Qi Huang, Shun-shan Feng, Xu-ke Lan, Chao-nan Chen, Yong-xiang Dong, Tong Zhou

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Keywords:Annular grooved projectile (AGP)Impact Firm embedding behavior Flow characteristics Microscopic tests

ABSTRACT Annular grooved projectiles (AGPs) have drawn ongoing concerns as an advanced penetrator for their excellent anti-rebound capability in impacting metal plates.They could become embedded solidly in the target surface during low-velocity impact.In this investigation,the firm embedding behavior of AGP was observed by impact experiments.Corresponding numerical simulations provided a better understanding of this process. Experimental and numerical results indicated that the firm embedding behavior of AGP was mainly due to the filling-material in the groove rather than the friction between the projectile and target, unlike traditional shape such as conical projectile. According to observation, firm embedding process can generally be subdivided into four stages: initial-cratering stage, groove-filling stage, fillingmaterial failure stage and rebound vibration stage. Moreover, the damage mechanics of target material around crater was obtained through microscopic tests. A comparison of the cross-sectional figures between the experiment and simulation proved that the analysis and the proposed method were reasonable and feasible, which further demonstrated that the firm embedding behavior has application potential in new concept warheads.

1. Introduction

In recent years, semi-armor-piercing high-explosive incendiaries (SAPHEIs) with delayed reactions have become important for reacting to various threats, including light armor aircraft,vehicles, and general support equipment [1]. The growing development of these multi-layer metal structures increases the need for multipurpose SAPHEI concepts. For instance, when a projectile penetrates a target, the goal is not to penetrate more plate layers,but to stop the projectile within the plate without rebound. The embedded projectile can facilitate delayed high-explosive reactions more reliably and controllably, resulting in more efficient damage.

Considerable research has been conducted on the armorpiercing penetration performance and protection effectiveness of multi-layer metal structures. Most of the studies in these fields concentrated on the ballistic limit, penetrator material strength,and projectile structure optimization [2e4] through impact tests,engineering analytical models, and numerical simulations [5e10].Backman and Goldsmith [11] summarized the experimental phenomena and proposed a phase diagram for projectile impact targets, which contained projectile states such as perforation,embedment or ricochet under various impact velocities, and obliquity degrees. Deng et al. [12,13] considered the ballistic performance of monolithic, double-, and three-layered metal plate impacts of different strength projectiles and discussed the effects of the projectile strengths and nose shapes. Using cavity expansion theory[14e20],a series of optimal projectile shapes were obtained by minimizing the instantaneous resistance force during penetration,and the projectiles exhibited good performances in impacting multi-layer targets or deep penetration.

However, most penetration performance studies did not consider the embedding mechanism [21]. As a special penetration phenomenon,it refers to a projectile becomes firmly embedded in a target instead of rebounding or perforating. So that the projectile become a solid obstacle and can be used for special applications,such as blockades or stable delayed explosions. In the case where the initial velocity of the projectile is lower than the ballistic limit,when the kinetic energy of the projectile is insufficient to penetrate the target, the rebound force of the target plate can cause the projectile to move backwards. If the projectile has sufficient antirebound capability to overcome the reverse motion, it can achieve firmly embedded behavior in target.In general,the friction on the surface between the projectile and target is not strong enough to prevent rebounding,so the embedment of traditional geometric projectile shapes (such as conical, ogive, and blunt nose) are not firm enough in low-velocity impact. Thus, a projectile with a new nose shape, called an annular grooved projectile (AGP), was proposed.

As mentioned above,AGP refers to a projectile that contains one or more annular grooves in its nose. In this study, the AGP was designed based on a conical shape and contained only one annular groove to simplify the analysis.Corresponding impact experiments were carried out using gas gun apparatus to achieve firm embedding behavior in a 2024-O plate. Numerical simulations were performed using the LS-DYNA software to investigate the dynamic response of the target material, especially the part filled into the groove during penetration. Moreover, the flow features of the target material around the crater were obtained through microscopic tests. These results proved that the firm embedding mechanism of the AGP is feasible.

