Experimental and Numerical Evaluation of
Thermal Performance of Steered Fibre Composite Laminates

139
For variable-stiffness panels a family of curves corresponding to various values of T
1
(from
0º to 90º in increments of 15º) is plotted in Figure 12. The lowest normalized value of stress-
resultant is 0.185, and is obtained for a variable stiffness configuration of T
0
= 85º and T
1
= 0º,
with normalized longitudinal deflection value of about 1.127. This value is 68% lower than
the lowest value of 0.577 obtained with a straight-fiber configuration, but with 12% increase
of normalized longitudinal deformation. Most variable stiffness panels with T
0
= 0º and T
1
in
the range of 0º to 45º have a higher stress resultant than the corresponding straight-fiber
configurations.

0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35
0
0.5
1
1.5
2
2.5
Normalized longitudinal deformation

30.5 cm away. The curvilinear tow paths that the fiber placement machine followed during
fabrication of these variable stiffness panels are shown in Figure 13. One panel has all 24,
0.32-cm-wide tows placed during fabrication. This results in significant tow overlaps and
thickness buildups on one side of the panel, and therefore it is designated as the panel with
T
1
= 0
o
T
1
= 15
o
T
1
= 90
o

Heat Transfer – Engineering Applications

140
overlaps. The fiber placement system’s capability to drop and add individual tows during
fabrication is used to minimize the tow overlaps of the second variable stiffness panel,
which is designated as the panel without overlaps. The third panel has a straight-fiber
[±45]
5s
layup and provides a baseline for comparison with the two variable stiffness panels.
The overall panel dimensions are 66.0 cm in the axial direction, and 62.2 cm in the transverse
dimension, as indicated by the dashed lines in the figure. Further details of the panel
construction are given in (Wu, 2006).
6.2 Test setup and instrumentation


Fig. 15. Composite panel instrumentation.

Heat Transfer – Engineering Applications

142
The panel response was measured during the thermal test with thermocouples and strain
gages, and these data were collected using a personal computer-based system. Panel front
and back surface temperatures were measured with five pairs of K-type thermocouples. The
average panel temperature is shown as a function of time as the dashed line in Figure 14.
The thermocouples, denoted as black-filled circles, are located at the corners and center of a
30.5-cm square centered on the panel, as shown in Figure 15.
Back-to-back pairs of electrical-resistance strain gages (each with a nominal ±1 percent
measurement error) are bonded to the panel surfaces using the procedures described in
(Moore, 1997). The locations of the strain gage pairs on each panel are also shown in Figure
15. The strain gages measure either axial strains (the open circles in the figure), or both axial
and transverse strains (the gray filled circles), and are deployed along the top edge, and
axial and transverse centerlines of the panels. The closely spaced axial gage pairs (locations
9, 10 and 11) on the panel with overlaps span a region of varying laminate thickness along
the transverse centerline. In addition to the axial gage pairs along the upper edge of the
baseline panel, biaxial gages are fitted at locations 4, 7 and 10 along the axial centerline.
6.3 Test results
The heating profile shown in Figure 14 is applied to the panels, and the resulting panel
thermal response is measured. An initial thermal cycle is performed for each panel to fully
cure the adhesives used to attach the strain gages to the panels. Since the strain gage
response is dependent on both its operating temperature and the motion of the surface to
which it is bonded, the thermal output of the strain gages themselves (Anon., 1993;
Kowalkowski et al., 1998) must first be determined. Strain data are recorded for gages
bonded to Corning ultralow-expansion titanium silicate (coefficient of thermal expansion 0 ±
3.06 x 10-8 cm/cm/ºC) blocks that are subjected to the same thermal loading. After

axial centerline, which have high axial CTEs and low transverse CTEs. Fig. 16. Strain vs. temperature at center of panel with overlaps. Fig. 17. Maximum strains for panel with overlaps.

