Multiscale Modeling of Nano-Reinforced Aerospace Adhesives

217 Pages·2013·14.19 MB·English

Multiscale Modeling of Nano-Reinforced Aerospace
Adhesives
by
Jacob Wernik, B.A.Sc
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Department of Mechanical and Industrial Engineering
University of Toronto
© Copyright by Jacob Wernik 2013
Multiscale Modeling of Nano-Reinforced Aerospace Adhesives
Jacob Wernik
Doctor of Philosophy
Department of Mechanical and Industrial Engineering
University of Toronto
2013
Abstract
In this work, the mechanical properties of carbon nanotube reinforced structural adhesives are
investigated both theoretically and experimentally. The theoretical investigations employ a novel
multiscale modeling technique that integrates the governing atomistic constitutive laws in a
continuum framework. This technique takes into account the discrete nature of the atomic
interactions at the nanometer length scale and the interfacial characteristics of the nanotube and
the surrounding polymer matrix. Fundamental to the proposed concept is the notion that atomic
bonds between two atoms act like load-bearing continuum elements, whereas individual atoms
can be represented by nodes of the related structure. Molecular dynamic interatomic potentials
were used to derive the constitutive behavior of the finite elements thereby reducing the
computational complexity of the problem while maintaining the accuracy of the model. The
governing formulations were developed to allow for the atomistic-based continuum modelling of
nano-reinforced structural adhesive bonds on the basis of a nanoscale representative volume
element that accounts for the nonlinear behaviour of its constituents; namely, the reinforcing
carbon nanotube, the surrounding adhesive and their interface. This model was used to evaluate the
constitutive response of carbon nanotubes with varied chiral indices, the load transfer and the
strengthening mechanisms between the nanotube and the surrounding adhesive as well as their
interfacial properties. The newly developed representative volume element was then used in
ii
analytical (Mori-Tanaka) and computational (finite element) micromechanical modeling
techniques to investigate the homogeneous dispersion of the reinforcing element into the adhesive
considered upon its mechanical properties. In this way, the model allowed for the prediction of the
full constitutive response of the bulk composite. The work is further extended experimentally to
establish the relative merits of using carbon nanotubes as mechanical reinforcements in structural
adhesive bonds. In this part of the research, we identified an appropriate dispersion methodology to
achieve a uniform distribution of the nanotubes in the epoxy matrix and evaluated its mechanical
properties. Scanning electron and transmission electron microscopy techniques were routinely used
to characterize the quality of the dispersion, the geometrical properties of the nanotubes, and the
fracture surfaces of the test specimens.
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Acknowledgments
I extend my appreciation and gratitude to Dr. Shaker Meguid for his expert advice, technical
guidance, financial assistance and continued support throughout the course of my research. I also
wish to thank all the past and present members of the Mechanics and Aerospace Design lab for
their friendship, advice and technical assistance. Furthermore, the financial support of the
National Science and Engineering Research Council Postgraduate Scholarship, the Mechanical
and Industrial Engineering Fellowship and the Joseph Bazylewicz Scholarship are gratefully
acknowledged. Finally, I would like to acknowledge the continued support and understanding of
my parents Marek and Miroslawa Wernik, to you I dedicate this thesis.
