Deformation mechanisms and energy absorption of polystyrene foams for protective helmets

Abstract

The deformation mechanisms and energy absorption capability of polystyrene foams and polycarbonate shells for protective helmets are experimentally studied with the aim of developing a comprehensive constitutive law to be implemented into FEM codes for impact analysis. Expanded polystyrene (EPS) of different densities are considered. Tensile and bending tests on both EPS and PC are performed. Static and dynamic compression tests on EPS are performed as well, according to both variable- and fixed-volume methods. Falling weight tests are performed on both plane PC and sandwich PC/EPS at different energy contents to investigate possible couplings. EPS dynamic-mechanical tests are also carried out at different frequencies to evaluate temperature and strain rate influence on material stiffness. The extensive scanning electron microscopy analysis allows the investigation of strain mechanisms responsible for energy absorption as well as the validation of existing theoretical models. It is demonstrated that the energy absorption capability of these materials can be controlled at two different stages: at the macroscopic scale, by choosing the foam density able to minimise the transferred load and the acceleration value in relation to the available absorbing volume; at the microscopic scale, by modifying EPS internal structure in terms of hollow bead dimensions and walls thickness.

Full text

Polymer Testing 21 (2002) 217–228 www.elsevier.com/locate/polytest
Product Performance
Deformation mechanisms and energy absorption of
polystyrene foams for protective helmets
Luca Di Landro
a,*
, Giuseppe Sala
1,b
, Daniela Olivieri
1b
a
“G. Natta” Politecnico di Milano, Department of Industrial Chemistry and Chemical Engineering,
Piazza Leonardo da Vinci, 32, 20133 Milan, Italy
b
Aerospace Engineering Department, Politecnico di Milano, Via La Masa, 34, 20158 Milan, Italy
Received 25 April 2001; accepted 27 June 2001
Abstract
The deformation mechanisms and energy absorption capability of polystyrene foams and polycarbonate shells for
protective helmets are experimentally studied with the aim of developing a comprehensive constitutive law to be
implemented into FEM codes for impact analysis. Expanded polystyrene (EPS) of different densities are considered.
Tensile and bending tests on both EPS and PC are performed. Static and dynamic compression tests on EPS are
performed as well, according to both variable- and fixed-volume methods. Falling weight tests are performed on both
plane PC and sandwich PC/EPS at different energy contents to investigate possible couplings. EPS dynamic-mechanical
tests are also carried out at different frequencies to evaluate temperature and strain rate influence on material stiffness.
The extensive scanning electron microscopy analysis allows the investigation of strain mechanisms responsible for
energy absorption as well as the validation of existing theoretical models. It is demonstrated that the energy absorption
capability of these materials can be controlled at two different stages: at the macroscopic scale, by choosing the foam
density able to minimise the transferred load and the acceleration value in relation to the available absorbing volume;
at the microscopic scale, by modifying EPS internal structure in terms of hollow bead dimensions and walls thickness.
2001 Elsevier Science Ltd. All rights reserved.
1. Introduction
Polymeric foams are extensively used in several appli-
cations such as impact-absorbing and thermal-acoustic
insulating materials. Possibly, the most common of such
foams is expanded polystyrene (EPS). Thanks to a con-
venient cost-benefit ratio, it is widely employed in the
packaging industry. Besides, owing to its outstanding
capability of energy absorption, it is also used in highly
demanding applications like head protective helmets.
The impact-protection function of modern helmets for
* Corresponding author. Tel.: +39-02-2399-3253; fax: +39-
02-2399-3266.
E-mail addresses: luca.dilandro@polimi.it (L. Di Landro),
giuseppe.sala@polimi.it (G. Sala).
1
Tel.: +39-02-2399-8361; fax: +39-02-2399-8334.
0142-9418/02/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.
PII: S0142 -9418(01)00073-3
motorcyclists (Fig. 1) is performed by both the stiff
external shell and the inner polymeric, rigid foam layer
[1–7]. The function of the stiff outer shell, generally
made of polycarbonate (PC), acrylonitrile-butadiene-
styrene copolymer (ABS) or polymer composites
(usually glass, graphite or aramidic fibres in epoxy or
polyester resins), is to distribute the impact energy over
a large area, thus avoiding concentrated loads. Also, a
significant share (34%) of the impact energy is dissipated
by the shell deformation [1,2]. The main function of the
polymeric foam inner layer, generally made of closed-
cells expanded polystyrene, is to absorb most of the
impact energy and to reduce to a minimum the load
transmitted to the head [6,7]. EPS parts with different
thicknesses and density can be found in the various pos-
itions of the helmet (top, rear, sides) to ensure adequate
comfort and protection to the driver. Moreover, different
thicknesses are often used to fit different head sizes to a

