Introduction to Stereological Principles

Although the fundamental relationships for stereology, the foundation of quantitative metallography, have been known for some time, implementation of these concepts has been restricted when performed manually due to the tremendous effort required. Further, while humans are quite good with pattern recognition, as in the identification of complex structures, they are less satisfactory for repetitive counting.

Many years ago, George Moore (1) and members of ASTM Committee E-4 on Metallography conducted a simple counting experiment. About 400 people were asked to count the number of times the letter “e” appeared in a paragraph without striking out the letters as they counted. The correct answer was obtained by only 3.8% of the people. Results were not Gaussian, however, as only 4.3% had higher values while 92% had lower values, some much lower. The standard deviation was 12.28. This experiment revealed a basic problem with manual ratings. In this case the subject was one very familiar to the test subjects, yet only 3.8% obtained the correct count. What degree of counting accuracy can be expected when the subject is less familiar, such as microstructural features? Image analyzers, on the other hand, are quite good at counting but not as competent at recognizing features of interest. Fortunately, there has been tremendous progress in the development of powerful, user-friendly image analyzers over the past two decades.


Introduction to Quantitative Metallography

For most of its history, metallographic observations have been largely qualitative in nature. The structure might be described as being relatively coarse or fine, or layered, or uniform. Particles might be labeled as globular or spheroidal, lamellar, acicular, or blocky. Microstructures were single-phase or duplex, and so forth.

Forty some years ago when I entered industry, chart ratings and visual examinations were the main approach toward quantitation. I can well remember the mill metallographers looking at spheroidized carbide tool steel structures and stating that it was, for example, 90% spheroidized (many raters would never say 100%, just as some teachers would never grade an essay at 100%!) or that it was 60% spheroidized and 40% lamellar tending to spheroidize. Or, without looking at the chart (a seasoned rater never did!), they would pronounce that the grain size was, for example, 100% 6 to 8 or perhaps 70% 8 and 30% 3 to 5 if it was duplex in appearance.


Image Analysis Measurements of Duplex Grain Structures

Several types of duplex grain size distributions in five different alloys were evaluated using image analysis. Most of the grain structures contained annealing twins. Those with straight interfaces could be recognized and deleted from the image, leaving only grain boundaries. One specimen exhibited curved twin boundaries, caused by deformation, and they could not be discriminated by the system as currently programmed. Grain areas were measured and grouped according to their relationship to the ASTM grain size scale. An area-weighted histogram was shown to be excellent for revealing the nature of the distribution, while a numerical-frequency histogram was insensitive. The intersection of these two curves separated only one of the four bimodal distributions. A deconvolution approach, using the area-weighted curve only, should be evaluated. An arithmetic grain area classification approach using 25 classes based on the data range, to split the two grain area populations based upon the intersection of the number percent and area percent curves, worked well for two of the four specimens. Image analysis detection of grains results in a small portion of the image (about 6-12%) assigned to the grain boundaries. In manual measurement methods, the area occupied by the grain boundaries is not considered, and it does not influence measurements. Thus, compared to manual methods, image analysis undersizes grains slightly producing a relatively small positive bias in the grain size number, which could be ignored, but can be eliminated or reduced.


Examination of Some Grain Size Measurement Problems


The measurment of grain size is performed nearly always on a metallographically prepared cross section, suitably etched to reveal the grain structure, using methods that pertain only to the grain cross sections. These measurements are termed planar and some may be converted mathematically into spatial estimates of the size of the three-dimensional grains. However, the vast majority of such work is planar where no assumptions about grain shape are required and grain size is described in one- or two-dimensional terms (intercept length, diameter, or area) based on sections through the grains. The most frequently used measurement methods are described in this paper and compared using the same images. These methods are the Jeffries planimetric method, the triple-point count method, and the Hetn intercept method. These methods base grain size on two-dimensional, zero-dimensional, and one-dimensional features
of the microstructure, resnectively (that is areas, points and lines),


Computer-Aided Microstructural Analysis of Specialty Steels

Computers are utilized in a variety of microstructural characterization functions – some are quite common, others are not. In this paper, three case studies of detailed specialty steel image analysis programs performed at Carpenter Technology Corporation will be reviewed. All involved computer-generated graphical analysis.


Automating the JK Inclusion Analysis

A procedure has been developed that through the use of the Leitz Texture Analyzer System (TAS) makes it possible to automatically obtain JK-inclusion ratings consonant with those obtained manually by ASTM E45, Methods A and D, which provide qualitative and quantitative data, respectively. In the new procedure, sulfide inclusions are detected by gray-level differences because image analysis techniques cannot distinguish between type-A sulfides and type-C silicates on the basis of morphological differences alone. Next, the stringered and globular oxides are seperated. Type-B and Type-C stringered oxides are seperated on the basis of the length of the largest oxides in a stringer. After each inclusion type has been isolated, the required measurement is made and the severity is calculated. For each type, the inclusions are further seperated according to thickness. Reproducibility of ratings with the new procedure is quite good, and the results obtained are in good agreement with those done manually.