Assessment of the ballistic response of honeycomb sandwich structures subjected to offset and normal impact

Nikhil Khaire , Gaurav Tiwari , Vivek Patel , M.A.Iqal

a Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi,110016, India

b Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur, 440026, India

c School of Mechanical Engineering, Dr.Vishwanath Karad MIT World Peace University, Pune, 411038, India

d Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India

Keywords:Honeycomb sandwich structure Offset impact Energy dissipation characteristic Deformation and failure mode Geometry effect

ABSTRACT In the present study, experimental and numerical investigations were carried out to examine the behavior of sandwich panels with honeycomb cores.The high velocity impact tests were carried out using a compressed air gun.A sharp conical nosed projectile was impacted normally and with some offset distance (20 mm and 40 mm).The deformation, failure mode and energy dissipation characteristics were obtained for both kinds of loading.Moreover, the explicit solver was run in Abaqus to create the finite element model.The numerically obtained test results were compared with the experimental to check the accuracy of the modelling.The numerical result was further employed to obtain strain energy dissipation in each element by externally running user-defined code in Abaqus.Furthermore, the influence of inscribe circle diameter and cell wall and face sheet thickness on the energy dissipation,deformation and failure mode was examined.The result found that ballistic resistance and deformation were higher against offset impact compared to the normal impact loading.Sandwich panel impacted at 40 mm offset distance required 3 m/s and 1.9 m/s more velocity than 0 and 20 mm offset distance.Also,increasing the face sheet and wall thickness had a positive impact on the ballistic resistance in terms of a higher ballistic limit and energy absorption.However, inscribe circle diameter had a negative influence on the ballistic resistance.Also, the geometrical parameters of the sandwich structure had a significant influence on the energy dissipation in the different deformation directions.The energy dissipation in plastic work was highest for circumferential direction, regardless of impact condition followed by tangential, radial and axial directions.

1.Introduction

Due to the integrity of high stiffness and strength with higher absorbed energy and moderately lightweight along with better thermal property and acoustic solution, sandwich panels are assessed in the aerospace industry for protection from debris and foreign object, military application and the automobile sector.Especially the sandwich panel with metallic honeycomb core has been extensively used in the vehicle and aerospace industry for protection purposes.These structures are frequently subjected to dynamic loadings over their service lives, such as projectile or debris impact and blast impact [1,2].

Over the past years, a lot of research has been conducted to examine the dynamic behavior of honeycomb core against high velocity impact loading [3-30].Kolopp et al.[3] examined the perforation resistance of the honeycomb core sandwich panels with aluminium and dry fabric face sheet.Authors have suggested that the choice of the front skin is foremost important to have high impact resistance and good absorbed energy.Arslan et al.[4]examined the ballistic performance of the sandwich structure with honeycomb core and functionally graded face sheet (aluminium and alumina) against high velocity impact.The study showed that using graded face sheets in the form of a ceramic fraction enhanced the impact resistance, damage mechanism and absorbed energy capability.Liaghat et al.[5] developed an analytical model to calculate the ballistic limit velocity against cylindrical nosed projectiles.This model was developed assuming the projectile's whole kinetic energy was dispersed in shearing the plug,crushing and folding the honeycomb and tearing the cell walls.Feli et al.[6]developed the analytical model by combining the equation of motion with the energy balance equation and the residual velocity,ballistic velocity and absorbed energy were obtained.Further,Alavi Nia et al.[7] performed several tests to examine how a cylindrical steel projectile affected the ballistic resistance of aluminium honeycomb panels.

Rahimijonoush A and Bayat M [8] conducted experimental and numerical studies on sandwich structure with titanium factsheet and aluminum honeycomb core.The study revealed that the impact velocity affects the failure mode of the face sheet.Tiwari et al.[9]and Khaire et al.[10] performed the experimental and numerical study for curve sandwich structure with the honeycomb core and proposed that the stress state was revealed to be an important factor for defining failure mode.Zang et al.[11] performed the comparative study for metallic sandwich plates with origami and honeycomb cores.Study proposed that irrespective of cell design their ballistic resistance was similar by comparing their relative densities.Want et al.[12]simulated the impact behavior of a curved sandwich with a coaxial and concentric honeycomb,and proposed that a curved sandwich with a concentric honeycomb performed better than a coaxial curved structure.

