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DOE OSTI2025

SEM Milestone Report for MARMOT Validation Project

MARMOT is a meso-scale fuel code under development by NEAMS designed to predict the microstructure evolution of fuel materials to determine updated thermal and mechanical property models. These updated models can be used by engineering scale codes such as BISON. To support its development and validation the MARMOT Validation Project (MVP) was initiated and consists of extensive microstructure and thermal characterization of U-10Zr fuel material before and at discreet levels of irradiation. This report summarizes the SEM and EDS characterization of the lowest burnup samples (1.5% FIMA) and how they compare to pre-irradiation SEM and EDS.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Mechanical Behavior of Neutron Irradiated Refractory Multi-Principal Element Alloys Processed via Spark Plasma Sintering

The search for advanced materials capable of withstanding the extreme conditions of Generation IV reactors is a critical area in materials science research. These reactors operate under severe environments, including high temperatures, corrosion, stress, and irradiation damage. Consequently, there is a need for innovative alloy systems to ensure the reliability and longevity of proposed Generation IV reactor components. Refractory multi-principal-element alloys (RMPEA) have emerged as a promising candidate due to their exceptional properties. These alloys, characterized by their composition of multiple principal elements in near-equiatomic ratios, exhibit superior resistance to irradiation damage, reduced void swelling, enhanced microstructural stability, and minimal irradiation-induced hardening. While initial studies on RMPEAs have shown promising results, most research has been limited to thin films, nanocrystalline microstructures, and ion irradiation, which do not accurately represent the behavior of bulk materials. To address this gap, our research focused on the neutron irradiation of bulk RMPEAs. We aim to conduct comprehensive post-irradiation examinations (PIE) of RMPEAs irradiated at the Advanced Test Reactor at Idaho National Laboratory. The RMPEAs were synthesized using spark plasma sintering (SPS) with mechanically alloyed metallurgical powder. The RMPEA specimens are a MoNbTi alloy system with additions of -Zr, and -ZrV. Furthermore, PIE consisted of mechanical testing and advanced materials characterization. The mechanical testing consisted of sub-sized tensile testing, micro- and nano- indentation. Microstructural characterization included scanning electron microscopy and transmission electron microscopy. Mechanical testing coupled with advanced microscopy techniques provides insight into phase morphology and its effects on the mechanical properties of the RMPEA specimens. The results indicate that both pristine and irradiated RMPEA specimens exhibited brittle behavior during tensile testing, which can be attributed to their heterogeneous microstructure. The SPS manufacturing process did not include any post treatment, which resulted in a heterogeneous microstructure. Energy-dispersive X-ray spectroscopy revealed the presence of intermetallic such as laves phases within the microstructure. Specifically, Ti-rich precipitates were observed in the MoNbTi specimen, while Mo-rich precipitates were found in the MoNbTiZrV specimen. Nano-hardness testing of pristine samples showed that the laves phases exhibited higher hardness values compared to the matrix phase, suggesting that precipitate hardening is likely the dominant hardening mechanism in these specimens. The results from this work will be used to build a finite element model to predict mechanical behavior of future MPEA compositions. Thus, enabling for a streamlined approach to developing novel MPEAs for the nuclear industry.

36 - MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Zircon (U-Th)/He Impact Crater Thermochronometry and the Effects of Shock Microstructures on Helium Diffusion Kinetics

