Effect of Target Arrangement and Target Materials Properties on Penetration Depth

: The article focuses on the development of the new calculation method of jet penetration into the target using ANSYS AUTODYN simulation. The jet formation and its penetration capability dependence on properties of targets are studied. Two kinds of steel armours Armox 440T and S235JR – in standardized plates of thickness 20 mm are used as materials of the target. The paper contains an analysis of the penetration depth in the targets containing the pure material plates set, combined material plates set and sets of Armox 440T plates with gaps 10 mm and 20 mm among individual plates. The theoretical results of simulation are compared with the results of experiments.


Introduction
Cumulative ammunition with shaped charge is widely used in armies all over the world to destroy numerous types of targets including tanks and other armoured vehicles. A typical modern shaped charge can penetrate steel armour to a depth measured in the diameters of the charge seven or more times.
Due to the relative independence of the jet penetration from impact velocity, the principle of the shaped charge is extensively used for various antitank ammunition or antitank systems, where the warheads have a relatively simple design. On the other hand, the ammunition does not require a weapon barrel loaded by high pressure, which makes the barrel production easier.
It is known that the jet formation and penetration depth in the target also depend on different parameters, such as the shaped-charge hollow angle α, the liner material

Materials and Methods
The jet formation theory is very complex. Many authors have published mathematical models capable to predict the penetration of the armour target by the shaped-charge jet. Penetration theories are given in works [2][3][4][5][6][7][8][9][10][11][12]. All of the models are often simplified, and they do not consider the character of materials too much, especially their dynamics character. In addition, heterogeneity in material properties was not mentioned in previous studies.
The Finite Element Model (FEM) was created using ANSYS AUTODYN [13] software, which is widely used in high explosive detonation simulations, high speed impacts, and other problems areas. The software includes its own material library; however, new materials can be added. The new material addition requires density, equations of state, strength models, and other material properties.  show the diagram of solution presented in this article. Based on AUTODYN, the collapse process is built to obtain the velocity and profile of jet, which is shown in Fig. 1. Then, the model was rebuilt using the jet velocity results from the jet formation model to solve the penetration problem in two ways:

Diagram of Solution
• using the gaps between the plates of target, • using the targets with different materials. Diagrams of these two cases are shown in Figs 2 and 3, respectively.

Materials Properties of PG-7V Warhead Parts
For simulation problems in this article, it is necessary to determine the characteristics of the main structural elements (parts), including materials of the PG-7V warhead, materials of the target and the materials of the air domain: • the case of warhead is made of Aluminium, • the booster charge is from PETN 1.77, • the explosive A-IX-I is used for main charge, • the liner is from CuOF-HC, • the new material properties have been added for wave shaper. Two kinds of armour steel were used for the target formation: Armox 440T and S235JR. Compositions and basic properties of Armox 440T were obtained from [14] and S235JR from [15].
Some parts used the material parameters taken from the ANSYS AUTODYN library and the remaining parts used the material parameters obtained from the experiments or from FEM, Inc. Tabs 1-5 introduce the properties of chosen materials.

Experiment Setup
The experiments were carried out by the Military Research Institute in Brno at the Bzenec shooting range. The number of PG-7V warheads had been limited, therefore the experiments were carried out according to Tab. 6. The warhead was placed in an optimal standoff distance from the target 180 mm. The target was built from 17 pieces of Armox 440 plates (20 × 200 × 200) mm, which is shown in Fig. 4. Fig. 5 shows the experimental setup when using target with air spaces between Armox 440T plates. The warhead is placed in an optimal standoff from the target. In these tests, the distances of gaps were 10 mm, resp. 20 mm. Fig. 6 shows the experimental setup when using S235JR target.

Simulation of Target Characteristics Effect on Penetration Depth
The process of the jet formation simulated in the FEM model described the Eulerian grid created a high-speed jet. Then the jet was transferred to the Lagrangian grid with the same coordinate system as in case of the Eulerian grid and the target made of steel armour plates from the Armox 440T was built using the ALE grid. The types of grids used were consulted with the experts from ANSYS company. The materials properties of the jet and target are introduced in Tab. 4 and Tab. 5.

Simulation of Target Characteristics Effect on Penetration Depth
The process of the jet formation simulated in the FEM model described the Eulerian grid created a high-speed jet. Then the jet was transferred to the Lagrangian grid with the same coordinate system as in case of the Eulerian grid and the target made of steel armour plates from the Armox 440T was built using the ALE grid. The types of grids used were consulted with the experts from ANSYS company. The materials properties of the jet and target are introduced in Tab. 4 and Tab. 5. Fig. 7 introduces the PG-7V model used for the jet formation simulation, which includes following parts: booster, case, wave shaper, main charge and liner. Using ANSYS AUTODYNE software, the FEM model was built up to determine the jet velocity, jet formation as well as the collapse process of the liner. All parts of the jet formation process model were described by an Eulerian grid. The model consists of 2 parts: PG-7V warhead and an air domain in front of it.

