Abstract
Table 1: Jeffries Planimetric Analysis on Three Principal Planes. 
If a specimen has been cold worked, or it did not recrystallize after hot working, the grains will not be equiaxed and extra care must be taken when assessing the specimen’s grain size. Always test a longitudinally oriented plane first to determine if the grains are, or are not, equiaxed. A lowcarbon sheet steel was tested in the asreceived condition (reportedly annealed), and after cold reductions in thickness of 12, 30 and 70%. Above 70% reduction, it can be quite difficult to reveal the ferrite grain boundaries well enough to get a precise measurement. Measurements were made on the three principal planes using the Jeffries planimetric method, the Abrams threecircle intercept method and the intercept method using directed parallel test lines.
Experimental Program
Grain size on each plane was evaluated using three methods defined in ASTM E112: Jeffries planimetric method, Abrams threecircle intercept method, and directed test lines (this method is defined in section 16 of E11210, “Specimens with Nonequiaxed Grain Shapes,” as illustrated in their Figure 7, and in E1382, Figure A1.3). Figure 1 shows examples of the microstructures.
Table 2: Abrams ThreeCircle Intercept Analysis on Three Principal Planes.

Results for grain size measured using the Jeffries planimetric method are given in Table 1. Note how the deformation affects the grain size measurements. While it is reasonably constant on the longitudinal plane, the grain size measurements get finer on the transverse plane and coarser on the planar surface as deformation increases. The average of the three planes is reasonably constant over the deformation range. The average for the N_{A} values on the three planes is calculated from the cube root of the product of the three N_{A} values. An arithmetic average of the N_{A} values could also be calculated and used to determine G.
Table 2 shows the results using the Abrams threecircle intercept method. Again, the grain size on the transverse plane becomes finer with increasing deformation while on the planar surface, the grain size becomes coarser with increasing deformation. But, the grain size on the longitudinal plane also became finer with increasing deformation. For the overall results, averaging the results from each plane, the grain size was constant for the annealed condition and reductions of 12 and 30% but finer for the 70% reduction specimen.
Table 3: Oriented Test Line Intercept Analysis on Three Principal Planes.

Table 3 shows the grain size measurements using the directed linear intercept method (illustrated in ASTM E 112) with test lines parallel to principle directions in each of the three principle test planes. The grain size can be calculated from the directed test lines of Figure 1 in two ways, as shown in Tables 3 and 5. In developing Table 3, the three principle directions were used, one on each plane: 0° on the longitudinal direction and 90° on the transverse and planar surfaces. But, all six directions can be used, as discussed below.
Table 4 lists the grain size measurements using all six directed test lines. The P_{L} values for the two measurements on each plane were computed as the square root of the product of the two values. Then, the three average values for each plane were averaged using the cube root of the product of the three values, as listed in Table 4. These four G values were the most consistent as a function of the specimen condition and test method used.
Conclusions
The experimental program verified that the longitudinal plane is best to use initially to determine if the grains in a specimen with unknown history are equiaxed or elongated. If they are equiaxed, measurements on any randomly chosen plane should reveal the same grain size within statistical precision. But, if they are not equiaxed, a carefully designed test plane program is required to obtain the true grain size in three dimensions. The test results showed that, using only the longitudinal plane, the Jeffries planimetric method yielded excellent results for all deformations while the Abrams threecircle intercept method gave consistent results for the annealed specimen and for the 12% and 30% reduction specimens, but gave a finer grain size rating for the specimen deformed 70%.
When the three principal directions (0° on longitudinal and 90° on the transverse and planar surfaces) were used for intercept counting, the grain size became coarser on the longitudinal plane with increasing cold reduction, became finer on the transverse plane with increasing cold reduction and was approximately constant for the planar specimens for the annealed, 12% and 70% reduction specimens, but slightly coarser for the 30% reduction specimen (possibly due to a counting error or from poorly etched boundaries). The overall average grain sizes using the intercepts on the three planes were very similar to those made using the Jeffries planimetric method for all four specimens. The threecircle intercept method gave average grain size numbers that were higher than by the planimetric method or when using either the three or six directed test lines for intercept counts. When the six principal test line directions were used to compute the average grain size for each specimen, the results were the most consistent of all methods used. Average grain size for a specimen should be calculated using the cube root of the product of the three measurements (or, the square root of the product of the two measurements per plane), rather than the simpler average of the sum of the measurements. The overall measured grain sizes for all four specimens were: 9.89 (planimetric method), 10.39 (threecircle intercept method), 9.92 (intercepts using three directed test lines) and 9.94 (intercepts using all six directed test lines).
Table 4: Grain Size Using All Six Oriented Test Lines. 
Figure 1: Ferrite grain structure (and cementite) in sheet steel specimens prepared on longitudinal (left column), transverse (center column) and planar surfaces (right column), in the asreceived condition (top row), and after 12% (second row), 30% (third row) and 70% (bottom row) cold reductions. The micrographs were taken at 500X (magnification bars are 20 μm long) after etching ~23 s with 2% nital, then an ~3 s immersion in Marshall’s reagent, followed by a 20 s immersion in 2% nital.
George Vander Voort has a background in physical, process and mechanical metallurgy and has been performing metallographic studies for 45 years. He is a longtime member of ASTM Committee E4 on metallography and has published extensively in metallography and failure analysis. He regularly teaches MEI courses for ASM International and is now doing webinars. He is a consultant for Struers Inc. and will be teaching courses soon for them. He can be reached at 18476237648, EMAIL: [email protected] and through his web site: www.georgevandervoort.com
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