Towards computational modeling of temperature field evolution in directed energy deposition processes

In modeling and simulating thermo-mechanical behavior in a directed energy deposition process, it often needs to compute the temperature field evolved in the deposition process since thermal history in the deposition process would affect part geometry as well as microstructure, material properties, residual stress, and distortion of the final part. This paper presents an analytical computation of temperature field evolved in a directed energy deposition process, using a single-bead wall as an illustrating example. Essentially, the temperature field is computed by superposition of the temperature fields generated by the laser source as well as induced from each of the past beads, where the transient solution to a moving heat source in a semi-infinite body is applied to describe each individual temperature field. For better characterization of cooling effect (temperature contribution from a past bead), a pair of positive and negative virtual heat sources is assigned for each past bead. In addition, mirrored heat sources through a reflexion technique are introduced to define the adiabatic boundaries of the part being built and to account for the substrate thickness. In the end, three depositions of Ti-6AL-4V walls with different geometries and inter-layer dwell times on an Optomec® laser engineered net shaping (LENS) system are used to validate the proposed analytical computation, where predicted temperatures at several locations of the depositions show reasonable agreement with the in situ temperature measurements, with the average prediction error less than 15%. The proposed analytical computation for temperature field in directed energy deposition could be potentially used in model-based feedback control for thermal history in the deposition, which could affect microstructure evolution and other properties of the final part.