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A Comprehensive Review on Finite Element Analysis of Laser Shock Peening

Laser shock peening (LSP) is a formidable cold working surface treatment that provides high-energy precision to enhance the mechanical properties of materials. This paper delves into the intricacies of the LSP process, offering insights into its methodology and the simulation thereof through the finite element method. This review critically examines various points, such as laser energy, overlapping of shots, effect of LSP on residual stress, effect of LSP on grain refinement, and algorithms for simulation extrapolated from finite element analyses conducted by researchers, shedding light on the nuanced considerations integral to this technique. As the significance of LSP continues to grow, the collective findings underscore its potential as a transformative technology for fortifying materials against mechanical stress and improving their overall performance and longevity. The discourse encapsulates the evolving landscape of the LSP, emphasizing the pivotal role played by finite element analysis in advancing our understanding and application of this innovative surface treatment.

36 MATERIALS SCIENCE↗

Rare Earth Element (REE) and Critical Mineral Fractions of Central Appalachian Coal-Related Strata Determined by 7-Step Sequential Extraction

Rare earth elements (REEs) and critical minerals (CMs) are used in many modern industries, including the automotive sector, generation and storage, clean energy, and defense. The demand for REEs is increasing, and the REE supply chain is unpredictable. The US has driven to assess non-conventional sources of REE (such as coal underclay) to identify domestic resources to stabilize this uncertainty in supply. Knowledge of the minerology, distribution, and modes of occurrence of REEs is integral to the assessment of non-conventional sources. Additionally, extraction techniques can be optimized and targeted when REE distribution in different solid fractions from source material is understood. In this study, four bituminous coal-related samples associated with the Lower and Middle Kittanning coal seams in the Appalachian Basin (US) underwent a seven-step sequential extraction procedure, primarily targeting the water-soluble, exchangeable, acid soluble, mildly reducible, moderately reducible, strongly reducible, and oxidizable fractions. The REE and other elements of interest from each extraction step were analyzed, and the percentages of element extracted from raw solids were calculated. REEs extracted from the total seven steps were reported as the extractable fraction, whereas the fractions in the residual solids were reported as the non-extractable fraction. Less than 6% of REE were extracted from three samples. Twenty-one percent of REE was extracted from the fourth sample, mainly from the steps targeting oxidizable and exchangeable phases. Co-extraction of critical metals (Co, Ni, Cu, and Zn) occurred during the oxidizable, exchangeable, acid soluble, and water-soluble steps for the four samples. In the extracted fractions, the four samples all exhibited a middle and heavy REE enrichment relative to light REE. The mobility of major cation (e.g., Ca, Fe, and P) and REE is associated with exchangeable, oxidizable, and acid soluble fractions. Non-extractable REE is likely held in refractory apatitic phases, and/or primary REE-phosphates (e.g., monazite and xenotime).

58 GEOSCIENCES↗

Removal of Iron from Pyrite-Rich Coal Refuse by Calcination and Magnetic Separation for Hydrometallurgical Extraction of Rare Earth Elements

In the metallurgical extraction of rare earth elements (REEs), the ratio of contaminant ions to REEs in the leachate dictates the cost and operational efficiency of the downstream processes. The current study investigated the potential iron contamination removal from the feed to the hydrometallurgical process by calcination followed by magnetic separation. The 2.20 specific gravity sink fraction of Baker coal seam coarse refuse was pulverized to finer than 180 μm, calcined at various temperatures, and separated into magnetic and non-magnetic fractions using a wet high-intensity magnetic separator at different field strengths. The untreated feed, calcined products, and their subsequent magnetic and non-magnetic fractions were subjected to acid leaching tests with 1.2 M sulfuric acid at 75 °C and 1% w/v solids concentration. The recovery of light and heavy rare earth elements (LREEs and HREEs, respectively) along with the concentration of common contaminant ions (Al, Ca, and Fe) were measured as output variables. The weight percent of magnetic material was maximized at approximately 29% by calcination at a temperature of 400 °C. Magnetic removal of this fraction using a field strength of 1.15 Tesla resulted in the rejection of 81% of the iron. Leaching of the magnetic fraction provided significantly higher Fe recovery relative to untreated feed material and the non-magnetic fraction. The non-magnetic fraction was subsequently calcined at 600 °C to dehydroxylate the clays and released the REE minerals in the same manner as the treatment of the original coarse refuse material. A comparison of the leachate elemental concentrations resulting from the leaching of both the calcined non-magnetic and original coarse refuse showed only a slight reduction in the iron content from the non-magnetic material. This finding combined with the REE loss in the magnetic fraction resulted in the conclusion that the magnetic removal step was unfavorable.

