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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Higher-Order Theory for Functionally Graded Materials

Functionally graded materials (FGM's) are a new generation of engineered materials wherein the microstructural details are spatially varied through nonuniform distribution of the reinforcement phase(s). Engineers accomplish this by using reinforcements with different properties, sizes, and shapes, as well as by interchanging the roles of the reinforcement and matrix phases in a continuous manner (ref. 1). The result is a microstructure that produces continuously or discretely changing thermal and mechanical properties at the macroscopic or continuum scale. This new concept of engineering the material's microstructure marks the beginning of a revolution both in the materials science and mechanics of materials areas since it allows one, for the first time, to fully integrate the material and structural considerations into the final design of structural components. Functionally graded materials are ideal candidates for applications involving severe thermal gradients, ranging from thermal structures in advanced aircraft and aerospace engines to computer circuit boards. Owing to the many variables that control the design of functionally graded microstructures, full exploitation of the FGM's potential requires the development of appropriate modeling strategies for their response to combined thermomechanical loads. Previously, most computational strategies for the response of FGM's did not explicitly couple the material's heterogeneous microstructure with the structural global analysis. Rather, local effective or macroscopic properties at a given point within the FGM were first obtained through homogenization based on a chosen micromechanics scheme and then subsequently used in a global thermomechanical analysis.

Aboudi, J.↗
NASA NTRS2014

Aeroelastic Tailoring of a Plate Wing with Functionally Graded Materials

This work explores the use of functionally graded materials for the aeroelastic tailoring of a metallic cantilevered plate-like wing. Pareto trade-off curves between dynamic stability (flutter) and static aeroelastic stresses are obtained for a variety of grading strategies. A key comparison is between the effectiveness of material grading, geometric grading (i.e., plate thickness variations), and using both simultaneously. The introduction of material grading does, in some cases, improve the aeroelastic performance. This improvement, and the physical mechanism upon which it is based, depends on numerous factors: the two sets of metallic material parameters used for grading, the sweep of the plate, the aspect ratio of the plate, and whether the material is graded continuously or discretely.

Dunning, Peter D.↗
NASA NTRS1999

Higher-Order Theory for Functionally Graded Materials

This paper presents the full generalization of the Cartesian coordinate-based higher-order theory for functionally graded materials developed by the authors during the past several years. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. The generalization outlined herein involves extension of the theoretical framework to enable the analysis of materials characterized by spatially variable microstructures in three directions. Specialization of the generalized theoretical framework to previously published versions of the higher-order theory for materials functionally graded in one and two directions is demonstrated. In the applications part of the paper we summarize the major findings obtained with the one-directional and two-directional versions of the higher-order theory. The results illustrate both the fundamental issues related to the influence of microstructure on microscopic and macroscopic quantities governing the response of composites and the technologically important applications. A major issue addressed herein is the applicability of the classical homogenization schemes in the analysis of functionally graded materials. The technologically important applications illustrate the utility of functionally graded microstructures in tailoring the response of structural components in a variety of applications involving uniform and gradient thermomechanical loading.

Aboudi, Jacob↗
NASA NTRS2003

Thermal Characterization of Functionally Graded Materials: Design of Optimum Experiments

This paper is a study of optimal experiment design applied to the measure of thermal properties in functionally graded materials. As a first step, a material with linearly-varying thermal properties is analyzed, and several different tran- sient experimental designs are discussed. An optimality criterion, based on sen- sitivity coefficients, is used to identify the best experimental design. Simulated experimental results are analyzed to verify that the identified best experiment design has the smallest errors in the estimated parameters. This procedure is general and can be applied to design of experiments for a variety of materials.

Cole, Kevin D.↗
NASA NTRS1995

Thermoelastic Theory for the Response of Materials Functionally Graded in Two Directions with Applications to the Free-Edge Problem

A recently developed micromechanical theory for the thermoelastic response of functionally graded composites with nonuniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fiber spacing in two directions. In contrast to currently employed micromechanical approaches applied to functionally graded materials, which decouple the local and global effects by assuming the existence of a representative volume element at every point within the composite, the new theory explicitly couples the local and global effects. The analytical development is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense. Results are presented that illustrate the capability of the derived theory to capture local stress gradients at the free edge of a laminated composite plate due to the application of a uniform temperature change. It is further shown that it is possible to reduce the magnitude of these stress concentrations by a proper management of the microstructure of the composite plies near the free edge. Thus by an appropriate tailoring of the microstructure it is possible to reduce or prevent the likelihood of delamination at free edges of standard composite laminates.

