**4. Discussion**

The existing experimental results suggested that the geometric characteristic size within a certain range would affect the physical characteristics of an LPBF-fabricated porous structure, including the morphology features, relative density, microstructure, and mechanical properties. This phenomenon can be explained through the simplified thermal transmission model in a laser powder bed fusion process (Figure 10). As a classical additive manufacturing method using a powder bed, three main thermal transferring forms occur during the LPBF process: thermal conduction from molten pool to part, thermal conduction from part to substrate, and thermal radiation from part to atmosphere [30]. It is important to note that thermal conduction between the part and the powder is negligible because the thermal conductivity coefficient of the metal powder is much smaller than that of the metal part [31]. Therefore, the as-built part could be regarded as a thermal container. According to Equation (1), the energy density is inversely proportional to the scan speed. The energy density represents its thermal source strength and the geometric characteristic size in a certain range reflects its own thermal storage volume and thermal-sinking capability. These two aspects will influence the temperature distribution of the as-built part. Higher energy density means that the molten pool will receive more heat from the laser beam, resulting in higher peak temperature, longer keeping time, and decreased undercooling degree [28]. A geometric characteristic size that is too small means that the molten pool and as-built part have a poor cooling condition, and less thermal storage volume and interfacial area with atmosphere and substrate, which results in a lower cooling rate. However, the phenomenon may gradually emerge when the geometric characteristic size is small enough (<1 mm).

**Figure 10.** Diagram of the thermal transmission model in the selective laser melting process. (**a**) Small geometric characteristic size; (**b**) large geometric characteristic size.

As shown in Figure 10, a higher energy density means that the molten pool has less surface tension and better wettability, absorbing more powder. Due to the layer-wise manufacturing method, the side surface generally bonds a large quantity of incompletely melted particles, which may need post treatment for further applications. Based on the above analysis, a geometric characteristic size that is too small may more easily cause the as-built part to gain more obvious size errors under the high-scan-speed conditions. This is because the newly forming part will remain at a high temperature for a longer time under the poor cooling condition. Then, the side wall of the part will bond more particles, resulting in an obvious size error. The relative density of the LPBF-built part is associated with pore deficiency. Too high a temperature of the molten pool with too high energy density will cause the evaporation of elements, generating pores with rounded shapes. Too high a cooling rate of the molten pool with too low an energy density will cause the incomplete fusion of powder, also generating pores with sharp shapes and incompletely melted particles. In addition, the poor cooling condition relating to too small a geometric characteristic size will aggravate pore generation under the condition of high energy density.

It is known that for metal materials, hardness is closely related to the microstructure. There is also a loose corresponding relationship between hardness and strength, namely, high hardness corresponding to high strength. High hardness is attributed to the refinement of the α/α' phase and β phase caused by rapid solidification, and much dislocation generation caused by residual stress in additive-manufactured Ti–6Al–4V parts [32]. The elastic modulus is associated with the residual stress level to a certain extent [33]. Based on the proposed thermal model, the higher energy density and small geometric characteristic size cause more thermal input and a poor cooling condition, respectively. This will weaken the grain refinement strengthening effect and decrease the residual stress, causing a decline in hardness and strength. A relatively low scan speed and small geometric characteristic size correspond to a low elastic modulus, which is partially due to the decrease of the residual stress [32].

As is known, the relative density is associated with the pore deficiency, and the porosity is associated with the size of the as-built struts of a porous structure. As shown in Figure 11, different from the porous structure with an *L*s value of 1.4 mm, the relative density and porosity of the porous structures with an *L*s value of 0.6 mm and a *v* of 700 mm/s were obviously less than those for the structures with a *v* of 1900 mm/s. This finding indirectly indicated that the struts of the porous sample with an *L*s value of 1.4 mm achieved more pores and larger positive size error under the *v* of 700 mm/s. In other words, a porous structure with an *L*s value of 0.6 mm and a *v* of 1900 mm/s had a better forming quality than did those with a *v* of 700 mm/s. These experimental results are in accordance with the results shown in Figures 3 and 4, confirming the validity of the above analysis to a certain extent.

**Figure 11.** A comparison of the relative density and porosity for samples in the verification experiment.
