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At least 1,315 records · Page 73

Lunar Origin: Role of Giant Impacts

The explanation that lunar origin involved giant impacts remains attractive. Large planetesimals are consistent with current accretion models, and may have been widely scattered in the early solar systems; their existence is a reasonably, assumption in Moon origin models. Isotopic data require the Moon's formation primarily from local material resembling Earth's upper mantle, not material from elsewhere in the solar system. Giant impacts are stochastic, class predictable events that would provide the required type of ejected Earth mantle material without requiring large moons to form near other planets (a problem with less stochastic processes). Such material may have mixed with incoming meteorites during lunar formation, affecting lunar chemistry.

Hartmann, W. K.↗

High-temperature thermal storage systems for advanced solar receivers materials selections

Advanced space power systems that use solar energy and Brayton or Stirling heat engines require thermal energy storage (TES) systems to operate continuously through periods of shade. The receiver storage units, key elements in both Brayton and Stirling systems, are designed to use the latent heat of fusion of phase-change materials (PCMs). The power systems under current consideration for near-future National Aeronautics and Space Administration space missions require working fluid temperatures in the 1100 to 1400 K range. The PCMs under current investigation that gave liquid temperatures within this range are the fluoride family of salts. However, these salts have low thermal conductivity, which causes large temperature gradients in the storage systems. Improvements can be obtained, however, with the use of thermal conductivity enhancements or metallic PCMs. In fact, if suitable containment materials can be found, the use of metallic PCMs would virtually eliminate the orbit associated temperature variations in TES systems. The high thermal conductivity and generally low volume change on melting of germanium and alloys based on silicon make them attractive for storage of thermal energy in space power systems. An approach to solving the containment problem, involving both chemical and physical compatibility, preparation of NiSi/NiSi2, and initial results for containment of germanium and NiSi/NiSi2, are presented.

Wilson, D. F.↗

Silicon Photo-Multiplier Readouts for Scintillators in High-Energy Astronomy

New scintillator materials have recently been shown to hold great potential for low-cost, reliable gamma-ray detectors in high-energy astronomy. New devices for the detection of scintillation light promise to make scintillator-based instruments even more attractive by reducing mass and power requirements,in particular, silicon photo-multipliers (SiPMs) are starting to become commercially available that offer gains and quantum efficiencies similar to those of photo-multiplier tubes (PMTs), but with greatly reduced mass, high ruggedness, low voltage requirements, and no sensitivity to magnetic fields. We have conducted laboratory tests of a sample of commercially available SiPMs coupled to LaBr3;Ce, a scintillator of relevance to to future high-energy astrophysics missions. We present results for gamma-ray spectroscopy. compare the SiPM performance to that of a PMT, and discuss the extent to which SiPMs offer significant advantages for scintillator-based space missions.

Bloser, Peter F.↗

A Solid State Zwitterionic Plastic Crystal With High Static Dielectric Constant

Solid materials with a high dielectric constant have a wide range of applications in the energy storage field. In this research, an imidazolium-based zwitterion is designed, synthesized, and confirmed to have a plastic crystal phase based on the following experimental and computational evidence: (i) the presence of long-range order with weak intermolecular forces and competing attractive-repulsive interactions along different crystallographic directions; (ii) the observation of more than one endotherm on heating including a solid-solid phase transition at T s-s = −26 °C and melting of the plastic crystal at T m = 72°C; (iii) a low entropy of fusion at melting (2.1 JK −1 mol −1 ); (iv) a strongly anisotropic morphology; (v) relatively fast dynamics originating from short-range degrees of freedom. Furthermore, it exhibits a very high dielectric constant in the plastic crystal solid state (147 at −10°C and 103 at 70°C) due to the rotational degrees of freedom of plastic crystals that arise from weak net intermolecular interactions of zwitterions due to only having two carbons between the anion and cation. This material conveniently remains in the plastic crystal phase within 50 K of ambient temperature. This discovery opens new opportunities in the search for solid-state high dielectric constant materials.

dielectric relaxation↗

Modeling and Measuring the Stress Distribution in Soft Magnetic Cores due to Epoxy Impregnation and Curing

