Effect of Adiabatic Shear on Penetration Properties of Water-back Plate

ZHU Hai-qing,LI Ying,ZHANG Xie-dong,ZHANG Hang

(School of Transportation,Wuhan University of Technology,Wuhan 430063,China)

Effect of Adiabatic Shear on Penetration Properties of Water-back Plate

ZHU Hai-qing,LI Ying,ZHANG Xie-dong,ZHANG Hang

(School of Transportation,Wuhan University of Technology,Wuhan 430063,China)

Adiabatic shear is one of the complicated damage mechanics of materials.In high strain rate situation,plastic deformation will bring temperature increasing,which makes the damage of the target plate is penetrated and melted.In this paper,adiabatic shear tests were designed,and a finite element model(FEM)based on Johnson-Cook method was set up,the experimental and numerical results were verified and compared to each other.Based on the FEM,the process of projectile penetrating water-back plate was analyzed,results indicated that：(1)In high strain rate loading,the temperature effect caused by adiabatic shear must be figured out;(2)The process of projectile penetrating liquid-filled tank can be divided into four distinct stages：mushrooming propagating,crushing,shearing and perturbing;(3)The residual velocity of the fragments considering adiabatic shear effect is smaller than that of without considering the effect.And the difference value is small when the initial velocity is slow,but will increase with the increasing of the initial velocity.

adiabatic shear;water-back plate;penetrating;residual velocity

0 Introduction

The liquid-filled tank is one of the main devices of naval ships,and it can be utilized as a protecting armor for the energy of projectile fragments will be absorbed by the liquid.The sketch of liquid-filled tank is shown in Fig.1.Recently,researchers started to focus on the mechanism of resistant penetrating fragments of liquid-filled tank.Projectiles with 600 m/s and 900 m/s penetrating aluminum tube and carbon fiber reinforced polymer tube(CFRP tube) were analyzed by Varas et al[1-4]through experimental and numerical methods,and high-speed camera were utilized to video the shock wave propagating.Projectiles with high-speed 1 000 m/s to 4 000 m/s impacting liquid-filled tank were experimented by Townsend et al[5],the damage level changed with the volume ratio of liquid and air was discussed.Most researches showed that when high-speed projectiles impacting liquid-filled tank,the shock wave with hugeenergy will occur and propagate in the tank,and cause huge damage to the whole tank.The global damage and global deformation phenomenon are the research targets,but the local deformation of the outer plate especially the adiabatic shearing has always been neglected.

Fig.1 Sketch of liquid-filled cabin

1 Dynamic compression and adiabatic shear tests

The research target of this paper is the material named 40CrNiMoA(steel4340)which is utilized to construct tanks.Split Hopkinson Pressure Bar(SHPB)method is utilized to get the dynamic stress-strain curves and damage modes.The SHPB testing setup is shown in Fig.2(a), the specimen is located between input bar and output bar,the striking bar impacts the input bar with a very high velocity,and the absorbing bar is utilized to handle the residential impact energy.The specimens are shown in Fig.2(b),designed from the previous tests carried out by Meyer[6],it is just like two cylinders overlapped together with different diameter,the upper cylinder is smaller and solid while the under cylinder is bigger and hollow.The upper cylinder is located toward to the input bar.

Fig.2 SHPB setup and specimens

The dynamic stress-strain curves of normal specimen and Meyer’s specimen during dynamic compression are compared in Fig.3.The initial yield points of the two types are almost the same,but because of the special dimensions of the Meyer specimens,this kind of specimen is utilized to highlight the shear properties.The local plastic deformation is much centralized and would lead to temperature rising.Generally,in low strain rate tests,plastic deformation is assumed in a constant temperature;while in high strain rate tests,there is almost 90% plastic deformation energy transferred to heat[7],the whole process usually called adiabatic shear.

Fig.3 Dynamic stress-stain curve of steel 4340 (strain rate=2 000 s-1)

Fig.4 Temperature rising with the dynamic deformation

The temperature increment could be calculated by Eq.(1),

where ΔT is the temperature increment of adiabatic shear;β is heat-energy conversion coefficient,the value is 0.9;ρ is the density of mild steel,the value is 7.85×103kg/m3;CPis the specific heat capacity of mild steel,the value is 0.45×103J/kg·℃.

