Experimental investigation on statistics of extremes for three-dimensional distribution of non-metallic inclusions

Abstract

A wide range of studies have shown that the lower bound of fatigue properties of high strength steels is determined by the maximum size of non-metallic inclusions that are present in a component. The maximum size of inclusions in a given component or material volume can be reasonably estimated using the statistics of extremes. However, as long as the estimation is based on microscope inspections of two-dimensional (2D) surfaces, there will be errors and uncertainties in estimating the maximum particle in a three-dimensional (3D) volume. In addition it has been recently found that in some steels the distribution of extreme defects is composed of a mixture of different particle types. The scope of this paper is to clarify the validity of 2D inspections on the basis of 3D distribution of inclusions in a modern super clean steel. The 3D distribution was obtained with a combination of inclusions detected with a repeated slicing procedure and of particles at fatigue fracture origin. The 3D distribution of inclusions is composed of a mixture of two types of particles having similar chemical compositions and different 3D morphological structures: one with a large population and another with few rare particles. The 3D large population can be accurately estimated from maximum inclusions on small polished sections, while in order to estimate the characteristic size of inclusions at fatigue fracture origin by 2D inspections it is necessary to adopt a minimum inspection area Scrit. In the case of the material examined in this study (SCM435 steel) this minimum inspection area is ~ 10 000 mm2.