Modeling of softsphere normal collisions with characteristic of coefficient of restitution dependent on impact velocity

This letter presents a theoretical model of the normal （head-on） collisions between two soft spheres for predicting the experimental characteristic of the coefficient of restitution dependent on impact velocity. After the contact force law between the contacted spheres during a collision is phenomenologically formulated in terms of the compression or overlap displacement under considera- tion of an elastic-plastic loading and a plastic unloading subprocesses, the coefficient of restitution is gained by the dynamic equation of the contact process once an initial impact velocity is input. It is found that the theoretical predictions of the coefficient of restitution varying with the impact velocity are well in agreement with the existing experimental characteristics which are fitted by the explicit formula.

Numerical simulation of the effects of the impact velocity on the particle deposition characteristics in cold gas dynamic spraying

In this study, the effects of the impact velocity on the particle deposition characteristics in cold gas dynamic spraying （CGDS） of 304 stainless steel （SS） on an interstitial free （IF） steel substrate are numerical simulated by means of a finite element analysis （FEA）. The results have illustrated that when the particle impact velocity exceeds a critical value at which adiabatic shear instability of the particle starts to occur. Meanwhile, the fatten ratio and impact crater depth （or the effective contacting area ） increase rapidly. The particle-substrate bonding and deposition mechanism can be attributed to such an adiabatic shear deformation induced by both the compressive force and the slide friction force of particle. The critical velocity can be predicted by numerical simulation, which is useful to optimize the CGDS processing parameters for various materials.

Velocity equation for grenades while impacting on dry sand media

This paper deals with the collision of sphere shape grenades with sand media.The central issue of the article is the establishing of an empirical velocity equation of the grenade while impacting on sand that is used to solve motion equations of the mechanical mechanism inside the impact grenade fuze.The paper focuses on impact velocities that are lower than 5 m s^(-1).An experiment was conducted to study the velocity of the grenade while impacting on dry sand.A high-speed camera video was used to capture the grenade positions.The grenade velocity in the impact process was generated from these video data.Some types of fitting curves are used to regress the velocity equation of the grenade while interacting with the sand media and the best-fitting model is chosen.The result shows the regression curve has a high correlation with the experiment data for grenade velocities below 5 m s^(-1).The received regression equation is useful for analyzing the working ability of the inertial mechanism inside the impact grenade or analyzing and choosing the appropriate parameters of each part in the inertial mechanism to meet the required characteristics of the mechanism.

Influence of impact velocity and impact attack angle of bullets on damage of human tissue surrogate--ballistic gelatin

Purpose Terminal performance of a bullet in human body is critical for the treatment of gunshot injury and optimization of bullet design.The effects of the impact velocity(v_(0))and the impact attack angle(δ_(0))of the bullet on its terminal performance was investigated,using a new evaluation method(called expansion method)based on the expansion of cracks and the permanent cavity wall in ballistic gelatin.Methods Ballistic gelatin was used to simulate human body.The 7.62 mm×39 mm rifle bullets with different v_(0)(600–76_(0)m/s)andδ_(0)(0°–6°)were fired into the gelatin blocks.The gelatin block was cut into slices of about 2_(0)mm thickness.The cracks and the permanent cavity on each slice were obtained manually.The damaged gelatin was determined using two methods:expanding the permanent cavity but ignoring the cracks,and expanding both the permanent cavity and the cracks.The relations between the damaged gelatin and v_(0)andδ_(0)were obtained using linear fitting method.Results According to the distribution of the damaged gelatin along the penetration depth,the damaged gelatin block could be divided into two parts:the less damaged part and the severely damaged part.The length of the less damaged part depends mostly onδ_(0);while the average damaged area of this part depends on bothδ_(0)as well as v_(0).The cracks contributed significantly to the total volume of damaged gelatin,particularly when the expansion was larger than 1.9 mm.The total damaged gelatin increases with v_(0),δ_(0)and the expansion extent.The average length of equivalent cracks grew with v_(0)andδ_(0)when considering the cracks,and decreased with v_(0)when ignoring the cracks.Conclusion The expansion method is suitable to investigate the influence of different factors of bullets on their terminal performance.The characteristics of the damaged gelatin have a linear relationship with the initial attack angle(δ_(0))and the initial velocity(v_(0))of the bullet.

