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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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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Time at Temperature Abstract and Intern Poster

Current NRC regulations for BWR operations dictate that any occurrence reaching the point of Departure from Nucleate Boiling (DNB) disqualifies the use of the fuel rod for further reactor operation. That criteria does not account for duration of rate of the power increase, the corresponding effects on material properties or rewetting that may occur. Previous Anticipated Operational Occurrences (AOOs) show short durations power increase that may require limited amounts of heat removal. Industrial experience has shown evidence that fuel can reach dryout yet continue to safely operate in regular reactor conditions. The gap in research into such occurrences is the motivation for a series of experiments, including this current work. Time-at-Temperature experiments aim to identify and characterize the microstructural changes in Zircaloy-2 under oxygen-free high temperatures. This work uses the FlashDSC instrument to rapidly ramp up and down the temperature of a focus ion beam (FIB) prepared large area lift-out (LALO) of Zircaloy-2 at a rate of 10,000 K/s to desired values. The focus is to characterize the microstructure evolution, if any, of Zircaloy-2 that may impact its performance under typical BWR conditions. This characterization includes analyzing grain structure and size, secondary phase particle (SPPs) size, shape, composition, and location using Transmission Electron Microscopy (TEM). Further data collection and analysis is in progress including diffraction pattern indexing and 4D STEM processing. While current results focus on the testing and characterizing unirradiated material, future plans include expansion to irradiated material to explore the effects of rapid transition rates seen in DNB and dryout conditions on irradiationg damage and defect annealing.

36 - MATERIALS SCIENCE↗
DOE OSTI2026

Robust dynamic operation of high temperature electrolysis solid oxide cells

Here, this study evaluates the durability of Ni/YSZ-supported SOECs under dynamic operating conditions relevant to real-world applications. Systematic tests were conducted to assess cell performance under steam cycling (3 to 75% humidified H 2 ), mode cycling between SOFC and SOEC operation, thermal cycling (150 to 750 °C at OCV, and 600 to 800 °C at 1.3V), and redox cycling (between 50% humidified H 2 and 50% humidified N 2 ). Steam cycling, mode cycling, and thermal cycling at OCV do not significantly accelerate performance degradation. Thermal cycling at 1.3V caused minimal damage within 600 to 800 °C. Full redox cycling (multi-hour oxidation holds) induced cell structural failure, while partial redox cycling (0.5 h holds) was tolerated. Extensive characterization revealed some material evolution, namely Sr and Co secondary phase formation, within the oxygen electrode due to La 0.6 Sr 0.4 Co 0.2 Fe 0.8 O 3-δ instability, especially for steam cycling and mode cycling. Minimal changes were identified within the Ni-YSZ fuel electrodes. These findings provide critical insights into SOEC reliability under dynamic conditions, supporting their application in dynamic or intermittent energy systems.

08 HYDROGEN↗
DOE OSTI2020

Imaging grain microstructure in a model ceramic energy material with optically generated coherent acoustic phonons

Characterization of microstructure, chemistry and function of advanced energy materials remains a challenge for instrumentation science with tremendous opportunity for new discoveries. This active area of research is starting to make considerable strides with examples ranging from methodologies that employ bright X-rays, electron microscopy and optical spectroscopy. However, further development of instruments, capable of multimodal measurements, is necessary to fully reveal complex microstructure evolution in realistic environments and dynamical systems that are far from equilibrium. In this regard, laser-based instruments have a unique advantage as multiple measurement methodologies are easily combined into a single instrument using standard optics. A new pump-probe method that uses optically generated acoustic phonons is expanding standard optical characterization by providing depth resolved information. Here we report on a noteworthy extension of this pump-probe method to image grain microstructure in ceria. Rich information regarding the orientation of individual crystallites is obtained by monitoring acoustic phonon velocities and noting how the polarization of the probe beam influences the detected signal amplitude. When paired with other optical microscopies, this methodology will provide new perspectives for optical characterization of ceramic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Microstructural, Corrosion, and Mechanical Characterization of Friction Stir Welded Al 6022-to-ZEK100 Mg Joints

