A Transfer Function for Relating Mean 2D Cross-Section Measurements to Mean 3D Particle Sizes
- PDF / 1,019,410 Bytes
- 5 Pages / 593.972 x 792 pts Page_size
- 102 Downloads / 183 Views
article size is an important input parameter in many microstructure evolution models,[1–6] yet it can only be directly measured in situ for a very small percentage of materials. While serial sectioning can be used to obtain the 3D attributes of polycrystalline materials, it is either prohibitively expensive or impractical for the majority of applications. Often, the researcher must instead utilize stereology to estimate the 3D sizes from observations on a 2D cross-section. Stereologically appropriate 2D measurements are either lineal intercepts (the chord length of linear probe intersections with volumetric features) or section areas (the intersection areas of a planar probe cutting through volumetric features).[7] The lineal intercepts or section areas can then be used to predict the 3D caliper diameter distributions using either the Cahn–Fullman or
A.R.C. GERLT, R.S. PICARD, A.E. SAURBER, A.K. CRINER, S.L. SEMIATIN and E.J. PAYTON are with the Materials and Manufacturing Directorate, Air Force Research Laboratory, WrightPatterson Air Force Base, OH 45433. Contact e-mail: [email protected] Manuscript submitted May 3, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS A
Johnson–Saltikov methods, respectively.[8] However, both techniques suffer from relatively large error propagation issues (e.g., as described in Reference 9). In the absence of sufficient 2D distribution data, many researchers will instead resort to estimating the mean 3D particle size through the use of a scalar multiplication factor, denoted here as j. These values are often based on geometric constants. For example, the diameter of a single sphere is equal to 1.5 times the average randomly oriented chord length through its volume. As such, multiplication of the mean 2D lineal intercept measurement by 1.5 to estimate the mean 3D particle size is an acceptable practice when the particles in a system can be reasonably approximated by a collection of uniformly-sized spheres. However, this multiplication factor is no longer accurate when the system contains spherical particles with a distribution of sizes. In fact, the correct value of j will always be less than 1.5 when the particle sizes follow a lognormal, gamma, or Rayleigh distributions.[7,10,11] Additionally, it is worth noting that non-spherical shapes have different caliper-size-to-intercept ratios. Uniform distributions of regular polyhedrons can have values of j ranging from 1.5 for a sphere to 2.25 for a cube,[7,12] with even higher values for shapes representing non-equiaxed grains: The proper multiplication factor for any distribution is therefore also a strong function of the expected particle shape and 3D distribution. An alternative multiplication factor focusing on polycrystalline grain structures was proposed by Mendelson in 1967 and took into account the effect of both particle shape and distribution.[11] Mendelson began by determining the correct j value for a uniform dispersion of tetrakaidecahedral particles, j0 = 1.7756, as this was expected to more accurately represent an equiaxed
Data Loading...
