Abstract: Single crystal superalloy turbine rotor blades are one of the core hot end components of aero-engines, which plays a decisive role in the thrust and performance of aero-engines. The additive repair technology of its service damage is one of the most challenging tasks in the field of special processing of aero-equipment. This paper systematically sorts out the additive repair process methods and application progress of single crystal superalloy turbine rotor blades of aero-engines; the hot crack defect problem that is easy to occur in single crystal alloy additive repair is summarized from the perspectives of hot crack formation mechanism, key influencing factors and control measures; and the research progress of single crystal alloy additive repair microstructure and performance is summarized. On this basis, the future development direction of single crystal superalloy turbine rotor blade additive repair is prospected, and it is pointed out that the design of alloy material composition for single crystal alloy repair, new process development and multi-objective collaborative optimization based on deep learning are important research directions in this field in the future.

Keywords: single crystal superalloy; turbine rotor blade; aero-engine; additive repair; hot crack; miscellaneous crystal

With the rapid development of my country’s aviation industry, the demand for high-performance and long-life engine components is increasing. Single crystal high temperature alloys have become important structural materials for manufacturing hot end components of aircraft engines due to their excellent high temperature strength and fatigue performance, creep resistance, corrosion resistance and oxidation resistance. As one of the core hot end components of aircraft engines, turbine rotor blades have the main function of converting the thermal energy of high temperature and high pressure gas into mechanical energy, driving the turbine shaft to rotate, and then driving the compressor and other accessories to work. They are the key link in determining the thrust and performance of aircraft engines.

Since single crystal high temperature alloy turbine rotor blades of aircraft engines have been in service for a long time in extremely harsh working conditions such as centrifugal loads, thermal stresses and high temperature corrosion, various local damages such as cracks, ablation, and wear are inevitable, which seriously affect their service performance and need to be replaced or repaired. However, the preparation process of single crystal high temperature alloy turbine rotor blades is extremely complicated, and the manufacturing cycle is long and the yield is low. Replacing new blades will cause great waste of materials and greatly increase costs. Therefore, single crystal high temperature alloy turbine rotor blade repair technology has become a research hotspot in the field of aircraft engine maintenance.

Due to the complex surface design, special microstructure characteristics and harsh operating load conditions of turbine rotor blades, the repair of service damage should not only consider restoring the blade geometry and maintaining the integrity of the single crystal, but also avoid metallurgical defects in the repair area and its bonding area with the substrate, so as to meet the stringent service requirements. The main problem of single crystal high temperature alloy repair is the formation of hot cracks and stray crystal defects. The generation of hot cracks will cause repair failure, and the introduction of stray crystals will greatly reduce the high temperature creep and fatigue resistance of single crystal high temperature alloys. In response to the above problems, domestic and foreign academic and engineering circles have carried out a lot of research work, and have achieved a series of research results in the dendrite solidification theory, hot crack formation mechanism and organizational performance control method of single crystal high temperature alloy turbine rotor blade repair area.

This paper systematically sorts out the repair process methods and application progress of single crystal high-temperature alloy turbine rotor blades for aero-engines. Aiming at the problem of hot crack defects that are easy to occur in single crystal alloy additive repair, the paper summarizes the research progress of single crystal high-temperature alloy additive repair structure and performance from the perspectives of hot crack formation mechanism, key influencing factors and control measures. On this basis, the future research direction and development trend of single crystal high-temperature alloy turbine rotor blades are prospected.

1 Research and application progress of single crystal high-temperature alloy turbine rotor blade repair methods

For the repair of single crystal high-temperature alloy turbine rotor blades for aero-engines, wire arc direct energy deposition (WA-DED), laser directed energy deposition (DED-L), laser powder bed fusion (LPBF) and brazing are generally used.

1. 1 WA-DED additive repair technology
WA-DED additive repair technology uses the high-temperature arc generated between the non-melting electrode (tungsten electrode) and the workpiece as a heat source to partially melt the surface of the repaired part to form a molten pool, and at the same time melt the welding wire (filler material) that is manually or automatically delivered to the front of the molten pool by the wire feeder. The molten welding wire flows into the molten pool through the front wall of the molten pool. As the arc moves forward, the molten pool gradually cools and solidifies to form a new metal layer, thereby realizing the layer-by-layer accumulation and repair of the material. During this process, inert shielding gases such as argon are continuously ejected through the welding gun nozzle, covering the arc, molten pool and heat-affected zone, forming a local gas protection layer, effectively isolating the air, and preventing the repair area from being oxidized and contaminated. WA-DED additive repair technology has the characteristics of high repair quality, flexible operation, and adaptability to all-position repair. It is one of the technologies widely used in the repair of single crystal high-temperature alloys.

Cai Zupeng used the WA-DED process to weld and melt DD407 single crystal alloy, and studied the influence of process parameters on solidification structure characteristics, impurity crystals and crack defects. He pointed out that arc heat input is the main factor affecting the microstructure of the melting zone. The use of smaller current and larger movement speed can effectively reduce the impurity crystal content in the melting zone and ensure the integrity of the single crystal. In addition, the crack types in the melting zone are mainly arc crater cracks and intercrystalline cracks, and the cracks are mostly concentrated in the impurity crystal area.

