CP620, Shock Compression of Condensed Matter - 2001edited by M. D. Furnish, N. N. Thadhani, and Y. Hone© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00

A MECHANISTIC STUDY OF DELAYED DETONATION IN IMPACTDAMAGED SOLID ROCKET PROPELLANT

E. R. Matheson1 and J. T. Rosenberg2

1 Aerothermal Design & Performance, Lockheed Martin Space Systems Company, Sunnyvale, CA 940892Reliability/Sustainability Engineering, Lockheed Martin Space Systems Company, Sunnyvale, CA 94089

Abstract. One method of hazard assessment for mass detonable solid rocket propellants consists ofimpacting right circular cylinders of propellant end-on into thick steel witness plates at varying impactvelocities. A detonation that occurs within one shock traversal of the cylinder length is termed a promptdetonation or a shock-to-detonation transition (SDT). At lower velocities, some propellants detonate attimes later than one shock transit, typically 1-5 shock transits. Because no mechanism for delayeddetonation has been fully confirmed and accepted by the detonation physics community, these low-velocity detonations are referred to as unknown-to-detonation transitions (XDTs). A leading theory,however, is that prior to detonation mechanically induced damage sensitizes the material through theformation of internal porosity which provides new mechanical reaction initiation sites (hot spots) andenhanced internal burn surface. To study this phenomenology, we have developed the Coupled Damageand Reaction (CDAR) model, implemented it in the CTH shock physics code, and simulated propellantimpact experiments. The CDAR model fully couples viscoelastic-viscoplastic deformation, tensiledamage, porosity evolution, reaction initiation, and grain burning to model the increased reactivity ofthe propellant. In this paper, CDAR simulations of propellant damage in spall and Taylor impact testsare presented and compared to experiment. An XDT experiment is also simulated, and implicationsregarding damage mechanisms and hydrodynamic processes leading to XDT are discussed.

INTRODUCTION

During impact testing of L/D=l cylindricalsamples of certain solid rocket propellants, twotypes of detonations are observed. Normal, orprompt, detonations occur at higher velocities andduring the first transit of the shock wave. For thesedetonations, chemical reaction rates dominate overrelease waves entering the sample from freeboundaries, and the mechanical behavior of thesolid propellant is readily characterized by its shockbehavior. Abnormal detonations are observed atlower velocities and typically occur after 1-5 shocktransits along the sample axis. For these delayeddetonations, release waves and ultimately tensilewaves can form in the solid propellant greatlycomplicating the sample response during impact.Because no mechanism for delayed detonation hasbeen fully confirmed and accepted by thedetonation physics community, these low-velocitydetonations are referred to as unknown-to-detonation transitions (XDTs). A leading theory1,however, is that prior to detonation mechanicallyinduced damage sensitizes the material through theformation of internal porosity which provides new

mechanical reaction initiation sites (hot spots) andenhanced internal burn surface.

To study phenomenology associated with XDT,we have employed the Coupled Damage andReaction (CDAR) model2"5 as implemented in theCTH shock physics code6. The CDAR model fullycouples viscoelastic-viscoplastic deformation,tensile damage, porosity evolution, reactioninitiation, and grain burning to model the increasedreactivity of damaged propellant. In this paper,CDAR simulations of propellant damage in spalland Taylor rod impact tests are presented andcompared to experiment. An XDT experiment isalso simulated, and implications regarding damagemechanisms and hydrodynamic processes leading toXDT are discussed.

SPALL MODEL CORRELATION

One-dimensional spall tests were performed forthe study material using PMMA flyers at increasingimpact velocities until full damage was achieved.Fig. 1 shows profiles of damage and solid volumefraction through the target material simulated with

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CDAR. In this case, the impact conditions are at thethreshold for full damage to occur at 6.0 jis. At thistime, the material exhibits a porosity of 2.0% at thelocation of 100% damage. At later times, thedamage profile remains unchanged whereas thevoids have fully closed. During the spall process,the tensile strain rates are very small or nonexistent.Moreover, the tensile strains remain very small overthe duration of the experiment. Thus, spall damageis necessarily modeled as a quasistatic stress failureof the binder system.

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0.2-

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——Damage—-Solid Volume

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0.995

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Position (cm)

FIGURE 1. Simulated damage and volume fraction profiles forthe interrupted spall test.

