2005 Vol. 25, No. 5
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2005, 25(5): 385-392.
doi: 10.11883/1001-1455(2005)05-0385-08
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Abstract:
To investigate the effects of shear stress to failure wave, series of experiments including oblique planar impact with inclination angle 10 and 15 degree, impact loading velocity ranging from 150 m/s to 400 m/s for K9 glass of central cut sample, are carried out in the present paper. Experimental results show that there existed a wave front with wave velocity exceeding that of longitudinal wave between the loading transversal wave and the unloading longitudinal wave. The wave has affected the amplitude of the unloading waves. Since the wave might be generated for the existing of central surface in central cut sample, some experiments including oblique planar impact with inclination angle 10 degree and impact loading velocity ranging from 70 m/s to 300 m/s for K9 glass of across cut sample are carried out in succession to eliminate the effect of central surface. In these experiments, the wave velocity of failure wave is determined to be 0.98-1.4 km/s and corresponding critical value for failure wave under combined pressure and shear impact loading are pressure 0.86-101 GPa and shear 0.053-0.071 GPa. All these show that shear stress may greatly decrease the critical value for failure wave. Some preliminarily discussions on dynamic friction coefficients and sliding velocity of impact surface are also conducted.
To investigate the effects of shear stress to failure wave, series of experiments including oblique planar impact with inclination angle 10 and 15 degree, impact loading velocity ranging from 150 m/s to 400 m/s for K9 glass of central cut sample, are carried out in the present paper. Experimental results show that there existed a wave front with wave velocity exceeding that of longitudinal wave between the loading transversal wave and the unloading longitudinal wave. The wave has affected the amplitude of the unloading waves. Since the wave might be generated for the existing of central surface in central cut sample, some experiments including oblique planar impact with inclination angle 10 degree and impact loading velocity ranging from 70 m/s to 300 m/s for K9 glass of across cut sample are carried out in succession to eliminate the effect of central surface. In these experiments, the wave velocity of failure wave is determined to be 0.98-1.4 km/s and corresponding critical value for failure wave under combined pressure and shear impact loading are pressure 0.86-101 GPa and shear 0.053-0.071 GPa. All these show that shear stress may greatly decrease the critical value for failure wave. Some preliminarily discussions on dynamic friction coefficients and sliding velocity of impact surface are also conducted.
2005, 25(5): 393-399.
doi: 10.11883/1001-1455(2005)05-0393-07
Abstract:
Oblique penetration/perforation of metallic plates by rigid projectiles with slender bodies and sharp nose shapes is studied in this paper. The mechanism of ductile hole enlargement dominates in whole penetration procedure. In the present model, the directional change is assumed to take place near the front surface when the projectile heading into the target and being subjected to asymmetric resistance. It clearly shows that the perforation of metallic plate is dominated by four non-dimensional numbers, i.e., the impact function I, the geometry function of projectile N , the non-dimensional thickness of target and the impact obliquity . Explicit formulae are obtained to predict the penetration depth, ballistic limit, residual velocity and directional change for the oblique penetration/perforation of metallic plates. The proposed model is able to predict the critical occurrence of ricochet. The predicted results are verified by comparing with available and independent experimental data and existing models.
Oblique penetration/perforation of metallic plates by rigid projectiles with slender bodies and sharp nose shapes is studied in this paper. The mechanism of ductile hole enlargement dominates in whole penetration procedure. In the present model, the directional change is assumed to take place near the front surface when the projectile heading into the target and being subjected to asymmetric resistance. It clearly shows that the perforation of metallic plate is dominated by four non-dimensional numbers, i.e., the impact function I, the geometry function of projectile N , the non-dimensional thickness of target and the impact obliquity . Explicit formulae are obtained to predict the penetration depth, ballistic limit, residual velocity and directional change for the oblique penetration/perforation of metallic plates. The proposed model is able to predict the critical occurrence of ricochet. The predicted results are verified by comparing with available and independent experimental data and existing models.
Investigation on mechanical properties of the composites of aluminum foam containing silicone rubber
2005, 25(5): 400-404.
doi: 10.11883/1001-1455(2005)05-0400-05
Abstract:
The aluminium foam containing silicone rubber was fabricated by infiltrating silicone rubber into the open-cell aluminum foam. The dynamic compressive experiments and quasi-static experiments were conducted on material test system and SHPB, respectively. The results show that the compressive stress-strain curves of the composites of aluminium foam containing silicone rubber are characterized by two distinct regions, i. e. elastic region and plateau region; and are more sensitive in strain rate, and larger oscillation in compression curve.
