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The effect of substrate orientation on stray grain formation in the (111) plane in laser surface remelted single crystal superalloys
Journal of Alloys and Compounds 800 (2019) 240e246
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The effect of substrate orientation on stray grain formation in the (111) plane in laser surface remelted single crystal superalloys J.C. Guo a, W.J. Chen a, R.N. Yang b, X.W. Lei a, W.J. Yao a, N. Wang a, * a The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, Department of Applied Physics, School of Natural and Applied Science, Northwestern Polytechnical University, Xi'an, 710072, China b Guiyang AECC Power Investment Casting Co., Ltd., Guiyang, 550014, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 April 2019 Received in revised form 3 June 2019 Accepted 4 June 2019 Available online 5 June 2019
Ni-base single crystal (SX) superalloys exhibit high Young modulus along the [111] crystallographic orientation, and this raise the question that how to avoid stray grain formation during laser repair of surface defects in (111) plane if SX turbine component is cast in [111] direction. In this study, laser remelting was conducted in different substrate orientations in (111) plane and the susceptibility of equiaxed stray grain to substrate orientation was determined. We define an angle x to show the substrate orientation variation by which x ¼ 0 , 30 , 60 , and 90 means the laser scanning direction along [112], [101], [211], and [110], respectively. It is found that with the increase of x, the susceptibility of equiaxed stray grain bottomed at 60 and then increases again. The theoretical calculated results confirm the experiment and show that it is caused by the x dependent variation in thermal gradient and dendrite growth velocity in different domains. We found that the optimized substrate orientation in (111) plane for laser remelting of SX superalloy is x ¼ 60 . Our results can provide an in-depth insight into the mechanism how to avoid stray grain formation in the future laser repair of SX components. © 2019 Elsevier B.V. All rights reserved.
Keywords: High-temperature Ni-base superalloys Laser processing Microstructure
1. Introduction Nickel-base superalloys have been broadly used for manufacturing the hot-section components in the gas turbine due to their superior mechanical properties at high temperatures [1e3]. To achieve superior service performances, this kind of material is often cast into single crystal (SX) form. Nevertheless, under the severe service conditions of high temperature and high pressure, tip and platform damages often take place. Due to the high cost of the single crystal components, effective repair techniques are more desirable than replacement [4e6]. The epitaxial laser metal forming process, in which metal powders are remelted and injected into a melt pool created by a moving laser beam [7e10], is an effective way for the repair. During this process, if specific solidification conditions are satisfied, the epitaxial growth of columnar cells/ dendrites along the original orientation in the substrate occurs and no equiaxed stray grains (SGs) will form. Otherwise, columnar-toequiaxed transition (CET) takes place and equiaxed SGs are produced, indicating the failure of the repairing process [11,12], as the
* Corresponding author. E-mail address: [email protected] (N. Wang). https://doi.org/10.1016/j.jallcom.2019.06.029 0925-8388/© 2019 Elsevier B.V. All rights reserved.
grain boundaries resulting from the SGs could lead to solidification cracking or lowered service performance [13e16]. It should be noted that the stray grains could form by columnar growth from incorrectly oriented grains (disoriented columnar grains) or non FCC phases. In the present paper, however, this is not what we concern. We will only focus on the equiaxed stray grain originated from CET dependent on the substrate orientation. The crystallographic direction of [001] is the normal casting direction of nickel-base single-crystal, and the aero engine blade grows along the [001] direction bodily. For this reason, the influence of substrate orientation on the formation of SGs based on (001) and (011) plans have been examined adequately. Qi et al. [17] studied laser depositions of Rene N5 powders on directionally solidified DZ125 substrates with the orientation variations in the transverse and longitudinal sections. They showed that the variation of substrate orientation influences the position of columnarto-equiaxed transition. DuPont et al. [18,19] demonstrated the effect of orientation on the formation of the SGs within the melt pool, and they moved the laser beam on the surface of CMSX-4 superalloys along [100], [110], and [120] crystallographic directions in (001) crystal planes. Their work revealed that the intersections of different dendrite domains are vulnerable sites for SG formation,
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and the location and number of intersections will control the overall SG formation. Mokadem et al. [20] performed laser welding of CMSX-4 SX superalloys along the [100] direction in various crystal planes ranging from (001) to (011) plane. It indicated that the equiaxed growth regime is extended when the substrate orientation effect is taken into account. Later on, the present authors [21,22] changed the laser beam directions in (100), (010), and (001) plane and showed that SG susceptibility varies strongly with the substrate orientation when laser scanning direction is rotated around [010] axis in (010) plane, whereas it changes slightly when laser scanning direction is rotated around [100] and [001] axes in (100) and (001) planes. As can be seen, the studies above focused mainly on the conventional crystallographic planes (001) and (011). Recently, substrate orientation in (111) plane arouse much interests since the Nibase superalloy possesses the best Young modulus in [111] crystallographic direction [23]. For this reason, the blade cast along [111] crystallographic direction could find some applications and has been proposed for manufacturing. Based on this, the repair of the aero engine blade on (111) plane should be considered in advance. Since the substrate orientation has drastic effect on the stray grain (SG) formation, optimal laser directions should be selected to obtain non-SG microstructure for a successful repair [18,19]. In the present study, we will concentrate on the contribution of the varied substrate orientation on SG formation in (111) plane. For such a purpose, different laser beam directions were selected on this plane during laser melting process. The solidification microstructures under these conditions were checked, and the underlying mechanism of orientations in (111) plane on the stray grain formation was determined.
241
crystallographic direction in (111) plane. x ¼ 0 , 30 , 60 , and 90 were used which means the laser scanned the sample along [112], [101], [211] and [110], respectively, as shown in Fig. 1. For the laser scanning directions via rotating x ¼ 30 , 60 , and 90 around [112] crystallographic direction in (111) plane, they will produce mirror orientations as those of x ¼ 30 , 60 , and 90 , therefore, the experiments on these angles are not necessary.
