Effects of Process Parameters on Microstructure and Cracking Susceptibility of a Single Crystal Super-Alloy Fabricated by Directed Energy Deposition

As an advanced material forming method, additive manufacturing (AM) has been rapidly developed in many industry fields. Due to the non-weldability of nickel-based single crystal (SX) super-alloys and complex solidification and stress conditions of AM process, hot cracks can easily form in depositions. Previous research focused on the additive manufacturing of single-track thin-walled SX samples, while effective solutions to fabricate crack-free multi-track SX block samples are still limited. Directed energy deposition (DED) technique was used to fabricate multi-track block samples in this work. The effects of the overlapping ratio, scanning velocity, and laser power on the microstructure and cracking susceptibility were analyzed. The experimental results demonstrated that improper process parameters play significant roles in the formation of high-angle grain boundaries and large internal stress, both of which will increase the cracking susceptibility. Crack-free SX multi-track block was successfully fabricated after adjusting the process parameters. These findings provide a guide to reduce the cracking susceptibility by controlling the process parameters, which aids in fabrication of large-scale crack-free SX blocks through DED technique.


H I G H L I G H T S
• The crack-free multi-track nickel-based single crystal superalloy block with 15 layers was successfully fabricated. • Improper overlapping ratio is the main reason for the occurrence of misoriented grains in the overlapping region • Appropriate laser power and scanning velocity effectively reduce the cracking susceptibility.

G R A P H I C A L A B S T R A C T
a b s t r a c t a r t i c l e i n f o

Introduction
Nickel-based single crystal (SX) superalloys are important materials for aeroengine SX turbine blades due to their excellent properties, such as high creep resistance, low oxidation rate, and high yield strength Materials and Design 198 (2021) 109296 [1,2]. With the development of nickel-based SX superalloys, the physical properties of SX superalloys are more and more demanding. Subsequently, a variety of precious metals elements, such as Hf, Re, and Ru, have been gradually added to the materials to improve their elevatedtemperature mechanical properties [3][4][5][6]. In general, the SX blade manufacturing process is extremely complicated. Traditionally, directional solidification and spiral crystal selection have been commonly used for the production of SX blades [7][8][9], both of which have a long production line, low productivity, and plenty of cast molds. Each SX aeroengine blade has a high cost. Thus, the total cost for updating a damaged or producing a new aeroengine can reach millions of dollars given that an aeroengine generally contains several hundred turbine blades [10][11][12]. Some researchers have recently developed Re-free (René N500) and low Re (René N515) nickel-based SX superalloys as a mean to reduce the production cost of SX blades [13][14][15]. With the development of technology, additive manufacturing (AM) has attracted great attention and is considered as an effective way to reduce the cost of SX blades [16][17][18]. In 2001, Gäumann et al. used laser metal forming (LMF) technique, as known as the directed energy deposition (DED) technique, to successfully fabricate the single-track thin-wall SX deposition by adjusting laser power and scanning velocity to obtain the suitable solidification condition for the growth of SX structures [17]. Nowadays, single-track thin-wall SX deposition with over a few centimeters in height can be fabricated by AM without any challenges, to which process models with reference values have also been reported [19,20]. However, single-track thin-wall depositions have reflected the width size limits, which has placed great restrictions on the repair and manufacturing of turbine SX blades. Since the track overlapping can easily increase the width, some researchers have tried to fabricate multitrack SX deposition by AM [21][22][23]. However, many cracks were detected in multi-track depositions due to the difficult weldability of the nickel-based SX superalloys [24] and the complex solidification and stress conditions of multi-track depositions [25] (Fig. 1). Fig. 1a shows the superalloys that have already been used in AM experiments [21][22][23][24][26][27][28]. SX superalloys must maintain a considerable number of strengthening phases (γ') to maintain optimal performance at high temperatures, of which Al and Ti are mainly used to form γ' (Ni 3 (Al,Ti)). Thus, the Al + Ti contents in nickel-based SX superalloys are normally maintained over 5.5 wt% [31]. While alloys with >4 wt% of Al + Ti contents are usually considered to be non-weldable because the increase of Al + Ti contents will contribute to the formation of the low-melting γ-γ' eutectic [24,32]. In the AM process, a molten pool will dissipate heat through the nearby solid, thus generating the heataffected zone (HAZ) (Fig. 1b). When the low-melting eutectic structures are remelted in HAZ, there is a strong possibility to form the liquation cracks [22,33]. In addition, temperature variations in the HAZ are unstable, thus producing inhomogeneous heat deformation and then deformation constraints, which eventually results in high internal stresses or thermal stress [34,35]. For the fabrication of the multi-track deposition, track overlaps can worsen the uneven thermal deformation (Fig. 1b). Region A is in a single HAZ, while adjacent region B is in two overlapping HAZs. In other words, region A will be heated once, and region B will be heated twice. Therefore, the internal stress will be concentrated in the overlapping region [36,37], which results in more complex stress conditions for multi-track blocks than for single-track thin-walls. Furthermore, as the molten pool dissipates heat downward, it also dissipates heat laterally along with adjacent deposition. Thus, there are both longitudinal and transverse temperature gradients during the solidification process (Fig. 1b), which can easily generate high-angle grain boundaries (HAGB) [23]. At the microscopic level, the formation of HAGBs can greatly promote the generation of solidification crack and liquation crack [22,38]. All these generate multi-track blocks that tend to crack more easily than single-track thin-walls. At one point, researchers tried to reduce the cracking susceptibility by adjusting the composition of superalloys [39]. However, the requirement of nickelbased single SX superalloy on the content of γ' greatly limits the adjustable range of the Al element. Moreover, nickel-based SX superalloys have complex compositions, and the reduction in the cracking susceptibility requires many complicated calculations and experiments. All these make it impossible to fabricate SX turbine blades by AM. In 2018, Korner et al. produced a crack-free SX (CMSX-4) rod with a diameter of 1 cm and a height of 8 cm using the selective electron beam smelting (SEBM) technique, to which the results demonstrated superior high-temperature mechanical properties compared to casting SX [27]. It is worth mentioning that large size SX blocks without cracking were fabricated without adjusting any elementary composition, which proved that HAGBs and cracks could be avoided by reasonable control of technological parameters in the AM process.
At present, minimal reports have discussed the fabrication methods and process models for multi-track SX deposition by AM, especially for the DED technique. Moreover, the effects of process parameters on the solidification structures and cracking susceptibility are not clear. In our previous work, we have analyzed the causes of hot cracks, including solidification cracks and liquation cracks, and revealed the important role of HAGBs in the initiation and propagation of hot cracks [22]. In this work, we aimed on epitaxial growth of crack-free SX block samples. The effects of major process parameters, including the overlapping ratio, scanning velocity, and laser power, on the microstructure and cracking susceptibility as well as their interrelationship were revealed. The effects of process parameters on microstructure and cracking susceptibility were analyzed through a series of analytical techniques, specifically optical microscopy (OM), scanning electron microscopy (SEM), and electron back-scattered diffraction (EBSD), to which their relationships were also assessed. The process parameters were optimized, and crackfree nickel-based SX superalloy blocks were successfully fabricated with this guide.

Experimental procedure
Directed energy deposition (DED) additive manufacturing technique was employed to fabricate the Re-free NBSCS with designed chemical composition, which was named CSU-B1 and reported in a previous article [22]. The nominal composition of the CSU-B1 alloy ingot is Ni-10Co-6.5 W-6.5Al-6Cr-6Ta-2.5(Mo + Hf)-0.05Si-0.05C-0.004B (wt %). The powders and substrates for the following experiments were fabricated from the same CSU-B1 ingots. The substrates were fabricated by Central South University, and the powders were manufactured by the Central Iron & Steel Research Institute of China. The powders were manufactured by the plasma rotating electrode process (PREP).
