Auxetic Polyurethane Foam (Fabrication, Properties and Applications)

Helwan University Faculty of Engineering, Mataria Mechanical Design Department

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 ELButch Tarek Hussien ELMahdy 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)

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 ElSeoudy ( )

Professor in Mechanical Design DepartmentFaculty of Engineering Suez Canal University

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

Professor in Mechanical Design DepartmentFaculty of Engineering, MatariaHelwan University

Prof. Dr. Eng.\ Alaa Mohammed ELButch ( Thesis Advisor ) Professor in Mechanical Design DepartmentFaculty of Engineering, MatariaHelwan University ( )

Assoc. Dr. Eng.\ Tarek Hussien ELMahdy ( Thesis Advisor ) Assoc. Prof. in Mechanical Design DepartmentFaculty of Engineering, MatariaHelwan University ( )

Cairo 2012

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 crosssections 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 quasistatic 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 quasistatic 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 %.

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/m 3, the energy absorbed was 3.98 kJ/m 3, 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 nosecone 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.

Table of Contents

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

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

iii

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

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 DivisionNuclear Research CentreEgyptian 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 EngineeringMataria, Helwan University for their support throughout the work.

Nomenclature

Symbol Definition unit

Vo Original volume mm 3

3 Vact Actual volume mm 3 Vmould Mould volume mm mbefore Mass of sample before the processing gram mafter Mass of sample after the processing gram 3 ρbefore Density of sample before the processing Kg/m 3 ρafter Density of sample after the processing Kg/m 3 ρf,ave Average density of sample after the processing Kg/m

CR before Theoretical compression ratio

CR act 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 3 To Modulus of toughness kJ/m E Modulus of elasticity kPa 3 Ed Dissipated energy kJ/m 3 Eabs Absorbed energy kJ/m

Symbol Definition unit

A (GConv.) Square grey conventional PU foam sample.

B (GAux. 100) Square grey auxetic PU foam sample at CR = 5.56 th,1 Batch

C (GAux. 80) Square grey auxetic PU foam sample at CR th,2= 6.94 St 1

D (GAux. 60) Square grey auxetic PU foam sample at CR th,3= 9.26

A* (YConv.) Square yellow conventional PU foam sample.

B* (YAux. 100) Square yellow auxetic PU foam sample at CR th,1= 5.56 Batch

C* (YAux. 80) Square yellow auxetic PU foam sample at CR th,2= 6.94 nd 2 D* (YAux. 60) Square yellow auxetic PU foam sample at CR th,3= 9.26

E (GConv.) Circular grey conventional PU foam sample

F (GAux. 100) Circular grey auxetic PU foam sample at CR th, 1= 2 Batch Batch

G (GAux. 80) Circular grey auxetic PU foam sample at CR th, 2= 2.5 rd 3 H (GAux. 60) Circular grey auxetic PU foam sample at CR th, 3= 3.33

E* (YConv.) Circular yellow conventional PU foam sample.

F* (YAux. 100) Circular yellow auxetic PU foam sample at CR th, 1= 2 Batch Batch

G* (YAux. 80) Circular yellow auxetic PU foam sample at CR th, 2= 2.5 th 4 H* (YAux. 60) Circular yellow auxetic PU foam sample at CR th, 3= 3.33

vii

List of Figures

Fig. No. Figure Title page

Fig. 1.1 (a) A material deformation with positive Poisson’s ratio, and 3 (b) A material deformation with negative Poisson’s ratio when stretched. 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: 7 (a) Conventional, and (b) Reentrant cell (Auxetic). Fig. 2.1 Conventional flexible PU foam samples with deferent densities and two 12 cross sectional areas Fig. 2.2 Isometric drawings with their dimensions for: 13 (a)Circular aluminium mould, and (b) Square aluminium mould. Fig. 2.3 Shows the circular and square moulds. 14 Fig. 2.4 Foam samples after conversion to auxetic: 15 (a) Circular auxetic samples, and (b) Square auxetic samples. Fig. 2.5 Samples after preparation for testing. 17 Fig. 3.1 Method to calculate the change in the transverse and longitudinal 21 directions to get the Poisson’s ratio in compression and tensile test for conventional and auxetic samples. Fig. 3.2 Zwick universal testing machine. 22 Fig. 3.3 a) Zwick resilience tester machine, and 23 b) Pendulum used for different tests. Fig. 3.4 (ad) Tensile test applied on the circular grey conventional (E) and auxetic 25 (F, G and H) PU foam samples at: a) No load, and b) Failure. Fig. 3.4 (eh) Tensile test applied on the circular yellow conventional (E*) and auxetic 26 (F*, G* and H*) PU foam samples at: a) No load, and b) Failure. Fig. 3.5 (ad) Compression test applied on square grey conventional (A) and auxetic 28 (B, C and D) PU foam samples at different compression strain levels: (0, 25, 50 and 75%). Fig. 3.5 (eh) Compression test applied on square yellow conventional (A*) and auxetic 29 (B*, C* and D*) PU foam samples at different compression strain levels: (0, 25, 50 and 75%). Fig. 3.6 Control panel of resilience tester machine 32

viii

Fig. No. Figure Title page

Fig. 4.1a Microstructure of grey square conventional and auxetic flexible PU foam 34 samples at 40X magnification. Microstructure of yellow Square conventional and auxetic flexible PU 34 Fig. 4.1b foam samples at 40X magnification Fig. 4.2a Microstructure of grey circular conventional and auxetic flexible PU foam 35 samples at 40X magnification Fig. 4.2b Microstructure of yellow circular conventional and auxetic flexible PU 36 foam samples at 40X magnification Fig. 4.3a Tensile stressstrain curve of a conventional grey PU foam sample (E) 38

Fig. 4.3b Tensile stressstrain curve of an Auxetic100 grey PU foam sample (F) 38

Fig. 4.3c Tensile stressstrain curve of an Auxetic80 grey PU foam sample (G) 38

Fig. 4.3d Tensile stressstrain curve of an Auxetic60 grey PU foam sample (H) 38

Fig. 4.3e Tensile stressstrain curves of conventional and auxetic grey PU foam 39 samples (E, F, G and H) Fig. 4.4a Tensile stressstrain curve of a conventional yellow PU foam sample(E*) 41

Fig. 4.4b Tensile stressstrain curve of an Auxetic100 yellow PU foam sample (F*) 41

Fig. 4.4c Tensile stressstrain curve of an Auxetic80 yellow PU foam sample (G*) 41

Fig. 4.4d Tensile stressstrain curve of an Auxetic60 yellow PU foam sample (H*) 41

Fig. 4.4e Tensile stressstrain curves of conventional and auxetic yellow PU foam 42 samples (E*, F*, G* and H*) Fig. 4.5a Compression stressstrain curve of a conventional grey PU foam sample 44 (A) at 25% compression strain Fig. 4.5b Compression stressstrain curve of an Auxetic100 grey PU foam sample 44 (B) at 25% compression strain Fig. 4.5c Compression stressstrain curve of an Auxetic80 grey PU foam sample 44 (C) at 25% compression strain Fig. 4.5d Compression stressstrain curve of an Auxetic60 grey PU foam sample 44 (D) at 25% compression strain Fig. 4.5e Compression stressstrain curves of conventional and auxetic grey PU 45 foam samples (A, B, C and D) at 25% compression strain Fig. 4.6a Compression stressstrain curve of a conventional grey PU foam sample 46 (A) at 50% compression strain

Fig. No. Figure Title page

Fig. 4.6b Compression stressstrain curve of an Auxetic100 grey PU foam sample 46 (B) at 50% compression strain Fig. 4.6c Compression stressstrain curve of an Auxetic80 grey PU foam sample 46 (C) at 50% compression strain Fig. 4.6d Compression stressstrain curve of an Auxetic60 grey PU foam sample 46 (D) at 50% compression strain Fig. 4.6e Compression stressstrain curves of conventional and auxetic grey PU 47 foam samples (A, B, C and D) at 50% compression strain Fig. 4.7a Compression stressstrain curve of a conventional grey PU foam sample 48 (A) at 75% compression strain Fig. 4.7b Compression stressstrain curve of an Auxetic100 grey PU foam sample 48 (B) at 75% compression strain Fig. 4.7c Compression stressstrain curve of an Auxetic80 grey PU foam sample 48 (C) at 75% compression strain Fig. 4.7d Compression stressstrain curve of an Auxetic60 grey PU foam sample 48 (D) at 75% compression strain Fig. 4.7e Compression stressstrain curves of conventional and auxetic grey PU 49 foam samples (A, B, C and D) at 75% compression strain Fig. 4.8a Compression stressstrain curve of a conventional yellow PU foam sample 51 (A*) at 25% compression strain Fig. 4.8b Compression stressstrain curve of an Auxetic100 yellow PU foam 51 sample (B*) at 25% compression strain Fig. 4.8c Compression stressstrain curve of an Auxetic80 yellow PU foam sample 51 (C*) at 25% compression strain Fig. 4.8d Compression stressstrain curve of an Auxetic60 yellow PU foam sample 51 (D*) at 25% compression strain Fig. 4.8e Compression stressstrain curves of conventional and auxetic yellow PU 52 foam samples (A*, B*, C* and D*) at 25% compression strain Fig. 4.9a Compression stressstrain curve of a conventional yellow PU foam sample 53 (A*) at 50% compression strain Fig. 4.9b Compression stressstrain curve of an Auxetic100 yellow PU foam 53 sample (B*) at 50% compression strain Fig. 4.9c Compression stressstrain curve of an Auxetic80 yellow PU foam sample 53 (C*) at 50% compression strain Fig. 4.9d Compression stressstrain curve of an Auxetic60 yellow PU foam sample 53 (D*) at 50% compression strain

Fig. No. Figure Title page

Fig. 4.9e Compression stressstrain curves of conventional and auxetic yellow PU 54 foam samples at 50% compression strain Fig. 4.10a Compression stressstrain curve of a conventional yellow PU foam sample 55 (A*) at 75% compression strain Fig. 4.10b Compression stressstrain curve of an Auxetic100 yellow PU foam 55 sample (B*) at 75% compression strain Fig. 4.10c Compression stressstrain curve of an Auxetic80 yellow PU foam sample 55 (C*) at 75% compression strain Fig. 4.10d Compression stressstrain curve of an Auxetic60 yellow PU foam sample 55 (D*) at 75% compression strain Fig. 4.10e Compression stressstrain curves of conventional and auxetic yellow PU 56 foam samples at 75% compression strain Fig. 4.11a One cycle Hysteresis stressstrain curve of a conventional grey PU foam 58 sample (A) at 25% compression strain Fig. 4.11b One cycle Hysteresis stressstrain curve of an Auxetic100 grey PU foam 58 sample (B) at 25% compression strain Fig. 4.11c One cycle Hysteresis stressstrain curve of an Auxetic80 grey PU foam 58 sample (C) at 25% compression strain Fig. 4.11d One cycle Hysteresis stressstrain curve of an Auxetic60 grey PU foam 58 sample (D) at 25% compression strain Fig. 4.11e One cycle Hysteresis stressstrain curves of conventional and auxetic grey 59 PU foam samples at 25% compression strain Fig. 4.12a One cycle Hysteresis stressstrain curve of a conventional grey PU foam 60 sample (A) at 50% compression strain Fig. 4.12b One cycle Hysteresis stressstrain curve of an Auxetic100 grey PU foam 60 sample (B) at 50% compression strain Fig. 4.12c One cycle Hysteresis stressstrain curve of an Auxetic80 grey PU foam 60 sample (C) at 50% compression strain Fig. 4.12d One cycle Hysteresis stressstrain curve of an Auxetic60 grey PU foam 60 sample (D) at 50% compression strain Fig. 4.12e One cycle Hysteresis stressstrain curves of conventional and auxetic grey 61 PU foam samples at 50% compression strain Fig. 4.13a One cycle Hysteresis stressstrain curve of a conventional grey PU foam 62 sample (A) at 75% compression strain

Fig. No. Figure Title page

Fig. 4.13b One cycle Hysteresis stressstrain curve of an Auxetic100 grey PU foam 62 sample (B) at 75% compression strain Fig. 4.13c One cycle Hysteresis stressstrain curve of an Auxetic80 grey PU foam 62 sample (C) at 75% compression strain Fig. 4.13d One cycle Hysteresis stressstrain curve of an Auxetic60 grey PU foam 62 sample (D) at 75% compression strain Fig. 4.13e One cycle Hysteresis stressstrain curves of conventional and auxetic grey 63 PU foam samples at 75% compression strain Fig. 4.14a One cycle Hysteresis stressstrain curve of a conventional yellow PU foam 65 sample (A*) at 25% compression strain Fig. 4.14b One cycle Hysteresis stressstrain curve of an Auxetic100 yellow PU 65 foam sample (B*) at 25% compression strain Fig. 4.14c One cycle Hysteresis stressstrain curve of an Auxetic80 yellow PU foam 65 sample (C*) at 25% compression strain Fig. 4.14d One cycle Hysteresis stressstrain curve of an Auxetic60 yellow PU foam 65 sample (D*) at 25% compression strain Fig. 4.14e One cycle Hysteresis stressstrain curves of conventional and auxetic 66 yellow PU foam samples at 25% compression strain Fig. 4.15a One cycle Hysteresis stressstrain curve of a conventional yellow PU foam 67 sample (A*) at 50% compression strain Fig. 4.15b One cycle Hysteresis stressstrain curve of an Auxetic100 yellow PU 67 foam sample (B*) at 50% compression strain Fig. 4.15c One cycle Hysteresis stressstrain curve of an Auxetic80 yellow PU foam 67 sample (C*) at 50% compression strain Fig. 4.15d One cycle Hysteresis stressstrain curve of an Auxetic60 yellow PU foam 67 sample (D*) at 50% compression strain Fig. 4.15e One cycle Hysteresis stressstrain curves of conventional and auxetic 68 yellow PU foam at 50% compression strain Fig. 4.16a One cycle Hysteresis stressstrain curve of a conventional yellow PU foam 69 sample (A*) at 75% compression strain Fig. 4.16b One cycle Hysteresis stressstrain curve of an Auxetic100 yellow PU 69 foam sample (B*) at 75% compression strain Fig. 4.16c One cycle Hysteresis stressstrain curve of an Auxetic80 yellow PU foam 69 sample (C*) at 75% compression strain

