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Simplified solution for stresses and deformations

A shortcut is presented to the classical Hertzian solution for local stress and deformation of two elastic bodies in contact, which employs simplified forms for the ellipticity and for the complete elliptic integrals of the first and second kinds as a function of the geometry. Unlike previously proposed simplified formulas whose range of applicability was limited to ellipticities equal to, or greater than one, the present method extends the range of validity to include ellipticities less than one; in which the semimajor axis in the elliptical contact lies in a direction parallel to the rolling, rather than being perpendicular, as in previous studies. An auxiliary shear stress parameter is also expressed in simplified form as a function of the geometry, permitting a shortcut calculation to be made for the location and magnitude of the maximum subsurface shear stress.

Hamrock, B. J.↗

Surface fatigue life of CBN and vitreous ground carburized and hardened AISI 9310 spur gears

Spur gear surface endurance tests were conducted to investigate CBN ground AISI 9310 spur gears for use in aircraft applications, to determine their endurance characteristics and to compare the results with the endurance of standard vitreous ground AISI 9310 spur gears. Tests were conducted with VIM-VAR AISI 9310 carburized and hardened gears that were finish ground with either CBN or vitreous grinding methods. Test conditions were an inlet oil temeprature of 320 K (116 F), an outlet oil temperature of 350 K (170 F), a maximum Hertz stress of 1.71 GPa (248 ksi), and a speed of 10,000 rpm. The CBN ground gears exhibited a surface fatigue life that was slightly better than the vitreous ground gears. The subsurface residual stress of the CBN ground gears was approximately the same as that for the standard vitreous ground gears for the CBN grinding method used.

Townsend, Dennis P.↗

Fretting Stresses in Single Crystal Superalloy Turbine Blade Attachments

Single crystal nickel base superalloy turbine blades are being utilized in rocket engine turbopumps and turbine engines because of their superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal nickel base turbine blade superalloys are PWA 1480/1493 and PWA 1484. These alloys play an important role in commercial, military and space propulsion systems. High Cycle Fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Blade attachment regions are prone to fretting fatigue failures. Single crystal nickel base superalloy turbine blades are especially prone to fretting damage because the subsurface shear stresses induced by fretting action at the attachment regions can result in crystallographic initiation and crack growth along octahedral planes. Furthermore, crystallographic crack growth on octahedral planes under fretting induced mixed mode loading can be an order of magnitude faster than under pure mode I loading. This paper presents contact stress evaluation in the attachment region for single crystal turbine blades used in the NASA alternate Advanced High Pressure Fuel Turbo Pump (HPFTP/AT) for the Space Shuttle Main Engine (SSME). Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. Blades and the attachment region are modeled using a large-scale 3D finite element (FE) model capable of accounting for contact friction, material orthotrophy, and variation in primary and secondary crystal orientation. Contact stress analysis in the blade attachment regions is presented as a function of coefficient of friction and primary and secondary crystal orientation, Stress results are used to discuss fretting fatigue failure analysis of SSME blades. Attachment stresses are seen to reach peak values at locations where fretting cracks have been observed. Fretting stresses at the attachment region are seen to vary significantly as a function of crystal orientation. Attempts to adapt techniques used for estimating fatigue life in the airfoil region, for life calculations in the attachment region, are presented. An effective model for predicting crystallographic crack initiation under mixed mode loading is required for life prediction under fretting action.

