PERGAMON

INTERNATIONAL JOURNAL OF IMPACT

ENGINEERING International Journal of Impact Engineering 26 (2001) 591-602

www.elsevier.com/locate/ijimpeng

NUMERICAL SIMULATION OF NON-PERFORATING IMPACTS ON SHIELDED GAS-FILLED PRESSURE VESSELS

DAVID PALMIERI*, FRANK SCI-IA~ER**, S T E F A N HIERMAIER** and MICHEL LAMBERT***

*University of Rome "La Sapienza", Aerospace Department, via. Eudossiana 16, 00184 Rome, Italy; "Ernst Mach Institut, Eckerstr. 4, D-79104 Freiburg i. Br., Germany; ""ESA-ESTEC, Postbus 299, NL-2200 AG Noordwijk,

The Netherlands

Abstract--In order to calibrate the output of hydrocode simulations of hypervelocity impacts on shielded gas-filled pressure vessels, Light Gas Gun impact experiments were performed. In a first step, tests were performed on so-called equivalent Whipple shield (EWS) configurations having basically the same set-up as the shielded pressure vessels (i.e. bumper thickness and - material, stand-off and backwall plate thickness and -material). Purpose was the determination of the impact conditions that lead to penetration into the backwall plate but not perforation of it or leakage through the impacted area. In a second step, impact tests on the corresponding shielded pressure vessels were performed with the same test conditions as the EWS. The purpose of the tests was the investigation whether leakage occurs when the vessel's front wall is not perforated, but just cratered. The test conditions lead to no leakage in all tests. The most important measured damage parameter was the crater depth of the deepest crater in the vessel's front wall/the backwall plate of the EWS, respectively. Hydrocode simulations were then performed to assess the capability of the numerical tool to correctly predict the damage on the impacted vessel surface. Normal impacts of aluminium spheres against shielded vessels were simulated using AUTODYN-2D, including and evaluating the effect of the static stress induced in the vessel walls by the inner pressure. Particular attention was focused on the exact determination of the maximum crater depth caused by the debris cloud impact on the vessel wall/the backwall plate of the EWS, respectively. Bumper and projectile were represented by SPH particles, the vessel shell was represented by a Lagrange grid. The results showed a very good agreement with the measured crater depths of the experiments. © 2001 Elsevier Science Ltd. All rights reserved.

Keywords: impact, numerical simulation, SPH, Lagrange, shielded gas-filled pressure vessels, Whipple shield, crater depth, leakage

INTRODUCTION

Pressurized vessels are widely used on board of spacecraft. The possibil i ty of hypervelocity impacts of meteoroids and orbital debris on pressurized components and the potential catastrophic damages resulting from it considerably increases the risk of mission failure. Impacts of particles on pressure vessels that result in catastrophic failure was extensively investigated during the past years, see e. g. [1]-[5]. The use of a shield can significantly decrease the probabili ty of a catastrophic failure, thus reducing the hazard to the surrounding components and the generation of additional debris [6]. However, the probabil i ty of impact of a large particle is fairly small. The focus was placed on investigating impacts of small particles on pressure vessels, having much higher fluxes in orbit than the large particles. It was noted that even perforation into a vessel and thus leakage of gas can be avoided when a moderate shielding is introduced. Therefore, the need arises to study adequate shielding systems for pressure vessels used onboard spacecraft, in order to keep up the system functionality by ensuring that no gas leakage occurs after impact. To this purpose the effect of a thin metall ic bumper spaced at some distance from the vessel shell was investigated in the present study.

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592 D. Palmieri et al. / International Journal of lmpact Engineering 26 (2001) 591--602

dp

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NOTATION AND ACRONYMS

projectile diameter [mm] vessel pressure (vacuum is reference pressure) [bar] maximum crater depth in vessels's front wall [mm] reference pressure: maximum pressure that can be sustained before yielding [bar] inner spacing between shield and front surface of PV [mm] vessel thickness [mm] shield thickness [mm] projectile velocity [km/s] impact angle (target surface normal corresponds to 0 °) [°] Hoop stress [MPa] projectile density [g/cm 3]

HYPERVELOCITY IMPACT TESTS Test samples

Test samples were cylindrical pressure vessels made of A1 2219 T851 alloy. The length of the vessels was 175 mm, the inner diameter was 75 mm, the wall thickness was 1.0 mm. The vessel tubes were manufactured from 1 mm thick Al-plates by rolling and welding along the axial joint. The bottom and top plates were then welded to the vessel tube. The vessels were inflated through a pressure inlet in the top. A pressure gauge was introduced into the vessel's top plate (Figure 1) for monitoring of the pressure decay in case the vessel wall is perforated by the impact. The shield of the vessel consisted of a 1.0 mm thick Aluminium plate both experiments, placed 10 mm and 25 mm, respectively, in front of the vessel.