2.2. Materials and experiment The second-generation nickel-based superalloy DD6 developed by China is chosen as the research subject in this study. The composition of DD6 is listed in Table 1 [24]. Fig. 2 presents the schematic illustration for producing the sample with the (111) plane. A SX cylindrical ingot with diameter of 15 mm, which was produced by a traditional casting method followed by standard heat treatment, is used. The primary trunk of dendrite grows along the long axis direction of the ingot and we define it as [001]. In this way, the standard crystallographic directions [100], [010], and [001] are defined, as shown in Fig. 2. Then the (111) plane can be determined and the plate samples with thickness of 2 mm were cut for experiments. The laser surface remelting experiments were performed by using a 1 kW continuous-wave Nd: YAG laser. The laser beam is a Gaussian heat source with radius close to 0.75 mm and power distribution of 2. During the experiments, a continuous flow of Ar2 gas was directed on the surface to reduce the oxidation. To examine the effect of substrate orientation on the SG formation ability, proper laser processing conditions such as the power and scanning velocity should be selected. According to the
2. Experiments 2.1. The selected orientations in (111) plane The variation in the substrate orientation can be performed by changing the laser scanning along different directions in the fixed (111) plane. We selected the substrate orientation by altering the laser scanning direction via rotating an angle x around [112]
Fig. 1. Schematic illustrations of (111) plane in fcc lattice and the laser scanning direction Vb.
Fig. 2. Schematic illustration for producing the substrate orientations of (111) plane.
Table 1 Nominal compositions of superalloy DD6 in wt. % [24]. Element
Cr
Co
Mo
W
Ta
Re
Nb
Ti
Al
Hf
Fe
Zr
S
Ni
DD6
4.3
9.0
2.0
8.0
7.5
2.0
0.5
e
5.6
0.1
e
e
e
Bal.
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theoretical predictions, if SGs do not form at initial orientation (x ¼ 0 ), they may not form at other orientations. Therefore, SGs are required to form at initial orientation x ¼ 0 , and then the situations at other orientations can be compared. For this purpose, different processing conditions have been tried and the selected parameters in the present work are: the beam power is 200 W and the scanning velocity is 5 mm/s. The experiments were then performed for varying laser scanning directions under this processing condition. A comparison experiment at a beam power of 150 W but same speed for the same orientations is also conducted to show the contribution of laser power. After the experiments, the samples were polished and etched by a solution of H2O þ HCl þ HNO3 in 1:2:1 ratio. The microstructures in the melt pool were then determined by optical microscopy in the transverse and longitudinal sections of the laser traces. Electron backscattered diffraction (EBSD) analysis was used for measuring the orientations in the weld pool to examine the stray grains. To further quantify the effect of substrate orientation, the areas of SGs and melt pool were measured at transverse sections, and the area fraction of SGs was used to evaluate SG susceptibility experimentally. 3. Results In this section, the transverse micrographs at different xs (0 , 30 , 60 and 90 ) will be presented, by which we will show the variation in SG susceptibilities for different substrate orientations for comparison. All the experiments were done by using the same laser velocity whereas the laser powers are 200 W and 150 W, respectively, as are presented below. 3.1. Laser melting at 200 W Fig. 3 shows transverse micrographs of the samples with different angles of x. For varied orientations, several domains with different preferred crystallographic directions are produced and their boundaries undergo continuous changes with the increasing angle. For x ¼ 0 , Fig. 3(a), three dendrite growth domains, [010], [100], and [001], form, and one domain intersection appears. SGs appear mainly within the [001] domain and near [010]/[001] and [100]/[001] boundaries, as the arrows mark. As will be shown later, the distributions of SGs and boundaries lines are functions of substrate orientation. This is an important factor contributing to the difference in SG susceptibility. With the increase of x, the competition of [010], [100], and [001] domains occurs. When x is increased to 30 , the [010]/[100] boundary tilts to the right side of the weld pool while the [001] domain moves to the same direction, leading to that the intersection of these dendrite domains towards upper right. This gives rise to a smaller [100] domain and a larger [010] domain while the size of [001] domain remains nearly unchanged. In this case, the stray grains are still produced near domain boundaries but their volume fraction decreases. When x reaches 60 , three dendrite growth domains, [001], [001], and [100], form. The [001] domain occupies the majority part in the center whereas the [100] and [001] domains with relative smaller sizes stay in the left and right corners. One cannot observe stray grains for this orientation. At x ¼ 90 , the [001]/[010] and [001]/[ 100] boundaries form in the left side. The [100]/[010] boundary moves to the right close to the centerline and the stray grains form again around the domain intersection and boundary lines. As to the SG formation for different substrate orientations, one typical characteristic is that with the increase of x under the current processing condition, the amount of SGs decreases firstly to x ¼ 60 at which nearly no SG forms, then increases again when x reaches to
Fig. 3. Transverse-section micrographs for different xs with the laser power of 200 W. (a) x ¼ 0 , (b) x ¼ 30 , (c) x ¼ 60 , and (d) x ¼ 90 .
90 . Fig. 4 presents the typical EBSD maps in the transverse-section of weld pool for x ¼ 0 and x ¼ 60 at 200 W, which correspond to Fig. 3(a) and (c). It can be seen clearly that the stray grain forms near [010]/[001] boundary and with [001] domain for x ¼ 0 whereas there is no stray grain for x ¼ 60 . To quantify the stray grain susceptibility as a function of substrate orientation, the area ratio of the stray grains to the weld pool, 4e, is measured for different xs. The results are given in Fig. 5. Clearly, the area ratio of the stray grains decreases firstly and then increases. 3.2. Laser melting at 150 W Fig. 6 shows transverse micrographs of the samples with x under the laser power of 150 W. With the increase of x, the variation trend of distribution of the various domains is similar to that of the high
Fig. 4. EBSD maps of welding pool transverse-section for different xs with the laser power of 200 W. (a) x ¼ 0 , (b) x ¼ 60 . The relevant directions [100], [010], [001] in (a) and (b) correspond to those in Fig. 3(a) and (c).
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processing condition, and we will discuss this aspect further in the following section.
