a. The ASTM defines grain size as the number of grains per square inch at (x 100), and this is given as:

n = 2Gn -1……………………………………………………. 1

Where n = number of grain per square inch at (x 100), and Gn = grain size number given as:

The International Organization of Standards (IOS) defines grain size as the number of grains per square millimeter at (x 1), and is given as

m = 8(2Gm )……………………………………………………………………………. 3

Where m = number of grains per square millimeter at (x 1) and

Gm = grain size number, given as:

But Gn and Gm are related by the equation [2, 4]

Gn = Gm — 0.045 ……………………………………………………………………………….. 5

The Jeffries method provides the value of N_ =number of grains per unit area which is an

A

equivalent of n or m. From this, the grain area, A and grain diameter, d can be obtained.

The Jeffries planetric method is generally employed by drawing a circle 79.8mm in diameter (i. e 5000mm2) on a photomicrograph or on a transparency placed on it. The magnification is adjusted to provide at least 50 grains within the test area. The number of grains falling within this area is counted and designated n, the number of grain intersecting the test circle is also counted and designated n2. The total of (n + n2)/2 is multiplied by the Jeffries factor f for the magnification with 79.8mm diameter circle to obtain an estimate of the number of grains per square millimeter.

This is given [4, 6] as:

N_ = f (П1 + П2 )/2………………………………………………………… 6

This is the value of N_ for each equiaxed grain. For non-equiaxed grains, grain count is done in

A

three mutually perpendicular planes (longitudinal N_ , transverse N_ and normal

A1 At

N_ directions). Then the number of grains mm3 is given as

A n

N_ =[ N_ + N_ + N_ ]/3…………………………………………………………. 7

A V A1 At An J

Therefore the value of f for any magnification is found using the equation

M2

5000………………………………………………..

The average grain area A is obtained from

A = — (in sq^m)

.9 10

N

_ 106 A = (in sq m) Na

Or

While the mean grain diameter d is obtained from

_ 1 d = A2

11

The ASTM grain size number is obtained from the formula [2]:

Gn = (3.322 log Na) — 2.95 …………………………………………………………….. 12

While the IOS grain size number can be obtained from Gm = Gn + 0.045 = (3.322log Na) — 2.95 + 0.045

= (3.322log Na) — 2.905 ……………………………………………………………….. 13

To obtain good results, the grain must be marked off, as they are counted to prevent miscounts. G is also usually rounded off to the nearest one-half unit. Also, the number of grains per unit area Na has been shown to be directly related to Lv the total length of grain edges per unit volume by [2, 4]

Lv = 4Na…………………………………………………………………………………………………. 14