Fig. 1. Pressure vessel and instrumented top cover plate. One unit on the scale corresponds to 10 mm

Testing

The tests were performed at the two-stage Light-Gas-Guns of the Ernst-Mach-Institute, Freiburg (Figure 2), [7], [8]. The purpose of the hypervelocity impact tests on shielded Aluminium pressure vessels was to create typical damage features for hypervelocity impacted

D. Palmieri et al. /International Journal of lmpact Engineering 26 (2001) 591-602 593

pressure vessels for comparison to numerical simulation runs. Subject of the tests was the creation of non-perforating impact damages in the vessel's front wall. The crater depths in the vessels should not exceed half of the vessel's wall thickness, i.e. 0.5 mm, at a normal impact velocity of 7 km/s. Leakage was to be avoided. Thus, the corresponding projectile diameters to cause the desired damage in the vessel's front wall were estimated from engineering equations and subsequently confirmed in "investigatory" impact tests on equivalent Whipple shield (EWS). An EWS is a Whipple shield that consists of a bumper that is equal to the bumper of the pressure vessel. The backwall plate of the EWS is made of the same or a comparable material as the pressure vessel wall having the same thickness (without curvature). An EWS is a suitable means of predicting impact damages to the front side of a shielded pressure vessels, at least when looking at normal impacts closely around the center of the pressure vessel.

Fig. 2. Medium two-stage light gas gun (MLGG) at EMI

The projectile diameters to fulfill the above mentioned requirement thus were determined experimentally to be 1.0 mm and 1.4 mm for the 10 mm and 25 mm shield stand-off, respectively, with EWS. As a next step, the impact tests on the shielded pressurized vessels were performed. In Table 1, the test parameters and test results of the EWS and PV tests are listed. The reference pressures listed there are the maximum pressures the vessels can sustain before yielding occurs. The reference pressure was calculated from the material parameters and the actual wall thicknesses considering the influence of the weld. Despite inflation pressures of 44.3 and 55.4 bar, and maximum penetration depths of 0.40 mm, none of the two vessels failed or leaked gas.

594 D. Palraieri et al. /International Journal of lmpact Engineering 26 (2001) 591-602

No. EMI No.

Table 1. Results of the impact tests on the shielded AI 2219 T851 PV

Shield Vessel/ Experimental parameters Damage backwall

plate at q ts S mat 1 pref dp mat I pp V cx P p/pref CH p .....

[mm] [mm] [bar] ram] [g/cm ~] [krn~] [o] [bar] [-] [MPa] [mm]

quivalent Whipple Shield Tests WS 3560 A1 1.0 10.0 A15754 1.0 A1 2.79 6.8 0 0.55 20 5754 2017

WS 3557 A1 1.0 25.0 A15754 1.4 A1 2.79 6.9 0 0.77 21 5754 2017

hielded Pressure Vessel Impact Tests PV 3573 AI 1.0 10.0 A12219 79.0 1.01 AI 2.79 7.0 5 44.3 0.56 165 0.40 20 5754 "1851 2017 _+0.03 PV 3559 A1 1.0 25.0 A12219 832 1.41 A1 2.70 6.9 40 55.4 0.67 207 0.38 21 5754 1"851 1098 +0.02

The impact of the projectile on the shield is recorded in Figure 3. The damages in the backwall plate of the EWS 20 and 21 and the wall of the pressure vessels 20 and 21 are shown in Figure 4 and 5.

Fig. 3. Image converter photographs of the impact of the projectile in test PV 20 (3573); frame separation is 1 us

D. Palmieri et al. /International Journal of lmpact Engineering 26 (2001) 591-602 595

EWS - Backwa l l PV - w a l l

Fig. 4. Impact damage in EWS backwall and PV wall, shield stand-off 10 mm, projectile diameter 1.0 mm

EWS PV Fig. 5. Impact damage in EWS backwall and PV wall, shield stand-off 25 mm,

projectile diameter 1.4 mm (top: shield, below: backwall/PVwall)

