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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Fabrication of freeform potassium dihydrogen phosphate crystals by belt-on-wheel polishing for spatially tailored polarization control in high-power lasers

Large-aperture (>30 cm) optical components that provide spatially tailored control of the properties of a laser beam, such as phase, polarization, and amplitude, have been the focus of much research and development in recent years. Such optics can improve energy throughput and target implosion efficiency in high-power laser systems conducting inertial confinement fusion research. Here, a method is demonstrated for fabricating freeform surface topographies into the birefringent crystalline material, potassium dihydrogen phosphate (KDP). Belt-on-wheel polishing with an oil-based fluid, developed to mitigate the deliquescent properties of KDP, is used to deterministically polish a freeform topography into KDP, enabling the fabrication of a wave plate with spatially arbitrary retardance. Testing of the laser-induced damage threshold of belt-on-wheel polished KDP was conducted at a wavelength of 351 nm and a pulse duration of 1 ns. The results revealed that the polished surfaces are highly resistant to laser-induced damage, making them suitable for large-aperture, high-power laser applications.

Urban, Nathaniel D. [Univ. of Rochester, NY (Unite↗
NASA NTRS2026

Tracing the Source of Carbon Oxides on the Large Moons of Uranus

The Uranian moons Ariel, Umbriel, Titania, and Oberon are enriched in CO 2 mixed with CO, but the origin(s) of these carbon oxides, be they primarily native or radiolytic, remain(s) uncertain. Using data collected by NIRSpec on the James Webb Space Telescope (JWST), we measured the spectral signature of CO 2 and other carbon oxides to help disentangle these hypotheses. Through comparison to laboratory data, we find that many of the detected spectral features are consistent with CO 2 ice, including 12 CO2 scattering peaks (4.15–4.26 μm), multilobe 13 CO 2 bands (4.35–4.43 μm), and CO 2 biphonon and triphonon modes (4.80–5.25 μm). Our measurements show that CO 2 and CO are concentrated on the trailing hemispheres of the inner moons Ariel and Umbriel, potentially supporting a radiolytic production hypothesis, consistent with prior ground-based results. However, many of the identified spectral features are only observed in thick crystalline ice deposits measured in the laboratory, which may be difficult to form via radiolysis of carbon-bearing material mixed in icy regoliths. Similarly, the data exhibit weak 4.02 and 4.40 μm bands, hinting at the presence of carbonate minerals and 13 CO 2 clathrates, respectively, possibly formed in the interiors of these moons. Furthermore, JWST has revealed that CO 2 is widespread at Uranus, present in its system of rings, ring moons, and irregular satellites, consistent with its largest moons accreting CO 2 and other carbon oxides from the Uranian subnebula. We conclude that exposed carbon oxides are potentially native, with their surface distributions shaped by charged particle irradiation and seasonal sublimation–condensation cycles.

Ice spectroscopy↗
DOE OSTI2026

Rapid Quantum Ground State Preparation via Dissipative Dynamics

Inspired by natural cooling processes, dissipation has become a promising approach for preparing low-energy states of quantum systems. However, the potential of dissipative protocols remains unclear beyond certain commuting Hamiltonians. This work provides significant analytical and numerical insights into the power of dissipation for preparing the ground state of noncommuting Hamiltonians. For quasi-free dissipative dynamics, including certain 1D spin systems with boundary dissipation, our results reveal a new connection between the mixing time in trace distance and the spectral properties of a non-Hermitian Hamiltonian, leading to an explicit and sharp bound on the mixing time that scales polynomially with system size. For more general spin systems, we develop a tensor network-based algorithm for constructing the Lindblad jump operator and for simulating the dynamics. Using this algorithm, we demonstrate numerically that dissipative ground state preparation protocols can achieve rapid mixing for certain 1D local Hamiltonians under bulk dissipation, with a mixing time that scales logarithmically with the system size. We then prove the rapid mixing result for certain weakly interacting spin and fermionic systems in arbitrary dimensions, extending recent results for high-temperature quantum Gibbs samplers to the zero-temperature regime. Together, these results show that dissipation can be a powerful tool for ground state preparation, with potential applications across condensed matter physics, quantum materials science, and beyond.

decoherence↗
DOE OSTI2026

EvoDiffMol: evolutionary diffusion framework for 3D molecular design with optimized properties

