Download Analysis of Advanced Integrated Composite Thermal Structures for

Analysis of Advanced Integrated Composite Thermal
Structures for Space Applications
L. DANGORA
ABSTRACT
Optical systems experience severe performance degradation when their support
structure or scientific instruments undergo shape distortion; thus, candidate materials
for these systems must be sufficiently stiff and thermally stable. Carbon-fiberreinforced polymers (CFRPs), with their high stiffness-to-weight ratios and near-zero
in-plane coefficients of thermal expansion (CTEs), are therefore appropriate for this
application. However, despite the low CTE of the composite, thermal gradients can
still stimulate warping of the structure. As such, the objective of the current research is
to improve temperature uniformity of the CFRP and thereby enhance its dimensional
stability.
The program objective is to be realized using active control of flow through an
interconnected network of channels embedded in the CFRP. Such vascular composites
are an emerging class of multifunctional materials that show promise in applications
for self-healing, structural health monitoring, and thermal regulation. However, due to
the fledgling state of the field, the technology lacks proper tools for design,
optimization, and analysis. This paper will introduce the application and describe
development of a computational tool for analysis of thermovascular composites.
INTRODUCTION
Carbon-fiber polymer-matrix composites (PMCs) have many characteristics that
make them attractive for use in a wide range of applications across the aerospace
industry (e.g., antennas, mirrors, lenses, solar panels, platforms, reflectors, and solar
sails) [1]. Benefits of using composite components include low mass, tailorable
material properties, good fatigue resistance, near-zero CTE, and high specific strength
and stiffness [2, 3]. Replacing metal parts with CFRPs can reduce the weight of
payloads launched to space while also meeting the specified stiffness requirements.
Furthermore, customizable design and flexibility in manufacture accommodates
fabrication of entire assemblies from composites parts, thereby facilitating CTE match
to mitigate thermal stresses buildup at the interface of dissimilar materials [1].
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Lisa Dangora, Naval Research Laboratory, 4555 Overlook Ave SW, Washington, DC 20375
TABLE I. DIMENSIONAL STABILITY OF SPACECRAFT COMPONENTS [1]
Application
Dimensional Change
Possible Effects
Antennas
600 με in length
Loss of signal
Microwave filters/waveguides
1–100 με in size
Loss of power
Optics and sensors/supports
10–100 με
Loss of pointing/tracking
Large space telescope
1 με between mirrors
Nonoperational
Lasercom systems
arc seconds of laser tilt
Mission impossible
Mirrors
0.1–10 με
Loss of resolution and
distortion of image
While PMCs are widely used in the aerospace industry, the primary applications
considered for the current research are composite optics and support structures.
Interest in large, lightweight, high-performance optical assemblies mandates the use of
CFRP to meet the size, weight, and stiffness requirements [1]. Optical systems in
general, whether spaceborne or ground-based, demand a high-level of dimensional
stability for reliable operation (e.g., Table I). For example, even a seeminglyinsignificant pointing error of 0.1° from the International Space Station (at an orbit
altitude of 200 miles) results in a ground error approximately one-third of mile wide.
Because these optical systems are highly sensitive to dimensional distortion, a critical
design aspect is shape stability under thermal loads. By combining the negative axial
CTE of carbon fiber with the positive CTE of the polymer matrix, CFRPs can be
designed to have near-zero planar coefficients of thermal expansion (Figure 1) [2].
However, image degradation depends not only on the magnitude of extensional strains
but also on its uniformity across the composite [4].
While local deviations in volume fraction or fiber orientation can cause the CTE to
vary over the part and compromise dimensional stability (Figure 2), such defects can
be tested and corrected for before system deployment. Furthermore, these
manufacturing errors are generally preventable by employing stringent processing
procedures. However, even when the composite design specifications are met, thermal
gradients can still stimulate structural deformations. Because properties of the
Figure 1. Candidate materials considered for the James Webb Space Telescope mirrors [5].
composite constituents vary nonlinearly with temperature (e.g., the matrix modulus of
elasticity and the fiber CTE), the local coefficient of thermal expansion may vary from
one end of the part to the other when thermal differentials present; as a result, the
composite will warp to reach a minimum energy state. Since, in this case, undesirable
shape distortions are not a result of fabrication error, they must be corrected for during
service of the part.
The current research proposes to actively cool composites in an effort to minimize
thermal gradients and thereby enhance shape stability. Analogous to the circulatory
systems of living organisms, a pervasive fluid network will be integrated into the
CFRP. The flow will be pumped through the closed loop network and the working
fluid’s latent heat of vaporization will be used to maintain isothermalization. As
vascular composites continue to be an emerging technology, there is a lack of
computation tools for their analysis. This paper will introduce a model under
development to assist with computer aided design and engineering of these systems.
