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