Effects of target strength on cratering process caused by impact of hypervelocity projectile

Rand, J. L.

English

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TEXAS ENGINEERING EXPERIMENT STATION 
T E X A S  A & M  U N I V E R S I T Y  
C O L L E G E  S T A T I O N  T E X A S  7 7 8 4 3  
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HYPERVELOCITY IMPACT EFFECTS 
SEMI-ANNUAL PROGRESS REPORT 
to the 
National Aeronautics and Space Administration 
Manned Spacecraft Center 
Research Performed Under NASA Grant NGR 44-001-106 
J.L.  Rand, Principal Investigator 
and Associate Professor of 
Aerospace Engineering 
March 16, 1971 
Texas A&M University 
Texas Engineering Experiment Station 
Space Technology Division 
INTRODUCTION 
This r e p o r t  desc r ibes  t h e  progress  under NASA g r a n t  NGR 44-001-106, 
Hyperveloci ty  Impact E f f e c t s  f o r  t h e  period of 1 September 1970 t o  28 
February 1971. This  g r a n t  w a s  awarded by NASA t o  i n v e s t i g a t e  t h e  e f f e c t s  
of t a r g e t  s t r e n g t h  on t h e  c r a t e r i n g  process  caused by t h e  impact of hyper- 
v e l o c i t y  p r o j e c t i l e s .  The ma jo r i t y  of experimental  s t u d i e s  i n  t h i s  area 
have been conducted us ing  1100-0 A l ,  which is a very  s o f t ,  commercially 
pure ,  aluminum, as t h e  t a r g e t  material. Unfortunately,  t h i s  m a t e r i a l  ex- 
h i b i t s  a y i e l d  s t r e n g t h  which i s  s e n s i t i v e  t o  t h e  r a t e  of loading.  In 
o r d e r  t o  c o r r e l l a t e  c r a t e r  dimensions such as depth and volume wi th  tar- 
I g e t  m a t e r i a l  i t  was found necessary by Gehring t o  use "dynamic hardness" 
va lues  f o r  t h e  t a r g e t  ma te r i a l .  These hardness  va lues  were obtained by 
measuring t h e  hardness  immediately ad j acen t  t o  t h e  c r a t e r  formed i n  a 
t a r g e t  a l r e a d y  subjec ted  t o  a hyperve loc i ty  impact. It was noted by this 
i n v e s t i g a t o r  t h a t  t h e  r a t i o  of "dynamic" t o  " s t a t i c "  hardness  repor ted  by 
Gehring i s  equal  t o  t h e  r a t i o  of t h e  maximum "dynamic" t o  " s t a t i c "  y i e l d  
stress repor ted  from wave propagat ion experiments. Since t h e  l a t e r  t e s t s  
a r e  economically and quick ly  performed it would appear  t h a t  pene t r a t ion  
equat ions should be based on dynamic y i e l d  stress r a t h e r  than  dynamic 
hardness.  
I n  o r d e r  t o  demonstrate t h i s  e f f e c t  a number of t a r g e t s  were made 
a v a i l a b l e  by t h e  Manned Spacecraf t  Center.  These t a r g e t s  had been i m -  
pacted by t h e  NASA-MSC l i g h t  gas  gun by a v a r i e t y  of p r o j e c t i l e s .  The 
t a r g e t s  were se lec ted  on t h e  b a s i s  of adequate documentation of p r o j e c t i l e  
s i z e ,  ve loc i ty  and dens i ty ,  a s  w e l l  a s  t a r g e t  configurat ion and material 
proper t ies .  
PROCEDURE 
The Aluminum t a r g e t s  were prepared by machining t h e  c r a t e r  l i p  and 
p l a s t i c a l l y  deformed a r e a  adjacent  t o  t h e  c r a t e r  down t o  the  o r i g i n a l  sur-  
face.  The t a r g e t s  considered were e i t h e r  f i n i t e  o r  semi- inf in i te  i n  thick- 
ness. The mate r i a l s  considered were e i t h e r  1100-0 o r  2024 Aluminum a l l o y ,  
After  machining the  t a r g e t s ,  c r a t e r  volumes were determined by metering 
a lcohol  in jec ted  i n t o  t h e  c r a t e r  u n t i l  t h e  l e v e l  of t h e  l i q u i d  reached the 
o r i g i n a l  su r face  of the  t a r g e t .  Cra ter  depths were determined by nlicrometer 
measurement from t h e  undisturbed surface.  This technique is  s imi la r  t o  tha t  
employed by Howell and ~ h i t t r o c k ' .  