2. Experiments investigation

2.1. Experimental setup

The ballistic impact experiments were performed in a compressed gas-gun facility at the Beijing Institute of Technology, as depicted in Fig. 1, and its detailed description can be found in previous work[22].In the tests,the projectiles were accelerated by compressed air, which can making it possible to determine the approximate striking velocity of the projectile in advance. A steel chamber with a metal target is fixed in front of the gun barrel;this chamber has a circular hole in line with the barrel,through which the projectile could pass into and penetrate the target.The target is sandwiched between a C-shaped clamping ring and a C-shaped support plate using 10 bolts, and the support plate is welded with steel plates to ensure its rigidity(Fig.2).Rubber plates were placed behind the target as a buffer to stop and recover the projectile after perforation. On one side of the target chamber was a transparent acrylic plate window through which a Phantom 710 high-speed camera (Vision Research, Inc. Wayne, New Jersey, USA) equipped with a flash unit could record the projectile action.The camera was placed in such a way that it could photograph the front and back of the target.The flash unit was placed between the window and the camera and provided an exposure time of approximately 21 ms. A copper wire connected to a trigger mechanism was connected to the gas gun muzzle. The wire was cut when the projectile passed through the muzzle,which in turn triggered the flash.Photographs were simultaneously manually captured using the camera at a frame rate of 44,000 fps.

2.2. Target and projectile

The annular grooved projectile (AGP) used in this study was designed based on a conical shape. The purpose of the groove structure was to provide space for the inflowing target material to achieve embedment in a low-velocity impact. Two structurally similar AGPs were used in the experiments. Their diameters were 10 mm and 16 mm,and corresponding nose length and total length were 1.5 times and 2.8 times the diameter,respectively.Dimensions of two AGPs are shown in Fig.3.They are made of a high-strength material, AISI 1045 steel, with an ultimate tensile strength of 625 MPa. These hardened steel projectiles experienced negligible inelastic deformation during the impact process and consequently can be considered as ‘rigid body’ [13]. Furthermore, the rounded structures at both ends of the groove and chamfer of the tip were designed to avoid stress concentration during penetration.

Considering the similarities in the dimensions, the target thickness in this study was consistent with projectile diameter.The length and width of targets were all 140 mm and corresponding dimensions are shown in Table 1. Target plates were composed of 2024-O aluminum alloy. After production of the plates heat treatments were applied to obtain tempers O (annealed), which gave a ductile superiority to the alloy.

Fig.1. Gas gun apparatus.

Fig. 2. Target carrier showing with its components: the clamping ring, the target plate and the support plate.

Fig. 3. Dimensions of 10 mm and 16 mm diameter AGPs (mm).

2.3. Experimental results and analysis

In the present tests, projectiles were fired in a velocity range from 154 m/s to 254 m/s. Eight shots on 2024-O aluminum target were carried out using the gas gun.The firm embedding behavior of the projectiles was evaluated by comparing their depth of penetration (DOP) and embedded firmness values. The experimental results, which included impact velocity V, initial projectile mass m and DOP, are listed in Table 1. It is worth noting that test number ds16 and ds10 represented AGP with diameters of 16 mm and 10 mm respectively.

Almost all the initial velocities were limited under its ballistic limit, only one shot (No. 3 in Table 1) perforated the target. In general, DOP refers to the depth of penetration of projectile when penetrating the thick target or semi-infinite target[11].However,inthis study,target thickness was smaller than the length of projectile nose, so the DOP was defined as the distance between projectile nose tip and the surface of target. In addition, test number ds16-1 and ds10-4 have similar dimensionless DOP and are selected to exhibit corresponding illustrative high-speed camera images,which are shown in Fig.4.It can be found that the AGPs were firmly embedded in target instead of rebounding after low-velocity impact.

Table 1 Experimental data of annular grooved projectiles (AGPs).

Fig. 5 exhibits two typical deformation of target material after penetration in detail,including the damage views of front and back faces of targets, firm embedding behavior of AGP, crater profile in cross section figures,etc.The magnified views shows that the target material is in close contacted with the projectile, and filled the annular groove structure completely. This phenomenon indicated that the AGP can effectively embedded in 2024-O aluminum plate because of the plastic deformation of filling-material in the groove.

