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AFY L-TR-69-39 AFWL-TR-69-38
COMPILATION OF HUGONIOT
EQUATIONS OF STATE
Brian J. Kohn
Lt. USAF
all _ |I TECHNICAL REPORT NO. AFWL-TR-69-38
AIR FORCE WEAPONS LABORATORYAir Force Systems Command
Kirtland Air Porce Base
New Mexico
This document is subject to special export controls and each transmittalto foreign governments or foreign nationals may be made only with priorapproval of AMV. (WLRP) Kirtland AFB, NM, 87117.
AFWL-TR-69-38
AIR FORCE WEAPONS LABORATORYAir Force Systems CommandKirtland Air Force Base
New Mexico
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This report is made available for study with the understanding thatproprietzry interests in and relating thereto will not be impaired. In caseof apparent conflict or any other questions between the Government's rightsand those of others, notify the Judge Advocate, Air Force Systems Command,Andrews Air Force Base, Washington, D. C. 20331.
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S__moo I
AFWL-TR-69-38
COMPILATION OF HUGONIOT EQUATIONS OF STATE
* Brian J. KohnLieutenant USAF
TECHNICAL REPORT NO. AFWL-TR-69-38
This document is subject to specialexport controls and each transmittalto foreign governments or foreignnationals may be made only with priorapproval of AFWL (WLRP), Kirtland AFB,NM, 87117. Distribution is limitedbecause of the technology discussed in
the report.
AFWI.-TR-69- 38
FOR EWORD
This report was prepared under Program Element 6.16.46.0l.H, Project 5710,Subtask RAS 1114 (15.025), and was funded by the Defense Atomic Support Agency(DASA).
Inclusive dates of research were June 1968 to January 1969. The report wassubmitted 4 March 1969.
Information in this report is embargoed tinder the US Export Control Act of1949, idministered by the Department of Commerce. This report may be releasedby departments or agencies of the US Government to departments or agencies offoreign governments with which the United States has defense treaty commitments,subject to approval of AFWL (WLRP), Kirtland AFB, NM, 87117.
This technical report has been reviewed and is approved.
BRIAN J. KOLieutenant, USAFProject Officer
HARRY F. RIZZO CLAUDE K. STAMBAUGHLt Colonel, USAF Colonel, USAFChief, Physics Branch Chief, Research Division
ii
AFWL-TR-69-38
ABSTRACT
(Distribution Limitation Statement No. 2)
Computer codes for predicting material response to shock loading in and abovethe elastic region of a material require a knowledge of the Hugoniot equationof state. Hugoniot and material data have been compiled from various sourceson materials Uf interest and prcsentcd in a form which condenses the neededcomputer code inputs to an easily accessible source.
iii
AFWL-TR-69- 38
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iv
AFWL-TR-69-38
CONTENTS
Section Page
INTRODUCTION 1
II HUGONIOT DATA REPRESENTATION 2
Form of the Equation of State 2
Experimental Determination of the Hugoniot 3
III MATERIAL PROPERTIES 6
Discussion of Material Strength 6
Significance ot the U - U Relationship 8S p
IV EQUATION OF STATE DATA AND GRAPHS 13
Aluminum 15
Aluminum (1060) 17
Aluminum (6061-T6) 19
Aluminum (2024) 21
24 ST Aluminum 23
921 T Aluminum 25
Antimony 27
AVCOAT II 29
Beryllium 31
Bismuth 33
Boron Nitride 35
Brass 37
Cadmium 39
Boron Carbide 41
Silicon Carbide 43
Tungsten Carbide 45
Carbon Phenolic 47
3-D Carbon Phenolic 49
Chromium 51
Cobalt 53
Copper 55
Durite 57
Epoxy 59
C-7 Epoxy 61
v
AFWL-TR-69-38
CONTENTS (cont'd)
Section Page
Exon 63
Hi-D Glass 65
Gold 67
Graphite, Commercial 69
Pyrolytic Graphite 71
Hafnium 74
Armco Iron 76
Iron 78
Lead 81
Lucite 83
Magnesium 85
Manganin 87
Molybdenum 89
Mylar 91
Nickel 93
Niobium 95
Nylon 97Palladium 99
Paraffin 101
AVCO Phenolic Fiberglass 103
GE Phenolic Fiberglass 105
Chopped Nylon Phenolic 107
Tape-Wound Nylon Phenolic 109
Quartz Phenolic 111
3-D Quartz Phenolic 113
X-Cut Crystalline Quartz 115
Phenolic Refrasil 117
Platinum 119
Plexiglass 121
Polyethylene 124
Polystyrene 126
RAD 58B 128
OTWR 132
Series 124 Resin 134
Silver 136
Stainless Steel Type 304 138
vi
AFWL-TR-69-38
CONTENTS (cont'd)
Section Page
Stainless Steel Type 304L 140
Steel, Mild EN3 142
Tantalum 144
Teflon 146
Thallium 148
Thorium 150
Tin 152
Titanium 154
Tungsten 156
TWSP 158
Uranium 3 wt pct Molybdenum 160
Vanadium 162
Zinc 164
Zirconium 166
V MATERIAL DATA REFERENCE SOURCES 168
REFERENCES 181
DISTRIBUTION 185
vi
vii
AFWL-TR-69-38
SYMBOLS AND UNITS
RHO ambient density (P0)(gm/cm3)
E sublimation energy (ergs/gm)
Sr Gruneisen coefficient (calculated from B VP 0 -Cp or observed
from shock wave experiments; dimensionless)
CL Longitudinal sound speed (cm/microsec)
C S transverse sound speed (cm/microsec)
C B bulk sound speed (cm/microsec)
B S adiabatic bulk modulus - p oC B2 (Megabars)
AMU shear modulus 0 C S2 (Megabars)
CO elastic Modulus (Megabars)
Y4U compression at which elastic limit is reached in terms of p
a thermal coefficient of expansion (volumetric)
Specific given in joules and at constant pressureheat (Cp)
S data pressure points (Megabars)
SCAL calculated stress (Megabars)
PCAL calculated hydrostatic pressure or, in the case of a simpleleast squares fit to P - v data, a stress term (Megabars)
V, V specific volume at final and initial compression, respectivelyo
ETA compressional term p/p 0or V /V (dimensionless)
U calculated particle velocity (cm/microsec)
YADD linear work hardening term (exprE sed at i - 0.2) (Megabars)
P (0/0)- 1 or (Vo/V) - 1 (a nondlimensional compression term)
Cl, Dl, S1 constants in cubic fit P - Cli + DlI 2 + SIp3 for first plasticwave, expressed in Megabars
C2, D2, S2 constants in cubic fit P = C2P 2 + D2p- + S2p 3 for secondplastic wave, expressed in Megabars
NOTE: All data points are referenced as to their source. Further, materialproperties available and included in this report are referenced as tosource.
