From Simple Shapes to Microstructural Grain Structure: An Inquiry

Based on serial sectioning data, materials microstructure can be reconstructed to digitally represent each grain in three dimensions. This paper attempts to calculate the average shape of the grains through Principal Component Analysis(PCA) , with a theoretical introduction to how this method can be generalized into calculating an average shape of the microstructure. Also investigated is the relation between the commonly assumed average shapes, sphere and ellipsoid, and the average shapes calculated, which for the current case proves to be very similar. Finally, the knowledge acquired from the first two steps is applied to creating new grain shapes which possess the characteristic of the microstructure.