Also, few studies mentioned the effect of the geometric parameter of aluminium honeycomb sandwich on the absorption of energy and ballistic resistance.Sun et al.[15] studied face sheet thickness and found that with an increase of thickness,absorption of impact energy increased however,the core thickness of the sheet seemed not to affect the absorbed energy.Moreover, increasing inscribe circle diameter and wall thickness reduces the absorbed energy.Zhang et al.[16]suggested that absorbed energy was higher for the impact loading compared to quasi-static loading.Also, the face sheet thickness has a considerably more influence than the core density, owing to the honeycomb's low density.Similarly,Khaire et al.[17]revealed that the involvement of core geometries on thicker skin sandwich panels was minimal; however, cell wall thickness and inscribe circle diameter had a significant impact on thinner skin sandwich panels.Buitrago et al.[18]suggested that the face sheet was the most essential factor in the absorption of energy.The top face sheet(46%)absorbed the most of the energy while the minimum by the core (13%) and remaining by the back face sheet(41%).

Moreover,some state of arts is available on the influence of the oblique impact on sandwich structure performance [21-26].Zhou et al.[21]examined the response of sandwich structure impacted at an angle of 45°-90°for the different nosed projectile.From the study, it was revealed that the projectile nosed and angle of obliquity has a significant influence on sandwich performance.Similarly, Chen et al.[22] and Zhou et al.[23] conducted an experimental investigation on the composite sandwich panel to find out the effect of the projectile impact angle on the ballistic performance.The impact angle had a significant impact on the ballistic performance, according to both studies.Ivanez et al.[24]explored the damage behavior of the honeycomb core sandwich structure against oblique impact at different velocities and angles.They suggested that with the increase in the impact angle, the damaged area was found to be decreased.Chen et al.[25] performed the multi-objective optimization study for the honeycomb sandwich structure at an impact angle of 45°and it was revealed that the absorbed energy of the optimized sandwich panel increased by 7.9% for 45°angle of impact and 12.4% for normal impact.

The above literature concluded that many experimental studies had been carried out for sandwich panels against high velocity impact.Also, most of the literature focused on the normal and oblique impact conditions however,the study on offset impact has not been reported in the literature.Moreover,the detailed absorbed energy in plastic deformation against different stretching directions (tangential, radial, axial and circumferential) is need to study for offset impact.Also, the effect of sandwich geometrical parameters on the absorbed energy in plastic works is rarely explored in the literature.Therefore,in this study,the deformation mechanism and absorption of energy during the plastic deformation against normal and offset impact were investigated.The experimentation was performed using a compressed air gun followed by finite element modelling in Abaqus/explicit solver.The conical nosed projectile was impacted at different velocities and offset distances.Furthermore, the energy dissipation in plastic works in tangential,radial,axial and circumferential directions was obtained by employing user-defined python code in Abaqus.Furthermore, the influence of thickness (cell wall and face sheet)and inscribe circle diameter was examined on energy dissipation characteristics.

2.Sample preparation and experimental set-up

Sandwich structures were composed of an aluminium alloy face sheet(1100-H12)and the aluminium alloy honeycomb core(3003- H18), see Fig.1.The circular face sheet diameter of 220 mm and thickness of 1 mm were used as the front and rear face sheets.The honeycomb core of 20 mm core thickness,0.05 mm thickness of cell wall and 3.2 mm inscribe circle diameter was used.The face sheet and honeycomb cell were joined together using SA80 epoxy resins.The conical nosed projectile (DCN = 19 mm, MCN = 52.5 gm and LCN = 50.8 mm) was adopted for high velocity impact.The projectile was made up of EN 24 steel subjected to a strain hardening process to improve the hardness up to 52 Rockwell to improve resistance to plastic deformation.

