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.

Normal Grain Growth in Three Dimensions: Monte Carlo Potts Model Simulation and Mean-Field Theory

2007 ◽  
Vol 550 ◽  
pp. 589-594 ◽  
Author(s):  
Dana Zöllner ◽  
Peter Streitenberger
Keyword(s):  
Field Theory ◽  
Grain Size ◽  
Monte Carlo ◽  
Distribution Function ◽  
Grain Growth ◽  
Mean Field Theory ◽  
Mean Field ◽  
Size Distribution Function ◽  
Three Dimensions ◽  
Self Similar

A modified Monte Carlo Potts model algorithm for single-phase normal grain growth in three dimensions in presented, which enables an extensive statistical analysis of the growth kinetics and topological properties of the microstructure within the quasi-stationary self-similar coarsening regime. From the mean-field theory an analytical grain size distribution function is derived, which is based on a quadratic approximation of the average self-similar volumetric rate of change as a function of the relative grain size as it has been determined from the simulation. The analytical size distribution function is found to be in excellent agreement with the simulation results.

scholarly journals Three dimensional grain size distribution during grain growth in aluminum.

1990 ◽  
Vol 40 (8) ◽  
pp. 612-618 ◽  
Author(s):  
Yoshimasa TAKAYAMA ◽  
Tatsumi TOZAWA ◽  
Hajime KATO ◽  
Hiroshi SHIRAI
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Growth ◽  
Grain Size Distribution ◽  
Three Dimensional
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