In addition,Fig.6 compares the shapes of AGPs before and after experiment. It is need to point out that the projectiles after experiment were separated by wire cutting and glued together subsequently. These projectiles had no significant deformation after gas gun tests.Therefore,it is reasonable to consider projectile as a rigid body in numerical simulation.

3. Simulation analysis

3.1. Constitutive relation and fracture criterion

A modified version of the Johnson-Cook (MJC) constitutive relation was used to model the target materials. The constitutive behavior is assumed to be isotropic and modelled with the von Mises yield criterion even though the materials exhibit some anisotropy [23]. The aluminum alloy was modelled as an elasticplastic material, exhibiting rate-dependent behavior. The equivalent stress is then expressed as

Fig. 4. Illustrative images captured using the high-speed camera.

where εeqis the equivalent plastic strain and(A,Q1,C1,Q2,C2,C,m)are model parameters.The dimensionless plastic strain rate is givenwhereis a user-defined reference strain rate.The homologous temperature is defined as,where T is the absolute temperature, Tris the room temperature and Tmis the melting temperature of the material.The temperature change due to adiabatic heating is calculated as

where r is the material density, Cpis the specific heat and c is the Taylor-Quinney coefficient that represents the proportion of plastic work converted into heat. Failure is modelled using a criterion proposed by Cockcroft and Latham (CL) [24].

where s1is the major principal stress,when s1≥0 and=0 when.It can be seen that failure cannot occur when there are no tensile stresses operating from Eq. . The model constant Wcis the value of W at failure.It should however be noted that owing to the anisotropic behavior of the material and the uncertainty in the calibration of the CL criterion, Wcshould not be regarded as a material characteristic [23]. In this study, the deviatoric stresses in the element are set to zero when W reaches its critical value Wcin a specified number of integration points.This is defined as material failure.However,the element continues to take compressive hydrostatic stresses until the time step size drops below a critical level. This is defined as element erosion.

The strain rate sensitivity of aluminum alloys is usually found to be small at room temperature [27,28]. While during penetration,which was assumed as an adiabatic shear process,the temperature of deforming material inside the groove would quickly reach its melt temperature according to the observation in simulation. In this case the strain rate sensitivity becomes important [26]. However, owing to the lack of tensile test data at elevated strain rates and temperatures, the strain rate sensitivity constant C was estimated and given a small and appropriate positive value [25] according to experimental results. Further, the temperature sensitivity parameter m was set to unity,implying a linear decrease in the flow stress with increasing temperature [23]. The constants in the JohnsoneCook model for 2024-O aluminum alloy used in this study are given in Table 2.

The hardened steel projectiles experienced negligible deformation during the impact experiments. Moreover, we mainly focuses on the deformation and flow characteristics of target materials inside the annular groove structure of projectile, in this case the projectile material was assumed to be rigid. The Young's modulus,Poisson's ratio and density of the projectile were taken as E?203 GPa,y?0.29 and r?7850 kg/m3, respectively[22].

Fig. 5. Deformation and crater profile of 2024-O aluminum targets.

Fig. 6. Comparison of the projectile structures before and after experiments. After the experiment, the projectile has no significant deformation and can be considered as rigid.

Table 2 Material constants for 2024-O aluminum alloy target [22,23,25,26].

3.2. Finite element model

All numerical simulations presented in the following were carried out using the nonlinear finite element code LS-DYNA 971.The projectile and the region in the target plate that undergo large plastic deformations were modelled using 2D Solid element type.The target plate was modelled somewhat smaller(50 mm×50 mm)than in the test (140 mm×140 mm). The discrepancy in results compared to the reduced model was found to be negligible. This significantly reduced the CPU time without compromising the results too much.

