We continue our multi-part discussion of quantitative metallography. We hope this information will be usable by many in their metallurgical investigations.
the most common measurements – determination of the amount of phases present – can
be done using three different methods. Areal analysis, developed by Delesse in
1848, says that the area percent of a phase on a 2-D plane is equal to its
volumetric percent – AA= VV. However, measuring
the area of a second phase is very tedious unless it is quite coarse. Lineal
analysis, developed by Rosiwal in 1898, says that the lineal fraction of test
lines in a phase on the 2-D plane is equal to its volumetric percent –
LL= VV. This is relatively easy to determine but still rather
around 1930, several people in different fields and countries showed that the
percentage of points on a test grid lying in the phase of interest was equal to
the volumetric percentage –
PP= VV. Of the three
methods, this is the most efficient technique. It gives the best
accuracy for the least effort when done manually. The point-counting technique
is described fully in ASTM E 562 (also ISO 9042). Image analyzers use
essentially the same procedure – the amount of a phase (usually called
the area fraction even if it really is a point fraction) is determined by the
number of picture elements, or “pixels,” in the phase of interest divided by the
total number of pixels (i.e. PP, usually expressed as a percentage).
size is perhaps the most commonly performed microstructural measurement,
although chart ratings are more commonly done than actual measurements (this is
changing). A recent ASTM inter-laboratory “round robin” showed that chart
ratings of grain size are biased; that is the ASTM grain-size number is 0.5-1 unit too low (see Appendix XI of E 112-10). No bias existed when planimetric
measurements were compared to intercept measurements by the same rater.
grain size number, G, is defined as: n = 2G-1
is the number of grains per square inch at 100X. To convert n to NA(the number of grains per square mm at IX), multiply n by 15.5. The ASTM grain-size
charts show graded series of grain structures of different types.
size can be measured by the Planimetric Method (developed by Jeffries in 1915
based upon earlier work by Sauveur) or by the Intercept Method (developed by
Heyn in 1904). In the Planimetric Method, a count is made of the number of
grains completely within a circle of known area and the number of grains
intersected by the circle to obtain NA. Then, NAis
related to G. This method is slow when done manually because the grains must be
marked when counted to obtain an accurate count.
Intercept Method, either straight lines, curved lines or circles are placed
over the structure and a count is made of either the number of grain-boundary
intersections (P) or the number of grains intercepted (N) by the line. P or N
is divided by the true line length, L, to determine PLor NL,
the number of intersections or interceptions per unit length (for a single-phased
structure). The reciprocal of PLor NLgives the mean
lineal intercept length, L, which is a measure of grain size that can be
converted to a G value. The Intercept Method is more efficient than the
Planimetric Method, yielding acceptable measurement precision (<10% relative
accuracy) in much less time. ASTM E 112 contains a complete description of
Introduction to Quantitative Metallography (part 3)
George Vander Voort is a consultant for Struers, Latrobe Steel and Scot Forge. He is also president of Vander Voort Consulting. Vander Voort has more than 40 years of industry experience and has authored more than 280 publications. A member of ASM International since 1966, he has won 34 awards for his work in metallography.