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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Shock initiation of low density polymer bonded explosive LX-14: A study of two morphologies

A series of six shock initiation experiments have been carried out on low density LX-14 powder in order to simulate a shock insult on the heavily damage polymer bonded explosive, LX-14. Two distinct morphologies were studied (tap density molding powder and machined swarf), both at the same density of 0.942 g/cm 3 , or 50.1% theoretical maximum density. The purpose of these experiments was to provide data to help make an assessment of the effects that damage has on the material sensitivity to a planar shock. This was achieved primarily by providing shock sensitivity data in the form of a Pop plot, and also reactants equation of state data, which aids in the determination of input conditions for both the experiments performed in this work and also future experiments of this material type. The experiments were of a cut-back format, consisting of four sample heights on each shot and diagnosed with optical velocimetry. The experiments were carried out at the Technical Area 40 Chamber 9 gas gun facility at the Los Alamos National Laboratory, where the LX-14 targets were subjected to Al 6061 and Oxygen Free High Conductivity copper impactors launched to velocities up to 2.14 km/s. Time corrected reactive growth wave profiles are presented in this paper along with the derivation of the following Hugoniot parameters for this explosive, where the molding powder and machine swarf are represented by the following linear equations, respectively, U s = 1.64 (±0.64)u p + 2.25 (±0.49) and U s = 0.87 (±.0.60)u p + 4.08 (±0.49). The results show that the steady increase in shock sensitivity with increasing void fraction reaches an inflection point beyond which the shock sensitivity begins to decease. This inflection point lies between 65% and 50% of the theoretical maximum density of the LX-14. In both cases, the damaged LX-14 was not as sensitive as expected, with a relative shock sensitivity of the molding powder being less than the pressed LX-14, and the machined swarf having a shock sensitivity that is comparable to pressed LX-14.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Estimation of cutting tool wear using an elastomeric tactile sensor

Machining performance of cutting tools and part quality are affected by the geometric condition of the cutting edge, which is influenced by thermomechanical loads experienced during the process. Tool condition monitoring (TCM) systems provide insight for timely replacement of cutting tools. However, existing TCM systems are expensive and require specialized equipment or sensors, hindering widespread adoption. A novel TCM system is developed herein using an elastomeric tactile sensor. Sensor images of the cutting edge are used to quantify wear using two distinct algorithms. In the first algorithm, the unworn and worn edges are identified based on Canny edge detect. In the second, the unworn edge is identified using edge detection while the region of wear is identified using a relative intensity method. In both cases, the maximum wear width is calculated based on an experimentally determined pixel to-physical distance scale. The TCM system is first used to estimate flank wear on a solid carbide helical end mill before evaluating its robustness by employing it to estimate insert wear of an indexable helical end mill. Measurements are also performed manually using an optical microscope and a high-resolution focus variation microscope for verification. The novel technique estimates flank wear in the solid carbide tool with a high accuracy of 98%. Larger discrepancies are observed for the inserts, however, with overlapping uncertainties. In conclusion, the technique shows promise in adaptability, automation, and closed loop control of machine tools.

Machining↗
NASA NTRS1947

Investigation of a Spoiler-Type Lateral Control System on a Wing with Full-Span Flaps in the Langley 19-Foot Pressure Tunnel

Tests of a partial-span model of a large bomber-type air1ane were conducted to determine the. aerodynamic characteristics of the wing equipped with full-span flaps and a retractable spoiler end aileron lateral control system. The arrangement consisted of (1) a double slotted flap extending over aproximate1y 86 percent of the wing semispan, (2) a 20-percent constant-percentage-chord aileron extending from the outboard end of the flap to the wing tip, and (3) a retractable spoiler, located at the 65-percent wing-chord station and extending from approximately 63 percent of the wing semispan to the wing tip. In addition, tests were made of a wing vent (of 1 and 2 percent of the wing chord located directly behind the spoiler), perforations in the spoiler, a blot or cut-out along the lower edge of the spoiler and spoilers of various spans. With full-span flaps deflected and with the 2-percent vent open or closed the initial stalling of the wing occurred at the tips, but with the vents closed there probably would be no appreciable loss in lateral control until maximum lift was reached. The l-percent vent increased the rolling effectiveness of the spoiler at small spoi1er deflections, particularly at high angles of attack with flaps deflected. With flaps deflected the 2-percent vent caused a large reduction in both the wing lift and rolling effectiveness of the spoiler at large angles of attack. However, at small angle of attack the 2-percent vent increased the rolling effectiveness of the spoiler at small spoiler deflections. The simultaneous operation of the spoiler and vent (in contrast to a vent fixed in the wing) would result in a large increase in the effectiveness of the spoiler and would avoid any loss in wing lift as in a fixed vent arrangement. The tests of the spoiler modifications revealed that (1) the spoiler perforations reduced the rolling-moment and yawing-moment coefficients but caused the spoiler hinge-moment coefficients to become more positive; (2) the spoiler slot had no notable effect on the rolling-moment and yawing-moment characteristics but produced a positive increase in the spoiler hinge-moment coefficients at large spoiler deflections; (3) the effects produced by the individual modifications were additive when the various modifications were combined. In general, progressively decreasing the spoiler span by removing the segments from the inboard end of the spoiler caused a decrease in rolling effectiveness approximately proportional to the span of the segment.