Accurate and precise age determination of impact cratering events remains challenging and often contentious; less than half of all known craters are regarded as accurately and precisely dated. Zircon (U-Th)/He (ZHe) dating of impactites can be employed to date medium to large impact structures as ZHe ages can be fully reset in minutes at T >1000°C, a plausible scenario in the central melt pool. In contrast, complete resetting of ZHe at 200-300°C, encountered near the crater margins or due to post-impact hydrothermal overprinting, may take >103-6 years. To test the reliability of ZHe impact dating, we have quantified the effects of shock-induced microstructures on helium diffusion kinetics in well-characterized variably shocked zircon. We investigated samples from two impact structures, the Chicxulub multi-ring crater and Ries complex crater, to compare diffusion kinetics from structures with different size, age, and hydrothermal system longevity. Shock microstructures were characterized by backscattered-electron imaging prior to determining the He diffusion kinetics by prograde and retrograde fractional-release experiments via light-bulb furnace with incremental step-heating (10°C) from 300°C to 600°C. Next, we examine the internal interconnectivity and sizes of the diffusion domains by EBSD. While we found that zircon with few shock microstructures exhibited no marked deviation from helium diffusion kinetics of undamaged zircon, zircon grains with planar microstructures and granular textures are characterized by a dramatic decrease in helium retentivity due to the reduction in the effective domain size and the introduction of interconnected fast diffusion pathways. A subset of grains were ZHe dated and showed that less deformed grains yielded a weighted mean age within error of the accepted impact ages, while the grains with planar microstructures or granular textures gave systematically younger ages. These new diffusion data and ZHe ages demonstrate that highly shocked grains are unsuitable for ZHe impact crater dating. Therefore, detailed characterization of impact-induced microstructures is critical for determining accurate ZHe impact ages and offers the possibility of investigating post-impact hydrothermal circulation.

Zircon↗

DOE OSTI2026

The effect of varying powder feedstock chemistry and printing atmosphere on the microstructure of additively manufactured nickel-based ODS alloys: Role on stabilization of cellular structures vs. oxide dispersion formation

Nickel-based alloys have a wide variety of structural applications due to their high corrosion resistance and mechanical strength which depend on solid solution strengthening, or the formation of oxides and/or intermetallic precipitation for their properties. In this study, the microstructure of six Ni–Cr–Y–Ti–Al powder batches designed for the production of oxide dispersion strengthened nickel were compared. These batches varied in chemistry and atomization technique used which included Gas Atomization Reactive Synthesis (GARS). The batches of powder were then consolidated via Additive Manufacturing (AM) Powder Bed Fusion using Laser Beam (PBF-LB) and characterized via transmission electron microscopy to elucidate the influence of powder feedstock (i.e. synthesis methodology and chemistry) on the PBF-LB microstructure. The study investigates (i) how the amount of yttrium and titanium additions in the powder feedstock and the addition of oxygen during the processing (through GARS) affect the microstructure of the powder itself and the AM printed microstructure, and (ii) how the control of oxygen addition in the printing atmosphere during the PBF-LB printing process itself is another important parameter for achieving the formation of the wanted oxide dispersion versus the stabilization of the cellular structure (often observed in AM processed alloys). Microstructural characterization of both powder particles and additively manufactured nickel alloys in this study provide important insights into the movement of yttrium within the material upon solidification, particularly along cell boundaries, and how yttrium behaves depending on alloy chemistry. When a threshold of yttrium content is reached within the system, yttrium consistently reacts to form an intermetallic along cell boundaries instead of forming oxide nanoparticles.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Microstructure-Based Understanding of High-Temperature Deformation Behaviors in Laser Powder Bed Fusion (LPBF) 316H Stainless Steel

This report presents the results of high-temperature mechanical property testing and microstructural analysis of laser powder bed fusion (LPBF) 316H stainless steel (SS) conducted during Fiscal Year 2025 (FY25) under the U.S. Department of Energy, Office of Nuclear Energy’s Advanced Materials and Manufacturing Technologies (AMMT) program. The study builds upon prior work by expanding the mechanical property test matrix and advancing a microstructure-based mechanistic understanding of LPBF 316H SS performance, with a focus on the solution annealed (SA, 1100°C for 1 hour) materials. High-temperature tension, creep, fatigue, and creep-fatigue tests were performed. Thermal aging studies were conducted. Advanced characterization techniques, including scanning electron microscopy (SEM), scanning transmission electron microscopy (STEM), and high-energy synchrotron X-ray diffraction, were employed to investigate the microstructural evolution during thermal aging and mechanical testing. It was discovered that the as-built (AB) LPBF 316H SS exhibited precipitation kinetics during thermal aging that are 10–100 times faster than its wrought counterpart due to the presence of high densities of preferred nucleation sites, while the precipitation kinetics in SA LPBF 316H was under investigation. The accelerated precipitation of embrittling phases such as sigma phase in LPBF 316H SS compared to its wrought counterpart led to significant impacts on creep ductility. The influence of laser printing parameters and build orientations on fatigue and creep-fatigue performance was observed. In assessing the creep-fatigue performance, it was discovered that the SA LPBF 316H samples failed in less than 200 cycles under 595°C, 0.5% (strain amplitude) with a 60-minute hold time. This work establishes a mechanistic framework for predicting the long-term behavior of LPBF 316H SS, supporting its rapid qualification under the ASME BPVC. The findings contribute to the broader goal of enabling the deployment of advanced materials in next-generation nuclear energy systems. An outlook for FY26 work, including continued aging studies, mechanical testing, and microstructural characterization, is provided.

