Shock-wave Deformation Research Articles

A New Type of Phase Transformations in the Process of Shockwave Deformation of Low-Carbon Steel

A New Type of Phase Transformations in the Process of Shockwave Deformation of Low-Carbon Steel

Effects of Internal Fluid on the Dynamic Behaviors of Double Cylindrical Shells Subjected to Underwater Explosion

Abstract Fluid-filled double cylindrical shells were widely used in the marine engineering field and their blast resistance was considerably concerned. In this paper, the dynamic behaviors of fluid-filled double cylindrical shells subjected to underwater explosion were studied through a combination of experimental and numerical methods. First, a series of comparative underwater explosion tests were carried out on the scaled empty and fluid-filled double cylindrical shells. Then, more detailed numerical simulations were developed to give more results, and the model was verified by comparing with the data gathered from tests. Based on the experimental and numerical results, the effects of internal fluid on the shock wave propagation process, deformation modes, dynamic response, and energy characteristics of structures were analyzed. It is shown that the internal fluid is helpful to resist the structural deformation of outer shell and significantly decreased the axial strains of inner shell. Meanwhile, the dynamic response of the inner shell of fluid-filled shells was more violent. Besides, the internal and kinetic energy of outer shell decreased markedly. Above results would provide a reference for the protection of fluid-filled structures.

Моделирование ударно-волновых эффектов в металлах на основе релаксационной модели с дислокационной кинетикой пластических сдвигов

In the range of weak shock waves (before absorption of elastic precursors by the shock wave) the effects of shock wave deformation of aluminum and beryllium alloys are numerically studied by the relaxation model with dislocation kinetics of plastic shear. Both the structure of non-stationary and stationary shock wave profiles are modeled. The plastic flow behind the front of elastic precursors is studied.

Numerical simulation of underwater explosion cavitation characteristics based on phase transition model in compressible multicomponent fluids

Underwater explosion cavitation has an important influence on the shock wave, explosion bubble, and structural deformation. The one-fluid model is usually used in underwater explosion cavitation. It is assumed that the cavitation is induced suddenly when the pressure is lower than the saturated pressure. The biggest deficiency of the model is that it is difficult to consider the temperature change in the cavitation domain. It is known that cavitation is sensitive to the temperature. In this paper, we study UNDEX cavitation characteristics based on the two-fluid model proposed by Chiapolino et al. (2017), which holds that the cavitation phenomenon is the result of the phase transition between the gas and liquid phases. This model is composed of the 4-equation model with phase transition relaxation, which is solved by a simple fractional step. In this article, we briefly introduce the compressible multiphase fluids model and successfully extent it to the engineering research field of underwater explosion cavitation. Through the quantitative analysis of the vapor phase content, it is suggested that the initial mass fraction of vapor phase in water should be set to less than 10−7. Meanwhile, it can be observed that the bulk cavitation near the free surface can evolve into a vortex ring until it collapses. Numerical results show that the collapsed pressure cannot be ignored relative to the shock wave in the bulk and local cavitation. Numerical results of this paper display that the phase transition model shows a great prospect of engineering application in underwater explosion cavitation.

Evaluation of Energy Absorption Capabilities of Polyethylene Foam under Impact Deformation.

Foams are widely used in protective applications requiring high energy absorption under impact, and evaluating impact properties of foams is vital. Therefore, a novel test method based on a shock tube was developed to investigate the impact properties of closed-cell polyethylene (PE) foams at strain rates over 6000 s−1, and the test theory is presented. Based on the test method, the failure progress and final failure modes of PE foams are discussed. Moreover, energy absorption capabilities of PE foams were assessed under both quasi-static and high strain rate loading conditions. The results showed that the foam exhibited a nonuniform deformation along the specimen length under high strain rates. The energy absorption rate of PE foam increased with the increasing of strain rates. The specimen energy absorption varied linearly in the early stage and then increased rapidly, corresponding to a uniform compression process. However, in the shock wave deformation process, the energy absorption capacity of the foam maintained a good stability and exhibited the best energy absorption state when the speed was higher than 26 m/s. This stable energy absorption state disappeared until the speed was lower than 1.3 m/s. The loading speed exhibited an obvious influence on energy density.

Modeling Ultrasound Propagation in the Moving Brain: Applications to Shear Shock Waves and Traumatic Brain Injury.