The symmetry in the problem was exploited by modelling only half the projectile and the plate. Plots of the 2D finite element meshes used in the simulations are shown in Fig.7.A refined mesh method was used in the impact region.Earlier studies have shown that perforation problems involving blunt projectiles causing shear localization are mesh-size sensitive, while the mesh-size dependency is less distinct for pointed nose projectiles causing failure by ductile hole growth[29,30].To check the mesh-size dependency in the current problem,simulations were run on 2024-O plates using respectively 32,64,128,256 and 512 square elements over the target thickness in the impact region.A constant impact velocity of 200 m/s was applied in these simulations.If less than 128 elements were used over the target thickness the mesh-size sensitivity was found to be strong because there is a nearly 20% deviation in DOP when going from 32 to 128 elements.However,a slight reduction in DOP of 5%was found when going from 128 to 512 elements over the target thickness.As a compromise between accuracy and CPU time,256 square elements(0.0625 mm×0.0625 mm)were used over the target thickness in this study.

The material was still allowed to take compressive hydrostatic stresses and failed elements were not eroded until their time step dropped below a user-defined critical level. In addition to failure caused by damage, the elements were also allowed to fail if the temperature reached the melting temperature of the material[31].Element erosion was used to prevent overly distorted elements which reduced the time step towards zero and could cause error termination.The critical time step for element erosion was set to 10 ns in this study.

Fig. 7. Finite element meshes of aluminum targets and projectiles used in the simulations.

Contact between the various parts was established using an automatic single surface contact algorithm available in LS-DYNA.The target was fully clamped at the boundary, and were assigned the Hourglass setting with the FlanaganeBelytschko stiffness[22].To validate the effect of friction between the projectile and target,typical simulations were run by keeping the coefficient of friction from 0 to 0.5 [32e35] between the contact surfaces at the impact velocity of 174 m/s.These simulations revealed that introduction of friction between the contact surfaces did not have significant influence on the ballistic resistance. In particular, a coefficient of friction of 0.5 resulted in a 4% reduction in DOP compared to the case where friction was not considered. Therefore, the effect of friction was considered negligible between the projectile and target.

3.3. Analysis of numerical results

Fig.8 shows the penetration process of the AGP impacting a 16 mm-thick 2024-O aluminum target at 174 m/s.This initial velocity condition was the same as that in test number ds16-1,as shown in Table 1 to compare the test results.Some typical physical behaviors of high ductile aluminum targets [36] during the penetration process were well-captured in the numerical simulation, such as petaling and denting of the impact surface. Based on the penetration process of the AGP, the target material did not fill into the groove until it was pressed by the upper surface(shown in Fig.13),and the stress of the filling-material was generally higher than surrounding area.

Fig. 9 shows the displacement and deceleration time-history curves of this process. Since the process of AGP vibrates in the target is much longer than that of penetrate, only the first 500 ms data was displayed and ignored the subsequent lengthy vibration curve segments. AGP maximum distance of rebound is limited to about 0.53 mm, then it enters the reciprocating vibration. This distance is related to the elastic recovery of target and the cavity volume of groove.

Different from conical projectile, the deceleration curve of AGP had a short and vibrating descent stage(marked by two red circles)before it reached the maximum. It represents the moment when the upper and lower edges of groove contacted the target respectively.The deceleration then rapidly increased to the peak value,at this moment the annular groove was completely filled by target material. After a wide pulse, deceleration decreases to 0 after fluctuation and became negative.It indicates that the material filled in groove provides resistance during rebounding,which exhibits an anti-rebound ability that made AGP firmly embedded in target.The corresponding motion of projectile is shown in displacement curve and will be discussed in detail in the next section.

There was good agreement between the simulated and experimental DOP,as shown in Fig.10,The penetration error was less than 5%, which indicates the accuracy of the simulation model. These over- and under-estimations may have been attributed to the anisotropy and thickness dependency of the mechanical properties of the 2024-O aluminum alloy[28,37],which were not considered in the simulations. However, these results are acceptable considering the complexity of the material flow behavior and the limitations of the constitutive relation and fracture criterion [7].

Fig. 8. Penetration process (where t provides the time after impact) of 2024-O aluminum targets impacted by a 16 mm annular grooved projectile with impact velocity 174 m/s.

Fig. 9. Displacement (left) and deceleration (right) history of annular grooves projectiles with impact velocity 174 m/s.

Fig. 10. Dimensionless DOP with different impact velocities in simulations and experiments.

