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© Copyright by Yanhouidé J. AHOSSIN GUEZO, 2013 All Rights Reserved

FRACTURE AND VISCOUS BEHAVIOR OF POLYPROPYLENE COMPOSITES COATING INSULATORS FOR DEEP WATER OIL PIPELINES

A Dissertation Presented to the Faculty of the Department of Civil and Environmental Engineering Cullen College of Engineering University of Houston

In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Civil Engineering

by Yanhouidé Jeannot AHOSSIN GUEZO December 2013

FRACTURE AND VISCOUS BEHAVIOR OF POLYPROPYLENE COMPOSITES COATING INSULATORS FOR DEEP WATER OIL PIPELINES ___________________________ Yanhouidé J. Ahossin Guezo Approved: ______________________________ Chairman of the Committee C. Vipulanandan, Professor, Civil and Environmental Engineering

Committee Members:

______________________________ Kaspar Willam, Professor, Civil and Environmental Engineering

______________________________ Yi-Lung Mo, Professor, Civil and Environmental Engineering

______________________________ Matthew A. Franchek, Professor, Mechanical Engineering Director of Subsea Engineering ______________________________ Thomas K. Holley, Professor, Chemical Engineering Director of Petroleum Engineering

______________________________ Suresh K. Khator, Associate Dean, Cullen College of Engineering

_________________________________ Kaspar Willam, Professor, Interim Chair, Civil and Environmental Engineering

ACKNOWLEDGEMENTS My decision of going back to school to pursue a PhD degree was one of the best decisions I made so far. It was made successful and bearable by the environment and the people I met at the Civil Engineering Department of Cullen College of Engineering. I broadened my knowledge of science by working with great professors and my horizon by making new friends. To my research and academic advisor, Dr. Cumaraswamy Vipulanandan, thank you for your guidance and for believing in me. All my considerations to Dr. Kaspar Willam, Dr. Yi-Lung Mo, Dr. Matthew A. Franchek, and Dr. Thomas K. Holley for serving in my committee. I want to gratefully acknowledge my fellow graduate students Shahriyar Beizaee, Dr.Giovanna Xotta, Florentia Kavoura, and Charan Tanneru for their friendship and support. Special thank you note to all the members of the CIGMAT (Center for Innovative Grouting and Materials) research group, especially to Bahar Basirat and Dongmei Pan. My research was made possible by the work of the best machinist and lab technician that any engineering department can expect, Jeffrey Miller and Gerald McTigret. Lastly, I would like to acknowledge the unwavering support, encouragement, love, and guidance I have received from my family throughout my life. I want to specifically express my deepest appreciation to my parents Christine Akuegninou and Eugene Guezo, my uncles Albert T. Ahossin and Bernard Amoussouga, my siblings Japhet Senamin, Jocelyne Bidossessi, Prisca Gueguede, and Judicael. A special note to my mum: I know you worried a lot about me even when I tried to hide all of the ordeals I was going through, thanks for everything.

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To my little sister Prisca Guéguédé

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FRACTURE AND VISCOUS BEHAVIOR OF POLYPROPYLENE COMPOSITES COATING INSULATORS FOR DEEP WATER OIL PIPELINES

An Abstract Of a Dissertation Presented to the Faculty of the Department of Civil and Environmental Engineering Cullen College of Engineering University of Houston

In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Civil Engineering

by Yanhouidé Jeannot AHOSSIN GUEZO December 2013

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ABSTRACT Over the past few decades, polymer composites are being used as subsea insulation coatings material in deep water oil pipelines. Failure of the insulation coating materials can significantly affect oil production. The major objective of this study was to characterize the physical and mechanical properties and quantify the effect of crack, strain rate and temperature on the visco-elasto-plastic behavior of the ductile polypropylene polymer (PP) with and without glass fillers in tension, compression, shear and bending. The density of the composite materials studied varied from 0.79 to 1.90 g/cc. The thermal conductivity of the coating insulators varied from 0.140 to 0.306 W/m.K. The effect of strain rate ( ) and temperature (T) on the nonlinear visco-plastic stress-strain behavior, yield strength (y), initial elastic modulus (Ei) and secant modulus at yield (Esy) of the materials (unfilled polypropylene, polypropylene with 65% glass filler and polypropylene with glass microsphere filler) was characterized and modeled. The tensile yield strengths of the materials varied from 3 to26 MPa. The rate of change in the tensile yield strength with temperature and strain rate were directly proportional to the yield strength and inversely proportional to the strain rate respectively. Crack growth and propagation in the multilayered polypropylene composite coating was investigated using the three dimensional Digital Image Correlation (3D DIC). Also the strain field ( ) development around the crack tip was investigated. A new concept based on Mode 1 strain rate amplification factor () was introduced to model the behavior of polymer composite with crack that increased the tensile yield strength, initial modulus and secant modulus at yield but reduced the strain energy density, at yield and failure, and the viii

ductility making the ductile coating materials stronger but more brittle. A three parameter constitutive relationship for polymer composites was developed to model the nonlinear visco-elasto-plastic and strain softening/hardening behavior of the polypropylene composites coating materials in function of strain rate ( ) and temperature (T).

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TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................................................................................ v  DEDICACE ....................................................................................................................... vi  ABSTRACT ..................................................................................................................... viii TABLE OF CONTENTS.................................................................................................... x LIST OF FIGURES ......................................................................................................... xiii  LIST OF TABLES ........................................................................................................ xxvii  1. INTRODUCTION .......................................................................................................... 1  1.1. 

General ................................................................................................................ 1 

1.2. 

Objectives ........................................................................................................... 3 

1.3. 

Organization ........................................................................................................ 3 

2. BACKGROUND AND LITERATURE REVIEW......................................................... 4  2.1. 

General ................................................................................................................ 4 

2.2. 

Polypropylene composites .................................................................................. 7 

2.3. 

Polypropylene composite behavior ..................................................................... 9 

2.4. 

Fracture mechanic ............................................................................................. 11 

2.5. 

Summary ........................................................................................................... 20 

3. MATERIALS and METHODS ..................................................................................... 22  3.1. 

Introduction ....................................................................................................... 22 

3.2. 

Materials ........................................................................................................... 22 

3.3. 

Experimental program ...................................................................................... 31 

3.4. 

The Digital Image Correlation (DIC) system (fundamentals and validation) .. 34 

3.5. 

Summary ........................................................................................................... 41 

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4. MATERIALS BEHAVIOR CHARACTERIZATION ................................................. 42  4.1. 

Introduction ....................................................................................................... 42 

4.2. 

Tensile properties of unfilled polypropylene (PP) ............................................ 42 

4.3. 

Tensile properties of polypropylene with glass microsphere filler ................... 48 

4.4. 

Tensile properties of polypropylene with 65% glass filler ............................... 50 

4.5. 

Compression test ............................................................................................... 53 

4.6. 

Composite behavior .......................................................................................... 57 

4.7. 

Summary and discussion................................................................................... 63 

5. FRACTURE CHARACTERIZATION ........................................................................ 67  5.1. 

Introduction ....................................................................................................... 67 

5.2. 

Tensile testing of unfilled polypropylene specimen with circular

5.3. 

Tensile testing of polypropylene with 65% glass filler specimens with circular

hole ......... 68 

hole         ......................................................................................................................... 83  5.4. 

Tensile testing of double edge grooved specimens without notches (DT) and

with notches (NDT) ...................................................................................................... 90  5.5. 

Bending test of notched composite beams ...................................................... 110 

5.6. 

Summary and discussion................................................................................. 118 

6. REPAIR METHODS .................................................................................................. 120  6.1. 

Introduction ..................................................................................................... 120 

6.2. 

Material parameters ........................................................................................ 120 

6.3. 

Specimen preparation...................................................................................... 120 

6.4. 

Testing procedure............................................................................................ 120 

6.5. 

Results ............................................................................................................. 121 

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6.6. 

Summary and discussion................................................................................. 121 

7. CONSTITUTIVE MODELLING ............................................................................... 123  7.1. 

Introduction ..................................................................................................... 123 

7.2. 

Material parameters ........................................................................................ 124 

7.3. 

Modeling of temperature (T) and strain rate ( ) sensitivity............................ 125 

7.4. 

Stress-strain relationship modelling................................................................ 140 

7.5. 

Summary ......................................................................................................... 148 

8. FINITE ELEMENT MODELLING............................................................................ 151  8.1. 

Introduction ..................................................................................................... 151 

8.2. 

Material parameters ........................................................................................ 151 

8.3. 

Constitutive Model.......................................................................................... 152 

8.4. 

Results ............................................................................................................. 153 

8.5. 

Summary and discussion................................................................................. 157 

9. CONCLUSIONS & RECOMMENDATIONS ........................................................... 158  10. REFERENCE ............................................................................................................ 161 

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LIST OF FIGURES Fig. 2-1: SEM micrograph of glass fiber reinforced polypropylene (Fu et al. 2000). ..... 8  Fig. 2-2: SEM micrograph of polypropylene syntactic foam. ............................................ 9  Fig. 2-3 : Sketch of the tensile test specimen (Roylance 2001). ....................................... 13  Fig. 2-4 : The fracture energy balance (Roylance 2001). ................................................. 14  Fig. 2-5: Fracture modes (Anderson 2004). ...................................................................... 16  Fig. 2-6: Stresses near the tip of a crack in an elastic material (Anderson 2004). ............ 16  Fig. 2-7: Flat surfaced notch in two-dimensional deformation field (all stresses depend only on x and y).

is any curve surrounding the notch tip,

, denotes the curved

notch tip. ................................................................................................................... 19  Fig. 2-8: Definition of crack tip opening displacement, t. .............................................. 20  Fig. 3-1: The subsea pipe with its thermal insulation layers in CIGMAT lab. PP: unfilled polypropylene, GF: polypropylene with 65% glass filler, GM: polypropylene with glass microsphere filler.(GM* was in the risers insulation). .................................... 23  Fig. 3-2: Published densities of polypropylene composites used for subsea pipe insulation and data of this study. PP: Unfilled polypropylene, GM: Polypropylene with glass microsphere filler, GF: Polypropylene with 65% glass filler. .................................. 24  Fig. 3-3: Published thermal conductivity of polypropylene composites used for subsea pipe insulation and data of this study. PP: Unfilled polypropylene, GM: Polypropylene with glass microsphere filler, GF: Polypropylene with 65% glass filler. .......................................................................................................................... 25  Fig. 3-4: FT-IR spectrum of the unfilled polypropylene. ................................................. 27  Fig. 3-5: FT-IR spectrum polypropylene with glass microsphere filler. .......................... 28 

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Fig. 3-6: FT-IR spectrum of polypropylene with 65% glass filler. .................................. 29  Fig. 3-7: SEM micrograph of Polypropylene with glass microsphere filler at high voltage acceleration (20 kV). (a)Magnification of 2.14 K X,(b) Magnification of 4.63 K X. ................................................................................................................................... 30  Fig. 3-8: SEM micrograph of Polypropylene with glass microsphere filler at lower voltage acceleration (10kV). (a) Magnification of 1.9 K X,(b) Magnification of 1.5 K X. ........................................................................................................................... 31  Fig. 3-9: SEM micrograph of Glass filled polypropylene. (a)Magnification of 11.85 K X,(b) Magnification of 122.99 K X. ......................................................................... 31  Fig. 3-10: Fracture of a deep water pipe insulation observed on the field during installation. ................................................................................................................ 32  Fig. 3-11: Test specimens: composites beam with and without notch, composite compression specimen, PP (white), GM and GF tensile specimens, tensile specimen with perforated centered circular hole, tensile double edges grooved without (DT) and with notches (NDT) specimens and compression specimens and creep specimens. ................................................................................................................. 33  Fig. 3-12: Speckle patterns examples on three different specimens. ................................ 37  Fig. 3-13: Tensile test setup for DIC accuracy validation. a.)Global view of the test setup in the INSTRON testing machine, b.)View of the clip-on extensometer and the strain gage on the specimen. ............................................................................................... 39  Fig. 3-14: Engineering stress-strain curves of PP (1DT-1)at two locations using strain gage, clip-on extensometer and 3D DIC system.a.)Full curves, b.) Curves in the strain range 0.000-0.010. .......................................................................................... 40 

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Fig. 3-15: Engineering stress-strain curves of PP (1DT-2)at two locations using strain gage, clip-on extensometer and 3D DIC system. a.)Full curves, b.) Curves in the strain range 0.000-0.010. .......................................................................................... 40  Fig. 3-16: Engineering stress-strain curves of GF (2DT-1) at two locations using strain gage, clip-on extensometer and 3D DIC system. a.) Full curves, b.) Curves in the strain range 0.000-0.010. .......................................................................................... 40  Fig. 4-1: Sketch of the tensile test specimen..................................................................... 43  Fig. 4-2: Tensile test setup in the INSTRON test machine. Global view of the setup with heating chamber, INSTRON control unit and Agilent data acquisition system. ...... 44  Fig. 4-3: Tensile test setup inside the INSTRON heating chamber.................................. 45  Fig. 4-4: Tensile engineering stress vs. engineering strain relationship of cyclically loaded PP at a nominal test strain rate of 0.100 min-1at 22oC................................... 46  Fig. 4-5: Engineering stress vs. engineering strain relationship of unfilled polypropylene at various strain rates and temperatures. ................................................................... 47  Fig. 4-6: Pictures of PP specimens at the end of tensile test at 22 and 60oC. ................... 47  Fig. 4-7: Engineering stress vs. strain of polypropylene with glass microsphere filler at various strain rates and temperatures. ....................................................................... 49  Fig. 4-8: Pictures of GM specimens at the end of tensile test at 22 and 90oC. ................. 49  Fig. 4-9: Tensile engineering stress vs. engineering strain relationship of cyclically loaded GF at a nominal test strain rate of 0.010 min-1. ............................................. 51  Fig. 4-10: Engineering stress vs. engineering strain relationships of polypropylene with 65% glass filler at various strain rates and temperatures. ......................................... 52  Fig. 4-11: Pictures of GF specimens at the end of tensile test at 22 and 60oC. ................ 52 

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Fig. 4-12: Pictures of compression specimen.. a.) Compression specimen with speckle for 3D DIC measurement, b.) Compression specimen instrumented with strain gage. . 53  Fig. 4-13: Compression specimen in the INSTRON testing machine. ............................. 54  Fig. 4-14: Strain field from the 3D DIC of the uniaxial strain of the composite specimen in compression at 0.003 min-1. (a.) Early stage in the elastic domain, (b.) Later state in the elastic domain, (c.) In the plastic domain. ...................................................... 55  Fig. 4-15: Compressive engineering stress vs strain relationships PP and GF at the nominal test strain rate of 0.003 min-1. ..................................................................... 56  Fig. 4-16: Compressive stress vs strain relationships of polypropylene with 65% glass filler at various strain rates and temperatures. .......................................................... 57  Fig. 4-17: Tests specimens’ sketches. a.) Typical composite beam specimen, b.) Shear test specimen. ............................................................................................................ 58  Fig. 4-18: Tests specimens’ sketches. a.) Typical composite beam specimen, b.) Four points bending setup. All dimensions are in mm. .................................................... 59  Fig. 4-19: Pictures of the interface shear test setup in the lab with the 3D DIC system . 59  Fig. 4-20: Pictures four points bending setup in the lab with the 3D DIC system. .......... 60  Fig. 4-21: Shear stress variation with time of the interface 1-2: Epoxy –GF interface ... 60  Fig. 4-22: Shear stress variation with time of the interface 2-3: GF –PP interface ......... 61  Fig. 4-23: Four points bending test. a.) Displacement rate of 0.015 in/min, b.) Displacement rate of 2.750 in/min. ........................................................................... 62  Fig. 4-24: Complete failure of the beam at the displacement rate of 2.750 in/min. ........ 62  Fig. 4-25: Moment and shear diagram of the four point bending with stress states in the elastic domain. .......................................................................................................... 63 

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Fig. 4-26: Comparison of engineering stress-strain relationship of unfilled polypropylene, polypropylene with 65% glass filler and polypropylene with glass microsphere filler at 22 and 90 oC at a strain rate of 0.030 min-1. ............................ 65  Fig. 4-27: Comparison of engineering stress-strain relationshipsof unfilled polypropylene, polypropylene with 65% glass filler and polypropylene with glass microsphere filler at 22 and 90 oC at a strain rate of 0.300 min-1........................................................... 65  Fig. 4-28: Published tensile yield strength of polypropylene composites used for subsea pipe insulation and data of this study obtained at a strain rate of 0.300 min-1. PP: Unfilled polypropylene, GM: Polypropylene with glass microsphere filler, GF: Polypropylene with 65% glass filler ......................................................................... 66  Fig. 5-1: Sketch of the tensile specimen with circular hole at the center. ........................ 69  Fig. 5-2: Test setup: (a.) DIC, and Agilent data acquisition system.. (b) Sspecimen held between grips. ........................................................................................................... 69  Fig. 5-3: Failure mode of PP with circular center hole. .................................................... 70  Fig. 5-4: Effect of circular center hole size on tensile engineering stress-strain relationship of unfilled polypropylene at 22oC and nominal test strain rate of 0.003 min-1. ......................................................................................................................... 71  Fig. 5-5: Effect of center hole size on engineering stress-strain relationship of unfilled polypropylene at 22oC and nominal test strain rate of 0.030 min-1. ...................... 71  Fig. 5-6: Yield strength variation with center circular hole diameter for unfilled polypropylene at........................................................................................................ 72  Fig. 5-7: Yield strength variation with the r/d ratio for unfilled polypropylene at 22oC and nominal test strain rate of 0.030 min-1. ..................................................................... 72 

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Fig. 5-8: Effect of center hole size on the ductility of unfilled polypropylene at 22oC and a strain rate of 0.030 min-1. ....................................................................................... 73  Fig. 5-9: Comparison of engineering stress-strain relationship at crack front (CF) with the global one (50.8 mm extensometer) of unfilled polypropylene specimen with 3.2 mm center hole. ......................................................................................................... 73  Fig. 5-10: Variation of the strain energy density with r/d . a.) Strain energy at yield, b.)Strain energy at failure. ........................................................................................ 75  Fig. 5-11: Effect of strain rate on the strain energy density. a.) Strain energy at yield, b.)Strain energy at failure. ........................................................................................ 76  Fig. 5-12: Location of the critical strain rate on tensile specimen with center circular hole. The deformed hole is shown. .................................................................................... 77  Fig. 5-13: Engineering stress-strain relationship of PP tensile specimen with a gage dimension of 95 mm x 24.5 mm x 12.7 mm and 2.4 mm circular hole at the center. ................................................................................................................................... 78  Fig. 5-14: Strain field from the 3D DIC of the uniaxial strain of a PP specimen with a 2.4 mm diameter center hole and a test strain rate of 0.03 min-1. a.) Early stage in the elastic domain, b.) Later state in the elastic domain, c.) In the plastic domain. ....... 78  Fig. 5-15: Picture of the PP specimen with 2.4mm center hole during test from the DIC, a) at crack initiation with the strain field superimposed, b.) at crack initiation stage, c.) after failure. .......................................................................................................... 79  Fig. 5-16: Engineering strain variation with time at locations from crack front (0.0 mm) horizontally (A-A) to the edge of the PP specimen. ................................................. 81 

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Fig. 5-17: Strain rate variation along A-A from crack front (0.0 mm) horizontally (A-A) to the edge of the PP specimen. The nominal test strain rate was 0.03 min-1. .......... 81  Fig. 5-18: Engineering strain variation with time from the top of the circular hole (0.0 mm) vertically (B-B) of the PP specimen. ................................................................ 82  Fig. 5-19: Strain rate variation along B-B from the top of the circular hole (0.0 mm) vertically (B-B) of the PP specimen. ........................................................................ 82  Fig. 5-20: Test setup in the INSTRON with the Agilent data acquisition system and the specimen held between grips. ................................................................................... 84  Fig. 5-21: Engineering stress-strain relationshipof GF tensile specimen with circular hole at the center at a nominal test strain rate of 0.085 min-1. ......................................... 85  Fig. 5-22: Strain field from the 3D DIC of the uniaxial strain of a GF specimen with a 2.4 mm diameter center hole and a test strain rate of 0.085 min-1. (a.) Early stage in the elastic domain, (b.) Later state in the elastic domain, (c.) In the plastic domain...... 85  Fig. 5-23: Picture of the GF specimen with 2.4mm center hole during test from the DIC, a) at crack initiation with the strain field superimposed, b.) at crack initiation stage, c.) after failure. .......................................................................................................... 86  Fig. 5-24: Engineering strain variation with time at locations from crack front (0.0 mm) horizontally (A-A) to the edge of the GF specimen. ................................................ 88  Fig. 5-25: Strain rate variation along A-A from crack front (0.0 mm) horizontally (A-A) to the edge of the GF specimen. The nominal test strain rate was 0.085 min-1. ....... 88  Fig. 5-26: Engineering strain variation with time from the top of the circular hole (0.0 mm) vertically (B-B) of the GF specimen. The nominal test strain rate was 0.085 min-1. ......................................................................................................................... 89 

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Fig. 5-27: Strain rate variation along B-B from the top of the circular hole (0.0 mm) vertically (B-B) of the GF specimen. The nominal test strain rate was 0.085 min-1. 89  Fig. 5-28: Sketch of : (a) symmetrically double edges grooved tensile specimen (DT) and (b) notched symmetrically double edges grooved tensile specimen (NDT). All dimensions are in mm. .............................................................................................. 92  Fig. 5-29: (a) Picture of the test setup in the INSTRON with the DIC, (b) Picture showing the instrumentation on the specimen......................................................................... 93  Fig. 5-30: a) DT specimen with speckles in the tensile grips at failure, b) NDT specimen with speckles in the tensile grips at testing. .............................................................. 93  Fig. 5-31: Location of the critical strain rate on DT tensile specimen. ............................ 94  Fig. 5-32: Location of the critical strain rate on NDT tensile specimen........................... 94  Fig. 5-33: Comparison of global engineering stress-strain relationship of DT and NDT specimens of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 min-1. ............................................................................................................... 95  Fig. 5-34: Comparison of engineering stress-strain relationship at CF of DT and NDT specimens of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 min-1. ............................................................................................................... 95  Fig. 5-35: Effect double semicircular grooves on the global engineering stress-strain relationship of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 and 0.050 min-1. .............................................................................................. 96  Fig. 5-36: Effect double semicircular grooves on engineering stress-strain relationshipat CF of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 and 0.050 min-1. ........................................................................................................ 97 

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Fig. 5-37: Strain field from the 3D DIC of the uniaxial strain of a DT GF specimen at a test strain rate of 0.020 min-1. (a.) Early stage in the elastic domain, (b.) Later state in the elastic domain, (c.) In the plastic domain. ...................................................... 98  Fig. 5-38: Picture of the GF DT specimen during test from the DIC, a)Before crack initiation b.) At crack initiation with the strain field superimposed, c.) After failure. ................................................................................................................................... 98  Fig. 5-39: Strain field from the 3D DIC of the uniaxial strain of a NDT GF specimen at a test strain rate of 0.020 min-1. (a.) Early stage in the elastic domain, (b.) Later state in the elastic domain, (c.) In the plastic domain. ...................................................... 99  Fig. 5-40: Picture of the GF NDT specimen during test from the DIC, a) before crack initiation with the strain field superimposed b.) at crack initiation, c.) at failure. .. 100  Fig. 5-41: Profile of the engineering strain along A-A evolution with time of GF DT specimen. The test nominal strain rate was 0.020 min-1. ........................................ 101  Fig. 5-42: Profile of the engineering strain along B-B evolution with time of GF DT specimen. The nominal test strain rate was 0.020 min-1. ........................................ 102  Fig. 5-43: Engineering strain variation with time at locations from the center (0.0 mm) horizontally along B-B of a DT GF specimen. The test nominal strain rate was 0.020 min-1. ....................................................................................................................... 102  Fig. 5-44: Strain rate variation along A-A from the crack front (0.0 mm) horizontally along A-A to the center of a GF DT specimen. The nominal test strain rate was 0.020 min-1. ............................................................................................................. 103 