Traumatic brain injury (TBI) studies on the living human brain are experimentally infeasible due to ethical reasons and the elastic properties of the brain degrade rapidly postmortem. We present a simulation approach that models ultrasound propagation in the human brain, while it is moving due to the complex shear shock wave deformation from a traumatic impact. Finite difference simulations can model ultrasound propagation in complex media such as human tissue. Recently, we have shown that the fullwave finite difference approach can also be used to represent displacements that are much smaller than the grid size, such as the motion encountered in shear wave propagation from ultrasound elastography. However, this subresolution displacement model, called impedance flow, was only implemented and validated for acoustical media composed of randomly distributed scatterers. Herein, we propose a generalization of the impedance flow method that describes the continuous subresolution motion of structured acoustical maps, and in particular of acoustical maps of the human brain. It is shown that the average error in simulating subresolution displacements using impedance flow is small when compared to the acoustical wavelength ( λ /1702). The method is then applied to acoustical maps of the human brain with a motion that is imposed by the propagation of a shear shock wave. This motion is determined numerically with a custom piecewise parabolic method that is calibrated to ex vivo observations of shear shocks in the porcine brain. Then the fullwave simulation tool is used to model transmit-receive imaging sequences based on an L7-4 imaging transducer. The simulated radio frequency data are beamformed using a conventional delay-and-sum method and a normalized cross-correlation method designed for shock wave tracking is used to determine the tissue motion. This overall process is an in silico reproduction of the experiments that were previously performed to observe shear shock waves in fresh porcine brain. It is shown that the proposed generalized impedance flow method accurately captures the shear wave motion in terms of the wave profile, shock front characteristics, odd harmonic spectrum generation, and acceleration at the shear shock front. We expect that this approach will lead to improvements in image sequence design that takes into account the aberration and multiple reflections from the brain and in the design of tracking algorithms that can more accurately capture the complex brain motion that occurs during a traumatic impact. These methods of modeling ultrasound propagation in moving media can also be applied to other displacements, such as those generated by shear wave elastography or blood flow.

Statistical analysis of deformation of a shock wave propagating in a local turbulent region

Direct numerical simulation is performed for analyzing the interaction between a normal shock wave and turbulence. The shock wave is initially located in a quiescent fluid and propagates into a local turbulent region. This flow setup allows investigation of the initial transition and statistically steady stages of the interaction. Shock deformation is quantified using the local shock wave position. The root-mean-square (rms) fluctuation in the shock wave position increases during the initial stage of the interaction, for which the time interval divided by the integral time scale increases with Mt2/(Ms2−1), where Mt is a turbulent Mach number and Ms is a shock Mach number. In late time, the rms fluctuation in the shock wave position hardly depends on the propagation time and follows a power law, [Mt2/(Ms2−1)]0.46, whose exponent is similar to the power law exponent of the rms pressure-jump fluctuation reported in experimental studies. Fluctuations in the shock wave position have a Gaussian probability density function. The spectral analysis confirms that the length scale that characterizes shock wave deformation is the integral length scale of turbulence. The fluctuating shock wave position is correlated with dilatation of the shock wave, where the correlation coefficient increases with Mt/(Ms − 1). In addition, the shock wave that deforms backward tends to be stronger than average and vice versa. Mean pressure jumps across the shock wave are different between areas with forward and backward deformations. This difference increases with the rms fluctuation in the shock wave position and is well-represented as a function of Mt2/(Ms2−1).

Mechanical joining behavior of Cu–Fe dissimilar metallic foils in laser shock clinching

Laser shock clinching is a novel joining method derived from laser shock forming in which the metal foil is plastically deformed under the pulsed laser induced shock wave, and then two or more metal foils can be joined together based on plastic deformation. However, the present researches are less concerned with the mechanical joining behavior of metal foils during incremental impacts of multiple laser pulses. In the present study, the mechanical joining behavior of pure copper foil and pre-pierced stainless steel sheet in laser shock clinching was investigated. A finite element model was established to analyze the material flowing and clinching behavior of metal foils under multiple laser pulses. Based on the validated model, the deformation stages, thickness change, and shock wave propagation features were studied. The temperature rise during clinching was assessed considering both the compression by shock wave and plastic deformation at high strain rates. It is revealed that the laser shock clinching process can be divided into three deformation stages, that is, free bulging forming, radial expansion, and formation of interlock. Both experimental and numerical results prove that the formation of clinched joints relies on the plastic deformation of the joining partner I. The thinnest region of the joint locates at the material of the joining partner I in contact with the upper corner of the joining partner II. In addition, there is no obvious influence of temperature increase on the mechanical properties of joining partners. Moreover, the shock wave propagation characteristics along axial direction and the influence of laser power density on interlock value and thickness distribution were also discussed.