Heat Transfer – Engineering Applications

144
Fig. 18. CTEs for panel with overlaps.
Fig. 19. Strain vs. temperature at center of panel without overlaps.
Experimental and Numerical Evaluation of
Thermal Performance of Steered Fibre Composite Laminates

145
The 20-ply laminate on the transverse centerline 12.7 cm on either side of the panel center
has a [±45/(±48)4]s layup. However, the measured axial CTEs (6.35 and 5.33 με/ºC) at gage
locations 6 and 8 there are much higher than the corresponding transverse CTEs (1.35 and
0.92 με/ºC). Since the CTEs of an [±45]5s orthotropic cross-ply laminate should all be equal,
the observed differences strongly suggest that the variable stiffness laminate CTEs can be
highly sensitive to relatively small changes in the fiber orientation angles.

Fig. 21. CTEs for panel without overlaps.
6.3.2 Baseline panel
Front and back surface axial and transverse strains at the baseline panel center are plotted as
functions of the panel temperature in Figure 22. The measured strains are linear and very
nearly equal, which is to be expected since the [±45]5s layup has the same response in both
the axial and transverse directions. The range of measured CTEs for the baseline panel is
from 2.34 to 3.40 με/ºC, with an average CTE of 2.92 με/ºC. The corresponding standard
deviation is 0.32 με/ºC, resulting in an 11 percent coefficient of variation. The maximum
temperature for the baseline panel thermal test is about 3.9 ºC lower than the maximum
temperature for the variable stiffness panels because the heating profile was terminated
when the temperature reached 65 ºC.
Experimental and Numerical Evaluation of
Thermal Performance of Steered Fibre Composite Laminates

147 Fig. 22. Strain vs. temperature at center of baseline panel.
6.4 Summary
The measured strain response at each gage location on each of the composite panels is
generally linear with increasing temperature. The membrane strain at each gage location is
defined and used to compute the laminate CTE at that location. The measured axial CTEs

Bis[4-diglycidylamino)phenyl]methane and Bis(4-aminophenyl) Sulphone”,
Macromolecules. Vol. 24, No. 11, pp. (3098-3110).
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976 Resin,” Journal of Composite Materials. Vol. 21, No. 3, pp. (243-261).
Duvaut, G, Terrel, G, Léné, F and Verijenko, V. (2000). Optimization of Fiber Reinforced
Composites. Composite Structures, Vol. 48, 2000, pp. (83-89).
Gürdal, Z and Olmedo, R. (1993). In-Plane Response of Laminates with Spatially Varying
Fiber Orientations: Variable Stiffness Concept. AIAA Journal, Vol. 31, (4), pp. (751-
758), 0001-1452.
Gürdal, Z, Haftka, RT and Hajela, P. (1999). Design and Optimization of Laminated Composite
Materials. John Wiley & Sons, Inc., New York, NY.
Gürdal, Z, Tatting, BF and Wu, KC. (2008). Variable stiffness composite panels: Effects of
stiffness variation on the in-plane and buckling response. Composite: Part A, Vol. 39,
2008, pp. (911-922).
Hetnarski, RB. (1996). Thermal stresses (I–IV). Amsterdam: Elsevier Science Pub. Co.
Hughes, T, Levit, I and Winget, J. (1982). Unconditionally stable element-by-element implicit
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Johnston, A. (1997). An Integrated Model of the Development of Process-Induced Deformation in
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Levitsky, M and Shaffer, B. (1975). Residual Thermal Stresses in a Solid Sphere Cast From a
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Gauges on Various Materials at Elevated and Cryogenic Temperatures. NASA TM-
1998-208739, October 1998.
Lee, W, Loos, A and Springer, S. (1982). Heat of Reaction, Degree of Cure, and Viscosity of
Hercules 3501-6 Resin”, Journal of Composite Materials. Vol. 16, pp. (510-520).
Experimental and Numerical Evaluation of
Thermal Performance of Steered Fibre Composite Laminates

