Elastic and Mechanical Properties of Expanded Perlite and Perlite/Epoxy Foams” Submitted by Miss

Home , Perlite

Elastic And Mechanical Properties

Of Expanded Perlite And

Perlite/Epoxy Foams

Haleh Allameh Haery

MIEngDes (UPM)

This thesis is submitted for the degree of

Doctor of Philosophy (Mechanical Engineering)

University of Newcastle, Australia

Faculty of Engineering and Built Environment

School of Engineering

February 2017

Statement of Originality

This is to certify that the thesis entitled “Elastic and Mechanical Properties of Expanded perlite and Perlite/Epoxy foams” submitted by Miss. Haleh Allameh Haery contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to this copy of my thesis when deposited in the University Library, being made available for loan and photocopying subject to the provisions of the Copyright Act 1968.

Haleh Allameh Haery

Statement of Collaboration

I hereby certify that the work embodied in this thesis has been done in collaboration with other researchers. I have included as part of the thesis a statement clearly outlining the extent of collaboration, with whom and under what auspices.

Statement of Authorship

I hereby certify that the work embodied in this thesis contains published papers of which

I am a joint author. I have included as part of the thesis a written statement, endorsed by my supervisor, attesting to my contribution to the joint publications.

Haleh Allameh Haery

Dedication

I dedicate this thesis to my parents, who have always loved and supported me

unconditionally.

Acknowledgments

I would like to express my sincere gratitude to my supervisors, Professor Erich Kisi and

Doctor Thomas Fiedler, for their help and support throughout my period of PhD study. I would like to take this opportunity to express my appreciation to my supervisor Erich, whose patience, kind words, complete support and professional advice have been a source of encouragement and a motivation to explore my ideas to their fullest depth. I would also like to thank Doctor Jubert Pineda for his mentorship and constructive advice which has helped me enormously.

I would like to take this opportunity to express my appreciation to the University of

Newcastle for granting me IPRS and Postgraduate Research scholarships during the four years of my study.

I would also like to gratefully acknowledge the assistance from the staff in the electron microscope and X-ray unit at the University of Newcastle, Australia.

Last, not the least, I want to thank my parents for their love, support and words of encouragement throughout studies.

List of Publications and Awards

Awards

1. 2016 Three Minutes Thesis Finalist (Faculty of Engineering and Built Environment); (University of Newcastle, Australia).

2. Runner Up - 2016 Three Minutes Thesis Faculty competition (Faculty of Engineering and Built Environment); (University of Newcastle, Australia).

3. Faculty of Engineering and Built Environment 2015 postgraduate research prize, Mechanical Engineering (University of Newcastle, Australia).

4. Faculty of Engineering and Built Environment 2014 postgraduate research prize, Mechanical Engineering (University of Newcastle, Australia).

5. Runner Up - 2015 Three Minutes Thesis Faculty competition (Faculty of Engineering and Built Environment); (University of Newcastle, Australia).

6. 2015 Three Minutes Thesis Finalist (Faculty of Engineering and Built Environment); (University of Newcastle, Australia).

Conference (Poster)

Haleh Allameh-Haery, Erich Kisi, Thomas Fiedler, “Characterization of perlite-epoxy foam cores for sandwich panels”, International Conference on Advances in Functional Materials", 29 June-3 July, 2015, Long Island, NY, USA.

Conference Papers H. A. Haery, and H. S. Kim, "Damage of hybrid composite laminates." SPIE Proceedings, Volume 8793, Aerospace Composites, 87931F-87931F-13 (2013)

Journal Papers

1. H. Allameh Haery, H. S. Kim, R. Zahari, E. Amini, Tensile strength of notched carbon/glass/epoxy hybrid composite laminates before and after fatigue loading. Journal of Industrial Textiles, 2014, 44(2): p. 307 – 331.

2. H. Allameh Haery, and H. S. Kim, Damage in hybrid composite laminates. Journal of Multifunctional Composites, 2013, 1(2): p.127-137.

3. H. Allameh Haery, E. Kisi, and T. Fiedler, Novel cellular perlite-epoxy foams: effect of density on mechanical properties. Journal of Cellular Plastics, Doi: 10.1177/0021955x16652110, 2016.

4. H. Allameh-Haery, C.M. Wensrich, T. Fiedler, and E. Kisi, Novel Cellular perlite-epoxy foams: effects of particle size. Journal of Cellular Plastics, Doi: 10.1177/0021955X16670528, 2016.

5. H. Allameh-Haerya, E. Kisi, J. Pineda, L. P. Suwal, T. Fiedler, Characterization and prediction of Elastic properties of green compacts of Expanded perlite particles. Journal of Powder Technology, 25 January 2017.

6. H. Allameh-Haery, E. Kisi, J. Pineda, L. P. Suwal, T. Fiedler, Elastic properties of perlite-epoxy foams. (Under review).

Table of Contents

Statement of Originality ...... 2

Statement of Collaboration ...... 3

Statement of Authorship ...... 4

Dedication ...... 5

Acknowledgments ...... 6

List of Publications and Awards ...... 7

Conference (Poster) ...... 7

Conference Papers ...... 8

Table of Contents ...... 9

List of Figures ...... 13

List of Tables...... 20

List of Symbols and Abbreviations ...... I

Abstract ...... 1

1 Chapter One: Introduction...... 4

2 Chapter Two: Literature Review ...... 9

Introduction ...... 9

The characteristics, manufacturing processes and applications of Perlite ...... 10

2.2.1 Introduction to perlite ...... 10

2.2.2 Expansion process ...... 12

2.2.3 The physical properties of perlite ...... 16

2.2.4 Chemical composition ...... 19

2.2.5 Applications ...... 24

2.2.6 Concluding Remarks ...... 41

Foams ...... 42

2.3.1 Introduction to foams and syntactic foams ...... 42

2.3.2 Manufacturing syntactic foams ...... 46

2.3.3 Particulate composites containing naturally occurring fillers ...... 50

Motivation and Problem Statement ...... 59

Research Objectives and Research Significance ...... 60

3 Chapter Three: Methodology ...... 61

Introduction ...... 61

Material ...... 62

3.2.1 Expanded perlite particles ...... 62

3.2.2 Epoxy resin ...... 63

Sample preparation ...... 64

3.3.1 Preparation of expanded perlite (EP) particle samples ...... 64

3.3.2 Preparation of solid perlite samples ...... 67

3.3.3 Preparation of resin samples ...... 67

3.3.4 Preparation of EP/epoxy foam samples ...... 70

Experimental Setup and Tests ...... 73

3.4.1 Mechanical testing on the packed beds of EP Particles ...... 73

3.4.2 Mechanical testing of EP/epoxy foams ...... 73

3.4.3 Elastic wave tests on EP particles ...... 75

3.4.4 Elastic wave tests on EP/epoxy foams and solid perlite ...... 79

Microstructural analysis ...... 81

Damage observation ...... 82

The theory of dynamic moduli measurement ...... 83

4 Chapter Four: Results ...... 86

Introduction ...... 86

Elastic properties of sintered solid perlite ...... 88

Properties of packed beds of EP particles ...... 91

4.3.1 Structural characterisation of EP particles ...... 91

4.3.2 Measurement of elastic moduli of packed EP particle beds using quasi-static

mechanical tests ...... 96

4.3.3 Measurement of elastic moduli of packed EP particle beds using elastic

waves 98

Mathematical models for prediction for Elastic properties of porous bodies 107

4.4.1 Phani Models ...... 109

4.4.2 Nielson Model ...... 113

4.4.3 Minimum solid area (MSA) models ...... 117

4.4.4 Gibson and Ashby Model ...... 121

Properties of epoxy resin ...... 124

Properties of EP/epoxy foams ...... 126

4.6.1 Microstructural characterisation of EP/epoxy foams ...... 126

4.6.2 Volume fraction of the epoxy in EP/epoxy foams ...... 128

4.6.3 Compressive response of EP/epoxy foams ...... 133

Damage analysis ...... 141

Measurement of the elastic moduli of EP/epoxy foams using elastic wave speed

147

5 Chapter Five: Discussion ...... 159

Introduction ...... 159

Manufacturing method ...... 160

Young’s modulus of packed EP particles ...... 163

Structural characterisation of EP/epoxy foams ...... 167

Compressive behaviour and compressive properties ...... 172

Damage mechanisms under compressive loading ...... 178

6 Chapter Six: Summary ...... 182

Conclusions ...... 182

Future Research ...... 186

References ...... 189

List of Figures

Figure 1.1. Schematic diagram illustrating the structure and composition of syntactic foams...... 4

Figure 2.1. (a) Unexpanded perlite (b) Expanded perlite. Both types were supplied by

Ausperl...... 11

Figure 2.2. Horizontal expander and handling system [30]...... 15

Figure 2.3. Vertical expander and handling system [30]...... 15

Figure 2.4. Cellular structure formed internally in expanded perlite particles...... 17

Figure 2.5. US expanded perlite use by application...... 24

Figure 2.6. Spherical gas tank farm in a petroleum refinery [116]...... 32

Figure 2.7. SEM image showing EP microspheres consisting of one or more microcellular bubbles [27]...... 37

Figure 2.8. (a) Closed cell Polyurethane foam [102], (b) Open cell Polyurethane foam [3].

...... 43

Figure 3.1. Durometer (Type D) for hardness test...... 63

Figure 3.2. Tapping device for measuring tapped density of EP particles...... 65

Figure 3.3. Prepared mould (a) The different parts of the mould (b) Assembled mould.

...... 66

Figure 3.4. Solid perlite sample (sintered perlite powders)...... 67

Figure 3.5. Mould for manufacturing epoxy resin samples for (a) compression and flexural tests and (b) tensile tests...... 68

Figure 3.6. A hand-made device for separating expanded particles from unexpanded and semi-expanded particles...... 71

Figure 3.7. Formation of two phases by buoyancy. The top phase is packed perlite particles and diluted binder and the bottom phase contained only diluted binder...... 72

Figure 3.8. Samples prepared using three particle size ranges; from the left, 1 - 2 mm, 2 -

2.8 mm and 2.8 – 4 mm...... 72

Figure 3.9. Schematic representation of the experimental set-up for measuring wave velocity in packed beds of EP particles...... 75

Figure 3.10. Examples of (a) P-wave and (b) S-wave signals in low density (0.12 g/cm3)

EP particle compacts and (c) P-wave and (d) S-waves in high density (0.3 g/cm3) EP particle compacts...... 78

Figure 3.11. Schematic representation of the ultrasonic experimental set-up for measuring wave velocity in solid perlite and EP/epoxy samples...... 79

Figure 4.1. Microscope images taken from the polished surface of sintered perlite. The polishing marks are designated on the picture in order not to be confused with porosity.

...... 88

Figure 4.2. SEM images showing the external structure of an EP particle: (a) in the 1 - 2 mm size range; (b) in the 2 - 2.8 mm size range; (c) in the 2.8 - 4 mm size range...... 92

Figure 4.3. SEM images showing the internal structure of an EP particle in the: (a) 1 - 2 mm size range; (b) 2 - 2.8 mm size range; (c) 2.8 - 4 mm size range; (d) 2 - 2.8 mm size range, illustrating natural reinforcement inside EP particle cells...... 93

Figure 4.4. Constrained modulus of packed EP particle beds as a function of compact density...... 97

Figure 4.5. The (a) Compression wave and (b) Shear wave velocities versus compact density...... 99

Figure 4.6. Formation of platy and fine particles as a result of the brittle crushing of cell walls...... 100

Figure 4.7. (a) Percentage of debris at each EP compact density. (b) Cumulative particle size distribution for entire compacts (EP particles and debris)...... 101

Figure 4.8. (a) Particle density versus particle size. This graph also includes debris density versus debris size; (b) Inter-particle porosity (excluding debris) versus compact density;

Figure 4.9. (a) Young’s modulus (E) of packed beds of EP particles versus compact density. (b) Poisson’s ratio of packed beds of EP particles versus compact density. In both graphs, the upper and right hand scales allow the normalised moduli versus porosity to be read from the same graphs...... 106

Figure 4.10. (a) Normalised Young’s modulus versus porosity (based on experimental moduli); (b) Normalised Poisson’s ratio versus porosity (based on experimental moduli);

Normalised Poisson’s ratio versus porosity (based on modified moduli)...... 112

Figure 4.11. (a) Shape factor versus compact porosity for the Phani and Neilson models applied to both the experimental moduli and modified moduli; (b) Modified Phani and

Nielson models for Young’s Moduli as a function of porosity; (c) Modified Phani and

Nielson models for Poisson’s ratio as a function of porosity...... 116

Figure 4.12. Hardness versus time curve used to determine the curing period of the diluted epoxy...... 125

Figure 4.13. Changes in the viscosity of epoxy + hardener diluted with acetone versus acetone content...... 125

Figure 4.14. Micrographs taken from the cross-sections of EP/epoxy foams with a density of 0.15 g/cm3 made with EP particles in the size ranges: a) 1 - 2mm; b) 2 - 2.8mm; and c)

2.8 - 4mm...... 127

Figure 4.15. (a) Foam density as a function of applied pressure. (b) Particle density as a function of compaction pressure...... 130

Figure 4.16. Volume fraction of epoxy versus density of the foam...... 131

Figure 4.17. Volume fraction of epoxy binder in EP/epoxy foams of type 2...... 133

Figure 4.18. Typical stress-strain curves for the different EP/epoxy foam densities of: (a)

Type 1; (b) Type 2; (c) Type 3...... 135

Figure 4.19. Properties of manufactured foams of type 1 ( ⃣ ), type 2 (◇) and type 3 (∆):

(a) Maximum stress versus foam density; (b) Effective modulus versus foam density; (c)

Modulus of toughness versus foam density...... 137

Figure 4.20. Confined modulus of EP particles ( ⃣ ) and confined modulus of the foams

(◇) as a function of the density of the packed bed of EP particles...... 138

Figure 4.21. Predicted elastic moduli of EP particles using the Voigt and Reuss models.

To quantify the particles’ contributions to the stiffness of the foam, the effective elastic modulus of the EP/epoxy foams as a function of foam density is presented...... 140

Figure 4.22. Schematic representation of failure in EP/epoxy foams...... 141

Figure 4.23. Macroscopic images showing (a) A sample of type 1 compressed to a strain of 12% (b) A typical remnant of the samples after the test...... 145

Figure 4.24. SEM images showing (a) Uncrushed EP particles in the wedge-like fractured side of a failed sample; (b) Cell walls of EP perlite particles fractured along a plane; (c)

Crushed cells in the central region of a uniformly compressed sample...... 146

Figure 4.25. Typical stress-strain curve for different EP/epoxy foam densities...... 147

Figure 4.26. The longitudinal wave and shear wave velocities versus foam density. .. 149

Figure 4.27. Young’s modulus of EP/epoxy foams versus foam density determined from the elastic wave speed (○) and mechanical tests (∆); and Young’s modulus of the EP particles versus foam density determined from the elastic wave speed (◇)...... 149

Figure 4.28. Volume fraction of the epoxy binder in the second series of EP/epoxy foams versus foam density...... 151

Figure 4.29. (a) stress-strain curves and (b) Young’s modulus measured from the gradient of the unloading path in Figure 4.29 (a) at different stress level in cyclic compressive tests conducted on a sample with density of 0.26 g/cm3...... 155

Figure 4.30. Poisson’s ratio of epoxy resin (••••), foam (○) and packed beds of EP particles ( ⃣ ) versus the foam density...... 157

Figure 5.1. Young’s moduli of the packed EP particle beds measured using mechanical tests and estimated using the Voigt and Reuss models...... 165

Figure 5.2. (a) Volume fraction of EP particles and (b) Porosity within inter-particle space

(by consideration of debris) and total porosity in type 2 EP/epoxy foams...... 169

Figure 5.3. A schematic representation of the internal structure of (a) low density and (b) high density EP/epoxy foams...... 171

Figure 5.4. Schematic representation of compressive stress-strain curves for a) an elastomeric, b) an elastic-plastic, c) a brittle foam [11]...... 172

Figure 5.5. Schematic representation of the compressive stress-strain curve for EP/epoxy foams...... 175

Figure 5.6. Compressive strength (a) and compressive modulus (b) plotted against density for currently available foams (Ashby et al., 2000) and results obtained for perlite-based foams ( )...... 177

List of Tables

Table 2.1. Typical physical properties of expanded perlite [23, 26, 39]...... 18

Table 2.2.Chemical composition of perlite (Percent) [22]...... 20

Table 2.3. Mineral phases detected in perlites of different origins...... 23

Table 2.4. Examples of perlitic sound insulation boards in which starch is used as binder

[69]...... 30

Table 3.1. Chemical composition [198] ...... 62

Table 3.2. ASTM D-695, ASTM D-638 and ASTM D-790 for measuring the compressive, tensile and flexural properties of epoxy resin...... 68

Table 4.1. Elastic properties of solid component of EP particles. For comparison, the corresponding data for obsidian by Manghnani et al. [213] are presented...... 90

Table 4.2. Bulk density and particle density measurements of EP particles ...... 91

Table 4.3. Cell dimensions of EP particles of 1 - 2 mm, 2 - 2.8mm and 2.8 - 4 mm size range. Each value is an average of 150 measurements...... 95

Table 4.4. Exponents of Eq. (4.3) and Eq. (4.4) for the three particle size ranges...... 96

Table 4.5. Physical parameters of mathematical models applied to the experimental and modified moduli. The physical parameters of the modified moduli are given in parenthesis...... 111

Table 4.6. Mechanical properties of cured epoxy resin with and without dilution by acetone...... 124

Table 4.7. Coefficients in Equations (4.21) and (4.22) for foam density Df and particle density Dp ...... 131

Table 4.8. Elastic properties of EP particles, epoxy resin and EP/epoxy foams...... 150

List of Symbols and Abbreviations

Item Description

EP Expanded perlite

Cp Compression wave velocity

Cs Shear wave velocity

CL Longitudinal wave velocity

휈 Poisson’s ratio

휈푐푟 Critical Poisson’s ratio

휈0 Poisson’s ratio at zero porosity

E Young’s modulus

E0 Young’s modulus at zero porosity

E* Constrained elastic modulus

G Shear modulus

G0 Shear modulus at zero porosity

K Bulk modulus

σcomp Compaction pressure

𝜌 Density

𝜌0 Density at zero porosity

ρc Composite density

ρp Particle density

ρg Density of the glass

ρtrue True density of the microspheres

ρe Epoxy density

Df foam density as a function of compaction pressure

DP Particle density as a function of compaction pressure tw Wall thickness of particle r Average radius of the microspheres

C Cell size dp EP particle diameter

𝜌퐸푃 EP particle density

𝜌푈푃 Density of fully dense perlite

휑 Angle of internal friction a Packing geometry dependent parameter

P Porosity

Pcr Critical porosity

Ptap Porosity of tapped packing state

Pgreen porosities of as-poured packing state

Constant related to pore morphology n0

Pore structure dependent parameter (shape factor) nE

훽 Pore structure dependent parameter (shape factor)

S Shape factor as a function of porosity

CSA Composite sphere assemblage b Constant related to particle stacking

푏′ Constant related to particle stacking

M Young’s, shear or bulk modulus

C Constant of proportionality

C Constant of proportionality

Ø Volume fraction of solid in the cell- struts

U ppe r Upper bound of Young’s modulus of EP particle EP

Low e r Lower bound of Young’s modulus of EP particle EP

σhyd Hydrostatic stress

σdev Deviatoric stress

δ Kronecker delta

λ, µ Lamé constants

III

Abstract

Syntactic foams are composite materials made by reinforcing a resinous matrix with hollow particles called microspheres. These materials are often used as the core material for sandwich panels, where a combination of low density, high compressive strength, high compressive deformation and high damage tolerance are required, e.g. in the aerospace, automotive and marine industries. Syntactic foams have superior mechanical and thermal properties but they are more expensive and denser than conventionally gas-blown foams.

The higher density and cost of syntactic foams is mainly due to the density and cost of the synthetically made microspheres. This problem can be mitigated by using light-weight naturally occurring particles which provide syntactic foams with similar properties but which are significantly cheaper. In this study, the potential of expanded perlite particles

(EP particles) in manufacturing light-weight syntactic foams is investigated. Perlite is a glassy volcanic rock of silicic composition and in its expanded form has a high porosity

(>95%), low density (~ 0.18 g/cm3) and offers excellent thermal and acoustical insulating properties, chemical inertness, physical resilience, fire resistance and water retention properties. These features, along with the fact that it is abundant and cheap make it a suitable candidate for manufacturing syntactic foams.

In this study, the structural, microstructural, physical and mechanical properties of EP particles were investigated. The elastic properties of packed EP particle beds were characterised by the isotropic elastic moduli Poisson’s ratio and Young’s modulus, calculated from elastic wave speeds along the axial (compaction) direction for a wide range of compaction densities. It was observed that during compaction to achieve different densities, some crushing of particles into smaller particles and platy debris

occurred. Consequently, analyses were conducted based on both the raw compaction densities and densities modified by the removal of debris from consideration, on the assumption that debris is non-structural. Based on the raw compaction densities, Young’s moduli of the packed EP particles were found to vary in the range 31.4 - 371.3 MPa, while based on the modified densities, they varied in the range 31.4 - 152.8 MPa for the compact densities ranging from 0.1 to 0.375 g/cm3. Poisson’s ratio of packed EP particles did not show a large variation with compact density in the range 0.1 - 375 g/cm3; Poisson’s ratio was about 0.3. The equation for Poisson’s ratio is independent of density, hence the values obtained based on the experimental and modified densities resulted in the same Poisson’s ratios.

Four analytical models were applied to predict the elastic moduli of packed beds of EP particles within the porosity range 84 - 95%. Models were assessed on their ability to successfully predict the elastic moduli of these highly porous bodies from the properties of solid perlite for both cases: using the raw compaction density and the modified density.

It was found that the Wang (Minimum Solid Area) model was able to estimate Young’s modulus, while the Gibson and Ashby model was reasonable for the average behaviour of both of the elastic moduli. The best agreement, however, was obtained through the

Phani model utilising our modified shape factor.

The impact of the research was broadened by dispersing EP particles in a matrix of epoxy resin and the manufacture of light-weight EP/epoxy foams. Foams were fabricated with three distinct particle size ranges and, within each size range, the samples covered a density range 0.15 - 0.45 g/cm3. The effects of particle size and foam density variations on the compressive strength, effective elastic modulus and modulus of toughness of the

EP/epoxy foams were investigated. The compressive properties of the EP/epoxy foams

showed a strong dependence on the foam density, but were almost independent of the particle size. The compressive strength of the EP/epoxy foams was found to vary linearly in the range 0.15 - 1.77 MPa with the foam densities ranging from 0.15 to 0.45 g/cm3.

However, the Young’s modulus and modulus of toughness of the EP/epoxy foams varied parabolically in the ranges 33 - 227 MPa and 0.01 - 0.35 MPa, respectively. The elastic properties of the EP/epoxy foams were characterised by adopting an isotropic model for the medium and measuring the elastic wave speeds (i.e. longitudinal and shear wave) in the axial direction (similar to the measurements of the particle beds). Quasi-static compressive test results were compared with those obtained by the elastic wave tests.

Both were observed to follow the same qualitative pattern, however the Young’s moduli measured using elastic waves were more than twice those obtained from the mechanical tests. Poisson’s ratio showed an increasing trend, ranging from 0.17 to 0.34 over the foam density range, and appeared to be influenced by the increase in contact surface area between the particles and the matrix as the foam density increased.

Post-test scanning electron microscopy (SEM), coupled with photogrammetry during the tests, were used to understand the behaviour of the foams under compressive load. The observations revealed the presence of three different failure modes for all of the foams, regardless of their particle size and density, however the strain to activate each mode was different for each foam type. In addition, the observations showed that the formation of wedge-like fragments in the foam samples under applied compressive stress were due to the effects of pure shear (i.e. the deviatoric components of the applied stress). However, the compressive deformation due to the effect of the hydrostatic components of the applied stress was concentrated in the middle of the foam samples.

1 Chapter One: Introduction

Foams are cellular solids where cells with solid ligaments and membranes pack together in three dimensions to fill space. These materials are widely found in nature, and have been in use for more than 5000 years, for example, the wooden artefacts found in Egypt’s pyramids or cork which has been used for the soles of shoes since Roman times [1]. These materials inspired engineers to synthesise light-weight, yet strong and stiff, cellular materials for various structural applications. Syntactic foams are a special class of cellular materials which are made by embedding hollow microspheres in a polymeric matrix or binder. They are identified as foams due to their cellular structure created by void space in both the polymer resin matrix and the hollow microspheres. The schematic structure of syntactic foams is presented in Figure 1.1.

Figure 1.1. Schematic diagram illustrating the structure and composition of syntactic foams.

Syntactic foams were initially developed in the 1960s as a buoyancy aid material for deep submergence applications where high hydrostatic pressures are involved [2]. They are generally used as the core material in sandwich plates and shells as an effective weight- saving design option for various structural applications [3], and in areas where a 4

combination of low density, high compressive strength, high compressive deformation and low moisture absorption are required, e.g. in naval, aeronautical, aerospace, civil and automotive applications [4-6].

There are a wide variety of hollow microspheres available for use in syntactic foams.

They are commonly made from glass, ceramic, carbon or any polymeric materials. The appropriate choice of microspheres can produce resinous foams with superior strength, stiffness, damage tolerance and chemical resistance. Preference is generally given to hollow glass microspheres due to their low density (~ 0.28 - 0.7 g/cm3 [7-9]), mechanical strength, stiffness, the regularity of the surface and their price, which is lower than other microspheres [8]. However, compared with conventionally gas-blown foams, syntactic foams have higher density and cost of production. This is mainly due to the cost of synthetically made hollow spheres. Cost and density are two main factors in the selection of materials, especially when production of weight-sensitive structural components in large quantities is involved. Hence, it would be worthwhile to find a light-weight material which has the potential to provide syntactic foams with similar specific properties, but which is significantly cheaper than other commercially available microspheres. One promising material is expanded perlite particles. Perlite is a glassy volcanic rock of rhyolitic composition normally comprised of 71-75% SiO2, 12.5-18% Al2O3, 4-5% K2O,

1-4% sodium and calcium oxides, lesser amounts of several metal oxides and 2-5% water by weight [10]. Upon rapid controlled heating in the range 760 - 1100°C, the combined water in perlite grains is vaporised, producing pressure that causes expansion of the perlite to 4 - 20 times its original volume. The expanded form of perlite has a low density (~ 0.18 g/cm3 [11]) and offers excellent thermal and acoustic insulating properties, chemical inertness, physical resilience, fire resistance and water retention properties [12]. In

addition, expanded perlite particles have a cellular structure mainly consisting of closed cells (sealed bubbles) which provide them with progressive crushing characteristics as opposed to the one-step crushing of microspheres [13]. This can be beneficial to preserving the cellular structure of the perlite-reinforced plastic/foam for a longer service life.

The present study focuses on the development of a light-weight foam material made by dispersing expanded perlite particles (hence called EP particles) in a matrix of epoxy resin. The structural, microstructural, and mechanical properties of EP particles and

EP/epoxy foams are investigated. Consequently, the potential of EP/epoxy foams as a novel class of engineering materials, especially for light-weight structural applications, are evaluated.

The layout of the remainder of the thesis, a significant portion of which is based on articles published by the author [14-16] while undertaking this study, are organised as follows:

Chapter 2 delivers an overview of the existing literature related to this work in two main sections. The first section gives a comprehensive overview of the physical properties, chemical properties, expansion process and applications of perlite particles. The second section outlines an overview of foams, syntactic foams and polymeric composites reinforced with different naturally occurring minerals, including perlite particles.

Subsequently, based on gaps in the current literature, the motivation for conducting the current project and the key objectives are highlighted.

Chapter 3 includes a description of the various raw materials used in manufacturing

EP/epoxy foams, fabrication techniques and testing procedures (i.e. quasi-static mechanical tests and elastic wave tests) used for characterisation of the mechanical and

physical properties of solid perlite (i.e. virtually pore free), packed beds of expanded perlite particles, and the novel EP/epoxy foams manufactured.

Chapter 4, firstly, outlines the experimental results related to tests performed on solid perlite, e.g. microscopy and elastic wave tests. Secondly, the experimental results relating to microscopy and mechanical and elastic wave tests, on packed beds of EP particles are discussed. Thirdly, the experimental results relating to mechanical and elastic properties of cured epoxy resin are presented. Fourthly, four mathematical models for the prediction of elastic properties of packed EP particle beds are introduced. The predictive ability of the models is evaluated and modifications are made to adapt to the morphology of the packed EP particles. Fifthly, the behaviour of the foams under quasi-static compressive loading, together with the consequences of different parameters (i.e. particle size and foam density) on the response of the foams, are investigated. Finally, the results of elastic wave tests on EP/epoxy foams are presented and a comparison with those obtained by the quasi-static tests is made.

