Three-dimensional grain topology-size relationships in a real metallic polycrystal compared with theoretical models

Grain topology-size relationships are of great significance for a better understanding of the polycrystalline microstructures and grain growth processes. However, experimental observations of the three-dimensional grain topology in real materials are extremely rare. In this paper, the topology and the size of 1215 three-dimensional grains in a real steel sample were quantitatively analyzed with the aid of serial sectioning technique. The results showed that a linear quantitative relationship exists between the number of the faces (F) and the mean tangent diameter of individual grains as theoretically predicted by DeHoff-Liu's model (Metall. Trans. 16A (1985) 2007). It can be written as F = 2.0 + (<F>-2) u(T), where u(T) is the normalized mean tangent diameter, <F> is the mean value of F averaged over all the grains. However, the experimental relationship became F = a + bu(e) + cu(e)(2) when the normalized sphere-equivalent diameter (u(e)) was used. Limitations of DeHoff-Liu's model and possible correlation between the two kinds of grain size parameters were also discussed in this paper. (C) 2002 Elsevier Science B.V. All rights reserved.