High velocity impact experimentation was performed on a compressed air gun at different velocities,see Fig.2.The complete experimental set-up consists compressed air reservoir, infrared sensors, clamped frame, ball actuator valve and data recorder.The test was carried out at velocities ranging from 40 to 145 m/s by varying the launching pressure and projectile length in the launcher barrel.A ball actuator valve was used as a trigger to open and close the barrel's airflow.The infrared sensors were used to measure the velocity during the impact.The sensors consist two sets,each with two receivers and two transducers, to measure the initial impact velocity as well as residual velocity after perforation.The projectile collector box filled with cotton was designed and placed back of the targets to collect projectiles and ejected fragments after the perforation.For ease in comparison labelling system was adopted and detailed incorporated in Table 1.For example,SF1.0-SH20-ST0.05-SL3.2 where SF-Face sheet thickness,SL-inscribe circle diameter, SH-core thickness, ST-cell wall thickness.

3.Finite element modelling

The 3D numerical model was developed in the Abaqus/explicit solver[27]to determine the ballistic resistance,failure mechanisms and energy dissipation characteristics against normal and offset impact loading,see Fig.3.The projectile was modelled as analytical rigid in the simulation, whereas the honeycomb core and face sheets were considered as a deformable body.Moreover, the adhesive layer was employed to examine the debonding phenomenon that occurred in high velocity impact.The face sheets and adhesive layers were modelled as a solid layer and meshed with the 8-noded solid element with reduced integration [28-31], see Fig.4.The honeycomb core was modelled as a surface element and meshed with the 4-noded shell element with reduced integration.For better accuracy and to capture proper failure mode, the projectile contact region with sandwich structure meshed finer and the noncontact zone was meshed coarser to save computational efficiency.The mesh size at the contact area between the face sheet and adhesive layers was used as 0.16 mm × 0.16 mm × 0.16 mm with an aspect ratio close to unity.

Fig.1.Specimens: (a) Flat sandwich panel; (b) Projectile with conical shape.

Fig.2.Schematic arrangement of the experimental test.

Moreover, the number of elements 4, 6, 9 and 12 were used across the thickness of the face sheet of thickness 0.7,1.0,1.5 and 2.0 mm, respectively and for the adhesive 2 layers across the thickness of 0.2 mm.This mesh size was selected from the mesh sensitivity study carried out by G.Tiwari et al.[32]for plate against high impact.The mesh sensitivity was examined for honeycomb through subsequent analysis by changing the mesh size from 0.15to 0.8 mm.The mesh size was considered by calculating the residual velocity at 125.6 m/s.The result of the convergence study was found that for the mesh sizes 0.2 and 0.15 mm, the change in residual velocity value was insignificant.As a result, the mesh size 0.2 mm × 0.2 mm was taken for the contact zone, whereas 2 mm×2 mm was used for the non-contact zone.Further,explicit surface-to-surface contact was employed between the conical projectile and sub-parts of the sandwich.The external projectile face used as the master surface, while the node base slave surface was considered for sandwich subparts at the contact zone.Also,to capture the debonding phenomenon, tie constraint was used between the sandwich subparts.The friction coefficient between sandwich structure subparts and projectiles was also used to consider the tangential interaction using a static-kinetic exponential decay algorithm with kinematic and static friction as 0.17 and 0.27[15].Also,an enhanced hourglass technique was used in the FE modelling to avoid hour glassing due to reduced integration.The sandwich structure was fixed in all six directions by providing encastered (U1, U2, U3, UR1, UR2, and UR3) conditions to the circumferential edges.

Table 1Nomenclature used for different terminologies used for structure.

Fig.3.Projectile impact: (a) Normal impact; (b) Offset impact.

Fig.4.Detail 3D FE of sandwich structure.

4.Constitutive model

The constitutive material model was formulated based on continuum damage mechanics and viscoplasticity, as suggested by Johnson and Cook[33].The model describes the relationship of von misses yield stress criterion with thermal softening due to adiabatic heating, isotropic strain hardening, linear thermo elasticity, strain rate hardening and associate flow rule.The model for yield stress criteria is defined as follows.

where T, T0and Tmeltare current temperature, transition temperature and melting temperature,respectively.In this study,the effect of heat was not considered.Therefore, the parameter m was considered to be zero for the honeycomb core and a similar approach was used by Sun.et al.[15].

4.1.Fracture model

In order to simulate the damage, two kinds of fracture models were employed for honeycomb core, adhesive and face sheet.Ductile damage was used for adhesive and honeycomb core,whereas the Johnson-Cook fracture model opted for face sheet.Both the fracture model is defined as follow.

