(Fabrication, Properties and Applications) · 2015. 11. 19. · HOSSAM IBRAHIM YOUSIF YOUSIF Instructor in the Egyptian Atomic Energy Authority ... • Can be used in the pumps and

Helwan University Faculty of Engineering, Mataria Mechanical Design Department

Auxetic Polyurethane Foam

(Fabrication, Properties and Applications)

By

Eng.\ HOSSAM IBRAHIM YOUSIF YOUSIF Instructor in the Egyptian Atomic Energy Authority

A Thesis submitted to Helwan University In Partial Fulfillment of the Requirements for the Degree of

Master of Science in Mechanical Design Engineering

Under Supervision of

Professor, Dr. Eng. Associate Professor, Dr. Eng.

Alaa Mohammed EL-Butch Tarek Hussien EL-Mahdy Vice Dean for students affairs Mechanical Design Department Faculty of Engineering, Mataria Faculty of Engineering, Mataria Helwan University Helwan University

Assistant Professor Eng.

Khaled Mohammed Zied Mechanical Design Department Faculty of Engineering, Mataria

Helwan University

Cairo 2012

Helwan University Faculty of Engineering, Mataria Mechanical Design Department

Auxetic Polyurethane Foam

(Fabrication, Properties and Applications)

By

HOSSAM IBRAHIM YOUSIF YOUSIF

Instructor in the Egyptian Atomic Energy Authority

A Thesis Submitted to Helwan University In Partial Fulfillment of the Requirements for the Degree of

Master of Science in Mechanical Design Engineering Approved by the Examining Committee:

Prof. Dr. Eng.\ Ramadan Ibrahim El-Seoudy ( )

Professor in Mechanical Design Department-Faculty of Engineering -Suez Canal University

Prof. Dr. Eng.\ Younes Khalil Younes ( )

Professor in Mechanical Design Department-Faculty of Engineering, Mataria-Helwan University

Prof. Dr. Eng.\ Alaa Mohammed EL-Butch ( Thesis Advisor )

Professor in Mechanical Design Department-Faculty of Engineering, Mataria-Helwan University

( )

Assoc. Dr. Eng.\ Tarek Hussien EL-Mahdy ( Thesis Advisor )

Assoc. Prof. in Mechanical Design Department-Faculty of Engineering, Mataria-Helwan University

( )

Cairo 2012

i

Abstract

Modern technology requires new materials of special properties. For the last two decades

there has been a great interest in a class of materials known as auxetic materials. An auxetic

material is a material that has a negative Poisson's ratio which means that this material expands

laterally when they subjected to a tensile force unlike most of the other traditional materials. This

material has superior properties over the traditional material such as high shear modulus and high

impact resistance, which makes this material a good candidate for many engineering applications.

In the present research work, auxetic flexible polyurethane polymeric foams having different

densities were fabricated from conventional flexible polyurethane polymeric foam at different

compression ratios. The microstructure of conventional and processed foams was examined by

optical microscope to compare between the two structures. The microstructure of processed foam

was compared with the one presented in the literature and it has shown the auxetic structure

configuration. This is the first time to produce auxetic foam in Egypt.

Conventional and auxetic foam samples having cylindrical and square cross-sections were

produced from foams having different densities (25 kg/m3 and 30 kg/m3). The compression ratios

used to produce the auxetic samples are (5.56, 6.94 and 9.26). Four mechanical tests were carried

out to get the mechanical properties for both conventional and auxetic foams. Two quasi-static

mechanical tests "tension and compression" and two dynamic mechanical tests "Hysteresis and

resilience" were carried out to compare between the conventional and auxetic foams.

The quasi-static tensile test was carried out at speed was adjusted to be position control rate

of 0.2 mm/s. The compression and hysteresis tests were carried out at strain control rate of 0.3 S-1.

The data recorded from the machine were stress and strain. The modulus of elasticity and Poisson’s

ratio of the test samples were obtained from tensile and compression tests. Poisson’s ratio of the test

samples was measured using video measurements using a dedicated Matlab and Get Data Graph

Digitizer programs.

Generally, the auxetic behaviour was observed for most of the processed foam. It has been

observed for all compression ratios and the yellow and the grey foam only. The obtained values of

Poisson’s ratios was between -0.27 and 0.74. The value of the modulus of elasticity for auxetic

foam was lower than the conventional foam. For example the grey auxetic foam (B) with a

compression ratio of 50% has a modulus of elasticity of 30.02 kPa which is lower than the

conventional foam sample (A) by 77.3 %.

ii

The energy absorbed of the foam was calculated using the compression and tensile test

results. It has been observed that auxetic foam has higher absorbed energy than the conventional

foam. For example for grey PU foam sample has a compression ratio of 5.56 and a density of 109.6

kg/m3, the energy absorbed was 3.98 kJ/m3, which is higher than the conventional PU foam sample

by 69.6%.

In the resilience test the value of resilience of the auxetic grey foam was higher than the

conventional foam. For example for grey foam has a compression ratio of 9.26 and a density of

125.5 kg/m3, the resilience percentage was 38% which is higher than the conventional foam by

7.7%.

The produced auxetic polymeric foam material has a potential to be used in the following areas:

• Biomedical field as dilator and artificial blood vessels [16].

• Car body parts (head rest and seats) and nose-cone of aircrafts [33,34].

• Body armour [35].

• Can be used in the packing of electronic equipment.

• Can be used in the pumps and Heat Exchangers fastenings as vibration absorbers.

• Can be used in the packing and seals of valves and pumps.

iii

Table of Contents

CHAPTER (1) INTRODUCTION AND LITERATURE SURVEY

1.1 Introduction ..................................................................................................................... 1 1.2 Literature survey............................................................................................................. 2

1.2.1 Negative poisson's ratio .............................................................................................. 2 1.2.2 Auxetic materials ........................................................................................................ 4 1.2.3 Flexible polyurethane (FPU) polymeric foams .......................................................... 5 1.2.4 Conventional flexible polyurethane (FPU) foam applications ................................... 6 1.2.5 Previous work ............................................................................................................. 7

1.3 The Objective of the research ...................................................................................... 10

CHAPTER (2) POLYURETHANE FOAM SAMPLES FABRICATION AND PREPARATION

2.1 Fabrication method of flexible Polyurethane foams .................................................. 11 2.2 Manufacturing technique of auxetic PU polymeric foam.......................................... 12 2.3 Adaptation dimensions of samples for testing ............................................................ 16 2.4 Samples label ................................................................................................................. 17

CHAPTER (3) POLYURETHANE FOAM TESTING AND MEASURING TECHNIQUES

3.1 Testing techniques......................................................................................................... 19 3.1.1 Compression ratio measurement............................................................................... 19 3.1.2 Density measurement................................................................................................ 19 3.1.3 Poisson’s ratio measurement .................................................................................... 20

3.2 Mechanical testing machines........................................................................................ 21 3.2.1 Zwick universal testing machine .............................................................................. 21 3.2.2 Zwick rebound resilience tester machine ................................................................. 22

3.3 Mechanical testing and methodology .......................................................................... 24 3.3.1 Tensile test and methodology ................................................................................... 24 3.3.2 Compression test and methodology.......................................................................... 27 3.3.3 Hysteresis test and methodology .............................................................................. 30 3.3.4 Resilience test and methodology .............................................................................. 31

CHAPTER (4) RESULTS AND DISCUSSION 4.1 Introduction.....................................................................................................................33 4.2 Microstructure of flexible PU foam samples .............................................................. 33 4.3 Tensile test of grey samples .......................................................................................... 37 4.4 Tensile test of yellow samples....................................................................................... 40

Abstract .......................................................................................................................................i Table of Contents........................................................................................................................iii Acknowledgments.......................................................................................................................v Nomenclature..............................................................................................................................vi List of Figures .............................................................................................................................viii List of Tables...............................................................................................................................xiv

iv

4.5 Compression test of grey samples................................................................................ 43 4.5.1 Compression strain at 25% ....................................................................................... 43 4.5.2 Compression strain at 50% ....................................................................................... 45 4.5.3 Compression strain at 75% ....................................................................................... 47

4.6 Compression test of yellow samples ............................................................................ 50 4.6.1 Compression strain at 25% ....................................................................................... 50 4.6.2 Compression strain at 50% ....................................................................................... 52

4.6.3 Compression strain at 75% ....................................................................................... 54 4.7 Hysteresis test of grey samples..................................................................................... 57

4.7.1 Compression strain at 25% and one cycle ................................................................ 57 4.7.2 Compression strain at 50% and one cycle ................................................................ 59 4.7.3 Compression strain at 75% and one cycle ................................................................ 61

4.8 Hysteresis test of yellow samples ................................................................................. 64 4.8.1 Compression strain at 25% and one cycle ................................................................ 64 4.8.2 Compression strain at 50% and one cycle ................................................................ 66 4.8.3 Compression strain at 75% and one cycle ................................................................ 68

4.9 Resilience test................................................................................................................. 71

4.10 General discussions of the test results ....................................................................... 73 4.10.1 Tensile tests ............................................................................................................ 73 4.10.2 Compression tests ................................................................................................... 74 4.10.3 Hysteresis tests........................................................................................................ 75 4.10.4 Resilience tests........................................................................................................ 75

CHAPTER (5) CONCLUSIONS AND FURTHER WORK 5.1 Conclusion ..................................................................................................................... 76 5.2 The applications of auxetic materials........................................................................... 79

5.2.1 Magnox nuclear reactors .......................................................................................... 79 5.2.2 Aerospace field ......................................................................................................... 79 5.2.3 Military ..................................................................................................................... 80 5.2.4 Industrial fields ......................................................................................................... 81 5.2.5 Biomedicine.............................................................................................................. 82

5.3 Further work ................................................................................................................. 83

REFERENCES References ....................................................................................................................... 84

APPENDICES Appendix A ...................................................................................................................... 87 Appendix B ...................................................................................................................... 88 Appendix C ...................................................................................................................... 89 Appendix D ...................................................................................................................... 90 Appendix E ...................................................................................................................... 91

v

Acknowledgments

I would first and foremost thank Allah for everything in my life. I wish Allah to accept this

work and make it useful for all of us. I would like to express my deepest of gratitude and

thankfulness to Prof. Dr. Alaa EL_Butch (Vice Dean for students affairs), Assoc. Prof. Dr. Tarek

EL_Mahdy (Associated Professor in the Mechanical Design Department) and Dr. Khaled

Mohammed Zied (Assistant Professor in the Mechanical Design Department) for their help,

support, guidance and continuous advising throughout this work.

I also wish to express my deepest thanks to Prof. Dr. Aly Karameldin Aly (internal

supervisor and Head of the Atomic Reactors Division-Nuclear Research Centre-Egyptian Atomic

Energy Authority) for his help, support and encouragement. I would also like to thank my friend

Eng. Ahmed Hassan for helping me to obtain the microstructure of conventional and auxetic foams.

I am grateful to my parents who have supported me throughout my entire life, along with

my wife, sister and brother for their support as well. Finally, I would like also to thank the members

of the Mechanical Design Department, Faculty of Engineering-Mataria, Helwan University for their

support throughout the work.

vi

Nomenclature

Symbol Definition unit

Vo Original volume mm3

Vact Actual volume mm3

Vmould Mould volume mm3

mbefore Mass of sample before the processing gram

mafter Mass of sample after the processing gram

ρbefore Density of sample before the processing Kg/m3

ρafter Density of sample after the processing Kg/m3

ρf,ave Average density of sample after the processing Kg/m3

CRbefore Theoretical compression ratio ---

CRact Actual compression ratio ---

ε Change in length divided by the original length. ---

Poisson’s ratio ---

R Resilience percentage %

H Sample height mm

W Sample width mm

D Sample diameter mm

L Sample length mm

σ Stress kPa

To Modulus of toughness kJ/m3

E Modulus of elasticity kPa

Ed Dissipated energy kJ/m3

Eabs Absorbed energy kJ/m3

vii

Symbol Definition unit

A (G-Conv.) Square grey conventional PU foam sample.

B (G-Aux. 100) Square grey auxetic PU foam sample at CRth,1= 5.56

C (G-Aux. 80) Square grey auxetic PU foam sample at CRth,2= 6.94

D (G-Aux. 60) Square grey auxetic PU foam sample at CRth,3= 9.26

1St B

atch

A* (Y-Conv.) Square yellow conventional PU foam sample.

B* (Y-Aux. 100) Square yellow auxetic PU foam sample at CRth,1= 5.56

C* (Y-Aux. 80) Square yellow auxetic PU foam sample at CRth,2= 6.94

D* (Y-Aux. 60) Square yellow auxetic PU foam sample at CRth,3= 9.26

2nd B

atch

E (G-Conv.) Circular grey conventional PU foam sample

F (G-Aux. 100) Circular grey auxetic PU foam sample at CR th,1= 2

G (G-Aux. 80) Circular grey auxetic PU foam sample at CR th,2= 2.5

H (G-Aux. 60) Circular grey auxetic PU foam sample at CR th,3= 3.33

3rd B

atch

E* (Y-Conv.) Circular yellow conventional PU foam sample.

F* (Y-Aux. 100) Circular yellow auxetic PU foam sample at CR th,1= 2

G* (Y-Aux. 80) Circular yellow auxetic PU foam sample at CR th,2= 2.5

H* (Y-Aux. 60) Circular yellow auxetic PU foam sample at CR th,3= 3.33

4th B

atch

viii

List of Figures

Fig. No. Figure Title page

Fig. 1.1 (a) A material deformation with positive Poisson’s ratio, and (b) A material deformation with negative Poisson’s ratio when stretched.

3

Fig. 1.2 Positive and negative poison’s ratio 4

Fig. 1.3 SEM images of PU foams (a) Conventional and (b) Auxetic. 5

Fig. 1.4 Applications for flexible Polyurethane Foams 6

Fig. 1.5 Idealized models for foam cells: (a) Conventional, and (b) Re-entrant cell (Auxetic).

7

Fig. 2.1 Conventional flexible PU foam samples with deferent densities and two cross sectional areas

12

Fig. 2.2 Isometric drawings with their dimensions for: (a)Circular aluminium mould, and (b) Square aluminium mould.

13

Fig. 2.3 Shows the circular and square moulds. 14

Fig. 2.4 Foam samples after conversion to auxetic: (a) Circular auxetic samples, and (b) Square auxetic samples.

15

Fig. 2.5 Samples after preparation for testing. 17

Fig. 3.1 Method to calculate the change in the transverse and longitudinal directions to get the Poisson’s ratio in compression and tensile test for conventional and auxetic samples.

21

Fig. 3.2 Zwick universal testing machine. 22

Fig. 3.3 a) Zwick resilience tester machine, and b) Pendulum used for different tests.

23

Fig. 3.4 (a-d) Tensile test applied on the circular grey conventional (E) and auxetic (F, G and H) PU foam samples at: a) No load, and b) Failure.

25

Fig. 3.4 (e-h) Tensile test applied on the circular yellow conventional (E*) and auxetic (F*, G* and H*) PU foam samples at: a) No load, and b) Failure.

26

Fig. 3.5 (a-d) Compression test applied on square grey conventional (A) and auxetic (B, C and D) PU foam samples at different compression strain levels: (0, 25, 50 and 75%).

28

Fig. 3.5 (e-h) Compression test applied on square yellow conventional (A*) and auxetic (B*, C* and D*) PU foam samples at different compression strain levels: (0, 25, 50 and 75%).

29

Fig. 3.6 Control panel of resilience tester machine 32

ix


Fig. 4.1a Microstructure of grey square conventional and auxetic flexible PU foam samples at 40X magnification.