viii
AFWL-TR-69- 38
UNIT CONVERSION RELATIONS
1 gm/cm3 (units of weight density) - 1 dyne-sec 2 /cm4 (units of mass density)
i gram = 1 dyne-sec 2 /cm (- 980.7 dynes at acceleration of 1 gravity)
I dyne - 1 gram - cm/sec 2
1 erg - I dyne - cm - 10 7 joules
1 calorie - 4.186 . 10 7 ergs - 4.186 • 105 mbar-cm3 per unit area
1 tap - 1 dyne-sec/cm2 - 1 bar-Pjsec
1 bar - 106 dynes/cm2 - 14.5 psi - 0.987 atmosphere
1 psi - 69,000 dynes/cm2 - 0.69 . 10 7 mbar - 70.31 grams/cm2
1 kbar - 103 bar - 109 dynes/cm2 (where kbar - kilobar)
1 mbar _ 103 kbar - 1012 dynes/cm2 (where mbar = megabar)
1 cal/gram~c - 1 BTU/lb0 F
1 ft/sec - 30.48 cm/sec - 30.48 x 10-6 cm/psec
ix
AFWL-TR-69-38
i p[
4 .
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AFWL-TR-69-38
SECTION I
INTRODUCTION
The study of shock wave propagation in solidR requires a knowledge of the
pressure-volume-energy (P-V-E) equation of state of the material under consid-
eration. Typically, the Mie-Gruneisan form of the equation of state is used
along with the Rankine-Hugoniot relations expressing the conservation of mass,
momentum, and energy. The Rankine-Hugoniot equations are not in themselves
adequate to uniquely determine the parameters; therefore, addiLional knowledge
of a material's behavior is necessary. This additional knowledge is given by
the Hugoniot of a material which defines all pressure-volume states obtainable
through a shock transition.
The Hugoniots included in this report represent data accumulated from
various sources and are reduced to a form usable in existing computer codes
for predicting material response to shock loading at pressures in and above
the elastic region of a material. The purpose of this report is therefore to
present the results of various investigations on materials of interest in a
form which condenses the needed computer code inputs to an easily accessible
source.
AFWL-TR-69-38
SECTION II
HUGONIOT DATA REPRESENTATION
1. FORM OF THE EQUATION OF STATE
The Mie-Gruneisen compressional equation of state can be written as
P P(V1 ) "r'(v) *( - EH(VH))(1
relating pressure-volume-energy through use of a reference curve, generally
chosen as the Hugoniot. In the above equation, P, V, E refer to any equilib-
rium position admissible in a complete equation of state; P1H' VH, EH refer to
states existing on the Hugoniot, and r(v), the Gruneisen coefficient, is
assumed to be a function of volume only.
The Hugoniot of a material defines all pressure-volume states obtainable
through a shock transition and can be represented in the form
PH "CU + D2 + Sj3 (2)
where C, D, S are constants, v - p/p - 1, and p0 , p - initial and final00
densities, respectively.
A description of the Hugoniot in terms of measurable quantities can be
obtained from the so-called "Jump" conditions which are statements of conser-
vation of mass, momentum, and energy across a shock front:
p U - P(U - U) conservation of mass (3)
P - P - p0 U; U conservation of momentum (4)0O Us Up
PU - 1/2 p U UE - Eop conservation of energy (5)p 0 p 0
where
p - density
Ua, Up a shock velocity, particle velocity, respectively
2
AFWL-TR-69-38
P pressure
E = energy
arid the subscript, o, refers to the undisturbed states.
By combining equations (3), (4), and (5), the Rankine-Hugoniot equation is
obtained relating energy to pressure and volume on the Hugoniot curve
EH E - 1/2 (PH + PO)(Vo- V) (6)
Combining equations (1), (2), and (6),
r - P~(~ (I _ r(v)Q)+ r(v)H * p 2 (E -Eo) (7)
In PUFF-type codes r(v) is assumed to be a constant, and E is set to zero.0
Equation (7) then becomes
P - (Cp + Dij2 + SiV3) .( -j: + rpE (8)
This, then, is a general equation of state used to describe material response
under dynamic loading.
2. EXPERIMENTAL DETERMINATION OF THE HUGONIOT
The above equations, however, are not sufficient to establish an equation
of state for a material without experimental data. This additional informa-
tion is generated through experimental measurements of the Hugoniot. Several
forms of Hugoniot data are used of which two will be considered here.