218 L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Fig. 1. Sketch of a motorcycle helmet.
single outer shell dimension (this means that persons
with larger heads and, presumably, higher weight, are
protected by lower EPS thickness). Therefore, different
combinations of density and thickness should be tested.
The main parameters which need to be considered in
the impact protection are the maximum impact energy,
the concentrated loads, and the accelerations transferred
to the head. The standards presently in force [8–13] usu-
ally consider these parameters as critical for the certifi-
cation of helmets for motorcyclists. The European Stan-
dard ECE 22-04 requires that motorcycle helmets
containing a false head of 5 kg mass should sustain
impacts up to a rate of 7.5 ms
⫺1
. Transferred acceler-
ations must be lower than 275 g and the HIC (Head
Injury Criterion) value, which considers load duration as
well, should not exceed 2400 [8].
The impact absorption capabilities can be tuned by
balancing the thickness and the density of the expanded
material. Increasing thickness can increase the
absorbable impact energy at the expense of helmet size,
comfort and aerodynamic performance. Increasing foam
density allows better energy dissipation at the expense
of higher accelerations and loads transferred. Owing to
these considerations, the optimisation of energy absorb-
ing capability of expanded foams can lead to a significant
improvement in the performance of sport helmets. In
addition, such an improvement might also be reflected
in the area of packaging, reducing protective foam vol-
umes with remarkable benefits on environmental and
transport costs. This optimisation requires a deep knowl-
edge of the relationship between the structure of the
expanded material, the deformation mechanics and the
energy absorption capability.
Motorcycle helmets EPS foam layers, as many pack-
aging protections, are usually produced in a two-stage
process. In the first stage, plastic pellets, containing a
low-boiling point hydrocarbon expander dissolved
within, are partially foamed to obtain pre-expanded
pearls. In the second stage, the pearls are sintered
together and expanded to the final density and shape in
a mould to produce the helmet part. A complex structure
results, consisting of sintered pearls a few mm in diam-
eter with dense and stiff walls between each other. The
pearls are made of small closed cells with dimensions of
the order of 100 µm. Therefore two sizes of unit cells
can be revealed, which are expected to deform inter-
actively. The foamed polystyrene parts are then inserted
into the plastic or composite helmet shells.
The deformation behaviour of foamed materials made
of closed cells can be described by simplified mechanical
models which refer to a network of beams [14,15]. These
models recognise different phenomena occurring during
the foam mechanical loading. Contributions derive from
elastic deflection of cell walls, air compression and buck-
ling of cell walls. These models, however, are often
applicable only to specific materials. In fact, polystyrene
foam structure is somewhat different from that described
by the models. Also, non-uniform deformation can be
observed during the compression of the material con-
sidered in this work, which is not taken into account by
the models.
In the following, the mechanical behaviour of poly-
styrene foams, dependent on thickness and density, is
studied. Plane EPS and coupled EPS/polycarbonate
samples are tested to investigate the relationship between
material characteristics and energy absorption mech-
anisms under different loading conditions. The results
can be employed for design and analysis of helmet
behaviour. The microscopic analysis of strain mech-
anisms points out different contributions dependent on
EPS structural parameters and suggests possible
improvements in the modelling of this cellular material.
2. Deformation mechanics
A general approach to the description of foam defor-
mation mechanisms can be found in [14]. The specific
considerations relevant to polystyrene foams are reported
and discussed in the following. The properties of cellular
solids depend on two separate sets of parameters:
앫those describing the structure of the foam, i.e. cell
size and shape, density and material distribution
between cells edges and faces;
앫those describing the intrinsic properties of the
material constituting the cell walls.
The main foam structural features are its relative den-
sity r*/r
b
(subscript brefers to bulk material properties,
asterisk to foam properties) and the proportion of open
and closed cells. The basic cells wall properties are bulk
density (r
b
), Young’s modulus (E
b
) and yield strength
(s
yb
).
Fig. 2 reports a compressive stress–strain curve typical
of elastomeric foams, showing linear elasticity (I) at low