Chapter 5 discusses the significance of the results in a broad context, including an evaluation of the advantages and disadvantages of the manufacturing method used in this study and possible alternative methods. Additional factors are discussed, such as: i) the

Young’s modulus of packed EP particle beds measured using the different methods; ii) the interior structure of EP/epoxy foams based on the experimental results; iii) the compressive behaviour and properties of EP/epoxy foams; and iv) the damage mechanisms during compressive tests. Moreover, a comparison is made with other commercially available foams, on the basis of their compressive properties, compressive behaviour and damage mechanisms.

Chapter 6 presents conclusions which may be drawn from the study. It also provides several suggestions for future work, which may be taken as a guide by students and researchers entering this area or wishing to pursue improved EP/epoxy foam manufacture and/or its properties.

2 Chapter Two: Literature Review

Introduction

This chapter is divided into four parts. The first part introduces the perlite material and provides comprehensive information about the process of expansion, its physical and chemical properties, as well as current commercial uses of perlite in three areas: construction, horticulture and industry. In the second part of this chapter, a review is conducted on previously developed polymer matrix foams and particulate composites which contained naturally occurring fillers, including perlite particles. The final two parts provide the motivation and main objectives of the current project based on gaps in the literature presented in the first and second parts.

The characteristics, manufacturing processes and applications of

Perlite

2.2.1 Introduction to perlite

Perlite is a glassy volcanic rock of silicic or rhyolithic composition, typically formed by the hydration of obsidian. Perlite occurs naturally in the form of block type-lava domes, restricted in area, which are formed by the extrusion of highly viscous magmas. Perlite deposits are restricted to Tertiary age, or younger, deposits of rhyolithic composition.

Rhyolithic glasses are unstable and devitrify1 with age into microcrystalline aggregates of quartz and feldspar, and transform to zeolites and other aluminosilicate minerals.

Therefore, the preservation of perlite is rarely found in rocks older than Tertiary age [17].

The name perlite is a derivation from the German word perlstein and is originally given to “certain glassy rocks (hyaloliparites, hyalo-rhyolites) characterized with numerous concentric cracks”, the ‘perl’, referring either to the resemblance of the broken-out fragments to pearls or to the pearly lustre of the surfaces [18]. Petrologically, the term

‘perlite’ refers to volcanic glasses in which cooling strain resulted in a concentric or onion structure of fracturing which may be visible to the naked eye or may only be observed under microscopes. This structure of fracturing is also known as perlitic [19].

Perlite is distinguished from other natural water-bearing glasses (e.g. obsidian, pumice and pitchstone) by the total water content of 2 to 5 wt% held within the glass structure, by the presence of a pearly lustre and by its onion skin perlitic fractures. The term,

1. The process in which a glass (noncrystalline or vitreous solid) transforms to a crystalline solid.

however, should be expanded to include the less dense textures of perlite which are related to the classical variety but rarely, or only microscopically, exhibit perlitic fractures, and which might not exhibit a pearly lustre. Textures of perlite may be commonly found in deposits ranging from the dense and classically fractured variety to vesiculated and pumiceous varieties which may not exhibit a pearly lustre or megascopic perlitic fracture

[20]. Commercially, the term ‘perlite’ has been applied to any naturally glass of igneous origin that will expand or ‘pop’ when heated quickly, forming a light-weight frothy material. However, this property is also present in some glassy rocks that do not have perlitic structure, and in some that are not primary in origin but are alteration products of rhyolite or obsidian [21].

Upon heating within its softening range of 760°C to 1100°C [10], the combined water in perlite grains is converted to steam and the perlite expands 4 - 20 times its original volume. Hence, it is called ‘expanded perlite’ (EP). Figure 2.1 illustrates the unexpanded and expanded forms of perlite.

(a) (b)

Figure 2.1. (a) Unexpanded perlite (b) Expanded perlite. Both types were supplied by Ausperl.

Expanded perlite has low thermal conductivity, high sound absorption, high resistance to heat, chemical inertness, physical resilience and water retention ability. More than half of the perlite produced is consumed in the construction industry as aggregate in insulation boards, acoustical ceiling tiles, plaster and concrete [17]. It is also used in horticulture and other applications like filtration, e.g. in the pharmaceutical and food industries, and as fillers in various processes and materials [22]. There have been many studies about the use of perlite in particular industrial and construction applications (e.g. [23], [24], and

[25]). However, few articles have been published which review perlite’s properties and its applications. Singh [26] conducted a review on the multifarious uses of perlite as a construction material. Barker and Santini [27] provided an overview of the world perlite deposits and activities. Therefore, this section of the chapter aims to provide a comprehensive overview on the characteristics and properties of perlite, as well as its applications. Hopefully, the information provided has the potential to rapidly fill the void in our understanding of perlite.

2.2.2 Expansion process

In general, the perlite expansion process involves rapid heating in a kiln to a softening point, and then rapidly cooling. The size to which the rock is crushed before heating depends on the composition of the perlite (e.g. water content), furnace design and the end- use for which the expanded perlite is required. Generally, perlite particles that pass 8- mesh (2.380 mm) and are retained on 30-mesh (0.595 mm) are suitable to be used as concrete aggregate; perlite particles that pass 14-mesh (1.410 mm) and are retained on

50-mesh (0.297 mm) are suitable to be used as plaster aggregate; and fine particles that pass 30-mesh (0.595 mm) are used for the lightest types of expanded product [28]. A

typical kiln feed contains perlite grains with diameters from 0.254 to 2.54 mm. It is customary to eliminate grains smaller than 25 µm, as they tend to produce very fine dust particles in the expanded product [21].

At the stage of heating perlite to the softening point, the combined water is vaporised, producing pressure that causes expansion of the perlite to 4 - 20 times its original volume leading to a significant reduction of its bulk density [29]. The heating may last from one to three minutes, at temperatures varying between 760°C and 1100°C. It can be carried out in either a rotary horizontal expander or a stationary vertical expander as both operate on the same principle. Figures 2.2 and 2.3 show schematics of horizontal and vertical expanders, respectively. Detailed descriptions of these two types of expander can be found in [30].

The heating rate for the expansion process may be optimised. If the perlite granules are heated too slowly, the combined water is removed through pores without much of a

‘popping effect’, leaving a slightly porous but relatively dense product. However, if the rate of heating is too high, the expansion of the water may be so violent that the perlite particles shatter and form numerous fines [31]. The optimum temperature at which perlite expansion occurs may depend on its chemical composition. Variations in the composition of the glass affect the softening point, the type and degree of expansion, the size of the bubbles and the wall thickness between them, as well as the porosity of the product [21].

Also, water content in perlite is another factor affecting the optimisation. It has been found that perlite containing excessive combined water is likely to shatter upon expansion, whereas perlite containing much less water is likely to produce higher density products [32]. A typical value of 3.2% to 3.7% combined water in perlite seems to work best in most conditions [27]. King et al. [33] reported that the water in perlite above 1.2%

is loosely held, and therefore is easily removable. However, as dehydration proceeds, the residual water (below 0.5%) is increasingly more firmly held, which is the effective portion in producing the expansion of perlite upon heating. Some form of pre-heating is generally used to reduce the effect of the initial thermal shock, and thus to reduce the amount of shattered material. It also drives off some of the loosely held water, brings the larger particles closer to their softening point, and thus reduces the time spent in the kiln in order to improve the fuel efficiency of the expander [34]. It also can lower the density of the final product, hence improve the insulating ability of the product. For coarse grades, in particular, preheating is important as these grades offer less surface area for heat transfer in a given amount of time, while intermediate and fine grades are not usually preheated [30].

Although it is possible to achieve some flexibility in the properties of the finished product properties through adjustment of furnace conditions and through preheating, it should be noted that all particles do not expand alike [27]. The characteristics of the final product, such as size, strength and density, depend on the initial granule size, granule water content and granule composition, together with the design and operation of the kiln and the heating rate [31]. When expanded perlite is cooled down, it is air classified to separate any unexpanded particles and fines. Depending on the intended end-use, the expanded perlite may be further size classified, surface treated or milled. For example, some expanded perlite is milled down to -100 mesh (0.15 mm) for use as a filter aid, especially in rotary pre-coat filtration [12]. Micronised perlite particles up to 2 μm can also be produced by milling for anti-block filler for polymeric film or as a reinforcing filler for polymers [35].

Figure 2.2. Horizontal expander and handling system [30].

Figure 2.3. Vertical expander and handling system [30].

2.2.3 The physical properties of perlite

Perlite textures may vary from classical (onion skin-like) to granular and pumiceous [27].

Classical, or onion skin perlite is the densest of the perlite types and is characterised by well-developed concentric fractures, a pearly-to-resinous lustre and a grey to bluish black colour. Granular perlite has a sugary or saccharoidal appearance, is microvesicular2 and highly fractured, with colours ranging from white to grey. Granular perlite is lighter than classical perlite, but denser than pumiceous perlite. Pumiceous perlite is extremely lightweight, white to light grey, frothy and commonly friable. All perlite types are mined, however the most common commercial one is in granular form [36]. It was found that the grain morphology affects the expansion ratio. Pumiceous perlite has a higher expansion ratio than granular perlite, but a lower expansion ratio than classical (onion skin-like) perlite. The granular perlite has a well distributed microvesicular texture that allows water vapour to escape easily, and thus only a small degree of perlite expansion occurs, considerably smaller than that of pumiceous and classical perlites. However, in classical perlite, the water vapour has difficulty in escaping through the successive onion skin-like layers. Therefore, the sudden vaporisation results in increasing pressure, thus blowing up the grain until it explodes and greatly expanding the grain [37]. The light-weight porous material with a cellular interior structure that perlite transforms into upon heating above

760°C, is shown in Figure 2.4.

2. Vesicular texture refers to the presence of small cavities called vesicles, which were originally gas bubbles in the liquid magma. This gas was initially dissolved in the magma but has come out of solution because of the pressure decrease during eruption or as the magma rose before eruption. The texture is often found in extrusive aphanitic, or glassy, igneous rock [Claudia Owen et al., 2010].

Figure 2.4. Cellular structure formed internally in expanded perlite particles.

Unexpanded ("raw") perlite has a bulk density ranging from 1.04 to 1.2 g/cm3, while expanded perlite typically has a bulk density of about 0.032 - 0.4 g/cm3. However, the true density of perlite does not change as significantly as expected [38]. Expanded perlite ranges from a fluffy highly porous (85 - 95 vol% [11, 39]) to glazed glassy particles having a low porosity [19]. Porosity3 provides expanded perlite with a volumetric and surface absorption capability. The porosity is an advantageous feature for drainage, aeration and retaining moisture and fertilizers in horticultural uses and landscaping [40].

However, the water absorption in thermal insulation applications is not desirable as the heat conductivity increases when the pores are filled with water [23]. The expansion process also creates a brilliant white colour in perlite, which is due to the reflectivity of the cellular structure. The brilliant white colour is also beneficial in light coloured, visible

3 Porosity is determined as the average ratio between the volume of pores and the total volume of the perlite grains [Topçu Işikdağ, 2006].

surface coatings. Colour is also of concern in filler applications, especially when the colour of the end product is important [27]. The typical physical properties of expanded perlite are given in Table 2.1.

Table 2.1. Typical physical properties of expanded perlite [23, 26, 39].

Typical Physical Properties

Colour White

GE brightness % 78

Refractive Index 1.5

Free Moisture, Maximum 0.5%

pH (of water slurry) 6.5 - 8.0

Specific Gravity 2.2 - 2.4

Wet density (kg/m3) 103

Bulk Density (Loose) 0.032 - 0.400 g/cm3

Mesh Size Available 4 - 8 mesh and finer

Softening Point 871 - 1093°C

Fusion Point 1260 - 1343°C

Unit weight 2.2 - 2.4 g/cm3

Specific Heat 0.20 kcal/kg°C

Thermal Conductivity at 75°F (24°C) 0.04 - 0.06 W/m·K

Solubility - Soluble in hot concentrated alkali and HF - Moderately soluble (<10%) in 1N NaOH - Slightly soluble (<3%) in mineral acids (1N) - Very slightly soluble (<1%) in water or weak acids

2.2.4 Chemical composition

Perlite is chemically inert, having an approximate pH of 7, and is mainly composed of silica, alumina and lesser amounts of several metal oxides (sodium, potassium, iron, calcium and magnesium). Table 2.2 gives the composition of perlite ores from different countries. As can be seen, although perlite from different origins exhibits considerable variation in composition, it is characterised by a high silica content (≥ 65%) and alumina content (11 - 18%) with about 7 - 8% of alkaline content [41]. Burriesci et al. [41] found that there are no traces of carbonate in perlite ore based on thermogravimetric analysis

[41] and another alumina silicate, tuff [42], and comparison between their weight loss curves. Considering the linearity and flatness of the weight loss curve in the range 700 -

900°C, a temperature range at which the decomposition of carbonate occurs, they considered that no carbonate should exist in perlite as, if it did, its presence should have shown a reduction in weight as was shown for tuff. Although this assumption is valid, referring to the weight loss curve for perlite in [41], the flatness is not well established.

Only three points in this range were used for both curves which does not seem satisfactory as every line with three points appears linear.

In addition to the above-mentioned compounds, trace amounts of some other elements were detected in perlite ores, which are usually less than 2% by weight. Typically, these elements include Arsenic, Boron, Beryllium, Barium, Chlorine, Chromium, Copper,

Gallium, Lead, Lanthanum, Manganese, Molybdenum, Nickel, Niobium, Neodymium,

Sulphur, Titanium, Thorium, Vanadium, Yttrium, Zirconium and Zinc [28-32].

Furthermore, the presence of trace amounts of rare earth elements (La, Ce, Pr, Nd, Sm,

Eu, Gd, Dy, Ho, Er, Yb, Lu) were detected in the analysis of the chemical composition

of perlite deposits from Trachilas (Greece) [43], Eastern Rhodope (Bulgaria) [44],

Nathrop (Colorado) and No Agua (New Mexico) [45].

Table 2.2.Chemical composition of perlite (Percent) [22].

Components New Mexico Greece China Turkey Iran Thailand

[29] [36] [37] [38] [39] [40]

SiO2 74.10 76.10 76.89 68.40 72.32 75.20

Al2O3 13.30 12.16 10.51 15.11 12.62 12.75

Na2O 3.20 3.62 0.80 1.62 2.96 2.85

K2O 4.60 3.03 8.25 4.05 5.02 5.12

CaO 0.60 1.21 0.12 1.72 0.66 0.38

Fe2O3 0.50 1.19 2.48 2.76 0.67 0.99

MgO 0.10 0.27 0.06 0.42 0.21 <0.10

TiO2 0.05 0.14 0.07 n.d. n.d. 0.14

MnO n.d. 0.05 0.04 n.d. 0.66 0.05

P2O5 n.d. 0.03 0.03 n.d. 0.13 <0.05

SO3 0.10 n.d. n.d. n.d. n.d. n.d.

H2O n.d. n.d. 0.31 4.92 n.d. 0.43

LOIa n.d. 2.19 0.64 n.d. 3.75 1.50

a. LOI, loss of ignition.

The chemical composition and physio-chemical properties of perlite (e.g. index of refraction, specific gravity, etc.) are comparable to those of obsidian and pumice.

However, perlite has a higher water content (generally about 3 - 4%) [41]. Water has an important role in the expansion process, not only by causing expansion of the grain during vaporisation, but also by reducing the viscosity of the grain [37]. It is reported that water 20

in perlite is in two forms, viz. molecularly dissolved water and hydroxyl groups. The ratio of these two species of water is variable in perlite [17]. King et al. [33] made an analogy between the molal entropy increase between 0 to 298 K in perlite and a number of substances containing water, either as water of crystallisation (e.g. in MgCl2.H2O) or as water as hydroxyl groups (e.g. in Mg(OH)2). The molal entropy increase in perlite was comparable to those compounds containing water of crystallisation. They did not conclude that the water in perlite is held similarly to the water of crystallisation, however, as they concluded that it is impossible that the large portion of the water in perlite is bound as hydroxyl groups. Later, Stolper [46] found that the concentration of hydroxyl groups increases rapidly with increasing total water content at low total water content (<2 wt%), but its concentration levels off or even decreases at a total water content higher than 3% by weight. On the other hand, the concentration of molecular water increases slowly at low total water content and more rapidly at a total water content higher than 3% by weight. Moreover, it was found that in water-bearing glasses having total water content of 4% by weight, the dissolved water is equally divided between the two species of water but in glasses with total water content of >4% by weight, more water is dissolved as molecular water. Saisuttichai and Manning [47] investigated the perlite ore from northeast of Lopburi (Thailand) and conducted Fourier transform infra-red spectroscopy on samples containing 3.40 wt% water, which showed higher molecular water than hydroxyl groups, which appeared to be consistent with Stolper’s findings. Roulia et al. [37] also studied perlite grains containing 3.48 wt% water from Trachilas (Greece) and the results showed consistency with Stolper’s findings as well. Therefore, the portion of hydroxyl and molecular groups in perlite ores vary depending on the total water content, and it is

not correct to generally suppose a larger portion of molecular water than hydroxyl groups without considering the total water content as some sources do (e.g. [21]).

Studies on the nature of the perlitic network have shown that perlite is mostly amorphous in nature, with a small amount of crystalline inclusions (e.g. quartz, feldspar and biotite).

Herskovitch and Lin [48] studied crude perlite from Milos Island4 and reported it to have

89.4% by volume of the amorphous phase and 10.6% by volume of the crystalline phases

(feldspars, biotite, quartz, magnetite and chlorite). The presence of crystals in crude perlite is correlated to its origin, as represented in Table 2.3. Crystalline silica (e.g. quartz, cristobalite and tridymite), though it is present in small amounts, is of concern during production and marketing. Crystalline silica is classified by the International Agency for

Research on Cancer (IARC) as a class 2A (probabale carcinogen) in humans when it is inhaled but not when it is ingested or contacted. In most commercial perlite deposits, however, the amount of crystalline silica is very low (<1-3 wt%). This can be even further lowered during processing and use, e.g. dilution in end product [49]. Though crude perlite comprises both amorphous and crystalline phases, the expanded perlite has been found to be clearly amorphous. X-ray diffraction analysis conducted by Barth-Wirsching et al. [50] and Chakir et al, [51] indicated that expanded perlite is amorphous. Roulia et al. [37] also found that the expansion of perlite, affected by rapid thermal treatment, only takes place in the amorphous phase of raw perlite and that crystallites do not expand and are rejected as unexpanded waste product. Chemical analysis of EP has shown a similar composition to crude perlite, but with a lower amount of combined water. It was found that the

4 Perlite was supplied by Habonim Industries, Moshav Habonim.

expansion of perlite results in a remarkable reduction in hydroxyl group content with a smaller reduction in molecular water [47].

Table 2.3. Mineral phases detected in perlites of different origins.

Origin Minerals

Socorro, New Mexico[29] feldspar, cristobalite, zeolites, fluoride

Searchlight, Nevada [29] feldspar, quartz, biotite, magnetite, limonite, zeolites

Korea [43] plagioclase, biotite, opaque minerals, traces of hornblende,

apatite, zircon and sanidine

Kawalan, Yemen [44] k-feldspar, plagioclase, pyroxenes, chlorite, quartz, serpentine

Sardinia, Italy [26] α-quartz, mica, feldspatiods

Milos Island, Greece [23] feldspar, quartz, biotite

Lopburi, Thailand [32] plagioclase and alkali feldspar, biotite, opaque minerals

In addition, it was found that, upon expansion, fluorine may be lost from perlite, presumably as HF, and it becomes increasingly available to water. The increase in the availability of fluorine to water may limit the use of such perlite in horticulture applications [47] as the detrimental effects of fluorine to plants are well-known [52]. It was also found that, upon expansion, the availability of Ca (Calcium) and Mg

(Magnesium) is reduced, but that the extractable K (Potassium) is increased (especially in highly potassic perlitic rhyolites). However, the increase in the water solubility of K on expansion can be useful in horticultural applications (e.g. as a possible slow-release source of potash) [47].

2.2.5 Applications

The low density, relatively low price and good insulating properties of perlite have led to the development of many commercial applications. Figure 2.5 illustrates the proportionate use of expanded perlite computed by the U.S. Department of the Interior

U.S. Geological Survey [92]. These applications can be classified into three general categories: construction applications, horticultural applications and industrial applications.

Figure 2.5. US expanded perlite use by application.

1. Includes acoustic ceiling panels, pipe insulation, roof insulation board, and unspecified formed

products.

2. Includes absorbents, laundries, paint texturisers, and other miscellaneous uses.

3. Estimated and reported data with specific use unknown

2.2.5.1 Construction applications

The low density, high heat insulating value, outstanding fire resistance and good sound absorbing properties of expanded perlite give it a number of construction applications mainly as formed products, concrete aggregate, masonry and cavity-fill insulation, and plaster aggregate. Construction uses of perlite account for about 60% - 70% of the total consumption in major markets. In the United States, the manufacture of formed products accounts for about 53% of total perlite use (see Figure 2.5 ). However, such a large demand for the use of perlite in formed products might not be seen in Europe due to differences in construction methods. In the US, most homes are constructed on a timber frame with extensive use of gypsum and insulating boards to form internal surfaces. There is much less use of brick or other masonry products for external walls, in comparison with

Europe. Therefore, there is less use of light-weight insulating plasters, mortars and loose fill insulation in the US, compared to Europe, which results in a higher percentage of perlite use for formed products in the US [53]. In the following sections, the different construction applications in which perlite is currently utilised, or is substituted for a traditional material, are explained.

Gypsum perlite-based plaster

Perlite, instead of sand, can be mixed with gypsum and water for plastering on a lath in order to provide a resilient wall or ceiling capable of withstanding stresses and thermal changes. Indeed, the manufacturing of gypsum-perlite and prefabricated gypsum boards has become one of the major uses of perlite. The plasters made of expanded perlite are characterised by their light-weight, ease of application and savings in structural steel.

They are resistant to cracking under stress, highly fire resistant and have excellent sound

absorbing properties [21]. It is claimed that gypsum-plaster made of expanded perlite aggregate weighs about one third of that conventionally made with sand, and has six times the thermal insulating value [54]. Perlite can also enhance the workability of plasters and mortars and can be used to create a texture on the finished surfaces [53].

Concrete

Concrete is a composite material and since around 75% of its volume is occupied by aggregate, the performance of concrete is greatly affected by the properties of the aggregate. The use of light-weight and porous aggregate as a constituent of concrete enables the production of light-weight concretes [55]. Light-weight concretes are economically beneficial, by reducing heat conductivity and unit weight. Reducing unit weight is especially beneficial in reducing the damage by earthquakes in high buildings

[56]. The low density of EP particles make them suitable for the production of light- weight concretes [57, 58]. At the same time, EP particles greatly improve thermal insulation, reduce noise transmission, and they are rot, vermin and termite resistant [59].

The high water absorption capability of EP particles can provide water for the hydration of cement in the later stages of curing, which is especially advantageous in concrete with low water/cement ratios [60]. EP particles can also have pozzolanic activity5 and can be used as a mineral admixture when finely ground [61]. The properties of light-weight

5 A pozzolan is a siliceous or siliceous and aluminous material which itself has little or no cement-like value but in finely divided form and in the presence of water will react chemically with calcium hydroxide (slaked lime) at ordinary temperatures and form compounds exhibiting cement-like properties [61,62].

concrete, however, are usually different from normal concretes. Sengul et al. [62] made light-weight concrete by partially replacing the natural aggregate (e.g. sand) with EP particles, from 0% to100% with 20% increments. The replacement of natural sand by EP particles resulted in a reduction in the unit weights by 8.4 - 80.8 % and a reduction in the compressive strength of the concrete by 40 - 99.7% due to the lower strength of the perlite.

Topçu and Işikdağ [56] also reported a reduction in compressive and splitting tensile strength of concrete by about 54% and 47%, respectively, for the replacement of the natural sand by 60% EP particles. The accompanying air entrainment was also effective in lowering the strength of the concretes. Not only the compressive strength, but also the modulus of elasticity were adversely affected. For the replacement of natural sand by EP in the range 20 - 60%, Sengul et al. [62] reported a reduction in the modulus of elasticity by 34 - 83%. This is due to the fact that the modulus of elasticity of concrete is a function of the modulus of elasticity of the constituents (i.e. hardened cement paste and concrete).

Concrete made with perlite aggregate may not be as strong as that made with pumice or heavier materials, however it may be used where compressive strength above about 13.79

MPa is not required [21]. On the other hand, increasing the expanded perlite ratio improves the thermal insulation of concrete by increasing the total porosity. Porosity is one of the factors affecting the thermal conductivity of concrete. Introducing enclosed pores reduces the thermal conductivity due to the low thermal conductivity of air [62].

These materials are beneficial in insulating spaces around heating, steam or coolant pipes; providing insulating bases for ovens, furnaces; cold storage tanks; and wherever light structural decks are desired [53].

Loose fill insulation

Another important construction application of perlite is as loose fill insulation. Perlite’s outstanding low density, thermal insulation and fire resistance allow it to be widely used as loose fill insulation in cavity walls and for filling cores, crevices, mortar areas and the air holes of masonry blocks. There are several other materials that can alternatively be used, such as fibre glass; expanded polystyrene foam, beads and panels; and vermiculite.

However, the valuable features of being non-settling and the free flowing behaviour of perlite make it more preferred [53]. Moreover, the use of perlite as loose fill in masonry construction has been proven to reduce the transmission of heat by as much as 50 - 70% when filling the cavities of concrete blocks. As already mentioned, there is a relationship between thermal conduction and density at various mean temperatures. Based upon the reported data, the density of 32 - 173 kg/m3 is recommended for loose fill insulation [63].

However, when using perlite as loose fill insulation, its ability to absorb moisture should be taken into account. Perlite moisture absorption can adversely affect the insulation value of expanded perlite, or increase settling problems within a conventional wall construction where perlite is used. Nevertheless, this problem has been alleviated by coating expanded perlite particles or adding a moisture repellent to the mix before its application into the wall. Coating the perlite particles with sodium silicate, for example, can improve the moisture resistance by closing the open pores of perlite and thus reducing the water retaining property [64]. Alternatively, it can be mixed with silicone (less than 5% by weight), a natural resin or Bitumen [65, 66]. However, silicon polymers are expensive and there are hazards associated with their use. Instead, the annealing of expanded perlite was found to be effective in reducing perlite’s water absorption [67]. In the annealing process, expaneded perlite is heated to a temperature sufficient to soften the perlite

surface (usually ranging from 426 to 537 °C [67]) and to heal many of the surface cracks and fissures. Sealing the surface fissures results in a reduction of water absorption.

Ceiling tiles

The use of ceiling tiles has had tremendous growth over the last few decades owing to the advantages it offers, like sound absorption, fire resistance, good thermal insulation, light reflectance and structural support. The increase in the use of ceiling tile systems has resulted in an increase in the use of perlite as a component of many kinds of ceiling tiles.

Standard ceiling tiles are typically made from a combination of mineral wool or slag wool, fibreglass, binders (e.g. starch), and sometimes inorganic fillers (e.g. mica, wollastonite, silica, calcium carbonate). Expanded perlite is added to the mixture to enhance the acoustic insulation, thermal insulation and fire resistance properties of the tile. Depending on the desired properties of the end product, the proportion of expanded perlite can vary from 0% to75% of the total mixture by weight. Moreover, perlite can be used to create different textures to the visible surface of the tile [53].

Starch is a well-known binder in ceiling perlitic tiles. The use of starch has been found useful for acoustic or sound insulation as these tiles do not bleed through or discolour the material if painted. Baig [68] used starch as a binder in making acoustic perlitic tiles and produced tiles with acceptable properties, improved drainage time and lower manufacturing costs. Denning et al. [69] also used starch in manufacturing insulation boards and reported an unexpected water repellence property. The product was soaked for three weeks and it was found that material had just slightly softened. It was also suggested that the addition of a water-repellent substance to achieve greater water repellence is possible. However, the addition of water repellent substances to acoustical boards is limited to those that would not discolour the board. Examples of sound

insulation boards made using starch are given in Table 2.4. However, the problem with the use of starch is that under certain environmental conditions, like increased temperature and humidity, the board loses its dimensional stability. To deal with this problem, latex binders were found to be useful. Kesky [70] and Deporter et al. [71] used latex binders in manufacturing perlitic ceiling tiles and reported perlite insulation boards made with latex binder show a higher MOR (Modulus of Rupture), higher breaking load, lower water absorption and better dimensional stability than perlitic ceiling tiles made with starch.

Examples of latex binders, having glass transition temperature ranging from about 30° C to about 110° C, and useful in ceiling tiles include polyvinyl acetate, vinyl acetate/acrylic emulsion, vinylidene chloride, polyvinyl chloride, styrene/acrylic copolymer and carboxylated styrene/butadiene [72].

Table 2.4. Examples of perlitic sound insulation boards in which starch is used as binder [69].