WING FLAPS, SLOTTED & AILERONS↗
NASA NTRS1985

Aerodynamics of sports balls

Research data on the aerodynamic behavior of baseballs and cricket and golf balls are summarized. Cricket balls and baseballs are roughly the same size and mass but have different stitch patterns. Both are thrown to follow paths that avoid a batter's swing, paths that can curve if aerodynamic forces on the balls' surfaces are asymmetric. Smoke tracer wind tunnel tests and pressure taps have revealed that the unbalanced side forces are induced by tripping the boundary layer on the seam side and producing turbulence. More particularly, the greater pressures are perpendicular to the seam plane and only appear when the balls travel at velocities high enough so that the roughness length matches the seam heigh. The side forces, once tripped, will increase with spin velocity up to a cut-off point. The enhanced lift coefficient is produced by the Magnus effect. The more complex stitching on a baseball permits greater variations in the flight path curve and, in the case of a knuckleball, the unsteady flow effects. For golf balls, the dimples trip the boundary layer and the high spin rate produces a lift coefficient maximum of 0.5, compared to a baseball's maximum of 0.3. Thus, a golf ball travels far enough for gravitational forces to become important.

Mehta, R. D.↗
NASA NTRS1993

Integrated tools for teleoperated satellite repair

Tools and tool handling techniques designed for demonstrating the use of the Advanced Teleoperation System at JPL in satellite repair operations are described in this paper. Our model for the repair demonstration is the Main Electronics Box (MEB) replacement on the Solar Maximum Satellite Repair (SMSR) procedure developed by NASA and successfully performed by the crew of Space Shuttle STS-13 in 1984. A summary of the repair procedure consists of uncovering thermal protection blankets on the satellite, removing screws from the MEB panel, opening the panel and clamping it in place, then removing electrical connectors from their sockets, cutting cords that hold electrical cables to the MEB panel, replacing the panel, and finally reversing the previous procedures. Methods for handling tools used in our SMSR procedure, along with details of the tool designs are discussed in this paper.

Das, H.↗
NASA NTRS1985

High-energy emission in gamma-ray bursts

Between February 1980 and August 1983 the Gamma-Ray Spectrometer on the Solar Maximum Mission Satellite (SMM) detected 72 events identified as being of cosmic origin. These events are an essentially unbiased subset of all gamma-ray bursts. The measured spectra of these events show that high energy (greater than 1 MeV) emission is a common and energetically important feature. There is no evidence for a general high-energy cut-off or a distribution of cut-offs below about 6 MeV. These observations imply a limit on the preferential beaming of high energy emission. This constraint, combined with the assumption of isotropic low energy emission, implies that the typical magnetic field strength at burst radiation sites is less than 1 x 10 to the 12th gauss.

Matz, S. M.↗
NASA NTRS1993

Cruise noise measurements of a scale model advanced ducted propulsor

A scale model Advanced Ducted Propulsor (ADP) was tested in NASA Lewis Research Center's 8- by 6-Foot Wind Tunnel to obtain acoustic data at cruise conditions. The model, designed and manufactured by Pratt & Whitney Division of United Technologies, was tested with three inlet lengths. The model has 16 rotor blades and 22 stator vanes, which results in a cut-on condition with respect to rotor-stator interaction noise. Comparisons of the noise directivity of the ADP with that of a previously tested high-speed, unducted propeller showed that the ADP peak blade passing tone was about 30 dB below that of the propeller, and therefore, should not present a cabin or enroute noise problem. The maximum blade passing tone first increased with increasing helical tip Mach number, peaked, and then decreased at a higher Mach number. The ADP tests with the shortest inlet showed more noise in the inlet arc than did tests with either of the other two inlet lengths.

