Applied nanoindentation in advanced materials
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Applied nanoindentation in advanced materials
John Wiley & Sons, c2017
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Includes bibliographical references and index
内容説明・目次
内容説明
Research in the area of nanoindentation has gained significant momentum in recent years, but there are very few books currently available which can educate researchers on the application aspects of this technique in various areas of materials science.
Applied Nanoindentation in Advanced Materials addresses this need and is a comprehensive, self-contained reference covering applied aspects of nanoindentation in advanced materials. With contributions from leading researchers in the field, this book is divided into three parts. Part one covers innovations and analysis, and parts two and three examine the application and evaluation of soft and ceramic-like materials respectively.
Key features:
A one stop solution for scholars and researchers to learn applied aspects of nanoindentation
Contains contributions from leading researchers in the field
Includes the analysis of key properties that can be studied using the nanoindentation technique
Covers recent innovations
Includes worked examples
Applied Nanoindentation in Advanced Materials is an ideal reference for researchers and practitioners working in the areas of nanotechnology and nanomechanics, and is also a useful source of information for graduate students in mechanical and materials engineering, and chemistry. This book also contains a wealth of information for scientists and engineers interested in mathematical modelling and simulations related to nanoindentation testing and analysis.
目次
List of Contributors xvii
Preface xxiii
Part I 1
1 Determination of Residual Stresses by Nanoindentation 3
P-L. Larsson
1.1 Introduction 3
1.2 Theoretical Background 5
1.3 Determination of Residual Stresses 12
1.3.1 Low Hardening Materials and Equi-biaxial Stresses 12
1.3.2 General Residual Stresses 13
1.3.3 Strain-hardening Effects 15
1.3.4 Conclusions and Remarks 15
References 16
2 Nanomechanical Characterization of Carbon Films 19
Ben D. Beake and TomaszW. Liskiewicz
2.1 Introduction 19
2.1.1 Types of DLC Coatings and their Mechanical Properties 19
2.1.2 Carbon Films Processing Methods 20
2.1.3 Residual Stresses in Carbon Films 21
2.1.4 Friction Properties of Carbon Films 22
2.1.5 Multilayering Strategies 23
2.1.6 Applications of Carbon Films 24
2.1.7 Optimization/testing Challenges 24
2.2 Factors Influencing Reliable and Comparable Hardness and Elastic Modulus Determination 24
2.2.1 The International Standard for Depth-sensing Indentation: EN ISO 14577-4 : 2007 24
2.2.2 Challenges in Ultra-thin Films 27
2.2.3 Indenter Geometry 28
2.2.4 Surface Roughness 28
2.3 Deformation in Indentation Contact 30
2.3.1 The Relationship Between H/E and Plastic and ElasticWork in Nanoindentation 30
2.3.2 Variation in H/E and Plasticity Index for Different DLC Films 31
2.3.3 Cracking and Delamination 32
2.3.4 Coatings on Si: Si Phase Transformation 33
2.4 Nano-scratch Testing 34
2.4.1 Scan Speed and Loading Rate 35
2.4.2 Influence of Probe Radius 36
2.4.3 Contact Pressure 36
2.4.4 Role of the Si Substrate in Nano-scratch Testing 38
2.4.5 Failure Behaviour of ta-C on Si 40
2.4.6 Film Stress and Thickness 43
2.4.7 Repetitive Nano-wear by Multi-pass Nano-scratch Tests 44
2.4.8 Load Dependence of Friction 46
2.5 Impact and Fatigue Resistance of DLC Films Using Nano-impact Testing 46