In view of the influence of repair alloy materials on WA-DED additive repair of single crystal alloy rotor blades, Churchman et al. used three filler materials, IN625, FM-92 and IN738, to perform additive repair on Rene N5 single crystal alloy. It was found that the weld shape is an important factor affecting the cracking incidence. Even if there are stray grains in the WA-DED deposited layer, cracks are not easy to occur. None of the three filler materials caused cracking problems. Based on the wear and crack damage of the tip of DZ125 directional alloy turbine blade, Qu Shen et al. used the WA-DED process to explore the applicability of traditional cobalt-based welding materials (Co-Cr-W, Co-Cr-Mo, GH605) and self-developed MGS-1 nickel-based welding materials. It was found that when cobalt-based welding materials were used for repair, thermal cracks were easily formed in the heat-affected zone, and the hardness of the repaired zone decreased significantly; when MGS-1 nickel-based welding materials were used, the crack problem in the heat-affected zone could be significantly reduced or even eliminated, and the tensile strength at 1000 ℃ reached 90% of the parent material strength, showing excellent repair quality and performance recovery effect. In terms of WA-DED additive repair applications, Canada’s Liburdi Group uses automatic wire feeding WA-DED additive repair equipment for blade repair, and has achieved the repair of high-, medium- and low-pressure turbine rotor blades of the RB211 engine. AECC Beijing Institute of Aeronautical Materials is at the leading level in China in the research of WA-DED additive repair of single crystal alloy turbine rotor blades. It has used precision arc welding to additively repair the tip damage of a gas turbine Rene N5 single crystal turbine rotor blade. The tip repair area after the size is restored is a directional columnar crystal (Figure 1). The repaired blade has been installed and applied.

1. 2 DED-L additive repair technology
DED-L additive repair technology uses a high-energy-density laser beam to heat and melt the substrate and the filler material coaxially delivered to the surface of the substrate to quickly form a local molten pool. As the laser heat source moves, the molten pool solidifies and the filler material is deposited. The unique advantage of DED-L technology lies in its highly flexible process control capability. It can not only customize the growth direction of the metal structure according to demand, such as preparing columnar crystal structure and single crystal structure, but also has the ability to quickly repair damaged parts, greatly improving production efficiency and material utilization. At the same time, DED-L technology can also flexibly control the alloy composition of the repair area by mixing metal powders of different properties, providing new design ideas and implementation methods for the organization control and performance improvement of the repair structure.

The high temperature gradient and solidification rate in the DED-L additive repair process of single crystal alloys can reduce the primary dendrite arm spacing and refine the γ′ phase. The refined γ′ phase can more effectively hinder dislocation movement, improve the high temperature strength and creep resistance of the material, and thus have a positive impact on the mechanical properties of single crystal materials or components. Gäumann et al. used DED-L technology to additively repair the crack damage of CMSX-4 single crystal turbine rotor blades, as shown in Figure 2, verifying the feasibility of this technology in the repair of single crystal high temperature alloy turbine rotor blades.

Vurgun et al. used DED-L technology to repair PWA1484 single crystal alloy turbine rotor blades using high temperature alloy powders of the same parent material. By adjusting the process parameters, the maximum repair height reached 2.3 mm, and the repair success rate was as high as 94.85%. Cardoso et al. used DED-L technology to deposit René N4 alloy on the surface of René N5 single crystal alloy and found that the deposited layer inherited the crystal structure and orientation of the single crystal matrix, forming a columnar dendrite solidification structure with obvious texture, which shows that it is also feasible to use heterogeneous filler materials for DEL-L repair on a single crystal high-temperature alloy matrix.

Wang et al. used DD407 single crystal high-temperature alloy as the object to compare the differences in microstructure and mechanical properties between DED-L and arc additive repair with depth. The results show that both repair areas can maintain single crystal epitaxial growth without obvious cracks and have similar fine-grained precipitates. During the DED-L process, a columnar crystal to equiaxed crystal transition phenomenon appeared at the top of the repair area. Kaierle et al. combined DED-L and laser remelting to successfully achieve deposition and remelting on the tip surface of CMSX-4 and PWA 1426 single crystal alloy turbine rotor blades to form a complete single crystal structure, providing a new method for repairing single crystal high temperature alloys.

Honeywell has successfully applied DED-L additive repair technology to the repair of turbine rotor blades for the LF507 engine of the Avro RJ regional jet series. The Fraunhofer Innovation Center in Germany has developed DED-L additive repair technology that can be used to repair rotor blade tip damage, as shown in Figure 3, and has formed additive repair, machining, precision polishing and non-destructive testing repair specifications. Domestically, the Shenyang Engine Design Institute and the Shenyang Liming Aero Engine Company have conducted research on the DED-L additive repair technology for the tip cracks of a certain type of engine turbine rotor blade. The repaired rotor blades have passed the 300-hour thermal shock test in a near-service environment and meet the overhaul blade failure inspection standards. The Beijing Institute of Aeronautical Materials of China Aero Engine Corporation has conducted research on the DED-L additive repair technology for DD6 and DD32 single crystal alloy turbine rotor blades with post-service tip wear and cracks, and repaired single crystal alloy blades without cracks and unfused defects, and the repaired area has obtained a near-single crystal directional structure, as shown in Figure 4.

1. 3 LPBF additive repair technology
LPBF additive repair technology uses the energy output of the laser to accurately control the beam trajectory through a scanning galvanometer, directly acting on the metal powder particles laid on the powder bed to achieve complete melting and layer-by-layer construction of a three-dimensional entity. LPBF technology significantly improves the surface finish and dimensional accuracy of repaired parts by using finer powder particle size and optimized laser beam spot size. Limited by the size of the printing room and the operating environment, its application scope is mainly for the repair of small, complex and extremely high precision parts.

