Application of Extreme Value Analysis for Two- and Three-Dimensional Determinations of the Largest Inclusion in Metal Samples

Abstract

The maximum size of single inclusion particles and clusters in an Fe–10 mass% Ni alloy deoxidized with Al or Ti/Al were examined using extreme value analysis. The results obtained from conventional two-dimensional observations of inclusions on a polished cross section of metal sample (the CS-method) were compared to those from three-dimensional investigations of inclusions on a film filter after electrolytic extraction (the EE-method). It was found that the EE-method can successfully be used as a reference method for estimation of the probable maximum size of single inclusion particles and clusters by using an extreme value distribution (EVD). The EVD results for single inclusion particles obtained from the EE-method agreed satisfactorily well with those from a conventional CS-method. However, this required identification as well as neglect of pores on an investigated cross section of a metal sample. The predicted maximum size of single inclusion particles in a 1 mm3 volume was confirmed by results from the EE-method.