Shock Wave and High Pressure Phenomena

For further volumes:

http://www.springer.com/series/1774

Founding Editor

R. A. Graham, USA

Honorary Editors

L. Davison, USA

Y. Horie, USA

Editorial Board

G. Ben-Dor, Israel

F. K. Lu, USA

N. Thadhani, USA

Shock Wave and High Pressure Phenomena

L.L. Altgilbers, M.D.J. Brown, I. Grishnaev, B.M. Novac, I.R. Smith, I. Tkach, and Y. Tkach:

Magnetocumulative Generators

T. Antoun, D.R. Curran, G.I. Kanel, S.V. Razorenov, and A.V. Utkin: Spall Fracture

J. Asay and M. Shahinpoor (Eds.): High-Pressure Shock Compression of Solids

S.S. Batsanov: Effects of Explosionon Materials: Modiﬁcation and Synthesis Under High-

Pressure Shock Compression

G. Ben-Dor: Shock Wave Reﬂection Phenomena

L.C. Chhabildas, L. Davison, and Y. Horie (Eds.) : High-Pressure Shock Compression of

Solids VIII

L. Davison: Fundamentals of Shock Wave Propagationin Solids

L. Davison, Y. Horie, and T. Sekine (Eds.): High-Pressure Shock Compression of Solids

V.L. Davison and M. Shahinpoor (Eds.): High-Pressure Shock Compression of Solids III

R.P. Drake: High-Energy-Density Physics

A.N. Dremin: Toward Detonation Theory

J.W. Forbes: Shock Wave Compression of Condensed Matter

V.E. Fortov, L.V. Altshuler, R.F. Trunin, and A.I. Funtikov: High-Pressure Shock Compres-

sion of Solids VII

B.E. Gelfand, M.V. Silnikov, S.P. Medvedev, and S.V. Khomik: Thermo-Gas Dynamics of

Hydrogen Combustion and Explosion

D. Grady: Fragmentation of Rings and Shells

Y. Horie, L. Davison, and N.N. Thadhani (Eds.): High-Pressure Shock Compression of

Solids VI

J. N. Johnson and R. Chere´t (Eds.): Classic Papersin Shock Compression Science

V.K. Kedrinskii: Hydrodynamics of Explosion

C.E. Needham: Blast Waves

V.F. Nesterenko: Dynamics of Heterogeneous Materials

S.M. Peiris and G.J. Piermarini (Eds.): Static Compression of Energetic Materials

M. Suc

eska: Test Methods of Explosives

M.V. Zhernokletov and B.L. Glushak (Eds.): Material Propertiesunder Intensive Dynamic

J.A. Zukas and W.P. Walters (Eds.): Explosive Effects and Applications

Jerry W. Forbes

Shock Wave Compression

of Condensed Matter

A Primer

With 212 Figures

Jerry W. Forbes

Energetics Technology Center

St. Charles, Maryland 20603

USA

ISBN 978-3-642-32534-2 ISBN 978-3-642-32535-9 (eBook)

DOI 10.1007/978-3-642-32535-9

Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2012954247

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Preface

This book is unique compared to others on shock wave physics of condensed matter

in that Chaps. 1, 2, and 3 are designed to q uickly get a physical scientist or engi neer

to understand how shocks interact with material boundaries and other shock waves

by presenting the steady one-dimensional (1-D) strain conservation laws. The

speciﬁc key technique p resented is shock wave impedance matching, which insures

conservation of mass, momentum, and energy. Early emphasis is given on the

meaning of shock wave and mass velocities in a laboratory coordinate system.

An overview of basic experimental techniques is presented in Chap. 4 on how to

measure pressure, shock velocity, mass velocity, compression, and internal energy

of steady 1-D shock waves. These ﬁrst four chapters allow the reader to understand

much of the shock wave literature, perform basic data analysis techniques, and

design simple 1-D shock wave experiments. The rest of the book will then tre at

thermodynamics, liquids and solids compression under shock loading, wave propa-

gation and stability, phase transitions, detonation of ener getic materials, time-

dependent ﬂow, and a few selected topics. Advanced treatments of condensed

matter under dynamic loading can be addressed by the reader once the ﬁrst-order

approaches presented in this book are understood.