Arakere, Nagaraj K.↗

Residual Stress Measurements After Proof and Flight: ETP-0403

The intent of this testing was to evaluate the residual stresses that occur in and around the attachment details of a case stiffener segment that has been subjected to flight/recovery followed by proof loading. Not measured in this test were stresses relieved at joint disassembly due to out-of-round and interference effects, and those released by cutting the specimens out of the case segment. The test article was lightweight case stiffener segment 1U50715, S/N L023 which was flown in the forward stiffener position on flight SRM 14A and in the aft position on flight SRM24A. Both of these flights were flown with the 3 stiffener ring configuration. Stiffener L023 had a stiffener ring installed only on the aft stub in its first flight, and it had both rings installed on its second flight. No significant post flight damage was found on either flight. Finally, the segment was used on the DM-8 static test motor in the forward position. No stiffener rings were installed. It had only one proof pressurization prior to assignment to its first use, and it was cleaned and proof tested after each flight. Thus, the segment had seen 3 proof tests, two flight pressurizations, and two low intensity water impacts prior to manufacturing for use on DM-8. On DM-8 it received one static firing pressurization in the horizontal configuration. Residual stresses at the surface and in depth were evaluated by both the x-ray diffraction and neutron beam diffraction methods. The x-ray diffraction evaluations were conducted by Technology for Energy Corporation (TEC) at their facilities in Knoxville, TN. The neutron beam evaluations were done by Atomic Energy of Canada Limited (AECL) at the Chalk River Nuclear Laboratories in Ontario. The results showed general agreement with relatively high compressive residual stresses on the surface and moderate to low subsurface tensile residual stresses.

Webster, Ronald L..↗

Advanced Gear Alloys for Ultra High Strength Applications

Single tooth bending fatigue (STBF) test data of UHS Ferrium C61 and C64 alloys are presented in comparison with historical test data of conventional gear steels (9310 and Pyrowear 53) with comparable statistical analysis methods. Pitting and scoring tests of C61 and C64 are works in progress. Boeing statistical analysis of STBF test data for the four gear steels (C61, C64, 9310 and Pyrowear 53) indicates that the UHS grades exhibit increases in fatigue strength in the low cycle fatigue (LCF) regime. In the high cycle fatigue (HCF) regime, the UHS steels exhibit better mean fatigue strength endurance limit behavior (particularly as compared to Pyrowear 53). However, due to considerable scatter in the UHS test data, the anticipated overall benefits of the UHS grades in bending fatigue have not been fully demonstrated. Based on all the test data and on Boeing s analysis, C61 has been selected by Boeing as the gear steel for the final ERDS demonstrator test gearboxes. In terms of potential follow-up work, detailed physics-based, micromechanical analysis and modeling of the fatigue data would allow for a better understanding of the causes of the experimental scatter, and of the transition from high-stress LCF (surface-dominated) to low-stress HCF (subsurface-dominated) fatigue failure. Additional STBF test data and failure analysis work, particularly in the HCF regime and around the endurance limit stress, could allow for better statistical confidence and could reduce the observed effects of experimental test scatter. Finally, the need for further optimization of the residual compressive stress profiles of the UHS steels (resulting from carburization and peening) is noted, particularly for the case of the higher hardness C64 material.

Shen, Tony↗

Glass sample characterization

The development of in-house integrated optical performance modelling capability at MSFC is described. This performance model will take into account the effects of structural and thermal distortions, as well as metrology errors in optical surfaces to predict the performance of large an complex optical systems, such as Advanced X-Ray Astrophysics Facility. The necessary hardware and software were identified to implement an integrated optical performance model. A number of design, development, and testing tasks were supported to identify the debonded mirror pad, and rebuilding of the Technology Mirror Assembly. Over 300 samples of Zerodur were prepared in different sizes and shapes for acid etching, coating, and polishing experiments to characterize the subsurface damage and stresses produced by the grinding and polishing operations.

Ahmad, Anees↗

Glass sample preparation and performance investigations

This final report details the work performed under this delivery order from April 1991 through April 1992. The currently available capabilities for integrated optical performance modeling at MSFC for large and complex systems such as AXAF were investigated. The Integrated Structural Modeling (ISM) program developed by Boeing for the U.S. Air Force was obtained and installed on two DECstations 5000 at MSFC. The structural, thermal and optical analysis programs available in ISM were evaluated. As part of the optomechanical engineering activities, technical support was provided in the design of support structure, mirror assembly, filter wheel assembly and material selection for the Solar X-ray Imager (SXI) program. As part of the fabrication activities, a large number of zerodur glass samples were prepared in different sizes and shapes for acid etching, coating and polishing experiments to characterize the subsurface damage and stresses produced by the grinding and polishing operations. Various optical components for AXAF video microscope and the x-ray test facility were also fabricated. A number of glass fabrication and test instruments such as a scatter plate interferometer, a gravity feed saw and some phenolic cutting blades were fabricated, integrated and tested.

