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Ballistic limit for oblique impact of thin sandwich panels and spaced plates

International Journal of Impact Engineering 35(2008)1339–1354

Ballistic limit for oblique impact of thin sandwich panels

and spaced plates

D.W.Zhou,W.J.Stronge ?

Department of Engineering,University of Cambridge,Cambridge,UK

Received 20September 2006;received in revised form 21May 2007;accepted 11August 2007

Available online 2September 2007

Abstract

Ballistic perforations of monolithic steel sheets,two-layered sheets and lightweight sandwich panels were investigated both experimentally and numerically.The experiments were performed using a short cylindrical projectile with either a ?at or hemispherical nose that struck the target plate at an angle of obliquity.A total of 170tests were performed at angles of obliquity 0–451.The results suggest that during perforation by a ?at-nosed projectile,layered plates cause more energy loss than monolithic plates of the same material and total thickness.There was no signi?cant difference in the measured ballistic limit speed between monolithic plates and layered plates during oblique impact perforation by a hemispherical-nosed projectile.

To develop understanding of the process of fracture development and perforation of a thin stainless-steel sheet resulting from oblique impact by a hard,?at-nosed projectile,numerical simulations by ABAQUS/Explicit ?nite element code were compared against the experimental fracture patterns,residual velocities and ballistic limits of perforated plates.Effects of projectile length-to-diameter ratio and spacing between layered plates struck by ?at-nosed projectiles were investigated.For projectiles of equal mass,a longer projectile (larger ratio of length to diameter,L /D 42)results in a drastic decrease in the ballistic limit speed for a double-layered plate.For thin,layered plates,the ballistic limit speed is affected signi?cantly by the spacing between layers.r 2007Elsevier Ltd.All rights reserved.

Keywords:Ballistic limit;Oblique impact;Metallic sandwich panel;Multilayer;Finite element analysis

1.Introduction

1.1.Ballistic impact on multi-layered plates

For armour that protects against perforation by projec-tiles,there has been a long dispute over the bene?ts of replacing monolithic plates by multi-layered plates either with or without spacing.Marom and Bodner [1]conducted tests on layered aluminium plates struck by round-nosed lead projectiles.Plugging failure was observed in the experiment and the resistance was characterized in terms of speed drop by the projectile during the perforation process.The results showed that multi-layered beams (without spacing)exhibited greater resistance to perforation than monolithic beams with equal areal density.This was because the laminated beams had lower shear resistance and

consequently larger overall deformation as a result of bulging and dishing—the signi?cant energy absorbing mechanisms.On the other hand,the layered beams without spacing were more ef?cient than separated beams of equal areal density because maintenance of contact between layered plates and increased bending stiffness increased the impact force acting on the projectile and thus led to greater deceleration and ?attening.Corran et al.[2]investigated the performance of multi-layered steel plates and found that layered plates without spacing were superior to monolithic plates when energy absorption was dominated by membrane stretching,rather than bending and shearing.

These conclusions con?ict,however,with the results by Radin and Goldsmith [3],which showed that ballistic resistance of adjacent layers of equal thickness of ductile aluminium plates were inferior to that of monolithic ductile aluminium plates of equal areal density when struck by blunt or conically nosed projectiles;this was considered to be due to the greater bending resistance of the monolithic

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?Corresponding author.

E-mail address:wjs@https://www.wendangku.net/doc/6e9097173.html, (W.J.Stronge).

plates.Spaced layers were reported to be less effective at resisting perforation than multi-layered plates without spacing.Gupta and Madhu [4]measured the post-perforation residual velocities of layered mild steel and aluminium plates and compared the data with those of monolithic plates of equal areal density.They found that multi-layered thin plates gave less loss of kinetic energy during perforation than did monolithic plates.For spaced plates,the loss of kinetic energy was less than that for the layered plates without spacing.Almohandes et al.[5]investigated the ballistic resistance of steel plates and concluded that monolithic targets are more effective than layered targets (either contacted or spaced layers)at the same total material thickness.

These experimental investigations of impact and perfora-tion have been analysed with a few numerical simulations using appropriate material constitutive relations and frac-ture criteria.Zukas and Schef?er [6]used both Lagrangian and Eulerian codes to simulate impact resistance of monolithic and multi-layered plates.Based on the simula-tion,the authors claimed that layering dramatically decreases the impact resistance of thin and intermediate thickness targets.The explanation was attributed to the difference in bending stiffness and stress wave propagation between monolithic plates and multi-layered plates.

A few analytical models have been proposed for investigating projectile perforation of layered plates sub-jected to impact [7–9].These models [7,8]used shear plugging as the fracture criterion—a mechanism that is not suitable for thin sheets of ductile materials where mem-brane stretching and tensile fracture dominate.Liang et al.[7]analytically investigated the ballistic impact of mono-lithic,double-and triple-layered targets under normal impact.The analysis was veri?ed by previously described experimental tests conducted by Almohandes et al.[5].It was reported that among these three targets,monolithic plates had the best ballistic performance.For two target layers,the worst ballistic performance corresponded to the case where the two layers were of equal thickness.Investigation of the effect of spacing showed that it slightly in?uenced the resistance to perforation of multi-layered targets.Elek et al.[8]subsequently presented a model for perforation of spaced multi-layered targets and concluded that a monolithic target had greater resistance than any other spaced multi-layered targets with equal areal density provided that there was no interaction between the individual layers during impact.For a double-layered target,the maximum resistance can be obtained for laminae of very different thickness,irrespective of whether the proximal surface is thin or thick.Elek’s analysis indicated a decreasing ballistic limit with increasing number of laminae,given any particular total target thickness.For normal perforation of spaced plates by cylindrical projectiles with a variety of nose shapes,the localized interaction model of Ben-Dor et al.[10]predicts very weak dependence of the ballistic limit velocity on plate spacing.A summary of the main conclusions of the above reviews is given in Table 1.