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Fig. 5-45: Engineering strain variation with time at locations from the center (0.0 mm) vertically (B-B) of the DT GF specimen. The test nominal strain rate was 0.020 min1

. .............................................................................................................................. 104 

Fig. 5-46: Strain rate variation along B-B from the center (0.0 mm) vertically along B-B of the GF DT specimen. The nominal test strain rate was 0.020 min-1. ................. 104  Fig. 5-47: Profile of the engineering strain along A-A evolution with time of GF NDT specimen. The test nominal strain rate was 0.020 min-1. ........................................ 106  Fig. 5-48: Profile of the engineering strain along B-B evolution with time of GF NDT specimen. The nominal test strain rate was 0.020 min-1. ........................................ 106  Fig. 5-49: Engineering strain variation with time at locations from the center (0.0 mm) horizontally along A-A of a NDT GF specimen. The test nominal strain rate was 0.020 min-1. ............................................................................................................. 107  Fig. 5-50: Strain rate variation along A-A from the crack front (0.0 mm) horizontally along A-A to the center of a GF NDT specimen. The nominal test strain rate was 0.020 min-1. ............................................................................................................. 107  Fig. 5-51: Engineering strain variation with time at locations from the center (0.0 mm) horizontally along B-B of a NDT GF specimen. The test nominal strain rate was 0.020 min-1. ............................................................................................................. 108  Fig. 5-52: Strain rate variation along B-B from the center (0.0 mm) vertically along B-B of the GF NDT specimen. The nominal test strain rate was 0.020 min-1. .............. 109  Fig. 5-53: Layered composite beams for four points bending test. a.) Typical specimen, b.) Beam specimen notched up to layer 3, c.) Beam specimen notched up to layer 2. ................................................................................................................................. 111 

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Fig. 5-54: Test setup for four point bending test in the INSTRON testing machine with the 3D DIC setup. a.)Global view, b.) Close view on the specimen with speckle during test................................................................................................................ 112  Fig. 5-55: Four points bending test configuration. ......................................................... 113  Fig. 5-56: Applied force vs. time. .................................................................................. 114  Fig. 5-57: Applied force vs. CTOD. .............................................................................. 114  Fig. 5-58: Applied force vs. time. The notch in the beam was stopped in PP layer as shown in Fig. 5-53(b).............................................................................................. 115  Fig. 5-59: Applied force vs. CTOD. The crack stopped in PP as shown in Fig. 5-53(b). ................................................................................................................................. 116  Fig. 5-60: Strain rate at crack tip vs. time. The crack stopped in PP as shown in Fig. 5-53(b)..................................................................................................................... 117  Fig. 5-61: Four points bending failed specimen. ............................................................ 117  Fig. 6-1: (a) Repaired tensile specimen, b.)Repaired tensile specimen in controlled temperature and pressure chamber.......................................................................... 121  Fig. 6-2: Comparison of engineering stress vs. strain of GF tensile specimen and the same specimen after repaired. Test conducted at the nominal strain rate of 0.003/min. . 122  Fig. 6-3: Comparison of engineering stress vs. strain of GF tensile specimen and the same specimen after repaired. Test conducted at the nominal strain rate of 0.003/min. . 122  Fig. 7-1: The material parameters on a typical engineering stress-strain relationship. .. 124  Fig. 7-2: Effect of temperature on yield strength (y) of unfilled polypropylene. ......... 127  Fig. 7-3: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of unfilled polypropylene. .............................................................................. 128 

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Fig. 7-4: Effect of temperature on yield strength (y) of unfilled polypropylene. ........ 128  Fig. 7-5: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of unfilled polypropylene. .............................................................................. 129  Fig. 7-6: Effect of temperature on yield strength (y) of glass microspheres filled polypropylene. ........................................................................................................ 130  Fig. 7-7: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of glass microspheres filled polypropylene. ................................................... 130  Fig. 7-8: Effect of temperature on yield strength (y) of polypropylene with glass microsphere filler. ................................................................................................... 131  Fig. 7-9: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with glass microsphere filler. ............................................. 131  Fig. 7-10: Effect of temperature on yield strength (y) of polypropylene with 65% glass filler. ........................................................................................................................ 132  Fig. 7-11: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with 65% glass filler. ................................................ 133  Fig. 7-12: Effect of temperature on yield strength (y) of polypropylene with 65% glass filler. ........................................................................................................................ 133  Fig. 7-13: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with 65% glass filler. ................................................ 134  Fig. 7-14: Effect of strain rate on yield strength (y) of unfilled polypropylene at 22oC. ................................................................................................................................. 135  Fig. 7-15: Effect of strain rate on initial elastic modulus (Ei) and secant modulus at yield (Esy) of unfilled polypropylene at 22oC. ............................................................... 135 

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Fig. 7-15: Effect of strain rate on yield strength (y) of polypropylene with glass microsphere filler at 22oC. ...................................................................................... 137  Fig. 7-16: Effect of strain rate on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with glass microsphere filler at 22oC. ................................ 138  Fig. 7-17. Effect of strain rate on yield strength (y) of polypropylene with 65% glass filler at 22oC. ........................................................................................................... 140  Fig. 7-18: Effect of strain rate on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with 65% glass filler at 22oC. ............................................ 140  Fig. 7-19. Original model normalized stress-strain relationship prediction. ................. 144  Fig. 7-20. Case: q=0 and p=1. ....................................................................................... 146  Fig. 7-21: Case: q=1 and p=0.5..................................................................................... 146  Fig. 7-22. New model normalized stress-strain relationship prediction. ....................... 147  Fig. 7-23: Comparison of the new model prediction and the experimental stress-strain relationship of GF. .................................................................................................. 148  Fig. 8-1: Uniaxial strain field evolution on the simulated GF specimen with a circular hole. ......................................................................................................................... 153  Fig. 8-2: Uniaxial strain field evolution on the simulated GF specimen with a circular hole. ......................................................................................................................... 153  Fig. 8-3: Uniaxial strain field evolution on the simulated GF DT specimen. ................. 154  Fig. 8-4: Comparison of strain fields from simulation with 3D DIC record of GF DT specimen. in the elastic domain.a.)FEM simulation, b.)DIC. ................................. 154  Fig. 8-5: Comparison of strain fields from simulation with 3D DIC record of GF DT specimen. in the plastic domain.a.)FEM simulation, b.)DIC.................................. 155 

xxv

Fig. 8-6: Uniaxial strain field evolution on the FEM simulated of GF NDT specimen. 155  Fig. 8-7: Comparison of strain fields from simulation with 3D DIC record of GF NDT specimen. in the elastic domain. a.)FEM simulation an , b.)DIC. .......................... 156  Fig. 8-8: Comparison of strain fields from simulation with 3D DIC record of GF NDT specimen. in the plastic domain.a.)FEM simulation, and b.)DIC. .......................... 156  Fig. 8-9: DIC strain field on the specimen. a.)Interface delamination, b.) Complete failure of the specimen. ...................................................................................................... 157  Fig. 8-10: ABAQUS strain field on the specimen. a.)Interface delamination, b.) VonMises. Stress. .......................................................................................................... 157 

xxvi

LIST OF TABLES Table 5-1: Summary table of strain rate amplification factor ..................................... 119  Table 7-1: Summary table of the thermal decay coefficient ........................................ 134  Table 7-2: Strain rate coefficients and reference parameters of unfilled and polypropylene with glass microsphere filler ................................................................................... 136  Table 7-3: Strain rate coefficients and reference parameters of the polypropylene with 65% glass filler ....................................................................................................... 139  Table 8-1: GF specimen with centered circular hole model material parameters. ......... 151  Table 8-2: GF DT model material parameters. ............................................................... 151  Table 8-3: GF NDT model material parameters. ............................................................ 152  Table 8-4: Four points bending model materials parameters.......................................... 152 

xxvii

1. INTRODUCTION 1.1.

General During the past few decades, the increasing use of structural polymer composites

has resulted in the need for better characterizations of the materials under working conditions. A strong driving force for new polymer composites is also due to the fact that they can successfully compete against metals. Added to this, polymer composites, with the ability to be relatively easily tailored designed, provide a wide range of applications. In the case of fiber glass-epoxy composites, the fiber choice, arrangement, and proportions are independently controlled by the fabricator. Such control or tailorability contributes to the importance of such composites. Polypropylene and its composites with mineral fillers (Zhou et al., 2002), glass fiber (Thomason et al., 1996), carbon fibers reinforced polypropylene (Amash et al., 1997), (Fu et al., 2000) and glass microsphere (Hansen et al., 2000) have many applications in the automobile, aerospace, appliances and subsea pipeline insulation (Guidetti et al., 1996). Also other commercial products in which creep resistance, stiffness, toughness and insulation are required, polypropylene composites are used. Most of these applications require good performance over a range of temperatures and deformation rates in addition to weight and cost savings. Therefore it has become important to quantify the effects of temperature as well as strain rate on the mechanical and fracture behavior of polypropylene and its composites. However,

polymer

composites filled with hard inorganic particles of nano- to micro-scale show a very complex variation of mechanical properties with increasing particle fraction (Zhou et al., 2002).

1

Polymer composites filled with inorganic particles to enhanced desired mechanical properties have been studied extensively (Fu et al., 2008). In particular, thermo mechanical behavior of polypropylene has been reported by many investigators in the past. The understanding of the structure-property relationships and deformation characteristics of polypropylene at different strain rates and temperatures were the focus of those studies. Many of the related studies in the literature are focused on polypropylene physical properties, its morphology and microstructure (Amash et al., 1997). With wide range of applications, better characterization, polypropylene and its composites are becoming more important (Sandler et al., 1998). Arruda et al. (1997) investigated the rate dependent deformation of polypropylene at room temperature under uniaxial compression. Duffo et al. (1991) investigated the tensile behavior of polypropylene in the temperature range between 20 and 150oC. The effects of temperature and strain rate on the tensile behavior of talc filled polypropylene were investigated by Zhou et al. (2002). The fracture toughness and failure mechanism of polymer filled with nano- to micro-scale size inorganic particles was investigated by Lauke et al. (2013). These studies gave insight to the required knowledge to assess polymer composites behavior, in this case polypropylene composite, for their application. However, there is very limited information on the modeling, the stress-strain relationship and fracture behavior of polypropylene glass composites.

2

1.2.

Objectives The overall objective of this work was to characterize and model the fracture and

mechanical behavior of polypropylene composites used as coating insulators for deepwater pipelines and risers. The specific objectives are as follows: (1) Characterize the behavior of polypropylene composites in terms of temperature and strain rate. (2) Investigate the effects of defects/cracks on the behavior of polypropylene and its composites. Also investigate a potential repair method. (3) Model the mechanical, fracture and stress-strain behavior of the polypropylene composites.

1.3.

Organization Chapter 2 summarizes the background information on polymers and polymer

composites with emphasis on polypropylene and polypropylene composites behavior modeling, structures and mechanics and a review of fracture mechanics. Chapter 3 involved the material identification and experimental program with emphasis on the 3D Digital Image Correlation (DIC) system usage. Chapter 4 presented the experimental tests which established the stress-strain behavior of the materials, the composites behavior and failure parameters of the materials. Chapter 5 involved the fracture behavior of polypropylene with and without glass fillers. Chapter 6 introduced a repair material with validation tests. In Chapter 7 constitutive models were developed for the thermomechanical behavior and stress-strain relationship of the materials. In Chapter 8 numerical simulation of tensile tests and bending of composite beams with and without cracks were evaluated. Chapter 9 summarizes the findings and conclusions of this study. 3

2. BACKGROUND AND LITERATURE REVIEW 2.1.

General The assessment of the deformation of a material during its practical application is

one of the driving reasons behind the development of material constitutive model. From the increase in the development of new composites polypropylene (PP), for specific thermo mechanical or chemical properties, came the needs to update the existing constitutive relationships or develop new models for behavior assessment and prediction for design. In the quest of new oil reserves to satisfy the increasing world energy demand, the petrochemical industry is looking more and more to the exploration of the offshore deep sea (between 500 and 1500 m) and ultra-deep sea (between 1500 and 3000 m) oil reserves (Bouchonneau et al., 2007). Consequently, one of the currently most challenging projects in the petroleum industry consists of exploiting oil resources at great depths, where production infrastructures are submitted to high hydrostatic pressures (up to 300 bar) and to low external temperatures (about 4°C at 3000 m) (Bouchonneau et al., 2010). Deep water developments usually consist of a number of wells with temperatures of up to 160oC, “tied back” to the production platform by means of pipelines and risers. The pipelines associated can be up to 100 km in length (Harte et al., 2004). One of the challenges of oil and gas exploitation in this subsea environment is to maintain the product leaving the wellheads hot since its flow and processing characteristics are temperature sensitive. Should its temperature fall below a particular value, problems may occur due to the formation of emulsions which produced water, and solids by wax deposition or the separation of ice-like crystals of gas hydrate in the case of high pressure

4

natural Gas. Therefore, it is necessary to design a system to prevent cooling of the oil coming from the wellheads and preserve the integrity of the pipeline despite its buckling on the seabed induced by the thermal expansion of the pipe wall due to the high temperature of the oil. One of the options is the thermal insulation of the pipeline to conserve the heat of the product (Collins 1989) and have a design to control the movement, lateral buckling and axial displacement, of the hot pipeline on the seabed (Bruton et al., 2008). There are three approaches to insulate flow line for deep water operation: pipe-in-pipe (inner and outer steel pipes with an insulating material in the annular space) - wet insulated flow lines (steel pipe with surrounding layers of exposed composite insulation) - and insulated flexible flow lines (a composite structure with a core of helically wound steel and extruded plastic layers and insulation added in the form of flexible wrapped syntactic insulation) (Hunter 2008). In the last decade, wet thermal insulation became the prevailing subsea pipeline insulation because of the material used. Glass microsphere technology and glass fiber reinforced polypropylene have fostered development of flow line insulation alternatives that reduce thermal conductivity and make deep water hydrocarbon recovery feasible. The thermo mechanical properties required for subsea pipe insulation make polypropylene and its composites a suitable material with the development of foamed polypropylene (syntactic foam) for subsea pipe insulation in the mid-eighties by Norsk Hydro (Hansen et al., 2000). It is essentially used for wet insulation (layered coatings). The coating is composed of thin layer of epoxy resin, intermediate layers of modified polypropylene copolymer (syntactic foam) and polypropylene. Polypropylene thermal

5

insulation can be of several layers coating (i.e. three layers (Guidetti et al., 1996), five layers (Bouchonneau et al., 2010), seven layers (Hansen et al., 2000)). From the manufacturing of the wet insulated pipes to their service environment at subsea, they are subjected to different thermo mechanical forces, stresses and strains ranges. During transportation, which induced transient forces; the whole insulated pipe goes through large bending deformation if we consider the extreme case of reel barging operation. This mode of transportation is both time and cost effective, but imposed severe mechanical strains on the insulated pipes as they are bent onto and straightened off the reel of the barge (Collins 1989). In service, the insulated pipes have to withstand the subsea high hydrostatic pressure (i.e. 3000 m induces 300 bar which is about 4400 psi) at 4oC from the interface with the sea and its lateral displacement and axial displacement because of the pipe buckling due to the thermal expansion of the steel pipe; with cycles of short downs and startups. From the above enumerated condition the following tests are performed for the development and evaluation of thermal insulation: tensile (Rizzi et al., 2000) – compression (Walley et al., 1994) – bending – hydrostatic crush pressure test – shear – sea water diffusion (Guidetti et al., 1996) and fracture toughness (Cartié et al., 2006) . Due to their functionality and availability, several rheological constitutive stressstrain or stress-stretch models have been developed through the years for polymers in an attempt to predict their behavior (Mooney 1940), (Valanis 1967), (Haward and Thackray 1968), (Ogden 1972), (Treloar et al., 1976), (Arruda and Boyce, 1993), (Arruda et al. 1995) and (Varghese and Batra 2009). These models were mainly developed for noncomposite polymer materials such as: rubber, polycarbonate (PC), polypropylene (PP)

6

an nd polymeth hylmethacry ylate (PMMA A). With thhe increase uused of polyymer compoosites caame the intrroduction off new constiitutive modeels (Cox 19552); (Vipulaanandan andd Paul 1990) (Mantrrala and Vip pulanandan 1995) 1 and (Z Zhou et al., 2002). It is to be mentiioned th hat the initiaal models, fo or non-comp posite polym mers materiaals, considerred the moleecular sttructure paraameters as driving d forcee for the maaterial macrroscopic defformation in both issotropic an anisotropic a behavior. b Th he fracture m mechanism aassessment oof these pollymer co omposites iss a necessity y for design n but a compplex issue siince they evvade the classsical method m due to their properties p such s as theeir strain rate dependent behavioor or microstructur m re (Gearing and a Anand 2004), 2 (Laukke and Fu 20013) and (de Morais 2011).

2.2.

Polyp propylenee composittes In un nderstanding the behavio our of compoosite polyproopylene, it iss very imporrtant to

cllearly quantiify the modiification to polypropylen p ne thermo-m mechanical pparameters innduced by y filling it with w inorganiic particles such as glasss fiber and gllass microspphere in the ccase of wet w thermal in nsulation. Polypropylene is a semicry ystalline the rmoplastic material wiith the mollecular fo ormula (C3H6) n

with: w

- A dennsity of 0.85 g/cm3 in thhe amorphouus state and 00.95 g/cm3 ccrystalline sttate (Maieer and Calafu ut 1999).

7

-

A mellting temperaature which varied betw ween 130 oC aand 171 oC ((Sperling 20006).

Mechanically M y, polypropy ylene is a viiscoelastic aand ductile ppolymer in bboth tensionn and co ompression and is classiified as tough h polymer. (i) i)

Glass fiber reinfo orced polyprropylene Glass fiber reinforced polypro opylene is uused in deep water pipeline to increaase the

th hermal insulation capaciity of the steel pipeline aand its stability. Glass G fiber iss a high streength brittle inorganic m material. Thee densities oof the ones uused in composites range r from approximateely 2.11 to 2.72 g/cm3 (Hartman et al. 1996). The composite wiith polyprop pylene as maatrix used gl ass fiber witth a density of 2.55 g/cm m3 (Fu et al. 2000) 2.62 2 g/cm3 (T Thomason and a Vlug 19996). Glass ffiber reinforcced polyproppylene iss a mixture of glass fib ber of variab ble length,

0.1mm to550 mm (Thhomason andd Vlug

1996) and low wer as 150 m  to 300 m  (Fu et al.. 2000), withh polypropyllene as matrrix, see Fig. F 2-1. Add dition of glaass fiber to polypropylen p ne increasess its stiffnesss but decrease its

ductility d (Lau uke and Fu 2013) 2

Fig. 2-1: SEM micrograph of o glass fiberr reinforced ppolypropylenee (Fu et al. 22000).

8

a.) (Boye ( et al. 2002) 2

b.) (Lefebvre et aal. 2009)

Fig. 2-2: SEM micrograph of o polypropyllene syntacticc foam.

(iii)

Synta actic polyprop opylene Syntaactic polypro opylene is a highly poroous material with good thhermal insullation

prroperty and lower density as shown in Fig. 2--2. Glass fibber reinforceed polypropyylene an nd glass miccrosphere po olypropylenee foam were initially devveloped for aeronauticaal and marine m strucctural and automotive a applicationns, (Rizzi eet al., 20000); (Mae 22008); (W Woldesenbett et al., 20 005). They have been the object of extensivve investigaations fo ollowing theeir manufactu uring processs and servicce loads requuirements. T Their introduuction in n deep waterr pipe thermaal insulation n systems reqquired the reeview of their behavior iin the new environm ment.

2.3.

Polyp propylenee compositte behavioor

2.3.1

Cox and a Krenchel model In thee modeling g of the ten nsile behavvior of polyymer compoosites, the most

ommonly ussed theory was w developeed by Cox (11952) and fuurther improoved by Krennchel co 9

(1964).

As clearly explained by Thomason (1996), Cox’s ‘shear lag’ model was

developed for aligned discontinuous elastic fibers in an elastic matrix. The applied load is transferred from the matrix to the fiber via interfacial shear stress, with the maximum shear at the fiber ends decreasing to zero at the center. Thus the tensile stress in the fiber is zero at the ends and maximum in the middle. However, the maximum tensile stress along the length of the fiber can never exceed the tensile stress in the matrix. Thus, although the efficiency of stress transfer increases with fiber length, it can never reach 100%. In order to accommodate this dependence of reinforcement efficiency on fiber length, Cox introduced a fiber length efficiency factor 1 into the ‘rule-of-mixtures’ equation for the composite modulus Ec. 1

(2-1)

,

where Ef, Em and Vf are the fiber and matrix stiffness and fiber volume fraction, respectively. The ‘shear lag’ theory developed by Cox gives

1

/

(2-2)

/

and



,

/

(2-3)

where L is the fiber length, Gm is the shear modulus of the matrix, r is the fiber radius and R is related to the mean spacing of the fibers. The r/R factor can be related to the fiber volume fraction Vf by

/



/

10

,

(2-4)

where Xi depends on the geometrical packing arrangement of the fibers. Krenchel extended this theory to take fiber orientation into account by adding a fiber orientation factor o into the ‘rule-of-mixtures’ equation, giving 1

.

(2-5)

Thomason et al. (1996) used of this model limited it accuracy to polypropylene with less than 40% inorganic filler (glass fiber) and predicted the composite polymers elastic modulus.

2.4.

Fracture mechanic Fracture mechanics is a fairly recent field of mechanics concerned with the study

of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. The foundation of fracture mechanics was first established by Griffith (1921) using the stress field calculations for an elliptical flaw in a plate developed by Inglis (1913) for the infinite plate loaded by an applied uniaxial stress (Budynas 1999). His work was on brittle material (glass) and introduce fracture mechanic, especially the linear elastic fracture mechanic (LEFM). Griffith’s theory was highly unrealistic because most materials present some ductility inducing some plastic flow at the crack tip. G. R. Irwin (1948) with his research group at the U.S. Naval Research Laboratory (NRL) in 1940s extended the Griffith’s LEFM theory to ductile materials by introducing the strain energy release rate (G), stress amplification factor and crack extension resistance curve or Rcurve. The latter is the attempt to elastic-plastic fracture mechanics. James R. Rice 11

(1968), from Brown University, developed the J-integral for non-linear elastic ductile material. The application of fracture mechanics resides in the detection of small cracks present during the fabrication of part or crack developed in service and their potential to grow into unstable cracks leading to catastrophic failure. The yield strength of the material, the working temperature and fatigue also play an important role in fracture mechanic failure. These latter makes the material brittle or reduce it yield stress respectively. 2.4.1

LEFM: Griffith’s work Griffith (1921) pioneering studies of fracture with glass (brittle material) was

based on Inglis’ calculation of stress concentrations around elliptical holes focusing on the crack tip. Griffith used an energy-balance approach to develop a fundamental approach to estimate fracture strengths. The strain energy per unit volume (U*) of stressed material is, ∗

.

(2-6)

If the material is linear (σ = E), then the strain energy per unit volume is

E 2  2 U   . 2 2E *

(2-7)

When a crack has grown into a solid to a depth a, a region of material adjacent to the free surfaces is unloaded and its strain energy released as shown in Fig. 2-3. Using the Inglis solution, Griffith was able to calculate the energy.

12

Fig. 2-3 : Sketcch of the tenssile test specim men (Roylancce 2001).

Approximatin A ng the unloaaded region ns near the ccrack flankss to trianglee of width a and height βa, the parameterr β can be selected s so aas to agree w with the Ingglis solutionn. For plane stress lo oading β = π. π The total strain s energyy U releasedd is then the strain energgy per un nit volume times t the vollume in both h triangular rregions:

U 

2 2E

 a2 .

