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20th international symposium on ballisticsorlando, fl, 2327 september 2002numerical simulation of the penetrationprocess of geopenetrators into predamagedconcrete targetsn. heider11ernst-mach-institut, eckerstr. 4, 79104 freiburg, germanytandem warhead systems consist of two components: a precursor shaped charge and a following kinetic energy (ke) projectile containing a high explosive filling. they are designed to penetrate hardened structures especially targets with concrete layers. the performance of the ke projectile depends strongly on the target damage due to the shaped charge jet penetration. at the moment there are no detailed reliable data about the damage available. this paper therefore analyses in a parametric way the influence of target damage (formation of crater hole as well as concrete material damage) on the achievable ke penetration performance. the simulations are based on an explicit modeling of the shaped charge jet crater with the crater profile deduced from experimental results. the crater shape and the damage level (reduced compressive strength of the concrete afterloading from the shaped charge jet) are varied parametrically. the numerical model is validated with experiments of ke projectiles intoplain concrete targets without pre damage. introductiona principal sketch of a tandem warhead system is shown in fig.1. the sequence of events during the impact of the tandem warhead is as follows: initiation of precursor shaped charge with jet formation interaction of jet with target (crater formation and damage of concrete around the crater) penetration of the following ke projectile into the pre damaged concrete target. a complete simulation of the tandem warhead function including the shaped charge jet penetration is given in 1. the theoretical description of the performance of the two tandem warhead components as a single weapon is already very good (within numerical as well as analytical modeling). some uncertainties still exist for the tandem system especially concerning the interaction of the ke projectile with the damaged target. the analytical and empirical modeling of the tandem system therefore requires some better understanding of the target damage and its influence on the time history of the ke projectile penetration process. due to the lack of detailed experimental and theoretical data on the damage distribution within the target it seems a reasonable approach to analyze the penetration process with the help of parametric variations of the relevant parameters describing the crater and the degree of damage in the concrete target material. this method allows the separate investigation of the influence of these physical parameters on the penetration depth of the ke projectile and a detailed understanding of the involved processes. fig.1 components of tandem warhead system fig.2 parameterization of carter profileexperimental basisthe simulation model is based on experimental results of concrete penetration with shaped charge jets and ke projectiles.the explicit modeling of the damaged concrete target requires information about typical crater profiles created by the impact of the shaped charge jet. the crater profiles are taken from experiments where shaped charges were fired against concrete targets at a stand off of 3 calibers. the crater profiles are not very sensitive to stand off as soon as the maximum penetration depth as a function of stand off is reached. even at high stand off values of 20 calibers the crater profiles are still similar to the corresponding ones at 3 calibers. the tests have been performed with 80 mm caliber charges with aluminum liners and point initiation. typical crater profiles have the following characteristics:biconical profile (see fig.2)spall crater at shaped charge jet impact surfaceerosion crater reaching to the final depth.the explicitly modeled crater profiles are derived from these data.the ke projectile penetration into undamaged concrete targets was used as avalidation case for the simulation model including the concrete material description. the following penetrator design was used:caliber 60mmlength 508mmmass 6039gthe target consisted of two concrete blocks of diameter 96cm, length 1m and a steel casing. the concrete compressive strength was 35n/mm2 . the experimental results were (see 2 and 3 for experimental details and interpretation of penetration depth within cavity expansion theory):impactvelocity 509m/secpenetration depth 114.5cmfig.3 shows the front and rear side of the target after impact of the ke projectile.fig.3 ke projectile impact test: front and rear side of concrete targetthe corresponding results from the simulation are shown in fig.4 with the configuration at the time of impact and after the penetrator came to rest. the calculated penetration depth is 119 cm and agrees very well the experimental value of 114.5cm. fig.4 simulation: ke penetrator at impact and at end of penetrationsimulation modelthe simulation model consists of the damaged target and the ke penetrator. the performance of the shaped charge jet is not explicitly modeled. instead the crater profile and the damage area around the crater are modeled explicitly. the simulation model used for this application is based on the erosion crater because the radius of the spall crater is significantly bigger than the radius of the ke projectile and thus has no influence on the ke projectile penetration. the crater used in the simulations is thus characterized by two diameters corresponding to target surface and the final penetration depth. these two parameters can be varied to study the influence of crater diameter on the penetration process.as no date are available about the damage produced in the concrete target due to the penetration of the shaped charge jet, the damaged region around the crater and the amount of strength reduction are additional variation parameters. the damaged area was assumed cylindrical with a certain depth and radius and a constant degree of damage within this area. these are three further variation parameters. the presented model parameters are deduced from experiments if possible and in the other cases are varied in a range that seems to be reasonable and interesting for he physical understanding.the simulation contains the three materials: original concrete target, damaged concrete target and the high strength steel penetrator case. the high strength steel is described with a johnson cook model for the deviatoric strength behavior. very important is the material description of concrete. for this