34

Fig. 4.1b Microstructure of yellow Square conventional and auxetic flexible PU foam samples at 40X magnification

34

Fig. 4.2a Microstructure of grey circular conventional and auxetic flexible PU foam samples at 40X magnification

35

Fig. 4.2b Microstructure of yellow circular conventional and auxetic flexible PU foam samples at 40X magnification

36

Fig. 4.3a Tensile stress-strain curve of a conventional grey PU foam sample (E) 38

Fig. 4.3b Tensile stress-strain curve of an Auxetic-100 grey PU foam sample (F) 38

Fig. 4.3c Tensile stress-strain curve of an Auxetic-80 grey PU foam sample (G) 38

Fig. 4.3d Tensile stress-strain curve of an Auxetic-60 grey PU foam sample (H) 38

Fig. 4.3e Tensile stress-strain curves of conventional and auxetic grey PU foam samples (E, F, G and H)

39

Fig. 4.4a Tensile stress-strain curve of a conventional yellow PU foam sample(E*) 41

Fig. 4.4b Tensile stress-strain curve of an Auxetic-100 yellow PU foam sample (F*) 41

Fig. 4.4c Tensile stress-strain curve of an Auxetic-80 yellow PU foam sample (G*) 41

Fig. 4.4d Tensile stress-strain curve of an Auxetic-60 yellow PU foam sample (H*) 41

Fig. 4.4e Tensile stress-strain curves of conventional and auxetic yellow PU foam samples (E*, F*, G* and H*)

42

Fig. 4.5a Compression stress-strain curve of a conventional grey PU foam sample (A) at 25% compression strain

44

Fig. 4.5b Compression stress-strain curve of an Auxetic-100 grey PU foam sample (B) at 25% compression strain

44

Fig. 4.5c Compression stress-strain curve of an Auxetic-80 grey PU foam sample (C) at 25% compression strain

44

Fig. 4.5d Compression stress-strain curve of an Auxetic-60 grey PU foam sample (D) at 25% compression strain

44

Fig. 4.5e Compression stress-strain curves of conventional and auxetic grey PU foam samples (A, B, C and D) at 25% compression strain

45


46

x



46


46


46


47


48


48


48


48


49

Fig. 4.8a Compression stress-strain curve of a conventional yellow PU foam sample (A*) at 25% compression strain

51

Fig. 4.8b Compression stress-strain curve of an Auxetic-100 yellow PU foam sample (B*) at 25% compression strain

51

Fig. 4.8c Compression stress-strain curve of an Auxetic-80 yellow PU foam sample (C*) at 25% compression strain

51

Fig. 4.8d Compression stress-strain curve of an Auxetic-60 yellow PU foam sample (D*) at 25% compression strain

51

Fig. 4.8e Compression stress-strain curves of conventional and auxetic yellow PU foam samples (A*, B*, C* and D*) at 25% compression strain

52


53


53


53


53

xi


Fig. 4.9e Compression stress-strain curves of conventional and auxetic yellow PU foam samples at 50% compression strain

54


55


55


55


55

Fig. 4.10e Compression stress-strain curves of conventional and auxetic yellow PU foam samples at 75% compression strain

56

Fig. 4.11a One cycle Hysteresis stress-strain curve of a conventional grey PU foam sample (A) at 25% compression strain

58

Fig. 4.11b One cycle Hysteresis stress-strain curve of an Auxetic-100 grey PU foam sample (B) at 25% compression strain

58

Fig. 4.11c One cycle Hysteresis stress-strain curve of an Auxetic-80 grey PU foam sample (C) at 25% compression strain

58

Fig. 4.11d One cycle Hysteresis stress-strain curve of an Auxetic-60 grey PU foam sample (D) at 25% compression strain

58

Fig. 4.11e One cycle Hysteresis stress-strain curves of conventional and auxetic grey PU foam samples at 25% compression strain

59


60


60


60


60


61


62

xii



62


62


62


63

Fig. 4.14a One cycle Hysteresis stress-strain curve of a conventional yellow PU foam sample (A*) at 25% compression strain

65

Fig. 4.14b One cycle Hysteresis stress-strain curve of an Auxetic-100 yellow PU foam sample (B*) at 25% compression strain

65

Fig. 4.14c One cycle Hysteresis stress-strain curve of an Auxetic-80 yellow PU foam sample (C*) at 25% compression strain

65

Fig. 4.14d One cycle Hysteresis stress-strain curve of an Auxetic-60 yellow PU foam sample (D*) at 25% compression strain

65

Fig. 4.14e One cycle Hysteresis stress-strain curves of conventional and auxetic yellow PU foam samples at 25% compression strain

66


67


67


67


67

Fig. 4.15e One cycle Hysteresis stress-strain curves of conventional and auxetic yellow PU foam at 50% compression strain

68


69


69


69

xiii



69

Fig. 4.16e One cycle Hysteresis stress-strain curves of conventional and auxetic yellow PU foam samples at 75% compression strain

70

Fig. 5.1 Bending behaviours of (a) Curvature behaviours in non-auxetic and (b) auxetic (double curvature-convex shape)

80

Fig. 5.2 Schematic of the principle of auxetic material used to human protection 81

Fig. 5.3 Dilator employing an auxetic end sheath. Insertion of finger and thumb apparatus causes the auxetic sheath to extend and expand laterally, thus opening up the surrounding vessel

82

Fig. 5.4 Deformation behaviour of artificial blood vessels: a) Conventional material, and b) Auxetic blood vessel

82

xiv

List of Tables

Table No. Description Page

Table 2.1 Square Sample types and description. 17

Table 2.2 Circular Sample types and description. 18

Table 4.1 Mechanical properties of the grey conventional and auxetic circular flexible PU foam samples (E, F, G and H) under tensile test.

39

Table 4.2 Mechanical properties of the yellow conventional and auxetic circular flexible PU foam samples (E*, F*, G* and H*) under tensile test.

42

Table 4.3 Mechanical properties of the grey conventional and auxetic square flexible PU foam samples (A, B, C and D) at 25% compression test.

45


47


49

Table 4.6 Mechanical properties of the yellow conventional and auxetic square flexible PU foam samples (A*, B*, C* and D*) at 25% compression test.

52


54


56

Table 4.9 Mechanical properties of the grey conventional and auxetic square flexible PU foam samples (A, B, C and D) at one cycle and 25% compression hysteresis test.

59


61


63

Table 4.12 Mechanical properties of the yellow conventional and auxetic square flexible PU foam samples at one cycle and 25% compression hysteresis test.

66


68


70

Table 4.15 (a - d)

Mean values of the resilience test for the conventional and three different types of auxetic PU foam samples for grey and yellow samples.

72

CHAPTER (1)

INTRODUCTION AND LITERATURE SURVEY

Chapter 1 “Introduction and Literature Survey”

1

1.1 Introduction

Modern technology requires new materials of special properties. One of the

reasons for interest in materials of unusual mechanical properties comes from the

fact that they can be used as matrices to form composites with other materials of

other required properties, e.g. electric, magnetic, etc. A new field of endeavour is

to study materials exhibiting Negative Poisson’s Ratio (NPR). Large-scale cellular

structures with NPR property were first realized in 1982 in the form of two-

dimensional silicone rubber or aluminium honeycomb structures deforming by

flexure of the ribs [1, 2].

In 1987, Lakes first developed the NPR polyurethane foam material with re-

entrant microstructure [3, 4]. This polymeric foam material had a Poisson’s ratio

of -0.7. These new types of materials were named Auxetics by [5], which, in

contrast to conventional materials (like rubber, glass, metals, etc.), expand

transversely when pulled longitudinally and contract transversely when pushed

longitudinally. People have known about auxetic materials for over 100 years, but

have not given them much attention. This type of material can be found in some

rock and minerals, even animal such as the skin covering a cow’s teats.

To date, a wide variety of auxetic materials has been fabricated, including

microstructure polymeric and metallic foam materials, microporous polymers,

carbon fibre laminates and honeycomb structures. A typical example is a well-

known synthetic polymer polytetrafluoroethylene (PTFE), which has been in use

for many years. Other materials possess the NPR property such as microporous

ultra high molecular weight polyethylene (UHMWPE), polypropylene (PP) [6, 7,

8, and 9], and several types of rocks [10].


2

However, their special characteristics are largely ignored. Only up until

recently, Lakes, Evans and other scientists’ work has attracted more attention to

these auxetic materials. These auxetic materials are of interest due to the possibility

of enhanced mechanical properties such as shear modulus, plane strain fracture

toughness and indentation resistance [3,11].

Therefore, studying these non-conventional materials is indeed important

from the point of view of fundamental research and possibly practical applications,

particularly in medical, aerospace and defence industries. In fact, some materials

with such anomalous (i.e. NPR) properties have been used in applications such as

pyrolytic graphite for thermal protection in aerospace, large single crystals of

Ni3Al in vanes for aircraft gas turbine engines, and so on.

1.2 Literature survey

1.2.1 Negative Poisson's ratio

It is well known that Poisson's ratio is defined by the ratio of the transverse

contraction strain to the longitudinal extension strain in a simple tension condition

[12, 13]. Poisson's ratio, also called Poisson ratio or the Poisson coefficient, is

usually represented as a lower case Greek nu " ", as shown in the equation (1).

(1)

Strain ) is defined in elementary form as the change in length divided by

the original length, as shown in the equation (2).

O (2)

Since most test specimens of engineering materials become thinner in cross

section when stretched, as shown in Figure (1.1a), Poisson’s ratio in this situation

is positive, typically around 0 to +0.5. The reason is that the inter-atomic bonds

realign with deformation.


3

However, some materials or structures contract in the transverse direction

under uniaxial compression, or expand laterally when stretched, see Figure (1.1b).

These materials or structures are said to have Negative Poisson's Ratios (NPR). A

typical example is a novel auxetic foam microstructure material, where a material

gets fatter when stretched.

This behaviour does not contradict the classical theory of elasticity, based on

the thermodynamic considerations of strain energy, the Poisson's ratios of isotropic

materials can not only take negative values, but can have a range of negative

values twice that of positive ones [12]. That is, the Poisson's ratio is bounded by

two theoretical limits, it must be greater than -1, and less than or equal to 0.5, this

is determined by the relation below.

-1 < ν ≤ 0.5

The upper bound of the Poisson’s ratio corresponds to rubber-like materials

with an infinite bulk modulus [3], while the lower bound stands for an infinite

shear modulus.

Figure (1.1) (a) A material deformation with positive Poisson’s ratio, and

(b) A material deformation with negative Poisson’s ratio when stretched.


4

1.2.2 Auxetic materials

Auxetics are materials that have a Negative Poisson's Ratio (NPR), i.e.

which when stretched, become thicker perpendicularly to the applied force. This

occurs because they contain hinge-like structures which flex when stretched. The

term auxetic derives from the Greek word α�ξητικός (auxetikos) which means,

"That which tends to increase," and has its root in the word α�ξησις, or auxesis,

meaning "increase”, as shown in Figure (1.2). This terminology was coined by

Professor Ken Evans [5].

Figure (1.2) Positive and negative poison’s ratio behaviour

Such materials are expected to have interesting mechanical properties such

as high energy absorption and fracture resistance. This may be useful in

applications such as body armor, packing material, knee and elbow pads, robust

shock absorbing material, and sponge mops. Auxetics can be illustrated with an

inelastic string wound around an elastic cord. When the ends of the structure are

pulled apart, the inelastic string straightens while the elastic cord stretches and

winds around it, increasing the structure's effective volume.


5

1.2.3 Flexible Polyurethane (FPU) polymeric foams

The first successful method to produce an auxetic material [3], which

involved the compression and heating to just above softening temperature point of

polyurethane foam. By doing this Lakes discovered that, this causes the foam to

become auxetic. The reason for its behavior had to do with re-entrant honeycomb

structure.

When looking at the foam before and after the heating and compression

though the use of a scanning electron microscope it was observed that ribs of the

cells in the foam collapsed inwards similar to the re-entrant honeycomb mentioned

in the previous section. It is due to this similar structure that it was stated to be the

cause of the auxeticity of the foam. Figure (1.3) shows SEM images of

conventional and auxetic Flexible Polyurethane (FPU) foams [14, 15].

Figure (1.3) SEM images of PU foams (a) Conventional, and (b) Auxetic.


6

1.2.4 Conventional FPU foam applications

Most of the flexible polyurethane foam produced is made for cushioning.

This includes furniture, packaging and transportation. Furnishings use

polyurethane foam for carpet underlay, bedding, and home furniture. The

transportation industry uses it in seating cushions for the airlines, trains, bicycles

and cars. It is also used in a wide range of other applications for cars such as sound

insulation and vibration dampening. Other applications include clothing, toys,

electronics and other applications for protection or cushioning issues, as shown in

Figure (1.4).

Figure (1.4) The applications of conventional flexible Polyurethane foams.


7

1.2.5 Previous work

Foams with re-entrant microstructures exhibited negative Poisson's ratios

(Auxetic) as well as greater resilience than conventional foams. The Auxetic

materials prepared using different techniques to evaluate their mechanical behavior

and structure [16]. The nonlinear stress - strain relationship for both conventional

and re-entrant “Auxetic” polymeric cellular solids depended upon the permanent

volumetric compression ratio during the processing procedure. The toughness of

re-entrant foam increased with permanent volumetric compression ratio [17].

Figure (1.5) shows Young's moduli of conventional and re-entrant open cell

foams are obtained by modelling the three-dimensional unit cell as an idealized 14-

sided unit cell. Young's modulus of re-entrant foams decreases with permanent

volumetric compression ratio in both modelling and experiments [18].

Figure (1.5) The idealized models for foam cells: (a) Conventional, and (b) Re-entrant cell

Anisotropic polymer foams have been prepared, which exhibit a Poisson's

ratio exceeding 1, and ratios of longitudinal to transverse stiffness exceeding 50%.

The foams are as much as 20 times stiffer in the longitudinal direction than the

foams from which they were derived. The transformation process involved

applying a uniaxial stress sufficient to produce 25% to 45% axial strain to open-

cell polyurethane foam, heating above the softening point, followed by cooling

under axial strain [19].


8

Different sizes of PU foams were compressed according to ASTM protocols

to determine their stiffness capabilities. It was found that the test results varied

according to the relation between the size of the test specimen and the test indenter

[20]. Pressure distributions on a seated were measured using a pressure-sensitive

array. Seated pressure distribution became more favourable with decreasing

sample density for both conventional and re-entrant foam blocks. Foam thickness

played a small role in the seated pressure performance of foam cushions [21].

Poisson's ratio of polyurethane foams decreased with compressive axial

strain and increased with tensile strain up to a maximum. The maximum Poisson's

ratio in tension decreased as cell size increases. The strain at which maximum

Poisson's ratio occurs, increased with cell size [22]. Various polyethylene foams

were subjected to thermo-mechanical processing with the aim of transforming

them into re-entrant materials exhibiting negative Poisson’s ratio. Poisson's ratio

vs. strain for these foams was similar to prior results for reticulated polyurethane

foams [23].

Poisson's ratio is defined as minus the ratio of transverse strain to

longitudinal strain in simple tension. For most materials, Poisson's ratio is close to

1/3. Negative Poisson's ratios are counterintuitive but permissible according to the

theory of elasticity. Such materials can be prepared for classroom demonstrations,

or made by students [24].

Static and dynamic characteristics of 0.027 g/cm3 density conventional open

cell polyurethane (PU), auxetic and iso-density “non-auxetic” foams were analyzed

[25]. The bulk properties of open cell polyurethane foam are studied in a

hydrostatic compression experiment under strain control. The bulk modulus in the

linear region is in reasonable agreement with the value calculated from

compression Young’s modulus and Poisson’s ratio. The linear region of behaviour

in hydrostatic compression corresponds to less than half the axial strain range

observed in axial compression [26].


9

Comparative analysis between the cyclic loading compressive “hysteresis”

behaviour of conventional, iso-density “non-auxetic” and auxetic “NPR”

thermoplastic polyurethane foams. The hysteresis loop tends to close itself as

function as the number of cycles N, while the slope of the dynamic stiffness

decreases with increasing N, therefore with decrease of dissipated energy. The

energy dissipated by the auxetic foams is significantly higher than the conventional

and iso-density foams at every number of cycles and loading level [27]. Auxetic

open cell polyurethane (PU) foams have been manufactured and mechanically

compressive tensile cyclic loading has been applied to measure tangent modulus,

Poisson’s ratios and energy dissipated per unit volume. The results are used to

obtain relations between manufacturing parameters, mechanical and hysteresis

properties of the foams [28].

Cyclic loading tensile behaviour was done to compare between the

conventional and auxetic thermoplastic PU foams. The results obtained shows that,

the auxetic foam has enhanced characteristics under static loading and tensile

fatigue compared to the conventional foam [29]. The auxetic structures and auxetic

polymeric materials have been designed and fabricated for diverse applications.

The emphasis is focused on the geometrical structures and models, particular

properties and applications of auxetic polymeric materials developed [30].

This exploratory paper presents some preliminary results on the use of full-

field deformation measurements on low density polymeric foams to identify the

evolution of Poisson’s ratio with compressive strain. Two types of foams were

tested: standard low density polyurethane foam and auxetic foam manufactured

from a similar precursor. 2D digital image correlation was used to measure the

strain field at the specimen’s surfaces. Then, Poisson’s ratios were identified using

a dedicated inverse method called the Virtual Fields Method (VFM) and the results

compared with the standard approaches [31].


10

��The�objective�of�the�research��

The main aim of this research is to fabricate new auxetic flexible

polyurethane polymeric foam with mechanical properties which are convenient to

the modern applications in different fields such as (medical, mechanical and

physical). Also, setting up a stress-strain curve of that material, so as to help the

designers, and engineers for using these materials correctly in the different

applications.

CHAPTER (2)

POLYURETHANE FOAM SAMPLES

FABRICATION AND PREPARATION

Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

11

2.1 Fabrication method of flexible Polyurethane foams

Solid foam is formed when gas is blown through solidifying plastic.

Depending on its ability to retain original shape after compression. Solid foam can

be classified as either flexible or rigid. Polyurethane foam is the most widely used

flexible foamed plastic, being used for thermal insulation and packaging materials,

cushions, bed mattresses, carpet backings and resilient floor coverings. This article

is based on the process used by Dunlop Flexible Foam in Auckland, although all

manufacturers use a similar process. Dunlop has been using a continuous process

since 1985, and has a daily capacity of more than 15 tons of polyurethane foam.