Example 1# 2# 3# 4#

Expanded perlite...... percent 67.5 62.5 49.6 60.0

Paper pulp fibre...... percent 22.5 27.5 28.9 30.0

Starch...... percent 10.0 10.0 20.0 10.0

Modulus of rupture ……kPa 357.84 488.84 409.55 536.41

Under floor insulation

Water repellent, dust-suppressed perlite produced in accordance with ASTM: C 549.81 is used for under floor insulation. Perlite under floor insulation can be employed under floating concrete floors, asphalt floors and floating board floors (thickness 6 - 10 cm). It is especially effective in the reduction of sound transmission in construction components,

from floor to floor, from floor to walls, from footsteps and from under floor piping systems. The neutral pH of perlite also prevents the development of corrosion in piping and electrical wiring that may be installed in the under floor area [63].

Fire resistant boards

Perlite’s outstanding properties of light weight and thermal insulation are used for producing light-weight insulation panels for fire protection where substantial weight saving is important, especially in the marine, aviation/aerospace and land/rail transport industries. For example, light-weight insulating materials that have high thermal insulation and fire resistance are suitable for components of vehicular interiors such as cabins and cargo holds, partitions and fire doors, or for transporting combustible materials

[73]. The thermal insulation boards discussed in [74] and [73] are representatives of these types of light-weight perlite-based insulation boards.

2.2.5.2 Horticultural applications

The chemical resistance and porosity of perlite are important features in horticulture applications when soils are wet for prolonged periods or where drainage, aeration and optimum moisture retention are required. The high brightness of finely ground perlite applied to the surfaces of seed blocks reflects light to the underneath of seedlings and helps with rapid and sturdy growth [27]. Perlite can be used as a soil amendment or alone as a medium for hydroponics. Studies have shown that outstanding yields can be achieved when perlite is used as a soil-less growing media in hydroponic systems. When used as an amendment, perlite’s high permeability, and low water retention can be beneficial and helps to prevent soil compaction. Other features of perlite advantageous for horticultural

applications are its neutral pH and the fact that it is sterile and weed-free. Perlite is also a good carrier for fertilizer, herbicides and pesticides and for pelletising seed [75].

2.2.5.3 Industrial applications

Perlite has a broad range of applications in industry. These include the use of perlite as fillers, filter aids, and in cryogenic and high temperature applications. Perlite is also used as silica-alumina source for the synthesis of zeolites. These applications are briefly described below.

Cryogenic applications

Expanded perlite particles contain countless glass-sealed particles, which accounts for its excellent insulating properties. Expanded perlite is a very effective insulator at temperatures below -100 °C and is widely used in insulated storage tanks containing liquid hydrogen, helium, oxygen and other gases [76]. Liquefied gas storage tanks (Figure

2.6) are spherical, double-walled vessels in which the space between the inner and outer wall is evacuated and filled with expanded perlite as the thermal conductivity of expanded perlite under evacuated conditions is many times lower than under non-evacuated conditions [53].

Figure 2.6. Spherical gas tank farm in a petroleum refinery [116]. 32

Perlite is not as hygroscopic as other siliceous powders and thus it is easier to prepare for vacuum applications. The low density and correspondingly high porosity (0.85 ≤ ѱ ≤

0.95) of expanded perlite are also two characteristic properties which make the material suitable for vacuum insulation [77]. Heat transfer through an evacuated porous material like perlite involves the simultaneous operation of the three transport mechanisms of thermal radiation, solid conduction and gas conduction. The radiant heat that passes through an EP particle originates at the hot boundary wall and from the neighbouring particles. This radiant energy is of a diffuse type, and, as it moves through the particle, it is scattered and partially absorbed. The absorbed radiation heats the particle. However, the scattering effect due to the symmetrical shape of typical vessels (e.g. concentric spheres or cylinders) is not of great importance in the thermal radiation problem of vessels filled with insulating porous particles [67]. To reduce the heating effect of radiation, the addition of opacifiers has been found to be effective. Alternatively, metallic powders can be added to the insulating particles to scatter and absorb radiation. Kropschot and Burgess

[78] found that the addition of 60 wt% aluminium powders (600 µm) can reduce thermal conductivity of perlite with a density of 64 kg/m3 by 50%.

Thermal energy is also transferred by conduction through the solid fraction of the EP particles. However, the solid heat conductivity of a porous insulation material is usually much smaller than the thermal conductivity of the pure solid fraction as the morphology of the material influences the heat transport [79]. In addition, the particle size was found to affect the solid conductivity of evacuated perlite beds. When the particle size decreases at a constant density, thermal conductivity decreases. The contact resistance increases with decreasing particle size because the greater strength and curvature of small particles

decreases the contact area and there are large numbers of contacts per unit length. In addition, at low temperatures, phonons carrying most of the heat energy have a long wave length with a long mean free path. If the particles become smaller than the mean free path of phonons, the scattering and collisions of phonons at the walls of particles becomes important and reduces the rate of heat transfer [80]. This effect is strengthened by the internal structure of perlite particles which are cellular. Therefore, reduction of the particle size increases the resistance to the flow of thermal energy inside each particle.

The morphology of perlite particles is also effective in the significant minimisation of gas convection. Convection is suppressed inside the particle pores, as the emerging buoyancy forces do not exceed friction [81]. Though gas convection is almost eliminated, depending on the level of vacuum there is some residual gas contributing to heat transfer by gaseous conduction. The small particle size of the powder limits the gaseous heat transfer in evacuated powders to free molecular gas conduction as the mean free path of the gas molecules, which describes the average distance a gas molecule travels between consecutive collisions, is large relative to the distance between surfaces of the adjacent particles. Aside from this, the reduction of pressure in high vacuum increases the mean free path of the gas molecules. In such conditions, gas molecules rarely collide with each other, thus the molecule to molecule conduction is eliminated. The energy is exchanged between the surface and the colliding molecules as the gas molecules travel unhindered between the confining walls of the adjacent solid particles. Therefore, the particle structure imposes an upper limit on the mean-free path within the insulation [82].

In addition to perlite’s low thermal conductivity, its free-flowing nature, the high strength/compaction resistance of the particles, the absence of shrinkage or slumping and the ease of handling and installing are features that make expanded perlite ideal for

cryogenic applications. Perlite is also very effective in insulating non-evacuated low temperature storage vessels for oxygen, nitrogen, liquefied natural gas, and similar products. The effective insulating properties of evacuated perlite are also utilised in some domestic refrigerators, in which evacuated plastic bags filled with perlite are used for insulation [83]. Other applications include the insulation of industrial cold boxes, test or processing equipment, and shipping containers and in food processing [53].

Fillers

One of the main industrial applications of expanded perlite is as fillers, in which its high surface area, permeability, low density and inertness and reinforcing characteristics can be very beneficial. Fillers are organic or inorganic particles added to materials (e.g. plastics, composite materials and concrete) to reduce the consumption of more expensive binder materials, and thus to improve the economics of the end product, in which case they are also called extenders. They are also used to improve some properties of the mixture by developing a beneficial chemical interaction with the host material; these are called functional fillers [84]. It is useful to distinguish between the three classes of perlite used in filler applications. One is produced by further milling and classifying expanded perlite to produce broken particles with jagged interlocking structures. These are, for example, used as insulating fillers in the manufacture of texture coatings, as anti-block6

6 Anti-block products are additives incorporated in plastic films to decrease the adhesion or blocking between touching layers of plastic films during fabrication, storage or use. This can be accomplished by slightly roughening the film surface by surface treatment with wax/polymers or by the inclusion of anti- block filler products into the plastic films [21].

fillers in plastic films, and as reinforcement fillers in polymers [85]. Another class of perlite used in filler applications is perlite hollow glass microspheres. Perlite microspheres consist of one or a few inner cells, in contrast with the large number of cells found in the larger, standardly produced expanded perlite particles. Perlite hollow glass microspheres are produced under stringent quality control conditions utilising special technologies. The feedstock for production of microspheres is crude perlite. Upon expansion, glassy, spherical-shaped hollow particles are produced, as shown in Figure

2.7. Microspheres generally have a diameter smaller than 140 microns, with the average between 30 and 70 microns. Depending on the desired properties, the microspheres can be further surface treated with either silicone or silane, which can increase the hydrophobicity (water repellency) of the microspheres. When perlite microspheres are used as fillers, a number of important characteristics are imparted into the end-product.

These include improved crack resistance, higher impact, nailing and stapling resistance, enhanced machinability and sanding features, finer texture with an increased workability, reduced weight and shrinkage, and a shortened drying time.

Examples of applications in which perlite microspheres as fillers are desired include in textured and acoustical coating mixes, adhesives and sealants, wall-patching compounds, thermo-set castings, syntactic foam, sheet moulding (SMC) and bulk moulding compounds (BMC), rotational moulding, stucco, fibre-reinforced product (FRP), spray and hand lay-up, specialty coatings and block filler paints [27]. Lastly, the third class is those which might be called basic or general light-weight perlite fillers, where traditional expanded perlite with sizes ranging from 500 to 2000 microns is used as fillers in products and mixes.

Figure 2.7. SEM image showing EP microspheres consisting of one or more microcellular

bubbles [27].

Filter aid

Perlite is chemically inert in many environments owing to the high silica content, usually greater than 70%, and are adsorptive, which make them excellent filter aids [9]. Filter aids are finely divided solids, chemically inert and light in weight. They help to control flow and remove finely distributed colloidal suspensoids from liquids. They can be used in two different ways, ‘precoating’ and ‘body feeding’. In the ‘precoating’ case, filter aids are applied as a thin layer over the filter before the suspension is filtered. This will enhance clarity and filter rate in the filtration process, and prevent gelatinous-type solids from clogging the filter medium, which can cause its resistance to become excessive.

Furthermore, it facilitates the removal of filter cake at the end of the filtration cycle. The second application method referred to as ‘body feeding’ involves the incorporation of a certain amount of filter aid to the suspension before filtration. The addition of filter aids increases the porosity of the slug, reduces the loading of undesirable particulate at the filter medium, reduces the resistance of the cake during filtering, and hence maintains the

desired flow rate. Depending upon the specific separation involved, perlite products may be used in precoating, body feeding, or both [31, 35].

The production of perlite filter aids involves careful selection of the ore, precise monitoring of crushing and screening, expansion, light milling to break the closed particles, followed by further screening and classification. This process produces fragments of perlite particles with a precisely controlled particle size distribution to give the desired clarity and flow rate in different applications. In most applications, perlite filter aids are used to filter solid particles having one micron or larger size [86].

Perlite competes with other filter media like diatomite, diatomaceous earth and cellulose.

However, it has found extensive niches in many applications due to the advantages it offers, like rapid filtration of viscous liquids, particle size distribution, high surface area, high porosity, inertness in most mineral and organic acids, low density compared to other filter media, and relative cheapness [53].

Perlite is particularly suitable for the filtration of viscous liquids such as edible oils, and this is one of its main applications. It is also used to remove fine solids like algae and bacteria from beer and filtering out yeasts and other fine solids from wine. Other applications include the filtering of various chemicals, pharmaceutical solutions, solid particulates from waste water streams, water for municipal systems and swimming pools, and the clarification of foodstuffs (e.g. sugar solutions and syrups) [53].

High temperature applications

Perlite insulation is used in a variety of high temperature applications such as in the steel and foundry industries (like hot topping, ladle topping and risering), in insulating formulations at a service temperature of up to 1000°C, and in the manufacture of refractory bricks or castables. 38

Both raw perlite and expanded perlite can be used in ladle topping applications, but the raw form is more common. As the perlite ore is added to the ladle, it reacts with the slag and allows easy removal of the slag layer. The expanded perlite can also act as an efficient insulating layer to maintain the temperature of molten metal during the steel making process.

In the hot topping of castings and risers, up to 20% perlite by weight is mixed with exothermic powders. This controls heat loss from the casting, and thereby prevents shrinkage cavities. Pre-formed boards for hot tops and hollow cylinders for risers also perform the same function as hot topping and risering powders and compounds.

Perlite is also used as a cushioning agent in foundry cores and moulding sand mixtures to compensate for the expansion of silica as it goes through phase changes at temperatures above 540 °C. It helps to minimise casting defects like buckles, veining, fissuring, and penetration, and to improve the venting of gases by increasing the permeability of core sand [53].

An additional use for perlite is in the manufacture of refractories by inducing porosity, reducing density and thermal conductivity where the average temperature does not exceed

1100 °C. At higher temperatures, perlite refractories are used as backup insulating layers for higher duty refractories [87].

Zeolite synthesis

Zeolites are a well-defined class of crystalline aluminosilicate minerals. They have three- dimensional structures arising from a framework of tetrahedral units of [SiO4] - and

[AlO4] arranged in a polyhedral structure linked by all corners [88]. Zeolites have been successfully used in the chemical industry, agriculture, aquaculture, and environmental protection because of their remarkable physical and chemical properties which include 39

molecular sieving, adsorption, catalytic and ion exchange functions. This has resulted in a great increase in demand for these products. There are more than 45 natural types of zeolite; however, only clinoptilolite, mordenite and chabazite and possibly phillipsite are currently used as commercial products. The use of zeolites in most industrial applications requires certain specifications. Thus, synthetic zeolites can be good solutions to provide the strict specifications imposed on adsorption and catalytic processes. Furthermore, it would be possible to maintain a constant composition of the products during zeolite synthesis, while natural zeolites usually show considerable chemical and mineralogical variation [89]. Consequently, zeolite synthesis from low-cost silica-alumina sources has been the aim of many studies. Synthetic zeolites can be produced from a variety of natural silica-alumina materials including acidic volcanic glasses, such as natural and expanded perlite and pumice (e.g. [90, 91]). Experimental investigations into the formation of zeolites from perlite have shown that this low-cost silica-alumina material is a suitable material for zeolite synthesis. It has been shown that perlite can be successfully used in the synthesis of the zeolites ZK-19, W, G, F, Na-Pc, HS, ZSM-5, A, V, Pc, Na-P1, P1,

K-G, Y, Analcime, sodalite octahydrate and calcium zeolite [50, 88, 89, 92-95].

Other industrial applications

Advantage can be taken of the mild abrasiveness of crude perlite in the production of soaps, cleansers, and polishes. Crude perlite is also used for the stone-washing of fabrics in the textile industry. Traditionally, pumice was used to age fabrics and to soften the finish. Perlite, however, has a softer impact on the fabric and produces less wear on industrial laundry equipment than pumice, which can be excessively abrasive to the fabric

[53].

Perlite uses also include its application in oil-gas, water and geothermal well cementing and grouting, where the perlite prevents lost circulation of drilling lubricants. Moreover, perlite is used as a porous support for catalysts and reagents in various chemical reactions

[19, 76].

2.2.6 Concluding Remarks

In Section 2.2, the physical and chemical properties of perlite, the process of its expansion and its application in construction, horticulture and industry were discussed. However, one of the main properties of this material, its mechanical properties, has been missed.

Although this material has found uses in various applications, to the author’s knowledge, barely any research has been conducted into the mechanical properties of perlite. Hence, one of the main gaps identified in the literature is perlite’s mechanical properties, such as strength, Young’s modulus and Poisson’s ratio in its expanded and unexpanded forms.

Foams

2.3.1 Introduction to foams and syntactic foams

A foam is an assembly of cells (i.e. small compartments) packed in three dimensions to fill space. Foams can be solid or liquid. In liquid foams, the cell walls are interconnected liquid films and there is gas inside the cells. Solid foams can be considered as a composite made of a solid and a fluid (i.e. mostly a gas but it can also be a liquid as is the case in live tissues) [96]. Gibson and Ashby [97] defined solid foams as cellular materials with a relative density, which is the density of the foam divided by the density of the solid from which the cells are made, of less than 0.3. For higher relative densities, there would be a transition from the cellular structure to solids containing isolated pores. If a solid from which the foam is made is contained in the cell edges only, and hence the fluid phase is interconnected, the foams are called open-celled. However, if the solid is not only contained in the cell edges but also in the cell walls, so that each cell is sealed off from its neighbours [97], the foams are called closed-celled. Of course, some foams contain a combination of closed and open cells. Examples of a typical open cell foam and a typical closed cell foam are illustrated in Figure 2.8. Most foams do not have regular packing of identical cells, and are comprised of cells with different sizes and shapes. The cell dimensions can vary, from less than one micrometre in microcellular materials up to millimetres. The thickness of the cell walls and edges can also vary from 1 to 10 µm as is the case in some polyurethane foams [98]. In foams, the thickness of the cell edge

(struts) is usually larger than that of the cell walls. This is due to the surface tension drawing more solid material to the cell edges during the foaming process [97]. The shape

of cells can also be more or less random due to differences in the cell dimensions, wall and edge thickness as well as their chemical composition [99-101]. However, a common pattern may be observed, for example in cork, the cells are usually prismatic and arranged in parallel columns on staggered bases [96].

(a)

(b)

Figure 2.8. (a) Closed cell Polyurethane foam [102], (b) Open cell Polyurethane foam [3].

Foam-like materials are very common in nature. Examples are cork, sponge, wood and coral. While natural cellular materials have been used for centuries, such as cork, which has been used as bungs for wine bottles since Roman times, mankind has made a wide

variety of cellular materials using polymers, metals, ceramics, and even composites via different foam processing techniques [97].

One of the main types of man-made cellular materials is polymeric foams. They are made by first heating a polymer into the liquid form, then gas bubbles are introduced. These are allowed to grow and when they have reached the required size the material is ‘solidified’ by cross-linking or cooling [97]. The gaseous phase is introduced by either mechanical stirring or by using blowing agents. There are two type of blowing agents: chemical blowing agents and physical blowing agents. Physical blowing agents are inert gases (e.g. nitrogen and carbon dioxide) forced into solution in the hot polymer at high pressure which expand into bubbles due to reducing pressure. Alternatively, low melting point liquids (e.g. methylene chloride) are mixed with a polymer and vaporised into bubbles on heating. Chemical blowing agents are additives which give-off gases due to either chemical reactions or thermal decomposition [97, 103]. Each of these processes can yield open or closed cell foams. It is the rheology and surface tension of the fluids in the melt which govern the final structure of the foam [97]. Polymeric foams can be categorised into two main groups, the thermoplastic and thermosetting foams. The thermoplastics can usually be reprocessed and recycled; however, thermosets are not recyclable as they are usually heavily cross-linked. Within these categories, the polymeric foams can be further classified as rigid, semi-rigid, semi-flexible or flexible. Furthermore, a solid polymeric foam can either be composed of closed (e.g. polystyrene foam used for coffee cups) or open cells (i.e. the polyurethane foam in seat cushions). Each polymeric foam possesses unique physical, mechanical and thermal properties, which are attributed to the polymer matrix, the cellular structure (i.e. cell density, expansion ratio, cell size distribution, cell geometry and cell integrity) and the gas composition (i.e. the molecular weight of the

constituting components) [104, 105]. These foamed polymers have excellent energy absorption characteristics and are widely used for shock mitigation in vehicles of all types, in packaging, in cushioning and as an insulation material. They are also widely used as cores in sandwich panels, where two relatively thin but stiff face sheets are attached on either side of a thicker light-weight core [3]. In combination with stiff and strong face sheets, they produce a construction with higher stiffness to weight and strength to weight ratios than a structure made of a thick single phase material [106].

It has been shown that a foamed resin with higher specific strength and modulus can be obtained if the resinous matrix is reinforced with different types of fillers, such as solid particles, hollow particles, short fibres, etc. [107-110]. However, producing low density core materials has increased interest in the use of low density fillers such as hollow glass microspheres [111]. Syntactic foams are a special class of closed cell foams made by embedding hollow particles in a polymer matrix. They have porosity in the form of closed cells, and are especially useful in applications where a combination of low density, high compressive strength and high damage tolerance is required [5]. Moreover, the porosity enclosed by the thin and stiff shells of hollow particles provides syntactic foams with low moisture absorption, low thermal and electrical conductivity, as well as high dimensional stability at elevated temperatures [112]. Most of these structural foams are rigid, although more ductile and even elastomeric syntactic foams can be manufactured using suitable hollow particles and matrix materials. There are a wide variety of hollow microspheres for use in syntactic foams. The diameters of the hollow microspheres ranges from 1 to

350 µm, though they are on average about 50 to 100 µm. Hollow microspheres are made from glass, ceramic or any polymeric material [2, 113]. Most polymers can be used in the manufacture of syntactic foams. Producing thermoplastic syntactic foams is generally

more difficult as these materials are usually melt processed. Syntactic foams are mostly processed from thermosetting polymers, many of which are available in a castable liquid

'prepolymer' form. The most prevalent thermosetting polymer matrices used in the manufacture of syntactic foams are the unsaturated polyester and epoxy resins, although the use of polyurethane, silicones, polyimides, phenol-formaldehyde and urea- formaldehyde have been reported [113-117]. In the following section, different methods used to manufacture syntactic foam are explained.

2.3.2 Manufacturing syntactic foams

The manufacturing process used to produce a syntactic foam is important in terms of the final product’s properties, ease of production and manufacturing cost. Various manufacturing methods are available for processing syntactic foams. These vary from the simple blending of components to the coating of particles by resin [113]. The particle and binder concentration are found to be crucial for ease of manufacturing. In addition, the choice of process parameters (temperature, mixing time and addition sequence) is considered influential in the manufacturing process [118].

The most common method of manufacturing syntactic foams involves the impregnation of the desired quantity of filler particles (e.g. hollow glass microspheres) in a thermoplastic polymer solution (polymer + solvent) or in liquid thermosetting prepolymers (which might contain solvent/viscosity control) [117]. This method ensures the uniform coating of individual particles by resin and hence, a uniform distribution of resin among particles can be achieved. As the filler particles (e.g. hollow-glass, organic or carbon microspheres) cannot withstand high pressure, it is practically not suitable to use extrude or injection-moulding of mixtures (slurry). Instead, the mixture is usually

‘cast’ to minimise particle damage. Solvent is evaporated before final curing, though the entire removal of solvent and minimisation of solvent entrapment is a particular challenge. There are several impregnation techniques in common use. In one method, particles of known mass are introduced to a resin solution. Subsequently, the solvent is removed to get a dough, which is transferred into the mould and allowed to be cured [119-

123]. In another method, the mould is filled with the desired quantity of particles and sometimes vibrated to facilitate particles packing [113, 124]. Subsequently, a premeasured amount of the resin solution is poured over the particles. The solution penetrates the porous regions between particles due to gravity and capillary forces, and sometimes with the aid of a vacuum. Another method is to first fill the mould completely with particles to measure particle quantity where different particle sizes provide different quantities [125]. Subsequently, the measured quantity of particles is mixed with the resin solution and the prepared mixture is poured evenly into the mould. To maintain the particles in a well dispersed state, compression is applied on top of the mould lid or with the aid of a vacuum. This method has the advantage of restricting the spheres from floating to the surface during the foam production. In this method, as in the previously explained methods, removal of the solvent before final curing is required. These methods have many disadvantages. Perhaps the most serious problem with excess solvent is drawing off resin from the microspheres during the solvent’s evaporation. As the resin and solvent solution is heavier than the microsphere, it tends to sink when the mixing action stops. This also promotes separation of the mixture into phases of equal density by increasing the tendency of microspheres to float to the top of the mixture, and the resin solution to sink to the bottom; the mixture must be mixed continuously to the point that it becomes stable [126]. Other problems include the potential environmental hazards and

health effects of volatile solvents, the formation of structural non-uniformities as a result of the solvent’s removal by heat, the difficulty in producing batch-to-batch homogenous syntactic foams owing to difficulty in the complete removal of excess solvent from the mixture before moulding, and the additional cost and energy associated with removal of the solvent and transporting the mixture to the moulding or curing equipment [127, 128].

The processing of syntactic foams from liquid thermosetting resins without using solvent has also been reported. This method has been found to be suitable for liquid polyesters and silicones [113, 129]. In this method, solid particles are directly mixed with a heat curable thermosetting resin, followed by casting into a desired shape and curing to a foam

[129-131]. The difficulty in this method is non-uniform distributions of particles in the matrix. To mitigate this problem, the mixture is heated to allow thermosetting resin to flow and to wet the particles and, hence, a more uniform distribution of particles throughout the matrix is obtained. In this method, it is important to keep the viscosity as low as possible to prevent the creation of air bubbles in the final product. Due to the increase in viscosity, the volume fraction of particles is limited (i.e. the higher the particle concentration, the higher the viscosity) and hence low density foams (ca. 0.3 g/cm3) can hardly be achieved. On the one hand, as the particle volume fraction increases, their tendency to float to the surface of epoxy decreases, which is a common problem in a simple mixture of epoxy and particles. It has been found that a volume fraction of between

35% to 65%, and preferably about 50%, is suitable to minimise the tendency of the mixture to separate into discrete phases [129]. Yet the volume fraction of hollow spheres is adjusted based on the composition, size, and shape of the particles.

When the resin is available in a powdered form, a solid mixture of hollow spheres and powdered thermoplastic (or powdered thermoset) is prepared by gentle shaking and

agitating actions [113, 132, 133]. In some cases, a suspending agent is used to facilitate mixing and is evaporated before moulding [113]. A weighted quantity of the mixture is then charged into a mould and heat pressed at a temperature range within which the resin powder melts and curing occurs. The volume fraction of particles is constant for each sample with the purpose of completely filling the mould with the closest particle packing possible. By holding the particle volume fraction constant, the density can be dependent on a single independent variable (either the resin or the voids volume fraction).

Thermoplastic syntactic foams can be manufactured by conventional melt processing techniques, such as extrusion or injection moulding [117, 134, 135], though many larger particles may be damaged by the high stresses and hydrostatic pressures associated with melt processing. Depending on the type of resin, sometimes post-curing after the moulding operation is required.

Another manufacturing method for syntactic foams consists of resin coating, vacuum filtration and polymer precipitation [136, 137]. In the coating step, particles are introduced into a resin solution (e.g. epoxy diluted with acetone) and left there for a measured amount of time to ensure good adsorption of resin on the surface of the particles. The mixture is subsequently vacuum filtered and rinsed with liquids while on the filter in order to precipitate epoxy on particle surfaces and to remove the solvent simultaneously by leaching. The result is a wet-sand like material which forms into finely divided coated particles after drying. These particles have a free-flowing behaviour and are used as a moulding powder. The resin film to particle ratio in the dry powder is determined by factors such as solution concentration (i.e. dilution ratio), particle/resin solution ratio, time of contact between the resin solution and the particles, and temperature. A predetermined quantity of dry coated spheres, calculated to produce a

close-packed syntactic foam, is loaded into the mould cavity, pressed to a desired volume, and cured. This method enables the production of different sample densities by changing the resin concentration while the particles are closely packed in a mould [2].

Syntactic foams have also been produced using spray-up equipment. In this method, resin

(or resin solution) and particles are sprayed using separate adjustable streams, meet and mix at some point while still in the air and accumulate as a syntactic foam on any desired surface. In this method, the density of the foam is controlled by changing the flow rate of each component [113, 138].

Last, but not least, is manufacturing syntactic foam based on the microsphere buoyancy disclosed in AU Patent No. 2003205443 [139]. This technique involves mixing microspheres with diluted epoxy resin. The mixture is subsequently left stationary for the self-packing of microspheres by buoyancy resulting in two phases, i.e. the top phase is composed of packed microspheres and diluted binder; and the bottom phase contains only diluted binder. The bottom phase is then drained from the bottom of the mould and the remaining top phase is allowed to be cured. This method has the advantage of ease of mixing of the microspheres with the epoxy.

2.3.3 Particulate composites containing naturally occurring fillers

Though these hollow particles provide the syntactic foams with a high strength to weight ratio, it is of interest to find a material which provides similar properties but which is significantly cheaper and has a lower carbon footprint. One type of promising material is naturally occurring volcanic glasses.

There are several studies which have investigated the mechanical behaviour of composites containing naturally occurring inorganic porous aggregates in a resinous

matrix. One naturally occurring volcanic aggregate is pumice, which is mainly comprised of silica (~ 60 wt%) and alumina (~ 16%) [140]. Pumice is formed during volcanic eruptions when molten rock is ejected into the air. The rapid depressurisation due to the violent expulsion of magma into the atmosphere causes the release of dissolved gases and the formation of magma froth. The simultaneous cooling and depressurisation freezes the bubbles in the matrix and turns the frothy-like magma into a porous ceramic [141, 142].

