Cunxin WANG , To SUO ,b,c,*, Yulong LI,b,c, Pu XUE ,b,c,Zhongbin TANG ,b,c

a School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

b Shaanxi Key Laboratory of Impact Dynamics and Engineering Application(IDEA), Northwestern Polytechnical University,Xi'an 710072, China

c Fundamental Science on Aircraft Structural Mechanics and Strength Laboratory, Northwestern Polytechnical University,Xi'an 710072, China

KEYWORDS 2618 aluminum plate;Damage characteristic;High-velocity impact;Johnson-Cook (J-C);Projectile forms

Abstract Ballistic impact tests were carried out with examined projectiles of the Ti-6Al-4V titanium alloy to investigate the impact response of the 2618 aluminum plates at a nominal velocity of 210 m/s. The inf luence of projectile forms and oblique angles on damage formation was particularly discussed by applying different loading conditions such as multiple projectile forms and oblique angles. Additionally, the numerical simulation method was employed to provide further insight into the characteristics of damage and target responses. The Johnson-Cook (J-C)constitutive model with revised failure parameters was used to support the simulations to assess target responses and characteristics of the damage created from different impact conditions.Results show that there is a signif icant transition in the deformation mode as changes of the projectile form are applied. Moreover, the cracks on the back of the 2618 aluminum alloy plates impacted by the solid plate projectile and the hollow blade projectile tend to locate at different positions,which are supposed to be inf luenced by local bending and stretching. The work in this paper may provide guidance for the design of fan blade containment systems.

1. Introduction

Designing a containment structure for a fan blade is important for aero-engines to improve safety and reliability despite the expensive and time-consuming process. The enormous cost of the full-scale containment test results in more extensive employment of the relatively inexpensive ballistic tests on metal and composite plates in original research. These impact tests can be used to demonstrate the effects of many factors on the ballistic performance and the failure mode of advanced aero-engine alloys,contributing to the design and optimization of containment systems.

Aluminum alloys are widely used in aircraft structures requiring energy absorption capability because of their excellent performances such as high plasticity and low weight.Combinations of aluminum alloys and woven fabrics are more weight-eff icient than pure metal materials, while maintaining the all-right ability to resist high speed impact. Therefore,the ‘‘soft-wall” containment concept in the gas turbine engine has been proposed and applied to satisfy increasingly stringent safety and weight requirements of gas turbine engines. Currently, metallic inner cases such as those using the aluminum alloys in the ‘‘soft-wall” containment system are always designed to be penetrated, and the released fan blade will be captured by outer high strength woven fabrics. Assuming the impacts from different releasing debris may result in distinct damage patterns, understanding the conditions to obtain a specif ic damage pattern and the ability to predict these patterns for more complex interactions would be benef icial.Thus,the impact response of aluminum alloys subjected to releasing fan blades or similar loads needs to be investigated,which can directly help to design a reliable and lightweight ‘‘soft-wall”containment system.

Since the 1970s, the efforts to explore the performance of aluminum alloys on ‘‘soft-wall” containment systems almost never stop.It caps more than 40 years of widespread concerns over the inf luence of projectile forms and oblique angles.Ambur et al.1,2reported the evaluation of aluminum which was used to contain fan blades released from gas turbine rotors; in addition, several impact tests were conducted with titanium projectiles to evaluate the uncontained engine failures,and a relationship between the ballistic limit and the oblique angle was developed. To investigate the effect of the oblique angle on the impact response of the 6061-T651 aluminum alloy and the 4340 steel plates,Piekutowski et al.3carried out experiments under normal and oblique impacts with an ogive-nose projectile, and both the projectile kinematics and deformations during the plate perforation were clearly shown.Bao et al.4presented a theoretical approach to investigate the perforation of the aluminum alloy foam target against the rigid and ogive-nosed projectile, and the results showed that the shank diameter, the shank length, and the caliberradius-head have signif icant inf luence on the perforating resistance force and the kinetic energy variation. Research also found that the failure mode was observed to be petal formation for the thin aluminum alloy targets. Moreover, the number and the shape of petals were changed due to an oblique impact, and the ballistic limit was improved when the oblique angle was increased.5-7

