Terminal Ballistics Zvi Rosenberg • Erez Dekel

Terminal Ballistics

Second Edition

123 Zvi Rosenberg Erez Dekel RAFAEL Ballistics Center Department of Engineering Haifa RAFAEL Ballistics Center Israel Haifa Israel

ISBN 978-981-10-0393-6 ISBN 978-981-10-0395-0 (eBook) DOI 10.1007/978-981-10-0395-0

Library of Congress Control Number: 2015960421

© Springer Science+Business Media Singapore 2012, 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made.

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This Springer imprint is published by SpringerNature The registered company is Springer Science+Business Media Singapore Pte Ltd. To the memory of our parents, Shmuel and Henya Rosenberg, and Nisim Dekel Preface

The high velocity impact of solid bodies has attracted a large amount of research over the past century by both military and civil engineers. These impacts, at hun- dreds to thousands of meters per second, involve large deformations of the impacting bodies which can result in their total destruction around the impacted area. The impact of projectiles on armored vehicles (at 1–2 km/s) and the impact of meteorites at space stations (at 10–20 km/s) are areas of much interest in this field. At impact velocities of a few meters per second, the structural response of the bodies is the relevant issue for safety engineers in the automotive industry. In order to study the effects of high velocity impacts, a special scientific discipline has been developed over the past 50 years, termed the dynamic response of solids to impulsive loading. This field involves several different disciplines such as elasticity and plasticity theories, hydrodynamics, high-pressure physics, material response to at high strain rates, fracture mechanics, and failure analysis. Several symposia dedicated to these issues were established during the last decades, such as the Hypervelocity Impact Symposia series, the International Symposia on Ballistics, the APS conferences on Shock Compression of Solids (in the USA), and the DYMAT conferences in Europe. In addition, several journals specifically dedicated to this field were established, such as the International Journal of Impact Engineering, since 1983, and the International Journal of Protective Structures (launched in 2010). All of these activities are focused on the dynamic response of solids to impulsive loading, by developing new experimental facilities and diagnostics, as well as advancing numerical simulations and analytical modeling. This book is focused on the subject of terminal ballistics which deals with the interaction between a moving object (the threat) and a protective structure (the target), at impact velocities in the range of a few hundreds to a few thousands of meters per second. At these velocities, the damage induced in the target is local, extending laterally to several projectile diameters, but it is concentrated along the direction of projectile’s motion. Thus, the target can be either perforated as is the case for thin targets, or deeply penetrated (for thick targets). These penetration/perforation issues are important for the armor engineer who looks for

vii viii Preface ways to minimize the extent of damage to the protected structure. Similarly, the anti-armor designer is concerned with the improvements in the lethality of the threats by increasing their velocities, masses, etc. The field of terminal ballistics covers a large range of scientific challenges and engineering applications, and we had to limit the number of the subjects which are discussed in this book. Naturally, most of the subjects we chose belong to armor issues, on which we worked for many years at the terminal ballistics laboratory in RAFAEL, a defense-related research institute in Israel. We wish to thank our colleagues for fruitful and exciting research during many years. In particular, we acknowledge the scientific collaborations with Y. Yeshurun, D. Yaziv, M. Mayseless, Y. Ashuach, and Y. Partom from RAFAEL, S.J. Bless, M.J. Forrestal, and N.S. Brar from the USA, and N.K. Bourne and J.F. Millett from England. We acknowledge the excellent work of M. Siman, R. Kreif, M. Rozenfeld, Y. Reifen, D. Kanfer, N. Yadan, D. Mazar, I. Shaharabani, and Y. Zidon, in performing many experiments in our laboratory for over 30 years. We also thank C.E. Anderson, A.J. Piekutowski, K. Poormon, T.J. Holmquist, T. Borvik, S. Chocron, K. Thoma, and A. Dancygier, for helpful discussions during the preparation of this book, and for sharing some of their best shadowgraphs which add so much to this book.

