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A geometrical interpretation of the grouping and variation rate terms of Reynolds stresses in compressible turbulent flow is presented. Examples of applications of the method are also given.
Two experiments are being conducted to observe the liquid/solid interface of He-4 near 1 K. Interesting instabilities are expected to occur when the solid is non-hydrostatically stressed. (1)A compact interdigital capacitor is used as a level detector to observe solid He-4 to which stresses are applied externally. The capacitor consists of 38 interlaced 50 m wide and 3.8 mm long gold films separated by 50 m and deposited onto a 5 mm by 5 mm sapphire substrate. The capacitor is placed on one flat end wall of a cylindrical chamber (xx mm diameter and xx mm long). The solid is grown to a known height and a stress is applied by a tubular PZT along the cylindrical axis. The observed small change in height of the solid at the wall is linearly proportional to the applied stress. The solid height decreases under compressive stress but does not change under tensile stress. The response of the solid on compressive stress is consistent with the expected quadratic dependence on strain. (2)Interferometric techniques are being developed for observing the solid He-4 surface profile. A laser light source is brought into the low temperature region via single mode optical fiber. The interference pattern is transmitted back out of the low temperature apparatus via optical fiber bundle. The solid He-4 growth chamber will be equipped with two PZT's such that stress can be applied from orthogonal directions. Orthogonally applied stress is expected to induce surface instability with island-like deformation on a grid pattern. Apparatus design and progress of its construction are described.
Laboratory tests were made to obtain information on the load-resisting properties of X76S-T aluminum alloy when subjected to static, impact, and repeated loads. Results are presented from static-load test of unnotched specimens in tension and in torsion and of notched specimens in tension. Charpy impact values obtained from bend tests on notched specimens and tension impact values for both notched and unnotched specimens tested at several different temperatures are included. The endurance limits obtained from repeated bending fatigue tests made on three different types of testing machine are given for unnotched polished specimens, and the endurance limits of notched specimens subjected to six different ranges of bending stress are also reported. The results indicated that: (a) polished rectangular specimens had an endurance limit about 30 percent less than that obtained for round specimens; (b) a comparison of endurance limits obtained from tests on three different types of machine indicated that there was no apparent effect of speed of testing on the endurance limit for the range of speeds used (1,750 to 13,000 rpm). (c) the fatigue strength (endurance limit) of the X76S-T alloy was greatly decreased by the presence of a notch in the specimens; (d) no complete fractures of the entire specimens occurred in notched fatigue specimens when subjected to stress cycles for which the mean stress at the notch during the cycle was a compressive stress; for this test condition a microscopic cracking occurred near the root of the notch and was used as a criterion of failure of the specimen. (e) as the mean stress at the notch was decreased from a tensile (+) stress to a compressive (-) stress, it was found that the alternating stress that could be superimposed on the mean stress in the cycle without causing failure of the specimens was increased.
An experimental study was conducted to assess the effects of heat treatment and cyclic mechanical loading on the tensile and compressive stress-strain behavior of six boron-aluminum composites having different laminate orientations and being subjected to different heat treatments. The heat treatments were as-fabricated, T6, and T6N consisting of T6 treatment followed by cryogenic quench in liquid nitrogen prior to testing. All laminates were tested in monotonic and cyclic compression, while the tensile-test data are taken from the literature for comparison purposes. It is shown that the linear elastic range of the T6- and T6N-condition specimens is larger than that of the as-fabricated specimens, and that cyclic loading in tension or compression strain hardens the specimens and extends the linear elastic range. For laminates containing 0-deg plies, the stress-strain behavior upon unloading is found to be nonlinear, whereas the other laminates exhibit a linear behavior upon unloading. Specimens in the T6 and T6N conditions show higher strain hardening than the as-fabricated specimens.
Hot-wire anemometer measurements of turbulent shear stresses in a Mach 3 compressible boundary layer were performed in order to investigate the effects of heat transfer on turbulence. Measurements were obtained by an x-probe in a flat plate, zero pressure gradient, two dimensional boundary layer in a wind tunnel with wall to freestream temperature ratios of 0.94 and 0.71. The measured shear stress distributions are found to be in good agreement with previous results, supporting the contention that the shear stress distribution is essentially independent of Mach number and heat transfer for Mach numbers from incompressible to hypersonic and wall to freestream temperature ratios of 0.4 to 1.0. It is also found that corrections for frequency response limitations of the electronic equipment are necessary to determine the correct shear stress distribution, particularly at the walls.
