Major Accomplishments in Composite Materials and Sandwich Structures (eBook)

Preface 5
Contents 11
Contributors 15
Chapter 1 19
Accelerated Testing for Long-Term Durability of Various FRP Laminates for Marine Use 19
1 Introduction 20
2 Accelerated Testing Methodology 20
2.1 Procedure of ATM 20
2.2 Applicability of ATM 22
2.3 Theoretical Verification of TTSP 22
3 Experimental Procedures 25
3.1 Preparation of Specimens 25
3.2 Tests 26
4 Results and Discussion 29
4.1 Creep Compliance 29
4.2 Flexural CSR Strength 30
4.3 Flexural Fatigue Strength 33
5 Conclusions 39
Navy Relevance 39
References 40
Chapter 2 42
Carbon Fiber–Vinyl Ester Interfacial Adhesion Improvement by the Use of an Epoxy Coating 42
1 Introduction 42
2 Materials and Methods 43
2.1 Materials 43
2.2 Methods 44
2.2.1 Microindentation Test 44
2.2.2 Thermogravimetric Analysis (TGA) 45
2.2.3 Dynamic Mechanical Thermal Analysis (DMTA) 45
2.2.4 Environmental Scanning Electron Microscopy (ESEM) 45
3 Preferential Adsorption of Some Constituents of the Matrix on the Carbon Fiber Surface and Its Influence on Interfacial Adhesion 46
3.1 Evidence of Preferential Adsorption of Some Constituents of the Matrix on the Carbon Fiber Surface 46
3.2 Influence on Interfacial Adhesion 46
3.2.1 Influence of the Concentration of the Initiator 47
3.2.2 Influence of the Concentration of the Promoter 48
3.2.3 Influence of the Concentration of the Accelerator 49
4 Influence of Cure Volume Shrinkage on Interfacial Adhesion 50
5 Improvement of Interfacial Adhesion by the Use of an Epoxy Coating 52
5.1 Optimization of the Coating Process 52
5.2 Interactions Between the Epoxy Coating and the Components of the Vinyl Ester Matrix 53
5.2.1 Influence of the Concentration of the Initiator 54
5.2.2 Influence of the Concentration of the Promoter 55
5.2.3 Influence of the Concentration of the Accelerator 55
5.2.4 Influence of Monomers 56
5.3 Influence of the Cure Volume Shrinkage with the Use of an Epoxy Coating 57
5.4 Qualitative Assessment of the Use of an Epoxy Coating on the Mechanical Properties of a Carbon Fiber–Vinyl Ester Composite Cured at High Temperature 58
5.5 Determination of the Optimal Thickness of the Coating by a Finite Element Analysis 60
5.6 Determination of the Thickness of the Interdiffusion Zone by a Nanoindentation Scratch Test 62
6 Conclusion 63
References 64
Chapter 3 66
A Physically Based Cumulative Damage Formalism 66
1 Introduction 66
2 Kinetic Crack Based Cumulative Damage and Life Prediction 68
3 A Special Form 72
4 Cyclic Fatigue 74
5 Probabilistic Generalization 76
6 Examples 77
7 Extended Life Examples 78
8 Conclusions 79
References 80
Chapter 4 81
Delamination of Composite Cylinders 81
1 Introduction 81
2 Materials and Specimens 82
3 Delamination Fracture Testing 85
4 Impact Testing of Cylinders 86
5 External Pressure Tests of Cylinders 86
6 Results and Discussion 89
6.1 Delamination Fracture Test Results 89
6.2 Influence of Impact 90
6.3 External Pressure Test Results 90
7 Conclusions 98
References 98
Chapter 5 100
Modeling of Progressive Damage in High Strain–Rate Deformations of Fiber-Reinforced Composites 100
1 Introduction 100
2 Progressive Damage Model 101
3 Implementation of the Damage Model 105
3.1 Brief Description of the Numerical Technique 105
3.2 Simulation of Material Failure 106
3.3 Energy Dissipation 106
3.4 Verification of the Code 107