These measurements a r e  tabula ted  i n  Table 1. The t a r g e t  i d e n t i f i c a t l s n  
corresponds t o  the  shot  numbers used by NASA i n  recording each shot .  lea .  
add i t ion ,  t h e  appropr ia te  p r o j e c t i l e  d a t a  a s  provided by NASA is  l i s t e d ,  
ANALYSIS 
I n  order  t o  develop confidence i n  these  da ta  and determine the  effects 
of t a r g e t  s t r eng th ,  t h e  da ta  were compared with d a t a  obtained by o the r  facili- 
t i e s  and reported e i t h e r  i n  t h e  l i t e r a t u r e  o r  con t rac t  r epor t s .  In order to 
examine a wide v a r i e t y  of da ta ,  a  penet ra t ion  equation commonly employed by 
NASA-MSC was used. I n  p a r t i c u l a r :  
where 
pd = pene t r a t ion  depth 
K = cons t an t  dependent on t a r g e t  m a t e r i a l  
d = p r o j e c t i l e  diameter 
P 
P~ 
= p r o j e c t i l e  d e n s i t y  
pt  = t a r g e t  d e n s i t y  
V = p r o j e c t i l e  v e l o c i t y  
HD = dynamu hardness  of t a r g e t  m a t e r i a l  
The e f f e c t s  of t h e  t a r g e t  m a t e r i a l  may be  separa ted  by d e f i n i n g  t h e  quan- 
t i t i e s  Q and KT: 
s o  t h a t :  Q = KT V 213 
The n o n l i n e a r i t y  i n  s i z e  s c a l i n g  due t o  p r o j e c t i l e  diameter w i l l  be  ignored 
f o r  t h e  moment. With t h e s e  d e f i n i t i o n s ,  a p l o t  of Q a s  a func t ion  sf V on 
log-log paper should appear a s  a  s t r a i g h t  l i n e  wi th  a  s lope  of  2 / 3 .  D i f -  
f e r e n t  l i n e s  w i l l  r ep re sen t  d i f f e r e n t  m a t e r i a l s  and t h e  s e p a r a t i o n  w i l l  be 
dependent on t h e  parameter,  f. When comparing 1100 and 2024 Aluminm al-  
loy ,  s i n c e  both have t h e  same nominal dens i ty ,  t h e  d i f f e r e n c e  i n  t h e  data 
a r e  a t t r i b u t a b l e  only  t o  s t r e n g t h  e f f e c t s .  The d a t a  t abu la t ed  i n  Table E 
i s  p l o t t e d  i n  F igure  1. The b e s t  s t r a i g h t  l i n e  wi th  a s l o p e  of 213 has 
been drawn through t h e  d a t a  po in t s .  Although t h e  d a t a  a r e  s eve re ly  scat- 
t e r e d  t h e  s t r a i g h t  l i n e s  ag ree  q u i t e  w e l l  wi th  t h e  d a t a  publ ished by 
3 4 2 Harperson , Goodman , sorensen5, and Howell , (Figures  2 through 5 ) .  The 
NASA d a t a  agrees  q u i t e  w e l l  wi th  o t h e r  repor ted  d a t a  and t h e  s c a t t e r  of 
d a t a  may be  a t t r i b u t e d  t o  t h e  f i n i t e  dimensions and r e s u l t i n g  s p a l l  of 
most t a r g e t s  examined. 
The sepa ra t ion  of t h e  two s t r a i g h t  l i n e s  f o r  1100 and 2024 Alunrinan 
a l l o y s  could not  b e  r e l a t e d  t o  t h e  " s t a t i c "  s t r e n g t h  of each material .  which 
r e s u l t e d  i n  Gehring's "dynamic hardness" va lues ;  however, i f  i t  i s  recognized 
t h a t  hardness  numbers a r e  d i r e c t l y  p ropor t iona l  t o  y i e l d  s t r e s s ,  then,  the  
dynamic hardness  may be  expressed as: 
5 - C a  S t a t i c  R 
where C i s  a cons tan t  r e l a t i n g  s t a t i c  harness  t o  s t a t i c  y i e l d  s t r e s s  and 
R is  t h e  r a t i o  of dynamic t o  s t a t i c  y i e l d  s t r e s s .  I n  t h i s  way, Q may be 
expressed i n  terms of t h e  s t a t i c  y i e l d  stress and r a t e  s e n s i t i v i t y  R: 
Q = K a  S t a t i c  
SUPPLEMENTARY ANALYSIS 
I n  t h e  process  of removing t h e  c r a t e r  l i p  and ad jacen t  a r e a  of p l a s t i c  
deformation, a d i s t i n c t  change i n  t h e  s u r f a c e  appearance was noted ,  figure 6. 
