Fractal Dimension Of Grain Boundaries Research Articles

The Study on the Quantification of Re-crystallized Structure Growth in FGHAZ of Mod. 9Cr-1Mo Steel during Creep by Fractal Dimension of Grain Boundaries

The Study on the Quantification of Re-crystallized Structure Growth in FGHAZ of Mod. 9Cr-1Mo Steel during Creep by Fractal Dimension of Grain Boundaries

Quantitative relationship between microstructure and mechanical properties in Nd: YAG transparent ceramics

In this work, stereology and fractals were applied to identify the quantitative relation between stereology parameters, fractal dimension, and mechanical properties of Nd: YAG transparent ceramics sintered at 1750 °C for 8–50 h. Mechanical properties and microstructure of the samples were investigated by using universal testing machine, micro-hardness tester, and scanning electron microscopy (SEM), respectively. When the ceramics were sintered at 1750 °C for 50 h, the compressive strength, flexural strength, and Vickers hardness reached 381.6 ± 5.2 MPa, 275.0 ± 5.5 MPa, and 1330.4 ± 18.5 MPa, respectively. Besides, the fracture toughness of ceramic samples was calculated by Vickers hardness. Micrographs of the sample surface and frequency distribution of crystal grains were analyzed by using metallographic image analyzer software. Findings suggest that compressive strength, flexural strength, and Vickers hardness linearly increase upon an increase in equivalent sphere diameter (D3S). However, compressive strength, flexural strength, and Vickers hardness decrease as a function of specific surface area per unit volume of the grains (SV) and discrete grains (SVP) and mean free distance (λ). Perimeter and area of crystal grains were obtained by using Image-Pro Plus image analysis software. The relationship between the fractal dimension of grain boundary and mechanical properties was analyzed based on the area-perimeter (small-island) method. When the grain boundary fractal dimension is close to 1.0, the geometry of ceramic grains tends to be regular, and mechanical properties of ceramic samples increases.

Influence of rapid annealing on the evolution of fractal abnormal grains in nanocrystalline Pd–10 at% Au

During abnormal grain growth, certain grains grow to much larger sizes than their neighbors. Usually, such abnormal grains expand in all directions at roughly the same speed, but in nanocrystalline Pd-10 at% Au, they appear to send forth dendritic offshoots into the surrounding matrix, resulting in highly irregular, fractal-like grain shapes. Exploiting the fast heating capabilities of a salt-bath oven, we have investigated the influence of heating rate on the evolution of fractal grain morphologies in nanocrystalline Pd-10 at% Au. In this material, the nanocrystalline matrix is stable at 170°C, but fractal grains appear within minutes at 200°C and 270°C, followed by fast growth until impingement. Surprisingly, the higher dwell temperature leads to a smaller average grain size in the fully impinged state. For the latter, no additional grain growth is observed at longer dwell times, but the fractal dimension of grain boundaries decreases with time at 270°C. These findings are consistent with abnormal grain formation being governed by a temperature-dependent nucleation process, upon which is superimposed the usual capillary driving force for grain growth; however, the mechanism by which boundaries migrate through the nanocrystalline matrix while retaining fractality remains unclear.

Study on Fractal Dimension of Grain Boundary of FGHAZ as the Indication of TypeIV Creep Damage

Study on Fractal Dimension of Grain Boundary of FGHAZ as the Indication of TypeIV Creep Damage

Fractal Dimension of Grain Boundaries and Mechanical Properties of the Metal of Oxygen Cylinders

We perform the quantitative fractal analysis of the grain boundaries in the microstructure of Ds steel of five oxygen cylinders with a period of operation from 18 to 52 years. Their fractal dimension is determined by the superposition of square cells of different sizes on the image of the selected grain boundary with computing the number of points of their intersection with this boundary (box method). We establish correlations between the fractal dimension of grain boundaries and the impact toughness, fracture pressure, and yield strength. The corresponding regression equations are deduced. We also analyze the fracture mechanisms connected with the fractal dimension of the grain boundaries.

Analysis of the fractal dimension of grain boundaries of AA7050 aluminum alloys and its relationship to fracture toughness

Quantitative analysis of the grain boundaries in partially recrystallized microstructures of heat-treated 7050 aluminum alloys has been performed. Fractal dimensions of the extracted grain boundaries were calculated by boxcounting method. Five different types of tear-tested materials rolled in different processes each at two orientations of 0o and 90o were studied. Efforts were made to connect the fractal dimensions of grain boundaries in the crack propagation direction to the fracture toughness (unit propagation energy, UPE, in tear test). The results show that there is a linear correlation between UPE and the fractal dimensions of the grain boundaries along the crack propagation direction for both 0o and 90o samples. The dependence corresponds well with the observation of transition from intergranular fracture to transgranular fracture with the increase of UPE. Quantitative analysis has also been performed on the micrographs to estimate the degree of recrystallization and the grain size in crack growth direction. No correlation between the fraction of recrystallized grains and the UPE could be detected.

Fractal Dimension of Grain Boundary during Heating Comparison between Images Analyses and Monte Carlo Simulation

There are few articles that mention fractal dimension in grain growth mechanism. Some authors build a simplified analytic model showing that initial fractal dimension of grain boundary has an influence on interface modification velocity. Nevertheless they postulate the relation where L is the grain length, c is a constant, s is grain size and the fractal dimension. The aims of this paper is to experimentally analyze by image analysis the fractal dimension of A5 aluminum sheet grain boundaries during heating and to simulate their evolution by a Monte Carlo method to validate experimental data.. It is shown by Monte-Carlo simulation and confirmed experimentally that the grain growth process decreases the fractal dimension of grain border. It can be concluded that it is very hazardous to build a model of grain growth without including the effect of grains morphology. The macroscopic fractal morphology of the grain structure could then be used to validate microscopic relation between Monte Carlo Steps time and real time.

