Studies have shown that using a preheating system minimizes tensile residual stresses [6,7,8,9,10,11,12], therefore improving the quality of the part and reducing part premature failure during building. A 510 Watt Nd-YAG laser was used by Liu et al.  to preheat yttria-stabilized zirconia ceramics to a maximum temperature of 2500 °C and observe a reduction in vertical cracks and porosity. Ali et al.  studied the effects of baseplate preheating on the residual stress formation, microstructure, and mechanical properties of Ti6A14V SLM-built parts using up to 800 °C baseplate preheating. They reduced residual stresses by 88.3% when preheating at 470 °C; furthermore, no substantial stresses were formed when preheating at 570 °C, 670 °C, and 770 °C. Roehling et al.  used an in situ annealing approach to reduce residual stresses in 316L steel bridges fabricated by LPBF using four laser diodes as preheating devices with 1.25 kW power each and observed that preheating at 625 °C substantially lowered residual stresses. Fries et al.  built crack-free tool inserts of WC-17Co at 900 °C baseplate preheating using an inductive heating device. They obtained microstructural and mechanical properties comparable to tools produced through conventional methods. Crack-free y-tiAl parts were built at 800 °C preheating by Calprio et al. , using an induction coil that heated the entire build volume. Saewe et al.  employed a baseplate preheating method that could heat up to 800 °C to process high special steel (HSS) and built crack-free samples when using 200 °C and 500 °C preheating temperatures. Meterns et al.  investigated the effects of elevated temperatures on the microstructure and mechanical properties of H13 tool steel, where a 300 W Yb:YAG fiber laser and baseplate preheating were utilized. Parts preheated at 400 °C had tensile strengths comparable to conventionally manufactured parts. Hardness was also improved over conventional materials.
In a crack growing from an initial defect, a quick tendency towards a crack front of circular or elliptical geometry is observed. A numerical study of the fatigue propagation of an inner crack with the geometry of a small circle in a round bar showed that it propagates retaining its original shape, but as it approaches the free surface, the part of the adjacent front grows faster, finally leading to a slight distortion of such circular geometry . In round bars that contain circular inner cracks and are subjected to tensile stress, an increase of relative crack eccentricity and of relative crack diameter raises the difference between the SIF values (caused by eccentricity) at the crack point closest to the bar surface and the crack point furthest from it .
Each point P of the crack front has been marked by the angle α corresponding to the arc of the circle between the point of the crack front farthest from the free surface and the point P itself (see scheme in Figure 2).
The dimensionless SIF Y increases with the relative crack diameter d/D (Figure 6), its value being greater for the notched specimens than for the smooth ones and, within the former, it increases with the notch axial semi-axis c. Therefore, the SIF decreases with the stress concentrator factor Kt contrary to what happens in the outer circumferential cracks . The effect of the notch on the SIF rises as the crack front approaches the free surface with increasing crack diameter d/D. The SIF results are closer between the sharp notched bar (c/b = 0.5) and the circular notched bar (c/b = 1) than between the circular notched bar (c/b = 1) and the blunt notched bar (c/b = 2), and these latter ones are closer than the SIFs between the smooth bar and sharp notched bar (c/b = 0.5). The effect of the notch on the SIF can be associated with the constraint loss on the crack front produced by the notch, the constraint becoming smaller as the axial semi-axis c of the notch increases (greater lack of material in the specimen in relation to the smooth bar).
In the case of the smooth bar, the increase in eccentricity does not produce a variation in the SIF value along the crack front, because the crack is far enough away from the free surface of the bar not to be affected by it. On the other hand, for the notched specimens, a continuous increase in the SIF value is observed from the point farthest from the free surface of the bar (minimum SIF) to the point closest to it (maximum SIF). The maximum SIF and the difference between maximum and minimum SIF (caused by the crack eccentricity in relation to the bar axis) both increase with the relative crack diameter, with the relative crack eccentricity, and with the elliptical notch axial semi-axis c.
Only the points of the crack front of maximum and minimum value of the SIF (diametrically opposed) have been considered. The calculation has been performed incrementally, keeping constant the maximum crack advance Δamax (corresponding to the point closest to the free surface) and obtaining the minimum crack advance Δamin (corresponding to the point farthest to the free surface) based on the relationship between the SIFs according to Paris law : 2b1af7f3a8