We have seen that one form of the Hugoniot is P1H - Cp + Dw2 + Sjj3. From
equation (3) we see that
0 (U S -s p
and from equation (4), if any two of the parameters P, Us, or U can be
measured, the third can be determined and a point on the Hugoniot can be found.
A series of such measurements then defines equation (2)
Another form for the Hugoniot may be found by solving equations (3) and (4)
for shock velocity and particle velocity.
3
9
AFWL-TR-69- 38
U5 s [(Co) P (9)
u~ P P/ U (10)
If a simultaneous experimental determination of U and U is made, there iss p
sufficient information to establish a point on the Hugoniot. A series of such
measurements will then define the entire curve.
For most materials a linear relationship has been noted where
U - c + u (11)s 0 p
C -U 5 intercept at zero pressure
X - slope of shock/particle velocity data
This alternate form may also be used to represent Hugoniot datA. C approxi-
mates the bulk sound speed given by
C 2 C - 4/3 C 2B L S
where
CL - longitudinal sound speed
CS - transverse sound speed
When U and U are linearly related, equation (2) can be written explicitly ins pterms of C and A. If equations (11) and (4) are combined and P is negligibly
small compared to P, then
P - Up (C + XUP) (12)
Equation (10) can be written in the form
00/ I1 [U /(C + U)] (13)
4
AFWL-TR-69- 38
Eliminating U between equations (12) and (13),P
Pc 2 C (i + 1)"P 0 0 (14)[i + 1J ( ) 2
where p /P - 1. This then gives the user two forms of the Hugoniot0
representation. One form gives a least squares fit to the data points
reported in the form
P Cp + DW2 + Sp 3
The second form is the relationship
U -C + XUs 0 p
5
AFWL-TR-69-38
SECTION III
MATERIAL PROPERTIES
1. DISCUSSION OF MATERIAL STRENGTH
The analytic functions for the Hugoniot so far discussed describe a
material's hydrostatic behavior. In some cases this hydrodynamic treatment
is a good approximation in the pressure regions of interest. For strong
materials with high elastic moduli it is necessary to include elastic response
in the calculations. In this treatment the Von Mises yield criterion is used
to describe an elastic region which, when exceeded, results in plastic or
hydrodynamic response of the material.
In figure I the Hugoniot elastic limit (HEL) of a material is the elastic
limit in stress-strain space. The stress-strain curve is taken to lie above
the hydrostat by a value equal to 2/3 Y0, where Y is the yield strength in
simple tension. In this report the Hugoniot elastic limit is found by either
of two methods. In the first case the HEL is observed directly by noting the
amplitude of the elastic precursor in a shock wave experiment when a material
is stressed above its elastic limit.
a stress
HEL
Hydrostat (P - C. + Dw2 + Sb2 )
•2/3 Yo0
YMU
Figure 1. Typical Stress-Strain Curve
6
AFWL-TR-69-38
In the second case an estimate of the HEL may be calculated from Y and
the elastic modulus. The elastic modulus is the slope of the stress-strain
* curve in the elastic region given by
PocB2 + 4/3 pCs 2Po CB 0 S
where
P CB 2 - bulk modulus
PocS2 - shear modulus
The Hugoniot elastic limit is then
HEL (PcB2 + 4/3 p C5 YMU
where YMU is the value of uat the elastic limit. Since the Von Mises yield
c):Iterion offsets the stress-strain curve from the hydrostat by 2/3 Y ,
HEL - PoCB2 • YMU + 2/3 0
and
YMU - (1/2) Yo/p 0 CS2
If U5 - U data are available, a hydrostatic pressure is calculated usings pequation (14) and the value 2/3 Y is added to the calculated hydrostat.
Should the experimental points still diverge from the predicted stress, a
purely empirical work hardening term, YADD, is calculated to give a final fit:
P -Cp + D2 + SP3 + 2/3 Y +2/3 (o2-•U YADD
Work hardening is assumed to be a linear function of the strain and YADD is
its value at P - 0.2. P is now a stress term taking into account material
strength and work hardening properties.
7
AFWL-TR-69-38
2. SIGNIFICANCE OF THE U - U RELATIONSHIPs p
As has been noted, the Hugoniots of many materials can be represented by
a linear U - U relationship, U - C + XUs p s 0 p
Departures from linearity can usually be traced to porosity, material
strength properties, or phase transitions. Phase transitions, for example,
whose effect may be difficult to observe in the p-v plane are quite noticeable
in the U - U plane.s p
Since the constant term, C0 , can be determined by direct measurement of
the acoustic wave velocities in an isotropic medium, the zero particle velocity
intercept may then be used to fit the data. Thus, the Hugoniot equation of
state of many materials may be described by p0 , C0 , and X. As has been pre-
viously discussed, use of the yield strength, Yof and a work hardening term,
YADD, improve the accuracy of the curve fit.
In some cases an adequate fit to the stress-strain data cannot be achieved
using equation (14) and a U - U relationship. Several reasons for thiss pdiscrepancy should be noted. In low pressure regions, material strength
properties tend to invalidate the use of equation (14). Also for some materials
the U - U relationship is not linear and has not been treated in this report.s p
For such cases a simple least square fit can be calculated for stress
versus compression. In all cases the linear term is the bulk modulus. Since
a least squares fit to the stress-p data is used, in these cases it is not
applicable to calculate a YADD.
All table data are explained under the section on symbols and units.
