International Journal of Impact Engineering 93 (2016) 153–165
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International Journal of Impact Engineering
j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / i j i m p e n g
Mechanisms of the penetration of ultra-high molecular weight
polyethylene composite beams
J.P. Attwood a, B.P. Russell a, H.N.G. Wadley b, V.S. Deshpande a,*
a
b
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge, UK
Department of Material Science & Engineering, School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22904, USA
A R T I C L E
I N F O
Article history:
Received 19 June 2015
Received in revised form 19 January 2016
Accepted 21 February 2016
Available online 8 March 2016
Keywords:
Ballistic penetration
Fibre composites
Indentation
Fracture
A B S T R A C T
A number of mechanisms have been proposed for the penetration of laminates comprising ultra-high
molecular weight polyethylene (UHMWPE) fibres in a polymeric matrix. Two-dimensional ballistic experiments are conducted in order to directly observe the transient deformation and failure processes
occurring immediately under the projectile via high-speed photography. Two sets of experiments were
conducted on [0°/90°]n laminate beams. First, back-supported and free-standing beams were impacted
by cuboidal projectiles of varying mass and fixed geometry. The observations indicate that in both cases,
failure occurs in a progressive manner, with plies first failing immediately under the impact zone. The
dynamic failure mode is qualitatively similar to that in a quasi-static indentation tests, and attributed
to tensile ply failure by the generation of indirect tension within the plies. Direct membrane stretching
is ruled out as failure that occurred with negligible beam deflection. In the second set of experiments,
the projectile mass was kept constant and its width varied. No dependence of the projectile width was
observed in either quasi-static indentation or dynamic penetration tests. This strongly suggests that failure
is not governed by a shear process at the edge of the projectile. The observations presented here therefore suggest that tensile ply failure by indirect tension rather than membrane stretching or shear failure
at the edges of the projectile is the dominant penetration mechanism in UHMWPE laminates.
© 2016 Elsevier Ltd. All rights reserved.
1. Introduction
Ultra-high molecular weight polyethylene (UHMWPE) fibre is one
of the highest specific strength materials available today [1,2]. These
materials are used to make ropes, sails, tear and cut resistant fabrics,
as well as in ballistic impact protection systems. For ballistic
applications, 10–20 μm diameter fibres are combined with
thermoplastic polymer matrices to form thin (~50 μm thick) unidirectional plies containing ~85% by volume fibres in a polymer
matrix. Examples include Dyneema® (the commercial name for
UHMWPE composites manufactured by DSM1) and Spectra made
by Honeywell.2 These unidirectional plies are typically combined
to form a [0°/90°] cross-ply laminate that is now extensively used
in ballistic protection applications.
A range of mechanisms has been proposed for the penetration/
failure of fibre composite beams and plates impacted by a nominally
rigid projectile. These include (Fig. 1): (i) tensile stretching failure
* Corresponding author. Department of Engineering, University of Cambridge,
Trumpington Street, Cambridge CB2 1PZ, UK. Tel.: +44 1223 332664; Fax: +44 1223
332662.
E-mail address: [email protected] (V.S. Deshpande).
1
DSM, Het Overloon 1, 6411 TE Heerlen, The Netherlands.
2 Honeywell Advanced Fibers and Composites, Morris Township, NJ, USA.
http://dx.doi.org/10.1016/j.ijimpeng.2016.02.010
0734-743X/© 2016 Elsevier Ltd. All rights reserved.
in a string-like mode as first modelled by Phoenix and Porwal [3]
and used to rationalise the Cunniff [4] scaling relationship; (ii) shearoff resulting in the formation of a plug [5]; and (iii) tensile fibre
failure by the generation of indirect tension due to the compressive loading under the projectile [6,7]. A Hertzian cone-crack type
fracture mechanism under the projectile as observed by Karthikeyan
et al. [2] in the context of fibre composites with high strength matrices such as conventional CFRP composites (and many ceramic
materials) has to-date not been reported for Dyneema® or the very
similar Spectra composites. A number of investigations [8–11] have
argued that the ratio of the thickness of laminate to the width of
the projectile dictates the operative mechanism in a given setting.
A number of studies have been conducted to measure the static
[12–14] and dynamic response [2,15–17] of UHMWPE fibres and
composites. For example, Russell et al. [12] have observed that
UHMWPE composites have tensile strengths of a few GPa but a shear
strength of only a few MPa. Moreover, they found that the tensile
strength of UHMWPE fibres displays nearly no strain rate dependence for strain rates up to 103 s −1. Similarly, continuum models too
have been proposed [18,19] to enable the modelling of penetration resistance of UHMWPE composites. While some penetration
calculations have had some success in making quantitative
predictions of the ballistic response [10], they have been unable
to reproduce the progressive failure processes reported by
Karthikeyan et al. [2].
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J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a) Membrane
failure
(b) Shear
(c) Indirect
tension
plugging
Buckling
Plug
Fibre
fracture
Filament
shear cutting
Fig. 1. Sketches of three penetration mechanisms for Dyneema® fibre composite beams. (a) Failure by tensile stretching in a string-like mode; (b) shear-off at the edges of
the projectile and the consequent formation of a shear plug; and (c) progressive tensile ply failure by indirect tension developed due to the compressive stresses under the
projectile.