The aluminium foam containing silicone rubber was fabricated by infiltrating silicone rubber into the open-cell aluminum foam. The dynamic compressive experiments and quasi-static experiments were conducted on material test system and SHPB, respectively. The results show that the compressive stress-strain curves of the composites of aluminium foam containing silicone rubber are characterized by two distinct regions, i. e. elastic region and plateau region; and are more sensitive in strain rate, and larger oscillation in compression curve.
2005, 25(5): 405-416.
doi: 10.11883/1001-1455(2005)05-0405-12
Abstract:
Cellular detonation in a straight tube was numerically studied, based on two-dimensional reactive Euler equations and detailed chemical reaction model. The 5th order WENO scheme was employed to resolve the convective terms, and the additive semi-implicit Runge-Kutta methods was used to treat the stiffness caused by the chemical source terms. The contours of density, pressure, temperature and typical species mass fraction as well as numerical cellular pattern etc. were obtained. The results show that, the different grid resolutions evidently influence the regularity of detonation cells and the equilibrium detonation mode number. As grid size increases, the detonation wave developes more irregular cells and more additional triple points. For the given gas mixtures, initial pressure, initial temperature and tube width, the final self-sustaining detonation mode number is converged to a fixed value. It is also independent of the variety of initial perturbations, provided that the initial perturbations are sufficiently strong to reproduce the self-sustaining cellular detonation. Detonation velocity ranges from 0.88DCJ to 1.5DCJ along the cell centerline, and the average detonation speed is only 0.88% different from the CJ value. The ratio of peak pressure to initial pressure ranges from 14 to 50 along the cell centerline. The average detonation speed and cell aspect ratio are remarkably agreeable with experimental values, but the computational cells are slightly smaller than the experimental cells. Some complicated detonation physics including transverse waves, un-reacted gas pocket, re-initiation of detonation cells etc. was recognized.
Cellular detonation in a straight tube was numerically studied, based on two-dimensional reactive Euler equations and detailed chemical reaction model. The 5th order WENO scheme was employed to resolve the convective terms, and the additive semi-implicit Runge-Kutta methods was used to treat the stiffness caused by the chemical source terms. The contours of density, pressure, temperature and typical species mass fraction as well as numerical cellular pattern etc. were obtained. The results show that, the different grid resolutions evidently influence the regularity of detonation cells and the equilibrium detonation mode number. As grid size increases, the detonation wave developes more irregular cells and more additional triple points. For the given gas mixtures, initial pressure, initial temperature and tube width, the final self-sustaining detonation mode number is converged to a fixed value. It is also independent of the variety of initial perturbations, provided that the initial perturbations are sufficiently strong to reproduce the self-sustaining cellular detonation. Detonation velocity ranges from 0.88DCJ to 1.5DCJ along the cell centerline, and the average detonation speed is only 0.88% different from the CJ value. The ratio of peak pressure to initial pressure ranges from 14 to 50 along the cell centerline. The average detonation speed and cell aspect ratio are remarkably agreeable with experimental values, but the computational cells are slightly smaller than the experimental cells. Some complicated detonation physics including transverse waves, un-reacted gas pocket, re-initiation of detonation cells etc. was recognized.
2005, 25(5): 417-422.
doi: 10.11883/1001-1455(2005)05-0417-06
Abstract:
The experimental study on arc windshield of fighter subjected to bird impact is presented. In order to understand the influences of boundary conditions and relative parts on dynamic response, the specimens include arc windshields and relative parts of fighters. The dynamic response process is recorded using the high speed video camera. The critical impact velocity for PMMA arc windshield is found. The displacement history and strain history of the dynamic response are obtained. The changing rules of displacement-velocity on key points are analyzed. The relationship between critical velocity and strain is given. Also, the value of the dynamic stress of windshield subjected to bird impact is computed. The valuable data are provided to engineers for designing, researching and producing new windshields with high crashworthiness.
The experimental study on arc windshield of fighter subjected to bird impact is presented. In order to understand the influences of boundary conditions and relative parts on dynamic response, the specimens include arc windshields and relative parts of fighters. The dynamic response process is recorded using the high speed video camera. The critical impact velocity for PMMA arc windshield is found. The displacement history and strain history of the dynamic response are obtained. The changing rules of displacement-velocity on key points are analyzed. The relationship between critical velocity and strain is given. Also, the value of the dynamic stress of windshield subjected to bird impact is computed. The valuable data are provided to engineers for designing, researching and producing new windshields with high crashworthiness.