Friction stir welded (FSW) aluminum–magnesium lightweight vehicle joints have gained significant interest due to their high strength-to-weight ratio. In this work, the corrosion resistance of this material is analyzed through electrochemical tests, which include open circuit potential (OCP) inspection and potentiodynamic polarization (PD) scanning. Weight loss measurements tested the corrosion rate of the FSW weld through cyclic corrosion testing (CCT) according to the standard SAEJ 2334. Mechanical properties were also investigated, including lap-shear strength, micro- and nano-hardness mapping, and true stress–strain curves as a function of local processing history. The electrochemical results indicate that the center weld zone’s corrosion property stays between the two base alloys. Indentation-based testing demonstrated that the weld zone behaves differently from base alloys. Lap shear strength surprisingly did not drop much even after eight weeks of cyclic corrosion tests, indicating that the joint did not allow any ingress of the electrolyte.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Phase Stability of Yttrium Titanium Oxide

This proposed study aims at elevating Idaho National Laboratory (INL)’s portfolio in nuclear material research on two major fronts: 1) expanding INL’s material characterization capabilities to provide holistic microstructural and microchemical characterization ranging from atomic scale to millimeter scale, and 2) filling the knowledge gap on the effect of microstructural evolution on material phase stability at extreme conditions resembling those inside nuclear reactors, using Yttrium-Titanium-Oxide (YTO) as a model material. Previous research indicated the kinetics of phase transition of YTO materials varies between bulk samples and powder samples, suggesting that microstructural characteristics such as defect, micro-strain, and crystallite size could play a significant role in phase transition. The effect of crystallite size on the thermodynamics of phase transition has been well documented for other ceramic materials at nanometer crystallite size, with potential impacts from surface and strain energy and defects. In this proposed study, we will perform microstructural (micro-strain, crystallite size, defects, phase) and microchemical (elemental mapping) analyses through in-situ high temperature measurements using X-ray diffraction (XRD; at millimeter scale for powder and bulk samples) and transmission electron microscopy (TEM, at nanometer scale and atomic scale for powder and thin foil samples), to provide a comprehensive view of the effect of microstructural and microchemical evolution on phase transition and phase stability of YTO materials. These findings will also establish a roadmap and provide new insights on the phase stability of other materials that are critical to nuclear energy and other renewable energy infrastructure. Besides advancing our understanding of this fundamental material science question, this project will also enable the development of state-of-the-art material characterization capabilities at INL/MFC for microstructural and microchemical analysis at high temperature conditions. The new collaboration between the High-Resolution Materials Characterization group at INL and the Electron Microscopy group at the University of Florida (UF) in this project will open the possibilities for more fruitful and synergetic cutting-edge nuclear material research in the future.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A practical guide to characterizing irradiated nuclear fuels using FIB tomography

We report focused ion beam (FIB) tomography with combined electron backscatter diffraction (EBSD) and energy dispersive x-ray spectroscopy (EDS) is a technique capable of statistically characterizing the microstructure and spatial compositional variation of nuclear fuel in three-dimensions (3D). The 3D visualization from FIB tomography provides a comprehensive picture of the interconnected microstructural and compositional features that can impact fuel performance. While these features are often characterized with surface examination, the complexity and relationship of fission products and grain boundary networks may not fully be captured by these 2D methods. This work presents a practical guide to FIB tomography that is tailored to nuclear fuel characterization. The steps used to collect and process the data are provided along with the scripts used to process the data. Additionally, suggestions for future characterization efforts utilizing this approach are given.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

In situ microstructural evolution in face-centered and body-centered cubic complex concentrated solid-solution alloys under heavy ion irradiation

