high strain rate evaluation of armor materialscradpdf.drdc-rddc.gc.ca/pdfs/unc92/p532809.pdf ·...

High Strain Rate Evaluation of Armor Materials

M. Nabil Bassim

Department of Mechanical and Manufacturing Engineering University of Manitoba, Winnipeg, Manitoba, Canada R3T 5V6 Canada

Project Manager: Madame Manon Bolduc

Contract number: W 7701-043128/001/QCA Scientific Authority: Manon Bolduc , 418-844-4000 Ext. 4621

Defence R&D Canada – ValcartierContract Report

DRDC Valcartier CR 2007-266December 2007

The scientific or technical validity of this Contract Report is entirely the responsibility of the contractor and thecontents do not necessarily have the approval or endorsement of Defence R&D Canada.

DRDC Valcartier CR 2007-266

High Strain Rate Evaluation of Armor Materials

M. Nabil Bassim

Department of Mechanical and Manufacturing Engineering

University of Manitoba, Winnipeg, Manitoba, Canada

R3T 5V6 Canada


Contract number: W 7701-043128/001/QCA

High Strain Rate Evaluation of Armor Materials Professor M.N Bassim Department of Mechanical and Manufacturing Engineering University of Manitoba, Winnipeg, Manitoba, Canada

R3T 5V6 Canada


Contract number (in full): W 7701-043128/001/QCA Contract Scientific Authority: Madame Manon Bolduc

Tel. No.: 1-418 844 4000 Ext. 4621

Author

Professor M.N. Bassim

Approved by

Madame Manon Bolduc

Defense Scientist

Approved for release by

Christian Carrier

Chief Scientist

Protective Statement: Unclassified

© Her Majesty the Queen as represented by the Minister of National Defence, 2007

© Sa majesté la reine, représentée par le ministre de la Défense nationale, 2007

DRDC Valcartier CR 2007-266 i

Abstract

This report gives results of investigations on high strain rate behaviour of materials with potential for use in armour plates. They include RHA steel plate, Tungsten A90S and Aluminium 5083 H131 alloys. Also considered were ceramics TiB-TiC, SiC-B and Alumina 98. The testing took place at strain rates in excess of 103 s-1 using both direct impact Hopkinson Pressure Bar (HPB) and Torsional Split Hopkinson Bar (TSHB). Both equipments were fully instrumented for retrieval of the incident, transmitted and reflected waves and for obtaining stress-strain curves. The testing results on the metallic materials produced stress-strain curves which are suitable for design at high strain rates. The ceramic materials proved to be too hard to machine. An alternative was to test Alumina 96 in torsion at high strain rates. The results from these tests are also included. Following testing, specimens were examined to determine the microstructural evolution during impact. In most cases, development of adiabatic shear bands, both of the deformed and transformed type were observed and reported. Crack initiation within these bands was also observed leading to fracture of specimen. Together with the described research, a part of the contract involved constructing a torsional Split Hopkinson Bar for delivery to Defence Research and Development Canada Valcartier (DRDC V). This equipment was delivered on schedule in December 2006.

Résumé

Ce rapport donne les résultats obtenus lors d’essais à taux élevés de déformation sur des matériaux offrant un potentiel comme plaques d’armure. Les matériaux inclus sont l’acier RHA, le tungstène A90S et l’alliage d’aluminium 5083H131. Les céramiques Ti-B-TiC, SiC-B et l’alumine 98 ont aussi été considérés. Les essais ont été conduits à des taux de déformation supérieurs à 103 s-1 utilisant une barre d’Hopkinson à impact direct ainsi qu’une barre d’Hopkinson en torsion. L’instrumentation des équipements utilisés permets de retracer les ondes incidentes, transmises et réfléchies et d’en déduire les courbes contraintes-déformations. Ces courbes obtenues sur les matériaux métalliques peuvent être utilisées dans la conception sous sollicitation à taux élevés de déformation. Dans le cas des céramiques, la dureté des échantillons était trop élevée pour permettre l’usinage aux dimensions requises. Comme alternative, des essais de torsion à haut taux de déformation ont été réalisés sur l’alumine 95. Les résultats sont inclus dans ce rapport. Suite aux essais, les échantillons ont été examinés afin de déterminer l’évolution de la microstructure durant l’impact. En général, le développement des bandes de cisaillement adiabatique sous forme de déformation ainsi que de transformation ont été observées. L’initiation de fissures dans ces bandes a aussi été observée causant la rupture finale de l’échantillon.

ii DRDC Valcartier CR 2007-266

En plus des travaux de recherche décrits précédemment, le contrat incluait la construction d’un appareil d’Hopkinson en torsion et sa livraison à Recherche et développement pour la défense Canada Valcartier (RDDC V). Cet appareil fut construit et livré en Décembre 2006

DRDC Valcartier CR 2007-266 iii

iv DRDC Valcartier CR 2007-266

Executive summary

In its effort to protect military personnel and improve the protection of its combat vehicles, Defence Research and Development Canada at Valcartier (DRDC Valcartier) has awarded a contract for three years to the University of Manitoba to study the behaviour of candidate armour plate materials during impact from a projectile at strain rates in excess of 103s-1. Stress-strain curves for such materials are used for design, in constitutive equations and in hydrocode simulation programs. The mechanisms of failure of such materials at high strain rates are determined in this contract. Also, duplicate equipment for testing materials at high strain rates in torsion, namely a torsional Split Hopkinson Bar, similar to one in operation in the laboratory of the principal investigator was constructed and delivered to DRDC Valcartier. The materials under consideration are metallic: RHA steel, Tungsten A90S alloy, Aluminium 5083 H131 alloy and ceramic: TiB-TiC, SiC-B and Alumina 98. The final report of the contract, which ended in March 31, 2007, describes the results obtained in this investigation. The main achievements are as follows: Testing of the metallic materials was completed. The testing took place using two types of Hopkinson Bar Systems described in detail in the report. One provides direct impact of a projectile on a cylindrical specimen while the other is a torsional bar which provides a shear wave in a thin walled specimen. All tests were conducted at strain rates in excess of 103s-1. The results obtained for the stress-strain curves of metallic materials are presented in the report. The steel appears to exhibit the highest strength, followed closely by the tungsten alloy. The aluminums alloy appears to have the lowest strength. In shear, from the torsion tests, the steel maintains the highest strength followed by the tungsten and the aluminium alloy. The second part of the report discusses the mechanisms of failure of the metallic materials in terms of occurrence of Adiabatic Shear Bands (ASB’s). This deformation mechanism which takes place at high strain rates is caused by the simultaneous occurrence of strain hardening and strain softening caused by adiabatic heating. This may cause a rise in temperature of the material by several hundreds degrees and may lead to simultaneous phase transformation causing the presence of transformed bands in the microstructure. Both transformed and deformed ASB’s were observed. The occurrence of ASB’s in the tested metallic materials is documented at length in the report. All materials tested showed some manifestation of ASB’s. Some of these ASB’s contained micro cracks which may have caused the eventual failure of the specimen. In tungsten, detachment of small conical fragments was observed. The outline of these fragments followed the path of ASB’s. The ceramic materials supplied by DRDC Valcartier were very hard and proved impossible to machine to produce torsional specimens. As an alternative, specimens

DRDC Valcartier CR 2007-266 v

made of Alumina 96, which is less hard, were machined and tested in torsion. The fracture profile of these specimens was similar to that for metallic materials. Stress-Strain curves were obtained for these ceramic specimens and included in the report. As part of the contract, a duplicate torsional Hopkinson bar was constructed and delivered to DRDC Valcartier in December 2006. The final report gives a detailed description of the operation of the system and the interpretation of the results obtained.

Bassim M.N. (2007), Principal Investigator. CR2007-266 Odeshi A.G. (2007), Research Associate DRDC-Valcartier

