scholarly journals Grain-Size Distribution Effects on the Attenuation of Laser-Generated Ultrasound in α-Titanium Alloy

Materials ◽  
2018 ◽  
Vol 12 (1) ◽  
pp. 102 ◽  
Author(s):  
Xue Bai ◽  
Yang Zhao ◽  
Jian Ma ◽  
Yunxi Liu ◽  
Qiwu Wang
Keyword(s):  
Grain Size ◽  
Titanium Alloy ◽  
Normal Distribution ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Fourth Power ◽  
Grain Sizes ◽  
Mean Grain Size ◽  
Log Normal ◽  
Log Normal Distribution

Average grain size is usually used to describe a polycrystalline medium; however, many investigations demonstrate the grain-size distribution has a measurable effect on most of mechanical properties. This paper addresses the experimental quantification for the effects of grain-size distribution on attenuation in α-titanium alloy by laser ultrasonics. Microstructures with different mean grain sizes of 26–49 μm are obtained via annealing at 800 °C for different holding times, having an approximately log-normal distribution of grain sizes. Experimental measurements were examined by using two different theoretical models: (i) the classical Rokhlin’s model considering a single mean grain size, and (ii) the improved Turner’s model incorporating a log-normal distribution of grain sizes in the attenuation evaluation. Quantitative agreement between the experiment and the latter model was found in the Rayleigh and the Rayleigh-to-stochastic transition regions. A larger attenuation level was exhibited than the classical theoretical prediction considering a single mean grain size, and the frequency dependence of attenuation reduced from a classical fourth power to an approximately second power due to a greater probability of large grains than the assumed Poisson statistics. The provided results would help support the use of laser ultrasound technology for the non-destructive evaluation of grain size distribution in polycrystalline materials.

scholarly journals Modified Gompertz sigmoidal model removing fine-ending of grain-size distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Rui Yuan ◽  
Bo Yang ◽  
Yingfei Liu ◽  
Lingyu Huang
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Cumulative Probability ◽  
Second Stage ◽  
Grain Sizes ◽  
Third Stage ◽  
Moments Method ◽  
Sigmoidal Model ◽  
Parameters Calculation

Abstract Because of the laboratory operating, the fineending of grain-size distribution (GSD) are simply combined as one point, which results in the information loss of the fine and very-fine clastic particles, and affects the geological parameters calculation of GSD. To remove the fine-endings, a modified Gompertz sigmoidal model is proposed in this paper. The first stage is establishing and solving the modified Gompertz sigmoidal model; the second stage is fitting and evaluating the cumulative probability and frequency of GSD; the third stage is calculating the geological parameters. Taking 113 samples for example, coefficients of determination (COD) between measured and fitted individual cumulative probability and frequency are bigger than 0.98980 and 0.97000 respectively, which proves the goodness of fitting results. By moments method using frequency data, the COD between fitted and measured mean is 0.97578, while CODs of sorting, skewness and kurtosis are in low values, which suggest that the fine-endings has little influence on the average grain-sizes of GSD and large influence on its geometry. Besides, modified Gompertz sigmoidal model offers another quick numerical way to calculate median, mean and sorting of GSD by graphical method using cumulative probability data. The proposed method is useful to remove the fine-endings and contribute to calculate the geological parameters of GDS.

scholarly journals Microstructural evolution in the fine-grained region of the Siple Dome (Antarctica) ice core

2011 ◽  
Vol 57 (206) ◽  
pp. 1046-1056 ◽  
Author(s):  
R.W. Obbard ◽  
K.E. Sieg ◽  
I. Baker ◽  
D. Meese ◽  
G.A. Catania
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Electron Backscatter Diffraction ◽  
Ice Core ◽  
Axis Orientation ◽  
Fine Grained ◽  
Depth Analysis ◽  
Siple Dome ◽  
Mean Grain Size

AbstractAn in-depth analysis of seven samples from the Siple Dome (Antarctica) ice core, using optical microscopy and electron backscatter diffraction, illustrates rotational recrystallization or polygonization in the fine-grained region of the core between 700 and 800 m. Between 640 and 700 m, the microstructure is characterized by a bimodal grain-size distribution and a broken girdle fabric with evidence of polygonization. From 727 to 770 m, mean grain size decreases and a single-maximum fabric is found, and, by 790 m, mean grain size has again increased and a multiple-maxima fabric manifests itself. We compare grain-size distribution, c- and a-axis orientation, and misorientation between adjacent grains. We found that misorientations between adjacent grains in the 727–770 m region were predominantly low-angle and typically around a common a-axis, suggesting polygonization. This conclusion is supported by radar evidence of a physical disturbance at 757 m, which may be correlated with higher than usual strain in the 700–800 m range. Below 770 m, larger less regular misorientations and textural evidence show that migration recrystallization is the primary recrystallization mechanism.

The Inverse Hall-Petch Effect—Fact or Artifact?