Understanding the effects of viscoelastic relaxation of stresses is critical in electric motor and inductor applications, where the magnetic material is fully or partially comprised of an amorphous phase and impregnated in an epoxy. Magnetic Amorphous Nanocomposites (MANCs) are a class of recently developed high-frequency magnetic materials that exhibit low magnetic hysteresis, high saturation flux density and very low AC magnetic losses. MANCs are formed as long, thin ribbons, a shape factor that minimizes eddy current-induced self-heating. This feature, in addition to their 1 GPa strength, and makes them attractive candidates for high-speed, high-power density, electric motors. MANCs are used in the form of tape-wound cores (TWCs). During the manufacturing process, the cores are impregnated with liquid epoxy between each layer of ribbon. Validated knowledge of the stresses imposed by the manufacturing process and during operation is necessary to understand motor performance limitations with respect to strength. Magnetostriction, the strain imposed by reversal of the magnetic field, also affects performance. When the epoxy cures, it contracts volumetrically by 8%, imposing radial and circumferential stresses that vary along the radial direction. To date, these stresses have received little attention in the literature. Here, we model the stress distribution throughout a TWC due to epoxy curing. Strain gauge measurements reported here indicate substantially lower tangential strain than model values, which is beneficial and which we attribute to viscoelastic relaxation of the epoxy layers. We will incorporate a constitutive model of this viscoelastic relaxation, and conduct more detailed strain measurements to understand how this takes

24 POWER TRANSMISSION AND DISTRIBUTION↗

Solvent–Solvent Correlations across Graphene: The Effect of Image Charges

Wetting experiments show pure graphene to be weakly hydrophilic, but its contact angle (CA) also reflects the character of the supporting material. Measurements and Molecular Dynamics simulations on suspended and supported graphene often reveal a CA reduction due to the presence of the supporting substrate. A similar reduction is consistently observed when graphene is wetted from both sides. The effect has been attributed to transparency to molecular interactions across the graphene sheet, however, the possibility of substrate-induced graphene polarization has also been considered. Computer simulations of CA on graphene have so far been determined by ignoring the material’s conducting properties. We improve the graphene model by incorporating its conductivity according to the Constant Applied Potential Molecular Dynamics. Using this method, we compare the wettabilities of suspended graphene and graphene supported by water by measuring the CA of cylindrical water drops on the sheets. The inclusion of graphene conductivity and concomitant polarization effects lead to a lower CA on suspended graphene but the CA reduction is significantly bigger when the sheets are also wetted from the opposite side. The stronger adhesion is accompanied by a profound change in the correlations among water molecules across the sheet. While partial charges on water molecules interacting across an insulator sheet attract charges of the opposite sign, apparent attraction among like charges is manifested across the conducting graphene. The change is associated with graphene polarization, as the image charges inside the conductor attract equally signed partial charges of water molecules on both sides of the sheet. Additionally, by using a non-polar liquid (diiodomethane), we affirm a detectable wetting translucency when liquid-liquid forces are dominated by dispersive interactions. Furthermore, our findings are important for predictive modeling toward a variety of applications including sensors, fuel cell membranes, water filtration, and graphene-based electrode materials in high-performance supercapacitors.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Nematic superconductivity in twisted bilayer graphene

Twisted bilayer graphene displays insulating and superconducting phases caused by exceptional flattening of its lowest energy bands. Superconductivity with highest T c appears near half filling of the valence band (n ≈ –2). The data show that in the large part of the superconducting dome near n = –2, threefold lattice rotation symmetry is broken in the superconducting phase, i.e., a superconductor is also a nematic. We perform a comprehensive analysis of superconductivity in twisted-bilayer graphene within an itinerant approach and present a mechanism for nematic superconductivity. We take as an input the fact that at dopings, where superconductivity has been observed, the Fermi energy lies in the vicinity of twist-induced Van Hove singularities in the density of states. We argue that the low-energy physics can be properly described by patch models with either six or twelve Van Hove points. We obtain pairing interactions for the patch models in terms of parameters of the microscopic model for the flat bands, which contains both local and twist-induced nonlocal interactions. Here, we show that the latter give rise to attraction in different superconducting channels. For six Van Hove points, there is just one attractive d-wave channel, and we find chiral d ± id superconducting order, which breaks time-reversal symmetry but leaves the lattice rotation symmetry intact. For twelve Van Hove points, we find two attractive channels, g and i waves, with almost equal coupling constants. We show that both order parameters are nonzero in the ground state and explicitly demonstrate that in this co-existence state the threefold lattice rotation symmetry is broken, i.e., the superconducting state is also a nematic. We find two possible nematic states, one is time-reversal symmetric, the other additionally breaks time-reversal symmetry. We apply our scenario to twisted bilayer graphene near n = –2 and argue that it is applicable also to other systems with two (or more) attractive channels with similar couplings as our reasoning for a nematic superconductivity is based on generic symmetry considerations.

