Multi-Fractal Behaviors in Grain Size Distribution of Low Silica Sinter

2012 ◽  
Vol 268-270 ◽  
pp. 344-347
Author(s):  
Yu Zhu Zhang ◽  
Qing Liu ◽  
Qing Jun Zhang ◽  
Jin Gang Liu ◽  
Wen Ling Mo ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Fractal Dimension ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Quantitative Measurement ◽  
Fractal Theory

Multi-fractal theory is used to detect fractal behaviors embedded in grain size distribution ofsinter with low SiO2. Impacts of SiO2, basicity, and MgO on structures of sinter ore are measured quantitatively by means of fractal dimension dm, d(1) and multi-fractal strength Δd. Increase of SiO2 induces decrease of fractal dimension and multi-fractal strength. While proper levels of carbon, basicity, and MgO lead to minimum values of fractal dimension and multi-fractal strength. This kind of quantitative measurement of structures in sinter ore can help us to investigate the relation of mechanical properties and structures in a quantitative way.

Influence of SiO2 Content on Fractal of Grain Distribution in Low Silicon Sinter

2011 ◽  
Vol 391-392 ◽  
pp. 269-273
Author(s):  
Qing Jun Zhang ◽  
Li Mei Jiang ◽  
Wen Ling Mo ◽  
Yu Zhu Zhang
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Fractal Theory ◽  
Fractal Characteristic ◽  
Important Index ◽  
Grain Distribution

Grain size distribution in the sinter is an important index sign to measure the quality of sinter. In this paper, according to the fractal theory and the contrast experiment of sinter, the fractal characteristic of grain size distribution of sinter with low SiO2is discussed. The relation between the fractal dimension and content of SiO2is proposed. Combine with the SEM graphs of the sinter with low SiO2, the relation between the fractal dimension and microstructure of sinter with low SiO2is also analyzed. Pass to the quantificational description of the grain size distribution of sinter with low SiO2, to predict and optimize the grain size constitution of sinter, and offer a new idea, a new way for the further thorough research of sinter ore.

scholarly journals A laboratory study of sediment deformation: stress heterogeneity and grain-size evolution

1996 ◽  
Vol 22 ◽  
pp. 167-175 ◽  
Author(s):  
Neal R. Iverson ◽  
Thomas S. Hooyer ◽  
Roger Leb. Hooke
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Normal Stress ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Local Stress ◽  
Large Strains ◽  
Self Similar ◽  
Deformation Stress ◽  
Stress Heterogeneity

In shearing sediment beneath glaciers, networks of grains may transiently support shear and normal stresses that are larger than spatial averages. Consistent with studies of fault-gouge genesis, we hypothesize that crushing of grains in such networks is responsible for surrounding larger grains with smaller grains. At sufficiently large strains, this should minimize stress heterogeneity, favor intergranular sliding and abrasion rather than crushing, and result in a self-similar grain-size distribution.This hypothesis is tested with a ring-shear device that slowly shears a large annular sediment sample to high strains. Shearing and comminution of weak equigranular (2.0–3.3 mm) sediment resulted in a self-similar grain-size distribution with a fractal dimension that increased with shear strain toward a steady value of 2.85. This value is significantly larger than that of gouges produced purely by crushing, 2.6, but it is comparable to values for tilts thought to be deforming beneath modern glaciers, 2.8 to nearly 3.0. At low strains, under a steady mean normal stress of 84 kPa, variations in normal stress measured locally ranged in amplitude from 50 to 300 kPa with wavelengths that were 100 times larger than the initial grain diameter. Crushing of grains, observed through the transparent walls of the device, apparently caused the failure of grain networks. At shearing displacements ranging from 0.7 to 1.0 m, the amplitude of local stress fluctuations decreased abruptly. This change is attributed to fine sediment that distributed stresses more uniformly and caused grain networks to fail primarily by intergranular sliding rather than by crushing of grains. Sliding between grains apparently produced silt by abrasion and resulted in a fractal dimension that was higher than if there had been only crushing.A size distribution with a fractal dimension greater than 2.6 is probably a necessary but not sufficient condition for determining whether a basal till has been highly deformed. Stress heterogeneity in subglacial sediment that is shearing through its full thickness should contribute to the erosion of underlying rock.

Multi-Class Grain Size Model for Forged Alloy 718 Aircraft Parts

2021 ◽  
Vol 1016 ◽  
pp. 499-508
Author(s):  
Christian Gruber ◽  
Peter Raninger ◽  
Martin Stockinger ◽  
Christian Bucher
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Base Alloy ◽  
Physical And Mechanical Properties ◽  
Initial Distribution ◽  
Alloy 718 ◽  
Process Data ◽  
Size Model

The evolution of microstructural features such as local grain size and local grain size distribution are essential in view of the final physical and mechanical properties of the nickel base alloy 718 for aircraft parts forged in a multi-step production route. Due to increasing standards and the need of the prediction of fracture mechanical properties, a multi-class grain size model for a more detailed microstructure prediction is necessary. Therefore, a multi-class model considers the real initial non-uniform grain size distribution and structure of the pre-material at the beginning of the forging process, which affects the evolution of grain sizes during thermo-mechanical treatment and leads to different results than commonly used uniform grain structures. The initial distribution is defined by grain classes according the ASTM standard. It is shown that the presence of different classes and distributions of grains are as import as the applied strain, strain rate and temperature on dynamic, meta-dynamic and static recrystallization. Additionally, dissolution processes of delta phase and grain growth kinetics are included in the model to properly indicate the recrystallized fractions and represent the resulting multi-class microstructure. A series of simulations with different initial distributions is discussed and compared with examined forged samples in terms of the resulting microstructure for typical forging parameters. Based on these results the microstructure model can be used in combination with collected process data to predict the resulting properties and for the design of new aircraft parts.

The Effect of Grain Size Distribution on the Mechanical Properties of Nanometals

2008 ◽  
Vol 140 ◽  
pp. 185-190 ◽  
Author(s):  
T.B. Tengen ◽  
Tomasz Wejrzanowski ◽  
R. Iwankiewicz ◽  
Krzysztof Jan Kurzydlowski
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Flow Stress ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Deformation Mechanisms ◽  
Average Grain Size ◽  
Significant Interest ◽  
Size Dispersion ◽  
The Relationship

Predicting the properties of a material from knowledge of the internal microstructures is attracting significant interest in the fields of materials design and engineering. The most commonly used expression, known as Hall-Petch Relationship (HPR), reports on the relationship between the flow stress and the average grain size. However, there is much evidence that other statistical information that the grain size distribution in materials may have significant impact on the mechanical properties. These could even be more pronounced in the case of grains of the nanometer size, where the HPR is no longer valid and the Reverse-HPR is more applicable. This paper proposes a statistical model for the relationship between flow stress and grain size distribution. The model considered different deformation mechanisms and was used to predict mechanical properties of aluminium and copper. The results obtained with the model shows that the dispersion of grain size distribution plays an important role in the design of desirable mechanical properties. In particular, it was found that that the dependence of a material’s mechanical properties on grain size dispersion also follows the HPR to Inverse-HPR type of behaviour. The results also show that copper is more sensitive to changes in grain size distribution than aluminium.

Enhanced Mechanical Properties of Multilayered Cu with Modulated Grain Size Distribution

2017 ◽  
Vol 20 (4) ◽  
pp. 1700849
Author(s):  
Bo Zheng ◽  
Xixun Shen ◽  
Huisheng Jiao ◽  
Qunjie Xu ◽  
Danhong Cheng
Keyword(s):  
Mechanical Properties ◽  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution
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