Atabay et al. used LPBF technology to prepare high-density crack-free Rene 77 single crystal high-temperature alloy. Scanning electron microscopy analysis showed that the microstructure of the sample was composed of columnar grains mainly arranged along the <100> direction, fine γ′ precipitate phase and spherical grain boundary carbides. Zhang Yu et al. used LPBF technology to epitaxially grow an alloy powder with a medium volume fraction of γ′ phase on a CM247LC single crystal substrate. It was found that when the width-to-depth ratio of the molten pool at the repair interface was greater than 4, the deposition area and the substrate could form a good bonding interface and a small grain orientation difference. By increasing the scanning rate and reducing the laser power, the crack density in the deposition area can be effectively reduced. The deposition structure is mainly columnar dendrites growing along the deposition direction. The higher the deposition layer, the smaller the cooling rate, the greater the dendrite spacing and grain orientation difference. By optimizing the printing parameters, a nickel-based single crystal high-temperature alloy deposition layer with low crack density, single grain orientation and excellent bonding with the single crystal substrate was finally obtained. Its tensile strength can reach 1094 MPa and its elongation can reach 21%.

Wang et al. used CM247LC filling material to perform additive repair on damaged SRR99 single crystal alloy turbine rotor blades (Figure 5). It was found that crack-free metallurgical bonding was achieved at the CM247LC/SRR99 interface, and the shrinkage cavity in the cast SRR99 area was effectively eliminated in the CM247LC repair area. Compared with the SRR99 matrix, the hardness of the repaired area increased by 8.62%. The tensile strength of the repaired sample was 791 MPa. The fracture occurred in the SRR99 matrix, indicating that the CM247LC/SRR99 interface has excellent metallurgical bonding strength.

1.4 Brazing additive repair technology
Brazing additive repair technology is to heat the high-temperature alloy and the low-melting point brazing material to above the melting point of the brazing material, and fill the liquid brazing material in the repaired area through capillary action to achieve the repair of the single crystal high-temperature alloy. At present, the more common single crystal high-temperature alloy repair brazing material mostly uses boron (B) as a melting point depressing element. However, due to the low solubility of B element in nickel-based high-temperature alloy, a large amount of low-melting point brittle boride is easily formed during the non-isothermal solidification process, which triggers the initiation and expansion of cracks and reduces the mechanical properties of single crystal high-temperature alloys.

Lang et al. [31] developed a Ni-40Cr-10Ta (atomic fraction/%) alloy as a filler material for single crystal high-temperature alloys, and achieved high-performance brazing of DD5 single crystal alloy. Compared with traditional brazing fillers containing B and Si elements, it avoided the formation of B- and Si-rich compounds and low-melting point eutectics, effectively improved the performance of the repaired area, and the tensile strength of the joint reached 654 MPa, which was 88.5% of the single crystal matrix, showing a good repair effect.

High entropy alloys have attracted extensive attention due to their unique composition and adjustable properties, and have great potential in reducing brittle intermetallic compounds in brazed joints. Ren et al. developed a Ni-Co-Cr-Al-Nb-Ti brazing filler metal with a melting point of 1155 °C and achieved the repair of DD6 single crystal superalloy under 1200 °C brazing conditions. After aging treatment, the alloying elements are distributed more evenly, the size of the interdendritic second phase is refined, and the γ+γ′ phase in the repaired area has the same orientation as the DD6 single crystal matrix, and the tensile strength at 980 °C can reach 559 MPa.

2 Research progress on thermal crack repair of single crystal superalloy turbine rotor blades

Since single crystal superalloys have relatively low shrinkage during the cooling process between liquid and solid phases, they often show high sensitivity to thermal cracks and a series of shrinkage defects. In addition, due to the rapid heating and cooling during the additive repair process, the tendency of thermal crack formation is further increased, which seriously affects the mechanical properties of single crystal alloy repair parts. At present, a variety of single crystal high temperature alloys that have been widely studied, such as CM247LC, CMSX-10, DD432, DD6, etc., are very prone to thermal crack defects during additive repair.

2.1 Study on the formation mechanism of thermal cracks in single crystal alloy additive repair
The crack defects generated during the additive repair of single crystal high temperature alloys mainly include solidification cracks and liquefaction cracks, and their typical characteristics are shown in Figure 6. Solidification cracks mainly occur in the mushy zone where liquid and solid phases coexist at the end of solidification. During the solidification process, the formation of dendrite structure inhibits the flow of residual liquid between dendrites. At the same time, under the action of thermal strain/stress caused by solidification shrinkage, the liquid film between dendrites is torn to form solidification cracks. In addition, due to the uneven distribution of alloying elements in the liquid, a low-melting-point liquid film is formed around the newly formed grains. These low-melting-point liquid phase films will reduce the solid-liquid interface energy and promote the generation of cracks by extensively wetting solid dendrites. Since the brittle grain boundaries cannot transmit residual tensile stress or shrinkage caused by cooling melt, two adjacent grains will separate and form solidification cracks. Han et al.’s research shows that solidification cracks generally initiate between grains and extend along high-angle grain boundaries (HAGBs>15°).