vi DRDC Valcartier CR 2007-266

Sommaire

Dans son effort pour protéger le personnel militaire et améliorer la protection des véhicules blindés, le secteur Recherche et Développement pour la Défense, Canada à Valcartier (RDDC Valcartier), a octroyé un contrat de recherche de trois ans à l’Université du Manitoba pour étudier le comportement de plusieurs matériaux utilisés dans la réalisation des plaques de blindage résistant à l’impact de projectiles balistiques produisant des taux de déformation de plus de 103s-1. Les courbes de contrainte-déformation de ces matériaux sont utilisées en design, dans les équations constitutives et dans les programmes de simulation numérique. Les mécanismes de rupture de tels matériaux à taux élevés de déformation ont été déterminés dans ce contrat. De plus, un appareil d’Hopkinson en torsion, semblable à celui utilisé lors de l’étude à l’Université du Manitoba, a été construit et livré au RDDC Valcartier. Les matériaux considérés sont des métaux : l’acier RHA, le tungstène et l’alliage d’aluminium Al 5083 ; et des céramiques : le carbure de bore, le carbure de silicone et l’alumine 98. Le rapport final du contrat ayant pris fin le 31 mars 2007 donne en détail les résultats obtenus dans ces travaux. Les accomplissements principaux sont : Les essais sur les matériaux métalliques ont été complétés. Ils ont été réalisés à l’aide de deux système Hopkinson décrits en détail dans ce rapport. L’un d’eux génère un impact direct de projectile sur un échantillon cylindrique, l’autre applique une torsion rapide générant une onde de cisaillement dans un échantillon à paroi mince. Tous les essais ont été réalisés à des taux de déformation supérieurs à 103 s-1. Les résultats obtenus de courbes contrainte-déformations sont donnés en détail dans ce rapport. L’acier montre la plus haute résistance à l’impact, suivi de près par le tungstène. L’alliage d’aluminium montre la plus faible résistance à l’impact. En torsion, l’acier est le plus résistant suivi par le tungstène et l’alliage d’aluminium. La deuxième partie du rapport discute des mécanismes de rupture des matériaux métalliques en termes d’apparition des bandes de cisaillement adiabatiques. Ce mécanisme apparait pour les alliages soumis à des taux élevés de déformation et sont causées par l’apparition simultanée d’un écrouissage et d’un amollissement due à un échauffement adiabatique. Le matériau subis alors une augmentation de température de plusieurs centaines de degrés qui entraine des changements de phase combinés résultant en des bandes transformées dans sa microstructure. Les deux types de bandes, déformées et transformées ont été observées. L’apparition des bandes de cisaillement adiabatique dans les essais sur les matériaux métalliques est décrite en détail dans ce rapport. Tous les matériaux métalliques testés ont montré la présence de ces bandes de cisaillement adiabatique. Certaines de ces bandes contiennent des microfissures pouvant être la cause de la rupture des échantillons. Dans le tungstène, le détachement de fragments coniques a été observé. Les contours de ces fragments suivent les lignes observées des bandes de cisaillement adiabatique.

DRDC Valcartier CR 2007-266 vii

Les matériaux céramiques fournis par RDDC Valcartier étaient très durs rendant l’usinage des échantillons pour les essais en torsion impossible. Afin d’étudier les céramiques, une solution alternative utilisant des échantillons d’alumine 96 moins durs a été utilisée. Les résultats montrent un profile de rupture de ce matériau similaire aux matériaux métalliques. Des courbes de contrainte-déformation ont été obtenues et sont inclues dans ce rapport. Comme stipulé dans le contrat, un appareil d’Hopkinson en torsion, semblable à celui utilisé dans le laboratoire de l’Université du Manitoba a été construit et livré au RDDC Valcartier. Une partie de ce rapport final est dédié au fonctionnement de cet appareil et à l’interprétation des résultats obtenus.

Bassim M.N. (2007), Principal Investigator. CR2007-266 Odeshi A.G. (2007), Research Associate DRDC-Valcartier.

viii DRDC Valcartier CR 2007-266

Table of contents

Abstract........................................................................................................................................ i

Executive summary ................................................................................................................... iv

Sommaire................................................................................................................................... vi

Table of contents ..................................................................................................................... viii

List of figures ............................................................................................................................. x

Acknowledgements ................................................................................................................. xiii

1. Introduction ................................................................................................................... 1

2. Experimental Procedure ................................................................................................ 2 2.1 Compression Test ............................................................................................. 2 2.2 Torsion Test...................................................................................................... 4

3. Experimental Results..................................................................................................... 6 3.1 Compression Test ............................................................................................. 6 3.2 Torsion Test.................................................................................................... 11 3.3 Microscopic Examination............................................................................... 15 3.4 Torsional Testing of Alumina ........................................................................ 29

4. Discussion of Experimental Results ............................................................................ 33

5. Construction of a new Torsional Hopkinson Bar ........................................................ 35 5.1 Specimen Mount............................................................................................. 35 5.2 Pulse generating System................................................................................. 35 5.3 The Clamping Mechanism ............................................................................. 36 5.4 Test Procedure ................................................................................................ 40 5.5 Calculation of Stress, Strain and Strain Rates ................................................ 40

6. CONCLUSION ........................................................................................................... 44

7. References ................................................................................................................... 45

DRDC Valcartier CR 2007-266 ix

List of symbols/abbreviations/acronyms/initialisms ................................................................ 48

Distribution list ......................................................................................................................... 49

x DRDC Valcartier CR 2007-266

List of figures

Figure 1. Direct Impact Hopkinson Pressure Bar System .......................................................... 3

Figure 2. Geometry of test specimen for compression test......................................................... 3

Figure 3. Torsional Split Hopkinson Bar System....................................................................... 5

Figure 4. Torsion test specimen.................................................................................................. 5

Figure 5. The effect of impact momentum on (a) strain rate and (b) total engineering strain.... 8

Figure 6. Stress-strain curves obtained from high strain-rate compression tests on RHA Steel 9

Figure 7. Stress-strain curves obtained from high strain-rate compression tests on the Tungsten A90S alloy........................................................................................................... 9

Figure 8. Stress-strain curves obtained from high strain-rate compression test on Aluminium 5083 alloy.......................................................................................................................... 10

Figure 9. Dynamic stress strain curves of all the three alloys in compression at a comparable impact momentum of about 45 kg.m/s.............................................................................. 10

Figure 10. Typical incident, reflected and transmitted waves recorded by the oscilloscope for RHA steel .......................................................................................................................... 12

Figure 11. Typical incident, reflected and transmitted waves recorded by the oscilloscope for Tungsten A90S alloy......................................................................................................... 12

Figure 12. Typical incident, reflected and transmitted waves recorded by the oscilloscope for Aluminium 5083 H131 alloy............................................................................................. 13

Figure 13. Dynamic stress-strain curves obtained for RHA Steel under torsional loading at different strain rates........................................................................................................... 13

Figure 14. Dynamic stress-strain curves obtained for Tungsten A90S under torsional loading at different strain rates....................................................................................................... 14

Figure 15. Dynamic stress-strain curves obtained for Aluminium 5083 H131 under torsional loading at different strain rates.......................................................................................... 14

Figure 16. Dynamic stress strain curves of the RHA steel, Tungsten A90S and Aluminium 5083 at comparable strain rates of approximately 1100 /s in torsion................................ 15

Figure 17. Optical micrograph showing the plate-like structure of the investigated RHA steel (as received) ...................................................................................................................... 16

DRDC Valcartier CR 2007-266 xi

Figure 18. Deformed ASB as observed in RHA steel subjected to an impact momentum of 46.6 kg.m/s ........................................................................................................................ 17

Figure 19. Optical micrographs showing overview of a parabolic shapes ASB observed on transverse section of RHA steel subjected to an impact momentum of 48 kg.m/s ........... 17

Figure 20. Optical micrographs showing ASB’s observed in RHA steel impacted at 48.5 kg.m/s at different magnifications..................................................................................... 18

Figure 21. Optical micrograph showing crack propagation along ASB in RHA steel subjected to impact momentum of 59.3 kg.m/s................................................................................. 18

Figure 22. Hardness outside and inside ASB’s in RHA steel as a function of impact momentum (IM) ................................................................................................................ 19

Figure 23. Optical macrograph of a sample impacted at 59.3 kg.m/s showing adiabatic shear failure and fusion of fragments along the ASB’s.)............................................................ 19

Figure 24. A schematic view of the longitudinal section of the sample impacted at 59.3 kg.m/s after failure under the high velocity impact showing the three fragments 1, 2 and 3 fused together along the shear bands (white strips). ......................................................... 20

Figure 25. Optical micrograph showing splashing and spreading of an ASB in RHA steel impacted at 59.3 kg.m/s..................................................................................................... 20

Figure 26. Microstructures of the Tungsten alloy showing equi-axed grains .......................... 22

Figure 27. Polished surface of impacted Tungsten A90S alloy showing detachment of small conical shaped fragment during impact............................................................................. 22

Figure 28. SEM-Micrograph showing fracture surface of Tungsten A90S alloy after high velocity impact .................................................................................................................. 23

Figure 29. SEM-Micrograph showing deformed band in Tungsten A90S alloy after high velocity impact .................................................................................................................. 23

Figure 30. SEM-Micrograph showing micro-voids and cracks on fracture surface of Tungsten A90S alloy after failure under high velocity impact ........................................................ 24

Figure 31. Optical micrograph showing the microstructure of the investigated Aluminium 5083 H131 alloy in as received condition ......................................................................... 25

Figure 32. Optical micrographs showing adiabatic shear band along transverse section of Aluminum 5083 H131 alloy impacted at 29.0 kg.m/s: (a) circular ASB close to the circumference. (b), (c) & (d) linear ASB across the cross section at different magnifications. (e) microstructure inside ASB and (f) microstructure outside ASB....... 26

Figure 33. Optical micrographs showing adiabatic shear band along transverse section of Aluminium 5083 H131 alloy impacted at 37.5 kg.m/s: (a) circular ASB close to the

xii DRDC Valcartier CR 2007-266

circumference. (b), (c), (d) linear ASB across the cross section at different magnifications, (e) Microstructure inside and outside ASB ............................................. 27

Figure 34. Optical micrographs showing adiabatic shear band along transverse section of Aluminum 5083 H131 alloy impacted at 43.5 kg.m/s: (a) (b), (c) ASB across the cross section at different magnifications. (d) Microstructure inside ASB and (e) Microstructure outside ASB ...................................................................................................................... 28

Figure 35. Torsional test specimens machined from the machinable Alumina 96................... 30

Figure 36. Typical incident, reflected and transmitted waves recorded by the oscilloscope during dynamic torsion test of alumina at high strain rate ................................................ 30