58 GEOSCIENCES↗

Element abundances in a gas-rich galaxy at z = 5: clues to the early chemical enrichment of galaxies

Element abundances in high-redshift quasar absorbers offer excellent probes of the chemical enrichment of distant galaxies, and can constrain models for population III and early population II stars. Recent observations indicate that the sub-damped Lyα (sub-DLA) absorbers are more metal-rich than DLA absorbers at redshifts 0 < z < 3. It has also been suggested that DLA metallicity drops suddenly at z > 4.7. However, only three DLAs at z > 4.5 and no sub-DLAs at z > 3.5 have “dust-free” metallicity measurements of undepleted elements. We report the first quasar sub-DLA metallicity measurement at z > 3.5, from detections of undepleted elements in high-resolution data for a sub-DLA at z = 5.0. We obtain fairly robust abundances of C, O, Si, and Fe, using lines outside the Lyα forest. This absorber is metal-poor, with [O/H] = −2.00 ± 0.12, which is ≳4σ below the level expected from extrapolation of the trend for z < 3.5 sub-DLAs. The C/O ratio is 1.8{sub −0.3}{sup +0.4} times lower than in the Sun. More strikingly, Si/O is 3.2{sub −0.5}{sup +0.6} times lower than in the Sun, whereas Si/Fe is nearly (1.2{sub −0.3}{sup +0.4} times) solar. This absorber does not display a clear alpha/Fe enhancement. Dust depletion may have removed more Si from the gas phase than is common in the Milky Way interstellar medium, which may be expected if high-redshift supernovae form more silicate-rich dust. C/O and Si/O vary substantially between different velocity components, indicating spatial variations in dust depletion and/or early stellar nucleosynthesis (e.g., population III star initial mass function). The higher velocity gas may trace an outflow enriched by early stars.

79 ASTRONOMY AND ASTROPHYSICS↗

A COMPARISON OF STELLAR ELEMENTAL ABUNDANCE TECHNIQUES AND MEASUREMENTS

Stellar elemental abundances are important for understanding the fundamental properties of a star or stellar group, such as age and evolutionary history, as well as the composition of an orbiting planet. However, as abundance measurement techniques have progressed, there has been little standardization between individual methods and their comparisons. As a result, different stellar abundance procedures determine measurements that vary beyond the quoted error for the same elements within the same stars. The purpose of this paper is to better understand the systematic variations between methods and offer recommendations for producing more accurate results in the future. We invited a number of participants from around the world (Australia, Portugal, Sweden, Switzerland, and the United States) to calculate 10 element abundances (C, O, Na, Mg, Al, Si, Fe, Ni, Ba, and Eu) using the same stellar spectra for four stars (HD 361, HD 10700, HD 121504, and HD 202206). Each group produced measurements for each star using (1) their own autonomous techniques, (2) standardized stellar parameters, (3) a standardized line list, and (4) both standardized parameters and a line list. We present the resulting stellar parameters, absolute abundances, and a metric of data similarity that quantifies the homogeneity of the data. We conclude that standardization of some kind, particularly stellar parameters, improves the consistency between methods. However, because results did not converge as more free parameters were standardized, it is clear there are inherent issues within the techniques that need to be reconciled. Therefore, we encourage more conversation and transparency within the community such that stellar abundance determinations can be reproducible as well as accurate and precise.

79 ASTRONOMY AND ASTROPHYSICS↗

The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element

Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar global oscillation eigenfunctions and eigenfrequencies. If the Lorentz force is added to the equilibrium equation of motion, stellar eigenmodes can couple. In quasi-degenerate perturbation theory, this coupling, also known as the direct effect, can be quantified by the general matrix element. We present the analytical expression of the matrix element for a superposition of subsurface zonal toroidal magnetic field configurations. The matrix element is important for forward calculations of perturbed solar and stellar eigenfunctions and frequency perturbations. The results presented here will help to ascertain solar and stellar large-scale subsurface magnetic fields, and their geometric configuration, strength, and change over the course of activity cycles.

