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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

Efficient Reformulation of HOTFGM: Heat Conduction with Variable Thermal Conductivity

Functionally graded materials (FGMs) have become one of the major research topics in the mechanics of materials community during the past fifteen years. FGMs are heterogeneous materials, characterized by spatially variable microstructure, and thus spatially variable macroscopic properties, introduced to enhance material or structural performance. The spatially variable material properties make FGMs challenging to analyze. The review of the various techniques employed to analyze the thermodynamical response of FGMs reveals two distinct and fundamentally different computational strategies, called uncoupled macromechanical and coupled micromechanical approaches by some investigators. The uncoupled macromechanical approaches ignore the effect of microstructural gradation by employing specific spatial variations of material properties, which are either assumed or obtained by local homogenization, thereby resulting in erroneous results under certain circumstances. In contrast, the coupled approaches explicitly account for the micro-macrostructural interaction, albeit at a significantly higher computational cost. The higher-order theory for functionally graded materials (HOTFGM) developed by Aboudi et al. is representative of the coupled approach. However, despite its demonstrated utility in applications where micro-macrostructural coupling effects are important, the theory's full potential is yet to be realized because the original formulation of HOTFGM is computationally intensive. This, in turn, limits the size of problems that can be solved due to the large number of equations required to mimic realistic material microstructures. Therefore, a basis for an efficient reformulation of HOTFGM, referred to as user-friendly formulation, is developed herein, and subsequently employed in the construction of the efficient reformulation using the local/global conductivity matrix approach. In order to extend HOTFGM's range of applicability, spatially variable thermal conductivity capability at the local level is incorporated into the efficient reformulation. Analytical solutions to validate both the user-friendly and efficient reformulations am also developed. Volume discretization sensitivity and validation studies, as well as a practical application of the developed efficient reformulation are subsequently carried out. The presented results illustrate the accuracy and implementability of both the user-friendly formulation and the efficient reformulation of HOTFGM.

Zhong, Yi

Higher-Order Theory: Structural/MicroAnalysis Code (HOTSMAC) Developed

The full utilization of advanced materials (be they composite or functionally graded materials) in lightweight aerospace components requires the availability of accurate analysis, design, and life-prediction tools that enable the assessment of component and material performance and reliability. Recently, a new commercially available software product called HOTSMAC (Higher-Order Theory--Structural/MicroAnalysis Code) was jointly developed by Collier Research Corporation, Engineered Materials Concepts LLC, and the NASA Glenn Research Center under funding provided by Glenn's Commercial Technology Office. The analytical framework for HOTSMAC is based on almost a decade of research into the coupled micromacrostructural analysis of heterogeneous materials. Consequently, HOTSMAC offers a comprehensive approach for analyzing/designing the response of components with various microstructural details, including certain advantages not always available in standard displacement-based finite element analysis techniques. The capabilities of HOTSMAC include combined thermal and mechanical analysis, time-independent and time-dependent material behavior, and internal boundary cells (e.g., those that can be used to represent internal cooling passages, see the preceding figure) to name a few. In HOTSMAC problems, materials can be randomly distributed and/or functionally graded (as shown in the figure, wherein the inclusions are distributed linearly), or broken down by strata, such as in the case of thermal barrier coatings or composite laminates.

Arnold, Steven M.

An innovative radial gradient material design using hot isostatic pressing for applications in extreme environments

Functionally graded materials (FGMs) are highly advanced continuous or discontinuous structures whose structural and material properties vary along a singular geometric dimension either in the axial or radial direction. Here, the radial gradient FGM design makes for an optimal structural design to incorporate a bi-metallic structure with a copper-based high entropy alloy (Cu-HEA) with good mechanical properties and high irradiation resistance, and Chromium (Cr) with great corrosion resistance. This study focuses on the experimental design of a metal powder loading mechanism to fabricate a bi-metallic radial gradient structure using Cu-HEA and 99.9 % pure Cr metal powders. The powder loading strategy uses custom-designed concentric cylindrical dividers to separate the individual compositions. Two benchtop trial runs were performed for design optimization. The optimized design was then implemented to eventually load the HEA and Cr powders for consolidation via powder metallurgy hot isostatic pressing (PM-HIP). The electron microscopy analysis reveals the successful fabrication of the radial gradient structure with the chemical mapping analysis, demonstrating the gradual composition shift from the HEA at the center to the pure-Cr at the periphery via a three-step gradient.