This book is a continuum mechanics approach treating liquids and isotropic

solids. The book primarily treats one-dimensional uniaxial compression to illustrate

key features of condensed matter response to shock wave loading. For materials in

equilibrium, a review of thermodynamics is done showing how the Hugoniot

pressure–volume (P-v) points ﬁt on the thermodynamic surface and how it relates

to other processes such as isothermal and isentropic compression. The ﬁrst-order

Maxwell solid model will be used to show ﬁrst-order features of time-dependent

behavior. Detonation shock waves in explosives is treated as a special overviewed

subject. Detonation physics is primarily based on experimental data so the experi-

mental properties of detonating explosives are emphasized. A unique summary

description of nonideal cylindrically shape d explosives is included. Finally, a few

selected subjects in shock wave physics are overviewed in the last chapter.

This text is not meant to be a historical account of shock wave physics but rather

it is put together from 20 years of teaching primer shock physics courses.

The material is from the authors experience in presenting to student s a cohesive

course of the subject so they can read the literature and look into more advanced

treatments on their own. It is inevitable that some of the organization is due to how

and when the author learned speciﬁc subjects. It is assumed that the reader has taken

undergraduate physics, mechanics, thermodynamics, advanced calculus, matrix

theory, and at least one other physical science course such as mechanical engineering,

chemistry, material science, or numerical computations.

St. Charles, MD, USA Jerry W. Forbes

vi Preface

Acknowledgments

There is a need for a shock wave primer for scientists and engineers who are new to

the ﬁeld. To address this need, I have developed a set of notes for teaching a basic

shock wave physics course over the last 20 years, beginning in 1992 at the Naval

Surface Warfare Center (NSWC) in White Oak, MD. I then taught this cours e at

The American University in Washington, DC, from 1994 to 1996 and at Lawrence

Livermore National Laboratory (LLNL) from 1996 to 2003, including 1 year

(1999–2000) for the University of California – Davis Department of Applied

Science located at LLNL. A revised course was taught as a web-based two-semester

fall and spring course for the Mechanical Engineering Department at the University

of Maryland for the 2004–2005, 2007–2008, and 2010–2013 school years.

Lawrence Livermore National Laboratory management was supportive in

presenting the in-house shock wave course from 1996 to 2003, especially

Dr. Randall Simpson of the Chemistry and Materials Science Directorate and the

Defense and Nuclear Technologies Directorate. The late Dr. David Hare and

Dr. Kevin Vandersall assisted at a number of these class presentations. Dr. Jon

Maienschein reviewed the 2003 set of class notes for clarity. Jacqy Turner expertly

and efﬁciently made drawings and typed and assembled this earlier version of class

notes for the courses given at LLNL. Most recently, Jason Forbes made numerous

drawings for this book. Richard Granholm gave suggestions for making Chaps. 1, 2,

3, and 4 of this book more readable. Dr. Craig Tarver gave suggestions improving

Chaps. 1, 9, and 10.

I wish to recognize the late Nathaniel Coleburn and John Erkman for being my

mentors at Naval Surface Warfare Center (NSWC)-White Oak Laboratory, and the

late Professor George Duvall who was my Ph.D. thesis advisor and mentor in shock

wave physics at Washington State University. In addition, Professor Yogendra

Gupta, Drs. James Asay, Dennis Grady, Craig Tarver, Neil Holmes, Larry Fried,

Joseph Zaug, and Stephen Shefﬁeld have generously answered my questions on

the fundamentals of high pressure science, shock wave, and detonation physics.

Dr. Shawn McGrane suggested a list of laser shock publications. Dr. Robert Graham,

Dr. Yuki Horie, and Professor Naresh Thadani and others have asked that I make

my course notes into a text book. I express my gratitude to all those who have taken

vii

the time to take one of my courses and all my colleagues who have encouraged me

to put together a primer text for Shock and Detonation Wave Physics. It is these

people, my family, and close friends who receive credit for my doing this book.