xii

Fig. No. Figure Title page

Fig. 4.16d One cycle Hysteresis stressstrain curve of an Auxetic60 yellow PU foam 69 sample (D*) at 75% compression strain Fig. 4.16e One cycle Hysteresis stressstrain curves of conventional and auxetic 70 yellow PU foam samples at 75% compression strain Fig. 5.1 Bending behaviours of (a) Curvature behaviours in nonauxetic and (b) 80 auxetic (double curvatureconvex shape) 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 82 apparatus causes the auxetic sheath to extend and expand laterally, thus opening up the surrounding vessel Fig. 5.4 Deformation behaviour of artificial blood vessels: 82 a) Conventional material, and b) Auxetic blood vessel

xiii

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 39 PU foam samples (E, F, G and H) under tensile test . Table 4.2 Mechanical properties of the yellow conventional and auxetic circular 42 flexible PU foam samples (E*, F*, G* and H*) under tensile test . Table 4.3 Mechanical properties of the grey conventional and auxetic square flexible 45 PU foam samples (A, B, C and D) at 25% compression test . Table 4.4 Mechanical properties of the grey conventional and auxetic square flexible 47 PU foam samples (A, B, C and D) at 50% compression test . Table 4.5 Mechanical properties of the grey conventional and auxetic square flexible 49 PU foam samples (A, B, C and D) at 75% compression test . Table 4.6 Mechanical properties of the yellow conventional and auxetic square flexible 52 PU foam samples (A*, B*, C* and D*) at 25% compression test . Table 4.7 Mechanical properties of the yellow conventional and auxetic square flexible 54 PU foam samples (A*, B*, C* and D*) at 50% compression test . Table 4.8 Mechanical properties of the yellow conventional and auxetic square flexible 56 PU foam samples (A*, B*, C* and D*) at 75% compression test . Table 4.9 Mechanical properties of the grey conventional and auxetic square flexible 59 PU foam samples (A, B, C and D) at one cycle and 25% compression hysteresis test. Table 4.10 Mechanical properties of the grey conventional and auxetic square flexible 61 PU foam samples (A, B, C and D) at one cycle and 50% compression hysteresis test. Table 4.11 Mechanical properties of the grey conventional and auxetic square flexible 63 PU foam samples (A, B, C and D) at one cycle and 75% compression hysteresis test . Table 4.12 Mechanical properties of the yellow conventional and auxetic square flexible 66 PU foam samples at one cycle and 25% compression hysteresis test. Table 4.13 Mechanical properties of the yellow conventional and auxetic square flexible 68 PU foam samples at one cycle and 50% compression hysteresis test . Table 4.14 Mechanical properties of the yellow conventional and auxetic square flexible 70 PU foam samples at one cycle and 75% compression hysteresis test . Table 4.15 Mean values of the resilience test for the conventional and three different 72 (a d) types of auxetic PU foam samples for grey and yellow samples.

xiv

CHAPTER (1)

INTRODUCTION AND LITERATURE SURVEY

Chapter 1 “Introduction and Literature Survey”

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). Largescale 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].

1 Chapter 1 “Introduction and Literature Survey”

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 nonconventional 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 interatomic bonds realign with deformation.

2 Chapter 1 “Introduction and Literature Survey”

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 rubberlike 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.

3 Chapter 1 “Introduction and Literature Survey”

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 hingelike structures which flex when stretched. The term auxetic derives from the Greek word αξητικός (auxetikos) which means, "That which tends to increase," and has its root in the word αξησις , 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.

4 Chapter 1 “Introduction and Literature Survey”

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 reentrant 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 reentrant 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.

5 Chapter 1 “Introduction and Literature Survey”

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.

6 Chapter 1 “Introduction and Literature Survey”

1.2.5 Previous work

Foams with reentrant 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 reentrant “Auxetic” polymeric cellular solids depended upon the permanent volumetric compression ratio during the processing procedure. The toughness of reentrant foam increased with permanent volumetric compression ratio [17].

Figure (1.5) shows Young's moduli of conventional and reentrant open cell foams are obtained by modelling the threedimensional unit cell as an idealized 14 sided unit cell. Young's modulus of reentrant 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) Reentrant 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].

7 Chapter 1 “Introduction and Literature Survey”

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 pressuresensitive array. Seated pressure distribution became more favourable with decreasing sample density for both conventional and reentrant 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 thermomechanical processing with the aim of transforming them into reentrant 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 isodensity “nonauxetic” 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].

8 Chapter 1 “Introduction and Literature Survey”

Comparative analysis between the cyclic loading compressive “hysteresis” behaviour of conventional, isodensity “nonauxetic” 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 isodensity 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].

9 Chapter 1 “Introduction and Literature Survey”

Theobjectiveoftheresearch

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 stressstrain 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”

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.

KirkOthmer, Encyclopedia of Chemical Technology (3rd Ed.), Vol 11, 8889.

11 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

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 TakiVita Company, 10 th 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) mm 3 and tolerances of ±1 mm, as shown in Figure (2.1).

D=50 mm and L =200 50 *50 mm 2 and L =200 a b

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.

12 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

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 mm 3, 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.

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

a b

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

13 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

a b

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 (AirCooled) 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].

14 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

a b Fig ure (2. 4) Foa m sa mp les afte r 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 (Aux100).

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 (Aux80).

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 (Aux60).

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.

15 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

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/m 3.

atatioiesiosofsalesfortestig

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).

16 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

Figure (2.5) Square samples after preparation for testing.

aleslabel

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.

17 Chapter 2 “Polyurethane Foam Samples Fabrication and preparation”

Table (2.1) Square samples ID and their description.

Batch Sample ID Definition

A (GConv.) Square grey conventional PU foam sample.

B (GAux. 100) Square grey auxetic PU foam sample at CR th,1= 5.56 First C (GAux. 80) Square grey auxetic PU foam sample at CR th,2= 6.94

D (GAux. 60) Square grey auxetic PU foam sample at CR th,3= 9.26 A* (YConv.) Square yellow conventional PU foam sample. B* (YAux. 100) Square yellow auxetic PU foam sample at CR = 5.56 Second th,1 C* (YAux. 80) Square yellow auxetic PU foam sample at CR th,2= 6.94

D* (YAux. 60) Square yellow auxetic PU foam sample at CR th,3= 9.26

Table (2.2) Circular samples ID and their description.

Batch Sample ID Definition E (GConv.) Circular grey conventional PU foam sample

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

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

H (GAux. 60) Circular grey auxetic PU foam sample at CR th, 3= 3.33 E* (YConv.) Circular yellow conventional PU foam sample.

F* (YAux. 100) Circular yellow auxetic PU foam sample at CR th, 1= 2 Forth G* (YAux. 80) Circular yellow auxetic PU foam sample at CR th, 2= 2.5

H* (YAux. 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”

Testigtechiques

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 (V o), the sample’s actual (final) volume after relaxation (V act ), and the volume of the mold (V mould ). The theoretical compression ratio (CR before ) is V o / V mould . The actual (final) compression ratio (CR act ) is Vo / V act . This tabulated in appendices (AD).

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 (AD).

19 Chapter “Polyurethane Foam Testing and Measuring Techniques”

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 quasistatic tests performed with a Zwick universal testing machine. The quasistatic 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)

20 Chapter “Polyurethane Foam Testing and Measuring Techniques”

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.

echaicaltestigachies

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 stressstrain 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.

21 Chapter “Polyurethane Foam Testing and Measuring Techniques”

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).

22 Chapter “Polyurethane Foam Testing and Measuring Techniques”

Technical characteristics: For DIN 53512 pendulum:

• Pendulum length: 200.4 mm. • Energy: 0.5 J

• Elevation angle: 90 degrees • Mass: 252 grams

• Impact velocity: 1,98 m/s • Shape of striker: half sphere

• Electr. Connection: 220V/50Hz • Diameter: 15mm

• Application: elastomers

a b

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

23 Chapter “Polyurethane Foam Testing and Measuring Techniques”

echaicaltestigaethoology

3.3.1 Tensile test and methodology Quasistatic 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 quasistatic 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 quasistatic 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 thermoplastic 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 strainstress 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.

24 Chapter “Polyurethane Foam Testing and Measuring Techniques”

a c

b d

Figure (3.4a) Conventional grey PU foam sample (E) Figure (3.4b) Auxetic100 grey PU foam sample (F) At: a) No load, and b) Failure. At: c) No load and d) Failure.

e g

f h

Figure (3.4c) Auxetic80 grey PU foam sample (G) Figure (3.4d) Auxetic60 grey PU foam sample (H) At: e) No load, and f) Failure. At: g) No load, and h) Failure.

25 Chapter “Polyurethane Foam Testing and Measuring Techniques”

i k

j l

Figure (3.4e) Conventional yellow PU foam sample (E*) Figure (3.4f) Auxetic100 yellow PU foam sample (F*) At: i) No load, and j) Failure. At: k) No load and l) Failure.

m o

n p

Figure (3.4g) Auxetic80 yellow PU foam sample (G*) Figure (3.4h) Auxetic60 yellow PU foam sample (H*) At: m) No load, and n ) Failure . At: o) No load, and p ) Failure .

26 Chapter “Polyurethane Foam Testing and Measuring Techniques”

3.3.2 Compression test and methodology

Quasistatic 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 quasistatic 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 quasistatic 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.

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

27 Chapter “Polyurethane Foam Testing and Measuring Techniques

a e i m

b f j n

c g k o

d h l p

Figure (3.5a) Compression test applied Figure (3.5b) Compression test Figure (3.5c) Compression test applied Figure (3.5d) Compression test applied on a conventional grey PU foam sample applied on an auxetic100 grey PU on an auxetic80 grey PU foam sample on an auxetic60 grey PU foam sample (A) at different compression strain foam sample (B) at different (C) at different compression strain (D) at different compression strain levels: compression strain levels: levels: levels: a) 0 % comp. e) 0 % comp. i) 0 % comp. m) 0 % comp. b) 25 % comp. f) 25 % comp. j) 25 % comp. n) 25 % comp. c) 50% comp. g) 50% comp. k) 50% comp. o) 50% comp. d) 75% comp. h) 75% comp. l) 75% comp. p) 75% comp.

Chapter “Polyurethane Foam Testing and Measuring Techniques”

a e i m

b f j n

c g k o

d h l p

Figure (3.5e) Compression test applied Figure (3.5f) Compression test applied Figure (3.5g) Compression test applied Figure (3.5h) Compression test applied on a conventional yellow PU foam on an auxetic100 yellow PU foam on an auxetic80 yellow PU foam on an auxetic60 yellow PU foam sample (A*) at different compression sample (B*) at different compression sample (C*) at different compression sample (D*) at different compression strain levels: strain levels: strain levels: strain levels: a) 0 % comp. e) 0 % comp. i) 0 % comp. m) 0 % comp. b) 25 % comp. f) 25 % comp. j) 25 % comp. n) 25 % comp. c) 50% comp. g) 50% comp. k) 50% comp. o) 50% comp. d) 75% comp. h) 75% comp. l) 75% comp. p) 75% comp.

Chapter “Polyurethane Foam Testing and Measuring Techniques”

3.3.3 Hysteresis test and methodology

Lowstrain rate hysteresis tests are like the quasistatic 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 lowstrain rate hysteresis tests were carried out at cycle speed was adjusted to be strain control rate of έ = 0.3 S1 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 lowstrain rate hysteresis tests were applied at different compressionhysteresis strain at (25, 50 and 75%) compression for all mentioned samples. The samples were cut in dimensions are (35×35×70) mm 3 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).

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.

30 Chapter “Polyurethane Foam Testing and Measuring Techniques”

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 strainstress 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 ε min and ε max 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) mm 3. 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).

31 Chapter “Polyurethane Foam Testing and Measuring Techniques”

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”

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 stressstrain 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 thermalcompression 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].

33 Chapter 4 “Results and Discussion”

A B

C D

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 auxetic100 foam sample. C: An auxetic80 foam sample. D: An auxetic60 foam sample.

A* B*

C* D*

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 auxetic100 foam sample. C*: An auxetic80 foam sample. D*: An auxetic60 foam sample.

34 Chapter 4 “Results and Discussion”

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.

E F

G H

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 auxetic100 foam sample. G: An auxetic80 foam sample. H: An auxetic60 foam sample.

35 Chapter 4 “Results and Discussion”

E* F*

G* H*

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 auxetic100 foam sample. G*: An auxetic80 foam sample. H*: An auxetic60 foam sample.

36 Chapter 4 “Results and Discussion”

4.3 Tensile test of grey samples

Figures (4.3a) to (4.3d) show the tensile stressstrain 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 stressstrain 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 “T o” (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/m 3); while the conventional foam sample (E) has mechanical properties values as (138.8%, 102.3 kPa, 0.48, 84.7910 kJ/m 3). 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 nondeformed, while the unit cell ribs in the auxetic foams are irregular (reentrant) and deformed (buckled) due to the previous processing technique, which occurs change in the foam density and porosity.

37 Chapter 4 “Results and Discussion”

Tensile Test of Conventional Grey Polyurethane Foam Sample [E] Tensile Test of Auxetic 100 Grey Polyurethane Foam Sample [F] 120 250 E:(TG-Conv.) F:(TG-Aux. 100)

100 200

150

60 Stress[kPa] Stress[kPa] 100

50 20

0 0 0 25 50 75 100 125 150 0 25 50 75 100 125 150 175 200 225 250 Strain [%] Strain [%] Fig. (4.3a) Tensile stressstrain curve of a conventional grey PU foam sample (E) Fig. (4.3b) Tensile stressstrain curve of an auxetic100 grey PU foam sample (F)

Tensile Test of Auxetic 80 Grey Polyurethane Foam Sample [G] Tensile Test of Auxetic 60 Grey Polyurethane Foam Sample [H] 150 180 H:(TG-Aux. 60)

160

120 140

120

90 100

80 Stress [kPa] Stress 60 Stress[kPa]

40 30

0 0 0 25 50 75 100 125 150 175 200 0 25 50 75 100 125 150 175 200 225 250 Strain [%] Strain [%] Fig. (4.3c) Tensile stressstrain curve of an auxetic80 grey PU foam sample (G) Fig. (4.3d) Tensile stressstrain curve of an auxetic60 grey PU foam sample (H)

Chapter 4 “Results and Discussion”

Tensile Test of Conventional and Auxetic Grey Polyurethane Foam Samples 250 E:(TGConv.) F:(TGAux. 100) G:(TGAux. 80) F 200 H:(TGAux. 60)

150 G

Stress [kPa] Stress 100 E

0 0 50 100 150 200 250 Strain [%]

Fig. (4.3e) Tensile stressstrain 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.

