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Semi-continuous approach for the modeling of thin
woven composite panels applied to oblique impacts on
helicopter blades
Pablo Navarro, Aubry Julien, Steven Marguet, Jean-François Ferrero,
Sandrine Lemaire, Patrice Rauch
To cite this version:
Pablo Navarro, Aubry Julien, Steven Marguet, Jean-François Ferrero, Sandrine Lemaire, et al.. Semi-
continuous approach for the modeling of thin woven composite panels applied to oblique impacts on
helicopter blades. Composites Part A: Applied Science and Manufacturing, Elsevier, 2012, 43 (6),
pp.871-879. �10.1016/j.compositesa.2012.01.020�. �hal-02143837�
Semi-continuous approach for the modeling of thin woven composite panels
applied to oblique impacts on helicopter blades
P. Navarro
a
, J. Aubry
a
, S. Marguet
b
, J.-F. Ferrero
b,
⇑
, S. Lemaire
c
, P. Rauch
c
a
Université de Toulouse/ICA/ISAE, 10 av. E. Belin, 31055 Toulouse Cedex, France
b
Université de Toulouse/ICA/UPS, 118 Rte de Narbonne, 31062 Toulouse, France
c
Eurocopter Marignane/BDD – Aéroport Marseille P., 13725 Marignane, France
In aeronautics, passenger safety and reliability of structures are essential aspects. In the specific case of
helicopters, blades are subjected to impact loadings. Modeling these phenomena continue to be difficult
and experimental tests often replace the prediction. The following work will focus on the experimental
and numerical study of an oblique impact on the skin of the blade. It is equivalent in a first approach
to an impact on a sandwich panel made up of a foam core and a thin woven composite skin. The objec-
tives are to identify the mechanisms of damage in the skin for this kind of loading and to develop a rep-
resentative modeling of the chronology of damage adapted to the modeling of the complete structure.
Thus, a semi-continuous F.E. explicit modeling has been developed. It relies on the development of a
specific damageable element at the bundles scale. Satisfactory numerical results are obtained. They allow
the identification of the damage mechanism of the woven skin.
1. Introduction
In the field of transport, particularly in aeronautics, the slightest
weakness in a part of the structure can have serious consequences.
Helicopter blades are particularly sensitive to impact loading. In-
deed, during flight, blades may be subjected to impacts with various
soft or hard bodies such as birds or hailstone. The impact velocity
can be up to several hundred meters per second. It is directly linked
to the rotational speed of the blades. The complexity of these im-
pacts is increased by the composition of the blades. A blade is made
up of a main spar with unidirectional glass–epoxy composite in the
leading edge; of a skin generally made of two or three plies of glass–
epoxy and (or) carbon–epoxy woven fabrics; of a polyurethane
foam core; of a glass–epoxy unidirectional composite trailing edge;
and of a protection made of stainless steel that covers the leading
edge. One or more composite carbon–epoxy ribs stabilize the skins.
Two kinds of impact can be distinguished. The first one is a frontal
impact on the leading edge. The second one, which is dealt with in
this study, is an oblique impact on the lower surface of the blade
(
Fig. 1).
An oblique impact is characterized by the angle of incidence of
impact, generally between 10° and 20°, caused by the inclination of
the blade in flight. Given the geometry of the impacted area, this
blade can be assimilated to a sandwich structure made up of a
foam core and a skin built up of two plies of woven glass/epoxy
composite.
Many experimental studies deal with the impact on laminate
panels for which the mechanisms of damage can be described in
three steps
[1]. Chronologically, the damage of the matrix precedes
delamination and failure of the fibers. Their relative influence de-
pends mainly on the characteristics of the fibers, the resin, the stack-
ing sequence and the applied loads
[2–6]. Woven laminates have
similar damage modes
[7], but a chronological classification cannot
be made as clearly as in the unidirectional laminate case. As for
sandwich structures
[8–10], the behaviors differ from those ob-
served in laminated panels, due to both the low thickness of the
skins and the presence of the core (foam or honeycomb) which sta-
bilizes them. Many failure modes have been brought to light:
– compression failure of the upper skin,
– foam compression with a tensile failure of the lower skin,
– shear failure of the foam coupled with a buckling of the upper
skin,
– shear failure of the foam coupled with a tensile failure of the
lower skin.
