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Composite Structures 66 (2004) 277–285
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The finite element analysis of composite laminates and shellstructures subjected to low velocity impact
Shiuh-Chuan Her *, Yu-Cheng Liang
Department of Mechanical Engineering, Yuan-Ze University, 135, Yuan-Tung Road, Chung-Li, Tao-Yuan Shian, Taiwan
Available online 5 June 2004
Abstract
In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-
DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading
and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination
are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and
spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported
boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with
greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection.
The impact response of the structure is proportional to the impactor velocity.
� 2004 Elsevier Ltd. All rights reserved.
Keywords: Finite element; Composite laminate; Shell structure; Impact; Contact force
1. Introduction
Advanced composite structures have been used
widely in many applications such as aerospace, sport
equipments, pressure vessels and automobile parts. It is
well known that composites are very suspectible to
transverse impact. Impact-induced damage may arise
during manufacture, maintenance and service operation.Low velocity impact could cause significant damage, in
terms of matrix cracking and delamination. Such dam-
age is very difficulty to detect by naked eye and can lead
to severe reductions in the stiffness and strength of the
structures. C scan and X-ray are the most popular
nondestructive testing methods to inspect the damage.
The behavior of composite structures subjected to
low velocity impact has been studied by numerousresearchers, including experimental, numerical and
analytical works. Most of the published literatures fo-
cused the impact analysis on flat plates [1–10]. Only a
few researches have been studied the low velocity impact
of laminate shells [11,12]. Analytical solutions for the
impact response of laminate plates are presented by
*Corresponding author. Tel.: +886-3-4638800x451; fax: +866-3-
455-8013.
E-mail address: [email protected] (S.-C. Her).
0263-8223/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruct.2004.04.049
Christorforou and Swanson [1], Cairns and Lagace [2],
and Prasad et al. [3]. A number of researchers have
deployed the finite element method for the solution of
impact on composite laminates [4–10]. In Ref. [8] the
authors have used a finite element formulation based on
the Saner’s shell theory to study the impact response and
damage of laminated cylindrical composite shells. While
in Ref. [11], the authors have adopted a 3-D brick ele-ment to investigate the effect of curvature on the dy-
namic response and impact-induced damage in
composite structures. By employing Disciuva’s com-
posite laminate theory with Hashin’s failure criterion,
Wang and Yew [12] calculated the distribution of
damage in each layer under the transverse impact.
Pierson and Vaziri [13] presented an analytical model to
predict the low velocity impact response of simple sup-ported composite laminates. Chun and Lam [14] pro-
posed a numerical method derived by Lagrange’s
principle and Hertzian contact law for the calculation of
dynamic response of laminated composite plates. A
hybrid stress finite element method was employed by
Goo and Kim [15] to simulate the dynamic behavior of
composite laminates under the low velocity impact.
In the present investigation, the ANSYS/LS-DYNAfinite element software is used to calculate the tran-
sient response of the impact on composite laminates,
278 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285
cylindrical and spherical shells. Deflection and contact
force are the major concerns in the impact response. A
modified Hertzian contact law for loading and unload-
ing processes during the impact period is adopted topredict the contact force. The numerical results are
compared with those existing literatures. The objective
of this research is to study the influence of the shell
curvature, clamped or simple supported boundary con-
dition, impactor velocity on the impact response of the
composite structures. Contact force and center deflec-
tion are presented for various parameters including shell
curvature, boundary condition and impactor velocity.
2. Contact force
The duration of an impact between two bodies occurs
at a very short of period, normally within a few micro
seconds. The transient response of the impact is inves-
tigated on the basis of the following assumptions:
(1) frictionless between the impactor and compositestructure;
(2) neglecting the damping affect in the composite struc-
ture;
(3) ignoring the gravity force during the impact period;
(4) rigid body for the impactor.
Contact force is the most important concern in the
impact analysis. In this study, the contact force is cal-culated, according to the loading and unloading pro-
cesses. During the loading phase, the contact force
follows the Hertzian contact law, and an expression
proposed by Tan and Sun [16] is adopted for the
unloading. These relations are given as
loading Fc ¼ ka1:5 ð1aÞ
unloading Fc ¼ Fma � a0am � a0
� �2:5ð1bÞ
where a denotes the indentation can be calculated by thedifference of the deflections between the composite
structure wsðtÞ and impactor wiðtÞa ¼ wiðtÞ � wsðtÞand k is the modified Hertzian contact stiffness which isdefined for a composite laminate, cylindrical shell and
spherical shell as follows [8]:
for cylindrical shell kcyl ¼4
3
½1=ri þ 1=2rcyl��0:5
½ð1� v2i Þ=Ei þ 1=E2�
for spherical shell ksph ¼4
3
½1=ri þ 1=rsph��0:5
½ð1� v2i Þ=Ei þ 1=E2�where E2 is the elastic modulus transverse to the fiberdirection and ri, vi, Ei are the radius, Poisson’s ratio andelastic modulus of the impactor, respectively. In the
unloading, Fm is the maximum contact force reached
during the impact, am is the maximum indentation
which corresponds to Fm and a0 is the permanent
indentation from the loading/unloading cycle. Expres-sions for the permanent indentation are [17]
for am < acr a0 ¼ 0
for am P acr a0 ¼ am 1
"� acr
am
� �2:5#
where acr is the critical indentation has been taken to be0.0083 mm for graphite/epoxy composite laminates [17].