36 MATERIALS SCIENCE↗

Dynamic, Adaptive, Systems and Materials: Complex, Simple and Emergent Behaviors

This program has been funded by DoE/BES for twenty years. It has moved into and out of various subjects as it has developed, but it has retained its focus on complexity and complex systems. The project has evolved in the following way: Self-Assembly and Biomimetic Self-Assembly: All self-assembling systems depend upon a minimum of two types of interaction: a repulsion and an attraction. For the familiar molecular systems, attractive interactions are typically hydrogen bonds and electrostatic interactions. Repulsive interactions include steric effects, hydrophobic effects (in biological systems), and charge-charge repulsion. We have expanded this repertoire to include surface interactions, magnetic interactions, and others. I list these systems in the order in which we have explored them: i) A key emphasis in current work is in understanding how the movement of ions in a magnetic field (the Lorentz effect) interacts with catalytic systems. We have demonstrated that an acceleration in rate of reduction of CO 2 to CO can be accomplished by applying an external magnetic field. This acceleration is largely due to the application of the Lorentz effect on mass transport at the catalyst’s surface. ii) We have also extensively explored the influence of electrostatics, as exhibited in self-assembling systems, by tribocharging. iii) Another key system involves surface tension effects; examples include interactions between heavy particles floating at a liquid-air interface, and interacting by changes in surface area; interactions of bubbles and bubble rafts, behaviors of bubble trains in microfluidic networks, and behaviors of microorganisms in constraining environments. iv) This work has intentionally de-emphasized biological systems; but it does include some work on protein-ligand interactions and interactions among microorganisms. v) We have also explored applications of some of these effects, these explorations include bubble rafts as diffraction gratings, exploration of the structures that can be obtained by tribocharging and uses of these structures in exploring nucleation and melting of crystals. vi) Although not a major focus of this work, several other topics have emerged and offer opportunities for future work. These include the behavior of bubble trains and bubble rafts in microfluidic systems. A particularly interesting example is the formation of bubble trains that repeat in the alteration of large and small bubbles according to rules we do not presently understand, but are uniquely large-period oscillating systems. These systems offer a new route into understanding the instabilities of the type represented by oscillations. vii) We have also begun exploratory projects on magnetic levitation (especially to determine molecular density), and information storage (in molecules). Magnetic Levitation: Self-assembling and biomimetic systems require both attraction and repulsion. We have used electrostatics (tribocharging), interfacial free-energies (surface tension and related forces) and others. Potential uses include reconfigurable diffraction gratings and liquid lenses; exploration of mechanisms in tribocharging; tunneling in EGaIn junctions; and bubble trains (especially in micro-fluidic systems). Examples of systems representing these topics is included in the following papers: Complexity: Disks rotating at a water-air interface; Benard-Marangoni effects; Vortex-Crystals from spinning magnetic disks (Marangoni effects); EGaIn Electrode to study quantum tunneling; Self-Assembly of electrostatically-charged metallic spheres (electrets); Dynamically reconfigurable lens; Using computational designs of ligands for enzymes; Electrostatic self-assembly by tribocharging; Monodisperse bubble trains in microchannel systems; Inverted dripping faucet; Flames; Printing of micro-organisms to regenerate the “ink” of printing device; Using micro-organisms to move loads (“microoxen”); Motion of bacterial swarms near surfaces; Making monodisperse particles in microfluidic systems; Coding/decoding of information stored in droplet trains in microfluidic networks; Magnetic levitation; and Information storage. i) Tribocharging. The change in focus of this work on electrets from the fundamentals of charging to applications of these materials in studying self-assembly using electrostatic interactions. ii) Bubbles in Microchannels. The realization that systems of bubbles in microchannels represented a major opportunity to study complexity in a very tractable system, and the development of a semi-quantitative theory of this subject. iii) Flames. The growth of “flames” remains an exploratory subject for the research, although their currently relatively little active work involving it ongoing. iv) Systems with Microorganisms. The removal of work in biological systems from this project. Based on work supported in this program, we now have a significant project on the development of microfluidic tools for studying C. elegans (a nematode), but this work was not appropriate for a program focused on complexity, and we developed separate support for it. (It is, however, an example of successful seeding of a new area by BES.) The work on electrets has gone through a period in which a part of the program was the subject of a MURI; the focus of this work was to develop materials that did not charge electrostatically on friction or contact. The MURI is now over, and the work on dynamic self-assembly (supported by BES) is the major focus. “Flames” has also enjoyed synergistic support, in terms of a project supported by DARPA on flame suppression (in the absence of extinguishing agents, using acoustic and electrostatic interactions). This work was helpful in understanding some of the basics of flames, but is entirely distinct from the BES focus in complexity. A growing interest is in the Lorentz effect. The Lorentz effect is the force exerted on charged particles (electrons, ions, charged molecules) when they move through a perpendicular magnetic field. The Lorentz effect is almost ubiquitous in modern technology: examples of applications include electric motors, dynamos, cathode ray tubes, many batteries, and most systems that control electrical currents with magnetic forces. We have begun to explore the Lorentz effect in electrochemical systems and heterogeneous catalytic systems involving charged organic species and inorganic ions. This work is still at an early stage, but initial studies that Lorentz effects can be large when ions move through magnetic fields, or magnetic fields move in the presence of ions.

