Propagation Properties of Shock Waves in Polyurethane Foam based on Atomistic Simulations

Porous materials are widely used in the field of protection because of their excellent energy absorption characteristics.In this work,a series of polyurethane microscopic models are established and the effect of porosity on the shock waves is studied with classical molecular dynamics simulations.Firstly,shock Hugoniot relations for different porosities are obtained,which compare well with the experimental data.The pores collapse and form local stress wave,which results in the complex multi-wave structure of the shock wave.The microstructure analysis shows that the local stress increases and the local velocity decreases gradually during the process of pore collapse to complete compaction.Finally,it leads to stress relaxation and velocity homogenization.The shock stress peaks can be fitted with two exponential functions,and the amplitude of attenuation coefficient decreases with the increase of density.Besides,the pore collapse under shock or non-shock are discussed by the entropy increase rate of the system.The energy is dissipated mainly through the multiple interactions of the waves under shock.The energy is dissipated mainly by the friction between atoms under non-shock.

NUMERICAL INVESTIGATION OF TOROIDAL SHOCK WAVES FOCUSING USING DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD

A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.

Experimental investigation on weak shock wave mitigation characteristics of flexible polyurethane foam and polyurea

In recent years,explosion shock wave has been considered as a signature injury of the current military conflicts.Although strong shock wave is lethal to the human body,weak shock wave can cause many more lasting consequences.To investigate the protection ability and characteristics of flexible materials and structures under weak shock wave loading,the blast wave produced by TNT explosive is loaded on the polyurethane foam with the density of 200.0 kg/m3(F-200)and 400.0 kg/m3(F-400),polyurea with the density of 1100.0 kg/m^(3)(P-1100)and structures composed of the two materials,which are intended for individual protection.Experimental results indicate that the shock wave is attenuated to weak pressure disturbance after interacting with the flexible materials which are not damaged.The shock wave protective capability of single-layer materials is dependent on their thickness,density and microscopic characteristics.The overpressure,maximum pressure rise rate and impulse of transmitted wave decrease exponentially with increase in sample thickness.For the same thickness,F-400 provides better protective capability than F-200 while P-1100 shows the best protective capability among the three materials.In this study,as the materials are not destroyed,F-200 with a thickness more than10.0 mm,F-400 with a thickness more than 4.0 mm,and P-1100 with a thickness more than 1.0 mm can attenuate the overpressure amplitude more than 90.0%.Further,multi-layer flexible composites are designed.Different layer layouts of designed structures and layer thickness of the single-layer materials can affect the protective performance.Within the research range,the structure in which polyurea is placed on the impact side shows the optimal shock wave protective performance,and the thicknesses of polyurea and polyurethane foam are 1.0 mm and 4.0 mm respectively.The overpressure attenuation rate reached maximum value of 93.3%and impulse attenuation capacity of this structure are better than those of single-layer polyurea and polyurethane foam with higher areal density.

THE INTERACTION BETWEEN SHOCK WAVES AND SOLID SPHERES ARRAYS IN A SHOCK TUBE

When a shock wave interacts with a group of solid spheres,non-linear aerodynamic behaviors come into effect.The complicated wave reflections such as the Mach reflection occur in the wave propagation process.The wave interactions with vortices behind each sphere's wake cause fluctuation in the pressure profiles of shock waves.This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres.A schlieren photography was applied to visualize the various shock waves passing through solid spheres.Pressure measurements were performed along different downstream positions.The experiments were conducted in both rectangular and circular shock tubes.The data with respect to the effect of the sphere array, size,interval distance,incident Mach number,etc.,on the shock wave attenuation were obtained.

Study of damage to a high concrete dam subjected to underwater shock waves

To study the effect of a strong underwater shock wave on a concrete dam, this research aims to improve hammer impact methods in model tests. Six 1:200 scale models were designed and tested under distributed impact loads. A device was deployed for a direct measurement of the impact force at the upstream face of the dams. The model dam bases were anchored to prevent displacement. The experimental results indicate that the top part of the concrete dam is a weak zone, and the impact failure initiates with a fracture on the top of the dam. The peak value of impact stress increases when the second crack appears in the concrete dam from the upstream face to the downstream face. And, the level of the second crack in the dam body is lower as the peak value of impact stress increases. In this study, dynamic analysis was conducted by calculating the results to verify the effectiveness of a device to directly measure the impact force. This method may be used to approximately forecast the damage of concrete dam and may also be useful in other engineering applications.

