hugoniot equation of state ~measurements for … · man u fact uring development 0 gener al k!0t...

HUGONIOT EQUATION OF STATES ~MEASUREMENTS FOR ELEVEN

(• MATERIALS TO FIVE MEGABARS

by -

F-H. Shipman .--A.H. Jones .

Materials & Structures Laboratory . - , U tL,.-"

Manufacturing Development, General Motors Corporation ---.

General Motors Technical Center, Warren, Michigan 48090

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4 7MSL-68-13

HUGONIOT EQUATION OF STATEMEASUREMENTS FOR ELEVEN

ii MATERIALS TO FIVE MEGABARS

byI W.M. Isbell

F.H. ShipmanA.H. Jones

Materials & Structures LaboratoryManufacturing Development, General Motors Corporation

General Motors Technical Center, Warre,., M"chigan 48090

1968, December

Prepared forDEPARTMENT OF THE ARMY

U.S. ARMY BALLISTIC RESEARCH LABORATORIESABERDEEN PROVING GROUND, MARYLAND 21005

UNDER CONTRACT DA-18•-40a-AMC-12I (X)

DASA File NoM. 1•Se"0

This dooaument has been approved for publio releame

and sale; its distribution is unlimited.

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MANUPACT URING C VFIOP.&5NT 4 C4w. AL MOTORi _U,,' POATION

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ABSTRACT

An experimental technique is utilized in which a Uight-gasgun is used to launch flat impactor plateso.to high velocities(u 8 km/sec) at specimens suspended at the muzzle of %he gun.Impact-induced shock waves at pressures to %, 5 megabarn arerecorded and are used to determine the shock state in tdLspecimen. The ability to launch unshocked, stress-frea slatplates over a wide and continuous velocity range, coupledwith the ability to launch impactor plates of the same miterialas the target, results in hugoniot measurements of relativelyhigh precision. Measurements were made on Fansteel-77 (a tung-sten alloy), aluminum (2024-T4), copper (OFHC, 99.99%), nickel(99.95%), stainless steel (type 304), titanium (99.99%), mag-,nesium (AZ31B), beryllium (S-200 and 1-400), uranium (depleted),Plexiglas, and quartz phenolic. The results are compared withthose of other researchers. .

Deviation from linear shock velocity - particle velocity was

found in aluminum beginning at I 1.0 megabars, probably attribu-table to melting in the shock front.

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TABLE OF CONTENTS

ABSTRACT Pg

LIST OF ILLUSTRATIONS v

LIST OF TABLES ix

SECTION I INTRODUCTION 1

A SECTION II EQUATION OF STATE MEASUREMENT 3

Theoretical Considerations 4

Experimental Techniques 8

Instrumentation 12

Target Design and Construction 15

SECTION III DATA ANALYSIS 22

Shock Wave Velocity 22

Impact Velocity 23

Hugoniot of the Impactor 23

SECTION IV EXPERIMENTAL RESULTS 24

Fanstee1-77 25

OFHC Copper 33

2024-T4 Aluminum 36

Depleted Uranium 49

Nickel 55

Type 304 Stainless Steel 62

Titanium 68

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TABLE OF CONTENTS (Continued)

Page 4Beryllium 75

AZ31B Magnesium 82

Plexiglas 87

Quartz Phenolic 92

SECTION V SUMMARY 97

Conclusions and Recommendations 101

ACKNOWLEDGEMENTS 102

REFERENCES 103

APPENDIX A DATA ANALYSIS PROCEDURES FOR THEDETERMINATION OF HUGONIOT STATESFROM SHOCK WAVE DATA 105

APPENDIX B ANALYSIS OF SYSTEMATIC MEASUREMENTERRORS 118I I

DD FORM 1473 DOCUMENT CONTROL DATA - R&D 127

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LIST OF ILLUSTRATIONS

Figure Page

1 Schematic of Shock Wave Parameters 5

2 Schematic of Symmetrical Impact Analysis 6

3 Schematic of Dissimilar MaterialsImpact Analysis 7

4 Layout of ARLG Gun Range 9

5 Target Chamber Set-up with ContinousWriting Streak Camera in Position 11

6 Top View of Target Chamber 11

7 X-ray Shadowgraphs of ProjectileBefore Impact 13

8 Schematic of Target & Impactor 16

9 Intrusion Angle of Elastic Edge RarefactionPoisson's Ratio 17

10 Photograph of Target 18

11 X-ray of Coaxial Shorting Pin 21

12 Shock Velocity vs Particle Velocityfor Fasteel-77 29

13 Shock Velocity vs Particle Velocityfor Fansteel-77 30

14 Pressure vs Particle Velocity for Fansteel- 7 7 31

15 Pressure vs Specific Volume for Fansteel-77 32

16 Shock Velocity vs Particle Velocityfor Copper 37

17 Shock Velocity vs Particle Velocityfor Copper 38

18 Pressure vs Particle Velocity for Copper 39

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LIST OF ILLUSTRATIONS (Continued)

Figure Page

19 Pressure vs Specific Volume for Copper 40

20 Shock Velocity vs Particle Velocity for2024-T4 Aluminum 44

21 Shock Velocity vs Particle Velocity forAluminum 45

22 Deviation of Aluminum Data from Linear Fit 46

23 Pressure vs Particle Velocity for Aluminum 47

24 Pressure vs Specific Volume for Aluminum 48

25 Shock Velocity vs Particle Velocity forUranium 50

26 Pressure vs Particle Velocity for Uranium 51

27 Pressure vs Specific Volume for Uranium 52

28 Shock Velocity vs Particle Velocity for Nickel 58

29 Shock Velocity vs Particle Velocity for Nickel 59

30 Pressure vs Particle Velocity for Nickel 60

31 Pressure vs Specific Volume for Nickel 61

32 Shock Velocity vs Particle Velocity for304 Stainless Steel 65

33 Pressure vs Particle Velocity for304 Stainless Steel 66

34 Pressure vs Specific Volume for304 Stainless Steel 67

35 Shock Velocity vs Particle Velocity forTitanium

36 Shock Velocity vs Particle Velocity forTitanium 72

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]Figure Page

37 Pressure vs. Particle Velocity forTitanium 73

38 Pressure vs Specific Volume forTitanium 74

39 Shock Velocity vs Particle Velocityfor Beryllium 78

40 Pressure vs Particle Velocity forBeryllium 79

41 Pressure vs Specific Volume forBeryllium 80

42 Shock Velocity vs Particle Velocityfor Magnesium 84

43 Pressure vs Particle Velocity forMagnesium 85

44 Pressure vs Specific Volume forMagnesium 86

45 Shock Velocity vs Parti.cle Velocityfor Plexiglas 89

46 Pressure vs Particle Velocity forPlexiglas 90

47 Pressure vs Specific Volume forPlexiglas 91

48 Shock Velocity vs Particle Velocityfor Quartz Phenolic 94

49 Pressure vs Particle Velocity forQuartz Phenolic

50 Pressure vs Specific Volume forQuartz Phenolic 96

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Figure Page

51 Compilation of Hugoniots 99

52 Compilation of Hugoniots 100

LIST OF ILLUSTPATIONS IN APPENDIX

f Figure

A-I Schematic of Equation of StateStudies Target 106

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LIST OF TABLES*o

Table Page

1 Summary of Materials Tested andPressure Ranges Examined 2

2 Calculated Minimum Design Anglesor Maximv-i Edge Rarefaction Angles 19

3 Chemical and Physical Propertiesof Fansteel-77 26

4 Hugoniot Data for Fansteel-77 28

5 Chemical and Physical Propertiesof OFHC Copper 34

6 Hugoniot Data for OFHC Copper 35

7 Chemical and Physical Propertiesof 2024-T4 Aluminum 42

8 Hugoniot Data for 2024-T4 Aluminum 43

9 Chemical and Physical PropertiesSof Depleted Uranium 53

10 Hugoniot Data for Depleted Uranium 54

11 Chemical and Physical Propertiesof Nickel 56

12 Hugoniot Data for Nickel 57

13 Chemical and Physical Properties of Type 304Stainless Steel 63

14 Hugoniot Data for Type 304 Stainless Steel 64

15 Chemical and Physical Proper,- ofTitanium 69

16 Hugoniot Data for Titanium 70

17 Chemical and Physical Properties ofS-200 and 1-400 Berylliums 76

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LIST OF TABLES (Continued)

Table Pae

18 Hugoniot Data for Beryllium 77

19 Hugoniot Data for AZ31B Magnesium 83

20 Hugoniot Data for Plexiglas 88

21 Hugoniot Data for Quartz Phenolic 93

22 Compilation of Hugoniot Data 98for Materials Tested

LIST OF TABLES IN APPENDIXES

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Table Page

1-B Systematic Error Parameters 120

2-B Summary of Systematic Errors 125

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SECTION I

INTRODUCTION

This report describes the experimental procedures and

presents the results of the work performed under contract

DA-18-001-AMC-1126(X). The work was sponsored by the U. S.

Army Ballistic Research Laboratories, Aberdeen Proving Ground,

Aberdeen, Maryland, during the period June 1966 to June 1968.

Very high pressure measurements were made to determine the

hugoniot equations of state of several metals, a composite

and a plastic. Results of these measurements are compared

with measurements made by Al'tshuler, McQueen, Skidmore and

others. This work extends the scope of a General Motors

sponsored research project reported earlier(1) which described

the use of a light-gas gun to obtain pressures substantially

above those reported by other researchers in this country.

The materials tested are copper (OFHC, 99.99%), nickel (99.95%),

titanium (99.95%), aluminum (2024-T4), stainless steel (type

304), magnesium (AZ31B), beryllium (S-200), beryllium (1-400),

Fansteel-77 (90% W, 6% Ni, 4% Cu), uranium (depleted), quartz

phenolic, and Plexiglas (Rohn and Haas II UVA). Table 1 lists

the measured pressure range for each material.

Section II of this report presents a detailed description of

the experimental techniques employed for the determination of

the hugoniot equations of state. Data analysis is brieflydescribed in Section III, with the details presented in Appan-

dix A. Appendix A also describes and lists the data analysis

computer program SHOVEL used to reduce the experiment data.

Included in Appendix B is a summary of %he results of an error

analysis.

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MSL-68-13 IExperimental results and comparison with other experiments arepresented in Section IV. Section V contains a summary of the

experimental results and conclusions.

TABLE 1

SUMMARY OF MATERIALS TESTED AND

PRESSURE RANGES EXAMINED

PRESSUR6 RANGEMATERIAL (Mb)

Fansteel-77 0.3 - 5.0

Copper (OFHC, 99.99%) 1.0 - 4.5

Aluminum (2024-T4) 0.5 - 2.2

Nickel (99.95%) 0.8 - 4.7

Stainless Steel (Type 304) 0.8 - 4.2

Titanium (99.95%) 0.4 - 2.7

Beryllium (1-400) 0.5

Beryllium (S-200) 0.3 - 1.6

Quartz Phenolic 1.3

Magnesium (AZ31B) 0.2 - 1.4

Plexiglas (Rohn and Haas, II UVA) 0.7 - 1.0

Uranium (depleted) 0.8 - 4.6

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SECTION II

EQUATION OF STATE MEASUREMENT

In the past two decades, high explosives have been used to

initiate compressive waves with amplitudes from tens of kilo-bars to several megabars in many materials. High explosive

plane wave generators placed either in direct contact with

the material or in contact with a "standard" material uponwhich the specimens were placed, were used to measure hugoniotstates to approximately 600 kilobars. Considerably higher

pressures were obtained from explosive systems in which the

high explosive was used to accelerate a thin flier plateacross a gap and then impact the specimen surface. In thismanner, pressures to approximately 2 megabars were generated

in materials of high density by McQueen and Marsh( 2 ) ofLos Alamos Scientific Laboratory (LASL). Hart and Skidmore

increased the pressure range of these measurements to over

5 megabars, using a radially converging explosive system whichaccelerated plates to high velocities at some expense in pre-cision; the converging shock wave system adding complexity to

(4)the analysis. Al'tshvler, et al, extended the range ofmeasurements to above 10 megabars, accelerating his flier plates

in an undisclosed fashion. Work in the United States has notprogressed above the 2 megabars reported by McQueen until this

study, which provides an extension of Lower pressure data toover 5 megabars.

For this study an "accelerated reservoir" light-gas gun was* used to accelerate flier plates to velocities extending above

8 kilometers per second. This method of experimentation offers

significant advantages over the explosive techniques previously

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used. Unshocked, stress-free impactors of similar or dissimilarmaterial to the specimen can be impacted over a wide and con-tinuous pressure range. Of significance is the simplicity ofthe calculation of the shock state in the specimen, usingeither symmetric impact assumptions or the measured hugoniotof the gun-launched impactor. For experiments in which theshock is created in a standard by either direct contact withexplosives or on being struck by an explosively acceleratedplate, the hugoniot point is less readily calculable. In thiscase, it is necessary to assume a form of the equation of statefor the standard in order to get the hugoniot point for thespecimen.

THEORETICAL CONSIDERATIONS

The application of the principles of conservation of mass,momentum, and energy across a discontinuity have led to thewell-known Rankine-Hugoniot equations. The equations were

derived originally for fluids, but may be applied to solids Iwhen the pressure P, is understood to represent the one-di-mensional stress normal to the wave front. These equationsmay be used to represent the discontinuous change of pressureP, density p, specific volume V, and internal energy E, acrossa shock front as they are related to the shock wave velocityUs, and the particle velocity behind the shock front u(Figure 1).

P - Po = PU sp (i p

PP U puu (2)0 s (SpS 0oUs = plUs-Up) (2)

E-E =1/2 (P + P) (Vo-V) (3)0 0

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Thus a measurement of the shock wave velocity and the particle

velocity associated with the shock wave provides sufficient in-

formation to calculate the chaiige in the thermodynamic stateof the specimen (assuming that steady state conditions prevail

behind the shock front).

Material At Material AtShock Conditions: Initial Conditions:-P 1 , P I , I J I ' E l , 1 O , P 0 , u 0 , E o

ShockFront

Velocity- Us

Figure 1 Schematic of Shock Wave Parameters

Although measurement of shock velocity is relatively straight-

forward, the measurement of particle velocity is more diffi-

cult experimentally. For this study, two techniques were used

to calculate the particle velocity associated with a measured

shock velocity. The first method applies by synmmtry. Foran impact of a specimen launched at velocity v onto a specimenof the same material a shock wave is induced with particle

velocity equal to one-half the impact velocity, or

u = 1/2 v (4)

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To rigorously apply this condition, it is necessary that theimpactor and specimen be in the same thermodynamic state,i.e., the impactor has not been shock heated nor subjectedto irreversible changes due to shock loading during accelera-tion. These conditions have been satisfied for this study.

