances thus effectively arresting the crack;Z-pin bridging in which fibers are introduced across the interlaminarsurfaces, liable to delaminate, artfully tapering off discontinuities whichare sources of potential delamination and the use of toughened epoxies.

6. Delamination driven structural failure: Certain loading scenarios cancause delamination growth if there is some preexisting delamination inthe structural component which in turn can lead to structural failure.Typically these are: Impact, cyclic loading (delamination due to fatigue),compressive loading causing localized buckling in the vicinity ofdelamination and dynamic loading in the presence of in-plane compression.Impact loading and any form of dynamic loading in the presence ofsignificant compressive stress in sandwich structures are known to triggerdelamination failure which is abrupt and total. These aspects have beendiscussed in several contributions.

The book has been divided into several sections to address the issuesmentioned in the foregoing. It has been a pleasure to work with a number ofauthors of international standing and reputation who had spent a great dealof effort in developing their respective chapters. The references cited at theend of each chapter should supplement and corroborate the concepts developedin the chapter. We hope that researchers and engineers who are concerned toapply state of the art technologies to composite structural analysis, designand evaluation of risk of failure will find this book useful and a valuablesource of insight.

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310

10.1 Introduction

The application of composite materials in the aircraft and automobile industrieshas led to an increase of research into the fracture behaviour of composites.One of the most significant mechanical properties of fibre reinforced polymercomposites is its resistance to delamination onset and propagation. It isknown that delamination can induce significant stiffness reduction leadingto premature failures. Delamination can be viewed as a crack propagationphenomenon, thus justifying a typical application of fracture mechanicsconcepts. In this context, the interlaminar fracture characterization ofcomposites acquires remarkable relevancy. There are several tests proposedin the literature in order to measure the interlaminar strain energies releaserates in mode I, mode II and mixed mode I/II. Whilst mode I has alreadybeen extensively studied and the Double Cantilever Test (DCB) test isuniversally accepted, mode II is not so well studied, which can be explainedby some difficulties inherent to experimental tests. Moreover, in many realsituations delaminations propagate predominantly in mode II, as is the caseof composite plates under low velocity impact (Choi and Chang, 1992). Thisgives relevancy to the determination of toughness propagation values insteadof the initiation ones commonly considered in design. Some non-negligibledifferences can be achieved considering the R-curve effects (de Morais andPereira, 2007). These issues make the fracture characterization in mode II anactual and fundamental research topic. However, problems related to unstablecrack growth and to crack monitoring during propagation preclude a rigorousmeasurement of GIIc. In fact, in the mode II fracture characterization teststhe crack tends to close due to the applied load, which hinders a clearvisualization of its tip. In addition, the classical data reduction schemes,based on beam theory analysis and compliance calibration, require crackmonitoring during propagation. On the other hand, a quite extensive FractureProcess Zone (FPZ) ahead of crack tip exists under mode II loading. Thisnon-negligible FPZ affects the measured toughness as a non-negligible amount

10Interlaminar mode II fracture

characterization

M. F. S. F. d e M O U R A, Faculdade de Engenharia daUniversidade do Porto, Portugal

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Interlaminar mode II fracture characterization 311

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itedof energy is dissipated on it. Consequently, its influence should be taken into

account, which does not occur when the real crack length is used in theselected data reduction scheme. To overcome these difficulties a new datareduction scheme based on crack equivalent concepts and depending only onthe specimen compliance is presented in the next section. The main objectiveof the proposed methodology is to increase the accuracy of experimentalmode II fracture tests on the GIIc measurements. In fact, a rigorous monitoringof the crack length during propagation is one of the complexities of thesetests.

