Qi Huang,Shun-shan Feng,Xu-ke Lan,Qing Song,Tong Zhou,Yong-xiang Dong

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

Keywords: Partial penetration Embedment behavior Ballistic impact Annular grooved projectile(AGP) Microscopic experiments

ABSTRACT Changing and optimizing the projectile nose shape is an important way to achieve speci fic ballistic performance.One special ballistic performance is the embedding effect,which can achieve a delayed high-explosive reaction on the target surface.This embedding effect includes a rebound phase that is signi ficantly different from the traditional penetration process.To better study embedment behavior,this study proposed a novel nose shape called an annular grooved projectile and defined its interaction process with the ductile metal plate as partial penetration.Speci fically,we conducted a series of lowvelocity-ballistic tests in which these steel projectiles were used to strike 16-mm-thick target plates made with 2024-O aluminum alloy.We observed the dynamic evolution characteristics of this aluminum alloy near the impact craters and analyzed these characteristics by corresponding cross-sectional views and numerical simulations.The results indicated that the penetration resistance had a brief decrease that was in fluenced by its groove structure,but then it increased signi ficantly-that is,the fluctuation of penetration resistance was affected by the irregular nose shape.Moreover,we visualized the distribution of the material in the groove and its in flow process through the rheology lines in microscopic tests and the highlighted mesh lines in simulations.The combination of these phenomena revealed the embedment mechanism of the annular grooved projectile and optimized the design of the groove shape to achieve a more firm embedment performance.The embedment was achieved primarily by the target material filled in the groove structure.Therefore,preventing the shear failure that occurred on the filling material was key to achieving this embedding effect.

1.Introduction

Semi-armor-piercing high-explosive incendiary(SAPHEI)[1]is a new concept ammunition,one of which includes annular grooved projectiles(AGPs)and that has obtained increasing attention for multifunctions in its firm embedment behavior with delayed reactions.AGPs not only can penetrate multilayer structures[2]like other traditional projectiles but also can effectively achieve embedment in the target without rebounding.In addition to this performance,the delayed high-explosive reaction could be more controllable and reliable.Therefore,the embedment process and characteristics of this novel penetrator are considerably important and require further research.

In this series of embedment-related studies,we defined the embedment process as “partial penetration” to distinguish it from “classical penetration” .Considerable research[3-6]of the latter has focused primarily on material properties of targets[7-9],ballistic limits of projectiles[10-12],or structure optimizations[13,14]focusing on the nose shape.Among these past studies,a famous phase diagram for projectile impact targets summarized by Backman and Goldsmith[15]categorized different experimental phenomena,including perforation,embedment,and ricochet under various initial conditions.Gupta et al.[16,17]investigated the effect of projectile nose shape,impact velocity,and target thickness on the deformation behavior of aluminum plates.Iqbal et al.[18]analyzed the failure mode of several double-nosed projectiles penetrating into the thin aluminum plates.Liu et al.[19]designed a double-ogive-nosed projectile and calculated the projectile’s penetration depth using an equivalent nose-shape coef ficient model.Deng et al.[20]analyzed the penetration performance of axisymmetric U-shape-nose grooved projectiles on aluminum targets.Kpenyigba et al.[21]studied the effect of projectile nose shape on the ballistic resistance of interstitial-free steel targets.Han et al.[22,23]discussed the effect of grooves on the double-nosed projectile during penetration.As for the role of groove,it generally is believed that it can provide space for the in flowing target material during the penetration process.Most ballistic experiments and numerical simulations,however,have concentrated on the perforation,and few studies have involved the embedment behavior of projectiles,particularly the partial penetration[24].As one of the ballistic modes between projectile and target,partial penetration shows the embedment,rather than intact perforation or rebound,of certain projectiles under certain impact conditions,including impact velocities,target material properties,or groove shapes.This process involves several physical phenomena and is more complex than classical impacts;thus,partial penetration is considered to be an innovative study that is derived from the classic penetration question.

