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2023 | Book

Behavior of Materials under Impact, Explosion, High Pressures and Dynamic Strain Rates


About this book

This book presents the results of experimental and theoretical studies of the destruction of solids under impact, explosion, high pressures, and strain rates. The content identifies the basic laws of the destruction of bodies under dynamic loads. The results of numerical studies were obtained using numerical methods on the Lagrangian, Euler, and ALE approaches to the description of the motion of continuous media. Numerical methods and mathematical models have been tested by comparison with experimental data and well-known analytical solutions (for instance, Rankin–Hugoniot laws). Experimental studies were performed on unique ballistic installations with the registration of fast processes (high-speed shooting). The results are used as new tests to verify the developing modeling methods. The research objects were metal multilayer plates, functionally graded materials, advanced, smart, and natural materials, etc. The book is interesting to specialists in the field of mathematical modeling and experimental methods for studying fast processes under dynamic loading.

Table of Contents

Chapter 1. “Algozit” Programming Environment for Continuum Mechanics Problem-Solving
The specific features of the “Algozit” programming environment for functional-object implementation of numerical experiment algorithms in continuum mechanics are investigated. Not only “Algozit” architecture is described, but also the technology providing visibility of complex algorithm representations with convenient program debugging, being based on visual programming of functional-object schemes, is proposed. Implementation of a mathematical model for multi-layer fabric package behavior under rigid element impact is described. Numerical modeling results and the correlation with physical experiment data are presented.
Valerii O. Kaledin, Anna E. Paulzen, Sergey V. Belov, Sergey V. Ponomarev
Chapter 2. Comparative Assessment of Underwater Explosion Resistance for GRP and CFRP Specimens
The results of experimental and computational studies on the resistance of glass reinforced plastic (GRP) and carbon fiber reinforced plastic (CFRP) specimens under proximity underwater explosions are given. Four groups of specimens made with different reinforcement materials were tested. The structure of reinforcement ensured quasi-isotropic properties of the material. Based on experimental data, the patterns of damage accumulation and failure for these materials are considered. The damage to material is assessed in terms of three criteria: damage to binder, rupture of individual fibers, and through-type fracture. Experiments have established that the resistance to the explosion of GRP specimens is much higher than that of the CFRP specimens under consideration in terms of individual fiber ruptures. Computer models have been developed and verified using LS-DYNA and AUTODYN software for the experimental conditions. Based on computer modeling, the details of the stress-strained state in GRP and CFRP are considered by the instant of damage initiation (rupture of fibers).
Andrey I. Dulnev, Ekaterina A. Nekliudova
Chapter 3. Numerical Study of the Geometric Distribution of Metal of Cumulative Lining
Based on the review of scientific and technical literature, the well-known facts about the course of the cumulation phenomenon and its features are presented, including elements of the hydrodynamic theory of cumulation. The known information on the geometric distribution of the metal of a cumulative lining during the operation of the cumulative charge is analyzed. The need to clarify the existing knowledge about the geometric distribution of the material in the jet-forming process is explained. The hypothesis of the jet-forming process by plastic deformation of lining material is proposed. A numerical experiment on the functioning of an axisymmetric cumulative charge is performed, and the data obtained on the geometric distribution of the lining metal are analyzed.
Ekaterina M. Grif, Anatoliy V. Guskov, Valeriya A. Kiryukhina, Konstantin E. Milevsky, Alena A. Nesterova
Chapter 4. About Mechanical Behavior and Effective Properties of Metal Matrix Composites Under Shock Wave Loading
In this work, the results of studying the mechanical behavior at the mesoscopic scale and effective properties of composites with aluminum matrix and reinforcing ceramic inclusions are submitted. Computer simulation of mechanical reaction of a representative volume of composite material, considered as an ensemble of the interacting structural elements (ceramic particles and metal matrix), is used for studying mechanisms of deformation and processes of the nucleation and growth of damage in metal–ceramic composites at the mesoscopic scale under the loading by shock waves. The mechanical behavior of aluminum matrix is described by the model of the damaged elastic–plastic medium. The model of the damaged brittle solid is used for ceramics. The problem is solved in the 2D statement with the application of finite-difference method. Results of numerical simulation have shown the formation of non-stationary and essentially non-uniform fields of stresses and strains at the mesoscopic scale. Generation of a dissipative structure at the mesoscopic scale in the composites under shock wave loading was revealed in the simulations. Cracks in ceramic particles, cracks between particles and matrix, and damage to the matrix can appear in composites under shock wave loading. The values of effective mechanical characteristics of composites were defined in this work.
