## 1 Introduction  
In recent decades, additive manufacturing (AM) technologies, also recognized as three dimensional (3D) printing, has attracted significant attention in different industries [1; 2]. In principle, in all-metal AM processes, at first, a solid model is sliced in multiple layers to generate a tool path for the printing machine. Thereafter, the 3D component is produced in a layer-wise process according to the sliced model data. In addition to the sliced model, two main elements are required to build a part: a feedstock material (metal powder or wire) and a heat source, which can be a laser, electron beam or electric arc [3]. In general, AM systems are categorized into two different classes: powder bed systems and powder/wire feed systems [4; 5]. In powder bed systems, a layer of powder is spread on the building platform or on the previously solidified layer and is selectively fused via an energy source that can be either electron beam or laser beam [6; 7; 8]. The ability to produce high-resolution features and internal channels, as well as precision dimensional control, are considered the main advantages of powder bed AM processes [5; 9; 10]. In contrast, in powder/wire feed systems, the material is fed directly inside a melt pool which is already formed by a focalized heat source on the substrate or on the already deposited layer. Directed energy deposition (DED), as a material feed process, uses a focalized heat source, that can be a laser or an electron beam, and a material which can be powder or wire while being delivered directly into the melt pool. It should also be highlighted that in the literature different names are generally reported for this process [11]. A summary of these names is listed in Table 1.  
In the DED process the deposition pattern is defined by the relative motion between the substrate and the deposition head. This motion can be obtained by moving only the deposition head, only the substrate, or both substrate and deposition head. The method used mainly depends on the size and the geometry of the substrate [24]. In particular, in the laser-powder DED process, which is known as the most versatile DED process, the powder feeding can be implemented by means of either a single nozzle, coaxial nozzle, or multi-nozzle configuration. The laser-powder DED process has gained considerable interest in recent years thanks to the possibility of repairing parts and production of functionally graded materials (FGM) by varying the alloying element content [25]. In addition to the abovementioned merits of this technology, by using the laser-powder DED process it would be also possible to design specific alloys through the in situ alloying process. In fact, it is possible to deliver various powders into the melt pool simultaneously and, as a consequence, achieve a new composition after solidification. Moreover, a high deposition rate, as well as a rather wide process window, make this process very promising, with respect to the other AM processes, to be employed for the production of large components. These flexibilities of the DED process in the production of net-shape parts and repair of high-value components have broadened its application in various sectors such as aerospace, transportation, medical, and defense. Despite the aforementioned merits, the DED process has a low powder efficiency and final rough surface that should be machined after the building process. Furthermore, previous works have shown that the thermal history of a part produced via the DED process has a marked effect on the microstructure and mechanical performance of components [26; 27; 28]. Therefore, the quality of DED parts is mainly defined by the building parameters used during the process. It is well-known that a large number of parameters can be varied in DED, and these include laser power, scan speed, powder feed rate, building atmosphere, deposition pattern, and many others.