Dynamic Damage and Fragmentation

Engineering structures may be subjected to extreme high-rate loading conditions, like those associated with natural disasters (earthquakes, tsunamis, rock falls, etc.) or those of anthropic origin (impacts, fluid–structure interactions, shock wave transmissions, etc.). Characterization and modeling of the mechanical behavior of materials under these environments is important in predicting the response of structures and improving designs.

This book gathers contributions by eminent researchers in academia and government research laboratories on the latest advances in the understanding of the dynamic process of damage, cracking and fragmentation. It allows the reader to develop an understanding of the key features of the dynamic mechanical behavior of brittle (e.g. granular and cementitious), heterogeneous (e.g. energetic) and ductile (e.g. metallic) materials.

David Edward Lambert is a member of the scientific and professional cadre of Senior Executives, and Chief Scientist of the Air Force Research Laboratory, Munitions Directorate, Eglin, USA.

Crystal L. Pasiliao is a Senior Research Scientist at the Air Force Research Laboratory, Munitions Directorate, Eglin, USA.

Benjamin Erzar is a Senior Research Scientist at the Commissariat à l’Energie Atomique, Gramat, France.

Benoit Revil-Baudard is a Research Scientist in the Department of Mechanical and Aerospace Engineering at the University of Florida, REEF, Shalimar, USA.

Oana Cazacu is Professor in the Department of Mechanical and Aerospace Engineering at the University of Florida, REEF, Shalimar, USA.

Preface xiii

Chapter 1. Some Issues Related to the Modeling of Dynamic Shear Localization-assisted Failure 1
Patrice LONGÈRE

1.1. Introduction 1

1.2. Preliminary/fundamental considerations 3

1.2.1. Localization and discontinuity 3

1.2.2. Isothermal versus adiabatic conditions 6

1.2.3. Sources of softening 9

1.2.4. ASB onset 22

1.2.5. Scale postulate 26

1.3. Small-scale postulate-based approaches 27

1.3.1. Material of the band viewed as an extension of the solid material behavior before ASB onset 28

1.3.2. Material of the band viewed as a fluid material 29

1.3.3. ASB viewed as a damage mechanism 31

1.3.4. Assessment 32

1.4. Embedded band-based approaches (large-scale postulate) 33

1.4.1. Variational approaches 34

1.4.2. Enriched finite element kinematics 38

1.4.3. Enriched constitutive model 41

1.4.4. Discussion 43

1.5. Conclusion 44

1.6. Acknowledgments 45

1.7. References 45

Chapter 2. Analysis of the Localization Process Prior to the Fragmentation of a Ring in Dynamic Expansion 53
Skander EL MAÏ, Sébastien MERCIER and Alain MOLINARI

2.1. Introduction 53

2.1.1. Fragmentation experiments 54

2.1.2. Fragmentation theories 54

2.2. An extension of a linear stability analysis developed in [MER 03] 59

2.2.1. Position of the problem 59

2.2.2. Classical linear stability analysis 60

2.2.3. Evolution of the cross-section perturbation 62

2.2.4. Analysis of the potential sites of necking 65

2.3. Outcomes of the approach 70

2.3.1. Effects of the loading velocity on neck spacing distribution 70

2.3.2. Effects of an imposed dominant mode in the initial perturbation 72

2.3.3. Comparison of the approach with numerical simulations 83

2.4. Conclusion 89

2.5. References 90

Chapter 3. Gradient Damage Models Coupled with Plasticity and Their Application to Dynamic Fragmentation 95
Arthur GEROMEL FISCHER and Jean-Jacques MARIGO