3. Verification of ANSYS/LS-DYNA
LS-DYNA is a general purpose transient dynamicfinite element program, specializes in contact related
problems such as impact and metal forming. ANSYS
adapts the LS-DYNA as the solver for the impact
problems, however, retains its own pre and post pro-
cesses formed the ANSYS/LS-DYNA. To solve the
impact problems by LS-DYNA, the required input data
can be classified into the following three categories:
1. Material properties: identified the material properties
for the impactor and target object, can be a rigid
body, isotropic material or composite material.
2. Initial and boundary conditions: specified the initial
conditions for the impactor such as impact velocity,
acceleration; boundary conditions for the target ob-
ject such as clamped or simple support.
3. Contact conditions: defined the type of contact andfriction coefficient, there are 18 different types of con-
tact can be chosen to accurately represent the physi-
cal model, among them surface to surface (STS)
and node to surface (NTS) are the most common use.
To verify the accuracy of LS-DYNA, a steel plate
impacted by a rigid ball is examined and compared with
literature result [18]. The Young’s modulus and Pois-son’s ratio of the steel plate are 200 GPa and 0.3,
respectively. The mass, radius and velocity of the
impactor are 0.0329 kg, 10 mm and 1 m/s, respectively.
The plate with length 200 mm, width 200 mm and
thickness 8 mm is clamped along the four edges. Three
different types of mesh using solid elements (SOLID
164) are proposed to conduct the convergence test.
Mesh 1 shows in Fig. 1 with 20 (length) · 20 (width) ·2 (height) ¼ 800 elements in plate and 32 elements in
impactor. Mesh 2 shows in Fig. 2 with 40 (length)· 40(width) · 2 (height) ¼ 3200 elements in plate and 32
elements in impactor. Mesh 3 shows in Fig. 3 with 80
(length) · 80 (width) · 2 (height) ¼ 12,800 elements in
plate and 256 elements in impactor. LS-DYNA is
capable of calculating the transient responses and pro-
Fig. 1. Finite element mesh 1 (20· 20 · 2).
Fig. 2. Finite element mesh 2 (40· 40 · 2).
Fig. 3. Finite element mesh 3 (80· 80 · 2).
Fig. 4. Contact force compared with Karas [18] with mesh 1.
Fig. 5. Contact force compared with Karas [18] with mesh 2.
Fig. 6. Contact force compared with Karas [18] with mesh 3.
S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285 279
vides the displacements and stresses distributions for
both impactor and plate. Thus, one can substitute the
impactor displacements, wiðtÞ and plate displacement
wsðtÞ at the impact points into Hertzian contact law Eq.(1a), to determine the contact force. Figs. 4–6 shows the
results of contact force associated with mesh 1, 2, and 3,
respectively. As shown from the figures, the numericalresults obtained by ANSYS/LS-DYNA can converge to
the analytical solution Kara [18], upon the mesh being
refined.
To demonstrate the capability of LS-DYNA software
in composite structure, the T300/934 [O/)45/45/90]2sgraphite/epoxy composite laminate subjected to low
velocity impact is investigated. The length, width and
thickness of the laminate are 76.2, 76.2 and 2.54 mm,respectively. The material properties of the composite
lamina are listed in Table 1 [6]. Impactor velocity, radius
and density are 25.4 m/s, 6.35 mm and 2800 kg/m3,
respectively. In the case of composite material, the
contact force is calculated by Eqs. (1a) and (1b),
according to the loading and unloading processes. Figs.
7 and 8 show the results of contact force with clamped
and simple supported boundary conditions, respectively.
Table 1
Material properties of T300/934 [6]
Exx
(GPa)
Eyy
(GPa)
Gxy
(GPa)
Vxy Vyz Density q(kg/m3)
145.54 9.997 5.689 0.3 0.3 1535.7
Fig. 7. Contact force T300/934 composite laminate with clamped
boundary condition.
Fig. 8. Contact force T300/934 composite laminate with simply sup-
ported boundary condition.
280 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285
Excellent agreement can be found between the LS-
DYNA results and Wu and Chang [6].