Fleischer and Zupan [142] used these aggregates in two sizes (4mm and 8mm) in a matrix of epoxy resin to manufacture a rigid cellular core material. Compressive tests were conducted and the mechanical response of the pumice–epoxy structure as a function of relative density was evaluated. However, due to the higher density of pumice (i.e. 1.056

- 1.075 g/cm3), the pumice/epoxy composites were quite dense. Sahin et al. [143, 144] manufactured PPS (Polyphenylene sulphide) composites reinforced with pumice powder

(<45 µm) at different mass concentrations (1, 5, and 10 wt%) and obtained considerable improvement in the thermal and mechanical properties of PPS reinforced with 1wt% pumice powder. It showed increases of 5.6%, 9.8% and 22.5% in the glass transition temperature, tensile strength and relative degree of crystallinity, respectively. Ramesan et al. [145] prepared a composite with various loadings of pumice powder (~ 60 µm) added to a polyvinyl alcohol (PVA) - polyvinyl pyrrolidone (PVP) blend, which is a biodegradable, water-soluble polymer, and for composites containing 10 wt% pumice powder they obtained higher AC electrical conductivity, dielectric constant and dielectric loss, thermal decomposition temperature, and of particular relevance, a higher tensile strength (~ 29.4 %) than the pure PVA/PVP blend. Alvarado et al. [146, 147] reinforced

PHBV, which is a naturally occurring biopolymer, with 12.8 wt% pumice particles

(~ 147μm) and manufactured PHBV-pumice composites which were stiffer (12.35%)

and more brittle than PHBV, experiencing almost no plastic deformation, in order to reduce the cost and density of the current PHBV-based materials for structural and non- structural applications. Examples of other studies focused on pumice-reinforced composites can be found in [148-151].

Another mineral aggregate of natural occurrence is vermiculite. Vermiculite resembles mica in appearance and mainly consists of silica (37 - 42 wt%), magnesium oxide (14 -

12 wt%), alumina (10 - 13 wt%), ferric oxide (5 - 17 wt%), water (8 - 18 wt%) and a lesser amount of ferrous oxide (1 - 3 wt%) [152]. When subjected to high temperatures

(>900° C), the water situated in the interlayer space is converted to steam which causes expansion of vermiculite particles to twenty or thirty times their original volume, giving so-called exfoliated or expanded vermiculite. Consequently, a highly porous material that is highly thermally insulating is formed which finds use in various industrial applications

[153, 154]. Jun et al. [155] used the fire retardant properties of expanded vermiculite, in combination with the low thermal conductivity of phenolic resin, in order to develop flame retardant insulating composites with a density range 0.12 - 0.22 g/cm3 and thermal conductivity of about 0.045 - 0.069 W/(mK). Verbeek and Du Plessis [156] used expanded vermiculite particles in combination with phenol formaldehyde resin and phosphogypsum to manufacture composites with a density as low as 0.986 g/cm3 and flexural strength as high as 3.04 MPa for building applications. Yu et al. [157] treated expanded vermiculite powders with benzyldimethyl-octadecyl-ammonium (ODBA) and mixed it with phenolic resin (98 wt%) to form a composite with better thermal properties than that of pristine phenolic resin. The thermal decomposition temperature of the phenolic/treated expanded vermiculite composite reached 482.6 °C in air, which was 48.7

°C higher than that of pristine phenolic resin. Zheng et al. [158] modified natural

powdered vermiculite (<54 µm) by cation exchange with quaternary phosphonium salts and blended it with polyethylene terephthalate (PET), which is a semicrystalline thermoplastic polymer, to form (PET)/phosphonium vermiculite composites with better mechanical properties than pure PET. The (PET)/phosphonium vermiculite composites containing 3% modified vermiculite showed higher tensile strength (17.4%) and stiffness

(35%) than pure PET. Patro et al. [159] dispersed natural powdered vermiculite (<25

µm) in either isocyanate or polyether based polyols to synthesise rigid polyurethane/vermiculite composites and achieved better mechanical and thermal properties than those of a rigid polyurethane foam without vermiculite powder. When 2.3 wt% vermiculite was dispersed in isocyanate, the polyurethane/vermiculite nanocomposites showed increases of 40% and 34% in their compressive strength and modulus, respectively, and a 10% decrease in their thermal conductivity. Qian et al. [160] modified natural powdered vermiculite (<4µm ) by cation exchange with long-chain quaternary alkylammonium salts and then dispersed it in polyether based polyols to synthesise a polyurethane/vermiculite nanocomposite with better mechanical and thermal properties than pure polyurethane foams having 30% rigidity. The composites containing

5.3 wt % vermiculite showed a >270% increase in tensile modulus, >60% increase in tensile strength, and a 30% reduction in N2 permeability than pure polyurethane foams.

There are several other studies in the literature focused on vermiculite-reinforced polymer composites with the same general results [161-166].

Last, but not least, another example of a naturally occurring mineral is volcanic ash.

Volcanic ash is made of tiny fragments of jagged rock, minerals and volcanic glass which is created during volcanic eruptions and deposited at the surface. These deposits are abundant, readily accessible, and are rich in silica and alumina. Volcanic ash is recognised

as a mesoporous material having significant porosity, an appropriate pore structure and high surface area, which increases the effect of surface adhesion when they are used as fillers in composites [167]. Bora et al. [168, 169] treated volcanic ash particles with 3- aminopropyltriethoxysilane (3-APTS) at various concentrations (1, 3 and 5 vol.%) and used these particles at two concentrations (i.e. 10% and 15%) to reinforce PPS composites. Treated volcanic ash/PPS composites which showed considerable improvement in their tensile and flexural properties with 3 vol.% coupling silane agent in comparison to untreated volcanic ash/PPS composites. Trinidad et al. [170] manufactured two polymeric matrix composites by mixing volcanic ash with epoxy resin and polyester resin, individually, and achieved slightly better mechanical properties for volcanic ash/polyester than volcanic ash/epoxy composites. The volcanic ash/polyester composites showed 9%, 2.3%, 5.6% and 6.5% higher compressive strength, hardness, modulus of elasticity, and modulus of rupture, respectively, than those of the volcanic ash/epoxy composites. Fidan [171] reported manufacturing polyvinyl chloride (PVC) composites reinforced with volcanic ash at various concentrations (5 - 25 wt%) which resulted in better thermal stability for PVC composites within the temperature range 25 - 600 °C.

Bora [172] fabricated PVC/volcanic ash composites by reinforcing PVC with volcanic ash at various mass contents (5 - 25 wt%) which led to an increase in the tensile and flexural modulus but a decrease in the tensile and flexural strength. All the properties showed significant reduction as a result of the temperature increase from -10°C to 50 °C.

Avcu et al. [173] outlined the manufacture of volcanic ash filled polyphenylene sulphide

(PPS) composites containing different volcanic ash concentrations (2.5 - 20 wt%). They reported improvement in the thermal, mechanical and residual mechanical properties of the PPS composite by an increase in the volcanic ash content, although erosion resistance

was decreased markedly. Cernohous [174] outlined the melt processing of polypropylene

(PP) with a blowing agent and volcanic ash particles at different mass concentrations (40

- 60 wt%) and produced thermoplastic foamed composites with a density range 0.65 -

0.78 g/cm3 and a flexural modulus in the range 3350 - 4120 MPa. Examples of other studies which have focused on composite materials made from a polymeric matrix reinforced with volcanic ash can be found in [175-180]. There are, however, few studies investigating the use of perlite particles in a resinous matrix. Lukosiute et al. [181] produced two composites, one was made of an epoxy resin matrix filled with unexpanded perlite particles at different volume fractions and another one made of an epoxy resin matrix reinforced with different volume fractions of plasticised PVC particles and unexpanded perlite particles. The unexpanded perlite particles used in this study had a mean size of 80 µm, specific weight of 2.37 g/cm3, density of 1.60 g/cm3 and a porosity of 32%. Perlite/epoxy composites have shown higher tensile strength, elastic modulus and bending strength but lower impact strength than those containing dispersed PVC particles. In addition, it was found that an increase in the perlite particle volume fraction from 7% to 41% increased the stiffness of the perlite/PVC/epoxy composites due to the higher stiffness of the perlite particles (i.e. 27.5 GPa [181]) compared with the epoxy matrix (i.e. 2.6 GPa). Sherman and Cameron [182] produced cores for building boards containing a high proportion of expanded perlite particles (85% by weight) in different matrices of acrylic resin, epoxy resin and urea-formaldehyde. They found that epoxy resin provided the core with a higher modulus of rupture and density than the other two resins.

However, the results were not comprehensive as their conclusions were only based on the two above-mentioned properties. Of all of the available options, perlite is considered the most promising filler.

There are several studies which have investigated the use of EP particles in composites for structural and non-structural applications. Lu et al. [183] manufactured a form-stable composite by direct impregnation of expanded perlite in paraffin, resulting in good thermal energy storage, thermal stability and thermal reliability for composites containing

60 wt% paraffin. Later, Lu et al. [184] manufactured a phase change material by depositing graphene oxide films on the surface of the expanded perlite/paraffin composite. The heat storage/release performance test results showed that the heat storage/release rate of the expanded perlite/paraffin composite with 0.5 wt% graphene oxide was twice as fast as that of the expanded perlite/paraffin composites because of the enhanced thermal conductivity. Karaipekli et al. [185] also manufactured a form-stable expanded perlite/paraffin composite material for latent heat thermal energy storage and found that adding 5 wt% expanded graphite could increase the thermal conductivity of the form-stable composite by about 46%. Shastri and Kim [186] used a pre-mould process, which was initially used by Kim [187] in manufacturing glass microsphere/epoxy syntactic foams and disclosed in AU Patent No. 2003205443 [139], for consolidation of expanded perlite particles with starch binder as a building material.

Using this method, they manufactured perlite/starch composites in the density range 0.1

- 0.4 g/cm3 and characterised the compressive strength and modulus to be in the range 0.1

- 1.5 MPa and 10 - 85 MPa, respectively, for this range of foam density. Arifuzzaman and

Kim [188] also produced composite foams for building applications using a similar method of manufacture, based on the buoyancy principle by dispersing expanded perlite particles in a matrix of sodium silicate. They manufactured these foam composites in the density range 0.2 - 0.5 g/cm3 and characterised the compressive strength and modulus to be about 2.8 MPa and 175 MPa, respectively, for the highest foam density containing

0.35 g/ml sodium silicate. Furthermore, they investigated the effect of expanded perlite particle size in three ranges, 1 - 2mm, 2 - 3mm and 3 - 4mm, on the compressive strength of the perlite/sodium silicate foams and found that the particle size did not significantly affect the compressive strength.

The light weight and porous structure of expanded perlite has also received attentions in manufacturing syntactic metal foams. Taherishargh et al. [11, 189, 190] produced low density syntactic foams as an effective energy absorber by the counter-gravity infiltration of expanded perlite particles with molten aluminium. They investigated the effect of expanded perlite particle size, particle shape and foam density, on the resulting properties of foams containing 62 - 65 vol% expanded perlite. Smaller expanded perlite particles resulted in a metallic foam with a refined cell wall microstructure, smaller cell size, fewer defects and an equiaxed dendritic morphology. In addition, the homogeneity of the cell geometry was found to increase with a decrease in particle size, resulting in more uniform plastic deformation. As a result, foams with smaller EP particles showed a smoother and steeper stress–strain curve and a higher plateau stress and energy absorption capacity.

Regardless of particle size, the mechanical properties (e.g. compressive strength, modulus of elasticity, energy absorption efficiency and plateau end strain) were found to increase with an increase in the foam density. This has also been reported in the literature for a variety of metallic foams [191-197]. The shape of expanded perlite particles was also found to affect the structural and mechanical properties of expanded perlite/aluminium syntactic foam [190]. The irregular shape of raw EP particles was turned into nearly spherical particles using a rotary tumbling machine. Use of rounded EP particles resulted in an increase in the modulus of elasticity, 1% offset yield stress, plateau stress and energy absorption by 38%, 24%, 14% and 19%, respectively. Image processing and

micro-computed tomography (µCT) revealed strut misalignment, missing cell walls, and surface roughness inside the pores for foams containing the raw particles, while a homogenous distribution of nearly spherical pores was observed for foams with rounded particles. Hence, the superior mechanical properties of the foams with rounded EP particles were ascribed to their homogenous distribution of pores and fewer structural defects.

In summary, EP perlite is considered to be a promising material in manufacturing polymer matrix syntactic foams with regards to its properties (i.e. chemical and physical) and applications, as explained in the first part of this chapter (see Section 2.2). Perlite, in its expanded and unexpanded forms, has been used in the manufacture of different composites; however very few studies have been conducted on the combination of EP particles with a resinous matrix, especially epoxy. Hence, there is a need for further investigation of the properties of foams made from perlite particles in a resinous matrix.

Motivation and Problem Statement

Despite the fact that hollow microsphere/epoxy syntactic foams are known to offer desirable properties for structural applications (i.e. high strength to weight ratio and high stiffness to weight ratio), the high cost of the synthetically made filler particles makes their production expensive. Considering the low density, abundance and low cost of expanded perlite particles, it would be beneficial to develop new light-weight foam cores for sandwich structures to replace conventional hollow microsphere/epoxy syntactic foams at a significantly lower price. In addition, considering the wide use of expanded perlite particles in different sectors of construction and industry, it would be worthwhile to investigate the elastic properties of these particles, which have received little attention in previous research.

Research Objectives and Research Significance

The main objectives of the current study are as follows:

i. To investigate the mechanical properties of packed beds of expanded perlite

particles.

ii. To introduce suitable models capable of predicting the elastic properties of

packed beds of expanded perlite particles.

iii. To introduce and characterise an economical, light-weight syntactic foam.

iv. To investigate the effects of different parameters such as the filler particle sizes

and foam density on the structure, microstructure and mechanical properties of

the new syntactic foams.

v. To investigate damage mechanisms that occur during mechanical tests and

understand the material’s behaviour under applied loads.

The significance of the current research study are as follows:

i. Producing a syntactic foam having properties comparable with other foams

available in the market but significantly cheaper.

ii. Producing a syntactic foam which can be moulded to accommodate different

shapes for different structural applications.

3 Chapter Three: Methodology

Introduction

This chapter begins with an introduction to the materials used in this study, followed by discussion of how these materials were used to prepare packed EP particle beds, sintered solid perlite, resin and EP/epoxy foam samples. Subsequently, all of the different tests used to characterise the sample properties (e.g. mechanical and elastic wave speeds) are explained in detail. Furthermore, the apparatus and procedure used for the microstructural and damage analysis are explained. Lastly, the theory of dynamic moduli measurement using the elastic wave speed is described.

Material

3.2.1 Expanded perlite particles

Expanded perlite particles (EP), shown in Figure 2.1 (b), were supplied by Industrial

Processors Limited (INPRO) and were sieved into the size ranges 1 - 2 mm, 2 - 2.8 mm and 2.8 - 4mm. The chemical composition of the perlite provided by the supplier is presented in Table 3.1.

Table 3.1. Chemical composition [198]

Constituent Percentage present

Silica 74%

Aluminium Oxide 14%

Ferric Oxide 1%

Calcium Oxide 1.3%

Magnesium Oxide 0.3%

Sodium Oxide 3.0%

Potassium Oxide 4.0%

Titanium Oxide 0.1%

Heavy Metals Trace

Sulphate Trace

3.2.2 Epoxy resin

The resin system used for binding perlite particles consisted of West System 105 Epoxy

Resin with 206 Slow Hardener, at a ratio of 5.36:1 by weight. To enable the manufacturing method, ease the distribution of perlite particles in the binder and control the binder content in the foam, the epoxy was diluted with acetone (Septone, ASA20).

Acetone was considered to be a suitable solvent as it has a less detrimental effect on the mechanical properties of cured epoxy in comparison with other solvents such as toluene, tetrahydrofuran, N-dimethylformamide (DMF) and ethanol [199, 200]. Fourier transform infrared spectroscopy (FTIR) also showed that the use of acetone does not seem to change the chemical structure of the liquid epoxy [199, 201]. The dilution with acetone at this ratio reduced the mix viscosity, which was measured using a RST-Brookfield rheometer.

In addition, dilution with acetone increased the curing time of the epoxy, which was investigated by monitoring hardness change using a Type D durometer, as shown in

Figure 3.1.

Figure 3.1. Durometer (Type D) for hardness test. 63

Sample preparation

3.3.1 Preparation of expanded perlite (EP) particle samples

3.3.1.1 Samples for structural characterisation of EP particles

The tapped density of EP particle beds of known mass were measured using a tapping device with a graduated measuring cylinder of 100 ml, shown in Figure 3.2. After every

20 taps, the cylinder was rotated to minimise any possible separation of the mass during tapping down. Five hundred taps were conducted for each density measurement, and the average of five measurements was considered.

Particle density was also measured using the wax-immersion method (ASTM C914-95).

It should be noted that due to the EP particles’ structure having both open and closed pores, measurements with an air pycnometer resulted in the wrong density. As expected, the value given by the air pycnometer lay between the particle density and the true density of the material. As the wax does not penetrate into the perlite pores, the wax-immersion method is considered to give the most accurate measurement of the perlite particle density.

Scanning electron microscopy was used to study the internal structure of perlite particles by cross–sectioning EP particles carefully. For this purpose, a number of particles were embedded in epoxy resin poured in a small mould of 30 mm diameter and 30 mm height.

Samples were ground and lapped to a 1m diamond finish. The ground samples were transferred into an ultrasonic cleanser to remove perlite dust created during the cutting and polishing. All samples were coated with gold before microscopy to avoid charging.

Figure 3.2. Tapping device for measuring tapped density of EP particles.

3.3.1.2 Samples for confined quasi-static compressive tests (oedometer tests)

A cylindrical compaction mould made of steel was manufactured to produce samples 35 mm in height and 30 mm in diameter for measuring the properties of packed EP particle beds. Figures 3.3 (a) and (b) show the constituent parts of the mould and the assembled form of the mould, respectively. Samples for each particle size were prepared for the density range 0.10 - 0.40 g/cm3 and three samples were prepared for each density. To this end, EP particles of known mass were transferred into the mould and compressive loading was transferred to the EP particles through a plunger moving vertically into the mould.

The compaction process was carried out with a constant displacement rate of 1.0 mm/min in a computer-controlled 5kN Shimadzu testing machine. The target compaction densities were achieved by controlling the mass of EP particles within a constant volume. To ensure homogeneity, specimens were compacted in three layers. To minimise friction between 65

the piston and the wall of the mould, lubricant oil was sprayed on the wall of the mould and the plunger.

(a) (b)

Figure 3.3. Prepared mould (a) The different parts of the mould (b) Assembled mould.

3.3.1.3 Samples for elastic wave tests on packed beds of EP particles

An aluminium cylindrical compaction mould was manufactured to produce samples of 45 mm ± 0.015 mm in height and 80 mm in diameter for measuring the elastic properties of packed beds of EP particles. The target compaction densities were achieved by controlling the EP particles’ mass within a constant volume. To ensure homogeneity and minimise variations in density, the specimens were compacted in several layers (up to five). The compaction process was carried out in a 5000kN computer-controlled Shimadzu testing machine using a constant displacement rate of 1.0 mm/min. Lubricant oil was used to minimise friction between the piston and the walls of the mould. Samples were prepared with a density range 0.10 - 0.35 g/cm3 and three samples were prepared for each density.

3.3.2 Preparation of solid perlite samples

Solid perlite was prepared by grinding 27 g of perlite particles with a mortar and pestle and sieving to <250 µm. The powder was transferred into a mould and uniaxially pressed into a pellet at 146 MPa. The pellets, resting on a bed of alumina powder, were heated at

10 °C/min to the sintering temperature of 1100 °C which was held constant for 12 hours.

Subsequently the samples were cooled at 10 °C/min to 450 °C and held for an hour.

Cooling continued at the same rate to 300 °C, at which temperature the furnace was turned off and the sample was left to cool slowly. The sintered pellet was cut and polished into samples 30 mm in diameter and 16 mm high, as shown in Figure 3.4. The densities of the prepared sintered pellets were measured at room temperature using the Archimedes method.

Figure 3.4. Solid perlite sample (sintered perlite powders).

3.3.3 Preparation of resin samples

To measure the compressive, tensile and flexural properties of epoxy resin, two groups of samples were prepared, one group for the undiluted epoxy resin and another group for epoxy resin diluted with acetone according to the ratio of 1 to 7 for epoxy + hardener to

acetone, respectively. Samples were prepared by pouring the epoxy resin into two moulds made of Acetal, as shown in Figure 3.5.

(a) (b)

Figure 3.5. Mould for manufacturing epoxy resin samples for (a) compression and flexural tests

and (b) tensile tests.

The moulds, shown in Figure 3.5, were designed to manufacture samples according to

ASTM D-695, ASTM D-638 and ASTM D-790 standards for measuring the compressive, tensile and flexural properties of epoxy resin, respectively, as shown in Table 3.2.

Table 3.2. ASTM D-695, ASTM D-638 and ASTM D-790 for measuring the compressive,

tensile and flexural properties of epoxy resin.

ASTM

D-695

T (Thickness) = 3.2±0.4 mm, W (Width of narrow section) = 12.7 mm,

LO (Length Overall) = 79.4 mm, WO (Width Overall) = 19 mm,

G (Gage length) = 38.1 mm, R (Radius of fillet) = 38.1 mm

ASTM

D-638

T (Thickness) = 3.2±0.4 mm, W (Width of narrow section) = 13 mm,

L (Length of narrow section) = 57 mm, WO (Width Overall) = 19 mm,

LO (Length Overall) = 165 mm, G (Gage length) = 50 mm, D (Distance between

grips) = 115mm, R (Radius of fillet) = 76 mm

ASTM

D-790

T (Thickness) = 3.2±0.4 mm, W (Width of narrow section) = 12.7 mm,

LO (Length overall) = 79.4 mm

3.3.4 Preparation of EP/epoxy foam samples

The basic principle for manufacturing EP/epoxy foam composites was based on the buoyancy method explained in AU Patent No. 2003205443 [139] for manufacturing glass microsphere/epoxy syntactic foams. The perlite particles provided by Industrial

Processors Limited (INPRO) contained some unexpanded and semi-expanded particles; thus a device was designed to separate the expanded particles, based on the winnowing technique. This device, shown in Figure 3.6, was made of two computer fans, which provided enough air pressure with respect to the density of EP particles, a sieve of 500

µm and a piece of PVC pipe, which was attached to the sieve. The air blown by the fans passed through the sieve mesh and lifted the less dense expanded perlite particles out of the PVC pipe, leaving the denser unexpanded particles behind. Separated EP particles, the epoxy + hardener and acetone were mixed at the ratio of 1:2:14 respectively, in a screw cap plastic container through gentle agitating and tumbling actions. This particular mixing ratio was adopted due to the buoyancy method and to producing light-weight foams containing a thin film of epoxy around the particles. The mixing container was then left stationary until particles floated to the surface resulting in two phases, i.e. the top phase of packed perlite particles and diluted binder, and the bottom phase containing only diluted binder, as shown in Figure 3.7. The top phase was separated by straining and transferred into a cylindrical steel mould which is shown in Figure 3.3. The same mould was used in preparing packed beds of EP particles (explained in Section 3.3.1.2) and

EP/epoxy foam samples in order for the dimensions to be comparable and to correctly measure the crushing strength of the EP particles during sample manufacturing (to be explained later in Section 4.6.2). The mould was designed to produce samples 35 mm high and 30 mm in diameter, according to ASTMC365/C365M – 11a. 70

Figure 3.6. A hand-made device for separating expanded particles from unexpanded and semi-

expanded particles.

Three types of EP/epoxy foam samples were manufactured for the density range 0.15 -

0.45 g/cm3 by changing the mass inside the mould while keeping the volume constant.

To achieve a constant volume, a universal testing machine was used to compress the mixtures of EP particles and the binder to the target height of 35mm. Figure 3.8 illustrates the foam samples having the same density but using three different particle size ranges.

Foams containing one particle size range were considered to be of one type. Foams of type 1, type 2 and type 3 were defined as foams made with particles in the size ranges of

1 - 2 mm, 2 - 2.8 mm and 2.8 - 4 mm, respectively. Five to eight samples were manufactured for each density and type of foam. The densities of the prepared foams were measured at room temperature after the curing time elapsed.

Figure 3.7. Formation of two phases by buoyancy. The top phase is packed perlite particles and

diluted binder and the bottom phase contained only diluted binder.

Figure 3.8. Samples prepared using three particle size ranges; from the left, 1 - 2 mm, 2 - 2.8

mm and 2.8 – 4 mm.

Experimental Setup and Tests

3.4.1 Mechanical testing on the packed beds of EP Particles

To measure the properties of the EP particles, oedeometric tests (confined compressive tests) were conducted on packed EP particle beds. As explained in Section 3.3.1.2, compaction was conducted in several layers, where each layer had virtually the same density and almost the same compaction load. Hence, the compaction load was in the same range for the whole of each sample. During the tests, experimental data were recorded by built-in aquisition software (Trapezium 2) in the form of force-displacement curves for each sample. These were subsequently converted to compaction stress-density curves based on the cross-sectional area of the plunger and the final height of the sample, measured using callipers after removing the compacted sample from the mould.

In addition, the compacted samples containing EP particles in the range 2 – 2.8 mm were used to measure the confined elastic modulus of the particles by cyclic loading-unloading of the pre-compacted particles to 10%, 15% and 20% of the maximum compaction force.

Three to four tests were conducted for each density.

3.4.2 Mechanical testing of EP/epoxy foams

Uni-axial (unconfined) compression tests were conducted on a computer-controlled 5 kN

Shimadzu testing machine. Samples were compressed at a crosshead speed of 0.5 mm/min at room temprature, which ranged from 23 to 25°C. During the tests, experimental data were recorded by the built-in aquisition software (Trapezium 2) in the form of force-displacement curves for each sample and these were then converted to engineering stress-strain curves, based on the intial cross-sectional area and height of the 73

test sample. To investigate the porosity dependent rigidity, the elastic gradient of the material was measured based on ISO 13314. In this standard, the elastic gradient is determined by loading and unloading between 20% and 70% of the maximum stress (σ20 and σ70). The unloading gradient, or so-called effective elastic modulus, was measured to alleviate two potential problems affecting the accuracy of the initial loading modulus.

Firstly, there might be some localised plasticity in the sample where cells yield at very low stress levels. This may result in contributions from both elastic and plastic deformation to the resulting modulus. Secondly, it is very likely that the sample’s surfaces touching the loading plates are not perfectly parallel. However, applying load at low strains will flatten the surfaces until complete contact is established (settling).

Consequently, when the load is released, the unloading gradient is purely elastic and not affected by localised plastic deformation and the settling effect [11]. To this end, one initial sample must be tested to obtain the maximum compressive stress (max). Then the next four samples were loaded to 70% of the maximum stress (σ70) and unloaded to 20% of the maximum stress (σ20).

Furthermore, a series of confined compression tests was conducted on cured EP/epoxy foams. For this purpose, samples were tightly enclosed in the cylindrical steel mould shown in Figure 3.3, with an inner diameter equal to the diameter of the sample. This mould was the same mould used for manufacturing the EP/epoxy foams. The diameter of the samples after curing were slightly bigger (30.1 ± 0.045 mm) than before curing (30 mm) which helped in tightly enclosing the foams.

3.4.3 Elastic wave tests on EP particles

To measure the properties of EP particle compacts, a compaction rig was designed to include transducers and particles. It consisted of a pair of aluminium rams located inside the top and bottom of the cylindrical aluminium die enclosing the compacted EP particles.

The rams were designed to have the same height as the transducer and a groove held the transducer tightly with the ram surface flush with the active element of the transducer. A schematic representation of the set-up is shown in Figure 3.9.

Figure 3.9. Schematic representation of the experimental set-up for measuring wave velocity in

packed beds of EP particles.

Elastic wave velocity measurements were carried out at a constant contact pressure equal to the average compaction stress at each density (see Section 3.4.1) using a computer- controlled Shimadzu testing machine. Two pairs of piezoelectric transducers (S-wave and

P-wave) with a nominal frequency of 1MHz were used to measure the compression, Cp, and shear wave, Cs, velocities in the axial direction throughout the sample. Each pair of transducers was placed in the rams and a thin layer of silicone grease was used to improve

the coupling between the specimen and the transducers. The experimental setup employed here is similar to the system used by Arroyo et al. for testing clayey rocks [202]. It included a programmable function generator (Thurlby Thandar® TTi – TG4001) to generate and transmit elastic waves as well as a digital oscilloscope (Tektronix® TDS

1001C-EDU) to acquire both input and output signals. Signal stacking was applied to both input and output waves to minimise random noise. Sine pulses with apparent frequency ranging from 5 to 40 kHz (100 V peak-to-peak) were used as the input signal.

Elastic wave velocities were estimated as the ratio of the travel length to the travel time.

The recorded input and output signals were used to estimate the travel time by considering the time delay between the start of the input signal and the start of the output signal

(details explained in [203]). The travel length is the height of the samples and was determined using callipers.

Examples of input and output signals for the low and high density EP particle compacts are given in Figure 3.10, where the arrival times for the P-waves (tP) and S-waves (tS) are indicated by vertical dashed lines. The arrival time tP was clearly identified as the

‘common first break time’ in the output signals, irrespective of the sample density. Two sets of input frequencies were used to determine the arrival time tS depending on the density of the EP particle compacts. Input frequencies up to 40 kHz were used in dense samples, whereas good quality output signals were obtained in low density samples (<

150 g/cm3) using frequencies up to 15 - 20 kHz. A step pulse of 10 Hz was also applied which, in combination with the sine pulses, helped to check the arrival time of the S- wave. The determination of the arrival time tS required extra care due to the influence of low-energy P-waves, which travel faster than S-waves, on the output signals. This phenomenon, known as the near-field effect [202, 204], is strongly frequency-dependent

and may lead to misleading estimates of tS if the arrival time of the P-wave is not available. From inspection of Figure 3.10 (b) and (d), it is clear that the arrival time of the

S-wave corresponds to the first important break time, whereas the small disturbance

(‘bump’) observed earlier in the output signals (clearer in the low density samples) is consistent with the arrival time tP previously estimated in Figure 3.10 (a) and (c).

