Crack-size and crack-orientation distributions of brittle materials.
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In this report, we derived a new theory by combining the previously obtained statistical theory fracture location with the multiaxial distribution function. Using this theory, we analysed not only 3 crack-size ditribution function but also the crack-orientation distribution. Both distribution function are considerably affected by the fracture criteria. Based on the above results, we suggested new proposition to non-destructive inspection of brittle materials like engineering ceramics.Keywords:
Brittleness
Rock brittleness plays an important role in rock engineering, thus it is practically valuable to assess rock brittleness accurately. Many brittleness indices have been developed, but few methods are developed for layered rocks. Based on energy evolution, the authors propose a new index for assessing brittleness of layered rocks. The new index indicates that high rock brittleness means elastic energy accumulated effectively before peak and dissipated abruptly after peak. For the sake of verifying the proposed method, a series of compression tests were performed. The results demonstrate that rock brittleness decreases gradually with increasing confining pressure. As orientation angle increases, rock brittleness weakens and then strengthens overall. The brittleness of the specimen with an orientation angle of 0° is slightly higher than that with an orientation angle of 90°. The new index was compared with three existing brittleness indices, and the results indicate that the proposed method can evaluate brittleness of layered rock effectively.
Brittleness
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Abstract To quantitatively evaluate the influence of high true three-dimensional stresses on the ductile–brittle behaviours of rock in deep underground engineering, a series of true triaxial compression tests with different stress levels were carried out on marble and four kinds of granite. The influences of true triaxial stress states ( σ 2 , σ 3 ) on the post-peak characteristics were analysed, and a new normalized ductile–brittle evaluation index was proposed based on post-peak energy conversion characteristics of rock under true triaxial stresses. The ductile–brittle behaviours of rock were divided into four qualitative levels, namely, ductile-brittleness, transitional, brittleness and super-brittleness, and the influences of true triaxial stress states on the ductile–brittle behaviours of rock were quantitatively investigated. The research shows that as σ 2 increases or σ 3 decreases (that is, the differential stress between σ 2 and σ 3 increases), the brittleness of rock increases, and its increase rate gradually decreases and tends to be stable, transforming from ductile-brittleness to transitional, brittleness and super-brittleness and resulting in super-brittleness being easily induced by low- σ 3 and high- σ 2 conditions. When the differential stress between σ 2 and σ 3 is small, the intrinsic characteristics of rock itself have an obvious influence on ductile–brittle behaviours. When the differential stress between σ 2 and σ 3 is large, all kinds of rocks can exhibit super-brittle behaviour. The change of stress controls the evolution of rock ductile–brittle behaviours, and high-stress controls rock brittleness. The rock brittleness under true triaxial stress is significantly higher than that under conventional triaxial stress at the same σ 3 . σ 2 induces an increase in rock brittleness and causes the decay rate of brittleness to decrease with increasing σ 3 , and σ 2 increases the upper limit of σ 3 for brittle failure of rock. The enhancement effect of σ 2 on rock brittleness must be considered when evaluating the brittle failure of deep surrounding rock under high-stress conditions; otherwise, the risk of brittle failure may be underestimated.
Brittleness
Differential stress
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Brittleness
Overburden pressure
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Accurately evaluation of brittleness characteristics of granite under different water content is of great significance to rock mass stability evaluation. The existing rock brittleness evaluation indices are summarized. The indices based on stress-strain curve are analyzed in detail. The brittleness of granite decreases with the increase of water content under uniaxial compression,but experiment results show that the indices which based on the stress-strain curve are difficult to accurately reflect the brittleness characteristics of granite under different water contents. So a new brittleness index Bd is proposed and can fully reflect the whole process of granite deformation and failure. Considering the whole process stress-strain curve and the post peak failure time,the new index Bd uses the peak strain to characterize the pre-peak brittleness characteristics and uses the post peak stress drop rate and the post peak strain growth rate to characterize the post-peak brittleness characteristics. It is proved by experiments that the index Bd can accurately reflect the trend that the granite brittleness decreases with the increase of water content. The new index Bd has superiority over the other brittleness indices. The research results can provide some references and help to enrich and improve the rock brittle characteristics evaluation methods.
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The values of the orientation distribution function and the data of the pole‐figure are correlated by products of particular conditional probabilities. One of the possible approximations of these products are obtained and demonstrated with the help of an example showing how the orientation distribution function can thus be obtained.
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In rock cutting mechanics, the effects of the rock and coal brittleness on the efficiency of cutting bits are examined by many researchers. There is no universally accepted brittleness concept as a measure of cutting efficiency. The effect of the brittleness on rock cutting has not been completely explained. The aim of this study is to correlate the relationships between Specific Energy (SE) and brittleness concepts. The applicability of various brittleness measurement methods for rock cutting efficiency has been investigated. In this study, the raw data derived from previous experimental studies were used, and the relationships between SE and brittleness concepts were investigated. The two previously used brittleness concepts, which are named as B1 (the ratio of compressive strength to tensile strength) and B2 (the ratio of compressive strength minus tensile strength to compressive strength plus tensile strength), and a new introduced brittleness concept named B3 (the area under line in relation to compressive strength and tensile strength) were evaluated in this study. The relations among these brittleness concepts for rock cutting efficiency were established using regression analysis. There is no correlation found between the SE values and the brittleness of B1 and B2 values. But, the SE is strongly correlated with the brittleness of B3. It was seen that the suggested brittleness of B3 concept could be used as an indicator in rock cutting efficiency analysis.
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Brittleness
Acoustic Emission
Overburden pressure
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Brittleness
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Brittleness
Indentation
Elongation
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The calculation of characteristics describing texture as well as relations between orientations and morphological features of microstructure are based on single orientation measurements. For such experimental data, it is essential to estimate the number of necessary measurements of single orientations for a statistically significant representation of the investigated quantity, which, in the present paper, is the orientation distribution function (ODF). In a previous article [Pospiech, Jura & Gottstein (1993) Mater Sci. Forum , 157–162 , 407–412], this number has been estimated by a criterion that is used here for a cubic and a hexagonal material. This approach is very useful since it allows one to estimate the minimum orientation number with or without referring to an ODF calculated from pole figures measured by X-ray or neutron diffraction.
Texture (cosmology)
Representation
Pole figure
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