@ARTICLE{Brożek_Marian_The_2003,
 author={Brożek, Marian and Oruba-Brożek, Ewa},
 number={No 3},
 journal={Gospodarka Surowcami Mineralnymi - Mineral Resources Management},
 pages={91-109},
 howpublished={online},
 year={2003},
 publisher={Komitet Zrównoważonej Gospodarki Surowcami Mineralnymi PAN},
 publisher={Instytut Gospodarki Surowcami Mineralnymi i Energią PAN},
 abstract={Theoretical tensile strength of brittle materials is 102-104 times larger than real strength. The particle structure, apart from the force of atomic bonds in an ideal crystal, affects real strength. A single-phase particle, spatially continuous and homogenous from the point of view of its chemical composition, is assumed to be the basis. A real particle is formed by means of introducing pre-existing microcracks and other geometrical and physical internal defects. The size distribution and number ofthese defects, affecting the particle strength, form the mechanical structure ofa particle. Since both the number and size ofpre-existing microcracks are randomvariables, respectively the particle tensile strength iś°"a random variable, described by Weibull's distribution. This paper has analysed the effect of particle structure on its tensile strength from the point of view ofthe weakest link theory and the statistical theory of fracture. In both cases for the distribution is obtained whose parameters are connected with the distribution ofmicrocracks lengths (formulas 5 and 15). The next part of the paper shows the results ofempirical tensile strength tests oflimestone and porphyry particles. The authors set distribution functions of tensile strength (formulas 20-22 and figures 3-5) and calculatedWeibull's moduli of the tested samples and the average particle strength. The average particle tensile strength is connected with the particle size by one of the formulas (25), depending on the fact whether particle fracture resulted from stimulating the volume, surface or edge microcracks. In case of limestone (one-component material) the particle fracture is caused by edge microcracks (formula 27a) while for porphyry (multi-component material) by surface microcracks (formula 27b). The dependence of crushing ratio on particle strength is described by an increasing power function (formulas 29-32). The exponent in this dependence is correlated with Weibull's modulus (formula 33). The presented results concern two raw materials. Further investigations will decide whether the obtained results are of general character, concerning all materials.},
 type={Artykuł},
 title={The effect of structure of mineral particles on their strength properties exemplified by limestone and porphyry},
 URL={http://ochroma.man.poznan.pl/Content/132553/PDF-MASTER/8_GSM_19_3_2003_Brozek_Wplyw.pdf},
 keywords={porphyry, limestone, tensile strength, Weibull's distribution, pre-existing microcracks, crushing ratio},
}