596 D. Palmieri et al. / International Journal of lmpact Engineering 26 (2001) 591--602

NUMERICAL SIMULATIONS

The purpose of the numerical simulations, performed with the AUTODYN-2D hydrocode in axial symmetry, was the prediction of the impact damage (i.e. crater depths) on the vessel shell. The capability of the model to reproduce the maximum craters depths and the extension of the cratered area on the external surface was analyzed. In order to combine the large deformations occurring after impact of the projectile against the shield with the lower deformation of the vessel walls subjected to impact with the fragment cloud, the standard Lagrange grid-based technique and the SPH technique was coupled. Thus, the projectile and the bumper plate were simulated using SPH discretization, the vessel wall respectively the EWS backwall plate were simulated using a Lagrange grid. The effect of pressurization of the vessel wall was investigated by a hoop stress boundary condition in the wall. The spatial resolution of the model was iteratively increased until a very good agreement with the experimental results was obtained. The results were also compared with those of the corresponding Equivalent Whipple Shield configurations.

Simulation of impact on pressure vessels

The hypervelocity experiments PV-20 (EMI shot No. 3753) and PV-21 (EMI shot No. 3559) were selected as references cases for the numerical simulations.

The Shock Equation of State and the Johnson-Cook strength model along with standard library data for the model parameters were used to simulate the material behavior. The failure criterion of maximum principal stress was used in tension only. The strength limit was 2.5 GPa. In order to simulate the craters formation in the vessel wall, Lagrangian cells were eroded after a geometric strain value of 250 % was reached.

The two experiments selected were initially simulated without considering the effect of the hoop stress induced in the vessel wall by the inner pressure (cases 20a and 21a, respectively). Only a sufficiently large central portion of the vessel was modeled with a fixing boundary at the end of the grid (see Fig. 6).

In these cases 16 SPH particles and 32 cells were set across the shield and vessel thickness, respectively. The debris cloud just after the impact with the vessel and the final crater shapes in the vessel wall around the impact center are shown in Fig. 7 for case 20a.

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D. Palmieri et al. /International Journal of lmpact Engineering 26 (2001) 591-602 597

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Three further simulations were performed for each experiment (cases 20b, 20c, 20d and 21b, 21c, 21d, respectively), in which the spatial resolution was varied. From the experiments it was known that no leakage occurred after impact. Thus, in the simulations, the inner fluid was not modeled. Instead the static stress wall resulting from the inner pressure was simulated by applying a stress boundary along the inner wall. However, if only a portion of the vessel would have been simulated as in cases 20a and 21a, the pressure loading would have induced an unrealistic bending on the structure. For this reason the whole axisymmetric half of the sphere was modeled (see Figs. 8 and 9).

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The original vessel was a cylinder. In 2D axial symmetry, the vessel is represented as a hollow sphere. The vessel formula delivers twice the wall stress for a cylinder compared to the stresses for a sphere if the inner pressure is the same. This problem was solved by applying twice the pressure to the simulated spherical pressure vessel: thus, the same wall stresses as in the cylindrical pressure vessels were obtained.

A certain problem concerning the computation times arises when a stress boundary condition is applied in a explicit code. The boundary condition causes stress waves which need to be

598 D. Palmieri et al. / International Journal of lmpact Engineering 26 (2001) 591-602

damped in order to get a static stress state. The number of explicit time steps until equilibrium is reached can be up to several thousand steps. The calculated equilibrium value matches very well the one predicted by the vessel theory (166 MPa).

The impact simulation was started, as soon as the stress damping was finished and the velocity of all of the points of the vessel grid was zero. Thus, the generated debris cloud impacted on the uniformly stressed vessel wall (see Fig. 10).

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Fig. 11. Stress field in impacted pressurized vessel.

After impact of the debris cloud, the instantaneous stress field in the vessel is given by the superposition of impact induced stress waves with the pre-existing static stress distribution (see Figure 11).

Simulation of impacts on Equivalent Whipple Shields (EWS)

For the simulation of impacts on EWS, the same approach was chosen as for the pressure vessels: A SPH model with particles of the same dimensions was chosen to simulate the projectile and the shield, and a Lagrange grid was chosen for the vessel wall. All the material models, including failure and erosion criteria, were exactly the same as in previous cases.

One simulation was performed for each of the two EWS experiments. The spatial resolution used in these two cases (indicated with 20W and 21W, respectively) was the same as in cases 20d and 21d, that is 20 SPH particles across the bumper and 40 cells across the back wall thickness. The dimension of SPH particles in the projectile was always set equal to the SPH particles in the bumper. It has to be noted that the only difference of these cases with respect to cases 20a and 21a, in which the effect of pressurization was not taken into account, is the plane geometry of the back wall.

