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At least 901 records · Page 50

Face Gear Technology for Aerospace Power Transmission Progresses

The use of face gears in an advanced rotorcraft transmission design was first proposed by the McDonnell Douglas Helicopter Company during their contracted effort with the U.S. Army under the Advanced Rotorcraft Transmission (ART) program. Face gears would be used to turn the corner between the horizontal gas turbine engine and the vertical output rotor shaft--a function currently done by spiral bevel gears. This novel gearing arrangement would substantially lower the drive system weight partly because a face gear mesh would be used to split the input power between two output gears. However, the use of face gears and their ability to operate successfully at the speeds and loads required for an aerospace environment was unknown. Therefore a proof-of-concept phase with an existing test stand at the NASA Lewis Research Center was pursued. Hardware was designed that could be tested in Lewis' Spiral Bevel Gear Test Rig. The initial testing indicated that the face gear mesh was a feasible design that could be used at high speeds and load. Surface pitting fatigue was the typical failure mode, and that could lead to tooth fracture. An interim project was conducted to see if slight modifications to the gear tooth geometry or an alternative heat treating process could overcome the surface fatigue problems. From the initial and interim tests, it was apparent that for the surface fatigue problems to be overcome the manufacturing process used for this component would have to be developed to the level used for spiral bevel gears. The current state of the art for face gear manufacturing required using less than optimal gear materials and manufacturing techniques because the surface of the tooth form does not receive final finishing after heat treatment as it does for spiral bevel gears. This resulted in less than desirable surface hardness and manufacturing tolerances. An Advanced Research and Projects Agency (ARPA) Technology Reinvestment Project has been funded to investigate the effects of manufacturing process improvements on the operating characteristics of face gears. The program is being conducted with McDonnell Douglas Helicopter Co., Lucas Western Inc., the University of Illinois at Chicago, and a NASA/U.S. Army team. The goal of the project is develop the grinding process, experimentally verify the improvement in face gear fatigue life, and conduct a full-scale helicopter transmission test. The theory and methodology to grind face gears has been completed, and manufacture of the test hardware is ongoing. Experimental verification on test hardware is scheduled to begin in fiscal 1996.

Source record↗

Simulations of the Modular Axisymmetric Scramjet Test Rig Under Reacting Flow Conditions

Simulations of the Air Force Research Laboratory (AFRL) Modular Axisymmetric Scramjet Test Rig (MASTeR) are presented. MASTeR is a parametric test article capable of investigating various scramjet cavity flameholder designs and fueling strategies with the goal to characterize and optimize flameholding capability. In the current work, three cavity aspect ratios, and two fueling strategies (upstream and in-cavity) with ethylene at a nominal facility pressure and temperature condition are evaluated. The reacting simulations are performed, and the resulting flow characteristics are discussed. For each configuration and fueling strategy, cavity residence time, entrainment rate, and fuel-air equivalence ratio are computed. The MASTeR geometry is defined in Engineering Sketch Pad (ESP) and the simulations use a sketch-to-solution (S2S) automated unstructured grid adaptation tool in VULCAN-CFD. This tool automatically generates a simulation grid from the ESP geometry and systematically adapts it to the numerical solution based on the Hessian error estimate of a specified flow field parameter. Reynolds averaged simulations (RAS) are used with a two-equation linear eddy viscosity and diffusivity model. The resulting database can be compared with the experimental data as those become available, and explored to develop models for cavity performance for scramjet propulsion design applications.

hypersonics↗

An experimental evaluation of S-duct inlet-diffuser configurations for turboprop offset gearbox applications

A test program, utilizing a large scale model, was run in the NASA Lewis Research Center 10- by 10-ft wind tunnel to examine the influence on performance of design parameters of turboprop S-duct inlet/diffuser systems. The parametric test program investigated inlet lip thickness, inlet/diffuser cross-sectional geometry, throat design Mach number, and shaft fairing shape. The test program was run at angles of attack to 15 deg and tunnel Mach numbers to 0.35. Results of the program indicate that current design techniques can be used to design inlet/diffuser systems with acceptable total pressure recovery, but several of the design parameters, notably lip thickness (contraction ratio) and shaft fairing cross section, must be optimized to prevent excessive distortion at the compressor face.

