مدل شبیه سازی برای یک ساختار پوشش EB-PVD با استفاده از روش سطح مجموعه

A comprehensive modeling approach to link machine dynamics, deposition, and substrate kinematics in an electron beam physical vapor deposition (EB-PVD) is presented in this paper. The machine dynamics in EB-PVD process are captured by finite element models, resulting in the prediction of evaporation rate and vapor distribution. The deposition process is modeled using the level set method, which is one of the computational techniques for tracking topographic evolution. The proposed simulation model is implemented in Matlab and is compared with experimental results published by other researchers. Results indicate that the proposed simulation model can be used to predict microstructure features such as zigzag and helical columnar shapes. The pitch of a zigzag microstructure can be predicted within 20% at the 0.3 to 6 μm level for Yttira-stabilized Zirconia (YSZ) coating.

Among the various deposition techniques, EB-PVD is versatile because it can simultaneously evaporate multiple materials of different types of compositions; it enables engineers to design tailored microstructures, such as functionally graded coatings and nano-laminated coatings; and new materials that could not be produced economically by conventional methods [2] and [3]. Coatings produced by the EB-PVD process usually have a good surface finish and a uniform microstructure. Singh and Wolfe [4] investigated the application of EB-PVD to the formation of net-shaped rhenium components with the shapes of ball, plate, and tube. EB-PVD can be a cost-effective solution for manufacturing surfaces with submicron and nano-sized microstructures with high hardness and strength as compared with chemical vapor deposition (CVD). There has been an acute need for developing a scientific basis for coating processes, especially models and techniques for their real-time control [5]. The theory of evaporation was first established by Hertz in 1882 followed by Langmuir in 1913 and Knudsen in 1915 to model the evaporation rates from free solid surfaces and liquids [6]. One of the key results in the theory of evaporation is the cosine law of emission which models the directionality of evaporating molecules [6]. The cosine model and its variants have been used in several evaporation applications to model coating thickness of simple planar substrates [7] and [8]. Bernier et al. [9] proposed a modified Knudsen’s cosine law of emission using experimentally measured thickness profiles of coatings deposited on stationary cylinders.

Numerical simulations indicate that the proposed integrated model using the level set approach can be used to predict the evolution phenomena with good accuracy for EB-PVD process. The validation has been performed against experimental results for microstructure features of EB-PVD deposition layers. It was found that there is good qualitative agreement between simulations and published, experimental results in the case of YSZ deposition on the flat work-piece with rotation. For YSZ layers deposited in high rotation speed, the amplitude and the pitch of the ‘zigzag’ structure in the evolution direction decreased, and the ‘vertical post’ columnar structure was achieved. In addition, the alternation of rotation direction increased the deposition rate and the pitch of a ‘zigzag’ structure. The ‘zigzag’ structures have significant implication in thermal barrier coatings, which makes the simulation model presented in the paper attractive for virtual design and process optimization. Potential directions of future research work include comprehensive experimental verification of the proposed model, which lead to future refinements of the models and predication accuracy. Simulation experiments in the paper illustrate the time and cost savings that could be potentially realized by using the model presented in the paper to reduce the experimentation cost while providing a much more scientific alternative to the prevailing practice of trial-and-error in the EB-PVD industry.