Setoodeh, S, Abdalla, M and Gürdal, Z. (2007). Design of variable stiffness composite panels
for maximum fundamental frequency using lamination parameters. Composite
Structures. Vol. 81, No. 2, pp. (283-291).
Setoodeh, S, Abdalla, M, IJsselmuiden, S and Gürdal, Z. (2009). Design of variable-stiffness
composite panels for maximum buckling load. Composite Structures. Vol. 87, No. ,
pp. (109-117).
Thornton, EA. (1992). Thermal structures and materials for high-speed flight. American Institute
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Heat Transfer – Engineering Applications

150
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Second International Symposium on Innovative Numerical Analysis in Applied
Engineering Sciences, Canada.
7
A Prediction Model for
Rubber Curing Process

improvements have been performed (e.g. Ding et al, 1996). Onishi and Fukutani
(2003a,2003b) performed experiments on the sulfur curing process of styrene butadiene
rubber with nine sets of sulfur/CBS concentrations and peroxide curing process for several
kinds of rubbers. Based on their results, they proposed rate equation sets by analyzing the
data obtained using the oscillating rheometer operated in the range 403 K to 483 K at an
interval of 10 K. Likozar and Krajnc (2007) proposed a kinetic model for various blends of
natural and polybutadiene rubbers with sulphur curing. Their model includes post-
crosslinking chemistry as well as induction and crosslinking chemistries. Abhilash et al.
(2010) simulated curing process for a 20 mm thick rubber slab, assuming one-dimensional
heat conduction model. Likazor and Krajnc (2008, 2011) studied temperature dependencies
of relevant thermophysical properties and simulated curing process for a 50 mm thick
rubber sheet heated below, and good agreements of temperature and degree of cure have
been obtained between the predicted and measured values.

Heat Transfer – Engineering Applications

152
The second type prediction method combines the induction and crosslinking steps in series.
The latter step is usually expressed by an equation of a form dε/dτ = f(ε,T), where ε is the
degree of cure, τ is the elapsed time and T is the temperature. Ghoreishy (2009) and Rafei et
al. (2009) reviewed recent studies on kinetic models and showed a computer simulation
technique, in which the equation of the form dε/dτ= f(ε,T) is adopted. The form was
developed by Kamal and Sourour (1973) then improved by many researchers (e.g. Isayev
and Deng, 1987) and recently the power law type models are used for non-isothermal, three-
dimensional design problems (e.g. Ghoreishy and Naderi, 2005).
Temperature field is governed by transient, heat conduction equation with internal heat
generation due to the curing reaction. Parameters affecting the temperature history are
dimensions, shape and thermophysical properties of rubbers. Also initial and boundary
conditions are important factors. Temperature dependencies of relevant thermophysical
properties are, for example, discussed in Likozar and Krajnc (2008) and Goyanes et

5. Comparisons of the distributions of the temperature history and the degree of cure
between the model calculated values and the measurements were performed.

A Prediction Method for Rubber Curing Process

153
2. Experimental methods
The most typical curing agent is sulfur, and another type of the agent is peroxide (e.g.
Hamed, 2001). In this section, summary of our experimental studies are described. Two
types of curing systems were examined. One is the styrene butadiene rubber with
sulfur/CBS system (Nozu et al., 2008). The other is the blend of styrene butadiene rubber
and natural rubber with peroxide system (Baba et al., 2008).
2.1 Styrene Butadiene Rubber (SBR)
Figure 1 illustrates the mold and the positions of the thermocouples for measuring the
rubber temperatures (rubber thermocouples). A steel pipe with inner diameter of 74.6 mm
was used as the mold in which rubber sample was packed. On the outer surface of the mold,
a spiral semi-circular groove with diameter 3.2 mm was machined with 9 mm pitch, and
four sheathed-heaters with 3.2 mm diameter, a ~ d, were embedded in the groove. On the
outer surface of the mold, silicon coating layer was formed and a grasswool insulating
material was rolled. The method described here provides one-dimensional radial heat
conduction excepting for the upper and lower ends of the rubber.
Four 1-mm-dia type-E sheathed thermocouples, A ~ D, were located in the mold as the wall
thermocouples. Four 1-mm-dia Type-K sheathed thermocouples were equipped with the
mold to control the heating wall temperatures. The top and bottom surfaces were the
composite walls consisting of a Teflon sheet, a wood plate and a steel plate to which an
auxiliary heater is embedded.
To measure the radial temperature profile in the rubber, eight type-J thermocouples were
located from the central axis to the heating wall at an interval of 5 mm. At the central axis
just below 60 mm from the mid-plane of the rubber, a type-J thermocouple was also located
to measure the temperature variation along the axis. All the thermocouples were led out