Polyurethane foam is the most widely used flexible foam plastic. It is used to

produce a wide variety of items including thermal insulation and packaging

materials, comfort cushions, bed mattresses, carpet backings and resilient floor

coverings. Tolylenediisocyanate (TDI) and polyalcohols are the basic ingredients

for the production of polyurethane foam. The basic reaction is as shown below:

Blowing agent, such as methylene chloride and water, and various additives are

also required steps.

Step 1 - Mixing of the raw materials

During production, the raw materials (Tolylenediisocyanate “TDI”, polyalcohol,

blowing agents and additives) are pumped from their own storage tank to a

common mixing chamber. Adequate dispersion can be achieved by the stirring of

high speed impeller installed in the mixer.

Kirk-Othmer, Encyclopedia of Chemical Technology (3rd Ed.), Vol 11, 88-89.


12

a b D=50 mm and L=200 50*50 mm

2 and L=200

Step 2 - Foam forming and settling

The foam gradually solidifies when travelling up the settling chamber by the action

of paper conveyor. It is then cut into 2.2 m long blocks by an electric cutter after

the foam is hardened.

Step 3 – Curing

The newly formed foam blocks are still very hot when transported to the storage

area. They must be cured at room temperature for at least 18 hours before further

processing.

2.2 Manufacturing technique of auxetic PU polymeric foam

The samples that were tested were produced from conventional foams. The

densities which used were White colour (16 kg/m3), violet colour (20 kg/ m3),

yellow colour (25 kg/ m3) and grey colour (30 kg/ m3). The samples were supplied

by the Taki-Vita Company, 10th of Ramadan, Egypt. The samples were cut from

each density in two different shapes; the first shape is circular cross sectional area

with dimensions are (D=50±1 mm and L=200±1 mm) while the second shape is

square cross sectional area with dimensions are (50×50×200) mm3 and tolerances

of ±1 mm, as shown in Figure (2.1).

Figure (2.1) Four different densities of the conventional PU foam samples with two cross sectional areas where: a) Circular cross sectional area, and b) Square cross sectional area.


13

The total numbers of samples used of each density are sixteen samples

which were divided into four batches. Every batch contains four samples from the

same density. Four square aluminium moulds with inner dimensions 30×30×150

mm3, and 1mm thickness were used backed by two wood square pistons for each

mould, which used to impose concurrent axial and radial compression on the

conventional PU foam samples.

Also, four cylindrical aluminium tube moulds (Di=30±0.2 mm, L=150±0.2 mm)

and 1 mm thickness were used to backed the sample by two wood circular pistons

for each mould. Figure (2.2) shows the drawing of the two moulds. The square and

cylindrical aluminium moulds are partially slotted along length from two ends to

lock the wood pistons by using screws after samples have been compression, as

shown in Figure (2.3).

Figure (2.2) Isometric drawings with dimensions for: a) Circular aluminium mould, and

b) Square aluminium mould.

a b


14

Figure (2.3) Aluminium tube moulds with their wood pistons where: a) Circular shape, and b) Square shape.

The inner walls of aluminium tube moulds were lubricated by vegetable oil

to prevent the conventional foam samples from surface wrinkles. The conventional

foam samples were packed gently inside the aluminium tube moulds to have

theoretically a constant radial compression ratio at three different positions of axial

compression ratios. Therefore, the samples compressed theoretically in axial

direction from its original length (200±1 mm) to imposed length (100, 80 and 60

mm).

The industrial furnace was preheated to 200 ºC for 5 minutes. After that the

foam samples and moulds assembly were placed into the furnace to heating at a

constant temperature (above softening temperature) about 200 ºC for 25 minutes.

The foam samples and moulds assembly were removed from the furnace to cool in

the ambient surrounding conditions (Air-Cooled) for 30 minutes and removed the

foam samples from the aluminium tube moulds. We stretched the samples gently in

each of the three orthogonal directions “make relaxation” to eliminate any

adhesion of the ribs, as shown in Figure (2.4). The above manufacture method is

adapted by [3,4].

a b


15

Figure (2.4) Foam samples after

conversion to auxetic foams where: (a) Circular auxetic samples, and (b) Square auxetic samples.

Important Notes

1. The previous procedures were done for each conventional foam density (square

and circular) samples. Those were compressed inside the four square and

circular moulds at a known compression ratios. The samples - moulds assembly

were placed together into furnace at the same time. The auxetic foams depend

on the compression ratio.

2. The above step was repeated to get more auxetic foam samples at different

compression ratios as following:

2.1- In the first time, four conventional foam samples were compressed by hand laterally inside the moulds and in the axial direction to reduce the length from 200 mm to 100 mm. This auxetic type named as (Aux-100).

2.2- In the second time, four conventional foam samples were compressed by hand laterally inside moulds and in the axial direction to reduce the length from 200 mm to 80 mm. This auxetic type named as (Aux-80).

2.3- In the third time, also four conventional foam samples were compressed by hand laterally inside moulds and in the axial direction to reduce the length from 200 mm to 60 mm. This auxetic type named as (Aux-60).

3. Therefore, Three different types of auxetic foam samples were fabricated

(Aux.100, Aux.80 and Aux.60) of each cross section (cylindrical and square)

and colour (density) of the conventional foams.

a b


16

4. Four polyurethane foam samples were prepared to be tested one conventional

(Conv.) and three different types of auxetic (Aux.100, Aux.80 and Aux.60) of

each cross section and colour.

5. The big wrinkles were found in the white and violet colour samples, which their

densities are 16 and 20 kg/m3 respectively. So, the yellow and grey colour

samples were used only in this research, which their densities are 25 and 30

kg/m3.

��a�tatio��i�e�sio�s�of�sa��les�for�testi�g�

In this research work, the dimensions of samples were adapted to adequate

the tests. So, in case the compression tests in order to prevent buckling. The length

of samples was 70±1 mm in order to vanish the buckling. From the trails of

experimental tests, we found the critical aspect ratio equals to 2.3. This depends on

the percentage of compression during the test. So, we used the following

dimensions for all samples:

The square samples are H=W=35±1 mm and L=70±1 mm, and

The circular samples are D=32±1 mm and L=70±1 mm.

These moulds have been manufactured from aluminium sheet thickness of 1 mm.

Three horizontal and vertical lines with equal distances were drawn by

marker pen to intersect in nine points. These points were used to calculate the

average deformation in axial and lateral directions. Therefore, the average

Poisson’s ratio “υ” was measured, as shown in Figure (2.5).


17

Figure (2.5) Square samples after preparation for testing.

��a��les�label�

The samples were divided into four batches. Every batch contains four

samples, one conventional sample (Conv.) and three auxetic samples (Aux.100,

Aux.80 and Aux.60). These samples were labelled as “A, B, C and D” for first

batch (grey square cross sectional samples), “A*, B*, C* and D*” for second batch

(yellow square cross sectional samples), “E, F, G and H” for third batch (grey

circular cross sectional samples) and “E*, F*, G* and H*” for forth batch (yellow

circular cross sectional samples). Tables (2.1) and (2.2) show the samples ID and

their definition for square and circular samples.


18

� Table (2.1) Square samples ID and their description.

� Table (2.2) Circular samples ID and their description.

Batch Sample ID Definition

A (G-Conv.) Square grey conventional PU foam sample.

B (G-Aux. 100) Square grey auxetic PU foam sample at CRth,1= 5.56

C (G-Aux. 80) Square grey auxetic PU foam sample at CRth,2= 6.94 First

D (G-Aux. 60) Square grey auxetic PU foam sample at CRth,3= 9.26

A* (Y-Conv.) Square yellow conventional PU foam sample.

B* (Y-Aux. 100) Square yellow auxetic PU foam sample at CRth,1= 5.56

C* (Y-Aux. 80) Square yellow auxetic PU foam sample at CRth,2= 6.94 Second

D* (Y-Aux. 60) Square yellow auxetic PU foam sample at CRth,3= 9.26

Batch Sample ID Definition

E (G-Conv.) Circular grey conventional PU foam sample

F (G-Aux. 100) Circular grey auxetic PU foam sample at CR th,1= 2

G (G-Aux. 80) Circular grey auxetic PU foam sample at CR th,2= 2.5 Third

H (G-Aux. 60) Circular grey auxetic PU foam sample at CR th,3= 3.33

E* (Y-Conv.) Circular yellow conventional PU foam sample.

F* (Y-Aux. 100) Circular yellow auxetic PU foam sample at CR th,1= 2

G* (Y-Aux. 80) Circular yellow auxetic PU foam sample at CR th,2= 2.5 Forth

H* (Y-Aux. 60) Circular yellow auxetic PU foam sample at CR th,3= 3.33

CHAPTER (3)

POLYURETHANE FOAM TESTING AND MEASURING TECHNIQUES

Chapter “Polyurethane Foam Testing and Measuring Techniques”

19

��Testi�g�tech�iques�

3.1.1 Compression ratio measurement

The sample dimensions were measured and recorded both before and after

processing. The compression ratio and spring back were determined by using the

sample’s initial (original) volume (Vo), the sample’s actual (final) volume after

relaxation (Vact), and the volume of the mold (Vmould). The theoretical compression

ratio (CRbefore) is Vo / Vmould. The actual (final) compression ratio (CRact) is Vo / Vact.

This tabulated in appendices (A-D).

3.1.2 Density measurement

The densities of the specimens were obtained measuring their dimensions

with a digital calliper (sensitivity ± 0.01 mm) and their weights (± 0.01 gram) with

an electronic balance. The tests were conducted at room temperature (27±2 °C) at

average (48±2 %) of humidity. The humidity level was not controlled during

testing. Since the specimens start to expand after the manufacturing process, it has

been necessary to measure the real density after two weeks. In fact, the differences

between the theoretical and actual volumetric compression ratios for the same

sample due to the viscoelastic behavior.

The dimensions of samples were measured with the digital calliper

(sensitivity ±0.01 mm). Since the foams tested were completed, the acquisition

process involved extreme handling care. The procedure used consisted of closing

the ends of the calliper at very low speed, and moving the calliper in a direction

perpendicular to the dimension measured. The measured dimensions were listed in

table of measurements, as shown in appendices (A-D).


20

A weight measure using an electronic balance (sensitivity ±0.01 g) followed,

and then the values obtained were used to calculate the density. It has to be noticed

that even if the different batches were made using the same parameters, the

densities of corresponding specimens were not the exactly same, due to a non

perfect repetitiveness of the manufacturing process.

3.1.3 Poisson’s ratio measurement

Poisson’s ratio were measured based on image data acquired with a

SAMSUN GPL20, 14.2 Megapixels, 5X zoom digital camera and processed by

using a new technique, the Get Data Digitizer and Matlab software. The images

were acquired during quasi-static tests performed with a Zwick universal testing

machine. The quasi-static tests (Compression and Tensile tests) were performed

using the Zwick universal testing machine. The Poisson’s ratio were measured by

cutting each sample in 70±2 mm length, and gluing it to the end clamp of the

machine with a Super Glue product in tensile test, and then stretched until breaking

or ungluing at 0.2 mm/s.

The test was recorded as a movie and we have taken captures at different

times (pictures cut) to compare (calibrate) it with the original photo to measure the

deformation occur in longitudinal and transverse strain during the testing. This

operation has been performed using the software of Get Data Digitizer and Matlab,

which calculate for every photo three values of transverse and three values of

length along the sample to get the output from the mean value in the two

directions, as shown in Figure (3). Once these data was calculated, it is possible to

calculate the Poisson’s ratio from equations (3) and tabulated in appendix (E)

for tensile test.

, and (3)


21

Figure (3.1) The calculation of the change in the transverse and longitudinal directions to get the Poisson’s ratio in compression and tensile test for conventional and auxetic samples.

��echa�ical�testi�g��achi�es�

3.2.1 Zwick universal testing machine

The machine used for the experiments is a Zwick universal testing machine,

which has enough displacement range and force to perform the experiments. A

picture of such a testing machine can be seen in Figure (3.2). The machine

basically consists of a motor, a load unit cell, a clamping system (different grips), a

lift system and a computer unit system. The load unit cell used in the experiments

is static at 10±0.001 kN.

The output data obtained was a relation between load and elongation to

evaluate the stress-strain curve and the mechanical properties of the conventional

and auxetic Polyurethane foams. The Zwick universal testing machine has been

used to carry out compression, hysteresis and tensile static tests on both

conventional and auxetic flexible Polyurethane foam samples.


22

Figure (3.2) Zwick universal testing machine.

3.2.2 Zwick rebound resilience tester machine

The Zwick resilience tester 5109 consists of a rebound, a screen monitor and

a control unit system. The output data obtained was used to measure the elasticity

behaviour as a mechanical property for elastomers and foams according to DIN

53512 Standard. This is digitally displayed directly in percentage (%). The Zwick

resilience tester is shown in Figure (3.3).


23

Technical characteristics:

• Pendulum length: 200.4 mm.

• Elevation angle: 90 degrees

• Impact velocity: 1,98 m/s

• Electr. Connection: 220V/50Hz

For DIN 53512 pendulum:

• Energy: 0.5 J

• Mass: 252 grams

• Shape of striker: half sphere

• Diameter: 15mm

• Application: elastomers

Figure (3.3) a) Zwick resilience tester machine, and b) Pendulums used for different tests.

a b


24

��echa�ical�testi�g�a��etho�ology�

3.3.1 Tensile test and methodology

Quasi-static tensile tests were carried out at a mean temperature of 27±2˚C

and relative humidity of 47±2%. Every sample should not be tested more than once,

and we have obtained the average data from three trial tests for same three

samples. The quasi-static tensile tests were carried out at speed was adjusted to be

position control rate of 0.2 mm/s.

The tensile tests have carried out on two different batches “cylindrical

flexible Polyurethane foam samples”, the first batch is four grey samples labelled

as (E, F, G and H), while the second batch is yellow samples labelled as (E*, F*,

G* and H*). The quasi-static tensile tests were applied until failure occurs in the

samples. The samples were cut in these dimensions (D=32±1 mm and L=70±1 mm).

Before starting the experiment, the top clamp end is moved up until there is enough

space for a sample to easily fit between them. In order to hold the samples in place,

a special addtion has been designed which is placed on top of the ends of the

samples [3]. The clamps used in the machine have a specific shape in order to

clamp the ends of the samples. The ends of sample were glued by using super glue

with a tee thermo-plastic section in order to hold the sample within the machine

grips.

By the way, the machine was adjusted to keep a constant distance of 70 mm

between the two grips. At this moment the samples were placed and locked

between the two special grips. There is no load between the clamps and the

sample, so the force of machine will be set to zero. After that the top clamp was

moved up. The data was acquired in displacement and force on the computer

monitor. With the knowledge of the initial sizes of the specimens it was then

possible to plot a strain-stress curve for every case. The static tensile tests applied

on the conventional and auxetic grey PU foam samples can be seen in figures

(3.4a) to (3.4d) and also, figures (3.4e) to (3.4h) show the tensile tests applied on

the conventional and auxetic yellow PU foam samples.


25

Figure (3.4c) Auxetic-80 grey PU foam sample (G)

At: e) No load, and f) Failure. Figure (3.4d) Auxetic-60 grey PU foam sample (H) At: g) No load, and h) Failure.

e g

f h

Figure (3.4a) Conventional grey PU foam sample (E) At: a) No load, and b) Failure.

Figure (3.4b) Auxetic-100 grey PU foam sample (F) At: c) No load and d) Failure.

a

b

c

d


26

Figure (3.4e) Conventional yellow PU foam sample (E*) At: i) No load, and j) Failure.

Figure (3.4f) Auxetic-100 yellow PU foam sample (F*) At: k) No load and l) Failure.

i k

j l

Figure (3.4g) Auxetic-80 yellow PU foam sample (G*) At: m) No load, and n) Failure.

Figure (3.4h) Auxetic-60 yellow PU foam sample (H*) At: o) No load, and p) Failure.

m o

n p


27

3.3.2 Compression test and methodology

Quasi-static compression tests were carried out at a mean temperature of

25±2 ˚C and relative humidity of 48±1 %. Every sample should not be tested more

than once, and we have obtained the average data from three trial tests for same

three samples. The quasi-static compression tests were carried out at speed was

adjusted to be strain control rate of 0.3 S-1.

Two different square batches were used, the one batch is four grey samples

labeled as (A, B, C and D), and the other batch is four yellow samples labeled as

(A*, B*, C* and D*). The quasi-static compression tests were applied on three

different compression strain levels (25, 50 and 75%) for all mentioned samples.

The samples were cut in dimensions are (35×35×70 mm). Before starting the

experiment, the top flat clamp end is moved up until there is enough space for a

sample to easily fit between them.


between the two flat grips. At this moment the samples were placed between the

two flat grips. There is no contact between the top clamp and the sample, so the

force of machine is measuring will be set to zero. The grips were lubricated to

minimize the friction between the contact surfaces. After that the top clamp was

moved lower. The data were acquired in displacement and force on the computer

monitor. With the knowledge of the initial sizes of the specimens it was then

possible to plot a stress strain curve for every case. The compression tests were

applied on square grey conventional and auxetic PU foam samples, as shown in

figures (3.5a) to (3.5d) and figures (3.5e) to (3.5h) for square yellow conventional

and auxetic PU foam samples.