A range of experimental studies to investigate the penetration
mechanisms of UHMWPE fibre laminates has also been recently conducted [16,17,20–22]. These investigations have primarily focused
on the ballistic resistance of plates. While high-speed photography enables the visualization of the transient deformation of these
plates, the geometry of the experiment prohibits direct imaging of
the dynamic deformation and failure processes at the critical locations, i.e. immediately under the projectile. Thus, these studies
have relied on post-test characterization to infer the dynamic failure
mechanisms. This leaves a number of uncertainties as the different failure modes (Fig. 1) cannot be definitely distinguished by posttest evaluations.
The aim of this study is to provide direct transient experimental observations and measurements to establish the failure and
penetration mechanisms in composites comprising ultra-high molecular weight polyethylene fibres. The outline of the study is as
follows. First we describe the experimental protocol to conduct “twodimensional” ballistic experiments on beams so as to directly observe
the region immediately under the impact site. Next we discuss the
experimental observations to quantify the effect of (a) the boundary conditions of the beams; (b) the mass of the projectile; and
(c) the projectile geometry. These observations are used to infer the
penetration mechanisms for impact velocities up to 650 ms−1.
2. Experimental protocol
The UHMWPE laminate used in this study was a commercial
grade denoted HB26 by the manufacturer DSM Dyneema®. The laminate comprises plies orientated in an alternating [0°/90°] stacking
sequence, with a ply thickness of 60 μm. Each ply is made up of 83%
by volume of SK76 fibres in a polyetherdiol-aliphatic diisocyanate
polyurethane (PADP) matrix. A detailed description of the process
used to manufacture the composite is given in References 12 and
23. Briefly, the steps are as follows:
(1) The UHMWPE fibres are produced by gel spinning followed
by hot drawing. Dissolved UHMWPE stock material is drawn
through a fine spinneret to produce filaments which are
quenched to form a gel-fibre. These fibres are drawn to form
a highly aligned fibre with a diameter of approximately
17 μm.
(2) The fibres are coated in a resin and laid up into [0°/90°/0°/90°]
sheets. The sheets are dried to remove the matrix solvent and
stacked to produce a laminate of the required areal density.
(3) The laminate is hot pressed and the matrix part melts to bond
the plies together, resulting in a plate with a density of
970 kg m−3 (these details are proprietary to DSM).
HB26 laminate material was supplied as 300 mm × 300 mm
× 12.4 mm thick sheets by DSM Dyneema®. These were then cut into
strips of length L = 300 mm and breadth b = 12.4 mm (and thickness t b equal to the sheet thickness) with a medium-fine bladed
band-saw. Due to the low shear strength and consequent ease with
which the material delaminates, cutting required the laminates to
first be sandwiched between two stiff plates (typically plywood).
This confinement prevented delamination and resulted in a high
quality finish with little discernible damage to the specimen edges.
The 300 mm beam length was selected to allow fibre fracture to occur
before the propagating stress waves reached the ends of the beam.
2.1. Experimental setup
A key aim of this investigation was to visualise the penetration
process and especially the failure processes immediately under the
projectile during an impact event. To achieve this aim, we designed two-dimensional (2D) experiments in which projectiles of
rectangular cross-section impacted a beam as sketched in Fig. 2a.
The breadth b of the projectile and beam was equal so that the experiment could be considered 2D, and the deformation and failure
processes under the projectile visualised by imaging of the side edge
of the beam is shown in Fig. 2b.
The projectiles were launched using a previously described gas
gun apparatus [2]. However, most gas gun setups have cylindrical
barrels and launch cylindrical projectiles. Cubical projectiles as required in this study could be launched using a sabot in a cylindrical
barrel but here we instead chose to use an aluminium barrel with
a square cross-section as sketched in Fig. 2a in order to reduce the
yaw, roll and (importantly) spin of the projectile about its longitudinal axis. The planarity of the impact of the cuboidal projectile was
confirmed by impact against a direct impact Hopkinson bar during
calibration of the setup. The beams were tested using two boundary support configurations:
(1) In the “back-supported” configuration (Fig. 2b), the beam was
adhered to a nominally rigid steel backing plate of thickness 45 mm using double-sided adhesive tape.
(2) In the “free-standing” configuration (Fig. 2b), the beam had
a free span of 250 mm, and a 25 mm length at each end of
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
155
PMMA window
Tubular steel
frame
Phantom high-speed camera
(a)
Steel collar for lasers
Nylon supports
in steel housing
Breech
Gun barrel
Support frame
Laser diodes
for velocity
measurement
Dyneema
sample
Gas cylinder
Sample cage
b = 12.4
Steel supports
25
(b)
Camera
b
b = 12.4
Steel
back
plate
b
w
250
300
w
Projectile
25
All dimensions in mm
Dyneema
sample
45
(drawing not to scale)
tb= 12.4
Free-standing case
Back-supported case
Fig. 2. (a) Sketch of the gas gun with a square barrel used to fire a cuboidal projectile. (b) The projectiles impacted “back-supported” and “free-standing” beams with a
high-speed camera used to obtain side-view images as indicated.
the beam was adhered to a rigid steel foundation using
double-sided adhesive tape.