1.2.Ballistic impact on sandwich panels

Although the sandwich plate is a variant of a multi-layered plate,there is still a considerable difference between a layered structure (with or without spacing)and sandwich

Table 1

Summary of ballistic impact on multi-layered plates Experiment Reference Proj.mat.Proj.nose shape Proj.radius (mm)Total thick (mm)No.of layers Impact speed (m/s)Results a Marom [1]Pure or alloy Al Round 2.81–101–3350–390D E a o D E b D E c o D E b Corran [2]Steel Flat 6.25 1.2–6.4140–220D E a o D E b

2.4–62–3Radin [3]

2024-0Al

Flat conical

6.25

3.2280–240

V a 504V b

4.836.44Gupta [4]Mild steel

Ogive 3.1 4.7–251–6800–870D E a 4D E b Al

6.1–401–6Almohandes [5]Steel,FRP

Ogive

7.62

1–5

706–826

D E a 4D E b D E c o D E b

Numerical simulation Zukas [6]RH armor

Round 6.531.81–6$1100

D E a 4D E b

Analytical analysis Liang [7]Same parameter and results as Almohandes [5]Elek [8]Steel Flat 2.8

3.452700–830

D E a o D E c

All the results are for normal impact,D E is the decrease in kinetic energy of the projectile and V 50is the ballistic limit.Superscripts are de?ned as a ?monolithic,b ?layered no space and c ?layered,spaced.

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1340

construction.The distinctive structure of sandwich panels requires a special treatment for analysing projectile impact problems.A few previous investigations of the ballistic limit of sandwich structures are described in Refs.[11–14]. Goldsmith et al.[11]conducted a series of tests on aluminium sandwich panels that were subjected to impact by cylinder–conical,?at and spherical projectiles.The core consisted of honeycomb or aluminium.The results showed that the ballistic limit of the sandwich panel was not signi?cantly affected by the type,cell size or wall diameter of the core microstructure.Perforation of the panel was related principally to piercing of the facesheets,i.e. identical facesheets produced the same ballistic limit irrespective of core https://www.wendangku.net/doc/6e9097173.html,mbert et al.[13]investigated hypervelocity impact damage to thin aluminium or CFRP composite facesheet sandwich panels with30–50mm thickness honeycomb cores.It was found that these sandwich panels are more resistant to perforation during hypervelocity impact than monolithic structures with the same thickness as the facesheets.

It should be mentioned that all the above research on ballistic perforation of multi-layered plates considered normal impact only.To the best of the present authors’knowledge,no experimental results were reported in the open literature about multi-layered targets under oblique impact.

1.3.Effect of projectile nose shape

In investigating the ballistic impact,the effect of projectile nose shape is an important factor.It has a strong effect on the failure mechanism of the plate,which is signi?cant in determining the resistance of a plate to penetration.The effect of the projectile’s nose shape on ballistic limit or energy absorption has been investigated by a number of papers[2,15–22]but this in?uence is still not completely formulated.Zukas et al.[18]investigated the effect of nose shape of long projectiles on the penetration of a thick plate(h/R?4where h is plate thickness and R is plate radius)that is made of rolled homogeneous(RH) armour with Brinell hardness number(BHN)380.The projectile of BHN555had a length-to-diameter ratio of10and a nose shape that was hemispherical,conical (401angle),?at or ogival.The results indicated that the more blunt the nose shape,the higher the ballistic limit;the ballistic limit for a?at-nosed projectile was approximately 6.5%larger than that for a hemisphere-nosed projectile. However,the difference in ballistic limit was very small, within4%,among the hemispherical,conical and ogive nose shapes.Wilkins[16]observed that for a thick plate (h/R41)the ballistic limit for a sharp rigid projectile was less than that for a?at projectile,whereas the opposite result was found for perforation of a thin plate target.It was explained in that paper that for thin plates,less energy is required for a?at cylinder to shear out a plug than for the sharp projectile to push material aside by ductile tearing and hole expansion,which involves friction force between the projectile and the plate.Wingrove[17] conducted impact perforation tests of2014-T6aluminium alloy targets and showed that?at projectiles perforated the target with the least resistance followed by hemispherical and ogive penetrators as long as the target thickness to projectile diameter ratio was less than1(h/R o1/2).Borvik et al.[15]investigated the ballistic limit of12mm thick steel plates that were perforated by20mm diameter projectiles with?at,hemispherical and conical noses(h/R41).The ballistic limit was about equal for hemispherical and conical projectiles,while it was considerably small for?at projectiles.Recently,Gupta et al.[21,22]perforated thin aluminium plates of0.5–3mm thickness by using projec-tiles with?at,ogive and hemispherical noses.The ballistic limit speed was found to be larger for hemispherical projectiles than that for?at projectiles,whereas the ogive-nosed projectile was found to be the most ef?cient penetrator.The effect of nose shape on ballistic limit is summarized in Table2.

1.4.Effect of obliquity

Most literature about the ballistic impact is focused on the normal impact of rigid projectiles on targets.Experi-mental data on oblique impact perforation are more limited

Table2

Comparison of effects of projectile nose shape on ballistic limits

Paper Plate material Thin or thick?a Results b

h/R

Zukas[18]RH armour?4V flat

504V hemis

%V conical

%V ogival

Wilkins[16]Steel41V flat

504V sharp

o1V flat

50o V sharp

Wingrove[17]Al(2014-T6)o2V flat

50o V hemis

=V ogival

Borvik[15]Steel 1.2V flat

50o V hemis

%V conical

Gupta[21]Al(1100-H12)0.1V flat

50o V hemis

a h/R is the ratio of the plate thickness h to the radius R of the cylindrical projectile.

b All the results are for monolithi

c plates under normal impact;V flat

50is the ballistic limit of a target struck by a?at-nosed projectile and other terms are in

a similar de?nition.