Johnson, R. Barry↗

Tectonics of the Outer Planet Satellites

Tectonic features on the satellites of the outer planets range from the familiar, such as clearly recognizable graben on many satellites, to the bizarre, such as the ubiquitous double ridges on Europa, the twisting sets of ridges on Triton, or the isolated giant mountains rising from Io's surface. All of the large and middle-sized outer planet satellites except Io are dominated by water ice near their surfaces. Though ice is a brittle material at the cold temperatures found in the outer solar system, the amount of energy it takes to bring it close to its melting point is lower than for a rocky body. Therefore, some unique features of icy satellite tectonics may be influenced by a near-surface ductile layer beneath the brittle surface material, and several of the icy satellites may possess subsurface oceans. Sources of stress to drive tectonism are commonly dominated by the tides that deform these satellites as they orbit their primary giant planets. On several satellites, the observed tectonic features may be the result of changes in their tidal figures, or motions of their solid surfaces with respect to their tidal figures. Other driving mechanisms for tectonics include volume changes due to ice or water phase changes in the interior, thermoelastic stress, deformation of the surface above rising diapirs of warm ice, and motion of subsurface material toward large impact basins as they fill in and relax. Most satellites exhibit evidence for extensional deformation, and some exhibit strike-slip faulting, whereas contractional tectonism appears to be rare. Io s surface is unique, exhibiting huge isolated mountains that may be blocks of crust tilting and foundering into the rapidly emptying interior as the surface is constantly buried by deposits from hyperactive volcanoes. Of the satellites, diminutive Enceladus is spectacularly active; its south polar terrain is a site of young tectonism, copious heat flow, and tall plumes venting into space. Europa's surface is pervasively tectonized, covered with a diverse array of exotic and incompletely understood tectonic features. The paucity of impact craters on Europa suggests that its tectonic activity is ongoing. Geysers on Triton show that some degree of current activity, while tectonic features that cross sparsely cratered terrain indicate that it may also be tectonically active. Ganymede and Miranda both exhibit ancient terrains that have been pulled apart by normal faulting. On Ganymede these faults form a global network, while they are confined to regional provinces on Miranda. Ariel, Dione, Tethys, Rhea, and Titania all have systems of normal faults cutting across their surfaces, though the rifting is less pronounced than it is on Ganymede and Miranda. Iapetus exhibits a giant equatorial ridge that has defied simple explanation. The rest of the large and middle-sized satellites show very little evidence for tectonic features on their surfaces, though the exploration of Titan's surface has just begun.

McKinnon, W. B.↗

A study of subsurface crack initiation produced by rolling contact fatigue

Results of subsurface crack initiation studies produced by pure rolling contact fatigue in 7075-T6 aluminum alloy are presented in this article. Microstructural changes and subsequent crack initiation below the contacting surface in cylindrical test specimens subjected to repeated rolling contact are illustrated. The rolling conditions are simulated in a three-dimensional elastic-plastic finite element model in order to estimate the plastic strains and residual stresses in the test material. The numerically estimated distribution of plastic strains in the model correlate well with the extent of microstructural changes observed in the test specimen. Results also indicate that a combination of plastic strains and low values of residual stresses is conducive to subsurface crack initiation and growth.

