Damage in woven-fabric composites subjected to
low-velocity impact
N.K. Naik*, Y. Chandra Sekher, Sailendra Meduri
Aerospace Engineering Department, Indian Institute of Technology, Powai, Mumbai-400 076, India
Abstract
The behaviour of woven-fabric laminated composite plates has been studied under transverse central low-velocity point impact
by using a modi®ed Hertz law and a 3D transient ®nite-element analysis code. The in-plane failure behaviour of the composites has
been evaluated by means of a failure function based on the Tsai-Hill quadratic failure criterion. The e€ect of fabric geometry on the
impact behaviour of woven-fabric composites has been studied. For comparison, the impact behaviour of balanced, symmetric,
crossply laminates made of unidirectional layers and unidirectional composites has been included. The studies have been carried out
with plate dimensions of 150 mm150 mm6 mm for a supported boundary condition. For these studies, incident impact velocities
of 3 and 1 m/s and an impactor mass of 50 gm have been used. It is observed that the in-plane failure function is lower for wovenfabric laminates than for crossply laminates, indicating that woven-fabric laminates are more resistant to impact damage.
Keywords: Impact behaviour; Polymer matrix composites; Textile composites; Failure criterion; Finite-element analysis; Fabrics
1. Introduction
One of the major concerns in designing composite
structures is their susceptibility to impact loading.
Fibre-reinforced polymer-matrix composites are known
to be highly susceptible to internal damage caused by
transverse loads, even under low-velocity impacts. The
composites can be damaged on the surface as well as
beneath the surface with relatively light impacts causing
barely-visible impact damage, while the surface may
appear to be undamaged to visual inspection. For the
e€ective use of ®bre-reinforced polymer-matrix composites for high-performance applications, understanding
the causes for the formation of such damage under lowvelocity impact and improving the damage-resistance
characteristics of the composites are important considerations which have been the topic of extensive research
for the last few years. Review articles on the impact
behaviour of polymer-matrix composites covering contact laws, impact dynamics, stress analysis, damage
mechanics, post-impact residual property characterisation and damage-resistance improvements are available
in the literature [1±5]. Many research publications are
available on the impact behaviour of polymer-matrix
composites covering speci®c aspects [6±33].
Matrix deformation and micro-cracking, interfacial
debonding, lamina splitting, delamination, ®bre breakage and ®bre pull-out are the possible modes of failure
in composites subjected to impact loading. Even though
®bre breakage is the ultimate failure mode, the damage
would initiate in the form of matrix cracking/lamina
splitting and would lead to delamination. Damage-free
composites are necessary for their e€ective use.
Traditionally laminated composites made of unidirectional (UD) layers were used for structural applications. These composites are characterised by high
speci®c sti€ness and high speci®c strength. But these
composites are highly susceptible to impact damage
because of their lower transverse tensile strength.
One of the ways of improving impact behaviour of
polymer-matrix composites is to use woven-fabric (WF)
layers instead of unidirectional layers. A woven-fabric is
a fabric produced by the process of weaving in which
the fabric is formed by interlacing the warp and ®ll
strands. The integrated nature of the fabric provides the
balanced in-plane properties. Woven-fabric composites
are characterised by high fracture toughness and ease of
handling. The transverse tensile strength of the WF
732
Nomenclature
a
‰BŠ
E11 , E22 , E33
ES
Eyy
I
F
f, F
fFg
fFm g
fm
G12 , G13 , G23
g
h
I
k
‰KŠ
Lx , Ly , Lz
m, M
‰MŠ
r
S12 , S13 , S23
t
tf
u, v, w
fUg
UI
fUm g
:
fUg
fU g
V0
V0f , Vf
strand width
strain shape function
Young's moduli w r t material
coordinate system
modulus of impactor
transverse modulus normal to the
®bre orientation of the uppermost
layer
impact force vector
scalar contact force
external force vector
force vector caused by the inertia
terms
peak contact force
shear moduli w r t material coordinate system
inter-strand gap
strand thickness
in-plane failure function
Hertz constant
sti€ness matrix of the plate
Lengths along X, Y and Z directions/plate dimensions
impactor mass
global mass matrix of the plate
radius of impactor
shear strengths w r t material
coordinate system
indicates any time `t'
duration of impact
displacements along X, Y and Z
directions
displacement vector of the plate
displacement caused by impact
force
displacement caused by inertia
force
velocity vector of the plate
acceleration vector of the plate
incident impact velocity
overall ®bre-volume fraction
composites is much higher than the UD composites.
This is one of the possible reasons for the superior
impact resistance characteristics of WF composites.
A number of studies are available on the impact
behaviour of UD laminated composites [1±33]. Even
though there are some studies on the impact behaviour
of WF composites [34±51], further studies are necessary
for their e€ective use in structural applications.
