Technical paperFinite element modeling of the electron beam welding of Inconel-713LC gas turbine blades
Introduction
Nickel-based superalloys are the materials of choice for hot section components of gas turbines, such as turbine discs, blades and vanes due their good creep resistance, tensile strength, and corrosion resistance. For aerospace applications, joining of the Ni-based superalloys is done by fusion welding process, such as gas Tungsten arc welding (GTAW), laser welding, and EBW. Among these techniques, EBW allows for achieving high-power density (5 × 108 W/cm2) at a small area (10−7 cm2) ensuring very small FZ and HAZ and, therefore, low-weld distortions. Moreover, the vacuum condition, which characterizes the EBW, avoids material contamination with air and results in high-quality welds making of EBW the most preferred technique for aero-engine [1]. However, in EBW as in any fusing welding operations, the presence of significant temperature gradients between the base metal, HAZ and FZ results in the production of residual stresses and distortions. Moreover, in the case of Ni-based superalloys the complex chemistry inherent to these alloys widens the solidification temperature interval and may result in cracking. The combination of residual stresses and solidification stresses may result in hot cracking after EBW [2]. The high cost of the material and the process does not allow for trial and error approach in optimizing the process and, therefore, modeling and simulations approaches are being used increasingly with continuous improvement brought on better heat source modeling and more reliable predictions on the influence of process parameters on the distribution of residual stresses and distortions. Finite element (FE) simulations have been the most common numerical method and many papers have been presented over a period of time to simulate the welding process [3], [4], [5], [6], [7], thermal [8], [9], and mechanical analyses [5], [8], [10], [11], [12].
The definition of welding process as a thermo-metallo-mechanically phenomenon essentially implies that there are various thermal, metallurgical, and mechanical processes happening simultaneously in the FZ and HAZ throughout the heating and cooling phases [12]. In EBW process, the incident beam of electrons hitting the workpiece evaporates the underlying material which results in the formation of a narrow and deep vapor cavity called “keyhole” [12], [13]. The heat flux distribution into the keyhole during EBW is a complex interaction between the high-energy density electron beam and metal in liquid or vapor state at different temperatures. Many analytical and numerical models of heat transfer and fluid flow have been developed in the literature. Wei and Shian [14] proposed an approximate three-dimensional heat-conduction model by satisfying interfacial energy and momentum balances at the keyhole cavity. Rai et al. [15] calculated the asymmetric keyhole profile through energy balance at keyhole walls considering multiple reflections of the laser beam within the keyhole, and the three-dimensional heat transfer and fluid flow in the weld pool. Rai et al. [16] suggested an energy balance model considering the variation of keyhole wall and calculated the fluid flow and heat transfer during EBW. He et al. [17] established a transient, three-dimensional numerical heat transfer and fluid flow model based on the solution of the equations of conservation of mass, momentum, and energy to calculate the temperature and velocity fields in the weld pool. Kaplan [18] and Zhao [19] calculated the asymmetric keyhole profile at high-welding speeds by considering energy balance at the keyhole walls. He and DebRoy [20] proposed a transient, three-dimensional numerical heat transfer and fluid flow model based on the solution of the equations of conservation of mass, momentum, and energy to calculate the temperature and velocity fields in the weld pool. Sudnik et al. [21] approximated the three-dimensional fluid flow in the weld pool by two-dimensional flows in horizontal and vertical planes. Zhang et al. [22] analyzed numerically the evolution of the weld pool, the keyhole shape and dimensions, and the fluid convection and temperature profiles in a plasma arc welding weld pool.
While many numerical models for heat transfer and fluid flow have been developed for keyhole mode laser and plasma arc welding [14], [15], [16], [17], [18], [19], [20], [21], [22], comprehensive heat transfer, and fluid flow models representing EBW is poorly defined due to complex interactions in liquid or vapor state at different temperatures. In addition, numerical models of keyhole of EBW available in the literature are often applicable to a limited range of welding parameters and/or materials. Therefore, many authors have simplified the calculation of thermal field by considering a pure thermal conduction model. Mazumder and Steen [23] proposed a three-dimensional heat conduction model for the calculation of temperature profiles in the workpiece. Huo et al. [24] developed a three-dimensional finite element model (FEM) for calculating EBW temperature using heat conduction model and stress fields of thin plates of BT20 Titanium alloy. The distortion and residual stresses induced during EBW of two Inconel 718 plates were predicted using a three-dimensional FEM and experimentally validated by Lundback [25]. He considered a combined conical and double ellipsoid heat source to model the heat input of the electron beam. Lacki et al. [8] performed simulation of EBW of 30HGSA steel tubes and employed empirical equation suggested by Lankalapalli et al. [26] to determine the amount of heat produced by electron beam. Although the EBW of several materials, such as Steel, Titanium, and Ni-based superalloys including Inconel-718 have been well investigated and reported [8], [24], [25], there are very limited data and information available on EBW simulation of Inconel-738LC in the open literature. A few number of EBW simulations have taken into account the industrial size of components with non-symmetric geometrical effects. It is worth mentioning that several studies in the aforementioned literature, have not modeled the heat source based on the data generated from experiments. It can reduce the level of heat source modeling accuracy, which is believed to have a significant influence on the prediction of residual stresses [27], [28].