Kumar, Arun M.↗

A Study of Some Factors Affecting Rolling-Contact Fatigue Life

A series of investigations using the fatigue spin rig to study the effect of several factors contributing to rolling contact fatigue life is summarized. Ball specimens of 1/2 and 9/16 inch diameter were tested at maximum theoretical Hertz compressive stresses in the range of 600,000 to 750,000 psi. Life was found to vary inversely with the tenth power of stress. In forging fiber studies, a greater concentration of failures and poorer life were observed where the greatest angle of intersection between the fiber flow lines and the surface occurred. This effect was independent of alloy composition. Higher lubricant viscosity was found to increase fatigue life, Lubricants having the same viscosity but of different base stock produced wide differences in life that correlated with the pressure viscosity coefficient of the lubricant. Higher temperature produced lower fatigue life. Dry powder lubricants produced poor fatigue life at 450 F; failure appearance indicated that the lubricant particles probably acted as minute stress raisers. In metallographic studies, nonmetallic inclusions were found to have a deleterious effect on fatigue life the inclusion size, location, composition, and condition of the matrix being contributing factors; failures were by shear cracking in the subsurface zone of maximum shear stress and eventual propagation into a shallow surface spall. Vacuum melting improved fatigue life, although a general correlation between cleanliness and fatigue life was not found. Life results for ten different bearing materials are presented.

Carter, Thomas L.↗

Constraints on the depth and geometry of the magma chamber of the Olympus Mons Volcano, Mars

The summit caldera of the Olympus Mons volcano exhibits one of the clearest examples of tectonic processes associated with shield volcanism on Mars. The radial distance from the center of the transition from concentric ridges to concentric graben within the oldest crater provides a constraint on the geometry and depth of the subsurface magmatic reservoir at the time of subsidence. Here, researchers use this constraint to investigate the size, shape, and depth of the reservoir. Their approach consists of calculating radial surface stresses corresponding to the range of subsurface pressure distributions representing an evacuating magma chamber. They then compare stress patterns to the observed radial positions of concentric ridges and graben. The problem is solved by employing the finite element approach using the program TECTON.

Zuber, Maria T.↗

Dynamic Fatigue of ULE Glass

Ultra Low Expansion (ULE) glass is used in a number of applications which require a low thermal expansion coefficient. One such application is telescope mirror elements. An allowable stress can be calculated for this material based upon modulus of rupture data; however, this does not take into account the problem of delayed failure. Delayed failure, due to stress corrosion can significantly shorten the lifetime of a glass article. Knowledge of the factors governing the rate of subcritical flaw growth in a given environment enables the development of relations between lifetime, applied stress and failure probability for the material under study. Dynamic fatigue is one method of obtaining the necessary information to develop these relationships. In this study, the dynamic fatigue method was used to construct time-to-failure diagrams for both 230/270 ground and optically polished samples. The grinding and polishing process reduces the surface flaw size and subsurface damage, and relieves residual stress by removing materials with successively smaller grinding media. This resulted in an increase in the strength of the optic during the grinding and polishing sequence. There was also an increase in the lifetime due to grinding and polishing. It was found that using the fatigue parameters determined from the 230/270 grit surface are not significantly different from the optically polished values. Although the lower bound of the polished samples is more conservative, neither time-to-failure curves lie beyond the upper or lower bound of the confidence limits. Therefore, designers preferring conservative limits could use samples without residual stress present (polished samples) to determine the fatigue parameters and inert Weibull parameters from samples with the service condition surface, to determine time-to-failure of the optical element.

Tucker, Dennis S.↗

Lifetime Predictions of a Titanium Silicate Glass with Machined Flaws

A dynamic fatigue study was performed on a Titanium Silicate glass to assess its susceptibility to delayed failure and to compare the results with those of a previous study. Fracture mechanics techniques were used to analyze the results for the purpose of making lifetime predictions. The material strength and lifetime was seen to increase due to the removal of residual stress through grinding and polishing. Influence on time-to-failure is addressed for the case with and without residual stress present. Titanium silicate glass otherwise known as ultra-low expansion (ULE)* glass is a candidate for use in applications requiring low thermal expansion characteristics such as telescope mirrors. The Hubble Space Telescope s primary mirror was manufactured from ULE glass. ULE contains 7.5% titanium dioxide which in combination with silica results in a homogenous glass with a linear expansion coefficient near zero. delayed failure . This previous study was based on a 230/270 grit surface. The grinding and polishing process reduces the surface flaw size and subsurface damage, and relieves residual stress by removing the material with successively smaller grinding media. This results in an increase in strength of the optic during the grinding and polishing sequence. Thus, a second study was undertaken using samples with a surface finish typically achieved for mirror elements, to observe the effects of surface finishing on the time-to-failure predictions. An allowable stress can be calculated for this material based upon modulus of rupture data; however, this does not take into account the problem of delayed failure, most likely due to stress corrosion, which can significantly shorten lifetime. Fortunately, a theory based on fracture mechanics has been developed enabling lifetime predictions to be made for brittle materials susceptible to delayed failure. Knowledge of the factors governing the rate of subcritical flaw growth in a given environment enables the development of relations between lifetime, applied stress and failure probability for the material under study. Dynamic fatigue is one method of obtaining the necessary information to develop these relationships. In this study, the dynamic fatigue method was used to construct a time-to-failure diagram for polished ULE glass.