In the high strain rate tests,in order to evaluate the temperature increment,the effect of heat conduction would be ignored.Fig.4 shows temperature rising tendency of adiabatic shear, the initial temperature is supposed to be indoor temperature 293 K(20℃),when strain rate is 1 000 s-1and plastic strain is 1.5, the temperature reaches 893K;when strain rate is 2 000 s-1and plastic strain is 1, the temperature reaches to 931 K.In those two cases,the temperature almost reaches the temperature for recrystallization of mild steel,and the high temperature will lead to decreasing of flow stress,so the effect of heat softening must be considered.

Fig.5 Finite element model of penetrating

2 Calculating model

2.1 Simulation model

A cylinder projectile sized diameter 10 mm and height 20 mm,meshed into 800 elements, the initial velocity v0is added to the projectile part.The steel plate with length 100 mm and thickness 5 mm,meshed into 4 000 elements.The water area is simulated through Euler model,50 mm long extend at the orientation of projectile’s initial velocity and 100 mm long extend along with the steel plate,meshed into 20 000 elements.The calculating model shown in Fig.5,and the calculating conditions listed in Tab.1.

Tab.1 Calculating conditions

2.2 Material model and parameters

A finite element model considering liquid-structure coupling effect is proposed through AUTODYN 2D,because of the high-speed impact loading,strain rate effect of steel material should be taken into account,Johnson-Cook model is one of the mostly accepted constitutive models to describe high strain rate,high temperature deformation process.

Due to simplicity and availability of material coefficients,the Johnson-Cook(JC)[8]material model implemented in AUTODYN was used in the present calculation.The material model should not be confused with the fracture model which will be discussed later.In the JC model,the equivalent stress σ is an explicit function of the equivalent plastic strain εeff,the temperature T,and the plastic strain rate ε˙.

The influence of the stress triaxiality in these models is based on the void growth equation proposed.The expression of J-C fracture strain[9]εfis

Parameters of steel 4340 are listed in Tab.2.

Tab.2 Parameters of steel 4340

Water is simulated by the Shock equation of state(EOS)provided by AUTODYN,parameters listed in Tab.3.

Tab.3 Parameters of water

3 Results and analysis

3.1 Penetrating process

From energy damage theory,the process of projectile penetrating liquid-filled tank can be divided into four stages(taking specimen No.4 for instance),shown in Fig.6：(1)Mushrooming propagating(0-2.26×10-3ms),projectile begins to contact to the steel plate,mushrooming phenomenon occurred at the bottom of the cylinder projectile,just like Taylor bar impact test.(2)Crushing(2.26×10-3-6.64×10-3ms),the projectile crushing into the steel plate, they begin to move together and distinct plastic deformation is formed,moreover,most plastic deformation energy transfers into heat,and lead to the temperature of the community increase. (3)Adiabatic shearing(6.64×10-3-14.94×10-3ms),the temperature reaches the critical adiabatic shearing temperature,and the steel plate begins to shear at the strain smaller than the static damage strain.(4)Perturbing(14.94×10-3-18.84×10-3ms),the steel plate is penetrated completely,projectile and the fragments of the steel plate crushing into the water,some kinetic energy will transfer from projectile to kinetic energy and potential energy of water,the velocity of the community will damp gradually,but the shock wave in water will strengthen rapidly.

Fig.6 Projectile penetrating steel plate(v0=1 300 m/s)

Fig.7 Temperature of the bottom of the projectile

Fig.8 Temperature of the steel plate

3.2 Discuss of the adiabatic shearing effect

The temperature increasing at the bottom of the projectile is shown in Fig.7,and temperature of the contact area of the steel plate is shown in Fig.8.The temperature-time curves indicate that：(1)The temperature of the whole community increases with the initial impacting velocity.(2)At the local contact area,temperature of peripheral is higher than that of center. (3)At a relative low impacting velocity(1 000 m/s),the materials at peripheral damage is earlier than materials at center area;but when the impacting velocity goes much higher(1 800 m/ s),a composite phenomenon will occur.

The temperature effects at different initial impacting velocity are shown in Fig.9.It is obvious that in the four diagrams,the velocity without considering temperature decreases faster than that with considering temperature.It is mainly because at the beginning,the temperature is increasing but not reaches the critical temperature yet,the damage mechanism manifests normal shearing;when the temperature high enough comes near the critical point the adiabatic shearing becomes the main damage cause.