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30

3.3.3 Hysteresis test and methodology

Low-strain rate hysteresis tests are like the quasi-static compression tests,

which were carried out at a mean temperature of 25±2˚C and relative humidity of

48±2 %. Every sample should not be tested more than once, and we have obtained

the average data from three trial tests for same three samples. The low-strain rate

hysteresis tests were carried out at cycle speed was adjusted to be strain control

rate of έ = 0.3 S-1 at lowering and rising.

Two different square batches were used, the one batch is four grey samples

labelled as (A, B, C and D), while the other batch is four yellow samples labelled

as (A*, B*, C* and D*). The low-strain rate hysteresis tests were applied at

different compression-hysteresis strain at (25, 50 and 75%) compression for all

mentioned samples. The samples were cut in dimensions are (35×35×70) mm3 to

implementation the test. Before starting the experiment, the top flat clamp end is

moved up until there is enough space for a sample to easily fit between them (the

initial reversal point was 0 % and upper reversal point was 50 % as strain control).


between the two flat grips. At this moment the samples were placed between the

two flat grips. There is no contact between the top clamp and the sample, so the

force of machine will be set to zero. The grips were lubricated to minimize the

friction between the contact surfaces.

After that the top clamp was moved lower until the determine compression

strain then the machine reverse its motion to return up “rising” to original position

(one cycle) with the same speed strain rate. The hysteresis test was implemented at

one, ten and twenty cycles at different compression strain levels 25, 50 and 75%

for all mentioned samples.


31

The data was acquired as displacement and force on the computer monitor

with sketch the relation between them. With the knowledge of the initial

dimensions of the samples it was then possible to plot a strain-stress curve for

every case. The low strain rate hysteresis tests on the samples are like the

compression tests. The dissipated energy was calculated from equation (4) at one

cycle and different compression strain levels for all PU foam samples.

(4)

where εmin and εmax are the minimum and maximum strain, respectively.

3.3.4 Resilience test and methodology

The Resilience Test was used to measure the elasticity behaviour of

elastomers. The resilience was determined previously by the equation (4). The

resilience test was carried out at a mean temperature of 25±2˚C and relative

humidity of 48±1%. The resilience value was obtained from the average data

acquired from three trial tests for same sample. Two different square batches were

used, as mentioned in compression and hysteresis tests, the one batch is four grey

samples labelled as (A, B, C and D), and the other batch is four yellow samples

labelled as (A*, B*, C* and D*). The resilience test was applied according to DIN-

53512 Standard for all samples.

The samples were cut in dimensions are (35×35×70) mm3. Before starting

the experiment, the resilience tester machine was set up. So, the tester the

resilience tester machine was switched on, select the mode as standard type (DIN

53512 Standard), select the mean average value , and then start the test, as

shown in the Figure (3.6).


32

The rebound strikes the sample six times per test, the one three strikes are

idle and the other three strikes are test. Every strike of the test will display its

elasticity value on the monitor screen. The mean value of elasticity was determined

by equation (5) and recorded on a monitor screen after the test finished.

(5)

Figure (3.6) Control panel of resilience tester machine.

CHAPTER (4)

RESULTS AND DISCUSSION

Chapter 4 “Results and Discussion”

33

4.1 Introduction

In this chapter, detailed test data are presented for conventional and auxetic

PU foam samples. First of all, the microstructure of the conventional and the

processed (auxetic) samples are examined to check if the auxetic microstructure is

obtained for the fabrication conditions presented in chapter 3. Also, the test data

for tensile, compression, hysteresis and resilience tests are presented and discussed

in the following section. The stress-strain curves for the first three tests of

polyurethane foam samples (tensile, compression and hysteresis) have been done,

while the other test (resilience) has been listed in tables. The values of the Young’s

modulus and Poisson’s ratio are extracted from the curves and presented in tables

for all samples.

4.2 Microstructure of flexible PU foam samples

Figures (4.1a) and (4.1b) show the microstructures of the square grey and

yellow of a conventional and three different types of auxetic PU foam samples.

The pictures were taken with an optical microscope facility. The grey and yellow

square conventional foam samples (A and A*) exhibit regular hexagonal unit cells

with straight ribs (ligaments), so a substantially isotropic distribution of the

principal axis of the cells in the various directions. While the grey and yellow

square auxetic foam samples (B, C, D, B*, C* and D*) show a more complex

compressive pattern and reduction of the cell sizes and exhibit irregular hexagonal

unit cells.

The reason behind that is due to the radial and axial thermal-compression

was done on the fabricated samples inside the moulds. So, the auxetic “fabricated”

PU foam samples lead to a reduction of the cell sizes and exhibit irregular

hexagonal unit cells as a global buckling of the cell ribs [2, 3, 20].


34

Figure (4.1a) Microstructure of square grey conventional and auxetic flexible PU foam samples at 40X magnification were: A: A conventional foam sample. B: An auxetic-100 foam sample. C: An auxetic-80 foam sample. D: An auxetic-60 foam sample.

Figure (4.1b) Microstructure of square yellow conventional and auxetic flexible PU foam

samples at 40X magnification were: A*: A conventional foam sample. B*: An auxetic-100 foam sample. C*: An auxetic-80 foam sample. D*: An auxetic-60 foam sample.

C* D*

B* A*

A

D C

B


35

Also, figures (4.2a) and (4.2b) show the microstructures of the circular grey

and yellow of a conventional and three different types of auxetic PU foam samples.

The pictures were taken with an optical microscope facility as mentioned above.

The circular conventional grey (E) and yellow (E*) PU foam samples exhibit

regular hexagonal unit cells with straight ribs.

The circular grey and yellow auxetic PU foam samples (F, G, H, F*, G* and

H*) show a more complex compressive pattern due to the radial and axial

compression operated in the mould. So, the auxetic foam samples lead to a

reduction of the cell sizes and exhibit irregular hexagonal unit cells. As mentioned

above for square samples.

Figure (4.2a) Microstructure of circular grey conventional and auxetic flexible PU foam samples at 40X magnification were: E: A conventional foam sample. F: An auxetic-100 foam sample. G: An auxetic-80 foam sample. H: An auxetic-60 foam sample.

E F

G H


36

Figure (4.2b) Microstructure of circular yellow conventional and auxetic flexible PU foam

samples at 40X magnification were: E*: A conventional foam sample. F*: An auxetic-100 foam sample. G*: An auxetic-80 foam sample. H*: An auxetic-60 foam sample.

E* F*

G* H*


37

4.3 Tensile test of grey samples

Figures (4.3a) to (4.3d) show the tensile stress-strain relationship of circular

grey conventional (E) and three different types of auxetic (F, G and H) PU

polymeric foam samples, until failure occur. For comparison between all tensile

stress-strain relationships of all circular grey PU foam samples, that are plotted in

one gragh, Figure (4.3e). The tensile test shows that, the auxetic foam samples

(F,G and H) give higher total strain and strength than the connventional foam

sample (E). So, the modulus of toughness “To” (Energy absorbed per unit volume

until failure of a sample equales to the area under stress strain curve) increased

more in the auxetic foams than the conventional foams.

Also, the results showed from image data processing that, the Poisson’s ratio

is positive for a conventional foam sample (E) but negative for auxetic foam

samples (F, G and H) at 2% of tensile strain. The mechanical properties of the

circular grey conventional and auxetic flexible PU foam samples (E, F, G and H)

are tabulated in table (4.1). It is clear that, the auxetic sample (F) gives the best

mechanical properties values of all auxetic samples such as the total tensile strain,

strength, poisson’s ratio and modulus of toughness (244.59%, 204.23 kPa, -0.26

and 203.53 kJ/m3); while the conventional foam sample (E) has mechanical

properties values as (138.8%, 102.3 kPa, 0.48, 84.7910 kJ/m3). The modulus of

elasticity of the conventional (E) foam sample (130.81 kPa) is higher than the

auxetic (F) foam samples (57.72 kPa) at 2% strain.

The reason behind that, because the ribs of the unit cells in the conventional

foams are regular hexagonal and non-deformed, while the unit cell ribs in the

auxetic foams are irregular (re-entrant) and deformed (buckled) due to the previous

processing technique, which occurs change in the foam density and porosity.

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

025

50

75

100

125

150

0

20

40

60

80

100

120

Strain [%

]

Stress [kPa]

Tensile Test of Conventional Grey Polyurethane Foam Sample [E]

E:(TG-Conv.)

F

ig. (

4.3a

) T

ensi

le s

tres

s-st

rain

cur

ve o

f a

conv

enti

onal

gre

y P

U f

oam

sam

ple

(E)

025

50

75

100

125

150

175

200

0

30

60

90

120

150

Strain [%

]

Stress [kPa]

Tensile Test of Auxetic 80 Grey Polyurethane Foam Sample [G]

F

ig. (

4.3c

) T

ensi

le s

tres

s-st

rain

cur

ve o

f an

aux

etic

-80

grey

PU

foa

m s

ampl

e (G

)

025

50

75

100

125

150

175

200

225

250

0

50

100

150

200

250

Strain [%

]

Stress [kPa]

Tensile Test of Auxetic 100 Grey Polyurethane Foam Sample [F]

F:(TG-Aux. 100)

F

ig. (

4.3b

) T

ensi

le s

tres

s-st

rain

cur

ve o

f an

aux

etic

-100

gre

y P

U f

oam

sam

ple

(F)

025

50

75

100

125

150

175

200

225

250

0

20

40

60

80

100

120

140

160

180

Strain [%

]

Stress [kPa]

Tensile Test of Auxetic 60 Grey Polyurethane Foam Sample [H]

H:(TG-Aux. 60)

F

ig. (

4.3d

) T

ensi

le s

tres

s-st

rain

cur

ve o

f an

aux

etic

-60

grey

PU

foa

m s

ampl

e (H

)


39

0 50 100 150 200 2500

50

100

150

200

250

Strain [%]

Stress [kPa]

Tensile Test of Conventional and Auxetic Grey Polyurethane Foam Samples

E:(TG-Conv.)

F:(TG-Aux. 100)

G:(TG-Aux. 80)

H:(TG-Aux. 60)

E

F

G

H

Fig. (4.3e) Tensile stress-strain curves of Conventional and auxetic grey PU foam samples (E, F, G and H)

Table (4.1) The mechanical properties of the circular grey conventional and auxetic flexible PU foam samples (E, F, G and H) under tensile test.

Samples εmax (%) σmax (kPa) E2% (kPa) υ2% To (kJ/m3) E :( TG-Conv.) 138.83 102.3 130.81 0.48 84.79 F :( TG-Aux.100) 244.59 204.23 57.72 - 0.26 203.53 G :( TG-Aux.80) 177.75 146.12 48.37 - 0.25 101.37 H :( TG-Aux.60) 219.42 169.92 35.30 - 0.23 133.86


40

4.4 Tensile test of yellow samples

Figures (4.4a) to (4.4d) show the tensile stress-strain relationship of the

circular yellow conventional (E*) and three different types of auxetic (F*,G* and

H*) PU foam samples, until failure occur. Figure (4.4e) shows the all above

mentioned figures in one plot to compare between them. The tensile tests show

that, the auxetic foam samples (F*,G* and H*) give higher strain and strength

values than the conventional foam sample (E*). So, the modulus of toughness “To”

(Energy absorbed per unit volume until failure of a sample = Area under stress

strain curve) is increased in auxetic foams more than conventional foams. Also, the

image data processing discoverd that, the poisson’s ratios are negative for auxetic

foam samples (F*,G* and H*) but positive for a conventional foam sample (E*).

Table (4.2) shows the mechanical properties of the circular yellow

conventional and auxetic flexible PU foam samples (E*, F*, G* and H*). The

auxetic foam sample (F*) gives the best mechanical properties values of all auxetic

samples such as the total tensile strain, strength, poisson’s ratio and modulus of

toughness (185.46%, 220.3 kPa, -0.27 and 277.28 kJ/m3); while the conventional

sample (E*) gives mechanical properties values of (79.31%, 73.77 kPa, 0.74, 36.19

kJ/m3). The modulus of elasticity of conventional (E*) foam sample (151.11 kPa)

is higher than auxetic (F*) foam samples (49.83 kPa) at 2% strain. The reason

behind that, the hexagonal unit cells are converted by the processing technique to

re-entrant unit cells, as mentioned previously.

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

010

20

30

40

50

60

70

80

0

10

20

30

40

50

60

70

80

Strain [%

]

Stress [kPa] Tensile Test of Conventional Yellow Polyurethane Foam Sample [E*]

E*:(TY-Conv.)

F

ig. (

4.4a

) T

ensi

le s

tres

s-st

rain

cur

ve o

f a

conv

enti

onal

yel

low

PU

foa

m s

ampl

e (E

*)

025

50

75

100

125

150

175

200

225

250

0

20

40

60

80

100

120

140

160

180

Strain [%

]

Stress [kPa]

Tensile Test of Auxetic 80 Yellow Polyurethane Foam Sample [G*]

G*:(TY-Aux.80)

F

ig. (

4.4c

) T

ensi

le s

tres

s-st

rain

cur

ve o

f an

aux

etic

-80

yell

ow P

U f

oam

sam

ple

(G*)

025

50

75

100

125

150

175

200

0

25

50

75

100

125

150

175

200

225

250

Strain [%

]

Stress [kPa]

Tensile Test of Auxetic 100 Yellow Polyurethane Foam Sample [F*]

F*:(TY-Aux.100)

F

ig. (

4.4b

) T

ensi

le s

tres

s-st

rain

cur

ve o

f an

aux

etic

-100

yel

low

PU

foa

m s

ampl

e (F

*)

025

50

75

100

125

150

175

200

225

250

0

25

50

75

100

125

150

175

200

225

250

Strain [%

]

Stress [kPa]

Tensile Test of Auxetic 60 Yellow Polyurethane Foam Sample [H*]

H*:(TY-Aux.60)

F

ig. (

4.4d

) T

ensi

le s

tres

s-st

rain

cur

ve o

f an

aux

etic

-60

yell

ow P

U f

oam

sam

ple

(H*)


42

0 50 100 150 200 2500

50

100

150

200

250

Strain [%]

Stress [kPa]

Tensile Test of Conventional and Auxetic Yellow Polyurethane Foam Samples

E*:(TY-Conv.)

F*:(TY-Aux. 100)

G*:(TY-Aux. 80)

H*:(TY-Aux. 60)

E*

F*

G*

H*

Fig. (4.4e) Tensile stress-strain curves of conventional and auxetic yellow PU foam samples (E*, F*, G* and H*)

Table (4.2) The mechanical properties of the circular yellow conventional and auxetic flexible foam samples (E*, F*, G* and H*) under tensile test.

Samples εmax (%) σmax (kPa) E2% (kPa) υ2% To (kJ/m3) E* :( TY-Conv.) 79.31 73.77 151.11 0.74 36.19 F* :( TY-Aux.100) 185.46 220.3 49.83 - 0.27 197.28 G* :( TY-Aux.80) 217.45 169.26 36.21 - 0.26 138.38 H* :( TY-Aux.60) 246.08 204.89 27.34 - 0.24 193.36


43

4.5 Compression test of grey samples

Quasi-static compression tests were applied on the square grey PU

conventional foam sample (A) and three different types of auxetic samples (B, C

and D) at three different compression strain levels (25, 50 and 75 %). The

compression tests show that the auxetic foam samples (B, C and D) give higher

strength and strain values than the conventional foam sample (A). So, the energy

absorbed is increased in auxetic foams more than conventional foams. Also, the

resullts found that, the poisson’s ratios are negative for auxetic foam samples but

positive for a conventional foam sample until 50% compression strain level.

Also, The results discovered that, at 75% compression strain level, the

conventional foam reversed to auxetic foam and gives a negative poisson’s ratio

and vice versa for Auxetic foam samples. The reason behind that, at high

compression strain level (75%), the regular hexagonal unit cells (conventional

foam) converted to re-entrant unit cells (auxetic foam), because the higher

compression strain makes the cell ribs buckled and behaves as the auxetic foam.

4.5.1 Compression strain at 25%

The quasi-static compression stress-strain relationship applied on the square

grey PU conventional foam sample (A) and three different auxetic foam samples

(B, C and D) at 25% compression strain level, as shown in figures (4.5a) to (4.5d).

For comparison between all square grey PU foam samples at 25% compression

stress-strain relationship, that are plotted in one gragh, figure (4.5e). The auxetic

foam sample (B) has a higher compression strain, strength, poisson’s ratio and

energy absorbed (22.78%, 13.56 kPa, -0.16, 1.22 kJ/m3) than conventional (A)

foam sample (24.41%, 4.48 kPa, 0.37, 0.9 kJ/m3), but the modulus of elasticity of a

conventional foam sample (A) is (132.35 kPa), while the auxetic foam sample (B)

is (30.87kPa), as shown in table (4.3).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.55

Strain [%]

Stress [kPa]Compression Test of Conventional Grey Polyurethane Foam Sample [A] at 25% Compression Strain

A (CG25%-Conv.)