Comparison of cross section figure in Fig. 11 shows the deformation of 2024-O target in simulation (right half) and experiment after penetration. The blue translucent area on the right exhibits the crater after removing projectile.It can be clearly found that the numerical result was approximately consistent with the experimental results,such as DOP,crater profile and the petaling on target surface.These deformation image shows that the crater surface was smooth and no cracks occurred nearby the filling-material in the groove under this DOP level.

Fig. 11. Deformation of 2024-O target of test number ds16-1 in simulation (blue translucent area on the right half) and experiment.

4. Discussion

4.1. Main stages of firm embedment

Fig.12. Velocity vector of target unit when the groove structure penetrated.

According to simulation results, the process of AGP firmly embedded into target can generally be subdivided in four stages:initial-cratering stage, groove-filling stage, filling-material failure stage and rebound vibration stage. Numerical and experimental results demonstrated that almost no shear fracture occurred on the filling-material in a small DOP.Therefore,it is reasonable to ignore the third stage when impact velocity is much lower than ballistic limit.In this section,the simulation of test number ds16-1 in Table 1 was also used as an example to analyze.

The first stage is consistent with the previous phase of normal penetration. The internal separations required for perforation initiate at the tip, then a hole in the target near the tip is enlarged continuously upon the trajectory of the projectile [11]. With the increasing DOP, target material on the surface was rapidly expanding radially and has not been filled into the groove structure until the groove structure contacts target surface. The velocity vector of target unit shown in Fig.12 clearly exhibits the tendency of material flowing. After that this process entered into groovefilling stage.

Groove-filling stage starts with the upper surface contacting the upheave target material, which is shown in Fig.13(a). The purple dotted line indicates the initial target material profile near the groove so as to observe the filling process.With the increase of DOP,part of the material continued to move radially, while other materials were filled into groove under the pressure of upper surface.It can be observed in Fig.13(b) and (c) that material unit closer to the groove contour obtained a higher velocity towards cavity,which means the target material had a tendency to move towards the groove.The blue dashed area outlines the region where greatly affected by the upper surface, so the stress of this area was much higher and resulting in higher velocities of some material units,which even up to 1.5 times the impact velocity. Therefore, the groove structure was rapidly filled with target material and this process entered into the next stage.

Fig.14. Deformation of target material when AGP velocity decreased to zero for the first time.

After reaching the maximum DOP,AGP has a rebound tendency and a long-term vibration due to the elastic recovery of target[21].This phenomenon is called rebound vibration stage,one of the most important stage in this process. In the case that projectile successfully prevented rebounding in the first vibration, it would embed into target.For conical projectile,the resistance only comes from friction between projectile and target is generally unstable and may not be sufficient to limit the rebound of the projectile at small DOP. However, AGP provides another relatively stable embedded method based on the plastic deformation of fillingmaterial in the groove.

Fig.15. Cross-section specimen(left)and microscopic images(right)of target material nearby projectile hole.

When the rebound phase begins, the filling-material stuck the groove and pressed its lower surface.At this moment,the pressure and friction directions are the same to prevent AGP from rebounding. If the resistance provided by the filling-material was less than its shear strength,a stable embedment behavior could be achieved. Fig.14 shows the clearly deformation of filling-material during the first vibration of the AGP, when the instantaneous velocity of penetration and rebound is zero,respectively.The process from Fig.14(a)to Fig.14(b)was shown in Fig.9 with a displacement of 0.53 mm.Then a long-term vibration with decreasing amplitude appeared until the kinetic energy exhausted, which did not affect the filling-material deformation and AGP firm embedment [21].According to simulation results, no further deformation of fillingmaterial in groove happened during reciprocating motion.

In addition, in the case when shear fracture occurred in fillingmaterial in a large DOP, it means that the material inside and outside the groove was completely separated,and the resistance is only provided by friction when rebounding.This situation is similar to a conical projectile. Therefore, the separation in a large DOP would be analyzed through microscopic tests.

4.2. Flow characteristics of target material

A deeper DOP experiment(Test No.5 in Table 1)was selected to observe the dynamic response and failure characteristics of fillingmaterial, to get a better understanding of this process. Moreover,microscopic tests were carried out to support the further study.