4.1.1.Johnson cook fracture model

Johnson and Cook[34]have incorporated the effect of strain rate and strain path to modify Hancock and Mackenzie's [35] fracture model and it is defined as follows:

4.1.2.Ductile damage model

It was employed in order to examine the failure of an adhesive layer and honeycomb core.The ductile damage model is a phenomenological model for forecasting the beginning of damage due to nucleation, voids formation, growth and amalgamation.It begins to occur when the following requirement is met,

where ωD-damage state variable(increases in response to plastic deformation).In the present study,shear failure strain criteria were used as failure criteria for damage evolution and the effect of temperature and strain rate were neglected [15].The shear failure strain values of 0.02 and 0.4 were used for the adhesive and the honeycomb core, respectively [15].Furthermore, the conical projectile was classified as a rigid analytical body.All the parameters used for sandwich sub-parts have been incorporated in Table 2.

5.Result and discussion

5.1.Residual and ballistic limit

To predict the accuracy of the finite element model,the obtained residual velocity and ballistic limit through experiments were compared for the sandwich structure at normal and offset impact against conical projectile.The variation in offset distance was taken as 0,20 and 40 mm.Table 3 depicts the obtained result of residual velocity against normal and offset impact, that further signified graphically in Fig.5.It was found that the created FE model accurately captured the residual value obtained in experimental tests with the maximum error of 8.72%for normal impact and 9.3%and 8.9%for offset impact.It was also discovered that the difference in the velocity drop at higher velocity was very low and almost the same in both impact loading.However, the difference in velocity drops between normal impact (0 mm) and offset impact (20 mm and 40 mm) gradually increased as the initial impact velocitydecreased.It was concluded that the velocity drop in case of offset impact was more compared to the normal impact.Furthermore,the target's ballistic limits were obtained for both the impact loadings,as shown in Table 4 and Fig.6.The ballistic limit obtained through simulation was over-predicted in both loadings compared to the experimentally obtained results.The difference in experimental and numerical ballistic values for normal impact was 2.5%.For offset distances of 20 mm and 40 mm,the respective difference was 2.3% and 2.6%.Further, Fig.6 portrays that the sandwich structure offered more ballistic resistance against offset impact than the normal impact.Sandwich panel impacted at 40 mm offset distance required 3 and 2.9 m/s, and 1.9 and 2 m/s more velocity experimentally and numerically than 0 and 20 mm offset distance.It was because near the neighbourhood of the edges of the sandwich panel,local bending rigidity and stiffness are higher than the centre point.As the centre point of impact was at the furthest distance from the sandwich structure boundary, the stiffness increased as the distance between the impact point and boundary decreased[37-39].

Table 2Material parameters of metallic sandwich structure.

Table 3Experimentally and numerically obtained residual velocity.

5.2.Visualization of penetration mode

The penetration and perforation modes for sandwich panels in both loading conditions were determined using experiments and numerical modelling.Figs.7-9 show the damage and failure mode of the sandwich structure of the front and rear face sheet of thickness 1 mm and inscribe circle diameter of 3.2 mm against normal and offset impact.It can be revealed that irrespective of impact loading, the failure process of sandwich structures was divided into three-phase that includes front face sheet perforation(dishing and damage), aluminium honeycomb core perforation(damage and crushing)and rear face sheet perforation(dishing and damage).

Phase 1: The front face sheet generally failed in the tensile damage with localised dishing.The penetrated front face sheet forms the petals due to the tensile stretching.Further, due to the dishing of the front sheet, progressive plastic deformation of the aluminium honeycomb core close to the front face sheet occurred and a slight buckle at the top of the honeycomb core happened,whereas the rear face sheet remained unaffected.Phase 2: In this phase,the honeycomb core absorbed part of the impact energy due to the combined effect ofcompression and crushing of the cell wall.The honeycomb core was deformed due to tensile and shear stress when the compressive strain was higher than the maximum failure strain.During the perforation, side crushing of the cell wall occurred as a projectile,along with petals of the front sheet,pushed the cell wall sideways.Due to this,the hole formed in the core was trapezoidal (the upper hole's diameter was larger than the lower hole).Phase 3: Similar to the front sheet, the rear sheet failed in dishing due to tensile or shear stretching.Further, the rear face sheet also failed in petalling due to tensile stretching.Additionally,the debonding of the core cell wall and rear face sheet occurred due to extensive contact force.