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

39 Chapter 4 “Results and Discussion”

4.4 Tensile test of yellow samples

Figures (4.4a) to (4.4d) show the tensile stressstrain 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/m 3); while the conventional sample (E*) gives mechanical properties values of (79.31%, 73.77 kPa, 0.74, 36.19 kJ/m 3). 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 reentrant unit cells, as mentioned previously.

40 Chapter 4 “Results and Discussion”

Tensile Test of Conventional Yellow Polyurethane Foam Sample [E*] Tensile Test of Auxetic 100 Yellow Polyurethane Foam Sample [F*] 80 250 E*:(TY-Conv.) F*:(TY-Aux.100) 225 70

200 60 175

50 150

40 125 Stress[kPa] Stress[kPa] 100 30

75 20 50

10 25

0 0 0 10 20 30 40 50 60 70 80 0 25 50 75 100 125 150 175 200 Strain [%] Strain [%] Fig. (4.4a) Tensile stressstrain curve of a conventional yellow PU foam sample (E*) Fig. (4.4b) Tensile stressstrain curve of an auxetic100 yellow PU foam sample (F*)

Tensile Test of Auxetic 80 Yellow Polyurethane Foam Sample [G*] Tensile Test of Auxetic 60 Yellow Polyurethane Foam Sample [H*] 180 250 G*:(TY-Aux.80) H*:(TY-Aux.60)

160 225

200 140

175 120

150 100

125 80 Stress[kPa] Stress[kPa] 100

60 75

40 50

20 25

0 0 0 25 50 75 100 125 150 175 200 225 250 0 25 50 75 100 125 150 175 200 225 250 Strain [%] Strain [%] Fig. (4.4c) Tensile stressstrain curve of an auxetic80 yellow PU foam sample (G*) Fig. (4.4d) Tensile stressstrain curve of an auxetic60 yellow PU foam sample (H*)

Chapter 4 “Results and Discussion”

Tensile Test of Conventional and Auxetic Yellow Polyurethane Foam Samples 250 E*:(TYConv.) F*:(TYAux. 100) F* G*:(TYAux. 80) H* 200 H*:(TYAux. 60)

G* 150

Stress [kPa] Stress 100

0 0 50 100 150 200 250 Strain [%]

Fig. (4.4e) Tensile stressstrain 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.

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

42 Chapter 4 “Results and Discussion”

4.5 Compression test of grey samples

Quasistatic 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 reentrant 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 quasistatic compression stressstrain 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 stressstrain 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).

43 Chapter 4 “Results and Discussion”

Compression Test of Conventional Grey Polyurethane Foam Sample [A] at 25% Compression Strain Compression Test of Auxetic 100 Grey Polyurethane F oam Sample [B] at 25% Compression Strain 5 14 A (CG25%-Conv.) B (CG25%-Aux.100) 4.5 12

10 3.5

3 8

2.5

6 Stress [kPa] Stress Stress [kPa] 2

1.5 4

1 2 0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.5a) Compression stressstrain curve of a conventional grey PU foam Fig. (4.5b) Compression stressstrain curve of an auxetic100 grey PU foam sample (A) at 25% compression strain sample (B) at 25% compression strain

Compression Test of Auxetic 80 Grey Polyurethane Fo am Sample [C] at 25% Compression Strain Compression Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 25% Compression Strain 8 5.5 C (CG25%-Aux.80) D (CG25%-Aux.60) 5 7

4.5

6 4

5 3.5

3 4 2.5 Stress [kPa] Stress Stress Stress [kPa] 3 2

1.5 2

1 1 0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%] Fig. (4.5c) Compression stressstrain curve of an auxetic80 grey PU foam Fig. (4.5d) Compression stressstrain curve of an auxetic60 grey PU foam sample (C) at 25% compression strain sample (D) at 25% compression strain

Chapter 4 “Results and Discussion”

Compression Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 25% Compression Strain 14 A (CG25%Conv.) B (CG25%Aux.100) B 12 C (CG25%Aux.80) D (CG25%Aux.60)

8 C

6 Stress [kPa] Stress D A 4

0 0 5 10 15 20 25 Strain [%]

Fig. (4.5e) Compression stressstrain 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.

3 Samples εmax (%) σmax (kPa) E2% (kPa) υ25% Eabs (kJ/m ) 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

4.5.2 Compression strain at 50%

Figures (4.6a) to (4.6d) show the quasistatic 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 stressstrain 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/m 3), 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).

45 Chapter 4 “Results and Discussion”

Compression Test of Conventional Grey Polyurethane Foam Sample [A] at 50% Compression Strain Compression Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 50% Compression Strain 7 50 A (CG50%-Conv.) B (CG50%-Aux.100) 45 6

5 35

30 4

3 Stress [kPa] Stress [kPa] 20

2 15

10 1 5

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%] Fig. (4.6a) Compression stressstrain curve of a conventional grey PU foam Fig. (4.6b) Compression stressstrain curve of an auxetic100 grey PU foam sample (A) at 50% compression strain sample (B) at 50% compression strain

Compression Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 50% Compression Strain Compression Test of Auxetic60 Grey Polyurethane Foam Sample[ D] at 50% Compression Strain 60 60 C (CG50%-Aux.80) D (CG50%-Aux.60)

50 50

40 40

30 30 Stress [kPa] Stress [kPa]

20 20

10 10

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%] Fig. (4.6c) Compression stressstrain curve of an auxetic80 grey PU foam Fig. (4.6d) Compression stressstrain curve of an auxetic60 grey PU foam sample (C) at 50% compression strain sample (D) at 50% compression strain

Chapter 4 “Results and Discussion”

Compression Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 50% Compression Strain 60 A (CG50%Conv.) B (CG50%Aux.100) 50 C (CG50%Aux.80) D (CG50%Aux.60)

30 Stress [kPa] Stress 20 B C D

10 A

0 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Fig. (4.6e) Compression stressstrain 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.

3 Samples εmax (%) σmax (kPa) E2% (kPa) υ50% Eabs (kJ/m ) 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

4.5.3 Compression strain at 75%

Figures (4.7a) to (4.7d) show the quasistatic 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). 47 Chapter 4 “Results and Discussion”

Compression Test of Conventional Grey Polyurethane Foam Sample [A] at 75% Compression Strain Compression Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 75% Compression Strain 20 350 A (CG75% -Conv.) C (CG75%-Aux.80) 18 300

14 250

12 200

150 Stress [kPa] 8 Stress [kPa]

6 100

50 2

0 0 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 Strain [%] Strain [%] Fig. (4.7a) Compression stressstrain curve of a conventional grey PU foam Fig. (4.7c) Compression stressstrain curve of an auxetic80 grey PU foam sample (A) at 75% compression strain sample (C) at 75% compression strain

Compression Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 75% Compression Strain Compression Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 75% Compression Strain 250 450 B (CG75%-Aux.100) D (CG75%-Aux.60)

400

200 350

300

150 250

200 Stress [kPa] Stress [kPa] 100

150

100 50

0 0 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 Strain [%] Strain [%] Fig. (4.7b) Compression stressstrain curve of an auxetic100 grey PU foam Fig. (4.7d) Compression stressstrain curve of an auxetic60 grey PU foam sample (B) at 75% compression strain sample (D) at 75% compression strain

Chapter 4 “Results and Discussion”

Compression Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 75% Compression Strain 450 A (CG75%Conv.) D 400 B (CG75%Aux.100) C (CG75%Aux.80) D (CG75%Aux.60) 350

C 300

250 B

200 Stress [kPa] Stress 150

100

50 A 0 0 10 20 30 40 50 60 70 80 Strain [%]

Fig. (4.7e) Compression stressstrain 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.

3 Samples εmax (%) σmax (kPa) E2% (kPa) υ75% Eabs (kJ/m ) 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

49 Chapter 4 “Results and Discussion”

4.6 Compression test of yellow samples

Quasistatic 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).

4.6.1 Compression strain at 25%

Figures (4.8a) to (4.8d) show the quasistatic compression stressstrain 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 stressstrain 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).

50 Chapter 4 “Results and Discussion”

Compression Test of Conventional Yellow Polyurethane Foam Sample [A*] at 25% Compression Strain Compression Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 25% Compression Strain 3 10 A* (CY25%-Conv.) C* (CY25%-Aux.80) 9

2.5 8

7 2

1.5 5 Stress [kPa] Stress Stress [kPa] Stress 4

1 3

2 0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.8a) Compression stressstrain curve of a conventional yellow PU foam Fig. (4.8c) Compression stressstrain curve of an auxetic80 yellow PU foam sample (A*) at 25% compression strain sample (C*) at 25% compression strain

Compression Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 25% Compression Strain Compression Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 25% Compression Strain 12 4.5 B* (CY25% -Aux.100) D* (CY25%-Aux.60)

4 10

3.5

8 3

2.5 6

2 Stress [kPa] Stress Stress [kPa]

4 1.5

1 2

0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.8b) Compression stressstrain curve of an auxetic100 yellow PU foam Fig. (4.8d) Compression stressstrain curve of an auxetic60 yellow PU foam sample (B*) at 25% compression strain sample (D*) at 25% compression strain

Chapter 4 “Results and Discussion”

Compression Test of Yellow Conventional and AuxeticPolyurethane Foam Samples at 25% Compression Strain 12 A* (CY25%Conv.) B* B* (CY25%Aux.100) 10 C* (CY25%Aux.80) D* (CY25%Aux.60) C*

Stress [kPa] Stress D* 4 A*

0 0 5 10 15 20 25 Strain [%]

Fig. (4.8e) Compression stressstrain 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. 3 Samples εmax (%) σmax (kPa) E2% (kPa) υ25% Eabs (kJ/m ) 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

4.6.2 Compression strain at 50%

Figures (4.9a) to (4.9d) show the quasistatic compression stressstrain relationship applied on the square yellow PU conventional foam sample (A*) and three different auxetic foam samples (B*, C* and D*) at 50% compression strain. For comparison between all square yellow PU foam samples at 50% compression stressstrain relationship, that are plotted in one gragh, Figure (4.9e). The auxetic 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).

52 Chapter 4 “Results and Discussion”

Compression Test of Conventional Yellow Polyurethane Foam Sample [A*] at 50% Compression Strain Compression Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 50% Compression Strain 5 50 A* (CY50%-Conv.) C* (CY50%-Aux.80) 4.5 45

4 40

3.5 35

3 30

2.5 25 Stress [kPa] Stress 2 Stress[kPa] 20

1.5 15

1 10

0.5 5

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%]

Fig. (4.9a) Compression stressstrain curve of a conventional yellow PU foam Fig. (4.9c) Compression stressstrain curve of an auxetic80 yellow PU foam sample (A*) at 50% compression strain. sample (C*) at 50% compression strain.

Compression Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 50% Compression Strain Compression Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 50% Compression Strain 40 50 B* (CY50%-Aux.100) D* (CY50%-Aux.60) 45 35

40 30 35

25 30

20 25 Stress [kPa] Stress Stress[kPa] 20 15

15 10

5 5

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 Strain [%] Strain [%]

Fig. (4.9b) Compression stressstrain curve of an auxetic100 yellow PU foam Fig. (4.9d) Compression stressstrain curve of an auxetic60 yellow PU foam sample (B*) at 50% compression strain. sample (D*) at 50% compression strain.

Chapter 4 “Results and Discussion”

Compression Test of Yellow Conventional and Auxetic Polyurethane Foam Samples at 50% Compression Strain 50 A* (CY50%Conv.) C* D* 45 B* (CY50%Aux.100) C* (CY50%Aux. 80) 40 D* (CY50%Aux. 60) B*

Stress [kPa] Stress 20

10 A* 5

0 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Fig. (4.9e) Compression stressstrain 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. 3 Samples εmax (%) σmax (kPa) E2% (kPa) υ50% Eabs (kJ/m ) 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

4.6.3 Compression strain at 75%

Figures (4.10a) to (4.10d) show the quasistatic compression stressstrain relationship applied on the square yellow PU conventional foam sample (A*) and three different auxetic foam samples (B*, C* and D*) at 75% compression strain. For comparison between all square yellow PU foam samples at 75% compression stressstrain relationship, that are plotted in one gragh, Figure (4.10e). The auxetic 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).

54 Chapter 4 “Results and Discussion”

Compression Test of Conventional Yellow Polyurethane Foam Sample [A*] at 75% Compression Strain Compression Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 75% Compression Strain 20 200 A* (CY75%-Conv.) B* (CY75%-Aux.100) 18 180

16 160

14 140

12 120

10 100 Stress [kPa] 8 Stress [kPa] 80

6 60

4 40

2 20

0 0 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 Strain [%] Strain [%] Fig. (4.10a) Compression stressstrain curve of a conventional yellow PU foam Fig. (4.10b) Compression stressstrain curve of an auxetic100 yellow PU foam sample (A*) at 75% compression strain. sample (B*) at 75% compression strain.

Compression Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 75% Compression Strain 300 Compression Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 75% Compression Strain C* (CY75% -Aux.80) 350 D* (CY75%-Aux.60)

250 300

250 200

200 150

Stress [kPa] 150 Stress [kPa] 100

100

50 50

0 0 10 20 30 40 50 60 70 0 Strain [%] 0 10 20 30 40 50 60 70 Strain [%]

Fig. (4.10c) Compression stressstrain curve of an auxetic80 yellow PU foam Fig. (4.10d) Compression stressstrain curve of an auxetic60 yellow PU foam sample (C*) at 75% compression strain. sample (D*) at 75% compression strain.