The fatigue lives of disk superalloys can be increased by shot peening their surfaces, to induce compressive residual stresses near the surface that impede cracking there. As disk application temperatures increase for improved efficiency, the persistence of these beneficial stresses could be impaired, especially with continued fatigue cycling. The objective of this work was to study the retention of residual stresses introduced by shot peening, when subjected to fatigue and high temperatures. Fatigue specimens of powder metallurgy processed nickel-base disk superalloy ME3 were prepared with consistent processing and heat treatment. They were then shot peened using varied conditions. Strain-controlled fatigue cycles were run at room temperature and 704 C, to allow re-assessment of residual stresses.
The author has identified the following significant results. A previously unmapped seismically active fault has been identified in south-central Alaska on the basis of ERTS-1 imagery. It can be traced for at least 120 km. An unmapped fault was found on the northwest flank of Mt. Sanford that is apparently a reverse fault. A large scale, seismically active fracture system has been identified in central Alaska on the basis of MSS imagery. The system consists of two sets of fractures which intersect at an angle of about 55 degrees. The dominant feature of the system is the Minook Creek fault, on which an earthquake of magnitude 6.5 occurred on October 29, 1968. A possible related feature is a 60 km long lineament near the Toklat River north of Mt. McKinley. These areas are all moderately seismically active. Focal mechanism studies of the 1968 earthquake revealed that left-lateral displacement had occurred on the Minook Creek fault due to compressive stress. A similarly oriented direction of compressive stress could be responsible for the entire fracture system.
In the present paper, the basic set of global intraplate stress orientation data is plotted and tabulated. Although the global intraplate stress field is complicated, several large-scale patterns can be seen. Much of stable North America is characterized by an E-W to NE-SW trend for the maximum compressive stress. South American lithosphere beneath the Andes, and perhaps farther east in the stable interior, has horizontal compressive stresses trending E-W to NW-SE. Western Europe north of the Alps is characterized by a NW-SE trending maximum horizontal compression, while Asia has the maximum horizontal compressive stress trending more nearly N-S, especially near the Himalayan front.
Ion exchange offers a pathway to impose residual compressive stresses to mitigate the electro-chemo-mechanical cracking of solid-state electrolytes such as lithium lanthanum zirconium oxide. This study uses a coupled multiscale framework (integrating density functional theory (DFT), molecular dynamics (MD), and continuum modeling) to examine how exchange ion size influences stress, diffusion, fracture toughness, and electronic properties. Larger isovalent ions (Na + , Ag + , K + ) were exchanged with Li + , with DFT confirming their preference for octahedral 96h sites and a linear relationship between ion size and chemical free expansion coefficient. MD simulations reveal stress and concentration effects on exchange ion diffusivity at elevated temperatures, with Na + and Ag + maintaining favorable mobility while K + showing concentration-dependent clustering. Continuum modeling predicts the range of fracture strength improvements and the required ion exchange concentration profile. It was shown that a 5% surface exchange concentration can induce ∼0.6 GPa of surface compressive stress using Na + and ∼1.0 GPa of surface compressive stress using Ag + . On the other hand, larger ion exchange species may penalize Li + diffusivity by increasing the activation volume and activation energy. Interestingly, Na + has a negligible penalty on Li-ion diffusivity. The room temperature Li + ion diffusivity is reduced by ∼40% with Ag + ion exchange. Electronic band structure analysis shows no size-dependent change in the bandgap, though Ag + introduces localized defect states near the valence band maximum. This study highlights ion size as a key factor in optimizing LLZO properties, offering a framework to improve the solid-state battery performance.
