Grain Size Characteristics
Grain Size measurement is complicated by a number of factors. First, the three-dimensional size of the grains is not constant and the sectioning plane will cut through the grains at random. Thus, on a cross-section we will observe a range of sizes, none larger than the cross section of the largest grain sampled. Grain shape also varies, particularly as a function of grain size. One of the earliest studies of grain shape was made by Lord Kelvin in 1887. He showed that the optimum space-filling grain shape, with a minimum surface area and surface tension, is a polyhedron known as a tetrakaidecahedron, which has 14 faces, 24 corners, and 36 edges. While this shape meets most grain criteria, it does not satisfy the required 120 degree dihedral angles between grains where three adjacent grains meet at an edge, unless the faces exhibit a minor amount of curvature. Another ideal grain shape, the pentagonal dodecahedron, agrees well with observations of grains, but is not a space filling shape.
It has twelve five-sided faces. However, it must be recognized that we are sampling grains with a range of sizes and shapes. In most cases, the grains observed on a polished cross-sectional plane exhibit a range of sizes around a central mean and individual measurements of grain areas, diameters, or intercept lengths exhibit a normal distribution. In the vast majority of cases, we merely determine the mean value of the planar grain size, rather than the distribution.
There are cases where the grain size distribution is not normal but bimodal, or "duplex." Also, our grain shapes can be distorted by processing procedures so that they are flattened and/or elongated. Different product shapes, and different processing procedures, can produce a variety of non-equiaxed grain shapes. This, of course, does influence our ability to measure the grain size.
Grain size measurement is also complicated by the different types of grains that can be present in metals, although their fundamental shapes are the same. For example, in body-centered cubic metals, such as Fe, Mo, and Cr, we have ferrite grains; in face-centered cubic metals, such as Al, Nickel, Copper, and certain stainless steel, we have austenite grains. The grains exhibit the same shapes and are measured in the same way, but we must be careful in describing what kind of grains we are measuring. In the face-centered cubic metals, we may observe so-called twin boundaries within the grains. Aluminum alloys, however, rarely exhibit twins. When twins are present, they are ignored if we are trying to define the grain size. However, if we are trying to establish a relationship between microstructure and properties, for example, strength, we must consider twin boundaries as they influence dislocation movement, just as grain boundaries do. Hence, we must recognize the intent of the work being performed.
In heat-treated steels, it is recognized that the grain size of the product of the heat treatment, usually martensite, is not measured or cannot be measured. For low-carbon steel, the martensite forms in packets within the parent austenite grains. In high-carbon martensites, we do not observe any convenient structural shape that can be measured. In most cases, we try to measure the size of the parent austenite grains that were formed during the high temperature hold during the heat treatment.
This is usually referred to as the "prior-austenite grain size" and it has been widely correlated to the properties of heat treated steels. The most difficult process here is the etching procedure needed to reveal these prior boundaries. Sometimes they cannot be revealed, particularly in low-carbon steel. In this case, it may be possible to measure the low-carbon lath martensite packet size, which is a function of the prior-austenite grain size.
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