Since the impact velocity is measured with high precision

(customarily n 0.05%), the particle velocity also can becalculated with similar precision. A series of tests areconducted over a range of different impact velocities, thehighest pressure being obtained at the highest impact velo-city (about 8 km/sec). Each test furnishes a point on thelocus of final compressed states known as the hugoniot.Figure 2 shows, in the pressure-particle velocity plane, agraphical description of the conditions of symmetrical impact.

Symmetrical Impedance MatchSchematic

Ta llet M/l

Hugonliot

St loeRelcd Impactorxi

UsP0 /Hugoniot

/ Particlevelocity Impact Velocity

Particle Velocity

Figure 2 Schematic of Symmetrical Impact Analysis

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To obtain pressures higher than those created by symmetrical

impact at the maximum launch velocity, it is possible to im-pact the specimen with a material of higher shock impedance(defined as the product of the initial density and the shockvelocity) and to calculate the resultant particle velocity and

pressure by an adaptation of the impedance matching techniquedeveloped by Walsh et al. With this technique, a measure-

ment of the velocity of the impactor material, the hugoniotof which hlas been previously measured, is sufficient, when

combined with a measurement of the shock velocity in the speci-

men material, to determine a point on the hugoniot of thespecimen. Figure 3 shows an impactor of known hugoniot strik-ing a specimen with velocity v. A single shock wave of velo-city U5 is induced in the specimen. The intersection of the

s4line poUs and the hugoniot of the impactor, centered at velo-

city v, determines the shock pressure and the particle velocity

in the specimen.

Impedance Match Schematic( Dissimilar Materials I

$ ToretHugenlot Reflected/Impactor

Hugonlot

us Ai*/I

A IParticle Velocity

Figure 3 Schematic of Dissimilar MaterialsImpact Analysis

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EXPERIMENTAL TECHNIQUES

The experimental determination of hugoniot equations of state

using the impedance match technique is based on the measure-ment of the shock velocity in the specimen and of the velocityof the impactor. With the techniques described below, thesetwo measurements can be made with precisions of approximately

0.5 and 0.05 percent respectively, resulting in hugoniots ofgood accuracy considering the limited number of tests conducted

on several of the materials.

The light-gas gun range and basic instrumentation have been

described in several other papers('( ''.8) and are again in-cluded here for completeness of this report.

Launching Techniques

The gun used to accelerate the impactor is an accelerated-reservoir light-gas gun with a launch tube bore diameter of

either 29 mm or 64 mm. This type of gun maintains a reason-ably constant pressure on the base of the projectile during

the launch, allowing a relatively gentle acceleration of the

impactor materials.

Figure 4 shows the layout of the range. The gun consists ofthe following major components:

1. Powder chamber2. Pump tube, 89 mm internal diameter by 12 m long

3. Accelerated-reservoir high-pressure coupling

4. Launch tube, either 29 m. internal diameter by8 m long or 64 mm diameter by 8 m long

5. Instrumented target chamber and flight range.

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Figure 4 Layout of ARLG Gun Range

When the gun is loaded for firing, gunpowder is placed in thepowder chamber and the pump tube is filled with hydrogen. The

hydrogen is compressed by a plastic nosed piston which has been

accelerated by the burnt gunpowder. In turn, the projectile isaccelerated by the release of the compressed hydrogen through

a high pressure burst diaphragm.

Prior to firing, the flight range and instrument chamber are

evacuated and then flushed with helium to approximately 10-2

Torr to eliminate any spurious effects due to gas build-up andionization between projectile and target. The sealing lips on

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the rear of the plastic sabot are pressed tightly against thesides of the launch tube by the high pressure gas and effectively

eliminate blow-by of the hydrogen gas. .1Careful attention to the condition of the launch tube is nec-

essary for successful firing in the high velocity ranges. Bore

linearity of better than 0.2 mm over the full 8 m length of thelaunch tube is maintained. Internal diameter is maintained con-stant to within 0.01 mm. Launch tubes are cleaned and honed

after each firing and are removed every 15 to 20 firings forreconditioning.

Figures 5 and 6 show the instrumentation chamber designed for

the high pressure studies. This chamber is connected to the

barrel of the gun through an 0-ring seal to allow free axial

movement of the launch tube. The target chamber and target arishook-mounted to prevent premature motion before projectile im-

pact. To facilitate this, several stages of mechanical iso- .

lation have been arranged in the barrel, I-beam support struc-

ture and the concrete foundation.

The impact chamber is a steel cylinder of 61 cm O.D. and 1.5 mlength. Physical access and instrument ports are precisely

machined in a horizontal plane and in planes 450 above the hori-

zontal. Two stations of six ports each are accurately spaced30.5 cm apart.

Operationally, the ports are closed against 0-ring vacuum sealswith Plexiglas or magnesium windows for optical and x-ray accessor with steel cover plates.

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I' rUo mrget Chamber Set-up with ContinousWritcing Streak Camera in Position

STATION#1 STATION

PHOTOMULTI PLIER DELAY #

LENS 30 NANOSECOND EXPOSURE

FITRFAHXkYUILAUNCH TUBE

PROJECTILE ::.:. .

X-RAY CAMERA 1. AGT ACCESS DOOR

LASER TRIGGER SYSTEM

Figure 6 Top View of Target Chamber

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INSTRUMENTATION

The impactor velocity measuring system consists of a laser trig-gering system and two short duration 'lash x-rays. With this

system, impactor velocities are measured accurate to 0.05%. The

triggering system consists of a neon-helium gas laser aimed ata photo-detector across the impact chamber orthog)nal to arA

intersecting the line of flight of the projectile. A photo-

multiplier monitors the laser light output through a •e. cf

xaasks and a narrow band optical filter. When light interruptionoccurs due to projectile passage, a sharp change of voltage level

is converted into a signal of sufficient amplitude to trigger aField Emission Corporation 30 nanosecond dual flash x-ray unit.The x-ray flash exposes a Polaroid film plate on the opposite

side of the chamber by means of a fluorescing intensifier screen-The trigger and x-ray flash system is toen duplicated to record

the passage of the projectile in the second field of view 30.5 cm

further down range.

The spacing between the two x-ray field centerlines is indicated

by fiducial wires which are measured by an optical comparatur towithin 0.2 rm. Measurements of the impactor face position rela-

tive to the window fiducials allow calculation of actua> pro-jectile position and travel over the time interval measured be-

tween flash exposures. Figure 7 is an example of the shadow-graphs of the two x-ray stations showing the projectile in free

flight before impact.

A second method is also employed to measure impactor velocity.

The time interval between the first x-ray flash and the impactof the projectile on the target is recorded electronically. Theimpactor and target positions are measured from the x-ray shadow-graphs and a velocity is calculated. Variations in measurements

between the two techniques are usually less than 0.05%.

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IMPACTOR TARGET

STATION #1 STATION #2

Figure 7 X-ray Shadowgraphs of ProjectileBefore Impact

The target is located approximately 60 cm from the launch tube

muzzle and is included in the #2 x-ray field of view. Measure-

ments of the shock wave transit time in the target are made us-

ing four coaxial self-shorting pins as sensors. The shortingof a pin results in a sharply rising current to ground which

produces a signal across the time-interval-meter input termina-

tion resistors. The circuit is so designed that each pin signalcan be seen on three output lines and is free of- any reflections

or ringing for several hundred nanoseconds. The individual cir-

cuits are "tuned" by the use of trimmer capacitors so that the

rise time of each signal is 1.0 ± 0.1 nsec to 12 volts. Thus

it is possible for the combined mechanical-electronic signalsystem to make use of the ± 1/2 nsec resolution of the time re-

cording instruments.

The shock wave transit time-interval-meters are Eldorado Model

793 counters. These counters have a specified time resolution

of ± 1/2 nsec and may be read digitally to the nearest nano-

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second. They require an input signal of 1 volt with a rise

time approximately 1 nsec. Although instrument stability isspecified to be one part in 10 for long term and five parts

in 106 for short term, in actual practice, the instruments arecalibrated prior to each shot over a period of about 10 minutes.

The shot is then fired within five minutes of completion ofthe calibration procedure.

The planarity of the shock wave induced in the target is de-pendent on the impactor flatness at: impact. The impactor sur-

face is machine lapped and then hand polished flat to0.5 x 10 mm. Tests performed with impactors of Fansteel-77and OFHC copper indicate the surface curvature after launch to

be less than the 5 nanosecond time resolution of the opticalrecording system at a launch velocity of 7 km/sec.

The impactor tilt relative to the target specimen front surface

is sensitive .:o 1*nich tube linearity and sabot alignment as 11 2well as to target alignment. The capability to adjust the

target position and perpendicularity relative to the launchtube centerlii a by an optical technique brings the average tiltat impact to approximately 0.005 radians (approximately 15 nano-

seconds of tilt at an impact velocity of 7 km/sec).

Because of the comparatively gentle acceleration of the pro-jecti.e to its terminal velocity, the impact.r plate is not

shock heated. In addition, free flight in an evacuated rangeprecludes aerodynamic heating. This accounts for the flatness

of the impactor after launch and significantly reduces thecomplexity of the experiment. The estimated temperatures riseduring launch of the order of 1C.

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TARGET DESIGN AND CONSTRUCTION

The 29 mm diameter of the launch tube places restrictions onthe diameter of the impactor plate and on the size of the speci-men which are severe enough to require a thorough study of theoptimization of target dimensions. In general, it is desirableto operate over as long a time base as possible for transit timemeasurements. However, the launch tube diameter controls theallowable specimen thickness. For larger specimens rarefactionsfrom both the unconfined edges and free rear surface of the im-

pactor plate could overtake the head of the shock wave beforemeasurements have been taken. To determira the maximum speci-men thickness which would still maintain an unrarefacted areaon the rear surface of the specimen on which sensors could beplaced to record wave arrival, the following analysis was used.

A typical estimate of the angle of intrusion of plastic rare-

faction waves from the specimen edges, a1 , is to assume that

tan a 1 (see Figure 8), and to ignore the elastic rarefac-tion wave system. Although for many materials this assumptionis justified, for some materials this criterion is inadequate;in particular, materials with a low Poisson's ratio should be

calculated more carefully.

The elastic wave velocity, Ce, is given by

c c .l 3 (-v) CK (5)e = Cp 1+v p

where v is Poisson's ratio and C is the plastic wave velocity,pwhich for strong shocks is a function of up, the particle velo-

city. Existing experimental results indicate that v is a weak

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/-Brass tounting.impactor / Block

" x StationSelf - Shorting No.

-s >x. Pin

SKecimen

E~ C!

a2

fA

4 ,- •xy

Figure 8 Schematic of Target and Impactor

S(6,91,10)function of the shock strength. To a good approxima-

tion, the elastic rarefaction angle, a2 , is

[ 1/2

tan a [2 2tana2 a + (K2-) 1 s P (6)

Figure 9 is a plot of a2 versus Poisson's ratio for the metals

listed in Table 2. The calculation assumes a value of tan

a1 = 0.7, taken from the work of Al'tsbuler(9), who notes that

for compressions greater than nu 1.3, tan aI becomes essentiallyU -U

constant at 0.70 ± .03 and -p is taken as unity - its maxi-U

mLm va2ue. Included in Figure 9 is a comparison of valr"ýs of

tan a 2 measured in this laboratory(10) for copper, aluminum,

titanium and beryllium. As these measurements fall below the

calculated line of the minimum allowable design angle, it is

felt that equation (6) provides a reasonably conservative design

critera. In practice, the design angle is chosen several de-

grees larger than the values listed.

16

EMANUFACTURING DEVELOPMENT* GENERAL MOTORS CORPORATION

MSL-68-13

S 70

~60

S50-

0i 0 caIlculiated ValuesMeasured Values

× 20 - 0 A ""iua t• • =0 Copper

A Tlitaum10- 4 Betyl~hm

C .. i I . I0.1 0.2 0.:J 0.4 0.5

POISSON'S RATIO

Figure 9 Intrusion Angle of Elastic Edge Rarefactionvs Poisson's Ratio

Impactor thicknesses were chosen to avoid rarefactions originat-

ing at the impactor free rear surface from overtaking the shock

wave until shock transit time measurements were complete. A

single impactor thickness was calculated which was adequate for

all materials and was used in all tests.

The target specimen was a machined and grouind disc with the im-

pact and rear surfaces machine lapped and hand polished to a

surface finish of 1 microinch rms or better. The lapping pro--3

cedure employed produced surface flatness within nu 1i0 mm.

Parallelism was maintained to \, 10-3 radians. The thicknessesof all specimens were measured to an accuracy of ± 0.5 x 10- mm.

The target specimen thicknesses at the pin stations were mea-

sured with a Zeiss light-section microscope employed as a com-

17

MANUFACTURING DEVELOPMENT * GLN ERAL MOTORS CORPORATION

MSL-68-13

parator. The use of the light-section microscope avoids the

problem of an indicator marring the specimen surface since no

physical contact is made with the surface. Rather, the vertical

position of a thin beam of light projected on the specimen is

compared with the position of the beam projected on a labora-

tory grade gage block and the specimen thickness is calculated.

The basic features of the target design employed in this work

are illustrated in Figure 10. Two coaxial shorting pins were

passed by the edge of the specimen disk with their cap faces

exactly in the plane of the specimen impact surface. These

pins were used to initiate the timing for the shock wave tran-

sit time measurement and to measure impactor tilt in terms

of the time interval difference between their respective clo-

sures.

Figure 10 Photograph of Target

18

U J MANUFACTURING DEVELOPMENT o GENERAL MOTORS CORPORATION

MSL-68-13

TABLE 2

CALCULATED MINIMUM DESIGN ANGLES

OR MAXIMUM EDGE RAPEFACTION ANGLES

CALCULATED FROM EQUATION (6)Minimum

Poisson's DesignMaterial Ratio Angle, a 2

Aluminum .332 470

Beryllium .055 580

Copper .356 450

Tantalum .342 460

Tungsten .280 500

Uranium .402 430

Titanium .304 480

Lead .430 410

Magnesium .306 490

Nickel .300 480

Steel (Mild) .290 490

Plexiglas .327 470

Two rear surface pins (or one, depending upon the target dia-meter) were mounted in line with the tilt pins to record the

shock wave arrival at the rear surface. All four pins were

mounted in a guide fixture which assured the proper geometricalspacing. The tilt pins were fixed in position in a dimension-

ally stable epoxy, while the rear surface pins were springloaded in place in the pin guide. The pin retainer and cable

bracket lent rigidity to the assembly to prevent accidental

damage to the pin shafts.