Liquidation cracks generally occur in the partially melted zone adjacent to the matrix metal fusion zone. During the heating process, due to the high temperature in this area, some low-melting-point phases are remelted into liquid phase films, involving the softening and liquefaction of γ-γ′ eutectic, unstable decomposition of coarse γ′ phase, thermally induced liquefaction of MC-type carbides, and dissolution of precipitated phases. Under the action of residual stress, these liquid phase films are prone to crack formation. Zhao et al. observed obvious liquefaction in the crack area of ​​Rene88DT alloy repaired by DED-L additive, showing a typical brittle intergranular fracture mode. The resolidified products in the crack contain a large amount of Ti, Al, Cr, Co and Ni, i.e., γ+γ′ eutectic. Li et al. verified the existence of liquid film and the propagation behavior of liquefaction cracks in the K465 alloy formed by DED-L, and found that cracks with a certain width started from the heat-affected zone and extended to the repair zone along the grain boundary or dendrite growth direction. Similar to solidification cracks, liquefaction cracks are also easy to propagate along HAGBs.

Lu et al. studied the formation mechanism of hot cracks in DED-L forming of CMSX-10 and DD432 single crystal high-temperature alloys, and concluded that the formation of hot cracks in the deposition zone of single crystal alloys depends on the stability of the liquid film, stress concentration and the combined effect of the precipitation phase at the grain boundary. The stability of the liquid film depends on the undercooling of dendrite solidification. When the undercooling of dendrite solidification at the grain boundary angle where a stable liquid film is formed is greater than the undercooling of the liquid film between dendrites inside the grain, a stable liquid film will be provided for the formation of intercrystalline crack sources; at the same time, the high level of stress concentration inside the deposition area drives the initiation and expansion of hot cracks; the Re-rich precipitate phase further promotes the formation of hot cracks by inhibiting liquid phase shrinkage through “pinning” and weakening the bonding strength between the phase and the matrix.

2. 2 Research on the method of suppressing hot cracks in single crystal alloy additive repair
The process parameters directly affect the solidification conditions and stress state of single crystal alloy additive repair, so process optimization is an important way to suppress hot cracks. Gäumann et al. and Lu et al. pointed out that since the grain boundary area of ​​single crystal materials is much smaller than that of polycrystalline materials, the sensitivity of single crystal materials to hot cracks is lower, and the introduction of impurities will significantly increase the sensitivity of hot cracks. Therefore, epitaxial growth can suppress the hot crack defects of single crystal alloy additive repair. Rong Peng et al. conducted multi-pass multi-layer deposition repair experiments using DED-L to explore the relationship between the cracking sensitivity of single crystal alloys and grain size. They found that grain size is an important factor affecting the formation of solidification cracks. A larger grain boundary angle will cause thermal cracks, while a smaller grain size can increase the critical grain boundary angle. As the laser scanning speed increases, the grain size decreases and the tendency of solidification cracks weakens. When the laser power is 250 W, the scanning speed is 2.5 mm/s, the single-layer lifting height is 100 μm, and the superposition rate is 4.1%, the solidification cracks can be completely eliminated, and defect-free repair of damaged single crystal blades can be achieved.

Chen et al. conducted DED-L experiments on DD407 single crystal alloy using two different cooling methods, air cooling and water cooling, and found that the epitaxial microstructure formed under air cooling conditions had almost no cracks, while under water cooling conditions, the thermal crack sensitivity of the deposited layer would increase due to the accumulation of thermal stress. Under water cooling, almost all cracks appeared in the overlapping area, and only a few cracks appeared in other areas. Element distribution analysis and grain boundary angle analysis show that microsegregation and large-angle grain boundaries lead to typical solidification hot cracks. The above research results show that by changing the cooling state during the single crystal repair process and reducing the accumulation of thermal stress, the generation of hot cracks can be effectively suppressed.

Lu Nannan et al. proposed a dynamic deposition strategy, which relieved the stress concentration in the deposition area and reduced the formation of grain boundaries by reducing the laser power (heat input) layer by layer, that is, the laser power was reduced from 1000 W in the first layer to 550 W in the last layer, and obtained a single crystal alloy deposition sample without crack defects.

3 Research progress on the repair organization and performance of single crystal high-temperature alloy turbine rotor blades

3. 1 Organization research of single crystal alloy additive repair

3. 1. 1 Organization characteristics of single crystal alloy additive repair
The typical organizational characteristics of single crystal alloy additive repair are shown in Figure 7. From bottom to top, it can be divided into the bottom metallurgical bonding zone (i.e., the bonding interface between the substrate and the deposited layer), the middle continuous epitaxial growth columnar crystal zone with the same orientation as the substrate, and the top equiaxed crystal zone. During the additive repair process, the formation of equiaxed grains hinders the epitaxial growth of [001] dendrites and destroys the integrity of single crystal growth. The high energy density heat source provides high temperature gradient conditions for the continuation of matrix columnar crystals and their continuous epitaxial growth. As the temperature gradient from the bottom to the top of the molten pool decreases and the solidification rate increases, the transformation from columnar to equiaxed can be observed at the top of the molten pool, forming miscellaneous crystals.

Lei et al. found that in the repair of single crystal high-temperature alloys, miscellaneous crystals basically exist in three typical locations: the outer surface of the deposition zone, the upper part of the deposition zone, and the bottom of the deposition zone, as shown in Figure 8 (a) to (d). The miscellaneous crystals on the outer surface of the deposition zone are mainly due to the fact that the incompletely melted single crystal powder adheres to the outer surface of the molten pool where the solid phase has not yet formed during the deposition process. This type of incompletely melted single crystal powder is equivalent to the nucleation point of the liquid phase at the solidification front of the columnar crystal, and finally forms equiaxed crystals on the side wall surface. This type of equiaxed crystal has a typical radial dendrite morphology, and its core is an unmelted solid phase. The upper impurities are mainly due to the equiaxed crystal structure formed with the increase of deposition height and the decrease of temperature gradient. For the impurities at the bottom of the fusion zone, during the deposition process, the solid phase matrix will melt under the irradiation of the laser. When the molten interface is distributed with a large number of precipitation phases and eutectic phases of low-melting-point elements, the position will collapse, as shown in Figure 8 (e) and (f). The direction of the temperature gradient at the collapse of the fusion interface will deviate from the original temperature gradient. During the growth of cellular crystals, the cellular crystals grow in the opposite direction of heat dissipation at the solid-liquid interface, that is, the cellular crystals grow in a direction perpendicular to the solid-liquid interface. Therefore, at the collapse of the fusion interface caused by large-sized precipitation phases and eutectic phases, the growth direction of the cellular crystals will be deflected, and then impurities at the fusion interface will be formed, as shown in Figure 8 (g)~(j).