In this paper, the impact behaviour of plain-weave
fabric-laminated composite plates supported on all the
X; Y; Z
XC , YC , ZC
XT , YT , ZT
, "
c
I
t
m
s
12 , 13 , 23
1 , 2 , 3
X , Y , Z
XY , XZ , YZ
12 , 13 , 23
Abbreviations
2D
3D
FEA
UD
CP
WF
WG
av
global coordinate axes
compressive strengths w r t material coordinate system
tensile strengths w r t material
coordinate system
di€erence between the displacement of the centre of the nose of
the impactor and that of the centre of the mid-surface of the plate
constants in Newmark time integration
strain
displacement of the centre of the
mid-surface of the plate
displacement of the tip of the
impactor
small increment in time
maximum displacement
Poisson's ratio
Poisson's ratio of the impactor
material
Poisson's ratios w r t material
coordinate system
density
normal stresses w r t material
coordinate system
normal stresses w r t global coordinate system
shear stresses w r t global coordinate system
shear stresses w r t material coordinate system
two-dimensional
three-dimensional
®nite-element analysis
unidirectional
balanced symmetric crossply
laminate (made of UD layers)
woven-fabric
weave geometry
average.
four sides and subjected to a transverse central point
load is studied. The studies have been carried out for
low-velocity impact loading. Stress state in the composite plate is evaluated using 3D transient ®nite-element
analysis. Initiation of damage and the location of
damage are predicted using an in-plane quadratic failure
criterion. The prediction model was validated with
experimental results in our earlier work [42,43]. Behaviour
of laminated composite plates made of di€erent plainweave fabrics under low-velocity impact is compared with
733
those of balanced symmetric crossply (CP) laminates
made of UD layers and also UD composites.
2. Governing equations
In the analysis of the composite plate, it is assumed
that the material of each layer is linearly elastic and
obeys the generalised Hooke's law. In the present study,
de¯ections of the plate are small in comparison to the
dimensions of the plate, and hence the small-de¯ection
theory is found to be valid for the impact analysis. For
small-strain theory the equilibrium equation for a body
in motion by neglecting the damping coecient is
written as
‰MŠ U ‡ ‰KŠfUg ˆ fFg
…1†
where ‰MŠ is global mass matrix, ‰KŠ issti€ness
matrix,
fFg is external force vector and fUg, U are the displacement and acceleration vectors.
or bulk deformations of the objects as a whole. The ®rst
attempt to incorporate a theory of local indentation was
based on a scheme suggested by Hertz [52], who viewed
the contact of two bodies as an equivalent problem in
elastostatics. A solution was obtained in the form of a
potential which described the stresses and deformations
near the contact point as a function of the geometrical
and elastic properties of the bodies. This result,
although both static and elastic in nature, has been
widely applied to impact situations where permanent
deformations are produced [53].
The contact force in case of impact between a hemisphere and a plane isotropic surface is obtained from
Hertz theory. In low-velocity impact, where the duration of impact is long in comparison to the period of the
lowest mode of vibration of the plate, the Hertz contact
law can be applied. In this case, Hertz theory which has
been modi®ed to apply for the case of impact on an
anisotropic surface like composites is used to calculate
the force caused by the impact on the plate. The Hertz
contact law can be expressed as
2.1. Contact force
f ˆ k3=2
The knowledge of force vector is important for the
solution of Eq. (1). For calculation of the force caused
as a result of impact on composite plate, the impactor is
modelled as an isotropic elastic body of spherical shape
and the target as a plane anisotropic surface. The
impactor is assumed to be rigid and of higher sti€ness
compared to the target in the direction of impact.
According to Davies et al. [20] the structure is expected
to respond dynamically away from the impactor, where
conventional theories of plates and shells can be applied
to predict the behaviour of the structure. It has been
found that near the point of impact the inertia forces are
small compared with those of impactor, so that
although the dynamic response of the structure may be
needed to ®nd the impactor-force history, the nature of
the stress ®eld can be analysed as if subjected to a
quasi-static force.
where f is the scalar contact force, `' is the di€erence
between the displacement of the centre of the nose of
the impactor and that of the centre of the mid-surface of
the plate and `k' is modi®ed Hertz constant whose value
can be calculated by [21,54,55]:
2.2. Contact law
3. Finite-element formulation for stress analysis
The classical treatment of impact phenomenon is
based primarily on the impulse-momentum law for rigid
bodies. The colliding objects are regarded essentially as
single mass points. Also, it is assumed that the contact is
instantaneous. This requirement can be met when the
contacting surfaces are ideal smooth planes located
normally to the relative velocity. In practice, however, it
is dicult to meet this requirement. Also, one of the
colliding surfaces is usually curved or non-planar. In
this case, the two bodies su€er a relative indentation in
the vicinity of the impact point in addition to the gross
3.1. Boundary conditions
kˆ
4 p
1
r
2
3
1 ÿ s 1 ÿ 2yx
‡
Es
Eyy
…2†
…3†
where yx ˆ ÿ ""xy
Here, r, s and ES are radius, Poisson's ratio and
modulus of impactor, respectively. Eyy is the transverse
modulus normal to the ®bre orientation in the uppermost composite layer.
The 3D ®nite-element analysis (FEA) code was used
to carry out the stress analysis of laminated composite
plates for the following boundary conditions.
Supported on all sides:
i. At X ˆ 0 and X ˆ Lx
u ˆ 0, v 6ˆ 0, w ˆ 0.
ii. At Y ˆ 0 and Y ˆ Ly
u 6ˆ 0, v ˆ 0, w ˆ 0.
734
The dynamic equilibrium equation (1) is expressed in
terms of ®nite-element formulation. For the modelling
of composite laminates, eight-noded linear isoparametric
brick elements with incompatible modes [56,57] were used.