Designing molecules with specific target properties remains a fundamental challenge in computational chemistry. While existing approaches show promise, most rely on simplified representations like SMILES strings or 2D graphs that lack essential three-dimensional geometric information. We present EvoDiffMol, a computational framework that integrates evolutionary algorithms with three-dimensional diffusion models for property-driven molecular generation. The method operates through adaptive evolutionary optimization, where population-based selection guides the generation process toward desired property landscapes. EvoDiffMol supports both unconstrained molecular design and scaffold-constrained generation that preserves fixed substructures while optimizing complementary regions. Comprehensive evaluation demonstrates exceptional performance, achieving the highest drug-likeness score (0.94) among all compared state-of-the-art methods while maintaining excellent validity, uniqueness, and novelty. Beyond single property optimization, the framework demonstrates flexible multi-property optimization capabilities, simultaneously controlling multiple molecular descriptors including synthetic accessibility, lipophilicity, topological polar surface area, and clinically relevant ADMET properties such as cardiotoxicity (hERG) and intestinal permeability (Caco-2). This adaptability spans from simple descriptors to practical pharmaceutical endpoints without requiring complete model retraining. The framework achieves precise control over target property values, generating molecules with properties closely matching specified targets for both single and multiple descriptors. Scaffold-constrained experiments preserve fixed molecular cores while maintaining effective property optimization. The three-dimensional representation offers advantages in maintaining structural validity during iterative optimization, with potential for geometry-aware applications in materials science and drug discovery.

3D molecular generation↗
NASA NTRS1992

On the isotopic signature of recent solar-wind nitrogen

One of the most intriguing discoveries yielded by the Apollo samples was evidence pointing towards a significant long-term change in the composition of the sun. Such a change, of the size inferred from the lunar sample data, is inconsistent with present theories of solar evolution. Consequently, there is much interest in exploring this phenomenon as closely as possible, to determine exactly what compositional changes have taken place and whether those changes really did take place in the sun, or whether the cause lies elsewhere. The reason why we can use the moon to analyze the elements in the sun is that the sun emits a stream of ions, known as the solar wind, whose composition, on average, is believed to be the same as that in the surface regions of the sun. When the solar-wind ions hit the surface of the moon, many of them penetrate a short distance into the dust grains lying on the lunar surface. Thus, after a grain has sat on the lunar surface for a while, it has a rim of material that is partly lunar and partly solar in composition. For most chemical elements, the difference between lunar and solar composition is so sufficiently small that the solar elements cannot be detected, but for a handful of elements that are missing from the moon, their solar 'signature' can be observed in samples of lunar soil brought back by the astronauts. Among those elements is nitrogen, the most common element in the air we breathe, but very rare indeed on the moon. Our analytical techniques are not sophisticated enough yet to enable us to analyze individual lunar soil grains for nitrogen, much less to zero in on just the nitrogen in the surface of such a grain. Consequently we are forced to analyze samples consisting of many different grains, each of which could have experienced its own individual history. This makes it difficult to identify the nitrogen implanted in grain surfaces, and also to define the age of a sample.

Kim, Y.↗
DOE OSTI2024

Landmark Publications in Analytical Atomic Spectrometry: Fundamentals and Instrumentation Development

The almost-two-centuries history of spectrochemical analysis has generated a body of literature so vast that it has become nearly intractable for experts, much less for those wishing to enter the field. Authoritative, focused reviews help to address this problem but become so granular that the overall directions of the field are lost. This broader perspective can be provided partially by general overviews but then the thinking, experimental details, theoretical underpinnings, and instrumental innovations of the original work must be sacrificed. In the present compilation, this dilemma is overcome by assembling the most impactful publications in the area of analytical atomic spectrometry. Each entry was proposed by at least one current expert in the field and supported by a narrative that justifies its inclusion. The entries were then assembled into a coherent sequence and returned to contributors for a round-robin review. A total of 48 scientists participated in this endeavor, contributing a combined list of 1055 individual articles spanning 17 sub-disciplines of spectrochemical analysis into what the current community views as “key” publications. Of these cited articles, 60 received nominations from four or more scientists, establishing them as the most indispensable reading materials. The outcome of this collaborative effort is intended to serve as a valuable resource not only for current practitioners in atomic spectroscopy but also for present and future students who represent coming generations of analytical atomic spectroscopists.