3.1.2 Theoretical study on the repair organization of single crystal alloy additive materials
During the solidification process, the latent heat of phase change is released. According to the different latent heat transfer paths, the solidification mode can be divided into two categories: one is directional growth along a specific direction, and the other is free growth without direction restriction. The grain morphology corresponding to these two crystal growth modes is columnar crystal and equiaxed crystal, respectively. During the epitaxial growth of single crystal alloy, if the solidification conditions change, causing the grain morphology to change from columnar to equiaxed transition (CET), miscellaneous crystals with different orientations and deviating from the substrate crystal direction will be formed in the repair area. In essence, the formation of miscellaneous crystals is the CET of grain morphology.

Since the 1980s, many scholars at home and abroad have carried out a series of theoretical and experimental studies on the CET phenomenon in the solidification process. Studies have shown that the compositional supercooling dendrite solidification theory is a major mechanism for the transformation of grain morphology from columnar crystals to equiaxed crystals. Under the columnar crystal growth mode, the heat flow direction is opposite to the growth direction of the dendrite, and the movement rate of the isotherm is the key factor in the migration speed of the solid-liquid interface. For alloy materials, if the solute distribution coefficient is lower than 1, a solute enrichment zone will form at the front of the solid-liquid interface, and the change in solute concentration will cause a change in the local equilibrium temperature. If the actual temperature is lower than the equilibrium temperature, the composition will be supercooled in this area, creating conditions for the formation of equiaxed crystals.

In 1984, Hunt first established the CET analytical model based on steady-state solidification conditions, combined with columnar crystal growth and equiaxed crystal nucleation and growth models, and created quantitative criteria between solidification parameters, material parameters, equiaxed crystal volume fraction and grain morphology. Based on this model, the grain morphology of the solidified structure can be determined according to different critical volume fractions. When the equiaxed crystal volume fraction at the front of the columnar crystal is 0.66%, the conditions for completely avoiding CET are shown in formula (1).
Where: G is the temperature gradient of the liquid metal at the solid-liquid interface front; N0 is the number of heterogeneous nucleation particles per unit volume; ΔTN is the critical undercooling of heterogeneous nucleation; ΔTC is the undercooling at the front of columnar crystal growth.

Kurz et al. pointed out that the core problem of repairing single crystal high-temperature alloys is to control the transformation of columnar crystals to equiaxed crystals during solidification. After comprehensively considering the effects of temperature diffusion, velocity distribution and phase change, they established the dendrite rapid solidification theory (KGT). Based on Kurz’s research, Vitek further established the relationship between process parameters and crystal growth through numerical calculation methods. This study combined the molten pool morphology with the 3D Rosenthal model to obtain the temperature gradient and solidification rate at each position inside the molten pool, revealing the influence of the molten pool morphology on the crystal growth direction. Compared with the average temperature gradient used by Kurz to evaluate the CET inside the molten pool, Vitek et al. used a local temperature gradient, which can more accurately determine whether the CET at a local position in the molten pool occurs.
In 2001, Gäumann et al. combined the KGT theory to expand the scope of application of Hunt’s CET model from steady-state solidification to rapid solidification conditions, and combined with the thermodynamic database, applied this model to the DED-L process of CMSX-4 single crystal high-temperature alloy. Since the temperature gradient and solidification rate of the DED-L process are relatively high, the effect of nucleation undercooling can be ignored, and the analytical model between the temperature gradient, the density of heterogeneous nucleation particles, the solidification rate and the equiaxed crystal volume fraction (φ) is obtained: (2). If φ<0.66%, the condition for completely avoiding CET can be obtained as follows: (3).
Where: KCET, a and n are related parameters of material properties. For CMSX-4 single crystal alloy, KCET=2.7×10’24 (K3.4/m4.4s), a=1.25×10’6K3.4/ms, n = 3.4.

According to the above Gäumann model, under the conditions of the selected single crystal alloy material, its solidification structure depends on the temperature gradient (G) at the solid-liquid interface front and the solidification rate (V) during the repair process. By adjusting G and V, the solidification structure can be regulated. This theory has been widely used in the continuous epitaxial growth of columnar crystals and the control of impurity crystals during the additive repair of single crystal high-temperature alloys.

3.1.3 Research on the influence of process parameters on the structure of single crystal alloy additive repair
The microstructure of the damaged repair area of ​​single crystal high-temperature alloy has a decisive role in the high-temperature mechanical properties of the repaired part. Obtaining complete epitaxial growth columnar crystals that are continuous with the single crystal matrix and have the same orientation through the additive repair process is the basis for the successful re-service of the repaired part. Controlling the continuous epitaxial growth of columnar crystals and avoiding the formation of impurity crystals during the additive repair process is the key to the repair of single crystal high-temperature alloys. In view of the problem of impurity crystal suppression in single crystal alloys, many scholars have carried out a lot of research work from the perspective of process parameter optimization.

