i

IMPACT CHARACTERISTIC AND ENERGY ABSORPTION OF AUXETIC

FOAM-FILLED SQUARE TUBES

SAEID MOHSENIZADEH

A project report submitted in partial fulfilment of the

requirements for the award from the degree of

Master of Engineering (Mechanical)

Faculty of Mechanical Engineering

Universiti Teknologi Malaysia

JANUARY 2015

ii

I declare that this project report entitled “Impact Characteristic And Energy

Absorption Of Auxetic Foam-Filled Square Tubes” is the result of my own research

except as cited in the references. The project report has not been accepted for any

degree and is not concurrently submitted in candidature of any other degree.

Signature : …………………….

Name : SAEID MOHSENIZADEH

Date : January 2015

iii

To my beloved parents and my dear brother, for their endless support and

encouragement.

iv

ACKNOWLEDGEMENTS

First and foremost, I would like to express gratitude to my supervisor Dr.

Zaini Ahmad for his valuable advices and constant support throughout this project.

I also would like to thank, PhD student, Mr. Mozafar Shokri Rad, Mr. Ali

Farokhi Nejad and PhD student, Mr. Roozbeh Alipour for their assistance during

this project.

Last but not least, a warm gratitude and sincere appreciation to my beloved

father, mother, brother and my grandmother peers for their endless support.

v

ABSTRACT

Auxetic materials have recently been gaining popularity within the research

community due to their enhanced mechanical properties, particularly energy

absorption performances. Unlike conventional materials, they exhibit a negative

Poisson’s ratio when subjected to a uniaxial loading. This present research

experimentally and numerically investigates the crush response and energy

absorption performances of auxetic foam-filled square tubes under axial loading.

For comparison, the crush response and energy absorption of empty and

conventional foam-filled squares tubes have also been examined with respect to

deformation modes and force displacement curve. Standard compression tests were

conducted on a series number of thin-walled tube samples. In addition to this, the

fabrication process of conventional and auxetic foam has also been described in this

project report. An additional compression test on conventional and auxetic foam has

also been conducted to observe the behavior of foam itself. It is evident that the

auxetic foam-filled square tubes are superior to empty and conventional foam-filled

square tubes in terms of energy absorption capacity. It shows that such tube is

preferable as an impact energy absorber due to their ability to withstand axial loads

effectively. Furthermore, it is found that the load capacity increases as the crush

length increases. Parametric study shows energy absorption increases as aspect ratio

increases whereas energy absorption decreases with increasing slenderness ratio.

The primary outcome of this study is design information for the use of auxetic

foam-filled square tubes as energy absorbers where impact loading is expected

particularly in crashworthiness applications.

vi

ABSTRAK

Bahan Auxetic baru-baru ini telah manjadi semakin popular dalam komuniti

penyelidikan kerana sifat mekanikal nya dipertingkatkan, terutamanya persembahan

sifat tenaga. Tidak seperti bahan konvensional, bahan ini menunjukkan nisbah

Poisson yang negatif apabila dikenakan beban ekapaksi. Kajian iniyans dilakukan

secara eksperimen dan berangka felah menyiasat kelakuan hentaman dan sifat

penyerapan tenaga tiab yans diisikan bahan auxetic di bawah paksi beban. Sebagai

perbandingan, sambutan menghancurkan dan tenaga penyerapan bagi tinb kasong

dan konvensional diisikan tius juga telah diperiksa berkenaan dengan mod ubah

bentuk dan lengkung anjakan. Ujian mampatan standard dijalankan ke atas beberapa

siri sampel tiub berdinding nipis. Di samping itu, proses fabrikasi baban

konvensional dan auxetic juga telah diterangkan dalam tesis ini. Ujian mampatan

tambahan pada babam konvensional dan auxetic juga telah dijalankan untuk

memerhatikan kelakuan baban itu sendiri. Ia adalah jelas bahawa auxetic yang telah