Simulation Model of Jet Formation
A coordinate system was built to determine positions of jet tip at any moment of jet moving. In this coordinate system, the 0x axis is axis of symmetry of the warhead, the rear edge of booster is chosen as 0y axis, and the origin is the intersection point of 0x and 0y axis. The coordinate system of the model was constructed as shown in

Jet Formation Simulation Results
All cases of simulation as well as experiments were performed when the warheads were located at the optimal standoff distance. According to technical documentation, the distance of the PG-7V warhead from the target to the rear edge of booster was between 318 mm and 332 mm, depending on the production precision of the warhead. Based on the simulation results, Fig. 9 shows the graph of the velocity and the profile of the jet in the optimal stand-off distance position. At this moment, the coordinates of the jet tip are (327; 0).  Fig. 10 shows the formed jet of the modified PG-7V warhead and the target model with gaps 10 mm between the plates of the target. In the same way, Fig. 11 shows the jet -target models assembled in the case where gaps are 20 mm.

Effect of Target Materials Properties on Penetration Depth
The model of penetration jet into the target made of Armox 440T is shown in Fig. 12. Series of Gauss points were set on the 0x axis to obtain the jet tip velocity and the state of the target at any moment of simulation time.

Fig. 12 Penetration model in case of Armox 440T target
In the same way, Fig. 13 shows the formed jet and target model at the optimal standoff distance at the moment of impact on the mixed target, which is formed alter-nately of 20 mm Armox 440T armour plates and 20 mm S235JR plates. Material properties of Armox 440T were determined experimentally.

Simulation of Air Spaces Effect between Plates of Target
The results indicate the state of the jet during the penetration process depending on time. Figs 15 and 16 show the state of jet -target system. The velocity of the jet depends on its length at 9.248 × 10 -2 ms of simulation time. In this case, the gaps size is 10 mm. The dependence of the penetration depth on the selected gaps between the plates of the target is shown in Fig. 17. In case of the 20 mm or greater gaps, the penetration depths do not change significantly. According to the trend of the graph, when the gaps between the plates further increase, the penetration depth will be less affected.  The dependence of the penetration depth on the selected gaps between the plates of the target is shown in Fig. 17. In case of the 20 mm or greater gaps, the penetration depths do not change significantly. According to the trend of the graph, when the gaps between the plates further increase, the penetration depth will be less affected.

Simulation of Target Materials Properties Effect
Figs 18-20 compare the jet velocities at the different penetration depths in all three cases of the plate arrangement of the target. At 120 mm penetration depth in the target formed by Armox 440T plates or the combination of Armox 440T and S235JR plates, the jet velocities and their structure are very similar. The jet tip velocity moving in the target formed by the Armox 440T and S235JR plate combination is 5 048 m s −1 . In case of the target composed only of Armox 440T plates, the jet tip velocity is 5 000 m s −1 and 6 920 m s −1 in case of the penetration into the S235JR plates.
The jet penetrating into the target composed of Armox 440T plates is divided into multiple sections (Figs 19 and 20). After the jet penetration at the depth of 200 mm into the S235JR plates, the jet tip velocity is 5 630 m s −1 . It is about 1.53 times greater than the jet tip velocity penetrating into the target from the Armox 440T plates and 1.41 times greater than the jet tip velocity penetrating into the target formed by Armox 440T and S235JR.
At 240 mm penetration depth in the S235JR plate target, the jet velocity is 5 160 m s −1 , which is 1.78 times greater than the jet tip velocity penetrating into the target from the Armox 440T plates and 1.49 times greater than the jet tip velocity penetrating into target from Armox 440T and S235JR plates.
Tab. 8 shows the comparison of time and the jet velocity simulation results depending on the penetration depth of three cases plate arrangement of the target. It can be seen from Figs 21-23 that the penetration depth in the target from the S235JR plates is greater than 400 mm. It is about 1.35 times higher than the penetration depth in the target from the Armox 440T plates (305 mm) and 1.3 times higher than that one in the target composed from the Armox 440T and S235JR plates with a penetration depth value of 320 mm.  Fig. 23 The target composed of S235JR plates after penetration

Comparison of Simulation and Experimental Results
The results of experiments carried out according to Tab. 6 and results of simulation are introduced in Tab. 9.
Comparing the penetration depth values in Tab. 9, the effect of the target material properties on the penetration depth is obvious. In case of penetration experiment using the S235JR plates, 20 plates were completely penetrated and the 21 st plate was partially penetrated. A comparison of the experimental results using the armour Armox 440T without gaps and using two different gaps is shown in Fig. 24. It is obvious that the penetration into the target decreases with larger gaps size of air space.
It is also obvious from Tab. 9 that the differences of the average experimental values and simulation results are not so high, i.e. in the range from 0.3% to 2.5%. In case of the composed target from two introduced steels, the difference is 12.8%.

Conclusion
In this article, the 2D simulation model using ANSYS AUTODYN was built to observe/study the effect of the target materials properties as well as the gaps sizes between target plates on the penetration depth values. Comparison of simulation and experimental results proves their very good correspondence with exception of the armour combination. Therefore, the ANSYS AUTODYN use for the penetration simulation of the armours of various properties and structures is possible and expedient when required input armour characteristics are known. Of course, the simulation results verification by the higher number of experiments is necessary. In this case, the higher number of PG-7V warheads or another HEAT ammunition for experiments were not available.
Despite the small amount of experiments, significant conclusions have been proved. The penetration depth of the target composed of the armour plates is comparable with that one of homogenous ballistic protection introduced for this ammunition. The regular gaps between the armour plates decrease the penetration depth. In spite of that, the penetration of armoured vehicles is still sufficient.