Dittmar, James H.↗
NASA NTRS2013

Combining Through-Thickness Reinforcement and Self-Healing for Improved Damage Tolerance and Durability of Composites

A study was undertaken to develop a prototype method for adding through-thickness hollow glass tubes infused with uncured resin and hardener in a carbon Z-pin through-thickness reinforcement field embedded in a composite laminate. Two types of tube insertion techniques were attempted in an effort to ensure the glass tubes survived the panel manufacturing process. A self-healing resin was chosen with a very low viscosity, two component, liquid epoxy resin system designed to be mixed at a 2-to-1 ratio of epoxy to hardener. IM7/8552 carbon epoxy double cantilever beam (DCB) specimens were cut from the hybrid Z-pin and glass tube reinforced panels and tested. In-situ injection of resin and hardener directly into glass tubes, in a staggered pattern to allow for 2-to-1 ratio mixing, resulted in partial healing of the fracture plane, but only if the injection was performed while the specimen was held at maximum load after initial fracture. Hence, there is some potential for healing delamination via resin and hardener delivered through a network of through-thickness glass tubes, but only if the tubes are connected to a reservoir where additional material may be injected as needed.

O'Brien, T. Kevin↗
DOE OSTI2024

Analytical insights into the interplay of momentum, multiplicity, and the speed of sound in heavy-ion collisions

We introduce a minimal model of ultracentral heavy-ion collisions to study the relation between the speed of sound of the produced plasma and the final particles' energy and multiplicity. We discuss how the particles' multiplicity N tot and average energy E tot / N tot is related to the speed of sound c s by c s 2 = d ln ( E tot / N tot ) / d ln N tot if the fluid is inviscid, its speed of sound is constant and all final particles can be measured. We show that finite rapidity cuts on the particles' multiplicity N and energy E introduce corrections between c s 2 and d ln ( E / N ) / d ln N that depend on the system's lifetime. We study analytically these deviations with the Gubser hydrodynamic solution, finding that, for ultrarelativistic bosons, they scale as the ratio of the freeze-out temperature T FO over the maximum initial temperature of the fluid T 0 ; the nonthermodynamic aspect of these corrections is highlighted through their dependence on the system's initial conditions. Published by the American Physical Society 2024

Physics↗
NASA NTRS1997

Planetary Aeronomy and Related Studies

Mercury atmosphere - Sprague and Hunten, in collaboration with Katharina Lodders of Washington University, proposed, mainly on cosmochemical grounds, that S atoms are an important constituent of the atmosphere (30 times more abundant than sodium). This paper has appeared in Icarus. We also suggest that condensed sulfur is an excellent candidate for the radar-bright polar caps, more plausible than water ice because the latter is only barely stable even in permanently-shadowed craters. The best prospect for detection of the vapor is through its resonance lines, a triplet near 1814 A. Mercury is too close to the Sun to be observed by any existing space telescope, but there is some prospect that the search could be made from a Shuttle-based spectrograph such as Lyle Broadfoot's USTAR. Sprague and Hunten have completed an elaborate data analysis of over 100 measurements of the Na D lines, obtained with the 61-inch telescope and our echelle spectrograph. Full account has been taken of the radiative-transfer problem that arises because the Na atmosphere is not optically thin. The output of this code is used in another program that makes an elaborate inverse interpolation in two angles and optical depth and computes the effect of the seeing (always bad for Mercury). The seeing is determined by fitting cuts across a computed image to part of the spectrum adjacent to the sodium lines, and typically ranges from slightly less than 4 arcsec to worse than 6 (diameter at l/e of a Gaussian). The final result is a list of Na abundances, with some information on spatial distribution. One particularly interesting result of further analysis is a strong abundance maximum in the morning relative to the afternoon, confirming an earlier result for potassium, based on much fewer measurements. The analysis are completed during the extension of the present grant. This work depends heavily on the Hapke parameters used to estimate the reflectance of Mercury's surface. The paper by Domingue et al. examines the credibility of the available parameters, which are derived from disk-unresolved photometry, and concludes that errors in the derived Na abundances could be as great as 30%.