4. Discussions In a laser weld pool, the formation of the stray grains in a specific domain with the preferred growth direction [hkl] during the laser remelting process is mainly controlled by the thermal gradient, Ghkl, and the growth velocity of dendrite, Vhkl. If these two parameters can be controlled properly, the local volume fraction of equiaxed stray grains, which is calculated by the following equation [25],
2
4pN0 f ¼ 1 exp4 3 Fig. 5. Variations in the experimental area ratio of the stray grains to the weld pool 4e and the calculated area-weighted average volume fraction 4of SGs with different xs.
laser power 200 W. Nevertheless, no SG forms in the weld pool of all substrate orientations in (111) plane, indicating that lower power under the same velocity condition could be beneficial to avoid CET. It should be bear in mind that although the smaller power could be helpful, it may not be suitable for laser repair of SX superalloy since a series of technological problems can be brought in such as incomplete melting of powder and higher surface roughness of the cladding layer during the process of laser forming. However, we present the results of 150 W here to show that different laser powers influence the stray grain susceptibility under the specific
1
1=n ðn þ 1Þ Gnhkl aVhkl
!3 3 5
(1)
will be smaller than a critical value related to the physical parameters of the materials. In this case, no stray grain will be produced. In the above equation, the value of a, n, and N0 are constants related to materials. Since no such experimental data are available for DD6 at present, we take the values from the work of Gaumann et al. for CMSX-4 [7] as a ¼ 1.25 106 K3.4/m,s, n ¼ 3.4, and N0 ¼ 2 1015/ m3. Ghkl and Vhkl are related to the isothermal thermal gradient Gsl and isothermal dendrite growth Vsl velocity in the weld pool:
Ghkl ¼ Gsl $cosjhkl
(2a)
Vhkl ¼ Gsl =cosjhkl
(2b)
where jhkl is the angle between the [hkl] preferred dendrite growth direction and normal vector to the solidification front. It should be stressed here under the fixed laser power and laser scanning velocity, the distributions of Gsl and Vsl do not vary with substrate orientation. However, the substrate orientation does change Ghkl and Vhkl via cosjhkl in Eq. (2). Thus, for elucidating the contribution of substrate orientation on stray grain susceptibility, the distribution of cosjhkl should be examined. According to the geometrical model proposed by Rappaz et al. ! ! ! [26], cosjhkl can be determined as n , u hkl . u hkl is the unit vector ! along the preferred dendrite growth direction [hkl] and n is the normal vector to the solidification front as given in Fig. 7, in which a schematic diagram of weld pool is presented to show the rela! tionship between associated angle and n . In (111) plane, since x ¼ 0 is defined to be parallel to [112], a matrix for transforming ! u 112 along [112] crystallographic reference system into a x-y-z reference system is given by
Fig. 6. Transverse-section micrographs for different xs with the laser power of 150 W. (a) x ¼ 0 , (b) x ¼ 30 , (c) x ¼ 60 , and (d) x ¼ 90 .
Fig. 7. Schematic illustration of weld pool diagram to show the relationship between ! associated angle and n in (111) plane.
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2
pffiffiffi 6 6 6 6 3 cosð60 þ xÞ 6 pffiffiffi 6 6 R ¼ 6 6 sinð60 þ xÞ 6 3 6 pffiffiffi 6 6 3 4 3
pffiffiffi 6 cosð60 xÞ 3 pffiffiffi 6 sinð60 xÞ 3 pffiffiffi 3 3
3 pffiffiffi 7 6 cosx 7 7 3 7 pffiffiffi 7 7 6 sinx 7 7 3 7 pffiffiffi 7 7 3 5 3
(3)
Now, in order to reveal the underlying mechanism of the substrate orientation on the stray grain formation in (111) plane, Gsl and Vsl were calculated by a 3-D steady-state heat transfer model which contains heat conduction and heat convection equations [21,22]. The Marangoni convection has quite slight effect and can be neglected under the present processing conditions [27]. After obtaining Gsl and Vsl, the distributions of Ghkl, Vhkl, and f were calculated according to Eqs. (1)e(3), then the area-weighted average volume fraction of equiaxed SGs, 4, was determined to show the stray grain formation ability as a function of substrate orientation [22]. Finally, the contribution of the orientation in (111) plane was discussed. The calculation method here has been described in detail in our previous work [21], and the physical parameters used in the calculation are listed in Table 2 [28]. Fig. 8. Variations in the distribution of thermal gradient Ghkl for different xs.
4.1. The distributions of Ghkl, Vhkl and f Fig. 8 shows the variation in the distribution of the thermal gradient with x in (111) plane. The calculated distributions of different dendrite domains with preferred crystallographic directions are marked by the dashed lines. It can be seen that the calculated dendrite domain distributions agree well with those obtained by experiment as shown in Fig. 3. For the Ghkl distributions in four situations (Fig. 8aed), the value of Ghkl increases from 3.42 105 to 1.05 106 K m1. Within the most parts in the weld pool, Ghkl ranges from 4.3 105 to 7.83 105 K m1. The minima of Ghkl exist in some positions, which vary with the substrate orientation. With the increases of x, the position of the minimum Ghkl moves from center part towards upper right. When x equals 60 , the right minimum region moves to upper right continuously and symmetric minimum region appears in the upper left edge, resulting in a symmetrical distribution of Ghkl. At x ¼ 90 , the dark blue region enlarges from the left side, forming an ideal mirror image of G distribution in comparing with that of x ¼ 30 . Fig. 9 gives the variations in distribution of the dendrite growth velocity, Vhkl, with x. It can be seen that near the weld pool boundary, Vhkl is the smallest and its value tends to be zero for all cases. With the position moves from the pool boundary to the center and upper part, Vhkl increases. For different xs, however, the intensities of the increase are different, resulting in different maximum value of Vhkl. Moreover, the position of the Vhkl maximum also varies with substrate orientation. For x ¼ 0 , Fig. 9(a), V increases and its value reaches 8.1 103 m/s at the domain
intersection in the center part. For x ¼ 30 , Fig. 9(b), the value of Vhkl can exceed 7.1 103 m/s at the domain intersection near the upper right region. For x ¼ 90 , Fig. 9(d), the situation is similar to that of the x ¼ 30 , except that the left and right region reverses. If x equals 60 , Fig. 9(c), however, the maximum value of Vhkl only can reach 6.1 103 m/s, and it locates in a small region in the upper center part of the weld pool.
Table 2 Physical parameters of DD6 used in the calculation of the temperature field [28]. Physical parameter
Unit
Value
Density Solidus temperature Liquidus temperature Thermal conductivity Specific heat of solid Coefficient of thermal expansion
Kg m3 K K W m1 K1 J kg1 K1 K1
8.78 103 1651 1672 22.3 600 1.41 105
Fig. 9. Variations in the distribution of dendrite growth velocity Vhkl for different xs.