The nose shape of projectile has a signi ficant in fluence on the penetration performance;to date,however,few studies have been conducted on the embedding mechanism of AGPs.In this study,we experimentally and numerically analyzed the flowing feature of a target made by ductile metal material close to the grooved outline and the deceleration characteristics of AGPs during partial penetration.This study obtained a better understanding of the embedding mechanism of AGP and achieved a more firm and reliable embedding effect.Accordingly,we based the projectile used in this study on the application of a certain SAPHEI,and we simpli fied its shape to a projectile with one annular groove on the head.We studied partial penetration through the way by which an AGP struck a ductile metal target at several velocities below its ballistic limit.We employed gas gun apparatus in ballistic impact tests to precisely control the initial velocity range of AGPs.We performed corresponding numerical simulations and microscopic experiments to observe the dynamic evolution characteristics of the target material around the crater.Therefore,we were able to clearly analyze the in flow process and distribution of the target material in a certain groove.To distinguish the target material inside and outside the groove,we defined the part that flowed into the groove as filling material.The results indicated that the plastic deformation of the filling material principally contributed to the embedding ability of the AGP.Furthermore,the results also revealed the embedment mechanism of the AGP impacting the ductile metal targets and optimized the design of the groove shape to achieve a more firm embedment.

2.Experimental study

We conducted all ballistic impact tests in a ballistic laboratory at Beijing Institute of Technology,and we used a gas gun apparatus to launch the AGPs(Fig.1).The detailed description of the experimental setup and the function of corresponding facilities is available in our previous work[25].We used a Phantom 710 high-speed camera operating at 44000 fps to measure the impact velocities of AGPs accurately.We recorded high-resolution videos of the partial penetration process.

We installed square targets on a C-shaped support plate by inserting four bolts in the target chamber.The support plate was welded to the bottom base structure to keep its stability during impact loading(Fig.2).Each shot was fired at the center of each target.The construction of a buffering shield located behind the target was used to stop and recover the possibly intact perforated projectile.

The dimensions of every target plates were 140 mm×140 mm×16 mm and all were made with 2024-O aluminum alloy.The chemical compositions(in weight%)of this metal[26,27]are shown in Table 1.To obtain ductile superiority instead of brittle fracture during partial penetration,the target plates underwent a heat treatment processes to achieve an annealed temper of O after production.Table 2 details the process.

Table 1 Chemical components of 2024 aluminum alloy.

Table 2 Heat treatment processes of 2024 aluminum alloy to obtain the temper O[26].

In the current tests,the aluminum alloy plates were impacted by AGPs shot at a variety of velocities.Cylindrical projectiles were 16 mm in diameter and had a nominal weight of 65 g(Fig.3).The nose length of each projectile was 1.5 times the diameter.The cylindrical cavity inside the projectile was designed for subsequent stretching tests and delayed explosion experiment,which we do not discuss in this study.The AGP material was AISI 1045 steel,which had an ultimate tensile strength of 625 MPa and was much higher than that of the target material.According to previous experiments[25],projectiles made with this relatively high-strength material experienced negligible inelastic deformation when penetrating 2024-O aluminum alloy,and as such,they were considered to be rigid[28].We used two-piece sabots made by nylon 66 to guarantee ideal acceleration conditions and reduce the yaw angle inside the firing barrel.

The annular groove structure originally was designed to provide sufficient room for the in flowing material.This structure was a possible obstacle during the rebound process caused by the elastic recovery of the target.In theory,AGP can contain grooves of arbitrarily shape and number.In contrast,to simplify the analysis,the AGP used in this study contained only one groove with a line-arc shape.Thus,the projectile was simpli fied into the three parts as shown in Fig.4.

The dimensions of a simpli fied annular groove structure can be characterized according to three main dimensionless parameters,namely,the groove relative positionL=l0/l,the relative widthW=lg/l,and the relative depthH=(r0-rg)/r,wherelg,l0,andrgare the width,center position,and bottom diameter of the groove,respectively.In particular,we took theL,W,Hin as 0.25,0.2,and 0.225.Other shapes and sizes of grooved structures and their effects will be analyzed in further studies.

3.Finite element model

We modeled the target materi al according to a modi f ied Johnson-Cook constitutive model.The quasi-static strain hardening was described by an extended Voce rule[29].According to comprehensive research on the aluminum alloy behavior presented by B?rvik[30-32],we modeled the constitutive behavior with the von Mises yield criterion,which we reasonably assumed to be isotropic,although the target material exhibited a little anisotropy[33].In the current paper,the equivalent stress is written as follows:

where εeqis the equivalent plastic strain,Ais the initial yield stress,QiandCiare hardening parameters,andis a dimensionless plastic strain rate,where0is a reference strain rate defined by user[34].T*is the homologous temperature and can be expressed by a function combined with the absolute temperatureT,the room temperatureTr,and the melting temperatureTmasT*=（T-Tr）/（Tm-Tr）.Candmare the model parameters related to the rate sensitivity and the thermal softening of the material,respectively[35].The temperature change due to adiabatic heating is expressed as follows

Fig.1.Gas gun apparatus.