8
AFWL-TR-69-38
Table I
MATERIAL IMPEDANCES
_mpedance
Material PoC 0Z -COCo)
Aluminum 2.7 0.544 1.469
Aluminum (1060) 2.703 0.524 1.416
Aluminum (6061-T6) 2.704 0.521 1.409
24ST Aluminum 2.785 0.5375 1.497
921 T Aluminum 2.828 0.5038 1.425
Aluminum (2024) 2.785 0.525 1.462
Antimony 6.6 0.2167 1.430
Avcoat I 1.1 0.1919 0.211
Beryllium 1.851 0.8078 1.495
Bismuth 9.79 0.132 1.292
Boron Nitride 2.142 0.255 0.546
Brass 8.45 0.3784 3.197
Cadmium 8.64 0.2465 2.130
Boron Carbide 1.92 0.2951 0.567
Silicon Carbide 2.32 0.285 0.661
Tungsten Carbide 15.02 0.5181 7.782
Carbon Phenolic 1.49 0.42 0.626
3-D Carbon Phenolic 1.34 0.3 0.402
Chromium 7.12 0.5295 3.77
Cobalt 8.82 0.48 4.23
Copper 8.93 0.392 3.501
Durite 1.38 0.2847 0.393
Epoxy 1.2 0.267 0.32
C-7 Epoxy 1.2 0.265 0.318
9
_; AFWL-TR-69- 38
Table I (cont'd)
Impedance
Material on C - 0oCO
Exon 1.681 0.1948 0.327
Hi-D Glass 6.2 0.3 1.86
Gold 19.24 0.3147 6.055
Graphite Commercial 1.628 0.1477 0.240
Pyrolytic Graphite 2.2 0.4145 0.912
Hafnium 13.31 0.295 3.926
Armco Iron 7.85 0.45 3.533
Iron (Same as Armco)
Lead 11.355 0.21 2.385
Lucite 1.181 0.2188 0.258
Magnesium 1.745 0.4545 0.793
Manganin 8.46 0.3803 3.217
Molybdenum 10.2 0.5163 5.266
Mylar 1.39 0.22 0.306
Nickel 8.86 0.4652 4.122
Niobium 8.58 0.4438 3.808
Nylon 1.14 0.2158 0.246
Palladium 11.95 0.3742 4.472
Paraffin 0.918 0.2968 0.272
AVCO Phenolic Fiberglass 1.9 0.1713 0.325
GE Phenolic Fiberglass 1.94 0.3276 0.636
Chopped Nylon Phenolic 1.21 0.2377 0.288
Tape-Wound Nylon Phenolic 1.22 0.3196 0.390
Quartz Phenolic 1.8 0.3156 0.568
3-D Quartz Phenolic 1.65 0.32 0.528
10
AFWL-TR-69- 38
Table I (cont'd)
Impedance
Material PO Co Z - PooC
X-Cut Crystalline Quartz 2.65 0.5728 1.518
Phenolic Refrasil 1.65 0.3007 0.496
Platinum 21.37 0.3636 7.770
Plexiglas 1.186 0.2745 0.326
Polyethylene 0.92 0.2931 0.270
Polystyrene 1.05 0.299 0.314
Polyurethane 1.265 0.207 0.262
RAD 58B 1.26 0.1202 0.151
OTWR 1.66 0.317 0.526
Series 124 Resin 1.22 0.2259 0.276
Silver 10.49 0.3305 3.467
Stainless Steel Type 304 7.896 0.4557 3.598
Stainless Steel Type 304L 7.903 0.4567 3.609
Steel, Mild EN3 7.84 0.3596 2.819
Tantaluip 16.6 0.33 5.478
Teflon 2.16 0.1424 0.308
Thallium 11.84 0.1887 2.234
Thorium 11.68 0.2174 2.539
Tin 7.28 0.2575 1.875
Titanium 4.51 0.4695 2.117
Tungsten 19.17 0.397 7.610
TWSP 1.66 0.3614 0.600
Uranium-3 wt pct Molybdenum 18.45 0.2553 4.710
Vanadium 6.1 0.5072 3.094
Zinc 7.14 0.3051 2.178
Zirconium 6.505 0.3757 2.444
11
K.
AFWL-TR-69-38
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12
AFWL-TR-69-38
SECTION IV
EQUATION OF STATE
DATA AND GRAPHS
13
AFWL-TR-69- 38
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14
= V 3 3D :- V
-w I 00.00000llk00 000 00 -I 0w nP& .* %Ob L '%4 %4nr.Il QO'%% %%* n*%. % 1% %
Q 0. 0 0. C.
