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Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition ASME 2012 IMECE

November 9-15, 2012, Houston, Texas, USA

IMECE2012-88476

SIMULATIONS OF THERMO-MECHANICAL CHARACTERISTICS IN ELECTRON BEAM ADDITIVE MANUFACTURING

Ninggang Shen and Kevin Chou Mechanical Engineering Department

The University of Alabama Tuscaloosa, AL 35487

ABSTRACT

In the direct digital metal manufacturing, Electron Beam Additive Manufacturing (EBAM) has been used to fabricate sophisticated metallic parts, in a layer by layer fashion, by sintering and/or melting metal powders. In principle, EBAM utilizes a high-energy electron beam to melt and fuse metal powders to build solid parts with various materials, such as Ti-6Al-4V which is very difficult to fabricate using conventional processes. EBAM is one of a few Additive Manufacturing (AM) technologies capable of making full-density metallic parts and has drastically extended AM applications.

The heat transfer analysis has been conducted in a simple

case of a single-scan path with the effect of powder porosity investigated. In the actual EBAM process, the scan pattern is typically alternate raster. In this study, a coupled thermo-mechanical finite element model was developed to simulate the transient heat transfer, part residual stresses of alternate raster during the EBAM process subject to a moving heat source with a Gaussian volumetric distribution. The developed model was first examined against literature data. The coupled mechanical simulation is able to capture the evolution of the part residual stresses in EBAM.

KEYWORD: Electron beam additive manufacturing, Finite element analysis, Residual stresses, Thermal stresses, Transient thermo-mechanical analysis

INTRODUCTION In recent years, Additive Manufacturing (AM) using

commercially available atomized metallic or alloyed powders

with a high-energy beam heat source has been developed to fabricate complex-shaped, multifunctional, or custom designed components. Various types of mechanical components can be built with such rapid fabrication technologies through computer controlled machines [1].

Titanium (Ti) and titanium alloys are materials with outstanding mechanical properties such as low density, high strengths, good chemical resistance and excellent biocompatibility. The combination of these properties in a special structure has many potential applications in the area of medical, aerospace, aeronautics and automotive systems. Generally, fabrications of these materials with conventional techniques are difficult due to their high melting point and extreme chemical affinity, especially at elevated temperatures [2].

Electron Beam Additive Manufacturing (EBAM) technology has been developed and commercialized [3], in which metallic powders are selectively molten by an electron beam, then rapidly self cooled and solidified; the detail of the process can be found in [1]. The electron beam can provide both high energy density and energy efficiency. In addition, product material properties are claimed to be comparable or even better than parts made by conventional means. Despite extensive advantages over conventional technologies, EBAM still exhibits several process/part deficiencies [4]. Hence, accurate physical models of both thermal and mechanical behaviors are required to investigate the thermo-mechanical phenomena and determine appropriate process parameters based on process variables that may potentially be correlated to the occurrence of the deficiencies.

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However, the simulation of thermal process in EBAM is still a challenging task because of the complex heat transport and physical mechanisms induced by an interaction among thermal, mechanical, and metallurgical phenomena. The state of the art in this field is the simulation with Level-Set Method, such as Qi and Mazumder [5], Wen and Shin [6]; or Volume-of-Fluid Method, such as Choi et al [7]. These two methods can precisely capture the convection in molten pools and even the free boundary problem. However, due to substantially high computational costs and limited commercial code access, Finite Element Analysis (FEA) is still the most efficient way to simulate the EBAM process. Due to the application of metallic powders in EBAM, the effects of powder porosity cannot be neglected. It is well known that thermal properties of metallic powder materials are significantly different from those of the corresponding solid bulk material [8]. In addition, sintering takes place in the powder bed in EBAM as it is usually preheated to about 700 to 800 °C before melting the powders. Thus, the effect of sintering should be considered as well.

