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The Numerical Simulation Research of Internal Curing Process for Fiber Winding Composite Shell
The Numerical Simulation Research of Internal Curing Process for
Fiber Winding Composite Shell
Jiazhong Xu, Xinying Wang*1, Ming Qiao, and Ying Yu
College of Automation, Harbin University of Science & Technology, Harbin, 150080, China
SUMMARY
Curing process has a great impact on molding quality of the fiber-winding composite shell. In order to improve
its curing quality and efficiency, a new curing process employed the method of heating the internal metal mandrel
with steam can be adopted, which is called internal curing process. This paper introduces the principle of internal
curing process and establishes the mathematical models of internal curing process, adopts ANSYS and APDL
to develop the 3-D transient numerical simulation program of internal curing to realize numerical simulation
of temperature, curing degree and residual strain, and analyze the influence of shell thick, fiber volume fraction
and film coefficient on the simulation results. Taking the cylinder shell as an example, numerical simulation and
experiment are carried out. This research provides theory basis and analysis method for the design, simulation
and parameter optimization of internal curing process.
1. INTRODUCTION
The combination of high specific
strength, high specific stiffness, easy
molding and outstanding designability
of thermoset composite shells with fiber
winding has made them an attractive
option for numerous high performance
applications in aerospace, military,
civil engineering, energy transmission
and pressure vessel molding, and has
brought great economic and social
benefits. Their molding process
directly determines their ultimate
performance and cost. At present,
the critical problems which restrict
the application and the development
of composite shells are composite
performance and manufacture cost1, 2.
In a good many molding methods
of thermoset composites, the wet
winding method which well realizes
the integration of low cost and high
efficiency is widely used in composite
shells molding. Traditionally, after
winding, fiber winding shells are
usually cured by external curing
process, which performs curing in
an autoclave or curing oven3. The
heat from the heating board of the
autoclave or curing oven is transferred
to the shell body through emission,
conduction and convection, and the
heat-transfer direction is from outer
surface to inner surface. Owning to the
large thermal inertia of the autoclave
or curing oven and the small thermal
capacity of the air used as heat-transfer
medium, the increase and decrease
rate of the shell temperature is slow
and the regulation and control of the
curing temperature is difficult. This
results in bad curing quality and low
product yield. Since the fiber winding
shell has the characteristic of hollow
structure and the mandrel material
is usually metal, we can adopt the
process of heating the mandrel inside
the composite shell to realize the
curing molding of the composite shell.
The above-mentioned curing process
is called internal curing process.
*Corresponding author: Tel: +86-451-86390585 Fax: +86-451-86390625.
E-mail address: [email protected]; [email protected]
Smithers Rapra Technology, 2011
©
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
In this paper, the internal curing process
using steam as the heating medium to
heat the mandrel is studied and the
principle of the internal curing process
is introduced. The selection and design
of curing process curve is an important
factor that affects the shell quality.
While, curing process is a complex
coupled process, which involves heat
conduction, exothermic chemical
reaction and mechanical-properties
changes of the composite. So in this
paper, heat conduction model, curing
kinetic model and residual strain model
for the internal curing process are
established. Based on the finite element
software ANSYS and APDL, the
numerical simulation program of the
internal curing process is developed.
The experimental testing and the
numerical simulation are conducted by
taking a cylindrical shell as an example.
Through simulation, the distributions
and histories of temperature, curing
degree and residual strain in the internal
curing process of the cylindrical
shell are analyzed and the influences
of thickness, fiber volume fraction
and film coefficient on temperature,
curing degree and residual strain of the
cylindrical shell are researched. This
study not only provides the theoretical
319
Jiazhong Xu, Xinying Wang, Ming Qiao, and Ying Yu
basis, but also supplies analytical
method for the design, simulation and
parameters optimization of the internal
curing process.
