2010 International Conference on Educational and Network Technology (ICENT 2010)
Finite Element Modeling of Carbon Fiber Reinforced Polymer Pressure Vessel
Wang Yingjun
Sun Minqing
School of Science, Wuhan University of Technology,
School of Science, Wuhan University of Technology,
No.122 Luoshi Rd. Wuhan 430070, P.R.C
No.122 Luoshi Rd. Wuhan 430070, P.R.C
[email protected]
[email protected]
Zheng Zixiong
Zhu Sirong
School of Science, Wuhan University of Technology,
School of Science, Wuhan University of Technology,
No.122 Luoshi Rd. Wuhan 430070, P.R.C
No.122 Luoshi Rd. Wuhan 430070, P.R.C
zzx [email protected]
[email protected]
_
This paper presents static analyses of pressurized CFRP
vessel with the aluminum liner, using the general FE analysis
software ANSYS. Parameters of the FE model are derived
Abstract-A finite element model of carbon fiber reinforced
polymer
(CFRP)
pressure
vessel
with
aluminum
liner
is
established by ANSYS finite element software. The outer
filament wound fibers are overwrapped by both hoop winding
from experimental tests. The analysis
agreement with the experimental results.
and helical winding methods. The safety is vital because of high
working pressure which is more than 35MPa. In the modeling
results
are
in
process, the number of filament winding layers is treated as
I.
composite laminates with thickness and wrap angle variations
of every unidirectional layer in the vessel section. The static
analysis of the vessel is conducted. Based on the maximum
A.
stress criteria, burst pressure of the vessel is predicted. There
CFRP vessel
In this study, the filament wound CFRP vessel with the
aluminum liner is shown in Fig.l. Metal liner is normally
made of elasto-plastic materials with a large plastic range,
such as 6061-T6 aluminum [6]. The reinforcement materials
are carbon fibers. One of the advantages of combining a
load-bearing metal liner with composite over-wrap is that it
can introduce internal stresses (compression in the liner and
is good agreement between model prediction and experimental
data.
Keywords- Finite Element; CFRP; Pressure Vessel
INTRODUCTION
Now CFRP wound pressure vessels with metal liner have
been widely used in many industrial areas such as aerospace,
aeronautics, and chemical engineering etc. Among their
applications, a common feature of such products is that they
must undergo a certain working pressure safely, which is
tension in the fibers) before the vessels are in service. This
process is known as 'autofrettage' in metal working, while it
is termed as 'sizing' in the composite pressure vessel
industry. After fabrication, a sizing pressure, higher than the
operating pressure, is applied such that the metal liner is
plastically deformed whereas the composite reinforcement is
more than 35MPa. Deformation and stress-strain analyses of
pressurized CFRP vessels must be conducted. Some fmite
element (FE) analysis methods have previously been
proposed to analyze the stress and deformation states of
CFRP vessels by other researchers. For example, Tomonori
et al. have carried out the failure analysis of a pressurized
FRP cylinder under transverse impact loading [1]. Aoki et al.
used solid elements and interface elements to study the
delamination in CFRP vessels [2]. While Hou et al. used
only solid elements to study several failure modes in CFRP
[3]. Krishnamurthy et al. proposed the shell elements to
investigate the impact response and damage of laminated
in its elastic range. The elastic unloading of the vessel leaves
the liner in compression and the composite reinforcements in
tension. By this method, in subsequent loading, the pressure
vessel can operate in the enhanced elastic range. And the
weight saving can be obtained; the weight of load-bearing
metal liner reinforced with composite over-wrap is about
50% of the entire metal pressure vessels with the same
volume.
B.
cylindrical composite
shells [4]. It is known that the accurate calculation
models of structures usually have a great deal of elements, as
a result, the calculation time will increase significantly.
Mesh Element
Before conducting an FE analysis, the element type must
first be decided upon. In the previous studies, solid and shell
elements were often used. A solid element requires that the
mesh division in the thickness direction must be the same as
the number of material layers. But it will take long
calculation time. A shell element does not require thickness­
direction mesh division, so the calculation time will be
shortened. Therefore, linear layered structure shell element
SHELL99 for CFRP and nonlinear layered structure shell
element SHELL91 for the inner metal are used in our study,
respectively. SHELL99 may be used for layered applications
of a structural shell model which allows up to 250 layers.
However, simplified models with less calculation time can
be inaccurate.
There are no uniform design standards for the design of
CFRP vessels all over the world [5]. DOT CFFC standard
has been adopted in many countries. The standard indicates
that the numerical calculation using fmite element method
should be performed to verify the design of CFRP vessels.
978-1-4244-7662-6/$26.00 © 2010 IEEE
FE MODEL OF THE VESSEL
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2010 International Coriference on Educational and Network Technology (ICENT 2010)
surfaces from 35MPa to burst pressure step by step. Strength
The element has six degrees of freedom at each node:
translations in the nodal x, y, and z directions and rotations
about the nodal x, y, and z-axes. The element is defmed by
eight nodes, average or comer layer thicknesses, layer
material direction angles, and orthotropic material properties.