3.5 Validation of the Mathematical Model 108
4 Parametric Studies on a Typical Laminated Composite 110
4.1 Effect of Mesh Size 111
4.2 Lay-Up Sequence 113
4.3 Target Thickness 115
4.4 Fiber Orientation 115
4.5 Delamination 118
4.6 Figure of Merit 118
4.7 Remarks 119
4.8 Limitations of the Model 119
5 Conclusions 120
References 121
Chapter 6 123
Post-Impact Fatigue Behavior ofWoven and Knitted Fabric CFRP Laminates for Marine Use 123
1 Introduction 123
2 Materials and Testing Methods 124
2.1 Materials and Molding Method 124
2.2 Specimens and Impact Test 125
2.3 Compression After Impact (CAI) Test and Post-Impact Fatigue (PIF) Test 126
2.4 Water Absorption Condition 127
3 Approach to Evaluate Damages 127
4 Impact Damage of CFRP Laminates 129
4.1 Plain Woven CFRP Laminate 129
4.2 Multi-axial Knitted CFRP Laminate 130
4.3 Three-Dimensional Characterization of Impact Damage Within CFRP Laminates 132
5 Compressive Strength and Fatigue Strength of Impact Damaged CFRP Laminates 133
5.1 Effect of Water Absorption on Post-Impact Fatigue Properties 133
5.2 Damage Evolution Mechanism in Plain Woven CFRP Laminates 134
5.3 Damage Evolution Mechanism in Multi-axial Knitted CFRP Laminates 138
5 Conclusions 140
References 141
Chapter 7 143
Dynamic Interaction of Multiple Damage Mechanisms in Composite Structures 143
1 Introduction 143
2 Modeling Multiple Delamination Fracture in Laminated and Multilayered Systems 145
2.1 Theoretical Approach 145
2.2 Energy Release Rate and Stress Intensity Factors in Homogeneous Orthotropic Beams 146
3 Interaction Effects of Multiple Delaminations on Fracture Parameters 149
3.1 Amplification and Shielding of the Energy Release Rate 149
3.2 Interaction Effects on Mode Ratio 151
3.3 Coupling of Interaction and Dynamic Effects 153
3.3.1 Dynamic Response of Beams with Single Stationary Delaminations 153
3.3.2 Dynamic Response of Beams with Multiple Stationary Delaminations 155
4 Interaction Effects of Multiple Delaminations on Crack Growth Characteristics and Macrostructural Behaviour 158
4.1 Local Instabilities and Strengthening Mechanisms 158
4.2 Stability of the Equality of Length of Systems of Equal Length Delaminations 159
4.2.1 Equally Spaced and Equal Length Cracks in Homogeneous Beams (Static Loading) 160
4.2.2 Equal Length and Unequally Spaced Cracks in Homogeneous Beams (Static Loading) 160
4.2.3 Dynamic Loading Conditions 161
Equally Spaced and Equal Length Cracks in Homogeneous Beams 161
Delamination Configurations Falling into the Stable Quasi-static Domain 162
Delamination Configurations Falling into the Unstable Quasi-static Domain 164
4.3 Crack Growth Characteristics in Systems of Unequal Length Cracks 165
5 Improving Mechanical Performance Through Controlled Delamination Fracture 166
5.1 Energy Absorption Through Multiple Delamination Fracture 166
5.2 Damage and Impact Tolerance 169
6 Indentation Response of Composite Sandwich Beams in the Presence of Skin Damage 171
6.1 Continuously Supported Sandwich Beam (F = 0) 172
6.2 Sandwich Beam with End Restraints (F Not Equal 0) 173
6.3 Characteristic Lengths 174
7 Conclusions 175
References 176
Chapter 8 179
A Review of Research on Impulsive Loading of Marine Composites 179
1 Introduction 179
2 Outline 180
3 Experimental Studies 181
3.1 Underwater Tests 181
3.1.1 Test Procedures and Instrumentations 181