High Velocity Impact Experiment on Ti/CFRP/Ti Sandwich Structure

Aircraft laminated composite components often suffer a variety of high velocity impacts with large quantity of energy,which usually affects aircraft behavior and would incur component damages,even disastrous consequences.Therefore,one investigates the impact resistance of a new type of composite material,Ti/CFRP/Ti sandwich structure,and launches impact tests by using an air gun test system.Then one acquires the critical breakthrough rate of the structure and analyzes the damages.The results show that the main failure mode of the front titanium sheet is shear plugging and brittle fracture of adhesive layer with fiber breakage,while the back titanium sheet is severely ripped.The rear damage is worse than the front one.Compared with traditional CFRP laminates,the critical breakthrough rate of Ti/CFRP/Ti sandwich structure is improved by 69.9% when suffered the impact of a bearing ball with 2mm radius.

Effect of Cycling Low Velocity Impact on Mechanical and Wear Properties of CFRP Laminate Composites

The mechanical and wear properties of CFRP laminate were investigated using a method of cycling low velocity impact, to study the trend and mechanism of impact resistance of the CFRP laminate under repeated impact during its service process. The interface responses of CFRP laminate under di erent impact kinetic energy during the cycling impact process were studied were studied experimentally, such as impact contact duration, deformation and energy absorption. The worn surface morphologies were observed through optical microscopy and a 3?D surface profiler and the cross?sectional morphologies were observed through SEM to investigate the mechanism of impact material dam?age. Based on a single?degree?of?freedom damping vibration model, the normal contact sti ness and contact damp?ing of the material in di erent wear stages were calculated. It shows the failure process of CFRP laminate damaged by accumulated absorption energy under the cycling impact of di erent initial kinetic energy. The results indicate that the sti ness and damping coe cients will change at di erent impact velocities or cycle numbers. The damage mechanism of CFRP laminates under cycling low kinetic energy is delamination. After repeated experiments, it was found that there was a threshold value for the accumulated absorption energy before the failure of the CFRP laminate.

Low Velocity Impact Response Analysis of Shape Memory Alloy Reinforced Composite Beam

The low velocity impact responses of shape memory alloy （ SMA ） reinforced composite beams were analyzed by employing the finite element method. The finite element dynamic equntion was solved by the Newmark direct integration method, the impact contact force was determined asing the Hertzian contact law, and the influence of SMA .fibers on stiffiwss matrix is studied. Numerical results show that the SMA fibers can effectively improve the low velocity impact response property of composite beam.

A DAMAGE ACCUMULATING MODELING OF FAILURE WAVES IN GLASS UNDER HIGH VELOCITY IMPACT

The failure wave phenomenon was interpreted in glass media under the high velocity impact with the stress levels below the Hugoniot elastic limit. In view of the plate impact experimental observations a damage-accumulating model predominated by the deviatoric stress impulse was proposed while Heaviside function was adopted in the damage-accumulating model to describe the failure delay in the interior of Materials. Features of the failure layer and propagation mechanism as well as their dynamic characteristics were further presented. The reduction in failure wave propagation speed is pointed out as the reflected rarefaction waves reflect again from the failure layer boundary.

Low Velocity Impact Response and Failure Assessment of Textile Reinforced Concrete Slabs

Present paper proposes a methodology by combining finite element method with smoothed particle hydrodynamics to simulate the response of textile reinforced concrete(TRC)slabs under low velocity impact loading.For the constitutive modelling in the finite element method,the concrete damaged plasticity model was employed to the cementitious binder of TRC and Von-Mises criterion was used for the textile reinforcement.Strain dependent smoothed particle hydrodynamics(SPH)was used to assess the damage and failure pattern of TRC slabs.Numerical simulation was carried out on TRC slabs with two different volume fraction of glass textile reinforcement to predict the energy absorption and damage by coupling finite element method with SPH.Parametric studies were also conducted for simulating the effect of number of textile layers in TRC under impact.It is concluded that the proposed methodology well predicts the damage in TRC slabs at various locations.The results were also analysed using two parameter Weibull distribution and the impact failure strength is presented in terms of reliability function.The results indicated that the Weibull distribution allows describing the failure in terms of reliability and safety limits.