Table 2
Material properties of T300/976 [7]
Exx
(GPa)
Eyy
(GPa)
Gxy
(GPa)
Gyz
(GPa)
Vxy Uyz Density q(kg/m3)
156 9.09 6.96 3.24 0.228 0.4 1540
Table 3
Strength of T300/976 [7]
Longitudinal tension Xt (MPa) 1520
Longitudinal compression Xc (MPa) 1590
Transverse tension Yt (MPa) 45
Transverse compression Yc (MPa) 252
Ply longitudinal shear Si (MPa) 105
4. Failure analysis
Impact induced damage is a very complicated phe-
nomenon. It requires a understanding of the basicmechanics and damage mechanism. Choi and Chang [7]
had investigated the impact damage by using a line-nose
impactor. Based on the previous studies, Choi and
Chang [7] summarized the impact damage mechanism as
follows:
1. Intraply matrix cracks due to shear or bending initi-
ate the damage.2. These matrix cracks propagate into the nearby inter-
face and cause the delamination between dissimilar
plies.
3. A shear matrix crack located in the inner plies of the
laminate can generate a substantial delamination.
4. A bending matrix crack located at the surface ply
generates a delamination along the first interface of
the cracked ply.
Although the damage mechanism of point-nose im-
pact is much more complicated than line-nose impact,
previous observations regarding the damage process is
still applicable. The sequence of impact damage incomposite laminate can be classified into two stages: (1)
bending or shear stresses initiate the micro cracks in
matrix, (2) propagation of the micro cracks into the
nearby interface yields to the delamination. Thus, in
order to predict the impact damage, two failure criteria
are proposed. Matrix cracking criterion is used to pre-
dict the initiation of damage, and delamination criterion
is adopted to estimate the damaged area. In this study,the failure criteria suggested by Choi and Chang [7] are
adopted and expressed as follows:
Matrix cracking criterion
n�ryy
nY
!2
þn�ryz
nSi
!2
¼ e2M eM P 1 failure ð2Þ
nY ¼ nYt if ryy P 0; nY ¼ nYc if ryy < 0
Delamination criterion
Da
n�ryz
nSi
!224 þ
nþ1�rxz
nþ1Si
!þ
nþ1�ryy
nþ1Y
!235 ¼ e2D
eD P 1 failure ð3Þnþ1Y ¼ nþ1Yt if ryy P 0; nþ1Y ¼ nþ1Yc if ryy < 0
The details of these criteria are given in the reference
cited above.
To verify the ANSYS/LS-DYNA in predicting the
impact damage, T300/976 graphite epoxy composite
were used for the study. The material properties and
strength of T300/976 are listed in Tables 2 and 3 [7],
respectively. Two types of ply orientation, [03/903/03/903/03] thickness 2.16 mm and [04/454/)454/904/)454/454/04]thickness 4.03 mm, are investigated. The length and
width of the specimen are 10 and 7.6 cm, respectively.
The specimen is clamped along the two parallel edges
and free for the other two edges as shown in Fig. 9. The
composite laminate is impacted by a steel ball with ra-
Fig. 9. Specimen used for failure analysis.
Fig. 10. Delamination area of T300/976 ½03=903=03=903=03� subjectedto 3.22, 4.0 and 6.7 m/s impact velocity.
S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285 281
dius of 0.635 cm at the center of the specimen. The
stresses were obtained by ANSYS/LS-DYNA finite
element software, and then substituted into the failurecriteria Eqs. (2) and (3) to determine the impact damage.
½03=903=03=903=03�
Various velocities were imposed to investigate the
effect of the impact velocity on the damage. It was foundthat there was no matrix crack or delamination when the
impact velocity was lower than 3 m/s. It shows that there
exists an impact velocity threshold for the laminate. Fig.
10 shows the delamination region of the composite
laminate subjected to an impact at three different impact
velocities. The dark area in the figure indicates the
location where the stresses were calculated by ANSYS-
LS/DYNA and satisfied the delamination criterion. Thedamaged area is heavily related to the impact velocity.
Multiple interfacial delaminations were found when the
impact velocity was greater than 3.0 m/s. The matrix
cracking at the bottom 0� plies was the first failure modeto be detected due to the bending stress. Then, a
delamination at the last interface between 903/03 ply
groups was predicted after the matrix cracking. Fol-
lowing that, the matrix cracking was also predicted inthe inner 90� and 0� groups which initiated the secondand third delaminations at the second and third inter-
faces. No matrix cracking was found at the top surface,
thus, there was no delamination at the first interface.
Fig. 10 shows the overall projected delamination area.
The predicted delaminations are correlated well with
Choi and Chang [7].