36 MATERIALS SCIENCE↗

NASA NTRS2020

Shock Deformation in Zircon, a Comparison of Results from Shock-Reverberation and Single-Shock Experiments

The utility of the mineral zircon, ZrSiO4, as a shock-metamorphic geobarometer and geochronometer, has been steadily growing within the planetary science community. Zircon is an accessory phase found in many terrestrial rock types, lunar samples, lunar meteorites, martian meteorites and various other achondrites. Because zircon is refractory and has a high closure temperature for Pb diffusion, it has been used to determine the ages of some of the oldest material on Earth and elsewhere in the Solar System. Furthermore, major (O) and trace-element (REE, Ti, Hf) abundances and isotope compositions of zircon help characterize the petrogenetic environments and sources from which they crystallized. The response of zircon to impact-induced shock deformation is predominantly crystallographic, including dislocation creep and the formation of planar and sub-planar, low-angle grain boundaries; the formation of mechanical {112} twins; transformation to the high pressure polymorph reidite; the development of polycrystalline microtextures; and dissociation to the oxide constituents SiO2 and ZrO2. Shock microstructures can also variably affect the U- Pb isotope systematics of zircon and, in some instances, be used to constrain the impact age. While numerous studies have characterized shock deformation in zircon recovered from a variety of terrestrial impact craters and ejecta deposits and Apollo samples, experimental studies of shock deformation in zircon are limited to a handful of examples in the literature. In addition, the formation conditions (e.g., P, T) of various shock microstructures, such as planar-deformation bands, twins, and reidite lamellae, remain poorly con-strained. Furthermore, previous shocked-zircon experimental charges have not been analyzed using modern analytical equipment. This study will therefore under-take an new set of zircon shock experiments, which will then be microstructurally characterized using state-of-the-art instrumentation within the Astromaterials Research and Exploration Science Division (ARES), NASA Johnson Space Center.

Erickon, T. M.↗

DOE OSTI2024

Deep-learning based artificial intelligence tool for melt pools and defect segmentation

Accelerating fabrication of additively manufactured components with precise microstructures is important for quality and qualification of built parts, as well as for a fundamental understanding of process improvement. Accomplishing this requires fast and robust characterization of melt pool geometries and structural defects in images. This paper proposes a pragmatic approach based on implementation of deep learning models and self-consistent workflow that enable systematic segmentation of defects and melt pools in optical images. Deep learning is based on an image-to-image translation–conditional generative adversarial neural network architecture. An artificial intelligence (AI) tool based on this deep learning model enables fast and incrementally more accurate predictions of the prevalent geometric features, including melt pool boundaries and printing-induced structural defects. We present statistical analysis of geometric features that is enabled by the AI tool, showing strong spatial correlation of defects and the melt pool boundaries. The correlations of widths and heights of melt pools with dataset processing parameters show the highest sensitivity to thermal influences resulting from laser passes in adjacent and subsequent layer passes. The presented models and tools are demonstrated on the aluminum alloy and datasets produced with different sets of processing parameters. However, they have universal quality and could easily be adapted to different material compositions. The method can be easily generalized to microstructural characterizations other than optical microscopy.

additive manufacturing↗

NASA NTRS1992

A preliminary characterization of the tensile and fatigue behavior of tungsten-fiber/Waspaloy-matrix composite