Figure 37. Dynamic stress strain curves obtained from torsional testing of Alumina 96......... 31

Figure 38. An alumina ceramic sample after failure under torsional loading at high strain rate31

Figure 39. Fracture surface of alumina ceramic after fracture in torsion at high strain rates. .. 32

Figure 40. A sketch of the constructed Split Hopkinson Bar ................................................... 37

Figure 41. Test specimen and the socket on the Kolsky bar .................................................... 38

Figure 42. Clamping Mechanism ............................................................................................. 38

Figure 43. Load release pin ...................................................................................................... 39

List of tables

Table 1. Experimental data sheet for high strain-rate compression test ..................................... 7

Table 2. Hardness inside and outside shear bands in Aluminium 5083 alloy after high velocity impact................................................................................................................................ 29

DRDC Valcartier CR 2007-266 xiii

Acknowledgements

We would like to thank the Department of National Defence for sponsoring this research. Also, we would like to thank the Scientific Authority, Madame Manon Bolduc for valuable guidance and technical input and comments. The technical support of Mr. Rejean Arsenault is also appreciated with gratitude. Prof. M.N. Bassim

xiv DRDC Valcartier CR 2007-266

DRDC Atlantic CR 2007-266 1

1. Introduction

This project was carried out to evaluate dynamic response of selected armor materials supplied by DRDC Valcartier to mechanical loading at high strain rates. The objective is to obtain relevant mechanical properties for these materials under extreme condition of high strain rates similar to that obtained in the military and defense applications. The materials were tested in compression using a direct impact Hopkinson Pressure Bar and in shear using a torsional Split Hopkinson Bar. Dynamic stress strain curves were generated for each investigated material under both loading modes. Microstructural evolution in the material at high strain rates was evaluated to determine their deformation and failure mechanisms. The materials supplied for investigation are metallic: Tungsten A90S, RHA plate, Aluminum 5083 H131 and ceramic: TiB-TiC, SiC-B and Alumina 98. All the three metallic materials were investigated both in compression and in shear at high strain rates. Results of both mechanical and microscopic investigations are presented in this report. However the ceramic materials are too hard for machining into test specimens and could not be investigated. In green state, the ceramic materials were mechanically too weak for machining. However an alternate ceramic material, namely machinable Alumina 96 (Rescor 960 supplied by Cotronics Corporation), was procured and tested in torsion at high strain rates. The results of the dynamic torsion test on the machinable alumina are presented in this report. The project was carried out with Professor M.N. Bassim as the principal investigator. He was assisted by a research associate, Dr. A.G. Odeshi and a postgraduate student, Ms Sahar Mirfakhraei. The major tasks of the projects are:

• Characterization of materials of interest, as supplied by DRDC Valcartier, at high strain rates using direct impact Hopkinson Pressure Bar and torsional Split Hopkinson Bar.

• Determination of relevant material properties from these test results • Design and fabrication of a torsional Split Hopkinson bar similar to that at the

University of Manitoba for DRDC Valcartier Periodic progress reports were required and provided throughout the duration of the project. Periodic meetings alternating between our facilities and DRDC facilities in Valcartier were also held in order to advance the work to meet schedule.

2 DRDC Valcartier CR 2007-266

2. Experimental Procedure

Detailed description of the Hopkinson bar systems used for this study has been provided in several publications by Dr M.N. Bassim et al. [1-15]. A brief but concise description of the systems is provided here.

2.1 Compression Test A schematic presentation of the testing system for the high strain-rate compression test using direct impact Hopkinson Pressure Bar is shown in Fig. 1. The test specimens are cylindrical specimens 9.5 mm in diameter and 10.5 mm long (Fig. 2). The samples were impacted by high velocity projectile constructed from AISI 4340 steel having a hardness value of 47 HRC. The weight of the projectile was 1.905 kg. A light gas gun fires the projectile, which travels through the gun barrel and strikes the specimen at a very high impact velocity, generating elastic waves, which travel through the specimen and are transmitted into the output bar. A strain-gauge connected to the output bar captures the strain-signal. A strain-pulse amplifier amplifies the strain-signal and sends it to an oscilloscope, which collects and stores the strain-data. The firing pressure was varied so that the projectile could strike the samples at impact velocities ranging between 20 and 32 m/s. Assuming constant volume and a linear variation of displacement with time and constant strain rate, the true stress (σ) and true strain (ε) at time t are given by the following expressions:

f

i(t ) t

ti i f

L ε In L - (L - L )( )

= (1)

ftt(t) i i f

(t)i i

P L - (L - L ) ( ) σ

A L= (2)

where Li and Lf are initial and final lengths respectively. The maximum strain in a specimen is directly proportional to the strain rate and length of the striker bar (l) as follows:

2 lC

ε ε= or Cε ε2l

= (3)

where C is the longitudinal wave propagation velocity in the transmitter bar. The global strain rates for each test were calculated as a function of total strain using equation 3 and are reported in Table 1. Dynamic stress strain curves for the materials in compression at high strain rates were generated using equations 1-3. After impact tests, some of the samples were cut, grinded, polished, etched and subjected to microscopic evaluation. The etching reagents used for microscopic investigations are listed as follows:

DRDC Valcartier CR 2007-266 3

• RHA Steel: 2 % Nital (2 % HNO3 in Methanol)

• Tungsten A90S alloy: Murakami’s reagent [100 mL Water, 10g NaOH, and 10g K3Fe (CN)6]

• Aluminum 5083 H131 alloy: 25ml Methanol, 25 ml HCl, 25 ml HNO3, 1 drop HF

Amplifier

Computer

Specimen

Firing Chamber

Striker bar Strain gage

Oscilloscope

Timer

Amplifier

Computer

Specimen

Firing Chamber


Oscilloscope

TimerTransmitter bar

Gun barrel

Amplifier

Computer

Specimen

Firing Chamber


Oscilloscope

Timer

Amplifier

Computer

Specimen

Firing Chamber


Oscilloscope

TimerTransmitter bar

Gun barrel

Figure 1. Direct Impact Hopkinson Pressure Bar System

10.5

mm

9.5 mm

10.5

mm

9.5 mm

10.5

mm

9.5 mm

Figure 2. Geometry of test specimen for compression test


2.2 Torsion Test Figure 3 shows the experimental set-up for the dynamic torsion test using a Split Hopkinson Bar. The testing system consists of incident and transmitter bar supported by Teflon bushings such that they are co-axial and can rotate freely. Test specimens are thin-walled tubes with hexagonal flanges as shown in Fig. 4. The hexagonal flanges of the specimens are slotted into the matching sockets at the specimen ends of the two bars, providing the required gripping mechanism for the specimen with the Kolsky bars. Incident and transmitter gages are attached to the bar at equidistance from the specimen and at a distance from the specimen such that overlapping of incident and transmitted waves is avoided. The system employs stored-torque technique of loading, in which the loading torque is stored between the clamp and the loading arm. The clamp is sufficiently tightened prior loading to prevent rotation of the incident bar as pure torsion load is applied by a hydraulic jack connected to a rotating wheel attached to the loading end of the incident bar. On attaining the desired angle of twist, the clamp is further tightened until the load release pin breaks and the stored torque is released generating elastic wave, which travels along the incident bar and deform the specimen. Incident strain gage captures the incident wave as it travels along the incident bar towards the specimen. On reaching the specimen/incident bar interface, part of the incident wave is transmitted through the specimen and propagates along the transmitter bar away from the specimen. The transmitted wave is captured by the strain gage on the transmitter bar. The remaining part of the incident wave is reflected back at the specimen/incident bar interface and captured by the incident gage. The pulse signal from the strain gages are amplified by the signal conditioner and recorded by a 20 MHz mixed-signal oscilloscope. The strain rate, strain and shear stress were calculated from the elastic wave signals captured as incident, reflected and transmitted waves using the equations that are described in section 5.5.


