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UNIVERSITI PUTRA MALAYSIA
MARYAM HOSSEINI
FK 2010 12
EXPERIMENTAL DETERMINATION OF FATIGUE LIFE FOR INTERNATIONAL RUBBER HARDNESS
DEGREE 60 ENGINE MOUNT RUBBER
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EXPERIMENTAL DETERMINATION OF FATIGUE LIFE FOR INTERNATIONAL RUBBER HARDNESS
DEGREE 60 ENGINE MOUNT RUBBER
By
MARYAM HOSSEINI
Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfilment of the Requirements for the Degree of Master of Science
January 2010
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Abstract of thesis presented to the Senate of Universiti Putra Malaysia in fulfilment of the requirement for the degree of Master of Science
EXPERIMENTAL DETERMINATION OF FATIGUE LIFE FOR INTERNATIONAL RUBBER HARDNESS
DEGREE 60 ENGINE MOUNT RUBBER
By
MARYAM HOSSEINI
January 2010
Chairman : Aidy Ali, PhD Faculty : Engineering
In the new millennium era, rubber materials are vigorously used in many industries
including automotive that cover a wide range of applications such as tires, seals, belts,
bushes and engine mounts. Rubber is an ideal material for many applications because it
can withstand very large strain with no permanent deformation or fracture.
The behavior of material under repeated loads differs from static loads. Elastomers fail
at cyclic stress or strain amplitude much lower than static stress or strain. It is based on
growth of cracks through the material. The fatigue analysis and its lifetime evaluation
are very important in design procedure to assure the safety and reliability of the rubber
components. Design of rubber against fatigue failure is one of the important topics to be
focussed for checking the failures during its operation life.
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Many mechanical and environmental factors could prolong the rubber fatigue life. The
fatigue failure process of materials is explained by two approaches including crack
initiation and crack propagation.
The present work deals with investigation of the fatigue behavior using rubber dumb-
bell test specimens under uniaxial loading. The material used in this study is a
vulcanized natural rubber with a typical engine mount formulation and the hardness of
International Rubber Hardness Degree 60. Test specimens were designed based on type
2 of MS ISO 37 standard and used for tensile and fatigue tests, both in ambient
temperature. Fatigue tests were conducted under the displacement controlled condition
with a sine waveform of 0.1 Hz and the ratio of the minimum displacement to the
maximum displacement was equal to zero. The experimental results were presented
under strain controlled condition.
For investigation of the fatigue damage behavior, a theoretical equation was developed
based on the continuum damage mechanics theory. The Ogden strain energy potential of
first order was used for defining a constitutive relation of the natural rubber. The
proposed theoretical formula was based on function of the strain range under cyclic
loading to determine the fatigue life of elastomeric material. The ability of predicted
fatigue life shows a reasonable agreement of 98% with experimental values. The
experimental results and theoretical equation were validated with the previous
experimental data which show a good agreement of 97% and 93% respectively.
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Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Master Sains
PENENTUAN JANGKA HAYAT LESU BAGI KEKERASAN GETAH
DARJAH 60 PADA PENDAKAP ENJIN
Oleh
MARYAM HOSSEINI
Januari 2010
Pengerusi : Aidy Ali, PhD Fakulti : Kejuruteraan
Dalam era alaf baru zaman kini, bahan seperti getah banyak digunakan di dalam
industri, termasuklah di dalam industri automotif yang meliputi pelbagai aplikasi seperti
tayar, kedap, talisawat, sesendal dan peredam enjin. Getah adalah bahan yang sesuai
digunakan kerana ia boleh menahan terikan yang sangat tinggi tanpa perubahan bentuk
yang kekal atau patah.
Perilaku sesuatu bahan dalam beban berulang adalah berbeza jika dibandingkan dengan
beban statik. Elastomer akan mengalami kegagalan pada nilai tegasan atau terikan
berkitar yang kurang berbanding nilai tegasan atau terikan dikenakan secara statik. Ini
berlaku disebabkan oleh tumbesaran keretakan pada sesuatu bahan. Analisis kelesuan
dan penentuan jangka hayat adalah amat penting semasa rekabentuk untuk memastikan
keselamatan bagi komponen getah. Rekabentuk komponen getah dan kegagalan
komponen disebabkan oleh kelesuan telah menjadi salah satu tajuk yang penting untuk
difokuskan bagi mengenal pasti tahap kegagalan semasa dalam operasi.