2005, 25(5): 423-429.
doi: 10.11883/1001-1455(2005)05-0423-07
Abstract:
The dynamic buckling of the implosion liners driven by magnetic pressure has been investigated experimentally and numerically. The study of the effect of material properties and dimensions and loading currents on liner buckling, using a capacitor bank as a driver, indicates that the mode number for buckling increases with the ratio of radius to thickness of a liner, and the yield strength to plastic hardening modulus, but keeps invariable with the increase of loading current, and that the magnitude of buckling increases with the loading current. The numerical simulation to the experimental results by an instant non-linear finite element method, shows basically an agreement between them.
The dynamic buckling of the implosion liners driven by magnetic pressure has been investigated experimentally and numerically. The study of the effect of material properties and dimensions and loading currents on liner buckling, using a capacitor bank as a driver, indicates that the mode number for buckling increases with the ratio of radius to thickness of a liner, and the yield strength to plastic hardening modulus, but keeps invariable with the increase of loading current, and that the magnitude of buckling increases with the loading current. The numerical simulation to the experimental results by an instant non-linear finite element method, shows basically an agreement between them.
2005, 25(5): 430-436.
doi: 10.11883/1001-1455(2005)05-0430-07
Abstract:
A non-overlapping frequency approach to analyze the time-frequency characteristics of vibration signals is presented by means of the discretized version of continuous wavelet transform based on a modified L-P (littlewood-paley) wavelet basis function, and it is used to study the time-frequency characteristics of blast vibrations in this work. Energy density distributions of vertical ground velocities for 80 kg TNT explosion on the ground surface varying with time show that at the moment of peak particle velocity arriving, the frequency range of blast vibrations is very wide, being the relatively narrow bands at the other moments, and the peak time-frequency energy just corresponds to the peak particle velocity arriving time of blast vibration. The power spectra of blast vibrations through wavelet transform method are agreement with those from Fourier transform. Additionally, the principle of modeling blast vibrations as random evolutionary processes by using the wavelet transform results is outlined.
A non-overlapping frequency approach to analyze the time-frequency characteristics of vibration signals is presented by means of the discretized version of continuous wavelet transform based on a modified L-P (littlewood-paley) wavelet basis function, and it is used to study the time-frequency characteristics of blast vibrations in this work. Energy density distributions of vertical ground velocities for 80 kg TNT explosion on the ground surface varying with time show that at the moment of peak particle velocity arriving, the frequency range of blast vibrations is very wide, being the relatively narrow bands at the other moments, and the peak time-frequency energy just corresponds to the peak particle velocity arriving time of blast vibration. The power spectra of blast vibrations through wavelet transform method are agreement with those from Fourier transform. Additionally, the principle of modeling blast vibrations as random evolutionary processes by using the wavelet transform results is outlined.
2005, 25(5): 437-444.
doi: 10.11883/1001-1455(2005)05-0437-08
Abstract:
Based on the two-dimensional axisymmetric Euler equations, the initiation and detonation process of CH4/O2/N2 premixed gas induced by reflected focusing shock wave over the parabolic reflector was investigated numerically, using the nonorthogonal structured meshes and an improved reactive wave propagation algorithm. The flow field structures of detonation process were described. The effects of different compositions of premixed gas, incident shock wave intensities and reflector shapes on initiation and detonation were discussed. The results showed that the reflected focusing shock wave produced a local high temperature and high pressure region in the vicinity of the reflector apex, the region could ignite the premixed gas and lead to the detonation. The low diluted concentration of premixed gas, the high incident shock wave Mach number and the deeper reflector were of benefit to form detonation.
Based on the two-dimensional axisymmetric Euler equations, the initiation and detonation process of CH4/O2/N2 premixed gas induced by reflected focusing shock wave over the parabolic reflector was investigated numerically, using the nonorthogonal structured meshes and an improved reactive wave propagation algorithm. The flow field structures of detonation process were described. The effects of different compositions of premixed gas, incident shock wave intensities and reflector shapes on initiation and detonation were discussed. The results showed that the reflected focusing shock wave produced a local high temperature and high pressure region in the vicinity of the reflector apex, the region could ignite the premixed gas and lead to the detonation. The low diluted concentration of premixed gas, the high incident shock wave Mach number and the deeper reflector were of benefit to form detonation.
