Satish K. Bapanapalli

Fiber Length and Orientation in Long-Fiber Injection-Molded Thermoplastics. Part I: Modeling of Microstructure and Elastic Properties

This article develops a methodology to predict the elastic properties of long-fiber injection-molded thermoplastics (LFTs). The corrected experimental fiber length distribution and the predicted and experimental orientation distributions were used in modeling to compute the elastic properties of the composite. First, from the fiber length distribution (FLD) data in terms of number of fibers versus fiber length, the probability density functions were built and used in the computation. The two-parameter Weibulls distribution was also used to represent the actual FLD. Next, the Mori—Tanaka model that employs the Eshelbys equivalent inclusion method was applied to calculate the stiffness matrix of the aligned fiber composite containing the established FLD. The stiffness of the actual as-formed composite was then determined from the stiffness of the computed aligned fiber composite that was averaged over all possible orientations using the orientation averaging method. The methodology to predict the elastic properties of LFTs was validated via experimental verification of the longitudinal and transverse moduli determined for long glass fiber injection-molded polypropylene specimens. Finally, a sensitivity analysis was conducted to determine the effect of a variation of FLD on the composite elastic properties. Our analysis shows that it is essential to obtain an accurate fiber orientation distribution and a realistic fiber length distribution to accurately predict the composite properties.

Micromechanical Analysis of Composite Corrugated-Core Sandwich Panels for Integral Thermal Protection Systems

termsA44 andA55 werecalculatedusinganenergyapproach.Usingtheshear-deformableplatetheory,aclosed-form solution of the plate response was derived. The variation of plate stiffness and maximum plate deflection due to changing the web angle are discussed. The calculated results, which require significantly less computational effort and time, agree well with the three-dimensional finite element analysis. This study indicates that panels with rectangular webs resulted in a weak extensional, bending, and A55 stiffness and that the center plate deflection was minimum for a triangular corrugated core. The micromechanical analysis procedures developed in this study were used to determine the stresses in each component of the sandwich panel (face and web) due to a uniform pressure load.

(Student Paper) Analysis and Design of Corrugated-Core Sandwich Panels for Thermal Protection Systems of Space Vehicles

A preliminary design process of an integral thermal protection system (ITPS) has been presented. Unlike the conventional TPS, the ITPS has both thermal protection as well as load bearing capabilities. The objective of this research work is to establish procedures and identify issues in the design of an ITPS. Corrugated-core sandwich construction has been chosen as a candidate structure for this design problem. An optimization problem was formulated as part of the design process with mass per unit area of the ITPS as the objective function and different functions of the ITPS as constraints. The optimization problem was solved by developing response surface approximations to represent the constraints. Response surface approximations were obtained from finite element (FE) analyses, which include transient heat transfer analyses and buckling analyses. A Matlab code (ITPS Optimizer) has been developed for generating the response surfaces, which has the capability to carry out hundreds of FE analyses, automatically, in conjunction with ABAQUS. Accurate response surface approximations could be obtained for the peak temperatures of the ITPS structure. It was found that response surface approximations for the smallest buckling eigen value of the whole structure were inaccurate. Therefore, the buckling modes were separated and similar buckling modes were grouped together. One response surface approximation was obtained for the smallest buckling eigen value of each group. The preliminary design process for the ITPS generates a design with areal density of approximately 10 lb/ft. Even though the ITPS has much higher load bearing capabilities, it is still on the heavier side when compared to conventional TPS (typical weight 2 lb/ft). New design changes have been proposed as part of the future work to make the ITPS lighter than the current design.

Comparison of Materials for an Integrated Thermal Protection System for Spacecraft Reentry

An integrated thermal protection system for spacecraft reentry based on a corrugated core sandwich panel concept fulfilling both thermal and structural functions is optimized for minimal mass. We seek the optimal dimensions and the best materials, but directly optimizing both continuous geometric parameters and discrete material choices is difficult. Accordingly the optimization problem is solved in two steps. In the first step, good candidatematerialsareselectedbasedmainlyontheirthermalperformance, obtainedfromasplineinterpolation of the maximum bottom face sheet temperature. Mild simplifying assumptions allowed a reduction of the number of variables in the interpolation to two nondimensional variables. In combination with a material database, this procedure allowed a graphical comparison and selection of candidate materials. In the second step, the geometry of the integrated thermal protection system panel is optimized for different combinations of the materials identified in step one. The optimization considers both thermal and structural constraints. The lightest panel employs aluminosilicate/Nextel 720 composites for the top face sheet and web corrugation and beryllium for the bottom face sheet. For the same thermal reentry environment, this design was found to be only about 40% heavier than a reference conventional thermal protection system that does not provide any structural load carrying capabilities.

Dimensionality Reduction Approach for Response Surface Approximations: Application to Thermal Design

of the maximum bottom face temperature is needed. The finite element model used to evaluate the maximum temperature depended on 15 parameters of interest for the design. A small number of assumptions simplified the thermal equations, allowing easy nondimensionalization, which together with a global sensitivity analysis showed that the maximum temperature mainly depends on only two nondimensional parameters. These were selected to be the variables of the response surface approximation for maximum temperature, which was constructed using simulations from the original nonsimplified finite element model. The major error in the two-dimensional response surface approximation was found to be due to the fact that the two nondimensional variables account for only part (albeit the major part) of the dependence on the original 15 variables. This error was checked and reasonable agreement was found. The two-dimensional nature of the response surface approximations allowed graphical representation, which we used for material selection from among hundreds of possible materials for the design optimization of an integrated thermal protection system panel.