High Entropy Alloys (HEAs)

High Temperature Materials for Chemical Propulsion Applications

Radiation or passively cooled thrust chambers are used for a variety of chemical propulsion functions including apogee insertion, reaction control for launch vehicles, and primary propulsion for planetary spacecraft. The performance of these thrust chambers is limited by the operating temperature of available materials. Improved oxidation resistance and increased operating temperatures can be achieved with the use of thermal barrier coatings such as zirconium oxide (ZrO2) and hafnium oxide (HfO2). However, previous attempts to include these materials showed cracking and spalling of the oxide layer due to poor bonding. Current research at NASA's Marshall Space Flight Center (MSFC) has generated unique, high temperature material options for in-space thruster designs that are capable of up to 2500 C operating temperatures. The research is focused on fabrication technologies to form low cost Iridium,qF_.henium (Ir/Re) components with a ceramic hot wall created as an integral, functionally graded material (FGM). The goal of this effort is to further de?celop proven technologies for embedding a protective ceramic coating within the Ir/Re liner to form a robust functional gradient material. Current work includes the fabrication and testing of subscale samples to evaluate tensile, creep, thermal cyclic/oxidation, and thermophysical material properties. Larger test articles have also being fabricated and hot-fire tested to demonstrate the materials in prototype thrusters at 1O0 lbf thrust levels.

Elam, Sandra

Analysis of Factors Affecting the Performance of RLV Thrust Cell Liners

The reusable launch vehicle (RLV) thrust cell liner, or thrust chamber, is a critical component of the Space Shuttle Main Engine (SSME). It is designed to operate in some of the most severe conditions seen in engineering practice. This requirement, in conjunction with experimentally observed 'dog-house' failure modes characterized by bulging and thinning of the cooling channel wall, provides the motivation to study the factors that influence RLV thrust cell liner performance. Factors or parameters believed to be directly related to the observed characteristic deformation modes leading to failure under in-service loading conditions are identified, and subsequently investigated using the cylindrical version of the higher-order theory for functionally graded materials in conjunction with the Robinson's unified viscoplasticity theory and the power-law creep model for modeling the response of the liner s constituents. Configurations are analyzed in which specific modifications in cooling channel wall thickness or constituent materials are made to determine the influence of these parameters on the deformations resulting in the observed failure modes in the outer walls of the cooling channel. The application of thermal barrier coatings and functional grading are also investigated within this context. Comparison of the higher-order theory results based on the Robinson and power-law creep model predictions has demonstrated that, using the available material parameters, the power-law creep model predicts more precisely the experimentally observed deformation leading to the 'dog-house' failure mode for multiple short cycles, while also providing much improved computational efficiency. However, for a single long cycle, both models predict virtually identical deformations. Increasing the power-law creep model coefficients produces appreciable deformations after just one long cycle that would normally be obtained after multiple cycles, thereby enhancing the efficiency of the analysis. This provides a basis for the development of an accelerated modeling procedure to further characterize dog-house deformation modes in RLV thrust cell liners. Additionally, the results presented herein have demonstrated that the mechanism responsible for deformation leading to 'dog-house' failure modes is driven by pressure, creep/relaxation and geometric effects.

Arnold, Steven M.

Thermo-Elastic Analysis of Internally Cooled Structures Using a Higher Order Theory

