Maxim Yu. Orlov, Viktor Glazyrin and Yuri N. Orlov
National Research Tomsk State University (TSU), Tomsk State University, Tomsk, Russia
(*)Email: [email protected]
ABSTRACT
In this work, numerical simulation of penetration of multilayer steel structures by a projectile is presented. The research objects were three-layer and four-layer steel plates. Projectiles had the same mass and diameter but different head part. The penetration of multilayer plates by a projectile was modeled in an elastic plastic lagrangian 2D statement using a non-commercial software package. Comparison of numerical results with experimental data was given. The post penetration analysis, including the time of the birth of the first foci of destruction, the time of penetration, the residual projectile velocity, the residual displacement were obtained numerically.
Keywords: multi-layered plates, projectile, post penetration analysis.
INTRODUCTION
At present time, multi-layer plates are used to protect civilian and military facilities. This is due to many reasons, including the unique ability of such structures to transform a falling shock pulse. Numerical results of the process of breaking through multilayer plates impacted by a 7.62 mm APM2 projectile are presented (Flores-Johnson, 2011). The influence of the shape of the projectile on the penetration of plates is studied in (Gupta N.K, 2008). According with a previous study impact resistance of steel bilayer plates was studied. The target was divided into the main layer and an additional layer. Moreover, the second layer was reinforcing. Ballistic performance steel plates impacted by 6.1 mm Smk projectile are presented (Glazyrin, 2006).
The current research objects are multi-layered plates in which the reinforcing layer is bilayer one. The additional layer consisted of two identical steel plates.
Mathematical model is based on phenomenological macroscopic model of continuum mechanics.
Governing equations is based on the fundamental laws conservation for: mass, momentum and energy. Elastic-plastic flow is given by the Prandl − Reis equations. The numerical solution is carried out in 2D statement for the axial symmetry by G.R. Johnson’s modified method. This method is based on lagrangian approach, and it allows simulate the task of deep penetration into heterogeneous structures, including modern protective structure.
The modification of the method include: algorithm erosion of triangulation elements, nodes splitting algorithm, and free surface constructing algorithm (Gerasimov A.V., 2007). According to the terminology of acad. V. Fomin method contains a new way for isolating discontinuity surfaces of materials. Before the numerical simulation conducted internal, qualitative and quantitative tests. The calculations were performed on the non-commercial software package Impact 2D. Before the calculations were carried out quantitative test only.
15, material’s plate is Steel 3 (In accordance with the Russian nomenclature of Construction materials). Projectile’s mass is 2.55 g. One diameter is 6.1 mm. The thickness of the layer in the multilayer plate was 2 mm.
Table 1 shows the numerical results. In addition to the values from Table 1, the time of the birth of the foci of fracture in materials, the air gap between the layers, the pressure at the control points, were obtained. The table shows the values for the three types of projectiles, including a projectile with an ogival nose, conical one and flat one. X is the designation of an additional layer. The first sample in the table is the homogeneous 6 mm plate.
Table 1 - Numerical simulation results Sample Penetration time
[µs] Residual
Velocity [m/s] Damage
[%] Hole diameter
[mm]
(6) 44/35/70 444/349/240 10.3/10.3/9.8 6.9/7.8/9.1
(2+2+2) 47/49/48 472/382/226 10.4/10.3/8.3 7.4/9.1/8.5
(X+2+2) 37/42/40 493/302/232 11.2/9.9/10.2 7.4/8.5/9.2
(2+X+2) 42/38/45 483/390/238 10.7/10.3/9.3 7.1/8.9/9.4
(2+2+X) 32/40/48 528/392/237 9.47/11.1/9.5 6.8/9.2/8.9
Numerical values for ogival nose/conical nose/flat nose/.
Thus, the research presents the result of breaking through multilayer plate by projectile.
Location additional layer in different parts of the plates have little effect on its impact resistance at a given initial velocity.
ACKNOWLEDGMENTS
The reported study was funded by RFBR according to the research project № 19-08-01152.
REFERENCES
Flores-Johnson E.A, Saleh M, Edwards L, Ballistic performance of multi-layered metallic plates impacted by a 7.62-mm APM2 projectile. Impact Engineering J, 2011, 38, p.1022- 1032
Gupta N.K, Iqbal M.A, Sekhon G, Effect of projectile nose shape, impact velocity and target thickness on the deformation behavior of layered plates. Impact Engineering J, 2008, 35, p.37-60
Orlov M Yu, Glazyrin VP, Orlov Yu N, Golubatnikov VV Modelling of the process penetration of steel barriers by elongated impactors Proceedings of the 7th International Conference on Mechanics and Materials in Design, Albufeira/Portugal 11-15 June 2017. Editors J.F. Silva Gomes and S.A. Meguid. pp. 1019-1020
Theoretical and experimental research of high-speed interaction of bodies. In Gerasimov AV (ed)/ Tomsk State University Publishing House, 2007, p/ 564
PAPER REF: 052
MODELING OF THE PROCESS OF EXPLOSIVE LOADING OF ICE
Viktor P. Glazyrin, Maxim Yu. Orlov and Yuri N. Orlov
National Research Tomsk State University, 36, Lenin Avenue, Tomsk, 634050, Russia
(*)Email: [email protected], [email protected]
ABSTRACT
In this paper, the problem of the effect of detonation products of an explosive charge located in ice or under water under ice on an ice block was solved. The charge is considered to be an explosive such as TNT and liquefied gas ethane. The behavior of ice is described by the basic system of equations of the mechanics of a deformable solid. The effect of explosive loading on a material is given in the approximation of the model of instantaneous detonation of an explosive charge. The aim of the research is to study the process of ice destruction, including the formation of the first foci of destruction, the time ice destruction, pressure and velocity at control points under action of detonation products (DP). By means of the author’s software package, computational experiments on modeling the process of explosive loading of ice cover were carried out and analyzed.
