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.

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.

Variable Elastic-Plastic Properties of the Grain Boundaries and Their Effect on the Macroscopic Flow Stress of Nano-Crystalline Metals

2009 ◽  
Vol 1224 ◽  
Author(s):  
Malgorzata Lewandowska ◽  
Romuald Dobosz ◽  
Krzysztof J Kurzydlowski
Keyword(s):  
Grain Size ◽  
Flow Stress ◽  
Grain Boundaries ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Distribution Functions ◽  
Boundary Misorientation ◽  
Plastic Properties ◽  
Nano Crystalline ◽  
Average Grain Size

AbstractThe paper reports new experimental results describing properties and microstructure of nanocrystalline metals. Nano- and sub-micron aluminium has been produced by hydrostatic extrusion at ambient tempearture. The structures have been quantified in terms of size of grains and misorientation of the grain boundaries. Different average size of grains, variable normalized width of grain size distribution and changing grain boundary misorientation distribution functions have been revealed depending on processing parameters. The results of the tensile tests showed that the average grain size, grain size distribution and the distribution function of misorientation angles influence the flow stress of obtained nano-metals. In order to explain the observed difference in the properties of nano- and micro-sized aluminium alloys, a Finite Element Method models have been developed, which assumes that both grain boundaries and grain interiors may accommodated elastic and non-linear plastic deformation. These models assumed true geometry of grains (which differed in size and shape). Also, variable mechanical properties of grain boundaries have been taken into account (elastic modulus, yield strength and work hardening rate). The results of modelling explain in a semi-quantitative way macroscopic deformation of nano-crystalline aggregates. In particular, they illustrate the importance of the interplay between properties of grain boundaries and grain interiors in elastic and plastic regime.

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.

scholarly journals EXPERIMENTAL EVALUATION OF STEREOLOGICAL METHODS FOR DETERMINING 3D GRAIN SIZE AND TOPOLOGICAL DISTRIBUTIONS

2011 ◽  
Vol 19 (2) ◽  
pp. 91 ◽  
Author(s):  
Guoquan Liu ◽  
Haibo Yu
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Experimental Evaluation ◽  
Single Phase ◽  
Experimental Methods ◽  
Grain Structure ◽  
Serial Sectioning ◽  
Topological Parameters ◽  
Selection Of

The conventional serial sectioning analysis and a set of modern stereological methods, including disector, selector, point-sampled intercepts, point-sampled area, and their combinations, have been used in this paper to measure the grain size, grain size distribution, topological parameters and their distributions in a spacefilling single-phase grain structure of steel. The results from different methods are compared and used to evaluate the methods quantitatively, based on which some suggestions will be given for selection of experimental methods in materials stereology research.

Ultrasonic Discrimination of Samples With Differently-Distributed Grain Sizes and Equal Average Grain Size

1994 ◽  
Vol 362 ◽  
Author(s):  
Denise Nicoletti ◽  
Aran Anderson
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Theoretical Development ◽  
Volume Distribution ◽  
Size Estimation ◽  
Grain Sizes ◽  
Average Grain Size ◽  
Distribution Parameters ◽  
Ultrasonic Techniques

AbstractMaterials can have distributions of grain sizes. These distributions can have effects on the material's mechanical properties that are more complicated than an average grain-size dependence. The omission of distribution effects on properties is understandable in view of the great amount of labor required in the experimental measurement of grain volume distribution, together with the predominantly two-dimensional nature of micrography-based grain-size estimation. Ultrasonic techniques have been used to nondestructively measure the grain size of materials on a scale of microns. We suggest using ultrasonic attenuation as an alternative to micrography for three reasons. One advantage is that the ultrasonic dependence on size is a true, three-dimensional dependence. Secondly, through careful selection of wavelength, various grain-size distribution parameters can be extracted. The third justification is that ultrasonic techniques are quick and nondestructive. Previous theoretical development will be reviewed, and the experimental verification will be presented. Through numerical modeling we show the advantages of using ultrasonic techniques that are sensitive to grain-size distribution parameters. We demonstrate that samples with equal average grain size but different grain-size distributions have significantly different attenuation wavelength dependencies.

Recrystallization of Oxygen Contaminated Al Films

1986 ◽  
Vol 71 ◽  
Author(s):  
G.J. Van Der Kolk ◽  
M.J. Verkerk
Keyword(s):  
Grain Size ◽  
Silicon Nitride ◽  
Substrate Temperature ◽  
Oxygen Partial Pressure ◽  
Partial Pressure ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Relative Increase ◽  
Partial Pressures ◽  
Average Grain Size

AbstractAl was evaporated at oxygen partial pressures, PO2, varying between 10−7 and 10−4 Pa on substrates of silicon nitride. The substrate temperature was varied between 20 °C and 250°C. The films were annealed at temperatures up to 500°C.For Al films deposited at 20°C, it was found that the average grain size decreases with increasing oxygen partial pressure. After annealing recrystallization was observed. The relative increase of grain size was less for higher values of pO2. Annealing gave rise to a broad grain size distribution.For Al films deposited at 250°C, the presence of oxygen caused the growth of rough inhomogeneous films. This inhomogeneous structure remained during annealing.

Macro and Microstructural Effects of the Application of an Induced Axial Magnetic Field During the Deposition of Aluminum Weld Beads

2009 ◽  
Vol 1242 ◽  
Author(s):  
M. A. García ◽  
V. H. López M. ◽  
R. García H. ◽  
F. F. Curiel L. ◽  
R. R. Ambríz R.
Keyword(s):  
Magnetic Field ◽  
Grain Size ◽  
Magnetic Fields ◽  
Weld Metal ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Axial Magnetic Field ◽  
Grain Structure ◽  
Bead Geometry ◽  
External Power Source

ABSTRACTIn this work, aluminum weld beads were deposited on aluminum plates of commercial purity (12.7 mm thick), using an ER-5356 filler wire. The aim of the experiments was to assess the effects that yield the induction of an axial magnetic field (AMF) during the application of the weld beads using the direct current gas metal arc welding process (DC-GMAW). An external power source was use to induce magnetic fields between 0 to 28 mT. The effects of the magnetic fields were assessed in terms of the macrostructural features of the deposits, morphology of the grain structure, grain size and grain size distribution in the weld metal. Macrostructural characteristics of the weld beads revealed that increasing the intensity of the magnetic induction to produce a magnetic field above 14 mT, leads to a significant loss of feeding material and there is a tendency of the deposits to increase their width and reduce penetration. Perturbation of the weld pool induced by the application of the AMF noticeably modified the grain structure in the weld metal. In particular, for the intensities of 5 and 14 mT, columnar growth was essentially non-existent. Grain size distribution plots showed, generally speaking, that the use of magnetic fields is an efficient method to produce homogeneous grain structures within the weld metal. Finite element analysis was used to explain the weld bead geometry with the intensity of the magnetic field.

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