Prediction of the Elastic—Plastic Stress/Strain Response for Injection-Molded Long-Fiber Thermoplastics

This article proposes a model to predict the elastic—plastic response of injection-molded long-fiber thermoplastics (LFTs). The model accounts for elastic fibers embedded in a thermoplastic resin that exhibits the elastic—plastic behavior obeying the Ramberg—Osgood relation and J-2 deformation theory of plasticity. It also accounts for fiber length and orientation distributions in the composite formed by the injection-molding process. Fiber orientation was predicted using an anisotropic rotary diffusion model recently developed for LFTs. An incremental procedure using Eshelbys equivalent inclusion method and the Mori—Tanaka assumption is applied to compute the overall stress increment resulting from an overall strain increment for an aligned-fiber composite that contains the same fiber volume fraction and length distribution as the actual composite. The incremental response of the latter is then obtained from the solution for the aligned-fiber composite by averaging over all fiber orientations. Failure during incremental loading is predicted using the Van Hattum—Bernado model that is adapted to the composite elastic—plastic behavior. The model is validated against the experimental stress—strain results obtained for long-glass-fiber/polypropylene specimens.

Comparison of Materials for Integrated Thermal Protection Systems for Spacecraft Reentry

An integrated thermal protection system (ITPS) for spacecraft reentry based on a corrugated core sandwich panel concept fulfilling both thermal and structural functions is optimized for minimal mass. We seek the optimal dimensions as well as the best materials, but directly optimizing both continuous geometric parameters and discrete material choices is relatively complex. Accordingly the optimization problem is solved in two steps. In a first step, good candidate materials are selected based mainly on their thermal performance. For this purpose a response surface approximation of the maximum bottom face sheet temperature is used. Mild simplifying assumptions allowed reducing the number of variables in the approximation to two nondimensional variables. In combination with a material database, this allowed graphical comparison of materials for the different sections of the ITPS panel. In a second part the geometry of the ITPS is optimized for different combinations of good potential materials from step one. This optimization considers both thermal and structural constraints. An ITPS panel based on alumino-silicate/Nextel 720 composites for top face sheet and web and beryllium for bottom face sheet was found to provide the lightest design.

Finite Element Based Method to Predict Gas Permeability in Cross-ply Laminates

A finite-element based method is developed to predict gas permeability in cross-ply laminates. Based on Poiseuilles Law and Darcys Law, the gas permeability is presented in terms of crack densities, microcrack opening displacements and an experimentally determined constant. The crack densities in each ply are predicted using finite element analysis based on energy concept of micro-fracture mechanics. The microcrack opening displacement of the representative volume element in cross-ply laminate is computed using three-dimensional finite element analysis. The normalized gas permeability in three laminates with different lay-ups are predicted and compared using the current model. Finally, a permeability-related material constant is quantified using the experimental results available in the literature.

Microcracking in Cross-Ply Laminates due to Biaxial Mechanical and Thermal Loading

DOI: 10.2514/1.20798 This paper presents a methodology to predict microcracking and microcrack density in both surface and internal plies ofa symmetriccross-ply laminateunder biaxial mechanical andthermal loadingconditions. Thethermoelastic properties of the microcracked laminates at different crack densities were determined by finite element analysis of the unit cells bounded by the microcracks. Analytical expressions for the stiffness and coefficients of thermal expansion as functions of crack densities were obtained in the form of response surface approximations. These analytical expressions were then used to predict the formation of a new set of microcracks by equating the change in strainenergyintheunitcellbeforeandaftertheformationofthemicrocrackstothecriticalfractureenergyrequired for their formation. Analytical expressions obtained as response surface approximations were also used to predict progressive microcracking. Both displacement and load control cases were considered along with thermal loading. Results from the current methodology agree very well with published data. Nomenclature

Micromechanical Analysis of Composite Truss-Core Sandwich Panels for Integral Thermal Protection Systems

A composite truss-core sandwich panel is investigated as a potential candidate for an Integral Thermal Protection System (ITPS). This multi-functional ITPS concept will protect the space vehicle from extreme reentry temperatures and will possess load carrying capabilities. The truss core is composed of two thin flat sheets that are separated by two inclined plates. Advantages of this new ITPS concept are discussed. The sandwich structure is idealized as an equivalent orthotropic thick plate continuum. The extensional stiffness matrix [A], coupling stiffness matrix [B], bending stiffness [D] and the transverse shear stiffness terms A44 and A55 are calculated through a strain energy and axes transformation approach. Using the Shear Deformable Plate Theory (SDPT) a closed form solution of the plate response was derived. The behavior of the stiffness and maximum plate deflection due to changing the web angle inclination is discussed. The calculated results, which require significantly less computational effort and time, agree well with the 3D finite-element analysis. The study indicates that panels with rectangular webs resulted in a weak extensional, bending, and A55 stiffness and that maximum plate deflection was greatest for 48 web angle configuration. The micromechanical analysis procedures developed in this study is to determine the unit cell stresses for each component (isotropic or composite) of the truss (face or web) that is caused by a uniform pressure load.