Instruments & Instrumentation↗
NASA NTRS2022

Optical properties of morphologically complex black carbon aerosols: Effects of coatings

Optical properties are computed for fractal-like aggregate black carbon (BC) aerosols coated with different substances. Two models are used for these aerosols: (i) the coated aggregate model (model I), where coating is added to the voids and surroundings of BC fractal-like aggregates; and (ii) the closed-cell aggregate model (model II), where coating is added concentrically to each monomer of BC fractal-like aggregates. Our results favor choosing the coated aggregate model (model I) to simulate scattering and absorption by coated BC aerosols because this model is morphologically more realistic, and because this model yields mass absorption cross section (MAC) and backscattering linear depolarization ratio (LDR) values that are consistent with field measurements. Moreover the corresponding computed degree of linear polarization (DoLP) and LDR values are very sensitive to changes in the coating volume fraction (fvol) and the coating refractive index (m). With the same absorbing BC core, the MAC value increases steadily with increasing fvol and m values. For example, using a density of 1.8 g/cm 3 and BC refractive index 1.95 + i0.79, the calculated MAC values for uncoated BC aggregates range from 6.2 to 6.8 m 2 /g at 0.55 µm. When coating material is applied to the BC aggregates, the calculated MAC values for model I particles increase to between 9.8 and 13.2 m 2 /g (depending on m) when fvol = 87.5%. The backscattering LDR values also tend to increase with the increasing m values for the shapes and sizes considered in our study. For model I particles, the backscattering LDR values span a wide range of 4.2–27.8% at a wavelength of 0.35 µm at fvol = 87.5% when m increases from 1.33 to 1.55. Our results are relevant to analyses of polarimetric and lidar observations of smoke particles, especially when these particles undergo hygroscopic growth.

Black carbon aerosols↗
DOE OSTI2026

The impact of aerosol mixing state on immersion freezing: insights from classical nucleation theory and particle-resolved simulations

Immersion freezing, initiated by ice-nucleating particles (INPs) in supercooled aqueous droplets, plays an important role in the formation of ice crystals within clouds. The efficiency of immersion freezing depends strongly on INP composition and, crucially, on the mixing state – how chemical species are distributed across the particle population. Here, we quantify the impact of aerosol mixing state on immersion freezing using a combined theoretical and particle-resolved modeling approach. We derive analytical expressions for the frozen fraction of internally and externally mixed INP populations based on classical nucleation theory, showing that the frozen fraction is sensitive to whether ice-active species are present in all particles or only in a subset of the population. We introduce a multi-species immersion freezing scheme into the particle-resolved model PartMC, using the water activity-based immersion freezing model (ABIFM) to compute freezing probabilities for mixed-composition particles. To improve computational efficiency, we implement a Binned Tau-Leaping algorithm and demonstrate an order-of-magnitude speedup with minimal accuracy loss. Simulations reproduce the analytical trends in limiting cases and extend the analysis to more general aerosol populations, where mixing state continues to exert a substantial control on frozen fraction. Sensitivity analyses across particle size, species type, and cooling condition reveal that the mixing state effect is most pronounced when small amounts of highly efficient INPs are mixed with less efficient materials. These findings underscore the need to represent aerosol mixing state explicitly in models of heterogeneous ice nucleation to reduce uncertainty in cloud-phase partitioning.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Direct observation of diamond formation in a shock-compressed high explosive

Understanding the formation timescale and structure of carbonaceous reaction products is critical for modeling the high-pressure equation-of-state of organic materials. We use the National Ignition Facility to shock-compress polycrystalline TATB (C 6 H 6 N 6 O 6 ) samples to ~70–130 GPa and ~4000–5500 K, employing in situ nanosecond X-ray diffraction to probe reaction products and velocimetry to measure transmitted compression wave profiles. Our diffraction data is consistent with the formation of diamond over timescales less than ~60 ns. This represents carbon condensation from a molecular explosive on timescales three times faster than previously reported and the earliest observation of diamond produced from reacting TATB. Reactive flow simulations with explicit chemistry reproduce the observed temporal structure within wave profiles to inform the distribution of P-T states. These findings provide direct evidence of ultrafast diamond formation in a reactive system at extreme conditions and provide new constraints for models of shock and detonation chemistry.