A microstructural study and a preliminary characterization of the room temperature tensile and fatigue behavior of a continuous, tungsten fiber, Waspaloy-matrix composite was conducted. A heat treatment was chosen that would allow visibility of planar slip if it occurred during deformation, but would not allow growth of the reaction zone. Tensile and fatigue tests showed that the failed specimens contained transverse cracks in the fibers. The cracks that occurred in the tensile specimen were observed at the fracture surface and up to approximately 4.0 mm below the fracture surface. The crack spacing remained constant along the entire length of the cracked fibers. Conversely, the cracks that occurred in the fatigue specimen were only observed in the vicinity of the fracture surface. In instances where two fiber cracks occurred in the same plane, the matrix often necked between the two cracked fibers. Large groups of slip bands were generated in the matrix near the fiber cracks. Slip bands in the matrix of the tensile specimen were also observed in areas where there were no fiber cracks, at distances greater than 4 mm from the fracture surface. This suggests that the matrix plastically flows before fiber cracking occurs.

Corner, Ralph E.↗

DOE OSTI2025

Bridging multimodal microscopy for advanced characterization on nuclear fuel using machine learning

Uranium dioxide (UO 2 ), widely used as driver fuel in light water reactors, experiences microstructure and property change by nuclear fission reactions. This paper bridges the characterization of fresh UO 2 fuel at different length scales, serving as a baseline for future post irradiation examination of irradiated UO 2 fuel. To characterize the microstructural change of nuclear fuel, modern approaches cover a wide range of length scales through different characterization techniques, such as mm scale for Synchrotron-based X-ray computed tomography (SXCT) and microscale for focused ion beam (FIB) and scanning electron microscopy (SEM). It is challenging to bridge the data and knowledge of the same sample in different length scales. This paper proposed a deep learning framework leveraging transfer learning to detect microstructural defects, trained from a sparse FIB, SEM, and SXCT images. The proposed model achieved superior performance in defect segmentation on multiscale microscopic data compared to four of the latest deep learning models.

36 MATERIALS SCIENCE↗

NASA NTRS2006

High-Performance Scanning Acousto-Ultrasonic System

A high-performance scanning acousto-ultrasonic system, now undergoing development, is designed to afford enhanced capabilities for imaging microstructural features, including flaws, inside plate specimens of materials. The system is expected to be especially helpful in analyzing defects that contribute to failures in polymer- and ceramic-matrix composite materials, which are difficult to characterize by conventional scanning ultrasonic techniques and other conventional nondestructive testing techniques. Selected aspects of the acousto-ultrasonic method have been described in several NASA Tech Briefs articles in recent years. Summarizing briefly: The acousto-ultrasonic method involves the use of an apparatus like the one depicted in the figure (or an apparatus of similar functionality). Pulses are excited at one location on a surface of a plate specimen by use of a broadband transmitting ultrasonic transducer. The stress waves associated with these pulses propagate along the specimen to a receiving transducer at a different location on the same surface. Along the way, the stress waves interact with the microstructure and flaws present between the transducers. The received signal is analyzed to evaluate the microstructure and flaws. The specific variant of the acousto-ultrasonic method implemented in the present developmental system goes beyond the basic principle described above to include the following major additional features: Computer-controlled motorized translation stages are used to automatically position the transducers at specified locations. Scanning is performed in the sense that the measurement, data-acquisition, and data-analysis processes are repeated at different specified transducer locations in an array that spans the specimen surface (or a specified portion of the surface). A pneumatic actuator with a load cell is used to apply a controlled contact force. In analyzing the measurement data for each pair of transducer locations in the scan, the total (multimode) acousto-ultrasonic response of the specimen is utilized. The analysis is performed by custom software that extracts parameters of signals in the time and frequency domains. The computer hardware and software provide both real-time and postscan processing and display options. For example, oscilloscope displays of waveforms and power spectral densities are available in real time. Images can be computed while scanning continues. Signals can be digitally preprocessed and/or post-processed by filtering, windowing, time-segmenting, and running-waveform-averaging algorithms. In addition, the software affords options for off-line simulation of the waveform-data-acquisition and scanning processes. In tests, the system has been shown to be capable of characterizing microstructural changes and defects in SiC/SiC and C/SiC ceramic-matrix composites. Delaminations, variations in density, microstructural changes attributable to infiltration by silicon, and crack-space indications (defined in the next sentence) have been revealed in images formed from several time- and frequency-domain parameters of scanning acousto-ultrasonic signals. The crack-space indications were image features that were not revealed by other nondestructive testing methods and are so named because they turned out to mark locations where cracking eventually occurred.