This  l i n e  of demarcation always appeared i n  t h e  1100 specimens and never i n  
t h e  2024 specimens. Therefore,  t h r e e  t a r g e t s  were sec t ioned  through the cen- 
t e r  of t h e  c r a t e r  and hardness  readings  obtained p a r a l l e l  t o  t h e  surface (0'1, 
normal t o  t h e  c r a t e r  (go0), and i n  between (45'). Measurements were made on 
a Tukon hardness  machine wi th  a 500 gm f o r c e  and Knoop hardness  values 
read as a func t ion  of d i s t a n c e  from t h e  f i n a l  c r a t e r  su r f ace ,  A p l a t  of 
t h e s e  hardness  readings  appears  i n  f i g u r e s  7 and 8. The t h i r d  specimen 
evidenced a distinct region of hardness comparable to the most strain hard- 
ened region at some distance from the crater. Additional targets will be 
examined to determine if this effect is peculiar to that one target due to 
same predictable wave interaction phenomenon. 
FUTURE WORK 
It has been realized by several researchers that the hydrodynamic theory 
could predict very well the initial stages of crater formation when the pres- 
sure is of the order of megabars, but during the later stages where the pres- 
sures drop down to the values comparable to material strength, the hydrody- 
namic theory can not be applied. 
Also it was observed, especially with small particle impacts, for a 
Pd given target and projectile combination, is not found to be a function of 
Pd P 
velocity but a= f (Vo) d1'18. Similar non-linear diameter size scaling ef - 
P 
fects were also observed with the target, projectile momentum ratio. To a 
first approximation, researchers felt that these non-linear size sealfng 
effects are attributable to the strain-rate sensitivity of the target material, 
Thus the importance of strength and strain-rate effects being realized, 
it is evident that such effects can come into hypervelocity impact calcula- 
tions only through a constitutive equation. A purely hydrodynamic constitu- 
tive equation neglects the strength and strain-rate effects whereas the hydro- 
dynamic-elastic-plastic constitutive equation neglects the strain-rate effects 
and thus fails to predict the non-linear effects. A hydrodynamic-elastfc- 
viscoplastic constitutive equation in its most general form proposed by Perzyna 6 
which takes into account the strength and strain-rate effects was applied to 
hypervelocity impact problems by Rosenblatt who got fairly encouraging results, 
I n  o rde r  t o  e s t a b l i s h  more c l e a r l y  t h e  s i g n i f i c a n c e  of s t r a i n  r a r e  
s e n s i t i v i t y  i n  t h e  c r a t e r i n g  process  a number of m a t e r i a l s  have been chosen 
which have exh ib i t ed  an  exagerated dynamic p l a s t i c  response. 
a )  1060 Aluminum i s  a commercially pure material which e x h i b i t s  a 
g r e a t e r  s e n s i t i v i t y  t o  rate than  1100. 
b)  6061 - T6 Aluminum a l l o y  i s  r e l a t i v e l y  i n s e n s i t i v e  t o  r a t e  and 
w i l l  be  used f o r  comparison. 
c )  1020 mild s t e e l  is s e n s i t i v e  t o  rate of loading  and has  an ex- 
tremely w e l l  def ined  y i e l d  po in t  when t e s t e d  s t a t i c a l l y .  
d )  Pure l ead ,  Pb, which is p e r f e c t l y  p l a s t i c  and s e n s i t i v e  t o  r a t e  
w i l l  be  considered.  
Nominal one inch  t h i c k  p l a t e s  of each m a t e r i a l  w i l l  b e  obtained.  Four 
by fou r  inch  t a r g e t s  w i l l  b e  c u t  from t h e s e  p l a t e s  and suppl ied  t o  NASA-MSC 
f o r  hyperve loc i ty  impact t e s t i n g .  The remainder of t h e  p l a t e  w i l l  be  mehiwed 
i n t o  c y l i n d r i c a l  specimens f o r  compression t e s t i n g .  