79 ASTRONOMY AND ASTROPHYSICS↗

NEUTRON-CAPTURE ELEMENT ABUNDANCES IN MAGELLANIC CLOUD PLANETARY NEBULAE

We present near-infrared spectra of 10 planetary nebulae (PNe) in the Large and Small Magellanic Clouds (LMC and SMC), acquired with the FIRE and GNIRS spectrometers on the 6.5 m Baade and 8.1 m Gemini South Telescopes, respectively. We detect Se and/or Kr emission lines in eight of these objects, the first detections of n -capture elements in Magellanic Cloud PNe. Our abundance analysis shows large s -process enrichments of Kr (0.6–1.3 dex) in the six PNe in which it was detected, and Se is enriched by 0.5–0.9 dex in five objects. We also estimate upper limits to Rb and Cd abundances in these objects. Our abundance results for the LMC are consistent with the hypothesis that PNe with 2–3 M {sub ⊙} progenitors dominate the bright end of the PN luminosity function in young gas-rich galaxies. We find no significant correlations between s -process enrichments and other elemental abundances, central star temperature, or progenitor mass, though this is likely due to our small sample size. We determine S abundances from our spectra and find that [S/H] agrees with [Ar/H] to within 0.2 dex for most objects, but is lower than [O/H] by 0.2–0.4 dex in some PNe, possibly due to O enrichment via third dredge-up. Our results demonstrate that n -capture elements can be detected in PNe belonging to nearby galaxies with ground-based telescopes, allowing s -process enrichments to be studied in PN populations with well-determined distances.

79 ASTRONOMY AND ASTROPHYSICS↗

A guide to the design of the virtual element methods for second- and fourth-order partial differential equations

Here we discuss the design and implementation details of two conforming virtual element methods for the numerical approximation of two partial differential equations that emerge in phase-field modeling of fracture propagation in elastic material. The two partial differential equations are: (i) a linear hyperbolic equation describing the momentum balance and (ii) a fourth-order elliptic equation modeling the damage of the material. Inspired by, we develop a new conforming VEM for the discretization of the two equations, which is implementation-friendly, i.e., different terms can be implemented by exploiting a single projection operator. We use C 0 and C 1 virtual elements for the second-and fourth-order partial differential equation, respectively. For both equations, we review the formulation of the virtual element approximation and discuss the details pertaining the implementation.

42 ENGINEERING↗

A high-order staggered finite-element vertical discretization for non-hydrostatic atmospheric models

Abstract. Atmospheric modeling systems require economical methods to solve the non-hydrostatic Euler equations. Two major differences between hydrostatic models and a full non-hydrostatic description lies in the vertical velocity tendency and numerical stiffness associated with sound waves. In this work we introduce a new arbitrary-order vertical discretization entitled the staggered nodal finite-element method (SNFEM). Our method uses a generalized discrete derivative that consistently combines the discontinuous Galerkin and spectral element methods on a staggered grid. Our combined method leverages the accurate wave propagation and conservation properties of spectral elements with staggered methods that eliminate stationary (2Δx) modes. Furthermore, high-order accuracy also eliminates the need for a reference state to maintain hydrostatic balance. In this work we demonstrate the use of high vertical order as a means of improving simulation quality at relatively coarse resolution. We choose a test case suite that spans the range of atmospheric flows from predominantly hydrostatic to nonlinear in the large-eddy regime. Our results show that there is a distinct benefit in using the high-order vertical coordinate at low resolutions with the same robust properties as the low-order alternative.

54 ENVIRONMENTAL SCIENCES↗

Slices: A Scalable Partitioner for Finite Element Meshes

A parallel partitioner for partitioning unstructured finite element meshes on distributed memory architectures is developed. The element based partitioner can handle mixtures of different element types. All algorithms adopted in the partitioner are scalable, including a communication template for unpredictable incoming messages, as shown in actual timing measurements.

partitioner finite element meshes parallel computi↗

Validating Finite Element Models of Assembled Shell Structures

The validation of finite element models of assembled shell elements is presented. The topics include: 1) Problems with membrane rotations in assembled shell models; 2) Penalty stiffness for membrane rotations; 3) Physical stiffness for membrane rotations using shell elements with 6 dof per node; and 4) Connections avoiding rotations.

membrane rotations↗

Integration of a Finite Element Model with the DAP Bone Remodeling Model to Characterize Bone Response to Skeletal Loading

NASA's Digital Astronaut Project (DAP) has developed a bone remodeling model that has been validated for predicting volumetric bone mineral density (vBMD) changes of trabecular and cortical bone in the absence of mechanical loading. The model was recently updated to include skeletal loading from exercise and free living activities to maintain healthy bone using a new daily load stimulus (DLS). This new formula was developed based on an extensive review of existing DLS formulas, as discussed in the abstract by Pennline et al. The DLS formula incorporated into the bone remodeling model utilizes strains and stress calculated from finite element model (FEM) of the bone region of interest. The proximal femur was selected for the initial application of the DLS formula, with a specific focus on the femoral neck. METHODS: The FEM was generated from CAD geometry of a femur using de-identified CT data. The femur was meshed using linear tetrahedral elements Figure (1) with higher mesh densities in the femoral neck region, which is the primary region of interest for the initial application of the DLS formula in concert with the DAP bone remodeling model. Nodal loads were applied to the femoral head and the greater trochanter and the base of the femur was held fixed. An L2 norm study was conducted to reduce the length of the femoral shaft without significantly impacting the stresses in the femoral neck. The material properties of the FEM of the proximal femur were separated between cortical and trabecular regions to work with the bone remodeling model. Determining the elements with cortical material properties in the FEM was based off of publicly available CT hip scans [4] that were segmented, cleaned, and overlaid onto the FEM.

