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Multiscale analysis in solids with unseparated scales: fine-scale recovery, error estimation, and coarse-scale adaptivity

There are several engineering applications in which the assumptions of homogenization and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. Here, we investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.

42 ENGINEERING↗

Effect of Heat Treatment on Microstructure and Mechanical Property of 316L Stainless Steel Produced by Laser Powder Bed Fusion

The advanced non-light water reactor designs (Gen IV reactors), including molten salt/ very high temperature/ sodium-cooled and lead-cooled fast reactors, typically operate at higher temperatures and more extreme radiation conditions than light water reactors. An intrinsic part of the deployment and progress of Gen IV reactor designs is selecting the most suitable structural material for a specific application. Additive manufacturing (AM), a fairly new process of making physical, three-dimensional objects from a computer design file, is going to completely change the way of design, build and certify nuclear systems. It offers a range of opportunities to produce complex geometries from existing materials, offers new routes for processing of previously difficult to process materials, allows for design of new high-performance materials, and finally facilitates hybridization of dissimilar materials. This emerging technology has successfully produced cars, wind turbine blade molds and even live cells. It could also open up big opportunities for the nuclear industry to quickly deploy technologies at a fraction of the cost. So far, AM techniques have been preliminarily applied in the field of nuclear reactors, including the classical parts such as the pressure vessel of a small reactor with 508-III steel, the bottom nozzle of a fuel assembly with 304L steel, the fuel cladding with zirconium alloy and the integrated impeller of a pump and the multi-channel valve body with 316L steel [6,7]. The AM applications for operating nuclear reactors started in auxiliary plant components and have slowly migrated to metallic reactors and core components, but many of these are not safety critical components. Although many parts used for nuclear reactors have been fabricated by AM techniques, practical applications in engineering are still a long way off due to the uncertainty factors focused on the processing, material properties, analysis methods and application standards, which feeds the safety and life-cycle of the nuclear reactor. Due to rapid, repeated heating and cooling during production, a high dislocation density was present in the AM material. This microstructure feature is unstable at elevated temperature while high temperature is one of the typical operation environments for nuclear reactors. Thus, it is important to understand the thermal effect on the microstructure of AM material. The objectives of this study are to investigate the effect of heat treatment on the microstructure and mechanical properties of 316L stainless steel produced by laser powder bed fusion additive manufacturing, and to determine an appropriate heat treatment practice that will be applied to the lightweight AM lattice-structured material with the same chemistry. The heat treatment study consisted of annealing the samples at a temperature range of 800 to 1200 oC with a 50 oC increment for different times (1-24 hours), followed by vacuum or air cooling. Microstructural characterization was carried out by Scanning Electron Microscope (SEM). Grain size and crystallographic orientation were investigated by Electron Backscatter Diffraction (EBSD). Vickers hardness tests with a 0.5 kg load were employed to determine the hardness of samples after different heat treatments. After heat treatment, the random crystallographic orientation was preserved, and the volume fraction of high-angle grain boundaries (grain boundary misorientation =15 oC) remained the same. The dislocation density decreased with annealing temperature due to recovery. The fine subgrain structures in the as-printed specimen were quite stable up to 1200 oC. Minimal recrystallization was observed up to 1200 oC. Recrystallization initiated only after 8.5 hours at 1200 oC. The SEM images did not show obvious dependence of microstructure on cooling rate. The hardness of the specimens decreased with increasing annealing temperature as a result of the decrease in dislocation density. It is interesting to note that the AM material showed very similar hardness to the wrought material when annealing at similar temperature, although the microstructures are very different. Annealing at 1050 oC for 1 hour followed by air cooling was selected as the heat treatment procedure for the lattice designed lightweight AM 316L material.

36 MATERIALS SCIENCE↗

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy↗

Achieving strength-ductility synergy in hierarchical aluminum metal matrix composites via friction extrusion

We report the fabrication of aluminum metal matrix composites (Al-MMCs) with hierarchical architectures via friction extrusion (FE), a scalable, single-step, solid-phase processing technique. Precursor pucks containing 0–15 vol% Al₂O₃ particles were extruded into fully dense AA6061-based composite rods. The FE induced a tree-ring-like architecture of concentric particle-rich and particle-lean bands, yielding refined grains in particle-rich regions and coarser grains elsewhere. At the nanoscale, magnesium in AA6061 selectively reacted with Al₂O₃ particles to form virus-like nodes, improving particle–matrix bonding. This multi-scale design strategy, combining mesoscale architecture, microscale grain refinement, and nanoscale interface engineering overcome the conventional strength–ductility trade-off. Tensile testing showed substantial increases in yield and ultimate tensile strengths while retaining high ductility ( > 20%). Enhanced strain hardening, driven by the accumulation of geometrically necessary dislocations at interfaces, contributed to the performance. The hierarchical microstructure produced by FE demonstrates a promising pathway for scalable fabrication of lightweight MMCs for structural applications requiring a combined high strength and ductility.

