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

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At least 1,243 records · Page 69
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Separating the Influence of Environment from Stress Relaxation Effects on Dwell Fatigue Crack Growth in a Nickel-Base Disk Alloy

Both environmental embrittlement and crack tip visco-plastic stress relaxation play a significant role in determining the dwell fatigue crack growth (DFCG) resistance of nickel-based disk superalloys. In the current study performed on the Low Solvus High Refractory (LSHR) disk alloy, the influence of these two mechanisms were separated so that the effects of each could be quantified and modeled. Seven different microstructural variations of LSHR were produced by controlling the cooling rate and the subsequent aging and thermal exposure heat treatments. Through cyclic fatigue crack growth testing performed both in air and vacuum, it was established that four out of the seven LSHR heat treatments evaluated, possessed similar intrinsic environmental resistance to cyclic crack growth. For these four heat treatments, it was further shown that the large differences in dwell crack growth behavior which still persisted, were related to their measured stress relaxation behavior. The apparent differences in their dwell crack growth resistance were attributed to the inability of the standard linear elastic fracture mechanics (LEFM) stress intensity parameter to account for visco-plastic behavior. Crack tip stress relaxation controls the magnitude of the remaining local tensile stresses which are directly related to the measured dwell crack growth rates. It was hypothesized that the environmentally weakened grain boundary crack tip regions fail during the dwells when their strength is exceeded by the remaining local crack tip tensile stresses. It was shown that the classical creep crack growth mechanisms such as grain boundary sliding did not contribute to crack growth, but the local visco-plastic behavior still plays a very significant role by determining the crack tip tensile stress field which controls the dwell crack growth behavior. To account for the influence of the visco-plastic behavior on the crack tip stress field, an empirical modification to the LEFM stress intensity parameter, Kmax, was developed by incorporating into the formulation the remaining stress level concept as measured by simple stress relaxation tests. The newly proposed parameter, Ksrf, did an excellent job in correlating the dwell crack growth rates for the four heat treatments which were shown to have similar intrinsic environmental cyclic fatigue crack growth resistance.

Dwell crack growth↗
NASA NTRSDate not supplied

Design Development of a Stable, Lightweight, Tall and Self-Deploying Lunar Tower

Deployable composite booms with spaceflight heritage are being investigated at the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) and the Massachusetts Institute of Technology (MIT) Space Resources Workshop for their potential to be vertically deployed in the lunar gravity field, in support of the NASA Artemis campaign. This paper reports new design development results—after the original presentation at the NASA 2020 BIG Idea Challenge—for a 16.5-meter-tall, compact, self-deploying composite tower intended to support the exploration of lunar permanently shadowed regions by nearby robotic assets or humans. Possible applications include vertical solar arrays and the provision of elevated lines-of-sight to science or engineering payloads, in support of nearby targets operating in areas of interest that may be hard to reach. Useful elevated payloads include radio repeaters, remote sensing and imaging, navigation and power beaming systems. However, while these lightweight rollable booms have an excellent height to mass ratio, they typically exhibit axial curvature upon deployment resulting in appreciable lateral dead-load deflection of the tip mass relative to the tower base. This static deflection increases with tower height and tip mass, not only constraining the value delivered by the tower but also endangering its integrity. To develop a competitive, lightweight deployable composite boom tower, a capability to correct static deflections during and after deployment will be required. In this paper, a deployable guy wire stability system will be presented for the MIT / LaRC self-erecting composite boom lunar tower that provides real time measurements, maintains tension both actively (during deployment) and passively (post-deployment), and can serve as a reconfigurable platform to test and trade alternative stability system configurations, such as with added spreaders inspired by sailing boat masts. Using a calibrated photogrammetry system, the natural lateral deflection of the boom tip relative to the boom base at different deployed heights was recorded for different configurations. With real-time force measurements it was found that tensioned guy wires can significantly reduce the static tip deflection of a deployable composite boom under dead load and can dampen a dynamic oscillation in under a minute. It was also found that control authority is greatest where it is needed most, i.e., for the lever arm closest to being opposite the direction of deflection. For a tower height of at least 11 m and spreader length of at least 60 cm, a solution of differential tension in all three arms exists and, in principle, provides sufficient control authority to correct or significantly reduce boom tip deflections. Notably, natural deflections occur almost entirely normal to the seams of the boom cross-section, but the natural boom tip lateral deflection under dead load upon deployment was approximately 5% of boom deployed length, exceeding the manufacturing acceptance specification of 1%. Ongoing and future work includes the further investigation towards mitigating manufacture-caused lateral deflection, trading of alternative guy wire system designs, as well as the design development of a second-generation tower incorporating a more capable boom design with the learnings from the proof-of-concept system presented here.

