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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]. _____________ 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. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 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