Cratering in low density targets, and comparisons of various hypervelocity projectile-target combination

Cannon, E. T.

Turner, G. H.

English

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CRATERING IN LOW-DENSITY TARGETS 
by Emerson T. Cunnon and Gerry H. Tzwner 
Prepared by 
UTAH RESEARCH & DEVELOPMENT CO., INC. 
Salt Lake City, Utah 
f Or 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION . WASHINGTON, D. C. . JUNE 1967 / 
; 
5” 
https://ntrs.nasa.gov/search.jsp?R=19670017226 2020-03-12T11:21:09+00:00Z
TECH LIBRARY KAFB, NM 
NASA CR- 798 
CRATERING IN LOW-DENSITY TARGETS 
By Emerson T. Cannon and Gerry H. Turner 
Distribution of this report is provided in the interest of 
information exchange. Responsibility for the contents 
resides in the author or organization that prepared it. 
Prepared under Contract No. NASw-1196 by 
UTAH RESEARCH & DEVELOPMENT CO., INC. 
Salt Lake City, Utah 
for 
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 
For sale by the Clearinghouse for Fcdcral Scientific and Technical Information 
Springfield, Virginia 22151 - CFSTI price $3.00 

ABSTRACT 
Craters were formed with aluminum, steel, nylon, 
and magnesium projectiles in targets made of rigid 
and flexible polyurethane foams, foamed glass, 
and natural pumice. The velocity range involved 
was 4.7 to 6.9 km/set. Crater dimensions and 
volumes were determined. Values of shear strength 
and shearing energy were determined for all target 
materials. Some comparison was done among dif- 
ferent projectile-target combinations to better 
understand the reasons for differences in crater 
shape. Values were determined for target mass 
displaced in a crater per unit of energy involved. 
It was found that projectiles of some materials are 
much more efficient in cratering than are others; 
steel projectiles being less efficient than the other 
types used by as much as a factor of one-half,, Plots 
were made showin 
c bpht) (PpVVSt) 
[ 9 
l/V0 and p/d being equal to 
where c and b are constants, 
V 1s crater volume, Vo is projectile volume, p is 
crater depth, d is projectile diameter, p is density, 
v is projectile velocity, s is shear strength, and 
the subscripts p and t denote projectile and target. 
It was found that in the volume relationship, b 
remains constant at l/2 for each target material, 
but c varies from 0.2 to 1 .O . In the depth relation- 
ship, b is l/3 for rigid targets and l/2 for flexible 
ones, with c varying from 0.025 to 0.3. 
iii 
CRATERING IN LOW-DENSITY TARGETS 
By Emerson T. Cannon and Gerry H. Turner 
Utah Research & Development Co., Inc. 
SUMMARY 
Craters were formed with aluminum, steel, nylon, and magnesium 
projectiles in targets made of rigid and flexible polyurethane foams, foamed 
glass, and natural pumice. The velocity range involved was 4.7 to 6.9. 
km/set. Crater dimensions and volumes were determined. Values of shear 
strength and shearing energy were determined for all target materials. Some 
comparison was done among different projectile-target combinations to better 
understand the reasons for differences in crater shape. Values were deter- 
mined for target mass displaced in a crater per unit of energy involved. It 
was found that projectiles of some materials are much more efficient in crater- 
ing than are others: steel projectiles being less efficient than the other types 
used by as much as a factor of one-half. Plots were made showing V/V, and 
p/d being equal to c [(pp/pt)(ppv2/St)) b where c and b are constants, V is 
crater volume, V, is projectile volume, p is crater depth, d is projectile 
diameter, p is density, v is projectile velocity, s is shear strength, and 
the subscripts p and t denote projectile and target. It was found that in the 
volume relationship, b remains constant at l/2 for each target material, but 
c varies from 0.2 to 1 .O. In the depth relationship, b is l/3 for rigid targets 
and l/2 for flexible ones, with c varying from 0.025 to 0.3. 
INTRODUCTION 
A limited amount of investigation has been done concerning crater- 
ing in materials having a specific gravity of less than one. Considerable in- 
terest is currently being shown in the formation of craters by high-velocity 
projectiles in low-density materials. This interest arises because of consider- 
ation being given to materials for shielding spacecraft, and because of a desire 
to determine lunar-surface properties. To better understand cratering processes 
in low-density materials, an experimental program has been carried out to 