The as-received sphere powders have a dendritic structure surface, and the powders had an average size of 69.41 ± 10.14 μm (Fig. 2c). An Ytterbium fiber laser (Nanjing Huirui Photoelectric Technology, Ltd., China; a wavelength of 1070 nm and a maximum laser power of 2 kW) was employed as the heat source for the manufacturing experiments. In addition, the laser produced a circular beam with a minimum diameter of 0.6 mm at the focal zone with a near Gaussian intensity distribution. Fig. 2a shows the schematic illustration of the DED process [22]. Fig. 2b presents the laser scanning path of block samples preparation; each layer followed a uniform S-scanning path direction. Directional solidified substrates used to fabricate block samples were disk-shaped with a diameter of 15 mm and a thickness of 2.5 mm with an upward crystal orientation of [001]. All the block samples were fabricated with 10 layers in height and 10 scanning tracks in each layer except for sample OS-1, which had a height of 15 layers. The sample OS-1 was fabricated by the optimized process parameters. Fig. 2d shows the macroscopic feature of a typical as-deposited block sample. It should be mentioned that it is necessary to obtain a molten pool with appropriate solidification conditions before the fabrication of SX block depositions. The method of obtaining suitable molten pool for the growth of SX structure is mainly based on the work of Gäumann et al., which is realized by adjusting laser power and scanning velocity [17]. In this work, when the laser power is 250-600 watts and the scanning velocity is 8-12 mm/s, the solidification conditions of the molten pool were suitable for the epitaxial growth of columnar grains. Fig. 3 shows a solidified molten pool with a laser power of 300 watts and a scanning velocity of 10 mm/s. The molten pool width (W) is 1030 μm and the height (H) is 311 μm (Note the molten pool consists of melted powders and the substrate). Although the equiaxed grains appears in the top of the deposition due to the temperature gradient drop during the final stage of the solidification, the equiaxed grains will be remelted under the next laser scanning and will not hinder the continuous growth of the columnar structures layer by layer, as has been demonstrated in our previous work [22]. Then molten pools (single track) were overlapped in order to obtain the block depositions, and different overlapping ratios (R) can be obtained by adjusting the track spacing (S). Fig. 4a shows the schematic diagram to calculate the overlapping ratio, wherein W is the width of a single track, S is the track spacing, and L is the overlapping length. The overlapping ratio is R (R= Table 1 shows the detailed process parameters with three types of samples with different numerations. Such as R 20 indicates that the sample was fabricated with a 20% overlapping ratio, and S 250-10 indicates that fabrication with a laser power of 250 W and a scanning velocity of 10 mm/s. In addition, OS-1 represents the sample fabricated by the optimized process. Fig. 4b shows the schematic diagram of measurement and calculation, where T is the height of 10 layers with one track, and there are 10 tracks in each layer. In addition, t is the average layer thickness and t = (T 1 + T 2 + T 3 … + T 10 )/(10 × 10).
The microstructural analysis samples were sectioned, mounted, polished, and etched by a mixture solution containing HCl (15 mL) + HNO 3 (10 mL) + CH 3 COOH (10 mL). The microstructures were investigated using a Leica optical microscope (OM) and a FEI Quanta 650 FEG scanning electron microscope (SEM) with an electron back-scattered diffraction (EBSD) detector. The EBSD analysis of the block samples had an accelerated voltage of 20 kV with a step size of 3 μm.

