How do you calculate grain number?

You calculate grain number (ASTM grain size number) primarily using the formula N = 2^(G-1), where 'N' represents the number of grains per square inch at 100X magnification, and 'G' is the ASTM grain size number.

Understanding Grain Size Number

The ASTM grain size number (G) is a measure used to quantify the average grain size in a polycrystalline material. A higher grain size number indicates a finer grain structure, which generally correlates with higher strength and hardness.

Steps to Calculate Grain Number (G)

Here's how you determine the ASTM grain size number:

1. Prepare the Sample: Polish and etch the material to reveal the grain boundaries under a microscope.

2. Image Acquisition: Capture a representative micrograph of the material at a magnification of 100X (standard magnification). If a different magnification is used, you will need to adjust your calculations accordingly.

3. Grain Counting (N): Determine the number of grains per square inch (N) on the micrograph at 100X magnification. There are several methods for this:

   • Jeffries Planimeter Method: Overlay a circle of known area on the micrograph and count the number of grains completely within the circle, plus half the number of grains intersected by the circle. Convert this count to grains per square inch at 100X.

   • Heyn Intercept Method: Draw several lines of known length randomly across the micrograph. Count the number of grain boundaries intersected by these lines. Divide the total line length by the number of intersections to get the average grain diameter. This can then be related to the ASTM grain size number.

   • Comparison Method: Compare the micrograph to a series of standard charts that depict known grain sizes at 100X magnification. Choose the chart that most closely matches the grain structure of the sample. This method provides a quick, visual estimate.

4. Calculation of Grain Size Number (G): Once you have 'N' (number of grains per square inch at 100X), use the formula to solve for 'G':

   • N = 2^(G-1)
   • log(N) = (G-1) * log(2)
   • log(N) / log(2) = G - 1
   • G = (log(N) / log(2)) + 1

   Since log base 2 of N, or log₂(N) is just log(N) / log(2), then:

   • G = log₂(N) + 1
   • G = 3.322 log₁₀(N) + 1 (since log₂(N) = 3.322 log₁₀(N))

Adjustment for Magnification

If the micrograph was taken at a magnification other than 100X (let's call it M), you need to adjust the grain count. The formula becomes:

N₁₀₀ = N_M * (M/100)²

Where:

• N₁₀₀ is the number of grains per square inch at 100X magnification.
• N_M is the number of grains per square inch at magnification M.
• M is the actual magnification used.

You would then use N₁₀₀ in the grain size number formula as described above.

Example

Suppose you count 64 grains per square inch (N = 64) at a magnification of 100X.

G = (log(64) / log(2)) + 1
G = (1.806 / 0.301) + 1
G = 6 + 1
G = 7

Therefore, the ASTM grain size number is 7.

Summary

Calculating the grain number involves preparing a sample, obtaining a micrograph (preferably at 100X), counting the grains per square inch, and then using the formula N = 2^(G-1) to determine the ASTM grain size number (G). Remember to adjust for magnification if necessary.