Initial coarsening of manganese sulfide inclusions in rolled steel during homogenization
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D URING hot-rolling of steel, manganese sulfide in-
clusions are flattened out and elongated in the rolling direction. A preliminary investigation showed that during a subsequent homogenization treatment these elongated plates coarsen by first becoming cylindrical. At
a later stage the cylindrical inclusions broke into seg-
ments which spheroidize and decrease in number with time. In this work the transition from flattened to cylindrical sulfides during high temperature homogenization of AISI 4340 low alloy steel was investigated. The transition from cylindrical to spherical morphology, which occurs at a later stage, was the object of a separate, parallel investigation. 1,2 Each one of these geometric transformations has been described theoretically to some extent, the main work on shape changes being by Nichols and Mullins 3 while that on particle size changes being by Lifshitz and Slyozov, 4 and Wagner. 5 Modifications of these theos -10 ries and other treatments have also been given Experiments on ovulation, defined as the breaking of a cylinder into spheres, and particle size coarsening have been conducted on a variety of materials 11-21 including manganese sulfide. 22-24 The theoretical treatment that applies to the present investigation was developed by Nichols and Mullins, 3 who considered the decay of circumferential perturbations of an infinite cylinder. The perturbation of interest is the one that describes a rod with a flattened
cross-section: r=R 0 +bsin20
[1]
where r and B are cylindrical coordinates of the rod surface, R o is the radius of the rod after the perturbation of amplitude S has decayed. The rate of decay is given by:
b/b = —k/Ró
[2]
where k and n are constants which depend on whether Y. V. MURTY and R. MEHRABIAN are Research Associate and Associate Professor, respectively, Dept. of Mining and Metallurgical Engineering, University of Illinois, Urbana, ILL. J. E. MORRAL and T. Z. KATTAMIS are Associate Professor and Professor, respectively, Dept. of Metallurgy, Institute of Materials Science, University of Conpecticut, Storrs, CT. Manuscript submitted February 19, 1975. METALLURGICAL TRANSACTIONS A
the shape change is controlled by surface or by volume 25 diffusion. Corresponding to Herring's scaling laws, n = 3 for volume and n = 4 for surface diffusion control. Although Eq. [2] was derived for small perturbations, in which case the surface Laplacian can be linearized, it will be applied, for the sake of simplicity, to all rods considered in this investigation. As mentioned above, the kinetics of shape changes in the solid state can be controlled by either volume or surface diffusion, depending on particle size or temperature. This dependence can be shown by considering the ratio of perturbation decay rates for surface diffusion, b s , and for volume diffusion, b: 3
b s2D S fvc2 b VDvR0
[3^
where D s and D v are surface and volume diffusion coefficients, f is the correlation factor for volume diffusion, v is the number of diffusing atoms per unit area and f1 is atomic volume. Be
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