Hardened silver steel (800 Vickers) projectiles impacted the beams
centrally and normally (with zero obliquity) in all cases. Two types
of projectile designs were used to investigate the effect of (a) projectile mass and (b) projectile impact face dimensions. In the study
of the effect of projectile mass, the projectile cross-section was kept
fixed at w = b = 12.4 mm as shown in Fig. 3a and the projectile mass
mp was varied between 22.2 g and 6.4 g by changing the length of
the projectile. A 0.5 mm chamfer was included on the impact face
of all projectiles as shown in Fig. 3a in order to reduce the stress
concentration at the edges of the projectile. For the two lowest masses
of 9.1 g and 6.4 g, a 10 mm long Nylon stabiliser was glued to the
rear of the steel projectile to ensure that the projectile did not change
pitch (yaw) upon exit from the gun barrel. The mass of the stabiliser
is included in the total mass of the projectiles listed in Fig. 3a. In
order to study the effect of the projectile impact surface dimensions, projectiles as sketched in Fig. 3b and of mass mp = 22.2 g were
machined from the hardened silver steel. In all cases, the depth was
kept fixed and equal to that of the beam, i.e. b = 12.4 mm , while the
width w varied between 3 mm and 12 mm. The length of the rear
section of the projectile was varied in order to retain a projectile
mass of 22.2 g.
2.2. Measurement protocols
Projectiles impacted the beams at velocities v0 in the range
50 ms−1–650 ms−1. The stand-off between the end of the square gun
barrel to the target was about 70 mm. Velocities were measured near
the exit of the barrel via a series of laser gates; see Fig. 2a. The first
gate was also used to trigger a model v1611 Phantom high-speed
camera and flash system. Images were recorded with inter-frame
times between 2.17 μs and 7.3 μs, and exposure time of 0.4 μs. These
images were used to infer the temporal evolution of the back face
deflections of the free-standing beams and the displacements of the
projectiles in addition to visualising the failure process near the impact
site.
In addition to these dynamic diagnostics, two types of analyses were also performed on the as-tested beams:
(1) Measurement of cut fraction
Dyneema® laminates are known to fail in a progressive manner
with an increasing number of plies failing (as measured from
the impacted end) with increasing projectile velocity until all
plies have failed at the ballistic limit. In order to accurately
measure the fraction of the plies that have failed (known as
the cut fraction f ), a small black triangle with a base of
s = 10 mm at the rear end of the beam and the apex at the
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J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
(b)
18.4
R = 0.5
12.4
18.4
mp= 22.2 g
Steel
R = 0.5
mp= 22.2 g
12.4
12.4
12.4
13.8
mp= 16.6 g
12.4
12.4
12
9.2
11
12.4
mp= 11.1 g
12.4
w=6
12.4
12.4
10
12.4
6.9
mp= 9.1 g
Nylon
15
12.4
10
12.4
12.4
4.6
11
12.4
w=3
mp= 6.4 g
12.4
All dimensions in mm
Fig. 3. Sketches of the projectile geometries used in this study. (a) Cuboidal projectiles with cross-sectional dimensions 12.4 mm × 12.4 mm and masses as indicated.
(b) Square-nosed projectiles of mass mp = 22.2 g and widths w = 3, 6 and 12 mm.
impacted end was stencilled onto one edge of each specimen, directly under the impact area at the centre of the beam,
as shown in Fig. 4. The width sc of the stencilled patch of the
edge of the cut zone as shown in Fig. 4 provides a direct
Spallation
Delamination
Impact
direction
s
sc
f=
sc
s
measure of the cut fraction via geometrical considerations.
In that analysis we assume that there is no permanent deformation of the uncut plies (consistent with measurements
of Russell et al. [12] which showed that the SK76 fibres display
an elastic/brittle response at strain rates in excess of about
1 s −1 ) and that the apex of the stencilled triangle is at the
centre of the impacted surface.
(2) X-ray tomography
The as-tested beams were imaged using an X-ray computed
tomography scanner (X-Tek 160 kV CT scanner) with scanning beam parameters of 40 kV and 80 μA. Stacks of images
were then generated, representing slices of the specimen at
approximately 0.5 mm intervals.
3. Effect of projectile mass
We proceed to detail the observations from the 2D impact experiments with projectiles sketched in Fig. 3a while focussing on
determining the mechanisms of projectile penetration.
3.1. Back-supported beams
Fig. 4. Sketch of the black triangle of base s = 10 mm stencilled on the side of the
beam with the apex at the centre of the impact site. The width sc at the edge of
the cut zone after the impact is used to estimate the cut-fraction f .
A montage of high-speed photographs showing the deformation of the beam immediately under the projectile is shown in Fig. 5a
and b for the 6.4 g projectile ( v0 = 335 ms −1) and 22.2 g projectile
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
157
(a) (i)
0 µs
5.88 µs
11.76 µs
17.64 µs
23.52 µs
29.40 µs
0 µs
5.88 µs
11.76 µs
17.64 µs
23.52 µs
29.40 µs
20 mm
(ii)
10 mm
(i)
(ii)
(b) (i)
0 µs
5.88 µs
11.76 µs
17.64 µs
0 µs
5.88 µs
11.76 µs
17.64 µs
23.52 µs
29.40 µs
20 mm
(ii)
23.52 µs
29.40 µs
10 mm
Fig. 5. A montage of high speed photographs showing the deformation/failure of the back-supported beams impacted by the (a) mp = 6.4 g projectile at v0 = 335 ms−1 and
(b) mp = 22.2 g projectile at v0 = 191 ms−1 . The time stamp on the images shows time t with t = 0 corresponding to the instant of impact. In each case, the images are shown
at two levels of magnification as indicated by the inset sketch.