Valerii V. Karakulov, Vladimir A. Skripnyak
Chapter 5. Shaped-Charge Treatment Effects Accompanying the Formation of Hard Structure and New Phase States in Coatings on Titanium
This paper presents the results of research on superhard coatings obtained by the interaction of high-speed powder clouds with a titanium substrate. High-speed powder clouds were obtained under conditions of a shaped-charge explosion. Shaped-charge synthesis was conducted using specially prepared mixtures containing atoms of nitrogen, carbon, and boron. The interaction of the initial mixture components and the substrate material yielded nitride, carbonitride, and boride phases that formed superhard coatings. The relationship between the mechanical properties of the investigated coatings and their structural state was established in this study. The specific features of the obtained layers were determined by the fact that they are multiphase coatings built into the crystalline structure of the titanium substrate. The microhardness of these layers varies in the range of 11–21 GPa.
Gulzara Kanzamanova, Sergey A. Kinelovskii, Alexander A. Kozulin
Chapter 6. Reactor 3D Software Performance on Penetration and Perforation Problems
To verify the REACTOR3D software package, numerous methodological numerical calculations of the processes of solids dynamic interaction have been carried out, and the comparison of the calculation results with the existing experimental data has been performed. The problem of the penetration of a high-strength elongated rod made of hardened steel into a massive target made of aluminum alloy has been solved, and a non-monotonic dependence of the penetration depth of the rod on the velocity, like the one in the experiment, has been obtained. The results of calculations for the collision of compact bodies of arbitrary shape with a massive target fit with good accuracy in the self-similar modeling Zlatin curve in dimensionless coordinates L/H (crater depth to the striker length) and E/Y (kinetic energy to the yield point). Based on numerical calculations, the engineering formula for the hole diameter in a thin target at a high-speed collision (2–5 km/s) with a metal sphere has been modified.
Aleksandr E. Kraus, Evgeny I. Kraus, Ivan I. Shabalin
Chapter 7. Numerical Simulation of Thermodynamic Parameters for Gold Alloys Under Shock-Wave Loading
The results of numerical experiments on modeling the shock-wave loading of alloys containing gold (Au) as a component are presented. The simulations were performed using the thermodynamical equilibrium model TEC. The model allows us to take into account the possibility of a polymorphic phase transition under the shock-wave action of the materials. It is essential for reliable simulating of thermodynamic parameters of composites and alloys containing such materials. The method allows us to describe the shock-wave loading of solid and porous alloys of various compositions. The calculations are performed for alloys of Au in combination with lead (Pb) and germanium (Ge), such as Au–Pb and Au–Ge. The calculated shock adiabat is compared with the available data from dynamic compression experiments.
K. K. Maevskii
Chapter 8. Numerical and Analytical Modeling of Two-Dimensional Water Flows Arising After the Dam Failure
The paper considers the gas-dynamic problem of the breakup of a special discontinuity for modeling two-dimensional isentropic water flows appearing after the destruction of the dam. The equations system of gas dynamics for polytropic gas considering the force of gravity with the polytropic index γ = 7.02 is used as a mathematical model. It is assumed that this model adequately describes two-dimensional water flows. With the help of non-stationary self-similar variables, the analytical solution to the problem is constructed in the area of rarefaction wave from the boundary of the resting gas to the gas-vacuum boundary in the form of convergent series. The first terms of the convergent series are used as the approximate conditions for the numerical statement of the problem, and the introduced error is estimated. Then the numerical modeling of the rarefaction wave is performed with the help of the explicit difference scheme.
Sergey L. Deryabin, Alexey V. Mezentsev
Chapter 9. Numerical Simulation of the Interaction of a Shock Wave with a Permeable Granulated Layer
Solutions to the problems of the action of plane shock waves on a deformable granular layer are obtained. The transformation of waves when passing through an elastoplastic granular layer with and without taking into account the change in the permeability of the layer due to its deformation is investigated. When solving problems, the dependence of the change in the permeability of a layer on its compression is used, which was obtained numerically when modeling the compression of symmetric fragments of granular layers in a spatial setting. A mathematical model is presented that describes in a one-dimensional approximation the interrelated processes of unsteady deformation of flat permeable granular layers, consisting of spherical particles, and wave processes in gas. The model is based on nonlinear equations of the dynamics of two interpenetrating continua. As the interphase forces, the drag forces are taken into account when the gas flows around the spherical particles and the Stokes friction forces. The numerical solution of the equations is carried out according to the modified scheme of S. K. Godunov, adapted to the problems of dynamics of interpenetrating media.