(a) (b)

Figure 3.10. Examples of (a) P-wave and (b) S-wave signals in low density (0.12 g/cm3) EP

particle compacts and (c) P-wave and (d) S-waves in high density (0.3 g/cm3) EP particle

compacts.

3.4.4 Elastic wave tests on EP/epoxy foams and solid perlite

A frame was designed to measure elastic wave velocities in EP/epoxy foams as well as the solid perlite samples. The frame consisted of a mobile top beam guided using a frictionless roller bearing, a stationary bottom beam and a pair of aluminium rams within which the sample was placed. Rams were designed to hold the transducers tightly while keeping the active element of the transducers at the same level as their surface. A schematic representation of the set-up is shown in Figure 3.11.

Figure 3.11. Schematic representation of the ultrasonic experimental set-up for measuring wave

velocity in solid perlite and EP/epoxy samples.

To improve the coupling between the transducer and the sample, a constant pressure was applied by adding a 5 kg dead weight to the mobile top beam; this will in turn enhance the quality of the output signals. Two pairs of piezoelectric transducers with a nominal frequency of 1MHz were used to measure the longitudinal, CL, and shear wave, Cs, velocities in the axial direction throughout the sample. Each pair of transducers was placed in the rams and acoustically coupled by a thin layer of silicone grease. Similar to

the experimental setup used for measuring the elastic properties of EP particles (see

Section 3.4.3), the experimental setup included a programmable function generator

(Thurlby Thandar® TTi – TG4001), a digital oscilloscope (Tektronix® TDS 1001C-

EDU) and an ultrasonic pre-amplifier OLYMPUS® (Panametrics 5656C, with a gain of

40dB). Signal stacking was applied to both the input and output waves to minimise random noise. Sine pulses with apparent frequency ranging from 10 - 50 kHz (100 V peak-to-peak) were used as the input signal. Elastic wave velocities were estimated in the same way explained in Section 3.4.3.

Microstructural analysis

Scanning electron microscopy (SEM) was used to study the internal structure of perlite particles and perlite-based foam samples before undergoing compression tests. The microstructure of expanded perlite particles was studied by carefully cross-sectioning the particles. For this purpose, a number of particles were embedded in epoxy resin poured in a small mould of 30 mm diameter and 30 mm height. After 24 hours curing, the sample was demoulded and the surface of the sample was carefully ground using 240, 320, 600,

800 and 1200 grit silicon carbide papers. A smooth, mirror like surface was subsequently achieved by polishing with 1µm diamond suspension in distilled water sprayed onto a polishing cloth. Perlite particles and epoxy resin are both non-conducting materials; hence the samples were coated with gold before microscopy. The internal structure of the perlite-based foams was studied by cutting a thickness of 3mm from the sample using a low speed silicon carbide saw. The thin slices were carefully ground by 800 and 1200 grit silicon carbide paper. To remove perlite dust created during cutting and polishing the sample, the thin slices were put into an ultrasonic cleaner for 10 minutes. They were then dried using a blow dryer and left in an oven at 35 °C for 2 hours. Lastly, the thin slices were coated with gold and were then ready for microstructural study by SEM.

Damage observation

Failure mechanisms of the newly developed foams were investigated using both macroscopic and microscopic observations. During the course of the mechanical testing experiments, a high resolution camera (Nikon D800E) was used to record an image of the compressed sample every 10s. This helped to closely follow the damage sequence and the failure process in the foam samples. Scanning electron microscopy was used after finishing the test to examine the fractured samples and to determine the failure modes. As the samples were mostly made up of perlite particles having a brittle nature, the fracture of the foam under compressive loading generated a large amount of broken pieces of particles (e.g. perlite dust). These loose particles can cause charging during electron microscopic observations. Thus, the fractured surface of the foam sample was exposed to a gentle blow of air before coating with gold. As the fractured samples had uneven surfaces with a porous structure, coating was also conducted from different directions and angles in several steps to avoid charging effects in the microscope.

The theory of dynamic moduli measurement

Elastic stress waves propagate in materials by inducing infinitesimal elastic deformation.

Hence, wave propagation equations which are based on elasticity theory can be used to measure the elastic moduli of a material if the elastic wave velocities and densities are measured independently [205, 206]. Two wave types propagate in extended elastic solids:

(i) compression waves in which the displacements are in the direction of the wave propagation, and (ii) shear waves in which the displacements are perpendicular to the direction of the wave propagation. In an isotropic linear elastic body, in which the propagating wave does not interact with the boundary of the medium, the compression wave or P-wave (CP) and shear wave or S-wave (CS) velocities are given by:

 C  (3.1) S 

M   2 C   (3.2) P  

where M is the constrained modulus, ρ is the density of the material, λ and µ are the Lamé constants. The Lamé constants are related to the stiffness tensor, 퐶푖푗푘푙, by:

Cijkl = [ ij  kl +  (ik  jl + il  jk )] kl (3.3) where 훿 is the Kronecker delta function defined as:

0 푓표푟 푖 ≠ 푗 훿 = { , 푖, 푗 = 1, 2, 3. 푖푗 1 푓표푟 푖 = 푗

Young’s modulus (E) and Poisson’s ratio (휈) can be expressed as a function of the density, compression wave velocity and shear wave velocity of the material as follows: 83

3C 2  4C 2  2 P S E  C S 2 2 (3.4) C P  C S

C 2  2C 2 P S   2 2 (3.5) 2(C P  CS )

When the characteristic dimensions of a body are not large compared with the wavelength, these equations no longer hold, and the velocities become dependent upon the frequency [207]. In the case of an unconstrained cylindrical bar (i.e. uniaxial conditions) with a radius much smaller than the wave length, the compression wave has a different velocity called the longitudinal velocity (or rod velocity) CL, given by [207]:

E C  (3.6) L 

However, the stiffness that controls shear waves in cylindrical bars is the same as the one in an infinite medium (i.e. Eq. (3.1)) [204]. Consequently, Poisson’s ratio is expressed as:

1  C L      1 (3.7) 2  C S 

In the current study, the above equations are used to characterise the elastic properties of packed EP particle beds and sintered perlite by assuming that the pores are air-filled voids which are randomly distributed and oriented throughout the medium. Hence, the commonly adopted assumption that the porous solid body exhibits isotropic elastic behaviour in a statistical sense will be adhered to.

With regards to the sample size and wave length, Eqs. (3.4) and (3.5) were used to characterise the elastic properties of packed beds of EP particles, whereas Eqs. (3.6) and

(3.7) were used to characterise the elastic properties of sintered perlite samples.

Moreover, Eqs. (3.6) and (3.7) were used to characterise the elastic properties of

EP/epoxy foams in the longitudinal direction (i.e. z-axis) by assuming that the particles

were randomly distributed and oriented throughout the foam and, thus, the EP/epoxy foams macroscopically exhibit isotropic elastic behaviour.

4 Chapter Four: Results

Introduction

In this chapter, the properties of solid perlite (pore free), packed EP particle beds, epoxy resin, and EP/epoxy foams are presented. The elastic properties of low porosity solid perlite and packed EP particle beds were characterized by means of elastic wave propagation along the the cylinder axis of the specimens. By adopting an isotropic model, the Young’s modulus and Poisson’s ratio were used to characterise the elastic response of the medium. Moreover, elasticity theory was used to estimate the properties of pore free solid perlite. Using these properties for solid perlite, porosity-elastic moduli relations were investigated using four analytical models. The models were compared with the experimental data from this study and their ability to estimate the elastic properties at different porosity levels was evaluated.

Mechanical properties of cured epoxy resin (before and after dilution with acetone) measured using quasi-static mechanical tests (according to ASTM standards) and elastic wave tests are also provided and discussed. In addition, the results from hardness and viscosity measurements for epoxy resin are presented and the effect of dilution on the curing time reported.

Following the above characterisation of the resin, the compressive properties of EP/epoxy foams characterised by quasi-static mechanical tests and the effects of density and particle size are reported and discussed. Post compression microscopic and macroscopic observations taken during the test are presented in order to understand the damage

mechanisms that occurred during the test and give additional insight into the material behaviour under compressive loading. Moreover, based on the results of mechanical tests, estimates for the contribution of the particle elastic modulus to the resulting foam effective elastic modulus are shown.

The elastic properties of Ep/epoxy foams were then characterised using elastic wave tests along the cylinder axis of the specimens in terms of Young’s modulus and the Poisson’s ratio are presented. Subsequently, a comparison is made between the properties obtained by mechanical and elastic wave tests. Furthermore, based on the results of the elastic wave tests, the contribution of the constituents’ properties to the resulting foam properties is discussed.

Elastic properties of sintered solid perlite

Using microscope images (shown in Figure 4.1) taken from the polished surface of the samples and an image processing technique (MATLAB, MathWorks, MA), the porosity of the sintered perlite samples was determined to be about 4%.

Figure 4.1. Microscope images taken from the polished surface of sintered perlite. The

polishing marks are designated on the picture in order not to be confused with porosity.

It has been shown that for porosity less than 5%, there is a linear relationship between the elastic moduli and the porosity [208-211]. Within this range (0 - 5%), elasticity theory successfully predicts the zero-porosity properties from the elastic moduli of porous solids, by the following relations [212]:

E  E0 (1 E P) (4.1a)

G  G0 (1c P) (4.1b)

  0 (1 P) (4.1c)

CL  CL0 (1 L P) (4.1d)

CS  CS0 (1 S P) (4.1e)

where  E 1/18(29 11 0 )

c  5 / 3

c  5 / 9 11 0 /181/(18 0 )

2  L 1/ 2 E  2  0 (2  0 ) (1  0 ) (1  0 ) (1  2 0 )1

 S 1/ 3

and E, G, ν correspond to Young’s modulus, shear modulus, and Poisson’s ratio, respectively, and subscript 0 refers to the zero porosity values of the properties. The resulting zero porosity values of the density ρ0, longitudinal wave velocity CL0, shear wave velocity CS0, Poisson’s ratio ν0, shear modulus G0 and Young’s modulus E0 of sintered perlite are shown in row 2 of Table 4.1. For comparison, the corresponding values from solid obsidian, measured by Manghnani et al. [213], are also presented. It can be seen that the measured wave velocity for perlite with 4% porosity is closer to obsidian than those for pore-free perlite. This might be due to the obsidian structure which is typically vesicle-poor [214] (i.e. <2.5% porosity [215]), though the percentage of the porosity was not reported by Manghnani et al. [213]. The comparison with obsidian

provides a benchmark for confidence in the measured values for the sintered perlite, especially Poisson’s ratio.

Table 4.1. Elastic properties of solid component of EP particles. For comparison, the

corresponding data for obsidian by Manghnani et al. [213] are presented.

𝜌 퐶퐿 퐶푆 퐺 퐸 휈

(g/cm3) (m/s) (m/s) (GPa) (GPa)

4% porosity Perlite 2.312 5616.44 3655.1 30.9 72.93 0.181

0% porosity Perlite 2.411 5836.75 3704.5 33.1 78.33 0.183

Obsidian [213] 2.357 5775 3608 30.7 75.16 0.180

Properties of packed beds of EP particles

4.3.1 Structural characterisation of EP particles

The bulk and particle densities of EP particles were measured according to the method given in Section 3.3.1.1 and an average of five measurements for each particle size range is presented in Table 4.2.

Table 4.2. Bulk density and particle density measurements of EP particles

particle size 1 - 2 mm 2 - 2.8 mm 2.8 - 4 mm

Bulk Density (g/cm3) 0.0703 0.0857 0.0939

Standard Deviation(g/cm3) 0.0003 0.0033 0.0007

Particle Density (g/cm3) 0.181 0.183 0.186

Standard Deviation (g/cm3) 0.016 0.010 0.004

Scanning electron microscopy (SEM) was used to characterise the microstructure of EP particles. SEM images taken from the outer surface of an EP particle at each size range are shown in Figure 4.2. As can be seen, the outer surface of the perlite particles is covered with both closed and open pores and has a froth-like structure.

(a) (b)

(c)

Figure 4.2. SEM images showing the external structure of an EP particle: (a) in the 1 - 2 mm size

range; (b) in the 2 - 2.8 mm size range; (c) in the 2.8 - 4 mm size range.

(a) (b)

Figure 4.3. SEM images showing the internal structure of an EP particle in the: (a) 1 - 2 mm size

range; (b) 2 - 2.8 mm size range; (c) 2.8 - 4 mm size range; (d) 2 - 2.8 mm size range, illustrating

natural reinforcement inside EP particle cells.

Examination of the different microscope images shows that the outer surface of the EP particles in the size range 1 - 2 mm contains more open pores than the other two size ranges.

Figures 4.3 (a) - (c) reveal that the interior of expanded perlites in all three size ranges has a three-dimensional cellular structure mainly composed of closed cells. Examination of the

micrographs also shows that EP particles in the size range 2.8 - 4mm are made up of polyhedral cells, mostly possessing pentagonal dodecahedron and tetrakaidecahedron geometries. However, the cells composing the structures of EP particles in the size range 1 -

2 mm and 2 - 2.8 mm do not appear to have a preferred geometrical shape; some are polyhedral and some are almost spherical. Micrographs taken from EP particles in the size ranges 2 - 2.8 mm and particularly 1 - 2 mm reveal the presence of inner cell reinforcement; fibre-like reinforcements spanning the walls of a cell (see Figure 4.3 (d)). This phenomenon was not observed in EP particles in the size range 2.8 - 4 mm. The governing conditions and formation mechanism of the fibrous cell reinforcement are not known at this stage.

Examination of the micrographs taken from EP particles of each size range, cell size, wall thickness and edge cell thickness7 were measured and are presented in Table 4.3. The measured values show larger thicknesses for the edge cells than for the walls. This can be ascribed to surface tension effects during the perlite expansion process which draws solid into the cell edges and leaves a thin wall framed by a thicker edge [11, 216]. It can be seen that the measured values are highest for particles in the size range 1 - 2 mm. This could explain the higher crushing resistance of this particle size range, illustrated later in Section

4.6.2.1.

7 Edge thickness: as defined by Gibson and Ashby [17]

Table 4.3. Cell dimensions of EP particles of 1 - 2 mm, 2 - 2.8mm and 2.8 - 4 mm size range. Each

value is an average of 150 measurements.

Cell Size Wall Thickness Edge Cell Thickness

1 - 2 mm 84.497 µm 0.532 µm 3.067 µm

Standard Deviation 13.437 µm 0.100 µm 0.725 µm

2 - 2.8 mm 61.107 µm 0.512µm 1.493 µm

Standard Deviation 9.397 µm 0.092 µm 0.438 µm

2.8 - 4 mm 53.494 µm 0.516 µm 2.425 µm

Standard Deviation 8.047 µm 0.092 µm 0.472 µm

Fine et al. [217] suggested a geometric relationship given by Eq. (4.2) for calculating the wall thickness of a glass hollow microsphere from its relative density (true density of a microsphere divided by the density of glass).

1 t   3 w 1 1 true  (4.2)   r  g  with 푡푤= wall thickness of the microspheres, r = average radius of the microspheres, ρtrue = true density of the microspheres, and ρg = density of the glass. Using the results presented in

Table 4.3 and measured particle densities presented in Table 4.2, Eq. (4.2) may be modified to adapt to the perlite morphology. Two Eqs. (4.3) and (4.4) are suggested for calculating the ratio of the wall thickness (tw) and cell size (C) to the EP particle diameter (dp) in terms of their relative density:

x tw  EP  1.5  1.5   (4.3) d p  UP 

y C  EP  1.5  1.5   (4.4) d p  UP  where 𝜌퐸푃 is the EP particle density and 𝜌푈푃 is the density of fully dense perlite. The exponents x and y for the three particle size ranges obtained by fitting the experimental results

(Table 4.3) to Eq. (4.3) and Eq. (4.4) are presented in Table 4.4.

Table 4.4. Exponents of Eq. (4.3) and Eq. (4.4) for the three particle size ranges.

x y

1 - 2 mm 1.25 1.075

2 - 2.8 mm 1.20 1.15

2.8 - 4 mm 1.20 1.17

4.3.2 Measurement of elastic moduli of packed EP particle beds using quasi-static mechanical tests

The elastic moduli of EP particles as a function of density were measured by conducting several loading-unloading compressive tests on packed beds of EP particles (explained in detail in Section 3.4.1). Considering the correlation coefficient (R2) of unloading gradients and the deviation between them, it was possible to determine the local yield point for that compacted sample. Below the determined yield point was considered to be the elastic region

where the confined elastic modulus could be measured. The results as a function of compact density are given in Figure 4.4.

Figure 4.4. Constrained modulus of packed EP particle beds as a function of compact density.

Since the particles used in this test were confined, the calculated unloading gradient was not identical to the elastic modulus of the packed bed of particles but a function of both their elastic modulus (EP) and Poisson’s ratio (휈). Considering 휀푦 = 휀푧 = 0, the confinement introduced by the wall of the cylinder, and 𝜎푦 = 𝜎푧, the unloading gradient (𝜎푥 /휀푥) or constrained elastic modulus E* is defined as [218]:

* (1  ) E  E (4.5) P (1  ) (1  2 )

There are various methods to determine Poisson’s ratio (휈) in the geotechnical literature. A common one [219] is given by Eq. (4.6):

k 2     ; k  tan 45   (4.6) 1 k  2  where 휑 denotes the angle of internal friction. However, it was found that the Poisson’s ratio

(휈) calculated from Eq. (4.6) overestimates the real value of this coefficient. Therefore, it is not applicable where the methods of theoretical elasticity are applied [220]. Sawicki and

Świdziński [220] proposed a method for determining the elastic moduli of particulate materials using confined compressive tests, with additional measurement of the lateral stresses. Although their method provides more exact solutions for the elastic moduli, it requires the conduct of biaxial compressive tests. Performing such tests was not possible in this study due to limitations of the testing machine. As a result, the study was extended to measure the elastic moduli of packed beds of EP particles using elastic waves, as explained in the next section.

4.3.3 Measurement of elastic moduli of packed EP particle beds using elastic waves

The compression and shear wave velocities of packed beds of EP particles at different densities are shown in Figure 4.5. As can be seen, both the compression and shear wave velocities reach a plateau for densities higher than 0.2 g/cm3. At lower densities, particles have more space available to move or rotate. At higher densities, the relative movement of particles is restrained as the particles reach an optimal structural arrangement (i.e. the particle fabric). Further compression reduces pore volumes between the EP particles by fracturing particles which produces both smaller cellular EP particles and fine platy debris such as that shown in Figure 4.6. Because of the closed cellular EP structure, microscopic analysis

conducted on EP particles in a previous study [15], indicated that debris does not form inside

EP particles i.e. the debris is restricted to the inter-particle spaces.

(a)

(b)

Figure 4.5. The (a) Compression wave and (b) Shear wave velocities versus compact density.

Figure 4.6. Formation of platy and fine particles as a result of the brittle crushing of cell walls.

The use of static density in Eqs. (3.1), (3.2), (3.4) and (3.6) can be justified only if the debris are mechanically linked to the particles [221]. If the debris particles are free moving, they should not be taken into account in the evaluation of the dynamic compact density.

Consequently, further investigation of the debris was undertaken. The debris concentration was investigated by separating the EP particles from the debris and measuring their relative masses at each compact density. Mechanical separation was ineffective without causing more particle fracture and debris. Therefore, the EP particle compacts were immersed in water for

24 hours to disperse. The dispersion resulted in two phases: a top phase comprising EP particles floating on the surface and sediment. The sediment was considered to be 100% debris due to its higher density (note the solid density of perlite in Table 4.1). Beakers containing the EP particles and sediment were placed in an oven at 120 °C for 24 h. The debris size was measured and found to be less than 212 µm which is used here to discriminate between particles and debris. To be sure that all the debris had separated from the EP particles, the samples were sieved and the fraction bellow 212 µm was added to the debris.

Figure 4.7 (a) illustrates the weight percentage of debris as the EP particle compact density 100

increases. This is also demonstrated by the particle size distribution measured after compaction which is shown in Figure 4.7 (b).

(a)

(b)

Figure 4.7. (a) Percentage of debris at each EP compact density. (b) Cumulative particle size

distribution for entire compacts (EP particles and debris).

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It can be seen that as the compact density increases due to the breakage of particles, the percentage of larger particles decreases and the amount of debris increases. This post compaction investigation revealed that the mass of EP particles that resisted crushing at densities higher than 0.2 g/cm3 remained relatively constant. This was very strongly correlated with the plateau region of the compression wave and shear wave velocity versus density curves, suggesting that only the EP particles contribute to sound wave propagation and the debris plays little role. This was further validated by investigating the evolution of the inter-particle porosity as compact density increases. To this end, the density of different

EP particles size ranges was measured using the wax immersion method. In this method, wax was melted in a 5ml measuring cylinder and kept at a constant temperature for each measurement. EP particles of known mass and size were immersed in the melted wax and their particle density was measured through the change in the wax’s volume. The results are shown in Figure 4.8 (a). Using the results shown in Figure 4.7 (b) and Figure 4.8 (a), the inter-particle porosity (excluding debris) within the total sample volume was calculated and is presented in Figure 4.8 (b). It can be seen that the inter-particle porosity does not change significantly as the compact density increases. This can be explained by the breaking of the original EP particles into smaller EP particles as the compact density increases. The smaller particles created new inter-particle porosity the increase of which was offset by the simultaneous production of debris. Considering the mass fraction of the debris at each compact density (see Figure 4.7 (a)) and the results shown in Figure 4.8 (a), the volume percentage of debris with respect to the total sample volume as well as with respect to the inter-particle porosity volume was calculated (Figure 4.8c). As can be seen, the debris does

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not occupy a significant portion of the total sample volume and the inter-particle porosity volume due to the very high density of the debris compared with the density of EP particles.

Therefore, the raw compact densities were modified by subtracting the debris mass from the total mass of the EP particles and new densities were calculated. The modified results are plotted along with the experimental results in Figure 4.5.

It should be noted that both of these results are useful. In practical situations, it is not usually feasible to separate the debris from the EP particles. However, the raw or experimental results are readily measured and reflect the effective state of the granular body. Hence, these results are of most practical interest. Otherwise, if the properties of pure EP particles are desired for more in-depth studies, the modified results are appropriate.

Young’s moduli of packed beds of EP particles, corresponding to the wave velocities in

Figure 4.5, calculated based on both raw compact density and modified density using Eq.

(3.4) is shown in Figure 4.9 (a). Figure 4.9 (a) also illustrates the normalised value of Young’s modulus (E/E0) versus the compact porosity. Both curves, calculated from the experimental and modified wave velocity results show that the Young’s modulus of packed beds of EP particles increases as the density of the compact increases. In addition, these two curves provide an upper and lower bound for Young’s modulus of EP particle compacts. In the authors’ view, the lower bound is closer to the true value considering the minor mechanical role of the debris.

Figure 4.9 (b) shows Poisson’s ratio of EP particle compacts as a function of compact density as well as the normalised Poisson’s ratio (휈/휈0) as a function of porosity. As the calculation of Poisson’s ratio is independent of density (Eq. (3.5)), the values obtained from the

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experimental and modified wave velocities resulted in the same Poisson’s ratios. Poisson’s ratio does not show as large a variation with density as Young’s modulus does within this range of compact density (or porosity). It increases up to density 0.25 g/cm3 followed by a decreasing trend however the changes are small (<10% over the whole range). There is no general consensus among researchers about the influence of porosity on Poisson’s ratio.

While some consider Poisson’s ratio as a constant [222], others claim it to be a function of porosity [223-225]. Such debates may arise from the fact that the Poisson’s ratio is usually derived as a function of two other elastic moduli (i.e. Young’s and shear moduli) whose relative dependence on porosity may intensify or supress the dependence of Poisson’s ratio on porosity. The evolution of Poisson’s ratio in the low density compacts seems to be affected by the pore character rather than the solid phase material properties. The compacted bed of

EP particles has a double-porosity structure; intra-particle porosity within the individual particles and inter-particle porosity between the perlite particles. Thus, there are two phenomena which contribute to Poisson’s ratio of the samples: Poisson’s effect of unit cells within individual particles and Poisson’s effect of the whole particle. This suggests that in the low density samples (ρ < 0.15 g/cm3), the bulk elastic response may be dominated by the

Poisson effect of cells as well as the compliance of the inter-particle contact region. The initial contact areas are relatively small and well separated, hence localised lateral deformation (Poisson effect) has a greater probability of intruding into the porous region between particles rather than straining the adjacent particle. Therefore, the overall lateral deformation is reduced, resulting in suppression of the Poisson’s ratio. Further increase in the density reduced the porosity between particles and increased the contact size along with

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increasingly more solid phase material being involved in load transfer throughout the bulk.

Consequently, the lateral deformation in both unit cells and individual particles contributes to the observed Poisson’s ratio.

(a)

(b) (c)

Figure 4.8. (a) Particle density versus particle size. This graph also includes debris density versus

debris size; (b) Inter-particle porosity (excluding debris) versus compact density; (c) Inter-particle

space filled by debris versus compact density.

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(a)

(b)

Figure 4.9. (a) Young’s modulus (E) of packed beds of EP particles versus compact density. (b)

Poisson’s ratio of packed beds of EP particles versus compact density. In both graphs, the upper and

right hand scales allow the normalised moduli versus porosity to be read from the same graphs.

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Mathematical models for prediction for Elastic properties of porous

bodies

A large number of empirical and semi-empirical models have been developed to explain the porosity dependence of material properties. The majority of these models are successful in predicting elastic properties within a porosity range of less than 38% (e.g. [222, 226, 227]) and some assume the vanishing of elastic properties at porosity of 50% (i.e. as a result of an implicit assumption of symmetry between pore and solid phase [228-231]). However, this is not valid as many granular and porous materials have measurable elastic properties for porosities greater than 50% (e.g. bodies made of hollow spherical particles [232]).

Consequently, models have been developed which cover the other end of the porosity spectrum (>50%). In this study, four of these models were used to predict the elastic properties of EP particle compacts of different densities. It is noteworthy that when choosing a model, three criteria were considered: (i) interpretation of the physical parameters of the model; (ii) whether standard relations of linear elasticity hold between all moduli; and (iii) the ability of the model to satisfy the boundary conditions. The boundary conditions include the prediction of the solid phase properties at zero porosity and the presence of a critical porosity, or percolation limit, at which particles no longer form a continuous network. Hence stiffness (i.e. E, G, K) goes to zero and the Poisson’s ratio approaches an asymptotic value.

This value has been found to be independent of the Poisson’s ratio of the solid phase but is dependent on the geometry of the solid phase at the critical porosity [233]. Experimental and numerical investigations have shown that, regardless of the solid phase Poisson’s ratio, the

Poisson’s ratio of a porous body asymptotically approaches a fixed value which has been 107

identified differently to be 0.2 [234-236] or 0.25 [223, 237]. Dunn [225] analytically investigated four different pore shapes as a function of the aspect ratio of a spheroid and found pore shape is another factor affecting the asymptotic behaviour of Poisson’s ratio. It was found that the asymptotic value for spherical and needle shaped pores is 0.2 while for disk-shaped pores and penny shaped cracks it is 0. With respect to experimental and analytical findings, the critical Poisson’s ratio is considered to lie in the range 0  cr  0.25

at critical porosity, Pcr . For a granular material, falls within the range of gravity induced packing states Ptap < Pcr < Pgreen, where Ptap and Pgreen are the porosities of the ‘tapped’ and

‘as-poured’ packing states [238]. In the evaluation of the models, the value of Pcr was considered to lie within these bounds in order to preserve its physical interpretation.

It should be noted that particle crushing and the production of debris is not taken into account in any of the models’ assumptions. Hence, it would be more appropriate to apply these models to the modified values. However, to investigate the effect of particle debris on the physical features of the models, the models were applied to moduli determined using both the raw compact densities (hereafter the experimental moduli) and moduli calculated using the modified densities, hereafter the modified moduli. In the following, each model and its physical features are explained, and the applicability of these models to the EP particle compaction data is discussed.

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4.4.1 Phani Models

Phani and Niyogi [239] derived a semi-empirical relation based on a simple model of applying a uniform state of stress on a porous body of constant cross-sectional area and constant length. This model has been found to agree well with the data from many polycrystalline brittle solids over a wide range of porosity [239-242] and is expressed by:

nE E  E0 (1 aP) (4.7) where E and E0 are Young’s modulus at volume fraction porosity P and zero, respectively, and a and nE are packing geometry and pore structure dependent parameters, respectively.

