Numerical simulation study on penetration performance of depleted Uranium (DU) alloy fragments

Fu-lin Zhu.Yang Chen.Gui-li Zhu

Sichuan Aerospace System Engineering Institute.Chengdu.610100.Sichuan.China

Keywords: Depleted uranium alloy Constitutive model Adiabatic shear Penetration performance Numerical simulation

ABSTRACT Due to its high strength.high density.high hardness and good penetration capabilities.Depleted uranium alloys have already shined in armor-piercing projectiles.There should also be a lot of room for improvement in the application of fragment killing elements.Therefore.regarding the performance of the depleted uranium alloy to penetrate the target plate.further investigation is needed to analyze its advantages and disadvantages compared to tungsten alloy.To study the difference in penetration performance between depleted uranium alloy and tungsten alloy fragments.firstly.a theoretical analysis of the adiabatic shear sensitivity of DU and tungsten alloys was given from the perspective of material constitutive model.Then.taking the cylindrical fragment penetration target as the research object.the penetration process and velocity characteristics of the steel target plates penetrated by DU alloy fragment and tungsten alloy fragment were compared and analyzed.by using finite element software ANSYS/LS-DYNA and Lagrange algorithm.Lastly.the influence of different postures when impacting target and different fragment shapes on the penetration results is carried out in the research.The results show that in the penetration process of the DU and tungsten alloy fragments.the self-sharpening properties of the DU alloy can make the fragment head sharper and the penetrating ability enhance.Under the same conditions,the penetration capability of cylindrical fragment impacting target in vertical posture is better than that in horizontal posture,and the penetration capability of the spherical fragment is slightly better than that of cylindrical fragment.

1.Introduction

Tungsten alloys are of high density,high strength,high hardness and can penetrate a certain strength of armor.They are widely used in armor-piercing projectiles.However.tungsten alloys are rare metals.expensive.lack of raw materials.and cannot be used on a large scale.Therefore.it is necessary to find a substitute for tungsten alloys.In recent years.many theoretical studies on depleted uranium alloys have been carried out all over the world.Eckmeyer[1]studied the effect of heat treatment on the properties of U-Ti alloys.It was found that the formation of uranium alloys and the solid solution enhancement effect of alloying elements in the solution can make the alloys twice stronger than other non-uranium alloys.Johnson and Cook[2]obtained data and fitted them through a large number of experiments.and proposed a J-C constitutive model.which gives the constitutive parameters of U-Ti alloy.He and Xiao [3]used the material testing machine and SHPB experimental device to study the compression mechanical behavior of UTi alloy at room temperature.and modified the Johnson-Cook model according to the experimental data.Yue and Qu [4]discovered that the DU alloy is more prone to adiabatic shearing and generate self-sharpness during the penetration process by studying the armor-piercing core material.which is more conducive to penetration.Shi Jie [5]and other scholars studied the forming mechanism of adiabatic shear band uranium-niobium alloys under impact load of artificial aging in different temperature via SHPB experiment.

Although there are many studies on DU alloys all over the world,most of them focus on the material"s own performance.and there are few reports on the penetration target of DU alloy as a killing fragment.

In this study,the self-sharpness theory of materials was used to analyze the penetrating properties of DU alloy and tungsten alloy.Then.the DU alloy fragments and tungsten alloy fragments weresimulated to penetrate Q235 steel based on ANSYS/LS-DYNA software,and the influence of target-impacting postures and shapes on penetration ability were analyzed.so as to provide a theoretical basis for the resource-rich DU alloy fragments to replace the resource-deficient tungsten alloy fragments.

2.Simulation model and parameters

2.1.Selection of material parameters

In the numerical calculation.the DU alloy.tungsten alloy and Q235 steel will produce large stress and strain.and the Johnson-Cook model widely used in engineering can accurately describe materials with the large strain and high strain rate[6].In this study,Johnson-Cook strength model was used.Its specific expression is shown in equation (1):

where:σ is the equivalent stress.ε is the equivalent strain.˙ε is the strain rate.˙ε0is the reference strain rate (for the convenience of calculation.the value can be 1); T*=(T -Tr)/(Tm-Tr) is the similar temperature; Tmand Trare the melting temperature and room temperature of the material,respectively.A is the yield stress under reference strain rate and reference temperature,B and n are the strain hardening coefficients.C is the strain rate hardening coefficient.and m is the temperature softening coefficient [7].

Johnson-Cook"s cumulative failure model expression is as follows:

In the formula:σ*=p/σεqis the ratio of hydrostatic pressure to equivalent pressure; D1-D5are the failure parameters of the material.