Aboudi, Jacob↗
NASA NTRS1994

Thermal analysis of a functionally graded material subject to a thermal gradient using the boundary element method

The boundary element method is utilized in this study to conduct thermal analysis of functionally graded composites, materials in which the internal microstructure or properties are explicitly tailored in order to obtain an optimal response, on the micromechanical (constituent) scale. A unique feature of the boundary element formulations used here is the use of circular shape functions to convert the two-dimensional integrations of the composite fibers to one dimensional integrations. Using the computer code BEST-CMS, the through the thickness temperature profiles are computed for a representative material with varying numbers of fibers and fiber spacing in the thickness direction. The computed temperature profiles are compared to those obtained using an alternate analytical theory which explicitly couples the heterogeneous microstructure to the global analysis. The boundary element results compared favorably to the analytical calculations, with discrepancies that are explainable based on the boundary element formulation. The results serve both to demonstrate the ability of the boundary element method to analyze these types of materials, and to verify the accuracy of the analytical theory.

Goldberg, Robert K.↗
NASA NTRS2003

Optimal Experiment Design for Thermal Characterization of Functionally Graded Materials

The purpose of the project was to investigate methods to accurately verify that designed , materials meet thermal specifications. The project involved heat transfer calculations and optimization studies, and no laboratory experiments were performed. One part of the research involved study of materials in which conduction heat transfer predominates. Results include techniques to choose among several experimental designs, and protocols for determining the optimum experimental conditions for determination of thermal properties. Metal foam materials were also studied in which both conduction and radiation heat transfer are present. Results of this work include procedures to optimize the design of experiments to accurately measure both conductive and radiative thermal properties. Detailed results in the form of three journal papers have been appended to this report.

Cole, Kevin D.↗
NASA NTRS2014

Aeroelastic Tailoring of Transport Aircraft Wings: State-of-the-Art and Potential Enabling Technologies

This paper provides a brief overview of the state-of-the-art for aeroelastic tailoring of subsonic transport aircraft and offers additional resources on related research efforts. Emphasis is placed on aircraft having straight or aft swept wings. The literature covers computational synthesis tools developed for aeroelastic tailoring and numerous design studies focused on discovering new methods for passive aeroelastic control. Several new structural and material technologies are presented as potential enablers of aeroelastic tailoring, including selectively reinforced materials, functionally graded materials, fiber tow steered composite laminates, and various nonconventional structural designs. In addition, smart materials and structures whose properties or configurations change in response to external stimuli are presented as potential active approaches to aeroelastic tailoring.

Jutte, Christine↗
NASA NTRS2003

Analysis of Photothermal Characterization of Layered Materials: Design of Optimal Experiments

In this paper numerical calculations are presented for the steady-periodic temperature in layered materials and functionally-graded materials to simulate photothermal methods for the measurement of thermal properties. No laboratory experiments were performed. The temperature is found from a new Green s function formulation which is particularly well-suited to machine calculation. The simulation method is verified by comparison with literature data for a layered material. The method is applied to a class of two-component functionally-graded materials and results for temperature and sensitivity coefficients are presented. An optimality criterion, based on the sensitivity coefficients, is used for choosing what experimental conditions will be needed for photothermal measurements to determine the spatial distribution of thermal properties. This method for optimal experiment design is completely general and may be applied to any photothermal technique and to any functionally-graded material.

Cole, Kevin D.↗
NASA NTRS2014

Electron Beam Freeform Fabrication of Titanium Alloy Gradient Structures

Historically, the structural optimization of aerospace components has been done through geometric methods. A monolithic material is chosen based on the best compromise between the competing design limiting criteria. Then the structure is geometrically optimized to give the best overall performance using the single material chosen. Functionally graded materials offer the potential to further improve structural efficiency by allowing the material composition and/or microstructural features to spatially vary within a single structure. Thus, local properties could be tailored to the local design limiting criteria. Additive manufacturing techniques enable the fabrication of such graded materials and structures. This paper presents the results of a graded material study using two titanium alloys processed using electron beam freeform fabrication, an additive manufacturing process. The results show that the two alloys uniformly mix at various ratios and the resultant static tensile properties of the mixed alloys behave according to rule-of-mixtures. Additionally, the crack growth behavior across an abrupt change from one alloy to the other shows no discontinuity and the crack smoothly transitions from one crack growth regime into another.

Brice, Craig A.↗
NASA NTRS2002

Efficient Reformulation of the Thermoelastic Higher-order Theory for Fgms

Functionally graded materials (FGMs) are characterized by spatially variable microstructures which are introduced to satisfy given performance requirements. The microstructural gradation gives rise to continuously or discretely changing material properties which complicate FGM analysis. Various techniques have been developed during the past several decades for analyzing traditional composites and many of these have been adapted for the analysis of FGMs. Most of the available techniques use the so-called uncoupled approach in order to analyze graded structures. These techniques ignore the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. The higher-order theory for functionally graded materials (HOTFGM) is a coupled approach developed by Aboudi et al. (1999) which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the original higher-order theory for two-dimensional elastic problems is developed and validated. The use of the local-global conductivity and local-global stiffness matrix approach is made in order to reduce the number of equations involved. In this approach, surface-averaged quantities are the primary variables which replace volume-averaged quantities employed in the original formulation. The reformulation decreases the size of the global conductivity and stiffness matrices by approximately sixty percent. Various thermal, mechanical, and combined thermomechanical problems are analyzed in order to validate the accuracy of the reformulated theory through comparison with analytical and finite-element solutions. The presented results illustrate the efficiency of the reformulation and its advantages in analyzing functionally graded materials.