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[4,18,23–28].Goldsmith[29]gave a comprehensive review on the non-ideal projectile impact on targets,treating oblique impact in particular.For oblique impact,the most frequently used parameters are non-dimensional velocity decreaseeV iàV RT=V R(where V i is the striking speed and V R is the residual speed)during perforation,exit angle of the projectile after perforation and the ballistic limit speed.In Ref.[18],a comparison of ballistic limits between normal impact and601obliquity showed that the ballistic limit at 601obliquity was approximately35–40%larger than that for normal impact depending on the projectile nose shapes. In a similar manner,Goldsmith and Finnegan[25]indicated that for cylindro-conical bullets perforating a3.175mm soft aluminium target the ballistic limit increased about34%as angle of obliquity increased from normal impact to531 obliquity impact.This paper also investigated the velocity decrease and at small initial obliquity(o301)it was independent of angle but changed rapidly at large angles of obliquity.Similar results were obtained by Awerbuch and Bodner[24]and Gupta and Madhu[4,26].According to Goldsmith and Finnegan[25],the exit angle of projectiles does not change much in comparison with the initial obliquity at the higher impact speed but usually is less than the initial angle at lower speeds.

The present paper gives a comparison of the ballistic impact resistance of stainless-steel sheets,i.e.monolithic, double-layered and sandwich sheets.In particular,effects of projectile nose shape,angle of obliquity and panel spacing on the ballistic resistance of layered plates and sandwich panels are addressed.In the following analysis, the damage mechanism of steel sheets and thin sandwich panels is?rst identi?ed.The ballistic limits of different types of plate are experimentally determined.With an appropriate selection of material constitutive relation and fracture criterion,the perforation sequence is numerically simulated.Effects of length-to-diameter ratio and spacing on ballistic limits of layered targets are discussed using the validated numerical analysis.

2.Experiment description

The experiment consisted of a cylindrical steel projectile with either?at or hemispherical-nose shape that was?red from an airgun and struck a clamped circular plate at an angle of obliquity of01,301or451.The angle of obliquity from normal a i is described in Fig.1.To examine the effect on the ballistic limit of the projectile mass and the length-to-diameter ratio,four projectiles with the same diameter but different lengths were considered for each nose shape. Table3gives a complete list of the projectile parameters used in the experiment.

A nitrogen gun with a bore diameter12.7mm was used to accelerate the projectiles to a range of impact speeds from50to150m/s.The cylindrical projectiles have a diameter of12.68mm.The missile speed was roughly controlled by varying both the gas pressure in the high-pressure cylinder that powers the gun and the location of the projectile in the barrel before?ring.The muzzle speed was measured by a digital timer,which measured the elapsed time between the breaking of two graphite leads that spanned the barrel at the muzzle;the distance between break-wires was50mm.The motion of the projectile was recorded by a high-speed camera with a frame speed of either4500or9000fps;this was supplemented by a mirror to re?ect the projectile movement(see Fig.2).By analysing the frames recorded by the high-speed camera,the residual speed of the projectile can be https://www.wendangku.net/doc/6e9097173.html,ing this measurement approach,an error of10%is introduced in the residual speed due to the displacement measurement.

Fig.1.Schematic of oblique impact.Table3

Projectile parameters used in the experiment

Name Nose Length(mm)Length/diameter Mass(g) F_1Flat18.7 1.520.5

F_1.5Flat28.1 2.230.8

F_2Flat37.4 2.941.0

F_2.5Flat46.8 3.751.3

H_1Hemisphere20.3 1.619.9

H_1.5Hemisphere30.5 2.429.9

H_2Hemisphere40.6 3.239.8

H_2.5Hemisphere50.8 4.0

49.8

Fig.2.Experimental set-up.

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To avoid the in?uence of the boundary,the diameter of the target plate was set to be about12times the diameter of the missile,which had a diameter of12.7mm.The target plates of square shape have small holes near the edge and were bolted in a special designed mount;this resulted in a circular plate of150mm diameter with clamped boundary condition.After the tests,the holes in the plate had little elongation;this showed that the plate boundary was well clamped and had little radial movement.While these target plates may not be large enough to entirely eliminate effects of boundary clamping on the ballistic limit,numerical simulations indicate that the in?uence of boundary effects is small.

The target plates consisted of316L stainless-steel sheets, including monolithic(0.5mm thickness),double layered in contact(either2?0.2or2?0.25mm thickness)and sandwich sheets.The sandwich sheets,named HSSA,are thin,lightweight structures with stainless-steel facesheets separated by a random arrangement of independent stainless-steel?bres.A schematic description of the material is shown in Fig.3.Adhesive bonding is used to connect the facesheet and the core.These panels have small thickness;consequently they can be pressed into3D curvature in a forming operation.The facesheet of the sandwich panel has a thickness of0.2mm and the?brous core is0.8mm thick.A detailed mechanical modelling of this material is given in Ref.[30].

A total of170tests were carried out for these different targets.For a speci?c impact,the number of impact tests varied from three to10depending on whether the ballistic limit speed was determined quickly.However,there were around20tests for each impact when steel and HSSA sandwich panels were struck by relatively short projectiles,

i.e.,F_1,F_1.5,H_1and H_1.5.