219L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Fig. 2. Typical compression stress–strain curve of a rigid
foam.
stresses, followed by a wide collapse plateau (II), which
leads to densification (III), where stress rises steeply.
(I) Linear elasticity holds for small (3–5%) strains and
is controlled by three different strains: bending of
cell edges, compression of gas trapped into the cells
and stretching of cell walls. In the case of com-
pressive load, the plateau is associated with cell
collapse owing to the onset of plastic hinges. Once
the cells have almost completely collapsed, oppos-
ing walls come into contact, further compressive
stresses arise, leading to the final region of bottom-
ing-out.
Young’s modulus E* is the initial slope of the
stress–strain curve and may be expressed as:
E∗
E
b
⫽E
c
∗
E
b
⫹E
g
∗
E
b
⫹E
f
∗
E
b
⯝f
2
·
冉
r∗
r
b
冊
2
(1)
⫹P
0
·(1−2n∗)
冉
1−r∗
p
b
冊
·E
b
⫹(1⫺f)·r∗
r
b
where:
r∗
r
b
⫽1,2·
冉冉
t
e
l
冊
2
⫹0,7·
冉
t
w
l
冊
2
冊
(2)
and fis the fraction of bulk materials pertaining to
the cell edges of thickness t
e
; the remaining frac-
tion, (1⫺f), constitutes the walls of thickness t
w
;l
is the edge length.
The first contribution, due to bending of cell
edges (E
e
∗), is computed from the linear-elastic
deflection of a beam of unitary length loaded at its
midpoint by a load F(Fig. 3a). When a uni-axial
stress is applied to the foam so that each cell edge
transfers the force F(Fig. 3b), the edge itself bends
and the linear-elastic deflection dof the structure
Fig. 3. Mechanical model for the deformation of a closed cell:
(a) un-deformed, (b) deformed.
as a whole is proportional to (Fl
3
)/(E
b
I), where Iis
the edge second moment of inertia (I⬀t
4
e
). The force
Fand the strain eare related to the compressive
stress sand the displacement dby the relationships
F⬀sl
2
and e⬀(d)/(l) respectively. It follows that the
elastic contribution to foam Young’s modulus is
given by E
e
∗=(s)/(e)⬀(E
b
t
4
)/(l
4
).
The second contribution, due to gas compression
(E
g
∗) is computed by considering a foam sample
of volume V
0
and relative density (r*)/(r
b
), whose
cells are filled with gas. If the sample is axially
compressed by the strain e, its volume decreases
from V
0
to V, where:
V
V
0
⫽1⫺e·(1⫺2n∗) (3)
The gas fills the cell space and is excluded from
the volume taken by the bulk cell edges and walls,
so its volume decreases from V
0
g
to V
g
, where:
V
g
V
0
g
⫽
1−e·(1−2n∗)−r∗
r
b
1−r∗
r
b
(4)
a Poisson’s ratio n*⬇0.33 is usually assumed [14].
The contribution to Young’s modulus is com-
puted from Boyle’s law. P
0
is the initial value of
gas pressure (usually atmospheric pressure), the
pressure Pdue to the strain eis given by
PV
g
=P
0
V
0
g
. The pressure which must be overcome
by the applied stress is P⬘=P⫺P
0
. Its contribution
to the modulus is given by E
g
∗=(dp⬘)/(de), which
is usually negligible compared to other contri-
butions. When transverse deformation is con-
strained as in confined compression tests, a Pois-
son’s ratio n*⬇0 should be assumed in Eq. (4).
In the last contribution, due to stretching of the
wall membranes (E
w
∗), the force Fcauses face
stretching proportional to d; the structure is linearly
elastic, so work
1
2
Fd, is done against the restoring
force caused face stretching proportional to

