Statistics of extremes analysis of nonmetallic inclusions based on 3D inspection

It is well known that the scatter of fatigue strength of high strength steels is caused by nonmetallic inclusions. The lower bound of the scatter of fatigue strength can be predicted by considering the maximum size of nonmetallic inclusions. Thus, it is of practical importance to estimate the maximum size of nonmetallic inclusions by appropriate inclusion rating methods. Most rational and convenient method to predict the maximum size of inclusions is the one based on the statistics of extremes. Therefore, recently the inclusion rating based on the statistics of extremes has been used by many industries, though the rating methods are mostly two-dimensional (2D) optical methods. It is known that the accuracy of the 2D method is lower than the exact 3D method. In addition, when multiple type inclusions having different chemical composition are contained in a material, the statistics of extremes distribution does not necessarily become a single straight line but become a bilinear line. The objectives of the present study are (1) to clarify the validity of the 2D method and (2) to establish the method to predict the maximum inclusion size when the statistics extremes distribution becomes bilinear. The results obtained show that the 2D method is basically correct as predicted by the computer simulation. When a bilinear distribution is obtained, it is necessary to determine the minimum inspection area S_crit for predicting the maximum size of the larger type inclusions, which become the fatigue fracture origins of components.