Peng-ru Li ,Qun-bo Fan ,,Xin-jie Zhu ,Hai-chao Gong

a School of Materials Science and Engineering,Beijing Institute of Technology,Beijing,100081,China

b National Key Laboratory of Science and Technology on Materials Under Shock and Impact,Beijing,100081,China

c Beijing Institute of Technology Chongqing Innovation Center,Chongqing,401135,China

Keywords: Titanium alloy targets Conoidal fracture Stress triaxiality Microscopic mechanism

ABSTRACT In order to understand the mechanism of conoidal fracture damage caused by a high-speed fragmentsimulating projectile in titanium alloy layer of a composite armor plate composed of titanium-and aluminum-alloy layers,the ballistic interaction process was successfully simulated based on the Tuler-Butcher and GISSMO coupling failure model.The simulated conoidal fracture morphology was in good agreement with the three-dimensional industrial-computed-tomography image.Further,three main damage zones(zones I,II,and III)were identi fied besides the crater area,which are located respectively near the crater area,at the back of the target plate,and directly below the crater area.Under the high-speed-impact conditions,in zone II,cracks began to form at the end of the period of crack formation in zone I,but crack formation in zone III started before the end of crack formation in zone II.Further,the damage mechanism differed for different stress states.The microcracks in zone I were formed both by void connection and shear deformation.In the formation of zone I,the stress triaxiality ranged from-2.0 to-1.0,and the shear failure mechanism played a dominant role.The microcracks in zone II showed the combined features of shear deformation and void connection,and during the formation process,the stress triaxiality was between 0 and 0.5 with a mixed failure mode.Further,the microcracks in zone III showed obvious characteristics of void connection caused by local melting.During the zone III formation,the triaxiality was 1.0-1.9,and the ductile fracture mechanism was dominant,which also re flects the phenomenon of spallation.

1.Introduction

Titanium alloy[1-3]is an excellent armor material with a low density,high strength,and high heat resistance.It is widely used in light armor structures.Under the conditions of projectile penetration,a titanium alloy target will show various macroscopic damage characteristics.Backman[4]et al.found that some of the most common failure modes observed in a metal armor were brittle fracture,conoidal fracture,spalling,plugging,front or rear petaling,and ductile hole enlargement.As one of the most common failure modes of a titanium alloy target,conoidal fracture

Greatly weakens the anti-penetration property of titanium alloy targets.

The mechanisms of conoidal fracture and spallation are similar,and both are considered to be typical dynamic tensile failure modes of materials under strong impact loads[5].There are many studies on spallation.The physical model of spalling was discussed in detail by Antoun[6]et al.It is related to shock waves.Rinehart et al.reported that the high strength compressive stress wave is re flected as a tensile one,thereby causing spalling.Bartus[7]et al.proved that the factors that determine the occurrence of spalling include the resistance of the material to fracture,the magnitude of the stress wave,and the shape of the stress wave.The conoidal fracture is identi fied by the following phenomenon;a cone crack that initially runs around the contact surface upon the impact of a projectile on the target plate at a high speed,rapidly spreads downward through the material,shearing out a complete cone of separated material.To study the microscopic mechanism of spalling,most studies performed flyer plate experiments.For example,Me-Bar and Boidin[8,9]carried out flyer impact experiments on Ti-6Al-4V samples,and in the interior of the plate,only the plane strain condition was observed.Experimental results show that the spallation mechanism occurs via the nucleation,growth,and coalescence of voids,which are connected as a result of shearing.In contrast,upon impact with a high speed projectile,a target plate exhibits a complex three-dimensional stress condition,so the underlying mechanism of conoidal fracture is more complex.However,few studies have focused

On the underlying microscale mechanism of conoidal fracture in titanium alloy targets.