As the impact velocity increases [11,12], the impact response
becomes localized and shear is the main failure mode.
To reduce certification and development costs, the aircraft
industry would like to use computational methods. This would en-
able them to predict structural integrity of composite structures
⇑
Corresponding author. Tel.: +33 5 6155 8645; fax: +33 5 6155 8178.
E-mail address:
Jean-Francois.Ferrero@isae.fr (J.-F. Ferrero).
1
under impact from soft or hard bodies. The simulation of impacts
on woven composite panels is performed using three major strat-
egies. The first one consists of modeling the structure at the panel
scale, using 2D elements and a homogenized orthotropic material
law
[13,14]. Damage parameters are introduced to represent the
breakage of the warp and weft fibers, the failure of the bundles
and the resin. These models are particularly efficient for ballistic
impacts on woven plates. The second strategy consists of building
models at a smaller scale to represent the details of the structure of
a woven ply. In
[15] the bundles are modeled with 3D solid ele-
ments in order to take into account the friction. In
[16] the scale
is lowered at the fiber scale. Each thread is modeled by a chain
of rod elements and the contact taken into account. These models
allow a good representation of the influence of the weaving, but for
longer computing times. The third approach consists of finding a
compromise between the two previous modeling scales. In
[17],
a representative pattern of the woven fabric is modeled with 3D
solid elements. The whole woven panel is modeled at a larger scale
and the calculation is conducted using a multi-scale method. This
method allows the representation of the resin cracking, the resin/
fiber interfacial debonding and the fiber breakage. Another multi-
scale method is described in
[18]. The fabric is represented at the
bundle scale with 3D solid elements in the impacted area. Else-
where, the fabric is modeled with 2D homogenized shell elements.
Using this strategy, the calculation time is reduced five fold.
A numerical modeling of the thin woven skin based on experi-
mental observations has been developed in this study. The model
presented here uses an original scale: the woven mesh fabric scale.
It allows a correct simulation of static indentations, low velocity
normal impacts and high velocity oblique impacts. It also permits
the identification of the damage scenario.
2. Experimental analysis
High velocity oblique impact tests have been performed in or-
der to identify the chronology of the damage mechanisms for the
thin woven composite skin. These tests have been carried out with
an air gun. The impactor is a 19 mm diameter steel ball with a mass
of 28 g. The core of the impacted panels is an aeronautical foam
(Rohacell A51). The two skins are made up of two plies of glass/
epoxy woven fabric (7781/913) prepregs oriented at 0–90° from
the firing direction. Special attention has been taken to balance
the proportions of warp and weft fibers in each direction. The com-
posite skin thickness is 0.7 mm. The material characteristics are gi-
ven in
Table 1.
The specimens are square, 200 mm on each edge, and 20 mm
thick. The sample is placed on a table tilted at 15° from the impact
axis (
Fig. 2). This value has been chosen to reproduce the flight
conditions of the helicopter blade. The impact velocity has been
varied from 60 m/s to 130 m/s, which corresponds to impact ener-
gies evolving from 50 J to 230 J.
These tests allow the observation of two states of damage to the
woven skin depending on the impact energy (
Fig. 3).
The first state of damage is observed under lower impact ener-
gies. Micro-cracking of the resin is visible using a scanning electron
microscope. However, no failure of the bundles is observed. The
impactor rebounds during the impact. The second level of damage,
obtained under greater impact energies, is characterized by the
damage of the resin and the breakage of fibers. For these energies,
the impactor either rebounds or perforates the skin. If the steel ball
rebounds, the resulting fracture surface is a longitudinal crack ori-
ented along the firing axis. For a given configuration of the sample,
the threshold between these different states of the skin depends on
the impact angle and on the mass and velocity of the impactor.
Furthermore, the analysis of the tests’ results brings to light the
mechanisms of damage of the thin woven composite skin (
Fig. 4).
Firstly, the damage of the skins begins with the apparition of
micro-cracking in the matrix resin. Then, once the resin is totally
damaged, the bundles, which are no longer stabilized, carry the
whole load. Finally, if the strain in the fibers reaches the ultimate
tensile strain, the fibers break and the skin tears. As the skin is
made up of 2 woven composite layers, no delamination is
observed.