3.1. Introduction 95

3.2. Theoretical aspects 96

3.2.1. Gradient damage models 96

3.2.2. Damage coupled with plasticity 106

3.2.3. Dynamic gradient damage 117

3.3. Numerical implementation 122

3.4. Applications 123

3.4.1. 1D fracture 124

3.4.2. Material behavior 124

3.4.3. Dimensionless parameters 126

3.4.4. 1D period bar 131

3.4.5. Cylinder under internal pressure 135

3.5. Conclusion 138

3.6. References 139

Chapter 4. Plastic Deformation of Pure Polycrystalline Molybdenum 143
Geremy J. KLEISER, Benoit REVIL-BAUDARD and Oana CAZACU

4.1. Introduction 143

4.2. Quasi-static and dynamic data on a pure polycrystalline Mo 144

4.2.1. Analysis of the quasi-static uniaxial tension test results on smooth specimens 147

4.2.2. Split Hopkinson pressure bar data 154

4.2.3. Taylor cylinder impact data 155

4.3. Constitutive model for polycrystalline Mo 158

4.4. Predictions of the mechanical response 162

4.4.1. FE. predictions of the quasi-static uniaxial tensile response for notched specimens 162

4.5. Conclusions 172

4.6. References 173

Chapter 5. Some Advantages of Advanced Inverse Methods to Identify Viscoplastic and Damage Material Model Parameters 177
Bertrand LANGRAND, Delphine NOTTA-CUVIER, Thomas FOUREST and Eric MARKIEWICZ

5.1. Introduction 177

5.2. Experimental devices for material characterization over a large range of strain rates 180

5.3. Identification of elasto-viscoplastic and damage material Parameters 184

5.3.1. Direct approach for material parameter identification 184

5.3.2. Inverse approaches for material parameter identification 192

5.4. Conclusions 204

5.5. Acknowledgments 205

5.6. References 205

Chapter 6. Laser Shock Experiments to Investigate Fragmentation at Extreme Strain Rates 213
Thibaut DE RESSÉGUIER, Didier LOISON, Benjamin JODAR, Emilien LESCOUTE,Caroline ROLAND, Loïc SIGNOR and André DRAGON

6.1. Introduction 214

6.2. Phenomenology of laser shock-induced fragmentation 215

6.3. Spall fracture 217

6.4. Microspall after shock-induced melting 222

6.5. Microjetting from geometrical defects 225

6.6. Conclusion 230

6.7. References 231

Chapter 7. One-dimensional Models for Dynamic Fragmentation of Brittle Materials 237
David CERECEDA, Nitin DAPHALAPURKAR and Lori GRAHAM BRADY

7.1. Introduction 237

7.2. Methods 242

7.3. Results 244

7.3.1. Mono-phase materials 244

7.3.2. Multi-phase materials 251

7.4. Conclusions 258

7.5. References 259

Chapter 8. Damage and Wave Propagation in Brittle Materials 263
Quriaky GOMEZ, Jia LI and Ioan R. IONESCU

8.1. Introduction 263

8.2. Short overview of damage models 264

8.2.1. Effective elasticity of a cracked solid 266

8.2.2. Damage evolution 268

8.3. 1D wave propagation 275

8.3.1. Problem statement 276

8.3.2. A single family of micro-cracks 278

8.3.3. Three families of micro-cracks 280

8.4. Two-dimensional anti-plane wave propagation 280

8.4.1. Anisotropic damage under isotropic loading 281

8.4.2. Anisotropic loading of an initial isotropic damaged material 284

8.5. Blast impact and damage evolution 286

8.6. Conclusions and perspectives 291

8.7. Acknowledgments 292

8.8. References 292

Chapter 9. Discrete Element Analysis to Predict Penetration and Perforation of Concrete Targets Struck by Rigid Projectiles 297
Laurent DAUDEVILLE, Andria ANTONIOU, Ahmad OMAR, Philippe MARIN, Serguei POTAPOV and Christophe PONTIROLI