THE APPLICATION OF COMPATIBLE STRESS ITERATIVE METHOD IN DYNAMIC FINITE ELEMENT ANALYSIS OF HIGH VELOCITY IMPACT

There is a common difficulty in elastic-plastic impact codes such as EPIC[2,3] NONSAP[4], etc.. Most of these codes use the simple linear functions usually taken from static problem to represent the displacement components. In such finite element formulation, the stress components are constant in each element and they are discontinuous in any two neighboring elements. Therefore, the bases of using the virtual work principle in such elements are unreliable. In this paper, we introduce a new method, namely, the compatible stress iterative method, to eliminate the above-said difficulty. The calculated examples show that the calculation using the new method in dynamic finite element analysis of high velocity impact is valid and stable, and the element stiffness can be somewhat reduced.

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 axe 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 unsymmetrical 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.

How does a woodpecker work? An impact dynamics approach

To understand how a woodpecker is able accelerate its head to such a high velocity in a short amount of time,a multi-rigid-segment model of a woodpecker＇s body is established in this study.Based on the skeletal specimen of the woodpecker and several videos of woodpeckers pecking,the parameters of a three-degree-of-freedom system are determined.The high velocity of the head is found to be the result of a whipping effect,which could be affected by muscle torque and tendon stiffness.The mechanism of whipping is analyzed by comparing the response of a hinged rod to that of a rigid rod.Depending on the parameters,the dynamic behavior of a hinged rod is classified into three response modes.Of these,a high free-end velocity could be achieved in mode II.The model is then generalized to a multihinge condition,and the free-end velocity is found to increase with hinge number,which explains the high free-end velocity resulting from whipping.Furthermore,the effects of some other factors,such as damping and mass distribution,on the velocity are also discussed.

Performance study of jute-epoxy composites/sandwiches under normal ballistic impact

This study is undertaken to explore the use of natural fiber Jute-epoxy(JE),Jute-epoxy-rubber(JRE)sandwich composite for ballistic energy absorption.Energy absorbed and residual velocities for these composites are evaluated analytically and through Finite Element Analysis(FEA).FE analysis of JE plates is carried out for different thicknesses(3,5,10 and 15 mm).JE plates and JRE sandwiches having the same thickness(15 mm) are fabricated and tested to measure residual velocity and energy absorbed.The analytical results are found to agree well with the results of FE analysis with a maximum error of 9%.The study on JE composite plate reveals that thickness influences the energy absorption.Experimental and FE analysis study showed that JRE sandwiches have better energy absorption than JE plates.Energy absorption of a JRE sandwich is about 71% greater than JE plates.Damages obtained from FEA and testing are in good agreement,SEM analysis confirms composites failed by fiber rupture and fragmentation.

Experimental investigation on anti-penetration performance of polyurea-coated ASTM1045 steel plate subjected to projectile impact

In this study,the anti-penetration performance of polyurea/ASTM1405-steel composite plate subjected to high velocity projectile was analyzed.Two kinds of modified polyurea material(AMMT-053 and AMMT-055)were selected and a ballistic impact testing system including speed measuring target system and high-speed camera was designed.This experiment was conducted with a rifle and 5.8 mm projectile to explore the effects by the polyurea coating thickness,the polyurea coating position and the glass-fiber cloth on the anti-penetration performance of polyurea/ASTM1405-steel composite plate.The result showed that the effects of polyurea coating position were different between two types of polyurea,and that the effects of glass-fiber position were disparate between two types of polyurea as well.For AMMT-053 polyurea material,it was better to be on front face than on rear face;whereas for AMMT-055 polyurea,it was better to be on rear surface although the difference was very subtle.Additionally,formulas had been given to describe the relationship between the effectiveness of polyurea and the thickness of polyurea coating.In general,AMMT-055 had better anti-penetration performance than AMMT-053.Furthermore,five typical damage modes including self-healing,crack,local bulge,spallation and local fragmentation were defined and the failure mechanism was analyzed with the results of SHPB test.Additionally,the bonding strength played an important role in the anti-penetration performance of polyurea/steel composite plate.

LOW VELOCITY RESPONSE CHARACTERISTICS OF COMPOSITE PLATE WITH EMBEDDED SHAPE MEMORY ALLOY

This paper analyzes the characteristics of utilizing shape memory e?ect (SME) of shape memory alloy (SMA) in improving the low velocity impact resistance performance of com- posite plate by using ?nite element method. The constitutive relation for SMA hybrid composite plates is presented. The analytic model of ?nite element for SMA composite plate subjected to low velocity impact is established. The modi?ed Hertz’s contact law is used to determine the impact contact force. The computing procedures for solving the ?nite element equation using Newmark direct integration method are given. The numerical modelling results show that the SMA can e?ectively improve the low velocity impact resistance performance of composite plate.