Relationship between cracking susceptibility and volume energy density
Firstly, cracks were observed in cross section, plan section, and side section views of all block samples (except OS-1). Cracks are of typical hot crack morphology, which is consistent with that observed in our previous work, including solidification cracks and liquation cracks [22], and cracks mainly appeared in the overlapping regions which could be easily observed in the cross-section view (Fig. 5a) and plan section view (Fig. 5b). Cracking susceptibility is usually reflected by the crack length/count density [40]. Samples with a large crack length/ count density indicate a high-degree cracking susceptibility. Thus, the cross section and plan section were used to get the crack length/count density of all block samples. Fig. 5 shows the sketch of the analysis of crack length density and crack count density of the deposited sample in different views. The cross section was obtained by bisecting the sample so as to avoid areas where the scanning velocity was unstable (the region of accelerating or decelerating). The plan section was from the bottom of the deposition (the first deposition layer) in order not to miss crack sources and also avoid the influence brought by the layers increasing. Fig. 5a and b   show typical metallographs of the deposited samples for analyzing the crack length/count density, Fig. 5c and d show the schematic diagrams of measurement. Where D CL is the crack length density and D CL = L/A; L is the sum of crack lengths in the statistical capture region, L = L 1 + L 2 + L 3 + … + L n ; A is the area of the statistical capture region, which is approximately the area of the cross or plain section view. All samples had cross-sectional areas of 7.994 × 10 6 μm 2 to 17.882 × 10 6 μm 2 , where the difference was observed in the deposition heights. All samples had plan-sectional areas of 23.562 × 10 6 μm 2 to 31.046 × 10 6 μm 2 . D CC is the crack count density and D CC = n/A; and n is the number of cracks in the statistical capture region.  Finally, the relationship between the crack length/count density (D CL and D CC ) and the volume energy density is shown in Fig. 6. The following equation is given to calculate the volume energy density, E V [40,41]: where E V is the volume energy density (J/mm 3 ), P is the laser power (W), S is the spacing between two central axes of two adjacent tracks (mm), v is the scanning velocity (mm/s), and t is the average layer thickness (mm). In general, there is a positive correlation between cracking susceptibility and volume energy density due to the thermal stress increases with the increase of volume energy density [40]. However, Fig. 6 shows that neither D CL nor D CC has a monotonic relationship with E V . Instead of that, three regions can be divided in Fig. 6a, which were named A1, A2, and A3, where the A2 refers to the status of low E V and low D CL , and A3 refers to the status of high E V and high D CL . A1 refers to the status of low E V and high D CL , which presents an unusual phenomenon. Samples R 20 , R 40 , and R 50 correspond to region A1, which are from the sample group R and includes R 20 , R 30 , R 40 , and R 50 , where R 20 , R 30 , R 40 , and R 50 were deposited by a laser power of 300 W, a scanning velocity of 10 mm/s, a powder feeding rate of 0.65 g/min, and different overlapping ratios of 20%, 30%, 40%, and 50%. Fig. 7 shows that sample R 30 has the highest energy density, but the lowest crack density. In addition, except the relationship between crack density and E V is not monotonous in this group, the relationship between overlapping ratio and E V is also not monotonous. It is worth mentioning that the change of the track spacing (S) will affect the stacking morphology of the depositions. With the decrease of S, the layer thickness (t) will increase, as shown in Table 1, which mainly determines the relationship between the overlapping ratio (R) and E V as shown in Fig. 7. Fig. 8 shows the crystal orientation and microstructure distributions of the samples with different overlapping ratios. On the whole, many misoriented grains and cracks were detected in R 20 , R 40 , and R 50 , while most crystal orientations of R 30 were well-aligned with a [001] orientation to the substrate except just a few stray grains as show in marked circle. Although there are many stray grains in samples R 20 , R 40 , and R 50 , the size of stray grains of R 20 (Fig. 8e) are much smaller and without obvious orientation compared with that of R 40 (Fig. 8g) and R 50 (Fig. 8h), which are similar with the misoriented grains of R 30 (Fig. 8f). Moreover, the stray grains of R 20 mainly presented in the overlapping regions, which could be identified by the track spacing (S). Combined the results in Fig. 8 with Fig. 7, it can be seen that the number of misoriented grains and crack density first decreased and then increased with the increase of overlapping ratio from 20% to 40%. Fig. 9 shows a comparison of the microstructure of the overlapping regions from the cross-section and plain section views of R 20 , R 30 , and R 40 . Equiaxed dendrite structures were observed in the overlapping region (P1 and P4) of R 20 in both the cross section (Fig. 9a) and plain section views (Fig. 9d), which corresponds to the fine grains in the EBSD analysis results (Fig. 8e). Fig. 9b and e show the columnar dendrite structures in the overlapping region (P2 and P5) of R 30 , and there were no cracks were observed. Locally oriented cellular dendrite structures were observed in the overlapping region (P3 and P6) of R 40 (Fig. 9c  and f), corresponding to the massive grains and HAGBs in EBSD analysis results (Fig. 8g).