3.Experiment results

3.1.Mode of fracture

In general,the failure mode for perforation depends on ductility of the target plate,the projectile nose radius and the plate thickness to projectile diameter ratio.Fracture modes of thin plates(h/R o1/2)are different from those intermediate or thicker plates where shear plugging is dominant.Figs.4–9give the fracture patterns of stainless-steel monolithic and sandwich sheets under the impact of projectiles with?at-and hemispherical-shaped noses.

In the case of a monolithic sheet,the fracture modes include discing(circumferential tensile crack around the contact area),petalling and hinging.Fig.4shows the failure of discing when a steel sheet is struck by a?at-nosed projectile,although there is no complete circumferential crack(3601)when the impact is oblique.When the circumferential crack initiates at a point of maximum stretching and advances along the periphery of the contact area until the ends of the crack are diametrically opposite, the crack then changes to a transverse tearing mode which forms a petal with two parallel cracks.As the projectile moves forward and the cracked material is forced to bend backward,a plastic hinge is formed.Hinges have also been observed by Goldsmith[31],Atkins et al.[32]and Crouch et al.[33].Fig.5gives failure modes of steel sheets struck by a hemispherical-nosed projectile at different angles of obliquity.Although tensile failure results in a hinge cap formed by a hemispherical-nosed projectile,there is typically additionally one dominant radial crack.This damage mode seems different from the cases of?at-nosed projectiles where oblique impact results in two parallel cracks in fracture mode III.

The failure mode of sandwich construction is more complicated than that of a monolithic steel sheet (see Figs.6and7).Apart from the above observed circum-ferential tearing failure mode of monolithic steel sheets in sandwich panels,debonding between facesheets and core occurs frequently.In addition to debonding,cracks in the front and rear facesheets sometimes develop in different patterns.As illustrated in Fig.8there is one circumferential crack in the front facesheet and a radial crack in the rear facesheet.Note that the tensile crack in the front facesheet is almost transverse to the direction of projectile motion, while the crack in the rear facesheet is parallel to projectile motion.As the striking speed increases,the cracks form a

Fig.3.SEM micrograph and schematic depiction of the?brous sandwich

structure(HSSA).

D.W.Zhou,W.J.Stronge/International Journal of Impact Engineering35(2008)1339–13541343

Fig.4.Fracture pattern of a monolithic steel plate struck by a projectile with ?at nose at angles of obliquity 0p a i p 45 :(a)V i ?97m =s,a i ?0 ;(b)V i ?65m =s,a i ?30 ;and (c)V i ?69m =s,a i ?45

Fig.5.Fracture pattern of a monolithic steel plate struck by a hemispherical-nosed cylinder at angles of obliquity 0p a i p 45 :(a)V i ?129m =s,a i ?0 ;(b)V i ?86m =s,a i ?30 ;(c)V i ?100m =s,a i ?45 (front view);and (d)V i ?100m =s,a i ?45 (rear

view).

Fig.6.Fracture pattern of the HSSA sandwich sheet struck by a ?at-nosed cylinder at angles of obliquity 0p a i p 45 :(a)V i ?81m =s,a ?0 ;(b)V i ?70m =s,a ?301;and (c)V i ?65m =s,a ?451.

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petal in each facesheet but these petals have different orientations (Fig.9).Fig.10gives the failure sequence of the HSSA sandwich panel when struck by a ?at projectile with L /D ?2.2at an obliquity of 301.It is interesting to note that the projectile changes rotation direction during perforation when the striking speed is close to the ballistic limit.Further discussion on the projectile rotation is given in Ref.[34].

3.2.Ballistic resistance

The resistance of structure to ballistic impact can be characterized by the ballistic limit and energy absorption during perforation.The ballistic limit of a plate impacted by a particular projectile is taken as the average of the lowest speed giving a complete perforation and the highest speed that gives partial or no perforation.In some cases where the target plates were cracked,the correspond-ing projectile incident speed was taken as the ballistic limit speed because it is the best available estimate.Values of the ballistic limit for various plates impacted by a range of projectiles are listed in Table 4.Fig.11also gives a comparison of the ballistic limit of different layered

plates as a function of angle of obliquity for a ?at-nosed projectile (F_1).

Residual velocities of various projectiles for monolithic plates and HSSA sandwich panels are given in Table 5.A curve of best ?t to the experiment data is given in Fig.18.The empirical formula employed in the best-?t curve is from Ref.[18]:

V R ?0;0p V i p V 50;

p 1eV p 2i àV p 250T1=p 2

;V i X V 50;((1)where V i ,V R and V 50are the striking,residual and ballistic limit velocities of the projectiles (in m/s).For non-deforming projectiles,p 2?2and p 1?M 1=M 1tM 0=3;where M 1is the projectile mass and M 0is the target material enclosed within a projection of the projectile prior to impact.Eq.(1)is obtained from conservation of energy for plugging where plug mass is M 0/3and energy required for perforation is independent of impact speed.

3.2.1.Effect of projectile nose shape

The effect of projectile nose shape on ballistic limit is shown in Fig.11.It can be seen that the ballistic limit for a hemispherical-nosed projectile is substantially larger than that for a ?at-nosed projectile,irrespective of the angle of obliquity or layering of the plates.Fig.12illustrates the effect of projectile nose shape on the post-perforation residual speed of projectiles.Under the same striking speed,the residual speed for the hemispherical-nosed projectile is substantially smaller than that for the ?at-nosed projectile,i.e.,more of the impact energy has been absorbed by fracture and ductile stretching.This further indicates that thin steel plates have more impact resistance to hemispherical-nosed projectiles in comparison with ?at-nosed projectiles.

Fig.7.Fracture pattern of HSSA sandwich sheet struck by a hemi-spherical-nosed projectile,V i ?73m =s,a i ?301:(a)front view;and (b)rear

view.