The relevant physical properties of the depleted uranium alloy,tungsten alloy and Q235 steel material were obtained from the SHPB experiment.and the parameters were from the literature[8-13].as shown in Table 1.

2.2.Finite element model

Fig.1.Finite element model.

The calculation model uses the fragments are cylindrical and spherical fragments with the same quality to penetrate the Q235 steel.The length/diameter ratio of the cylindrical fragments is 1,and the diameters are Φ6.1 × 6.1 and Φ7 mm.respectively.The fragments are flat. and the target plate size is 100 mm × 100 mm × 15 mm.Using Solid 164 elements to divide grids.and the Lagrange algorithm is used between the fragment and the semi-infinite target plate,and the contact type is defined as erosion contact (*CONTACT-ERODING-SURFACE-TO-SURFACE).In order to improve the calculation accuracy,the mesh is densitied at the center of the target.the size of the encryption area is 0.4 mm,and the size of the non-dense area is 3.0 mm.a total of 193471 nodes and 182500 elements are obtained.The cylindrical fragment grid size is 0.2 mm,and a total of 11916 nodes and 10500 elements are obtained; The spherical fragment grid size is 0.2 mm,which is divided into 12691 nodes and 11664 elements.The outer boundary of the target plate is set as stress non reflection boundary to simulate an infinite region.and the unit system is cm-g-μs-Mbar.The structure of the finite element model is shown in Fig.1.

3.Material self-sharpness analysis

Compared with tungsten alloy.DU alloy has obvious selfsharpness.The main reason is that the adiabatic shear sensitivity of DU alloy material is bigger than that of tungsten alloy.which is more prone to adiabatic shear failure.resulting in the continuous peeling and detachment of bullet head along the shear band,so that the warhead is getting sharper and sharper.as shown in Fig.2(a),this is also the reason why the DU alloy has a higher penetration capability.However.due to the characteristics of tungsten alloy materials,“mushroom heads”are often formed during the piercing process.As shown in Fig.2(b).adiabatic shear failure occurs only under high strain rates,so the piercing capability is relatively lower.

Tungsten alloys and DU alloys undergo plastic deformation after stress,and rapidly produce strain hardening and thermal softening effects.However.due to the high melting point of tungsten.softening requires greater deformation and higher temperature.Therefore,it is defined according to Ref.[14]formulas of adiabatic shear parameters for different materials:

Table 1 Material model parameters.

Fig.2.Penetration Process Comparision of tungsten alloy and DU alloy.

Among them,K and Cpare the thermal conductivity and specific heat capacity of the material,respectively,h is the gate width of the shear band.and ˙ε is the initial shear strain rate.The smaller the value of k,the more likely it is to form an adiabatic shear band.And when the strain rate and the shear bandwidth are the same.the value of K/Cpdetermines the relative tendency of different materials to form adiabatic shear bands.The smaller the ratio,the easier it is.The data in Table 2 lists the adiabatic shear parameters of different materials.It can be seen from the table that the ratio of uranium is significantly smaller than that of tungsten,so it is easier to form adiabatic shear bands.This is consistent with the results in the literature [15]that can promote the formation of adiabatic shear bands at lower strain rates.Therefore.DU alloys are more likely to form adiabatic shear bands than tungsten alloys.

Therefore.based on the above.the adiabatic shear failure mechanism of the two materials under dynamic compression conditions can be described as follows: The process of projectile penetration into the target is a high strain rate process.Under this condition,the entire deformation time of the material is very short.Most of the plastic work is converted into heat.and there is not enough time disperse the heat into the surroundings.resulting in an increase in the temperature of the material.The process is approximately adiabatic.According to the Johnson-Cook constitutive equation in (1).the stress of the material increases with the increase of strain and strain rate,and decreases with the increase of temperature.namely strain strengthening effect.strain rate strengthening effect and temperature thermal softening effect.Under high strain rate conditions.when the temperature of the adiabatic process rises to a certain extent.and the temperature softening effect of the material exceeds the hardening effect of strain and strain rate,thermoplastic instability begins to occur,that is,adiabatic shear fails.However,tungsten alloy is a material that is sensitive to strain rate and temperature.When the strain is small,elastic deformation and uniform plastic deformation occur.theflow stress greatly increases.and obvious strain hardening effect appears.As the strain and strain rate increase.the tungsten alloy will produce strong non-uniform plastic deformation.Due to the extremely short deformation time,the deformation work is almost completely converted into heat,and the temperature rises rapidly.At this time.the thermal softening effect gradually takes the leading role.and the strain hardening effect is weakened.Thereafter.the deformation of the tungsten alloy has it develops in two directions:one is the overall thermal softening of the tungsten alloy head to form a “mushroom head”.as shown in Fig.2(b).and the other is to form a local adiabatic shear band along the direction of the maximum shear force.as shown in Fig.3.Moreover.under dynamic compression conditions.tungsten alloys form adiabatic shear fractures by means of transgranular cleavage fracture.It is more difficult for tungsten alloys to achieve a large number of transgranular cleavage fractures.Therefore.the ability of tungsten alloys to form adiabatic shear failure to achieve self-sharpening properties of armor piercing is worse than that of DU alloys.