220 L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
1
2
E
b
e
2
V
w
, where eis the strain caused by stretching
of a cell wall, and V
w
is the volume of bulk material
pertaining to a cell face (V
w
⬀l
2
t
w
).
The same procedure leads to the expression of
shear modulus G*:
G∗
E
b
⬇3
8
冋
f
2
·
冉
r∗
r
b
冊
2
⫹(1⫺f)·r∗
r
b
册
(5)
The contribution due to gas pressure disappears
because pure shear is not expected to produce any
change in volume.
(II) Foams made of materials possessing a plastic yield
point show a ductile failure as well if loaded
beyond their linear-elastic regime. Plastic collapse
gives the stress–strain curve a wide horizontal pla-
teau, where the strains are no longer recoverable.
Such a feature is exploited in energy-absorbing sys-
tems.
The load inducing plastic collapse in a closed-
cell foam depends on three different mechanisms.
When the bending moment acting at cell walls
exceeds the allowable moment of the edges, there
is an onset of permanent hinges, cell wall plastic
stretching occurs and pressure of fluid contained
into the cell increases.
The plastic hinges onset when the cell walls
allowable bending moment is overcome (Fig. 4).
To evaluate its contribution to the overall com-
pressive strength, the plastic collapse has to be con-
sidered. The cell displacement dparallel to the
compression axis produces the work Fd, the edge
rotation is proportional to d/land the plastic work
due to the evolution of plastic hinges is pro-
portional to M
p
d/l, so the following relationship
holds:
Fd⬀M
p
d
l(6)
Because Fand dare proportional to sl
2
and el
Fig. 4. Mechanics of closed cell plastic collapse: wall stretch-
ing +edge bending.
respectively, the contribution given by the plastic
hinges to the collapse strength is expressed as:
s
h
pl
s
yb
⫽Cf
3
2
冉
r
r
b
冊
(7)
where C⬇0.3 is experimentally measured in open-
cell foams.
Perpendicular to the compression axis, the walls
are tensioned and the corresponding plastic work
Fdis proportional to s
yb
dt
w
l. The contribution of
cell wall plastic stretching to the collapse strength
can be expressed as:
s
w
pl
s
yb
⫽C∗(1⫺f)r∗
r
b
(8)
where C*=1.
Pressure Pof the gas contained into the cells
increases during compression due to the continu-
ously reducing volume available. If the initial
pressure P
0
of gas in the cell is equal to room press-
ure, the contribution to the applied stress is given
by:
s
g
pl
s
yb
⫽P−P
0
s
yb
(9)
In conclusion, the collapse strength can be
expressed as:
s
pl
∗
s
yb
⫽s
h
pl
s
yb
⫹s
w
pl
s
yb
⫹s
g
pl
s
yb
⬇0,3·f
3
2
·
冉
r∗
r
b
冊
3
2
(10)
⫹(1⫺f)·r∗
r
b
⫹P−P
0
s
yb
(III) At large compressive strains, when the cells are
completely collapsed, the opposing cell walls
are crushed together and the constituent
material is compressed as well. As a conse-
quence, the stress–strain curve rises steeply and
its slope tends to E
b
.
Fig. 5. Compression load–deformation curves in static, free-
volume conditions of EPS at different densities.