Figure 1. Schematic diagram of internal curing process
2.1 PRINCIPLE OF INTERNAL
CURING PROCESS
The internal curing process discussed in
this study is similar to mandrel heating
molding process of thermoplastic
composite with dry winding4. The
heating mandrel molding process uses
electric heating mandrel to heat and
cure thermoplastic composite from
inner to outer. There is no exothermic
reaction in the molding process of
thermoplastic composite, so it is
different from the curing process of
thermoset composite discussed in this
paper. The internal curing principle of
cylindrical composite shell is shown in
Figure 1. The shell body consists of
many layers of fiberglass soaked with
thermoset epoxy resin. The mandrel
is a hollow metal pipe with even wall
thickness. The hollow steel pipe with
small holes is used for feeding saturated
steam, compressed air and cooling
water. After winding, the steam used for
heating the mandrel is fed into the inner
cavity of the mandrel through small
holes at the steel pipe wall. The heated
mandrel transfers the heat to winding
layers, where occurs exothermal crosslinking reaction. During curing, the
shell body makes a rotary motion for
uniform heating of the shell body and
to prevent accumulation of uncured
liquid resin at the undersurface of the
shell due to gravity.
Compared with traditional external
curing, the internal curing process
has the following evident advantages:
The heat in the inner cavity of the
mandrel directly transfers to the
fiberglass layers to be cured through
the metal mandrel with small thermal
resistance. This heat transfer approach
can quickly increases the temperature
of the shell and rapidly causes the
gelling and curing reaction of the epoxy
resin so as to effectively shorten curing
320
time. Furthermore, it can precisely
control the curing history according
to curing process curve, which greatly
improves curing efficiency and curing
quality.
During the internal curing process,
the heat of the mandrel transfers to
the shell, and then the resin viscosity
reduces, which is helpful to fiber
soaking and micro-bubbles flowing
out. During this stage, a rich resin
layer with good penetrability resistance
and corrosion resistance is formed as
a result of the migration of the resin
molecules from outer surface to inner
surface. However, for the external
curing process, the migration direction
of the resin molecules is just opposite,
which always causes the lack of resin
at the inner surface.
When the shell is cured by the internal
curing process, the hot heating medium
makes the metal mandrel expand
quickly, and the fiber winding layers
which tightly wrap the mandrel become
the constraint of mandrel expansion.
Thus in the gelling process, the shell is
under the inner pressure, which not only
tightens the fiber, but also compacts the
shell structure.
3. CURING PROCESS
MODEL
3.1 Heat Conduction Model
In the curing process, temperature
distribution in a composite shell is
determined by the heat conduction
rate of the composite and the heat
generation rate of curing reaction.
Temperature field analysis of the
internal curing process is a heat
conduction problem with nonlinear
internal heat source determined by
the generated heat of exothermal
curing reaction of resin matrix. The
law of Fourier heat conduction and
the principle of energy balance can be
used to establish the heat conduction
model6, 7:
(1)
Where r is density of the composite;
c is specific heat; T is absolute
temperature; kx, ky and kz are heat
conduction coefficient along the
directions of x, y and z respectively;
Hr is total reaction heat of resin; α is
curing degree; da/dt is derivative α
with respect to time.
3.2 Curing Kinetic Model
Curing reaction of resin is a complex
chemical phenomenon, so most
equations about reaction kinetics are
established on the basis of empirical
models. Generally, the curing kinetic
model of epoxy resin can be expressed
as5, 7:
(2)
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
The Numerical Simulation Research of Internal Curing Process for Fiber Winding Composite Shell
Where k1 and k2 are reaction rate
constants defined by the Arrhenius
Equation:
(3)
(4)
Where A1, A2 are pre-exponential
factors; E1, E2 are activation energies;
R is universal gas constant; m, n are
constants associated with reaction
rate orders. These parameters are all
obtained by experiments.
It is found from Equation (1) and (2),
in the curing kinetic model there is a
temperature variable and in the heat
conduction model the internal heat
source term is the function of curing
degree. So there is a strong coupled
relationship between the temperature
and the curing degree.
3.3 Residual Strain Model
In the curing process, thermal and
mechanical properties vary with the
temperature and the curing degree.
Therefore, strain field analysis of
composite winding layers in curing
process is a coupled thermal and
structural problem following with the
characteristic of material nonlinearity8.
The residual strain mainly consists
of thermal strain caused by thermal
expansion and contraction of the
composite and chemical shrinkage
strain caused by curing shrinkage of
the resin9.
Where h is total volume shrinkage
of the resin, in this paper, it is -0.05.
thermal analysis element SOLID70 to
structural analysis element SOLID45.