2005, 25(5): 445-450.
doi: 10.11883/1001-1455(2005)05-0445-06
Abstract:
An investigation of detonation wave diffraction over a divergent nozzle was carried out experimentally and numerically. The experiment was conducted in a detonation tube with double exposure holographic interferometric measurement, which offers better resolution and quantitative information as well, in comparison with conventional flow visualization such as schilieren method. Adaptive finite volume method combined with kinetic chemical reaction model was programmed to simulate the flow field. The numerical results agree fairly well with the experimental measurements. It was found that detonation diffraction has quite a lot of flow feature compared with shock wave diffraction, including the detachment of reaction front and leading shock wave and reignition phenomena. The divergent angle and initial pressure have great influence to the flow field of detonation diffraction. The lower initial pressure, the earlier the detachment of chemical reaction front and leading shock wave will happen.
An investigation of detonation wave diffraction over a divergent nozzle was carried out experimentally and numerically. The experiment was conducted in a detonation tube with double exposure holographic interferometric measurement, which offers better resolution and quantitative information as well, in comparison with conventional flow visualization such as schilieren method. Adaptive finite volume method combined with kinetic chemical reaction model was programmed to simulate the flow field. The numerical results agree fairly well with the experimental measurements. It was found that detonation diffraction has quite a lot of flow feature compared with shock wave diffraction, including the detachment of reaction front and leading shock wave and reignition phenomena. The divergent angle and initial pressure have great influence to the flow field of detonation diffraction. The lower initial pressure, the earlier the detachment of chemical reaction front and leading shock wave will happen.
2005, 25(5): 451-456.
doi: 10.11883/1001-1455(2005)05-0451-06
Abstract:
Dynamic mechanical behaviors of 45 steel have been studied with the split Hopkinson pressure bar(SHPB) and static material test system over a wide range of strain rates and temperatures. The Johnson-Cook constitutive relationship parameters are determined through these experiments. The parameters are validated by comparison between the Taylor experiments and the simulations. The consistency between experimental observation and numerical simulation indicates that the parameters obtained can describe the large strain mechanical behavior of 45 steel under high speed deformation.
Dynamic mechanical behaviors of 45 steel have been studied with the split Hopkinson pressure bar(SHPB) and static material test system over a wide range of strain rates and temperatures. The Johnson-Cook constitutive relationship parameters are determined through these experiments. The parameters are validated by comparison between the Taylor experiments and the simulations. The consistency between experimental observation and numerical simulation indicates that the parameters obtained can describe the large strain mechanical behavior of 45 steel under high speed deformation.
2005, 25(5): 457-460.
doi: 10.11883/1001-1455(2005)05-0457-04
Abstract:
The influence of the modal dispersion of a signal fiber on velocity measurement in VISAR is theoretically analyzed and discussed in detail. A mathematical analysis model about the interfering contrast decreased by model dispersion is set up. The dispersion contrast factor varied with fringe constants and velocity increment is calculated. The results show: (1) the larger the fringe constants, the smaller the influence of the modal dispersion of a signal fiber; (2) the larger the measured velocity ,the larger the influence of the modal dispersion; (3) the influence of the modal dispersion of a multimode step-index fiber is larger than one of a multimode graded-index fiber. After this research, the efficient methods that decrease the influence of the modal dispersion of a signal fiber is put forward. This play an important role in improving interfering contrast and measuring precision in VISAR.
The influence of the modal dispersion of a signal fiber on velocity measurement in VISAR is theoretically analyzed and discussed in detail. A mathematical analysis model about the interfering contrast decreased by model dispersion is set up. The dispersion contrast factor varied with fringe constants and velocity increment is calculated. The results show: (1) the larger the fringe constants, the smaller the influence of the modal dispersion of a signal fiber; (2) the larger the measured velocity ,the larger the influence of the modal dispersion; (3) the influence of the modal dispersion of a multimode step-index fiber is larger than one of a multimode graded-index fiber. After this research, the efficient methods that decrease the influence of the modal dispersion of a signal fiber is put forward. This play an important role in improving interfering contrast and measuring precision in VISAR.