(a)
(b)
Figure 2. Variation in coefficients of thermal distortion of a graphite PMC as a function of (a) fiber
orientation and (b) fiber volume fraction. Note fiber and matrix properties are found in [2].
VASCULAR COMPOSITES
While the science of microfluidics has been extensively investigated for decades,
only recently have efforts been made to marry these hydraulic systems with composite
structures [6]. There are a number of ways to fabricate vascular composites (e.g.,
removable solid cores, non-removable hollow cores, micromachining, sacrificial
components) [7]. Early developments in this research area investigated the use of
cylindrical cores incorporated in the ply schedule to create channels within the
composite during curing. Non-removable cores, such as hollow glass fibers and
metallic tubes, are left in the composite, but typically have weak interfacial strength
between the core and the matrix. To eliminate this interface, removable cores have
also been explored. Nevertheless, these methods are limited to straight, discrete
channels with no interconnectivity.
Micromachining can instead be used to create more complex networks [7];
however, microcracking introduced during machining of the composite can
significantly compromise the structural performance. Furthermore, the high pressures
required to drive the flow create a need for strong interlaminar bonds, which is best
attained through single-step composite curing. If two laminate halves are cured
individually, micromachined, and adhered together, the bond strength will be weaker.
Therefore, more favorable approaches to fabrication have been developed in recent
years involving the use of sacrificial material, such as direct ink writing [8] and
vaporization of sacrificial components (VaSC) [9]. These techniques offer good
flexibility in network design with the ability to create interconnectivity and vary
channel size.
Using these sacrificial methods in conjunction with an additive manufacturing
processes, such as fused deposition modeling (FDM), allows for intricate and precise
network design at practical production rates with automated processing. The
vasculature can be introduced into commercially-available, aerospace-grade materials
that are already commonly employed for construction of space-bound components.
Furthermore, the technology can be incorporated into industry-standard structural
members (e.g., sandwich panels and grid structures) with minor modification to
conventional fabrication procedures.
Computational tools will be necessary for design of the fluid-channel network as
well as for thermohydraulic and structural analyses of the vascular composite. The
hybrid thermostructure will require tradeoffs between optimal structural performance
and optimal thermal performance. Due to the large number of system parameters and
their interdependency, design optimization is best accomplished through numerical
simulation [6]. However, because vascular composite technology is still an emerging
field of study, the research area lacks the computational framework for such analyses.
Without the aid of a system model, technology development would require
extensive experimental programs implemented on a case-by-case basis. The current
work seeks to bridge this gap by developing a computer program that can link the
design to analyses for material mechanics, fluid dynamics, and heat transfer. The
eventual goal is to use structural and thermohydraulic analyses to influence the design
in an automated optimization process. However, only one facet of this optimization
program, i.e. the thermal-mechanical model, has been developed to date. The
following describes this section of code and the steps taken to link the vascular
composite design to a finite element model for mechanical and thermal stress analysis.
(a)
(b)
Figure 3. (a) Ply stack and (b) discretized zones for zone-based model
THERMOMECHANICAL MODEL
The program presented here is intended to convert the vascular composite design
into a zone-based finite element (FE) model that can be used to analyze structural and
thermal responses of the laminate. The zone-based approach is a common technique
used to analyze composite laminates with commercial finite element solvers (e.g.,
Nastran, Abaqus, LS-DYNA). Using this method, the composite part is discretized
into zones. Each zone is assigned its own effective properties, which can be influenced
by factors such as local fiber orientation, volume fraction, and thickness. Consider, for
example, a simple plate made from three plies with borders as shown in Figure 3a.
There will be different thicknesses and effective laminate properties depending on
which plies are present in a given location. For this rudimentary case, the laminate can
be classified by four zones (Figure 3b), each having its own properties. This zonebased modeling approach will be used to analyze vascular composites but, instead of
considering locations of ply drop-off and misalignment, the zones in this instance will
be defined by the local void content created by the presence of channels, which are
needed to accommodate the fluid network.
In its current state, each network-design iteration is read into the MATLAB code
as an image file (Figure 4a). The program scales the pixels to fit user-defined
dimensions of the composite plate, and then meshes the image (Figure 4b) by defining
nodal locations and elemental connectivity. The image is converted to greyscale and
(a)
(b)
Figure 4. (a) Image of network design and (b) mesh grid overlaid on image of 100-mm by 75-mm plate.
pixels are assigned a value based on their color; values range from zero to one and are
associated with greyscale ranging from black to white. All black pixels are considered
to be composite whereas all white pixels are taken to be voids.