Chapter 4 “Results and Discussion”

Compression Test of Yellow Conventional and Auxetic Polyurethane Foam Samples at 75% Compression Strain 350 A* (CY75%Conv.) B* (CY75%Aux.100) D* 300 C* (CY75%Aux.80) D* (CY75%Aux.60) C* 250

200 B*

150 Stress [kPa] Stress

100

50 A* 0 0 10 20 30 40 50 60 70 80 Strain [%] Fig. (4.10e) Compression stressstrain 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. 3 Samples εmax (%) σmax (kPa) E2% (kPa) υ75% Eabs (kJ/m ) 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

56 Chapter 4 “Results and Discussion”

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 stressstrain behaviour observed upon deformation typically includes a significant strain energy contribution, with the area enclosed by the hysteresis loop corresponding to the dissipated energy (E d) for each cycle. For any given cycle (N), the dissipated energy per unit volume is calculated by using equation (4) in chapter 3. Hysteresis stressstrain 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 stressstrain 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).

57 Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional Grey Polyurethane Foam Sample [A] at 25% Compression Strain Hysteresis Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 25% Compression Strain 5 14 A (HG25%-Conv.) B (HG25%-Aux.100) 4.5 12

10 3.5

3 8

2.5

6 Stress [kPa] 2 Stress [kPa]

1.5 4

2 0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.11a) One cycle Hysteresis stressstrain curve of a conventional grey PUfoam Fig. (4.11b) One cycle Hysteresis stressstrain curve of an auxetic100 grey PU foam sample (A) at 25% compression strain. sample (B) at 25% compression strain.

Hysteresis Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 25% Compression Strain Hysteresis Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 25% Compression Strain 8 5 C (HG25%-Aux.80) D (HG25%-Aux.60) 4.5 7

4 6 3.5

5 3

4 2.5 Stress [kPa] Stress [kPa] 2 3

1.5 2 1

1 0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.11c) One cycle Hysteresis stressstrain curve of an auxetic80 grey PU foam Fig. (4.11d) One cycle Hysteresis stressstrain curve of an auxetic60 grey PU foam sample (C) at 25% compression strain. sample (D) at 25% compression strain.

Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 25% Compression Strain 14 A (HG25%Conv.) B B (HG25%Aux. 100) 12 C (HG25%Aux. 80) D (HG25%Aux. 60)

8 C

6 Stress [kPa] Stress D A 4

0 0 5 10 15 20 25 Strain [%] Fig. (4.11e) Hysteresis stressstrain 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. 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

4.7.2 Compression strain at 50% and one cycle

Figures (4.12a) to (4.12d) show the hysteresis stressstrain 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 comparison between all square grey PU foam samples at one cycle and 50% 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).

59 Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional Grey Polyurethane Foam Sample [A] at 50% Compression Strain Hysteresis Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 50% Compression Strain 7 50 A (HG50%-Conv) B (HG50%-Aux.100) 45 6

5 35

30 4

3 Stress [kPa] Stress [kPa] 20

15 2

1 5

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%]

Fig. (4.12a) One cycle Hysteresis stressstrain curve of a conventional grey PU foam Fig. (4.12b) One cycle Hysteresis stressstrain curve of an auxetic100 grey PU foam sample (A) at 50% compression strain. sample (B) at 50% compression strain

Hysteresis Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 50% Compression Strain Hysteresis Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 50% Compression Strain 60 60 C (HG50%-Aux.80) D (HG50%-Aux.60)

50 50

40 40

30 30 Stress [kPa] Stress [kPa]

20 20

10 10

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%]

Fig. (4.12c) One cycle Hysteresis stressstrain curve of an auxetic80 grey PU foam Fig. (4.12d) One cycle Hysteresis stressstrain curve of an auxetic60 grey PU foam sample (C) at 50% compression strain sample (D) at 50% compression strain

Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional and Auxetic Gray Polyurethane Foam Samples at 50% Compression Strain 60 A (HG50%Conv.) D B (HG50%Aux. 100) C 50 C (HG50%Aux. 80) D (HG50%Aux. 60) B

30 Stress [kPa] Stress 20

10 A

0 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Fig. (4.12e) Hysteresis stressstrain 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

4.7.3 Compression strain at 75% and one cycle

Figures (4.13a) to (4.13d) show the stressstrain 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 comparison between all square grey PU foam samples at one cycle and 75% compression, that are plotted in one gragh, Figure (4.13e). The auxetic foam sample (B) have a higher dissipated energy (19.82 kJ/m 3) than the conventional foam sample (A) (3.08 kJ/m 3), as shown in table (4.11).

61 Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional Grey Polyurethane Foam Sample [A] at 75% Compression Strain Hysteresis Test of Auxetic 100 Grey Polyurethane Foam Sample [B] at 75% Compression Strain 20 250 A (HG75%-Conv) B (HG75%-Aux.100) 18

16 200

12 150

10 Stress[kPa] 8 Stress [kPa] 100

4 50

0 0 0 15 30 45 60 75 0 15 30 45 60 75 Strain [%] Strain [%]

Fig. (4.13a) One cycle hysteresis stressstrain curve of a conventional grey PU foam Fig. (4.13b) One cycle hysteresis stressstrain curve of an auxetic100 grey PU foam sample (A) at 75% compression strain. sample (B) at 75% compression strain.

Hysteresis Test of Auxetic 80 Grey Polyurethane Foam Sample [C] at 75% Compression Strain Hysteresis Test of Auxetic 60 Grey Polyurethane Foam Sample [D] at 75% Compression Strain 350 450 C (HG75%-Aux.80) D (HG75%-Aux.60)

400 300

350

250 300

200 250

200 150 Stress[kPa] Stress [kPa]

150 100

100

50 50

0 0 0 15 30 45 60 75 0 15 30 45 60 75 Strain [%] Strain [%]

Fig. (4.13c) One cycle hysteresis stressstrain curve of an auxetic80 grey PU foam Fig. (4.13d) One cycle hysteresis stressstrain curve of an auxetic60 grey PU foam sample (C) at 75% compression strain. sample (D) at 75% compression strain.

Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional and Auxetic Grey Polyurethane Foam Samples at 75% Compression Strain 450 A (HG75%Conv.) 400 B (HG75%Aux. 100) D C (HG75%Aux. 80) D (HG75%Aux. 60) 350

300 C

250 B 200 Stress [kPa] Stress 150

100

50 A 0 0 10 20 30 40 50 60 70 80 Strain [%]

Fig. (4.13e) Hysteresis stressstrain 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

63 Chapter 4 “Results and Discussion”

4.8 Hysteresis test of yellow samples

The stressstrain behaviour observed upon deformation typically includes a significant strain energy contribution, with the area enclosed by the hysteresis loop corresponding to the dissipated energy (E d) for each cycle. The quasistatic 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).

4.8.1 Compression strain at 25% and one cycle

Figures (4.14a) to (4.14d) show the stressstrain hysteresis curves of the 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/m 3) than the conventional foam sample (A*) (0.34 kJ/m 3), as shown in table (4.12).

64 Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional Yellow Polyurethane Foam Sample [A*] at 25% Compression Strain Hysteresis Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 25% Compression Strain 3 12 A* (HY25%-Conv.) B* (HY25% -Aux.100)

2.5 10

2 8

1.5 6 Stress [kPa] Stress [kPa] Stress

1 4

0.5 2

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.14a) Hysteresis stressstrain curve of a conventional yellow PU foam Fig. (4.14b) Hysteresis stressstrain curve of an auxetic100 yellow PU foam sample (A*) at 25% compression strain and one cycle. sample (B*) at 25% compression strain and one cycle.

Hysteresis Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 25% Compression Strain Hysteresis Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 25% Compression Strain 10 4.5 C* (HY25%-Aux.80) D* (HY25% -Aux.60)

9 4

8 3.5

7 3

6 2.5

Stress [kPa] Stress 4 [kPa] Stress

1.5 3

1 2

1 0.5

0 0 0 5 10 15 20 25 0 5 10 15 20 25 Strain [%] Strain [%]

Fig. (4.14c) Hysteresis stressstrain curve of an auxetic80 yellow PU foam Fig. (4.14d) Hysteresis stressstrain curve of an auxetic60 yellow PU foam sample (C*) at 25% compression strain and one cycle. sample (D*) at 25% compression strain and one cycle.

Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional and Auxetic Yellow Polyurethane Foam Samples at 25% Compression Strain 12 A* (HY25%Conv. B* B* (HY25%Aux. 100) 10 C* (HY25%Aux. 80) D* (HY25%Aux. 60)

8 C*

Stress Stress [kPa] D* 4 A*

0 0 5 10 15 20 25 Strain [%] Fig. (4.14e) Hysteresis stressstrain 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

4.8.2 Compression strain at 50% and one cycle

Figures (4.15a) to (4.15d) show the stressstrain hysteresis curves of the square yellow 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 comparison between all square yellow PU foam samples at one cycle and 50% compression, that are plotted in one gragh, figure (4.15e). The auxetic foam sample (B*) have a higher dissipated energy (3.42 kJ/m 3) than the conventional foam sample (A*) (0.88 kJ/m 3), as shown in table (4.13).

66 Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional Yellow Polyurethane Foam Sample [A*] at 50% Compression Strain Hysteresis Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 50% Compression Strain 5 40 A* (HY50%-Conv.) B* (HY50%-Aux.100) 4.5 35

4 30 3.5

25 3

2.5 20 Stress [kPa] Stress 2 Stress[kPa] 15

1.5 10 1

5 0.5

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%]

Fig. (4.15a) Hysteresis stressstrain curve of a conventional yellow PU foam Fig. (4.15b) Hysteresis stressstrain curve of an auxetic100 yellow PU foam sample (A*) at 50% compression strain and one cycle. sample (B*) at 50% compression strain and one cycle.

Hysteresis Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 50% Compression Strain Hysteresis Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 50% Compression Strain 50 50 C* (HY50%-Aux.80) D* (HY50% -Aux.60) 45 45

40 40

35 35

30 30

25 25

Stress [kPa] Stress 20 [kPa] Stress 20

15 15

10 10

5 5

0 0 0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Strain [%]

Fig. (4.15c) Hysteresis stressstrain curve of an auxetic80 yellow PU foam Fig. (4.15d) Hysteresis stressstrain curve of an auxetic60 yellow PU foam sample (C*) at 50% compression strain and one cycle. sample (D*) at 50% compression strain and one cycle.

Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional and Auxetic Yellow Polyurethane Foam Samples at 50% Compression Strain 50 A* (HY50%Conv.) D* C* 45 B* (HY50%Aux. 100) C* (HY50%Aux. 80) 40 D* (HY50%Aux. 60) B* 35

Stress [kPa] Stress 20

A* 5

0 0 5 10 15 20 25 30 35 40 45 50 Strain [%] Fig. (4.15e) Hysteresis stressstrain 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. Samples Dissipated Energy (kJ/m3) A* :( HY50%Conv.) 0.88 B* :( HY50%Aux.100) 3.42 C* :( HY50%Aux.80) 3.48 D* :( HY50%Aux.60) 2.38

4.8.3 Compression strain at 75% and one cycle

Figures (4.16a) to (4.16d) show the stressstrain hysteresis curves of the square yellow 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 comparison between all square yellow PU foam samples at one cycle and 75% compression, that are plotted in one gragh, figure (4.16e). The auxetic foam sample (B*) have a higher dissipated energy (17.62 kJ/m 3) than the conventional foam sample (A*) (2.44 kJ/m 3), as shown in table (4.14).

68 Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional Yellow Polyurethane Foam Sample [A*] at 75% Compression Strain Hysteresis Test of Auxetic 100 Yellow Polyurethane Foam Sample [B*] at 75% Compression Strain 20 200 A* (HY75%-Conv.) B* (HY75%-Aux.100) 18 180

16 160

14 140

12 120

10 100 Stress [kPa] Stress [kPa] 8 80

6 60

4 40

2 20

0 0 0 15 30 45 60 75 0 15 30 45 60 75 Strain [%] Strain [%]

Fig. (4.16a) Hysteresis stressstrain curve of a conventional yellow PU foam Fig. (4.16b) Hysteresis stressstrain curve of an auxetic100 yellow PU foam sample (A*) at 75% compression strain and one cycle. sample (B*) at 75% compression strain and one cycle.

Hysteresis Test of Auxetic 80 Yellow Polyurethane Foam Sample [C*] at 75% Compression Strain Hysteresis Test of Auxetic 60 Yellow Polyurethane Foam Sample [D*] at 75% Compression Strain 300 350 C* (HY75%-Aux.80) D* (HY75%-Aux.60)

300 250

250 200

200

150

150 Stress [kPa] Stress [kPa]

100 100

50 50

0 0 0 15 30 45 60 75 0 15 30 45 60 75 Strain [%] Strain [%]

Fig. (4.16c) Hysteresis stressstrain curve of an auxetic80 yellow PU foam Fig. (4.16d) Hysteresis stressstrain curve of an auxetic60 yellow PU foam sample (C*) at 75% compression strain and one cycle. sample (D*) at 75% compression strain and one cycle.

Chapter 4 “Results and Discussion”

Hysteresis Test of Conventional and Auxetic Yellow Polyurethane Foam Samples at 75% Compression Strain 350 A* (HY75%Conv.) B* (HY75%Aux. 100) D* 300 C* (HY75%Aux. 80) D* (HY75%Aux. 60) C* 250

200 B*

150 Stress [kPa] Stress

100

50 A*

0 0 15 30 45 60 75 Strain [%] Fig. (4.16e) Hysteresis stressstrain 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.

Samples Dissipated Energy (kJ/m3) A* :( HY75%Conv.) 2.44 B* :( HY75%Aux.100) 17.62 C* :( HY75%Aux.80) 22.90 D* :( HY75%Aux.60) 21.54

70 Chapter 4 “Results and Discussion”

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.

71 Chapter 4 “Results and Discussion”

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. Auxetic100 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. Auxetic80 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. Auxetic60 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 %

72 Chapter 4 “Results and Discussion”

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 stressstrain data.

73 Chapter 4 “Results and Discussion”

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 1015 % 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 wellknown 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. Postbuckling 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 stressstrain curve showed different behavior which consists of mainly two regions:

a. Linear elastic region which follows the theory of elasticity, and

b. Postbuckling of the unit cell wall or what so called densification of the foam in which the foam behaves like solid polymer.

74 Chapter 4 “Results and Discussion”

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”

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%.

76 Chapter “CONCLUSIONS AND FURTHER WORK”

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 stressstrain 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 wellknown plateau while for all processed auxetic samples, the stressstrain curve showed different behavior which consists of mainly two regions, linear elastic region and postbuckling 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.

77 Chapter “CONCLUSIONS AND FURTHER WORK”

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.

78 Chapter “CONCLUSIONS AND FURTHER WORK”

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 nosecone 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).