Computer Oscilloscope Signal conditioner

Strain gage Strain gage

Clamp

Loading armTransmitter bar Incident bar

Specimen



Clamp


Specimen



Clamp

Loading arm



Clamp


Specimen

Transmitter bar Incident bar

Specimen



Clamp


Specimen



Clamp


Specimen



Clamp


Specimen



Clamp

Loading arm



Clamp


Specimen

Transmitter bar Incident bar

Specimen



Clamp


Specimen

Figure 3. Torsional Split Hopkinson Bar System

16.0

mm

φ 13.8 mm

φ 13.0 mm 3.8 mm

6.0 mm

6.0mm

16.0

mm

φ 13.8 mm

φ 13.0 mm 3.8 mm

6.0 mm

6.0mm

Figure 4. Torsion test specimen


3. Experimental Results

3.1 Compression Test The experimental data for the compression tests are presented in Table 1 while Figure 5 shows the comparative evaluation of the engineering strain and strain rates produced in the investigated alloys as a function of the impact momentum of the striker bar. The higher the firing pressure of the gun, the higher is the impact momentum. The higher the impact momentum, the higher is the strain rates generated in the specimen. These curves show that Tungsten A90S alloy exhibits the highest resistance to plastic deformation at high strain rates while Aluminum 5083 alloy shows the least resistance. The slopes of linear plot of engineering strain against impact momentum are 0.020, 0.014, and 0.012 for Aluminum 5083, RHA steel and Tungsten A90S respectively, indicating that ductility of the aluminum alloy is most sensitive to increase in impact load. Typical stress-strain curves obtained from high strain-rate compression tests on the three investigated metallic alloys are presented in Figs. 6-8. The flow stress increases initially with strain, reaching a maximum and decreases with subsequent increase in strain. Thermal softening as a result of the conversion of impact energy to thermal energy dominates the later stage of deformation leading to observed drop in flow stress at high strain values. Impact momentum shows a considerable influence on the ultimate flow stress of RHA steel and Tungsten A90S alloy. While the tungsten alloy fracture at high impact momentum, the maximum flow stress shows a remarkable decrease with increasing impact momentum at impact momentum in excess of 55 kg.m/s. On the contrary, ultimate flow stress increases with impact momentum impact momentum values lower than 55 kg.m/s. In the range of impact momentum studied, change in impact momentum does not have any significant influence on the maximum flow stress of the aluminum alloy. The influence of impact momentum on the dynamic flow stress of the materials is determined by the simultaneous effects of strain hardening and thermal softening on deformation. Complex interactions between both phenomena control the plastic deformation behavior of metallic materials at high strain rates. The initial increase in maximum flow stress with increasing impact momentum is traceable to the increasing strain hardening effect of the increased deformation load. At very high impact momentum, strain hardening effects are increasingly overshadowed by thermal softening effects of increased thermal energy. Microstructural examination (Section 3.3) shows that adiabatic heating and occurrence of adiabatic shear bands dominate the deformation behavior of the aluminum alloy for all the range of the applied impact momentum. This dominant role of adiabatic shear banding on flow stress accounts for the little or no dependence of flow stress of the aluminum alloy on impact momentum as observed in Fig. 8. Comparative stress strain curves for the three alloys at comparable impact momentum of about 45 kg.m/s are presented in Fig. 10. Aluminum alloy exhibits the lowest ultimate flow stress of the three materials, while RHA steel has a slightly higher ultimate flow stress than the tungsten alloy.


Table 1. Experimental data sheet for high strain-rate compression test

Sample No Material

Lo (mm)

Do (mm)

Area (mm2)

Pressure (kPa)

Time (ms) Lf

Impact Velocity

(m/s2)

Impact Momentum

(kg/m.s)Nominal

Strain

Strain rate (/s)

S. 1-00 RHA steel 10.46 9.39 69.278 180 12.73 7.52 21.60 41.954242 0.28107 2818.203

S. 1-01 RHA steel 10.49 9.39 69.278 200 12.03 7.29 22.86 44.39547 0.30505 3058.659

S. 1-02 RHA steel 10.48 9.43 69.87 200 11.99 7.2 22.94 44.543578 0.31298 3138.117

S. 1-03 RHA steel 10.66 9.46 70.315 220 11.47 6.96 23.98 46.56299 0.34709 3480.175

S. 1-04 RHA steel 10.75 9.43 69.87 240 11.1 6.78 24.77 48.11509 0.3693 3702.871

S. 1-05 RHA steel 10.54 9.35 68.689 280 10.24 6.12 26.86 52.156006 0.41935 4204.731

S. 1-06 RHA steel 10.61 9.47 70.464 320 9.48 5.43 29.01 56.337289 0.48822 4895.206

S. 1-07 RHA steel 10.51 9.39 69.278 340 9.26 5.37 29.70 57.675756 0.48906 4903.622

S. 1-08 Aluminium 5083 H131 10.65 9.41 69.574 200 11.74 2.42 23.42 45.492121 0.77277 7748.307

S. 1-09 Aluminium 5083 H131 10.54 9.43 69.87 180 12.29 2.48 22.38 43.456265 0.76471 7667.451

S. 1-10 Aluminium 5083 H131 10.66 9.45 70.166 140 14.23 3.64 19.33 37.531799 0.65854 6602.927

S. 1-11 Aluminium 5083 H131 10.6 9.46 70.315 100 16.23 4.68 16.94 32.906808 0.55849 5599.799

S. 1-12 Aluminium 5083 H131 10.6 9.42 69.721 80 18.55 5.92 14.82 28.79124 0.44151 4426.868

S. 1-13 Aluminium 5083 H131 10.63 9.33 68.396 80 18.65 5.98 14.75 28.636863 0.43744 4386.077

S. 1-14 Aluminium 5083 H131 10.65 9.39 69.278 80 18.36 5.73 14.98 29.089188 0.46197 4632.038

NS - 1 Aluminium 5083 H131 10.55 9.42 69.721 100 16.18 4.54 17.00 33.008498 0.56967 5711.874

S. 1-15 Tungsten A 90S 10.44 9.52 71.21 200 12.14 8.43 22.65 43.993204 0.19253 1930.421

S. 1-16 Tungsten A 90S 10.53 9.47 70.464 220 11.77 8.33 23.36 45.376168 0.20893 2094.84

S. 1-17 Tungsten A 90S 10.6 9.66 73.319 240 11.17 8.15 24.62 47.813563 0.23113 2317.484

S. 1-18 Tungsten A 90S 10.52 9.56 71.809 280 10.36 7.64 26.54 51.551882 0.27376 2744.943

S. 1-19 Tungsten A 90S 10.52 9.57 71.96 320 9.65 7.1 28.50 55.344819 0.3251 3259.62

S. 1-20 Tungsten A 90S 10.5 9.62 72.713 340 9.38 6.87 29.32 56.9379 0.34571 3466.362

Al. 2-00 Aluminium 5083 H131-L 10.4 9.49 70.762 200 11.74 2.44 23.42 45.492121 0.76538 7674.256

Al. 2-01 Aluminium 5083 H131-L 10.5 9.48 70.612 180 12.4 2.76 22.18 43.070766 0.73714 7391.086

Al. 2-02 Aluminium 5083 H131-L 10.48 9.5 70.911 180 12.34 2.68 22.29 43.280186 0.74427 7462.595

Al. 2-03 Aluminium 5083 H131-L 10.58 9.5 70.911 180 12.4 3.18 22.18 43.070766 0.69943 7012.98

Al. 2-04 Aluminium 5083 H131-L 10.5 9.5 70.911 180 12.45 2.8 22.09 42.897791 0.73333 7352.889

Al. 2-05 Aluminium 5083 H131-L 10.6 9.46 70.315 150 13.3 3.33 20.68 40.156203 0.68585 6876.78

Al. 2-06 Aluminium 5083 H131-L 10.62 9.5 70.911 150 13.33 3.38 20.63 40.065829 0.68173 6835.505

Al. 2-07 Aluminium 5083 H131-L 10.5 9.5 70.911 150 13.32 3.64 20.65 40.095908 0.65333 6550.756

Al. 2-09 Aluminium 5083 H131-T 10.5 9.5 70.911 150 13.27 3.38 20.72 40.246986 0.6781 6799.035

Al. 2-10 Aluminium 5083 H131-T 10.52 9.54 71.509 150 13.34 3.5 20.61 40.035795 0.6673 6690.798

Al. 2-11 Aluminium 5083 H131-T 10.6 9.5 70.911 150 13.34 3.42 20.61 40.035795 0.67736 6791.648

Al. 2-12 Aluminium 5083 H131-T 10.54 9.52 71.21 150 13.29 3.36 20.69 40.186418 0.68121 6830.31

Al. 2-13 Aluminium 5083 H131-T 10.5 9.52 71.21 180 12.38 2.92 22.21 43.140347 0.7219 7238.298

Al. 2-14 Aluminium 5083 H131-T 10.53 9.5 70.911 180 12.43 3.03 22.12 42.966814 0.71225 7141.5

Al. 2-15 Aluminium 5083 H131-T 10.6 9.5 70.911 180 12.45 3.2 22.09 42.897791 0.69811 6999.748

Al. 2-16 Aluminium 5083 H131-T 10.6 9.5 70.911 200 11.85 2.76 23.21 45.069831 0.73962 7415.95

St. 2-17 RHA Steel - L 10.68 9.45 70.166 400 8.6 3.4 31.98 62.102035 0.68165 6834.657

St. 2-18 RHA Steel - L 10.68 9.5 70.911 360 9.01 3.5 30.52 59.276082 0.67228 6740.774

St. 2-19 RHA Steel - L 10.68 9.5 70.911 360 9 3.48 30.56 59.341944 0.67416 6759.551

St. 2-20 RHA Steel - L 10.68 9.48 70.612 360 9 3.6 30.56 59.341944 0.66292 6646.891


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(b) Figure 5. The effect of impact momentum on (a) strain rate and (b) total engineering strain


RHA Steel

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Figure 6. Stress-strain curves obtained from high strain-rate compression tests on RHA Steel

Tungsten A 90S

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Figure 7. Stress-strain curves obtained from high strain-rate compression tests on the Tungsten A90S alloy


Aluminium 5083 H131

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Impact Momentum: 43.3 kg.m/sImpact Momentum: 40.1 kg.m/s

Figure 8. Stress-strain curves obtained from high strain-rate compression test on Aluminium 5083 alloy

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Al 5083 (IM: 45.5 kg.m/s)

Figure 9. Dynamic stress strain curves of all the three alloys in compression at a comparable impact momentum of about 45 kg.m/s


