SPALLATION STUDIES ON SHOCK LOADED U-6 WT PCT NB. Page: 4 of 5
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The CHARADE full damage model results
presented in the following figures 1-4 generally160-
140.
120-
par
vel
(ml 80
se
c) 60
40
20
0
340
320 -
300 -
280
260-
240-
c: 220
a, 200-
E180-
- 160 -
> 140 -
S120-
80
60
40 -
20 -
0-U-6% Nb
Shot 9, 34 kbar
/data
calcuation
0 1 2 3 4 5 6 7
time(usec)
U-6% Nb Shot 12, 82 kbar
data
calcuation0 1 2 3 4
time(usec)5 6 7
FIGURE 2. Calculated and measured free surface particle
velocity profiles.
capture successfully the behavior near the spall dip.
Hence, the damage initiation and part of the
subsequent damage growth are modeled well. In
particular, most of the VISAR trace of the weakest
impact, in Fig. 3, in which mostly inclusion cracking
occurred, is successfully modeled. For the stronger
impacts, the smooth rise and turn over after the spall
dip is not modeled well. The sudden peak in the
calculated turn over for shot 9, for example, is
caused by the achievement of fracture. The measured
peak height is achieved in the calculation, so the
overall dissipation in the model is correct, but thedetails of late damage evolution and the transition to
fracture are not modeled so well. This is probably
due to not including the twinning plasticity that is
known to occur at a few per cent strain in this alloy
(8). Twinning plasticity is different from the generic
"dislocation" plasticity in the model. Twinning
plasticity modeling is a likely area of future progress.
The same set of full damage evolution
parameters was used for all of the fits. The values
used are: o =5/ps, c=6 kbar, y = 7 kbar, and n=1.5.
The seed (initial) porosity, po is 0.02. and the spall
porosity is 17.3 %. The large model seed porosity
(whose value was not critical) corresponds well to
the large inclusions, having a volume of about 1%,
seen in the micrographs [1]. The initial value of -
18.3 kbar of the "pressure threshold", (2/3)y ln p0
corresponds, in this modeling, which lacks an
explicit void nucleation component, to the pressure
to crack the carbides and nucleate a void. The y
value, thus, is being made to serve two purposes, the
void cracking and void growth. The model will be
generalized to overcome this problem. The spallation
porosity used is smaller than the 30% used for many
fcc metals. We note that shot 27 is somewhat better
modeled by changing n to 1.0, but the standard
parameter set is close to the best for the other shots.
As mentioned earlier, this parameter set does best
on the void nucleation and early damage evolution.
Shot 19 is a good example, the recovered sample of
which showed mostly void cracking.
The parameter values for the matrix power law
plastic strain rate relation are as follows: y =
3x104/s , ryf = 1.2 kbar , and Tyb= 1.0 kbar. These
two yield stresses are smaller but comparable to the
yield stress of 2 kbar or more found in conventional
low strain rate testing on different U6Nb material
(9). Values of 2 kbar produce a noticeable calculated
Hugoniot elastic limit, in disagreement with the
VISAR data. Including twinning plasticity in the
model might resolve this problem. However, it
would have to be triggered in shock waves at a
smaller stress than is seen in conventional
mechanical testing (8).
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TONKS, D. & AL, ET. SPALLATION STUDIES ON SHOCK LOADED U-6 WT PCT NB., article, January 10, 2001; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc724544/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.