10.2 Static mode II fracture characterization

There are three fundamental experimental tests used to measure GIIc. Themost popular one is the End Notched Flexure (ENF), which was developedfor wood fracture characterization (Barrett and Foschi, 1977). The test consistson a pre-cracked specimen under three point bending loading (see Fig. 10.1).

a δ, P

ENF 2h

L L

δ, P

ELS 2h

a

L

δ, P

4ENF 2h

a d

L L

10.1 Schematic representations of the mode II tests.

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itedUnstable crack propagation constitutes one of the disadvantages of the ENF

test. Another possibility is the End Loaded Split (ELS) test which is based oncantilever beam geometry (see Fig. 10.1). Although the ELS test involvesmore complexities during experiments relatively to the ENF test, it providesa larger range of crack length where the crack propagates stably. In fact, theENF test requires a0/L>0.7 to obtain stable crack propagation (Carlsson etal., 1986), whereas in the ELS test a0/L>0.55 is sufficient (Wang and Vu-Khanh, 1996). However, both of these tests present a common difficultyrelated to the crack length measurement during the experimental test. Differentmethods have been proposed in literature to address these difficulties.Kageyama et al. (1991) proposed a Stabilized End Notched Flexure (SENF)test for experimental characterization of mode II crack growth. A specialdisplacement gage was developed for direct measurement of the relativeshear slip between crack surfaces of the ENF specimen. The test was performedunder constant crack shear displacement rate, which guarantees stable crackpropagation. Yoshihara et al. (Yoshihara and Ohta, 2000) recommended theuse of Crack Shear Displacement method (CSD) to obtain the mode II R-curve since the crack length is implicitly included in the CSD. Tanaka et al.(Tanaka et al., 1995) concluded that to extend the stabilized crack propagationrange in the ENF test, the test should be done under a condition of controlledCSD. Although the CSD method provides the measurement of the mode IItoughness without crack length monitoring, this method requires a servovalve-controlled testing machine and the testing procedure is more complicatedthan that under the loading point displacement condition. Alternatively theFour Point End Notched Flexure test (4ENF) (Fig. 10.1) can be used toevaluate the mode II R-curve. This test does not require crack monitoring butinvolves a more sophisticated setup and larger friction effects were observed(Shuecker and Davidson, 2000). In the following, a summary of the classicalreduction schemes used for these experimental tests is presented.

10.2.1 Classical methods

Compliance calibration method (CCM)

The CCM is the most used. During the test the values of load, applieddisplacement and crack length (P-δ-a) are registered in order to calculate thecritical strain energy release rate using the Irwin-Kies equation (Kanninenand Popelar, 1985)

G PB

dCdaIIc

2 =

2 10.1

where B is the specimen width and C = δ/P the compliance. In the ENF andELS tests a cubic relationship between the compliance (C) and the measuredcrack length a is usually assumed (Davies et al., 2001)

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itedC = D + ma3 10.2

where D and m are constants. GIIc is then obtained from

GP m a

BIIc

2 2

= 3

210.3

For the 4ENF test a linear relationship (Yoshihara, 2004) between thecompliance (C) and the measured crack length a is used

C = D + ma 10.4

being D and m the respective coefficients. It should be noted that relationsC = f(a) given by Equations 10.2 and 10.4 are based on the beam theoryapproach, as it will be shown in the next sub-section. GIIc is given by

G PB

mIIc

2 =

210.5

The three tests require the calibration of the compliance in function of thecrack length. This can be done by measurement of crack length duringpropagation or, alternatively, considering several specimens with differentinitial cracks lengths to establish the compliance–crack length relation, whichis regressed by cubic (Equation 10.2) and linear (Equation 10.4) functions.

Beam theory

Beam theory methods are also frequently used to obtain GIIc in mode II tests.In the case of ENF test Wang and Williams (1992) proposed the CorrectedBeam Theory (CBT)

Ga P

B h EIIcI

2 2

2 31

= 9( + 0.42 )

1∆

610.6

where E1 is the axial modulus and ∆I a crack length correction to account forshear deformation

∆ I1

13

2

= 11

3 – 21 +

hEG

ΓΓ( )

10.7

with

Γ = 1.18 1 2

13

E EG

10.8

where E2 and G13 are the transverse and shear moduli, respectively. In theELS case a similar expression is proposed (Wang and Williams, 1992)

