Estimating the crush zone size under a cutting tool in coal

Summary As part of an effort to understand the mechanics of fine fragment formation in coal, which is important in studies of respirable dust due to mining, fracture toughness measurements and the strain energy density (SED) theory were applied to calculate the crush zone size under a cutting tool in coal. This zone is the major source of fine fragments in the 1 to 10 µm size range. The model used in these calculations is a boundary element program containing a failure criterion based on the SED theory. The boundary element program calculates linear elastic stresses at numerous points in the coal material ahead of a cutting bit. These stresses are then input to a subroutine called critical flaw length and orientation (CFLO) which uses the SED theory to determine the CFLO for a small crack at the boundary element stress computation point. The extent of crushing is based on earlier postulates about the role of inherent flaws in a fragmentation process. To form 1 to 10 µm fragments requires firstly a local stress strong enough to activate flaws with a characteristic length less than 1 to 10 µm and secondly, a flaw density sufficient to provide an average spacing between flaws also on the order of 1 to 10 µm. The locus of active 10 µm flaws represents the maximum possible extent of fine fragmentation in the 10 µm or less size range assuming that a sufficient inherent flaw density exists. The approach offers a first order approximation to the extent of crushing under a tool tip. The size and shape of the crush zone volume is affected by the attack angle and geometry of the tool.     

The macungie Sinkhole,Lehigh valley Pennsylvania: Cause and repair

A dramatic sinkhole collapse measuring some 100 feet in diameter by 41 feet deep occurred suddenly in the Borough of Macungie on June 23, 1986. The sinkhole collapse resulted in a major disruption of traffic, utility services, as well as a major health and safety hazard. Continual growth of the sinkhole could have resulted in almost certain damage or loss to more than 17 residences adjacent to the sinkhole collapse. Stabilization and repair costs totaled some $450,000 and required almost three months to restore utility services, roadway, and parking areas.     

Temporal features in thunder days in the United States

1901–80 data for the contiguous U.S. show that secular variability of thunder days was very much less than that of precipitation or of frequency of extra tropical cyclones. Overall, there may have been a slight decline, but more evident was an increase to the thirties followed by a falling off, broken only by a peak in the seventies. These up-and-down movements were evident in most months of the year and regions of the U.S. The general decrease, however, was clear only in the South East and replaced by an increase in the Upper Great Lakes region. Secular variation in thunder day frequency was slightly correlated positively with that of extra tropical cyclone frequency and negatively with sea level pressure. The analysis also confirmed well known seasonal and regional patterns of thunder activity.     

Fractal analysis of long-range paleoclimatic data: Oxygen isotope record of pacific core V28-239

R/S analysis of the oxygen isotope curve of Pacific core V28-239 yields a fractal dimension of 1.22. This value is considered to characterize global climatic change over the last 2 million years as expressed by changing O¹⁸ ratios and confirms that climatic variations are characterized by long-term persistence. The fractal dimension of 1.22 compares favorably with the approximate fractal dimension of 1.26 for annual precipitation records for nine major cities in the United States. Although the precipitation and oxygen isotope data are measured in different physical units and recorded at different time scales, fractal analysis allows for a mathematical comparison of the two phenomena. Additionally, since the fractal dimensions of the oxygen isotope and precipitation records are similar, it is implied that such fractal dimensions are characteristic of climate change over the spectral range of 10 to 10⁶ years. Given this temperature curves based on fractal parameters of long-term O¹⁸ data could be constructed which would allow examination of characteristics of temperature variation over tens and hundreds of years. Such studies may allow the establishment of limits on natural temperature variation and document the persistence of temperature trends through time. If these trends and limits can be resolved, long-range climatic prediction is feasible.     

A modeling of the structure and compressibility of quartz with a molecular potential and its transferability to cristobalite and coesite

Several computer models of quartz were developed and tested. A simple model based on a potential energy function, derived in large part from quantum mechanical calculations on the molecule H₆Si₂O₇, was found to reproduce the compressibility curve for quartz up to pressures of 8 GPa. The potential includes quadratic expressions for the SiO bond lengths, the OSiO angles and a parameter spanning the SiOSi angle together with an exponential OO repulsion term for non co-dimer O atoms. The variations in the cell edges and in the SiOSi angle, as a function of pressure, parallel observed trends when the bond lengths and angles calculated for the molecule are used as rgressor values. Poisson ratios calculated using the model match those observed. Two configurations for quartz related by the Dauphiné twin law are generated as minimum energy structures of the model with about equal frequencies as observed in nature. It is shown that the model, devised for quartz, can also be applied to the silica polymorph cristobalite, giving reasonable estimates of its compressibility curve, structural parameters and its negative Poisson ratio. When the observed bond lengths and angles are used as regressor values, the model generates the absolute coordinates of the atoms and the cell dimensions for quartz to within 0.005 Å and those of cristobalite to within 0.001 Å, on average, both at zero pressure. When applied to coesite, the model yields a zero pressure structure that is close to that observed but which is significantly softer than observed. The resulting SiO bond lengths are linearly correlated with f _s (O), as observed for coesite, despite the use of a single bond length and a single SiOSi angle as regressor values in the calculation. When the structures are optimized assuming P1 space group symmetry and triclinic cell dimensions, the resulting frameworks of silicate tetrahedra exhibit the translational, rotational and reflection symmetries observed for quartz, cristobalite and coesite. The fact that the resulting frameworks exhibit observed space group symmetries is evidence that the symmetry adopted by the silica polymorphs can be explained by short ranged forces.     

Bond length and radii variations in fluoride and oxide molecules and crystals

Molecular orbital calculations completed on fluoride molecules containing first and second row cations have generated bond lengths, R, that match those observed for coordinated polyhedra in crystals to within ～0.04 Å, on average. The calculated bond lengths and those observed for fluoride crystals can be ranked with the expression R=Kp ^?0.22, where p=s/r, s is the Pauling strength of the bond, r is the row number of the cation and K=1.34. The exponent -0.22 (≈ -2/9) is the same as that observed for oxide, nitride and sulfide molecules and crystals. Bonded radii for the fluoride anion, obtained from theoretical electron density maps, increase linearly with bond length. Those calculated for the cations as well as for the fluoride anion match calculated promolecule radii to within ～0.03 Å, on average, suggesting that the electron density distributions in the vicinity of the minima along the bond paths possess a significant atomic component despite bond type. Bonded radii for Si and O ions provided by experimental electron density maps measured for the oxides coesite, danburite and stishovite match those calculated for a series of monosilicic acid molecules. The resulting radii increase with bond length and coordination number with the radius of the oxide ion increasing at a faster rate than that of the Si cation. The oxide ion within danburite exhibits several distinct radii, ranging between 0.9 and 1.2 Å, rather than a single radius with each exhibiting a different radius along each of the nonequivalent bonds with B, Si and Ca. Promolecule radii calculated for the coordinated polyhedra in danburite match procrystal radii obtained in a structure analysis to within 0.002 Å. The close agreement between these two sets of radii and experimentally determined bonded radii lends credence to Slater's statement that the difference between the electron density distribution observed for a crystal and that calculated for a procrystal (IAM) model of the crystal “would be small and subtle, and very hard to determine by examination of the total charge density.”