In the authors’ previous work [9], a thermal model was developed by finite element method, using ABAQUS software, to investigate the effects of porosity-dependent metallic powder thermal properties in the thermal process of EBAM. The heat source was modeled as a conical volumetric heat flux under the workpiece top surface and the intensity is distributed in Gaussian distribution horizontally and decays linearly with penetration depth based on the review of the work about Electron Beam Welding (EBW) [10-12]. To simulate the effect of convection in FEA, Taylor et al. [13], De and DebRoy [14] increased the thermal conductivity in the molten pool. A user subroutine coded in FORTRAN was applied to take account of the latent heat of fusion, temperature dependent and porosity dependent thermal properties of solid or powder materials, and the material state change. The porosity dependent thermal properties of the powder were modeled based on the emissivity model of Sih and Barlow [8] and thermal conductivity model of Tolochko et al. [15]. The thermal part of the thermo-mechanical analysis just succeeds the previous work.

The mechanical behaviors of EBAM parts, such as implants, were tested and numerically studied with FEA [16, 17], but the mechanical process within the powder bed during the melting and cooling procedures have not been investigated to date due to the limitation of the machine and the harsh experimental environment. Since the mechanical state in the EBAM process originates from thermal conditions, a thermo-mechanical model is very indispensable in order to obtain more thorough understanding of EBAM. Thermo-mechanical models with FEA have been widely used for the residual stress prediction in arc welding of stainless steel and carbon steel [18, 19]. The similar work were presented for EBW of Ti-6Al-4V [11] and Inconel-706 [10]. Most of them coupled thermo-mechanical analysis, which meant the heat generated by deformation was also considered. In addition, the complex viscoplastic behaviors of materials were usually simplified with rate-independent isotropic hardening or bilinear hardening model according to different assumptions from those authors. Furthermore, as the additive nature of BEAM, the technique of element activation layer by layer is required to capture the process characteristics. Zhang and Chou [20, 21] investigated

the Fused Deposition Modeling process, which consisted of the heat and mass transfer phenomena coupled with mechanical loading and phase changes by FEA using element activations to simulate the mechanical and thermal phenomena in FDM and to further anlayze residual stress and part distortion simulations.

In this research, a series of porosity effect included in thermo-mechanical FEA were conducted for multiple conditions in EBAM to simulate the effect of thermal cycles on the residual stress distribution and deformation. The residual stress distribution was initially predicted by simulations of single-pass scan at one layer and then a multi-layer raster scan. Then, the effects of thermal cycles on the residual stress distribution during one raster-scan layer and between rwo consecutive layers were evaluated by a multi-layer raster scan simulation.

MATHEMATICAL-PHYSICAL MODEL Heat Transfer Model

With the assumption of negligible molten flow during the solidification process, the governing equation of heat transport during the EBAM process is generally thermal conduction dominated [9]. The latent heat of fusion was considered in this model to trace the solid/liquid interface of the molten pool. The fraction of liquid determines how much of the latent heat of fusion is going to be included in the enthalpy calculation. The liquid fraction was determined with the interpolation between the solidus and liquidus temperatures. When the temperature droped between the solidus and liquidus temperatures, the latent heat of fusion was modeled as an additional term of the internal thermal energy per unit mass [9].

Heat Source Intensity Modeling In the EBAM process, a cavity containing metal-ion plasma

is created in the powder layer due to the material evaporation resulting from the high energy density of the electron beam. The molten material ahead is removed under the effect of vapor pressure and surface tension. Then, the electron beam penetrates deeper to form the so-called “keyhole” effect. To simulate the heat input distribution, the electron beam is typically modeled as a conical moving heat source with Gaussian distributed intensity at each depth level and the intensity decays linearly with the increase of the depth [9]. To apply the heat source in the FEA model, a user subroutine of DFLUX was developed in FORTRAN. This subroutine can read the simulation time and determine the beam center position, raster direction before each calculation, so that the domain of the volumetric heat flux can be determined. The magnitude of the heat flux at each nodule will be interpolated with the heat source equation [9].

MATERIAL PROPERTIES Properties of Solid Bulk Materials

The material in this study was Ti-6Al-4V powder with temperature dependent material properties applied. Figure 1 shows the temperature dependent density, thermal conductivity and specific heat [22] and the mechanical properties [11] below the melting point. The emissivity of Ti-6Al-4V was estimated from literature; Yang et al. experimentally calibrated the emissivity of Ti-6Al-4V as 0.7 [22]. Since this was a coupled

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thermo-mechanical analysis, heat generated by deformation was considered. Based on the studied condition, modeling of complex viscoplastic behavior was not considered and an isotropic kinematic hardening model was taken into account. Further properties not deatiled here are listed in Table 1.

