World Journal of Engineering
STRESSES DEVELOPMENT IN AN ADVANCED GRIDSTIFFENED PLATE DURING THE CO-CURING PROCESS
Ren Mingfa, Huang Qizhong and Chen Haoran
State key laboratory of structural analysis for industrial equipment,
Dalian university of technology, Dalian 116024, China.
where Q is an interior heat source which
associates with the cure law of polymer depicted
by a cure kinetic equation, as follow
.
d d
Q  Vm H r
 f  A, E , T ,   (2)
,
dt
dt
where  is the density of the resin; Vm
respresents the volume fraction of the resin; H r is
the total heat liberated for complete cure; d dt
is designated as the cure rate and it is a function of
the pre-exponential coefficient A , the activation
energy E , the temperature T and the degree of
cure  .
The CHILE(cure hardening instantaneously linear
elastic) model is used to analyses the polymer as it
goes through the curing process. The composite
constituents used in this study are AS4 fiber and
3501-6 resin. The elastic modulus of 3501-6 resin
is given by
Em  (1   ) Em0   Em
(3)
Introduction
Advanced grid-stiffened structure (AGS) is a
kinds of composite lattice structures which has
been applied in aerospace and marine, due to the
advantages of light weight, high stiffness and
strength, durability and etc. In order to attain their
full potential, more and more AGS parts are
manufactured with a great size means that a much
more dimensional stability and product quality are
required. The soft-mould aided co-curing process
which simultaneously cures the skin part and the
ribs part of an AGS in a silicon rubber mould is a
promising manufacturing technique for reducing
cost and improving quality. Silicon rubber was
chosen as the tooling material due to its high
coefficient of thermal expansion, when heated
during cure, the rubber expanded, providing out of
plane, or lateral, pressure to the ribs. The
development of stresses during the co-curing
process of composite directly impacts on the
product quality such as dimensional stability and
structural performance [1]. Though well-suited
parameters of manufacturing techniques for an
AGS with a precision size and low residual
stresses could be determined by trial-and-error
process, it is a time-consuming and costly process
and unable to propose a reasonable strategy for
reducing residual stresses. Based on the process
mechanics of composites, numerical simulation is
a positive solution for investigating the stresses
development and improving the manufacturing
techniques for an AGS.
wehere the E m0 and Em are the assumed fully
uncured and fully cured temperature dependent
resin modulus, respectively. Then the material
properties of unidirectional plies are determined
by the mechanical properties of their constituent
resin and fiber using micromechanics equations
from Bogetti et al [2]. The residual strain induced
by volumetric shrinkage of matrix during the cocuring process can be expressed as
1
(4)
 ch  1    3  1
where  and  denote the cure degree and
volumetric shrinkage of matrix 3%, respectively.
 ch denotes the shrinkage residual strain. Based
on the aforementioned equations, the stresses
development of an AGS could be investigated by
a solution combines the finite element method and
the finite difference method.
Equations and model
Assumed the temperature is equilibrium in local at
any time, the heat transfer differential equation
with an interior heat source could be expressed as
T
 
T  .
c

(1)
 K ij
Q
t xi 
x j 
Results and discussion
The simulation of the development of residual
953
World Journal of Engineering
stresses of an AS4/3501-6 plate stiffened by isocuring process. It can be seen that the magnitude
orthogonal grids during the co-curing process was
of stress  x in rib center, within 2MPa, is much
conducted based on a 2D FE model as shown in
less that in skin center, within 16MPa, due to the
figure 1. The skin part and the rib part are
pressure caused by the silicon rubber with a
manufactured by unidirectional sheets with a
higher CTE 200e-6/c. The magnitude of vertical
sequence [0/±45/90]5s and [0]80, respectively. The
stress in skin center is constant while that in rib
thickness of sheet is 0.125mm, the width of rib is
center vary, due to the boundary conditions.
5mm, and the cell size is 5×10cm. The boundary
conditions is that the bottom is constrained and
applied the temperature as cure cycle, the top is
applied a pressure 0.6MPa and a convection with
500w/(m k), both of the left and right applied a
symmetrical condition. It illustrates that there is
an un-uniform distribution field of temperature
and cure degree in the AGS cured by the
manufacture recommend cure cycle. Due to the
exothermic cross-linking reaction, two overshoots
Figure 2 Effect of shrinkage on the stress and strain in skin
are observed while the cure degree is aggressive
center during the co-curing process
increasing at where the cure temperature is hold.
According to the CHILE model and the chemical
strain model, the development progress of resin
modulus and chemical strain is similar to the cure
degree.
Figure 3 Stresses development in the AGS during the cocuring process
Conclusion
Figure 1 Variation of temperature and cure degree in the
AGS during the co-curing process
There is a non-uniform distribution of temperature
and cure degree which would cause a gradient in
stresses and distortion in the AGS during the cocuring process. The shrinkage would partly reduce
the magnitude of stress and strain. The silicon
rubber mould with an appropriate CTE may also
reduce the magnitude of stress which could
improve the quality of AGS.
According to the results show in figure 1, the
cross-linking reaction would be finished in 2.7
hours means that the constitutive and volume
shrinkage of the AGS would be constant after it is
cured for 2.7 hours. Figure 2 shows the progress
of traverse stress  x and traverse strain  x in skin
center of AGS considering the shrinkage and the
non-shrinkage during the co-curing process. It can
be seen that the shrinkage would reduce the
magnitudes of stresses and strain while the crosslinking reaction is happening. The magnitude of
stress considering the non-shrinkage increases as
the temperature and offsets the stress considering
the shrinkage gradually.
Figure 3 shows the stresses development in the
AGS considering the shrinkage during the co-
REFERENCES
[1] N. Ersoy, T. Garstka, K. Potter, et al.
“Development of the properties of a carbon
fibre reinforced thermosetting composite
through cure”, Compos. Part A, 41, 401409(2010).
[2] T. A. Bogetti and J. W. Gillespie, “ProcessInduced Stress and Deformation in Thick954
World Journal of Engineering
Section Thermoset Composite Laminates”, J.
Compos. Mater. 26, 626-660(1992).
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