2.5.1 Compositionally Graded a-C and a-C:H Coatings on M42 Tool Steel 49
2.5.2 DLC/Cr Coating on Steel 51
2.5.3 PACVD a-C:H Coatings on M2 Steel 51
2.5.4 DLC Films on Si-film Thickness, Probe Geometry, Impact Force and Interfacial Toughness 52
2.6 Wear Resistance of Amorphous Carbon Films Using Nano-fretting Testing 54
2.6.1 Nano-fretting: State-of-the-art 55
2.6.2 Nano-fretting of Thin DLC Films on Si 55
2.6.3 Nano-fretting of DLC Coatings on Steel 57
2.7 Conclusion 58
References 59
3 Mechanical Evaluation of Nanocoatings under Extreme Environments for Application in Energy Systems 69
E.J. Rubio, G. Martinez, S.K. Gullapalli, M. Noor-A-Alam and C.V. Ramana
3.1 Introduction 69
3.2 Thermal Barrier Coatings 70
3.2.1 Nanoindentation Characterization of TBCs 72
3.2.2 Mechanical Properties of Hafnium-based TBCs 74
3.3 Nanoindentation Evaluation of Coatings for Nuclear Power Generation Applications 76
3.3.1 Evaluation ofW-based Materials for Nuclear Application 77
3.4 Conclusions and Outlook 80
Acknowledgments 81
References 81
4 Evaluation of the Nanotribological Properties of Thin Films 83
ShojiroMiyake and MeiWang
4.1 Introduction 83
4.2 Evaluation Methods of Nanotribology 83
4.3 Nanotribology Evaluation Methods and Examples 84
4.3.1 Nanoindentation Evaluation 84
4.3.2 Nanowear and Friction Evaluation 88
4.3.2.1 Nanowear Properties 89
4.3.2.2 Frictional Properties with Different Lubricants 91
4.3.2.3 Nanowear and Frictional Properties, Evaluated with and without
Vibrations 95
4.3.3 Evaluation of the Force Modulation 98
4.3.4 Evaluation of the Mechanical and Other Physical Properties 102
4.4 Conclusions 108
References 108
5 Nanoindentation on Tribological Coatings 111
Francisco J.G. Silva
5.1 Introduction 111
5.2 Relevant Properties on Coatings for Tribological Applications 116
5.3 How can Nanoindentation Help Researchers to Characterize Coatings? 116
5.3.1 Thin Coatings Nanoindentation Procedures 118
5.3.2 Hardness Determination 120
5.3.3 Young's Modulus Determination 123
5.3.4 Tensile Properties Determination 124
5.3.5 Fracture Toughness inThin Films 125
5.3.6 Coatings Adhesion Analysis 126
5.3.7 Stiffness and Other Mechanical Properties 127
5.3.8 Simulation and Models Applied to Nanoindentation 128
References 129
6 Nanoindentation of Macro-porous Materials for Elastic Modulus and Hardness Determination 135
Zhangwei Chen
6.1 Introduction 135
6.1.1 Nanoindentation Fundamentals for Dense Materials 135
6.1.2 Introduction to Porous Materials 137
6.1.3 Studies of Elastic Properties of Porous Materials 138
6.2 Nanoindentation of Macro-porous Bulk Ceramics 140
6.3 Nanoindentation of Bone Materials 143
6.4 Nanoindentation of Macro-porous Films 144
6.4.1 Substrate Effect 145
6.4.2 Densification Effect 147
6.4.3 Surface Roughness Effect 149
6.5 Concluding Remarks 151
Acknowledgements 151
References 151
7 Nanoindentation Applied to DC Plasma Nitrided Parts 157
Silvio Francisco Brunatto and CarlosMauricio Lepienski
7.1 Introduction 157
7.2 Basic Aspects of DC Plasma Nitrided Parts 160
7.2.1 The Potential Distribution for an Abnormal Glow Discharge 160
7.2.2 Plasma-surface Interaction in Cathode Surface 161
7.2.3 Electrical Configuration Modes in DC Plasma Nitriding 162
7.3 Basic Aspects of Nanoindentation in Nitrided Surfaces 163
7.4 Examples of Nanoindentation Applied to DC Plasma Nitrided Parts 167
7.4.1 Mechanical Polishing: Nanoindentation in Niobium 169
7.4.2 Surface Roughness: Nanoindentation in DC Plasma Nitrided Parts 170
7.4.2.1 Nanoindentation in DC Plasma Nitrided Niobium 170
7.4.2.2 Nanoindentation in DC Plasma Nitrided Titanium 174