The initial setup and the debris cloud just before impacting the back wall are shown in Fig. 12 for case 21W, while the craters on the central part of the back wall are shown in Fig. 13 (left side), together with a detail of the deepest one on the impact axis (right side).

D. Palmieri et al. / International Journal of lmpact Engineering 26 (2001) 591-602 599

MATERIAL

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Results and comparison with experiments

All the simulated cases are summarized in Table 2. In particular, two damage parameters were extracted from the simulation runs: the maximum crater depth and the extension of the cratered area on the vessel surface. The choice of these parameters is related to the availability from the experimentally impacted samples. The comparison between experiment and result is given in Table 3.

Table 2. Simulation cases

Case Nr. of SPH particles Nr. of Lagrangian cells through Static stress in through shield thickness vessel thickness vessel wall (MPa)

20a 16 32 0 20b 16 32 165 20c 16 40 165 20d 20 40 165 21a 16 32 0 21b 16 32 207 21c 16 40 207 21d 20 40 207

20W 20 40 0 21W 20 40 0

600 D. Palmieri et al. /International Journal of Impact Engineering 26 (2001) 591-602

Table 3. Comparison between numerical and experimental results \

Case Exp. Nr. Maximum crater depth (mm) Diameter of craterized area (mm) Exp. Sim. Exp. Sim. (erosion) Sire. (pl. strain)

1 0.4 0.378 19 11.2 16.2 1 0.4 0.573 19 10.3 15.6 1 0.4 0.525 19 13.6 17.9 1 0.4 0.404 19 13.8 20.0 2 0.38 (*) 0.650 38 19.2 30.2 2 0.38 (*) 0.885 38 22.5 31.8 2 0.38 (*) 0.630 38 21.3 35.9 2 0.38 (*) 0.520 38 24.3 35 3 0.43 0.449 13 12.8 17.4 4 0.55 0.544 42.4 23.9 34.3

20a 20b 20c 20d 21a 21b 21c 21d 20W 21W

(*) A projectile offset of 24 mm from ideal normal trajectory was observed

Maximum crater depth The maximum crater depth measured in the impact tests was the distance from the original

reference surface of the vessel to the deepest point of the crater bottom. The same criterion was adopted for the determination of the numerical value, in order to have consistent data for the comparison.

From the simulated test cases that included the stressed walls, it can be clearly seen that a significant improvement of the prediction of the maximum crater depth can be obtained by increasing the spatial resolution. The numerical value for case 20d is very close to the experimental one. Unfortunately the value determined in experiment 21 is not directly comparable with the simulation results, because - for technical reasons - the projectile impacted 24 mm off the center trajectory into the shielding. This caused the fragment cloud to impact on the vessel surface at an angle of about 40 degrees with respect to the normal to its curved surface,

Thus the data were compared to the experimental EWS result: There it was found that the maximum crater depth in case 21d matches very well with the experimentally measured depth of test 21W on the EWS. The comparison of a hypervelocity experiment on a pressure vessel with the corresponding EWS works fine, as can be seen for example from the results of tests 20 and 20W, showing similar values at least with regard to the maximum crater depth. Comparing simulation test cases 20d and 21d with cases 20W and 21W respectively, proves that the simulations with and without pressure load give quantitatively similar results, at least when the spatial resolution exceeds a certain level. The latter results are also in good agreement with the experiments.

The two simulation cases in which no pressure was considered (20a and 21a) show better agreement with the experiments than those including the pressure with the same spatial resolution (20b and 21b respectively). This might suggest that the introduction of a pressure load in the back wall requires a finer model to obtain the same degree of correspondence.

Cases 20a and 21a also compare well with cases 20W and 21W and the corresponding experiments on the EWS. In fact, the only difference between the two couple of simulations is to be found in the curved vessel surface. However, in a limited zone around the debris cloud impact point, where the maximum crater depth is always located, this effect isnot considered to be relevant.

As already found for the pre-loaded vessels, it can be seen that the increase of spatial resolution in simulations 20W and 21W leads to a better agreement with experiments.

D. Palmieri et al. /International Journal of lmpact Engineering 26 (2001) 591-602 601

Extension of cratered area on the vessel surface The crater formation in the vessel's or the EWS backwall plate is calculated by material

deformation and by erosion of the Lagrange cells when a fixed value of the geometric strain is reached. This value is basically a numerical necessity with no direct physical meaning. To some extent it represents the physical mechanisms when failed material is eroded. In some cases it is difficult to make a distinction between a small crater, produced for example by the erosion of only one cell, and a highly distorted region of the grid eventually just below the erosion limit. This causes problems for the exact determination of the cratered zone in the simulations.