3.1.2 Response of Marine Structural Materials to Underwater Blast Loading 183
3.2 In-Air Tests 185
3.2.1 Test Procedures and Instrumentations 185
3.2.2 Response of Marine Structural Materials to In-Air Shock and Blast Loading 187
4 Theoretical and Computational Studies 191
4.1 Analysis of Marine Panels 191
4.1.1 Panel Response to Free Field Blast Loading 191
4.1.2 Fluid–Structure Interaction in Sandwich Composites 194
4.2 Analysis of Full-Scale Marine Structures 196
5 Closing Remarks 198
References 201
Chapter 9 205
Failure Modes of Composite Sandwich Beams 205
1 Introduction 206
2 Sandwich Materials Investigated 207
2.1 Facesheet Materials 207
2.2 Core Materials 207
3 Facesheet Failure 214
4 Facesheet Debonding 217
5 Core Failures 221
6 Indentation Failure 224
7 Facesheet Wrinkling Failure 228
8 Failure Mode Interaction 230
9 Conclusions 232
References 233
Chapter 10 236
Localised Effects in Sandwich Structures with Internal Core Junctions: Modelling and Experimental Characterisation of Load Response, Failure and Fatigue 236
1 Introduction 236
2 Prediction of Failure in Sandwich Structures with Core Junctions 238
2.1 Failure Criteria for Sandwich Core Materials 238
3 Core Junctions in Sandwich Panels Subjected to In-Plane Loading 242
3.1 Test Specimens 242
3.2 Material Properties 244
3.3 Experimental Investigation – Part 1: Quasi-static Tests 248
3.4 Finite Element Analyses (FEA) 252
3.5 Experimental Investigation – Part 2: Fatigue Tests 259
3.6 Discussion and Conclusions (In-Plane Loading) 261
4 Core Junctions in Sandwich Panels Subjected to Transverse Shear Loading 262
4.1 Sandwich Test Specimens 262
4.2 Experimental Results – Part 1: Quasi-static Tests 263
4.3 Finite Element Analyses (FEA) 269
4.4 Experimental Results – Part 2: Fatigue Tests 277
4.5 Discussion and Conclusions (Transverse Shear Loading) 282
5 Summary and Conclusions 282
References 283
Chapter 11 285
Damage Tolerance of Naval Sandwich Panels 285
1 Introduction and Background 285
2 Fracture of Foam Core Materials 287
3 Disbonds in Sandwich Beams 288
4 Impact Damage in Sandwich Beams 291
5 Interface Disbonds in Sandwich Panels 293
6 Impact Damage in Sandwich Panels 297
7 Damage Tolerance Scheme for Naval Sandwich Structures 302
References 307
Chapter 12 310
Size Effect on Fracture of Composite and Sandwich Structures 310
1 Introduction 310
2 Size Effect on the Tensile Strength of Notched Fiber–Composite Laminates [23] 313
2.1 Introduction 313
2.2 Experimental 314
2.3 Size Effect 315
2.4 Conclusions 317
3 Size Effect on the Flexural Strength of Fiber–Composite Laminates [34] 318
3.1 Introduction 318
3.2 Size Effect 318
3.3 Experimental Studies 320
3.4 Conclusions 321
4 Size Effect on the Compression Strength of Fiber–Composite Laminates [42] 321
4.1 Introduction 321
4.2 Experimental 322
4.3 Conclusions 325
5 Size Effect on Fracture of Polymeric Foams [45] 325
5.1 Introduction 325
5.2 Experimental 326
5.3 Size Effect 327
5.4 Conclusions 331
6 Size Effect on Compressive Strength of Sandwich Panels [54] 332
6.1 Introduction 332
6.2 Experimental 332
6.3 Size Effect 334
6.4 Conclusions 336
7 Size Effect of Cohesive Delamination Fracture Triggered by Sandwich Skin Wrinkling [55] 337
7.1 Introduction 337
7.2 Size Effect 337
7.3 Conclusions 341
References 341
Chapter 13 344
Elasticity Solutions for the Buckling of Thick Composite and Sandwich Cylindrical Shells Under External Pressure 344