Ga P

B h EIIcI

2 2

2 31

= 9( + 0.49 )∆

410.9

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itedFor the 4ENF test the beam theory leads to the following equation (Silva,

2006)

C dE I

d a d L d L = 24

(18 – 20 + 60 – 6 )1

2 2 10.10

where I is the second moment of area and d represents the distance betweeneach support and its nearest loading actuator (Fig. 10.1). Using Equation[10.1] GIIc can be obtained from

G P dE B hIIc

2 2

12 3 = 9

1610.11

In summary, the application of beam theory to ENF and ELS tests involvesthe crack length, which does not occur in the 4ENF test. However, it shouldbe emphasized that 4ENF setup is more complex. Also, friction effects(Shuecker and Davidson, 2000) and system compliance (Davidson and Sun,2005) can affect the results. Owing to these drawbacks of the 4ENF test, theENF and ELS tests emerge as the most appropriate to fracture characterizationof composites in mode II. In this context, a new data reduction scheme, notdepending on the crack length measurements, is proposed in the followingsection for these experimental tests.

10.2.2 Compliance based beam method (CBBM)

In order to overcome the difficulties associated to classical data reductionschemes a new method is proposed. The method is based on crack equivalentconcept and depends only on the specimen compliance. The application ofthe method to ENF and ELS tests is described in the following.

ENF test

Following strength of materials analysis, the strain energy of the specimendue to bending and including shear effects is

UM

E Idx

GBdy dx

Lf

f

L

h

h

= 2

+ 20

2 2

0

2

2

13∫ ∫ ∫ τ 10.12

where Mf is the bending moment and

τ = 32

1 – 2

2

VA

yc

i

i i

10.13

where Ai, ci and Vi represent, respectively, the cross-section area, half-thicknessof the beam and the transverse load of the i segment (0 ≤ x ≤ a, a ≤ x ≤ L or

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itedL ≤ x ≤ 2L). From the Castigliano theorem, the displacement at the loading

point for a crack length a is

δ = = (3 + 2 )8

+ 3

10

3 3

313

dUdP

P a LE Bh

PLG Bhf

10.14

Since the flexural modulus of the specimen plays a fundamental role on theP-δ relationship, it can be calculated from Equation 10.14 using the initialcompliance C0 and the initial crack length a0

Ea L

BhC

LG Bhf =

3 + 2

8–

310

03 3

3 013

–1

10.15

This procedure takes into account the variableness of the material propertiesbetween different specimens and several effects that are not included inbeam theory, e.g., stress concentration near the crack tip and contact betweenthe two arms. In fact, these phenomena affect the specimen behavior andconsequently the P-δ curve, even in the elastic regime. Using this methodologytheir influence are accounted for through the calculated flexural modulus.On the other hand, it is known that, during propagation, there is a regionahead of crack tip (Fracture Process Zone), where materials undergo propertiesdegradation by different ways, e.g., micro-cracking, fibre bridging and inelasticprocesses. These phenomena affect the material compliance and should beaccounted for in the mode II tests. Consequently, during crack propagationa correction of the real crack length is considered in the equation of compliance(10.14) to include the FPZ effect

Ca a L

E BhL

G Bhf

= 3( + ) + 2

8 +

310

FPZ3 3

313

∆10.16

and consequently,

a a aCC

aCC

Leq FPZcorr

0 corr03 corr

0 corr

3

1/3

= + = + 23

– 1∆

10.17

where Ccorr is given by

C CL

G Bhcorr13

= – 3

1010.18

GIIc can now be obtained from

GP a

B E hfIIc

2eq2

2 3 = 9

1610.19

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itedThis data reduction scheme presents several advantages. Using this

methodology crack measurements are unnecessary. Experimentally, it is onlynecessary to register the values of applied load and displacement. Therefore,the method is designated as Compliance-Based Beam Method (CBBM).Using this procedure the FPZ effects, that are pronounced in mode II tests,are included on the toughness measurement. Moreover, the flexural modulusis calculated from the initial compliance and initial crack length, thus avoidingthe influence of specimen variability on the results. The unique materialproperty needed in this approach is G13. However, its effect on the measuredGIIc was verified to be negligible (de Moura et al., 2006), which means thata typical value can be used rendering unnecessary to measure it.