Fig.2.Target supports.

whereρis the material density;χis the Taylor-Quinney coef ficient,which refers to the proportion of plastic work converted into heat;andCpis the speci fic heat of target material.The Cockcroft and Latham(CL)fracture criterion[36]was used to model failure and can be expressed as follows:

whereσ1is the major principal stress,〈σ1〉=σ1whenσ1≥0,and〈σ1〉=0 whenσ1<0.Eq.(3)shows that failure will not occur when no tensile stresses are operating.Wcis the model constant about the value ofWat failure.Note that,according to the material’s anisotropic behavior and the uncertainty in the calibration of the CL criterion[26],Wcshould not be considered as a material characteristic.To determine the constitutive relation and the failure criterion for 2024-O aluminum alloy used in this study,we employed LS-DYNA,and the corresponding constants in the MJC model are given in Table 3.

Table 3 Main material constants for 2024-O aluminum alloy target[25,26,37].

As mentioned,the hardened AGP made by high-strength steel experienced negligible deformation during ballistic tests.Furthermore,the dynamic evolution characteristics of ductile metal material during the partial penetration process is the major focal point in this study,so we assumed that the projectile was rigid in numerical simulations.The density,Young’s modulus,and Poisson’s ratio of the projectile material were considered asρ=7850 kg/m3,E=203 GPa,andυ=0.29,respectively[25].

We performed all numerical simulations in this study using LSDYNA 971,a widely used nonlinear finite element(FE)software program.Considering the axisymmetry in this ideal penetration simulation without yaw or obliquity,we modeled only half of the projectiles and plates.Moreover,we modeled the target plate as a smaller(50×50 mm2)plate instead of a full-size plate(140×140 mm2).Theoretically,two-dimensional(2D)simulations might have an acceptable deviation compared with threedimensional(3D)simulations,which generally are used in classic penetration research.Previous studies[38],however,have indicated that 2D simulations exhibit a good agreement with realistic a phenomenon and could reduce the CPU running time signi ficantly without overly affecting the results[26].Therefore,we determined that this simpli fied method was reasonable and feasible in partial penetration studies.

Fig.3.Dimensions of the AGP and corresponding conical projectile(dotted contour instead of the groove structure).All measures are in mm.

Fig.4.The simpli fied contour of an AGP nose shape.

Fig.5 shows the FE meshes that contained a re fined mesh method used in the numerical simulations.The mesh size in the impact region(Zone I)was signi ficantly smaller than that of other regions(Zone II).Earlier studies[39]have evaluated the mesh-size dependency and the effect of friction in this problem.The results have shown that an element size of 0.0625×0.0625 mm2is the ideal choice for the impact region when considering the compromise between calculation accuracy and CPU running time.Moreover,we ignored the effect of friction between the AGP and the target because changing the coef ficient of friction from 0.5 to 0 resulted in a mere 4%reduction in depth of penetration(DOP).We applied an automatic-single-surface contact algorithm to describe the contact between the AGP and the target[40].We assigned a target edge with an hourglass setting using the Flanagan-Belytschko stiffness[25]and fully clamped the target by limiting displacement,velocity,and acceleration in all directions.

Fig.5.FE meshes and corresponding re fined mesh method of different regions used in simulations.

4.Results

The experimental data,including initial projectile massm,impact velocityvi,rebound velocityvr,initial kinetic energyEi,and DOP,are listed in Table 4.In particular,we controlled the initial velocities of projectiles below the ballistic limit using the gas gun to prevent intact perforation.

Table 4 Partial penetration data of a 16 mm 2024-O aluminum alloy plate impacted by AGPs.

Typical high-speed video images of a projectile with 140.7 m/s are shown in Fig.6.After a relatively long period(t>3 ms)of observation,the projectile kept embedding in the target instead of rebounding.This phenomenon revealed that the AGP had an embedding ability at low-velocity impact.Photographs of three typical embedded AGPs are shown in Fig.7,and a signi ficant difference in depth of penetration can be observed comparatively.As the initial speed increased,the global bending of the metal plate gradually became obvious when the impact velocity was higher than 140 m/s.Note that the projectile’s rebound velocity in No.1 was zero,but it was not firmly embedded because it fell off during manual shaking.Other AGPs(Nos.2-7)also were shaken manually but did not fall from the target.This indicated that an unignorable cavity existed between the embedded AGPs and the target,which further explained that the annular groove structure was not filled completely by the ductile material.The remaining two AGPs(Nos.8-9)were sufficiently firmly embedded and could not be shaken loose.This embedment firmness needs to be evaluated further and will be a topic of a future study.