1 Introduction 344
2 Formulation 346
3 Pre-buckling State 352
4 Perturbed State 357
5 Solution of the Eigen-Boundary-Value Problem for Differential Equations 359
6 Results and Discussion 361
References 367
Chapter 14 369
An Improved Methodology for Measuring the Interfacial Toughness of Sandwich Beams 369
1 Introduction 369
2 Test Methods Considered 370
3 Geometries Considered 371
4 Finite Element Modeling 372
5 MCSB Evaluation 374
6 Preliminary Evaluation of the TSD Test 375
7 Data Reduction in the MP Test 376
8 TSD and MP Experiments 380
9 Mechanical Attachments 382
10 Conclusions 383
References 383
Chapter 15 385
Structural Performance of Eco-Core Sandwich Panels 385
1 Introduction 386
2 Design of Test Specimens 386
2.1 Short Beam Shear Test Specimen 387
2.2 Four-Point Flexure Test Specimen 388
2.3 Edgewise Compression Test Specimen 390
3 Fabrication of Sandwich Panel and Specimen 394
4 Tests 395
4.1 Short Beam Shear Test 396
4.2 Four-Point Flexure Test 396
4.3 Edgewise Compression Test 397
5 Test Results and Discussion 399
5.1 Short Beam Shear Test 399
5.2 Four-Point Flexure Test 400
5.3 Edgewise Compression Test 405
6 Concluding Remarks 409
References 410
Chapter 16 411
The Use of Neural Networks to Detect Damage in Sandwich Composites 411
1 Introduction 411
2 Nondestructive Evaluation 412
2.1 Thermography Based NDE 413
2.1.1 Modeling 414
2.1.2 Validation 415
2.1.3 Test Cases and Results 416
2.2 Vibrations Based NDE 417
2.2.1 Modeling 418
2.2.2 Validation 420
2.2.3 Test Cases and Results 421
3 Artificial intelligence (AI) in Damage Detection 422
3.1 Neural Network Based Damage Detection 423
3.1.1 Thermographic Based NN Implementation 424
3.1.2 Curvature Based NN Implementation 426
3.1.3 Multi-component NN Implementation 426
3.2 Testing and Evaluation 428
4 Conclusions 431
References 432
Chapter 17 434
On the Mechanical Behavior of Advanced Composite Material Structures 434
1 Introduction 435
2 High Strain Rate Effects on Composite Material Properties 435
3 Composite Sandwich Structures 438
References 442
Chapter 18 443
Application of Acoustic Emission Technology to the Characterization and Damage Monitoring of Advanced Composites 443
1 Background 443
2 Sample Acoustic Emission Applications 445
2.1 Edgewise Compression Tests of Polycore Sandwich Material 445
2.1.1 Background 445
2.1.2 Testing 446
2.1.3 Discussion of Results 446
2.1.4 Concluding Remarks 451
2.2 Isogrid Construction 451
2.2.1 Background 451
2.2.2 Testing 452
2.2.3 Discussion of Results 453
2.2.4 Concluding Remarks 457
2.3 Flexural Fatigue of Foam-Cored Composite Sandwich 458
2.3.1 Background 458
2.3.2 Testing 458
2.3.3 Results and Discussion 458
2.3.4 Concluding Remarks 461
3 Conclusion 462
References 462
Chapter 19 465
Ballistic Impacts on Composite and Sandwich Structures 465
1 Introduction 465
2 Models Based on Assumptions Regarding the Penetration Resistance 466
2.1 Constant Penetration Resistance 468
2.2 Assumption 2: Kinetic Energy Absorbed by Ejecta 470
2.3 Poncelet’s Assumption 474
2.4 Penetration Force Increases Linearly with the Velocity 475
2.5 Penetration Force Varies with v and v2 476
2.6 Summary 476
3 Projectile-Target Interaction Models 477
3.1 Normal Pressure on the Surface of the Projectile 477
3.2 Blunt-Ended Projectile 478
3.3 Conical-Tipped Projectile 478