determine the effect of various target properties on the observed crater. The 
results of that investigation are presented in this report. 
EXPERIMENTAL METHODS 
Spherical projectiles were accelerated by a light-gas gun to veloc- 
ities between 4.7 and 6.9 km/set. The high-speed projectiles were allowed 
to hit a specified target in an evacuated range at room temperature. The pro- 
jectiles which were used in the experimental program were stainless steel 
(l/16 inch, 3/32 inch and l/8 inch in diameter), aluminum (l/16 inch and l/8 
inch in diameter), nylon and magnesium (both l/8 inch in diameter). The size 
of the projectile used for a particular shot was mainly based on the “stopping 
power” of the target. The target materials were chosen by their density (less 
than one gm/cm3) and their availability. A series of rigid polyurethane foams 
having densities of 0.034, 0.065, 0.072, 0.082, 0.16, 0.27, 0.32 and 0.62 
gm/cm3 was supplied by Goodyear at no cost. Flexible polyurethane (density 
0.0 80 gm/cm3), foamed glass (0.15 gm/cm3) and natural pumice (0.51 and 
0.65 gm/cm3) were obtained locally. All types of the above-mentioned pro- 
jectiles were fired into each type of target where it was practical. 
Crater dimensions were determined by cross-sectioning the targets. 
Crater volumes were calculated from the measurement of these cross-sections 
at intervals along the axis of the crater. Because the diameter of each crater 
was not constant, it was necessary to consider average values for a number 
of segments in each crater when calculating its volume. Target material 
densities were calculated from the volumes and weights of uniformly shaped 
specimens. 
The shear strength of each target material was determined. This was 
done by measuring, with a Universal testing machine, the maximum force nec- 
essary to shear a one-inch diameter plug from a specimen. Figure 1 is a sketch 
of the testing apparatus. The energy used in shearing the specimen was calcu- 
lated for each test by plotting force as a function of distance traveled by the 
die, and then calculating the area under the curve. A typical force-distance 
diagram is shown in Figure 2. Two or more tests were made with each material 
and the specimen thickness was varied by a factor of two. Good agreement 
was shown in most instances. The results of these tests are presented in 
Table I. The numbers given are either averages or represent, in our’ opinion, 
the most reliable value. Values are given for two different energy relation- 
ships; energy per unit area used in shear up to the point of maximum stress, 
which we define as the yield point, and energy per unit area used in shear 
during the entire punching operation. As examples of actual values obtained, 
the data concerning the rigid polyurethane foams are shown in Figures 3 and 
4. Figure 3 shows shear strength as a function of material density, and 
Figure 4 shows energy used in shear as a function of material density. 
2 
- 
Dial 
Indicator 
l-inch Diameter Die 
\ Guide Plates 
Sample 
Shear Plate 
I Base 
Force 
Testing 
e Machine 
\ Head 
Figure 1. Diagram of the apparatus used in 
shear testing low-density materials. 
- 
O- 
o- 
C- 
I 
.04 
I I I I I 
.08 .12 .16 .20 024 
Distance (inch) 
Figure 2. Plot of force applied as a function of distance 
moved by the die in testing a 0.25 6-inch thick 
rigid polyurethane foam of density 0.27 g/cm3. 
3 
TABLE1 
SHEARSTRENGTHANDSHEARING-ENERGYDATA 
FOR LOW-DENSITYTARGET MATERIALS 
Target Material 
Shearing Total 
Energy to Shearing 
Density Shear Strength Yield Point 
(g/cm3) (dyne/cm2) 
Energy 
(Joule/cm2) (Joule/cm2) 
Rigid Polyurethane Foam 
II II II 
Flexible II 
FoamedGlass 
Natural Pumice 
II II 
0.034 
0.065 
0.072 
0.082 
0.16 
0.27 
0.32 
0.62 
0.080 
0.15 
0.51 
0.65 
4.2 x106 
5.7 
5.9 
6.4 
13 
35 
52 
200 
11 
1.8 
3.3 
3.9 
0.081 0.26 
0.092 0.41 
0.10 0.46 
0.11 0.53 
0.20 0.99 
0.32 1.45 
0.53 1.56 
1.39 1.41 
0.12 0.16 
0.045 0.14 
0.015 0.077 
0.090 0.21 
250 r 
/ 
I I 
I - 
50 
I I I I I I 
0 
0 .3 .4 
Material Density (g/cm3) 
.5 .6 
Figure 3. Shear strength as a function of material density for rigid polyurethane foams. 
2.0 
1.5 
1.0 
.5 
0 To&l shearing ehergy per unlit area to pukch through ‘specimen 
I 
v Shearing energy per unit area to yield point 
0 
0 
.2 .3 .4 .5 .6 .7 
Material Density (g/cm3) 
Figure 4. Total shearing energy per unit area required to punch through a specimen 
and shearing energy per unit area used to the specimen yield point, as 