7.4.2.3 Nanoindentation in DC Plasma Nitrided Martensitic Stainless Steel 175
7.4.3 Nitrogen-concentration Gradients: Nanoindentation in DC Plasma Nitrided Tool Steel 176
7.4.4 Crystallographic Orientation: Nanoindentation in DC Plasma Nitrided Austenitic Stainless Steels 177
7.5 Conclusion 178
Acknowledgements 179
References 179
8 Nanomechanical Properties of Defective Surfaces 183
Oscar Rodriguez de la Fuente
8.1 Introduction 183
8.1.1 The Role of Surface Defects in Plasticity 183
8.1.2 Experimental Techniques for Visualization and Generation of Surface Defects 184
8.1.3 Approaches to Study and Probe Nanomechanical Properties 185
8.2 Homogeneous and Heterogeneous Dislocation Nucleation 186
8.2.1 Homogeneous Dislocation Nucleation 186
8.2.2 Heterogeneous Dislocation Nucleation 188
8.3 Surface Steps 190
8.3.1 Studies on Surface Steps 191
8.4 Subsurface Defects 194
8.4.1 Sub-surface Vacancies 195
8.4.2 Sub-surface Impurities and Dislocations 195
8.5 Rough Surfaces 197
8.6 Conclusions 200
Acknowledgements 200
References 200
9 Viscoelastic and Tribological Behavior of Al2O3 Reinforced Toughened Epoxy Hybrid Nanocomposites 205
Mandhakini Mohandas and AlagarMuthukaruppan
9.1 Introduction 205
9.2 Experimental 206
9.2.1 Materials 206
9.2.2 FTIR Analysis 208
9.2.3 Results and Discussion 209
9.2.3.1 Viscoeleastic Properties 210
9.2.3.2 Hardness and Modulus by Nanoindentation 214
9.3 Conclusion 219
References 220
10 Nanoindentation of Hybrid Foams 223
Anne Jung, Zhaoyu Chen and Stefan Diebels
10.1 Introduction 223
10.1.1 Motivation 223
10.1.2 State of the art of Nanoindentation of Metal and Metal Foam 226
10.2 Sample Material and Preparation 230
10.2.1 Al Material and Coating Process 230
10.2.2 Sample Preparation for Nanoindentation 231
10.3 Nanoindentation Experiments 232
10.3.1 Experimental Setup 232
10.3.2 Results and Discussion 232
10.4 Conclusions and Outlook 239
Acknowledgements 240
References 240
11 AFM-based Nanoindentation of Cellulosic Fibers 247
Christian Ganser and Christian Teichert
11.1 Introduction 247
11.2 Experimental 248
11.2.1 AFM Instrumentation 248
11.2.2 AFM-based Nanoindentation 250
11.2.3 Comparison with Results of Classical NI 255
11.2.4 Sample Preparation 256
11.3 Mechanical Properties of Cellulose Fibers 257
11.3.1 Pulp Fibers 257
11.3.2 Swollen Viscose Fibers 259
11.4 Conclusions and Outlook 265
Acknowledgments 265
References 266
12 Evaluation of Mechanical and Tribological Properties of Coatings for Stainless Steel 269
A.Mina, J.C. Caicedo,W. Aperador, M. Mozafari and H.H. Caicedo
12.1 Introduction 269
12.2 Experimental Details 270
12.3 Results and Discussion 271
12.3.1 Crystal Lattice Arrangement of -TCP/Ch Coatings 271
12.3.2 Surface Coating Analysis 272
12.3.3 Morphological Analysis of the -TCP-Ch Coatings 274
12.3.4 Mechanical Properties 276
12.3.5 Tribological Properties 279
12.3.6 SurfaceWear Analysis 280
12.3.7 Adhesion Behaviour 281
12.4 Conclusions 283
Acknowledgements 283
References 283
13 Nanoindentation in Metallic Glasses 287
Vahid Nekouie, Anish Roy and Vadim V. Silberschmidt
13.1 Introduction 287
13.1.1 Motivation 287
13.1.2 Nanoindentation Studies of Metallic Glasses 288
13.1.2.1 Pile-up and Sink-in 291
13.1.2.2 Indentation Size Effect 293
13.2 Experimental Studies 296
13.2.1 Nano Test Platform III Indentation System 296
13.2.2 Calibration 297
13.2.2.1 Frame Compliance 298
13.2.2.2 Cross-hair Calibration 298
13.2.2.3 Indenter Area Function 298
13.2.3 Experimental Procedure 301
13.2.4 Results and Discussion 301
13.3 Conclusions 307
References 308
Part II 313
14 Molecular Dynamics Modeling of Nanoindentation 315