Fig.5.Residual velocity for different impact velocity:(a)0 mm;(b)20 mm;(c)40 mm.

Table 4Experimental and numerically obtained ballistic limit.

Fig.6.Ballistic limit for the different normal and offset impact.

Fig.10 shows the experimental failure mode of the sandwich panel impacted at 0, 20, and 40 mm and it was observed that the rear face sheet underwent large deformation regardless of the type of impact loading.It happened because the rear face sheet experienced more contact force than the core and front face sheet.Figs.11 and 12 show comparative results of failure modes and found that the all-failure pattern was similar in experimental and numerical analysis.Numerical results precisely captured the ductile hole, petals formation, core crushing and buckling in both the impact cases.Also, from Figs.13 and 14, it was found that the number of petals formed was found to be independent of the impact distance.Four petals on the front and rear face-sheet were observed experimentally and numerically against normal and offset impacts.In addition, the petal thinning happened in both impact cases from tip to root.

Similarly, Fig.15 illustrates the rear face sheet's transverse deformation at a velocity close to the ballistic limit.Further,it was concluded that the rear face sheet deformation of the sandwich decreased with the increase in the offset distance and it happened since near the boundary edge stiffness was higher compared to the centre [37-39].Compared to 0 mm, the deformation of the rear face sheet was decreased by 5.8%and 12.5%for 20 mm and 40 mm offset distances,respectively.

5.3.Absorption of energy during plastic deformation

The current numerical modelling for the sandwich panel is required to provide a careful examination of the absorbed energy against projectile impact.The projectile's kinetic energy, assumed to be absorbed as strain energy (internal energy) by the sandwich panels, can be considered the contribution of local and global deformations.The local absorbed energy was regarded as the absorbed energy in the localize failure mechanism such as petaling,plugging and shear, whereas the global energy involves the absorbed energy in global dishing [36,40,41].

In present investigation, the user-defined algorithm written in python code for the sandwich panel was used to calculate the amount of absorption of strain energy.The strain energy was estimated at an elemental level in three tangential and normal directions by multiplying the stress,strain and element volume,see Fig.16.The absorbed energy in the axial (Eaxial), radial (Eradial),tangential(Etangential)and circumferential(Ecircumferential)directions make up total strain energy.The amount of absorbed energy in various directions was calculated as follows:

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Absorbed energyplastic=Eradial＋Eaxial＋Ecircumferntial

Fig.8.Process of perforation for 20 mm offset impact during the projectile impacted at velocity 121.6 m/s.

Fig.9.Process of perforation for 40 mm offset impact during the projectile impacted at velocity 118.3 m/s.

Fig.17 portrays the energy dissipation in a different direction for the sandwich panel to find the effect of offset impact.The energy dissipation was observed to accelerate as the offset distance was increased and it was higher at 40 mm, followed by 20 and 0 mm offset distances.

For a 40 mm offset distance,compared to 0 mm and 20 mm,the dissipation of energy in the radial direction was 23.3% and 9.42%higher,respectively.For the axial direction,it was 17.33%and 11.11%more, for the circumferential direction, the respective increment was 26.30% and 13.53% and for the tangential direction, the corresponding increment was 15.72% and 10.72%, respectively.Moreover,in the circumferential direction dissipated energy was higher irrespective of the offset distance.As the crack propagation in the radial and circumferential direction is mainly caused due to circumferential stresses, hence the energy absorption was higher correspondingly [32].The dissipations of energy for all sandwich panel component are depicted in Fig.18.It can be seen that irrespective of offset distance,the energy dissipation was highest in all four directions for the rear face sheet and subsequently for the front face sheet and honeycomb core.

6.Parametric study

Fig.10.The failure mode sandwich structures: (a) 0 mm; (b) 20 mm; (c) 40 mm.

Fig.11.Detail experimental and numerical sandwich structure's cross-sectional view at 0 mm (normal impact).

Fig.12.Detail experimental and numerical sandwich structure's cross-sectional view at 20 mm offset impact.

Fig.14.Petals formed at rear facesheet different offset distance:(a)0 mm;(b)20 mm;(c) 40 mm.