Keywords: ice, model, modelling, velocity, barrier, penetration, detonation, destruction
INTRODUCTION
The modern development of the Arctic and the northern territories of Russia requires the deepening of our knowledge in the field of physics and ice mechanics by conducting theoretical and experimental studies on the behavior of ice under various types of loading, in particular under impulse action. Certain results in this direction can be obtained by conducting large-scale model and field experiments. However, it is necessary to note the technical complexity and high cost of such experiments, as well as the impossibility of obtaining detailed information on the spatial and temporal distribution of stress fields, deformations and areas of damage in the ice samples under consideration. Therefore, a theoretical approach based on mathematical modeling of processes is of particular importance in terms of these studies (Gerasimov, 2007).
In the paper (Orlov, 2017) with the help of the original computer program (Glazyrin, 2018), penetration metal ball into the ice block was studied. The calculated values of stresses and strains in the samples correspond to the experimental data.
RESULTS AND CONCLUSIONS
The physical formulation of the problem is formulated as the action on the ice plate of detonation products of an explosive charge placed in ice or in water under ice. As a charge, explosives of the TNT type and liquefied gas ethane SZHG are considered. Ice thickness is 80 cm.
The medium considered is assumed to be compressible, isotropic with the absence of mass forces, internal heat sources and heat conduction (Zelepugin, 2017). An elastic-plastic model is used with the Prandtl − Reis plastic flow equations associated with the von Mises yield condition. The equation of state of Walsh is used. The effect of porosity on the stress-strain state
gradient distribution of strength, the initial anisotropy, as well as the effect of temperature on the strength and fragmented selection of zones of destruction. The model of destruction is based on a deterministic approach and takes into account the joint formation of damage by the type of spall and damage by the type of shift. The effect of explosive loading on the material is set in the approximation of the model of instantaneous detonation of the explosive charge.
The numerical solution of the stated boundary value problem is carried out in 2D for axial symmetry by the Johnson’s method. The method contains a modified algorithm for splitting nodes, erosion triangle elements, restructuring the free surface, etc. (Gerasimov, 2007). To test the mathematical model and determine the necessary constants, task of penetration of 4.5 mm steel ball into the ice block was solved. The impact velocity varied from 100 m/s to 200 m/s.
The objects of study were the freshwater ice block, as well as thick ice (300 cm) and ice on the water. By means of author’s uncommercial software package, the task of the destruction of an ice block by an explosive charge placed under ice in water was solved. The modelling was carried out for the “Ice − Water – Explosives” system at different detonation velocity and explosive substance masses. The depth of explosive laying was 80, 50, 40 and 0 cm, the masses of explosives were 6, 10 and 14 kg, the detonation velocity was 4.6 km/s and 6.9 km/s.
The numerical results allow us to estimate the degree of damage to the ice cover, to determine the values of the velocity of the elements of the free ice surface and the pressure at any point of water and ice, depending on the depth of the explosive charge. It has been established that the action of DP of a TNT charge, which is equal in mass to the charge of SZHG, under the same initial conditions, causes almost two times more ice destruction.
ACKNOWLEDGMENTS
The reported study was funded by RFBR according to the research project № 19-08-01152.
REFERENCES
Gerasimov A.V., GlazyrinV.P., Orlov M. Yu. and others. Theoretical and experimental research of high-speed interaction of bodies/ Tomsk State University, 2007, pp. 564.
Orlov M.Yu, Orlova Yu.N., Bogomolov G.N., Glazyrin V.P. Research of the behavior of ice on water under explosive loads. IOP Conf. Series: Journal of Physics: Conf. Series 919 (2017) 012006 doi :10.1088/1742-6596/919/1/012006.
Viktor P. Glazyrin, Maxim Yu. Orlov, Yuri N. Orlov Analysis of the penetration of the barriers by impactors with an explosive substanсe // Proceedings IRF2018: 6th International Conference Integrity-Reliability-Failure, Lisbon/Portugal 22-26 July 2018, р. 893-898.
Zelepugin S.A., Ivanova O.V., Yunoshev A.S., Zelepugin A.S. Numerical simulation for the propagation and action of shock waves during explosive synthesis // IOP Conf. Series:
Materials Science and Engineering, 2017, Vol.894, no. 012033, p. 1-8. doi: 10.1088/1742-6596/894/1/012033.
Skripnyak V.V., Skripnyak V.A., Skripnyak E.G. and Vaganova I.K. Mechanical response of ZrB2–based ultra-high temperature ceramics to shock pulse loadings in a wide temperature range. IOP Conf. Series: Journal of Physics: Conf. Series 1115 (2018) 042016, https://
doi:10.1088/1742-6596/1115/4/042016.
PAPER REF: 053