221L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
When the relative foam density increases, the Young’s
modulus increases as well, the plateau stress is raised and
the strain, at which densification begins, reduces (Fig. 5).
3. Materials
In the following, both PC and EPS will be considered.
PC is a mostly amorphous thermoplastic polymer
(embrittlement range ⫺5/⫺25°C, glassy temperature
135–140°C, melting range 220/260°C, thermal degra-
dation 280/320°C), which can be moulded and injected
(20 000–30 000 molecular weight) or thermoformed
(60 000 molecular weight). PC is a ductile material,
which possesses high mechanical strength (s
ult
⬇60 MPa,
e
ult
⬇100%), hardness and toughness, good workability,
thermal stability and transparency. It maintains its mech-
anical characteristics over a wide range of temperatures
(⫺100/+135°C). On the other hand, it shows low UV
endurance, mainly in hot–wet environments and low
chemical resistance to alkaline solvents. Also, it is
hygroscopic and needs to be dried before extrusion or
injection. During production, PC granules are mixed with
thermal and UV stabilisers and organic pigments, then
the outer helmet shell is injection-moulded at 260°C.
EPS raw material (0.628 g/cm
3
density) consists of styr-
ene beads containing dissolved pentane, which is the
main agent responsible for expansion. They are collected
in a pre-expander where a first expansion is carried out
with air and vapour at 0.5 bar pressure. The value of
temperature and the share between air and vapour influ-
ence the material density. Then, pre-expanded styrene is
air-dried and stocked into a container, where it is stabil-
ised at 30–35°C for 48 h. Finally, it is injected (7 bar
pressure) into a closed mould, where vapour is injected
as well (1–2 bar) to sinter together the beads walls. In
the meantime, the mould is cooled by water circulation
to avoid further expansion of the pentane, which at the
end is totally discharged. The complete work-cycle takes
150 s.
4. Experiments
EPS samples of four different nominal specific
weights were considered, namely 28, 40, 55 and 70 g/l.
Actual values were computed after weight and volume
measurements. Values of 31±1, 42±1, 58±1, 71±1 g/l
were measured respectively.
EPS static compression tests were performed accord-
ing to ASTM D1621-73 standard with an Instron 4302
dynamometer at 23°C at a cross-head rate of 2.5
mm/min.
Dynamic compression tests were performed with a
drop tower, 13.57 kg flat-head falling mass and 30 KJ
impact energy. 100 mm diameter and 30 mm thickness
cylindrical samples were used. Both static and dynamic
tests were performed according to free- and confined-
volume methods. In the latter case, the samples were fit-
ted to a cylindrical steel frame not allowing radial expan-
sion during compression.
Falling weight tests were performed according to
ASTM D3029-84 with a 15.9 mm diameter hemispheri-
cal impactor at different impact energy levels from 15
KJ up to failure on both plane PC and sandwich PC/EPS
specimens of different thickness and density. The speci-
mens consisted of injection moulded PC disks 100 mm
in diameter and 3.4 mm in thickness coupled with EPS
cylinder 100 mm in diameter, 25, 30, 35, 40 mm in thick-
ness and 28, 40, 55, 70 g/l in density. The specimens
were constrained to a flat steel plate and impacted by a
13.9 kg mass falling from variable height.
EPS torsional dynamic-mechanical tests were perfor-
med according to ASTM D4065-95 standard with a
Rheometrics RDA II Mechanical Spectrometer at differ-
ent frequencies between 0.1 Hz and 10 Hz, within
⫺120/+110°C temperature range on 28 and 70 g/l den-
sity samples and within +30/+110°C temperature range
on 40 and 55 g/l density samples to estimate temperature
and strain rate influence on material stiffness. The upper
temperature limit depends on material properties: in fact,
approaching T
g
(110°C), PS begins to soften and pre-
vents the instrument measuring the torque. 10×50×2mm
prismatic specimens were used.
Tensile and bending tests on both EPS and PC were
performed as well in accordance with UNI 8071, ASTM
D638-86 and ASTM D790-86 respectively
5. Mechanical behaviour
Fig. 5 reports the results of free-volume static com-
pressive tests on foams of different densities. The curves
show three characteristic regions, corresponding to linear
elasticity, quasi-perfect plasticity and densification. The
lower the density, the wider the plastic plateau, suited
for energy absorption. From stress–strain curves, the
elastic modulus, compressive strength and specific
absorbed energy were computed and plotted vs. foam
density showing linear dependence (Fig. 6). It can be
observed that, the deformation being equal, higher den-
sities absorb higher energy contents but transfer larger
force values. To obtain the same energy absorption,
lower thickness of high-density foam is sufficient, while
low-density foams lead to lower transferred loads (Fig.
7a,b), provided densification is not occurring.
Fig. 8 shows the results of confined-volume tests,
while Table 1 summarises the dependence of foam
characteristics on test conditions. Small differences can
be noted (less than 10%) owing to the fact that, even in
free-volume tests, only outer cells are really free to
expand transversally, while inner ones suffer a constrain-