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List of Abbreviations
3D Three-dimensional PA6 Polyamide – 6 (Nylon 6)
ABC Atomistic-based continuum PANI Polyaniline
AFM Atomic force microscopy PE Polyethylene
CNT Carbon nanotube PMMA Polymethyl methacrylate
DCB Double cantilever beam PmPV Poly-m-phenylenevinylene
DGEBA Diglycidyl ether of bisphenol A PS Polystyrene
DLS Double lap shear PVP Polyvinylpyrrolidone
DWCNT Double-walled carbon nanotube QM Quantum mechanics
FEM Finite element method RVE Representative volume element
Glass Laminate Aluminum
GLARE SAB Structural adhesive bond
Reinforced Epoxy
HPC High powered computing SEM Scanning electron microscopy
Scanning transmission electron
ISS Interfacial shear strength STEM
microscopy
LJ Lennard-Jones potential SWCNT Single-walled carbon nanotube
MD Molecular dynamics TEM Transmission electron microscopy
MM Micromechanics TETA Triethylene tetramine
MWCNT Multi-walled carbon nanotube vdW van der Waals
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List of Notations
α Aspect ratio of fiber e Applied strain
r
a Delamination length {ε} Strain vector
v
a Acceleration of particle i
i ε Strain tensor
kl
A CNT cross-section area
ε Average fiber strain
f
Strain concentration factor for
A
o matrix ε Average matrix strain
o
Strain concentration factor for Young’s modulus of composite
A
f fiber E with randomly orientated
inclusions
Dilute strain concentration factor
A dil
f for fiber Longitudinal Young’s modulus
Ef ,
L of representative fiber
Dilute strain concentration factor
Adil
o for matrix Transverse Young’s modulus of
Ef ,
T representative fiber
Transformation matrix for 3D
A
ij space F DCB correction factor
b DCB specimen thickness Fv Force acting on particle i
i
Bounding surface of
B F Total shear force
τ
representative fiber
F Total axial force
σ
[B] Derivatives of shape functions
Shear modulus of composite
C Stiffness tensor of composite
G with randomly orientated
inclusions
C Stiffness tensor of matrix
0
G Critical strain energy release rate
C , Cf Stiffness tensor of fiber IC
f ijkl
Longitudinal shear modulus of
Gf
D Diameter of representative fiber L representative fiber
{d} Displacement vector Transverse shear modulus of
Gf
T representative fiber
[D] Elasticity matrix
G Fiber pull-out energy
f
δ Crack opening displacement
γ Shear strain
Δ DCB correction factor
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I Identity tensor t CNT wall thickness
Plane-strain bulk modulus of Δt Time step size
Kf
representative fiber
τ Interfacial shear strength
i
L Length of representative fiber
U Internal energy
L Initial CNT length
o
v Volume fraction of matrix
0
m Mass of particle i
i
v Volume fraction of fiber
f
M Moment
V Volume of representative fiber
Components of outward normal
nj vector to boundary B V (rv) Total potential energy of atomic
system
N DCB correction factor
W External work
[N] Shape functions
Local coordinate system of
x
j representative fiber
P Applied load
X Global coordinate system
Π Total potential energy i
Total strain energy of
r Bond length χ
representative fiber
v
R Chiral vector
Angles of coordinate
φ, Φ
1 transformation
S Eshelby tensor
r
Lennard-Jones potential
σ Average stress of composite μ, ψ

parameters
σ Stress tensor
ij D β, k Modified Morse potential
e, θ
and k parameters
{σ} Stress vector sextic
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Table of Contents
Acknowledgments ........................................................................................................................... ii
List of Abbreviations ...................................................................................................................... v
List of Notations ............................................................................................................................ vi
Table of Contents ......................................................................................................................... viii
List of Tables ................................................................................................................................ xii
List of Figures .............................................................................................................................. xiii
List of Appendices ..................................................................................................................... xxiii
Chapter 1 Introduction and Justification ......................................................................................... 1
1.1 Paradigm shift in Composite and Airframe Design ............................................................ 1
1.2 Justification of the Study .................................................................................................... 4
1.3 Objective of the Study ........................................................................................................ 5
1.4 Method of Approach ........................................................................................................... 6
1.5 Layout of Thesis ................................................................................................................. 8
Chapter 2 Literature Review ......................................................................................................... 10
2.1 Carbon Nanotubes ............................................................................................................. 10
2.1.1 Structure of CNTs ................................................................................................. 10
2.1.2 Mechanical Properties ........................................................................................... 12
2.2 Nano-Reinforced Composites ........................................................................................... 15
2.2.1 Dispersion and Functionalization ......................................................................... 15
2.2.2 Experimental Investigations of the Mechanical Properties .................................. 19
2.3 Existing Multiscale Models and Theoretical Characterization of Nanocomposites ......... 26
2.3.1 Atomistic Modeling .............................................................................................. 27
2.3.2 Continuum Modeling ............................................................................................ 29