9.1. Introduction 297

9.2. Discrete element model 299

9.2.1. Definition of interactions 299

9.2.2. Constitutive behavior of concrete: Discrete element model 300

9.2.3. Linear elastic constitutive behavior 301

9.2.4. Nonlinear constitutive behavior 302

9.2.5. Strain rate dependency 305

9.3. Simulation of impacts 307

9.3.1. Impact experiments 307

9.3.2. Modeling of impact experiments 308

9.4. Conclusion 311

9.5. References 311

Chapter 10. Bifurcation Micromechanics in Granular Materials 315
Antoine WAUTIER, Jiaying LIU, François NICOT and Félix DARVE

10.1. Introduction 315

10.2. Application of the second-order work criterion at representative volume element scale 318

10.3. From macro to micro analysis of instability 322

10.3.1. Local second-order work and contact sliding 322

10.3.2. Role of strong contact network in stable and unstable loading directions 323

10.3.3. From contact sliding to mesoscale mechanisms 326

10.3.4. Micromechanisms leading to bifurcation at the representative volume element scale 329

10.4. Diffuse and localized failure in a unified framework 331

10.4.1. Diffuse and localized failure pattern 331

10.4.2. Common micromechanisms and microstructures 332

10.5. Conclusion 334

10.6. References 335

Chapter 11. Influence of Specimen Size on the Dynamic Response of Concrete 339
Xu NIE, William F. HEARD and Bradley E. MARTIN

11.1. Introduction 339

11.2. Materials and specimens 341

11.3. Experimental techniques 343

11.3.1. Kolsky compression bar theory and set-up 343

11.3.2. Pulse shaping technique 345

11.4. Results and discussion 350

11.4.1. Pulse shaper design for Kolsky compression bar systems 350

11.4.2. Rate and specimen size effect on failure strength 355

11.5. Conclusion 360

11.6. Acknowledgments 362

11.7. References 362

Chapter 12. Shockless Characterization of Ceramics Using High-Pulsed Power Technologies 365
Jean-Luc ZINSZNER, Benjamin ERZAR and Pascal FORQUIN

12.1. Introduction 365

12.1.1. Presentation of the silicon carbide grades 367

12.2. Principle of the GEPI generator 368

12.3. Dynamic compression of ceramics 370

12.3.1. Lagrangian analysis of velocity profiles 371

12.3.2. Experimental results 372

12.4. Dynamic tensile strength of ceramics 374

12.4.1. Experimental methodology and data processing 375

12.4.2. Characterization of two silicon carbide grades 377

12.4.3. Post-mortem analyses of damaged samples 378

12.5. Conclusions 380

12.6. Acknowledgments 381

12.7. References 381

Chapter 13. A Eulerian Level Set-based Framework for Reactive Meso-scale Analysis of Heterogeneous Energetic Materials 387
Nirmal KUMAR RAI and H.S. UDAYKUMAR

13.1. Introduction 387

13.2. Numerical framework 390

13.2.1. Governing equations 390

13.2.2. Constitutive model for HMX 390

13.2.3. Reactive modeling of HMX 393

13.2.4. Level set representation of embedded interface 395

13.2.5. Image processing approach: Representing real geometries 395

13.3. Results 398

13.3.1. Grid refinement study 400

13.3.2. Collapse behavior of voids present in the pressed HMX material 401

13.3.3. Criticality conditions for Class III and Class V samples 403

13.3.4. Meso-scale criticality conditions for pressed energetic materials 405

13.4. Conclusions 411

13.5. Acknowledgments 412

13.6. References 412

Chapter 14. A Well-posed Hypoelastic Model Derived From a Hyperelastic One 417
Nicolas FAVRIE and Sergey GAVRILYUK

14.1. Introduction 417

14.2. A general hyperelastic model formulation 418

14.3. Evolution equation for the deviatoric part of the stress tensor: neo-Hookean solids 420

14.3.1. Expression of tr(b) as a function of the invariants of S 421

14.3.2. Hypoelastic formulation 423

14.4. Conclusions 424

14.5. Acknowledgments 425

14.6. References 425

Appendix A: Case a = 0.5 429

List of Authors 433

Index 437

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