Mathematical modeling of a melt pool driven by an electron beam
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I. INTRODUCTION
PHYSICAL vapor deposition (PVD) assisted by an electron beam is one of several methods currently used to apply coatings of a wide variety of materials from metals to ceramics to semiconductors.[1–5] The focus of this article is on ZrO2 based thermal barrier coatings (TBCs) that are applied to aircraft components subjected to high-temperature environments. This process is performed using several different hardware configurations.[6] This article shall consider one particular configuration, shown in Figure 1. The heat source, a scanning electron beam generated by a 270 deg electron-beam gun, is directed onto an ingot of yttria stabilized zirconia (YSZ). The electron beam is traced rapidly over the top surface of the ingot such that it forms a molten pool and evaporates. To maintain a supply of YSZ for a prolonged deposition process, the ingot is fed continuously upward through a water-cooled copper crucible. Hardware being coated by the TBC material is usually rotated above the melt pool to promote uniform coatings. An over-source heater is used to control the temperature of the hardware being coated. Of interest to the aircraft engine manufacturing industries is attaining better control over this process.[7] It is known that the microstructural characteristics of TBCs vary according to the conditions under which they are manufactured.[8] Further, it is understood that TBCs with certain microstructures are more effective and reliable. Three of the most important process parameters that impact TBC microstructure are the temperature of the hardware being coated, the mass flux of source material impinging upon the D. SIMON, formerly Graduate Student, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, is Member of Research Staff, Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723. U. PAL, Associate Professor, is with the Department of Manufacturing, Boston University, Boston, MA 02215. Manuscript submitted January 2, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS B
hardware, and the temperature of the impinging vapor.[7,9] Consequently, it is highly desirable to be able to control these parameters during TBC production. Industrial attempts at the control of this process have been based upon the statistical analysis of coatings fabricated under various conditions. This approach has allowed coating manufacturers to develop a set of bounds on their process parameters inside which they can expect to produce acceptable TBCs. To some degree, this approach has also allowed these manufacturers to optimize their process parameters. To move to the next level of process control, a better understanding of the process is needed first. The need for this understanding is the motivation behind this investigation and the development of the forthcoming reduced order models. Of course, a full understanding of the PVD process also requires an investigation of the vapor transport and deposition processes.[10,11,12] This investigation, however, will focus sol
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