Shock Waves: Measuring The Dynamic Response Of Materials

SHOCK W A V E S Measuring the Dynamic Response of Materials

SHOCK IAIAV=S Measuring the Dynamic Response of Materials

William M. Isbell ATA Associates, USA

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Imperial College Press

Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

SHOCK WAVES: MEASURING THE DYNAMIC RESPONSE OF MATERIALS Copyright © 2005 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 1-86094-471-X

Printed in Singapore by World Scientific Printers (S) Pte Ltd

Dedication To my wife, Virginia, who spent countless hours preparing the draft of the original manuscript, then spent as many additional hours as a computer-widow, while I finalized the work.

Preface The 1950s and 1960s are sometimes referred to as the "Golden Age of Shock Wave Physics," characterized by ample private and government funding and with new insights and discoveries arriving on a regular basis. . . an exciting period, indeed. After a period of relative quiet during the 1970s, shock wave research resumed its expansion in the 1980s, with substantial support shown for the science worldwide. To some degree, however, the emphasis had changed from basic to applied studies. While numerous studies of a basic nature were still being pursued, the application of shock wave research to practical matters such as spacecraft shielding, fragmentation of spacecraft by explosions and by impact with space debris, and the development of advanced kinetic energy weapons, has provided a major support for the research efforts. Perhaps the most significant advance during this period was in the incorporation of physical models of shock wave behavior into finite difference and finite element routines, run both on supercomputers and on desktop personal computers. The capabilities of these routines to provide three-dimensional representations of complex target and projectile geometries have produced quantitative answers in areas previously not studied. Support for these computer techniques and the models they employ has grown in proportion to their utility. New launchers and diagnostics have become available to the experimenter, substantially expanding measurement capability. Nanograms are launched at 100 km/s by Van de Graaff generators, milligrams are launched at 15-30 km/s by exploding foils and by laser acceleration, and grams are launched at 10-13 km/s by three-stage guns. As with their predecessors at lower velocities, new insights will be obtained into material behavior, pushing back the frontiers.

vii

Contents Dedication Preface Acknowledgments

v vii xv

1 Introduction 1.1 1.2 1.3 1.4 1.5

Foreword Motivation for Research Chapter Organization Convention for Units References

1 2 3 4 5

2 Characteristics of High-Intensity Waves 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

2.9

Foreword Description of Shock Wave Formation Rankine-Hugoniot Relations Attenuation Waves Constitutive Relations High Pressure Region: Mie-Gruneisen Equation of State Elastic-Plastic Flow in Uniaxial Strain Time-Dependent Effects 2.8.1 Strain Rate 2.8.2 Spallation References

ix

7 7 8 11 12 13 15 17 17 18 20

x

Shock Waves: Measuring the Dynamic Response of Materials

3 Experimental Techniques for Measurement of the Dynamic Properties of Materials 3.1 3.2 3.3

Introduction Stress-Strain-Strain-Rate Studies Uniaxial Stress Tests 3.3.1 Low-Rate Testing 3.3.2 Medium-Rate Testing 3.3.3 High-Rate Testing 3.4 Multi-Axial Stress Tests, Biaxial Machine 3.4.1 Confined Pressure Device 3.5 High Heating Rate Tests 3.5.1 Heating and Testing Machine 3.5.2 Temperature Measurement 3.5.3 Strain Measurement 3.6 Ultrasonics Measurements 3.6.1 Elastic Wave Velocities 3.7 Equation of State and Wave Profile Studies 3.8 Gas Guns 3.8.1 Compressed-Gas Gun, 102 mm 3.8.2 Compressed-Gas Gun, 63.5 mm 3.8.3 Light-Gas Gun 3.9 Instrumentation 3.9.1 X-Cut Quartz Gages 3.9.2 ManganinGage 3.9.3 Streak Camera Techniques 3.9.4 Laser Velocity Interferometer 3.9.5 Slanted Resistance Wire 3.9.6 Magnetic Wire Gage 3.10 Spall Tests 3.10.1 Recovery Tests 3.10.2 Room Temperature Testing 3.10.3 Elevated Temperature Testing 3.10.4 Metallographic Examination 3.11 References

23 23 24 24 24 26 28 29 29 29 31 32 34 35 39 40 40 42 44 47 47 51 52 55 57 58 60 61 62 63 64 66

xi

Contents

4 Dynamic Response of Materials at Low and Moderate Stresses (. T = an°c

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4. Dynamic Response of Materials at Low and Moderate Stresses

