Parametric study on mass loss of penetrators

Earth penetration weapon （EPW） is applicable for attacking underground targets protected by reinforced concrete and rocks. With increasing impact velocity, the mass loss/abrasion of penetrator increases, which significandy decreases the penetration efficiency due to the change of nose shape. The abrasion may induce instability of the penetrator, and lead to failure of its structure. A common disadvantage, i.e. dependence on corresponding experimen- tal results, exists in all the available formulae, which limits their ranges of application in estimating the mass loss of penetrator. In this paper, we conduct a parametric study on the mass loss of penetrator, and indicate that the mass loss of penetrator can be determined by seven variables, i.e., the initial impact velocity, initial nose shape, melting heat, shank diameter of projectile and density and strength of target as well as the aggregate hardness of target. Further discussion on factors dominant in the mass abrasion of penetrator are given, which may be helpful for optimizing the target or the projectile for defensive or offensive objectives, respectively.     

Stability analyses of the mass abrasive projectile high-speed penetrating into concrete target. Part Ⅰ： Engineering model for the mass loss and nose-blunting of ogive-nosed projectiles

The mass loss and nose blunting of a projectile during high-speed deep penetration into concrete target may cause structural destruction and ballistic trajectory instability of the penetrator,obviously reducing the penetration efficiency of penetrator.Provided that the work of friction between projectile and target is totally transformed into the heat to melt penetrator material at its nose surface,an engineering model is established for the mass loss and nose-blunting of the ogive-nosed projectile.A dimensionless formula for the relative mass loss of projectile is obtained by introducing the dimensionless impact function I and geometry function N of the projectile.The critical value V c0of the initial striking velocity is formulated,and the mass loss of projectile tends to increase weakly nonlinearly with I/N when V0〉V c0,whilst the mass loss is proportional to the initial kinetic energy of projectile when V0     

Experimental and theoretical investigation of the failure behavior of a reinforced concrete target under high-energy penetration

The dynamic mechanical properties of concrete and reinforced concrete targets subjected to high-speed projectile impact loading have a significant influence on the impact resistance of protective structures.In this study,high-speed projectile penetration and perforation of concrete and reinforced concrete structures was carried out to determine the high-energy impact loading.The failure behaviors of projectile penetration and perforation of the concrete and reinforced concrete targets were investigated,and the destruction characteristics of the targets were measured.An analytical model was established using the principle of minimum potential energy.The results show that the theoretical predictions are consistent with the experimental data,indicating that the energy method is effective for predicting the dynamic mechanical properties of concrete and reinforced concrete targets under high-speed projectile penetration.     

A spherical cavity expansion model for penetration of ogival-nosed projectiles into concrete targets with shear-dilatancy

A dynamic spherical cavity-expansion penetration model is suggested herein to predict the penetration and perforation of concrete targets struck normally by ogivalnosed projectiles.Shear dilatancy as well as compressibility of the material in comminuted region are considered in the paper by introducing a dilatant-kinematic relation.A procedure is first presented to compute the radial stress at the cavity surface and then a numerical method is used to calculate the results of penetration and perforation with friction being taken into account.The influences of various target parameters such as shear strength,bulk modulus,density,Poisson’s ratio and tensile strength on the depth of penetration are delineated.It is shown that the model predictions are in good agreement with available experimental data.It is also shown that the shear strength plays a dominant role in the target resistance to penetration.     

PREDICTION OF PROJECTILE PENETRATION AND PERFORATION BY FINITE CAVITY EXPANSION METHOD WITH THE FREE-SURFACE EFFECT

With a target treated as the incompressible Tresca and Mohr-Coulomb material, by assuming that cavity expansion produces plastic-elastic and plastic-cracked-elastic response region, the decay function for the free-surface effect is constructed for metal and geological tar- gets, respectively. The forcing function for oblique penetration and perforation is obtained by multiplying the forcing function derived on the basis of infinite target assumption with the de- cay function. Then the projectile is modeled with an explicit transient dynamic finite element code and the target is represented by the forcing function as the pressure boundary condition. This methodology eliminates discretizing the target as well as the need for a complex contact algorithm and is implemented in ABAQUS explicit solver via the user subroutine VDLOAD. It is found that the free-surface effect must be considered in terms of the projectile deformation, residual velocity, projectile trajectory, ricochet limits and critical reverse velocity. The numerical predictions are in good agreement with the available experimental data if the free-surface effect is taken into account.     