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Apparently, the calculated minimum Ghkl and maximum Vhkl locate at the domain intersection, and their values for different substrate orientation are presented in Fig. 10. At x ¼ 60 , the minimum Ghkl has largest value and the maximum Vhkl has the smallest value. By using the data of thermal gradient and growth velocity for every point in different domains with preferred growth direction, the distributions of local fraction of equiaxed SGs (4) at the solidification front as a function of x are calculated and the results are given in Fig. 11. For all orientations, near the fusion line, 4 is quite small and its value is less than 0.1, and this is attributed to the large thermal gradients and very small velocities. However, with the position departs from the fusion line, 4 increases and reaches a maximum value at domain intersection. The positions of the maxima vary with x. For x ¼ 0 , as shown in Fig. 11(a), the maximum 4 locates at domain intersection in the center region. For x ¼ 30 , it moves to the right side of the weld pool, and the value of 4 is smaller than x ¼ 0 . The situation of x ¼ 90 is similar to that of x ¼ 30 , where the maximum 4 is on the left side of the weld pool. However, for x ¼ 60 , two maxima of 4 move to both sides nearly outside of the melt pool, where the value of 4 is smaller than 0.41 in all positions. This indicates that it is a feasible way to avoid CET by altering the value of x.
4.2. Overall CET susceptibility After obtaining the local value of 4, the overall CET tendency within a melt pool can be determined by the area-weighted average volume fraction of equiaxed SGs 4[21,22]. The calculated 4 as a function of x is plotted in Fig. 5, in which the results of x ¼ 30 , 60 , and 90 are also presented for comparison. Clearly, the calculated 4 is symmetrical with the variation of x for the rotations around the x ¼ 0 . When x equals 0 , 4 has a maximum value, indicating that CET is most sensitive along this substrate orientation. With the increase of jxj value, 4 decreases initially till x reaches j60 j and then increases to j90 j. A minimum value existing at x ¼ j60 j reveals that SG susceptibility is weakest in this orientation, and this is in agreement with the experiment results as shown in Fig. 3, indicating that the [211] direction corresponding to x ¼ 60 in (111) plane is the most invulnerable orientation to the stray grains. Next we will analyze why the variation of the substrate orientation results in different stray grain susceptibilities.
Fig. 10. Variations in Ghkl minimum and Vhkl maximum with x.
Fig. 11. Variations in the distribution of 4 with x.
4.3. The underlying mechanism of the contribution of substrate orientation in (111) plane From Eq. (1), one can see that smaller Ghkl and larger Vhkl result in large value of f, and in such a case, CET will occur easily and equaixed stray grains are inclined to be produced. Due to this reason, the locations which have the minimum value of Ghkl and the maximum value of Vhkl could be the most susceptible position to equiaxed stray grains. As shown in the above sections, Ghkl minima and Vhkl maxima as well as their distributions vary with x. For different substrate orientations, the minimum Ghkl and the maximum Vhkl always appear at the domain intersection, which leads to a maximum f there, as shown in Figs. 8 and 9. This indicates that the intersection points are the most vulnerable locations to CET. The value of Ghkl increases and that of Vhkl decreases along the domain boundaries from the domain intersection, and the former increases further and the later decreases further within the domain inside, respectively, suggesting that the CET ability weakens in the sequence of domain intersection, domain boundary, and domain inner part. Bearing this point in the mind, we can understand why CET susceptibility changes with the substrate orientation and why x ¼ 60 has no stray grains whereas the other three have. For x ¼ 0 , 30 or 90 , there is one domain intersection in the weld pool although its position changes. At the domain intersection, the thermal gradient and the growth velocity reaches the minimum and the maximum values, respectively. However, for x ¼ 60 , the situation is quite different. The domain intersection moves to the right side nearly outside the weld pool. There is the other mirror domain intersection appears in the left side. Moreover, the Ghkl minima reaches its maximum and Vhkl maxima reaches its minimum for x ¼ 60 as Fig. 10 presents. That means Gnhkl =Vhkl in such a case is much larger than those in other three ones and it results in a relatively smaller local volume fraction and areaaverage volume fraction of equiaxed stray grain, as shown in Figs. 11(c) and Fig. 5. This is the reason why the substrate
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orientation of x ¼ 60 is the most invulnerable to the stray grain. In general, as discussed in our previous work [21,22], the number and location of the intersection points determine the magnitude of 4. Reducing or even eliminating the intersection points would lower 4 and finally leads to a lower value of 4. In the (111) plane, we found that the x ¼ 60 laser scanning direction can provide an ideal orientation for remelting of SX superalloys, i.e., the (111)/[211] substrate orientation, under which the area-average volume fraction of equiaxed SGs is minimum. 4.4. The effect of the laser power As for the laser remelting with the laser power of 150 W, the trend of the change of the domain distributions at different substrate orientation is similar to that of 200 W. Since the power difference is not large, the sizes of weld pools in the two situations also have no apparent discrepancy. However, it is hard to find stray grains under the small laser power condition. In order to reveal the underlying mechanism, the area-weighted average volume fraction of equiaxed SGs 4 for the case of 150 W was calculated and the results are presented in Fig. 5. It can be seen that the change in 4 as a function of x is similar to that at high laser power. Nevertheless, its absolute value is smaller. This shows that under the small laser power condition, the variation in 4 agrees well with the experimental results. Combining the results given in Figs. 3 and 4, a critical value of 4 ¼ 4c should exist for DD6 under the present processing conditions, as indicated by the dash line in Fig. 5. Below the dash line, no stray grain forms under the situation of jxj ¼ 60 for 200 W and those of all xs for 150 W. If the processing conditions are changed, the values of 4 for different substrate orientations could vary. As a result, the possibility of stray grain formation could also be different. However, the situation that 4 has the smallest value at jxj ¼ 60 in (111) plane will not change, no matter how the processing conditions vary. That means, the laser scanning along [211] and [121], corresponding to x ¼ 60 and x ¼ 60 , are the best beam directions for the repair of SX superalloys in (111) crystallographic plane. 5. Conclusion In the (111) plane, the effect of substrate orientation on CET in a laser weld pool for single crystal superalloys is investigated for different x as we defined. It is shown that CET depends evidently on the substrate orientation. With the increase of x, the susceptibility of equiaxed stray grain decreases to 60 and then increases again. The theoretical calculated results indicate that it is the x dependent variation in thermal gradient and dendrite growth velocity in different domains that results in the different stray grain susceptibility. Both the experimental and theoretical investigations reveal that the optimized substrate orientation in (111) plane in the laser remelting of SX superalloy is x ¼ 60 and it will be the best direction in the future laser repair of SX components in (111) plane. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 51671160 and 51801160), the Aviation Science Foundation (Grant No. 2017ZF53066), and the Fund of the Innovation Base of Graduate Students of NPU. We would like to thank the Analytical & Testing Center of Northwestern Polytechnical University for the EBSD map determination.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
The effect of substrate orientation on stray grain formation in the (111) plane in laser surface remelted single crystal superalloys J.C. Guo a, W.J. Chen a, R.N. Yang b, X.W. Lei a, W.J. Yao a, N. Wang a, * a The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, Department of Applied Physics, School of Natural and Applied Science, Northwestern Polytechnical University, Xi'an, 710072, China b Guiyang AECC Power Investment Casting Co., Ltd., Guiyang, 550014, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 April 2019 Received in revised form 3 June 2019 Accepted 4 June 2019 Available online 5 June 2019
Ni-base single crystal (SX) superalloys exhibit high Young modulus along the [111] crystallographic orientation, and this raise the question that how to avoid stray grain formation during laser repair of surface defects in (111) plane if SX turbine component is cast in [111] direction. In this study, laser remelting was conducted in different substrate orientations in (111) plane and the susceptibility of equiaxed stray grain to substrate orientation was determined. We define an angle x to show the substrate orientation variation by which x ¼ 0 , 30 , 60 , and 90 means the laser scanning direction along [112], [101], [211], and [110], respectively. It is found that with the increase of x, the susceptibility of equiaxed stray grain bottomed at 60 and then increases again. The theoretical calculated results confirm the experiment and show that it is caused by the x dependent variation in thermal gradient and dendrite growth velocity in different domains. We found that the optimized substrate orientation in (111) plane for laser remelting of SX superalloy is x ¼ 60 . Our results can provide an in-depth insight into the mechanism how to avoid stray grain formation in the future laser repair of SX components. © 2019 Elsevier B.V. All rights reserved.