36 MATERIALS SCIENCE↗

Structural Characteristics and Phase Evolution of Calcium-Reduced (Sm,Zr)(Fe,Co,Ti) 12 Particles

Magnetic materials are essential for applications in electronics, energy conversion and many other industrial and technological sectors. Among the permanent magnets, rare-earth magnets exhibit the strongest properties and dominate the market shares in related applications. However, due to the increasing cost and unstable supply, the research on reducing the rare-earth elements in magnets attracts significant increasing interest. Rare-earth-lean samarium transition metal (TM) compounds (SmTM 12 or 1:12 for short) have made breakthroughs in 2020 and the (Sm,Zr)(Fe,Co,Ti) 12 monocrystalline particles synthesized by a Ca reduction of elemental oxides at high temperature demonstrated an order of magnitude improvement in coercivity at room temperature. In this study, we made structural analysis of (Sm,Zr)(Fe,Co,Ti) 12 particles to elucidate the impact of synthesis conditions, microstructure and phase transformation on the evolution of magnetic properties.

36 MATERIALS SCIENCE↗

The Riddle of Dark LLZO: Cobalt Diffusion in Garnet Separators of Solid‐State Lithium Batteries

Abstract Solid‐state batteries (SSBs) with a Li 7 La 3 Zr 2 O 12 (LLZO) garnet electrolyte are attracting much attention as robust and safe alternative to conventional lithium‐ion batteries. Technical challenges in the practical implementation of garnet SSBs are related to the need for high‐temperature sintering, which often leads to undesirable chemical reactions with the cathode material. While these reactions are well understood for composite cathodes, very little is known about similar processes between cathode and separator during battery fabrication. This work focuses on understanding the processes between the composite LiCoO 2 ‐LLZO cathode and the LLZO separator and how they affect the battery performance. The extensive diffusion of Co‐ions within LLZO, which leads to the often‐observed LLZO darkening, is shown to have a significant impact on ionic conductivity, electronic conductivity, and dendrite stability of the separator. Experimental data coupled with large‐scale molecular dynamics simulations uncover the diffusion mechanism for Co‐ions and identify secondary phases that form during these interactions. In addition to extensive Co‐ion diffusion within the grains, a non‐uniform segregation of Co‐ions at grain boundaries is found leading to the formation of three distinct Co‐containing phases. This work offers a general approach to studying the fundamental ion diffusion processes that occur during the fabrication of oxide SSBs.

electrochemical properties↗

Bayesian optimization of entropy-stabilized metal fluoride conversion cathodes and their synthesis

Fluoride-based conversion cathodes are promising for next-generation Li ion batteries because of their high voltage and energy densities. High entropy earth abundant fluoride cathodes are attractive for sustainable battery because of the potentially higher cycling stability. While Ni and Co containing equimolar alloys stabilized by high entropy were considered previously, Ni and Co free non-equimolar metal alloy compositions might offer new opportunities to increase materials stability and average voltage. This opportunity was pursued using Bayesian optimization of average voltage for the computational prediction of (Fe x1 Cu x2 Zn x3 Mn x4 Mg x5 )F 2 cathode chemistries. Theoretical voltage, room temperature free energy, and electronic structure of potentially high voltage compositions were computed using density functional theory calculations. Here, the experimental realization of non-equimolar quinary Co and Ni free fluorides with stable rutile single phase and improved conversion reaction voltage by up to 28 % compared to the equimolar alloy demonstrated the power of Bayesian optimization methods for the computationally guided experimental synthesis of fluoride cathodes. Finally, non-equimolar cathode chemistries were found with cycling stability superior to known multi-element fluorides.