Effect of overlapping ratio on solidification structures and cracking susceptibility
The difference of solidification structure types was caused by the change of solidification conditions, temperature gradient (G) and solidification rate (R) were considered as determinants of the solidification structure types [17,42]. With the change of G n /R, the solidification structure type also changed correspondingly (Fig. 10a), where n is the material coefficient and can be about 3.4 for SX superalloys [17]. As the Gaussian laser was used in this experiment, the energy input gradually decreased from the center of the laser beam to the edge (Fig. 10b). The temperature gradient (G Z ) distribution of the single-track molten pool exhibited a similar trend with the laser energy distribution [26]. However, when the track was overlapped, the liquid in the overlapping region dissipated heat along with the adjacent deposition, resulting in a horizontal temperature gradient (G Y ). Therefore, the vector sum of the temperature gradients was that: G≈ . Note that there was still G X , since it was too small compared to G Z and G Y , and thereby G X can be reasonably ignored [23]. When the track spacing (S) was very large, such as with R 20 , a lower temperature gradient (G) appeared in the overlapping region. Moreover, a small overlapping ratio reduced the heat accumulation, resulting in a large solidification rate (R). The ratio of G n /R thus decreased, forming equiaxed dendrite structures. With the decreasing of S, the energy input in the overlapping region increased and subsequently converted the equiaxed structures to columnar structures given that the value of G n /R was larger than K CET . K CET is a certain value of G n /R when the equiaxed grains began to transform into columnar grains or vice versa [17]. Columnar grains have preferential growth and always tend to grow in the direction of the maximum temperature gradient (G Z ), which is consistent with the preferential orientation [42,43]. Thus, the horizontal heat flow hardly affected the growth of columnar grains, as shown in Fig. 8f and Fig. 9b. The higher temperature gradient (G), such as R 40 , appeared in the overlapping region when the track spacing (S) was very small. Furthermore, the heat accumulation increased with the overlapping ratio, resulting in a small solidification rate (R). Excess G n /R results in columnar grains to cellular grains transformation. Cellular grains generally grow in the direction of heat flow [42,43], which corresponds to the direction of the vector sum of the temperature gradients (Fig. 10b), thus resulting in a large angle with a [001] orientation (Fig. 9c).
On the one hand, the appearance of different solidification structures in the overlapping region undoubtedly directly led to the generation of HAGBs (Fig. 8). According to previous work, the appearance of HAGBs prolonged the presence of residual liquid between the dendrites [38] and also increased the solidification shrinkage stress at the solid-liquid interface [22], which contributes the formation of solidification cracks. On the other hand, the HAGBs of HAZ regions will intensify the deformation constraint between grains to produce concentrated stress, which provides driving force for the propagation of liquation cracks [35]. Moreover, in this work, cracks were always captured with stray grains (misoriented grains), which further proved the promotion of HAGBs for the generation of hot cracks ( Fig. 8 and Fig. 9). Therefore, the overlapping ratio mainly affected the solidification conditions (the value of G n /R) of the overlapping region and determined the solidification structure types. Small (20%) overlapping ratio resulted in the transformation of columnar structures to equiaxed structures and excessive overlapping ratio (≥ 40%) produced cellular structures, both of which formed HAGBs, which increased the cracking susceptibility.