Keywords: High-temperature Ni-base superalloys Laser processing Microstructure
1. Introduction Nickel-base superalloys have been broadly used for manufacturing the hot-section components in the gas turbine due to their superior mechanical properties at high temperatures [1e3]. To achieve superior service performances, this kind of material is often cast into single crystal (SX) form. Nevertheless, under the severe service conditions of high temperature and high pressure, tip and platform damages often take place. Due to the high cost of the single crystal components, effective repair techniques are more desirable than replacement [4e6]. The epitaxial laser metal forming process, in which metal powders are remelted and injected into a melt pool created by a moving laser beam [7e10], is an effective way for the repair. During this process, if specific solidification conditions are satisfied, the epitaxial growth of columnar cells/ dendrites along the original orientation in the substrate occurs and no equiaxed stray grains (SGs) will form. Otherwise, columnar-toequiaxed transition (CET) takes place and equiaxed SGs are produced, indicating the failure of the repairing process [11,12], as the
* Corresponding author. E-mail address: [email protected] (N. Wang). https://doi.org/10.1016/j.jallcom.2019.06.029 0925-8388/© 2019 Elsevier B.V. All rights reserved.
grain boundaries resulting from the SGs could lead to solidification cracking or lowered service performance [13e16]. It should be noted that the stray grains could form by columnar growth from incorrectly oriented grains (disoriented columnar grains) or non FCC phases. In the present paper, however, this is not what we concern. We will only focus on the equiaxed stray grain originated from CET dependent on the substrate orientation. The crystallographic direction of [001] is the normal casting direction of nickel-base single-crystal, and the aero engine blade grows along the [001] direction bodily. For this reason, the influence of substrate orientation on the formation of SGs based on (001) and (011) plans have been examined adequately. Qi et al. [17] studied laser depositions of Rene N5 powders on directionally solidified DZ125 substrates with the orientation variations in the transverse and longitudinal sections. They showed that the variation of substrate orientation influences the position of columnarto-equiaxed transition. DuPont et al. [18,19] demonstrated the effect of orientation on the formation of the SGs within the melt pool, and they moved the laser beam on the surface of CMSX-4 superalloys along [100], [110], and [120] crystallographic directions in (001) crystal planes. Their work revealed that the intersections of different dendrite domains are vulnerable sites for SG formation,
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and the location and number of intersections will control the overall SG formation. Mokadem et al. [20] performed laser welding of CMSX-4 SX superalloys along the [100] direction in various crystal planes ranging from (001) to (011) plane. It indicated that the equiaxed growth regime is extended when the substrate orientation effect is taken into account. Later on, the present authors [21,22] changed the laser beam directions in (100), (010), and (001) plane and showed that SG susceptibility varies strongly with the substrate orientation when laser scanning direction is rotated around [010] axis in (010) plane, whereas it changes slightly when laser scanning direction is rotated around [100] and [001] axes in (100) and (001) planes. As can be seen, the studies above focused mainly on the conventional crystallographic planes (001) and (011). Recently, substrate orientation in (111) plane arouse much interests since the Nibase superalloy possesses the best Young modulus in [111] crystallographic direction [23]. For this reason, the blade cast along [111] crystallographic direction could find some applications and has been proposed for manufacturing. Based on this, the repair of the aero engine blade on (111) plane should be considered in advance. Since the substrate orientation has drastic effect on the stray grain (SG) formation, optimal laser directions should be selected to obtain non-SG microstructure for a successful repair [18,19]. In the present study, we will concentrate on the contribution of the varied substrate orientation on SG formation in (111) plane. For such a purpose, different laser beam directions were selected on this plane during laser melting process. The solidification microstructures under these conditions were checked, and the underlying mechanism of orientations in (111) plane on the stray grain formation was determined.
241
crystallographic direction in (111) plane. x ¼ 0 , 30 , 60 , and 90 were used which means the laser scanned the sample along [112], [101], [211] and [110], respectively, as shown in Fig. 1. For the laser scanning directions via rotating x ¼ 30 , 60 , and 90 around [112] crystallographic direction in (111) plane, they will produce mirror orientations as those of x ¼ 30 , 60 , and 90 , therefore, the experiments on these angles are not necessary.