Anatoliy V. Kochetkov, Ivan A. Modin
Chapter 10. Research of the Behaviour of Multi-layered Steel Targets Impacted by High-Velocity Projectiles
This paper presents a numerical investigation of the ballistic performance of monolithic, double-, and triple-layered metallic plates impacted by a 6.1-mm projectile at the velocity of 500 m/s. The behaviour of materials is described by elastic–plastic model with a deterministic failure concept. The modified Lagrangian method for penetration and perforation problems is used. All the finite-element simulations are conducted with non-commercial 2D computer code Impact. A good agreement in terms of penetration depth of projectile was obtained between experiment and calculation. We obtained computed values of perforation duration of targets, residual projectiles velocity, damage level, hole diameter, and time of nucleation foci destruction. It was found by numerical modelling that ballistic performance for some multi-layered plates was greater for monolithic plates ones. An attempt to clarify this effect was performed in the chapter.
Maxim Yu Orlov, Talgat V. Fazylov
Chapter 11. Approaches to Determining the Load on a Free Body of Finite Mass upon Impact of a Highly Porous Cylinder
The study aims to evaluate approaches to determining the load on movable barriers of nuclear power plant structures when a military aircraft strikes. The load on such structures may differ significantly from that calculated for impact at rigid wall. The initial stage of interaction is considered, that is, the deformation of the nose compartment containing the onboard equipment (OE). The purpose of the work was to determine the applicability of simplified approaches to mechanical equivalents of OE. Additionally, the effect of the mobility of the barrier on the loading history was shown. Several simplified approaches to determining the load on a movable barrier were considered. Firstly, this is an approach in which the aircraft is considered as a one-dimensional rigid-plastic rod (Riera’s approach) with an addition in the form of iterative load correction. Secondly, there is the authors’ one-dimensional model. The results of the simplified approaches were compared with 3D simulation in the LS-DYNA program package results. In the calculations in the LS-DYNA package, finite element models of impactors with direct geometric porosity assignment were used. The approaches considered can be used to assess the impact of barrier movements.
Yulian V. Popov, Georgy V. Belov, Vladimir A. Markov, Vladimir I. Pusev, Viktor V. Selivanov
Chapter 12. Comprehensive Experimental and Theoretical Study of High-Speed Entry into Water and Movement of Supercavitating Strikers at Gunfire Start
This paper presents the capabilities of a hydroballistic stand to carry out comprehensive experimental and theoretical studies of high-speed water entry and motion in it of supercavitating strikers during cannon launches. The main technical solutions developed and applied in the study of high-speed throwing of one or several supercavitating strikers are presented. The following processes can be investigated on the hydroballistic stand: acceleration of an inert striker or group of strikers in the ballistic barrel channel in a given mode and obtaining the required initial velocity; movement of strikers on the air part of the ballistic track and separation of the leading devices; entry into the water under different conditions; motion of inert strikers in the water environment; mutual influence of strikers on trajectories in case of group movement; interaction of inert strikers with underwater obstacles. To study and analyze the processes in each of the research areas, mathematical models and software packages have been developed to describe with high accuracy the processes accompanying high-speed throwing, motion and interaction of a single striker or a group of supercavitating strikers in water, as well as with various underwater obstacles.
Aleksandr N. Ishchenko, Viktor V. Burkin, Aleksey S. D’yachkovskiy, Konstantin S. Rogaev, Ivan S. Bondarchuk, Anton Yu. Sammel’, Alexey D. Sidorov, Evgeniy Yu. Stepanov, Andrey V. Chupashev, Vladimir Z. Kasimov, Leonid V. Korol’kov
Chapter 13. The Study of the Slow Deformation Wave Propagation from the Faults Having Different Inclinations to the Loading Axis
In our research, the complete mathematical model for describing the processes of generation and propagation of slow deformation waves combines dynamic equations of solid mechanics and specific constitutive equations of geomedium rheology with a cellular automata algorithm. According to the algorithm, the cumulative plastic strain in any neighboring calculation cell needs to exceed a certain threshold to provide the plastic deformation propagation. Fault zones—narrow elongated areas inclined to the axis of the load application—were defined as the areas where plastic deformation can be generated. As a result of the conducted research, it was found that the shape of the deformation fronts depends on the angle between the fault and the axis of the load application, type of loading (compression or tension) as well as the choice of the implementation of the algorithm of cellular automata for the transmission of slow perturbation. It is shown as well that the choice of the variant of the neighborhood models of cellular automata only slightly affects the shape of the propagating fronts of slow perturbations in the medium.
