Shaped Charges Engineering Fundamentals

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Shaped Charges Engineering Fundamentals

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Preface

This book originated from a series of short courses, sponsored by Computational Mechanics Associates, taught on this subject over the last four years. The voluminous notes developed for these courses became the core of this book.

It is our intent that this book provide an introduction to the basic aspects of shaped charges. We did not aim to provide exhaustive coverage of the subject. This would be an impossible task since much of the literature in this field is either classified or proprietary, insofar as specific items of hardware are concerned. What was obvious to us, from the first course onward, was the existence of a rieed for a basic text in this area. Thus, this book is not intended to be a "design handbook." We consistently stress the fundamental principles that must be understood before leaping into hardware design. This book will not tell the reader how to design or improve a specific hardware device. It does stress the principles and ideas that must be mastered to achieve such objectives.

The authors assume a basic background in the sciences, such as would be obtained in a first degree science or engineering curriculum in the United States. We assume also the ability to fluently convert between English and metric units as we mix both throughout the book, primarily for the sake of convenience.

Also, we deviated from the norm by relegating many figures and illustrations to the final chapter, our picture book of shaped charges. Those interested only in a brief introduction to the shaped charge field, without mathematical concepts and the like, should read Chapters 1-3 and 14. Other chapters may then be selected at will, depending on individual interest.

The authors are grateful to their many colleagues over the years, at the Ballistic Research Laboratory and elsewhere, who gave unselfishly of their time while allowing us to profit from their knowledge and experience. We also thank those who were instrumental in expediting this material for publication. Special thanks are due to B. Dale Trott, who provided an excellent review and critique of portions of the text; Steven Segletes, who generated Figures 12-19 of Chapter 5; and Manfred Held, Ben Pernick, and Chris W eickert, who generously provided considerable data and illustrations. Special thanks is also due to Dr. Pei Chi Chou, who co-authored (with WPW) in the open literature some of the material discussed in Chapters 8 and 9.

TOC

1 INTRODUCTION TO THE SHAPED CHARGE CONCEPT 1
1.1 The Shaped Charge Concept, 2
1.2 Introduction to Shaped Charges, 4
1.3 The Nomenclature, 8
References, 9
2 HISTORY OF SHAPED CHARGES 11
2.1 The Early History, 11
2.2 The Munroe Effect, 12
2.3 Early Shaped Charge Development, 13
2.4 The World War II Era, 14
2.5 The Post World War II Era, 20
Key to Agencies and List of Abbreviations, 1950, 22
Key to Abbreviations, 22
References, 27
3 APPLICATIONS 32
3.1 Military Applications, 32
3.2 Specialized Applications, 32
3.3 Current Applications, 37
References, 42
4 THE GURNEY VELOCITY APPROXIMATION
4.1 The Gurney Expressions, 46
4.2 Extensions of the Gurney Method, 57
4.3 The Taylor Angle Approximation, 63
4.4 Applicability of the Gurney and Taylor Methods, 66
References, 68
5 SHAPED CHARGE JET FORMATION
5.1 The Birkhoff et al. Theory, 72
5.2 Comments on the Birkhoff et al. Solution, 77
5.3 The PER Theory, 78
5.4 Generalization of Shaped Charge Jet Formation Model, 89
5.5 A Sample Calculation, 92
Appendix A The Hydrodynamic Assumption Justification, 96
References, 97
6 THE VISCO-PLASTIC JET FORMATION THEORY 101
6.1 The Visco-Plastic Concept, 101
6.2 The Visco-Plastic Model, 102
6.3 The Equations for the Visco-Plastic Jet Formation Model, 104
6.4 Jet Coherency, 106
References, 108
7 COMMENTS ON EXPLOSIVE WELDING, BONDING AND FORMING
7.1 Explosive Forming, 111
7.2 Explosive Welding and Bonding, 111
References, 116
8 THE BREAKUP OF SHAPED CHARGE JETS
8.1 Hydrocode Simulation, 118
8.2 Analytical Jet Breakup Models, 120
8.3 Semi-Empirical Formulas, 121
8.4 The Chou-Carleone Model, 123
8.5 Maximum Jet Velocity, 127
References, 127
9 SHAPED CHARGE JET PENETRATION MODELS 130
Notation, 130
9.1 Introduction, 131
9.2 Shaped Charge Jet Penetration, 132
9.3 Variable-Velocity Jets, 137
9.4 Particulated Jets, 143
9.5 Compressible Models, 147
9.6 The Virtual Origin Concept, 148
9.7 Rod Penetration Models, 149
Appendix A Radial Hole Growth, 156
References, 159
References Appendix A, 167
10 OTHER ASPECTS OF SHAPED CHARGES 171
10.1 Fabrication of Shaped Charge Liners, 171
10.2 Shaped Charge Precision Assembly, 178
10.3 Scaling of Shaped Charges, 185
10.4 Shaped Charge Jet Temperature Studies, 191
References, 193
11 COMPUTATIONAL ASPECTS OF EXPLOSIVE- METAL INTERACTIONS 196
11.1 The Governing Equations, 202
11.2 Spatial Discretization, 217
11.3 Mesh Description, 222
11.4 Numerical Integration, 237
11.5 Artificial Viscosity, 238
11.6 Material Models, 243
11.7 Material Failure, 247
References, 259
12 WAVE PROPAGATION CODES FOR SHAPED CHARGE STUDIES 266
12.1 Summary of Wave Propagation Code Characteristics, 274
12.2 Code Selection Criteria, 280
12.3 Applications, 285
References, 293
Bibliography: Production Computer Codes, 295
13 SHAPED CHARGE GENERALITIES 309
13.1 Shaped Charge Variables, 309
13.2 The Explosive Fill and Initiation Mode, 313
13.3 Jet Characteristics, 319
References, 323
14 EXAMPLE APPLICATIONS 329
14.1 Conical Shaped Charge Liners, 329
14.2 Shaped Charge Liner Collapse and Jet Formation, 343
14.3 Shaped Charges with Hemispherical Liners, 351
14.4 Explosively Formed Penetrators, 358
14.5 Blasting and Shaped Charges, 365
14.6 Special Applications and Effects, 373
14.7 Shaped Charge Jet Collisions, 388
References, 389
INDEX 391