Abstract. 1 Introduction

Transcription

1 Lagrangian simulation of linear shaped demolition charge formation G.A. Gazonas U.S. Army Research Laboratory Weapons Technology Directorate Aberdeen Proving Ground, MD 21005, USA Abstract This paper outlines the results of a combined numerical and experimental study of linear shaped demolition charge (LSC) formation [1]. The demolition charge was composed of a mild steel liner, filled with castable Composition-B (CompB) high explosive (HE). The Lagrangian hydrocode, EPIC92, predicted a jet tip velocity of 5.2 km/s at 12 ^is. Subsequent experiments showed that jet tip velocities ranged from 3.3 to 3.52 km/s as determined from flash radiography and a special electrical makewire circuit test fixture. Thus, EPIC92 overpredicted jet tip velocities by 50% due to computational inaccuracies resulting from a highly distorted mesh in the collapsing liner. The problem was reanalyzed in 3-D using the Lagrangian hydrocode DYNA3D94, and jet tip velocites were overpredicted by only 15% at 12 is. The work attests to the importance of conducting experiments in order to verify baseline hydrocode simulations. 1 Introduction Military demolition operations use a variety of shaped charge geometries (e.g. cylindrical, linear, curvilinear and flexilinear) for the clearance of obstacles and barriers, the destruction of facilities and materiel, the construction of roads and trenches, and in land clearance and quarrying. In this study, the Navy was interested in assessing the predictive capabilities of Lagrangian-based hydrocodes in modeling jet tip formation in the Mk-7 Mod 8 demolition charge. One of the motivations of the current study was to assess the accuracy of hydrocodes in problems with limited experimental data, such as in demolition work, where data can be both hazardous and costly to obtain.

2 362 Structures Under Shock And Impact The Mk-7 Mod 8 demolition charge (Figure 1) consists of a mild steel container (liner)filledwith plastic explosive (e.g. C-4). A blasting cap is typically placed on the top surface of the explosive to initiate the charge. The charge may w N- Figure 1: Critical dimensions of the Mk-7 Mod 8 demolition charge [1],[2]. be used individually or linked together in a continuous series if a long linear cut is desired. Linking several individual charges together in series is achieved by connecting the short leg of one charge to the long leg of an adjacent charge. In this configuration, the charge has a uniformly short standoff distance on the order of 1.1 in (28 mm). The dimensions of the Mk-7 Mod 8 charge are: N=80, W= 1.00 in (25.4 mm), T=0.053 in (1.35 mm), H=1.12 in (28.45 mm), L=6.0 in (152.4 mm), and D=1.06 in (26.92 mm). The experimental determination of optimal jet cutting properties for a particular demolition operation requires parametric variation of design variables such as the liner material, liner geometry, standoff distance, and explosive properties. Since experiments can be costly and hazardous to conduct, there is a strong motivation to develop numerical methods which employ hydrocodes to assist in the development of demolition procedures. The explicit Lagrangian hydrocode, EPIC-2 (Elastic Elastic Impact Calculations, hereafter referred to as EPIC92 to denote the 1992 version of the code) [3], was used to initially model the plane strain jet formation of the Mk-7 Mod 8 demolition charge since this code has successfully predicted jet tip velocities (to within 5%) in explosively loaded hemispherical lead liners [4], The jet tip velocity was experimentally determined both by flash radiography, and from a special test fixture designed to measure the jet velocity using a makewire circuit. Experimental determination of jet tip velocity was compared with the EPIC92 jet tip velocity predictions in order to assess EPIC92 computational accuracy for jet tip formation. It was found that the hydrocode overpredicted the jet tip velocity by 50%. Doubling the liner element density led to an overprediction of the tip velocity by 68%. This led to the decision to compare results with another Lagrangian-based hydrocode in order to assess the plane strain modeling assumptions in the initial EPIC92 computations. The DYNA3D hydrocode [5] (hereafter