In order to optimize the oblique impact response of a helicopter
blade, a study of the influence of the various parameters (materials
and impact conditions) on the amount of damage must be carried
out. Therefore, a numerical modeling has been developed.
Fig. 1. Section of a blade and materials used. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 1
Characteristics of the materials.
Woven fabric (7781/913) Foam (Rohacell A51)
Density (kg/m
3
) 1900 Density (kg/m
3
)52
Elastic modulus (MPa) E
x
= E
y
17,000 Elastic modulus (MPa) 70
Shear modulus (MPa) 3000 Shear modulus (MPa) 19
Poisson ratio 0.13 Compressive strength (MPa) 0.9
Tensile strain limit 0.025 Tensile strength (MPa) 1.9
15°
Composite
sandwich
panel
Impact axis
Fig. 2. Presentation of the oblique impact tests.
2
3. Modeling presentation
3.1. Principle
In light of previous observations, a semi-continuous modeling
for the thin woven composite blade skin has been suggested. It re-
lies on the chronology identified experimentally. The idea is to
build a modeling which can represent the behavior of the undam-
aged woven skin (a continuous panel) as well as that of the dam-
aged skin (non-stabilized bundles). Therefore, the modeling has
been developed at the woven fabric mesh scale. As a consequence
of the same warp and weft distribution, no distinction has been
made between the modeling of the two membrane directions. As
delamination is not predominant, only one element is taken
through the thickness. The bundles are represented by the use of
1D rod elements. This truss structure is stabilized by a damageable
2D element, which has been fully developed (
Fig. 5).
The plate theory gives the normal forces per unit length (vector
N) and the bending moments per unit length (vector M) of the wo-
ven skin. They are obtained from the membrane and bending
strains (respectively vectors
e
and k) by the introduction of three
constitutive matrices A, B and C (1):
N
M
¼
AB
B
t
C
e
k
with N ¼
N
xx
N
yy
N
xy
8
>
<
>
:
9
>
=
>
;
; M ¼
M
xx
M
yy
M
xy
8
>
<
>
:
9
>
=
>
;
;
e
¼
e
xx
e
yy
e
xy
8
>
<
>
:
9
>
=
>
;
; k ¼
k
xx
k
yy
k
xy
8
>
<
>
:
9
>
=
>
;
ð1Þ
A is the constitutive matrix of the membrane behavior and C the
constitutive matrix of the bending behavior. B represents the mem-
brane-bending coupling. In this study the skin is a balanced woven
laminate, so that B =0.
Matrix’s micro cracking
Longitudinal crack
Energy (J)
115
95
57
Firing direction
Bouncing of
the impactor
Perforation of
the skin
Damage of
the resin
Damage of the resin
+ Fibre breakages
Fig. 3. Influence of the impact energy on the damage of the skin. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of
this article.)
Resin damage
No stabilized bundles
Fibre breakage
Fig. 4. Damage mechanisms of the woven skin. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
3
For the membrane loading, the stiffness of the woven skin is
represented by both the rods and the 2D shell elements. However,
for the bending and transverse shear loading, the rods do not have
any influence (2):
A ¼ A
shell
þ A
rod
C ¼ C
shell
ð2Þ
where A
shell
and C
shell
are respectively the constitutive matrix of the
membrane behavior and the bending behavior of the 2D shell ele-
ment. A
rod
is the stiffness of the rod elements. The matrix A
shell
rep-
resents the stiffness of the resin. The matrix C
shell
represents the
stiffness of the whole skin. The damage mechanisms (micro-crack-
ing of the resin between and inside the bundles) are taken into ac-
count by damaging the matrices A
shell
and C
shell
.
The connection between the 1D and 2D elements is made at the
nodes. The interaction between the bundles and the resin is
neglected.