ELS test

Following a procedure similar to the one described for the ENF test, theapplied P-δ relationship is

δ = = (3 + )2

+ 3

5

3 3

31 13

dUdP

P a LBh E

PLBhG

10.20

In order to include the root rotation effects at clamping and the details ofcrack tip stresses or strains not included in the beam theory, an effectivebeam length (Lef) can be achieved. In fact, considering in Equation 10.20 theinitial crack length (a0) and the initial compliance (C0) experimentallymeasured, it can be written

Ca

Bh E

L

Bh EL

BhG003

31

ef3

31

ef

13 –

3

2 =

2 +

35

10.21

To take account for the FPZ influence a correction to the real crack length(∆aFPZ) should be considered. From Equation 10.20 the compliance (C)during crack propagation can be expressed as

Ca a

Bh E

L

Bh EL

BhG –

3( + )2

= 2

+ 3

5FPZ

3

31

ef3

31

ef

13

∆10.22

Combining Equations 10.22 and 10.21, the equivalent crack length can begiven by

a a a C CBh E

aeq FPZ 0

31

03

1/3

= + = ( – )2

3 + ∆

10.23

GIIc can now be obtained from

GP a

B h EIIc

2eq2

2 31

= 9

410.24

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itedFollowing this procedure GIIc can be obtained without crack measurement

during propagation which can be considered an important advantage. Equation10.24 only depends on applied load and displacement during crack growth.Additionally, the influence of root rotation at the clamping point and singularityeffects at the crack tip are accounted for, through initial compliance C0.During propagation, the effect of FPZ on the compliance is also includedusing this methodology. In this case (ELS test) it is necessary to measure thelongitudinal modulus.

10.2.3 Numerical simulations

In order to verify the performance of the CBBM on the determination of GIIc

of unidirectional composites, numerical simulations of the ENF and ELStests were performed. A cohesive mixed-mode damage model based on interfacefinite elements was considered to simulate damage initiation and propagation.A constitutive relation between the vectors of stresses (σ) and relativedisplacements (δ) is postulated (Fig. 10.2). The method requires local strengths(σu,i, i = I, II, III) and the critical strain energy release rates (Gic) as inputteddata parameters [8, 9]. Damage onset is predicted using a quadratic stresscriterion

σσ

σσ

σσ σ

σσ

σσ σ

I

,I

2II

, II

2III

, III

2

I

II

, II

2III

, III

2

I

+ + = 1 if 0

+ = 1 if 0

u u u

u u

≤10.25

where σi, (i = I, II, III) represent the stresses in each mode. Crack propagationwas simulated by a linear energy criterion

GG

GG

GG

I

Ic

II

IIc

III

IIIc + + = 1 10.26

Basically, it is assumed that the area under the minor triangle of Fig. 10.2 isthe energy released in each mode, which is compared to the respective criticalfracture energy represented by the bigger triangle. The subscripts o and urefer to the onset and ultimate relative displacement and the subscript mapplies to the mixed-mode case. More details about this model are presentedin de Moura et al. (2006).

Three-dimensional approaches (Figs 10.3 and 10.4) were carried out toinclude all the effects that can influence the measured GIIc. The interfaceelements were placed at the mid-plane of the specimens to simulate damageprogression. Very refined meshes were considered in the region of interestcorresponding to crack initiation and growth. The specimens’ geometry and

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itedσ i

σ u,i

σ um,i

σ om,i

Gi

δo,i

Gic

Pure modemodel

i = I, II, III

Mixed-modemodel

δ i

δum,i δu,i

10.2 Pure and mixed-mode damage model.

10.3 The mesh used for the ENF test: global view and detail of therefined mesh at the region of crack initiation and growth.

material properties and are listed in Tables 10.1, 10.2 and 10.3, respectively.An analysis of G’s distributions at the crack front showed a clear predominanceof mode II along the specimens’ width, although some spurious mode IIIexists at the specimens edges (de Moura et al., 2006 and Silva et al., 2007).