The void fraction of each element is calculated by averaging color values of all
pixels bounded by that element. To accommodate pixels that are segmented by
gridlines, and are therefore common to multiple elements, the value of a given pixel is
weighted relative to its area contained within each element. The elements are then
grouped into bins associated with their void content. A single bin group will contain
all elements having a void fraction within the bounds of the bin range. The resolution
of the bin range is user-defined; a higher resolution value will create a more accurate
model. For example, using bins with a void fraction range of 5% creates a maximum
of 20 possible element groups whereas a 1% bin range generates 100 possible groups.
When the elements in Figure 4b are grouped into 5% bins, only five element sets are
created, as illustrated by the color mapping of Figure 5a. By increasing the resolution
to 1%, the number of element sets quadruples (Figure 5b) and the material definitions
can better characterize all elements to which they are assigned. Alternatively, the grid
resolution of the mesh can be enhanced to improve accuracy of the model (Figure 5c).
The user can also specify the number of plies affected by the channels; the
remaining plies in the layup are assumed to be void-free. For example, if the network
is designed to be minimally invasive on the structure, the channel diameters may be
less than the thickness of a single ply; therefore, only one ply out of the stack-up will
have a void content greater than zero. If, on the other hand, the channel diameter is
greater than the thickness of a single layer, the sacrificial filament for the network may
nest within multiple plies during manufacture. Therefore, the void content determined
from the network image (e.g., Figure 4) is only relevant to the plies affected by the
channels; the remaining plies have zero void fraction.
The sum of the void content in all of the ply layers through the thickness is
normalized by the number of plies in the layup to achieve an average void volume
fraction for the composite. To demonstrate with values, consider an element with an
average pixel color value of 0.75 (i.e., a 75% void fraction), and note that the channels
are assumed to nest within two of the six ply layers; the average void content for that
element in the composite is 25% (given by 2×0.75/6). While the bin groupings were
determined based on the void content of a single layer that is affected by the network
channels, the average void fraction for the element (through the entire thickness of the
composite) is used in the calculation of material properties.
To save on computational time, material properties are calculated once for a
pristine composite without any voids; knockdown factors are later applied to account
for the void content. A strength of materials micromechanical model is employed to
calculate the engineering constants of a unidirectional (UD) lamina from the
constituent properties; the rule of mixtures and the modified rule of mixtures are used
to determine the contributions of the fibers and matrix to the overall response of the
lamina. The UD lamina properties and ply schedule are then used with classical
lamination theory (CLT) to populate the laminate stiffness matrix (a.k.a., ABD matrix)
and determine the global engineering constants for the composite. These baseline
composite properties are modified using the rule of mixtures to account for the void
volume fraction that defines each element set.
(a)
(b)
(c)
Figure 5. FE model of vascular composite with coarse 5-mm grid at (a) low bin resolution and (b) high
bin resolution, and (c) fine 1-mm grid with coarse bin resolution. Note elements are colored by material.
Figure 6. MSC Nastran heat transfer analysis of M55J/RS3 vascular composite subject to uniform
surface heat flux of 50 W/m2. (1-mm element size with 5% bin resolution)
After all the information is calculated, it is organized for output. First, the nodes
are defined by an identifier (ID) and global position (x, y, z). Next, the shell elements
are given an identifier and are defined by the four node IDs at the shell corners. The
element sets are then named and listed, and the sets are assigned section properties.
Lastly, the material properties are defined for each section. The program then exports
the model information to a text file that can subsequently be imported into commercial
FE preprocessors (e.g., FEMAP and Abaqus/CAE), where boundary and loading
conditions can be applied, and it is ready for analysis and post-processing (e.g.,
Figure 6). Because the elements are already grouped into sets, allocating the
constraints is quick and easy. However, the code can easily be modified to apply
boundary and loading conditions to the part, eliminating the need for a FE
preprocessor; this will become important when all facets of the optimization program
are complete because execution of the finite element analyses can be fully automated.
SUMMARY AND FUTURE WORKS
A computational tool was developed to generate a finite element model from an
image file of a vascular composite network design. The code meshes the image by
generating node locations and assigning element connectivity. Using a zone-based
approach, the program groups elements into sets based on the local void volume
fraction. Material properties are calculated using the rule of mixtures and classical
lamination theory. The program then outputs a text file that can be read into
commercial finite element software for additional preprocessing or analysis.
The code is intended to be a single section of a larger optimization program. For
robust predictions, the portion of code presented here should be linked to a
thermohydraulic analysis, whose outputs (e.g., local pressurization and heat transfer
coefficients) will be required as inputs to the thermomechanical model described in
this paper. Ultimately, it is the goal of this research to generate an automated process
that uses computer aided engineering (CAE) to systematically influence the computer
aided design (CAD) of these systems.
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