The results of previous studies showed that a backplate restraint can effectively inhibit the conoidal fracture of the titanium alloy layer,thereby improving the ballistic

Anti-penetration property.Fanning[11]et al.studied the ballistic performance of a 7.62-mm-diameter armor-piercing projectile that penetrates a timetal LCB titanium alloy specimen.The results showed that when an aramid plate is used as the back support,the extent of conoidal fracture damage could be controlled or it could be prevented,thus resulting in an effective armor system.Furthermor,in most previous studies,traditional experimental procedures and microscopic observations were employed to study the conoidal fracture,but the systematic,intensive,quantitative

Research on the conoidal fracture mechanism was not carried out.

In this study,considering the light weight and excellent antipenetration property,an aluminum alloy was used to fabricate the back plate,and then,the conoidal fracture behavior of the titanium alloy TC4 layer upon impact with a high-velocity projectile was analyzed.Furthermore,the combination of numerical simulation and experimental analysis was used to reveal the underlying mechanism quantitatively.

2.Experimental details

The experiment was conducted using a ballistic gun,velocitymeasuring system,and target platform,as shown in Fig.1.Further,a fragment-simulating projectile made of 35CrMnSi steel,with a length and diameter of 15 mm,was used.The projectile has one wedge-shaped end and a flat end.The geometric model and relevant dimensions are shown in Fig.2.The projectile velocity was 1199 m/s.In order to realize a distinctly conoidal fracture in the titanium alloy layer,the projectile was made to impact the composite target plate with the flat end.The polyurethane adhesive was used to bond the titanium-and aluminum-alloy plates,and the hot pressing of the target was completed at 120°C for 2 h.The thickness of the titaniumand aluminum-alloy plates are 20 and 10 mm,respectively.The length and width of the target plate are 200 mm.The ballistic gun was used to launch the fragment-simulating projectile,and the projectile launch speed was controlled by adjusting the charge amount.In the experiment,the ballistic gun was fixed on a gun frame,and the muzzle was set at a height in line with the center of the target to ensure stable shooting and to ensure that the projectile movement was perpendicular to the target.

3.Finite element analysis

Simulation was performed using ANSYS/LS-DYNA.In order to reduce the number of grids and calculation time,the 1/2 model was used to establish the finite element model,as shown in Fig.3.The whole finite element models are divided into 616,560 elements,in which the titanium target plate is composed of 469,600 elements,the number of elements for the aluminum target plate is 204,800 elements and the projectile body is composed of 2160 elements.

3.1.Material models

In the LS-DYNA simulation,the MAT_PLASTIC_KINEMATIC[12]constitutive model was used for the fragment-simulating projectile,and the speci fic material parameters are shown in Table 1.In order to simulate the strain strengthening,strain rate strengthening,and thermal softening behavior of the titanium-andaluminum-alloy plates during the processof penetration,the MAT_JOHNSON_COOK constitutive model[13]was selected as the material model,and the material parameters used in the simulation are listed in Tables 2 and 3.The equation of state was used to describe the relationship between the volume and pressure during deformation.The model for contact between the projectile body and the target plate was defined as CONTACT_ERODING_SURFACE_TO_SURFACE,and the model for the contact between the titanium and aluminum alloy plates was defined as CONTACT_AUTOMATIC_SURFACE_TO_SURFACE.

Table 1 Material properties of projectile.

Table 2 Material properties of titanium alloy.

Table 3 Material properties of aluminum alloy.

3.2.Failure criterion

In the case of a Ti-6Al-4V target,the very-high-speed collision of a projectile results in a high impact force and plastic deformation in the target area.All loads will cause the target plate to be damaged,thus introducing a stress-strain coupling failure based on cumulative damage effects.

It was the day before Thanksgiving -- the first one my three children and I would be spending without their father, who had left several months before. Now the two older children were very sick with the flu, and the eldest1 had just been prescribed bed rest for a week.

The stress-accumulation-induced damage of the Ti-6Al-4V titanium alloy

Corresponds to the Tuler-Butcher failure model[14].

whereα=2 andK=17.5 MPa2s are material constants,σ0=1100 MPa is the defined stress threshold,tis the loading time,andσtis the stress load as a function of time.