2.3.3 Existing Multiscale Modeling Techniques ........................................................... 32
2.4 The Need for the Current Studies ..................................................................................... 36
2.4.1 CNT Dispersion .................................................................................................... 36
2.4.2 Interfacial Characteristics and Load Transfer ....................................................... 37
2.4.3 Theoretical Models ............................................................................................... 38
2.4.4 Multifunctionality and Self-Health Monitoring .................................................... 38
Chapter 3 Multiscale Modeling of Nanocomposites Using Atomistic-Based Continuum
Method ..................................................................................................................................... 40
3.1 Molecular Dynamics ......................................................................................................... 40
3.1.1 Two-body (pair) potentials ................................................................................... 42
3.1.2 Many-body Potentials ........................................................................................... 44
3.1.3 Time Stepping ....................................................................................................... 47
3.2 The Finite Element Method .............................................................................................. 49
3.3 Representative Volume Element ....................................................................................... 50
3.3.1 Atomistic-based Continuum Representation of CNT Structures .......................... 51
3.3.2 Atomistic-based Continuum Representation of Interfaces ................................... 54
3.3.3 Homogenized Epoxy Matrix Representation ........................................................ 57
3.3.4 Assembled RVE .................................................................................................... 60
Chapter 4 Interfacial Characterization of Nano-Reinforced Adhesives Using Atomistic-Based
Continuum ................................................................................................................................ 61
4.1 Nanotube Pull-out ............................................................................................................. 61
4.2 Interfacial Representation ................................................................................................. 62
4.3 Epoxy Matrix Representation ........................................................................................... 63
Chapter 5 Micromechanical Determination of Effective Mechanical Properties of
Nanocomposites ....................................................................................................................... 66
5.1 The Representative Fiber .................................................................................................. 66
5.1.1 Representative Fiber Constitutive Model ............................................................. 67
5.1.2 Boundary Conditions ............................................................................................ 68
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5.1.3 Material Property Summary .................................................................................. 70
5.2 Micromechanical Analysis Using Mori-Tanaka Formulations ......................................... 71
5.2.1 Mori-Tanaka Method for Unidirectionally Aligned CNTs ................................... 72
5.2.2 Mori-Tanaka Method for Randomly Orientated CNTs ........................................ 75
5.2.3 Orientational Averaging ........................................................................................ 76
5.2.4 Effective Engineering Constants of Nanocomposite ............................................ 78
5.3 Micromechanical Analysis Using Large Scale Hybrid Monte-Carlo FEA Simulations .. 79
5.3.1 Representative Fiber Constitutive Model ............................................................. 79
5.3.2 Monte-Carlo Computational Cell ......................................................................... 81
Chapter 6 Experimental Investigations ......................................................................................... 85
6.1 Fabrication of Nano-Reinforced SABs ............................................................................. 85
6.1.1 Materials Used ...................................................................................................... 85
6.1.2 Dispersion Methodology and Specimen Fabrication ............................................ 91
6.2 Mechanical Characterization of Nano-Reinforced SABs ................................................. 92
6.2.1 Dogbone Tensile Testing ...................................................................................... 92
6.2.2 Tensile Button Testing .......................................................................................... 93
6.2.3 Double Lap Shear Testing .................................................................................... 93
6.2.4 Double Cantilever Beam Testing .......................................................................... 94
Chapter 7 Analysis of Results and Discussions ............................................................................ 97
7.1 Numerical Predictions ....................................................................................................... 97
7.1.1 Constitutive Response and Fracture Behavior of CNT ......................................... 97
7.1.2 ABC Model Validation Using Molecular Dynamics .......................................... 105
7.1.3 Interfacial Characteristics ................................................................................... 108
7.1.4 Effective Linear Elastic Properties of Nano-Reinforced Adhesives ................... 127
7.1.5 Full Constitutive Response Predictions .............................................................. 135
7.2 Experimental Findings .................................................................................................... 142
x