Hunten, D. M.↗
DOE OSTI2024

Applications of Lifted Nonlinear Cuts to Convex Relaxations of the AC Power Flow Equations

Here, we demonstrate that valid inequalities, or lifted nonlinear cuts (LNC), can be projected to tighten the Second Order Cone (SOC), Convex DistFlow (CDF), and Network Flow (NF) relaxations of the AC Optimal Power Flow (AC-OPF) problem. We conduct experiments on 38 cases from the PGLib-OPF library, showing that the LNC strengthen the SOC and CDF relaxations in 100% of the test cases, with average and maximum differences in the optimality gaps of 6.2% and 17.5% respectively. The NF relaxation is strengthened in 46.2% of test cases, with average and maximum differences in the optimality gaps of 1.3% and 17.3% respectively. We also study the trade-off between relaxation quality and solve time, demonstrating that the strengthened CDF relaxation outperforms the strengthened SOC formulation in terms of runtime and number of iterations needed, while the strengthened NF formulation is the most scalable with the lowest relaxation quality improvement due to these LNC.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1988

Simulated impact damage in a thick graphite/epoxy laminate using spherical indenters

A study was made to determine the extent of fiber damage caused by low-velocity impact of spherical impactors to a very thick graphite/epoxy laminate. The laminate was cut from a filament wound case being developed for the Space Shuttle solid rocket motors. The case was wound using a wet process with AS4W graphite fiber and HBRF-55A epoxy. Impacts were simulated under quasi-static conditions by pressing hemispherically shaped indenters against the laminate at different locations. The contact force and indenter diameter were varied from location to location. The forces were chosen for each indenter diameter to produce contact pressures below and above that required to initiate damage. After the forces were applied, the laminate was cut into smaller pieces so that each piece contained a test site. The pieces were then deplied and the individual plies examined to determine the extent of fiber damage. Broken fibers were found in the outer layers directly beneath the contact site. The locus of broken fibers in each layer resembled a crack normal to the direction of the fibers. The maximum length and depth of the cracks increased with increasing contact pressure and indenter diameter. The internal stresses in the laminate were calculated using Hertz's law and Love's solution for pressure applied on part of the boundary of a semi-infinite body. The maximum length and depth of the cracks were predicted using a maximum shear stress criterion. Predictions and measurements were in good agreement.

Poe, C. C., Jr.↗
NASA NTRS1989

Microscopic deformation in a heated unidirectional graphite-epoxy composite

Both in-plane and out-of-plane displacements were determined in patches of the toughened 1962-ERLX epoxy bounded by three closely packed high-modulus P75S graphite fibers. The P75S/1962-ERLX composite was unidirectional, with an average fiber volume of 60 percent. On heating to 44 C from room temperature, the epoxy confined between clusters of three fibers sank in a trough beneath the plane of the fiber ends by 50-120 nm. When the maximum temperature achieved in the prior thermal cycles exceeded 100 C the depth of the trough increased. However, when cycles exceeding 100 C were followed by thermal cycles of decreasing amplitude, chosen to reduce interfacial stress relaxation, the depth of the trough decreased. The results illustrate the feasibility of deducing quantitative data on local deformation from high-resolution strain measurements on cut surfaces.

Morris, W. L.↗
NASA NTRS1945

Effects of Wing and Nacelle Modifications on Drag and Wake Characteristics of a Bomber-Type Airplane Model

