Statistical characterisation of inclusions in metals: From 2D to 3D

Inclusions play a significant role in certain failure processes and material specifications. Therefore, characterising the largest inclusions in a finite volume of metal from observations on polished surfaces is a key problem facing industry and research. Current efforts to predict the largest inclusions expected to occur in a volume based on light microscopy investigations of polished surfaces are dominated by the simple heuristic model developed by Murakami and his collaborators. In the present paper, an alternative and comprehensive statistical model for inclusion characterisation based on block maximum sampling from polished surfaces is presented. The relation between the observations (two-dimensional) and the actual inclusions (three-dimensional) is transparently modelled. Furthermore, similarities and differences with an existing popular model are explored. The presented model offers deeper insight with the convenience of two-dimensional inspections.