Thermo-mechanical model development and validation of directed energy deposition additive manufacturing of Ti–6Al–4V
Introduction
Directed energy deposition (DED) [1] is an additive manufacturing process that creates parts through the layer-by-layer addition of material. DED uses a high intensity energy source, such as a laser, to create a melt pool into which metal powder or wire is injected. The melt pool follows a pattern to fill each layer, progressively building the part. Several processes are included in this standard classification, such as laser powder forming, laser engineered net shaping (LENS), direct metal deposition, and laser consolidation. The resulting complex thermal history influences the microstructure, material properties, residual stress, and distortion of the final part. In an effort to understand these phenomena, many researchers have used finite element analysis (FEA) to model the DED process and study its effects on the part [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17].
FEA modeling of DED is inspired by weld modeling, since it is a similar process that has been studied extensively [18], [19], [20]. Although many of the weld modeling studies are directly applicable to DED modeling efforts, the convection models used are not applicable. Some weld studies have achieved useful results by neglecting convection while others have applied free convection uniformly on all exposed surfaces. These approaches lead to small errors in weld modeling because of the small amount of filler material relative to the substrate, which allows most of the heat to be conducted away from the bead into the parts being joined. In contrast, filler material makes up the majority of a part built using DED, resulting in longer processing times and higher temperatures that allow for a greater amount of heat loss through convection. Consequently, greater errors can occur from inaccurate convection models in DED simulations. Complex convection models are required because of the inert gas jets often used to protect the laser optics, to shield the molten material from oxidation, and to aid in delivering powder to the melt pool. The heat transfer literature demonstrates that these types of jets create localized forced convection that is influenced by a variety of factors [21], [22], [23].
The literature shows inconsistent implementation of convection in DED models. Heat loss due to convection is assumed negligible and excluded in some models [24], [25], [26], [27]. Convection is incorporated in other models by assuming it is uniformly distributed over all surfaces and equal to free convection in air (≃10 W/m2/°C) [5], [6], [10], [28], [29], [30], [31], [32], [33] while others have applied a higher uniform convection [34], [35], presumably to account for the greater amount of surface convection caused by the inert gas jets. Some researchers have considered the complexity of forced convection when modeling DED. Ghosh and Choi used the empirical equation defined by Gardon and Cobonque [36] to account for the forced convection [37]. Zekovic and co-workers included forced convection when modeling a thin wall deposition by using computational fluid dynamics (CFD) to calculate the convection acting on the surface [8]. However, there was no experimental effort to validate the CFD results for their process. Furthermore, no work has been found in the literature that develops a measurement-based forced convection model.
This work proposes that measurement-based convection is a necessary component in an accurate model of the DED process. To demonstrate this, a thermo-mechanical model for DED of Ti–6Al–4V is developed that implements measurements of the convection generated by an Optomec® LENS system. The thermo-mechanical model is validated using in situ temperature and deflection measurements, as well as post-process measurements of the residual stress of three different depositions with varying geometry and dwell times. An additional convection model that assumes free convection is developed to illustrate the importance of implementing forced convection in the thermo-mechanical model.
Section snippets
Thermal model
The DED process is simulated by first solving the thermal history of the process using a three dimensional transient thermal analysis [17]. The governing heat transfer energy balance is written as:
where ρ is the material density, Cp is the specific heat capacity, T is the temperature, t is the time, Q is the heat source, r is the relative reference coordinate, and q is the heat flux vector, calculated as:
where k is the thermal conductivity of the material.
Table 1
Calibration and validation depositions
Single track thin walls of Ti–6Al–4V are deposited using an Optomec® LENS MR-7 system with a 500 W IPG Photonics fiber laser. The deposition occurs in a chamber with an argon atmosphere that has an oxygen content of less than 15 parts per million. A 30 L/min argon jet is used to supply argon to the chamber, to protect the laser optics, and to shield the melt pool. The Ti–6Al–4V powder delivered to the melt pool is assisted by four argon jets that have a combined flow rate of 4 L/min. These four
The FEA solver
The FEA analysis is performed using CUBIC (Pan Computing LLC), a Newton–Raphson based solver developed specifically to model additive manufacturing technologies. The hybrid “quiet”/inactive element activation method is used to simulate the deposition of material during the DED process [39]. The model initially includes all the elements in the substrate. Before each layer is deposited, its elements are introduced into the set of equations. When the elements of a layer are first introduced, they
Simulation cases
Table 3 presents the convection models used to simulate each case to illustrate the impact of the convection model on the simulation results. The forced convection model is developed from measurements of the distribution of h (Appendix A) and is presented in Fig. 6 for a single wall deposition (Case 1 or 3) when it is half complete. This convection model is independent of the deposition material. Fig. 6 presents the distribution of the value of h acting on a single wall deposition (Case 1 or 3)
Thermal history
Fig. 7 presents the simulated temperature distribution at the middle of each deposition using the forced convection model. The deposition of a single wall with no dwell between layers (Case 1) generates the highest temperature, since the heat is input quickly and the mass of the deposition is relatively small. The deposition of a second wall with no dwell (Case 2) experiences high temperatures in the wall, but lower temperatures in the substrate compared to the first wall in Case 1. This is due
Conclusions
Experimentally measured surface convection is implemented into a thermo-mechanical model of DED additive manufacturing. Three different thin-wall cases, with different geometries and dwell times, are made to validate the thermo-mechanical model. To illustrate the need for the measurement-based forced convection model, a second model is developed that assumes free convection on all surfaces, which is a common approach used in the literature.
Comparisons between in situ temperature measurements
Acknowledgments
J.C. Heigel is supported by the National Science Foundation under Grant No. DGE1255832. This work is also supported in part by the Office of Naval Research, under Contract No. N00014-11-1-0668. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Office of Naval Research.
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