An ultrasonic method for reconstructing the two-dimensional liquid-solid interface in solidifying bodies
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I.
INTRODUCTION
THERE exists
a need to sense the shape of the liquidsolid boundary in solidifying strands during continuous casting and in the subsequent thermomechanical processing of metals and alloys, m Previous research on fully solidified AISI 304 stainless steel has demonstrated the ability of an ultrasonic approach to reconstruct the internal temperature profiles for solid bodies both in the laboratory t21 and in a steel mill. I31 Noncontact techniques based on the use of electromagnetic acoustic transducer (EMAT) techniques and laser-generated ultrasound were u s e d . 14-8] Here, we report on the extension of this ultrasonic approach to solidifying bodies, where knowledge of the solid shell thickness during continuous casting could allow faster casting rates, reduced incidence of breakouts, and better control of metallurgical defects (macrosegregation, hot cracking, etc.). Our approach is based upon the significant difference in the ultrasonic velocity in solid and molten metal, 191 which can vary from 10 to 20 pet. The time of flight of an ultrasonic pulse traversing a solidifying body depends upon the ultrasonic velocities sampled by the ray. Thus, the time of flights of a suitable set of rays through the body can be used to determine the distribution of ultrasonic velocity over a cross section of the body. If the object is solidifying, the known difference in velocities in the solid and liquid states can be used to determine the liquid-solid boundary within the cross section. We have explored the use of an iterative least-squares method for finding the liquid-solid interface rather than a more conventional tomographic method which would require a much larger number of rays. The approach we utilized, which was found to be both simple and robust, was to regard the boundary of intersection between the liquid region and the plane of the ultrasonic rays as an approximately elliptical shape and to then determine the F.A. MAUER, Physicist, S.J. NORTON, Physicist, and D. PITCHURE, Metallurgical Technician, are with the Metallurgy Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. Y. GRINBERG, Metallurgist, is with the Atomic Energy Commission, Israel. H.N.G. WADLEY, Professor, is with the Department of Materials Science, University of Virginia, Charlottesville, VA. Manuscript submitted May 3, 1990. METALLURGICAL TRANSACTIONS B
best elliptical boundary (in the least-squares sense) consistent with the ultrasonic measurements. Independent metallographic measurements of the liquid-solid interface indicate that the shape of the computed elliptical boundary and the actual boundary were in good agreement ( + 2 pct). II.
METHOD AND APPARATUS
Previous attempts to locate the liquid-solid interface in partially solidified bodies have generally been based on pulse-echo techniquesJ 1~ These methods rely on detection of an echo from the liquid-solid interface. Unfortunately, because of the spatially extended nature of the liquid-solid boundary in alloys, the echo amplitude is small and is
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