3.4 Spherical Tipped Projectile 480
3.5 Effect of Friction 482
4 Factors Affecting the Ballistic Limit 482
4.1 Effect of Laminate Thickness and Projectile Diameter 483
4.2 Effect of Stacking Sequence 485
4.3 Effect of Obliquity 486
4.4 Effect of Projectile Density 487
5 Models Based on Static Test Results 488
6 Energy – Balance Models 490
7 Numerical Models 493
8 Impact on Sandwich Structures 494
9 Conclusions 496
References 496
Chapter 20 502
Performance of Novel Composites and Sandwich Structures Under Blast Loading 502
1 Introduction 503
2 Material Systems 505
2.1 Laminated Composites 505
2.1.1 E-Glass Vinyl Ester Composite (EVE) 505
2.1.2 Carbon Fiber Vinyl Ester Composite (CVE) 506
2.2 Layered Composites 506
2.2.1 Polyurea Layered Materials 506
2.3 Sandwich Composites 506
2.3.1 Polyurea Sandwich Composites 506
2.3.2 Sandwich Composites with 3D Woven Skin 506
2.3.3 Core Reinforced Sandwich Composites 507
2.3.4 Sandwich Composite with a Stepwise Graded Core 508
2.3.5 Pre-damaged Sandwich Composite 509
3 Experimental Setup 509
3.1 Shock Tube 509
3.2 Loading and Boundary Conditions 510
3.3 Pre-damage Procedure 511
3.4 High Speed Imaging 512
3.5 Blast Energy Calculation Procedure 513
4 Results and Discussion 513
4.1 Blast Resistance of Laminated Composites 513
4.2 Blast Resistance of Layered Composites 516
4.2.1 PU/EVE Layered Material 517
4.2.2 EVE/PU Layered Material 518
4.3 Blast Resistance of Sandwich Composites 519
4.3.1 Polyurea Based Sandwich Composites 519
4.3.2 Sandwich Composites with 3D Skin and Polymer Foam Core 522
4.3.3 Sandwich Composite with E-Glass Fiber and Polymer Foam Core 528
4.3.4 Sandwich Composites with Stepwise Graded Foam Cores 528
4.3.5 Pre-damaged Sandwich Composites 534
5 Summary 537
References 538
Chapter 21 540
Single and Multisite Impact Response of S2-Glass/ Epoxy Balsa Wood Core Sandwich Composites 540
1 Introduction 540
2 Experimental 541
2.1 Specimen Fabrication 541
2.2 High Velocity Impact Set Up 542
3 Model Description 542
3.1 Mesh Generation and Contact Definition 542
3.2 Composite Progressive Failure Model and Strain Softening Characteristics 544
3.2.1 Wood Material Model 544
4 Results and Discussion 546
4.1 Single Site Projectile Impact 546
4.1.1 Single Project Impact: Balsa Wood Core Only 546
Experiment 546
Simulation 547
4.1.2 Single Projectile Impact: Sandwich Composite 548
4.2 Simultaneous 0.30 and 0.50 Caliber Three Projectile Impact on the Sandwich Specimens 555
4.3 Delamination Factor, Sd for Multisite Impact Prediction 561
4.4 Fiber and Wood Damage 564
5 Summary and Conclusions 565
References 566
Chapter 22 569
Real-Time Experimental Investigation on Dynamic Failure of Sandwich Structures and Layered Materials 569
1 Introduction 569
2 Experimental Procedure 573
2.1 Materials and Specimens 573
2.2 Experimental Setup 575
3 Results and Discussion 576
3.1 Failure Process of Short Model Sandwich Specimens with Equal Layer Widths 576
3.2 Failure Process in Long Model Sandwich Specimens 578
3.3 Effect of Impact Speeds 582
3.4 Dynamic Failure Mode Transition 583
3.5 Dynamic Interface Debonding Ahead of a Main Incident Crack 585
3.6 New Progress on Dynamic Crack Branching 588
3.6.1 Special Experiments for Dynamic Crack Kinking and Branching 588
3.6.2 Dynamic Crack Branching and Kinking from aWeak Interface 588
3.6.3 Dynamic Crack Branching Initiated from a Notch Subjected to High Impact Loading 590