79 Chapter “CONCLUSIONS AND FURTHER WORK”

5.2.3 Military

The Defence Clothing and Textile Agency (DCTA) in Colchester, which is responsible for research into hightech 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 outofplane 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 (domelike 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 nonauxetic and (b) auxetic (double curvatureconvex 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 bulletproof helmets or vests more resilient to knocks and shrapnel.

80 Chapter “CONCLUSIONS AND FURTHER WORK”

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 bulletproof 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, "pressfit" 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.

81 Chapter “CONCLUSIONS AND FURTHER WORK”

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).

82 Chapter “CONCLUSIONS AND FURTHER WORK”

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

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.2542, 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.10381040, 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. DApply 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. 636642, 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.19061914, 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), 40394047, 2000.

(10) Nur, A. and Simmons, G., “The effect of saturation on velocity in low porosity rocks”, Earth Planet Sci. Lett., vol.7, pp.183193, 1969.

(11) Evans, K.E., “Tailoring the negative Poisson’s ratio”, Chem. Ind., vol.20, pp.654657, 1990.

(12) Fung, Y.C., “Foundations of Solid Mechanics”, PrenticeHall, 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 Reentrant foam materials with a negative Poisson’s ratio: Experiment and Analysis”, Int. J. Fracture, vol. 80, pp.7383, 1996.

(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.57255736, 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. 44064414, 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. 46784684, 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. 23972401, 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. 219224, 1998.

(21) A. Lowe, and R. S. Lakes. "Negative Poisson's Ratio Foam as Seat Cushion Material." Cellular Polymers, vol.19, pp.157167, 2000.

(22) YunChe 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. 373385, 2001.

(23) Brandel, B. and Lakes, R. S. "Negative Poisson’s ratio polyethylene foams”, Materials Science, vol. 36, pp. 58855893, 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. 5058, 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.

(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. 10521063, 2010.

(31) Pierron, F. "Mechanical properties of low density polymeric foams obtained from fullfield 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. 3149, 2008.

(33) K. Evans and A. Alderson, “Auxetic materials: Functional materials and structures from lateral thinking", Advanced Materials, vol. 12, no (9), pp. 617628, 2000.

(34) G. Stavroulakis, “Auxetic behaviour: Appearance and engineering applications", Physica Status Solidi (b), vol. 242, no 3, pp. 710720, 2005.

(35) P. McMullan, S. Kumar, and A. Grifin, “Textile fibres engineered from molecular auxetic polymers", World, vol. 8, pp. 12, 2000.

APPENDICES

Appendix A: Densities and compression ratios of samples (First Batch)

Square Grey Samples ( Aux.100, Aux.80 and Aux.60)

3 3 3 S. No Li=200 (mm) Vc) i mafter (gram) Vafter (mm ) ρafter (Kg/m ) ρave (kg/m ) Vc) f,ave 1 16.096 33*36*126 149688 107.53 2 Aux.100 4.883 15.604 34*36*125 153000 101.99 109.59 3.44 3 15.923 33*34*119 133518 119.26 1 16.616 34*36*111 135864 122.30 2 Aux.80 6.1035 15.72 35*36*115 144900 108.49 113.81 3.56 3 15.573 34*36*115 140760 110.64 1 16.145 35*36*102 128520 125.62 2 Aux.60 8.138 16.37 35*36*100 126000 129.92 125.46 3.93 3 15.378 35*36*101 127260 120.84

3 3 3 3 Vbefore =500000 mm , V 1,mould =61440 mm , V 2,mould =81920 mm and V 3,mould =102400 mm

Appendix B: Densities and compression ratios of samples (Second Batch)

Square yellow Samples (Aux.100, Aux.80 and Aux.60)

3 3 3 S. No Li=200 (mm) Vc) i mafter (gram) Vafter (mm ) ρafter (Kg/m ) ρave (kg/m ) Vc) f,ave 1 12.436 36*37*136 181152 68.65 2 Aux.100 4.883 12.65 35*35*130 159250 79.43 76.51 3.08 3 11.921 34*35*123 146370 81.44 1 12.605 35*35*109 133525 94.40

2 Aux.80 6.1035 11.999 35*36*116 146160 82.09 94.89 3.76 3 12.867 33*34*106 118932 108.19 1 12.647 36*36*110 142560 88.71 2 Aux.60 8.138 12.091 35*36*114 143640 84.18 89.98 3.63 3 12.364 35*35*104 127400 97.05

3 3 3 3 Vbefore =500000 mm , V 1,mould =61440 mm , V 2,mould =81920 mm and V 3,mould =102400 mm

Appendix C: Densities and compression ratios of samples (Third Batch)

Cylindrical Grey Samples (Aux.100, Aux.80 and Aux.60)

3 3 3 S. No Dm= 30(mm) Vc) i mafter (gram) Df Lf Vafter (mm ) ρafter (Kg/m ) ρave (Kg/m ) Vc) f,ave 1 11.634 31.51 121 94368.529 123.283 2 Aux.100 5.555 11.715 30.88 121 90597.730 129.308 126.13621 4.23 3 11.731 31.19 122 93237.764 125.818

1 11.589 31.83 109 86739.506 133.607 2 Aux.80 6.944 11.68 31.51 107 83455.153 139.955 137.43299 4.63 3 11.702 31.83 106 84346.880 138.737 1 11.584 32.47 102 84448.206 137.173 2 Aux.60 9.259 11.71 32.47 101 83620.282 140.038 137.41052 4.62 3 11.741 32.79 103 86956.885 135.021

3 3 3 3 Vbefore =392699.1 mm , V 1,mould =42411.5 mm , V 2,mould =56548.7 mm and V 3,mould =70685.8 mm

Appendix D: Densities and compression ratios of samples (Forth Batch)

Cylindrical yellow Samples (Aux.100, Aux.80 and Aux.60)

3 3 3 S. No Dm= 30 (mm) Vc) i mafter (gram) Df Lf Vafter (mm ) ρafter (g/mm ) ρave (kg/m ) Vc) f,ave 1 9.726 30.88 116 86854.02 111.98

2 Aux.100 5.555 9.814 31.04 118 89263.80 109.94 108.96 4.37 3 9.786 31.19 122 93237.76 104.96 1 9.766 31.83 109 86739.51 112.59 2 Aux.80 6.944 9.774 31.35 106 81840.41 119.43 120.65 4.79 3 10.030 31.19 101 77188.64 129.94

1 9.741 31.83 93 74007.10 131.62 2 Aux.60 9.259 9.731 31.51 94 73314.35 132.73 127.30 5.06 3 10.025 32.47 103 85276.13 117.56

3 3 3 3 Vbefore =392699.1 mm , V1,mould =42411.5 mm , V2,mould =56548.7 mm and V3,mould =70685.8 mm

Appendix E: Measurement of Poisson’s ratio in tensile test.

Original 2 % Strain Grey Samples Time) movie max ε2% εmax Time ε=2% νε=2% Xo Yo X1 Y1

Conv. (E) 390 138.8 5.62 39 69 37 76 0.51 Aux.100 (F) 571 244.59 4.67 43 68 44 74 0.26

Aux.80 (G) 360 2% 177.75 4.05 41 59 42 65 0.24 Aux.60 (H) 447 219.4 4.07 38 57 39 63 0.25

Original 2 % Strain Yellow Samples Time) ε ε Time ν movie max 2% max ε=2% ε=2% Xo Yo X1 Y1 Conv. (E*) 209 79.3 5.27 40 69 37 76 0.74 Aux.100 (F*) 600 185.4 6.47 42 67 43 73 0.27

Aux.80 (G*) 443 2% 217..45 4.07 41 59 42 64 0.29 Aux.60 (H*) 538 246 4.37 39 57 40 63 0.24

ﻣﻠ ﺨ ﺺ اﻟ ﺮ ﺳﺎﻟﺔ ﺑﺎﻟﻠ اﻟ ﻐﺔﻌ ﺮﺑﻴﺔ ﺑﺎﻟﻠ ﻐﺔ اﻟ ﺮ ﺳﺎﻟﺔ ﻣﻠ ﺨ ﺺ

اﻟﺘﻜﻨﻮﻟﻮﺟﻴﺎ اﻟﺤﺪﻳﺜﺔ ﺗﺘﻄﻠﺐ ﻣﻮاد ﺟﺪﻳﺪة ﻧﺎت ﺧﻮاص ﻣﻴﻜﺎﻧﻴﻜﻴﺔ ﺧﺎﺻﺔ. ﻓﻲ اﻟﻌﻘﺪﻳﻦ اﻟﻤﺎﺿﻴﻴﻦ ﻛﺎن اﻟﻤﺎﺿﻴﻴﻦ اﻟﻌﻘﺪﻳﻦ ﻓﻲ ﺧﺎﺻﺔ. ﻣﻴﻜﺎﻧﻴﻜﻴﺔ ﺧﻮاص ﻧﺎت ﺟﺪﻳﺪة ﻣﻮاد ﺗﺘﻄﻠﺐ اﻟﺤﺪﻳﺜﺔ اﻟﺘﻜﻨﻮﻟﻮﺟﻴﺎ ﻫﻨﺎك إﻫﺘﻤﺎم ﻛﺒﻴﺮ ﻟﻔﺌﺔ ﻣﻌﻴﻨﺔ ﻣﻦ اﻟﻤﻮاد اﻟﻤﻌﺮوﻓﺔ ﺑﺎﺳﻢ اﻟﻤﻮاد اﻟﻤﺘﻤﺪدة اﻟﺤﺠﻢ materials.( )Auxetic اﻟﻤﻮاد ).Auxetic materials( اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪدة اﻟﻤﻮاد ﺑﺎﺳﻢ اﻟﻤﻌﺮوﻓﺔ اﻟﻤﻮاد ﻣﻦ ﻣﻌﻴﻨﺔ ﻟﻔﺌﺔ ﻛﺒﻴﺮ إﻫﺘﻤﺎم ﻫﻨﺎك اﻟﻤﺘﻤﺪدة اﻟﺤﺠﻢ ﻫﻲ اﻟﻤﻮاد اﻟﺘﻲ ﻟﺪﻳﻬﺎ ﻧﺴﺒﺔ ﺑﻮاﺳﻮن اﻟﺴﻠﺒﻴﺔ وﻫﻮ ﻣﺎ ﻳﻌﻨﻲ أن ٥ﻫﺬ اﻟﻤﻮاد ﻳﺰﻳﺪ ﻣﻘﻄﻌﻬﺎ ﻇﺪﻣﺎ ﻣﻘﻄﻌﻬﺎ ﻳﺰﻳﺪ اﻟﻤﻮاد ٥ﻫﺬ أن ﻳﻌﻨﻲ ﻣﺎ وﻫﻮ اﻟﺴﻠﺒﻴﺔ ﺑﻮاﺳﻮن ﻧﺴﺒﺔ ﻟﺪﻳﻬﺎ اﻟﺘﻲ اﻟﻤﻮاد ﻫﻲ اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪدة ﺗﻌﺮض ﻟﻘﻮة اﻟﺸﺪ و ﻳﻨﻜﻤﺶ أﺛﻨﺎﺀ ﻗﻮة اﻟﻀﻔﻂ، وﻫﺬا ﺧﻼﻓﺎ ﻟﻤﻌﻈﻢ اﻟﻤﻮاد اﻟﺘﻘﻠﻴﺪﻳﺔ اﻷﺧﺮى. ﻫﺬه اﻟﻤﻮاد ﻟﻬﺎ اﻟﻤﻮاد ﻫﺬه اﻷﺧﺮى. اﻟﺘﻘﻠﻴﺪﻳﺔ اﻟﻤﻮاد ﻟﻤﻌﻈﻢ ﺧﻼﻓﺎ وﻫﺬا اﻟﻀﻔﻂ، ﻗﻮة أﺛﻨﺎﺀ ﻳﻨﻜﻤﺶ و اﻟﺸﺪ ﻟﻘﻮة ﺗﻌﺮ ض

ﺧﺼﺎﺋﺺ ﻣﺘﻔﻮﻗﺔ ﻋﻠﻰ اﻟﻤﻮاد اﻟﺘﻘﻠﻴﺪﻳﺔ ﻣﺜﻞ زﻳﺎدة ﻣﻌﺎﻣﻞ اﻟﻘﺺ، أرﺗﻔﺎع ﻣﻘﺎوﻣﺔ اﻟﺼﺪم، ﻗﺪرة .ﻋﺎﻟﻴﺔ ﻋﻠﻰ إﻣﺘﺼﺎص اﻷﻫﺘﺰازات و اﻟﺼﻮت ﻣﻤﺎ ﻳﺠﻌﻞ ﻫﺬه اﻟﻤﻮاد ﻧﺎت أﻫﻤﻴﺔ ﻛﺒﻴﺮة ﻓﻰ ﻛﺜﻴﺮ ﻣﻦ اﻟﺘﻄﺒﻴﻘﺎت اﻟﻬﻨﺪﺳﻴﺔ. اﻟﺘﻄﺒﻴﻘﺎت ﻣﻦ ﻛﺜﻴﺮ ﻓﻰ ﻛﺒﻴﺮة أﻫﻤﻴﺔ ﻧﺎت اﻟﻤﻮاد ﻫﺬه ﻳﺠﻌﻞ ﻣﻤﺎ اﻟﺼﻮت و اﻷﻫﺘﺰازات إﻣﺘﺼﺎ ص