Tucker, Dennis S.↗

An Evanescent Microwave Probe for Super-Resolution Nondestructive Imaging of Metals, Semiconductors, Dielectrics, Composites and Biological Specimens

Using evanescent microwaves with decay lengths determined by a combination of microwave wavelength (lambda) and waveguide termination geometry, we have imaged and mapped material non-uniformities and defects with a resolving capability of lambda/3800=79 microns at 1 GHz. In our method a microstrip quarter wavelength resonator was used to generate evanescent microwaves. We imaged materials with a wide range of conductivities. Carbon composites, dielectrics (Duroid, polymers), semiconductors (3C-SiC, polysilicon, natural diamond), metals (tungsten alloys, copper, zinc, steel), high-temperature superconductors, and botanical samples were scanned for defects, residual stresses, integrity of brazed junctions, subsurface features, areas of different film thickness and moisture content. The evanescent microwave probe is a versatile tool and it can be used to perform very fast, large scale mapping of a wide range of materials. This method of characterization compares favorably with ultrasound testing, which has a resolution of about 0.1 mm and suffers from high absorption in composite materials and poor transmission across boundaries. Eddy current methods which can have a resolution on the order of 50 microns are restricted to evaluating conducting materials. Evanescent microwave imaging, with careful choice of operating frequency and probe geometry, can have a resolution of up to 1 micron. In this method we can scan hot and moving objects, sample preparation is not required, testing is non-destructive, non-invasive and non-contact, and can be done in air, in liquid or in vacuum.

Pathak, P. S.↗

Effect of grinding on the fatigue life of titanium alloy (5 Al-2.5 Sn) under dry and wet conditions

The principal factors in the performance of aerospace materials are strength-to-weight ratio, fatigue life, fracture toughness, survivability and, of course, reliability. Machining processes and, in particular, grinding under adverse conditions have been found to cause damage to surface integrity and affect the residual stress distribution in the surface and subsurface region. These effects have a direct bearing on the fatigue life. In this investigation the effects of grinding conditions on the fatigue life of Titanium 5 Al-2.5Sn were studied. This alloy is used in ground form in the manufacturing of some critical components in the space shuttle's main engine. It is essential that materials for such applications be properly characterized for use in severe service conditions. Flat sub-size specimens 0.1 inch thick were ground on a surface grinding machine equipped with a variable speed motor at speeds of 2000 to 6000 rpm using SiC wheels of grit sizes 60 and 120. The grinding parameters used in this investigation were chosen from a separate study. The ground specimens were then fatigued at a selected stress and the resulting lives were compared with that of the virgin material. The surfaces of the specimens were examined under a scanning electron microscope, and the roughness and hardness were measured using a standard profilometer and microhardness tester, respectively. The fatigue life of the ground specimens was found to decrease with the increase in speed for both dry and wet conditions. The fatigue life of specimens ground under wet conditions showed a significant increase at the wheel speed of 2000 rpm for both the grit sizes and thereafter decreased with increase profilometry, microhardness measurements and scanning electron microscopic examination.