Zeng et al.’s research results on DED-L additive repair of DD6 single crystal alloy showed that faster powder feeding rate and higher laser power had a positive effect on the epitaxial growth of columnar dendrites and the elimination of stray grains, while the effect of scanning speed on stray grains was not obvious. They pointed out that the residual stress caused by complex thermal cycles was not the direct cause of the formation of stray grains. The rapid movement of dislocations caused many fine grains near the fusion line to grow in different morphologies. Dislocations moved to the boundaries of columnar grains and gradually formed subgrain boundaries. In addition, the difference in the content of elements that form carbides and adjacent γ/γ′ eutectics between the dendrite core and the dendrite interregion led to the orientation misalignment of the two, which appeared as stray grains on the mesoscopic scale. Lu Nannan and Xu et al. respectively explored the effects of laser power and scanning speed on the microstructure of DED-L repaired CSU-B2 and CMSX-10 single crystal high-temperature alloys through process experiments. The ratio of the length of the continuously grown columnar crystals to the overall height of the deposition area was used to quantitatively characterize the epitaxial growth rate, i.e., r=h/H. It was pointed out that laser power and scanning speed would jointly affect the microstructure of DED-L single crystal alloys. High laser power and low scanning speed would help to increase the epitaxial growth height and reduce the epitaxial growth rate. When the laser power was greater than 600 W in the scanning speed range of 8-14 mm/s, the epitaxial growth rate was higher than 92%.

Liang et al. theoretically calculated the microstructure involving powder feeding and pointed out that a moderate powder feeding rate can effectively inhibit the formation of impurities. Lu Nannan found that as the powder feeding rate increased, the epitaxial growth height first increased and then decreased, and the epitaxial growth rate decreased significantly. Chen et al. studied the effect of powder feeding state on the quality of single crystal repair. The results showed that unstable powder feeding would change the distribution of stray particles in the molten pool, and the melting and flow of metal powder affected the local solidification conditions. The simulation experimental results showed that the injection of powder caused the melt to cool locally, thereby promoting the formation of stray crystals. At the same time, the research results of Liu et al. showed that by changing the laser defocus and tilting the laser incident angle, the local solidification conditions can be adjusted and the formation of stray crystals can be suppressed.

Regarding the effect of scanning path on stray crystals inside single crystal alloys, there are different views in the reported research results. Xu et al. conducted DED-L additive repair on CSU-B2 single crystal alloy and pointed out that compared with the unidirectional scanning method, the epitaxial growth rate of single crystal alloy prepared by the bidirectional scanning method is higher, reaching 97.4%. On the contrary, Chen et al. [60] took DD5 single crystal alloy as the research object and found that the bidirectional laser scanning mode hindered the continuous epitaxial growth of columnar dendrites. During the multi-layer laser cladding process, the change in the laser scanning direction leads to changes in local solidification conditions such as heat accumulation and heat flow direction, which will cause the epitaxial dendrites to deflect along the laser scanning direction or rotate along the epitaxial growth direction. Wei et al. also found that fiber texture was formed during unidirectional laser beam scanning, and when the laser scanning direction rotated 180°, the texture growth direction rotated 90°.

The research results of Wang et al. showed that in the DED-L process, a sufficiently high laser power was required to ensure that the impure crystal area on the surface of the previous deposition layer was completely melted, which was the prerequisite for eliminating impure crystals. Wang Huijun et al. studied the distribution of impure crystals in the remelting zone of DD6 single crystal alloy at different powers and found that the increase in laser power led to a decrease in temperature gradient, which in turn induced the transformation of columnar crystals to equiaxed crystals. The generation of impure crystals at the junction of dendrites was caused by the temperature gradient at the junction of dendrites being smaller than that at other places and the change in the direction of the temperature gradient. Liu et al. established a self-consistent three-dimensional mathematical model to predict the crystal growth and microstructure formation during the multi-layer and multi-pass laser powder deposition process of single crystal alloys. They found that the overlap rate of the laser scanning path is the key parameter affecting the continuity and consistency of the epitaxial columnar dendrite growth in the repair area. Both too small and too large overlap ratios will lead to residual impurities in the previous deposition layer.

3.1.4 Study on the influence of matrix orientation on the structure of single crystal alloy additive repair
During the process of additive repair of single crystal high temperature alloys, when the columnar dendrites in the molten pool grow epitaxially along the molten pool boundary, their direction is not strictly parallel to the temperature gradient, but they choose to grow in a preferred direction consistent with the matrix. Therefore, the matrix orientation is a key factor in controlling the epitaxial growth of columnar crystals and inhibiting the formation of impurities.

Wang Lei et al. compared the impurity formation ability of (001) and non-(001) oriented DD6 single crystal alloys during additive repair. The local solidification variables that control the microstructure were obtained through numerical calculations, and the volume fraction of impurities was used as a quantitative single crystal integrity index. The results show that compared with the (001) crystal plane, most non-(001) crystal planes can promote the epitaxial growth of columnar crystals, thereby obtaining better single crystal integrity. Guo et al. [66] compared and analyzed the influence of matrix orientation on the sensitivity of impurity formation of DD6 single crystal alloy by changing the laser scanning direction on three traditional crystal planes (001), (011) and (111). They pointed out that on the (011) and (111) crystal planes, the laser scanning direction has a significant effect on impurity formation, while on the (001) crystal plane, its effect is smaller. The three crystal planes show different CET sensitivities, and the tendency of impurity crystal formation decreases in the order of (111) > (001) > (011). It is pointed out that DED-L additive repair along the [011ˉ] direction on the (011) crystal plane can effectively inhibit the formation of impurity crystals.