Fig.6.Typical illustrative images of a 16 mm 2024-O aluminum alloy plate impacted by an AGP at 140.7 m/s,captured by the high-speed camera.

Fig.7.Embedment situation of AGPs(Test No.1/5/9);a signi ficant difference in depth of penetration can be observed comparatively in the images from left to right.

Typical simulations of the partial penetration of 16-mm-thick 2024-Otargets impacted by the AGPs at 185 m/s are shown in Fig.8.The impact velocity(185.0 m/s)was the same in this test as that in test No.9(185.3 m/s;given in Table 4)to facilitate comparison of results.The simulation captured some of the typical physical behaviors of high-ductile aluminum targets under low-velocity impact loading,such as petals and denting on the impact surface[41].According to the brief observation of partial penetration,a visible cavity appeared between the annular groove and the target material in the early stages of penetration.With increasing DOP,the target material gradually filled the cavity when pressed by the upper surface(marked in Fig.12).This process also explains the reason why the von Mises stress of the target material inside the groove generally was higher than that of the surrounding area.

The results from a large number of numerical simulations are represented by the dimensionless DOP versus impact velocity curves in Fig.9,and the experimental DOP data are given for comparison.Moreover,the horizontal dashed line represents the DOP at which the annular groove structure completely penetrated the plate.A short area under this line(see the magni fied view in Fig.9)shows that the AGP had a slightly higher DOP because a cavity in the groove caused a decrease in the axial resistance.With the increasing impact velocity,the extrusion surface(marked in Fig.12)of the annular groove structure affected the penetration resistance.

Generally,we achieved good agreement between the simulations and experiments,which indicated the feasibility and accuracy of the simulation model for partial penetration.The over-and under-deviations may have been caused by the thickness dependency and anisotropy of the material properties of 2024-O aluminum alloy[9,42].These results,which were caused by a complex in flowing process of the ductile metal material,remain acceptable when considering the limitations of the constitutive relation and fracture criterion[43].

We selected a series of tests(No.4/6/9 in Table 4)and conducted corresponding simulations to analyze the deceleration characteristics(deceleration against time and penetration depth curves is shown in Fig.10).Fig.10 clearly shows that the partial penetration could be divided into two distinct stages according to the positive and negative deceleration value:the invasion phase and the rebound phase.The time information in the impact tests shown in Fig.6 revealed that the rebound duration was much longer than the invasion process(i.e.,only the first 450μs of data).Fig.10a shows the invasion stage and one complete rebound phase.In general,the deceleration curves increased gradually in the early period,but an ephemeral descending phase occurred in which the annular groove structure barely contacted the target.The partial penetration situation at this moment is indicated by the inset in Fig.10.The deceleration value then rapidly reached its peak after the upper surface contacted the target.We observed that the higher the initial speed,the longer the deceleration lasted at the peak,but the duration of the entire partial penetration was similar.The deceleration value also re flected the resistance of the projectile during partial penetration.As shown in Fig.10b,during the early period of partial penetration,the resistance against the penetration depth in the three cases had a similar trend.After the projectile tip perforated the metal plate,the sparse wave from the back surface of plate caused a signi ficant difference in resistance.The fluctuation of force maintained a good correlation with the shape of the warhead.Under the same penetration depth when the annular groove structure contacted the target surface,the resistance showed almost the same decrease,and then quickly reached the peak as the penetration depth increased.

Fig.8.Penetration process of 16 mm 2024-O aluminum alloy plate impacted by an AGP with an initial velocity of 185 m/s,where t refers to the time after impact.

Fig.9.A comparison of DOP data between experimental and simulated results of a series of AGPs.

Fig.10.Deceleration history of AGPs at three different initial velocities.

Moreover,the deceleration curve became negative and fluctuated at the rebound phase of partial penetration.This was signi ficantly different than the traditional penetration process.According to the analysis of the simulation and experiment results,the negative deceleration was caused primarily by the interaction between the filling material in the groove and the elastic recovery of the target during the rebound phase[39],which limited the reverse movement of the projectile and thus achieved the firm embedment behavior.This situation also is shown in the insert in Fig.10.In addition,as the initial velocity increased,the negative peak did not show a visible difference.Because the rebound was caused by the elastic recovery of the ductile metal plate,we considered that during partial penetration,the AGP’s reverse deceleration reached a maximum value and was related to the material properties of the metal plate.These curves showed the characteristics of the partial penetration process and further provided an intuitive explanation for the embedment mechanism of the AGP.