3 Structures Under Shock And Impact 363 referred to as DYNA3D94 to denote the 1994 version of the code) was selected for this phase of the study of the LSC jet formation problem. The DYNA3D94 jet tip velocity predictions were found to be within 15% of those experimentally measured. Computations and experiments are presented in this paper in the order they were conducted. 2 EPIC92(94) computations Computations were initially performed using the explicit Lagrangian hydrocode, EPIC92 [3], that has been used in the analysis of terminal ballistic and hypervelocity impact problems. The EPIC finite element hydrocode was originally developed by Alliant Techsystems Inc., Brooklyn Park, Minnesota (formerly Honeywell, Inc.) for the Ballistic Research Laboratory (BRL) in 1977, and has seen continuous use and development since then [6]. The initial grid for the jet formation problem which consisted of 1,485 nodes and 2,732 constant strain triangles was generated from the charge geometry given in the Introduction. The liner consisted of 5 composite elements through the liner thickness. Each composite element contains four constant strain triangles. Computations proceeded through three phases: pre-processor, main cycle and post-processor corresponding to manual input, EPIC92, and RSCORS routines, respectively. The distortional behavior of the 1006 mild steel liner material was modeled using the Johnson-Cook viscoplastic constitutive model [7] together with a von Mises initial yield condition (Figure 2). The dilatational behavior of the mild steel was modeled using the Mie-Gruneisen equation of state (EOS). In EPIC92, an isotropic hardening rule governs subsequent yield surface behavior coupled with a radial-return algorithm. Because of the high strain rates encountered in shaped charge jet problems, temperature fields in bodies modeled using EPIC92 are adiabatic (dq = 0, i.e., there is no heat flow within the body) and thermal softening of a material element is directly proportional to the amount of accumulated plastic work. The dilatational behavior of the CompB detonation products was modeled using the Jones-Wilkins-Lee (JWL) EOS (Figure 3), together with the programmed burn model. In the model, the entire cross section of the charge was simultaneously detonated in order to approximate a plane detonation wave traveling along the length of the charge. Interpenetration between the HE and liner was prevented by alternately defining the interface nodes for these materials using master and slave sidelines. In the original analysis [1], the liner was composed of 5 composite elements through the liner thickness. For the current study, the jet formation was reanalyzed using EPIC94 with 11 composite elements through the liner thickness (Figure 4). An interesting feature of the simulation shows that the jet accelerates from a velocity of about 5.6 km/s at 5 pis to 6.0km/s at 20 is (Figure 5). This 7% increase in velocity is nonphysical since the jet is fully formed at 5 is. Additionally, doubling the liner element density produced an even greater jet tip velocity

4 364 Structures Under Shock And Impact I CJ Point ( ) r 5.0 = l s' Plastic Strain V/V. Figure 2: Adiabatic flow stress versus equivalent plastic strain for 1006 mild steel as a function of strain rate [1]. Figure 3: JWL EOS for CompB[l]. that overpredicted the observed value by 68% at 12 pa. Use of the automatic mesh rezoner, available in the EPIC94 hydrocode, reduced the jet tip velocity from 4.7 km/s to 3.8 km/s at 4 (is. However, computations beyond 4 is were not possible due to numerical instabilities associated with an extremely small integration time increment due to mesh distortion. The explosive was eliminated from the simulation at 10.1 is. 3 Experiments LSC Jet Tip Velocity (Makewire Circuit) The jet tip velocity of the LSC was determined by measuring the travel time of the jet as it consecutively severed three parallel double-lead wires, fastened to a plexiglas test fixture (Figure 6). As each wire was impinged by the electrically conductive jet, a circuit was completed that sent a signal to an oscilloscope from which the travel time and velocity of the jet could be deduced. A breakwire circuit was not used because it might interact with the electrically conductive jet. A uniform standoff distance was assured by elevating the short legs of the liner with wooden spacers. The charge was detonated at one end by hotwire initiation of two layers of C-6 Detasheet explosive that were press fit onto the CompB. Each layer of Detasheet was about 6-mm thick. The Detasheet is composed of 68% PETN, 28% acetyl tributyl citrate, and 8% nitrocellulose [8], The test fixture was supported by a 1 -in (25.4 mm)-thick rectangular witness plate composed of RHA. As the jet tip cut through each double-lead, the wires were bridged, thus completing the electrical makewire circuit. When the circuit was completed, a 67.5-volt signal was simultaneously discharged from a battery to a Nicolet model 2090 oscilloscope. Two separate experiments were conducted to estimate the jet

5 Structures Under Shock And Impact Figure 4: EPIC94 simulation results (axes in meters x " " % 4000' ^ Position (m) Figure 5: EPIC94 jet velocity versus axial position (denser liner).