2.2. Materials and experiment The second-generation nickel-based superalloy DD6 developed by China is chosen as the research subject in this study. The composition of DD6 is listed in Table 1 [24]. Fig. 2 presents the schematic illustration for producing the sample with the (111) plane. A SX cylindrical ingot with diameter of 15 mm, which was produced by a traditional casting method followed by standard heat treatment, is used. The primary trunk of dendrite grows along the long axis direction of the ingot and we define it as [001]. In this way, the standard crystallographic directions [100], [010], and [001] are defined, as shown in Fig. 2. Then the (111) plane can be determined and the plate samples with thickness of 2 mm were cut for experiments. The laser surface remelting experiments were performed by using a 1 kW continuous-wave Nd: YAG laser. The laser beam is a Gaussian heat source with radius close to 0.75 mm and power distribution of 2. During the experiments, a continuous flow of Ar2 gas was directed on the surface to reduce the oxidation. To examine the effect of substrate orientation on the SG formation ability, proper laser processing conditions such as the power and scanning velocity should be selected. According to the
2. Experiments 2.1. The selected orientations in (111) plane The variation in the substrate orientation can be performed by changing the laser scanning along different directions in the fixed (111) plane. We selected the substrate orientation by altering the laser scanning direction via rotating an angle x around [112]
Fig. 1. Schematic illustrations of (111) plane in fcc lattice and the laser scanning direction Vb.
Fig. 2. Schematic illustration for producing the substrate orientations of (111) plane.
Table 1 Nominal compositions of superalloy DD6 in wt. % [24]. Element
Cr
Co
Mo
W
Ta
Re
Nb
Ti
Al
Hf
Fe
Zr
S
Ni
DD6
4.3
9.0
2.0
8.0
7.5
2.0
0.5
e
5.6
0.1
e
e
e
Bal.
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theoretical predictions, if SGs do not form at initial orientation (x ¼ 0 ), they may not form at other orientations. Therefore, SGs are required to form at initial orientation x ¼ 0 , and then the situations at other orientations can be compared. For this purpose, different processing conditions have been tried and the selected parameters in the present work are: the beam power is 200 W and the scanning velocity is 5 mm/s. The experiments were then performed for varying laser scanning directions under this processing condition. A comparison experiment at a beam power of 150 W but same speed for the same orientations is also conducted to show the contribution of laser power. After the experiments, the samples were polished and etched by a solution of H2O þ HCl þ HNO3 in 1:2:1 ratio. The microstructures in the melt pool were then determined by optical microscopy in the transverse and longitudinal sections of the laser traces. Electron backscattered diffraction (EBSD) analysis was used for measuring the orientations in the weld pool to examine the stray grains. To further quantify the effect of substrate orientation, the areas of SGs and melt pool were measured at transverse sections, and the area fraction of SGs was used to evaluate SG susceptibility experimentally. 3. Results In this section, the transverse micrographs at different xs (0 , 30 , 60 and 90 ) will be presented, by which we will show the variation in SG susceptibilities for different substrate orientations for comparison. All the experiments were done by using the same laser velocity whereas the laser powers are 200 W and 150 W, respectively, as are presented below. 3.1. Laser melting at 200 W Fig. 3 shows transverse micrographs of the samples with different angles of x. For varied orientations, several domains with different preferred crystallographic directions are produced and their boundaries undergo continuous changes with the increasing angle. For x ¼ 0 , Fig. 3(a), three dendrite growth domains, [010], [100], and [001], form, and one domain intersection appears. SGs appear mainly within the [001] domain and near [010]/[001] and [100]/[001] boundaries, as the arrows mark. As will be shown later, the distributions of SGs and boundaries lines are functions of substrate orientation. This is an important factor contributing to the difference in SG susceptibility. With the increase of x, the competition of [010], [100], and [001] domains occurs. When x is increased to 30 , the [010]/[100] boundary tilts to the right side of the weld pool while the [001] domain moves to the same direction, leading to that the intersection of these dendrite domains towards upper right. This gives rise to a smaller [100] domain and a larger [010] domain while the size of [001] domain remains nearly unchanged. In this case, the stray grains are still produced near domain boundaries but their volume fraction decreases. When x reaches 60 , three dendrite growth domains, [001], [001], and [100], form. The [001] domain occupies the majority part in the center whereas the [100] and [001] domains with relative smaller sizes stay in the left and right corners. One cannot observe stray grains for this orientation. At x ¼ 90 , the [001]/[010] and [001]/[ 100] boundaries form in the left side. The [100]/[010] boundary moves to the right close to the centerline and the stray grains form again around the domain intersection and boundary lines. As to the SG formation for different substrate orientations, one typical characteristic is that with the increase of x under the current processing condition, the amount of SGs decreases firstly to x ¼ 60 at which nearly no SG forms, then increases again when x reaches to
Fig. 3. Transverse-section micrographs for different xs with the laser power of 200 W. (a) x ¼ 0 , (b) x ¼ 30 , (c) x ¼ 60 , and (d) x ¼ 90 .
90 . Fig. 4 presents the typical EBSD maps in the transverse-section of weld pool for x ¼ 0 and x ¼ 60 at 200 W, which correspond to Fig. 3(a) and (c). It can be seen clearly that the stray grain forms near [010]/[001] boundary and with [001] domain for x ¼ 0 whereas there is no stray grain for x ¼ 60 . To quantify the stray grain susceptibility as a function of substrate orientation, the area ratio of the stray grains to the weld pool, 4e, is measured for different xs. The results are given in Fig. 5. Clearly, the area ratio of the stray grains decreases firstly and then increases. 3.2. Laser melting at 150 W Fig. 6 shows transverse micrographs of the samples with x under the laser power of 150 W. With the increase of x, the variation trend of distribution of the various domains is similar to that of the high
Fig. 4. EBSD maps of welding pool transverse-section for different xs with the laser power of 200 W. (a) x ¼ 0 , (b) x ¼ 60 . The relevant directions [100], [010], [001] in (a) and (b) correspond to those in Fig. 3(a) and (c).
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processing condition, and we will discuss this aspect further in the following section.