Over time, the investigations on FE modeling techniques have caused wide concerns since the developments of available advanced computer codes.With the support from the Aircraft Catastrophic Failure Prevention Program of the Federal Aviation Administration (FAA), the research on generic material models used in high-speed impact simulations has been carried out as part of the uncontained engine failure events.8Furthermore,more research programs have been launched to improve the understanding of metal fragments impact and penetration,which helps to design the reliable fragment barriers in case of rotor failures.9-11It has been shown that the sets of parameters can considerably affect the prediction of ballistic performance.In addition,the failure modes of the containment system have been investigated with the assist of simulations. Zhang et al.12,13conducted some ballistic impact tests combined with the numerical simulations, f inding that the global dishing and the local ductile tearing are the main failure modes of two kinds of Ti-6Al-4V casing. Research by Kelly and Johnson11also indicated that the failure of aluminum plates changes from dishing and petaling to plugging as the thickness of the plate increases. Teng and Wierzbicki14presented a numerical failure analysis for an aircraft engine containment panel impacted by a titanium gas turbine engine fragment. Afterwards, the formation of an indentation/gouging channel on the proximal surface of the panel and the growth of a crack on the distal surface were successfully captured.

In the present work,in support of designing a containment structure for the fan blade,the ballistic impact responses of the 2618 aluminum plates were investigated via both experimental and numerical methods.The purpose is to identify and analyze both the concepts and the mechanisms of the failure by impacting the targets with a wedge-shaped projectile, a solid plate projectile and a hollow blade projectile, respectively.For this class of simple targets, changing the projectile form and the oblique angle, rather than increasing the thickness,may be the key to inf luencing the damage in and behind the targets. Therefore, a series of ballistic impact tests were performed launching different Ti-6Al-4V titanium projectiles against the 2618 aluminum alloy plates to investigate the damage formation on the projectiles and the target plates, thus helping to determine the combined effect of projectile forms and oblique angles. In addition, numerical simulations were conducted to gain additional insight into the characteristics of damage generated from the impact. The work can help to obtain a better understanding of the impact responses of the 2618 aluminum alloy plates, and provide guidance for the design of fan blade containment systems.

2. Experimental procedure

In the ballistic impact tests, the 2618 aluminum alloy plates with thicknesses of 22 mm, 28 mm, and 38 mm were used.All the target plates were cut into square plates with a geometry of 550 mm×550 mm and attached to two 25 mm-wide support frames on the two parallel sides, thus leaving a 550 mm×500 mm free target area, as shown in Fig. 1(a). It is worth mentioning that there was no support frame on the top and the bottom edges of the target plates, which would help to avoid the cutting process caused by the sliding Ti-6Al-4V titanium alloy projectile during the impact. To measure the in-plane strain history, eight strain gauges were stacked on the back side of each plate.Meanwhile,the normal def lections of two points on the back side of each target plate were measured by two XGL-VS laser displacement sensors.In addition,a high-speed camera was installed in front of the target to monitor the impact process.The 1.475 kg wedge-shaped projectile, the 0.846 kg solid plate projectile, and the 0.846 kg hollow blade projectile were employed (see in Fig. 1(b)) to determine the combined effect of projectile forms and oblique angles on the impact response.For the purpose of applying the same vertical impact energy, the 1.475 kg wedge-shaped projectiles were launched towards the target with an angle of 35° while the others impacted the target normally. The one stage air gun with a 200 mm caliber used in the ballistic tests can accelerate the projectile to a maximum velocity of 280 m/s, as shown in Fig. 2. The projectile was supported by a polyurethane foam shell in an aluminum sabot and accelerated by the compressive air in the gun barrel. As can be seen,it is very diff icult to control the f lying posture of the noncylindrical projectile during the high-velocity impact experiments.Moreover,both the mass and the strength of the brittle polyurethane foam shell were much smaller and can be neglected compared with the Ti-6Al-4V projectile. Therefore,the foam shell was launched to the target together with the projectile.

Fig. 1 Schematic diagrams of target plate and projectiles.

Fig. 2 Schematic diagram of testing device-pneumatic gun system.