Fig.8.Fracture pattern of the HSSA sandwich sheet struck by a hemispherical end cylinder,V i ?80m =s,a i ?451:(a)front view;and (b)rear

view.

Fig.9.Fracture pattern of the HSSA sandwich sheet struck by a hemispherical end cylinder,V i ?100m =s,a i ?451:(a)front view;and (b)rear view.

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3.2.2.Effect of angle of obliquity

As observed from Fig.11,a general trend of the ballistic limit curve for both nose shapes and all combinations of layering is an initial decrease and a subsequent increase with increasing angle of obliquity.For a ?at-nosed projectile,the ballistic limit speed initially decreases with

angle of obliquity as the failure mechanism transforms from shear around the entire periphery of the projectile nose (plugging)to tensile tearing under an edge of the obliquely penetrating projectile.Less energy is required to initiate the less extensive initial crack that develops from an oblique impact on a thin metal sheet.At large angles of obliquity,an increasing ballistic limit with increasing angle of obliquity occurs because of the increasing size of the

Table 4

Comparison of measured ballistic limits of different targets Plate

Proj.

Obliquity

Ballistic limit (m/s)a F_1

F_1.5F_2F_2.5Monolithic Flat 0968572–Monolithic Flat 3057544840Monolithic Flat

4566–––Monolithic Hemisphere 0125–––Monolithic Hemisphere 308677–63Monolithic Hemisphere 45103–––Sandwich Flat 078635851Sandwich Flat 3052474339Sandwich Flat

4562–––Sandwich Hemisphere 0110–––Sandwich Hemisphere 307468–53Sandwich Hemisphere 4584–––Double layer 1Flat 083–––Double layer 1Flat 3066–––Double layer 2Flat 089–––Double layer

Flat 3069

–

10%measurement

error.

Fig.10.Perforation of an HSSA sandwich sheet struck by a ?at-nosed cylinder at obliquity of 301(F_1.5),V i ?53:8m =

Fig.11.Ballistic limits of structures struck by ?at-and hemispherical-nosed cylinders (F_1,H_1)compared with ?nite element simulation.

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perforation and a large in-plane force that resists projectile displacement parallel to the plate surface.The long traces of sliding and paths of tearing seen at large angles of obliquity (Figs.4and 5)are evidence of increased energy required for perforation with increasing angle of obliquity.More observations are given in Ref.[34].These trends for variation of the ballistic limit speed with angle of obliquity

were also exhibited by the ?nite element (FE)simulation of perforation shown in Fig.11.

https://www.wendangku.net/doc/6e9097173.html,parison of ballistic limits of different plates

For a stainless-steel plate struck at normal obliquity by a ?at-nosed projectile,Fig.11shows that the ballistic limit speed of the monolithic panel is the largest,while the ballistic limit speed of the sandwich panel is smaller.A double-layered sheet (either 2?0.25or 2?0.2mm)has a ballistic limit between that of a monolithic steel sheet and sandwich plate.However,for a ?at-nosed projectile at an impact obliquity of 301,the double-layered sheet clearly has a larger ballistic limit than a monolithic plate.Both the 2?0.25and 2?0.2mm double-layered plates have ballis-tic limits 17%and 12%larger than the monolithic sheet,respectively.This observation demonstrates that for oblique impact of thin stainless-steel plates by ?at-nosed projectiles at an angle of obliquity smaller than 451,double-layered structures are more effective in resisting projectile perforation than monolithic plates of the same total material thickness.A comparison of the ballistic limits of sandwich panels and monolithic sheets also supports this conclusion.As seen in Fig.11,for both ?at-and hemispherical-nosed projectiles,the ballistic limit of monolithic sheets is 23%larger than that of HSSA sandwich sheets at normal obliquity.This percentage decreases to 13%for an angle of obliquity 301and 7%for 451.

4.Numerical simulation 4.1.General description

In order to understand the perforation process,ABAQUS/Explicit was employed to simulate both mono-lithic plates and layered plates under projectile impact.Details of various simulation cases are given in Table 6.A numerical simulation of oblique impact requires a 3D model of the plate deformation.Since membrane stretching is a main mechanism of energy absorption,four-node shell elements (S4R)with reduced integration were used.Shell elements have also been used by Lee and Wierzbicki [35]to simulate fracture of thin plates under impulsive loading.Both the plate and the projectile are symmetrical.Conse-quently,only half of the plate with a symmetric boundary along a diameter was considered.A typical element size of 0.2mm was used near the perforated area.

Table 6

Simulation cases to validate the numerical model Projectile a Obliquity (deg.)Plate

F_10and 30Monolithic (0.5mm)

F_1

0and 30

Spaced double layer (0.2+0.8+0.2mm)

Details of the plate material properties are referred to in Table 6.a

The projectile has a radius of 6.34mm and a length of 20.8mm.

Table 5

Residual speed of projectiles for different plates Plate Proj.Striking speed (m/s)a Residual speed (m/s)a Monolithic

F_1

53.713.454.627.259.232.962.230.169.543.1Sandwich F_1

60.733.266.144.568.131.981.747.3Monolithic F_1.5

67.948.582.171.699.290.8Sandwich F_1.5

53.834.363.146.374.560.184.269.5104.889.8Monolithic H_1.5

85.633.891.235.0100.850.6110.671.8HSSA H_1.5

70.2 2.396.056.3106.8

75.9

10%measurement

error.

Fig.12.Measured residual speed curves for different plates struck by different projectiles (F_1.5,H_1.5)at an angle of obliquity 301.