Fig.9 Temperature effects on the attenuation of projectile’s velocity

4 Verification and discussion

In order to verify the proposed viewpoint that plastic deformation in high strain rate load-ing condition will lead to temperature increasing,tests including projectile penetrating steel plate target and water-back target were accomplished.The residual fragments were collected, the penetrating hole had been measured,and the post test specimen and fragments were shown in Fig.9.It was obvious that the fragments must be serious heated for its melt area and the grey-blue spots on the steel target indicated that the steel was melted during the penetrating.

When the projectile penetrating the steel plate completely,the projectile-steel plate fragments community will crush into the water,so the velocity will decrease gradually.The beginning velocity of the community called residual velocity,temperature effects on residual velocity is shown in Fig.10：(1)The overall tendency of the bar charts indicated that the residual velocity considering adiabatic shear effect is smaller than that of ignoring the adiabatic shear effect;(2)The difference value of the two conditions will increase with the increase of the initial velocity of the projectile.

Fig.10 Melt area of fragment and target

Fig.11 Temperature effect on residual velocity

5 Conclusions

In this paper,the adiabatic shear tests under dynamic loading were utilized to study the temperature effect caused by plastic deformation.Through the finite element model of the water-back plate,the whole process of projectile penetrating liquid tank was simulated considering fluid-structure interaction.The results indicated that：

(1)In high strain rate loading,the temperature effect caused by adiabatic shear must be figured out;

(2)The process of projectile penetrating liquid-filled tank can be divided into four distinct stages：mushrooming propagating,crushing,shearing and perturbing;

(3)The residual velocity of the fragments considering adiabatic shear effect is smaller than that of without considering the effect.And the difference value is small when the initial velocity is slow,but will increases with the increasing of the initial velocity.

Acknowledgements

Research was sponsored by the financial support of Natural Science Foundation of China (No.51408450),the Fundamental Research Funds for the Central Universities(No.2014-yb-20),and the open fund of the State Key Laboratory of Nonlinear Mechanics(LNM201505).

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绝热剪切效应对背水靶板的抗侵彻特性影响的研究

朱海清，李营，张谢东，张行
（武汉理工大学交通学院，武汉430063）

绝热剪切效应是材料破坏的重要机理之一。文章开展了动态冲击作用下的材料绝热剪切试验，计算了绝热条件下材料的塑性温度升高。建立了背水靶板的FEM全流固耦合模型，采用考虑了温度效应的Johnson-cook模型开展了爆炸破片侵彻舰船液舱舱壁过程的计算。结果表明：（1）材料在高应变率下的绝热温升不可忽略；（2）弹体侵彻背水靶板过程可分为4个典型阶段，分别为墩粗凿坑阶段、碰撞形成速度共同体阶段、绝热剪切阶段和扰动液体阶段；（3）考虑温度效应的剩余速度明显小于不考虑温度效应的剩余速度；速度较低时，是否考虑温度效应预测的剩余速度值差异较小，随着初始速度的增大，差异逐渐增大。

绝热剪切；背水靶板；抗侵彻特性

U661.4

：A

国家自然科学基金资助项目（51408450）；中央高校基本科研业务费专项资金（2014-yb-20）；非线性力学国家重点实验室开放基金（LNM201505）

朱海清（1988－），女，武汉理工大学博士研究生；

1007-7294（2017）03-0352-09

U661.4

：A

10.3969/j.issn.1007-7294.2017.03.010

李营（1988-），男，武汉理工大学博士生，通讯作者，E-mail：liying@whut.edu.cn；

张谢东（1964-），男，博士，武汉理工大学教授；

张行（1980-），女，博士，武汉理工大学讲师。

Received date：2016-11-18

Foundation item：Supported by the Natural Science Foundation of China(No.51408450);the Fundamental Research Funds for the Central Universities(No.2014-yb-20);and the open fund of the State Key Laboratory of Nonlinear Mechanics(LNM201505)

Biography：ZHU Hai-qing(1988-),female,Ph.D.candidate of Wuhan University of Technology;

LI Ying(1988-),male,Ph.D.candidate,corresponding author,E-mail：liying@whut.edu.cn.