19

Ii MANUFACTURING DEVELOPMENT * GENERAL MOTORS CORPORATION

MSL-68-13

The four-pin targets, in conjunction with the four Eldoradoone-nanosecond time interval meters, produced four values of

the shock wave transit time. From these four values a sin-'-shock wave velocity in the specimen was calculated and, by a

system of cross-checking, an indication of the precision ofthe measurement was available.

The degree of non-planarity of impact between target and impactor

is calculated by comparing shock transit times recorded by thecounters started by each of the two front surface pins. The

time difference between the shorting of the front surface pins,

Att (which, when combined with the impact velocity, yields thetttilt angle, 0) is calculated from Att = tl_-C-t A-c = t l_B-tAB,

where ti-c is the time recorded on the counter started by pin #1

and stopped by pin C (Figure 10a).

For the highest velocity tests (7-8 km/sec), it was necessary

to lighten the projectile by reducing the diameter and the thick-

ness of the impactor plate. The target designed for these high-est pressure shots had a slightly smaller diameter and thickness

and was provided with only one coaxial shorting pin on the rear

surface.

The coaxial self-shorting pins employed in this work as sen-sors consisted of a one millimeter diameter tube of brass sur-

rounding a teflon sleeve and a copper inner conductor. The

pins were connected to RG174 50 cable by soldered joints andwere made self-shorting by the placement of a brass cap over

the sensing end, which left a small gap (on the order of 0.050± .002 mm) between its inner face and the flat end of the inner

conductor. When a large amplitude stress wave reaches the cap

face, the cap is set into motion and the gap is closed at the

Model CA-1039, Edgerton, Germeshausen and Grier, SantaBarbara, California.

20

U.3 n mA i A , 6 M D e r A.n Lr M TI R J R T

MSL-68-13

free surface velocity of the cap material. The pin gaps weremeasured by x-ray shadowgraphy, of which Figure 11 is an exampl!,and the measurements were employed in the shock velocity calcu-lations for corrections to pin closure times.

Figure 11 X-ray of Coaxial Shorting Pin

21

MAN U1FACT URNG G.VELOPMENT * GENEKAL MOTORS CORPORATION

MSL-68-1 3

SECTION III

DATA ANALYSIS

The analysis of the experimental data obtai,-.. '.n the research

program is basz' upon the impedance match solution for the

determination of particle velovity, pressure, energy and volume

of the shock state in the specimen. The requisite information

in the analysis is the shock wave velocity, the impact velocity,

and the hugoniet of the imnpactor. A general description of the

method of data analysis is given here, with the detailed equa-

tions presented in Appendix A.

IIj SHOCK WAVE VELOCITY

The measurements relevant to shock wave velocity are the target

I thickness and the shock wave transit time interval. In order tocalculate the shock wave transit time, it is necessary to make

refinements upon the recorded time interval.

Two sources of refinement to the measurement are:

(i) Inclusicn of the effects of shock wave tilt resultingfrom r-n-planar projectile impace on the target.

(ii) Correction for the differences of closing times of

coaxial pins with different gaps, which involves:

(a) Calculation of the interaction of theimpactor with the two front surface pins

A (b) Calculation of the interaction of thei specimen material with the two rear sur-

face pins.

22

i


MSL-68-13

To calculate the closing velocity of the cap for the direct

impact of the projectile material on the front surface pins,

an impedance match solution is applied, using the impact velo-

city, the hugoniot of the impactor and the hugonioi: of the cap

material (brass).

The pin gap correction for the interaction of the rear surface

pins and the specimen is based on the impedance match solution

of the shock wave in the target being transmitted into the pin

material. The hugoniot of the specimen must first be estimated

to provide the necessary constants. The shock transit time is

first calculated with no pin gap corrections and a preliminary

hugoniot point is determined for the specimen. This hugoniot

point is then used to calculate pin interactions and, through

a series of iterations (usually two) the preliminary hugoniot

point is modified until satisfactory convergence is reached

(differences < 0.01%).

IMPACT VELOCITY

Measurement of impact velocity has been discussed earlier under"Instrumentation". Theý flash x-ray system-used furnishes high

precision velocity determination providing the projectile main-

tains a constant velocity during the time of measurement. A

check on this premise is provided by the seconding system which

measures velocity over a longer baseline. No evidence of pro-

jectile acceleration or deceleration during its free flighthas been observed.

HUGONIOT OF THE IMPACTOR

Measurement of impactor hugoniots for tests in which specimens

are impacted with dissimiliar materials are discussed in the

following section "Experimental Results".

23


U MSL-68-13

SECTION IV

EXPERIMENTAL RESULTS

The experimental work effort was first concent•:ated on the

measurement of the hugoniots of the three materials to be used

as impactor plates for dissimilar material impacts. The ma-

terials were chosen to (i) cover a range of shock impedances,

(ii) be easily obtainable and consistent in their material pro-

perties from batch to batch, and (iii) to coincide with stand-

ards chosen by other laboratories. The materials investigated

were Fansteel-77 (a tungsten alloy), OFHC copper, and 2024-T4

aluminum. The ratio of shock impedances of the copper and

Fansteel-77 with respect to the aluminum is approximately 1:2:4.

These three materials were more thoroughly investigated than

the remaining materials so that errors in the impedance match

solution for materials impacted by these standards would be

minimized.

A typical test series for the determination of the hugoniot of

a specimen material, for instance nickel, began with a series

of shots using nickel for both impactor and target over the

full velocity range of the gun. To obtain pressures higher

than those created by like-like impact at the highest velocity,

the series continued with impacts using a material of higher

impedance than the specimen; in the case of nickel, Fansteel-77

was used. Impact velocities were adjusted to space the shots

over the pressure range to be investigated.

In the following section, the experimental data are presented

in tabulated and graphical form. Fits to the shock velocity

vs particle velocity data have been made by the method of least

24

II

SMA N U FA C T U RIN G D EVELO PM EN T * G EN E R A L M O TO R S C O R PO R A TIO N f

MSL-68-13

squares and are listed tor each material. The tabulations in-

clude measured and calculated parameters and an indication ofthe "weighting factor" used in the least square fits. In

general, test results were weighted according to whether thetarget had single or double pins, the double pin targets gen-

erally having a higher weighing factor due to the redundant

measurements of shock wave velocity.

The tabulated data also include the impactor material and theimpact velocity. Additional figures are included to illustrate

comparison with other researchers.

FANSTEEL-77

Fansteel-77, a tungsten alloy composed nominally of 90% tungs-

ten, 6% nickel, and 4% copper was employed as the standard for

the highest pressure tests. Fansteel-77 was chosen over pure

tungsten because the metallurgical stracture reduces the brittle-ness of the material (which can cause plate fracture during

launch) while maintaining high strength and density.

In the initial work the quality control of the Fansteel-77

stock material presented several problems. The material isproduced by powder metallurgical techniques which include

pressing and sintering of a billet of the material. Theporosity of the surface of the billet was found to be scmewhatdependent upon the compacting pressure prior to sintering.

The core of the billet, however, was found upon metallographic

examination to exhibit essentially no porosity, and sample to

sample variations in density were less than 0.5% when the out-side 1 mm was removed from a 50 mm diameter bar. The chemical

and physical properties of Fansteel-77 are presented in Table 3.

25

A4

NM A N L) A C T U R I N G DEVELOPMENT 0 GENERAL M O T O R S C O R P 0 R A T I O N

TABLE 3

CHEMICAL AND PHYSICAL PROPERTIES

OF FANSTEEL-77

Chemical Properties

Element Wt %

W 90 ±.l

Cu 3.8 ±.6

Ni 6.1 ±.2

Physical Properties

Yield Strength (0.2% elong.) 85,000 psi (imin)

Ultimate Tensile Strength 98,000 psi (min)/

Density 17.01 ± .01 gm/cm

Poisson's Ratio: 0.286*

Acoustic Velocities : Longitudinal, C1 = 5.049 km/sec

Shear , C = 2.765 km/secs

Bulk , C = 3.912 km/sec0

Ultrasonic tests were performed by J. Havens andR. Lingle of this laboratory.

26


MSL-68-13

The test series on Fansteel-77 resulted in a hugoniot over the

pressure range .35 Mb to 5.0 Mb. Symmetric impacts were used

on all tests so that particle velocity may be assumed to be

one-half the impact velocity. Both second and third order fits

were made to the data; however, the linear relationship

Us = C + Su describes the data with the root mean square (RMS)p

deviation not significantly larger than the higher order fits.

The relationship is given by:

U = 4.008 + 1.262 u km/secs p

RMS deviation of U was ± 0.021 km per second for the seventeen5

data points. The results are presented in Table 4.

The data points taken are displayed in the U vs u planes p

in Figure 12. In one shot the velocity was not measured

directly with the x-ray system and instead was calculatedfrom the gun firing parameters. Estimates made in this man-

ner are quoted with standard errors in velocity of ± 2%.

In Figures 13, 14 and 15 are displayed the data for Fan-

steel-77 compared with the data obtained by researchers of

the Ballistics Research Laboratory of the United States Army,

Aberdeen Proving Grounds and the data of Hart and Skidmore' 3 '

for a tungsten alloy similar to Fansteel-77.

The Ballistics Research Laboratories data are in excellent

agreement with the results obtained here. The hugoniot mea-

sured by Hart ar" Skidrure has the quadratic form:

2U = 2.95 + 2.47 u - 0.342 u 2 (km/sec)

p p*

Mr. George Hauver, private communication.

27


MSL-68-13

•'01

tyu.........4 c4 4v; 4rZ q

N 4 MN N N N C4NC

co- f r' 0l .4 .4 f- tn 0 0 -4 4~ f- -0 in ~co 4 ~ a M 0 4% &A 1 (4 C4 C4 N- 1- i WD In V

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- 28

MANUFACTURING DEVELOPMENT 0 GENERAL MOTORS CORPORATION 10

MSL-68-13

O I I I I

I MATE.RIAL - FNWTEF1 77 - GM

C)1

i o

L)LnLO1

I II

Lj9

-J-Lr)

cr2

10 2.0" M. 4.0 5.0 GIG 7-0PARTICLE VELOCITY -KM/SEEL

Figure 12 Shock Velocity vs Particle Velocityfor Fansteel-77

29

M A N U F A C T U R I N G DEVELOPMENT e GENERAL MOTORS C O R C ' R "A T

MSL-68-13-

I ATERIAL - FR6E.

S~:)l

Ln,

Li

•I•&--BRL[ Po . 17. 01

1 -- HART S KID MO RE (REIP. 3) Co - 16.8

44

•.0 P.,C 110 4,0C 5,0 G.61oPARTICLE VEL{nCITY -KM/SEE

Figure 13 Shock Velocity vs Particle Velocity for Fansteel-77

30

MANUFACTURING DEVELOPMENT S GENERAL MOTORS CORPORATION

MSL-68 -13

MATERIP - FA%7SEEL1!

IlD

8

rnm

CL

a A--BRI, PO . 17.01

*-HART SKIDMORE (RES. 3) P . 16.8

: I,F• ' 200 3,00 4.00 9.CC 6!00 I.0t

PARTii__LE VELDEITY KM/,, L

Figure 14 Pressure vs Particle Velocity for Fansteel-77

31


MSL-68-13

MAIERIAL - FANSTEE

Cz2

0-GIG PANSTEEL-77 00 . 17.01

S--RL P0 = 17.01

H-EA•T SKIDMORE (REP. 3) P0 . 16.8

"A" 4.0.50.04 0 .s 0.07 0.06 0.01

SPEEIFTTE VOLUME - E/EGM

Figure 15 Pressure vs Specific Volume for Fansteel-77

32

M A N LVACT 1nlIN G DEVELOPMENT * GENERAL MOTORS CORPORATION

MSL-68-13

and falls below the present data at lower values of up. Thisbehavior is not readily explainable since the intercept ofthe J.inear fit to the present work, C = 4.008 km/sec., is inoagreement with the bulk sound velocity measured ultrasonically,

Co = 3.912 km/sec.

It is interesting to note that the hugoniots for pure tungsten(as measured by LASL) and for Fansteel-77 are quite similar,the LASL linear fit for tungsten being given by:

Us = 4.029 + 1.237 up km/sec

although the density of the tungsten is 13% higher than that ofF~nnteel-77.

OFHC COPPER

OFHC copper of 99.99% purity is employed as a standard forthe intermediate and high pressure ranges in the hugoniotexperiments of a number of laboratoriec. Physical character-istics of the copper are described in Table 5. The results oftwelve tests are presented here in Table 6. The linear fit tothe data in the U - U plane is given by:s p

U = 3.964 + 1.463 up km/sec

Root Mean Square Deviation of Us 0.009 km/sec for 12 datapoints. The hugoniot equation recently published by LASL( 1 2 )

is given by:

U = 3.940 + 1.489 u km/secs p

in close agreement with the present results.

33

3

-4A

MAIIUFACTURING OEV�LOPMENT e G�NERAL MOTORS CORPORATION

M�L-b8-i3 j�1

TABLE 5

CHEMICAL & PHYSICAL PROPERTIES*

OF OFHC COPPER

�1I

Chemical Compc�iticn

Element Wt %

Iron 0.0003Sulphur 0.0025 £

Silver 0.0010Nickel 0.0006Antimony 0.0005Lead 0.0006Copper Remainder

Physical Properti'�s

Density 8.930 gm/cm3

Poisson's Ratio: 0.332

Acoustic Velocities: Longitudinal., C1 = 4.757 km/sec

Shear , = 2.247 km/sec

Bulk , C = 3.99 km/sec

0

* Based on mar.ufacturers specifications.