3. Experimental results

In the present work,15 ballistic impact tests were conducted to characterize the ballistic performance of the 2618 aluminum alloy plates and identify the combined effect of projectile forms and oblique angles. Fig. 3 shows the measurement of normal def lections on the back side of the target plates and the def lection-time curves of the 2618 aluminum alloy plates impacted by hollow blade projectiles under the oblique angle of 90°. It should be noted that all the def lections of the 2618 plates are parallel to the through-thickness direction.The testing results are summarized in Table 1,in which the peak def lection denotes the maximum value on each def lection-time curve for point D1. As can be seen, the peak def lections of the 2618 plates impacted by the wedge-shaped projectiles are signif icantly larger than those of the 2618 plates impacted by the solid plate projectiles and the hollow blade projectiles because of the larger impact energy and more serious damage.In addition,as the thickness increases,the peak def lections of the 2618 plates impacted by the wedge-shaped projectiles show no signif icant decrease. However, those of the 2618 plates impacted by the solid plate projectiles and the hollow blade projectiles decrease considerably as the thickness increases. For plates impacted by the solid plate projectiles and the hollow blade projectiles, the increased structural stiffness induced by the increased thickness can also signif icantly affect the peak def lections when the velocities of the projectiles are lower than the critical penetration velocity. However, for plates impacted by wedge-shaped projectiles, the effect of increased structural stiffness is weakened since the velocities of the projectiles are higher than the critical penetration velocity.5

Fig.3 Normal def lections measurement and results of 2618 aluminum alloy plates impacted by hollow blade projectiles under an oblique angle of 90°.

Table 1 Results of ballistic impact tests for 2618 aluminum alloy plates.

3.1. Plates impacted by wedge-shaped projectiles

Fig.4 illustrates the typical damage morphologies of the plates when the target plates were impacted with wedge-shaped projectiles under the oblique angle of 35°.As can be seen,all the plates were severely damaged and penetrated.It should be noticed that the wedge-shaped projectiles were prone to rollover during the impact which may result in secondary damage on the front surface of the target plate. Since the projectile was enwrapped by the foam shell, the detailed process of the contact between the projectile and the target is hard to observe via the high speed camera. However, from the deformation of the projectile and the photos collected by the high-speed camera (Fig. 5), it can be assumed that the edge of the wedge-shaped projectile may have contacted with the target plate f irst during the impact,leading to the obvious bend and warp of the plates.Even signif icant damage was found on the target plates,and the reduced mass of the Ti-6Al-4V wedge-shaped projectile was only 0.004 kg,which can be attributed to the obvious gap of the yield strength between the Ti-6Al-4V and the 2618 aluminum alloy.In the following sections, combined with numerical simulation results,the detailed impact and damage process will be discussed.

The damage morphologies suggest that there are two kinds of impact damage on the 2618 aluminum alloy plates; i.e. the global deformation and the local damage, as shown in Fig. 4(b) and (c). Seen from the characteristics of the damage morphologies, the global deformation mainly involves bending and stretching in most regions of the plate while the local damage is mainly characterized by an obvious dent on the front surface and a crack or a perforation induced by bidirectional stretching on the back of the plate. In brief, the damage of the 2618 aluminum alloy plate mainly involves the perforation resulted from global bending of the plane and the dent induced by in-plane cutting. Therefore, it is believed that the kinetic energy of the projectile is mainly absorbed by these two processes during the impact events.

3.2. Plates impacted by solid plate projectiles and hollow blade projectiles

Fig. 4 Typical damage morphologies of 2618 aluminum alloy plates impacted by Ti-6Al-4V wedge-shaped projectile.

Fig. 5 Typical high-speed photographs (tests 1-2) of 2618 aluminum alloy plate perforated by wedge-shaped projectiles under oblique angle of 35°.

Fig. 6 shows the damage morphologies of the 2618 aluminum alloy plates when the target plates were impacted with solid plate projectiles and hollow blade projectiles under an oblique angle of 90°. It can be seen that none of the target plates impacted by solid plate projectiles and hollow blade projectiles were perforated even when the same vertical energy was applied. For plates impacted by solid plate projectiles, each 22 mm 2618 aluminum alloy plate was damaged with not only a smooth dent on the front surface but also an obvious crack on the back (Fig. 6(a)-(b)).Results also show that the global bending deformation and the cracks induced by the bidirectional stretching in 28 mm 2618 aluminum alloy plates were weakened compared with those of 22 mm 2618 aluminum alloy plates (Fig. 6(c)). Furthermore, the 38 mm 2618 aluminum alloy plate was damaged with the shallowest dent on the front surface, and no obvious crack on the back was found as shown in Fig. 6(d). Similarly, the 22 mm and 28 mm plates (Fig. 6(e)-(g))impacted by hollow blade projectiles were also damaged with a dent and a crack while each 38 mm plate (Fig. 6(h)) was only damaged with the shallowest dent. It is worth mentioning that the cracks on the back side tended to be generated at different locations when the target plates were impacted by solid plate projectiles and hollow blade projectiles. The details and reasons will be discussed with a combination of the numerical simulation analysis in the following section.