4. NUMERICAL
SIMULATION AND
EXPERIMENTAL TEST
In this paper, finite element method
combined with finite difference
method is used to solve the strong
coupled heat conduction model and
curing kinetic model. Based on the
thermoelastic theory, indirect method
is adopted to solve residual strain, that
is, temperature field obtained from the
thermal analysis is imposed on the
shell as a body force to solve thermal
strain, and chemical shrinkage strain
is imposed as an initial strain at every
calculation step to solve residual strain
field of every calculation step.
4.1 Material
Taking cylindrical composite shell
as an example, numerical simulation
and analysis of temperature, curing
degree and residual strain during
internal curing process are carried out.
In the simulation, inner radius of the
cylindrical shell is 50 mm, outer radius
is 60 mm, axial length is only taken
100 mm, and fiber volume fraction is
60%. Thermophysical properties and
cure kinetic parameters of the material
constituted the shell are separately
listed in Table 1 and Table 2.
4.3 Experimental Test
In order to test correctness of the
temperature field and the residual
strain field simulation, we have
temperature and strain experiment
using sensors at the same size
4.2 Numerical Simulation
Suppose resin flow is not taken into
account. Thermal boundary conditions
are: temperature of the inner surface
of the shell is equal to temperature of
the mandrel or the steam; effective
film coefficient of the outer surface
is 8.0W/(m2/°C); the head and the
end face are assumed to be adiabatic
boundary conditions. The finite element
discretization of the shell model is
presented in Figure 2. SOLID70 is
chosen as the element type of thermal
analysis. Sweep-meshing method is
adopted to mesh the shell, and 1000
elements and 1331 nodes are obtained.
For the analysis of residual strain, the
model of thermal analysis is still used
except switching the element type from
Figure 2. Finite element discretization
of the shell model
Thermal strain can be described as9:
(5)
Where b is effective thermal expansion
coefficient.
Chemical shrinkage strain can be
calculated by the following equation10:
(6)
Table 1. Thermophysical properties of glass fiber/epoxy resin
Density kg/m3
Specific heat J/
(kg·°C)
epoxy resin
1200.0
7900.0
8.65
glass fiber
2600.0
690.0
0.270
Film coefficient W/
(m2/°C)
Table 2. Cure kinetic parameters of the composite
m
0.839
n
1.159
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
A1, s-1
1.76×10
5
A2 , s-1
3.901×10
5
ΔE1/mol
6.498×10
4
ΔE2 J/mol
5.399×10
4
Hr J/kg
7.02×105
321
Jiazhong Xu, Xinying Wang, Ming Qiao, and Ying Yu
cylindrical shell. Figure 3 is the
comparison chart of curing simulation
result and experiment result about
outer surface of the shell. From the
figure we can see that they are very
close to each other. The biggest
temperature and residual strain
discrepancy in whole curing process
is respectively no more than 4.05 °C
and 0.0011, which is mainly the result
of not taking heat absorbing of the
mandrel into account.
5. SIMULATION RESULTS
AND DISCUSSION
5.1 Profiles
Temperature, curing degree and residual
strain profiles of the shell at the time of
600 s, 1260 s and 3000 s are respectively
illustrated in Figure 4a, b and c.
Figure 3. Comparison of simulation result and experiment result about outer surface. (a) temperature comparison; (b)
residual strain comparison
Figure 4. Profiles of temperature, curing degree and residual strain at different time
322
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
The Numerical Simulation Research of Internal Curing Process for Fiber Winding Composite Shell
When curing time is 600 s, profiles
of temperature, curing degree and
residual strain are shown in Figure 4a.
The inner surface has the highest
temperature and its curing degree is
0.36. But the temperature of the outer
surface is only 39.66 °C and its curing
degree is only 0.02. So at this time,
the influence of resin curing reaction
is little. This indicates the temperature
increase of the outer surface from initial
temperature 35.00 °C to the current
temperature 39.66 °C is essentially
caused by heat conduction, and the
residual strain increment which is
0.0452 is almost induced by thermal
expansion. Though the residual strain
of the inner surface is under the
influence of curing shrinkage, it is still
higher than that of outer surface.
Figure 4b is the profiles of temperature,
curing degree and residual strain at
the time of 1260 s. At the moment,
curing degrees of inner surface and
outer surface are all above 0.94 and the
shell is about to be fully cured. This
is because small film coefficient and
heat conductivity, the generated heat of
curing reaction can not be transferred
timely, causing temperature increase
of the outer surface and further crosslinking reaction of the resin. As a result,
the curing degrees of inner surface
and outer surface are nearly the same.