34

MAN UFACTURING DEVELOPMENT 0 GENERAL MO0TO0R S CO0R POR A TIO N

U ~M5T.-F.R-l I

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U ~C. UU0035 UC


MSL-68-13

The data are presented in Figure 16, which now includes a legend

to indicate the impactor material used. The use of diffeientimpactors provides a good method for cross-checking the hutioniotsof the standards as suggested by McQueen(II). The hugoniot es-tablished by Fansteel-77 impacting copper is indistinguishable

from the copper on copper tests. This both checks the accuracywith which the Fansteel-77 hugoniot was determined and providesadditional confidence in the use of impedance matching tech-niques as used in this experimentalsystem. A single test wasconducted- using 2024- aluminum as an iiactor. Al! tests wereused in the calculation of the fit given above. The resulting

hugoniot displays a very small RMS deviation, (0 0.1% in shock-velocity). --

Figures 17, 18 and 19 compare the present data with the dataof Al1tshuler( 9 ,1 3 ), Walsh 'and McQueen Agreement within"" 2% in the linear fit was obtained -(i.e., the reported shock Jvelocities are within " 2% of the values predicted by the pre-

sent linear fit). -

A close examination of the data indicates a small (< 1%) devi-ation from a linear fit begiuining at u 2.4 km/sec. It is

p_likely that this deviation is associated with melting in thes - kfront (see the following discussion or. 2024-T4 aluminum).This phenomenon will be discussei more fully in a forthcoming

report._

2024-T4 ALUMINUM

The hugoniot ecperiments performed on 2024424 aluminum extendover a pressure-range of 0.45 to 2.2 Mb. Fourteen tests werecondu'fted, employing the following impactors: Fansteel-77 -

5 tests; OFHC copper - 5 tests; and 2024-T4 -luminum 4 tests.In addition, Shot No. 98 from the series on copper is i:acluded

36

-MANUFACTURING D-EVELOP-MENT *GENERAL MOTORS CORPORATION

MSL-68-13

.1 - -4 MATERIAL CUCR{R - GM '

A' Liwf'

LLJ?>

H-Abb MATEh~RIAL:-COPPER 4

1.0 C. 4;G G. f- ( 7.01PAIRTIELIE VELOCITY -KM,/SEC

Figuri 1`i6 Shock Velocity vs Particle Velocity for Copper

* 37

M ANU-FACT URING DEVELOPMENT -0 G ENERAL MOTO RS COORPORATION

MSL-68.--13

I MATERIAL- LPIFER

0 -o i cOI CPPER aaH P0.89+-WALSH RICE MCQUMB (REY. 5) 00 . 6.90

13- AL'T KOR4ER BAKAN0VA (REP. 13) oi-i .9Al-ALT XOREI4R BRAZHNIX (RU?. 9) P i 0.93

s.s.-NCgU~E= HARSH (REF. 2) P0 -16.90

6-

Li

LLA

3.0 4.0 1A. 610- 7.0PARTILLE VELOCITY -KM/SEQ

Figure 17 Shock Velocity vs Particle Velocity for Copper

38

MANUFACTU.RING DEVELOPMENT 9 GENERAL MOTORS CORPORATION

MSL-68-13

MATERIAL-OMR-

0 ~OPHC COPPsiR Gm- D0 8.930

+ - UALH RICE woCuEnm (Imp. 5) 00 8.900 -ALIT ICONGR BAicANOVA (RP 13) :::.944.1 -JMCQUEE NARS (REP. 2) 00 - 8.90

WLn

_Lf

S _ _ ___ __

Figjig PA00 PfI 3-00~ 4 T, EeG-0

MANUFACTURING DEVELOPMENT * GENFRAL MOTORS CORPORATION

MSL-68-13 ji

Ktt

1 07 O1C COPPE.R N• P- a .93+ - NAli- R.x,-XCwMuz (RaE. 5) PC . 8.90

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We M4.W HA jrS 2)PC-.0

U-1 nI

.J , •++

UM- .o

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Figure 19 Pressure vs Specific Volume for Copper

40

MAN UFACTURING DEVELOPMENT * GENERAL MOTORS CORPORATION

MSL-6 8-131

as a cross-check by reversing the impactor and specimen materialsand impacting an aluminum plate into a copper target. IZ the

hugoniot of the copper is assumed to be known the state in the

aluminum may be calculated.

The chemical and physical properties of 2024-T4 aluminum are

tabulated in Table 7 and the data are presented in tabular formin Table 8. The measured initial density of the aluminum was

2.783 ± .001 gm/cm •

Figures 20 and 21 are a plot in the Us - Up plane of hex ex-perimental results. The linear fit is from LASL, Reference 22.A departure from linear behavior is seen, beginning at

U = 3.5 km/sec (P 1 megabar), where shock velocity 'allsPbelow the line representing a linear fit to the data. Althoughthe dAta-shows scatter, it is felt that the trend of the datain this region is beyond experimental error. The linear fit ofLASL, Us = 5.328 + 1.338 up, to data below this pressure range,was compared to the. present data by calculating deviations ofthe& 4ata from this fit. The deviations are plotted in Figure 22along with other high- pressure data from Russian researchers.Only the ten tests showing least internal scatte. and tilt are

plotted.

Urlin(15) has proposed a model for melting in the front of ashock wave and predicts an observable effect on the linearUs - u relation. For aluminum the melting is calculated tobegin at aPproximately 1 megabar. The present data followsthe ti•d predicted by Urlin, although whether melting, ex-perimental inaccuracy, or other phenomena is the explanationfor the large deviations found between Up = 3.5 to 4.5 ki/secremains to be verified.

The: comparison of hugoniot data from other workers (9,13,14,16)

is shown in. Figures 21, 23 and 24, and displays the area ofdivergence.

41

A'...|.. i i I [ • V 1 •

MANUFACTURING DEVELOPMENT * G-E N E RA L MO-TORS C O R PO RAA I O-N

MSL-6 8-13

If all the present data points are combinied the data may

be represented by the equation:

Us = 5.471 + 1.310 up

Root Mean Square Deviation = + .022 km/sec for 11 data r.ints.d

TAALE`'~7

CHEMICAL & PHYSICAL PROPERTI'ES

OF 2024-T4 ALUMINUM

Chemical Composition

Element Wt %

Silicon 0.5Iron 0.5Copper 3.8 - 4.9Mangan~se 0.3 - 0.9Magnesium 1.2 - 1.8Chromium 010Zinc 0.25A-luminum Remainder

Physical Properties

Yield Strength 47,000 psi

Ultimate Tensile Strength 68,000 psi

Hardness (Brinell No.) 1203

Density (measured) 2.783 4m/cm


Acoustic Velocities: Longitudinal, C1 = 6.38 km/sec

Shear , Cs = 3.20 km/sec

Bulk , CO = 5.20 km/sec

Based on Alcoa Aluminum Handbook and specimen certification.

42

M-A NU FA C TUR I NG DOE V ELPM E NT C GC NE'A L MO0TO0R . CO0R PO0RAT'r1O0N

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]Figure 24- Pressure vsý Spej 1 .fcV~~ frAuii

48 --

6UVACLOP-M1N1 '0 GENERAL MOTORS CORPO-RATIONJ

* ~MSfr68-13

DiPL~tiD tRAMIUM

Five- tesits- Were pe!rfortme4 for t-he determination of tkhe hugo-

ftiot-Jdf_ dAepleted - uranium -dier -the pressure range.O9- to 4.6

444~as ýh-- -t -_g&tcr were- etrOFHC copper 6r Fan-

st~1.71. 6~irn~i rqaterial iimpict -tests- -ketep~om

~ -- Fi~frs 2,Z6 rnd- 27'. -xc11ent -agrev-

~ wiW hehigl, p6rassulre (above-2 miegabarsl)

Skdire 46Ad Mris (1?

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fIid"P s-~~] b~ are-,summarized- in Table9, dtehg

oni~~~~~~~t~ dt-r- iTal10 Itwsnted-that the

-'-kbbhlýy Ia~jpo' f -ox-idized rapid-ly,ý turning from a light

ta badar&-blui -broncoo- That this oxide layer is very

-thin, ma&y -be dAiousre bthfd tatsveral 'swipes of

the s-rf Ace- -on- w 4,1: ~I~ig at& remrnOves thedarkkene~d layer.

- h ln'~ tt to e tH - bfi -dt ýi~- iv~h by th qation:

=2.-4- + .8 p ~sc-

R'otMen Sqqareý Devat*4 -=±.09km/sec for 5 data p6ins

- . Sidor ' dtafo 5data poifits is included in the figures- - and is fitb the,,q4AdrAt,16 equaion-:

2)2U56 -1ina 2.55- f16 MASu is 20901 (+ 1.3 u.0 k/e

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010 3,0 4.0 5;.0 G,0 1.0PARTICLE VELOCITY ,M/SECE-

Figure 25 Shock Velocity vs Particle Velocity forU-a-iumn

50

MANUFACTURING DEVELOPPiENT * GENERAL MOTORS CORPORATION

MSL-68-13

S. . ... _ _ _ _ _ _ _ _

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I.Figure 26 Pressure vs Particle Velocity for Uranium

51

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MSL-68-13

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Figure 27 Pressure vs Specific Volume for Uranium

52

I

MANUFACTURING nOyiePMEN T 0 E NERAL MOTOS CORPORATION

MSL-6•=i3

TABLE 9

CHEMICAL AND PHYSICAL PROPERTIES OF DEPLETED URANIUM

Chemical Properties

EemntWt (Aluminum 9Boron 0.3Cadmium 0.3Chromium 3Copper 8Ii'on 10Magnesium 2Manganese 15Molybdenum 2Nickel 20Lea&Silicon 40Samarium 1Uranium wt % 99.8%

Physical Properties:•

Yield (0.1% elongation) 47,250 psi

Tensile Strength 124,000 psi

Density (measured 18.951 gm/cm3


Acoustic Velocities: Longitudinal, C1 = 2.97 km/s-cShear 'Cs = 1.20 km/secBulk , CO = 2.63 km/sec

53

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454


MSL-68-13

NICKEL

Five tests were performed to obtain-hugoniot data for nickel.Three of the tests empJnyed nickel impactors and two impactors

were of Fansteel-77. The nickel was purchased under specifi-cation ASTM-B-160-61 as 99.5% purity. The chemical and mech-anical properties of the material are listed in Table 11.

The experimental data are tabulated in Table 12 and displayedin Figures 28, 29, 30 and 31. The least squares linear fit to

the data is:

Us = 4.456 + 1.555 up km/sec

Root Mean Square Deviation = ± 0.012 km/sec for 5 data points.

The data of McQueen and Marsh (2) Walsh(5), and Al'tshuler (18)

are also displayed in the figures and show reasonable agree-

ment with the present data. The data of Al'tshuler extendsover a wider pressure range (1.1 to 9.2 megabars) than the

General Motors data. The Al'tshuler data is best fit by a

quadratic curve:

u= 4.370 + 1.775 up -0.047 up2 km/secUs

Sigma Us = 0.008 km/sec for 4 data points.

57I

55

I mM•m • m ~ m

W M AN UI-ACT URING DEVELOPMENT * GENERA L MOTORS CORPORATiON

S~ MSL-68-i3

TABLE 11

c CHEMICAL AND PHYSICAL PROPERTIES OF NICKEL

~Chemical Properties

SElement Weiqht I

Carbon 0.11SMangane~se 0.26SIron 0,09SSulphur 0. 005

!!Silicon 0.02Copper 0.02

SNickel 99.47

• Physical Properties

SYield Strength 82,500 psiS~at 0,2% Elongation

Tensile Strength 89,000 psi


SPoisson's Ratio: 0.300

SAcoustic Velocitiest Longitudinal, C1 = 5.76 km/sec

SShear ,Cs = 3.08 km/secSBulk ,Co = 4.53 km/sec

N 56

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Figure 28 Shock Velocity vs Particle Velocity for Nickel

s4 '

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MSL-68-13

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IFigure 29 Shock Velocity vs Particle Velocity for Nickel

59

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"",A N U FACT U'ING DEVELOPMENT 0 GENERAL MOTORS COR-PORAT ION

MATORT - NICKEL

C•am •o 8I O .164

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Figure 30 Pressure vs Particle Velocity for Nickel

60

MANUFA,-TURING DEVELOPMENT eGENERAL MOTORS CORPORATIONj

MSL- 68-13

MATERIA - wiDfEL

5Il NWQUhl "W.~H fRZI. 2) o - '.86

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if~MS L- 68-13

TYPE 304 STAINLESS STEEL

The composi 1..on and i,.--hanicý 1 irope-ti es of Tyr~e -304 Stain-

c 's Steel are presented in Table la. The me~asured~ density

is 7.905 gm/cm .The hugoniJot data over a pressure .-:nge of

0.3 tr~ 4.3 megabars are 2isted in Table 14 and are pres~entedgraph~ically in Figures 32, 33 and 34. The' linear hugon."Lot

fit is given by:

Us= 4.722 + 1.441 up km/sec

Root Mean Square Deviation of U = ~0.023 km/sec _for _4 d&taS.

points.

Also displayed are the data from the U. S. Army BallisticsResearch Laboratories (1)for comt.arison with the presen~

results. Although the pressure ranges tested are barely ovrer,

lapping, the extrapolation of the present dat to lower pres-

sures is in reasonable agreement with the Ballistics -Research

Laboratories rpsqlts.

62


MSL-68-13

TABLE 13

CHEMICAL AND PHYSICAL PROPERTIES OF TYPE 304

STAINLESS STEEL


Element Weiqht

Carbon 0.065Manganese 1.62Po6sphorous 0.029Sulphur 0.028Silicon 0.49Nickel 8.80c "hromium 8.73Molytdenum 0.-14

Iron, 69.86O~ther .(CO 0.•070

Mechhaical, ̀Proprties

Yield Strength 55,-000 psiTensile Strength 90,500 psi

Hardness BHN 192Density 7.905 gm/cm3

Poisson's Ratio: 0.290Acoustic Velocities: Longitudinal, C1 = 5.74 km/sec

Shear , C = 3.12 km/secBulk , C = 4.47 km/sec

Si .63

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MATERIAL - 3D4 STAINLES5 SEEL

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SFi gure 32- Shock Velocity vs Particle Velocity forS304- Stainless steel

65

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Aw MST_,-6A-!3 I

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PARTICLE VELOCITY - KM/EEC

Fiqure 33 Pressure vs Particle Velocity for304 Stainless Steel

66

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1MSL-68-13

r MATERT& - 304 STAINISC-M

M

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Figure 34 PressurevsSeicVouefr304 tailess Steel

67

f

MANUFACTURING DEVELOPMENT * GENERAL MOTORS CORPOATION

MSL-68-13

TITAN IUM

Three hugoniot tests were performed on titanium over a pressure

range of 0.4 to 2.7 Megabars. The chemical and physical proper-

ties of the titanium samples are listed in Table 15.. The hug-

oniot data are presented in Table 16 and in Figures 35, 36, 37

and 38. The linear fit to the hugoniot is given by:

U= 4.692 + 1.126 u km/secs p

Root Mean Square Deviation of Us 0.014 km/sec for 3 data

points.