Roth, Don↗

NASA NTRS2020

A Computational Study to Investigate the Effect of Defect Geometries on the Fatigue Crack Driving Forces in Powder-Bed AM Materials

Powder-bed additive manufacturing (AM) processes are associated with the formation of multiple types of process-specific pores, including but not limited to lack-of-fusion (LoF) and keyhole pores. The performance of an AM component is dependent on the type of pores, their density and their proximity to the free surface, and other heterogeneities in the microstructure. In order to characterize the influence of porosity on the mechanical behavior of AM materials, it is imperative to quantitatively analyze the heterogeneous strain accumulation in the vicinity of porosity. Process-specific microstructure models are generated using SPPARKS, an open-source process simulation code. Spherical keyhole or irregular LoF pores are embedded into the microstructure models, which are meshed and input into a finite element code, ScIFEN, to solve for the heterogeneous strain localization in the vicinity of the pores. Given the non-smooth geometries of LoF pores, they readily promote strain accumulation in their vicinity thereby increasing the propensity of initiating fatigue cracks.

Saikumar R Yeratapally↗

DOE OSTI2026

Degradation science: Integrating modeling and experiments to predict localized corrosion processes (Annual Progress Report)

Additively manufactured (AM) eutectic high-entropy alloys (EHEAs), such as nano-lamellar AlCoCrFeNi 2.1 , have excellent strength, ductility, and wear resistance even at elevated temperatures, but their corrosion behavior in aggressive acids at different length scales remain poorly understood. This work investigates the corrosion behavior of laser powder bed–fused (L-PBF) AlCoCrFeNi 2.1 as a function of annealing temperatures, probing degradation mechanisms from nanoscopic to macroscopic length scales. The alloy is dual phase consisting of a ductile FCC L1 2 phase and a high-strength BCC B2 phase. Rapid solidification during L-PBF produces a far-from-equilibrium nano-lamellar structure with nearly homogeneous elemental distribution, which tends to evolve upon annealing toward Cr/Co/Fe-enriched FCC and Al/Ni-enriched B2. Three conditions were studied: as-printed, 600 °C/5 h, and 1000 °C/1 h, over which B2 lamellae coarsen, lamellar spacing increases, and elemental segregation becomes more prominent. Microstructure and chemistry were characterized by scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS), while in-situ electrochemical atomic force microscopy (EC-AFM) was used to link early (<5 h) local dissolution to microstructure after exposure in sulfuric acid. EC-AFM highlights preferential dissolution of the BCC/B2 phase where the surrounding matrix is Cr-depleted and directly quantifies the dissolution rates within individual phases, tracks the transition from early nano-scale attack to partial repassivation, to correlate height differences with current and impedance responses. To monitor longer-term behavior (up to 96 h), ex-situ AFM, SEM, and confocal imaging were combined with conventional bulk electrochemical tests, bridging nanoscale observations to micro/meso-scale damage morphologies. At the meso-scale, the deepest dissolution channels align with the build-direction lamellae and melt-pool boundaries, indicating that printing directionality guides the propagation of these localized corrosion sites. Annealing modifies corrosion by restructuring BCC/FCC phase fractions, lamellar spacing, and Cr/Al segregation, thereby changing the cathode/anode ratio and passive film stability. The results clarify how as-printed and annealed nano-lamellar architectures differ in their susceptibility to selective dissolution; how elemental segregation competes with residual stresses along the build direction. With these insights, future work will use CALPHAD-guided alloy modification to stabilize higher Cr contents in the B2 phase while retaining a dominant FCC+B2/BCC microstructure, with the goal of designing mechanically robust, corrosion-resistant EHEAs for safety-critical applications to leverage the LLNL’s broader national and global security mission.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Bridging length scales in hard materials with ultra-small angle X-ray scattering – a critical review