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The numerical model employed a uniform thickness plate with clamped edge that represents the boundary condition in this experiment.The ABAQUS/Explicit general contact algorithm was employed to simulate the contact between the projectile and plate.This contact algorithm was also used to simulate the interaction of the two faceplates in a double-layered plate.During the perforation,the petal,that develops,bends until it comes into contact with the non-perforated area of the plate.The self-contact algorithm was used to consider this interaction.Friction is neglected in the simulation since sensitivity studies show that the result was not sensitive to the friction coef?cient.

The experiments employed a hardened projectile,which had no observable plastic deformation after perforating the plate;consequently the projectile was modelled as an elastic body.The projectile had a Young’s modulus of 210GPa and a Poisson ratio of 0.3.Densities of the projectile and plate were taken as 7800kg/m 3.

4.2.Material constitutive relation and failure criterion In general,the response of material under high-speed impact involves consideration of the effect of strain,strain rate and temperature,i.e.,s ?f e ;_

;T T.(2)

The Johnson–Cook material model was used in the

present simulation to simulate the sandwich facesheets and single/layered panels.This empirical model decouples the effect of strain,strain rate and temperature,namely,

s ??A tBˉ n 1tC ln _ _ 0

?1à^y m ,(3)where s is the ?ow stress;ˉ is the equivalent plastic strain;

and C and _

0are material properties measured at transition temperature.Parameters A ,B and n are determined from

the uniaxial tension test in last section.Parameter ^y

represents the adiabatic heating and this effect is ignored in the analysis.Previous work by Borvik et al.[36]and Gupta et al.[21]has shown that adiabatic effect can be ignored in this range of speed.

It has been shown that localization of the deformation and strain-softening behaviour of the material causes mesh dependence in simulation of continuum damage mechanics [37].Mesh re?nement results in a smaller width of the localization band and reduces the global energy dissipa-tion.The damage thus localizes in a zone of vanishing volume and consequently the energy dissipation decreases to physically unrealistic values.However,Needleman [38]has shown that pathological mesh dependence does not occur in numerical simulation for rate-dependent solids because material rate dependence implicitly introduces a length scale into the governing equations.

The basic form of a strain-based fracture model in FE analysis is to de?ne the damage in an element:

o D ?Z d ˉ

ˉ f

,(4)

where ˉ f is the equivalent plastic strain to fracture and

d ˉ is an increment of equivalent plastic strain.Th

e state variable o D increases monotonically with plastic deformation proportional to the incremental change in equivalent plastic strain.Fracture is assumed to occur when o D ?1.0.

The equivalent fracture strain ˉ f es m =ˉs Tto be used in FE analysis strongly depends on stress triaxiality s m =ˉs ;where s m is the hydrostatic or mean stress and ˉs is the VonMises equivalent stress.In simulations of sheet metal deformation,it has been shown in Ref.[39]that the following fracture criterion can be used when stress triaxiality is in the range of

13p s m ˉs p 23,i.e.,Z ˉ f

s m

ˉs d ˉ ?D c ,(5)where D c is a critical damage value for a material.Once D c

is determined,the fracture strain at other stress triaxiality can be obtained by ˉ f ?

D c

s m =ˉ

s .(6)

One approach to obtain the critical damage value D c is to use the fracture strain in the uniaxial tension test.For the uniaxial tension test,stress triaxiality is taken as 0.33since the material has very small thickness.Thus,the damage value D c is approximated as

D c ?13

ˉ f es m =ˉs T.

(7)The sandwich panels used in these tests had a core consisting of randomly oriented stainless-steel ?bres.The ?brous core of the sandwich panel can be represented as a compressive anisotropic plastic material [30].The present simulation employed a material model similar to that developed by Xue and Hutchinson [40],which was developed based on the Deshpande–Fleck model [41].ABAQUS subroutine VUMAT has been implemented to simulate the plastic deformation and core failure [42].Fracture of the ?brous core is simulated by deleting elements once the strain fracture criterion is satis?ed.Because simulation results suggest that the kinetic energy of the projectile is predominately absorbed by stretching of the facesheets,the effect of the ?brous core in the sandwich panel is solely to provide spacing between the two facesheets.

4.3.Determination of facesheet and panel material properties

The uniaxial tensile test was performed to identify the material properties to be used in the numerical simulation.Flat,dog-bone specimens were cut from thin sheets.During the test,several tensile coupons were cut from the sheets in two orthogonal directions but no appreciable differences in properties were found.Therefore,the

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stainless-steel sheets used in these experiments were considered to be isotropic.A drawing of the specimen is presented in Fig.13.Two types of panel material were investigated as described in previous sections,i.e.,HSSA sandwich panels (1.2mm total thickness)and 316L stainless-steel sheets (0.5mm thickness).This thickness gives the same areal density between sandwich panels and monolithic plates.An Instron machine was employed to exert the tensile loading (at a strain rate of 0.001s à1)until the specimen was fractured.The elongation of the specimen was recorded by a laser extensometer.Fracture patterns of the specimen are given in Fig.14.

Since necking reduces the cross-section of the specimen during a tensile test,the true stress–strain curve was obtained by numerical simulation with a trial-and-error approach until the numerical calculation of the load and necking deformation corresponded well with the test data on the test specimen.A large number of runs were needed to obtain the plastic stress–strain coef?cients which provide the experimental force–de?ection curve.The calibration procedure is summarized below:

1.Obtain the true stress–strain curve from the experi-mental force–displacement curves,using transformation rules from engineering to true measures.

2.Fit the above obtained stress–strain curve with the following analytical model:s ?E ; p Y ;s ?A tB n ;

X Y ;

((8)

where E is the Young’s modulus,e Y is the yielding strain and parameters A ,B and n are to be determined.3.Simulate the tensile test using the above ?tting curve and compare the calculated load–de?ection curve with experiment.