In the figures are grarhical compa:.isons of the data of

Krupnikov120) Walsh15), and LASL( 1 2 ) with the present

work.

Krupnikov: U= 4.8S + 1.11 u km/sec (0.8 to 2.8 Mb)Krpikv s p•

Walsh: Us = 4.590 + 1.259 u km/sec (0.7 to 1.4 Mb)

LASL: U = 4.877 + 1.049 u km/sec (0.8 to 1.1 Mb)s p

A surprisingly large spread in slope and intercept is seen,

consolidation of all the data above yields a linear fit:

U = 4.695 + 1.146 us p

Root Mean Square Deviation of Us = - 0.045 km/sec for 13 data

points, deviating but very little from the General Motors

data alone.

68

Iii

MANUPACTURn!H DLVPtlU T U FACTUi.At UfTrnm tOR lfATInN

TABLE 15

Q-EMICAL AND PHYSICAL PROPERTIES OF TITANIUM


Element Weiqht %

Carbon 0.02Nitrogen 0.010Iron 0.25Oxygen 0.115 - 0.123Titanium 99.60

Mechanical Properties

Yield Strength 50,000 - 55,500 psiat 0.2% Elongation

Tensile Strength 75,600 - 76,300 psi



Acoustic Velocities: Longitudinal, C1 = 6.118 km/sec

Shear , Cs = 3.246 km/sec

Bulk , C = 4.83 km/secis 0

69

I2

MAN UFACTURIN6 DEVELOPMENT 0 GENERAL MOTORS CORPO~RATION

414

-4J 4

U) 000(.40 H4 t-

0 0

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MSL-6 8-13

C'3

MATERIAL TITPJNILN - G

C-?

Li

Lfcn

UT

0+

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r6o 1.0 2.0 3-0 4-, ;.0 6.0 1.0PARITILLE VELOCLITY - KM.-SEE

Figure 35 Shock Velocity vs Particle Velocity for

Titanium

71

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MS L-68-13

TEJ•IAL - TITANU

r,• 0 GH Po a 4.501

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A UMCE MARSH (CRZ. 2) po a 4.51

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>-

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Figure 36 Shock Velocity vs Particle Velocity forTitanium

72

MANUFACTURING DEVF tLp.P.M ENT e - TRAL OTO RS CO RPOA TO

M&TBUIM- TIMTN"

0. an Gpo a 4.508

0 YUUVZXOV MAX. SM6. (M2P. 20) po a 4.50

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SFigure 37 Pressure vs Particle Velocity for

S~Titanium

73

• '73


MSL-68-1sUA

NAM& - TITMIfW

0 St ON P 4.S08

X XUPMRIXOV MR. NWAZ. (MV1. 20) * 4.50

a MCQUZUDI-NASN (Ixr. 2) P0 a 4.51

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(L

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Figure 38 Pressure vs Specific Volume forTitanium

74

MANUFACTURING DEVELOPMENTo GENERAL MOTORS CORPORATION

MSL-68-13

'BERYLLIUM

Hugoniot. experiments were performed on two types of beryllium,e designated as S-200 and 1-400, having nominal compositions ofj 2% and 4% BeO respectively.

The chemical and physical properties of the beryllium speci-mens as furnished by the supplier, Brush Beryllium Co., are

listed in Table 17. The specimen preparation presented some-what of a problem in that dust and small fragments of the

material are considered toxic. All polishing and lapping ofsamples were performed in closed and vented work areas.

The beryllium presented the most diffi';ult case for accuratehugoniot measurements with a restricted target size becausethe elastic release wave velocity is relatively high and the

target thickness is thus necessarily less than that for othermaterials. (See Figure 9 for the maximum angle of intrusionof the side rarefactions).

The hugoniot data presented in Table 18 include seven testson S-2001 the material of major interests and one comparison

test on 1-400. The impactors for the test series were OFHCcopper.(3 tests) and Fansteel-77 (5 tests). The data arepresented graphically in Figures 39, 40 and 41. A linearfit was made to the data for the S-200 beryllitu:

U = 8.390 + 0.975 u km/sec

Root Mean Square Deviation of U5 ± 0.017 km/sec for 7 datapoints.

75


MSL-68-13

TABLE 17

CHEMICAL AND PHYSICAL PROPERTIES OF S-200 A)b1-400 BERYLLIUMS


Material 1-400 S-200

Beryllium Oxide 3.96 2.00

Carbon 0.18 0'.126

Iron 0.16 0•163

Aluminum 0.04 0.054

Magnesium 0.02 0.035

Silicon 0.04 0.080

Manganese 0.01

Beryllium 95.77 98.18

Other 0.10 0.04 max

Mechanical Properties

Yield Strength 56,000 psi 37,500 psi

Ultimate Tensile

Strength 66,700 psi 57-,700 psei3 3

Density 1,881 gm/cm3 1.857 gm/cm


Acoustic Velocities: Longitudinal, C1 = 12.83 12.916 3

Shear , C9 = 8.80 8.86

Bulk , C = 7.83 7.87

76

A~NU FACTU~iN-6 DELVELUIPMEIN1i 0 G'EN FRAL MO-TORS CORPORATION s

0 -o0%CD , -0 0M cW nU m CnU in

g -0 '- r- in 'W-!- Nok .0 O 0 o - t- c

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N iWjt~8- 13

ý9 IMTERIM - 9R0tLIUM

8-200 SUYLLIUH PC a 1.613

1 1-400 •LIU M Ok P a 1.661

"qi LZL (W3?. 12) PC a 1.150

4 1

oru

UI

PARTICLE VELOCITY - M/SEC

Figure 39 Shock Velocity vs Particle Velocityfor Beryllium

79

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MANUFACTURING DEVELOPMENT * GENERAL MOT ORS CORPORATION

MSL-68-13

IATERIAL - BERYLIW

8 8-2o01 ByZRYLLIUM WP 0 . 1.851

* --400 SERYLLIUM ON p0o 1.881

IF , LAL (Ur3. 12) 00 " 1.150

M///

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c 0 1 .00 2 I ,, I I

3.0 1O0 2,000 4.00 5.00 G,00 7.00PARTICLE VELOCITY - KM/EEC

SFigure 40 Pressure vs Particle Velocity for

Beryllium

79

11 M A NL- FFA CT U RIN G DFV_ 1-PM, ET & c N T Z R A L MOTORS CORPO'RATION

MSL-6 8-13

IATERIML - NRYALILM

I0 tS -200 BERYLLIUM ON -1.851

LL

* 1400B!RLLZK N p0 1.61l"" .- if L' ZAB? (RE1P. 12) pO •' 1.6501

LoJ(L

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SPECIFIE VOLUME - CC/GM

Figure 41 Pressure vs Specific Volume forBeryllium

80

MANUFACTURING DEVELOPMENT * GENERAL MOTOPS CORPORATION

MSL-68-13

The 1-400 beryllium is slightly more dense (" 1.3%) than the

S-200 beryllium due to a greater percefitage of the heavier

beryllium oxide compound. The data point is slLghtly above

the fit of the S-200.

A comparison of the data with that of LASL(12) on a beryllium

of similar BeO content shows a significant difference in the

slopes of two linear fits, the- slope LASL's data indicating

a somewhat "stiffer" hugoniot than the present data

(U s = 7.998 + 1.124 up). The reason for this difference is

difficult tG determine. The possibility of edge rarefactions

affecting the measurements on the GM specimens was checked by

firing several tests with specimens substantially thinner thanthe value dictated by the analysis in Section II. No signifi-

cant differences in the measured values were noted.

1

81 a

'1

MANUFACTURING DEVELOPMENT 0 GENERAL MOTORS CORPORATION JMSL-68-1:3

AZ31B MAGNESIUM

Four hugoniot tests werE performed on AZ31B magnesium toolingplate (po = 1.773 gm/cm ) material. The nominal composition

of thr- material is Mg 96.0%, Al 3.0%, and Zn 1.0%. The datashows more scatter than was found in tests with other metals.

The hugoniot data are presented in Table 19 and in Figures

42, 43 and 44. The hugoniot is described by the linear Iequation:

Us = 4.551 + 1.209 up km/sec

Root Mean Square Deviation of U = ± 0.083 km/sec for 4 data

points.

The figures compare graphically the measured values with the(21)AZ31B magnesium data of the LRL Compiler and the data on

99.5% pure magnesimn by LASL( 1 2 ). Linear fits to the oher

data are:

U = 4.516 + 1.256 up km/sec (LASL, P0 = 1.745 gm/cm3

Us = 4.648 + 1.198 up km/sec (LRL Compiler, p0 = 1.78 gm/cm3

82

MAN UFACT URING DEVELOPMENT 0GENERAL MOTORS CORPORATION

Z4SL-6 8-13

4. 5 in t - In0 0 in r4

0 0 N-Vin f0(.. 0%

V ~ en m n 0 %0

P ~0 >~'ar -AH V 10 i

0>4

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0 o r 0 0c N

0 ok¶

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& H 0 m H~ n (r: H0 0 N

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MANUFACTURING DEVELOPMEN * GENERAL MOTORS CORPORATION

MSL-68-13

MATRJIAL -WDGfIWM

0 W 0o, 1.776

+ LRL (Wt?. 21) 00 a 1.78, -QUZW .•WH (RX. 22) Po-1.745

u.

(-.

Li

LU

LU

S~t !

"".3. 4. 9,0 6-0 /

PARTICLE VELOCITY - KM/SEC

Figure 42 Shock Velocity vs Particle Velocity for Magnesium

84

if MANUFACTURING DEVELOPMENT 0 GENERAL MOTORS CORPORATION

MSL-68-13

MATERI&A. - WOIWLl

0 GI4 00 0 1.776

+4 LPL (W1. 21) o, a 1.745

I4 * COUM3 *MR3 (33U. 22) P .4

k

V /

-:1) II

Ln,LdCLf

+_

1.00 2.00 3,00 4.0 0 .• G.Cr, I .c

PARTIELE VFLOLITY - KM/SEE

Figure 43 Pressure vs Particle Velocity for MagnesiumI

MANUFACTURING DEVELOPMENT 0 GENERAL MOTORS CORPORATIONSa. e .-

MATERINX tMtASILJ. GH P 0 - 1.776

+ LI (Mri. 21) a0 1.71

s]e uscoUz M XWS (Mir. 22) 0, a 1.745

24 4

IT

ii++

'A I\

i, 19 0 3 N 0.33 (.. 0.43 0.48 00 -SPECIFIC VOLUME - CC/GM

Figure 44 Pressure vs Specific Volume for Magnesium

86

2'

if ~MAN UFACTURING DEVELOPMrN M 0~4PA MTOR 0 nOA~O

MSL-68-13

PLEXIGLAS

The Plexiglas tested was identified as Rohm and Haas Type II

UVA. Only two tests were performed, which served to provide

•I a check on the extrapolation of the data of Hauver( 2 3 ) takenabove the phase transition at %, 0.2 megabars, (line A of Fig-ure 45) into the higher pressure region investigated by

(23)Bakanova (line B). The data are listed in Table 20.

Fits to the above data are

Us = 3.51 + 1.25 up km/sec (Hauver) (2.8 < up < 3.5)

Ip

Us - 3.10 + 1.32 u k m/sec (Bakanova) (3.0 < up < 8.0)

Figures 45, 46 and 47 display the present data as comparedto that of Hauver and Bakanova with the line representing

Bakanova's data between 3.0 < U < 8.0 km/sec. The twodata points determined in the present work are in good

agreement with the data of Bakanova (difference in shockvelocity less than 0.4%) and also are in agreement withthe extrapolation of Hauver's data (difference in shockvelocity of less than 2% at a pressure of 1.0 megabar).

S87

M AHUFACTUtING DEVELOPMENT 0 GENERAL MOTORS CORPORATION

II In

G>oo fn0 )

> 4)

,'40

o14

44,

0 4)N rz4 0q 41 8

Ou -ri4

41

a' o

90 0

('4 1

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MSL-68-13

S~~MAIMI& - RDIGI•/

* C-?

0 umovx (CR. 23) P) a 1.1/

+ HMNEn (DI. 22) Po a 1.16

LiU1C

C H

LJ

CD

.0"LiLIT

rC.0 1.0 2.0 3.0 4.0 6.00 7.0PARTICLE VELOEITY -KM!SEC

Figure 45 Shock Velocity vs Particle Velocityfor Plexiglas

89

AA

4--

-6-

41t.1

0 UAKINOVA------23)----1-

+ M 0 3V00 4-00.522) 0. - 1.16

PATCL7EOCT.M,/E

Fi u e46 P e s re v ati l eoct8o

Plexgla

90I

MANUFACTURING DEVELOPMENT G GENERAL MOTORS CORPORATION

MSL-68-13

MATERIk - REIGA

0 BAJA0VA (Mr. 23) P0 " 18

+ CAU)V (REP. 22) p0 1.18

U.•

S5

IK

LiJ

A j

SPECIFIC VOLUME - E/GMW

Figure 47 Pressure vs Specific Volume forPlexiglas

91

mJ

M AN U F AC U URING DEVELOPMENT 0 GENERAL MOTORS CORPORATIONMSL-68-13

QUARTZ PHENOLIC

A single test was performed to locate a very high pressure

point on the hugoniot of quartz phenolic. Lower pressure work

was performed at this laboratory under Contract AF04-(694)-807

under directorship of the U.S. Air Force Ballistics Systems

Division and is reported in Reference 25. All of the data are

listed in Table. 21 and are displayed in Figures 48, 49 and 50.

A pnase change in clearly evident beginning at a pressure of

nu 0.2 megabars. The data point obtained is on the higher pres-

sure phase of the hugoniot.

The linear fit to the upper portion of the hugoniot is given

by :

U= 1.949 + 1 364 up km/sec

Root Mean Square Deviation of Us = ± 0.016 km/sec for 5 datapoints.

The initial density of the quartz phenolic is 1.80 gm/cm 3

The properties of the high pressure phase suggests that this

may be related to the propezties of quartz under high pressure,

i.e., the high pressure9 polymorph-stishovite . The tests

were made with layup directions of the quartz cloth in the

phenolic matrix both parallel and perpendicular to the shock

front, but orientation effects on the wave velocity are ap-

parently neg..igable at these pressures.

