Efficient measurement of microstructural surface area using trisector
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To emphasize the preceding sampling requirements, the composite test probe is called "trisector." It is also shown that independent random sections are not useful for estimation of Sv of anisotropic microstructural surfaces, in general. Further, two perpendicular vertical sections are also not generally useful for a reliable estimation of S~ in anisotropic microstructures.
I.
INTRODUCTION
MICROSTRUCTURES contain internal surfaces or boundaries. The total area of the internal boundaries of interest per unit microstructural volume Sv is an important microstructural attribute. The microstructural parameters, such as mean intercept grain size, H,21 mean free path, [3j surface area averaged particle size, 14] etc., that often correlate to mechanical and physical properties are directly related to Sv. In the composite materials, microstructural damage features, such as microcracks and delaminations, can be quantified in terms of their total surface area per unit volume. Smith and Guttman, ISl Saltykov,161and Duffin et al. tTJ have given the following assumption-free equation for the unbiased estimation of Sv from the measurements performed on the randomly oriented and located metallographic sections. Sv = 2PL
[1]
where PL is the average number of intersections of a randomly oriented and located test line of unit length with the observed microstructural boundaries of interest. Equation [1] is applicable to isotropic as well as anisotropic microstructures. In isotropic microstructure (i.e., no preferred geometric orientation), the number of intersections of a test line with the internal boundaries does not depend on the test line orientation (direction). Further, if the microstructure is homogenous (i.e., no significant systematic variations in the microstructure from ARUN M. GOKHALE, Professor, is with the School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245. WILLIAM J. DRURY, formerly Graduate Student, School of Materials Science and Engineering, Georgia Institute of Technology, is Vice-President, PL Technologies, Inc., Atlanta, GA 30361. Manuscript submitted July 9, 1992. METALLURGICALAND MATERIALS TRANSACTIONS A
one location in the specimen to another), then parallel metallographic planes at different locations in the specimen present statistically similar two-dimensional microstructures. It follows that for isotropic homogenous microstructures (for example, well-annealed copper), the average number of intersections of a test line with the internal boundaries of interest does not vary significantly with orientation of test line and metallographic plane or with the location of metallographic plane in the specimen. In such a case, PL can be estimated with high precision from the measurements performed on parallel test lines uniformly distributed in a single metallographic plane and Sv can be calculated by using Eq. [1]. However, microstructures are often homogenous but anisotropic. For example, grain boundaries in an extruded copper wire, elongated inclusions in a rol
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