Kalsar, Rajib [Pacific Northwest National Laborato↗

Direct Measurements of Ionic Transport Behavior of Dual-Layer Porous Electrodes

To improve power and cycling performance of lithium-ion batteries, dual-layer or porosity-gradient electrodes have been proposed. By engineering a higher porosity close to the separator, the intention is to improve ion transport where it is most impactful. In this research, MacMullin numbers of two dual-layer anode samples are tested using an impedance measurement technique developed previously. To characterize the microstructure of each layer independently, we developed an improved transmission-line model that accounts for each layer's properties.Virtual experiments using COMSOL Multiphysics to simulate impedance measurements are used to examine and improve the accuracy of the numerical inversion procedure. The results for the two dual-layer anodes studied show that MacMullin numbers follow expected trends, though the anodes are quite different from each other.

Dual-Layer Electrodes↗

Laser Powder Bed Fusion Microstructure Surrogate Model

SAND2025-11467O The Laser Powder Bed Fusion (LPBF) Microstructure Surrogate Model is a machine-learning-based tool. It predicts statistics of microstructures that are produced by the LPBF additive manufacturing process. It includes a series of codes for training, testing, and analyzing the model as well as utility scripts for handling data. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Moser, Daniel [Sandia National Lab. (SNL-CA), Live↗

Development of GRCop-84 for Rocket Engine Applications

GRCop-84 (Cu-8 at.% Cr-4 at.% Nb) has been under development at the NASA Glenn Research Center for several years. The alloy possesses a unique combination of good thermal conductivity, high elevated temperature strength, long creep lives and long low cycle fatigue lives. The alloy is also more oxidation resistant than pure copper and most competitive alloys. The combination of properties has attracted attention from major rocket engine manufacturers who are interested in the alloy for the combustion chamber liner in their next generation of regeneratively cooled engines. It is also a strong candidate for various components in hypersonic vehicles, which also experience very high heat flux conditions. This presentation will discuss the alloy design strategies used to develop GRCop-84 and the various processing routes available for manufacturing components. The microstructure and mechanical properties of the alloy will be reviewed, as well as the results of actual hot fire testing of subscale rocket combustion chambers. The use of environmental and thermal barrier coatings to extend the performance to even higher levels will also be discussed.

Ellis, David L.↗

Effects of Exposures on Superalloys for Space Applications

The industry is demanding longer term service at high temperatures for nickel-base superalloys in gas turbine engine as well as potential space applications. However, longer term service can severely tax alloy phase stability, to the potential detriment of mechanical properties. Cast Mar-M247LC and wrought Haynes 230 superalloys were exposed and creep tested for extended times at elevated temperature. Microstructure and phase evaluations were then undertaken for comparisons.

Gabb, Tim↗

Advanced cast aluminum alloys for automotive engine application with superior high-temperature properties

A high fatigue strength aluminum alloy comprises in weight percent copper 3.0-3.5%, iron 0-1.3%, magnesium 0.24-0.35%, manganese 0-0.8%, silicon 6.5-12.0%, strontium 0-0.025%, titanium 0.05-0.2%, vanadium 0.20-0.35%, zinc 0-3.0%, zirconium 0.2-0.4%, a maximum of 0.5% other elements and balance aluminum plus impurities. The alloy defines a microstructure having an aluminum matrix with the Zr and the V in solid solution after solidification. The matrix has solid solution Zr of at least 0.16% after heat treatment and solid solution V of at least 0.20% after heat treatment, and both Cu and Mg are dissolved into the aluminum matrix during the heat treatment and subsequently precipitated during the heat treatment. A process for heat treating an Al—Si—Cu—Mg—Fe—Zn—Mn—Sr-TMs alloy comprises heat treating the alloy to produce a microstructure having a matrix with Zr and V in solid solution after solidification.

36 MATERIALS SCIENCE↗

Containment strategy for subsurface H 2 storage based on time-dependent soft solids

Here, we propose an innovative containment strategy based on time-dependent soft solids, namely 2 wt% Laponite suspensions, to reinforce natural subsurface seals and engineer flow barriers, with an eye toward making H 2 subsurface storage scalable and geographically agnostic. This suspension can be injected at its initial low viscosity and elasticity into a porous medium, allowing for easy pumping and targeted delivery. Once inside the target zone, it matures into a soft solid with much higher viscosity and elasticity, acting as a potential flow barrier. We discuss the rheological properties of the suspensions and demonstrate that hydrogen does not adversely affect their microstructure, but rather increases the suspensions’ viscosity and elasticity. Moreover, the suspensions enhance the rock samples’ compressive strength, while hydrogen exposure increases their stiffness and ductility. The ability of rock samples saturated with the suspensions to contain higher injected gas pressures is enhanced by aging at higher temperatures.