Parametric Analysis of A Submerged Cylindrical Shell Subjected to Shock Waves

In this study, an FEM-SBFEM （scaled boundary finite element method） coupling procedure proposed by Fan et al. （2005） is adopted to obtain the dynamic responses of a submerged cylindrical shell subjected to plane step or exponential acoustic shock waves. The coupling procedure can readily be applied to three-dimensional problem, however for clarity, the problems to be presented are hmited to two-dimeusional domain. In the analyses, the cylindrical shell is modeled by simple beam elements （using FEM）, while the effects of the surrounding infinite fluid is modeled by the SBFEM. In it, no free surface and seabed are involved. Compared with Fan and his co-authors＇ works, the FEM-SBFEM coupling procedure is further verified to be feasible for shock waves by benchmark examples. Furthermore, parametric studies are performed and presented to gain insight into effects of the geometric and material properties of the cylindrical shell on its dynamic responses.

IMPROVEMENT OF MATERIALS WELDABILITY BY SHOCK WAVES

The weldability is an important property to metal materials. Materials weldability becomes worse with the yield strength increasing. The experimental results indicate that the specific shock waves treatment could improve the weldability of steels such as 16MnR, SM 58Q, e.g. increase the notch toughness of coarse grains zone in HAZ and decrease cold cracking sensibility. The work would explore initially the mechanisms of improvement of weldability by shock waves. The further study on the low alloy high strength steel WEL TEN80 indicates that the shock waves may increase the material weldability on this grade of trength.

A Study on Super Speed Forming of Metal Sheet by Laser Shock Waves

Metal sheet plastic deformation or forming is gener at ed through a mechanical pressure or a thermal variation. These pressure variatio ns or thermal variations can be created by a variety of means such as press form ing, hydroforming, imploding detonation and so on. According to the magnitude of the strain rates all these forming methods can be divided into quasi-static fo rming and dynamical forming. Up to now there are no reports of forming methods w ith the strain rates above 10 5sec -1, even though the exploding forming. In this article, we work on a dynamic super-speed forming method driven by lase r shock waves and advanced a novel concept of laser shock forming. The initial o bservation of the laser shock forming is done through a bugle testing with speci mens of SUS430 sheet metal, using a neodymium-glass laser of pulse energy 10J～ 3 0J and duration of 20 ns (FWHM). The investigation revealed that the plastic de formation during the laser shock forming is characterized as ultrahigh strain ra te up to 10 7sec -1. We indicate that plastic deformation increases nonlin early when the energy density of the laser varies. By investigating the hardness and residual stress of the surfaces, we conclude that laser shock forming is a combination technique of laser shock strengthening and metal forming for introdu cing a strain harden and a compressive residual stress on the surface of the wor k-piece, and the treated surface by laser shock forming has good properties in fatigue and corrosion resistance. This technique can achieve forming wit h or without mould.

Numerical Simulation of the Protective Effect of Complex Boundaries Toward Shock Waves in a 3D Explosive Field

A numerical method is presented that simulates 3D explosive field problems. A code MMIC3D using this method can be used to simulate the propagation and reflected effects of all kinds of rigid boundaries to shock waves produced by an explosive source. These numerical results indicate that the code MMIC3D has the ability in computing cases such as 3D shock waves produced by air explosion, vortex region of the shock wave, the Mach wave, and reflected waves behind rigid boundaries.

THE INTERACTION BETWEEN SHOCK WAVES AND FOAM IN A SHOCK TUBE

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.

STABILITY OF VISCOUS SHOCK WAVES FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

We study the large-time behavior toward viscous shock waves to the Cauchy problem of the one-dimensional compressible isentropic Navier-Stokes equations with density- dependent viscosity. The nonlinear stability of the viscous shock waves is shown for certain class of large initial perturbation with integral zero which can allow the initial density to have large oscillation. Our analysis relies upon the technique developed by Kanel~ and the continuation argument.

Research on the distribution characteristics of explosive shock waves at different altitudes

There are great differences in the distribution characteristics of shock waves produced by ammunition explosions at different altitudes.At present,there are many studies on plain explosion shock waves,but there are few studies on the distribution characteristics of plateau explosion shock waves,and there is still a lack of complete analysis and evaluation methods.This paper compares and analyzes shock wave overpressure data at different altitudes,obtains the attenuation effect of different altitudes on the shock wave propagation process and proposes a calculation formula for shock wave overpressure considering the effect of altitude.The data analysis results show that at the same TNT equivalent and the same distance from the measuring point,the shock wave overpressure at high altitude is lower than that at low altitude.With the increase in the explosion center distance of the measuring point,the peak attenuation rate of the shock wave overpressure at high altitudes is smaller than that at low altitudes,and the peak attenuation rate of the shock wave overpressure at high altitudes gradually intensifies with increasing proportional distance.The average error between the shock wave overpressure and measured shock wave overpressure in a high-altitude environment obtained by using the above calculation formula is 11.1389%.Therefore,this method can effectively predict explosion shock wave overpressure in plateau environments and provides an effective calculation method for practical engineering tests.