Fig

. (4.

5a)

Com

pres

sion

str

ess-

stra

in c

urve

of

a co

nven

tion

al g

rey

PU

foa

m

sam

ple

(A)

at 2

5% c

ompr

essi

on s

trai

n

05

10

15

20

25

012345678

Strain [%]

Stress [kPa]

Compression Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 25% Compression Strain

C (CG25%-Aux.80)

Fig

. (4.

5c)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-8

0 gr

ey P

U f

oam

s

ampl

e (C

) at

25%

com

pres

sion

str

ain

05

10

15

20

25

02468

10

12

14

Strain [%]

Stress [kPa]

Compression Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 25% Compression Strain

B (CG25%-Aux.100)

Fig

. (4.

5b)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-1

00 g

rey

PU

foa

m

sam

ple

(B)

at 2

5% c

ompr

essi

on s

trai

n

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.55

5.5

Strain [%]

Stress [kPa]

Compression Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 25% Compression Strain

D (CG25%-Aux.60)

Fig

. (4.

5d)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-6

0 gr

ey P

U f

oam

sam

ple

(D)

at 2

5% c

ompr

essi

on s

trai

n


45

0 5 10 15 20 250

2

4

6

8

10

12

14

Strain [%]

Stress [kPa]

Compression Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 25% Compression Strain

A (CG25%-Conv.)

B (CG25%-Aux.100)

C (CG25%-Aux.80)

D (CG25%-Aux.60)

A

B

D

C

Fig. (4.5e) Compression stress-strain curves of conventional and auxetic grey PU foam samples (A, B, C and D) at 25% compression strain.

Table (4.3) shows the mechanical properties of the grey conventional and auxetic square flexible PU foam samples (A, B, C and D) at 25% compression.

Samples εmax (%) σmax (kPa) E2% (kPa) υ25% Eabs (kJ/m3) A :( CG25%-Conv.) 24.41 4.48 132.35 0.37 0.90 B :( CG25%-Aux.100) 22.78 13.56 30.87 -0.16 1.22 C :( CG25%-Aux.80) 22.77 7.44 24.49 -0.14 0.64 D :( CG25%-Aux.60) 22.17 4.95 20.02 -0.13 0.45


Figures (4.6a) to (4.6d) show the quasi-static compression tests applied on

the square grey PU conventional foam sample (A) and three different auxetic foam

samples (B, C and D) at 50% compression strain. For comparison between all

square grey PU foam samples at 50% compression stress-strain relationship, that

are plotted in one gragh, Figure (4.6e). The auxetic foam sample (B) have a higher

strain, strength, poisson’s ratios and energy absorbed (44.82%, 47.44 kPa, -0.11,

7.52 kJ/m3) than a conventional foam sample (48.97 %, 6.35 kPa, 0.07, 2.01

kJ/m3), but the modulus of elasticity of a conventional foam sample (A) is (132.03

kPa), while the auxetic foam sample (B) is (30.02 kPa), as shown in table (4.4).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

30

35

40

45

50

01234567

Strain [%]


A (CG50%-Conv.)

F

ig. (

4.6a

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f a

conv

enti

onal

gre

y P

U f

oam

s

ampl

e (A

) at

50%

com

pres

sion

str

ain

05

10

15

20

25

30

35

40

45

50

0

10

20

30

40

50

60

Strain [%]

Stress [kPa]


C (CG50%-Aux.80)

F

ig. (

4.6c

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-80

grey

PU

foa

m

sam

ple

(C)

at 5

0% c

ompr

essi

on s

trai

n

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


B (CG50%-Aux.100)

F

ig. (

4.6b

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-100

gre

y P

U f

oam

s

ampl

e (B

) at

50%

com

pres

sion

str

ain

05

10

15

20

25

30

35

40

45

50

0

10

20

30

40

50

60

Strain [%]

Stress [kPa]


D (CG50%-Aux.60)

F

ig. (

4.6d

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-60

grey

PU

foa

m

sa

mpl

e (D

) at

50%

com

pres

sion

str

ain


47

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

Strain [%]

Stress [kPa]


A (CG50%-Conv.)

B (CG50%-Aux.100)

C (CG50%-Aux.80)

D (CG50%-Aux.60)

A

B

CD

Fig. (4.6e) Compression stress-strain curves of Conventional and auxetic Grey PU foam samples (A, B, C and D) at 50% compression strain

Table (4.4) The mechanical properties of the grey Conventional and auxetic square flexible PU foam samples (A, B, C and D) at 50% compression test.

Samples εmax (%) σmax (kPa) E2% (kPa) υ50% Eabs (kJ/m3) A :( CG50%-Conv.) 48.97 6.35 132.03 0.07 2.01 B :( CG50%-Aux.100) 44.82 47.44 30.02 -0.11 7.52 C :( CG50%-Aux.80) 45.81 53.45 24.70 -0.07 6.70 D :( CG50%-Aux.60) 44.72 55.49 20.58 -0.05 5.41


Figures (4.7a) to (4.7d) show the quasi-static compression tests applied on

the square grey PU conventional foam sample (A) and three different auxetic foam

samples (B, C and D) at 75% compression strain. For the comparison between all

samples at 75% compression strain level, that are plotted in one gragh as shown in

figure (4.7e). The auxetic foam sample (B) has higher compression strain, strength,

poisson’s ratio and energy absorbed (69.37 %, 228.37 kPa, 0.09, 31.75 kJ/m3) than

conventional (A) foam sample (73.99 %, 19.56 kPa, -0.02, 4.62 kJ/m3). The results

discovered the modulus of elasticity of a conventional foam sample (A) is (132.98

kPa), but the auxetic foam sample (B) is (30.56 kPa), as shown in table (4.5).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

010

20

30

40

50

60

70

80

02468

10

12

14

16

18

20

Strain [%]


A (CG75%-Conv.)

F

ig. (

4.7a

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f a

conv

enti

onal

gre

y P

U f

oam

s

ampl

e (A

) at

75%

com

pres

sion

str

ain

010

20

30

40

50

60

70

0

50

100

150

200

250

Strain [%]

Stress [kPa]


B (CG75%-Aux.100)

F

ig. (

4.7b

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-100

gre

y P

U f

oam

s

ampl

e (B

) at

75%

com

pres

sion

str

ain

010

20

30

40

50

60

70

0

50

100

150

200

250

300

350

Strain [%]

Stress [kPa]


C (CG75%-Aux.80)

F

ig. (

4.7c

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-80

grey

PU

foa

m

sam

ple

(C)

at 7

5% c

ompr

essi

on s

trai

n

010

20

30

40

50

60

70

0

50

100

150

200

250

300

350

400

450

Strain [%]

Stress [kPa]


D (CG75%-Aux.60)

F

ig. (

4.7d

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-60

grey

PU

foa

m

sa

mpl

e (D

) at

75%

com

pres

sion

str

ain


49

0 10 20 30 40 50 60 70 800

50

100

150

200

250

300

350

400

450

Strain [%]

Stress [kPa]


A (CG75%-Conv.)

B (CG75%-Aux.100)

C (CG75%-Aux.80)

D (CG75%-Aux.60)

A

B

C

D

Fig. (4.7e) Compression stress-strain curves of conventional and auxetic grey PU foam samples (A, B, C and D) at 75% compression strain

Table (4.5) The mechanical properties of the grey conventional and auxetic square

flexible PU foam samples (A, B, C and D) at 75% compression test.

Samples εmax (%) σmax (kPa) E2% (kPa) υ75% Eabs (kJ/m3) A :( CG75%-Conv.) 73.99 19.56 132.98 -0.02 4.62 B :( CG75%-Aux.100) 69.37 228.37 30.56 0.0 9 31.75 C :( CG75%-Aux.80) 68.28 299.32 24.26 0.03 37.30 D :( CG75%-Aux.60) 64.17 399.09 20.96 0.01 37.08


50

4.6 Compression test of yellow samples

Quasi-static compression tests were applied on the square yellow PU

conventional foam sample (A*) and three different auxetic foam samples (B*, C*

and D*) at different compression strain levels (25, 50 and 75 %). The compression

tests show that the auxetic foam samples (B*, C* and D*) give the higher strength

and strain values more than the conventional foam sample (A*). So, the energy

absorbed is increased in auxetic foams more than conventional foams. Also, we

found that the poisson’s ratios are negative for auxetic foam samples but positive

for a conventional foam sample until 50% compression strain level. The results

discovered that, at 75% compression strain level, the conventional foam reversed

to auxetic foam and gives a negative poisson’s ratio and vice versa for auxetic

foam samples. The reason behind that mentioned previously in item (4.5).


Figures (4.8a) to (4.8d) show the quasi-static compression stress-strain

relationship applied on the square yellow PU conventional foam sample (A*) and

three different auxetic foam samples (B*, C* and D*) at 25% compression strain.

For comparison between all square yellow PU foam samples at 25% compression

stress-strain relationship, that are plotted in one gragh, Figure (4.8e). The auxetic

foam sample (B*) have a higher strain, strength, poisson’s ratios and energy

absorbed (23.49 %, 11.26 kPa, -0.22 and 1.03 kJ/m3) than a conventional (A*)

foam sample (24.42 %, 2.85 kPa, 0.11 and 0.54 kJ/m3), but the modulus of

elasticity of a conventional foam sample (A*) is (56.11 kPa), while the auxetic

foam sample (B*) is (27.50 kPa), as shown in table (4.6).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

0

0.51

1.52

2.53

Strain [%]

Stress [kPa]

Compression Test of Conventional Yellow Polyurethane Foam Sample [A*] at 25% Compression Strain

A* (CY25%-Conv.)

Fig

. (4.

8a)

Com

pres

sion

str

ess-

stra

in c

urve

of

a co

nven

tion

al y

ello

w P

U f

oam

s

ampl

e (A

*) a

t 25%

com

pres

sion

str

ain

05

10

15

20

25

02468

10

12

Strain [%]

Stress [kPa]

Compression Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 25% Compression Strain

B* (CY25%-Aux.100)

Fig

. (4.

8b)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-1

00 y

ello

w P

U f

oam

s

ampl

e (B

*) a

t 25%

com

pres

sion

str

ain

05

10

15

20

25

0123456789

10

Strain [%]

Stress [kPa]

Compression Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 25% Compression Strain

C* (CY25%-Aux.80)

Fig

. (4.

8c)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-8

0 ye

llow

PU

foa

m

sam

ple

(C*)

at 2

5% c

ompr

essi

on s

trai

n

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.5

Strain [%]

Stress [kPa]

Compression Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 25% Compression Strain

D* (CY25%-Aux.60)

Fig

. (4.

8d)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-6

0 ye

llow

PU

foa

m

sa

mpl

e (D

*) a

t 25%

com

pres

sion

str

ain


52

0 5 10 15 20 250

2

4

6

8

10

12

Strain [%]

Stress [kPa]

Compression Test of Yellow Conventional and AuxeticPolyurethane Foam Samples at 25% Compression Strain

A* (CY25%-Conv.)

B* (CY25%-Aux.100)

C* (CY25%-Aux.80)

D* (CY25%-Aux.60)

A*

D*

C*

B*

Fig. (4.8e) Compression stress-strain curves of Conventional and auxetic Yellow PU foam samples (A*, B*, C* and D*) at 25% compression strain.

Table (4.6) The mechanical properties of the yellow conventional and auxetic square flexible PU foam samples (A*, B*, C* and D*) at 25% compression.

Samples εmax (%) σmax (kPa) E2% (kPa) υ25% Eabs (kJ/m3) A* :( CY25%-Conv.) 24.42 2.85 56.11 0.11 0.54 B* :( CY25%-Aux.100) 23.49 11.26 27.50 -0.22 1.03 C* :( CY25%-Aux.80) 22.81 9.59 23.20 -0.18 0.74 D* :( CY25%-Aux.60) 22.23 4.20 16.61 -0.13 0.40







foam sample (B*) have a higher strain, strength, poisson’s ratios and energy

absorbed (47.01 %, 38.94 kPa, -0.14 and 6.50 kJ/m3) than a conventional (A*)

foam sample (48.43 %, 4.56 kPa, 0.03 and 1.48 kJ/m3), but the modulus of

elasticity of a conventional foam sample (A*) is (56.35 kPa), while the auxetic

foam sample (B*) is (27.03 kPa), as shown in table (4.7).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

30

35

40

45

50

0

0.51

1.52

2.53

3.54

4.55

Strain [%]

Stress [kPa]

Compression Test of Conventional Yellow Polyurethane Foam Sample [A*] at 50% Compression Strain

A* (CY50%-Conv.)

Fig

. (4.

9a)

Com

pres

sion

str

ess-

stra

in c

urve

of

a co

nven

tion

al y

ello

w P

U f

oam

sam

ple

(A*)

at 5

0% c

ompr

essi

on s

trai

n.

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

Strain [%]

Stress [kPa]


B* (CY50%-Aux.100)

Fig

. (4.

9b)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-1

00 y

ello

w P

U f

oam

sam

ple

(B*)

at 5

0% c

ompr

essi

on s

trai

n.

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


C* (CY50%-Aux.80)

Fig

. (4.

9c)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-8

0 ye

llow

PU

foa

m

sam

ple

(C*)

at 5

0% c

ompr

essi

on s

trai

n.

05

10

15

20

25

30

35

40

45

05

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


D* (CY50%-Aux.60)

Fig

. (4.

9d)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-6

0 ye

llow

PU

foa

m

sam

ple

(D*)

at 5

0% c

ompr

essi

on s

trai

n.


54

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]

Compression Test of Yellow Conventional and Auxetic Polyurethane Foam Samples at 50% Compression Strain

A* (CY50%-Conv.)

B* (CY50%-Aux.100)

C* (CY50%-Aux. 80)

D* (CY50%-Aux. 60)

A*

B*

C*D*

Fig. (4.9e) Compression stress-strain curves of conventional and auxetic yellow PU foam samples (A*, B*, C* and D*) at 50% compression strain.

Table (4.7) The mechanical properties of the yellow conventional and auxetic square flexible PU foam samples (A*, B*, C* and D*) at 50% compression test.

Samples εmax (%) σmax (kPa) E2% (kPa) υ50% Eabs (kJ/m3) A* :( CY50%-Conv.) 48.43 4.56 56.35 0.03 1.48 B* :( CY50%-Aux.100) 47.01 38.94 27.03 -0.14 6.50 C* :( CY50%-Aux.80) 45.78 49.30 23.73 -0.10 5.78 D* :( CY50%-Aux.60) 43.90 47.91 16.33 -0.06 4.61







foam sample (B*) has higher strain, strength, poisson’s ratio and energy absorbed

(70.24 %, 186.81 kPa, 0.06 and 26.68 kJ/m3) than a conventional (A*) foam

sample (73.29 %, 19.13 kPa, -0.08 and 3.7 kJ/m3). The modulus of elasticity of a

conventional foam sample (A*) is (55.51 kPa), but the auxetic foam sample (B*) is

(27.64 kPa), as shown in table (4.8).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

010

20

30

40

50

60

70

80

02468

10

12

14

16

18

20

Strain [%]

Stress [kPa]Compression Test of Conventional Yellow Polyurethane Foam Sample [A*] at 75% Compression Strain

A* (CY75%-Conv.)

Fig

. (4.

10a)

Com

pres

sion

str

ess-

stra

in c

urve

of

a co

nven

tion

al y

ello

w P

U f

oam

s

ampl

e (A

*) a

t 75%

com

pres

sion

str

ain.

010

20

30

40

50

60

70

0

50

100

150

200

250

300

Strain [%]

Stress [kPa]


C* (CY75%-Aux.80)

Fig

. (4.

10c)

Com

pres

sion

str

ess-

stra

in c

urve

of

an a

uxet

ic-8

0 ye

llow

PU

foa

m

sam

ple

(C*)

at 7

5% c

ompr

essi

on s

trai

n.

010

20

30

40

50

60

70

80

0

20

40

60

80

100

120

140

160

180

200

Strain [%]

Stress [kPa]


B* (CY75%-Aux.100)

Fig

. (4.

10b

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-100

yel

low

PU

foa

m

sam

ple

(B*)

at 7

5% c

ompr

essi

on s

trai

n.

010

20

30

40

50

60

70

0

50

100

150

200

250

300

350

Strain [%]

Stress [kPa]


D* (CY75%-Aux.60)

Fig

. (4.

10d

) C

ompr

essi

on s

tres

s-st

rain

cur

ve o

f an

aux

etic

-60

yell

ow P

U f

oam

s

ampl

e (D

*) a

t 75%

com

pres

sion

str

ain.


56

0 10 20 30 40 50 60 70 800

50

100

150

200

250

300

350

Strain [%]

Stress [kPa]

Compression Test of Yellow Conventional and Auxetic Polyurethane Foam Samples at 75% Compression Strain

A* (CY75%-Conv.)

B* (CY75%-Aux.100)

C* (CY75%-Aux.80)

D* (CY75%-Aux.60)

A*

D*

C*

B*

Fig. (4.10e) Compression stress-strain curves of conventional and auxetic yellow PU foam samples (A*, B*, C* and D*) at 75% compression strain.