25 ENERGY STORAGE↗

Redox Chemistry Mediated Control of Morphology and Properties in Electrically Conductive Coordination Polymers: Opportunities and Challenges

Coordination polymers (CPs) and metal–organic frameworks (MOFs) have attracted significant research interest in the past several decades due to their reticular structures and modularity. However, realizing electrically conductive CPs or MOFs with comparable properties to classic conducting organic polymers has only been a recent development. This emerging class of materials has found wide appli-cation in many fields due to combined features of structural rigidity, chemical tunability, porosity, and charge transport. Alongside many studies revealing myriad design approaches to access these materials, the role that redox chemistry plays in both material synthesis and modulation of electronic properties has been an emerging theme. This perspective provides a brief overview of select examples where redox chemistry medi-ates control of morphology and properties in electrically conductive CPs/MOFs. Here, the challenges and limitations in this area are also discussed. Particular challenges include the characterization of redox states in these materials and measuring and understanding highly correlated elec-tronic properties and other unusual physical phenomena which may be important for potential applications.

36 MATERIALS SCIENCE↗

Superconductivity at carrier density 10 17 cm – 3 in quasi-one-dimensional Li 0.9 Mo 6 O 17

Superconductivity is a fascinating phenomenon that involves an attractive interaction by which electrons are paired and can move without electrical resistance below a critical temperature T c . A paradigm for understanding superconductive pairing, the successful “BCS” theory, developed more than 65 years ago, is challenged by certain classes of materials for which parameters (e.g. the value of T c , the density of electrons, etc.) fall outside the range for which BCS theory is applicable. The study of such materials is important because new physics may be revealed and because superconductivity has many potential applications in sensing and electronics. Superconductivity at very low carrier density is a rare and fascinating phenomenon that is of considerable importance and interest in condensed matter physics. The conditions of high density of states and effective screening of Coulomb repulsion, both key ingredients of stable Cooper pairing in the BCS theory, may not be met at low carrier density. Thus, such systems may also harbor unconventional electron pairing (e.g. non-phononic) or pairing without phase coherence as a precursor to Bose-Einstein condensation. An intriguing route toward extreme low-density (and possibly unconventional) superconductivity may be found in quasi-one-dimensional metals for which density-wave instabilities compete for the ground state and can lead to gapping of substantial portions of the Fermi surface (FS), leaving a residual (reconstructed) FS comprising a very small carrier density. Our work highlights a novel material in this unusual category: Li 0.9 Mo 6 O 17 (T c =2 K) (also known as "lithium purple bronze" or "LiPB"). We present both electrical and thermoelectric magnetotransport measurements that reveal superconductivity to occur at carrier density 2 x10 17 cm -3 , among the lowest known for any superconductor, and four orders of magnitude lower than is expected from its chemical valence and band structure. With its exceptionally large ratio of superconducting to Fermi temperature, T c /TF ≳ 0.1, LiPB is properly placed at the top of a very small group of superconductors (including cuprates, heavy-fermion and Fe-based superconductors) for which this ratio falls in the BCS-BEC crossover regime and for which pairing is believed to be spin mediated.

36 MATERIALS SCIENCE↗

SurFE-XD (Surface curvature-driven Finite Elements model for Diffusion under eXtreme conditions)

SurFE-XD is a mesoscale finite element framework to model surface diffusion under mutliphysics environments. The code uses legacy C++ library dolphin wrapped with python in a FEniCS driven unified form language and just-in-time (JIT) compilation setting. The purpose of the release is to attract wide-ranging usage of the code along with publication supplementation to support reproducibility of scientific data. SurFE-XD has been originally conceived under the LDRD-DR funding for “High-Gradient (C-BAND) Breakdown tolerant accelerator materials project. Currently SrFE-XD support electrostatics and Thermo-elasticity driven surface diffusion kernels. Releasing the code will also enable to include contributions from other physical regimes e.g., plasticity and electrodynamics etc as well portability to GPU-based platforms.