diisi adalah lebih baik daripeda tiub kosong dan tiub berisi konvensional

penyerapan tenaga. Ini menunjukkan bahawa tiub itu adalah lebih baik sebagai

penyerap tenaga kesan kerana kemampuan mereka untuk menahan beban paksi

berkesan. Tambahan pula, didapati bahawa kapasiti beban yang meningkat di mana

panjangnya bertambah menghancurkan. Kajian parametrik menunjukkan

penyerapan tenaga bertambah apabila nisbah aspek meningkat manakala

penyerapan tenaga berkurangan dengan peningkatan nisbah kelangsingan. Hasil

utama kajian ini adalah maklumat reka bentuk untuk penggunaan auxetic yang

penuh dalam tiub sebagai penyerap tenaga di mana kesan dijangka terutamanya

dalam aplikasi hentaman.

vii

TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENTS iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF ABBREVIATIONS xvi

1 INTRODUCTION 1

1.1 Introduction 1

1.2 Background of the Study 2

1.3 Problem Statement 4

1.4 Objective 4

1.5 Scopes of the Study 4

1.6 Importance of the Study 5

1.7 Structure of the Thesis 5

2 LITERATURE REVIEW 6

2.1 Introduction 6

2.2 Fabrication of Auxetic Materials 9

2.2.1 Methods for the Conversion of Polymeric

Foams 9

2.2.1.1 Multi-Pase Auxetic Fabrication 10

2.2.1.2 Solvent Based Auxetic

viii

Fabrication 11

2.2.1.3 Vac-Bag Auxetic Fabrication 11

2.2.1.4 Dual Density Auxetic Fabrication 12

2.2.1.5 Fabrication of Auxetic Closed-

Cell Foam 13

2.2.1.6 Manufacturing Parameters of the

Auxetic Foams 13

2.2.2 Fabrication Methods of Metallic Foams 14

2.2.3 Microporous Polymer Fiber 14

2.2.4 Fabrication of Polymeric Composite 16

2.2.5 Molecular Auxetic Polymers 18

2.3 Geometrical Structures and Models 20

2.3.1 Proposed Structures for Modeling the

Foams 21

2.3.2 Re-Entrant Structures 23

2.3.2.1 Two-Dimensional Re-Entrant

Structure 23

2.3.2.2 Three-Dimensional Re-Entrant

Structures 24

2.3.3 Chiral Structure 25

2.3.4 Star-Shape Structure 26

2.3.5 Rotating Units 27

2.3.6 Angle-Ply Laminates 28

2.3.7 Hard Molecules 28

2.3.8 Microporous Polymer Mode 28

2.3.9 Liquid Crystalline Polymer Model 29

2.3.10 Disordered Structures 29

2.4 Experimental on Auxetic Materials 30

2.5 Application of Auxetic Materials 33

2.6 Thin-Walled Structures 37

2.7 Energy Absorption Indicators 39

2.7.1 Peak Force, FMAX 39

2.7.2 Energy Absorption, EA 40

ix

2.7.3 Crush Force Efficiency, (CFE) 40

2.7.4 Specific Energy Absorption, (SEA) 41

2.8 Comparison Energy Absorption of Thin Walled

Structures on Varying Geometry 42

3 RESEARCH METHODOLOGY 44

3.1 Introduction 44

3.2 Research Methodology and Procedure 44

3.3 Experimental Methodology 45

3.3.1 Fabrication Process of Polyurethane Foam 46

3.3.2 Modified Fabrication Process of Auxetic

Foam 46

3.3.3 Determination of Poisson’s Ratio 48

3.3.4 Effect of Various Hydraulic Pressure,

Heating Time and Heating Temperature on

Auxeticity of Foams 51

3.4 Specimens Preparation 52

3.4.1 Material Properties of Tubes and Foams 53

3.4.2 Quasi-Static Compression Test on

Specimens 56

3.5 FE Simulation 57

4 RESULTS AND DISCUSSION 61

4.1 Introduction 61

4.2 Experimental Results 61

4.2.1 Experimental Results of Aluminum Tube

(25x25x50) 63