deployable composite boom↗
NASA NTRSDate not supplied

Disorder to Order in Interface Patterns: Thermal Noise to Limit Cycle Transition in Dendrite Sidebranch Formation

Thin sample directional solidification experiments have been carried out in the model succinonitrile-camphor system to examine the origin of secondary branches in dendrite morphologies. Thermal noise at the dendrite tip creates interface instabilities which amplify to form sidebranches. This is accepted as the primary mode of sidebranching in dendritic growth from an undercooled melt and occurs in directional solidification of dendrites. The proposed limit cycle couples the growth of the tip with the initiation of the sidebranch. Directional solidification of curved interfaces is a driven dissipative system with the potential to form a limit cycle. Two sets of experiments were performed, the first holding velocity constant and evolving the gradient and the second imposing oscillating velocities around the natural period of sidebranching. Both experimental methods were found to characterize a transition from disordered sidebranching induced by thermal noise to ordered sidebranching produced by the limit cycle mechanisms. This is the first quantitative measurement of previously hypothesized limit cycle growth. These experiment sets have been quantitatively analyzed for dynamic behavior seen in limit cycles. High-quality data sets of the tip and instability enable the measurement of the FFT and analysis through a power spectrum. At low gradients, the sidebranches are found to be excited by thermal noise far away from the tip. As the gradient increases and velocity is held constant, the distance between the instability and tip decreases until limit cycle growth is found between the tip of the primary dendrite and the first forming sidebranch. An alternative to the deterministic limit cycles seen in experiments of gradient evolution is a limit cycle actively driven through the square wave oscillation of velocity. Crucial observations of the solidified microstructure conclude that this produced periodic interconnected bridges between the primary dendrites. This is a finding with potentially significant implications for commercial applications.

Trevor Lyons↗
DOE OSTI2024

Wind turbine performance enhancement with minimal structural load penalty: A design philosophy

The performance benefits of using tip devices on wind turbines has been well-documented. However, previous studies show that adding blade tip devices such as winglets leads to a significant increase in blade root bending moment, potentially requiring structural reinforcement with cost and weight drawbacks. A new and unique design philosophy for retrofit blade tip devices for wind turbines is presented. By balancing generated aerodynamic and centrifugal loads, these devices offer an increase in power production without the need for structural reinforcement. Predicted performance and cost benefits of using retrofit blade tip devices on the National Renewable Energy Laboratory 5 MW reference wind turbine are shown. Finally, the addition of blade tip devices resulted in significant improvements in the coefficient of power (C p ) and annual energy production (AEP).

17 WIND ENERGY↗
DOE OSTI2023

Stable electrospray signal on a microfabricated glass chip with three-dimensional open edge and tiered depth geometries

This paper presents the microfabrication and performance of a three-dimensional electrospray ionization (ESI) emitter tip made from glass, which achieves stable current signals important for chemical analysis. Our novel microfabrication process and custom-built signal conditioning hardware provides the advantage of providing accurate features and steady signals. The fabrication process relies on standard microfabrication techniques (i.e., deposition, photolithography, and wet etching). This fabrication method involves the novel application of two layers of positive and negative photoresists in addition to Parafilm® wax tape. Open edge and tiered depth details were successfully created from a multilayer planar mask. This is a benefit for integrated miniaturized and microfluidic systems that often require micro features for their functionality but relatively large millimeter size features for their physical periphery. We demonstrate the fundamental performance of electrospray with this microfluidic chip. The emitter tip was fixed on a linear axis stage with high resolution (10 μm) to finely control the tip distance from a metal counter electrode plate. Further, a custom printed circuit board system was built to safely control four voltages applied to the microchip ports from a single high voltage power supply. To readily form the electrospray, non-aqueous solvents were used for their low viscosity and a constant voltage of +2.7 kV was applied to the sheath electrospray microchannel. The liquid being sprayed was 80/20 (v/v) methanol/acetonitrile with 0.1% acetic acid in the sheath microchannel and with ammonium acetate (10–40 mM) in its remaining microchannels. The electrospray signal was measured in response to varying the distance (1.4 to 1.6mm) between the electrospray emitter tip and a metal counter electrode plate in addition to the varying concentration of the background electrolyte, ammonium acetate. Stable and repeatable electrospray signal showed linear relationships with emitter tip distance and concentration (r 2 ≥ 0.95).