222 L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Fig. 6. Elastic modulus (E), compressive stress (s
c
) and spe-
cific absorbed energy (W) as a function of foam density.
Fig. 7. Comparison between maximum load reached by differ-
ent foams after (a) iso-strain or (b) iso-energy deformations
(impact energy 50J).
Fig. 8. Compression load–deformation curves in static, con-
fined-volume conditions. The estimated contribution of trapped
air is indicated.
ing effect. Fig. 8 reports the estimated contribution of
air trapped in the cells. The contribution to elastic modu-
lus due to gas trapped in the cells can be expressed as:
E
g
⫽P
0
(1−2n)
冉
1−r
r
b
冊
and E
g
⫽P
0
冉
1−r
r
b
冊
(11)
in the case of free- and confined-volume tests, respect-
ively. Since r/r
b
is small and P
0
equals room pressure,
the contribution due to gas pressurisation can be neglect-
ed.
Tensile tests on EPS show that the material is charac-
terised by brittle behaviour (failure occurs perpendicu-
larly to load axis, with no detectable shrinkage); tensile
strength linearly depends on foam density (Fig. 9).
Fig. 10 shows the results of free-cross-volume
dynamic compression tests. The tests were performed at
30 J impact energy on 30 mm thick cylindrical speci-
mens made with EPS of different density. At a parity of
impact energy, the higher the density, the higher the elas-
tic modulus and peak load, the lower the crushing. Static
and dynamic behaviour is compared in Table 2. Dynamic
compression gives notably larger crushing and smaller
peak load, while the elastic modulus is not affected by
the strain rate.
Comparing the results of free- and confined-volume
dynamic compression, it appears that the latter condition
gives elastic modulus and peak load somewhat higher
(about 10%), while crushing is slightly lower, mainly in
the case of lighter EPS’s.
Falling weight tests were performed on both thin cir-
cular PC flat panels and PC+EPS sandwich specimens.
The results of tests on plain PC plates showed that elastic
modulus remains practically constant, while peak load
and plastic component of crushing increase linearly with
energy content (Fig. 11). Two different sets of tests were
carried out on PC+EPS specimens: at a parity of density
(28, 40, 55 and 70 g/l) and energy content (40, 55, 67
and 75 J respectively) to investigate the influence of
thickness; at a parity of thickness (40 mm) and energy
(75 J) to investigate the influence of density. Peak loads
are plotted vs. thickness in Fig. 12, while their depen-
dence on density is shown in Fig. 13 together with crush-
ing values. It was observed for all densities that, when
the specimens do not reach bottoming out (that is if the
specimen is not completely crushed), the value of thick-
ness has limited influence on both peak load and crush-
ing. However, in the lower range of thickness and/or
density, the impact energies employed (Figs. 12 and
13—open markers) led to bottoming out. It can be con-
cluded that a minimum thickness value exists for every
density and energy content necessary to avoid complete
crushing. Therefore, thickness influences the maximum
amount of energy that can be absorbed, rather than the
absorbing mechanism itself: in fact, far away from bot-
toming out, the values of peak load and crushing are
comparable. Besides, the deformed shape is not influ-
enced by thickness, but notably depends on density: low-
density EPS provides a distributed co-operation in
absorbing energy, while heavier EPS contributes to
energy absorption only through brittle failure of cells
close to the impact point. The evaluation of peak load
and crushing vs. density at constant thickness and impact

223L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Table 1
Results of static compression tests
Nominal density (g/l) E(MPa) W(J/cm3) s
c
(MPa)
Free Confined Free Confined Free Confined
28 6.5 7.4 0.11 0.12 0.19 0.20
40 11.9 14.1 0.17 0.18 0.31 0.32
55 21.3 23.0 0.25 0.28 0.46 0.53
70 32.3 34.7 0.38 0.39 0.70 0.71
Fig. 9. EPS tensile strength as a function of density.
Fig. 10. Compression load–deformation curves in dynamic,
free-volume conditions.
Table 2
Results of static and dynamic compression tests
Nominal density (g/l) Crushing (mm) Max load (kN) E(MPa)
Static Dynamic Static Dynamic Static Dynamic
28 14.8 20.0 2.2 2.0 6.5 6.3
40 10.2 14.8 2.8 2.2 11.9 12.2
55 7.3 11.7 4.0 3.4 21.3 21.3
70 5.1 10.3 5.8 4.0 32.3 32.3
Fig. 11. Maximum load and crushing as a function of impact
energy in falling weight tests on PC plates.
Fig. 12. Peak load as a function of thickness for EPS at differ-
ent densities (open markers indicate that bottom out occurred).