C.J. Ruestes, E.M. Bringa, Y. Gao and H.M. Urbassek
14.1 Introduction 315
14.2 Methods 316
14.2.1 The Indentation Tip 318
14.2.2 Control Methods Used in Experiment and in MD Simulations 319
14.2.3 Penetration Rate 320
14.3 Interatomic Potentials 321
14.3.1 Elastic Constants 321
14.3.2 Generalized Stacking Fault Energies 322
14.4 Elastic Regime 324
14.5 The Onset of Plasticity 325
14.5.1 Evolution of the Dislocation Network 325
14.5.2 Contact Area and Hardness 327
14.5.3 Indentation Rate Effect 328
14.5.4 Tip Diameter Effect 329
14.6 The Plastic Zone: Dislocation Activity 329
14.6.1 Face-centered Cubic Metals 329
14.6.2 Body-centered Cubic Metals 330
14.6.3 Quantification of Dislocation Length and Density 331
14.6.4 Pile-up 333
14.6.5 Geometrically-necessary Dislocations and the Identification of Intrinsic Length-scales from Hardness Simulations 334
14.7 Outlook 336
Acknowledgements 337
References 337
15 Continuum Modelling and Simulation of Indentation in Transparent Single Crystalline Minerals and Energetic Solids 347
J.D. Clayton, B.B. Aydelotte, R. Becker, C.D. Hilton and J. Knap
15.1 Introduction 347
15.2 Theory: MaterialModelling 349
15.2.1 General Multi-field Continuum Theory 349
15.2.2 Crystal Plasticity Theory 350
15.2.3 Phase FieldTheory for Twinning 351
15.3 Application: Indentation of RDX Single Crystals 352
15.3.1 Review of PriorWork 353
15.3.2 New Results and Analysis 354
15.4 Application: Indentation of Calcite Single Crystals 356
15.4.1 Review of PriorWork 359
15.4.2 New Results and Analysis 361
15.5 Conclusions 364
Acknowledgements 365
References 365
16 NanoindentationModeling: From Finite Element to Atomistic Simulations 369
Daniel Esque- de los Ojos and Jordi Sort
16.1 Introduction 369
16.2 Scaling and Dimensional Analysis Applied to IndentationModelling 370
16.2.1 Geometrical Similarity of Indenter Tips 370
16.2.2 Dimensional Analysis 371
16.2.3 Dimensional Analysis Applied to Extraction of Mechanical Properties 372
16.3 Finite Element Simulations of Advanced Materials 374
16.3.1 Nanocrystalline Porous Materials and Pressure-sensitive Models 375
16.3.2 Finite Element Simulations of 1D Structures: Nanowires 378
16.3.3 Continuum Crystal Plasticity Finite Element Simulations: Nanoindentation of Thin Solid Films 380
16.4 Nucleation and Interaction of Dislocations During Single Crystal Nanoindentaion: Atomistic Simulations 383
16.4.1 Dislocation Dynamics Simulations 383
16.4.2 Molecular Dynamics Simulations 385
References 386
17 Nanoindentation in silico of Biological Particles 393
Olga Kononova, Kenneth A. Marx and Valeri Barsegov
17.1 Introduction 393
17.2 ComputationalMethodology of Nanoindentation in silico 395
17.2.1 Molecular Modelling of Biological Particles 395
17.2.2 Coarse-graining: Self-organized Polymer (SOP) Model 396
17.2.3 MultiscaleModeling Primer: SOP Model Parameterization for Microtubule Polymers 398
17.2.4 Using Graphics Processing Units as Performance Accelerators 399
17.2.5 Virtual AFM Experiment: Forced Indentation in silico of Biological Particles 401
17.3 Biological Particles 403
17.3.1 Cylindrical Particles: Microtubule Polymers 403
17.3.2 Spherical Particles: CCMV Shell 404
17.4 Nanoindentation in silico: Probing Reversible Changes in Near-equilibrium Regime 406
17.4.1 Probing Reversible Transitions 406
17.4.2 Studying Near-equilibrium Dynamics 407
17.5 Application of in silico Nanoindentation: Dynamics of Deformation of MT and CCMV 409
17.5.1 Long Polyprotein - Microtubule Protofilament 409
17.5.2 Cylindrical Particle - Microtubule Polymer 411