( v0 = 191 ms −1 ), respectively, with t = 0 corresponding to the
instant of projectile impact with the beam. In Fig. 5, images taken
at different levels of magnification are included so as to show the
deformation modes at a range of length scales. These images at different magnifications are from the same test. The photographs are
taken on the side of the beam opposite to where the black triangle was stencilled and the final cut-fraction f ≈ 0.25 in both cases
in Fig. 5. Upon impact, a dark region appears directly under the projectile. This is attributed to the development of a micro-texture as
the fibres orientated along the beam length (x-axis) extrude outward
due to their lower transverse compliance; see Fig. 6. As this extrusion progresses, it changes the appearance of the imaged face of the
beam which in turn affects the reflective properties of the surface
of the beam as sketched in Fig. 6c. This change in appearance gives
(a)
an indication of the time for the shock wave emanating from the
impact face to reach the rear face of the t b = 12.4 mm beam. This
transit time is estimated to be ≈ 5 μs from the images in Fig. 5 though
there is considerable uncertainty associated with this measurement. To within the accuracy of the measurement the deduced shock
wave speed was about 2500 ms −1 . For both cases shown in Fig. 5,
failure is seen to initiate at the contact surface between the projectile and beam. This failure then progresses further through the
beam thickness, though the view of this process is later impeded
by ejected debris.
The variation of the fraction of plies f cut by the projectile as
a function of the projectile velocity vo is plotted in Fig. 7a for five
projectile masses mp in the range 6.4 g to 22.2 g. For a given value
of mp two critical velocities can be defined: the minimum velocity
(b) Even surface illumination
t1
(c) Stress-induced micro-texture
0o plies are
squeezed out
o
90 ply
0o ply
Projectile
Light
Shadowed
region
Light
t2 > t1
Dark region
x
y
t3 > t2
y
z
z
Uncompressed
Compression
x
Fig. 6. The mechanism by which a dark patch develops immediately under the impacted region and propagates to the rear of the beam. Sketches of (a) the propagation of
the dark patch as seen in Fig. 5, (b) the undeformed surface with even illumination and (c) the extrusion of alternate plies that causes changes in the reflectivity of the
imaged surface and results in the appearance of the dark patch.
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J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
1.0
m = 22.2 g
p
Cut fraction f
0.8
16.6
11.1
0.6
9.1
6.4 g
0.4
0.2
0
0
100
200
300
400
500
600
700
800
700
800
Projectile velocity v0 (ms-1)
(b)
Cut fraction f
Pre
d
0.6
on
0.8
Pr
ed
icti
ictio
n
1.0
Experiment
0.4
22.2 g
11.1 g
mp = 22.2 g
mp = 11.1 g
0.2
0
0
100
200
300
400
500
600
Projectile velocity v0 (ms-1)
Fig. 7. (a) The measured cut-fraction f versus impact velocity vo for the backsupported beams impacted by projectiles of mass mp in the range 6.4 g to 22.2 g.
(b) Comparison between the measured cut-fractions and that predicted by the energy
balance model for the mp = 11.1 g and 22.2 g projectiles.
Vc at which the first failure of plies is observed such that f = 0+ ,
and the minimum velocity at which all plies have failed with f = 1,
denoted as the penetration velocity Vp . The cut fraction f rises
smoothly from 0 to 1 as v0 is increased from Vc to Vp with both
Vc and Vp increasing with decreasing mp .
O’Masta et al. [22] performed spherical projectile impact studies
against UHMWPE cross-ply plates, and were therefore unable to
perform the direct observations of the mechanisms reported here.
Nevertheless, they suggested that a simple energy balance based
on a quasi-static penetration measurement might suffice to predict
the f versus v0 relation. In order to test this hypothesis, we performed a quasi-static penetration test using an indenter of crosssectional dimensions identical to the projectiles as sketched in the
inset of Fig. 8. The beam was again placed on a nominally rigid
foundation and the applied load P measured via the load cell of
the test machine and the displacement δ of the indenter measured via a laser extensometer. This measured P versus δ curve is
plotted in Fig. 8. After an initial approximately linear increase in
P with increasing δ , a peak load is attained at δ c ≈ 2.5 mm. This
peak load corresponds to the instant when plies are immediately
in contact with the indenter fracture as discussed by Scott [8]. Subsequently, continued penetration occurs by a series of discrete ply
failure events which result in the saw-tooth type P versus δ
response seen in Fig. 8.
A montage of photographs showing the deformation of the beam
immediately under the indenter is included in Fig. 9a and shows
the progressive failure process under the indenter. Each load peak
in Fig. 8 corresponds to a ply failure event where plies immediately in contact with the indenter fail in tension by the indirect tension
mechanism proposed by Attwood et al. [7]. These failed plies then
recoil back to let the indenter through. The mechanism by which
this indirect tension fracture occurs under the indenter is illustrated in the sketch in Fig.9b.
A comparison of the quasi-static images in Fig. 9a with the highspeed images in Fig. 5 suggests a similarity in the deformation/
failure mechanisms, i.e. ply failure under both static and dynamic
loading is via the indirect tension failure mechanism. Given this similarity in the failure modes, a simple model for the cut fraction in
the dynamic tests can be proposed via an energy balance of the form
δ
1
mp v02 = ∫ P dδ .