functions of material density for rigid polyurethane foams. 
RESULTS 
Crater Shape 
General variations in crater shape are illustrated by comparing 
cross-sections of craters formed in rigid polyurethane foams of various 
densities and craters formed with projectiles of different materials. Figure 
5 compares the shapes of craters formed in a foam of density 0.32 g/cm3 
by l/8-inch diameter projectiles of nylon, magnesium, aluminum and steel. 
This sketch shows that crater depth is approximately proportional to projec- 
tile mass and thus to projectile momentum. The jagged crater walls with 
nylon, magnesium, and aluminum projectiles seem to indicate that the pro- 
jectiles were fragmented. The smooth walls of the crater formed by the 
steel projectile seem to indicate that the projectile remained intact. Figure 
6 compares the shapes of craters formed in foams of densities 0.16, 0.27, 
0.32, and 0.62 g/cm3 by l/l 6-inch diameter steel projectiles. Of interest 
in this sketch is the change in crater depth between targets of densities 
0.16 and 0.27. This difference in shape suggests a possible change in 
cratering mechanism. Data concerning projectile velocity, mass and energy; 
and crater depth and volume, are tabulated in Figures 5 and 6. 
Crater Size 
The size, or volume, of a crater is naturally dependent upon the 
density of the target material. As a more consistent method of comparing 
size with other factors, the target mass displaced by the crater (the product 
of target density and crater volume) is considered. Figure 7 shows target 
mass displaced per unit of energy as a function of target density for the 
impact of aluminum, steel, nylon and magnesium projectiles into rigid poly- 
urethane foams. Best-fit straight lines, obtained by the least-squares 
method, are drawn through the data points. The vertical positions of the 
lines might be considered as a measure of the cratering efficiency of the 
projectile material: aluminum projectiles are thus most efficient, and steel 
projectiles are least efficient. The slopes of the lines are governed by 
changes in target material properties which change as the density changes. 
Shear strength is considered to be important in this regard and, as shown 
in Figure 3; it increases non-linearly with target density. 
Values of target mass displaced per unit of energy, or cratering 
efficiency, were calculated for craters formed by aluminum, nylon, magne- 
sium, and steel projectiles into foamed-glass and flexible polyurethane 
7 
Projectile Projectile Projectile Impact Projectile Crater Crater 
Materials Mass Velocity Energy Depth Volume 
hd (km/set) (Joule) (cm) (cm31 
Nylon 20 5.64 320 2.0 2.2 
Magnesium 30 5.61 470 2.5 2.2 
Aluminum 47 5.55 720 5.5 6.5 
Steel 131 5.43 1930 24.5 10.0 
Figure 5. Sketch showing the actual shapes and sizes of craters 
formed in rigid polyurethane foam of density 0.32 g/cm3 
by l/8-inch diameter projectiles of different materials. 
Projectile Projectile Crater Crater 
Velocity Energy Depth Volume 
(km/set) (Joule) (cm) (cm31 
5.45 
5.94 290 8.0 1.1 
2.9 0.5 
Figure 6. Sketch showing the actual shapes and sizes of craters formed 
in rigid polyurethane foams of various densities by l/16-inch 
diameter steel projectiles having a mass of 16.3 mg. 
I I I I I I 
V l/l 6” Aluminum 
V l/8” Aluminum 
: ;;;r;:::; 
0 3/32” Steel 
III l/8” Nylon 
0 l/8” Magnesium 
Steel - 
0 
Figure 7. 
.l .2 .3 .4 
Target Density (g/cm31 
.5 .b .7 
Target mass displaced per unit of energy as a function of target density for 
the impact of aluminum, steel, nylon and magnesium projectiles into rigid 
polyurethane foams. 
foam targets. These values are given in Table II. They are averages of at 
least four craters with each projectile and target combination. 
TABLE II 
AVERAGE VALUES OF CRATERING EFFICIENCY 
FOR SEVERAL PROJECTILE-TARGET COMBINATIONS 
Projectile Craterinq Efficiency (q/Toule) 
Material Foamed-Glass Tarsets Flexible Polyurethane Foam Tarqets 
Nylon 5.2 x 10-Z 0.57 x 10-3 
Aluminum 4.3 0.59 
Magnesium 3.6 
Steel 3.0 0.76 
Cratering efficiency has been related to the energy used in shear- 
ing . It was found that for targets of rigid polyurethane foam and foamed glass, 
target mass displaced by the crater per unit of energy is a linear function of 
total shearing energy; the relationship being approximated by the equation 
CE = d - 1 .O Etotal (1) 
where CE = Cratering efficiency 
Etotal = Total energy to shear 
d = A constant for each projectile material. 
