Interface mechanics of CNT and nanorope reinforced composites

INTERFACE MECHANICS OF CNT AND NANOROPE REINFORCED COMPOSITES KHONDAKER SAKIL AHMED NATIONAL UNIVERSITY OF SINGAPORE 2012 INTERFACE MECHANICS OF CNT AND NANOROPE REINFORCED COMPOSITES KHONDAKER SAKIL AHMED (B.Sc. Eng., BUET) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. Khondaker Sakil Ahmed 25 February 2013 ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my supervisor, Associate Professor Ang Kok Keng, for his invaluable guidance, interesting discussion, constructive advices, commitment, patience and encouragement which helped me immensely in the completion of my PhD research work. Working with him has been rewarding and enjoyable. Through many pleasant conversations with him, I have also learnt countless things beyond academic matters. I would like to thank the examiners of my thesis, Professor Quek Ser Tong (NUS) and Assistant Professor Pang Sze Dai (NUS) for spending their valuable time in reading and evaluating my thesis. My gratitude also goes to my undergraduate thesis supervisor, Professor Tahsin Reza Hossain (BUET) who first inspired me to continue my study and pursue PhD from NUS. The financial support and the facilities provided by National University of Singapore to carry out this research are greatly acknowledged. It’s a pleasure to thank my colleagues, Dr. K M A Sohel, Dr. Md Tarik Arafat, Dr. Zakaria Mohammad Amin, Dr. Jahidul Islam, Aziz Ahmed, Mohammad Abdul Hannan, Md. Shakhawat Hossain Khan not only for sharing knowledge and suggestions but also the encouragement that I received in my difficult time. Last but not least, my warm gratitude goes to my parents and my beloved wife for being the best support to hurdle all the obstacles throughout the course of my PhD research work. i TABLE OF CONTENTS ACKNOWLEDGEMENT i TABLE OF CONTENT ii SUMMARY vii LIST OF TABLES x LIST OF FIGURES xi LIST OF SYMBOLS xviii CHAPTER 1: INTRODUCTION 1.1 General Remarks 1.2 CNT/Polymer Interface 1.3 Objective and Scope 1.4 Organization of the Thesis CHAPTER 2: LITERATURE REVIEW 12 2.1 Introduction 12 2.2 Properties of Carbon Nanotubes 13 2.2.1 Bonding Structure of CNT 13 2.2.2 Geometric Properties of CNT 15 ii 2.3 Previous Experimental Works 17 2.4 Analytical Studies on CNT Reinforced Composites 25 2.4.1 Atomistic Simulation 25 2.4.2 Finite Element Method 29 2.4.3 Continuum Mechanics Modeling 32 2.4.3.1 Pull-out Models 32 2.4.3.2 Shear-lag Models 35 2.5 Conclusion 38 CHAPTER 3: CNT/MATRIX INTERFACE 40 3.1 Introduction 40 3.2 Categorization of CNT/Matrix Interface 41 3.3 Formulation 42 3.4 Radial Stress due to Poisson’s Contraction 49 3.5 Thermal Residual Stress 53 3.6 van der Waals Interactions 54 3.6.1 Cohesive Law for Graphene/Polymer Interface 56 3.6.2 Carbon Nanotube Polymer vdW Interaction 59 3.7 Conclusion 63 iii CHAPTER 4: PULL-OUT MODEL FOR NANOCOMPOSITE 65 4.1 Introduction 65 4.2 Pull-out Model for Perfectly Bonded Interface 68 4.2.1 Analytical Model 68 4.2.2 Results & Discussion 75 4.3 Pull-out Model for Imperfectly Bonded Interface 84 4.3.1 Extended Pull-out Model 85 4.3.2 Solution for Debonded Region 86 4.3.3 Solution for Perfectly Bonded Region 91 4.3.4 Analytical Results & Discussion 92 4.3.5 Parametric Study 98 4.4 Conclusion 105 CHAPTER 5: SHEAR-LAG ANALYSIS 107 5.1 Introduction 107 5.2 Proposed Shear-lag Model 108 5.3 Results & Discussions 122 5.3.1 Effect of Coefficient of Friction 124 5.3.2 Effect of Aspect Ratio 126 iv 5.3.3 Effect of CNT/matrix Young’s Modulus Ratio 128 5.3.4 Effect of vdW Interaction 130 5.4 Interface Crack Propagation 132 5.4.1 Analytical Model for Static Crack Propagation 134 5.4.2 Crack Propagation vs. Debonded Length 137 5.5 Conclusion 138 CHAPTER 6: NANOROPE REINFORCED COMPOSITES 140 6.1 Introduction 140 6.2 Proposed Model for Nanorope Reinforced Composite 143 6.3 Results & Discussions 161 6.3.1 Comparison of Results 163 6.3.2 Stress Components of the Nanorope Reinforced Composite 165 6.4 Parametric Study 168 6.4.1 Perfectly Bonded Rope/Resin Interface 168 6.4.1.1 Effect of Aspect Ratio 168 6.4.1.2 Effect of Rope/Resin Radius Ratio 170 6.4.1.3 Effect of CNT/matrix Young’s modulus ratio 172 6.4.2 CNT/CNT Non-bonded Interface v 174 6.4.2.1 Effect of Coefficient of Friction 174 6.4.2.2 Effect of Aspect Ratio 176 6.4.2.3 Effect of vdW Interaction 178 6.5 Conclusion 180 CHAPTER 7: CONCLUSIONS AND RECOMMENDATIONS 182 7.1 Concluding Remarks 182 7.2 Recommendations 189 REFERENCES 192 LIST OF PUBLICATIONS 204 vi SUMMARY Carbon