4. Numerical modeling and validation

4.1. Finite-element models

Because of the excellent ability of nonlinear analysis, all the numerical models in this study were developed with the commercial software ABAQUS. Three different FE models were developed to investigate the detailed impact performance of the 2618 aluminum alloy plates,while several modeling parameters, such as contact options, damage evolution, were examined. To f ind an optimized mesh for stability, accuracy, and eff iciency of the impact analysis, the mesh pattern and size dependency were examined f irst. It is important to mention that one quarter of the target plate models and the projectile were not chosen; instead, they were caused by the oblique angle. These models were cost effective 3D models, where a nearly perfect impact with an oblique projectile orientation can be modeled successfully.Both the target plate and the projectile were established with the eight-node reduced integrated hexagonal solid elements (C3D8R).

Fig. 6 Typical damage morphologies of the target plates.

The in-plane mesh pattern was kept the same for all the models, and the central part of each target plate was divided into three different regions where the mesh density gradually coarsens from the inner region (the potential impact region)to the outer region. Mesh transitions between these regions were good enough to prevent stress wave ref lections from the boundary of the regions. Theoretically, simply ref ining the mesh can not necessarily improve the accuracy since the material model parameters were calibrated for a specif ic mesh size and the mode of failure changes during the simulation. Furthermore, there was no clear theoretical guideline on the required mesh density for the range of impact events covered in this study. Considering the softening effects and the mesh dependent failure algorithms, the only reasonable methodology to f ind the most appropriate mesh size was trial,the results of which are compared against a controlled test data. Subsequently, it is possible to arrive at an optimum after experimenting with different meshings and draw some guidelines for that particular case.Thus,the in-plane mesh for each target plate was modeled with one mesh density while many more had been experimented during the calibration runs. For mesh patterns along the thickness direction, the number of through thickness elements was chosen to be 22 for the 22 mm target plate as a baseline since the implementation of the reduced integration solid elements required at least three elements through the thickness to be able to capture accurate bending deformation modes.Correspondingly,the 28 mm plate meshed with 28 elements while the 38 mm plate meshed with 38 elements through the thickness,respectively.A viscous based stabilization method was used during the simulations to prevent hourglass modes of the reduced integration elements. Contact behavior between the projectile and the target plate was attained by using a penalty based single surface type contact algorithm which adopted a nodal constraint formulation with an element erosion scheme.

4.2. Material models

A more sophisticated material model was necessary for the targets to simulate ballistic impact responses, thus the Johnson-Cook (J-C) constitutive model and the failure model were employed to describe the responses of the 2618 aluminum and the Ti-6Al-4V titanium alloy. The J-C constitutive model is a strain-rated and temperature-dependent (adiabatic assumption)visco-plastic model,and the formulation is empirically based. The J-C constitutive model represents the f low stress with an equation of the form15

where σ and ε are the effective stress and plastic strain, ˙ε*is the normalized effective plastic strain rate, n denotes the work hardening exponent, and A, B, C and m are the constants of the material where their physical meanings are described in previous work.16Quantity T* is def ined as

where Tmis the melting temperature, and Tris the reference temperature typically taken as 293 K.

Damage in the J-C material model is a special failure criterion widely used in simulations. Theoretically, the J-C failure model should consider the stress triaxiality, the strain rate,and the temperature, and the damage in the J-C constitutive model is derived from the following cumulative damage law17

where Δε is the increment of the effective plastic strain during an increment in loading,D=0 is assumed to be the initial status,and failure occurs when the failure parameter D exceeds 1.The strain at the fracture can be def ined as17

where σ*denotes the mean stress normalized by the effective stress often referred to as stress triaxiality, and ˙ε*is the normalized effective plastic strain rate. Parameters D1, D2, D3,D4, and D5are the fracture constants of the material. Both the failure strain and the accumulation of damage are functions of stress triaxiality, strain rate, and temperature. Failing elements are then removed from the FE model with an element erosion algorithm.