17.5.3 Spherical Particle - CCMV Protein Shell 416
17.6 Concluding Remarks 421
References 424
18 Modeling and Simulations in Nanoindentation 429
Yi Sun and Fanlin Zeng
18.1 Introduction 429
18.2 Simulations of Nanoindention on Polymers 430
18.2.1 Models and Simulation Methods 430
18.2.2 Load-displacement Responses 431
18.2.3 Hardness and Young's Modulus 433
18.2.4 The Mechanism of Mechanical Behaviours and Properties 437
18.3 Simulations of Nanoindention on Crystals 441
18.3.1 Models and Simulation Methods 442
18.3.2 The Load-displacement Responses 444
18.3.3 Dislocation Nucleation 446
18.3.4 Mechanism of Dislocation Emission 449
18.4 Conclusions 455
Acknowledgments 456
References 456
19 Nanoindentation of Advanced Ceramics: Applications to ZrO2 Materials 459
Joan Josep Roa Rovira, Emilio Jimenez Pique andMarc J. Anglada Gomila
19.1 Introduction 459
19.2 IndentationMechanics 460
19.2.1 Deformation Mechanics 460
19.2.2 Elastic Contact 461
19.2.3 Elasto/plastic Contact 462
19.3 Fracture Toughness 462
19.4 Coatings 463
19.4.1 Coating Hardness 463
19.4.2 Coating Elastic Modulus 464
19.5 Issues for Reproducible Results 464
19.6 Applications of Nanoindentation to Zirconia 465
19.6.1 Hardness and Elastic Modulus 466
19.6.2 Stress-strain Curve and Phase Transformation 467
19.6.3 Plastic Deformation Mechanisms 468
19.6.4 Mechanical Properties of Damaged Surfaces 468
19.6.5 Relation Between Microstructure and Local Mechanical Properties by
Massive Nanoindentation Cartography 471
19.7 Conclusions 472
Acknowledgements 472
References 473
20 FEM Simulation of Nanoindentation 481
F. Poehl, W. Theisen and S. Huth
20.1 Introduction 481
20.2 Indentation of Isotropic Materials 482
20.3 Indentation of Thin Films 489
20.4 Indentation of a Hard Phase Embedded in Matrix 490
References 495
21 Investigations Regarding Plastic Flow Behaviour and Failure Analysis on CrAlN Thin Hard Coatings 501
Jan Perne
21.1 Introduction 501
21.2 Description of the Method 501
21.2.1 Flow Curve Determination 502
21.2.1.1 Nanoindentation Step 502
21.2.1.2 Yield Strength Determination 502
21.2.1.3 Flow Curve Determination by Iterative Simulation 503
21.2.1.4 Determination of Strain Rate and Temperature Dependency 503
21.2.2 Failure Criterion Determination with Nano-scratch Analysis 503
21.3 Investigations into the CrAlN Coating System 504
21.3.1 Flow curve dependency on chemical composition and microstructure 504
21.3.2 Strain Rate Dependency of Different CrN-AlN Coating Systems 506
21.3.3 Failure criterion determination on a CrN/AlN nanolaminate 507
21.4 Concluding Remarks 509
References 511
22 Scale Invariant Mechanical Surface Optimization 513
Norbert Schwarzer
22.1 Introduction 513
22.1.1 Interatomic Potential Description of Mechanical Material Behavior 513
22.1.2 The Effective Indenter Concept and Its Extension to Layered Materials 514
22.1.3 About Extensions of the Oliver and Pharr Method 514
22.1.3.1 Making the Classical Oliver and Pharr Method Fit for Time Dependent Mechanical Behavior 515
22.1.4 Introduction to the Physical Scratch and/or Tribological Test and its Analysis 515
22.1.5 Illustrative Hypothetical Example for Optimization Against Dust Impact 515
22.1.6 About the Influence of Intrinsic Stresses 516
22.2 Theory 517
22.2.1 First Principle Based Interatomic Potential Description of Mechanical Material Behavior 517
22.2.2 The Effective Indenter Concept 521
22.2.3 An Oliver and Pharr Method for Time Dependent Layered Materials 522
22.2.4 Theory for the Physical Scratch and/or Tribological Test 533
22.2.5 From Quasi-Static Experiments and Parameters to DynamicWear, Fretting and Tribological Tests 534