5.Discussion

We selected several cross-section images of AGP partial penetration tests to exhibit a partial penetration process.We arranged these images by ascending impact velocity(Fig.11).In general,the target material was in close contact with the projectile and eventually filled the annular groove structure almost completely.The gap in the groove explained why the AGP could be manually shaken but remained firmly embedded in the target.

Fig.11.Deformation and crater pro files of a variety of 16-mm-thick 2024-O aluminum alloy plates.

5.1.In flow process of the target material

The magni fied views in Fig.12 show,in detail,the deformation of three 16-mm-thick 2024-O aluminum alloy plates after ballistic impact tests,including the evolutionary characteristics of the material and the changes in cavity volume.With increasing DOP,the target material was pressured by the extrusion surface(red line)so that the target material gradually filled from the top to the bottom along the contour of the groove.Because the embedding ability was caused primarily by the plastic deformation of the filling material[39],a relatively blunt extrusion surface on the groove was necessary for the target material to flow in.This phenomenon indicated that the groove shape was an important factor to achieve embedment behavior.

A comparison between the simulation and experiment images is shown in Fig.13.The bottom labels,Nos.2-9,correspond to the test numbers in Table 4.The simulation images show the main penetration process of AGP with a 185 m/s impact velocity.These images show that the AGPs did not have a subsequent rebound process,and the experimental images show the various final states of the target subjected to different impacts.The good agreement of the shape of the filling material between numerical and experimental results illustrated that the various experiments could approximately re flect the dynamic process of partial penetration.Note the irregular deformation of the filling material near the lower surface in experimental images.This deformation was caused by an extrusion during AGP reverse movement,but the simulations did not contain the subsequent rebound process.During this period,the filling material acted on the lower surface,and the plasticity deformation energy and friction work offset the rebound kinetic energy of the projectile.This phenomenon revealed the embedment mechanism of AGP.

Fig.12.The target material flows from the upper surface to the lower surface.

Fig.13.A comparison of the filling material in the groove between various experiments and one continuous simulation with an impact velocity v=185 m/s.

Moreover,the experimental and numerical results in No.9 both showed that small cracks occurred at the ends of the groove.These cracks represented that the shear fracture of the filling material started on a relatively high DOP.If the filling material was sheared completely and the projectile could not penetrate the plate,the antirebound resistance came only from friction.In this case,the embedded firmness decreased to a level similar to that of a conical projectile.

5.2.In flow volume of the target material

Fig.14.The contour of un filled cavity in the groove of various experiments.

We extracted the contours of the cavity in the groove using Photoshop software(Fig.14).The cavity volumeVccan be calculated by integrating the contour shape.We took the moment when the target material contacted the upper surface of the groove as the initial time to record the in flow process,as shown by the No.2 test.At this moment,the material was not affected by the groove and the cavity volume was defined asVc0.With the continuous in flow of target material,the instantaneous cavity volumeVcicontinued to decrease until it reached a minimum value.Therefore,the instantaneous volume of the in flow materialVficould be calculated asVfi=Vc0-Vci.We de f ined the f ill ratio asVti/Vci,which could describe the real-time situation of the f illing material.Moreover,those parameters(given in Table 5)exhibited the relationship between the in f low situation of target material and the DOP of the AGP.

Table 5 The relationship between the volume of filling material in the groove and depth of penetration.

The experimental data shown in Table 5 can be fitted and are shown in Fig.15.The fitting curve showed that in the early stage of partial penetration,the volume of the filling material and the DOP of the AGP had an approximately linear relationship,which was related to the effect of the extrusion surface.As the DOP increased,the fill rate reached a critical value.This value generally was affected by several factors,including elastic modulus and failure of target material,volume and extrusion surface shape of groove structure,and impact velocity of the projectile.The fill rate could be defined as one of the indicators to quantify the embedment firmness and this will be discussed in detail in future research.When the kinetic energy of the AGP was not sufficient to increase its DOP,and the projectile moved in reverse because of the overall elastic recovery of the target.At this stage,the filling material acted on a lower surface of the groove and absorbed the remaining kinetic energy of the projectile through its plastic and elastic deformation.As a result,the groove was dif ficult to be completely filled with the target material after the experiments,which indicated that the projectile could be shaken manually but remain firmly embedded on the target.

Fig.15.The relationship between the volume of filling material and the depth of penetration.