Further,to simulate the macroscopic cracks in the sample,the GISSMO damage model[15]related to the generalized incremental stress was applied to the finite.

Fig.2.Finite element model and dimensions of fragment-simulating projectile.

Fig.3.Finite element model of projectile and target plate.

Element model:

wherenis the nonlinear damage accumulation index,Δεpis the equivalent plastic strain increment,Dis the damage variable(the initial value of the damage variable is zero,and when the damage variable reaches 1,the corresponding element in the finite element model is deleted),andεfis the material-fracture-equivalent plastic strain related to the stress triaxiality.The stress state of the material is characterized by the stress triaxialityσ*,and the calculation formula is as follows:

wherepis the hydrostatic pressure andσeffis the equivalent stress.The GISSMO failure model of the titanium alloy layer is shown in Fig.4.As a dimensionless parameter,σ*re flects the stress state of materials.If its value is negative,shear fracture plays a dominant role,whereas in the case of highσ*values,the ductile fracture with void expansion is dominant;further,in the caseσ*of values between the above two states,the fracture mode is a combination of shear and ductile fracture modes.When the stress state changes,the fracture strength,the equivalent failure strain,and the mode of fracture failure change.

Fig.4.Fracture curve of the equivalent strain and stress triaxiality.

4.Failure mechanism analysis

4.1.Macroscale morphologies

To analyze the internal damage,the crater area was cut into a 40 mm×40 mm×20 mm cuboid specimen,and analyzed using the GE Phoenix v|tome|x C Industrial CT system with a power of 500 W.Fig.5 displays the obtained three-dimensional image.Fig.6 displays the two-dimensional section plane,which is cut from the 3D reconstructed model.Fig.6(a)and(b)show the central sections of the titanium alloy carter from different perspectives,respectively.From Fig.6(b),it is clear to find the conoidal-fracture macroscopic failure characteristics.The cracks are located in a cylindrical region with a diameter of 33.84 mm and a length of 18.05 mm(the volume is about 1.62×104mm3).Furthermore,annular discontinuous flaky crack zones are found at the periphery and the lower part of the crater area.In addition,a signi ficant tendency of material separation is observed at the bottom of the sample.

To further analyze the crack initiation mechanism,the titanium alloy layer was cut into half along the impact direction,and its macroscopic features are shown in Fig.7.The figure shows that the projectile clearly does not fully penetrate the plate:the maximum penetration depth is 14.5 mm.A large number of cracks were generated in the lower part of the crater.Further observation of the failure characteristics of the titanium alloy layer revealed that the macroscopic crack morphology changed obviously with a change in the penetration depth and location during the process of penetration.In order to facilitate the analysis of the conoidal-fracture macroscopic failure characteristics,the target with macrocracks was divided into three regions according to morphological characteristics:zones I,II,and III.The main crack in zone I was located near the crater area and was at an angle of about 30°to the impact direction;further,there were sub-cracks perpendicular to the main crack.The cracks of zone I with a length of 20 mm and a maximum width of 1 mm were distributed in the surrounding crater.The cracks in zone II were at an inclination of nearly 45°with respect to the impact direction and were located at the bottom of the plate;the cracks had a length of about 10 mm,and a maximum width of about 1 mm.Further,cracks in zone III were relatively small,with a length of 12 mm and a width of less than 0.5 mm.

Fig.5.Industrial computed tomography image of titanium alloy sample.

Fig.6.The central section of the titanium alloy carter:(a)from one perspective;(b)from another perspective.

Fig.7.Macroscale morphological features along the cross section in penetration channel.

