Features of the linear intercept method used for measuring the grain size in WC–Co hardmetals

Abstract

Several WC–Co hardmetals with varying WC grain size distributions were analyzed to measure the mean grain size using the linear intercept (L) and planimetric (dJ ) methods. Additional measurements included the equivalent diameter (deq ) and mean chords (dch ) for all grains, and separately, for grains intersected by the line. The findings show that mean sizes and size distributions of grains intersected by the line differ from those of all grains. This discrepancy is attributed to the linear intercept method’s rule for drawing secants, leading to “shadowing” where finer grains are obscured by coarser ones. The relationship between the mean sizes of all grains and those intersected by the line can be quantified using the “shadow” function S, which depends on the coefficient of variation (cv ) of the WC grain size distribution, as d a/d l = 1 – S. Experimental data illustrate that the mean equivalent diameter deq correlates with the linear intercept method L through equation deq /L = 1.4(1 – S), and the relationship between the mean grain size dJ and L are described by the equation dJ /L = 1.4(1 – S)\(\sqrt {1 + c_{\rm{v}}^2} \). The analysis of grain distributions by the equivalent diameters and mean chords showed that they equally describe the alloy grain size distribution. The length distribution of random chords obtained using the linear intercept method differs from the alloy grain size distribution due to the shadow effect, and also because the length distribution of random chords is always broader than the mean grain chord distribution. It is demonstrated that the length distribution of random chords is a convolution of the grain size distribution function and a function related to the grain shape.