Bagchi, Soumendu↗

High-Temperature Alkaline Water Electrolysis

Hydrogen production for mobile and energy storage applications from water electrolysis is attractive due to its high efficiency, fast ramp rates, and potential for the clean energy economy. However, current hydrogen production from electrolysis comprises only a small fraction of the global hydrogen market due to the high cost associated with expensive stack materials (membrane, catalyst, and bipolar plates) and electricity consumption of the commercial electrolysis systems. In this project, we aimed to develop a high temperature alkaline water electrolyzer (HTAWE) that can simultaneously reduce the electrolyzer cost (by adopting cheap material) and improve energy efficiency (by enabling high-temperature operation).

08 HYDROGEN↗

Organic Solvent Free Process to Fabricate High Performance Silicon/Graphite Composite Anode

Cycling stability is a key challenge for application of silicon (Si)-based composite anodes as the severe volume fluctuation of Si readily leads to fast capacity fading. The binder is a crucial component of the composite electrodes. Although only occupying a small amount of the total composite mass, the binder has major impact on the long-term electrochemical performance of Si-based anodes. In recent years, water-based binders including styrene-butadiene rubber (SBR) and carboxymethyl cellulose (CMC) have attracted wide research interest as eco-friendly and low-cost alternatives for the conventional poly(vinylidene difluoride) (PVDF) binder in Si anodes. In this study, Si-based composite anodes are fabricated by simple solid mixing of the active materials with subsequent addition of SBR and CMC binders. This approach bypasses the use of toxic and expansive organic solvents. The factors of binder, silicon, and graphite materials have been systematically investigated. It is found that the retained capacities of the anodes are more than 440 mAh/g after 400 cycles. These results indicate that organic solvent free process is a facile strategy for producing high performance silicon/graphite composite anodes.

Fang, Chen (ORCID:0000000321011991)↗

Chlorination processing of local planetary ores for oxygen and metallurgically important metals

The use of chlorine to extract, reclaim, and purify metals has attractive possibilities for extraterrestrial processing of local planetary resources. While a complete cyclic process has been proposed for the recovery of metallurgically significant metals and oxygen, herein the chlorination step of the cycle is examined. An experimental apparatus for reacting refractory materials, such as ilmenite, in a microwave induced plasma is being built. Complex equilibria calculations reveal that stable refractory materials can, under the influence of a plasma, undergo chlorination and yield oxygen as a by-product. These issues and the potential advantages for plasma processing in space are reviewed. Also presented is a discussion of the complex equilibria program used in the analysis.

Lynch, D. C.↗

CARES/Life Ceramics Durability Evaluation Software Enhanced for Cyclic Fatigue

The CARES/Life computer program predicts the probability of a monolithic ceramic component's failure as a function of time in service. The program has many features and options for materials evaluation and component design. It couples commercial finite element programs--which resolve a component's temperature and stress distribution--to reliability evaluation and fracture mechanics routines for modeling strength-limiting defects. The capability, flexibility, and uniqueness of CARES/Life have attracted many users representing a broad range of interests and has resulted in numerous awards for technological achievements and technology transfer. Recent work with CARES/Life was directed at enhancing the program s capabilities with regards to cyclic fatigue. Only in the last few years have ceramics been recognized to be susceptible to enhanced degradation from cyclic loading. To account for cyclic loads, researchers at the NASA Lewis Research Center developed a crack growth model that combines the Power Law (time-dependent) and the Walker Law (cycle-dependent) crack growth models. This combined model has the characteristics of Power Law behavior (decreased damage) at high R ratios (minimum load/maximum load) and of Walker law behavior (increased damage) at low R ratios. In addition, a parameter estimation methodology for constant-amplitude, steady-state cyclic fatigue experiments was developed using nonlinear least squares and a modified Levenberg-Marquardt algorithm. This methodology is used to give best estimates of parameter values from cyclic fatigue specimen rupture data (usually tensile or flexure bar specimens) for a relatively small number of specimens. Methodology to account for runout data (unfailed specimens over the duration of the experiment) was also included.

Nemeth, Noel N.↗