224 L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Fig. 13. Maximum load and crushing as a function of EPS
density in falling weight tests on PC+EPS samples at a parity
of impact energy.
energy, reported in Fig. 13, shows that the higher the
density the higher the peak load and the lower the crush-
ing value. Also, the higher the density the lower the
amount of EPS contributing to energy absorption.
The dynamic-mechanical tests on EPS give results
qualitatively similar to those on bulk polystyrene: elastic
modulus remains notably constant up to temperatures
close to T
g
(110°C), when stiffness falls to negligible
values. Working within 0.1/10 Hz frequency and
⫺120/+120°C temperature ranges, the material master
curves can be drawn by horizontally shifting the curves
along the log frequency scale [16,17]. G⬘,G⬙and tan d
master curves of 28 g/l EPS at 30°C reference tempera-
ture are shown in Fig. 14. Within the usual temperature
working range (that is between ⫺20°C and +50°C), stiff-
ness is negligibly influenced by testing rate: in fact, the
change of two decades in testing rate induces a stiffness
variation smaller than 7%. In Fig. 15 G⬘modulus at 1
Hz and 30°C is plotted vs. EPS density. Shear modulus
is strongly dependent on material density; as indicated
by Eq. (5) a parabolic function seems to adequately fit
the experimental results.
Fig. 14. G⬘,G⬙, tan dmaster curves of 28 g/l EPS at 30°C
reference temperature.
Fig. 15. G⬘values at 30°C, 1 Hz as a function of EPS density.
6. Microscopic analysis
SEM microscopic analysis was performed on three
different kinds of PC+EPS specimens. Preliminary
analysis on undeformed 28 and 70 g/l samples was car-
ried out to determine the expanded morphology (cells
mean dimensions and manufacturing defects). Further
analysis allowed investigation of deformation features
and stability limits after free cross-section partial and
complete static compression tests. The last analysis
focused on the deformation mechanism generated by
concentrated loads on 70 g/l samples after the falling
weight test. In each case the whole thickness of the
samples was analysed.
EPS consists of a two-level structure, the first being
represented by pre-expanded beads sintered together; the
second by closed cells within the beads. SEM analysis
allowed measurement of cell average dimensions, that is
320 and 130 µm for 28 g/l and 70 g/l EPS, respectively.
The expansion process induces non-uniform cell dis-
tribution, leaving more dense, deformed cells close to
bead boundaries (Fig. 16). The analysis of partially com-
pressed EPS (25% strain) showed that, before
densification occurs, the through-the-thickness perma-
nent deformation is not uniform, but is concentrated just
in correspondence to sample outer surfaces and beads
boundaries (Fig. 17). This suggests that cell buckling is
due to the presence of these pre-deformed cells. At 25%
strain the cells within the beads did not show evidence
of permanent deformation. At a higher compression
stage, once densification occurs, complete, permanent
cell wall buckling is observed. It should be noticed that
the boundaries between the beads, made of bulk material,
buckle as well, thus contributing to energy absorption.
Fig. 18 shows 70 g/l EPS after being falling weight
impacted. A surface brittle fracture can be observed. Per-
manent deformation, which is larger in correspondence
to the impact surface, extends far beyond the crack tip,

225L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Fig. 16. SEM micrograph of an undeformed 70 g/l EPS speci-
men.
showing preferential buckling of those cells close to the
bead boundaries.
These analyses show that the plateau typical of EPS
stress strain curves is the result of a progressive, non-
uniform buckling of cells and bead walls, which both
positively contribute to energy absorption. In fact, it
Fig. 17. SEM micrograph of a 70 g/l EPS specimen after
static compression.
seems reasonable to consider the dimensions of pre-
expanded beads, together with the material density, as a
significant parameter affecting EPS energy absorption
capability.

226 L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
Fig. 18. SEM micrograph of EPS+PC after a falling weight impact: EPS fracture zone.
7. Conclusion
Some conclusions can be drawn about the deformation
mechanisms and the energy absorption capability of
polystyrene foams (EPS) and polycarbonate (PC) shells
for protective helmets, and some suggestions for the
design improvement can be given.
The comparison between mechanical characteristics
measured through free- and confined-volume static com-
pression tests shows no appreciable differences: this
means that, although EPS used for protective helmets is
loaded in confined-volume conditions, the free-volume
tests prescribed by standards still provide reliable results.
Also, the static, dynamic and dynamic-mechanical
tests performed on EPS show that an increase of some
orders of magnitude in the strain rate produces only a
slight increase in the elastic modulus: this means that the
use of characteristics measured through static tests does
not lead to significant design errors.
Dynamic tests on PC+EPS sandwich specimens show
that, once minimum thickness of EPS layer is chosen for
absorbing the prescribed energy content, its value does