An investigation on anti-impact and penetration performance of basalt fiber composites with different weave and lay-up modes

The woven basalt fiber composites(WBFC) and the unidirectional [0°/90°/45°/-45°]s basalt fiber composites(UBFC) were prepared by hot-pressing.Three-point bending test,low velocity impact test,and ballistic test were performed to the prepared composites.After the tests,the specimens were recovered and analyzed for micromorphology.Three-point bending tests show that both the bending strength and stiffness of the WBFC surpass those of the UBFC.Low velocity impact test results show that the low velocity impact resistance to hemispherical impactor of the UBFC is higher than that of the WBFC,but the low velocity impact resistance to sharp impactor of the UBFC is lower than that of the WBFC.For the ballistic test,it can be found that the ballistic property of the UBFC is higher than that of the WBFC. After the tests,microscopic analysis of the specimens was applied,and their failure mechanism was discussed.The main failure modes of the UBFC are delamination and fibers breakage under the above loading conditions while the main failure mode of the WBFC is fibers breakage.Although delamination damage can be found in the WBFC under the above loading conditions,the degree of delamination is far less than that of the UBFC.

A TWO-DIMENSIONAL LAGRANGIAN TECHNIQUE FOR FLOW FIELD MEASUREMENT UNDER HIGH DYNAMIC PRESSURE

In this paper,a two-dimensional(2-D)Lagrangian technique for flow field measurement under high dynamic pressure is presented,which includes a set of experimental device and 2-D Lagrange composite manganin-constantan ring gages.With this kind of gage,the histories of pressure and radial displacement can be measured simultaneously at different Lagrange positions in an axisymmetric shock loading flow field. The technique has some advantages over the 1-D one,such as,simplified loading device,continuously adjust- able output pressure,no restriction on sample length and the availability for the study of lateral rarefaction in shock propogation.As a preliminary application,the processes of 2-D shock initiation and attenuation in compacted TNT are measured.

High velocity impact of metal sphere on thin metallic plate using smooth particle hydrodynamics(SPH)method

The modeling of high velocity impact is an important topic in impact engineering.Due to various constraints,experimental data are extremely limited.Therefore,detailed numerical simulation can be considered as a desirable alternative.However,the physical processes involved in the impact are very sophisticated;hence a practical and complete reproduction of the phenomena involves complicated numerical models.In this paper,we present a smoothed particle hydrodynamics(SPH)method to model two-dimensional impact of metal sphere on thin metallic plate.The simulations are applied to different materials(Aluminum,Lead and Steel);however the target and projectile are formed of similar metals.A wide range of velocities(300,1000,2000,and 3100 m/s)are considered in this study.The goal is to study the most sensitive input parameters(impact velocity and plate thickness)on the longitudinal extension of the projectile,penetration depth and damage crater.

Numerical modeling of high velocity impact applied to reinforced concrete panel

A numerical simulation of a high-velocity impact of reinforced concrete structures is a complex problem for which robust numerical models are required to predict the behavior of the experimental tests.This paper presents the implementation of a numerical model to predict the impact behavior of a reinforced concrete panel penetrated by a rigid ogive-nosed steel projectile.The concrete panel has dimensions of 675 mm675 mm200 mm,and is meshed using 8-node hexahedron solid elements.The behavior of the concrete panel is modeled using a Johnson-Holmquist damage model incorporating both the damage and residual material strength.The steel projectile has a small mass and a length of 152 mm,and is modeled as a rigid element.Damage and pressure contours are applied,and the kinetic and internal energies of the concrete and projectile are evaluated.We also evaluate the velocity at different points of the steel projectile and the concrete panel under an impact velocity of 540 m/s.

MECHANISM OF WAVE FORMATION AT THE INTERFACE IN EXPLOSIVE WELDING

Some of the main progress on the investigation of the mechanism of the wave formation in explosive welding at the Institute of Mechanics is summarized and otters'previous works are re- viewed.Our systematic experiments and analysis do not substantiate the theory of wave formation based on Karman vortex-street analogy or Helmholtz instability.On the contrary,they show that materi- al strength insensitive to strain rate plays an important role.A simple hydro-plastic model is presented to explain the main features regarding the interracial wave formation and to estimate the magnitude of wave length.The result is in broad agreement with experiment.