This model satisfies the boundary conditions: E = E0 at P = 0, and E= 0 at P = Pcr = 1/a.

Rice [243] theoretically derived the values of Pcr to be 0.785, 0.964 and 1.0 for the cubic staking of cylindrical, spherical and hexagonal pores, respectively. Knudsen [244] studied the contact area as a function of bulk density and calculated the value of Pcr for rhombohedral, orthorhombic and cubic packing of spherical particles to be 0.26, 0.397 and 0.476, respectively. From the theoretically derived values of Pcr and the existing relationship between Pcr and parameter a (i.e. Pcr = 1/a), the value of a lies in the range1  a  3.85. For random packing with isolated spherical pores, the constants a and were found to be about

1 and 2, respectively [239]. However, the increase in corresponds to the transition of pores from being spherical to being more interconnected.

Phani and Sanyal [245] derived a relation between the shear modulus and Young’s modulus of an isotropic porous solid based on the Mori–Tanaka mean-field approach, in which the

109

elastic properties are obtained by subjecting the inclusion (i.e. pores) to an effective stress or strain field. This relation is given by:

n0 2 E 1 2  E   G   (1 )  0   G (4.8) 3 0 E 3  E  0  0  0  

where G is the shear modulus, E is predicted from Eq. (4.7) and n0 is a constant for a given

data set of a porous material related to pore morphology. The value of n0 can be evaluated using the experimentally measured values of E and G at a single porosity value. This model satisfies the boundary conditions: G = G0 when E = E0 at P = 0, and G = 0 when E = 0 at P

= Pcr.

Predicted values of Young’s moduli from Eq. (4.7) along with the ones for shear moduli from

Eq. (4.8) were used to evaluate Poisson’s ratio by,

E   1 (4.9) 2G as a function of porosity. The required data for pore-free solid phase (i.e. E0, G0 and ν0) were obtained from Table 4.1. Non-linear regression coefficients to fit the model to the experimental and modified moduli are presented in Table 4.5. The regression value for nE in both cases (i.e. based on the experimental and modified moduli) was indicative of the compacts’ pore structure being non-spherical and partially interconnected. The regression value of the constant a (i.e. Pcr = 1/a) gives a Pcr of 1.0. For packed beds of EP particles, the range Ptap < Pcr < Pgreen was experimentally determined to be 0.96 < Pcr < 0.98. Thus, the estimated value of Pcr by Eq. (4.7) is slightly higher than the expected range.

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Table 4.5. Physical parameters of mathematical models applied to the experimental and modified

moduli. The physical parameters of the modified moduli are given in parenthesis.

Model Name Physical Parameters

Phani a = 1 (1); nE = 2.8 (3.095); n0 = 1.104 (1.053); Pcr = 1 (1)

Nielsen β = 0.24 (0.12); Pcr = 0.965 (0.979)

1 Rice bʹE = 0.036 (0.02); bʹG = 0.0327 (0.02); Pcr = 0.976 (0.978)

Wang b = 3 (3.63); c = 3.1(3.08); d = 0.95 (1); Pcr = 1 (1)

Gibson-Ashby C1 = 0.1 (0.068); C1ʹ = 0.1 (0.072); C2 =0.037 (0.026);

C2ʹ = 0.039 (0.0276); Pcr = 1 (1)

1. The subscript E in bʹE refers to Young’s modulus and subscript G in bʹG refers to shear modulus

Application of the Phani model to both the experimental and modified moduli is illustrated in Figures 4.10 (a) - (d). In both cases, Young’s modulus values predicted by Eq. (4.7) show a considerable deviation (see Figures 4.10 (a) and (c)). Although the predicted Poisson’s ratios (Figures 4.10 (b) and (d)) do not follow the same trend as the experimentally measured values, they show slightly better agreement with the ones obtained based on the modified densities. It should be noted that Poisson’s ratio is a small quantity dependent on the differences of other elastic moduli and is hence very sensitive to errors in them [212]. The considerable deviation from the experimental moduli of values predicted by the Phani model might be ascribed to the effect of the shape factor nE as a single parameter to reflect the

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change in porosity as compaction proceeds. This effect is discussed in more detail in Section

4.4.2.

(a) (b)

Figure 4.10. (a) Normalised Young’s modulus versus porosity (based on experimental moduli); (b)

Normalised Poisson’s ratio versus porosity (based on experimental moduli); (c) Normalised

Young’s modulus versus porosity (based on modified moduli); (d) Normalised Poisson’s ratio

versus porosity (based on modified moduli).

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4.4.2 Nielson Model

Nielsen [246] proposed a model for predicting the elastic moduli of porous materials based on the composite sphere assemblage (CSA) approach. CSA considers a porous body to be constituted of congruent composite elements consisting of a spherical pore embedded in a concentric spherical shell of matrix material. It is assumed that the composite spheres are available in an infinite range of sizes and they are distributed in a way where smaller composite spheres fill all the interstices between larger spheres. This model was originally introduced by Hashin and assumed the applied stress on the assembled body is uniformly distributed (hydrostatic) around each inclusion so that strains can be calculated to obtain the elastic moduli for the body. Nielsen set forth to predict the elastic moduli for porous materials by assuming two types of composite elements: one as described above and the other one made of a spherical matrix embedded in a concentric spherical shell of pore. These two types of CSAs defined two bounds of continuous solid phase (isolated pores) and continuous pore phase (isolated solid phase) where transition between them (different mixtures of them) results in porous material with a wide range of porosity of any geometry. The Nielsen model for Young’s modulus and Poisson’s ratio are expressed as:

2E (1 P)(5  7)(P  P) E  0 0 cr (4.10) 2 (5 0  7)(Pcr  P)  Pcr P( 0 1)(15 0 13)

2 (5  7)(P  P)  P P( 1)(5  3)   0 0 cr cr 0 0 (4.11) 2 (5 07)(Pcr  P)  Pcr P( 0 1)(15 0 13) where 훽 is a shape factor characterising the ability of the material to transfer stress and providing information on the shape of the pores and their inter-connectivity. The shape factor

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훽 is in the range 0< β <1. The lower bound, 훽 = 0, is when the pore phase totally surrounds the solid phase (i.e. particle) while the upper bound, 훽 = 1, corresponds to when the solid phase completely surrounds the pore phase (i.e. isolated pores). Hence, the lower value of 훽 correlates with highly interconnected pores and smaller contact areas between particles, while higher values of 훽 indicates that pores are becoming increasingly more isolated.

The Nielsen model satisfies the boundary conditions at zero porosity and correctly predicts both of the solid phase elastic moduli (i.e. E = E0, 휈 = 휈0). It also predicts the presence of the critical porosity at which Young’s modulus goes to zero and Poisson’s ratio is given by

5 0  3  Cr  . Given that Poison’s ratio for an isotropic elastic material lies in the 15 0 13 physically realistic range 0 ≤ 휈0 ≤ 0.5, this model predicts critical Poisson’s ratio to lie in the range 0.09 ≤ 휈푐푟 ≤ 0.23, which does not cover the expected range 0 ≤ 휈푐푟 ≤ 0.25.

This limited range may have a significant effect on the quality of predicted values for

Poisson’s ratio.

Non-linear regression analysis was conducted to fit the Nielson model to the experimental and modified moduli and the results are shown in Table 4.5. The predicted values of Pcr for both the raw compact and modified densities were within the specified range 0.96 < Pcr <

0.98 and the low value of 훽 is representative of a high-volume fraction of pores compared to the solid phase. Figures 4.10 (a) and (b) show that the agreement between the Neilson model and the experimental moduli is not very good. In the case of Poisson’s ratio, the discrepancy can be attributed to the low value of νcr (i.e. 0.09 ≤ 휈푐푟 ≤ 0.23) and the shape factor β.

Similar to nE in the Phani model, the shape factor β in the Nielson model is used as a single

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value to accommodate microstructural change during the compaction of compacts of different densities and with a wide range of pore shapes and geometries. This problem might be alleviated by solving Eqs. (4.7) and (4.10) point by point. The results of this calculation for both of the shape factors (nE and β) as a function of porosity are presented in Figure 4.11

(a). As can be seen, both shape factors change as a function of porosity and the results show the opposite of what was expected. At lower porosity 훽 approaches zero while at successively higher porosities, where the structure is open and interconnected, it approaches 0.5 for the experimental moduli and exceeded the upper bound of unity for the modified moduli. Similar to 훽, the evolution of the shape factor nE with porosity does not follow the expected behaviour defined by Phani and Niyogi. To accommodate these differences, the shape factors were expressed as a function of porosity P, given by:

2 3 n1 S(P) 1P 2 P 3P 4 P  .... n P (4.12) where S is a shape factor, either nE or β and 휂푛 (n = 1, 2, 3, ...) are empirical constants.

Applying the modified form of the shape factor in Eq. (4.12) to the experimental and modified moduli up to n = 4, both Nielson’s and Phani’s models were replotted and are presented in Figures 4.11 (b) and (c). It can be seen that both Nielson’s and Phani’s models for Young’s modulus show close agreement with the experimental moduli when the shape factor was defined as a function of porosity. In the case of Poisson’s ratio, the modified form of the shape factor improved the results of the Phani model but not those from the Neilson model (see Figure 4.11 (c)). Therefore, as the Nielson model does not exhibit good agreement with both the Young’s modulus and Poisson’s ratio, it is not considered to be a good model for the prediction of the elastic properties of EP particle compacts.

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(a) (b)

(c)

Figure 4.11. (a) Shape factor versus compact porosity for the Phani and Neilson models applied to

both the experimental moduli and modified moduli; (b) Modified Phani and Nielson models for

Young’s Moduli as a function of porosity; (c) Modified Phani and Nielson models for Poisson’s

ratio as a function of porosity.

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4.4.3 Minimum solid area (MSA) models

The minimum solid area (MSA) model assumes that the macroscopic elastic response is related to the load-bearing area of the solid phase material. The key assumption in MSA models is that normalised elastic moduli scale according to the minimum area of solid phase

E per unit area in a plane perpendicular to the direction of the applied load, i.e.  MSA. In E0 this context, a common approach is to assume an idealised microstructure, including the regular stacking of solid particles in a void matrix, and the regular stacking of pores (spheres, cylinders, etc.) in a solid matrix. The initial and major development of such models was

Knudsen’s model [244]. Knudsen investigated the ideal microstructure of three particle stackings (i.e. simple cubic, orthorhombic and rhombohedral) and found that the stacking of particles, and hence the pores, is significant. In addition, plotting of the resultant models as a function of porosity on semi-log plots for low to intermediate porosity was approximated by:

bP E  E0 e (4.13) where b is related to particle stacking and hence is a function of pore shape, geometry and alignment with respect to the stress axis. This equation has been criticised [227] for not satisfying the boundary condition that E = 0 at P = 1. However, such criticism is only valid when critical porosity occurs, at about unity. Anderson [247] analytically proved the existence of such exponential dependence on porosity from strain analysis of isolated ellipsoidal pores. He stated that Eq. (4.13) becomes invalid at very high pore fractions where constant b does not reflect pore interactions occurring as the concentration of pores increases. 117

Rice [243] discussed that this relationship (Eq. (4.13)) provides a good approximation for effective properties up to 1/3-1/2 of 푃/푃푐푟 and holds true for all elastic moduli. In attempts to estimate the minimum solid area for higher porosity, Rice and Wang proposed two equations. Rice [248] suggested that the role of pores and solid phase material can be exchanged (i.e. stacking of pores rather than particles) leading to the theoretical equation:

' b (1P / Pcr ) M  M 0 (1 e ) (4.14) where M is the Young’s, shear or bulk moduli and 푏′ is related to the pore stacking. Rice discussed that 푏′ decreases as b increases. For instance, for spherical pores in cubic stacking, the value of b is 2.7 while the value of 푏′ is 0.5. For other pore shapes and stackings, the values of b and 푏′ can be obtained from Figure 2 in [248]. This model predicts zero stiffness as the porosity goes to unity, but it does not satisfy the zero porosity boundary condition

′ since (1 − exp (−푏 (1 − 푃/푃푐푟)) does not go to unity as P goes to zero. Rice explained this by expressing that Eq. (4.14) is a continuation of Eq. (4.13) for higher porosity values and no extrapolation between them is required.

Wang [222] used the ideal model of spherical particles in a simple cubic stacking developed by Knudsen [244] and modified it for real microstructures. The modifications account for misalignment of the uniaxial applied stress, which induces shear and hinge effects at the neck

(the small contact area between two particles). Wang derived a complex relation between porosity and Young’s modulus, and proposed an approximate solution to his exact solution which could satisfactorily cover a wide range of porosity, as given by:

2 3 E  ES exp[(bP  cP  dP  ...)] (4.15)

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where b, c and d are empirical constants. Brown et al. [249] analytically derived the value of b for different idealised pore geometries and orientations and proposed a similar equation to

Wang’s model, but in the context of strength, as given by:

1 2 1 3 1 j ln( / 0 )  bi Pi  (bi Pi )  (bi Pi )  (bi Pi ) (4.16) i 2! i 3! i j! i

where bi is related to the pore geometry and orientation of the ith kind of pore and Pi is the contribution made by pores of the ith kind to the total porosity. Therefore, the constants of

Eq. (4.15) can be expressed in terms of the constants of Eq. (4.16). Wang has shown that the proposed equation with a quadratic exponent can predict the Young’s modulus of a porous material up to a porosity of 38% [222] and additional higher order terms can be included for higher porosities.

The Wang model with a cubic exponent was used for the prediction of elastic moduli of EP particle compacts. Non-linear regression analysis was conducted to fit the Wang and Rice models to the experimental and modified moduli. The results are presented in Table 4.5. The critical porosity value predicted by the Wang model is slightly higher than the specified range

0.96 < Pcr < 0.98, while the value predicted by the Rice model (for both shear and Young’s moduli) is within the range. As shown in Figures 4.10 (a) and (c), the Rice model shows very close agreement with the experimental moduli, however, it did not show such agreement with the modified moduli. Similarly, the Wang model shows better agreement with the experimental moduli than with the modified Young’s modulus values (see Figures 4.10 (a) and (c)). The regression parameters in Wang’s model for the experimental Young’s moduli in terms of the constants in Eq. (4.16), correspond to; b - cylindrical pores aligned

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perpendicular to the loading direction; c - oblate pores (with a ratio of about 0.8) in a cubic stacking; and d - a combination of about 70% cubical pores in <100> orientation with 30% cylindrical pores parallel to the loading direction [250-252], respectively. The interpretation of the regression parameters in Wang’s model for the modified Young’s moduli is similar to those for the experimental moduli, except for constant b (3.63) which corresponds to a combination of about 77% cubical pores in <110> direction with 23% cubical pores in <111> direction. This approximation seems reasonable with respect to the cell shape in EP particles

(Figure 4.3) and the fact that pores can have different directions in a real packing of particles.

The predicted Young’s and shear moduli based on both experimental and modified moduli were found to lie within the simple cubic and rhombohedral packing of pores. For comparison, a similar range of values can be acquired from Figure 2 in [248]. Rice discussed how porous bodies are better modelled by combining two or more idealised pore structures, as opposed to just one. Consequently, the values of 푏′ (Table 4.5) can be ascribed to different combinations of these two pore packing geometries (e.g. simple cubic and rhombohedral) and their interaction as porosity evolves. Poisson’s ratio values were calculated using the predicted Young’s and shear moduli values from Eq. (4.14) and then combining them using

Eq. (4.9). Poisson’s ratio values predicted by the Rice model based on raw compact density show close agreement with the experimentally measured Poisson’s ratio values. However, the deviation of Young’s and shear moduli values predicted by the Rice model based on modified moduli resulted in poor predictive results for Poisson’s ratio (see Figures 4.10 (b) and (d)). As a whole, the Rice model was shown to be successful in predicting the elastic properties of EP particle compacts only when the raw compact density is considered

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4.4.4 Gibson and Ashby Model

Gibson and Ashby derived a semi-imperial model for the relationship between elastic moduli and porosity by employing dimensional arguments (using standard beam theory) for a cellular solid. For simplicity, they assumed cell struts and walls of uniform dimensions, while in reality these will usually be tapered toward, and thinner in, the centre (i.e. due to the effect of surface tension during the foaming process). The correction for this tapering was implemented by arranging the cubic cells in a staggered stacking, so that their members meet at their midpoint. This model has been shown by many authors (e.g. [253-258]) to successfully predict the elastic moduli of closed cell foams, which are given by the following expression:

E 2 (4.17)  C  2 1 P  C ' (1)(1 P) E 1 1 0

G 2 2 ' (4.18)  C2 1 P  C2 (1)(1 P) E0

Where 퐶 and 퐶′ are constants of proportionality, Ø is the volume fraction of solid in the cell- struts ,which can be obtained from the relative area of the struts and faces on a plane section as explained in [259], and the remaining fraction (1− Ø) is the solid contained in the cell faces. The quadratic term describes the contribution of the cell struts bending to the modulus and is the same for open cell foams. The linear term corresponds to the cell walls’ lateral

′ ′ stretching. Gibson and Ashby suggested 퐶1 and 퐶1 should be about unity and 퐶2 and 퐶2 should be about 3/8 for porous materials with 휈0 = 0.33, where these satisfy the boundary

′ conditions at P = 0 and P = Pcr = 1. However, the values of 퐶1 and 퐶1 will change based on

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the volume fraction of solid in the cell struts, the variable geometries of the foam and uncertainty in the value of the solid Young’s modulus, E0 [97]. As a result, the values of these constants depend on the type of foam and vary from one foam to another.

The Gibson–Ashby relation provides a good approximation for the cellular structure of the

EP particles shown in Figure 4.3. For a given porosity and solid fraction of cell struts (Ø =

′ 0.78), the regression analysis yielded the values 퐶1 and 퐶1 in Eq. (4.17) for both the experimental and modified Young’s moduli (see Table 4.5). Application of the Gibson and

Ashby model to the experimental and modified Young’s moduli is presented in Figures 4.10

(a) and (c). This model shows good agreement with the experimental Young’s modulus values. In the case of the modified Young’s moduli, the Gibson and Ashby model demonstrates fair agreement with the moduli for porosity higher than 0.87, while for lower porosity a considerable deviation is observed.

′ G 3 Gibson and Ashby suggested that if 퐶1 and 퐶1 are about unity and  , which holds true E 8 for polycrystalline metallic materials [260], Poisson’s ratio of the foam is about 0.33. Since

′ constants 퐶1 and 퐶1 are not unity (see Table 4.5), this relation does not hold and Poisson’s ratio should be calculated using two elastic moduli. For this purpose, the Young’s moduli from Eq. (4.17) along with the shear moduli predicted from Eq. (4.18) were used to calculate

Poisson ratios by Eq. (4.9). For a given porosity and solid fraction of cell struts (Ø = 0.78),

′ the regression analysis yielded the values of 퐶2 and 퐶2 in Eq. (4.18) for both the experimental

′ and modified shear moduli (see Table 4.5). It is noteworthy that although 퐶1 and 퐶1 are not unity, the ratio of the shear to Young’s moduli is almost 3/8, which gives implicit satisfaction of the boundary condition (explained above). The results for Poisson’s ratio are presented in 122

Figures 4.10 (b) and (d). As can be seen, the Poisson’s ratio values predicted by the Gibson and Ashby model show good agreement with both the experimental and modified Poisson’s ratios. Overall, the Gibson and Ashby model gives a satisfactory means of predicting the elastic properties of EP particle compacts based on the experimental and modified moduli.

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Properties of epoxy resin

The mechanical properties of the cured epoxy resin, with and without dilution with acetone, were measured according to the specified ASTM standards and are presented in Table 4.6.

Table 4.6. Mechanical properties of cured epoxy resin with and without dilution by acetone.

Properties Epoxy/Hardener Epoxy/Hardener/Acetone

Hardness (Shore D) ASTM D-2240 82 57

Compression yield ASTM D-695 103 MPa 3.40 MPa

Compressive modulus ASTM D-695 3170 MPa 1002 MPa

Tensile strength ASTM D638 45.40 MPa 7.50 MPa

Tensile elongation ASTM D-638 7.3 % 3.20%

Tensile Modulus ASTM D-638 2910 MPa 1834.7 (2022.4) 1 MPa

Flexural strength ASTM D-790 184 MPa 35.70 MPa

Flexural Modulus ASTM D-790 7365 MPa 1370 MPa

Poisson’s ratio 0.39 (0.37) 0.41 (0.38)2

Density 1.18 1.14 (g/cm3)

1 & 2. The measured properties using elastic wave tests are given in parenthesis.

Dilution with acetone changed the curing time of the epoxy which was investigated by monitoring hardness change using a durometer (type D). The results presented in Figure 4.12 are indicative of a minimum curing time of 45 days for diluted epoxy as no change in hardness was observed after this period. The dilution with acetone at this ratio reduced the

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mix viscosity of epoxy resin+hardner from 1.80 Pas (with no acetone) to 0.0067 Pas (with

90 wt% acetone); viscosity was measured, shown in Figure 4.13, using RST-Brookfield rheometer and the data were subsequently analysed using the Bingham model [261]. The point for 100% epoxy + hardener is not shown in the graph due to scale limitations.

Figure 4.12. Hardness versus time curve used to determine the curing period of the diluted epoxy.

Figure 4.13. Changes in the viscosity of epoxy + hardener diluted with acetone versus acetone

content. 125

Properties of EP/epoxy foams

4.6.1 Microstructural characterisation of EP/epoxy foams

Scanning electron microscopy was used to examine the microstructure of foam samples before undergoing compression tests. Figure 4.14 shows micrographs taken from cross- sections of the three foam types with the same density. It can be seen that the epoxy has filled the space between the particles and did not penetrate into the perlite particles, which explains the low density of the foams. The SEM images also show good bonding between the perlite particles and the epoxy binder as few gaps were seen at their interfaces. However, this may not have a significant effect on the resulting properties (mechanical, physical, etc.). This can be due to the porous structure as well as the size and volume fraction of the perlite particles.

The porous structure of perlite inhibits a continuous layer of adhesion between the particle and matrix, compared with if there is a solid continuous surface. Regarding the particle size, it has been reported [262] that particles of smaller size have a higher surface area to volume ratio leading to better interfacial interaction with the matrix. The maximum of such interactions for spherical and near-spherical particles was achieved at the size range of nanometer and submicrometer particles [120, 263-265]. It was found that the particle contents in the range 25 - 30 vol% provided the maximum interfacial interaction between the filler (particle) and the matrix. At higher particle content, the overlap of interfacial adhesion between adjacent particles reduced the overall filler-matrix interfacial interaction [263]. In the present study, however, the size of the particles ranged from 1 to 2, 2 to 2.8 and 2.8 to 4 mm and the volume fraction ranged from 46 to 58% (to be explained in Section 5.4).

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Therefore, adhesion between the particles and the epoxy cannot be considered to have had a notable effect on the resulting mechanical properties. This will be investigated further in

Section 4.6.3.

(a) (b)

(c)

Figure 4.14. Micrographs taken from the cross-sections of EP/epoxy foams with a density of 0.15

g/cm3 made with EP particles in the size ranges: a) 1 - 2mm; b) 2 - 2.8mm; and c) 2.8 - 4mm.

In addition, an examination of the micrographs shows fewer gaps (marked on Figure 4.14) between the epoxy binder and the EP particles in the foams of type 1 and 2 than foams of 127

type 3. Hence, it is expected that cracks initiate and develop faster under compressive loading in the foams of type 3 than in the other two types of foam. This will be investigated in detail in Section 4.7.

4.6.2 Volume fraction of the epoxy in EP/epoxy foams

In the following, the volume fraction of the epoxy binder in EP/epoxy foams is quantified by employing an estimation method as well as the measured experimental values. However, the comparison of the results and a discussion of the ability of the estimation method to quantify this parameter are held over until Section 5.4.

4.6.2.1 Estimating the volume fraction of epoxy in EP/epoxy foams from the foam

density

The volume fraction of epoxy Ve in the foams was calculated theoretically from the rule of mixtures given in Eq. (4.19):

Ve  (c  P )/(e  P ) (4.19) where ρc is the composite density, ρp is the particle density and ρe is the epoxy density. It should be noted that the particle densities presented in Table 4.2 cannot be used in Eq. (4.19) since these densities only refer to undeformed particles. During the sample manufacturing process, the compaction pressure effectively changed the density and density distribution of the EP particles (see Figure 4.8 (a)). Therefore, a modified version of Eq. (4.19) was used to estimate the volume fraction of epoxy in the manufactured foams:

(4.20) Ve  D f  DP /e  DP 

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where Df and Dp are the foam density and particle density as a function of compaction pressure (σcomp), respectively:

D f  f (comp ) ; Dp  f ( comp )

To obtain the particle density as a function of compaction pressure, a group of samples, which only contained perlite particles was prepared. To this end, EP particles of known mass were compacted in the same mould used for manufacturing the EP/epoxy foam samples. As the compaction proceeded, the change in height, and hence density, were calculated as a function of compaction pressure. Results illustrating the particle density versus compaction pressure are shown in Figure 4.15 (a).

Using the experimental results and the assumption that there was little or no ingress of epoxy into the EP particles, the foam density Df and particle density Dp as a function of compaction pressure (𝜎푐) can be expressed by the following equations:

D  C  2  C   C (4.21) f 1 C 2 C 3

D    2    P 1 C 2 C 3 (4.22)

The coefficients Ci and αi for the foam density Df and particle density Dp were determined using least squares fitting. The coefficients for the foam density and particle density containing EP particles of three particle size ranges are given in Table 4.7.

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(a)

(b)

Figure 4.15. (a) Foam density as a function of applied pressure. (b) Particle density as a function of

compaction pressure.

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Table 4.7. Coefficients in Equations (4.21) and (4.22) for foam density Df and particle density Dp .

2 2 Particle 퐶1 퐶2 퐶3 푅 훼1 훼2 훼3 푅 size range -0.0114 0.1268 0.1549 0.9876 -0.0078 0.1188 0.125 0.9908 1-2mm -0.0129 0.1313 0.1456 0.9759 -0.0174 0.1574 0.0874 0.9807 2-2.8 mm

2.8-4 mm -0.0146 0.1405 0.1329 0.9792 -0.0066 0.1065 0.1016 0.9908

Using Eqs. (4.21) and (4.22), the particle density and the corresponding foam density at each pressure level were calculated, substituted in Eq. (4.20) and subsequently the volume percentage of epoxy (Ve) was calculated. Figure 4.16 illustrates the volume percentage of epoxy as a function of foam density for the three types of foam.

Figure 4.16. Volume fraction of epoxy versus density of the foam.

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The results show that foams of type 3 have the highest volume percentage of epoxy. In contrast, foams of type 1 show the lowest volume percentage of epoxy versus density. The volume percentage of epoxy increases with the foam density in the range of 0.15 - 0.4 g/cm3 for foams of type 3 but reaches a maximum earlier at 0.38 g/cm3 for type 1 foams. At higher densities, though, a gradual decrease in the volume fraction of epoxy is observed, which will be discussed in Section 5.4.

4.6.2.2 Calculating the volume fraction of epoxy in EP/epoxy foams

The volume fraction of epoxy in each foam sample was calculated from the difference between the mass of the foam and the mass of the EP particles in that foam. Next, the mass of the epoxy was divided by the density of the cured epoxy binder (i.e. 1.14 g/cm3) to get the volume of the epoxy. Dividing the volume of the epoxy by the total sample volume gives the volume fraction of the epoxy binder in that foam sample. Following this procedure, the volume fraction of the epoxy binder in the three types of EP/epoxy foams were calculated and are presented in Figure 4.17. Figure 4.17 shows that the volume percentage of epoxy within the EP/epoxy foams was between 1.9% and 6% and was mostly in the range 2% - 5%.

Though it seems the volume fraction is almost constant, a decreasing trend in the type 1 and

2 EP/epoxy foams and a polynomial trend in the type 3 foams can be noticed. Overall, the results presented in Figure 4.17 show that epoxy occupies a very small portion of the

EP/epoxy foams which explains their low density.

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Figure 4.17. Volume fraction of epoxy binder in EP/epoxy foams of type 2.

4.6.3 Compressive response of EP/epoxy foams

Compressive stress-strain curves for the three types of EP/epoxy foams in the density range

0.15 - 0.48 g/cm3 are illustrated in Figure 4.18. The stress-strain curves show a similar trend, with the maximum stress occurring in the strain range of 0.03 - 0.07, followed by strain- softening. The stress-strain curves were used to evaluate the maximum stress, effective elastic modulus, and modulus of toughness for different foam densities and these are presented in Figure 4.19. Maximum stress is the peak value in the stress-strain diagram; effective elastic modulus is the unloading gradient (details explained in Section 3.4.2); and the modulus of toughness is the area under the stress-strain diagram which indicates the strain-energy density absorbed by the material before it fractures [266]. The compressive stress shows a linearly increasing trend with density (Figure 4.19 (a)), while the effective

1 elastic modulus (Figure 4.19 (b)) and the modulus of toughness (Figure 4.19 (c)) show (𝜌)2 and 𝜌2 trends, respectively. In addition, the results show that the compressive stress and the 133

effective elastic modulus of EP/epoxy foams are independent of the particle size range.