Bone Remodeling↗

Developing Procedures to Implement Geometric Imperfections Beyond Right Circular Cylindrical Shells in Finite Element Method Models

Analysis of aerospace structures is frequently conducted using nominal dimensions and frequently assumes ideal conditions in loading, contact, constraints, et cetera. Off-nominal dimensions and nonideal conditions, however, are present in all structures. These are the result of widely ranging causes from coefficient of thermal expansion mismatches, manufacturing tooling anomalies, to assembly procedures that inadvertently alter the structure. Specifically, geometric imperfections can have potentially significant influence on the response of a structural test article observed in an experiment versus the response given by a numerical simulation. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS) was previously presented as a set of Python scripts to calculate and implement as-manufactured geometric midsurface and thickness imperfections into finite element method (FEM) shell models of nominally right circular cylinders. By taking advantage of the simple shape of a right circular cylinder, interpolations of the measured data points were able to be performed along directions that aligned to the cylindrical coordinate system axes of the entire structure. By taking advantage of the shell representation of the real structure as opposed to modeling using a continuum representation, the thickness variation was able to be implemented by shell section definitions instead of having to modify the position of multiple nodes in the thickness direction. Py_TIGIRS is a useful tool that established a procedural example on how to implement geometric imperfections in right circular cylindrical shell structures. Three new procedures, each expanded from concepts established in Py_TIGIRS, are proposed for various test-article designs and are intended to broaden the range of structures that can be modeled with measured geometric imperfections in the structural analysis community. Each test-article design introduces new challenges to successfully implement geometric imperfections into a FEM model. The first test-article design consists of a carbon fiber reinforced polymer square plate with a hat-shaped stiffener co-cured on one side. This test-article design was for a novel seven-point bend test that was also previously presented. Manufacturing and cure-cycle imperfections are observed using digital image correlation (DIC) techniques. As thermal expansion coefficient mismatches between the plate and stiffener materials were anticipated, a thermal analysis study with continuum shell and solid elements was conducted to capture the global shape observed prior to testing. The second test-article design is of a similar hat-stiffened plate configuration, but with a side length ratio near 3:1 with elongation in the stiffener direction. The test article was used to characterize the response to uniaxial compressive loading in the direction of the stiffener. Due to differing manufacturing steps, a thermal analysis like the one developed for the seven-point bend configuration was unable to mimic the observed geometric imperfections. Instead, a strategy based on applying deformations directly to the structure during analysis was developed for continuum shell and solid element representation of a stiffened panel.

Geometric imperfections↗

Algorithmic Detection of Elemental Biosignatures

Machine learning models that classify a sample as indicative or non-indicative of life could play an important role in life-detection missions. Their predictions result from agnostic algorithms and thereby add redundancy to judgements resulting from human expertise. Additionally, their important features can reveal the most informative measurements within the operational constraints of a life-detection mission. The Ladder of Life Detection (Neveu 2018) identifies the need for an understanding of how combinations of multiple biosignatures affect overall confidence. The present work provides a starting point to answer this need, and future work will expand the data types to obtain even more predictive combinations of features. Elemental abundance was chosen as a starting set of features due to its availability in diverse sample types, which are needed to train a generalizable model. A standardized dataset was collected, including 35 non-indicative, e.g., lunar rock, basalt; 19 indicative mixed, e.g., seawater, agricultural soil; 46 indicative non-alive, e.g., coal, chalk; and 10 indicative alive, e.g., biofilm, bacteria. This dataset could be valuable for complementary biosignature research. The samples were standardized to the same limit of detection of a simulated mission scenario. Four classification models were used: k-nearest neighbors (KNN), logistic regression (LR), linear support vector machines (SVM), and Gaussian naïve Bayes (GNB). To obtain feature importances, KNN was run on three principal components of the training data and LR and SVM were run with L1 and L2 regularization. The performances and feature importances of the six model variants on 40:60 train to validation ratios were assessed with Monte Carlo simulations. ROC AUC and mean accuracy scores ranged between 82% - 94%, with sensitivity greater than specificity. For indicative of life predictors, all models had C and Ca as strong and Cl as medium; a majority of models had N, K, and P as medium. For non-indicative of life predictors, all models had Si as strong, and a majority of models had Mg, Al, and Ti as medium. Varied elements were Fe (slightly non-indicative), H (slightly indicative), O (widely varied), Na, Mn, and S. These results serve as a proof of concept and suggest important elemental signals beyond merely the CHNOPS of Earth-based life.