Thermocouple Steel plate
Mold
74.6
a
b
c
d
Wood Plate
Thermocouple
A
B
C
D
Thermal
insulator
Teflon sheet
Φ
74.6
240
120
Rubber thermocouples
60

Fig. 1. Experimental mold and positions of rubber thermocouples for SBR

Ingredients wt% wt%
Polymer (SBR) 53.8 51.6
Cure agent (Sulfur) 1.0 5.0
Vulcanization accelerator 0.9 0.9
Reinforcing agent (Carbon black) 31.9 30.6

2.2 Styrene Butadiene Rubber and Natural Rubber blend (SBR/NR)
Figure 3 illustrates cross-section of the mold which consists of a rectangular mold with inner
dimensions of 100mm×100mm×30 mm and upper and lower aluminum-alloy hot plates
heated by steam. Rubber sample was packed in the cavity.

x
0
30
5
L

Fig. 3. Experimental mold and hot plates for SBR/NR
Energy transfer in the rubber is predominantly one-dimensional, transient heat conduction
from the top and bottom plates to the rubber. To measure the through-the-thickness
temperature profile along the central axis in the rubber, type-J thermocouples were located
at an interval of 5 mm. Two wall thermocouples were packed between the hotplates and the
rubber. All the thermocouples were led out through the mold and connected to the data
logger, and the temperature outputs were subsequently recorded to 0.1K. The blend
prepared includes 70 wt% styrene butadiene rubber (SBR) and 30 wt% natural rubber (NR).
The peroxide was used as the curing agent. Ingredients are listed in Table 2.
To locate the rubber thermocouples at the prescribed positions rubber sheets with 5 mm
thick were superposed appropriately.
Experiments were conducted under the condition of the heating wall temperature 433 K by
changing the heating time in several steps from 50 to 120 minutes in order to study the
dependencies of the degree of cure on the heating time. After the heating was terminated,
the rubber was led out from the mold then immersed in ice water. The rubber was sliced 3
mm thick × 30 mm long in the vicinity of the central axis. Test pieces were prepared with
dimensions of 3mm×3mm×3mm at x= -10, -5, 0, 5 and 10 mm, where the coordinate x is

Heat Transfer – Engineering Applications

rr r d











(2)
subject to
T = T
init
for τ = 0 (3a)
T = T
w
(τ) for τ > 0 and r = r
M
(3b)
T/r = 0 for τ > 0 and r = 0 (3c)
where
r
is the radial coordinate,

is the time，ρ is the density, c is the specific heat, λ is
the thermal conductivity, T
M

w
(t) for τ > 0 and x = ±L (5b)
where x is the coordinate defined as shown in Fig. 3. The second term of the right hand sides
of equations (2) and (4), dQ/dτ, show the effect of internal heat generation expressed as
dQ/dτ = ρΔH dε/dτ (6)
where ΔΗ is the heat of curing reaction and

is the degree of cure.
3.2 Curing reaction kinetics
Prediction methods for the degree of cure ε in equations (2) and (4) have been derived by
Onishi and Fukutani(2003a,2003b) and the models are adopted in this chapter.
3.2.1 Styrene Butadiene Rubber (SBR)
Curing process of SBR with sulfur has been analyzed and modeled by Onishi and Fukutani
(2003a). A set of reactions is treated as the chain one which includes CBS thermal
decomposition.
Simplified reaction model is shown in Fig. 4, where α is the effective accelerator, N is the
mercapt of accelerator, M is the polysulfide, RN is the polysulfide of rubber, R* is the active
point of rubber, and RX is the crosslink site. Fig. 4. Simplified curing model for SBR
The model can be expressed by a set of the following five chemical reactions.
k
1
a → N
k
2
N + a → M
k
3