92

A-MANUFACTURING DEVELOPMENT * GENERAL MOTORS CORPORATIONj

MSL-68-13

-HI 14

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MATIRIAL - OJARTZ Mal.IC

0 GH PRZS•NT (J.LKYUP) po 1.60

A GM (AV. 24) (J.YMUP) pa " 1.80

a GH (R,'. 24) (1-LAYUP) Pa 1.Co

'-.4

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L2

Liq• ILij

---- 4---------- -- I

3. 1.0 ?.0 3,0 4,0 5.0 6-0 7.0

PARTICLE VELOCITY - KM/SEE

I.

Figure 48 Shock Velocity vs Particle Velocityfor Quartz Phenolic

94

'. A W U " A fýT U R I N C DEVELOPMENT 0 GENERAL MOTORS CO :ýOl1ATIONBV' YiSL-66-13

I

i 4i ~~MAIIUT - UA O Wq 4LE

0 Q( PIt•8I• (J.,LAYUP) PC 1..0

&A , (UP. 24) (.LAYW) PC o 1.80

8 04 (N3?. 24) (CL&YUP) Po- 1.80

|I

- - I

.4 °

ry

I k U II I

S-.)co 1.00 2.00 3,00 4-0 0 0 G.00 7.00PARTICLE VELOCITY - KM/SEL

Figure 49 Pressure vs Particle Velocity forQuartz Phenolic

95

'-3

M A N U F A C T U R I N G DEVELOPMENT e GENERAI M 0 T 0aS P, 0 R PAA T

MSL-68-13

S• ,, I I, ., I . I-

MATERI&L - •WA FMIC

S6P( am 383r ({J.LLtA ) Po a 1.8s

A ON IRV. 24) (J L ,YUP) P0 a 1.6s0

0 OR (331. 24) (=IAY'ur) Po " 1.60

-4

4, UJ-(13Ld

El2f

¢,--,,••1... , -- --------- ,----+ ..SSEII VOLUME - E/GM

Figure 50 Pressure vs Specific volume forQuartz Phenolic

96

MANUFACTURING DEVELOPMENT a PEtJEnAL un TOAD5 COR POAT 0

MSL-68-13

SECTION V

SUMMARY

The research program has resulted in the relatively high pre-cision determination of the high pressure hugoniot equations

of state of eleven materials. The estimated error for shock

velocity measurements with the experimental system was 0.2%

to 0.6%. Estimated error in calculation particle velocity

was 0.05% for like-like impact, but somewhat higher for

dissimilar materials impact (see Appendix B).

Table 22 summarizes the results of the experimental program in

terms of the constants of the linear hugoniot equation

Us = CO + Su Also included are the pressure ranges mea-

sured and the RMS deviations of the measurements. Figures

51 and 52 show the data points obtained, displayed in theP vs u plane.

p

Comparisons have been made of the data with that of other

researchers. Space does not permit the inclusion of all

data available for comparison and the data quoted is selected

principally on the basis of pressure ranges studied and simi-

larity of the materials in terms of density and composition.

The onset of melting in the shock front is evidenced by only

very small changes in the measured parameters, shock velocity

and particle velocity. Accordingly, very accurate data are

required to substantiate theoretical predictions of the melting

phenomenon. Although the linear fits to the high pressure data

reported here are useful for calculating shock wave propagation,

it is likely that several of the materials experience melting

at the higher pressures, and the linear approximations become

less accurate.

.17

rUAT~.. c r 1P~4 GENCRAL MOTORS COR FORAT iOm

MSL-6a-l I

2' ~4.a, 4

'.40 0 44.4 911A A 0 am.4

0' 11t.. W.4 4 0

-A 4.

E-44

W2n

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Go -4 P- m t N N Cfl

E-4 - .4 .

0.~0

In0 1. 0 0 00 .In r-w0ý a 0 0m 00 00 0 1ý014c

r: a;. 4 04 a; 0 0 0 0z 4

I*44

2 0

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9.4 r - P4 H4r 0 4 41

r6 4 4

E4 ~ ~ ~ ~ 1 __ __ _ 4___ __ __ _ __ __ __ __ _ __ __ __ __ _

0>99

MANUAC~~V. DEELOMEN G!NikAL MOJ1ORS CORPORATION

MAMAERI- 3 -L

ULcU

Ur)3

9 20

'i~ARf1~E L6E~Y - ~QMEA 'c

Figure 51 Compilation Of Hugoniots

99

MANUFACTURING DEVELOPMENT 0GENERAL MOTORS CORPORATION

iL-6 8-13

MATO&L4 GM P -IIIOVNC COPPXRI

UJIC. 2024-T4

ALLWHM4U

FARTIELE VELOCITY - /SE

Figure 52 Compilation of HugoniJots

.100


MSL-68-13

CONCLUSIONS AND RECOMMENDATIONS

The research program has, by the attention to detail necessaryto produce high precision measurements in multimegabar hugoniot

determination, provided the opportunity to work out the diffi-culties and reduce the errors in a relatively new experimentalsystem, the use of a light-gas gun for shock wave measurements.Although some problems still remain, the light-gas gun system isnow better developed and more efficient than when the programbegan.

On the whole, good agreement was found with the data of otherinvestigators. However, several•-interpretive problems arestill unresolved. The behavior of the aluminum alloy 2024-T4in the pressure range t, 1 megabar should be investigated fur-ther. The small differences in the slopes of aluminum andcopper as -measured by gun-launched impactor and by explosivetechniques may be significant and need further investigation.The large differences in slope- .,f the beryl-liz and the nickelhugoniots when compared with other researchers are beyond theestimated experimental errors and need further systematic tests.

1

! 101

3 MANUFACTUR1,G oEVELOPMENT . GENERAL MOTORS CORPORAT ON 0

MSL-68-13 I

ACKNOWLEDGEMENTS IThe authors gratefully acknowledge the invaluable assistanceof a number of people; in particular, the light-gas gun crew,J. Paavola, J. M. Hessel, H. G. Reynolds, and their supervisorA. R. McMillan, and the talented abilities of J. W. Thomlinsonand W. D. Fershman, who constructed the delicate target systems.R. Lingle and J. R. Havens supplied measurements of acoustic

velocities and Dr. C. J. Maiden supplied helpful criticism.

Numerous helpful suggestions on material selection and data

interpretation were provided by Dr. S. M. Taylor, the contracttechnical monitor, and by Mr. G. E. Hauver, both of the U.S.Army Ballistic Research Laboratories.

102

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I U I MANUFACTURINb DEVELOFPMENT ; GEN, RAL MOTORS CORPORATION

MSL-68-13

3 1REFERENCES1. Jones, A. H., Isbell, W. M. and Maiden, C. J., J.A.P.,

Vol. 37, p. 3493 (1966),

2. McQueen, R. G. and Marsh, S., J.A.P., Vol. 31, p. 1253(1960).

3. Hart and Skidmore, I. C. (LRL Compendium) 1965.

4. Al'tF'uler, L. V., Krupnikov, K. K. and Brazhnik, M. I.,Soviet Phyp. -JETP, Vol. 34, p. 614 (1958).

5. Walsh, J. M., Rice, M H., McQuepn, R. G. and Yarger, F. L.,Phys. Rev., Vol. 108, p. 196 (1957).

6. Isbell, W. M., Shipman, F. H., and Jones, A. H., "Use of aLight-Gas Gun in Studying Material Behavior at Megabar Pres-sures", Symposium High Dynamic Pressure, Paris, Prance,September, 1967.

7. Jones, A. H., Isbell, W. M. and Shipman, F. H., "MaterialProperties Measurements for Selc-ted Materials", ContractNAS2-3427 National Aeronautics and Space Administration,Ames Research Center, Moffett-Field, California, April, 1968.

8. Lingle, A. and Jones, A. H., "Triggering System at theMuzzle of an Accelerating Light-Gas Gun", TR65-65, ONDefense Research Laboratories, Santa Barbara, California,September, 1965.

9. Al'tshuler, L. V., Kormer, S. B. and Brazhnik, M. I.,Soiet Phys. - JETP, Vol. I, 766 (1960).

i0. Curran, D. R., J.A.P., 34 (9), 2677 (1963).

11. McQueen, R. G., Marsh, S. P. ar.d Carter, W. J., "The Deter-mination of New Standards for Shock Wave Equation-af-StateWork", Symposium High Dynamic Pressure, Paris, France,September, 1967.

12. McQueen, R. G., Marsh, S. P., Carter, W. J., Fritz, J. N.and Taylor, J. W., "High Velocity Impace Phanomenon",edited oy E. V. Colen, Academic Press Inc., N. Y. (in press).

13. Al'tshuler, L. V., Kormer, S. B. and Bakanova, A. A.,Soviet Phys. - JETP, Vol. 11, p. 573 (1960).

103

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M A N U FA C T U RIN G DEVELOPMEI1T G tENERAL MOTORS CORPORATION

MSL-68-13Ii

14. Kormer, S. B., Funtikov, A. I., Urlin, V. D. and Kolesni-kcva, A. N., Soviet Phys. - JETP, Vol. 15, p. 477 (1962).

15. Urlin, V. D., Soviet Phys. - JETP, Vol. 22, No. 2,

p. 341.

16. March, S. P., Private communication with LRL.

17. Skidmore, I. C. and Morris, E., "TheziLodynamics ofNuclear Materials", p. 173-216, Vienna, 1962.

18. Al'tshuler, L. V., Bakanova, A. A. and Trunin, R. F,Soviet Phys. - JETP, Vol. 16, p. 65 (.962).

19. Minor, E. E., Private communication, 1968.

20. Krupnikov, K. K., Bakanova, A. A., Brazhnik, M. I. andTrunin, R. F., Soviet Phys. - JETP, Vol. 3, p. 205 (1963).

21. Van Thiel, M., "Compendium of Shock Wave Data", UCRL-50108 (2 Vols.) ed., Lawrence Radiation Laboratory,University of California, Livermore, California, 1966.

22. McQueen, R. G. and Marsh, S. P, Report No. GM.,-6-566,p. 51-62 (1964), Los Alanto- Scientific Laboratory, GMX-6.

23. Hauver, G. E. and Melani, A., B.R.L. Report No. 1259 (1964),Ballistics Research Laboratory, Aberdeen Proving Grounds,Aberdeen, Maryland.

24. Bakanova, A. A., Dudoladov, I. P. and Trunin, R. F.,Fizika, Tverdogo Tela, Vol. 7, p. 1616 (1965).

25. isbell, W. M., Froula, N. H., Shipman, F. P., FundamentalMaterial StdyX, Vol. III, "Shock Wave Propagation andEquation of State Measurements of Quartz Phenolic", Tech-nical Report TR67-07, Vol. III, February, 1967 pieparedon Contract No. AF04-(694)-807 for Ballistic SystemsDivision Norton AFB, California 92409.

26. Wacklerle, J., J.A.P , Vol. 33, p. 922 (1962).

104

awi

A

II

IL

APPEND IXES

MANUFACTURING DEVELOPMENT A GENERAL MOTORS CORPORATION

E l MSL-68--13

APPENDIX A

DATA ANALYSIS PROCEDURES FOR THE

DETERMINATION OF HUGONIOT STATES

FROM SHOCK WAVE DATA

INTRODUCTION

The fo'lowing is a detailed description of the data analysis

method employed for the determination of hugoniot state data

derived from the experimental system described in the main

body of this report. The first part of this appendix pre-

sents the equations and assumptions employed in Lhe analysis

and the second part describes a computer routine written to

perform the calculations.

Experiment Analysis

Figure A-I illustrates the system schematically with the follow-

ing nomenclature:

v = impact velocity cm/psec

b = pin cap thickness cm

g = pin gap cm

h = target thickness cm

x = pin position on line 1-A cm

0 = impactor tilt radians

D = shock velocity in target cm/!sec

105


MSL-68-13

Ito rass Mounting1lmpactor Block"\ StationSelf - Shorting NStton

"Pin

""/ TargetSpecimen

a

I

1 -Cast

Epoxy

b

Figure A-i Schematic of Equation of State Studies Target

Two cases of pin correction are necessary; the first involves

the "start" pins 1 and A which are struck by the impactor directly.

The second case involves the rear surface pins B and C, which

receive the shock transmitted by the target material; and thus

have closing velocities diffe-ent from pins 1 and A.

The times to pin closure are given by:

t! =_bl + gl (A-l)

U 2 uspin pin

tA= X3tanO + bA + gA (A-2)

v 'spin pin

106

$


MSL-6 8-13

!I(X D

B-(X-h~tan;ý 0) tanG + eB (A-3)sec(=Vo) +•~~~T -. • •Upt Upt

DI= (X 3-hctaG 0) tan + sec(v) + h 2 Up (A-4)Sv -D U 2 u

spt Pt

where subscripts 1, A, B, C refer to pin locations, and

Uspin - pin cap shock velocity induced by impactor

Upin = pin cap partical velocity induced by impactor

U = pin cap shock velocity induced by target

Upt= pin cap particle velocity induced by target

Usi and upin are evaluated by the impedance match solutionfor the direct impact of the projectile material into the pinmaterial. The particle velocity derived from this analysis is:

u= B - r-B2 -4A C (A-5)

P 2A

where A = P p- Popin Spin (A-6)

B p C + p .C + 2p C vop op opin pin OP op

C v v(C + Spv)op op p

andOU =C + S uspin pin pin pin ,A-7)

107

&I A N U F A C T U R I N G D E V F L O P M E N T G E N E R A L M O T O R S C O R P 0 A I 1O N

the impactor hugoniot being given by:

' U~sp = op + pU PAS

For the pin gap velocity correction of the wave interaction be-tween the specimen and the rear surface pins on the impedancematch solution is employed again. Although the equations are

similar to those already derived, the hugoniot state of thespecimen must first be estimated and then determined byiteration.

The first approximation of the shock velocity is found by the

following procedure: Subtracting Equation (A-6) from Equation(A-7) we obtain

tan 0 v [t bA -bl 1 A-g1 A-9SX3 (A-t spin pinj

Neglecting several small corrections, the approximate shockvelocity in the target at Station B is given by

' ... +ta 0 (A-10)DB =hB/[tB-tl) v tan 0 + U spin iU (Ab

spin pin]

The particle velocity, u', at this shock velocity is given byEquation (A-5), 4here-

A S

B p C + PotD + 2P Spv (A-lI)opVop + opSp

Cp PV(C +S v)op op p

108

IMANUFACTURiNG DcEVELOPMENT * GENERAL MOTORS CORPORATION

The first approximation of the shock pressure is given by:

P'= otD'u' (A-12)

The approximate shock and particle velocities thus obtainedare used in the more exact solution for shock velocity given

by Equation (A-13). The results may be iterated several times

until the desired convergence is reached. With the convergencetest set at 0.01% usually only two iterations are required.

