## 1 Introduction  
Metallic additive manufacturing (MAM) is a family of technological processes where metallic components are manufactured by the successive deposition of cross-sections (or layers) of the final part until it is built [1]. This classification encompasses a considerable variety of processes, varying in complexity, productivity and cost; the present study focuses on direct energy deposition (DED), a process where the feedstock, which may be powdered (DED) or a wire (wDED) metallic compound, is melted by a heat source as it is being inserted into the melting pool [2]. The heat-source is usually a solid-state laser or a fibre laser [3], although an electron beam may be employed. In order to prevent corrosion phenomena, a localised inert atmosphere is created by the coaxial ejection of an inert gas--typically argon. DED technologies may be compared to selective laser melting (SLM), another well-established MAM process, which produces parts through the successive melting of evenly spread metallic powder layers: at each cross-section, a thin coat (usually around 30 um is spread by a powder roller or rake) before the heat source melts the powder as it is diverted through a system of mirrors to follow the cross-section of the built part. While DED features increased productivity at the cost of decreased part accuracy and surface finishing [4], often being named a near-net shape process [5], SLM is capable of producing more complex geometries, as it not only has better dimensional fidelity but also is capable of producing support structures [6]. Due to the aforementioned characteristics, SLM is capable of producing structural components with geometries of extreme complexity, such as implicit surfaces or internal porosities demanded by the aerospace [7] and biomedical [8] industries. However, due to the absence of a powder bed, DED is capable of depositing in existing surfaces with complex shapes, granting it the flexibility required for repairing applications [9] and surface cladding [10]. DED processes feature a considerable amount of processing variables, including the laser power, powder feeding rate, laser scanning speed, carrier gas flow rate, shielding gas flow rate, nozzle angle and nozzle-to-substrate distance, among others [2]. Furthermore, complex parameters may be analysed: researchers [11] have indicated a total of fourteen relevant dimensionless numbers that may be obtained to ascertain the deposition quality, efficiency and productivity; additional, non-dimensionless variables may be computed from the process parameters [2], translating them into concepts with physical significance that aids the development of optimised process parameter windows. The current work mentions the energy density \(E\),  
\[E=\frac{P}{v_{s}\times d_{s}} \tag{1}\]  
in which \(P\) is the laser power, \(v_{s}\) is the scanning speed and \(d_{s}\) is the laser spot size. The successful production of components through this technology thus revolves around the optimisation of the aforementioned variables for each material-substrate combination and its subsequent analysis, a process common for both DED and SLM technologies that is often expensive and time-consuming as it is based on trial-and-error depositions [2]. DED has already been used in depositing nickel-based super alloys, such as Inconel 625 [12; 13] and Inconel 718 [14], 316L stainless steel [15], tool steels, such as AISI H13 [16], as well as in developing functionally graded materials (FCMs), which are components whose chemical and/or conditions show a spacial variation across the component [17]; SLM, on the other hand, has also been used to successfully deposit precipitation-hardened steel, such as 17-4 PH [18], Ti6 Al4V [19], 316L stainless steel [20], nickel super alloys [21] and aluminium alloys [22], among others.