2
0
(3.1)
250
P, δ
Load P (kN)
200
b =12.4 mm
150
t b= 12.4 mm
100
w = 12.4 mm
50
0
0
2
4
6
8
10
12
Displacement δ (mm)
Fig. 8. The measured quasi-static load P versus displacement δ response of the indentation of a Dyneema® beam on a nominally rigid foundation as sketched in the inset.
The cross-sectional dimensions of the rigid indenter are identical to those in Fig. 3a.
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
159
indenter
δ = 0 mm
δ = 0.5 mm
δ = 1 mm
δ = 3 mm
10 mm
(b)
Inter-laminar shear
Poisson's
expansion
Cubical punch
Pull-in
X
Void
Tension
Bulge Void
Compression
Z
Fig. 9. (a) Montage of images from the quasi-static test of Fig. 8 showing the deformation and failure of the plies immediately under the indenter. Images are shown for
four values of the displacement δ . In the first image, the darkened region immediately under the projectile is a result of a shadow due to the flash used in the high-speed
photography. (b) Sketch of the indirect tension failure mechanism by which plies fail due to the compressive stresses under the indenter. This image is adapted from a figure
appearing in Reference 19.
Equation (3.1) gives the penetration depth δ as a function of the
impact velocity vo . With the cut-fraction f in this quasi-static test
defined as
f≡
δ − δc
, δ c ≤ δ ≤ tb
tb − δ c
(3.2)
such that f = 0 if δ ≤ δ c and f = 1 when δ = t b , Eqs. (3.1) and (3.2)
directly provide predictions of the vo − f relation. These predictions are included in Fig. 7b for mp = 11.1 g and 22.2 g. It is clear that
while the model adequately predicts the velocity Vc at the onset
of cutting (at-least in the mp = 22.2 g case), it substantially overpredicts the penetration velocity Vp .
This discrepancy between the measurements and predictions can
be understood by examining X-ray tomography (XCT) images of the
beams impacted by the mp = 11.1 g projectile shown in Fig. 10 for
six values of vo with f varying between f = 0.01 and 1. The XCT
images show the mid-plane of the beam as illustrated in the inset
in Fig. 10.3 At low impact velocities ( v0 ≤ 208 ms −1), failed plies are
seen on the impacted face of the beam and the number of failed
plies increases with increasing v0 . However, when the impact velocity rises to v0 ≈ 250 ms −1 , a second failure mode initiates with
plies now failing on both the impacted face and rear face (i.e. the
face supported in the foundation) of the beam but with plies in
between remaining intact. As the impact velocity is increased further,
the number of plies failing on both the impacted and rear faces increases until at v0 = Vp ≈ 344 ms −1 all the plies of the beam have failed.
We now divide the total cut fraction f into two parts: the fraction
3
The images seem to suggest shear failure at the edges of the projectile. However,
this would have resulted in a shear plug that is not observed. Thus, we argue in Section
4 that failure is actually by indirect tension with complete disintegration of the material under the projectile, giving the impression that failure initiated at the edge
of projectile.
fb of the plies that have failed on the rear face and f f that have
failed on the impacted face such that f ≡ fb + f f . The variation of
both f and fb with v0 for the mp = 11.1 g projectile is plotted in
Fig. 11. At low impact velocities, fb ≈ 0 , but as we approach the penetration velocity Vp , fb becomes a significant component of f . We
emphasize that the curves for f and fb do not extrapolate beyond
Vp ≈ 344 ms −1 when all plies within the beam have failed. Recall
that in the quasi-static indentation test, ply fracture on the rear surface
was never observed. In the dynamic tests, ply fracture occurs on the
rear surface due to the compressive stress enhancement that occurs
as the shock wave that initiates from the projectile impact (and propagates to the rear face), reflects from the rigid foundation. This
mechanism is of course not present in the quasi-static tests and the
model associated with Eqs. (3.1) and (3.2). Therefore, the model overpredicts Vp as it does not account for the ply failure at the rear surface
that becomes increasingly important with increasing impact velocity.
3.2. Free-standing beams
The most commonly accepted view of failure of Dyneema® or
Spectra beams/plates is via a membrane stretching mechanism as
proposed by Phoenix and Porwal [3] and used to rationalise the
Cunniff [4] scaling. This mechanism is sketched in Fig. 12 and involves two key processes: (i) upon impact of the projectile, a
longitudinal elastic wave propagates outward at a speed c L ; and
(ii) this longitudinal wave is followed by a slower wave travelling
at c p and marks the edge of the expanding portion of the beam that
has deflected. Tensile strains build up in the portion of the beam
engulfed by the longitudinal wave, with the maximum tensile strain
occurring in the section immediately under the projectile. The beam
fails when the strain reaches the material failure strain and therefore failure is a binary event, with either failure of the complete beam
cross-section or all plies remain intact.
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J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
(c)
(b)
5 mm
5 mm
5 mm
(d)
(e)
5 mm
(f)
5 mm
5 mm
Fig. 10. X-ray tomography images of the mid-plane of the as-tested back-supported beams impacted by the mp = 11.1 g projectile at (a) v0 = 160 ms−1 ( f = 0.01) ; (b) v0 = 208 ms−1
( f = 0.08) ; (c) v0 = 250 ms−1 ( f = 0.24); (d) v0 = 298 ms−1 ( f = 0.54); (e) v0 = 308 ms−1 ( f = 0.73) ; and (f) v0 = 344 ms−1 ( f = 1.0) . The inset shows a sketch of the imaged
plane.