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This situation is illustrated for example in Fig. 14, showing two near zones where the formation of a crater could be eventually predicted for case 20d. The lower one is generated by the erosion of three cells, while the upper one is only due to the material plastic deformation, but no cells are eroded.

In the attempt to overcome these difficulties, the extension of the cratered area reported in Table 3 was determined according to two different criteria. In the first one (erosion) the boundary of the cratered area is given by craters that are generated by the erosion of at least one ceil. In the second case the boundary of the cratered area is given by craters where the physical failure strain of the material (0.11 for the A12219-T851 vessels) is reached.

This latter approach seems to agree generally better with the experimentally determined extensions of the cratered area. Again, the simulation cases with the highest spatial resolution match best the experimental test results.

CONCLUSIONS

Experimental and numerical investigation of the hypervelocity impact on pressure vessels has been performed. The first tests were performed on equivalent Whipple shields (EWS) and later on shielded pressure vessels with the same test conditions as the EWS. The purpose of the tests was the investigation whether leakage occurs when the vessel's front wall is not perforated but impacted and damaged by craters. The test conditions lead to no leakage in all tests. The most important measured damage parameter was the crater depth of the deepest crater in the vessel's front wall or the backwall plate of the EWS respectively.

602 D. Palmieri et al. /International Journal of lmpact Engineering 26 (2001) 591-602

Hydrocode simulations were then performed to assess the capability of the numerical tool to correctly predict the damage on the impacted vessel surface. Normal impacts of aluminium spheres against shielded vessels were simulated using AUTODYN-2D, including and evaluating the effect of the static stress induced in the vessel walls by the inner pressure. Particular attention was focused on the exact determination of the maximum crater depth caused by the debris cloud impact on the vessel wall and the backwall plate of the EWS respectively. Bumper and projectile were represented by SPH particles, the vessel shell was represented by a Lagrange grid. After performing a systematic mesh refinement, the simulated crater depths were predicted to within less than 2 % with respect to the measured crater depths of the experiments. Thus, the AUTODYN code has proven its principle capability to simulate such complex test cases and potentially can be used for the simulation of non-perforating impacts on shielded gas-filled pressure vessels that cannot be simulated experimentally by Light Gas Gun technology, i. e. in velocity ranges in excess of 10 km/s. There is some uncertainty in what concems the determination of the radial extension of the impact damage on the vessels' respectively the backwall plate's surface. This is related to the definition of what is considered a impact crater in the simulation when the cells of the mesh are just deformed (in contrast to eroded). Here, some general procedure needs to be developed in order to be able to compare experimental and numerical results.

REFERENCES [1] Hiermaier S., Schiller F. Hypervelocity Impact Fragment Clouds in High Pressure Gas - Numerical and

Experimental Investigations. Int. J. Imp. Engng., 1999, 23(1): 391-400. [2] Sch~ifer F, Schneider E, Lambert M. An Experimental Study to Investigate Hypervelocity Impacts on Pressure

Vessels. ESA SP'-393, Proc. Second European Conference on Space Debris, ESOC, Darmstadt, 1997: 435- 443.

[3] Schiller F., Schneider E., Lambert M. Hypervelocity Impacts on Cylindrical Pressure Vessels - Experimental Results and Damage Classification. PVP-Vol. 351, Structures under Extreme Loading Conditions, Proc. 1997 ASME Pressure Vessels and Piping Conference, Orlando, FL, USA, 1997.

[4] Whitney J. P. Hypervelocity Impact Tests of Shielded and Unshielded Pressure Vessels, NASA JSC, JSC 32294, 1993.

[5] Friesen L.J. Hypervelocity Impact Tests of Shielded and Unshielded Pressure Vessels, Part II. NASA Johnson Space Center, JSC 27081, July 1995.

[6] Schiller F., Schneider E. Impact Testing - Impact on Pressure Vessels, Hypervelocity Impacts on Aluminum Pressure Vessels", Report No. EMI-HVI-PV1001, Emst-Mach-Institut, Freiburg, Germany, May 15, 1996.

[7] Crozier W. D., Hume W. High Velocity Light Gas Gun. J. of Appl. Phys. 1957, 28. [8] Stilp A. Review of Modem Hypervelocity Impact Facilities. Int. J. of Impact Engng. 1987; 5,613-621.