Effect of scanning velocity on solidification structures and cracking susceptibility
Scanning velocity plays a significant role in cracking susceptibility. The region A3 in Fig. 6a refers to the status with high E V and high D CL . Firstly, the scanning velocity has a direct influence on the average layer thickness (Fig. 11a) and E V (Fig. 11b). With the increase of the scanning velocity, the average layer thickness significantly decreased, though the E V increased. In general, the increase in energy density elevated the produced thermal stress, which increased the cracking susceptibility [33,40]. In fact, the relationship between the crack density and the energy density is not monotonous, as evinced by a comparison of Fig. 11c and d to Fig. 11b.  The sample deposited with a scanning velocity of 10 mm/s had the second-highest energy density, but the smallest crack density. The crack density first decreased and then increased with the increasing scanning velocity (Fig. 11c and d). Since the scanning velocity determines the duration of the laser energy at a certain position, it has a decisive effect on the solidification rate (R) of the molten pool, such that the solidification structures will also be affected. Fig. 12 shows the microstructure of primary dendrites in the center of tracks of the samples with different process parameters, which is from the plan section of the deposition's bottom. The area method was used to calculate the spacing of primary dendrites, as shown in the following equation [44]: where λ 1 is the primary dendritic spacing (μm), A is the area of the region being counted (μm 2 ), and N is the number of primary dendrites (N > 900). The cooling rate and solidification rate can be estimated by the following equations [45][46][47][48][49]: where △T 0 is the solidification interval (K), D is the liquid diffusivity (m 2 /s), Γ is the Gibbs-Thomson coefficient (m·K), k is the partition coefficient (k = 0.8), G is the temperature gradient (K/m), R is the solidification rate (m/s), and V is the cooling rate (K/s). These thermo-physical parameters for estimating the cooling rate are shown in Table 2. The values of the cooling rate corresponding to the different scanning velocities can be estimated by the primary dendritic spacing values. Fig. 13a indicates that the value of primary dendrite spacing was greatly affected by the scanning velocity as compared to the laser power. Fig. 13b shows the relationship between the scanning velocity and cooling rate. The cooling rates of the samples deposited with a scanning velocity of 8 mm/s were within 1600 K/s. The cooling rates increased to 3400 K/s when the scanning velocity increased to 10 mm/s. The cooling rates even increased to 7600 K/s at a higher scanning velocity of 12 mm/s. These indicate the dependence of the scanning velocity on the cooling rate. In general, the excessive cooling rate significantly increases the internal stress [50], thereby resulting in cracking as a way to release the internal stress. Based on this information, the degree of the internal stress can be judged generally based on the crack size (Fig. 14a, d, and g). Fig. 14 shows the microstructure and cracks in samples with different scanning velocities. Three samples (S 350-12 , S 350-10 , and S 350-8 ) were deposited with the same laser power of 350 W, and different scanning velocities of 12 mm/s, 10 mm/s, and 8 mm/s, respectively. The opening width and length of the crack in S 350-12 (Fig. 14a) were significantly greater than those in S 350-10 (Fig. 14d) and S 350-8 (Fig. 14g),  Temperature gradient 3 × 10 6 (K/m) [49] which reflects the excessive internal stress. Although the crack size in S 350-8 was small, many stray grains in S 350-8 were still detected (Fig. 14h). In addition, the grain morphologies of the interlaminar zone were significantly different from those of S 350-12 (Fig. 14b) and S 350-10 (Fig. 14e). More and more stray grains were detected as the scanning velocity decreased, as observed through a comparison of Fig. 14c, f, and i. The appearance of stray grains hindered the continuous growth of the columnar grains, wherein cracks were observed with the HAGBs (Fig. 14i). With continuous layer-by-layer deposition, heat accumulation is inevitable, which can result in a decrease in the temperature gradient [50]. An extremely small scanning velocity can increase the laser working capacity per unit length, thus inputting more energy and resulting in increased heat accumulation. Although a reduced scanning velocity will result in a lower solidification rate (R), the  temperature gradient (G) change has a greater impact on the value of G n /R at the n of approximately 3.4 [17]. Therefore, the decrease in G n /R can transform columnar grains to equiaxed grains, thus forming HAGBs that ultimately increase the cracking susceptibility. In general, the effect of the scanning velocity on the cracking susceptibility can be divided into two aspects: (1) the high scanning velocity increases the cracking susceptibility by increasing internal stress; and (2) the low scanning velocity promotes the formation of stray grains.