10.4 The mesh used for the ELS test.

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ited

Appropriate values of critical strain energy release rates were considered foreach of the three modes, respectively (see Table 10.3). Consequently, theefficacy of the proposed data reduction scheme can be evaluated by itscapacity to reproduce the inputted GIIc from the P-δ results obtainednumerically.

The application of the CBBM is performed by three main steps. The firstone is the measurement of the initial compliance C0 from the initial slope ofthe P-δ curves (Figs (10.5) or (10.7)). This parameter is then used to estimatethe flexural modulus in the ENF test (Equation 10.15). The next step is the

Table 10.1 Specimens’ geometry

L (mm) b (mm) h (mm) a0 (mm)

ENF 100 10 1.5 75ELS 100 10 1.5 60

Table 10.2 Material properties

E1 E2 = E3 ν12 = ν13 ν23 G12 = G13 G23

(GPa) (GPa) (GPa) (GPa)

150 11 0.25 0.4 6 3.9

Table 10.3 Strength properties

σu,i (i = I,II,III) GIc GIIc GIIIc

(MPa) (N/mm) (N/mm) (N/mm)

40 0.3 0.7 1.0

P (

N)

140

120

100

80

60

40

20

00 2 4 6 8 10

δ (mm)

10.5 P-δ curve of the ENF specimen.

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itedevaluation of the equivalent crack length (Equations 10.17 or 10.23) in function

of the current (C) and initial compliance (C0). Finally, the R-curves, Figs(10.6) and (10.8), can be obtained from Equations 10.19 and 10.24, respectively.It should be noted that crack propagation occurs after peak load in both tests.During crack growth P decreases with the increase of equivalent crack length.This originates a plateau on the R-curves, which corresponds to the criticalstrain energy release rate in mode II (GIIc). These plateau values are comparedwith the reference value (Figs (10.6) and (10.8)), which represents the inputtedGIIc. The excellent agreement obtained in both cases demonstrates the

GII (CBBM)

GIIc (Reference value)

GII

(N/m

m)

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.075 80 85 90 95 100

aeq (mm)

10.6 R-curve of the ENF specimen.

P (

N)

70

60

50

40

30

20

10

00 2 4 6 8 10 12 14 16

δ (mm)

10.7 P-δ curve of the ELS specimen.

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effectiveness of the CBBM as a suitable data reduction scheme to determineGIIc, without crack length monitoring during propagation. As the ENF test ismuch simpler to execute than the ELS one, it can be concluded that using theCBBM, the ENF test is the most suitable for the determination of GIIc and itshould be considered as the principal candidate for standardization.

10.3 Dynamic mode II fracture characterization

The research on dynamic crack propagation in composites has become thefocus of several authors in the recent years. The dynamic fracturecharacterization of composites is not easy to perform. In fact, it is experimentallydifficult to induce high speed delamination growth in a simple and controlledmanner (Guo and Sun, 1998). However, the determination of dynamic fracturetoughness of composites is of fundamental importance in the prediction ofthe dynamic delamination propagation in composite structures. In addition,it is known that the impact delamination is mainly governed by mode IIfracture (Wang and Vu-Khanh, 1991). However, there are several unclearphenomena related to dynamic crack propagation. One of the most importantissues is related to the influence of rate effects on the propagation of dynamiccracks. An example of this occurrence is the dynamic delamination propagationoccurring in composites submitted to low velocity impact. In this case, rateeffects in the FPZ can interact with the well known rate-dependency ofpolymers leading to a very complicated phenomenon. In addition, Kumarand Narayanan (1993) verified that when glass fibre reinforced epoxy laminatesare impacted, the total delamination area between the various plies multipliedby the quasi-static energy release rate exceeds the energy of the impacting

10.8 R-curve of the ELS specimen.

GII (CBBM)

GIIc (Reference value)

GII

(N/m

m)

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.060 65 70 75 80 85 90 95

aeq (mm)