Fig.15.Transverse deformation of rear facesheet deformation for different offset distance.

Fig.16.Cylindrical coordinate system used for energy dissipation in different direction.

Fig.17.The absorbed energy in plastic works at different offset distance.

Table 5Ballistic limit for different sandwich parameters obtained through numerical simulation.

The parametric investigation using the numerical method can significantly minimize the number of resources needed and the expense of the experimental analysis.As a result, the proposed model was used to examine the effect of a thickness(face sheet and cell wall) and inscribe circle diameter on the performance of sandwich panels against conical projectile.The impact resistance of these geometries was studied in terms of rear face deformation,residual velocity, dissipation of energy and ballistic resistance.

6.1.Impact resistance

In this part, the effect of geometrical parameters on impact resistance was explored by obtaining ballistic limit, velocity drop(residual velocity)and transverse deformation of the rear sheet,as mentioned in Table 5.

6.1.1.Effect of face sheet thickness

The four specimens of sandwich structure with face sheet thickness of 0.7,1.0,1.5 and 2.0 mm were studied to examine how it affects the structure's impact resistance.Fig.19(a) depicts the relationship between residual velocity and face sheet thickness,demonstrating that as the ascend in face sheet thickness, the residual velocity of the panel decreases.In addition, the variation in the ballistic limit with face sheet thickness is illustrated in Fig.20(a)and it was observed that the sandwich panel's ballistic limit increased with the increase in face sheet thickness.The ballistic limit for 2 mm sheet thickness was ascended by 97.6%, 60.6% and 31.7%compared to the thickness of 0.7,1 and 1.5 mm,respectively.Furthermore, Fig.21(a) depicts the variation of rear sheet transverse deformation and shows that it decreased as sheet thickness increased.For the thickness of 1, 1.5, and 2 mm, the respective decrement was 6.14%,16.58%,and 27.1%,respectively,compared to the thickness of 0.7 mm.It is due to the fact that by increasing the face sheet thickness,the overall stiffness of the structure increased,which led to a decrease in the face sheet deformation and increased ballistic limit.

The impact resistance of ST-1, ST-2, ST-3 and ST-4 was investigated to examine the behaviour of cell wall thickness.Fig.19(b)depicts residual velocity and cell wall thickness, indicating that increasing cell wall thickness results in a decrease in residual velocity;however,compared to the sheet thickness,the effect of cell wall thickness was found marginal.Furthermore, for different cell wall thicknesses, the fluctuation of ballistic limit was investigated(see Fig.20(b)) and found that it increased as the thickness of the cell wall increased.For 0.05, 0.07, and 0.09 mm, the respective increments were 3.34%,7.74%,and 12.08%,respectively,as compared to 0.03 mm.Furthermore, Fig.21(b) shows the deformation in the transverse direction for the rear face sheet obtained with the variation in cell wall thicknesses.It is seen that the rear face sheet transverse deformation declined with an increase in cell thickness.As the thickness of the cell wall increased from 0.03 to 0.09 mm,the transverse deformation decreased by 2.3 mm.Increasing the thickness of the cell wall increased the crushing strength and stiffness of the core.Also, projectile require higher velocity to perforate the thicker cell wall due to the increase in the contact area,which increases the perforation resistance in terms of impact velocity drops, higher ballistic limits and lower transverse deflection.

Fig.19.Residual velocity obtained through numerical simulation: (a)Sheet thickness;(b) Inscribe circle diameter; (c) Wall thickness.

Fig.20.Ballistic limit obtained through numerical simulation: (a)Sheet thickness;(b)Inscribe circle diameter; (c) Wall thickness.

Fig.21.Transverse deformation obtained through numerical simulation: (a) Sheet thickness; (b) Inscribe circle diameter; (c) Wall thickness.