227L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
not represent a crucial design parameter any more: in
fact, above this threshold, the overall behaviour does not
depend on thickness.
By contrast, EPS density is the crucial parameter
influencing energy absorption capability, being respon-
sible for the basic mechanisms of deformation and fail-
ure, as well as for the values of acceleration and
maximum crushing. Low-density EPS provides a distrib-
uted co-operation in absorbing energy, while high-den-
sity EPS contributes to energy absorption only through
brittle failure of cells close to the impact point: this
implies higher peak loads.
It can be concluded that high-density EPS are able to
absorb larger amounts of energy than low-density EPS
can do, but transfer higher accelerations and forces local-
ised at the impact point. On the other hand, to absorb
the same amount of energy, lighter EPS need thicker lay-
ers, to be compliant with cost, size and aerodynamics
constraints.
Given the amount of energy to be absorbed, the opti-
mal design should define the value of EPS density able
to minimise the acceleration and peak load, once the
allowable thickness and maximum crushing are pre-
scribed.
Considering the main mechanisms responsible for the
energy absorption capability, SEM analysis shows that
the crushing of EPS cells is not uniform through-the-
thickness, but is localised at the borders between pre-
expanded beads, since pre-crushed cells can always be
found, even in un-deformed specimens. The basic mech-
anisms leading to energy absorption consist of the wall
buckling of both cells and pre-expanded beads. The latter
phenomenon can be explained if pre-expanded beads are
assimilated to elementary cells, the walls separating the
beads being made of bulk material. This means that, at
a parity of overall EPS density, the size of pre-expanded
beads influences the deformation and the amount of
energy that can be absorbed: in fact, smaller beads imply
smaller free-deflection length of pre-expanded beads
walls and higher buckling load. Also, if the wall surface
is increased, the number of potential plastic hinges is
increased and the volume of EPS co-operating to energy
absorption is increased as well.
By contrast, it should be considered that, at a parity
of overall density, a wider contact surface between pre-
expanded beads (that is smaller pre-expanded beads)
implies larger elementary cells, larger free-deflection
length and lower buckling loads.
Finally, it can be concluded that EPS energy absorp-
tion capability can be controlled at a macroscopic level
by choosing a density able to minimise acceleration, but
compatible with volume allowable for absorption, and at
a microscopic level by managing the sizes of internal
structure in terms of elementary cells and pre-
expanded beads.
An alternative approach could consist of the adoption
of a functionally graded material, that is an EPS whose
density changes continuously through the thickness of
the layer devoted to energy absorption.
Acknowledgements
The authors wish to thank OPTICOS Srl, NOLAN Spa
and General Electric Plastics for having supplied the
materials and the samples, and Mr. Pardi for his help in
performing SEM analyses.
References
[1] A. Gale, N.J. Mills, Effect of polystyrene foam liner den-
sity on motorcycle helmet shock absorption, Plastics and
Rubber Processing and Applications 5 (1985) 101–108.
[2] A. Gilchrist, N.J. Mills, Modelling of the impact response
of motorcycle helmets, International Journal of Impact
Engineering 15 (3) (1994) 201–218.
[3] J.A. Medding, B.J. Love, Evaluation of collisional damage
in polystyrene foam construction using a dual hammer
impact test, Polymer Engineering and Science 36 (9)
(1996) 1286–1289.
[4] P.R. Stupack, J.A. Donovan, Deformation and energy
absorption of polymer foams as a function of 2-D indenter
and absorber geometry, Polymer Engineering and Science
34 (10) (1994) 857–864.
[5] W.A. Jemian, B.Z. Jang, J.S. Chou, Testing, simulation
and interpretation of materials impact characteristics, in:
S.L. Kessler, G.C. Adams, S.B. Driscoll, D.R. Ireland
(Eds.), Instrumental Impact Testing of Plastic and Com-
posite Materials, ASTM STP 936, American Society for
Testing Materials, Philadephia, 1987, pp. 117–143.
[6] M.J. Tzeng, M.C. Lee, Mechanical properties of impact
absorbing liner of motorcycle helmets, American Society
of Mechanical Engineers, New York 98 (1989) 381–384.
[7] J. Miltz, O. Ramon, Energy absorption characteristics of
polymeric foams used as cushioning materials, Polymer
Engineering and Science 30 (2) (1990) 129–133.
[8] ECE 22-04 Economic Commission for Europe No. 22.
Uniform regulations for the permission of the protective
helmets for drivers and passengers of motorcycles and
motorfahrraedern.
[9] BSI–BS 6658. British standard specification for protective
helmets for vehicle users, 1985.
[10] AS 1698. Australian standard for protective helmets for
vehicle users, 1988.
[11] DOT 72-6. Motor vehicle safety standard number 218
(motorcycle helmets).
[12] NF S72-305. Casques de protection pour usages de motor-
cycles, velomototeurs et cyclemoteurs.
[13] SNELL M-95. 1995 standard for protective headgear (for
use with motorcycles and other motorised vehicles).
[14] L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and
Properties, Pergamon, Oxford, 1988.
[15] N.C. Hilyard, Mechanics of Cellular Plastics, Applied
Science Publisher, London, 1982.

228 L. Di Landro et al. / Polymer Testing 21 (2002) 217–228
[16] J.D. Ferry, Viscoelastic Properties of Polymers, 2nd ed.,
Wiley, New York, 1970.
[17] T. Murayama, Dynamic Mechanical Analysis of Poly-
meric Materials, Elsevier Scientific Publishing Company,
Amsterdam/Oxford/New York, 1978.