Clarke, Samantha M. [Lawrence Livermore National L↗
DOE OSTI2026

Scalable multiplexed machine learning gas sensor chips for food classification

Multiplexed gas sensor arrays combined with machine learning have unlocked previously inaccessible applications for scent-based sensing. Current platforms are limited by overlapping sensing materials with similar compositions, leading to highly correlated responses, or multistep deposition processes that hinder scalability. In this work, we developed a 16-element monolithic chip with fully distinct sensing layers, enabling a truly heterogeneous array. The system consists of highly sensitive carbon nanotube field effect transistors that are functionalized through a single-step microdispensing method compatible with automated pipetting systems. The resulting chip produces characteristic signal patterns in response to object-specific scent profiles and, when combined with machine learning algorithms, can perform automated object identification. We demonstrate the classification of 16 different objects, including food spoilage and nut allergens, with a 92.6% overall prediction accuracy.

Bassil, Carla [University of California, Berkeley,↗
DOE OSTI2026

FY26 Progress on Demonstration of a Multiphysics Steady State Capability for Modeling Core Radial Expansion in SFRs

Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. This report summarizes recent progress on developing a multiphysics, MOOSE-based workflow to predict core bowing and associated reactivity feedback. Significant new capabilities in the reactor physics code Griffin - sodium backfill and pin power reconstruction for deformed geometries - were applied in this effort. This year’s work included verification, code comparisons, sensitivity studies, and coupled demonstrations that advance the state of MOOSE-based core bowing workflow. Griffin’s sodium backfill capability was verified by demonstrating that its automated treatment of geometry expansion and material-density updates reproduces manual calculations exactly, confirming solid mass conservation and proper coolant backfilling in expanded geometries. Reconstructed pin powers were compared for Griffin’s ductheterogeneous and ring-heterogeneous treatments in single-, seven-, and nineteen-assembly cases, with best agreement observed in lower-leakage configurations and the duct-heterogeneous approach offering substantially lower computational cost. Thermal-hydraulic sensitivity sensitivities showed that MOOSE SCM, SAM, and CFD are expected to produce similar deformation predictions despite variances in their temperature predictions, and that explicit treatment of inter-assembly flow becomes increasingly important as gap flow rate increases. Finally, coupled demonstrations on small multi-assembly configurations using Griffin, MOOSE Solid Mechanics, MOOSE SCM, and Heat Conduction produced physically consistent reactivity feedback from thermal expansion and bowing. The coupled demonstrations simulated grid plate expansion as well as resultant core bowing at full power conditions. Simplifications were made in current workflow, namely the assumption of instantaneous full power conditions following hot zero power, and pre-expanding the Griffin geometry axially due to lack of an axial fuel pin expansion model and temperature feedback to Griffin.

Wozniak, Nicholas↗
DOE OSTI2026

Delamination recycling of multilayer plastic films: Solvent-assisted separation pathways and recovery of solid polyolefins

Multilayer plastic films are excellent packaging materials due to the bound layers of multiple polymers, with each different polymer contributing to the film properties. Desirable properties lead to continuously growing demand for multilayer films. Multilayer plastic films are typically single-use and, as such, their increased production and disposal have led to waste management problems. Multilayer films are not currently recyclable primarily due to the multiple bound polymers. This work advances delamination as a recycling process to separate and sequester valuable polymers from multilayer films, facilitating the incorporation of these polymers into the circular economy. We effect delamination in a physical process that preserves targeted polymers as solid film, hence retaining their embodied energy. This work documents three different pathways of inducing delamination of multilayer films, with appropriate solvents disrupting adhesion between adjacent layers or dissolving a minor component of the film in less than an hour and at temperatures below 90°C, and where all initial polyethylene is maintained in its solid form throughout the process and is recovered at high purity. Solvent-based delamination is exemplified on commercial multilayer films with majority polyethylene (PE), and polyethylene terephthalate (PET) or ethylene vinyl alcohol copolymer (EVOH) or nylon also present. Solvent-based delamination is an energy-efficient and environmentally friendly recycling process that improves upon dissolution-precipitation recycling, since delamination involves very little dissolution and no precipitation, and is superior to pyrolysis which breaks down the polymers, while delamination keeps polymer chains intact. Furthermore, delamination recycling can contribute to the sustainable use of multilayer films as they continue to protect our food and medicine.