D tan O -hBtan 0

Sb gB VB

+ (A-13)

Uspin 2 upin Uspt 2 Upt

The particle velocity, up is calculated by Equation (h-S) with:

A p Sop p

B p C + P U +2p Sv (A-14)op op ot s P5

C op V(Cop py)

Pressure is calculated from

P =p Uu (A-15)ot S p

where it is assumed that P0 =0

109-

MANUFACTURING DEVELOPMENT 0 GENERAL MOTORS CORPORATION j5 ~MSL-68-13j

The procedure is then applied to analyze the data from pins 1, 1A and C, A, 1, and B, and A, 1 and C using the appropriate values

of g, h, b, and X.

The procedure described above is a retinement upon the simplestform of average velocity determination (i.e. distance/time)where the time term is corrected for impactor tilt. The above

refinement results in an average effect on U5 of ,v 0.2% comparedwith the simplest form. The overall effect on a shot basis hasbeen found for metals such as copper and Fansteel-77 to reducedata scatter about a linear form of the hugoniot in Us-Up.

Data Analysis Program - SHOVEL

The computer program described below is written in Mark IFortran for use on the General Electric Timesharing ComputerService. This Fortrn is very similar to Fortran IV used on

m.ny computers and provides some convenience for adapting to

teletype I/O.

The program has two sections and one subroutine. The firstportion of the program is merely an operator convenience toconvert all input data into the required units and formats.The latter portion calculates the shock velocity at each sta-tion. The subroutine COMPUT is in the form of the quadraticsolution that results in a meaningful value of up.

p

1101

MANUFACTURING 0FlVFLnPME:NT e-MC EEAL I IAI11CROATO

MSL-68-13

Definition of Terms

The terms presented below are in the following order:

1. Values required as input2. Intermediate terms3. Output values

1.INPUT TERMS

TERM NAME UNITS

Shot No. SHOT ID RUNTn.pactor Material MATLP (2) HTarget Material MATLT(2) HImpactor C CZERO km/secImpactor S~ 0SP 3 fImatrpp RPgm/cm 3Target p 0RT gm/cm3

Pin 1-B 2ime DTB lisecPin 1-C DTC iisecPin 1 height Hl in.Pin A height HA in.Pin B height HB in.Pin C height HC in.Pin 1 gap G1 in.Pin Agap GA in.Pin Bgap GB in.Pin Cgap GC in.Pin 1-C Spacing Xl in.Pin 1-B Spacing X2 in.Pin 1-A Spacing X3 in.

D H2D H3

Impactor to Window #1 Ref. Spacing Ll cts.Impactor to Window #2 Ref. Spacing L2 cts.X-ray Flash Time Interval TSIl lisec.X-ray #1 to Pin C Time Interval TS12 1isec.Front Surface Shim Thickness (If Used) SHIM in.Tilt Time Interval TILT lisec.Approximate Slope of Target Hugoniot SI(S=1.5 if zero)Pin Combination COMBO HComputer Run No. RUNS I

I -Integer, D -Dummy, H -Holorith Field


MSI,.-6 8-13

2. COMPUTED TERMS

TERM NAME UNITS

X-ray 1 Scale Factor F1 in/ctX-ray 2 Scale Factor F2 in/ct,Window Fiducial Spacing D inImpact Velocity W ft/secImpact Velocity W1 ft/secImpact Velocity V cm/ljsecD USTARPin and Po RPIN gm/cmPin Material Hugoniot Slope SPINPin Material CO C0PIN km/secPin Cap Thickness B1 in 3Specific Volume (initial) SVOL0 cm /gmQuadratic Solution Term AQuadratic Solution Term BQuadratic Solution Term CParticle Velocity of Pin Cap UPIN cm/psecShock Velocity of Pin Cap USPIN cm/psecImpactor Tilt THETA radiansFirsv Approximation Us (B Station) USBI cm/psecFirst Approximation up UBI cm/psecFirst Approximation P PBl MbFirst Approximation Pl RTI gm/cm3

First Approximation Sound Velocity C2 cm/psecParticle Velocity Induced by Target UPT cm/psecShock Velocity, Induced by Target USPT cm/psecShock Wave Tilt in Target THETI radians

3. OUTPUT TERMS

B Shock Velocity USB I:m/secB Particle Velocity UB km/secB Pressure PB MbB Relative Volume VOLSpecific Volume SVOL cm /gm

112

A4

S A MANUFACTURING DEVELOPMENT N GENERAL MOTORS CORPORATION

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The term labeling is essentially identical for the "C" station

calculations with the output being:

C Shock Velocity USC km/secC Particle Velocity UC km/secC Pressure PC MbC Relative Volume VOLl 3C Specific Volume SVOLI cm /gm

SThe "D" station calculation employs the C station approximate

velocity and corrects for the time interval difference between

B and C. The output terms are:

Shock Velocity US km/secParticle Velocity U km/secPressure P MbRelative Volilme VOL2Specific Volume SVOL2 cm /gm

Additional output terms:

D Station Calculation of Shock Tilt THET3 Radians

Calculated Impactor Tilt Time Interval TILT1 •sec% Difference of (B-C)/C Shock Velocities DIFF %

The Mark II Time Sharing System allows chaining of programs and

SHOVEL is continued as SHOVEN and an external file INFORM is used

as the data source. Up to seven files may be linked and called

in process.

113

I 4i.b JE V E L P M ENT G* E4 E 0A L WMOfTORSC (,RP C RA T 1O0I

MSL-68--13

SHIOVEL

100 COMMtON U*A.B*C110 REAL DIIENSION r4ATLPCL$)# MATLTC2)120 INTEGER SHOTRJNCOt4BOoRUNS1 30C140 200 READ( It* 40) SHOT& RUNrMATLPC I) j, ATh.PC2).*MA~TTC l)*?9ATLT(2)150 READ( I)CZERO. SPRP.-RT,#DTS.DTC.1f1I4FA.14B.ICs~lGAGgeGC.X1.g2* X3*160 +R*82I.3*2,PLI ,L2*TSI 1,,TSI2.SI4IM* TILT* S

180 40 FORMATCSX.IS.I2*4A6)196C200 PRINTs"ENTER PIN COMBINATION' (I START~ a 7 A START 4 ) AND RUN NO-"P.10 INPUT 30. COMBO*RUNS2 20C230 30 FORMAT(2AI)240C250CMPTV COMPOTE TILT AND VELOCITY252 PRINT 61. CZERO, SPD if?.RPD DYS. DTC-tI6B ,ICDGI.GAGB.oGCXI. X2iK3s254 *TILTPS256 61 FORv4ATC////6F5 3.s27. 5.476. 4//SF6. 4/1/)26 SC270 17CL1)46#48#46280 46 F'1v,4756E-033F22.4771Ir.03iD2II.9951290 1 7CL2) 41 v42* 41300 41 Dla(lI*FI+L2*F2+D)/12og316 VELl=CDI/TSIl)*IeflE+86320 42 D2uCLl*$I*D+II2*F24.9537*SIIIN)/12.0330 VEL2smCD2/CTSI2-DTC))*loSE+06340 1 FCL2) 43#44a 43350 44 GO TO 45360 43 W=VEL1;Vl,4VEL2j370 GO TO 49380 45 IW*VEL2IWIUO0*1390 .UO TO 49400 4S READCI)W410 W110*0I430CTC CONVERT INPUT TO CGS4 40C450 49 V=CW/3*281)*l.0E*62460 CZERO=CZERO*l.0E+05JUSTARUUSTAR*1 .OfbSS470 DTBUDTB*.o@ES06IDDTCu TC*I.SES96JTILTOTILTý*16E- 6

Ai80 H8141*2* 54; F4A=HA*2. 54JH348K*2* 54; iI.C*8C*O2. 544-SO RPIN z8o 41; SPIN* 1*42) CSPIN*3& SE+05D81=5e OSE-035iO GI=GI*2. 543GAzGA*2.S45GBEGB*2*54iGCOGC*2.S4

V510 XIinXI*2..54iX2yK2*2.543X3xg3*-&No54S29 TI1ET330. 01SVOLS*oU ./RI3 SVOLUO. 63SVOL IsO.S

I4CS COMPUTE SHOCK VELOCITY

569 IF DT8)11l1.10S0

114t

a' ~SHO~VEL CJNJTINUED

570 11 1JB~a0.0sPBu0.0IUIS3.--0.0VOL~c0s0

580 GO MO 5

600 1000 8= RP*CZERG+RPIM.*C0Pt1'.2*RP*SP*V610 A=RP*SP-RPI4'*SP~ilJCsRP*V*CCZERO+SP*V)620 CALL COMP1JT630 UIN ;UP~CPNSt*UI640 THIETAu(V/X3)*(TILT-CGA-GI)/C2*UPIN))650 US81=C!I8-HD/CTB-X2*THETAlV)660 1001 B=RP*CZEROGRT*USBI +2*RP*SP*VJ AuRP*SP670 G=RP*V*CCZERO+SP*V)680 CALL COMPUT690 UBI=U;PBI=RT*USB1*UBI700 RTI*(RT*USBI)/CUSRI-UBZ'710 C2wSISR~4+(UB-F1/SI*2720 IF(S)SOPSOAS1

2 130 50 S-ml#5740 St BWtRPIN*COPIý'e.RTI*C2+2*RTI*S*U8IIAtS*RTI-SPIN*RPIN750 C5S*RTI*UB1**2+RTI*C2*UBI+PB1760 CALL COMPIJT770 UPT=Uj IJSPT=COPIN +SPIN*UPT780 THETlwCUSBl/V)*THETA790 DELTIuOT8-THfETA*(K2-C48-N1)*THETI)/V800 DELTI=DELTI ,B1/USPliN.Gl/C(2*UPi'4)- B1/USPT- GB/C2*UPT)810 USB=x(HB-H1)*SQRTCTHETI**2.1)/DELTI820 3 IF(.000l-(ABSC(USB-US8I)/USB)))1002.,1003, 1003830 1002 USBlwUSB840 GO TO 1003850 1003 B8RP*CZERO+RT*USB+2*RP*SP*VSA=RP*SP;CzRP*V*(CZERO*SP*V)860 CALL COM'PUT870 UBs Ul PB=RT*USB*UBJ VOL= Il-UB/USB880 SVOLOm Ia /RT;SVOL:VOL/RT390C900 5 IF(DTC)6p6,,7910 6 USC .0OSUC=0.03PC=0.0;VOLI=0.01TILThTlLr*1.0E*06?US0.03Lk10.0920 TILTIz0.0JUSBzUSB*1.0E.05IUBuUB*1.0E.05 P82PB*1 .0Z-12930 Pz .0.JVOL2 0. 0940 SVOL I -0o 01SVOL2= *0;0D IFFVOe0.950 GO TO 2960C970 7 8zRP*CZERO4RPIN'*COPIý'J+2*RP*SP*V980 AtR*PRI4SI';=PVCZR+PV990 CALL COMPUT1000 UPI NZ U;USPP~nmC PI N+SPINi*UPIN1010 T-{ETA=(V/X3)*(TILT-CGA-G1)/(2*UPPJ'))1020 USCI=(HC-4i1)/CDTC-XI$THETA/V)1 030 1004 B=RP*CZERO+RT*USCI+2*RP*SP*VIAtRP*SP1040 C=RP*V*CCZERO+SP*V)1050 CALL COM4PUT1060 UCI=LJ;PCI1RT*USCI*UCI

115

1107 RT2=(iRT*USCI1/(USCt1-UC.1)1080 C3=LISC I*SQRTc. 49+c( USCI-UCI)/USCI)**2)1090 8z*RPIN*C0PI,.4.RT2*C3+2*RT2,*S*L'C13AsS*RT2-SPIN*RPIN1100 C.-S*RT2*UCI**2.RT2*C3*UCIPCI1 110 CALL. COM'PUT1 120 UPT1xUs USPTI*COPIN+SPW,'*UPTI1130 THET23(IJSCI/V)*THETA1 140 DE ~ T-TEA(Xt-VCHI*TE2/1150 DET=ET+IUPNG/2UPN-IUPIG/2U't1160 US*H-l*QTTHT*21/ET1 170 4 IFC.0001-(ABS(CUSC-USCz)/USC)),100S,,006.,a@61180 1005 USC3-LJSC1190 GO TO 10041200 1006 8WRP*CZERO+RT*USC+2*RP*SP*VSA3RP*SP;C2RP*V*CC;ZERO.SP*V)1210 CALL COMPUTI 220 UCEUa PCoRT*USC*UC; VOLI= 1-UC/USC1230 UgwU8*t.0E-SsUS~aiUS8*1.0E-05;pgup8*logE-g21240 UCU*.90;S*S*Ie-Sp:p*~gg1250 DELT=(OELTI-DELT2).1.GE.061269 TILT=TILT*1.OE,0612703 TILTIsCDTBeDTC)*x3/Oc2-Xl)I,.,E+,61 280 DIFFPO.SISVOLIOVOL,/RTI 293C1 3090)1310 IF(DTB)70,70,*211320 70 TIT*.s~aoU=@OP~@VL**1330 Go TO 21340 21 USI=(14C-H1)/DTC1353 BuRP*CZERORT*USI,2*RP.SP*V;A*RP*SP1360 CuRP*V*CCZEJtOSP*V)1370 CALL COM'PUT1 380 UI=UPlltRT*USI*U11390 1007 RT3=(RT*USI)/(USI-UI)1400 C42USI*SQiRTC.494CCUStsU1)/USI)**2)1410 IFCS)2P2,22#231420 22 S-1.51 4:30 23 8~RPIH'*Cl3PE[+RT3*C,'4+2*RT3*S*U13A2S*RT3-SPIN*RPIN'1 440 C=S*RT3*U1**2+RT3*C4*Ul+Pl1 450 CALL C04PiJT1 460 UJPTx UD USPTUC0PIt+SPIN*UPT1470 DTILT=DTB-CNB-H41)/uS1.81/usPLN*GI/C2*uPIN')-B1/IUSPT-GgV(2*UPT)I 490 Tý4ET3=V*DTILT/X21490 S4IM T-NT0CXI-*S T4T/)V9/SI+l/?Ulv1-500 $'-F1/USP1'-GC/(2**UPT)1510 LIj4-l*grl@(UITE3V*2/RI1 520 B=RP*CZERO*RT*US.2*RP*SP*VsAuRP*SP1 530 C=RP*V*CCZERO+SP*V)1 540 CALL COMPUTt553 U=UIP=RT*US*U1560 IFC.-0G01-(ABS((US-USI)/US)))I088.IS09,10109