Table 2 Adiabatic shear parameters of U、W.

Fig.3.ASB forming process under dynamic compression loading in tungsten alloy.

4.Simulation analysis

4.1.Analysis of fragment penetration process

In order to analyze the penetrating performance of DU and tungsten alloy fragments in Q235 steel target plate,the simulation calculation and analysis were carried out when the fragmentation velocity of DU and tungsten alloy was 1350 and 1400 m/s.When DU and tungsten alloy fragments were at a velocity of 1350 m/s.the penetration process is shown in Fig.4.respectively.

It can be seen from Fig.4 (a) that in the initial stage of penetration(t=4 μs).the fragment opened a crater slightly larger than the bullet diameter in the target plate,and a bulge appeared on the front end surface of the target plate,and a spherical shock wave was generated in the target plate.As the penetration deepens(t=10 μs),the mesh near the contact surface was deleted for failure result from excessive deformation.the plastic deformation and small shear strain occurred on the fragment head.and the crater radius became significantly larger; in the middle of penetration(t=44 μs).due to the self-sharpening properties of the DU alloy,the fragment head gradually became sharp.and the crater radius gradually decreased to form a tapered hole;in the later penetration stage (t=70 μs).the steel target material in contact with the cone surface of the fragment undergone shear failure and broke,and the rear end surface of the target plate was cracked due to the bulging,and the target plate was cut into two small plug blocks; the two small plug blocks were completely off the target as the fragments continue to advance.At (t=130 μs).the fragment penetrates the target plate.

It can be seen from Fig.4(b)that under the same conditions,the penetration performance of the tungsten alloy fragments and the DU alloy fragments during the initial penetration is slightly different; during the middle of penetration.the head of thetungsten alloy fragments does not become sharp.but gradually becomes round.It indicates that its self-sharp characteristic is worse than that of DU; as the fragment penetration deepens.the crack occurs on the back side of the target.but the fragment does not penetrate the target.Under the same conditions.the DU alloy can penetrate the target plate.while the tungsten alloy cannot,indicating that the penetration performance of the tungsten alloy fragments is slightly lower than the DU alloy fragments.Note that the penetration progress is basically a damage and fracture process[16-22].

Fig.4.The Penetration Process of Fragments: DU alloy(a).tungsten alloy(b).

4.2.Fragment penetration velocity analysis

It can be seen from Fig.5 that in the initial stage of fragment penetration.the velocity attenuation is very fast due to the large target plate resistance when the crater is opened.and the difference begins to appear after 10 μs.Under the same velocity condition.the tungsten alloy penetration velocity decays significantly faster than that of DU alloy.After 100 μs,the two tend to be stable,the residual velocity of the DU alloy fragments is 129.1 and 172.4 m/s.respectively corresponding to an initial penetration velocity of 1350 and 1400 m/s,and the remaining maximum kinetic energy is 0.015 times of the initial kinetic energy,while the residual velocity of the tungsten alloy fragments is 0 and 147.1 m/s.and the remaining maximum kinetic energy is 0.011 times of the initial kinetic energy.Therefore,the residual penetrating ability of the DU alloy fragments is 1.36 times of the tungsten alloy fragments.

Fig.5.Cylindrical fragmentation velocity-time Curve (Vertical penetration).

4.3.Effect of fragmentation target-impacting posture on penetration performance

In addition to further demonstrating that the penetrating power of DU alloy is superior to tungsten alloy.this simulation is mainly compared with (4.1) simulation to study the effect on penetration result with the fragmentation in horizontal attitude.

The penetration process of DU alloy fragments and tungsten alloy fragments on Q235 steel is basically the same as (4.1).but in the early stage of penetration.the horizontally penetrating fragment head is a curved surface,and the self-sharp effect is not very obvious.but with the penetration deepens.cracks occur on the back of the target plate.At the same time,it can be found that the sharpness of the fragment head in horizontal penetration is not as good as that in vertical penetration.The main reason may be that the contact surface in the horizontal penetration is curved rather than plane.