4.On the basis of the error between FEM and experiment,adjust the true stress–strain curve (parameters A ,B and n )for a better ?t to the experimented load–de?ec-tion curve.Numerical simulation of the tensile test was performed by ABAQUS/Explicit due to the instability problem in the implicit method when representing ductile fracture.The monolithic stainless-steel specimen was meshed by CPS4R plane stress elements.In the case of the HSSA sandwich

panel,only two facesheets with thicknesses of 0.2mm each were incorporated in the FE model since the core has a negligible stretching stiffness.One end of the sample was ?xed and the other end was extended at a displacement loading in the uniaxial direction.

For use in the numerical simulation,relevant parameters were obtained for monolithic steel panels and HSSA facesheets.The true stress–strain curves for these two panels are given in Fig.15.These stress–strain relations give the best ?t for the experimental load–displacement curves for 316L stainless steel and HSSA that are shown in Fig.16.Note that the stainless steel and HSSA specimen had different cross-section areas.A mesh sensitivity study was also carried out and it was shown that the mesh used is ?ne enough to simulate the tensile test.By comparing the measured displacement at fracture of the specimen with the

Fig.13.Geometrical con?guration and dimension of a specimen for material and fracture

calibration.

Fig.14.Fractured specimens of uniaxial tensile test.(a)316L stainless-steel sheets and (b)HSSA sandwich

sheet.

Fig.15.Tensile true stress–strain curves for the monolithic steel and HSSA sandwich sheet.

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calculated displacement and evaluating the corresponding ?nite strain in the region of necking,we obtained an estimate for the experimental fracture strain.This fracture strain for the monolithic steel sheets and HSSA facesheets was identi?ed as 0.49and 0.35,respectively.

The parameter C in Eq.(3)for the strain rate effect (Table 7)is determined by Nordberg [43].On the basis of a comparison of 12high-strain rate tests of stainless steel,Nordberg suggested an empirical formula for the material constitutive relation of stainless steel.This formula is similar as Eq.(3)except that the thermal effect is ignored.The relevant material properties are given in Table 7.4.4.Validation of numerical model

The calculated fracture pattern and deformation of a monolithic plate perforated by ?at-and hemispherical-nosed projectiles striking at a 301angle of obliquity are shown in Fig.17.The fracture patterns and extent of fracture are almost the same as those obtained experimen-tally (Figs.4b and 5b ).It can be seen that the numerical and experimental fracture patterns agree.

Fig.18gives a comparison of residual velocities between experimental and FE analyses for target plates struck at angle of obliquity of 301.FE analysis is in general within 20%of the experiment.For the ballistic limit,Table 8shows that the calculated ballistic limit speed is within 10%of the experimental results.

4.5.Discussion

4.5.1.Effect of projectile nose shape

4.5.1.1.Flat-nosed projectile.The experimental results in the previous section show that for ?at-nosed projectiles,a double-layered plate has more impact resistance than a monolithic plate of the same material thickness in terms of both ballistic limit and speed drop.To develop under-standing of the observed behaviour,the validated numer-ical model was employed to investigate the impact force during perforation.During plate perforation,a nose force acts on the projectile’s nose where it initially contacts the plate.After the plate is perforated and the projectile is passing through the plate,it is subjected to a side force where it moves against the plate.During perforation,the nose and side forces cause the projectile to rotate and thus affect the ballistic limit speed.

Fig.19illustrates the impact force during perforation of two types of plates (monolithic and double-layered plates in contact)by a ?at-nosed projectile travelling at a moderately large impact speed (40%larger than the ballistic limit speed)and striking at a 301angle of obliquity.One of the most notable differences in Fig.19is that the impact force generated by a double-layered plate is much larger than that by a monolithic plate.An observation of the deformation of the double-layered plate (without space)from FE analysis indicated that individual plates do not fail simultaneously;this asynchrony increases the penetration resistance because,when the ?rst plate is

Fig.16.A comparison of experimental and numerical load–displacement relations for tensile specimen used to develop the stress–strain curve in Fig.15

Fig.17.Fracture pattern on distal surface of a monolithic plate after perforation by (a)a ?at-nosed shape projectile,V i ?65m =s,a i ?301and (b)a hemispherical projectile,V i ?86m =s,a i ?301(t ?1ms after initial contact).

Table 7

Summary of material properties Specimen A (MPa)B (MPa)C _ 0(s à1)n m ˉ f Monolithic plate 27012500.070.0010.7200.46HSSA facesheet

270

1250

0.07

0.001

0.73

0.32

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perforated,the second faceplate is stretched without fracture initiation.This stretching causes strain hardening and thus the resistance of the second plate to perforation is increased.These effects hence lead to a larger average impact force than that for a monolithic plate.

With increasing impact speed,the impact duration in both cases becomes shorter and the effect of the asynchrony in fracture in layered plates becomes insignif-icant.Therefore,the nose force for both monolithic and layered plates of equal material thickness will be identical; the difference in energy loss in perforation of these two structures will thus be negligible.As an example,the calculated residual speed of these two different panels is illustrated in Fig.20.The difference of residual velocities between these two plates becomes smaller with increasing impact speeds.

4.5.1.2.Hemispherical projectile.When a projectile with

a hemispherical nose shape strikes a plate,Fig.21shows that the difference in the impact force between monolithic and layered sheets is insigni?cant(maximum10%differ-ence).For comparison with the?at-nosed projectile,the striking speed is40%larger than the ballistic limit speed.

Fig.18.Variation of residual speed with striking speed for a?at-nosed projectile(F_1)striking on monolithic steel plates and HSSA sandwich panels at a301angle of obliquity.(a)0.5mm monolithic steel plate and(b) HSSA sandwich

sheet.Fig.19.Calculated force on the?at-nosed projectile(F_1,L/D?1.64) during perforation of monolithic and layered sheets at an impact speed of 80m/s and an initial angle of obliquity of301.

