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Chapter 4: Problem 50

Following is a schematic micrograph that represents the microstructure of some hypothetical metal.Determine the following: (a) Mean intercept length (b) ASTM grain-size number, \(G\)

Short Answer

Expert verified
#tag_title#Answer#tag_content#The general steps to calculate the mean intercept length and ASTM grain-size number for a given schematic micrograph are: 1. Count the number of grains and intercepts per line for a few randomly chosen lines within the micrograph. 2. Calculate the mean intercept length using the formula: Mean Intercept Length (L_m) = Total length of the lines / Total number of intercepts. 3. Estimate the number of grains per square inch at 100x magnification (N) by taking the inverse of the mean intercept length (1/L_m), and multiplying this value by a scaling factor (100x). 4. Calculate the ASTM grain-size number (G) using the formula: G = log2 (N+1).

Step by step solution

01

Count the Grains and Intercepts Per Line

First, count the number of grains and the intercepts per line for a few randomly chosen lines within the schematic micrograph. You will need to count both the grains and the intercepts in order to calculate the mean intercept length and ASTM grain-size number. Counting grain boundaries can be challenging, but doing it for several lines will improve the accuracy of the final result.
02

Calculate Mean Intercept Length

To calculate the mean intercept length, use the following formula: Mean Intercept Length (\(L_m\)) = Total length of the lines / Total number of intercepts Calculate the mean intercept length using the intercept counts from step 1. This will give you the average length of a line segment that touches two grain boundaries within the microstructure.
03

Estimate Number of Grains Per Square Inch at 100x Magnification (N)

To calculate N, we first need to determine the grains per unit area (grains/square inch) in the schematic micrograph. To do this, follow these steps: 1. Take the inverse of the mean intercept length (\(1/L_m\)) to obtain a value in "lengths per unit area." 2. Multiply this value by a scaling factor (100x), so you obtain grains per square inch at 100x magnification. With this value for N, we can now calculate the ASTM grain-size number (G).
04

Calculate the ASTM Grain-Size Number (G)

Now, using the value of N calculated in step 3, use the following formula to calculate the ASTM grain-size number: \(G = \log_2 (N+1)\) The result will give you the ASTM grain-size number for the given schematic micrograph of the hypothetical metal. Keep in mind that the results for the mean intercept length and ASTM grain-size number will highly depend on the schematic micrograph you have. Carefully follow these steps with your given micrograph to obtain accurate results.

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