purpose the rht model, developed at emi is used .concrete has the following experimental material properties: tensile strength is 1/10 of compressive strength shear strength is pressure dependent damage development (failure surface depends on damage due to preloading) porosity and existence of micro cracks between mortar and aggregatesthe description of these phenomena requires a complex model for the characterization of concrete. the emi rht model includes the static as well as the dynamic range and thus can be used for the penetration processes of ke penetrators.the following gives a short summary of the main properties of the model: porous equation of state limit surfaces pressure dependent (elastic, failure and residual strength) limit surfaces depend on all 3 invariants of stress tensor strain rate effectsfig.5 shows the schematic location of the different limit surfaces in the stress space especially the change of the failure surface due to damage development. damage occurs as soon as the failure surface in the stress space is reached during a loading process. in the uniaxial compression test damage occurs in the stress strain diagram in the region following the maximum compression stress. the material behavior is then characterized by macroscopic crack development. the following phenomena have to be described: reduction of the failure surface with increasing damage (material with a complete damage can not sustain any tensile stresses any more) reduction of elastic constantsin the following the presented modeling parameters are varied and their influence on the ke penetration depth is analyzed.simulation resultsthe simulation variants analyzed are shown in fig.6. the reference case is simulation 1 with the original undamaged concrete target. varied is the crater profile (simulation 2 and 7) and the damaged area around the crater (spatial extend and damage level, simulations 3 to 6 and 8 to 12). in addition a simulation 13 was performed with a semi infinite target to get information about the influence of the target size on the penetration performance. influence of the crater diameter: fig.7 shows the penetration depth of the ke projectile as a function of the crater radius on the impact surface. the penetration depth from the simulation in the undamaged target is 1198mm (the corresponding experimental value is 1145mm). modeling of the eroded crater profile (without damage in the region around the crater) gives an increase to 1251mm (crater radius 11.2mm) or 1404mm (crater radius 22.4mm). small hole diameters (compared with the projectile diameter) lead only to a small increase of the performance of the penetrator. only hole diameters approaching half of the penetrator caliber significantly increase the penetration depth.influence of strength reduction: fig.8 shows the penetration depth as a function of time for several simulations. here the reference configuration 1 is compared with the simulation 6 where the model shows only a strength reduction (from 35mpa for the original concrete to 10mpa for damaged concrete) but no crater hole in the target. the penetration depth increases from 1198mm to 1377mm. the increase is nearly as high as for simulation 2 with the crater profile modeled (penetration depth for simulation 2 is 1404mm). the strength reduction with a spatial extension of 2 penetrator calibers around the impacting projectile thus leads already to a significant performance increase.combination of crater profile and strength reduction: fig.8 contains the simulations 1,3 and 4. this corresponds to the situation where crater profile and strength reduction occur together. the penetration depth increases from 1198mm (reference case) to 1458mm (simulation 3 with small damage area) and finally to 1467mm (simulation 4 with bigger damage area). comparison with the former results shows that the combined effect leads to a relatively small additional increase of penetration.material damage or crater hole alone give already most of the achievable performance gain. the combination shows an overmatch for the simulated configuration. variation of the damage level from 10mpa to 5mpa gives an additional penetration depth increase (simulation 4 - 1467mm compared with simulation 5 - 1490mm). it is important to note that there is no linear addition of the contributions from damage and crater hole to the total penetration. the whole target damage in front of the penetrator determines the performance independent by which effect it is caused. if there is already a significant damage due to eroded material an additional material damage has only minor influence. on the other hand material damage alone is sufficient to increase the penetration depth significantly.fig.6 simulated crater profiles and damaged target areasinfluence of spatial extension of damage zone: the radial as well as the axial extension of the damage zone is varied. for the axial extension the two values of 637mm and 1000mm were selected. the crater hole profile itself was not changed. the dependence of the penetration on the radial extension of the damaged area is shown in fig.9. there is a sort of plateau formation at a radial distance of around 2 projectile calibers with a penetration increase of around 250mm. the 2 significantly lower values at the radial distance at 50mm correspond to the axial damage extension of 637mm.this shows the importance of the radial as well as the axial extension of the damaged target regions on the penetration. fig.5 schematic representation of fig.7 ke projectile penetration aslimit surfaces of concrete a function of crater radius fig.8 time history of ke fig.9 ke projectile penetration asprojectile penetration a function of damage radiusinfluence of target dimension: a final simulation 13 was done which modeled a target with semi infinite extension (simulated with corresponding boundary conditions). the penetration is 1104mm and has to be compared with the value of 1198mm from the reference simulation 1. it gives an impression of the expected variation of performance of ke projectiles in real targets where different impact conditions are found. the decrease of penetration is due to the higher confinement and the reduced effects from the target boundaries.summarythe performance of the precursor shaped charge in a tandem warhead systems leads to a weakening of target (formation of crater hole and material damage). the development of engineering codes for the description of the tandem system requires a detailed understanding of the separated effects. therefore a finite element model was developed that is based on experimental res