3.2 Torsion Test Typical elastic wave signals as captured by the strain gages, amplified by the signal conditioning/amplifying system and recorded by the oscilloscope are shown in Figs. 10-12. Only a very small fraction of the incident wave is transmitted through the specimen, whereas the greater fraction is reflected back at the specimen/incident bar interface. Thus the angular rotation at the incident end of the specimen is greater than at the transmitted end causing high strain rate deformation of the thin wall tubular specimen. The fractions of transmitted waves are much smaller for aluminum alloy than for the other two alloys. Differences were observed in the shape of the reflected and transmitted waves for each of the alloys. The curves presented in Figs. 10-12 are typical of the respective alloys. The two peaks observed in the reflected signals of RHA steel and tungsten alloy can be traced to yield phenomenon occurring as a result of preferential segregation of solute atoms in distorted regions near dislocations, forming solute atmosphere. The temperature increase during plastic deformation of the alloys at high strain rate increases the mobility of these solute atoms. The solute atmosphere hinders dislocation motion and increase strength until the stress becomes large enough to break dislocation free from solute atmosphere resulting in increased dislocation mobility and reduced stress. The more mobile dislocations can now move freely without increase in strength until work hardening becomes significant again, when stress start to increase with further strain. Yielding effect is more common in BCC metals such as steel and tungsten alloy than alloys of FCC metals such as aluminum as evident in the reflected elastic wave signal in Fig. 10-12. Figs. 13-15 show some of the dynamic stress-strain curves obtained from torsion tests on the materials at strain rates ranging between 950 and 1500 s-1. The result is similar to that obtained in compression test. Plastic deformation is characterized by simultaneous occurrence of strain hardening and thermal softening. At high strain rates thermal softening quickly cancels the effect of strain hardening and lower flow stress as observed in compression tests. The point at which thermal softening dominates the strain hardening is influenced by strain rates. Fig 16 shows a comparative evaluation of the dynamic stress strain curves of the three alloys at strain rate of approximately 1100 /s. RHA steel exhibits the highest ultimate flow stress rate followed by the tungsten alloy at this strain rate, while aluminum shows the least flow stress. As observed in compression test, the difference in the values of flow stresses for the steel and tungsten alloy and which of the two has a higher flow stress is significantly influenced by the strain rate. This may be due to the complex interactions between strain hardening and thermal softening leading ultimately to thermo-mechanical instabilities, stress collapse and occurrence of adiabatic shear bands in materials undergoing plastic deformation at high strain rates.


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Figure 10. Typical incident, reflected and transmitted waves recorded by the oscilloscope for RHA steel

Tungsten A90S

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Figure 11. Typical incident, reflected and transmitted waves recorded by the oscilloscope for Tungsten A90S alloy


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Figure 12. Typical incident, reflected and transmitted waves recorded by the oscilloscope for Aluminium 5083 H131 alloy

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Figure 13. Dynamic stress-strain curves obtained for RHA Steel under torsional loading at different strain rates


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Figure 14. Dynamic stress-strain curves obtained for Tungsten A90S under torsional loading at different strain rates

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Figure 15. Dynamic stress-strain curves obtained for Aluminium 5083 H131 under torsional loading at different strain rates


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RHA steel - 1080 /sTungsten A90S-1120 /sAluminum 5083 - 1130 /s

Figure 16. Dynamic stress strain curves of the RHA steel, Tungsten A90S and Aluminium 5083 at comparable strain rates of approximately 1100 /s in torsion

3.3 Microscopic Examination Typical optical micrograph of the investigated RHA steel in as received condition is shown in Fig. 17. The steel has a plate-like microstructure that is typical of martensite or bainite. Some of the impacted samples were grinded and polished for visual and microscopic examinations. The microscopic investigation of impacted RHA steel shows that adiabatic heating leading to material instability and strain localization along narrow bands play a prominent role in plastic deformation and fracture behavior of the material at impact momentum exceeding 44.5 kg.m/s. Such narrow bands of intense strain localization occurring in materials at high strain rates are called adiabatic shear bands. Two types of adiabatic shear bands are commonly reported in metallic materials: deformed shear band and transformed shear bands. Whereas no adiabatic shear band was observed in samples impacted at a momentum below 44.5 kg.m/s, deformed shear bands were observed in RHA steel sample impacted at 46.6 kg.m/s

(Fig. 18). At higher impact momentum, transformed shear bands were observed in the steel specimens. Transformed bands are also called white etching bands because of their white color when viewed under an optical microscope after etching. Figure 19 shows the overview of a parabolic shaped transformed shear band observed on the transverse cross section of a RHA steel impacted at a momentum of 48 kg.m/s. The transformed shear bands in the steel, as observed under an optical microscope at different magnifications are presented in Fig. 20. The plate-like morphology observed in the parent material and outside the shear bands could not be observed inside the transformed shear bands under an optical microscope. The thickness of the adiabatic


shear band was observed to increase with increasing impact momentum. Failure of the steel at high strain rates is initiated by cracks which form and propagate along the adiabatic shear bands (Fig. 21). Results of hardness measurement on the steel samples show the adiabatic shear bands to have higher hardness value than the bulk material and the hardness of the shear bands was observed to increase with increasing impact momentum as shown in Fig. 22. Figure 23 shows a RHA steel specimen that failed at a high impact momentum of 59.3 kg.m/s. Although this material fractured into three parts, total fragmentation did not occur as a result of high temperature fusion of the fragments. A schematic view of fused fragments after impact is shown in Fig. 24, with arrows indicating shear flow directions. This observation suggests a temperature increase of up to the melting point of the steel inside the shear bands during deformation. Visual observation of the specimen after impact also indicates melting in the material during the high velocity impact. Results of microscopic evaluation of this test specimen show splashing and spreading of materials inside the shear band (Fig. 25). This indicates high fluidity of the materials inside shear bands during testing at the impact momentum of 59.3 kg.m/s.

Figure 17. Optical micrograph showing the plate-like structure of the investigated RHA steel (as received)


ASBASB

Figure 18. Deformed ASB as observed in RHA steel subjected to an impact momentum of 46.6 kg.m/s

Figure 19. Optical micrographs showing overview of a parabolic shapes ASB observed on transverse section of RHA steel subjected to an impact momentum of 48 kg.m/s


Figure 20. Optical micrographs showing ASB’s observed in RHA steel impacted at 48.5 kg.m/s at different magnifications

Figure 21. Optical micrograph showing crack propagation along ASB in RHA steel subjected to impact momentum of 59.3 kg.m/s


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Inside Deformed band (IM = 41.9 kg.m/s2)

Inside deformed band (IM = 44.5 kg.m/s2)

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Hardness (HV)

Figure 22. Hardness outside and inside ASB’s in RHA steel as a function of impact momentum (IM)

Figure 23. Optical macrograph of a sample impacted at 59.3 kg.m/s showing adiabatic shear failure and fusion of fragments along the ASB’s.)


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Figure 24. A schematic view of the longitudinal section of the sample impacted at 59.3 kg.m/s after failure under the high velocity impact showing the three fragments 1, 2 and 3 fused together along the shear bands (white strips).

Figure 25. Optical micrograph showing splashing and spreading of an ASB in RHA steel impacted at 59.3 kg.m/s


Typical microstructure of the investigated Tungsten A90S alloy, in as received condition, showing equi-axed grains is presented in Fig. 26. When impacted at a momentum exceeding 50 kg.m/s fragments broke off from the diametrical surface of the tungsten specimens leaving behind a conical shaped cavity on the impacted surface as shown in Fig. 27. Scanning electron microscopic examination of the surface of the cavity shows a ring-like structure (Fig. 28). The centre of the cavity has a smooth fracture surface as against a coarse surface with more micro-voids and micro-cracks at the peripheral regions of the cavity. The conical shape of the cavity is similar to that of transformed shear bands that we observed in cylindrical AISI 4340 steel specimens after high velocity impact in a previous investigation [9]. It is suggested that extreme strain localization along shear band caused immediate cracking and fracture of the tungsten alloy at high strain rates. Scanning electron microscopic examination of impacted tungsten confirms the occurrence adiabatic shear band at the point where the fragments are detached from the test specimens [Fig. 29]. The deformed bands in the tungsten alloy consist of elongated grains as against equi-axed grain microstructure that is retained in the bulk material after impact. Micro-voids and micro-cracks were observed on the fracture surface of the tungsten specimens as against void- and crack-free surface observed on polished surface of the bulk materials (Fig. 30). Fracture of the tungsten alloy could be traced to formation and coalescence of these micro-voids and -cracks as ASB’s propagate in the material. As in the case of RHA steel, hardness measurement also shows a higher hardness value inside the shear band region than in the bulk material. For example for the sample impacted at 55.3 kg.m/s, the hardness values inside and outside shear band are 806 and 698VH respectively. Microstructures of the Aluminum 5083 H131 alloy consist of fine precipitates embedded in a continuous matrix (Fig. 31). On impact, the alloy shows clear evidence of strain localization and occurrence of adiabatic shear bands for all range of apllied impact momentum (Figs. 32-34). The intensity of the strain localization increases as impact momentum increases from 28 to 45 kg.m/s. ASB’s in the aluminum alloy appear darker than the bulk material and the precipitates are larger and more closely packed inside the shear bands than in the bulk material. This suggests coarsening of the precipitates at the elevated temperature produced by adiabatic heating inside the shear bands during deformation at high strain rates. In most cases, coalescence of precipitates showing alignment in shear flow direction can be observed inside the shear bands (Fig. 33). Shear flow directions are clearly noticeable inside and within the vicinity of the shear bands. Hardness measurement on impacted aluminum alloy (Table 2) shows that hardness values are higher inside the shear bands than outside as in the case of RHA steel and Tungsten A90S alloy. However, no cracking was observed inside the shear bands formed in the aluminum alloy during impact. Thus, the shear bands formed in the aluminum alloy is less susceptible to cracking than those that form in the RHA steel and Tungsten A90S alloy.