According to the data in Table 3 and Fig.6.comparing the vertical target-impacting with the horizontal target-impacting,whether the DU fragment or the tungsten fragment.at the same initial velocity.the target plate is not penetrated.or the target is penetrated in vertical target-impacting.not in horizontal.or the target is penetrated in both cases.but the remaining velocity in vertical target-impacting is higher.Seen from the analysis of Fig.7(tungsten on the left and DU on the right).in the case when the target plate is not penetrated.the DU alloy fragments cause shear cracking on the target plate while the W alloy does not,only causes cracking on the back surface of the target plate,and the penetration depth of the DU alloy is significantly larger than that of tungsten fragments.The results are consistent with section 3 self-sharpness analysis.Therefore.under conditions of horizontal targetimpacting.the penetration ability of DU alloy fragments is still better than that of tungsten alloy.and it can also be said that the penetration capability of vertical target-impacting is better than that of horizontal target-impacting.

After penetration.the shape comparison between the DU fragment and the tungsten fragment is shown in Fig.8(DU on the left and tungsten on the right).It can be seen from Fig.8 that the head of the DU fragment is sharper than the tungsten fragment.This result is in good agreement with the self-sharpness analysis in chapter three.

4.4.Effect of fragment shape on penetration performance

From the simulation results of (4.3).it can be seen that the target-impacting posture of the fragment has an influence on the penetration result.and the horizontal penetration ability of the fragment is slightly lower than that of the vertical penetration.In order to avoid adverse effects.this group of simulations will be vertically penetrated with the cylindrical shape in(4.1)as a control group.simulating spherical fragments of the same quality penetrating the Q235 target.so that there is no difference between vertical penetration and horizontal penetration.The simulation velocities are 1350 and 1400 m/s.

It can also be seen from Fig.9 that the penetration velocity of the tungsten alloy fragments is attenuated rapidly.This is because in the middle of penetration process.the temperature gradually increases with the advancement of the penetration; for tungsten alloy material.the strain rate sensitivity reduces as temperature increases,causing the head of the fragment to be rounded,which in turn leads to a decrease in its penetration ability.In contrast,as thetemperature of the DU alloy fragments increases.its strain rate increases.and the plastic deformation increases.resulting in adiabatic shearing.which makes the fragment head sharper and the penetration ability enhanced.

Table 3 Effect of target-impacting attitude on penetration performance.

Fig.6.Cylindrical fragmentation velocity-time curve (horizontal penetration).

Fig.7.Penetration Comparison of DU and fragment.

Fig.8.Comparison of DU and Tungsten fragment shapes.

Fig.9.Spherical fragment velocity-time curve.

According to Table 4.the residual velocities of the spherical DU alloy fragments are 152.9 and 272 m/s.respectively.while the residual velocities of the spherical tungsten alloy fragments are 18.2 and 178 m/s,respectively,both of which penetrate the target plate.The maximum residual velocity of the spherical DU alloy fragment is 1.58 times of that of the cylindrical shape.and the remaining maximum kinetic energy is 0.038 times of the initial kinetic energy;while the maximum residual velocity of the spherical tungsten alloy fragment is 1.21 times of that of the cylindrical shape,and the remaining maximum kinetic energy is 0.016 times of the initial kinetic energy.Therefore,the maximum residual penetration of the DU alloy fragments is 2.375 times of the tungsten alloy fragments.Under the same conditions.the higher the velocity.the better the penetrating ability.When the velocity and quality is the same.the penetrating performance of the spherical fragment is superior to that of the cylindrical fragment.

5.Conclusions

1) It was found that during the penetration process of the DU alloy fragments and tungsten alloy fragments.the self-sharpening property of DU alloy makes the fragment head sharper and improves the penetrating ability of the DU alloy fragments.

2) Under the condition of the same variables.the penetration performance of the DU alloy fragments is superior to that of the tungsten fragments whatever kind the penetration is.

3) When the other variables are the same and the initial velocity is 1400 m/s.the residual penetrating ability of the cylindrical DU alloy fragments is 1.36 times of that of the tungsten alloy fragments.The residual penetrating ability of the spherical DU alloy fragments is 2.375 times of that of the tungsten alloy.Therefore,the penetrating performance of the DU alloy fragments is better than that of tungsten alloy fragments.

4) The shapes of the fragment will have an effect on the penetration results.Under the same conditions of other variables.the maximum residual velocity of the spherical DU alloy fragment is 1.58 times of that of the cylindrical fragment; the maximum residual velocity of the spherical tungsten alloy fragment is 1.21 times of that of the cylindrical fragment.

Table 4 Effect of fragment shape on penetration performance.

Declaration of competing interest

I declared that there has no conflicts of interest to this work.I declare that I do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Acknowledgement

This study did not receive any funding from funding agencies in the public.commercial or non-profit sectors.