5.3.Distribution of the target material

To obtain a better understanding of partial penetration,we performed microscopic tests of the target material to analyze the dynamic evolution characteristics.We employed a chemical etchant called Keller reagent[25]in microscopic tests to obtain a clear observation.According to the different DOP,we selected three typical specimens of targets near the crater from tests No.6,No.8,and No.9.The cross-sections of these three specimens,which were immersed in the Keller reagent,are shown in Fig.16.Corresponding microscopic images are shown in Fig.17.

Fig.16.Cross-section specimen(bottom)of three 2024-O aluminum alloy plates(top)in tests No.6,No.8,and No.9.

The “rheology lines” of the target material can be observed clearly in Fig.17.These lines showed an “S-bent” shape around the interface inside and outside the groove and were more pronounced as the DOP increased.In tests No.6 and No.8,the lines were connected inside and outside the groove,whereas in test No.9 they were not.Also,cracks appeared in the penetration direction and the interface was signi ficantly brighter compared with the surrounding region.This phenomenon suggested that this part of the material underwent a large deformation of stretching and shearing,which caused a higher temperature on the interface during penetration.Furthermore,a large amount of heat was generated in the target material inside the groove on a relatively large DOP penetration,which resulted in a re finement of material grain and inconspicuous rheology lines.

Fig.17.Grain microscopic images of three specimens in tests No.6,No.8,and No.9.

Fig.18.Highlighted meshes mark the six horizontal lines,which are 0.5,1,2,3,4,and 5 mm away from the target surface.

The related simulation showed similar results and enabled us to analyze the dynamic processes of partial penetration.We marked six horizontal lines through the highlighted meshes in the target,which are shown in Fig.18.Because the groove width was 5 mm,the distance between the mesh lines and the target surface was set to 0.5,1,2,3,4,and 5 mm.

The bending,stretching,and shear deformation of the six highlighted lines,shown in Fig.19,further exhibited the dynamic evolution characteristics of the target material impacted by an AGP with an initial velocity of 185 m/s.Although we deleted the fracture meshes in the simulation,the highlighted lines showed good agreement with the rheological lines observed in the microscopic experiment.The highlighted lines illustrate the distribution of the material in the groove and provide an intuitive explanation for the partial penetration on the metal target.

Fig.19.Dynamic evolution characteristics of target material of a 16-mm-thick 2024-O aluminum alloy plate impacted by an AGP with an impact velocity of 185 m/s,where t provides the time after impact.

Moreover,the material deformation re flected the fact that shear failure would happen at a relatively large DOP so that a relatively high-velocity impact should not be considered in partial penetration.

6.Conclusions

To examine the embedment behavior under low-velocity impact,we investigated the partial penetration of AGPs impacting medium-thickness 2024-O aluminum alloy plates under corresponding ballistic velocities through a series of ballistic tests,numerical simulations,and corresponding microscopic experiments.The results showed how an annular groove structure affected deceleration and rebound behavior when the initial velocity of projectile was below its ballistic limit,which helped to achieve the embedment phenomenon.Overall,the following conclusions of partial penetration were drawn:

(1)During the partial penetration of AGPs impacting ductile metal targets,the target material gradually filled from the top to the bottom along the contour of the groove because of the compression of the grooved upper surface.This result indicated that the grooved shape was an important factor to achieve this embedment behavior.

(2)The penetration resistance during partial penetration brie fly decreased when the grooved structure contacted the target surface,and then it increased signi ficantly to the maximum.This result indicated that the fluctuation of penetration resistance was affected by the special nose shape.

(3)The bottom filling material underwent plastic deformation when the AGP moved in reverse because of the overall elastic recovery of the target.For a certain embedded AGP,the peak value of deceleration during the rebound phase was related primarily to the target condition instead of the projectile’s initial velocity.

(4)The distribution of the material in the groove and its in flow process could be visualized clearly through the rheology lines in microscopic tests and the highlighted mesh lines in the simulations.The results indicated that the embedment was achieved mainly by the target material filled in the groove structure;therefore,preventing shear failure from occurring on the filling material was key to achieving the embedment behavior.

The firmness of embedment could be characterized by the filling situation of the target material in the groove,which was closely related to many factors,including the material properties of the target,the shape of the groove,the impact velocity,and the DOP.Further numerical and experimental research should be carried out,however,to support these findings.

Declaration of competing interest

The authors declare that they have no con flict of interest.

Acknowledgments

The financial support of this research is from the National Natural Science Foundation of China(NSFC)[No.11472053 and 11872121].