42 ENGINEERING↗
DOE OSTI2025

Plant-microbial interplay for organic nitrogen mediated by functional specificity of root compartments

The organic form of nitrogen (N) is a critical intermediate in mutualistic and competitive root-microbial interactions, mediated by extracellular enzymes. Visualization of the hotspots of organic N and proteolytic activity might be valuable for revealing root functional specificity in N acquisition and transformation at the level of individual roots and compartments. For the first time, we used time-lapse amino-mapping and zymography to co-localize and map the spatial distribution of amino-N and leucine aminopeptidase (LAP) activity in the soil and different root parts of maize (Zea mays L.). Amino-N distribution was mainly associated with seminal roots and root tips, where it overlapped with LAP activity hotspots. In the lateral roots and bulk soil, however, LAP activity was decoupled from amino-N. Distinct functional traits revealed themselves as the highest amino-N content and LAP activity in seminal root tips and as the largest relative extent of the rhizosphere in lateral root tips. Co-localized amino-N and LAP activities highlighted different nutrient acquisition strategies mediated by root-microbe interactions, depending on the root compartment. Seminal roots and their tips appeared to adopt mutualistic strategies, potentially attracting root-associated microorganisms through releasing oligo- and polypeptides. In contrast, lateral roots, with amino-N detected only at their tips, demonstrated stronger N competition, relying on the enzyme activity of the rhizosphere microbial community for N acquisition. These insights emphasized the role of root functional specialization in shaping plant-microbe interactions, offering pathways to enhance nutrient use efficiency.

Maize (Zea mays L.)↗
DOE OSTI2025

Scanning Electrochemical Microscopy for Kinetic Investigations in Viscous Deep Eutectic Solvents: Identifying Practical Approach Curves and Deviations from Electron Transfer Models

Determining heterogeneous electrochemical electron transfer (ET) kinetics in electrolytes with a wide range of physical properties is of great interest for achieving high-performance redox flow batteries. Among such electrolytes, concentrated hydrogen-bonded electrolytes (CoHBEs), including deep eutectic solvents (DESs), have recently garnered significant attention. Unfortunately, traditional Tafel analysis using macroelectrodes often encounters issues with mass transfer limitations in CoHBEs with high viscosities, thereby restricting kinetic analysis to a narrow potential window. Here, in this work, we introduce a methodology for evaluating ET kinetics in viscous DES using the scanning electrochemical microscopy (SECM). We first determined practical solutions to SECM tip positioning in ethaline DES, which yield pseudopositive feedback responses. Lattice Boltzmann method (LBM) simulations helped us rationalize the impact of the fluid and concentration fields, as well as tip geometry, tip approach velocity v, and the solvent viscosity ηs, on the shape of the approach curves. In addition to successfully recreating approach curves over a variety of conditions, we found that approaching a conductor ensured a practical point where the normalized tip response (Ni T = 2) converged at L = 0.7 within ∼10% error regardless of tip velocity. With positioning capabilities at hand, we investigated the kinetics of Fe 3+ /Fe 2+ redox couple in aqueous and the ethaline media. The experimental kinetic results were interpreted using the Butler–Volmer (BV) and Marcus–Hush–Chidsey (MHC) models. For ethaline, a nonideal kinetic behavior was observed, potentially attributed to solvent dynamics within DESs or to the interplay of chloride anions in the charge transfer process.

electrodes↗
DOE OSTI2023

Fine scale sampling reveals early differentiation of rhizosphere microbiome from bulk soil in young Brachypodium plant roots