The speci fic distribution feature of cracks at zone I,zone II and zone III is obtained as shown in Fig.8.Fig.8(a)is the cross-section of the sample,and the sample is divided along the green line to obtain a cross-section as shown in Fig.8(b).The middle diameter of the crater is about 19.05 mm.Zone I shows conical penny-shaped cracks,in which the middle diameter is 31.00 mm,which is about 1.63 times of the crater.Zone II is located at the bottom of the target plate,and the middle diameter is 16.39 mm.Meanwhile,Fig.8(b)shows that the diameter of Zone III is 18.45 mm,and its size is similar to the diameter of the middle of the crater.

Fig.8.The cross-section of the sample.(a)The central section of the titanium alloy carter;(b)the pro file chart of the central section.

4.2.Simulation results

The simulated ballistic-performance results and penetration depths are shown in Fig.9.The projectile did not fully penetrate the titanium plate,but induced the conoidal fracture.Table 4 shows the comparison of two ballistic tests and simulation results,and the relative error between the experimental penetration depth and the simulated penetration depth is 12.41%and 14.19%,respectively,which is generally acceptable.Meanwhile,the failure characteristics of both experiments are similar to the simulated result,which further proves that the relevant conclusions are reliable.

Table 4 Comparison of two ballistic tests and simulation results.

Fig.9.Simulation results and penetration depths.

4.3.Microscale fracture mechanism analysis

4.3.1.Triaxiality analysis

The time-history analysis results for the stress triaxiality and the timeline of

Crack propagation are shown in Fig.10.In zone I,the distance between the tip of the main cracks and the target surface was approximately 4 mm,with sub-cracks growing perpendicular to the main crack.The plate underwent substantial plastic deformation upon penetration by the projectile,and the stress triaxiality in the shear region was between-2.0 and-1.0.From Fig.4,it can be seen that the target material was in the shear fracture mode.During the penetration process,the shear stress dominate regions gradually decrease,at the same time gather below the projectile.In contrast,the red part,i.e.,the area with triaxiality greater than 0,increased signi ficantly from 18μs;from 18μs to 100μs,the triaxiality in this zone was between 0 and 0.5 in this period,corresponding to the mixed mode of shear and ductile fracture.Further,from 22μs to 40μs,in zone III,cracks initiated and expanded gradually;the triaxiality was relatively large,i.e.,between 1.0 and 1.9,indicating that the ductile fracture mode was dominant.Notably,the period in which cracks exist in zone III is dependent on the other two zones,and this period is within the period in which zone II exists.

4.3.2.Analysis of microscale mechanism of crack damage in zone I

In Fig.11(a),a scanning electron microscopy(SEM)image of zone I is shown,and the morphological features of the scanning area are shown in Fig.11(b).The surface of the crack in the area enclosed by red lines was rough and showed connected voids.Further,another crack in the area enclosed by the blue lines had a smooth surface and sharp tip,indicating that the shear crack propagates as a result of shear deformation.Moreover,SEM observation revealed that most of the cracks were accompanied by adiabatic shear bands,thus indicating the main cause of the cracks.Under the condition of loading at a high strain rate,the temperature rise of the shear band was extremely high.Because of the extremely uneven deformation in the band,many hot spots with abnormal temperature existed.At some hot spots,microvoid nucleation occurred under tensile or shear stress.As is shown in Fig.11(c),upon projectile impact under a high-strain-rate loading,voids nucleated at the interface between theαphase andβphase in the titanium alloy target plate.

Fig.10.Time-history analysis of stress triaxiality and timeline of crack propagation.