Experimental investigation of penetration performance of shaped charge into concrete targets

In order to develop a tandem warhead that can effectively destroy concrete targets, this paper explores the penetration performance of shaped charges with different cone angles and liner materials into concrete targets by means of experiments. The penetration process and the destruction mechanism of concrete targets by shaped charges and kinetic energy projectiles are analyzed and compared. Experimental results suggest that both kinetic energetic projectile and shaped charge are capable of destroying concrete targets, but the magnitudes of damage are different. Compared with a kinetic energy projectile, a shaped charge has more significant effect of penetration into the target, and causes very large spalling area. Hence, a shaped charge is quite suitable for first-stage charge of tandem warhead. It is also found that, with the increase of shaped charge liner cone angle, the depth of penetration decreases gradually while the hole diameter becomes larger. Penetration depth with copper liner is larger than of aluminum liner but hole diameter is relatively smaller, and the shaped charge with steel liner is between the above two cases. The shaped charge with a cone angle of 100° can form a jet projectile charge （JPC）. With JPC, a hole with optimum depth and diameter on concrete targets can be formed, which guarantees that the second-stage warhead smoothly penetrates into the hole and explodes at the optimum depth to achieve the desired level of destruction in concrete targets.     

An engineering formula on the calculation of oblique penetration by long-rod projectile

Based on the concept supposed in this paper that damage of a target is determined by momentum rather than by stress, an engineering .formula on the calculation of oblique penetration by long-rod projectile is established. The results calculated from this formula show good agreements with experimental data.     

NORMAL EXPANSION THEORY FOR PENETRATION OF PROJECTILE AGAINST CONCRETE TARGET

Based on the equations which describe the dynamic behavior of material under high-velocity and high-pressure shock, corresponding equations at shock front whose surface is general space curve surface were established. For concrete material, a normal expansion theory was proposed by which some deceleration about time history of the projectile can be analytically given. This normal expansion theory is not only suitable for spherical and cylindrical-nose projectile, but also suitable for other general nose projectile, for example conical nose or ogive-nose. And it is not only suitable for perpendicular shock but also for oblique shock.     

Numerical simulation of bubble breakup phenomena in a narrow flow field

Based on the boundary integral method, a 3D bubble breakup model in a narrow flow field is established, and a corresponding computation program is developed to simulate the symmetrical and asymmetrical bubble breakup. The calculated results are compared with the experimental results and agree with them very well, indicating that the numerical model is valid. Based on the basic behavior of bubbles in a narrow flow field, the symmetrical and asymmetrical bubble breakup is studied systematically using the developed program. A feasibility rule of 3D bubble breakup is presented. The dynamics of sub-bubbles after splitting is studied. The influences of characteristic parameters on bubble breakup and sub-bubble dynamics are analyzed.     

Research on abrasion of debris flow to high-speed drainage structure

As one weak topic in research of debris flow, abrasion of debris flow shortens obviously application life of control structure composed of concrete. High-speed drainage structure, one of the most effective techniques to control giant debris flow disaster, has shortened one-third application life due to abrasion by debris flow. Based on velocity calculation method founded by two-phase theory, research of abrasion mechanism of debris flow to high-speed drainage structure was mode. The mechanism includes both abrasion mechanism of homogeneous sizing and shearing mechanism of particle of debris flow to high- speed drainage trough structure. Further abrasion equations of both sizing and particle were established by Newton movement theory of debris flow. And abrasion amount formula of the high-speed drainage trough structure is set up by dimensional analysis. Amount to calculating in the formula is consistent with testing data in-situ, which is valuable in design of high-speed drainage structure.     

Analytical models for the penetration of semi-infinite targets by rigid, deformable and erosive long rods

A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.     

Large eddy simulation of fuel injection and mixing process in a diesel engine

The large eddy simulation(LES) approach implemented in the KIVA-3V code and based on one-equation sub-grid turbulent kinetic energy model are employed for numerical computation of diesel sprays in a constant volume vessel and in a Caterpillar 3400 series diesel engine.Computational results are compared with those obtained by an RANS(RNG k-ε) model as well as with experimental data.The sensitivity of the LES results to mesh resolution is also discussed.The results show that LES generally provides flow and spray characteristics in better agreement with experimental data than RANS;and that small-scale random vortical structures of the in-cylinder turbulent spray field can be captured by LES.Furthermore,the penetrations of fuel droplets and vapors calculated by LES are larger than the RANS result,and the sub-grid turbulent kinetic energy and sub-grid turbulent viscosity provided by the LES model are evidently less than those calculated by the RANS model.Finally,it is found that the initial swirl significantly affects the spray penetration and the distribution of fuel vapor within the combustion chamber.     

Dynamic torsional response of pre-strained end bearing pile embedded in pre-strained isotropic saturated soil medium

The influence of initial strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated through the linearized theory of small elastic perturbation superposed on largely stressed bodies. The governing equations for soil, based on Blot＇s poroelasticity theory, are derived in the cylindrical coordinates, and the pile is modeled by using the one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of both twist angle and time history of velocity response are obtained by using of separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle, and velocity response at the top of the pile is carried out.     