6.1.3.Effect of inscribe circle diameter

To analyse the effect of inscribe circle diameter on the impact resistance, samples SL-1, SL-2, SL-3 and SL-4 were studied numerically.Fig.19(c) shows the effect of inscribe circle diameter on the residual velocity.It was observed that the drop in the residual was increased with an increase in the inscribe circle diameter.In the same way,the effect of inscribe circle diameter on the ballistic limit was obtained, see Fig.20(c), and it was found that as the inscribe circle diameter increased,the ballistic limit decreased.Compared to SL-1,the ballistic limit of inscribe circle diameter SL-2,SL-3 and SL-4 were decreased by 4.49%,7.02%and 9.41%,respectively.In addition,Fig.21(c) shows the effect of inscribe circle diameter on rear face sheet transverse deformation.It was observed that the rear face sheet transverse deformation was increased with ascend in the inscribe circle diameter.By increasing inscribe circle diameter from 3.2 to 9.2 mm, the transverse deformation was increased by 2.1 mm.It was due to the fact that by increasing inscribe circle diameter,the stiffness of the core decreased.Also,the projectile has to crush fewer corners and cell walls when perforating the larger inscribe circle diameter.Due to this, the structure's overall perforation resistance decreases, which results in higher transverse deformation and lower ballistic limit.

6.2.Effect on energy dissipation characteristic

This part explored the influence of geometrical factors on energy dissipation in the circumferential, tangential, radial and axial directions.Moreover, the energy contributions of distinct layers(face sheet and core) and absorbed energy in global and local deformation were calculated mentioned in Tables 6 and 7.

6.2.1.Effect of face sheet thickness

Figs.20(a)and 21(a)illustrates the effects of face sheet thickness on the absorbed energy of the sandwich structure.In Fig.22(a),as the thickness of the face sheet ascends, the sandwich structure's absorbed energy increased.Similarly,from Fig.23(a),the SAE of the sandwich structure was ascended with an increasing thickness ofthe face sheet.Further,Fig.24(a)represents the involvement of the sandwich parts in the absorbed energy that was calculated for the different thicknesses of the face sheet.The absorbed energy of the rear face sheet was maximum, regardless of face sheet thickness,followed by the front sheet and core.Furthermore,the contribution from the core was insignificant with the face sheet thickness variation.The absorbed energy was found maximum for circumferential direction, regardless of face sheet thickness, followed by tangential,radial and axial directions,see Fig.25(a).The dissipation of energy ascended in all four directions as the face sheet thickness ascended.The dissipation of energy for SF-4 in the axial direction was comparatively higher than the face sheet thickness of SF-3,SF-2 and SF-1 and the corresponding increment was 115.2%,158.3%,and 239.6%,respectively.Similarly,for circumferential direction,energy dissipation was 66.3%,180.1% and 388.6% higher, for radial direction, energy dissipation was 72.3%,143.15% and 215.6% higher and in tangential direction it was 31.3%,102.5%and 163.5%higher for SF-2, SF-3 and SF-4 face sheet, respectively.

Table 6Absorbed energy and SAE for different sandwich parameters obtained through numerical simulation.

Table 7Numerically obtained absorbed energy by the face sheet and core.

6.2.2.Effect of cell wall thickness

Figs.22(b)and 23(b)portray the relationship between cell wall thickness and energy dissipation for sandwich panels.Fig.22(b)the absorbed energy of the sandwich structure was improved with the increase in thickness of the cell wall.Compared to ST-1, the absorbed energy in ST-2,ST-3 and ST-4 was 10.2%,19.7%and 27.6%higher,respectively.However, from Fig.23(b), the SAE of the sandwich structure was descended with an increasing cell wall thickness.The SAE in ST-2,ST-3 and ST-4 was descended by 10.2%,19.7%and 27.6%higher, respectively, compared to ST-1.The effect ofthe cell thickness was found to be less significant compared to the sheet thickness,and it was because the core has a lower relative density than the face sheet.Also, the contribution of the sandwich parts to the absorbed energy was calculated for the different cell thicknesses,see Fig.24(b).With increasing cell thickness,the contribution from the core was increased while the contribution from the face sheet almost remained constant.Further, the effect of cell wall thickness on energy dissipation in a different direction was obtained, see Fig.25(b).Regardless of cell wall thickness, dissipation ofenergy was found to be higher in the circumferential direction,subsequently tangential, radial and axial directions.It was also discovered that as the thickness of the cell wall increases, the dissipation of energy also increased in all directions.For ST-4, the energy dissipation in the axial direction was 17.14%,29.3%and 61.2%higher for ST-2, ST-3 and ST-4, respectively.Similarly, for circumferential direction,energy dissipation was 66.3%,180.1%and 388.6%higher, for radial direction, energy dissipation was 72.3%,143.15%and 215.6% higher and in tangential direction it was 10.2%, 22.8%and 36.5%, for ST-2, ST-3 and ST-4, respectively.