This paper presents the results of a study on the thermomechanical behavior of internally cooled silicon nitride structures. Silicon nitride is under consideration for elevated temperature aerospace engine applications. and techniques for lowering the operating temperature of structures composed of this material are under development. Lowering the operating temperature provides a large payoff in terms of fatigue life and may be accomplished through the use of thermal barrier coatings (TBC's) and the novel concept of included cooling channels. Herein, an in-depth study is performed on the behavior of a flame-impinged silicon nitride plate with a TBC and internal channels cooled by forced air. The analysis is performed using the higher order theory for functionally graded materials (HOTFGM), which has been developed through NASA Glenn Research Center funding over the past several years. HOTFGM was chosen over the traditional finite element approach as a prelude to an examination of functionally graded silicon nitride structures for which HOTFGM is ideally suited. To accommodate the analysis requirement% of the internally cooled plate problem, two crucial enhancements were made to the two-dimensional Cartesian-based version of HOTFGM. namely, incorporation of internal boundary capabilities and incorporation of convective boundary conditions. Results indicate the viability and large benefits of cooling the plate via forced air through cooling channels. Furthermore, cooling can positively impact the stress and displacement fields present in the plate, yielding an additional payoff in terms of fatigue life. Finally, a spin-off capability resulted from inclusion of internal boundaries within HOTFGM; the ability to simulate the thermo-elastic response of structures with curved surfaces. This new capability is demonstrated, and through comparison with an analytical solution, shown to be viable and accurate.

Arnold, Steven M.

Fabrication of ceramic to metal graded structure for high temperature CSP receiver application using solid state additive manufacturing

The overarching goal of this project is to come up with an innovative joining solution for integration of SiC ceramic to structural materials such as stainless steels (SS)/Ni-base alloys, where intimate metallurgical bonding between SiC ceramic and the structural metallic alloy is demonstrated at the interface. Implementation of a simple, yet robust joining method would help in increasing the application space of SiC in a high-temperature CSP (concentrated solar power) plant, especially in the receiver section. This research goal has been achieved by creating a functionally graded material (FGM) interface between SiC and the selected structural material with the help of powder metallurgy (PM) approach and demonstrate intimate metallurgical bonding between monolithic RB-SiC and 316L stainless steel alloy blanks.

36 MATERIALS SCIENCE

High-Fidelity Micromechanics Model Developed for the Response of Multiphase Materials

A new high-fidelity micromechanics model has been developed under funding from the NASA Glenn Research Center for predicting the response of multiphase materials with arbitrary periodic microstructures. The model's analytical framework is based on the homogenization technique, but the method of solution for the local displacement and stress fields borrows concepts previously employed in constructing the higher order theory for functionally graded materials. The resulting closed-form macroscopic and microscopic constitutive equations, valid for both uniaxial and multiaxial loading of periodic materials with elastic and inelastic constitutive phases, can be incorporated into a structural analysis computer code. Consequently, this model now provides an alternative, accurate method.

Aboudi, Jacob

High-Fidelity Generalization Method of Cells for Inelastic Periodic Multiphase Materials

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress said inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model, and with finite-element results for transverse loading.

Aboudi, Jacob

HFGMC Enhancement of MAC/GMC

Additional information about a mathematical model denoted the high-fidelity generalized method of cells (HFGMC) and implementation of the HFGMC within version 4.0 of the MAC/GMC software has become available. MAC/GMC (Micromechanics Analysis Code With Generalized Method of Cells) was a topic of several prior NASA Tech Briefs articles, version 4.0 having been described in "Comprehensive Micromechanics-Analysis Code - Version 4.0" (LEW-17495-1), NASA Tech Briefs, Vol. 29, No. 9 (September 2005), page 54. MAC/GMC predicts elastic and inelastic thermomechanical responses of composite materials. MAC/GMC utilizes the generalized method of cells (GMC) - a model of micromechanics that predicts macroscopic responses of a composite material as functions of the properties, sizes, shapes, and responses of its constituents (e.g., matrix and fibers). The accuracy of the GMC is limited by neglect of coupling between normal and shear stresses. The HFGMC was developed by combining elements of the GMC and a related model, denoted the higher-order theory for functionally graded materials (HOTFGM), that can account for this coupling. Hence, the HFGMC enables simulation of stress and strain with greater accuracy. Some alterations of the MAC/GMC data structure were necessitated by the greater computational complexity of the HFGMC.

Arnold, Steven M.