Rangaswamy, Partha↗

High-Frequency Focused Water-Coupled Ultrasound Used for Three-Dimensional Surface Depression Profiling

To interface with other solids, many surfaces are engineered via methods such as plating, coating, and machining to produce a functional surface ensuring successful end products. In addition, subsurface properties such as hardness, residual stress, deformation, chemical composition, and microstructure are often linked to surface characteristics. Surface topography, therefore, contains the signatures of the surface and possibly links to volumetric properties, and as a result serves as a vital link between surface design, manufacturing, and performance. Hence, surface topography can be used to diagnose, monitor, and control fabrication methods. At the NASA Glenn Research Center, the measurement of surface topography is important in developing high-temperature structural materials and for profiling the surface changes of materials during microgravity combustion experiments. A prior study demonstrated that focused air-coupled ultrasound at 1 MHz could profile surfaces with a 25-m depth resolution and a 400-m lateral resolution over a 1.4-mm depth range. In this work, we address the question of whether higher frequency focused water-coupled ultrasound can improve on these specifications. To this end, we employed 10- and 25-MHz focused ultrasonic transducers in the water-coupled mode. The surface profile results seen in this investigation for 25-MHz water-coupled ultrasound, in comparison to those for 1-MHz air-coupled ultrasound, represent an 8 times improvement in depth resolution (3 vs. 25 m seen in practice), an improvement of at least 2 times in lateral resolution (180 vs. 400 m calculated and observed in practice), and an improvement in vertical depth range of 4 times (calculated).

Roth, Don J.↗

Emplacement of Volcanic Domes on Venus and Europa

Placing firmer constraints on the emplacement timescales of visible volcanic features is essential to obtaining a better understanding of the resurfacing history of Venus. Fig. 1 shows a Magellan radar image and topography for a putative venusian lava dome. 175 such domes have been identified, having diameters that range from 19 - 94 km, and estimated thicknesses as great as 4 km [1-2]. These domes are thought to be volcanic in origin [3], having formed by the flow of a viscous fluid (i.e., lava) onto the surface. Among the unanswered questions surrounding the formation of Venus steep-sided domes are their emplacement duration, composition, and the rheology of the lava. Rheologically speaking, maintenance of extremely thick, 1-4 km flows necessitates higher viscosity lavas, while the domes' smooth upper surfaces imply the presence of lower viscosity lavas [2-3]. Further, numerous quantitative issues, such as the nature and duration of lava supply, how long the conduit remained open and capable of supplying lava, the volumetric flow rate, and the role of rigid crust in influencing flow and final morphology all have implications for subsurface magma ascent and local surface stress conditions. The surface of Jupiter's icy moon Europa exhibits many putative cryovolcanic constructs [5-7], and previous workers have suggested that domical positive relief features imaged by the Galileo spacecraft may be volcanic in origin [5,7-8] (Fig. 2). Though often smaller than Venus domes, if emplaced as a viscous fluid, formation mechanisms for europan domes may be similar to those of venusian domes [7]. Models for the emplacement of venusian lava domes (e.g. [9-10]) have been previously applied to the formation of putative cryolava domes on Europa [7].

timescales↗

Cryovolcanic Emplacement of Domes on Europa

Here we explore the hypothesis that certain domes on Europa may have been produced by the extrusion of viscous cryolavas. A new mathematical method for the emplacement and relaxation of viscous lava domes is presented and applied to putative cryovolcanic domes on Europa. A similarity solution approach is applied to the governing equation for fluid flow in a cylindrical geometry, and dome relaxation is explored assuming a volume of cryolava has been rapidly emplaced onto the surface. Nonphysical sin- gularities inherent in previous models for dome relaxation have been eliminated, and cryolava cooling is represented by a time-variable viscosity. We find that at the onset of relaxation, bulk kinematic viscosities may lie in the range between 10(exp 3) and 10(exp 6) sq m/s, while the actual fluid lava viscosity may be much lower. Plausible relaxation times to form the domes, which are linked to bulk cryolava rheology, are found to range from 3.6 days to 7.5 years. We find that cooling of the cryolava, while dominated by conduction through an icy skin, should not prevent fluids from advancing and relaxing to form domes within the timescales considered. Determining the range of emplacement conditions for putative cryolava domes will shed light on Europa's resurfacing history. In addition, the rheologies and compositions of erupted cryolavas have implications for subsurface cryomagma ascent and local surface stress conditions on Europa.

volcanism↗