3.7 Dynamic Crack Kinking and Penetration at an Interface 591
3.7.1 Weak Interfaces with Different Interfacial Angles 591
3.7.2 Modeling of Dynamic Failure Modes Across an Interface 593
3.7.3 Mode Mixity of the Kinked Interfacial Crack 595
3.8 Two-layer Specimens with Direct Impact on the BrittlePolymeric Layer 597
4 Conclusions 598
References 599
Chapter 23 602
Characterization of Fatigue Behavior of Composite Sandwich Structures at Sub-Zero Temperatures 602
1 Introduction 602
2 Experiments 604
2.1 Specimens 604
2.2 Static Flexure Tests 604
2.3 Flexural Fatigue Tests 606
3 Finite Element Modeling 608
4 Results 609
4.1 Static 4-Point Bending 609
4.2 Flexural Fatigue 611
4.3 Fatigue Life at Low Temperatures 611
4.4 Stiffness and Damping at Low Temperatures 612
4.5 Fatigue Failure Modes 617
5 Finite Element Analysis 617
6 Conclusions 619
References 620
Chapter 24 622
Impact and Blast Resistance of Sandwich Plates 622
1 Introduction 623
2 Response to Uniform Pressure 624
3 Response to Impact 627
3.1 Medium Velocity Impact at Different Contact Locations 627
3.2 Response to Impact at Support 630
3.3 Effect of Indenter Shape, Interlayer Moduli and Thickness 632
3.4 Energy Released by Interfacial Cracks 637
4 Response to Impulse or Blast Loads 640
4.1 Geometry and Material Properties 641
4.2 Finite Element Models 645
4.3 Response to a Full Span Pressure Impulse 646
4.4 Energy Absorption 649
4.5 Effect of Change in Total Mass 651
4.6 Performance Comparison of Polyurea and Polyurethane 651
5 Conclusions 652
References 653
Chapter 25 657
Modeling Blast and High-Velocity Impact of Composite Sandwich Panels 657
1 Introduction 657
2 Impulsively-Loaded Sandwich Panels 658
2.1 Phase I – Through-Thickness Wave Propagation 660
2.1.1 Transmission and Reflection at Interfaces 660
2.1.2 Elastic and PlasticWaves in Foam 662
2.1.3 Local Indentation 663
2.2 Phase II – Global Bending/Shear 664
2.2.1 System Lagrangian 665
2.2.2 Bending/Shear Strain Energy Potential 665
2.2.3 Equations of Motion 666
2.3 Transient Deformations 667
2.3.1 Local Core Crushing: Phase I Response 668
2.3.2 Global Bending/Shear: Phase II Response 670
2.4 Damage Initiation 670
3 High-Velocity Impact of Sandwich Panels 673
3.1 Phase I: Local Indentation 675
3.1.1 Through-Thickness Wave Propagation 675
3.1.2 Local Indentation 675
Kinetic Energy 676
Potential Energy 677
Equation of Motion 678
3.2 Phase II: Global Bending/Shear 679
3.2.1 Kinetic Energy 680
3.2.2 Global Bending/Shear Energy 680
3.2.3 Equations of Motion 681
3.3 Comparison with Finite Element Analysis 682
4 Conclusions 683
Appendix A Uniaxial StrainWave Speed in an Orthotropic Plate 683
Appendix B Momentum and Kinetic Energy of Core During Phase I 684
Appendix C Elastic Strain Energy and Plastic Work in Core 685
References 686
Chapter 26 687
Effect of Nanoparticle Dispersion on Polymer Matrix and their Fiber Nanocomposites 687
1 Introduction 687
2 Effect of Dispersion on Polymer Matrix 688
2.1 Materials 691
2.2 Fabrication 691
2.3 Microstructural and Mechanical Characterization Techniques 692
2.4 Morphological Characterization 692
2.5 Mechanical Characterization 694
3 Mechanical Behavior of FRP Nanocomposites 695
3.1 Materials and Fabrication 698
3.2 Mechanical Characterization Techniques 698
3.2.1 Compression 698
3.2.2 Tension 699
3.2.3 DCB 699
3.2.4 ENF 699