Algorithmic↗

Modeling the Stochastic Response of Fiber Reinforced Composites with Varied Representative Volume Element Sizes

Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to variability and flaws during manufacturing, making failure predictions difficult. These flaws may occur at the microscale where mechanical properties vary locally due to regions of fiber clusters and matrix pockets. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using a reduced order micromechanical model and NASA’s Multiscale Analysis Tool (NASMAT). Mesoscale models were created with equivalent element sizes to microstructures and properties sampled from microscale simulation results. Results showed how microscale size affects certain mechanical properties. Also shown is how well mesoscale models agree to experiments when using stochastic element properties and varying element size.

microstructure↗

Application of Solar Electric Propulsion to the Low Thrust Lunar Transit of the Gateway Power and Propulsion Element

NASA has committed to returning to the moon, landing the first woman and the next man on its surface. To support a sustained lunar presence, NASA is designing an orbital platform to be assembled in a semi-stable orbit near the moon called the Near Rectilinear Halo Orbit (NRHO). This platform is known as the Gateway and its purpose it to support missions primarily to the lunar south pole. As NASA continues to study ways to reduce the cost of lunar exploration, a simplification implemented in 2020 was combining the first two elements of the Gateway together onto a single commercial launch vehicle (CLV). When launched together, the Power and Propulsion Element (PPE) and NASA’s Habitation and Logistics Outpost (HALO) make up the Co-Manifested Vehicle (CMV). The PPE, a high-power Solar Electric Propulsion (SEP) Stage, will propel the combined stack from a low elliptical orbit to a semi stable orbit near the moon known as a Near Rectilinear Halo Orbit (NRHO). A transit of such a large mass, delivered to the moon from a single launch vehicle is only made possible by the use of the highly efficient SEP low thrust propulsion system. Delivering the same mass via more traditional chemical propulsion systems would require multiple launches and significantly more propellant. This paper captures an overview of the PPE’s SEP system, the lunar transit it will perform to deliver these first two elements of NASA’s Gateway to the NRHO with a comparison of a chemical system performing the same lunar transit to illustrate how SEP enables NASA’s Gateway.

electric propulsion↗

Multiphysics Simulations of the Complex 3D Geometry of the High Flux Isotope Reactor Fuel Elements Using COMSOL

A research and development project is ongoing to convert the currently operating High Flux Isotope Reactor (HFIR) of Oak Ridge National Laboratory (ORNL) from highly-enriched Uranium (HEU U3O8) fuel to low-enriched Uranium (LEU U-10Mo) fuel. Because LEU HFIR-specific testing and experiments will be limited, COMSOL is chosen to provide the needed multiphysics simulation capability to validate against the HEU design data and calculations, and predict the performance of the LEU fuel for design and safety analyses. The focus of this paper is on the unique issues associated with COMSOL modeling of the 3D geometry, meshing, and solution of the HFIR fuel plate and assembled fuel elements. Two parallel paths of 3D model development are underway. The first path follows the traditional route through examination of all flow and heat transfer details using the Low-Reynolds number k-e turbulence model provided by COMSOL v4.2. The second path simplifies the fluid channel modeling by taking advantage of the wealth of knowledge provided by decades of design and safety analyses, data from experiments and tests, and HFIR operation. By simplifying the fluid channel, a significant level of complexity and computer resource requirements are reduced, while also expanding the level and type of analysis that can be performed with COMSOL. Comparison and confirmation of validity of the first (detailed) and second (simplified) 3D modeling paths with each other, and with available data, will enable an expanded level of analysis. The detailed model will be used to analyze hot-spots and other micro fuel behavior events. The simplified model will be used to analyze events such as routine heat-up and expansion of the entire fuel element, and flow blockage. Preliminary, coarse-mesh model results of the detailed individual fuel plate are presented. Examples of the solution for an entire fuel element consisting of multiple individual fuel plates produced by the simplified model are also presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Excited State Effects in Nucleon Matrix Element Calculations

We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge g{sub A} and for the first moment of the isovector unpolarized parton distribution x{sub u-d}. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using N{sub f} = 2+1+1 maximally twisted mass Wilson fermions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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