ata
z~h xPPPP z 9 --111
U. u. 1 m CM, "00000 00 110 aE oa, 10 , 10
4I- m 0, Z P CPO, co war.-*su wt .*5
-~ ~ ~ - W 0 P ~ 4P O u N.N~U U ih hi -0 h
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en IL
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on N9 v- a,-' ,- 0Mi 3
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49 V)C a -" % N I 0 W hNi PuM 7 NINrstN N .a C
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OX 9 0 2 z I W.aaao
InaN 4,.,.v 0 a- ý w- .su ew rt An* 1...-
15
AFWL-TR-69-38
200RLUMINUM2.000
1.800
1.600
•1.400
1-2 .00Lu
w
1.000
.800
.600
.400
.200
.080 .160 .240 .320 .400 .480 .560 .640 .720 .800MU
16
inI
C.Ahmin nnnyMuI Y(1-
ID Cb NN 4 44044404444u*44 44
Z ~ ~ ~ a M rtu hi hi hi hi aih ih ih i ih ih
" z " Uz 1 z I1% C % *c 0C, 13C 2(
hi II I II
I w cLlm- @ 6I
0 0 4M P
j U" h U-
o~ C 0 M0 ft - a ft 0~ a 0 D0- D OC,0C0 u E l in v+# 0 * *-
K~~W a 44 0MI or ------ -t -a -- - -
-ý -i M. *tlQ4q.0o4p- 4 - qp-4-. 4in *0it-*cmonaM In . In -. l 10 4U -6 Eq0 q n 0 (M -
* .4 U0 r) in0A CL U * 0A -dig n M5 0mAýfm(d 0 64 M0
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ct X It En # Mopo OUnr *** *4*(** ***MfuCU U) .~4 M CU CD ( i i Nh"hI AihihihiPhihihihi
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4 4A49 _
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K00op*c 0Cn : 0 0 aSI SS SS IIS 3
U C o to *. *4 0 * a .~ * 0 0
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2x M. .0( U vNP NM-YMi
AFWL-TR-69- 38
.700 RLUMINUM (1060)
.630
.560
-, .490m
L0a:E
n .420O)
LJ
.350
.280
.210
.140
.070
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SECTION V
MATERIAL DATA REFERENCE SOURCES
Aluminum
E Reference 39
CL, CS Reference 11
Cp, B Handbook of Physics and Chemistry
Ir Reference 40
Y Taken from a materials handbook0
Aliminum (1060)
CL' CS Reference 46
CB Reference 24
8Cp, Reference 46
r Reference 46
Composition (percent) A1/Si/Fe/Cu/Mn/Mg/Zn/Ti/99.13/0.25/0. 35/0.05/0.03/0.03/0.05/0.03
Aluminum (6061-T6)
CLCS Reference 46
Cp, 8 Reference 46
r Reference 46
Hugoniot Elastic Limit Reference 20
Composition (percent) AI/Mg/Si/Cu/Cr/97.9/l.0/0.6/0.25/0.25
24ST Aluminum
Cp8 0 Reference 13
r Reference 43
168
AFWL-TR-69-38
921-T Aluminum
CLI CS Reference 20
Cpr 8 Reference 20
Reference 20
Aluminum (2024)
CL. C Reference 20L*S
Cp, a Reference 20
r Reference 20
Hugoniot Elastic Limit Reference 20
CB Reference 20JB
Antimony
Cp, Handbook of Physics and Chemistry
r Calculated from Cp, 8
Y Handbook of Physics and Chemistry
*Phase transitions at 115 Kb and 135 Kb not indicated in this report. SeeJournal of Applied Physics, Vol 39, No. 7, "Dynamic Observations of the Courseof a Shock Induced Polymorphic Phase Transition in Antimony."
Avcoat
CL, CS Reference 46
Cp, a Reference 46
r Calculated from Cp, 8
Beryllium
E Reference 39
CL9 CS Handbook of Physics and Chemistry
Cp,8 Handbook of Physics and Chemistry
r Calculated from C., B
Y Taken from a materials handbook
169
"AFWL-TR-69-38
Bismuth
E Reference 39s
CL, CS Reference 39
Cp, B Reference 13
r Reference 40
*Phase transition not indicated in this report.
Boron Nitride
E Data from McDonnell Douglas Corporations
r Reference 44
Brass
CL, CS, Cp, a, Yo Handbook of Physics and Chemistry
r Calculated from Cp, B
Cadmium
E Reference 39s
CL, CS Reference 13
CP, Reference 40
r Reference 40
Boron Carbide
E 6Data from McDonnell Douglas Corporation(estimate)
r Reference 48
Silicon Carbide
E Data from McDonnell Douglas Corporation* (estimate)
CL, CS Reference 20
F Reference 48
170
AFWL-TR-69-38
Tungsten Carbide
E Data from McDonnell Douglas Corporations (estimate)
CL, CS Reference 20
Reference 48
Carbon Phenolic
E Reference 44s
CL,CS Reference 46
Cp, 8Reference 46
Calculated from Cp. a
Chromium
E Reference 39s
CL, CS Reference 13
Cp, a Handbook of Physics and Chemistry
r Reference 20
Cobalt
E Reference 39S
Cp, 8Reference 13
Calculated from Cp, 0
Copper
E Reference 39S
CL. CS Reference 13
Cp, 6 Handbook of Physics and Chemistry
y Reference 20
Y Handbook of Physics and Chemistry0
171
AFWL-TR-69- 38
Epoxy
CL, CS Reference 20
CB Reference 26
8 Reference 48
AVCO Phenolic Fiberglass
CL 0.435 cm/microsec (a-direction), 0.272cm/microsec (c-direction) Reference 43
Cp, 8 Reference
GE Phenolic FiberglassCL 0.434 cm/microsec (a-direction), 0.333
cm/microsec (c-direction) Reference 43
C S Calculated from CL" CB (approximate)
Cp, a Reference 46
r Reference 46
Gold
E Reference 39s
CL" CS Reference 46
Cp, Reference 40
r' Reference 46
Y Taken from a materials handbook0
Pyrolytic Graphite
E Estimated for medium to low pressures
sReference 44
8 Reference 43
r Calculated from Cps a
*For further data see (1) AFWL-TR-64-42, Reference 36; (2) AFWL-TR-64-92,Vol II, Reference 38; (3) Boeing D2-90099, Reference 29; (4) Journal ofApplied Physics, Vol 34, No. 4, 844 (1963), Reference 35
172
A*
AFWL-TR-69- 38
Hafnium
E Reference 39
CL' CS Reference 20
CPO Reference 40
r Reference 40
Iron
E Reference 39s
CL, CR Reference 21LCS
Cp, a Reference 40
r Reference 20
Hugoniot Elastic Limit Taken from Reference 20 where elasticlimit varies from 15 kbar for FINE GRAINHARD to 9 kbar for LARGE GRAIN SOFT iron
*The low pressure data below the phase transition at 130 kbar is Armco Iron.Material properties indicated for Armco Iron and Iron have been consideredthe same.
