One, Two, and Three-Dimensional Universal Laws for Fragmentation due to Impact and Explosion

2002 ◽  
Vol 69 (6) ◽  
pp. 854-856 ◽  
Author(s):  
A. Carpinteri ◽  
N. Pugno
Keyword(s):  
Particle Size ◽  
Energy Dissipation ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Three Dimensional ◽  
Brittle Materials ◽  
Fractal Particle

Based on the fractal particle size distribution, a fragmentation theory for quasi-brittle materials is herein developed. The results are three simple and powerful universal laws for the multiscale energy dissipation under impact and explosion fragmentation for one, two, and three-dimensional bodies, respectively. The three-dimensional law unifies the most important and well-known fragmentation theories. As an example, it has been applied to the prediction of the devastated area due to asteroid impacts on earth as a function of the energy released in the collision.

scholarly journals Effect of fractal particle size distribution on the mobility of dry granular flows

AIP Advances ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 095113
Author(s):  
Zhiqiang Lai ◽  
Dong Chen ◽  
Enhui Jiang ◽  
Lianjun Zhao ◽  
Luis E. Vallejo ◽  
...  
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Granular Flows ◽  
Fractal Particle

scholarly journals Laser Triangulation in 3-Dimensional Granulometric Analysis

2016 ◽  
Vol 61 (1) ◽  
pp. 15-27 ◽  
Author(s):  
Adam Heyduk
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Particle Surface ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Conveyor Belt ◽  
Laser Triangulation ◽  
Depth Maps ◽  
Coal Particles

Abstract The measurement of the particle size distribution plays an important role in mineral processing. Due to the high costs and time-consumption of the screening process, modern machine vision methods based on the acquisition and analysis of recorded photographic images. But the image analysis methods used so far, do not provide information on the three-dimensional shape of the grain. In the coal industry, the application scope of these methods is substantially limited by the low reflectivity of the black coal particle surface. These circumstances hinder proper segmentation of coal stream surface image. The limited information contained in two-dimensional image of the raw mineral stream surface, makes it difficult to identify proper size of grains partially overlapped by other particles and skewed particles. Particle height estimation based on the shadow length measurement becomes very difficult in industrial environment because of the fast movement of the conveyor belt and because of spatial arrangement of these particles, usually touching and overlapping. Method of laser triangulation connected with the movement of the conveyor belt makes it possible to create three-dimensional depth maps. Application of passive triangulation methods (e.g. stereovision) can be impeded because of the low contrast of the black coal on the black conveyor belt. This forces the use of active triangulation methods, directly identifying position of the analyzed image pixel. High contrast of the image can be obtained by a direct pointwise laser lighting. For the simultaneous identification of the entire section of the raw material stream it is useful to apply a linear laser (a planar sheet of the laser light). There have been presented basic formulas for conversion of pixel position on the camera CCD matrix to the real-word coordinates. A laboratory stand has been described. This stand includes a linear laser, two high-definition (2Mpix) cameras and stepper motor driver. The triangulation head moves on the rails along the belt conveyor section. There have been compared acquired depth maps and photographic images. Depth maps much better describe spatial arrangement of coal particles, and have a much lower noise level resulting from the specular light reflections from the shiny fragments of the particle surface. This makes possible an identification of the coal particles partially overlapped by other particles and obliquely arranged particles. It enables a partial elimination or compensation of image disturbances affecting the final result of the estimated particle size distribution. Because of the possibility of the reflected laser beam overriding by other particles it is advantageous to use a system of two cameras. Results of the experimental research confirmed the usefulness of the described method in spite of low reflectance factor of coal surface. The fast detection of changes in particle size distribution makes possible an on-line optimization of complex technological systems - especially those involving coal cleaning in jigs - thus leading to better stabilization of quality parameters of the enrichment output products. An additional application of the described method can be achieved by measuring the total volume of the stream of the transported materials. Together with the measurement signal from the belt conveyor weight it makes possible to estimate the bulk density of the raw mineral stream. The low complexity of the signal processing in the laser triangulation method is associated with the acquisition of high contrast images and analysis based on simple trigonometric dependencies.

Particle-Size Distribution of CdSe Quantum Dots Determined by Photoluminescence Spectroscopy

1989 ◽  
Vol 164 ◽  
Author(s):  
E.N. Prabhakar ◽  
C.A. Huber ◽  
D. Heiman
Keyword(s):  
Quantum Dots ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
State Energy ◽  
Energy Levels ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Electron Hole ◽  
Electron Hole Pair

AbstractParticle-size distribution effects on the energy levels of semiconductor quantum dots are investigated. By examining the low temperature photoluminescence spectra of microcrystals of the binary semiconductor CdSe embedded in a glass matrix, the distribution of energy levels due to three-dimensional confinement is determined. Calculations of the electron-hole pair ground state energy provide a relation between confinement energy and particle diameter. This allows conversion of the photoluminescence lineshape directly into a distribution of particle radii and facilitates analysis of the observed properties of the material. With extension to other systems the technique can become a valuable tool in the study of semiconductor microparticle composites.

Particle size distribution effects on the solid particle erosion of brittle materials

Wear ◽  
1981 ◽  
Vol 71 (3) ◽  
pp. 363-373 ◽  
Author(s):  
D.B. Marshall ◽  
A.G. Evans ◽  
M.E. Gulden ◽  
J.L. Routbort ◽  
R.O. Scattergood
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Solid Particle ◽  
Brittle Materials ◽  
Solid Particle Erosion ◽  
Particle Erosion

Effect of Particle Size Distribution on the Properties of Sand Mold by Three Dimensional Printing

2012 ◽  
Vol 190-191 ◽  
pp. 467-470
Author(s):  
Huo Ping Zhao ◽  
Chun Sheng Ye ◽  
Zi Tian Fan
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Three Dimensional ◽  
Sand Mold ◽  
Silica Sand ◽  
Three Dimensional Printing ◽  
Comprehensive Properties ◽  
Effect Of Particle Size ◽  
Dimensional Printing

In this study, three dimensional structures are fabricated by a self-developed three dimensional printing machine with eight different particle size distribution scrubbed silica sand. In order to evaluate particle size distribution effect on the properties of sand mold, the physical and mechanism properties of printed specimens, including weight, gas evolution, air permeability, tensile strength and compressive strength, were measured. The mechanism of effect was analyzed and studied. The results show that the printed specimens from the 80-140 mesh sand powder have the best comprehensive properties. Both wider and narrower particle size distribution adversely affects the properties of printed specimens.

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