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itedmass. This suggests that under high crack speeds, delamination propagates

at lower toughness which leads to larger damaged areas. In order to explainthis behaviour, Maikuma et al. (1990) suggest that the calculation of criticalstrain energy release rate should account for the kinetic energy (Ekin) inEquation 10.26

G PB

dCda

dEBdaIIc

2kin=

2 – 10.27

The kinetic energy expression can be obtained from

E B hdw x

dtdx

Lt

kin0

2

= 12

2 ( )ρ ∫

10.28

where ρ and Lt are the mass density and the total length of the specimen,respectively, t represents the time and w(x) the displacement field. The quasi-static approach may provide an adequate approximation to the dynamicproblem if the contribution of kinetic energy is small.

Wang and Vu-Khanh (1995) have suggested that the dynamic fracturebehaviour of materials depends on the balance between the energy releasedby the structure over a unit area of crack propagation (G) and the materialresistance (R), which can be viewed as the energy dissipated in creating thefracture surface. When unstable crack growth occurs, the difference G-R isconverted into kinetic energy. If G increases with crack growth the crackspeed also increases because more energy is available. Crack arrest willoccur when G becomes lower than R and, consequently, no kinetic energy isavailable for crack growth. Thus, it can be affirmed that fracture stabilitydepends on the variations of the strain energy release rate and the materialsresistance during crack growth. On the other hand, the fracture resistance ofpolymer composites is generally sensitive to loading rate. Under impact loador during rapid delamination growth, the strain rate at the crack tip can bevery high and the material toughness significantly reduced. The fracturesurface exhibited ductile tearing and large scale plastic deformation of thematrix. The dynamic fracture surface in the initiation exhibits less plasticdeformation; during propagation even less deformation is observed. It wasalso verified that plastic zone size at the crack tip diminishes with increasingrate. Consequently, the decrease in mode II interlaminar fracture toughnessis attributed to a transition from ductile to brittle matrix dominated failurewith increasing rate.

The decreasing trend of toughness with increase of crack speed was alsoobserved by Kumar and Kishore (1998). The authors used a combination ofnumerical and experimental techniques on the DCB specimens to carry outdynamic interlaminar toughness measurements of unidirectional glass fibreepoxy laminate. They observed a sharp decrease of dynamic toughness values

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itedrelatively to the quasi-static ones. In fact, they measured dynamic toughness

initiation values of 90–230 N/m2 against quasi-static values of 344–478N/m2. Propagation values of 0–50 N/m2 were obtained for crack speed rangingbetween 622–1016 m/s.

The majority of the experimental studies consider unidirectional laminates.Lambros and Rosakis (1997) performed an experimental investigation ofdynamic crack initiation and growth in unidirectional fibre-reinforcedpolymeric-matrix thick composite plates. Edge-notched plates were impactedin a one-point bend configuration using a drop-weight tower. Using an opticalmethod the authors carried out a real-time visualization of dynamic fractureinitiation and growth for crack speeds up to 900 m/s. They verified that theelastic constants of the used material are rate sensitive and the measuredfracture toughness values are close to those typical of epoxies. This wasconsidered consistent, because in unidirectional lay-ups crack initiation andgrowth occurs in the matrix.

Tsai et al. (2001) used a modified ENF specimen to determine the modeII dominated dynamic delamination fracture toughness of fiber compositesat high crack propagation speeds. A strip of adhesive film with higher toughnesswas placed at the tip of interlaminar crack created during laminate lay-up.The objective was to delay the onset of crack extension and produce crackpropagation at high speeds (700 m/s). Sixteen pure aluminium conductivelines were put on the specimen edge side using the vapour deposition technique,to carry out crack speed measurements. The authors concluded that the modeII dynamic energy release rate of unidirectional S2/8553 glass/epoxy compositeseems to be insensitive to crack speed within the range of 350 and 700 m/s.The authors also simulated mixed mode crack propagation by moving thepre-crack from the mid-plane to 1/3 of the ENF specimen thickness ofunidirectional AS4/3501-6 carbon/epoxy laminates. The maximum inducedcrack speed produced was 1100 m/s. They found that that the critical dynamicenergy release rate is not affected by the crack speed and lies within thescatter range of the respective static values.