This study characterizes the microstructural evolution of single-phase complex concentrated solid-solution alloy (CSA) compositions under heavy ion irradiation with the goal of evaluating mechanisms for CSA radiation tolerance in advanced fission systems. Three such alloys, Cr 18 Fe 27 Mn 27 Ni 28 , Cr 15 Fe 35 Mn 15 Ni 35 , and equimolar NbTaTiV, along with reference materials (pure Ni and E90 for the Cr-FeMnNi family and pure V for NbTaTiV) were irradiated at 50 K and 773 K with 1 MeV Kr ++ ions to various levels of displacements per atom (dpa) using in-situ transmission electron microscopy. Cryogenic irradiation resulted in small defect clusters and faulted dislocation loops as large as 12 nm in face-centered cubic (FCC) CSAs. With thermal diffusion suppressed at cryogenic temperatures, defect densities were lower in all CSAs than in their less compositionally complex reference materials indicating that point defect production is reduced during the displacement cascade stage. High temperature irradiation of the two FCC CSA resulted in the formation of interstitial dislocation loops which by 2 dpa grew to an average size of 27 nm in Cr 18 Fe 27 Mn 27 Ni 28 and 10 nm in Cr 15 Fe 35 Mn 15 Ni 35 . This difference in loop growth kinetics was attributed to the difference in Mn-content due to its effect on the nucleation rate by increasing vacancy mobility or reducing the stacking-fault energy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Microstructure and mechanical behavior of a TiC nanoprecipitate strengthened V Alloy

The V-4Cr-4Ti (V44) alloys have been proposed as the prime candidate structural material for self-cooled liquid Li blanket and other designs for fusion energy applications. However, the applications of the V44 alloy are limited to a narrow operation temperature window, due to reduction in creep strength at or above 700 °C and susceptibility to irradiation hardening and embrittlement when irradiated below 400 °C. Here, in this work, we explore the feasibility of designing a novel V alloy to form a high number density of TiC nanoprecipitates, in order to simultaneously improve creep strength and provide defect sinks to mitigate irradiation hardening. Computational thermodynamics was used to design a new alloy (V44C) to achieve our goal of high TiC nanoprecipitates density within the alloy V44 matrix. To ensure scalability, the new alloy was made through arc-melting and ingot-casting followed by hot forging, cold rolling and heat treatments of homogenization and precipitation aging. The microstructure was characterized by SEM, TEM, XRD and APT, confirming the existence of nanoprecipitates predicted in the thermodynamic calculations. In addition to microstructural evaluation tensile properties at room temperature and 700 °C, and Charpy impact energy at room temperature were measured. The microstructure and mechanical properties were then compared with those from a historic reference V44 alloy. The tensile strength improvement in V44C was rationalized based on particle and solid solution strengthening mechanism. The fracture behavior was discussed based on the fractography results and necking deformation behavior.

Alloys development↗
DOE OSTI2024

A new paradigm in electron microscopy: Automated microstructure analysis utilizing a dynamic segmentation convolutional neutral network

Over the past half century, the transmission electron microscope enabled insight into the fundamental arrangements and structures of materials. State-of-the-art electron microscopes can acquire large image datasets across multiple imaging modalities. However, the manual annotation process for feature or defect quantification may not be feasible with the modern microscope. Convolutional neural networks emerged to characterize individual microstructural features from an image in a cost-effective, consistent manner. However, many of these neural network approaches rely on thousands to hundreds of thousands of manual annotations of each feature type across hundreds of images to train the network for adequate performance. This work focused on the development and application of a pixel-wise defect detection machine-learning dynamic segmentation convolutional neural network with associated automated acquisition and postprocessing to identify microstructural features rapidly and quantitatively from a small initial dataset incorporating multiple imaging modes. The approach was demonstrated for characterization of superalloy 718 from both single image acquisition on multiple detectors to in-situ evolution captured with a single detector on a standard desktop computer to demonstrate the low barrier to entry required for widespread adoption. Pixel-by-pixel class identification was excellent with strong identification of chemically distinct phases, structurally distinct phases, and defect structures, thus demonstrating the new paradigm of machine learning-assisted characterization.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Kink mechanism in Cu/Nb nanolaminates explored by $\mathcal{in}$ $\mathcal{situ}$ pillar compression

