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Grain Size Distributions in Normal Grain Growth

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Published/Copyright: May 5, 2013
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Practical Metallography
From the journal Practical Metallography Volume 47 Issue 11

Abstract

An analytical distribution function characterising the grain sizes of polycrystalline microstructures is presented. Contrary to standard mathematical probability functions that are still often used for description of experimentally obtained size distributions, this one is based on a statistical mean-field theory of grain growth and is fully consistent with the fundamental physical conditions of total-volume conservation and the existence of a finite average grain volume. It is found that this distribution function describes the grain size distribution obtained by Monte Carlo Potts model simulations better than standard mathematical distributions. Additionally, two-dimensional plane sections from the simulated three-dimensional grain structures are considered and compared with experimental data, and the analytic size distribution function is also compared with an experimental grain size distribution for pure iron obtained by serial sectioning.

Kurzfassung

Vorgestellt wird eine analytische Verteilungsfunktion, die die Korngrößen von polykristallinen Mikrostrukturen beschreibt. Im Gegensatz zu mathematischen Standard-Wahrscheinlichkeitsfunktionen, die noch immer häufig zur Beschreibung experimentell erhaltener Größenverteilungen eingesetzt werden, basiert diese Funktion auf einer statistischen Theorie des mittleren Feldes (Mean-Field-Theorie) für Kornwachstum und steht vollkommen in Einklang mit den grundlegenden physikalischen Bedingungen der Erhaltung des Gesamtvolumens und der Existenz eines endlichen mittleren Kornvolumens. Es wurde herausgefunden, dass diese Verteilungsfunktion die durch die Monte-Carlo-Potts-Modellsimulationen erhaltene Korngrößenverteilung besser beschreibt als mathematische Standardverteilungen. Ferner wurden zweidimensionale ebene Schnitte der simulierten dreidimensionalen Kornstrukturen betrachtet und mit experimentellen Daten verglichen. Des Weiteren wird die analytische Größenverteilungsfunktion mit einer experimentellen Größenverteilung für reines Eisen verglichen, die durch Serienschnitte erhalten wurde.

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Peter Streitenberger studied physics and received his doctoral degrees in 1980 and 1989. He spent research visits at foreign universities and is lecturing physics at Magdeburg University. His research activities focus on microstructural instabilities due to growth and coarsening, stress-driven diffusion at lattice defects and decohesion.

Dana Zöllner studied lectureship for grammar schools for mathematics, physics and computer science. She received her doctorate in physics in 2006 and works now as a research assistant at the Otto-von-Guericke-university Magdeburg focussing on grain growth in nanocrystalline metals.

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Received: 2008-4-2
Accepted: 2010-3-19
Published Online: 2013-05-05
Published in Print: 2010-11-01

© 2010, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents/Inhalt
  2. Inhalt / Contents
  3. Editorial
  4. Editorial
  5. Technical Contributions/Fachbeiträge
  6. Grain Size Distributions in Normal Grain Growth
  7. EBSD-Gefügeuntersuchungen an Aluminiummatrix-Verbundwerkstoffen
  8. Influence of the Metallic Die Graphite Layer Thickness in the Microstructure of Aluminium Bronze Alloy
https://doi.org/10.3139/147.110100

Articles in the same Issue

  1. Contents/Inhalt
  2. Inhalt / Contents
  3. Editorial
  4. Editorial
  5. Technical Contributions/Fachbeiträge
  6. Grain Size Distributions in Normal Grain Growth
  7. EBSD-Gefügeuntersuchungen an Aluminiummatrix-Verbundwerkstoffen
  8. Influence of the Metallic Die Graphite Layer Thickness in the Microstructure of Aluminium Bronze Alloy
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