Split Hopkinson Bar Studies
Split Hopkinson Bar Studies
Split Hopkinson Bar Studies
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Cavendish Laboratory<br />
Fracture & Shock Physics<br />
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong> <strong>Studies</strong> of a<br />
Nitrocellulose-based PBX System<br />
AWE Nitrocellulose Meeting<br />
April 2007<br />
D.R. Drodge, D.M. Williamson, W.G. Proud<br />
1
Overview<br />
Materials: EDC37 and NC-K10<br />
Technique: <strong>Split</strong>-<strong>Hopkinson</strong> Pressure<br />
<strong>Bar</strong> with Pulse Shaping and<br />
Temperature Control.<br />
Results & Discussion<br />
2
Sample Materials<br />
3
EDC37: 91% HMX<br />
filler, 9% NC-K10<br />
binder<br />
NC-K10: plasticised<br />
nitrocellulose<br />
Motivation: examine<br />
sub-T g behaviour<br />
to extend current<br />
data set.<br />
Sample Materials<br />
DMTA figure courtesy of Dr D. Williamson<br />
4
Story So Far<br />
We already have EDC37 data for:<br />
Fixed T (room temp), varying strain<br />
rates<br />
Fixed strain rate (10 -3 s -1 ), varying T<br />
(D.M. Williamson et. al., paper awaiting publication)<br />
… ramp up strain rate, drop T, see what<br />
happens…<br />
5
Storage Modulus<br />
Viscoelastic Response<br />
Glassy<br />
T g Transition<br />
Rubbery<br />
Melt<br />
Temperature OR Loading Time Period<br />
6
Not-so-subtle differences…<br />
Strain Rate vs. Loading Frequency<br />
Small strain vs. strained to failure<br />
Pure polymer vs. filled polymer…<br />
F 0 sin(wt)<br />
THUD!<br />
1T<br />
7
Storage Modulus<br />
Current Data…<br />
Glassy<br />
T g Transition<br />
Rubbery<br />
Melt<br />
Temperature OR Loading Time Period<br />
8
Plan…<br />
Use high strain-rate apparatus to<br />
raise the transition temperature<br />
Use cooling chamber to induce<br />
glassy behaviour<br />
Find something out.<br />
9
Apparatus<br />
10
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
Sample<br />
Striker Input Output Trapper<br />
Gauges measure strain in <strong>Bar</strong>s<br />
11
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
Striker Input Output Trapper<br />
Particle<br />
Velocity<br />
Sample<br />
Gauges measure strain in <strong>Bar</strong>s<br />
Z<br />
SAMPLE STRAIN<br />
Strain<br />
E<br />
Stress<br />
Sample Dim’s<br />
A<br />
Force<br />
SAMPLE STRESS<br />
12
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
Gauge Voltage / V<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
-0.1<br />
-0.2<br />
-0.3<br />
60 110 160 210 260 310 360<br />
Time / microseconds<br />
Input Gauge<br />
Output Gauge<br />
13
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
Gauge Voltage / V<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
0<br />
-0.1<br />
-0.2<br />
-0.3<br />
Incident<br />
Transmitted<br />
60 110 160 210 260 310 360<br />
Time / microseconds<br />
Input Gauge<br />
Output Gauge<br />
Reflected<br />
14
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
Gauge Voltage / V<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.1<br />
-0.1<br />
-0.2<br />
-0.3<br />
Incident<br />
0<br />
60 110 160 210 260 310 360<br />
F I<br />
F R<br />
v L<br />
Transmitted<br />
Time / microseconds<br />
L<br />
v R<br />
F T<br />
Input Gauge<br />
Output Gauge<br />
Reflected<br />
15
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
ε&<br />
=<br />
vR − vL<br />
L<br />
F I<br />
F R<br />
v L<br />
L<br />
v R<br />
F T<br />
σ =<br />
F<br />
A<br />
(assumes equilibrium)<br />
T<br />
S<br />
16
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
σ<br />
σ<br />
L<br />
R<br />
