## 1 Introduction
Nevertheless, the literature mainly focuses on residual stresses, microstructure evolution and fatigue resistance. The parts manufactured by SLM are prone to a significant amount of induced residual stresses because of the high temperature gradients involved in the process: This phenomenon is amplified in the case of Ti6 Al4V, due to its poor thermal conductivity. Thus, residual stress increases with the increasing number of layers [18]. Moreover, the scan strategy was proven to have a great influence on the residual stresses: The authors of [19] observed the correlation between the scan length and the residual stresses intensity, while [20] observed that residual stresses are larger along the scan direction than the perpendicular one, due to the larger thermal gradient. Since residual stresses originate from thermal gradients, the typical way to relieve them after the SLM process is a high-temperature stress-relief heat treatment [21]. The fatigue properties of as-built Ti6 Al4V are similar to those of cast and wrought material, even without a HIP treatment [14]. Obviously, the fatigue life of AM parts increases when the surface-finishing level is enhanced, since the fatigue is a surface-induced critical phenomenon; then AM components need surface-finishing operations before service [22]. Thus, the low surface quality is one of the major challenges for AM industrialization. Milling and sandblasting are common solutions, but they have some drawbacks: SLM products typically have complex geometry; thus, the geometry freedom is lost when a machining toolpath must be planned. Meanwhile, sandblasting has lower repeatability and surface-finishing accuracy, being a manual operation that depends on the operator's skills. In such a scenario the barrel finishing (BF), which belongs to the family of mass-finishing technology, showed improvements of the mechanical performance of SLM parts [23]. It is typically used for finishing operations, from radiusing and deburring to very fine finishing. This technique consists in loading a charge composed by the components to be finished, media, water and compound within a rotating barrel: The relative motion between the charge components permits the micro-removal of the material performing the finishing operation [24]. The fixturing of the parts during the process is not necessary and therefore it is suitable for components in a variety of sizes, shapes and materials. Moreover, it requires a low investment cost, as well as very low maintenance costs [25]. For these characteristics, it is suitable for the finishing of AM parts [26]. The abrasive action is generated by the rotation of the barrel: As the barrel rotates, the charge is moved upward, until the force of gravity overcomes the tendency of the mass to stick together, and a layer slides down [27]. Depending on the filling and the rotational speed, six motions take place: sliding, slumping, rolling, cascading, cataracting and centrifuging [28]. Only two of these motions, i.e., rolling and cascading, permit a continuous flow, in the form of avalanches, providing the desired soft mechanical action of BF. Hence, adequate process parameters must be chosen. No theoretical model can help in this step, because the process parameters strictly depend upon the charge characteristics. The different motions can be described through the Bed Behavior (BB) diagram which is a map of the attainable motions as a function of the filling percentage and the rotational speed [28]. This BB diagram must be developed experimentally for each charge. The present study aims to quantify the improvements on the static mechanical properties of SLM Ti6 Al4V parts achievable with thermal treatments and BF finishing operation, thus acting both on residual stresses and surface finish quality levels. The specimens were fabricated in three different directions: vertical, horizontal and diagonal.