(2-8)

This T strain en nergy is liberated by craack growth. B But in formiing the crackk, bonds muust be brroken, and the t requisitee bond energ gy is in effecct absorbed by the mateerial. The suurface en nergy (S) asssociated with h a crack of length a (annd unit depthh) is:

S  2 a ,

(2-9)

2 where w γ is th he surface en nergy (e.g., Joules/m J ) aand the factoor 2 is needeed since twoo free

su urfaces havee been formeed. The totall energy assoociated withh the crack iss then the suum of S (positive) an nd U (negatiive) as preseented in Fig. 2-4.

13

Fig. 2-4 : The fracture eneergy balance (Roylance 2 2001).

As A the crack grows longeer (a increasses), the quaadratic depenndence of sttrain energyy on a ev ventually do ominates the surface energy, and beyyond a criticcal crack lenggth ac the syystem caan lower its energy by letting l the crrack grow sttill longer. U Up to the pooint where a = ac, th he crack will grow only y if the stresss in increaseed. Beyond that point, tthe crack beecome un nstable cracck; growth is spontaneo ous and catastrophic. Thhe value of the critical crack leength can be found by seetting the derrivative of thhe total enerrgy S + U to zero,

f (S  U )  2  a  0 . E a 2

(2-10)

When W this con ndition is saatisfied the crrack becomees unstable, and the stresss is written as σf

f 

2E . a

(2-11)

This T energy balance b apprroach was deerived for briittle materials. 2.4.2

Irwin n’s work Since most of thee engineering g materials ppresent som me ductility, Irwin (1948) and

Orowan O (194 49) suggesteed that in a ductile matterial, the vvast majorityy of the releeased 14

strain energy was absorbed not by creating new surfaces, but by energy dissipation due to plastic flow in the material near the crack tip. They concluded that catastrophic fracture occurs when the strain energy is released at a rate sufficient to satisfy the needs of all these energy “sinks,” and denoted this critical strain energy release rate by the parameter Gc (Roylance 2001). The Griffith equation can then be rewritten in the form

f 

EGc , a

(2-12)

where Gc is the critical strain energy release rate, σf the stress level and a the size of the flaw. For application, a is calculated and any crack with length equal to ac becomes unstable and propagate catastrophically;

ac 

Gc E

 2

.

(2-13)

During inspection of all the length of the cracks are checked and compare to the critical value. 2.4.3

LEFM: Stress Intensity Factor While the energy-balance approach provides a great deal of insight to the fracture

process, an alternative method that examines the stress state near the tip of a sharp crack directly has proven more useful in engineering practice. Three distinct modes of crack propagation exist, as shown in Fig. 2-5. A tensile stress field gives rise to mode I, the opening crack propagation mode.

15

Fig. 2-5: Fractu ure modes (A Anderson 2004 4).

This mode m is the most m commo on in practicce. Mode II is the slidingg mode, is ddue to n-plane sheaar. Mode IIII is the tea aring mode,, which arisses from ouut-of-plane shear in (B Budynas 199 99). Mode I is a norm mal-opening mode, whilee modes II and III are shear slliding modes. The semi--inverse metthod developped by Wesstergaard shoows the opeeningmode m stressess to be:

Fig. 2-6: Stressses near the tiip of a crack in i an elastic m material (Andderson 2004).

x 

KI   3  cos 1  sin sin   ... , 2 2 2  2 r

(2-14)

y 

KI   3 cos 1  sin sin 2 2 2 2 r

(2-15)

16

   ... , 

 xy 

KI  3  cos cos sin ... , and 2 2 2 2 r 0

z    ( x   y )

(if plane stress ) . (if plane strain )

(2-16)

(2-17)

For distances close to the crack tip (r ≤ 0.1a), the second and higher order terms indicated by dots may be neglected. At large distances from the crack tip, these relations cease to apply and the stresses approach their far-field values that would be obtained when the crack was not present. KI is the stress intensity factor and was introduced by Irwin (1948). The subscript I indicate the crack opening mode, and similar relations apply in modes II and III. Note that each stress component is proportional to the constant KI, the stress intensity factor. If KI is known, the entire stress distribution at the crack tip can be computed with the equations. KI completely characterizes the crack tip conditions in a linear elastic material (Budynas 1999). The denominator factor (2πr)−1/2 shows the singular nature of the stress distribution. The critical stress intensity factor value beyond which the crack becomes unstable and propagates rapidly is denoted KIc. This critical stress intensity factor is then a measure of material toughness. The failure stress σf is then related to the crack length a and the fracture toughness by

f 

K Ic

 a

,

(2-18)

where α is a geometrical parameter equal to 1 for edge cracks and generally on the order of unity in other situations. Expressions, for α, are tabulated for a wide variety of specimen and crack geometries, and specialty finite element methods are available to

17

compute it for new situations. The stress intensity and energy viewpoints are interrelated, as can be seen by comparison below (with α = 1),

f 

EGc K  Ic  K Ic2  EGc . a a

(2-19)

This relation applies in plane stress; it is slightly different in plane strain, K Ic2  EGc (1  2 ) .

2.4.4

(2-20)

Elastic-plastic fracture mechanics For engineering material with nonlinear elastic and inelastic behavior under

operating load, the LEFM assumptions may not apply: -

the plastic zone at the crack tip may be as big as the crack,

-

size and shape of the plastic zone may change with the applied load. As Suresh (1991) clearly stated, the stress intensity factor K provides a unique

characterization of the near-tip fields under small-scale yielding conditions, while the corresponding loading parameter for the characterization of monotonic, nonlinear fracture in rate-independent materials is the J-integral proposed by Rice (1968).

(i)

J-integral Consider a cracked body subjected to a monotonic load. Assuming that the

tractions T are independent of crack size and that the cracks faces are traction-free, the line integral J along any contour Γ which encircles the crack tip, as shown in Fig. 2-7, is given by

18

n NOTCH

y=X

t



2

X = X1

Fig. 2-7: Flat surfaced notch in two-dimensional deformation field (all stresses depend only on x and y). Γ is any curve surrounding the notch tip, Γ , denotes the curved notch tip.

.

,

(2-21)

where u is the displacement vector, y is the distance along the direction normal to the plane of the crack, s is the arc length along the contour, T is the traction vector and the strain energy density of the material. The stresses ij are related to the .

is

as followed (2-22)

For a material which is characterized by linear or nonlinear elastic behavior, J is independent of the path Γ taken to compute the integral.

(ii)

Crack Tip Opening Displacement (CTOD) J-integral treats the presence of large deformations as an integral part of analytical

formulations that comprehensively describe the state of plastic stresses and strains. The crack tip opening displacement (t=CTOD), as shown in Fig. 2-8, is a measure of fracture toughness of solid materials that undergo ductile-brittle transition and elastic-plastic or fully plastic behavior as in larges structures (ships, pressure vessels). Subsequently, the

19

critical stress and crack size might be predicted using this technique, provided that a critical value of CTOD(t=c) is known (Perez 2004).

t



.

45°

Fig. 2-8: Definition of crack tip opening displacement, t. Using Dugdale model t can be expressed in term of the stress intensity factor,

,

(2-23)

or in term of the J integral (Suresh 1991), ,

(2-24)

where dn is a function of , y and n. dn ranges in value from about 0.3 to 0.8 as n, the strain hardening exponent is varied from 3 to 13.

2.5.

Summary

(1) Polymer materials have good engineering properties and have been the target of numerous studies.

20

(2) New polymer composites tailored, at micro- and nano-scale level, for specific functions such as polypropylene composites used in subsea insulation system, requires the review of the existing models and the development of new ones. (3) Cox model, extended by Krenchel, is generally used for the macro structural elastic parameters of thermoplastic polymer composites. (4) Fracture mechanic study of materials which covers the linear and plastic behavior of materials, from the work of Griffith to CTOD, will be considered for the fracture characterization of the new polymer composites.

21

3. MATERIALS and METHODS 3.1.

Introduction The development of material engineering is accompanied by a growing demand

for routine testing for the assessment of chemical composition, physical and mechanical properties of new materials as well as for quality control of the manufacturing processes. Coatings are mostly made of polymers and hence their functional properties and durability mainly depend on polymer chemical composition and supermolecular structure (Farrukh 2012). The polymer composites in this study were characterized with Fourier Transformed Infra-Red (FT-IR) spectroscopy and Scanning Electron Microscope (SEM) tests. The materials densities, thermal conductivity, mechanical and fracture properties were measured. The contactless three dimensional Digital Image Correlation (3D DIC) system was used to measure the strain and crack growth in the test specimens.

3.2.

Materials The coated steel pipe had an outer diameter (OD) of 20 cm (7.9 in) and the thermal

insulation was 6.6 cm (2.6 in) thick as shown in Fig. 3-1. The four layers were as follows: (1) one layer of fusion bonded epoxy resin - (2) a thick layer of polypropylene with 65% glass filler was one type of (deep water pipes) insulation and polypropylene with glass microsphere was the second type of insulation (risers) – (3) a layer of unfilled polypropylene and (4) an outer layer of solid polypropylene (4). The materials investigated, in this study, were unfilled polypropylene (PP), polypropylene with glass microsphere filler (GM) and polypropylene with 65% glass filler (GF).

22

The polypropylen p ne polymer coating c matterials were obtained froom deep-waater oil pipelines with h a multilayeers polyprop pylene compposite insulattion as show wn in Fig. 3--1. The mpany to CIG GMAT. pipes with thee coating inssulation weree supplied byy an oil com

Fig g. 3-1: The subsea pipe with its theermal insulattion layers iin CIGMAT lab. PP: unnfilled poly ypropylene, GF: G polypropy ylene with 65% % glass fillerr, GM: polyprropylene withh glass micrrosphere fillerr.(GM* was in i the risers innsulation).

3.2.1

Densiity

(i) Unfillled polyprop pylene (PP) PP bu ulk density was 800 kg g/m3 and coompared to the commoon density oof PP he literature as a shown in Fig. 3-2. reeported in th (ii) Polyp propylene wiith glass miccrosphere filller (GM) The average a bulk k density of GM was 7885 kg/m3. Itt was nearlyy the same aas the u poly ypropylene due to the proportion and the siize of the glass density of unfilled microsphere m filler. f

23

(iii)Polypropylene with 65% glass filler (GF) The average bulk density of GF was 1950 kg/m3. It was 2.4 higher than the density of PP. It was developed to provide stability to the subsea pipeline besides its thermal properties. A similar polypropylene composite used in subsea pipeline coating had a density of 2300 kg/m3 (Guidetti et al., 1996). The material densities of the current study are compared to the densities of different polypropylene composites, used for subsea pipe insulation as reported in the literature as shown in Fig. 3-2, (Cartié et al., 2006), (Hansen and Delesalle 2000), (Guidetti et al., 1996), (Bouchonneau et al., 2007), (Boye et al., 2002), (Harte et al., 2004), and (Woldesenbet 3

et al., 2005). The densities of PP with and without foams varied from 500 to 900 kg/m .

2500

Cartie et al. (2006) Hansen et al. (2000)

GF

Guidetti et al. (1996)

2000

Bouchonneau et al. (2007)

Density (kg/m3)

Hansen et al. (2002) Harte et al. (2002) 1500

Woldesenbet et al. (2005) This study PP & GM

1000

500 PP, Foam & syntactic PP 0 0

1

2

3

4

5

6

7

8

9

10

Data sets

Fig. 3-2: Published densities of polypropylene composites used for subsea pipe insulation and data of this study. PP: Unfilled polypropylene, GM: Polypropylene with glass microsphere filler, GF: Polypropylene with 65% glass filler.

24

3.2.2

Thermal conductivity The thermal conductivity of each material was measured using the KD2 Pro

Thermal Properties Analyzer. The thermal conductivity of the unfilled polypropylene (PP), polypropylene with glass microsphere filler and polypropylene with 65% glass filler were determined to be 0.160, 0.140 and 0.306 W/m.K respectively. The results are compared to the published thermal conductivity values of polypropylene and its composites in Fig. 3-3, (Hansen and Delesalle 2000), (Guidetti et al., 1996), (Boye et al., 2002), (Bouchonneau et al., 2007), and (Harte et al., 2004). GM thermal conductivity was the lowest. GF had the highest value when compared to the published values in the literature.

0.50 Hansen et al. (2000) Guidetti et al. (1996) Hansen et al. (2002)

Thermal conductivity (W/m.K)

0.40

Bouchonneau et al. (2007) GF

Harte et al. (2004) This study

0.30

PP

0.20

GM

0.10

0.00 0

1

2

3

4

5

6

7

8

9

10

Data sets Fig. 3-3: Published thermal conductivity of polypropylene composites used for subsea pipe insulation and data of this study. PP: Unfilled polypropylene, GM: Polypropylene with glass microsphere filler, GF: Polypropylene with 65% glass filler.

25

3.2.3

Fourier Transformed Infra-Red Spectroscopy (FT-IR) In this study, FT-IR was used to confirm the chemical nature and components of

the polymer composites. The equipment used was the Thermo Nicolet 4700 FT-IR spectrometer. Almost any compound having covalent bonds, whether organic or inorganic, absorbs various frequencies of electromagnetic radiation in the infrared region of the electromagnetic spectrum. This region lies at wavelengths longer than those associated with visible light, which range from 400 to 800 nm, but lies at wavelengths shorter than those associated with microwaves, which are longer than 1 mm. The vibrational portion of the infrared region is the one of interest here. It included radiations with wavelengths () between 2.5 m and 25 m. The wavenumbers ( ) rather than wavelength (m) was used. Wavenumber is expressed as reciprocal centimeter (cm-1) and is calculated by taking the reciprocal of the wavelength expressed in centimeters, ̅

.

(3-1)

Wavenumbers are directly proportional to the energy (a higher wavenumber corresponds to a higher energy) (Pavia et al. 1979). Since each type of bond has a specific natural frequency of vibration, and two of the same type of bond in two different compounds are in two slightly different environments, no two molecules of different structure have the exactly the same infrared spectrum. Even if some of the frequencies absorbed in two cases might be the same, in no case of two different molecules will their infrared spectra be identical. Therefore, the infrared spectrum can be used as the equivalence of fingerprint for molecules. By comparing the infrared spectra of two substances thought to be identical, you can establish whether they are, in fact, identical. If their infrared spectra coincide peak for peak (absorption for absorption), in most cases the

26

two substances will be identical (Pavia et al. 1979). In terms of wavenumbers, the vibrational infrared extends from about 4000 to 400 cm-1. When Fourier Transform is used to post process the data, the infrared spectroscopy is referred to as FT-IR.

(i) Unfilled polypropylene (PP) The FT-IR spectrum for unfilled polypropylene is shown in Fig. 3-4. The absorbing group and vibrations characteristic of polypropylene were identified: - a (CH2) corresponding to the peak at wave number 2916 cm-1 - a (CH3) to 2959 cm-1 - s (CH3) to 2881 cm-1 - s (CH2) to 2841 cm-1 - a (CH3) to 1460 cm-1 - s (CH3) to 1376 cm-1 - w (CH2- CH) to 1357 and 1328 cm-1 (Farrukh 2012). (Note: s‐stretching vibration symmetrical; a‐ asymmetrical; s‐deformation vibration symmetrical; a‐ asymmetrical; w‐ wagging vibration).

% Transmittance

100

1358 99

2877

2868 1462

98

1377

97 2951 2918 96 3000

2750

2500

2250

2000

1750

Wavenumbers (1/cm) Fig. 3-4: FT-IR spectrum of the unfilled polypropylene.

27

1500

1250

1000

(ii) Polypropylene with glass microsphere filler (GM) The FT-IR spectrum of the polypropylene with glass microsphere filler is shown Fig. 3-5. The absorption band peaks of polypropylene can be observed, as marked, besides the glass, Si-O-Si, infra-red spectra between the wavenumbers 800 and 1250 cm1.

% Transmittance

100 99 2883 98

2839

1358

2951 2918

1460 1375

97 96 95 1034 94 3000

2750

2500

2250

2000

1750

1500

1250

1000

750

Wavenumbers (1/cm) Fig. 3-5: FT-IR spectrum polypropylene with glass microsphere filler.

(iii) Polypropylene with 65% glass filler (GF) The FT-IR spectrum of the polypropylene with 65% glass filler is shown Fig. 3-6. The absorption band peaks of polypropylene can be observed, as marked, besides the glass, Si-O-Si, infra-red spectra between the wavenumbers 800 and 1250 cm-1. The position and shape of the absorption peak assigned to the stretching vibration mode of the glass, Si-O-Si, bridge are dependent on the oxygen content (Tomozeiu 2005). This explains the difference in the absorption band of the glass particle in GF, Fig. 3-6 and GM, Fig. 3-5.

28

100

% Transmittance

99

1356

2839 2877

98

1458

2951 97 2920

1375

96 1163

95 94 93 92 3000

1076 2750

2500

2250

2000

1750

1500

1250

1000

750

Wavenumbers (1/cm) Fig. 3-6: FT-IR spectrum of polypropylene with 65% glass filler.

FT-IR spectroscopy is one of the best appropriate tests for identification of polymer and additives. It was necessary to use scanning electron microscope to check the micro-structure of the polymer composites. 3.2.4

Scanning Electron Microscope (SEM) For more than 70 years since its invention, Scanning Electron Microscopes

(SEMs) have evolved from relatively simple devices with a resolution of 50 nm to sophisticated computer – controlled systems with wide analytic potentialities and resolutions of 1-2 nm to sub-nm in some particular cases. At the present time, it is hard to conceive of a science field which would not employ methods and instruments based on the use of fine focused e-beams. Well instrumented and supplemented with advanced methods and techniques, SEMs provide possibilities not only of imaging but quantitative measurement of object topologies, local electrophysical characteristics of semiconductor structures and performing elemental analysis (Viacheslav Kazmiruk 2012). 29

In thiss work, we used u SEM to o verify the m microstructur ure of the pollymer compoosites in nvestigated. A SEM LE EO 1525 waas used. It iis a high reesolution fieeld emissionn gun sccanning elecctron microsscope (FEGS SEM) approppriate for im maging and aanalysis of nnanosccale materialls. The speciimens were coated with platinum. (i) Glasss microsphere filled polyypropylene ((GM) The SEM S microg graph at 20 kV k voltage aacceleration of GM is shhown in Figg. 3-7 an nd at 10 kV V is shown in Fig. 3-8 . In Fig. 3-7 (a), glass m microspheress and particlles of brroken glass microspheree embedded in the polyppropylene m matrix has beeen identifieed. At higher resolution as show wn in Fig. 3--7 (b), the gllass microsppheres are ass big as 30  m in diameter. (ii) Polyp propylene wiith 65% glasss filler (GF)) The SEM S results of GF are shown in F Fig. 3-9 (a) and (b). In Fig. 3-9 (a)), the polypropylen ne matrix has been clearrly be identiified separattely from thhe glass partticles. The T concentration of the glass particlles justified tthe 65% vollume fractionn calculated from th he bulk denssity. The glaass particles average sizee is less thann 1 m as obbserved at hhigher reesolution in Fig. F 3-9 (b)..

a.)

b.)

Fig. 3-7: SEM micrograph of o Polypropyllene with glasss microspherre filler at higgh voltage acceleeration (20 kV V). (a)Magniffication of 2.114 K X,(b) M Magnification of 4.63 K X.

30

a.)

b.)

Fig. 3-8: SEM micrograph of o Polypropyllene with glasss microspherre filler at low wer voltage acceleeration (10kV V). (a) Magniffication of 1.99 K X,(b) Maagnification oof 1.5 K X.

a.)

b.)

Fig. 3-9: SEM micrograph of o Glass filled d polypropyleene. (a)Magniification of 11.85 K X,(b) Magn nification of 122.99 1 K X.

3.3.

Expeerimental program From analysis of o the defo ormation hi story of thhe insulatedd pipe from m its

manufacturin m ng and transp portation to its i service coondition, andd the review w of the publlished liiterature, an experimental programm med was esttablished to investigate the failure m mode ob bserved on the t field as shown s in Fig g. 3-10.

31

Fig. 3-10: Fraccture of a deep p water pipe insulation i obsserved on thee field during installation.

The T experimeental program m was design ned to: (i) Deteermine the unfilled u pollypropylene,, polypropyylene with gglass microsphere fillerr and polypro opylene with h 65% glasss filler stresss-strain relattionship in ttension at vaarious strain rates variatiion and tem mperatures annd stress-strain relationsship in comp pression. (ii) Deteermine the co omposite behavior at neear room tem mperature wiith: Four pointts bending of layered com mposite beam ams and Interface shear s test. (iii) Charracterize thee fracture beh havior of thee materials bby conductioon: Tensile tesst on specim mens with perrforated centtered circulaar hole, Tensile tesst on symmeetrically doubble edge groooved (DT) sspecimens annd, Tensile teest on sym mmetrically notched doouble edge grooved ((NDT) specimenss and Four pointts bending teest on notcheed compositees beams.

32

The T differentt types of specimens useed are shownn in Fig. 3-111.

Fig. 3-11: Tesst specimens:: composites beam with and without notch, compposite compreession specimen, PP (white), GM M and GF tensile speciimens, tensille specimen with peerforated centtered circularr hole, tensilee double edgges grooved without (DT T) and wiith notches (N NDT) specimeens and comppression speciimens and creeep specimens.

3.3.1

Instru umentation All th he tests were displacemen nt controlledd and were iinstrumentedd in consequuence.

A strain gagee based clip p-on extenso ometer and conventionaal strain gagges were used to measure m axial and laterall strain. The load was reecorded usinng a load celll. These seensors were w all conn nected to an n Agilent daata acquisitioon (DAQ) syystem. Thee data acquissition sy ystem was controlled by y a laptop wh hich was set to record thhe sensors siggnals at speccified tiime intervalss. A Diigital Imagee Correlatio on (DIC) ssystem was used to m monitor thee full deformation field f at the surface s of the specimenss. In contrastt to the clip--on extensom meter, which w was mechanically m y attached to o the test sppecimens, optical measuurement devvices, su uch as DIC, operate co ontactless. Optical O technniques are pparticularly suitable forr soft

33

polymeric materials, as local stress concentrations arising from the indentation of the specimen and the weight of an attached mechanical extensometer are entirely avoided. The DIC system was specially used for the bending and fracture tests to capture the deformation field (strain field) and the crack growth (direction and size) with the loading. High temperature tensile tests were performed in an INSTRON heating chamber. The temperatures inside the heating chamber and at the specimens’ surface were separately monitored using two different thermocouples. The extensometer used was specially designed to withstand high temperature.

3.4. The Digital Image Correlation (DIC) system (fundamentals and validation) The deformation fields at the surface of the specimens were monitored using a Full-Field Strain Analysis (FFSA) system commonly referred to as Digital Image Correlation (DIC). The DIC system ARAMIS 3D was used. An optical deformation analysis system developed by GOM (Gesell-shaft für Optische Messtechnik). The 3D DIC system consists of two high speed cameras for recordings the images (type Titanar 2.8/50), a trigger box to control the cameras and a computer for data acquisition and post processing. The cameras were mounted on a tripod and arranged so that two adjacent faces of the specimen were visible to both cameras simultaneously. This arrangement allows measurement of out-of-plane displacement in addition to in-plane strains on the specimen surface (Grytten et al., 2009). Image recording is done simultaneously with the analog input from the load cell and the extensometer. The DIC cameras system was consequently fixed relative to the test machine in this configuration.

