Finite element model for unified EB–PVD machine dynamics

Abstract

The present paper presents finite element models to describe machine dynamics, such as electron beam (EB) generation in an EB gun, EB scanning on the surface of an ingot, melting process of the ingot, and vaporisation and deposition on the surface of a substrate during EB-PVD process. Based on physical models, the finite element models relate the input power to the EB gun and the temperature profile of the ingot surface, the temperature profile to the shape of vapour plume, and the vapour distribution to the coating thickness. The two deposition process models have been investigated for predicting the coating thickness and compared to experiments performed for simple shaped substrates. With preliminary studies, it is found that the presented models are suitable for a cost efficient computation and can aid in assessing process parameters.

Simulation model for an EB-PVD coating structure using the level set method

“…Here the speed of evolution means the increment of surface thickness in unit time, which is calculated from the thickness increment after one simulation iteration. From the machine dynamics model the evaporated mass a v and the beam collimation parameter n are obtained; and from the substrate kinematics model the two angles, ϕ and θ; and the distance r are obtained (see [13]). It should be noted that ϕ and θ represent the dependency of the speed function F on the geometric relation between a substrate and a vapor source.…”

“…The unified model of EB-PVD process developed by the authors [13] uses a finite element model to combine various dynamic aspects of an EB-PVD machine as well as deposition process and substrate kinematics. As shown in Fig.…”

“…In this paper, the level set approach is extended into the EB-PVD process to develop computational models which are efficient compared to MC techniques. First, an FEM-based unified EB-PVD machine dynamic model from our prior work [13] is summarized in Section 2. Section 3 illustrates the level set method and the derivation of an evolution speed function in the EB-PVD process.…”

“…The kinetics of evaporation and vapor transport as well as deposition rate were simplified in reduced order models and a macroscopic balance was established between the intermediate process parameters, such as ingot temperature and deposition rate, and the input parameters [12]. The authors have developed a simulation tool to predict the coating thickness for simple geometric shapes such as the flat plate and the cylinder coated with titanium and tungsten, respectively [13,14]. The microscopic process of coating growth, however, cannot be accurately predicted using these models for the EB-PVD process.…”

Evaluation of mixed oxide formation and sintering behavior in thermal barrier coatings on nickel‐based superalloy

“…Therefore, different failure mechanisms can cause damage to this coating system. Some of the most emergent mechanisms in plasma sprayed thermal barrier coatings are bond coat oxidation and thermally grown oxide (TGO) formation [9][10][11], top coat sintering [12], phase transformation in layers [13][14][15], spinel formation [16,17] and residual stress [18,19]. Experimental studies show that damage to coating commonly results from the combination of different failure mechanisms, which are caused by mechanical, thermal, and metallurgical effects.…”