Lead
E Reference 39s
CL, CS Reference 13
Cp 8 Reference 40
I' Reference 46
Lucite
CL' CS Reference 20
Magnesium
E Reference 395
CL' CS Reference 17
Cp, 8 Handbook of Physics and Chemistry
173
ATWL-TR-69- 39
Magner•',= (cont'd)
Y Handbook of Physics and Chemistry0
r Reference 40
Mangai in
Cp, a Reference 22
r Calculated from Cp,
Composition (percent) Cu/Mn/Ni/84/12/4
Molybdenum
E Reference 39s
C P Reference 40S
r Reference 40
Mylar For at.ditional data see References 29and 23
Nickel
E Reference 39s
CL, Cs Reference 13
Niobium
E Reference 395
CL, CS Reference 20
Cp, 8 Reference 40
r Calculated from Cp, 6
Nylon (Polyamide--C6 HI1 N 0)
CS Reference 46
C1 Calculated from CS, CB
Cp, 8 Reference 46
r Reference 46
174
AFWL-TR-69- 38
Palladium
E Reference 39Es
C1 , Cs Reference 20
C 8, a Reference 40
I, Calculated from Cp, a
Paraffin
Cp, 8 Handbook of Physics and Chemistry
Chopped Nylon Phenolic
CL Reference 43 (c-direction)
C S Calculated from CL, CB
Cp, 8 General Electric Cincinnati TestingLaboratory information
Calculated from CPO 8
Tape-Wound Nylon Phenolic
CP, 8 General Electric Cincinnati TestingLaboratory information
Calculated from CpI 8
X-Cut Crystalline Quartz All data taken from Reference 49
Quartz Phenolic
Es, CPO 8 Data from McDonnell Douglas Corporation
F Calculated from Cp, 8
3-D Quartz Phenolic
E Data from McDonnell Douglas Corporationfor Phenolic Quartz--35 percent resin,
P0 N 1.68
175
AFWL-TR-69- 38
Platinum
E Reference 39
CL, CS Reference 17CCS
Cp8 a Reference 13
Calculated from Cp, 8
OTWR
E ApproximateS
CL Reference 43 (a-direction)
C S Calculated from CL, CB
Cp8 Reference 46
r Calculated from Cp, 8 (AFUL-TR-65-188data)
Phenolic Refrasil
E Reference 44 (Phenolic Resin data)s
Tape-Wound Silicon Phenolic
E Data from McDonnell Douglas Corporations for Phenolic Quartz--35 percent resir.,
Po = 1.68
Plexiglas
CL, CS Reference 20
Cp8 8 Reference 46
r Reference 46
Polyethylene
E AFWL-TDR-64-42B
CL, CS Reference 46
CpI 8 Reference 46
r Reference 46
176
AFWL-TR-69-38
PolystyreneData from McDonnell Douglas Corporation
Polyurethane
CL, CS Reference 20
RAD 58B
CL Reference 43
CS Calculated from CL, CB
Reference 43
Silver
E Reference 39S
C', CS Reference 13
CPO a Reference 40
F Calculated from Cp.
Stainless Steel Type 304L
CL, CS Reference 20
C 8 AFWL notes on Stainless Steel
r Calculated from C., a
Composition (percent) Cr/Ni/18/8
Stainless Steel Type 304
CL, CS Reference 20
Cp, r, r Valuea used as for Stainless SteelType 304L
Hugoniot Elastic Limit Reference 20
Steel, Mild EN3
Handbook of Physics and Chemistry
Composition (percent) Fe/C/Mn/98.75/0.25/1.0
177
AFWL-TR-69-38
Tantalum
E Reference 395
CLCS Reference 13
Cp,8 Reference 40
r Reference 40
Teflon
Es Data from AVCO Corporation
CS Reference 46
CL Calculated from CS, CB
Cp. 8 Reference 46
r Reference 46
Thallium
Cp8 Handbook of Physics and Chemistry
r Reference 40
Thorium
E Data from McDonnell Douglas Corporation
Cp, B Handbook of Physics and Chemistry
r Reference 40
Hugoniot Elastic Limit Reference 20
Tin
E Reference 39
CL, Cs Reference 13
CpI 6 Handbook of Physics and Chemistry
Reference 40
178
AFWL-TR-69-38
Titanium
E Reference 39S
C, *Handbook of Physics and ChemistryLp, • Handbook of Physics end Chemistry
r Reference 40
*The phase transition at 175 kbar is not indicated in this report. SeeReference 20.
Tungsten
E Reference 39
CLs Cs, 8, CP, Yo Handbook of Physics and Ckamistry
r Calculated from Cp, a
Uranium-Molybdenum Alloy
C Reference 20H C' CS
Cp, a Reference 20
r Reference 20
Vanadium
E Reference 395
Cp, a Reference 40
r Reference 40
Zinc
Ee Reference 39
CL, CS Handbook of Physics and Chemistry
CPO a Handbook of Physics and Chemistry
r Reference 40
179
AFWL-TR-69-38
Zirconium
E Reference 39U
CLt CS Reference 20
Cp8 Reference 40
r Reference 40
180
180
AFWL-TR-69-38
REFERENCES*
1. Unpublished data from the Air Force Weapons Laboratory Gas Gun Facility.
2. Wagner, M. H., Waldorf, W. F., Jr., Loule, N. A., Determination ofHugoniot Equations of State for Polymers and Reentry Vehicle Materialsand Investigations of Fracture Phenomena, AFSWC-62-66, Vol I, Air ForceForce Weapons Center, Kirtland AFB, NM.
3. Marsh, S. P., taken from private communication, Los Alamos.
4. Lawrence Radiation Laboratory Data.
5. McQueen, R. C., Marsh, S. P., "Equation of State for Nineteen MetallicElements from Shock-Wave Measurements to Two Megabars," Journal ofApplied Physics, Vol 31, No. 7.