The process can be also seen from the
temperature profile: temperature of
the outer surface is higher than that
of the inner surface, which indicates
generated heat of curing reaction is
great at the outer surface. In addition,
residual strain of the outer surface
is obviously greater than that of the
inner surface arising from temperature
increase of the outer surface.
transfer direction is from outer surface
to inner surface. The residual strain has
the same distribution characteristic as
the temperature, while it is caused by
thermal expansion.
5.2 History Curves
In order to clearly illustrate histories of
temperature, curing degree and residual
strain in the internal curing process, we
choose central nodes of inner surface,
middle surface and outer surface as the
research object.
Their temperature, curing degree and
residual strain histories of the three
central nodes in the internal curing
process are presented in Figure 5 and
Figure 6.
As shown in Figure 5, at the beginning
of curing, the temperature of inner
surface is the highest, and the heat
is transferred from inner surface to
outer surface. During this period,
crosslinking reaction rate of the resin
is very slow and curing reaction
heat is little. With the increase of the
temperature, the cross-linking reaction
rate is getting faster and faster and the
curing reaction heat is getting more and
more. Due to the poor heat conductivity
of resin matrix, the generated heat
of curing reaction is not transferred
timely, and then obvious temperature
peak and uneven temperature gradient
is appeared. Figure 5 shows that at
the time of 1260 s the temperature of
outer surface reaches the peak value
147.65 °C which is higher than mandrel
Figure 5. Histories of temperature and curing degree
Figure 6. History of residual strain
The profiles of temperature, curing
degree and residual strain at the time
of 3000 s are shown in Figure 4c.
The resin is fully cured and the
exothermic reaction is finished. Current
temperature distribution is similar to
initial temperature distribution, that is
to say, the temperature of outer layers
is higher than inner layers because heat
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
323
Jiazhong Xu, Xinying Wang, Ming Qiao, and Ying Yu
temperature about 17.65 °C. In the
whole curing process, slope change of
curing degree curve of inner surface is
the minimum and curing time is the
longest, which indicate that curing
rate of inner surface is the slowest. But
outer surface, affected by generate heat
of curing reaction and heat conduction
of the composite, is cured quickly and
its curing degree is approached to 1.0 in
a short time. After curing, exothermic
reaction is finished and temperature
change is gentle. In the stage of cooldown, owing to small heat conductivity,
when temperature of inner surface is
cooled down to 90 °C, the temperature
of outer surface is still up to 117.45 °C.
Figure 6 is the history of residual strain.
At the initial stage of temperature
increasing, composite is heated to
expand inducing that the strain is
positive and it increases gradually
with the increase of temperature. When
curing reaction is started, generated
heat of curing reaction increases
composite temperature. Meanwhile,
cure shrinkage is taken place because of
curing reaction, and the cure shrinkage
strain is negative, so the positive
strain decreases gradually. In the
stage of post-curing, residual strain of
composite varies with its temperature
which is the result of thermal expansion
and contraction.
Figure 7. Curves of temperature and curing degree with different thicknesses
Figure 8. Curves of residual strain with different thicknesses
5.3 Influence of Thickness
Figure 7 and Figure 8 are the histories
of temperature, curing degree and
residual strain at the central node of the
shell with three different thicknesses
of 8.0 mm, 10.0 mm and 12.0 mm. As
shown in Figure 7, the temperature of
the 8.0 mm thick shell first exceeds
the dwell temperature and reaches the
highest temperature peak. In addition,
its curing reaction is first started, but the
curing time is the longest. Accordingly,
the strain peak appears the earliest and
the final residual strain is the smallest.
The 10.0-mm-thick shell takes the
second place. While for the 12.0 mm
thick shell, it is the last one to exceed
the dwell temperature and also the last
one to start the curing reaction, but it
finishes curing reaction in the shortest
324
time. Its strain peak is the last one to
appear and the final residual strain is
the highest, as shown in Figure 8.
