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–Liuʹs model (Metall. Trans. 16A (1985) 2007). It can be written as F=2.0+(〈F〉-2) uT, where uT 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+bue+cue2 when the normalized sphere-equivalent diameter (ue) was used. Limitations of DeHoff–Liuʹs model and possible correlation between the two kinds of grain size parameters were also discussed in this paper.