Owing to their exceptional properties, hard materials such as advanced ceramics, metals and composites have enormous economic and societal value, with applications across numerous industries. Understanding their microstructural characteristics is crucial for enhancing their performance, materials development and unleashing their potential for future innovative applications. However, their microstructures are unambiguously hierarchical and typically span several length scales, from sub-ångstrom to micrometres, posing demanding challenges for their characterization, especially for in situ characterization which is critical to understanding the kinetic processes controlling microstructure formation. This review provides a comprehensive description of the rapidly developing technique of ultra-small angle X-ray scattering (USAXS), a nondestructive method for probing the nano-to-micrometre scale features of hard materials. USAXS and its complementary techniques, when developed for and applied to hard materials, offer valuable insights into their porosity, grain size, phase composition and inhomogeneities. We discuss the fundamental principles, instrumentation, advantages, challenges and global status of USAXS for hard materials. Using selected examples, we demonstrate the potential of this technique for unveiling the microstructural characteristics of hard materials and its relevance to advanced materials development and manufacturing process optimization. We also provide our perspective on the opportunities and challenges for the continued development of USAXS, including multimodal characterization, coherent scattering, time-resolved studies, machine learning and autonomous experiments. Our goal is to stimulate further implementation and exploration of USAXS techniques and inspire their broader adoption across various domains of hard materials science, thereby driving the field toward discoveries and further developments.

36 MATERIALS SCIENCE↗

NASA NTRS2016

Additive Manufacturing and Characterization of Polylactic Acid (PLA) Composites Containing Metal Reinforcements

Additive manufacturing of polymeric systems using 3D printing has become quite popular recently due to rapid growth and availability of low cost and open source 3D printers. Two widely used 3D printing filaments are based on polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS) systems. PLA is much more environmentally friendly in comparison to ABS since it is made from renewable resources such as corn, sugarcane, and other starches as precursors. Recently, polylactic acid-based metal powder containing composite filaments have emerged which could be utilized for multifunctional applications. The composite filaments have higher density than pure PLA, and the majority of the materials volume is made up of polylactic acid. In order to utilize functionalities of composite filaments, printing behavior and properties of 3-D printed composites need to be characterized and compared with the pure PLA materials. In this study, pure PLA and composite specimens with different metallic reinforcements (Copper, Bronze, Tungsten, Iron, etc) were 3D printed at various layer heights and resulting microstructures and properties were characterized. Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) behavior of filaments with different reinforcements were studied. The microscopy results show an increase in porosity between 3-D printed regular PLA and the metal composite PLA samples, which could produce weaker mechanical properties in the metal composite materials. Tensile strength and fracture toughness behavior of specimens as a function of print layer height will be presented.

brass↗

NASA NTRS2000

Characterizing the Use of Ultrasonic Energy in Promoting Uniform Microstructural Dispersions in Immiscible Mixtures

Gravity driven separation and preferential wetting precludes uniform microstructural distributions during solidification processing of immiscible, liquid-liquid mixtures. Historically, it is, however, established that liquid/liquid suspensions can be established and maintained by utilizing ultrasound. Following a brief introduction the results of experiments on immiscible mixtures subjected to ultrasonic energy during solidification processing will be compared and evaluated in view of a recently developed mathematical model. The presentation continues by discussion of scaling the model to commercial viability and concludes with the implications of such processing in a microgravity environment.

Grugel, R. N.↗

NASA NTRS2001

Characterizing the Use of Ultrasonic Energy in Promoting Uniform Microstructural Dispersions in Immiscible Mixtures

Grugel, R. N.↗

NASA NTRS1993

The influence of a microgravity environment on the dendritic morphology during directional solidification of hypoeutectic Al-Si alloys

NASA grant NAGW-2540 provided the opportunity to evaluate and extend ongoing studies of directionally solidified Al-Si alloys. Microstructural development was further characterized in terms of solidification processing parameters; novel relationships between processing and development of dendrite trunk diameters and tertiary dendrite arm spacings were found. This has resulted in three publications (one in print, one in press, and one in review). Microstructural development under conditions of controlled acceleration during directional solidification has been investigated; this has culminated in a Master's degree and will be submitted for publication. The above work not only contributes to our understanding of solidification phenomena but also defines the processing parameters for a successful microgravity experiment while providing a data base to which mu g samples can be unequivocally compared and evaluated.

Grugel, Richard N.↗

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↗