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Banyak faktor mekanikal dan persekitaran boleh mempengaruhi jangka hayat lesu bagi
getah. Kegagalan komponen getah disebabkan oleh kelesuan dapat diterangkan melalui
dua pendekatan, iaitu permulaan retak dan rambatan retak.
Kerja terkini melibatkan siasatan penentuan kelesuan menggunakan spesimen dumbel
yang dikenakan beban pada satu arah. Getah yang digunakan ialah getah asli yang telah
divulkankan dengan kekerasan International Rubber Hardness Degree 60, formulasi
yang biasa digunakan di dalam komponen peredam enjin. Spesimen direka mengikut
spefikasi berdasarkan MS ISO 37 jenis 2, dan digunakan dalam ujikaji regangan dan
kelesuan dengan keadaan suhu persekitaran. Ujian kelesuan dijalankan dengan
kawalan terikan menggunakan bentuk gelombang sin berfrekuensi 0.1 Hz dan nisbah
terikan minimum dan terikan maksimum bersamaan dengan sifar. Keputusan ujikaji
ditunjukkan dalam keadaan kawalan terikan.
Di dalam siasatan kerosakan disebabkan oleh kelesuan, satu persamaan teori telah
dihasilkan berdasarkan teori kontinum mekanik kerosakan. Potensi tenaga terikan
Ogden peringkat pertama digunakan untuk menentukan hubungan konstitutif bagi getah
asli. Formula teori yang dicadangkan ialah berdasarkan fungsi antara julat terikan
dengan bebanan berkitar untuk menentukan jangka hayat elastomer. Perbandingan
keputusan eksperimen dan jangka hayat yang diramalkan mencapai persetujuan
sebanyak 98%. Keputusan eksperimen dan teori disahkan oleh keputusan eksperimen
yang telah dijalankan dahulu dan menunjukkan kesepakatan yang baik, iaitu masing-
masing 97% dan 93%.
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ACKNOWLEDGEMENTS
I would like to express my sincere appreciation to all those who encouraged me and
made it possible for me to complete this thesis.
First and foremost, I would like to express my deep gratefulness to my supervisor Dr.
Aidy Ali for his guidance, constructive comments, invaluable advices and suggestions to
complete my research successfully. My sincere appreciation is also extended to the
committee member, Prof. Dr. Ir. Barkawi Sahari for his guidance and suggestions
throughout my research.
My sincere thanks also go to the Malaysian Rubber Board (MRB) for providing rubber
materials, dumb-bell test specimens and some experiments for this study. All of these
supports are highly appreciated.
I wish to express my profound gratitude to Prof. Dr. Waqar Asrar, Head of Department
of Mechanical Engineering and Dr. Kassim Abdulrahman Abdullah, Assistant
Professor, at International Islamic University Malaysia (IIUM) for supporting through
permission to use the fatigue test machine of their laboratory.
Finally, I would like to express my heartiest gratitude and appreciation to my beloved
family for support, encouragement and understanding throughout my studies, without
their love, it would not be possible for me. I am very thankful to my husband, Mansour,
and my son, Amir hossein, for their lasting love, support and patience.
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I certify that a Thesis Examination Committee has met on 7 January 2010 to conduct the final examination of Maryam Hosseini on her thesis entitled “Experimental Determination of Fatigue Life for International Rubber Hardness Degree 60 Engine Mount Rubber” in accordance with the Universities and University Colleges Act 1971 and the Constitution of the Universiti Putra Malaysia [P.U.(A) 106] 15 March 1998. The Committee recommends that the student be awarded the Master of Science.
Members of the Thesis Examination Committee were as follows:
Mohd Sapuan bin Salit, PhD Professor Faculty of Engineering Universiti Putra Malaysia (Chairman)
Nor Mariah binti Adam, PhD Associate Professor Faculty of Engineering Universiti Putra Malaysia (Internal Examiner)
Nawal Aswan bin Abdul Jalil, PhD Lecturer Faculty of Engineering Universiti Putra Malaysia (Internal Examiner)
Shahrum Abdullah, PhD Associate Professor Faculty of Engineering Universiti Kebangsaan Malaysia (External Examiner)
BUJANG KIM HUAT, PhD
Professor and Deputy Dean School of Graduate Studies Universiti Putra Malaysia Date: 11 March 2010
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This thesis was submitted to the Senate of Universiti Putra Malaysia and has been accepted as fulfilment of the requirement for the degree of Master of Science. The members of the Supervisory Committee were as follows: Aidy Ali, PhD Senior Lecturer Department of Mechanical and Manufacturing Engineering Faculty of Engineering Universiti Putra Malaysia (Chairman) Barkawi Sahari, PhD Professor Department of Mechanical and Manufacturing Engineering Faculty of Engineering Universiti Putra Malaysia (Member)
HASANAH MOHD GHAZALI, PhD
Professor and Dean School of Graduate Studies Universiti Putra Malaysia Date: 8 April 2010
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DECLARATION
I declare that the thesis is my original work except for quotations and citations which have been duly acknowledged. I also declare that it has not been previously, and is not concurrently, submitted for any other degree at Universiti Putra Malaysia or at any other institutions.