Because the adiabatic shear band was closely related to the loading condition,the numerical simulation method was used for the in-depth study of the target stress state.The shear stress nephogram and the maximum principal stress nephogram are shown in Fig.12.From 4μs to 6μs,the shear stress remained concentrated in zone I,and the red and blue areas in the figure re flected the shear stress in the opposite directions.From Fig.12(a)and(c),we can see that the maximum value was about 0.9 GPa.Moreover,compared with the shear stress,the principal stress in this area was relatively dispersed,with the maximum value of about 0.2 GPa(Fig.12(b)and(d)).Furthermore,the formation of cracks in zone I was mainly due to the shear stress.The shear stress nephogram from 10μs to 40μs is shown in Fig.13.During the period from 10μs to 20μs,the shear stress of the plate was about 1.0 GPa,and then,it decreased continuously.At 30μs,the maximum value of the shear stress was about 0.7 GPa,while at 40 μs,the maximum value was about 0.5 GPa.The shear stress decreased with time,and simultaneously the shear stress concentration area changed.At 10μs,the maximum shear stress existed in the main stress area of the crater,and it existed at an angle of~45°to the impact direction.Moreover,with the penetration of the projectile,the stress peak position migrated to the interior of the target plate from 20μs.The corresponding failure features are as shown in Fig.11(a):several sub-cracks grew along the direction perpendicular to the main shear crack.

Fig.11.Microscale morphologies in zone I:(a)SEM scanning area in zone I;(b)microscale morphology at 200×magni f ication;and(c)microscale morphology at 500×magni f ication.

Fig.12.Shear stress nephogram and the maximum principal stress nephogram of zone I:(a)shear stress nephogram at 4μs;(b)maximum principal stress nephogram at 4μs;(c)shear stress nephogram at 6μs;and(d)maximum principal stress nephogram at 6μs.

4.3.3.Analysis of microscale mechanism of crack damage in zone II

The microstructural characteristics in zone II are shown in Fig.14.The area enclosed by white lines in Fig.14(a)was observed by SEM,and the morphological features of the area are shown in Fig.14(b).A microcrack with a smooth surface and sharp tip was located at the interface between the adiabatic shear band and the matrix.Under the applied stress,the deformation of the matrix part and the shear band was not synchronous,forming an elongated microcrack.In the shear band,discontinuous voids connected to the microcrack are visible.Fig.14(c)shows the voids in the matrix,mainly in the sharp interface area between theαphase andβphase.

To further study the mechanism of crack formation in zone II,a simulation-based quantitative analysis was carried out.As mentioned in Section 4.3.1,during the period from 18μs to 100μs,continuous damage occurred in zone II,and the triaxiality was between 0 and 0.5,which corresponded to the mixed mode of ductile fracture and shear fracture.Further,from 16μs to 18μs,cracks began to emerge in zone II.The effective plastic strain nephogram is shown in Fig.15(a)and(c).In this period,the effective plastic strainεin zone II is higher than the principal stress,with a value of about 0.3.Further,from 18μs to 100μs,the effective plastic strain accumulate with time until the element is deleted due to the target back-surface bulge.The principal stress vector nephogram of zone II at 16μs and 18μs are shown in Fig.15(b)and(d),respectively.The first and second principal stresses were the circumferential and radial tensile stresses,corresponding to the maximum values of 2.86 GPa and 2.03 GPa,respectively.Furthermore,the third principal stress with a value of about 0.98 GPa was the compressive stress along the impact direction.Under the joint action of high stress and strain,the whole of zone II exhibited both tensile and shear stresses with a mixed failure mode of ductile fracture and shear fracture.In the case of high stress,the dislocation at the interface caused stress concentration,whereas in the case of high strain,separation occurs due to the incongruous plastic deformation of theαphase andβphase and voids emerged simultaneously at the interface between theαphase andβphase.

4.3.4.Analysis of microscale mechanism of crack damage in zone III

Fig.13.Shear stress nephogram from 10μs to 40μs.

Fig.14.Microscale morphologies in zone II:(a)SEM scanning area in zone II;(b)microscale morphology at 200×magni f ication;and(c)microscale morphology at 1500×magni f ication.

The microstructural characteristic of zone III are shown in Fig.16.The area enclosed within white lines in Fig.16(a)was observed by SEM,and the morphological features of this area are shown in Fig.16(b).There were discontinuous voids in the crack,most of which are formed owing to the local melting,and which is caused by the sharp rise in the temperature due to friction between the projectile and the target.The crack surface was rough,and void connection is evident.Fig.16(c)shows the voids in the matrix,which mainly appear in the interface area between theαphase and βphase,and the voids expand along the direction perpendicular to the impact direction.

