ON THE NEW METHOD OF REPRESENTATION OF THE MIXTURE OF SEVERAL AUSTENITE GRAIN SIZES

Abstract

In indicating austenite grain size, the hitherto-used method is sufficient in case all the grains are of almost uniform size, but if there are different sizes of grains mixed up, the old method is of no effect at all, and when the author try to use it forcibly, the following faults will come out: -
(1) Even if it is of uniform grains, there is no way of ascertaining it.
(2) When grains of large size and of small size are mixed up closely as well as uniformly in the microscopic field, it is to be represented as of uniform grains (microscopic mixed grains), though it seems to be of mixed-up grains.
(3) As the sample is looked in its section, small-size grains will naturally be seen more than those that actually are, while large size grains are less.
(4) There is no way of estimating the volume fractions of large-size and small-size grains contained in a sample.
(5) Discrepancy in the number of grain sizes obtained by the hitherto-used method denotes only the differences of average grain sizes in different visual fields, and does not exactly represent the grade of the mixed-up grains. (macroscopic mixed grains.)
In order to make up these shortcomings and to represent mixed-up grains exactly, the author accordingly tried to work out distribution function i.e. g(r) of radii of grains contained in a sample following method: -
Drawing a random line on the top of each microscopic photo of a sample, at the same time-making the ensemble of length of intercepts {Li} where L is lineal traverse of length limited by grain boundaries, the distribution function of Li, i.e. f(L) is to be finally found out.
When applying the theory actually, the intercepts are first classified into three groups (large length of intercept which is denoted by Λ₀): small intercepts (below Λ0/4), medium intercepts (from Λ₀/4 to Λ₀/2) and large intercepts (over Λ₀/2) and the author count fractions of these intercepts α', β' and γ'. And by use of the values of theseα', β' and γ', the following quantities are obtained.
(1) Volume fraction of small grains (its diameters extend from V₀/8 to Λ₀/4) α, medium grains (from Λ₀/4 to Λ₀/2) β, and large grains (above Λ₀/2) γ.
(2) The radius of such sphere as gives the average value of total grains volumes.
(3) The degree of mixed grains.
(4) The surfacial area of grains boundaries in the unit volume.
(5) The average value of lengths of intercepts calculated out theoretically from the g(r) which is obtained by f (L).
In this study, equations and figures or tables giving the above mentioned values are proposed.
Further, if there is the greater discrepancy between (5) and the actual average length of intercept over 5%, the classification into three groups will be at fault, and therefore it should be classified into more groups, and the equation thereof are also here proposed.