Each node has 3 degrees of freedom. The solution of the
dynamic equation was obtained using an implicit directintegration technique like Newmark's method [57].
3.2. Stress calculation
For calculating the stresses, the ‰BŠ matrix is initially
evaluated at the Gauss points and using this matrix,
strains are calculated. These strains are then extrapolated to the nodes. To overcome the discontinuity of
the strain values between two elements because of the
use of Co type of ®nite-element, the strain at any node is
calculated as the sum of the strains obtained at that
node from all the surrounding elements, divided by the
number of surrounding elements. These nodal strains
are used to calculate the stresses at the nodes. In case of
node lying on the interface the in-plane normal stresses
and shear stress are calculated by simply multiplying
with the elasticity matrix of the particular layer. But the
transverse normal stress and transverse shear stresses
are calculated by using the average elasticity matrix of
the two layers. The values of stresses YZ and XZ are
not exactly zero at the top and bottom surfaces and that
of Z is not zero at the bottom, since the equilibrium
equations are not explicitly enforced. These can be
made exactly zero at the top and the bottom surfaces by
back-substituting the values of in-plane normal stresses
in the equilibrium equations and then solving the
resulting partial di€erential equations for Z , YZ and
XZ by applying the appropriate boundary conditions.
Numerical techniques like ®nite di€erence can be used
to obtain their solution. However, the discrepancy seen
at the top and the bottom was found to be very small to
make any di€erence in the failure calculations and
hence was neglected in the present study.
3.3. Newmark time integration
For the solution of the dynamic equation, Newmark
time integration is used. The dynamic equation can be
written at time t ‡ t as
‰MŠ U t‡t ‡ ‰KŠ Ut‡t ˆ Ft‡t
…4†
The acceleration and velocity vectors at time t ‡ t
are obtained by the following expressions:
n : o
1
Ut‡t ÿ fUt g ÿ …t† Ut
…t†2
n o
1 1
ÿ U t
ÿ
2
n
o
U t‡t ˆ
…5†
n:
o n: o
n
n o
n
oo
U t‡t ˆ U t ‡ …t† …1 ÿ † U t ‡ U t‡t
…6†
where and are the constants, which are in this case
chosen to be 0.25 and 0.5, respectively [57]. Then this
method is also called the constant average acceleration
method or the trapezoidal method. Substituting Eq. (5)
in the dynamic equation (4).
1
‰
M
Š
Ut‡t ˆ FIt‡t ‡ Fm
…7†
‰K Š ‡
t
2
…t†
Fm
t
1
1 n: o
Ut
fU t g ‡
ˆ ‰ MŠ
2
…t†
…t†
n o
1
ÿ 1 U t
‡
2
…8†
In Eq. (4) the only unknowns are the de¯ection fUg
and force fFg at time `t ‡ t'. Rest of the terms, i.e.
velocity, displacement and acceleration at time `t' are all
known. As there are two unknowns and only one equation, another equation is developed using Hertz contact
law.
4. Solution procedure
The force caused by the impact of a sphere on a plate
cannot be expressed by a simple analytical function of
time. Hence, the force Vs time curve is idealised by a
suitable step curve having constant forces F1, F2, F3, ...
over equal time intervals. That means, it is assumed that
the continuous action of the force is replaced by a series
of constant forces F1, F2, F3, .... each acting for a time
interval `t'. Here, F1, F2, F3 ... are the forces at time,
(nt), where n=1, 2, 3 ... . At any time `t' the force at
that instant is obtained by the superposition of the
e€ects of the previous impulses at that time `t' with the
impulse at the same time `t'.
In the present impact problem, the algorithm given in
Ref. [58] was followed to save the computation time.
First, the response of the plate to a unit impulse of time
duration `t' is calculated for the entire time history
and stored in the memory. After that the non-linear
Hertz law is applied at every time step to calculate the
impact force. The impact force at any time `t' is calculated from the impactor and plate displacements of the
previous time step.
4.1. Response of plate to unit impulse
The exact procedure for getting the response of the
plate as a result of a unit impulse of time duration `t'
is given as follows. It is seen in Eq. (7) that the force
vector consists of the force caused by an external force
735
applied as well as the inertia force caused by the mass of
the plate. Hence the displacement vector is written as
sum of the displacements caused by the external applied
load as well as by the inertia force [55].
…9†
Ut‡t ˆ UIt‡t ‡ Um
t‡t
Substituting Eq. (9) in Eq. (7),
‰KŠ ‡
1
‰MŠ UIt‡t ‡ Um
t‡t
2
…t†
I m
ˆ Ft‡t ‡ Ft
…10†
The impact force is calculated using the Hertz contact
law which during the loading phase is given by
…11†
where t‡t is the indentation depth at any instant of
time.
At any time `t ‡ t'
…12†
The above equation is approximated by its value calculated from the plate and impactor displacements at
time `t' given as below:
t‡t ˆ It ÿ ct
…t …t
0
t
1
X
X
f
dtdt ÿ
Fj cj
0m
jˆt
jˆ1
!3=2
…15†
Here, Fj is a dimensionless quantity de®ned as (fj /unit
force).