Further analysis of the stress state in zone III revealed that in the range of 22μs-40μs,as mentioned in Section 4.3.1,the triaxiality of zone III was between 1.0 and 1.9,corresponding to the ductile fracture mode.The hydrostatic pressure nephogram and the principal stress vector nephogram are shown in Fig.17.It can be seen that zone III was affected by the high hydrostatic pressure,which was about 2.0 GPa.During this period,while withstanding severe plastic deformation without failure,the titanium alloy material has a high energy density.Because of the adiabatic characteristics of localized deformation,with the extremely high temperature rise in the shear band,the shear band became an ideal place for the generation of defects such as voids.At the same time,the principal stress vector nephogram showed that in zone III,the threedimensional principal stresses were all tensile stresses:The first principal stress was perpendicular to the surface of the plate and is about 2.22 GPa.The second principal stress was parallel to the plate surface and perpendicular to the impact direction,and was about 2.01 GPa.The third principal stress was tensile stress along the impact direction and was about 0.95 GPa.Under this state of stress,the internal defects of the target material increased,and cracks were generated after the tensile stress continued to increase for a certain period of time,resulting in the failure of the target material.The stress state also revealed spallation in the target plate:upon projectile impact,the pressure stress wave was transmitted from the titanium alloy layer with a high impedance to the aluminum alloy plate with a low impedance,and the reflection on the free surface formed the tensile stress wave,which led to the threedimensional tensile stress state in the titanium alloy layer when the tensile stress wave propagated back,and promoted the growth and extension of the voids.Thus,cracks were formed,which eventually led to spalling.

Fig.15.Effective plastic strain nephogram and principal stress vector nephogram of zone II:(a)effective plastic strain nephogram at 16μs;(b)principal stress vector nephogram at 16μs;(c)effective plastic strain nephogram at 18μs;and(d)principal stress vector nephogram at 18μs.

Fig.16.Microscale morphologies in zone III:(a)SEM scanning area in zone III;(b)microscale morphology at 200×magni f ication;and(c)microscale morphology at 2000×magni f ication.

5.Conclusion

In this study,by using ANSYS/LS-DYNA software,through the finite element numerical simulation of the penetration process combined with the comparative analysis of the experimental results,the mechanism of the conoidal fracture in the titanium alloy layer of a composite armor plate composed of titanium-and aluminum-alloy layers during the penetration of a high-speed fragment-simulating projectile was analyzed.The cracks were distributed in three zones,depending on their shapes and locations:zones I,II,and III located near the crater region,at the back of the target plate,and directly below the crater region,respectively.The simulation results showed that the crack in zone II began to form at the end of the period of crack formation in zone I,but its growth did not end when crack damage began in zone III.Furthermore,the failure mechanism was different in different regions.In Zone I,the triaxiality is in the range of-2.0 to-1.0,and the shear mechanism was dominant.The voids in the shear band formed cracks by nucleation,growth,and extension or shear elongation.In zone II,the microcracks formed by shear elongation and void connection appeared,and the triaxiality was in the range 0-0.5.In this zone,the three-dimensional principal stress shows two dimensional tension stress and one dimensional compression stress,and microcracks gradually generate under the joint action of shear stress and tensile stress.In zone III,microcracks were obviously formed by the connection of voids formed by local melting.The triaxiality was between 1.0 and 1.9;the ductile fracture mechanism was dominant,and the three-dimensional principal stress was tensile stress,which caused spallation of the plate.

Fig.17.Hydrostatic pressure nephogram and principal stress vector nephogram at different time in zone III.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to in fluence the work reported in this paper.

Acknowledgement

This work was supported by the National Natural Science Foundation of China(Grant No.51571031).