On Ptolemaic metric simplicial complexes

We show that under certain mild conditions, a metric simplicial complex which satisfies the Ptolemy inequality is a CAT(0) space. Ptolemy's inequality is closely related to inversions of metric spaces. For a large class of metric simplicial complexes, we characterize those which are isometric to Euclidean space in terms of metric inversions.Comment: 13 page

Complex surfaces plated by thin-film deposition in one operation

Ion plating deposits thin film on complex surface in one operation. The ionized materials follow electric lines of force to all points on the objects, uniformly plating the surface from all sides simultaneously

Characterization of erosion of metallic materials under cavitation attack in a mineral oil

Cavitation erosion and erosion rates of eight metallic materials representing three crystal structures were studied. The erosion experiments were conducted with a 20-kHz ultrasonic magnetostrictive oscillator in a viscous mineral oil. The erosion rates of the metals with an fcc matrix were 10 to 100 times higher than that of an hop-matrix titanium alloy. The erosion rates of iron and molybdenum, with bcc matrices, were higher than that of the titanium alloy but lower than those of those of the fcc materials. Studies with scanning electron microscopy indicated that the cavitation pits were initially formed at the grain boundaries and precipitates and that the pits formed at the junction of grain boundaries grew faster than the others. Transcrystalline craters formed by cavitation attack over the surface of grains and roughened the surfaces by multiple slip and twinning. Surface roughness measurements showed that the pits that formed over the grain boundaries deepened faster than pits. Computer analysis revealed that a geometric expression describes the nondimensional erosion curves during the time period 0.5 t (sub 0) t 2.5 t (sub 0), where t (sub 0) is the incubation period. The fcc metals had very short incubation periods; the titanium alloy had the longest incubation period

Characterization of erosion of metallic materials under cavitation attack in a mineral oil

Cavitation erosion and erosion rates of eight metallic materials representing three crystal structures were studied using a 20-kHz ultrasonic magnetostrictive oscillator in viscous mineral oil. The erosion rates of the metals with an fcc matrix were 10 to 100 times higher than that of an hcp-matrix titanium alloy. The erosion rates of iron and molybdenum, with bcc matrices, were higher than that of the titanium alloy but lower than those of the fcc metals. Scanning electron microscopy indicates that the cavitation pits are initially formed at the grain boundaries and precipitates and that the pits that formed at the triple points grew faster than the others. Transcrystalline craters formed by cavitation attack over the surface of grains and roughened the surfaces by multiple slip and twinning. Surface roughness measurements show that the pits that formed over the grain boundaries deepended faster than other pits. Computer analysis revealed that a geometric expression describes the nondimensional erosion curves during the time period 0.5 t(0) t 2.5 t(0), where t(0) is the incubation period. The fcc metals had very short incubation periods; the titanium alloy had the longest incubation period

Cavitation Erosion of Copper, Brass, Aluminum and Titanium Alloys in Mineral Oil

The variations of the mean depth of penetration, the mean depth rate of penetration, MDRP, the pit diameter 2a and depth h due to cavitation attack on Al 6061-T6, Cu, brass of composition Cu-35Zn-3Pb and Ti-5A1-2.5Sn are presented. The experiments are conducted in a mineral oil of viscosity 110 CS using a magnetostrictive oscillator of 20 kHz frequency. Based on MDRP on the materials, it is found that Ti-5Al-2.5Sn exhibits cavitation erosion resistance which is two orders of magnitude higher than the other three materials. The values of h/a are the largest for copper and decreased with brass, titanium, and aluminum. Scanning electron microscope studies show that extensive slip and cross slip occurred on the surface prior to pitting and erosion. Twinning is also observed on copper and brass

The mechanism of erosion of metallic materials under cavitation attack

The mean depth of penetration rates (MDPRs) of eight polycrystalline metallic materials, Al 6061-T6, Cu, brass, phosphor bronze, Ni, Fe, Mo, and Ti-5Al-2.5Sn exposed to cavitation attack in a viscous mineral oil with a 20 kHz ultrasonic oscillator vibrating at 50 micron amplitude are reported. The titanium alloy followed by molybdenum have large incubation periods and small MDPRs. The incubation periods correlate linearly with the inverse of hardness and the average MDPRs correlate linearly with the inverse of tensile strength of materials. The linear relationships yield better statistical parameters than geometric and exponential relationships. The surface roughness and the ratio of pit depth to pit width (h/a) increase with the duration of cavitation attack. The ratio h/a varies from 0.1 to 0.8 for different materials. Recent investigations (20) using scanning electron microscopy to study deformation and pit formation features are briefly reviewed. Investigations with single crystals indicate that the geometry of pits and erosion are dependent on their orientation

Cavitation pitting and erosion of aluminum 6061-T6 in mineral oil water

Cavitation erosion studies of aluminum 6061-T6 in mineral oil and in ordinary tap water are presented. The maximum erosion rate (MDPR, or mean depth of penetration rate) in mineral oil was about four times that in water. The MDPR in mineral oil decreased continuously with time, but the MDPR in water remained approximately constant. The cavitation pits in mineral oil were of smaller diameter and depth than the pits in water. Treating the pits as spherical segments, we computed the radius r of the sphere. The logarithm of h/a, where h is the pit depth and 2a is the top width of the pit, was linear when plotted against the logarithm of 2r/h - 1

Solid spherical glass particle impingement studies of plastic materials

Erosion experiments on polymethyl methacrylate (PMMA), polycarbonate, and polytetrafluoroethylene (PTFE) were conducted with spherical glass beads impacting at normal incidence. Optical and scanning electron microscopic studies and surface profile measurements were made on specimens at predetermined test intervals. During the initial stage of damage to PMMA and polycarbonate, material expands or builds up above the original surface. However, this buildup disappears as testing progresses. Little or no buildup was observed on PTFE. PTFE is observed to be the most resistant material to erosion and PMMA the least. At low impact pressures, material removal mechanisms are believed to be similar to those for metallic materials. However, at higher pressures, surface melting is indicated at the center of impact. Deformation and fatigue appear to play major roles in the material removal process with possible melting or softening

Morphology of an aluminum alloy eroded by a jet of angular particles impinging at normal incidence

The erosion of an aluminum alloy impinged by crushed glass particles at normal incidence was studied. The erosion patterns were analyzed by scanning electron microscopy, energy dispersive X-ray spectroscopy, and surface profilometer measurements. From the analysis of specimens tested at various driving gas pressures and time intervals, four distinct erosion regions were identified. A study of pit morphology and its relationship to cumulative erosion was made. Cutting wear is believed to be the predominant material removal mechanism; some evidence of deformation wear was found during the incubation period

A study of the nature of solid particle impact and shape on the erosion morphology of ductile metals

Impulsive versus steady jet impingement of spherical glass bead particles on metal surfaces was studied using a gas gun facility and a commercial sand blasting apparatus. Crushed glass particles were also used in the sand blasting apparatus as well as glass beads. Comparisons of the different types of erosion patterns were made. Scanning electron microscopy, surface profilometry and energy dispersive X-ray spectroscopy analysis were used to characterize erosion patterns. The nature of the wear can be divided into cutting and deformation, each with its own characteristic features. Surface chemistry analysis indicates the possibility of complex chemical and/or mechanical interactions between erodants and target materials