Theoretical study of post-shock stress relaxation and shock wave deformation around a pore in single and poly-crystalline α-RDX

The mechanical properties and shock dynamics of α-hexahydro-1,3,5-trinitro-1,3,5-triazine (α-RDX) are simulated by molecular dynamics (MD). Based on the simulation results, the equation of state, Hugoniot curve and isoentropic curve for α-RDX are calculated, and the microscopic structure of shock wave is investigated, including the wave profile and the shock front deformation. First, we prove that the shock wave profile is determined by the viscoelastic equation of α-RDX, and develop a method to inverse the viscoelastic coefficients from the velocity profile calculated by MD. Two stress relaxation mechanisms are obtained: the boundary scattering and molecular rotation. The boundary scattering mechanism shows that the damping time of stress relaxation is determined by the particle size of polycrystal. Second, we find that the pore collapse induces rarefaction wave after the shock front. The rarefaction wave function is evaluated by using the Riemann invariant method, and the shock front deformation is derived from the superposition rule of shock wave and rarefaction wave. A physical picture to describe the nanoscale pore collapse process for α-RDX is obtained.

Intensification of shock damage through heterogeneous phase transition and dislocation loop formation due to presence of pre-existing line defects in single crystal Cu

In general, shock wave deformation studies of perfect single crystals may cause disagreement with the experimental findings as the complete elimination of all defects in the metallic system is not possible in reality. Here, we have studied the influence of edge and screw dislocations on the intensification of damage produced during the propagation of shock at various velocities. Various analyses have been performed such as common neighbor analysis, atomic strain analysis, stress analysis, and kinetic energy mapping to investigate the underlying plastic deformation mechanisms. Results have revealed that the presence of edge dislocations has caused intensified damage through localized amorphization and phase transition. In comparison with the perfect crystal, the presence of pre-existing edge dislocations has incurred an additional damage of ∼17% to the specimen region. On the other hand, the presence of screw dislocations in the specimen causes damage through shear bands and dislocation loop formation, which is found to constitute greater than 80% of the specimen region.

Statistics of overpressure fluctuations behind a weak shock wave interacting with turbulence

The overpressure fluctuations behind a weak shock wave interacting with turbulence are studied by wind tunnel experiments, where a spherical shock wave propagates in grid turbulence. The experiments are conducted for various values of the shock Mach number MS0 of the shock wave and turbulent Mach number MT of the grid turbulence. The experimental results show that the root-mean-squared peak-overpressure fluctuation divided by the averaged peak-overpressure, σΔp/⟨Δp⟩, where the inherent noise caused by the experimental facility is removed, follows a power law of MT2/(MS02−1). The probability density functions of the overpressure fluctuations are close to the Gaussian profile for a wide range of MT2/(MS02−1). A shock deformation model based on the deformation due to nonuniform fluid velocity is proposed for the investigation of the influences of turbulence on the shock wave. The deformation changes the cross-sectional area of the ray tube, which is related to the shock Mach number fluctuation of the area. The model for a weak shock wave yields the relation σΔp/⟨Δp⟩≈(1/3)[MT2/(MS02−1)]1/2, which agrees well with the experimental results. The model also predicts the Gaussianity of the peak-overpressure fluctuations behind the shock wave interacting with Gaussian velocity fluctuations. Good agreements between the model and experiments imply that the change in the shock wave characteristics by the interaction with turbulence is closely related to the shock wave deformation caused by the fluctuating turbulent velocity field.

Amplification and attenuation of shock wave strength caused by homogeneous isotropic turbulence

We study the pressure increase across a planar shock wave with shock Mach numbers Ms of 1.1, 1.3, and 1.5 propagating through homogeneous isotropic turbulence at a low turbulent Mach number (Mt ∼ 10−4) based on direct numerical simulations (DNSs). Fluctuation in the pressure increase, Δp′, on a given shock ray is induced by turbulence around the ray. A local amplification of the shock wave strength, measured with the pressure increase, is caused by the velocity fluctuation opposed to the shock wave propagating direction with a time delay, while the velocity in the opposite direction attenuates the shock wave strength. The turbulence effects on the shock wave are explained based on shock wave deformation due to turbulent shearing motions. The spatial distribution of Δp′ on the shock wave has a characteristic length of the order of the integral scale of turbulence. The influence of turbulent velocity fluctuation at a given location on Δp′ becomes most significant after the shock wave propagates from the loc...

