Grain size estimation in anisotropic materials
- PDF / 380,480 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 108 Downloads / 234 Views
I.
INTRODUCTION
ALMOST all of the important mechanical properties of polycrystalline materials depend on grain size. Consequently, grain size estimation is the most frequently performed quantitative microscopic measurement. It follows that reliable estimation of grain size is of significant theoretical and practical interest.[1,2] Grain size is usually calculated from the measurements performed on metallographic planes through the three-dimensional microstructure. The stereological relationships between two-dimensional grain size measurements and three-dimensional microstructural parameters are known, but often not recognized or appreciated. The most popular measures of grain size are mean grain intercept (L3) and ASTM grain-size number (G), calculated from the mean grain intercept. Mean grain intercept (L3) is the average value of the chord length generated by intersections of grains and straight test lines of all possible different orientations and locations in the specimen. Thus, the mean grain intercept is a quantitative measure of the overall ‘‘scale’’ of the grain structure. In a single-phase material, the mean grain intercept is simply equal to the reciprocal of the average number of intersections between test lines of all possible orientations and locations per unit test line length (I L), and it is related to the total grain boundary area per unit volume (SV) in a straightforward manner. Smith and Guttman[3] have given the following general stereological equation for an unbiased estimation of total surface area of any type of microstructural interface per unit volume of specimen (SV) from the measurements performed on randomly oriented and located metallographic planes through the microstructure: SV 5 2 I L
[1]
As mentioned earlier, I L is the average value of the number of intersections of test lines and grain boundaries of interest per unit test line length. The mean grain intercept (L3) and the ASTM grain-size number (G) can be calculated from
BILLY RAY MORRIS, formerly Graduate Student, School of Materials Science and Engineering, Georgia Institute of Technology, is Graduate Student, Department of Mechanical Engineering, University of California, Davis, Davis, CA 95616. ARUN M. GOKHALE, Professor, is with the School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245. GEORGE F. VANDER VOORT, Director, Research and Technology, is with Buehler Ltd., Lake Bluff, IL 60044. Manuscript submitted March 12, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
the average intersection count (I L) using the following equations:[4–11] L 3 5 [1/I L] 5 [2/SV]
[2]
G 5 26.64571 [log L 3] 2 3.298
[3]
In Eq. [3], L3 is expressed in millimeters. The value of I L can be experimentally estimated by performing intersection counting on test lines of different random orientations and locations, placed on randomly oriented and located metallographic planes. In a homogeneous microstructure (i.e., no systematic gradients from one location to another) a statistically similar two-di
Data Loading...