4.2.2 Experimental Results of Aluminum Tube

(50x50x50) 65

4.3 FE Analysis and Validation 67

4.3.1 FE Results of Aluminum Tubes (EAT, CFFT,

AFFT) 67

4.3.2 Comparison Initial Peak Load of Tube

(25x25x50) 71

4.3.3 Specific Energy Absorption of Tube(25x25x50) 71

x

4.3.4 Crush Force Efficiency (Load Ratio) 72

4.4 Parametric Study 73

5 CONCLUSION 77

REFERENCES 78

xi

LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Discovery and development of auxetic materials 20

2.2 Important applications of auxetic materials 37

3.1 Poisson’s ratio for various hydraulic pressures, heating time

and heating temperature.

52

3.2 Tubes material properties 54

3.3 Material properties of foams 56

4.1 Parametric study (a) Thickness ratio, (b) Height ratio. 74

4.2 Crashworthiness indicators; (a) various thickness, (b) various

height 76

xii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

1.1 (a) Honeycomb structure with positive Poisson’s ratio,

(b) Re-entrant structure with negative Poisson’s ratio

3

1.2 Reaction of conventional and auxetic materials into the

vicinity of the impact

3

2.1 Conventional and auxetic material 6

2.2 Differences between (a) a positive and (b) a negative

Poisson’s ratio material

7

2.3 (a) Timeline for the discovery of natural and man-made

auxetic materials, (b) areas where auxetic materials have

been discovered and their size (adapted from Ref. (Evans,

2000)).

8

2.4 The microstructure of the closed-cell foam. Left: free

foaming, Right: under compression.

13

2.5 The structure used for modeling polymeric auxetic

materials 15

2.6 The specially designed extrusion rig 16

2.7 Helical auxetic yarn 17

2.8 Force-displacement diagram for auxetic and conventional

polypropylene fibers

18

2.9 Close packed structure of hard cyclic hexamers 19

2.10 Molecular structures of auxetic materials 19

2.11 Proposed structures for modeling the foams in 2D case;

(a) hexagonal honeycomb, (b) diamond-shaped

honeycomb, (c) rotation of rigid units model

21

2.12 Rotation of rigid units structure: (a) the conventional

xiii

model for conventional foams, (b) the rotation of rigid

units model for auxetic foams, (c) an idealized model

22

2.13 Proposed structures for modelling the foams in 3D case;

(a) rhombic dodecahedron, (b) tetrakaidecahedron, (c)

elongated dodecahedron structures

22

2.14 Basic geometry of re-entrant structures 23

2.15 Two-dimensional re-entrant structures 24

2.16 Three-dimensional re-entrant structures 25

2.17 Chiral structures with different cells; (a) made by the

same units, (b) Made by different symmetrical units

26

2.18 A typical type of star-shaped auxetic structure 26

2.19 Different geometries of rotating units 27

2.20 Auxetic laminated angle-ply composite: (a) Structure, (b)

Model.

28

2.21 Liquid crystalline polymer model: (a) Undeformed shape,

(b) Deformed shape.

29

2.22 A typical disordered auxetic structure made of different

auxetons. 30

2.23 SEM images of conventional and auxetic foam

specimens. (a): conventional foam, (b): auxetic open cell

foam.

31

2.24 Optical microscopy of polyester urethane foam. 32

2.25 Schematic of the laser system used for measuring

Poisson’s ratio.