34

3.4.1

Fundamentals Computer vision based deformation measurement systems rely on digitizing

images into pixels and tracking them in space and time using powerful algorithm (Sutton et al., 2009). The accuracy of conventional extensometer and strain gage are well known and are easily determined. On the other hand, the resolution and accuracy of the optical measurement devices depend on the computer vision hardware (distance, objective, camera resolution and light system) and the software for the images processing (digitization, tracking algorithm and post processing method). In addition we have to include any physical disturbance between the cameras setup and the test equipment such as test machine vibration and any effect of optical interference between the cameras and the specimen. In short, any environmental condition is of importance. Farther are the cameras from the target surface, more accuracy problem is encountered. In this study, only 3D DIC was used. Therefore out of plane deformation was not a concern, as it is in the case of 2D DIC. These established the limitations on the accuracy of the DIC. Hence in this study the DIC results were compared to the strain gage and the mechanical clip-on extensometer results at specific locations on the specimen. As clearly stated by Jarabek (2010) and detailed by Sutton et al. (2009), DIC is based on the principle of comparing speckle pattern structures on the surface of the deformed and the undeformed sample or between any two deformation states. For this purpose, a virtual grid of subsets of a selected size and shape, consisting of certain pixel gray value distributions, is superimposed on the preexisting or artificially sprayed on surface pattern and followed during deformation by an optical camera system. In this manner, information on the in-plane local strain distribution is gained without assuming 35

the constitutive behavior of the material a priori. Furthermore, this method is independent of specimen geometry and can also be applied to complex parts and geometries to monitor the deformation of components in service. Therefore, a full deformation field is obtained from which a trove of deformation information could be extracted: full displacement field and full strain field for small and large deformation, extensometer strain, area strain for strain gage, localized strain for strain concentration and evolution. In computer vision or stereovision, a point is uniquely identified among a trove of locations by its unique surroundings. Consequently, every point is unique because of the configuration of the point surrounding it is unique. Also a point exists as identifiable entity because of the contrast of color between it and it surroundings. As Sutton et al. (2009) stated it, the ideal surface texture should therefore be isotropic, i.e., it should not have a preferred orientation, meaning no repeating textures which would lead to misidentification (misregistration). Consequently, the preferred texture should be nonperiodic. 3.4.2

Requirements: speckle pattern and calibration Therefore, for a complete description of the deformation field on the target

surface, a random speckle pattern is necessary. These requirements naturally lead to the use of random textures. The patterns commonly applied typically resemble laser speckle patterns to some degree. However, the patterns used in digital image correlation adhere to the surface and deform with the surface, and therefore no loss of correlation occurs even under large translations and deformations (Sutton et al., 2009).

36

The specimens were w prepared d for the usse of the DIC C by complletely coatinng the taarget surfacees with a white w coating g, using thee commerciially availabble white RU USTOLEUM O Flatt Protective Enamel E and left to dry. Then the dryy white coatted surfaces were caarefully spraayed over with w the blacck RUST-OL LEUM Flat Protective E Enamel to ccreate th he random speckle s patteerns shown in Fig. 3-122. The randoom speckless are a blackk and white w contrasst with variab ble gray inteensity distribbution.

Fig. 3-12: Specckle patterns examples on three differennt specimens..

The use u of 3D DIC D measureement adds the additionnal step of ccalibration tto the prrocess which consists in n taking thee relative poosition of thee two camerras to each other in nto account. This processs is done by y taking a seeries of pictu tures simultaaneously witth the tw wo cameras of a calibraated target with w grid w with defined shaped dotts. Then the DIC detecting algo orithm calcu ulates how accurately a thhe targeted ddots are uniqquely detecteed by he two cameras. th 3.4.3

Post-p processing The principle p of any DIC system s is too use the rrandom grayy value inteensity

distribution of o the pattern n on the objeect and to ovverlay a gridd of subsets or facets on it. In th he two pictu ures recordeed simultaneously by tthe camerass, each subsset has a unnique in ntensity distribution. Th he calibration function eenables the detection oof the positioon of

37

each subset in the 3D space. In a series of images recorded during a test, the pattern becomes deformed according to the specimen deformation, and the subsets can be detected in each image according to the intensity distribution calculated and determined in the reference image. As the size and shape of the subsets changes when the target object is strained, the strain field on the specimen surface in longitudinal and transverse direction may be obtained by continuously analyzing the speckle pattern and the deformed subsets. The algorithm applied to identify the subsets in each picture is of great importance for the accuracy of the strain field (Jerabek et al., 2010). From the numerous software specific adjustable parameters of a DIC system, the most important one affecting the result accuracy is the size of the subsets. As the subset size determines and is equivalent to the minimum local gauge length, and since there is no systematic procedure, the definition of an adequate subset size is based on operator experience and judgment. In this study, overlapping quadratic subsets with variable size and step were. Longitudinal and transverse strain values are obtained for each of the subsets, implying constant strain values within a given subset (Sutton et al., 2009). 3.4.4

Validation The deformation obtained from the 3D DIC system was compared to the

measurements of clip-on extensometer and strain gage from a series of tensile tests to establish the 3D DIC accuracy. The tests were displacement controlled tensile tests. The setup was as shown in Fig. 3-13. The load cell signal was sent simultaneously to the data acquisition (DAQ), which monitored the strain gage and the extensometer signals, and to the DIC analog signal monitoring unit.

38

a.) b.) Fig. 3-13: Ten nsile test setup p for DIC acccuracy validattion. a.)Globaal view of thee test setup in the INS STRON testin ng machine, b.)View b of thee clip-on exteensometer andd the strain gaage on the t specimen.

Digitaal strain gag ge and exten nsometer weere created iin the post-pprocessing oof the DIC D data to super imposse the real strain s gage aand clip-on extensometeer locations. The DIC D computeed strain vallues are com mpared to thhe physical sstrain gage aand extensom meter values in Fig g. 3-14, Fig. 3-15 and Fiig. 3-16. Thee data were rrecorded at a frequency 1Hz. 2 Hz and 2Hzz respectivelly. As sh hown in Fig g. 3-14 (a), the total eengineering stress-strainn curves loook all dentical. Thee curves in 0.000-0.010 0 strain range are plotted iin Fig. 3-14 (b) which sshows id noticeable vaariations up to t 0.002 straain. In the seecond case, DIC and strrain gage records were w near peerfect in Figg. 3-15 (b). In the thiird case, theere were fluuctuations w which sttabilized at about a 0.001 strain.

39

15

Engineering stress e (MPa)

Engineering stress e (MPa)

25

20

15 Strain gage DIC Strain gage

10

Extensometer DIC Extensometer

5

0 0.00

0.40

0.80

1.20

10

Strain gage 5

DIC Strain gage

0 0.000

1.60

0.002

0.004

0.006

0.008

0.010

Engineering strain e

Engineering strain e

a.)

b.)

Fig. 3-14: Engineering stress-strain curves of PP (1DT-1)at two locations using strain gage, clipon extensometer and 3D DIC system.a.)Full curves, b.) Curves in the strain range 0.000-0.010. 15

Engineering stress e (MPa)

Engineering stress e (MPa)

25

20

Strain gage DIC Strain gage

10

15 Extensometer

10

Strain gage DIC Strain gage

5

DIC Extensometer 0 0.00

0.20

0.40

0.60

5

0 0.000

0.80

Engineering strain e

a.)

0.002

0.004

0.006

0.008

Engineering strain e

0.010

b.)

Fig. 3-15: Engineering stress-strain curves of PP (1DT-2)at two locations using strain gage, clipon extensometer and 3D DIC system. a.)Full curves, b.) Curves in the strain range 0.000-0.010. 20

Engineering stress e (MPa)

Engineering stress e (MPa)

20

15

15

10

10

Extensometer Strain gage 5

DIC Strain gage DIC Extensometer

0 0.000

0.020

0.040

0.060

0.080

Strain gage DIC Strain gage

5

0

0.100

0.000

Engineering strain e

0.002

0.004

0.006

0.008

0.010

Engineering strain e

a.) b.) Fig. 3-16: Engineering stress-strain curves of GF (2DT-1) at two locations using strain gage, clipon extensometer and 3D DIC system. a.) Full curves, b.) Curves in the strain range 0.000-0.010.

40

It was decided to, conservatively, set the accuracy of the 3D DIC readings to be completely reliable at strain higher than 0.002 strain. In the case of strain values lower than 0.002, accuracy level check will have to be done case by case.

3.5.

Summary The materials, unfilled polypropylene (PP), polypropylene with glass microsphere

filler (GM) and polypropylene with 65% glass filler (GF), density and thermal conductivity were determined and compared to the published data. 3D Digital Image Correlation system used for deformation field monitoring was introduced and its accuracy relative to clip-on extensometer and strain gage was set. (1) FT-IR and SEM were used to characterize their nature and structure. (2) The glass microsphere fillers GM diameter was as high as 30 m and the glass filler in GF was as small as 200 nm. (3) The experimental program was laid out following the objective of the study. (4) The 3D Digital Image Correlation (DIC) system, used in the study, was presented with its advantage of monitoring the full deformation field on the surface of the test specimens. The DIC accuracy limit was set to be matching the accuracy of conventional strain gage and clip-on extensometer at strain level higher than 0.002.

41

4. MATERIALS BEHAVIOR CHARACTERIZATION 4.1.

Introduction Polymer and polymer composites behavior have been commonly reported in

compression (Arruda et al., 1997) (Shim and Mohr 2011) (Boyce et al., 1994), tension Zhou et al., 2002) (Ramsteiner and Theysohn 1985), shear (Boyce et al., 1994) (Gearing and Anand 2004) and bending (Rizzi et al., 2000). Following the objective of this study, the unfilled polypropylene (PP), the polypropylene with glass microsphere filler (GM) and the polypropylene with 65% glass filler (GF) tensile behaviors were determined at various strain rates from 0.002 to 0.300 at 22, 60 and 90oC and the compression stress-strain relationship of PP and GF were determined at a near room temperature. With the knowledge of the tensile and compressive stress-strain behavior of the insulation materials, interface shear tests and four points bending tests were conducted to determine the point of fracture initiation in the insulation system and the mechanical conditions which triggered it.

4.2.

Tensile properties of unfilled polypropylene (PP) Uniaxial direct tensile tests were conducted on PP specimens at various strain rate

from 0.003/min to 0.300/min at 22oC (71.6oF), 60oC (140oF) and 90oC (194oF). All the specimens were checked for homogeneity and weighted before testing. The strain rate was calculated as followed .

(4-1)

42

4.2.1

Specimens preparation The uniaxial tensile test specimens were dogbone shaped as shown in Fig. 4-1.

Specimens, of each material, were machined directly from the insulation layers. Since the layers were applied by coating, no directional effect was expected and was not considered in preparing the specimens. They were machined out from the longitudinal direction of the pipe, and were 162.0 mm in total length with 82.0 mm for tapered gage (L), 10 mm width (d) and 6.4 mm in thickness (t). All the tested specimens were visually checked for homogeneity.

d L

t

y z x

Fig. 4-1: Sketch of the tensile test specimen.

4.2.2

Testing procedure The uniaxial axial direct tensile tests were displacement controlled conducted

with an INSTRON servohydraulic test machine equipped with a heating chamber as shown in Fig. 4-2. Two thermocouples were installed inside the heating chamber, one on the chamber wall and the other on the surface of the test specimens. Equilibrium of the

43

teemperature readings r fro om the two thermocoupples was reaached beforee performing the un niaxial tensiile tests. A strain gaug ge based clipp-on extensoometer withh 50.8 mm ((2 in) gage length with w 25.4 mm m travel (1 in) was useed to measurre the axial strain alongg with sttrain gage (10 mm long g) as shown n in Fig. 4-33. The tests were perfoormed up to 50% sttrain. An ad dditional 4 mm m long strrain gage, pperpendicular ar to the axial direction,, was in nstalled on the samplee to measurre the laterral deformattion. The sstrain rates were caalculated by y recorded th he strain from m the extensoometer withh time. The sstrain rates oof the teest were then n varied betw ween 0.002/m min and 0.3000/min and the test tempperature werre 22, 60 and 90oC.

Fig. 4-2: Tensiile test setup in the INSTR RON test macchine. Globall view of the setup with heeating cham mber, INSTRO ON control unit u and Agileent data acquisition system m.

44

Fig. 4-3: Tensiile test setup inside i the INS STRON heatiing chamber.

4.2.3

Resullts Tensille cyclic loaading, unload ding and relloading was conducted on a specim men at

near room tem mperature att 22oC as sho own Fig. 4-44 . The material, PP, hadd an elasto-pplastic behavior. As it was obsserved, theree is a graduual decay off the elasticc modulus inn the reeloading sections. This observation was shown in the workk of Grytten eet al. (2009)). The en ngineering stress-strain s relationship p of PP is noonlinear in tthe elastic doomain. The yield sttrength was taken to be the stress at a the point of maximum m change enngineering sstress, which w corresp ponded in most m cases to o the maximuum stress inn the engineeering stress-sstrain cu urve. The PP P specimenss went throu ugh a full drrawing up too the failure, no neckingg was ob bserved.

45

20

Engineering stress e (MPa)

E3

E2

E1

E4

16

12

8

4

0 0.00

0.05

0.10

0.15

0.20

0.25

Engineering strain e Fig. 4-4: Tensile engineering stress vs. engineering strain relationship of cyclically loaded PP at a nominal test strain rate of 0.100 min-1at 22oC.

The engineering stress-strain relationship of PP at different temperature and strain rate are shown in Fig. 4-5. After yielding, the stress-strain relationship was nearly perfectly plastic behavior at all strain rates and temperatures. Quantifying the temperature effect, at the same strain rate, the overall stress level decreased with increasing temperature. At a strain rate of 0.300 min-1 the yield strength was 25.6 MPa at 22oC and 10.0 MPa at 90oC, a 61% decrease in yield strength for about 300% increase in temperature. On the other hand, the yield strength increased with increasing strain rate at 22oC, but no variation was observed with increasing strain rate at 60 and 90oC within the strain rate range studied. At 60 and 90oC, a volume increase of the specimens was observed during test and remained permanent as shown in Fig. 4-6. This precluded the use of any “no volume” change criteria to model the material behavior at within these

46

teemperature ranges. r The studied PP was w a visco-elasto-plasttic material in tension. B Based on n lateral straain measurem ment, the Poisson ratio w was 0.3 at neear room tem mperature.

30 0 0.300/m min T22 0.030/m min T22

Engineering stress e (MPa)

25 5

0.003/m min T22 0.300/m min T60

22 oC

20 0

0.030/m min T60 0.300/m min T90

15 5

60 oC 0.030/m min T90

10 0

90 oC

5

0 0.00

0.10

0.20

0.30

0.40 0

0.50

0.60

0.70 0

0.80

E Engineering g strain e Fig. 4-5: Engin neering stresss vs. engineeriing strain relaationship of uunfilled polyppropylene at variou us strain ratess and temperaatures.

90 0oC

22oC

Fig. 4-6: Picturres of PP speccimens at the end of tensille test at 22 annd 60oC.

47

4.3.

Tensile properties of polypropylene with glass microsphere filler Uniaxial direct tension tests were conducted on GM specimens at variable strain

rate

between 0.003/min and 0.300/min and at 22oC (71.6oF), 60oC (140oF) and 90oC

(194oF). All the specimens were checked for homogeneity and weighted before testing. 4.3.1

Specimens preparation Unless otherwise specified, the polypropylene with glass microsphere filler (GM)

tensile specimens were prepared as described in section 4.2.1. 4.3.2

Testing procedure Unless otherwise specified, the testing procedure is the same as specified in

section 4.2.2. 4.3.3

Results In the case of GM, with a density of 0.79 g/cm3, it was observed that the

engineering stress-strain relationship is nonlinear in both elastic and inelastic domain as shown in Fig. 4-7. The initial yielding was followed by nearly perfectly plastic state with some slight increase in stress level near the fracture point in some cases. Quantifying the temperature effect, at the same strain rate, the overall stress level decreased with increasing temperature; i.e. at a strain rate of 0.300 min-1 the yield strength was 9.0 MPa at 22oC and 4.0 MPa at 90oC, a 56% decrease in strength for about 300% increase in temperature. The stress level increase with increasing strain rate at all temperatures in the strain rate range studied. The addition of glass microsphere in this proportion to polypropylene decrease it yield strength besides increasing its thermal insulation properties. The nonlinear behavior was more pronounced.

48

At 60 and 90oC, a volume inccrease of thee specimens was observeed during tesst and reemained permanent as observed o in Fig. F 4-8. Thiis precludedd the use of any “no voluume” ch hange criterria to model the materiaal behavior at within thhese temperaature ranges. The sttudied GM was a visco o-elasto-plasstic materiall in tension.. Based on the lateral sstrain measurement m t, the Poisson n ratio was 0.25 0 at near rroom temperrature.

10 0.300/miin T22

Engineering stress e (MPa)

22 2 oC

8

0.150/miin T22 0.030/miin T22 0.030/miin T60

6

60 0 oC

0.300/miin T60 0.300/miin T90 0.030/miin T90

90 0 oC

4

2

0 0.00

0 0.10

0.20

0.30

0.40 0

0.50

0 0.60

0.70

0.80

E Engineering s strain e Fig. 4-7: Engin neering stresss vs. strain of polypropylenne with glass microsphere filler at varioous strain n rates and tem mperatures.

22oC

90oC Fig. 4-8: Picturres of GM specimens at th he end of tensiile test at 22 aand 90oC.

49

4.4.

Tensile properties of polypropylene with 65% glass filler Uniaxial direct tension tests were conducted on GF specimens at variable strain

rate

between 0.003/min and 0.300/min and at 22oC (71.6oF), 60oC (140oF) and 90oC

(194oF). All the specimens were checked for homogeneity and weighted before testing. 4.4.1 Specimens preparation Unless otherwise specified, the polypropylene with 65% glass filler tensile specimens were prepared as described in section 4.2.1. 4.4.2

Testing procedure Unless otherwise specified, the testing procedure is the same as specified in

section 4.2.2. 4.4.3

Results Tensile cyclic loading, unloading and reloading was conducted on a specimen at

near room temperature at 22oC as shown Fig. 4-9. The material, PP, has an elasto-plastic behavior. As it was observed, there is a decay of the elastic modulus in the reloading sections. GF engineering stress-strain relationships were nonlinear in both elastic and inelastic domain as shown in as shown in Fig. 4-10. The initial yielding was followed by a sudden drop in the stress level and a steady decrease in the stress level until fracture at all strain rates and temperatures. Quantifying the temperature effect, at the same strain rate, the yield strength decreased with increasing temperature. When the strain rate was 0.300 min-1 the yield strength was 16.0 MPa at 22oC and 6.8 MPa at 90oC, a 58% decrease in strength for about 300% increase in temperature. The stress level increased with increase in strain rate at all temperatures within the strain rate range studied. The

50

65% addition of glass to polypropylene decrease it yield strength and made the resulting composite stiffer and more brittle at near room temperature, 22oC. The nonlinear behavior was more pronounced. At 60 and 60oC, a volume increase of the specimens was observed during test and remained permanent as observed in Fig. 4-11. This precluded the use of any “no volume” change criteria to model the material behavior within these temperature ranges. The studied GF was a visco-elasto-plastic ductile material in tension. Based on the lateral strain measurement, the Poisson ratio was 0.3 at near room temperature.

Engineering stress e (MPa)

16 14 12 10 8 6 4

tot

2 0 0.00

p

0.02

0.04

0.06

0.08

0.10

Engineering strain e

Fig. 4-9: Tensile engineering stress vs. engineering strain relationship of cyclically loaded GF at a nominal test strain rate of 0.010 min-1.

51

18 0..300/min T22

16

Engineering stress e (MPa)

14

0..100/min T22 22 oC

0..030/min T22 0..005/min T22

12

0..300/min T60 0..100/min T60

10 60 oC

8

0..030/min T60 0..300/min T90 0..100/min T90

6 90 oC 9

0..030/min T90

4 2 0 0..00

0.10

0.20

0.30

0.4 40

0.50

0.60

0 0.70

0.80 0

E Engineerin ng strain e Fig. 4-10: Eng gineering stresss vs. engineeering strain reelationships off polypropyleene with 65% % glass fillerr at various sttrain rates and d temperaturees.

Fig. 4-11: Pictu ures of GF sp pecimens at th he end of tenssile test at 22 and 60oC.

52

4.5. 4

Com mpression test t Comp pression testts were cond ducted on cyylindrical laayer compossites specim mens to

determine the stress-straain relationsship of eachh material: unfilled poolypropylenee (PP), polypropylen ne with glass microspherre filler (GM M) and polyprropylene with 65% glass filler (G GF). 3D Dig gital Image Correlation C (DIC) system m was used tto monitor thhe strain fieldd.

4.5.1

Specimens prepa aration c n specimenss were corred throughh the full tthickness off the The compression

nsulation witth the steel pipe p as show wn in Fig. 44-12(a). Thee compressioon specimens had in 50 mm for diameter d and d 100 mm for f height w with the steeel layer. Thee total insullation height was 70 mm. PP is the white layer on topp, GF is thee middle layyer and the llower grreen layer is the epox xy. The com mpressions specimens w were preparred for 3D DIC measurement m t as describeed in sectio on 3.3.2. Thhe axial straains in eachh layer weree also measured m usin ng strain gag ges as shown n in Fig. 4-112(b).

a.)

b.)

Fig. 4-12: Pictu ures of comprression specim men.. a.) Com mpression speecimen with sspeckle for 3D D DIC measuremen nt, b.) Compreession specim men instrumennted with strain gage.

53

4.5.2

Testin ng procedurre The compression tests were conducted c w with an INST TRON servoohydraulic teesting

machine m at co onstant nom minal strain rates, r nom, oof 0.003 minn-1 as shownn in Fig. 4-113. A raandom speck kle pattern was w applied, as describedd in section 3.3.2 on thee surface as show in n Fig. 4-12((a). The macchine load cell c and straiin gages siggnals were rrecorded witth the Agilent A data acquisition a system. s The sttrain field was w measured d using 3D D DIC system m to overpasss the bulgingg that th he specimens go through h under comp pression. Thhe load cell ssignal was allso amplifiedd and seent to the analog input of the DIC sy ystem.

Fig. 4-13: Com mpression speecimen in the INSTRON teesting machinne.

4.5.3

Resullts The uniaxial u com mpression deeformation ffield output from the 3D D DIC is shhown

Fig. F 4-14. The T DIC reeconstructed d the 3D vieew of the ccylindrical ssample from m the cu urvature of the specklee. The threee layers off polymer in Fig. 4-122(a) deform mation differences caan be noticeed in Fig. 4--14 (a), incluuding the boottom steel w which is thee dark

54

blue. The bullging of the specimen s ex xplained the increase of diameter in Fig. 4-14 (cc) and

Engineering g g axial strain e ((%))

(d d).

b.)

c.)

d.)

Engineering g g axial strain e ((%))

a.)

Fig. 4-14: Straain field from m the 3D DIIC of the uniiaxial strain oof the compoosite specimeen in co ompression att 0.003 min-1. (a.) Early sttage in the elaastic domain,, (b.) Later sttate in thee elastic domain, (c.) In the plastic dom main.

Comp pressive cycclic loading g, unloadingg and reloaading was conducted on a sp pecimen at near n room teemperature at a 22oC as sshown in Figg. 4-15. The material, PP P and GF G had an elaasto-plastic behavior. b Bo oth PP and G GF engineeriing stress-strrain relationnships

55

were nonlinear in both elastic and inelastic domain. The initial yielding was followed by gradual hardening. The hardening was more pronounced in the case of PP. The PP compressive yield strength was 34.5 MPa, 1.9 times the tensile yield strength which was 18 MPa at the same test strain rate of 0.003 min-1. The GF Compressive yield strength was 41 MPa, 2.9 times the tensile yield strength which was 14 MPa at the same test strain rate of 0.003 min-1. The addition of 65% of glass to polypropylene increase its compression strength

and made the resulting composite

stiffer at near room temperature. The strain gage record is compared to the 3D DIC in Fig. 4-16. Both results compared quite well.

50

Engineering stress e (MPa)

PP (DIC) 40

GF (DIC)

30

20

10

0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Engineering strain e Fig. 4-15: Compressive engineering stress vs strain relationships PP and GF at the nominal test strain rate of 0.003 min-1.

