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.

Experimental Investigation and Numerical Simulation of Air-Breathing Mode for Laser Propulsion

Laser propulsion is a new concept technique of propulsion and will have important application in future space technology. There are two main driving types: the air-breathing mode and the rocket ablation mode. Vertical flight experiments have been carried out with a simple paraboloid type lightcraft in the air-breathing mode by TEA-CO_2 laser. In simulation a new model is used for LSD/LSC wave, the result shows that the momentum coupling coefficient increases with the increase of the pulse energy.

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.

A three-stage model for the perforation of finite metallic plates by long rods at high velocities

A three-stage theoretical model is presented herein to predict the perforation of a thick metallic plate struck normally by a long rod at high velocities. The model is suggested on the basis of the assumption that the perforation of a thick metallic plate by a long rod can be divided into three stages:(1) initial penetration;(2) plug formation and (3) plug slipping and separation. Various analytical equations are derived which can be employed to predict the ballistic limit, residual velocity and residual length of the long rod. It is demonstrated that the present model predictions are in good agreement with available experimental results for the perforation of finite steel targets struck normally by steel as well as tungsten alloy long rods at high velocities. It is also demonstrated that the dynamic maximum shear stress of a plate material has strong effect on plug formation and plug thickness which, in turn, exerts considerable influence on the residual velocities and lengths of a long rod at impact velocities just above the ballistic limit.

Enhanced effect of dimension of receptor-ligand complex and depletion effect on receptor-mediated endocytosis of nanoparticles

We present an extended analytical model including the depletion effect and the dimension of ligand-receptor complex, aiming to elucidate their influences on endocytosis of spherocylindrical nanoparticles （NPs）. It is found that the dimension of ligand-receptor complex （δ） and the depletion effect interrelatedly govern the optimal conditions of NP endocytosis. The endocytosis phase diagram constructed in the space of NP radius and relative aspect ratio indicates that the endocytosis of NP is enhanced evidently by reducing the optimal radius and the threshold radius of endocytosed NP. Meanwhile, through thermodynamic and kinetic analysis of the diffusion of receptors, the dependence of diffusion length on depletion effect and the dimension of ligand-receptor complex can be identified in great detail. For small aspect ratio, diffusion length decreases with increasing concentration c of small bioparticles in cellular environment. Endocytosis speed corresponding to large radius R and high concentration c of small bioparticles strongly depends on the increasing （2r-δ）. These results may show some highlights into the conscious design of NPs for diagnostic agents and therapeutic drug delivery applications.

Dynamic Properties of Fiber Reinforced Cement Mortar

Based on the shear wave tracing(SWT) technique proposed by Tang Z P, particle velocity gauge and the dual internal measurement for pressure and shear waves (IMPS) system are applied to investigate the responses of fiber reinforced cement subjected to impact loading. Series of experiments are conducted. The results show that there exist four critical points, A, B, C, D, in p-V Hugoniot curves. They correspond to the Hugoniot elastic limit (HEL) of the material, the critical point for shear strength limit and transition from damage state to failure state, void collapse, and solid compression, respectively. The critical point B is difficult to be aware of and never reported. However, it can be clearly disclosed with SWT method. Based on the analyses of shear strength, it can be concluded that the transversal wave, especially the unloading transversal wave, is especially important for the dynamic damage investigation of brittle materials.

The theory of compression–shear coupled composite wave propagation in rock

The wave velocity analysis of rock medium is the main method used to explore the internal compositions in the crust and research seismic.In this paper,a compression–shear coupled nonlinear elastic constitutive relation is established,which is consistent with the mechanical properties of rock and mineral medium under high pressure.On this basis,numerical solutions of the wave equation and plane wave analytical solutions for the primary and secondary wave velocities are obtained.As is indicated by the comparison with the linear elastic constitutive theory,the results reflect the compression–shear coupling characteristics of the rock,including the stress path effect and the compression–shear coupling wave effect.With different parameter values,the velocity of the secondary wave changes from lower than that of the elastic shear wave,to higher than that of the elastic shear wave.The research results are expected to provide meaningful explanations for the physical mechanisms of the supershear wave and sub-Rayleigh wave,and guidance for the detection of rock and soil composition and the observation of seismic waves.