33

2.26 Collision energy absorbing thin-walled components 38

2.27 Crush box structures (thin-walled structure) 39

3.1 Established design process flow 45

3.2 Different stages of PU foam fabrication process 46

3.3 Hydraulic oil pump and thick-walled aluminum cylinder 47

3.4 Sizing and covering polyurethane foam 47

3.5 Conversion of Honeycomb Micro Structure to Re-entrant

Micro Structure 48

3.6 Heating step 48

xiv

3.7 Compression test set-up (a) High speed camera (b)

Tested sample (c) Processed image

49

3.8 The auxetic foam specimen under ith compression stage 50

3.9 Specimen’s configuration 53

3.10 Tensile test 53

3.11 True Stress-Strain curve; (a) Aluminum tube (25x25x50),

(b) Aluminum tube (50x50x50) 54

3.12 Compression test on foam 55

3.13 Material properties of foams; (a) conventional foam, (b)

auxetic foam

55

3.14 Instron compression test machine 57

3.15 Deformation modes of specimen 57

3.16 Geometry representation; (a) Empty square aluminum

tube, (b) Foam

58

3.17 Boundary conditions 59

3.18 Mesh convergence study 60

4.1 A typical relationship of force versus displacement of

axial crushing behavior with progressive folding 62

4.2 Deformation mode of square tube (25x25x50) 63

4. 3 Load–displacement curve of aluminum tubes(25x25x50) 64

4. 4 Energy absorption capacity of tubes (25x25x50) 65

4.5 Deformation mode of square tube (50x50x50) 65

4.6 Load–displacement curve of aluminum tubes (50x50x50) 66

4.7 Energy absorption capacity of tubes (50x50x50) 66

4.8 Comparison among numerical and experimental

deformations; (a) EAT, (b) CFFT, (c) AFFT

68

4.9 load-displacement curve; (a) EAT, (b) CFFT, (c) AFFT 69

4.10 Comparison of energy absorption capacity of

experimental and finite element; (a) EAT, (b) CFFT, (c)

AFFT 70

4.11 Effect of foam as a filler on the initial peak load 71

4.12 Comparison specific energy absorption of (EAT, CFFT,

AFFT) 72

xv

4.13 Comparison crush force efficiency of (EAT, CFFT,

AFFT)

73

4.14 Paramedic study variables 74

4.15 Parametric study according to; (a) Thickness ratio, (b)

Height ratio 75

xvi

LIST OF ABBREVIATIONS

EA - Energy Absorption

SEA - Specific Energy Absorption

CFE - Crush Force Efficiency

EAT - Empty Aluminium Tube

CFFT - Conventional Foam-Filled Tube

AFFT - Auxetic Foam-Filled Tube

CHAPTER 1

INTRODUCTION

1.1 Introduction

Higher requirements of improving the crashworthiness efficiency of vehicle

structures have drawn growing attention to minimize injuries of drivers and

passengers in crashing events. The utilization of the energy absorption devices with

high crashworthiness capacity and desirable deformation characteristics has become

more and more prevalent. In this respect, energy absorbers allow the vehicle

structures to maximize absorption of the kinetic energy yielded during the impact

process and to minimize the impact forces transferred from vehicle structure to

occupants. Over the past decades, research interests in crashworthiness have resulted

in a series of systematic investigations into crash responses of various thin-walled

tubal structures with different cross-sectional geometries and wall materials via

analytical, experimental and numerical approaches. From the energy absorption point

of view, tubal structures are capable of carrying substantial loads for leading to

desired deformation, which are much higher than the corresponding ultimate or

buckling loads (Abramowicz & Wierzbicki, 1988).

Advanced materials are playing an increasingly important role in improving

crashworthiness of thin-walled structures. Auxetic material as a filler of tubes is

considered as new candidates for energy absorbers.

2

1.2 Background of the Study

Materials can be divided into two basic categories: structural or functional.

Development of structural materials is focused on improving their mechanical or

physical properties, often with a saving in weight or cost. By contrast, functional

materials are designed to detect and/or respond to events or stimuli that occur during

their lifetime. These materials often display novel and counterintuitive behavior.

Materials that contract when heated, and those that expand when subjected to

hydrostatic pressure. For example is a remarkable class of materials known as

auxetic materials (Evans, 1991(b)), when stretched lengthways, these materials get

fatter rather than thinner.

As well as this unique characteristic, auxetic materials have enhanced

mechanical and physical properties, which mean that they can actually be classified

as both structural and functional materials.

