A Mathematical Model for Determination of Lamellar Spacing in Materials of Poly-Grain Microstructures

Based on the assumption of spherical grains in polycrystalline materials and the theory of metallography, a mathematical model was developed to calculate the quantitative relationship between apparent and true values of the lamellar spacing cutting through the grain randomly. The results indicate that the grain sizes of most polycrystalline materials are much larger than their lamellar spacings, the ratio of an average apparent value to a true one can be characterized by the corrected coefficient k. The ratio of the apparent lamellar spacing to the grain size reduces from 0.05 to 0.0001, and k increases from 1.5391 to 1.5707, which gradually tends to be π/2. When the ratio of the apparent lamellar spacing to the grain size is smaller than 0.001, value k can be considered as a constant of π/2. The amount of work will be decreased adopting the present model to get the true value of lamellar spacing compared with the conventional methods.