The deformation/failure of the free-standing beams impacted by
the mp = 6.4 g ( vo = 423 ms −1 ) and mp = 22.2 g ( vo = 342 ms −1 ) projectiles is shown in Fig. 13a and b, respectively, via a series of highspeed photographs at different levels of magnification similar to those
in Fig. 5 (here the images at the different magnifications are from
different tests). The deformation/failure process as identified from
these images differs from the Phoenix and Porwal [3] mechanism
summarised above in the following respect. Phoenix and Porwal [3]
Cut fractions f and fb
1.0
assume that initial elastic deformation occurs in a membrane mode
with a spatially uniform tensile strain being generated across the
beam cross-section. Thus, failure of the beam must be a binary event
with all or no plies failing. In contrast, it is clear from Fig. 13 that
failure occurs in a progressive manner similar to the back-supported
case with the propagation of the darkened region (associated with
failed plies). Here, plies in contact with the projectile failed first,
and this failure front then propagated through the beam thickness.
This is a brittle failure mechanism and the propagation of this brittle
failure front (with failure due to indirect tension) is similar to that
observed during cavity expansion with micro-cracking etc. [24,25].
The distance the failure front propagates through the beam thickness
0.8
0.6
tb
Mp
Total cut fraction f
Vo
0.4
cL
tb
0.2
Back face cut fraction fb
0
0
50
100
150
200
250
300
350
400
Mp
cp
mp
-1
Projectile velocity v0 (ms )
Fig. 11. The variation of the total cut-fraction f and the cut-fraction fb of the plies
at the rear face as a function of the impact velocity vo for the back-supported beam
impacted by the mp = 11.1 g projectile.
V
Fig. 12. Sketches showing the elastic string-like deformation mode assumed in the
Phoenix and Porwal [3] analysis. The progression of the longitudinal and deflection waves travelling at c L and c p , respectively ( c L > c p ), is indicated.
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
161
(i)
0 µs
7.29 µs
14.58 µs
21.87 µs
20 mm
43.74 µs
(ii)
(i) (ii)
(iii)
0 µs
5.88 µs
0 µs
2.17 µs
0 µs
7.29 µs
11.76 µs
17.64 µs
23.52 µs
10 mm
(iii)
4.34 µs
8.68 µs
13.02 µs
10 mm
(b) (i)
14.58 µs
29.16 µs
20 mm
51.03 µs
(i) (ii)
(ii)
(iii)
0 µs
10 mm
5.88 µs
11.76 µs
17.64 µs
23.52 µs
2.17 µs
4.34 µs
8.68 µs
13.02 µs
(iii)
0 µs
10 mm
Fig. 13. A montage of high speed photographs showing the deformation/failure of the free-standing beams impacted by the (a) mp = 6.4 g projectile at v0 = 423 ms−1 and
(b) mp = 22.2 g projectile at v0 = 342 ms−1 . The time stamp on the images shows time t , with t = 0 corresponding to the instant of impact. In each case, the images are
shown at three levels of magnification as indicated by the inset sketch.
increases with increasing vo . Importantly, it is clear that plies fail
very early in the deformation history when the beam deflection is
much smaller than its thickness, clearly showing that failure is not
occurring in a membrane or string-like mode.
The temporal evolution of the displacements of the projectile
(which behaves as a nominally rigid body) and the maximum deflection of the rear face of the beam for the two cases in Fig. 13 are
plotted in Fig. 14. Recall from Fig. 5 that it takes approximately 5 μs
for the wave emanating from the projectile/beam interface to reach
the rear face of the beam and thus the back face deflection of the
beam only initiates after this initial transient. Subsequently, the displacement rates of the projectile and back face of the beam are nearly
equal for both cases. The difference in the displacements of the back
face of the beam and the projectile is equal to the penetration of
the projectile into the beam. Thus, the data in Fig. 14 suggest that
the majority of the penetration occurs within the first 5 μs after
impact, with the beam and projectile moving together subsequently.
The cut fraction f of the free-standing beams is plotted in Fig. 15
as a function of the impact velocity vo for three projectile masses
mp . Again, both Vc and Vp increase with decreasing mp , though
unlike the back-supported case (Fig. 7a), the results in Fig. 15 suggest
that the vo − f curves are reasonably independent of mp for
mp ≥ 16.6 g .
It is worth emphasising here that while penetration of the beam
occurs in both the back-supported and free-standing cases by the
indirect tension mechanism, no ply failure at the rear surface is observed in the free-standing case. This is because the compressive
stress wave reflects as a tensile wave from the free rear face of the
free-standing beams and hence does not generate the compressive stresses required to activate the indirect tension mechanism
at the rear face.
3.3. Comparison between back-supported and free-standing beams
The measurements of Vc and Vp as a function of the projectile
mass mp are included in Fig. 16 for both the back-supported and
free-standing beam cases. Two key features are evident from this
summary: (i) for a given mp , both Vc and Vp are higher for the
162
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
1.0
25
m = 22.2 g
p
0.8
20
Projectile
Cut fraction f
Displacement ∆ (mm)
mp= 6.4 g
15
10
Back face
5
0.6
16.6 g
0.4
6.4 g
0.2
0
0
10
20
30
40
50
60
70
0
80
0
Time t (μs)
(b)
100
300
400
500
600
700
800
Projectile velocity v0 (ms-1)
25
Fig. 15. The measured cut-fraction f versus impact velocity vo for the freestanding beams impacted by projectiles of mass mp in the range 6.4 g to 22.2 g.
mp= 22.2 g
Displacement ∆ (mm)
200
20
Projectile
In the limit of a heavy projectile, mb mp → 0 and v f → vo , i.e. we
expect the relative velocity between the beam and the projectile
to become insensitive to mp with increasing mp . This is the reason
for the reduction in the sensitivity of Vc and Vp to mp at high values
of the projectile mass in the free-standing beam case.