Mcdill, Paul L.↗

Effects of regenerator geometry on pulse tube refrigerator performance

This paper gives results of the cooling performance of a double-inlet pulse tube refrigerator using various regenerators. The same pulse tube was used for all the experiments and measured 4.76 mm in diameter and 46.2 mm in length. A commercial linear compressor with a swept volume of 4 cm3 was used in these experiments. The operating conditions were held constant at a mean pressure of 2.0 MPa and a frequency of 54 Hz. Using finite difference software called REGEN3.1, developed at NIST, and recent experiment results, we optimized a series of regenerators based on dimensions, materials and screen packing. The values used for calculating the thermal conduction through stacked screens by REGEN3.1 were based on recent experimental results from NIST. The regenerator tubes were designed using 316 stainless steel and titanium materials. The regenerator matrices investigated were 400-mesh and 500-mesh stainless steel screen. The valve settings for both orifices were adjusted to minimize the no-load temperature for all regenerators. A cooling capacity curve from 0 to 3 W was also determined. The performance of the pulse tube refrigerator using the different regenerators is discussed. The experimental results from the various regenerators are evaluated and compared with their corresponding numerically calculated coefficient of performance (COP) and regenerator design as determined by REGEN3.1.

NASA Discipline Life Sciences Technologies↗

Interference Drag Associated with Engine Locations for Multidisciplinary Design Optimization

This research aims to quantify the interference drag for various engine locations on a traditional “tube and wing,” 150-passenger commercial aircraft flying at 35,000 ft and Mach 0.8. Engine locations are varied in the chord wise, span wise, and vertical directions near the wing, both under and above the wing, as well as along the fuselage. Euler simulations are performed with representative powered modern engines. The results are intended to supplement empirical drag estimates suitable for multidisciplinary design environments. Large interference drag increases, as compared to the isolated air frame and engine geometry, are found to occur when the engine is placed directly above or below the wing. Interference effects are significantly reduced, and in some instances result in benefits compared to the isolated bodies, when the engines are placed fore or aft of the wing. Interference drag increases are partially explained by flow channels leading to choked flow and shock interactions between bodies.

Blaesser, Nathaniel J.↗

Practical considerations in waverider applications

This paper proposes a practical perspective for waverider shapes with respect to their use in the commercial and military aerospace industry. Also, integration problems that must be considered when deriving these shapes for operational aircraft are discussed and general approaches to solving them are suggested. The inverse design methodology that is used to generate waverider geometries is discussed as a potentially powerful tool for the aerospace industry in the design of practical operational high-speed (Mach 4 to 25) aircraft. Further, it is suggested that unless this methodology proves to be a valuable tool in the near future, it will not likely find a customer in the aerospace industry and may become no more than an interesting academic study in aerodynamic optimization.

Stevens, Daniel R.↗

Dynamics of a split torque helicopter transmission

Split torque designs, proposed as alternatives to traditional planetary designs for helicopter main rotor transmissions, can save weight and be more reliable than traditional designs. This report presents the results of an analytical study of the system dynamics and performance of a split torque gearbox that uses a balance beam mechanism for load sharing. The Lagrange method was applied to develop a system of equations of motion. The mathematical model includes time-varying gear mesh stiffness, friction, and manufacturing errors. Cornell's method for calculating the stiffness of spur gear teeth was extended and applied to helical gears. The phenomenon of sidebands spaced at shaft frequencies about gear mesh fundamental frequencies was simulated by modeling total composite gear errors as sinusoid functions. Although the gearbox has symmetric geometry, the loads and motions of the two power paths differ. Friction must be considered to properly evaluate the balance beam mechanism. For the design studied, the balance beam is not an effective device for load sharing unless the coefficient of friction is less than 0.003. The complete system stiffness as represented by the stiffness matrix used in this analysis must be considered to precisely determine the optimal tooth indexing position.