Dynamic response and microstructure evolution of the finite steel target subjected to high velocity impact by copper explosively formed projectile

AbstractThe dynamic deformation of the finite steel target subjected to high velocity impact of copper explosively formed projectile is investigated by optical, scanning, and transmission electron microscopy. Morphology analysis of fracture surfaces indicates that the copper remainder plated to the crater wall shows extremely plastic deformation, which consists of elongated parabolic dimples, and the mild carbon steel target exhibits excellent brittle features that material fails mainly along the cleavage facets on the rear surface of target under strong impact of explosively formed projectile. In the surface of crater, the whole part of copper remainder and partial material of steel target undergoes completely dynamic recrystallization. The layer thickness of dynamic recrystallization zone, which displays an extreme plastic flow in solid state, is about 21.3 μm in steel target, and the average size of the refined grains significantly decreases to approximately 200 nm. Theoretically calculated results indicate that the temperature increase is associated with shock wave and plastic deformation of steel target and can reach 1352 K, which is 0.75Tm (where Tm is the melting temperature of steel target). The change in microhardness from the crater wall to the matrix of target is consistent with micro‐deformation of grains, and maximum microhardness is observed on the interface between dynamic recrystallization and severe plastic deformation zones of steel target.

ВОЗМОЖНОСТИ АДДИТИВНО-СУБТРАКТИВНО-УПРОЧНЯЮЩЕЙ ТЕХНОЛОГИИ

The accurate shape obtaining is the most significant, but far from being the only problem which is solved at parts produc-tion. Not less important are also such properties as elasticity, plasticity, strength and durability and so on. It is well-known that high-temperature influence upon billet material which follows any of known processes of additive processing ad-versely affects the above-mentioned properties. The most significant task of additive techniques is ensuring material qua-litative structure and high operating properties in a part manufactured at multiple increase of productivity. The purpose of theoretical and practical researches carried out consists in the development of the technology in which to the processes of additive and subtractive treatment there is added a process of hardening with shock wave deformation that allows structuring, strengthening, compacting the material of a layer grown forming compressive stresses instead of tensile residual stresses of thermal origin. The growth of a part is carried out by means of arc deposition with wire materi-al. Such an approach ensures productivity by an order higher, but has such drawbacks as defects of structure, considerable porosity and low accuracy in comparison with powder additive techniques. The drawbacks mentioned are compensated by strengthening and machining in the course of product manufacturing. The research methods - a comparative analysis of the structure of iron-carbon material manufactured with the use of additive-subtractive techniques and additive-subtractive strengthening techniques. Results and conclusions. In strengthened material, in contrast to non-strengthened one there are no practically hidden cavities. The dimensions of phase elements of ferrite and pearlite in material manufactured according to the technology with strengthening decrease by more than five times. Hardness of material grown with strengthening exceeds more than twice hardness of material manufactured without strengthening.

Change of the kinetics of shock-wave deformation and fracture of VT1-0 titanium as a result of annealing

The paper presents the results of measurements of shock-wave compression profiles of VT1-0 titanium samples after rolling and in the annealed state. In the experiments, the pressure of shock compression and distance passed by the wave before emerging to the sample surface were varied. From measurements of the elastic precursor decay and compression rate in a plastic shock wave of different amplitudes, the plastic strain and the corresponding shear stresses in the initial and subsequent stages of high-rate deformation in an elastoplastic shock wave are determined. It is found that the reduction in the dislocation density as a result of annealing reduces the hardness of the material but significantly increases its dynamic yield strengh, corresponding to the strain rate above 104 s–1. With a reduction in the strain rate, this anomalous difference in the flow stresses is leveled off.

Special Features of the Mechanical Characteristics of Al–Al2O3 Composites Produced By Explosive Compaction of Powders Under Shock-Wave Deformation

The results obtained from investigations into the special features inherent in the mechanical characteristics (Hugoniot elastic limit and spall strength) observed under shock-wave loading of Al–Al2O3 composite samples produced by an explosive powder compaction technique are presented. Embedding 10 wt.% of aluminum oxide in the aluminum matrix has been found to increase the Hugoniot elastic limit as opposed to the commercialgrade AD1(Al 1013) aluminum alloy.