Aigerim A. Kazakbaeva, Igor Yu. Smolin
Chapter 14. Fictitious Absorption Method in a Dynamic Problem for a Layer Weakened by a Crack
A layer or layered medium with a fracture or fracture system serves as a model for various natural structures, such as geological and structural elements. The use of the provisions from the theory of the vibration strength «viruses» allows us to construct systems of integral equations (IE) for layered media with flat defects. And to solve aforementioned integral equations we can apply the fictitious absorption method (FAM). The purpose of the work presented is to construct a solution for the integral equation of the steady-state oscillation problem on an elastic layer caused by vibration of the edges of an internal fracture with finite dimensions and zero thickness using a modified FAM. In the paper, we present an algorithm for solving the IE with a growing kernel symbol for the vibration problem of a singular flat fracture in a layer, which can further be used to solve equation systems of dynamic problems for a package of layers with discontinuity in their connections. The FAM, being a semi-analytical method, makes it possible to investigate the features of the IE solutions and take them into account during the development of numerical algorithms.
Ilya S. Telyatnikov, Alla V. Pavlova
Chapter 15. Computer Simulation of Related Problems of Sintering Low-Temperature Ceramics
This paper presents an approach to computer simulation of related problems of sintering low-temperature composites. The developed approach makes it possible to numerically calculate the values of shrinkage, concentration of components, and porosity of a sintered compact. The research results have shown that in the formation of the structure of a sintered low-temperature composite material, a decisive contribution is made by the possibility of forming a refractory frame of refractory components of the mixture. The developed modeling scheme makes it possible to estimate the values and nature of residual stresses in the material during the preparation of the initial compact of the sintered sample and the thermal destruction of the binder. The uniqueness of the developed integrated approach lies in the possibility of using a wide range of dispersed elements with various magnetic, thermodynamic, mechanical, and other properties as a refractory component.
Aleksandr O. Tovpinets, Vladimir N. Leitsin, Maria A. Dmitrieva, Anastasia V. Puzatova
Chapter 16. Experimental Investigation of Ice Sample Behaviour When Reinforced with Polypropylene Void Rods
The purpose of this work is an experimental study of the behaviour of ice reinforced with tubular polypropylene rods. It is important to note that polypropylene is a fairly light material compared to rebar, which simplifies its delivery to the Northern regions with harsh climatic conditions. Improvements in experimental studies are presented. The experimental curves are described for various schemes of amplifying samples with polypropylene pipes. The behaviour of the curves and the formation of cracks in the ice matrix are compared with the results of photo and video shooting of the samples. It has been experimentally established that the most optimal scheme is with four pipes in cross section. As a result of the research, it is obvious that polypropylene, when used as surface reinforcement of ice, can not only increase the bearing capacity, but also significantly increase the plasticity of ice samples. The original results obtained can be used to develop recommendations for the construction and operation of reinforced ice cover as ice crossings and bearing platforms.
Alexey S. Vasilyev, Vitaliy L. Zemlyak, Victor M. Kozin
Chapter 17. Mathematical Modeling of Deployment Dynamics of Large Transformable Space Structures
Large-sized space structures with transformable configuration are multilink systems consisting of a large number of interconnected elements. The structures are delivered into space orbits in a folded, tightly packed transport state and after that the deployment takes place which occurs under the action of force actuators to bring them into a working position. Dimensions of the transformable space structures in transport and operating states can differ tens of times. The transformation of space structures occurs due to the use of various force actuators. In the process of opening such systems, dynamic shock loads occur on their elements. As active elements of force actuators, it is proposed to use materials with the shape memory effect. Some characteristics are obtained from quantitative and qualitative studies of wires made of titanium nickelide which have a shape memory effect. These characteristics are important for the application of the wires as force actuators to ensure controlled deployment of the transformable space structures. The procedure of the force actuator calculation is proposed, which is based on the mathematical model of its operation and takes into account the obtained experimental data.
Vladimir N. Zimin, Alexey V. Krylov, Georgy N. Kuvyrkin, Artur O. Shakhverdov
Chapter 18. Estimation of Uncertainty for Measurement of Ship Ice Resistance in Ice Basin
Evaluation of the ship’s ice capability is closely related to how accurate the ice resistance measurements of the ship hull that breaks the ice. Traditional methods for estimating the error of indirect measurement of this characteristic are too conservative and unacceptable for practical application. The problem of measurement uncertainty for ice resistance can be solved by detailed consideration of all measured characteristics and the environment of ship operation under experimental investigation. This study presents the results of numerous towing tests of a standard ship model in solid-level ice in the Ice Basin of Krylov State Research Centre. Each experiment involved measurements of physical and mechanical ice properties. The obtained data were used to study the measurement errors in evaluations of the main ice properties and ship ice resistance, and possible ways to reduce the same were examined.
Aleksei A. Dobrodeev
Behavior of Materials under Impact, Explosion, High Pressures and Dynamic Strain Rates
Maxim Yu. Orlov
Visakh P. M.
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