4. Discussions In a laser weld pool, the formation of the stray grains in a specific domain with the preferred growth direction [hkl] during the laser remelting process is mainly controlled by the thermal gradient, Ghkl, and the growth velocity of dendrite, Vhkl. If these two parameters can be controlled properly, the local volume fraction of equiaxed stray grains, which is calculated by the following equation [25],
2
4pN0 f ¼ 1 exp4 3 Fig. 5. Variations in the experimental area ratio of the stray grains to the weld pool 4e and the calculated area-weighted average volume fraction 4of SGs with different xs.
laser power 200 W. Nevertheless, no SG forms in the weld pool of all substrate orientations in (111) plane, indicating that lower power under the same velocity condition could be beneficial to avoid CET. It should be bear in mind that although the smaller power could be helpful, it may not be suitable for laser repair of SX superalloy since a series of technological problems can be brought in such as incomplete melting of powder and higher surface roughness of the cladding layer during the process of laser forming. However, we present the results of 150 W here to show that different laser powers influence the stray grain susceptibility under the specific
1
1=n ðn þ 1Þ Gnhkl aVhkl
!3 3 5
(1)
will be smaller than a critical value related to the physical parameters of the materials. In this case, no stray grain will be produced. In the above equation, the value of a, n, and N0 are constants related to materials. Since no such experimental data are available for DD6 at present, we take the values from the work of Gaumann et al. for CMSX-4 [7] as a ¼ 1.25 106 K3.4/m,s, n ¼ 3.4, and N0 ¼ 2 1015/ m3. Ghkl and Vhkl are related to the isothermal thermal gradient Gsl and isothermal dendrite growth Vsl velocity in the weld pool:
Ghkl ¼ Gsl $cosjhkl
(2a)
Vhkl ¼ Gsl =cosjhkl
(2b)
where jhkl is the angle between the [hkl] preferred dendrite growth direction and normal vector to the solidification front. It should be stressed here under the fixed laser power and laser scanning velocity, the distributions of Gsl and Vsl do not vary with substrate orientation. However, the substrate orientation does change Ghkl and Vhkl via cosjhkl in Eq. (2). Thus, for elucidating the contribution of substrate orientation on stray grain susceptibility, the distribution of cosjhkl should be examined. According to the geometrical model proposed by Rappaz et al. ! ! ! [26], cosjhkl can be determined as n , u hkl . u hkl is the unit vector ! along the preferred dendrite growth direction [hkl] and n is the normal vector to the solidification front as given in Fig. 7, in which a schematic diagram of weld pool is presented to show the rela! tionship between associated angle and n . In (111) plane, since x ¼ 0 is defined to be parallel to [112], a matrix for transforming ! u 112 along [112] crystallographic reference system into a x-y-z reference system is given by
Fig. 6. Transverse-section micrographs for different xs with the laser power of 150 W. (a) x ¼ 0 , (b) x ¼ 30 , (c) x ¼ 60 , and (d) x ¼ 90 .
Fig. 7. Schematic illustration of weld pool diagram to show the relationship between ! associated angle and n in (111) plane.
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2
pffiffiffi 6 6 6 6 3 cosð60 þ xÞ 6 pffiffiffi 6 6 R ¼ 6 6 sinð60 þ xÞ 6 3 6 pffiffiffi 6 6 3 4 3
pffiffiffi 6 cosð60 xÞ 3 pffiffiffi 6 sinð60 xÞ 3 pffiffiffi 3 3
3 pffiffiffi 7 6 cosx 7 7 3 7 pffiffiffi 7 7 6 sinx 7 7 3 7 pffiffiffi 7 7 3 5 3
(3)
Now, in order to reveal the underlying mechanism of the substrate orientation on the stray grain formation in (111) plane, Gsl and Vsl were calculated by a 3-D steady-state heat transfer model which contains heat conduction and heat convection equations [21,22]. The Marangoni convection has quite slight effect and can be neglected under the present processing conditions [27]. After obtaining Gsl and Vsl, the distributions of Ghkl, Vhkl, and f were calculated according to Eqs. (1)e(3), then the area-weighted average volume fraction of equiaxed SGs, 4, was determined to show the stray grain formation ability as a function of substrate orientation [22]. Finally, the contribution of the orientation in (111) plane was discussed. The calculation method here has been described in detail in our previous work [21], and the physical parameters used in the calculation are listed in Table 2 [28]. Fig. 8. Variations in the distribution of thermal gradient Ghkl for different xs.
4.1. The distributions of Ghkl, Vhkl and f Fig. 8 shows the variation in the distribution of the thermal gradient with x in (111) plane. The calculated distributions of different dendrite domains with preferred crystallographic directions are marked by the dashed lines. It can be seen that the calculated dendrite domain distributions agree well with those obtained by experiment as shown in Fig. 3. For the Ghkl distributions in four situations (Fig. 8aed), the value of Ghkl increases from 3.42 105 to 1.05 106 K m1. Within the most parts in the weld pool, Ghkl ranges from 4.3 105 to 7.83 105 K m1. The minima of Ghkl exist in some positions, which vary with the substrate orientation. With the increases of x, the position of the minimum Ghkl moves from center part towards upper right. When x equals 60 , the right minimum region moves to upper right continuously and symmetric minimum region appears in the upper left edge, resulting in a symmetrical distribution of Ghkl. At x ¼ 90 , the dark blue region enlarges from the left side, forming an ideal mirror image of G distribution in comparing with that of x ¼ 30 . Fig. 9 gives the variations in distribution of the dendrite growth velocity, Vhkl, with x. It can be seen that near the weld pool boundary, Vhkl is the smallest and its value tends to be zero for all cases. With the position moves from the pool boundary to the center and upper part, Vhkl increases. For different xs, however, the intensities of the increase are different, resulting in different maximum value of Vhkl. Moreover, the position of the Vhkl maximum also varies with substrate orientation. For x ¼ 0 , Fig. 9(a), V increases and its value reaches 8.1 103 m/s at the domain
intersection in the center part. For x ¼ 30 , Fig. 9(b), the value of Vhkl can exceed 7.1 103 m/s at the domain intersection near the upper right region. For x ¼ 90 , Fig. 9(d), the situation is similar to that of the x ¼ 30 , except that the left and right region reverses. If x equals 60 , Fig. 9(c), however, the maximum value of Vhkl only can reach 6.1 103 m/s, and it locates in a small region in the upper center part of the weld pool.
Table 2 Physical parameters of DD6 used in the calculation of the temperature field [28]. Physical parameter
Unit
Value
Density Solidus temperature Liquidus temperature Thermal conductivity Specific heat of solid Coefficient of thermal expansion
Kg m3 K K W m1 K1 J kg1 K1 K1
8.78 103 1651 1672 22.3 600 1.41 105
Fig. 9. Variations in the distribution of dendrite growth velocity Vhkl for different xs.