6 366 Structures Under Shock And Impact Figure 6: Plexiglas makewire test fixture for velocity measurement [1] Table 1. Jet tip velocity measurements [1]. Shot # 1 2 Stations 1 to 2 2 to 3 1 to 3 1 to 2 2to3 1 to 3 Interstation Distance (mm) Travel Time (Us) average: Jet Tip Velocity (km/s) tip velocity which was found to average 3.52 ±0.10 km/sec (Table 1). This velocity was relatively constant over a total flight distance of about 4 in (100 mm). Jet Tip Velocity (Orthogonal X-rays) The jet tip velocity of the LSC was also determined by an orthogonal x-ray measurement method so that a direct comparison could be made to the electrical makewire measurement method. The LSC was suspended by two nylon ropes with radiographic film cassettes oriented at right angles to the charge. Several

7 Structures Under Shock And Impact 367 attempts to obtain orthogonal radiographs of the jet as it formed were unsuccessful because the lateral radiographic film cassettes were damaged by laterally projected fragments of the steel liner which left crater-like imprints on the interior wall of the test facility. Hence, jet tip velocity had to be estimated from a single radiograph (Figure 7, oriented horizontally). The front and back legs of the LSC are visible at the left of the radiograph as well as the horizontal 4.0 in fiducial mark. Knowing the distance from the base of the LSC to the tip of the jet, one can determine the jet tip velocity from information about the test system time delays. Test system time delays were estimated at 3 (is for predetonation electrical delay, 3 Lis for Detasheet burn delay, 3 (is to 6 [is for CompB burn delay, and 5 is for jet formation delay. The jet formation delay was the time required for the jet to emerge from the base of the LSC at a given cross section once the detonation wave reached that cross section, and was included in the delay times since all distances were measured from the base of the LSC. The jet formation delay was determined from the hydrocode computations. The total time delay thus ranged from 14 [is to 17 is. The radiograph flash time occurred at 73.5 [is so that the total travel time ranged from 56.5 [is to 59.5 us. The distance traveled by the jet was determined to be mm from the radiograph, hence jet tip velocity was estimated to range from 3.3 km/s to 3.5 km/s. Figure 7: X-ray radiograph of LSC (axial view) at 73.5 ps [ 1 ]. 4 DYNA3D94 computations Computations were then performed using the explicit Lagrangian hydrocode, DYNA3D94 [5], developed by the Lawrence Livermore National Laboratory (LLNL) in The code is in use by the aircraft industry (Boeing) and the

8 368 Structures Under Shock And Impact attempts to obtain orthogonal radiographs of the jet as it formed were unsuccessful because the lateral radiographic film cassettes were damaged by laterally projected fragments of the steel liner which left crater-like imprints on the interior wall of the test facility. Hence, jet tip velocity had to be estimated from a single radiograph (Figure 7, oriented horizontally). The front and back legs of the LSC are visible at the left of the radiograph as well as the horizontal 4.0 in fiducial mark. Knowing the distance from the base of the LSC to the tip of the jet, one can determine the jet tip velocity from information about the test system time delays. Test system time delays were estimated at 3 (is for predetonation electrical delay, 3 tis for Detasheet burn delay, 3 ^is to 6 (is for CompB burn delay, and 5 iis for jet formation delay. The jet formation delay was the time required for the jet to emerge from the base of the LSC at a given cross section once the detonation wave reached that cross section, and was included in the delay times since all distances were measured from the base of the LSC. The jet formation delay was determined from the hydrocode computations. The total time delay thus ranged from 14 (is to 17 (is. The radiograph flash time occurred at 73.5 (is so that the total travel time ranged from 56.5 (is to 59.5 (is. The distance traveled by the jet was determined to be mm from the radiograph, hence jet tip velocity was estimated to range from 3.3 km/s to 3.5 km/s. Figure 7: X-ray radiograph of LSC (axial view) at 73.5 (is [1]. 4 DYNA3D94 computations Computations were then performed using the explicit Lagrangian hydrocode, DYNA3D94 [5], developed by the Lawrence Livermore National Laboratory (LLNL) in The code is in use by the aircraft industry (Boeing) and the