Figure 26. Microstructures of the Tungsten alloy showing equi-axed grains

Figure 27. Polished surface of impacted Tungsten A90S alloy showing detachment of small conical shaped fragment during impact


Figure 28. SEM-Micrograph showing fracture surface of Tungsten A90S alloy after high velocity impact

Cavity

ASB

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ASB

Figure 29. SEM-Micrograph showing deformed band in Tungsten A90S alloy after high velocity impact


Figure 30. SEM-Micrograph showing micro-voids and cracks on fracture surface of Tungsten A90S alloy after failure under high velocity impact


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Figure 31. Optical micrograph showing the microstructure of the investigated Aluminium 5083 H131 alloy in as received condition


(a) (b)

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Figure 32. Optical micrographs showing adiabatic shear band along transverse section of Aluminum 5083 H131 alloy impacted at 29.0 kg.m/s: (a) circular ASB close to the circumference. (b), (c) & (d) linear ASB across the cross section at different magnifications. (e) microstructure inside ASB and (f) microstructure outside ASB


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Figure 33. Optical micrographs showing adiabatic shear band along transverse section of Aluminium 5083 H131 alloy impacted at 37.5 kg.m/s: (a) circular ASB close to the circumference. (b), (c), (d) linear ASB across the cross section at different magnifications, (e) Microstructure inside and outside ASB


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Figure 34. Optical micrographs showing adiabatic shear band along transverse section of Aluminum 5083 H131 alloy impacted at 43.5 kg.m/s: (a) (b), (c) ASB across the cross section at different magnifications. (d) Microstructure inside ASB and (e) Microstructure outside ASB


Table 2. Hardness inside and outside shear bands in Aluminium 5083 alloy after high velocity impact

Impact Momentum (kg.m/s)

Avarage hardness outside the shear bands (HV)

Average hardness inside the shear bands (HV)

45.5 137.0 157.0

43.5 127.0 154.037.5 142.0 154.032.9 131.0 158.028.8 127.5 153.528.7 132.0 148.529.1 130.5 142.5

3.4 Torsional Testing of Alumina The ceramic materials provided for investigation were too hard and could not be machined into test specimens. As an alternative, machinable Alumina 96 (Rescor 960) was procured from Cotronics Corporation and machined into torsion test samples (Fig. 35) for high strain rate evaluation. The alumina samples were tested in torsion using torsional Hopkinson Bar described in Section 3.2. Typical incident, reflected and transmitted wave signals captured and recorded by the oscilloscope during testing of the ceramic material are shown in Fig. 36. The transmitted pulse signal through the specimen is much smaller compared to those obtained from testing of metallic materials. Large portion of the elastic wave signal transmitting through the specimens are consumed in fracturing them. Only very small fraction of pulse signal actually transmits through the specimen on to the transmitter bar. Dynamic stress strain curves obtained from the high strain-rate torsional testing of the alumina ceramic are presented in Fig. 37. All the ceramic specimens fractured during testing. Results of our investigations show that ultimate stress increases with increasing strain rate and decreases with increasing wall thickness of the tubular specimen. Figure 38 shows fragment of a test piece after rupture in torsion at high strain rate. Although this specimen was not completely crushed, most of the tested samples eventually crumble into multiple smaller fragments, especially at higher strain rates or during withdrawal from the sockets of the Kolsky bars after testing. The fracture pattern displayed by the sample shown in Fig. 38 is of particular interest because the outline of the fracture path is similar to that which is observed in metallic materials that failed at high strains by adiabatic shear banding. Strain localization might therefore be one the damaging mechanism in the alumina ceramic. Characteristic feature of the fracture surface of fragmented alumina shows intergranular fracture with noticeable evidence of debonding of the ceramic particles along the path of crack propagation (Fig. 39). The high temperature, resulting from adiabatic heating, and intense strain localization within the shear bands is possibly responsible for degradation of the bonding between ceramic particles leading to crack initiation and fracture.


Figure 35. Torsional test specimens machined from the machinable Alumina 96

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Figure 36. Typical incident, reflected and transmitted waves recorded by the oscilloscope during dynamic torsion test of alumina at high strain rate


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Figure 37. Dynamic stress strain curves obtained from torsional testing of Alumina 96

Figure 38. An alumina ceramic sample after failure under torsional loading at high strain rate


Figure 39. Fracture surface of alumina ceramic after fracture in torsion at high strain rates.


4. Discussion of Experimental Results

Plastic deformation and failure of the investigated metallic material at high strain rates is dominated by occurrence of adiabatic shear bands. Adiabatic shear bands (ASBs) are regions of intense localized deformation in materials subjected to plastic deformation at high strain rates. Adiabatic shear band occurs when the heat generated during the deformation in a particular region is retained causing a local rise in temperature. When the local condition is such that the effect of thermal softening due to the adiabatic heating is greater than the strain-hardening effect of plastic deformation, a condition of thermo-mechanical instability resulting in intense shear strain localization occurs. Occurrence of adiabatic shear bands is an undesirable phenomenon because adiabatic shear band constitute microstructural defects which can trigger premature failure at high strain rates, resulting in a sudden and catastrophic failure of even a normally ductile material. As observed in the investigated RHA steel and tungsten alloy, adiabatic shear bands act as preferential crack initiation and propagation site. Therefore, formation of adiabatic shear bands can be regarded as initiation of failure. Most materials failure at high strain rates has been traced to strain localization and occurrence of adiabatic shear bands. For example, perforation of a steel shell by ballistic fragments and fragmentation of steel casement after explosion have also been traced to shear strain localization and adiabatic shear banding [16,17]. Two types of adiabatic shear bands have been identified in the literature: deformed band and transformed bands. Deformed bands appear as severely distorted region showing extensive shear deformation. This is the type of shear bands that we observed in the aluminum and tungsten alloy and in the RHA steel subjected to impact momentum below 47 kg.m/s. The transformed bands observed in the RHA steel impacted at higher momentums are common to hardened steel and Titanium alloys. They are called transformed bands because they are considered to be products of phase transformation occurring due to high temperature increase inside the shear bands during deformation. The transformed bands are also called white etching bands because of their white color when observe under an optical microscope after etching. The temperature rise as a result of adiabatic heating during plastic deformation at high strain rates is given by equation (4) [16]:

τdγρCβdT

V

= (4)

where Cv is the specific heat and β is the Taylor-Quinney coefficient, i.e the fraction of the plastic work converted into heat that results in temperature rise. Armstrong and Zerilli [18,19] suggested that a local rise in temperature and softening can be produced when a dislocation pile-up pierces through a grain boundary creating a site for shear band initiation. Depending on the plate thickness that is struck by a projectile, analyses by Chen et al [20] shows that a temperature rise of up to 1527 °C can be attained in the localized zone of a target plate and cause strain localization along narrow bands. This temperature is high enough to cause phase change in the steel and lead to changes in strength and other mechanical properties.


In the present study, a correlation is observed between the results of mechanical tests and microstructural evaluation. For example as the impact momentum of RHA steel and tungsten increases, the maximum flow stress increases until the impact momentum applied is high enough to trigger the formation of adiabatic shear bands. Beyond this impact momentum, the flow stress is dominated by extreme strain localization and occurrence of adiabatic shear bands. For all the applied impact momentum during the testing of the aluminum alloy, plastic deformation is dominated by adiabatic heating and occurrence of adiabatic shear bands and no significant change in maximum flow stress was observed as impact momentum was increased within the range of the applied impact momentum. The increased strain hardening effect of increase impact momentum is mostly neutralized by increased thermal softening and the associated thermo mechanical instability that lead to occurrence of adiabatic shear bands. This explains the reason why no noticeable increase in ultimate flow stress is observed for the aluminum alloy as impact momentum was raised within the range of the applied impact momentum. Microstructural examinations show that all impacted aluminum samples contain fully developed adiabatic shear bands. Transformed bands observed in high strength steels after deformation at high strain rates steels have been reported to contain very fine sub-grains of a few hundreds nanometer size [21-23]. Zurek [23] attributed the white color of transformed bands to resolution limit of optical microscope in resolving the nanosized subgrains inside the shear bands. A number of theories have been propounded to explain the nano sized subgrains that are observed in the white etching bands; Cho et al [22] attributed the formation of the very fine cells in transformed bands to elongation and fragmentation of the existing grains along shear band propagation path during deformation. Many authors [23-27] have also suggested that microstructural evolution at high strain rates begin with a homogeneous distribution of dislocations that rearrange themselves into dislocation cells which eventually become elongated sub-grains that subsequently break down into equi-axed microcrystalline structure as strain increases. The high hardness observed inside the shear bands, as observed in this study, is attributed the extreme fine structure that are characteristic of white etching bands. Since other investigators [24,25] have observed high dislocation density inside adiabatic shear bands, increased dislocation can also contribute to the high hardness of shear bands. The mechanism of crack initiation and propagation inside adiabatic shear bands is discussed in details in one of our recent publications [9]. As reported in section 3.4, the outline of the fracture path in the investigated alumina is similar to that which is observed in metallic materials that failed at high strains by adiabatic shear banding. This suggests that strain localization might therefore the damaging mechanism in the ceramic material. Occurrence of inelastic deformation and strain localization in ceramic materials at high strain rates have been reported in the literature [28-34]. Meyers et al. [28] suggested that shear localization in ceramic materials is a direct consequence of avoiding dilatation that accompanies homogeneous deformation. Intergranular fracture and debonding of the ceramic particles observed along the crack propagation path can be traced to combined effect of high temperature and intense shear deformation inside the high shear band, which degrade the glassy material that usually bonds alumina particles together.