Table (4.8) The mechanical properties of the yellow conventional and auxetic square flexible PU foam samples (A*, B*, C* and D*) at 75% compression.

Samples εmax (%) σmax (kPa) E2% (kPa) υ75% Eabs (kJ/m3) A* :( CY75%-Conv.) 73.29 19.13 55.51 -0.08 3.70 B* :( CY75%-Aux.100) 70.24 186.81 27.64 0.06 26.68 C* :( CY75%-Aux.80) 65.61 273.70 23.00 0.05 34.58 D* :( CY75%-Aux.60) 63.59 314.82 16.51 0.02 33.75


57

4.7 Hysteresis test of grey samples

A useful quantity for the estimation of fatigue behaviour in cellular foams is

the energy dissipation. In sandwich structures with polymeric foam core, it is

expected that the viscoelastic behaviour of the foam plays an important role in

absorbing and dissipating energy especially during dynamic loading [14]. The

stress-strain behaviour observed upon deformation typically includes a significant

strain energy contribution, with the area enclosed by the hysteresis loop

corresponding to the dissipated energy (Ed) for each cycle. For any given cycle

(N), the dissipated energy per unit volume is calculated by using equation (4) in

chapter 3. Hysteresis stress-strain tests were applied on the square grey PU

conventional foam sample (A) and auxetic foam samples (B, C and D) at one cycle

and different compression strains (25, 50 and 75 %).

4.7.1 Compression strain at 25% and one cycle

Figures (4.11a) to (4.11d) show the hysteresis stress-strain curves of the

square grey PU conventional foam sample (A) and three different auxetic foam

samples (B, C and D) at one cycle and 25% compression strain level. For

comparison between all square grey PU foam samples at one cycle and 25%

compression, that are plotted in one gragh, figure (4.11e). The conventional (A)

and auxetic (B) foam samples have almost the same dissipated energy (0.56 kJ/m3),

as shown in table (4.9).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.55

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional Grey Polyurethane Foam Sample [A] at 25% Compression Strain

A (HG25%-Conv.)

Fig

. (4.

11a)

One

cyc

le H

yste

resi

s st

ress

-str

ain

curv

e of

a c

onve

ntio

nal g

rey

PU

foam

sam

ple

(A)

at 2

5% c

ompr

essi

on s

trai

n.

05

10

15

20

25

012345678

Strain [%]

Stress [kPa]

Hysteresis Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 25% Compression Strain

C (HG25%-Aux.80)

Fig

. (4.

11c)

One

cyc

le H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

80 g

rey

PU

foa

m

s

ampl

e (C

) at

25%

com

pres

sion

str

ain.

05

10

15

20

25

02468

10

12

14

Strain [%]

Stress [kPa]

Hysteresis Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 25% Compression Strain

B (HG25%-Aux.100)

Fig

. (4.

11b

) O

ne c

ycle

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-10

0 gr

ey P

U f

oam

sam

ple

(B)

at 2

5% c

ompr

essi

on s

trai

n.

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.55

Strain [%]

Stress [kPa]

Hysteresis Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 25% Compression Strain

D (HG25%-Aux.60)

Fig

. (4.

11d

) O

ne c

ycle

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-60

gre

y P

U f

oam

sa

mpl

e (D

) at

25%

com

pres

sion

str

ain.


59

0 5 10 15 20 250

2

4

6

8

10

12

14

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 25% Compression Strain

A (HG25%-Conv.)

B (HG25%-Aux. 100)

C (HG25%-Aux. 80)

D (HG25%-Aux. 60)

B

A

C

D

Fig. (4.11e) Hysteresis stress-strain curves of conventional and auxetic grey PU foam samples (A, B, C and D) at 25% compression strain at one cycle.

Table (4.9) The mechanical properties of the grey conventional and auxetic square

flexible PU foam samples (A, B, C and D) at one cycle and 25% compression hysteresis test.


Figures (4.12a) to (4.12d) show the hysteresis stress-strain curves of the

square grey PU conventional foam sample (A) and auxetic foam samples (B, C and

D) at one cycle and 50% compression strain for every sample alone. For


compression, that are plotted in one gragh, figure (4.12e). The auxetic foam sample

(B) have a higher dissipated energy (3.98 kJ/m3) than the conventional foam

sample (A) (1.21 kJ/m3), as shown in table (4.10).

Samples Dissipated Energy (kJ/m3) A :( HG25%-Conv.) 0.57 B :( HG25%-Aux.100) 0.56 C :( HG25%-Aux.80) 0.30 D :( HG25%-Aux.60) 0.23

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

30

35

40

45

50

01234567

Strain [%]

Stress [kPa]


A (HG50%-Conv)

Fig

. (4.

12a)

One

cyc

le H

yste

resi

s st

ress

-str

ain

curv

e of

a c

onve

ntio

nal g

rey

PU

foa

m

sa

mpl

e (A

) at

50%

com

pres

sion

str

ain.

05

10

15

20

25

30

35

40

45

50

0

10

20

30

40

50

60

Strain [%]

Stress [kPa]


C (HG50%-Aux.80)

Fig

. (4.

12c)

One

cyc

le H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

80 g

rey

PU

foa

m

sam

ple

(C)

at 5

0% c

ompr

essi

on s

trai

n

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


B (HG50%-Aux.100)

Fig

. (4.

12b

) O

ne c

ycle

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-10

0 gr

ey P

U f

oam

sam

ple

(B)

at 5

0% c

ompr

essi

on s

trai

n

05

10

15

20

25

30

35

40

45

50

0

10

20

30

40

50

60

Strain [%]

Stress [kPa]


D (HG50%-Aux.60)

Fig

. (4.

12d

) O

ne c

ycle

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-60

gre

y P

U f

oam

sam

ple

(D)

at 5

0% c

ompr

essi

on s

trai

n


61

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional and Auxetic Gray Polyurethane Foam Samples at 50% Compression Strain

A (HG50%-Conv.)

B (HG50%-Aux. 100)

C (HG50%-Aux. 80)

D (HG50%-Aux. 60)

A

B

C

D

Fig. (4.12e) Hysteresis stress-strain curves of conventional and auxetic grey PU foam samples (A, B, C and D) at 50% compression strain at one cycle.

Table (4.10) The mechanical properties of the grey Conventional and auxetic square flexible PU foam samples (A, B, C and D) at one cycle and 50% compression hysteresis test.

Samples Dissipated Energy (kJ/m3) A :(HG50%-Conv.) 1.21 B :(HG50%-Aux.100) 3.98 C :(HG50%-Aux.80) 3.44 D :(HG50%-Aux.60) 2.79


Figures (4.13a) to (4.13d) show the stress-strain hysteresis curves of the

square grey PU conventional foam sample (A) and auxetic foam samples (B, C and

D) at one cycle and 75% compression strain for every sample alone. For


compression, that are plotted in one gragh, Figure (4.13e). The auxetic foam

sample (B) have a higher dissipated energy (19.82 kJ/m3) than the conventional

foam sample (A) (3.08 kJ/m3), as shown in table (4.11).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

015

30

45

60

75

02468

10

12

14

16

18

20

Strain [%]

Stress [kPa]


A (HG75%-Conv)

Fig

. (4.

13a)

One

cyc

le h

yste

resi

s st

ress

-str

ain

curv

e of

a c

onve

ntio

nal g

rey

PU

foa

m

s

ampl

e (A

) at

75%

com

pres

sion

str

ain.

015

30

45

60

75

0

50

100

150

200

250

300

350

Str

ain

[%

]S

tra

in [

%]

Str

ain

[%

]S

tra

in [

%]

Stress [kPa]


C (HG75%-Aux.80)

Fig

. (4.

13c)

One

cyc

le h

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

80 g

rey

PU

foa

m

sam

ple

(C)

at 7

5% c

ompr

essi

on s

trai

n.

015

30

45

60

75

0

50

100

150

200

250

Strain [%]

Stress [kPa]


B (HG75%-Aux.100)

Fig

. (4.

13b

) O

ne c

ycle

hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-10

0 gr

ey P

U f

oam

sam

ple

(B)

at 7

5% c

ompr

essi

on s

trai

n.

015

30

45

60

75

0

50

100

150

200

250

300

350

400

450

Strain [%]

Stress [kPa]


D (HG75%-Aux.60)

Fig

. (4.

13d

) O

ne c

ycle

hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-60

gre

y P

U f

oam

sa

mpl

e (D

) at

75%

com

pres

sion

str

ain.


63

0 10 20 30 40 50 60 70 800

50

100

150

200

250

300

350

400

450

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 75% Compression Strain

A (HG75%-Conv.)

B (HG75%-Aux. 100)

C (HG75%-Aux. 80)

D (HG75%-Aux. 60)

A

B

C

D

Fig. (4.13e) Hysteresis stress-strain curves of conventional and auxetic grey PU foam samples (A, B, C and D) at 75% compression strain and one cycle.

Table 4.11 The mechanical properties of the grey conventional and auxetic square

flexible PU foam samples (A, B, C and D) at one cycle and 75% compression hysteresis test.

Samples Dissipated Energy (kJ/m3) A :( HG75%-Conv.) 3.08 B :( HG75%-Aux.100) 19.82 C :( HG75%-Aux.80) 23.21 D :( HG75%-Aux.60) 20.94


64

4.8 Hysteresis test of yellow samples

The stress-strain behaviour observed upon deformation typically includes a

significant strain energy contribution, with the area enclosed by the hysteresis loop

corresponding to the dissipated energy (Ed) for each cycle. The quasi-static stress-

strain hysteresis tests were applied on the square yellow PU conventional foam

sample (A*) and auxetic foam samples (B*, C* and D*) at one cycle and different

compression strains (25, 50 and 75 %). As mentioned before in item (4.7).



square yellow PU conventional foam sample (A*) and auxetic foam samples (B*,

C* and D*) at one cycle and 25% compression strain for every sample alone. For

comparison between all square yellow PU foam samples at one cycle and 25%

compression, that are plotted in one gragh, Figure (4.14e). The auxetic foam

sample (B*) have a higher dissipated energy (0.49 kJ/m3) than the conventional

foam sample (A*) (0.34 kJ/m3), as shown in table (4.12).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

0

0.51

1.52

2.53

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional Yellow Polyurethane Foam Sample [A*] at 25% Compression Strain

A* (HY25%-Conv.)

Fig

. (4.

14a)

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

con

vent

iona

l yel

low

PU

foa

m

sam

ple

(A*)

at 2

5% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

05

10

15

20

25

0123456789

10

Strain [%]

Stress [kPa]

Hysteresis Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 25% Compression Strain

C* (HY25%-Aux.80)

Fig

. (4.

14c)

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-80

yel

low

PU

foa

m

sam

ple

(C*)

at 2

5% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

05

10

15

20

25

02468

10

12

Strain [%]

Stress [kPa]

Hysteresis Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 25% Compression Strain

B* (HY25%-Aux.100)

Fig

. (4.

14b

) H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

100

yell

ow P

U f

oam

sam

ple

(B*)

at 2

5% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

05

10

15

20

25

0

0.51

1.52

2.53

3.54

4.5

Strain [%]

Stress [kPa]

Hysteresis Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 25% Compression Strain

D* (HY25%-Aux.60)

Fig

. (4.

14d

) H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

60 y

ello

w P

U f

oam

s

ampl

e (D

*) a

t 25%

com

pres

sion

str

ain

and

one

cycl

e.


66

0 5 10 15 20 250

2

4

6

8

10

12

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional and Auxetic Yellow Polyurethane Foam Samples at 25% Compression Strain

A* (HY25%-Conv.

B* (HY25%-Aux. 100)

C* (HY25%-Aux. 80)

D* (HY25%-Aux. 60)

A*

B*

C*

D*

Fig. (4.14e) Hysteresis stress-strain curves of conventional and auxetic yellow PU foam samples (A*, B*, C* and D*) at 25% compression strain and one cycle.

Table (4.12) The mechanical properties of the yellow Conventional and auxetic square flexible PU foam samples at one cycle and 25% compression hysteresis test.

Samples Dissipated Energy (kJ/m3) A* :( HY25%-Conv.) 0.34 B* :( HY25%-Aux.100) 0.49 C* :( HY25%-Aux.80) 0.36 D* :( HY25%-Aux.60) 0.22







(B*) have a higher dissipated energy (3.42 kJ/m3) than the conventional foam

sample (A*) (0.88 kJ/m3), as shown in table (4.13).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

05

10

15

20

25

30

35

40

45

50

0

0.51

1.52

2.53

3.54

4.55

Strain [%]

Stress [kPa]

Hysteresis Test of Conventional Yellow Polyurethane Foam Sample [A*] at 50% Compression Strain

A* (HY50%-Conv.)

Fig

. (4.

15a)

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

con

vent

iona

l yel

low

PU

foa

m

sam

ple

(A*)

at 5

0% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


C* (HY50%-Aux.80)

Fig

. (4.

15c)

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-80

yel

low

PU

foa

m

sam

ple

(C*)

at 5

0% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

Strain [%]

Stress [kPa]


B* (HY50%-Aux.100)

Fig

. (4.

15b

) H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

100

yell

ow P

U f

oam

sam

ple

(B*)

at 5

0% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

05

10

15

20

25

30

35

40

45

50

05

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


D* (HY50%-Aux.60)

Fig

. (4.

15d

) H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

60 y

ello

w P

U f

oam

s

ampl

e (D

*) a

t 50%

com

pres

sion

str

ain

and

one

cycl

e.


68

0 5 10 15 20 25 30 35 40 45 500

5

10

15

20

25

30

35

40

45

50

Strain [%]

Stress [kPa]


A* (HY50%-Conv.)

B* (HY50%-Aux. 100)

C* (HY50%-Aux. 80)

D* (HY50%-Aux. 60)

A*

B*

C*D*

Fig. (4.15e) Hysteresis stress-strain curves of conventional and auxetic yellow PU foam samples (A*, B*, C* and D*) at 50% compression strain and one cycle. Table (4.13) The mechanical properties of the yellow conventional and auxetic square flexible PU foam samples at one cycle and 50% compression hysteresis test.








(B*) have a higher dissipated energy (17.62 kJ/m3) than the conventional foam

sample (A*) (2.44 kJ/m3), as shown in table (4.14).

Ch

apte

r 4

“R

esu

lts

and

Dis

cuss

ion

”

015

30

45

60

75

02468

10

12

14

16

18

20

Strain [%]

Stress [kPa]Hysteresis Test of Conventional Yellow Polyurethane Foam Sample [A*] at 75% Compression Strain

A* (HY75%-Conv.)

Fig

. (4.

16a)

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

con

vent

iona

l yel

low

PU

foa

m

s

ampl

e (A

*) a

t 75%

com

pres

sion

str

ain

and

one

cycl

e.

015

30

45

60

75

0

50

100

150

200

250

300

Strain [%]

Stress [kPa]


C* (HY75%-Aux.80)

Fig

. (4.

16c)

Hys

tere

sis

stre

ss-s

trai

n cu

rve

of a

n au

xeti

c-80

yel

low

PU

foa

m

sam

ple

(C*)

at 7

5% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

015

30

45

60

75

0

20

40

60

80

100

120

140

160

180

200

Strain [%]

Stress [kPa]


B* (HY75%-Aux.100)

Fig

. (4.

16b

) H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

100

yell

ow P

U f

oam

sam

ple

(B*)

at 7

5% c

ompr

essi

on s

trai

n an

d on

e cy

cle.

015

30

45

60

75

0

50

100

150

200

250

300

350

Strain [%]

Stress [kPa]


D* (HY75%-Aux.60)

Fig

. (4.

16d

) H

yste

resi

s st

ress

-str

ain

curv

e of

an

auxe

tic-

60 y

ello

w P

U f

oam

s

ampl

e (D

*) a

t 75%

com

pres

sion

str

ain

and

one

cycl

e.


70

0 15 30 45 60 750

50

100

150

200

250

300

350

Strain [%]

Stress [kPa]


A* (HY75%-Conv.)

B* (HY75%-Aux. 100)

C* (HY75%-Aux. 80)

D* (HY75%-Aux. 60)

A*

B*

C*

D*

Fig. (4.16e) Hysteresis stress-strain curves of conventional and auxetic yellow PU foam samples (A*, B*, C* and D*) at 75% compression strain and one cycle. Table (4.14) The mechanical properties of the yellow conventional and auxetic square flexible PU foam samples at one cycle and 75% compression hysteresis test.



71

4.9 Resilience test

The Zwick Resilience Tester was used to determine the resilience (elasticity)

of the foam samples. The output data obtained were used to measure the elasticity

behaviour as a mechanical property for elastomers and foams (Conventional and

auxetic flexible Polyurethane foams) according to DIN 53512 Standard. The mean

value of elasticity (resilience) is determined by equation (5) in chapter 3.

This is digitally displayed directly in percentage (%). Table (4.15) shows the

mean values of resilience for the square conventional and three different auxetic

samples. The three types of auxetic grey and yellow foam samples (B, C, D, B*,

C* and D*) give a higher resilience (elasticity) of the conventional foam samples

(A and A*), but (Aux.60) was released the highest values of resilience than the

other auxetic grey and yellow samples. It is attributed to the buckling of the auxetic

foam unit cells during the processing.


