Liquid Inclusion Distortion by Lens Shape Effect: In Situ Observation and Quantification on LCAK Steels Using HT-CSLM
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Changes in the size of nonmetallic inclusions during steel processing are expected to affect steel properties. As examples, Ma et al.[1] found that fatigue resistance was markedly worse if alumina inclusions larger than 0.2 mm2 were present and Zhang et al.[2] observed fatigue initiation by spherical calcium aluminates larger than 20 lm in a Cr-Mn-V low-alloy steel. In contrast, small inclusions can aid grain refinement by nucleating ferrite.[3] Confocal laser scanning microscopy allows in situ observation of oxide particles on the surface of liquid steel.[4,5] However, the presence of the liquid–gas interfaces is expected to change the shape of liquid droplets from spherical (within liquid steel) to lens shape (Figure 1) at the steel–gas interface. The shape of micron-sized oxide droplets is controlled by surface and interfacial tension (and not by gravity).[6] The angles
MAURO E. FERREIRA, PETRUS CHRISTIAAN PISTORIUS, and RICHARD J. FRUEHAN are with the Center for Iron and Steelmaking Research, Department of Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213. Contact e-mail: [email protected] Manuscript submitted May 21, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS B
shown in Figure 1 depend as follows on the surface and interfacial tensions[6]: c2ML ¼ c2M þ c2L 2cM cL cos a
½1
cML sin b ¼ cL sin a
½2
In these equations, cM is the surface tension of the liquid metal; cL is the surface tension of the liquid oxide; cML is the metal-oxide interfacial tension; and the angles a and b are defined in Figure 1. Because of its lens shape, a droplet at the steel surface would have a larger diameter than a spherical inclusion of the same volume within the liquid steel. This ratio of lens diameter to sphere diameter (denoted by q in this paper) is calculated readily from the geometric relationships for a spherical cap,[7] as summarized in Figure 2 and Eqs. [3] through [5]. Equation [5] gives the volume of the spherical cap. a ¼ R sina
½3
h ¼ Rð1 cosaÞ ¼ að1 cosaÞ =sina
½4
Vcap ¼
ph 3a2 þ h2 6
½5
The total volume of the lens-shaped droplet is the sum of the volumes of the upper cap (in the gas phase) and the lower cap (in the liquid metal); the upper and lower caps have the same base radius a but different heights (h) because, in general, a „ b. Literature values of surface and interfacial tensions were used to evaluate the expected ratio q = a/rsphere, where rsphere is the radius of a spherical droplet (within the liquid steel) which would have the same volume as a lens (with radius a) at the steel surface. Values are summarized in Table I. From these values, q is expected to be between 1.6 and 2.2. That is, the radius of the lensshaped droplet is expected to be approximately twice the radius that the same volume of liquid oxide would have when completely immersed in liquid steel. Samples of calcium-treated aluminum-killed steel were used to test this relationship. The steel was prepared by melting 600 g of electrolytic iron in an MgO crucible unde
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