However, a small deviation was observed for the modulus of toughness (Figure 4.19 (c)).

Similar behaviour was observed in Perlite/sodium silicate [188] (explained in Section 2.3.3).

Foams of type 1 and 2 show a slightly higher energy absorption capacity. This can be seen by comparing the stress-strain curves for the three types of foams (Figure 4.18). The stress- strain curves for foams made with EP particles of 2 - 2.8 mm (Figure 4.18 (b)) show a plateau for a significant range of strain and thus a higher energy absorption capacity. This can be ascribed to the morphology of EP particles in the range of 1 - 2 mm and 2 - 2.8 mm which have a larger edge cell thickness (Table 4.3) and contain internal fibre reinforcement (Figure

4.3). Other factors contributing to the increase in the modulus of toughness are better bonding of smaller particles with epoxy when used in foams (Figure 4.14) and slightly higher epoxy volume fractions in the type 1 and 2 foams (Figure 4.17).

(a)

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(b)

(c)

Figure 4.18. Typical stress-strain curves for the different EP/epoxy foam densities of: (a)

Type 1; (b) Type 2; (c) Type 3.

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(a)

(b)

136

(c)

Figure 4.19. Properties of manufactured foams of type 1 ( ⃣ ), type 2 (◇) and type 3 (∆): (a)

Maximum stress versus foam density; (b) Effective modulus versus foam density; (c) Modulus of

toughness versus foam density.

Considering the high volume fraction of EP particles in the manufactured foams, the EP’s properties could have a significant contribution in the resulting foam properties. To measure this contribution as a function of density, several loading-unloading confined compressive tests were conducted on packed beds of EP particles as explained in detail in Section 4.3.2.

As discussed earlier, however, the moduli obtained from these tests were not equal to the

Young’s modulus; they were a function of both the Young’s modulus and Poisson’s ratio.

Therefore, to find the stiffness contribution of EP particles to the effective stiffness of

EP/epoxy foams, a series of additional confined tests was conducted on the EP/epoxy foams, as explained in Section 3.4.2. As the experimental results have already proven that the

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effective elastic moduli of the EP/epoxy foams are independent of particle size, the confined tests were only conducted on the foams of type 2. The measured confined modulus of the EP particles and the EP/epoxy foams as a function of the particle density are presented in Figure

4.20.

Figure 4.20. Confined modulus of EP particles ( ⃣ ) and confined modulus of the foams (◇) as a

function of the density of the packed bed of EP particles.

As can be seen in Figure 4.20, for foams having the same combined mass of EP particles per unit volume as the packed bed samples of EP particles, the effective elastic modulus is generally lower. This is due to friction and interaction between the EP particles. The inclusion of the epoxy as a matrix reduced the friction between EP particles; however, this reduction could not be quantified. The measured effective elastic moduli of the EP/epoxy foams are much closer to the elastic moduli of EP particles than to that of epoxy (1002 MPa). This is clearly indicative of the significant role of EP particles in the stiffness of the EP/epoxy foams 138

and can be ascribed to the high-volume fraction of the EP particles (88 - 94 Vol%) in these foams (i.e. type 2). Though the stiffness provided by the EP particles in the EP/epoxy foams

푈푝푝푒푟 퐿표푤푒푟 cannot be measured using quasi-static mechanical tests, an upper 퐸푃 and a lower 퐸푃 bound can be predicted using the Voigt and Reuss models given by Eq. (4.23) and Eq. (4.24).

The Voigt and Reuss models have been shown to set the upper and lower bounds of the elastic moduli for most particulate micro- and nano-composites [262]. It has been shown that all experimental and predicted values (using models like Kerner [267], Counto [268], Guth [269] and Paul [270]) fall between these bounds:

Lower Ec  EeVe E p  (4.23) 1Ve 

Upper Ec Ee 1Ve  E p  (4.24) Ee  EcVe where E is the elastic modulus and the subscripts p, e and c stand for particle, epoxy and composite, respectively. Figure 4.21 shows an upper and a lower bound for the elastic modulus of EP particles at each foam density. To quantify the contribution of EP particles in the resulting foam stiffness, the effective elastic modulus of the foams as a function of foam density is illustrated. Note that the Reuss model assumes a state of uniform stress and the

Voigt model a state of uniform strain. In solid materials, a perfectly elastic 100% dense system of interacting grains, where each grain is anisotropic and under the Reuss condition, suffers strain (or displacement) singularities or gaps at the grain boundaries. Likewise, the

Voigt condition would lead to stress singularities in the grain boundaries [271]. With regards to the results presented in Figure 4.21, two things can be inferred. Firstly, the EP/epoxy foams show Reuss-like behaviour similar to metals, but are atypical of non-plastic materials. In 139

metals, a Reuss-like state can be maintained because deformation which would lead to displacement singularities can be accommodated through localised plastic deformation. In a similar manner, in EP/epoxy foams the accommodation is through local EP cell wall collapse at the boundaries between particles. The local failure associated with the cell wall collapse releases the stress concentration without affecting the whole structure of the EP particle, which on average behaves in a Reuss-like fashion. Secondly, the particles make a significant contribution to the resulting elastic modulus (or stiffness) of the EP/epoxy foams.

Figure 4.21. Predicted elastic moduli of EP particles using the Voigt and Reuss models. To

quantify the particles’ contributions to the stiffness of the foam, the effective elastic modulus of the

EP/epoxy foams as a function of foam density is presented.

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Damage analysis

The macroscopic observations taken during the tests coupled with post-test microscopic observations were used to understand the deformation mechanisms of the EP/epoxy foams under compressive loading. Figure 4.22 shows a schematic representation of the damage sequence in the EP/epoxy foam samples, which is irrespective of their density and type.

However, the strain of occurrence was different for each type of foam, as denoted by the strain range at which each damage step occurred.

a) b) c) d)

Type 1 ε =5.0-6.8% ε =7.9-10.0 % ε =11.0-13.0 % ε =28.0-40.0 %

Type 2 ε =5.6-7.2% ε =8.0-11.0% ε =12.0-13.0% ε =30.0-46.0%

Type3 ε =3.8-4.2% ε =5.3-6.2% ε = 8.9-10.0% ε =27.0-28.0 %

Figure 4.22. Schematic representation of failure in EP/epoxy foams.

As can be seen, damage started and developed faster in the type 3 foam samples. This can be explained by two factors: interfacial bonding between the particles and the epoxy binder, and the volume fraction of epoxy. Microscopic observations (explained in Section 4.6.1) showed 141

that there is better interfacial adhesion between the particles and the binder as the EP particles get smaller in size. Foams of type 2 and 1 have the higher resistance to the formation and propagation of cracks than foams of type 3. This may be due to the better interfacial adhesion between the particles and the binder and the higher volume fraction of epoxy in comparison with the type 3 foams. According to the macroscopic observations, cracks started to develop in the foam when the stress reaches its maximum, at strains of about 3.8 to 7.0% (Figure 4.22

(a)). Cracks on the wall of the sample developed in the direction of the applied load, while shear type cracks originated from the upper and lower rims. After reaching the maximum stress, inelastic deformation occurred as the sides of the sample barrelled outward under compressive loading. The barrelling effect became more prominent in the samples with larger particle size. For foams of the same type, the barrelling effect reduced as the density increased. As the compressive load increased, the cracks on the sample wall joined together and caused the formation of longitudinal cracks (see Figure 4.22 (b)) due to secondary tensile stresses. These secondary tensile stresses are normal to the applied load and are generated due to transverse deformation (Poisson effect) [272]. Longitudinal cracks resulted in longitudinal splitting along the rim of the sample. At the same time, shear type cracks propagated through the foam and converged at the central part of the sample where horizontal cracks were generated due to the pure compression (see Figure 4.22 (c)). This type of shear failure is common in brittle materials such as ceramics and concrete during compression testing due to the restraining effect of friction on the upper and lower surfaces. The eventual joining of the longitudinal splitting and shear cracks in the sample gave rise to the formation of wedge-like fragments on the sides of the samples (see Figure 4.22 (d)). The development

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and formation of the wedge-like fragments can be better understood by analysing the uniaxial compressive state of stress, assuming frictionless compression:

 0 0   (4.25) ij   0 0 0  0 0 0 where σ is the applied stress. The state of stress can be decomposed into hydrostatic (σhyd) and deviatoric (σdev) stress components:

   2  0 0 0 0  3   3        (4.26) ij   hyd   dev   0 0    0 0   3   3        0 0 0 0  3   3 

The deviatoric stress components can be further divided into two parts, both representing a state of pure shear [124]:

 2  0 0    3  0 0 0   2      0 0  0 0  (4.27)  3   3   0 0 0  0 0     3 

As can be seen, the hydrostatic stress component produces pure compression while the deviatoric component gives rise to shear stresses in the material. The effect of the deviatoric and hydrostatic components of applied stress on the damage of EP/epoxy foams can be observed in the macroscopic pictures such as Figure 4.23, taken from a type 1 sample compressed to a strain of 12%. In these pictures, the propagation of shear cracks from the

143

upper rim and the formation of longitudinal splitting on the wall of the sample can be observed. Figure 4.23 (b) displays the remnants of the sample, which is typical of all of the samples after the tests, showing the significant role of shear and compressive stresses on the failure modes. The shear stress (the deviatoric component) is responsible for the formation of shear cracks in the foams while the compressive stress (hydrostatic component) gives rise to the formation of horizontal cracks. Post-test micrographs taken from the failed samples provide further evidence for the effects of shear and compressive stresses on the failure modes. Figure 4.24 shows the SEM micrographs taken from the wedge-like side of the sample. As can be seen, the particles are uncrushed (Figure 4.24 (a)) and cell walls seem to be fractured along a plane (Figure 4.23 (b)) which could be due to shearing in the sample.

On the other hand, micrographs from the centre of the sample (Figure 4.24 (c)), where horizontal cracks dominate, show a significant difference. A large proportion of the cell walls are crushed which is a typical feature of failure under compression.

(a)

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(b)

Figure 4.23. Macroscopic images showing (a) A sample of type 1 compressed to a strain of 12%

(b) A typical remnant of the samples after the test.

(a) (b)

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(c)

Figure 4.24. SEM images showing (a) Uncrushed EP particles in the wedge-like fractured side of a failed sample; (b) Cell walls of EP perlite particles fractured along a plane; (c) Crushed cells in the

central region of a uniformly compressed sample.

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Measurement of the elastic moduli of EP/epoxy foams using elastic

wave speed

Elastic properties of the EP/epoxy foams were characterised by means of elastic wave propagation (compression and shear) along the cylinder axis of the specimen. In addition, a new series of quasi-static compressive tests were conducted on the EP/epoxy foams in parallel, as the EP particles previously used (Sections 4.6.1 - 4.6.3) were from a different batch. Having all of the samples made from the same particle batch ensured that a more reliable comparison could be made between the properties obtained from the mechanical and elastic wave tests. Compressive stress-strain curves for the new EP/epoxy foams with different densities are illustrated in Figure 4.25.

Figure 4.25. Typical stress-strain curve for different EP/epoxy foam densities.

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Stress-strain curves were used to evaluate Young’s modulus of the foams from the unloading gradient (explained in detail in Section 3.4.2). The results for Young’s modulus obtained using the quasi-static tests are illustrated as a function of foam density in Figure 4.27 and the average values are tabulated in Table 4.8. The Young’s moduli obtained for the new series of EP/epoxy foams were very close to the ones manufactured from another batch of EP particles, presented in previous Section 4.6.3. Determination of Poisson’s ratio of the foam by installation of regular strain gauges was not possible. The strain gauges had a tendency to debond during the compressive test (un-confined one) due to minimal surface contact afforded by voids on the surface of the foam. Therefore, the work was extended to characterise the complete elastic properties of EP/epoxy foams by measuring the velocity of the passage of elastic waves (i.e. longitudinal and shear waves) in the axial direction for a wide range of foam densities. The longitudinal and shear wave velocities of EP/epoxy foam at different foam densities are shown in Figure 4.26. Similar to Figure 4.5 for packed EP particles, both velocities reached a plateau for densities higher than 0.2 g/cm3. This was investigated in packed EP particle beds (details explained in Section 4.3.3) and was ascribed to the relatively constant mass of EP particles which resisted crushing at densities higher than

0.2 g/cm3. In addition, the inter-particle porosity was found to be about 50 Vol%, excluding debris, and in the range 40 - 50 Vol% including debris for compact densities in the range 0.1

- 0.375 g/cm3. In EP/epoxy foams the inter-particle porosity is filled with 3 - 5 Vol% epoxy, as shown in Figure 4.28. A very similar behaviour to the wave velocities in the EP particle compacts (Figure 4.5) is indicative of the dominant role of the EP particles in wave propagation.

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Figure 4.26. The longitudinal wave and shear wave velocities versus foam density.

Figure 4.27. Young’s modulus of EP/epoxy foams versus foam density determined from the elastic wave speed (○) and mechanical tests (∆); and Young’s modulus of the EP particles versus

foam density determined from the elastic wave speed (◇).

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Table 4.8. Elastic properties of EP particles, epoxy resin and EP/epoxy foams.

EP particles EP/epoxy foams

Density Elastic wave tests1 Mechanical tests2 Elastic wave tests

(g/cm3) 퐸 (MPa) 휈 퐸 (MPa) 휈 퐸 (MPa) 휈

0.15 35.6 0.277 54.7 - 115.2 0.172

0.20 130.3 0.287 102.2 - 246.7 0.194

0.25 210.3 0.295 145.2 - 359.7 0.219

0.30 275.6 0.300 175.6 - 454.5 0.245

0.35 326.4 0.301 199.7 - 531.6 0.274

0.40 362.5 0.300 223.7 - 591.6 0.305

0.42 372.8 0.299 253.9 - 610.8 0.318

Density Epoxy resin (Diluted with acetone)

(g/cm3) Mechanical tests Elastic wave tests

1.14 퐸(MPa) 휈 퐸(MPa) 휈

1834.7 0.42 2022.4 0.38

1. Elastic properties of the EP particles are given as a function of the corresponding EP/epoxy foam density.

2. Elastic properties of the EP/Epoxy foams are given as a function of the EP/epoxy foam density

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Figure 4.28. Volume fraction of the epoxy binder in the second series of EP/epoxy foams versus

foam density.

Isotropic elastic properties of the foams were investigated in terms of two elastic constants E and ν, given by Eqs. (3.6) and (3.7), and illustrated as a function of foam density in Figures

4.27 and 4.30, respectively. For comparison, the Young’s modulus results obtained from elastic wave tests are plotted with the ones determined from quasi-static mechanical tests

(Figure 4.27). Both plots follow the same qualitative pattern and show that the Young’s modulus increases with the foam density. However, the measured Young’s moduli from the elastic wave speed are more than twice the values obtained by mechanical tests. Williams and Johnson [273] also reported dynamic moduli (measured using elastic wave tests) were about twice the static moduli for cancellous cell composites. They ascribed this discrepancy to a difference in the strain rate. The difference in strain rate can influence the results for a continuous material by about 10 - 15% [274], which is consistent with the measured values for epoxy resin (Table 4.6), and for granular material by up to about 40% [275]. Nevertheless,

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the observed discrepancy (≥ 100%) cannot be attributed only to the strain rate difference.

There are three other possible hypotheses to explain such a discrepancy. The first is the deformation mechanism of the EP particles during unloading. The foams contain a high- volume fraction of EP particles, consequently not all of the interstices between the particles are filled with epoxy and some particles are in direct contact with each other. In this case (in the absence of epoxy between particles), Hardin [276] explained that both elastic and plastic deformation occurs during the unloading of particulate materials and strain cannot be separated into discrete elastic and plastic components. This will in turn adversely affect the

Young’s modulus measured using quasi-static mechanical tests.

The second possible explanation for this discrepancy could be the strain level at which

Young’s modulus was measured by the mechanical and elastic wave tests. It was hypothesised that loading to 70% of the maximum stress (ISO 13314), which was about 3% strain, could deteriorate the microstructure of EP/epoxy foams by local failure of EP particle cell walls which leads to lowering the stiffness of the material. On the contrary, the material displacements produced by the passage of elastic waves are in the order of a few angstrom

[277], and hence Young’s modulus was measured at very low strains and not affected by microstructural deterioration. To test this hypothesis, one sample with a density 0.26 g/cm3 was loaded to 70% of the maximum load and while the load was held constant, longitudinal elastic waves were propagated through the sample and Young’s modulus was measured. The result, which is designated by a filled black circle in Figure 4.27, not only does not show a lower Young’s modulus value in comparison with previously measured ones but a slightly higher value than the average ones. This result invalidates the above hypothesis and shows

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that loading to 70% of the maximum load does not adversely affect the Young’s modulus and should even provide slightly higher moduli by compressing the foam to a higher density.

This is also demonstrated by conducting cyclic compressive tests on a sample with a density of 0.26 g/cm3. The specimen was loaded to 2.5% of the maximum load, and then unloaded at the same crosshead speed to 2N load. The loading-unloading continued to 70% of the maximum load with a load increment of 2.5%, as shown in Figure 4.29 (a). It can be seen that as the stress increases, the gradient of the unloading path gets steeper which is measured and presented in Figure 4.29 (b). It clearly shows that loading to 70% of the maximum load does not detoriorate the internal microsturcture of EP/epoxy foam but makes the foam stiffer.

Nevertheless, these results show that ISO 13314 cannot give a unique Young’s modulus for

EP/epoxy foams, but only the particular elastic modulus of the material at 70% of the maximum load.

The third hypothesis relates to the deformation of the epoxy ligaments, as well as the deformation of the perlite cell struts. In mechanical testing where the effective Young’s modulus (EMech) is determined from the unloading gradient between 70% and 20% of the

1 maximum load, the unloading displacement is proportional to the compliance . As E Mech

Young’s modulus measured by the elastic waves (EWave) is bigger than the Young’s modulus measured by mechanical tests EWave > EMech, the mechanical testing case is more compliant

1 1  . If the true compressive modulus is taken as EWave , then a larger unloading EWave E Mech displacement (mechanically) is observed than was expected from the pure compressive value,

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1 which would be proportional to . One simple way for a mechanical system to show a EW ave large elastic displacement is in bending or buckling. The epoxy ligaments are oriented so as to respond by bending/buckling (n = 1, both ends of a column pinned). However, wave velocity measurements use small displacements so that direct compressive displacement is the same as the bending displacement. A similar situation occurs within EP particle struts.

This is supported by the experimental results in Sections 4.3.2 and 4.3.3 where the constrained modulus of packed beds of EP particles was measured using quasi-static mechanical and elastic wave tests. That result also showed that for the density range 0.17 -

0.37 g/cm3, the constrained modulus measured using elastic waves was higher than that measured by the mechanical tests by up to about 25%. Therefore, the combined effects of the strain rate difference, yielding of EP particles during unloading, and the buckling deformation in both EP particles and epoxy ligaments may result in a much lower

‘mechanical test’ modulus than the one measured by elastic wave tests.

Notwithstanding, both these properties (i.e. static and dynamic moduli) are useful. For applications where the material is subjected to compressive load, the stiffness of the material is characterised by Young’s modulus obtained using quasi-static mechanical tests. On the other hand, when they are used in a vibrating structure, for example, for sound absorption in buildings, inside the fuselages of aeroplanes and in machinery enclosures, the true elastic properties measured by the elastic wave tests are of importance.

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(a)

(b)

Figure 4.29. (a) stress-strain curves and (b) Young’s modulus measured from the gradient of the

unloading path in Figure 4.29 (a) at different stress level in cyclic compressive tests conducted on a

sample with density of 0.26 g/cm3.

To evaluate the relative contribution of EP particles to the stiffness of EP/epoxy foams,

Young’s modulus of the EP particles measured in Section 4.3.3 were plotted with those of the EP/epoxy foams in Figure 4.27. For foam densities of 0.15 g/cm3 and 0.2 g/cm3, the EP 155

particles contribute to the stiffness of the EP/epoxy foams by 12% and 49%, respectively.

For higher foam densities, however, this contribution reached a constant value of about 62%.

There are three main factors contributing to the stiffness of EP/epoxy foams: i) epoxy binder, ii) EP particles, and iii) the interaction between the EP particles and epoxy binder. The role of the epoxy binder in the stiffness of EP/epoxy foams seems to be almost constant with respect to the constant range (3 - 5%) of the epoxy volume fraction in EP/epoxy foams, as shown in Figure 4.28. However, the contribution of EP particles and the interaction between the EP particles and epoxy binder appear to be variable. This might be ascribed to the number of contact points and the contact size (or contact surface area) among the EP particles as well as the contact size between the EP particles and the epoxy binder. As particles are crushed into smaller particles during foam densification, the number of contact points per unit volume as well as the contact size will increase among the particles, and also between the EP particles and the binder. These result in more mechanical bonds between the constituents and hence an increase in the stiffness of EP/epoxy foams. In low density foams (< 0.2 g/cm3), a greater portion of large EP particles exist (see Figure 4.7) and thus a smaller number of contact points and smaller contact size are present in comparison to foams at higher densities. Beyond 0.2 g/cm3, the intra-particle volume becomes constant. This will be discussed in Section 5.4.

The Poisson’s ratio of EP/epoxy foams, corresponding to the wave speed measurements in

Figure 4.26, were calculated using Eq. (3.7) and are presented in Figure 4.30. It can be seen that Poisson’s ratio of the foams monotonically and almost linearly increases with respect to the foam density. This is indicative of the material’s increasing resistance to change in volume rather than to distort under uniaxial load.

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Figure 4.30. Poisson’s ratio of epoxy resin (••••), foam (○) and packed beds of EP particles ( ⃣ )

versus the foam density.

To investigate the effect of the constituent materials on the foam Poisson’s ratio, Poisson’s ratio of EP particles and the cured diluted epoxy resin are also plotted on the same figure.

Poisson’s ratio of the foams begins lowest, intersects with the Poisson’s ratio of EP particles at 0.38 g/cm3, and approaches the Poisson’s ratio of the epoxy binder with increase in the foam density. Conversely, Poisson’s ratio of the packed EP particles is almost constant with increase in the foam density. However, when the particles and epoxy are combined, the resultant Poisson’s ratio is far from constant. Without epoxy, rotation can occur about the points of contacts between the particles – the inclusion of the epoxy elastically constrains these motions. This situation is similar to the assumptions considered in [278] concerning the elastic behaviour of granular materials as assemblies of randomly distributed particles. Figure

157

5 in [278] shows that Poisson’s ratio increases by decreasing ks/ kn ratio, where ks is the resistance of a contact between two particles to shear displacement and kn is the resistance of a contact to compression along a line connecting the centre of the two particles. The decrease in ks/ kn can be due to: i) increase in kn, ii) decrease in ks, or iii) concurrent increase in kn and decrease in ks. At this stage, it is suggested that the decrease in ks/ kn is responsible for the observed increase in Poisson’s ratio with increase in foam density, however it is not clear which case (i, ii or iii) is active. This will be investigated by numerical simulation in a future study.

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5 Chapter Five: Discussion

Introduction

In Chapter 4, there was a very focused discussion of each specific result. In this chapter, the results from the previous chapters will be discussed in a broader context, which includes: a)

Comparison of the manufacturing methods for EP/epoxy foams with other syntactic foams; b) Comparison of Young’s moduli of packed EP particle beds found experimentally using the oedometric tests and elastic wave tests, as well as the ones predicted using the Voigt and

Reuss models; c) Analysis of the method for estimation of the volume fraction of epoxy binder in the EP/epoxy foams; d) Comparison of the compressive properties of EP/epoxy foams with the foams discussed in the literature; e) Comparison of the damage modes in

EP/epoxy foams under compressive loading with a variety of existing foams.

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Manufacturing method

In this study, EP/epoxy foams were manufactured by the buoyancy method (AU Patent No.

2003205443 [139]), as described in Section 3.3.4. Alternative methods for manufacturing foams were reviewed in Section 2.3.2. In comparison with those methods, the buoyancy method used here has several advantages. These include avoiding breakage of the fragile EP particles during mixing with the epoxy prior to pressing. This is essential for the very low density foams but is also useful for the high density foams. In addition, this method offers the homogeneous distribution of EP particles in the matrix, the feasibility of manufacturing foams with density as low as 0.15 g/cm3 and ease of manufacture.

On the other hand, this method has some drawbacks. In this method, the mixture of EP particles and diluted epoxy binder creates a two-phase system where just the top phase is used and the bottom phase is disposed of. Even though 2 - 5 vol% of the epoxy binder is present in the EP/epoxy foams, a large amount of acetone is required to dilute the epoxy binder (the mixing ratio is explained in Section 3.3.4). This is a large waste of materials as the residual bottom phase, including a large amount of acetone, is thrown away. The second problem is the curing time which is significantly longer (40 days) than the competing methods mentioned in Section 2.3.2 which require from less than 2 days and up to 7 days.

The third problem is compressing EP particles of different mass within a constant volume to obtain different densities. The compression causes breakage and crushing of EP particles and thus reduces the properties which are pertinent to the cellular structure of EP particles, such as the thermal and acoustic insulating properties.

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Of the alternative methods explained in Section 2.3.2, two methods are considered suitable for EP/epoxy foams. The first one involves the filling of a mould with a desired quantity of particles and pouring a pre-measured amount of epoxy over the particles. The other is to fill a mould completely with particles and then measure their mass. This is followed by mixing the particles with an epoxy solution and then transferring the mixture to a mould. Both methods have the advantage of using a small amount of acetone which is contrary to the buoyancy method. In addition, the first method has the advantages of avoiding particle fracture and having accurate information regarding the volume fraction of particles and binder. The second method also has the advantage of a homogeneous distribution of particles within the foam as well as restricting the particles from floating to the surface during foam production. These methods, however, have several disadvantages in addition to those mentioned in Section 2.3.2. The first method has the potential for an inhomogeneous distribution of particles owing to the separation of phases due to differences in the constituent densities. Moreover, there is a possibility of binder concentrating in the lower part of the foam due to gravity, especially as the particles are free to move and do not completely fill the mould. The second method has a high potential to break particles during mixing with the epoxy binder before the moulding process, which is especially of concern for manufacturing of the lowest density foams.

Taking these factors into consideration, the first method, with the constraint of filling the mould completely, has the greater potential for EP/epoxy manufacture. Here, different foam densities could be achieved by using different particle sizes, which have different densities

161

in Figure 4.8 (a), within a constant volume. In addition, using a low viscosity epoxy is suggested rather than diluting standard epoxy with acetone.

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Young’s modulus of packed EP particles

Considering the high-volume fraction of EP particles in the EP/epoxy foams, the Young’s modulus of packed beds of EP particles were required to be determined. For this purpose, oedometer tests (confined quasi-static compressive tests) were conducted on packed EP particle beds, as detailed in Section 4.3.2. However, since the particles in this test were confined, the calculated unloading gradient was equal to the constrained modulus of the packed particle beds and a function of both their Young’s modulus (EP) and Poisson’s ratio

(휈), given by Eq. (4.5). As it was not possible to obtain Poisson’s ratio by oedometer tests, attempts were made to estimate the Young’s modulus of packed EP particle beds using the

푈푝푝푒푟 Voigt and Reuss models (i.e. Eqs. (4.23) and (4.24)) which give an upper 퐸푝 and a lower

퐿표푤푒푟 퐸푝 bound, shown in Figure 4.18. To characterise the complete elastic properties, the work was extended to investigate the elastic properties of packed EP particle beds by measuring the velocity of the passage of elastic waves (i.e. compression and shear) in the axial direction for a wide range of compaction densities.

Compression and shear wave velocity measurements and Eqs. (3.4) and (3.5) were used to measure the Young’s modulus and Poisson’s ratio of a packed bed of EP particles at each compact density (see Figure 4.9). Having determined the Poisson’s ratio of the EP particle beds, the constrained moduli obtained earlier using the oedometer tests were converted to

Young’s modulus, hereafter referred to as the quasi-static Young’s modulus. However, this

Young’s modulus is an estimate as the Poisson’s ratios obtained by the elastic wave tests would be slightly different from the ones that could be obtained from quasi-static testing; 163

Poisson’s ratio from a quasi-static test is expected to be slightly higher. It has been found that

Young’s modulus is dependent on the strain rate or frequency of the tests [1]. Generally,

Young’s modulus increases with strain rate or frequency of the tests. This will in turn result in a lower Poisson’s ratio, as shown for the epoxy in Table 4.6, which was attributed to the difference in the deformation rate of the specimens [2, 3].

For comparison, the estimated Young’s modulus of packed EP particles from the quasi-static tests were re-plotted with the ones predicted using the Voigt and Reuss models as a function of the foam density, as shown in Figure 5.1. In addition, Young’s moduli obtained using the elastic wave tests, in terms of both the experimental compact density and the modified density, are shown in Figure 5.1. As the density is not involved in the calculation of Young’s modulus from the mechanical results, the mechanical results cannot be modified to reflect the correction of density excluding debris.