For numerical simulations of the dynamic crack propagation the cohesivedamage models emerge as the most promising tools. The major difficulty isthe incorporation of the rate-dependent effects in the constitutive laws.Corigliano et al. (2003) developed a cohesive crack model with a rate-dependent exponential interface law to simulate the nucleation and propagationof cracks subjected to mode I dynamic loading. The model is able to simulatethe rate-dependent effects on the dynamic debonding process in composites.The authors concluded that the softening process occurs under larger relativedisplacements in comparison to rate-independent models. They verified thatthe type of rate-dependency can affect dynamic crack processes, namely thetime to rupture and fracture energy. They also state that these effects diminishwhen inertial terms become dominant.

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itedIn summary, dynamic fracture toughness characterization of composite

materials has been the centre of attention of several authors with no apparentconsensus on the results. Although the majority of the studies point to adecrease of the fracture toughness with increasing load rate there is nounanimity about this topic. Some authors observed the opposite trend(Corigliano et al., 2003) and others detected no remarkable influence ofcrack speed on toughness (Tsai et al., 2001). Although some of thesediscrepancies can eventually be explained by different behaviour of the testedmaterials, and the attained crack speed values, it is obvious that more profoundstudies about the subject are necessary.

10.4 Conclusions

Interlaminar fracture characterization of composites in mode II acquiresspecial relevancy namely under transverse loading such as low velocityimpact. Up to now there is no standardized test in order to measure thecritical strain energy release rate in mode II. Due to their simplicity, the ENFand ELS tests become the principal candidates to standardization. However,they present a common difficulty associated with crack monitoring duringpropagation which is fundamental to obtaining the R-curves, following theclassical data reduction schemes. To surmount these difficulties a new datareduction scheme based on specimen compliance is proposed. The methoddoes not require crack length measurement during propagation, and accountsfor the effects of the quite extensive FPZ on the measured critical strainenergy release rate. Numerical simulations of the ENF and ELS testsdemonstrated the adequacy and suitability of the proposed method to obtainthe mode II R-curves of composites. Due to its simplicity the ENF test isproposed for standardization.

Little work has been done on dynamic fracture of composite materials,namely under mode II loading. This is due to experimental difficulties relatedto inducing high crack speeds in a monitored way. Although the majority ofthe published works point to a decrease of the dynamic toughness withincrease of crack speed, it appears that dynamic toughness can be similar tothe respective quasi-static value up to a given crack speed (Tsai et al., 2001).Undoubtedly, more research about this topic is necessary. In fact, an unsafestructural design can occur if the quasi-static values of toughness are used ina dynamically loaded structure.

10.5 Acknowledgements

The author thanks Professors Alfredo B. de Morais (UA, Portugal), JoséMorais (UTAD, Portugal) and Manuel Silva for their valorous collaboration,advices and discussion about the matters included in this chapter. The author

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itedalso thanks the Portuguese Foundation for Science and Technology for

supporting part of the work here presented, through the research projectPOCI/EME/56567/2004.

10.6 References

Barrett JD, Foschi RO (1977), ‘Mode II stress-intensity factors for cracked wood beams’,Engng. Fract. Mech., 9: 371–378.

Carlsson LA, Gillespie JW, Pipes RB (1986), ‘On the analysis and design of the endnotched flexure (ENF) specimen for mode II testing’, J Compos Mater, 20: 594–604.

Choi HY, Chang FK (1992), ‘A model for predicting damage in graphite/epoxy laminatedcomposites resulting from low-velocity point impact’, J Compos Mater, 26: 2134–2169.

Corigliano A, Mariani S, Pandolfi A (2003), ‘Numerical modelling of rate-dependentdebonding processes in composites’, Compos. Struct., 61: 39–50.

Davidson BD, Sun X (2005), ‘Effects of friction, geometry and fixture compliance on theperceived compliance from three- and four-point bend end-notched flexure tests’, J.Reinf. Plastics Compos., 24: 1611–1628.