MARYAM HOSSEINI Date:
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TABLE OF CONTENTS
Page DEDICATION ii ABSTRACT iii ABSTRAK v ACKNOWLEDGEMENTS vii APPROVAL viii DECLARATION x LIST OF TABLES xiii LIST OF FIGURES xiv LIST OF ABBREVIATIONS xviii
CHAPTER
1 INTRODUCTION �
1.1 Introduction 1 1.2 Problem Statement 2 1.3 Hypothesis 4 1.4 Research Objectives 6 1.5 Scope of Study 6 �.6 Layout of the Thesis 6
2 LITERATURE REVIEW 7 2.1 Introduction to Elastomer 7 2.2 Elastomer Types 8 2.3 Compounding 9 2.4 Elastic Properties 10 2.4.1 Elastic Properties at Small Deformations 11 2.4.2 Elastic Properties at Large Deformations 14 2.5 Viscoelasticity 15 2.6 Tensile Stress-Strain 17 2.7 Hyperelastic Models 19 2.7.1 Polynomial Model 22 2.7.2 Reduced Polynomial Model 23 2.7.3 Ogden Model 24 2.7.4 Mooney-Rivlin Model 24 2.7.5 neo-Hookean Model 25 2.7.6 Yeoh Model 26 2.7.7 Arruda and Boyce Model 27 2.7.8 Van der Waals Model 28 2.8 Durability of Rubber 29 2.9 Life Prediction Methodology 30 2.10 Initiation and Propagation of Cracks 32 2.10.1 Fatigue Crack Nucleation 32 2.10.2 Fatigue Life and Crack Growth 34
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2.10.3 Fatigue Crack Growth 36 2.11 Existing Predictors for Fatigue Crack Nucleation 39 2.11.1 Classical Fatigue Life Predictors 40 2.11.2 Plane-Specific or Critical Plane Approach 47 2.12 Summary 50
3 METHODOLOGY 53 3.1 Introduction 53 3.2 Material Description 55 3.3 Form of Test Piece for Tensile Stress-Strain and Fatigue Tests 57 3.3.1 Static Test Specimen 58 3.3.2 Fatigue Test Specimen 60 3.3.3 Forming the Specimen 61 3.3.4 Measurement of Test Pieces 65 3.4 Mechanical Properties Test Description 66 3.4.1 Tensile Test Procedure 67 3.4.2 Fatigue Test Procedure 76 3.5 Analytical Solution 84 3.6 Summary 85
4 RESULTS AND DISCUSSION 87 4.1 Introduction 87 4.2 Tensile Test Results 88 4.2.1 Tensile Test with Extensometer 88 4.2.2 Tensile Test without Extensometer 91 4.3 The Hyperelastic Constitutive Model for Material Characterization 94 4.4 Fatigue Test Results 98 4.5 Analytical Solution for the Fatigue Life of Elastomeric
Materials 102
4.5.1 Continuum Damage Mechanics Theory 102 4.5.2 Assumptions for Damage and Fatigue of Elastomers 103 4.5.3 The Damage Model 104 4.6 Limitation and Range of Parameters in Fatigue Life Equation 109 4.7 Validation and Verification 112 4.8 Mechanism of Failure 114 4.9 Effect of Hardness on Stress-Strain Properties 116 4.10 Heat-Aging Effects on Hardness and Stress-Strain Properties 119 4.11 Summary 124
5 CONCLUSIONS AND RECOMMENDATIONS 126 5.1 Conclusions 126
5.2 Recommendations 127
REFERENCES 129 BIODATA OF STUDENT 137 PUBLICATION 138