Delamination Analysis of Composite Laminates Wei Ding A thesis submitted in conformity with the requhments for the degree of Doctor of Phiiosophy Graduate Department of Chemical Engineering and Appiied Chemistry University of Toronto @ Copyright by Wei Ding 1999 National Library BiMiothèque nationale 14 dan, du Canada Acquisitions and Acquisitions et Bibliographie Senrices services bibliographiques 395 Wellington Street 395, rue Wellington OttawaON K1AON4 Ottawa ON K1A ON4 Canada Canada The author has granted a non- L'auteur a accordé une licence non exclusive licence allowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distribute or sell reproduire, prêter, àistribuer ou copies of this thesis in microform, vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or otherwise de celle-ci ne doivent être imprimes reproduced without the author's ou autrement reproduits sans son permission. autorisation. Delamination Analysis of Composite Laminates Wei Ding Doctor of Phiiosophy, 1999 Department of Chernical Engineering and Appüed Chemietry University of Toronto Abstract A combined theoretical and experimental study has been conducted on the delamination of fibre reinforced polymenc composites. The main objectives were to gain a better understanding of the physical orîgin of delamination fhcture toughness and to develop theoretical models to predict the critical strain energy release rates of delamination in composite materials. Of the many energy dissipation mechanisms present in the delamination process, crack tip plastic deformation was determined to be the most critical one. Two analytical beam models, based on the double cantilever beam @CB) specimen and the end notched flexure (ENF) specimen, were developed. A frsicture criterion, based on the skof the crack tip plastic zone, was incorporated into thae beam models so that the mode 1 and mode II cntical strain energy release rates of composites can be predicted using the corresponding resin and fibre properties as well as composite structural parameters. A complete set of mechanical tests were perfiormed on five polymeric composite systems, including both thermoset and thennoplastic systems, and on their correspbnding neat polymer resins. The theoretical predictiom for delamination kture toughness nom the present anaiytical models agreed very well with the data obtained in the present experiments and those in the literature over a wide range of composite laminates. Acknowledgments 1 am especiaily gratefiù to my supervisor, Professor M.T. Kortschot, for his support, encouragement and guidance throughout this work. Special thanks go to Professor M.R. Piggott for allowing the use of his labomtory facilities and for his insightfd advice and discussion on composite materiais. 1wouid aiso like to thank Professor D.E. Cormack for taking tirne fiom his busy schedule to be the chair of the reading cornmittee, giving me valuable advice and guidance. 1greatly appreciate the assistance and helpfidness of Mr. S. Law and Mr. S. Dai in my experimental work. 1 would like to thank dl rny fiends and colleagues, Chengjie Zhang, Ning Yan, Gus Trakas, Saeed Douroudiani, Dennis Cicci and the present MTK group for their interesthg and inspiring conversations and discussion. The hcial assistance fiom the Govemment of Ontario in term of Ontario Graduate Scholarships (OGS) and the National Science and Engineering Research Council of Canada (NSERC) is also greatly appreciated. , Finally, 1 would like to thank my wife, Yigping, for her patience, understanding and support. Table of Contents Abstract Acknowledgments Table of Contents Nomenclature viii List of Tables xii List of Figures 1 Introduction 2. Literature Review 2.1 Delambation Testing 2.1.1 Mode1 2.1.2 Mode II 2.1.3 Mode III 2.1.4 Mixed Mode 2.2 MaterialEffects 2.3 Fractography 2.4 Summary Theoretical Modelling 3.1 Introduction 3.1.1 Delamination Mechanisms 3.1.2 Present Work 3.2 Mode 1 Delamination Model 3.2.1 Introduction 3.2.2 Mathematical Development 3.2.3 Failure critenon 3.3 Mode II Delamination Model 3.3.1 Introduction 3.2.2 Mathematical Development 3.2.3 Failure criterion 4. Experimental Studies 4.1 Testing and Equipment 4.1.1 Polymer Tensile Test 4.1.2 Single-edge Notched Bend Test (SENB) 4.1.3 Mode 1 Delamination Test 4.1.4 Mode II Delamination Test 4.1.5 Fractography 4.2 Materials and Sample Preparation 4.2.1 Materials Selection 4.2.2 Preparation of Tensile Specimens 4.2.3 Preparation of SENB Specimens 4.2.4 Preparation of Mode 1 and Mode II Specimens 4.2.5 Preparation of Specimens for Microscopie Studies 5. Experimental Results 5.1 Introduction 5.2 Experimental redts 5.2.1 PolymerTensileTest