We report Nano metallic laminates (NMLs) exhibit different failure modes depending on the loading conditions due to their mechanical anisotropies. Kinking is a typical failure mode in many NMLs compressed along a layer-parallel direction. However, a detailed description of the microstructure evolution during kink band (KB) formation and an in-depth understanding of the formation mechanisms are lacking. In this work, the KB process is investigated in Cu/Nb NMLs by in situ micro pillar compression in the scanning electron microscope (SEM) along a layer-parallel direction. Post-mortem S/TEM and transmission Kikuchi diffraction (TKD) analyses show that kink banding leads to significant microstructure changes characterized by an accumulation of geometrically necessary dislocations (GNDs) and of tilt geometrically necessary boundaries (GNBs) near KB boundaries (KBBs). The distinct microstructure evolution implies that KB formation is facilitated by the inhomogeneous microstructures resulting in constrained deformation modes. Specifically, dislocations active on slip planes nearly parallel to the interfaces make a major contribution to kink evolution after the onset of kinking. Once layer-parallel slip systems are activated, preexisting lattice dislocations and dislocations nucleating from interfaces will accumulate as GNDs near KBBs via the stochastic storage of lattice dislocations that have certain Burgers vectors. GNDs can further transform into GNBs via cross-slip and climb driven processes near the KBB. Furthermore, GNBs near KBBs can grow by incorporating more GNDs or by coalescence to accommodate the KB evolution. We further hypothesize that microstructural perturbations and their ensuing stresses can initiate KB formation in Cu/Nb NMLs.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Which way does the dendrite grow? Competition among epitaxy, preferred growth direction, and thermal gradients in powder bed fusion additive manufacturing

The as-processed microstructure of metal alloy parts manufactured through laser powder bed fusion (LPBF) is heavily derived from the cellular dendritic solidification. The growth direction of dendrites within the melt pool is determined through competition among epitaxial growth, preferred growth directions, and maximum thermal gradients. However, the dominant factor and the specific role of each in developing melt pool microstructures remain unknown. Here, in this study, we performed single laser track scans on an SS316L single crystal substrate and combined experimental characterization of microstructure and crystal orientations with Computational Fluid Dynamics simulations of thermal gradients to evaluate the role of each factor in determining dendritic growth direction and evolution. Our results reveal that epitaxial growth dominates microstructure development by preferentially growing along a single 〈100〉 variant of the single crystal substrate adjacent to the melt pool boundary. Under LPBF’s highly curved and rapidly evolving thermal field, this preferential dendrite variant selection and its continued growth from the melt pool boundary to the centerline are governed by the local temperature gradient magnitude at the solid-liquid interface, rather than by the instantaneous maximum temperature gradient direction alone. Using these findings, we successfully predict changes in the dendrite growth direction with changing laser scan direction on a single crystal substrate, and show that the geometric melt pool centerline can deviate from the microstructural centerline because asymmetric local temperature gradient magnitudes transiently limit growth, resulting in different dendrite travel distances on each side of the melt pool.

36 MATERIALS SCIENCE↗
DOE OSTI2020

STEM Characterization of Dislocation Loops in Irradiated FCC Alloys

In this study, we demonstrate the methodology systematically developed for dislocation loop (perfect and faulted loops) imaging and analysis in irradiated face-centered-cubic (FCC) alloys using scanning transmission electron microscopy (STEM). On-zone [001] STEM imaging was identified as the preferred choice for its accuracy and effectiveness based on the comparison with other dislocation loop imaging techniques including: (i) on-zone STEM imaging using other major low-index zone axes, (ii) kinematic two-beam conditions bright field imaging near the [001] zone axis in conventional TEM (CTEM) mode, and (iii) Rel-Rod CTEM dark-field (DF) imaging near the [011] zone axis. The effect of STEM collection angle on the contrast formation of dislocation loops was also investigated. The developed method was confirmed by imaging all populations of perfect and faulted loops of types a/2$\langle$110$\rangle${110} and a/3$\langle$111$\rangle${111} found in an ion irradiated Ni40Fe40Cr20 alloy. The proposed STEM-based technique can easily identify said loops with a size greater than 10 nm without any assumptions such as those commonly made using the conventional Rel-Rod CTEM-DF technique. The recommended methodology in this study is developed as a quick and convenient tool that can be generally applied to irradiated FCC-based materials due to their common crystallography.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Deformation Mechanism Transition in Additively Manufactured Compositionally Graded Fe-Base Alloys