Abstract For a deeper and comprehensive understanding of the composition and function of rhizosphere microbiomes, we need to focus at the scale of individual roots in standardized growth containers. Root exudation patterns are known to vary along distinct parts of the root even in juvenile plants giving rise to spatially distinct microbial niches. To address this, we analyzed the microbial community from two spatially distinct zones of the developing primary root (tip and base) in young Brachypodium distachyon grown in natural soil using standardized fabricated ecosystems known as EcoFABs as well as in more conventional pot and tubes. 16S rRNA based community analysis showed a strong rhizosphere effect resulting in significant enrichment of several OTUs belonging to Actinobacteria, Bacteroidetes, Firmicutes and Proteobacteria. However, microbial community composition did not differ between root tips and root base or across different growth containers. Functional analysis of bulk metagenomics revealed significant differences between root tips and bulk soil. The genes associated with different metabolic pathways and root colonization were enriched in root tips. On the other hand, genes associated with nutrient-limitation and environmental stress were prominent in the bulk soil compared to root tips, implying the absence of easily available, labile carbon and nutrients in bulk soil relative to roots. Such insights into the relationships between developing root and microbial communities are critical for judicious understanding of plant-microbe interactions in early developmental stages of plants.

Acharya, Shwetha M.↗
DOE OSTI2021

Evaluating the Influence of Rotor-Casing Eccentricity on Turbine Efficiency Including Time-Resolved Flow Field Measurements

Abstract The clearance that exists between the casing and turbine blade tips is one of the key drivers of efficiency in gas turbine engines. For this reason, engine manufacturers utilize precise manufacturing techniques and may use clearance control systems to minimize tip clearances to reduce associated losses. Despite these efforts, turbines typically exhibit some nominal casing ovality or rotor-casing eccentricity, and changes to blade tip clearance during operation commonly occur due to thermal and mechanical stresses. The present study investigates non-axisymmetric tip clearance effects by creating a rotor-casing eccentricity in a one-stage axial test turbine operating in a continuous-duration mode at engine-relevant conditions with engine representative hardware. A magnetic levitation bearing system was leveraged to move the turbine shaft to vary the rotor-casing eccentricity without test section disassembly. The results of this study indicate that rotor-casing eccentricity does not affect overall turbine efficiency over the range that was tested, but does locally influence efficiency and the rotor exit flow field. Comparisons of flow angle and secondary flow kinetic energy (SKE) agreed with previous studies and existing analytical methods, respectively. Collectively, these results indicate that tip clearance can be studied locally on an eccentric rotor.

Engineering↗
DOE OSTI2023

Multipurpose active scanning probe cantilevers for near-field spectroscopy, scanning tunnel imaging, and atomic-resolution lithography

In this work, we report progress on developing a multipurpose scanning probe cantilever applying gallium nitride nanowires as the probe tip. Gallium nitride nanowires possess high potential as probes due to their straight profile, tunable electrical and optical properties, high Young’s Modulus, durability, and high-yield fabrication process. Their wide bandgap enables them to be pumped to emit ultraviolet pulses which can be used for optical imaging and spectroscopy. They can be doped during growth to be electrically conductive, and their sharp tips obtained during epitaxial growth enable confinement of a high electric field at tip–sample interface. Their sharp tips are obtained during fabrication by their epitaxial growth which eliminates the need for postprocess sharpening that is typically required for standard STM tips. We present results of using gallium nitride nanowires for scanning tunnel microscopy applications of atomic-resolution imaging and lithography, and atomic force microscopy applications of imaging and lithography in vacuum and atmospheric environments.

