Damaging Effects of Weapons and Ammunition

Igor A. Balagansky, DSc, is Professor of the Gas Dynamic Devices Department at Novosibirsk State Technical University in Russia. He has authored over 100 scientific publications and is a Federal Expert in Science and Technology for the Russian Ministry of Science and Higher Education.

Preface xv

I Introduction 1

I.1 Ammunition Types and Characteristics of Their Damaging Effect 1

I.1.1 Basic Concepts and Definitions 1

I.1.2 Types of Ammunition and Their Damaging Effects 2

I.2 Generalized Characteristics of the Damaging Effect 3

I.2.1 Degrees of Damage 3

I.2.2 Contact and Remote Ammunition 4

I.2.3 Generalized Characteristics of Contact Ammunition 4

I.2.4 The Accumulation of Damage 5

I.2.5 Generalized Characteristics of the Damaging Effect of Remote Ammunition 6

I.2.6 Specified Zone of Target Damage 8

I.3 Evaluation of the Effectiveness of Shooting 9

I.3.1 The Concepts of Combat Effectiveness of Weapons 9

I.3.2 Classification of Targets, Typical Efficiency Indicators 9

I.3.3 Dispersion During Shooting 10

I.3.4 Scheme of Two Groups of Errors 12

I.3.5 Probability of Damaging a Single Target 14

I.3.5.1 Damaging the Target with a Single Shot 14

I.3.5.2 Damaging the Target with Multiple Shots 16

I.3.6 Evaluation of the Effectiveness of Firing on a Group Target 18

I.3.7 Evaluation of the Effectiveness of Firing at Area Target 21

I.3.7.1 Fraction of Damage U with One Shot 22

I.3.7.2 Determining the Average Damage Fraction at Multiple Shots 29

I.4 Self-assessment Questions 29

References 30

1 Fragmentation Ammunitions 31

1.1 Basic Concepts and Definitions. General Information 31

1.1.1 Classification of Fragmentation Ammunition 31

1.1.2 High-explosive Fragmentation Projectiles of Field Artillery 32

1.1.3 Brief Description of Other Classes of Fragmentation Ammunition 35

1.2 The Mechanics of High-speed Deformation and Destruction of Shells Under the Action of an Explosion 38

1.3 Modeling the Processes of Explosive Fragmentation of Shells Using Standard Samples 46

1.3.1 The Basic Theorem of the Dimensional Theory 46

1.3.2 Dimensional Analysis for Fragmentation Processes 47

1.3.2.1 Chemical Composition 47

1.3.2.2 Grain Size 47

1.3.3 Ratios for the Total Number of Fragments 49

1.3.4 Standard Fragmentation Cylinders 50

1.3.5 The Main Grades of Fragmentation Steels 53

1.3.5.1 Group of Carbon Steels 53

1.3.5.2 Siliceous Steels 54

1.3.5.3 Сhromic Steels 54

1.3.5.4 Silicon–Manganese Steels 54

1.3.6 Prospects of Using Manganese Austenitic Steels to Improve Fragmentation Quality 54

1.4 Statistical Models of the Fragment Fields and the Fragment Spectra 57

1.4.1 Fields of Fragment Dispersion, Methods of Controlling the Fields of Dispersion 57

1.4.2 Laws of Fragment Distribution by Mass 63

1.4.2.1 Numerical Distributions 63

1.4.2.2 Mass Distributions 65

1.4.3 Analytical Representation of Fragment Distribution Laws 66

1.4.3.1 Weibull Distribution 66

1.4.3.2 The Mott Law 67

1.4.4 Distribution of Fragments by Shape 67

1.5 External Ballistics of Fragments 68

1.6 Kinds of the Damaging Effect of Fragments 71

1.6.1 Ignition Effect of Fragments 72

1.6.2 Initiating Action of Fragments 73

1.6.3 Effects of a Dense Flow of Fragments 73

1.7 Laws of Target Damage with Fragments 73

1.8 Specified Zone of Target Damage with Fragmentation Munitions 77

1.8.1 The Area of the Specified Zone 77

1.9 Methods for Optimizing the Parameters of Fragmentation Munitions 79

1.9.1 The Method of Bauman Moscow State Technical University (bmstu) 79

1.9.2 Warhead Optimization for the C-13 Unguided Aircraft Missile 84

1.10 Vulnerability Characteristics of Objects to the Effects of Fragments, Determination of Safe Distances 85