Microstructure-dependent deformation and fracture behavior was investigated for an additively manufactured compositionally graded alloy (CGA) printed using the laser-directed energy deposition (L-DED) method to explore an alternative approach for dissimilar metal joints in nuclear energy systems. The electron backscatter diffraction (EBSD) maps from scanning electron microscopy (SEM) display a clear microstructural transition with decreasing austenite-forming elements (Ni and Mn), from an austenite (γ) dominant structure, to a complex composite structure containing ferrite (α), martensite (α') and retained austenite, and then to a fully ferritic structure. EBSD data were recorded in situ during tensile testing in SEM, and the evolution of the deformation mechanism and microstructure was characterized using Kikuchi diffraction pattern analysis. Complementary analysis for high-resolution features was also performed using scanning transmission electron microscopy (STEM). The Ni/Mn-rich austenite-dominant microstructures showed a complex deformation mechanism of two-step martensitic transformation (γ→ε→α'), whereas the minor austenite phase retained in the ferrite and/or martensite matrix showed a single transformation route (γ→α'). Ordinary dislocation glide and twinning via partial dislocation glide were observed in the austenite deformation. Meanwhile, the ferrite and martensite grains deformed mainly by ordinary dislocation slips and grain rotation. Furthermore, static tensile fracture was also highly dependent on local composition and phase constituents.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The application of synchrotron micro-computed tomography to characterize the three-dimensional microstructure in irradiated nuclear fuel

This research demonstrated the first time that synchrotron X-ray micro-computed tomography (μ-CT) was utilized to analyze the three-dimensional (3-D) morphology of the microstructure of irradiated nuclear fuel. Both absorption contrast and propagation-based phase contrast enhanced μ-CT techniques were evaluated. Porosity and phase region volumes were determined in neutron irradiated uranium 10 wt.% zirconium (U-10Zr) using propagation-based phase contrast enhanced μ-CT. Volumes were determined by image processing software and algorithms, with the porosity volume subsequently compared to the ASTM E562 method. The 3-D porosity of a small region (~ 8 x 10 5 µm 3 ) located in the intermediate fuel redistribution zone that was removed via a focused ion beam was determined to be 7.2% via image processing. A detailed 3-D analysis of the porosity with respect to volume and morphology was provided. Five growth stages of pore evolution were observed including: nucleation, growth, coalescence, interconnected porosity, and extended/interconnected porosity. Four distinct phase regions were identified, including the pores, via both absorption contrast and propagation-based phase contrast enhanced μ-CT. A quantitative comparison of fuel swelling between this localized microscopic U-10Zr fuel region, previously irradiated in the Fast Flux Test Facility, and historic U-10Zr fuels irradiated in the Experimental Breeder Reactor-II (EBR-II) was conducted. It was determined that for similar burnups, the localized swelling in this microscopic fuel region was 7.7%, which was approximately one-half of the value of the macroscopic swelling reported in EBR-II irradiated fuel. With the advent of new specimen preparation tools for irradiated materials, as well as advances in characterization techniques, researchers can now obtain previously inaccessible microstructural insight into irradiated fuels. This possibility naturally lends itself to improved fuel performance models for the nuclear community.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

A Review of Existing and Emerging Methods for Lithium Detection and Characterization in Li-Ion and Li-Metal Batteries

Whether attempting to eliminate parasitic Li metal plating on graphite (and other Li-ion anodes) or enabling stable, uniform Li metal formation in ‘anode-free’ Li battery configurations, the detection and characterization (morphology, microstructure, chemistry) of Li that cannot be reversibly cycled is essential to understand the behavior and degradation of rechargeable batteries. In this review, various approaches used to detect and characterize the formation of Li in batteries are discussed. Each technique has its unique set of advantages and limitations, and works towards solving only part of the full puzzle of battery degradation. Going forward, multimodal characterization holds the most promise towards addressing two pressing concerns in the implementation of the next generation of batteries in the transportation sector (viz. reducing recharging times and increasing the available capacity per recharge without sacrificing cycle life). Such characterizations involve combining several techniques (experimental- and/or modeling-based) in order to exploit their respective advantages and allow a more comprehensive view of cell degradation and the role of Li metal formation in it. Additionally, it is also discussed which individual techniques, or combinations thereof, can be implemented in real-world battery management systems on-board electric vehicles for early detection of potential battery degradation that would lead to failure.

