Ferrostatic Pressure

In continuous casting, ferrostatic pressure is generally accepted as the primary force holding the solidfying shell in contact with the copper mold. This in con- trast to the behavior of a pool of solidifying metal on a chilled surface and its tendency to freeze and bow upwards [128]. The ferrostatic pressure load is di- rectly proportional to the depth below the meniscus, with the largest pressure experienced at the metallurgical length. The exact load may vary slightly from grade to grade with changes in density of the liquid steel, but it is on the order of magnitude of about 0.03 MPa.

Ferrostatic pressure is the continuous casting analog of hydrostatic pressure. From the top of the meniscus to the metallurgical length, the solidification front experiences this pressure as a result of the liquid steel pool above it. This fer- rostatic pressure helps keep the solidifying shell in good contact with the mold copper, however the presence of ferrostatic pressure is not always enough to resist the shells attempts to pull away from the mold, especially in situations where there is local shell thinning or a drop in heat transfer.

This study demonstrates that in the general absence of ferrostatic pressure, the tendency for depression formation induced by a reduced heat transfer region is indeed substantially greater. This study also shows that application of the ferrostatic pressure as a traction on the liquid is feasible if setup correctly. It has also demonstrated that the difference between the pulling and pushing application is negligible for this model.

A.1.1

Magnitude

To examine the effect of ferrostatic pressure on the formation of depressions, the magnitude of the applied load was varied. A case was run with 10% of the expected value of the pressure applied to the domain. While this boundary condition is clearly not representative of casting on earth, it does allow us to imagine what the ferrostatic pressure is preventing or allowing.

A.1.2

Application Location

Application of the ferrostatic pressure in previous works has primarily applied it as a traction to the steel surface which contacts the mold as shown in Fig- ure A.1. This applied traction pulls the steel shell towards the mold according to the ABAQUS user subroutine DLOAD and assuming a constant casting speed, is directly proportional to time below meniscus.

The purpose of this applied traction (as opposed to what some might consider more realistic in application on the solidification front) is primarily numerical sim- plification, and to ease the difficulties sometimes encountered with other methods such as tracking the liquid/solid boundary nodes, or large deformation of the weak liquid elements.

Application of the ferrostatic pressure using the pushing method is shown in Figure A.2. The steel-mold contact face is a free surface. The opposite face, has ferrostatic pressure traction applied.

Figure A.2: Ferrostatic pressure applied pushing on domain

The free moving edge of the domain is constrained to remain vertical; However, when applying the ferrostatic pressure as a traction pushing on the free liquid surface, that surface also must be constrained to maintain a straight line.

Results of this small study are shown in Figure A.3. It was found that the size of the depression observed with ferrostatic pressure applied pushing on the liquid, it was observed that the size of the depression was about 10% smaller than when it pulls on the surface. This demonstrates that this method of ferrostatic pressure application is reasonable for this situation.

(a) Pulling (b) Pus hing (c) 10% Pulling (d) 10% Pushing Figure A.3: Results of v aried ferrostatic pressure applic ation

Appendix B

ABAQUS Operational Notes, Input Files &

Scripts

During the course of this work, the author has spent considerable time trou- bleshooting and exploring solidification modeling using ABAQUS commercial fi- nite element software. This appendix contains some notes and recommendations for its successful operations, as well as example input files for the work conducted. The importance of reading and understanding the documentation cannot be em- phasized enough, for convenience portions of this chapter contain large excerpts (some summarized) from the ABAQUS documentation collection.

There is also a section containing the following codes: ABAQUS input files, the GAPCON subroutine written in FORTRAN, and examples of Python script files that can be used to run batch jobs for parametric studies, subject to the following copyright:

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