Chemical Recycling↗
DOE OSTI2026

Atomic Evolution of Hydrogen Intercalation Wave Dynamics in Palladium Nanocrystals Revealed by Liquid-Phase Transmission Electron Microscopy

Solute-intercalation-induced phase separation creates spatial heterogeneities in host materials, a phenomenon ubiquitous in batteries, hydrogen storage, and other energy devices. Despite many efforts, probing intercalation processes at the atomic scale has been a significant challenge. By utilizing liquid-phase transmission electron microscopy (TEM), we study hydrogen (de)intercalation in palladium nanocrystals as a model system and have achieved unprecedented atomic-resolution imaging of hydrogen intercalation wave dynamics. Our observations reveal that intercalation wave mechanisms, instead of shrinking-core mechanisms, prevail at ambient temperature for palladium nanocubes ranging from ∼60 nm down to ∼10 nm. Systematic image analysis uncovers the atomic evolution of the hydrogen intercalation wave, transitioning from nonplanar and inclined boundaries to those closely aligned with {100} planes. Our kinetic Monte Carlo simulations demonstrate that the observed intercalation wave dynamics correspond to sorption pathways minimizing the lattice mismatch strain at the phase boundary. In conclusion, unveiling the atomic intercalation pathways holds profound implications for engineering intercalation-mediated devices and advancements in energy sciences.

Lee, Daewon [Lawrence Berkeley National Laboratory↗
DOE OSTI2026

RADAI: A Large-Scale Realistic Dataset for Radiation Detection Algorithm Development

Open, realistic datasets are essential for developing and benchmarking radiation detection algorithms, yet they remain scarce. The Radiological Anomaly Detection and Identification (RADAI) project was develop to create datasets that meet the training and testing needs for sophisticated radiation detection algorithms. The RADAI dataset is a large-scale synthetic resource that integrates high-fidelity Monte Carlo simulations with realistic urban scenarios to capture both background variability and source signatures. RADAI models construction-material NORM, people and vehicles, urban clutter, and dynamic environmental effects such as cosmic-ray and rain-induced transients, and they provide list-mode detector data with motion and response modeling suitable for algorithm training and evaluation. The RADAI project resulted in three publicly-released complementary datasets together with an online scoring portal for standardized performance assessment and an open software toolkit that supports data access, augmentation, model development, and evaluation. These resources enable reproducible comparisons across methods and promote rigorous studies at the scale required by contemporary machine learning. By grounding algorithm development in realistic, well-documented conditions, RADAI supports progress toward more robust detection, identification, and localization in complex urban environments.

Ghawaly, James M. [Division of Computer Science an↗
NASA NTRS1977

Calculations of the Moon's Thermal History at Different Concentrations of Radioactive Elements, Taking Into Account Differentiation on Melting

Calculations of the thermal history of the moon were carried out by solving the thermal conductivity equation for the case in which the heat sources are the long-lived radioactive elements Th, U, and K 40 . The concentrations of these elements were adjusted to give four variations of the heat flow: 1.35 x 10 -8 and 0.91 x 10 -6 cal cm -2 s -1 (I and I**), 0.61 x 10 -6 (variant II, the terrestrial mixture of Lyubimova and Starkova), and 0.236 x 10 -6 (variant III, the chondrite model of Urey and MacDonald). In the same calculations, we considered layering of the differentiated material with transport to the surface of the radioactive elements after the temperature of the layer rose to 200 K above the melting temperature, which is considered in five variants that differ in the amount of transported radioactive elements: 100 percent ( n = 1), 80 percent n = 0.8), 40 percent, 20 percent ( n = 0.6, 0.4, 0.2). During fusion the heat capacity and heat conductivity were changed. We considered two variants of an initially cold (273 K) and hot (900 K) Moon. Calculations show that the interior of the Moon was heated to melting during the first 0.7 to 2.3 x 10 9 years. The maximum fusion involved practically the entire Moon to a distance from 15 to 45 km beneath the surface, and started 3.5 to 4.0 x 10 9 years ago (I, I**), or 2.5 to 3.0 x 10 9 years ago (II, III) and continued for 1 to 2 x 10 9 years. Today the Moon is cooling. The current thickness of the solid crust is from 150 to 200 km and the heat flow exceeds the stationary value 1.5 fold. Apparently the most realistic variant is II (terrestrial mixture) for an initially hot Moon, and gives, regardless of the moderate concentration of radioactive elements, a heat flow of 0.9 to 0.95 x 10 -6 cal cm -2 s -1 , which agrees with the radioastronomical measurements of Troitsky and Krotikov and with the Apollo 15 data.