An investigation of a model of a large four-engine bomber was conducted in the Langley 19-f'oot pressure tunnel to determine the effects of several wing and nacelle modifications on drag characteristics and air­ flow characteristics at the tail. Leading-edge gloves, trailing-edge extensions, and modified nacelle afterbodies were tested individual ly and in combination. The effects of the various modifications were determined by force tests, tuft observations, and turbulence s1ITveys in the region of the tail. Tests were made with fixed and natural transition on the wing and with propellers operating and propellers off. Most of the tests were con- ducted at a Reynolds number of approximately 2.6 x 106. The results indicated that application of certain of the modifications provided worth-while improvements in the characteristics or the model. The flow over the wing and flaps was improved, the drag was reduced, and the turbulence in the region of the tail was reduced. Trailing-edge extensions were the most effective individual modification in improving the flow over the wing with wing flaps neutral, cowl and intercooler flaps clos ed. Modified nacelle afterbodies were the most effectiv8 individual edification in reducing drag with either fixed or natural transition on the wing; however, trailin6-edge extensions were slightly more effective with fixed transition. Combinations of either leading­ or trailing-edge extensions and modified afterbodies were more effective than either modification alone. With cowl and intercooler flaps open, trailing-edge extensions with modified afterbodies provided substantial improvement in flow and drag characteristics. With wing flaps deflected, enclosing the flap behind the inboard nacelle within an extended afterbody or cutting the flaps at the nacelle appeared. to be the most promising methods of improving the f low over the flaps and the tail. Although the results of hot-wire-anenometer surveys were not conclusive in regard to buffeting characteristics, the modifications did educe the turbulence at the tail with wing flaps both neutral and deflected. The modifications, as a rule, were favorable to maximum lift. Appreciable reductions in longitudinal stability of the model were caused by addition of leading -edge gloves and tr ailing -edge extensions.

Neely, Robert H.↗
DOE OSTI2020

Simple, compact, high-resolution monochromatic x-ray source for characterization of x-ray calorimeter arrays

X-ray calorimeters routinely achieve very high spectral resolution, typically a few eV full width at half maximum (FWHM). Measurements of calorimeter line shapes are usually dominated by the natural linewidth of most laboratory calibration sources. This compounds the data acquisition time necessary to statistically sample the instrumental line broadening and can add systematic uncertainty if the intrinsic line shape of the source is not well known. To address these issues, we have built a simple, compact monochromatic x-ray source using channel cut crystals. A commercial x-ray tube illuminates a pair of channel cut crystals that are aligned in a dispersive configuration to select the Kα1 line of the x-ray tube anode material. The entire device, including the x-ray tube, can be easily hand-carried by one person and may be positioned manually or using a mechanical translation stage. The output monochromatic beam provides a collimated image of the anode spot with magnification of unity in the dispersion direction (typically 100 μm–200 μm for the x-ray tubes used here) and is unfocused in the cross-dispersion direction so that the source image in the detector plane appears as a line. We measured output count rates as high as 10 count/s/pixel for the Hitomi soft x-ray spectrometer, which had 819 μm square pixels. We implemented different monochromator designs for energies of 5.4 keV (one design) and 8.0 keV (two designs), which have effective theoretical FWHM energy resolution of 0.125 eV, 0.197 eV, and 0.086 eV, respectively; these are well-suited for optimal calibration measurements of state-of-the art x-ray calorimeters. We measured an upper limit for the energy resolution of our Cr Kα1 monochromator of 0.7 eV FWHM at 5.4 keV, consistent with the theoretical prediction of 0.125 eV.

47 OTHER INSTRUMENTATION↗
NASA NTRS2013

A Hybrid Fiber/Solid-State Regenerative Amplifier with Tunable Pulse Widths for Satellite Laser Ranging