Davies P, Blackman BRK, Brunner AJ (2001), Mode II delamination. In: Moore DR,Pavan A, Williams JG, editors. Fracture Mechanics Testing Methods for PolymersAdhesives and Composites, Amsterdam, London, New York: Elsevier; 307–334.

de Morais AB, Pereira AB (2007), ‘Application of the effective crack method to mode Iand mode II interlaminar fracture of carbon/epoxy unidirectional laminates’, CompositesPart A: Applied Science and Manufacturing, 38: 785–794.

de Moura MFSF, Silva MAL, de Morais AB, Morais JJL (2006), ‘Equivalent crack basedmode II fracture characterization of wood’, Engng. Fract. Mech., 73: 978–993.

Guo C, Sun CT (1998), ‘Dynamic mode-I crack propagation in a carbon/epoxy composite’,Composites Science and Technology, 58: 1405–1410.

Kageyama K, Kikuchi M, Yanagisawa N (1991), ‘Stabilized end notched flexure test:characterization of mode II interlaminar crack growth’. In: O’Brien TK, editor. CompositeMaterials: Fatigue and Fracture, ASTM STP 1110, Vol. 3. Philadelphia PA: ASTM,p. 210–225.

Kanninen MF, Popelar CH (1985), Advanced Fracture Mechanics, Oxford: OxfordUniversity Press.

Kumar P, Narayanan MD (1993), ‘Energy dissipation of projectile impacted panels ofglass fabric reinforced composites’, Compos. Struct., 15: 75–90.

Kumar P, Kishore NN (1998), ‘Initiation and propagation toughness of delaminationcrack uncder an impact load’, J. Mech. Phys. Solids, 46: 1773–1787.

Lambros J, Rosakis AJ (1997), ‘Dynamic crack initiation and growth in thick unidirectionalgraphite/epoxy plates’, Composites Science & Technology, 57: 55–65.

Maikuma H, Gillespie JW, Wilkins DJ (1990), ‘Mode II interlaminar fracture of thecenter notch flexural specimen under impact loading’, J. Compos. Mater., 24: 124–149.

Schuecker C, Davidson BD (2000), ‘Effect of friction on the perceived mode II delaminationtoughness from three and four point bend end notched flexure tests’, ASTM STP,1383: 334–344.

Silva MAL (2006), ‘Estudo das Propriedades de Fractura em Modo II e em Modo III daMadeira de Pinus pinaster Ait.’, Master Thesis, FEUP, Porto.

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itedSilva MAL, Morais JJL, de Moura MFSF, Lousada JL (2007), ‘Mode II wood fracture

characterization using the ELS test’, Eng. Fract. Mech., 74: 2133–2147.Tanaka K, Kageyama K, Hojo M (1995), ‘Prestandardization study on mode II interlaminar

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polymeric composites’, Composites Science & Technology, 61: 87–94.Yoshihara H, Ohta M (2000), ‘Measurement of mode II fracture toughness of wood by

the end-notched flexure test, J Wood Sci., 46: 273–278.Yoshihara H (2004), ‘Mode II R-curve of wood measured by 4-ENF test’, Engng. Fract.

Mech., 71: 2065–2077.Wang H, Vu-Khanh T (1991), ‘Impact-induced delamination in [05, 905, 05] carbon

fiber/Polyetheretherketone composite laminates’, Polymer Engineering and Science,31: 1301–1309.

Wang H, Vu-Khanh T (1995), ‘Fracture mechanics and mechanisms of impact-induceddelamination in laminated composites’, J. Compos. Mater., 29: 156–178.

Wang H, Vu-Khanh T (1996), ‘Use of end-loaded-split (ELS) test to study stable fracturebehaviour of composites under mode II loading’, Compos. Struct., 36: 71–79.

Wang Y, Williams JG (1992), ‘Corrections for Mode II Fracture Toughness Specimens ofComposite Materials’, Composites Science & Technology, 43: 251–256.

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