The Analysis of Adhesively Bonded Advanced Composite Joints Using Joint Finite Elements

The design and sizing of adhesively bonded joints has always been a major bottleneck in the design of composite vehicles. Dense finite element (FE) meshes are required to capture the full behavior of a joint numerically, but these dense meshes are impractical in vehicle-scale models where a course mesh is more desirable to make quick assessments and comparisons of different joint geometries. Analytical models are often helpful in sizing, but difficulties arise in coupling these models with full-vehicle FE models. Therefore, a joint FE was created which can be used within structural FE models to make quick assessments of bonded composite joints. The shape functions of the joint FE were found by solving the governing equations for a structural model for a joint. By analytically determining the shape functions of the joint FE, the complex joint behavior can be captured with very few elements. This joint FE was modified and used to consider adhesives with functionally graded material properties to reduce the peel stress concentrations located near adherend discontinuities. Several practical concerns impede the actual use of such adhesives. These include increased manufacturing complications, alterations to the grading due to adhesive flow during manufacturing, and whether changing the loading conditions significantly impact the effectiveness of the grading. An analytical study is conducted to address these three concerns. Furthermore, proof-of-concept testing is conducted to show the potential advantages of functionally graded adhesives. In this study, grading is achieved by strategically placing glass beads within the adhesive layer at different densities along the joint. Furthermore, the capability to model non-linear adhesive constitutive behavior with large rotations was developed, and progressive failure of the adhesive was modeled by re-meshing the joint as the adhesive fails. Results predicted using the joint FE was compared with experimental results for various joint configurations, including double cantilever beam and single lap joints.

Stapleton, Scott E.

Functionally Graded Adhesives for Composite Joints

Adhesives with functionally graded material properties are being considered for use in adhesively bonded joints to reduce the peel stress concentrations located near adherend discontinuities. Several practical concerns impede the actual use of such adhesives. These include increased manufacturing complications, alterations to the grading due to adhesive flow during manufacturing, and whether changing the loading conditions significantly impact the effectiveness of the grading. An analytical study is conducted to address these three concerns. An enhanced joint finite element, which uses an analytical formulation to obtain exact shape functions, is used to model the joint. Furthermore, proof of concept testing is conducted to show the potential advantages of functionally graded adhesives. In this study, grading is achieved by strategically placing glass beads within the adhesive layer at different densities along the joint.

Stapleton, Scott E.

Development of direct ink write radially graded alumina/zirconia

Functionally graded materials (FGMs) are of interest in multiple fields, yet many materials combinations are limited by coefficient of thermal expansion (CTE) mismatch. Here, a radially graded alumina/yttria-doped zirconia (Al 2 O 3 /8YZ) FGM is used to demonstrate processing strategies to mitigate CTE and sintering behavior differences between these oxides. FGM materials are especially sensitive to ink stability during printing, as all components (in this case, Al 2 O 3 and 8YZ) must be stabilized in the same dispersant or additive solution. Thus, this system is also ideal to demonstrate ink optimization best practices. Materials were characterized throughout processing to correlate the effects of common additives on both the ceramic particle suspensions and final sintered components. Aggregation observed in the initial additive-containing suspensions were present in the sintered component. The differences in sintering onset temperature and shrinkage rate resulted in internal stresses within the sintered component, which ultimately caused mechanical failure of the component under low stress. In conclusion, a processing strategy was recommended to mitigate the sintering behavior mismatch of alumina and 8 wt% yttria-stabilized zirconia.

Lamm, Benjamin W. [Oak Ridge National Laboratory (

Systematic analysis of melt pool dynamics in laser processing of mixed powder feedstocks

Functionally graded materials (FGMs) fabricated via additive manufacturing of blended powders offer the potential to spatially tailor properties for new technologies, such as fusion first-wall systems, turbine blades, and spacecraft. However, processing these materials is difficult due to the multiplicity of processing parameters to optimize, all of which must be changed as substrate material, powder feedstock compositions, and melt pool dynamics evolve. Here, this work systematically evaluates the qualitative and quantitative effects of these variables on the melt pool size, shape, composition, and particle distribution in an exemplar Ti-Ta system, and connects the experimental results to Marangoni flow behavior and phenomena observed in other systems. Increasing laser power linearly increases melt pool size and layer thickness, driving engineering considerations such as part/geometrical tolerances. Decreasing laser velocity changes the melt pool shape from lenticular to convex and reduces chemical homogeneity due to extreme thermal and compositional gradients between the melt pool center and boundaries. Thermophysical property differences between the powder feedstock and substrate material, as well as the directionality of the gradient, affect dilution and melt pool dynamics, which in turn affect the melt pool boundary characteristics, shape, and uniformity. Mixed powder feedstocks of intermediate compositions do not behave according to linear interpolations between single-material endpoints, instead building taller and wider melt pools. As such, it is recommended to quantify process maps for at least one intermediate composition in the FGM or multi-material system of interest to ensure optimized processing parameters, predictable melt pool sizes and shapes, and compositional and spatial precision.