Engineering↗
DOE OSTI2020

PDRD Project 19039 - All metal vacuum scroll pump development for tritium

Currently the United States relies on a single source, foreign company, Eumeca (formerly Normetex) for the supply of an all metal vacuum scroll pump to process tritium. This “one of a kind”, all metal, vacuum scroll pump utilizes no “wetted”, polymeric materials that degrade prematurely when exposed to tritium. U.S. based vacuum scroll pump suppliers typically utilize a polymer, Teflon®, as a tip seal material at the edge of the scroll impellers for proper pump function. Teflon® is known to degrade within a relatively short time frame (approximately 1 year) when continually exposed to tritium gas. This degradation results in “flaking” of the Teflon® material which results in particulate contamination of the process gas stream. While filtration of the particulate is possible, doing so requires additional maintenance which is costly in a glovebox environment. In addition, filtration can degrade pumping system performance as particulate collects in the filter media over time. To date, all of the well established U.S and European based vacuum scroll pump manufacturers have been uninterested in developing an all metal vacuum scroll pump that does not use a polymeric scroll tip seal. This position is taken as the vacuum scroll pump manufacturers do not see a large enough market to make it profitable for them to develop and market an all metal vacuum scroll pump. In the mid 2000s, one company, Air Squared, Inc., a small Original Equipment Manufacturer (OEM) specializing in design and fabrication of custom scroll vacuum pumps and compressors, was willing to pursue the effort. The first design effort incorporated Vespel® as a polymeric tip seal material. Results of this effort led to realizing the affect that the Met-Bel MB-601 metal bellows pump has on performance when used as a backing pump for an all metal vacuum scroll pump without a scroll tip seal. As a result, Air Squared subsequently designed an all metal vacuum scroll pump without a tip seal material for evaluation. Although the initial, all metal version of the Air Squared pump was found deficient in regard to scroll impeller stiffness, which resulted in scroll contact, general design and pump performance was verified to be adequate. SRS PDRD Project 19039 was launched in 2019 as a 3rd attempt with Air Squared, Inc. in regard to development of an all metal vacuum scroll pump for consideration as an equivalent to the Eumeca/ Normetex pump. The effort specified 300 series stainless steel for the scroll impellers, all metal sealing, and design to meet tritium throughput and ultimate vacuum requirements. In addition, a 60 psig design pressure rating requirement was specified for the pump containment boundary. The 3rd generation Air Squared pump has been designed, fabricated, and has received preliminary testing. Preliminary testing has indicated proper leak tightness and pump performance. However, work continues regarding development of a pumping chamber containment bellows that can be subjected to 66 psig without damage to the bellows. Work will continue in 2020 and 2021 to pursue a pumping chamber containment bellows that meets the pressure rating requirement.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Ab Initio Molecular Dynamics Insights into Stress Corrosion Cracking and Dissolution of Metal Oxides

Oxide phases such as α-Fe2O3 (hematite) and α-Al2O3 (corundum) are highly insoluble in water; however, subcritical crack growth has been observed in humidity nonetheless. Chemically induced bond breaking at the crack tip appears unlikely due to sterically hindered molecular transport. The molecular mechanics of a crack in corundum with a reactive force field reveal minimal lattice trapping, leading to bond breaking before sufficient space opens for water transport. To address this, we model a pre-built blunt crack with space for H2O molecule adsorption at the tip and show that it reduces fracture toughness by lowering the critical J-integral. Then, we explore stress-enhanced dissolution to understand the mechanism of crack tip blunting in the oxide/water system. Density functional theory combined with metadynamics was employed to describe atomic dissolution from flat hematite and corundum surfaces in pure water. Strain accelerates dissolution, stabilizing intermediate states with broken bonds before full atom detachment, while the free energy profile of unstrained surfaces is almost monotonic. The atomistic calculations provided input for a kinetic model, predicting the shape evolution of a blunt crack tip, which displays three distinct regimes: (i) dissolution primarily away from the tip, (ii) enhanced blunting near but not at the apex, and (iii) sharpening near the apex. The transition between regimes occurs at a low strain, highlighting the critical role of water in the subcritical crack growth of oxide scales, with dissolution as the fundamental microscopic mechanism behind this process.

Chemistry↗
NASA NTRS1973

Radially leaned outlet guide vanes for fan source noise reduction

Two quiet engine program half scale fans one with a subsonic and the other with a supersonic fan tip speed at takeoff were run with 30 degree leaned and radial outlet guide vanes. Acoustic data at takeoff fan speed on the subsonic tip speed fan showed decreases in 200-foot sideline noise of from 1 to 2 PNdb. The supersonic tip speed fan a takeoff fan speed, however, showed noise increases of up 3 PNdb and a decrease in fan efficiency. At approach fan speed, the subsonic tip speed fan showed a noise decrease of 2.3 PNdb at the 200-foot sideline maximum angle and an increase in efficiency. The supersonic tip speed fan showed noise increase of 3.5 PNdb and no change in efficiency. The decrease in fan efficiency and the nature of the noise increase largely high frequency broadband noise lead to the speculation that an aerodynamic problem occurred.