A chemical etchant used in microscopic tests was Keller reagent(95 ml H2O t 2.5 ml HNO3t 1.5 ml HCl t 1.0 ml HF). The crosssection specimen of target material nearby the crater, which was shown in Fig.15,was immersed in the Keller reagent repeatedly to obtain clear micrographs.

A slender crack located nearby the lower surface of groove can be clearly observed in Fig. 15. It shows that the shear fracture is generated from lower surface. Furthermore, four typical (A/B/C/D)regions were selected to observe the microstructure of target material after penetration. Those microscopic images were shown in Fig.16 to Fig.18 respectively.

Fig. 16 exhibits the grain microstructure away from the cater.The A region is almost unaffected by penetration and can be approximated considered as its initial shape.Instead,B/C/D regions are distributed along the crater in order.

Observed the grain along penetration direction of B region in Fig.17(a),it shows that grain closed to the crater is slender than its initial shape.Moreover,stretching direction of the elongated grains is approximately parallel to penetrate direction.It implies that the stretching was caused by radial extrusion and axial friction during penetration.However,the stretching direction of grain in the center has a tendency to bend toward the crater,which was shown by the blue arrow.From the blue arrow segment to the red dotted line,the bend tendency of stretching was no longer apparent. It suggested that this phenomenon was caused by the petaling formed on target surface.

Fig.16. Grain microscopic images of A region.

Fig.17. Grain microscopic images of B and C region.

Fig. 17(b) shows the grain located near the upper surface of groove.An obvious light area(circled by a red dotted ellipse)can be easily found and it was brighter than surrounding material. It suggests that the temperature of this area is higher during penetration. Combined with numerical results, it is speculated that the high temperature was caused by high stress and large deformation of target material during penetration.

Fig.18 exhibits the grain of D region.Six more details(Fig.18(a)to Fig. 18(f)) with enlarged scale distributed in the groove were selected to observe the dynamic response of the filling-material.For instance, Fig.18(a) and Fig.18(c) are immediately adjacent to groove profile, Fig.18(b) and Fig.18(f) are located in both ends of the crack, while Fig.18(d) and Fig.18(e) are situated in the groove center. According to these details,process of target material filling into groove can be accurately described.

Cracks can be observed clearly between the material inside and outside the groove.The grain in Fig.18(b) and Fig.18(d) was more slender than that in Fig.18(a)and Fig.18(c),while grain in Fig.18(e)was similar as its initial shape. As a typical instance, Fig. 18(d)shows the smooth transition of grain from regular to slender approaching crack. This phenomenon indicated that the contribution of extrusion and slip friction are almost works near the contact surface. Good agreement between experiment and simulation is shown in Fig.19.Furthermore,compared with simulation results in Fig.13, stretching direction of the elongated grain was consistent with the velocity vector direction of the target unit.

5. Conclusions

The firm embedding behavior of annular grooved projectile impacting 2024-O aluminum alloy plates with low-velocity were studied. Based on the experimental and numerical observations,the following conclusions are drawn:

Fig.18. Grain microscopic images of D region.

Fig.19. Crack shape observed in simulations and microscopic tests.

(1) Compared with the traditional conical shape, the annular grooved projectile (AGP) can become solidly embedded in the target surface during low-velocity impacts.

(2) Experimental and simulated results indicated that the firm embedment behavior was mainly due to plastic deformation of the filling-material rather than friction between the projectile and target.

(3) Material flow process can generally be subdivided into four stages: initial-cratering stage, groove-filling stage, fillingmaterial failure stage and rebound vibration stage.

(4) The flow characteristics of target material around crater was obtained through microscopic tests and it exhibited firm embedding mechanism of AGP.

Firm embedment behavior is a creative application in new concept warheads. However, it is a complex process that is influenced by the target material, groove size, target thickness, and impact velocity. Therefore, further theoretical and experimental research must be carried out to support the findings in this study.

Acknowledgements

This study was financially supported by the National Natural Science Foundation of China [grant number 11472053].