116

'A C U ~G iJL V tL VM Er ti G EN E RAL MO0TO0R S C 0 PP f)R A 1 61

MSL-68-1 3

SHOVEL CONTINUED

1570 1008 USIZUSIUI=UUPIxpt530 (01 1010071590 1009 VOL2=1-U/US3L~wti*1.0E.05JUSsUS*1.0E-05JF"zP*'.0E-121600 SVOLlwV0Ll/RTSV0L2wV0L2/fRT1610 OI.-V=(ABSCCLJSB.USý/Ur)C)?*100.01620 $USE SI4OVENJ

SI4OVJE4

1760C OUTPUT STATEMENTS FOR SHOVEL; 710OC1720 2 PRINT 60j-S40To RUNS,,COMBO* MATLTC I)*M4~TLTC2) aMATLPC I)*MATLP(C2).3730 *f.TPRPp SVOLO*W*TI(ET3,,VpTILT* WI*TILTI#DIFP.17 40 *USB, UB. PB.VOL. SVOL. USC. UCPC, V3L 1.SVOL I.US.U. P. V3L2 SVO)Lg1 750C2760C OUTPUT FORMrAT1 770C1780 60 FOR41AT(/////////10Xs911S4OT NO. v15pl0Xp84RLllN NO* PAW/17~90 +10XP1711PIN COMBINATIONt *AliaXp71I- START*//1800 *SK.I144TARGET MATLo- *2A6*1810 *4K, 131IPROJ* MATL,- #2A6//8Xv91IDENStTY- .F6e3, lXv511G4l/'^.X,*1 820 *+I1DENSI TY- * F6. 3,1 K. 5PGN/CC//SX. 8KVOLUP4E- * F6. 4.1K. 51CC/GM.v1830 4/////5X.18IIPROJECTILE VEL. * Et2*5#1840 *IX.6IIFT/SEC.AK. 13HSI4OCK TILT = #F9*6//S3XvEl295. 1K.61Cl4/SECp1 859I +04K.13'ITILT MEAS. = F9.6//23X.El2e5. IX6. 6(T/SEC. 4Xp1860 +13HTILT CALCe = F9*6///SX.21JS4OCX( VEL. SCATTER = vF7.3.Ip 1X4.'.1870 +//////2Xv44Z( Ao4XvlHSHfOC-( VEL. 4l(.vleRPART* VEt.. 7X.F84PRESSUR2Z1 880 +4K. 4'-iV/V05K.,6HV:)LUMEf/l0X.6HKM/sV'--C.8X.6HIIMfSEC. I Xj, 8MEG'I "R.S,1 890 +1 3K. SHCC/ GM*/f//1 900 +2X. 1318.6X(.F8.4. 6X.F~8.4. 8X. Pl~o.6; KP9lX V8. 51X,,*//1 910 *2X 1'4C.6X.P5. 4.6X.P8.4.8X.F10,.6,lX.F9.5. IKVBS5//1 9P0 +2X. 1110,6X.*8. 4.6X.*8. 4.8X.P~I0 £ 1X.P'9. 5. 1K.F3 5//////)1930 GO TO 2001940 EN D1950 SUBROUTINE COMPUT1960 C04M0.'J U#A*B*Ct970 U~CB-SQRTCB**2-4*A*C))/C2*4)

1980 RETURN1990 ENDP-000 $FILE INFORM

117

f f 1 M 14 1 G E N E 9R A L M O T 0 R S C- Ri

Ii

APPENDIX B

ANALY SIS OF SYSTEMATIC MEASUREMENT EHRORS

iAn analysis of systematic errors in the eitperimental system

z,• performed. Each of the 22 parameters involved in the cal-culation of a hugoniot equation of state point from information

obtained using the light gas gun system was considered and an Iestimated error was calculated. These errors were combined

mathematically to yield an average systematic error for the 4hugoniot parameters calculated; pressure, particle velocity,

shock velocity, and volume. Errors in measurement of impactvelocity were also calculated.

Two cases were considered: (1) dissimilar impact, in which the

hugoniot point is calculated from the impact velocity, the shock

wave velocity, and the measured hugoniot for the impactor and

(2) symmetric impact, in which only the impact velocity and the

shock wave velocity are necessary for the calculation.

Since the error analysis is dependent on the shock impedances

of the specimen and the impactor as well as on the pressureattained, a complete error anelysis could be performed for eachdata point. This formidable task was avoided by calculating

errors involved in an "average" data point, and briefly examin-

ing the errors at the limits of the system. As the variance

in errors at the limits do not substantially change the values

for the average case, only the average case is reported.

T'-e parameters operated upon involved a measurement made on coppez

with a Fansteei-77 impactor or a copper impactor launched at 6km/sec.

The method is a statistical procedure called the analysis of variance.!

The authors are indebted to Mr. W. L. Rearick of SystemsAnalysis: Manufacturing Development, for his assistance inthe formulation of the system error analysis procedure.

118

UM A N U FA CT U PI N G DEVELOPMENT * GENERAL MOTOR-S C0RP0RAT0N

MSL-68-13

By definition the standard error of the variable, x, is given

by:

Y n G2xi/n (a)SE 1 xi

where a xi is the deviation of the ith term from some f(x).

When a I a 2' 0n are mutually dependent, the variance of

x is then:

G a2C12 + Cr2 + *..+ a2(b)

with an2 denoting the nth element component of x.

In the present case, a a (or standard deviation) is determined

for the system components of all the mutually dependent variables,listed in Table 1-B.

The variances of mutually independent variables may be determined

using the rules presented below,. By definition the mean, xi' ofa variable, x, is given by:

lix = (xl + x2 + x " " X )/n (C)

where xl, x 2 , . . xn are element components of a statisticaldistribution.

If the variance of x and y are small compared their means, i.e.,2«x << 1x' and independent, the following rules may be employed

to determine the variances of the sums, products and quotients

of variables x and y:

119

3 IA NL FA C 7UR I NG DEVELOPMENT 0 GENERAL MO0TO0R S CO0R PO0R A T nON

MSL-68-13

z - -

z ____________________________ ____________________________

0

(n'C4 tn NH N' '

to co r. .- . 1w C NH 0 LAL('40 0 .q.HO 00 U,~ 0 0 0 HHO

H) C4HH; nt C l H a 24 c -

Or40 00 0CH

" ~ ~ ~ ~ ~ OW r4C 4( 4C4C 4D 4 H 04 0 C O H 4r4r%a. 6a~u afe 44 &a 4a La Is 4(

.~ ~ r e ...... .... ......

0 ~~04 0 -r.OH 0 00O

Cl) rC4 r'4C'(4'4'4 HZ ~ toU' $4' 0~ $'4 H.(e'4 14N

H) r-0 HHC HH4 toI 1 H (H .-AH

al D. W 0 4J 4)04 04 o4

0 0 4A40 000014941 4 H.- OW t ))D HM Uflm

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.14i4 V4) E4) 0 I) 4J4 u4C4~~~0 040 $4$ Zr r

-H -1~ -H - .4"

0HE4 E4 0 ErfE4 aCW14 N H

120

MANUFACTURING DEVELOPMENT * GENERAL MOTORS COR PORATION T0

MSL-68-13

IuwA to1 00 u

Ng

00

O 3NH CN

H O '4 tq •NOO0 O Oql s 110 0 (l Nm L4C

>f

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0 ". Nl-Io o o- N"

cQ E-4 c4 c4 mI a4 ,-D tn f4 m-,I,

o . . ,.4,- .

~~r- _ _ _ _ _ _ _ _o

cn N HNNCNH4N N4C4 4N H H

O 0 H HH HH4 rJ

HH

0) 0 044E-4 43 00 C U

"4-)0 4

a) W (d i~ 44)D E-~4 >4 0

*rl-A .$4-H M (4-) H

Hz rHHWW M 3040 0 Q r

u r oe qt r) rf4 D 40 E4..0 M O 4I Q0 0 ad

(d P4A E-i14 0 0~ E-l 'U0 E-f a02 CAE-4 $4U 0 4JO H Z HE-4 EnCAH

Ci H.

121

S..A N U FCT L G P Vl E T G E N E k A L M O 10 R S C 0 R P O R A T I O N•11 HMSL-68-13

T

Addition: •2 = 2 a 2 (d)_y x y

2 20 2+ 21 2o 2 2 }Multiplication: a xy 2 x Y y 2 y x (e)

2 axP +a Yi II2]j2+ 22•'

Division: a 2 0x P +0.. (f)Ix/ =4(f)

"y-i where in (f), y >>O

t

The present analysis was carried out using the tabulated valuesp

op and a of Table 1-B. The variance of each term of equations •.1 through 4 was determined and then combined to yield the re-sultant variance for each operation.

Impact Velocity: v = y/z (1)

Impactor Tilt: tan = - v-(

Shock Velocity: Us = h sec 1--)/[(T-Tn)11 V

v + Uspin 2Upin

b gn

Uspt 2*upt

Symmetrical Condition Particle Velocity: u 1/2v (4)

122I-

MuM A N U FA C T URI NG D EVE LO PM M NT Y G E N E R A L MO T O R C R P 0 R A T IN

MSL-68-13

To determine the variance resulting from the impedance mismatch

solution for the particle velocity, it is necessary to know thevariances of the terms of the hugoniot equation of the standard.Since the hugoniot equation is itself a statistical inference,

the following approach was used:

nu. = ?n •(g)Pup 1 n

where n is the number of data employed in the least squares

analysis. The variance is then given by:

2 n (u -" 2 (h)Up 1 piup

For an equation in the form:

C' U =C +S (i)S 0 up

the variances of the zeroth and first order terms using

equation (a) are given by:

22 se(j)•Co n

22 se (k)Cp aup

The analysis of variance is then applied to equation 5a through

5c.

Impedance mismatch particle velocity:

u = 24A (5)Up 2A

123

UAN UFACTUkiNG DEVELOPMENT 0 GENERAL MOTORS CORPORATION

MSL-6_8-13

A = Pop Sp (5a)

B = P opC op+PotUs+2p op.Spv (5b)

o =P op vP U5 v2pc)C=PopCopv+P opSpV2 p5c)

To determine the variance of the square root operation, the

binomial expansion is used; i.e.

a 2V, 2 + a2 (1)

The variances are then determined for the reinaininghugniot

relations.

Shock Pressure: P = U (6),ot

Shock Specific Volutme': V = (7)

Pot

Table 2-B presents a summary of the systematic error analysis.

The percent error column shows the marked difference in the -

Saccuracy with which measurements can be performed on symmetric

(Case 2) versus dissimilar material (Case 1) experiments. The '

larger errors involved in the :dissimilar material tests (Case 1)

concern the errors in the hugoniot of the impactor material.

For tests using impactor materials with precisely measured.

hugoniots these errors will -be correspoadingly smaller.

1-24 - -

M MA NU FAC TU R ING 0 9v 1 1 9)M 8:HT E GR AL M 0 OR 5 COR POR A TIO N

no 11-L-68-133

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125

(Page.126is b-anJ

21 ~ r

UNCLASSIFIEDSecurity ClaSsification

-~~~ (SecuritY c. Casification of litte, body of abstract and Indexing annotatlion muset be entered wdhen theo~voralI report Is cieaeliieI.ORIGINATING ACTIVITY (Corporate author~) (25. REPORT SECURITY CLASSIFICATIONManufacturing Development UCASFEGeneral Motors Corporation a,1RUGM Technical Center, Warren, Michigan 48090

3. REPORT TITLE

HUGON lOT EQUATION OF STATE MEASUREMENTS FOR ELEVEN MATERIALSTO FIVE MEGABARS

4. oEscflipTIVE NOTES (Ty'po of report end inclusive dates)

Final Report 1966, June - 1968, December.AUTHOR(IS) (First name, Mtddle Inftiet, lest neme)

Isbell, W. M., Shipman, F. H., Jones., A. H.

0. REPORT DATE 70. TOTAL NO. OF PAGES T7b. NO. OF REFS

1968 December 125 I26OS. CONTRACT OR GRANT NO. 5.ORIGINATOR'$ REPORT NUWDfER(S)

DA-18-00l-AMC-1126 (X)b. PROJECT NO. MSL-6 8-13DASA Subtask No. 15.025_________________

C. S~b. OTHER REPORT NO(S) (Any other nuombr Mhat Mars be 0841#10dthis report)

U ftu doo Wzmnt bes been apprqV.d :for public r01383mi~ r~l~its d~istri±bution 18 UnImalted.

4t- UPPLMENTRY NTESAbereen rovig 1. SIONSORING MILITARV ACTIVITY

tISUPLMENAR N r ounbedsn Parovingd Department of the ArmyGrond,0arlad. U.S. Army Ballistics Research

21005. 1Laboratories13. ANSTRACT Aberdeen Proving Ground, Maryland

21005

An exner-imental technique is utilized in which a light-gas gun isused to launch flat impactor plates to high velocities (',, 8 km/sec)at specimens suspended at the muzzle of the gun. Impact-inducedshock waves at pressures to "u 5 megabars are recorded and are usedto determine the shock state in the specimen. The ability to launchunshocke"a, stress-free flat plates over a wide and continuous velocityrange, coupled with the ability to launch impactor plates of the samematerial as the target, results in hugoniot measurements of relativelyhigh precision. Measurements were made on Fansteel-77 (a tungstenalloy), aluminum (2024-T4), copper (DFHC, 99.99%), nickel (99.95%),stainless steel (type 304), titanium (99.99%), magnesium (AZ3lB),beryllium (S-200 and 1-400), uranium (depleted), plexiglas, andquartz phenolic. The results are compared with those of otherresearchers.

Deviation from linear shock velocity - particle velocity was foundin aluminum beginning at n, 1.0 megabars, probably attributable tomelting in the shock front.

473~~~a 1678E ~ O tS. 1 JAI*55 WWIC1 isUUDIv~ *g*o #0m 41,W 127 UNCLASSIFIED~sinao

=

U ~UNCLASSIFIED Isocuity classification _____

14. LINK A L11NK 0 LINK CKe-y- - - -

I FHugoniot Equation of State

Shock Wave PropagationMegabar Dynamic Pressure Measurements

S~UNCLASSIFIED S 5128 ;,-• "

I

hugoniot equation of state ~measurements for … · man u fact uring development 0 gener al k!0t...

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