9 Structures Under Shock And Impact 369 automobile industry (Volvo, Saab, General Motors, and Japanese manufacturers) for crash and safety modeling [9]. The finite element computational grid consisted of 75,447 nodes and 65,000 hexahedral elements with a rigid-wall symmetry plane oriented parallel to the axis of the LSC (Figure 8). The liner consisted of 10 hexahedral elements through the liner thickness. Computations proceeded through three phases: pre-processor, main cycle and post-processor corresponding to PATRAN, DYNA3D94, and TAURUS routines, respectively. The Johnson-Cook material description for the DYNA3D94 simulation was identical to that used in the EPIC94 simulation, however the dilatational behavior of the mild steel was modeled in DYNA3D94 with a slightly different implementation of the Mie-Gruneisen EOS. Further, the CompB was detonated at a single centrally located point on one end of the LSC, rather than on the entire cross section of the charge, as in the plane strain simulation. Slidelines were defined at the interface between the liner and the HE, with the liner interface nodes defined as the master surface and the HE interface nodes defined as the slave surface. The liner failure that was observed in the field tests was modeled using the "node spotwelded to surface" slideline feature in DYNA3D94. With this feature, nodes along a "failure" surface are released when a predefined level of the normal and shear failure strength of the liner is exceeded [5]. Runs were conducted on a 32-bit Silicon Graphics computer, and were terminated at 20 (is since this is the length of time it takes the detonation wave to traverse the length of the LSC. Unlike the plane strain simulation where the jet was fully formed at 5 os (Figure 4), the 3-D simulation predicted a fully formed jet at 10 ^s positioned about 0.5 in (12.7 mm) from the end where detonation was initiated (Figure 8). Some interesting features of the 3-D simulation include a jet tip contour that is parabolic along the length of the LSC, and rapid expansion of the detonated CompB on unconfined surfaces. The detonation wave front is also not planar as was assumed in the plane strain simulation since pressure contours (not shown here) are lobe-shaped when viewed in cross section at selected locations normal to the axis of the LSC. A plane wave has a uniform pressure contour in the plane of observation (cross section). The simulation also shows that the liner fragment begins to form at 5 jis by "peeling" off the main body of the LSC at a velocity of about 2 km/s. 5 Discussion and conclusions Maximum jet tip velocity predictions using DYNA3D94 overestimated the observed velocity of 3.5 km/s by 15% at 12 jis, whereas EPIC94 predictions overestimated the observed velocity by 68% at 12 is (Figure 9). The relatively poor performance of the EPIC94 hydrocode in predicting the LSC jet tip velocity is surprising in view of the fact that others have predicted jet tip velocities in explosively loaded hemispherical lead liners to within 5% of observed velocities^]. Further, jet tip velocity predictions using both CST and Pugh-

10 370 Structures L'nclcr Shock And Impact t = O.Ojisec t = 5 fisec t = 10 (isec Figure 8: DYNA3D94 simulation showing jet tip and fragment formation. Eichelberger-Rostoker (PER) 2-D axisymmetric elements for explosively loaded conical copper liners were virtually identical to observed velocities [10]. An important difference between the current LSC problem, and previous work [4], is that in this work the liner geometry consists of a sharp "v-notch", whereas the hemispherical liner problem has a smoothly varying liner geometry which mitigates the overly stiff behavior of EPIC94 tetrahedral elements. Use of the automatic rezoner, available in EPIC94, reduced the jet tip velocity to within 8.5% of the observed value. However, EPIC94 computations beyond 4 (is were not possible due to numerical instabilities associated with requiring a vanishingly small integration time increment [1]. Further efforts to investigate the LSC problem in 3-D using EPIC94 were abandoned and the problem was readdressed using DYNA3D94. Since DYNA3D94 hexahedralfiniteelements are more susceptible to hourglass modes than EPIC94 tetrahedral finite elements, there were some initial reservations about using DYNA3D94 to solve the LSC problem. Furthermore, DYNA3D94 employs a Jaumann objective stress rate (co-rotational) formulation