1.10.1 Methods of Efficiency Estimation 85

1.10.2 Characteristics of Target Vulnerability to Fragment Action 88

1.10.3 Determining Safe Distances 89

1.11 Self-assessment Questions 90

References 92

2 Ammunitions with Shaped Charges 93

2.1 Basic Concepts and Definitions. General Information 93

2.1.1 Artillery Projectiles 94

2.1.2 Engineering Mines with Shaped Charges 94

2.1.3 Anti-tank-guided Missiles (ATGM) 98

2.1.4 Anti-tank Bombs and Cluster Submunitions 99

2.2 Fundamentals of Cumulative Effects 100

2.2.1 The Phenomenon of Cumulation 100

2.2.2 The Cumulative Effect in Explosives Charges with Cavities 103

2.2.3 Hydrodynamic Theory of Shaped Charges 107

2.2.3.1 Theory of Jets of Ideal Fluid 107

2.2.3.2 Theory of Shaped Charge Jet Formation 109

2.2.3.3 PER-theory 110

2.2.4 Limitations of Hydrodynamic Theory 111

2.2.4.1 The “Reverse” Cumulation Mode 111

2.2.5 Accounting for Compressibility of the Liner Material 112

2.3 Explosion Loading of Shaped Charge Liners, Their Throwing, and Collapse 114

2.3.1 Calculation of Throw Velocity and Rotation Angle of a Shaped Charge Liner 114

2.3.1.1 The Planar Case 114

2.3.1.2 The Case of Axial Symmetry 116

2.3.2 Investigation of a Shaped Charge with a High-modulus Ceramic Tube 117

2.3.2.1 Experiments 117

2.3.2.2 Numerical Modeling 119

2.4 Formation, Tension of Metal Jets, and Their Penetration into Targets 122

2.4.1 Movement and Breaking of Shaped Charge Jets 122

2.4.2 Penetration of Shaped Charge Jets into Barriers 123

2.5 The Influence of Design Parameters and Manufacturing Technology of Shaped Charges on the Penetration Effect 125

2.5.1 Shaped Charge Liner 125

2.5.2 High-explosive Charge and Case 126

2.5.2.1 HE Charge 126

2.5.2.2 The Shape of HE Charge 127

2.5.2.3 HE Charge Case 127

2.5.3 Detonation Front Control 127

2.5.4 Shaped Charge Manufacturing Technology 128

2.5.4.1 Reasons for Longitudinal–Transverse Instability of Detonation Wave Propagation 130

2.5.4.2 Longitudinal–Transverse Instability of Initiating Shock Waves 131

2.6 Influence of the Operational Conditions of Ammunitions with Shaped Charges on Their Damaging Effects 132

2.6.1 Standoff Distance 132

2.6.2 The Effect of Rotation on the Shaped Charge Effect 133

2.7 Formation and Effect of Explosively Formed Projectiles 134

2.8 The Effect of Ammunition with Shaped Charges on the Armor of Modern Tanks 136

2.8.1 Characteristics of Modern Tank Armor 136

2.8.2 Interaction of Shaped Charge Jets with Explosive Reactive Armor 138

2.8.2.1 External Dynamic Protection 139

2.8.2.2 Built-in Dynamic Protection 139

2.8.2.3 Dynamic Protection Embedded into the Armor 139

2.9 Methods for Evaluating the Effectiveness of Ammunition with Shaped Charges 141

2.10 Self-assessment Questions 142

References 143

3 High-explosive Ammunitions 145

3.1 Basic Concepts and Definitions. General Information 145

3.1.1 Artillery Projectiles 147

3.1.2 Artillery Mines 147

3.1.3 Aviation Bombs 150

3.1.4 Volumetric Explosion Ammunition 152

3.2 Parameters of an Air Shock Wave During the Explosion of High Explosives 156

3.2.1 Physical Phenomena Accompanying the Explosion of a Charge in the Air 156

3.2.2 Air Shock Wave (ASW) Parameters 159

3.2.3 Overpressure, Specific Impulse, and Time of Action of the Air Shock Wave 161

3.2.3.1 Overpressure 162

3.2.3.2 Time of Action of the Shock Wave 164

3.2.3.3 Specific Impulse 164

3.2.4 Influence of Conditions of the Explosion of Explosive Charge on Blast Action 166

3.2.4.1 The Charge Shape 166

3.2.4.2 Own HE Charge Velocity 166

3.2.4.3 Properties of the Soil 167

3.2.4.4 The Khariton Layer 167