=<br />
=<br />
F<br />
A<br />
T<br />
S<br />
F I +<br />
A<br />
S<br />
F<br />
R<br />
F I<br />
F R<br />
v L<br />
L<br />
Do Front and Back<br />
v R<br />
stresses match?<br />
…if not, we have a problem<br />
F T<br />
17
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
Shallower Pulses = Reach Equilibrium Sooner<br />
Copper Shim (annealed at 450C for 2hrs)<br />
Place on end of input bar to cushion blow<br />
Strain<br />
0 20 40 60 80 100 120<br />
Time / μs<br />
18
<strong>Split</strong> <strong>Hopkinson</strong> Pressure <strong>Bar</strong><br />
5000<br />
4000<br />
3000<br />
2000<br />
1000<br />
0<br />
-1000<br />
-2000<br />
-3000<br />
-4000<br />
Smoothed Pulse (timeshifted)<br />
Reflected Force<br />
0 20 40 60 80 100 120 140<br />
Transmitted Force<br />
Incident Force<br />
Two-Wave Force<br />
19
Other considerations<br />
Friction. Mitigate by lubrication with<br />
appropriate substance (silicon<br />
grease)<br />
Inertia. Demonstrated* to be<br />
negligible for strain rates below<br />
105s-1 provided sample geometry is<br />
sensible.<br />
*G.T. Gray III (2000) – ASM Handbook vol. 8<br />
20
Heating / Cooling System<br />
Thermocouple on output bar.<br />
21
Heating / Cooling System<br />
22
3mm Length<br />
8mm Diameter<br />
EDC37 Samples<br />
Supplied in disc form by AWE<br />
23
NC-K10 Samples<br />
Supplied as ~1mm thick sheets by AWE<br />
Make double-thickness sheet<br />
Punch out ~3mm diameter discs<br />
Place between lubricated bars and<br />
squeeze<br />
Measure dimensions using<br />
sophisticated multichromatic<br />
photometric array<br />
24
NC-K10 Samples<br />
25
NC-K10 Samples<br />
Obtain height and width.<br />
Thickness well defined…<br />
Diameter less so… hence<br />
stress is subject to error<br />
26
Results<br />
27
EDC37 Results<br />
28
Near-constant failure strain<br />
Failure<br />
29
EDC37 Results<br />
30
EDC37 Strength<br />
31
EDC37 Strength<br />
Glassy?<br />
Glass<br />
Transition<br />
Rubbery<br />
32
EDC37 Modulus Estimate<br />
Usually, elastic behaviour occurs<br />
before sample equilibrium reached<br />
Pulse Shaping allows earlier<br />
equilibrium<br />
Stress-strain gradient offers<br />
estimate of elastic modulus<br />
33
EDC37 Modulus Estimate<br />
34
EDC37 Modulus Estimate<br />
Glassy<br />
?<br />
T g Transition<br />
Rubbery<br />
35
NC-K10 Results<br />
36
NC-K10 Results<br />
“Yield Stress” taken as zero for “melt”<br />
Stresses have near 10% error from poorly defined<br />
sample diameter/area<br />
37
Combined Strength Results<br />
38
Combined Strength Results<br />
Lower T g ??<br />
Bizarre shape<br />
39
Conclusions<br />
<strong>Hopkinson</strong> <strong>Bar</strong>s allow detailed study of<br />
viscoelastic effects in high rate impact<br />
around the glass transition<br />
EDC37 Failure Stress continues to rise<br />
below T g<br />
High rate modulus estimates describe a<br />
near-ideal viscoelastic master curve at<br />
low strains<br />
NC-K10 Failure Stress peaks at<br />
T ~ -60C, then decreases<br />
Binder transition at lower T than EDC37,<br />
sharper<br />
40
Extension<br />
Cold machining to produce better<br />
NC-K10 specimens from new<br />
material<br />
High-speed photography and softrecovery<br />
techniques to confirm<br />
failure modes<br />
Simultaneous diametric<br />
measurements to find Poisson’s<br />
Ratio<br />
Investigate crystal behaviour at low<br />
temperatures<br />
41
Acknowledgments<br />
D.R. Drodge and D.M. Williamson<br />
thank AWE<br />
W.G. Proud thanks QinetiQ<br />
42
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