SHELL91 may be used for layered applications of a
of composite vessel is mainly decided by that of filament­
wound composite layer. Many studies indicated the stress
was the main failure factor for CFRP vessels [8-13].Thus,
the stress of the first CFRP layer (the inner CFRP ply near
the Al liner) is used to defme the strength criterion of the
CFRP vessel. The maximum stress of the first CFRP ply
must satisfy:
structural shell model or for modeling thick sandwich
structures. Up to 100 different layers are permitted to choose
as the sandwich option turned off.
half
a m ax
The FE model is shown in Fig. 1. In this study, only a
symmetrical model is used so as to reduce the
Where, a max
calculation time. This model consists of 3,010 nodes, 903
III.
2
Material
Number
Shell91
Nonlinear shell
Aluminum
903
Shell99
Linear layer shell
CFRP
910
1210
RESULTS AND DISCUSSION
As shown in Figure 3 and 4, the equivalent stress of the
liner is 208.85MPa, which is less than 276MPa as the
working pressure 35MPa is applied. And the stress of the
first CFRP ply is 459.567Mpa, which is less than 1210 MPa.
The burst pressure is predicted further. As shown in
Table I. Element Description
Element Description
=
MPa[5].
The model of the whole structure is established using
fmite element analysis software ANSYS [7]. Through setting
the boundary conditions and contact forms, the different
components are meshed using corresponding element types.
The detail is given in Table I.
Element type
au are the maximum stress of the first
CFRP ply and ultimate stress, respectively. Here, au
SHELL91 elements and 910 SHELL99 elements.
No.
'
� au
Figure 5 and 6, as the inner pressure increases up to 65MPa,
the maximum tensile stress of the first CFRP ply reaches
121OMPa. The results show that the vessel will be destroyed
in this case, so the pressure, 65MPa, is regarded as the burst
pressure. An experiment on the real CFRP vessel has been
done by Energy Materials Co. Ltd., Liaoning, China. The
analysis results are in agreement with the experimental
results.
C. Material definition
The outer layer, CFRP is assumed to be orthotropic and
elastic. The inner metal layer is defmed to be isotropic,
elastic perfectly plastic materials which the yield stress is
276 MPa. The detailed material properties are shown in
Table 2.
IV.
CONCLUSION
In this study, the fmite element model of a filament
wound CFRP pressure vessel with aluminum liner is
established using fmite element software ANSYSIO.0. All
components of the CFRP layer and inner metal layer are
meshed using nonlinear layered shell elements and linear
Table 2 Material properties of unidirectional plate and A I
CFRP
Aluminum
Density(kg/m3)
1570
2750
Ex(GPa)
128
Ey(GPa)
10.5
layered shell elements, respectively. The study presents a
method to analyze such vessel subjected to internal pressure
loading. Based on the maximum stress criteria, burst
Ez(GPa)
10.5
pressure of the vessel is predicted. There is good agreement
between model prediction and experimental measurement.
GX
(GPa)
5.0
Gy= (GPa)
5.0
G zx
(GPa)
5.0
V xy (GPa)
0.28
V yz (GPa)
0.40
V zx (GPa)
0.02
Y
II.
69
ACKNOWLEDGMENT
Project
supported
by
the
National
Natural
Science
Foundation of China (Grant No. 50878169, 50878170)
REFERENCES
0.32
ANALYSIS
This analysis of CFRP vessels includes two loading cases:
One is an inner working pressure 35MPa analysis (case 1);
the other is burst pressure prediction (case 2). In the burst
pressure prediction, the pressure is applied to the inner
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[3]
Hou JP, Petrinic N, Ruiz C. A delamination criterion for laminated
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2069-74.
260
2010 International Coriference on Educational and Network Technology (ICENT 2010)
Krishnamurthy KS, Mahajan P, Mittal RK. A parametric study of the
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[5]
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[6]
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[4]
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Fig.1 The part of the vessel
Fig.2 The FE of the vessel
2.023
25.004
47 _ 985
97.4
97.901
D
97.83
D
97.879
[]
93.689
D
0 90.464
90.521
D
0 90.568
90.044
c
0
70.966
93.947
116_ 928
139.909
51.063
102.126
153_ 189
204_ 252
255.315
306_ 378
35? _ 441
208.852
Fig.3 The equivalent stress of the liner under case 1(/MPa)
408.504
459_ 567
Fig.4 The stress of the first CFRP ply under case l(IMPa)
261
2010 International Coriference on Educational and Network Technology (ICENT 2010)
6.323
273·
°
% .669
ZD
275.569
0
275.585
o
124.999
275.585
275.585
o
360.933
o
o
164.558
275.596
°
275.597
o
275.599
319.647
o
o
204.117
243.676
273.676
o
283.234
196.536
o
322.793
362.352
Fig.5 The equivalent stress of the liner under case 2(/MPa)
o
268.953
403.429
537.905
672.382
806.858
941. 334
1076
1210
Fig.6 The stress of the fIrst CFRP ply under case 2(IMPa)
262