Bansal, Yogesh↗
NASA NTRS2001

User's Manual and Final Report for Hot-SMAC GUI Development

A new software package called Higher Order Theory-Structural/Micro Analysis Code (HOT-SMAC) has been developed as an effective alternative to the finite element approach for Functionally Graded Material (FGM) modeling. HOT-SMAC is a self-contained package including pre- and post-processing through an intuitive graphical user interface, along with the well-established Higher Order Theory for Functionally Graded Materials (HOTFGM) thermomechanical analysis engine. This document represents a Getting Started/User's Manual for HOT-SMAC and a final report for its development. First, the features of the software are presented in a simple step-by-step example where a HOT-SMAC model representing a functionally graded material is created, mechanical and thermal boundary conditions are applied, the model is analyzed and results are reviewed. In a second step-by-step example, a HOT-SMAC model of an actively cooled metallic channel with ceramic thermal barrier coating is built and analyzed. HOT-SMAC results from this model are compared to recently published results (NASA/TM-2001-210702) for two grid densities. Finally, a prototype integration of HOTSMAC with the commercially available HyperSizer(R) structural analysis and sizing software is presented. In this integration, local strain results from HyperSizer's structural analysis are fed to a detailed HOT-SMAC model of the flange-to-facesheet bond region of a stiffened panel. HOT-SMAC is then used to determine the peak shear and peel (normal) stresses between the facesheet and bonded flange of the panel and determine the "free edge" effects.

Yarrington, Phil↗
NASA NTRS1995

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

Pindera, Marek-Jerzy↗
NASA NTRSDate not supplied

Combining Data with Physical Knowledge for Uncertainty Quantification in Certification and Reliability Analysis

Unifying empirical data with predictive models can enable engineering cost-savings through certification by analysis and reliability-based design. Both concepts require rigorous uncertainty quantification (UQ) and robust understanding and treatment of relevant physics. Combining sampling-based UQ algorithms with high-fidelity simulations creates a computational bottleneck that is often alleviated through the use of machine learning (ML). ML can be used to create computationally efficient surrogates for simulations of complex or high-dimensional physical interactions (e.g., multi-phase interactions associated with melt pools in laser powder bed fusion or spatially-dependent material properties in functionally graded materials). However, negative side effects of ML may include a lack of interpretability and negative correlation between event rarity and simulation accuracy due to a lack of training data. As such, it is important to infuse ML algorithms with physics-based guardrails to provide confidence in their predictions. This talk will provide a brief review of recent NASA research at this intersection of physics-based simulation, ML, and UQ with a focus on certification and reliability analysis.

uncertainty quantification↗
NASA NTRS2018

Coupled Thermomechanical Micromechanics Modeling of the Influence of Thermally Grown Oxide Layer in an Environmental Barrier Coating System

Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting critical components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) from extreme thermal/chemical environments. However, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination. Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting silicon based ceramic matrix composite (CMC) components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) such as silicon carbide from extreme thermal/chemical environments. In a typical CMC/EBC system, an EBC may or may not be adhered to an underlying substrate with a bond coat (e.g., silicon). Irrespective, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination, recession, chemical attack and dissolution, thermo-mechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites and will be used herein to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer in EBC/CMC systems without a silicon bond coat. To accomplish this a sensitivity study is conducted to examine the influence of uniformly and non-uniformly grown oxide layer on the associated driving forces leading to mechanical failure (spallation) of EBC layer when subjected to isothermal loading, recession, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites (Aboudi et al., 1999, Composites B). For example, HOTFGM was previously used (Arnold et al, 1995, NASA CP 10178, paper 34), to assess interlaminar stresses (including free edge effects) in a substrate with a thermal barrier coating (TBC). In this study, HOTFGM micromechanics analyses will be used to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer between a silicon carbide substrate and a ytterbium disilicate EBC. In order to realistically simulate TGO growth, an evolution law will be incorporated into HOTFGM. In addition, the effect of TGO roughness will be explored consistent with previous TBC work (Pindera et al., 2000. Material Science and Engineering, A284, pp. 158-175). This model represents a first step in developing a robust analysis tool that can ultimately be used to design durable EBC systems. Additional failure modes will be considered as part of a future work.

environmental barrier coating↗