CP620, Shock Compression of Condensed Matter - 2001 edited by M. D. Furnish, N. N. Thadhani, and Y. Horie © 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00 LONG-ROD MOVING-PLATE INTERACTION Y. Partom Rafael, P.O. Box 2250, Haifa 31021 Israel Understanding the mechanics of interaction of a long rod projectile with a forward moving plate at an angle is essential to understanding long rod interaction with an explosive reactive armor cassette. To investigate the mechanics of such an interaction we use AUTODIN2D/EULER in plane geometry, although the problem is 3D. We assume that this is a satisfactory approximation, as we're only interested in the main features, and are not comparing fine details to experimental results. From the simulations we learn that the interaction never reaches steady state. Initially each material splits into two streams, and the interaction plane is perpendicular to the rod. But with time the interaction plane rotates slowly, until it becomes parallel to the rod, which is then able to continue moving forward without interruption. During this process interacting rod material of length AL is diverted at an angle and becomes ineffective for penetrating the main target. We made many such runs to determine the dependence of AL on the parameters of the problem. This dependence makes it possible to predict AL for a variety of rod-plate situations. We use AUTODYN2D/EULER in plane geometry. The problem is 3D, but AUTODYN3D/EULER was not fully debugged when we did this work. WE know that plane geometry is sometimes only a crude approximation to a 3D problem, but we believe that it can reproduce the correct physical picture. Using an Euler grid, it is more efficient to apply to the problem a Galilean velocity transformation, so that the interaction region is almost stationary and doesn't move out of the grid. Referring to Fig. 1, Vp is the rod velocity, Vt the plate velocity, and 6 is the angle between the rod and its projection on the plate. INTRODUCTION The outcome of the interaction of a long rod projectile with an explosive reactive armor cassette depends mainly on its interaction with the forward moving plate (FMP) of the cassette. The outcome of this interaction depends on many parameters such as: rod velocity, diameter, density and strength; obliquity angle; plate velocity, thickness, density and strength. In what follows we use computer simulations to study the physical picture of the interaction, and to perform an extensive parameter study of the problem. From the results we formulate a procedure to predict the performance of the FMP on degrading the penetration capacity of the rod. V P. Rod Plate SIMULATIONS FIGURE 1. Velocity transformation. * Work done while on sabbatical leave at SwRI, San Antonio, TX. 1283 We first decompose Vt into Vt and Vt and then apply to the system the velocity -V t . The transformed velocities Vp and Vt are shown in Fig. 2 and given in (1). FIGURE 2. Transformed velocities. Vt' = V t /tan9 ; V t "=V t /sin0 v;=v p -v t f f =v p -v t /sine (1) We see that the transformed problem is that of two interacting streams. In Fig. 3 we show material location plots every 100 jus from an AUTODYN run. The grid cells are 1x1 mmxmm throughout. The initial projectile is Hp=10 mm thick tungsten alloy with pp=17.0 g/cm3, Yp(flow stress)=1.2 GPa, Gp(shear modulus)=140 GPa? STFp(strain to failure)=0.1 and Vp =0.75 km/s. More projectile material is fed in from the boundary at the same velocity up to a total length of 300 mm (L/H=30). The plate is at an angle of 30°, is Ht=10 mm thick, is made of steel with pt=7.83 g/cm3, Yt=1.0 GPa, Gt=80 GPa? STFt=0.5 and Vt'=0.75 km/s. More plate material is fed in from the boundary at the same angle and velocity. From Fig. 3 we see that both rod and plate split into two streams of unequal thickness. For the rod the upper branch is thicker, while for the plate the lower branch is thicker. The interaction surface rotates slowly clockwise until it finally breaks up, and the two flows slide past each other. In this run the length of the rod that stays approximately straight and aligned with the x direction is 34 mm, so that AL=266 mm of the length is diverted and becomes ineffective for penetrating the main target. We repeated the run with different values of V p , and in Fig. 4 we show results for AL as a function of Vp for runs with Vt=0.5 km/s. We see from Fig. 4 that for Vp <0.73 km/s, the entire rod (300 mm) is diverted away from its original direction, most of it upwards. For Vp >0.73 km/s only part of the rod is diverted. We also see that AL is quite sensitive to FIGURE 3. Material location plots for a run with Vp'=Vt'=0.75 km/s. 1284 g/cm3, pp=17.0 g/cm3. Around the nominal set we evaluate the partial derivatives dajdxj by giving each