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245
Apparently, the calculated minimum Ghkl and maximum Vhkl locate at the domain intersection, and their values for different substrate orientation are presented in Fig. 10. At x ¼ 60 , the minimum Ghkl has largest value and the maximum Vhkl has the smallest value. By using the data of thermal gradient and growth velocity for every point in different domains with preferred growth direction, the distributions of local fraction of equiaxed SGs (4) at the solidification front as a function of x are calculated and the results are given in Fig. 11. For all orientations, near the fusion line, 4 is quite small and its value is less than 0.1, and this is attributed to the large thermal gradients and very small velocities. However, with the position departs from the fusion line, 4 increases and reaches a maximum value at domain intersection. The positions of the maxima vary with x. For x ¼ 0 , as shown in Fig. 11(a), the maximum 4 locates at domain intersection in the center region. For x ¼ 30 , it moves to the right side of the weld pool, and the value of 4 is smaller than x ¼ 0 . The situation of x ¼ 90 is similar to that of x ¼ 30 , where the maximum 4 is on the left side of the weld pool. However, for x ¼ 60 , two maxima of 4 move to both sides nearly outside of the melt pool, where the value of 4 is smaller than 0.41 in all positions. This indicates that it is a feasible way to avoid CET by altering the value of x.
4.2. Overall CET susceptibility After obtaining the local value of 4, the overall CET tendency within a melt pool can be determined by the area-weighted average volume fraction of equiaxed SGs 4[21,22]. The calculated 4 as a function of x is plotted in Fig. 5, in which the results of x ¼ 30 , 60 , and 90 are also presented for comparison. Clearly, the calculated 4 is symmetrical with the variation of x for the rotations around the x ¼ 0 . When x equals 0 , 4 has a maximum value, indicating that CET is most sensitive along this substrate orientation. With the increase of jxj value, 4 decreases initially till x reaches j60 j and then increases to j90 j. A minimum value existing at x ¼ j60 j reveals that SG susceptibility is weakest in this orientation, and this is in agreement with the experiment results as shown in Fig. 3, indicating that the [211] direction corresponding to x ¼ 60 in (111) plane is the most invulnerable orientation to the stray grains. Next we will analyze why the variation of the substrate orientation results in different stray grain susceptibilities.
Fig. 10. Variations in Ghkl minimum and Vhkl maximum with x.
Fig. 11. Variations in the distribution of 4 with x.
4.3. The underlying mechanism of the contribution of substrate orientation in (111) plane From Eq. (1), one can see that smaller Ghkl and larger Vhkl result in large value of f, and in such a case, CET will occur easily and equaixed stray grains are inclined to be produced. Due to this reason, the locations which have the minimum value of Ghkl and the maximum value of Vhkl could be the most susceptible position to equiaxed stray grains. As shown in the above sections, Ghkl minima and Vhkl maxima as well as their distributions vary with x. For different substrate orientations, the minimum Ghkl and the maximum Vhkl always appear at the domain intersection, which leads to a maximum f there, as shown in Figs. 8 and 9. This indicates that the intersection points are the most vulnerable locations to CET. The value of Ghkl increases and that of Vhkl decreases along the domain boundaries from the domain intersection, and the former increases further and the later decreases further within the domain inside, respectively, suggesting that the CET ability weakens in the sequence of domain intersection, domain boundary, and domain inner part. Bearing this point in the mind, we can understand why CET susceptibility changes with the substrate orientation and why x ¼ 60 has no stray grains whereas the other three have. For x ¼ 0 , 30 or 90 , there is one domain intersection in the weld pool although its position changes. At the domain intersection, the thermal gradient and the growth velocity reaches the minimum and the maximum values, respectively. However, for x ¼ 60 , the situation is quite different. The domain intersection moves to the right side nearly outside the weld pool. There is the other mirror domain intersection appears in the left side. Moreover, the Ghkl minima reaches its maximum and Vhkl maxima reaches its minimum for x ¼ 60 as Fig. 10 presents. That means Gnhkl =Vhkl in such a case is much larger than those in other three ones and it results in a relatively smaller local volume fraction and areaaverage volume fraction of equiaxed stray grain, as shown in Figs. 11(c) and Fig. 5. This is the reason why the substrate
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orientation of x ¼ 60 is the most invulnerable to the stray grain. In general, as discussed in our previous work [21,22], the number and location of the intersection points determine the magnitude of 4. Reducing or even eliminating the intersection points would lower 4 and finally leads to a lower value of 4. In the (111) plane, we found that the x ¼ 60 laser scanning direction can provide an ideal orientation for remelting of SX superalloys, i.e., the (111)/[211] substrate orientation, under which the area-average volume fraction of equiaxed SGs is minimum. 4.4. The effect of the laser power As for the laser remelting with the laser power of 150 W, the trend of the change of the domain distributions at different substrate orientation is similar to that of 200 W. Since the power difference is not large, the sizes of weld pools in the two situations also have no apparent discrepancy. However, it is hard to find stray grains under the small laser power condition. In order to reveal the underlying mechanism, the area-weighted average volume fraction of equiaxed SGs 4 for the case of 150 W was calculated and the results are presented in Fig. 5. It can be seen that the change in 4 as a function of x is similar to that at high laser power. Nevertheless, its absolute value is smaller. This shows that under the small laser power condition, the variation in 4 agrees well with the experimental results. Combining the results given in Figs. 3 and 4, a critical value of 4 ¼ 4c should exist for DD6 under the present processing conditions, as indicated by the dash line in Fig. 5. Below the dash line, no stray grain forms under the situation of jxj ¼ 60 for 200 W and those of all xs for 150 W. If the processing conditions are changed, the values of 4 for different substrate orientations could vary. As a result, the possibility of stray grain formation could also be different. However, the situation that 4 has the smallest value at jxj ¼ 60 in (111) plane will not change, no matter how the processing conditions vary. That means, the laser scanning along [211] and [121], corresponding to x ¼ 60 and x ¼ 60 , are the best beam directions for the repair of SX superalloys in (111) crystallographic plane. 5. Conclusion In the (111) plane, the effect of substrate orientation on CET in a laser weld pool for single crystal superalloys is investigated for different x as we defined. It is shown that CET depends evidently on the substrate orientation. With the increase of x, the susceptibility of equiaxed stray grain decreases to 60 and then increases again. The theoretical calculated results indicate that it is the x dependent variation in thermal gradient and dendrite growth velocity in different domains that results in the different stray grain susceptibility. Both the experimental and theoretical investigations reveal that the optimized substrate orientation in (111) plane in the laser remelting of SX superalloy is x ¼ 60 and it will be the best direction in the future laser repair of SX components in (111) plane. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 51671160 and 51801160), the Aviation Science Foundation (Grant No. 2017ZF53066), and the Fund of the Innovation Base of Graduate Students of NPU. We would like to thank the Analytical & Testing Center of Northwestern Polytechnical University for the EBSD map determination.
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