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Thermal Analysis of Epoxy based Fibre-reinforced Composites at Cryogenic Temperatures Thermal Analysis of Epoxy based Fibre-reinforced Composites at
Cryogenic Temperatures
B S R Murthy, Member
Dr A Rama Krishna, Non-member
B V Rama Krishna, Non-member
Epoxy based fibre-reinforced composite materials are general choice for use as supports and standoffs in super-conducting
energy storage magnets to take up compressive loads with minimum thermal loss. As these composites are generally
fabricated at moderate temperatures (100 C
o
- 200 C
o
) use of these materials at low temperatures induces severe thermal
stresses, which are of great concern considering the stability of composite structures. For analysis of the thermal stresses,
temperature distribution across these composite thick plates is to be obtained. A physical model is presented for this
purpose. A two-dimensional finite element model with a quadrilateral element in ANSYS 5.4 is considered for this
analysis. The results obtained are plotted in longitudinal and transverse directions for three different fibre materials with
epoxy as matrix material. Finally, it is concluded that the temperature distribution is non-linear in transverse direction
whereas uniform temperature field is obtained in the longitudinal direction for the given thermal loading in the physical
model.
Keywords: Fibre-reinforced composites; Cryogenic temperatures; Thermal stresses; Temperature distribution
B S R Murthy is with Mechanical Engineering Department, Nagarjuna
Institute of Technology, Vijayawada; Dr A Rama Krishna is with
Mechanical Engineering Department, Andhra University College of
Engineering, Visakhapatnam 530 003; and B V Rama Krishna is with IIT
Bombay, Mumbai 400 076.
This paper was received on November 5, 2002. Written discussion on the
paper will be entertained till April 30, 2004.
INTRODUCTION
The typical applications of epoxy-based composite laminated
plates are as insulators, mechanical supports and composite
tubes in combination with metal tubes as thermal standoffs in
large size super-conducting underground energy storing
magnets (to store 1000 MW to 10 000 MW) at cryogenic
temperatures. As these composites are fabricated at 100
o
C to
200
o
C , their use at low temperatures creates thermal stresses.
Temperature distribution data of thermal analysis is required
in the coupled field analysis finally to obtain and analyze
thermal stresses. It is, therefore, proposed to take up a heat
conduction problem using finite element method to obtain
temperature distribution data of a laminated epoxy-based
composite support at cryogenic temperatures.
Assumptions
(i) The temperature distribution is piece wise linear
across each layer (as the layers are thin compared to
entire laminate thickness).
(ii) The layers are stacked arbitrarily and the adjacent
layers are perfectly bonded and adhesive bond is of
negligible thickness. The geometry is referred to as
orthogonal coordinates (x, y, z) with x-y plane
coinciding with the mid-plane of the laminate and
z-axis transverse to the plate.
DESCRITIZATION OF THE PHYSICAL MODEL
A thick plate of dimensions (L � B � H ) consisting of N
number of layers as shown in the Figure 1, forms the domain for
descritization into finite elements. The problem of heat
conduction is solved by two-dimensional finite element
Figure 1 Physical model of fibre reinforced laminated plate with
thermal loading
146
IE (I) Journal�MC
B
77k
ADIABATIC
Convection Boundary h T T
(
) analysis. A two-dimensional eight-noded iso-parametric
quadrilateral element having thermal degree-of-freedom
(element type plane 77 in ANSYS 5.4) is chosen for heat
conduction problem.
The entire laminated composite plate with N layers is sub-
divided into number of eight-noded quadrilateral elements.
Typically each layer consisted of one or two or three rows of
elements and the plate consisted of five layers.
HEAT CONDUCTION PROBLEM
In the present investigation, the laminated composite plate is
considered to be a support in a super-conducting magnet that
supports a liquid nitrogen dewar at 77 K on its top. So a steady
temperature of 77 K condition is imposed on the top surface of
the laminated composite plate. Convective boundary
conditions are taken on the sides of the plate. At the bottom it
rests on the insulated wall of the super-conducting magnet. So
an adiabatic heat flow condition is imposed on the bottom
surface of the laminated composite plate.
MATERIAL PROPERTIES USED
Composite Material
K
L
, W/mk
K
T
, W/mk
Epoxy-Carbon
0.524
0.28
Epoxy-Kevlar
1.090
0.19
Epoxy-Glass
0.700
0.10
The boundary conditions are implemented and the problem is
solved using Frontal solver in ANSYS 5.4. The temperature
distribution results are obtained in the general postprocessor.
The analysis is conducted for composite plates made up of
epoxy-carbon, epoxy-kevlar and epoxy-glass materials. The
results so obtained are plotted [Figure 2].
Figure 2 shows the variation of temperature across the thickness
of the epoxy-carbon, epoxy-kevlar, and epoxy-glass composite
plates, with an aspect ratio L/B = 1.6, subjected to uniform
temperature 77 K on its top surface, adiabatic heat flow condi-
tion at its bottom and convective heat flow condition of its sides.
These values are computed taking fibre volume fraction of 0.6
and an orientation angle of 0
o
. The temperature variations
across the plate thickness are significantly non-linear for epoxy-
carbon compared to epoxy-kevlar and epoxy-glass. This
phenomenon can be attributed to very low conductivity values
of these materials, which are comparable with thermal
insulator materials particularly in transverse direction.
Further, the variation in temperature distribution behaviour
between epoxy-carbon and the remaining two can be attributed
to the significant anisotropy of thermal property for epoxy-
kevlar and epoxy-glass in comparison to epoxy-carbon. The
temperature is found to decrease up to 50% of plate length
in x-direction and increases gradually thereafter.
In the y-direction along the thickness, the temperature decreases
steadily up to 90% of the height and noses down up to edge as
depicted in Figure 3. This phenomenon can be understood, as
the material is a thermal insulator with low conductivity
allowing minimum heat loss.
CONCLUSIONS
1. The two-dimensional thermal field obtained in
unidirectional epoxy-based composite plates reveals that the
temperature variation along the breadth (or thickness) direction
is significantly non-linear for epoxy-carbon in comparison to
epoxy-kevlar and epoxy-glass. This phenomenon can be
attributed to very low thermal conductivity values of these
materials, which are comparable with conductivity values
thermal insulator materials particularly in transverse direction.
Further, the variation in temperature distribution behaviour
between epoxy-carbon and the remaining two can be attributed
to the significant anisotropy of thermal properties for epoxy-
kevlar and epoxy-glass in comparison to epoxy-carbon.
2. The thermal analysis on composite support also indicates
that the temperature distribution in length direction is linear
and straight representing a steady-state temperature field. The
temperature dropped down at the end, where nitrogen dewar at
77 K is supported. This phenomenon can be understood, as the
material is a thermal insulator with low conductivity allowing
minimum heat loss.
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Vol 84, January 2004
147
Figure 3 Temperature against Y/B for uni-directional composite plate
EPOXY CARBON
EPOXY GLASS
EPOXY KEVLAR
0.00 0.20 0.40 0.60 0.80 1.00
Y/ B
400
300
200
100
0
T
emperature
Figure 2 Temperature against X/L for uni-directional composite plate
0.00 0.20 0.40 0.60 0.80 1.00
X / L
EPOXY CARBON
EPOXY GLASS
EPOXY KEVLAR
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300.00
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