15
10
Back face
4. Effect of projectile geometry
5
0
0
10
20
30
40
50
60
70
80
Time t (μs)
Fig. 14. Measurements of the displacements Δ of the projectile and maximum deflection of the rear face of the free-standing beam as function of time t with t = 0
corresponding to the instant of impact. The measurements are shown for (a) the
mp = 6.4 g projectile at v0 = 423 ms−1 and (b) the mp = 22.2 g projectile at
v0 = 342 ms−1 (i.e. the two cases in Fig. 13).
The results presented above clearly show that tensile failure in
a stretching string-like mode does not describe the failure mode of
the Dyneema® beams impacted by a rigid projectile. The failure mode
has instead been argued to be indirect tension due to the compressive stresses generated by the impacting projectile. Another failure
mode suggested by Cheeseman and Bogetti [5] was shear failure at
the edges of the projectile. While the high speed images in Section
3 suggest that this is not the operative mode, the images are
free-standing beam case compared to the back-supported case; and
(ii) Vc and Vp are more sensitive to mp in the back-supported case,
with these critical velocities becoming nearly independent of mp
for mp ≥ 16.6 g in the free-standing beam case.
To rationalise observation (i), note that the interfacial pressure
between the projectile and beam generates the stress required to
trigger the indirect tension failure mechanism. This pressure is set
by the relative velocity between the projectile and the beam, with
a higher relative velocity giving rise to a higher pressure. The relative velocity between the beam and the projectile in the backsupported case is equal to the projectile velocity as the beam is
stationary. Thus, in the back supported case, a lower projectile velocity compared to the free-standing case is required to generate
the interfacial pressure required to cause failure by indirect tension.
In order to develop a qualitative understanding of observation (ii),
consider an unsupported beam of mass mb impacted by a projectile of mass mp and at a velocity vo . The beam and projectile acquire
a common velocity v f as time t → ∞ and v f are given by momentum conservation as
vf =
vo
.
1 + mb mp
(3.3)
Projectile velocity (ms-1)
700
600
VP
500
Free
400
Back supported
300
VC
Free
200
Back supported
Free
100
Back supported
0
0
5
10
15
20
25
Projectile mass mp (g)
Fig. 16. Summary of the measurements of the critical velocity Vc to initiate failure
in the beam and the velocity Vp for complete penetration in the back-supported and
free-standing beams as a function of the projectile mass mp . We emphasize that
the lines through the date are to aid the eye in terms of the trends rather than definite fits on the variation of Vp or Vc with mp .
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
(a)
163
p / p0
p0
w
1
Indenter
nose
x'
x
-1
2
0
x
w
1
2
(b)
1600
P, δ
w = 3 mm
Presure p0 (MPa)
1400
b
1200
1000
tb
800
600
w
400
6
200
12
p0 =
0
0
2
4
6
8
10
P
(bw)
12
Displacement δ (mm)
Fig. 17. (a) Plane strain indentation of an elastic beam on a rigid foundation by a frictionless flat-bottomed rigid indenter. The sketch shows the contact pressure distribution and the definition of the co-ordinate systems x and x ′ . (b) The measured quasi-static nominal contact pressure p0 versus indentation depth δ for three indenter
widths w . The inset shows a sketch of the test geometry for indentation on a rigid foundation.
sufficiently blurred by the impact debris to leave some doubt. In
this section, we provide further evidence to show that shear failure
mode is not an operative in these experiments.
Consider the plane strain quasi-static indentation of a backsupported isotropic elastic beam by a frictionless flat-bottomed rigid
indenter of width w as shown in Fig. 17a. For an applied normal
load P , the contact pressure distribution is given by [26]
4.1. Quasi-static indentation
p0
p=
π 1−
4 x2
w2
(4.1)
where p0 ≡ P w is the nominal contact pressure and x is the position measured from the center of the indenter as shown in Fig. 17a.
Defining x ′ ≡ x + w 2 , the contact pressure pe in the limit x ′ → 0+
is given by
pe ≡
H
p w 1
= 0
,
2π
x′
x′
(4.2)
i.e. the contact pressure is asymptotically unbounded at the edge
of the indenter with the magnitude of the singularity H ≡ ( p0 √ w ) 2π .
We thus anticipate shear failure at the edges of the indenter to occur
when this magnitude reaches a material specific value Hc and thus
the nominal contact pressure at failure p0f is expected to scale as
p0f =
projectile are not perfectly sharp since the asymptotic fields associated with this scaling hold at distances from the edge of the
indenter on the order of the chamfer radius. This is analogous to
the fact that singular crack tip fields adequately characterize the fields
around blunt cracks (or notches) at distances away from the crack
tip on the order of the crack tip radius [27].