ﻓﻲ ﻫﺬا اﻟﺒﺤﺚ اﻟﻤﻘﺪم، ﺗﻢ ﺗﺼﻨﻴﻊ ﻓﻮم اﻟﺒﻮﻟﻲ ﻳﻮرﻳﺜﺎن اﻟﻤﺮن اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ ﻧﺎت اﻟﻜﺜﺎﻓﺎت اﻟﻤﺨﺘﻠﻔﺔ ﻣﻦ اﻟﻤﺨﺘﻠﻔﺔ اﻟﻜﺜﺎﻓﺎت ﻧﺎت اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد اﻟﻤﺮن ﻳﻮرﻳﺜﺎن اﻟﺒﻮﻟﻲ ﻓﻮم ﺗﺼﻨﻴﻊ ﺗﻢ اﻟﻤﻘﺪم، اﻟﺒﺤﺚ ﻫﺬا ﻓﻲ ﻓﻮم اﻟﺒﻮﻟﻲ ﻳﻮرﻳﺜﺎن اﻟﻤﺮن اﻟﺘﻘﻠﻴﺪي ﺑﻨﺴﺐ إﻧﻀﻐﺎط ﻣﺨﺘﻠﻔﺔ. ﺗﻢ ﻓﺤﺺ اﻟﺘﺮﻛﻴﺐ اﻟﺒﻨﺎﺋﻲ ﻟﻜﻼ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم ﻣﻦ ﻟﻜﻼ اﻟﺒﻨﺎﺋﻲ اﻟﺘﺮﻛﻴﺐ ﻓﺤﺺ ﺗﻢ ﻣﺨﺘﻠﻔﺔ. إﻧﻀﻐﺎط ﺑﻨﺴﺐ اﻟﺘﻘﻠﻴﺪي اﻟﻤﺮن ﻳﻮرﻳﺜﺎن اﻟﺒﻮﻟﻲ ﻓﻮم واﻟﻤﺘﻤﺪد ﺑﺄﺳﺘﺨﺪام اﻟﻤﺠﻬﺮ اﻟﻀﻮﺋﻲ ﻟﻠﻤﻘﺎرﻧﺔ ﺑﻴﻨﻬﻢ. ﺗﻢ ﺗﺤﻘﻴﻖ ﻫﺬا ﻣﻘﺎرﻧﺔ ﺑﺄﻋﻤﺎل ﺳﺎﺑﻘﺔ أﺧﺮى وأﻇﻬﺮت ﻧﻔﺲ وأﻇﻬﺮت أﺧﺮى ﺳﺎﺑﻘﺔ ﺑﺄﻋﻤﺎل ﻣﻘﺎرﻧﺔ ﻫﺬا ﺗﺤﻘﻴﻖ ﺗﻢ ﺑﻴﻨﻬﻢ. ﻟﻠﻤﻘﺎرﻧﺔ اﻟﻀﻮﺋﻲ اﻟﻤﺠﻬﺮ ﺑﺄﺳﺘﺨﺪام واﻟﻤﺘﻤﺪد اﻟﺸﻜﻞ ﻟﻠﺘﺮﻛﻴﺐ اﻟﺒﻨﺎﺋﻰ ﻟﻜﻼ ﻣﻦ اﻟﻔﻮم اﻟﻌﺎدى و اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ. ﻫﺬه ﻫﻲ اﻟﻤﺮة اﻷوﻟﻰ ﻹﻧﺘﺎج اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﻔﻮم ﻹﻧﺘﺎج اﻷوﻟﻰ اﻟﻤﺮة ﻫﻲ ﻫﺬه اﻟﺤﺠﻢ. اﻟﻤﺘﻤﺪد و اﻟﻌﺎدى اﻟﻔﻮم ﻣﻦ ﻟﻜﻼ اﻟﺒﻨﺎﺋﻰ ﻟﻠﺘﺮﻛﻴﺐ اﻟﺸﻜﻞ

اﻟﺤﺠﻢ ﻓﻲ ﻣﺼﺮ.

ﺗﻢ ﻗﻄﻊ و ﺗﺠﻬﻴﺰ ﻣﺠﻤﻮﻋﺔ ﻋﻴﻨﺎت ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي ﺑﻜﺜﺎﻓﺘﻴﻦ ﻣﺨﺘﻠﻔﺘﻴﻦ، اﻟﻜﺜﺎﻓﺔ اﻻوﻟﻰ ﺻﻔﺮاﺀ اﻟﻠﻮن اﻟﻠﻮن ﺻﻔﺮاﺀ اﻻوﻟﻰ اﻟﻜﺜﺎﻓﺔ ﻣﺨﺘﻠﻔﺘﻴﻦ، ﺑﻜﺜﺎﻓﺘﻴﻦ اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم ﻣﻦ ﻋﻴﻨﺎت ﻣﺠﻤﻮﻋﺔ ﺗﺠﻬﻴﺰ و ﻗﻄﻊ ﺗﻢ ٢٥( )٣ﻛﺠﻢ\م و اﻟﺜﺎﻧﻴﺔ رﻣﺎدﻳﺔ اﻟﻠﻮن ٣٠( ).٣ﻛﺠﻢ\م وذﻟﻚ ﺑﻤﻘﻄﻌﻴﻦ ﻣﺨﺘﻠﻔﻴﻦ ﻣﻦ ﻛﻞ ﻛﺜﺎﻓﺔ، اﻟﻤﻘﻄﻊ اﻻول اﻟﻤﻘﻄﻊ ﻛﺜﺎﻓﺔ، ﻛﻞ ﻣﻦ ﻣﺨﺘﻠﻔﻴﻦ ﺑﻤﻘﻄﻌﻴﻦ وذﻟﻚ داﻧﺮى ' )D=50mm, و اﻟﻤﻘﻄﻊ اﻟﺜﺎﻧﻰ ﻣﺮﺑﻊ ر ,W=H=50mm ). ﺗﻢ ﺿﻐﻂ ﺗﻢ ). ﻫﺬه اﻟﻌﻴﻨﺎت داﺧﻞ ﻗﻮاﻟﺐ ﻣﻦ اﻷﻟﻤﻮﻧﻴﻮم ﻧﺎت ﻣﻘﻄﻊ داﺋﺮى )D=30mm( و اﻷﺧﺮ ﻧﺎت ﻣﻘﻄﻊ ﻣﺮﺑﻊ ﻣﻘﻄﻊ (H=w =30mm )، ﺗﻢ ﺿﻌﻂ اﻟﻌﻴﻨﺎت ﻓﻰ اﻻﺗﺠﺎه اﻟﻤﺤﻮري ﻣﻦ ٠ ٠ ٢ ﻣﻢ إﻟﻰ ( ٠ ٠ ١ ، ٠ ٨ و ٠ ﻣﻢ)٦ ﻟﻠﺤﺼﻮل ﻋﻠﻰ ﺛﻼث ﻧﺴﺐ اﻧﻀﻐﺎط ﻣﺨﺘﻠﻔﺔ. ﺗﻮﺿﻊ اﻟﻘﻮاﻟﺐ ﺑﺎﻟﻌﻴﻨﺎت داﺧﻞ اﻟﻔﺮن ﻟﻠﺘﺴﺨﻴﻦ ﻋﻨﺪ درﺟﺔ ﺣﺮارة ﺛﺎﺑﺘﺔ ٠ ٠ ٢ درﺟﺔ ﻣﺌﻮﻳﺔ ﻟﻤﺪة ٥ ٢ دﻗﻴﻘﺔ. ﺑﻌﺪ ذﻟﻚ ﻳﺘﻢ ﺗﺒﺮﻳﺪ اﻟﻘﻮاﻟﺐ ﺑﺎﻟﻌﻴﻨﺎت ﻓﻰ اﻟﻬﻮاﺀ ﻟﻤﺪة ٥ دﻗﻴﻘﺔ١ ﺛﻢ ﻳﺘﻢ ﻧﺰع اﻟﻌﻴﻨﺎت اﻟﻌﻴﻨﺎت ﻧﺰع ﻳﺘﻢ ﺛﻢ دﻗﻴﻘﺔ١ ٥ ﻟﻤﺪة اﻟﻬﻮاﺀ ﻓﻰ ﺑﺎﻟﻌﻴﻨﺎت اﻟﻘﻮاﻟﺐ ﺗﺒﺮﻳﺪ ﻳﺘﻢ ذﻟﻚ ﺑﻌﺪ دﻗﻴﻘﺔ. ٢ ٥ ﻟﻤﺪة ﻣﺌﻮﻳﺔ درﺟﺔ ﻣﻦ اﻟﻘﻮاﻟﺐ و ﺷﺪﻫﺎ ﻓﻰ اﻟﺜﻼث إﺗﺠﺎﻫﺎت ﻹزاﻟﺔ اﻹﺟﻬﺎدات اﻟﻤﺨﺘﺰﻟﺔ. ﺑﺬﻟﻚ ﻳﺘﻢ اﻟﺤﺼﻮل ﻋﻠﻰ ﺛﻼث أﻧﻮاع ﺛﻼث ﻋﻠﻰ اﻟﺤﺼﻮل ﻳﺘﻢ ﺑﺬﻟﻚ اﻟﻤﺨﺘﺰﻟﺔ. اﻹﺟﻬﺎدات ﻹزاﻟﺔ إﺗﺠﺎﻫﺎت اﻟﺜﻼث ﻓﻰ ﺷﺪﻫﺎ و اﻟﻘﻮاﻟﺐ ﻣﻦ ﻣﺨﺘﻠﻔﺔ ﻣﻦ اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ وﻫﻢ ,Aux.80 and Aux( )60.Aux.100 ﺑﺜﻼث ﻧﺴﺐ إﻧﻀﻐﺎط ﻣﺨﺘﻠﻔﺔ ٦،٩٤،٥،٥٦( و )٩،٢٦ ﻋﻠﻰ اﻟﺘﺮﺗﻴﺐ.

ﺗﻢ ﺗﻘﺴﻴﻢ اﻟﻌﻴﻨﺎت اﻟﻰ أرﺑﻊ ﻣﺠﻤﻮﻋﺎت ﻛﻞ ﻣﺠﻤﻮﻋﺔ ﺗﺤﺘﻮى ﻋﻠﻰ أرﺑﻊ .ﻋﻴﻨﺎت (ﻋﻴﻨﺔ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪى اﻟﻔﻮم ﻣﻦ (ﻋﻴﻨﺔ .ﻋﻴﻨﺎت أرﺑﻊ ﻋﻠﻰ ﺗﺤﺘﻮى ﻣﺠﻤﻮﻋﺔ ﻛﻞ ﻣﺠﻤﻮﻋﺎت أرﺑﻊ اﻟﻰ اﻟﻌﻴﻨﺎت ﺗﻘﺴﻴﻢ ﺗﻢ وﺛﻼث ﻋﻴﻨﺎت ﻣﺨﺘﻠﻔﺔ ﻓﻰ ﻧﺴﺐ اﻹﻧﻀﻐﺎط ﻣﻦ اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ اﻟﻨﻲ ﺗﻢ ﺗﺼﻨﻴﻌﺔ)، اﻟﻤﺠﻤﻮﻋﺔ اﻻوﻟﻰ ذو ذو اﻻوﻟﻰ اﻟﻤﺠﻤﻮﻋﺔ ﺗﺼﻨﻴﻌﺔ)، ﺗﻢ اﻟﻨﻲ اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد اﻟﻔﻮم ﻣﻦ اﻹﻧﻀﻐﺎط ﻧﺴﺐ ﻓﻰ ﻣﺨﺘﻠﻔﺔ ﻋﻴﻨﺎت وﺛﻼ ث اﻟﻤﻘﻄﻊ اﻟﻤﺮﺑﻊ و اﻟﻠﻮن اﻟﺮﻣﺎدى، اﻟﻤﺠﻤﻮﻋﺔ اﻟﺜﺎﻧﻴﺔ ذو اﻟﻤﻘﻄﻊ اﻟﻤﺮﺑﻊ و اﻟﻠﻮن اﻷﺻﻐﺮ، اﻟﻤﺠﻤﻮﻋﺔ اﻟﺜﺎﻟﺜﺔ ذو اﻟﺜﺎﻟﺜﺔ اﻟﻤﺠﻤﻮﻋﺔ اﻷﺻﻐﺮ، اﻟﻠﻮن و اﻟﻤﺮﺑﻊ اﻟﻤﻘﻄﻊ ذو اﻟﺜﺎﻧﻴﺔ اﻟﻤﺠﻤﻮﻋﺔ اﻟﺮﻣﺎدى، اﻟﻠﻮن و اﻟﻤﺮﺑﻊ اﻟﻤﻘﻄﻊ اﻟﻤﻘﻄﻊ اﻟﺪاﺋﺮى و اﻟﻠﻮن اﻟﺮﻣﺎدى و اﻟﻤﺠﻤﻮﻋﺔ اﻟﺮاﺑﻌﺔ ذو اﻟﻤﻘﻄﻊ اﻟﺪاﺋﺮى و اﻟﻠﻮن اﻷﺻﻐﺮ. ﺗﻢ اﺀﻋﺪاد وﺗﺠﻬﻴﺰ اﺀﻋﺪاد ﺗﻢ اﻷﺻﻐﺮ. اﻟﻠﻮن و اﻟﺪاﺋﺮى اﻟﻤﻘﻄﻊ ذو اﻟﺮاﺑﻌﺔ اﻟﻤﺠﻤﻮﻋﺔ و اﻟﺮﻣﺎدى اﻟﻠﻮن و اﻟﺪاﺋﺮى اﻟﻤﻘﻄﻊ اﻟﻌﻴﻨﺎت ﺑﺤﻴﺚ ﺗﻜﻮن اﻟﻌﻴﻨﺎت ﻧﺎت اﻟﻤﻘﺎﻃﻊ اﻟﻤﺮﺑﻌﺔ ﺑﺎﻷﺑﻌﺎد اﻟﺘﺎﻟﻴﺔ (H=w =35mm, L=70mm ) و ) اﻻﺧﺮى ﻧﺎت اﻟﻤﻘﺎﻃﻊ اﻟﺪاﺋﺮﻳﺔ ﺑﺎﻷﺑﻌﺎد اﻟﺘﺎﻟﻴﺔ (D=32mm, L=70mm). ﺗﻢ ﺗﻄﺒﻴﻖ أرﺑﻌﺔ اﺧﺘﺒﺎرات ﻣﻴﻜﺎﻧﻴﻜﻴﺔ ﻟﻠﺤﺼﻮل ﻋﻠﻰ اﻟﺨﻮاص اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ ﻟﻠﻔﻮم اﻟﺘﻘﻠﻴﺪي و اﻟﻤﺘﻤﺪد و اﻟﺘﻘﻠﻴﺪي ﻟﻠﻔﻮم اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ اﻟﺨﻮاص ﻋﻠﻰ ﻟﻠﺤﺼﻮل ﻣﻴﻜﺎﻧﻴﻜﻴﺔ اﺧﺘﺒﺎرات أرﺑﻌﺔ ﺗﻄﺒﻴﻖ ﺗﻢ اﻟﺤﺠﻢ ﻟﻤﻌﺮﻓﺔ ﺳﻠﻮك ﻛﻼ ﻣﻨﻬﻢ. ﺗﻢ ﺗﻨﻐﻴﺬ اﺛﻨﻴﻦ ﻣﻦ اﻻﺧﺘﺒﺎرات اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ اﻻﺳﺘﺎﺗﻴﻜﻴﺔ اﻟﺸﺪ” ”واﻟﻀﻐﻂ واﺛﻨﻴﻦ ”واﻟﻀﻐﻂ اﻟﺸﺪ” اﻻﺳﺘﺎﺗﻴﻜﻴﺔ اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ اﻻﺧﺘﺒﺎرات ﻣﻦ اﺛﻨﻴﻦ ﺗﻨﻐﻴﺬ ﺗﻢ ﻣﻨﻬﻢ. ﻛﻼ ﺳﻠﻮك ﻟﻤﻌﺮﻓﺔ اﻟﺤﺠﻢ ﻣﻦ اﻻﺧﺘﺒﺎرات اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ اﻟﺪﻳﻨﺎﻣﻴﻜﻴﺔ اﻟﺘﺨﻠﻔﻴﺔ” ”واﻟﻤﺮوﻧﺔ ﻟﻌﻤﻞ اﻟﻤﻘﺎرﻧﺔ ﺑﻴﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي واﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ واﻟﻤﺘﻤﺪد اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم ﺑﻴﻦ اﻟﻤﻘﺎرﻧﺔ ﻟﻌﻤﻞ ”واﻟﻤﺮوﻧﺔ اﻟﺘﺨﻠﻔﻴﺔ” اﻟﺪﻳﻨﺎﻣﻴﻜﻴﺔ اﻟﻤﻴﻜﺎﻧﻴﻜﻴﺔ اﻻﺧﺘﺒﺎرات ﻣﻦ ﺗﻢ ﺗﻨﻐﻴﺬ اﺧﺘﺒﺎر اﻟﺸﺪ اﻻﺳﺘﺎﺗﻴﻜﻲ ﺑﻤﻌﺪل ﺗﺤﻜﻢ ﻓﻰ اﻟﺴﺮﻋﺔ ﻳﺴﺎوى ،٢ ٠ ﻣﻠﻢ ا ﺛﺎﻧﻴﺔ .و ﺗﻢ ﺗﻨﻐﻴﺬ اﺧﺘﺒﺎرات اﻟﻀﻔﻂ اﺧﺘﺒﺎرات ﺗﻨﻐﻴﺬ ﺗﻢ .و ﺛﺎﻧﻴﺔ ا ﻣﻠﻢ ٠ ،٢ ﻳﺴﺎوى اﻟﺴﺮﻋﺔ ﻓﻰ ﺗﺤﻜﻢ ﺑﻤﻌﺪل اﻻﺳﺘﺎﺗﻴﻜﻲ اﻟﺸﺪ اﺧﺘﺒﺎر ﺗﻨﻐﻴﺬ ﺗﻢ