2005, 25(5): 461-466.
doi: 10.11883/1001-1455(2005)05-0461-06
Abstract:
In order to get the damage mode and resist character of spacecraft shield structure by the high-velocity impact of space debris, a two-stage light gas gun with non-powder projection was used to launch Al-sphere projectiles impacting on aluminum alloy Whipple shield. By analyzing damage mode in different impact velocity ranges, the laws of penetration hole diameter and cratered area diameter depending on projectile diameter and impact velocity were observed. At the same time, the ballistic limit curves of the Whipple shield in a velocity range from 0.5 km/s to 5.5 km/s was obtained. Comparing to the predicted curve from Christiansen ballistic limit equation, the experimental minimum critical projectile diameter is slightly greater than the prediction.
In order to get the damage mode and resist character of spacecraft shield structure by the high-velocity impact of space debris, a two-stage light gas gun with non-powder projection was used to launch Al-sphere projectiles impacting on aluminum alloy Whipple shield. By analyzing damage mode in different impact velocity ranges, the laws of penetration hole diameter and cratered area diameter depending on projectile diameter and impact velocity were observed. At the same time, the ballistic limit curves of the Whipple shield in a velocity range from 0.5 km/s to 5.5 km/s was obtained. Comparing to the predicted curve from Christiansen ballistic limit equation, the experimental minimum critical projectile diameter is slightly greater than the prediction.
2005, 25(5): 467-471.
doi: 10.11883/1001-1455(2005)05-0467-05
Abstract:
By using one-dimensional finite different hydrodynamic code coupled with four spall models, spall in ductile metal has been studied. Numerical simulation results indicate that: (1)Cut-off model and simple damage accumulation model can qualitatively describe some physical essences of spall fracture, but remain apparent discrepancies from the experimental results due to the damage influence on the material properties being neglected; However, because of using a few parameters, they are still useful to solve engineering problems without considering higher precision. (2) NAG model and FJB damage degree function model based on statistical micro-damage mechanics have a good ability of description of the process of damage evolution, and the computed free-surface velocity profiles consist with the experimental measurements very well.
By using one-dimensional finite different hydrodynamic code coupled with four spall models, spall in ductile metal has been studied. Numerical simulation results indicate that: (1)Cut-off model and simple damage accumulation model can qualitatively describe some physical essences of spall fracture, but remain apparent discrepancies from the experimental results due to the damage influence on the material properties being neglected; However, because of using a few parameters, they are still useful to solve engineering problems without considering higher precision. (2) NAG model and FJB damage degree function model based on statistical micro-damage mechanics have a good ability of description of the process of damage evolution, and the computed free-surface velocity profiles consist with the experimental measurements very well.
2005, 25(5): 472-476.
doi: 10.11883/1001-1455(2005)05-0472-05
Abstract:
The process of explosives (wrapped coarse granule TNT, =1.547 g/cm3) shock initiation and extinguishment was experimentally investigated and analyzed by Lagrange method in the case of small partition assay. The state equations of explosive and reaction products are all based on JWL state equations. The value-time relations of u,v,e on every Lagrange position are obtained and the parameters in the reaction rate equation have been determined, which utilizies the ignition and growth model.The reaction rate obtained by Lagrange method indicates that there are partly reactions when the shock wave extinguishs in the solid explosives.
The process of explosives (wrapped coarse granule TNT, =1.547 g/cm3) shock initiation and extinguishment was experimentally investigated and analyzed by Lagrange method in the case of small partition assay. The state equations of explosive and reaction products are all based on JWL state equations. The value-time relations of u,v,e on every Lagrange position are obtained and the parameters in the reaction rate equation have been determined, which utilizies the ignition and growth model.The reaction rate obtained by Lagrange method indicates that there are partly reactions when the shock wave extinguishs in the solid explosives.
2005, 25(5): 477-480.
doi: 10.11883/1001-1455(2005)05-0477-04
Abstract:
The meshing method of spherical fragment penetrating target by LS-DYNA is introduced. With the material models of tungsten spherical fragment and LY-12 aluminum alloy target, simulation analysis of spherical fragments penetrating at different initial velocities and incident angles are made, from which the penetration charts, and the ricochet charts are obtained and discussed. The critical incident angles both for penetration and for ricochet are determined, and the terminal velocity and terminal angle of the penetrated fragments are analyzed as well.
The meshing method of spherical fragment penetrating target by LS-DYNA is introduced. With the material models of tungsten spherical fragment and LY-12 aluminum alloy target, simulation analysis of spherical fragments penetrating at different initial velocities and incident angles are made, from which the penetration charts, and the ricochet charts are obtained and discussed. The critical incident angles both for penetration and for ricochet are determined, and the terminal velocity and terminal angle of the penetrated fragments are analyzed as well.