Krantz, Timothy L.↗

Pool and flow boiling in variable and microgravity

As is well known, boiling is an effective mode of heat transfer in that high heat flux levels are possible with relatively small temperature differences. Its optimal application requires that the process be adequately understood. A measure of the understanding of any physical event lies in the ability to predict its behavior in terms of the relevant parameters. Despite many years of research the predictability of boiling is currently possible only for quite specialized circumstances, e.g., the critical heat flux and film boiling for the pool boiling case, and then only with special geometries. Variable gravity down to microgravity provides the opportunity to test this understanding, but possibly more important, by changing the dimensional and time scales involved permits more detailed observations of elements involved in the boiling process, and perhaps discloses phenomena heretofore unknown. The focus here is on nucleate boiling although, as will be demonstrated below, under but certain circumstances in microgravity it can take place concurrently with the dryout process. In the presence of earth gravity or forced convection effects, the latter process is usually referred to as film boiling. However, no vapor film as such forms with pool boiling in microgravity, only dryout. Initial results are presented here for pool boiling in microgravity, and were made possible at such an early date by the availability of the Get-Away-Specials (GAS). Also presented here are some results of ground testing of a flow loop for the study of low velocity boiling, eventually to take place also in microgravity. In the interim, variable buoyancy normal to the heater surface is achieved by rotation of the entire loop relative to earth gravity. Of course, this is at the expense of varying the buoyancy parallel to the heater surface. Two questions which must be resolved early in the study of flow boiling in microgravity are (1) the lower limits of liquid flow velocity where buoyancy effects become significant to the boiling process (2) the effect of lower liquid flow velocities on the Critical Heat Flux when buoyancy is removed. Results of initial efforts in these directions are presented, albeit restricted currently to the ever present earth gravity.

Merte, Herman, Jr.↗

Aerostructural Weight Estimation for a Transonic Truss-Braced Wing using the Higher-fidelity Conceptual Design and Structural Optimization Tool

Continued development and enhancements of the Higher-fidelity Conceptual Design and structural optimization (HCDstruct) tool has been driven largely by advanced aircraft concepts of interest to NASA. While previous versions of HCDstruct were limited to hybrid wing body (HWB) and generalized tube and wing (TW) aircraft concepts, the latest version of HCDstruct supports the analysis of Truss-Braced Wing (TBW) aircraft concepts, where users can model both high and low wing configurations as well as strut and jury geometries parametrically. Additionally, new methods for modeling advanced composite materials within HCDstruct have been implemented. These recent tool enhancements were demonstrated for an independent assessment of the NASA/Boeing SUGAR Phase VI Mach 0.8 Transonic Truss-Braced Wing (TTBW) concept.

Zachary D. Windous↗

The Aerodynamic Optimization of Wings at Subsonic Speeds and the Influence of Wingtip Design

Some of the objectives of modern aircraft development are related to the achievement of reduced fuel consumption and aircraft noise. This investigation is mainly concerned with the aerodynamic aspects of aircraft development, i.e., reduction of induced drag. New studies of wing design, and in particular wing tips, are considered. Induced drag is important since, in cruising flight, it accounts for approximately one-third of the entire drag for the aircraft, and one-half while climbing. A survey is presented for the wing geometries and wing tip designs studied, and theoretical investigations of different planar wings with systematically varied wing tip forms are conducted. Attention is also paid to a theoretical study of some planar and nonplanar wings and their comparison with experimental data.

Zimmer, H.↗

Overview of Additively Manufactured TPS Proposed Flight Test and Earth Re-Entry Capsule Design

A flight mechanics overview is presented of an Earth flight test designed to investigate a novel, 3D printed thermal protection system (TPS) that is currently in development at NASA as part of the Additive Manufacturing of Thermal Protection Systems project. The project is pioneering a method to print a thermal protection system onto an entry vehicle forebody one layer at a time. This method reduces labor and complexity as compared to traditional manufacturing methods while increasing mission-dependent customization of through-depth materials properties. The flight test has three objectives. First, subject the forebody stagnation point of a capsule equipped with additively manufactured TPS (AMTPS) material to peak heat fluxes in excess of 100 $W/cm^2$. Second, capture in-flight data to enable flight reconstruction and AMTPS material thermal response model improvement. Third, recover the capsule with data storage and forebody AMTPS intact to enable post-flight inspection and analysis of AMTPS performance. The flight test trajectory is designed to achieve a peak stagnation point, cold-wall, entry heat flux of 135~$W/cm^2$. Flight mechanics simulations are performed using the Program to Optimize Simulated Trajectories II (POST2) and Monte-Carlo analysis yields statistical percentiles on vehicle performance at key points along the trajectory. Based on the flight mechanics analysis presented in this paper, a prototype capsule was designed, partially fabricated, and underwent preliminary component stress testing in preparation for fabrication of the flight unit capsule. The capsule outer mold line is a modified version of the heritage Mars Microprobe geometry. The capsule has a 0.356~m diameter, a 30~kg mass, and a hypersonic ballistic coefficient of 300~$kg/m^2$. Sensor selection is guided by flight dynamics simulations with the goal of resolving the re-entry heating pulse. On-board instrumentation include forebody and aftbody pressure sensors and thermocouples, a 9-axis IMU, a GPS receiver, and an Iridium satellite modem, all of which collect and store data throughout flight via on-board avionics systems. A two-stage parachute system is designed to decelerate the capsule to touchdown velocities that will not result in significant fracture or deformation of the charred AMTPS material at ground impact.