parameter a displacement Ax,- and running the simulation. We then evaluate the derivatives by: projectile velocity. For the above plate velocity (0.5 km/s at 30°), the range 0.5<VP<0.8 km/s is equivalent to 1.5<VP<1.8 km/s (also shown in Fig. 4), which is the ordnance range for long rod projectiles. We see that for the high end of this range the FMP is only partly effective in diverting the rod. Beyond Vp=2 km/s only a small part of the rod would be diverted. ^foj __ \ i /displaced ——-— — -f r J V J''displaced \ i /nominal 7 \———— ,~^ (:)) V JAiominal Two examples of the displaced and nominal hyperbolas are shown in Figs. 5 and 6. —»— Nominal, (y-71.6Xx-0.7)=10.37 --»—Yp=2.0 GPa, (y-72.3Xx-0.75)=6.58 300 260 S1 200 b. 100 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Transformed projectile velocity (km/s) 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 Transformed projectile velocity (km/s) FIGURE 4. Diverted projectile length versus transfbrmed projectile velocity for Hp/Ht=l, Vt=0.5 km/s and 0=30°. FIGURE 5. AL versus V p . Nominal runs (circles) and runs with displaced Yt (squares). Curves are the fitted hyperbolas. PARAMETER STUDY Nominal, (y-71.6Xx-0.7)= 10.37 Vt prime =1.386 km/s, (y-81.4Xx-1.25)=9.84 Performing many runs like that described in the previous section, but with different values of the parameters, we find that for all the cases that we checked, the AL(VP ) relation is always a hyperbola-like curve that can be fitted with: (AL-a 1 )(v;-a 2 ) = a 3 (2) where ai (i=l,3) depend on the material and kinematics parameters. Denoting the parameters by Xj we have: a^a^xj i = l,3 ; j = l,10 (3) To first order approximation we can express ai(Xj) by: *i = (ai)nom 1 nal + Z^-( X J-( X j)nominJ Transformed prqectile velocity (km/s) FIGURE 6. Same as Fig. 5 but with Vt' displaced to 1.386 km/s. The partial derivatives extracted in this way are shown in Table 1. To check our prediction procedure using these partial derivatives we performed additional simulation runs in which we used the nominal set of parameters, but with the rod and plate materials interchanged. In Fig. 7 we compare the results <4> relative to a nominal set of parameters Xj. The nominal set of parameters we use is Vt =0.866 km/s, 9=30°, Hp=Ht=10 mm, Yt=1.0 GPa, Yp=1.2 GPa, STFt=0.5, STFP=0.1, pt=7.83 1285 obtained from the runs to those predicted from the partial derivatives. We see from Fig. 7 that the prediction is not ideal, but in view of the large change in density relative to the nominal case, it is satisfactory. In subsequent work use this approach in a model to predict the performance of explosive reactive cassettes against long rod projectiles. TABLE 1. Partial derivatives of parameters ai in (2) with respect to material parameters i=2 i=l i=3 Xj displace ment 0.7 Nominal 71.6 10.37 mm km/s mm2/|is 8i 67.4 0.75 0.5 GPa Displ. ai 8.13 -8.40 0.10 -4.48 dai/dYt 72.3 0.75 Displ. ai 0.8 GPa 8.58 0.875 0.0625 -2.24 dai/dYp -0.4 0.4 5 g/cc - 5 g/cc 5 mm 0.52 km/s 5 mm 5 degrees Displ. ai dai/dSTFt Displ. ai dai/dSTFt Displ. ai daj/dpt Displ. ai da/dpp Displ. ai dai/dHp Displ. ai daJdVt 70.8 2.0 64.1 -18.75 111.8 8.04 88.7 -3.42 74.1 -0.5 81.4 18.85 0.75 -0.125 0.7 0 0.90 0.04 0.85 -0.03 0.7 0 1.25 1.058 7.80 6.425 10.14 - 0.575 11.86 0.298 11.97 -0.32 14.02 0.73 9.84 -1.019 Displ. ai dai/dHt Displ. ^ dai/dO 65.7 -1.18 56.0 -3.12 0.75 0.01 0.65 -0.01 22.51 2.428 10.12 -0.05 SUMMARY We use AUTODYN2D/EULER in plane geometry to study the phenomenology of long rod interaction with a forward moving plate. The essence of the phenomenology is that part or the entire projectile is diverted from the original direction, and thereby becomes less effective in penetrating the main target. In reality, the diverted projectile is bound to break into several fragments. Performing many simulation runs with different sets of parameters we conclude that, the relation AL(Vt ) can always be fitted by an hyperbola with three parameters en that depend on the problem parameters Xj. We evaluate the partial derivatives da/dxj numerically, and are able to predict ai(Xj) using a first order approximation. Applying this approach to realistic situations of long rod interaction with an explosive reactive cassette (not reported here), we find that potential benefit of such cassettes against long rods cannot be fully exploited because of practical geometrical constrains. 600 -. 500 REFERENCES — Nominal — — Simulation, interchanged materials — Predicted from partial derivatives This reference list is empty, as we couldn't find anything relevant to the subject in the open literature. £ 400 I = 300 K 200 I 100 Q 0.6 0.8 1 1.2 1.4 1.6 1.8 2.2 Transformed projectile velocity (km/s) FIGURE 7. Results of check runs. 1286
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