Kazin, S. B.↗
NASA NTRS1973

Computational fracture mechanics

Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.

Rice, J. R.↗
NASA NTRS1975

Operating characteristics of a hollow-cathode neutralizer for 5 and 8 centimeter-diameter electron bombardment mercury ion thrusters

Thin-tip 0.3-cm-outside-diameter hollow-cathode neutralizers were used to investigate causes of neutralizer tip erosion experienced in thruster endurance tests. Bell-jar tests indicated that neutralizers with new rolled tantalum foil inserts coated with an emissive mixture eroded very little over the neutral flow rates investigated (3 to 10 mA) for simulated 5- and 8-cm-diameter thruster neutralizer conditions. Tip erosion rates of neutralizers operated with no insert or emissive mixture increased by two orders of magnitude for both configurations as the neutral flow rate decreased. Spectroscopic analysis of the discharge plasma from neutralizers operated with inserts coated with the emissive mixture detected tungsten at all neutral flow rates for both thruster neutralizer conditions. The only source of tungsten was the tip. Therefore, detection of tungsten indicated neutralizer tip erosion. Barium, an element of the emissive mixture, was detected at low neutral flow rates for the 5-cm-diameter thruster neutralizer operating condition only.

Weigand, A. J.↗
NASA NTRS1975

Experimental quiet engine program

Full-scale low-tip-speed fans, a full-scale high-tip-speed fan, scale model versions of fans, and two full-scale high-bypass-ratio turbofan engines, were designed, fabricated, tested, and evaluated. Turbine noise suppression was investigated. Preliminary design studies of flight propulsion system concepts were used in application studies to determine acoustic-economic tradeoffs. Salient results are as follows: tradeoff evaluation of fan tip speed and blade loading; systematic data on source noise characteristics and suppression effectiveness; documentation of high- and low-fan-speed aerodynamic and acoustic technology; aerodynamic and acoustic evaluation of acoustic treatment configurations, casing tip bleed, serrated and variable pitch rotor blades, leaned outlet guide vanes, slotted tip casings, rotor blade shape modifications, and inlet noise suppression; systematic evaluation of aerodynamic and acoustic effects; flyover noise projections of engine test data; turbine noise suppression technology development; and tradeoff evaluation of preliminary design high-fan-speed and low-fan-speed flight engines.

Cornell, W. G.↗
NASA NTRS1975

The effect of circumferential distortion on fan performance at two levels of blade loading

Single stage fans designed for two levels of pressure ratio or blade loading (rotor tip D-factor of 0.43 and 0.54) were subjected to screen-induced circumferential distortions of 90-degree extent. Both fan rotors were designed for a blade tip speed of 425 m/sec, blade solidity of 1.3 and a hub-to-tip radius ratio of 0.5. Circumferential measurements of total pressure, temperature, static pressure, and flow angle were obtained at the hub, mean and tip radii at five axial stations (three between the screen and rotor and behind rotor and stator blade rows). Rotor loading level did not appear to have a significant influence on rotor response to distorted flow. Losses in overall pressure ratio due to distortion were most severe in the stator hub region of the more highly loaded stage. At the near stall operating condition tip and hub regions of (either) rotor demonstrated different response characteristics to the distorted flow. No effect of loading was apparent on interactions between rotor and upstream distorted flow fields.

Hartmann, M. J.↗
NASA NTRS1976

Analysis of contact pressures attainable using indentors which are bodies of revolution

The elastic behavior of a conical indentor with a rounded tip pressed against a flat anvil has been analyzed. It is found that when the radius of contact extends beyond the rounded tip, the contact radius increases much more rapidly as the pressure increases than it does for the case of a fully spherical or parabolic tip. Consequently, the pressure achieved for a rounded conical tip for a given applied force is considerably less than for a spherical or parabolic tip.

Ruoff, A. L.↗