72

Table (4.15a to 4.15d) The mean values of the resilience test for the conventional and three different types of auxetic PU foams for grey and yellow samples.

a. Conventional foam sample (grey and yellow) Conventional grey sample (A) Conventional yellow sample (A*)

Resilience test %

First strike 34.4 33.8 35.2 34.2 34 31 Second strike 36.2 34 35.8 34.4 34.2 32.2 Third strike 35.6 35.4 35.4 33 33.8 30.8

Average test value (%) 35.4 34.4 35.4 34.2 34 31.3

Final mean value ( ) 35.07 % 33.17 %

b. Auxetic-100 PU foam sample (grey and yellow) Auxetic-100 grey sample (B) Auxetic-100 yellow sample (B*)

Resilience test %

First strike 37.4 36 36.4 37.4 37.8 38 Second strike 39.8 36 37.8 39 37.2 36.2 Third strike 37.6 38.4 37 37.6 38.6 37.2

Average test value (%) 38.2 36.8 37 38 37.8 37.1

Final mean value ( ) 37.33 % 37.91 %

c. Auxetic-80 PU foam sample (grey and yellow) Auxetic-80 grey sample (C) Auxetic-80 yellow sample (C*)

Resilience test %

First strike 37.8 38 37.4 38.4 38 37.4 Second strike 37.2 36.2 39 38 37.8 38.6 Third strike 38.6 37.2 37.6 39.2 39.2 37.8

Average test value (%) 37.8 37.1 38 38.5 38.3 37.9

Final mean value ( ) 37.63 % 38.23 %

d. Auxetic-60 PU foam sample (grey and yellow) Auxetic-60 grey sample (D) Auxetic-60 yellow sample (D*)

Resilience test %

First strike 37.2 38 38.2 39.6 40.6 40.2 Second strike 37.8 38.6 38.4 40 40.4 39.8 Third strike 38.4 38 37.6 38 41.4 38.2

Average test value (%) 37.8 38.2 38 39.2 40.8 39.4

Final mean value ( ) 38.00 % 39.80 %


73

4.10 General discussions of the test results

4.10.1 Tensile tests

The tensile test was carried out on grey and yellow samples having circular

cross section. The tests were carried out on conventional and processed auxetic

foam at different compression ratios. Generally speaking, the conventional foam

showed higher tensile modulus and less total strain than the auxetic foam. The

reason behind that, the unit cell of the auxetic foam has taken an irregular

hexagonal shape as shown in Figure (4.1) and (4.2). The unit cell of the auxetic

foam takes the shape of almost the reentrant hexagonal unit cell. The degree of

irregularity depends on the compression ratio. The effect of the tensile force on the

auxetic unit cell is that the force tends to return the unit cell to its original shape

first up to a certain strain level and then the behavior of the foam changes to that of

the conventional foam.

The strain level required to change the foam from auxetic to conventional

caused that the total strain is higher than that of the conventional foam. Also, the

fracture stress of the auxetic foam is higher than that of the conventional foam and

this combined with the high fracture strain has been reflected on the amount of the

energy absorbed until fracture.

For both grey and yellow auxetic foams, the effect of the compression ratio

has a significant effect on Young’s modulus. It has been observed that the modulus

has decreased by 45%, meanwhile the compression ratio increased by 40%.

However the effect of the compression ratio on Poisson’s ratio is less significant

and it has decreased by 11%, meanwhile the compression ratio increase by 40%.

Also it was expected that the amount of energy absorbed to be increases, as the

compression ratio increase however a discrepancy in calculation was observed and

this can be referred to the errors during integration of the stress-strain data.


74

4.10.2 Compression tests

The compression test is carried out on grey and yellow samples using three

strain levels 25%, 50% and 75% for both conventional and processed auxetic

foam. The reason behind the use of these three strain levels is to observe that how

the processed foam will retain the auxetic behavior [32]. For both grey and yellow

auxetic samples, the auxetic behavior has been retained for up to 50% compression

while it has been converted into conventional for 75%. The reason behind that, the

high compression strain level of the auxetic foams was at 75% compression. At

this compression strain level the material has started to behave as a solid polymeric

PU material. Thus has been noticed also that the auxetic samples does not reach the

required strain level, but it reaches to from 10-15 % which is less than that of the

conventional foam.

Generally, for both grey and yellow samples, the conventional foam showed

a typical stress strain curve with the well-known plateau with the three regions of

the deformation mechanism explained by Gibson and Ashby [2] as follows:

a. Linear elastic region which follows the theory of elasticity,

b. The plateau, which is formed because of the elastic buckling of the unit cell walls,

c. Post-buckling of the unit cell wall or what so called densification of the foam in which the foam behaves like solid polymer.

For all processed auxetic samples, the stress-strain curve showed different behavior

which consists of mainly two regions:

a. Linear elastic region which follows the theory of elasticity, and

b. Post-buckling of the unit cell wall or what so called densification of the foam in which the foam behaves like solid polymer.


75

This behavior can be referred to that the elastic buckling of the wall cells

does not occur due to the irregularity of the unit cell which takes the form of a re-

entrant hexagon. The effect of the compression ratio on the value of the Poisson’s

ratio is found to be reduced in the negativity as the decrease of the compression

ratio. For example of yellow foam at a strain level of 25% the value of Poisson’s

ratio has decreased from -0.22 to -0.13 as the compression is reduced by 40%. Also

as the compression ratio decrease, the value of Young’s modulus increase.

4.10.3 Hysteresis test

The hysteresis test is carried out on grey and yellow samples using three

strain levels 25%, 50% and 75% for both conventional and processed auxetic

foam. The reason behind the use of these three strain levels is to observe that how

much the energy lost during unloading due to hysteresis in the polymer. The

energy lost is affected by the strain level and the compression ratio of the

processed foam, for both grey and yellow auxetic samples.

4.10.4 Resilience test

In the resilience test the average value of the resilience for the conventional

yellow foam is 33.17 %, meanwhile the grey foam showed slightly higher value of

35.07 % which is attributed to the increase of the foam density.

The average resilience value of grey and yellow auxetic foams are around

38.15 %, which showed slight effect of the compression ratio and which is

influence affect the density of the foam. However the value of the resilience of the

auxetic yellow foam is higher than that of the conventional foam by 16.6 %. The

same observations were made for the grey foam and the value of resilience

increase over the conventional foam by 7.7 %.

However, it was expected to obtain a higher value of the resilience for the

denser foam. This can be referred to the test errors or the defects obtained during

the fabrication of the auxetic foam. Some samples showed melting spots on the

surface of the samples.

CHAPTER (5)

CONCLUSIONS AND FUTURE WORK

Chapter � “CONCLUSIONS AND FURTHER WORK”

76

5.1 Conclusions

Based on present results, the following can be concluded:

1- The present work is focusing on the development of new class of

polymeric flexible foam called auxetic foam which has negative Poisson’s ratio.

The foam is successfully fabricated using commercial conventional Polyurethane

PU foam.

2- The foam has been fabricated from foam has different densities.

However, low density foam was not suitable for the fabrication technique used in

the present work which mainly depends on the heat treatment of the conventional

foam.

3- The microstructure of the conventional foam and the processed foam

has been examined first to compare both of the conventional and the processed

foam and second to ensure that the auxetic behavior will be obtained. The

microstructure of the processed foam showed the auxetic microstructure presented

in the literature. Several mechanical tests have been carried out to obtain the

mechanical properties of the foam. The tests carried out on the yellow and the grey

foam are; tensile, compression, hysteresis and resilience tests. The following

remarks have been concluded:

3.1- From the tensile test, for both grey and yellow auxetic foams, the

effect of the compression ratio has a significant effect on Young’s modulus. It has

been observed that the modulus has decreased by 45% as the compression ratio

increased by 40%. However the effect of the compression ratio on Poisson’s ratio

is less significant and it has increase by 11% in negativity as the compression ratio

increase by 40%.


77

Also, it was expected that the amount of energy absorbed to be increases as

the compression ratio increase however a discrepancy in calculation was observed

and this can be referred to the errors during integration of the stress-strain data.

Auxetic foam has higher strength, modulus of toughness and low modulus of

elasticity compared with conventional foam at tensile test.

3.2- From the compression test for both grey and yellow auxetic samples,

the auxetic behavior has been retained for up to 50% compression while it has been

converted into conventional for 75%. The reason behind that for 75% compression

and high compression ratio of the auxetic foam is that the material has started to

behave as a solid polymeric PU material.

Generally for both grey and yellow samples, the conventional foam showed

a typical stress strain curve with the well-known plateau while for all processed

auxetic samples, the stress-strain curve showed different behavior which consists

of mainly two regions, linear elastic region and post-buckling of the unit cell wall

or what so called densification of the foam in which the foam behaves like solid

polymer.

The effect of the compression ratio on the value of the Poisson’s ratio is

found to be reduced in the negativity as the decrease of the compression ratio. For

example for grey foam at a strain level of 25% the value of Poisson’s’ ratio has

decreased from -0.22 to -0.13 as the compression is reduced by 40%. Also as the

compression ratio decrease, the value of Young’s modulus increase.

3.3- In the hysteresis test, three strain levels are used to evaluate how

much the energy lost during unloading due to hysteresis in the polymer is affected

by the strain level and the compression ratio of the processed foam. For both grey

and yellow auxetic sample have higher dissipated energy than conventional foams

at high compression hysteresis test for both types of foams.


78

3.4- In the resilience test the average value of the resilience for the

conventional yellow foam is 33.1 while the grey foam showed slightly higher value

of 35% which is due to the increase of the foam density. For the auxetic foam the

average value of the resilience for the yellow and the grey foams are around 38%

which showed slight effect of the compression ratio which mainly affect the

density of the foam. However the value of the resilience of the auxetic yellow foam

is higher than that of the conventional foam by 13%.

The same observations were made for the grey foam and the value of

resilience increase over the conventional foam by almost the same amount.

However It was expected to obtained a higher value of the resilience for the denser

foam. This can be referred to the test errors or the defects obtained during the

fabrication of the auxetic foam. Some samples showed melting spots on the surface

of the samples.


79

5.2 The applications of auxetic materials

5.2.1 Magnox nuclear reactors

Currently auxetic materials are used in the moderators of magnox nuclear

reactors because they have the maximum shear modulus to protect the graphite

rods from damage that could be caused by an earthquake [33].

5.2.2 Aerospace field

Commonly when an auxetic material is subjected to a bending moment the

result is a double curvature deformation, better known as synclastic curvature,

shown in the previous figure (5.1a). This behavior coupled with the great impact

resistance of auxetic material makes it suitable for the aerospace field in these

things, the nose-cone of airplane, the sandwich panels used in the wings, and the

duct lines in the wings themselves or car body parts [33, 34].

In aerospace industry it is useful for the manufacture of space structures

such as large antennas and sun shields that could be launched into space in a closed

compact form and then “open up” at a later stage in space. (Grima, et al, 2005).

Currently, energy dissipating material is used for cushioning the impact of

all airborne supplies in order to ensure that they arrive on the ground safely and are

fully functional. Materials with NPR (e.g. auxetics) possess much better impact

resistance, indentation resistance and energy absorption properties.

Therefore, a material with NPR might be potentially applied to aircraft

equipment protection such as cargo drop to prevent the damage due to high energy

absorption. (Athiniotis & Cannon, 2006).


80

5.2.3 Military

The Defence Clothing and Textile Agency (DCTA) in Colchester, which is

responsible for research into high-tech clothing for the military, has been looking

into the use of auxetic textiles for military purposes. The military applications of

auxetic material have been looked into, especially with material that has the

auxeticity in the out-of-plane direction. The interest is driven by the fact that

impact resistance is improved, so the material could be applied to things like body

armor, bullet proof vests and in field bandages, and wound pressure pads [35].

A normal material responds to this by attempting to shrink in the

perpendicular direction, so the edges tend to curl upwards, leading to formation of

a saddle shaped surface (anticlastic curvature), as shown in figure (5.1a). But in

auxetic materials the response is to cause the edges to curve downwards, that is

convex shape (dome-like shape), which is the same direction as the bending force

Figure (5.1b). So, the convex shapes are more appropriate than saddle shapes for

sandwich panels for aircraft or automobiles [3, 4].

Figure (5.1) Bending behaviors of (a) Curvature behaviors in non-auxetic and (b) auxetic (double curvature-convex shape) (after Lakes, 1987; Evans, 1990; Cherfas, 1990).

Body armor made from auxetic materials could give the similar protection

for military personnel in the battlefield, but it would be thinner and lighter and

conform better to the synclastic double curvatures of the human body.. (Burke, 1997; McMullan, 2004).

Another promising application area is using auxetic polymers to make

bullet-proof helmets or vests more resilient to knocks and shrapnel.


81

When an auxetic helmet suffers an impact from one direction, material

should flow in from other directions to compensate for the impact. Therefore, head

injuries may be prevented or be less severe figure (5.2).

Figure (5.2) Schematic of the principle of auxetic material used to human protection. (After Alderson, 1999).

Auxetic materials have also been identified as candidate materials for use in

electromagnetic launcher technology to propel such projectiles. And the intended

recipient of the projectile might benefit from a bullet-proof vest and other personal

protective equipment formed from auxetic material because of their impact

property enhancements.

5.2.4 Industrial fields

The counterintuitive property of auxetic materials, namely, lateral expansion

under longitudinal tensile loads, is essential from the point of view of modern

technology. Many applications for auxetic materials have been designed in various

fields of human activity, from vascular implants, strain sensors, shock and sound

absorbers, "press-fit" fasteners, gaskets and air filters, to fillings for highway

joints. Materials containing inclusions of negative stiffness constitute another class

of systems with unusual mechanical properties. The recent interest in such systems

has its origin in their very high damping properties.


82

5.2.5 Biomedicine

The biomedical field has also taken interest in auxetic materials for

application in dilator and artificial blood vessels [16]. Used as a dilator for opening

the cavity of an artery or similar vessel has been described for use in heart surgery

(angioplasty) and related procedures as seen in figure (5.3).

Figure (5.3) Dilator employing an auxetic end sheath. Insertion of finger and thumb apparatus causes the auxetic sheath to extend and expand laterally, thus opening up the surrounding vessel. (after Moyers, 1992; Alderson, 1999).

Artificial blood vessel if is made of conventional material, it tends to

undergo a decrease in wall thickness as the vessel opens up in response to a pulse

of blood flowing through it figure (5.4a). This could lead to rupture of the vessel

with potentially catastrophic results. However, if an auxetic blood vessel is used,

the wall thickness increases when a pulse of blood flows through it figure (5.4b).

Figure (5.4) Deformation behaviour of artificial blood vessels: a) Conventional material, and b) auxetic blood vessel.. (after

Evans & Alderson, 2000).


83

5.3 Further work

The following topics could be a good opportunity on further

research on auxetic foam:

1. Fabrication of full size foam for some specific applications.

2. Fabrication of auxetic foam from other types of traditional foam such as metallic foam which will be good candidate for automotive industry applications.

3. Modeling of the behavior of the auxetic foam using analytical methods and finite element method and comparing the behavior with the one observed during the mechanical tests

4. Carrying out other tests such as acoustic and vibration damping test of the auxetic foam.

REFERENCES

84

References

(1) Gibson, L. J., Ashby, M. F., Schajer, G. S. and Robertson, C. I., “The mechanics of two dimensional cellular materials”, Proceedings of The Royal Society of London, vol. 382, pp.25-42, 1982.

(2) Gibson, L.J. and Ashby, M.F., “Cellular Solids: Structure and Properties”, Pergamn Press, London, 1988.

(3) Lakes, R.S. (1987a), “Foam structures with a negative Poisson's ratio”, Science, vol. 235, pp.1038-1040, 1987.

(4) Lakes, R.S. (1987b), “Polyhedron cell structure and method of making same”, Int. Patent Publ. No. WO88/00523, May 1987.

(5) Evans, K.E., Nkansah, M.A., Hutchinson, I.J. and Rogers, S.C., “Molecular network design”, Nature, vol.353, pp.124, 1991.

(6) Caddock, B.D. and Evans, K.E., “Microporous materials with negative Poisson’s ratio: I. Microstructure and mechanical properties”, J. Phys. D-Apply Phys., vol. 22, no(12), pp. 1877- 1882, 1989.

(7) Pickles, A.P., Alderson, K.L. and Evans, K.E., “The effects of powder morphology on the processing of auxetic polypropylene PP of negative Poisson’s ratio”, Polym. Eng. & Sci., vol. 36, no (5), pp. 636-642, 1996.

(8) Alderson, K. L., Webber, R.S. and Evans, K.E., “Novel variation in the microstructure of auxetic microporous ultra high molecular weight polyethylene, Part 2: Mechanical properties”, Poly. Eng. Sci., vol.40, no(8), pp.1906-1914, 2000.