nanotubes are expected to be ideal reinforcements of high strength and lightweight smart composites because of their extremely high Young’s modulus, mechanical strength. Since there is a huge difference in strength and stiffness between CNT and most other potential polymer matrix, the mechanics involved at the nanotubes/matrix interface plays an important role in affecting the strength of the nanocomposite. The main goal of this study is to investigate mechanics involved at the interface as well as examine key factors controlling the interface strength of CNT and nanorope reinforced composites. Initially, an analytical pull-out model is developed to investigate the mechanism of stress transfer from CNT to polymer matrix for chemically (perfectly) bonded interface which is extended for non-bonded CNT/polymer interface as well. Stress transferring ability of nanotube in the nonbonded interface is controlled by mechanical interlocking, thermal residual stress, Poisson’s contraction and van der Waals (vdW) interaction. Closed form analytical solutions for different stress components are derived. The proposed continuum-based analytical model is able to predict critical values of key interface parameters such as effective embedded length and critical CNT/polymer Young’s modulus ratio. In addition, the influence of vdW interaction at the non-bonded CNT/polymer interface is investigated which is found to be significant in influencing the composite strength. The analytical result shows that the stress transferring potential of nanotube is smaller in the non-bonded than in the perfectly bonded part of the interface. Parametric study shows that parameter dependency of stress transferring is comparatively high in the perfectly bonded region than the debonded interface. In addition, stress transferring of CNT through the non-bonded interface is almost independent of volume fraction of CNT in the nanocomposite. The proposed extended pull-out model can be readily vii Chapter Conclusion at the nanoscale. Thus, experimental investigations on single nanotubes (pull-out, fragmentation and peeling) to understand the mechanics of the interface and nature of interaction between polymer and carbon nanotube would be useful contribution to the literature. In particular, experimental works that can examine the influence of key interface factors would be highly recommended. In addition, it is important to explore whether Atomic Force Microscopy (AFM) or Transmission Electron Microscopy (TEM) can be employed to capture the interface behavior accurately. 191 REFERENCES Ailin, L., Wang, K.W. and Bakis, C.E. Multiscale damping model for polymeric composites containing carbon nanotube ropes. Journal of Composite Materials, 44(Compendex), pp.2301-2323.2010. Ajayan, P.M., Schadler, L.S., Giannaris, C. and Rubio, A. Single-Walled Carbon Nanotube–Polymer Composites: Strength and Weakness. Advanced Materials, 12(10), pp.750-753. 2000. Ashrafi, B. and P. Hubert. 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K, Interface characteristics of nanorope reinforced polymer composites. Computational Mechanics, 2013: p. 1-15. DOI 10.1007/s00466-0130833-z 3. Ang K. K. and Ahmed K. S., An improved shear-lag model for carbon nanotube reinforced polymer composites. Composites Part B: Engineering DOI:10.1016/j.compositesb.2013.01.016 4. Ahmed K. S. and Ang K. K., An Extended Pull-out Model for Imperfectly Bonded Carbon Nanotube in Polymer Composite, 2013, Computational Mechanics. (Reviewed: Minor Revision) 5. Ang K. K. and Ahmed K. S., Static Crack Propagation in Non-bonded CNT/Matrix Interface, 2013. (Under Preparation) Conferences 1. Ang K. K., Ahmed K. S,; Interface Characteristics of Nano-rope Reinforced Composites, Proceedings of the Twenty-fourth KKCNN Symposium on Civil Engineering, December 14–16, 2011, Hyogo, Japan; pp293-296 2. Ahmed K. S*., Ang K. K.; An Improved Pullout Model for Carbon Nanotube Reinforced Composites, Proceedings of the Twenty-third KKCNN Symposium on Civil Engineering, November 13–15, 2010, Taipei, Taiwan; pp.41-44 3. Ahmed K. S.*, Ang K. K.; Load Transfer Mechanism of Nanotube Reinforced Composite Considering Coulomb Friction and van der Waals Interactions, Proceedings of the Twenty-second KKCNN Symposium on Civil Engineering, October 31–November 2, 2009, The Imperial Mae Ping Hotel, Chiang Mai, Thailand, pp.331-336 [...]