ESTIMATION OF INTEGRAL MIXED SURFACE CURVATURE FROM VERTICAL METALLOGRAPHIC SECTIONS

The integral mixed curvature Q(v) of a population of surfaces in a mic rostructure is defined as follows. Q(v) = integral integral[3(K-1)(2) + 2K(1)K(2) + 3(K-2)(2)] ds/4. The integration is over all surface ele ments of int-rest in; unit volume of microstructure. K-1 and K? are th e principal normal curvatures of a surface element of area ds. A new s tereological relationship is derived for the estimation of integral mi xed curvature, Q(v), of population of smooth surfaces from the measure ments on the vertical metallographic sections. On the vertical section s, sample the boundary elements by using vertical straight test lines, and measure curvature k of only those boundary elements that intersec t these lest lines. From these data. compute the sum of the square of the curvatures, and divide it by the total test line length. Let [(k(2 )) over bar](L) be the average value of this parameter in the vertical sections. It is shown that, Q(v) = 2[(k(2)) over bar](L). The stereol ogical relationship is geometrically general and it is applicable to a ny arbitrary collection of smooth surfaces. (C) 1998 Acta Metallurgica Inc.