Measurement of the mean grain size in a metal by using fractal dimensions

We propose a method for the automated determination of mean grain size on the basis of analysis of digital metallographic images of the microstructure of operated 12Kh1MF steam-pipeline steel. Measurements of the fractal dimension of grain boundaries of the metal form its basis. It enables one to automate calculations and analyze metallographic images with unclosed and broken grain boundaries without their interactive editing.

Calculation of the fractal dimension of grain boundaries in nanocrystalline Pd

The geometric structure of grain boundaries in nanocrystalline Pd has been analysed in terms of power-law relationships. The power laws yielded exponents that were interpreted as fractal-like dimensions. The box-counting fractal dimension, , was computed for three images digitized from published transmission electron micrographs; the average result was . An average site occupation probability, p, was estimated for the lattices in the images, by determining the relationship between p and for pseudo-random fcc lattices. The results of further numerical simulations suggested that the grain boundaries had a box-counting fractal dimension of . The extent to which fractal theory is valid for nanocrystalline Pd is evaluated.

Fractal dimension of grain boundary in CuAu alloys refined by platinum addition

Irregularity of the grain boundaries in CuAu alloys refined by platinum addition was estimated by fractal analysis. The fractal dimension increased with decreasing the grain size, which introduced by platinum addition. The grain refinement produced more complexity in microstructure.

Effects of Cold Work on the Fractal Dimension of Grain Boundaries in Pure Iron

The effects of cold work on the fractal dimension of grain boundaries (FDGB) were investigated using cold-worked (cold-upsetted) specimens of pure iron. The change in the grain-boundary configuration with cold work was analysed principally by the coarse-graining method (CGM) using line segments in this study. The FDGB was estimated from the relationship between the length of grain perimeter and the scale length in fractal analysis in the scale range from about 5 x 10 -7 to 3 x 10 -6 m, which was correlated to the size range of slip line spacing (4.5 x 10- 7 to 3.4 x 10 -6 m) in the cold-worked specimens of pure iron. The FDGB increased from about 1.05 to 1.15 with increasing amount of cold work (ACW) in the range from 0% to about 50% of cold reduction, but it remained almost unchanged when the ACW exceeded about 50%. The increase of the FDGB was associated with an increase of the density of slip lines within the grains due to the cold work, since the slip lines caused steps and ledges on the grain boundaries, which resulted in an increase of the FDGB. The box-counting method gave a slightly larger value for the FDGB than the CGM.

冷間加工した純鉄試料における粒界のフラクタル次元

The effects of the amount of cold work on the fractal dimension of grain boundary were investigated using specimens of the commercial pure iron cold-upsetted in the range from 0% to about 85%. The fractal dimension of grain boundary was estimated principally by approximating the length of the grain perimeter (the length of grain boundaries which belonged to a grain) by line segments.The length of the grain perimeter, L, in each specimen decreased with an increase of the scale of the analysis, r, in the range from about 5×10−7m to about 3×10−6m (region I) and above about 1×10−5m (region III) of r, while it showed a constant value, Lp, between about 3×10−6m and about 1×10−5 m of r. Total datum points of several grains were unified by dividing L by Lp and by plotting L⁄Lp against r. The fractal dimension of grain boundary was obtained by using the datum points in region I, since the change in the grain-boundary configuration with cold work was associated with the slip in the grains. The fractal dimension of grain boundary increased from about 1.05 to about 1.15 with increasing amount of cold work in the range from 0% to about 50% of cold reduction, but it was almost constant above 50% cold work. The box-counting method gave a little larger values of the fractal dimension of grain boundary than the coarse-graining using line segments. The shape change of grains with cold work was also examined and interpreted by a simple analysis in this study.

Characterization of grain-boundary configuration and fracture surface roughness by fractal geometry and creep-rupture properties of metallic materials

Grain-boundary configuration in heat-treated specimens and fracture surface roughness in creep-ruptured specimens of several kinds of metallic material were quantitatively evaluated on the basis of fractal geometry. Correlations between the fractal dimension of grain boundary, that of fracture surface profile, the creep-rupture properties and the fracture mechanisms of the alloys are discussed. In heat-resistant alloys, the fractal dimension of a nominally serrated grain boundary was always larger than that of a straight grain boundary in the same alloy. The relative importance of the ruggedness of grain boundaries was estimated by the fractal dimension difference between these two grain boundaries. There was a quantitative relationship between the increase of the fractal dimension of the grain boundary and the improvement of rupture ductility and rupture strength owing to grain-boundary serration in the alloy. A similar correlation was also found between the increase in the fractal dimension of the fracture surface profile and the improvement of the creep-rupture properties, since in some cases the fractal dimension of the fracture surface profile was correlated with that of the grain boundary. Both grain boundary and fracture surface profile were assumed to exhibit a fractal nature between one grain boundary length (upper bound) and an interatomic spacing (lower bound). In carbon steels with ferrite-pearlite structure, according to the increase in pearlite volume fraction, the rupture ductility decreased and the fracture mechanism changed from transgranular fracture in pure iron and low-carbon steels to intergranular fracture at ferrite-pearlite grain boundaries in medium-carbon steels, and further to intergranular fracture at pearlite grain boundaries in high-carbon steels. The correspondence between the fractal dimension of the grain boundary and that of the fracture surface was confirmed in ruptured specimens of ferrite-pearlite steels when the grain boundary was the fracture path.