5.4 Influence of Fiber Volume
Fraction
Figure 9 and 10 is the histories of
temperature, curing degree and residual
strain at the central node of the shell
whose fiber volume fractions are
respectively 40%, 50% and 60%. Before
the temperature reaches the dwell
temperature, the curing reaction rate is
very slow and generated heat of curing
reaction is little. As shown in Figure
9 and 10, the temperatures and strains
of different fiber volume fractions are
almost the same. When the temperature
of the central node exceeds the dwell
temperature, the shell with the fiber
volume fraction of 40% has the earliest
and the highest temperature peak, and
the curing reaction rate is the fastest,
but the residual strain is the highest.
The shell under the condition of the
fiber volume fraction is 50% takes the
second place. When the fiber volume
fraction is 60%, the shell has the lowest
and the latest temperature peak, and the
curing reaction rate is the slowest, but
the residual strain is the lowest. Figure 9
and 10 shows that the temperature
peak values under the three different
conditions are 146.65 °C、143.54 °C
and 141.27 °C and the residual strain
peak values are respectively 0.0183,
0.0181 and 0.0176.
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
The Numerical Simulation Research of Internal Curing Process for Fiber Winding Composite Shell
5.5 Influence of Film
Coefficient
The histories of temperature, curing
degree and residual strain at the
central node of the shell whose film
coefficients are 1.0 W/(m2/°C), 8.0 W/
(m2/°C) and 20.0 W/(m2/°C) are shown
in Figure 11 and Figure 12. When the
film coefficient is 1.0 the shell has the
earliest and the highest temperature
peak. It takes the longest curing time
and its residual strain is the highest.
With the film coefficient of 20.0, the
shell has the lowest and the latest
temperature peak. In this case, the
curing time is the shortest and the
residual strain is the highest. All of the
above is because under the condition
of the same thickness, the bigger the
film coefficient, the greater the heat
dissipating capacity, the slower the
temperature increasing rate. Therefore,
the appearance and the amplitude of
temperature peak are reduced, the
curing rate is slowed down and the
residual strain is decreased.
Moreover, film coefficient has little
influence on the shell at early-curing,
but it has great influence on the shell
at post-curing. As shown in Figure 11
and Figure 12, when curing time
is 800 s, under the condition of the
film coefficients are 1.0 and 20.0, the
temperature discrepancy is 3.5 °C,
and the residual strain discrepancy is
0.0009. While, at the curing time of
2500 s, their temperature and residual
strain discrepancy are 20.8 °C and
0.0065.
Figure 9. Curves of temperature and curing with different fiber volume fractions
degree Figure 10. Curves of residual strain with different fiber volume fractions
Figure 11. Curves of temperature and curing degree with different film
coefficients
6. CONCLUSIONS
The internal curing process models of
thermoset composite are established,
and three-dimensional transient
numerical simulation is carried out. The
simulation result and the experiment
data agree well with each other, which
indicate the correctness of the method
adopted in this paper.
From the numerical simulation and the
analysis of the internal curing process
Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011
325
Jiazhong Xu, Xinying Wang, Ming Qiao, and Ying Yu
Figure 12. Curves of residual strain with different film coefficients
of the cylindrical shell, we can get the
following conclusions: the heat of the
mandrel and generated heat of curing
reaction are transferred from inner
to outer layer by layer, making the
curing rate get faster and faster and
the curing time get shorter and shorter
from inner to outer. The residual strain
of internal curing process is influenced
by temperature of the composite and
chemical shrinkage of the resin.
The thicker the shell, the later the
curing starting, the slower the curing
rate, the higher the temperature
peak and the final residual strain. In
the stage of early-curing, the shell
under the condition of different fiber
volume fractions is almost cured
simultaneously. In the fast-curing
stage, the lower the fiber volume
fraction, the faster the curing rate, the
earlier and the higher the temperature
peak and the residual strain. With
the increase of the film coefficient,
generated heat of curing reaction is
reduced, curing time is prolonged
and residual strain is decreased. The
film coefficient has little influence on
early-curing but has great influence on
post-curing.
326
This research not only provides new
idea for the realization of composite
shell with fiber winding molding
with high efficiency, high quality and
low cost, but also supplies theoretical
basis and analytical method for
design, simulation and parameters
optimization of internal curing process.
ACKNOWLEDGEMENTS
This work is supported by National
Nature Science Foundation of China
(Number: 50902039).
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Polymers & Polymer Composites, Vol. 19, Nos. 4 & 5, 2011