TAYLOR ROD IMPACT TESTCORRELATION

Taylor impact experiments were performed onpropellant rods of various L/D ratios. Fig. 2 showsdamage inflicted on a propellant sample withZ/D=1.27. The upper image in Fig. 2 is of theimpact face revealing an approximately circum-ferential macrocrack. In the lower image, thesample was sliced along its axis revealing the samemacrocrack running a short distance up the sample.In both views, it can be observed that there are largeenergetic crystals decohered from the propellantbinder system. For the spall tests, decohesipndamage was not readily apparent since the tensilestrains were very low relative to the Taylor tests.

The Taylor rod impact experiment wassimulated using CDAR, and Fig. 3 shows contoursof damage in the sample at some time after impact.At this time, the sample has just begun to reboundfrom the aluminum impactor and has experiencedmaximum radial strains at the impact face. Grayregions in Fig. 3 correspond to decohesion damagelevels. In CDAR, decohesion damage may

limited to a specified level. Here, it was set toreflect the change in modulus of the propellantobserved in dynamic tensile tests. Decohesion ismodeled as occurring abruptly when tensile strainsexceed the value at which the modulus is observedto decrease suddenly in the tensile tests.

The black regions in Fig. 3 are sites whereCDAR has predicted full damage due to binderscission. Two forms of scission are predicted byCDAR in Fig. 3:1) strain failure of the binder at theimpact face, and 2) stress failure on-axis near theback surface. The damage profile at the front facequalitatively agrees well with the damage shown inFig. 2. There is a circumferential macrocrackpredicted at the mid-radius that is penetrating somedistance along the axis. There is also full damagepredicted at the radial periphery of the impact face.Fig. 2 shows some material missing at theperiphery. If scission damage near the rear of thesample occurred, it was not reported. In this region,CDAR predicted that the tensile stress state wasvirtually uniform in all directions, and the stress wasgreater than that for the 1-D spall threshold.Considering that it does not conform to the usualconcept of a spall plane and that it occurs over asmall region, it may not have been readily detected.

i)' View of ini

b) of

FIGURE 2. Damaged propellant recovered from a Taylor rodimpact experiment.

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than scission damage. Fig. 4 also shows that there isa low level of porosity and only decohesion damageon-axis where the detonation initiates in Fig. 5. Thisis quite different from the DDT-like mechanismpostulated in Ref. 1.

FIGURE 3. Simulated damage contours for end-on impact of acylindrical sample in a Taylor rod impact experiment.

XDT IMPACT CORRELATION

Impact-induced XDT was studied previouslyusing the programmed XDT technique . The XDTexperiment studied in Ref. 7 is simulated here usingthe CDAR model. The propellant sample was25mm in diameter, L/D=1, and fired from a shotgunonto a steel witness plate. The witness plate was 3.2mm thick, and there was a PVDF stress gageembedded on the sample shotline between thewitness plate and a thick steel backing plate.

Fig. 4 shows damage and solid volume fractioncontours immediately prior to the initiation ofdetonation. The sample has experienced decohesiondamage throughout, and there is some peripheralscission damage. The solid volume fraction contourshows a low level of porosity evolution on-axis nearthe front face. Near the rear surface, there is a highdegree of porosity due to decohesion, but thescission damage is insufficient to form a spall plane.

Fig. 5 shows gas pressure contours at four times.The upper-left quadrant shows that the initialreaction occurs near the front face about 2/3 of theway from the axis. In the upper-right quadrant, thereactive wave has propagated to the axis. The twolower quadrants reveal that the detonation initiateson-axis at the impact face and propagatesspherically away from that point. The lower-rightquadrant also indicates that there is a fairly largeregion ahead of the detonation front that hasinitiated reaction. Examination of gas mass fractioncontours prior to detonation shows that there is atrivial amount of gas present, and the gas has anegligible effect on hydrodynamic processes.

There is scission damage shown in Fig. 4 in thesame vicinity as the site where reaction initiates.Since it occurs later and does not propagate to theaxis as does the reaction, it appears that reactioninitiation is supported by decohesion damage rather

FIGURE 4. Simulated damage and solid volume fractioncontours for an XDT impact experiment.

FIGURE 5. Simulated gas pressure contours for an XDTimpact experiment.