(9) Alderson, K.L., Fitzgerald, A.F. and Evans, K.E., “The strain dependent indentation resilience of auxetic microporous polyethylene”, J. Mat. Sci., vol. 35, no(16), 4039-4047, 2000.

(10) Nur, A. and Simmons, G., “The effect of saturation on velocity in low porosity rocks”, Earth Planet Sci. Lett., vol.7, pp.183-193, 1969.

(11) Evans, K.E., “Tailoring the negative Poisson’s ratio”, Chem. Ind., vol.20, pp.654-657, 1990.

(12) Fung, Y.C., “Foundations of Solid Mechanics”, Prentice-Hall, p.353, 1968.

(13) Beer, F.P., Johnston, E.R., Jr. and DE Wolf, J.T., “Mechanics of Materials”, McGraw Hill, vol. 84, 2001.

(14) Choi, J.B and Lakes, R.S., “Fracture toughness of Re-entrant foam materials with a negative Poisson’s ratio: Experiment and Analysis”, Int. J. Fracture, vol. 80, pp.73-83, 1996.

85

(15) Chan, N. and Evans, “Microscopic examination of the microstructure and deformation of conventional and auxetic foams”, J. Mater. Sci., vol.32, no (21), pp.5725-5736, 1997.

(16) Friis, E. A., Lakes, R. S., and Park, J. B., “Negative Poisson's Ratio Polymeric and Metallic Foams”, Journal of Materials Science, vol. 23, pp. 4406-4414, 1988.

(17) Choi J. B. and Lakes R. S., “Nonlinear properties of polymer cellular materials with a negative Poisson's ratio”, J. Materials Science, vol. 27, pp. 4678-4684, 1992.

(18) Choi J. B. and Lakes R. S., “Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative poisson’s ratio”, Int. J. Mech. Sci., vol. 37, pp. 51-59, 1995.

(19) Lee, T. and Lakes, R. S., “Anisotropic polyurethane foam with Poisson's ratio greater than 1”, Journal of Materials Science, vol. 32, pp. 2397-2401, 1997.

(20) Beth A. Todd, PhD; S. Leeann Smith, BS ; Thongsay Vongpaseuth, BS. "Polyurethane foams : Effects of specimen size when determining cushioning stiffness." Journal of Rehabilitation Research and Development vol. 35, pp. 219-224, 1998.

(21) A. Lowe, and R. S. Lakes. "Negative Poisson's Ratio Foam as Seat Cushion Material." Cellular Polymers, vol.19, pp.157-167, 2000.

(22) Yun-Che Wang, Roderic Lakes, and Amanda Butenhoff. "Influence of Cell Size on Re-Entrant Transformation of Negative Poisson's Ratio Reticulated Polyurethane Foams" Cellular Polymers, vol. 20, pp. 373-385, 2001.

(23) Brandel, B. and Lakes, R. S. "Negative Poisson’s ratio polyethylene foams”, Materials Science, vol. 36, pp. 5885-5893, 2001.

(24) R. S. Lakes and R. Witt. "Making and characterizing negative Poisson's ratio materials", International Journal of Mechanical Engineering Education, Vol. 30, pp. 50-58, 2002.

(25) F. Scarpa*, J. Giacominº, Y. Zhang*, and P. Pastorino. "Mechanical Performance of auxetic Polyurethane Foam for Antivibration Glove Applications", Cellular Polymers, vol. 24, 2005.

(26) B. Moore, T. Jaglinski, D.S. Stone§ and R.S. Lakes. "On the Bulk Modulus of Open Cell Foams", Cellular Polymers, vol. 26, 2007.

(27) Abderrezak Bezazi 1, Fabrizio Scarpa. "Mechanical behaviour of conventional and negative Poisson’s ratio thermoplastic polyurethane foams under compressive cyclic loading", International Journal of Fatigue (Elsevier), vol. 29, pp. 922–930, 2007.

(28) Matteo Bianchi Æ Fabrizio L. Scarpa Æ. "Stiffness and energy dissipation in polyurethane auxetic foams", J Mater Sci., vol. 43, pp. 5851–5860, 2008.

86

(29) Abderrezak Bezazi, Fabrizio Scarpa. "Tensile fatigue of conventional and negative Poisson’s ratio open cell PU foams", International Journal of Fatigue, vol. 31, pp. 488-494, 2009.

(30) Yanping Liu and Hong Hu. "A review on auxetic structures and polymeric materials", Scientific Research and Essays, vol. 5, no (10), PP. 1052-1063, 2010.

(31) Pierron, F. "Mechanical properties of low density polymeric foams obtained from full-field measurements", EPJ Web of Conferences (EDP Sciences), 2010.

(32) R.D.Widdle Jr., A.K. Bajaj and P. Davies “Measurement of the Poisson’s ratio of flexible Polyurethane foam and its influence on a uniaxial compression model", sciencedirect, vol. 46, pp. 31-49, 2008.

(33) K. Evans and A. Alderson, “Auxetic materials: Functional materials and structures from lateral thinking", Advanced Materials, vol. 12, no (9), pp. 617-628, 2000.

(34) G. Stavroulakis, “Auxetic behaviour: Appearance and engineering applications", Physica Status Solidi (b), vol. 242, no 3, pp. 710-720, 2005.

(35) P. McMullan, S. Kumar, and A. Grifin, “Textile fibres engineered from molecular auxetic polymers", World, vol. 8, pp. 12, 2000.

APPENDICES

A

pp

end

ix A

: D

ensi

ties

and

com

pres

sion

rat

ios

of s

ampl

es (

Fir

st B

atch

)

Vb

efor

e=50

0000

mm

3 , V1,

mou

ld=

6144

0 m

m3 , V

2,m

ould

=81

920

mm

3 an

d V

3,m

ould

=10

2400

mm

3

Sq

uar

e G

rey

Sam

ple

s (

Au

x.10

0, A

ux.

80 a

nd

Au

x.60

)

S. N

o L

i=20

0 (m

m)

Vc)

i m

afte

r (g

ram

) V

afte

r (m

m3 )

ρ aft

er (K

g/m

3 ) ρ a

ve (

kg/m

3 ) V

c)f,

ave

1 16

.096

33

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126

1496

88

107.

53

2 15

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34

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125

1530

00

101.

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3.44

1 16

.616

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111

1358

64

122.

30

2 15

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9.92

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8.

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7260

12

0.84

125.

46

3.93

A

pp

end

ix B

: D

ensi

ties

and

com

pres

sion

rat

ios

of s

ampl

es (

Sec

ond

Bat

ch)

Vb

efor

e=50

0000

mm

3 , V1,

mou

ld=

6144

0 m

m3 , V

2,m

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920

mm

3 an

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3

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Sam

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s (A

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7400

97

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8 3.

63

A

pp

end

ix C

: D

ensi

ties

and

com

pres

sion

rat

ios

of s

ampl

es (

Thi

rd B

atch

)

Vb

efor

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2699

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411.

5 m

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62

A

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ص خ ة مل ل سا ر ل ة ا غ ل ل ا ة ب ي ب ر ع ل ا

كان الماضيين العقدين في خاصة. ميكانيكية خواص نات جديدة مواد تتطلب الحديثة التكنولوجيا

المواد ).Auxetic materials( الحجم المتمددة المواد باسم المعروفة المواد من معينة لفئة كبير إهتمام هناك

ظدما مقطعها يزيد المواد ٥هذ أن يعني ما وهو السلبية بواسون نسبة لديها التي المواد هي الحجم المتمددة

لها المواد هذه الأخرى. التقليدية المواد لمعظم خلافا وهذا الضفط، قوة أثناء ينكمش و الشد لقوة تعرض

ى متفوقة خصائص على .عالية قدرة الصدم، مقاومة أرتفاع القص، معامل زيادة مثل التقليدية المواد عل

الهندسية. التطبيقات من كثير فى كبيرة أهمية نات المواد هذه يجعل مما الصوت و الأهتزازات إمتصاص

من المختلفة الكثافات نات الحجم المتمدد المرن يوريثان البولي فوم تصنيع تم المقدم، البحث هذا في

التقليدي الفوم من لكلا البنائي التركيب فحص تم مختلفة. إنضغاط بنسب التقليدي المرن يوريثان البولي فوم

نفس وأظهرت أخرى سابقة بأعمال مقارنة هذا تحقيق تم بينهم. للمقارنة الضوئي المجهر بأستخدام والمتمدد

المتمدد الفوم لإنتاج الأولى المرة هي هذه الحجم. المتمدد و العادى الفوم من لكلا البنائى للتركيب الشكل

مصر. في الحجم

اللون صفراء الاولى الكثافة مختلفتين، بكثافتين التقليدي الفوم من عينات مجموعة تجهيز و قطع تم

الاول المقطع كثافة، كل من مختلفين بمقطعين وذلك ).٣كجم\م ٣٠( اللون رمادية الثانية و )٣كجم\م ٢٥(

ضغط تم ).W=H=50mm, ر مربع الثانى المقطع و )D=50mm, ' دانرى مربع مقطع نات الأخر و )D=30mm( دائرى مقطع نات الألمونيوم من قوالب داخل العينات هذه

)H=w =30mm،( إلى مم ٢ ٠ ٠ من المحوري الاتجاه فى العينات ضعط تم )للحصول مم)٦ ٠ و ٨ ٠ ، ١ ٠ ٠

٢ ٠ ٠ ثابتة حرارة درجة عند للتسخين الفرن داخل بالعينات القوالب توضع مختلفة. انضغاط نسب ثلاث على

العينات نزع يتم ثم دقيقة١ ٥ لمدة الهواء فى بالعينات القوالب تبريد يتم ذلك بعد دقيقة. ٢ ٥ لمدة مئوية درجة

أنواع ثلاث على الحصول يتم بذلك المختزلة. الإجهادات لإزالة إتجاهات الثلاث فى شدها و القوالب من

مختلفة إنضغاط نسب بثلاث )Aux.100, Aux.80 and Aux.60( وهم الحجم المتمدد الفوم من مختلفة

الترتيب. على )٩،٢٦ و ٦،٩٤،٥،٥٦(

التقليدى الفوم من (عينة .عينات أربع على تحتوى مجموعة كل مجموعات أربع الى العينات تقسيم تم

ذو الاولى المجموعة تصنيعة)، تم الني الحجم المتمدد الفوم من الإنضغاط نسب فى مختلفة عينات وثلاث

ذو الثالثة المجموعة الأصغر، اللون و المربع المقطع ذو الثانية المجموعة الرمادى، اللون و المربع المقطع

وتجهيز اءعداد تم الأصغر. اللون و الدائرى المقطع ذو الرابعة المجموعة و الرمادى اللون و الدائرى المقطع

H=w( التالية بالأبعاد المربعة المقاطع نات العينات تكون بحيث العينات =35mm, L=70mm( و

).D=32mm, L=70mm( التالية بالأبعاد الدائرية المقاطع نات الاخرى

المتمدد و التقليدي للفوم الميكانيكية الخواص على للحصول ميكانيكية اختبارات أربعة تطبيق تم

واثنين ”والضغط الشد” الاستاتيكية الميكانيكية الاختبارات من اثنين تنغيذ تم منهم. كلا سلوك لمعرفة الحجم

الحجم والمتمدد التقليدي الفوم بين المقارنة لعمل ”والمرونة التخلفية” الديناميكية الميكانيكية الاختبارات من

الضفط اختبارات تنغيذ تم .و ثانية ا ملم ٠ ،٢ يساوى السرعة فى تحكم بمعدل الاستاتيكي الشد اختبار تنغيذ تم

علاقة عن .عبارة هى الاختبار ماكينة من المسجلة البيانات وكانت .١ث- ٠ ،٣ مقدارة تحكم بمعدل والتخلفية

تم وقد والضغط. الشد لأختبارات بواسون ونسبة المرونة معامل على الحصول تم الانفعال. و الاجهاد بين

لمعرفة مختلفة أزمنة عند وذلك الاختبار أثناء المسجل الفليم من الصور تقطيع بأستخدام بواسون نسبة قياس

).Get Data Graph Digitizer( برنامج بأستخدام الطولى و العرضى التفير

نسب عند التقليدى الفوم من أفضل الحجم المتمدد الفوم سلوك أن النتائج أوضحت قد وعموما،

نسب من تجريبيا عليها الحصول تم التي القيم وكانت والرمادي. الأصغر الكثافتين لكلتا و المختلفة الانضغاط

الحجم المتمدد للفوم المرونة معامل أن أيضا الاختبارات أوضحت ،.).٧٤ و ٠،٢٧(- بين تتراوح بواسون

7.0 ٠ إنفعال نسبة ظد ح اللون الرمادية الحجم المتمددة الفوم عينة المثال سبيل على التقليدي. الفوم من أقل

ر.٧٧،٣ بمقدار التقليدي الفوم من أقل هو الذي و باسكال كيلو ٣٠،٠٢ مرونة معامل لديها

المتمدد الفوم أن لوحظ وقد الضفط. و الشد أختبار نتائج باستخدام للفوم الممتصة الطاقة حساب تم

نسبة لدية اللون الرمادي الفوم المثال سبيل .على التقليدي الفوم من أعلى للطاقة إمتصاص يملك الحجم

ه٦ إنضغاط ، ي ٣كجول\م٣،٩٨ كانت الممتصة الطاقة كذلك .٣كجم\م ١٠٩،٦ كثافة و ه الفوم من أعلى وه

من أعلى الرمادي اللون نات الحجم المتمدد للفوم المرونة قيمة أن الاختبارات أثبتت ر.٦ ٩،٦ بنسبة التقليدي

٩،٢٦ أنضغاط نسبة لدية الذى الرمادي اللون نات الحجم المتمدد الفوم المثال سبيل .على التقليدي الفوم

ه وكثافة ، ر.٧,٧ بنسبة التقليدي الفوم من أعلى هي و /٣٨ مرونة نسبة أعطى ،٣كجم\م ١٢ه

التالية: المجالات في لاستخدامه إمكانية لدية الحجم المتمدد الفوم

الطبية. المجالات فى يستخدم أن يمكن ٠التثبيت. وأربطه الحرارية المبادلات المضخات، فى الاهتزازات لامتصاص يستخدم أن يمكن ٠والمضخات. الصمامات فى وعازل كحشو أيضا يستخدم أن يمكن ٠الداخل. من الطائرات تبطين و عزل فى يستخدم أن يمكن ٠الرأس. ساند و السيارات مقاعد تصنيع فى يستخدم أن يمكن ٠للجسم. الواقية الدروع في يستخدم أن يمكن ٠غيرها. و المنزلية الأثاثات مثل المنزلية التطبيقات من كثير فى يدخل أن يمكن ٠الإلكترونية. الأجهزة لحماية كحشو يستخدم أن يمكن ٠

حلوان جامعة بالمطرية الهندسة كليةالميكانيكي التصميم قسم

المتمدد البوليوريثان فوم وتطبيقات خواص وتعيين صنيع

إعداد

يوسف يوسف إبراهيم حسام ا المهندسالذرية الطاقة هيئة - النووية البحوث مركز - الذرية المفاعلات بقسم معيد

حلوان جامعة - بالمطرية الهندسة كلية إلى مقدمة رسالة

الميكانيكى التصميم فى الماجستيير رسالة على الحصول متطلبات من كجزء

العربية مصر جمهورية٢٠١٢


المتمدد البوليوريثان فوم وتطبيقات خواص وتعيين تصنيع

إعداد

يوسف يوسف إبراهيم حسام ا المهندس



: الممتحنين لجنة من يعتمد

) ( السعودى السيد إبراهيم رمضان ا الدكتور الأستاذ

السويس. قناة جامعة - الهندسة كلية - الميكانيكى التصميم و الانتاج هندسة بقسم أستاذ

) ( يونس خليل يونس ا الدكتور الأستاذ

حلوان. جامعة - بالمطرية الهندسة كلية - الميكانيكى التصميم هندسة بقسم أستاذ

) ( (مشرف) البطش أحمد محمد علاء ا الدكتور الأستاذ

حلوان جامعة - بالمطرية الهندسة كلية - الحللاب لشئون الكلية وكيل و - الميكانيكى التصميم هندسة بقسم أستاذ

) ( (مشرف) المهدى حسين طارق ا المساعد الأستاذ

حلوان جامعة - بالمطرية الهندسة كلية - الميكانيكى التصميم هندسة بقسم مساعد أستاذ



المتمدد البوليوريثان فوم وتطبيقات خواص وتعيين تصنيع

إعداد

يوسف يوسف إبراهيم حسام ا المهندسالذرية الطاقة هيئة - النووية البحوث مركز - الذرية المفاعلات بقسم معيد



إشراف تحت

البطش أحمد محمد علاء ٠د٠أ الميكانيكى التصميم بقسم أستاذ

الحللاب و التعليم لشئون الكلية وكيلحلوان جامعة المطرية- هندسة

د. م. المهدى حسين طارق أ. الميكانيكى التصميم بقسم مساعد أستاذ

الميكانيكى التصميم قسم رئيسحلوان جامعة المطرية- هندسة

زيد محمد خالد د.

الميكانيكى التصميم بقسم مدرسحلوان جامعة المطرية- هندسة


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