4.3. Determination of material model parameters

The J-C constitutive parameters, as well as the failure parameters, were determined based on the results from the quasi-static and the dynamic experiments, respectively. The quasi-static experiments were performed using the CSS44100 electronic universal testing machine with a maximum load capacity of 100 k N. The split Hopkinson pressure bar and the tensile bar were also employed on the dynamic compressive and tensile experiments at different strain rates, respectively.

To determine the fracture behaviors under different stress triaxialities, the cylinder specimens with different notch radii and pure torsion specimens were employed. Fig. 7(a) shows the specimens with different notch radii for the tension experiments,where r is the radius of the minimum cross-section,and R is the radius of the circumferential notch. Theoretically, the variations of the strain at the circumferential area were not the same when the same loading speed was applied, as shown in Fig. 7(b). Thus, the corresponding FE models based on the acquired J-C constitutive parameters were performed to revise the loading speed for each kind of specimen, which was supported to avoid the strain rate effect. The strain rate of the quasi-static experiment was set to 10-3/s, thus the loading speeds of the specimens with 1.5 mm,2.0 mm,2.5 mm notches were set to 0.00135 mm/s, 0.0015 mm/s, 0.0017 mm/s,respectively.

In previous works, the equivalent failure strain is always calculated by the Bridgman's method18

where d0and d denote the initial and the f inal diameters of specimens, respectively. However, the accuracy of the equivalent failure strain was always inf luenced by many factors such as necking and uncertainty in the measure since the deformation of the notch area was complicated. Fig. 7(c) illustrates the strain distribution of the 2618 aluminum alloy specimens with 1.5 mm notches in the tensile tests using the FE model.Results indicate that the largest strain concentrated on the surface of the circumferential area, thus the equivalent failure strain was revised by introducing the maximum strain on the surface before the appearance of the fracture. Considering the practical application of damage evolution in FE models,the equivalent failure strain can depict the local failure of the structures established with a large number of small elements.In fact, the stress triaxiality was not constant during the tensile deformation.19,20Consequently, the stress triaxialities were revised by using the FE models and the captured images.Fig. 8(a) sketches the relationships between the stress triaxiality and the strain for the 2618 aluminum alloy specimens with three kinds of notches. Results indicate the stress triaxiality increases to a stable value accompanying the plastic deformation. The stress triaxialities of the tensile specimens with notches can be revised by replacing Bridgman's results with the stable stress triaxialities calculated by the FE model. In addition,the stress triaxiality of the smooth specimen can also be revised using the captured images,as illustrated in Fig.8(b).Since the results from the tensile experiments showed that the increase of stress triaxiality was almost uniform after the necking happened, the revised stress triaxiality of the smooth specimen can be calculated by

where t1is the time spent from the initial state to the start of the necking, t2is the time spent from the initial state to the appearance of the fracture, R denote the radius of notch, 2a is the real-time diameters of specimens.By calculating the pixels, Eq. (6) can be replaced with

Fig.7 Specimens with different notch radii for quasi-static tensile experiments,determination of loading speeds and strain distribution simulated by FE model.

Fig. 8 Correction methods of stress triaxialites.

where N1and N2denote the number of pixels corresponding to t0and t1,respectively. Since the maximum strain concentrated on the surface of the circumferential area as mentioned above,the Digital Image Correlation (DIC) method was applied to measure the strain f ield, and the maximum strain in the strain f ield calculated before the fracture can be considered as the failure strain, as shown in Fig. 9. Dynamic tensile tests were conducted to obtain parameter D4of the J-C failure model.It should be noted that the fracture induced by the multiple stress wave needed to be avoided to ensure the accuracy of the strain at the fracture. Thus, the pulse width of the stress wave was improved in the dynamic experiments to guarantee the fracture induced by the single stress wave, which can be validated by checking the high-speed video.Moreover,parameter D5of the J-C failure model can be determined based on the results of the quasi-static tensile tests at the temperatures of 373 K, 473 K, and 573 K, respectively.