Experimental and numerical study on protective effect of RC blast wall against air shock wave

Prototype experiments were carried out on the explosion-proof performance of the RC blast wall.The mass of TNT detonated in the experiments is 5 kg and 20 kg respectively.The shock wave overpressure was tested in different regions.The above experiments were numerically simulated,and the simulated shock wave overpressure waveforms were compared with that tested and given by CONWEP program.The results show that the numerically simulated waveform is slightly different from the test waveform,but similar to CONWEP waveform.Through dimensional analysis and numerical simulation under different working conditions,the equation for the attenuation rate of the diffraction overpressure behind the blast wall was obtained.According to the corresponding standards,the degree of casualties and the damage degree of the brick concrete building at a certain distance behind the wall can be determined when parameters are set.The above results can provide a reference for the design and construction of the reinforced concrete blast wall.

Blast waveform tailoring using controlled venting in blast simulators and shock tubes

A critical challenge of any blast simulation facility is in producing the widest possible pressure-impulse range for matching against equivalent high-explosive events.Shock tubes and blast simulators are often constrained with the lack of effective ways to control blast wave profiles and as a result have a limited performance range.Some wave shaping techniques employed in some facilities are reviewed but often necessitate extensive geometric modifications,inadvertently cause flow anomalies,and/or are only applicable under very specific configurations.This paper investigates controlled venting as an expedient way for waveforms to be tuned without requiring extensive modifications to the driver or existing geometry and could be widely applied by existing and future blast simulation and shock tube facilities.The use of controlled venting is demonstrated experimentally using the Advanced Blast Simulator(shock tube)at the Australian National Facility of Physical Blast Simulation and via numerical flow simulations with Computational Fluid Dynamics.Controlled venting is determined as an effective method for mitigating the impact of re-reflected waves within the blast simulator.This control method also allows for the adjustment of parameters such as tuning the peak overpressure,the positive phase duration,and modifying the magnitude of the negative phase and the secondary shock of the blast waves.This paper is concluded with an illustration of the potential expanded performance range of the Australian blast simulation facility when controlled venting for blast waveform tailoring as presented in this paper is applied.

Effects of bi-kappa distributed electrons on dust-ion-acoustic shock waves in dusty superthermal plasmas

The basic properties of dust-ion-acoustic （DIA） shock waves in an unmagnetized dusty plasma （containing inertial ions, kappa distributed electrons with two distinct temperatures, and negatively charged immobile dust grains） are investi- gated both numerically and analytically. The hydrodynamic equation for inertial ions has been used to derive the Burgers equation. The effects of superthermal bi-kappa electrons and ion kinematic viscosity, which are found to modify the basic features of DIA shock waves significantly, are briefly discussed.

Research advances in enhanced coal seam gas extraction by controllable shock wave fracturing

With the continuous increase of mining in depth,the gas extraction faces the challenges of low permeability,great ground stress,high temperature and large gas pressure in coal seam.The controllable shock wave(CSW),as a new method for enhancing permeability of coal seam to improve gas extraction,features in the advantages of high efficiency,eco-friendly,and low cost.In order to better utilize the CSW into gas extraction in coal mine,the mechanism and feasibility of CSW enhanced extraction need to be studied.In this paper,the basic principles,the experimental tests,the mathematical models,and the on-site tests of CSW fracturing coal seams are reviewed,thereby its future research directions are provided.Based on the different media between electrodes,the CSW can be divided into three categories:hydraulic effect,wire explosion and excitation of energetic materials by detonating wire.During the process of propagation and attenuation of the high-energy shock wave in coal,the shock wave and bubble pulsation work together to produce an enhanced permeability effect on the coal seam.The stronger the strength of the CSW is,the more cracks created in the coal is,and the greater the length,width and area of the cracks being.The repeated shock on the coal seam is conducive to the formation of complex network fracture system as well as the reduction of coal seam strength,but excessive shock frequency will also damage the coal structure,resulting in the limited effect of the enhanced gas extraction.Under the influence of ground stress,the crack propagation in coal seam will be restrained.The difference of horizontal principal stress has a significant impact on the shape,propagation direction and connectivity of the CSW induced cracks.The permeability enhancement effect of CSW is affected by the breakage degree of coal seam.The shock wave is absorbed by the broken coal,which may hinder the propagation of CSW,resulting in a poor effect of permeability enhancement.When arranging two adjacent boreholes for CSW permeability enhancement test,the spacing of boreholes should not be too close,which may lead to negative pressure mutual pulling in the early stage of drainage.At present,the accurate method for effectively predicting the CSW permeability enhanced range should be further investigated.