For the most part, the mechanical test results lie in between the two wave speed determined moduli which could be considered as upper and lower bounds for constrained moduli of EP particle compacts. For a compacted density of 0.1 g/cm3, the constrained moduli determined from mechanical tests is higher than those determined by elastic wave tests. This indicates that an additional resistance to displacement is present in the mechanical tests, i.e. the unloading response observed in the previous work was not truly elastic. It has been widely discussed in the literature that particulate materials yield during unloading, and consequently the true elastic behaviour is restricted to infinitesimal increments of unloading [4, 5].

Therefore, the measurement of elastic properties, especially in low density (high porosity) compacts where the size of inter-particle contacts is very small is best performed by elastic

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wave velocity measurements. In addition, Young’s modulus for a density of 0.1 g/cm3 measured by quasi-static tests do not fall within the bounds of the Voigt and Reuss models which are a simple test of validity. The predicted values of Young’s modulus for most particulate micro- and nano-composites [6] are found to fall within the identified upper and lower bound by the Voigt and Reuss models. The predicted values which fall within these bounds are considered to be valid. Hence, with regards to the elastic wave Young’s moduli and Voigt and Reuss estimations, the quasi-static Young’s moduli for the compacts with a density higher than 0.15 g/cm3 are considered to be valid.

Figure 5.1. Young’s moduli of the packed EP particle beds measured using mechanical tests and

estimated using the Voigt and Reuss models.

Within this range (0.15 - 0.37 g/cm3), the Young’s moduli determined by elastic waves are higher than those determined by the mechanical tests. As these two types of measurement impose strains that differ by 3 - 5 orders of magnitude and occur at widely differing strain rates, they explore different aspects of a material’s behaviour [7, 8] which can influence the 165

results for a continuous material by about 10 - 15% [7], and for a granular material by up to

40% [9]. Nevertheless, the lower and upper bounds determined by the experimental and modified Young’s moduli using elastic-wave tests appear to provide a reasonable range in which the Young’s moduli of packed EP particles can be explored.

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Structural characterisation of EP/epoxy foams

The manufactured EP/epoxy foams had a structure of a packed EP particle bed with the epoxy resin partially filling the interstices. Therefore, the experimental results on the packed EP particle beds presented in Section 4.3.3 helped to understand the structure of packed EP particles and hence the EP/epoxy foams. As mentioned in Section 4.6.3, since the properties of EP/epoxy foams show almost no dependency on particle size, type 2 foams were chosen and the rest of the tests, including the elastic wave speed test, were conducted on this type of foam. Hence, this discussion on the structure of the EP/epoxy foam is based on experiments conducted on only the type 2 foams, with the assumption that other foam types behave similarly.

Using the calculated inter-particle porosity shown in Figures 4.8 (b) and (c), the volume fraction of EP particles in EP/epoxy foams was calculated and is presented in Figure 5.2 (a).

It can be seen that the volume fraction of EP particles increase with the foam density, reaching a peak at a density of 0.375 g/cm3, and then start to decrease for higher foam densities. This can be explained by fracturing of more EP particles into smaller particles and debris, as shown in Figure 4.7, which results in a reduction of the volume of EP particles and hence their fraction in the EP/epoxy foams at high densities (> 0.375 g/cm 3).

In addition, the percentage of porosity at each foam density was calculated as the sum of the inter-particle porosity and the intra-particle porosity. The inter-particle porosity at each foam density was calculated by subtracting the sum of the volume fraction of the EP particles

(Figure 5.2) and the epoxy binder (Figure 4.17) from the total sample volume:

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Vsample  (VParticle  Vepoxy ) Interparticle Porosity  (5.1) Vsample

Intra-particle porosity was calculated by:

 EP Porosity inside one particle size  Pi  1 * f i (5.2)  solid perlite

n Intraparticle Porosity   Pi (5.3) i1 where ρEP is the density of an EP particle of a certain size presented in Figure 4.8 (a),

𝜌solid perlite is the density of the pore free perlite given in Table 4.1, and fi is the fraction of that particle size within a compact. The calculated inter-particle porosity from Eq. (5.1) and the intra-particle porosity from Eq. (5.3) were added together and the total porosity of the

EP/epoxy foams at each density was calculated and is presented in Figure 5.2 (b).

The volume percentage of epoxy in the EP/epoxy foams was estimated using a method introduced in Section 4.6.2.1, and the results for three types of EP/epoxy foams were presented in Figure 4.16. In addition, the epoxy volume fractions in three types of EP/epoxy foams were measured based on experimental data (explained in detail in Section 4.6.2.2) and are shown in Figure 4.17. Both the results showed that the volume fraction of epoxy is influenced by the EP particle size. However, while the estimated values show significant change in epoxy volume fraction with density, the experimentally measured ones show only a slight change in epoxy volume fraction with density. Moreover, the experimentally measured values show that the measured epoxy volume fractions for the type 1 foams were slightly higher than the type 2 and type 3 foams, and that the measured values for the type 2 foams were slightly higher than the type 3 ones. This is reasonable given the fact that smaller

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particles have a bigger surface area per unit volume and thus a larger amount of epoxy is required to cover those surfaces.

(a)

(b)

Figure 5.2. (a) Volume fraction of EP particles and (b) Porosity within inter-particle space (by

consideration of debris) and total porosity in type 2 EP/epoxy foams.

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The estimated values (Figure 4.16) were reasonable for the average behaviour of type 1 and

2 foams of, however they show a significant deviation with the experimentally measured values for type 3 foams. This indicates that there is a particle size limitation, and that the estimation method does not give a reasonable trend for the foams made with EP particles larger than 2.8 mm.

Considering the epoxy volume fraction, the inter-particle and intra-particle porosity as well as the investigation of SEM images, it can be concluded that EP/epoxy foams have a structure which is schematically drawn in Figure 5.3. The porosity inside the EP particles is not drawn but the figure shows how the inter-particle porosity is distributed. In addition, it shows that the epoxy resin is drawn to the EP particles by surface tension while keeping the inter-particle space relatively open. Hence, it can be seen that low density EP/epoxy foams have a similar interior structure to high density foams, but at a different scale. Moreover, it should be noted that though the particle volume fraction in different density foams varies in the range 46 -

58%, the resultant foam density is mainly caused by the density of the EP particles. The higher the foam density, the larger the portion of smaller particles and debris that were shown to have higher densities (Figure 4.8 (a)). Accordingly, the total foam porosity decreases from

91 Vol% to 79 Vol% while the inter-particle porosity reduces from 50 Vol% to 37 Vol%.

This clearly shows that the intra-particle porosity is constant for foams of different density

( 41 - 42 Vol%). Therefore, while the experimental results on the packed EP particles showed

(Figure 4.8 (b)) that the inter-particle porosity was almost constant excluding debris, the real compact structures, which included the debris, had a constant intra-particle porosity. Overall, the porous structure of the EP particles contributed to the porosity of the EP/epoxy foams by

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as much as about 42% and the rest of the foam porosity is related to the packing of EP particles and the void spaces between particles.

(a) (b)

Figure 5.3. A schematic representation of the internal structure of (a) low density and (b) high

density EP/epoxy foams.

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Compressive behaviour and compressive properties

A schematic representation of the compressive stress-strain curves for elastomeric, elastic- plastic, and brittle single-phase foams (i.e. foams that are manufactured from one type of material) is shown in Figure 5.4. They show linear elasticity at low stress levels, followed by a long stress plateau regime truncated by a regime of densification where the stress rises steeply. The gradient of this regime (the initial slope of the stress-strain curve) is considered as Young’s modulus. The linear elastic region is followed by a plateau region which characterises the energy absorption capacity of a foam through the deformation of cells. The final regime of densification is associated with the touching of opposite collapsed cell walls and if compression continues to a higher strain (called densification) the stress-strain curve should reach the elastic response of the solid material from which the cell walls are made.

(a) (b) (c)

Figure 5.4. Schematic representation of compressive stress-strain curves for a) an elastomeric, b) an

elastic-plastic, c) a brittle foam [11].

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As can be seen, no drop after the peak stress has usually been observed in the stress-strain curves for elastomeric foams (Figure 5.4 (a)), while a small drop in elastic-plastic foams

(Figure 5.4 (b)) and a significant drop in the brittle foams or foams with little plasticity

(Figure 5.4 (c)) has been observed. It has also been found that increasing the foam density increases the Young’s modulus and plateau stress, but shortens the strain at which densification occurs [10, 11].

Similar to the single-phase foams explained above, the stress-strain curves for syntactic foams start with an approximately linear region corresponding to the elastic behaviour of the foam until the peak stress is reached. Peak stress designates the point of crack initiation. In some stress-strain curves, the peak stress is followed by a sharp stress drop while in others there is only a slight decrease in the stress level. The sharper stress drop suggests that it is more difficult for cracks to initiate in the matrix which is more prominent as the matrix volume fraction and the strain rate increases [12]. On the contrary, increasing the volume fraction of hollow microspheres decreases the stress drop after the peak stress [13]. These imply that the failure initiation in syntactic foams does not depend on the strength of the hollow microspheres, but is mainly related to the properties of the polymeric matrix. After this decrease, a plateau region starts at which the stress becomes nearly constant for further compression. The plateau region corresponds to the energy absorption in the process of the collapse of cells comprising a microsphere and its surrounding epoxy resin. Syntactic foams with higher volume fractions of hollow microspheres show a larger plateau region. When a significant portion of the microspheres are crushed, further compression results in the densification of the foam which is visible as an upward trend in the stress-strain curve

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following the plateau region. This point is considered the failure point for syntactic foams because at this point most of the load bearing microspheres have been crushed. It is worth noting that these three distinct regions are found to be influenced by the strain rate of the test and the geometry of the samples. As the strain rate increases, the plateau stress level and energy dissipation capacity of the foam increases [14, 15]. Gupta [12, 16] investigated the effects of the specimen aspect ratio on the fracture behaviour and compressive properties. It was found that the peak compressive strength depends on the mechanical properties of the hollow microspheres and matrix resin, and is independent of the specimen aspect ratio.

However, the specimen behaviour during compression shows remarkable differences with respect to the aspect ratio. Specimens with low aspect ratio show no drop after the peak stress and show a shorter plateau region, while specimens with high aspect ratio either show a small decrease after peak stress and a larger horizontal plateau region [16] or a large drop and no plateau regime [12].

A schematic representation of the stress-strain curves in the current study is presented in

Figure 5.5. The damage mechanisms causing these features will be discussed in Section 5.6.

Similar to the foams explained above, there is a linear elastic region ending in a peak stress.

The peak stress is followed by a significant drop in stress i.e. strain softening. Similar behaviour was noticed in the compressive stress–strain curves of expanded perlite/starch foams [17], cenosphere/epoxy syntactic foams [12] and pumice/epoxy composites [18].

Following the strain softening, the stress becomes nearly constant for further compression in the plateau region. Contrary to the single-phase foams and syntactic foams discussed previously, there is no densification regime in the stress-strain curves of EP/epoxy foams.

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The point at the end of the plateau where the stress started to decrease continuously is the failure point (designated in Figure 5.5) for EP/epoxy foams. At this point, the major portion of the structure has collapsed and the remnants are incapable of bearing substantial amounts of load. The compressive stress-strain curves (see Figure 4.18) also show that an increase in a foam’s density increases the peak stress, Young’s modulus, the energy absorption capacity and hence the modulus of toughness of the EP/epoxy foam. This behaviour is similar to the single phase foams and syntactic foams discussed above.

Figure 5.5. Schematic representation of the compressive stress-strain curve for EP/epoxy foams.

To compare the compressive properties of the newly manufactured perlite-based foams with currently available foams, Ashby diagrams of the average compressive strength and modulus of the foams as a function of density are presented in Figure 5.6. The perlite-based foams are illustrated by small red ellipses which set them apart from the other foams. A line with a slope of one is drawn in both Figures 5.6 (a) and (b). All materials lying on lines with this

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𝜎 퐸 slope have the same specific strength ( 퐶) or specific modulus ( 퐶), respectively. Specific 𝜌 𝜌 properties provide a better comparison of different foams having different densities. As shown in Figure 5.6 (a), the specific compressive stress of the newly developed foams in the density range 300 - 440 kg/m3 (0.300 - 0.440 g/cm3) is comparable with that of alumina foam (0.745 g/cm3), aluminium-silicon carbide foam (0.27 g/cm3), closed cell Phenolic foam

(0.035 g/cm3), and closed cell polypropylene (PP) foam (0.030 g/cm3). The specific modulus, however, is lower than alumina foam and aluminium-silicon carbide foam and higher than the other two above-mentioned foams. In addition, the specific compressive stress of the

EP/epoxy foams in the density range of 300 - 440 kg/m3 (0.300 - 0.440 g/cm3) is comparable with EP/starch foam (0.3 g/cm3 and 0.375 g/cm3) [17] and EP/sodium silicate foam containing 0.20 g/ml sodium silicate (0.3 g/cm3 and 0.4 g/cm3) [19] while both foams have lower specific compressive modulus than that of EP/epoxy foams. Additionally, Figure 5.6

(b) does shows that the specific compressive modulus of perlite-based foams in the density range of 155 - 440 kg/m3 (0.155 - 0.440 g/cm3) is comparable with that of rigid closed cell polyurethane foam (0.24 - 0.6 g/cm3), closed cell polyethylene terephthalate (PET) foam

(0.108 - 0.15 g/cm3), closed cell Phenolic foam (0.12 g/cm3), hollow glass microsphere/epoxy syntactic foams (0.139 and 0.27 g/cm3), and closed cell polystyrene (PS) foam (0.05 g/cm3).

Therefore, the newly developed perlite-based foams may be adaptable for applications where similar or better properties can be achieved using this economically advantageous material.

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(a)

(b)

Figure 5.6. Compressive strength (a) and compressive modulus (b) plotted against density for currently available foams (Ashby et al., 2000) and results obtained for perlite-based foams ( ).

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Damage mechanisms under compressive loading

Post-test microscopy observations, coupled with macroscopic observations taken during the tests, revealed the presence of three different failure modes (i.e. longitudinal splitting, shear failure, and compression failure) for all of the EP/epoxy foams regardless of their particle size and density. However, the strain to activate each mode was different for each foam type.

In addition, these observations helped to understand the damage sequence and its correlation with the peak stress, strain softening, plateau region and failure point of the stress-strain curves for EP/epoxy foams, shown in Figure 5.5. The peak stress is the point at which cracks started to appear in the specimens, due to shear stresses in the form of shear type cracks originating from the sample corners, by secondary tensile stresses in the form of longitudinal cracks, and by compressive stresses in the form of horizontal cracks in the sample centre (as explained in Section 4.7). The strain softening might be due to the combined effects of the very low density of the EP/epoxy foams, the small EP cell wall thickness (0.512 - 0.532 µm), the brittle nature of the EP particles, and the brittleness and low volume fraction of the epoxy matrix. Moreover, the development and propagation of longitudinal cracks in the samples causes disintegration of the sample structure which was even more prominent in samples with lower density due to easier lateral deformation under secondary tensile stresses. These together make the foam incapable of bearing a substantial amount of compressive load as the strain increases. The plateau region corresponds to where: i) shear cracks propagated and meet horizontal cracks in the sample centre; ii) longitudinal cracks meet and form longitudinal splitting; and iii) the remaining part of the sample, which is in the shape of an

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hourglass, underwent uniform compressive deformation. The failure point which led to the end of the plateau region corresponds to the formation of wedge-like fragments by the intersection of the longitudinal splitting and shear cracks in the sample and the completion of the collapse of the EP particles along with the surrounding resin matrix.

It is worth noting that similar modes of failure were observed in cenosphere/epoxy [12] as well as in hollow glass microspheres/epoxy syntactic foams under compressive load [16, 20].

On the other hand, in perlite/A356 syntactic foams with densities lower than 1.06 g/cm3 similar modes of failure to the EP/epoxy foams were observed [21]. At higher densities, however, cells deformed layer by layer (e.g. by buckling or bending of the cell walls), in a uniform manner and no shear or wedge-like failure modes were observed [22]. This was explained by the brittle behaviour of the cell walls in foams with densities lower than 1.06 g/cm3. In higher density foams, strain hardening occurred in deformed cell walls which resulted in the successful transfer of stress from the distorted layer of cells to the adjacent areas and thus uniform growth of damage through the whole sample block. Shear-like failure has also been commonly observed in metal foams showing ductile behaviour [23]. For example, in cenosphere/aluminium syntactic foams [24] during compression, deformation was observed to initiate from the upper and lower corners of the sample and developed along the plane of shear at an angle of approximately 45° towards the centre of the sample where compression failure was dominant due to the concentration of the compressive stress in this region. The sheared zone grew layer by layer during deformation and the maximum deformation was observed to occur within the sheared zones and in the centre of the samples.

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However, the fully developed wedge-like failure observed in the EP/epoxy foams was absent

[22].

In metal foams with little plasticity, e.g. Zn−22Al alloy foam [25], the deformation mechanisms mainly consist of brittle crushing and crumbling of cell walls, cell wall tearing and large shear fracture. In all these foams after an initial linear elastic region, the stress-strain curve is characterised by a significant drop in load resistance at the onset of plastic deformation and jagged, oscillatory plateau behaviour associated with the progressive crushing of brittle cell walls (see schematic representation in Figure 5.4 (c)). This is the opposite of what has been observed in ductile metal foams which show little or no drop in load at the beginning of plasticity and smooth plateau behaviour before densification [11].

Polymeric viscoelastic foams have been shown to behave differently [11, 26-29]. These may be further categorised as elastomeric, elastic-plastic or brittle foams. In these materials, linear elastic deformation is controlled by cell struts bending and if they contain closed cells, by cell wall stretching. Under compressive loading, the elastic deformation is followed by the collapse of the cells by elastic buckling in elastomeric foams (e.g. EPDM foam [30]), plastic buckling of cell walls in elastic-plastic foams (e.g. rigid polyvinyl chloride foam [31]), and brittle crushing of the cell walls and formation of shear fractures in brittle foams (e.g. rigid polyurethane [32] and epoxy-based polymeric foams [33]). Deformation mechanisms associated with elastomeric and elastic-plastic foams, particularly the elastic buckling deformation of cell walls and the formation of plastic hinges, was not observed in the

EP/epoxy foams. However, the crushing of cells in the EP/Epoxy foams is similar to what has been observed in other brittle foams.

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The role of the different structural components in the failure is also of interest. X-ray microtomography was recently used in conjunction with finite element modelling in order to study the progressive collapse of glass hollow sphere reinforced epoxy samples under compressive loads [34]. In that study, it was clearly demonstrated that the glass spheres near the centre of the sample are the first to collapse and transfer load to the surrounding epoxy and spheres. Following this, some sphere collapse along 45 degree planes, analogous to our shear planes, was also evident. It is possible that the perlite particles within the samples in the current study underwent a similar collapse sequence, commencing in the central region leading to the shear cracks and splitting, essentially the reverse of the sequence described in

Section 4.7. However, as the core of the sample is not visible in our work, we are unable to clarify this at present. In contemplating the damage sequence, it is necessary to note some fundamental differences between the tomographic study and the work reported here. The volume fraction of glass cenospheres used was quite low (0.3), the cenospheres had quite thick walls (15 microns) compared with perlite (0.32 microns), and perlite is a multi-cellular particle. Therefore, perlite particles under load begin to crush far more easily than cenospheres, however as multi-cellular particles, they can exist in a variety of intermediate states between uncrushed and crushed i.e. they can crush progressively, cell by cell.

These comparisons serve to highlight that failure by a combination of shear, compression and longitudinal splitting observed in this work is characteristic of porous structures consisting of brittle cell walls, although these may be represented to different degrees in different systems.

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6 Chapter Six: Summary

Conclusions

This study investigated the potential of expanded perlite particles (EP particles) in the manufacture of light-weight syntactic foams. The structural, microstructural and physical properties of EP particles were characterised. Two geometrical relationships were suggested for relating the micro-structure of EP particles to their macroscopic properties (Section 4.3.1).

In section 4.3.2, the elastic modulus of packed EP particles beds were measured using quasi- static mechanical tests. However, as the test was conducted in a confined situation, the calculated unloading gradient was not identical to the Young’s modulus of the packed bed of particles but a function of both their Young’s modulus and Poisson’s ratio. Hence in section

4.3.3, the elastic properties of packed EP particles beds, in terms of two isotropic elastic moduli (Young’s modulus and Poisson’s ratio), were characterised using elastic wave speed measurements along the axial direction. Particle distributions within EP particle compacts after compaction showed that as the compact density increases, the percentage of larger particles decreases due to breakage into smaller particles accompanied by the production of debris. Despite this process, it was found that the inter-particle porosity remains relatively constant with increasing compact density. The mass % of debris rises to quite high levels owing to the high mass density of the debris particles, however, the volume of debris never exceeded 20% of the available inter EP-particle space. Due to the formation of debris, the

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experimental compact densities were modified by deducting the debris mass from the total mass of EP particles and new densities were calculated. Young’s moduli calculated based on the experimental and modified density values showed a decrease with porosity. However,

Poisson’s ratio was relatively independent of porosity.

The properties of solid perlite were investigated by sintering powdered perlite into low porosity solid samples and the application of elasticity theories (Section 4.2). The elastic properties of solid perlite were found to be very close to those for solid obsidian reported by

Manghnani et al. [20]. Using these properties of solid perlite, the porosity-elastic moduli relations were investigated in Section 4.4. Four analytical models predicting the elastic moduli of packed beds of EP particles from the properties of the parent material were investigated. Although these models were not developed to explicitly handle debris, the

Wang, Rice, and Gibson and Ashby models showed reasonable agreement with the experimental moduli. However, none of the original models predicted the modified moduli well although the Wang model and the Gibson and Ashby models gave a reasonable average trend. It was shown that modifying the Phani model shape factor and expressing it as a function of porosity can provide a satisfactory means of predicting the elastic properties of

EP particle compacts based on both the experimental and the modified densities.

The ultimate purpose of the EP particles was for the formation of syntactic foams. Thus, the research was extended in Section 4.6 by producing light-weight foams synthesised by dispersing EP particles in a matrix of epoxy. Three types of foams containing different sized particles were fabricated for a density range of 0.15 - 0.45 g/cm3. Quasi-static compressive tests were conducted on the EP/epoxy foams and the effects of particle size and foam density

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variation on the compressive properties were investigated. The compressive stress and effective elastic modulus were shown to be independent of the particle size. However, a slight variation was observed in modulus of toughness as foams made with EP particles in the size range 2 - 2.8 mm showed a slightly higher energy absorption capacity. On the contrary,

EP/epoxy foams showed a strong dependence of the compressive properties on the foam density. The strength increased linearly, peaking at 1.77 MPa, whereas the effective elastic modulus and modulus of toughness increased at parabolically increasing and decreasing rates, respectively. In Section 4.7, post-test SEM observations coupled with photogrammetry during the tests revealed the presence of three different failure modes for all of the foams, regardless of their particle size and density. However, the strain to activate each mode was different for each foam type.

The specific compressive stress of perlite–epoxy foams in the density range of 0.3 - 0.44 g/cm3 was found to be comparable with that of foams such as alumina (0.745 g/cm3), aluminium–silicon carbide (0.27 g/cm3), closed cell phenolic foam (0.035 g/cm3), and closed cell PP foam (0.030 g/cm3). The specific compressive modulus, however, was found to be lower than alumina foam and aluminium–silicon carbide foam but higher than closed cell phenolic foam and closed cell PP foam. In addition, the specific compressive stress of the

EP/epoxy foams in the density range 0.300 - 0.440 g/cm3 is comparable with EP/starch foam

(0.3 g/cm3 and 0.375 g/cm3) [186] and EP/sodium silicate foam containing 0.20 g/ml sodium silicate (0.3 g/cm3 and 0.4 g/cm3) [188] while both foams have lower specific compressive modulus than that of EP/epoxy foams. Nevertheless, the specific compressive modulus of perlite–epoxy foams in the density range 0.155 - 0.44 g/cm3 was found to be comparable with

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those of a number of rigid closed cell foams made from polyurethane (0.4 g/cm3), PET (0.15 g/cm3), phenolic (0.12 g/cm3) and PS (0.05 g/cm3) materials.

In the additional work presented in Section 4.8, the elastic properties of EP/epoxy foams were characterised by means of elastic wave propagation (compression and shear) along the the cylinder axis of the specimens. By adopting an isotropic model, the Young’s modulus and Poisson’s ratio were used to characterise the elastic response of the medium. The young’s moduli obtained using quasi-static compressive tests were compared with those obtained using elastic wave tests. Both followed the same qualitative pattern, however the Young’s moduli measured using elastic waves were more than twice the values obtained by mechanical tests. This discrepancy was explained by the combined effects of the strain rate difference, strain level, yielding of EP particles during unloading, and buckling deformation in both EP particles and the epoxy ligaments. Poisson’s ratio showed an increasing trend with the foam density and appeared to be influenced by the increase in contact surface area between the particles and the matrix as the foam density increased.

In summary, all of the objectives of the current research listed in Section 2.5, have been addressed:

vi. EP particles were introduced as a cost-efficient porous filler to produce light-weight

syntactic foams.

vii. Structural, microstructural, physical, and mechanical properties of EP particles were

characterised.

viii. Three models suitable for predicting the elastic properties of packed beds of EP

particles were introduced. Two of which (i.e. Wang, and Gibson and Ashby) were

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considered to give an average reasonable trend and the other one (i.e. Phani) with our

modified shape factor was introduced to give the best agreement with the data

generated in this study.

ix. An economical light-weight EP/epoxy foam was manufactured.

x. Microstructural, structural, and mechanical properties of EP/epoxy foams were

characterised using the optical and scanning electron microscopy, quasi-static

compressive tests and elastic wave speed tests.

xi. The effects of the EP particle sizes and foam density on mechanical properties and

behaviour of the foam was investigated.

xii. Damage mechanisms occurring during the tests and behaviour of EP/epoxy foams

under compressive loads were investigated.

Future Research

The mechanical properties (e.g. compressive strength and stiffness) of EP/epoxy foams will be improved by improving the bonding between the EP particles and the epoxy binder. Since inorganic fillers such as EP particles generally have a poor affinity with organic resins, they cannot be chemically bonded and the bonding between the EP particles and the resin is through the mechanical retention in their irregular pores. To improve the adhesion, the EP particles could be initially coated with organic compounds and then embedded in the resin matrix. Organic compounds which have three or more ethylenically unsaturated groups, such as acrylates or methacrylates of polyhydric alcohols, have been found to be very effective in bonding inorganic fillers to organic resins [150]. Since not all of the ethylenically unsaturated

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groups in the organic compounds are consumed during the coating step of the EP particles, the coated EP particles would be very reactive and could be chemically bonded to organic resins. As a result of concurrent mechanical and chemical bonds between the EP particles and the epoxy resin, significant improvement in the compressive strength, compressive stiffness and bending strength of the EP/epoxy foams is expected. The mixing ratio of the organic compounds to the EP particles varies in the range 20:80 - 80:20 and the optimum value should be found by experimentation. To this end, the coated EP particles need to be embedded in the matrix of epoxy. However, a different manufacturing method rather than the buoyancy method used in the current study, is recommended. Due to problems associated with the buoyancy method such as an increased curing time, and the breakage and crushing of EP particles at the compression step, it would be well worth investigating other methods.

One promising method would be the filling of a mould completely with the closest particle packing possible and then pouring a pre-measured amount of resin solution over the particles.

However, instead of diluting the epoxy with acetone which degrades the mechanical properties and greatly increases the curing time (see Section 4.5), a low viscosity resin such as CRACKBOND® SLV-302 can be used. This epoxy resin has a viscosity of 195 cP at 24°C and a curing time of 7 days. This manufacturing method would have the advantage of a quicker curing time and a significant reduction in the breakage and crushing of EP particles.

In addition, it would be easy to calculate the volume fraction of the epoxy and EP particles which was a challenge in the current study. Such EP/epoxy foams should be fabricated with different particle size ranges (e.g. 0.710 – 1 mm, 1 - 1.18 mm, 1.8 - 1.40 mm and 1.40 - 2.0 mm) to cover a density range of 0.15 - 0.45 g/cm3. The structural, microstructural, mechanical

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and thermal properties of the foams would be investigated, and the optimal mixing ratio of the organic compounds to EP particles, in terms of the resultant properties, would be determined. Moreover, as one of the main applications of syntactic foams is to use as the core material in sandwich plates and shells, additional work to attach a stiff skin to the top and bottom of the core should be undertaken. The skin itself could be a composite of one of three types: i) glass fibre/epoxy, ii) carbon fibre/epoxy, and iii) hybrid glass/carbon/epoxy. The prepared panels would then be subjected to flexural and fatigue tests, and the results would be analysed and the best sandwich panels determined.

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