56

50

Engineering stress e (MPa)

GF (SG) 40

GF (DIC)

30

20

10

0 0.00

0.01

0.02

0.03

0.04

0.05

Engineering strain e Fig. 4-16: Compressive stress vs strain relationships of polypropylene with 65% glass filler at various strain rates and temperatures.

4.6.

Composite behavior A special shear test configuration was designed to assess the shear capacity of the

interfaces between the layers. Four point bending tests were conducted on the layered composites beams cut out of the pipe insulation system. The four points bending test was selected because it provided, for analysis, a domain of pure bending moment, two locations of maximum shear and two locations of combined maximum shear bending moment as shown in Fig. 4-25.

57

4.6.1

Specimens preparation Prismatic specimens of constant rectangular cross section were cut out of the

insulated pipe in the longitudinal direction. The specimens which had all the insulation layer and the steel, were use interface shear tests and the specimens with only the insulation materials as layers were used four points bending. The composite beams were approximately 362 mm (14.25 in) long, 70 mm (2.76 in) high in average, and 38 mm (1.5 in) width. Layer 0 is steel, layer 1 is the epoxy, layer 2 is the GF, the layer 3 is the unfilled polypropylene (PP) and layer 4 is the solid polypropylene.

Notch up to the interface

362 38

70

4 0

1

3

2

2

3 4

1

a.)

b.)

Fig. 4-17: Tests specimens’ sketches. a.) Typical composite beam specimen, b.) Shear test specimen.

4.6.2

Testing procedure The interface shear and four points bending tests were displacement controlled.

The load was measured with a load and the 3D DIC system was used to monitor the deformation along with strain gage. The specimens target surface were prepared for the 3D DIC deformation field monitoring as described in 3.3.2. The four points bending test

58

was w setup as shown in Figg. 4-18 (a) an nd the interfface shear teest was setupp as shown inn Fig. 4--18 (b). Tw wo interfacess were testeed: the inteerface betweeen the epooxy and thee GF,

in nterface 1-2, and the inteerface betweeen the GF annd PP, interfface 2-3.

P

P

101.6 mm (4'') 4 0 3 2

304.8 mm m (12'') 1

a.)

b.)

Fig. 4-18: Testts specimens’ sketches. a.) Typical com mposite beam specimen, b.)) Four points ben nding setup. All A dimension ns are in mm..

ures of the in nterface shear test setup in tthe lab with tthe 3D DIC syystem . Fig. 4-19: Pictu

59

Fig. 4-20: Pictu ures four poin nts bending seetup in the labb with the 3D D DIC system m.

4.6.3

Interfface shear tests results The in nterfaces beh haviors were quasi britttle when faillure occurreed. Thereforee, the

sh hear stressess are plotted with the tim me. The interrface 1-2, eppoxy-GF, shhear test is shhown in n Fig. 4-21. No N failure waas recorded. It sustainedd the shear foor of 12 MPaa. This inteerface iss considered as full bond ded interfacee. 14.0

Shear stress (MPa)

12.0 10.0 8.0 6.0 4.0 2.0 0.0 0

250

500

750

1000

1250

Time (sec) ( Fig. 4-21: Sheaar stress variaation with tim me of the interrface 1-2: Eppoxy –GF inteerface

60

The interface 2-3 shear tests results are shown in Fig. 4-22. The shear capacity the varied between 0.75 to 1.25 MPa and the failure were brittle. 1.6

Shear stress (MPa)

1.2

0.8

0.4

0.0 0

100

200

300

400

Time (sec) Fig. 4-22: Shear stress variation with time of the interface 2-3: GF –PP interface

4.6.4

Four points bending tests results It was observed that the beam failed by fracture of layer 2 right below the loading

point at the loading rate of 0.578 in/min or higher as shown in Fig. 4-23 (b) . The crack then propagates through the layer 2, layer 3 and 4 to the complete failure of the composite beam. At low loading rate of 0.015 in/min no failure was observed despite large deformation as shown in Fig. 4-23 (a). It was then concluded that polypropylene with 65% glass filler of layer 2 stress-strain relationship depends on the strain rate of loading.

61

a.)

b.)

Fig. 4-23: Fou ur points bend ding test. a.) Displacement D t rate of 0.0155 in/min, b.) D Displacementt rate of 2.750 2 in/min.

Fig. 4-24: Com mplete failuree of the beam at the displaccement rate oof 2.750 in/miin.

From the momentt and shear diagram, d seee Fig. 4-25, tthe crack staarted in layeer 2 at th he location of o maximum m stress and strain: the llocation of ccombined m maximum bennding moment m and maximum m sh hear force in n the tensile zzone.

62

xy

Shear V

xy

xy

xy

+P -P

+ TOP

xx

xx

xx

(C)

(C)

(C)

xx

xx

xx

(T)

(T)

(T)

xx

xx

xx

(C)

(C)

(C)

xx

xx

xx

(T)

(T)

(T)

+PL/3

Moment M BOT.

= TOP

BOT.

xy

xy

xy

xy

xy

xy

xy

xy

Fig. 4-25: Moment and shear diagram of the four point bending with stress states in the elastic domain.

4.7.

Summary and discussion (1) The comparison of the engineering stress-strain relationships of all three materials at a strain rate of 0.030/min and temperatures of 22oC and 90oC is shown in Fig. 4-26. The unfilled polypropylene has the highest yield strength at both temperature followed by the polypropylene with 65% glass filler.

63

(2) As expected, polypropylene with 65% glass filler has the highest elastic modulus and polypropylene with glass microsphere filler the lowest elastic modulus. (3) The addition of the glass microsphere to polypropylene in this case decreased it elastic modulus but maintained it ductility, at 22oC. The same observations were recorded at the strain rate of 0.300/min as shown in Fig. 4-27. The stress levels are consequently higher due to the strain rate level. (4) The tensile yield strengths of the materials are compared to the published data in Fig. 3-2. (5) The compressive yield strengths of PP and GF are respectively 2 and 3 times higher that their tensile yield strength. (6) From the results of the four points bending tests, it was concluded that the fracture initiation in the composite layered beams is dependent on stress concentration and strain rate level. It initiated inside the polymer composite layer, here GF, and then propagates through layers and interfaces. It is only noticed when it reaches the surface. Since the fracture initiates in the internal insulation layer, it is then difficult, almost impossible to be detected before it breaks out. It then requires a control over the mechanical parameters which trigger it: the stress level and strain rate level.

64

25 PP 0.030/min T22

Engineering stress e (MPa)

GF 0.030/min T22

20

GM 0.030/min T22 PP 0.030/min T90 GF 0.030/mim T90

22 oC

15

GM 0.030/min T90

10

90 oC

5

0 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

Engineering strain e Fig. 4-26:

Comparison of engineering stress-strain relationship of unfilled polypropylene, polypropylene with 65% glass filler and polypropylene with glass microsphere filler at 22 and 90 oC at a strain rate of 0.030 min-1. 30 PP 0.300/min T22 GF 0.300/min T22

Engineering stress e (MPa)

25

GM 0.300/min T22 PP 0.300/min T90

20

GF 0.300/mim T90 22 oC

GM 0.300/min T90

15

10

90 oC

5

0 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

Engineering strain e Fig. 4-27: Comparison of engineering stress-strain relationships of unfilled polypropylene, polypropylene with 65% glass filler and polypropylene with glass microsphere filler at 22 and 90oC at a strain rate of 0.300 min-1.

65

40 Hansen et al. (2005)

Tensile yield strength y (MPa)

35

Guidetti et al. (1996)

30

Hansen et al. (2002) GF

This study

25 20

PP

15 GM

10 5 0 0

1

2

3

4

5

6

7

8

9

10

Data sets Fig. 4-28: Published tensile yield strength of polypropylene composites used for subsea pipe insulation and data of this study obtained at a strain rate of 0.300 min-1. PP: Unfilled polypropylene, GM: Polypropylene with glass microsphere filler, GF: Polypropylene with 65% glass filler

66

5. FRACTURE CHARACTERIZATION 5.1.

Introduction Behavior of brittle and ductile materials will be very much affected by cracks and

voids defects in the materials. Also the behavior will be affected by the size, shape and orientation of the cracks. Since the materials go through drawing instead of necking under direct tension, two additional stress concentration specimens were designed considering the work of Popov (1976) and Frocht (1933). A symmetrically double edge grooved (DT) and a symmetrically notched double edge grooved (NDT) tensile specimens were designed. The former (DT) specimens were used to determine stress concentration factors by Frocht using the photoelasticity (Frocht 1933). The stress concentration due to the presence of cracks are relatively high when the material behaves the material behaves elastically. Inelastic behavior tends to reduce these factors. The configurations of these specimens allowed high local stresses concentration due to the abrupt change in the cross-sectional area. We, consequently, created known locations of stress concentration where we monitored the effect of stress level evolution with the material deformation and failure. Furthermore, due to the presence of voids in the materials such as glass microsphere or debonding between the matrix (PP) and the glass particles, it is important to investigate cracks in the materials. Voids coalescence at the microstructural level in materials with periodic distributions of voids was the basis of Tvergaard (1982) modification of Gurson yield criterion for porous material (Jirasek and Bazant 2001). A Digital Image Correlation system was used to monitor the full deformation field at the surface of the specimens.

67

5.2.

Tensile testing of unfilled polypropylene specimen with circular hole Tensile tests were conducted on specimens with center hole to determine the effect

of strain rate on the failure. Unfilled polypropylene material was used in this study. The focus was on the quantification of the strain rate variation, due to the stress concentration, around the hole and its effect on the material stress-strain behavior and failure. 5.2.1 Specimens preparation The material used in this study was the unfilled polypropylene. The tensile specimen, as shown in Fig. 5-1, with gage section dimensions 75.0 mm x 14 mm x 5.5 (l x d x t) mm were machined directly from the insulation layer. The center hole of diameter 1.6 mm and 3.2 mm were drilled using a drilling machine. If r is the radius of the hole and d the width of the specimen, the ratio r/d is indicative of the stress concentration around the center circular hole (Popov 1976). 5.2.2 Testing procedure The tensile tests were conducted with a screw driven type testing machine at the nominal strain rates, nom, of 0.003 and 0.030 min-1 as shown in Fig. 5-2. A random speckle pattern was applied, as described in section 3.3.2, on two of the specimen’s surface afterwards. The machine load signal and the strain gage based clip-on extensometer signal were recorded via an Agilent data acquisition system. The load cell signal was also amplified and sent to the analog input of the DIC system.

68

d L

t

Hole y z x

Fig. 5-1: Sketcch of the tensiile specimen with w circular hole at the ceenter.

a.) a

b.)

s (a.) DIC, and Agilen nt data acquissition system... (b) Sspecim men held betw ween Fig. 5-2: Test setup: gripss.

5.2.3

Resullts As sho own in Fig. 5-3 (b), all the t specimenns failed alonng the planee perpendicuular to

th he displacem ment direction n which wen nt through thhe circular ceenter hole w with necking..

69

a.)

bb.)

Fig. 5-3: Failurre mode of PP P with circulaar center holee.

The engineering stress-strain s relationshipps of the PP specimens w with circularr hole of diameter 0.0, 0 1.6 and 3.2 3 mm are shown s in Figg. 5-4. The ttest at the noominal strainn rate was w 0.003 min-1. The en ngineering sttrain e, recoorded here, is the globaal strain obtained frrom the clip p-on extensometer which spannedd 50.8 mm over the ciircular hole.. The en ngineering stress s was caalculated at th he center hoole line wherre the materiial failed. The engineering e tensile yield strength  y and the apparent ellastic modullus E in ncreased witth the diametter of the cirrcular hole w with the testss conducted at a strain raate of 0.003/min. This T was a hardening behavior. IIn contrary,, the apparent ductilityy () ore brittle beehavior. y increased bby 20 from 00.0 to decreased draastically. This was a mo 1.6 mm diam meter and by y 30% from 0.0 to 3.2 ddiameter holle as plottedd in Fig. 5-66. The ap pparent ducttility decreassed by 37% from 0.0 too 1.6 mm diaameter hole and stabilizzed as sh hown in Figg. 5-8. The in ncrease of th he yield strenngth with thhe hole diam meter was coounter in ntuitive. Thee same obserrvation was recorded att a strain ratte of 0.030/ min as show wn in Fig. F 5-5 with a 20% incrrease of y and a about 600% decreasee in apparennt ductility .The

70

yield strength increase with center hole diameter seems to stabilized at hole diameter of 3.2 mm as observed in Fig. 5-6. PP transitioned from visco-elasto-plastic ductile behavior to a visco-elasto-plastic brittle with fracture hardening behavior. The following tests

were set to investigate this transitional behavior of the material. 30 dia. 3.2 mm dia. 1.6 mm

Engineering stress e (MPa)

25

dia. 0.0 mm 20

15

= 0.003/min

10

5

0 0.00

0.05

0.10

0.15

0.20

0.25

0.30

Engineering strain e

.

Fig. 5-4: Effect of circular center hole size on tensile engineering stress-strain relationship of

unfilled polypropylene at 22oC and nominal test strain rate of 0.003 min-1. 30 dia. 3.2 mm

Engineering stress e (MPa)

25

dia. 1.6 mm dia. 0.0 mm

20

15

10

5

0 0.0

0.1

0.2

0.3

0.4

0.5

Engineering strain e

Fig. 5-5: Effect of center hole size on engineering stress-strain relationship of unfilled polypropylene at 22oC and nominal test strain rate of 0.030 min-1.

71

30

Yield strength y (MPa)

25

20 0.030/min

15

0.003/min 10

5

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Center hole diameter (mm)

Fig. 5-6: Yield strength variation with center circular hole diameter for unfilled polypropylene at 22oC and nominal test strain rate of 0.030 min-1.

30

Yield strength y (MPa)

25

20 0.030/min

15

0.003/min 10

5

0 0.00

0.02

0.04

0.06

0.08

0.10

0.12

r/d

Fig. 5-7: Yield strength variation with the r/d ratio for unfilled polypropylene at 22oC and nominal test strain rate of 0.030 min-1.

72

10

0.030/min

Apparent ductility 

8

0.003/min

6

4

2

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Hole diameter (mm)

Fig. 5-8: Effect of center hole size on the ductility of unfilled polypropylene at 22oC and a strain rate of 0.030 min-1. 30

Engineering stress e (MPa)

25

20

0.003/min CF 0.030/min CF

15

0.030/min Global 0.003/min Global

10 = 3.2 mm

5

0 0.00

0.05

0.10

0.15

0.20

0.25

Engineering strain e

Fig. 5-9: Comparison of engineering stress-strain relationship at crack front (CF) with the global

one (50.8 mm extensometer) of unfilled polypropylene specimen with 3.2 mm center hole.

The global stress-strain curves of the specimens with the stress-strain curve at the crack front are shown in Fig. 5-9. It was observed that the elastic modulus were higher at the crack front compare to the global ones. After the yield point, most of the deformation

73

was localized in the center hole horizontal line plane. This justified the large deformation recorded at the crack front point.

(i)

Strain energy density

The strain energy density at yield (Uy) and at failure (Uf) was calculated, following equations (5-1) and (5-2), from the stress-strain relationship shown in Fig. 5-4 and Fig. 5-5. The results are plotted in Fig. 5-12 and Fig. 5-13. Both strain energy density, Uy and Uf, decreased with r/d, the size of the crack, but increased with the strain rate. The

effect of strain rate on the strain energy density was shown by plotting the products . with r/d as shown in Fig. 5-13. (5-1) (5-2) 0.8

Strain energy at yield Uy (MPa)

and .

0.6

0.030/min

0.4

0.003/min 0.2

0.0 0.00

0.02

0.04

0.06

r/d a.)

74

0.08

0.10

0.12

Strain energy at failure Uf (MPa)

8.0

6.0

0.030/min

4.0

0.003/min 2.0

0.0 0.00

0.02

0.04

0.06

0.08

0.10

0.12

r/d b.) Fig. 5-10: Variation of the strain energy density with r/d . a.) Strain energy at yield, b.)Strain energy at failure.

0.025

(MPa/min)

0.020

0.015

0.010 0.030/min 0.003/min

0.005

0.000 0.00

0.02

0.04

0.06

r/d a.)

75

0.08

0.10

0.12

0.250

(MPa/min)

0.200

0.150 0.030/min 0.003/min

0.100

0.050

0.000 0.00

0.02

0.04

0.06

0.08

0.10

0.12

r/d b.) Fig. 5-11: Effect of strain rate on the strain energy density. a.) Strain energy at yield, b.)Strain energy at failure.

(ii)

Strain rate effect

Due to the observations above, the full deformation field from the DIC system was studied. The PP tensile specimens used, had gage section dimensions of 95.0 mm x 24.5 mm x 12.7 mm with a circular center hole with a diameter of 2.4 mm. The global engineering stress-strain relationship and at the crack front are plotted in Fig. 5-13. The ratio r/d is equal to 0.05 for this specimen. Unfilled polypropylene tensile stress-strain behavior was proven to be strain rate dependent which was quantified by the increase of the yield strength y, initial elastic modulus Ei, secant modulus at yield Esy and the decrease of the ductility at near room temperature with the strain rate increase. Therefore, the strain evolutions at critical

76

locations, shown in Fig. 5-12, were extracted from the strain field and the strain rates were calculated. The strain field variations in the elastic and plastic domains are shown in Fig. 5-14. As expected, there is a clear variation in the distribution of the axial strain. Around

the circular hole the axial strain is higher in the horizontal A-A plane (yh) than in the vertical B-B plane (yv) in both elastic and plastic domains. This was expected based on the stress concentration around a circular hole in a flat bar under tension (Popov 1976). The ratio, ,

(5-3)

was about 3.4 in the elastic domain, as shown in Fig. 5-14(a), and 27.5 in the plastic domain as shown in Fig. 5-14(c). This ratio change is of an order of 8. It is to mention that these ratios are just indicative of the changes. It was concluded that there is a strain rate distribution effect in the tensile stress-strain behavior of these PP specimens. The circular center hole induced a strain gradient in the GF material behavior in tension, which reached an order of 8 at failure.

B

A

Points of strain rate calculation

A Crack front (CF)

B

Fig. 5-12: Location of the critical strain rate on tensile specimen with center circular hole. The deformed hole is shown.

77

30

Engineering stress e (MPa)

25 DIIC Extensometeer

20

DIIC Crack front 15

= 0.03 30/min 10

= 2.4 mm

5

0 0.00

0.05

0.10

0.15

0.20

0.25

Engineering g strain e

Engineering axial strain e (%)

Fig. 5-13: Eng gineering stresss-strain relatiionship of PP P tensile speciimen with a ggage dimensioon of 95 mm m x 24.5 mm m x 12.7 mm and 2.4 mm ccircular hole at the center.

(a)

(b)

(c)

Fig. 5-14: Straain field from m the 3D DIC C of the uniaxxial strain off a PP specim men with a 2.44 mm diam meter center hole and a test t strain ratee of 0.03 minn-1. a.) Early stage in the eelastic dom main, b.) Lateer state in the elastic domaiin, c.) In the pplastic domaiin.

78

(a)

(b)

(c)

Fig. 5-15: Pictu ure of the PP specimen with 2.4mm cennter hole duriing test from tthe DIC, a) att crack k initiation with w the strain field superim mposed, b.) at crack initiatiion stage, c.) aafter failu ure.

(iiii)

Strain n rate profilee The engineering e strain s evoluttions with tiime along thhe horizontaal line A-A aat six

lo ocations from m the crack front (0.0 mm) m to the specimen eddge are plottted in Fig. 5-16. The T positionss were given n in legend. All the currves presenteed two distinnct sections. The fiirst section spanned s from m 0 to 38 secc into the tesst, and the seection spanneed from 42 ssec in th he test to thee end. The in ntersection of the two zonnes is the yielding pointt of the speciimen. The T curves were w accurateely approxim mated as biliinear. The sllope of in eaach section iis the lo ocal strain raate . Thereffore, we iden ntified that loocally, at thiis critical loccations, theree was a lower strain rate

before yield and a higher aafter yieldinng. The arroow, in Fig. 5-16,

ndicated thatt the yielding g process pro opagated froom the crackk front to thee edge. in

79

The strain rate

was calculated at each point and plotted in Fig. 5-17. The strain

rate before yielding was about 0.040 min-1 close to the nominal test strain rate 0.030 min1

. The maximum strain rate

on A-A was at the crack front and was calculated to be

1.043 min-1. The ratio of the maximum strain rate to the nominal test strain rate ,

(5-4)

is 35 and is characterized as a strain rate amplification factor. The stress-strain behavior of the material governing the fracture is the behavior of the material at the strain rate of



=

.

The engineering strain evolutions with time along the vertical line B-B at six locations, from the center top of the circular hole (0.0 mm) vertically, are plotted in Fig. 5-18. The positions were given in legend. All the curves presented one distinct section.

The curves were accurately approximated as linear. The slope of the line is the local strain rate . The strain rate

was calculated at each point and plotted in Fig. 5-19. The

average strain rate was about 0.035 min-1 close to the nominal test strain rate 0.030 min-1. They were not much variation compare to the value in section A-A. The maximum strain rate

on B-B was 0.039 min-1.The strain rate profile in the A-A direction is the one

controlling the failure mechanism of the specimen with the circular defect.

80

0.25 H1 - 0.0 mm

Engineering strain e

0.20

H2 - 1.6 mm H3 - 3.4 mm

0.15

H4 - 5.2 mm H5 - 6.8 mm

0.10

H6 - 8.6 mm

0.05

0.00 0

10

20

30

40

50

60

Time (sec) Fig. 5-16: Engineering strain variation with time at locations from crack front (0.0 mm)

horizontally (A-A) to the edge of the PP specimen.

1.20 After yielding

Strain rate (e/min)

1.00

Before yielding

0.80

0.60

0.40

0.20

0.00 0

2

4

6

8

10

(A-A) Length (mm) Fig. 5-17: Strain rate variation along A-A from crack front (0.0 mm) horizontally (A-A) to the

edge of the PP specimen. The nominal test strain rate was 0.03 min-1.

81

0.040 V1 - 0.0 mm

Engineeirng strain e 

V2 - 1.8 mm 0.030

V3 - 3.8 mm V4 - 5.5 mm V5 - 7.3 mm

0.020

V6 - 9.6 mm

0.010

0.000 0

10

20

30

40

50

60

Time (sec) Fig. 5-18: Engineering strain variation with time from the top of the circular hole (0.0 mm)

vertically (B-B) of the PP specimen.

0.05

Strain rate (e/min)

0.04

0.03

0.02

0.01

0.00 0

2

4

6

8

10

12

(B-B) Length (mm) Fig. 5-19: Strain rate variation along B-B from the top of the circular hole (0.0 mm) vertically (B-

B) of the PP specimen.

82

5.3. Tensile testing of polypropylene with 65% glass filler specimens with circular hole Tensile tests were conducted on specimens with center hole to determine the effect of strain rate and strain rate variation on the failure mode of these specially configured specimens. Polypropylene with 65% glass filler material was used in this study. We focused on the quantification of the strain rate variation, due to the stress concentration, around the hole and its effect on the material stress strain behaviour and failure. 5.3.1 Specimens preparation The material used in this study was the polypropylene with 65% glass filler. The specimens were as shown in Fig. 5-1, with gage section dimensions 95.0 mm x 25.4 mm x 17.2 mm with a center hole diameter of 2.4 mm. Unless otherwise specified, the specimens were prepared the same way as detailed in section 5.2.1. The ratio r/d was 0.05. 5.3.2 Testing procedure The tests were conducted with an INSTRON servo hydraulic testing machine under displacement control at a strain rate of 0.085 min-1. Unless otherwise specified, the testing procedure was as detailed in section 5.2.2. 5.3.3 Results (i)

Strain rate effect

The full deformation field from the DIC system was studied. The global engineering stress-strain relationship and at the crack front are plotted in Fig. 5-21.