Zvi Rosenberg Erez Dekel Contents

Part I Experimental and Numerical Techniques 1 Experimental Techniques ...... 3 1.1 The Terminal Ballistics Lab ...... 3 1.1.1 Laboratory Guns ...... 3 1.1.2 Projectiles and Targets ...... 5 1.1.3 Diagnostics for Terminal Ballistics...... 7 1.2 Determination of the Dynamic Properties ...... 9 1.2.1 Equation of State Measurements ...... 10 1.2.2 Dynamic Strength Measurements ...... 12 1.2.3 Diagnostics ...... 15 1.3 The Common Threats in Terminal Ballistics ...... 23 2 Material Models for Numerical Simulations ...... 27 2.1 General Description ...... 27 2.2 Material Properties ...... 29 2.2.1 The Equation of State ...... 29 2.2.2 The Constitutive Relations ...... 32 2.2.3 Failure of Ductile Materials ...... 35 2.2.4 Failure of Brittle Materials ...... 42 2.2.5 The Spall Failure...... 45

Part II Penetration Mechanics 3 Rigid Penetrators...... 51 3.1 The Mechanics of Deep Penetration ...... 51 3.2 The Penetration Model for Rigid Long Rods ...... 61 3.2.1 Impact at the Ordnance Velocity Range ...... 62 3.2.2 High Velocity Impact: The Cavitation Phenomenon . . . . . 67 3.3 The Cavity Expansion Analysis ...... 75

ix x Contents

3.4 The Penetration of Short Projectiles ...... 83 3.4.1 The Influence of the Entrance Phase ...... 83 3.4.2 A Numerically Based Model for the Entrance Phase Effect ...... 88 3.5 The Impact of Spheres ...... 95 3.5.1 Rigid Sphere Impact ...... 96 3.5.2 The Impact of Non-rigid Spheres...... 99 3.6 The Effect of Friction ...... 102 3.7 The Optimal Nose Shape ...... 104 3.8 Concrete Targets ...... 105 3.9 The Deep Penetration of Deforming Rods ...... 114 3.10 The Transition to Finite-Thickness Targets ...... 122 4 Plate Perforation ...... 125 4.1 General Description ...... 125 4.2 The Perforation of Ductile Plates by Sharp Nosed Rigid Projectiles ...... 127 4.3 Plate Perforation by Spherical Nosed Projectiles ...... 145 4.4 Plate Perforation by Blunt Projectiles ...... 148 4.5 Forced Shear Localization and Adiabatic Shear Failure ...... 166 4.6 The Perforation of Concrete Slabs by Rigid Projectiles ...... 169 4.7 The Catastrophic Failure of Thin Panels by Hydrodynamic Ram...... 179 5 Eroding Penetrators...... 183 5.1 The Penetration of Shaped Charge Jets ...... 184 5.2 The Penetration of Eroding Long Rods...... 187 5.2.1 The Allen–Rogers Penetration Model ...... 190 5.2.2 The Alekseeνskii-Tate Penetration Model ...... 197 5.2.3 The Validity of the AT Model...... 203 5.2.4 The L/D Effect ...... 207 5.2.5 Other Penetration Models ...... 211 5.3 Scaling Issues in Terminal Ballistics...... 216 5.4 Penetration at the Hypervelocity Regime...... 223 5.5 Plate Perforation by Eroding Rods ...... 227 5.6 Perforation of Thin Plates at the Hypervelocity Regime ...... 234

Part III Defeat Mechanisms 6 Defeat by High Strength Targets ...... 239 6.1 Definitions ...... 239 6.2 Metallic Targets...... 240 6.3 Ceramics for Armor ...... 245 6.3.1 Ceramics Against AP Projectiles ...... 245 6.3.2 The Interaction of Ceramics with Long Rods ...... 255 Contents xi

6.3.3 Numerical Simulations ...... 263 6.3.4 Ceramics Against Shaped Charge Jets ...... 271 6.4 Woven Fabrics as Armor Materials ...... 274 7 Asymmetric Interactions ...... 287 7.1 Defeating AP Projectiles ...... 290 7.2 Defeating Long Rods ...... 296 7.2.1 Perforation of Inclined Plates ...... 296 7.2.2 Ricochet of Long Rods ...... 297 7.2.3 The Interaction of Long Rods with Moving Plates ...... 303 7.2.4 The Impact of Yawed Rods ...... 311 7.3 Defeating Shaped Charge Jets ...... 321 7.3.1 The Explosive Reactive Armor (ERA) ...... 321 7.3.2 Passive Cassettes ...... 330 7.3.3 The Hole Diameter in a Plate Impacted by a Jet ...... 334