2000 ◽  
Vol 634 ◽  
Author(s):  
Carl C. Koch ◽  
J. Narayan
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Computer Simulations ◽  
Nanocrystalline Materials ◽  
Grain Sizes ◽  
Average Grain Size

ABSTRACTThis paper critically reviews the data in the literature which gives softening—the inverse Hall-Petch effect—at the finest nanoscale grain sizes. The difficulties with obtaining artifactfree samples of nanocrystalline materials will be discussed along with the problems of measurement of the average grain size distribution. Computer simulations which predict the inverse Hall-Petch effect are also noted as well as the models which have been proposed for the effect. It is concluded that while only a few of the experiments which have reported the inverse Hall-Petch effect are free from obvious or possible artifacts, these few along with the predictions of computer simulations suggest it is real. However, it seems that it should only be observed for grain sizes less than about 10 nm.

Topology Based Growth Law and New Analytical Grain Size Distribution Function of 3D Grain Growth

2007 ◽  
Vol 558-559 ◽  
pp. 1183-1188 ◽  
Author(s):  
Peter Streitenberger ◽  
Dana Zöllner
Keyword(s):  
Grain Size ◽  
Distribution Function ◽  
Size Distribution ◽  
Grain Growth ◽  
Grain Size Distribution ◽  
Three Dimensional ◽  
Size Distribution Function ◽  
Change Rate ◽  
Grain Sizes ◽  
Self Similar

Based on topological considerations and results of Monte Carlo Potts model simulations of three-dimensional normal grain growth it is shown that, contrary to Hillert’s assumption, the average self-similar volume change rate is a non-linear function of the relative grain size, which in the range of observed grain sizes can be approximated by a quadratic polynomial. In particular, based on an adequate modification of the effective growth law, a new analytical grain size distribution function is derived, which yields an excellent representation of the simulated grain size distribution.

Statistical analysis of the parameters and grain size distribution functions of single-phase polycrystalline materials

2020 ◽  
Vol 86 (4) ◽  
pp. 39-45
Author(s):  
S. I. Arkhangelskiy ◽  
D. M. Levin
Keyword(s):  
Grain Size ◽  
Distribution Function ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Single Phase ◽  
Distribution Functions ◽  
Grain Structure ◽  
Polycrystalline Materials ◽  
Grain Sizes ◽  
Average Grain Size

A statistical analysis of the grain size distribution is important both for developing theories of the grain growth and microstructure formation, and for describing the size dependences of various characteristics of the physical and mechanical properties of polycrystalline materials. The grain size distribution is also an important characteristic of the structure uniformity and, therefore, stability of the properties of the products during operation. Statistical Monte Carlo modeling of single-phase and equiaxed polycrystalline microstructures was carried out to determine the type of statistically valid distribution function and reliable estimates of the average grain size. Statistical parameters (mean values, variances, variation coefficient) and distribution functions of the characteristics of the grain microstructure were obtained. It is shown that the distribution function of the effective grain sizes for the studied polycrystal model is most adequately described by γ-distribution, which is recommended to be used in analysis of the experimental distribution functions of grain sizes of single-phase polycrystalline materials with equiaxed grains. The general average (mathematical expectation) of the effective grain size (projection diameter) with γ-distribution function (parameters of the distribution function are to be previously determined in analysis of the grain structure of polycrystalline materials) should be taken as a statistically valid and reliable estimate of the average grain size. The results of statistical modeling are proved by the experimental data of metallographic study of the microstructures of single-phase model and industrial materials with different degree of the grain structure heterogeneity.

On the Grain Size Distribution of MnO Doped ZnO Ceramics

2007 ◽  
Vol 336-338 ◽  
pp. 2361-2362
Author(s):  
Shu Ai Li ◽  
Da Nian Liu ◽  
Jiang Hong Gong
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Sintering Temperature ◽  
Grain Morphology ◽  
Holding Time ◽  
Grain Sizes ◽  
Different Temperatures ◽  
Doped Zno ◽  
Zno Ceramics

A series of MnO-doped ZnO with different grain sizes and grain morphologies were prepared by sintering the samples at different temperatures for different holding times. The grain size distribution for each sample was determined. It was found that, although the grain size increases and the grain morphology varies with the sintering temperature and/or the holding time, the normalized grain size distribution keeps invariable.

scholarly journals On the dynamics of farm size distribution in Finland

1975 ◽  
Vol 47 (6) ◽  
pp. 454-461
Author(s):  
Devendra Sahal
Keyword(s):  
Normal Distribution ◽  
Size Distribution ◽  
Farm Size ◽  
Time Period ◽  
Farm Structure ◽  
Log Normal ◽  
Log Normal Distribution

This study attempts to explain why farm structure in Finland is what it is. The static aspects of size distribution are summarised by means of log-normal distribution and tested with respect to data on more than 500 communes for years 1959 and 1969. As to the dynamic aspects, despite some correlation between percentage growth and size at the beginning of the time period and which is believed to be partly spurious, the observed phenomena do not seem to be incompatible with the proposed version of law of proportionate effect. The latter need not be observed at every point in time.

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