3.2. Formulation
The specific shell element has been developed from
Belytschko’s formulation
[19]. It is based on the theory of bending
of shells. To increase stability and to avoid hourglass strain modes,
the element incorporates four integration points. As this 2D ele-
ment is considered as homogenous in the thickness direction, the
transverse shear strain has been calculated using Hencky-Mindlin’s
theory. The membrane/bending/shear distinction is made when
choosing the values of the corresponding elastic modulus, respec-
tively E
M
, E
F
and G
T
. The normal forces per unit length and the
bending moments per unit length are calculated using the consti-
tutive matrix for a plane stress state. An explicit code is used for
the modeling. Eq. (3) gives the values of the forces and moments
at the iteration t +
D
t, which are calculated from their values at
the previous iteration:
N
xx
ðt þ
D
tÞ
N
yy
ðt þ
D
tÞ
"#
¼
N
xx
ðtÞ
N
yy
ðtÞ
"#
þ
e E
M
ðtÞ
D
t
1
v
2
1
v
v
1
"#
_
e
xx
_
e
yy
"#
M
xx
ðt þ
D
tÞ
M
yy
ðt þ
D
tÞ
"#
¼
M
xx
ðtÞ
M
yy
ðtÞ
"#
þ
e
3
E
F
ðtÞ
D
t
12ð1
v
2
Þ
1
v
v
1
"#
_
k
xx
_
k
yy
"#
Q
xx
ðt þ
D
tÞ
Q
yy
ðt þ
D
tÞ
"#
¼
Q
xx
ðtÞ
Q
yy
ðtÞ
"#
þ
D
t K
y
G
T
ðtÞe
10
01
"#
2
_
e
xz
2
_
e
yz
"#
ð3Þ
where
_
e
ij
and
_
k
ij
represent respectively the strain rates in membrane
and bending, Q
ij
is the transverse shear, e the thickness of the panel,
t
the Poisson’s ratio of the fabric and
D
t the time step. The elastic
modulus E
F
, which represents the bending stiffness, is that of the
woven composite oriented at 0/90°. The elastic modulus E
M
is that
of the resin and the transverse shear modulus G
T
is that of the whole
skin. These two moduli are given by the manufacturer of the woven
fabrics. K
y
is a transverse shear correction factor. It is value is set to
5/6.
Concerning in-plane shear behavior, it has been observed
experimentally that pseudo-plasticity was the predominant phe-
nomenon. Therefore, the in-plane shear forces per unit length are
calculated from the in-plane shear elastic strain (4):
N
xy
ðtÞ¼e
D
t G
M
2
e
e
xy
M
xy
ðtÞ¼
e
3
6
D
t G
M
k
e
xy
(
with
e
e
xy
¼
e
t
xy
e
p
xy
k
e
xy
¼ k
t
xy
k
p
xy
(
ð4Þ
where G
M
is the in-plane shear modulus. It is given experimentally
by a tensile test of the woven fabric oriented at ±45°.(
e
e
xy
; k
e
xy
) are
the in-plane shear elastic strains, (
e
t
xy
; k
t
xy
the in-plane shear total
strains and (
e
p
xy
; k
p
xy
) the in-plane shear plastic strains. The calcula-
tion of these strains is carried out in two principal steps. Firstly,
in an elastic prediction step, the strain increment is assumed to
be purely elastic. Secondly Eq. (5) is used to verify the nature of
the stress computed under the elastic prediction:
f ¼j
r
xy
jR
r
0
ð5Þ
where
r
xy
is the in-plane shear stress,
r
0
the plastic strength and R
the hardening variable.
If f > 0, a plastic correction is carried out using a Newton–Raphson
iterative scheme to find the value of the plastic strain, as defined
in
[20].
The micro-cracking of the resin is represented by the degrada-
tion of the 2D elements. Due to the thin nature of the skin, the
damage can be assumed to be the same throughout its thickness.
The evolution of the membrane, bending and transverse shear
modulus due to damage is described by a single parameter (d).
As developed in
[21],(d) is a function of the energy release rate
Y, obtained by differentiating the elastic energy W
e
with respect
to the damage (6):
E
M
ðtÞ¼ð1 dÞE
M
E
F
ðtÞ¼ð1 dÞE
F
G
T
ðtÞ¼ð1 dÞG
T
Y ¼
1
2
@W
e
@d
; d ¼
hY Y
0
i
P0
Y
c
ð6Þ
where Y
0
controls the damage initiation and Y
c
the damage evolu-
tion from the initiation to the failure, as defined in
[22]. Classically
(d) varies between 0 (no damage) and 1 (entirely damaged).
The fibers have been modeled using rod elements, which have
been integrated in the formulation of the 2D specific element. A
linear elastic material law with brittle failure in tension has been
chosen. As shown in [23], tensile failure properties for woven fab-
Fig. 5. Modeling principle. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
4