As a result of the non-linear nature of the above
equation, analytical solution is not possible and the
solution is obtained numerically by small time increment method, then Eq. (15) becomes
ft‡t
!3=2
n
t
1
X
X
t2 X
c
ˆ k V0 t ÿ
Dnÿj‡1 Fj ÿ
Fj j
m jˆ1
jˆt
jˆ1
…16†
The summation in the second term of the Eq. (16)
arises from the double integration term and, for a linear
continuous approximation of force/time curve can be
expressed as
n
X
Dnÿj‡1 Fj ˆ 2‰…n ÿ 1†F1 ‡ …n ÿ 2†…F2 ÿ F1 † ‡ :::Š
jˆ1
4.2. Calculation of impact force
t‡t ˆ It‡t ÿ ct‡t
Substituting Eq. (14) and Eq. (13) in Eq. (11),
ft‡t ˆ k V0 t ÿ
To proceed with the solution, it is necessary to prescribe the right hand side force vectors. It must be noted
that fFm g at time `t' is known since the displacement,
acceleration and velocity vectors at time
`t'
are known.
Also the force caused by the impulse FI during time
t ˆ 0 to t ˆ t is of unit magnitude. After the ®rst time
step `t' the external applied force is made zero. The
left-hand-side matrix contains the e€ective sti€ness
matrix, which is decomposed only once before the
iterations are begun. This decomposed matrix is used to
calculate the displacements of the plate with di€erent
right-hand-side force vectors at each time step. Newmark time integration scheme is used to get the displacement history of the plate over the required time
period.
ft‡t ˆ k…t‡t †3=2
the impactor and `f' is the contact force caused by
impact.
…t …t
f
It ˆ V0 t ÿ
dtdt
…14†
m
0 0
…13†
Here, ct is the displacement of the centre of the midsurface of the plate in the direction of the impact. It is the
displacement of the tip of the impactor at any time `t'.
The position of the tip of the impactor at any time `t'
after the contact between the plate and impactor has
taken place is given in Eq. (14), where the double integral signi®es the resistance of the plate to the motion of
1
‡ …Fn ÿ Fnÿ1 ‡ Fnÿ2 ÿ :::†
3
…17†
The solution of Eq. (16) is obtained by the following
approximation scheme [53,59]. At time t ˆ t, the force
is assumed to be a function of only the local compression and not the de¯ection of the plate. Hence the force
is calculated as
ft ˆ k…V0 t†3=2
…18†
Then the force at time t ˆ 2t is calculated from the
known displacements of plate and impactor at time
t ˆ t. Similarly, force at any time `t ‡ t' is calculated
by substituting the impactor and plate displacements of
the previous time step using Eq. (17).
The value of ct , already available from the response
history of the plate, calculated for a unit impulse of
duration `t', is multiplied by the impactor force to get
the displacement of the plate under the impact load. At
any time `t' the displacement of the plate is obtained by
taking a summation of the products of the impact force
and the displacement response of the plate due to the
unit load up to that time `t' as shown by the double
summation sign in the third term of the Eq. (16).
736
5. Results and discussion
The results have been obtained using the inhouse
FEA code developed for impact analysis. This program
was used to analyse the woven-fabric composite plates
under impact loading. For comparison, the results for a
[0/90]S crossply laminates made of UD layers and [0]n
UD composites are also presented. For all the cases, the
loading was through a point load acting at the centre of
the plate.
Joshi and Sun [7] have analysed the impact behaviour
of composite beams. They used ®nite-element analysis
based on 2D plain-strain formulation. In the present
analysis, impact behaviour of composite plates has been
analysed using eight-noded linear isoparametric brick
elements with incompatible modes. The present analysis
is based on solution of equilibrium equations tending
towards exact solution.
The schematic arrangement of WF laminated composite plate geometry is shown in Fig. 1. For the present
study, a square plate of 150 mm150 mm6 mm thickness was considered. Supported boundary condition was
considered for all the cases.
A steel spherical impactor with radius 6.5 mm, modulus of elasticity of 200 GPa and Poisson's ratio of 0.3
was considered.
Di€erent plain-weave fabric laminated composite
plates were considered for the impact studies. The
weave geometrical parameters considered are presented
in Table 1. Laminate con®guration C2 was considered
for all the laminates [60±65]. E-glass/epoxy and T300/
5208 carbon/epoxy materials were used for the studies.
Five weave geometries were considered for the studies
with di€erent strand width (a), strand thickness (h) and
inter-strand gap (g). All the laminates were made with
balanced fabrics with the same geometrical and material
parameters along both warp and ®ll directions. The
ratio (g=a) was 0.1 for all the cases. The ratio (h=a) was
varied in the practical range from 0.01 to 0.25. The
Table 1
Plain-weave fabric structurea
Weave geometry
WG06
WG07
WG02
WG08
WG10
a
Warp strand
Fill strand
h=a
g=a
h=a
g=a
0.01
0.05
0.10
0.15
0.25
0.1
0.1
0.1
0.1
0.1
0.01
0.05
0.10
0.15
0.25
0.1
0.1
0.1
0.1
0.1
a=2.0 mm.
fabric thickness was minimum for WG06 and maximum
for WG10. For the other fabrics it was in between.
As given in Tables 1±8, materials WG06, WG07,
WG02, WG08 and WG10 refer to plain-weave fabric
laminates. Materials CP0.65, CP0.40 and CP0.70 refer to
balanced symmetric crossply laminates made of UD layers. Materials UD0.65 and UD0.70 refer to UD composites. The last letter `G' refers to E-glass as reinforcing
material and `C' refers to T300 carbon as reinforcing
material. The elastic and strength properties are given in
the Tables 2±5 [60±66].