11

4.1.4 Release Wave Behavior A complete understanding of wave propagation requires study of release wave behavior. Most previous studies have been conducted using impactors of the same material as the target. Thus, the measured release wave behavior is irretrievably linked with the compressive wave behavior in the impactor. An alternate and better technique for the study of release waves is shown in Figure 4.8, in which a square input wave has been induced in the material by the impact of a fused quartz disc. Fused quartz exhibits shock compressive behavior in the stress regime of -0-3 GPa in which the Hugoniot is concave downward, in contrast to most materials where the derivative of the stress-particle velocity curve is positive. The result is that, upon reflection of a shock wave from a free surface, a rarefaction shock is formed, rather than the customary rarefaction fan. Impact of a fused quartz disc on a sample thus produces a nearly instantaneous release wave at the impactor-specimen interface, allowing formation of release waves that are not related to the shape of the compressive wave. In the compressive portion of the wave in the sample, the elastic precursor decay is evident as the shock wave progresses into the material. On the release portion of the wave, the behavior of the elastic-plastic wave system can be followed in detail. The waves are dispersive in nature and decay of the elastic release wave is indicated. The profiles in Figure 4.8 have been adjusted to show the same maximum interface velocity and to coincide at release wave arrival time. Modeling the unloading wave requires knowledge of subsequent yield behavior of the material. Shown in Figure 4.9 are results of a study of the Bauschinger effect and its dependence upon strain and aging time. The Bauschinger effect can be evaluated in terms of the ratio of yield in tension on reload over the yield in compression on preload. For 6061-T6 aluminum, this ratio changes at low strains (< 2%), showing a decrease with increasing strain. The Bauschinger effect is also time dependent, and aluminum shows reload yield recovery as time between preloading in tension and reloading in compression is increased.

78

Shock Waves: Measuring the Dynamic Response of Materials

Figure 4.8. Wave Profiles in 6061-T6 Aluminum

Figure 4.9. Bauschinger Effect in 6061-T6 Aluminum

4. Dynamic Response of Materials at Low and Moderate Stresses

4.1.5

79

Fracture

Spall fracture usually results from the reflection of compressive stress waves from relatively low-impedance interfaces (normally a free surface) and their subsequent interaction. Analysis of spall fracture in metals requires consideration of a number of factors, most important of which are material properties, stress-time history, and test technique (i.e., stress pulse generation method). The spall fracture data were obtained by flat-plate impact, where uniaxial strain conditions exist. These studies were conducted using both active and passive methods. Active techniques provide quantitative, time-resolved data on the influence of internal fracture or spall surfaces on stress wave profiles [3]. The primary instrumentation used is the laser velocity interferometer, which provides a time history of free surface motion. Passive techniques involve the recovery and examination of shock-loaded specimens. Metallographic examination establishes the type and degree of damage, which can be correlated with impact parameters such as velocity, impactor thickness, and target thickness. A qualitative assessment of the spall behavior of the four metals is given in Figure 4.10. Each material exhibited ductile failure, although the nature of the plastic flow accompanying void formation differs. The aluminum and titanium specimens were taken from plate stock, and void growth and coalescence were influenced by the grain structuring resulting from the rolling process. There was very little dispersion of voids around the spall plane in the copper, while the tantalum showed sizable voids at appreciable distances from the nominal spall plane.

Figure 4.10. Spall Fractures

80

Shock Waves: Measuring the Dynamic Response of Materials

Spall tests were conducted using quasi-rectangular waves arising from symmetric impact. To study the dependence of the spall thresholds on time duration, tests were conducted using different impactor thicknesses to provide different pulse widths. For these tests, the ratio of impactor to target thickness was kept constant. A summary of the impact velocity necessary to create incipient spall is shown in Figure 4.11.

Figure 4.11. Spall Threshold Results

4.1.6

Degraded Properties

For the formulation of complete constitutive relations, it is important to establish the influence of material temperature as well as time-attemperature on strength, stiffness, and other material properties. The effect of heating rate on yield strength of 6061-T6 aluminum is shown in Figure 4.12. The yield at 20°C is compared with yield at 260°C and at 370°C. The data indicate that degradation of yield at elevated temperature has three distinct regimes. At high heating rates (>l°C/s for 260°C), the yield shows little dependence on heating rate, suggesting an almost instantaneous decrease in yield as temperature increases. At intermediate

4. Dynamic Response of Materials at Low and Moderate Stresses

81

rates (10~4 to l°C/s), a time-dependent softening occurs and the yield decreases with decreasing heating rate due to diffusion processes. At low heating rates (