Table8

Comparison of ballistic limits between experiment and numerical modelling for?at-nosed projectile

Plate Impact obliquity Experiment(m/s)Numerical(m/s) HSSA07881

Monolithic plate096105

HSSA305255

Monolithic plate3057

58Fig.20.Calculated residual speed vs.striking speed for a monolithic plate,double-layered sheet in contact and a spaced layer sheet(2mm space)struck by a?at-nosed projectile(F_1,L/D?1.64)at an angle of obliquity of301.

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This similarity indicates that these two structures will have similar impact resistance,giving negligible difference of the residual speed and ballistic limit between a monolithic plate and a double-layered plate.

4.5.2.Effect of projectile length-to-diameter ratio for oblique perforation

The result in the last section considers a projectile with a length-to-diameter ratio of1.64,which is relatively short.

The present section investigates the effect of the projectile length-to-diameter ratio on the ballistic impact of plates of the same mass.The length-to-diameter ratio can affect perforation because of increasing moment of inertia about a transverse axis and decreasing mass per unit cross-sectional area as projectile length increases.Fig.22gives a comparison of residual speed of a?at-nosed projectile for two length-to-diameter ratios,i.e.,L/D?1.64and4.67. Details of the geometric con?guration are presented in Table9.For both monolithic and layered sheets,it can be seen that the ballistic limit decreases rapidly with increasing length-to-diameter ratio.However,with increases of the striking speed,the effect of the length-to-diameter becomes insigni?cant.This might be because the in?uence of projectile rotation about a transverse axis is smaller for a higher striking speed since the impact event is so short. 4.5.3.Effect of spacing between layers

When the facesheets are thin,a sandwich structure can be treated as a spaced layered panel with membrane stretching as the dominant energy absorption mechanism for thin facesheets.As reviewed earlier,for normal impact spacing between layered plates has an adverse effect on resistance to ballistic impact.However,with an appro-priate space between two layers,the resistance of plates to oblique impact could be improved due to rotation of the projectile.The numerical model was employed to investi-gate this effect for thin plates.The spaced double-layered plate had a spacing of2mm between facesheets.A comparison of the residual speed for spaced double-layered plates,double-layer plates in contact and monolithic plates are shown in Fig.20.It can be seen that the spaced plate causes more projectile energy loss during perforation than layered sheets in contact,which in turn has much more resistance in comparison with a monolithic plate.Fig.23 illustrates the sequence of the perforation of the spaced sheet.It can be seen that during the perforation of the layer that?rst contacts the projectile,the projectile rotates towards the normal to the plate(pitch).Since it is more dif?cult to perforate a plate under normal impact,the resistance of the spaced sheet is improved in comparison with a monolithic sheet of similar material thickness.

5.Conclusions

This experimental study compared the ballistic resistance of monolithic plates,double-layered sheets and sandwich panels.The main?ndings are summarized below.

(i)At angles of obliquity0–451,a?at-nosed projectile has

a smaller ballistic limit than a hemispherical projectile

as a consequence of more localized deformation near the penetrating corner of the projectile’s nose.

(ii)For oblique impact by a?at-nosed projectile at angles of obliquity0–451,layered plates have a larger ballistic limit than monolithic plates composed of the same

Fig.21.Calculated impact force on a hemispherical projectile(F_1,L/ D?1.64)for an impact speed of120m/s and an initial angle of obliquity of301

Fig.22.Calculated residual speed of a monolithic plate and double-

layered sheet in contact struck by?at-nosed projectiles with L/D?1.64

and4.67at an angle of obliquity of301.t?0,0.12ms,0.24ms and

0.48ms.

Table9

Projectile properties with different length to diameter ratio

Projectile name Diameter(mm)Length(mm)Length/diameter Mass(g)

F_Proj112.720.8 1.6420.6

F_Proj28.941.6 4.6720.6 D.W.Zhou,W.J.Stronge/International Journal of Impact Engineering35(2008)1339–1354

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material and having the same total material thickness (Fig.11).

(iii)For oblique impact by hemispherical-nosed projectiles, monolithic plates and sandwich panels have nearly the same ballistic limit speed.

FE simulations of oblique impact of cylindrical projec-tiles on thin panels(monolithic steel plate or double-layered sheet)generally resulted in a ballistic limit speed within20%of experimental results.Achievement of this accuracy required re?nement of material constitutive relations(including failure criterion across a range of projectile nose shapes and target con?gurations)and incorporation of strain-rate dependence.

This validated numerical model was used to investigate the energy loss in perforation of thin monolithic and layered plates struck at angles of obliquity0–451by?at and hemispherical-nosed projectiles.For a?at-nosed projectile,it was found that the ballistic resistance for layered sheets is much larger than that of a monolithic sheet.A large length-to-diameter ratio of the projectile causes a decrease in the ballistic limit of both monolithic and layered metallic sheets because inertia limits rotation of the projectile(pitch)that develops during perforation. The effect of L/D on the ballistic limit speed decreases, however,with increasing impact speed above the ballistic limit.For oblique impact of?at-nosed projectiles,spacing of layered plates increases the ballistic limit speed because it results in more rotation of the projectile around a transverse axis(pitch)during perforation;for hemisphe-rical-nosed projectiles,spacing of layered plates does not signi?cantly affect the ballistic limit speed.Both hemi-spherical-and?at-nosed projectiles penetrating thin metallic plates(either monolithic or layered)have a minimum ballistic limit speed at an angle of obliquity between301and451from normal.

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