Dissimilar

The Effect of Interface Roughness and Oxide Film Thickness on the Inelastic Response of Thermal Barrier Coatings to Thermal Cycling

The effects of interfacial roughness and oxide film thickness on thermally-induced stresses in plasma-sprayed thermal barrier coatings subjected to thermal cycling are investigated using the recently developed higher-order theory for functionally graded materials. The higher-order theory is shown to be a viable alternative to the finite-element approach, capable of modeling different interfacial roughness architectures in the presence of an aluminum oxide layer and capturing the high stress gradients that occur at the top coat/bond coat interface. The oxide layer thickness is demonstrated to have a substantially greater effect on the evolution of residual stresses than local variations in interfacial roughness. Further, the location of delamination initiation in the top coat is predicted to change with increasing oxide layer thickness. This result can be used to optimize the thickness of a pre-oxidized layer introduced at the top coat/bond coat interface in order to enhance TBC durability as suggested by some researchers. The results of our investigation also support a recently proposed hypothesis regarding delamination initiation and propagation in the presence of an evolving bond coat oxidation, while pointing to the importance of interfacial roughness details and specimen geometry in modeling this phenomenon.

Pindera, Marek-Jerzy

End Effects and Load Diffusion in Composite Structures

The research carried out here builds on our previous NASA supported research on the general topic of edge effects and load diffusion in composite structures. Further fundamental solid mechanics studies were carried out to provide a basis for assessing the complicated modeling necessary for large scale structures used by NASA. An understanding of the fundamental mechanisms of load diffusion in composite subcomponents is essential in developing primary composite structures. Specific problems recently considered were focussed on end effects in sandwich structures and for functionally graded materials. Both linear and nonlinear (geometric and material) problems have been addressed. Our goal is the development of readily applicable design formulas for the decay lengths in terms of non-dimensional material and geometric parameters. Analytical models of load diffusion behavior are extremely valuable in building an intuitive base for developing refined modeling strategies and assessing results from finite element analyses. The decay behavior of stresses and other field quantities provides a significant aid towards this process. The analysis is also amenable to parameter study with a large parameter space and should be useful in structural tailoring studies.

Horgan, Cornelius O.

Development of HVOF Sprayed Erosion/Oxidation Resistant Coatings for Composite Structural Components in Propulsion Systems

Thermally sprayed coatings are being studied and developed as methods of enabling lightweight composites to be used more extensively as structural components in propulsion applications in order to reduce costs and improve efficiency through weight reductions. The primary goal of this work is the development of functionally graded material [FGM] polymer/metal matrix composite coatings to provide improved erosion/oxidation resistance to polyimide-based polymer matrix composite [PMC] substrates. The goal is to grade the coating composition from pure polyimide, similar to the PMC substrate matrix on one side, to 100 % WC-Co on the other. Both step-wise and continuous gradation of the loading of the WC-Co reinforcing phase are being investigated. Details of the coating parameter development will be presented, specifically the high velocity oxy-fuel [HVOF] combustion spraying of pure PMR-11 matrix material and layers of various composition PMR-II/WC-Co blends onto steel and PMR-15 composite substrates. Results of the HVOF process optimization, microstructural characterization, and analysis will be presented. The sprayed coatings were evaluated using standard metallographic techniques - optical and scanning electron microscopy [SEM]. An SEM + electron dispersive spectroscopy [EDS] technique has also been used to confirm retention of the PMR-II component. Results of peel/butt adhesion testing to determine adhesion will also be presented.

Knight, R.