... energy for graphene/polymer interface Cohesive energy per unit length of CNT Shear Modulus Volume fraction of CNT Volume fraction of polymer Equilibrium distance between CNT and polymer Length of CNT Indices representing CNT Coefficient of friction Nanometer ( ) Number of carbon atom per unit area of CNT Number of molecule per unit volume of polymer Poisson’s ratio CNT/ matrix interface gap beyond equilibrium... Effects of CNT on the tribological properties of nanocomposites 21 Fig 2.6: SEM micrographs showing fracture morphologies of aluminum oxide coating reinforced with (a)4 wt% CNTs and (b) 8 wt% CNTs 22 Fig 2.7: Molecular structure of crystalline PE /CNT composite: (a) A crosssection of the central region of the sample and (b) a side view of the CNT and two nearby PE chains 26 Fig 2.8: Schematic of the... well as the objective and scope of study Chapter 2: This chapter provides a brief literature review on the current state of the art on CNT and CNT reinforced composites The review focuses on both experimental investigations and analytical studies of CNT reinforced composites Subsequently, a detailed discussion of the available analytical models and tools to investigate the CNT reinforced composite is... theories in micromechanics modeling and fiber -reinforced composites to the study of CNT 5 Chapter 1 Introduction reinforced polymer composites (Qian et al 2000; Liu 2003; Liu and Chen 2003; Chen 2004) and explained the behavior of the composite from a mechanics point of view Widely used continuum models include the shear-lag and pull-out models These are commonly used in the study of fiber reinforced composite... between CNT and matrix, which largely influences the reinforcing potential of CNT and nanorope in polymer composites Both perfect and imperfect bonding at the interface between CNT and matrix will be studied The scope of this study include  To develop an analytical pull-out model of the CNT reinforced composite The pull-out model will be used to investigate the stress transferring mechanism from CNT to... different interface gap 179 Fig.6.11b: Interfacial shear stress distribution of inner nanotube for different interface gap 179 xvi LIST OF SYMBOLS Radius of Carbon Nanotube ă Radius of Nanorope Lattice constant of graphite Angstroms ( ) Ratio of Young’s modulus Thermal coefficient of expansion of CNT Thermal coefficient of expansion of polymer Radius of representative volume element Chiral vector Diameter of. .. understand the source of interface strength and the mechanics involved at the nanotube/matrix interface 2 Chapter 1 Introduction Fig 1.1: (a) Fractured specimen of CNT epoxy showing the CNT being pulled out of the matrix (Ajayan et al 2000); (b) TEM image of an internal fracture (Jin et al 1998) 1.2 CNT/ Polymer Interface Generally, bonding at the CNT/ matrix interface depends on the type of synthesis, catalyst... components 94 Fig 4.9a: Comparison of average axial stress of CNT of different models 96 Fig 4.9b: Comparison of interfacial shear stress distribution of CNT 96 Fig 4.10: Variation of normal cohesive stress by van der Waals interaction along the embedded length of CNT Fig 4.10b: Interfacial shear stress of CNT for different Aspect Ratio xiii 97 98 Fig 4.11a: Axial stress of CNT for different debond length... accuracy, seems to be a good approach for investigating both perfectly and imperfectly bonded CNT/ matrix interface 1.3 Objective and Scope In view of the preceding discussion, the main objective of the present study is to determine the interface characteristics of carbon nanotube (CNT) and nanorope reinforced composites using classical continuum mechanics in the elastic regime This 6 Chapter 1 Introduction... vector Diameter of the CNT d Distance between two non-pair atom Temperature change Characteristics bond length of -CH2Critical separation gap at CNT/ matrix interface E Modulus of elasticity of composite Є Potential energy between two non-bonded pair of atom/molecule Modulus of elasticity of effective fiber Modulus of elasticity of polymer matrix Modulus of elasticity of hollow CNT Electron-volt ( xvii . (a)4 wt% CNTs and (b) 8 wt% CNTs 22 Fig. 2.7: Molecular structure of crystalline PE /CNT composite: (a) A cross- section of the central region of the sample and (b) a side view of the CNT and two. INTERFACE MECHANICS OF CNT AND NANOROPE REINFORCED COMPOSITES KHONDAKER SAKIL AHMED NATIONAL UNIVERSITY OF SINGAPORE 2012 INTERFACE. Effect of CNT/ matrix Young’s modulus ratio 172 6.4.2 CNT/ CNT Non-bonded Interface 174 vi 6.4.2.1 Effect of Coefficient of Friction 174 6.4.2.2 Effect of Aspect Ratio 176 6.4.2.3 Effect of