Fig. 6 compares simulated and experimental x-ray records of the expanding detonation products.The simulation exhibits a radial jet-like structuresimilar to that in the experiment. The simulationalso shows the witness plate crater which compareswell with the crater photographic record in Ref. 7.

Fig. 7 compares the axial stress on-axiscomputed by CTH at the PVDF gage location withthe experimental gage record. The simulation showsa precursor to the detonation similar to the data butoccurring somewhat early. The precursor pulsecauses the pores to close generating a significant

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gas pressure. However, the mass fraction of gas isso low the hydrodynamics are unaffected. It is thesolid pressure in response to the compressive pulsethat is generating hot spots leading to thedetonation. CTH also computed a peak stress due tothe detonation that is in very good agreement withthe data. The simulated pulse is probably widerbecause the interface between the witness andbacking plates which provides a path for transverserelease waves to unload the gage was not modeled.

FIGURE 6. Experimental versus simulated flash x-ray recordfor an XDT impact experiment.

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CTH Axial StressPVDF Gage Record

TimeFIGURE 7. Experimental versus simulated flash x-ray recordfor an XDT impact experiment.

DISCUSSION AND CONCLUSIONS

This study demonstrates that material damageenhances material reactivity in CDAR to produceXDT-like responses in solid rocket propellants. Inthe XDT simulation, CDAR predicted thatdecohesion damage rather than macrocracks due tobinder scission is responsible for XDT. In Ref. 1,

DDT-like behavior was postulated as a possiblecause for XDT, but it appears that themicrostructure in conjunction with the bindertoughness is the cause. For the Taylor testsimulation, CDAR underpredicted the increase insample volume observed in shadowgraphs. It isthought that adding pressure-dependent shear andshear-induced dilatation into the CDAR constitutivemodels might solve this problem8. Inclusion ofthese processes in CDAR may be important forpredicting XDT under all impact conditions.

REFERENCES

1. Green, L. G., James, E., Lee, E. L., Chambers, E. S.,Tarver, C. M., Westmoreland, C, Western, A. M.,Brown, B., "Delayed Detonation in Propellants fromLow Velocity Impact," Seventh Symposium(International) on Detonation, Annapolis, MD, 16-19 June 1981, pp. 256-264.

2. Olsen, E. M., Rosenberg, J. T., Kawamoto, J. D.,Lin, C. F., and Seaman, L., "XDT Investigation byComputational Simulation of Mechanical ResponseUsing a New Viscous Internal Damage Model,"Eleventh Symposium (International) on Detonation,Snowmass, CO, 30 August - 4 September, 1998, pp.170-178.

3. Matheson, E. R., Drumheller, D. S., and Baer, M.R, "An Internal Damage Model for Viscoelastic-Viscoplastic Energetic Materials," in ShockCompression of Condensed Matter - 7999, edited byM. D. Furnish, L. C. Chhabildas, and R. S. Hixson,AIP Conference Proceedings 505, New York, 1999,pp. 691-694.

4. Matheson, E. R., Drumheller, D. S., and Baer, M.R., "A Coupled Damage and Reaction Model forSimulating Energetic Material Response to ImpactHazards," in Shock Compression of CondensedMatter - 1999, edited by M. D. Furnish, L. C.Chhabildas, and R. S. Hixson, AIP ConferenceProceedings 505, New York, 1999, pp. 651-654.

5. Matheson, E. R., Drumheller, D. S., and Baer, M.R., "A Viscoelastic-Viscoplastic Distention Modelfor Granulated Energetic Materials," Proceedingsof the JANNAF 18th Propulsion SystemsHazards Subcommittee (PSHS) Meeting, CocoaBeach, FL, 18-21 October, 1999.

6. Hertel, E. S., et al, "CTH: A Software Family forMulti-Dimensional Shock Physics Analysis," inProceedings of the 19th International Symposium onShock Waves 1, edited by R. Brun and L. D.Dumitrescu, pp.377-382.

7. Matheson, E. R., Rosenberg, J. T., Ngo, T. A., andButcher, G., "Programmed XDT: A New Techniqueto Investigate Impact-Induced Delayed Detonation,"Eleventh Symposium (International) on Detonation,Snowmass, CO, 30 August - 4 September, 1998, pp.162-169.

8. Drumheller, D. S., Private Communication.

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