D2 Metallography and Microscopy

Topic

Metallography—the experimental method described by this model—involves preparing and microscopically examining a polished section of the metal sample, revealing grain boundaries through appropriate chemical or electrolytic etching. Using this microscopic image, the linear intercept method (in accordance with ASTM E112) measures the metal's grain size by counting how many grain boundaries are crossed by a line of known length drawn across the image. If this line crosses more grain boundaries as it traverses the image, the linear intercept method yields a smaller measured grain size; conversely, if it crosses fewer boundaries, the measured grain size is larger.

In addition to revealing the metal's grain boundaries, the microscopic image also shows the area fraction occupied by any second phase present in the microstructure. Delesse's principle relates this observed area fraction to the actual volume fraction of that second phase within the metal's total volume; according to this principle, the two fractions are equal on average, provided the observed section was taken randomly with respect to the metal's microstructure. Thus, if the area fraction of the second phase measured on the image is higher, Delesse's principle implies that the actual volume fraction of that phase is also higher.

For this reason, the current model—which began by addressing metallography and grain size—supplies the grain size value directly obtained via the linear intercept method to another model in the set that describes the metal's grain size. The fact that this same stereological count—based on the Delesse principle—serves to relate a two-dimensional observation to an actual volumetric quantity allows it to be reused for the same purpose in a different material model—specifically, one describing the fractography of a composite material—to verify the length of the fiber actually embedded within the fracture surface.

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