S t r e s s - s t r a i n - s t r a i n  r a t e  d a t a  w i l l  be  obta ined  us ing  both s tandard  
(Balwin) t e s t i n g  machines and a  s p l i t  Hopkinson p re s su re  ba r .  These data 
w i l l  be  analyzed and s u i t a b l e  v i s o p l a s t i c  models w i l l  be  used t o  analyti-s 
c a l l y  desc r ibe  t h e  m a t e r i a l s .  I f  a t  a l l  pos s ib l e ,  t h e s e  models w i l . 1  be used 
t o  p r e d i c t  t h e  f i n a l  c r a t e r  geometry r e s u l t i n g  from impact of s p h e r i c a l  pro- 
j e c t i l e s  a t  v e l o c i t i e s  from 3 t o  6 kmlsec. 
It is hoped t h a t  t h e  r o l l  of s t r a i n  r a t e  s e n s i t i v i t y  w i l l  b e  clearly 
e s t a b l i s h e d  so  t h a t  a d d i t i o n a l  confidence may b e  placed i n  t h e  p e n e t r a t i o n  
s c a l i n g  equat ions  p r e s e n t l y  being used. 
ACKNOWLEDGEMENTS 
The target preparation and crater measurements reported here were ae- 
complished by Mr. Charles Nelson with the assistance of Mr. Roy E. Sewall. 
Mr. Nelson is presently studying for his Master of Science degree in Aero- 
space Engineering and is supported under this grant. Mr. Sewall io eomplet- 
ing the requirements for a Bachelor of Science degree in Aerospace Engineer- 
ing and is supported by the Space Technology Division. 
The future work in identifying the roll of strain rate sensitivity In 
the hypervelocity cratering process will be accomplished by Mr. Basavarislju 
Chakrapani. Mr. Chakrapani is in Mechanical Engineering and will prepare 
his Ph.D. dissertation on this problem while supported by this grant, The 
dynamic stress-strain relations will be obtained by Mr. James S. Wilbeck, 
Mr. Wilbeck is a candidate for the Master of Science degree in Aerospace 
Engineering. He holds a NDEA fellowship and receives supplemental support  
from the Space Technology Division. Mr. Nelson will prepare his msters 
thesis on the characterization of the materials with the appropriate viseo- 
plastic models. 
REFERENCES 
1. "Hypervelocity Impact Studies Against Apollo - Types Structures Up to 
16.5 km/secH, General Motors Corporation, G.M. Defense Research 
Laboratories, 1965. 
2. Howell, W.G. and Whittrock, E.P., "~ypenrelocity Impact Data For 
Cratering Studies"; Mechanics Division, Denver Research Institute, 
Denver, Colo., 1966. 
3. Halperson, S.M.; Seventh Hypervelocity Impact Symposium; pp. 253-256, 
4 .  Goodman, E.H., Liles, C.D., Sixth Symposium On Hypervelocity Impact, 
p. 563. 
5. Sorensen, N.R., Seventh Hypervelocity Impact Symposium, p. 313. 
6. Perzyna, P., "The Constitutive Equations for Rate Sensitive Plastic 
Materials," Quarterly of Applied Mathematics, Vol. 20, No. 4, 1963, 
pp, 321-332. 
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TABLE I 
Hypervelocity Impact Data 
PROJECTILE TARGET 
TARGET NO. MATERIAL DIAMETER 
( i n . )  
Alum . I25  
Alum 
Alum 
Pyrex 
Pyrex 
Pyrex . 
Alum 
Bronze 
Alum 
Alum 
Pyrex 
Lowden 
Lowden 
Pyrex .I252 
- Pyrex .I254 
Alxrm -1253 
VELOCITY 
(Km/sec) 
THICKNESS 
( i n .  ) 
7.56 Alum ,500 - 
7.08 1100 .375 
6.60 1100 .500 
DEPTH 
.258 
,274 
.294 
. I56  
.I77 
.095 
.270 
. I43  
.I75 
.I93 
,105 
.443 
,394 
.357 
.368 
.391 
TABLE I 
PROJECTILE 
TARGET NO. MATERIAL DIAMETER 
( i n , )  
3177 Glass .009 
3274 Pyrex .062 
3277 Pyrex .062 
3913 Glass .0660 
Hypervelocity Impact Data 
TARGET 
VELOCITY THICKNESS DEPTH 
(Km/sec) ( i n . )  '-1 
1100 .375 . I16  
7.89 1100 .500 . I88  
7.92 1100 .500 . I84  
7.26 Alum ,294 . I71  
VOLUME 3 
.00305 
.0168 
,0153 
,0122 
* V ( KM/SEC 1 5 6 7 8 9 10 FIG 

FIG 
FIG 






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