6. Lundergren, C. D., The Hugonict Equation of State of 6061-T6 Aluminumat Low Pressures, Research Report SC-4637 (RR), Sandia Corporation,September 1961.
7. Anderson, G. D., Doran, D. G., Fahrenbructi, A. L., Equation of Steae ofSolids--Aluminum and Teflon, AFWL-TR-65-147, Air Force Weapons Labora-tory, Kirtland AFB, NM, December 1965.
8. Al'tshuler, L. V., Kormer, S. B., Bakanova, A. A., Trunin, R. F.,"Equation of State for Aluminum, Copper, and Lead in the High PressureRegion," Soviet Physics/JEPT 11, p. 573, 1960.
9. Taken from progress report No. 11, DA-49-146-XZ-280O
10. Al'tshuler, L. V., Kormer, S. B., Bakanova, A. A., Trunin, R. F.,"Equation of State for Aluminum, Copper, and Lead in the High PressureRegion," Soviet Physics/JEPT 11, p. 766, 1960.
11. Skidmore, I. C., Morris, E., Thermodynamics of Nuclear Materials, p. 173FF, 1962.
12. Fowles, G. R., "Shock Wave Compression of Hardened and Annealed 2024Aluminum," Journal of Ap2pled Physics, Vol 32, p. 1475, 1961.
13. Walsh, J. M., Rice, M. H., McQueen, R. G., Yarger, F. L., '"Shock-WaveCompression of Twenty-Seven Metals," Physical Review, Vol 108, No. 2,pp. 196-216, October 1957.
14. Al'tshuler, L. V., Bakanova, A. A., Trunin, R. F., "Shock Adiabats andZero Isotherms of Seven Metals at High Pressures," Soviet Physics/JEPT,Vol 15, p. 65, 1962.
*References 2 through 18 are taken from LRL Compendium of Shock Wave Data.
181
r
AFWL-TR-69-38
REFERENCES (cont'd)
15. Al'tshuler, L. V., Bakanova, A. A., Trunin, R. F., "Shock Adiabats andZero Isotherms of Seven Metals at High Pressures," Soviet Physics/JEPT,Vol 15, p. 65, 1962.
16. Al'tshuler, L. V., Krupnikov, K. K.. Brazhnik, M. I., "Dynamic Compressi-bility of Metals under Pressure from 400,000 to 4,000,000 Atmospheres,"Soviet Physics/JEPT, Vol 7, p. 614, 1958.
17. McQueen, R. G., Marsh, S. P., Report No. GMX-6-566, Los Alamos ScientificLaboratory, pp. 51-62, 1964.
18. Krupnikov, K. K., Bakanova, A. A., Soviet Physics/JEPT, Vol 8, p 205, 1963.
19. Rinehart, J. S., Compilation of Dynamic Equation of State Data for Solidsand Liquids, Technical Publication 3798, US Naval Ordnance Test Station,May 1965.
20. McQueen, R. G. et al., High Velocity Impact Phenomena, R. Kinslow, ed.,Academic Press, NY (taken from preprint copy).
21. Taylor, John W., Rice, M. H., "Elastic-Plastic Properties of Iron,"Journal of Applied Physics, Vol 34, p. 364, 1963.
22. Keough, D. D., Procedure for Fabrication and Operation of Manganin Shockrressure Gages, AFWL-TR-68-57, Air Force Weapons Laboratory, Kirtland AFB,t l, August 1968.
23. Louie, N. A., Kinney, W. W. , Reid, R. D., Jr., Dynamic Properties ofMaterials, AFWL-TR-68-101, Air Force Weapons Laboratory, Kirtland AFB, NM,196g.
24. Hunsun, D. E., Barker, L. M., "Dynamically Determined Pressure-VolumeRelationships for Aluminum, Copper, and Lead," Journal of Applied Physics,Vol 37, pp. 1652-1660, 1966.
25. Andersou, G. D., Fahrenbruch, A. L., Equation of State of Solids, II--Aluminum and Teflon," AFWL-TR-67-43, Air Force Weapons Laboratory, KirtlandAFB, NM, Soptember 1967.
26. Guess, T. R., Some Dynamic Mechanical Properties of an Epoxy, SandiaCorporation, New Mexico, SC-DR-68-343, 1968.
27. Los Alamos Scientific Laboratory, private communication.
28. Wackerle, J., "Shock-Wave Compression of Quartz," Journal of AppliedPhysics, Vol 33, No. 3, 1962.
29. See Boeing Document, Equation of State of Mylar, Boeing-D2-90099, 1962.
30. Wagne:, N. H., Louie, N. A., Determination of Hugoniot Equation-of-Statefir Polymers and Reentry Vehicle Materials and Investigations of kracturePheosena, SWC-TDR-62-66, Vol II, Air Force Special Weapons Center,Kirtland AFB, 1•4, August 1962.
182
AFWL-TR-69-38
REFERENCES (cont'd)
31. Hartman, W. F., Smith, J. H., Response of Several Ablation Materials toDynamic Loading, SC-4647, Sandia Corporation, NM, January 1962.
32. Bancroft, D., Peterson, E. L., Minshall, S.. "Polymorphism of Iron atHigh Pressure," Journal of Applied Physics, Vol 27, No. 3, 1956.
33. Isbell, W. M., Froula, N., Shipman, F. H., Shock Wave Propagation andEquation-of-State Measurements of Quartz Phenolic, Final Report, BSD-TR-67-25, Vol 3, 1967.