08 HYDROGEN↗

A novel digital lifecycle for Material‐Process‐Microstructure‐Performance relationships of thermoplastic olefins foams manufactured via supercritical fluid assisted foam injection molding

Abstract This research significantly enhances the applicability of thermoplastic olefins (TPOs) in the automotive industry using supercritical N 2 as a physical foaming agent, effectively addressing the limitations of traditional chemical agents. It merges experimental results with simulations to establish detailed material‐process‐microstructure‐performance (MP2) relationships, targeting 5–20% weight reductions. This innovative approach labeled digital lifecycle (DLC) helps accurately predict tensile, flexural, and impact properties based on the foam microstructure, along with experimentally demonstrating improved paintability. The study combines process simulations with finite element models to develop a comprehensive digital model for accurately predicting mechanical properties. Our findings demonstrate a strong correlation between simulated and experimental data, with about a 5% error across various weight reduction targets, marking significant improvements over existing analytical models. This research highlights the efficacy of physical foaming agents in TPO enhancement and emphasizes the importance of integrating experimental and simulation methods to capture the underlying foaming mechanism to establish material‐process‐microstructure‐performance (MP2) relationships. Highlights Establishes a material‐process‐microstructure‐performance (MP2) for TPO foams Sustainably produces TPO foams using supercritical (ScF) N 2 with 20% lightweighting Shows enhanced paintability for TPO foam improved surface aesthetics Digital lifecycle (DLC) that predicts both foam microstructure and properties DLC maps process effects & microstructure onto FEA mesh for precise prediction

Engineering↗

Location specific solidification microstructure control in electron beam melting of Ti-6Al-4V

Relationships between prior beta grain size in solidified Ti-6Al-4V and melting process parameters in the Electron Beam Melting (EBM) process are investigated. Samples are built by varying a machine-dependent proprietary speed function to cover the process space. Optical microscopy is used to measure prior beta grain widths and assess the number of prior beta grains present in a melt pool in the raster region of the build. Despite the complicated evolution of beta grain sizes, the beta grain width scales with melt pool width. The resulting understanding of the relationship between primary machine variables and prior beta grain widths is a key step toward enabling the location specific control of as-built microstructure in the EBM process. Control of grain width in separate specimens and within a single specimen is demonstrated.

42 ENGINEERING↗

Electro-strengthening of the additively manufactured Ti–6Al–4V alloy

Structure-property-processing relationship has been studied in additively manufactured Ti–6Al–4V alloy. The processing was performed using in-situ electron microscope (EM) at a moderate current density of 5 × 105 A/cm2 applied for 5 min, and by suppressing Joule heating with massive heat sinks such that the temperature rise was <180 °C and the mechanical properties were not compromised. Overall, the results show that while the grain size increased by ~15%, the nanohardness increased by 16%. This is attributed to the pronounced dislocation generation, regeneration, and clustering as well as defect healing. Ultimately, there is a reduction in the residual strain and a significant increase in the intrinsic strength as evidenced by the high Taylor factor of the electric current processed specimen. This novel processing technique represents an alternative pathway for active controlling of microstructure and internal defects for parts that might be sensitive to high-temperature processing or conventional methods.

36 MATERIALS SCIENCE↗

Laser Intensity Profile Effects on the Solidification Microstructure of Ti-6Al-4V and Ti-5553

Traditional machining of Ti-6Al-4V and Ti-5Al-5Mo-5V-3Cr (Ti-5553) is challenging due to high chemical reactivity, adiabatic shear band formation, and material cost. Titanium is attractive because of its high tensile strength, low density, corrosion resistance, and ability to withstand extreme temperatures. Selective Laser Melting (SLM) is capable of manufacturing geometrically complicated parts at a lower expense. Exceptional tolerances can be obtained with properly tuned processing parameters. Alterations on scan parameters permit microstructure and melt pool control. Single track laser melting experiments were performed on Ti-6Al-4V and Ti- 5553 using elliptical intensity profiles. Results show that maintaining constant energy density but increasing power results in a melt pool failing to penetrate the substrate for Ti-5553. Increasing laser energy density increases melt pool width and can increase powder bed denudation. Comparing Ti64 and Ti-5553 microstructures contributes to a better understanding of rapid solidification in titanium.

36 MATERIALS SCIENCE↗

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE↗

Kernel Enriched Meshfree Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Laboratory of the Rockies (NLR), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. References: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

97 MATHEMATICS AND COMPUTING↗