25 ENERGY STORAGE↗
DOE OSTI2022

Understanding radiation effects in friction stir welded MA956 using ion irradiation and a rate theory model

We report an outstanding challenge in the manufacturing and joining of oxide dispersion strengthened steels is retaining the nanofeatures in the alloy throughout the fabrication and welding process. MA956 was friction stir welded with two different sets of welding parameters, resulting in a medium and high heat input. After welding, 5 MeV Fe ++ ion irradiations were performed at doses ranging from 50 to 200 dpa in the temperature range of 400 to 500°C. Post-irradiation characterization was performed with scanning transmission electron microscopy and energy-dispersive x-ray spectroscopy to investigate the Y-Al-O dispersoids, voids, and dislocations. After welding, the dispersoid microstructure coarsened, resulting in fewer and larger dispersoids regardless of heat input. After irradiation, the dispersoid behavior in the welded material was sensitive to temperature, exhibiting growth behavior attributed to Ostwald coarsening at 500 °C but a mixture of nucleation and more muted growth at 400 and 450 °C, attributed to competing mechanisms of radiation-enhanced diffusion and Ostwald coarsening. Void swelling correlated to heat input; being more prevalent in the welded conditions occurring at lower doses and in higher values relative to the base material. The low values of swelling despite microstructure coarsening caused by welding demonstrate the excellent swelling resistance of MA956, even after welding with the highest swelling values of 0.5% noted in the stir zone high heat input condition at 450 °C, 200 dpa. The dislocation behavior was inconsistent: the strongest trend was that network density was higher for welded versus base material, and an increase in loop diameter with temperature was observed. A rate theory model based on the observed microstructure suggests at high temperature interstitial loss to sinks was more likely to be dominant compared to mutual annihilation via point defect recombination, because of an increase of the radiation diffusion coefficient with temperature regardless of initial welded microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Evaluation of microstructural changes in fresh cement paste using AC impedance spectroscopy vs. oscillation rheology and 1H NMR relaxometry

AC impedance spectroscopy (ACIS) is a promising technique for monitoring the microstructure evolution of fresh cement paste in real-time. This paper compared the change of bulk electric resistivity (ρ{sub bulk}) obtained from ACIS with the developments of storage modulus (G′) and the mean transverse relaxation times (T{sub 2}) of fresh Portland cement pastes within 5 h. It was found that the three different phases (Phase I, II, and III) on the microstructural build-up process of fresh paste can be accurately distinguished by analyzing ρ{sub bulk}, as well as G′ and T{sub 2}. The use of ρ{sub bulk} fails to characterize the microstructural changes in Phase I due to the great sensitivity on the electrical conductivity of the interstitial solution. However, it can successfully reflect the developing features of microstructure in Phases II and III, and reliably evaluate the impacts of water to cement ratio, superplasticizer, and supplementary cementitious materials on the microstructural development.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Simulation toolkit for digital material characterization of large image-based microstructures

In this paper, an efficient image-based simulation toolkit for material characterization is presented, which is scalable to work from personal computers to workstations. The effective thermal conductivity, elasticity, and permeability are evaluated employing a computational homogenization framework based on the Finite Element Method (FEM). Two complementary open-source packages are presented: one developed in Python, which can convert digital images into voxel meshes (pyTomoviewer); the other developed in Julia, that can run numerical simulations to compute effective material properties (chpack). Also, a CUDA C version of chpack is provided (chfem_gpu). They were designed to deal with large multi-phase models, so strategies were devised to minimize their memory footprint, while avoiding a high toll on execution time. The voxel-based approach significantly simplifies the FEM meshes and allows efficient matrix-free implementations. In that sense, to handle large linear systems of equations, the element-by-element (EBE) technique is adopted, in conjunction with a low-memory implementation of the Preconditioned Conjugate Gradient (PCG) method. Finally, the code was thoroughly tested on an artificial geometry made of a square array of cylinders, for which analytical solutions exist, as well as on a real micro-tomographic reconstruction of FiberForm TM , a carbon preform commonly used in thermal protection systems.

36 MATERIALS SCIENCE↗