Fig.22.Absorbed energy obtained through numerical simulation:(a)Sheet thickness;(b) Inscribe circle diameter; (c) Wall thickness.

Fig.23.SAE obtained through numerical simulation for (a) sheet thickness; (b)inscribe circle diameter; (c) wall thickness.

Fig.24.Absorbed energy by the facesheet and core: (a) Sheet thickness; (b) Inscribe circle diameter; (c) Wall thickness.

Fig.25.The absorbed energy in plastic works at four deformation direction for (a)Sheet thickness, (b) Inscribe circle diameter; (c) Wall thickness.

6.2.3.Effect of inscribe circle diameter

To find out the effect of inscribe circle diameter of the honeycomb core on energy dissipation in a different direction, inscribe circle diameter varied from 3.2, 5.2,7.2,and 9.2 mm.Compared to SL-1, the absorbed energy in SL-2, SL-3 and SL-4 was reduced by 8.2%,16.7%and 23.6%,respectively,see Fig.22(c).However,the SAE of the sandwich structure was ascended with an increasing inscribe circle diameter, see Fig.23(c).The SAE in SL-2, SL-3 and SL-4 ascended by 10.02%, 12.7%, and 23.6% higher, respectively,compared to SL-1.Also, the contribution of the sandwich parts to the absorbed energy was calculated for the different inscribe circle diameters, see Fig.24(c).With increasing inscribe circle diameter,the contribution from the core was decreased while the contribution from the face sheet almost remains constant with the increasing inscribe circle diameter.The influence of the inscribed circle diameter on energy dissipations was also graphically shown in Fig.25(c).It describes that irrespective of inscribe circle diameter, the energy dissipation in the axial direction was least and highest in the circumferential direction.Also,it was observed that the inscribe circle diameter has a marginal effect on the energy dissipation and with increasing inscribe circle diameter,the energy dissipation was decreased.For SL-1, the energy dissipation in the axial direction was 11.4%,19.3%and 47.4%higher than SL-2,SL-3 and SL-4, respectively.Similarly, for circumferential direction, energy dissipation was 4.6%, 10.6% and 16.4% higher, for radial direction,energy dissipation was 12.6%, 19.7% and 41.1% higher and in the tangential direction, it was 8.9%,16.03% and 22.4% than SL-2, SL-3 and SL-4, respectively.

7.Conclusions

The present work investigated the deformation mechanism and energy dissipation in plastic work against normal and offset impact numerically and experimentally.The experimentation was performed using a pneumatic gun followed by FE modelling in Abaqus/Explicit software.The conical nosed projectile was used and impacted at various velocity ranges.The important conclusions which have been drawn from the study are as follows.

(1) The sandwich structure offered more resistance against the offset impact than the normal impact.The drop in the residual velocity and ballistic limit was higher in offset impact.Sandwich panel impacted at 40 mm offset distance required 3 and 2.9 m/s and 1.9 and 2 m/s more velocity experimentally and numerically than 0 and 20 mm offset distance.

(2) In both normal and oblique impact conditions,the face sheet failed in localized dishing with petal formation, while the core failed during cor crushing.However, the transverse deformation of the rear sheet was more in normal impact than the 20 mm and 40 mm offset impact distance.

(3) The energy dissipation in plastic work was highest for circumferential direction, regardless of impact condition,followed by tangential, radial and axial directions.Similarly,the rear face sheet dissipates more energy than the core and front face sheet.

(4) From a parametric study,it was observed that the face sheet and wall thickness had a positive impact on the ballistic resistance in terms of a higher ballistic limit.However,inscribe circle diameter had a negative influence on the ballistic resistance.

(5) An increasing face sheet thickness increased the absorbed energy and SEA, while increasing wall thickness decreased the SAE and increased the absorbed energy.In contrast to wall thickness, increasing inscribe circle diameter, the SAE was increased and absorbed energy decreased.

Declaration of competing interest

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