Results of magnetoacoustic emission (MAE) and magnetoacoustic (MAC) measurements performed with an unembrittled HY-80 steel specimen are presented. The MAE measurements were obtained by applying an ac magnetic field of 20 Hz parallel to the uniaxial stress axis. The effects of tensile stress were shown to monotonically decrease the peak amplitude of the MAE burst, and they were consistent with the predicted trend based on the tensile stress-induced domain alignment. The effects of compressive stress were found to increase the peak amplitude of the MAE burst initially and to eventually decrease as the magnitude of compressive stress increased.
A chart is presented for the coefficient in the formula for the critical compressive stress at which cross sectional distortion begins in a thin-wall tube of rectangular section symmetrical about its two principal axes. The energy method of Timoshenko was used in the theoretical calculations required for the construction of the chart. The deflection equation used in this method was selected to give good accuracy. The exact values given by solution of the differential equation were calculated for a number of cases and it was found that the energy solution was correct to within a fraction of 1 percent. The calculation of the critical compressive stress at stresses above the elastic range is also discussed. In order to demonstrate the use of the formulas and the chart in engineering calculations, several illustrative problems are included.
Charts are presented for the coefficients in the formulas for the critical compressive stress at which cross-sectional distortion begins in thin-wall columns of I-, Z-, channel, and rectangular-tube sections. The energy method of Timoshenko was used in the theoretical calculations required for the construction of the charts. The deflection equations were carefully selected to give good accuracy. The calculation of the critical compressive stress at stresses above the elastic range is briefly discussed in order to demonstrate the use of the formulas and the charts in engineering calculations. Two illustrative problems are included.
Compressive surface layers were formed on hot-pressed silicon carbide and nitride. The objective of these treatments was to improve the impact resistance of these materials at 1590 K (2400 F). Quenching was used to form compressive surface layers on silicon carbide. The presence of the compressive stresses was demonstrated by slotted rod tests. Compressive stresses were retained at elevated temperatures. Improvements in impact resistance at 1590 K (2400 F) and flexural strength at room temperature were achieved using cylindrical rods 3.3 mm (0.13 in.) in diameter. Carburizing treatments were used to form the surface layers on silicon nitride. In a few cases using rectangular bars improvements in impact resistance at 1590 K (2400 F) were observed.
We investigated the relationship between stratigraphy, stress, and microseismicity at the Hydraulic Fracture Test Site-1. The site comprises two sets of horizontal wells in the Wolfcamp shale and a deviated well drilled after hydraulic fracturing. Regional stresses indicate normal/strike-slip faulting with E-W compression. Stress measurements in vertical and horizontal wells show that the minimum principal stress varies with depth. Strata with high clay and organic content show high values of the least compressive stress, consistent with the theory of viscous stress relaxation. By integrating data from core, logs, and the hydraulic fracturing stages, we constructed a stress profile for the Wolfcamp sequence, which predicts how much pressure is required for hydraulic fracture growth. We applied the results to fracture orientation data from image logs to determine the population of pre-existing faults that are expected to slip during stimulation. We also determined microseismic focal plane mechanisms and found slip on steeply dipping planes striking NW, consistent with the orientations of potentially active faults predicted by the stress model. This case study represents a general approach for integrating stress measurements and rock properties to predict hydraulic fracture growth and the characteristics of injection-induced microseismicity.
When rapid oscillation of blanket wearing looms at Chatham Manufacturing Company caused significant metal fatigue, the company turned to NC/STRC for a NASA data bank computer search. The search pinpointed tensile stress, and suggested a built-in residual compressive stress as a solution. "Shot peening," bombarding a part with a high velocity stream of very small shot to pound and compress the part's surface, was found to be the only practical method for creating compressive stress. The method has been successful and the company estimates its annual savings as a quarter million dollars.
