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Purpose The purpose of this paper is to develop, apply and validate a mesh-free graph theory–based approach for rapid thermal modeling of the directed energy deposition (DED) additive manufacturing (AM) process. Design/methodology/approach In this study, the authors develop a novel mesh-free graph theory–based approach to predict the thermal history of the DED process. Subsequently, the authors validated the graph theory predicted temperature trends using experimental temperature data for DED of titanium alloy parts (Ti-6Al-4V). Temperature trends were tracked by embedding thermocouples in the substrate. The DED process was simulated using the graph theory approach, and the thermal history predictions were validated based on the data from the thermocouples. Findings The temperature trends predicted by the graph theory approach have mean absolute percentage error of approximately 11% and root mean square error of 23°C when compared to the experimental data. Moreover, the graph theory simulation was obtained within 4 min using desktop computing resources, which is less than the build time of 25 min. By comparison, a finite element–based model required 136 min to converge to similar level of error. Research limitations/implications This study uses data from fixed thermocouples when printing thin-wall DED parts. In the future, the authors will incorporate infrared thermal cameramore »data from large parts. Practical implications The DED process is particularly valuable for near-net shape manufacturing, repair and remanufacturing applications. However, DED parts are often afflicted with flaws, such as cracking and distortion. In DED, flaw formation is largely governed by the intensity and spatial distribution of heat in the part during the process, often referred to as the thermal history. Accordingly, fast and accurate thermal models to predict the thermal history are necessary to understand and preclude flaw formation. Originality/value This paper presents a new mesh-free computational thermal modeling approach based on graph theory (network science) and applies it to DED. The approach eschews the tedious and computationally demanding meshing aspect of finite element modeling and allows rapid simulation of the thermal history in additive manufacturing. Although the graph theory has been applied to thermal modeling of laser powder bed fusion (LPBF), there are distinct phenomenological differences between DED and LPBF that necessitate substantial modifications to the graph theory approach.« less

The objective of this paper is to experimentally validate the graph-based approach that was advanced in our previous work for predicting the heat flux in metal additive manufactured parts. We realize this objective in the specific context of the directed energy deposition (DED) additive manufacturing process. Accordingly, titanium alloy (Ti6Al4V) test parts (cubes) measuring 12.7 mm × 12.7 mm × 12.7 mm were deposited using an Optomec hybrid DED system at the University of Nebraska-Lincoln (UNL). A total of six test parts were manufactured under varying process settings of laser power, material flow rate, layer thickness, scan velocity, and dwell time between layers. During the build, the temperature profiles for these test parts were acquired using a single thermocouple affixed to the substrate (also Ti6Al4V). The graph-based approach was tailored to mimic the experimental DED process conditions. The results indicate that the temperature trends predicted from the graph theoretic approach closely match the experimental data; the mean absolute percentage error between the experimental and predicted temperature trends were in the range of 6% ∼ 15%. This work thus lays the foundation for predicting distortion and the microstructure evolved in metal additive manufactured parts as a function of the heat flux.more »In our forthcoming research we will focus on validating the model in the context of the laser powder bed fusion process.

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