34. Isbell, W. M., Froula, N., Shipman, F. H., Shock Wave Propagation andEquation-of-State Measurements of Quartz Phenolic, Final Report, BSD-TR-67-25, Vol 3, 1967.
35. Doran, D. G., "Hugoniot Equation of State of Pyrolytic Graphite to 300Kilobars," Journal of Applied Physics, Vol 34, No. 4, p. 844, 1963.
36. Allen, R. G., Goodwin, L. K., Study of X-Ray Countermeasure Methods,Final Report, AFWL-TDR-64-42, Air Force Weapons Laboratory, Kirtland AFB,NM, June 1964.
37. Morgan, D. T., Rockowitz, M., Atkinson, A. L., Measurement of GruneisenParameter and the Internal Energy Dependence of the Solid Equation ofState for Aluminum and Teflon, AFWL-TR-65-117, Air Force Weapons Labora-tory, Kirtland AFB, NM, 1965.
38. Morgan, D. T., Rockowitz, M., Atkinson, A. L., Measurement of the GruneisenParameter and the Internal Energy Dependence of the Solid Equation ofState of Aluminum and Teflon, AFWL-TR-65-117, Air Force Weapons Laboratory.Kirtland AFB, NM, October 1965.
39. Stull and Sinke, Thermodynamic Properties of the Elements, AmericanChemical Society, Washington, 1956.
40. Seitz, F., Turnbull, D., Solid State Physics, Vol 16, Academic Press, 1964.
41. "The Compressibility of Pyrolytic Graphite," US Naval Ordnance Laboratory,J. Chem. Phys., Vol 40, p. 71, 1963.
42. Penning, J. R., Davies, F. W., Hugoniot Equation of State of Mylar, takenfrom preprint of Boeing Document D2-125304-1.
43. Asay, J. R., Darr, A. J., Arnold, N. D., Guenther, A. H., Ultrasonic WaveVelocity-Temperature Studies in Several Plastics, Plastic Foams and NoseCone Materials, AFWL-TR-65-188, Air Force Weapons Laboratory, Kirtland AFB,NM, March 1966.
44. Radiation Damage Study (RADS), Vol 5, Final Report, Material Data Handbook,BSD-TR-66-372, 1966.
45. Louie, N. A., Anderson, W. H., Experimental Fracture Studies and Equation-of-State Measurements, Final Report, RTD-TDR-63-3102, Air Force WeaponsLaboratory, Kirtland AFB, NM, March 1964.
183
AFWL-TR-69-38
REFERENCES (cont'd)
46. Asay, J. R., Urzendowski, S. R., Guenther, A. H., Ultrasonic and ThermalStudies of Selected Plastics..Laminated Materials, and Metals, AFWL-TR-67-91, Air Force Weapons Laboratory, Kirtland AFB, NM, January 1968.
47. Crotwell, G. P., Jr., Hugoniot Data on Several Materials, AFWL-TR-68-82,Air Force Weapons Laboratory, Kirtland AFB, NM, October 1968.
48. Toulaukian, Y. S., Thermodynamic Properties of High Temperature SolidMaterials, 6 Volumes, Thermophysical Properties Research Center, PurdueUniversity, Macmillan, 1967.
49. Bakken, L. H., Anderson, P. D., Memo, "Correction of Equation of StateValues in SCL-TM-67-118," Sandia Corporation, New Mexico, 1968.
184
;mj.•gj .T TTRfl,
securi ty Classification
DOCUMENT CONTROL DATA. R & 0(Security classification of title, body of abstrac I mnd indexifig mnnotatlon nlw.t be enterd w1 he,. til overall report II classilledl
1 ORIGINATING ACTIVITY (Corporate author) 2a0. REPORT SECURITY CLASSIFICATION
Air Force Weapons Laboratory (WLRP) 2b. GROUP .T rTPTKirtland Air Force Base, New Mexico 87117
3. REPORT TITLE
COMPILATION OF HUCONIOT EQUATIONS OF STATE
4 DESCRIPTIVE NOTES (7ype of report and Inclusive date.)
.Turn lQ1A-+Tnin.ry 1QRQS. AU THORI (FirS t name, middle initial. last name)
Brian J. Kohn, Lieutenant, USA"
8. REPORT DATE 74. TOTAL NO. MF PAGES REFS
a•.4 10•198[ 49.CON4AT -C-TSOR GRANT NO. go ORIGINATOR'S REPORTNUMBER(S)
b, PROJECT NO. 5710 AFWL-TR-69-38
c Subtask No. RAS 1114 (15.025) 9b. OTHER REPORT NOIS) (Any ot.her nu•b•s that may be ase•. edthis report)
d.
10 DISTRIBUTION STATEMENT This document is subject to special export controls and eachtransmittal to foreign governments or foreign nationals may be made only with priorapproval of AFWL (WLRP), Kirtland AFB, NM, 87117. Distribution is limited becauseof the technologv discussed in the report.11, SUPPLEMENTARY NFTES 12. SPONSORING MILITARY ACTIV'TYCI
AFWL (WLRP)Kirtland AF8, NM 87117
I, ABSTRACT
(Distribution Limitation Statement No. 2)Computer codes for predicting material response to shock loading in and above theelastic region of a material require a knowledge of the Hugoniot equation of state.Hugoniot and material data have been compiled from various sources on materials ofinterest and presented in a form which condenses the needed computer code inputs toan easily accessible source.
£
DD NOV .,1473 UNCLASSIFIEDSecurstv CIad s• i-•a',,n
14 9 N tN LINK CRE~V WORD$
PRNOL[ OT ROLE WT ROLE W T
HugoniotMie-Gruneisen equation of stateElastic limitHydrostat 9
Stress-strain
II
A
UNCIASSIFIF)Security Classification