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Standard Operation Procedure for measuring
average ASTM grain size of non-equiaxed grain structure

Methods

1. Lineal Intercept Procedure
2. Circular Intercept Procedures
• Hilliard Single-Circle Procedure
• Abrams Three-Circle Procedure

Procedure

Generally, for non-equiaxed structure, more information can be obtained by making separate size determinations along parallel line arrays that coincide with all the three principal directions of the specimen. Therefore, longitudinal (l), transverse (t) and plane (p) specimen sections are used. The number of intersection was counted. (An interception is a point where a test line is cut by a grain boundary.)

# Lineal Intercept Procedure

1. The average grain size is estimated by counting the number if grains intercepted by one or more straight lines sufficiently long enough to yield at least 50 intercepts.
2. It is desirable to select a combination of test line length and magnification such that a single field will yield the required number of intercepts.
3. Usually the straight test lines will lie inside the grains, precision will be reduced if the average count per test line is low. If possible, use either a longer test lines or a lower magnification.
4. Use the test lines of known lengths and count the number of intersection on three to five blindly selected and widely separated fields and then an average number of intersections is calculated for all the principal directions planes l, t and p.
5. Mean number of interceptions per unit length, NL, on the fields of longitudinal (NL(l)), transverse (NL(t)) and planar (NL(p)) planes were thus calculated. (formula shown below)

# Hilliard Single-circle Procedure

1. A single circle was used as test line. This will eliminate the problem of being bias when counting of the grain boundaries as in the Lineal Intercept method.
2. The test circle diameter should never be smaller than the largest observed grain.
3. Do not use a small test circle as it is rather inefficient as a great many fields must be evaluated to obtain a high degree of precision.
4. A small reference mark is placed at the top of the circle to indicate the place to start and stop the count.
5. Use the test lines of known circumferences (length) and count the number of intersection on three to five blindly selected and widely separated fields until sufficient counts are obtained to yield the required precision.
6. Repeat the previous step for all the principal directions planes l, t and p.
7. The mean number of interceptions per unit length, NL, on the fields of longitudinal (NL(l)), transverse (NL(t)) and planar (NL(p)) planes were thus calculated. (formula shown below)
8. Recommended 35 counts per circle with the test circle applied blindly over as large a specimen area as feasible until the desired total number of counts is obtained.

# Abrams Three-Circle Procedure

1. From experiment finding that a total of 500 counts per specimen normally yields an acceptable precision.
2. Consists of three concentric and equally spaced circles having a total of 500mm
3. Use the circular test lines of known circumferences (length) and count the number of intersection on at least five blindly selected and widely separated field.
4. Separately record the count of the intersections per pattern for each of the tests.
5. Repeat the previous step for all the principal directions planes l, t and p.
6. Mean number of interceptions per unit length, NL, on the fields of longitudinal (NL(l)), transverse (NL(t)) and planar (NL(p)) planes were thus calculated. (formula shown below.

Calculation of results

• Use the following equation to find NL(n) for each principal direction plane

NL(n) =   Ni / (L/M)
NL = mean number of interceptions per unit length,
Ni = the number of interceptions counted on the field,
L = the length of the test line(s) used,
n = the principal direction plane, and
M = the magnification.

• Take the equation below to find the average NL,:

NL = (NL(l) . NL(t) . NL(p) ) 1/3

• Calculate the mean lineal intercept Lm, for each field using the following equation:

Lm = 1/ NL

• Determine ASTM grain size number using the following equatio

G = (-6.6457 log10 Lm) – 3.298

References

1. ASTM E 112 – Standard test methods for determining average grain size, p229-251 (NTU)
2. Grain size measurement, p85-  (NUS TN689.2 Pra)
3. ASTM E 930-92 – Standard test methods for determining the largest grain observed in a metallographic section (ALA grain size), p666-670 (NTU)
4. ASTM E 1181-87 – Standard test methods for characterizing duplex grain sizes, p725-738 (NTU)
5. ASTM E 1382-97 – Standard test methods for determining average grain size using semiautomatic and automatic image analysis, p855-878 (NTU)
6. BS DD 44:1975 – Methods for the determination of grain size of non-ferrous alloys, p3-10 (NTU, BS)
7. JIS H 0501 – Methods for estimating average grain size of wrought copper and copper alloys, p261-165 (NTU)
8. Metal Handbook (Metallography) – Grain size & particle distribution, p129-134

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