O I Ornatskaya↗
DOE OSTI2026

Time-Resolved Neutron Imaging for Hydrogen Uptake in Subsurface Lithologies

Geologic hydrogen production and underground storage are increasingly important for meeting rising energy demands while providing clean-combustion advantages. However, hydrogen’s high diffusivity and propensity for leakage through porous media necessitate direct evaluation of its transport behavior in subsurface materials. Whereas X-ray microcomputed tomography (μCT) studies often employ contrast agents or surrogate gases, this study leverages neutron transmission radiography/CT to observe hydrogen migration in situ. This work represents the first demonstration of real-time neutron radiography of hydrogen migration in reservoir and caprock lithologies. Cylindrical cores of Indiana limestone, Amherst Gray sandstone, and Tumey shale were subjected to constant-pressure hydrogen charging and scanned in real time using high-resolution neutron radiography. Results indicate immediate hydrogen infiltration in sandstone and limestone, with homogeneous distribution detected throughout their pore structure. In contrast, hydrogen remained largely absent from fine-grained shale under the same pressure, except in an apparently localized fracture zone, where neutron signatures confirmed the presence of hydrogen. Subsequent neutron CT of the sandstone sample, using image subtraction against an uncharged reference, corroborated hydrogen distribution patterns. Even under lowpressure, single-phase conditions, distinct neutron imaging signatures of hydrogen were achieved. These preliminary findings underscore the potential of neutron imaging for advancing subsurface hydrogen migration research.

08 HYDROGEN↗
DOE OSTI2026

Emergence of low-energy spin waves in superconducting electron-doped cuprates

In order to fully utilize the technological potential of unconventional superconductors, an enhanced understanding of the superconducting mechanism is necessary. In the best performing superconductors, the cuprates, superconductivity is intimately linked with magnetism, although the details of this coupling remain elusive. Here, we address this gap by studying the electron-doped cuprate Nd 1.85 Ce 0.15 CuO 4−δ that has an antiferromagnetic ground state when synthesized and only becomes superconducting after a reductive annealing process. Using neutron spectroscopy, we show that the as-grown crystal exhibits a large spin pseudogap in the magnetic fluctuation spectrum. Annealing removes defects introduced by the commonly employed synthesis method and significantly reduces the spin pseudogap. While the spin pseudogap in the annealed sample likely arises from superconductivity, in the as-grown sample it results from the absence of long-wavelength spin waves. These results reveal a direct connection between defects, magnetism, and superconductivity, offering new insight into the mechanisms underlying high-temperature superconductivity and guiding the design of improved superconducting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2025

Mechanics of Preloaded Bolt Tensile Loading With Focus on Load Introduction Factor

The bolt tensile and joint separation loads are directly influenced by the locations at which the external loads enter the clamped members of a preloaded bolted joint (PBJ) and the associated load-paths through the joint. This physical load introduction mechanism affecting the bolt tensile loading is typically represented in the bolt tensile load equation, in part, by a load introduction factor (LIF), which was shown by H.M. Lee of Marshall Spaceflight Center to be a natural product of the bolt tensile load equation using a linear spring stiffness model. This LIF, being a function of load-path stiffness, has subsequently been denoted as the stiffness-based LIF (SBLIF), providing a framework to calculate the LIF using whatever load-path stiffness approximations are appropriate. Expanding upon the work of Lee, it is shown that the SBLIF and the joint stiffness factor are functions of the stiffnesses of the same load-paths and regions within a PBJ, and thus they should not be treated as independent variables. Mathematical expressions for the SBLIF are presented. Comparisons are shown between the analytically calculated SBLIF, the analytically calculated geometric LIF (GLIF), which is a simple clamped-member thickness ratio, the experimentally derived LIF, and the LIF determined by finite element analysis (FEA). Using experiment and FEA as a benchmark, the SBLIF, using traditional load-path stiffness approximations, enables a more accurate prediction of bolt tensile loading than the GLIF, although it can be unconservative near joint separation. The GLIF generally attributes more of the externally applied tensile load to the bolt than does the SBLIF, potentially resulting in heavier and/or more costly bolted joints. Mathematical relationships between the SBLIF and the GLIF are developed. Supplemental material is provided in the appendixes where the historical practice of using the joint compressive stiffness in place of the joint tensile stiffness is evaluated. The appendixes include step-by-step examples demonstrating the calculation of the SBLIF using traditional stiffness approximations and conclude with the development of the joint diagram in terms of the SBLIF, culminating into formulas for the key features of a joint diagram, which is useful for programming.

Load Path↗