UNIVERSITY OF CALIFORNIA Los Angeles The Interface Energy and Particle Size Effects on Nanocomposites A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Civil Engineering by Yinghui Zhu 2019 © Copyright by Yinghui Zhu 2019 ABSTRACT OF THE DISSERTATION The Interface Energy and Particle Size Effects on Nanocomposites by Yinghui Zhu Doctor of Philosophy in Civil Engineering University of California, Los Angeles, 2019 Professor Jiann-Wen Ju, Chair Currently, the advancement of nanotechnology provides new insights into the structures with the characteristic length in the nanometer scale. Due to their large specific area, the nano-structures may possess desirable features. Therefore, scientists attempt to employ the nano-structures as the reinforcements in the composite materials; i.e., nanocomposites, to achieve improved properties. It is well known that the local atomic environment at the matrix-reinforcement interface is different from its setting associated with the interior due to the accommodation of two different materials. As a consequence, the free energy associated with the interface is different from that associated with the interior. Since the nanocomposites have much larger interface area than the traditional ii composites, the interface energy effect becomes one of the main factors that determine the mechanical properties. The objective of the present study is to research on the effective (overall) elastic, elastoplastic and elastoplastic damage behavior of nanocomposites by considering the interface energy effect. Firstly, a nanomechanical framework is proposed in Chapter 3 to investigate the effective elastic behavior of nanocomposites containing randomly distributed spherical particles. The interface energy effect is simulated by the zero-thickness membrane interphase between the matrix and the reinforcement together with the interface stress. In addition, classical micromechanical homogenization procedures are incorporated to determine the volume averaged effective properties. Secondly, the elastic nanomechanical framework in Chapter 3 is extended to consider the more sophisticated spheroidal particle reinforced nanocomposites in Chapter 4. The spheroidal particles are assumed to be aligned and randomly distributed in the matrix. Thirdly, the effective elastoplastic behavior of the spherical particle reinforced nanocomposite is studied in Chapter 5. The effective secant moduli are obtained for the nanocomposite with the elastoplastic matrix and the elastic reinforcements. In Chapter 6, the elastoplastic damage performance of the continuous fiber reinforced nanocomposites is investigated. Interface debonding is considered as the damage type that occurs in the nanocomposites. The progressive debonding of the interface and the volume fraction evolution of debonded fibers are presented. The results show that the effective mechanical properties of nanocomposites are dependent upon the total interface area. The interface energy effect increases with the rising total interface area in the composite and becomes negligible when the dimensions iii of the reinforcements are in micrometer scale. Further, classical micromechanical solutions can be obtained when the interface energy effect is neglected. iv The dissertation of Yinghui Zhu is approved. Ertugrul Taciroglu Jian Zhang Ajit K. Mal Jiann-Wen Ju, Committee Chair University of California, Los Angeles 2019 v TABLE OF CONTENTS ABSTRACT OF THE DISSERTATION .................................................................................... ii LIST OF FIGURES ...................................................................................................................... xi LIST OF TABLES ...................................................................................................................... xvi Acknowledgments ..................................................................................................................... xvii VITA ......................................................................................................................................... xviii 1. INTRODUCTION ..................................................................................................................... 1 1.1 Composite Materials .......................................................................................................... 2 1.1.1 Definitions .............................................................................................................. 2 1.1.2 Structures of composite materials .......................................................................... 2 1.1.3 Development of composite materials ..................................................................... 4 1.1.4 Classification of composite materials ..................................................................... 6 1.1.5 Applications of composite materials ...................................................................... 7 1.2 Micromechanics of Composite Materials ........................................................................ 12 1.3 Interface Energy and Nanocomposites ............................................................................ 13 1.4 Scope and Delimitations .................................................................................................. 15 1.5 References ....................................................................................................................... 18 vi 2. LITERATURE REVIEW ....................................................................................................... 21 2.1 Micromechanics of Heterogeneous Materials ................................................................. 21 2.1.1 Eigenstrain ............................................................................................................ 21 2.1.2 Eshelby inclusion theory and equivalent principle principle ............................... 24 2.1.3 Determination of the effective moduli .................................................................. 25 2.1.4 Direct Eshelby method ......................................................................................... 27 2.1.5 Mori-Tanaka method ............................................................................................ 28 2.1.6 Self-Consistent method ........................................................................................ 30 2.1.7 Direct particle interaction model .......................................................................... 32 2.2 Nanomechanics of Heterogeneous Materials .................................................................. 33 2.2.1 Interface energy and interface stress .................................................................... 33 2.2.2 Interface models ................................................................................................... 35 2.2.3 Interface stress model ........................................................................................... 36 2.3 References ....................................................................................................................... 39 3. INTERFACE ENERGY EFFECT ON THE EFFECTIVE ELASTIC MODULI OF SPHERICAL PARTICLE-REINFORCED NANOCOMPOSITES ....................................... 42 3.1 Introduction ..................................................................................................................... 43 3.2 Equivalent Inclusion Method with Interface Energy Effect ............................................ 45 3.3 Interface Boundary Conditions ........................................................................................ 47 vii 3.4 Effective Elastic Moduli of the Composite ..................................................................... 51 3.5 Discussions ...................................................................................................................... 55 3.6 Conclusions ..................................................................................................................... 64 3.7 References ....................................................................................................................... 65 4. INTERFACE ENERGY EFFECT ON EFFECTIVE ELASTIC MODULI OF SPHEROIDAL PARTICLE REINFORCED NANOCOMPOSITES .................................... 68 4.1 Introduction ..................................................................................................................... 69 4.2 Interface Discontinuity Conditions for Spheroids ........................................................... 73 4.3 Interface Discontinuities .................................................................................................. 75 4.4 Effective Moduli of Spheroidal Particle Reinforced Composites ................................... 83 4.5 Nanomechanics Examples and Discussions .................................................................... 85 4.5.1 Analytical solutions of effective moduli for the 2-phase spherical-particle- reinforced nanocomposite ............................................................................................. 85 4.5.2 Numerical solutions of effective elastic stiffness for the 2-phase spheroidal- particle-reinforced nanocomposite ................................................................................ 86 4.6 Conclusions ..................................................................................................................... 90 4.7 References