Fig. 10(a)-(b) show the true stress versus true strain curves of the 2618 aluminum alloy and the Ti-6Al-4V titanium alloy tested at different strain rates. In addition, the f itted curves are added for comparison.The parameters of the J-C constitutive model were listed in Table 2,and the reference strain rates for both materials were set as 0.001. Fig. 10(c)-(h) show the relationships between the failure strain,the revised stress triaxialities, the strain rates, and the temperatures of the 2618 aluminum alloy and the Ti-6Al-4V titanium alloy.The Bridgman equivalent failure strains were added for comparison. Finally,the revised J-C failure parameters of the 2618 aluminum alloy and the Ti-6Al-4V titanium alloy can be obtained by f itting the results, as listed in Table 2.

4.4. Simulation results

Fig. 9 Strain f ields calculated using DIC method and micro speckles.

Fig. 10 Statistical interpretation of test results of 2618 aluminum alloy and Ti-6Al-4V titanium alloy.

By adopting the user subroutine VUMAT with J-C failure criteria, the impact responses of the Ti-6Al-4V titanium alloy projectile and the 2618 aluminum alloy plate were examined.It should be noted that Hillerborg's stress-displacement relationship at the beginning of the damage generation was implemented into the user subroutine VUMAT, which can help to reduce the mesh dependence. The responses are illustrated by demonstrating the in-plane strain histories, where they can be compared to the ballistic test data. The perforation of the 2618 aluminum alloy target impacted by the wedge-shaped projectile under an oblique angle of 35° is illustrated in Fig. 11(a), and the comparison between the measurements and computations is shown in Fig.12(a).As can be seen,a cutting type of deformation mode was observed in the front surface (impact surface) of the target plate, and the 2618aluminum alloy failed mostly in shear. Meanwhile, there are signif icant global bendings in the target plate, resulting in tensile failures in the backside of the 2618 aluminum alloy.

Table 2 Parameters of J-C constitutive and failure model for 2618 Aluminum alloy and Ti-6Al-4V titanium alloy.

Fig. 11 Comparison of damage morphologies between the experiments and simulations.

Fig. 12 Comparison of in-plane strain histories (strain gauge 2 and strain gauge 4) between the measurements and computations.

For plates impacted by solid plate projectiles and hollow blade projectiles, simulations show no perforations of the targets,which is the same as the experiments.The comparison of experimental and numerical time series for the 2618 aluminum alloy plate impacted by the hollow blade projectile under an oblique angle of 90° is illustrated in Fig. 13. As is shown, the attitude of the hollow blade projectile in the impact process corresponds well to the results from the high-speed photography.Since it is diff icult to observe the target response from the high-speed photography due to the foam, the comparison of the failure mode, the dents formation, the perforation shape of the 2618 aluminum alloy plates, and the damage of the Ti-6Al-4V titanium alloy projectiles in the simulations are provided.Fig.11(b)shows the damage of the solid plate projectile and the hollow blade projectile under an oblique angle of 90°,which corresponds well to the test results. In addition, as shown in Fig. 11(c), the damage morphology and the size of the target plates are also comparatively coincident with the experiments. Moreover, the cracks on the back of the target plates are predicted well, and both the experiments and the simulations indicate that the possible initiating origin and the propagation direction of the cracks for the plates impacted by the solid plate projectile and the hollow blade projectile are different.To verify the accuracy of the model,the comparisons between the measured strain and the output strain in the test are shown in Fig.12(b)and(c),and it can be seen that not only the levels but the tendencies of the strain histories from the experiments and the simulations show good agreement.In conclusion, the failure mode, the dent formation, the perforation shape,the in-plane strain histories of the 2618 aluminum alloy plates,and the damage of the Ti-6Al-4V titanium alloy projectiles in the simulations all correspond well to the test results,which can be attributed to the revised J-C failure parameters.

Based on the results from both the experiments and the simulations, the reasons why the impact with the same vertical energy was not able to keep the same damage are mainly considered to be the projectile attitude and the failure mode. For the 2618 aluminum alloy plate impacted by the wedge-shaped projectile under the oblique angle of 35°, the perforation appears in company with the rollover of the projectile. Generally,the target plate will suffer more impact energy. However,it should be noted that the statistics of energy absorption show an interesting trend. Table 3 lists the energy absorption of the 22 mm plates under different projectile forms and obliquities.As can be seen, the energy absorption of the plates impacted by the wedge-shaped projectile is less than that of the plates impacted by the solid plate projectile and the hollow blade projectile, although the plates impacted by wedge-shaped projectile suffer more damage. Fig. 14 illustrates the deviation of the stress triaxiality for three representative f inite elements at the failure zone.It is shown that the type of failure and deformation drastically changes as the projectile form and the obliquity changes, and the failure fully depends on the multi-axial state of the stress. Specif ically, stretching and bending types of deformation patterns change into shearing and spalling types of deformation when the projectile form and the obliquity are changed from the wedge-shaped projectile under the oblique angle of 35°to the solid plate projectile and the hollow blade projectile under the oblique angle of 90°. Therefore, the deformation of the 2618 plate impacted by the wedge-shaped projectile is less than that of the plates impacted by the solid plate projectile and the hollow blade projectile, resulting in the differences in energy absorption.