A three-dimensional numerical study on instability of sinusoidal flame induced by multiple shock waves

The instabilities of a three-dimensional sinusoidally premixed flame induced by an incident shock wave with Mach = 1.7 and its reshock waves were studied by using the Navier-Stokes (NS) equations with a single-step chemical reaction and a high resolution, 9th-order weighted essentially non-oscillatory scheme. The computational results were validated by the grid independence test and the experimental results in the literature. The computational results show that after the passage of incident shock wave the flame interface develops in symmetric structure accompanied by large-scale transverse vortex structures. After the interactions by successive reshock waves, the flame interface is gradually destabilized and broken up, and the large-scale vortex structures are gradually transformed into small-scale vortex structures. The small-scale vortices tend to be isotropic later. The results also reveal that the evolution of the flame interface is affected by both mixing process and chemical reaction. In order to identify the relationship between the mixing and the chemical reaction, a dimensionless parameter, , that is defined as the ratio of mixing time scale to chemical reaction time scale, is introduced. It is found that at each interaction stage the effect of chemical reaction is enhanced with time. The enhanced effect of chemical reaction at the interaction stage by incident shock wave is greater than that at the interaction stages by reshock waves. The result suggests that the parameter can reasonably character the features of flame interface development induced by the multiple shock waves.

Numerical and experimental investigation into the evolution of the shock wave when a muzzle jet impacts a constrained moving body

The gun-track launch system is a new special launch device that connects the track outside the muzzle.Because it is constrained by the track,the characteristics of development of the muzzle jet differ from those of the traditional muzzle jet.Specifically,it changes from freely developing to doing so in a constrained manner,where this results in an asymmetric direction of flow as well as spatio-temporal coupling-induced interference between various shock waves and the formation of vortices.In this background,the authors of this article formulate and consider the development and characteristics of evolution of the muzzle jet as it impacts a constrained moving body.We designed simulations to test the gun-track launch system,and established a numerical model based on the dynamic grid method to explore the development and characteristics of propagation of disturbances when the muzzle jet impacted a constrained moving body.We also considered models without a constrained track for the sake of comparison.The results showed that the muzzle jet assumed a circumferential asymmetric shape,and tended to develop in the area above the muzzle.Because the test platform was close to the ground,the muzzle jet was subjected to reflections from it that enhanced the development and evolution of various forms of shock waves and vortices in the muzzle jet to exacerbate its rate of distortion and asymmetric characteristics.This in turn led to significant differences in the changes in pressure at symmetric points that would otherwise have been identical.The results of a comparative analysis showed that the constrained track could hinder the influence of reflections from the ground on the muzzle jet to some extent,and could reduce the velocity of the shock waves inducing the motion of the muzzle as well as the Mach number of the moving body.The work here provides a theoretical basis and the requisite technical support for applications of the gun-track launch system.It also sheds light on the technical bottlenecks that need to be considered to recover high-value warheads.

Evolution of shock waves formed by laser-induced breakdown in air

The evolution of shock waves produced by 7 ns laser pulses in air is investigated by time-resolved shadowgraph. A nodular structure of the shock wave is observed. It is found that the origin of the structure is the multi-longitudinal- microfocus caused by the astigmatism of the laser beam. The spherical shock waves formed by each microfocus expand gradually and collide with each other, resulting in the nodular structure of the shock wave.

Dynamic Response of Stiffened Plates with Holes Subjected to Shock Waves and Fragments

The power field of shock waves and fragments is analyzed and set up, and the damage modes of stiffened plates are put forward. According to the structural characters of the stiffened plates investigated and the properties of the shock waves and fragments, the experiments on the shock waves acting on the stiffened plates (penetrated and non-penetrated by fragments) are mainly conducted. The dynamic response rules of stiffened plates with holes under shock waves and fragments loading are obtained. The results show that the penetration of fragments into stiffened plates hardly affects their deformation produced by shock waves..