Figure 1 Temperature dependent thermal and mechanical properties

Properties of Metallic Powder Layers Thermal properties of metallic powders are significantly

different from those of the solid bulk material. Research indicated that the specific heat and latent heat of fusion of powders could be considered the same as those of the solid material [4, 8, 15]. The emissivity of powder is modeled as the combination of the solid bulk emissivity and the emissivity of the gap or cavity between adjacent powder particles. The weight of each component is determined by the area fraction of the surface that is occupied by the radiation emitting holes [9]. The thermal conductivity of powders only considered the effective thermal conductivity due to thermal radiation and heat transfer through powder necks. Material State Change

The material state change was implemented using a subroutine of UMATHT. An internal state variable, working as a material index, was defined to specify the material as either powder or solid at any time frame simulated. The material index can be either 0 or 1 (0 – powder, 1 – solid). The changing criterion was: the material is molten and under cooling. The subroutine reads the material index of each node to determine the correct material properties to be assigned before each calculation. As the state change in EBAM can only be one-way (i.e., from powder to solid), the material index will be locked as 1 once the material becomes solid.

NUMERICAL MODEL IMPLEMENTATION Model Configuration

Two 3D FEA thermo-mechanical models were developed with ABAQUS to simulate the thermal process, thermal stress evolution, residual stress distribution and deformations in a single straight scan path and multi-layer crossed raster scan. Both of the melting and cooling phases were included in these

models. The preheating stage was simplified and set at as the thermal initial conditions (ICs).

In the melting phase, although these two simulations are different from each other, they share a similar idea about the model configuration within one scan (i.e. within one layer). The models were divided into two basic domains, substrate and metallic powder layer on top. Figure 2 shows the general model configuration and boundary conditions (BCs). Domain A (light) is a thin powder layer on the top of the substrate; Domain B (dark) is the substrate. As the vacuum surroundings, convection between the powder layer and environment is ignored. Hence, only radiation was considered between the powder/part and surroundings. The substrate and powder layer were assigned with a uniform temperature distribution of Tpreheat as the thermal initial condition. The temperature of solid substrate bottom was confined as a constant temperature of Tpreheat as the thermal boundary condition. For the single straight scan path simulation, the electron beam heating occurs at the top surface of a powder layer and traverses along the x-axis at a constant speed for a certain distance (6 mm in this simulation). For the multi-layer alternate raster scan, two sequential layers wee simulated and the alternate raster scan is shown in Figure 3. The raster pattern was in an area of 4 × 2 mm2 and the width of the raster was the same as the beam diameter. Since each scan (or layer) of both simulations was considered as an intermediate scan (or layer) in a continuous multi-layer part building, the substrate was considered as solid bulk which was solidified from the powder in previous melting scans. In this study, all the substrate thickness was 10 mm which is much smaller than the actual substrate thickness. Therefore, only the top section of an actual substrate was simulated; all the geometric degrees of freedom (DOFs) were confined at the bottom of the substrate. The contact between the solid bulk material and powders was assumed as the solid, since all the powders were preheated to be sintered before each scan.

After melting, it is the cooling phase. In the single straight scan simulation, all materials were simply under cooling until the temperature dropped to the room temperature. The displacement constraints at the bottom were kept due to the same reason above. The thermal boundary condition at the bottom was redefined which decayed with time from the Tpreheat of 750 °C to the room temperature. The cooling time was set as 10 hours in this simulation. In the multi-layer alternate raster simulation, there were two cooling steps; the first cooling was the heat self-balance corresponding to a few seconds break between two sequential scans for new powder layer spreading; the second one was the final cooling step to the room temperature. The time for the first cooling step was set as 10 sec which is approximately the duration for new powder spreading in the EBAM process. The thermal boundary conditions were the same as those in the melting step. The second cooling step was defined as the same as the final cooling step in the single straight scan simulation.

The element activation technique was applied to simulate the material addition in the multi-layer crossed raster scan simulation. The second layer powder was modeled at the very first beginning, but was deactivated during the melting phase of the first layer. It was later reactivated at the second melting phase and the initial temperature was also Tpreheat. Then, the

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heating started again from the same starting point with the alternate raster direction and the same raster width.