Flight Mechanics↗

S3D: An interactive surface grid generation tool

S3D, an interactive software tool for surface grid generation, is described. S3D provides the means with which a geometry definition based either on a discretized curve set or a rectangular set can be quickly processed towards the generation of a surface grid for computational fluid dynamics (CFD) applications. This is made possible as a result of implementing commonly encountered surface gridding tasks in an environment with a highly efficient and user friendly graphical interface. Some of the more advanced features of S3D include surface-surface intersections, optimized surface domain decomposition and recomposition, and automated propagation of edge distributions to surrounding grids.

Luh, Raymond Ching-Chung↗

A Computational Approach for Model Update of an LS-DYNA Energy Absorbing Cell

NASA and its contractors are working on structural concepts for absorbing impact energy of aerospace vehicles. Recently, concepts in the form of multi-cell honeycomb-like structures designed to crush under load have been investigated for both space and aeronautics applications. Efforts to understand these concepts are progressing from tests of individual cells to tests of systems with hundreds of cells. Because of fabrication irregularities, geometry irregularities, and material properties uncertainties, the problem of reconciling analytical models, in particular LS-DYNA models, with experimental data is a challenge. A first look at the correlation results between single cell load/deflection data with LS-DYNA predictions showed problems which prompted additional work in this area. This paper describes a computational approach that uses analysis of variance, deterministic sampling techniques, response surface modeling, and genetic optimization to reconcile test with analysis results. Analysis of variance provides a screening technique for selection of critical parameters used when reconciling test with analysis. In this study, complete ignorance of the parameter distribution is assumed and, therefore, the value of any parameter within the range that is computed using the optimization procedure is considered to be equally likely. Mean values from tests are matched against LS-DYNA solutions by minimizing the square error using a genetic optimization. The paper presents the computational methodology along with results obtained using this approach.

Horta, Lucas G.↗

Frequencies and Flutter Speed Estimation for Damaged Aircraft Wing Using Scaled Equivalent Plate Analysis

Equivalent plate analysis is often used to replace the computationally expensive finite element analysis in initial design stages or in conceptual design of aircraft wing structures. The equivalent plate model can also be used to design a wind tunnel model to match the stiffness characteristics of the wing box of a full-scale aircraft wing model while satisfying strength-based requirements An equivalent plate analysis technique is presented to predict the static and dynamic response of an aircraft wing with or without damage. First, a geometric scale factor and a dynamic pressure scale factor are defined to relate the stiffness, load and deformation of the equivalent plate to the aircraft wing. A procedure using an optimization technique is presented to create scaled equivalent plate models from the full scale aircraft wing using geometric and dynamic pressure scale factors. The scaled models are constructed by matching the stiffness of the scaled equivalent plate with the scaled aircraft wing stiffness. It is demonstrated that the scaled equivalent plate model can be used to predict the deformation of the aircraft wing accurately. Once the full equivalent plate geometry is obtained, any other scaled equivalent plate geometry can be obtained using the geometric scale factor. Next, an average frequency scale factor is defined as the average ratio of the frequencies of the aircraft wing to the frequencies of the full-scaled equivalent plate. The average frequency scale factor combined with the geometric scale factor is used to predict the frequency response of the aircraft wing from the scaled equivalent plate analysis. A procedure is outlined to estimate the frequency response and the flutter speed of an aircraft wing from the equivalent plate analysis using the frequency scale factor and geometric scale factor. The equivalent plate analysis is demonstrated using an aircraft wing without damage and another with damage. Both of the problems show that the scaled equivalent plate analysis can be successfully used to predict the frequencies and flutter speed of a typical aircraft wing.