5. Construction of a new Torsional Hopkinson Bar

Included in the contract is the design and fabrication of a torsional Split Hopkinson Bar similar to the one at the University of Manitoba for DRDC-Valcartier. This equipment was fabricated on schedule in December 2006. Although the geometry of torsion test specimens is complex and they are more expensive to produce than compression test specimens, torsional Hopkinson Bar may be preferred to Hopkinson Pressure Bar (compression) for the following reasons;

• Poisson's ratio effects of uni-axial loading are eliminated

• No geometric dispersions during wave propagation along the bar as in case of uni-axial compressive loading

• Torsional bar is more suitable for investigating hard and brittle ceramic materials

A sketch of the fabricated torsional Hopkinson Bar is shown in Fig. 40. The equipment is made of two bars (incident and transmitter bars) made of Aluminum 6061-T6 alloy. Each of the bars is 1.829 m long and has a diameter of 25.4 mm. The bars are suspended on a series of Teflon bushing that line stainless steel stands, which are in turn attached to a 4 m long I-beam. Incident and transmitter gages are attached to the two bars at equidistance from the specimen and at a distance from the specimen such that overlapping of incident and transmitted wave is avoided. The system employs stored-torque technique of loading, in which the loading torque is stored between a clamp and the loading arm. The clamp is sufficiently tightened prior loading to prevent rotation of the incident bar as pure torsion load is applied by a hydraulic jack connected to a rotating wheel attached to the loading end of the incident bar. On attaining the desired angle of twist, the clamp is further tightened until the load release pin breaks and the stored torque is released generating elastic wave, which travels along the incident bar and deform the specimen at a strain rate which can be in excess of 103 s-1, depending of the amount of torque stored in the loading arm.

5.1 Specimen Mount The incident and transmitter bars are machined to have hexagonal sockets that will provide a lock-in system that and enables a rigid contact between the hexagonal flanged specimens, incident and transmitter bars (Fig. 41). With this type of specimen lock-in system, the need for the use of screws or rigidity-increasing compounds such as epoxy or glycol phthalate is eliminated.

5.2 Pulse generating System The torsional pulse generating system consists of mechanical jack, locker, clamp and the loading end of the input bars for torque storage. The loading pulse is produced by clamping the incident bar at a distance of about 540 mm from the point of application of torque. The angle of twist can be measured directly with the aid of an attached


compass as torque is applied using the hydraulic jack; the corresponding maximum shear strain on the surface of the bar is given by:

Lcφγ = (5)

where L is the length of storage bar and c radius of the storage bar and φ is the applied angle of twist. The total stored torque (T) in the storage bar prior to loading of the test specimen be calculated as follows:

LJG T φ

= (6)

On breaking the load release pin, the stored torque is released in form of two equal and opposite torsional pulses. One of the pulses propagates from the clamp towards the specimen while the other pulse propagates towards the clamping mechanism. As the incident pulse travels along the bar towards the specimen, it is detected and captured by the strain gage mounted on the incident bar as incident pulse. On reaching the specimen, part of the pulse will propagate through the specimen on to the transmitted bar. The transmitted pulse will be detected and captured by the strain gage mounted on the transmitter bar. Part of the pulse that reach the specimen will be reflected back along the incident bar and captured by the strain gage mounted on the input bar. The wave signals can be captured, recorded and stored by means of high frequency mixed signal oscilloscope or any other suitable signal capturing device.

5.3 The Clamping Mechanism The design of the clamp, as shown in Fig. 42, is one of the most important aspects of the torsional Hopkinson bar for good results. The clamp must be able to hold the desired torque without slipping. The clamp must also release the stored torque rapidly enough to produce a sharp fronted stress pulse traveling towards the specimen, i.e. the incident pulse should rise instantly to a constant amplitude and drop off immediately to zero at the end of the pulse. For an ideal clamp a square loading pulse should be generated. However, in practice a finite time is required to achieve maximum torque in the loading pulse and to reduce the torque to zero at the end of the incident wave. The clamp is tightened by a notched using a notched load-release pin shown in Fig. 43. The pin is constructed from Aluminium 6061-T6 alloy. In order to initiate the pulse after the required torque has been stored, the load applicator at the base of the clamp is tightened until the bolt fractures and the stored torque is released.


Figure 40. A sketch of the constructed Split Hopkinson Bar


Figure 41. Test specimen and the socket on the Kolsky bar

Front view Side ViewFront view Side View

Figure 42. Clamping Mechanism


Figure 43. Load release pin


5.4 Test Procedure The procedure for conducting tests using the torsional Hopkinson bar system is itemized in the sequence below:

• Ensure that the jacking mechanism is at its lowest position and close the pressure release valve of the hydraulic jack

• Loose the clamp release applicator, insert the notched load release pin into the clamp and tighten the pin as much as possible

• Tighten the load applicator with a wrench to sufficiently clamp the incident bar such that the input bar does not rotate beyond the clamp when torque is applied at the loading end.

• Check and adjust the data acquisition system to confirm proper connection and readiness to capture single event data

• Apply the torsional load on the incident bar up to the clamp using the hydraulic jack until the desired angle of twist is attained

• Insert the sample between the incident and transmitter bars and twist the transmitter bar in clockwise direction (looking down towards the clamp) to eliminate any slack that might exist at the interface between the specimen and either of the two bars

• Set the trigger voltage for data capturing

• Tighten the load applicator further until the load release pin fractures and release the stored torque that generates the elastic waves that travels through the incident bar and deform the specimen at high strain rates

5.5 Calculation of Stress, Strain and Strain Rates The mathematical relation between the shear strain and voltage recorded by the strain gages are derived from equipment calibration. This is carried out by connecting the transmitter and an incident bar with a solid hexagonal rod. While keeping the end of the transmitter bar fixed. Torque is applied using the loading arm at increasing angles of twist and corresponding voltage measurement by the strain gages recorded. A linear plot of shear strain against the signal strength in voltage can be use to determine the mathematical relationship between the voltages detected by the strain gages and the corresponding value of shear strains on the bars.

The shear strain in the specimen is given by the difference in rotation between its two ends divided by its length.

s s 1s

s

D - Dγ = 2L2φ φ

(7)


φ1 and φ2 are the angles of twist in the incident and transmitter bars respectively. Ds is the mean diameter of the thin walled specimen and Ls is its length. The value of φ2 can be determined from the shear strain measured at the surface of the transmitter bar as follows:

T

2 2

D Dγ = 2 x 2C t

∂φ ∂φ=

∂ ∂ (8)

D is the diameter of the incident and transmitter bars and C is the wave propagation velocity in the bar and it is given by:

GCρ

= (9)

From equation (8),

2

t

T0

2C γ (t)dtD=φ ∫ (10)

The angle of twist in the incidence bar φ2 can be computed from the difference in strains due to the incidence and reflected pulses. Thus

[ ]1

t

I R0

2C γ (t)-γ (t) dtD

φ = ∫ (11)

The minus sign is necessary because the reflected pulse travels in the opposite direction of the incidence pulse. Differentiating equation (7) and substituting equations (10) and (11):

{ }[ ]R(t)I(t)T(t)s

ss(t) γ- γ- γ

DLD C γ = (12)

For a homogeneous strain state in the specimen, the transmitted pulse is the difference between the incident and reflected pulses, i.e. )( RIT γγγ −−≈ and equation 6 reduces to:

(t)γDLD 2C

γ Rs

ss(t) = (13)

Integration of equation (12) gives the value of strain )(tsγ in the specimen. Thus strain in the specimen at time t is given by

{ }[ ]dtDL

CDt

sR(t)I(t)T(t)

0s(t) γ- γ- γ γ ∫= (14)


Equation (14) can be simplified to a more workable form as follows:

{ }ss(t) T(t) I(t) R(t)

s

CDγ γ - γ - γ ∆tL D

= ∑ (15)

Analysis by Kolsky, as outlined by Hartley [29], also shows that the stress in the thin-walled tube to be given by:

sss tD

Ts)(

22π

τ = (16)

where ts and Ts are wall thickness and average Torque respectively. The average torque in the specimen is also given by the average torque at the interface with the incident bar (T1) and at the interface with the transmitter bar (T2):

)( 2121 TTTs += (17)

Torques can be given in term of strain at the surface of the bar. At the surface with the incident bar, the torque is given by:

16)(3

1RIDGT γγπ −

= (18)

The negative sign for Rγ is required due to the fact that the reflected pulse travels in the –x direction. The torque at the surface with the transmitter bar in terms of strain is given by:

16

3

2TDGT γπ

= (19)

Substituting equations (17), (18) and (19) in equation (16), the stress in the thin walled specimen is:

( )3

s(t) ( ) ( ) ( )2s s

GDτ 16D t I t R t T tγ γ γ= − + (20)

For a homogeneous system of strain, transmitter pulse can be expressed as the difference between incident and reflected pulses and the equation (20) reduces to

3

s(t) 2s s

GDτ 8D t Tγ= (21)


Homogeneous sate of strain can hardly be achieved in the bar at high strain rates, so the assumption of homogeneous state of strain is better discarded for higher accuracy of test data. Thus strain, strain rate and stress in the specimen as function of time can be determined using equations (12), (15) and (20).