Fig. 13 Comparison of experimental and numerical time series for the 2618 aluminum alloy plate impacted by hollow blade projectile under oblique angle of 90°.

Table 3 Energy absorption of the 22 mm plates.

It is found that the cracks on the back of the 2618 plates locate at different positions when the target plates were impacted with the solid plate projectile and the hollow blade projectile under the oblique angle of 90°, as shown in Fig. 11(c). Consequently, it is necessary to combine the experiments with the simulations to investigate the deformation process,based on the consistency between the simulations and the available experimental measurements. Fig. 11(c) shows the plastic strain distributions which can be considered as the reason why the crack on the back does not tend to keep the same location during the experiment of various projectile forms. To be specif ic, the solid plate projectile and the hollow blade projectile will deform in different forms as shown in Fig. 11(b),resulting in the different impact responses of the 2618 plate.For the hollow blade projectile, the deformation concentrates on the top and the bottom edges, and the deformation near the central part of the hollow blade projectile is less than that near the edges, leading to the larger local bending and plastic deformation of the central part than that of the other regions.However,the difference between the central part and the edges of the solid plate projectile is smaller, particularly for the deformation region. For this reason, the most serious local bending of the plate impacted by the solid plate projectile concentrates on the region near the edge of the projectile, leading to the movement of the maximum plastic strain location from the center to both sides.In addition,due to the existence of an undeformed area on the 2618 plate caused by the hollow area of the projectile, the front of hollow blade projectile will stretch the plates during the impact, also contributing to the plastic strain localization in the central region.

Fig. 14 Deviation of stress triaxiality for three representative f inite elements at the failure zone.

5. Conclusions

The ballistic impact tests were conducted to characterize the ballistic performance of the 2618 aluminum alloy plates, and to identify the combined effect of projectile forms and oblique angles. In addition, simulations were carried out using ABAQUS as an explicit dynamics FE code incorporating the J-C constitutive model and failure parameters. Conclusions based on the tests and the simulations can be drawn as follows:

(1) A new experimental and numerical method was carried out to determine the Johnson-Cook(J-C)failure parameters of the 2618 aluminum alloy and the Ti-6Al-4V titanium alloy. The comparisons between the ballistic impact tests and the simulations were also made.Results show the failure mode, the dent formation, the perforation shape of the 2618 aluminum alloy plates, and the damage of the Ti-6Al-4V titanium alloy projectiles in the simulations all correspond well to the experiments,thus proving the accuracy of the J-C failure parameters.The method to obtain the revised J-C failure parameters is worth reference.

(2) Both the experiments and the simulations indicate that the deformation mode tends to change under different impact conditions. It is observed that changing the wedge-shaped projectile to a solid plate projectile and a hollow blade causes the change of deformation patterns from stretching and bending to shearing and spalling. Consequently, the energy absorption is also inf luenced by the combined actions of projectile forms and obliquities during the impact.

(3) The cracks on the back of the 2618 plates impacted by the solid plate projectile and the hollow blade projectile under the oblique angle of 90°tend to locate at different positions, and the simulation results show an excellent correlation. It can be considered as the differences of most serious local bending locations.Furthermore,since there always exists an undeformed area in the impact zone when the target plate is impacted by the hollow blade projectile, the target plate will be stretched by the front of the hollow blade projectile and thus lead to the local plastic strain concentration in the center location of the impact zone on the back of the target plate.

Acknowledgements

The writers would like to acknowledge Xiang Wang of Jiangsu TieMao Glass Co., LTD in China. This work was performed under the f inancial support from the National Natural Science Foundation of China(No.11772268,11522220,11627901 and 11527803).