Spherical bubble dynamics in a bubbly medium using an Euler–Lagrange model

For applications involving large bubble volume changes such as in cavitating flows and in bubbly two-phase flows involving shock and pressure wave propagation, the dynamics, relative motion, deformation, and interaction of bubbles with the surrounding medium play crucial roles and require accurate modeling. We present in this paper a fundamental study of the dynamic oscillations of a “primary” bubble in a bubbly mixture using a two-way coupled Euler–Lagrange model. It addresses a simplified spherical configuration while using the full three-dimensional code. A main objective of the study is to investigate how the dynamics of a “primary” bubble is affected by the presence of a surrounding bubbly medium and how it differs from its behavior in a pure liquid. This helps elucidate the physics at play for this relatively simple configuration. The model simulates the mixture as a continuum and solves the corresponding Navier Stokes equations with grids moving with the interface of the primary bubble wall. The surrounding microbubbles are tracked in a Lagrangian fashion accounting for their volume evolution. The two-way coupling between the bubbly medium and the primary bubble dynamics is realized through the local density of the mixture obtained from the tracking of the microbubbles and the determination of their volumes and spatial distribution.The simulations clearly indicate that the surrounding microbubbles absorb energy emitted from the primary bubble during its oscillations. This results in a reduction of the maximum radius and the period of oscillations of the primary bubble as compared to the dynamics in the pure liquid. Also, accounting for the dynamics of the field bubbles brings out the presence in the two-phase medium of a phase shift between density and pressure distributions. Such a shift is not captured by two-phase homogeneous medium models. These effects increase with increase in the mixture void fraction and in the initial bubble sizes in the mixture. The numerical observations are found to be in good qualitative agreements with previously published experimental data (Jayaprakash et al., 2011) investigating spark generated bubble dynamics in a bubbly medium.

Response of shock wave deformation in AA5086 aluminum alloy

The AA5086 aluminum alloy sheets with different starting textures were subjected to shock wave deformation with an input impulse of ~0.2 Ns. Microstructural examination indicate no significant change in grain size; however, the evolution of substructure manifesting intra-granular misorientation was evident. The improvement in hardness indicates the absence of recovery and strain hardening during shock deformation. Shock deformed samples show characteristic texture evolution with high Brass {110}〈112〉 component. The study demonstrates the viability of high velocity forming of AA5086 aluminum alloy sheet using shock wave.

Deformation and fracture mechanisms and structural changes in coarse-grained copper under shock-wave loading

Results of experiments on shock-wave deformation of M2 copper under uniaxial loading are presented. Light, scanning, and transmission electron microscopy methods are used to reveal specific features of mechanisms of deformation and fracture of copper during the formation of a main spall crack. The parameters of spall strength, damage, and self-similarity of the spall crack contour are determined.

The deformation and mixing of several Ni/Al powders under shock wave loading: effects of initial configuration

The shock wave initiation of ultra-fast chemical reactions in inorganic powder mixtures requires the reactants to be blended within the shock front or shortly behind it. As such, the details of particle deformation are crucial to understanding the sequence of events leading up to the shock initiation of these systems. It is known that the initial configuration of a powder (i.e. the mixture composition and particle morphology) can have a significant effect on the degree of mixing that is achieved under shock wave loading. However, it is difficult to fully resolve this mixing behaviour in shock compression experiments due to the time and length scales involved. In this work, the shock wave deformation and mixing of six distinct Ni/Al powders are studied at the particle level using finite element simulation. Attention is focused on the Ni/Al interfaces that are formed since overall mixture reactivity depends on the specific amount of reactant interfacial area and on conditions induced at those interfaces. The analysis reveals (i) a rank ordering of the powders based on reactant interfacial area formation, (ii) a scaling relation for the rate of Ni/Al interface production and (iii) the distributed nature of Ni/Al interface temperature and dislocation density over a range of shock stress. Finally, it is shown that particle velocity differentials tend to develop across Ni/Al interfaces when the compacted powders are reshocked by reflection waves. The velocity differentials stem from the heterogeneity of the aggregates and are hypothesized to drive fragmentation processes that enable ultra-fast reactions on a sub-microsecond time scale.