Efficient measurement of microstructural surface area using trisector

Abstract

It is shown that just three appropriately chosen metallographic sections can yield an efficient and reliable estimate of the total area of the internal microstructural boundaries per unit volume Sv in a microstructure having an arbitrary and unknown anisotropy and geometry. The following sampling scheme is required. (1) Choose a reference direction (called “vertical axis”) such that most of the surface elements of interest are not parallel to the selected reference direction (vertical axis). (2) Observe the microstructure on three metallographic sections that are mutually at an angle of 120 deg and contain the vertical axis. (3) Superimpose a set ofcycloid shape test lines on these metallographic sections (called vertical sections) such that the cycloid minor axis is parallel to the vertical axis, and estimate the average number of intersections between these test lines and the microstructural boundaries per unit test line length, [PL c]3. The surface area per unit volume Sv is given by Sv = [PL c]3 To emphasize the preceding sampling requirements, the composite test probe is called “trisector. ” It is also shown that independent random sections are not useful for estimation of Sv of anisotropic microstructural surfaces, in general. Further, two perpendicular vertical sections are also not generally useful for a reliable estimation of Sv in anisotropic microstructures.