A discussion of the spacing of inclusions in the volume and of the spacing of inclusion nucleated voids on fracture surfaces of steels

Abstract

When fracture is by micro-void coalescence and the fine-scale microstructure of a steel is held constant the toughness of the steel is determined by the characteristics of the inclusions in the steel. Three inclusion characteristics which influence toughness are the inclusion volume fraction, the inclusion spacing and the resistance of the inclusions to void nucleation. A measure of the inclusion spacing which is often used in assessing the effect of inclusion spacing on toughness is the average nearest-neighbor-distance between the inclusions in the volume. One can also determine an inclusion spacing by determining the average spacing of inclusion nucleated voids on the fracture surface. The first objective of this work was to determine the spacing of the inclusion nucleated voids on the fracture surface and compare it to the average nearest-neighbor-distance between inclusions in the volume. The spacing of such voids on the fracture surface is about 2.5 times the average nearest-neighbor-distance between inclusions in the volume. The fraction of the fracture surface covered by voids which actually contain inclusions is very small, about 0.03. That this number is so small suggests the possibility that many inclusion particles are simply not retained on the fracture surface. To examine this possibility the sizes of all voids containing inclusions were measured and the size of the smallest void which contained an inclusion was determined. It was then assumed that all voids which were of this size and larger and which did not contain an inclusion were actually nucleated at an inclusion. The number of such voids was then determined. Thus, the number of voids which were nucleated by inclusions was taken to be this quantity plus the number of voids actually containing inclusions. Based on this assumption one can show that the fraction of the inclusions actually retained on the fracture surface is very small, that the spacing of such voids on the fracture surface is very close to the average nearest neighbor spacing of inclusions in the volume and that the fraction of the fracture surface covered by such voids ranges from 0.36 to 0.64 for the four steels investigated, which is considerably larger than the fraction of the fracture surface covered by inclusions which actually contain inclusions, about 0.03 for the four steels examined.