References ...... 341 Introduction

The science and engineering of impacting bodies have a large range of applications depending on their type and their impact velocities. At very low velocities, these impacts can be limited to the elastic range of response, with practically no damage to the impacted bodies. In contrast, at very high impact velocities these bodies experience gross deformation, local melting, and even total disintegration upon impact. Various scientific and engineering disciplines are devoted to specific areas in this field such as vehicle impacts, rain erosion, armor and anti-armor design, spacecraft protection against meteorites, and the impact of planets by large meteors at extremely high velocities. In order to follow these different events, the researcher has to be acquainted with diverse scientific fields which include elasticity and plasticity of solids, fracture mechanics, and the physics of materials at high pres- sures and temperatures. Terminal ballistics is the generic name for the science and engineering of impacts which are of interest to armor and anti-armor engineers. The relevant impact velocities usually range between 0.5 and 2.0 km/s, the so-called ordnance velocity range. These are the velocities at which projectiles are launched against personnel armored vehicles and buildings, by rifles and guns. The impact velocities of shaped charge jets are within the hypervelocity range of 2.0–8.0 km/s, and their interaction with armor is also of major interest to both armor and anti-armor engineers. This book is devoted to the science of terminal ballistics, as it is defined here, through the various threats which operate in the battlefield. The science of terminal ballistics started with the works of the great mathe- matician Leonard Euler (1745) and the British engineer Benjamin Robins (1742), who analyzed data for the penetration of steel cannonballs in soil as a function of their impact velocity. In the following two centuries, until the Second World War, the field of terminal ballistics was based on empirically derived relations between the penetration depth and the impact velocity of various projectiles into different targets. The reviews of Hermann and Jones (1961) and Backman and Goldsmith (1978) summarize many of these empirical formulas which were sug- gested over this period. During the years of WW-II, scientists in the USA and UK have analyzed the penetration process of shaped charge jets and rigid steel pro- jectiles into armor plates, through analytical models which were based on physical

xiii xiv Introduction considerations. These models identify the main force exerted on the projectile during penetration, which is then inserted in its equation of motion. The aim of these models was to reduce the mathematical description of a complicated three-dimensional problem, to a simple form which retains the essential physics of the penetration process. This simplification results in either a low-dimensional system of ordinary differential equations, or a few one-dimensional partial differ- ential equations which can be easily solved. The models can be tested by controlled experiments, in which the parameters are varied in a systematic way, in order to establish the non-dimensional parameters of the process. With these analytical models, data correlation is made easy and extrapolations to areas beyond the ability of experimental facilities are possible. On the other hand, analytical models require some compromise to be made, limiting their use to ideal cases where only a single mechanism is at work. Still, analytical models have been used successfully in order to account for the data and to reduce the number of the necessary experiments in terminal ballistics. Since the advancements in numerical simulations, the role of analytical models seems to decline as the codes are getting better and more efficient. Our strong belief is that analytical modeling is crucial for the field of terminal ballistics in order to understand the physics involved, and to highlight the important parameters which influence these processes. Throughout this book, we bring examples where physically based models play a major role in simplifying complex interactions. These models are derived either through experimental observations or through numerical simulations. Our approach is that numerical simulations can be viewed as the “perfect experiments,” with which one can change a single parameter at a time and find its influence on the investigated process. We shall demonstrate the usefulness of these numerical studies for the construction of numerically based models and for the critical examination of existing models. Note that the term “model,” as it is often used in the literature, is somewhat confusing since it is applied both for the description of material properties (material modeling) and for the analytical account of the process itself (the engineering model). For both applications, these models should be physically based, with parameters which can be calibrated by well-defined exper- iments. A valid material model should be applicable for a variety of experimental configurations, and an engineering model has to account for the behavior of dif- ferent materials in a given experiment. The book is divided into three parts. Part I includes a description of the terminal ballistics laboratory and the main diagnostic tools which are used in this field. It also summarizes several material models which are frequently used in numerical simulations. Part II is devoted to the field of penetration mechanics, dealing with the basic processes which take place upon the impact and penetration of various projectile/target combinations. Part III describes the working principles behind several armor concepts which are designed to defeat some of the more common threats.