The in-house FEA code developed was ®rst run with
di€erent meshes for convergence study. Based on the
study, a mesh of 20208 was adopted for all the cases.
The code was run for an impact problem solved by
Karas [55,67] for an isotropic material. The results
obtained by the present in-house FEA code and that
obtained by Karas were compared, and a good correlation
was obtained [42,43].
The code was also used to obtain the failure for a
material given by Lammerant and Verpoest [26] and
tested under quasi-static loading for a crossply laminate
[0/90]S, made of HTA/6376 toughened carbon/epoxy.
They observed damage initiation in the form of a matrix
cracking/lamina splitting in the bottom layer right
under the point of the loading. This ®rst matrix cracking/lamina splitting appeared at a displacement of 1
mm. Using the present code, it was observed that the
failure had just initiated in the form of a matrix cracking/lamina splitting in the bottom most layer for a displacement of 1 mm [42,43].
5.1. Impact loading
Fig. 1. Woven-fabric laminated composite plate geometry.
Response plots of E-glass/epoxy laminates are presented for supported boundary conditions in Fig. 2.
Contact force and displacement plots are given in Figs.
3 and 4, respectively. It can be seen from Fig. 3 that multiple contacts occur for both WF and CP laminates. The
peak contact force was more for WF laminates. Corresponding plate and impactor displacements are nearly the
same for the WF and CP laminates considered.
It was observed that the loss of contact takes place
when the plate starts moving with a higher velocity
737
Table 2
Elastic properties of composites: E-glass/epoxya
Material
E11 (GPa)
E22 (GPa)
E33 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
12
13
23
Vf
(kg/m3)
UD
UD
UD
WG06G
WG07G
WG02G
WG08G
WG10G
48.0
44.6
30.9
21.7
21.4
20.8
19.9
18.1
15.3
13.4
8.3
21.7
21.4
20.8
19.9
18.1
15.3
13.4
8.3
8.5
8.6
8.7
8.8
9.0
5.1
4.4
2.8
3.91
3.91
3.92
3.92
3.94
5.1
4.4
2.8
4.1
4.1
4.2
4.2
4.2
5.8
5.0
3.0
4.1
4.1
4.2
4.2
4.2
0.315
0.317
0.327
0.169
0.171
0.173
0.178
0.189
0.315
0.317
0.327
0.280
0.279
0.279
0.278
0.276
0.332
0.342
0.395
0.280
0.279
0.279
0.278
0.276
0.65
0.6
0.4
0.4
0.4
0.4
0.4
0.4
2112
2040
1750
1750
1750
1750
1750
1750
a
Densities of E-glass ®bre=2620 kg/m3 and epoxy resin=1170 kg/m3.
Table 3
Elastic properties of composites: T300/5208 carbon/epoxya
Material
E11 (GPa)
E22 (GPa)
E33 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
12
13
23
Vf
(kg/m3)
UD
UD
UD
WG06C
WG07C
WG02C
WG08C
WG10C
162.0
150.7
94.1
53.1
50.3
44.2
38.0
28.8
14.9
13.3
7.9
53.1
50.3
44.2
38.0
28.8
14.9
13.3
7.9
8.0
8.1
8.2
8.4
8.6
5.7
4.9
2.8
3.79
3.79
3.79
3.79
3.79
5.7
4.9
2.8
3.7
3.7
3.7
3.7
3.7
5.4
4.8
2.7
3.7
3.7
3.7
3.7
3.7
0.283
0.287
0.309
0.055
0.058
0.064
0.073
0.093
0.283
0.287
0.309
0.074
0.073
0.072
0.071
0.070
0.386
0.390
0.436
0.074
0.073
0.072
0.071
0.070
0.7
0.65
0.4
0.4
0.4
0.4
0.4
0.4
1583
1554
1406
1406
1406
1406
1406
1406
a
Densities of T300 carbon ®bre=1760 kg/m3 and epoxy resin=1170 kg/m3.
Table 4
Strength properties of composites: E-glass/epoxya
Material
XT (MPa)
YT (MPa)
ZT (MPa)
S12 (MPa)
S13 (MPa)
S23 (MPa)
XC (MPa)
YC (MPa)
ZC (MPa)
Vf
UD
UD
UD
WG06G
WG07G
WG02G
WG08G
WG10G
1297
1197
798
315
290
250
230
210
27.8
27.7
27.1
315
290
250
230
210
27.8
27.7
27.1
27.1
27.1
27.1
27.2
27.3
39.2
38.7
36.8
28
28
28
28
28
39.2
38.7
36.8
28
28
28
28
28
38
37
36
28
28
28
28
28
820
740
480
210
196
183
170
120
150
145
140
210
196
183
170
120
150
145
140
140
140
140
140
140
0.65
0.6
0.4
0.4
0.4
0.4
0.4
0.4
a
XT and YT values for WF composites are at pure matrix block failure.