واﻟﺘﺨﻠﻔﻴﺔ ﺑﻤﻌﺪل ﺗﺤﻜﻢ ﻣﻘﺪارة ،٣ ٠ .١ث- وﻛﺎﻧﺖ اﻟﺒﻴﺎﻧﺎت اﻟﻤﺴﺠﻠﺔ ﻣﻦ ﻣﺎﻛﻴﻨﺔ اﻻﺧﺘﺒﺎر ﻫﻰ .ﻋﺒﺎرة ﻋﻦ ﻋﻼﻗﺔ ﻋﻦ .ﻋﺒﺎرة ﺑﻴﻦ اﻻﺟﻬﺎد و اﻻﻧﻔﻌﺎل. ﺗﻢ اﻟﺤﺼﻮل ﻋﻠﻰ ﻣﻌﺎﻣﻞ اﻟﻤﺮوﻧﺔ وﻧﺴﺒﺔ ﺑﻮاﺳﻮن ﻷﺧﺘﺒﺎرات اﻟﺸﺪ واﻟﻀﻐﻂ. وﻗﺪ ﺗﻢ وﻗﺪ واﻟﻀﻐﻂ. اﻟﺸﺪ ﻷﺧﺘﺒﺎرات ﺑﻮاﺳﻮن وﻧﺴﺒﺔ اﻟﻤﺮوﻧﺔ ﻣﻌﺎﻣﻞ ﻋﻠﻰ اﻟﺤﺼﻮل ﺗﻢ اﻻﻧﻔﻌﺎل. و اﻻﺟﻬﺎد ﺑﻴﻦ ﻗﻴﺎس ﻧﺴﺒﺔ ﺑﻮاﺳﻮن ﺑﺄﺳﺘﺨﺪام ﺗﻘﻄﻴﻊ اﻟﺼﻮر ﻣﻦ اﻟﻔﻠﻴﻢ اﻟﻤﺴﺠﻞ أﺛﻨﺎﺀ اﻻﺧﺘﺒﺎر وذﻟﻚ ﻋﻨﺪ أزﻣﻨﺔ ﻣﺨﺘﻠﻔﺔ ﻟﻤﻌﺮﻓﺔ ﻣﺨﺘﻠﻔﺔ أزﻣﻨﺔ ﻋﻨﺪ وذﻟﻚ اﻻﺧﺘﺒﺎر أﺛﻨﺎﺀ اﻟﻤﺴﺠﻞ اﻟﻔﻠﻴﻢ ﻣﻦ اﻟﺼﻮر ﺗﻘﻄﻴﻊ ﺑﺄﺳﺘﺨﺪام ﺑﻮاﺳﻮن ﻧﺴﺒﺔ ﻗﻴﺎ س اﻟﺘﻔﻴﺮ اﻟﻌﺮﺿﻰ و اﻟﻄﻮﻟﻰ ﺑﺄﺳﺘﺨﺪام ﺑﺮﻧﺎﻣﺞ Get Data Graph Digitizer.( )Get( ﺑﺮﻧﺎﻣﺞ ﺑﺄﺳﺘﺨﺪام اﻟﻄﻮﻟﻰ و اﻟﻌﺮﺿﻰ اﻟﺘﻔﻴﺮ

وﻋﻤﻮﻣﺎ، ﻗﺪ أوﺿﺤﺖ اﻟﻨﺘﺎﺋﺞ أن ﺳﻠﻮك اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ أﻓﻀﻞ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪى ﻋﻨﺪ ﻧﺴﺐ ﻋﻨﺪ اﻟﺘﻘﻠﻴﺪى اﻟﻔﻮم ﻣﻦ أﻓﻀﻞ اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد اﻟﻔﻮم ﺳﻠﻮك أن اﻟﻨﺘﺎﺋﺞ أوﺿﺤﺖ ﻗﺪ وﻋﻤﻮﻣﺎ، اﻻﻧﻀﻐﺎط اﻟﻤﺨﺘﻠﻔﺔ و ﻟﻜﻠﺘﺎ اﻟﻜﺜﺎﻓﺘﻴﻦ اﻷﺻﻐﺮ واﻟﺮﻣﺎدي. وﻛﺎﻧﺖ اﻟﻘﻴﻢ اﻟﺘﻲ ﺗﻢ اﻟﺤﺼﻮل ﻋﻠﻴﻬﺎ ﺗﺠﺮﻳﺒﻴﺎ ﻣﻦ ﻧﺴﺐ ﻣﻦ ﺗﺠﺮﻳﺒﻴﺎ ﻋﻠﻴﻬﺎ اﻟﺤﺼﻮل ﺗﻢ اﻟﺘﻲ اﻟﻘﻴﻢ وﻛﺎﻧﺖ واﻟﺮﻣﺎدي. اﻷﺻﻐﺮ اﻟﻜﺜﺎﻓﺘﻴﻦ ﻟﻜﻠﺘﺎ و اﻟﻤﺨﺘﻠﻔﺔ اﻻﻧﻀﻐﺎط ﺑﻮاﺳﻮن ﺗﺘﺮاوح ﺑﻴﻦ ٠،٢٧(- و ،.).٧٤ أوﺿﺤﺖ اﻻﺧﺘﺒﺎرات أﻳﻀﺎ أن ﻣﻌﺎﻣﻞ اﻟﻤﺮوﻧﺔ ﻟﻠﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد ﻟﻠﻔﻮم اﻟﻤﺮوﻧﺔ ﻣﻌﺎﻣﻞ أن أﻳﻀﺎ اﻻﺧﺘﺒﺎرات أوﺿﺤﺖ ،.).٧٤ و ٠،٢٧(- ﺑﻴﻦ ﺗﺘﺮاوح ﺑﻮاﺳﻮن أﻗﻞ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي. ﻋﻠﻰ ﺳﺒﻴﻞ اﻟﻤﺜﺎل ﻋﻴﻨﺔ اﻟﻔﻮم اﻟﻤﺘﻤﺪدة اﻟﺤﺠﻢ اﻟﺮﻣﺎدﻳﺔ اﻟﻠﻮن ح ﻇﺪ ﻧﺴﺒﺔ إﻧﻔﻌﺎل ٠ 7.0 ﻟﺪﻳﻬﺎ ﻣﻌﺎﻣﻞ ﻣﺮوﻧﺔ ٣٠،٠٢ ﻛﻴﻠﻮ ﺑﺎﺳﻜﺎل و اﻟﺬي ﻫﻮ أﻗﻞ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي ﺑﻤﻘﺪار ر.٧٧،٣ ﺑﻤﻘﺪار اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم ﻣﻦ

ﺗﻢ ﺣﺴﺎب اﻟﻄﺎﻗﺔ اﻟﻤﻤﺘﺼﺔ ﻟﻠﻔﻮم ﺑﺎﺳﺘﺨﺪام ﻧﺘﺎﺋﺞ أﺧﺘﺒﺎر اﻟﺸﺪ و اﻟﻀﻔﻂ. وﻗﺪ ﻟﻮﺣﻆ أن اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﻔﻮم أن ﻟﻮﺣﻆ وﻗﺪ اﻟﻀﻔﻂ. و اﻟﺸﺪ أﺧﺘﺒﺎر ﻧﺘﺎﺋﺞ ﺑﺎﺳﺘﺨﺪام ﻟﻠﻔﻮم اﻟﻤﻤﺘﺼﺔ اﻟﻄﺎﻗﺔ ﺣﺴﺎب ﺗﻢ اﻟﺤﺠﻢ ﻳﻤﻠﻚ إﻣﺘﺼﺎص ﻟﻠﻄﺎﻗﺔ أﻋﻠﻰ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي .ﻋﻠﻰ ﺳﺒﻴﻞ اﻟﻤﺜﺎل اﻟﻔﻮم اﻟﺮﻣﺎدي اﻟﻠﻮن ﻟﺪﻳﺔ ﻧﺴﺒﺔ ﻟﺪﻳﺔ اﻟﻠﻮن اﻟﺮﻣﺎدي اﻟﻔﻮم اﻟﻤﺜﺎل ﺳﺒﻴﻞ .ﻋﻠﻰ اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم ﻣﻦ أﻋﻠﻰ ﻟﻠﻄﺎﻗﺔ إﻣﺘﺼﺎص ﻳﻤﻠﻚ اﻟﺤﺠﻢ

إﻧﻀﻐﺎط ،ه٦ ه و ﻛﺜﺎﻓﺔ ١٠٩،٦ .٣ﻛﺠﻢ\م ﻛﺬﻟﻚ اﻟﻄﺎﻗﺔ اﻟﻤﻤﺘﺼﺔ ﻛﺎﻧﺖ ٣ﻛﺠﻮل\م٣،٩٨ وﻫ ﻲ أﻋﻠﻰ ﻣﻦ اﻟﻔﻮم ﻣﻦ أﻋﻠﻰ اﻟﺘﻘﻠﻴﺪي ﺑﻨﺴﺒﺔ ٩،٦ ر.٦ أﺛﺒﺘﺖ اﻻﺧﺘﺒﺎرات أن ﻗﻴﻤﺔ اﻟﻤﺮوﻧﺔ ﻟﻠﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ ﻧﺎت اﻟﻠﻮن اﻟﺮﻣﺎدي أﻋﻠﻰ ﻣﻦ أﻋﻠﻰ اﻟﺮﻣﺎدي اﻟﻠﻮن ﻧﺎت اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد ﻟﻠﻔﻮم اﻟﻤﺮوﻧﺔ ﻗﻴﻤﺔ أن اﻻﺧﺘﺒﺎرات أﺛﺒﺘﺖ ر.٦ ٩،٦ ﺑﻨﺴﺒﺔ اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي .ﻋﻠﻰ ﺳﺒﻴﻞ اﻟﻤﺜﺎل اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ ﻧﺎت اﻟﻠﻮن اﻟﺮﻣﺎدي اﻟﺬى ﻟﺪﻳﺔ ﻧﺴﺒﺔ أﻧﻀﻐﺎط ٩،٢٦ ٩،٢٦ أﻧﻀﻐﺎط ﻧﺴﺒﺔ ﻟﺪﻳﺔ اﻟﺬى اﻟﺮﻣﺎدي اﻟﻠﻮن ﻧﺎت اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد اﻟﻔﻮم اﻟﻤﺜﺎل ﺳﺒﻴﻞ .ﻋﻠﻰ اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم

وﻛﺜﺎﻓﺔ ١٢ه،ه ،٣ﻛﺠﻢ\م أﻋﻄﻰ ﻧﺴﺒﺔ ﻣﺮوﻧﺔ /٣٨ و ﻫﻲ أﻋﻠﻰ ﻣﻦ اﻟﻔﻮم اﻟﺘﻘﻠﻴﺪي ﺑﻨﺴﺒﺔ ر.٧,٧ ﺑﻨﺴﺒﺔ اﻟﺘﻘﻠﻴﺪي اﻟﻔﻮم ﻣﻦ أﻋﻠﻰ

اﻟﻔﻮم اﻟﻤﺘﻤﺪد اﻟﺤﺠﻢ ﻟﺪﻳﺔ إﻣﻜﺎﻧﻴﺔ ﻻﺳﺘﺨﺪاﻣﻪ ﻓﻲ اﻟﻤﺠﺎﻻت اﻟﺘﺎﻟﻴﺔ: اﻟﻤﺠﺎﻻت ﻓﻲ ﻻﺳﺘﺨﺪاﻣﻪ إﻣﻜﺎﻧﻴﺔ ﻟﺪﻳﺔ اﻟﺤﺠﻢ اﻟﻤﺘﻤﺪد اﻟﻔﻮم

٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم ﻓﻰ اﻟﻤﺠﺎﻻت اﻟﻄﺒﻴﺔ. اﻟﻤﺠﺎﻻت ﻓﻰ ﻳﺴﺘﺨﺪم ٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم ﻻﻣﺘﺼﺎص اﻻﻫﺘﺰازات ﻓﻰ اﻟﻤﻀﺨﺎت، اﻟﻤﺒﺎدﻻت اﻟﺤﺮارﻳﺔ وأرﺑﻄﻪ اﻟﺘﺜﺒﻴﺖ. وأرﺑﻄﻪ اﻟﺤﺮارﻳﺔ اﻟﻤﺒﺎدﻻت اﻟﻤﻀﺨﺎت، ﻓﻰ اﻻﻫﺘﺰازات ﻻﻣﺘﺼﺎص ﻳﺴﺘﺨﺪم أن ﻳﻤﻜﻦ ٠ ٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم أﻳﻀﺎ ﻛﺤﺸﻮ وﻋﺎزل ﻓﻰ اﻟﺼﻤﺎﻣﺎت واﻟﻤﻀﺨﺎت. اﻟﺼﻤﺎﻣﺎت ﻓﻰ وﻋﺎزل ٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم ﻓﻰ ﻋﺰل و ﺗﺒﻄﻴﻦ اﻟﻄﺎﺋﺮات ﻣﻦ اﻟﺪاﺧﻞ. ﻣﻦ اﻟﻄﺎﺋﺮات ﺗﺒﻄﻴﻦ و ﻋﺰل ﻓﻰ ﻳﺴﺘﺨﺪم ٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم ﻓﻰ ﺗﺼﻨﻴﻊ ﻣﻘﺎﻋﺪ اﻟﺴﻴﺎرات و ﺳﺎﻧﺪاﻟﺮأس. ﺳﺎﻧﺪ ٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم ﻓﻲ اﻟﺪروع اﻟﻮاﻗﻴﺔ ﻟﻠﺠﺴﻢ. اﻟﻮاﻗﻴﺔ اﻟﺪروع ﻓﻲ ﻳﺴﺘﺨﺪم ٠ ﻳﻤﻜﻦ أن ﻳﺪﺧﻞ ﻓﻰ ﻛﺜﻴﺮ ﻣﻦ اﻟﺘﻄﺒﻴﻘﺎت اﻟﻤﻨﺰﻟﻴﺔ ﻣﺜﻞ اﻷﺛﺎﺛﺎت اﻟﻤﻨﺰﻟﻴﺔ و ﻏﻴﺮﻫﺎ. و اﻟﻤﻨﺰﻟﻴﺔ اﻷﺛﺎﺛﺎت ﻣﺜﻞ اﻟﻤﻨﺰﻟﻴﺔ اﻟﺘﻄﺒﻴﻘﺎت ﻣﻦ ﻛﺜﻴﺮ ﻓﻰ ﻳﺪﺧﻞ ٠ ﻳﻤﻜﻦ أن ﻳﺴﺘﺨﺪم ﻛﺤﺸﻮ ﻟﺤﻤﺎﻳﺔ اﻷﺟﻬﺰة اﻹﻟﻜﺘﺮوﻧﻴﺔ. اﻷﺟﻬﺰة ﻟﺤﻤﺎﻳﺔ ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﺟﺎﻣﻌﺔ ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔﺑﺎﻟﻤﻄﺮﻳﺔ ﻗﺴﻢ اﻟﺘﺼﻤﻴﻢاﻟﻤﻴﻜﺎﻧﻴﻜﻲ اﻟﺘﺼﻤﻴﻢ ﻗﺴﻢ

ﺻﻨﻴﻊ وﺗﻌﻴﻴﻦ ﺧﻮاص ﻓﻮموﺗﻄﺒﻴﻘﺎت اﻟﺒﻮﻟﻴﻮرﻳﺜﺎناﻟﻤﺘﻤﺪد اﻟﺒﻮﻟﻴﻮرﻳﺜﺎن ﻓﻮم وﺗﻄﺒﻴﻘﺎت ﺧﻮاص وﺗﻌﻴﻴﻦ ﺻ ﻨ ﻴ ﻊ

إﻋﺪاد

اﻟﻤﻬﻨﺪس ا ﺣﺴﺎم إﺑﺮاﻫﻴﻢ ﻳﻮﺳﻒﻳﻮﺳﻒ ﻳﻮﺳﻒ إﺑﺮاﻫﻴﻢ ﺣﺴﺎم ا اﻟﻤﻬ ﻨﺪ س ﻣﻌﻴﺪ ﺑﻘﺴﻢ اﻟﻤﻔﺎﻋﻼت اﻟﺬرﻳﺔ - ﻣﺮﻛﺰ اﻟﺒﺤﻮث - اﻟﻨﻮوﻳﺔ ﻫﻴﺌﺔ اﻟﻄﺎﻗﺔ اﻟﺬرﻳﺔ اﻟﻄﺎﻗﺔ ﻫﻴﺌﺔ - اﻟﻨﻮوﻳﺔ اﻟﺒﺤﻮث ﻣﺮﻛﺰ - اﻟﺬرﻳﺔ اﻟﻤﻔﺎﻋﻼت

رﺳﺎﻟﺔ ﻣﻘﺪﻣﺔ إﻟﻰ ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔ - ﺑﺎﻟﻤﻄﺮﻳﺔ ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﻛﺠﺰﺀ ﻣﻦ ﻣﺘﻄﻠﺒﺎت اﻟﺤﺼﻮل ﻋﻠﻰ رﺳﺎﻟﺔ ﻓﻰ اﻟﻤﺎﺟﺴﺘﻴﻴﺮ اﻟﺘﺼﻤﻴﻢاﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﻓﻰ اﻟﻤﺎﺟﺴﺘﻴﻴﺮ رﺳﺎﻟﺔ ﻋﻠﻰ اﻟﺤﺼﻮل ﻣﺘﻄﻠﺒﺎت ﻣﻦ ﻛﺠﺰﺀ

ﺟﻤﻬﻮرﻳﺔ ﻣﺼﺮ اﻟﻌﺮﺑﻴﺔ ﻣﺼﺮ ﺟﻤﻬ ﻮر ﻳﺔ ٢٠١٢ ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﺟﺎﻣﻌﺔ ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔﺑﺎﻟﻤﻄﺮﻳﺔ ﻗﺴﻢ اﻟﺘﺼﻤﻴﻢاﻟﻤﻴﻜﺎﻧﻴﻜﻲ اﻟﺘﺼﻤﻴﻢ ﻗﺴﻢ

ﺗﺼﻨﻴﻊوﺗﻌﻴﻴﻦ ﺧﻮاص ﻓﻮموﺗﻄﺒﻴﻘﺎت اﻟﺒﻮﻟﻴﻮرﻳﺜﺎناﻟﻤﺘﻤﺪد اﻟﺒﻮﻟﻴﻮرﻳﺜﺎن ﻓﻮم وﺗﻄﺒﻴﻘﺎت ﺧﻮاص وﺗﻌﻴﻴﻦ ﺗ ﺼ ﻨ ﻴﻊ

إﻋﺪاد

اﻟﻤﻬﻨﺪس ا ﺣﺴﺎم إﺑﺮاﻫﻴﻢ ﻳﻮﺳﻒﻳﻮﺳﻒ ﻳﻮﺳﻒ إﺑﺮاﻫﻴﻢ ﺣﺴﺎم ا اﻟﻤﻬ ﻨﺪ س

ﻳﻌﺘﻤﺪ ﻣﻦ ﻟﺠﻨﺔ :اﻟﻤﻤﺘﺤﻨﻴﻦ

اﻷﺳﺘﺎذ اﻟﺪﻛﺘﻮر ا رﻣﻀﺎن إﺑﺮاﻫﻴﻢ اﻟﺴﻴﺪاﻟﺴﻌﻮدى ( )

أﺳﺘﺎذ ﺑﻘﺴﻢ ﻫﻨﺪﺳﺔ اﻻﻧﺘﺎج و اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ - ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔ - ﺟﺎﻣﻌﺔ ﻗﻨﺎة اﻟﺴﻮﻳﺲ. ﻗﻨﺎة ﺟﺎﻣﻌﺔ - اﻟﻬﻨﺪﺳﺔ ﻛﻠﻴﺔ - اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ

اﻷﺳﺘﺎذ اﻟﺪﻛﺘﻮر ا ﻳﻮﻧﺲ ﺧﻠﻴﻞﻳﻮﻧﺲ ( )

أﺳﺘﺎذ ﺑﻘﺴﻢ ﻫﻨﺪﺳﺔ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ - ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔ ﺑﺎﻟﻤﻄﺮﻳﺔ - ﺟﺎﻣﻌﺔ ﺣﻠﻮان. ﺟﺎﻣﻌﺔ - ﺑﺎﻟﻤﻄﺮﻳﺔ اﻟﻬﻨﺪﺳﺔ ﻛﻠﻴﺔ - اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﻫﻨﺪﺳﺔ ﺑﻘﺴﻢ

اﻷﺳﺘﺎذ اﻟﺪﻛﺘﻮر ا ﻋﻼﺀ ﻣﺤﻤﺪ أﺣﻤﺪ اﻟﺒﻄﺶ (ﻣﺸﺮف) ( ) ( ( ﻣﺸﺮف)

أﺳﺘﺎذ ﺑﻘﺴﻢ ﻫﻨﺪﺳﺔ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ - و وﻛﻴﻞ اﻟﻜﻠﻴﺔ ﻟﺸﺌﻮن اﻟﺤﻠﻼب - ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔ ﺑﺎﻟﻤﻄﺮﻳﺔ - ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﺟﺎﻣﻌﺔ - ﺑﺎﻟﻤﻄﺮﻳﺔ اﻟﻬﻨﺪﺳﺔ ﻛﻠﻴﺔ - اﻟﺤﻠﻼب ﻟﺸﺌﻮن اﻟﻜﻠﻴﺔ وﻛﻴﻞ و - اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﻫﻨﺪﺳﺔ

اﻷﺳﺘﺎذ اﻟﻤﺴﺎﻋﺪ ا ﻃﺎرق ﺣﺴﻴﻦ اﻟﻤﻬﺪى (ﻣﺸﺮف) ( )

أﺳﺘﺎذ ﻣﺴﺎﻋﺪ ﺑﻘﺴﻢ ﻫﻨﺪﺳﺔ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ - ﻛﻠﻴﺔ اﻟﻬﻨﺪﺳﺔ ﺑﺎﻟﻤﻄﺮﻳﺔ - ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﺟﺎﻣﻌﺔ - ﺑﺎﻟﻤﻄﺮﻳﺔ اﻟﻬﻨﺪﺳﺔ ﻛﻠﻴﺔ - اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﻫﻨﺪﺳﺔ

إﻋﺪاد

اﻟﻤﻬﻨﺪس ا ﺣﺴﺎم إﺑﺮاﻫﻴﻢ ﻳﻮﺳﻒﻳﻮﺳﻒ ﻳﻮﺳﻒ إﺑﺮاﻫﻴﻢ ﺣﺴﺎم ا اﻟﻤﻬ ﻨﺪ س ﻣﻌﻴﺪ ﺑﻘﺴﻢ اﻟﻤﻔﺎﻋﻼت اﻟﺬرﻳﺔ - ﻣﺮﻛﺰ اﻟﺒﺤﻮث اﻟﻨﻮوﻳﺔ - ﻫﻴﺌﺔ اﻟﻄﺎﻗﺔ اﻟﺬرﻳﺔ اﻟﻄﺎﻗﺔ ﻫﻴﺌﺔ - اﻟﻨﻮوﻳﺔ اﻟﺒﺤﻮث ﻣﺮﻛﺰ - اﻟﺬرﻳﺔ اﻟﻤﻔﺎﻋﻼت ﺑﻘﺴﻢ

ﺗﺤﺖ إﺷﺮاف

٠د٠أ ﻋﻼﺀ ﻣﺤﻤﺪ أﺣﻤﺪ اﻟﺒﻄﺶ أ.م.د. ﻃﺎرق ﺣﺴﻴﻦاﻟﻤﻬﺪى ﺣﺴﻴﻦ ﻃﺎر ق أﺳﺘﺎذ ﺑﻘﺴﻢ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ أﺳﺘﺎذ ﻣﺴﺎﻋﺪ ﺑﻘﺴﻢ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﺑﻘﺴﻢ ﻣﺴﺎﻋﺪ وﻛﻴﻞ اﻟﻜﻠﻴﺔ ﻟﺸﺌﻮن اﻟﺘﻌﻠﻴﻢ و اﻟﺤﻠﻼب رﺋﻴﺲ ﻗﺴﻢ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﻗﺴﻢ رﺋﻴﺲ ﻫﻨﺪﺳﺔ اﻟﻤﻄﺮﻳﺔ- ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﻫﻨﺪﺳﺔ اﻟﻤﻄﺮﻳﺔ- ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﺟﺎﻣﻌﺔ اﻟﻤﻄﺮﻳﺔ- ﻫﻨﺪﺳﺔ

د. ﺧﺎﻟﺪ ﻣﺤﻤﺪ زﻳﺪ ﻣﺤﻤﺪ ﺧﺎﻟﺪ د. ﻣﺪرس ﺑﻘﺴﻢ اﻟﺘﺼﻤﻴﻢ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﻤﻴﻜﺎﻧﻴﻜﻰ اﻟﺘﺼﻤﻴﻢ ﺑﻘﺴﻢ ﻣﺪر س ﻫﻨﺪﺳﺔ اﻟﻤﻄﺮﻳﺔ- ﺟﺎﻣﻌﺔ ﺣﻠﻮان ﺟﺎﻣﻌﺔ اﻟﻤﻄﺮﻳﺔ- ﻫﻨﺪﺳﺔ

ﺟﻤﻬﻮرﻳﺔ ﻣﺼﺮ اﻟﻌﺮﺑﻴﺔ ﻣﺼﺮ ﺟﻤﻬ ﻮر ﻳﺔ ٢٠١٢