A fiber/solid-state hybrid seeded regenerative amplifier, capable of achieving high output energy with tunable pulse widths, has been developed for satellite laser ranging applications. The regenerative amplifier cavity uses a pair of Nd:YAG zigzag slabs oriented orthogonally to one another in order to make thermal lensing effects symmetrical and simplify optical correction schemes. The seed laser used is a fiber-coupled 1,064-nm narrowband (<0.02 nm) diode laser that is discretely driven in a new short-pulsed mode, enabling continuously tunable seed pulse widths in the 0.2-to-0.4-ns range. The amplifier gain unit consists of a pair of Brewster-cut 6-bounce zigzag Nd:YAG laser slabs, oriented 90deg relative to each other in the amplifier head. This arrangement creates a net-symmetrical thermal lens effect (an opposing singleaxis effect in each slab), and makes thermo-optical corrections simple by optimizing the curvature of the nearest cavity mirror. Each slab is pumped by a single 120-W, pulsed 808-nm laser diode array. In this configuration, the average pump beam distribution in the slabs had a 1-D Gaussian shape, which matches the estimated cavity mode size. A half-wave plate between the slabs reduces losses from Fresnel reflections due to the orthogonal slabs Brewster-cut end faces. Successful "temporal" seeding of the regenerative amplifier cavity results in a cavity Q-switch pulse envelope segmenting into shorter pulses, each having the width of the input seed, and having a uniform temporal separation corresponding to the cavity round-trip time of approx. =10 ns. The pulse energy is allowed to build on successive passes in the regenerative amplifier cavity until a maximum is reached, (when cavity gains and losses are equal), after which the pulse is electro- optically switched out on the next round trip The overall gain of the amplifier is approx. =82 dB (or a factor of 1.26 million). After directing the amplified output through a LBO frequency doubling crystal, approx. = 2.1 W of 532-nm output (>1 mJ) was measured. This corresponds to a nonlinear conversion efficiency of >60%. Furthermore, by pulse pumping this system, a single pulse per laser shot can be created for the SLR (satellite laser ranging) measurement, and this can be ejected into the instrument. This is operated at the precise frequency needed by the measurement, as opposed to commercial short-pulsed, mode-locked systems that need to operate in a continuous fashion, or CW (continuous wave), and create pulses at many MHz. Therefore, this design does not need to throw away or dump 99% of the laser energy to produce what is required; this system can be far smaller, more efficient, cheaper, and readily deployed in the field when packaged efficiently. Finally, by producing custom diode seed pulses electronically, two major advantages over commercial systems are realized: First, this pulse shape is customizable and not affected by the cavity length or gain of the amplifier cavity, and second, it can produce adjustable (selectable) pulse widths by simply adding multiple seed diodes and coupling each into commercial, low-cost fiber-optic combiners.

Coyle, Barry↗
NASA NTRS2020

Simple, Compact, High-Resolution Monochromatic X-Ray Source for Characterization of X-Ray Calorimeter Arrays

X-ray calorimeters routinely achieve very high spectral resolution, typically a few eV full width at half maximum (FWHM). Measurements of calorimeter line shapes are usually dominated by the natural linewidth of most laboratory calibration sources. This compounds the data acquisition time necessary to statistically sample the instrumental line broadening and can add systematic uncertainty if the intrinsic line shape of the source is not well known. To address these issues, we have built a simple, compact monochromatic x-ray source using channel cut crystals. A commercial x-ray tube illuminates a pair of channel cut crystals that are aligned in a dispersive configuration to select the Kα1 line of the x-ray tube anode material. The entire device, including the x-ray tube, can be easily hand-carried by one person and may be positioned manually or using a mechanical translation stage. The output monochromatic beam provides a collimated image of the anode spot with magnification of unity in the dispersion direction (typically 100 μm–200 μm for the x-ray tubes used here) and is unfocused in the cross-dispersion direction so that the source image in the detector plane appears as a line. We measured output count rates as high as 10 count/s/pixel for the Hitomi soft x-ray spectrometer, which had 819 μm square pixels. We implemented different monochromator designs for energies of 5.4 keV (one design) and 8.0 keV (two designs), which have effective theoretical FWHM energy resolution of 0.125 eV, 0.197 eV, and 0.086 eV, respectively; these are well-suited for optimal calibration measurements of state-of-the art x-ray calorimeters. We measured an upper limit for the energy resolution of our Cr Kα1 monochromator of 0.7 eV FWHM at 5.4 keV, consistent with the theoretical prediction of 0.125 eV.

M A Leutenegger↗
NASA NTRS1988

Simulated impact damage in a thick graphite/epoxy laminate using spherical indenters

The extent of fiber damage due to low-velocity impacts was determined for very thick graphite/epoxy laminates. The impacts were simulated by pressing spherical indenters against the laminates. After the forces were applied, the laminate was cut into smaller pieces so that each piece contained a test site. Then the pieces were deplied and the individual plies were examined to determine the extent of fiber damage. Broken fibers were found in the outer layers directly beneath the contact site. The locus of broken fibers resembled cracks. The cracks were more or less oriented in the direction of the fibers in the contiguous layers. The maximum length and depth of the cracks increased with increasing contact pressure and indenter diameter. The length and depth of the cracks were also predicted using maximum compression and shear stress criteria. The internal stresses were calculated using Hertz's law and Love's solution for pressure applied on part of the boundary of a semi-infinite body. The predictions and measurements were in good agreement.

Poe, C. C., Jr.↗