Figure 2 FEA model configuration and BCs in melting phase

Figure 3 Schematic of the alternate raster scan pattern applied in multi-layer analysis

Model Validations Due to lack of EBAM experimental results, the model

validation was conducted by simulating an electron beam welding process of Inconel-706 [10]. Ferro et al. [10] conducted the experiments of the EBW process of 5 mm thick Inconel-706 plates and developed a 3D FE model to predict the keyhole geometry and the residual stress distribution. Figure 4 shows the simulated thermal analysis results and comparisons. In the experiments, three holes were drilled at different depths from the side of the plate for three thermocouples. Figure 4-d just shows the comparison of experimentally measured data and the simulated temperature histories from the author. Figure 5 shows the simulated residual stress profiles of experimental measurements and simulations, at the center of the bead along the direction of the bead cross section, from Ferro et al. [10] and from the authors. Figure 6 is the comparison of simulated longitudinal residual stress field.

Figure 4 Simulated thermal analysis results comparisons: (a) Temperature fields from authors; (b) Temperature fields from Ferro et al. [10]; (c) simulated temperature profiles along the direction of the bead cross section.; (d) Simulated temperature histories of the three thermocouples from authors comparing to the experimental measurements.

Figure 5 Residual stress profiles of experimental measurements and simulation results from Ferro et al. [10] and from the authors at the center of the bead along the direction of the bead cross section.

Figure 6 Simulated 3D longitudinal residual stress field comparisons: a) from Ferro et al. [10]; b) from the authors.

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Table 1 Material Property List Used in Simulations. Parameters Values Solidus temperature, TS (°C) 1605 [23] Liquidus temperature, TL (°C) 1665 [23] Latent heat of fusion, Lf (kJ/Kg) 440 [23] Electron beam diameter, Φ (mm) 0.4 Absorption efficiency, η 0.9 [4] Scan speed, v (mm/sec) 400 [1] Acceleration voltage, U (kV) 60 [1] Beam current, Ib (mA) 0.002 [1] Powder layer thickness, tlayer (mm) 0.1 [4] Porosity, φ 0.3 Beam penetration depth, dP (mm) 0.1 Preheat temperature, Tpreheat (°C) 750 [1]

The thermal part of the duplicated model is fairly close to the model in the literature. The magnitude and distribution of the residual stresses are comparable. Therefore, all the results indicate that the thermo-mechanical FE model developed by the authors is capable of conducting the thermo-mechanical analysis for the process with elevated temperatures.

RESULTS AND DISCUSSION Adequate process parameters were determined for EBAM

with Ti-6Al-4V [1], such as the scan speed, acceleration voltage, beam current, layer thickness, and preheat temperature, etc., all listed in Table 1. Then, the powder layer porosity was set as constant 0.3 in this study.

Single Straight Scan Simulation A single straight scan simulation was conducted first to

investigate the thermo-mechanical phenomena for a simple condition. Figure 7-a shows the temperature field and the molten pool geometry at the end of the melting phase. The molten pool geometry is at the upper right corner with a different legend. The molten pool size is about 780 × 400 ×100 μm3 (L × W × H) with a shape tail. Figure 7-b shows the temperature profile along the scan center line from the beam center to the tail. The plateau within 1 mm length is noted due to the latent heat of fusion.

Figure 7 Simulated temperature fields, molten pool geometry and temperature profile.

The corresponding thermal stress distributions for both longitudinal and transverse directions are shown in Figure 8. Within the solidified materials, both of the components of the thermal stresses are tensile, but the magnitude of the transverse component is smaller. This may indicate that the thermal

contraction in the transverse direction is smaller than that in the longitudinal direction. The compressive stress occurs at the electron-beam front and underneath for both components. This is because the top materials were heated and expanded first, so that the material just under the powder layer was suppressed. When the temperatures dropped and contraction happened, the stress underneath released by about 20-40%, but still kept compressive.

Figure 8 Simulated thermal stress fields of single straight scan just before cooling: a) Longitudinal stress; b) Transverse stress.

Figure 9 Simulated temperature history and thermal stress histories close to the beam center point.