Table 5
Strength properties of composites: T300/5208 carbon/epoxy
Material
XT (MPa)
YT (MPa)
ZT (MPa)
S12 (MPa)
S13 (MPa)
S23 (MPa)
XC (MPa)
YC (MPa)
ZC (MPa)
Vf
UD
UD
UD
WG06C
WG07C
WG02C
WG08C
WG10C
1744
1622
1013
565
500
405
365
345
52.6
52.0
49.5
565
500
405
365
345
52.6
52.0
49.5
49.5
49.5
49.5
49.5
49.5
107.8
106.4
100.5
66
66
66
66
66
107.8
106.4
100.5
66
66
66
66
66
100
99
96
66
66
66
66
66
1650
1525
940
420
370
300
255
240
260
250
220
420
370
300
255
240
260
250
220
220
220
220
220
220
0.7
0.65
0.4
0.4
0.4
0.4
0.4
0.4
compared to the velocity of the impactor, i.e. the displacement of the plate exceeds that of the impactor
causing a separation between the two. They once again
come into contact when the plate reverses its direction
of motion and starts coming back towards its original
position. However, it may be noted that the loss of
contact does not signify the end of impact event. During
the impact event there can be a number of contacts
738
Table 6
Impact behaviour of composites: E-glass/epoxya
Material
WG10G
WG08G
WG02G
WG07G
WG06G
CP0.65G
CP0.40G
UD0.65G
a
b
c
Plate
thickness,
LZ (mm)
Peak
contact
force, fm (N)
Max.
displacement,
m (mm)
Duration of
impact,b tf
(ms)
Time to
reach
fm (ms)
Time to
reach m
(ms)
Maximum
failure
in-plane
function
Time to
reach (ms)
I1 (bottom)
I2 (top)
Peak I1
Peak I2
6.0
6.0
6.0
6.0
6.0
5.0
6.0
5.0
1220
1215
1213
1193
1200
927c
880
854c
0.628
0.610
0.602
0.598
0.595
0.113c
0.600
0.107c
871
844
831
825
822
66c
1030
61c
798
776
763
758
754
66c
78
61c
430
418
412
409
408
66c
514
61c
0.033
0.029
0.025
0.018
0.016
1.000
0.545
1.000
0.207
0.107
0.094
0.083
0.072
0.08c
0.066
0.073c
789
766
754
751
745
66c
110
61c
801
769
764
756
755
66c
104
61c
(938)
(907)
(893)
(885)
(888)
(66c)
(962)
(61c)
M=50 gm, V0 =3 m/s; plate dimensions: LX =150 mm, LY =150 mm, simply supported.
Duration of impact is given at contact force, F ˆ 0. The quantity in parentheses indicates duration of impact at plate displacement, w ˆ 0.
Indicates the values at in-plane failure.
Table 7
Impact behaviour of composites: E-glass/epoxya
Material
WG10G
WG08G
WG02G
WG07G
WG06G
CP0.65G
CP0.40G
UD0.65G
a
b
Plate
thickness,
LZ (mm)
Peak
contact
force, fm (N)
Max.
displacement,
m (mm)
Duration of
impact,b tf
(ms)
Time to
reach
fm (ms)
Time to
reach
m (ms)
6.0
6.0
6.0
6.0
6.0
5.0
6.0
5.0
393
391
392
388
388
298
275
364
0.210
0.204
0.201
0.199
0.199
0.201
0.205
0.201
902
876
863
858
854
1026
1068
1000
823
798
784
780
774
72
102
648
442
429
422
419
418
492
526
500
(940)
(910)
(895)
(888)
(884)
(962)
(966)
(940)
Maximum
failure
in-plane
function
Time to
reach (ms)
I1 (bottom)
I2 (top)
Peak I1
Peak I2
0.003
0.002
0.002
0.002
0.001
0.131
0.058
0.143
0.019
0.009
0.009
0.007
0.007
0.009
0.007
0.011
811
104
103
103
103
118
136
116
813
790
776
772
766
96
122
658
M=50 gm, V0 =1 m/s; plate dimensions: LX =150 mm, LY =150 mm, simply supported.
Duration of impact is given at contact force, F ˆ 0. The quantity in parentheses indicates duration of impact at plate displacement, w ˆ 0.
Table 8
Impact behaviour of composites: T300/5208 carbon/epoxya
Material
WG10C
WG08C
WG02C
WG07C
WG06C
CP0.70C
CP0.40C
UD0.70C
a
b
Plate
thickness,
LZ (mm)
Peak
contact
force, fm (N)
Max.
displacement,
m (mm)
Duration of
impact,b tf
(ms)
Time to
reach fm
(ms)
Time to
reach
m (ms)
6.00
6.00
6.00
6.00
6.00
5.32
6.00
5.32
371
379
405
441
437
369
305
399
0.187
0.169
0.159
0.151
0.148
0.134
0.149
0.119
757
693
656
622
618
664
762
628
645
551
525
512
495
472
114
540
357
325
308
296
485
340
394
398
(778)
(703)
(662)
(629)
(612)
(614)
(702)
(708)
Maximum
failure
in-plane
function
Time to
reach (ms)
I1 (bottom)
I2 (top)
Peak I1
Peak I2
0.002
0.002
0.002
0.002
0.001
0.019
0.010
0.032
0.006
0.007
0.006
0.004
0.003
0.003
0.003
0.004
631
570
546
519
516
124
150
530
631
568
545
518
515
96
120
534
M=50 gm, V0 =1 m/s; plate dimensions: LX =150 mm, LY =150 mm, simply supported.