Effect of laser power on cracking susceptibility
Laser power is an important processing parameter that determines the laser energy input and has a significant effect on the volume energy density (E V ). The high-volume energy density of region A 3 was caused by both the excess scanning velocity and the excessive laser power. Fig. 15a and c show the relationship between the crack length/count density and the volume energy density. Firstly, the volume energy density significantly increased with the laser power and crack density, especially at increases from 300 W to 400 W. In general, the increase of energy input can increase the thermal stress and increase the cracking susceptibility [33,40]. However, the lowest energy input showed a higher crack density (S 250-10 ). The unfused voids were detected in S 250-10 , and some voids became crack sources ( Fig. 15b and d). The insufficiently low energy input prevented the powder from fully melting, resulting in unfused voids. Some voids in HAZ easily resulted in stress concentration and eventually lead to cracking. However, the thermal stress level in S 250-10 was relatively low due to the low energy input, and the formation of some microcracks generally did not result in excessive expansion (Fig. 15b and d).
The laser energy is the heat source to melt materials, including powders and the substrate. One part of the input energy was used to melt materials, another was lost since the laser is reflected by materials, a third was transferred to the environment by heat conduction, and the rest were stored in the sample. The relationship can be expressed as E i = E m + E R + E t + E r , where E i is the total energy input, E m is the energy to melt materials, E R is the lost energy by reflection, E t is the energy transferred by heat conduction, and E r is residual energy in samples; all energies have units of J. For a certain material, E m , E R , and E t are determined by the mass, the laser reflectivity, and the thermal conductivity, respectively. Ideally, E m is expected to be infinitely close to E i . However, it is impossible to avoid excessive energy inputs such as E R , E t , and E r . In addition, cracking can release the residual energy (E r ). Therefore, decreasing the residual energy (E r ) can reduce the cracking susceptibility, and the value of energy density can express the level of E r . As such, it is particularly important to choose the most appropriate laser power. Fig. 16 shows a method to optimize the laser power. All samples correspond to those shown in Fig. 15, which were deposited with a scanning velocity of 10 mm/s, an overlapping ratio of 30%, and a powder feeding rate of 0.65 g/min. The average layer thickness can represent the level of energy input in a certain range (Fig. 16a). The average layer thickness increased with the laser power and eventually tended to a stable value due to the limitation of the powder feed rate. The functional relationship can then be characterized by fitting the data in Fig. 16a, as presented in the results in Fig. 16b, to which the following fitting equation was formed: where t is the average layer thickness; P is the laser power; and H, K, and b are constants with values of 0.20440, −1.10767, and 87.85197, respectively. As such, the t can be calculated using the equation E V ¼ P SÂtÂv , which can be replaced by Eq. (4) to obtain the functional relationship between the laser power (P) and volume energy density (E V ) (Fig. 16d). The minimum value of the volume energy density was measured to be 252 J/mm 3 , which can be obtained by using this function, and the corresponding laser power value was 272 W. It is worth mentioning that when the volume energy density was approximately equal to 252 J/mm 3 , the corresponding laser power range was 262-284 W. A comparison of the calculated results ( Fig. 16c) with the experimental results (Fig. 16d) indicates that the two trends were different under the condition of <272 W. The low energy input resulted in incomplete fusion defects, which affected the sample layer thickness, but this effect was neglected in the calculations. To avoid any unfused defects, the applicable laser power range was modified to 272-284 W.