Results 52.2 SENB Test Results 5.2.3 Mode 1 and Mode II Test Resuits 5.2.4 Fractography 6. Model Application and Discussion 6.1 Introduction 6.2 Mode 1 Mode1 Application 6-2-1 Model Evaluation 6.2.2 Theoretical Predictions and Discussion 6.3 Mode II Mode1 Application 6.3,l Model evaluation vii 6.3.2 Theoretical prediction and discussion 6.4 Conclusions 7. Conclusions 8, Recommendations 123 9, References 124 Appendices A Mathematical details of mode 11 beam model --- Elastic /plastic case 133 B Mathematical development for mode II beam model - Elastic case 138 Nomenclature Sym bol Definition crack length the dope of a plot of normalized crack length (ah)vs. the cubic root the compliance the MCC method specimen width constants in the solutions of goveming differential equations compliance compliance of the EM: specimen calculated by the mode II mode1 compliance of the ENF specimen calculated by the classical beam theory constants in the solutions goveming differential equatiom constants in the solutions goveming differential equations Young's modulus Young's modulus of fibres Young's modulus of ma& Young's moduius of the composite beam in the fibre direction Young's modulus of the composite beam perpendicuiar to the fibre direction shear modulus of the composite beam shear modulus of fibres shear modulus of matrix strain energy release rate seain energy release rate of mode 1, II, and III strain energy release rate caiculated by classical beam theory cntical strain energy release rate critical strain energy release rate of mode 1, II and III half thickness of the barn specimen stifiess of the elastic foundation in the mode 1 mode1 stress intensity factor critical stress intensity factor length of the crack tip plastic zone critical lengths of the crack tip plastic zone in mode 1 and II half length of the ENF specimen the slope of a least square regression line used in compliance calibration in ENF test foundation spring constants in mode 1 and II models bending moment the dope log compliance vs. log crack length in the CC method ratio between the critical sizes of the crack tip plastic zone in the mode 1 delamination and in the resin fiacture ratio between the cntical sizes of the crack tip plastic zone in the mode II delamination and in the resin kture extemal Ioad extemal load at the onset of plastic deformation radius of the crack tip plastic zone in resin hcture cntical radius of the crack tip plastic zone in resin kture glas-transition temperature extemal energy interna1 energy including both elastic and plastic energy fibre volume fiaction deflections of the beams work of hcture length of the elastic shear spring foundation correction coefficients for large deflection and transverse shear deflection of the beam deflection of the beam at the onset of plastic defiornation the x-intercept of a plot of the cube root of the specimen cornpliance vs. the mck length in the MBT method the area of the crack surface parameter used in the mode 1model shear correction coefficient in the mode II model Poisson's ratio density of composite material density of fibres density of matrices Yield stress of the spring foundation shear stress on the center surface of the ENF specimen Yield shear stress of the spring foundation xii List of Tables Table 5.1 Tensile strengths of al1 neat resins Table 5.2 Tensile moduli of al1 neat resins Table 5.3 SENB test results of neat resin materials Table 5.4 Mode 1 and mode II delamination test redts Table 6.1 Comparisons of GKof the present composite systems Table 6.2 Matenal properties of the reshs and fibre volume fiactions of the composite systems Table 6.3 Comparisons of G,of previous composite systems Table 6.4 Materials properties of three typical composite laminates Table 6.5 Comparisons of C, and G, values between the finite element results and the present solutions Table 6.6 Comparisons of C, and G,,values between the present results and the finite element solutions Table 6.7 Cornparisons of C, and G, values between the present results and the finite element solutions Table 6.8 Cornparisons of the cornpliance and the G, of ENF specirnens Table 6.9 Comparisons of G, of the present composite systems Table 6.10 Comparisons of Gnc of the previous composite systems List of Figures Figure 1.1 Basic delamination modes Figure 2.1 Mode 1 delamination test method Figure 2.2 Mode II delamination test method Figure 2.3 Mode III delamination test methods Figure 2.4 Mixed-mode delamination test methods Figure 3.1 An optical micrograph of a petrographic thin section of a rubber- toughened AS4lpolycarbonate composites. The plastic zone is observed using cross polarized light.