Principal parametric resonance of axially accelerating rectangular thin plate in magnetic field

Nonlinear parametric vibration and stability is investigated for an axially accelerating rectangular thin plate subjected to parametric excitations resulting from the axial time-varying tension and axial time-varying speed in the magnetic field. Consid- ering geometric nonlinearity, based on the expressions of total kinetic energy, potential energy, and electromagnetic force, the nonlinear magneto-elastic vibration equations of axially moving rectangular thin plate are derived by using the Hamilton principle. Based on displacement mode hypothesis, by using the Galerkin method, the nonlinear para- metric oscillation equation of the axially moving rectangular thin plate with four simply supported edges in the transverse magnetic field is obtained. The nonlinear principal parametric resonance amplitude-frequency equation is further derived by means of the multiple-scale method. The stability of the steady-state solution is also discussed, and the critical condition of stability is determined. As numerical examples for an axially moving rectangular thin plate, the influences of the detuning parameter, axial speed, axial tension, and magnetic induction intensity on the principal parametric resonance behavior are investigated.     

A STUDY ON THE COUNTER-INTUITIVE BEHAVIORS OF PIN-ENDED BEAMS UNDER PROJECTILE IMPACT

The counter-intuitive behaviors of pin-ended beams under the projectile impact are investigated with ANSYS/LS-DYNA in this paper. It studies in detail their displacement-time history curves, final deformed shapes, energy relationships and projectile impact velocity ranges related to their counter-intuitive behaviors. The influences of the impact positions on their counterintuitive behaviors are also discussed. The results show that no matter where the impact position on the beam is, the counter-intuitive behaviors of pinned beams will occur as long as the impacting velocity lies within a proper range. Corresponding to the occurring of the counter-intuitive behaviors, the rebounding number in the displacement history curves of the beams decreases from a few times to zero with an increase of the impact velocity. The final deformation modes of the beam corresponding to the counter-intuitive behaviors will appear in symmetrical and unsym-metrical forms no matter where the impact position is; the impact velocity of the first-occurring of the counter-intuitive behaviors of the beam increases slowly with the deviation of the impact position away from the mid-span.     

THE PERTURBATION FINITE ELEMENT METHOD FOR SOLVING THE PLANE PROBLEM IN CONSIDERATION OF LINEAR CREEP

In this paper, amethod (PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, prestressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on. In the presented method, the assumption made in the general increment method that variables remain constant in a divtded time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased. Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.     

NORMAL PERFORATION OF A THIN INFINITE PLATE BY A FLAT-HEADED CYLINDRICAL PROJECTILE

Analytical formulae for calculating the stress acting on the contact surface between projectile and target and for calculating the moving velocity of this contact surface under impact are both suggested in this paper. These formulae can be thought of as a generalization of the well-known Hopkins and Kolsky's theory in plastic domain. And then, an analytical formula for calculating ballistic limit is also suggested. It is also proved in this paper that the shear stress acting on the cylindrical surface of the plug is distributed uniformly.     

Normal perforation of a thin infinite plate by a flat-headed cylindrical projectile

Analytical formulae for calculating the stress acting on the contact surface between projectile and target and for calculating the moving velocity of this contact surface under impact are both suggested in this paper. These formulae can be thought of as a generalization of the well-known Hopkins and Kolsky’s theory in plastic domain. And then, an analytical formula for calculating ballistic limit is also suggested. It is also proved in this paper that the shear stress acting on the cylindrical surface of the plug is distributed uniformly.     

Minimum Control Energy of Spatial Beam with Assumed Attitude Adjustment Target

The dynamic analysis on the ultra-large spatial structure can be simplified drastically by ignoring the flexibility and damping of the structure.However,these simplifications will result in the erroneous estimate on the dynamic behaviors of the ultra-large spatial structure.Taking the spatial beam as an example,the minimum control energy defined by the difference between the initial total energy and the final total energy in the assumed stable attitude state of the beam is investigated by the structure-preserving method proposed in our previous studies in two cases:the spatial beam considering the flexibility as well as the damping effect,and the spatial beam ignoring both the flexibility and the damping effect.In the numerical experiments,the assumed simulation interval of three months is evaluated on whether or not it is long enough for the spatial flexible damping beam to arrive at the assumed stable attitude state.And then,taking the initial attitude angle and the initial attitude angle velocity as the independent variables,respectively,the minimum control energies of the mentioned two cases are investigated in detail.From the numerical results,the following conclusions can be obtained.With the fixed initial attitude angle velocity,the minimum control energy of the spatial flexible damping beam is higher than that of the spatial rigid beam when the initial attitude angle is close to or far away from the stable attitude state.With the fixed initial attitude angle,ignoring the flexibility and the damping effect will underestimate the minimum control energy of the spatial beam.