Wang et al. introduced the substrate orientation into the Gäumann model and established a numerical model combining the substrate orientation and the sensitivity of equiaxed crystal formation during single crystal epitaxial growth to predict the formation trend of impurity crystals in the molten pool. It is proposed that the impurity crystals can be controlled by selecting the optimized single crystal substrate lattice orientation. Combining the results of laser surface remelting and single layer deposition experiments under different substrate orientations and the finite element simulation of local temperature gradient and solidification rate, it is pointed out that the (001)/[110] and (01 3)/[100] substrate orientations can effectively inhibit the formation of impurity crystals.

Liu et al. established a three-dimensional crystal growth model for the DED-L process of DZ125 directional alloy, and combined with process experiments, deeply studied the microstructure and crystal growth behavior of the deposited layer under different matrix crystal orientations. The results show that in the longitudinal section of the molten pool, the change of the matrix crystal orientation mainly affects the position of the transformation from columnar crystal to equiaxed crystal, while in the transverse section, it mainly affects the preferential growth direction of columnar crystal. In the longitudinal section, when the inclination angle of the matrix orientation changes from -30° to +30°, the epitaxial growth rate of columnar crystal increases approximately linearly from 9% to 94%. In the transverse section, when the inclination angle of the matrix orientation changes from 0° to +45°, the transition line of the preferential epitaxial growth direction of columnar crystal moves from the edge of the molten pool to the central axis. At the same time, Liu et al. studied the effect of the tilt angle on the microstructure and crystal growth behavior of the single crystal thin-walled structure DED-L for the special non-vertical structures such as the tilted sidewall and twisted sidewall of the DD6 single crystal alloy, and pointed out that the formability of the oblique thin-walled structure is limited to a narrow range (≤30°). Excessive tilt angles (≥40°) cannot maintain the balance of the molten pool, resulting in a poor quality, unformed molten pool. Through the continuous epitaxial growth of ultrafine columnar dendrites, the thin-walled structure continues the [001]/[100] crystal orientation of the single crystal matrix.

Wang et al. studied the effect of matrix orientation at different rotation angles on the solidification structure of the single crystal alloy DED-L process by rotating the DD3 single crystal matrix around the x-axis, y-axis, and z-axis (corresponding to the [100], [010], and [001] crystal orientations, respectively). The results show that the substrate orientation affects both the temperature gradient G and the growth rate V in the dendrite growth direction, and G is more sensitive to changes in substrate orientation than V. Therefore, the effect of substrate orientation on dendrite epitaxy and heterocrystal formation mainly depends on the change of G. Starting from the [100]/(001) initial state, when rotating around the y axis, CET changes strongly with the change of substrate orientation, while when rotating around the x or z axis, CET hardly changes. The reason for this difference is that when rotating around the y axis by 45°, there is no intersection of dendrites with different orientations in the molten pool, while when rotating around the x or z axis, at least one intersection appears. G is lowest at the dendrite intersection, so the number and position of dendrite intersections jointly affect the trend of the entire CET. Reducing the intersections or transferring them to positions with high temperature gradients is conducive to avoiding CET and inhibiting heterocrystal formation.

In addition, the geometry of single crystal alloy damage may change the heat dissipation conditions during additive repair. Chen et al. simulated the angle β between the growth direction of columnar crystals and the direction of heat flow (the angle between the [001] crystal direction and the laser axis) by preparing and rotating cylindrical specimens to solve the problem of single crystal alloy repair with complex geometry. As shown in Figure 9 (a), the influence of the heat flow angle β on the formation of stray grains was systematically explored. The results show that columnar dendrites tend to grow epitaxially along the crystal direction close to the heat flow. In the epitaxial columnar dendrite region, stray grains are generated when β exceeds the critical value of 30° (Figure 9 (b)). The repair principle of ensuring that β is not greater than 30° through geometric design was proposed.

3.2 Performance study of single crystal alloy additive repair
For the performance evaluation of single crystal alloy additive repair, Ci et al. successfully prepared crack-free DD32 single crystal alloy from a substrate and conducted medium-temperature tensile tests. The results show that the fracture of the medium-temperature tensile test is a cleavage fracture, and the fracture area is the substrate; while the fracture mode in the high-temperature tensile test is a microporous aggregation fracture, and the fracture area is the deposition layer. The reason for the different fracture modes is that the crack origins are different. As shown in Figure 10, in the medium-temperature tensile test, the coarse MC carbide fragments generated crack sources and further extended the cracks in the substrate. Due to the low melting point, the γ+γ′ eutectic is easy to crack and extend the fracture in the high-temperature tensile test.

Qin Renyao et al. [72-73] experimentally investigated the microhardness distribution of DED-L additively repaired DD6 single crystal high temperature alloy and found that the microhardness of the additively repaired area can reach 450~470HV, which is significantly higher than the DD6 single crystal matrix (402~413HV). This is due to the fact that the repair material contains higher alloying elements such as C, Cr, Co, Hf, and Re. The intergranular MC carbides formed have significant dispersion strengthening effects. At the same time, the higher Cr, Co and Re contents also have strong solid solution strengthening effects in the γ matrix phase.