3.2.4.5 The Shell of the HE Charge 168

3.3 Reflection of Shock Waves from Barriers and Flow Around Barriers 168

3.3.1 Reflection of a Shock Wave from a Barrier 168

3.3.1.1 Normal Reflection 168

3.3.1.2 Oblique Reflection of SW 170

3.3.2 Flow Around Barriers 176

3.4 Determination of Parameters of an Air Shock Wave During Detonation of Fuel–Air Mixtures 178

3.4.1 General Information About Fuel–Air Mixtures 178

3.4.2 Parameters of an Explosion of Fuel–Air Mixtures in the Detonation Mode 183

3.4.2.1 Parameters of FAM Detonation Inside the Cloud 183

3.4.2.2 Parameters of a Detonation Explosion at the Boundary of the FAM Cloud 186

3.4.2.3 Parameters of the Air Shock Wave During FAM Detonation 188

3.5 Evaluation of the Damaging Effect of Shock Waves on Various Objects 190

3.5.1 Criteria of the Damaging Effect of Shock Waves 190

3.5.2 Characteristics of Target Vulnerability to Blast Effects 192

3.5.2.1 Parameters of the Destruction of Buildings and Other Objects 192

3.5.2.2 Parameters of Human Damage 196

3.5.2.3 Determination of the Degree of Damage of Enemy Personnel 200

3.6 Explosion in Water 202

3.6.1 The Physical Picture of an Explosion in the Water 202

3.6.2 Basic Parameters of an Underwater Explosion 205

3.6.3 The Damaging Effect of an Underwater Explosion 207

3.7 Underground Explosion 209

3.7.1 The Physical Picture of an Underground Explosion 209

3.7.2 Parameters Characterizing the Explosion Process in the Ground 211

3.7.3 The Damaging Effect of an Explosion in the Ground 218

3.7.3.1 Explosion for Ejection 218

3.7.4 Destruction of Underground Structures 218

3.7.4.1 Seismic Action of the Explosion 219

3.8 Self-assessment Questions 222

References 223

4 Penetrating Ammunitions 225

4.1 Basic Concepts and Definitions. General Information 225

4.1.1 Armor-piercing Artillery Projectiles 225

4.1.2 Armor-piercing Caliber Projectiles 226

4.1.3 Sub-caliber Armor-piercing Projectiles 228

4.1.4 Concrete Piercing Artillery Projectiles 233

4.1.5 Weapons and Ammunition for Damaging Extremely Resistant Targets 235

4.1.6 Ammunition of Small Arms 236

4.2 Interaction of Impactors with Targets 238

4.2.1 Classification of Dynamic Penetration Conditions. Main Factors 240

4.2.2 Impact Velocity 240

4.2.3 Mechanical Properties 240

4.2.4 The Geometry of the Impactor and the Barrier 241

4.2.5 The Angle of Impact 241

4.2.6 Other Factors 241

4.2.7 Plug Formation 243

4.2.8 Viscous Crater Formation (Puncture) 244

4.2.9 Ballistic Limit 245

4.2.10 Peculiarities of a High-velocity Impact 250

4.2.11 Damaging Effect of the Impactors on the Living Force 254

4.3 Formulation of Penetration Problems and Ways to Solve Them 255

4.4 Shock with Long Rods 258

4.4.1 Segmented Impactors 263

4.4.2 Telescopic Impactors 263

4.5 Peculiarities of Collision with Thin Targets (Screens) 264

4.6 Self-assessment Questions 266

References 267

5 Numerical Simulation of High-speed Processes 269

5.1 Introduction. Basic Concepts 269

5.2 The System of Equations of Continuum Mechanics 273

5.3 Behavior of Materials Under Intense Dynamic Loads 277

5.3.1 Elastic Medium 278

5.3.2 Hydrodynamic Model 279

5.3.3 Elastoplastic, Viscoplastic, and Elastoviscoplastic Models 281

5.3.4 Dislocation Models 283

5.4 Numerical Methods for Solving Dynamic Problems 286

5.5 Short Introduction to ANSYS AUTODYN 293

5.5.1 Choice of the Numerical Method 294

5.5.1.1 Lagrange Solvers 294

5.5.1.2 Euler Solvers 294

5.5.1.3 ALE (Arbitrary Lagrange Euler) Solver 296

5.5.1.4 Mesh Free Solver 297

5.6 Numerical Modeling Example 297

5.6.1 Experimental Data 298

5.6.2 Numerical Simulation 299

5.7 Self-assessment Questions 305

References 306

Appendix A 309

Index 329