It was also found that cratering efficiency is a non-linear function of the 
shearing energy required to yield; this relationship being 
CE= . = 
1 + 2.0 Eyield 
(2) 
where CE = Cratering efficiency 
Eyield = Shear energy to yield 
c =. A constant for each projectile material. 
11 
Target Shear Strength Considerations 
Sorensen* established, by dimensional analysis methods, rela- 
tionships correlating target and projectile properties and parameters. These 
relationships concern craters formed in metals by projectiles of the same or 
different metals. 
- = 0.12 (?) ‘“[g) o.845 V 
VO 
(3) 
and 
z = 0.311 (EX) 1’6(Pos;2) o*282 
tihere 
v = Crater volume 
v, = Projectile volume 
Pp = Projectile density 
Pt = Target density 
V = Impact velocity 
St = Target shear strength. 
On the basis of these relationships, the data concerning cratering 
in low-density materials were reduced and plotted with V/V0 and p/d on the 
ordinate as functions of [ bpht) (Pp v2/st)] on the abscissa. Data for the 
ratio V/V, are shown in Figure 8, and those for p/d are shown in Figure 9. 
Individual data points are shown in Figures 8 and 9 for rigid polyurethane 
foams, but are omitted for flexible polyurethane foam, foamed glass and 
natural pumice D 
For the volume relationship, it was found that 
V 9 
[(Ii i] 
Pp v2 m 
v, 
= c 
5 % 
* Sorensen# N. R., “Systematic Investigation of Crater Formation in Metals, ” 
Seventh Hypervelocity Impact Symposium Proceedings, Vol. VI, p 281, 1965 
12 
10’ 
10: 
V 
vO 
10: 
1 
I I I I 
l/l 6 ” Aluminum 
3/3 2 ” Aluminum T 
Fi 
l/l 6” Steel 
3/32” Steel 
0 l/8” Steel 
l/8” Nylon 
l/8” Magnesium 
. 
Foamed Glass 
and Pumice 
. 
Polyurethane Foam 
(c = 0.2) 
IU” I” 
Figure 8. Log-log plot showing V/V, as a function of (pp/pt) (pp v2/St) for craters formed in rigid 
and flexible polyurethane foams, foamed glass, and pumice by aluminum, steel, nylon 
and magnesium projectiles. Individual data points are shown only for rigid polyurethane 
foam. 
F 
bb 
10: 
10 
: 
10 
I I I I 
l/l 6 ” Aluminum 
l/8” Aluminum 
l/l 6” Steel 
3/32” Steel 
l/8” Steel 
l/8” Nylon 
l/8” Magnesium 
Flexible Polyurethane Foam 
;= .025[$2(k$.)1’2 
0 
Figure 9. Log-log plot showing p/d as a function of (pp/pt)(~p v2/St) for craters formed in rigid 
and flexible polyurethane foams, foamed glass, and pumice by aluminum, steel,. nylon, 
and magnesium projectiles. Individual data points are shown only for rigid polyurethane 
foam. 
where 
C = a constant for each target material. 
Values for c are 1 .O for rigid polyurethane foam, 0.2 for flexible 
polyurethane foam, and 0.5 for foamed glass and natural pumice. The data 
agree well with these equations with the steel data showing the most scatter. 
This relationship indicates that crater volume is proportional to projectile 
momentum and to (l/pt St) li2. 
For the depth relationship, it was found that for rigid polyurethane 
foam, foamed glass, and natural pumice targets 
3 = c[(s$~)j 1’3 (6) 
c being 0.3 -for rigid polyurethane and 0 .l for foamed glass and natural pumice. 
For flexible polyurethane 
% = 0.025[( 2) [$)11’2 (7) 
CONCLUSIONS 
The shape and size of a crater formed in a low-density materialvary 
considerably with different projectile-target combinations. In rigid polyure- 
thane foams, the cratering data which compare target mass displaced per unit 
of energy with target density show that steel projectiles are less efficient (by 
a factor as low as one-half) than aluminum, magnesium, or nylon projectiles. 
With foamed-glass targets, approximately the same results are obtained. This 
suggests that projectile properties, perhaps strength, are important in this 
regard. 
Target shear strength is seen to be a factor in correlating data from 
the various target and projectile combinations investigated. Plots of dimen- 
sionless relationships showing V/V, and p/d as being equal to 
v"/st,l b show consistency in the data from each type of target 
15 
material. However, for the volume relationships, different coefficients were 
found for the different targets. Different coefficients and exponents were 
found for the penetration data. This does not agree with similar relationships 
with cratering in metals in which c and b remain constant for all projectile- 
target combinations. 
Utah Research & Development Co., Inc. 
1820 South Industrial Road 
Salt Lake City, Utah, February 8, 1967 
16 NASA-Langley, 1961 - 23 CR-798 


Cratering in low-density targets

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