Finally, I want to thank my wife Cynthia for showing great patience with my doing

this project as it extended much beyond my early predictions of its completion date.

viii Acknowledgments

Contents

1 Introduction to Shock Wave Physics of Condensed Matter ....... 1

1.1 Introduction ....................................... 1

1.2 General Assum ptions . . . ............................. 1

1.3 Brief History of Shock Field in the United States of America . . . 2

1.4 Practical Value of Shock Field ......................... 3

1.5 Techniques for Producing 1-D Plane Shock Waves . . . . . . . . . . 4

1.6 Dynamic Versus Static Compression . .................... 5

1.7 Select Areas of Shock Wave Research . . . . . . . . . . . . . . . . . . . . 5

1.8 What Does a Shock Wave in Condensed Matter Look Like? . . . . 6

References ............................................ 8

2 Plane One-Dimensional Shock Waves ....................... 13

2.1 Deﬁnition of a Plane One-Dimensional Shock Wave ......... 13

2.1.1 A More Practical Deﬁnition for a Steady Shock Wave . . . 13

2.2 Practical Des cription of U

, E, P and Disturbance Velocity ... 14

2.3 Conservation Equations for a 1-D Plane Steady Shock Wave . . . 16

2.4 A Single Shock Wave Deﬁnes Only One (P, v) Point on

a Hugoniot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Two Plane Shock Waves 1-D Conservation Relations . . . . . . . . . 20

2.6 Wave Stability ..................................... 21

2.6.1 Necessary Condition for a Shock Wave to Form . . . . . . . 22

References ............................................ 29

3 Impedance Matching Technique ........................... 31

3.1 Waves Response to Material Interfaces and Intersection

with Other Waves .................................. 31

3.1.1 Practical Uses for Impedance Matching . . . . . . . . . . . . 31

3.2 Distance-Time (x-t) Wave Propagation Diagrams ........... 31

3.3 Introduction to Principal P-u Curves with Initial State

(P ¼ 0, u ¼ 0).................................... 33

3.4 Introduction to P-u Curve with Initial State (P

)......... 34

3.5 P-u Curves for Materials with U

¼ A+bu

.............. 36

3.6 P-u Diagram for a Shock Crossing a Boundary into a Material

of Higher Impedance . . . ............................ 37

3.7 Impedance Matching Treatment of Rarefaction Waves ....... 38

3.8 Impedance Matching for a Shock Reaching a Free Surface . . . . 39

3.9 Impedance Matching for a Flyer Plate Hitting a Stationary

Plate of the Same Material ........................... 41

3.10 Disturbance Velocity in a 1-D Eulerian Cartesian

Coordinate System Fixed in Space . ..................... 42

3.10.1 Symmetric Impact Example . . . . . . . . . . . . . . . . . . . . 42

3.10.2 Disturbance Velocity for General Case ............ 44

3.11 Impedance Matching for Four Basic Cases . . . . . . . . . . . . . . . . 45

3.12 Impedance Matching for Thin Foils . . ................... 48

3.12.1 Summary of the Practical Lessons for Thin Foils ..... 49

3.13 Impedance Matching for Multiple Waves Is an

Approximation .................................... 52

3.14 Wave-Wave Interaction and Contact Discontinuity .......... 53

References ............................................ 57

4 Experimental Techniques ................................ 59

4.1 Selected Experimental Techniques to Measure Shock Wave

Parameters ....................................... 59

4.2 Explosive and Flyer Plate Shock Driver Systems . . . . . . . . . . . 59

4.3 Laser Shock Drivers ................................ 62

4.4 Early Impedance Matching Experiments . . ............... 63

4.5 Shock Velocity Measurements ......................... 64

4.6 Free Surface Velocity Measurement Using a Streak Camera . . . 66

4.7 Electromagnetic Particle Velocity Gauge ................. 67

4.8 Laser Velocity Interferometry ......................... 68

4.9 VISAR.......................................... 68

4.10 ORVIS .......................................... 69

4.11 Fabry-Perot ...................................... 70

4.12 Heterodyne System . . ............................... 71

4.13 Optical Windows on Test Samples . ..................... 72

4.14 Quartz Stress Gauge ................................ 72

4.15 Quartz Gauge Technique for Measuring Low

Pressure Hugoniot . ................................. 74

4.16 Quartz Gauge Technique for Measuring the Hugoniot

of a Thin Material .................................. 75

4.17 Manganin Stress Gauge . ............................. 75

4.18 Other Stress Gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.19 Proton Radiography for Accurate Density Measurements

of Shock Wave . . . . . . . . . . .......................... 80

4.20 Issues for Making Temperature Measurements Behind

Shock Waves . .................................... 80

4.21 Error Analysis for Experiments . . . . . . . . . . . . . . . . . . . . . . . . 82

4.22 Random Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

x Contents