6. CONCLUSION

The response of selected armor materials to plastic deformation at high strain rates both in torsion and in compression is evaluated. Dynamic stress strain curves are generated to provide information on mechanical properties of the material in both loading modes. Microstructural evolution in the materials during high strain-rate deformation is also investigated. It is evident that the plastic deformation and failure of the materials is controlled by the phenomenon of adiabatic heating leading to thermal softening and strain localization along adiabatic shear bands. Occurrence of adiabatic shear bands shows considerable influence on dynamic stress-strain curves for the materials and cause failure at high strain rates. As major component of the part of the contract, a torsional Split Hopkinson Bar similar to the one that was used in executing this contract was constructed and delivered on schedule to DRDC-Valcartier in December 2006. The equipment is capable of achieving strain rates in excess of 103s-1. A unique advantage of this equipment is that it can be used to investigate ceramic material in amour plate use.


7. References

1. M.N. Bassim, Study of the formation of adiabatic shear bands in steels, Journal of materials Processing Technology 119 (2001) 234-236

2. H. Feng, M.N. Bassim, Finite element modeling of the formation of adiabatic shear bands in AISI 4340 steel. Materials Science and Engineering A Vol. 266 (1999) 255-260.

3. M. Nabil Bassim and N. Panic, High strain rate effects on the strain of alloy steels, Journal of Materials processing Technology, Vol. 92-93, 481-485

4. A. G. Odeshi, G. M. Owolabi and M.N. Bassim, Effects of particulate reinforcement and strain-rates on deformation and fracture behaviour of Aluminium 6061-T6 under high velocity impact, Materialwissenchaft und Werkstofftechnik, 38 (2007), 66-69

5. M.N. Bassim, M. Bolduc, A.G. Odeshi and S. Mirfarkraei, Microstructural Evolution in High Strength Materials at High Strain Rates , Journal De Physique IV 134 (2006) 1097-1103.

6. G. M. Owolabi, A. G. Odeshi, M.N.K. Singh and M.N. Bassim, Dynamic shear band formation in Aluminum 6061-T6 and Aluminum 6061-T6/Al2O3 composites, Material Science and Engineering A, 457 (2007) 114-119

7. A.G. Odeshi, G.M.Owolabi, M.N.K. Singh, M.N. Bassim, Deformation and fracture behaviour of metal matrix composites during dynamic mechanical loading, Accepted for publication in Metallurgical and Materials Transactions A- Physical metallurgy and Materials Science

8. A.G. Odeshi, M.N. Bassim, S. Al-ameeri, Effect of heat treatment on adiabatic shear bands in a high strength low alloy steel, Materials Science and Engineering A 419, (2006) 69-75.

9. A. G Odeshi., S. Al-ameeri, S. Mirfakhraei, F. Yazdani and M.N. Bassim, Deformation and Failure Mechanism in AISI 4340 Steel under Ballistic Impact, Theoretical and Applied Fracture Mechanics, Vol. 45, No 1 (2006) 18-24.

10. Odeshi. A. G., M.N. Bassim, S. Al-ameeri and Q. Li, Dynamic shear band propagation and failure in AISI 4340 steel, Journal of Materials Processing Technology, Vol. 169, No 2 (2005) 150-155.

11. Odeshi. A. G., S. Al-ameeri and M.N. Bassim. The effect of high strain rate on plastic deformation of steel subjected to ballistic impact, Journal of Materials Processing Technology, Vol. 162-163C (2005) 385-391


12. Q. Li, P. Zmudzki, S. Al-ameeri, Bassim M.N. Morphology of adiabatic shear bands in cylindrical specimens of AISI 4340 steel impacted by Hopkinson pressure bar, Materials Science and Technology 20 (2004) 676-678

13. L. Qiang, M.N. Bassim, Effects of strain and strain-rate on the formation of the shear band in metals, Journal de Physique IV 110 (2003) 87-91

14. Q. Li, Y.B. Xu, M.N. Bassim, Dynamic mechanical properties in relation to shear band formation in titanium alloy-Ti117, Materials Science and Engineering A 358 (2003) 128-133

15. A.G. Odeshi, G.M. Owolabi, M.N.K. Singh and M.N. Bassim, Deformation and fracture behaviour of metal matrix composites during dynamic mechanical loading, accepted for publication in Metallurgical Transaction A, March 2006

16. Y. Bai, B. Dodd (1992) Adiabatic Shear Localization, Pergamon Press, New York

17. S.E. Schonfeld and T.W. Wright, A failure criterion based on material instability, Int. J. Solids Struct. 40 (2003), pp. 3021–3037.

18. R. Armstrong, W. Arnold, F. Zerilli, Dislocation Mechanics for shock-induced plasticity, Conference proceeding, TMS 2007: Annual Meeting and Exhibition, Orlando Florida, Feb 25-March 2007, p. 29

19. R. W. Armstrong and F. J. Zerilli, Dislocation mechanics aspects of plastic instability and shear banding, Mechanics of Materials 17 (1994) 319-327.

20. X. W. Chen, Q.M. Li, S.C. Fan, Initiation of adiabatic shear failure in a clamped circular plate struck by a blunt projectile, Int. J Impact Eng. 31 92005) 877-893

21. J.L. Derep, Microstructure transformation induced by adiabatic shearing in armour steel, Acta Metall. 35 (1987) 1245-1249

22. K.M Cho, S. Lee, S.R Nutt, J. Duffy, Adiabatic shear band formation during dynamic torsional deformation of an HY-100 steel , Acta Metall. Mater. 41 (1993) 923-932

23. A.K. Zurek, The study of adiabatic shear band instability in a pearlitic 4340 steel using a dynamic punch test, Metallurgical and Material Transactions 25A, (1994) 2483-2489

24. M.A Meyers, Y.B. Xu, Q. Xur, M.T. Perez-Prado, T.R McNellley, Microstructural evolution in adiabatic shear localization in stainless steel, Acta Mater. 51 (2003) 1307-1325

25. M.A Meyers, V.F. Nesterenko, J.C. LaSalvia, Q Xue, Shear localization in dynamic deformation of materials: microstructural evolution and self-organization, Mater. Sc. Eng A 317 (2001) 204-225


26. V.F. Nesterenko, M.A. Meyers, J.C. LaSalvia, M.P. Bondar, Y.J. Chen, Y.L. Lukyanov, Shear localization and recrystallization in high-strain, high strain-rate deformation of tantalum, Mater. Sc. Eng. A 229 (1997) 23-41

27. D. R. Chichili, K.T. Ramesh, K.J. Hemker, Adiabatic shear Bband localization in α-titanium: experiments, modeling and microstructural evolution, J Mech. Phys. Solids 52 (2004) 1889-1909

28. 4. M.A. Meyers, V.F. Nesterenko, J.C. LaSalvia and Q. Xue, Shearl localization in dynamic deformation of materials: microstructural evolution and self organization, Mater. Sci. Eng. A317 (2001), 204-225.

29. C.J. Shih, V.F Nesterenko and M.A. Meyers, High strain-rate deformation and comminution of silicon carbide, J. Appl. Phys. 83, (1998), 4660-4671.

30. V.F. Nesterenko, M.A Meyers, and H-C Chen, Shear localization in high-strain-rate deformation of granular alumina, Acta Met. 44 (1996), 2017-2026.

31. C.J. Shih, M.A. Meyers, V.F. Nesterenko, High strain-rate deformation of granular silicon carbide, Acta Mater. 46 (1998), 4037-4065

32. C.J. Shih, M.A. Meyers, V.F. Nesterenko and S.J Chen, Damage evolution in dynamic deformation of silicon carbide, Acta Materailia 48 (2000) 2399-2420

33. D.R. Curran, L. Seaman, T. Copper and D.A. Shockey, Micromechanical model for comminution and granular flow of brittle material under high strain rate application to penetration of ceramic targets, Int. J. Impact Eng. 13, (1993) 53-83

34. K.A. Hartley, J. Duffey, R.H. Hawley, in ASM Handbook (1985), 218


List of symbols/abbreviations/acronyms/initialisms

DND Department of National Defence DRDC Defence Research and Development Center SHB Split Hopkinson Bar SHPB Split Hopkinson Pressure bar TSHB Torsional Split Hopkinson bar ASB Adiabatic Shear Band ASB’s Adiabatic Shear Bands

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