83

Fig. 5-20: Test setup in the IN NSTRON with the Agilent daata acquisition system and thee specimen helld betw ween grips.

The T polyprop pylene with 65% 6 glass fiiller (GF) tennsile stress-sstrain behaviior was provven to be strain ratee dependent which was quantified bby the increease of the yyield strengtth y, in nitial elastic modulus Ei, secant mod dulus at yielld Esy and thhe decrease oof the ductillity at near room tem mperature with w the strain rate increease. Thereefore, the strrain evolutioons at crritical locatiions, shown in Fig. 5-122, were extraacted from tthe strain fieeld and the sstrain raates were callculated. The sttrain field variations in the elastic aand plastic ddomains are shown in F Fig. 4-

17. As expeccted, there iss a clear varriation in thee distributionn of the axial strain. Arround th he circular hole h the axiaal strain is higher h in thee horizontall A-A plane (yh) than iin the vertical B-B plane p (yv) in n both the elastic e and pllastic domaiins. This waas expected bbased on n stress con ncentration around a a circcular in flat bbar under tennsion (Popoov 1976). The raatio

was 15.2 1 in the elastic domaiin, as shownn in Fig. 4-117 (a), and 3386 in

th he plastic do omain as sho own in Fig. 4-17 (c). Thhis ratio channge is of an order of 25. It is to o mention th hat these ratio os are just in ndicative of the changess. It was conncluded that there

84

iss a strain rate r distribu ution effect in the tenssile stress-sttrain behaviior of thesee GF sp pecimens. The T circularr center hole induced a strain grradient in tthe GF material

behavior in teension, whicch reached an order of 25 at failure. 18

Engineering stress e (MPa)

15

12 DIC Ex xtensometer

9

DIC Craack front = 0.085/min

6

3

0 0.00

= 2.4 2 mm 0.05

0..10

0.15

0 0.20

0.25

0.30

0.35

Engineering g strain e

Engineering axial strain e (%)

Fig. 5-21: Eng gineering stresss-strain relatiionshipof GF F tensile speciimen with circcular hole at tthe cen nter at a nomiinal test strain n rate of 0.0855 min-1.

(a) (b) (c) Fig. 5-22: Straain field from m the 3D DIC C of the uniaxxial strain of a GF specim men with a 2.44 mm diam meter center hole h and a teest strain rate of 0.085 minn-1. (a.) Early stage in the eelastic dom main, (b.) Latter state in thee elastic domaain, (c.) In thee plastic domain.

85

(a)

(b) b)

(c)

Fig. 5-23: Pictu ure of the GF F specimen wiith 2.4mm cennter hole duriing test from the DIC, a) aat cracck initiation with w the strain n field superim mposed, b.) aat crack initiattion stage, c.)) after faillure.

(iii)

Strain n rate profilee The engineering e strain s evoluttions with tiime along thhe horizontaal line A-A aat six

lo ocations from m the crack front (0.0 mm) m to the specimen eddge are plottted in Fig. 5-24. The T locations positions were given n in legend. All the cuurves presennted two distinct seections. The first section n spanned frrom 0 to 14ssec into the test, and thee section spaanned frrom 16 sec in i the test to o the end. Th he intersectioon of the tw wo zones is tthe yielding point of the specim men and the curves weree accuratelyy approximat ated as bilineear. The slope of i the local strain s rate . Therefore, we identifieed that locallly, at this crritical eaach section is lo ocations, theere was a lo ower strain rate

befoore yield andd higher aftter yielding.. The

86

arrow, in Fig. 5-24, indicated that the yielding process propagated from the crack front to the edge. The strain rate

was calculated at each point and plotted in Fig. 5-25. The strain

rate before yielding was about 0.125 min-1, in the A-A plan, which 47% higher than the nominal test strain rate of 0.085 min-1. The maximum strain rate,

, on A-A plan was

at the crack front and was calculated to be 2.840 min-1. The ratio of the maximum strain rate to the nominal test strain rate is 33. The stress-strain behavior of the material governing the fracture is the stress-strain behavior of the material at the strain rate of  =

.

The engineering strain evolutions with time along the vertical line B-B at six locations, from the center top of the circular hole (0.0 mm) vertically, are plotted in Fig. 5-26. The locations positions were given in legend. All the curves presented one distinct

section and were accurately approximated as linear. The slope of the line is the local strain rate

. The strain rate

was calculated at each point and plotted in Fig. 5-27. The

average strain rate was about 0.035 min-1 which is 59% lower than the nominal test strain rate 0.085 min-1. It was concluded that, in the case of GF, most of the deformation in the specimen took place near the A-A plane. There were not much variation compare to the

value in section A-A. The maximum strain rate

on B-B was 0.043 min-1. The strain

rate profile in the A-A direction is the one controlling the failure mechanism of the specimen with the circular defect.

87

0.30

H1 - 0.0 mm H2 - 2.9 mm

Engineneing strain e 

0.25

H3 - 5.7 mm 0.20

H4 - 8.6 mm H5 - 10.9 mm

0.15

H6 - 12.1 mm

0.10 0.05 0.00 0

5

10

15

20

25

Time (sec) Fig. 5-24: Engineering strain variation with time at locations from crack front (0.0 mm)

horizontally (A-A) to the edge of the GF specimen. 3.00 After yielding

Strain rate (e/min)

2.50

Before yielding

2.00 1.50 1.00 0.50 0.00 0

2

4

6

8

10

12

(A-A) Length (mm) Fig. 5-25: Strain rate variation along A-A from crack front (0.0 mm) horizontally (A-A) to the

edge of the GF specimen. The nominal test strain rate was 0.085 min-1.

88

0.014 V1 - 0.0 mm

Engineering strain e 

0.012

V2 - 1.5 mm V3 - 3.4 mm

0.010

V4 - 5.6 mm 0.008

V5 - 7.7 mm V6 - 10.8 mm

0.006 0.004 0.002 0.000 0

5

10

15

20

Time (sec) Fig. 5-26: Engineering strain variation with time from the top of the circular hole (0.0 mm)

vertically (B-B) of the GF specimen. The nominal test strain rate was 0.085 min-1.

Strain rate (e/min)

0.05

0.04

0.03

0.02

0.01

0.00 0

2

4

6

8

(B-B) Length (mm)

10

12

Fig. 5-27: Strain rate variation along B-B from the top of the circular hole (0.0 mm) vertically (B-

B) of the GF specimen. The nominal test strain rate was 0.085 min-1.

89

5.3.4 Summary (1)

All the centered circular hole specimens failure surface were through the hole perpendicular to the axial displacement planes.

(2)

Due to the circular hole, there was strain gradient and strain rate variation in the specimen under tension. The maximum strain gradient  was 25.

(3)

A strain rate amplification factor was defined to be equal to the ratio of the maximum strain rate recorded at the crack tip and the nominal strain rate of the test. The maximum strain rate was recorded at the location of crack initiation. was determined to be 33 in this PP specimen.

(4)

The PP stress-strain behavior was proven to be strain rate dependent and brittle at higher strain rate in chapter 3 at near room temperature.

5.4. Tensile testing of double edge grooved specimens without notches (DT) and with notches (NDT) Tensile tests were conducted on symmetrically double edge grooved without notch (DT) and with notched (NDT) specimens to determine the effect of strain rate and strain rate variation on the failure mode of these specially configured specimens. Unfilled polypropylene (PP) and polypropylene with 65% glass filler (GF) were used. We focused on the quantification of the strain rate variation due to stress concentration in these two types of specimens.

90

5.4.1 Specimens preparation The material used in this study was the polypropylene with 65% glass filler (GF). Two types stress concentration specimens were used. The first shown in Fig. 5-28 (a) (DT) had gage section dimensions of 82.0 mm x 25.4 mm x t (l x d x t) mm; the second shown in Fig. 5-28 (b) (NDT) had a gage dimensions of 75 mm x 20.3 mm x t .All the specimens were machined directly from the insulation layer. The semicircular edge groove had a consistent radius of 6.35 mm through the specimens. The r/d ratio was 0.25 for the DT specimens and 0.31 for NDT specimens unless otherwise specified. The notches in NDT specimens are 2 mm wide and 3 mm deep. All the specimens were visually checked for homogeneity before testing. 5.4.2 Testing procedure The tests were conducted on an INSTRON servo hydraulic testing machine under displacement control. Unless otherwise specified, the testing procedure was as detailed in section 5.2.2. The test setup in the INSTRON with the DIC system and the instrumentation on a test specimen in the tension grips is shown in Fig. 5-29. As it can be seen in Fig. 5-29(b), the specimens were also instrumented with the strain gage and extensometer besides the speckle to monitor their deformation. 5.4.3 Results A failed DT specimen still in the tension grip is shown in Fig. 5-30(a). The failure plane was perpendicular to the displacement direction and went through the center of the two semicircular grooves. The crack initiated at the yield strength. The two metallic legs spanning over the grooves are the clip of the extensometer. A NDT specimen in test

91

stage is shown in Fig. 5-38 (b). The speckles at the surface of the specimen are for the DIC system. The global engineering stress-strain relationship of DT and NDT specimens are plotted in Fig. 5-33 and their stress-strain curves at the crack front (CF) are plotted in Fig. 5-34. The crack fronts (CF) are defined in Fig. 5-31 and Fig. 5-32. It can be observed that

the NDT were brittle and had higher elastic modulus and DT specimen presented. The ductility of DT and NDT were 4and 2 respectively. An order of 2 increases, the notches of NDT made the specimens more brittle and stiffer. This difference in the behavior of DT an NDT specimens were investigated by studying the deformation field obtained from the DIC. The strain rate variations in DT and NDT specimens were studied at specific locations as specified in Fig. 5-31 and Fig. 5-32 respectively.

d L

3

r L

r 2

t

t d

y z x

a.)

b.)

Fig. 5-28: Sketch of : (a) symmetrically double edges grooved tensile specimen (DT) and (b) notched symmetrically double edges grooved tensile specimen (NDT). All dimensions are in mm.

92

a.)

bb.)

Fig. 5-29: (a) Picture P of the test setup in the INSTRON N with the DIIC, (b) Picturre showing the insttrumentation on the specim men.

a.)

b.)

Fig. 5-30: a) DT D specimen with w speckless in the tensilee grips at failuure, b) NDT sspecimen withh speeckles in the teensile grips at testing.

93

B Points of strain rate calculation A

A Crack front (CF)

B

Fig. 5-31: Location of the critical strain rate on DT tensile specimen.

B Points of strain rate calculation A

A Crack front (CF)

B

Fig. 5-32: Location of the critical strain rate on NDT tensile specimen.

94

18 0.02/min 2DT - 2

16

0.02/min 2DT - 3 0.02/min 2NDT - 1

14

Engineering stress e (MPa)

0.02/min 2NDT - 3

12 10

= 0.020/min

8 6 4 DT

NDT

2

GLOBAL BEHAVIOR

0 0.00

0.02

0.04

0.06

0.08

0.10

Engineering strain e Fig. 5-33: Comparison of global engineering stress-strain relationship of DT and NDT specimens of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 min-1. 18

Engineering stress e (MPa)

16 14 12

0.02/min 2DT - 2

10

0.02/min 2DT - 3

= 0.020/min

0.02/min 2NDT - 1

8

0.02/min 2NDT - 3

6 4 DT

2 0 0.00

NDT

CRACK FRONT

0.10

0.20

0.30

0.40

Engineering strain e Fig. 5-34: Comparison of engineering stress-strain relationship at CF of DT and NDT specimens of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 min-1.

95

(i)

Strain rate (DT)

The full deformation field from the DIC system was studied. The global engineering stress-strain relationship and at the crack front, for GF DT specimens, are plotted in Fig. 5-35 and Fig. 5-36 respectively for nominal test strain rate of 0.020 min-1 and 0.050 min-1. At higher strain rate, the specimen became brittle. 65% glass filled polypropylene tensile stress-strain behavior was proven to be strain rate dependent which was quantified by the increase of the yield strength y, initial elastic modulus Ei, secant modulus at yield Esy and the decrease of the ductility at near room temperature with the strain rate increase. Therefore, the strain evolutions at critical locations, shown in Fig. 5-31, were extracted from the strain field and the strain rates were calculated. 18

Engineering stress e (MPa)

0.02/min (2DT - 2)

16

0.02/min (2DT - 3)

14

0.05/min (2DT - 7)

12 10 8 6

GLOBAL BEHAVIOR

4 2 0 0.00

0.02

0.04

0.06

0.08

0.10

Engineering strain e

Fig. 5-35: Effect double semicircular grooves on the global engineering stress-strain relationship of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 and 0.050 min-1.

96

18

Engineering stress e (MPa)

16 14 12 0.02/min (2DT - 2)

B

10 A

8

A

0.05/min (2DT - 7)

B

6

0.02/min (2DT - 3)

CRACK FRONT

4 2 0 0.00

0.10

0.20

0.30

0.40

Engineering strain e

Fig. 5-36: Effect double semicircular grooves on engineering stress-strain relationshipat CF of polypropylene with 65% glass filler at the nominal test strain rate of 0.020 and 0.050 min-1.

The strain field variations of GF DT, at the nominal test strain rate of 0.020 min-1, in the elastic and plastic domains are shown in Fig. 5-37. As expected, there is a clear variation in the distribution of the axial strain. The axial strain is higher in the horizontal A-A plane (yh) than in the vertical B-B plane (yv) in both the elastic and plastic domains. This was expected based on stress concentration study on DT specimen (Frocht 1933). As it was observed in Fig. 5-38, a crack initiated at the center of one semicircular groove (a). The failure plane is as detailed above. The ratio

was 16.9 in the elastic domain, as shown in Fig. 5-37(a), and 193 in

the plastic domain as shown in Fig. 5-37 (c). This ratio change is of an order of 11.4. It is to mention that these ratios are just indicative of the changes. It was concluded that there is a strain rate distribution effect in the tensile stress-strain behavior of GF DT specimens.

97

The T semicirccular groovees induced a strain graadient in thhe GF mateerial behavior in

Engineering axial strain e

teension, which reached an n order of 11 1.4 at failuree.

(a) (b) (c) Fig. 5-37: Straain field from the 3D DIC of o the uniaxiaal strain of a D DT GF specim men at a test strain -1 ratee of 0.020 min . (a.) Early y stage in the elastic domaain, (b.) Laterr state in the eelastic dom main, (c.) In th he plastic dom main.

(a)

(b)

((c)

Fig. 5-38: Pictu ure of the GF F DT specimen during test from the DIC C, a)Before crrack initiationn b.) At crack initiatio on with the strain field supperimposed, cc.) After failurre.

98

(iii)

Strain n rate (NDT) T) The strain field variations v off GF NDT, at the nom minal test strain rate of 00.020

min m -1, in the elastic and plastic domains are shoown in Fig. 55-39. As exppected, theree is a cllear variatio on in the disstribution off the axial strain. The axial strain is higher in the horizontal A--A plane (yh t vertical B-B plane (yv) in bothh the elasticc and y ) than in the plastic domaiins. As it waas shown in Fig. F 5-40(b), a crack initiiated at the u upper cornerr both notches and propagated towards thee center (c)). The failurre plane waas horizontal and d nt direction as a it was in thhe case of D DT specimens. particular to displacemen The raatio

was virtually v infiinite in the eelastic domaain, as show wn in Fig. 5-339(a),

nd 1220 in absolute a valu ue in the plastic domain as shown inn Fig. 5-39(c)). It is to meention an th hat these ratiios are just indicative i off the changees. It was cooncluded thaat there is a sstrain raate distributiion effect in n the tensilee stress-strainn behavior of GF NDT T specimens. The

notches inducced a strain gradient, in the GF matterial behaviior in tension, which reaached

Engineering axial strain e

viirtually 1220 0 at failure.

(a) (b) (c) Fig. 5-39: Straain field from m the 3D DIC C of the uniaxxial strain of a NDT GF sspecimen at a test straain rate of 0.0 020 min-1. (a.) Early stage in the elasticc domain, (b.) Later state in the elasstic domain, (c.) ( In the plastic domain. \

99

(a)

(b)

(c)

Fig. 5-40: Pictu ure of the GF F NDT specim men during tesst from the DIC, a) before crack initiation with the strain fiield superimp posed b.) at crrack initiationn, c.) at failuree.

(iiii)

Strain n rate profilee (DT) The axial a engineeering strain, e, profile hhorizontally along A-A iin time is pllotted

in n Fig. 5-41. It is 50% higher at the edges symm metrically, thhe cracks froont, to the ccenter before yieldin ng and 30% % higher afteer yielding. The profilee of e alonng B-B in tim me is plotted in Fig g. 5-42. It caan be observ ved that all th the deformattions are at tthe center off B-B n the failure plane A-A., the intersecction of bothh axes. on The engineering e strain s evoluttions with tiime along thhe horizontaal line A-A aat six lo ocations from m the centerr (0.0 mm) to t the specim men edge , tthe crack froont, are plottted in

Fig. F 5-43. Th he locations positions were w given iin legend. A All the curvees presentedd two distinct sectio ons. The firsst section sp panned from m 0 to 40sec into the testt, and the seection panned from m 50 sec in the test to the end. Thhe intersecttion of the ttwo zones iis the sp

100

yielding point of the specimen and the curves were accurately approximated as bilinear. The slope of each section is the local strain rate . Therefore, we identified that locally, at these locations, there was a lower strain rate

before yield and higher after yielding. The

arrow, in Fig. 5-43, indicated that the yielding process propagated from the cracks front, from the edges, to the center where they met. The strain rate

was calculated at each location and plotted in Fig. 5-44. The

strain rate before yielding was about 0.040 min-1, in the A-A plan, which was 50% higher than the nominal test strain rate of 0.020 min-1. The maximum strain rate,

, on A-A

plan was at the crack front and was calculated to be 0.630 min-1. The ratio of the maximum strain rate to the nominal test strain rate is 31.5. The stress-strain behavior of

the material governing the fracture is the stress-strain behavior of the material at the strain rate of 

=

0.25 67 sec

Engineering strain e

0.20

63 sec 50 sec

0.15

38 sec 0.10 B

A

0.05

A

B

0.00 0

5

10

15

20

25

30

35

(A-A) Distance (mm) Fig. 5-41: Profile of the engineering strain along A-A evolution with time of GF DT specimen. The test nominal strain rate was 0.020 min-1.

101

0.20

Engineering strain e

67 sec 0.16

63 sec 50 sec

0.12

38 sec

0.08

B

A

A

B

0.04

0.00 0

20

40

60

80

100

(B-B) Distance (mm) Fig. 5-42: Profile of the engineering strain along B-B evolution with time of GF DT specimen. The nominal test strain rate was 0.020 min-1. 0.25

Engineering strain e 

H1 - 0.0 mm H2 - 2.9 mm

0.20

H3 - 5.7 mm H4 - 8.6 mm

0.15

H5 - 10.9 mm H6 - 12.1 mm

0.10

0.05

0.00 0

10

20

30

40

50

60

70

80

Time (sec) Fig. 5-43: Engineering strain variation with time at locations from the center (0.0 mm) horizontally along B-B of a DT GF specimen. The test nominal strain rate was 0.020 min-1.

102

0.70

Strain rate (e/min)

0.60 0.50 0.40

After yielding 0.30

Before yielding 0.20 0.10 0.00 0

2

4

6

8

10

12

14

(A-A) Length (mm) Fig. 5-44: Strain rate variation along A-A from the crack front (0.0 mm) horizontally along A-A to the center of a GF DT specimen. The nominal test strain rate was 0.020 min-1.

The engineering strain variations with time along the vertical line B-B at five locations, from the center top (0.0 mm) vertically along B-B, are plotted in Fig. 5-45. The locations positions were given in legend. All the curves presented two distinct sections and were accurately approximated as linear bilinear. The slope of the line is the local strain rate . The strain rate

was calculated at each point and plotted in Fig. 5-46. The

average strain rate was about 0.027min-1 which is 35% higher than the nominal test strain rate 0.020 min-1. It was concluded that, in the case of GF, most of the deformation in the DT specimen took place near the A-A plane. There were not much variation compare to

the value in section A-A. The maximum strain rate

on B-B was 0.500 min-1 at the

intersection of B-B and A-A. The strain rate profile in the A-A direction is the one controlling the failure mechanism of the GF DT specimens.

103

0.25

V1 - 0.0 mm V2 - 3.2 mm

Engineering strain e 

0.20

V3 - 6.4 mm 0.15

V4 - 10.2 mm V5 - 16.4 mm

0.10

0.05

0.00 0

20

40

60

80

Time (sec) Fig. 5-45: Engineering strain variation with time at locations from the center (0.0 mm) vertically (B-B) of the DT GF specimen. The test nominal strain rate was 0.020 min-1.

0.60

Strain rate (e/min)

0.50

After yielding Before yielding

0.40

0.30

0.20

0.10

0.00 0

3

6

9

12

15

18

(B-B) Length (mm) Fig. 5-46: Strain rate variation along B-B from the center (0.0 mm) vertically along B-B of the GF DT specimen. The nominal test strain rate was 0.020 min-1.

104

(iv)

Strain rate profile (NDT)

The axial engineering strain, e, profile horizontally along A-A in time is plotted in Fig. 5-47. It is 95% higher at the edges symmetrically to the center before yielding, and 50% higher after yielding. The profile of e along B-B in time is plotted in Fig. 5-48. It can be observed that all the deformations are at the center of B-B on the failure plane A-A., the intersection of both axes. The engineering strain evolutions with time along the horizontal line A-A at six locations from the center (0.0 mm) to the specimen edge, the noche, are plotted in Fig. 5-49. The locations positions were given in legend. All the curves presented two distinct

sections. The first section spanned from 4.5 to 6.5 sec into the test, and the section spanned from 7.25 sec in the test to the end. The intersection of the two zones is the yielding point of the specimen and the curves were accurately approximated as bilinear. The slope of each section is the local strain rate . Therefore, we identified that locally, at these locations, there was a lower strain rate

before yield and higher after yielding. The

arrow, in Fig. 5-49, indicated that the yielding process propagated from the cracks front, from the edges, to the center where they met. The strain rate

was calculated at each location and plotted in Fig. 5-50. The

strain rate before yielding was about 0.288 min-1, in the A-A plan, which was 1304% higher than the nominal test strain rate of 0.020 min-1. The maximum strain rate,

,

on A-A plan was at the crack front and was calculated to be 4.712 min-1. The ratio of the maximum strain rate to the nominal test strain rate is 235.6. The stress-strain behavior

of the material governing the fracture is the stress-strain behavior of the material at the strain rate of 

=

105

0.14 5 sec

Engineering strain e

0.12

6 sec 0.10 7 sec 0.08

9 sec

0.06 0.04 0.02 0.00 0

5

10

15

20

25

30

(A-A) Length (mm) Fig. 5-47: Profile of the engineering strain along A-A evolution with time of GF NDT specimen. The test nominal strain rate was 0.020 min-1.

0.12 5 sec

Engineering strain e

0.10

6 sec 7 sec

0.08

9 sec

0.06 0.04 0.02 0.00 0

10

20

30

40

50

60

70

80

(B-B) Length (mm) Fig. 5-48: Profile of the engineering strain along B-B evolution with time of GF NDT specimen. The nominal test strain rate was 0.020 min-1.

106

0.14 H1 - 0.0 mm

Engineering strain e 

0.12

H2 - 1.7 mm H3 - 3.5 mm

0.10

H4 - 5.8 mm 0.08

H5 - 8.1 mm H6 - 9.2 mm

0.06 0.04 0.02 0.00 0

2

4

6

8

10

Time (sec) Fig. 5-49: Engineering strain variation with time at locations from the center (0.0 mm) horizontally along A-A of a NDT GF specimen. The test nominal strain rate was 0.020 min-1.