3.2.5 Low Velocity Impact 699
3.3 Compressive Properties 699
3.3.1 Off-Axis Compressive Strength 699
3.3.2 Longitudinal Compressive Strength 700
3.4 Tensile Properties 702
3.5 Fracture Toughness 703
3.6 Impact Resistance 705
4 Conclusion 706
References 707
Chapter 27 710
Experimental and Analytical Analysis of Mechanical Response and Deformation Mode Selection in BalsaWood 710
1 Introduction 711
2 Experimental 712
2.1 Microstructural Features of Balsa Wood 712
2.2 Specimen Preparation and Geometry 714
2.3 Quasi-Static Testing Method 715
2.4 Dynamic Testing Method 716
3 Results and Discussion 717
3.1 Stress–Strain Response 717
3.1.1 End Effects 719
3.1.2 Initial Failure and Progressive Deformation 719
3.1.3 Densification 721
3.1.4 Energy Dissipation Capacity 724
3.2 Failure Modes 726
3.3 Strength Models Based on Failure Modes 727
3.3.1 Elastic Buckling 727
3.3.2 Plastic Buckling 729
3.3.3 End-Cap Collapse 729
3.3.4 Kink Band Formation 730
3.4 Comparison with Quasi-Static Experiments 731
3.5 Models for Inertial Stress Enhancement 732
3.5.1 Background 732
3.5.2 Buckling 734
Model Parameters 738
3.5.3 Kink Band Formation 739
Model Parameters 741
3.6 Comparison of Inertia-Based Models with Dynamic Data 741
4 Conclusions 745
References 747
Chapter 28 749
Mechanics of PAN Nanofibers 749
1 Introduction 749
2 Experimental Methods and Materials 751
2.1 Nanofiber Fabrication 751
2.2 Mechanical Experiments with Single Polymeric Nanofibers 752
2.2.1 Background 752
2.2.2 Nanoscale Tension Experiments with Individual Polymeric Nanofibers 753
2.2.3 Resolution in Force and Nanofiber Extension Measurements 754
2.2.4 Loadcell Calibration 756
3 Fabrication vs Mechanical Behavior of PAN Nanofibers 757
4 Mechanical Instabilities During Cold Drawing of PAN Nanofibers 760
5 Effect of Strain Rate on the Mechanical Deformation of Nanofibers 761
6 Origins of Surface Rippling in Electrospun PAN Nanofibers 763
7 Molecular Alignment in Electrospun PAN Nanofibers 765
8 Conclusions 767
References 767
Chapter 29 771
Characterization of Deformation and Failure Modes of Ordinary and Auxetic Foams at Different Length Scales 771
1 Introduction 771
2 The Multi-scale Speckle Photography Technique 772
3 Studies of Ordinary Foams 774
3.1 Size Effect on Mechanical Properties of Foam Composites 774
3.2 Crack Tip Deformation in Foam at Different Length Scales 778
4 Studies of Auxetic Foams 781
4.1 Introduction 781
4.2 Auxetic Polyurethane Foam 782
4.3 Auxetic PVC (H45) Foam 782
4.3.1 Manufacturing the Auxetic PVC Foam 782
4.3.2 Mechanical Properties of Auxetic PVC Foam 783
Uniaxial Test 783
Shear Test 786
Impact Test 787
Indentation Tests 787
References 789
Chapter 30 791
Fracture of Brittle Lattice Materials: A Review 791
1 Introduction 791
1.1 Fracture Mechanics Concepts 792
1.2 Outline of this Review 793
2 Classical Beam Theory 793
2.1 The Hexagonal Lattice 794
2.2 Other 2D Lattices 795
2.3 Statistics of Brittle Failure 795
3 Generalised Continuum Theories 796
4 Finite Element Modelling 797
4.1 Stress Analysis 797
4.2 Boundary Layer Analysis 799
4.2.1 Extrapolation of 2D Results to 3D Lattices 802
4.2.2 Sensitivity of Fracture Toughness to Imperfections 802
5 Atomic Lattice Models for Crack Dynamics 803
6 Representative Cell Method 804
7 Experimental Studies on Fracture Toughness 805
8 Concluding Remarks 806
References 806
Author Index 809