½04=454=�454=904=�454=454=04�
The quasi-isotropic laminate was tested at the impact
velocity of 7.8 m/s. The delamination at each interface is
shown in Fig. 11, except the second interface between
45� and )45� ply groups measured from the top surface.The first delamination was initiated at the last interface
between 454/04 ply groups, and appeared to be the
largest area. Delaminations with relatively smaller sizes
were also found at other interfaces except the second
interface, where no delamination was predicted. It seems
that the first delamination governed the overall delam-
ination size and was more sensitive to the impact
velocity than the other delaminations. It is interesting to
see that the delamination shown in Fig. 11 is oriented
itself along the fiber direction of the bottom ply group of
the delaminated interface.
5. Impact analysis of laminated shells
A doubly curved laminated shell structure subjected
to an impact by a steel ball is shown Fig. 12. The curves
of the shell structure are represented by radii of R1 andR2.
Fig. 12. Laminated shell structure geometry [8].
Fig. 11. Delamination area at each interface of T300/976 ½04=454=454 � 904=� 454=454=04�.
282 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285
The numerical examples are considered to demon-
strate the capability of ANSYS/LS-DYNA on the im-
pact analysis of a laminated shell structure. A variety of
examples are presented to study the impact responses.
The parameters included in this study are the curvature
of the shell, boundary condition and the impact velocity.The composite material properties AS/H3501 are show
in Table 4 [8]. The lay up for the laminated shell is a four
layer symmetric cross ply with stacking sequence [0/90/
90/0] and thickness 2.54 mm. The impactor is a steel ball
with radius of 6.35 mm and density of 7870 kg/m3. Two
special types of shell structure (cylinder and sphere) are
considered in this study. The geometric properties used
are a ¼ b ¼ 25:4 mm, for a cylindrical shell R1 ¼ 1 andfor a spherical shell R1 ¼ R2 ¼ R. The finite elementmesh is shown in Fig. 13.
Table 4
Material properties of AS/H3501 [8]
Exx
(GPa)
Eyy
(GPa)
Gxy
(GPa)
Gyz
(GPa)
Vxy Density q(kg/m3)
144.8 9.65 7.10 5.92 0.3 1389.2
Fig. 13. Finite element mesh for shell structure.
Fig. 14. Contact force for different radius of cylindrical shell.
Fig. 15. Contact force for different radius of spherical shell.
Fig. 16. Central deflection for different radius of cylindrical shell.
Fig. 17. Central deflection for different radius of spherical shell.
Fig. 18. Contact force of cylindrical shell with clamped and simply
supported boundary conditions.
S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285 283
Fig. 14 shows the effect of the ratio of the radius to
arc length R=a on the contact force for a cylindrical
shell. The impactor velocity is 30 m/s and the shell is
clamped. For the three ratios R=a, the contact force isvirtually the same during the first contact. However,
there is a small difference in the second contact, the
contact force occurs earlier and for a longer period time
when the radius of cylinder is decreasing. This may be
due to the stiffening effect on the cylinder as the radius is
decreasing, results to a higher natural frequencies and
earlier contact. The contact force shown in Fig. 14 is in
good agreement with the results presented in Ref. [8].Fig. 15 shows the effect of the ratio R=a on the contactforce for a spherical shell. The trend of contact force for
the spherical shell is similar to the cylindrical shell. Figs.
16 and 17 show the central deflection of the cylindrical
and spherical shell, respectively.
Fig. 19. Contact force of spherical shell with clamped and simply
supported boundary conditions.
Fig. 20. Contact force of cylindrical shell subjected to different impact
velocity.
Fig. 21. Contact force of spherical shell subjected to different impact
velocity.
Fig. 22. Central deflection of cylindrical shell subjected to different
impact velocity.
Fig. 23. Central deflection of spherical shell subjected to different
impact velocity.
284 S.-C. Her, Y.-C. Liang / Composite Structures 66 (2004) 277–285
A comparison between clamped and simply sup-
ported boundary conditions for a cylindrical and
spherical shell is shown in Figs. 18 and 19, respectively.
The velocity of impactor is 30 m/s and the ratio of radius
to arc length R=a is equal to 5. The second contact forthe clamped boundary condition occurs earlier than the
simply supported boundary condition. The earlier con-
tact is due to the stiffer boundary condition on theclamped edges.
The effect of impact velocity on the contact force is
shown in Figs. 20 and 21 for a cylindrical and spherical
shell, respectively. The ratio R=a is 5 and boundary
condition is clamped. The contact force is increased
proportion to the impact velocity, while the contact
period is virtually unchanged. Figs. 22 and 23 show the
central deflection of the cylindrical and spherical shell,
respectively.
6. Conclusions
The composite laminated plate and shell structuressubjected to low velocity impact have been analyzed
using ANSYS/LS-DYNA finite element software. The
impact responses are presented for the contact force and
central deflection. The numerical results are in good
agreement with the results found in the literatures. The
results show that the contact force is proportion to the
impactor velocity. However, the contact period is
dependent on the stiffness of the laminated structuresuch as the curvature and boundary condition.
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