5.00

Strain rate (e/min)

4.00

3.00 After yielding Before yielding

2.00

1.00

0.00 0

2

4

6

8

10

(A-A) Length (mm) Fig. 5-50: Strain rate variation along A-A from the crack front (0.0 mm) horizontally along A-A to the center of a GF NDT specimen. The nominal test strain rate was 0.020 min-1.

107

The engineering strain variations with time along the vertical line B-B at five locations, from the center (0.0 mm) vertically along B-B, are plotted in Fig. 5-51. The locations positions were given in legend. All the curves presented two distinct sections and were accurately approximated as linear bilinear. The slope of the line is the local strain rate . The strain rate

was calculated at each point and plotted in Fig. 5-52. The

average strain rate was about 0.270min-1 which is 1250% higher than the nominal test strain rate 0.020 min-1. It was concluded that, in the case of GF, most of the deformation in the NDT specimen took place near the A-A plane. There were not much variation

on B-B was 4.7 min-

compare to the value in section A-A. The maximum strain rate 1

at the intersection of B-B and A-A. The strain rate profile in the A-A direction is the

one controlling the failure mechanism of the GF DT specimens. 0.10 V1 - 0.0 mm

Engineeirng strain e 

0.08

V2 - 3.2 mm V3 - 6.4 mm

0.06 V4 - 9.6 mm 0.04

V5 - 13.3 mm

0.02

0.00 0

2

4

6

8

10

Time (sec) Fig. 5-51: Engineering strain variation with time at locations from the center (0.0 mm) horizontally along B-B of a NDT GF specimen. The test nominal strain rate was 0.020 min-1.

108

5.00

After yielding

Strain rate (e/min)

4.00

Before yielding 3.00

2.00

1.00

0.00 0

2

4

6

8

10

12

14

(B-B) Length (mm) Fig. 5-52: Strain rate variation along B-B from the center (0.0 mm) vertically along B-B of the GF NDT specimen. The nominal test strain rate was 0.020 min-1.

5.4.4 Summary (1)

All DT specimens’ failure surface was through the semicircular groove center and perpendicular to the axial displacement planes.

(2)

Due to the circular hole, there was a strain gradient and a strain rate variation in the specimen under tension. The maximum strain gradient  was 11.4.

(3)

The maximum strain rate was recorded at the location of crack initiation at the grooves center. The strain rate amplification factor was determined to be 31.5 in this DT GF specimen.

109

(4)

In the case of the NDT specimens, the failure surface was through the notches end corner and perpendicular to the axial displacement planes.

(5)

Due to the notches, there was a strain gradient and a strain rate variation in the specimen under tension.

(6)

The maximum strain gradient  was 1224. The maximum strain rate was recorded at the location of crack initiation at the grooves center.

(7)

The strain rate amplification factor was determined to be 235.6 in this NDT GF specimen.

(8)

The stress-strain behavior of the material governing the fracture is the stress-strain behavior of the material at the strain rate of 

5.5.

=

Bending test of notched composite beams Four points bending tests were performed on notched beam specimens, machined

out through the full depth of the insulations (composite beams) to investigate the fracture behavior of GM and PP. The four point bending test imposed a mode I fracture at the crack. The crack tip opening displacement (CTOD) and strain rate at the crack tip variation were studied. 5.5.1 Specimens preparation The composite beams were approximately 362 mm (14.25 in) long, H mm high in average, and 38 mm (1.5 in) width as shown in Fig. 5-53 (a). The beam specimens were

110

cut out from the pipe insulation in the longitudinal direction through the full depth. The resulting specimens were composite beams as shown in Fig. 5-55. They were 362 mm (14.25 in) long, 70 mm (2.76 in) high and 38 mm (1.5 in) width. There were two types: one with with layer 2 in GF materials and the second with layer 2 in GM. Type 1: Layer 1 was a 5.4 mm thick epoxy, layer 2 was 45.7 mm thick polypropylene with 65% glass filler, layer 3 was 14.4 mm unfilled polypropylene and layer 4 was 4.5 mm solid polypropylene. Type2: Layer 1 was a 7.9 mm thick epoxy, layer 2 was 31.8 mm thick polypropylene with glass microsphere filler, layer 3 was 22.2 mm unfilled polypropylene and layer 4 was 4.8 mm solid polypropylene. 362 38

H

1 2 3 4

a.)

b.)

c.)

Fig. 5-53: Layered composite beams for four points bending test. a.) Typical specimen, b.) Beam specimen notched up to layer 3, c.) Beam specimen notched up to layer 2.

All the notches were rectangular with 1.5 mm wide as shown in Fig. 5-53 (a). The four points bending test was selected because it provided, for analysis, a domain of pure bending moment, two locations of maximum shear and two locations of combined maximum shear and maximum pure bending moment as shown in chapter 4. The

111

sp pecimen preeparation forr 3D DIC measuremen m nt was as sppecified in cchapter 3 seection 3.3.2.

5.5.2

Testin ng procedurre Four points p bendiing tests on the notchedd beam werre conductedd at displaceement

co ontrolled on n an INSTRO ON machinee as shown in Fig. 5-544 and Fig. 55-55. Quasi static monotonic m an nd cyclic load were perrformed. A random speeckle patternn was applieed, as described in section 3.3..2 on the sp pecimens forr DIC meassurement. The machine load d acquisittion system and was also, in derivaation, siignal was reecorded via an Agilent data am mplified and d sent to the analog inpu ut of the DIC C system. Thhe DIC imagges were recoorded att frequency set dependin ng on the teest displacem ment rate. The tests werre conductedd at a displacement rate of 0.382 and 1.27 mm m (0.05in) per min.

a.)

b.))

Fig. 5-54: Testt setup for fou ur point bendiing test in thee INSTRON ttesting machinne with the 3D DIC C setup. a.)Gllobal view, b..) Close view on the specim men with specckle during teest

112

P

P

101.6 mm (4'') 1 2 3 304.8 mm (12'')

4

Fig. 5-55: Four points bending test configuration.

5.5.3 Results The crack tip opening displacements (CTOD) were monitored at the accuracy of 0.0001 mm with the 3D DIC. The measurement CTOD of was done as described in section 2.4.4. The materials had visco-elasto-plastic behavior which precluded successively the use of LEFM and J-Integral method for fracture characterization.

(i)

Quasi static monotonic loading

The quasi static monotonic tests results are shown in Fig. 5-56, PP had a brittle fracture behavior and GM had a ductile fracture behavior. From the plots of applied force with the CTOD in Fig. 5-57 the critical CTOD (c) were determined: -

for PP c = 4 mm,

-

for GM c = 1.14 mm.

113

20000 17500 15000

Force (N)

12500 No crack

10000

PP start crack (B 1-1 N) PP mid crack (B 2-2 N)

7500

GM start crack (B 3-1 N)

5000 2500 0 0

250

500

750

1000

1250

1500

1750

Time (sec)

Fig. 5-56: Applied force vs. time.

15000

12500

Force (N)

10000

PP start crack (B 1-1 N)

7500

PP mid crack (B 2-2 N) GM start crack (B 3-1 N)

5000

2500

0 0

3

5

8

10

CTOD (mm)

Fig. 5-57: Applied force vs. CTOD.

114

13

15

18

(ii)

Monotonic cyclic and pushover loading

From the monotonic quasi static test it was recorded that the specimen, shown in Fig. 5-53(b), cracked at about 7000 N and became unstable at 7400 N at a displacement

rate of 1.27 mm/min. The monotonic cyclic test was then conducted on a similar beam specimen with the maximum load maintained 7000 N when the crack opened as the same displacement rate of 1.27 mm/min. Five cycles were performed and then the specimen was loaded up to failure (pushover). The load evolution with time of the monotonic cyclic loading and the pushover loading (precracked) is shown in Fig. 5-58. It showed that the consistent displacement rate of 1.27 mm/min maintained a consistent loading rate in both tests.

8000 Cyclic Precracked

Force (N)

6000

4000

2000

0 0

200

400

600

800

1000

Time (sec) Fig. 5-58: Applied force vs. time. The notch in the beam was stopped in PP layer as shown in Fig. 5-53(b).

115

In the five cycles the CTOD was maintained under c , as expected, at 1.2 mm and cracked the specimen without reaching instability. The strain rate at the crack tip was monitored and plotted with time in Fig. 5-60. It was constant in all loading stage and defined as 0.07

.

In the pushover case, the specimen failed at CTOD of 1.84 mm. More than 50% decreased from the monotonic quasi static loading c. In the other hand, the strain rate at 2.37

failure

.

33.9.

The ratio

7500

Force (N)

6000

4500 Cyclic 3000

Precracked

1500

0 0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

CTOD (mm) Fig. 5-59: Applied force vs. CTOD. The crack stopped in PP as shown in Fig. 5-53(b).

116

350

Strain at Crack Tip (%)

300 250 200

Cyclic Precracked

150 100 50 0 0

200

400

600

800

1000

Timee (sec)

Fig. 5-60: Straain rate at cracck tip vs. timee. The crack sstopped in PP P as shown in Fig. 5-53(b).

Fig. 5-61: Fourr points bending failed speecimen.

5.5.4

Summ mary (1) Un nfilled polyp propylene (P PP) was conffirmed to haave a brittle fracture behhavior in four pointts bending, despites thhe ductility observed inn it stress-sstrain relationship.

117

(2) Polypropylene with glass microsphere filler (GM) has stable crack grow in fracture. The critical COTD parameter for fracture variation with cyclic load was quantified. (3) The strain rate amplification factor in the case of notched in the PP layer, was 33.9. This value is within the range

5.6.

Summary and discussion (1) In all cases, the crack initiated in the specimens at the maximum recorded stresses which were considered the yield strength of the materials. (2) There is a strain rate variation in the specimen as expected which quantified with the factor . The strain rate variation was quantified by the strain amplification factor which values are summarized in Table 5-1. (3) The strain rate amplification factor  , 33.9, obtained from the four point bending test was within the range of the values of specimens with circular hole and DT specimens for both PP and GF. (4) The GF stress-strain behavior was proven to be strain rate dependent and brittle at higher strain rate in chapter 3 at near room temperature. This observation was justified in this fracture analysis.

118

Table 5-1: Summary table of strain rate amplification factor SPECIMENS

MATERIALS

r/d

Test (/min)

Max (/min)



GF

0.50

0.020

0.68

34.0

GF

0.50

0.065

2.04

31.4

GF

0.25

0.020

0.65

32.5

GF

0.25

0.020

0.68

34.0

GF

0.25

0.020

0.63

31.5

GF

0.25

0.050

1.98

39.6

PP

0.25

0.020

0.55

27.5

GF

0.05

33.0

PP

0.05

35.0

GF

0.31

0.020

4.7

235.0

PP

0.31

0.020

4.7

235.0

119

6. REPAIR METHODS

6.1.

Introduction Repair materials were investigated for the polypropylene composites.

Polypropylene materials are chemically difficult to be bonded. As requirement for the subsea condition, the require method has to make use of filler material which can withstand the pressure and the temperature.

6.2.

Material parameters Commercially available cyanoacrylate ester was selected as a repair material. The

product was supplied by ACCRAbond Inc. Cyanoacrylate ester is a chemically active liquid that reacts rapidly with other weakly alkaline materials to form hard plastic. Its bonding is a polymerisation process which is activated by alkaline, or moisture, materials to form a hard plastic. The stiffness and resistance to high temperature are the requirements of the repair method.

6.3.

Specimen preparation The specimens were prepared and initialy test up to failure, in tension, as described

in Chapter 4 section 4.2.1 and section 4.2.2 unless otherwise specified.

6.4.

Testing procedure Once the failed specimens were bonded the bonding was tested in a chamber under

high hydrostatic pressure and temperature to simulate the subsea condition. The tensile 120

tests on the repaired specimens were conducted as specified in Chapter 4 section 4.4.2 unless otherwise specified. The tests were conducted at a 0.003 min-1, a quasi-static monotonic loading.

Control temperature and pressure chamber

Repaired specimen

a.)

b.)

Fig. 6-1: (a) Repaired tensile specimen, b.)Repaired tensile specimen in controlled temperature and pressure chamber.

6.5.

Results The tests results are shown in Fig. 4-7 and Fig. 6-3. Since the specimens were

failed, the controlling parameter was the deformation sustained by the repaired specimens. The specimens bonds sustained 100% of the initial deformation sustained by the intact specimens. The residual stresses were 50% of the material yield strength in both cases.

6.6.

Summary and discussion Cyanoacrylate gave initial satisfactory results as a repair material. It sustained the

high temperature and pressure and provides the required ductility.

121

18

Engineering stress e (MPa)

16 14 12 Original 0.090/min

10

Repaired 0.003/min

8 6 4 2 0 0.000

0.005

0.010

0.015

0.020

Engineering strain e

0.025

0.030

Fig. 6-2: Comparison of engineering stress vs. strain of GF tensile specimen and the same specimen after repaired. Test conducted at the nominal strain rate of 0.003/min.

Engineering stress e (MPa)

20

16 Original 0.300/min

12

Repaired 0.003/min

8

4

0 0.000

0.004

0.008

0.012

0.016

0.020

Engineering straine

Fig. 6-3: Comparison of engineering stress vs. strain of GF tensile specimen and the same specimen after repaired. Test conducted at the nominal strain rate of 0.003/min.

122

7. CONSTITUTIVE MODELLING 7.1.

Introduction The assessment of the deformation of a material during its practical application is

one of the driving reasons behind the development of material constitutive model. From the increase in the development of new composites polypropylene (PP), for specific thermo mechanical or chemical properties, came the needs to update the existing constitutive relationships or developed new ones for behavior assessment and prediction for design. Polypropylene composites, mainly polypropylene with glass filler and with glass microsphere filler, used in deep sea pipeline insulation system are the subject of this work. Based on the experimental results presented in chapter 4 and 5: -

stress-strain relationships of the materials were nonlinear in the elastic and inelastic domains;

-

none of the materials showed a clear necking up to the failure of the test specimens;

-

addition of glass particles and glass microsphere to polypropylene increased the elastic modulus, but the yield strength and yield strain were reduced along with the ductility, a constitutive models were developed for yield strength (y), initial elastic

modulus (Ei) and secant modulus at yield (Esy) for polypropylene and glass filled composites in term of strain rate and temperature. A new stress-strain relationship was

123

proposed to model the nonlinear behavior of the composites considering the temperature and strain rate dependency of the material using the three parameters. Influence of the strain rates on the mechanical properties was quantified through the model parameters The nonlinear visco-elasto-plastic, the strain rate and temperature dependency behavior of the composites was considered for the stress strain relationship modeling.

7.2.

Material parameters Three parameters, initial elastic modulus (Ei), yield strength (y) and yields strain

(y) were determined from the stress-strain relationships. The initial modulus is the Young’s modulus and was determined as the initial slope of the stress-strain relationship. The yield strength was the maximum stress sustained by the specimen in the engineering stress-strain relationship. The secant modulus at yield (Esy) was obtained by dividing the yield strength by the yield strain as shown in Fig. 7-1. 6

Engineering stress e (MPa)

5

Ei

y

4

3

Esy

2

1

y 0 0.00

0.10

0.20

0.30

0.40

0.50

0.60

Engineering strain e

Fig. 7-1: The material parameters on a typical engineering stress-strain relationship.

124

7.3.

Modeling of temperature (T) and strain rate ( ) sensitivity From the experimental in chapter 4 shown in Fig. 4-5, Fig. 4-7 and Fig. 4-10 it

was concluded that the investigated unfilled polypropylene (PP), polypropylene with 65% glass filler (GF) and polypropylene with glass microsphere filler (GM) tensile stress-strain behaviors were temperature and strain rate sensitive. The yield strain in all three cases increased with increasing temperature in the temperature range considered. These observations are similar to the observations of Zhou et al. (2002) on unfilled and talc-filled polypropylene. A general dependency of glassy polymers stress-strain behavior on strain rate and temperature was also presented by Arruda et al. (1995). In this study, from the analysis of the tensile tests results described above, we proceeded to model the temperature and strain rate sensitivity of the yield strength, y, the initial elastic modulus, Ei, and the secant modulus at yield, Esy, of each material. For the model, the following assumptions were made: - the first assumption was: all three parameters are function of the strain rate independently of the temperature ; and consequently can be modeled using a single function

specific to each parameter;

- the second assumption was: the temperature effect on all three parameters can be modeled using a single two variables function of the form of the first function

,

which is a modifier

values, and specific to each parameter.

Therefore, the yield strength, y, Ei and Esy, of each material can be modeled using the following functions: . .

, ,

, , and 125

(7-1) (7-2)

.

,

.

(7-3)

7.3.1 Unfilled polypropylene (PP) temperature sensitivity In the case of PP, for about 300% increase of the temperature from 22 to 90oC, the yield strength y decreased by 52% at a strain rate of 0.030 min-1 and 60% at a strain rate of 0.300 min-1 as shown in Fig. 4-26 and Fig. 4-27 respectively. In the same order of analysis, the initial elastic modulus Ei decreased by 69 and 71% and the secant modulus at yield Esy decreased by 60 and 67%. From the observation of the tests data, y, Ei and Esy showed an exponential decay that can be represented as follows: ,

(7-4) →

→



(7-5)

, →



→



, then

(7-6) ,

(7-7)

where is the decay parameter. The variation of ln(y) with T shown in Fig. 7-2 where the relationship was linear,  was 0.0141. Hence the parameter  was independent of the temperature for PP. Test results indicated that  was a function of strain rate ( ) and the proposed relationship is as follows:

. ,

where a and b are material parameters. 126

(7-8)

Variations of ln(i) with T and ln(sy) with T are shown in Fig. 7-3. The relationships are linear, and  is equal to 0.0188. 4.0

0.300/min

ln(y) (MPa)

0.030/min 3.0

2.0

1.0 20

40

60

Temperature

80

100

(oC)

Fig. 7-2: Effect of temperature on yield strength (y) of unfilled polypropylene.

The solution to equation (7-4), the exponential rate of change is as followed: .

where

,

(7-9)

is the yield strength at the reference temperature To and is the function

defined in equation (6-1) . To is 22oC in this study, and by definition T = T-To. multiplier exponential function is Similarly,

,

,

,

,

The

in equation (7-1). ,

and

in equation (7-2) and (7-3) are respectively

defined as followed: . .

and

(7-10)

,

(7-11)

127

where Eio and Esyo are the initial elastic modulus and secant modulus at yield respectively at the reference temperature To. The results of the temperature sensitivity models equations (7-9), (7-10) and (7-11), for PP, are plotted with the tests result for PP in Fig.

8.0

8.0

7.0

7.0

6.0

5.0

Ei

6.0

Esy

5.0

0.300/min 0.030/min

4.0

ln(Esy) (MPa)

ln(Ei) (MPa)

7-4 and Fig. 7-5.

4.0

3.0

3.0 20

40

60

Temperature (oC)

80

100

Fig. 7-3: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of unfilled polypropylene. 30

Yield Strength y (MPa)

0.300/min 25 0.030/min 20 15 10 5 0 20

40

60

Temperature

80

(ȯC)

Fig. 7-4: Effect of temperature on yield strength (y) of unfilled polypropylene.

128

100

2000 0.300/min

1500

1500

0.030/min

1000

1000

500

500

Ei Esy

0

Secant Modulus at yield Esy (MPa)

Initial Elastic Modulus Ei (MPa)

2000

0 20

40

60

80

100

Temperature (oC)

Fig. 7-5: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of unfilled polypropylene.

7.3.2 Polypropylene with glass microsphere filler (GM) temperature sensitivity In the case of GM, for a about 300% increase of the temperature from 22 to 90oC, the yield strength y decreased by 50% for a strain rate of 0.030 min-1 and 65% for a strain rate of 0.300 min-1 as shown in Fig. 4-26 and Fig. 4-27 respectively. In the same order of analysis, the initial elastic modulus Ei decreased by 81 and 85% and the secant modulus at yield Esy decreased by as 77 and 85%. Following the same procedure described in the case of PP in section 7.3.1, y, Ei and Esy were modeled using the equation (7-7) as shown in Fig. 7-6 and Fig. 7-7. From Fig. 7-6,  for y was determined to be 0.0123, and = was conservatively

determined to be 0.0181 for Ei and Esy from Fig. 7-7. The results of the temperature sensitivity models equations (7-9), (7-10) and (7-11), for GM, are plotted with the tests result for PP in Fig. 7-8 and Fig. 7-9.

129

3 0.300/min

ln(y) (MPa)

0.030/min 2

1

0 20

40

60

80

100

Temperature (oĊ) Fig. 7-6: Effect of temperature on yield strength (y) of glass microspheres filled polypropylene.

8.0   0.030/min

7.5

  0.300/min

7.0 6.5

Ei

6.0 6.0 5.5

ln(Esy) (MPa)

ln(Ei) (MPa)

7.0

5.0

5.0

Esy 4.0

4.5 4.0

20

40

60

80

100

Temperature (oĊ) Fig. 7-7: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of glass microspheres filled polypropylene.

130

10

Yield Strength y (MPa)

0.300/min 8

0.030/min

6

4

2

0 20

40

60

Temperature

80

100

(oĊ)

Fig. 7-8: Effect of temperature on yield strength (y) of polypropylene with glass microsphere filler. 2000

Initial Elastic Modulus Ei (MPa)

0.030/min 1500

1500

1000

1000

Ei 500

500

Secant Modulus at yield Esy (MPa)

2000 0.300/min

Esy 0

0 20

40

60

80

100

Temperature (oĊ) Fig. 7-9: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with glass microsphere filler.

131

7.3.3 Polypropylene with 65% glass filler (GF) temperature sensitivity In the case of GF, for a about 300% increase of the temperature from 22 to 90oC, the yield strength y decreased by 50% for a strain rate of 0.030 min-1 and 50% for a strain rate of 0.300 min-1 as shown in Fig. 4-18 and Fig. 4-19 respectively. In the same order of analysis, the initial elastic modulus Ei decreased by 53 and 59% and the secant modulus at yield Esy decreased by as 67 and 67%. Following the same procedure described in the case of PP, y, Ei and Esy were modeled using the equation (6-7) as shown in Fig. 7-10 and Fig. 7-11. From Fig. 7-10,  for y was defined, using equation (6), as followed: 0.0145

0.015. .

(7-12)

From Fig. 7-11., = was conservatively determined to be 0.0265 for Ei and Esy.

3.0

0.300/min 0.090/min 0.030/min

ln(y) (MPa)

2.5

2.0

1.5

1.0 20

40

60

Temperature

80

100

(oĊ)

Fig. 7-10: Effect of temperature on yield strength (y) of polypropylene with 65% glass filler.

132

The results of the temperature sensitivity models equations (7-9), (7-10) and (7-11), for GM, are plotted with the tests results, for GF, in Fig. 7-12 and Fig. 7-13.

9

9 0.300/min 0.030/min

8

7

7

Ei

6

5

6

ln(Esy) (MPa)

ln(Ei) (MPa)

8

5

Esy

4

4 20

40

60

80

100

Temperature (oĊ) Fig. 7-11: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with 65% glass filler. 20

0.300/min

Yield Strength y (MPa)

0.090/min 0.030/min

15

0.003/min 10

5

0 20

40

60

Temperature

80

100

(oĊ)

Fig. 7-12: Effect of temperature on yield strength (y) of polypropylene with 65% glass filler.

133

3750

3750

0.090/min

3000

3000

0.030/min 2250

2250

0.003/min

1500

1500

750

750

Ei

Secant Modulus at Yield Esy (MPa)

Initial Elastic Modulus Ei (MPa)

0.300/min

Esy 0

0 20

40

60

80

100

Temperature (oĊ) Fig. 7-13: Effect of temperature on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with 65% glass filler.

7.3.4 Summary The result of the temperature sensitivity models equations (7-9), (7-10) and (7-11) are all in good agreement with the data of PP, GM and GF.