Duration of impact is given at contact force, F ˆ 0. The quantity in parentheses indicates duration of impact at plate displacement, w ˆ 0.
between the impactor and the plate, but the impact
event can be considered to be over only when the
impactor displacement reverses its sign and the contact
between the impactor and the plate is lost during the
upward motion of the plate and the impactor, or the
plate returns to its original position, whichever takes
place later. In the present case, it can be seen that, for
WF laminates, the contact between the plate and the
impactor was lost even before the plate returned to its
original position. On the other hand, for CP laminates,
739
Fig. 2. Response of E-glass/epoxy laminates, CP0.40G and WG02G
to unit impulse Ð simply supported.
Fig. 4. Variation of impactor and plate displacements with time at
X ˆ LX /2 and Y ˆ LY /2 for E-glass/epoxy laminates, CP0.40G and
WG02G Ð simply supported.
Fig. 3. Variation of contact force with time at X ˆ LX /2 and Y ˆ LY /2
for E-glass/epoxy laminates, CP0.40G and WG02G Ð simply supported.
the contact between the plate and the impactor was lost
beyond the original position. In the present study, only
the ®rst impact was considered and hence the calculations were stopped after the impactor displacement
reversed its sign and the contact between the impactor
and the plate was lost, or the plate returned to its original position, whichever took place later.
5.2. In-plane stress plots
The plots for the variation of the stresses (X and Y )
through the thickness of the plate are given in Figs. 5±7
for the WF and CP laminates. For WF laminate, time
interval 763 ms corresponds to time to reach peak contact
Fig. 5. Variation of X and Y through the plate thickness at X ˆ LX /
2 and Y ˆ LY /2 for E-glass/epoxy laminate, WF, (0)S, WG02G Ð
simply supported.
force. Time interval 500 ms is during the separation
period. For CP laminate, time interval 78 ms corresponds to time to reach peak contact force. In this case
also time interval 500 ms is during the separation period.
For the incident impact velocity and mass of the
impactor considered for these two cases, stresses
induced were not sucient to cause damage in the
740
plates. From Figs. 5±7, it can be seen that the magnitudes of compressive normal stresses in the upper layers
of the laminate are more than the magnitudes of the
tensile normal stresses in the lower layers. This is
because of the compression of the upper layers during
the impact event when the contact exists between the
impactor and the plate. But during the separation period the magnitudes of the stresses in the upper and the
lower layers are identical. From Fig. 5, it can be seen
that the variation of X and Y through the plate
thickness is identical for WF composites. This is because
the WF composites have balanced properties in both
warp and ®ll directions.
Variation of stresses (X and Y ) along LY at peak
contact force is presented in Figs. 8±11 for WF and CP
laminates. From X and Y plots it can be seen that near
the centre the stresses are compressive in the upper layers and tensile in the lower layers. But the sign changes
towards the end of the plate. The magnitude of XY is
seen to be a very small quantity.
5.3. In-plane failure function plots
The three possible macro modes of damage initiation
that can occur in the composite laminate under impact
load are:
i. Initiation of matrix cracking/lamina failure caused
by in-plane stresses. In-plane tensile normal stresses and shear stress can lead to matrix cracking/
lamina failure in the lower layer whereas in-plane
compressive normal stresses and the shear stress
can lead to matrix cracking/lamina failure in the
upper layer. These matrix cracks initiated within
the layer can lead to delamination when these
cracks reach the neighbouring interface.
ii. Initiation of delamination caused by the tensile
nature of Z and other interlaminar shear stresses.
iii. Crushing of upper layers caused by impact loading.
Fig. 6. Variation of X through the plate thickness at X ˆ LX /2 and
Y ˆ LY /2 for E-glass/epoxy laminate, CP, [0/90]S, CP0.40G Ð simply
supported.
Out of these three possible modes of damage initiation, only the ®rst mode, i.e. the in-plane failure mode,
Fig. 7. Variation of Y through the plate thickness at X ˆ LX =2 and
Y ˆ LY /2 for E-glass/epoxy laminate, CP, [0/90]S, CP0.40G Ð simply
supported.
Fig. 8. Variation of X along LY at peak contact force for E-glass/
epoxy laminate, WF, (0)S, WG02G Ð simply supported.
741
has been considered in the present study. Damage
initiation caused by Z , XZ and YZ is being studied
separately.
The damage initiation would occur in the form of
matrix cracking/lamina splitting either in the bottom
layer or in the top layer. Hence, an in-plane failure criterion by Tsai±Hill [68] was used for damage initiation
studies. An in-plane failure function, I, based on Tsai±
Hill criterion is de®ned as follows:
1
XT
2 2 2 2
12
1
2
‡
‡
ÿ
ˆI
YT
S12
XT YT
Here 1 , 2 and 12 are the induced in-plane stress
components and XT , YT and S12 are the normal and inplane shear-strength values.
The damage initiation takes place when the value of
in-plane failure function, I just exceeds unity. In-plane
failure function plots are presented in Figs. 12±15 for
WF and CP laminates. Failure has not taken place for
the plate geometry and impact parameters considered
for both WF and CP laminates. In-plane failure function value is very high for CP laminates as compared to
Fig. 9. Variation of Y along LY at peak contact force for E-glass/
epoxy laminate, WF, (0)S, WG02G Ð simply supported.