11 Structures L niter Shock And Impact Time (microseconds) Figure 9: Comparison of maximum jet tip velocity versus time. [11] which has been criticized for generating non-physical oscillatory shear stress in certain materials that undergo finite simple shear [12]. Despite these concerns, the DYNA3D94 hydrocode predicted jet tip velocity within 15% of the observed value. However, the DYNA3D94 solution was obtained at a relatively high cost that averaged 8 CPU hours/solution is. In contrast, the solution cost for the EPIC94 plane strain simulation averaged only 0.2 CPU hours/solution (is. Studies are currently underway to quantify the effects of these potential instabilities for this class of problems. An interesting feature of the 3-D simulation shows a jet tip contour that is parabolic along the length of the LSC. This feature of the simulation may explain why linear cuts made in RHA and mild steel plates with the LSC were less deep near the edges of cut [1]. Also, the detonation wave front was not planar as assumed in the plane strain simulation, since pressure contours were lobe-shaped when viewed in cross section at selected locations normal to the axis of the LSC. Finally, the DYNA3D94 simulation successfully modeled the formation of the laterally projected liner fragments using the "failure" criterion associated with spotwelded nodes. These laterally projected liner fragments "peeled away" from the main liner body at 2 km/s, and formed rectangularly shaped craters in the wall of the test facility. 6 Acknowledgments The work [1] was supported by the Naval Explosive Ordnance Disposal (NAVEOD) Technology Center, Indian Head, MD. The author thanks Dr. Steven B. Segletes of ARL for conducting EPIC92 simulations [1], and Messrs. Steven R. Stegall and Carl V. Paxton for making LSC velocity measurements [ 1].

12 372 Structures Under Shock And Impact 1 References 1. Gazonas, G.A., Segletes, S.B., Stegall, S.R. & Paxton, C.V. Hydrocode simulation of the formation and penetration of a linear shaped demolition charge into an RHA plate, ARL-TR-788, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, July, Department of the Navy EODB/Department of the Army TM/U.S. Air Force TO 60A Explosive Ordnance Disposal Procedures, Shaped Charges: General Information, September, Johnson, G.R., Stryk, R.A., Pratt, D.E. & Schonhardt, J.A. User Instructions for the 1992 Version of the EPIC Code, Alliant Techsystems, Inc., Brooklyn Park, MN, October, Walters, W. P., Jonas, G.H. & Zukas, J.A. Explosive loading of lead hemispherical liners, Computers and Structures, 1985, 20, Hallquist, J.O. & Whirley, R.G. DYNA3D Users Manual (Nonlinear Dynamic Analysis of Structures in Three Dimensions), UCID-19592, Rev. 5, Lawrence Livermore National Laboratory, Livermore, CA, May Johnson, G.R. High velocity impact calculations in three dimensions, Journal of Applied Mechanics, 1977, 99, Johnson, G.R. & Cook, W.H. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures, and pressures, Engineering Fracture Mechanics, 1985, 21, Asay, B.W., Ramsay, J.B., Anderson, M.U. & Graham, R. A. Shock response of the commercial high explosive detasheet, Shock Waves, 1994, 3, Randers-Pehrson, G. Terminal Effects Division TAP Report, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, December, Johnson, G.R., Stryk, R.A. & Nelson, C.A. Simplified Shell Elements and a Pugh-Eichelberger-Rostoker (PER) Shaped Charge Link for EPIC-2, Honeywell, Inc., Brooklyn Park, MN, AFATL-TR-90-08, June, Hallquist, J.O. Theoretical Manual for DYNA3D, UCID-19401, Lawrence Livermore National Laboratory, Livermore, CA, March, Dienes, J.K. A discussion of material rotation and stress rate, ActaMechanica, 1986,65, 1-11.