The thermal decay

coefficients for PP, GM and GT are given in Table 7-1. Table 7-1: Summary table of the thermal decay coefficient .

 Material

y

Ei

Esy

Polypropylene (PP)

0.0141

0.0188

0.0188

0.0123

0.0181

0.0181

0.0145*

0.0265

0.0265

Polypropylene with glass microsphere filled(GM) Polypropylene with 65% Glass filler (GF)

*This value is a constant in an function.

134

7.3.5 Unfilled polypropylene (PP) coupled strain rate and temperature sensitivity The relationship between y and ln( ) is shown in Fig. 7-14, and Fig. 7-15 shows the relationship between Ei, Esy and ln( ) of PP at 22oC. They showed that y, Ei and Esy are linear functions of ln( ) at room temperature. 27

Yield Stress (MPa)

25 23 21 19 17 15 -8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

ln( ̇) (e/min)

Fig. 7-14: Effect of strain rate on yield strength (y) of unfilled polypropylene at 22oC.

Initial Elastic Modulus Ei (MPa)

Ei 1500

375

1000

250

125

500

Esy

Secant Modulus at Yield Esy (MPa)

500

2000

0

0 -8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

ln( ̇) (e/min)

Fig. 7-15: Effect of strain rate on initial elastic modulus (Ei) and secant modulus at yield (Esy) of unfilled polypropylene at 22oC.

135

The slopes of these linear functions quantified the strain rate sensitivities of the yield strength, the initial elastic modulus and the secant modulus at yield respectively of PP. Consequently, the following equations are the

functions of equation (7-1), (7-2)

and (7-3) for PP:

.

,

.

(7-13)

, and

(7-14)

,

(7-15)

.

where, yoo, Eioo and Esyoo are reference y, reference Ei and reference Esy of PP taken to be the value of these parameters at the reference temperature To (22oC) and at the reference strain rate

which is taken to be 0.003/min in this study.

the slopes of the plots

vs.

,

vs.

and

vs.

,

and

are

respectively. These

parameters were determined from the experimental results plotted in Fig. 7-14, and Fig. 7-15 and are given in Table 7-2. Table 7-2: Strain rate coefficients and reference parameters of unfilled and polypropylene with glass microsphere filler yoo

Eioo

Esyoo

(MPa)

(MPa)

(MPa)

Polypropylene (PP)

21.5

1380

Polypropylene with glass microsphere filled(GM)

7.5

552

Material

o

-1 (min ) To ( C)

ay

ai

asy

515

0.996

84.31

3.01

0.030

22

207

0.791

731.61

73.73

0.030

22

Substituting Equation (7-13) into (7-9) gave:

.

.

Similarly: 136

.

(7-16)

.

. .

, and

(7-17)

.

(7-18)

.

Equations (7-16), (7-17) and (7-18) established the strain rate and temperature sensitivity of yield strength, initial elastic modulus and secant modulus at yield of unfilled and polypropylene with glass microsphere filler. Similar relationships were proposed by Zhou et al. (2002) to fit their tensile test data of unfilled and 40% filled polypropylene with test specimens machined from pallets of both materials. 7.3.6 Polypropylene with glass microsphere filler (GM) coupled strain rate and temperature sensitivity From Fig. 7-16 and Fig. 7-17, we can observe that GM parameters have linear relationship with ln( ). Therefore, equations (7-13), (7-14) and (7-15) are valid to model the variation of GM y, Ei and Esy parameters. vs.

vs.

,

and

vs.

,

and

are the slopes of the plots

plotted in Fig. 7-16 and Fig. 7-17, and are

given in Table 7-2. 10

Yield Stress y (MPa)

9

8

7

6

5 -4.0

-3.0

-2.0

-1.0

0.0

ln( ̇) (e/min)

Fig. 7-16: Effect of strain rate on yield strength (y) of polypropylene with glass microsphere filler at 22oC.

137

The complete coupled models for GM y, Ei and Esy parameters are also given by Equations (7-16), (7-17) and (7-18).

2000

Ei

1500

1500

1000

1000

500

500 Esy

Secant Modulus at Yield Esy (MPa)

Initial Elastic Modulus Ei (MPa)

2000

0

0 -4.0

-3.0

-2.0

-1.0

0.0

ln( ̇) (e/min)

Fig. 7-17: Effect of strain rate on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with glass microsphere filler at 22oC.

7.3.7 Polypropylene with 65% glass filler (GF) coupled strain rate and temperature sensitivity The relationship between y and tanh( ) is shown in Fig. 7-18 and Fig. 7-19 shows the relationship between Ei, Esy and tanh( ) of the polypropylene with 65% glass filler at 22oC. The three parameters are linear functions of tanh( ) with strain rate in percentage. A tangent hyperbolic function was adopted from the observation of the evolution of the experimental test results. It was recorded that, within the range of strain rate studies, y, Ei and Esy evolved exponentially up to a certain value and then stabilized up to the end of the domain of interest. Consequently the relationships in Equations (719), (7-20) and (7-21) were adopted,

138



.

.

.

. .

,

(7-19)

, and

(7-20)

.

(7-21)

,

where , a scaling factor for the test strain rate, is a material parameter. Here  is equal to 100. Therefore the strain rate was expressed in %/min. The parameters calculated from the experimental results plotted in Fig. 7-18 and Fig. 7-19 are given in Table 7-3. Table 7-3: Strain rate coefficients and reference parameters of the polypropylene with 65% glass filler Material Polypropylene with 65% Glass filler (GF)

yoo

Eioo

Esyoo

(MPa)

(MPa)

(MPa)

15.6

3520

1460

ay

ai

asy

2.584

1607.70

588.49

o

-1 (min ) To ( C)

0.030

22

Substituting Equation (7-19) into (7-9) gave:

.

.

.

.

(7-22)

.

.

.

and

(7-23)

.

(7-24)

Similarly:



.

.

.

Equations (7-22), (7-23) and (7-24) established the strain rate and temperature sensitivity of yield strength, initial elastic modulus and secant modulus at yield of polypropylene with 65% glass filler.

139

17

Yield Stress y (MPa)

16

15

14

y = 2.5842x + 13.1 R² = 0.9456

13

12 0.0

0.2

0.4

0.6

0.8

1.0

1.2

tanh( ̇) (%/min)

Inital Elastic Modulus Ei (MPa)

4000

4000

Ei 3000

3000

2000

2000

Esy 1000

1000

0

0 0.0

0.2

0.4

0.6

0.8

1.0

Secasnt Modulus at yield Esy (MPa)

Fig. 7-18. Effect of strain rate on yield strength (y) of polypropylene with 65% glass filler at 22oC.

1.2

tanh( ̇) (%/min) Fig. 7-19: Effect of strain rate on initial elastic modulus (Ei) and secant modulus at yield (Esy) of polypropylene with 65% glass filler at 22oC.

7.4.

Stress-strain relationship modelling The interest in developing an analytical model is to provide an appropriate stress-

strain model that can be used for any kind of composite polymer with variables in

140

function of the three parameters: the yield strength (y), yield strain (y) and the initial elastic modulus (Ei). The model has to take into account the nonlinear behavior in the elastic and inelastic domains and the strain rate and temperature dependency of the stressstrain relationship. Also volume conservation should not be imposed based on the experimental results in chapter 4 at higher temperatures. Consequently, yield criteria based on the assumptions of plastic incompressibility and no effect of yield of the hydrostatic component of stress has to be abandoned. Gurson’s yield criteria and flow rules for porous ductile media and it modified version has to be applied to the materials.

7.4.1 Original model The model proposed by Vipulanandan et al. (1990) has the parametric ability to take into account the requirements, but it have been best used for strain softening materials for which it was purposely developed. It was introduced to model the stressstrain relationship of epoxy and polyester polymer concrete behavior in compression. It was presented as followed , then

1

(7-25)

(7-26)

where y is the yield strain, y the yield strength, i the uniaxial stress and i uniaxial strain. The parameters p and q are functional variable of the material, different from the known hydrostatic pressure q and deviatoric stress p in constitutive modeling.

141

They are

function of the initial modulus Ei and the secant modulus at yield Esy which in turn can be defined ad followed: ,

, ,

(7-27)

,

, and

(7-28)

.

(7-29)

The model imposed at all time that ,

(7-30)

and .

(7-31)

Normalizing the stress by yield stress and the strain by the yield strain, and ̅

(7-32)

.

(7-33)

Equation (7-26) became 1

̅

̅

.

(7-34)

Mantrala introduced a modification transforming stress-strain model which provided the following relationship 1

̅

in which q is defined as,

142

̅

,

(7-35)

,

(7-36)

0 ; 1 .

q is, therefore, a direct quantification of the

material nonlinear elastic stress-strain

behavior , and p is a material property. The condition in equation (7-30) was satisfied. The normalized stress-strain relationships, of the model prediction, are shown in Fig. 7-20 for values of q and range of p.

1.2

q = 0.15 1.0

0.20

i/y

0.8

0.6

p 0.4

0.2

0.01 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

i/y

a.) 1.2

q = 0.20 1.0

0.20

i/y

0.8

0.6

p 0.4

0.2

0.01 0.0 0.0

0.5

1.0

1.5

2.0

i/y

b.)

143

2.5

3.0

3.5

4.0

4.5

1.2

q = 0.25 1.0

0.20

i/y

0.8

0.6

p 0.4

0.2

0.01 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

i/y

c.) Fig. 7-20. Original model normalized stress-strain relationship prediction.

The model have been successfully used for strain-softening behavior materials such as polymer concrete in (Mebarkia et al. 1992), (Wei et al. 1992), (Barros et al. 1999) (Neves et al. 2005), (Bencardino et al. 2008) and (Usluogullari et al. 2011). The use of the model for mainly strain softening behavior is due to its limitation to accurately predict strain-hardening behavior observed in material such as polymer, polymer composite, metals in tension and compression.

7.4.2 Modified model The following expression was adopted from the modification of Mantrala model to account for both softening and hardening observed in the polymer composites experimental results in chapter 4 and 5, 1

̅

̅ .

144

(7-37)

The condition in equation (7-30) is satisfied and the expression of q given in equation (7-36) as a ratio of the secant modulus at yield (Esy) and of the initial modulus (Ei) is maintained. Therefore the new model parameters are the same as the original ones.

The parameter n controls the rate of hardening and is equal to be 2 for the studied materials based on the experimental data, 1

̅

̅ , then

(7-38)

,



1

(7-39)

, .

(7-40)

In the case of hardening model, the second order component of the denominator (

̅ ) controls the hardening and the plastic strain rate. A hardening polymer, in tension,

has a sudden drop in stiffness, right after the yield point in large strain deformation as observed in the experimental result in chapter 3. This behavior is capture by the ̅ component.

maximum of the denominator polynomial due to 0 →

0





1 →

→





1

,

(7-41)

, as shown in

,

(7-42)

Fig. 7-21.

0 →

1



0.5 →



→

145

1

, as shown in Fig. 7-22.

1

1

Fig. 7-21. Case: q=0 and p=1.

1

1

Fig. 7-22: Case: q=1 and p=0.5.

The tangent modulus is:

.

(7-43)

p is a material parameter. In this study p was related to the normalized strain energy

density (

) as follows, ̅.

(7-44)

satisfies the conditions in Fig. 7-21 and Fig. 7-22 and a is a correction parameter. The normalized stress-strain relationship, of the new model prediction, is shown in Fig. 7-23 for values of q and range of p.

146

2.0

0.900

q = 0.150

i/y

1.5

p 1.0

0.5

1 - q = 0.850 0.0 0

5

10

15

20

25

30

35

40

45

50

55

60

i/y

a.) 2.0

0.900

q = 0.200

i/y

1.5

p 1.0

0.5

1 - q = 0.800 0.0 0

5

10

15

20

25

30

35

40

45

50

55

60

i/y

b.) 2.0

0.900

q = 0.30

i/y

1.5

p 1.0

0.5

1 - q = 0.700 0.0 0

5

10

15

20

25

30

35

40

45

50

i/y

c.)

Fig. 7-23. New model normalized stress-strain relationship prediction.

147

55

60

7.4.3 Modified model application The parameter q varied from 0.415 to 0.200 for PP, from 0.600 to 0.100 for GM material and for 0.600 to 0.190 for PP in tension for the temperature range of 22 to 90oC. The model is applied to predict GF experimental stress-strain relationship. The modeling was done case by case. The parameters y, Ei and Esy were, each, directly calculated from the experimental result for each stress strain relationship. From the experimental data, the correction parameter a = 0 for GF. 18 0.300/min T22 0.100/min T22

Engineering stress e (MPa)

16 14

0.030/min T22 22 oC

0.005/min T22 0.300/min T60 The model

0.100/min T60

12

0.030/min T60 0.300/min T90 0.100/min T90

10 60 oC

0.030/min T90

8 6 90 oC

4 2 0 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

Engineering strain e Fig. 7-24: Comparison of the new model prediction and the experimental stress-strain relationship of GF.

7.5.

Summary The effect of temperature and strain rate ( ) on the tensile behavior of the PP, GM

composite and GF composite were modeled. Also the nonlinear stress-strain relationship model was developed.

148

(i)

Parameters represent the change in the material properties (y, Ei,

Esy) on the temperature and are summarized in Table 7-1.The yield strength (y), the

initial elastic modulus (Ei) and the secant modulus at yield (Esy) of the stress-strain relationship PP, GM and GF were modeled. (a) For all three materials (PP, GM, GF),  and were the highest, hence of the three material parameters, Ei and Esy are the most influence, equally, by the temperature. y was the least influence by the temperature. (b) GF were the highest followed by the PP value. Consequently GF was the most influenced by the temperature followed by PP, and GM was the least sensitive to temperature. Order of temperature sensitivity of GF, PP and GM were in accordance with the thermal conductivity results presented in Chapter 3.

(ii)

Parameter a (ay, ai, asy) represents the dependence of material properties (yo, Eio,

Esyo) on the tensile strain rate ( ) and are summarized in Table 7-2 and Table 7-3.

(a) For all three materials (PP, GM, GF), GF was the least sensitive to strain rate. Its parameter (yo, Eio, Esyo) stabilized faster following the tangent hyperbolic function. Considering ay parameter, PP was the most sensitive of the three materials to strain rate.

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(iii)

The proposed stress-strain relationship model captured quite well the nonlinear

behavior of the materials and took into account the strain rate and temperature dependency from the modeling of its material parameters (y, Ei, Esy). From the range of the test strain rates, it was assumed that the tensile test were nearly isothermal (Arruda et al. 1995). In the evolution of the yield strength and the elastic moduli with the strain rate, it was understood that these parameters cannot infinitely increase with increasing strain rate. There are limits and these limits appeared earlier in the composite with glass inclusion.

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8. FINITE ELEMENT MODELLING 8.1.

Introduction The interest of the numerical modeling lays in the assessment of numerical

simulation for future parametric analysis. The strain field variations on the specimens, obtained from the 3D DIC in Chapter 5, were verified using 3D finite element modeling. The four points bending test of notched layered beam was also simulated using FEM. The numerical simulations were done using ABAQUS.

8.2.

Material parameters The material parameters for each model were obtained from experiments which

results were presented in Chapter 4 and 5. The GF tensile specimen with 2.4 mm diameter centered circular hole studied in section 5.3 was numerically model with the material parameter shown in Table 8-1. Table 8-1: GF specimen with centered circular hole model material parameters. 3

Type

Material

Density (kg/m )

2A17

Polypropylene with 65% Glass filler (GF)

1950

y

Esy

(MPa)

(MPa)

15.5

901

y

u



0.017

0.04

0.3

The GF DT tensile specimen, analyzed in section 5.4, was modeled using the material parameters summarized in Table 8-2. Table 8-2: GF DT model material parameters. 3

Type

Material

Density (kg/m )

2DT

Polypropylene with 65% Glass filler (GF)

1950

y

Esy

(MPa)

(MPa)

15

938

151

y

u



0.016

0.15

0.3

The GF NDT specimen tensile specimen analyzed in section 5.4 was also modeled and the material parameters are shown in Table 8-3. The notched composite beam layered material parameters are summarized in Table 8-4. Table 8-3: GF NDT model material parameters. 3

Type

Material

Density (kg/m )

2NDT

Polypropylene with 65% Glass filler (GF)

1234

y

Esy

(MPa)

(MPa)

15.8

1234

y

u



0.013

0.15

0.3

y

u



Table 8-4: Four points bending model materials parameters. y

Ei

(MPa)

(MPa)

800

14

2000

0.07

1

0.28

Polypropylene with 65% Glass filler (GF)

1950

14

2750

0.005

1

0.25

3

Polypropylene (PP)

800

19

1700

0.011

1

0.3

4

Solid PP

800

-

2000

-

-

0.11

3

Layer

Material

Density (kg/m )

1

Epoxy

2

8.3.

Constitutive Model Linear elastic and linear elastic perfectly plastic model were used for the material.

The secant modulus at yield (Esy ) was used as the young modulus instead of the initial elastic modulus(Ei) for the tensile specimens . Von-Mises yield criteria was used in all cases. The strain rate dependency of the materials behavior was not considered. In the beam model, the interfaces 1-2 and 3-4 were modelled as tied: no slip no debonding. The interface 2-3 was modeled using tangential and normal stiffnesses. The unfilled polypropylene (layer 3) was modeled using XFEM (extended finite element method) to allow crack growth. The maximum principle stress criterion was used for the crack initiation. Fracture was not considered in the numerical modeling of the tensile specimens.

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8.4. 8

Resu ults The strain s field evolution was w of interrest in the nnumerical ssimulation.

Mesh

seensitivity analysis was done d for all th he models.

8.4.1

GF sp pecimen witth 2.4 mm centered circcular hole The sttrain field vaariation due to stress conncentration aaround the hhole was capptured

ass shown in Fig. 5-28. The T numericcal model caaptured com mpressive strrain as expeected, based on Kirsch work (1898), but th his was not rrecorded wiith the DIC as shown inn Fig.

8-2 (a) and (b b). The orderred 10-4 may y be out of raange.

Fig. 8-1: Uniax xial strain fielld evolution on o the simulatted GF specim men with a ciircular hole.

a.)

b.)

Fig. 8-2: Uniax xial strain fielld evolution on o the simulatted GF specim men with a ciircular hole.

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8.4.2

GF DT D specimen n The strain s field variation du ue to stress concentratiion around the semicirrcular

grrooves was captured as shown in Fig. F 8-3. Thee numerical model captuured compreessive sttrain as expeected, based on Kirsch work w (1898) , but this waas not recordded with thee DIC ass shown in Fig. 8-2 (a)) and (b). At A the same oorder of straain in the pllastic domaiin, as sh hown in Fig. 8-5, the nu umerical mod del was stilll showing coompressive strain. The sstrain distributions were comp pletely diffeerent. The sstrain rate ddependency of the maaterial behavior maarked the difference. d The T experim mental resuult (DIC) sshowed thatt the deformations were concen ntrated along g the center line.

Fig. 8-3: Uniax xial strain fielld evolution on o the simulatted GF DT sppecimen.

a.)

b.))

parison of straain fields from m simulation with 3D DIC C record of G GF DT specim men. Fig. 8-4: Comp in th he elastic dom main.a.)FEM simulation, s b..)DIC.

154

a.)

b.)

Fig. 8-5: Comp parison of straain fields from m simulation with 3D DIC C record of GF F DT specimeen. in the pllastic domain n.a.)FEM simu ulation, b.)DIIC.

8.4.3

GF NDT N specimeen. Same observation n as in the caase of GF D DT specimenn, but accenttuated. The sstrain

fiield variation ns are shown in Fig. 8-6. As shownn in Fig. 8-77 and Fig. 8-88, the strain field distributions were w differeent and was justified by tthe viscous nnature of GF F material.

Fig. 8-6: Uniax xial strain fielld evolution on o the FEM simulated of G GF NDT speccimen.

155

a.)

b.)

Fig. 8-7: Comp parison of straain fields from m simulation with 3D DIC C record of G GF NDT speciimen. in thee elastic domaain. a.)FEM simulation an , b.)DIC.

a.))

b.))

parison of straain fields from m simulation with 3D DIC C record of G GF NDT speciimen. Fig. 8-8: Comp in thee plastic domaain.a.)FEM siimulation, andd b.)DIC.

8.4.4

Four points bend ding The fo our points bending test results r from m the DIC aree shown in Fig. 8-9 (aa) and

(b b). The beam m failed by crack c openin ng first followed by delaamination at the interfacce 2-3 an nd then com mplete failurre as shown n in Fig. 8-99 (b). The ccomplete faailure was by the development of full deptth crack through layer 2 under thee load appliccation pointss, the maximum m strress locationss.

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The numerical n mo odel captured d the crack oopening and delaminatioon at the inteerface c througgh layer 2. 2-3, but didn’’t capture thee full depth crack

a.)

b.)

Fig. 8-9: DIC strain s field on n the specimen. a.)Interfacee delaminatioon, b.) Compllete failure off the specim men.

a..)

b.)

AQUS strain field on the specimen. a.)IInterface delaamination, b.) Von-Mises. Fig. 8-10: ABA Streess.

8.5. 8

Summary and discussion (1) Th he numericaal modeling gave insightt in the behaavior of these polypropyylene co omposites at constant strain rate. (2) An n accurate numerical parametric analysis wiill require consideratioon of viscous naturre of thesee polypropyylene compposites and the strain rate mplification factor . am

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9. CONCLUSIONS & RECOMMENDATIONS The objective of this study was investigated the behavior of polypropylene composite coating insulators at various strain rate. The thermal conductivity of unfilled polypropylene (PP), polypropylene with microsphere filler (GM), and polypropylene with 65% glass filler (GF) were 0.160, 1.40 and 0.306. Three dimensional Digital Image Correlation system was used to monitor the full strain field on the tensile, compressive, shear and bending specimens. Based on the experimental results, the following conclusions were advanced: (1) The unfilled polypropylene (PP), polypropylene with glass microsphere filler (GM) and polypropylene with 65% glass filler (GF) tensile engineering stressstrain relationships were strain rate and temperature dependent. The yield strength (y), initial elastic modulus (Ei) and secant modulus at yield (Esy) decreased with increasing temperature and increased with increasing strain rate in tensile test. (2) Polypropylene with 65% glass filler had the highest elastic modulus and polypropylene with glass microsphere filler had the lowest elastic modulus. (3) Addition of the glass microsphere to polypropylene in this case decreased it elastic modulus but maintained the ductility at 22oC. (4) The compressive yield strength of PP and GF were two to three times higher than the yield strength. (5) The fracture initiation in the layered composite beams is dependent on stress concentration and strain rate level. It initiates inside the polymer composite layer, here GF, and then propagates through layers and interfaces. It is only

158

noticed when it reaches the surface. Since the fracture initiates in the internal insulation layer, it is then difficult, almost impossible to be detected before it breaks out. It then requires a control over the mechanical parameters which trigger it: the stress level and strain rate level. (6) Stress concentration around the crack, due to defect, induced strain rate gradient in the polymer composites which increase y, Ei and Esy but made the ductile polymer more brittle in fracture. The strain energy density at yield and failure reduced with the crack size, but increased with the strain rate. (7) A strain rate amplification factor was defined to be equal to the ratio of the maximum strain rate recorded at the crack tip to the nominal test strain rate. controlled the fracture of the polymer.

(8) Repairing of cracks using a rapid setting polymer was evaluated. The repaired composite maintained 100% of its initial failure strain. (9) The proposed stress-strain relationship model captured quite well the nonlinear behavior of the materials and took also into account the strain rate and temperature dependency from the modeling of the material parameters (y, Ei, Esy). This study opened the door to future work on polymer composites used in subsea. Mainly, how to control the deformation of the insulated pipeline, before installation (transportation) and at service condition, to maintain the deformation rate below the point of the development of large strain rate? The developed constitutive

159

equations can be parametrically updated for other polymer composites or materials displaying similar behavior.

160

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