Fig. 11. Variation of Y along LY at peak contact force for E-glass/
epoxy laminate, CP, [0/90]S, CP0.40G Ð simply supported.
Fig. 10. Variation of X along LY at peak contact force for E-glass/
epoxy laminate, CP, [0/90]S, CP0.40G Ð simply supported.
Fig. 12. Variation of in-plane failure function, I with time at the centre
for E-glass/epoxy laminate, WF, (0)S, WG02G Ð simply supported.
742
Fig. 13. Variation of in-plane failure function, I along LY at peak
contact force for E-glass/epoxy laminate, WF, (0)S, WG02G Ð simply
supported.
Fig. 15. Variation of in-plane failure function, I along LY at peak
contact force for E-glass/epoxy laminate, CP, [0/90]S, CP0.40G Ð
simply supported.
of the lower transverse tensile strength. Woven-fabric
laminates are characterised by balanced and equal
properties along both warp and ®ll directions. The tensile failure strength along the transverse direction is signi®cantly higher for WF laminates leading to a
signi®cant reduction in in-plane failure function. It is
interesting to note that the in-plane failure initiates from
the bottom surface for CP laminated composites whereas
it initiates from the top surface for the WF laminates.
Woven-fabric laminates have balanced in-plane properties, but the compressive strength properties for the WF
laminates are much lower than the tensile strength
properties. The upper layer is under compressive stresses for the WF laminates, and hence the failure initiates
on the upper layer.
5.4. E€ect of fabric geometry on impact behaviour of
composites
Fig. 14. Variation of in-plane failure function, I with time at the centre
for E-glass/epoxy laminate, CP, [0/90]S, CP0.40G Ð simply supported.
WF laminates. This indicates that WF laminates are
more impact-damage resistant compared to CP laminates. From Figs. 12 and 13, it is seen that the in-plane
failure function value is higher for the top layer (I2)
than for bottom layer (I1) for the WF laminate. On the
other hand, it is seen from the Figs. 14 and 15, that the
in-plane failure-function value is higher for the bottom
layer (I1) than for the top layer (I2) for the CP laminate.
For the CP laminate the in-plane failure can initiate in
the form of matrix cracking/lamina splitting in the
lower layer during impact because of in-plane tensile
stresses. The damage initiates in the lower layer because
Impact behaviour of di€erent plain-weave fabric
composites made of E-glass/epoxy and T300/5208 carbon/epoxy is presented in Tables 6±8.
Weave geometries WG06, WG07, WG02, WG08 and
WG10 indicate plain-weave fabric composites with
decreasing in-plane modulus of elasticity values. The
maximum displacement and maximum in-plane failure
function decrease with the increase in in-plane modulus
of elasticity for both E-glass/epoxy and T300/5208 carbon/epoxy laminates. Nominal plate thickness considered
was 6 mm for all these cases. [0/90]S and [0]n laminate
results are also presented in Tables 6±8 for comparison.
CP0.65G, UD0.65G, CP0.70C and UD0.70C laminate
thickness values were changed as shown in Tables 6±8.
This was done to have the same mass for all the plates.
743
For CP0.65G and UD0.65G the laminates were failing for the plate dimensions and the impact parameters
considered for E-glass/epoxy at V0 ˆ 3 m/s (Table 6).
The in-plane failure was initiating in the bottom layer in
the form of matrix cracking/lamina splitting. For Eglass/epoxy, the peak contact force was more for all the
plain-weave fabric laminates considered compared to
UD and CP laminates (Tables 6 and 7). For T300/5208
carbon/epoxy, UD and CP laminates were not failing for
the plate dimensions and the impact parameters considered (Table 8). But, the in-plane failure function is
higher for UD and CP laminates compared to WF laminates. From the Tables 6±8, it is clear that the in-plane
failure would initiate from the top surface for all the
plain-weave fabric laminates, whereas it would initiate
from the bottom surface for the UD and CP laminates.
6. Conclusions
The behaviour of WF laminated composite plates has
been studied under transverse central low-velocity-point
impact. For this, a ®nite-element formulation is presented.
For the plate geometry and impact conditions considered, it is observed that:
i. Multiple contacts between the impactor and the
composite plate occur during the impact event.
ii. Maximum displacement and maximum in-plane
failure function decrease with the increase in inplane modulus of elasticity for both E-glass/epoxy
and T300/5208 carbon/epoxy laminates.
iii. The magnitudes of compressive normal stresses X
and Y in the upper layers of the laminate are
higher than the magnitudes of tensile normal
stresses X and Y in the lower layers.
iv. The in-plane failure function is lower for the WF
laminates than for UD and CP laminates indicating
that the WF laminates are more impact resistant.
v. In-plane failure function is higher on the top layer
than on the bottom layer for WF laminates. It
indicates that in-plane failure would initiate on the
top layer for WF laminates.
vi. In-plane failure function is higher on the bottom
layer than on the top layer for UD and CP laminated composites. It indicates that in-plane failure
would initiate on the bottom layer for the UD and
CP laminated composites.
Acknowledgements
This work was supported by the Structures Panel,
Aeronautics Research & Development Board, Ministry
of Defence, Government of India, Grant No. Aero/RD134/100/10/95-96/890.
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