Dynamic thermo-mechanical behaviors of SME TiNi alloys subjected to shock loading

Dynamic thermo-mechanical coupling behaviors of shape memory TiNi alloy in the strain rate ranging from 300 s^−1 to 2000 s^−1 are investigated by the split Hopkinson pressure bar(SHPB)device with an infrared(IR)detection system.In stress–strain space,dynamic response shows a strong strain hardening property,however,in stress–temperature space,transformation path is particularly sensitive to the strain rate.The corresponding temperature evolution measured synchronously shows that local temperature increased associated with the forward phase transition,and it would keep the loading maximum value unchanged or decreased for unloading,depending on the strain rate.Besides,local temperature evolution was consistent with the transformation stress and its values at different points are the same.Temperature evolution and transformation deformation mechanism is then analyzed by a simple one-dimensional model.The results show that latent heat and dissipated energy are responsible for temperature variation.Furthermore,the temperature evolution with strain rate reveals that with the increase of strain rate,the phase transformation deformation mechanism undergoes a transformation from phase transition fronts propagation during lower strain rates to combination of local nucleation and front propagation during middle strain rate and to uniform nucleations during higher strain rates.The results are helpful for a passive shape memory alloy(SMA)micro-valve design.

Combined stress waves with phase transition in thin-walled tubes

The incremental constitutive relation and governing equations with combined stresses for phase transition wave propagation in a thin-walled tube are established based on the phase transition criterion considering both the hydrostatic pressure and the deviatoric stress. It is found that the centers of the initial and subsequent phase transition ellipses are shifted along the sigma-axis in the sigma tau-plane due to the tension-compression asymmetry induced by the hydrostatic pressure. The wave solution offers the 'fast' and 'slow' phase transition waves under combined longitudinal and torsional stresses in the phase transition region. The results show some new stress paths and wave structures in a thin-walled tube with phase transition, differing from those of conventional elastic-plastic materials.

Predicting the penetration of long rods into semi-infinite metallic targets

Analytical equations are presented herein to predict the penetration of semi-infinite metallic targets struck normally by long rods at high velocities for Yp<S where Yp is the rod strength and S is the static target resistance.The equations are derived based on energy balance method.It is assumed that the kinetic energy loss of a long rod is related to the energy dissipated by the plastic deformations in the target,the energy consumed by the long-rod penetrator itself and the energy carried by the eroded rod debris.Secondary penetration is also examined in the present paper due to the fact that the eroded rod debris forms a tube which can penetrate the target further if the density of the rod is greater than that of the target and the impact velocity is high enough.The present analytical equation is found to be in good agreement with the experimental data for a wide range of impact velocities.

Study on the propagation of coupling shock waves with phase transition under combined tension-torsion impact loading

Phase transition can strongly change the stress wave propagation features. In this paper, the characteristic wave propagation under combined tension and torsion impact loading was studied with a simplified constitutive model of phase transition considering both pressure and shear stress. The results showed that for loading from the austenitic phase to the mixed phase, the wave propagation was similar to that in the elasto-plastic materials. However, for an instantaneous loading from the austenitic phase or mixed phase directly to the martensitic phase, a coupling shock wave(CSHW) with phase transition was predicted due to the second phase strengthening effect, which has barely been studied before. Through analysis of the constitutive equations with phase transition and the discontinuity conditions of shock waves, the control equations of the generalized Hugoniot curve was obtained and the CSHW problem with phase transition was solved analytically. An independent numerical simulation of step loading along a NiTi thin walled tube suffering a combined tension-torsion impact loading was given to prove the existence of CSHW. The simulation discloses the formation mechanism of CSHW and the adjusting process of the stress state ahead of CSHW, which reflects the intrinsic characteristic of materials with strong nonlinear constitutive behavior.

PETALLING OF A THIN METAL PLATE STRUCK BY A CONICAL-NOSED PROJECTILE

A theoretical study is presented herein on the petalling of a fully-clamped thin metal plate struck by a rigid conical-nosed projectile. It is assumed that the energy absorbed in the petalling process consists of two parts, one part is due to the local deformation during the hole formation and the other is from the global response such as bending and membrane stretching. Various energy absorbing mechanisms are delineated and an approximate equation for the ballistic limit is obtained. It transpires that the predictions from the present model are in good agreement with test data available when the is taken into account. sensitivity of the strain rate of the material