2
[N][α] – k
3
[M]
d[RN]/dτ = k
3
[M] – k
4
[RN]
d[R*]/dτ = k
4
[RN] – k
5
[R*]
d[RX]/dτ = k
5
[R*]
where [α],[N],[M],[RN],[R*] and [RX] are the molar densities of appropriate species. Initial
conditions of equation (8) are [α] = 1 and zero conditions for the rest of species. Rate
constants k
i
(i = 1～5) in the set were expressed using the Arrhenius form as
k
i
= A
i
exp(-E
i
/RT) (9)
where A

1.166×10
4
1.387×10
-1
3.827
2
k
3.159×10
13
1.466×10
4
5.492×10
8
9.973
3
k
2.182×10
7
8.401×10
3
1.880×10
9
9.965
4
k
1.089×10
7
8.438×10
3
1.160×10


1.243×10
8
1.095×10
4

2
k
1.007×10
15
1.826×10
4

3
k
9.004×10
2
6.768×10
3

4
k
2.004×10
6
8.860×10
3

5
k
1.000×10


k
4
RX* + R → RX + PR
k
5
PR + R*→ RX
which leads the following rate equation set
d[R]/dτ = - k
1
[R] – k
3
[PR][R] – k
4
[RX*][R]
d[R*]/dτ = k
1
[R] – k
2
[R*]
d[PR]/dτ = k
2
[R*] – k
3
[PR][R] + k
4
[RX*][R] – 2k
5
[PR]
2

be adopted for estimating the SBR/NR system. SBR
SBR/NR
Sulfur 1 wt% Sulfur 5wt%
Density ρ (kg/m
3
) 1.165×10
3
1.024×10
3

Thermal conductivity l (W/mK) 0.33 0.20
Specific heat capacity c (J/kgK) 1.84×10
3
1.95×10
3

Heat of reaction ΔΗ (J/kg) 1.23×10
4
3.99×10
4
2.78×10
4Table 5. Physical properties used for prediction
The density ρ was determind using the mixing-rule. The thermal conductivity λ was
measured using the cured rubber at 293K. DSC measurements of the specific heat capacity c
060120180
0
50
100
150
Elapsed time (min)
Temprerature T (℃)
Heating wall
0
10
20
30
35
r mm
Predicted T
R
Measured T
wFig. 6. Temperature profile for cured SBR, Method A 060120180
0
50
100
150

shows a sharp increase and takes a maximum then decreases moderately. It can also be seen
that the onset of the heat generation takes place, for example, at τ = 15 minutes for r = 35
mm, and at τ = 65 minutes for r = 0mm. This means that the induction time is shorter for
nearer the heating wall due to slow heat penetration. Another point to note here is that the
symmetry condition at r = 0, equation (3c), leads to the rapid increase of T
R
near r = 0 after τ
= 60 minutes is reached as shown in Fig.7. The degree of cure ε increases rapidly just after
the onset of curing, then approaches gradually to 1 as shown in the lower part of Fig.8.
Figure 9 shows the profiles of rubber temperature and that of degree of cure, both are model
calculated results. An overall comparison of the Figs. 9(a) and 9(b) indicates that the
progress of the curing is much slower than the heat penetration. The phenomenon is
pronounced in the central region of the rubber. Temperature profiles at τ = 90 and 105
minutes were almost unchanged, thus the two profiles can not be distinguished in the
figure.
0
1
2
3
4
060120180
0.0
0.5
1.0
Heat generation rate dQ/d

(W/m

0.5
1.0
010203040
0
50
100
150
Degree of cure

75
60
45
90
Radial distance r (mm)
= 105 min
r = r
M
30 15
Temperature T (℃)
15
r = r
M
30
45
60
Radial distance r (mm)
75
= 0 min
= 90, 105 min