Figure 10 Simulated residual stress fields of single straight scan: a) Longitudinal stress; b) Transverse stress.

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Figure 9 shows the comparisons between the history of the temperatures and both thermal stress components at a point at the beam center track and close to the starting point on the top surface. It indicates that each point undergoes the compressive stress first due to the thermal expansion and then tensile stress due to the contraction after solidification. Figure 10 shows the final residual stress distributions. The stresses in the solidified materials keep almost uniformly tensile and the magnitudes increase to about 250 MPa. The stresses in the material underneath releases, except at the start and end location of the scan (being compressive). The compressive stresses extended deeper into the substrate.

Multi-Layer Alternate Raster Scan Simulation In reality, hundreds of thousands scans with alternate raster

pattern are processed to build a part in EBAM, so the thermo-mechanical model of multi-layer alternate raster scanning was developed to capture the complex temperature history and stress evolutions more close to the reality. Two scans in two layers were simulated in this task. Figure 11 shows the simulated temperature fields, the molten pool geometry and its cross section. The peak temperature is about 2570 °C which is about 100 °C higher than that of the single straight scan. The residual heat from the previous track of this scan leads to this increase. And it results in a molten pool that is longer, about 1050 μm vs. only about 780 μm in the single straight scan. However, the width and depth of the molten pool do not change too much and the magnitude still keeps the same level generally. Nevertheless, the molten pool does not have the tail-like shape any more. Figure 12 shows the simulated fields and the cross sectional view of both thermal stress components at the end of the first layer. The magnitudes of both components are similar to those in the single straight scan for both layers. The stress just under the powder is still compressive, but the magnitude has dropped almost 50% and the compressive stress goes deeper due to heat dissipation along the depth direction. The tensile stress is in the top surface layer except the beam scan front. Figure 13 shows the thermal stress field at the end of the interval between the two layers. The magnitudes of tensile stress become greater due to the cooling; the compressive stress become a litter higher, with a deeper stress zone Figure 14 shows the simulated residual stress fields and the cross sectional view for the multi-layer crossed raster scan. Both the magnitudes are close to those for the single straight scan path, but the penetration of the tensile stress zone is deeper. Therefore, the multiple scans may not change the magnitude of the residual stresses too much, but lead to a deeper tensile stress zone in the substrate.

Figure 11 Simulated temperature fields and molten pool geometry for raster scan: a) the temperature fields of layer-1; b) the cross sectional view of the field in a).

Figure 12 Simulated thermal stress and its cross sectional view.

Figure 13 Simulated thermal stress fields and their cross sectional views at the end of the break between two sequential layers: a) Longitudinal stress; b) Transverse stress.

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Figure 14 Simulated residual stress fields and their cross sectional views: a) Longitudinal stress; b) Transverse stress.

CONCLUSIONS In this research, two 3D thermo-mechanical FE models are

developed. In EBAM, the powder bed will be heated time and time again that may significantly affect stress evolutions. The major findings can be summarized as follows. 1) Since the electron beam is going back and forth with the

raster scan pattern, the residual heat in previous track increase the size of the molten pool in length from about 780 μm to 1050 μm with respect to the single straight scan and the peak temperature is about 100 °C higher than that in the single straight scan. The sharp tail of the molten pool does not occur for the alternate raster scan.

2) For a certain location in the powder layer, the stress goes to compressive first due to the thermal expansion from the lateral materials and becomes compressive due to the contraction after the solidification in both single straight scan path and multi-layer alternate raster scan pattern. The stress in the underneath keeps compressive.

3) Tensile residual stress is always in the solidified materials due to the contraction and the compressive stress extends deeper into the substrate, even to the bottom, for both single straight scan and multi-layer alternate raster scan. The maximum magnitudes for both components are about ± 250 MPa, respectively. However, the multi-layer alternate raster scan has deeper tensile stress penetration. Future work of this research will require temperature and

residual stress measurements for comprehensive model validations. Besides, the potential improvements discussed in previous work [9], the mechanical boundary conditions are to be investigated in details.

ACKNOWLEDGMENT This research is supported by NASA, No. NNX11AM11A,

and is in collaboration with Marshall Space Flight Center (Huntsville, AL), Advanced Manufacturing Team.

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