Fabrication of the crack-free single crystal superalloy block sample
The process parameters were adjusted according to the discussion results on the effect of process parameters on cracking susceptibility. Crack-free multi-track SX block sample OS-1 with 15 layers was produced, which was deposited with a laser power of 280 watts, an overlapping ratio of 32%, a scanning velocity of 10 mm/s, and a powder feeding rate of 0.65 g/min. In addition to the optimization results of the laser power used, the overlapping ratio was reasonably increased according to the results of sample R 30 . The increase in overlapping ratio from 30% to 32% appropriately increased G n/ R of the overlapping region to avoid the transformation from columnar grains to equiaxed grains. Fig. 17a shows the crystal orientation distribution of the sample OS-1 with 15 layers in the cross-section view. The crystal orientation of the deposition was consistent with that of the substrate, except that the top surface was distributed with stray grains, and no crack was observed. Compared with samples of just 10 layers, the results of the sample OS-1 indicate that the process was indeed optimized. Although the location of the overlapping regions can still be identified by a slight color difference (such as the region b), the crystal orientation measurement results showed that crystal misorientation angles were within 6°along the [001] direction (Fig. 17a). The crystal misorientation mainly appeared in overlapping regions, especially when the height of the deposition increased, as shown in Fig. 17b and c. Fig. 17c corresponds to the region c in Fig. 17a, which is an overlapping region near the substrate, and shows columnar grains with a highly uniform orientation. Fig. 17b corresponds to the region b in Fig. 17a, which is an overlapping region in the middle of the sample, indicating that the growth orientation of the columnar grains in the overlapping region was different from the region of track center. This difference occurred layer by layer mainly because the temperature gradient (G) was gradually decreasing due to the heat accumulation during the continuous deposition. On the whole, G gradually decreased, the solidification structure of the overlapping region will be affected first since its energy input and G were smaller than those of the central region.

Conclusions
The present work successfully fabricated crack-free multi-track SX block by adjusting the process parameters based on the relationship between the process parameters, microstructure, internal stress, and cracking susceptibility. The main research conclusions are as follows: (i) The overlapping ratio was the most important process parameter to determine the type of solidification structure in the overlapping region. An extremely small (20%) overlapping ratio produced a low G n /R in the overlapping region, which resulted in the transformation of columnar structures into equiaxed structures to form HAGBs. Conversely, an extremely large (>40%) overlapping ratio increased G n /R in the overlapping region, which resulted in the formation of cellular structures and subsequently HAGBs, both of which increased the cracking susceptibility. (ii) For the scanning velocity, an excess scanning velocity (12 mm/s) created an extremely high cooling rate (approximately 7000 K/ s), thereby resulting in large internal stress, large size cracks, and high crack length density. However, a too small scanning velocity (8 mm/s) contributed to the increase of heat accumulation and eventually led to interlaminar stray grains and resulted in the formation of HAGBs, thus increasing the cracking susceptibility. (iii) For the laser power, the laser power is the most important process parameter to determine the energy input. Large laser power (>300 W) resulted in a high volume energy density, which contained more residual energy and may eventually be released through cracking. Conversely, an extremely small laser power (<250 W) produced incomplete fusion defects, which can likely be crack sources under re-heated. The experimental data were fitted and calculated, of which the results estimated the range of applicable laser power to be 272-284 W. In this work, a laser power of 280 W was finally proved to be appropriate.

Author statement
Zhipeng Zhou, Qian Lei, and Lan Huang were responsible for the concept and experimental design. Zhipeng Zhou finished the experiments and the manuscript. Huan Qi provided the additive manufacturing equipment and technical support for the fabrication of samples. Zhou Yan, Zi Wang, Yijing Shang, and Yunping Li gave valuable advice and help for the experimental design and data analysis. Qian Lei, Lan Huang, Yong Liu, and Liang Jiang supervised the project. All authors do the contribution for the data interpretation and writing.

Declaration of competing interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, "Effects of process parameters on microstructure and cracking susceptibility of a single crystal superalloy fabricated by directed energy deposition".