2π Hc
.
w
(4.3)
This inverse square root scaling of the nominal contact pressure at failure with the width of the indenter is thus expected to
be a hallmark of the shear failure mechanism and we present measurements in this section to test this scaling. We emphasize here
that the scaling (4.3) is applicable even when the edges of the
Heat-treated silver steel indenters were used to perform indentation tests similar to those described in Section 3.1. A summary
of the measured nominal contact pressure p0 versus the indenter
displacement δ is plotted in Fig. 17b for three indenter widths in
the range 3 mm ≤ w ≤ 12.4 mm . The p0 − δ curves are similar to the
P − δ relationship seen in Fig. 8 and comprise an initial elastic
region with first ply failure setting the initial peak pressure at displacement δ c = 2.4 mm . The subsequent saw-tooth response is due
to discrete ply failure events. It is clear from Fig. 17b that the initial
peak contact pressure is independent of the indenter width w . Moreover, to within the inherent variability of the subsequent failure
events there is also no evidence of a dependence of the contact pressure on w . Recall that the analysis presented above suggests that
the contact pressure at failure for the w = 3 mm indenter is expected to be about double that of the w = 12.4 mm indenter. This
is clearly not the case and thus these results suggest that ply failure
under the indenter does not occur via a shear failure mechanism
at the edges of the indenter but rather via the indirect tension mechanism consistent with the images in Fig. 9.
4.2. Impact measurements
Projectiles of mass mp = 22.2 g and geometry sketched in Fig. 3b
were impacted normally and centrally on the back-supported and
164
J.P. Attwood et al./International Journal of Impact Engineering 93 (2016) 153–165
1.0
All dimensions in mm
11
12.4
w
w
0.2
w= 3
in
nd
ta
-S
ee
Ba
ck
-S
up
po
0.4
g
rte
d
0.6
Fr
Cut fraction f
0.8
6
12
0
0
100
200
300
400
500
(not to scale)
Projectile velocity v0 (ms-1)
Fig. 18. The measured cut-fraction f as a function of the impact velocity vo for projectiles of mass mp = 22.2 g impacting the back-supported and free-standing beams.
The loading geometry is included in the inset and results are presented for three projectile widths w = 3, 6 and 12 mm.
free-standing beams employed in Section 3. Three projectile widths
w = 3, 6 and 12 mm were used in this study. The measured cutfraction f versus impact velocity vo is plotted in Fig. 18 for both
the free-standing and back-supported beam cases. Similar to the
results of Section 3, for any given vo , the cut fraction f is significantly larger in the back-supported case compared to the freestanding case with both Vc and Vp also lower in the back-supported
case. However, the results show no dependence of the cut-fraction
on the width w of the projectile to within the variability in the measurements. Thus, again similar to the quasi-static indentation there
is no evidence that shear failure at the edges of the projectile is the
operative penetration mode in these experiments.
5. Concluding discussion
Experimental observations of the deformation/failure processes of ultra-high molecular weight polyethylene (UHMWPE) fibre
laminates impacted by nominally rigid projectiles are reported. The
transient processes are visualised by performing two-dimensional
(2D) experiments on beams and using high-speed photography to
image immediately under the impact site. Two sets of experiments were conducted by firing the projectiles normally and
centrally on back-supported and free-standing beams. In the first
set, cuboidal projectiles of fixed cross-sectional area were employed with masses in the range 6.4 g to 22.2 g while in the second
series the projectile mass was fixed at 22.2 g and the width of the
projectile varied.
For projectiles of fixed geometry, the velocity at which first failure
is observed and the velocity at which complete penetration occurs
both decrease with increasing projectile mass for both the backsupported and free-standing cases. The high-speed photographs
clearly show that in both cases, failure occurs in a progressive
manner: Ply fracture initiates at the interface between the projectile and the beam and propagates to the rear of the beam. The failure
process is similar to that in a quasi-static indentation test and attributed to tensile failure of the plies by an indirect tension
mechanism wherein the transverse compressive stresses generate
tensile stresses due to a mismatch in the properties between the
alternating 0° and 90° plies. Tensile failure due to membrane
stretching is ruled out as failure is shown to occur when the deflection of the beams is negligible and no ply failure occurs late in
the deformation when the deflections are significant. Two key differences between the free-standing and back-supported cases are
observed: (i) the cut fraction of the back-supported beams is higher
compared to the free-standing beams at the same projectile impact
velocity; and (ii) at high impact velocities, plies are observed to fail
on the rear surface of the back-supported beams due to stress wave
reflections from the rigid foundation while this mode is not observed in the free-standing beams.
In the second set of experiments, no observable dependence of
the projectile width was observed in both the quasi-static indentation and dynamic penetration responses. This suggests that failure
in these beams is not governed by the high stress concentrations
at the edges of the projectile. This is also consistent with the observation that failure by the formation of shear plugs was never
observed. Together, the observations reported here demonstrate that
neither tensile failure by membrane stretching nor shear plugging
is operative in these 2D beam experiments. Penetration and failure
occur by tensile ply failure via the indirect tension mechanism.
Acknowledgements
This research was funded by the Defense Advanced Research Projects Agency (DARPA) under grant number W91CRB-11-1-0005
(Program manager, Dr. J. Goldwasser). We are grateful to DSM for
the supply of the materials used in this study. Dr B.P. Russell was
supported by a Ministry of Defence/Royal Academy of Engineering Research Fellowship (Grant Number RG60007).
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