Part of the redesign of the SRMs for the Space Shuttle involved the substitution of three new capture cylinders for three of the previously used cylinders. These new cylinders mate with the old standard case segments in each of the three field joints. The new capture cylinders contain an integral capture latch on the tang end which mates with a case clevis during stackup at KSC. The capture cylinders also contain a groove in the capture latch to provide for a third 0-ring in the joint and are designed to achieve a metal-to- metal interference fit between the capture latch and the mating clevis. An unexpected fretting problem has occurred on the tang capture feature and the inner clevis leg interference fit surfaces on flight hardware since STS-26. Varying degrees of fretting damage have been found on the case segments from different flight motors. Fretting is a wear phenomena that occurs when two tightly fitting metal surfaces are subject to cyclic relative motion of extremely small amplitudes (generally less than 0.010-inch) in the absence of adequate lubrication. It is adhesive ("cold" - welding) in nature and vibration is its essential causative factor. This problem has manifested itself on the flight motors as a series of pits and axial gouges on the inside diameter (ID) surfaces of the inner clevis legs and the outside diameter (OD) surfaces of the tang capture features. The problem occurs in varying degrees of severity in all of the field joints. It is not believed that fretting is a flight safety issue. However, it could become a reusability issue if left unattended. Fretting has been encountered in other industries for many years and measures that will prevent or reduce it have been devised. These include: elimination or reduction of vibration (amplitudes and/or frequencies), elimination of slip, improved lubrication between parts, increased surface separation, increased interference, inducing residual compressive stresses in the surfaces of the mating parts, and employing non-fretting interference shims. Looking at each of these separately; vibration and slip occur in varying degrees and magnitudes in the field joints (as part of the roll-out, launch, flight, splashdown, flotation, and/or tow back) and are difficult to define or eliminate. Improved lubrication is something that was evaluated since it would be the simplest change to incorporate, but little or no improvement was found. Increasing surface separation would defeat the purpose of the interference fit. The effect of increasing the interference fit is unknown. Additional shot peening and/or surface rolling to impart residual compressive stresses in the joints undoubtedly would alter the characteristics and finish of the sealing surfaces of the motor cases. Also, experimental data' indicate that the tangs and clevises already have residual compressive stress fields on their surfaces yet fretting occurs. These stresses probably result from the case machining and the glass beading used to clean these surfaces.
We performed finite element analyses on a model of the Phenolic Impregnated Carbon Ablator (PICA) heatshield from the Stardust sample return capsule (SRC) to predict the thermal stresses in the PICA material during reentry. The heatshield on the Stardust SRC was a 0.83 m sphere cone, fabricated from a single piece of 5.82 cm-thick PICA. The heatshield performed successfully during Earth reentry of the SRC in January 2006. Material response analyses of the full, axisymmetric PICA heatshield were run using the Two-Dimensional Implicit Ablation, Pyrolysis, and Thermal Response Program (TITAN). Peak surface temperatures were predicted to be 3385K, while the temperature at the PICA backface remained at the estimated initial cold-soak temperature of 278K. Surface recession and temperature distribution results from TITAN, at several points in the reentry trajectory, were mapped onto an axisymmetric finite element model of the heatshield. We used the finite element model to predict the thermal stresses in the PICA from differential thermal expansion. The predicted peak compressive stress in the PICA heatshield was 1.38 MPa. Although this level of stress exceeded the chosen design limit for compressive stresses in PICA tiles for the design of the Orion crew exploration vehicle heatshield, the Stardust heatshield exhibited no obvious mechanical failures from thermal stress. The analyses of the Stardust heatshield were used to assess and adjust the level of conservatism in the finite element analyses in support of the Orion heatshield design.
Flywheel energy storage offers an attractive alternative to battery systems used in space applications such as the International Space Station. Rotor designs capable of high specific energies benefit from the load carrying capacity of hoop wound carbon fibers but their long-term durability may be limited by time-temperature dependent radial deformations. This was investigated for the carbon/epoxy rotor material, IM7/8552. Coupon specimens were sectioned from filament wound panels. These were tested in compression and tension at room temperature (RT), 95 and 135 C for strain rates from 5x10(exp -6) per second to 5x10(exp -3) per second. Time, temperature and load sign dependent effects were significant transverse to the fiber. At -0.5 percent strain for 72 hr, compressive stresses relaxed 16.4 percent at 135 C and 13 percent at 95 C. Tensile stresses relaxed only 7 percent in 72 hr at 135 C for 0.5 percent strain. Using linear hereditary material response and Boltzmann s principle of superposition to describe this behavior is problematic if not intractable. Micromechanics analysis including the effects of processing residual stresses is needed to resolve the paradoxes. Uniaxial compressive stress relaxation data may be used to bound the loss of radial pre-load stresses in flywheel rotors.