The key to auxetic behavior is a value known as Poisson's ratio. It determines

how the thickness of the material changes when it is stretched lengthways. When an

elastic band is stretched the material becomes thinner, giving it a positive Poisson's

ratio. Indeed, most solids have a Poisson's ratio of around 0.2-0.4. Poisson's ratio is

determined by the internal structure of the material. For example, consider a two­

dimensional honeycomb deforming by hinging of the ribs forming the network (see

Figure 1.1). For the conventional hexagonal geometry (see Figure 1.1(a)), the cells

get longer in the x-direction and close up along the y-axis when the material is

stretched along the x-axis, giving a positive value for Poisson's ratio. Modifying the

honeycomb cell geometry to adopt a 're-entrant' structure (see Figure 1.1(b)) means

that the network gets longer in both the x- and y directions when it is stretched,

giving it a negative Poisson's ratio and making the material auxetic (Almgren, 1985).

3

(a) (b)

Figure 1.1 (a) Honeycomb structure with positive Poisson's ratio, (b) Re-entrant

structure with negative Poisson's ratio (www.hkrita.com).

Auxetic materials are interesting both because of their novel behavior and

because of enhancements in other material properties that are related to Poisson's

ratio. For example, hardness can be increased in an auxetic material (see Figure 1.2).

When an object hits an auxetic material and compresses it in one direction, the

auxetic material also contracts laterally material 'flows' into the vicinity of the

impact. This creates an area of denser material, which is resistant to indentation.

Importantly, elasticity and hence auxetic behavior does not depend on scale.

Deformation can take place at the macro-, micro- or even molecular level; this means

that we can not only consider auxetic materials, but also auxetic structures.

Figure 1.1 Reaction of conventional and auxetic materials into the vicinity of the

impact

4

1.3 Problem Statem ent

Thin-walled tubes with different filler are widely used as energy absorbing

structural components in high-volume automotive and aviation industries. Large

deformation occurred when exposed to the crash event, so auxetic material as filler

has been paid attention by automotive industries with the aims of weight reduction

and increasing energy absorption capacity. A large number of experimental works

has been done on auxetic materials, fabricated with a number of modified methods.

In the present research, attempt has been done to do analytical and finite element

modeling, modifying the fabrication process, also effect of foam as filler on thin-

walled tubes have investigated the energy absorption capacity.

1.4 Objective

The primary objective of this thesis is to examine the crush response and

energy absorption capacity of auxetic foam-filled square tube under axial loading

1.5 Scopes of the Study

The scope of this project includes the following aspects:

a) Develop preliminary models of thin walled tubes (empty and foam

filled)

b) Fabrication of auxetic foam and testing samples

c) Conduct quasi-static compression test on the samples

d) Develop detailed FE model and validate the FE model

e) Conduct a series of parametric study on energy absorption of empty

and filled tubes with respect to varying geometry

5

1.6 Im portance of the Study

As the advancement in automotive technology, number of accident is in rise,

this automatically increases the importance over the safety of the drivers and

passengers. This made automotive engineers to develop structures which can reduce

or eliminate the effect of accident on occupant.

Tubular structures provide the widest range of possible energy absorbing

systems for any simple structure. Apart from their use as energy absorbers, their

common existence as structural elements implies in strict energy absorption

capability in the largest part of the vehicles structures. This study focuses on energy

absorption capacity of foam-filled tube on vehicles.

1.7 S tructure of the Thesis

Chapter 2 involves some of the literatures reviewed and provides the reader

with a general understanding of the auxetic material and crashworthiness concepts,

are introduced in Chapter 2, the methodology used in this research and the

established process of fabricating auxetic foam, experimental tests, and simulation

are explained in Chapter 3.

Comparison of energy absorptions of empty tube, conventional foam-filled

tube and auxetic foam-filled tube for two different geometries and validation of finite

element analysis with experimental tests are presented in Chapter 4.

Finally a conclusion is made in Chapter 5 through comparison of energy

absorptions of empty tube, conventional foam-filled tube and auxetic foam-filled

tube.

78

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