Journal of Materials Science

, Volume 30, Issue 14, pp 3668–3673 | Cite as

Fractal nature and quantitative evaluation of microstructures in metallic materials

  • M. Tanaka


The fractal nature of microstructures was investigated using metallic materials containing second-phase particles, grain-boundary reaction (GBR) nodules or creep voids. The area fraction of the precipitates or the creep voids in the specimens was correlated with the scale of the analysis. The microstructures of these specimens exhibited a fractal nature between the lower and the upper critical scales, and could be regarded as the aggregate of the unit pattern with the size of the upper critical scale. The fractal dimension of a given microstructure was generally larger in specimens containing a larger area fraction of the second phase. The lower critical scale was close to the average size of second-phase particles or GBR nodules or the size of a large creep void. The upper critical scale, above which the area fraction of the precipitates or the creep voids did not show a scale dependence, was generally much larger than the average size and the average spacing of the precipitates, but it was almost the same as or a fair degree smaller than the grain size in specimens containing the second-phase particles or the GBR nodules. In the creep-ruptured specimens, the upper critical scale was much larger than the initial grain size and the grain size at rupture. The true area fraction of the second phase or the creep voids corresponding to the upper critical scale was also obtained.


Grain Size Nodule Microstructure Fractal Dimension Material Processing 
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Copyright information

© Chapman & Hall 1995

Authors and Affiliations

  • M. Tanaka
    • 1
  1. 1.Department of Mechanical EngineeringMining College, Akita UniversityAkitaJapan

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