In this work, a comprehensive three-dimensional non-linear FEM of EBW of Inconel-713LC nickel-based super alloy gas turbine blades has been developed in ABAQUS to determine the temperature, thermal and residual stresses, and distortions. Both main and cosmetic welding pass have been considered. A particular effort has been made to determine an accurate model for the heat input through experimental analysis. Thermal and residual stresses were precisely measured in HAZ and FZ to determine the regions that are highly vulnerable for hot and cold cracking, respectively. Moreover, an extensive sensitivity analysis was carried out to understand the correlation between the EBW parameters and residual stresses and consequently distortions.
Section snippets
Material and part geometry
Inconel 713LC is an investment cast low-carbon nickel-based alloy that is ideally suited for gas turbine blades in hot sections of power generation and aircraft gas turbines. Inconel 713LC offers outstanding resistance to thermal fatigue and good castability while offering exceptional rupture strength at 1700 °F (927 °C) [17], [29].
Fig. 1 (a) illustrates the schematic view of the welded blades and the weld line. The blade length is 32.5 mm.
Lindgren [31], [32] and Dong [33] have both shown that
Heat transfer governing equation
The heat transfer governing equation (Fourier's law), for the weld joint in a coordinate system with a positive x-direction moving electron beam can be written as:where x, y, z are the Cartesian coordinates; ρ is the density of the material; cp is the specific heat capacity; k is the heat conductivity; T is the transient temperature; is the heat source intensity in the material. The density of the material, specific heat capacity, and heat conductivity
Structural analysis governing equations
In the present investigation, the Johnson–cook material model equation (Eq. (7)) was used to describe the plastic material properties of the material [47].
In above equation, A represents the yield stress value at room temperature. B and n are coefficients which define the shape of the plastic curve and generally are found by material characterization. The second multiplier equation is related to strain rate effect (ε). The third equation which is important in
Thermal analysis
Fig. 5 illustrates the temperature distribution of the EBW at an arbitrary time step. In this picture, the temperatures above melting point at 1315 °C are shown in yellow and those below 145 °C are shown with grey color. It can be seen that the EBW effect on the part is localized to a narrow band. Due to the asymmetric shape of the parts, mainly caused by positioning of the blades, the temperature distribution is asymmetric.
To better distinguish the weld pool, elements with temperature higher
Experimental measurement of residual stresses
In order to verify the accuracy of the FEM calculations, an experimental determination of the residual stress for the blades after welding was carried out using the hole drilling method (HDM). This method is well standardized and widely used by industry to measure residual stresses [50]. One pair of welded blades has been used for residual stress measurements. Residual stress measurements were made in the FZ and HAZ by a certified laboratory (Stresscraft Ltd.). The hole diameters were about 1.8
Sensitivity analysis
To reduce the level of tensile stresses, known as one of the main cracking factors in FZ and HAZ, it is imperative to quantify the influence of the weld parameters on residual stress generation and distribution. The primary processing parameters in the EBW are the beam current, accelerating voltage, focusing lens current (focal beam spot size), welding speed, and vacuum level [31], [34]. The weld joint quality depends on the proper selection of these parameters that influence residual stresses,
Summary and conclusion
An uncoupled three-dimensional FEM were developed to predict the stresses and distortions generated during and after EBW of gas turbine blades. On the basis of cross-sections obtained from optical macrographs, the use of a conical heat source with Gaussian distribution along with a hollow sphere with linear distribution was adopted. The model was validated by experimental analysis (HDM) and a published numerical analysis [2]. Both main weld and cosmetic thermal cycles were considered to
Acknowledgments
Support from Siemens Canada Limited and Mitacs are gratefully acknowledged.
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