22.2.6 Including Biaxial Intrinsic Stresses 537
22.3 The Procedure 540
22.4 Discussion by Means of Examples 544
22.5 Conclusions 555
Acknowledgements 555
Referencess 556
23 Modelling and Simulations of Nanoindentation in Single Crystals 561
Qiang Liu,Murat Demiral, Anish Roy and Vadim V. Silberschmidt
23.1 Introduction 561
23.2 Review of IndentationModelling 564
23.3 Crystal PlasticityModelling of Nanoindentation 565
23.3.1 Indentation of F.C.C. Copper Single Crystal 567
23.3.2 Indentation of B.C.C. Ti-64 569
23.3.3 Indentation of B.C.C. Ti-15-3-3 571
23.4 Conclusions 573
References 574
24 Computer Simulation and Experimental Analysis of Nanoindentation Technique 579
A. Karimzadeh,M.R. Ayatollahi and A. Rahimi
24.1 Introduction 579
24.2 Finite Element Simulation for Nanoindentation 580
24.3 Finite Element Modeling 580
24.3.1 Geometry 580
24.3.2 Material Characteristics 581
24.3.3 Boundary Condition 582
24.3.4 Interaction 582
24.3.5 Meshing 582
24.4 Verification of Finite Element Simulation 583
24.4.1 Nanoindentation Experiment on Al 1100 584
24.4.2 Comparison Between Simulation and Experimental Results for Al 1100 584
24.4.2.1 Load-displacement 584
24.4.2.2 Hardness 588
24.5 Molecular Dynamic Modeling for Nanoindentation 591
24.5.1 Simulation Procedure 592
24.6 Results of Molecular Dynamic Simulation 595
24.7 Conclusions 597
References 597
25 Atomistic Simulations of Adhesion, Indentation andWear at Nanoscale 601
Jun Zhong, Donald J. Siegel, Louis G. Hector, Jr. and James B. Adams
25.1 Introduction 601
25.2 Methodologies 604
25.2.1 Density FunctionalTheory 604
25.2.1.1 The Exchange-correlation Functional 605
25.2.1.2 PlaneWaves and Supercell 606
25.2.2 Pseudopotential Approximation 606
25.2.3 Molecular Dynamics 607
25.2.3.1 Equations of Motion 607
25.2.3.2 Algorithms 608
25.2.3.3 Statistical Ensembles 608
25.2.3.4 Interatomic Potentials 608
25.2.3.5 Ab initio Molecular Dynamics 609
25.2.4 Some Commercial Software 611
25.2.4.1 The VASP 611
25.2.4.2 The LAMMPS 611
25.3 Density Functional Study of Adhesion at the Metal/Ceramic Interfaces 612
25.3.1 Calculations 612
25.3.2 Effect of Surface Energies in theWsep 614
25.3.3 Conclusions 615
25.4 Molecular Dynamics Simulations of Nanoindentation 616
25.4.1 Empirical Modeling 616
25.4.1.1 Modeling Geometry and Simulation Procedures 617
25.4.1.2 Results and discussions 618
25.4.1.3 Conclusions 622
25.4.2 Ab initio Modeling 622
25.4.2.1 Modeling Geometry and Simulation Procedures 622
25.4.2.2 Results and Discussions 624
25.5 Molecular Dynamics Simulations of AdhesiveWear on the Al-substrate 628
25.5.1 Modeling Geometry and Simulation Procedures 629
25.5.2 Results and Discussions 630
25.5.2.1 One CommonWear Sequence 630
25.5.2.2 Thermal Analysis for theWear Sequence 631
25.5.2.3 Wear Rate Analyses 632
25.6 Summary and Prospect 636
Acknowledgments 638
References 638
26 Multiscale Model for Nanoindentation in Polymer and Polymer Nanocomposites 647
Rezwanur Rahman
26.1 Introduction 647
26.2 Modeling Scheme 648
26.2.1 Details of the MD Simulation 649
26.3 Nanoindentation Test 650
26.4 Theoretically and Experimentally Determined Result 651
26.5 Multiscale of Complex Heterogeneous Materials 651
26.5.1 Introduction to Peridynamics 652
26.5.2 Nonlocal Multiscale Modeling using Peridynamics: Linking Macro- to Nano-scales 654
26.6 MultiscaleModeling for Nanoindentation in Epoxy: EPON 862 655
26.7 UnifiedTheory for MultiscaleModeling 658
26.8 Conclusion 658
References 659
Index 663
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