Ren et al. studied the wear behavior of SRR99 single crystal alloy repair parts and compared them with their cast alloys. They found that the size of the γ′ precipitation phase of the single crystal superalloy prepared by DED-L was one order of magnitude lower, and its wear rate and friction factor were 75% and 20% lower than those of the cast alloy, respectively. The improvement in wear performance was due to its higher dislocation density, finer γ′ phase deposition and the formation of gradient structure. Yang et al. and Lei et al. studied the hot corrosion behavior of DED-L nickel-based single crystal superalloy in a fuel gas environment and compared it with the corrosion behavior of the substrate. They pointed out that the deposited single crystal layer was composed of a γ (Ni) matrix and rich spherical γ′ (Ni3Al) nanoparticle phases. The hot corrosion resistance of the deposited part was better than that of the substrate part. This was due to the finer γ′ phase, higher volume fraction of the γ′ phase and the tighter synergistic effect of the corrosion products in the deposition area.

4 Conclusion

In summary, additive manufacturing provides an advanced, efficient and high-quality repair method for single-crystal high-temperature alloy turbine rotor blades. So far, the research on additive repair of single-crystal high-temperature alloys and their rotor blades has mainly focused on the repair of hot crack formation mechanism, the influence mechanism of recrystallization and epitaxial growth of grains, and the analysis of finite basis performance. On this basis, the WA-DED and DED-L methods have been successfully used at home and abroad to achieve the repair and application of single-crystal high-temperature alloy turbine rotor blade tip damage. At present, each additive manufacturing method has its own advantages in repairing single crystal superalloys and their turbine rotor blades, but there are still some technical bottlenecks: (1) The poor formability of single crystal superalloy additive manufacturing and the thin-walled characteristics of turbine blades and the structural constraints of damaged parts make it very easy for thermal cracks to occur during the repair of single crystal alloy turbine blades using the same parent material filler material by WA-DED, DED-L and LPBF methods; (2) The thin-walled characteristics of turbine blades and the structural constraints of damaged parts lead to the inevitable presence of large residual stress in the additive repair part of single crystal alloy turbine blades, which makes it easy to recrystallize and crack during subsequent surface finishing or heat treatment. Therefore, how to use additive manufacturing technology to achieve efficient and high-quality repair of single crystal superalloy turbine rotor blades, obtain ideal epitaxial growth repair organization and excellent joint performance, and effectively improve the repair qualification rate, still needs to be further studied. In order to realize the wide application of additive repair technology in the field of deep repair of single crystal superalloy turbine rotor blades of aircraft engines, the following three directions will be the focus of future research.

(1) Design of special alloy material composition for single crystal alloy additive repair based on process characteristics In the existing research and application of single crystal alloy turbine rotor blade additive repair, the filler material used is generally a commercial single crystal alloy material with the same or similar composition as the matrix. The composition and proportion of such materials are designed and developed based on traditional casting or forging technology, and the characteristics of micro-area metallurgy, non-equilibrium solidification and repeated thermal cycles under the action of high energy density heat source in the additive repair process are not fully considered. These factors are closely related to the stress state of the repair area and the matrix bonding area, the solidification parameters and solid phase transformation during the repair process, and directly affect the metallurgical quality, solidification structure and service performance of the single crystal alloy repair part. Therefore, according to the characteristics of the additive repair process, comprehensively considering factors such as thermal crack sensitivity, single crystal integrity and strengthening mechanism, combined with the material thermodynamic database, designing and preparing special single crystal alloy repair alloy materials will be an important research direction in the field of single crystal alloy turbine rotor blade additive repair.

(2) Development of new additive repair processes based on the characteristics of single crystal alloy materials
At present, the heat source mode used in DED-L additive repair of single crystal high-temperature alloys is mainly concentrated on Gaussian beam energy distribution, that is, the heat source energy is high in the center and low at the edge. Under this heat source characteristic, the molten pool has high superheat and coarse solidified dendrite structure, which can easily cause problems such as increased thermal stress in the repair area of ​​single crystal alloys and reduced high-temperature mechanical properties. With the rapid development of beam shaping technology, various types of laser heat sources with special energy distribution characteristics have been designed and developed, such as annular beams, ellipsoidal beams, inverse Gaussian beams, etc. The above heat source types have been initially applied in the field of metal additive manufacturing, and their beneficial effects in shape control and shape control have been verified. Given the similarities between the metallurgical processes of DED-L repair and additive manufacturing, it is an important research direction in the field of single crystal alloy repair to develop new DED-L processes, explore the mechanism of action of different heat source modes on metallurgical defects, crystal growth and residual stress of single crystal alloy and its turbine blade repair, and design the energy distribution form of laser heat source based on the material characteristics of single crystal alloy.

(3) Multi-objective collaborative optimization of additive repair of single crystal alloy turbine rotor blades based on deep learning

At present, for the process optimization problems in single crystal alloy additive repair, a single optimization target (thermal cracks, impurity crystals, columnar crystal epitaxial growth control, etc.) is often used, and the experimental design often follows the single variable principle. On the one hand, the process optimization for a single target does not consider the synergistic change factors of other target performance, which may weaken other performance indicators; on the other hand, due to the large number of process parameters in single crystal alloy additive repair, including heat source power, scanning speed, powder feeding rate, substrate orientation, molten pool shape, etc., the workload of single variable experimental design is large, and there is a lack of consideration of the interaction between parameters, which affects the comprehensive performance of single crystal alloy repair parts. Therefore, another important research direction in the field of single crystal alloy repair is to use deep learning methods, comprehensively consider the interactions between process parameters to design experiments, establish a multi-objective collaborative optimization prediction model for single crystal alloy turbine rotor blades, and achieve control over the comprehensive performance of repaired parts.