Krishnamurthy, Thiagarajan↗

Assessment of a Bidirectional Reflectance Distribution Correction of Above-Water and Satellite Water-Leaving Radiance in Coastal Waters

Water-leaving radiances, retrieved from in situ or satellite measurements, need to be corrected for the bidirectional properties of the measured light in order to standardize the data and make them comparable with each other. The current operational algorithm for the correction of bidirectional effects from the satellite ocean color data is optimized for typical oceanic waters. However, versions of bidirectional reflectance correction algorithms specifically tuned for typical coastal waters and other case 2 conditions are particularly needed to improve the overall quality of those data. In order to analyze the bidirectional reflectance distribution function (BRDF) of case 2 waters, a dataset of typical remote sensing reflectances was generated through radiative transfer simulations for a large range of viewing and illumination geometries. Based on this simulated dataset, a case 2 water focused remote sensing reflectance model is proposed to correct above-water and satellite water-leaving radiance data for bidirectional effects. The proposed model is first validated with a one year time series of in situ above-water measurements acquired by collocated multispectral and hyperspectral radiometers, which have different viewing geometries installed at the Long Island Sound Coastal Observatory (LISCO). Match-ups and intercomparisons performed on these concurrent measurements show that the proposed algorithm outperforms the algorithm currently in use at all wavelengths, with average improvement of 2.4% over the spectral range. LISCO's time series data have also been used to evaluate improvements in match-up comparisons of Moderate Resolution Imaging Spectroradiometer satellite data when the proposed BRDF correction is used in lieu of the current algorithm. It is shown that the discrepancies between coincident in-situ sea-based and satellite data decreased by 3.15% with the use of the proposed algorithm.

LISCO(LONG ISLAND SOUND COASTAL OBSERVATORY)↗

Calibration and Validation of a Finite ELement Model of THor-K Anthropomorphic Test Device for Aerospace Safety Applications

The THOR anthropomorphic test device (ATD) has been developed and continuously improved by the National Highway Traffic Safety Administration to provide automotive manufacturers an advanced tool that can be used to assess the injury risk of vehicle occupants in crash tests. Recently, a series of modifications were completed to improve the biofidelity of THOR ATD [1]. The updated THOR Modification Kit (THOR-K) ATD was employed at Wright-Patterson Air Base in 22 impact tests in three configurations: vertical, lateral, and spinal [2]. Although a computational finite element (FE) model of the THOR had been previously developed [3], updates to the model were needed to incorporate the recent changes in the modification kit. The main goal of this study was to develop and validate a FE model of the THOR-K ATD. The CAD drawings of the THOR-K ATD were reviewed and FE models were developed for the updated parts. For example, the head-skin geometry was found to change significantly, so its model was re-meshed (Fig. 1a). A protocol was developed to calibrate each component identified as key to the kinematic and kinetic response of the THOR-K head/neck ATD FE model (Fig. 1b). The available ATD tests were divided in two groups: a) calibration tests where the unknown material parameters of deformable parts (e.g., head skin, pelvis foam) were optimized to match the data and b) validation tests where the model response was only compared with test data by calculating their score using CORrelation and Analysis (CORA) rating system. Finally, the whole ATD model was validated under horizontal-, vertical-, and lateral-loading conditions against data recorded in the Wright Patterson tests [2]. Overall, the final THOR-K ATD model developed in this study is shown to respond similarly to the ATD in all validation tests. This good performance indicates that the optimization performed during calibration by using the CORA score as objective function is not test specific. Therefore confidence is provided in the ATD model for uses in predicting response in test conditions not performed in this study such those observed in the spacecraft landing. Comparison studies with ATD and human models may also be performed to contribute to future changes in THOR ATD design in an effort to improve its biofidelity, which has been traditionally based on post-mortem human subject testing and designer experience.

Putnam, J. B.↗

Low subsonic aerodynamic characteristics of five irregular planform wings with systematically varying wing fillet geometry tested in the NASA/Ames 12 foot pressure tunnel (LA65)

An experimental and analytical aerodynamic program to develop predesign guides for irregular planform wings (also referred to as cranked leading edge or double delta wings is reported; the benefits are linearization of subsonic lift curve slope to high angles of attack and avoidance of subsonic pitch instabilities at high lift by proper tailoring of the planform-fillet-wing combination while providing the desired hypersonic trim angle and stability. Because subsonic and hypersonic conditions were the two prime areas of concern in the initial application of this program to optimize shuttle orbiter landing and entry characteristics, the study was designated the Subsonic/Hypersonic Irregular Planforms Study (SHIPS).

Ball, J. W.↗

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

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

Superalloy↗